UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Application of the HF precision-velocity technique to the study of [delta] Scuti variables Yang, Stephenson 1985-12-31

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1986_A1 Y36.pdf [ 14.47MB ]
Metadata
JSON: 1.0053461.json
JSON-LD: 1.0053461+ld.json
RDF/XML (Pretty): 1.0053461.xml
RDF/JSON: 1.0053461+rdf.json
Turtle: 1.0053461+rdf-turtle.txt
N-Triples: 1.0053461+rdf-ntriples.txt
Original Record: 1.0053461 +original-record.json
Full Text
1.0053461.txt
Citation
1.0053461.ris

Full Text

c APPLICATION OF THE HF PRECISION-VELOCITY STUDY OF 6 SCUTI  TECHNIQUE TO THE  VARIABLES  by STEPHENSON YANG M.Sc.,  University  of  B r i t i s h Columbia,  1980  B.Sc,  University  of  B r i t i s h Columbia,  1976  A THESIS  SUBMITTED IN PARTIAL FULFILMENT OF  THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES Department  We a c c e p t to  of  Geophysics  this the  thesis  conforming  standard  OF BRITISH  October ©  as  reqjaiire'd  THE UNIVERSITY  and'Astronomy  COLUMBIA  1985  Stephenson Yang,  1985  In presenting this thesis in partial fulfilment  of the requirements for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or  by his or  her  representatives.  It  is understood that copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  DE-6(3/81)  • In  conventional radial-velocity  calibration guiding  in stellar  errors.  imposing  the  The most R-branch  calibration  errors lines  (3-0)  c a n be of  suitable  a  reservoir  by p l a c i n g  the s t e l l a r  then  maintain  a  beam. The at  constant  In  high  the e f f e c t  lines  can  relative of  the  of l i n e  minimised using  positions  minimise  the e f f e c t  between  the  The  filled  and to  the avoid  to the c e l l i s  0°C and t h i s  would  inside  cell.  utilised  the  to provide  the  HF  b l e n d i n g between t h e two s e t s  of  lines  difference  have  spectra  and  accuracy  be  of  was  found  The means  modified used  studies the  the to  line  to  differences  accuracy  increase l i n e a r l y  depth  i i  A  and s c a l e  that  line  spectra.  can a l s o  Simulation  confirmed  s/n  HF  technique.  of small o f f s e t profiles.  or  numerical  a r e measured by  function  measurement would  the  performing stellar  line-position  Furthermore,  belong  t h e imposed  of s p e c t r a l  line  spectra  the  is  by  Fahlman-Glaspey d i f f e r e n c e  of  at  spectra with  standard  Fahlman-Glaspey  artificial  Connected  the  o f HF.  monel c e l l  pressure  the s t e l l a r  lines,  cancellations  on  by  s/n s p e c t r a .  reducing  be  band  100°C i n o r d e r  HF m a i n t a i n e d  Meanwhile, the R e t i c o n d e t e c t o r necessary  wavelengths  an a b s o r p t i o n c e l l  o f t h e HF m o l e c u l e s .  of l i q u i d  eliminated  natural absorption lines  s a p p h i r e windows a r e m a i n t a i n e d polymerisation  largely  known  wavelength  by c o l l i m a t i o n and  vibration-rotation  i s achieved  w i t h HF g a s i n t o  techniques,  spectra i s limited  These  absorption  spectra. to  ABSTRACT  with  with of both  profiles.  decrease  with  increasing  linewidths  when t h e  equivalent  w i d t h s were  held  constant. A method temperature involves  has  been  directly  calculating  from  on  the  line  measure  observed  been c a l c u l a t e d  strengths  i n order  the  o b s e r v e d HF l i n e  relative  gas  pressure.  collisional linewidths between  line  This  dependence  of  linewidths. published  Poor and  The  5  lOkms" . Since 1  ±0.1kms"  1  Scuti  would  about  ±0.00l  study  of  6  m  to  (1-0),  was  be the  theory  on  calculate  HF  h a s been  achieved  ( 2 - 0 ) , and (3-0)  on t h e  collisional  line  are  0.3^  Scuti  of 0.05  5  to calculate ATC  used  a study  HF  line  dependence  temperature  self-broadened  obtained  between  the  shifts.  Nevertheless,  wavelengths of t h e r e f e r e n c e  stars  5  most  This  (3-0)  derived.  small-amplitude  than  enables  corrected  than  v  strengths  was  agreement  Scuti  Am  gas  v a l u e s can a l s o  Good agreement  (3-0)  periods of l e s s  amplitude  HF  lines.  their  cutoff-free  calculated  have been  HF  t o study  and p u b l i s h e d  also the  pressure-shift lines  shifts.  the c a l c u l a t e d  linewidths.  A  broadening  and l i n e  the  f o r t h e (3-0) HF l i n e s  the gas temperature. These t h e o r e t i c a l  used w i t h  for  to  t h e r a t i o s between t h e o b s e r v e d HF  strengths. Theoretical have a l s o  devised  m  be  i n the l i g h t Scuti  a  v  value  by  type A  typically  a velocity  2K/Am  stars,  already  and s p e c t r a l stars  and  the  distinguished  pulsation o r F.  have  2K a m p l i t u d e i s about  velocity equivalent  light of  less  92kms~ mag~ 1  precision to a  a  of  precision  c u r v e . Hence one c a n improve  pulsations  with  the  use  The  of  1  just of the  precision  radial-velocity enable  techniques.  the study  The  of i n d i v i d u a l  HF  technique  spectral  would  lines  for  also  profile  variations. The  star  20 CVn  observed  using  1.4kms  was o b t a i n e d  of  _1  l^kms"  2K/Am  t h e HF  nonradial The  for  40kms~ mag~ 1  the other f o r 20  1  p Pup i s a 0.141  found  variations  to vary  are  at  near  effective  minimum  temperature star  o  1  observed  a t CFHT.  for  Ca  the  i n phase w i t h  These g i v e  light.  "features"  about  imply  are  and at  H I a  across  was  1  lines. of  in  the  the broadened  line  0 Cas i s a 0.104  a t CFHT.  7kms"  1  while  The Ca I I the value  and  of  about Ca  cycle. variable measured  2%  II  of  the  line.  The  movement This  of  would  i n the s t a r .  broad-line 5 Scuti has  the  Line-profile  profile.  X8662 l i n e  the  c a n be c o n s i d e r e d  o f 4.3kms"  level  observed  of  the p u l s a t i o n  X8750  These  maximum l i g h t  the e x i s t e n c e of n o n r a d i a l p u l s a t i o n star  1%  by t h e v a r i a t i o n s over  lines  curve.  and  v a r i a t i o n s c a n be c h a r a c t e r i s e d a s t h e t e m p o r a l  observed  a  variable  broad-line 6 Scuti  A 2K a m p l i t u d e  been  0.5%  The v a r i a t i o n s  of the s t a r  8 Scuti  the l i g h t  between  E r i i s a 0.082  which  c o n t i n u u m , have  The  of  a value  of the s t e l l a r  a r e s t r o n g e s t near  I I X8662  variations  suggest  value  while  lines.  6 D e l type  s p e c t r a l - t y p e v a r i a t i o n s caused  The  A 2K  variable  CVn w h i c h c o u l d  intensities  levels  c o n t i n u u m . The l i n e s  as  a t CFHT.  f o r t h e Ca I I X8662 l i n e  a t CFHT. The l i n e  have been  weakest  6 Scuti  pulsation. star  observed  6 D e l type  d  technique  was o b t a i n e d  1  of about  v  i s a 0.122  variable  a 2K v a l u e  of  f o r t h e H I X8750 and t h e o t h e r  iv  metallic found  lines  i s about  4.5kms~ .  t o l a g the other v e l o c i t y  Line-profile  variations  curves  which a r e  continuum,  have  variations  c a n be c h a r a c t e r i s e d  broad-line  phase c o i n c i d e s  the n a r r o w - l i n e  been  The H I v e l o c i t y  1  observed  with  at a level  in  the  Ca  as l i n e w i d t h the v e l o c i t y  phase c o i n c i d e s w i t h  v  by a b o u t  curve  was  2% i n p h a s e . o f 1% o f  II  the  line.  The  variations. minimum  the v e l o c i t y  The  while  maximum.  Table 1.  of  Contents  Introduction  1  1.1 The measurement 1.2 C o n v e n t i o n a l  of s t e l l a r  radial-velocity  1.3 Modern p r e c i s i o n  Coude o p t i c a l  1.3.2  Infrared  heterodyne  1.3.3 Measurement Infrared  fibre  1.3.6 F a b r y - P e r o t  1.3.8  1.4 D e l t a S c u t i 1.4.1  6  oscillations spectrometer  interferometer  7 ....9 10 11  lines  Imposing a r t i f i c i a l  6  technique  techniques  1.3.7 Use o f t e l l u r i c  4  6  Transform  1.3.5 M o d i f i e d M i c h e l s o n  techniques  1  feed  of the s o l a r  Fourier  velocities  techniques  radial-velocity  1.3.1  1.3.4  radial  15  calibration  lines  variables  16 18  Introduction  19  1.4.2 M a i a s e q u e n c e ?  20  1.4.3  20  6 D e l p h i n i anomalies  1.4.4 C o e x i s t e n c e  of p u l s a t i o n  1.4.5 M o d e l s o f 6 S c u t i  and m e t a l l i c i s m  stars  ..21 22  1.4.6 P e r i o d - l u m i n o s i t y - c o l o u r r e l a t i o n  24  1.4.7 L i g h t  24  and v e l o c i t y  1.4.8 S y s t e m a t i c s 1.5 O s c i l l a t i o n  amplitudes  of 6 S c u t i  stars  25  modes  -..26  1.5.1 Mode c l a s s i f i c a t i o n 1.5.2 Mode  identification  1.5.2.1  26 techniques  Period ratios  30  1.5.2.2 Use o f t h e p u l s a t i o n 1.5.2.3 L i n e p r o f i l e vi  30  analysis  c o n s t a n t Q ...31 32  1.5.2.4 Use o f s i m u l t a n e o u s l y  observed  data  33  1.5.2.5 Use o f p o l a r i s a t i o n 1.6 S p e c t r o s c o p i c 1.6.1  observations  Difficulties  with  measurements ..38  of D e l t a  Scuti stars  low-amplitude  v a r i a b l e s .38  1.6.2 R e c e n t o b s e r v a t i o n s 1.6.3 Use o f p r e c i s i o n r a d i a l - v e l o c i t y techniques 2.  The HF a b s o r p t i o n 2.1  cell  40 42  system  45  Introduction  2.2 C h o o s i n g  45  the d e t e c t o r  45  2.3 The Ret i c o n d e t e c t o r 2.3.1  .38  47  Introduction  47  2.3.2 Dark c u r r e n t  49  2.3.3 L i n e a r i t y 2.3.4 F i x e d  i n response  line  2.3.5 R e d u c t i o n  ...50  pattern  51  of readout  2.3.6 The i n c o m p l e t e  noise  readout  52  phenomenon  54  2.3.7 The p e r s i s t e n c e phenomenon  59  2.3.8 C o s m i c - r a y  60  events  2.4 The g a s a b s o r p t i o n  system  61  2.4.1  Choosing  2.4.2  P h y s i c a l and c h e m i c a l  2.4.3 S a f e t y  the absorbing  precautions  2.4.4 The a b s o r p t i o n 2.4.5 The c e l l  gas  61  p r o p e r t i e s o f HF  on w o r k i n g  with  HF  cell  of the gas h a n d l i n g  2.4.7 P l a c e m e n t  of the c e l l  vii  66 67  windows  2.4.6 O p e r a t i o n  ....66  71 system  75 80  3.  The HF s p e c t r u m  82  3.1  82  Introduction  3.2 M o l e c u l a r 3.2.1  constants  Basic  f o r HF  equations  83  and c o n s t a n t s  3.2.2 D e r i v a t i o n s o f new c o n s t a n t s wavelengths 3.3 The t e m p e r a t u r e 3.3.1  and p r e s s u r e  83 and 86  o f t h e HF g a s  94  Introduction  3.3.2 HF l i n e 3.3.2.1  94  strength  96  Basic  96  equations  3.3.2.2 The H e r m a n - W a l l i s  factors  97  3.3.2.3 D e r i v a t i o n o f g a s t e m p e r a t u r e  ....101  3.3.2.4 D e r i v a t i o n o f t h e g a s p r e s s u r e 3.4 The c o l l i s i o n a l l y b r o a d e n e d 3.4.1  ...104  linewidths  109  Introduction  3.4.2 T h e o r i e s  109  on c o l l i s i o n a l  line  3.4.3 The A n d e r s o n - T s a o - C u r n u t t e 3.4.3.1  Basic  ..111  (ATC) t h e o r y  ..113  approach  3.4.3.2 C o l l i s i o n  113  cross  3.4.3.3 The c o l l i s i o n  section  efficiency  3.4.3.4 C u t o f f p r o c e d u r e parameter 3.4.3.5 The c u t o f f - f r e e  115 function  f o r small  impact  theory  3.4.3.6 B a s i c f o r m u l a t i o n s theory 3.4.4 S u r v e y  broadening  116 117 118  of s i m p l i e d  120  o f e x p e r i m e n t s and c a l c u l a t i o n s ...121  3.4.5 The c a l c u l a t i o n shifts  o f l i n e w i d t h s and  3.4.6 C a l c u l a t e d l i n e w i d t h s  viii  line  f o r t h e HF l i n e s  122 ...124  3.4.7 C a l c u l a t e d  line  shifts  f o r t h e HF l i n e s  3.4.8 S h i f t - c o r r e c t e d r e f e r e n c e 3.4.9 D o p p l e r and c e l l - w a l l 4.  HF d a t a 4.1  wavelengths  ..127  ....130  broadening  130  reduction  133  Introduction  4.2 P r e p r o c e s s i n g 4.2.1  133 of R e t i c o n  Baseline  spectra  subtraction  133  4.2.2 Use o f " e x t r a - r e a d o u t " 4.2.3 R e l a t i v e g a i n 4.2.3.1  133  points  135  correction  Line-normalisation  4.2.3.2 Use o f s t e p  136 procedure  136  lamps  137  4.2.4 F l a t - f i e l d i n g 4.3 R e d u c t i o n 4.3.1  138  o f HF d a t a  Continuum  141  rectification  141  4.3.2 L i n e - p o s i t i o n d e t e r m i n a t i o n 4.3.2.1  Line  4.3.2.2 L i n e  145  cancellations p o s i t i o n i n standard  145 spectra  150  4.3.2.3 Use o f t h e d e r i v a t i v e o f t h e l i n e profile 151 4.3.2.4 The F a h l m a n - G l a s p e y d i f f e r e n c e technique  156  4.3.2.5 L i n e - p r o f i l e  160  4.3.2.6 O p t i m i s i n g  variations  difference function  ...162  4.3.2.7 E r r o r e s t i m a t i o n  164  4.3.2.8 D i s p e r s i o n  165  4.3.3 E f f e c t i v e  rest  4.3.4 B a r y c e n t r i c 4.4 S i m u l a t i o n  relation  wavelengths  corrections  studies  169 171 176  ix  5.  6.  7.  4.4.1  Basic  approach  176  4.4.2  Noise  generation  176  4.4.3  Reduction  4.4.4  The  effect  of  s/n  4.4.5  The  effect  of  line  4.4.6  The  effect  of  linewidth  4.4.7  Theoretical line-position  The  Delta  S c u t i v a r i a b l e 20  5.1  Introduction  5.2  Variabilities  5.3  The  observations  5.4  The  data  5.5  The  radial  5.6  Discussion  202  The  Delta  212  6.1  Introduction  6.2  Variabilities  6.3  The  observations  217  6.4  The  data  221  6.5  The  line-profile  6.6  The  radial  6.7  Discussion  The  Delta  7.1  Introduction  265  7.2  The  observations  265  7.3  The  data  267  7.4  The  radial  of  the  artificial  spectra  177 179  depth  179 182 accuracy  CVn  184 188 188  of  20  CVn  189 192  reduction  •  velocities  193 197  S c u t i v a r i a b l e p Pup  ....212 of  p Pup  212  reduction variations  velocities  222 242 263  Scuti variable o  reduction velocities  x  1  Eri  265  273  7.5 The l i n e - p r o f i l e  8.  variations  279  7.6 D i s c u s s i o n  281  The D e l t a  284  8.1  S c u t i v a r i a b l e 0 Cas  Introduction  284  8.2 The o b s e r v a t i o n s  286  8.3 The d a t a  288  reduction  8.4 The r a d i a l  velocities  8.5 The l i n e - p r o f i l e  290  variations  8.6 D i s c u s s i o n  298 303  BIBLIOGRAPHY  305  INDEX  326  xi  List  of T a b l e s  2. 01  The U B C - b u i l t  3. 01  Published molecular constants  3. 02  Adopted m o l e c u l a r c o n s t a n t s  3. 03  Vacuum wavenumbers f o r t h e (3-0) band  3. 04  SSTP w a v e l e n g t h s  3. 05  The a ^ s and t h e M.'s  f o r HF  3. 06  Herman-Wallis  f o r t h e (3-0) band  3. 07  Line  3. 08  L i n e w i d t h s o f t h e (1-0) band  o f HF  125  3. 09  Linewidths  o f t h e (2-0) band  o f HF  125  3. 10  L i n e w i d t h s o f t h e ( 3 - 0 ) band  o f HF  126  3. 1 1  Line  3. 1 2  Shift-corrected  3. 1 3  Line  5. 01  Parameters  5. 02  Mid-exposure  5. 03  Relative  6. 01  Parameters  6. 02  Mid-exposure  6. 03  Relative  radial  velocities  o f p Pup ( I )  255  6. 04  Relative  radial  velocities  o f p Pup ( I I )  257  7. 01  Parameters  7. 02  Mid-exposure  7. 03  Relative  8. 01  Parameters  8. 02  Mid-exposure  8. 03  Relative  1872-Reticons  54 f o r HF  f o r t h e (3-0) band  f o r t h e (3-0) band  factors  o f t h e (3-0) band  shifts  o f HF  o f HF  o f HF  o f HF  o f HF  o f t h e (3-0) band  f o r 20 CVn  velocities  spectra  o f 20 CVn  f o r p Pup  105  1 29 131 131  1 92 202 213  t i m e s and e x p o s u r e s f o r p Pup  for o E r i  219  266  1  times f o r the o velocities  1  E r i spectra  of o E r i 1  f o r /J Cas  269 274 285  t i m e s f o r t h e 0 Cas s p e c t r a  radial  100  190  t i m e s f o r t h e 20 CVn  radial  91 93  wavenumbers and w a v e l e n g t h s  f o r the R-branch  radial  91  98  s t r e n g t h s o f t h e (3-0) band  shifts  87  velocities  xii  o f 0 Cas  289 295  List  of F i g u r e s  2. 01  Residuals  2. 02  The  2. 03  Time d e c a y o f t h e p e r s i s t e n c e  phenomenon  58  2. 04  Stellar  of X8700  63  2. 05  Fringe pattern  cell  73  2. 06  Attempts  2. 07  Schematic  of a g e n e r a l i s e d  3. 01  The  (3-0)  vibration-rotation  3. 02  The  temperature  d e p e n d e n c e o f HF l i n e  3. 03  The  temperature  dependence of the  4. 01  The  first  derivative  o f t h e HF  4. 02  The  first  derivative  o f t h e p Pup  4. 03  The  first  derivative  o f t h e 38 E r i s p e c t r u m  4 .04  The  effect  o f s/n on a c c u r a c y  180  4. 05  The  effect  of l i n e  181  4. 06  The  effect  of l i n e w i d t h  4. 07  s/n  as a f u n c t i o n  5. 01  The  20 CVn  5. 02  The  Ca  I I X8662 v e l o c i t y c u r v e o f 20 CVn  198  5. 03  The  Fe  I X8689 v e l o c i t y  199  5. 04  The  mean v e l o c i t y c u r v e  5. 05  Velocity  difference  ( Ca I I c u r v e - mean c u r v e  5. 06  Velocity  difference  ( mean c u r v e  - Fe I c u r v e  )  205  5. 07  Velocity  difference  ( Fe 1 c u r v e  - S i 1 curve  )  206  5. 08  Velocity  difference  ( Fe I c u r v e - S I  6. 01  The  p Pup  6. 02  The  unoptimised  from  persistence  spectra  incomplete  56  readout  57  phenomenon  i n the region from d e f e c t i v e  to f l a t - f i e l d  window  74  the f r i n g e s  depth  HF  77  system band o f HF  84 108  strengths  128  linewidths  1 52  spectrum  1 53  spectrum  154  on a c c u r a c y  183  on a c c u r a c y  of s i g n a l  185  ( i n adcu)  spectrum  194  curve  of 20 CVn  o f 20 CVn from  weak  curve  lines  )  )  200 204  207 218  spectrum Ca I I X8662 v e l o c i t y  xiii  curve  223  6. 03  The  6. 04  Uncertainties  i n t h e Ca I I X8662 l i n e  6. 05  Uncertainties  i n t h e Fe I X8689 l i n e  6. 06  The  unoptimised  6. 07  The  Ca  II X8662 l i n e  6. 08  The  Fe  I X8689 l i n e p r o f i l e s  6. 09  The  Si  I X8752 and Fe I X8757 l i n e  6. 10  The  Si  I X8752 and Fe I X8757  6. 1 1  The  Si  I and Fe I r e s i d u a l s  unoptimised  Fe I X8689 v e l o c i t y  Fe I X8757  224  curve  226  positions  227  positions  228  velocities  profiles  and t h e i r  residuals  and t h e i r  residuals  231 232 233  profiles  234  residuals  235  from BJD2445356  244  6. 1 2 The  o p t i m i s e d Ca I I X8662  6. 13  The  o p t i m i s e d Fe I X8757  6. 14  The  o p t i m i s e d Ca I I X8662 v e l o c i t y  6. 15  The  o p t i m i s e d H I X8750 v e l o c i t y  6. 16  The  o p t i m i s e d Fe I X8689 v e l o c i t y  6. 17  The  mean o p t i m i s e d Fe I v e l o c i t y  curve  249  6. 18  The  mean o p t i m i s e d S i I v e l o c i t y  curve  250  6. 19  The  mean o p t i m i s e d S I v e l o c i t y  6. 20  The  o p t i m i s e d Ca I I v e l o c i t i e s  from  t h e 22nd  252  6. 21  The  o p t i m i s e d Ca I I v e l o c i t i e s  from  the 25th  253  6. 22  Errors  6. 23  Velocity  7. 01  The  o  7. 02  The  Ca  7. 03  The  H I X8750 v e l o c i t y  7. 04  The  velocity  7. 05  The  Ca  7. 06  The  residuals  8. 01  The  P Cas  1  uncertainties  i n t h e HF d i s p e r s i o n difference  245  uncertainties  247  curve  248  curve  251  curve  260  fits  ( Ca I I c u r v e  - Fe I c u r v e  )  261 268  E r i spectrum I I X8662 v e l o c i t y  curve  246  curve  curve  of o  I I X8662 l i n e  curve  1  of o E r i 1  27 1  of o E r i  E r i from  1  weak  lines  272 277  profiles  o f t h e Ca I I X8662 l i n e  270  profiles  278 287  spectrum  xiv  8.02  The Ca I I X8662 v e l o c i t y  curve  8.03  The H I X8750 v e l o c i t y  8.04  The Fe I X8689 v e l o c i t y  8.05  The v e l o c i t y  8.06  Uncertainties  8.07  The Ca I I X8662 l i n e p r o f i l e s  o f 0 Cas  291  c u r v e o f 0 Cas  292  c u r v e o f 0 Cas  293  c u r v e o f 0 Cas from weak l i n e s i n t h e Ca I I X8662 l i n e p o s i t i o n s  xv  and t h e i r  residuals  294 299 301  Acknowledgements I would l i k e for  t o thank  h i s assistance,  involved ranges  guidance,  i n every part  i f not a l l t h e  data  discussed  supervisor support,  D r . Gordon  o f t h e DAO  HF s y s t e m  image g u i d i n g  in this  is  participation to  performing  at the t e l e s c o p e  f o r the  to  thank D r . B r u c e C a m p b e l l  for his  a s s i s t a n c e . He and D r . W a l k e r a r e r e s p o n s i b l e HF p r o j e c t . D r . C a m p b e l l  designed,  CFHT HF s y s t e m w i t h  the data  which  was b a s e d . D r . C a m p b e l l problems  He  thesis.  I would a l s o l i k e  the  Walker  and p a t i e n c e .  o f t h e HF p r o j e c t . H i s  from h i s d e s i g n  most  my  also  associated  built,  the  data  whole  and o p e r a t e d  discussed  discovered  with  f o r the  in this  and s o l v e d reduction  the  thesis many  of  of  the  spectra. I would a l s o l i k e Screiber  for  responsible in  this  their  Mr.  some o f t h e d a t a - r e d u c t i o n  absorption  cell  both  and  appreciation the  assistance.  t h e s i s while  DAO  t o thank Mr. J o h n Amor and Mr. D i e t e r  Mr. D i e t e r  and t h e CFHT.  I  t o Mr. Ron J o h n s o n  Amor  built  gas-handling also  like  been  discussed t h e DAO  systems to  express  f o r h i s t e c h n i c a l support  HF for my of  instrumentations. I would  graduate  like  students  t o thank for their  Dr. help  Friedhelm  with  performed  some  r e m o v i n g HF from  of the dangerous  tasks  the a b s o r p t i o n - c e l l system.  xvi  Aubke  and h i s  t h e DAO HF s y s t e m . D r .  Aubke h a s made a v a i l a b l e , on many o c c a s i o n s , and  has  techniques  Scrieber  current would  John  his  laboratory  of r e p l a c i n g  or  I  would  Underhill,  like  Greg  J a s o n Auman, helpful  t o e x p r e s s my Fahlman,  and  discussion  Garry  Joslin,  Grant  Hill,  their  on t h i s  thesis.  A l l the f a c u l t y , graduate  i n t h e department  like  and t h i s  Daniel  Thibault,  the  bottle  like  to  losing this  in his  empty by t h e  e x p r e s s my  thesis.  also  Victoria  carried  sympathy  I would  like  on t h e t h e o r y o f  like  t o go  t o John that  occasions, I  staffs  on o b s e r v i n g  would  Observatory  like in  facilities.  b o t h DAO a n d  Colin  thank  Victoria  the  observing bottle  Unfortunately, it. I who  would  has  been  I have been w o r k i n g t h e work o f  variations.  trips.  Walker  I  would  I  like  on Phil  would  some  of  like  to  f o r t h e use o f  I would a l s o  the  and  i n Mauna  I would a l s o  CFHT f o r  Bennett,  to  their thank  who, on  many  our equipment.  to  Telescope Corporation their  Nicol  i n the P h y s i c s department  leak-tested  Phil  S i e p who l e t us borrow  p o w e r - s p e c t r u m - a n a l y s i s program. technical  I  Millward,  HF l e c t u r e  own c a r .  spectral-type  thank Dr. Tad U l r y c h and  the  the  t o acknowledge  t o t h a n k Mr. B i l l  equipment  with  t i m e we r e c e i v e d  one b e e r f o r e v e r y week  Bennett  his  was  their  P e t e r W h a i t e , D e n n i s C r a b t r e e , and  Zoran N i n k o v to  and  thesis.  t o thank Zoran Ninkov, C h r i s  Enrico Kindl,  from Vancouver  guidance  have o f f e r e d  t o t h e HF p r o j e c t  John N i c o l ,  DAO. Once,  Ovenden,  for  G e r r y G r i e v e . Many o f them have a s s i s t e d at  Michael  Anne  Richer  h e l p a n d encouragement especially  Anthony M e r e r ,  to Drs.  Harvey  s t u d e n t s , and s t a f f s  would  appreciation  their  Dominion  the Kea like  Canada-France-Hawaii for extensive  use  t o thank t h e s t a f f s  support.  xvi i  Astrophysical  Murray  Fletcher  of at has  been v e r y  helpful  occasions,  he has t o r e - c o a t  observing  r u n . He  on t h e p r o j e c t . the like the  t o our  observing  has a l s o  Dr.  l i t e r a t u r e references t o acknowledge  Batten  t h e work  support dedicate  and  this thesis  over  numerous  before  helpful  DAO  star  On  train  our  discussion  has a l s o  provided  0 C a s . I would  of D r . M i c h a e l  De  also  Robertis  on  program.  t o acknowledge  patience  very  of  f o r the  barycentric-correction I would l i k e  t h e r e d coude  provided  Allan  a t DAO.  the  my  late parents  years.  I  t o t h e memory o f them.  xvi i i  would  for  their  like  to  memory of my parents  Chapter  1  INTRODUCTION  1.1  THE In  MEASUREMENT OF 1842,  the ocean observer on a  Doppler  frequency  i s on  moving  observed This  Christian  wave who  STELLAR RADIAL V E L O C I T I E S  shore  s h i p . He  effect.  If  frequency  has  and  one  or  rest  relative  as e m i t t e d by  a  effect  f r e q u e n c y . The  the observed  0  frequency  shifted As  an  application  [1842], F i z e a u motions  star  attempts  between  trustworthy dispersion  as  that  the  is the  ship. Doppler  the  actually  light  observed  )  (1.1)  of  light sight  star. of the and  f  0  i s the  i s c , and  and  star. the  If v  star the  measurement  instruments a v a i l a b l e  1  is  is  of  negative, moving  frequency  i s red  the  observer.  t h e n would  Doppler  t o measure  the  unsuccessful  produce any  called  w o u l d be  were many to  the  direction  g i v e n by  t h e method  1887  v  or r a d i a l  the p r i n c i p l e  b o d i e s . There  emitted  This i s generally  is positive,  of  the in  w o u l d be moving away from  1863  velocity  known  in  of the  difference  of  [1870] o u t l i n e d  of c e l e s t i a l  difference  f r e q u e n c y , and  i s blue s h i f t e d  the  stationary  o b s e r v e r who  the v e l o c i t y  ( 1 - v/c  velocity  and  a  relating  gives:  line  towards the o b s e r v e r . I f v  by  by an  the  from  velocity  i n the  radial  seen  the star  f i s the observed  velocity  seen  that on  considers  between t h e o b s e r v e r and  the  that  noted  f = f term  is  been commonly  on E a r t h , t h e D o p p l e r  The  that  f r e q u e n c i e s depends  phenomenon  d e r i v e d formulae  star.  a  single The  low  introduce errors  2 many t i m e s not  until  stellar of  larger  than  1890 t h a t  the v e l o c i t i e s  the f i r s t  reliable visually  the s t e l l a r  a Bootis In  sodium D l i n e s ,  (Keeler  light  the Doppler  velocity  the v e l o c i t y star.  stellar  Einstein  postulated that  effect  the  star  of s p e c i a l  relativity: 2  of the s t a r  is  1.2 w i l l  2  )  (1.2)  v w h i l e tf> i s t h e a n g l e  and t h e o b s e r v e r ' s  Equation  velocity  f r a m e s of r e f e r e n c e and  ( 1 - (v/c)cos<* ) / / ( 1 - ( v / c )  0  velocity  10th 1890 on t h e b r i g h t  i s t h e same i n a l l v e l o c i t y  f = f  the  the f i r s t  [1894]).  1905, A l b e r t  derived  The  determined  v e l o c i t i e s were o b t a i n e d . B a s e d on t h e d i s p l a c e m e n t s  measurement was"made on A p r i l  of  t o be m e a s u r e d . I t was  l i n e of s i g h t  give  a non-zero  between  direction Doppler  to  shift  even when 0 i s 9 0 ° : The  radial  comparing against  the observed its  Generally, could  velocity  of a  frequency  corresponding  the t r a n s v e r s e  star  c a n be  of a s t e l l a r s p e c t r a l  laboratory  component  of  rest  by line  frequency.  a stellar  velocity  c o n t r i b u t e t h e e q u i v a l e n c e o f a few t e n s o f m e t r e s p e r  second  to  velocity  the  observed  inferred  Doppler  directly  from  shift.  the true  Correction  t r a n s v e r s e Doppler  be made value  for this  i f the p a r t i c u l a r of  the  applications, the  Doppler  radial  effect  star.  w o u l d have  motion.  the  the shift  of the  In  i n the r e l a t i v e  therefore,  unimportant.  Doppler  requires the  stellar  interested  velocities; would be  radial velocity  application  one i s o n l y  radial effect  true  Therefore,  the observed  does n o t r e p r e s e n t  in  estimated  to  precise most change  second-order  3  The  radial  velocity  the c e n t r e of t h e Hence t h e relative  Sun a s t h e  observed  the value  generally  not  value which physical  for f  the rest  takes  effects  is  stellar  velocity  has  0  to  used  normally  stellar  the measured v e l o c i t i e s  of  addition  t o t h e I.A.U. s y s t e m  earlier  Lick  systems  (Fletcher  still  et a l .  star  displayed imply  a  relative Doppler variable  i s essentially by i t s s p e c t r a l  p h y s i c a l motion to  the  effect stars  atmospheric  observer  as may,  motions caused  include  need  standard  (Pearce  the various [1982],  stars.  standard  and  same  There  are  stars.  In  there are the  recent  photoelectric a l .  of the  star's centre  by  implied the the  [1979], estimate  Doppler  But i t may n o t  by s t e l l a r  and  [1955]),  lines.  p a r t , be  0  t o be a p p l i e d t o  by t h e  by  f  [1982]).  radial-velocity  the  is  spectral  redshift,  Beavers et  defined  experienced in  technical  t o p l a c e them on t h e  Neese e t a l . [ 1 9 8 5 ] ) . The o b s e r v e d of a  These  radial-velocity  s y s t e m and  An e f f e c t i v e  conditions (Dravins  radial-velocity  systems  centre.  1.1 and 1.2  gravitational  i n order  several  f o r the  and t h e s o l a r  many m i n o r  used.  used  reference.  corrected  i n Equations  account  photospheric  the  frame o f  be  observer  z e r o - p o i n t c o r r e c t i o n s may  system w i t h  has t r a d i t i o n a l l y  laboratory value.  into  blending effects,  detailed Minor  value  m o t i o n between t h e  Moreover,  line  of a s t a r  effect  necessarily of  gravity  velocity.  stellar result  pulsation.  lines of  The in  stellar  4 1.2 CONVENTIONAL The  conventional  involves  simply  as w e l l a s  into  generally  well  alter  of  effect  line  A  slit  slit  the c o l l i m a t o r . cause  focus  of  the  spectroscopy,  and  different  (Tull  stellar  nonuniform  focus  error  t o remove  the  which can  also is  and  optical  mirror  [ 1 9 6 9 ] ) . The  telescope  refraction  and  image  the  in  t h e camera  (Petrie  and  paths  will use of  Fletcher  in  imperfections cause  variable  emission  the  i n the Coude  beams may  and t h e c o l l i m a t o r  Zonal  will  conventional  comparision  of  i n the d i s p e r s i o n  miscollimation  In  on  illumination  as w e l l as i n s t a b i l i t i e s  detector.  camera  shifts  atmospheric  spectrograph,  spectrograph  how  s e r i o u s of these  include variations  differently.  d e p e n d s on  problems of t h e  displacements  illuminated  The  Inconsistent  cause  the s t e l l a r  lines.  of the spectrograph.  with  problems  spectral  illumination  out-of-focus  line  is  i n t e r m s o f uneven  and s p e c t r o g r a p h ,  spectrograph  slightly  This  The most  changing  will  spectral  [1967]). Other  emission  these  relation  of r e f e r e n c e  c a n be u s e d  by t r a c k i n g  by t h e  slightly  spectrograph's  dispersion  atomic  positions.  positions  which t r a n s l a t e s  positions  lines  velocities  line  dispersion relation  of g u i d i n g e r r o r  unavoidably  radial  yet unpredictable effects  c a n be c a u s e d  telescope  of  of s p e c t r a l  The  cathode  the entrance  seeing.  and  the  a derived  systematic  guiding  also  wavelengths.  hollow  spectral  across  and  t h e measurement  the reference s p e c t r a l  various  the  determination  d e r i v e d from  e.g.  accuracy  TECHNIQUES  the d i s p e r s i o n r e l a t i o n  positions  lines  RADIAL-VELOCITY  follow will in  be the  spectral  reference  line  5 spectra  will  also  displacement  of  profile  the  of  asymmetry problems  suffer  the  velocities Fletcher  spectral  and  are  Griffin  [1976,1978], Campbell and W a l k e r  The of  method  radial velocity  i s about  ±l00ms"  [ 1 9 6 7 ] . T h i s was slit  and h e n c e  per p l a t e internal  Photoelectric  a  [1981],  1  to  ±0.07kms~ .  Higher  1  detector  as  t e c h n i q u e s c a n be f o u n d Baranne  in  a  and  et  value  in  error as  precision  a l . [1979],  technique plane  of  about  cross-correlation [1974], G r i f f i n  Beavers  and  and  Eitter  of v a r i o u s  I n f a c t , most methods a i m t o 1  be  [1983].  i s to achieve better  110ms" , o r i n some c a s e s , 11ms"  the  can  Gray  e t a l . [ 1 9 8 2 ] . The o b j e c t i v e  in precision.  Fletcher  spectrograph's  precision  van C i t t e r s  r a d i a l v e l o c i t y methods  1  photographic  mask a t t h e f o c a l  these p h o t o e l e c t r i c  1  about  and  measurement  cross-correlation  have a c h i e v e d  1  the  t h e same  spectrograph  ±l00ms~  and  Serkowski  the guiding-induced external  using a  1100ms" . R e v i e w s o f  i n the  narrowing  of  precision  radial  [1983],  by t h e c o n v e n t i o n a l  and a s p e c t r a l  [1977], and F l e t c h e r  the  Petrie  Campbell  a s r e p o r t e d by P e t r i e  Reticon  methods  [1974],  of  of  [1973],  attained  the spectrum  Gunn  Reviews  [1967],  Griffin  between the  degree  d e t e r m i n a t i o n of  Prevot  ever  ±0.3kms~  o f about  using  instrumental  some  [1973]).  and  a c h i e v e d by  about  error  achieved  1  reducing  of  the  dependent  [1985].  highest precision  stellar  by  et a l  if  exhibits  Griffin  discussed  intensity  lines  accurate conventional  [1967],  Campbell  severe  spectrograph  (Griffin in  from  in precision.  than  achieve  6 1.3 MODERN PRECISION RADIAL-VELOCITY TECHNIQUES Non-conventional  radial-velocity  classified  into  roughly  whether a  spectrograph  precision  radial-velocity  over  many o t h e r s a s h o r t time  rely  marks on on  scale.  In almost  Dravins  has  limit  the the  i n the s t e l l a r  out line  1  motions  and w a v e l e n g t h  involve  imposing  light  of the  relative  formation  itself  instruments  velocities. small  scale  region  would  velocities  (Dravins  the  techniques,  would e s p e c i a l l y  shifts  on  of  that  measurement o f a b s o l u t e  ±500ms" . Convective asymmetries  pointed  be  n o t . Most  a l l of these  accurate  can  depending  the s t e l l a r  the s t a b i l i t y  t o measure  inhomogeneities  or  techniques  the o b j e c t i v e i s [1975]  main c a t e g o r i e s  is utilised  wavelength c a l i b r a t i o n while  two  methods  to  about  cause  line  [1982]).  1.3.1 COUPE OPTICAL FIBRE FEED Heacox collimation input  [1983,1984] errors  by  lamp i s a l s o goal  scrambling  to the spectrograph.  t h e Coude s p e c t r o g r a p h  of t h i s  used  eliminated  t h e image  technique  guiding of the  T h i s was a c c o m p l i s h e d  w i t h an o p t i c a l  at the  the  fibre.  t e l e s c o p e end o f  i s to achieve  by  and  stellar feeding  The c o m p a r i s o n the f i b r e .  a precision  of  The about  tSOrns" . 1  1.3.2 INFRARED HETERODYNE The  wind  velocities  TECHNIQUE in  t h e atmosphere  been m e a s u r e d by i n f r a r e d  heterodyne  emission  950cm"  lines  a t about  1  o f Venus  measurement  (Betz  et a l .  have  of the [1976]).  C0  2  A  7 review  of  Blaney  infrared  [1975].  telescope combined  is  Basically,  combined  beam i s t h e n  which g e n e r a t e s radio then by  a  frequency  i s then  outputs are 6ms"  can  1  systematic laser.  with focused  motion  for  into  C0  2  a  which  frequency  the  laser.  The mixer  over  the  current  shift  is  caused  only  channels  for  instability  of  whose  various C0  2  i s the  r e g i o n such  at  of  the  o f t h i s method  visible  The  precision  correcting  i n the spectral  vary with  in  from  current  the Doppler  disadvantages  are  2  computer. A  frequency  lines  C0  40 i n d e p e n d e n t  e.g.  lines  beam  found  t h e o b s e r v e r and Venus.  after  errors  velocities  The r a d i o  achieved  by t e l l u r i c  unblended  frequency  multiplexed into be  infrared stablised  between  analysed  c a n be  on a HgCdTe p h o t o d i o d e  difference  One o f t h e main  crowding  a  and c o r r e c t e d  the r e l a t i v e  detection  the  bandwidth.  amplified,  signal  heterodyne  that  specific  radial  motion  of the  the barycentric  observer.  1.3.3  MEASUREMENT OF THE SOLAR OSCILLATIONS Various  160  minutes  methods and t h e 5  These o s c i l l a t i o n s 2ms" , 1  placed that  strip  the l i g h t  remain  Severny  beam  w o u l d become p o l a r i s e d would  minutes  et  in front  from  the  used  period  a c r o s s the Sun.  i n the solar  only  been  have v e l o c i t y  respectively.  pole-to-pole  have  to  measure  pulsation  amplitudes  o f t h e Sun.  of  a l . [1976] A circular  the  1ms"  observed polariser  of the spectrograph  central  while the l i g h t  portion from  and  1  a is  such  o f t h e Sun  the polar  rim  u n a f f e c t e d . Two p h o t o m u l t i p l i e r s a r e s e t on t h e  8  wings of a m a g n e t i c a l l y then of  insensitive  be m e a s u r e d by c o m p a r i n g  the  phot'omultipliers  internal  accuracy  circular  half  reported  t o be a b o u t  different  technique  of the solar  Brooks  the d i f f e r e n c e  at  of t h i s  disk  a l .  absorption  a  a n d an  is  left-  cell  longitudinal  Zeeman c o m p o n e n t s .  vapour of  field  The  intensity  first  light  the vapour  light  is  which  light  varying  wavelength of  t h e Zeeman  velocity  is  magnetic  field  that  can  would p l a c e  simply  The  and  one c a n i f only apply  a*  the  intensity light Zeeman  hence  the  sample  the  a  radial  constant  t h e two Zeeman components on  t h e maximum s l o p e  The  difference  i n the i n t e n s i t i e s of the scattered a n d a*  by  the  wings near  by t h e a'  in a  optical  shifted  the  sampled  vapour  the incident  field  components,  light  and  the  photomultipliers.  the magnetic  one  a'  l i g h t re-emitted  to  which  i s placed  excites  l i n e p r o f i l e . However,  desired,  metal  the  an  through  The s o l a r  controlled  light  proportional  component. By  with  modulator  produces  and t h e  pulsation.  i s then passed  at the wavelength of the p a r t i c u l a r  whole a b s o r p t i o n  was  optical,  isolated  polarisation.  solar  i s m e a s u r e d by c o o l e d  scattered  inner  ring  an  S r , Na, o r K. The v a p o u r c e l l  magnetic  resonance of  is  through a temperature  containing  i t s outer  used  electro-optical  or right-handed  then passed  against  The  compare t h e  measure t h e s o l a r  line  f i l t e r . The s o l a r  produces  output  polarisations.  to  [1976]  interference polariser  i n the  1  et  an  s h i f t s can  0.5ms~ .  r e s o n a n t - s c a t t e r i n g method t o Basically,  l i n e . Doppler  of the s o l a r  i . e . the short  line  and l o n g  profile. light  as  wavelength  9  components, w i l l line.  A  using  this  of  give the r a d i a l  precision  of  better  or a v a r i a n t  t h i s method c a n be  Fossat  and  Roddier  [1970], Grec  applied  to the  detectable fraction  [1980],  of  10  this  scattered  light  of the i n p u t  flux.  Grec  Transform  measure p r e c i s i o n beam i s d i v i d e d  path of  path d i f f e r e n c e  is  is  fainter  that  optical  only  be  a  velocities.  have  Basically,  recombined  Brault  generally  continuously  as  varied  by a l a s e r  the  The  numerically  together ratio  [1984].  to  after  h a s been v a r i e d .  s p e c t r o s c o p y have been and  used  one o f t h e beams  The  stellar applying  the  Hall  (  to s/n  the  t r a n s f o r m of  itself  can  be  Fourier  interference patterns  Reviews  g i v e n by Connes et  a  resultant  inverse  achieve ).  The  with  going through  starlight.  t o t h e o u t p u t . Many o f t h e s e  signal-to-noise  small  or dual  spectrum  added  the  two beams u s i n g a beam s p l i t t e r  spectrum.  be  very  be  stellar  the  can  since  been  the Fourier  transform  The  the  path  by  Snider  SPECTROMETER  pattern i s essentially  recovered  [1961],  cannot  flux  interference stellar  application  i t  stellar  would  m o v i n g m i r r o r and i s m o n i t o r e d same  achieved  e t a l . [1978].  e n t r a n c e a p e r t u r e s . The two beams a r e l a t e r the o p t i c a l  be  a l . [1976],  spectrometers  radial  into  et  and B r o o k s  1.3.4 INFRARED FOURIER TRANSFORM Fourier  can  _ 1  absorption  method. F u r t h e r  method  times  1 1  ±1ms  of the  i n Blamont a n d R o d d i e r  [1971],  et a l .  main d i s a d v a n t a g e  than  of t h i s found  velocity  the on  [1970] and  a l . [1979] u s e d  required Fourier Ridgway  the K i t t  Peak  10 Fourier in  spectrometer  bright  and  N 0  late  type  to observe stars.  were u s e d a s  2  t h e CO band  Telluric  p r e c i s i o n o f 20ms"  Hall  [1981] i n t r o d u c e d  the  stellar  lines  on t h e  better  than  required of  beam t o  s/n (==400) c a n be a c h i e v e d  Peery  atmospheric  velocity  fom t h e  However,  the  effect  precision  t o only  of  about  modified  [1983]  Michelson  radial-velocity stablised  of  line  has a  c o n t r o l unit to maintain  fibre  o p t i c feed  has  the  output  another  i s used  Velocities and T i  limited  and R i n g to  beam  fixed  i s used  search  for  The  path  I. the  the f i x e d  path  to observe  of the  the input  of  with  difference.  in a A  image. i s the  i s used t o  fringe pattern  the i n t e n s i t y  a  small  difference;  by an i n t e r f e r e n c e f i l t e r  intensity  used  temperature  in conjunction  used t o scramble  isolated  [1978]  s i g n a l f o r t h e i n t e r f e r o m e t e r . One d e t e c t o r  observe  hours  t o study the  Fe I ,  blending  Forrest  servo  input  the  INTERFEROMETER  a reference  line  several  i n 19 P s c .  variations in bright stars.  i s also  stars,  be  1  fact,  absorption  after  CO, HF,  interferometer  laser  into  0.4kms~ .  and  interferometer  cell  precision to  spectroscopy  gradient  lines  1.3.5 MODIFIED MICHELSON Forrest  a Tauri.  absorption  for bright only  a  telescope.  [1978] has u s e d F o u r i e r  were m e a s u r e d  An  even  1  a 4m  reference the  2  They o b t a i n e d  absorption  2  expected  I0ms~ . A p p a r e n t l y ,  i n t e g r a t i o n with  stellar  a N 0  H 0,  2  f o r the K giant  1  impose a r t i f i c i a l  s p e c t r u m . They  1  of CH„, C 0 ,  wavelength standards.  radial-velocity and H i n k l e  lines  (3900-4500cm~ )  while  the input.  A  11 radial-velocity change  i n the  output. will  The  then  the  output  of  intensity  intensity  The  1.5m  system  was  obtained  for  obtained  f o r twelve  two  Connes  A  on  while  other  spectrograph  and  an  The  seasons  3.8m  by  hence the UKIRT  telescope  to search 2ms"  of  about  20ms"  for was  1  of  has  t o be t e s t e d .  still the a  the  was  1  stability  with  beat  the  radial  about  scrambler.  laser  a  detectors  of  proposed  image  to a stable  the  that  interferometer  produce  two  i n a program  stars.  observing  the  f r i n g e s and  precision  [1983,1984]  servo-controlled  use  system  of  vacuum  a  echelle  A  tunable  mixing  w o u l d be  laser used  to  the i n t e r f e r o m e t e r .  FABRY-PEROT TECHNIQUES The  for  used  stars  between n i g h t s and  1.3.6  the  will  f r i n g e s move t h r o u g h between  Tenerife telescope  oscillations.  referenced  as  difference  stellar  monitor  the a b s o r p t i o n l i n e  g i v e t h e p h a s e of  velocity. and  shift  PEPSIOS s p e c t r o m e t e r  stellar  measure t h e  oscillations  (Traub  r e t r o g r a d e wind  Carleton  [ 1 9 7 9 ] ) . The  Mack e t  al.  has  PEPSIOS s y s t e m  [1963].  The  linked  a  transmittance orders.  The  series by  to  incident filter  before  The  of  spectrum  scanning  the  search  a  (Traub  consists  of  and  are  order  of  single  train  i s accomplished  by  by  three  parasite  i s p r e m o n o c h r o m a t i s e d by  e n t e r i n g the  to  etalons  a l l the neighbouring  starlight  interference  to  been d e s c r i b e d  s p a c i n g s . The  isolate  suppressing  on V e n u s  has  spectrometer  e t a l o n s of d i f f e r e n t  been u s e d  e t a l . [1978]) as w e l l as  velocities  Fabry-Perot in  also  of  an  etalons.  varying  the  12  pressure  of  the  N  photomultiplier short-term  3ms"  10ms"  is  will  imply  etalon.  the  variations  line.  without  et  a l .  [1978]  radial-velocity The  described  spectrometer  i n p u t t o the system  t e l e s c o p e . An absorption  line.  accomplished  by  The a  of  line output  precision  larger  a  et a l . [1978],  Fabry-Perot  is  used  this  o f 10ms" . 1  fibre to  from  an  system  is  of  the  In f a c t ,  in  mode between t h e  case  inflection output  i s used  in rapid  p o i n t s of  intensity  the l i n e  will  c h a n g e . The s t a b i l i t y than  X/1000 on t i m e  IRFC  of the system  scale  oscillations 20ms" about  1  to  4ms~  1  as a  on t h e 1.9m  search  for  Scuti  f o r the  was a c h i e v e d  change  two  in  the  radial-velocity  i s s u p p o s e d t o be b e t t e r  on t h e s h o r t e r t i m e  i n Ap and 5  was a c h i e v e d  The  gap  the scanning  o f d a y s t o weeks w h i l e  The s y s t e m was u s e d  telescope  profile.  be i n t e r p r e t e d  X/10000 c a n be e x p e c t e d to hours.  chopping  the  isolate  etalon  servo-controlled variation  and  stellar  between t h e p l a t e s o f t h e F a b r y - P e r o t . this  than  stars.  i s f e d by an o p t i c a l  scanning  the  a  i n the  t h a t has a p r e c i s i o n  interference f i l t e r  GaAs detect  p o i n t of  values  Reay e t a l . [ 1 9 8 3 a , 1 9 8 3 b ] , A t h e r t o n Wells  To  change. A  f o r a Bootis while bright  cooled  scanning,  A change  radial-velocity  f o r other  A  detector.  a half-intensity  a  was a c h i e v e d  1  as  Fe I X6678  were f o u n d  1  used  .set a t  e.g. the  intensity of  is  i n each  radial-velocity  spectrometer profile  gas  2  6 Scuti  scale  variable star  1.5m  radial-velocity  A precision  f o r the b r i g h t  than  of minutes  SAAO a n d t h e  rapid  stars.  better  of  about  p Pup  while  Canopus.  13 Serkowski  [1972,1976] p r o p o s e d  measure r a d i a l polarised  by  temperature of  velocities.  a Wollaston stablised  polarisation.  stellar  light  polarisation wavelength  and to  a tilting  s t e e p change  as  a  function  each  Wollaston  the  etalon  Digicon  image t u b e  of  method  reductions wavelength  orders.  are  The  both  is  One  is  of  plane the  angle  of  Hence  the  the  spectrum  half-wave  is  used while  out  scanned  t h e main  the by  a  disadvantages  system  a l s o dependent  plate  element  to sort  The  The  etalon is  then  the o p t i c a l  ia  a  of p o l a r i s a t i o n .  used  complicated.  calibration  in  resolution  output  detector.  very  the p o s i t i o n  prism. A Fabry-Perot spectral  through  retarder,  wavelength.  to  linearly  r o t a t e s the  a rotating  spectrograph  i s that  in  angle  through  individual  echelle  passed  the  element  position  passed  from  of  resolution  unique  various  this  I t i s then  emergence  method  is first  phase r e t a r d e r which  Upon  i s then  isolate  prism.  a  of  a calcite  starlight  has  encoded w i t h a starlight  The  a polarimetric  and  the  data  accuracy  in  the  on  the  stellar  flux. Serkowski [1979a,1979b] spectrometer  modified into  spectrometer. wavelength  [1977,1978]  The  and  the a  polarimetric Fabry-Perot  Fabry-Perot  calibration  since  the  prism  The  starlight  before  d e p e n d e n c e of  passes  r e a c h i n g the radial  the  through  et  al.  radial-velocity radial-velocity  interferometer  t r a n s m i t t e d maxima depend o n l y on etalon.  Serkowski  provides  wavelengths  of  specifications a rotating  of  on  the p o s i t i o n  of  the the  reversion  Fabry-Perot. This eliminates  velocities  the  the  the star  14 in  the  entrance  spectrometer of  uses  the r o t a t i n g  also  provide  calibration  spectrum the  reversion identical  The  by an  echelle  interferometer transmitted in  of the  later  illuminated was  of  intensified  instead record  in  a  eight  later  260A  i s then  of  (CCD) o f  is  512x320  pixels  as  eighteen  echelle  McMillan  [1984]). A p r e c i s i o n  latest  version  integrated  an  N0  the  s o u r c e was  used  to c a l i b r a t e  the  in  absorption  2  An a r r a y  device  centred  at  of  Fabry-Perot  tube 42x342  (CID) was  about  can  spectrum  X4230.  the i n t e n s i t i e s maxima. The  used  It  The  the cell  of  the spectrometer.  Fabry-Perot  the spectrometer  then  i n s t e a d . A D i g i c o n image  of  the  output  image s c r a m b l e r  r e c o n s t r u c t e d from  wavelength-calibrated version  the  a  of  orders simultaneously.  and  on  is  wavelength  the d e t e c t o r .  version  from  the  the  cathode  charge-injection  echelle  c o v e r s about spectrum  as  will  s p o t s . The s c a n n i n g  the  system,  by a lamp i s "used used  that  of the spectrometer  the  light  Fabry-Perot  tilting  hollow  Fabry-Perot. With  originally  pixels  by  changing  version  version  the  bright  instead  incident  s p e c t r o g r a p h such  maxima. An F e - A r  the e a r l i e r  tilts  is  star,  from  the  image s c r a m b l e r  than  a  of  image s c r a m b l e r  when  realised  hereby  fibre  version  illumination  of rows o f  is  later  p r i s m . The  output  consists  spectrum  A  an o p t i c a l  lamp, r a t h e r  Fabry-Perot. dispersed  aperture.  of  The the  most  recent  charge-coupled  device  uses  a  the  d e t e c t o r and  can  record  o r d e r s s i m u l t a n e o u s l y (Smith et a l . [1983], o f 5ms"  of the s p e c t r o m e t e r .  sunlight  1  i s expected  Initial  has a c h i e v e d a p r e c i s i o n  test  for with  o f about  this disk 6ms"  1  1 5 while  short  exposures of  gave a p r e c i s i o n  1.3.7  absorption telluric the in  lines  as  lines are  poor  Griffin e.g.  imposed  Reticons,  [1980]), bright  on Venus  and  set  stellar  have  spectrum  of  been  for stellar  the  problems  result  with  the  the  Barker  wind  e t Cochrane  oscillations  i n the  [1982a,1983]).  used  in  detectors,  measure  (Smith  lines  before  photographic  used  to  the  eliminated.  electronic  technique  of t e l l u r i c  Since  of  precision Modern  telluric  most o f t h e  (Young e t a l . [ 1 9 7 9 ] ,  search  use  methods c a n be  a T a u r i and a B o o t i s  stars  most common  to  the  [1973],  telluric-absorption-line velocities  on t h e  characteristics  limited  to  references.  the spectrograph,  Griffin  the  proposed  wavelength  photometric  and  [1973]  radial-velocity  e m u l s i o n s have  telescope  LINES  Griffin  s t a r l i g h t enters  The  a small  1  and  conventional  with  o f 40ms~ .  USE OF TELLURIC Griffin  Arcturus  i s the  0  2  The  band  at  X6300. One  disadvantage  technique stable  i s that  enough  precision  is  bands and overlap  as  a  strengths differently  of  different  from  bands  ) i s not  i f very  other the  as  lines  atmospheric  2  high  absorption  elements  t o produce a  wavelengths  telluric  under d i f f e r e n t  2  s p e c i e s of  absorption The  ( 0 , H 0  calibrator  Weak l i n e s  isotopic  spectrum.  telluric-absorption-line  spectrum  wavelength  required.  various  the  the t e l l u r i c  the reference  complicated  of  well  will  rather  as  also  conditions. 0  may  the vary  2  lines  1 6 will  grow w i t h z e n i t h  distance while the H 0  lines  will  grow w i t h h u m i d i t y . The b l e n d i n g o f t e l l u r i c  lines  w i t h weak  2  stellar  lines  and t e l l u r i c  stellar  lines  w i t h weak t e l l u r i c  shifts and  depending  on  lines  conditions.  demonstrated  by  pressure  will  also  telluric  lines.  pressure  i n d u c e d s h i f t s o f more  be  observing,  with a  lines  difficult  absorption  with the  but line  under  caused  10"  not  by  type  line  star  been  atmospheric  2  reference reported  angstrom  f o r the  a  by  with  to  the  problem.  the the  blends  The  an u l t i m a t e p r e c i s i o n  artificial  by  spectrum.  be u s e f u l  is  reduce telluric  for  short  of  about  conditions.  LINES  e t a l . [1982] and C o c h r a n e  impose  caused  stellar of  by  observing  i . e . one c a n o n l y  the  atmospheric  telluric  n u m e r i c a l l y removing  removal  eliminate  can  obtained  t h e same  problems  'cleaner'  be p e r f e c t  lines  the  spectrum  technique should s t i l l  excellent  Cochrane  telluric  under  1.3.8 IMPOSING A R T I F I C I A L CALIBRATION  method  has  have  n u m e r i c a l l y removing  numerical  scale calibration 1  than  line stars  of the  [1979]  of  of the  effect  Walker  reduced  and can never  effect  10ms"  fictitious  Changing  the blending  c a n be  Nevertheless,  time  and  telluric  Similarly,  lines  stellar  by  s a y , an e a r l y  conditions.  the  This  the wavelength  problems  reduced  spectrum  stellar  Campbell  cause  velocity  [1983].  affect  blending  probably line  Campbell  as the b l e n d i n g  lines.  2  The  lines  the t o p o c e n t r i c  atmospheric  A-band 0  as w e l l  also  [1984] d e s c r i b e d  calibration  lines  on  a the  1 7  spectrum  before  artificial  the s t a r l i g h t  absorption lines,  temperature-stablised optical  fibre  scramble the  the input  scrambled  Fabry-Perot by  rest  the  contains  a  t o form  identical  except  output  only  Octicon spectrum The  the  which  The  two  the output that  in  beam.  one  of the  while  two beams.  is  maxima  each  i n the  of  which  are  back  the  reflected  by t h e l o s s beams  beam of the  are  then  tilted  such  that  w a v e l e n g t h by h a l f Consequently,  minima  the free  from  range  of each a b s o r p t i o n  1 500A and  i f the e r r o r  is  and  precision  measurement of  the  an The  X6820.  reference  increase the p r e c i s i o n  i n each l i n e  expected  stellar  of  minimum  i s c e n t r e d a t about  s e v e r a l hundred  the the  separated  spectral  are the  1872-Reticons p l a c e d end-to-end.  wide b a n d p a s s w i l l  The  Each  Both F a b r y - P e r o t s  Fabry-Perot.  the depth  i s eight  in  Each  etalon.  reflecting  reflected  contains absorption  c o v e r s about  distributed. 1  completely  50% o f t h e c o n t i n u u m . The d e t e c t o r t o be u s e d  result  1ms" .  into  interference  i n w a v e l e n g t h by h a l f  availability  lines  to  Fabry-Perot  The s p e c t r u m  range  the F a b r y - P e r o t is  divided  maxima a r e d i s p l a c e d i n  spectrum  each other  first  a b s o r p t i o n minima c a u s e d  recombined  spectral  here  An  by g u i d i n g o r s e e i n g v a r i a t i o n s . The  the  maxima.  transmitted  used  background while  beam.  imposed  a r e f o r m e d by two  etalons in r e f l e c t i o n .  again  separate  a black  transmitted  free  is  transmits  absorbed of  caused  on  is  case,  The  image. T h i s e l i m i n a t e s t h e v a r i a t i o n s  starlight  falls  in this  Fabry-Perot  scrambler  illumination  beam  enters the spectrograph.  of  i s randomly  technique  is  18 An gas  absorption c e l l  has  lines  been u s e d  on  the  to  filled  spectrum  before  The  generated  are  by  controlling  t h e HF  gas.  described  Details  in  of  later Yang and  measure t h e  relative  for o s c i l l a t i o n s  search  stars  and  internal  precision  o b t a i n e d on  the  value  was  obtained  velocities  of a t i m e  data  ±12ms~ from curve  1.4  observed (Campbell  the  scatter T  and  Walker  i n the  VARIABLES  8  of  Campbell  Campbell  a Boo  in  the )  to  [1984], The  f o r data  1  [1983]).  This  the  measured  s p e c t r a . The  precision  observing  seasons  [ 1 9 8 5 ] ) . T h i s v a l u e was  measured  and  in  al.  ±6ms"  to  Scuti  a l . [1985]).  i s about  al.  technique  technique  et  scatter  n i g h t s and  Ceti.  DELTA SCUTI  the  series  over  Campbell  ( I r w i n and  from  et  of  of are  technique  Walker e t  technique  same n i g h t  1  of  the  Yang  ( extra-solar planets ?  [1983],  [1985],  of  the  stars. HF  X8700  technique  variations  the  the  pressure  [1983] a p p l i e d t h e  been a p p l y i n g  Walker  used  in bright  (Campbell  Campbell  for  Campbell  f o r low-mass c o m p a n i o n s  solar-type  and  thesis.  radial-velocity  to  also  [1983]  enters  at about  temperature  this  (HF)  absorption  starlight  absorption c e l l of  Walker  I r w i n and  W a l k e r have  the  t h e HF  variables. search  the  fluoride  reference  absorption lines  chapters  [1982] and  hydrogen  impose a r t i f i c i a l  spectrograph. stablised  with  relative  i s about derived  radial-velocity  19 1.4.1  INTRODUCTION The  are  Delta  one g r o u p o f  periods light  of l e s s  The  than  forthis  large-amplitude referred  Vel variables  have a  typical  5 Scuti  the  main  while  >0.3  instablity  strip  t o about  edge o f t h e s t r i p  about  strip.  or  variables  than  10  luminosity from  V.  are  magnitude.  less  I t ranges  in  Cepheids,  5 Scuti  0.05  i s a lower  from  variables  dwarf  i s generally  instability  sequence  )  The  ranges  0.8 m a g n i t u d e  stars,  of  pulsation  t y p e A o r F.  the small-amplitude  amplitude  variables  by  of v a r i a b l e s  magnitude  a s RRs  amplitude  the Cepheid  and s p e c t r a l  group  (  Cepheid  distinguished  a magnitude t o  to  V  radial-velocity The  stars  0.3 day  thousandths of  generally  of  or U l t r a s h o r t - P e r i o d  variable  amplitude  several  AI  Scuti  The  kms" . 1  extension just  below  2.5 m a g n i t u d e s above  i t . The b l u e  h a s been d e t e r m i n e d by B r e g e r  [1977] t o be  8000K on t h e ZAMS a n d 8400K a t a b s o l u t e v i s u a l m a g n i t u d e  of  0.65.  at  The r e d  absolute found  inside  open  star  a t 7500K  the i n s t a b i l i t y  the  5  phenomenon. ( ZZ C e t i  greater Scuti  In  stars  strip  ), t h e  than  0.01  i n the  usually  Population  I objects.  two-solar-mass  stars  a  found  a  Persei  Galaxy.  of the s t a r s variable  a r e t h e most  stars  normal pulsators numerous  variables  They a r e g e n e r a l l y I  suggests  and  dwarf  6 Scuti  been  cluster  t o be  common  white  stars  Population  have  magnitude. T h i s  the  5 Scuti  a n d 6950K  to one-third  is  after  pulsators  be  the  have been  pulsation  fact,  Scuti  e.g.  one-quarter  type of  to  on t h e ZAMS  o f 1.7. 5  clusters  [ 1 9 7 8 ] ) . About  with amplitude that  is  v i s u a l magnitude  in  (Slovak  edge  that  are  considered are  just  20 evolving  o f f t h e main  sequence.  There  i s a subgroup of  the  variables  l e d by SX Phe w h i c h r e s e m b l e s P o p u l a t i o n  II  stars  in  kinematics  In  fact,  their  several  variables  cluster  to Cen o r  and  Irkaev  and low  are  metal  probably  are objects  abundances.  members  in  of  the  globular  the g a l a c t i c halo  (Frolov  [1984a]).  1.4.2 MAIA SEQUENCE ? Struve of  Maia  (20 T a u ) v a r i a b l e s  HR d i a g r a m of  quite  pulsations  common  (Breger  which would  as c o o l  the speculation  existence  the existence fill  of a  t h e space  that  a s B5  (Smith  nonradial  the Maia  variables  [1977])  pulsation  is still  [1979]). S t u d i e s of v a r i a b i l i t i e s (B7III),  7 UMi  (A3II-III),  not  have  7 CrB  the  photometric Tippets  variations  and  [1983]). This candidate, of  s t a r s may o n l y  Wilcken is  1.4.3 6 DELPHINI Some 5 S c u t i all 6  V e t o and  recent  by K h o l o p o v  may  concentrated (AOIV),  on t h e  Peg  i n the  detectable [1970],  [1981],  with another  review  r  lies  show  Kovacs  be  time, the  of 7 CrB (Percy  the s i t u a t i o n  a L y r (A0V). A  Vega h a s been g i v e n  while not  e.g. the case  [1970],  also  occasionally  has  conclusive  ( A 5 I V ) , and 0 S e r ( A 2 V ) . One o f t h e d i f f i c u l t i e s that  i n the  existence  f o r a l l B and A s t a r s . A t t h e p r e s e n t  of  20 T a u  fact  sequence  between t h e (5 Cep a n d 5 S e t s t a r s . The  nonradial  increased  on  [1955] h a s p r o p o s e d  Veto  probable variability  [1984].  ANOMALIES variables Del  also  stars are  have  6 D e l type  8 Scuti  anomalies  variables.  Delta  21 Delphini A  or  s t a r s are  F.  The  6 Delphini and  Sc  are  subgiant  degree  s t a r s but  relative  t o Fe  that  the  Eggen  6 Del i n Am  diffusion  theory  quiescent  and  ionisation  and  Cr  [1976] and  evolved  slowly  z o n e may  would  Consequently, settling rise  and  produce  under  influence  others  photospheric  soon as  convection  10  (Vauclair  depletion  however a l s o  implies  agrees very  well  Am  not  s t a r s do  of  with  Fe.  have  He  mixing  of  suggested abnormal by  in  He  a II  settle  convection elements.  gravitational  some e l e m e n t s the  the  II  the In  i n the  of  downward  pressure,  explains  other  [1982]).  helium  the  Ca  marginal  i t s tendency to  the  y e a r s a f t e r the  3  to  sink  in  earths  been e x p l a i n e d  outer  observed  elements. M e t a l l i c i s m ,  '1.4.4 COEXISTENCE OF The  will  layers. This  o v e r a b u n d a n c e of as  the  to  a  s t a r s . The  destroys  normally  the  rare  be  Vauclair  due  upward r a d i a t i o n  while  Am  r o t a t i n g s t a r , the disappear  the  [1979]  s t a r s have g e n e r a l l y and  among  m e t a l l i c i s m and  Kurtz  (Vauclair  and  relative in  type  underabundant  also  similarities  downward g r a v i t a t i o n a l l y . T h i s which  Zr,  may  s t a r s are  abundances  Y,  spectral  varies  they are  Sr,  There  the  s t a r s of  metallicism  while  i n T i , V,  Because of properties,  of  giant  generally,  overabundant.  underabundance  or  in fact,  disappearance  of  will  stellar  undercan the  and occur  He  II  [1976]).  PULSATION AND helium that the  pulsate.  METALLICISM  from the  the  star  He will  observational Several  II  ionisation  not  fact  m a r g i n a l Am  pulsate. that  zone This  classical  s t a r s have been  22  found star  to p u l s a t e HR3321  has  period  of  (Kurtz  [1984]).  Am-like  55  5  been  found  [1979],  [1981] have  suggested  f o r the Am  as  residual  6 Del  stars.  enough d r i v e  an  the  due  Cox  6 Scuti  problem  variable  of  existence  0.006 of  for  Valtier  et a l .  that  With  et  [1979b],  with  theoretical  and  incomplete  from  both  [1979],  Saez e t  al.  pulsation  can  w h i c h a r e more e v o l v e d  to occur  than  the  there w i l l  enhanced H as  settling  or  a  pulsating  al.  mild metallicism,  Am  magnitude  the  the  m e t a l l i c i s m and  stars  to  the m a r g i n a l  t o e x p l a i n t h e c o e x i s t e n c e of  for pulsation He  a  fact,  amplitude  metallicism.  Stellingwerf  in  be  poses a  w h i c h has  and  classical  to  Similarly, stars  interpretation  coexist  [1978]);  m i n u t e s and  Del  pulsation  (Kurtz  recent  be well  upward  mixing.  1.4.5  MODELS OF 6 Scuti  ionisation  zone a t  another  coincidence second  computed the mass  from  observed  from  5 . 2 x 1 0 K and  Z  by  by  the  the H  S t e l l i n g w e r f [1979] p o i n t e d o u t  ionisation  zone a t flux  theoretical  from  A wide 0.2  with  the  other  range of 3.0 of  II  ionisation that  caused  5  models  to  (the content t o 0.001  1.5X10 K  He  frequency  observables  there  by  the  of  edge. P u l s a t i o n a m p l i t u d e s ,  c o n s t a n t s , and  the  0.01  mainly  partly  4  values.  ranging  ranging  driven  of maximum p h o t o n  pulsation  composition  is  minor d r i v i n g  helium  ratios,  STARS  pulsation  1.2X10"K.  zone a t is  6 SCUTI  the  period  are  often  for comparision  with  models w i t h  solar  masses  elements h e a v i e r  have been c l a i m e d  stellar and  the  than  He)  to agree  with  23 the o b s e r v a t i o n s .  N o n l i n e a r approaches  models a r e o f t e n results,  required  the  artificial  mechanisms),  (Stellingwerf  [1980],  Some  of  the  well  a s why  Fitch  and  Percy  other  modes  some modes a p p e a r that  radial  and n o n r a d i a l modes.  to  o u t why some s t a r s  in stars  of the  strips  as w e l l  variabilities. of  5  Scuti  of  as the r o l e Recent stars  in  are pulsators  if  the  in  [ 1 9 8 0 ] , Cox  a n d Hodson  [1981], Tsvetkov  and  Cox [ 1 9 8 4 b ] ,  [1980], F i t c h  the  theoretical  and  on  e t a l . [1980],  recent e f f o r t  observational  the  aspects [1975],  Stellingwerf  [1980],  [I982ab], Andreasen  The most  instability  Peterson  [ 1 9 7 9 ] , Cox e t a l . [ 1 9 7 9 a , 1 9 7 9 b ] ,  Fitch  include  and d i f f u s i o n  Stellingwerf  [1980], K u r t z [ 1 9 8 0 ] , Andreasen  or i f they  on t h e t h e o r e t i c a l  found  is  the s t a r s  problems  of  be  resonance  velocity  Other  of r o t a t i o n  be  may  s t r i p are not  that  strip  as  example,  One o f t h e p r o b l e m s  t h e edges  discussions can  amplitudes  there i s a  high rotational  determination  involve  and n o n r a d i a l ) ,  i n the i n s t a b i l i t y  i n an a p p r o p r i a t e b i n a r y s y s t e m .  a better  the  physics  the p u l s a t i o n  where  instability  t h e y have a s u f f i c i e n t l y are  input  A n t o n e l l o [1982] h a s s u g g e s t e d part  the  (i.e.  multimode p u l s a t i o n  between  lower  of  and d i s a p p e a r . F o r  excited  the  Current  problems  (radial  preferentially  variables.  parameters  theoretical  [1980] h a s s u g g e s t e d  find  stars.  [1980]).  current  excited  theoretical  on t h e t r e a t m e n t  t h e mechanisms w h i c h g o v e r n  the p a r t i c u l a r  Scuti  viscosity  dissipation  and  the 5  however, depend v e r y much  opacities,  finding  for  i n the  Dziembowski  Percy  [1980],  et a l .  [1983],  t o compare  properties  between of  both  24 high-amplitude found  and low-amplitude  i n Andreasen  [1983].  the h i g h - a m p l i t u d e 5 Scuti  1.4.6  metal-poor,  8  metal-rich,  and  on  double-mode  M Other  i s a period-luminosity-colourrelation  Scuti  relation  stars.  = -3.052 l o g P - 8.456  y  d e t e r m i n a t i o n s of a n d Bregman  Frolov  and I r k a e v  each  radial  [ 1 982b]. T ^  [1979]  gives  the  following  The  ( b - y ) - 3.121  t h e PLC r e l a t i o n  [1975], A n t o n e l l o and Conconi [1984b].  pulsation  In f a c t ,  stars  This agrees pulsation  those  are  [1978] a n d  relations  by  [1982], and  PLC r e l a t i o n s  mode by Gupta  corresponding  (1.3)  include  given  Tsvetkov  between  a r e a l s o g i v e n . The p e r i o d - g r a v i t y  8 Scuti  1.4.7  Breger  (PLC) f o r  :  Breger  relation  a n c  *  of the  g i v e s a s l o p e between 0.030 day a n d 0.035 d a y .  well  with  constant Q  the expected  radial  fundamental  o f 0.035 day ( B r e g e r  0  mode  [1980b]).  LIGHT AND VELOCITY AMPLITUDES Antonello et  between t h e colours  v  visual  light  v  found  amplitude  and  v  + 7.54(6c,) (b-y) 0  i s the peak-to-peak v i s u a l  relation  replaced  have  will  by t h e p e r i o d  a  relationship  the  narrow  band  stars:  = 2.06(8c,)oM  t e r m Am  above  a l . [19813  of t h e 8 S c u t i  logAm The  includes a discussion  be  PERIOD-LUMINOSITY-COLOUR RELATION  the  log  It also  v a r i a b l e s can  stars.  There  for  6 Scuti  be  simplified  0  " 1.91  light i f  a m p l i t u d e . The  the  u s i n g t h e PLC r e l a t i o n .  (1.4)  colours  are  25 There velocity  i s also  amplitude  92kms" mag1  is  a  a  for  1  typical  nonradially  2K.  value  45kms~^ag" .  large  difference  found  t o be  in  the  generally excited about  6 Scuti  and  periods  stable  and  pulsation  proposed  the  amplitudes  small  the  beating  that  the  the  value use  is  this  distinguish  stars  complex  pulsation  c u r v e s . These  question  amplitudes.  AI  are  various  however, a  rotation  HR6434, an  are  structures  e f f e c t s from t h e  is s t i l l ,  stellar  in  to  this  For  to  a l l 6 Scuti  radial-velocity  of  [1982] has  able  values  s p i t e of  the  shown t h a t  of  pulsators.  modes. T h e r e  stability  two  be  the  a value  pulsators.  may  in almost  in  and  v  s t a r s , a more t y p i c a l  the  nonradial  light  radial  Am  given  [1982b] has  f a c t , one  a t t r i b u t e d to  the  [1969] has  the  between  pulsation  believed  for  In  1  The  Breger  pulsating  radial  r e l a t i o n between  IK/hm^. S m i t h  about  between  linear  Breger  is responsible Vel  -like  6  for  Scuti  star.  1.4.8  SYSTEMATICA OF From t h e  constant 25%  of  Q,  the  pulsate  statistical  Antonello  and  low-amplitude  i n the  available  6 SCUTI  radial  r e s u l t s on  draw  some  properties. i n many  s t a r s . For  Pastori (i.e. <  6 Scuti  [1981] 0.3  radial  of  the  found  pulsation that  magnitude)  variables  s t a r s with determined  about  about  mode. B a s e d upon a l l  analyses,  conclusion  Several  distribution  fundamental  modes f r o m m u l t i p e r i o d i c to  STARS  Breger their  modes a r e  stars pulsating  pulsation  [1980b] was general  in  able  pulsation  simultaneously mainly  the  the  excited higher  26  radial  overtones,  may a l s o  be  dominant  present.  for  instability over  the  with  strip.  The in  overtone  fundamental  mode  is  the  5  Scuti  found  in  stars  stars  have  cool  instability  modes.  the  and l o w e r  part  Nonradial pulsation  The  fundamental  r e v i e w s of  radial the  modes a l t h o u g h  radial  radial  fundamental  stars  entire  nonradial  the  c a n be  strip.  Not  AI V e l s t a r s the  properties  of  first  overtone  mode.  the  Scuti  Fitch  [1976],  Eggen  Wolff  [1983],  and B r e g e r and S t o c k e n h u b e r  of  eigenfunctions  stellar  (r 6 <p)  pulsation  are  r  the  Frolov  Recent can  be  [1975],  [1979,1980a,1980b,1980c], [1983].  with  the  the  have  P^(cos0)  first for  the  spherical  of  The  The a n g u l a r  numbers, harmonics  functions  Y'(0,0)  real  the  spherical  Y^(0,<£),  being  kind.  frequencies.  quantum  i n the  harmonics  The f u n c t i o n  orders  which c h a r a c t e r i s e  p r o p o r t i o n a l to  spherical  exp(/ai).  the  Breger  [1973],  the  MODE CLASSIFICATION The  of  al.  variables  in  OSCILLATION MODES  1.5.1  r  B a g l i n et  8  only  coexists  mainly  i n Leung  [1979],  often  pulsate  found  1.5  all  nonradial pulsation  and  [1970],  of  modes  the  is  polar  of  equal  Associated a are  parts,  the  radial  to  the  harmonics  m=-l,...,0,.../, The  modes  coordinates distance  r,  dependence  p'(cos0)exp(/m0)  Legendre  Polynomials  eigenvalues  oscillation  quantum n u m b e r s ,  indices.  normal  and a t e m p o r a l  terms  spherical  the  which angular  /=0,1,2,...,  while are  (2/+1)-fold  the the  are  azimuthal azimuthal  degeneracy  of  /  27 i n m c a n be l i f t e d  by t h e r o t a t i o n  of the s t a r . A review  m-splitting  h a s been g i v e n by Cox [ 1 9 8 4 a ] .  corresponds  t o waves t r a v e l l i n g i n t h e o p p o s i t e d i r e c t i o n t o  the  stellar  travelling to  rotation  case  of n o n r a d i a l  to quadrupole are  also  m<0  i n t h e same d i r e c t i o n .  the s p e c i a l  case  while  corresponds The /=0 mode  of r a d i a l p u l s a t i o n .  dipole  The c o n d i t i o n  of  oscillation  while  1=2,3  i n the  displacement  from  and  £=1,2  are  respectively. 14  the  modes  There  also  cause  four  a. 2  an  infinite  The  p r o p a g a t i o n zones the envelope with  of  2  the r e s t o r i n g  the  orbit,  of  2  usually  the  oscillation  pressure  of  the  (acoustic) variations. situated  v a l u e s of t h e s e  modes  k ( t h e number o f r a d i a l n o d e s )  large  force.  of  nonradial  spectrum  due t o p r e s s u r e  t h e s t a r . The a  have m a i n l y  vertical  variations.  modes have g r a v i t y  The p r o p a g a t i o n z o n e s  .and  motions  The v a l u e s  f o r t h e p-modes i n c o m p a r i s o n  t h e g-modes. The g o r g r a v i t y as  i n binary  spheroidal type  p r e s s u r e and d e n s i t y  are generally  modes,  o f t h e p-modes a r e g e n e r a l l y  / v a l u e s . The p-modes  a  force  increasing  as l a r g e  overtone  [1979]).  discrete  p-modes a r e  modes w i t h t h e r e s t o r i n g  of  Each  +  to  of  the  pulsation  hyperfine s p l i t t i n g s  types  (p,f,g ,g~).  corresponds  second  ( F i t c h and W i s n i e w s k i  are  oscillations  eigenvalues  first  T i d a l e f f e c t s on t h e v a r i a b l e  A u r , may  pulsation  as w e l l  There  t h e c e n t r e of  while  increase  correspond  t h e r a d i a l quantum numbers k, w h i c h d i s t i n g u i s h t h e  t o the fundamental  in  corresponds  The /=1 mode i s t h e  s t a r . The k=0 mode c o r r e s p o n d s  The  waves  and o c t u p o l e o s c i l l a t i o n s , r e s p e c t i v e l y .  number o f n o d e s  e.g.  to  m>0  with  (buoyancy)  o f t h e g-modes  28  are  generally  given  /  situated  value,  increases.  the  The  a  as  well  For  the  g -modes,  the  g~-modes.  a  The  oscillatory  i n the  lowest  k  value  effects  of  variations  as  those  of  stellar  models,  waves on a f l u i d for  in  the  by  and g - m o d e s .  the  f-modes  sphere.  (vortex-like)  and c a r r y  The  radial  nonradial  (Smith  a  c a n be  to  Their  +  star  while  only with  and  for  l>2.  and  are  In s i m p l e  modes may a l s o  no  intermediate homogeneous  be  surface present  [1978]  toroidal  have modes driven  atmospheric  Saio  [1982]).  %(r,t)  c a n be e x p r e s s e d  = a(r)  P^(cos0)  = b(r)  d ( P ' ( c o s 0 ) )/dd  e  The  i n f o r m a t i o n from one  [1981],  Ji ,  the  density  c o n s i d e r e d as  motions  the  convectively  exist  of  are  horizontal  i  ir.  g -modes  the  a class  are  are  ,t ) = (  f  the  for  modes  They a r e R o s s b y - l i k e waves  i(r  r  l,  the  P a p a l o i z o u and P r i n g l e  displacement  oscillations  negative  the  of  values  2  Toroidal  are  2  pressure  p-  forces.  another  the  the  rotating stars.  to  a  node)  their  Coriolis  depth  radial  r-modes d e s i g n a t i o n  slowly  modes  as  a rotating pulsator.  given  only  on  k  implies  in  f-modes  a p p r o a c h 0 as  variations.  oscillatory  no  a  and d e n s i t y  of  (i.e.  For  horizontal  while  2  star.  mainly  r a d i a t i v e regions  well  between  have  a <0  or K e l v i n  the  g-modes  The e i g e n f u n c t i o n s  The f  the  the  usually  condition  unstable.  regions.  of  are p o s i t i v e  2  be  i n t e r i o r of  small pressure  dynamically  unstable  values  2  as  +  can  the  g-modes  motions  g~-modes  in  £ ) 0  due as  exp(/tn )  exp(/m0) exp(/m0)  to  spheroidal  : (1.5) (1.6) (1.7)  29  = imb(r)  In a  air)  = <//(')/r  bir)  =  constant the  C  air)  and  and  i//(r)  \j/ir)  e.g.  i n Cox  horizontal  r  l  +  ]  L a  k  r  2  part  [1971]  and  c o n s t a n t s and velocity  Kubiak  with the  change  is  -  0  of  xir)  =  r  l  ]  L b  they  b(r)/a(r) the  are =  both  functions i n the  [1958].  by power  pulsating  [1978],  simply  +  The  The f u n c t i o n s  Walraven  be a p p r o x i m a t e d  ratio  then  mode. The  respectively.  i n Ledoux and  and  a mnc  of t h e d i s p l a c e m e n t  [ 1 9 8 4 ] ) . In most m o d e l s w i t h a t h i n Osaki  i s a function  the p u l s a t i o n  k  o =  fl,  i n the n o n - r o t a t i n g case.  direction,  given  frequency  [1980] and  f-modes, t h e y can =  (1.10)  with angular  are the r a d i a l  x ( r ) are  t h e p- and  (1.8) (1.9)  s t r u c t u r e and  bir)  and  radial  star  i s given  stellar  sin0  2  i s the eigenfrequency  0  /  (dx/dr)/(/)r)  rotating  where a  ( c o s 0 ) expdmcj))  P  k  r  2  For  series  (Clement  k  envelope  e.g.  treated  as  (Q/0.116) .  The  2  time  derivative  of  Hr,t). R e c e n t d i s c u s s i o n s on can  be  found  Cox  [1976],  the  theories  i n Ledoux and W a l r a v e n P a p a l o i z o u and  Pringle  [1966],  [1978], T a s s o u l  [1978],  [ 1 9 7 9 ] , Unno e t a l . [ 1 9 7 9 ] ,  [1979],  Cox  [1980],  et a l .  [1982],  Perdang  Goupil  [1984],  Aikawa  [1984a].  and  [1981], Blacher  [1984],  pulsation  [1958], C h r i s t y  Dziewbowski  Stothers  of s t e l l a r  Fitch  Saio  [1982],  [1982],  Clement  and  Wisniewski Barranco  Buchler  [1984],  and  and Cox  30 1.5.2 MODE IDENTIFICATION 1.5.2.1 P e r i o d Mode  ratios  identifications  accomplished can  modes p r e s e n t  identify  ratios  One  looking  at  p u l s a t i o n modes  Cox  and  Hodson  [1980]).  = 0.81  higher  evolves  with  overtone p u l s a t i o n  that  the  result  ratios  with  would  existence  of  and  Stellingwerf  et  ratios  e.g.  pulsation.  between  may  From  depletion  the  stellar  the fundamental  ratio  and  i n VZ Cnc c o u l d be  effect.  pulsation period  any o b s e r v e d p e r i o d the  almost  V474 Mon h a s s u g g e s t e d  arise  as the s t a r  specific  ratio ratio  radial  equally-spaced  has  been  which  does  mode  i n d i c a t e the presence of n o n r a d i a l three  and  theoretical  that from  checked  = 0.76  Ambiguities  found  Fitch  i n c r e a s e s . Cox [1984b] h a s p o i n t e d  nonradial  any o f  c a n be  P T / P O  pulsations.  ratio  [1979],  a l . [1980],  of the v a r i a b l e  of such e v o l u t i o n a r y  determined. Generally, agree  [1975],  the l a r g e observed p e r i o d  No s p e c i f i c  a c o m b i n a t i o n of  models  ratios.  a downwards h e l i u m  first out  simplest  e t a l . [1983] have  the period  using  several  f o r a v a r i e t y of s t e l l a r  radial  zones,  pulsation  period  period  outer  different  method  Theoretical  (Peterson  overtone  no s i n g l e  be  common  period  for radial  can  most  Observed periods  models, Andreasen  not  the  [1980], Andreasen  c e r t a i n "magic"  stars  The p u l s a t i o n modes o f  of  have been computed  and  for  Scuti  however, have been d e t e r m i n e d  methods i s  P2/P1  5  a l l the  i n the s t a r .  s e v e r a l methods.  for  for  by s e v e r a l m e t h o d s . U s u a l l y ,  unambiguously  stars,  TECHNIQUES  period  modes.  frequencies  the presence of nonradial  modes  The in with  31  m-splitting  due t o s t e l l a r  [1979]). D e t a i l e d indicated radial with  that  rotation  analysis  by B a l o n a  observed  to  distinguish  narrow  band  pulsation formula  log  pulsation  period  Breger  a n d Bregman  and  modes.  indices  [1973], and  T  eff'  from  a n c  ^  ^  c  a  e  n  [1975,1979],  [1979].  fundamental  + logT  b Q l  the c a l i b r a t i o n s  Crawford  Relyea  M  A  f  nonradial and  Stellingwerf  ^  e  c  and Q  v a l u e s of l e s s  modes. The  pulsation  Q values  modes  [1979] a n d F i t c h  o n l y f o r normal  a  l  c  u  have  l  a  t  e  c  ^  of H a r r i s  o f 0.033  than  with [1963],  [1977],  p u l s a t i o n . While  day i t  first  and will  i s not overtone  0.025 day  forvarious been  stars.  t h e uvbyj3  may  stellar  computed  [ 1 9 8 1 ] . T h i s method c a n n o t  t o t h e SX Phe s u b g r o u p s i n c e  valid  main  (1.11)  Breger  Q value  radial  f  pulsation  are  the  [1975]:  radial  applied  the  using the following  t h e c a s e , Q = 0.025 day may i n d i c a t e  models  With  knowing  always  imply  c a n be  Q = -6.454 + l o g P + 0.5 l o g g  0  indicate  oscillation  P, Q c a n be c a l c u l a t e d  q u a n t i t i e s M^ jf  Philip  constant Q of a v a r i a b l e  photometry,  +0.1  t h e uvby0  constant Q  between  uvby0  from  modes  m-splitting.  The  Allen  a n d S t o b i e [1980b] h a s  mode w h i l e t h e o t h e r two a r e n o n r a d i a l d i p o l e  1.5.2.2 Use o f t h e p u l s a t i o n  The  Stobie  o f t h e t h r e e f r e q u e n c i e s , one i s an o v e r t o n e  rotational  used  (Shobbrook a n d  by be  calibrations  32  1.5.2.3 L i n e Line  profile  profile analysis  instantaneous pulsating can  be  to  to  linewidth  is  large  variations  distorted  by  a  reliable  than  velocities,  The  points.  pulsations  intrinsic  fitted line  half  computed  derivative  in  changes  o f £(r ,t)  frequency,  and  each  theoretical  like  widths. divided  into  c h a n g e s due  the  grid  more  unperturbed  is  p o i n t . The generally  atmospheres. from  the  s e t o f t h e modal  The time  constants  l i n e a r l y added. Each p r o f i l e  at  f o r the e f f e c t  other  from a l l  stellar  line profile.  is  been  of  l i m b d a r k e n i n g , and  visible  This  amplitude.  i s then c o r r e c t e d  profiles  have  The e f f e c t  rotation,  entire  of  parameters  calculated  pulsation  point  the  square  f o r a given  each g r i d  the perturbed  series  with each g r i d  model  are  s u p e r i m p o s e d modes c a n be  all  line  of r a d i a l - v e l o c i t y  stellar  radial-velocity  of  mode.  upon  only  series  is first  imposed  but  which  line-profile  radial  tend  time  profiles  the  pulsations  w i d t h s , and e q u i v a l e n t  then  from  a  the  profiles  e.g.  variations  time  by  s t e l l a r disk  profile  modes  pulsation  The e f f e c t  is  across  of l i n e  nonradial  line p r o f i l e associated  unperturbed  (I,m),  while  fitting  theoretical  many g r i d  pulsation  specified just  series  The o b s e r v e d  generated  t o examine  velocities  radial-velocity  generally  theoretically  to  identify  the opposite.  profiles  radial  of  s t e l l a r s u r f a c e . A time used  show  p r o v i d e s means  distribution  p u l s a t i o n s cause small  analysis  disk  A time  effects-.  Summation  the g r i d will  series  of s t e l l a r  points  then of l i n e  of over  provide  a  profiles  33 can  be  for  generated The  £ { r , t ) .  irrelevant. long  of  pose a  are  not  and  Smith  high  the  series.  time  degrees  v a r i a b l e s with problem  [1982] of  two  for this  identification  5  of  dominant  this  the  effect  failed of  r e d u c e d by  the  case as  in  to  or  f i t , modes  v a r i a b l e 20 imaging  projected  on  Smith  Generally,  the  pulsation  for  However,  the  as  w e l l as  the  conclusive.  The  CVn. the  In  this  line  rotational  [1980] line  (/,m) not  there  the  nonradial  were  as  large  the  model  is  well  t o the  Campos and  variables.  modes  Doppler  low  Due  accomplished.  f o r the  the  data  freedom  modal c o n s t a n t s  superimposed  method a l s o  s/n  method  either radial  of  this  or more s u p e r i m p o s e d  data.  was  expression  method, e s p e c i a l l y i f  Scuti  mode  identification secondary  used  the  of  i n the  in  t  requires  enough o b s e r v a t i o n a l  profiles  the  for  available  <j> v a l u e s  the  parameter  T h i s method  multiperiodic will  varying time  time coverage  number  the  by  case,  profile  v e l o c i t y of  is the  star. 1.5.2.4 Use  of  simultaneously  Dziembqwski  [1977],  [1979a,1979b,1980a], Balona [1981]  have  variations pulsating  derived  in  light,  s t a r . The  brightness variations.  [1979b] o b t a i n e d are  the  colour,  S t a m f o r d and  radial is  f o r AL/L, and  Watson  for  velocity  the of  a  that  the  surface  to  the  colour  Balona  and  Stobie  proportional  pulsations,  expressions  brightness,  and  Stobie  expressions  major a s s u m p t i o n  radial  and  [ 1 9 8 1 ] , and  colour,  are  data  Balona  linearised  variations For  observed  AF/F,  and  AV  r  which  radial-velocity variations,  34  respectively.  The e x p r e s s i o n s a r e :  AL/L  = e|/(f + 4fcos\//+4) c o s ( a * + T ? )  AF/F  = ef c o s ( a « + ^ )  AV  = 0.708eaR  r  (1.12)  2  (1.13)  cos(af-7r/2)  o  (1.14)  tanr? = f sini///( 2 + f c o s ^ )  (1.15)  where a =  frequency  e =  semi-amplitude  ty = p h a s i n g  between  c o l o u r and v e l o c i t i e s  TJ = p h a s i n g  between  light  R  0  = equilibrium  f = scaling With  simultaneous  one c a n s o l v e f o r t h e four  equations  above  f o r the  unknowns  to the  0  and S t o b i e  data  of  the  o f t h e two n o n r a d i a l modes  to obtain a value  Similarly,  and B a l o n a  for  and A V  AV,  AC,  radial-velocity  the r a d i a l  r  which had  from  variations,  the  been  removing  the data.  They  f o r the r a d i u s of the s t a r . Balona  [1981] have o b t a i n e d  which  a n d 77 i n  mode i . e .  for nonradial pulsation,  [1979a,1980a]  data,  [1980b] a p p l i e d t h e  V474 Mon  to isolate  were a b l e  only  e, f , ty, R ,  prewhitened effects  amplitude  c o l o u r , and r a d i a l - v e l o c i t y  above. Balona  equations  velocities  r a d i u s of t h e s t a r  factor  light,  and  are the  light,  respectively.  The  and  Stobie  expressions colour,  and  expressions  are: AV = 1.086e P ^ ( c o s i ) F  v  cosiat+ty^)  AC = (1 . 0 8 6 e P ^ ( c o s i ) F / A ) c  AV  r  = aR eP^(cosi)F 0  R V  (1.16)  cos(at+<t> )  cos(ar-ir/2)  c  (1.17) (1.18)  35  F„sinc6„ =  -(fb.sin^)  (1.19)  F„cos</>„ = -(fb,cosi//+(2 + / ) (/-1 )b, )  (1.20)  F sin0  = -(fb^sin*//)  (1.21)  = - ( f b cosi//+(2 + / ) (/-1 ) ( b j - 2 1 , ) )  (1.22)  c  c  F cosc6 c  F  c  /  (2-0)12+1-51  RV  3  + 7 4 . 6 Q ( / (/ + 1 ) / 2 ) ( ( 2 - 0 ) I b I  (2-/3)1 , + 1 .5/51 jl  n  0 .23)  + /3I )  2  2  3  (1.24)  2  (1.25)  c o s 0 P. (cos©) dcost? n  where 0 = the limb-darkening  coefficient  1 = the i n c l i n a t i o n angle ty = p h a s e l a g o f t h e f l u x A = factor  r e l a t i n g AC w i t h s u r f a c e  P^ = L e g e n d r e P o l y n o m i a l Simultaneous provide  light,  three  colour,  amplitudes  five quantities  f o r the  unknowns i n  f,  /,  however, c a n be integer. value  For  ty,  placed  ty-ti/2  (6  and  e,  Scuti  and  between  light  difference  V  which  R V  and  between  respectively. generated  (0 -<6 ),  colour light  Theoretical  on t h e p l o t  and  differences  equations which  A, and  on t h e  brightness  r a d i a l - v e l o c i t y data  two p h a s e  above  radius  of o r d e r /  and  f o r / from t h e p o s i t i o n  (0y-0^)  r e l a t i v e to the  R .  Some  0  value of /  stars),  of the data are  the  variations  and  radial-velocity  l i n e s of c o n s t a n t  f o r each d i s c r e t e  six  constraints, i t is  an  identify  a  on a p l o t phase  i.e.  have  since  one c a n  can  between  difference the  phase  variations,  f a n d ty c a n  value  of /  be  using  36 rough e s t i m a t e s values  of  pulsator only all  by  /,  implies  for  the  of  and  between  v  from the  the  refinement ratio  of  Balona  5  the  p o s i t i o n of and  Burki  amount  of  required  colour,  and  radial  obtain.  The  method  particular  prewhitened  to  rather  S t a m f o r d and equations also  the  for  the  determined  i . e . 0 ~<6 =O V  can  data  still  ty^n,  on  Mayor  get  ratios.  method  of  to  the  I  can  be  between plot is  examining  for  [1981] a l s o  mode-typing.  normally  best  applied  of  This  Mon this  the  i s the  main large  of  light,  difficult to  a time, hence the  e a c h mode.  this  applied  data  are  a the  v a r i a b l e s V474  Simultaneous  mode a t  isolate  v  This  v a r i a b l e HD37819. One  also  an  t/» —0^,<O  a plot  method of m o d e - t y p i n g  is  for  C  i s s i m i l a r to a  amplitude  velocities  to  only  data  one  have  makes t h e  to  data  tedious. Watson  for nonradial v a r i a t i o n s of  w a v e l e n g t h dependence found  v a r i a t i o n of  have s u c c e s s f u l l y a p p l i e d  data.  pulsation  odd  For  amplitude  technique  the  I >2.  which  R V  light  and  this  one  the  reliable  mode a n a l y s i s  d i s a d v a n t a g e s of  analysis  V  less  m o d e - t y p i n g method t o  be  F /F  v e l o c i t y and  Scuti.  For  0  i s then  variations  implies  a l . [1980b,1981]  extensive and  of  R.  p h a s e d i f f e r e n c e p l o t e.g.  c  c  area  Nevertheless,  corresponding  the  et  /.  e.g.  variation  brightness  c6 ~0 >O  quantities Fy/F  unknowns  projected  light  / from t h e  / =0  identified  other  The  surface  values  estimate  the  however, t h e  i s zero.. the  odd  of  nonradial  [1981]  pulsation the  rederived but  all  taking  into  e f f e c t i v e g r a v i t y as  i n the  limb-darkening  pulsations,  the  the  above account  well  as  function.  assumption  that  the They the  37  variations  of  surface  variations  of  colour  effect  surface  of  is  to  affect  correction  factors  mode-typing  [1981],  (0 ~0  )  V  lines  R V  or the  on  [1981]. possible  the  F /F v  i n the the  [1980b].  They  derivation,  for  V  for  plot,  values factor  the  /.  for  the  observed  from P a r s o n s rotational  of  radial  velocity  field.  field  and  (<j>^-<j> ) c  the  in  of  /  Balona is  less  be  The  mean  limb-darkening inadequate  out  effect  and p u l s a t i o n  than  cannot  the  becomes  /<2,  new rather  variations of  but  Stobie  the  will  also pointed  for  also [1981]  and  with  />3  vs  theoretical  new method  variations  velocity  is  by S t a m f o r d  Balona  centre-to-limb  [1972] c a n be u s e d  generated his  even  of  most  with  the  as  profile.  They  in  S t a m f o r d and Watson  that,  the  he  values  radial-velocity  line  small  from t h e but  the  mode-typing  from t h o s e  odd  result  from  the  /  Mon u s i n g  out  surface  his too  the  studied  conjunction  from c u r r e n t model a t m o s p h e r e s  correction  velocity  R  identification  simply of  higher  between  in  distorted  same  pointed  when t h e  wavelengths function  V  d a t a on V474 the  is  identify  F /F  are  on  Nevertheless,  new d e r i v a t i o n .  mode  inferred  effect  [1981]  new d e r i v a t i o n  still vs  c  plots  obtained almost  be  In the  Mode d i s c r i m i n a t i o n  re-analysed  insecure  the  be u s e d  one c a n  p r o p o r t i o n a l to  variations  result.  to  method.  Watson  that  the  are  i n v a l i d . Balona  gravity  method and c o n c l u d e d cases  brightness  that  the  of  1.31  velocity  provided that the  the  pulsational  38 1.5.2.5 Use  of  p o l a r i s a t i o n measurements  Mode-typing has  not  Watson  yet  by  measuring  been a p p l i e d  to  [1980] have shown  amplitude  of  the  the  the  that  polarisation  5 Scuti at  variations  s t a r s . Stamford  visible  wavelengths,  p o l a r i s a t i o n v a r i a t i o n s w o u l d be  for  detection  i n even most B s t a r s e x c e p t  has  been mode-typed  using  t h i s method  too  and the  small  f o r BW  Vul  which  Odell  and  Tapia  by  [ 1 9 8 1 ] . P o l a r i s a t i o n v a r i a t i o n s have been r e p o r t e d  for  peculiar  (Haefner  large-amplitude  et  a l . [1976]).] A  by  Watson  1.6  recent  v a r i a b l e SX  discussion  low-amplitude amplitude generally many  of  of  the  8 Scuti  of  the  l e s s than the  generally  variables  I0kms~  method  is  given  STARS  of  the  short the  pulsation  phase-smearing  effects  radial-velocity profile  has  is  of  the  usually d i f f i c u l t .  The  and  1  can  be  This  and  of  on  c u r v e . The  the  in  both  the  e f f e c t of  been s t u d i e d  by  is  2kms~  for  the  order  of  to a v o i d  line  1  need  of  period  three  h o u r . The  l i m i t e d to at  order  2K,  main p u l s a t i o n  j u s t one  is generally period  l e s s than  implies  i s of  order  variations  variations,  s p e c t r o s c o p y . The  i n each spectrum of  spectroscopic  variables.  very  w h i l e many a r e  line  DELTA SCUTI  radial-velocity  very-high-dispersion  20%  the  D I F F I C U L T I E S WITH LOW-AMPLITUDE VARIABLES Observation  time  of  Phe  [ 1983].  SPECTROSCOPIC OBSERVATIONS OF  1.6.1  is  5 Scuti  the  hours  exposure  most  10%  or  significant  profiles  and  the  e x p o s u r e t i m e upon  the  Huang and  Struve  [1955].  39 f o r )3 Cas and p  Except  variables  are  certainly  imposes  attainable  s/n i n e a c h  is  to  obtain  periods.  an  than  very  stringent  spectrum.  average  i s only  observations  a l l the other  brighter a  Not t a k i n g  improvement of  not  Pup, however,  limitation of  each  any s y s t e m a t i c  observations are required  b i n . This  i f one  wants  will  be  c o n s i d e r e d . The will  be  precise  very  worse  correct  and a l m o s t  multiperiodic.  other  of the  without  Cycle-to-cycle  in  i f the  are  velocities  knowledge  variations  each  effects  radial  prior  impossible  many  actual  - 1  /n when  phasing  difficult  period  than  0.1  number  The  kms .  to  the  reduced  from  improvement  effect,  t o be  for  1  many  error  curve  kms"  over  the  t h e mean r a d i a l - v e l o c i t y 1  the  implies  phase b i n of example  on  of /n where n i s t h e  phase  This  improvement  r a d i a l - v e l o c i t y curve  by a f a c t o r  Scuti  magnitude.  One method  i n t o account  in  third  8  of  variable  may  also  the is be  present. The u s e o f systems has measured spectral  photoelectric  enabled  for  several  has  difficult  to get  spectral  a  mask  characteristics Difficulties broad  narrow  line  l i n e s with  radial-velocity  spectral  type  a perfect  match  variables.  the  also  be e n c o u n t e r e d  vsini  greater  "dip"  can  than  between  during  than  No  if  i f the It is  the v a r i a b l e changing  1  with  cycle.  In f a c t , the  and  spectral  the v a r i a b l e  30kms~ .  be  proper  FO.  the p u l s a t i o n  be a c h i e v e d  to  i s available  earlier  e s p e c i a l l y with  of the v a r i a b l e  will  scanner-type  radial-velocity variations  "mask" f o r t h e v e l o c i t y s c a n n e r  variable  the  the  radial-velocity  DAO  has no RVS  40 s y s t e m on  the b r o a d - l i n e  Furthermore, the  one c a n n o t  scanner-type  asymmetry  variable study  line  Cas (Ninkov  line-profile  systems. Although  o f t h e mean  j3  [1982]).  variations  some i n f o r m a t i o n on  profile  c a n be i n f e r r e d  the  by B u r k i  and  cross-correlation  function  Mayor  one s t i l l  examine t h e i n d i v i d u a l  profiles. velocity the  cannot  The v a r i a t i o n s may be  i n both  different  radial-velocity  for  scanner  e.g.  the p r o f i l e different  the  from  shape o f t h e [1981],  with  and t h e  lines.  line radial  Generally,  t e c h n i q u e has been a p p l i e d  to the large-amplitude 8 S c u t i  only  stars.  1.6.2 RECENT OBSERVATIONS Recent photographic the  simultaneous  light  8 D e l , p Pup, a n d 6 and  Wehlau  variations  simultaneous Bessell  8  addition  to  distribution  also  measured  and  used  plates profile  in  to  the  radial-velocity 20  h i s study  data  by N i s h i m u r a  e t a l . [1976],  t o show t h e of  Abt  14  of the  of the  [1969],  respectively.  radial-velocity [1965]. D r a v i n s  variations et  energy  was  light  of  [1969] was e Cep u s i n g  a l . [1977]  also and  28 And,  P e n f o l d [1971],  Breger  in  variables  analysis  Simultaneous  Aur.  scanner  d a t a were o b t a i n e d f o r t h e v a r i a b l e s  CVn, a n d HR7331  Breger  variables.  Leung  obtained  on  spectrum  variations  of  radial-velocity  data  p Pup, 8 D e l , a n d 8 S e t . A c u r v e - o f - g r o w t h applied  [1967].  a l . [1968]  radial-velocity  a photoelectric  t h e Coude and l i n e  the  et  include  measurements  and D a n z i g e r  Del. Chevalier  light  [1969]  and r a d i a l - v e l o c i t y  S e t by K u h i  [1967] of  spectroscopic observations  measured  and able the the  41 radial-velocity Ca I I K l i n e This  may  variations  emission  be  of  p Pup.  They  also  a t a c e r t a i n phase o f t h e  caused  by  shocks  a t m o s p h e r e . Shock g e n e r a t e d  propagating  e m i s s i o n has a l s o  i n VZ Cnc by G a r b u z o v a n d M i t s k e v i c h [ 1 9 8 4 ] . variations  of the  variables  measured  by V a l t i e r  observed  the evolved  et a l . [1979].  core  splitting  with  "bumps"  in  and  Preston  Duncan  variations plates.  HR432, HR515,  6 Scuti  been  Radial-velocity and HR8006  y Boo.  i n both  radial-velocity  They  5 Del A  and 6 D e l  The s u s p e c t e d v a r i a b l e  the photographic  plates  the  by  [1979] line  conjunction Meanwhile,  radial-velocity  B with  j3 A r i was a l s o Barbiano Di  were  found  curves.  measured  the  observed  Auvergne e t a l .  star  [1979]  pulsation.  through  i n t h e Ca I I and H I p r o f i l e s i n the  reported  photographic observed  Belgioso  with  et a l .  [1983]. Recent  photoelectric  observations variations Imbert  include  of  variations  RRs  measured  stars  Simultaneously  radial-velocity  the v a r i a b l e s  p  Mayor  Van  light  d a t a on V474 Mon were  [1980b].  and  by  the p h o t o e l e c t r i c  photoelectric  Burki  of the  o f HD200925. S i m u l t a n e o u s  radial-velocity Stobie  t h e measurement  several  [1980]  radial-velocity  Pav, HD37819,  radial-velocity Citters  [1976].  radial and  velocity  photoelectric  o b t a i n e d by B a l o n a and observed  d a t a were and 5 S e t  [ 1 9 8 0 , 1 9 8 1 ] , and  scanner  Balona  also  light obtained  by K u r t z et  and for  [1981],  a l .  [1981],  respectively. Campos a n d S m i t h detector  to  measure  [1980] and S m i t h both  the  [1982] u s e d  radial-velocity  a Reticon and  the  42 line-profile  variations  28  Tau,  And,  14 Aur  44 A,  and  intensified variations also  20  of  20  CVn.  Pasinetti  The demand  that  5 Scuti  kms  values  to  equivalent  ±0.5  achieve to  the  28  Aql,  used  an  were  servo-controlled to  measure  by  the  International Fracassini  and  e t a l . [1983] t o o b s e r v e  of  several  5 Scuti  ratio 1  in  the  1  the  variables.  of  6  (Breger  ±0.01  a precision  w o u l d mean more  than  Scuti  kms"  about  radial-velocity  variables. to l i g h t  of  For  many  amplitude if  is  one  can  better  curves, ±0.001  it  mag  many of  in precision  of  ±0.0001  an  order  mag  a  pointed  than  would  i n the  t h e methods  which  is  be  light  r a d i a l - v e l o c i t y techniques  in fact, 1  have  [1980] has  precision  of  variables  should  [ 1 9 7 9 ] ) . Hence,  radial-velocity  this;  6 Scuti  precision  of v e l o c i t y  to a p r e c i s i o n  achieve  the  observations  radial-velocity  almost  having  Set,  variations  The  used  kms" . Heacox  c u r v e . Most modern p r e c i s i o n certainly  was  6  radial-velocity  a  Pup.  of many of  study  1  -1  Mon,  a l . [1983]  light  p  of a p p l y i n g  the  kms" mag" a  (IUE)  radial-velocity  stars,  achieve  et  spectrometer of  emissions  advantages  92  V474  [1983a] u s e d  Fracassini  of a t l e a s t  techniques  B,  Pup,  PRECISION RADIAL-VELOCITY TECHNIQUES  s m a l l 2K  the  about  K line  OF  precision  Del  Simultaneous  variations  [1982] and  USE  p  variables  Nishimura  CVn.  Explorer  I I H and  1.6.3  6  radial-velocity  Ultraviolet  ±0.1  A,  o b t a i n e d . Reay e t a l .  radial-velocity  out  Del  the  R e t i c o n d e t e c t o r t o measure t h e  Fabry-Perot  Mg  6  of  can can  equivalent  i n the photometry. T h i s  of m a g n i t u d e  improvement  in  43 the  ability The  its  t o study  HF a b s o r p t i o n  application  Individual the  study  as  the  line  the  profiles  determination spectral  technique study  be a c h i e v e d  and  with only able  can a l s o  of  lines.  with  unseen  be  different  studied.  spectral  l i n e s may h e l p  the p u l s a t i n g  stellar  Van  Hoof e f f e c t  ( v a n Hoof  phase l a g s spectral  between  the  t o probe  velocities for  o f about  ±50  s/n f o r t h e reduction.  pulsation  1  pulsation lines  amplitude  of  the s t r u c t u r e of  the  i s characterised  by  r a d i a l - v e l o c i t y curves of the m e t a l l i c  the .structure  ms"  One w o u l d  a t m o s p h e r e . The o b s e r v a t i o n [1957]) which  a  spectrum  low-amplitude  one t o s t u d y  l i n e s e . g . h y d r o g e n and  be u s e d  well  on d i f f e r e n t s p e c t r a l  The d i f f e r e n t  of  allows  s t a r s would n o t be  a moderate  previously  in  variables.  v a r i a t i o n s as  radial  Broad-line  only  suitable  Scuti  profile  a m o d e r a t e amount o f d a t a  to detect  also  also  8  very  be o b t a i n e d . T h i s  precise  modes. The e f f e c t s o f p u l s a t i o n can  of  is  f o r t h e HF t e c h n i q u e . A p r e c i s i o n  can  be  to  cell  pulsation.  of the i n d i v i d u a l l i n e  individual problem  the 6 Scuti  different  lines,  of the p u l s a t i n g  could stellar  atmosphere. Presently, stars are values.  b a s e d on  observed  offers  photometric  Spectroscopic  determination  radial  most o f t h e e x i s t i n g m o d e - t y p i n g s o f 5 S c u t i  of  the  data  can  nonradial  another  These w i l l  mode.  star  pulsations.  independent  enable  give  pulsation  2K v a l u e o f a 6 S c u t i and  studies  method  one t o s t u d y ,  e.g. using another One  the  Q  .independent can  use  the  to discriminate  between  Line-profile  analysis  f o r mode using  discrimination.  spectroscopic  data,  44  the  systematics  the  instablility  with  the  HF  aperture  of t h e  6  S c u t i s t a r s at d i f f e r e n t  strip.  Many  technique  similar  if  to that  8 Scuti  one  of  s t a r s can  uses a  the  CFH  3.6m  It  report  Chapter choose  the  Reticon on  two  of  noise  this  detector  detector  and  the  for  and  d e r i v a t i o n of  improved the  derivation from the  observed  followed  by  calculation describes  r e d u c e HF the  of  o  1  HF  six  E r i while  the  reports Chapter  HF on  p  eight  r e p o r t s on  directly collision  in  four order  procedure  is also  five  /3 C a s .  to  discussion barycentric reports  v a r i a b l e 20 seven  is  eventual  data  technique,  Chapter  the  Chapter  The  to the  Pup.  enables  and  Reticon  technique  hence  three. This  shifts.  Chapter  the  strengths  pressure  accuracy.  of  and  line  formulation  difference  velocity  emphasis  describes  of m o l e c u l a r  There  The  persistence  This  spectra.  to  gas.  three  i n Chapter  described.  criteria  the  band. The  theory  the  technique.  f o r HF  t e m p e r a t u r e and  for  Fahlman-Glaspey and  and  Chapter  to preprocess  s/n  Several  a description  l i n e w i d t h s and  is also  a p p l i c a t i o n of  Chapter  gas  theoretical  the  the  also calculated.  procedure  data  (3-0)  an  study.  constants  is also described  optimum  corrections, the  f o r the  s p e c t r a . The  a  the  to achieve  molecular  relative  self-broadening  on  new  HF  particular  readout, gives  with  absorption  with  operation.  band a r e  of  reference  also  its  wavelengths (3-0)  the  two  the  thesis discusses  incomplete  phenomenon. C h a p t e r cell  on  is also discussed  reduction,  absorption  to  the  of  studied  telescope.  studied using  o b j e c t i v e here  be  telescope  5 S c u t i v a r i a b l e s have been i s the  parts  reports  on CVn. on  Chapter THE  2.1  2  HF ABSORPTION CELL SYSTEM  INTRODUCTION One c a n e l i m i n a t e most o f t h e p r o b l e m s a s s o c i a t e d  the  use  This an  of t e l l u r i c  i s accomplished  absorption  cell  would  cell  be  lines  i n the  enters  pressure  of  generated  absorption  telluric  lines.  technique  can  absorbing  gas. Moreover,  lines  telescope  the spectrograph.  the  absorbing lines  Blending  Since  gas will  can be  problems  be m i n i m i s e d  with  a  as opposed  s t e l l a r spectra with  absorption  lines  as  absorption  lines  c a n be e a s i l y  very  reference  lines.  are generated  w e l l as s p e c t r a  beam  before  the  t h e t e m p e r a t u r e and be  controlled,  more s t a b l e in  to the  choice case  or without  generated.  the the  the t e l l u r i c - l i n e  careful  with  than  only These  of with  the the  the  imposed  the  imposed  spectra  u s e f u l i n removing the l i n e - b l e n d i n g - i n d u c e d e r r o r s  line-position  by  c o n t a i n i n g a s e l e c t e d g a s . The a b s o r p t i o n  placed  lines,  wavelength  i f the reference  starlight  telluric  as  with  are in  measurements.  2.2 CHOOSING THE DETECTOR Measuring high the  very  accurate  signal-to-noise ratios dominant  in  order  be  detected.  dynamic  source  to achieve  T h i s would  range.  positions requires  f o r the s p e c t r a . Photon  of noise high  line  i n high  s/n s p e c t r a .  noise i s  Therefore,  s / n , l a r g e numbers o f p h o t o n s imply  very  must  t h e d e t e c t o r must have a l a r g e  I t i s also d e s i r a b l e f o r the detector  45  t o have  46 a  linear  order  response.  that  shifts), tubes,  High p o s i t i o n a l  instrumental  as  seen  would  not  induced  in t e l e v i s i o n occur.  The  detective  quantum e f f i c i e n c y  detector  should  suitable  for  detector  of  the  spectral  region  most CCDs. The  Reticon  transfer  sensing area  (diode)  Reticon out  readout single  s/n  the  CCD  e.g.  as  aspect  the  negates over  the  can  be  f u t u r e , the  accomplished  n o i s e of CCD  the  pixel.  noise  spectra.  can  75%  in  CCD. the  Johnson  the  the  only  be  added  The  Reticon  the  The  Reticon than a  pointed  a column of such  same as  source also  of  In  the  t h a t of in  any  noise has  CCD  that  three p i x e l s  t h i s manner.  array  CCDs.  low-readout-noise  chip  At  dominant  and  inefficient  [ 1 9 8 4 a ] has  i s the  the  plates  very-low-readout-noise  summed column  i s not  than  n e c e s s i t y t o sum  summation a l o n g  in  X8000  i s higher  of  available  present,  The  for spectroscopy The  within  above  the  many  ratio)  the  array.  in  have t h e  found  the  in  the  photographic not  of  photons.  of  This  high  configuration  photodiode  h i g h as  i s more s u i t a b l e  pixels  i n the  same c o l u m n readout  as  a l s o does  of  area  important  most  Reticon  (Walker et a l . [ 1 9 8 5 ] ) .  that,  pixels  CCD of  be  (large  square-shaped p i x e l  advantage  satisfies  problem  shape  c o l u m n of  is  a  image  have  number of d e t e c t e d  detectors  rectangular  the  in  in  (raster or  should sensing  (Walker e t a l . [ 1 9 8 5 ] ) .  most c o n v e n t i o n a l  charge  can  detectors  and  This  is a linear  Reticon  shifts  type  large  which  spectral  detector  to maximise the  mentioned c r i t e r i a DQE  be  i s important  (DQE). The  spectroscopy.  consideration The  also  stability  in  a the  case, high  excellent  47 geometrical  stability,  a large charge  storage  l a r g e dynamic  range, as w e l l as having  s p a c e between  diodes.  2.3 THE RETICON  2.3.1  DETECTOR  is  self-scanned diode array  the  i s a large  n-doped s i l i c o n silicon  chip.  at regular on  the  the  array.  chip When a  diodes, at  to  The c h i p  bottom  reverse  a space-charge  bias  between  silicon.  Absorption  of  the  electrons  semiconductor) within pairs.  I f these  p-doped  and  partially  the  n-doped s i l i c o n ,  depletion  silicon,  thin  as  effective of 5  a 300jum  the  the  drift  number  i n the  t h e whole  surface  and  form  carriers  of the  applied  sufficient  will  to the  is  created  the  p-doped  energy  band  of  (to the  electron/hole a r e formed  to the d e p l e t i o n  move by d i f f u s i o n effectively  in  region  t h e b i a s . And i f t h e y a r e f o r m e d  r e s u l t s i n having  of  photodiodes  conduction  f r e e charge  common  reflectivity  n-doped  thick p-doped  and a The  volts i s  they a l s o w i l l  region. This  fabricated  (depletion region)  they w i l l  discharge  anode.  of  silicon  channels of  covers  2  the s i l i c o n  excess  the  i s mainly  photons with into  group  ( I D A ) . The  number o f  layer  interface  a  the surface  l a y e r of S i 0  the  raise  I t has  reduce t h e  of  integrated c i r c u i t  to the  A transparent  name arrays  i n t e r v a l s on  channels corresponds  of  scale  substrate.  substrate  array.  commercial  or i n t e g r a t e d diode  a single silicon  gold  no dead ( i n s e n s i t i v e )  INTRODUCTION Reticon  on  capacity i . e .  in  t othe no d e a d  48  s p a c e between d i o d e s . a  set  exposure  restore of  the  the  time,  original  a  shift  analog  output  Higher  electron/hole  too  register  the  i n t o the  long  I f the  substrate  pointed  out  interference  finish case,  of  effects  the  chip  in order proper  The the  This  the  would be  leads  to a  density  of  surface  Consequently,  chip  the  blue  reduced the of  The  amplified  i . e . beyond back  interfere  because  the the with  [1976] such rear  have a v e r y  fine  reflections.  In  any  remove  any  absorption  of  spectrum.  by  reaching  responsive  silicon  is  the  p r o c e d u r e can  created  from  arrays,  f r o m the  (red)  photons  thick is  the  penetration  Geary  recombination the  line.  effects.  required to  before  each  generate  the  and  This  calibration  measure  lower energy  reflected  to produce c o l l i m a t e d  recombine  to  a longer  the  small.  electron/hole pairs  (RQE). The near  for  fringe pattern  p h o t o n s can  layer.  are  flat-field  small-amplitude  tend  fringing  that,  to  (rebiasing  output  generation  the  a  is first  t h a n the  be  of  give  wavelength of  p h o t o n s may  required  computer.  p h o t o n s have  silicon.  the  gold  surface  in a  after  to connect  video  line  photons  incoming photons to produce has  video  for electron/hole pair  red c u t o f f , bottom  red  again  In a r e a d o u t  i t s appropriate  (blue)  charge  i s clocked  p a i r s more e a s i l y  p h o t o n s . Hence  of  photons.  for storage  energy  is rebiased  potential will  s i g n a l from t h e  then d i g i t i s e d  diode  amount  5 volts  s e q u e n t i a l l y to  depth  the  number of a b s o r b e d  diodes),  diode  and  the  When t h e  the the  space-charge  quantum  efficiency  centres  is  (Geary  p h o t o n s , w h i c h have s h o r t  higher [1976]).  penetration  49  depths, is  a r e more s e r i o u s l y  still  dominated  response  in  increased charges the  far  the red  recombination  have t o t r a v e l  be  will  loss  will  result  increasing chosen  in  rather  gradual  by  t h e HF  i s dominated  adjacent  d i o d e s due  t o be v e r y  2.3.2  DARK CURRENT  by  It  as a d d i n g dark  extra  nonlinear  r e g i o n and  hence  spatial  resolution  with  at  spectral  the  The  from  point-spread  d i o d e s has  a r r a y . The  amount'of d a r k  by  the diode a r r a y .  than  into  when f r e e  the  layer.  system.  on  Thermal  the width  average  well  time. This  diode  c u r r e n t , however, c a n A t an  charges  space-charge  a l s o have a much  the  been  [1980]).  t h e number o f a b s o r b e d  leakage  (the  o f t h e a r r a y as  leakage  thermal  between  saturated  with exposure  amount o f  region  cross talk  exists  range  (hot d i o d e s ) can  diffuse This  Simpson  Some o f t h e d i o d e s  cooling  directly  spillover  dynamic  would  above.  effect.  of the dependence of the  depletion  the  instrumental  n o i s e component  current i s also  because  longer distance  will  to d i s c h a r g e the  the e f f e c t i v e an  the  there  of  ( T a l m i and  thermally generated reduces  by  completely discharged)  small  The  free charges,  Dark c u r r e n t ( t h e r m a l l e a k a g e ) are  affected  free charges  fact,  silicon.  With  loss  this  be  response  layer.  t h e one  to charge  layer  found  the  program, the  function  space-charge  the  of  the  space-charge  than  In  course,  to the  to reach the  wavelength.  for  also  due  a h i g h e r chance t h a t  adjacent pixels  Of  reflectivity  l o n g d i s t a n c e of t r a v e l  also to  the  by  affected.  be  of  is the  photons. higher in  the  reduced  o p e r a t i n g temperature  of  50 -130°C w i t h almost  negligible  cooling energy et  of  longer  N  (Vogt e t  a l . [1978],  however, w i l l  [1978] r e p o r t e d  (redward  Vogt  becomes  [1981]). the  bandgap  of the photons.  drop  in  t h e RQE  i s about  Vogt  in  o f X7000) w i t h c o o l i n g . 90K  The  the  The  peak  80%  a t about  X7000  readout  errors  from  [1976]).  To  avoid  large  differential  heating  dark  from  signal  systematic (Campbell  "charge  prevents  s u r f a c e . The  UBC  of  array  frost  zeolite,  absorbing  the  will  residue  [1981]). Temperature detectors  is  then gas  when  stability maintained  heater/diode-temperature-sensor  on  housing  pumped w i t h a m e c h a n i c a l  material,  as w e l l  (Vogt  provides temperature  formation built  a l . [1981])  the  (cold  pump. The  readouts. insulation  cooled box)  cooled  good  UBC  to  vacuum et  built  ±0.2°C  loop  first pumping  (Campbell  of the  array  is  cryogenic  generate a  as  [1981]),  a r e t u r n e d o f f between  f o r the a r r a y the  et  pumping" e f f e c t s  p u l s e s to the a r r a y  Vacuum h o u s i n g  rough  current  increase  depth  a marked  for Reticons cooled to  clock  the dark  as t h e p e n e t r a t i o n  wavelengths  (Geary  and  cooling,  2  the a r r a y ,  as w e l l  al.  RQE  liquid  (Campbell  by al.  Reticon by  a  et  al.  [1981]).  2.3.3  LINEARITY IN RESPONSE The  by G e a r y and  linearity  [1976], Campbell  Simpson  nonlinear  of t h e R e t i c o n r e s p o n s e  [1980],  dark  current  and  [ 1 9 7 7 ] , Vogt Vogt  been  examined  et a l . [1978],  [1981].  i n the s i g n a l  has  will  Talmi  Existence  of  the  certainly  produce  51 a nonlinear imperfect  removal  (baseline) the  response. of  from t h e  properly  cooled,  removed  data.  the  fixed  Furthermore,  converters  with  signal  of  the  result  proper  procedure.  d e p e n d s on  the  array  photodiode.  Reticon  photodiode  over the  the  i s 3.2  pcoul  of  sufficient  saturation  2x10  of  can  be  and the  data Reticon  to saturate  c h a r g e of a  or  Reticon  response  range  The  can  four orders  The  charge  and  output  calibration  dynamic  signal  amplifiers  instrumental  amount o f  silicon  in  from  pattern  the  is linear  nonlinearities  reduction  2.3.4  additive  also  c h a r a c t e r i s t i c s . Generally, with  magnitude. Small  a  RL-1872F/30  equivalent  photons.  additive fixed  pattern  7  FIXED LINE PATTERN The  output  signal  component. I t i s clock-driver amplitude pattern  of  has  multiples be  of  very  signal  is  removed by obtained  this  the  kept  shortly  output  stable  video  and  lines. of t i m e  the  the  initial  B e c a u s e of  the  the  lines.  The  readout array  it a  It,  i f the  can  of  clock of  be  readout  the data  fixed second  the  easily  frame  self-heating  the  in  however,  second  residual  s u b t r a c t i o n of  fixed  periods  temperature  Consequently,  small-amplitude  remain a f t e r  spatial  subtracting off  [1976]). a  output  of  i s u s u a l l y l a r g e . The  long periods  constant.  after  video  waveform w i t h  over  numerically  capacitive coupling  the  pattern  number of  are  an  of  onto  fixed  constant  phenomena,  still  result  a saw-tooth  (Walker e t a l . other  the  contains  signals  waveforms  Reticon  can  the  analog-to-digital  have n o n l i n e a r  can  N o n l i n e a r i t y can  and  pattern readout  52  (baseline).  This  calibration  and  2.3.5  readout  d o m i n a t e d by the Johnson  300  AQ  i s the  double CDS  rms  n o i s e AQ  of  restoring  i s given  by  (2.1) equivalent  i s about  operating  the  diode  with  of  the  respect  video  (CDS)  signal  f o r the  signal  of  150K.  In  KTC  been  subject  noise  line  which  minimised  after  i s the  r e b i a s i n g the  before  the  by  than  Walker et of  line and  measured  is typically  et a l . [1974],  nth diode  video  a s s o c i a t e d with  processing technique  (White  less  i s no  conventional  to ground both  T h i s would  the  sampling  i f there  a r r a y , however, t h e  the  signal  Hence,  r e s e t n o i s e would be  to  has  kelvin  pF.  temperature  the  diode  0.6  photons  i n pF  in  T h i s problem  the measured  amount  temperature  the  [1985] u s i n g  shift-register  the  di.ode c a p a c i t a n c e  i s the  capacitance  pF.  The  is  diode,  /(kTC)  9  r e b i a s i n g each d i o d e .  c h a r g e of  in  T  i s monitored  The  the  constant  voltage  50  of  Boltzmann's  schemes of  shunt  resistance  k i s the  readout  after  rebiasing a  i s i n number of  capacitance  a t an  In  diode.  stray capacitance,  e"  Reticon  noise.  uncertainty  = 2.5x10  C  other  cooled  [1985]:  AQ  diode  properly  (KTC)  i n the  a p p l i e d to the  Where  instrumental  procedure.  of a  reset  an  proper  READOUT NOISE  noise  Walker et a l .  removed w i t h  noise  the  switch causes charges  be  data-reduction  REDUCTION OF The  The  can  the about al.  correlated  Geary  difference (n-1)th diode  [1979]). between (with  53 the  video  (n-l)th signal  line  diode  Within video Only the  uncorrelated and  with  a  m a g n i t u d e as The (adcu)  with  nth  factor  of  Reticon  the  spectra this  remains. T h i s  the of  of B e t e l g e u s e  alternate  capacitance  the  per  variance  diode  per  amplifiers.  factor  can  between  i s the of  same  convertor  units  of a s h o r t  order  and  levels, The  method.  make  needs  i n two  By  can  a  to of  ways. and  conversion DAO  computing  plot  conversion  the  the  f o r the U B C - b u i l t  s l o p e . Walker  exposed t o  to  heavy m o d u l a t i o n one  in  a s a t u r a t e d diode  obtained  of  the  t h e number  accomplished for  dark  for  p h o t o n s , one  et a l . [1985]).  calibration  reset  the  s a t u r a t i o n charge,  signal. the  be  of a d c u  spectra  the  difference.  readout  In  between a d c u  a d c u was  signal  reciprocal  i n the  from  the d i f f e r e n c e  number of d e t e c t e d  two  against  noise  line line).  the  (Walker  of  video  of  per  between  range  variance be  e"  video  diode.  from  specified  detector  residual large  185  the  in analog-to-digital  number  manufacturer  the  the  measured  1872-Reticon d e t e c t o r o p e r a t i n g  the  the  from  i s removed to  the  to the  interval,  diode  photons. This  Knowing b o t h  diode  and  and  DAO  know t h e c o n v e r s i o n equivalent  and  2 a d c u rms  mode  comparison  the  sample  obtained  UBC-built  line)  disconnected  t h a t of a s i n g l e  It i s  gain  nth  n o i s e due  noise  short-circuited  video  characteristic  is easily  current high  the  readout  exposure.  the  i s correlated  (n-l)th  noise  diode  short double  line the  t o the  connecting  (n-l)th  the  capacitor  connected  after  ( w i t h the  shunt  i.e.  the  factor  a  signal  will  e t a l . [1985]  same s i g n a l  level  The  number  large  the  then used for of  54 TABLE 2.1 U B C - b u i l t  1872-Reticons  ********************************************************** Telescope DAO  e"/adcu  1,2m/l.8m  ( h i gain)  e"/adcu  ( l o gain)  185  185x5  CFHT 3.6m  250  250x3.5  UBC  150  150x3.5  0.4m  ********************************************************** strong in  absorption lines  the s i g n a l  levels.  was o b t a i n e d .  This  in  the spectrum  A conversion agrees  very  factor well  calibration  and i m p l i e s a n o i s e  level  photons  a single  Recent  in  electronics less has  than  have  noise 2.1  their  the  CFHT R e t i c o n  this  the three  e'/adcu c o n v e r s i o n  Reticon-control  unit.  reduced  range  with  of only  the  previous  370 e q u i v a l e n t  improvements  the readout  in  noise  the  to  be  CFHT R e t i c o n  characteristics.  lists  and  shifted  further  the  o f 180 e" p e r a d c u  320 e q u i v a l e n t p h o t o n s . The U B C - b u i l t  similar Table  readout.  provided  a r e based software  by one b i t )  current UBC-built  factors.  The v a l u e s  on " r e a l "  adc  Reticons  listed  units.  The  u s e s a " p s e u d o " adc u n i t  which  i s equivalent  for CFHT  (logically  t o two " r e a l "  Hence t h e  corresponding  conversion  pseudo u n i t  w o u l d be h a l f  of those  factors  listed  adc  based  on  i n Table  2.1.  2.3.6 THE INCOMPLETE READOUT PHENOMENON It  h a s been r e p o r t e d t h a t  remain a f t e r al.  [1978]).  readout  a  readout This  l a g , however,  a residual  (Livingston  phenomenon was f o u n d  et  charge  can  a l . [1976],  still  Vogt  et  readout  or  of  incomplete  to  be n e g l i g i b l e  by  Geary  55 [1976] and rebiased after  T a l m i and  Simpson  back t o t h e o r i g i n a l  a readout,  exposure.  eliminated  by  The  allow  readout  to  erasure  r e a d o u t s can  are  fully  al.  [ 1 9 7 8 ] ) . The  residual  incomplete  having  charged  more  also  will  This w i l l  raise  level  The the  off  front glow  of the  exposures at  the  exposure.  low  cause  in  the  be  array  reduced  rate  or  for  the  Multiple  a l l  exposure  a quick  diodes  (Vogt  et  sequence  of  of  the  array.  c u r r e n t as w e l l to  the  reduced  that  self-heating  of t h e d a r k  as a  rebiasing.  o f an  volts)  contaminate  scan  to insure  start  incomplete This  path  image  time  reach  The After  readout. Figure  of  as  it  temperature  for  a Hg  by  a r c spectrum.  This i s  i s switched  to eliminate  readout  strong  this  behind  by  shows  arc  any  after  saturated  and  however, s h o u l d  can  be  a  the  would  then  incompleteness  this  remnant  any  represent  of t h e  spectrum  be dark  o f f the u n d e r l y i n g b a s e l i n e , readout  in  performing  would be lines  a But  spectrograph blocked o f f  readout,  in  with  setting  d u r a t i o n , the a r c  first  subtracting  2.1  been e x a m i n e d  R e t i c o n i s set to continue  the  second  has  accomplished  to the  ( r e a d o u t s ) . The  left  readout  is  slicer.  t h e a r c . The  detected  residuals  can  used  of t h e e x p o s u r e  positions  discarded.  signal  of  the o p t i c a l  from  be  long exposure  t h e end  and  for  Reticon.  relatively  readout  (5  not  again.  effect  DAO  before  the  time  equilibrium  will  power d i s s i p a t i o n  however,  take  charge  complete  b e f o r e the  readouts,  would  same e f f e c t  a sufficiently  for  I f the d i o d e s are  operating potential  i t would have t h e  response. Moreover, the next  [1980].  first  together  Figure  2.1  Residuals  from  incomplete  readout.  57  Figure  2.2  The  persistence  phenomenon  R0B = 2. T = 37.5s  R0H = 3. T=62.5s R0H = 4. T=87.5s  R0H=5. T = 112.5s R08=6. T = 137.5s  R0W = 7. T = 162.5s  R0H=8. T=212.5s  R0H=9. T=262.5s  RO» = 10. r = 312.5s  'R0H = 11. T=362.5s  R0H = I2. T=412.5s >i*m»m n » * w m > » » » 1 * 4 w * m n p Q ^ _ ) 3  7 = 452 5s  ^ ^ R 0 t t = !4. T=512.5s I^OOOe" per 100s H ^ ^ I ^ N M * ^ ! ' ^ n^m.!*^ 100  _i  500  i_  900 Pixel M  1300  1700  PQJ^ 5 = 1  y=562 5s  Figure  2.3  Time decay  of  the. p e r s i s t e n c e  phenomenon.  is 1«  SQOI  jad  .a  59 w i t h an u n s a t u r a t e d Hg a r c s p e c t r u m . in  the  remnant  saturated  in  the f i r s t  ( e a c h of a b o u t saturated  spectrum  would  would  5  i n the  first  i s 2x10 e~, t h i s  would  signal  could  by  7  multiple  be r e t a i n e d  This  is a  to  equally  lines  lines  lines  correspond t o p o s i t i o n s  imply that  large  almost  effect.  of  saturation 1% o f t h e  the incompleteness of a  rather  not  strong  readout. Since the  charge  readout.  correspond  r e a d o u t . The  1.8xl0 e")  lines  The s h a r p weaker  single  Consequently,  e r a s u r e r e a d o u t s s h o u l d n o r m a l l y be u s e d .  2.3.7 THE PERSISTENCE PHENOMENON Figure after  2.2  shows  the incomplete  the  time  elapsed  for  each  spectrum.  a readout  the f i r s t  the  since  line  persist  readouts  number  readout a r e a l s o  saturated  readout  The a p p a r e n t  is  and shown  would  a l l scaled  have  to the  higher noise  the a r t i f a c t of  t i m e . One c a n o b s e r v e  i n F i g u r e 2.2 t h a t  arc  readout  The s p e c t r a a r e  of s p e c t r a  exposure  subsequent  The  the i n i t i a l  The i n i t i a l  couple  of  test.  t i m e o f 100 s e c o n d s .  from a s h o r t e r series  readout  number RO#=0.  same e x p o s u r e in  the r e s u l t  from  scaling  this  the r e s i d u a l s at the p o s i t i o n s  for a  long  time  and  after  time of many  readouts. This persistence  phenomenon does n o t have t h e same  characteristics  effect  discussed  as  earlier.  the The  effect  of  cannot  performing multiple  readouts.  elapses.  forthis persistence  The r e a s o n  unknown. T h e r e creation  states  in  be  I t would d e c a y  h a s been s u g g e s t i o n t h a t  of surface  incomplete  readout  reduced only as  phenomenon i tresults  the s i l i c o n  by time  is still from  by t h e  the  initial  60 light  e x p o s u r e . The  electron/hole  pairs  would d i f f u s e  towards  the d e p l e t i o n  time  Figure  2.3  scale.  phenomenon. In view exposures  for  a  exposure. This is  long  2.3.8  and  of t h i s ,  certain  the  one  only  time  really  regions  over a  decay  long  of  the  should delay  time  important  these  after  a  i f t h e new  new  strong exposure  weak.  COSMIC-RAY EVENTS  diode will  from  the  produce  width,  pairs  passage  a  can of  be  generated  a cosmic  ray  narrow e m i s s i o n s p i k e  superimposed  on  the  spectrum  (Vogt e t a l . [ 1 9 7 8 ] ) , l o n g  Johnson  [1984b],  emission  spikes  high  however,  in  (Vogt  frequency  (around  p i c k u p s . Cosmic-ray UBC-built  Reticons  fact,  can  plot  one in  s p i k e s can  be  events on  2.2.  seen  The  sampling  i n the  p e r hour their  Their at  pixel  occurrence DAO  and  positions  t h e r e can al,so be  the spectrum  affected.  observed  sharp of  noise  with series.  the time  the In  series  but  typical  at  T=463s.  of about  i n R e t i c o n spectrum twice t h i s  four  the r e s u l t  a t T=263s and each  to  frequency)  on  in  Because  that  most n o t i c e a b l e  spectra  about on  c a n be out  event  pixels  i n two  or time  of t h e s e s p i k e s  cosmic-ray spikes are generally  height.  been  exposures  two  one  c a n a l s o be  have  long  see a few  Figure  the  silicon  [1981]).  pointed  the s p e c t r a  the  of s e v e r a l  exposures  has  in  e v e n t . Such  f r e q u e n c y of s u c h o c c u r r e n c e i s a b o u t  hours  The  region  amount o f  is especially  Electron/hole  the  shows  from  2000e~  i s about  a t CFHT.  ten  Naturally,  a r e random. A t  s p i k e s c a u s e d by a l p h a p a r t i c l e s  in  times,  from  the  61 •nuclear are of  very  of  ray  photons. A  detectors  [1976], Walker  et  [1976], Campbell Percival  and  C o c h r a n and  2.4.1  al.  A suitable  lines  i n the  length  the  very  few  fairly  evenly 150  Livingston [1979],  Simpson  [1980],  e t a l . [1981 ],  absorption  spectral  line  fixed  absorption  the  one  reference  lines  absorption  in  Vogt  angstroms  by  the  as  as  path in  metre. I t  the  strong  most  same  the  A  stellar will  t o be  at  has  region.  coverage  array  simple  spectrum  spectral  a  be  convenient  telescope  p r e f e r a b l y be the  reference  is desirable for lines  have  Reticon  of c o u r s e ,  length.  stellar  should  Reticon  where t h e  be  cell  across  should  The  strength,  the  lines  wavelength  region  absorption  while  cell  efficiency.  absorption  i s about  strong  in  the  r e g i o n . The  weak l i n e s  reference  and  al.  GAS  quantum  should  the  of  et  Walker et a l . [1985].  least  installations spectrum  [1976],  the  Reviews  et a l . [1978], Geary  at  a  for  Geary  [1981], Campbell  in  detective  by  [1985].  in Livingston  [1980], Talmi  for  has  limited  thousands  d i s c u s s i o n on  i n Ninkov  found  [1976],  gas  lines  lines  be  ABSORBING  absorption  spectral  found  These  ABSORPTION SYSTEM  CHOOSING THE  high  be  [ 1 9 8 3 ] , and  detector.  s e v e r a l hundreds of  [1977], Vogt  Barnes III  GAS  i n the  more d e t a i l e d  can  Nordieck  [1981], Timothy  THE  e v e n t s of  phenomenon can  Reticon  2.4  r a d i o a c t i v e elements  energetic  equivalent  cosmic on  decay  Coude the with some The  distributed of  about  reciprocal  62 dispersion important to  be  commonly between f o r the  should  still  also  too  be  between t h e  the in  polyatomic  m o l e c u l e s would  case,  should the  a  the  not  be  such that This  is  (HF)  the  by  telluric  order  Walker  to  absorbing  the  HF  criteria. region  For  also  There are spectral  X8700 r e g i o n a  given  gives  wavelength than  region and  a  in  several  between F5  the  the  around K.  two  conventional  weakly-blended  Figure  X8700 2.4  range  or  of band  linear  the  i s to  In  molecule  be  of  chosen minimal.  line-blending  lines. hydrogen  suggested  fluoride  by  Gerhard  vibration rotation most  of  the  change,  blue  the  spectral  stellar  ' s t a r s of  shows s e v e r a l  band  mentioned  l a r g e r Doppler  strong  for  the  the  telluric  radial-velocity  f a c t o r of  blended blending  l i n e s would be  fulfils  it  i s o t o p i c bands  region  (3-0)  lines  The  of  stable  as  there  rotational  band  avoid  gas  low  above c r i t e r i a .  [1979] s e l e c t e d  R-branch of  i n the  to  variable  C a m p b e l l and be  other  spectral  in  by  by  or  be  diatomic  the  absorption  the  contamination  H e r z b e r g . The of  satisfy  contaminated  problems caused  of  to  by  stars. A  gas  high  found. C o n v e r s e l y ,  constrained the  also  spectrum  reference  features.  reference  important  be  is  r e l a t i o n . But  stellar  selected  m o l e c u l e . Moreover  any  l i n e s not  v e l o c i t i e s of  from  this  can  It  l i n e s i n the  reference  strong  structure  A/mm.  gaps between t h e  l i n e s i s , however,  topocentric  10  dispersion  lines  f o r the  with  reference  the  stellar  and  c a l i b r a t i o n of  sufficient  desirable  heavily  the  in  structure  where u n b l e n d e d is  number of  sufficient  frequency  2 A/mm  X8700  shift  region.  l i n e s in  spectral typical  in  the type  spectra  63  Figure  25% 8660  2.4 S t e l l a r  spectra  I  I  8695  i n the region  I 8730  Wavelength  o f X8700  8765  64 in  this  region stars  spectral are  v a r i o u s Fe  of e a r l i e r  N I lines lines  is  spectral  also  particular  bands of DF reasons,  been c o n s i d e r e d diatomic there  i s an  deliver  other  be  large HF  has  diatomic  parameters  [1982], may  after be  an  There are lines. handle.  HF  F5,  i n the  most  absorption  low  reflectivity  aluminum,  the  reflectance  of  Because t h e r e  use  the  dip  (3-0)  overcoated are  up  to  the  region. has  study  of  lasers  (Hough  molecules.  to  [1977]). completely  Wavelengths  and  i n the  band  are  Cochrane et  al.  have a l s o c o n c l u d e d  and  that  in  using  is  not  at  the  the  (3-0)  HF  easiest  to  must a l s o be t h e HF  heated  For  X8700 i s  aluminum ten or  freshly o n l y about  is more  very  to  molecules.  band a l s o c o i n c i d e s w i t h  of aluminum.  reflectance  band  Moreover,  of HF  lines  t o a v o i d p o l y m e r i s a t i o n of  X8700 r e g i o n of  the  gas.  d a n g e r o u s gas  The  the  of t h e most  Moreover, the a b s o r p t i o n c e l l  100°C i n o r d e r  towards  [1958]).  in chemistry.  search,  telluric  infrared  for  densities  for other  no  absorption  the  suitable  some d i s a d v a n t a g e s  is a  almost  in  i n the  power  suitable  and  (Kuipers  interest  extensive  s e v e r a l Paschen  same s p e c t r a l  spectrum  shapes  the  For  stable isotope while  a l s o been one  for  X8662 l i n e .  II  lines  region except  other  molecules  t h e most  than  not  specific  the  P - b r a n c h of t h e  no  line  in  t h e Ca  spectral  the  stellar  There are  t h e HF  much b e t t e r known t h a n  HF  type  are  increased  Consequently, studied  to  molecular  and  present.  l o c a t e d . F l u o r i n e has  similar  prominent  I lines  w a v e l e n g t h where t h e  molecular For  are  in this  longer  r e g i o n . The  the  deposited 89%.  much  reflections  The lower. in  a  65 Coude-Reticon very  high.  improve  The  on  badly  on  of  that  be  readily  of  the  of  loss in  silver  high  through-put silver  the  within  implies  use  the  reflectance optics  system, the  DAO  at  is  red  not  c o n d i t i o n s a t CFHT w h i l e UBC  the  0.4m  DAO  t h r o u g h - p u t . One  lines  can  absorption  depth one  has  imply a  few  cells  about  to  the  use  This  to a l l e v i a t e  help  deteriorate  present  are  too  the  lines. the  To  such  to  telluric matters.  lines  Coude much  that  i s t o use  the  the  the  path  the  t h e HF  (4-0)  region  HF  spectral wavelength  the  available  (4-0)  HF  the  line  l e n g t h and cell.  been red  band. More  however,  is  the  same amount of  absorption in  not  the  improve  problem  increase  absorption  of m u l t i - p a s s  red  by  10-15% i n d e p t h compared t o a b o u t (3-0)  would  o p t i c s have now  improve  time,  short  This  deterioration  helped  (3-0)  the  to  the  the  the  over  silver  a i r c o n d i t i o n i n g system Gold  to The  re-surfaced.  rapid  be  Coude t r a i n  observed  increase  more  complicate  1.22m  may  At  f o r the  an  X6750 i n s t e a d of  This  calibration.  only  freshly  T h i s may  telescope.  way  a l s o be  coverage.  The  however,  been o b s e r v e d on  drier  band a t  98%.  r e f l e c t a n c e Coude t r a i n  high  are  mandatory.  the  e i t h e r CFHT or UBC.  (4-0)  over  becomes  surfaces  they  at  are  is  telescope,  train  used at  reflecting  a week a f t e r  o p t i c s has  the  thro.ugh-put  almost  a v a i l a b l e at a l l times.  red  used at  red  X8700  1.22m  the  lines 60-70%  strength, this  There are of  X6750  will also to  66 2.4.2  PHYSICAL AND Hydrogen  chemical boiling  is  will  the  will Being  readily  an  metals  acid,  to  catalyst  2.4.3  and  is toxic.  by  and  one  at  be  and  or  escape cloth  from may  phase  skin.  One  immediately  i s very who to  has  save  administered  e x p o s u r e t o HF  liquid  the  contact  a drenching  corrosive  glass.  Steel  above  65°C.  It  is  [1950,1964].  cause  limit  level.  life.  with shower  in either  HF  the  In t h e  of w a t e r .  amount event through  Inhalation  of  immediately  the vapour  attack must  coughing  penetrating  t o the v i c t i m  will  a  chemical  vapour, b r e a t h i n g  and  of  also  and  s h a r p and  one's  heat  HF  usually  v a p o u r . HF  corrosive  a high  hydroxides  v a p o u r can  serious toxic  It  air  physical  WORKING WITH  gas  i n t o moist  i s very  salts.  b r e a t h i n g . The  t o below a  cannot  the  also  a  its  o x i d e s and  fluoride  or  a  b e c a u s e of  temperatures  I n h a l a t i o n of HF  oxygen must be  after  HF  t h e v a p o u r , however, w i l l  clothing  100%  gas  silicates,  r e a c t i o n s . The  of hampered  inhalation  that  will  has  temperatures.  fact,  of HF  react with  water  In  and  in l i q u i d  o f HF "have been d e s c r i b e d i n Simons  a sense  dry  will  for organic  o d o u r of of  corroded HF  be  i n w a t e r . HF  attack quartz,  a c i d ) has  colourless  i t can  fumes. T h e r e  SAFETY PRECAUTIONS ON HF  It i s  agent.  is dissolved  form  properties  hydrofluoric  f o r water, a leak  rapidly  HF  r a n g e of o b s e r v a t o r y  strong dehydrating  when HF  be  HF.  1 9 . 5 1 ° C . Hence  produce v i s i b l e  will  (anhydrous  simply  normal  affinity  release and  of  p o i n t of  a very  strong  fluoride  formula  phase over  CHEMICAL PROPERTIES OF  or  unprotected be  subjected  A  physician  67  s h o u l d be even  if  consulted the  as soon  injury  appears  p r e c a u t i o n s must be Availability  of  g o g g l e s , and  head  have a f u l l w i t h HF. the  HF  as a r e s u l t discussion  adequate  gas  coverings  may  accidents  is  safety involved.  resistant  can  t o sudden  One  gloves,  should  still  on t h e s a f e t y  happen  pressure  p r e c a u t i o n s as w e l l  data sheet  on h y d r o g e n  exposure  fluoride  as  e.g.  buildup detailed  recommended  i s given by  also  working  w i t h c o n t a m i n a n t s . A more  published  the  i n the  Matheson  P r o d u c t s company.  2. 4."4  THE The  ABSORPTION CELL HF  system  a gas a b s o r p t i o n  (sample  line)  is essentially cell  of l i q u i d  which HF.  This  a closed  system  consisting  i s connected to a  reservoir  reservoir  be m a i n t a i n e d a t a c o n s t a n t t e m p e r a t u r e gas  pressure  absorption  cell  (HF  vapour  itself will  operating  t e m p e r a t u r e . The  different  than that  system c o n s i s t s connecting of  exposure,  a t a l l t i m e s when  i n t h e c a s e of a c c i d e n t a l  of  HF  is essential.  procedure  Gas  any  Adequate  wherever  masks, HF  e x p l o d e due  of r e a c t i o n  after  be m i n o r .  clothing  with caution,  equipment  to  t a k e n when and  c o v e r a g e of  Even  as p o s s i b l e  HF  proof.  of  also  will  the  cell.  The  be m a i n t a i n e d a t a c o n s t a n t  sample  various control  s y s t e m . The  HF  to ensure a constant for  temperature  of t h e HF  t u b i n g s f o r use  from t h e  pressure)  of l i q u i d  of the  line.  The  c e l l may gas  handling  v a l v e s , manometer,  i n the i n t r o d u c t i o n whole s y s t e m  has  and to  be  and  removal be  leak  68 The  absorption c e l l  itself  w i t h windows a t b o t h e n d s . by  the  amount of  available  entrance  slit  in  the  generally  about  one  metre.  should  large  enough t o  be  light  beam.  This  occur  when t h e c e l l  accomplished  two  is  different  The  the c e l l  other is  end  about  i s about  of c e l l , 1.0cm.  smaller  at the  guiding  beam.  HF  to  the  diameters  tetramers are  and  Davis  Huong and Wiggins of  70°C  [1953], Smith Couzi  monomeric HF  however,  inside  has the  molecules  not  HF  of the  system  size  with  of  the  a t one  end  at  cell  available  the  at  addition  cyclic  hexamers  (HF)  D i s c u s s i o n s on be  Herget  Bartell  Hobbs  greatly  of  chain  m o l e c u l e s can  and  also  shaped  shaped  and  is  i n t h e way  the  slit,  t o form p o l y m e r s  temperatures. HF  is  zig-zag  [1958,1959],  would  Coude  a cell  diameter  getting  2  [1969], Janzen  polymers  cell  would  d i a m e t e r . The  (HF) ,  [ 1 9 7 1 ] , and H i n c h e n  these  vignetting  diameter  ring  of gaseous  is  of t h e  ( M e r e d i t h [ 1 9 7 2 b ] ) . In  dimers  a l s o p r e s e n t at lower  polymerisation  This  t h e beam. A t CFHT, t h i s  to avoid  the  Coude  the p a r t i c u l a r  have a t e n d e n c y  than  fl  the  the s p e c t r o g r a p h " e n t r a n c e  outside  s m a l l end  ( H F ) , and  diameter  t o match  large  towards  monomers,  that  into  of  4.0cm w h i l e t h e s m a l l e r d i a m e t e r  The  less  inside  telescope,  gas m o l e c u l e s  temperatures  front  tube  is limited  observatory.  with a large  1.22m inside  in  accommodate  c o n v e r g i n g Coude beam. The of  space  particular  i s moved  a metal  l e n g t h of the c e l l  to ensure  by a c e l l  u s e d a t t h e DAO  The  is basically  found et a l .  reduce  f o r the  the  the  in Jarry [1960],  [ 1 9 6 9 ] , Himes  [ 1 9 7 9 ] , The  6  and  presence number  f o r m a t i o n of  of the  69  reference  absorption  cell  to  has  greater  be  than  (Kuipers  lines.  Consequently,  h e a t e d and  100°C  in  maintained  order  [ 1 9 5 8 ] , Herndon e t  t h e HF  to  at  absorption  a  minimise  temperature  polymerisation  a l . [ 1 9 6 2 ] , M e r e d i t h and  Smith  [1974]). Operation heating  coils  handling  temperature  high temperature  wrapped a r o u n d  system.  temperatures  stable  at the  A  at  thermocouple  both  control  unit  temperature.  It  applied  t o the  several  hours  equilibrium average  for  non-uniform the  cell.  the  was f o u n d  of  to  used  that  would  a  of  the  maintain provide  the c e l l  minimise system.  voltage It  takes  to  reach  process.  The  two ends o f t h e  cell  rather  of  profile  a l o n g any c r o s s - s e c t i o n cell  the s t e l l a r  cell  the i n s u l a t i o n .  forced the  stable  a  c o n c e i v a b l e f o r t h e HF g a s t o have a  a stable  to  to maintain  cell.  even has t h e e n t i r e  applied  feed-back  o f t h e HF gas i n s i d e  The h e a t e d a b s o r p t i o n  Continuous  the  the  temperature  condition  by gas  monitor  be s u f f i c i e n t .  i s thermally  from t h e s u r r o u n d i n g s i n o r d e r t o minimise seeing  of the  A  the heating  o b t a i n e d from that  part  cell.  originally  the s t a r t  temperature  i s also quite  of  was  and  i s used  the temperature  may n o t be t h e same a s It  ends  heating c o i l  after  the c e l l  i s accomplished  cell  image.  An e a r l i e r placed  t h e danger of The s y s t e m  a possible  a t CFHT  version  t o the  cover. HF  on t h e  This also helps i s used  o f t h e HF  i n a polyethylene  a i r circulation polyethylene  insulated  i t s effect  temperature. F i b r e g l a s s  This  of  outdoor also  to  system  covering. was helps  gas l e a k a g e from  uses a p l e x i g l a s s cover  to  then to the  instead  70 of  the p o l y e t h y l e n e c o v e r i n g . At  used  room t e m p e r a t u r e ,  i n chemistry  Jaffe  experiments  of  Nickel  one s u c h  is  construction associated Kuipers Couzi  fluorides  of  gas  (Naude  HF  been  formed  and i t has cells  system  [1958],  systems  fluoride  (Hinchen  Rollefson  Kel-F  for  [1979]).  systems  the  Nielsen  i n chemistry  is  temperatures.  construction  and  et a l .  [1972b],  [ 1 9 7 6 ] ) . Monel  a l . [1956],  [ 1 9 6 4 ] , Huong  Kel-F  one o f  (copolymers of also  and gas  handling  [1979],  Wickliffe  the  cells  properties  and  i s monel et a l .  Bartell  et  of  (Kuipers et a l . [ 1 9 6 2 ] , Mason  and Wiggins  a l . [1972],  Differential  CFHT  and  gas DAO.  f o r both the c e l l thermal expansion  gas  leakage a t  Couzi [1971],  metals  i t h a s been c h o s e n  at  and  Guelachvili  resistant  and the a s s o c i a t e d  cause  gas  [ 1 9 6 9 ] , Huong a n d  t h e most HF  systems  could  has  handling  Consequently,  HF  and  o f HF  Spellicy  gas h a n d l i n g s y s t e m . metals  et  the  material  a d v a n t a g e o u s t o use t h e same m e t a l  different  parts  [ 1 9 6 4 ] . The most common  [ 1 9 7 0 ] , Himes  o f t h e HF c e l l  f o r both  of  a n d Hobbs  experiments  [1967], Janzen  Meredith  or  o f HF c e l l s  [1958], Herndon  [1969], Wiggins  system  i n Bryce  surface. f o r the  Rothschild  D i s c u s s i o n s on  contruction  [1956], K u i p e r s  the  after  been u s e d  (Kuipers  [1974], Hinchen  c a n be f o u n d  on  and c h l o r o t r i f l u o r o e t h y l e n e )  f o r the c o n s t r u c t i o n  [1950],  become HF r e s i s t a n t  absorption  handling  h a d been  and V e r l e g e r  [ 1 9 6 9 ] ) . The f l u o r o c a r b o n p o l y m e r  been u s e d  high  has  metal  [1958], Smith  vinylidene  used  HF a b s o r p t i o n c e l l s  e t a l . [ 1 9 6 5 ] ) . Some m e t a l s  a coating  and  steel  the  at  f o r the handling It  is  and t h e between various  71 joints  i n the  gauge u s e d  2.4.5  THE The  system.  i n t h e gas  h a n d l i n g system  t r a n s p a r e n t windows  in  f o r the c e l l  on  the  spectral  windows f o r t h e  have a l s o  been  Mason and  Nielsen  used  used  [1969],  however, u s e d  HF  Many t y p e s  of  r e g i o n , have been u s e d  on  cell.  (Adams and  calcium  fluoride  V e r l e g e r [1950],  Plexiglass  property  [1956],  t h e DAO  rapidly  for  HF  cells  (Herget et  [1976], Hinchen  and  Hobbs is  temperatures.  f o r t h e HF  Couzi  cells  [1979]). HF  [1966]).  after The  Their  reacting  most  common  experiments Mann e t  al.  [1966],  Wiggins  Spellicy  et  [1974],  resistant  al.  Guelachvili  S a p p h i r e has  Consequently, at both  Rao  [1971],  Hinchen  very  Rao  on  been  system.  a l . [i960],  Wiggins  [1972b],  and  quality  operating chosen  Himes and  Meredith  Kuipers  also  in chemistry  [ 1 9 6 1 ] , Herndon e t a l . [ 1 9 6 2 ] , Webb and  [1972],  [1958],  and  windows have  on  deteriorated  of s a p p h i r e  a l . [1970],  used  windows  Smith  Huong  at the h i g h o p e r a t i n g temperatures.  t y p e s o f window u s e d  optical  chloride  F i s h b u r n e and  windows were once u s e d  transmission  [1964]  a l l t h r e e t y p e s o f window d e p e n d i n g  used  (Naude and  Silver  windows.  region. Plexiglass  et  must a l s o  Rothschild  Katz  the wavelength  made  resistant.  [ 1 9 6 7 ] ) . K u i p e r s e t a l . [1956] and  [1958]  are  pressure  be  chemistry experiments.  polyethylene  w i t h HF  the  a r e a l s o HF  at the h i g h o p e r a t i n g t e m p e r a t u r e s .  window, d e p e n d i n g cells  as  CELL WINDOWS  resistant  HF  C o n t r o l v a l v e s as w e l l  the  high  s a p p h i r e windows  were  CFHT and  DAO.  at  excellent  The  sapphire  windows a r e a l s o made w i t h optimum t r a n s m i s s i o n a t t h e  X8700  72 region.  Teflon  gaskets  are  (tetrafluoroethylene  used  to s e a l  the  polymers)  windows  rings  onto the  or  absorption  cell. Thin easily  windows  heated  give  to  higher  the  however, more f r a g i l e  operating and  have  during  have t h e  a d v a n t a g e of m i n i m i s i n g  pattern  Basically, Fringe  a thin  had  windows. F i g u r e  2.5  and  HF  the  window. F i g u r e in  the  respectively, taken with beam. The i s not  are  not  the  an  loaded  adequate  empty HF out  dividing Figure  of the  2.6c  dividing  of  a  Lyrae  ( c o n t a i n i n g HF)  to reduce  percent  the  cell the  of  after by  the the  beam. F i g u r e  spectrum shows t h e spectrum  etalon.  a Lyrae  taken  the  an  2.5c a  thin with  defective the  empty  and  cell  (no  are,  flat-field  lamp  absorption  cell  i s wavelength  continuum. F i g u r e a  in  lamp s p e c t r u m  techniques  in Figure  2.5b  residual  of  in Figure  2.6a  by  the 2.5b  that  shows with  with  the  pattern  after  in Figure  2.5a.  fringe pattern by  to  taken  taken  shows t h e  the  dependent  lamp s p e c t r u m  2.6b  HF)  2.5d  residual fringe pattern  dividing  another  windows.  defective  with  and  fringe pattern  windows  taken without  taken  under  interference  perfectly reproducible. Flat-fielding  fringe pattern  cell  of  beam. F i g u r e s  spectrum  much below one the  i n the  observed  and  i s that  are,  thin  containing  spectrum  They  Thick  of  with  spectrum cell  more  a Fabry-Perot  observed  i s the 2.5b  effect  as  are  to crack  process.  the  act  absorption  2.5a  cell  been  known  poor q u a l i t y  shows t h e  beam. F i g u r e  absorption  from  window can  patterns  without  tightening-down  generated  and  temperature.  been  pressure  fringe  the  transmission  those  in  after Figures  73  74  75  2.5a  and 2.6a. F i g u r e  spectrum  in Figure  2.6d shows t h e r e s u l t  2.5c by t h o s e  in Figures  2.4.6 OPERATION OF THE GAS HANDLING The into  HF s y s t e m h a s  the surroundings  be v e r y  react  with  entire  system.  vulnerable  to this  molecules with rest  variable the  time  of  a i r i n t o the  leaks  The  i n the system can  is  damage  pressure  is  desirable  lines.  impossible  rough s e a r c h  be a c c o m p l i s h e d  control valves  to  l e a k s when t h e s y s t e m known t o  check  using  This  become  help  to correct at for  possible  the  pressure  isolate,  loose  a  leak-tester is  vibration-induced  transported.  during  one a t  s y s t e m on a s i n g l e  to minimise  i s being  HF  highly  on t h e s y s t e m . I t  t o mount t h e whole g a s h a n d l i n g will  of the  b o t h b r o a d e n and a l t e r t h e  i s almost  f o r a more d e t a i l e d  metal p l a t e . This  can  especially  Collision  s e l e c t e d s e c t i o n s of the system. A helium  required  in  (corrosion) to the  gauge  reference  reduction. A  gauge and t h e v a r i o u s time,  severe  HF  error  HF s y s t e m  gas  Contaminants e.g. water vapour can  of c o r r o s i o n .  of the  of data  o f HF  leak  type  systematic  leak  d i s a s t r o u s to the o p t i c s  f o r e i g n gases w i l l  wavelengths  A  be  t h e HF and c a u s e  HF  2.5a and 2.5d.  could  undesirable.  the  SYSTEM  t o be l e a k - p r o o f .  most o b s e r v a t o r i e s . A also  of d i v i d i n g  J o i n t s have been  transportation  of  the  HF  system. There a r e s e v e r a l  operation  modes f o r  t h e HF  system.  They a r e : (a) d i s t i l l a t i o n bottle  of  sufficient  HF  from t h e  i n t o t h e HF r e s e r v o i r (sample  lecture  line).  76  (b) i n t r o d u c t i o n absorption pressure sample (c)  gas  using a melting  gas  t h e sample a l l t h e HF  of  t h e HF  gas  system  Operations  of  near  an  exhaust  f o r t h e modes 2.7  This  large  distillation associated  with  system  are  immersed are  this  observe  The  Kel-F  helps  valve  V6  to  amount o f  bottle  i s closed  for  after  t u b e . A lamp  the l i q u i d  i n the  colour  imply t h a t  is usually  seen  t h e HF  e.g.  most of  the  valves in a  good  the Kel-F  into  the  tube  and  required  the  i s probably  HF  HF  to h e l p  should  liquid  V5  Kel-F  of the l i q u i d  liquid on  HF  valve  o f HF  v a l v e s V6  the l e v e l  t u b e . Pure  any  achieving  d i s t i l l e d over  HF the  control  the system. With  HF  up  ( a ) , a l l the c o n t r o l  translucent  tube would  especially  speed  i s the  lecture  closed  the e n t i r e  visible  is  be  throughout  m e t h a n o l - d r y - i c e bath, the  Any  should  (d).  be m e a s u r e d by e x a m i n i n g  colourless.  This  very  used  initially  o p e n e d . The  tube can in  in a  system  only  tubings are  Products. It  vacuum t h r o u g h o u t  used  generalised  t i m e s . F o r t h e o p e r a t i o n mode the  operation  of a  the commercial  f r o m M a t h e s o n Gas  HF  the  schematic  diameter  process.  (d) a r e  the  (a) and  monel  cell  system.  fume-hood.  shows t h e  system. H a l f - i n c h  the  involves only  infrequently.  system.  gas the  the a b s o r p t i o n  from  (a) and  Figure  heated  line.  ( c ) . Modes  recommended  the  i c e bath around  from  (b) and  performed  into  m a i n t a i n i n g a c o n s t a n t HF  a l l t h e HF  (d) r e m o v i n g  modes  HF  line.  into  Normal usage  the  c e l l and  by  condense back  of  in  be the  contaminated  gure  2.7  Schematic  of  a generalised  HF s y s t e m  78 and  s h o u l d be d i s c a r d e d . T h i s  closing  V6  valve  liquid-nitrogen  bath.  opening valves V 1 system  into  and  immersing With  cold  vacuum  first  trap  in  a  pump  turned  on,  remove a l l t h e  HF from  the  t r a p . The vacuum pump a n d c o l d  a m e t h a n o l - d r y - i c e bath) can o f HF  the  the  and V 4 w i l l  the c o l d  distillation  c a n be a c c o m p l i s h e d by  also  be u s e d  from t h e l e c t u r e  trap ( i n  t o speed  bottle  into  up  the  the Kel-F  tube. If  t h e HF v i s i b l e  distilled  into  t h e sample  methanol-dry-ice  Kel-F  tube until  distilled  into  liquid  t h e sample  an  such  cell.  form and  that  line  line.  some  after  This also  sample  and  the  This  a l l t h e HF from  of is  gas  liquid  HF g a s  HF  HF  has 6  about  into  cm  still  i s released  into  limit  additional  coatings  been 3  system. A f t e r  the Kel-F  remain the  also  surface  completing  and r e s i d u a l  system  t h e vacuum pump a n d c o l d  valve V 3  opened  line,  and a  any f o r e i g n  HF i n  methanol-dry-ice gas  i n the  is tube  i n the  absorption  required of the  the  v a l v e V 3 c a n be c l o s e d i s removed u s i n g  of  on t h e volume o f t h e  HF i s  on t h e i n n e r  be  HF i n t h e sample  would  a lower  Initially,  handling  transfer  a  sample  The p r o c e d u r e c a n  s h o u l d be s u f f i c i e n t  imposes  the f l u o r i d e  sample  i t c a n be  HF f o r t h e HF s y s t e m a t DAO. The amount d i s t i l l e d  known v o l u m e . T h e r e  sample  transfer  amount  line.  m o n i t o r e d by t h e i n t e r m e d i a t e  line  bath around  line.  appropriate  t h e sample  i s clear,  With valve V 6 c l o s e d  line.  or l i q u i d - n i t r o g e n  into  repeated  of  tube  o p e n i n g v a l v e s V 4 and V 3 w i l l  line, the  i n the Kel-F  cell  transfer,  the rest  bath  to  of the  trap.  With  around  the  system can  also  be  79 removed u s i n g  t h e pump and c o l d t r a p . T h i s  brief  s i n c e the vapour p r e s s u r e  process  dry-ice also  temperature. Using  freeze  any  trapped  liquid  air. A  distill  higher  p u r i t y HF  lecture  bottle  is  be a  very  o f HF i s n o n - z e r o a t  nitrogen,  however,  would  more i n v o l v e d p r o c e d u r e  from t h e  described  should  by  standard  Wickliffe  commercial and  to HF  Rollefson  [1979]. For of  operation  the system  cold  c a n be  trap, Kel-F  and  V4 a r e c l o s e d  The  HF  f o r the e n t i r e duration cell  of about  the  condensation.  V3  will  introduce  is  placed  pressure  around  gas e n t e r s  windows w i t h  the  the atmospheric  into the  to  amount o f HF l e a k i n g gauge  rather  t o monitor  o f HF i s g i v e n  remove V2  and bath  ensure a constant  pressure  out.Valve  this  gas  be t h e v a p o u r p r e s s u r e  operation.  system  coloured  A melting-ice  360 mm Hg. The f a c t  margin of s a f e t y t o the  pressure  line  is  may be r e l a t e d t o  into the c e l l .  sample  less  pressure  Brown  opening valves  HF g a s  the  i f the c e l l  With a heated c e l l ,  is  the  operating  ' h e a t - g u n ' may  a t 0°C a n d i s a b o u t  leak  the  a  HF  will  the c e l l .  has  HF p r e s s u r e .  air  substantial  be o p e n e d t o  by J a r r y a n d D a v i s  extra  develops,  than having  of  the pressure  a d d e d an  I f a leak  V7 c a n  the  that  V1  operation.  t o the i n t r o d u c t i o n of  i n the system. T h i s w i l l  than  to  pump,  The v a l v e s  of the  heated  c o n d e n s a t i o n s on t h e windows  problem. Heating the  be  parts  t h e vacuum  o f t h e HF g a s c a n o c c u r  h e a t e d when t h e HF  liquid  must  100°C p r i o r  gas. Condensation  not  removed. T h e s e a r e  t u b e , a n d HF l e c t u r e b o t t l e .  absorption  temperature HF  mode ( b ) , most o f t h e n o n - e s s e n t i a l  The  [1953] :  allow vapour  80  log  1 0  P  = A - B / ( C + t  where  )  P = HF v a p o u r  (2.2)  p r e s s u r e i n mm Hg  A = 8.38036 ± 0.10896 B = 1952.55 ±  125.85°  C = 335.52 ± 8.15° t In  order  everytime, distilled can  to  maintain  one  uses d i s t i l l e d  water  more  consistent  water  and i c e formed  line  sample  iine  may c a u s e  can  to l i q u i d  gases  (c), collecting  be a c c o m p l i s h e d  clotting  foreign  from  temperature  smaller  pieces  i n the i c e bath.  o p e r a t i o n mode  sample  temperature  f o r t h e i c e b a t h . A more s t a b l e  being used  For  nitrogen  of the  trap.  remove a l l HF from  by  t h e HF back slowly  into the  freezing  temperature. Rapid  system  i n t h e system  vacuum pump a n d c o l d to  a  i n °C  be m a i n t a i n e d i f t h e i c e i s c r u s h e d i n t o  before  or  = temperature  the  freezing  by f r o z e n HF. R e s i d u a l  HF  c a n a g a i n be removed w i t h t h e  Similarly,  t h e system,  for operation  mode (d)  t h e vacuum pump a n d  cold  t r a p a r e u s e d w i t h v a l v e s V1, V2, V3, V4, V5, a n d V7 o p e n e d . Dry  air  system and  or n i t r o g e n  by o p e n i n g v a l v e  cold  output  t r a p would  be i n t r o d u c e d  V8. I n t h i s  be r e p l a c e d  to flush  c a s e , t h e vacuum  by a  gas through a sodium-hydroxide  exhaust  2.4.7  can a l s o  tubing  t o bubble  solution  the pump the  and i n t o  an  image s l i c e r  is  fume-hood.  PLACEMENT OF THE CELL Instead  generally  of the  conventional s l i t ,  used t o reduce  the  loss  an  i n through-put  caused  by  81  poor the  seeing  c o n d i t i o n s . The image  amount o f g u i d i n g  cell  i s placed  image s l i c e r .  the l a s t  cell  can  respect  avoid iris  to  that  exposures. This  can  respect  off  t h e image  by a s m a l l  align  the c e l l  light  along  with  the  cell  path  and the i r i s .  the  easily  of the c e l l i n order  on  to  the  well  the alignment  lamp  aligned  of the  iris  through  the  mirror  slicer.  i s accomplished  This  sky or r e f l e c t i n g  by  light  The image s l i c e r  may a l s o  be  aperture  purpose.  To  the l i g h t  for this  in place,  from b e h i n d  o p t i c s . Alignment  by v i e w i n g  use  i s generally  blue  HF  i s a l i g n e d a g a i n s t the for  t h e image s l i c e r  t h e beam  way o f t h e v i e w i n g accomplished  circular  and  the primary  at the  o f t h e dome.  mirror  be a c c u r a t e  place  diaphragm  the telescope  the i n s i d e  replaced  in  by v i e w i n g  flat  the  a c c u r a t e l y and  the c e l l  t o t h e beam. A t DAO,  from b e h i n d  pointing  is  iris  be c h e c k e d  iris  has t o  reduce  a n d DAO,  beam. The a l i g n m e n t  vignetting. Generally, diaphragm  with  t h e beam  Coude  a l s o be  moved i n o r o u t o f t h e Coude with  would a l s o  e r r o r . A t b o t h CFHT  between The  slicer  one c a n s h i n e  t h e image s l i c e r  of the c e l l  rays  by  c a n t h e n be  coming through  both  Chapter THE HF  3.1  vibration-rotation state  (X 2 ) 1  +  l e v e l ) and the  o f HF  u=3  between  i.e.  carried  band,  as  Kirkpatrick  the  and S a l a n t  to  Rao  The  Mann  band  (ground  the second overtone  were  [1935].  v  is  the  et  al.  [1961]  bands  Since  of the  [1967a]  measured  vibration-rotation  photographed  then,  the  wavenumbers measured.  a l . [1979]  from t h e (1-0) t h r o u g h  [ 1 9 7 6 ] , Naude and  Webb  Verleger  flame  while  spectra,  23  through  (9-4).  Deutsch  (1-0),  (2-1),  and  (3-2)  from  HF  only  measured  laser  a l s o observed  the  HF  laser  (2-1)  while bands.  transitions  band. The most  recent  p e r f o r m e d by F i s h b u r n e  t h e (4-0) and  82  transitions  t h e (1-0) and  t o t h e (6-5)  measurement o f t h e (3-0) band was [1966] who  et a l .  et a l . [1962],  from  by  from (1-0)  Kwok e t a l . [1970] measured Sengupta e t  was band  ( 3 - 0 ) , a n d t h e (4-0) bands  the bands  HF  (3-0)  bands have been  measured,  ranging  of  vibrational  study  first  a l . [1956], Herget  the (2-0),  different  Rao  v=0  level  second overtone  [ 1 9 6 8 ] , and G u e l a c h v i l i  [1950] m e a s u r e d  the  electronic  (1-0) and t h e (2-0) bands were m e a s u r e d by T a l l e y  [1950], K u i p e r s et and  from  o f t h e (1-0) f u n d a m e n t a l )  the v a r i o u s v i b r a t i o n - r o t a t i o n  The  arise  ground  experimental  (that  (4-0)  the  where  earliest band  lines  the v i b r a t i o n a l  o u t by Imes [ 1 9 1 9 ] .  well  in  they belong  vibration-rotation  vibration-rotation  reference  transitions  quantum number. The  of  SPECTRUM  INTRODUCTION The c h o s e n w a v e l e n g t h  as  3  and  (5-0) b a n d s . P u r e  83 rotational  transitions  o f HF  K u i p e r s e t a l . [1956], Mason and Sengupta  Nielsen  et  [1959], D i Greening  [1967],  to  the  transitions  in  form  transitions)  the  the  f o r HF.  vibration-rotation running  bands  is  and  the  lines  (or  -J") f o r the l i n e s  (or  J') a r e , r e s p e c t i v e l y ,  and  t h e upper  Douglas  rule  AJ=±1  with  AJ=+1  J  transitions the  There  is  band a r e i l l u s t r a t e d equal  transitions  J o h n s and Barrow  band  and  provided  t o J^+1  for  the  being  the  give  rise  while  AJ=-1  no Q - b r a n c h  (AJ=0  The v a r i o u s t r a n s i t i o n s  i n d e x number m i s  and  c o n s t a n t s f o r HF.  R-branch of  P-branch.  by  [1967b],  [1970],  references also  selection  quantum number. The  lines  [1973],  of the above  rotational  rotational  [1964], Deutsch  Meanwhile, e l e c t r o n i c  derived molecular  vibration-rotation  observed  and Y a r d l e y  and D o u g l a s  [ 1 9 7 9 ] . Most  The  Akitt  been  by S a f a r y e t a l . [ 1 9 5 1 ] ,  Lonardo  experimentally  also  Rothschild  a l . [1979].  have been o b s e r v e d  have  i n the  (3-0)  i n F i g u r e 3.1. (or  The  o r J') f o r  i n t h e R - b r a n c h . And i t t a k e s on t h e v a l u e s o f - J ^ i n the P-branch. the  (u=3) v i b r a t i o n a l  J^  ( o r J " ) and  J v a l u e s i n t h e lower  J^  (u=0)  level.  3.2 MOLECULAR CONSTANTS FOR HF  3.2.1  BASIC EQUATIONS AND The  wavenumber o f a l i n e c a n be o b t a i n e d d i r e c t l y  the d i f f e r e n c e levels.  CONSTANTS  The  J-rotation  between  term level  the p a r t i c u l a r  value  T(u,J)  i s t h e sum o f  for  upper the  a vibration  and lower u-vibration term  from energy and  G(u) and  a  84  Figure  3.1  The  Ti«  (3-0)  —  "II  II  ° i'  vibration-rotation  IIII II I'  l:i: •  *  band  II a  to  II  2  —vrA . Il  —v— O ~ 'l  of  HF  85  rotation  term  Fy(J) :  T(w,J) = G(v)  + F (J)  (3.1)  y  G(i>) = co (u+1/2) •  x  e  (u+1/2)  e e  + co y ( y + 1 / 2 ) e e  2  3  F  (J) = B j ( j + 1 )  - D J (J+l) 2  y  3  u> ,  co x ,  e  anharmonic listed  The  -  3  be  power s e r i e s  Barrow  co z  4  are  some  of  the  constants  are  e e  values of  these  a n h a r m o n i c c o n s t a n t s c a n be f o u n d [1979], c a n be  expressed  o f (u+1/2) w i t h t h e a n h a r m o n i c c o n s t a n t s [1950],  Rao  and Mantz  [1972],  as  Johns  [ 1 9 5 9 ] ) . The a n h a r m o n i c c o n s t a n t s t h e m s e l v e s  expressed  in  be  terms  of  the  between t h e Dunham  [ 1 9 3 2 ] . The t e r m can  (3.3)  c o n s t a n t s B , D , and H  (Herzberg  coefficients,  y  The  3.1. O t h e r  rotation  correspondence  H  e  and  i n Huber and H e r z b e r g  coefficients and  co y , e'e  constants.  referenced  in  e  i n Table  L^JMJ+1 )  2  y  terms  (3.2)  y  + H J (j+1 ) The  - co z (u+1/2)" e e  y  Dunham  value T(u,J) as  expressed  coefficients.  a n h a r m o n i c c o n s t a n t s and  corrections,  more  can well  be f o u n d as G(u),  explicitly  can  using  in  The  Dunham Dunham  B , D ,  and  y  the  Dunham  coefficients: = I . Y. ( u + 1 / 2 ) J ( J + l )  T(u,J) G(u) v  =  v  =  v  =  B  D  H  i  = Z Y i  Z  i  i 1 (  Y  -2 Y i  Z  i  Y  (u+l/2)  i 0  u  +  /  1  )  2  i 3  (  d' l/2) u  +  l  /  2  )  (3.4)  m  (3.5)  1  ( - >  1  +  i 2  m  1  3  6  (3.7)  1  (  3  ,  8  )  86 L  The  v  -^iY^to+l^)  =  (3.9)  1  v a l u e s f o r most o f t h e Dunham c o e f f i c i e n t s c a n be  i n Webb a n d Rao [ 1 9 6 8 ] . V a l u e s in Deutsch  t e r m s o f B^, u£, Formulae  6  by Dunham al.  Y  0 8  Y ,  for  2ft  and  a^ u s e d  from  a r e from  line-strength  are  in a  The in  a,,...,  in  the  et  Tipping potential  Sandeman  [1940]. with  6  i n the  calculation used  are  forY  [1962] w h i l e t h o s e  from  and l i n e w i d t h  taken ,  Y  1 5  ,  for  Y  0 7  ,  and T i p p i n g [ 1 9 8 3 ] .  0 6  Formulae  Bouanich  [1978a].  p r o v i d e a easy  l e v e l s which w i l l  way  to  be r e q u i r e d ' i n  calculations.  CONSTANTS AND  3.3, one  and  been c a l c u l a t e d  Dunham c o e f f i c i e n t s  Equation  [1962], Niay  o f ( a , ) . The v a l u e s f o r t h e  Ogilvie  3.2.2 DERIVATIONS OF NEW  lines  constants  between  given  Woolley  t h e v a r i o u s energy  Using  found  expressed  Ogilvie  and Koo [ 1 9 7 6 ] . The f o r m u l a e  These c a l c u l a t e d  any  and  the other c o e f f i c i e n t s are taken  compute  usually  c o e f f i c i e n t s have  constants  1 6  are  up t o t h e o r d e r  a r e taken  and Y  c a n be  respectively.  Woolley  formulae  c^  Dunham  from O g i l v i e  [1978a],  conversion  a^  contributions potential  Sandeman [ 1 9 4 0 ] ,  Bouanich  The  Theoretical  are  and t h e Dunham p o t e n t i a l  [1932],  constants  and  coefficients  1 3  f o r t h e Dunham c o e f f i c i e n t s have been p u b l i s h e d  [1977],  [1983],  0  [1967b] and Mann e t a l . [ 1 9 6 1 ] ,  Dunham a n h a r m o n i c  a .  f o r Y „ and Y  found  WAVELENGTHS  c a n d e r i v e t h e wavenumbers  (u-0) v i b r a t i o n - r o t a t i o n  band. The  of  wavenumbers  f u n c t i o n s o f t h e v and J v a l u e s , t h e band c e n t r e v ( t h e  wavenumber  0  corresponding  to  which  would  be  the  pure  87  Table  3.1 P u b l i s h e d m o l e c u l a r  constants  f o r HF  *************************************************** reference co  = 41 3 8 . 7 6 6 6 cm"  Webb a n d Rao [1968]  = 8 9 . 8 8 cm"  Webb a n d Rao [1968]  = 0.90 cm- i  Webb a n d Rao [1968]  1  e  co x e  e  co y e  7  e  co z e  B  e  a e  = - 0 . 0 1 1 0 cm'  1  e  = 20.9561 cm' = 0.798 cm" 1.27x10"  D  e  cm'  2  1  Webb a n d Rao [1968]  1  Ogilvie  a n d Koo [1'976]  cm"  Ogilvie  a n d Koo [1976]  Ogilvie  a n d Koo [1976]  Ogilvie  a n d Koo [1976]  = 0.0021497 cm"  H  = 1.6445x10"  e  5  7  cm"  1  = 0.9168A  v  0  (1-0)  = 3961.4229±0.00025  v  0  (2-0)  = 7750.7949±0.0015  0  (3-0)  = 11372.807±0.007  cm"  (4-0)  = 14831.627±0.007  cm"  v  v  0  a n d Koo [1976]  Webb a n d Rao [1968]  = 6.133X10"  r  Ogilvie  1  1  0  e  Webb a n d Rao [1968]  cm" cm"  B  0  = 20.559743±0.000014  D  0  = (2. 1 2 0 4 8 0 ± 0 . 0 0 0 0 4 6 ) x l 0 '  H  0  = ( 1 . 6 6 5 3 1 0 . 0 0 6 4 ) X 1 0 " cm"  L  0  = (1.8110.12)x10-  cm'  1  H, = ( 1 . 5 9 4 2 1 0 . 0 0 6 8 ) X 1 0 "  7  Guelachvili  [1976]  Guelachvili cm"'  3  1  1  1  cm  3  cm"  1  1 1  [1976]  Sengupta  e t a l . [1979]  Sengupta  e t a l . [1979]  Sengupta  e t a l . [1979]  Guelachvili  1  D, = ( 2 . 0 6 3 9 9 6 + 0 . 0 0 0 0 5 6 ) X 1 0 "  [1976]  F i s h b u r n e a n d Rao [1966]  1  cm" '  B, = 1 9 . 7 8 7 4 7 8 1 0 . 0 0 0 0 1 4 cm"  Guelachvili  F i s h b u r n e a n d Rao [1966]  1  1  7  11  1  [1976]  Sengupta  e t a l . [1979]  Sengupta  e t a l . [1979]  88  L, = ( 1 . 4 6 ± 0 . 1 1 ) x 1 0 "  cm"  1 1  B  2  = 19.034931±0.000032  D  2  = (2.00958±0.00011)x10"  H  2  = (1.523±0.013)x10"  L  = (1,32±0.12)x10  _ 1 1  2  cm"  B  = 18.2995±0.0005  cm"  1  3  D  3  = (1.948±0.006)X10"  H  3  = (1.43±0.10)X10"  B„ = 1 7 . 5 8 2 9 ± 0 . 0 0 0 7 D„  cm"  cm"  = (1.911±0.006)x10-  H, = ( 1 . 2 3 ± 0 . 1 5 ) X 1 0 "  1  1  1  1  [1976]  Sengupta  e t a l . [1979]  Sengupta  e t a l . [1979]  Sengupta  e t a l . [1979]  F i s h b u r n e and Rao  [1966]  F i s h b u r n e and Rao  [1966]  Mann e t a l . [1961]  1  F i s h b u r n e a n d Rao  1  cm'  3  7  cm"  cm"  3  e t a l . [1979]  Guelachvili  1  3  cm'  7  cm"  7  Sengupta  1  cm"  [1966]  F i s h b u r n e and Rao  1  [1966]  Mann e t a l . [1961]  1  ************************************** vibrational H , 0  transition),  L , B , D , 0  y  have  H ,  y  given  and L . F o r example,  y  a  and t h e r o t a t i o n y  power-series  wavenumbers. The r e c e n t l y B ,  D ,  are  listed  y  y  other  and H  i n Table  rotation  (2-0),  3.1. The  most  Mann e t a l .  values  the  of v a r i o u s  v,  values  the c a l c u l a t i o n 0  Sengupta constants  and L  0  0  have  been  e t a l . [1979], i m p l i e s v, 0  from p u b l i s h e d basically  molecular  constants  bands  f o r the  B , 3  D , 3  H , 3  experimental  and L  3  that  accurately  that  only  remain  wavenumbers.  a l e a s t - s q u a r e s problem t o f i n d  [1973],  i s required for  o f t h e wavenumbers. The f a c t  H ,  0  0  c o n s t a n t s c a n be f o u n d i n Mann e t a l . [ 1 9 6 1 ] ,  A s e t of c o n s i s t e n t  B , D ,  [1961]  ( 3 - 0 ) , and (4-0) recent  0  for  F i s h b u r n e a n d Rao [ 1 9 6 6 ] , and D i L o n a r d o and D o u g l a s  for  D ,  0  representation  published  f o r the (1-0),  y  constants B ,  the values  determined  the f i v e t o be The  by  molecular determined  problem  the f i v e  is  constants  89  which would minimise between  the  calculated  the  experimental  optimal  values  [1976], data, D  3  As  for H  B ,  Sengupta  the  Equation  can  then  H  0  H,  has  1 . 4523x 1 0" cm." 7  value  of  of  been g i v e n 1  uncertainties first  time  _ 1  as  y  by  a  of  the  to  by  Albritton  of  the  the  et  al.  experimental  f o r v0 ,  values  B , 3  i s to d e r i v e  data  H ,  and  H,,  0  The  function  formula  and the  solve for  for H  and  H  Y ,  and  Y  for  t>>3  This  is  1 3  terms H  of 3  u, H ,  i n terms of  only  experimental  Sengupta  constants  determined.  L  3  using  et a l . are  method  of a  the  [1979].  within  the  i s also  the  is limited  by  values. This The  A value Similarly,  3  from  2 3  and  for  H  from  2  1 f  0  derived for H .  is calculated  y  3.8.  Rank e t a l . [ 1 9 6 5 ] .  of  is  determine  l e a s t - s q u a r e s method  Equation  rotation  3  of  in  i = 2.  derived  that L  (3-0)  "state  theory  0 3  using  constants  their  A to  solve for Y , to  i s subsequently 1 1  the  i s described  of  of  can  t e r m s up  1.39x10" cm  the  one  approximation  improved m o l e c u l a r Most  values  for H  used  program  the  optimisation process.  evaluated  solving  A similar and  i n the  3  and  optimisation  for  A b e t t e r approach  3  residuals  lines by  The  accuracy  independently  3  with  be  been  the  of  [1966],  i s given  the  L .  improved  3.8  essentially 2  D  has  gives reasonable  e t a l . [1979],  in  H .  L  and  3  With  and  3  Rao  u s i n g the  from  and  3  on  the  used  constants.  constants  procedure  for H  vQ ,  only  and  w e l l as  review  squares  wavenumbers  the  expected  not  values  A  molecular  the  but  for  the  accomplished  Fishburne  method a s  [1984].  estimate  be  o p t i m i s a t i o n program  optimisation Moore  from  of  wavenumbers of  v a l u e s . T h i s can  those  art"  sum  experimental  m e t h o d s . The band a r e  the  90 having  accurate  rotation  constants  Hence, t r u n c a t i o n e r r o r s a r e the  i=2  term  After  final with  residual  new  old  than  obtained  fit  the  residual of  i f one  the  (3-2) add  band c e n t r e .  molecular  constants are experimental  calculated J^,  and  with  m values  The  vacuum  w a v e l e n g t h s by air  wavelength, p r e s s u r e . The Table  3.4  band  small  i n the  final  listed  even  data  in Table  are also  index,  however, air  r e l e v a n t formulae  is  and  the - 1  in  with  the  slightly order may  be  Sengupta  Table the  e.g.  for 3.3  the lists  wavenumbers  corresponding  J^,  listed.  be  refractive  from  values  3.2.  f o r each  can  mean  the problem  adopted  c o n s t a n t s . The  wavenumbers  The  optimisation process.  vacuum wavenumbers and  line  -1  improvement  the adopted  the  is  The  compatible  forced fourth  experimental  The  temperature,  lists  in a  three  ±0.02 c m  ±0.005 c m this  the  3  3.1.  from  more unknowns i n t o  knowing t h e  refractive  A  L ,  wavenumbers  to  obtained  i n c l u d e s the  however, w i l l  the  to  successful.  in Table  fact,  the d a t a .  (3-2)  both  2.  up  other  are a l l  i s reduced  constants  and  3  the  very  experimental  c o n s t a n t s . In  a l . [1979] on  This,  the  H  to d e r i v e  values given  molecular  the  1, and  using only  for  three constants  v a l u e s , however,  polynomial  et  f o r the  molecular  smaller  derived values  data. T h i s proves  between  the  i n t r o d u c e d by  i s used  experimental  calculated using  the  results their  the  procedure  from  f o r u = 0,  equations.  adopting  optimisation constants  i n the  only  converted index a  of t h e a i r .  function  pressure,  and  are  in Edlen  given  into  s t a n d a r d - a i r wavelengths  of  air The the  water-vapour [1966].  f o r both  the  91 Table  3.2 A d o p t e d m o l e c u l a r  constants  f o r t h e (3-0) band  ****************************************** = 1 1372.81 08  cm-  B  0  = 20.559743  cm"  D  0  = 2.12048xl0"  H  0  =• 1 .6653x1 0- c n r  L  0  = 1.81x10"  B  3  = 18.30016  D  3  = 1.9551X10"  H  3  -  L  3  = 1. 39x10"  1  cm'  3  7  1  cm'  1 1  1  cm"  1  1  cm"  3  1.4523x10- cm" 7  1  cm"  1 1  1  1  ************************************************************ Table  3.3 Vacuum  wavenumbers  f o r t h e (3-0) band o f HF  ************************************************************ J  i  J  f  m  experimental  calculated  3  2  -3  1 1236. 129 cm"  2  1  -2  11286.120 cm" ~  1 1 286.1211 cm"  1  0  -1  11331.707 cm"  1  1 1331.6998 cm"  0  1  1  11409.413 cm"  1  1 1409.4033 cm"  1  2  2  11441.428 cm"  2  3  3  11468.841  3  4  4  11491.616 cm"  1  1 1491.621 3 cm"  4  5  5  11509.714 cm"  1  11509.71 1 9 cm"  5  6  6  11523.092 cm"  1  11523.0911  6  7  7  11531.735 cm'  1  11531.7330 cm"  7  8  8  11535.614 cm"  1  1  cm"  1  1  1  1 1236.1296 cm"  1 1441.4304 cm" 1 1468.8493 cm"  cm"  11535.6160 cm"  ************************************************************  92  experimental  and  corresponding  air refractive  the is  calculated  spectroscopic standard at  760  torrs,  15°C,  values  indices.  as The  temperature  and  well  as  the  "standard a i r "  and  pressure  or  (SSTP)  zero water-vapour pressure  (Edlen  [1966]). Before can  be  the  the  obtained,  stellar  spectrum  E a c h HF  velocity  has on  The  and  are  one  line  measurement.  lines  radial  of a p a r t i c u l a r  to convert the  wavelengths  into  between  an  positions  ways of e x p r e s s i n g t h e  dispersion relation  polynomial  the p o s i t i o n s  lines.  f i t between The  accuracy  depends c r i t i c a l l y the d i s p e r s i o n affect the  on  most  simple  line-position corresponding  of  Systematic experimental Meanwhile,  how  well There  are  would  zero-point  errors from  measurements w o u l d a l s o  be  determination represents that  of  accuracy  a  introduced  the  can  HF  of how  errors  a  accuracy  latter, the  also and  the of  of  line  systematic  Fishburne  experimental  simplest  of  The  may  position  r e p r e s e n t a t i o n . Two  the  be  HF  w a v e l e n g t h s of  many c a u s e s  the c r i t e r i a  The  i s i n terms of  are  the  the  spectrum.  the  polynomial  and  This  random  of  this  absolute wavelengths.  values  and  the p o l y n o m i a l  measurements  determined.  the  a radial-velocity  causes  d e p e n d s somewhat on are  of  relation.  the a c c u r a c y  on  between one  a b s o l u t e w a v e l e n g t h . One  of  wavelength  i s the d i s p e r s i o n r e l a t i o n .  provides a correspondence  measurement and  HF  a  t h e w a v e l e n g t h - c a l i b r a t i o n marks on  line  line  t h e measured p o s i t i o n  spectrum  relationship  stellar  exist Rao  their course,  positions effect. in  the  [1966].  in these  wavelength  into  polynomial  the  93  Table  3.4  SSTP w a v e l e n g t h s  f o r t h e (3-0) band o f HF  ******************************************* refractive  index  m  exper i m e n t a l  calculated  8  8666.4256A  8666.4241 A  1.00027467  7  8669.3408A  8669.3423A  1 .00027467  6  8675.8433A  8675.8440A  1 .00027467  5  8685.9275A  8685.9291A  1.00027466  4  8699.6069A  8699.6029A  1.00027466  3  8716.8828A  8716.8765A  1.00027465  2  8737.7680A  8737.7662A  1.00027464  1  8762.2864A  8762.2939A  1.00027463  -1  8822.3731A  8822.3788A  1.00027460  -2  8858.0087A  8858.0078A  1.00027458  -3  8897.4193A  8897.4189A  1.00027457  ************************************************************ dispersion  f i t . This  experimental contain  values  shifts  from  line-to-line  pressure-induced is  condition to adopt  not  would  be  a  Fishburne  and Rao  wavelength  differential appropriate  o f t h e HF c e l l .  the  corrections zero-point  can error  data  applications  and  amount  more  of  then may  be still  applied to exist  in  of F i s h b u r n e especially  A  the adopted  in  Rao  [1966].  relative  these  constants  very  shift small  reference  by z e r o - p o i n t e r r o r and  by  satisfactory  molecular  them.  also  operation  reference wavelengths. Appropriate  w a v e l e n g t h s . T h i s would be c a u s e d experimental  caused  particular  from  The  [1966] m i g h t  The  It i s probably  the wavelengths c a l c u l a t e d  t o be t h e a b s o l u t e  effect.  variations  shifts. for  random  For  i n the most  radial-velocity  94  works, however, Further  improvement  achieved taken  shifts  caused  from  typical  reciprocal residual  HF  pressure  slight  imply  spectrum  ±0.00224A  can  be  shifts  are  case  for  the  o f t h e HF c e l l .  temperature  and  Small  pressure  be d i s c u s s e d  in  detail  values  d i s p e r s i o n f i t was a p p l i e d  taken  at  was from  obtained  an i m p r o v e d  CFHT  for  the f i t  were  used  wavelengths.  The A  rms  when  the  as  the  of ± 0 . 0 0 1 5 5 A  rms r e s i d u a l  values  to  Coude.  0.0713A/pixel.  3.4  Table  when t h e c a l c u l a t e d  the reference  the  4.8A/mm o r  w a v e l e n g t h s . An i m p r o v e d  was o b t a i n e d used as  polynomial  d i s p e r s i o n was  of  reference  3.4  from T a b l e  The i m p r o v e d  were  f i t may  r e p r e s e n t a t i o n of the d i s p e r s i o n r e l a t i o n .  THE TEMPERATURE AND PRESSURE OF THE HF GAS  3.3.1  INTRODUCTION One  of the t e c h n i c a l  the i n a b i l i t y  t h e HF  gas  measured w i t h surface gas  by  line  especially  This point w i l l  order  experimental  is  is  adequate.  wavelengths  pressure-induced  This  be  i n the chapter. A third  3.3  should  t h e mean o p e r a t i o n c o n d i t i o n o f t h e c e l l c a n  be c o r r e c t e d .  later  values  the r e f e r e n c e  a t t h e 360 t o r r s  deviations  a  on  account.  application  also  adopted  when l i n e - t o - l i n e  into  line  the  with  t o measure t h e t e m p e r a t u r e  accurately  inside  the  the thermocouple  is  temperature  inside  difficulties  the c e l l  of the c e l l .  cell. only  t h e HF  technique  and p r e s s u r e The  the  temperature  mean  The t e m p e r a t u r e  of  outside  of the  c a n be q u i t e d i f f e r e n t . M o r e o v e r ,  HF  there  95  may  not  be  a  cross-section profile This  may a l s o  stellar  This  be v a r i a b l e  along the length  HF m o l e c u l e s  Hence, d e p e n d i n g  HF g a s f o r m i n g t h e HF r e f e r e n c e  the c e l l  and  with respect  Coude s e e i n g ,  of the  are introduced  the e f f e c t i v e lines  t o the s t e l l a r  temperature  as  the  into  the  temperature  the of  different.  such as a l i g n m e n t  beam, t h e  stability  cell.  p a t h of  c a n be  factors  the  temperature  on t h e p a r t i c u l a r  beam t h r o u g h t h e c e l l ,  on  t h e windows a s w e l l  T h i s d i f f e r e n c e may depend on many of  profile  cross-sectional  t h e c a s e near  where c o l d e r  heated c e l l .  temperature  of the c e l l .  i s especially  location  the  uniform  atmosphere  of the c e l l ,  as w e l l  a s t h e f o c u s o f t h e beam. The m e a s u r e d p r e s s u r e i s s u b j e c t e d to  zero-point  variations It the  error  o f t h e manometer a s w e l l  of t h e i c e b a t h around  at the v a r i o u s  temperature  would  affect  Boltzmann  energy  affected in  determine  This  HF  by h a v i n g t o compare  s t r e n g t h and shape.  the  HF l i n e s can  Maxwellian the  relative  are  be  also  variations of  in  course,  which  due  t o temperature to  energy would  the  as w e l l level also  the  in  lines.  would  are  pressure-induced line  distribution the  positions,  HF l i n e s  sensitive  explicitly  velocity  temperature,  The  o f t h e HF  the o b s e r v a t i o n a l  line  for  f o r the  o f HF, a c h a n g e  strength  reduce  Assuming  distribution  levels  the l i n e  Many n u m e r i c a l t e c h n i q u e s t o to  line.  any l o n g - t e r m HF p r o j e c t .  temperature-dependent  population  e.g.  temperature  i s important to maintain a constant temperature  HF g a s t h r o u g h o u t  usual  t h e sample  as  data be  different shifts  of  variations.  variations  i n the  as i m p l i c i t l y  from  population.  The  affect  the  relative  96  number o f monomers both  the l i n e  ( H F ) , and  s t r e n g t h as  t h e s e problems can temperature observed  and  well  as  pressure  of  With  corrections  the  known  can  (HF) . This  affects  6  the p r e s s u r e s h i f t s .  be m i n i m i s e d  spectrum.  line-shift  hexamers  i f one  can  HF  directly  gas  determine  temperature  be made  at the  All  from  and  time  the the  pressure,  of  the  data  reduct ion.  3.3.2  HF  LINE STRENGTH  3.3.2.1  Basic  The  line  equations s t r e n g t h of a v i b r a t i o n - r o t a t i o n  unit-atmosphere has  been  gas  g i v e n by  p r e s s u r e and Meredith  in units  [1972b]  of  and  line  per  (atm.cm )" 2  Pugh  and  1  Rao  [1976] a s : S(m)  =  { ( 1 .01 325X1 0 { exp(  6  ) 8ir |m|yN /  -E(u ,J )/kT i  )  i  |<u. J . |/z(r) | u J > | f  c = speed h  of  = Planck  (3hcpZ) }  3  2  f  }  (3.10)  light  constant  k = Boltzmann's c o n s t a n t T = temperature v  =  in  wavenumber o f  m = the  running  kelvin line  index  of  the  line  N = number o f a b s o r b i n g m o l e c u l e s P = gas  pressure  Z = total E(u.,J.)  cm  3  i n atmospheres  partition = energy  per  function level  of t h e  lower  state  97  u(r) Equation  3.10  = electric uses the  double primes) indicate The  the matrix  moment. E q u a t i o n  factor  f  of  (or s i n g l e  of induced  and  at  level,  of  3.10 d o e s n o t t a k e emission  by  i  (or  prime)  also  the  electric  into  account  however,  (Pugh  the  is  transitions  moderate t e m p e r a t u r e s  to  respectively.  not i n c l u d i n g  factor,  1 for vibration-rotation  infrared  subscript  element  {1-exp(-hev/kT)}. This to  function  and k e t | > r e p r e s e n t a t i o n s a r e  express  effects  close  convention  and s u b s c r i p t  bra < |  used t o  the  moment  t h e l o w e r and upper e n e r g y  Dirac  dipole  dipole  very  i n the and  Rao  [1976]). 3.3.2.2 The H e r m a n - W a l l i s Herman and W a l l i s electric be  dipole  written  i  f  term  factor.  function  c a n be  dipole  discussed  |<u |M(r)|y >| i  f  is  2  formulae al.  matrix  a  directly  factor  from t h e and  [1977,1978b] who  has a l s o  f o r the matrix were  (1-0),  first (2-0),  elements.  given  or  ratio  been given Direct  by Herman  (3-0),  F  rotation  method h a s  expressions  f o r the  (3.11)  f  elements. This  f o r the factors  [1958]  and  F(o.,» ,m)  the Herman-Wallis  calculated  by B o u a n i c h  theoretical  can  2  F(v^,v^,m):  between t h e t h e o r e t i c a l v i b r a t i o n - r o t a t i o n electric  factor  the  2  F(v^,v^,m) It  |<v^J^ | u ( r ) | v > |  of a v i b r a t i o n a l  interaction  out that  f  =  The  elements  as the product  \<v J \n(r)\v J >\ i  [1955] have p o i n t e d  matrix  vibration-rotation  factors  and  et  (2-1)  98  Table  3.5 The a . ' s and t h e M 's  f o r HF  i  **************************************** a, == -2.2538 a  2  == 3.4882  a  3  == -4.4986  a„ == 4.704 a  5  == -2.91  a  6  == -1.76  M  0  == 1.80306  M, == 1.39366 M  2  == -0.0583  M  3  == -0.8861  M« == -0.599 M  5  == -0.931  ************************************************************ transitions. given  by  Improvements  Toth et  [1970a], T i p p i n g  on t h e s e  a l . [1969,1970], and F o r b e s  Tipping  [1976],  Ogilvie  [1982], and O g i l v i e  of  these  Ogilvie  in  F(u The  i f  u ,m) f  functions  [1980],  also  give  expansion  Dunham p o t e n t i a l  and  internuclear  constants  Herman [1972b], and  Several for  the  c a n be e x p r e s s e d  in m : (3.12)  2  f  B(v^.v^)  been  Tipping  formulae  The f a c t o r  f  C(v^.v^)  and  [1983].  = 1 + C(ui,u )m + D(uifu )m  terms of t h e e q u i l i b r i u m  and  a l .  and T i p p i n g  transitions.  t e r m s o f a power s e r i e s  Tipping  have  [1971], M e r e d i t h  et  recent publications  higher-overtone  formulae  are  expressed  separation  a ^ ' s , < U j | n( r ) | u ^>,  r  g  in  , the  B^,  u> , e  the  99 M^'s. The M^'s a r e t h e c o e f f i c i e n t s expansion  of the e l e c t r i c n(r)  The  values  Spellicy  i  Sileo  [1980].  Meanwhile,  et  e  f o r these  [1974],  and  a l . [1961],  series  d i p o l e moment:  = I. M [ ( r - r ) / r ] have  Meredith  Cool  (3.13)  i  g  's  e t a l . [1972],  i n t h e power  been  evaluated  and Smith  [1976],  and  [1973], L i e  Ogilvie  et  t h e a ^ ' s have been e v a l u a t e d  Webb a n d Rao [ 1 9 6 8 ] ,  by  and O g i l v i e  Mann  a n d Koo  Table  Ogilvie  e t a l . [1980] a s w e l l a s t h e v a l u e s o f t h e a ^ ' s  Ogilvie  <v^\n(r)  and  thevalues  a l .  [1976].  from  3.5 l i s t s  by  Koo [ 1 9 7 6 ] .  |i>f> c a n a l s o  be  of t h e M 's  from  i  The  vibrational  expressed  factor  i n terms o f  these  constants: <v \u(r) L  | i> > = L  i  f  M <u i  i  | (r/r ) e  1  | u >  (3.14)  f  f o r t h e e x p e c t a t i o n v a l u e s <v^ | ( r / r ) | u ^ > i n  Formulae  1  ?  t e r m s o f B , cj , t h e a ^ ' s , a n d M^'s a r e g i v e n  i nTipping  [1973].  i n Niay e t  g  g  al.  More g e n e r a l e x p r e s s i o n s c a n be f o u n d  [1979]. The  Herman-Wallis  published derive  f o r the  their  experimental  3.5.  procedure  values  and  2  D(u^,y^),  factors  from  <v^\n(r)\v^>  a  least-squares data,  are also  listed  The  i n Table  can the  values  These a r e l i s t e d  in  optimisation  optimal values  a n d 6.3528x10-* a r e d e t e r m i n e d respectively.  between  <v^\u(r)\v^>  and  e t a l . [1972].  Applying  explicitly  HF. One, however,  the ratios  on t h e e x p e r i m e n t a l  -1 . 0 7 8 8 x l 0 -  have n o t been  (3-0) band o f  m e a s u r e d by S p e l l i c y Table  factors  of  for C(i> u )  least-squares  3.5. T h e o r e t i c a l  i f  f  fitted values  100  Table  3.6 Herman-Wall i s  factors  f o r t h e (3-0) band  o f HF  ********************************************** m  experimental  least-squares  -4  1 .0676  1.0533  -3  1 .0301  1.0381  -2  1 .0086  1.0241  -1  1.0068  1.0114  1  0.9969  0.9899  2  0.9908  0.9810  3  0.9601  0.9734  4  0.9920  0.9670  5  0.9386  0.9619  6  0.9668  0.9581  7  0.9546  0.9556  fitted  ************************************************************ for  the Herman-Wallis f a c t o r s  the  formulae  [1982],  given  Tipping  [1969].  The  experimental be c a u s e d  experimental  the  and  values the  i n T i p p i n g and  [1971],  between  i s not  very  inadequacies  choosing  calculation  appropriate.  Forbes  v a l u e s may a l s o  view o f t h e s e , for  independently  agreement  by  have been c a l c u l a t e d  and  the  Ogilvie  Toth  et a l .  theoretical  satisfactory. of  the  may  theories.  The  carry sizeable  temperature  and  This  errors.  the l e a s t - s q u a r e s f i t t e d  o f gas  using  may  In  factors be  more  101  3.3.2.3 D e r i v a t i o n o f g a s t e m p e r a t u r e For  two  lines,  vibration-rotation strength  as given  Sdn,)  band,  and  v a r e known  i f  u  between  their  line  simply be:  f f  2  accurately  (3.15) (3.16)  2  2  / » F ( v , o ,m )  m,)  i  between  f  factors,  level  a n d t h e wavenumbers  o f HF. The d i f f e r e n c e i n o f t h e two J s t a t e s  i s simply  values  by h e . V a l u e s  known. Hence,  (3.17)  2  the l e v e l  thecorresponding  3.3 m u l t i p l i e d  )  {|m |p ]  ground v i b r a t i o n a l  values  same  2  f o r t h e (3-0) band  E -E,,  between  the  3.10 w i l l  2  m v a l u e s , Herman-Wallis  the  in  2  / S ( m ) = A B exp( [ E - E , ] / k T  B = F(u  energy,  m,  the r a t i o  by E q u a t i o n  A = {|m,|p.} /  The  m,  the difference  of  i  n  Equation  f o r B , D , H , and L 0  0  0  i f t h e two l i n e s  o f J ^ , t h e temperature  in  have  are  0  different  T c a n be c a l c u l a t e d  from  E q u a t i o n 3.15. The  Beer-Lambert  describes  law  gives  the transmission  of  the r e l a t i o n radiation  which  through  a  homogeneous g a s a s : I(p)  The  terms  I  intensity,  0  = I  and  e x p ( -K(p)pL  0  l(i>)  coefficient.  absorption  path,  gas.  The  line  Expressions Lorentzian, et  al.  The  f o r K(P)  The  K(P)  and  line  is  the  The t e r m L i s t h e l e n g t h o f t h e  depends in  line  on  the  and V o i g t p r o f i l e s  [1980].  function  and p i s t h e p r e s s u r e shape  (3.18)  a r e t h e continuum  respectively.  absorption  )  of the  the  form  cases  of  have been g i v e n  strength  S  absorbing of  K(P).  Gaussian, by M a n d i n  i s simply  the  1 02 integrated Lowry and  absorption coefficient F i s h e r [1982], S = ;  The  relationship  width By  i s given  limits  in  the  of  the  3.20  determine  the  L  are  temperature between  s e t s of  [1972]. about  spectrum  0.6%  performed  number.  The  dispersion  0  i  n  e  3.18  3.19 0  is  simply  be  used of  3 6 8 . 2 ± 4 . 3 K have  i s simply  the  wavenumbers  positions.  the  This  gives: |df/dx|  gas.  The  equation  dx  Average  (3.20) spectrum. 3.15  when,  in  the  p the  ratios  temperatures  been c a l c u l a t e d  of  for  the  et  al.  temperature  of  in S p e l l i c y  assumed  to  constants  considers only  strengths published with  line  Equation  one  the  the  "with  strengths.  agree  over  rectified  the  [1968].  spectrum,  the  the  determination,  These  and  line  Ln(l(x)/I )  temperature  line  the  f i t between t h e  the c o r r e s p o n d i n g  line  Korb et a l .  be  l  equivalent  100°C. The  for  [1982] and  c a n c e l l e d from  the  s t r e n g t h and  can  can  3 6 0 . 9 ± 1 . 4 K and two  line  3.19  function I ( x ) / l  Equation  (3.19)  of  (-1/pL) J  [1976],  d»  the p o l y n o m i a l and  Rao  [1982]):  dispersion  with Equations  S =  and  K(U)  e  between  pixel  lines  together  The  n  in Equation  - derivative of  i  i n Overend  considering  integral  l  Overend  (Pugh and  procedure obtained  a l l t h e HF  of  well  the  with  from  lines  absorption  temperature  has  also  been a p p l i e d t o a t y p i c a l  t h e CFH  have been  with  respect  373.7±0.7K expected  Coude.  The  line  set at p o s i t i o n s to  the  limits of  continuum.  i s obtained. T h i s agrees temperature  of  HF  100°C.  only A very The  1 03  accuracy  of  accuracy  the  of  essentially the  lines.  of  the  the  measured  The  This  broadened  wings of the l i n e s  for  the c h o i c e  the e f f e c t s  from  is  may  line  s t r e n g t h and  Korb  e t a l . [1968] and G i v e r  equivalent  [1982]  curve-of-growth procedure Nevertheless,  multiplicative measurements  those  changes  In in  probably The can  have  by  have  t h e use o f  by  the  Blendings at  the  been  and  the  no  of t h i s ,  the temperature,  widths  present i n the effect  use  of in Rao of  strengths.  between  line  procedure,  any  equivalent-width on  Ogilvie  the  monitor  the p r e s e n t  result.  factors and  mean t e m p e r a t u r e to  the  been d e s c r i b e d  ratios  from  by  for  suggested the  the  the  curves  generated  t o measure t h e l i n e  values  would  i n t h e measurement  other Herman-Wallis  increase spite  mainly  e t a l . [ 1 9 8 2 ] . Pugh and have  of  placement  method t o c o r r e c t  systematic error  theoretical  10K.  lines  used  are  s t r e n g t h s and  w i d t h has  only  would  [1982], c o u l d as  since  are  Meanwhile,  line  f a r wings of t h e l i n e  Overend  which  limits. Correction  iterative  of the  strengths  hampered  broadening  loss  the  i s i n the  become s i g n i f i c a n t  line  on  the l o g a r i t h m  line profiles.  of  [ 1 9 7 2 ] . An  [1976] and  strengths  widths of  on m e a s u r e d  instrumental  Meredith  critically  main s o u r c e o f e r r o r  continuum.  restrict  line  the e q u i v a l e n t  collisionally far  p r o c e d u r e depends  Tipping  by a s  the  e.g.  much  relative  procedure  is  adequate. difference be more  between easily  the  equivalent  measured  from  a  width  of  difference  104  spectrum  (Campbell [1984a]).  HF l i n e s  in  a particular  examining  the  subtracting  a "standard"  the  then  lines.  spectrum  and l i n e  be  These can then to  that  produced  by  The  would  known  have  respect  be u s e d  to  calculated  line  to  HF l i n e s  in  equivalent  strengths  these  determine for  of by  HF s p e c t r u m .  Relative  with  strengths  be measured  spectrum  strengths.  calculated  relative  s p e c t r u m can  difference  "standard"  widths  Consequently,  the  a  can  "standard" temperature  "standard"  HF  spectrum.  3 . 3 . 2 . 4 D e r i v a t i o n of The HF evaluated strength 3.11. N/p  gas  if  in  unit-atmosphere  Equation  partition  p  pressure Equation  can c a l c u l a t e  By a s s u m i n g  in  gas  pressure  one  per  the  function  ideal  gas  3.10  would  the  using  law  can  theoretical  the  become 3.10  HF g a s , 1/kT.  and  the  The  c a n be  be line  E q u a t i o n s 3.10  for  Z in Equation  3.20  term total  expressed  as: Z(T) The e n e r g y value  = L Lj  level  obtained  Dunham  together  (1  E(u,J)  constants  is  be  In  10"  1 8  listed  is  Table  )  the  3.11,  from  calculated term  Equation  3.14  which  1  1.6095xl0~  are  used  are  esu.cm  2 1  o b t a i n e d when t h e 3.5  term  the  g  of  (3.21)  from t h e  <v^ \(r/r ) |v^>  A value  esu.cm)  using  Equation  for  [1973].  in  3.4  calculated  formulae  in Tipping  debye  -E(o,J)/kT  through Equation  can  with  exp(  c a n be c a l c u l a t e d  coefficients.  <t>^|M(r)|vj>  given  (2J+1)  v  various in  the  105 Table  3.7 L i n e s t r e n g t h s o f t h e (3-0) band o f HF  ***************************************** m  experimental.  calculated  -3  0.0235 cm" a t m "  1  0.02285 cm" a t m "  -2  0.0245 cm" a t m "  1  0.02467 cm" a t m "  - 1  0.0164 cm" a t m "  1  0.01697 cm" a t m "  1  0.0193 cm" a t m "  1  0.01970 cm- a t r r r  2  0.0327 cm" a t m "  1  0.03324 cm" a t m "  3  0.0353 cm" a t m "  1  0.03574 cm" a t m "  4  0.0287 cm- a t m "  1  0.02903 cm" a t m "  5  0.0188 cm" a t m "  1  0.01881  6  0.0099 cm" a t m "  1  0.00996 cm" a t m "  7  0.0039 cm" a t m "  1  0.00437 cm" a t m "  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  cm" a t m " 2  2  2  ************************************************************ calculation. 1.628x10"  T h i s agrees  experimental  matrix  element  Rosmus  [1980].  line  including  the  temperature.  given  in  0.467atm  c a n be  factor  then  Table  theoretical found  also  o f HF.  terms  be  S p e l l i c y et The  taken  both  i n Werner  and on  account  by  into  Equation  a  atmosphere values  of and  f o r the  are  corresponding values  line  function  the experimental  experimental  calculated  emission  theoretical as  per unit  a l . [1972]  [1972]. this  into  known,  of  for  of induced  calculated  3.7 l i s t s  The  values  referenced  be  value  et a l .  {1-exp(-hc?/kT)}  l i n e strengths  data.  Spellicy  The m i n u t e e f f e c t  a l l these  s t r e n g t h s can  (3-0) band  and  s t r e n g t h can  3.10. W i t h  calculated  the experimental  esu.cm m e a s u r e d by  21  Other  the  with  to  used  those the the  106 temperature  of  360.9K  obtained  from  the  temperature-determination  method d e s c r i b e d e a r l i e r .  agreement  s e t s of v a l u e s  very  between t h e  two  comparing  of  the  the  HF  theoretical  The  has  procedure  used e a r l i e r  In  fact,  that p a r t i c u l a r  in  this  calculation.  than  f o r t h e gas  the  expected  statistical  obtained the  that  value  earlier  there  is  a  implies line  the  and  source  equivalent-width the  spectrograph. continuum the  360  torrs.  well the  as  the  is  of  result  the  the  of  Systematic  3%  errors  spectrum c o u l d  large discrepancy.  The  the result  suggest of  fact  et a l .  for  that  [1972],  i n the  by  a  theoretical  error  measurements c a u s e d  is  strengths  The the  relative  only  with  line  Spellicy  used  small  existence  between  HF  lower  The  would s t r o n g l y  of e r r o r i s p r o b a b l y  of  17%  excellent  error factor.  agreement  is torrs  associated  ratios  The  order  f o r the  300.4±0.7  value  error  CFHT  determination.  i s about  here  the  "standard"  This  of  the  strength.  temperature  of  by  against line  temperature  determined  systematic  strengths.  of  unit-atmosphere  determination,  good  calculations  for  is  determined  pressure.  with  problem  multiplicative  be  strength  A value  as  temperature the  line  i n the  standard  determined  can  been a p p l i e d t o t h e  spectrum  obtained  gas  measured  corresponding  is  3.7  good. Pressure  in  in Table  The  measured in  the  scattered  light  the  Coude  in  the  not  be  CFH  placement the  e r r o r caused  sole by  the  of  cause fact  107 that  the  chosen  line  continuum  should  be  logarithm the  of  line  factor  the  spectrum  the  f a c t o r . One  in  calculation  dispersion  of  understand  the  the  cell. of  The  the  i s the  absorption  length  the  ones f r e s h l y sample  cell,  be  in  windows and  factors  the  (HF)  lines.  absorption  length,  It  and  be  heated  of  the the  as  from  rather towards  cell sample  the  the the  correct.  w e l l as  cell  the  length  same  i s conceivable in  of  that  quite  contribute  where  effect  not  hexamers  6  not  the  windows as  numbers  location the  the  is  to this  in  measured  assumption  may  in  length  an used  is  f a c t o r used path  of  error  become  strengths  i s the  i n t o the  be  has  that near line  the the than the they the is  reducing  the  effective  hence r e d u c i n g  the  observed  strengths. Although absolute  line  the  large error  length  however,  significant  path  cm  This  path  connected. This  line  100  would t h e n  the  since  would  absorption  cell.  would  observed absorption may  of  introduced  monomers. They  line  any  m o l e c u l e s near  line  true  computation  multiplicative  of  optical  absorption  c o l d e r HF  the  multiplicative  multiplicative  effective  The  i n the  placement  the  existence  chosen value  of  at  Furthermore,  small  the  of  not  s p e c t r u m . However, i t i s d i f f i c u l t  parameter. Another calculation  the  of  are  i s used  continuum  additive the  small.  strengths,  in  limits  s t r e n g t h method  determinations  should  pressure  i s not be  determination  possible, relative possible.  One  can  using  this  pressure use  the  109 method t o with  monitor  respect  to  for  various  lines  the  line-strength  line-strength band o f HF.  At  about  100°C,  HF  the  lines  in  strength with  pressure  of  t h e gas  measured  line  between be  of  temperature  equal  unit-atmosphere  to  line  the  F i g u r e 3.2' shows for  the of  |m|<5  in  would d e c r e a s e lines  each line  of  m>6  individual  corresponding  the  line,  the  pressure  theoretical  value i s  a given  THE  COLLISIONALLY BROADENED LINEWIDTHS  the  to  s t r e n g t h and  strength. This  would  Meanwhile,  proportional  for  3.4.1  with  o p e r a t i o n temperature  directly  the  The  strengths  studied  temperature.  measured  spectrum.  the l i n e  be  while  s t r e n g t h s . For the  pressure  with temperatures  the c e l l  is  HF  calculations.  increase  would  can  variations  (3-0)  ratio  constant  temperature.  INTRODUCTION The  p r e s s u r e o f t h e HF  linewidths  of  theoretical  broadening pressure for  HF  t h e gas  "standand"  d e p e n d e n c e of  strength with  the  of a  in  temperature  the  the  that  variations  relative  theoretical  3.4  the  each  is  as  collisionally a  HF  line.  function  of  also  This  be d e t e r m i n e d  involves  induced l i n e  calculating  linewidths.  The  both  temperature  and  the  much r e l a t e d shifts.  both  from  broadened  amount o f b r o a d e n i n g  A very  f u n c t i o n s of  can  lines.  o f t h e g a s . The  collisionally shifts  t h e HF  gas  One  is-  different  phenomenon needs t o know  temperature  and  is  the these  pressure  in  1 10 order  t o make c o r r e c t i o n s  to the reference  shifts,  to a certain  of  reference wavelengths.  the  direction  extent, determine  and magnitude  the u l t i m a t e  They a r e  f o r each  wavelengths.  accuracy  different  r e f e r e n c e HF  in  to  determine  constituents  of  the intermolecular  the gas  e.g. the  o c t o p o l e moments o f many m o l e c u l e s this  manner.  linewidths and  application  of m o l e c u l e s  temperature  the broadened also  The  important  linewidths  design  as t h e  study  planetary applied  atmospheres.  t o determine  atmosphere helium  Jupiter  collisionally The  atmosphere  broadened studied Varanasi  broadened pressure  can a l s o  methane l i n e s  can  and F i s h e r  transfer  Colmont  e t a l . [1971]) .  concentration  linewidths and  of  molecular  terrestrial  and  has  been  i n the  from CH  3  the  lines in  of  helium (Varanasi  the  Jovian  from the b r o a d e n i n g of t h e Meanwhile,  in C0  on Venus  well  distribution  temperature  [1971]).  as  [ 1 9 8 3 ] ) . Abundances  of  from  [1982]). I t i s  theory  determined  HC1 a n d HF l i n e w i d t h s  for application  in  in  broadened  i n the atmosphere,  be d e t e r m i n e d  (Margolis  and  c a n be d e t e r m i n e d  ozone d e n s i t y  be  quadrupole  The CO  Line-broadening  (Monnanteuil and  in  [1971]).  the  the  and o p e r a t i o n  the study of p o l l u t a n t s radiative  between  theoretical  exhaust  lasers,  of  of  (Lowry  c a n be  have been d e t e r m i n e d  i s numerous.  i n combustion  to the  forces  electric  both  line.  In c h e m i s t r y , t h e s t u d y o f l i n e w i d t h s a n d s h i f t s used  The  2  (Shaw  collisionally  atmospheres and L o v e l l  have been [1969],  111  3.4.2  THEORIES ON The  shape  interaction  of  spectral  of e a c h  surrounding generally  COLLISIONAL LINE BROADENING  individual  molecules. been  divided  high-pressure  statistical  theory  first however,  [1895]  Lorentz  and  summarised [1951],  and  These  molecule  to  collisions  be  given was  [1906].  impact  [ 1 9 5 8 ] , and  Fano  [1966],  [1967ab,1968],  Zaidi  broadening  by  Impact Michelson  impact  theories  Foley  [1946]  and  Mizushima  assume  the  radiating  and  formal  have  quantum-mechanical [I958ab], Kolb  been  given  by  Ross  B e z z e r i d e s [ I 9 6 7 a b ] , Murphy and  Boggs  [ 1 9 6 8 ] , D i Giacomo and  [1977],  and  B o u l e t and  Gordon Robert  Tarrini [1973],  [1978],  [1970], Smith  and  of  statistical  [ I 9 7 5 a b ] , and broadening Leavitt  m e c h a n i c s and by  Davies  theories  [ 1980],  Zaidi and  quantum many-body [1972],  Davies  O l i [1978], Recent  include  Breene  and  f o r m u l a t i o n s u s i n g the  a l . [ 1 9 8 3 ] . More e l a b o r a t e f o r m u l a t i o n s i n v o l v i n g  given  the  process i s  et  have been  are  that  the o s c i l l a t i o n  [1963]. Recent  et a l . [I971ab], N i e l s e n  [ 1 9 7 6 ] , Lam  the the  [1935].  considered  Baranger  approximation  have  and  Statistical  oscillator  by  other  cases:  broadening  theories  in  with  the  Early  classical  [1966], Gordon  al.  in  by  effects  Margenau  first  been g i v e n  binary-collision  Smith  by  Formulations  framework have  molecule  limiting  broadening.  a r e s t r o n g enough t h a t  interrupted.  Griem  a  two  (interruption)  expanded early  be a l t e r e d  radiating  into  impact  broadening,  can  Line-broadening  low-pressure  was  lines  [1981],  Boggs  [1972],  Leavitt  and  Clough the  use  techniques  [1975],  Roney  r e v i e w s on Rabitz Korff  et  line  [1974],  [1981 ] , and  11 2  Buffa  and  Tarrini  Anderson semiclassical  [1983].  [1949]  applied  impact  theory  perturbation and  methods  produced  to  a  computational  expressions  for general pressure broadening.  T h i s was  extended  Tsao  et a l .  [1969],  [1981]. Hewitt  [1976],  Leavitt Frost  by  [1980],  and and  [ 1 9 7 6 ] , and  theory  to  extensions  [1963],  Herman and  widely  and  impact  theory  l i n e w i d t h s and [1963],  Jarecki  and  [1967a] p r o d u c e s  linewidths  with experimental m o d i f i e d ATC  Leavitt not  and  Korff  better  considered premises (QFT)  than  method  w i d e l y used have  to  be  a l l  self-broadened H 0 2  difference  between  three lines.  on  more  the  ATC  is  the  broadened and  in better ATC  Boggs  agreement  formalism.  produce is  The  [1977],  a s good  if  generally  acceptable  physical  Quantum F o u r i e r  Transform  [1975]  has  not  been  m e t h o d s . Mandin e t a l . to  found and  most  also  methods They  [1970b],  Boulet et a l .  Murphy  can  theory  two  Ben-Reuven e t  and M a c G i l l i v r a y  ATC  by D a v i e s  as t h e o t h e r  applied  by  the e a r l y  t h e o r y . The  proposed  noble-gas  of c o l l i s i o n a l l y  (Frost  The  Early  Herman  theory  which are  founded  t h e MB  include  (ATC)  [ 1 9 8 1 ] ) , however,  agreement.  Anderson  [1975].  than  theories  calculate  and  method p r o p o s e d  results  the  shifts.  et a l . [1973],  computation  MB  to  Tipping  Anderson-Tsao-Curnutte f o r the  line  shifts  Herman  l i n e w i d t h s . The  later  of  T i p p i n g [1970], Levy  used  Robert  Korff  calculation  Herman  [ 1 9 7 3 ] , and The  [1962],  B o u l e t e t a l . [1977] e x t e n d e d  the  pressure-induced al.  Leavitt  permit of  Curnutte  later  the  that  QFT  [1980]  calculation  t h e r e i s not  methods,  as  while  of much the  11 3  results and  from  t h e MB method a r e s y s t e m a t i c a l l y  MacGillivray  gives poorer (Cattani  Korff  (Van  Frost  line  and Weisskopf [1966],  t h e MB  method  The m o d i f i e d MB  method  and M a c G i l l i v r a y  t o t h e m o d i f i e d ATC  Vleck  found  shifts.  method  [ 1981 ] have shown t h a t  of G o r d o n of  calculated  [1972],  comparable and  [1977] have a l s o  that  [1977]),  however, i s  i n accuracy.  early  [1945]),  t o o low. F r o s t  Leavitt  phase-shift  theories  the s e m i c l a s s i c a l  theory  a n d t h e MB t h e o r i e s a r e a l l l i m i t i n g  cases  t h e m o d i f i e d ATC t h e o r y .  3.4.3  THE ANDERSON-TSAO-CURNUTTE 3.4.3.1  Basic  The  impact  approach  ATC  approach  theory uses  with  molecules  the time, enables  the  the states  by  transitions  shifting  interval  their  between  one t o t r e a t  on  translation degrees can  freedom  generally  A  used  or  molecular  radiative  causing  process,  scales.  collisions since  The from  to treat  the  the  translational  internal motion  classical  the c o l l i s i o n .  This  they  molecular  t h e m o l e c u l e s . Quantum  straight-line for  radiating)  This  be d e c o u p l e d  the  (or  successive c o l l i s i o n s .  would t h e n  while  collisions  with  time  used  the  i n comparision  different  be  classically.  short  In  the  phases  the i n d i v i d u a l  of freedom of  then  d u r a t i o n of  i s assumed t o be  perturbation  approximation.  of the absorbing  as u n c o r r e l a t e d w i t h t h e occur  a semiclassical  the binary-impact  approximation,  which a f f e c t  (ATC) THEORY  internal mechanics  degrees is  of  treated  trajectory  is  procedure  is  11 4 quite al.  common  f o r most  [1976],  classical  semiclassical  however, have p r o p o s e d trajectory.  (collision  matrix)  The  theories.  t h e use o f a  time-evolution  which  describes  i s e x p a n d e d by p e r t u r b a t i o n  approach  t o o b t a i n a s i m p l e and p r a c t i c a l The  considered  i n the  molecules  are  molecules the case  phenomenon  distinguishable  from can  radiators.  In t h i s  with a zero  perturber  still case,  system.  and  the e f f e c t  t h e amount o f  inelastic  ATC  theory.  distinction  would  broadening  collision The  by  the  perturber  the  radiator  early  i s changed  i sunaltered.  be  a n d one o f  the  as  the  among  transferred  energy  of  the  This  are  effect  [1971]),  of the e x c i t e d  T h i s would i n c r e a s e  relative  ATC  can  become m e a n i n g l e s s .  effects  Sharma  In  the  interaction.  collision  most  is  between  state.  broadening  i n which the d i r e c t i o n  radiator energy  i n the i n t e r n a l  t h e upper  line  ATC  computational  c a n be  of s h o r t e n i n g the l i f e t i m e  [1966],  considered effect  excitation  perturber-radiator  and  to another  considered  The  radiator  or broadening  (Gordon  from  i n the  of foreign-gas broadening.  be  n e t change  two-molecule  distinct  case  one m o l e c u l e  molecules  state  Normally,  curved  collision  o f s e l f - b r o a d e n i n g , however, e x c i t a t i o n  transferred  has  of resonance  ATC t h e o r y .  as i n the  theory  et  operator  the  dynamics  procedure.  Smith  t o the case Both  elastic  c o n s i d e r e d by of  the  reorientation  however,  theories.  of  This  is  not  i s the  o f a n g u l a r momentum o f t h e  i n the c o l l i s i o n  while the  internal  1  3.4.3.2 C o l l i s i o n In per  t h e ATC  of c m  section  line  shift  of t h e p e r t u r b e r  8  and i n  collision  7 =  ( 1 .01 325x1 0 )N/(27rcp)  fg v F ( v ) a ( v )  8 =  ( 1 . 0 l 3 2 5 x l 0 ) N / ( 2 7 r c p ) SQ v F ( v ) a ( v )  6  R  dv  cross  :  (3.23)  = a (v) + / aj(v)  (3.24)  R  is  F(v)  real  the  part  p a r t . The  because of  is  Maxwellian  f o r the r e l a t i v e  the  imaginary  collision  (3.22)  dv  6  distribution  the  gas p r e s s u r e  a r e r e l a t e d t o t h e complex  -1  function  o (v)  t h e l i n e w i d t h 7 and  a(v) :  a(v) The  section  theory,  unit-atmosphere  units  R  cross  1 5  the  of  v . The  a(v) while  function  Ojiv)  'i s  f u n c t i o n o ( v ) i s a complex  noncommutative  matrix  velocity  velocity  probability  (Herman  distribution  quantity  characteristic  [1963]). c a n be  The  of  integration  removed  the  the over  i f one u s e s t h e  approximation: /Q v F ( v ) o ( v ) <v> The t e r m <v>  = • ( 8kT /  by o n l y  investigated pointed fact  by  out t h a t  function.  near This  may  a few  the  t h a t , a t room  t o peak  and  many  the  (3.26) velocity  affect  percent.  small  error  temperature, of  condition  the may  and M  i s a very the  This  researchers.  peak  (3.25)  (TTM) )  the molecule. T h i s  approximation  linewidth  a(<v>)  i s t h e mean c o l l i s i o n  r e d u c e d mass o f used  dv =* <v>  is  calculated has  [1974]  the r e s u l t  the c r o s s velocity not  commonly  point  Rabitz  be  i s the  section  of  been has the tends  distribution valid  in a l l  1 16 applications. out  that  even  calculation introduced Hewitt  Buffa  of  use  of  the  velocity  3.4.3.3 The  impact  and  collision  sum  between t h e  zeroth  t e r m S,(b,v) the  S^bjv)  0  linewidth  vanish  the  degrees  powers  term S  in  between  integration  over  i s r e l a t e d to  and  where b  the  theory,  S(b,v)  is  of  interaction  the  radiator: (3.27)  a f t e r the i s zero.  0  w o u l d be  Frost  that  The  second  order  first  order  a contributor  [1976]  S,(b,v)  has  shown  freedom. real  those  S ( b , v ) has  a l s o 'been  for  imaginary part  functions  from  of  r e f e r r e d to a  R  and  of line  the  internal  S ( b , v ) . The 2  as" t h e can  to  second  shift  al.  unless  Contribution  part the  the  to that  et  would v a n i s h  contributions of  the  is  some a p p l i c a t i o n s . B o u l e t  the  The  a(v)  ATC  truncated  S , ( b , v ) and  as:  Meanwhile,  2  comes f r o m the  2  function.  be  + S , ( b , v ) + S ( b , v ) +...  order  term S ( b , v ) while  2  in  shifts.  considers  vibrational  can  S(b,v),  perturber  [1977] have r e m a r k e d one  the  i s i m a g i n a r y and  line can  error  function  section  In  is usually  t e r m . The  the  difference  numerical  function  expanded  S(b,v) = S  only  cross  parameter.  potential  for  calculations.  efficiency  efficiency  perturbation  The  explicit  i s good  large  significant  pointed  distribution.  collision  collision  a  line-shift  f o u n d no  <v>  [1983] have a l s o  approximation  linewidths,  i n t o the  the  Tarrini  i f the  [1976]  The  and  the order  are  from  function  interruption  t h e n be  written  11 7  V a  V  =  )  L  vJ 2  I  (  v  )  L  =  vJ 7  p 2  vJ 2  P J,  7  °R( ^2,J ) 2  (3.28)  ° i ^ >  2 )  (3.29)  v  2  V9  v  2 >  o (v,u ,J )  = J Q 27rb R e { S  a (v,u ,J )  = /Q  R  2  I  2  2  2  2nb  J  (b,v, v , J 2  2  2  ) } db  [S (b,v,» ,J )+ 1  2  2  Im{S (b,v,u ,J )}] 2  -r  P„  U J 2  The  2  2  db  (3.31)  = ( 2 J + 1) exp( - E ( u , J ) / k T ) / Z(T) 2  2  (3.32)  2  2  v  variables  rotational  partition 3.4.3.4  The  refer  function  of  the  Z(T) i s  f o r small  S (b,v)  and  perturber,  simply  however, w i l l  diverge  ATC t h e o r i e s ,  S (b,v)  f o r small  2  i s real  for b^b  impact  produced  2  2  the v i b r a t i o n a l  the  total  from E q u a t i o n 3 . 2 1 .  procedure  S (b,v)=1  to  number  function  function  assuming  2  quantum  Cutoff  The  and J  2  respectively.  then  (3.30)  0  by  parameter  t h e ATC  values  theory,  o f b. In  and a c u t o f f  early  procedure  of  i s used. E q u a t i o n 3 . 3 0 would  become: a (v,y ,J ) R  The  2  term  defined  S (b,v) 2  of  the  = *bg +  f£  b  the c u t o f f  is  0  by  considers  2  the  the  o  27rb R e { S ( b , v , u , J ) } 2  condition  contribution  as w e l l ,  2  impact that  parameter  S (b ,v)=1.  of the  the c o n d i t i o n  db  2  2  0  imaginary  defining  b  0  would  (3.33) and If  is one  part  of  be  one  followings:  Re{S (b ,v)} 2  0  = 1  (Re{S (b ,v)}) 2  0  2  (3.34)  + (lm{S (b ,v)}) 2  0  2  = 1  (3.35)  118  Re{S (b ,v)} 2  Equation  3.34  was  while Equation Herman and  +  0  |lm{S (b ,v)}| = 1 2  u s e d by Sharma  3.36  was  [1970b]. Equation  summarised  in  [1977] have  X(b,v) =  a cutoff  function  1 - exp( - S ( b , v ) 2  Tipping  and  and  natural  criteria  are  MacGillivray  p r o c e d u r e would  i s replaced  2  efficiency  Frost  [1971]  i s more  used. Other c u t o f f  that  i f S (b,v)  by  however,  [1974].  suggested  be n e c e s s a r y collision  Rabitz  and C a l e d o n i a  recommended 3.35,  has been more w i d e l y  (3.36)  0  by a new  not  convergent  X(b,v): )  (3.37)  Re{X(b,v)} =  1 - cos(Im{S (b,v)})exp(-Re{S (b,v)}) 2  (3.38)  2  Im{X(b,v)} = sin(Im{S (b,v)})exp(-Re{S (b,v)}) 2  The  function  S (b,v) 2  X(b,v)  for large  would approach  most  framework  is  given  [1981].  over  a l l values  cutoff-free internal al.  by  Leavitt  A S(b,v)  b  and  the  ATC  and L e a v i t t  and  of  vibrational  [ 1 9 7 3 ] ) has a l s o  formulation [1980]  which i s b  has  t h e o r y . . The e f f e c t  The c o l l i s i o n  small  theory  sophisticated  Korff  1 for  b.  3.4.3.5 The c u t o f f - f r e e The  (3.39)  2  motion of been  efficiency  bound  been  in  and  integrable  derived  for  of a n h a r m o n i c i t y  the  in  the m o l e c u l e ( G i r a u d  included  function  i n the  the et  formulation.  i s given as:  S(b,v) =  1 - exp(-/A  i +  /A -S°^ f  e r  -S^  e r  -S  m i d d l e  )  (3.40)  119  The  subscripts  optical  state  transition, for  i and of  the  contributors  Leavitt  [1980]". They  intermolecular  A,  various  electric  Higher-order Schawlow to  r  ,  and  quadrupole,  the  each  Some h i g h e r  "resonance  Ig (&).  The  how  spectral  line  i  d  of  the  d  l  e  expressions are  the  k  close  order  colliding  e.g.  and  in  b-dependent molecules  dipole-quadrupole,  and  functions  polarizability,  octopole  moments.  i n Townes  [ 1 9 6 7 ] , The  and  contributors  i s the  collision-induced  t e r m s a l s o d e p e n d on  is also  the  given  Clebsch-Gordan c o e f f i c i e n t s  functions"  variable  m  possible  Racah c o e f f i c i e n t s . There various  final  summarised  Buckingham  to  s  functions  i n t e r a c t i o n s are  corresponding  a measure  e  constants  S ( b , v ) a l s o d e p e n d on  n  t  and  i n t e r a c t i o n s . These are  molecular  [1975] and  transition.  U  dipole-dipole,  dipole,  initial  most d e t a i l e d  p o t e n t i a l between  electric  the  S°  are  quadrupole-quadrupole of  the  particular  r e s p e c t i v e l y . The  the  e.g.  f r e f e r to  a  fn(k),  the  d e p e n d e n c e on gn(k),  If  the  (k),  and  r e s o n a n c e p a r a m e t e r and  various  states  are  to  is  exact  resonance:  k  = 27rb/(hv)  ( E  - E?  + E  A  - E  A  - E  + E  A  - Ef  B  i n d i c a t e the  A  B  )  (3.41a)  )  (3.41b)  or  k The  27rb/(hv)  superscripts  after f  =  the  refer  molecule, state  of  A and  collision, to  the  ( E  r e s p e c t i v e l y . The  upper and  respectively. the  B  The  perturber.  lower  before  subscripts  states  subscript The  states  of  the  i  and  active  2 indicates  resonance  and  the  functions  120  9 ^)  f (/c) and Ig (A;)  a  r  e  n  n  even  functions  a r e odd. E x p l i c i t  n  while  expressions  resonance  functions  in  terms o f  functions  are given  in Leavitt  the modified  [1980],  given  [1976] a n d M e s s e r e t a l . [ 1 9 8 2 ] .  Basic  formulations  Less elaborate used  in  the  linewidths. real in  part  of s i m p l i e d  expressions  calculations  Spellicy  broadened  with thec u t o f f  have  self-broadening  for  S(b,v)  in  the  been  (3-0)  HF  only  the  procedure  3 . 3 3 . A more s o p h i s t i c a t e d b u t s t i l l  expression  are  theory  [1972] c o n s i d e r e d  et a l .  series  functions  f o r S(b,v)  of  of S(b,v) together  Equation  simple  the resonance  the Bessel  Power-  for  3.4.3.6  and  for a l l  approximations i n Frost  some o f  I f (A:)  rather  case  of  c a n be f o r m u l a t e d a s :  Re{S(b,v)} = Z.  [ Zj  f  A,(v) f , U ) +  b-'c^  Z_j b - c 6  Zj  2 : j  b- c  A (v)  f U ) ~+  A (v)  f U)  2  2  8  3 j  3  3  ]  (3.42)  Im{S(b,v)} = -Z  f  [ Zj b-'c^  A,(v)  If,U)  + +  Zj  b- c  2 : j  A (v)  It (k)  Zj  b- c  3 : j  A (v)  If (*)  6  8  3  = (4/9)  A (v)  = (4/45)  u 6  A (v)  = (1/25)  6* [ 2 7 r / ( h v ) ]  3  simplified  M" [ 2 7 r / ( h v ) ] 2  2  2  2  A,(v) 2  This  i  3  (3.44)  2  [27r/(hv)]  S(b,v) i n c l u d e s  (3.43)  ]  (3.45)  2  (3.46)  2  contributions  from  only  121  the  intermolecular  electric  dipole-quadrupole, interactions.  The  upper and lower i n t o account states.  and  quadrupole-quadrupole  contributions states  dipole-dipole,  of the  active  collision-induced  The f u n c t i o n s A , ( v ) ,  are  summed  2  the  to  take  molecule  transitions  A (v),  over  from  those  and A ( v ) a r e  taken  3  from T s a o a n d C u r n u t t e  [ 1 9 6 2 ] . The p a r a m e t e r s ju and 6 i n  the  above  formulae  are  the  quadrupole  moments,  respectively.  Clebsch-Gordan c o e f f i c i e n t s and Herman  [1963].  application  3.37  o f t h e ATC  lines  broadened  have been measured  and H e r g e t  et  band. L o v e l l a l s o measured lines.  measured  [1972]  (3-0) b a n d s ,  the  (2-0) band have been  lines  (3-0) b a n d . J a f f e  be  cutoff-free  of  Kuipers  both the  et  [1958]  t o the  (1-0)  l i n e w i d t h s of l i n e s  measured  line  (1-0) band HF  shifts  line  shifts and  [1979] a n d  for  the l i n e s  e t a l . [1956], Wiggins e t a l .  have  i n t h e (2-0)  by G u e l a c h v i l i  Walker  [1979]  a l . [1972]  Self-induced  HF  self-broadened  belonging  and S p e l l i c y  [1978]. Meanwhile, Campbell and the  Benedict  3.46 c a n  of s e l f - b r o a d e n e d  respectively.  [1983] have m e a s u r e d  in  [1962] and H i n c h e n and Hobbs  the self-broadened  and  are  and s h i f t s  by many r e s e a r c h e r s .  the linewidths  Meredith  n  3.39 i n a  linewidths  o f HF  and Herget  c j's  CALCULATIONS  a l . [1962] m e a s u r e d  l i n e w i d t h s and s h i f t s  and  theory.  3.4.4 SURVEY OF EXPERIMENTS AND Collisionally  given  3.42 t h r o u g h  through  dipole  The  and a r e  Equations  used with E q u a t i o n s  electric  in  Smith  Campbell in  [1970],  the and  1 22 Pine  [1980]  shifts  of t h e HF  and  Lovell  C0  induced  2  measured  and S m i t h  [1978]  HCl-induced  lines  Hough  shifts  include  [1977].  calculated the et  by  the  Calculations lines  in  Jarecki Smith  DF-induced  3.4.5  THE  (1-0),  (1-0),  (2-0),  and  [1974],  linewidths  self-induced Contributions collision in  i n the  3.39  l i n e w i d t h s and s h i f t s from  3.42  et a l .  intermolecular f u n c t i o n were  through  3.46.  The  and  [1972]  the l i n e s  shifts  Boulet for  (3-0)  the  bands.  and s h i f t s  for  were made  also  in  by  [1980].  calculated  (1-0) band.  LINE  efficiency has  (1-0)  [1963]  [ 1 9 7 7 ] , and P i n e  meanwhile,  for lines  and  efficiency  Equations  f o r the  (2-0) bands  CALCULATION OF LINEWIDTHS AND  3.38  and  and  2  (2-0) b a n d s .  for  linewidths  [1975], J a r e c k i  Meredith  Equations  N -,  2  l i n e w i d t h s and  The c u t o f f - f r e e c o l l i s i o n in  C0 -,  Herman  linewidths  and  2  G u e l a c h v i l i and  and S p e l l i c y  of r a r e - g a s - i n d u c e d  the (0-0),  and  and  (1-0)  bands, r e s p e c t i v e l y . M e a n w h i l e ,  (0-0),  and Herman  lines.  the  H -,  2  linewidths  Benedict  the self-broadened  Shaw  i n the  the N -,  i n t h e (1-0) and  a l . [1977] c a l c u l a t e d t h e in  (2-0) b a n d s .  of the l i n e s measured  [1972]  and  a l . [1972] measured  of s e l f - b r o a d e n e d those  linewidths  the r a r e - g a s - ,  for lines  (3-0)  and  of t h e (1-0) HF  Meredith  (2-0) and  lines  et  [1973]  have measured  Calculations HF  and V a r a n a s i  linewidths  2  i n t h e (1-0)  l i n e w i d t h s and s h i f t s  band. M e r e d i t h  Smith  lines  [1969]  D -induced  the rare-gas-induced  been  SHIFTS  function used  to  described calculate  f o r t h e (3-0) HF interactions taken  lines. to  t o be t h o s e  d i p o l e moment  the given  f o r HF  was  123 taken This The  t o be  1 .80306x10-  i s the  same as  quadrupole  esu.cm  18  the c o e f f i c i e n t  moment f o r  HF  also  and  Cool  [1973],  and  Muenter  Benedict  [1976],  and  Gauss-Laguerre-quadrature semi-infinite  3.44. over In  The  the v e l o c i t y  Boulet  and  of  Equations  3.25  numerical considers greater  a l l  than  to account  computing  for  of  and  levels.  The  establishes  can  then  3.42  and  and  was  3.36.  used  by  however,  of the The  In f a c t , even a t  a common d a t a b a s e  of  calculation factors  sufficient  can on  be  the  Benedict  and  1200K, l e s s  than  states  the  in  explicit  Boltzmann  in rotational  evaluations  r e f e r e n c e d by  3.43  energy-level population at  amount o f c o m p u t a t i o n  one  be  many  for  integration  J=23. T h i s s h o u l d be  that  method r e q u i r e s  used  calculation,  w h i c h have  [1963] have p o i n t e d out are  to the  velocities.  HF.  molecules  was  quadrature  [1976]  32-point  Equations  instead  100°C f o r  of the  A  Equations  used  over  most o f t h e of  are  r e s o u r c e s , the approximation  was  u=0  of  actual  contributions  that  temperature  Herman  In t h e  integration  [ 1 9 7 0 ] . They  Boulet et a l .  applied  Gauss-Laguerre  3.26  and  integration  integration  Ramus  Meredith  numerical  in  and  [1973]).  [1963].  distribution  limited  Dymanus  Herman  be  [1976].  observed  i n Werner and  Klemperer by  3.5.  the  L i e [1974],  also  a 7-point  et a l .  because  0.3%  range  same method can  fact,  low  Leeuw and  r e f e r e n c e d i n the c a l c u l a t i o n s  and  the  2  [1980]).  in Table  t o be  v a l u e s f o r the c o n s t a n t s a r e g i v e n Sileo  (De  taken  Other  - 2 6  et a l .  listed  0  of  Smith  esu.cm  was  M  value  [1980],  2.21X10  (Ogilvie  J>20.  various  greatly  the energy  the v a r i o u s p a r t s of  energy  reduced levels.  the  The  if This  computer  1 24 p r o g r a m and  h e n c e w o u l d e l i m i n a t e any  repeated  energy-level  calculat ion. The linewidth as  the  7  calculated and  shift,  halfwidth  absorbance.  From  K(V)  function  of  functions  l ( p ) and  respectively. line-shape  unit-atmosphere  linewidth is  the  50%  of  of  the  line  at  definition 3.18,  maximum of I  the  The  in Equation  at h a l f  are  respectively.  the  halfwidth  5  and  are  0  Reviews  parameters  the  the  the on  t h e maximum line  line  absorbance  l i n e w i d t h w o u l d be  the  function - L n ( I ( v ) / l ) .  The  0  line  and  the  are  defined  continuum  definitions  given  in  intensity, of  Meredith  various  [1972]  and  Mandin e t a l . [1980].  3.4.6  CALCULATED LINEWIDTHS FOR To  test  linewidths  A gas  consistently  in for  In  taken  for lines  lines  from  the  (2-0)  than  of  and  the c a l c u l a t e d  and  and  373.15K has the  3.8  b a n d . The  values  lists  is excellent.  experimental  values  in  by  the  For  are  for  lines  linewidths values  the  good  lines  3.9  lines  are  between  quite  Table  f o r the  the  several  agreement  w i t h m<6.  are  values  linewidths is  lines  agreement  been u s e d  agreement  The  bands  experimental  experimental  [1962].  experimental  procedure,  (2-0)  calculated  experimental  Herget  f o r the R-branch band, t h e  computational  P - b r a n c h . The  (1-0)  and  LINES  (1-0)  i s b e t t e r . Table  i n the  HF  compared a g a i n s t t h e  the  i n the  Lovell  the c a l c u l a t e d especially  then  general,  lower  the  i n the  temperature  the R-branch the  and  lines  They a r e  calculations.  percent  theory  f o r the  calculated. values.  the  THE  in  lists in  the  125 Table  3.8 L i n e w i d t h s  of  the  (1-0)  band o f HF  ***************************************** m  calc.  expt.  -1  0.4336 c r r r a t n r  1  0.462 cm" 'atm"  1  0.4310 c m " a t m "  1  0.458  cnr'atnr  2  0.501 6 c r r r ' a t m -  1  0.501  cnr'atm-  3  0.5133 c m - ' a t m - '  0.563  cnr atnr  4  0.4555 c r r r a t r r r  1  0.454  cnr atrrr  5  0.3636 c m - a t n r  1  0.345  cm" atm"  6  0.2821  cm-'atm-  1  0.259  cm-'atm"  7  0.2058 c m - ' a t m '  1  0.173  cm" atm"  1  1  1  1  1  1  1  1  ************************************************************  Table  3.9 Linewidths  of  the  (2-0)  band of HF  ************************************************************ m  calc.  expt.  -1  0.4263 c r r r a t m -  1  0.4090 c m - ' a t m " '  0.406  cm-'atm"  2  0.4586 c m - ' a t m "  1  0.464  cm-'atm"'  3  0.4696 c m - ' a t m "  1  0.471  cm^atm"  1  4  0.4268 c m - ' a t m "  1  0.419  cm" atm"  1  5  0.3493 c m - ' a t m "  1  0.347  cnr'atm  6  0.2738  7  0.2064 c m - ' a t m "  1  0.184  cm" atm"  1  8  0.1536 cm" atm"  1  0.140  cm- atm"  1  1  cm"'atm"  1  0 . 4 5 9 cm" a t m "  1  1  "  1  1  1  - 1  1  1  1  ************************************************************  1 26 Table  3.10 L i n e w i d t h s  o f t h e (3-0) band o f HF  ***************************************** m  calc  expt.  -2  0.4492 cm- a t m "  1  0.506 cm" a t m"  -1  0.4136 cm" a t m "  1  0.447 cm" ' a t n r  1  0.3975 cm" a t m "  1  0.397 cm" atm"  2  0.4268 cm" a t m "  1  0.443 cm" atm"  3  0.4473 cm" a t m "  1  0.453 cm" atm"  4  0.4201 cm" a t m "  1  0.412 cm" ^ t m "  5  0.3514 cm" ^ t i r r  6  0.2820 cm" a t m "  1  0.254 cm" ^ t m "  7  0.2187 cm" a t m "  1  0. 1 64 cm" atm"  1  1  1  1  1  1  1  1  1  0.331 cm" atm"  1  1  1  1  1  1  ************************************************************ (2-0)  b a n d . The e x p e r i m e n t a l  taken  from  given  i n Table  Spellicy for  Meredith  the R-branch l i n e s than  calculation  3.3  temperature  It  proportional  invers-ely  the  c a n be  from  v.  proportional  the  from  i s quite  good  t h e agreement i s  less  sophisticated  et a l . [1972], the (3-0) seen  linewidth band.  from  For to  variations  The  result  Equation  3.22  with  is  not  that 7  o f t h e p e r t u r b e r n,  constant  gas  temperature  pressure, T  t o / T . Hence 7 w o u l d be i n v e r s e l y  The t e m p e r a t u r e  are  values a r e taken  Of c o u r s e ,  t o t h e number d e n s i t y  velocity  proportional t o v/T.  result  case,  f o r t h e (3-0) band i s  t h e agreement  w i t h m<6.  shows  for  unexpected.  gas  the  Again,  by S p e l l i c y  Figure  The r e s u l t  3.10. The e x p e r i m e n t a l  e t a l . [1972].  much b e t t e r  the  [1972].  linewidths, in this  dependence of  while  and n  v  is  is is  proportional  the c o l l i s i o n  cross  1 27  section  i s small  considered be  f o r the very  here. Meanwhile,  directly  s m a l l change  the observed  p r o p o r t i o n a l to  Smith  [1974],  nonlinearity interest  Smith  is  and  very  small  over  are  (Meredith  and  [1974]).  the  should  Linewidths  dependence  Meredith  temperature  linewidths  the pressure.  known t o have a n o n l i n e a r p r e s s u r e  in  But  pressure  the  range  of  here.  3.4.7 CALCULATED L I N E SHIFTS FOR THE HF LINES In  comparing  band a g a i n s t [1962],  the c a l c u l a t e d  the experimental  t h e agreement  only  t o t h e same o r d e r  tend  t o be  The  f o r the  i s poor.  from line  [1978]  Boulet  e t a l . [1976].  Table  shifts  f o r t h e (3-0)  a r e taken  from  slight  agreement  between  Although are based appear  with  shifts.  and  Tarrini  approximation  et a l .  shifts  with  m>4.  the c a l c u l a t e d  same  the experimental  values  or the c a l c u l a t e d  values  3.11  lists  the  the c a l c u l a t e d  calculated values  [1979],  and  in  in  There  experimental  f o r the l i n e w i d t h s and  theory, more  the  calculated  accurate  shifts  linewidths  that those  of  T h i s phenomenon h a s been commented on by [1983]  line  m<5.  t o be s i g n i f i c a n t l y  line  for lines  C a m p b e l l and W a l k e r  the c a l c u l a t i o n s  on t h e  (1-0)  i s agreement  band. The e x p e r i m e n t a l  table  for lines  Herget  o f m a g n i t u d e . The c a l c u l a t e d  and S m i t h  values  from  f o r the  Generally, there  (2-0) band a g a i n s t  Guelachvili  is  values  i s t h e same when c o m p a r i n g  from  the  shifts  p r o g r e s s i v e l y too p o s i t i v e  situation  shifts  line  to  Equation  be  a  consequence  3.25 i n s t e a d  of  "of  the Buffa  using  performing  the an  gure  3.3  The  t e m p e r a t u r e dependence of t h e  linewidths  1 29 Table  3.11 L i n e  shifts  o f t h e (3-0) band o f HF  ********************************************* m  calc.  expt.  -2  +0.0288 cm  -1  +0.0763 cm" 'atm"  1  +0.0763 cm" a t m "  1  +0.0445 cm" atm"  2  +0.0061  cm" a t m "  1  +0.0070 cm" 'atm"  3  -0.0237 cm" a t m "  1  -0.0140 cm" atm"  4  -0.0046 cm" ' a t m  5  +0.0281  cm" a t m "  6  +0.0541  7  -  1  atm"  1  1  1  1  1  1  1  -0.0171  cm" atm"  1  -0.0201  cm" atm"  cm" a t m "  1  -0.0101  cm" atm"  +0.0758 cm" a t m "  1  -0.0121  cm" atm"  - 1  1  1  1  1  1  1  1  ************************************************************ explicit ignores terms  velocity the  are  i n t e g r a t i o n . The  terms / A ^ pure  and / A ^  imaginary  contribute  towards the l i n e  Boulet  a l . [1976],  et  together  calculated are  in  fact,  line  better  shifts  d i r e c t i o n with  Campbell and Walker theory  like  result  i s beyond  it  with  will  that  and  These  hence  will  linewidths.  sophisticated  integration,  have  theory produced  (1-0) a n d (2-0) bands the  Boulet  also  3.40.  and not the  a more  f o r the  agreement  line  shifts  velocity  f o r l i n e s w i t h m>4,  calculated shift  shifts  from E q u a t i o n  quantities  using  with e x p l i c i t  s i m p l i f i e d theory  which  experimental values.  e t a l . [1976] have p r o d u c e d  i n t h e (2-0) band w h i c h a g r e e i n those of  In  t h e (3-0)  band measured  [ 1 9 7 9 ] . The u s e o f a more  the by  sophisticated  by L e a v i t t  [1980] t o i m p r o v e t h e c a l c u l a t e d  the scope  of t h i s  significantly  deplete  initial  the  study.  available  In  fact,  computing  1 30 resources  which  fruitfully  utilised  3.4.8  3.12  standard-air  pressure  of  adopted  shifts  are  [1979].  time,  be  more  data r e d u c t i o n .  vacuum  of t h e  (3-0)  a t a gas  wavenumbers  band l i n e s .  temperature  This i s accomplished  of C a m p b e l l listed  in  The  and  3.6.  35/9T,  range  Campbell  and  by a p p l y i n g  the  [1979] t o  the  Listed  dependence  are a l s o  Walker  are l i n e a r  [1979].  from T a b l e  the e a r l i e r rms  shifts  considered here. This  and  wavelengths  the  3.12  dispersion  residual  is  1  listed  use  from  of t h e  in  from  and the  Table  Campbell the by  shift-corrected  reduced  the  o f t h e s t a n d a r d HF  an  of  been d e m o n s t r a t e d  further  to  Table  i n p r e s s u r e over  has  reduced  in  ±0.001 55A"  improvement  residual spectrum. down  from  to  ±53ms~  1  in velocity.  DOPPLER AND There  has  f i t  ±0.00128A. T h i s c o r r e s p o n d s to ±44ms"  The  T h e s e have  a s g i v e n by C a m p b e l l  temperature  shifts,  and  100°C  Walker  Table  shifts  of  These a r e the e x p e r i m e n t a l v a l u e s taken  [1983]. Again,  3.4.9  present  the  the unit-atmosphere  unit-atmosphere  The  torrs.  wavenumbers  Walker  in  lists  for shifts  360  experimental  small  the  spectral  wavelengths  been c o r r e c t e d  3.13.  on  at  SHIFT-CORRECTED REFERENCE WAVELENGTHS Table  3.13  would,  are  CELL-WALL BROADENING other  line-broadening  molecular c o l l i s i o n  broadening.  Townes and  [ 1 9 7 5 ] . The  Schawlow  are the Doppler  broadening  and  These two  mechanisms are  besides  summarised  more s i g n i f i c a n t  the c o l l i s i o n  broadening  in ones with  131  Table  3.12  Shift-corrected  wavenumbers  and w a v e l e n g t h s  ***************************************  V  m  X  1  1 1 4 0 9 . 4 2 4 4 cm  2  11441.4337 cm"  3  11468.8426 cm  - 1  4  11491.6132 cm  - 1  8699.6090A  5  1 1 5 0 9 . 7 0 2 4 cm  - 1  8685.9363A  6  11523.0863  cm"  1  8675.8476A  7  11531.7272 cm'  1  8669.3466A  8762.2777A  - 1  8737.7637A  1  8716.8815A  ************************************************************ Table  3.13  Line  shifts  f o r t h e R - b r a n c h o f t h e ( 3 - 0 ) band  ************************************************************  m  95/3T  5  1  -0.0342  A.atnr  1  -0.115 mA.K"  1  atnr  2  -0.0053  A.atnr  1  +0.013 mA.K"  1  atnr  3  +0.0106  A.atnr  1  +0.036 mA.K"  1  atnr  4  +0.0129  A.atnr  1  -0.006 mA. K"  1  atnr  5  +0.0152  A.atnr  1  -0.044 mA.K"  1  atm"  6  +0.0076  A.atnr  1  -0.084 mA.K-  'atnr  7  +0.0091  A.atnr  1  -0.082 mA.K"  1  atnr  ************************************************************ the  absorption  the  motion  of has  cell  wall.  of the m o l e c u l e  the r a d i a t i o n been g i v e n  being  i n Townes  Doppler broadening i n the d i r e c t i o n  a b s o r b e d . The and Schawlow  i s caused  parallel  to that  Doppler h a l f w i d t h [1975] a s :  by  7  D  1 32  7  D  (v/c)  =  v/( (2kT/M) l n 2 )  The  term M  the  operation  temperature  the  order  0.02cm"  also  i n t h e above  of  broadened  absorption  cell  absorption rigorous 7  w  but  treatment  adequate  In t h e above  constant,  100°C o f t h e HF the  (3-0) l i n e s .  The  colliding  The c o l l i s i o n  would  hence  to c a l c u l a t e  cause  line  has  At  7  of  been  are  against  the  interrupt  the  broadening.  [1953].  given  is  D  lines  the w a l l - c o l l i s i o n  Danos and G e s c h w i n d  expression  mass.  cell,  molecules  and  by  i s the m o l e c u l a r  in  halfwidth A  simpler  Townes  and  V  w  =  (A/V) • (  equation, is  and M  A  (RT) /  3  i s the t o t a l  t h e volume  i.s  (8ir M)  of  the molecular  the  ) inside cell,  mass. The  (3.48) s u r f a c e area of R  is  value  the  gas  of 7  is w  generally  A  [1977] a s : 7  cell,  the  process  of  for  wall.  h a s been g i v e n  Schawlow  the  by  1  equation  (3.47)  much l e s s  than  the pressure-broadened  width.  Chapter HF  4  DATA REDUCTION  4. 1 INTRODUCTION The  most t i m e - c o n s u m i n g p a r t  reduction  of  velocities. velocities complex  the The  in  the  data  in  spectra  is  data-reduction  roughly  two  parts  not  accomplished  The  through  Reticent  (Yang  the  Reticon part  from  these  exclusive  since  needed data  two  second  information  is  procedure.  the  The  into  the  be  would  case.  divided  mutually  information  program  which  involves preprocessing  are  to  in  the  r e d u c t i o n of use  [1980],  of  Pritchet  the the et  [1982]).  PREPROCESSING OF  BASELINE As  has  too minute  high-precision be  more  techniques.  r e d u c t i o n but  radial-velocity  continuum-rectification  4.2.1  can  t o be  conventional  made f o r e f f e c t s  the  radial-velocity  4.2  procedure  i n t o c o n t i n u u m - r e c t i f i e d spectra while  s p e c t r a . The  al.  in  result  involves deducing  the  radial  data  part  is  p r e c i s i o n r e q u i r e d f o r the  than  procedure  program  radial  conventional  first  HF  relative  data-reduction  have t o be  data-reduction p a r t s . The  the  the  spectra to obtain  high  detailed  Considerations  affect  very  causes  and  important  observed  of  RETICON  SPECTRA  SUBTRACTION  m e n t i o n e d p r e v i o u s l y , an  t o be  removed  from  e a c h raw  133  additive fixed Reticon  line  pattern  spectrum. T h i s  can  1 34  be a c c o m p l i s h e d by  subtracting  taken  t h e d a t a e x p o s u r e . In many  this  shortly dark  exposure  starlight of  after  still  of  can simply  incident  the longer  especially  be  data exposure  t h e CFH R e t i c o n  light  after  for fainter  There c o u l d taken w i t h  be  drifts  lines.  objects.  adc u n i t s depending  be  best  exposure  time  difficult  to  the as  the  achieve  physical  state  Moreover, baseline  one  the  would  i n the use  events. Generally,  dark  for  between  use  as w e l l  be s u f f i c i e n t .  has  of  would  the  same  is  usually  exposures.  Besides  in  time,  t h e same  data  t h e mean  Reticons,  of  a  long  many  order to of  dark reduce  cosmic-ray  shorter  constant f o r  the  exposures.  The c h a r a c t e r i s t i c s  become q u i t e  the  output  time. I t  as the e f f e c t on  of  the  This  and  the subtraction  a l l  spectra  of the order  may n o t r e m a i n  depending  electronics  between  of t e l e s c o p e  baseline  off  exposure.  exposure  longer  available  and b l o c k  generally  is  exposure,  i s now  the exposure  the  This  The amounts  spectrum.  want t o  the n o i s e c o n t r i b u t i o n  amplifier  on  of the R e t i c o n  exposures  exposure would  are  data  for  the e f f i c i e n c y  both  times.  in this  characteristics  A dark  differences  dark b a s e l i n e  lowering  enough f o r  close  with  response  detected  A shutter  also different  The d i f f e r e n c e s  if  signal  the b a s e l i n e  exposure  are  applications,  the s u b t r a c t i o n .  will  during  several the  It  zero-point  different  zero-point video  system.  from t h e d e t e c t o r  exposure  exposure  the s p e c t r a l  however, w o u l d be more d e s i r a b l e . on  (baseline)  a short  any p h o t o n  would n o t a f f e c t  the case  dark  on t h e R e t i c o n . The l i n e a r  t h e R e t i c o n means t h a t  short, e x p o s u r e  a  of  dark the  exposures  135 longer of  than  similar  the  s e v e r a l hundred exposure  shorter  times,  exposures  calibration  seconds.  Dark b a s e l i n e  however, a r e s t i l l  such  as those  exposures  desirable for  f o r the  incandescent  lamps.  4.2.2 USE OF "EXTRA-READOUT" POINTS The  effect  minimised (Walker the but  of  et a l . [1983]).  result  of  without  readout  addressing  or  It i s  o b t a i n e d both  photodiodes. for  residuals  Basically,  performing  the v a r i o u s output  points  zero-point  drifts  There each  These  and a f t e r  are  about  output  i n these  sequences  28  video  line.  By  comparing  the  minor z e r o - p o i n t  drifts  can  be n u m e r i c a l l y  each output  line.  I t h a s been f o u n d  lamp e x p o s u r e s , "extra-readout" the  sensitive  The  shift  photon  signal  registers  on  and would d e t e c t p h o t o n s  high. Generally, this  effect  amount o f z e r o - p o i n t d r i f t s . contain  the  light  signals  caused  Reticon are i f the l i g h t  i s small  in  the  calibration in  by t h e also  second  these fact light  intensity i s  i n comparison  Some R e t i c o n s  for  p o i n t s a r e not  also detected  points. This i s possibly  the  exposure,  corrected  i n incandescent is  1872  subtracting  baseline  "extra-readout" that  points  of the  "extra-readout" points after dark  from  "extra-readout"  from  video  individual  "extra-readout"  useful  are  Reticon  the v o l t a g e s  the readouts  be  points  on t h e  ones  that  also  points  the  sampling  lines.  before  readout  rebiasing  essentially video  these  the c o r r e s p o n d i n g  perfect.  can  o r c o r r e c t e d by t h e u s e o f " e x t r a - r e a d o u t "  photodiodes.  are  the  are also set  with the known t o of  the  1 36 "extra-readout" points. the in  readouts  these p o i n t s  accumulated residual  the  charges  readouts  set  of t h e  1872  are  of  t o be  1872  a  The  left  i n the  signal  of t h e  signal  T h i s behaves  output  be  as  video l i n e s  Consequently,  " e x t r a - r e a d o u t " p o i n t s may  after  amount of  function  photodiodes.  the p h o t o d i o d e s .  zero-point-drift  4.2.3  photodiodes.  i s found  in  the  in  of the  These are the p o i n t s o b t a i n e d  if  after  the  second  unsuitable for  use  corrections.  RELATIVE GAIN CORRECTION 4.2.3.1 L i n e - n o r m a l i s a t i o n p r o c e d u r e The usually  relative  5%.  This implies  is slightly  different  for  each  relative  and  constant from  a  has  each  t o be  constant  use  a  of  over  This i s  i s taken  a l l output  drift  simple  which  numerical  line-normalisation correct  t h e two  of e a c h  output  also  additive  additive  process  effects. line  the  The  be c o m p l i c a t e d i s an  to  normalisation to the  output  lines.  output  the  simple  where  ratio line  each  between and  the  multiplicative by any  effect. or  perfectly  residual One  cannot  multiplicative decouple  To c o m p l i c a t e m a t t e r s , has  video  multiplicative  process  t o be  are that  output  essentially  the p a r t i c u l a r  however, would  a  numerically  line-normalisation  the mean s i g n a l  zero-point  is  multiplicative  applied  video l i n e .  normalisation  mean s i g n a l  gains effect  different  multiplicative  effect,  amplifiers  to within  The  effect  the output  adjusted only  the g a i n line.  g a i n s of  and  the g a i n  a s m a l l d e p e n d e n c e on  the  1 37 accumulated  signal  nonlinearity. 5x10" gain  8  The  level. change  p e r adc u n i t  levels  over  significant In effect  where  conventional i s corrected  by d i v i d i n g  level.  or e i g h t - l i n e  may e x i s t  in this  spectrum c o n t a i n s levels  quite  division  by  incorrect lines.  a  gain  subtraction  to  spectral  lamp  series  of  or  a  signal additive  Several  fact  problems  that  the  data  have  signal  signal  level,  spectrum  pattern  gains  would  cause  t o the s p e c t r a l  from  the  the accuracy  baseline  of a  simple  the r e l a t i v e gains  effect  lamps  i s through  spectra. lamp  exposed  to a d i f f e r e n t  spectra  should cover  factors  a  process.  continuous  One c a n c a l c u l a t e  is  continuum  t o be a p p l i e d  affect  nonlinearity lamp  same  multiplicative  One method t o c a l i b r a t e  incandescent  higher  s p e c t r u m by  the continuum  additive  4.2.3.2 Use o f s t e p  the small  at  high  relative  l i n e s which w i l l  from  corrections  line-normalisation  and  the  p r o c e d u r e . The  would a l s o  about  i n the  signal  the data  the  continuous  Residual  range  i s then a p p l i e d .  different  small  saturation. techniques,  process  a  typically  accumulated  exposed  normalisation  is  I t becomes g r e a t e r  lamp s p e c t r u m A four-  is  the signal  the  f r a c t i o n of  effect  i n gain  mode o f t h e R e t i c o n .  signal  This  Basically, spectra  signal  level.  the e n t i r e  one  with  a n d hence  step  obtains  each  The s e r i e s  range o f s i g n a l  the m u l t i p l i c a t i v e  f o r each spectrum  t h e use of  a  of  them  of  lamp  levels.  line-normalisation f o r each  different  1 38  signal  level.  A polynomial  can  then  be u s e d  t o f i t the  normalisation  f a c t o r s as a f u n c t i o n of s i g n a l l e v e l s  in  each  separate  video  be  used  to  effects  correct  provide the'  a good  f i t over  high-gain  mode  are  needed  fits  lamp  indicated corrected.  levels.  region  the  near  filters lamp  flat  This  in  for  spectrum.  adequate  Reticon.  range i n  the  entire ten  or  t h e f i t . The g o o d n e s s the q u a l i t y of the  any  readout in  to  Higher-order  to cover  baselines  should  be u s e d  zero-point points  of lamp for  drift  should  the continuous  as  also  lamp  be  spectra  f a c t o r s are c a l c u l a t e d should  i . e . have  i s usually  infrared  i n the data  order  And  where t h e n o r m a l i s a t i o n relatively  the  dark  the extra  The  nonlinearity  up t o s a t u r a t i o n . U s u a l l y ,  spectra.  by  and  generally  d e p e n d s on  spectra. Appropriate  can then  the e n t i r e s i g n a l l e v e l  are required  polynomial  these  are  of  range of s i g n a l l e v e l more s p e c t r a  gains  i n d i v i d u a l point  polynomials  polynomials  the  These p o l y n o m i a l s  the r e l a t i v e  f o r each  First-order  line.  a  small  range  in  signal  t h e c a s e when one i s w o r k i n g  and a t  high  dispersions.  have t o be u s e d t o p r o d u c e a f l a t  be  in  Otherwise,  region  i n the  spectra.  4.2.4 FLAT-FIELDING After  dark b a s e l i n e  s u b t r a c t i o n and a p p l i c a t i o n o f  various  l i n e - n o r m a l i s a t i o n procedures,  to  flat-fielded.  be  sensitivity  This  v a r i a t i o n s as  is  to  w e l l as  the data  remove  still  the have  diode-to-diode  non-uniformities  i n the  1 39 Reticon on  and s p e c t r o g r a p h  the Reticon  the  surface  response.  detector  This  at  would a l s o  is  CFHT.  response across application  s p e c t r a l responses.  especially  Removal  by n u m e r i c a l l y  incandescent  lamp  well  the necessary  have been  division.  Care  f r o m b o t h t h e lamp identically. illuminate stellar the  dividing  be t a k e n  It i s especially  a  However, s m a l l  slicer  inside the  as  preprocessing the beams  i l l u m i n a t e a l l the  optics  f o r t h e lamp beam t o  a one  (Campbell  still  array  as the  to a c e r t a i n extent  which c r e a t e s  may  c a n be  s p e c t r u m by an  of the R e t i c o n  beams a r e n o t i d e n t i c a l l y  et  exist  by  dimensional a l .  i f the  [1981]). lamp  and  matched.  beams was to, u s e t h e lamp  t o match t h e lamp a n d  light  reflected  o f f the  o f t h e dome. The lamps were mounted on t h e t o p end o f  telescope.  telescope  E a c h lamp s p e c t r u m was a l s o t a k e n a t t h e same  orientation  flat-field on  the  the l i g h t  One method p r e v i o u s l y u s e d a t DAO stellar  a l s o ease  subtraction  t o ensure  important  Fabry-image  effects  the  lamp s p e c t r u m b e f o r e  beam. T h i s h a s been a c h i e v e d  of  in  line-normalisation  e x a c t l y t h e same p a r t  equivalent  the data  of  Reticon  Flat-fielding  Dark b a s e l i n e  and t h e s t a r  u s e o f an image  stellar  non-uniformities  applied to this  should  to the  s p e c t r u m would  spectrum.  particles  the u n i f o r m i t y  relevant  rectification.  accomplished  should  of  the Reticon  of continuum  as a l l  alter  Dust  how w e l l  as  the  lamp s p e c t r a were  particular  obtained.  t h e lamp s p e c t r u m would  caused  by a d u s t  particle  major  disadvantages  of  This  claim  flat-field  on t h e R e t i c o n this  star.  method  the  Excellent is  response  a r r a y . One o f  to  obtain  based  the  matched  1 40 flat-field generally use  the  lamp  spectra  needed. mean  This  of  The b r i g h t  by warming up t h e  that  very  i s especially  o f many  contribution.  is  long  lamps would as  are  bad when one wants  these spectra  dome a s w e l l  exposures  to  reduce  a l s o degrade  to  noise  the seeing  a t t r a c t i n g moths t o  the  telescope. A n o t h e r method CFHT and  DAO. An  telescope  exit  the  last  this  i s adopted a t iris  pupil  element  diaphragm  formed  i n the  p u p i l would  the present  produce  is  stellar  Coude t r a i n .  object  Coude t r a i n . a beam w h i c h  because  can  Otherwise, mean v a l u e  lens  be  divided  out  t o be a d j u s t e d f o r  d i v i d i n g each p o i n t would  in  be s u f f i c i e n t  short.  the  If  the  i n the  f i t o f t h e lamp lamp  spectrum.  t h e lamp s p e c t r u m to  of the  as i s the case  polynomial from  is  illuminating  mis-collimation  slope,  a low o r d e r  which  the  match t h e s t e l l a r  The lamp e x p o s u r e s a r e g e n e r a l l y  s p e c t r a l region,  spectrum  needs  both  isolate  A lamp will  of s l i g h t  lamp s p e c t r u m h a s a s i g n i f i c a n t blue  to  by t h e c o n v e r g i n g  beam. The p o s i t i o n o f t h e d i a p h r a g m each  used  time at  produce  by  the  a  normalised  s p e c t r u m by t h e  flat-field  flat-field. After  d i v i d i n g the s t e l l a r  lamp, a f o u r - c h a n n e l s  additive line-normalisation  c a n be a p p l i e d  t o remove any  This  is a  order  generally o f an  very  adc u n i t  small  small  or l e s s .  residual line  c o r r e c t i o n and I f the  procedure pattern. i s of  lamp s p e c t r u m  the was,  however, n o t t a k e n a t t h e same p h y s i c a l s t a t e o f t h e R e t i c o n as  the  stellar  line-normalisation  would  spectrum, not  reduce  the the  four-channels residual  line  141 p a t t e r n . T h i s can was t a k e n  when t h e  temperature  when t h e  line  after  to  degrading  a  liquid-N may be  5% o f  the  stellar  the  process  Nyquist  reaching  refill.  useful  this  i t should to  The  n o t be  An  in  frequency  spectrum. should  spectrum  of  2  i s of poor q u a l i t y ,  about  line-normalisation  the process  normalisation  I f t h e lamp s p e c t r u m  smoothed  lamp o r s t e l l a r  R e t i c o n was i n  equilibrium  eight-channels case.  occur  be  avoid  additive  applied  to arc  spectra.  4.3  REDUCTION OF HF DATA  4.3.1  CONTINUUM RECTIFICATION There a r e four types  observing  run i n order  o f s p e c t r a one h a s t o o b t a i n  t o produce a r e l a t i v e  measurement. T h e s e a r e t h e s t e l l a r lines,  the s t e l l a r  continuous  spectra with  lamp s p e c t r a  lamp s p e c t r a w i t h o u t are  used  velocities  f o r the  imposed HF  lines.  For is  used  coverage  stellar  procedure  lines  in  a t a l l times i s used is is  spectrograph  in  at both  the  same  achieved such  imposed  HF l i n e s ,  and t h e  radial  aligning  that the a r c l i n e  Ar I  with  spectral  DAO and CFHT where t h e  by  continuous  t o measure  the spectrum  The  the  spectra  t h e HF p r o g r a m s . I n f a c t ,  4.8A/mm.  HF  A l l these  greater c o n s i s t e n c y , the i d e n t i c a l  dispersion coverage  no imposed  t h e imposed HF l i n e s .  i n the data-reduction  radial-velocity  spectra with  w i t h HF l i n e s ,  i n an  the  region  the  same  reciprocal  identical  spectral  the  Reticon  X 8 6 6 7  would  and always  142 locate  at  array.  Furthermore,  of  the  t h e same  spectra  criteria  pixel  to avoid  due  a r e used  to  I  X8689.  position are  This  of the a r c  focal  the Reticon. focus  i n the  plane,  focus  the  same  The Hartmann mask i s  to  monitor  when d i f f e r e n t  parts  the  of  pixel  of the  beam  masked o f f . In most HF  programs, a s t e l l a r  used as a r a d i a l - v e l o c i t y for  that  standard for  standard  same s t a r . S i m i l a r l y , an  reference  spectrum spectra  for  HF  spectrum  is  generally  (or reference)  spectrum  HF s p e c t r u m  lines  in  pseudo-continuum  a l l spectra.  rectification stellar  of  spectra  the  t h e imposed HF l i n e s .  Pseudo-continuum  of  standard  the  techniques. polynomial  This  signal  paucity  of  polynomial case  i s achieved  i n the  of  by  same a s  good fit  a v a i l a b l e continuum  with  in  conventional  points  a  Each the  points.  Due  the  points,  a  lines  More  are  particular  a p p l i c a t i o n and a h i g h e r - o r d e r  low-order  e.g.  to the  lamp s p e c t r u m  HF l i n e s .  to  is especially  and broad  i s a continuous continuum  taken  t o have  A s i m i l a r p r o c e d u r e c a n be a p p l i e d  HF s p e c t r u m w h i c h  stellar  rectification  taken  used. T h i s  strong  data  i n the spectrum.  f i t i s generally  i s generally  standards  d i v i d i n g t h e s p e c t r u m by  several neighbouring  f o r the spectra  a Lyr.  is  f i t t o the continuum p o i n t s  continuum point mean  spectra  a  These  are generally  without the  i s used as  c a n a l s o be u s e d a s t h e s p e c t r a l  s p e c t r a . The s t a n d a r d  of  Reticon  on t h e same a r c l i n e  essentially  line  on t h e  any i n c o n s i s t e n c y  optimum  is  o f 351  the curved  to focus  always used t o o b t a i n Fe  position  polynomial  those  standard  imposed  available  the  in  with this  f i t can  1 43 be  used.  broad  Again,  the continuum p o i n t s a r e chosen  w i n g s o f t h e HF  lines.  A g e n e r a l way t o c o n t i n u u m first  to divide  stellar  the data  spectrum.  spectrum  by  an  i s a l s o performed  rectified original ratio of  data data  spectrum spectrum  spectrum  the  these  spectrum  The p a t t e r n s  data  spectrum  is  night.  going  become  features  in  fits  features. It  the  section.  fits A  from  numerically  smoothed.  simpler  cubic-spline  f i t r a t h e r than  the  shape as  patterns.  spectrum one  data  observing  visible  when  the  taken  can  i s only  on  actually  when one ±20ms"  polynomial spectrum  however, s u b d i v i d e polynomial  residual  such  fringe  i . e . b e t t e r than  complicated  individual  between t h e p o l y n o m i a l  standard  A single  the  the general  on a n o t h e r  applications,  s e c t i o n s and a p p l y  t o each  taken  In most  important.  A  one d i v i d e s t h e  to a  small  others).  f i t . The  even  compared  i m p o s s i b l e . One c a n , smaller  and  fitted  by d i v i d i n g  a r e much l e s s  f o r very high p r e c i s i o n  t h e y may the  these  i s then  features  p a t t e r n s a p p e a r when  by a s t a n d a r d  ignore a l l  many  standard  contains the  or  obtained  function  variations  or run.  same  then  by t h i s  date  the  spectrum  (polynomial  response,  low-spatial-frequency  spectrum  ratio  is  standard  HF  spectrum  generally contains besides  spectral  Generally,  is  spectrum  rectified  i f the data  function  a data  by t h e r e c t i f i e d  by t h e  The r e s i d u a l  appropriate  rectify  spectrum  Division  imposed HF l i n e s .  to avoid the  1  is that  f i t to a l l is  usually  the spectrum  into  or s i n u s o i d a l f u n c t i o n  The d i s c o n t i n u o u s different method  joints  s e c t i o n s can is  to  use  be a  pseudo-piecewise-polynomial  1 44 fit.  The  g o o d n e s s of  dependent  on  particular why  the  Other  data  factors  velocity,  and  spectrum that  be  This  spectrum  spectrum  i s one  is usually  of  t h e main  the  former  c o r r e c t e d by if  the  same  star. include  focus,  radial  g e n e r a l l y kept  to a  the  equipments while  the  numerical  methods. However,  one  of  are  very  reasons  match  instrumental p r o f i l e , The  is  matches  t h a t of t h e  affect  alignment  have d i f f i c u l t i e s  residual  standard  would  dispersion.  careful  can  the  between t h e  minimum by latter  well  spectrum.  standard  differences  will  how  f i t t o the  there are  intrinsic  line-profile  variations. Radial-velocity  dispersion  to  matching  s p e c t r u m . T h i s , however, r e q u i r e s t h e  at  rough r a d i a l - v e l o c i t y  better  standard  corrections  applied  least  the  and  method would be  spectrum  the  use  the p o s i t i o n s  of  and  spectra.  Based  procedure  can  standard  interpolation spectrum this  to  variable-star different  corresponding  produce a  method  would spectra  velocities.  polynomial  and  produce  It i s  knowledge  fit  spectral  i n the  the be  lines  cubic-spline  A more  standard  spectrum.  f i t between t h e  sinc-interpolation  method  produce the matching  two  lines  i s again  s e t s of  line  i s g e n e r a l l y used  s p e c t r u m . The  same  However,  complicated  difficult  s u i t a b l e method  data  a p p l i e d t o the  different also  between  f i t , an  for  may  for  t o r e p r e s e n t a l l the h i g h e r - f r e q u e n c y  variations.  of  polynomial  rather  where  better  of a p o l y n o m i a l  b e t t e r matching become  a  be  d i s p e r s i o n "information. A  on  then  to  can  have  a  single  dispersion  the  of  a  positions.  A  with  use  the  procedure  f i t is  to  also  1 45 applied The  to the  final  effects  continuum  residual of  spectrum  poor  "overlooked"  rectification  line  i n the continuum  discussed  in  line-position  more  t h e HF  probably  cancellations.  continuum p o i n t s . Imperfect be  will  of  fit  detail  determinations  still  later  contain  These  by c a r e f u l  cancellation  spectra.  can  be  c h o i c e of  the  between  when  lines ' will  i t s effect  on  i s examined.  4.3.2 LINE-POSITION DETERMINATION 4.3.2.1 L i n e The lines.  cancellations  data  stellar  Blendings  s p e c t r a have  between t h e  seriously  affect  from  spectra. Dividing  the  matched  small residual  line  of  positions  spectrum  with  difference  c a n be  lines  by  f o r each  technique  line  spectrum  one  lines  by t h e HF  left.  lines.  .cancellations  stellar  comparing  still  The  HF-free  spectrum.  line  d e s c r i b e d by  ignore  by  the  line  stellar This  means o f  Fahlman and  be  stellar  the r e l a t i v e  this  the  spectrum  and t h e r e w o u l d  individual  profiles,  by  One c a n s i m p l y  comparing  is  spectrum  line  d e r i v e d from  the standard  Since  individual matched  to imperfect  stellar  obtained  accomplished  [1973],  due  unaffected s t e l l a r  positions  data  would  measurement  give a s t e l l a r  a s e r i o u s problem.  few a f f e c t e d  plenty  the  stellar  of l i n e s  line-position  free of the contaminations  w o u l d n o t be the  two s e t s  s t a n d a r d HF s y s t e m w i l l  essentially Any  any d i r e c t  b o t h HF and  is the  Glaspey  corresponding  i t i s not necessary  t o use t h e  a s t h e r e f e r e n c e s p e c t r u m . The o r i g i n a l  146  standard  spectrum  difference the is  is sufficient  i n the  dispersion  narrow w i d t h o f t h e negligible.  spectrum spectra  In  of t h e same s t a r .  position.  Relative  individual the  used  line  spectra  comparison any  The  HF  spectrum  t e c h n i q u e by against  the  data  used  lines  can  by a  . line  determined  f o r each  consistent  for a l l  t h e n make  direct  t h e need  of  be m e a s u r e d w i t h  the  the  in pixel  such  that  achieved  if  A  rough  single  HF  increase  The  position. it  would  o f t h e HF line  optimal values  free  the  amount  of  the  contaminations by  dividing  which The  has amount  produce lines  used.  after can For  would of  been of  minimal  of s h i f t can  l i n e s . However, t h i s in  the  stellar  cancellation is  in  spectrum.  matched  be m i n i m i s e d  mean s h i f t  work, d i f f e r e n t  for different  lines  almost  s t e l l a r spectrum  division. a  by  also  spectrum  significant  relative  t h e HF  spectrum  i n the neighbourhood  used  data  t h e same  t h o s e i n t h e s t a n d a r d HF  an HF  shifted is  comparing  residual  refined  that  without  the s t e l l a r l i n e s .  data spectrum  shift  for a l l other  can  can a l s o  spectrum  w i l l give  numerically  One  these v e l o c i t i e s  line positions  the s t e l l a r  the  star.  profile  correction.  c o n t a m i n a t i o n s by by  velocities  over  t h e same s t a n d a r d  each  internally  of t h e same  spectrum  Dividing  s h o u l d use spectrum  Any  the s p e c t r a  stellar line  determine  be  purpose.  T h i s w i l l ensure  radial  between  difference  to  will  additional  data  one  as t h e c o m p a r i s o n  are  between  individual  fact,  criteria  f o r the  the be more be  imply a required  1 47  computation used  individual  spectrum  f o r e a c h HF l i n e - p o s i t i o n  different applied used  line.  to numerically lines  No used,  imperfect  line  a variety  line-profile Reticon  be  can a l s o  be  on  the  line-cancellation  technique  is  always  be  small  residuals  due  to  c a n c e l l a t i o n s . These r e s i d u a l s a r e caused  of  small  effects.  variations,  of  the  These  imperfect  serious limitations  nonzero-width  to  the contaminations  s p e c t r a , and i m p e r f e c t  t h e most  has  lines.  which  will  is  Moreover,  calculation  same t e c h n i q u e  minimise  by t h e HF  matter  there  The  cancellation  determination.  difference-technique  t o each  stellar  by  when  include  intrinsic  preprocessing  of  the  d i s p e r s i o n m a t c h . One  i s an e f f e c t  instrumental  caused  profile  by  of the  and  line  out  that  blendings.  the  Campbell  and W a l k e r  observed  spectrum  between  the  profile  I ( X ) . For  and  the  HF  intrinsic  symbol stellar  *  is  the  convolution  spectrum with  the  instrumental  [S(X)H(X)]*I(X). flat-fielding-type  spectrum  observed  respectively.  denotes c o n v o l u t i o n . with  stellar  H(X), the  H(X)*I(X),  spectrum  pointed  actually  the i n t r i n s i c  spectrum  S ( X ) * I ( X ) and  [1985] have  imposed  HF l i n e s  Consequently, division  line  technique  spectra The  Similarly,  S(X) are  operation  the  observed  would t h e n  be  cancellation  by  is  not  quite  correct i . e . * S(X)*I(X)  (4.1)  {[S(X)H(X)]*l(X)}/[S(X)*l(X)] * H(X)*I(X)  (4.2)  {[S(X)H(X)]*I(X)}/[H(X)*I(X)]  1 48 Equality there the of  in Equations  i s no  blending  4.1  between  4.2  the  these  conditions  lines  especially  for  stellar the  profile  w i d t h of  image s l i c e r  the  the  Reticon.  equality  contribute The  in  to  the  residual  strengths  is  between  linewidths, criteria  the  used  blendings also variations blended  of  with  velocity  of  Earth's  It  to  is  the the  orbital  by  Equations in  determine  line  of  the and  stellar ignore case HF  of  lines the the  is  l i n e s , the  slit  resolution  loss  that  the  and  relative HF  line  lines,  the  radial-velocity  stellar  as  the  lines will  apparent  with  the  of  line  type  the  line  not  since  one  stellar  stellar be  and  star.  any These to  dependent. HF  affected  radial  cancellation  by  critical  be  barycentric  rotation,  contamination  problem cannot  hence  cancellations.  apparent  Earth's  by  nullify  line  spectral  contamination  The  The  imperfect  more s e r i o u s l y  stars.  positions.  residual  e f f e c t of  HF  line  cause the  The  the  the  radial-velocity variations  r a d i a l v e l o c i t y and  attain.  and  intrinsic  be  either  positions,  changes  from  or  line  lines  motion,  lines  to  4.2  the  star. Different  star  red  and  stellar  relative  HF  if  projected  blendings  4.1  function the  the  the  line  residual  only  l i n e s blended with  and  change w i t h the  HF  impossible  f i x e d by  i s the  a  and  later-spectral-type  instrumental the  hold  n a r r o w . However,  i s almost  a l w a y s be  would  stellar  instrumental p r o f i l e i s very  There w i l l  of  and  line  residuals can  on  simply  l i n e s . In  the  residuals  on  ignored. There are  only  149 a  few  HF l i n e s  i n the  spectrum. Campbell  [1985] have s t u d i e d t h e p r o b l e m a more p a s s i v e the  effect  and n u m e r i c a l l y than  instrumental S(X),  order  compute  H(X)*I(X),  the  artificial  [S(X)H(X)]*I(X).  different  blending line  relative  i s not  position  stellar-HF  severe,  generated  corrections  are necessary  has  then  be  residuals. only  direct  in  S(X)*I(X),  ratio  line  correct  generated  The  spectrum constructed  p o s i t i o n s . I f the  c o r r e c t i o n to  any m e a s u r e d the observed  HF and  Generally,  these  i f one wants t o a c h i e v e  p r e c i s i o n of b e t t e r than  also studied the e f f e c t  adopted  Appropriate  spectra  c a n be made by c o m p a r i n g  artificially  velocity  can  Walker  of  I(X) are f i r s t  {[S(X)H(X)]*I(X)}/[S(X)*I(X)] for  method  deconvolution.  H ( X ) , and  and  They  s t a b l e method t o  obvious  profile  artificial to  the  in detail.  and  ± 2 0 m s " . Young  [1978]  1  of l i n e  shifts  a  due t o  line  blending. When one i s c o m p a r i n g observing  runs,  imperfect  s p e c t r a taken  that  I t h a s been the  stellar  some o b s e r v i n g  noticed lines  runs.  generally  difficult  comparison  between  stellar)  taken  different  c a n c e l l a t i o n s of the  l i n e s c a n a l s o be c a u s e d by c h a n g e s runs.  from  i n I ( X ) between  in spectra  may a p p e a r Correction  and  may  the standard  i n the d i f f e r e n t  stellar  o f t h e same more a s y m m e t r i c  for  have  this  to  effect  rely  spectra  (both  observing  runs.  on HF  the star in is the and  1 50 4.3.2.2 L i n e p o s i t i o n The  line  generally  i n standard  positions  spectra  i n the  determined  standard  by  the  spectra  are  criterion  of  intensity-weighted centre-of-gravity: x = ( I. I The  measured  line  x. ) / ( L. I ? )  n  position  intensity  corresponding  power  would  n  be  centre-of-gravity result  in  summation a  the  such  emission  lines.  considered  variations interested star,  limits  line  n=2  as  lines.  is  between  in  would  for may in  variable occur. the  the c r i t e r i o n  If  relative  one radial  and as  intensity-weighted it  by i t s  is utilised  stars  use  Equation  appear  position.  with each p o i n t weighted shape  line  rectified  that  e s t i m a t i o n of the l i n e  The  c o i n c i d e with  specified  absorption lines  of the l i n e  could  a b s o r p t i o n . To  is  where  is  a  I t c a n be of the  intensity.  a s compared  l i n e - p r o f i l e - f i t t i n g techniques. This  important  usual  profile  be c o n t i n u u m  criterion  The  and a l o n g - w a v e l e n g t h  i f these  to  the  to arc  line  x^.  s i m p l y a s t h e a r i t h m e t i c mean p o s i t i o n  profile  No t h e o r y  has  for  condition  The a d v a n t a g e o f t h e  centre-of-gravity  most  limit  definition  that  nonparametric  The  zero-percent  spectrum  one  i s the pixel  t h e whole l i n e  I t would be o p t i m a l  inverted  line  over line  line-position  4.3,  to  dispersion f i t  i s carried  of  and. 1^  the p o i n t or  equal  a better  the p o s i t i o n s the  to  criterion.  short-wavelength  limit.  i s x,  (4.3)  to  especially  line-profile  i s , however, velocities  o f how one would d e t e r m i n e  only of  the  the line  151 positions  i n the standard  spectrum  4.3.2.3 Use o f t h e d e r i v a t i v e The  main  weakness  centre-of-gravity This  i s not a s e r i o u s  as  the  HF  zero-percent  spectrum  absorption  however, would l i m i t stellar locate of  lines. line  be  digital choose  easily  etc.  positions  minimum o f  the f i r s t  derivative  Figures  4.1, 4.2, a n d 4.3  the  spectrum, the  HF  spectrum,  respectively.  that  positions  the  minimum  in  the  sharply  defined.  p Pup  to the  examining  the d e r i v a t i v e  profile,  the  line  profile,  of  the  t h e two  line limits  maximum  i n the  will  maximum  positions.  absorption.  t h e two l i m i t s  In f a c t  correspond  and are  line  The  pixel  by  simply  are obtained  also  of  derivative  spectrum. F o r a symmetric  limits  and  figures  profiles  of  to  t h e 38 E r i  the  positions  is  derivative  line  the  profile.  from t h e  to  they  from  the l i n e  The z e r o - c r o s s i n g s  for  p e r c e n t a g e of l i n e  that  maximum  spectrum, and  corresponding  positions  the  I t c a n be seen  i . e . "peak"  two  of  to  the p o s i t i o n s  approach  show t h e f i r s t  derivative  spectrum correspond absorption  with  f o r the  criterion  good e x c e p t  coinciding  nearly  limits  such as u s i n g  and p r a c t i c a l  lines  blendings,  unambiguously measured  d a t a . A more e a s y the  to place  are  line  of  found. L i n e  use a c o n s i s t e n t  Criteria  of  for isolated  positions  the a b i l i t y  and  intensity-weighted  problem  c a n be  absorption  profile  the requirement  where  should  limits.  50% l i n e  cannot  One  the  is  limits. in  of the l i n e  of  criterion  i s not important.  have for a  the  line same  Gaussian  to the p o s i t i o n s  1 52  Figure  4.1 The f i r s t  derivative  of  the HF  spectrum  15  1 55 defining the  the  a halfwidth  standard-deviation  profile.  Of  profile,  one  where m  i s greater  equivalent effect  course, can  in order  of  the  nearest  pixel,  two  one  s p e c t r u m . The  d e r i v a t i v e of  a  s p e c t r u m S(X)  first of the  /wT(a>). S i m i l a r l y ,  the  before  i t can  The not  the  sensitive  if  positions terms w i l l at  the  of  the of  to  ma,  line  would depth.  however,  wants  to  i n the  become  the  to  find  second  a spectrum  The  locate  numerically  the  the the the  derivative be  easily  Fourier Transform  method.  inverse  second  Transform  be  can  Fourier  Transform  derivative is  of  -CJ T(CJ). 2  s p e c t r u m may  have  the  For  simply low  t o be  s/n  smoothed  used.  most  to the  shown t h a t  result  be  method of  determination  has  the  derivative  line  i t s F o u r i e r T r a n s f o r m T(a>),  d e r i v a t i v e i s simply  data,  is  and  inverse Fourier  will,  can  using  m=v/(21n2)  line  the  more p r e c i s e l y t h a n  zero-crossings  computed n u m e r i c a l l y  Gaussian  corresponding  one  limits  where a i s  i n c l u d e more of  h a l f the  blendings If  profile,  f o r the  e.g.  at  corresponding  For  to  one  halfwidth  greater.  positions  line  limits  than  line  proportionally  the  parameter  choose  to the  of  of  intensity-weighted ideal  relative choice  for line  centre-of-gravity  very  positions.  of  line  limits.  e r r o r terms  will  be  limits  are  zero-percent  a l s o be  cancelled  not line  high  It is  introduced  chosen  quite  Fahlman  to  absorption.  i f both l i m i t s  p o s i t i o n s w h i c h have t h e  precision  [1982]  into  the  at  the  be The are  same p e r c e n t a g e of  error chosen line  1 56 a b s o r p t i o n . None achieved.  of  The  computational  line  even  sufficient  nonsymmetrical  line  desirable  of r e l a t i v e l i n e  sensitive  the  limits  but  estimation  accuracy  would  still  not  the  limits  The  further  t o use  preserve  general  determine  the  lines  probably  The  maximum  two  line  of t h e  finding  the is  by  Fahlman  the  mathematically  intuitively  the  of  the  Similar  of  line  technique two  to  spectral  between  the  position  between  A  technique  [1973].  difference  them.  In  fact,  function  is  t o f i n d i n g t h e maximum o f  the  function  (Fahlman  technique  f o r the  less  criterion.  is,  [1984]).  I t can  calculated  t o the c e n t r e - o f - g r a v i t y  The  however,  a t t r a c t i v e a s i t c a n be e x p r e s s e d  estimate  is  nonparametric  function  at-  Glaspey  least-squares minimisation.  error  which  difference-function  and  equivalent  difference-function  occur  f o r the  cross-correlation.  relative shift  minimum  cross-correlation  of  will  method  described  of  of  technique  between  technique  be  complicate the  the  cross-correlation  profiles  corresponding to similar  the  position  can  placement  and n o n p a r a m e t r i c  relative  easy  presence  p r o p e r t y of the c e n t r e - o f - g r a v i t y  most  is  an  a method  positions  i n the  easily between  is  4.3.2.4 The F a h l m a n - G l a s p e y d i f f e r e n c e The  be  sum  accuracy.  determination to  if  profiles will  p r o b l e m . I t i s more  can  to  limits  procedure,  with  conditions  necessity  non-integer-valued  defined  these  also  in  more terms  provide  relative line  an  shift.  method, t h e a c c u r a c y o f  157 a  line-shift  measurement w i t h  t e c h n i q u e depends on i.e.  the  amount  conclusion, of  the  the  of  This  difference-function  equivalent  width  information  however, does not  noise.  the  point  in  include  will  be  of  the any  the  line  line.  This  consideration  discussed  later  in  the  chapter. Basically, shifted and of  (displaced  subtracted s q u a r e s of  over  the  the  data  in pixel  from the  the  shift  of  of  the  s,  shift  corresponding  sum  D(s) The  term  the  data  The  the  minimum sum  of  values  the for s  [ A(X-)  generally  results.  Interpolation  spectrum  s h i f t e d by  easily shifted  accomplished  T r a n s f o r m of  the  the  residuals:  has  by  the  the  Fourier  i s simply  This  procedure  then  function of  the  (4.4)  2  i  in  to  amount. Shift the T(o>)  in  the the  non-integer  for high used  the  function  would produce  technique,  be  can  r e s i d u a l s . As  required to  each  difference  which  exp( io)s ) T ( w ) , where B(X).  ]  sum  for  value  at p i x e l  the  a non-integer  s p e c t r u m B(X+s)  T r a n s f o r m of  of  The  is a  on  intensity  squares  One  which  amounts  spectrum  computed  i  shift  various  spectrum.  cross-correlation are  is  - B(X +s)  minimum o f  optimal the  takes  by  numerically  difference  f u n c t i o n D(s)  s q u a r e s of  i s the  would g i v e  of  = I.  A(X^)  spectrum A(X).  case  of  i n the  profile  and  is  spectrum A(X).  line  formulate a d i f f e r e n c e  B(X)  position)  standard  residuals  particular  different  spectrum  precision produce  This  can  theorem.  a be The  inverse  Fourier  is  Fourier  the  i s equivalent  to  the  1 58 sine  interpolation.  shape  f o r both  where s  and B(X)  A(X)  Glaspey  h(\+s-s )  [1973] D(s)  assumption,  means  difference parabola  integer  carries  portion  corrected  to  functions. steps  This  fits,  approximations  near  the  f u n c t i o n s . The  position  found  by  numerically  derivative roots  is  of not  computation, and  apply  the  Generally, applied  the  shift.  The  0  the  Taylor  t h a t s~s  be  to  minimum  of  of  for fit.  values, o f  dispense  with  s  function very  good  difference  difference roots  to  Discrimimating  Conceivably,  are  difference  the  the  any  Generally,  the  t h e minimum  is  0  explicitly  however, a r e s t i l l  optimisation techniques  the d i f f e r e n c e  f i t to  the d i f f e r e n c e  polynomial  one c a n  s-s .  14 d i f f e r e n t  solving  a problem.  of  minimum o f  can  fits  about  minimum. The p a r a b o l a  order  sixth-order polynomials  better  pixel  when  o f t h e method.  i s u s i n g about  o f 0.05  this  always t r u e s i n c e  shifts  s/n HF d a t a ,  Fahlman  parabola  assumption  i s almost the  provide  is a  the optimal  0  under  polynomial  the a d d i t i o n a l  of  that  line  A(X-s ),  =  shift.  to the f i r s t  before a p p l i c a t i o n  the high  found  4.4  line  o p t i m a l and t h e  to  s m a l l . T h i s assumption  in  shown  second-order  corresponds  expansion  for  have  function i s  identical  would mean B(X)  i n Equation  a  of  relative  i s T a y l o r expanded  0  This  assumption  i s the i n t r i n s i c  0  and  An  with  is the the  increased  the polynomial f i t  to find  t h e minimum o f  function directly. the  to individual  difference lines.  function  The summation  technique in  is  Equation  159  4.4 If  i s best  t o be p e r f o r m e d  the l i n e  only  a  limits  partial  over  f o r the  line  summation  profile,  calculation  of a d i f f e r e n c e  summed o v e r  t h e whole p r o f i l e .  the  result  of  difference shift any  pure  position  other  relative  line  shift  accuracy  i n the placement  of  intrinsic  small  will  of  different  to that  residuals  from  4.4  i n Equation  contribution  for  Therefore,  consistent  criterion  sensitive  the l i n e  limits. i n the  whole l i n e  c o r e w o u l d be  the  profile  information  is  determination limits,  the  blendings.  limitations positions velocities.  on and  result.  more  effects In  of the  decreases  limits  the  Consequently,  the  hence  caused this  the accuracy hence  line  will  fact,  cases  c o r e . The s q u a r i n g  However,  acute  In  the  small  utilised, and  to  are usually  the  of  a  function. a  covering the  the more  more  velocity  more  accurate  the wider be  relative  work,  a d e q u a t e . Of c o u r s e ,  used,  will  line-cancellation line  is  or  difference  radial-velocity  to define  same  the c a l c u l a t e d  very  further  relative  this  t h e whole p r o f i l e  from t h e w i n g s t o t h e d i f f e r e n c e  Consequently,  of  shift,  be m i n i m a l a t t h e  residuals  the l i n e  the  are  spectrum a t the f a r wings of the l i n e compared  in  But i f t h e r e s i d u a l s  not  shifts,  result  over  that  summed o v e r  is  are defined  line-position  of t h e p r o f i l e .  profile.  than  should also  as t h a t  part  it  function  relative  function  t h e whole l i n e  the  the  line  imperfect  by i n c r e a s e d  stellar-HF  is  the  one  of  t h e measured  accuracy the l i n e  of  the  limits  for  major  HF  line  measured the  HF  160 lines  are usually  more r e s t r i c t e d t h a n  ones  used  the  for  measurements limits  in  corresponding o f maximum  generally  used.  the  centre-of-gravity  the standard  positions  Less  to  and minimum restrictive  case,  less  severe. For the s t e l l a r for  in  4.3.2.5 L i n e - p r o f i l e  l i m i t s may  lines,  of  of  be u s e d  the  profile the  variations  line  different function  profile. parts of the  criterion  to  in  The  to  variations.  than  limits  profile  type of p r o f i l e choose  also  be  will and  limits also  to  In t h i s by  displacement  of  be d i f f e r e n t  at  also  be  v a r i a t i o n s . Hence limits  p a r t i c u l a r part  The  produced  will  is  in  applied  4.4 a r e  line  technique  sample a  The l i n e  the  a  becomes  variations.  by p u r e  residuals  the  difference-function criterion  for  c a n be q u a n t i f i e d  Equation  rather  of  is  variations,  the l i n e  technique can  residuals  In  limits  used  measure t h e s e p s e u d o r a d i a l - v e l o c i t y v a r i a t i o n s . case,  for  line-position  are also  radial-velocity  function  is  effect  t h e same l i n e  line-profile  to define  relative  difference  the  technique.  important. L i n e - p r o f i l e v a r i a t i o n s terms  by  variations  case  criterion  line  the d e r i v a t i v e  centre-of-gravity  the d i f f e r e n c e - f u n c t i o n  consistent  s e t of  imperfect l i n e - c a n c e l l a t i o n  the  the  A  indicated  measurements i n t h e s t a n d a r d s p e c t r u m  In  line-position  b r o a d - s t e l l a r - l i n e spectra.  this  used  spectrum.  twice that  imposed HF l i n e s from the  the corresponding  for  essentially of t h e  determine  the  a  the the the  profile relative  161  contributions  toward  t h e measured p s e u d o r a d i a l  from  different  p a r t s of the p r o f i l e .  most  t y p e s of  profile  the  line  The  core a r e g r e a t e r than  measured  variations limits'  would  relative  then  be  coverage  line-profile  make  stars  a  or  comparison w i t h model  the  in  between  results  calculations,  narrow-line spectra  the  line  limits  as  maximum and minimum profile. be  to ensure  And  that  limits  t h e same  f o r t h e same hence  the s h i f t s to  i n the f i r s t  on  i s the  stellar main  are applied  line  and  by  "features"  different  limits.  with  without  or i s to  broader  with  of the  line  severity  choose  line  limits in  the  line  t o be t h o s e detail  and c r i t e r i a  a l l of the  r e a s o n why  in Equation  to the data  spectra  the standard spectrum A ( X ) .  line may  of  chosen  the  limits  This i s a computational line  to  the l i n e  coinciding  a r e always  of  complicated.  derivative  the  the  the  i s important  criterion  the p o s i t i o n s  the standard spectrum.  used  choose  the. a d o p t e d  depending  b l e n d i n g s . The l i n e on  to  For b r o a d - l i n e s p e c t r a ,  possible  the  from  i t  In g e n e r a l ,  variations,  the  where  would be even more  criterion  profile  wings.  for  core  cases  in near  on t h e shape and p h a s e  have a c o n s i s t e n t for  to  are characterised  moving a c r o s s t h e l i n e , To  amplitude  between  curve  variations  the v a r i a t i o n s  proportional  the e f f e c t s  radial-velocity  As f o r example,  those a t the l i n e  radial-velocity  wings. S i m i l a r l y , the  variations,  velocity  are  spectra. 4.4  B(X) and  that not  1 62 4.3.2.6 O p t i m i s i n g Besides shifts,  line-profile  there  contribute  difference function  are other  preprocessing, phenomenon  small  induced  differences  between  the to  should  a first  such  or that  approximation  One o f  corrected the  These the  of  i s limited  by  the only  accomplished  t h e two  depth or  effective  i s to formulate  and  from  accuracy  by n o r m a l i s i n g  t h e most  detector's  profiles.  s/n o f t h e s p e c t r a . T h i s c a n be  = S. [ ( A U j J - a )  term a  i s t h e mean  line  limits,  over  the  estimate  persistence  i n the  instrumental  removed  or  data  spectra  equivalent  yet  still  a modified  very  difference  E(s) :  E(s)  and b i s  line  limits.  - 0(B(X + s ) - i )  ]  i  of the spectrum  (4.5)  2  A(X) over  t h e mean o f t h e s p e c t r u m The  f o r the i n t r i n s i c  calculated is  the  be  procedures  function  could  rectification,  and B(X) t o have t h e same l i n e  simple  which  by i m p e r f e c t  dark c u r r e n t  continuum  function  width e t c .  The  caused  t o measure s p e c t r a l s h i f t s  finite  A(X)  effects  non-zero o f f s e t s  imperfect  difference  effects  presence of  response,  function  systematic  t o t h e r e s i d u a l s and t h e d i f f e r e n c e f u n c t i o n .  They a r e t h e v e r y  effects  v a r i a t i o n s and r a d i a l - v e l o c i t y  term  relative  as the p o s i t i o n of D ( s ) ' s  s' line  is  B(X+s')  the  shift  the  initial  s. 0  Iti s  minimum. The t e r m 0  a s c a l e f a c t o r t h a t w o u l d m i n i m i s e E ( s ' ) . An a n a l y t i c  expression  for  0  can  be d e r i v e d  9E(s,/3)/3/J  = 0 a t s = s' . One o b t a i n s :  0 = [ I . A U . j B U . + s ' ) - nab ] /  from  the  condition  163  [  Z^BU.+s' ) LiA(Xi)  E(s)  D(j)  -  2  -  2/3(fl-/3i)EiB(Xi +5 ) + -  4.7  Equations  4 . 6 and 4 . 5 ,  rewritten  it  c a n be  The  is two  The  s'  the  than  E(s),  This  such  different  than  are  function  A(X) then  over  except  b, o r /3 n o t c l o s e of  D{s)  applying of  5 / .  lines  E(s)  a  scale This  function.  be an In  is  to the  B(X+s).  improved  fact,  E(s") the  i n c a s e s where  the  a  t o o n e . Of  with  more  between  i . e .  the consequences for  t h e need  and B(X+s)  s", w o u l d  large  that  information  avoids  The d i f f e r e n c e s  small  E(s)  and c a l c u l a t i n g  depth  shift  D(s').  corrections  aware  form  in minimising the difference  are usually  than  and  to  The f u n c t i o n  difference  line  for the optimal  be  D(s).  t o B(X)  offset  of minimal  less  from  limits.  equivalent  same b a s i c  of a d j u s t i n g  required  rather  respectively.  shifts  or  modify  position  should  the l i n e  are mathematically  modified  results  values  over  the  value  always  points  from  to  estimate  of  constructed  the result  procedure  (4.8)  computational  additional  same mean  2  easy  to  basically  (4.7)  n(a-pb)  i n a more  in obtaining  residuals.  02I.B(X.+s)2  2ZiA(Xi)B(Xi+^)  and 4 . 8  computed apply  +  ZiB(Xi+^)2  Equations  factor  2(a-/36)L.A(Xi)  n i s t h e number  is  ( 4 . 6 )  2/3ZiA(Xi)B(Xi+5)  L.A(X.)2  term  ]  2  -  + The  - nb  2  being  quite  course,  in applying intrinsic  one E(s)  profile  164  variations. 4.3.2.7  Error  The the  minimum o f  minimal  effect  estimation  mean  of noise  square  present  noise-free  data,  zero.  will  This  the d i f f e r e n c e  the  in  happen  s =  s".  function  can p r o v i d e  measured  relative  The  a measure o f  shift.  function  the  minimum v a l u e  Fahlman  under  is  of  would  be  correlated  r e s i d u a l goes of the  [1984]  to  difference  the accuracy  t h e minimum o f t h e d i f f e r e n c e  the  In t h e c a s e  i f the noise that  represents  possible  the spectra.  B(X) s u c h  zero at  that  residual  minimum o f t h e  also  between A ( X ) and  function  in  the  has p o i n t e d  function  follows  out a x2 v  distribution of E(s)  case  v .= 2 ( « ~ 1 )  with  or other  d e g r e e s o f f r e e d o m . In  modified  number o f d e g r e e s o f f r e e d o m  difference  functions, the  would be d e c r e a s e d  number o f a d d i t i o n a l e s t i m a t e d p a r a m e t e r s e.g.  a, b,  and /3. S i n c e  true  shift  s, 0  E(s")  With  f o r equivalence  can  be e v a l u a t e d  and  the  standard deviation a  This  implies  that  minimal d i f f e r e n c e standard the  shape  deviation of the  =  i s only  i s also  minimal d i f f e r e n c e . 68.3%  s"  an  to that  the  estimate  f o r the  f o r the  interval,  true e.g.  one s t a n d a r d d e v i a t i o n ,  one c a n t h e n  v  by  i n the formula  an e s t i m a t e  a confidence  the  g e t an e s t i m a t e  x2  for  a of E ( s " ) : Ejis")  there  /  x2  (4.9)  i s a 6 8 . 3 % chance t h a t  would l i e  within  a  c a n t h e n be t r a n s l a t e d difference  function  the  true  of E ( s " ) .  This  directly  from  into a  standard  1 65  deviation a  f o r t h e measured o p t i m a l  standard  velocity. minimum  The  f o r the  reciprocal  should  effective very  deviation  also  s/n o f t h e  small,  then  of  shift  measured the  provide  s/n  hence,  relative  radial  difference  an  for  the  in A ( X )  noise  B ( X ) is  of  function  estimate  s p e c t r a . I f the  the  s " , and  is  essentially  b/ySEis").  4.3.2.8 D i s p e r s i o n The from  absolute  line  position  i s then  line  line  position  with  by  dispersion  higher-  thirdor  small  lines.  order  line  shifts  lower-order This  is  polynomial  number o f HF l i n e s  weighted dispersion  by  the  fit.  spectrum.  The  of  imperfect  blendings To  measurement,  their  wavelengths  square  induced  polynomials  imposed by t h e  f i t  i s not  The  HF  be  the  absolute by  the  collisions. a r e used fact  feasible  that  i t s line  depth  F o r c o n s i s t e n c y , t h e same w e i g h t  to a  f o r the  i n the spectrum. Each l i n e of  the  polynomial  f i t would  molecular  and  translate  w a v e l e n g t h s c o r r e c t e d f o r any  differential  t h e HF  the  calibration.  dispersion  temperatureand pressure-dependent  fit  to  be c a l c u l a t e d . A  positions against  i n the  adopted absolute  Generally,  line  a wavelength  derived  respect  f o r the e f f e c t  has t o  the  wavelengths used  or  with  the standard  caused  into  relation  provide  on  c a n be  the instrumental p r o f i l e .  t o t h e HF l i n e  would  shift  corrected  position  dispersion  o f any l i n e  line  cancellations  convolution  fit  position  i t s relative  absolute  the  relation  in  is the  i s used  1 66 for  the  choice  same l i n e of  Fahlman  the  i n a l l of  weighting  [1984] t o be  the  difference  the  detailed  spectrum  be  from  The  stellar that  line.  deviation  of  of  50ms"  f o r the  1  the  s p e c t r u m and  l i n e s in  by  about  10  the the  to  shift  order  of  the  corresponds  HF  to  be  mean  dispersion  evaluated  at  any  observed wavelength spectrum are  25  a  velocities.  i t can  to give  HF  Without  f i t of  f i t i s b a s i c a l l y the  position  from each o t h e r  This  by  minimising  reference-wavelength  Coude.  CFHT  shown  m u l t i - l i n e case.  the  The  particular  been  in a dispersion  f o r the line  has  achieved  dispersion  relation  f o r the  standard  standard deviation  The  a d i r e c t c o n s e q u e n c e of  function  a  spectra.  function  l i n e - p o s i t i o n or  corrections, 0.0015A can  the  of  separated  a n g s t r o m s . Hence  only  the  l o w - f r e q u e n c y components o f  the  dispersion  relation  are  c a l i b r a t e d by  High-frequency  structure  may  still  structure  be  the  present  could  be  the  s p e c t r o g r a p h as  the  Reticon  photometric w o u l d be  dispersion  r e s u l t of  well  as  i r r e g u l a r spacing  response across  manifested  as  velocity  p r e c i s i o n of  high-frequency  each  an  dispersion'  very-high-precision  1  accuracy can  relation  of  the  in  the  the  spacings a  w a v e l e n g t h s have  to  more be  between  For  Hence i f  cause a d i f f e r e n c e  r e s u l t s can  within  photodiode  centres.  ±3x10""A.  of  This  shape o f  individual  optical  ±l0ms" ,  structure  i n the  differences  photodiode's  measured t o  relation.  optical effects  photodiodes. Differences  each  mean  lines.  i n the  the  between  be  HF  than  affected.  from  the the  ± 3 x 1 0 " "A,  167  To  decrease  structure is  the  in relative  always a l i g n e d  positions  on  effects  of  the  radial-velocity  such that  the R e t i c o n  work, t h e  array  i . e . having  spectral  region  at  dispersion  relation  c a n be  i m p r o v e d by  lines  stellar  wavelengths  the  same  into  are the shift  iterative  procedure  dispersion  relation  achieve  internal  applied  to variable  different account  line  particular be  zero.  inversely  This  residual is  at  each  terms  from  the  correcting  the zeroth-order  at  the p a r t i c u l a r  in  t h e spectrum, t h e r e would And N  t h e n be  evaluated  observed  stellar  by  for line  the  i n order to  t h i s cannot  mean term  such  Hence  zero  weight  from  that  then  is the  fits  but  residual lines  dispersion  stellar line. would  the  a l l  w a v e l e n g t h measurements  wavelength  the  relation  f o r N HF  be N d i f f e r e n t  a particular  the  t h e HF l i n e  dispersion to give  into  in  i s to  dispersion  of  be  l i n e s c a n have  retaining  HF l i n e p o s i t i o n .  different  an  between  structure  line  the p o s i t i o n  high-order  relations.  HF  accomplished  with  Hence  i t s separation  stellar line. A different for  the  ad hoc way t o t a k e  a stellar line  with  including  velocity  intermediate-frequency  generated  wavelength  used  where d i f f e r e n t  of  mean  wavelengths  c o n s i s t e n c y . Of c o u r s e ,  wavelength c a l c u l a t i o n  can  be  and t h e d e r i v e d  stars  The  a l l lines.  v e l o c i t i e s . One s i m p l e the  e a c h HF  apparent  to  same  f i t . In t h i s c a s e , t h e  for  has  the  a l l times.  the d i s p e r s i o n  velocity  Reticon  t h e HF l i n e s a r e a t t h e same  identical  stellar  high-frequency  be  can The the  1  68  weighted average ot these N wavelengths. Each weight is inversely proportional to the separation between the particular HF line and the stellar line as well as directly proportional to the square of the HF line depth. Generally, the result of this weighted wavelength is different by about several metres per second in velocity from those obtained directly through the mean dispersion relation. Campbell et a l . [1981] have studied in detail the high-frequency structure of the dispersion relation. A Fabry-Perot etalon was used to impose a fringe pattern on incandescent lamp spectra. The fringes are about one angstrom apart and their relative wavelengths can be derived from their order numbers. These can then be compared to those calculated from the mean dispersion relation which was derived from the HF lines. By tilting the Fabry-Perot etalon, the fringes can be made to move along the Reticon array. This enables the relative wavelengths at different pixel positions to be calculated. The high-frequency structure in the dispersion relation can be examined by calculating the residuals AX between the mean dispersion relation wavelengths and the Fabry-Perot wavelengths. Campbell et a l . [1981] found high-frequency structure with AX ranging between ±0.001$ and ±0.002A . This is larger than the point-to-point scatter for AX of about ±0.00012A which could be caused by the errors in the fringe wavelengths. A single structure is generally greater h  >  169 than  100  pixels  constant  within  between  nights.  Fabry-Perot  in width. the  I t s shape a l s o a p p e a r s  same o b s e r v i n g  Consequently,  fringe  patterns  h i g h - f r e q u e n c y components This  would  provide  wavelengths  a c c u r a c y of  Campbell  [1984] has  relative  radial-velocity  can  improve  4.3.3  only  lines  found work,  that  the  nightly  the  relation.  AX  to  the  relation.  necessary  better  the v e l o c i t y  the  unless  one  than  120ms" .  In  for  low-amplitude  1  the n i g h t l y precision  t h e most solar  of  these  recently  line  line  has  to  lines.  For  solar-type  by  for  lists  one  measured  list  Identifications solar  measured wavelengths  into velocities,  wavelengths  second  these  corrections  by a b o u t  1ms" .  of  stellar  1  lines  standard  air  pressure  of  refractive  and can  be  f o r other  c a t a l o g u e by  exclusively  i.e.  index  a r e t h o s e on  found  lines  wavelengths  at a  temperature  torrs. over  The  smooth  temperature  and  in  S t . John  the  [1973]. earlier et  al.  are referenced  in  Phelps  [1982].  It  lines  and  f o r HF  refractive  of  rest  spectra,  Breckinridge  which are d e f i n e d with the  760  stellar  by Moore e t a l . [1966] and  t o use  the  know t h e e f f e c t i v e  wavelengths  lines  M.I.T. w a v e l e n g t h  adequate  stellar  rest  Pierce  [ 1 9 2 8 ] . Most w a v e l e n g t h s  is  not  varies  E F F E C T I V E REST WAVELENGTHS To c o n v e r t  the  terms  be  use  t h e mean d i s p e r s i o n  is  fact,  can  dispersion  correction  are generally  a t an  but  to c a l i b r a t e  These c o r r e c t i o n s aiming  one  of the  d e r i v e d from  night  to  15°C  change air  and  index  of  an  air  the  air  pressure  are  in  1 70 implicitly  corrected  wavelengths are constant  can  f i t when  consistently.  Basically,  used  refractive  coefficients  i n the d i s p e r s i o n  index  of the  fitted  use s t a n d a r d - a i r  than  at  atmosphere.  For  line,  a  given  particular  criteria  spectral  the  standard  and  then adopt  effective  several to  dispersion  the  rest  derived  i t may n o t be  onto a s t e l l a r radial-velocity  interested  standard  the  positions  and  these  effective  wavelengths as long  are  for  same  In  in be  velocities  i s c a l i b r a t e d by high  may  precision,  show  velocity  however, one i s o n l y  i s not dependent  a s t h e same c o n s i s t e n t  star.  the  technique.  r a d i a l v e l o c i t i e s . The  relative velocities  out  cannot  i n t h e HF  stars  on  wavelengths  wavelengths as  With the  standard  dependent.  positions  rest  to place  stars.  wavelength  velocities  a l l applications,  i n the r e l a t i v e  the  include  the l i n e  r a d i a l - v e l o c i t y system which  In almost  the derived  one  line  possible  possible  IAU r a d i a l - v e l o c i t y  variations.  wavelength that  s t a r . As p o i n t e d  absolute  from less  the catalogue  down t o t h e p r e c i s i o n  Moreover,  used  are far  and d i s p e r s i o n  f o r that  one  60%  least-squares-fitted  wavelengths the  measure  f i t to  a l l the  applications  f a c t o r s . These  resolution,  spectrum using  one,  accurate  of  all  l i n e s . Hence, t h e e f f e c t i v e  type,  One c a n p e r f o r m a  even  i n almost  the e f f e c t i v e  used  b l e n d i n g s w i t h weaker  Chapter  in  almost  r e l a t i o n . Hence  the observatories  one s t a n d a r d  also  included  an  e . g . a i r p r e s s u r e a t CFHT i s a l w a y s a b o u t  s h o u l d a d o p t d e p e n d s on  is  is  dispersion  wavelengths  even when t h e c o n d i t i o n s standard  factor  standard-air  some  stellar  accuracy on  the  values spectra,  171 different this  stellar  lines  may have  different  case,  one i s i n t e r e s t e d  i n the r e l a t i v e  variations  i n the i n d i v i d u a l  stellar  velocities.  In  radial-velocity  lines.  4.3.4 BARYCENTRIC CORRECTIONS Before any  one c a n make u s e  application,  barycentric observer's  one  has t o  velocities. motion  with  times  of the observed that  barycentre  observer's  the  solar  with  i . e . to  heliocentric  velocity  would  planets  A  c o r r e c t i o n s has  become  important  13ms  i s convenient  -1  system  (Gordon  to perform  calculations  system, a s t a r  apply  in  with  right  the  frame o f and  calculate by  Gordon  20ms .  With  - 1  for  long-term  can cause a  velocity  [1976]). most  the  (or d i r e c t i o n  to  of  t h e p e r t u r b a t i o n s by  especially  of about  the  velocities  of about  variation  coordinate  only  been g i v e n  o f t h e HF t e c h n i q u e ,  i.e.  reached  program  The p l a n e t a r y p e r t u r b a t i o n s  position  topocentric  the barycentre  heliocentric  computer  the  involves correcting  techniques  projects.  It  have  respect to  an a b s o l u t e a c c u r a c y  the h i g h p r e c i s i o n the  the  b a r y c e n t r i c date  system. T h i s  with  obtain  dates.  I t has  convert  of  r e s p e c t t o t h e Sun a s t h e v e l o c i t y  heliocentric  [1976].  starlight  position  the barycentre  into  system. C o n v e n t i o n a l  corrections reference  f o r the  one s h o u l d  of the the s o l a r  the  involves correcting to  them  in  observed  velocities  the  velocities into  respect  system. S i m i l a r l y ,  time  convert  This  solar  the  of the observed  of the v e l o c i t y  equatorial  c o s i n e s ) . In t h i s  ascension  and  rectangular coordinate  a and d e c l i n a t i o n  5 will  1 72  have t h e d i r e c t i o n c o s i n e s  If  and (  V  X  component  v = sina cos5  (4.11)  w = sin6  (4.12)  barycentric  V  V  Z  K  respectively,  contribution  = - ( uV  + vV  V  = -M  sina  +  cos5  cosa  sin6  - V  x x  V  fi  = -V  V  fc  = •( V  o  V  and v e l o c i t y  the star  and  a  will  x  2  + v  line  + >vV y  have  a  tangential-velocity  2  )  (4.13)  z  (4.14) sina  y  sin5  + V  cos6  z  (4.15)  )  (4.16)  of wavelength  X will  be D o p p l e r  shifted  by  v e l o c i t i e s t o X': (X/X') = • ( 1 - V / c 2  V  = V  2  2  + V  x  + V  2  y  2  ) / ( 1 + V^/c )  (4.17) (4.18)  2  z  V ' = - ( u ' V + v ' V + w ' V ) r x y z  (4.19)  ii'  = u + ( 1/c) ( V + u V ) + ( 1 /2c ) ( K « + V V )  (4.20)  v'  = v + (1/c)(V  (4.21)  2  x  r  — 2V  2  — V  The  V^. i n  r  rather  (4.22)  2  z  4.23 a r e  Equations  v e l o c i t y and i n c l u d e s  of V  + (1/2c )(Kw+V V ) r  (4.23)  4.17 t h r o u g h  radial  r  r  2  Equations term  r  2  r  z  K  J C  + v V ) + ( 1 / 2 C ) (icv+VV )  w' = w + ( 1 / c ) ( V + w V )  use  are  fc  V„ r Q  coordinate  V :  A spectral the  (4.10)  ' ^'  radial-velocity  t  u = cosa cos5  the observer's  (x,y,z)  (u,v w):  taken  4.17 a n d the  from Stumpff 4.19 i s  the  [1979]. apparent  e f f e c t of a b e r r a t i o n .  t h a n V£, i n E q u a t i o n  4.17 w o u l d  introduce  The an  1 73  error  in  AX/X  contribution Stumpff  of from  [1979]  up V  10~ . also  pointed  in high-precision  barycentric  velocity  velocity  the  Earth's  The  vector  and  (T^,T  V W ,T^) The  simultaneous  by  is  observer's  the  barycentric  v e l o c i t y due  well  to  to  are  Heliocentric  given to a  given  in  the  r e s u l t s generated  by  the  z  JPL  DE200.  equations  y  a  z  n  d  the  order  for  and  to  the  of  correction  At  is  =  ( 1/c  of  minor has  JPL  barycentric are  the  planets.  method  42cms"  of.  been  has  been  DE96.  The  for  the  1  coordinates.  also  calculated  [1980].  the  added  performs  motion  (x,y,z)  coordinates  i n Stumpff  be  It  ephemeris program  time  common o r i g i n  has  diurnal  of  reduce  correction  At  are  ,E )  p r i n c i p a l and  X  earlier  velocities  to  the  velocity the  (V >V >V )  5  order  the  2 4 )  of  (E^E  the  4.6X10" AU  program  starlight  of  -  velocity  [1977,1979,1980]. T h i s  errors and  of  calculate  Stumpff  velocities  as  ( 4  rotation  program  i n t e g r a t i o n of  maximum  The  both  observer's  diurnal  ephemeris  an  In  of  4.17.  contribution  Earth's barycentric  A l m a n a c . They a r e  against  the  the  d a i l y values  Moon a s  algorithm  the  compared  by  this  m e a s u r e m e n t s . The  i s the  z  is  relativistic  and  ,E )  x  Astronomical  given  Equation  - ( V V V V V V  (E ,E  telescope.  An  and  in  Doppler  rotation: (  Sun  that  i s composed  Earth  second-order  included  out  significant  of  The  8  is  fc  has  to  at to  of the  the  reception barycentre,  observed  of  the  a  time  time.  This  simply: )  ( ux  +  vy  + wz  rotational velocity  of  )  (4.25) the  telescope  can  be  174 calculated  from the f i g u r e  C = 1 / •( cos ^ 2  T = T T T where  (  -T  x  T  y  )  27r/p  of the E a r t h :  + (1-f)  sin 4>  2  )  2  (4.26) (4.27)  ( aC + h ) costf>  sinty  (4.28) (4.29)  COSty  0  z  (4.30)  a = e q u a t o r i a l radius of the Earth f = flattening  factor  f o r the E a r t h  p = sidereal  rotation  p e r i o d of the E a r t h  <p = g e o d e t i c  latitude  of the observatory  h = e l e v a t i o n of the observatory ty = l o c a l Equation enables latitude  mean s i d e r e a l  4.26 i s t a k e n  from G u r n e t t e  t h e use of g e o d e t i c i n Equation found  and  Boksenberg  [1984].  adopted v a l u e s  for a l l  latitude  It  4.10  through  if  heliocentric  from S t u m p f f  the  precision  [1980] i s  velocity  appropriate pointed  calculate  Almanac by  Vohden  t h e I.A.U.  newly  constants used  and t i m e c o r r e c t i o n s  velocities  and  positions  i n the equations.  Although  derived  to  4.30 c a n a l s o be  velocities  It  geocentric  the relevant astronomical  radial  used  formulae  also contains  to obtain h e l i o c e n t i c  are  [1974],  r a t h e r than  i n the Astronomical  a and f . E q u a t i o n s  the corresponding  and W o o l l e y  4.27. The l a t e s t  p and ty c a n be  e.g.  time  the  calculated  final  (E^,E^,E ) z  precision  i n the  c o r r e c t i o n s d e p e n d s v e r y much on t h e u s e o f  stellar  out that  high,  i n the  coordinates  the E-terms  (a,5).  Stumpff  of a b e r r a t i o n  [1980]  must  first  has be  1 75 removed the  from the  aberration  orbit  stellar  terms  be  formula  Boksenberg be  on  old  old  applied  be  are and  Vohden and  taken  from  the  new  applied  also  proper motions t o the  new  Boksenberg  course,  i f the  new  FK5  possible  The  p o s i t i o n s should the  precession,  [ 1 9 8 4 ] . Of  s o u r c e of be  referenced  calculated the  velocity  accordingly.  have been  applied  positions,  the  (Ex,E  to  produce  if  true  old  1950  be  [1979] has choice  found  pointed  of  (a,5).  same e q u a t o r  (a,6)  is  equator be  and  corrected  should  nutation  same c o r r e c t i o n s must a l s o  components.  the  are  components  Similarly,  precession  proper motions  to the If  proper  will  i n the  ,Ez).  on  corrections  Stumpff  error  are  based  the  s y s t e m can  p o s i t i o n s and  catalogue.  be  2000  convert  also  subsequent  to  equinox  and  motions  any  Corrections  to  catalogue.  should  proper  constants,  Formulae  However,  i n Vohden  proper motion  new  Earth's  fundamental  2000 FK5  i s given  on  elliptical  the  p o s i t i o n s must  i f the  the  catalogue.  equinox  of  effect  These  in  FK4  E-terms  constants.  another  velocity  the  used.  from the  precessed  the  I f the  to  out  for  in  the  of  [1984]). present  effect  made  necessary  e q u i n o x as  ellipticity  precession  precession  positions  be  always  (a,6).  the  constants  not  the  remove t h e  in  m o t i o n s must  in  are  [ 1 9 8 4 ] . The  precession the  to  E-terms c o r r e c t  Boksenberg  absent  included  based  and  by  p o s i t i o n s which are  they w i l l The  caused  (Vohden  aberration  p o s i t i o n . The  also  be  corrections and  applied  equinox to  the  1 76 4.4. SIMULATION  4.4.1  STUDIES  BASIC APPROACH The  precision  d e p e n d s on spectrum, noise  many  of  events.  effects  Artificial  These  the  with  can  apply  then  measure t h e intrinsic accuracy  4.4.2  One  include  i s through  the  of  the  the measurent  and  can  on  these  be  line  the (when  the e f f e c t  be  simulation. numerically One  procedures  spectra. line  of the  i n c l u d e d or e x c l u d e d .  artificial can  of  to study  data-reduction  position  position  the  of n u m e r i c a l  spectra  various  s/n  s i m p l e s t ways  the v a r i o u s e f f e c t s  line  of  line  of  effects,  t h e use  measurement  the  l i n e , the width  of t h e  absorption  generated  is  to  Since  the  known,  the  assessed.  NOISE GENERATION The  spectra  two  o f n o i s e t o be  readout  n o i s e of  n o i s e . The  readout  noise  pixel  are  types the  pixels  i n the can  be  a Standard  s p e c t r u m . The obtained  350e".  The  distribution. Standard The  through  i s taken  photon  noise  However,  as  Normal d i s t r i b u t i o n mean v a l u e  of  i n c l u d e d i n the t h e R e t i c o n and  would a f f e c t  amount of  Normal p r o b a b i l i t y  the d i s t r i b u t i o n  used.  line-position  is included), line-blending  various  of  stellar  factors.  the depth  cosmic-ray  shot  of  noise  a random-number  t o be  the  The  follow  a computational  f o r each  mean  a  with value  n o i s e of Poisson  convenience,  random-number g e n e r a t o r  this distribution  the  generator  t h e mean r e a d o u t  should  photon  equally a l l  readout  distribution.  artificial  i s the  a  is also  square  root  1 77 of  the  This  amount of  is  large  detected  actually a  that  should  approach the  Gaussian  the  line  simplicity, in  this  are  level  as  by  simplicity,  more r e a l i s t i c  over  4.4.3  line  mean o f  can  taken  is applied  positions  This  the  use  artificial  data  and  into  the  have t h e  same  spectra.  Each  of  noise mean  of  in a l l cases.  been assumed t o  For have  response. For  spectra,  i n t o account  ARTIFICIAL  line  same s i g n a l l e v e l  has  the  spectra  the by  overlapping  a  non-zero  integrating trapezoidal  individual pixel.  t o measure t h e  A different  lamp  effect  i s used  For  considered  b a s e l i n e s . The  Reticon  with  the  THE  of  be  profile  is  stellar the  eight  spectra  simulation  method w h i c h  technique.  line  a delta-function-type  f u n c t i o n of  involves  the  individual pixel  hence  simulation.  lamp s p e c t r a  contains  flat-field  REDUCTION OF The  f o r the  flat-field  of  theorem  distribution  same manner f o r d i v i s i o n  spectrum the  Limit  the  f o r l a r g e numbers. A  absorption  continuum  each p i x e l  the  response  the  each  w i d t h and  w i d t h of  i n the  using  generated  isolated  pixel.  considering  probability  been u s e d  s p e c t r u m . The  line  reduction  any)  study. A r t i f i c i a l  line  generated  zero  an  a l s o generated  signal  (or  has  particular  Central  Normal d i s t r i b u t i o n  shape  only  the  good a s s u m p t i o n p h o t o n s . The  Poisson  initial  absorption  four  very  number of d e t e c t e d  states  photons at  of  t o the  on  the  real  spectra  these a r t i f i c i a l Fahlman-Glaspey  artificial other  SPECTRA  standard  spectra. difference  spectrum of  a t t r i b u t e s i s generated  s p e c t r u m . The  standard  i s used  spectrum,  for  the each  however,  178 has  the  line  the  data  spectrum  continuum function shift  centred at p i x e l is pixel  rectified  between  4.4  them.  The  the  derivative  the  standard  limits  also  standard-deviation At  least  five  five  estimation values  the  measure of t h e The error of  did  the  intrinsic  d e r i v e d by  predicted  error 4.9  The  of  ones first  case, 6  the  is  line  used  the  standard  value  can  the  profile.  to  shift  produce in  each  d e v i a t i o n of  these  -1.3535 w o u l d  also  lie  l i e almost  the  used  on  error  the  give  'a  In  exactly  over  technique.  Out  these error  24  cases bounds  cases,  at the boundary of the e r r o r  92%  estimate  u s u a l one-o  the  of  the  another  to study  Fahlman-Glaspey  i n 27  outside  bounds. T h e r e f o r e ,  r a t h e r than  of  spectra, only  4.9.  i s good  be  the Fahlman-Glaspey  shifts  i m p l i e s t h a t the  level,  of  relative  the  where  spectra are  are  the  in  the Gaussian  in  difference  In t h i s  ±5,  applications  Equation  shifts  Equation  spectra  are  minimum  to  of  these  used  profile.  measurements  intrinsic by  two  position  accuracy.  intrinsic  This  of  the a r t i f i c i a l  predicted  by  parameter  independent  method on  and  line  simulation t r i a l s  estimate  636  maximum  of t h e a c c u r a c y .  from  line  unoptimised  limits  correspond  pairs  independent  . the  line  to  line  the  i s a p p l i e d t o measure t h e  corresponding of  while  151.3535. The  before  in Equation  150  estimate  of a l l  the given  applications.  g i v e s a 2a  level.  the  confidence  179 4.4.4  THE The  effect  varying other can  the  of  S/N s/n  signal  on  level  the of  parameters constant.  be  their The  EFFECT OF  error  a  deviation  Figure  i s in  m e a s u r e m e n t s . The 0.4  with  of  used  respect  a" The  linear  a  relation  error  is  error  here  term  (  in  deviation  is  the  simulation  in s/n.  standard line-shift  has  a depth  of  line  all  spectra  plotted against  1  by  1.  of The  is 4 pixels.  The  gives:  (s/n)  -1.71  (4.31)  unexpected. Campbell  a relation  i s simply  standard  the  which s t a t e s t h a t  inversely proportional  zeroth-order would  i s not  keeping  generated  continuum  5 of  plot  = 0.1306  1  [1979] have g i v e n  the  the  examined  independent  i n the  to  f i t of  the  six  standard-deviation-halfwidth straight-line  of  be  while  p i x e l s and  from  line  s/n  shows a "  unit  can  spectra  from  4.4  calculated  the  The  measured d i r e c t l y continua.  accuracy  a x  to the  c  Equation  s/n.  x dispersion  4.31  i s nearly  and  Walker  the  velocity  The  velocity  ) /  X. . The  zero  as  one  expect.  4.4.5  THE The  Figure  EFFECT OF effect  4.5  depths are  of  line  where a " in  LINE DEPTH  1  d e p t h on  Each  f r a c t i o n s of  point  on  the  i n d e p e n d e n t measurements linear  f i t of  the  accuracy  i s plotted against the  standard-deviation-halfwidth 1350.  the  plot  of  gives:  d e p t h . The  c o n t i n u u m . The 4 p i x e l s and  graph of  line  i s examined  the  is  the  relative  a  line s/n  result line  of of  in  line  has  a  about five  shift.  A  180 Figure  4.4 The e f f e c t  O CD  of  s/n  on  CD Ul C\J  accuracy  CD CD —.  (,I3XTd) D t  gure  4.5  The e f f e c t  of  ( .I3Xjd) t  line  D  x  d e p t h on a c c u r a c y  1 82  a" This  relation  [1979]  4.4.6  i s again  have  velocity  Figure  given  e r r o r and  THE The  = 457.7  1  not  an  of  4.6  where  equivalent  of  w i d t h of  l i n e w i d t h on a  pixels about  line  and  line  1350.  The  preserve - extremal  the  result  of  of  points  the  trend  expect  included that  line  i n each  (±6)  limits  of  within  shows  keeping  the  spectrum  the  equivalent  the  with  5 being  The  case s/n  i n the  is  varied  to  positions  at  i n each case are choosing  the  4  spectra  in Figure  4.6  is  the  m e a s u r e m e n t s . The  a  - 0.00185 + 0.0091  2  and  8 is  the  line  line  fit  readout  number of p i x e l s .  The  the  noise  would  would  when more p i x e l s  more n o i s e  has  the  are  the  fact  (readout  equivalent  been  increase  photon n o i s e ,  One  i s b e c a u s e of  while  line  (4.33)  unexpected.  This  w o u l d add  measurement  c o n t e n t ) of  not  increase  limits.  each a d d i t i o n a l p i x e l  amount of  4.6  such t h a t  line-shift  v e l o c i t y e r r o r to  (information  as  depth  the  gives:  photon) t o the  The  The  line  independent  Figure but  same  in  against  linewidth  0.4.  between  the  the  i s examined  line.  d e r i v a t i v e . Each p o i n t  five  between  the  depth being  a = 0.000386 The  the  i s adjusted  i s the  accuracy plotted  6 of  same c r i t e r i o n  first  the  is  changing  linewidth  the  relationship  Walker  depth.  width constant.  of d i f f e r e n t  (4.32)  LINEWIDTH  effect  effect  10.1  u n e x p e c t e d . C a m p b e l l and  standard-deviation-halfwidth the  depth) -  inverse  line  EFFECT OF  (line  kept  linearly  however, would  and  width  constant. with  the  increase  183  Figure  4 . 6 The e f f e c t  of  linewidth  (|3XTd)  D  on  accuracy  184 faster  than  mainly  b e c a u s e of  the  as  linewidth  increases  the  pixel  also  linearly  the  4.7  fact  that  shows  s/n.  A  and  preprocessing equivalent  the  readout  equal  the  of  the  noise  of  4.7  This  becomes  is  shallower  photon n o i s e  data.  A  350e~  at  each  also  been  mode of  signal  i s used  are  used  the  CFHT  the eight  in  factor  used. T h i s  (in  in  assumes t h a t  conversion  a d c u has  high-gain  between  lamps  of a l i n e  detected  performed  of  the  the  of  factor  250 is  1872-Reticon.  shape w i t h photons per detected  one  halfwidth  of  halfwidth  in  consider depth  at  the  d.  = N  h  a  If. N  ( 1 - d/2  line  halves  the  noise  line  pixels  i s the  the  and  in  each  profile be  number of S  line,  i s the  of  bisection  h.  triangular absorption  continuum,  ( 1 - d/2  the  bisection is essentially  i n e a c h h a l f of  S = N  for  possible  this  amount of  f o r the  a line  5S  the  i n t o two well  The  can  photons  profile  profile.  this  expression  p o s i t i o n of  p h o t o n s . How  Let  pixel  simplified  measurement. One  line  i s a f f e c t e d by  line  continuum.  simplicity,  a  p o s i t i o n i s the  which d i v i d e s the  number o f  be  derived  a line-position  determine a value the  line  conversion  flat-field  [1982] has  accuracy  bisector  half  of p i x e l s .  THEORETICAL LINE-POSITION ACCURACY  definition  can  of  to the  Walker the  four  photons per  appropriate  4.4.7  the  hence  c a l c u l a t i o n . Moreover, F i g u r e baselines  number  increases.  Figure a d c u ) and  with  to at For line  detected number  t h e n one  of  obtains:  )  (4.34)  ) 8h  (4.35)  adcu  (hi  gain)  186  US)  (6/0 o = Equation  4.36  assumption the  full  6h  Equation  4.38  profile,  a,  In  the  of  would  OJ=16,  in  Equation  imply  of  4.4,  s/n  about  about  4.38  a  would  1.5x10"  however, g i v e s 1700.  It  under  the should  then  p i x e l . The  3  an  i s not  accuracy unexpected  of  an  specific  studies  give  measurements. shape  by  give  Consider  With a  at  high Figure  rf=0.4  and  line-position  4xl0"  that  a  for  a  photons.  simulation of  the  estimation  1700.  imply  cosmic-ray  still  results.  about  in  similar  a  line  accuracy  of  position  estimate  16000x250 d e t e c t e d s/n  line  spike.  line-position  simulation  is  a  simulation  4.38  and  w o u l d become  accuracy  the  is  profile.  line  of  4.36  approximating  the  which N  then  Figure of  while  line  level. A  effect  measurement  relative  and  against  Equation  accuracy  the  4.38  uncertainty  i n a cosmic-ray  order-of-magnitude  comparison  4.7  of  function,  an  case  gives  criterion  continuum  the  good  a triangular  i s the  in Equation  photons  4.38  this  the  is a  continuum  i n the  which  study  5S  for  uncertainty  l i n e at  the  symmetric  that  bh  This  t e r m CJ i n E q u a t i o n  simple  fact  as  to  accuracies  triangular  s/n  the  line-position  spite  least  in t h i s  used  equivalent  only  p r o f i l e at  o f the  amount of  noise.  line  same  t h i s case,  photon  the  i s the  line-position  (4.37) (4.38)  The  i s the  Equation  ) )  data.  2h  In  absolute  only  which  be  d/2  s/n  states  halfwidth  method can  to  ( 1 -  ( N  = |/(w/(2tf(l-d/2)))  w i d t h of  measurement  (4.36)  = h /  2  for high  equal  event.  S  considers  w o u l d be  the  =  2  3  the  study  pixel  in  for a  simulation  187 study  should  realistic simulation  give  noise study  a lower  contributions e.g. readout  from t h e f l a t - f i e l d upon t h e Hence, the  use of  a  should  for  the p r e c i s i o n ,  have been  included  n o i s e and n o i s e  standard  spectrum  s/n s t a n d a r d  increase.  with  spectrum  since i n the  contribution  s p e c t r u m . The s i m u l a t i o n s t u d y  i f a much h i g h e r  precision  value  the is  is  based  same  s/n.  available,  Chapter THE  5.1  DELTA SCUTI VARIABLE 20  CVN  INTRODUCTION The  Scuti  star  20  variable  Canum V e n a t i c o r u m with  Parameters  f o r 20  parameters  can  Baglin  al.  et  8  be  [ 1972]  20  CVn  spectral X4481  are type  weaker and  and  than  anomalously  20  CVn  have  of  [1976] i s h i g h e r t h a n  20 CVn  pointed  there  that  reported  values  20 CVn.  Membership  0.45  of about  for M  v  5.1.  by  strong  [1979],  and  Bregman  Jaschek  [1982].  that  t h e Ca  Hoffleit in  11  of  t h e Mg and  by  Dickens  Abundance  Hauk  determined v a l u e of Leung  t h e Hyades  visual would  0.44  w h i l e Stromgrens photometry  1.27.  188  al.  et  al. Kurtz  f o r the  [1970]  magnitude imply  et  by  i s a d i s c r e p a n c y between t h e absolute  II  Jaschek  CVn.  [ 1 9 7 6 ] , and  lines similar  20  be a member.  Other  Breger  other s t a r s  f o r [Fe/H]  may  f o r the in  and  t h e more t y p i c a l  Hyades o f w h i c h out  on  Kurtz  0.80  Table  Breger  been p e r f o r m e d  [1975],  value  in  abundances.  c l a s s . Meanwhile,  been commented  Ishikawa  [ 1 9 8 5 ] . The  Hoffleit  luminosity  be  [1971],  HR5017 ) i s a 8  [1982b],  [1978],  those  to of  in  have p o i n t e d o u t  has  analyses  about  Gupta  line  [1982]  CVn,  summarised  in Tsvetkov  [1972],  Morgan and  Abt  are  found  [1970],  ( AO  D e l p h i n i - t y p e anomalous  CVn  [ 1 9 7 5 ] , Leung  in  5  has  various M  of  v  a value  gives a  of  value  189 5.2  V A R I A B I L I T I E S OF The  star  20  20 CVn  CVN  was  first  r e p o r t e d t o be  Wehlau e t a l . [1966] and D a n z i g e r light  curves  f o r 20  CVn  Dickens  [1967],  Breger  Gonzalez  [1981],  Chun  [1982b].  et  period Am  of  v  about  period  0.0292  m  was  measured  photometric  amplitude  [1972]  a  gave  frequency  Hence b o t h  recalculated  of  the b r i g h t n e s s v a r i a t i o n s  in  light  was  measured t o  a v a l u e of 0.031  An a m p l i t u d e  the p e r i o d over  and  a V  of 0.022  v  m  has  of been  [1981] by B o s s i  amplitude  and t h e p h o t o m e t r i c  f o r Am «  m  to a c o l o u r  amplitudes  m  1  8.2183  amplitude  in yellow  An  of  a l . [1983] have o b s e r v e d  day"  [1976]  m  and 0 . 0 4 . B o s s i e t a l . [1983] have of 8.21  to' be s t a b l e  Penfold  o f 0 . 0 3 5 . Shaw  variations.  for  f o r the s t a r .  m  by  a  o f f t h e V d a t a o f Pena and G o n z a l e z  0.02  by  photometric  suggested  h a s been s t a n d a r d i s e d  e t a l . [ 1 9 8 3 ] . Chun e t between  and  o f 0.12168 day o r a f r e q u e n c y  a l s o measured  = 0.20  measured  al.  amplitude  m  (b-v)  et  day t o g e t h e r w i t h an  be 0 . 0 l 9 6 . S m i t h [1982b] a d o p t e d light  and  pulsation  day and an a m p l i t u d e  the b l u e w h i l e the amplitude  This  Bossi  and  a  m  the  and  Pena  performed  o f 20 CVn  and 0.14  a period  for  1  data  0.03 . V a l t i e r  of 0.135  determined day"  0.13  [1976],  have been  been  Other  by D a n z i g e r  radial-velocity  have  [1966].  by  e t a l . [1983].  photometric  between  Shaw  variations  time-series observations  Early  been g i v e n  a l . [1983],  Simultaneous  [1971] and N i s h i m u r a  and D i c k e n s  [1969],  [1983]. R a d i a l - v e l o c i t y Smith  have  a variable  determined  of  amplitude  0.0174 . m  appear  t h e 14 y e a r s span o f o b s e r v a t i o n s . P e n f o l d  [1971] o b t a i n e d a r a d i a l - v e l o c i t y  amplitude  2K of  1.5km" . 1  190 Table  5.1  Parameters  f o r 20 CVn  **************************************** Reference HD number  : 115604  SAO number DM number  : 44549 : +41  2380  R.A.  (1950)  :  13  Dec.  (1950)  : 4 0 ° 50'  Annual p a r a l l a x  h  15  18.151  m  s  7.483"  : +0.19"  Proper motion  in R . A . :  -0.127"/yr  Proper motion  in Dec. :  +0.0l7"/yr  b  1T  :  102.73°  :  75.52°  Spectral Radial Vsini M  y  T  e  type  : F3 I I I - I V  velocity = <5 k m s  = 7.4 kms" - 1  = +0.5 f  log  f  = 7500K g = 3.7  B r o a d band V =  photometry 7 3  al.  [1981]  Smith  [1982b]  Smith  [1982b]  Eggen  [1979]  Kurtz  [1976]  Kurtz  [1976] et  al  [1965]  m m  U - V = +0. 5 0  m  V - R = +0. 2 5  m  I  1  Pena e t  Iriate  B - V = +0. 3 0  V Infared  (cgs)  4.  '  = +0. 4 0  photometry  :  m  Verma e t  al.  [1983]  191  H  =  4.17  m  K =  3.95  m  Intermediate 0 =  band p h o t o m e t r y  2.780  b - y =  0.180  =  0.231  m  c,  =  0.913  m  =  Kurtz  [1976]  m  m,  5m,  :  -0.035  m  m  ***************************************** Smith  [1982b]  1.3kms~ Shaw  1  and  a  [1976].  0.127  day  determine night  measured  Nishimura their  a 2K  value  of  light  0.37  that  the  light  data  is  same a s  that given  by  e t a l . [1983]  measured a p e r i o d  of  spectroscopic  data.  6 Scuti  [1971],  shift  is  the  the  simultaneously  (Breger  also one  photometric t o be  a  phase  and  light  fraction  of  the  behind  the  minimum  lags  observed  spectroscopic  et a l .  at about This  and  the  can  d a t a . From  radial-velocity  d e f i n e d as  Nishimura  One  there appears  radial-velocity  by  from  1  radial-velocity  velocity.  stars  the  1.7kms"  maximum o c c u r s  minimum r a d i a l for  of  p e r i o d between  maximum. The  photometric the  amplitude  of  Penfold  c u r v e s . T h i s phase period  velocity  simultaneous  o b s e r v a t i o n s by shift  radial  p e r i o d which  from  of  a  [1983] i n d i c a t e  0.1  period  is a typical  et a l . [1976]).  before  and that the  phase-shift value  192 Table  5.2 M i d - e x p o s u r e  times  f o r t h e 20 CVn  spectra  ************************************** #  24 J a n 83 UT+  Barycentric  0  (1 3 : 1 1:30 .20)  2445359. 0520520  2h  1 4m 00s  East  1  :33 :22 .89) (1 3  2445359. 0672461  1h  52m  04s  East  2  ( 1 3:50 :38 .61 )  2445359. 0792343  1h  34m  45s  East  3  (1 4 :07 :49 .78)  2445359. 0911698  1h  1 7m 31s  East  4  (1 4 :25 :07 .75)  2445359. 1031841  1h  00m  5  (14 :42 : 16 .58)  2445359. 1150925  Oh 42m  59s  East  6  :59 :25 .59) (1 4  2445359. 1270030  Oh 25m  47s  East  7  (1 5 : 1 6:31 .50)  2445359. 1388777  Oh 08m  38s  East  8  (15 :33 :42 • 47)  2445359. 1.508109  Oh 08m  36s  West  9  (1 5 :50 :56 .96)  2445359. 1627849  Oh 25m  53s  West  10  (1 6 :08 :07 .57)  2445359. 1747139  Oh 43m  06s  West  JD  hour angle  1 0s E a s t  ************************************************************ 5.3 THE  HF  OBSERVATIONS  The s t a r  20 CVn was  absorption  cell  telescope spectra slicer.  observed  at  the  on t h e 2 4 t h o f J a n u a r y  was The  obtained  with  spectrograph  The CFHT RL1872F/30  Reticon  of the  4.8A/mm a t  about  X8700. T h i s  0.07lA/pixel  on  gives a projected s l i t  the  (Brealey et was  used  3.6m  s e r i e s of and  f/7.4 al.  image Coude  [1980]).  unintensified  The g r a t i n g i s b l a z e d  d i s p e r s i o n i n the f i r s t corresponds  the Reticon width  Coude t r a i n was  detector  spectrograph.  X8000 and g i v e s a r e c i p r o c a l of  1983 UT. The t i m e  used  spectrograph  the focus  Canada-France-Hawaii  the red  four-grating-mosaic  at  s p e c t r o s c o p i c a l l y with the  to  array.  of about  order  a dispersion The image  at  of  slicer  33a ( C a m p b e l l e t a l .  193 [1985]). a  The 15M w i d t h o f a R e t i c o n  resolution  spectrum  series  o f 0.12168 day  of t e n s p e c t r a  spectra These  without  also  the s t e l l a r  shown. E a c h  the spectra 5.2  Table lines.  for  #0 by u s i n g  spectrum  barycentric  radial  #1.  For  times l a g  in  each  one-tenth  the  h o u r s ) . The  time  Stellar  lamp  and  were a l s o  numerically  obtained. spectrum  removed  are  s p e c t r u m h a s a mean s/n o f a b o u t  t h e continuum.  20 CVn  Approximate  from spectrum  o r HF l i n e s  The m i d - e x p o s u r e  i n Table 5.2.  a r e summarised  i sthe  (2.92  imply  spectrum  5.1. The mean s t e l l a r + H F  stellar+HF on  f o r each  about  HF l i n e s  then  coverage  one p e r i o d .  t h e imposed  266 a t e a c h p o i n t of  covered  a r e shown i n F i g u r e  with e i t h e r  time  This corresponds to  "cycle-count" period  would  The s p e c t r a l  130A. The e x p o s u r e  i s about  1000 s e c o n d s .  was  0.16A.  of about  pixel  spectrum without velocities  times #0  in  t h e imposed  HF  Spectrum  can s t i l l  be  measured  the dispersion  relation  this  observations,  s e t of  the h e l i o c e n t r i c  times  determined the 2.0  by a b o u t  seconds.  5.4  THE DATA REDUCTION The  d a t a were p r o c e s s e d a n d r e d u c e d u s i n g  described is  i n the previous chapter.  calculated  with the line  f o r t h e time s e r i e s  t h e HF l i n e s  numerically  radial-velocity shape  Fahlman-Glaspey relative  shifts  A mean s t e l l a r  spectrum  of s p e c t r a . T h i s  spectrum  removed h a s been c h o s e n  standard spectrum.  and p o s i t i o n  references  difference of i n d i v i d u a l  the procedure  I t p r o v i d e s both  i n the a p p l i c a t i o n  technique spectral  t o be the  of  the  i n determining the lines.  The c h o i c e  of  Figure  5.1 The  20 CVn  spectrum  195 using is  a mean s p e c t r u m  would  i m p l y an i n c r e a s e d  used as t h e s t a n d a r d spectrum.  would b r o a d e n relative very  the  t o those  small  spectral  case  lines  a m p l i t u d e . Moreover,  because  i n a second  the d a t a - r e d u c t i o n procedure, between  individual  spectra  t h e mean s p e c t r u m . lines  are  values  the  numerical  the  data  spectrum  #0.  The amount  minimise stellar  the t o t a l  value of  in  the  particular  The  should would  result  computation The has  is  over  better  f o r the  stellar minimum  positions,  chosen  This  the  l i n e s a r e a c h i e v e d by appropriately to  shifted  spectrum  such t h a t  positions  i t  lines  procedure of shifted  f o r each  would  HF  a  mean  f o r the dividing standard  cancellations. individual  line  However,  this  computation  i.e.  cancellations. numerical  #0  of a l l the  is essentially  A similar  amount o f  and  profiles.  a l l the s t e l l a r  line  shifts forming  HF l i n e  over the  the  before  maximum  applied  o f an o p t i m a l s h i f t  by more t h a n one o r d e r o f m a g n i t u d e .  unadjusted  been u s e d  limits  an  of  velocity  t o a c h i e v e n u m e r i c a l HF l i n e  the  cost  "pass" or i t e r a t i o n  by an a p p r o p r i a t e l y  in  increase  velocity  by  division  data spectrum.  application  of the very small  the  the spectrum.  shift  i s used  effect i s  of s h i f t  residual  the d a t a spectrum spectrum  This  of the s t e l l a r  spectrum  spectrum  lines  spectrum.  of t h e l i n e  d e t e r m i n a t i o n of  cancellations  each  spectrum  to the  derivative  dividing  before  mean  line  those c o r r e s p o n d i n g  effect  the  be c o r r e c t e d  The c h o s e n  i n the f i r s t  In  in  the r e l a t i v e  can  spectrum  The p h a s e - s m e a r i n g  i n the i n d i v i d u a l  in this  s/n  for  difference the s t e l l a r  function lines  from E q u a t i o n  i n the a p p l i c a t i o n  4.4 of  1 96 the Fahlman-Glaspey d i f f e r e n c e that  the  measurement  line-profile of  variations  minimising  differences  of  any  would n o t  the  and the m o d i f i e d  to  small. This  profile for to  variations  the s t e l l a r  lines  profile.  width.  are  The l i n e  twice as broad  chosen  limits  f o r the  as t h o s e  A typical  of l i m i t s  relative  HF  line  function  polynomial  h a s been u s e d  the s p e c t r a . T h i s  any  small  caused  variation  for  the s t e l l a r  X8763, S i I X8718, the  are  of  the  7 pixels chosen  in  to  be and  profile.  i n width.  4.5. The  the  The  modified of  to f i t the d i s p e r s i o n r e l a t i o n s  of  the  the p o s s i b i l i t y  measured v e l o c i t i e s  that  could  be  between t h e d i s p e r s i o n f i t s . curves  have  been  obtained  Ca I I X8662, Fe I X8675, X8689,  X8728, X8742,  the  corresponding  t h e maximum  16 " p i x e l s  X8752, S  I X8680,  mean s y s t e m i c observed  X8710,  X8695, Mg  and N I X8683. The s/n  s p e c t r a a r e t o o low f o r a d e t e r m i n a t i o n  measured over  limits  same o r d e r  radial-velocity  curve. A  found  The l i n e  measured u s i n g  X8776, A l I X8773, X8774,  velocity  the  little  derivative  to  the  using  of t h e l i n e  should minimise in  lines  lines  Equation  by i n c o n s i s t e n c i e s  Individual  about  are  from  all  HF  case,  of v e r y  i s about  derivative  is  shifts  difference  first  by  artifacts  f u n c t i o n were  t o be t h o s e  corresponding  i n the f i r s t  by  derived  of l i m i t s  ensure  caused  In any  lines.  i n the  set  minimum v a l u e s set  i n the  minimum  A typical  shift  be an i n d i c a t i o n  happening  t h e maximum and  line  function.  difference  may  i s to  be a f f e c t e d  velocities  unmodified  This  velocity  the d i f f e r e n c e between  be v e r y  technique.  velocity  cycle.  This  I of  o f t h e H I X8750 o f 9.532kms" was  1  is  obtained  by  1 97 averaging  the  velocities  spectra.  It i s different  by  [1982b],  Smith  velocity rather  of the  absolute  subtracting  a mean v e l o c i t y  X8662  line  is  measurement  estimate with  i s derived  the  based  Figure each  on t h e  these 1  other  ±0.3kms~ . 1  about  weaker  for  the  obtained  by  except  velocity  error  chapter.  line  i s calculated  precision.  The  line error  theoretical  error  estimate  have  radial-velocity  X8689,  is  shown  in  uncertainty  in  is  about  uncertainties  for  between  and  precision,  ±0.1 a  weighted  f o r t h e weak l i n e s i . e .  The c h o s e n w e i g h t  i s proportional  l i n e d e p t h and i n v e r s e l y  II  obtained  measurements  t o i n c r e a s e the  mean  This  The  mostly  the  The  estimate  The  Fe I  l i n e s are  curve  Ca  _ 1  one-standard-deviation  In o r d e r  o n l y on  ±0.093kms .  line-position  even weaker  velocity  velocities  5.2.  each  this effective  t h e Ca I I l i n e .  the  in  method.  all  the  the  line.  based  Figure  from t h e f o r m a l  curve  individual  curve  in  average v e l o c i t y lines  is  mean o n e - s t a n d a r d - d e v i a t i o n  ± 0 . l 0 4 k m s ~ . The the  is  i n the p r e v i o u s  5.3. The of  curve  uncertainty  to calculate  been d e s c r i b e d curve  shown  Fahlman-Glaspey  formulations  in  sufficient  f o r the p a r t i c u l a r  radial-velocity  one-standard-deviation position  measured  1  VELOCITIES  The r e l a t i v e II  a l l the  interested  relative  are  radial-velocity  from  o f 7.4kms"  Hence  velocities  relative  Ca  lines  i s only  star.  purpose. A  5.5 THE RADIAL  the  from t h e v a l u e  G e n e r a l l y , one  variations  than  of a l l  for  each  t o the square  of  p r o p o r t i o n a l t o the square  of  mean  one-standard-deviation  1 98  Figure  5.2  The  Ca  II  X8662  velocity  curve  of  20  CVn  CO LO CO LO ^* CNJ Q ~~)  CD  C  ,.sui>|  D  Ad  aAjiejad  199 Figure  5.3  The  Fe  I  X8689 v e l o c i t y  curve  of  20  CVn  + CJ) L O C D L O  CM Q  ~i  CO  CO CO CD  00  QJ  (_> CD  CM  SUJ>I Ad  aAjiejay  200  Figure  5.4  T h e mean  velocity  curve  o f 20 CVn  from  weak  lines  + CD LO CO LO  C\l Q  ~>  CO  C  D  201 uncertainty 0.083kms  for  this  measurements. T h i s Dispersion contribute  fits  to  This  is  obtained  if  uncertainty  account,  the  error  for  t h e Ca I I  c u r v e would be  the  velocities  shown i n F i g u r e s  in  small.  shifts  Large guiding  i n the  HF l i n e  was n o t o b s e r v e d . positions pixel  (that  over  In  of the  through  smooth  out  any  exposure-meter  for  value  5.2 t h r o u g h  course,  i t would  each exposure.  intensity  output  In t h i s  lists  5.4. The  errors  inconsistencies are have c a u s e d  large  small  the  from t h e exposure  ±0.042  guiding  image  In  uniform  case,  about  line  error  slicer.  would a l s o h e l p  effects.  t o use  This  o f t h e HF  i s only  o f 1000 s e c o n d s  be b e t t e r  5.3  between t h e s p e c t r a .  of  was r a t h e r  into  the corresponding  t h e rms s c a t t e r  short-term  output  relation  _ 1  use  the  about  X8717 l i n e )  the  from  of  t h e e n t i r e time s e r i e s . T h i s  realised  is  measurements.  ± 0 . 1 1 1 k m s . Table  positions  i n the  value  calculated  e r r o r s would  fact,  moderate exposure time  Of  similar  t h e m i d - e x p o s u r e t i m e s due t o g u i d i n g  very  is  A  dispersion  while  of a l l  error  have an u n c e r t a i n t y  per v e l o c i t y point  1  would  by t h e u n c e r t a i n t i e s i n  is  of the  t h e mean c u r v e would  ±0.102kms"  standard  o f t h e HF l i n e - p o s i t i o n  uncertainty  5.4.  uncertainties  measurements.  standard  estimates  this  t h e mean  of  line-position  i n the spectra  the  and i s c a u s e d m a i n l y  line-position  contribution  i s shown i n F i g u r e  to  1  a  the s t e l l a r  t h e HF l i n e s  ±60kms"  points.  HF  Taking  fits  has  from  mean c u r v e  about  dispersion the  curve  per v e l o c i t y point  _1  velocity  mean  any  case,  f o r each  meter.  to the  exposure.  a w e i g h t e d mean  the weight  The  could  be  time the  202 Table  5.3 R e l a t i v e  radial  velocities  o f 20 CVn  **************************************** #  Ca I I X8662  •  .  Fe I X8689  mean weak  lines  0  -0.188 kms"  1  -0.302 kms"  1  -0.344 kms"  1  1  -0.519 kms"  1  -0.605 kms"  1  -0.547 kms"  1  2  -0.934 kms-  1  -0.568 kms"  1  3  -0.327 kms"  1  1  -0.249  kms"  1  4  +0.071  kms  - 1  -0.078 k m s  - 1  +0.001  kms  - 1  5  +0.484 k m s  - 1  +0.414 k m s  - 1  +0.376  kms  - 1  6  +0.677 kms"  +0.525 k m s  - 1  +0.541  kms  - 1  7  +0.630 k m s  - 1  8  +0.450 kms'  9  +0.011  10  -0.354 k m s  .  -0.478 k m s  -0.309 kms"  1  +0.660 kms"  1  +0.661  kms  1  +0.437 kms"  1  +0.446  kms"  1  1  +0.022 kms"  1  +0.027  kms"  1  -0.345  kms'  - 1  kms"  - 1  -0.347 k m s  - 1  - 1  1  ************************************************************ 5.6 DISCUSSION The Ca amplitude Figure with  II  of  velocity  1.4kms"  5.4 h a s  1  curve  while the  an a m p l i t u d e o f  t h e v a l u e o f 1.3kms"  Fe I X4476 and  1  t o remove  caused  the length  of each  of  correction  t h e dominant  less  s e v e r e phase  smear  as  As i n S m i t h  2K  curve  in well  from the  [1982b],  the phase-smearing e x p o s u r e . In  the exposure  than i n the  any c a s e ,  time s h o u l d  case i n Smith  15% a n d  20% o f t h e p e r i o d  of  [1982b] h a s e s t i m a t e d  that,  the 10% cause  [1982b]  as the even  no  effect  s m a l l . The u s e o f  w h i c h u s e d between exposure. Smith  velocity  a  by S m i t h [1982b]  i s probably very  period  has  1  Fe I I X4508 l i n e s .  i s applied  required  mean  5.2  1.2kms" . These a g r e e  derived  correction by  i n Figure  length  in  that  203 case,  t h e amount  of r e d u c t i o n  phase  smear would  be  Figure Ca  11  5.5  gives  There  BJD2445359.08. shortward small  seen  from  to  be  The  II  line  the o t h e r l i n e s  the  difference  that  appears Ca  from  a  appears  not appear  to  aberrant  velocity  point.  order to  sampling  the  the  same  criteria  have  line  because  of the r o u n d - o f f e r r o r  limits.  This  However,  technique  to determine  sensitive  to  the  discretisation and  error  i t i s minimal  d e v i a t i o n s may part The  choice  be c a u s e d  of the p u l s a t i o n Ca  other  II l i n e lines;  extrema  of  meaning  than  t h e Ca  has  was  therefore, the in  II l i n e  has  an  by  by  the  one  may  perfectly  very  Moreover,  this  that  line  a  II  velocities.  a  than  the  by  the  different  Furthermore,  quite  have been  line  different  shape  have  II  observed  determined  potential may  the  i s not  the other l i n e s .  and  line,  a l l  c u r v e . The  t h e Ca  limits  is  Fahlman-Glaspey  the f a c t by  single  integer-valued  the  different  excitation  from t h o s e of the o t h e r l i n e s  at  that  positions  derivative  the case of  result  determine  velocity  the l i n e  profile  be  from each  limits.  sampled  a slightly  can  s e v e r e f o r t h e b r o a d Ca  f o r a mean  still  line  fact,  of a  be a c h i e v e d  of  of l i n e  is less  ensure  imposed  relative  The  at  shifted  wavelengths  to  not  use  be 1  phenomenon  could  the  to  the e f f e c t  been u s e d  stellar  line  limits.  be  pulsation  deviation  points.  BJD2445359.08 does  the weak  0.37kms~ . In  shorter  neighbouring v e l o c i t y  identical  by  between  t h e mean of  marked  by a b o u t  towards  In  v a l u e s caused  10%.  c u r v e and  gradual trend  from  than  the v e l o c i t y  X8662 v e l o c i t y  lines.  a  less  i n t h e 2K  different  formed  at  a  204 Figure  5 . 5 Velocity  difference  ( Ca  I I curve  - mean  curve  )  9 1  CO  o  -  -  1  o  CD O  I  -  -  o  cn cu  /  a  CM ra  QJ  V  ZX  a ra cu  -  1,  -  o  /  \  O  I  -  -  \ \  CD CD  \  o  CD  o  CD  CD  /  C_J  CD CN  CD O  OO  >  —  CD CD CD  1 CD  LD  CD  O  LO CM  in  O  O  O  CD  CD  LD  (,.SUJ>|)  CD LO CO LO C\l Q  &>  CM CO CD CO  CO  C\J  33U3J9J JTQ  CD  AlJ30J3/\  ~o CO  205  Figure  5.6  Velocity  difference  ( mean c u r v e  -  Fe I c u r v e  )  9 1  CO  CO  T  CD  o  A /  .—•  ?  O  CD  1 o  (XI  (\l <•—i  \  CO  CD  &>  /  CNJ  /  o  -  Q  CD  f  o  CD  1 Q  \  oo  OO CD  \  b /  CD CD  CO CD -  CD LO CO LO  O  CO CD  \ i CD LD  LD (XI  CD CD  LO (NJ  CD LO  CD  CD  CD  CD  CD  (,.SUI>|) 3 J U 3 J 3 J J T Q  AlT30T3/\  ~1 CD  206  Figure  5.7  Velocity  difference  ( Fe  I curve  - Si I curve  )  cn cu cr  CO 4CO  o cr  ro  QJ  LO CM Q -) CO  cn cu tr  QJ  Li-  ra QJ  cr >  CJ CD  CM  o LO  LO C\J  CO  CD  Ul CM  CD Ul  O  O  CD  O  CD  (,.sw>|)  3JU3J3JJTQ  AIT:JOT3/\  207 5.8 Velocity  Figure  difference  ( Fe  I curve  - S I  curve  I  )  CO  1  CD  \ ©  CD  / T  C\J  QJ  t=  •  -  CD  CD  -  -  CD  \  CD  QJ  U_ u_  an  o  OO CD  Q  CD  CO CD CD  4  ••  >  /  1  QJ EH  CO CD  CO CD  /  CD  CD 1  1  LD  LD CM  CD CD  LD CM  LD  CD  CD  CD  CD  CD  CD  (,.SUI>J)  3DU3J3JJTQ  + CD LO CD LO  "3-  1  .—I  r H  -  1  1 cn  tz  CM  1  CD  I  QJ  CD  CD  AJTDQJ3/\  CM CD ~D CO  208 different other  r e g i o n of the p u l s a t i n g  hand,  the  propagation  atmosphere c o u l d a l t e r deduced  velocity  shortward-shifted reported Dravins  emission  shocks  in  In  i n the  5 D e l type  a l . [1977].  been o b s e r v e d  a t m o s p h e r e . On t h e  t h e Ca I I l i n e  displacement.  i n another et  of  stellar  the  profile  and h e n c e  fact,  shock-generated  Ca I I  K line  6 Scuti  variable,  Shock-generated  emission  i n the large-amplitude  pulsating  has  Abt  found  [1972].  offered begin  to  At the p r e s e n t ,  f o r the to  be a n o m a l o u s i n  observed  speculate  on  Cnc  i n 20  CVn  s t r e n g t h by Morgan  and  or s o l e l y  to the 6 Scuti  Figure  5.6 g i v e s  the v e l o c i t y  mean c u r v e Figure Fe  a n d t h a t d e r i v e d from  5.7 shows  I curve  the v e l o c i t y  in  F i g u r e 5.8. T h e r e a p p e a r s  in  any o f t h e s e  curve  three  i s probably  precision.  ±36ms  Figure  while  F i g u r e 5.8  smaller by  .  scatter  the fact  difference  of the s t a r . between  between  while  the  the  t h a t t h e Fe I l i n e s  the  of the  has a s t a n d a r d  is  deviation in  because of t h e i r  of  ±l09ms~ 1  caused  each  individual  d e v i a t i o n of ± 7 0 m s ~ .  do c o n t r i b u t e  shown  deviation  d e v i a t i o n of  i s probably  mean  difference  the scatter  indication  a standard  i n F i g u r e 5.6  the  t h e mean o f t h e Fe I l i n e s .  In f a c t ,  has a s t a n d a r d  be even  to  t o be no s y s t e m a t i c  F i g u r e 5.6  t o w a r d s t h e mean c u r v e  related  and t h e mean S I c u r v e  curves.  5.7 h a s  one c a n n o t  pulsation  difference  a reasonable  velocity _ 1  is  and t h e t h e mean S i I c u r v e  between t h e mean Fe I c u r v e  e x p l a n a t i o n can  fact,  it  metallicism  also  VZ  In  whether  by  has  8 Set v a r i a b l e ,  no c o n c r e t e  effect.  been  p Pup,  ( G a r b u z o v and M i t s k e v i c h [ 1 9 8 4 ] ) . The Ca I I l i n e s have been  the  1  The  partially  significantly  l a r g e number.  209 The cause the  short  large  data.  uncertainty  from  variation  in  Likelihood  the  of  period  of  0.130  or  given  the are  The  uncertainty  b e c a u s e of  n i g h t s . The night  of  effect  on  Smith  caused  period  of  CVn  the  by  0.122  can  a  second  .  Bossi  by  between t h e  d  amplitudes  0.0054 ,  respectively.  disagree  with  m  the  of The  velocity  5.4  of  from  the  values et  be  carries  al.  purely a  large  Moreover,  radial-velocity  different  before,  of  Nishimura  h e r e may  be  a  results  Bossi  the  to  gives  These  time c o v e r a g e .  quite  on  different  s i n u s o i d a l on  t h e y were  monotonically the  beating  period modulating  the  primary  et  al.  this  one  to  photometric main  .  period  that  Maximum  . S i m i l a r l y , an  and  achieved  [1982b] a t t r i b u t e d  i n the  0 . 1 4 3 . The  be  - 1  be  cyclic  II  result  [1982b],  can  a mean p e r i o d  different  were f o u n d  night  modulation a beat  day  reported  velocities  while  decreasing.  20  7.69  limited  from  and  Figure  of  pulsation  the  has  in  gives  too  derived  one  Ca  0.1266  two  Smith  derived  [1982b]  the  the  agreement  accidental.  variations  not  will  almost  spectroscopic  [1976],  [ 1 9 8 3 ] . However, any  Smith  of  series  period  periodogram  v e l o c i t y curve  well with  Shaw  The  a period  frequency  [1983] and  by  change of  . Averaging  time  "cycle-count"  a n a l y s i s of  gives  a mean  observed  pulsation period  velocities.  mean  0.1336  agree very al.  observed  5.2  the  the  a pseudo  power-spectrum  in Figure  analysis  et  the  of  i n any  Nevertheless,  inferred  curve  duration  [1983]  amplitude period  the  two  and  identification  w h i c h may a  periods  period  ratio, of  have  the  reported be  caused  second p e r i o d are  0.0200  however, second  m  at and  would  overtone  210 radial  pulsation  Gonzalez value  as  the  [1981]. T h i s  day f o r 20 CVn.  to Equation  1.11,  20  CVn. T h i s  or  even n o n r a d i a l Tsvetkov  peculiar large  Applying  implies pulsation  [1984] h a s  6 Scuti  Q value  a  first  placed  between  and  period  of 2 days  nonradial  period  20  found a sharp s e p a r a t i o n radially  their  value  has  suggested  _1  nonradial. of  using  The the  This  the l i n e s  typing  star  condition there reason  was  that  adopted  1  t h e dominant  i s in spite  deserves  more  characteristics improved. T h i s  the of  nine  stars a l l  have  evolutionary  Smith v  radial  [1982b]  values  a  has  f o r the  s t a r s . B a s e d on a [1982b]  mode i n 20 CVn i s  probably  that  Smith  pulsation  the  sharpness  [1982b] from mode  short  time  Reticon with  isstill  unclear  observations.  s e t of data wind  together  of  f o r 20 CVn, S m i t h  of t h e f a c t  60-knot  the  list  t h e common  5 Scuti  extensive  was p o o r when t h i s a strong  pulsation  analysis.  n a t u r e o f 20 CVn's  for  radial  t h e 2K/Am  i n 20 CVn h a s p r e v e n t e d line-profile  5.1  [1982b] h a s s u g g e s t e d  Furthermore,  between  of 42kms mag"  of  0.025 day f o r  calculated  and n o n r a d i a l l y p u l s a t i n g  low  Tsvetkov  i n Table  CVn i n a  a n d hence e x c l u d e d ratios.  derived  f o r 20 CVn.  masses a n d p u l s a t i o n m a s s e s . S m i t h beat  of  overtone  and  a Q value  the parameters  v a r i a b l e s . These p e c u l i a r  discrepancies  Pena  was b a s e d on t h e i r  hand, h a s a d o p t e d  one o b t a i n s  value  by  the p u l s a t i o n constant.  [ 1 9 8 2 b , 1 9 8 4 ] , on t h e o t h e r 0.041  oscillation  mode t y p i n g  day f o r Q,  o f 0.02  main  also  coverage. CFH  t h e improved  The s k y  was t a k e n . I n f a c t ,  w h i c h was  at  and  have  the  The since  through-put  main noise been  of the  21 1 CFH  r e d Coude  possible  with  train the  implies  that higher  same i n s t r u m e n t a l s e t u p  s/n at  data CFH.  are  now  Chapter THE  6.1  6  DELTA SCUTI VARIABLE p PUP  INTRODUCTION The  star  c Argus  p Puppis  by Reese  (  HR3185  [1903]. I t  )  has a l s o  is a  5 Scuti  6 D e l p h i n i - t y p e anomalous a b u n d a n c e s . are  summarised  summarised Gupta  in  in  Tsvetkov  [1978],  Antonello  et  Table  Breger  p Pup  and  Ti  Breger  and J a s c h e k  I I , and V I I abundances appear  Bidelman  Leung  [1970],  Baglin  et a l . analysis  [1976]. A s l i g h t l y  [ 1 9 5 1 ] , McNamara  t o be s l i g h t l y  and Augason  Morgan a n d Abt [1972] have p o i n t e d o u t t h a t p Pup when compared  to stars  enhanced  of s i m i l a r  [1976]  t h e Ca I , Sc  II,  deficient.  [1951] has g i v e n p Pup a MK c l a s s i f i c a t i o n  However, B i d e l m a n  Bessell  f o r [Fe/H]. Kurtz that  are  [1983],  [1975],  elements  Pup  Moon  by G r e e n s t e i n [ 1 9 4 8 ] ,  determined  f o u n d among t h e l i g h t e r  parameters  and  [1979],  with  for p  [ 1 9 8 2 ] . Abundance  [ 1 9 7 0 ] , and K u r t z  v a l u e o f 0.54 h a s been also  Bregman  h a s been p e r f o r m e d  [1969], Breger  Halprin  called  variable  Parameters  Additional  [1982b],  a l . [1981 ] ,  [1972], and H o f f l e i t of  6.1.  been  of F 6 I I .  [1962],  and  Ca I I i s weak i n  spectral  type.  6.2 V A R I A B I L I T I E S OF p PUP The radial  star  p  Pup was f i r s t  velocities  [1928].  In f a c t ,  by Reese Spencer  range  o f 11.6 kms"  first  reported  by  1  for  reported to exibit  [1903] and  Jones  Campbell  [1928] h a s d e r i v e d  p Pup. P h o t o m e t r i c  Cousins  [1951]  212  and  variable and a  velocity  variations  Eggen  Moore  were  [1956,1957].  213 Table  6.1  P a r a m e t e r s f o r p Pup  *************************************** Reference HD  number  SAO DM  : 67523  number number  : 175217 : -23  6828  R.A.  (1950)  : 8  5  Dec.  (1950)  : -24° 9'  h  Annual p a r a l l a x  24.798  m  s  32.312"  : +0.031"  P r o p e r m o t i o n i n R.A.  : -0.088"/yr  P r o p e r m o t i o n i n Dec.  :  /  : 243.15°  : i  b  : 4.40°  lz  Spectral Radial Vsini M  =  v  T  +0.048"/yr  e  f  log  f  type  : F5  velocity = 14  kms'  Hp  = 46  kms  1  +1.7 = 7100K g = 3.25  (cgs)  B r o a d band p h o t o m e t r y : V == 2. 8 2  Infrared  Morgan  and Abt  Eggen  [1979]  Kurtz  [1976]  Eggen  [1979]  Kurtz  [1976]  Kurtz  [1976]  Iriate  [1972]  e t a l . [ 1 965]  m  B -- V =  +0. 4 4  u -- V =  +0. 6 3  v  -- R =  +0.  v  -- I =  +0. 5 8  37  m  m  m  photometry :  m  Verma e t a l . [1983]  214  H =  2.02  K =  1.99  m  I n t e r m e d i a t e band p h o t o m e t r y : 0 =  2.715  [1979]  m  b - y = 0.260 m,  = 0.215  m  c,  = 0.730  m  8m,  Eggen  = -0.040  m  m  *************************************** Light  curves  [1963],  Thulsassi  Radial-velocity [1956],  p Pup  for  Doss  Fracassini  also  h a v e been  [1957],  by  radial-velocity  Reay and  have been p e r f o r m e d [1977],  Weiler  Fracassini [1983].  and  emission  Pasinetti  et  al.  [1980],  and  has  been  radial-velocity Simultaneous  time-series  observations  [1966], D r a v i n s  [1983].  the Mg  Bessell  and  II  H and  and  have  et  [1969]  photoelectic  continuum.  lines  [1981]  [1973].  by S t r u v e  [1979] w i t h t h e C o p e r n i c u s  the  et a l .  oscillation  radial-velocity  at the  Ponsen  Smith  and K u h i  of  by  [1983a].  and S t o b i e  been o b s e r v e d  of  al.  observation  and O e g e r l e  observations  et  by D a n z i g e r  simultaneous  have  given  Fabry-Perot  photometric  and B a l o n a  spectrum-scanner lines  and  e t a l . [ 1 9 8 3 ] . The v e l o c i t y  spectrometer  performed  given  Campos  measured w i t h a s e r v o - c o n t r o l l e d  al.  been  [ 1 9 6 9 ] , and T r o d a h l  curves  Buscombe  have  Emission  K lines  by  satellite.  IUE  been  Fracassini  given et  by al.  215 The  early  Observatory  radial-velocity  (Reese  [1903],  data  Campbell  suggested  a radial-velocity  data  S t r u v e e t a l . [1956] has  from  suggested  a v a l u e of  the  radial-velocity  The  photometric  amplitude of  0.l07  and  reanalysed  to  be  than  has  amplitude  the  minimum.  a  300K  with the the  amplitude in  Kuhi  amplitude  of  0.15  variation  of  280K. Minimum l i g h t  v a l u e of  radial-velocity by  0.075 i n p h a s e . B e s s e l l  variation  of  130K  and  an  was  amplitude can  minimum l a g s  and  an  amplitude  [1963]  has  photometric  curve  the  is  sharper  descending  a t X4050  m  and found  s t e e p . Bappu  [1959]  together  temperature.  v a l u e of  b e f o r e maximum  1  show  The  spectroscopic observations  a t X4566,  9.5kms~ . One  and  colour  [1966] g i v e a 2K  [1969] m e a s u r e d a l i g h t 2K  and  light  equally  the  which  (3.3712 h o u r s )  d  0.16  also  maximum.  maximum s l i g h t l y  of  and  a period  and  [1951]  Ponsen  rising  Danziger  of  The  m  photometric  m  1  light  together with h i s  simultaneous  0.08  Cousins  of 0.127 .  variation  9.7kms~ .  0.1409  the  d  of the curve are almost light  of  i n p h a s e by  0.14089 .  The  1  of  of 0.14088141  Both  [1928])  [1956,1957] m e a s u r e d an of  Lick  Moore  amplitude  behind  by  the  o f 8.4kms~ .  t h e amount  data  sinusoidal  measured a  with  period  derived a period  nearly  branches  a  a l l the e a r l y  a blue-light  as  observations m  an  2K  a period  minimum l a g s  o f 0 . 1 4 6 . Eggen  m  d a t a and  0.14  and  amplitude  S t r u v e e t a l . [1956] m e a s u r e d  from  radial  see  1  to occur  from  m  his  t h e maximum of  a radius  at  velocity.  0.130  [1969] has  light  effective-temperature found  of  11kms" , a  by  Bessell  a t X4255, and data  that  the l i g h t  reported a  variation  about  of  a the  curve  temperature 1.6xl0 km. fl  216 Thulasi  Doss  [1969] has  in  t h e narrow p a s s  The  corresponding  0 . 12  m r  curve  and  bands a t  amplitudes  given with a was  an  corresponding relative  full  amplitude  minimum and  the  of  (c!,b-y)-diagram  from  0.06  wave p r o p a g a t i n g al.  [1977],  detector,  and  Fe  Fe  linewidth  and  Campos  or  0.l02  m  and  maximum and has  Trodahl  of  et  the  at  m  175K.  A  for  al.  the  [1977]  radial-velocity  the  Dravins  et  al.  loop t r a v e l l e d  wing of t h e  K  i n p h a s e b e f o r e maximum l i g h t .  It  the  stellar Smith  Smith  Smith  2K  of  [1980] d i d  difference  of  minimum.  been s t a n d a r d i s e d t o a c o l o u r  of  a  et  Reticon  both  the  the  lines was  1  detect 5%  any  of  the  amplitude  Am  between t h e  This light (b-v)  shock  11.5kms"  than  a light 0.08  of  not  greater  a  (Dravins  measured  value  adopted  by  With  variations  variation  radial-velocity  atmosphere  [1980]  I I X4508. A  caused  [1982]).  line-profile  [1982b] has  is  Ca  of  II  the e m i s s i o n  and  by  cycle.  i n the b l u e  that  a phase  of given  Dravins  between  0.105  and  in  line-profile  continuum. Smith of  pulsation.  of  p Pup  0.28  and  radial-velocity  determined.  320K. A p e r i o d  the  [1977],  Campos  I X4476  of  variation  through  Hill  m  maximum. A t e m p e r a t u r e  [1977] r e p o r t e d e m i s s i o n  been s u g g e s t e d  0.14 ,  m  0.033 was  AR/R.  X5875.  effective-temperature  d u r i n g the p u l s a t i o n  a t about  variations  0.l7 ,  amplitude  of a b o u t  v light  measured  profile  light  variations  phase l a g  has  The  as  effective-temperature variation  measured a  line  given  amplitude  measured a  radius  was  were  a l s o d e r i v e d f o r the  [1977]  X4850 and  photometric  X3858, X4310, X4720, and  111  was  Sullivan  the  0.09 , r e s p e c t i v e l y .  0.14088067  160K  observed  = 0.20.  y  light  amplitude Reay  et  217  al.  [1983a]  used  radial-velocity variations  of  observations, than  a  servo-controlled  spectrometer p  Pup.  there  the p r i n c i p a l  t o measure t h e  From 226  was no  evidence  p e r i o d o f 0.141  20ms . F r a c a s s i n i  of h i g h - d i s p e r s i o n o b s e r v a t i o n s time  series covers  exposure  for  pulsation  (3.76  was f o u n d  hours)  of p e r i o d i c i t i e s  .  This  a time  was  t o be p r e s e n t  c y c l e and i t i n c r e a s e d w i t h  10  lines. the  minutes.  during  of  series  pulsation cycle; about  of  other  i s to a limit  o f t h e Mg II H and K  one c o m p l e t e  each spectrogram  Mg I I e m i s s i o n  radial-velocity  e t a l . [1983] have r e p o r t e d  - 1  The  minutes  Fabry-Perot  the  The  entire  increasing luminosity.  6.3 THE OBSERVATIONS The HF  star  p Pup was o b s e r v e d  absorption  cell  at ' the  telescope  on t h e 22nd,  The  series  time  of  c o n d i t i o n s and w i t h time  series  procedures without  were  stellar  the  Canada-France-Hawaii  3.6m  24th, and 25th  s p e c t r a were  CVn d e s c r i b e d used. S t e l l a r  obtained  earlier. and  numerically  of each exposure  under  setups  1983  same  as f o r the observing  lamp s p e c t r a  with  These a r e  spectrum with  UT.  the  Similar  were o b t a i n e d .  6.1. The mean s t e l l a r + H F  o r HF l i n e s  of January  t h e same i n s t r u m e n t a l  t h e imposed HF l i n e s  in Figure  length  on 20  s p e c t r o s c o p i c a l l y with  and shown  either  the  removed a r e a l s o shown.  i s either  600, 750, o r 900  The  seconds.  These correspond,  r e s p e c t i v e l y , t o 0.05, 0.062, a n d 0.074 o f  the  p e r i o d o f 0.141 day (3.37 h o u r s ) .  "cycle-count"  coverage and  i n "the  69% o f t h i s  three  nights  is,  The t i m e  r e s p e c t i v e l y , 83%,  112%,  p e r i o d . Each spectrum has f o r each p o i n t  at  218 Figure  6.1  The  p Pup  spectrum  219 Table  6.2 M i d - e x p o s u r e  t i m e s and e x p o s u r e s  f o r p Pup  ******************************************* #  Barycentric 22 Jan  JD  exposure  hour  angle  83 UT+  1  (09 :31 :43 .26)  2445356. 9011222  600s  Oh 52m  20s E  2  (09 :42 : 1 1.42)  2445356. 9083927  600s  Oh 41m  50s E  3  (09 :52 :37 .84)  2445356. 9156430  600s  Oh 31m  22s E  4  (10 :03 :04 .25)  2445356. 9228932  600s  Oh 20m  53s E  5  (10 : 13 :36 .83)  2445356. 9302148  600s  Oh  6  ( 1 0:24 :04 .30)  2445356. 9374773  600s  Oh 00m  7  ( 1 0:34 :31 .05)  2445356. 9447314  600s  Oh  8  (10 :44 :56 .65)  2445356. 9519722  600s  Oh 21m  06s W  9  (10 :55 :22 .31 )  2445356. 9592138  600s  Oh 31m  33s W  1 0  (1 1 :05 :48 .43)  2445356. 9664606  600s  Oh 42m  01 s W  1 1  ( 1 1: 16 : 15 .70)  2445356. 9737208  600s  Oh 52m  30s W  12  ( 1 :26 1 :41 .86)  2445356. 9809681  600s  1h 02m  58s W  1 3  ( 1 1:37 :07 .68)  2445356. 9882115  600s  1h 1 3m 26s W  1 4  :33 .18) ( 1 :47 1  2445356. 9954511  600s  1h 23m  52s W  1 5  (1 1 :57 :33 .18)  2445357. 0027053  600s  1h 34m  21 s W  16  (12 :08 :26 .45)  2445357. 0099568  600s  1h 44m  49s W  1 7  (12 :20 :39 .13)  2445357. 0184369  600s  1h 57m  04s W  24 J a n  1 Om 1 9s E 1 Os W  1 Om 39s W  83 UT+  18  (08 :05 :52 .14)  2445358. 8415243  900s  2h  19  (08 :21 :37 .01 )  2445358. 8524604  900s  1h 54m  44s E  20  (08 :43 :45 .99)  2445358. 8678423  900s  1h 32m  32s E  21  (08 :59 :22 .30)  2445358. 8786793  900s  1h 1 6m 53s E  22  (09 : 14 :58 .28) • 2445358. 8895125  900s  1h 01m  14s E  23  (09 :30 :35 .19)  900s  Oh 45m  35s E  2445358. 9003565  1 Om 32s E  220  24  (09 :44: 54. 45)  2445358. 9103017  750s  Oh 31m  25  (09 :57: 52. 83)  2445358. 9193108  750s  Oh  26  (10 : 1 2:1 1 03) .  2445358. 9292438  900s  Oh 03m  27  (10 :27: 52. 65)  2445358. 9401423  900s  Oh  28  (1 0 :43: 28. 79)  2445358. 9509774  900s  Oh 27m  31 s W  29  (10 :58: 55. 78)  2445358. 9617065  900s  Oh 43m  00s W  30  : 1 4:23. 19) (1 1  2445358. 9724405  900s  Oh 58m  30s W  31  (1 1:29: 58. 27)  2445358. 9832633  900s  1h 1 4m 08s W  32  (1 1:45: 26. 52)  2445358. 9940071  900s  1h 29m  39s W  33  :00: 53. 85) (1 2  2445359. 0047401  900s  in  45m  09s W  34  (1 2 : 1 6:21 . 09)  2445359. 0154722  900s  2h 00m  39s W  35  :31 : 48. 55) (1 2  2445359. 0262068  900s  2h  25 J a n  1 3s E  1 8m 1 3s E 52s E  1 1m 52s W  1 6m 09s W  83 UT+  36  (08 :24: 20. 19)  2445359. 8543583  900s  1h 48m  04s E  37  (08 :39: 45. 69)  2445359. 8650702  900s  1h 32m  36s E  38  (08 :55: 12. 65)  2445359. 8757990  900s  1h 1 7m 06s E  39  (09 : 1 0:39. 09)  2445359. 8865218  900s  1h 01m  37s E  40  (09 :26: 18. 42)  2445359. 8973938  900s  Oh 45m  56s E  41  (09 :41 : 48. 19)  2445359. 9081551  900s  Oh 30m  23s E  42  (09 :57: 19. 29)  2445359. 9189318  900s  Oh  43  (10 : 12:48. 85)  2445359. 9296907  900s  Oh 00m  44  (10 :28: 19. 31 )  2445359. 9404600  900s  Oh  45  (10 :43: 45. 62)  2445359. 9511813  900s  Oh 31m  ***********************************************  1 4m 50s E 43s W  1 6m 1 6s W 44s W  221 the continuum, nights, length  a mean  s/n o f 690, 800, and 400 f o r t h e t h r e e  respectively. of exposure  6.2. S p e c t r u m imposed  HF  spectra other  f o r each  radial  u s i n g the spectra.  heliocentric  spectrum  time  as w e l l  Again  as  velocities dispersion  For  the  times l a g  in  the  can  case  of  relations p  the b a r y c e n t r i c  CVn,  from  these  data  times  the  20  determined Pup  the  i n Table  without  be measured  entire  as  a r e summarised  #17, #18, and #19 a r e t h e s p e c t r a lines.  approximate  The m i d - e x p o s u r e  f o r the  set,  the  by a b o u t  0.9  second.  6.4 THE DATA The  REDUCTION  data  procedures  were p r o c e s s e d  which  #17 h a s  been  spectrum  for  were a p p l i e d  chosen  to  relative  a l l the p  spectrum  shifts  taken  reduce  Pup  standard  spectra  measured v e l o c i t i e s compare  the  directly  The reduction  between  measured  between  additional  ensures  the  the  same  Spectrum  radial-velocity  standard  provides  r e f e r e n c e s used  These time  using  t h e 20 CVn d a t a .  data. I t  on t h e same n i g h t ,  a l l three  reduced  the  of i n d i v i d u a l  HF s t a n d a r d s p e c t r u m . to  to  be  l i n e - s h a p e and l i n e - p o s i t i o n the  and  spectral  in  both  determining  lines.  A  lamp+HF  t h e 2 4 t h , was u s e d  two s t a n d a r d s p e c t r a series.  The  internal  of  time a  three  time  which  were u s e d  as  were  of  consistency  the three  velocities  use  the used  identical for  the  One  can  series.  particular  series  the  line  without  any  correction.  same  criteria  were u s e d  t o choose  the l i n e  for  limits  the  20  CVn  f o r both  the  222 stellar is  and HF l i n e s .  about  10  function stellar  pixels  from  in  In  than  Doppler  imaging,  an  from  20  relative  of  the  CVn. B e c a u s e  function  used  4.5  was  the  used  lines  of the  I X8686,  by s u b t r a c t i n g period.  a  In  between  line-profile  for  order  o f mean v e l o c i t y  the use  of  than  in  difference  t h e t h e HF  c u r v e s were  lines.  subsequently  any  to  from  X8764, S I  X8742, and  different  was u s e d  X8671, The  line  was  calculated  preserve  I  X8752.  particular  mean v e l o c i t y  data  of  Ca I I X8662, H I X8750, Mg  X8728,  velocity  are  effect  modified  for  the  Fahlman-Glaspey  to detect  radial-velocity lines  for  i s less desirable  However,  limits  difference  the s t e l l a r  X8710, X8713, X8757,  Si  radial  consistency value  unmodified  initially  be e a s i e r  CVn.  Equation  X8680, X8695,  observed  was  p Pup,  20  i t may  X8719, Fe I X8689,  obtained  in  f o r the s t e l l a r  relative  The  of  difference  of  Individual obtained  width.  line  i f t h e y a r e p r e s e n t . Hence i n i t i a l l y ,  case  function  s e t of s t e l l a r  the a p p l i c a t i o n  those  optimising  the  typical  4.4  the case  broader  variations  in  Equation  lines  technique.  A  the  nights,  over  internal the  f o r a l l t h r e e time  an  same  series.  6.5 THE LINE-PROFILE VARIATIONS Figures  6.2  and 6.3  the n i g h t of the 24th lines,  respectively.  one-standard-deviation each value  stellar is  the  show t h e v e l o c i t y  f o r t h e Ca I I X8662 a n d t h e Fe I X8689 The  Ca  II. c u r v e  uncertainty  line-position formal  c u r v e m e a s u r e d on  error  has  of about  measurement. estimate  an  average  ±0.17kms" The  derived  1  in  uncertainty from  the  223  Figure  6.2  The  unoptimised  Ca  II  X8662 v e l o c i t y  curve  + CO LD  CO LO  "3" -d-  CM Q  "~) CO  siu>|  AcJ 3 A T ; e j 3 d  224 Figure  6.3  The  unoptimised  Fe  I  X8689 v e l o c i t y  curve  + 00  LO CO LO  CN o  -)  CO  SUI>J  3ATie|3y  225 Fahlman-Glaspey comparison obtained  to the  p Pup l i n e s  the  major in  value  6.3  than  about  line-position  measurement. value  ±0.09kms~  of about  be  t h e Fe  I  one-standard-deviation  ±0.31kms~ This  1  that  can.not  Similarly,  an  in  in  1  i s much ±0.1kms~  1  each  stellar  larger  than  obtained  the  f o r the  CVn d a t a . Figures  measurement  6.4 and 6.5 uncertainties  respectively. the  effect  spectra.  and  Each of  caused This  uncertainty  by  is  value  by  show t h e i n d i v i d u a l  line-position  for  Fe I  these  inversely  and  Walker  6.5,  t h e Ca  curves  differences  the r a t i o  proportional  in by  rising  The  minima o f t h e v e l o c i t y  Comparing  and  d e c r e a s i n g branches of  explained i f there  i s a correlation  u n c e r t a i n t i e s and t h e l i g h t by about  X8757 v e l o c i t y corresponding  0.08 i n curve.  curve  curve.  This effect  near can  the  velocity  which l e a d s t h e  velocity  phase. F i g u r e Superimposed  line-position  and  the middle of  t o occur  between  s/n  (Campbell  the v e l o c i t y  curve.  the  uncertainty  F i g u r e s 6.3  u n c e r t a i n t y appear  for  each  the spectrum's  s p e c t r u m ' s s/n  t h e minima o r maxima o f t h e v e l o c i t y  curve  multiplying  t h a t t h e u n c e r t a i n t i e s peak n e a r  the  between  that the v e l o c i t y  to the  curves,  been c o r r e c t e d  t h e s/n  between  [ 1 9 7 9 ] ) h a s been u s e d .  one s e e s  II and  has  accomplished  a mean s / n . The a s s u m p t i o n  is  be  value  t h e 20 CVn l i n e s  has  of  large  of about  f o r the discrepancy.  Figure  corrresponding  a very  s/n 20 CVn d a t a . The f a c t  a r e broader  reason  is  corresponding  uncertainty  20  It  f o r t h e much l o w e r  the  curve  technique.  6.6 shows on t h e  uncertainties.  t h e Fe  plot It  is  I  a r e the evident  226  Figure  6.4  Uncertainties  i n t h e Ca II X8662  line  positions  cz o  -—1 •4—1  (_>  c  . — »  CD  cu  CJ  cz QJ  (_ U-  rCD  TD  CD  CU  u— _ H  +  00  cn CD  (_ +-»  cn JC  LD CO LD  CO CD  C\J  CD  a  +-•  —>  CO  —1  ' — '  CD CD  CD CO  r <  CD  00 \—1 h-1 CD  O  -•  LD CO  CL CD ZZ)  CL  a  ( _sm>j) t  A;ujeiJ33un  AJTDOJ3A  Figure  6.5 U n c e r t a i n t i e s  ex  a o •M  i n t h e Fe I X8689 l i n e  positions  0  C D  QJ (_)  C  QJ _ QJ CD u_  ^  Ol —I  oo  \  CD  \ _  ro l_  CD CO  CO  r-»  9  CO CO  CO CO CO oo CD  CO  CO  oo  CD  QJ  in  LO  .. oo CX  oo  C D  C L  CD LD CD  CM  CD CD  o  CD  in  (,.sui>i) A i u T e u a D u n  AJTDOJ3A  BJD2445358+  229 from  the p l o t  correlated.  t h a t the  The  the v e l o c i t y uncertainty with  the  coincides The after line  uncertainty curve  curve curve  light  by  would  with  the  light  line-position  be  p h a s e or  error  technique.  The  by  line-profile  'smoother'  or  than  that, in  this  however,  the  residuals  from  technique  two in  phase  BJD2445358.9  the  individual  will  curve  by  the  of  the  caused  curve  with  with  the as  the  or same sole  b e c a u s e of  the  profile  variations,  the  process  of  trend w i l l  be  the case  the  the  hence would n o t the  contribute  is partly  random. The  cases. This i s probably  limited  them a r e  s p e c t r a would h a v e a  In  residuals  s/n  random n o i s e  technique's  are  the  variations  curve  i s d e r i v e d from  velocity  the  a p p e a r more p r e c i s e  simple  positions.  r e s i d u a l s and  which the  will  systematic  line  of  derived  t h a t most of  with  of  In t h e  the measured  these  but  i n the d i f f e r e n c e d  residuals,  the  out  intrinsic  systematic  corresponding  the case  and  variations  uncertainty. This  smooth t r e n d .  the  a  leading  Hence  variations. A velocity  variations  formal e r r o r  of t h e  residuals  180°  estimate  s t r o n g l y suggest  line-profile  the  line-profile  formal  systematic  standard  to  uncertainties  fact  phase.  are  minimum.  between t h e  error,  Fahlman-Glaspey  source  in  t o be  u n c e r t a i n t y peak n e a r  In a d d i t i o n  this  estimated  i s measured  0.07  in  the v e l o c i t i e s  d e r i v e d u n c e r t a i n t i e s a r e measures of  profiles.  simple  and  about  c u r v e . The  differencing  towards  uncertainties  of  systematic minimising  reflected limited  formal  error  sum  the  of  s/n,  estimate  squares  of  between  the  explanation for Figure  6.6  appears  distinguish  in  more p r e c i s e t h a n  its  230 formal  error  technique  type of  and  linewidth  variations.  seriously. objective  Of to  line-profile produce The is  variations  in  those  the v e l o c i t y  variations.  curve  the  be s i m i l a r other  in  line  those  and  at a  why  the  phase. T h i s  would  BJD2445358.9  ( n e a r v e l o c i t y maximum)  at  BJD2445358.97  velocity than  explain  the  line-profile  correlate  velocity  with  may  be  variations  not  related  over  each X8662  variations  after  spectrum. F i g u r e line  for  this profile taken  can best  each  plot  subtracting  photometric peak than  6.7a shows spectrum  that  curve  the rather  the  result  of  variations.  The  the temperature  and  the  cycle.  be e x a m i n e d  line  the region after  at  that  i . e . a stacked  a mean  near  that  be  to  which  suggest  the p u l s a t i o n  series difference-spectrum residuals  variations  that  the l i g h t  may  the  the  i s stronger  profile  time  parametrise  uncertainty  surface-velocity-field  Line-profile  the  spectra  pulsation-generated variations  more  be  similar  c u r v e • would  variations  spectral-type  may  ( n e a r v e l o c i t y minimum). The f a c t  uncertainties  with  curve  t a k e n a t BJD2445358.85  shape t o  v e l o c i t y minimum  shape  variations.  n e a r a v e l o c i t y minimum. I t i s e x p e c t e d  will  on  the  line  line-profile  pseudo v e l o c i t y  much  affect  i t  to  the  line-depth  velocity  cases,  Systematic  s t a n d a r d p r o f i l e was  like  complicated  the d e r i v e d  of  very  seriously  O t h e r more  course,  systematic  depends  would n o t  affect  use  sensitivity  variations  variations  would  The  Simple  v e l o c i t y curve.  variations  may  imply.  to l i n e - p r o f i l e  the  derived  estimates  from plot  profile of  correcting  t h e Ca for  a of  from II the  231  6.7  The  Ca  II  X8662 l i n e  profiles  and  their  residuals  (b)  0.86784  (a)  0.87868  0.88951  0.90036  0.91030 0.91931  0.92924 0.94014  0.95098 0.96171  0.97244  0.98326  0.99401  8662  6663  1.00474  1.01547  0.5X  '1.02621  8662  8663  232  Figure  6.8  The Fe I X8689 l i n e  profiles  and t h e i r  (b)  (a) 0.86784 0.87868 0.88951 0.90036 0.91030 0.91931 0.92924 0.94014 0.95098 0.96171 0.97244 0.98326 0.99401 1.00474 1.01547 1.02621  Mean  1.01547  8687  1.02621  8689  8687  8689  residuals  gure  6.9 The S i I X8752 and Fe I X8757 l i n e  profiles  '0.90112 '0.90839 '0.91564 0.92289 '0.93021 "0.93748 '0.94473 '0.9S197 '0.95921 "0.96646 '0.97372 '0.98097 "0.98821 '0.9954S "1.00271 '1.00996 "Heart  10X  8748  8750  8752  8754  8756  8758  gure  8748  6.10  The S i I X8752 and Fe I X8757  8750  8752  8754  8756  8758  residuals  gure  8748  6.11  The S i I and Fe I r e s i d u a l s  8750  8752  8754  8756  from BJD2445 356  8758  236 measured v e l o c i t y  shifts.  a Gaussian transfer mid-exposure indicated after The line  subtracting  profiles  of  Fe  I  Fe  I  mean  Figures  X8689  line  Figure  6.9  X8757 l i n e s  and  profiles  i n each  plot  f o r t h e same  J a n u a r y . The  the  indicated It the  and  can  be  seen  from  variations  can  i n the l i n e  a l l  than t h e i r  the  mean l i n e  6.11  shows t h e  the data  were u s e d and  of the to  are 22nd  produce  6.11.  The  from BJD2445356  mean l i n e  of  the  6.10,  be  and  6.11  are  characterised  maxima a t b o t h  But  lines  width  near  lines the  a r e weaker  Near t h e nodes o f t h e l i g h t profiles  as  BJD2445358.90  absorption  profile.  line  that  depth or e q u i v a l e n t  the s t e l l a r  profiles.  variabilities  X8752  corresponding  the n i g h t  6.8b,  minimum a t BJD2445358.97, t h e s t e l l a r their  residuals,  but  6.10  one  series  of the S i I  lines  of days  Figures  Near t h e l i g h t  BJD2445359.03,  over  their  Figure  profiles  Figures  represents  6.11.  variations  the l i n e s .  6.10.  o b s e r v e d on  times i n f r a c t i o n  line-profile  stronger  both  in Figure  systematic of  in  fifteen  show t h e t i m e  and  spectral  same mean l i n e  residuals  mid-exposure  series  It  s p e c t r u m . The  residual  spectrum.  averaged  shows t h e r e g i o n  i s shown i n F i g u r e  of  6.8b  is  residuals  from each  profile  plot  from t h e t i m e  shows t h e  t h r o u g h #35.  residual  taken  6.7b  by The  from BJD2445358  the average of the  #21  line  smoothed  has a a of ± 0 . 0 7 5 & .  profile  t o be  6.8a  have been  of days  mean l i n e  the  respectively. and  a  i s chosen  cycle.  which  spectrum. F i g u r e  from s p e c t r u m  approximately  spectra  in fraction  f o r each  pulsation  function  time  mean p r o f i l e  The  from  their  are light than  curve, mean  237 profile  are minimal.  different in  between  the l i n e  level  depth  plot  variations  line The  t h e Ca I I  a r e more  appears rest  at the  of the  line-intensity  the  of  o f 0.5% o f t h e c o n t i n u u m .  residual  variations.  light  of t h i s  variations  X8662 l i n e  are  only at  continuum in  The  than  inner core  variations  a r e o n l y about  small reverse v a r i a t i o n s  be  seen  two  the  minimum.  than  0.3%  I X8689  of show  line.  0.8% o f t h e c o n t i n u u m .  at the inner l i n e  weaker  to  of  X8757 l i n e s  a s t h e Fe  or  spectral  the r e s t  less  Fe I  the  respect  the l i g h t  is  stacked  line-depth  of the  than  near  X8752 and  The  these  The  a  line  shows t h a t  simple  i s shallower  Si I  However t h e a m p l i t u d e s  level.  F i g u r e 6.8b  small reversal  line-intensity  in  The  t h e r e v e r s e manner w i t h  It  are  lines.  maxima b u t d e e p e r  t h e c o n t i n u u m . The similar  in  the v a r i a t i o n s  The s t r o n g Fe I X8689  complicated  t o vary  amplitude  1%  line  of the l i n e .  near  of  the v a r i o u s s t e l l a r  shows v a r i a t i o n s  line  The a m p l i t u d e s  lines  but  core at  a  can a l s o smaller  amplitude. Similar reported  in  but the  SX Phe ( S t o c k  minimum l i g h t  while  near  known  variables.  light  vary  as The  between F5  [1971],  the  the  Haefner  were a l s o maxima o f  maxima.  variations  over  This a  type  and K1 o v e r  8  have  Set  been  variable  et a l . [1976]).  found the  t o be m i n i m a l line  same  pulsation  spectral-type  spectral  variations  large-amplitude  intensities  line-intensity well  amplitude  peculiar  and T a p i a  absorption-line  occured  larger  a pulsation  at  intensities sequence  cycle  variation  of l o n g - p e r i o d  The  is  in  also  Cepheid  Cepheids  cycle.  of  can  Naturally,  238 the c o r r e s p o n d i n g larger  than  Cepheids in  in  line-intensity  this  i s essentially  the e f f e c t i v e  p Pup, about  case  the  of p  caused  temperature  full  variations Pup. The  by  their  over  the  are very  larger  effect  much l a r g e r pulsation  effective-temperature  much in  change  cycle.  amplitude  is  In only  280K. The  observed  lines  o f Ca  I I , Fe I , S i  known t o have s t r o n g e r i n t e n s i t i e s slightly weaker  later  in  stars  Therefore, caused  (or c o o l e r ) than  if  by  cycle,  temperature  earlier  the observed  mainly  pulsation  of  the the  minima  variations  is  that  temperature  (almost c o i n c i d i n g  exactly  i s observed  the  continuum  level  particular stellar  temperature and  stellar  lines  line  and  a very simple  effect  of  K,,  opacity d  stronger  at  maxima) and with  light  line-intensity  observed of  energy-level  linear  both  line the  population  depth stellar of  Considering only variations,  theory to account  i s much  larger  one  f o r the  spectral-type variations.  KC  opacity  of  the  than  the weak can main  Assuming the  line  one o b t a i n s :  = l  Ad/d  an  transition.  the observed  the continuum  affect  s m a l l temperature  derive  be  were  i n p Pup.  dependence  the  type.  over  with l i g h t  sequence  also  variations  (almost c o i n c i d i n g  the  Temperature v a r i a t i o n s through  then  type  are  spectral  variations  should  maxima  lines  hotter)  line-intensity  are  of s p e c t r a l  p Pup. These (or  lines  weaker a t t e m p e r a t u r e minima). T h i s  in stars  I , and S I  K  /  (  l  K  +  c  K  = (1-d) ( A  (6.1)  )  K /  /  K /  -  A K  C  A  C  )  (6.2)  239  K  = A exp( - E / k T  L  L \ K  A K  K  )  (6.3)  (AT/T)  (6.4)  L  1  =  n  = (E /kT) L  1  / K  C  H  / K  = An ./n _ H  c  H  +  n  e / H  (6.6)  n  K_  = n  n _  = ( v/(n K .)  H  H  n  / n _  e  (6.7)  H  3  H  (6.5)  H  H  ) / K .  (6.8)  H  A n . / n . = (1/2) (AK^/K^) - ( A K _ / K - )  (6.9)  log(K _)  (6.10)  H  H  H  = -(x -)d  H  ~(x )e  =  AK _/K  =2.3  H  H  AK /K H  H  H  - ( 3 / 2 ) l o g f l + ...  u  log(K )  H  - (3/2) l o g S + ...  (AT/T)  = 2.3 (AT/T)  where  H  [  (6.11)  Cx -)0 + 0.65 ] H  [ (x )0 + 0.65 ] H  6 = 5040 / T n = n  H  + h  e  n  e  = e l e c t r o n number  n  H  = number d e n s i t y  density of H  n _  = number d e n s i t y  o f H"  n  = number d e n s i t y  of H  H  H +  d = line  +  depth  T = temperature i n k e l v i n k = Boltzmann's  constant  = low e n e r g y l e v e l X H  X  u  = 0.75 ev = 13.6 ev  of the l i n e  (6.12) (6.13)  240 Equation  6.2  is  obtained  Equation  6.1.  the  line  opacity i s proportional  the  particular  Basically,  energy  independent  of  effect  induced  of  stating  continuum  t o the  i s the of  respectively, K  and  H  equations and  6.13  H~  and  form  is  is  et  been  6.8. given  star  by  Allen  temperature  and  the  Kuhi  [1966]  determinations. determination  of  and  The T  6.2,  observed i s the  is  6.4,  is  ions. This  is a  the  by  and Kurtz  stellar bound-free  and  6.7  are,  constants,  manipulating that  considering and  line  6.11  6.5, For  the  are  Saha  Equations 6.10  6.9,  [1976].  as  can  then  6.12,  and  g i v e n by  AT  is  Danziger  most  probably  6.11,  Ad/d  p Pup,  with  6.12  and  depth  change AT/T  value  agrees  recent  7100K  i n the  weak l i n e s .  observed it  most  opacity  assumption  of E q u a t i o n s  relative  evaluated using Equations  essentially  and  [1973].  the  ±140K. T h i s  is  the  6.10  a  about  the  by  Equations  change  of  considering  6.6  by  relative  f o r any  the  where  derived  The  in  free-free  The  6.13  neglected  6.5  with  6.3  [1972]).  continuum  respectively.  be  al.  obtained  the d e r i v a t i v e s  f u n c t i o n of  in Equation  of t h e d i s s o c i a t i o n  6.8  6.9  i n the  is  A  Equations  together  of E q u a t i o n  are  mainly  ions.  6.8  F6  that  term  the  an  of  Equation  6.7  derivative  for  result  Equation  e<  that  stating  of  at  Equation  the d e f i n i t i o n s  H  i s simply  o b t a i n e d by  6.3.  derivative  t o t h e number of atoms  has  is  the  number d e n s i t y of t h e H"  the  K -.  Equations n>>n  Equation  6.3  (Johnson  6.4  assumption  transitions  The  emission  assumption  proportional reasonable  Equation  temperature  of  the  considering  level.  formulation. Equation derivative  by  the  other best  Therefore,  241 knowing E  and d f o r a  L  line,  the corresponding  Ad/d c a n  be  calculated. The  maximum  X8757 l i n e depth  is  l i n e - d e p t h change  i s about about  10% o f  v a l u e s a r e then temperature The  very  theory  would t h e n  value  well with  of  is  between larger  the c a l c u l a t e d  s i n c e the  weak l i n e s . X8752  This  12 l i n e ;  able for  to predict these  2.83ev.  o f -0.081 f o r agree  one c o n s i d e r s  Ad/d f o r t h i s  superimposed  Si I line  direction  even  T h i s i s not  valid  on  X8750 l i n e  also  line i s  discrepancy  be a p p l i e d  the H I  the  v a l u e s becomes  i s only  f o r the  to the S i the  the theory  of the l i n e - d e p t h  is  I  broad  opacity  has t o be t a k e n  6.1. N e v e r t h e l e s s ,  the  is  at  at into  still  variations  lines.  a line  AK^/K^  line  ± 0 . 0 3 . The  theory  is  therefore,  Examining Equations for  is  a l s o cannot  line  i n Equation  Ad/d  AT=-140K. T h e s e  good when  value  simple  the wavelength of the account  for  and t h e observed  The t h e o r y  line.  Paschen  for this  when one c o n s i d e r s t h e Ca I I X8662 l i n e .  unexpected  line  minimum and -0.08  The c a l c u l a t e d  the observed  the  I  values.  not as  s t r o n g Fe I X8689 l i n e .  Fe  observed  g i v e Ad/d a v a l u e  +0.081  the observed  agreement  ±0.08 w h i l e  continuum, the  value  L  i n the  continuum. Since  +0.08 a t t e m p e r a t u r e  and a  The  the  maximum. The E  simple  AT=+140K  0.8% of t h e  observed  with a s u f f i c i e n t l y  w o u l d be l a r g e r  a direction  6.2 and  change  opposite d i r e c t i o n  than  6.4, one c a n o b s e r v e  l a r g e E ^ v a l u e , the e f f e c t of  t h a t of A K / K «  f o r Ad/d. The l i n e with  that  C  c  This w i l l  would t h e n  respect t o the other  vary  lines.  cause i n the  I t would  242 become  strongest  at  temperature  maxima  condition  i s true  t e m p e r a t u r e m i n i m a . The X8750 l i n e  which  unexpected  since  has it  a  value  i s well  become p r o g r e s s i v e l y  weaker  (or c o o l e r )  Pup.  stronger types. and  Examining  Paschen  one line,  respect  residuals Si  I  p  i n s t a r s of  6.11,  with  than  can the  to  stacked  other  make q u i t e  of  the  a contrast  that  observed  variations,  observed  amplitude and  have t o be  taken  6.6  THE  precision  into  4.4. of  The this  unable  the  to  the  not lines later  progressively spectral  in Figure  opposite the  6.10  of  the  direction H  I  X8750  r e s i d u a l s of  other  variations. of  hydrogen  theory  the  direction. predicted  account The  In the  for  the  effects  of  h y d r o g e n atoms  would  account.  the  individual line the  the  shown i n F i g u r e s  unmodified  line-depth  difference  v a r i a t i o n s would profile  and  Since  simple  and  6.3 from  affect  the  line  shifts.  cause d i f f e r e n c e s  between  the  relative  standard  r e s i d u a l s have m a n i f e s t e d  estimates.  6.2  function  v a r i a t i o n s would  method t o measure  line-depth  error  is  r a d i a l - v e l o c i t y curves  The  fact,  simple  hence d e p l e t i o n  measured u s i n g  Equation  In  of  the  i n the  is  position  fact,  with  the  it  This  (or h o t t e r )  i n the In  Paschen  s p e c t r a l types  the  at  RADIAL V E L O C I T I E S  The are  lines.  the  plots  at  go  which v a r i e d  fact  ionisation  earlier  that  f o r the  they are  residual  observe  the  that  Moreover,  weakest  12.04ev.  i n s t a r s of  v a r i a t i o n s do  X8752 l i n e  spite  known  slightly  the  of  and  line  i n t o the  line-depth  profile.  large  variations  formal should  243 not  alter  still  be  the  line  p o s i t i o n , the  minimal at  where t h e r e  is  difference  the  a perfect  function,  perfect  make i t more  difficult  minimum p o s i t i o n of way  line-profile and  the  line-intensity  variations  function  Equation  shifts. line  This  profile  standard  the  6.12  profile  difference stellar  and  6.13  estimates  would  the  Ca  II  corresponding  unoptimised  can  that  observe  line-intensity Figures  6.12  have a l s o those the  the  6.13.  from t h e  20  CVn  a p p l i c a t i o n of  stellar  l i n e s has  Figures velocity  been a  6.14,  curves  for  6.15, the  then  in measuring  the  the  effect  difference  relative  scale  of  the  individual  minimal. Consequently,  the  has  been a p p l i e d  i n the  Fe two  residual  line  be  p Pup  figures  periodic  trends largely  and  formal are  in  set. Therefore,  modified  difference  re-measure  spectra.  6.4  Figures  formal  I X8757 l i n e  Figures  have  to  derived  in  smaller  the  the  the  ones  data  in  would  modified  the  Moreover, the  become much  than  The  from  these  variations  and  will  X8662 and  Comparing  This  measure t h e  subsequently  respectively.  profiles.  order,  the  that  positions  show  f o r the  such  function  line  use  to  case  function.  first  function  linearly  line  •modified all  difference  the  should  i n the  shallower  less precise  i s to  4.5  the  match.  difference to  function  p o s i t i o n as  match between  to minimise,  from  shift  however, w o u l d be  case w i t h the  One  same  difference  error  positions,  against  the  and  6.6,  one  by  the  caused  disappeared error  in  estimates  agreement  with  i t appears  that  function  to  the  success. and Ca  6.16 II  show t h e X8662, H  I  measured r e l a t i v e X8750, and  Fe  I  244  Figure  6.12 The o p t i m i s e d  Ca II X8662  uncertainties  + CO LO CO LO C\l Q —)  CO  LD  CD  LO O  CD  (,.sui>i) A i u j e u a j u n  CD CD CD  AIT30J3A  245  Figure  6.13  The o p t i m i s e d Fe I X8757  uncertainties  s—,  cr o  — i •M CJ  cr  .—i  CD  UQJ CJ  cr  TP  QJ l_ CU lota-  CO CD  cu  CO —I pz -•H 4—'  CL  a  CO CO  .  CD  JZ +-> — 1  - —  CO LO CO  •  CO  CD  CD  00  LO CM  CD CM  LO  CD  LO CD  O  (,.su>|)  AjUjeiJ33UH  AJT30J3A  p Pup : Ca I I  X8662  (with o p t i m i s e d d i f f e r e n c e  0.85  0.89  0.93  0.97  1.01  0.85  0.89  0.93  0.97  1.01  BJD2445358+  function)  p Pup : H I  X 8 7 5 0 (with o p t i m i s e d d i f f e r e n c e  function)  0-85  0.89  0.93  0.97  1.01  0.85  0.89  0.93  0.97  1.01  BJD2445358+  248 Figure  6.16  The o p t i m i s e d  Fe I X8689 v e l o c i t y  curve  rr o  —i  +-• '—i u CD •  £Z  ZD  U -  QJ  U  CZ QJ l_ QJ ij_ CO  U_  —1 CD  TD TD  00  QJ  LD  cn  00  ••H  E=  •M  LD  CD CD  CL a CD  CM  a ~o  _c  CQ  —1 ' — '  cn  CO CD CO r<  CD  OO •  CD  i ( i i QJ Li_ LD OO « • CL CD  ZD  Q_  (,.sui>|)  Ad  3AjieT3cj  249  Figure  6.17  The  mean o p t i m i s e d  Fe  I velocity  curve  + CO LO  00  LO CM  a  —> m  (,.sui>|)  Ad  3AT;ej3^  250  Figure  6.18  The mean o p t i m i s e d  S i I velocity  curve  + CO LO CO LD C\l Q —> CO  (,.sui>l)  Ad  3AT ej3y +  251  Figure  6.19  The mean o p t i m i s e d  S I velocity  curve  + CO LO CO LO  Q  —)  CO  (,.SUI>|) Ac!  3AT BT3cJ +  252  Figure  6.20  The o p t i m i s e d  Ca II  velocities  from  the  22nd  + CD LO CO LO  CM  a CO.  (,.sui>|)  Ad  3AT;GT3^  p Pup : Ca I I 0.82  — i i  X8662  (with o p t i m i s e d d i f f e r e n c e  0.86  0.90  1 i  1 i  4  »'  2  '  0.94 1 1  -  1 — 1—  -  \  \  /  " \  /  2  0.98  0  /  0  function)  -  <*  4  i  0.82  1  0.86  1  0.90  1  0.94  BJD2445359+  L_  0.98  254 X8689 l i n e s ,  respectively.  t h e mean v e l o c i t y S I,  respectively.  Figures  c u r v e s from  lines  6.20 and the n i g h t s  A l l the v e l o c i t i e s  X8750, Fe I X8689, and Mg  are l i s t e d  derived  from  mean  X8757, and X8764 v e l o c i t i e s .  inversely error also  Similarly, weighted  each mean  velocities.  HF  line  night  of the  estimate on  shown  spectra. are  X8686,  effect  is  most  6.22  dispersion removed  of t h i s ,  n o t random. The coinciding  of the  X8728,  X8713,  depth  mean  and  formal  of  X8742, velocity  data.  from and  was  the X8752  derived  errors  with  the u n c e r t a i n t i e s  30ms~  shows t h e i n d i v i d u a l fit.  The r e l a t i v e  the  result  plot.  appear  caused  the  error  dependence  The low  values  o f t h e h i g h s/n o f  one c a n o b s e r v e  the l i g h t  probably  of  f o r t h e d a t a t a k e n on t h e  1  from  6.22 a r e t h e  maximum  line  was d e r i v e d  mean S I  was a b o u t  been  In s p i t e  square  was  have been c h o s e n t o  o f t h e mean  i n t r o d u c e d by  i n t h e HF  i n Figure  Table  o f t h e Fe I , S i I , and S I  I velocity  24th. F i g u r e  t h e s/n h a s  in  I  mean o f t h e X8680 a n d X8695 v e l o c i t i e s .  mean e r r o r positions  are l i s t e d  over a l l t h r e e n i g h t s  Meanwhile, each  the weighted The  the  25th,  m e a s u r e m e n t s . The same w e i g h t h a s  line  mean S i of  II  t h e Ca I I X8662, H  The w e i g h t s  t o the  i n the l i n e - p o s i t i o n f o r each  t h e Ca  o f t h e X8689, X8710,  the square  proportional  been u s e d  from  to  and  6.4. E a c h mean Fe I v e l o c i t y  the weighted  be p r o p o r t i o n a l  show  o f t h e 22nd and  I X8719 l i n e s  i n Table  o f Fe I , S i I ,  6.21  from  6.3 w h i l e a l l t h e mean v e l o c i t i e s lines  6.17, 6.18, and 6.19 show  c u r v e s from t h e  respectively.  X8662 v e l o c i t y  Figures  to  that  be p e r i o d i c  minimum o f by  the  the,  errors  with  p Pup.  the  the This  line-intensity  255 Table  6.3  Relative  radial  velocities  of  p Pup  (I)  ***************************************** #  Ca  II  \8662  H I  1  -1 .118  kms'  1  + 0. 1 06 kms"  1  -1 . 268  kms"  2  + 0 .245  kms"  1  + 0. 014  kms"  1  + 0. 168  3  + 1.484  kms  1  + 1 .710  kms"  1  4  + 2 .590  kms"  1  + 1 .973  kms"  5  + 3 .702  kms"  1  + 3 . 425  6  + 4 .525  kms"  1  7  + 4 .771  kms"  8  + 4 .758  9  X8750  Fe  I  X8689  Mg I  X8719  1  - 0 . 885  kms"  1  kms"  1  + 0. 186  kms"  1  + 1 .483  kms"  1  + 1 .516  kms"  1  1  + 2. 651  kms"  1  + 2. 582  kms"  1  kms"  1  + 3 . 798  kms"  1  + 3 . 598  kms"  1  +4. 806  kms"  1  + 4. 560  kms"  1  + 4. 349  kms"  1  1  + 4. 100  kms"  1  + 4. 856  kms"  1  + 4. 630  kms"  1  kms"  1  + 4. 151  kms"  1  + 4. 629  kms"  1  + 4. 529  kms"  1  + 4 .079  kms"  1  + 3 . 323  kms"  1  + 3. 846  kms"  1  + 3 . 947  kms"  1  10  + 2 .898  kms"  1  + 2. 256  kms"  1  + 2. 756  kms"  1  + 2. 705  kms"  1  1 1  + 1.521  kms"  1  + 0. 1 36 kms"  1  + 1 .1 38 kms"  1  + 0. 928  kms"  1  1 2  - 0 .213  kms"  1  -1 . 060  kms"  1  - 0 . 602  kms"  1  - o . 828  kms"  1  1 3  -1 .948  kms"  1  - 2 . 650  kms"  1  - 2 . 429  kms"  1  - 2 . 271  kms"  1  14  -3 .220  kms"  1  - 3 . 179 kms"  1  - 3 . 702  kms"  1  - 3 . 873  kms"  1  1 5  -4 .105  kms"  1  - 4 . 1 93 kms"  1  - 4 . 571  kms"  1  - 4 . 802  kms"  1  16  -4 .361  kms"  1  - 5 . 561  kms"  1  - 4 . 837  kms"  1  - 4 . 855  kms"  1  17  -4 . 1 37 kms"  1  - 4 . 270  kms"  1  - 4 . 614  kms"  1  - 4 . 641  kms"  1  18  - 4 .644  kms"  1  - 4 . 308  kms"  1  - 4 . 793  kms"  1  - 4 . 600  kms"  1  19  - 4 .386  kms"  1  - 4 . 386  kms"  1  - 4 . 1 29 kms"  1  - 4 . 045  kms"  1  20  -2 .791  kms"  1  - 2 . 791  kms"  1  - 2 . 413  kms"  1  - 2 . 402  kms"  1  21  + 0 .448  kms"  1  + 0. 448  kms"  1  - o . 645  kms"  1  - 0 . 738  kms"  1  22  + 1.915  kms"  1  + 1 .915  kms"  1  + 1 .391  kms"  1  + 1 .484  kms"  1  23  + 2 .845  kms"  1  + 2. 845  kms"  1  + 3. 1 62 kms"  1  + 3 . 024  kms"  1  24  + 4 .082  kms" • +4. 082  kms"  1  + 4. 339  kms"  1  + 4. 383  kms"  1  25  + 4 .221  kms"  + 4. 221  kms"  1  + 4. 802  kms"  1  + 4. 845  kms"  1  _  1  1  256  26  + 3.878 kms"  27  + 2.613 kms"  28  + 0 .781  29  -1 .424 kms"  30  -3 .007 kms"  31  -3 .898 kms"  32  -3 .893 kms"  33  -2 .970 . kms" -2 .970 kms"  34  -1 .677 kms"  35  + 0 .821  36  -2 .114 kms"  37  -0 .336 kms"  38  + 1.383 kms"  39  + 2 .907 kms"  40  + 4 .204 kms"  41  + 4.489 kms"  42  + 3.633 kms"  43  + 1.862 kms"  44  -0 .553 kms"  45  -2 .856 kms"  +3 .878 kms"  1  + 2.613 kms"  1  kms"  + 0 .781  1  kms"  -1 .424 kms"  1  -3 .007 kms"  1  -3 .898 kms"  1  -3 .893 kms"  1  1  kms"  1  1  1  1  1  1  1  1  1  1  1  1  -1 .677 kms" + 0.821  kms"  -2 .616 kms" + 1.087 kms" + 0 .057 kms" + 3.627 kms" + 5 .117 kms" + 4 .478 kms" + 2 .262 kms" + 1.544 kms" + 0.930 kms" -2 .930 kms"  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  + 4.247 kms" + 2.497 kms" + 0.019 kms" -2 .458 kms" -4 .099 kms" -4 .776 kms" -4 .230 kms" -3 .045 kms" -1 .105 kms" +0 .937 kms" -2 .253 kms" -0 .362 kms" + 1.590 kms" + 3.173 kms" + 4.328 kms" + 4.512 kms" + 3.676 kms" + 1.870 kms" -0 .637 kms" -3 .124 kms"  **********************************************  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  +4. 391  kms"  1  +2. 715 kms"  1  + 0.235 kms"  1  -2. 1 97 kms" -3. 879 kms"  1  1  -4. 869 kms" -4. 495 kms" -3. 1 53 kms" -1 . 1 16 kms" + 0.908 kms" -1 . 895 kms" -o. 556 kms" +1 . 209 kms" + 3. 1 54 kms" + 4. 487 kms" + 4. 752 kms" + 3.876 kms" + 2.076 kms" -0. 214 kms" -2. 837 kms"  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  257  Table  6.4  Relative  radial  velocities  of  p Pup ( I I )  ***************************************** mean of  Si  1  -0.855  kms"  1  -0.950  kms"  1  +0.341  kms"  1  +0.462 kms"  3  +1.508 kms"  1  +1.715  kms"  1  + 1 .846 kms"  4  +2.694 kms"  1  +2.956  kms"  1  +3.056  kms"  5  +3.824 kms"  1  +3.968 kms"  1  +4.007  kms"  6  +4.600  kms"  1  +4.695  kms"  1  +4.793 kms"  7  +4.860  kms"  1  +4.976  kms"  1  +5.002 kms"  8  +4.655  kms"  1  +4.871  kms"  1  +4.767  kms"  9  +3.866  kms"  1  +4.107  kms"  1  +4.017  kms"  1 0  +2.793 kms"  1  +2.713 kms"  1  +2.803 kms"  1 1  +1.162 kms"  1  +1.309  kms"  1  +1.244 kms"  1 2  -0.571  kms"  1  -0.651  kms"  1  -0.603  kms"  1 3  -2.384  kms"  1  -2.234  kms"  1  -2.332  kms"  1 4  -3.674  kms'  1  -3.447  kms"  1  -3.663  kms"  1 5  -4.526  kms"  1  -4.310  kms"  1  -4.518  kms"  1 6  -4.761  kms"  1  -4.629  kms"  1  -4.799  kms"  1 7  -4.544  kms"  1  -4.256  kms"  1  -4.629  kms"  18  -4.772  kms"  1  -4.768  kms"  1  -4.686  kms"  '19  -4.097  kms"  1  -3.964  kms" '  -4.046  kms"  - 2 . 3 7 9 kms"  1  -2.267  kms"  1  -2.211  kms"  #  mean of  1  -1.119  kms"  2  +0.211  20  .  Fe I  I  mean o f S kms"  21  -0.592  kms"  1  -0.378  kms"  1  -0.440  kms"  22  +1.456  kms"  1  +1.652 kms"  1  +1.585  kms"  23  +3.191  kms"  1  +3.322 kms"  1  +3.283 kms"  24  +4.362 kms"  1  +4.450' kms"  1  +4.460  kms"  25  +4.798 k m s '  1  +4.746  1  +4.791  kms"  kms"  258  26  +4.228  kms"  27  +2.519  kms"  28  +0.058  29  +4.116  kms"  1  •+4.319  kms"  1  1  +2.548  kms"  1  +2.551  kms"  1  kms"  1  +0.176  kms"  1  +0.141  kms'  1  -2.457  kms'  1  -2.367  kms"  1  -2.277  kms"  1  30  -4.094  kms  -3.948  kms"  1  -3.972  kms"  1  31  -4.720  kms"  -4.464  kms"  1  -4.646  kms"  1  32  -4.196  kms  -4.100  kms"  1  -4.138  kms"  1  33  -2.964  kms"  1  -2.767  kms"  1  -2.862  kms"  1  34  -1.041  kms"  1  -0.875  kms"  1  -0.917  kms"  1  35  +0.987  kms"  1  +1.086  kms"  1  +1.146  kms"  1  36  -2.220  kms"  1  -1.990  kms"  1  -1 .955, kms"  1  37  -0.361  kms"  1  -0.178  kms"  1  -0.319  kms"  1  38  +1.534 kms"  1  +1.807  kms"  1  +1.639  kms"  1  39  +3.155  kms"  1  +3.398 kms"  1  +3.077  kms"  1  40  +4.262 kms"  1  +4.439  kms"  1  +4.151  kms"  1  41  +4.500  kms"  1  +4.512 kms"  1  +4.393 kms"  1  42  +3.689  kms"  1  +3.562 kms"  1  +3.647  kms"  1  43  +1.803 kms"  1  +1.887  kms"  1  +1.718  kms"  1  44  -0.701  kms"  1  -0.901  kms"  1  -0.895  kms"  1  45  -3.136  kms"  1  -3.096  kms"  1  -3.230  kms"  1  -  -  1  1  1  1  ****************************************  259 variations standard would  of  the  spectrum  then  affect  stellar are  lines.  Line cancellations  i m p e r f e c t and  t h e HF  line-position  A p e r i o d - s e a r c h i n g procedure velocities technique very  of  all  three  r e q u i r e s evenly  appropriate for  several this  n i g h t s . The  present  determine  this  set  p e r i o d of  a number of t r i a l  each case,  a  The of  velocity  A p e r i o d of  velocities. quite  well with  [1963] and Doss  the  of  Ca  not  which spreads  used  program used  by  Ninkov  some  measured  s h o r t time  [1985] t o  [1978]. and  in  point.  best  plot  f o r t h e Ca this  given  determined  d  on  significance  coverage,  0.14088141  0.14088067  in  I t i s based  which g i v e s the  be  over  f o r each v e l o c i t y  was  II  Entropy  hence w o u l d  according to  t h e p e r i o d of value  and  Cygnus X-1.  one  0.14095  In view of t h e  Maximum  computer  is calculated  a g a i n s t phase  The  to the  p e r i o d s are attempted,  optimum p e r i o d would t h e  criteria.  agrees  by by  II  Ponsen Thulasi  [1969]. The  while The  phase  residuals  p r o g r a m g i v e n by Morbey  Basically,  the  determinations.  of data  initially  computer  resulting  applied  data  period-finding  orbital  t h e a l g o r i t h m and  was  nights. spaced  a n a l y s i s was  the  the  by  Ca  I I X8662 v e l o c i t i e s  the v a l u e  f o r the  corresponding  velocities  are  These are given  by  [1980],  values  9.46,  M e a n w h i l e , t h e Mg  H  f o r the and  I X8719 l i n e  Danzinger  than and  respectively.  value  I X8750 v e l o c i t i e s  9.23,  a l l lower  have a 2K  Kuhi  I,  S i I,  a  2K  value  [1966]  and  Struve  11  1  8.35kms . _1  and  S  I  of  9.64kms~ .  and  11.5kms~  Campos et  9.08kms"  respectively.  1  v a l u e s of  However,  is  9.41kms~ ,  has  the  Fe  of  al  1  and [1956]  1  Smith and  260 Figure  6.22  Errors  i n the  HF  dispersion  fits  Q 1  60  X  P  cr  OT  -  _  cn i_  ©  QJ CL  cn  /  —H  -CD  (TT)  n:  CD  a  t  oo  -O  CD  cD  1_ CD "O  CD  -  -  o /  CO CD  CM  a  © 0  OT  /  ~0 CD  0 CD CO  v,  cr cn +-» W  LO  ..  CO  CTL ZD  CD  L O  00  CL  a  1  (JO O  1  1  C\J  CD  + CO LO CO LO  O  1  CD CD  CD  (^su)]) A i u j e u a o u n  AITDOJSA  261 Figure  6.23  Velocity  difference  ( Ca II  curve  -  Fe I c u r v e  0  h  o  Q  CO QJ  en  rr  ro  CD N  QJ  O  r-  / Q Q  CO CJ)  CD CD  1  6  N.  N  o  CD  ©  I  CM CD CO CD OO  y 0  00  ei  CD CO  y  /  CD  I—I  CD  © /  ro <->  CM a CO  QJ  <<  + CO LD CD LD  LD CO  LD  00  CL C D ZD  Q_  1  CD  i  i  i  i  in  CM  LQ  CD CD  LO  CM  CD LO  CD  CD  CD  CD  CD  (,.SMI>|) 3 3 U 3 J 3 J J J P  1  A1T30J3A  1  )  262  Bessell  [1969]  have  measured  9.5kms~ , r e s p e c t i v e l y . 1  the e f f e c t spectrum Figure Ca  of phase  reported  6.23  In  lines.  the other This  velocity  observed  effect It  the  about  minima. t o be  observed  more  is  a  rather  lines.  behind  discussed  be  of the  H I curve appears  Hoof  each  between  the  of the  two  large  points.  used  observed  cast  systematic  check  found  in  further  i n Chapter  other eight.  of  on  the  But  the  velocity of  five  from  the  the  any c a s e ,  the  those  H I velocity  variable  X8750  or  shape t h a n  i s similar  the  those  reality  phenomenon. In  the other curves  the  of the lower s/n.  the  phenomenon o f t h e  effect  trend  velocities  because  I  doubt  phenomenon.  t o have a d i f f e r e n t The  H  i n phase w i t h  H I  of  comparing the  the  however,  o r 2%  o f a few i s o l a t e d  The  to  curve,  by  phase-lag  X8662  c u r v e s of a l l  0.003  T h i s may  i s not the r e s u l t  cannot  repeatabilty  lagging  been  period.  t h e Ca I I  However,  n i g h t s a r e of poorer q u a l i t y  the other  The e f f e c t  obtained  curves.  consecutive velocity  van  is  velocity  of  they  and  of  the  plot  differences,  c u r v e s by  value  reality  And  difference  The H I X8750 v e l o c i t y  maximum a p p e a r s  the other  other  9.7,  time  6% o f  a r e i n phase w i t h t h e v e l o c i t y  corresponding  points.  exposure  o n l y about  of t h e a m p l i t u d e  other m e t a l l i c  velocity  v a l u e s of  2K v a l u e s i s v e r y e v i d e n t i n t h e p l o t .  velocities  period.  was  The  mean Fe I v e l o c i t i e s .  spite  lags a l l  smearing.  here  2K  The d i s c r e p a n c y c o u l d n o t have  shows t h e v e l o c i t y  I I and t h e  different  the  to the stars.  of  curve  classical This  is  263 6.7 DISCUSSION Using  the  93kms" mag" 1  Smith  would  conclusion analysis  the  rather  imply  radial  a  mean  parameters  from  in  fundamental  values  [1982b],  arrived  at  theoretical same  imply  v  same  [1980] i n  and  an  f o r p Pup.  by B r e g e r  respectively,  the  by  2K/Am  f o r p Pup. The  for log g  pulsation  f o r l o g g. T s v e t k o v  p Pup a g a i n s t  f o r the  one c a n c a l c u l a t e  0.044 a n d 0.0395 day q u o t e d Tsvetkov  This  obtained  1  discussed i n Kurtz  3.53  6.1,  radial  of  their  the p u b l i s h e d values of the  0.03 d a y f o r p Pup. T h i s v a l u e w o u l d of  value  parameter.  v  value  pulsation  a  profiles.  of  Table  2K/Am  large  T h i s h a s been  value  lines,  by Campos a n d S m i t h  i s a discrepancy  g parameter.  I  of 103±12kms~'mag"  This  was o b t a i n e d  t h e Fe  f o r the  value  o f p Pup's l i n e  There  Using  of  obtained  with  [1982b].  parameter  log  is  1  would agree  2K v a l u e  The v a l u e s  [1982b] who compared  of  other of  identification  were c a l c u l a t e d  conclusion  the  a Q value  a n d Bregman  mode-dependent  [1976].  of  [1975] a n d  using  higher  the  ^  v a l u e s , has  fundamental  of also  radial  pulsat ion. Because of variablities, study the with  i t s b r i g h t n e s s , sharp  p Pup  the 6 Scuti  identification the  attainable  would  of a  unique  The h i g h  study  impose  of  5  problems  Scuti  limitations curve  affect  both  on  of 5 Scuti the  and  simple  opportunity  s/n d a t a  few a d d i t i o n a l  i n the v e l o c i t y  variations  a rather  pulsation.  spectroscopic  variations  profile  offers  lines,  has  enable  associated  stars. the  Profile precision  variables.  stellar  to  and  The HF  264 line-position be  the  fields.  determinations.  result The  of  cause  phase w i t h  the  variations  can  the  core  of  pulsation-generated  temperature  would a l s o  T h e s e v a r i a t i o n s may  variations  over  surface the  line-profile variations light  also  t h e Fe  be  curve very  and  not  has  pulsation  and  as  the  indicated.  only  velocity  these  the v e l o c i t i e s .  complicated  I X8689 l i n e  not  cycle are  in  These  reversal  at  Chapter  7  THE DELTA SCUTI VARIABLE o  7.1  INTRODUCTION The  5 Scuti value et  star  o  Eridani  1  variable.  o f 96kms"  Other  Halprin  Hoffleit  and J a s c h e k  and  Moon  Bregman  reported  can  [1978],  been  t o be  done on  amplitude  intermediate-band  y  [1975]  photometry.  They  found  represented  by is  determined  t o be 0.0815  about  o f 0.1291  7.2 THE The  o  b  the  0.05  m  and  Baglin  few  star  was  light  first et a l .  was f o u n d  m  the  in  the  Jorgensen star  curves  oscillation. the  et a l .  [1982]. Very  photometry.  that  [1982b],  by J o r g e n s e n  0.02  reobserved  i n Table  and  E r i . This  1  vsini  [1981], Breger  and J a s c h e k  simple p e r i o d i c  amplitude  the star  [1979],  of about  and  Norgaard-Nielsen  a  Tsvetkov  Antonello et a l .  a  i s g i v e n by B a g l i n  1  in  a photometric v a r i a b l e  [1971]. A l i g h t  period  found  Breger  Hoffleit  broad-line  E r i a r e summarised  1  be  [1983],  [ 1 9 7 5 ] , and  s t u d i e s have  for o  ) is a  [1982] q u o t e  w h i l e a v a l u e o f 98kms~  1  parameters  [1972], Gupta  HF  ( 38 E r i , HR1298  a l . [1973]. Parameters  7.1.  of  ERI  1  dominant  (1.96 h o u r s ) . T h e r e may  . No s t u d y o f t h e s p e c t r o s c o p i c  and  with  uvby  cannot The  light  period be a  be  is  second  variations  h a s been r e p o r t e d .  OBSERVATIONS star  absorption  o  1  E r i was o b s e r v e d cell  at  t e l e s c o p e on t h e 2 5 t h o f  the January  265  spectroscopically  with the  Canada-France-Hawaii 1983 UT. A t i m e  series  3.6m of  266 Table  7.1  Parameters f o r o  1  Eri  ****************************************** Reference HD  number  SAO DM  : 26574  number  : 131019  number ': -7  R.A.  (1950)  Dec.  (1950)  764 4  9  h  25.321  m  : -6° 57'  Annual p a r a l l a x  s  59.675"  : +0.033"  Proper  m o t i o n i n R.A.  :  +0.004"/yr  Proper  m o t i o n i n Dec.  :  +0.083"/yr  : b  199.32°  : -38.39°  JI  Spectral Radial Vsini M  =  v  T  e f f  log  type  : F2  velocity = 98  kms"  II-III  = 11  kms  Breger -1  Baglin  1  +1.85  Eggen  = 7300K g = 3.9  (cgs)  B r o a d band p h o t o m e t r y V = 4. 0 5  m  B - V =  +0 . 3 3  m  u -  V =  +0 . 4 7  m  v -  R =  +0 . 3 2  m  v -  I =  +0 . 4 8  m  I n t e r m e d i a t e band p h o t o m e t r y /3 =  Eggen  2.730  m  [1979] [1979] e t a l . [1973] [1979]  Breger  and Bregman  [1975]  Breger  and Bergman  [1975]  Iriate  e t a l . [1965]  Eggen  [1979]  267  b  - y = 0. 197'"  m,  = 0.l92  m  c,  =  m  6m,  0.789  = -0.013  m  ***************************************  spectra  were o b t a i n e d under  same i n s t r u m e n t a l discussed Stellar lines  a n d lamp  spectrum  the  h o u r s ) . Each  spectra  in  T a b l e 7.2  lines. these  650  seconds. This period  using  o  1  HF  exposure  corresponds to 0.0815  lines  time  day  the  The m i d - e x p o s u r e  for about (1.96  velocities dispersion  set  l a g the b a r y c e n t r i c  262  times  of  #1 and  #2  w i t h o u t t h e imposed  HF  i n T a b l e 7.2. S p e c t r u m  E r i spectra  radial  #3. F o r t h i s  7.1. The mean  s t e l l a r or  of  HF  s p e c t r u m has a mean s/n o f a b o u t  a r e summarised  spectra  the  used.  t h e imposed  in Figure  shown. The  at the continuum.  a r e the  p r o c e d u r e s were  and w i t h o u t  a r e shown  also  stellar+HF  Approximate  spectrum times  with  "cycle-count"  each p o i n t  the  7.3  was  observing  with either  removed a r e  spectrum  one-tenth  in  spectra  were o b t a i n e d . T h e s e  numerically  and w i t h t h e  s e t u p s a s f o r t h e d a t a on 20 CVn and p Pup  earlier. Similar  stellar+HF  each  t h e same c o n d i t i o n s  can  be m e a s u r e d  relation  of o b s e r v a t i o n s , t i m e s by a b o u t  4.4  from  determined the  for  heliocentic  seconds.  THE DATA REDUCTION The  d a t a were p r o c e s s e d a n d r e d u c e d u s i n g  p r o c e d u r e which  were a p p l i e d  w i t h t h e 20 CVn  reduction,  the  identical  t o t h e 20 CVn d a t a . I n f a c t ,  t h e mean s t e l l a r s p e c t r u m of  as the ,  268  Figure  7.1 The o  1  Eri  spectrum  269 Table  7.2 M i d - e x p o s u r e  times  f o r the o  E r i spectra  1  ******************************************* #  25 Jan  83 UT+  1  (04 :53: 26 .22)  2445359. 7059216  1h  23m  45s  East  2  (05 :05: 05 .73)  2445359. 7140171  1h  1 2m 03s  East  3  (05 :26: 1 1.87)  2445359. 7286704  Oh 50m  54s  East  4  (05 :37: 27 .27)  2445359. 7364868  Oh 39m  36s  East  5  (05 :51 •37 .86)  2445359. 7463308  Oh 25m  23s  East  6  (06 :02 55 .48)  2445359. 7541730  Oh  1 4m 04s  East  7  (06 : 1 4 1 1.26)  2445359. 7619939  Oh 02m  46s  East  8  (06 :25 26 .90)  2445359. 7698132  Oh 08m  31s  West  9  (06 :36 42 .96)  2445359. 7776373  Oh . 1 9m 49s  West  10  (06 :47 59 .41 )  2445359. 7854660  Oh 31m  08s  West  1 1  (06 :59 • 1 7.50)  2445359. 7933136  Oh 42m  27s  West  12  (07 : 10 :33 .25)  2445359. 8011341  Oh 53m  45s  West  Barycentric  hour a n g l e  JD  *********************************************************** time  series  standard  has  been  spectrum.  numerically position  chosen This  to  be  spectrum  removed and i t p r o v i d e s references  in  both  the  pulsation  related  20  any  CVn,  It  line  c a n be  standard  line-profile  corrected  procedure.  in  lines  the line-shape of  In a d d i t i o n t o  caused  having will  are s t e l l a r  As i n t h e c a s e o f by  the  velocity  t h e mean s p e c t r u m w i l l a second  and the  one c y c l e  i f there  variations.  i n forming  HF  application  spectrum  broadening  phase-smearing e f f e c t  reduction  the  s / n , t h e mean s p e c t r u m a v e r a g e d o v e r  be a more a p p r o p r i a t e  small.  radial-velocity  has  Fahlman-Glaspey d i f f e r e n c e technique. a higher  the  iteration  of  be the  270 Figure  7.2  The  Ca  II  X8662  velocity  curve  of  o1  Eri  C\J C M  CD  1  1  1  o / CD p  ei  >  P + cn  CD  LD CO LD  1  ? 1  LD  LT)  —  C M Q  ~ D QQ  \ CO  -  -  CD  \ \  r-- —  \  _  \]  CD  l  l l  CD  CM-  ,.SUI>I  Ad  CM  3AJjej3^  CD  271 Figure  7.3 The H I X8750 v e l o c i t y  c u r v e o f o'  Eri  C M C M  C D  I  +  01  LO CO LO  C M Q  ~D CD  LO 00  UJ  00 00 C M  C M  ,.sui>(  Ad  3Aj  +  eT3^  272  Figure  7.4  The v e l o c i t y  c u r v e of  —<  o  1  E r i from weak  O  1  lines  1  1  1  G |  CO (AJ  CD  CD  r-  CO LO CO CO CO  r<  cn co  CO CO  r< CD CO CO CO r<  CD  i  ?  o  /  LO  00  LO  /  CD  •^r csi CD  ~D  CO  CO  CO  \  b \  QJ  CO  + co LO CO LO  6  CO  LU  CD  CD  \  V h  CD l  l  CD l  CD  ,.siu>| AcJ  3AueT3cj  273 7.4  THE  RADIAL VELOCITIES  The used HF  same c r i t e r i a  limits  the  lines.  A typical  s e t of  in  w i d t h . The 4.4  application  was  used  obtained  f o r the s t e l l a r  These are p r e s e n t e d s/n  of  velocity even  the  f o r the  X8695, Fe  by  lines.  Table  the  through  T h i s has  low 7.3  7.4.  been  equal  2K  lists The  values  from  similar  s/n.  estimate  over  11kms  is  -1  error  ±63ms~ . 1  CVn  and  The  II c u r v e  HF  agrees p  Pup  H I  to  uncertainty  lines.  In  fact, X8680,  weaker  shown i n is  Figures  11.947kms" . 1  It i s  of a l l  the  approximately [1979].  dispersion  fits with  sets  7.2  one  partially  for these  which  has  ±1.34kms"  measurement. T h i s i s t h e  the Fahlman-Glaspey  were X8750.  S I  This i s  data  of  line  reasonable  very well  in Figure  the  respectively.  by Eggen  i n the  This  t h e 20 Ca  quoted  in  curves  t h e mean v e l o c i t y cycle.  from  i n F i g u r e 7.4,  the v e l o c i t i e s  as  80  lines  amplitudes  the observed  line-position from  lead  mean s y s t e m i c v e l o c i t y  one-standard-deviation stellar  a l l  mean s t a n d a r d  spectra  to  variations.  velocity  i s about  and  7.3,  I X8728 g i v e n  and  t o measure  and  of the  stellar  lines  I I X8662  curve  the c y c l i c  t o the v a l u e of The  Si  calculated  l i n e s averaged  Ca  were  function  technique  t o o low  mean v e l o c i t y  discern  caused  limits  f o r t h e o t h e r weaker s t e l l a r  I X8689, and  barely  the  radial-velocity  lines  are  reduction  stellar  i n F i g u r e s 7.2  spectra  curves  line  the  relative  CVn  difference  of the Fahlman-Glaspey  Individual  The  for  20  for both  stellar  unmodified  shifts.  the  line  t o choose  Equation  7.2  f o r the  here  pixels  can  used  an 1  the have  average in  formal  t e c h n i q u e . The  of  large  each error value  274 Table  7.3 R e l a t i v e  radial  velocities  of o E r i 1  ***************************************** #  Ca I I X8662  H I X8750  mean weak  lines  1  -2.068 kms'  1  -2.136 kms"  1  -0.369  kms"  1  2  -0.855 kms"  1  -1.060 kms"  1  -0.369  kms"  1  3  +0.475 kms"  1  -0.434 kms"  1  +0.028  kms"  1  4  +1.168 kms"  1  +1.060 kms"  1  +0.123  kms"  1  5  +2.162 k m s  +1.942 k m s  - 1  +0.757  kms'  1  6  +1.968 kms"  1  +1.015 k m s  - 1  +0.370  kms  7  +1.797 kms"  1  +2.163 kms"  1  +0.298  kms"  1  8  +0.517 kms"  1  +0.620 kms"  1  +0.164  kms"  1  9  -0.129 kms~  1  -0.504 kms"  1  +0.058  kms"  1  10  -1.212 kms"  1  -1.172 kms"  1  -0.638 kms"  1  11  -1.849 kms"  1  -0.923 kms"  1  -0.225  kms'  1  12  -1.974 kms"  1  -0.571  1  -0.196  kms"  1  - 1  kms"  - 1  *********************************************************** here The  may  signify  the  corresponding values  7.4 a r e ± 1 . 5 6 k m s " Periodogram analyses in  1  f o r the 1  and  Maximum  g i v e a mean p e r i o d  from  Norgaard-Nielsen time  may n o t secondary period  series be  curves  and ± 1 . 7 9 k m s " ,  F i g u r e 7.2, o r a mean  different  the  e x i s t e n c e of l i n e - p r o f i l e  [1975]. here,  In  from  power-spectrum t h e Ca I I  curve  o f 11.39 d a y " . T h i s 1  v a l u e of  view of t h e  0.0815  is  given  by  short duration  of  t h e d i s c r e p a n c y between t h e two v a l u e s  significant.  p e r i o d may c a u s e  t o be o b s e r v e d  and  respectively.  o f 0.088  the photometric  i n F i g u r e s 7.3  Likelihood  frequency  variations.  over  The  effect  of  beating  an a p p a r e n t l y d i f f e r e n t t h e s h o r t t i m e window.  by  the  primary  275  Both  H I c u r v e s have  t h e Ca I I and  4 . 3 k m s . The w e a k - l i n e  curve  _1  in  F i g u r e 7.4 has a 2K  of  1.2kms~  at  BJD2445359.746 and BJD2445359.785.  two  i f one i g n o r e s t h e e f f e c t  1  velocity  rather be  genuine  differences  of t h e v e l o c i t y  of  line-profile  i n the amplitudes  pixels  between  have been c a u s e d  i n the l i n e l i m i t s  result  of  such  choice  of  the l i n e  The  a  been  variations.  the various  lines.  limits  s h o u l d be  r e a l i t y of is  the v e l o c i t y  dip  effect.  A  The  in even the  i n the the  a t BJD2445359.754  much s m a l l e r  i n t h e Ca I I c u r v e . A s i m i l a r  t h e form  of a v e l o c i t y  first  reported i n the v e l o c i t y  a l . [1968].  radial-velocity  peak n e a r  d i p near  velocity  The  type  mean  curves  out are  the  velocity curve  curves  1.1kms"  d i p may  1  be  of other  curve  6 Scuti  i s generally maximum  minimum.  This  o f 14 Aur by  or a was  Chevalier  been o b s e r v e d  i n the  o f HR432 and HR515 by V a l t i e r  et a l .  by A u v e r g n e associated  in  o f phenomenon h a s  the v e l o c i t y  "bumps" have a l s o  [1979] and i n 7 Boo by  bumps  small f o r  The "bump" i n t h e r a d i a l - v e l o c i t y  pointed  the e r r o r  more p r o b a b l e . T h i s d i p o f a b o u t  local  et  of  i s too small to a l t e r  Moreover,  may  velocity  by t h e u n c e r t a i n t i e s  reported i n the r a d i a l - v e l o c i t y  stars. in  broad  r e l a t i v e l y large  present  these  curve.  the H I curve is  points  The r e a l i t y o f  the c h o i c e of the v a r i o u s l i n e l i m i t s . A d i f f e r e n c e  velocity  value  i n the v e l o c i t i e s . N e v e r t h e l e s s , they effect  curves c o u l d not  several  of  p o i n t s may be somewhat u n c e r t a i n i n view o f t h e  large error  the  a 2K a m p l i t u d e  Auvergne e t a l . [1979], et a l . with  the  [1979] t h a t splitting  I t has the  of  been  velocity  the  line  276  profiles. commonly line for  The  splitting  known as t h e  splitting  and  of  shock  of  line  where  requires  only  However,  i n the  a  longer this  time  The for  for  lines  t h e gas  a thick  may  layer  of  be o b s e r v e d when t h e small continuum  velocity  atmosphere.  with  has y e t  observed  bump  Auvergne  et a l .  phase-smearing  i t will  time  to return  i s not  a  i t would  where  take a  to e q u i l i b r i u m .  rise  by K a r p  period  been done  of  i s strong  Within  f o r the  as p r o n o u n c e d Boo.  enough  [1975b].  [ l 9 7 5 a b ] , however, days. 5  No  Scuti  as those  This could  i n the observed c u r v e .  and  predicted  13 of K a r p  12  the  splitting  depths. T h e o r e t i c a l l y in Figure  gas  much  a considerable distance  temperature  [1979] i n 7  effect  the  h e a t e d g a s . Hence, l i n e  seen  result.  equilibrium.  the atmosphere  formed,  travel  will  to  wave  because  formed,  to return  (Karp  t h e shock  rise  are  The  propagation  accelerate  temperature  are  calculations  Cepheid  calculation  be  As  is  predicted  models  i s c a u s e d by t h e  weak l i n e s  optical  "bumps" may  theoretical a  hydrodynamic  region higher in  t i m e , t h e shock  produce  at  the  very short  c o r e s of the s t r o n g  can  splitting  i n the atmosphere,  region  i n Cepheids  "bumps" have been  by d e t a i l e d  the d e c r e a s i n g d e n s i t y . A  In t h e  profile  " C h e s h i r e - C a t " l i n e s phenomenon.  waves i n t h e s t e l l a r  moves o u t w a r d  line  the v e l o c i t y  Cepheid v a r i a b l e s  [ I 9 7 5 a b ] ) . The  of the  are  similar  stars.  The  observed  by  be c a u s e d  by  gure  7.5 The Ca II X8662 l i n e  profiles  0.70592 0.71402 0.72867 0.73649 0.74633 0.75417 0.76199 0.76981 0.77764 0.78547 0.79331 0.80113  Mean  8660  8665  8670  278 Figure  7.6 The r e s i d u a l s  o f t h e Ca II X8662 l i n e  profiles  0.70592 0.71402  0.72867 0.73649  0.74633 0.75417 0.76199 0.76981 0.77764 0.78547  0.79331 0.80113 8660  8665  8670  279 7.5  THE  LINE-PROFILE VARIATIONS  Figure  7.5  spectrum a f t e r The  spectra  shows t h e r e g i o n  which  fraction  of  been  has a  days  flatter  line  profiles either the  from  of  while  spectrum.  observed  variations  is  variations  are  continuum.  The  the  result  across first  have  Since  the eleven in  the  have symmetric  line  profiles  a mean  The  about  velocities, is  the l i n e  centre  the  the  about  The 1% t o  systematic 2%  of  i s r a t h e r weak i n  feature  to enter  f e a t u r e can  It i s strongest  fades  the  c a n be c h a r a c t e r i s e d  This  and  a l l  line-profile  an a b s o r p t i o n  of t h i s  mean  the average of  movement o f  wavelength  strength  shows  observed spectra cover  of  wavelength  to the long  7.6  from  variations  profile.  towards  profile  7.6.  dominant  skewed  line  Figure  short  centre.  have  in  moves from t h e  line  the p r o f i l e s  evident  The  towards  this  of  the l e v e l  in  from  nature  at  time  each  The  core.  #9.  evident  transfer  for  spectra.  line  spectrum  are  radial  i t has y e t  #3  indicated  the s u b t r a c t i o n  of temporal  spectrum  is  long wavelengths. Figure  s p e c t r a as  broadened  mid-exposure  Some  the  subtracting  the l i n e two  others.  or the  for  The  each  shifts.  Gaussian  Some o f  after  spectrum chosen the  than  variation  a  variations  others  the s h o r t  cyclic  for  by  BJD2445359  the s p e c t r a .  cores  residuals  each one  plot  smoothed  a o f ±0.1A.  spectrum. L i n e - p r o f i l e "stacked"  II l i n e  c o r r e c t i n g f o r t h e measured v e l o c i t y  have  function  o f t h e Ca  the  best  s i d e of the  be  as  feature the  rotationally seen as  it  line  core  in  s i d e of t h e l i n e  core  in  f e a t u r e grows a s as  it  i t moves away f r o m  i n spectrum  #5.  After  moves the  spectrum  280 #9,  the feature  also the  see another first  shown  in  the  short  time  of  the  Hence  in  representative  of  the  would be  7.6 c a n the  One c a n core  The  not  also that  and  be  the  a mean s p e c t r u m  true  of  the  contribute was u s e d  for  of  the  interpreted  variations.  profile  as  feature  positions  not  true  line  core.  would  the shapes  of  the l i n e  is  mean s p e c t r u m  Figure  those  plot  core.  v a r i a t i o n s . Because  feature  towards the  to  variations  residual  the p r o f i l e  series,  shown  to enter  was moving o f f t h e l i n e  subtraction.  identical  starting  "stacked"  significantly  feature  a s i t moves o f f t h e l i n e  feature  feature  representation  the  fades  without averaged  as  A  better  the  imposed  over  several  cycles. The is very  type of l i n e - p r o f i l e s i m i l a r to those  v a r i a t i o n s e x h i b i t e d by o E r i 1  found  i n t h e Oe s t a r  et a l . [1979,1981b], Ninkov e t [1983])  and  the  0  Cephei  [1981a,1982], F r a s e r profile t o be  caused  by  observed  nonradial  this  1  a  [1983],  in  the p u l s a t i o n  s e r i e s and t h e s m a l l  however, difficult  imply  that  a  Smith  unique  Penrod et a l .  [1985]).  The  considered the  profile  suggests the presence  t h e s t a r . One o f t h e  usual  mode f o r a s e t o f d a t a  such  and t h e i r  counterparts.  number  i f not i m p o s s i b l e .  (Walker  p u l s a t i o n s . Hence  E r i strongly  generated  Vir  (Walker  and  stars are generally  i s to f i t the observed p r o f i l e s  to t h e o r e t i c a l l y time  in o  p u l s a t i o n modes  ways t o i d e n t i f y as  nonradial  a l . [1983], Vogt star  a l .  v a r i a t i o n s i n these  variations of  et  $ Oph  of s p e c t r a  residuals  The r a t h e r  short  available  here,  mode i d e n t i f i c a t i o n  The l a r g e number  of  may  be  parameters  281 necessary  in  combination as w e l l . alone not  the f i t  would e n a b l e  o f modes t o f i t t h e s m a l l d a t a  In any c a s e ,  mode i d e n t i f i c a t i o n  i s treacherous even  a variety  take  (Smith  into  [1981]).  account  o f modes  set,a l l  equally  by l i n e  profiles  This conclusion  any  or  doubt  does  about  the  a p p r o p r i a t e n e s s and c o r r e c t n e s s o f t h e m o d e l .  7.6 DISCUSSION W i t h some s i m p l e the p u l s a t i o n This  a  nonradially  most two s u c h  one  time,  /=3 o r 4. Of c o u r s e , the  reality  then  probably  o f t h e weaker  second  fourth  feature. A variety  in  order  to  allow  this The  observed  v a r i a t i o n s a r e caused  Tesseral |m|.  axis  modes a r e a l s o  first  Some o f t h e s e a s s u m p t i o n s  modes and low i v a l u e s  that  since  at  or four  any such imply  have t o be of  assumption by a s i n g l e  the is  that  angle  of s i g h t  made  the mode.  between  i.e  t o be u n i m p o r t a n t  third  observed  nonradial  inclination  and t h e l i n e assumed  stellar  f e a t u r e o r any u n s e e n  M o r e o v e r , t h e r e h a s t o be a l a r g e rotation  the  be 2 o r 1. T h i s d e p e n d s on  interpretation  variations.  s t r i p of  T h i s would  of assumptions  profile  star's  feature in  i n the p r o f i l e  surface.  / could also  on  most t h r e e  at  variations.  one c a n r e a s o n  at  the s t e l l a r  or  the  wave  features are v i s i b l e  waves on  observed  the observed  pressure  i s the case,  there are  travelling  by t h e  c a n make a g u e s s  by a p o l e - t o - p o l e a z i m u t h a l  travelling  If this  one  by i n t e r p r e t i n g  7.6 t o be c a u s e d  surface. at  mode s u g g e s t e d  i s accomplished  Figure  assumptions,  i=*90°.  i.e. /  =  are quite r e a l i s t i c . Tesseral  would cause  only small  line-profile  282 distortions The by  (Smith  pulsation  Breger  From t h i s  mode  in o  based  the  on t h e  Q value. value  the  by  radial value  1  I  [1982b],  low v a l u e  radial  be  lines,  first  was  only  also  v  o f 4.3kms"  large  data  set  partially the  dependent  provided  the  observed  here  a  value  of  criterion  would  suggest  However, i f one u s e s t h e  f o r 2K/Am  v  i s too  c o n c r e t e c o n c l u s i o n on t h e n a t u r e  as i s the  becomes  implies nonradial pulsation  present  overtone  the  value  he  compared  obtains  i n the c a l c u l a t i o n ,  the value  1  parameter. Using  this  pulsation  mode  pulsation  one  Table  pulsation.  the  [1982b]  radial  in  0.0241 d a y . And  the t h e o r e t i c a l  f o r the s t a r .  [1982b],  of  identification  f o r t h e 2K/Am  Smith  to  t h e 2K v a l u e  o f t h e Fe I l i n e s  The  mode  Tsvetkov  H  t o be 0.025 day  the dominant  overtone  Q value  overtone  I I and  pulsation  Smith  This  first  Ca  1  given  first  against  agreement. Using  86kms" mag"  in  This  here.  using the parameters  identified  pulsation  pulsation.  v a l u e s . The  for  they  [1982b] o b t a i n e d a  observed  best  value,  i s not the case  Q was c a l c u l a t e d  [1975]  E r i t o be t h e  1  identified radial  constant  a n d Bregman  7.1.  Tsvetkov  [1981]). T h i s  1  case  26kms"'mag" . 1  f o r the s t a r .  limited  of o  2K  Eri's  to  provide  a  pulsation.  A  more e x t e n s i v e d a t a  s e t i s r e q u i r e d f o r that purpose.  A much  longer  with  higher  s/n  time  series  would be  CFHT. The s k y data  desirable.  T h i s can  c o n d i t i o n was  s e t was t a k e n .  earlier,  s h o r t e r exposure  As w i t h  t h e r e was a s t r o n g  seeing. Furthermore,  still  times  be a c c o m p l i s h e d  r a t h e r poor a t the other 60-knot  the readout  and  t h e time  observations wind c o u p l e d  at this  reported with  poor  n o i s e o f t h e R e t i c o n a t CFH  283 has  since  been  red  Coude  train  reduced. has  also  An  improved  been  through-put  realised.  f o r the  CFH  Chapter THE  8.1  DELTA SCUTI VARIABLE fl CAS  INTRODUCTION The  star  broad-line vsini  fl Cas  6 Scuti  are  (  variable.  Baglin  quote  summarised  Breger  [1972],  Breger  [1982].  In s p i t e  done  a  on  and  fl  indicated  amplitude  0.04  magnitude  velocity. star's  radial-velocity [1965] who Abt  also  fainter  for  independent.  The  Gupta  and  Parameters  for  parameters  [1970],  Baglin  Hoffleit very  first  few  a  period  of  and  o f 0.10430 day  a scatter  velocity.  A  has  monitored that any  velocity  the  there  of  at  of  has  i s no  22"  be  and and  a V  a  amplitude  suggested Cas's  radial  away have  is  a  radial in  1  the early Abt  velocity.  i n the  f o r fl C a s .  V  Jaschek  the  evidence  a  photometric  been g i v e n by  star's  s c a t t e r may  284  fl  have  to  of ± 2 . l 2 k m s ~  b i n a r y motion  companion  and  review  measurements on fl Cas  Jaschek  day  M e l l o r [1917] has  variability  al.  studies  The  0.104  and  et  reported  [1966].  on  are  [1978], H a l p r i n  Millis  based  )  Hoffleit  Additional  by  the  to indicate  optical  and  _ 1  was  a period  [1965] c o n c l u d e d  velocities  a  [ 1 9 7 5 ] , and  f o r fl C a s .  T h i s was radial  e t a l . [1972] g i v e i t  magnitude. Meanwhile, H o f f l e i t  [1982] have q u o t e d  period  a  i t s brightness,  observations of  is  Leung  It  107A  of 7 0 k m s .  [1982b],  Cas.  " ADS  [1965]  8.1.  [1979],  variable  27 d a y s  value  Bregman of  HR21,  Abt  in Table  photometric  0.06  while  1  i n Tsvetkov  [1983],  been  Cassiopeiae  72kms~  [1982]  summarised Moon  fl  v a l u e of  Jaschek  of  8  radial  The  much  probably  been c a u s e d  by  285 Table  8.1  P a r a m e t e r s f o r 0 Cas  ***************************************** Reference HD  number  SAO DM  : 432  number number  : 21133 : +58  R.A.  (1950)  Dec.  (1950)  3  0  6  h  29.742  m  : 58° 52'  Annual p a r a l l a x  s  26.497"  : +0.072"  P r o p e r m o t i o n i n R.A.  :  P r o p e r m o t i o n i n Dec.  : -0.177"/yr  /JJ.  : 117.52°  b  : -3.27°  z l  Spectral Radial Vsini M T  =  v  e  f  log  type  : F2  velocity = 72  kms  +0.526"/yr  III-IV  = 11.8  kms"  Morgan 1  Baglin  -1  +1.35  Eggen  = 7100K  f  g = 3.7  Broad  Eggen  (cgs)  band p h o t o m e t r y V = 2. 2 8  [1979] e t a l . [1973] [1979] [1975]  B r e g e r and Bergman  [1975]  e t a l . [1965]  m  m  +0.  u -  V =  +0. 4 5  m  v -  R =  +0. 3 1  m  v -  I =  +0. 5 2  m  34  I n t e r m e d i a t e band p h o t o m e t r y  [1972]  B r e g e r and Bregman  Iriate  B - V =  0 = 2.709m  and Abt  Eggen  [1979]  286  b - y = 0.216"  1  ID,  = 0 . 1 77  c, = 0.785  m  m  6m, = -0.003  m  ************************************** irregular v a r i a b i l i t y  typical  f o r an e a r l y F s t a r .  8.2 THE OBSERVATIONS The HF  s t a r 0 Cas was observed  absorption  cell  at  t e l e s c o p e on the 21st of was among the f i r s t  the October  s p e c t r o s c o p i c a l l y with  the  Canada-France-Hawaii  3.6m  1980 UT. T h i s s e t of  o b s e r v a t i o n s made with three  instruments  of the o b s e r v a t o r y . These are the four-grating-mosaic Coude spectrograph,  the UBC-built  available  at  the  F/7.4  CFHT 1872-Reticon, and the  CFHT H F - a b s o r p t i o n - c e l l system. Only aluminum Coude were  data  time.  Hence  the  mirrors  transmission  e f f i c i e n c y of the Coude t r a i n a t X8700 was only about 20% of what i t c o u l d  have been. N e v e r t h e l e s s ,  s p e c t r a were obtained and o  1  and  instrumental  the time s e r i e s  under e s s e n t i a l l y s i m i l a r  of  conditions  setup as the e a r l i e r d i s c u s s e d data s e t  E r i . S i m i l a r o b s e r v i n g procedure were a l s o used. lamp s p e c t r a with and without  on  Stellar  the imposed HF l i n e s  were  o b t a i n e d . These a r e shown i n F i g u r e 8.1. The mean s t e l l a r + H F spectrum with  e i t h e r the  s t e l l a r or  HF l i n e s  numerically  removed are a l s o shown. The  exposure time  T h i s corresponds  f o r each spectrum  t o about one-tenth  was 850  seconds.  the " c y c l e - c o u n t " p e r i o d  Uavelength  to  CO  288 of  0.104 day  series  covered  stellar+HF point  at  spectra  spectrum the  lag  two  has a  continuum.  the 0  Approximate spectra  about  The t w e n t y  mean s/n The  Cas s p e c t r a  radial  using  spectra. For t h i s  the b a r y c e n t r i c  can  times  s e t of data,  t i m e s by a b o u t  each  of  the  #1, #13,  and  imposed HF  be m e a s u r e d  relations  Each  344 i n  8.2. S p e c t r u m the  time  periods.  of about  without  dispersion  i n the  mid-exposure  velocities  the  spectra  "cycle-count"  a r e summarised i n T a b l e  #19 a r e  other  (2.5 h o u r s ) .  lines.  from  determined  these  f o r the  the h e l i o c e n t r i c  2.4  times  seconds.  8.3 THE DATA REDUCTION The d a t a w h i c h were  were  processed  and  reduced using  s i m i l a r t o those a p p l i e d  to the o  only  d i f f e r e n c e s between t h e two d a t a  fact  that  data. the  step-lamp s p e c t r a  Hence, t h e  gain  normalisation  process  pattern. ideal and in  match  in  the s i g n a l  observing necessary  they  used  this  the Reticon's  level  is  The  case  a rather  at  procedure  a less  significant  times  normalisation  identical  data  between  After  additive  between t h e  different  upon  eight-line than  stellar  difference  lamp a n d s t e l l a r  eight-line  were  an  c a u s e d by  f o r t h e lamp+HF s p e c t r a . A l l o t h e r  reduction  relies  procedure.  remove  response  between t h e  were t a k e n  night.  to  was p r o b a b l y  lamp s p e c t r a . T h e r e  Moreover,  and  This pattern  i n c l u d e the  s p e c t r u m , an e i g h t - l i n e  was  The  were n o t a v a i l a b l e f o r t h e 0 Cas  m u l t i p l i c a t i v e four-line normalisation by t h e lamp  E r idata.  reductions  correction in  flat-fielding  1  procedures  spectra.  during was  the not  processing the o  1  Eri  289 Table  8.2  Mid-exposure times  f o r the  /3 Cas s p e c t r a  ************************************** #  21 O c t 80 UT+  B a r y c e n t r i c JD  hour a n g l e  1  (05:43 :45)  2444533 .7423178  2h 47m 00s E a s t  2  (06:24 :00)  2444533 .7702693  2h 06m 38s E a s t  3  ( 0 6 : 3 9 :55)  2444533 .7813227  1h 50m 41s E a s t  4  ( 0 6 : 5 5 :20)  2444533 .7920287  1h 35m 1 3s E a s t  5  (07: 10 :45)  2444533 .8027348  1h 1 9m 46s E a s t  6  ( 0 7 : 2 6 :05)  2444533 .8133830  1h 04m 23s E a s t  7  (07:41 :30)  2444533 .8240891  Oh 48m 56s E a s t  8  (07:56 :55)  2444533 .8347952  Oh 33m 28s E a s t  9  (08:12 :20)  2444533 .8455013  Oh 1 8m 00s E a s t  10  (08:27 :45)  2444533 .8562074  Oh 02m 33s E a s t  1 1  (08:43 :15)  2444533 .8669714  Oh 1 3m 00s West  12  ( 0 8 : 5 8 :40)  2444533 .8776774  Oh 36m 38s West  13  ( 0 9 : 1 5 :30)  2444533 .8893673  Oh 45m 20s West  14  (09:33 :30)  2444533 .9018674  1h 03m 23s West  1 5  (09:48 :55)  2444533 .9125735  1h 18m 50s West  16  (10:04 :20)  2444533 .9232796  1h 34m 1 8s West  17  ( 1 0 : 1 9 :45)  2444533 .9339857  1h 49m 45s West  18  ( 1 0 : 3 5 :10)  2444533 .9446917  2h 05m 1 3s West  19  (10:51 :56)  2444533 .9563353  2h 22m 02s West  20  (11:11 :10)  2444533 .9696919  2h 41m 19s West  ***********************************************************  290  and  0  Cas  data  reduction,  t o be  spectrum  provide  In  fact,  both  application  the l i n e - s h a p e  cycles  would  s/n, t h e  be a  more  the  Eri  1  series  standard  and p o s i t i o n  has  spectrum.  references in  the  t e c h n i q u e . In a d d i t i o n t o  mean s p e c t r u m  averaged  appropriate standard  there are s t e l l a r pulsation  o  n u m e r i c a l l y removed and would  of the Fahlman-Glaspey  a higher  to  of the time  the r a d i a l - v e l o c i t y  h a s t h e HF l i n e s  having  8.4  identical  t h e mean s t e l l a r s p e c t r u m  been c h o s e n This  set.  related  over  two  spectrum  line-profile  if  variations.  THE RADIAL V E L O C I T I E S The  same  reduction  criteria  which  were a g a i n u s e d  here  were u s e d t o choose  b o t h t h e s t e l l a r and HF l i n e s . A t y p i c a l limits  is  difference  about function  application relative  of  stellar  I I X8662, H I  Si  I  lines, set,  weaker  mean v e l o c i t y  Individual  As  curve  the v e l o c i t i e s  shown  velocity  to  the  measure relative  f o r the s t e l l a r  lines  S I X8680, X8695, 8.3, and  8.4  case with the  c u r v e was  i s shown  in  and  show  the  f o r t h e Ca I I , H I , and Fe  i n the  i.e. a l l lines  T h i s mean c u r v e  systemic  line  8.2,  line  unmodified  4.4 was a g a i n u s e d  shifts.  Eri  1  limits for  The  technique  X8742. F i g u r e s  o  s e t of s t e l l a r  Fahlman-Glaspey  radial-velocity  lines  Equation  the  the l i n e  width.  X8750, Fe I X8689,  respectively.  a  in  c u r v e s were o b t a i n e d  Ca  X8728,  pixels  from  the  radial-velocity  relative  50  for  except  formed  from  o  1  Eri  those of  t h e Ca I I and H I  i n F i g u r e 8.5. T a b l e 8.3  i n F i g u r e s 8.2  through  o f /3 Cas i s 1 1 . 9 k m s . _1  Thijs was  data the  lines.  lists  8.5. The  I  a l l mean  calculated  P Cas : Ca I I  X8662  C  0.75  0.80  0.85  0.90  0.95  0.75  0.80  0.85  0.90  0.95  BJD2444533+  fB  p Cas : H I A.8750 0.75  0.80  0.85  0.90  0.95  0.75  0.80  0.85  0.90  0.95  BJD2444533+  C i rt)  293  Figure  8.4  The Fe I X8689 v e l o c i t y  c u r v e of  0 Cas  + CO CO LO  CM Q ~> CO  (,.SI0)j) A1TD0J9A  3ATiej3y  294  Figure  8.5  The  velocity  curve  of  p Cas  from  weak  lines  CO CO LO CM Q  —) CO  (  (  SUJ)j)  AlTD0J9/\  3ATlEJ3y  295  Table  8.3 R e l a t i v e  radial  velocities  o f /? Cas  ********************************************* #  Ca  II  X8662  1  +1 . 524 kms"  2  + 3. 236 kms"  3  342 kms" +1 .  4  - o . 774  H I X8750  X8689  mean weak l i  kms"  1  + 0. 794 kms"  1  +0 .715 kms"  1  + 1.558 kms"  1  449 +1 .  kms"  1  + 1.641  1  + 0 .818 kms"  1  +1 . 093 kms"  1  + 0 .960 kms"  kms"  1  -1 .072 kms"  1  -1 . 403 kms"  1  -1 .293 kms"  5  -3. 1 92 kms"  1  -1 .460 kms"  1  -0. 916 kms"  1  -1 .236 kms"  6  -3. 139  kms"  1  -1 .650 kms"  1  -2. 590 kms"  1  -2 .563 kms"  7  -1 . 903 kms"  1  -1 .957 kms"  1  -1 . 041  kms"  1  -0 .962 kms"  8  -0. 426 kms"  1  -0 .708 kms"  1  -0. 613 kms"  1  -0 .505 kms"  9  +1 . 391  kms"  1  +0 .397 kms"  1  + 1 .190 kms"  1  + 1.323 kms"  10  + 2. 684 kms"  1  + 1.530 kms"  1  + 2. 201  kms"  1  + 2 .025 kms"  1 1  + 2. 572 kms"  1  + 2 .365 kms"  1  646 kms" +1 .  1  + 1.691  12  462 kms" +1 .  1  + 1.126 kms"  1  527 kms" +1 .  1  + 1.508 kms"  1 3  -0. 017 kms"  1  + 0 .61 1 kms"  1  -1 . 094 kms"  1  -0 .947 kms"  14  -2. 363 kms"  1  -1 .056 kms"  -1 . 580 kms"  1  -1 .673 kms"  1 5  -2. 934 kms"  1  -2 .083 kms"  1  -1 . 741  kms"  1  -2 .095 kms"  1 6  -2. 059  1  -1 .422 kms"  1  -1 . 182 kms"  1  -1 .230 kms"  17  -0. 707 kms"  1  -0 .210 kms"  1  kms"  -0 .655 kms"  18  541 +1 .  kms"  1  +0 .281 kms"  1  19  + 2. 321  kms"  1  + 2 .440 kms"  20  + 2. 295 kms"  1  + 1.652 kms"  kms"  1  +0 .989  Fe I  1  1  1  - o . 541  826 kms" +1 .  1  +1 . 093 kms" + 0. 620 kms"  1  1  1  kms"  kms"  + 1.705 kms" + 1.019  kms"  + 0 .560 kms"  ***********************************************************  296 a s t h e mean v e l o c i t y one  observed #3  spectrum 11.8kms in  _1  cyclic  #13.  through  quoted  variation  which  This value  by Eggen  is  averaged  over  represented  agrees  with  by  that  [1979] a n d t h e o t h e r v a l u e s  of  given  Abt [1965]. The  HF  o f t h e ' Ca I I X8662 l i n e  mean e r r o r  line-position  with  those  introduced  measurements i s a b o u t  of  the  one-standard-deviation line-position formal  other  uncertainty i s about  estimate  derived  t e c h n i q u e . The  large  value  variations.  H I X8750 and  ±60ms" . 1  data  measurement  error  line-profile  by t h e u n c e r t a i n t i e s  each  The  mean  the  II  X8662  This i s the  - 1  may s i g n i f y  Fahlman-Glaspey the  The c o r r e s p o n d i n g  Fe I X8689 l i n e s  agrees  Ca  ±0.65kms . by  This  sets.  for  i n the  presence  of  values f o r the  are ±1.2kms"  1  and  iSkms" , 1  respectively. Periodogram,  Maximum  Likelihood,  power-spectrum a n a l y s e s g i v e t h e Ca I I c u r v e day  - 1  given time  .  This  discrepancy possible primary The  agrees  by M i l l i s series  in Figure  both  here  the photometric I n view and i n  period  Ca I I c u r v e  p e r i o d may to  Millis The  cause  be o b s e r v e d  o f 0.101  period  i n amplitude  The  2K a m p l i t u d e velocity  over  effect  an  curves  of  9.94 0.104  over  the  the  is  a  different  t h e s h o r t time  window.  tendency t o  cycles.  H I X8750  about  small  o f b e a t i n g by  apparently  t h e two o b s e r v e d  of both  from  of  [1966],  i n F i g u r e 8.2 d o e s show a s l i g h t  decrease  Entropy  of the s h o r t d u r a t i o n of the  i s not s i g n i f i c a n t .  second  weak-line  a mean p e r i o d  Maximum  8.2, o r a mean f r e q u e n c y  with  [1966].  and  and t h e  4.5kms . _1  The  mean 2K  297 amplitude  of  the  decreased  from a v a l u e o f a b o u t  a v a l u e of about is  usually The  cycles.  It  may  effect might  why  w h i c h have b o t h The  _1  X8662  curves  uncertainties  the choice  in  of  limits  is  too small  to a l t e r  lines.  Moreover,  velocity  c u r v e . The  photosphere  over  the  lowest  presumably than  the other  excitation lower  potential  and  over  a larger  range  in  from  be s m a l l  i s probably of depths  the  the  line  such  broad  f o r the  mean  related  to  i n the  stellar  hence  t o p of t h e  the  would  photosphere  has t h e  presumably  the other  by  the  The Ca I I X8662  and  I X8750 l i n e  hence would  between  spectral-line  pixels  the r e s u l t  to the  than  This curves  caused  various  potential  l i n e s . The H  i n the photosphere  formed  be s o l e l y  and r a n g e  closer  i f the  and p r e c i s i o n .  should  excitation  observed  observed  which the l i n e s a r e formed.  be formed  two  was any l o w e r .  several  phenomenon  i n the depth  has  even  effect  differences  the  another  i n the other v e l o c i t y  of the  difference  the  curve  cannot  A  cycle to  T h i s phenomenon  v e l o c i t y amplitudes  various velocity  limits.  been  amplitudes  i n the  however,  b e a t i n g by  have  II v e l o c i t y  lower  cycle.  over  even  curve,  i n the f i r s t  1  small  i t i s not seen  difference  7kms~  e f f e c t of  i s very not  velocity  i n the second  as t h e  i n t h e Ca  explain  II  6kms  explained  period.  precision  Ca  highest  be  formed  lines. It i s  of photospheric depths  than  also the  others. In velocity  spite  of the amplitude  i s in  weak m e t a l l i c  phase w i t h  difference,  t h e Ca I I  t h e mean v e l o c i t y  curve of  l i n e s . The H I X8750 v e l o c i t y c u r v e ,  X8662 the  however,  298  lags  both  0.002  t h e Ca  or  2%  phenomenon in  of  reaches Hot also  rising  and  THE  line  formation the  stellar  phase. is  potentials  lines  Scuti  times. would to  curves  different  have a l s o 6  wave  turbulence  excitation  of  not  pressure  depths at d i f f e r e n t  lines  the the  in  effect  between v e l o c i t y  large-amplitude  of  behind  pulsation  atmospheric  shifts  form  found  been  the which  ionisation reported  variable  SX  in Phe  LINE-PROFILE VARIATIONS likelihood by  of  the  line-profile large  line-position  each  that  formal  measurements.  i n t h e Ca  spectrum.  every  minima  phase  the  This  effect  i n the  that  t h a t the  of  Hoof  several percent  out  about  period.  lagging  by  by  e t a l [1976]) .  indicated  cannote  or  fact  excitation  uncertainties  with  curves  pointed  the  from  peculiar  stellar  for  t o t h e van  i s usually  curves  components  derived  The been  by  Different  (Haefner  8.5  It  curve  photometric  d i s p l a c e t h e c e n t r e s of h i g h e r  states the  [1957] has  different  violet. are  velocity  caused  mean w e a k - l i n e  related  velocity  metallic-line  solely  and  the p r i n c i p a l  variables.  hydrogen-line  Hoof  curve  i s probably  /3 C e p h e i  Van  11  velocity  i n the  maxima and  i n the u n c e r t a i n t y c u r v e  decreasing  different  than  branch  error  of  the  has  F i g u r e 8.6  Figures  already  estimates  II X8662 l i n e - p o s i t i o n  Comparing  the peaks  variations  8.2  for  the  shows  the  measurements and  8.6,  u n c e r t a i n t y curve minima.  coincide  Furthermore,  c o i n c i d e with velocity  one  every  curve.  t h e phenomenon r e p o r t e d e a r l i e r  the rising  This  i n p Pup.  is In  299  Figure  8.6  Uncertainties  i n t h e Ca II X8662 l i n e  positions  Q \  to cn  LO CO  _  o  O  y  o cn  O OO  o  <1 /  CO CO LO  er  in oo  a  _  •-.  LO  00 O  CM Q  —)  CD  0  er CM  £  CD  •  co  CO  CD  00  0  >  ro CD  / /  LO in ro CJ  -  /  -  LO CD  1  LO  1  1  1  1  O O  LO  CD LO  LO CN  ^_  CD  0  O  (,-SUI>|) AlUTEJJ33UH  A1J30J3A  300 that  case, the  line-depth  line-profile  variations  variations  which  are  in  are  i n the form  phase  with  the  of  light  curve. Figure profile plot  8.7a shows t h e  f o r each  have  been  region  of the  s p e c t r u m . The l i n e aligned  with  profile  respect  for  t h e measured  velocity  have a l s o  been  smoothed  a Gaussian  has a a o f ± 0 . 1 A .  which days  from BJD2444533  Figure line  8.7b  profile  stacked level  residuals  after  from e a c h  spectrum.  I t can  plot  of the continuum.  by p h a s e  dependent  spectra  near  that  linewidth  with respect  n e a r BJD244453.81  and  line  the  show  cores are  show a g a i n o n l y  The  profiles  n e a r BJD244453.86,  the  mean p r o f i l e  in  dependent  the spectra  the  profiles  than  pattern  mean  from  this  the  The  line  characterised  repeats  The  line-profile However,  profiles  i n the  the  profile near  residuals.  however, a r e n a r r o w e r cores are  1%  d e e p e r . The  w i t h no p r o f i l e  than same  variations  n e a r b o t h BJD244453.88 and BJD244453.94 w h i l e n e a r BJD244453.91  t h e mean p r o f i l e .  narrower  a  are at  profile.  random n o i s e  are broader  One c a n a l s o  n e a r BJD244453.96 a r e s t a r t i n g of  be seen  obvious  as deep.  BJD244453.84  phase  spectrum.  a r e b r o a d e r t h a n t h e mean not  and t h e  i n f r a c t i o n of  c a n be  no  t o t h e mean  profiles  function  and l i n e - d e p t h v a r i a t i o n s .  BJD244453.78  by  spectra  subtracting  the v a r i a t i o n s  The v a r i a t i o n s  The  f o r each  shows t h e  residual  difference  indicated  other  transfer time  line  stacked  each  shifts.  The m i d - e x p o s u r e  i s also  in this  to  correcting  by  Ca I I X8662  notice  that  t o show t h e  l i n e w i d t h s and d e e p e r  line  and  cores.  shallower  the  profiles  characteristics  301 Figure  8.7  The Ca II  X8662  line  profiles  and t h e i r  residuals  (b)  I"  "0.74232  (a)  0.74232 0.77027 0.78132 0.79203 0.80273 0.81338 0.82409 0.8348O 0.84550 0.85627 0.86697 0.87768 0.88937  0.80273 ^_  0.81338 82409 0.83480  WVVW\/\A\/ Wv/W84550 V  0.85627 0.86697  0.90187 0.91257 0.92328 0.93399 0.94469 0.95634  0.87768 0.88937 0.90187 0.91257  0.96969  0.92328 Mean  0.93399  v\/VwA/v ^ A/A/n  10%  0.95634 0.96969  8658  8662  8666  8658  8662  8666  302  The  observed  certainly  explain  uncertainty velocity in  sequence  Figure  variations,  o f F i g u r e 8.6.  in Figure  8.6  near-zero  the p a t t e r n d i s p l a y e d  curve  curve  as  one  well  relative  radial  shallower  8.2 a g a i n s t i t s u n c e r t a i n t y  curve  as  line  Similar variations  that  have  their  variations the  of the  have  variations  line  of  and  which a r e near  the  linewidths  larger  the  maxima w h i l e b r o a d e r  velocity  m i n i m a . In t h i s [1952],  which  Van Hoof  in  and  theoretical agree  with  and  the line  correlated  i n /3 C a s .  velocity  Naturally,  line-profile  TJ A q l t h a n  in 0  Cas.  l i n e p r o f i l e s do show t h e same narrower  and d e e p e r  lines  and s h a l l o w e r l i n e s o c c u r  particular  the  line-profile  radial-velocity  variables.  here  times  with  observed  type of v e l o c i t y  the  velocity  Deurinck  linewidths  TJ A q l . T h e s e t h e o r e t i c a l  both  the t h e o r e t i c a l  type of v a r i a t i o n s  and  the  with the  profiles  ones o b s e r v e d  a r e many  Nevertheless,  a r e near  generated  the i d e n t i c a l  as the  amplitudes  mean  which  spectra  correlation  f o r the Cepheid  display  as the  depths.  pulsation-distorted  profiles  ones  a r e t h e ones w i t h narrow  [1952]  observations  also  have  the  broader  while the  which  depths  the spectra  velocity  line-profile  the spectra  c u r v e have been r e p o r t e d i n C e p h e i d Deurinck  of  v e l o c i t i e s were  characteristics  and  sequence  l i n e w i d t h s and l i n e  l i n e depths  deeper  Comparing  the  radial  maximum r a d i a l v e l o c i t y and  i n the l i n e - p o s i t i o n X8662  p r o f i l e . Furthermore,  minimum  could  t h e Ca I I  can observe  w h i c h have s i m i l a r line  of l i n e - p r o f i l e v a r i a t i o n s  model g i v e n by van  line-profile variations  are  near near Hoof the  303 direct by  result  a  pure  observed  radial  the  by  radial  one  uses  pulsation  line-profile 0.  mode.  generated  T h i s suggests  variations  |3  in  Cas  that  may  the  also  be  pulsation.