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Spectral variations of 12 Lacertae Allison, Andrea Mary-Anne 1976

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SPECTRAL VARIATIONS OF 12 LACEBTRE  by  Andrea Mary-Anne A l l i s o n  E.Sc. , Loyola of Montreal,  1974  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOB THE DEGREE OF MASTER OF SCIENCE  i n the Department of GEOPHYSICS  and ASTRONOMY  He accept t h i s t h e s i s as conforming  to the  reguirecl standard  The U n i v e r s i t y  of B r i t i s h  April,  Columbia  1976  (c) Andrea Mary-Anne Allison, 1976  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  f u l f i l m e n t o f the requirements f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, the L i b r a r y s h a l l I  f u r t h e r agree  make i t f r e e l y a v a i l a b l e  that permission  I agree  that  f o r r e f e r e n c e and study.  f o r e x t e n s i v e copying o f t h i s  thesis  f o r s c h o l a r l y purposes may be granted by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . of  this  thesis  It  i s understood that  f o r f i n a n c i a l gain s h a l l  copying or p u b l i c a t i o n  not be allowed without my  w r i t ten pe rm i ss i on .  Department o f  GEOPfl^SlCS  The U n i v e r s i t y o f B r i t i s h  2075 Wesbrook Place Vancouver, Canada V6T 1W5  ftA>P  Columbia  flSTftOflOflly  Abstract Observations of the made  at  both  high  Isocon  television  cycles  of  1972. at  the  Cephei s t a r  12  Lacertae  time and s p e c t r a l r e s o l u t i o n camera.  pulsation  The  observations  have  been  with an Image  cover  complete  on two c o n s e c u t i v e n i g h t s i n October  The s p e c t r a l r e g i o n covered i n c l u d e s the two S i i n c l i n e s  j 4553 and  /J 4568.  The l i n e p r o f i l e v a r i a t i o n s have been s t u d i e d i n d e t a i l ; i n p a r t i c u l a r the l i n e doubling at c e r t a i n phases of the p u l s a t i o n . Wavelength s h i f t s of the separate components were measured and a d i s c o n t i n u o u s r a d i a l v e l o c i t y curve was o b t a i n e d .  iii  f a b l e of Contents page Introduction  1  The  7  Observations  Preprocessing  of the  Data  9  Line P r o f i l e V a r i a t i o n s  28  fiadial  54  Velocity  Measures  66  Discussion Summary and  Conclusions  73  Bibliography  76  Appendix A  78  iv  L i s t of Tables page I.,  Observed P r o p e r t i e s of  12 Lac  5  11(a).  Fiducial  Shift  C o r r e c t i o n s f o r Oct.  15.  22  11(b).  Fiducial  Shift  C o r r e c t i o n s f o r Oct.  16,  23  V  L i s t of F i g u r e s page 1a.  Mean Spectrum  f o r October 15 data.  10  1b.  Mean Spectrum f o r October 16 data.  11  2a.  Time s e r i e s seguence of s p e c t r a f o r October 15  13  data. 2b.  Time s e r i e s seguence of s p e c t r a f o r October 16  14  data. 3a.  Variance v s ± S i g n a l f o r October 15 data.  15  3b.  Variance v s ^  16  4a.  Contour p l o t o f l e f t  S i g n a l f o r October 16 data. F i d u c i a l mark f o r October  17  15 data. 4b.  Contour p l o t of r i g h t F i d u c i a l mark f o r October  18  15 data. 4c.  Contour p l o t of l e f t  F i d u c i a l mark f o r October  19  16 data. 4d. .. Contour p l o t of r i g h t F i d u c i a l mark f o r October  20  16 data, 5a.  Time s e r i e s of E e c t i f i e d s p e c t r a f o r Oct.  15.  26  5b.  Time s e r i e s of E e c t i f i e d s p e c t r a f o r Oct.  16.  27  6a.  Time s e r i e s of r e c t i f i e d  s p e c t r a f o r Oct.  15,  30  6b.  Time s e r i e s of r e c t i f i e d s p e c t r a f o r Oct.  15.  31  7a,  Time s e r i e s of r e c t i f i e d  s p e c t r a f o r Oct., 16.  32  7b,  Time s e r i e s of r e c t i f i e d  s p e c t r a f o r Oct,  33  8a,  Contour p l o t o f S i I I I \ 4553 l i n e f o r Oct.  15.  35  8b.  Contour p l o t of S i I I I \ 4568 l i n e f o r Oct.  15.  36  8c.  Contour p l o t of S i I I I \ 4553 l i n e f o r Oct.  16.  37  8d.  Contour p l o t o f S i I I I } 4568 l i n e f o r Oct.  16.  38  16.  vi  9a.  Bifference plots c f r e c t i f i e d  s p e c t r a f o r Oct.  40  spectra  41  15. 9b.  Difference  p l o t s of r e c t i f i e d  f o r Oct.  16. Second d e r i v a t i v e p l o t s f o r the data of Oct.  15.  42  Second d e r i v a t i v e p l o t s f o r the data c f Oct.  15.  43  Second d e r i v a t i v e p l o t s f o r the data c f Oct.  16.  44  Second d e r i v a t i v e p l o t s f o r the data of Oct.  16.  45  L i n e depth, h a l f - w i d t h , and asymmetry v s for  Oct.  15.  and asymmetry v s  for  4568.  15. : S i I I I  Line depth, h a l f - w i d t h , and asymmetry v s for  Oct.  16.  Oct.  16.  49  A  Time  50  A  Time  51  A  Time  52  S i I I I /I 4553.  Line depth, h a l f - w i d t h , for  Time  S i I I I ^4553.  Line depth, h a l f - w i d t h , Oct.  A  and asymmetry v s  S i I I I } 4568.  R a d i a l v e l o c i t y curve f o r S i I I I ) 4553 f o r Oct.  58  15. R a d i a l v e l o c i t y curve f o r S i I I I ^ 4568 f o r Oct.  59  15. R a d i a l v e l o c i t y curve f o r S i I I I ^ 4553 f o r Oct.  60  16. R a d i a l v e l o c i t y curve f o r S i I I I  4568 f o r Oct.  61  16. Gaussian f i t t o input data f o r block  #10 of  62  #10 of  63  Figure 5a. Gaussian f i t t o input data f o r block Figure 5b.  vii  15a.  B a d i a l v e l o c i t y curve ^4553 f o r Oct.  15b.  64  (centroid) f o r S i I I I  65  15.  B a d i a l v e l o c i t y curve A 4553 f o r Oct.  (centroid) f o r S i I I I  16.  A.  1  Deconvolved spectrum f o r block # 3 of F i g u r e 5a.  80  A.  2  Deconvolved spectrum f o r block # 9 of F i g u r e 5a.  81  A. 3  Deconvolved spectrum f o r block #10 of F i g u r e 5a.  82  A.4  Deconvolved spectrum f o r block #12 of Figure 5a.  83  A.5  Deconvolved spectrum f o r block # 1 of F i g u r e 5b.  84  A.6  Deconvolved spectrum f o r block # 3 of Figure 5b.  85  A.7  Deconvolved spectrum f o r block # 5 of Figure 5b.  86  A.8  Deconvolved spectrum f o r block #13 of Figure 5b.  87  A.9  Deconvolved spectrum f o r block #14 of F i g u r e 5b.  88  Deconvolved spectrum f o r block #15 of Figure 5b.  89  A.  10  viii  Acknowledgments I would l i k e t o thank my s u p e r v i s o r Gordon l a l k e r patience  and  Glaspey and  Greg  discussions. computer available.  support. Fahlman  Drs.  programs I  I  would  very much l i k e  f o r taking  part  in  for his  to thank John many  helpful  Fahlman and Glaspey a l s o wrote many o f the used  would  and  also  I  like  thank to  them thank  a s s i s t a n c e with part of the data a n a l y s i s .  f o r making  Tad U l r y c h f o r h i s I thank t h e N a t i o n a l  Research C o u n c i l f o r support from a postgraduate s c o l a r s h i p . thank  them  I  Graham H i l l o f the Dominion A s t r o p h y s i c a l Observatory f o r  a l l o w i n g me t o use data he o r i g i n a l l y  obtained.  Finally  l i k e to thank the graduate students of the department always w i l l i n g  t o answer my many g u e s t i o n s .  I would  who  were  1  12 l a c e r t a e , a l s o known as the v a r i a b l e s t a r is  a  member  of  the  few  hundredths  period  v a r i a t i o n s i n both  light  The l i g h t v a r i a t i o n s 4m are u s u a l l y  only a  of a magnitude and the r a d i a l v e l o c i t y  2K range from 5 km/sec to 150 km/sec giving, a l a r g e The  £ Cephei s t a r s range  luminosity curves  classes  are  multiple review  II-III-IV.  (1966), and Percy  The Cephei  The  light  variables  been w r i t t e n  radial  velocity  but many of the s t a r s shon phenomenon.  by Struve  General  (1955) , U n d e r h i l l  properties  and s p e c t r a l v a r i a t i o n s of the  are  d i f f e r e n t from the other i n t r i n s i c  Whereas  mechanisms  2K/Am r a t i o .  (1967) as w e l l as o t h e r s .  pulsation  variables.  guite  the  pulsational  modes  and  excitation  of such s t a r s as the C l a s s i c a l Cepheids and BB Lyrae  s t a r s are well understood, those of the yet  and  p e r i o d i c i t y and some show a beat have  amplitudes  i n s p e c t r a l type from B0.5-B2 and have  approximately s i n u s o i d a l  articles  Lacertae,  Cephei c l a s s o f variables.... These are a  group of s t a r s which show short and r a d i a l v e l o c i t y .  DD  cephei s t a r s  a r e not  known with any c e r t a i n t y .  The  suspected  cause  of  pulsation  v a r i a b l e s i s envelope i o n i z a t i o n . about  by  elements  regions such as  in  modulation  brought  the s t e l l a r envelope c o n t a i n i n g  abundant  hydrogen  ionization  can  have  pulsations,  and  under  f o r some of the c o o l e r  and the  the  The f l u x  helium  proper proper  in  various  phasing  stages  of  for driving  of  conditions  can  induce  2  pulsational  instability  in a star.  The  /? Cephei s t a r s a r e very  hot  (Te 20,000-25,000°K) ana so t h i s would not apply.  no  H i o n i z a t i o n zone and the He* i o n i z a t i o n zone l i e s t o o c l o s e  to the s t e l l a r s u r f a c e to be e f f e c t i v e  theoretical  (1973a).  this  course  is  is  traversed  post-main  given  in  seguence  model in  calculations  they  i n the s h e l l hydrogen  is  suspected  find  an S-shaped manner i n the  evolution:  once  burning phase.  d e f i n i t e l y i n which of these 3 stages the it  in  Lesh and Aizenman  in  the  burning phase, once i n the secondary c o n t r a c t i o n  once  but  location  Cephei s t a r s occupy a very narrow  diagram and by  region  of  hydrogen and  diagram  They f i n d t h a t the  s t r i p i n the H-R that  H-fi  is  (Cox,1974).  A good d i s c u s s i o n of /? Cephei s t a r s and t h e i r the  There  core phase,  I t i s not known  cephei  stars  are,  that the p u l s a t i o n i s connected with the  s t r u c t u r a l changes caused by one of these stages of e v o l u t i o n .  I t has sometimes been thought t h a t the ft Cephei s t a r s a  'peculiar'  Aizenman normal define  type  of s t a r but both Watson (1972) and Lesh and  (1973b) attempt to show t h a t the  B type s t a r s .  Satson  Cephei  stars  are  (1972) uses the (0e,log g) plane to  the /5 Cephei i n s t a b i l i t y  and Aizenman  were  strip.  (1973b) t h a t the p Cephei  He concludes as do Lesh stars  differ  from  the  n o n v a r i a b l e s t a r s only i n t h e i r s t a t e o f e v o l u t i o n .  Various  attempts  have been made towards  understanding the  nature of the p u l s a t i o n .  A b r i e f summary of t h i s  found  Radial  in  Cox  (1974).  work  can  be  and n o n - r a d i a l modes have been  3  examined as w e l l as i n t e r a c t i o n s between the two observed  recently  Aizenman, Cox conclude  in  and  proposed lesh  e x c i t a t i o n mechanisms are found  {1975) and Osaki  (1974).  t h a t i n model c a l c u l a t i o n s f o r a 10 H (g )  0  to  For T  spectra f o r t f . 2  to a c c o u s t i c a l or pressure discrete two  2  (p) modes.  p o s i t i v e eigenvalues  possibilities  which  are a l l p o s i t i v e and  there  is  not  (T  2  this:  in  z  2  two  For T  If  there  p  modes  have  s m a l l , t h e r e are  2  is  to g r a v i t y or g  convective +  modes.  The If  c o n v e c t i v e s t a b i l i y , the s o l u t i o n s correspond  separating  2  is  suggested  <T  becomes n e g a t i v e .  and  2  whereby  which  There i s  <*  ).  2  3  the  long  Non-linear  to in  stages  of  or  radial  harmonic  if  the  (described  as  s t a r s are massive s t a r s i n  core hydrogen burning. large-scale unstable  g  -  convective modes  mode  p e r i o d g* modes can  have been shown to agree with o b s e r v a t i o n s .  (1974) assumes t h a t the P Cephei late  results  A l l these  e x c i t e a sh'orter p e r i o d s t a b l e mode: f , p, modes  non-radial  i n t e r m e d i a t e fundamental or f mode with a p o s i t i v e  eigenvalue T ^ coupling  the  thus the s t a r i s d y n a m i c a l l y s t a b l e .  -  an  This  >0) .  arise.  unstable c o n v e c t i v e modes g ; V addition  oscillations  l a r g e the s o l u t i o n s correspond  2  s t a b i l i t y , the s o l u t i o n s correspond T  lower  a f o u r t h order problem where the eigenvalue v~  e n t e r s n c n - l i n e a r l y i n the c o e f f i c i e n t s . distinct  s t a r , the  ( Considering only  the a d i a b a t i c case, the eguations of motion f o r reduce  in  Aizenman et a l . .  modes are unstable a g a i n s t n o n - r a d i a l  +  the e a r l y s h e l l hydrogen burning s t a g e s .  case  the  phenomenon.  Two  gravity  to e x p l a i n  The  Osaki the  b a s i c mechanism i s  motion  in  the  core  ) i s o s c i l l a t o r y and i f the  4  frequency of one of the c o n v e c t i v e with  the  whole  eigen-freguency  star,  then  oscillation  this  of  a  modes  happens  to  coincide  n o n - r a d i a l o s c i l l a t i o n of the  resonance  may  o f the s t a r , which may  excite  a  non-radial  be observable a t the  stellar  surface.  A few p r o p e r t i e s o f 12 l a c are mentioned symbols  E1  and  respectively.  be  binary  spectroscopic  I t was f i r s t  (Adams,  1912)  broadening of the l i n e s at c e r t a i n phases. the  absorption  velocity  lines  2K  i s large  (Struve, 1950  c o n s i d e r the v a r i a t i o n s over one duration  4h  p e r i o d i c i t y of section.  The  38m).  The  12  will  Lac  thought  because  It  was  of  found  and to the that  are double at maximum and minimum r a d i a l  but the e f f e c t i s measurable  amplitude  I.  P2 correspond to the primary period 4h 38m  secondary p e r i o d 4h 44m a  i n Table  only ).  cycle  whole be  when  In my of  reviewed  variable  work I w i l l  just  pulsation  (of  the  question  the  of  in  the the  multiple discussion  Host of the work done on 12 Lac has been p h o t o m e t r i c ,  i n c l u d i n g an I n t e r n a t i o n a l Campaign i n 1952.  These e f f o r t s have  mainly  accurate  been  directed  determinations. (1961) ,  De  towards  Among these are Path  Jager  (1962),  (1962) , Jerzykewicz (1963), Some  spectroscopic  and Zebergs and  et a l (1976) .  Ciurla  period  (1938), O p o l s k i and  Ciurla  (1962), O p o l s k i and  Ciurla  (1973),  and  Sato  (1973).  work has been done by Struve (1950), Struve  (1955), De Jager  Grabowski  Earning  more  (1966), Beres  (1957), Grabowski (1965), Grabowski  (1966),  Opolski  (1969) and  Heard  5  Table Ij.  Observed P r o p e r t i e s of 1.2 L a c  |  !  RE  i  !  B1.5 I I I i  1  i  i  B2 I I I  J  2  5.25  |  2  5.18  |  4  -3.61  I  1  | SYMBOL  MK S p e c t r a l Type  V i s u a l Magnitude  1  !  V  |  !  Absolute Magnitude  Log  of Period (days)  R a d i a l V e l o c i t y Range (km/sec)  I  !  -4.0  |  2  i  !  '4.15  |  4  1  l o g P1|  -.705  1  4  I  2K  |  36 (P1)  J  2  I  15 (P2)  |  2  J  -.135  |  4  1  -.140  |  2  1  .074  I  B-V Colour Index  1  B-V  1 Amplitude of L i g h t Curve  1  !  A m  !  E f f e c t i v e Temperature Parameter=5040/T K  I  01tra-Violet  I  Colour  i  Index Apparent  Rotational  Broadening  (km/sec)  J  2  .042 (P2)|  2  .214  1  I U-B  (P1) |  | I  -.945  !  |  4  I  I  v sinij  79  I  4  j  j  29  |  2  References 1. 2. -. 3. 4.  A  Lesh and Aizenman (1973) Percy (1967) O p o l s k i and Grabowski (1966) H i l l (1967) .  6  The  primary  dispersion,  aim  of my  i n v e s t i g a t i o n was  detail  Vul and same  look  high time and high s p e c t r a l r e s o l u t i o n  of 12 Lacertae and examine the l i n e more  to  than had  ^Cephei,  detection  two  previously other  doubling  been done.  f> Cephei  system were analyzed  stars  the p u l s a t i o n c y c l e were detected i n both  high  observations  feature  in  Observations obtained  by Goldberg  12 Lac, r a p i d s p e c t r a l v a r i a t i o n s o c c u r r i n g  at  with  (1973).  much of  BB the  As i n  at c e r t a i n phases of  stars.  7  The  Observations  The Isocon  o b s e r v a t i o n s were  taken  using  a  t e l e v i s i o n camera as a d e t e c t o r .  refrigerated  The  onto the photocathode o f the Isocon tube and predetermined  time.  An  electron  t a r g e t normal to the spectrum., The of  a  image  spectrum i s imaged integrated  for  r e a d i n g beam then scans data i s d i g i t i z e d  by  a the  means  12 b i t a n a l o g - t o - d i g i t a l c o n v e r t e r and s t o r e d on magnetic  tape.  Each scan g i v e s  cathode.  The  system  840 is  data  points  monitored  by  over an  70  mm  of  I n t e r d a t a Hodel 4  computer which d i s p l a y s the spectrum on an o s c i l l o s c o p e . period  observations  i n t e g r a t i o n p e r i o d are detailed  description  of  the  taken of  dark  after  the  current the  the  star  over data.  Short  the  same  A  more  system i s given by Walker e t a l  A  (1972) .  The  o b s e r v a t i o n s were taken using the coude spectrograph  of  the 48 i n c h t e l e s c o p e of the Dominion A s t r o p h y s i c a l Observatory, Victoria. gratings  The was  96 i n c h camera with a mosaic of four 800 used i n the second o r d e r .  In a d d i t i o n a t r a n s f e r  l e n s which magnifies a small r e g i o n of the spectrum and the  curvature  photocathode 0.5  A/mm.  fiducial  The  of  the  useable  1973 area  ) was of  time  for  the  12  the  used g i v i n g a d i s p e r s i o n of tube  face  marks g i v e s a s p e c t r a l coverage of -25  integration  matches  f o c a l plane to the curvature of the  (Richardson,  The  line/mm  Lac  was  between  the  30.87 sees.  576  A.  i n d i v i d u a l frames were obtained on October 15,1972 O.T.  and  688  8  on  October  16,  1972  U.T.  4h55m and 5h53m r e s p e c t i v e l y . 4h38m.  Thus  pulsation. lines  The t o t a l time of o b s e r v a t i o n s was The primary p e r i o d of 12  Lac  is  the o b s e r v a t i o n s cover more than one c y c l e of t h e  The wavelength  \ 4553 and } 4568.  region examined showed the two S i I I I  9  ElgEfQggssing  The  of the Data  average of the dark c u r r e n t f o r each n i g h t was  by an  11  point  (an a r b i t r a r y number)  then  subtracted  from a l l of the s p e c t r a .  the two  n i g h t s are shown i n F i g u r e s  running  mean smoothing was  either  end  of  reference  markers to monitor any  and  data 430  They  are  pieces  numbers on  of  and  was  mean s p e c t r a f o r  1(b). The  A  5-point  two  d i p s at  a l s o show up on the most  likely  black  tape  which  serve  changes i n the scanning  the wavelength a x i s correspond  p o i n t s i n the spectrum.  are  The  This  the s p e c t r a are f i d u c i a l markers on the face  These  840  1{a)  mean.  a p p l i e d to the data.  the tube.  p a t t e r n . . The  running  smoothed  due  The  of as  raster to  the  t i n y b l i p s at p o i n t s  -290  spectrum  of  a  calibration  lamp.  to "dust"  specks on the face of  the  tube.  In order the  time-series  duration. f i n a l sum data  to see the l i n e p r o f i l e changes  The was  point  s p e c t r a i n each block normalized  interval  from  block was  divided  was  within  1000.. T h i s i n t e r v a l was to  affecting by  were added together  such t h a t the sum  lines  intensity  the data  a  cycle,  s p e c t r a were grouped i n t o blocks of equal  from the s p e c t r a l  spectrum.  during  prevent  any  A 5 point running  average  of  the  chosen away  ratio.  in  line  In a d d i t i o n each calibration  mean smoothing was  to improve the s i g n a l t o noise  the  specified  variations  the n o r m a l i z a t i o n .  the  a  and  time  lamp  a l s o a p p l i e d to  12 LACERTAE  12  2(a)  The  seguence of s p e c t r a f o r each n i g h t are shown i n F i g u r e s  and  2(b).  Each spectrum  i n d i v i d u a l exposures.  The  signal  to  The  is  a  20.6  They  noise  found  indicated signal  is  that  shown  system by  there  to  is  hold  i n F i g u r e s 3 (a) and  values were s e l e c t e d  Thus the a d d i t i o n  of  40  c h a r a c t e r i s t i c s of the image i s o c o n  r e l a t i o n s h i p from s p e c t r a with s t r o n g relationship  mean  s i g n a l to noise r a t i o i s -75:1.  have been d i s c u s s e d f o r the U.E.C. (1973).  minute  et  al  a l i n e a r s i g n a l t o noise absorption  for  3 (b).  Buchholz  the  12  lines. Lac  For the variance  This  s p e c t r a as analysis,  from a l i m i t e d data p o i n t i n t e r v a l .  of N frames of data g i v e s a/F  improvement  in  the s i g n a l t o n o i s e .  The  scanning  vary with time artificial have  this  (Fahlman and Glaspey,  1973).  T h i s can produce an  wavelength s h i f t i n the spectrum.  some  velocity.  p a t t e r n of the camera reading beam i s known to  estimate The  of  this  shift  for  I t i s important measures  purpose.  Figures  i n t o 20  A two-dimensional  4(a),  minute  distribution  radial  f i d u c i a l marks mentioned p r e v i o u s l y are used  4(b),  blocks  4(c) and 4 ( d ) . as  for  Figure  of the l i n e s i s mapped.  l i n e s are a measure of  intensity;  lower i n t e n s i t y , i e . a b s o r p t i o n .  for  (wavelength,time) p r e s e n t a t i o n  i n contour form of the area around the f i d u c i a l marks in  of  to  The 2  The  smaller  is  shown  data i s guantized  and  the  intensity  l a b e l s on the numbers  contour  indicating  From these f i g u r e s one  can  c l e a r l y the r a s t e r s h i f t during the p e r i o d of o b s e r v a t i o n .  see  14  Figure 3(a).  Variance  vs. signal for October 15 data.  cn  -w  in  »•• •-  ixJCE E r 2  IS  o  0.0  I  2.4  i—  I  4.8  S I G N A L  7.2  9.6  ~1 12  Figure 3(b). Variance vs. signal for October 16 data.  0)  0.0  "1— 2.4  -1 4.8  S I G N A L  "1 1.2  ~T"~ 9.6  ~1 12  17  Figure 4(a). Contour plot of l e f t Fiducial mark for October 15 data.  Figure 4(b). Contour plot of right Fiducial mark for October 15 data.  o  E~T  4.95  1  5.93  1  6.91  1  1  7.B9  TIME UT  8.B7  MRS.)  1  9.85  1  10.  Figure 4(c).  Contour plot of l e f t Fiducial mark for October 16 data.  Figure 4(d).  Contour p l o t of r i g h t F i d u c i a l mark f o r October 16 data.  21  The  displacements are c a l c u l a t e d using a program  by Fahlman and Glaspey  (1973).  The spectrum to be  s y s t e m a t i c a l l y s h i f t e d r e l a t i v e to a reference to  find  that  be  is  applied  measured  is  spectrum i n order  s h i f t which minimizes, i n a l e a s t squares sense,  the d i f f e r e n c e s between differencing  described  to  the  two  spectra.  The  done i n the F o u r i e r domain. the  absorption  line  is  shifting  and  The c o r r e c t i o n to found  by  linear  i n t e r p o l a t i o n between the measured s h i f t s of the f i d u c i a l s . mean spectrum was used as the s t a n d a r d . and  left  fiducial  marks  The  The s h i f t s of the r i g h t  as w e l l as the slope o f the s t r a i g h t  line fitted  through the s h i f t s are given i n Tables 11(a) and  (b).  values  The  of  p o i n t s , however the  the  shifts  accuracy  of  are the  guaranteed to -0.1 of a sample p o i n t . a  linear  two  shift  reference  linear  across  points,  expansion  will  discussion.  be  t o three  technique  can  decimal only  be  I t i s necessary to assume  the face of the tube s i n c e we only have  Thompson  (1974) found  o f the camera reading  p u t t i n g upper l i m i t s to the r a d i a l point  given  II  returned  to  apparent  beam which  velocity  later  an  in  necessitated  variations.  the  The s h i f t c o r r e c t i o n s were not  ^non-  radial  applied  This  velocity until  the  a c t u a l r a d i a l v e l o c i t y measures were made.  another i n s t r u m e n t a l what  problem a s s o c i a t e d  appears t o be microphonics.  with i s o c o n data i s  The g l a s s t a r g e t i s only 2/4m fL  t h i c k , and i t i s suspected that the scanning by the reading  beam  c o u l d cause the t a r g e t to v i b r a t e .  Shat r e s u l t s i s a s i n u s o i d a l  v a r i a t i o n imposed on the spectrum.  Unfortunately  of the microphonic v a r i a t i o n i s rouqhly  the  the same as  frequency  22  F i d u c i a l S h i f t C o r r e c t i o n s f o r Oct...  Table 11  T"  r  i  1 Block | I  No.  I  1  j  Fiducial  Shift  j  Slope  Bight  I  (Shift/Pt)  Left  J  (70-124)  1  (685-730)  j  1  1•  I  -2.472  1  -6.064  |  -0.0059  I  2.  J  -0. 833  1  -4.287  |  -0.0057  i  3.  |  0.269  1  -2.743  J  -0.004 9  I  4.  |  0.791  |  -1.907  J  -0.0044  I  5.  |  0. 683  J  -0.396  J  -0.0018  I  6.  |  0. 653  I  -0.252  I  -0.0015  I  7.  j  1.032  I  0.008  |  -0.0017  18.  I  0.492  I  0.539  |  0.0001  J  9.  |  -0.016  l  1.255  |  0.0021  1 10.  |  0.239  I  1.429  |  0.0020  111.  J  0.207  l  1.739  I  0.0025  I  12.  I  0.085  I  2.033  |  0.0032  I  13.  I  -0.521  |  2.635  I  0.0052  I  14.  I  -1.165  J  2.819  |  0.0065  t  ,  J.  j.  _  x  :  23  Table I I b.  1 Fiducial Shift  |  Slope  left  Bight  |  (Shift/Pt)  (70-124)  (685-730)  | Block | |  Do.  J  |  F i d u c i a l S h i f t C o r r e c t i o n s f o r Oct.  i, 1  J  —  *  I  .320  1  -4.000  |  -0.0071  1 2 .  |  .035  1  |  -0.0058  I  3.  I  .287  -2.220  |  -0.0041  1  4.  |  . 187  ! !  -3.500  -1.360  |  -0.0025  1  5.  J  .212  !  -0.760  |  -0.0016  1 6 .  1  .183  1  0 . 182  |  0,0000  1 7 .  |  .300  0.820  J  0.0008  1  8.  |  ,162  1.100  |  0.0015  1  9.  I  .020  1. 380  |  0.0022  1 10.  J  -.061  1.300  I  0.0022  I 11.  I  .131  1. 586  |  0.0024  I 12.  |  -.041  2.110  |  0.0035  113.  |  -.232  2.180  |  0,0040  I 14.  J  -.315  2.240  I  0.0042  I 15.  I  -.500  2.400  I  0.0048  | 16.  |  -.417  2.620  |  0.0050  J 17.  J  -.842  2.655  |  0.0057'  I  1  1.  A -  !  •!  !  ! !  1  ! ! ! ! ! „ J.  i  16.  _  i 1  J  24  that  of  the  s p e c t r a l l i n e s and so cannot tie f i l t e r e d out.  v i s u a l i n s p e c t i o n of the data was which  c a r r i e d out and  to determine  the amplitude volume  an o b j e c t i v e c r i t e r i a  of the e f f e c t was  of data  omitted,  p r o h i b i t e d any other approach.  No s i g n i f i c a n t change was  the  signal  to  together,  o r i g i n a l data  intact.  and  so  the data using a bandpass f i l t e r  c u t o f f p o i n t of the f i l t e r  frequency  The  was  15  this  was  for  Oct.  16  c u t o f f was  procedure.  The  continuum by a l e a s t squares points  in  the  it  was  decrease  decided  to  use  decided to  the  filter  t r u n c a t e d with a l a n c z o s window The high  frequency  chosen as the frequency  where the  25  per  cent  it  was  28  of  db.  the  For  Nyguist  per c e n t .  spectrum  i s removed from spectra  f i t cf  4th  The  were order  the s p e c t r a by rectified  to  polynomials  which r e p r e s e n t r e a l continuum.  continuum f i t using the same p o i n t s was 20  records  low  s e t at zero.  i n s t r u m e n t a l response  rectification  The sequence of  of a s i n g l e block of data f e l l below -32  the data cf Oct. and  as  noted other than a  i n s t e a d of using the running mean smoothing.  freguency,  rejection  with the r e j e c t e d  f u r t h e r a n a l y s i s of the data, i t was  power spectrum  was  n o i s e r a t i o where l e s s e r numbers of records  were averaged  For  for  It  o f t e n hard to e s t a b l i s h , but the  s p e c t r a as i n F i g u r e 2 were recomputed  the  frames  shewed a marked s i n u s o i d a l p a t t e r n were r e j e c t e d .  difficult  in  those  fi  determined  for  each  a a to new of  minute b l o c k s to compensate f o r any f l u c t u a t i o n s i n the  i n s t r u m e n t a l response.  The  sequence of  rectified  spectra  for  25  the two  n i g h t s are shown i n F i g u r e s 5(a)  and  5(b).  Figure 5(b).  Time series of R e c t i f i e d spectra for Oct.  16.  28  Line P r o f i l e  The  Variations  line  remarkable.  profile The  the  If  the  i s r e a l l y going  this  1)  Series"  "Time  F i q u r e s 5(a)  and  5(b).  true  " p i c t u r e " of the  2)  The  Contour  technigue has a  Difference  differences  of  the  has  the  of  discrete  wavelength  I  have  chosen  a  An  the  following:  example of t h i s i s shown i n useful  in  qiving  a  spectral lines. A  preliminary  description  of  this  marks.  This  e f f e c t i v e method of showing immediately  the  i n t e n s i t y changes.  P l o t . - From each block of data data and  of a time s e r i e s p l o t .  4) The  difficulty,  Such a diaqram i s  mean spectrum of a l l the  form  series"  a l r e a d y been given f o r the f i d u c i a l  wavelength s h i f t s and  the  i s sampled at  are changing with time as i s  These are  Plot.-  Plot.-  particularly  The  "time  two-dimensional  ways of i l l u s t r a t i n g the l i n e p r o f i l e v a r i a t i o n s , both quantitative.  is  quite  a problem t o c o r r e c t l y v i s u a l i z e what  q u a l i t a t i v e and The  are  on.  a i d i n overcoming  number of  a  spectral features  case here, i t i s o f t e n  To  cycle  data a l l o w s much freedom  of data: a c e r t a i n wavelength r e g i o n  blocks.  a  What we have e s s e n t i a l l y i s a  time i n t e r v a l s - r e s u l t i n g i n  3)  over  d i q i t i z e d form of the  i n presentation. set  variations  between i n d i v i d u a l  Second D e r i v a t i v e . -  The  time s e r i e s i s taken.  the  is  subtracted  r e s u l t i s given i n  the  This i s very u s e f u l i n showing  the  blocks. second d e r i v a t i v e of  each  block  T h i s " l i n e sharpening" technique  important c h a r a c t e r of sometimes beinq able  to  resolve  29  i n d i v i d u a l components from blended 5)  Finally  a  quantitative  lines.  description  of the  changes can be given i n terms of measures of l i n e width, asymmetry and e q u i v a l e n t  1) The Time S e r i e s As  depth,  half-  width.  s t a t e d i n t h e p r e v i o u s s e c t i o n F i g u r e s 5(a) and 5(b)  individual  resolution,  s p e c t r a : each spectrum a 20 minute  exposures.  a  smaller  In  time  order  to  minute  numbers  mean of  of  records  12  corresponding  decrease  one  this  averages  individual  are  few  obtain  mean of  better  time  s p e c t r a : each block  exposures.  averaged  together,  i n s i g n a l to noise. number  of  #48 F i g .  from sharp presence  there  is  indicated.  a  U n f o r t u n a t e l y when  records,  evidence  for 6,  7.) n e v e r t h e l e s s one sees c l e a r l y the development  line of  a  Because l e s s e r  microphonics i s present i n some of the blocks (eg. #28 F i g . and  are  sampling i n t e r v a l was c o n s i d e r e d .  F i g u r e s 6 and 7 are a s e r i e s o f r e c t i f i e d 6  profile  Plot.  a s e r i e s of r e c t i f i e d 40  line  two  to  broad  line  components  phase.  In  particular,  the  at c e r t a i n phases i s very c l e a r l y  I t i s a l s o p o s s i b l e t o monitor the  relative  growth  and d e c l i n e of the components.  From  l o o k i n g at these l i n e p r o f i l e s one sees that the l i n e  at )4568 appears broader than that a t J 4553. slight  to a  n o n - l i n e a r i t y i n d i s p e r s i o n a c r o s s the f a c e of the tube.  T h i s i s probably due to the use of the )4568  T h i s i s due  t h e d i s p e r s i o n i s -.045 A/pt.  .051 A/pt.  transfer  lens.  Around  ; at J4553 i t i s c l o s e r to  S i 111 4568  S i 111 4553  4568  S i 111  4553  Ill  4568  Si 1 1 1 ^  4553  34  2) The  Contour  Plot.  p l o t s of the data b l o c k s of F i g u r e 5  Contour Figure  8.  Each s p e c t r a l l i n e  amount  of  information  At  the  beginning  symmetric. the  be  of  lines  separately.  gathered  observation  This i s indicated  contour  shown  from  such  in  A great a  two-  Consider F i g u r e 8 (a):  dimensional d i s p l a y . A)  can  i s contoured  are  the  line  by the symmetric  i s sharp  and  distribution  of  on both s i d e s of the minimum contour l i n e  of  100. B) As the c y c l e progresses, the l i n e becomes b r o a d e r — s h o w n by a g r e a t e r spread i n the equal i n t e n s i t y contour C) The nature of the asymmetry Around ^ 6 h r s . U.T.  plots.  can  also  lines.  be  seen  the contour l i n e s  from  on the blue s i d e  of the a b s o r p t i o n peak are more widely separated than the  red s i d e .  to the b l u e . block  T h i s i s confirmed from 8.  F i g u r e 5(a) by  wavelength  E)  A  displacement  rough  obtained. minima  is  the f i r s t lines-  shifts  idea  of  half i t  i e . the  wing  looking  at  obvious  wing to the red.  from  looking  at  the  lines.  the v a r i a t i o n s i n l i n e depth can a l s o Figure  8(d).  very approximately  crosses  line  are  of the contour  Take f o r example indicated  on  Towards the end o f o b s e r v a t i o n the  asymmetry r e v e r s e s i t s e l f showing an extended  vertical  those  Thus there i s an asymmetry with an extended  numbers 5 , 6 , 7 , and  D) The  these  successively  gets deeper.  l i n e gets shallower again.  The  path  of  by the dashed l i n e . lower  valued  be  line In  contour  As the c y c l e p r o g r e s s e s the  35 Figure  8(a). Contour plot of S i 111 4553 line for Oct. 15.  36 Figure 8(b).  C o n t o u r p l o t o f S i 111 4568 l i n e f o r O c t . 15.  •37  Figure 8 ( c ) .  Contour p l o t of S i 111 4553 for Oct. 16.  Figure 8(d).  Contour  plot of Si 111 4568 for Oct. 16.  39  3) The  Difference Plot.  D i f f e r e n c e p l o t s f o r the b l o c k s of F i g u r e 5 Figure  9.  The  mean  spectrum  e s s e n t i a l l y that of F i g u r e removed. is  The  1  subtracted  with  the  in  from each block, i s  instrumental  response line  I t resembles a s i n u s o i d whose  wavelength i s egual to the width of the more  given  d i f f e r e n c e spectrum of a d i s p l a c e d s p e c t r a l  e s s e n t i a l l y an S shaped curve.  show  are  line.  These  diagrams  c l e a r l y than any of the o t h e r s , the i n d i v i d u a l  changes at d i s c r e t e time i n t e r v a l s .  The  basically  which are very s e n s i t i v e  first  derivative  p o s i t i o n changes.  The  plots  difference  block  second d e r i v a t i v e p l o t s  plots  described  are to  below  are more s e n s i t i v e to p r o f i l e changes.  4) The  Second D e r i v a t i v e . The  second d e r i v a t i v e p l o t s of the data blocks of F i g u r e 5  are shown i n F i g u r e s 10 and The  data was  28  per  first  cent  derivative  of  was  the  found  necessary.  Nyguist.  When  you  apply  the  to 25 or second  The  n o i s i e r the data the worse the  noise l e v e l .  to 20? of the  looking  The  2nd d e r i v a t i v e  in  components.  the growth  Consider f o r example  A 4553:  a) In the f i r s t  was  Nyguist.  at the p l o t s one sees immediately  development of the two  F i g u r e 10 (a)  problem.  t h a t a 5 point smoothing gave the best compromise  addition f i l t e r e d  and  m o d i f i c a t i o n was  to a s e t of data each s l i g h t change i n slope becomes  between r e s o l u t i o n and  From  One  5 point smoothed i n s t e a d of f i l t e r e d  greatly amplified. It  11.  4 blocks only one component i s present.  in  40 Figure 9 ( a ) .  Difference plots of r e c t i f i e d spectra f o r Oct.  15.  Figure 9(b).  Difference p l o t s of r e c t i f i e d spectra for Oct.  J6o  46  B) In the f i f t h blue  block a component i s beginning  to develop on the  side.  C)  In  blocks  7,8, and 9 t h i s blue component continues t o grow  and  i n c r e a s e i n amplitude.  D) In block 10 the redward c o n t i n u e s to decrease  component  i n amplitude  begins  i t s decline  i n blocks 11,12, and 13.  E) In block 14 you have e s s e n t i a l l y only one component  The ^4568. This  situation  is  a little  more confused  suspected  d e r i v a t i v e technique  to  be  more  a  present.  when you lock a t  At times three components a c t u a l l y seem t o is  and  character  be  of  present.  the  second  than any r e a l s p e c t r a l f e a t u r e .  5) Q u a n t i t a t i v e Measurements. The  equivalent  indication  of  the  line profiles.  width, degree  line  depth,  half-width  and  an  of asymmetry were measured from the  The b l o c k s of f i g u r e s 6 and 7 were used t o  give  a more d e t a i l e d a n a l y s i s c f the v a r i a t i o n s .  Eguivalent integration spectra.  widths  between  for  the  continuum  This result  l i n e s were determined and  line  Nevertheless, r e l a t i v e  width  made  be  n i g h t s of appears  remain  e g u i v a l e n t width during  the  measures  of  t o a very good approximation.  observation, tc  the  rectified  w i l l be i n f l u e n c e d by i n a c c u r a c i e s i n the  continuum f i t . can  from  by area  the  eguivalent  constant  over  the  widths entire  eguivalent For the two  of  the  cycle.  d i d not vary by more than - 1 % on the  observation  period.  This  is  in  lines The  average  agreement with  47  Huang's (1955) r e s u l t f o r T Sco (2K-80-120 km/sec) and (1973) r e s u l t f o r Bw  The minimum The  line  results  equivalent  Vul(2K*150 km/sec).  depth  intensity  was and  are  defined  as  the  difference  in  Figure  absolute  12.  Again,  good  relative  comparisons.  h a l f - w i d t h was'defined  half-width  normalized  b l o c k s of data. was  1.21  A and  The 1;36  f o r S i I I I A 4568 was  the the  allows  period i s  width of the l i n e at  Hhat i s p l o t t e d i n F i g u r e 12  to  1.  12.  as the f u l l  the half-peak i n t e n s i t y l e v e l . the  for  procedure  The extent of one  shown by the dotted l i n e s i n Figure  The  as  measures are not p o s s i b l e but  i n t e r n a l c o n s i s t e n c y of the continuum f i t t i n g very  between  the continuum i n t e n s i t y s e t equal to  shown  widths,  Goldberg's  is  the mean h a l f - w i d t h f o r a l l the  mean h a l f - w i d t h W f o r the S i I I I ^ 4553 l i n e A f o r Oct. 1.16  15 and Oct.  A and  1.32  16 r e s p e c t i v e l y .  A f o r Oct.  15 and Oct,  W 16  respectively.  The  asymmetry i s d e f i n e d as i n the paper  (1976). midpoint  It  is  of the  normalized  taken as the displacement width  at  half-depth.  by the mean width  The  was times  taken  to be t h a t of minimum i n t e n s i t y .  when t h e r e are a c t u a l l y two  p o s i t i o n i s not r e a l l y meaningful  components and  et  al  result  is  again  A p o s i t i v e measure  of asymmetry means t h a t the core i s to the red The  Heard  of the core from the  at h a l f depth.  value means the core i s to the v i o l e t .  by  and  a  negative  p o s i t i o n of the core N a t u r a l l y at present  the  those core  t h i s shows up as i n c r e a s e d  48  s c a t t e r i n the p o i n t s as shown most c l e a r l y 12(d).  i n Figures  12 (c) and  Figure 12(a).  Line depth, half-v/idth, and asymmetry vs. time f o r Oct. S i 111  4553  =3 Q ©  o  o ®  ©®(b©  0  ©  a  (!)  ^  ©  •a  CD ©  ©Q©©  G)  ©  FFI  ©  UJ  ©  a  © © °  UJ  ©  O  ©  ffl  m  ©  ©  © © 0  •—i  in  —4  l— Q  °©©e>  i—«  ©O  cr. •_!  ©  0  O O ©  0  ©  Q  ° ©  0  ©  o©  LU-  ©O©  n: a  ©  ©© © ffiOffl  ©Q© ©  Q,®  ©  © ©©  o  a  a© 0)  © ©  2: >— CO cr  **>  © < V ©  0  O  f  f  l  © V  ©~  ®©  0  „©/*© © © Q Q)  ~  O  ©  oo  ©  ©  ©  ©  ©  ©°  ©  ©  ° o©  0  0  1  ?.83  -1 4.81  1 5.79  1— 6.77  TIME UTCHRS;  7.75  8.73  Figure 12(b).  Line depth, half-width, and asymmetry vs. time f o r Oct S i 111  4568  9  13 ,  ©  (DO©  LU  a  CD  (!) ©  (Do ©Q  UJ  CD  »  a©  ©  ©  © ©  'ffi  © ©  ©  in  —«  in  I— Q •—c  ©  © © (5  x i—  0  a  0  ©  Q  a©  ©a  ©  O©  GC --4  :  a  © ©  a ©a©  w  ©  ©  " ©  ©  "  ©  fflfl)  ©  ©  a  a  ^G^O  ©a a  ©  in "1 0  cn  F— UJO z: >-. CO (X  a  ©  o  © ° ©^  e  •  a  a  © ©o  © ©  ©  w  a ©  a ©  o  © ®  ©  ca a  a  a.  ©  ©  © © © ©a a © © a,  ©  a  ?.83  4.81  5.79  6.77  TIME UT(HRS)  7.75  8.73  51 Figure .12(c).  Line depth, half-width, and asymmetry vs. time f o r Oct. 16. 4553  S i 111  9  © ~ 0  ©  © ©® _o ©  in  m ,  m --^  ©  ©©  ©  ©  ©ca ©  a© o  ©o©  ©  a  QL.  O  ©  ©  UJ  ©  ©  © ©  ©  ©  v  ©  © ©  ©©  ©«. " ©  ©  © ©  ©  O  ~ ©  ©o 0  0  i  in  —4  in  IE" r-  4  ©o©  a  C9  °  0  o ©  CE -_J UJ"  ©  ©  ©  ©  0  O  6  ©o©  ©  © © ©  ©  © ©-  ~©  ©  ©  m t— a  0 © ^  .  .  a  ffl  ©  ©  a a  °  © ©  ©  ©  o V  ©  "  ©  .in  ©  cn  ©  i—  °  °  © >— CO d  ©  o ©  „  ^  ©o  Q  0  ©  ©  o  u  o  u  ©  o © o  ©a ©  ©  a©  5.93  1 7.89  TI:E UTIHRS)  1 8.87  ©  ©  ©  a  0  0  o. i  4.95  i  ©  (n  -1 6.91  o  ©  ©  >-  0 ©  ©  9.85  10.83  Figure 12(d).  Line depth, half-width, and asymmetry vs. time for Oct. 16. Si 111 4568  9  o  m Q_ UJ Q  © *  UJ  Q  ,©Q  °  © ©  (9  ©  ©  0  ©  ©Q 0  CD©  °  © ©©  o©  0  © © © © © © o ©  IT)  —<  ' o  ©  _©  m  o  ° D  ©&Q©  °  I  ©  in  »—  a  ©^  © ©0  CE iii—  ° O Q ©,  °© °© © ©  ©© ©  ©  1  ° °~o  i— Q  ©  ©  a ©  ©  ©  o © ©  ©  ©^  ©  0  •3  © a  >— CO <x  ©  a  ©  ©  ©  I— UJO  ©  © ° o ©  ©  D  0  ©o  © Q  °  ©  ©Q©  © c©  CO CD.  o  a |  o o© ©  i I 4.95  1 5.93  1 6.91  ©  ©  1 7.89  TIME UT(HRS)  1 8.87  ©  ©  °  1 9.85  1 10.83  53  I t i s important with  the  points  t o have some idea of the  p l o t t e d i n F i g u r e 12,  I  approximately course  have  error  throughout  s m a l l block t o block  can use t o estimate bars  i n the p l o t .  of  the  s a i d before t h a t the e q u i v a l e n t  constant  the  associated  T h i s can be obtained a  number of ways; one i s from a c o n s i d e r a t i o n widths,  error  cycle.  equivalent  width remains There  v a r i a t i o n s and i t i s these  the e r r o r s of the p o i n t s i n F i g u r e  are  of  t h a t one 12.  The  are - 2 to 3 times the diameter o f the symbols used  54  The  R a d i a l V e l o c i t y Measures  The  broadening  of the l i n e s at c e r t a i n  be due t o the presence  cf two  the  amplitude  radial  The  double  very  velocity  in  this  star  r a d i a l v e l o c i t y amplitude  at  (Goldberg,  certain 1973).  authors  are  improved  The  observations  spectral  and  time  phases  is  In 12 Lac  the  Radial velocity  an attempt was  separate  described  here  resolution.  In  however, light  have  of  the  for  BW  made to measure the r a d i a l v e l o c i t i e s of the  components.  A new Tad  One  from the p o s i t i o n of  d i s c o n t i n u o u s v e l o c i t y curve obtained by Bruce Goldberg Vul  Vul  a l l continuous.  u s u a l l y measure the wavelength s h i f t  l i n e minimum.  In BH  i s on the order of 150 km/sec.  i s considerably l e s s .  curves obtained by v a r i o u s would  unresolved components.  nature of the s p e c t r a l l i n e s  evident  phases i s assumed to  method of d e c o n v o l u t i o n developed  Dlrych  (Clayton and O l r y c h , 1S76)  A b r i e f d e s c r i p t i o n of t h i s method and of the deconvolved  was  by Rob  Clayton  a p p l i e d to the  and data.  diagrams shewing examples  s p e c t r a are given i n Appendix A.  The  results  are g u i t e amazing.  The  wavelength s h i f t s f o r each component were measured from  the p o s i t i o n s of l i n e This  technigue  Corrections for  was  minimum  from  applied  shifts  and  the  deconvolved  spectra.  to the b l o c k s of F i g u r e s 6 and non-linearities  in  the  scanning  r a s t e r d i s c u s s e d i n a previous s e c t i o n were a p p l i e d to the A  reference  velocity  of  -20  km/sec was  7.  data.  somewhat a r b i t r a r i l y  55  taken as the further  stillstand  described  velocity  in  the  (the  Discussion  t h e r e f o r e view the a c t u a l  numbers  instead  changes,  the  spectrum is  in  was  amplitude taken but was  motion  within  term  with  'stillstand  section). caution  A  and  r a s t e r s h i f t s i n the c a l i b r a t i o n spectrum  Each  line  was  .  interest  Also, large  were found which would  case.  considered  separately.  velocity  measures l i n e  p o s i t i o n s were  nearest  instrumental  channel.  the e r r o r s i n v e l o c i t y are estimated be  In  determined  From  r a s t e r s h i f t and the d i s c r e t e sampling  should  must  calibration  The r e s u l t i n g r a d i a l v e l o c i t y curves are p l o t t e d i n 13.  a  Figure  the  radial  only  to  consideration  the  of the  i n t e r v a l mentioned above, to  be  -  7  km/sec.  It  noted t h a t the e r r o r s w i l l be l a r g e r where t h e r e are  two components present; the s c a t t e r i s very s m a l l when there only  is  consider  primary  the framework of the s t a r  l i m i t the accuracy i n any  One  wavelength  not used s i n c e our  1  one  component  present.  Because  of  p o i n t s t h e r e i s some guestion as t o the exact stillstand  velocity.  f o r the two  lines  For t h i s reason  ( ^4553  and  the s c a t t e r i n the location  an average  ^4568  )  is  was  of  velocity not  F u r t h e r remarks cn the v e l o c i t y curve are reserved t i l l  the curve  obtained. the next  section.  The  deconvolution  technigue  used  to  separate  components uses the Maximum Entropy method c f s p e c t r a l (  a  very  brief  description  the  two  analysis  of t h i s i s given i n Appendix A).  T h i s g i v e s g u i t e accurate p o s i t i o n  measurements  but  does  not  56  provide true v a l u e s f o r the i n t e n s i t i e s of the components.  A  synthetic  Glaspey  was  profile  fitting  method  developed  line  John  used t o determine the i n t e n s i t i e s of the components.  D e t a i l s of the technigue can be found i n Glaspey g t Each  by  profile  was  reconstructed  by  al  adding  (1S76).  two  Voigt  components, both of the same width but with d i f f e r e n t  velocities  and amplitudes, and c o n v o l v i n g t h e i r  Modulation  Transfer  Function  of  components was chosen compared  to  a  the  components  was  velocities  used  The  which  gave  profile  p r o f i l e gave a s a t i s f a c t o r y  then  the  width the  The  those  permitted  to  the Voigt  best  f i t when  doppler  taken to be constant throughout were  of  at sharp l i n e phase.  f i t .  s p e c t r a . , Only two parameters, were  with  isoccn.  as that  line  sum  obtained  from  A Gaussian  width  of  the  the c y c l e .  The  the  deconvolved  the amplitudes of the components,  vary i n order to o b t a i n a *good» f i t .  Because of the l a r g e volume of data to be analyzed an fitting  procedure  was  used.  The  method  c o n s i s t s of determining the values of the A1  and  least  amplitude  A2 which y i e l d a minimum f o r the f u n c t i o n Of  is essentially input  of  data  the sum  profile  automatic squares parameters  2  ( whereof  of squares of the d i f f e r e n c e between and the f i t t i n g  method d e s c r i b e d by Bevington  profile).  (1969) was  2  the  The q r i d search  used.  The l i n e depths of the separate components are shown i n the upper plots  p l o t s of F i g u r e 13. correspond  The symbols used i n  the  line  to the two components i n the v e l o c i t y  depth curves.  Examples of the Gaussian p r o f i l e f i t to the i n p u t data are shown  57  i n F i g u r e s 14(a) the  plus(+)  Gaussian  and  14(b),  signs.  The Gaussian curve i s i n d i c a t e d  The r e s u l t i n g d i f f e r e n c e curve  ) i s shown below the l i n e  component (s) i s marked by the  The p o s i t i o n of the  readily  compare  my  the  centroid  of the l i n e  measuring (j -(A1  are'the wavelength p o s i t i o n s of  c  the  the  wavelength  Oct.  15 and Oct.  16 r e s p e c t i v e l y .  the  shift  +42 J L ) / (A1+A2) ; X  and  two  The  components).  r e s u l t i n g curves f o r A 4553 are shown i n F i g u r e s 15(a) for  velocity  with t h a t obtained by other o b s e r v e r s , I have p l o t t e d  v e l o c i t y curve as obtained by from  ( observed-  arrows.  In order to be able t o more curve  profile.  by  and  15(b)  13(a).  I 4.81  Radial v e l o c i t y curve f o r S i 111 4553 f o r Oct.  5.79  I 6.77  . TIME UT  MRS)  1  i 7.75  1 8.73  15.  13(b).  <  Radial v e l o c i t y curve f o r S i 111  4568 f o r Oct. 15,  «  o ° o o  X  <  ~  -  * o°°o  °  K  *  * «  o  °o o o  <  o  o  «  oo o  O O  4.81  5.79  6.77  TIME UT MRS)  o  o  ooo o o  O Oo  7.75°  8.73  Figure 13(c).  Radial v e l o c i t y curve f o r S i 111 4553 f o r Oct.  oO  o ^ o  o  oo o  o  O  o  16.  oo oo  oo  (V) I E •• I—  a. a -Ja'  o°o  o °  o  UJ  «  °<^o 4  <  o  apx  a a. in  o <  CJ UJ CO  oo  4 «  do  o o  4  o  o  'a.  oo  O Oo  ooo  UJ2. CE i—i  o  cn ens  0  o  ° ° o o o  o  o °o  o  o 4  oo  i  44 4  4 < 4  4  4  4 4  o o in. i  4.95  5.93  5.91  7.89  TIME UT  8.87  MRS.)  9.85  10  Radial v e l o c i t y curve f o r S i 111  Figure 13(d).  4568 f o r Oct. 16.  °o o 0  o° o ° °o o o  o _ oo o u  0  oo  O  O  °  o o °  oo  o 0  >  o°°  °  o  0  o o  « «  r  /  o o  K  < o  oo  o  o  o O  o  OO  O  ° °o o o o  o  ooo  o  O  °  o  ° °  O  O 0  o oo 4.95  I  5.93  oo o  1 o 6.91  °  1 7.89  TIME UT  1 8.87<  MRS)  1  «  R"  9.85  10  Figure 14(a).  Gaussian f i t to input data f o r block Figure 5a.  S i 111  4553  12 LRC  #10  63  64  Figure 15(a).  Radial velocity curve (centroid) for Si 111  4553 for Oct. 15.  01  o in.  Q  0, D  B3 in  a  U  03  • Q  ts  03 Q  UJ CO  Q  at  •  'in. i  a  a  •  O Oa  cn I—I  C3 Q  l  Q •  • a  a in rn.  3.83 i  4.81  5.79  TIME UT  6.77  MRS)  m 7.75  1 8.73  Figure 15(b).  Radial v e l o c i t y curve (centroid) f o r S i 111  4553 f o r Oct. 16.  o in" 0  a in"  o  -  •a  a  o  cm  o  U  UJ  CO  cn  CQQJ  m  CD  2 °  CQQ  o  i  _tD  a  ta  oo  ODD  o  D  DO  O Oa  CD  0  LuS. Q  cn •a cn . 01 i  ft. CO  in tn.  95  1 5.93  1 6.91  1 7.89  TIME UT  1 8.87  MRS)  1 9.85  1 10.83  66  Discussion  Throughout  this  discussion  obtained by Bruce Goldberg The  two  I w i l l use the v e l o c i t y  (1973) f o r BH  discontinuous  nature  stillstand  the descending  branch  on  and  radial velocity  2)  v e l o c i t y f c r 12 evidence  for a  of the v e l o c i t y curve.  BM V u l t h e r e i s a p e r i o d of -40 minutes the  V u l f o r comparison.  most prominent f e a t u r e s of my observed  Lac a r e 1) i t s  curve  duration  r e g a i n s approximately  during  constant.  In  which  Because of  the s c a t t e r i n the data p o i n t s i t i s not c l e a r i n the case of 12 Lac whether or not*the constant.  v e l o c i t y during  Nevertheless  •stillstand  1  is  really  as t h i s f e a t u r e i s q u i t e pronounced i n  BH V u l I w i l l use the term  •stillstand*  i n my d i s c u s s i o n .  In d e s c r i b i n g t h e v a r i o u s f e a t u r e s of the v e l o c i t y curves I w i l l i n d i c a t e i n b r a c k e t s [ ] which component I am r e f e r r i n g t o : x or o.  Consider F i g u r e s 13(c) and 13(d):  1) The s t i l l s t a n d discontinuity splitting  [o]first  preceding  takes p l a c e the  at  -5  stillstand  h r s D.T.  results  The  from  the  £o]  of the l i n e i n t o two components.  2) There i s evidence  f o r a blue s h i f t f o l l o w i n g  stillstand  at  T h i s e f f e c t i s more obvious  i n F i g u r e 13(d)  for  -6.5  hrs  \ 4568.  phase  O.T.  The • f l a t t e n i n g ' o f the  o f maximum blue s h i f t  e v i d e n t i n V4568. maximum For these  blue  shift  velocity  as observed.in  For /i 4568 the amplitude and the s t i l l s t a n d  A 4553 i t i s only h a l f t h i s amount. observations  whether  this  curve  near  the  BW V u l i s a l s o g u i t e difference  between  v e l o c i t y i s -30 km/sec. I t i s not  discrepency  clear  from  i s i n t r i n s i c or  67  instrumental, 3) The r a p i d r i s e of one component [ o ] to  maximum  redshift  is  seen p r i o r t o a renewal of the c y c l e . 4) A f t e r the r e d - s h i f t e d component reaches a maximum v e l o c i t y i t seems  to  experience  a blue s h i f t before  seen p a r t i c u l a r l y i n F i g u r e effect  is  continues  not  This i s  13(c) f o r f x ] at - 6 h r s D.T.  seen i n EH V u l , i n f a c t the o p p o s i t e  to be r e d - s h i f t e d .  It  is  suspected  s h i f t i s not r e a l and t h a t what r e a l l y few  f a d i n g away.  This  occurs; i t  that  the  blue  happens i s t h a t the f i r s t  p o i n t s have been o v e r c o r r e c t e d f o r r a s t e r s h i f t .  T h i s point  i s f u r t h e r e x p l a i n e d i n #6 below. 5)  For  and  are able t o see the d i s c o n t i n u i t y reappear  D.T.)  t h i s night we have more than one c y c l e of the p u l s a t i o n  as  a  component  [x]  develops  (  having  at  -9.5  the  hrs  stillstand  velocity.  Consider  Figures  13(a) and 13(b):  6) I might note that i n F i g u r e of o b s e r v a t i o n km/sec).  a t -4 h r s . D.T. seem  Se are seeing  pulsation  just s l i g h t l y  branch  cycles).  should The  run.  be  (by  -10  the  same  shift  near  the  of the c y c l e  (at  least  corrections beginning  of  for were the  In p a r t i c u l a r the c o r r e c t i o n f o r the f i r s t few  b l o c k s were on the  order  of  p o i n t s were at - -25 km/sec. expansion  high  more than one c y c l e of the  fiducial  g r e a t e r than 2 sample p o i n t s only observing  abnormally  and thus the v e l o c i t i e s at the beginning  on the ascending consecutive  13(a) the p o i n t s a t the beginning  15  km/sec  - i e . the  uncorrected  I t i s p o s s i b l e t h a t the n o n - l i n e a r  of the camera reading beam might be more s e r i o u s near  68  the s t a r t of o b s e r v a t i o n on a p a r t i c u l a r o b j e c t . 7) There seems stillstand  to  be  evidence  for  a  large.  a p o s s i b l e cause f o r the s c a t t e r measurements  is  the  profile have  width  changes  the  components  s h i f t s determined In  a  but  the  radial  velocity  different with  widths time.  and/or  cases, This i s  be  the d e c o n v o l u t i o n technigue most  likely  not  the  The wavelength  by the deconvolution method would then  few  t h r e e components.  in  shape assumed f o r one component.  Perhaps the two components  situation  following  i n p o i n t (2) f o r the other n i g h t ' s data.  8) The s c a t t e r i n F i g u r e 13(b) i s very  error,  shift  [ o ] p a r t i c u l a r l y i n F i g u r e 13(a) f o r /] 4553 at -7.75  hrs as noted  of  blue  a  real  in  yielded physical  more a f u n c t i o n of the p r o f i l e shape assumed f o r  the v a r i o u s components.  The l i n e p r o f i l e and r a d i a l v e l o c i t y changes correlated. 12(b),  Compare F i g u r e s 12 and 13.  13(a)  and  13(b).  fit  the  are  directly  Consider F i g u r e s 12(a),  beginning of the ascending  branch o f the v e l o c i t y curve the l i n e s are s h a r p e s t , deepest and e s s e n t i a l l y symmetrical. O.T.  as  broader the  the  begin  the s t i l l s t a n d the  phase occurs  at  wing to the r e d .  to double  velocity. redshifted  At - 5.5  hrs.  as a component £ o ] develops  T h i s component i n c r e a s e s i n component  £x]  fades  hrs.  i n F i g u r e s 12(a) and 12(b) a t -6.5 h r s .  O.T.)  O.T. having  intensity  away.  s t i l l s t a n d t h e . l i n e s become sharper and deeper again clearly  -4  progresses the l i n e s become shallower and  with an extended  lines  while  cycle  The deepest  During  (shown very but  less  69  so  than  at  blue s h i f t  the beginning of the ascending branch. following  stillstand  extended  wing  to  [o]  the  there blue.  is  During the  an  asymmetry  showing  an  narrower  and deeper p r i o r to the renewal of the c y c l e .  same t h i n g i s seen f o r the data of October  I t i s very i n t e r e s t i n g and  Figures  13 (c)  and  15(b).  of  and  Figure  15  are  a  As  one  velocity  of  resulting  mere towards the  the s t r o n g e r component.  For F i g u r e 13(a) the v e l o c i t y  is  Figure  km/sec;  velocity  amplitude  wavelength  for  determined  15 (a)  the  star  a  curve  and-  15 (b)  for  a  The  showing  the  much  evidence  in  s t i l l s t a n d on the descending  curve.  I w i l l present  of the period d e t e r m i n a t i o n s i n 12 Lac.  (De Jager^ 195 3) t r i e d to e x p l a i n by means of a sum  of two  of  0.19308883  beat p e r i o d P=8.908 days.  the  independent  f r e q u e n c i e s being not f a r from each other. periods  i s - 45 km/sec.  to be  Because of i t s importance  summary  De Jager  it  whole g u e s t i o n of the m u l t i p l e p e r i o d i c i t y of 12 Lac i s  very complex. short  from  There does not appear  branch of the v e l o c i t y  The  15(a)  amplitude  s h i f t s from the c e n t r o i d w i l l thus be much l e s s than  the t r u e value. Figures  straight  the v e l o c i t i e s f o r the separate components.  ( c e n t r o i d ) v e l o c i t y i s weighted  70  15(a)  »hen the two components are of  component becomes s t r o n g e r than the other, the  -  Much the  16.  to compare F i g u r e s 13(a)  egual i n t e n s i t y , the v e l o c i t i e s i n average  The l i n e s then get  In  a  1953  variability  of  o s c i l l a t i o n s with  His components  days(Pl) and 0.197367 days(P2) In consequence,  here  one ought  to  with  g i v e the expect  /  70  t h a t the amplitudes values and  of  of b r i g h t n e s s and r a d i a l v e l o c i t i e s , and the  [ 0 - C ] c a l c u l a t e d f o r maxima or minima of b r i g h t n e s s  radial velocities  days  should  change  from the  period  0.19308883  or  0.197367  a c c o r d i n g t o the phase o f the beat p e r i o d .  T h i s d i d not occur, and i n 1957 De Jager  (De J a g e r ,  1957)  found  the e x i s t e n c e of the t h i r d o s c i l l a t i o n i n the s t a r with a p e r i o d of  0.15583  three  days.  Rakosch  independent  values  of  the  0.15292 days). variations  (1960) confirmed the presence  oscillations  periods  with  (0.19308997  He a l s o found  (0.118644  but  a  days).  new A  slightly  determination  of  period  large  f o r colour  independent o s c i l l a t i o n s ; (0.19308883  days  and  two  of  12  with  0.197358  Lac.  by  Barning  uncertainties Jerzykiewicz period  probably  involved. (1963)  not  Opolski  and  the  They suggest short  Ciurla  Any (  known  periods  The  real  and  period  because o f t h e many  Ciurla  (1973)  longest  found with  (1961,  1962),  t h a t the s h o r t a  period  of  curve  P1 (0.19308883), P2 (0.197367) and P3  (0.15583) r e p r e s e n t no more than a observed  (1963) f o r the  t h a t the components o f the l i g h t  periods  and  days), and two a d d i t i o n a l ones  (0.19308858 days) v a r i e s p e r i o d i c a l l y  8.876 days. with  is  compiled  His r e s u l t i s four  previously  with p e r i o d s 0.182127 days and 25.85 days. found  index  number of o b s e r v a t i o n s  (1963) were used by Barning  variability  different  days, 0.19737253 days and  obtained during the " I n t e r n a t i o n a l L a c e r t a Weeks" p u b l i s h e d by De Jager  of the  formal  description  o f the  v a r i a b i l i t y of 12 Lac.  periods determined  from previous r a d i a l v e l o c i t y  curves  such as F i g u r e s 15(a) and 15(b) ) should be re-examined.  The  71  v e l o c i t y curve i s c l e a r l y d i s c o n t i n u o u s and t h i s s p l i t t i n g i n f l u e n c e any period  determinations.  There have been undertaken  a  towards  phases.  might  number  of  explaining  theoretical  the  line  investigations  splitting  at c e r t a i n  -  1) The double l i n e s are formed i n d i f f e r e n t p a r t s of the disk 2)  star's  (McNamara and Gsbbie, 1961; Huang, 1955). They  arise  from  two  l a y e r s , one above the other  (Odgers,  1955; Goldberg, 1973). 3) They are the ccnseguences  cf  non-radial  pulsation  (Osaki,  1971) .  As mentioned b e f o r e , Huang width  in  T Sco  did  not  (1955) found t h a t the e g u i v a l e n t  vary  throughout  i n t e r p r e t e d t h i s to mean that the s p l i t t i n g due  to  different  macroscopic  motion:  the  cycle.  He  of l i n e p r o f i l e s  is  the two streams must be moving i n  parts of the s t a r ' s d i s k  instead  of  one  above  the  other.  In  (2)  the motion i s r a d i a l .  The i n t e r p r e t a t i o n i s based  on the f o l l o w i n g p i c t u r e : An atmosphere velocity  which  is  ejected  with  high  a f t e r t r a v e l l i n g outwards f o r a time then  falls  back i n t c the general s t e l l a r photosphere at high speed. time  at  the  stillstand  phase  the  v i s i b l e and then another atmosphere  For  a  s t e l l a r s u r f a c e proper i s  i s e j e c t e d , (Goldberg,  1973).  The paper by Heard e t a l (1976) mentions work by Hatson and  72  Stanford that extends Osaki's work and shows t h a t at moderate t o l a r g e amplitude, n o n - r a d i a l p u l s a t i o n can produce  line  splitting  of the type observed i n EH V u l and now seen i n 12 Lac.  Both gualitative  the  non-radial  and  radial  explanations  d e s c r i p t i o n of the l i n e s p l i t t i n g .  to be done t o decide which i s the c o r r e c t  offer  a  More work needs  interpretation.  73  Summary and C o n c l u s i o n s  The seen The  broadening of the l i n e p r o f i l e s at  to  be  due  is  in  the  radial  velocity  curve  preceding  i s due t o the growth of a component at the s t i l l s t a n d  velocity.  The  velocity  phases  t o the presence of two unresolved components.  discontinuity  stillstand  certain  curve  line  splitting  should  prove  and  a  consequent  strong  discontinuous  incentive  for  more  t h e o r e t i c a l and o b s e r v a t i o n a l i n v e s t i g a t i o n s .  There i s one very s i g n i f i c a n t d i f f e r e n c e BW V u l . and  BS Vul appears to be s i n g l y  radial  velocity  changes  between 12 Lac and  periodic.  The l i n e p r o f i l e  repeat from c y c l e  to c y c l e .  The  amplitude of the v e l o c i t y curve remains c o n s t a n t .  12 Lac has  (supposedly ) a number of p e r i o d s .  velocity  amplitude i s v a r i a b l e .  On Oct.  amplitude  i s -70 km/sec; on Oct.  16 i t i s  15 the t o t a l -  80  r a d i a l v e l o c i t y curves and l i n e p r o f i l e v a r i a t i o n s from  cycle  to  cycle.  Cn  Oct.  16  the  to  that  on Oct.  accurately  amplitude  15.  variation.  In  the  p e r i o d (s)  choosing  r a d i a l theory t h i s d i f f e r e n c e  in  of  velocity The  do not repeat amplitude  much  More o b s e r v a t i o n s should be  determine  radial  km/sec.  velocity  s e p a r a t i o n at s t i l l s t a n d between the components i s than  The  larger  undertaken  radial  velocity  between any r a d i a l or  velocity  amplitude  must  nonbe  considered.  An  interesting  side  r e s u l t of t h i s i n v e s t i g a t i o n  i s that  74  though the v e l o c i t y amplitude i n broader ( The  one  16  i s g r e a t e r on Oct.  resulting  l i n e s , the l i n e p r o f i l e s at the sharp l i n e phase  component present ) have the same width  same Gaussian  f o r both n i g h t s .  p r o f i l e gave a s a t i s f a c t o r y f i t f o r both  sets  of data.  Another  important  result  is  that  r a d i a l v e l o c i t y curve i s much g r e a t e r than obtained.  Heard  et  al  amplitude  amplitude  what  was  of the  previously  (1976) f i n d t h a t the amplitude 43  v e l o c i t y v a r i e s s l i g h t l y from splitting  the  km/sec  35  to  of the  km/sec.  of the components shows t h a t the t r u e r a d i a l  The  velocity  i s about twice that obtained p r e v i o u s l y .  Hith regards to 12 l a c i t i s  proposed  that  a  number  of  t h i n g s be done: 1)  As  summarized  in  the  D i s c u s s i o n s e c t i o n there has been a  great amount of work done through light  and  examining  the  r a d i a l v e l o c i t y curves f o r m u l t i p l e p e r i o d i c i t y .  Any  researcher  who  attempts  explaining  the  line  should  keep  in  mind  discontinuous v e l o c i t y  to  use  profile the  the years,  and  line  these  on  periods  radial  in  velocity  splitting  and  a  variations consequent  curve.  2)  Hore o b s e r v a t i o n s should be undertaken at t h i s high  and  time r e s o l u t i o n .  of  c y c l e s , one  I f one  spectral  had o b s e r v a t i o n s of a l a r q e  number  would have a c l e a r e r i d e a of whether the  scatter  ( p a r t i c u l a r l y at s t i l l s t a n d 3)  model  ) was  i n t r i n s i c or i n s t r u m e n t a l .  L i n e s of other elements should be observed;  He lJi4471 and the hydroqen l i n e s .  Two  in particular  possible motivations  for  75  this  line  of  investigation  l i n e s i n some ft Cephei Zebergs  stars  are:  1) the presence of emission  ( u n d e r b i l l , 1966)  (1955) have shown that the hydrogen  descending  branch  of the v e l o c i t y  and  lines  2) Struve lag  on  and the  curve.  Observations of other /§ Cephei  s t a r s should most d e f i n i t e l y  be obtained at high s p e c t r a l and time r e s o l u t i o n i n order t c see if  any  line  splitting  occurs.  A  complete  c l a s s i c a l ft Cephei s t a r s i s given i n U n d e r b i l l the s t a r s are very b r i g h t short(<6  hours)i  could be observed  A  (1966).  of the  18  All  of  (>6th magnitude) and t h e i r p e r i o d s are  complete c y c l e  i n one  list  (or more) of the  night of o b s e r v a t i o n .  pulsation  76  Adams, W.S. 1912, Ap.J.,  35 ,  179.  Aizenman, H.L., Cox, J.P. and Lesh, J.R. 1975, Ap.J., 197 , 399. Barning, F . J . f l . 1962,  B.A.N., J7 , 22.  Beres, K. 1966, Acta A s t r . , 16 ,  161.,  Bevington, P.R. 1969, Data Seduction and E r r o r A n a l y s i s f o r the P h y s i c a l Sciences (McGraw-Hill). Buchholz, V.L., Walker, G.A.H., Auman, J.R. and Isherwood, B.C. 1973, i n A s t r o n o m i c a l Observations with T e l e v i s i o n type Sensors, e a . J . a . Glaspey and G.A.H. Walker (Oniv. o f B r i t i s h Columbia, I n s t , o f Astronomy and Space S c i e n c e ) , p. 199. C i u r l a , T. 1973, Acta A s t r . , 21 * 367. C l a y t o n , B.W. and D l r y c h , T.J. 1976, i n p r e p a r a t i o n . Cox, J.P. 1974, Reports cn Progress i n P h y s i c s , 37 , 563. De Jager, C. 1953, E.A.N., J2 .1957, .  , 81.  B.A.N., 13 ,  1963, E.A.N., 17 ,  149. 1.  Fahlman, G.G. and Glaspey, J.W. 1973, i n Astronomical Observations with T e l e v i s i o n - t y p e Sensors, ed. J.W. Glaspey and G.A.H. Walker (Univ. of B r i t i s h Columbia, I n s t , of Astronomy and Space S c i e n c e ) , p. 347. F a t h , E.A. 1938, Pop. A s t r . , 46 , 241. Glaspey, J.W., E i l e k , J.A., Fahlman, G.G. and Auman, J.R. 1976, Ap.J., 203 , 335. Goldberg, E.A. 1973, PhD. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia. Grabowski, B. 1966, Acta A s t r . , 16 , 309. .1969,  Acta A s t r . , J9 , 23.  Heard, J . F . , Hurkens, R.J., Percy, J.R. and Porco, M. 1976, t o be p u b l i s h e d . Hill,  G. 1967, Ap.J. Suppl., 14 , 263.  Huang, S.S. 1955, P.A.S.P., 67 , 22.  '  77  Jerzykiewi.cz, M.  1963,  Seta A s t r . , 13 , 253.  Kanasewich, E.B. 1973, Time Sequence A n a l y s i s i n Geophysics U n i v e r s i t y of A l b e r t a Press) . Lesh, M.I. and Aizenman, J.B. 22 , 229. 26  • , 1.  flcNamara,  —  D.fl. and Gebbie,  Odgers, G.J.  1955,  1973a, A s t r o n . and  Astrophys.,  . 1973b, A s t r o n . and  Astrophys.,  K.B.  1961,  .  .  Osaki, Y.  1971,  Pub.  .  1974,  Ap.J., J89  1967,  215. ,  231.  Acta A s t r . , 12 ,  269.  1966, J6  , 303.  A s t r . Sec. Japan,  23 , 485.  , 469.  J.B.A.S.C., 61 ,  Bakosch, K. 1960> A.N.,  9,  Acta A s t r . , JM  1962,  O p o l s k i , A. and Grabowski, B.  Percy, J.B.  P.A.S.P., 73 , 56.  P u b l . B.A.O., 10 , No.  O p o l s k i , A. and C i u r l a , T. 1961,  (The  285,  117.  211.  B i c h a r d s o n , E.fl. 1973, i n Astronomical Observations with T e l e v i s i o n - t y p e Sensors, ed. J.W. Glaspey and G.A.H. Walker (Univ. of B r i t i s h Columbia, I n s t , of Astronomy and Space S c i e n c e ) , p. 433. Sato, N.  1973,  Astrophys. and  S t r u v e , 0. 1951, >. 1955,  ftp.J.,  1974,  U n d e r h i l l , A.P. 1966, D. B e i d e l Co.).  , 135.  V. 1955,  B.Sc. The  215.,  , 589.  P.A.S.P., 67  S t r u v e , 0. and Zeberqs, Thompson, I.B. Columbia.  113  Space S c i . , 24 ,  Ap.J., 122  ,  134.  T h e s i s , U n i v e r s i t y of  British  E a r l y Type S t a r s (Dordrecht, H o l l a n d :  Walker> G.A.H., Auman, J.B., Buchholz, V.L., Goldberg, B.A., Gower,*A.C, Isherwood, B.C., Knight, B. and Wright, D. 1972, Advances i n E l e c t r o n i c s and E l e c t r o n P h y s i c s , 33E , 819. Watson, B.D.  1972,  Ap.J. Suppl., 24 ,  167.  78  ADjjendix  In that  A  any  method o f d e c o n v o l u t i o n one  you  have  a  knowledge  components.  A Gaussian  data  profile  a t the  the  two  assumption  is  shape t h r o u g h o u t  new  are  made  decrease/increase  The  profile  sharpest  components  the  requirements  profile  phase was  assumed  to  the  intensity,  shape best  used.  be  equal;  components still  retain  of  f i t  The  the to  a  widths  of  as  w e l l the  though the  is  they  same  profile  this  'power  cycle.  method i s e s s e n t i a l l y  1) The  data  2)  autoccvariance function  The  the  the  which qave t h e  line  that  in  of  of  i s t r e a t e d as a power  this: spectrum.  is  obtained  from  spectrum*. 3)  The  the  assumed  <4) The  autocovariance profile  obtain  shape f o r one  Maximum E n t r o p y  autocorrelation the  One  function  coefficients  the which  by a t i m e  magnitude  of the  employ domain  also  of  puts  power t h r o u g h a limit  cn  the  amplitude  spectrum  of  i s then  obtained  above a r e u s e d  where  the  directly  to  coefficients.  a  of  conventional  smoothing  of  deconvolution  the a u t o c o r r e l a t i o n  window o r a s m o o t h i n g of  F o u r i e r Transform on  the  component.  computed  drawbacks  window which i s b a s e d leakage  by  Power s p e c t r u m  prediction-errcr  of  technigues  i s weighted  the  true  i s t h a t they spectrum.  s i d e l o b e s i n the resolution.  The  do  the not  This  transfer  sguared design leads  a to  f u n c t i o n and  Maximum E n t r o p y  Method  79  estimator  retains  a l l the estimated l a g s without smoothing and  uses Weiner optimum f i l t e r which  will  theory t o design a p r e d i c t i o n  whiten the input power spectrum.  output power and the response of the  The  accuracy  of  the  positions  filter  (Kanasewich,  shown  i n the f o l l o w i n g F i g u r e s .  to be c o n s i d e r e d as a power  spectrum  Some  results  The.data must be i n v e r t e d which  accounts  f o r the  pseudo-emission  line  the  The middle p l o t shows the deconvolved spectrum.  i n p u t data.  spectrum.  1969).  I t i s estimated t h a t  p o s i t i o n s are determined t o t 1 sample p o i n t .  are  i t is  depends on the number of  s i n u s o i d s i n the a u t o c o r r e l a t i o n f u n c t i o n . the  From the whitened  prediction  p o s s i b l e t o compute the input power spectrum  filter  The bottom graph i s a p l o t o f  The top graph i s the r e c o n s t r u c t e d p r o f i l e . , T h i s i s obtained by c o n v o l v i n g the deconvolved spectrum shape  for  one component.  with  the  assumed  profile  The data blocks c o n s i d e r e d are those  of F i g u r e s 5(a) and 5(b) f o r \ 4553.  Figure A . l  Deconvolved spectrum for block // 3 of Figure 5a.  Figure A.2  0.0  Deconvolved spectrum f o r block // 9 of Figure 5  50.0  100.0  POINTS  150.0  200.0  Figure A.3  Deconvolved spectrum f o r block # 10 of Figure 5a  Figure A.4  Deconvolved spectrum for block # 12 of Figure 5a.  Figure A.5  Deconvolved spectrum f o r block # 1 of Figure 5b.  o  O.D  50.0  100.0  POINTS  150.0  200.0  Figure A. 6  I  O.D  Deconvolved spectrum for block // 3 of Figure 5b  1  50.0  1  100.0  POINTS  1  150.0  I  200.0  86  Figure A. 8  Deconvolved spectrum for block // 13 of Figure 5b.  I  1  0.0  50.0  1 100.0  POINTS  1 150.0  1 200.0  Figure A. 9  Deconvolved spectrum for block it 14 of Figure 5b.  Figure  A.10  Deconvolved spectrum f o r block # 15 of Figure 5b.  

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