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The kinematics of carbon stars in the large and small magellanic clouds Joslin, Garry Douglas 1983

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T H E K I N E M A T I C S OF IN L A R G E AND  CARBON  STARS  THE  SMALL  MAGELLANIC  CLOUDS  by  GARRY DOUGLAS B.Sc,  A  THESIS  JOSLIN  Queen's U n i v e r s i t y ,  SUBMITTED  IN PARTIAL FULFILMENT  T H E REQUIREMENTS MASTER  1980  FOR  THE DEGREE  OF  OF S C I E N C E  in T H E F A C U L T Y OF GRADUATE (Department  We  of Geophysics and  accept to  this  thesis  the required  T H E U N I V E R S I T Y OF July  ©Garry  Douglas  STUDIES Astronomy)  as conforming standard  BRITISH  COLUMBIA  1983  Joslin,  1983  ii In  presenting  requirements  this for  an  of  British  it  freely available  agree for  that  I  by  understood  that  his  that  or  be  her or  shall  fulfilment at  the  Library  shall  and  study.  I  copying  granted  by  publication be  the  of  allowed  of  of  C  eo p  <; 'cs  The U n i v e r s i t y o f B r i t i s h 1956 Main M a l l Vancouver, Canada V6T 1Y3  DE-6  (3/81)  t  a»\C^  Columbia  make  further this  head It  this  without  permission.  Department  the  University  representatives.  not  of  the  extensive  may  copying  f i n a n c i a l gain  degree  reference  for  purposes  or  partial  agree  for  permission  scholarly  in  advanced  Columbia,  department  for  thesis  / s y V o n o ^  thesis  of  my  is  thesis my  written  Abstract Radial  velocities  star  spectra.  Small  Magellanic Clouds  Westerlund, McCarthy  Blanco  curves  indicated  that  gradient  of  be  10.4  mass the  the  limit  of  When  populations and  Weiss  major This  was  Mo  when  LMC  taken  the  (Eggen,  of Bar  the  to  possibility participating  the that  with  a  velocity higher  i n the  LMC  inclination SMC  in streaming  field motions  of  angle  (1977).  velocities  The  velocity  was  found a  disk-shaped with  of  stellar  Feitzinger along  the  in object  age.  eccentricity  with  similar 1962).  findings The  Bar  also the of  to  lower  model  other  gradient  contained from  Philip  placed  Blanco  were  dispersion  Blanco,  decrease  previous  and  of  axis  in orbital  McCarthy  catalogues  catalogue of  velocity  increase with  the  L y n d e n - B e l l , Sandage  field  the  this  from  and  body.  orbits,  a  Large  radial  major  of  well  Blanco,  West  radial  attributed  agreed  solid  compared  an  which  a  carbon  (1978),  and  the  were  increase  the  derived  employing  as  dispersions  Bar.  circular  9  in  of  i n the  Crabtree  along  interpreted  galaxy  higher  stars  correlate  our  and  like  to  age  SMC  rotates  sample  located  Sanduleak  found  object own  an  and  stars  the  (1979)  axis was  in  and  the  For  6.0X10  were  upon  carbon  for a  listed  Richer  LMC  carbon  stars were  (1980)  km/sec/deg.  LMC.  and  based  the  determined  carbon  Olander,  and  Rotation  These  were  the  in  compared.  the The  field  was  and  the  which  were  SMC  stars  opposite  velocity  field  SMC  for  ends  of  the  iv  Table  of  Contents  Abstract Table  i i i  of  Contents  List  of  Tables  List  of  Figures  .  iv v vi  Acknowledgements  Chapter  I  Introduction  Chapter  Chapter  Reduction, Radial  1  Methodology  Velocity  and  Catalogue  5  of  the  LMC  as  D e s c r i b e d by  Carbon  Stars  17  IV  Radial Large  Chapter  Motivation  III  Rotation  Chapter  and  II  Data the  viii  Velocity and  Small  Dispersions in  the  Magellanic Clouds  58  V  Conclusions  Appendix  I:Geometrical Predictions  Bibliography  71  of  Radial  Velocity  ....  75  79  V  List Table  Tables  I Spectra  Table  of  Parameters  ;  ..  5  II Radial  Velocities  of M a g e l l a n i c  Cloud Carbon  Stars  ....  11  Table III Solid Table  Body  Parameters  v s . Age  o f t h e LMC  28  Gradient  Object  45  V Mass  Table  Curve  IV Velocity  Table  Rotation  of the Large Magellanic  Cloud  48  VI Flat  Rotation  Curve  Parameters  f o r t h e LMC  56  vi  List Star  of Figures  Fig.  I  Carbon  Spectrum  Fig.  II  X-Y Map f o r WORC C a r b o n  Fig.  I l l  X-Y Map f o r S - P C a r b o n  Fig.  IV  X-Y Map f o r H I I R e g i o n s  21  Fig.  V  X-Y Map f o r S t a r s  22  Fig.  VI  X-Y Map f o r S t e l l a r  Fig.  VII  X-Y Map f o r P l a n e t a r y  Fig.  VIII  Solid  Body  Rotation  Curve  : WORC C a r b o n  Fig.  IX  Solid  Body  Rotation  Curve  : S-P C a r b o n  Fig.  X  Solid  Body  Rotation  Curve  : HII Regions  31  Fig.  XI  Solid  Body  Rotation  Curve  : Stars  32  Fig.  XII  Solid  Body  Rotation  Curve  : Stellar  Fig.  XIII  Solid  Body  Rotation  Curve  : Planetary  Nebulae  Fig.  XIV  Velocity  Mean  Difference  : WORC C a r b o n  Stars  Fig.  XV  Velocity  Mean  Difference  : HII Regions  37  Fig.  XVI  Velocity  Mean  Difference  : Stars  38  Fig.  XVII  Velocity  Mean  Difference  : Stellar  Fig.  XVIII  Velocity  Mean  Difference  : Planetary  Fig.  XIX  Solid  Body  Rotation  Curve  : S-P S t a r s  (0=60°)  Fig.  XX  Solid  Body  Rotation  Curve  : S-P S t a r s  (9=120°)  Fig.  XXI  Flat  Rotation  Curve  : WORC C a r b o n  Fig.  XXII  Flat  Rotation  Curve  : S-P C a r b o n  Fig.  XXIII  Flat  Rotation  Curve  : HII Regions  52  Fig.  XXIV  Flat  Rotation  Curve  : Stars  53  Fig.  XXV  Flat  Rotation  Curve  : Stellar  Fig.  XXVI  Flat  Rotation  Curve  : Planetary  Fig.  XXVII  Velocity  Standard  7 Stars  19  Stars  20  Clusters  23  Nebulae  Deviation  24 Stars Stars  . . . 30  Clusters  Clusters  . . . 33  Stars  Clusters Nebulae  : WORC S t a r s  .. 34 36  ....  Nebulae  Stars  .. 29  39  . . . 40 .. 41 . 42 50 51  54 ... 55 60  vii  Fig.  XXVIII  Velocity  Standard  Deviation  : HII  Fig.  XXIX  Velocity  Standard  Deviation  : Stars  Fig.  XXX  Velocity  Standard  Deviation  : Stellar  Fig.  XXXI  Velocity  Standard  Deviation  : Planetary  Fig.  XXXII  Geometry  of  Disk  Models  Regions  61 62  Clusters Nebulae  .  63 64 77  viii  Acknowledgements  I  wish  supervisor  to and  encouragement both  aided  from  whose  greatly  i n the in  and  Professors  UBC.  Special  thank  follow  my my  and  my go  plots  me  supporting  me  to as  Many  area  fellow  I wish  that  Nicol, thesis.  and  Lois,  to  thank  and dream  and  my  thesis Dr.  beginning classes,  gratitude i n astronomy  not  least,  Jan  to at  routine  encouraging,  fiance,  M.  criticisms  plotting  but  reality.  to  For  my  students  for  patient  through  whose  graduate  this  helpful  I extend  constantly a  made  thesis.  Last  my  His  also  astronomy  graduate  to John  Vancouver I made  of  has  thanks  this  interaction,  for this  and  of  as  project.  discussions  parents, Maurice  following  for acting  this  preparation  informal  dreams  Richer  enjoyable.  the  thanks  the  H.  suggesting  insightful  the  produced  Dr.  beginning to completion  and  education  discussions  to  for  educational  Ovenden  my  thank  I  wish  me  to  Moore,  for  encouraging  and  1  CHAPTER I  INTRODUCTION  The  purpose  velocities Magellanic these  were  radial  As  important  galactic Aaronson  contrast  closely  ,  the  of  o f carbon  stars  stars  a small  catalogue stars  to the derived program  ,  stars Richer,  McCarthy  of carbon  and stars SP) .  are  very  of galactic  potentially  dynamics.  In recent  i n t h e WORC a n d BMB c a t a l o g u e s (Richer,  1980; Cohen these  Olander,  e t a l 1981)  of  I carbon  stars  found  i n thedisk  carbon  stars  taken  to  of  (1977 , h e r e a f t e r  majority  , many  and Small  Olander,  sample  radial  kinematics  the  WORC) a n d B l a n c o  carbon  the  i n the Large  v a r i o u s models  The m a j o r i t y  theunderstanding  correspond  stars  most  from  Westerlund  i t has closely  with 1979;  been  found  correspond t o  of our  own  galaxy.  t h e SP c a t a l o g u e  Population II carbon  stars  found  more  in  the  o f t h e M i l k y Way. Recent  the  stars  derive  investigate  fitting  hereafter  group  and Mould  the  to  thecatalogues of Westerlund,  carbon  Population  halo  by  to  theSanduleak-Phi1ip  in  comparisons  In  and then  (1978,  a stellar  was  of carbon  ( 1 9 8 0 , h e r e a f t e r BMB) w i t h from  that  sample  thesis  velocities.  from  Crabtree  taken  this  galaxies  taken  Blanco  a  Clouds  two  stellar  and  of  of  AND M O T I V A T I O N  studies  o f t h e LMC a n d SMC b y BMB  WORC a n d SP c a t a l o g u e s a r e o n l y  number  of  carbon  stars  Furthermore  these  stars,  luminous  than  M =-3.5. T  that from  Since  are  a small present  a l l present  thedistance  have sample in  shown  that  of the total the  Clouds.  indications,  a r e more  modulus  o f t h e LMC  i s  2  18.6 LMC  (Allen should  Carbon  Clouds  1981) a l l l a t e  be d e t e c t a b l e u s i n g  stars  outline  kinematics  in fine  detail.  the case  possibly  of the M i l k y II  observable Way  and  carbon  stars  I carbon kinematic  these  indicators  disks  of  also  the  describe the kinematics  of the halos  and  the  a n d SMC.  time,  i n a l l three  observable small  sample  are  part  serious stars  study  i s  much  a candidate  stars,  therefore  They  less  have  found  b e t h e much  of the halo  for this  an a b s o l u t e faint  area  predominantly needed  probe  found  these  this of A  i n the  clusters of  o f t h e LMC.  a n d SMC.  these  RR  area  Lyrae  study.  of about  RR +1.0  Population II  i n t h e SP c a t a l o g u e  for this  at  be r e q u i r e d f o r a  magnitude  i n t h e LMC  galaxy  the halo.  of kinematic  visual  they  population  T h e number  would  SMC.  our  exists  has been that  and  because  t o probe  find  than  objects are  of  large  which  Magellanic  LMC  There  p o p u l a t i o n o f t h e LMC.  are therefore rather  carbon  (1982).  of the k i n e m a t i c s  however,  with  no  old globular clusters  of the halo however,  galaxies,  indicators  and Hartwick  are also  Lyraes,  t h e LMC  of these  of very  by C o w l e y  objects  of  velocity  LMC  and  halos  to  f o r both the  important  accurately also  enough  and Small  stars,  i n the  equipment.  and numerous  the Large  are  present  t e l e s c o p e s and  luminous  the  stars  carbon  present  of both  of P o p u l a t i o n  the oldest  Population  type  a r e t h e r e f o r e both  the  In  disk  ,  of  , could  kinematic  research. This a  thesis  sample  of  catalogues. these  stars  i s based  carbon  Through  upon  stars  the derived radial  taken  photometry  ( R i c h e r e t a l 1979  and  from  the p r e v i o u s l y d e s c r i b e d  spectral  ; Richer  velocities for  classification  1 9 8 1 ) i t was  found  of that  3  all  those  galactic  stars  Population  separate be  more  group like  that  LMC  were  taken  also  of  the  curves  are  perhaps  A  gradient  of that  these the  disk  LMC.  This  (1982)  plane  different  finding  of  this  participate  a  found  to  to  evidence  i n the rotation  nebulae.  stars.  by  in and  compared  and  The with  Carbon  in  this  the  planetary  the  velocity  noted. stars  indicates  found  stellar  disk  axis by  of  i n the  by o l d  rotation  in  population.  II carbon the  of  Freeman  as described  disk-like  the population  that  i n the rotation  preferred  o f t h e LMC  of the  objects,  objects  only  in  i n the  early  evidence  of the younger that  These  carbon  carbon  of  rotation  luminous  age  other  stellar  (1979),  not p a r t i c i p a t e any  two  determined  objects  were  was  upon  and Weiss  of  i n age  curve  component  thesis,  group  rotation  contradiction  that  other  type  group  about  from  to  as  other  and p l a n e t a r y  disk  type  to  purposes.  between  of halo  showed  on  of objects  exceeded  based  galactic  regions,  on  not r o t a t e  clusters  undergo  clusters  do  halo  were  , i t was  similar  Feitzinger  i n t h e LMC  the  curves  based  oldest  being  group's  i s in  that  globular  not  a n d do  of  based  analysis  objects  they  classes  correlation  similar  were  were: HII  the  similar  treated  which  rotation  curves  stellar  curves  nebulae.  A  stars  of these  were  stars  f o r comparison  age  probably  comparison,  galactic  catalogue  stars,  SP  of r o t a t i o n  i n that  generated  rotation  stars  of  stars  were  stars.  Rotation  increasing  rotation  II  carbon  manner.  late-type  the  type  These  the remaining  i n t h e LMC  from  order  from  the examination  the disk  similar  a n d WORC c a t a l o g u e s  I objects.  descriptions  populations a  t h e BMB  Population  Through simple  from  stars LMC,  a  The do was  4  taken and  as  kinematic  photometric  Population All study in  exhibited  to two  from  also  and  to galactic  compare  the v e l o c i t y  stars  field  velocity  orientation  of  field.  be the  field  BMB  the small  plane  being  in  this  km/sec. in  of these  enough  LMC  o f 27.8  17 c a r b o n The  of  field fields  that  they  across  the  the opportunity stars  i n these  contained km/sec. stars  difference  terms two  B a r West  velocity  the  dispersion  understood  as  observed  presented  in  contained  43.6  stars  found  d i s p e r s i o n s of the carbon  B a r West  of  cases  This  stars The  in radial  rotation.  a velocity  dispersion can  carbon  t h e r e f o r e were  s t u d i e d i n t h e SMC  dispersion  sight.  BMB  with  Bar  changes  carbon  LMC.  s t u d i e d . In both  systematic  r e g i o n s . The  of these  Cloud  t h e BMB  i n diameter no  substantiated the spectroscopic  i n the  Magellanic  due  carbon Bar  taken was  23'  field  objects  the Small  were  that  identification  II halo  t h e LMC  were  evidence  the  in  The with  24 BMB a  velocity different  g a l a x i e s t o our l i n e  of  5  C H A P T E R I_I DATA The  pertinent  program  data  stars,  Date  REDUCTION  for  used  Telescope  AND  a l l the  in this  ESO  Dec/76  CTIO  Jan/78  CTIO  ,  both  are given  Table  I  Stars  Jan/78  stars  study  Standard  )btained  METHODOLOGY  Program  standards  i n Table  and  1.  Dispersion  Spectral  Stars  Range  3.6m  0  21  126 A/mm  4m  5  3  50 A/mm  5000-7000  A  9  8  90 A/mm  5000-7200  A  6  6  90 A/mm  3000-5000 A  22  90 A/mm  5000-7200  10  5  25 A/mm  5600-6400 A  4m  1 7  5000-7200 A  A  Dec/78  CTIO  4m  9  20  90 A/mm  5000-7200 A  Jan/80  CTIO  4m  10  20  90 A/mm  5000-7200  A  Oct/80  CTIO  4m  9  19  90 A/mm  5000-7200  A  Of are  this  total  WORC s t a r s ,  stars.  The  velocities above  52 s p e c t r a  actual  were  To  proved obtain  o f program  a r e BMB  number  finally  a m o u n t a s some  spectra  sample  of  derived  spectra  stars  carbon  duplicated  velocities  46 o f t h e s p e c t r a  a n d 26 s p e c t r a stars  was s l i g h t l y  irreducible forradial the radial  stars,  f o r which smaller  t h e same  velocity  are  stars  SP  radial  than  the  a n d a few  purposes.  of t h e program  stars, the  6  plates  were  plates  was  reduced  independantly  same  reduced taken  series  taken  Firstly, Comparator. HeNeAr all  i n the  on a s e p a r a t e  at different  the standard Employing  discernible I shows  densitometer identified  lines  for  the  the spectrum  lines  positions.  This  yielded  wavelength.  From  this  stellar were the  lines  known  of  third  were  lines  then  the  the  spectrum  in  the  side  A  wavelengths  this  that  were  fitted  was  position  spectrum to  was  these  between p o s i t i o n  and  wavelengths  the  As t h e r a d i a l  for  on  mean  the calculated  corrected  and  e n t i t l e d RADVEL  polynomial  stars,  and  of the s t e l l a r  the  selected  were m e a s u r e d .  lines  tasks.  relationship  of  Abbe  spectrum  star  program  determined.  then  of  stellar  relationship,  were  shifting  the  order a  of was  m e a s u r e d on a n  program  A computer  f o r the standard  stellar  doppler  a  were  sides  o f one  on e i t h e r  and  spectra  the positions  the following  determined  series  run and t h e r e f o r e were  the s t e l l a r  some  to perform  arc  stars  on b o t h  in  Each  dispersions.  carbon  lines  are indicated.  employed  , as  the Comparator,  tracing  then  manner.  observing  of the others  a r c comparison  Figure  following  velocities  wavelengths  observer  to  of  motion  heliocentric  of by rest  wavelengths. The then the the  standard  combined stellar  greater was  i n order  lines.  standard  identified  wavelengths  stars  resulted  than  not used.  If a  line  was  a mean  a  process  rest  standard the line resulted  deviation  deviation  in  was c o n s i d e r e d in a  set  of  stars  wavelength  identified in less  i f the standard  30 k m / s e c , This  a l l the standard  to determine  or in  from  than  50%  were for of  of the l i n e s velocity  inaccurate  of and  approximately  F i g . I. Spectrum o f BMB B a r West 99 taVpn a t an A A ™  spectrum exhibits some o f the features t$5L o f that were used f o r r a d i a l v e l o c i t y determination!  TU-  carbo7ste S  8  thirty  standard  wavelengths  A/mm)  spectra  and  the  higher  lines  employed  considered  velocities  again  employing  this  program then  spectrum  of  compared lines star of  found was  a  the  no  i n the standard further  The  computed shifts  line  doppler  then  t h e mean  discarded  velocity  standard  corrected  These  and  determination It  was  number  are listed noticed  that  along of  lines  until  with  lines  of  program  Angstroms),  two  spectral was  a l l  then  doppler  determined. radial  velocities  deviation  from  t h e mean  remaining  t h e mean.  mean  then  the position  the  standard  from  from  the  same  a l l the  deviations  in  the  furthest  until  i n the  wavelengths  to  were  lines  were  0 a n d +12  continued  and the  velocities, the  due  a l l the  to a heliocentric  measured  velocity  be  pairs  velocities  one a t a t i m e  1.5  wavelengths rest  by  previously,  observed  between  process  line  determined  of the l i n e s  between  considered  Individual  within  to  stars.  described  limit  for  and were  to the arc  a predetermined  shift  were  I f the line  (typically  for a l l possible  computed mean.  than  indicators  determined  126  spectral  polynomial  These  stars.  and the comparison  RADVEL  order  previously  considered the l i n e  feature.  A s was  star.  These  of the program  RADVEL.  (90 a n d  wavelengths  spectra.  stars  a third  program  standard  program  the wavelengths  the  standard  RADVEL  then  the program  dispersion  velocity  the v e l o c i t i e s  fitted  with  t o be g o o d  of the  determined  of s i x t y  ( 5 0 a n d 25 A/mm)  to determine  The  and  i n excess  dispersion  were  f o r the lower  of  the  were  then  lines  were  This velocity  velocity  for  the standard used  and  in  that  star.  deviation  the  was  in  velocity  i n Table I I . when  the i n i t i a l  reduction process  was  9  applied  to  the  wavelength spectrum These  standard  for  was  the  taken  neutral  stars  same  of  for  image-intensifier  filters the  had  the  standard  had  not  the  position  in  standard  passed  the  the  To  correct  for  the  density  filter  the  following  of  standard  series every  other  series  of  therefore  series plates  a  determined. mean  compared  plates.  being  All  mean  the  shift  dV(m,n)  velocity  density  series  those a  shift  m'  was  the  in  values  of  for  was  given  between  total for  number the  of  This  which  shift  would  by  carried  neutral  out.  determined  The  for  present  particular  that then  any  summed  series  two  to  of  series  set each  in  for  two  in  result  the  frequency  any  of  from both  shift  and  line  was  yield  a  plates. of  plates  m  where  k  k  series  final  lines  relative  between  (( I d v ( n , m ) ) / k  by  These  series.  lines  s h i f t s were  the  acceptable  i d e n t i f i c a t i o n wavelengths  For  shift  filters.  spectrum  for,  produced  k  and  to  was  star's  spectrograph.  filter.  in  reduce  level  corrected  shift  compared,  velocity  to  comparison  wavelengths the  a  the  arc  procedure  relative velocity  velocity The  of  with  density  s h i f t i n g the  the  from  velocity  to  shifts  standard  necessary  to  of  i f not  identification  was  to  the  neutral  spectrum  neutral  shifts  systematic when  were  effect  spectrum,  velocity  line  attached  relative  through  of  systematic  star's  unfortunate stars  were  different  filters  intensity the  the  stellar  through  density  there  of  -  ( I dV(n,m'))/k),  plates  involved.  relative velocity  This  s h i f t s of  resulted  each  series  stars. This  correction  the  effect  velocities  of  of  a l l the  was the  then  applied  neutral  program  stars  to  each  density consistent  series filters  to  correct  making  relative  to  the one  10  another.  However,  this  d i d not c o r r e c t  velocities.  This  the  of the s o l i d  I  velocity carbon  velocity radial  the  a t t h e same  point  The  agree  with  to series,  order  of  Small  Although  comparing  curve  Centre  in  the  LMC  adopted  these  in  the  Magellanic  mean  velocity  the size  This  curves  corrected  analysis Clouds.  of  stars  o f 274.5  radial  and  were km/sec  correction  correction  velocities listed  final  of other  (Fietzinger  in  Population  the weighted  of the c o r r e c t i o n  velocity  final  by  of the  with  of the r o t a t i o n  the average  10 k m / s e c .  the f i n a l ,  employed  accomplished  rotation  Radio  the weighted  series  was  was  error  r a d i a l v e l o c i t i e s of the carbon  Centre.  It  body  indicators  Radio  to  correction  at  velocity  1979). to  stars  final  f o r a zero-point  mean known Weiss  adjusted at  varied was  of  the from the  to the v e l o c i t i e s l e d  i n Table I I . velocities  the kinematics  that  of the Large  were and  11  T A B L E I_I RADIAL  WORC No.  VELOCITIES  OF L A R G E M A G E L L A N I C  CLOUD CARBON  STARS  RA  Dec.  Measured  Standard  No. o f  Adopted  (1975)  (1975)  Velocity  Deviation  Lines  Velocity  2  04  39.1  -70  10.0  275. 1  20.4  1 7  297.2  13  04  50.6  -70  25.6  254.3  22.6  8  240.8  40  04  59.0  -65  57.7  214.4  16.7  15  200.9  46  05  00.4  -70  15.8  256.5  28.5  7  243.0  51  05  01 .3  -66  52.9  315.3  27. 1  10  301 .8  54  05  01 .9  -70  33.8  210.1  29.7  13  232.3  56  05  02. 1  -70  53.3  207.0  20.2  18  229.2  64  05  02.7  -65  11.1  292.7  24.9  23  314.8  65  05  02.8  -66  26.5  279.9  24.6  1 5  302. 1  84  05  07. 1  -69  58.2  236.9  15.5  25  239.6  105  05  11.7  -65  16.1  322.7  19.7  1 7  309. 1  1 06  05  1 1 .7  -66  52.7  272.3  18.7  37  274.9  106  05  1 1 .7  -66  52.7  286.8  21.5  20  30'9.0  106  05  11.7  -66  52.7  268.3  13.7  54  276.7  107  05  11.8  -65  09.8  350.4  21.4  7  336.9  108  05  12.1  -65  47.6  287.5  29.6  1 2  273.9  11 2  05  12.9  -65  43.3  298.6  26.2  1 1  285.0  1 12  05  12.9  -65  43.3  313.5  19.6  15  300.0  115  05  13.8  -72  55. 1  261 .6  22.9  1 2  248.0  131  05  17.2  -64  48.5  314.6  11.2  13  301 .0  134  05  18.5  -70  57.7  264.5  25.9  1 1  251 .0  137  05  19.8  -65  04.2  353.7  30.4  1 4  340. 1  12  157  05  26. 1  -73  19.8  197.6  22.7  17  219.8  186  05  35.2  -71  01 .4  298.3  21.7  15  284.8  186  05  35.2  -71  01 .4  253.6  20. 1  20  256.2  190  05  38.0  -70  49. 1  187.5  30.5  22  209.7  192  05  38.2  -72  09.3  232. 1  34.9  10  218.6  210  05  49.6  -71  39.2  194.3  31.8  1 7  216.5  214  05  51 .8  -72  31.7  279.8  18.8  21  266.2  229  05  05.9  -69  27.2  238.3  23.8  21  260.5  237  06  08.8  -68  15.9  256. 1  38.8  14  242.5  239  06  09.2  -73  50. 1  272.0  27.0  1 2  258.6  239  06  09.2  -73  50. 1  278.3  20.5  1 2  264.7  248  06  12.0  -68  58.7  276.5  19.7  20  298.7  256  06  13.7  -67  28.4  323.3  30.8  1 4  309.8  271  06  16.9  -67  29.7  389.9  38.6  8  376.3  272  06  17.1  -68  13.2  376.4  37. 1  9  362.9  287  06  23.5  -68  35.9  296.7  29.5  1 3  283.2  294  06  24.6  -68  46.8  260.7  23.7  16  282.9  296  06  26.8  -71  41.8  311.6  19.7  17  298.0  300  06  29.6  -70  55.5  338.3  23.2  8  324.7  50 06  09.2  -73  50  234.8  32.8  10  221 .3  W  13  BMB  Bar  St  NO.  RA  Dec.  Measured  Standard  (1950)  (1950)  Veloc i t y  Deviation  No.  of  Adopted  Lines  V e l o c i'  1  05  06.8  -69  10.4  288.1  44.1  6  254.7  9  05  07.5  -69  07.2  250.3  31 .9  9  216.9  1 1  05  07.5  -69  15.6  249.8  26.6  8  216.4  25  05  0 8 . 1;  -69  13.7  228.9  24.0  9  195.5  29  05  08.2  -69  03.7  209.5  46.9  7  206.3  31  05  08.3  -69  18.5  298. 1  26.8  7  264.7  32  05  08.3  -69  09.4  203.7  38.7  7  200.5  33  05  08.3  -69  19.2  270.2  39.4  6  236.8  35  05  08.4  -69  17.0  204.5  32.2  5  171.1  37  05  08.5  -69  02.0  210.1  19.5  7  1 76.7  41  05  08.6  -69  09.5  250.3  33. 1  9  216.9  47  05  08.8  -69  12.3  305.5  24.0  8  272. 1  54  05  09.0  -69  01 .3  264.8  19.4  6  261 .6  58  05  09. 1  -69  17.4  229.7  27.8  5  226.5  67  05  09.3  -69  18.6  234.2  35.5  5  230.9  70  05  09.5  -69  11.8  251.1  19.1  7  217.7  76  05  09.6  -69  15.2  244.5  23.9  6  241 .3  87  05  09.9  -69  11.8  227.7  27.6  6  194.4  89  05  09.9  -69  08.2  292.0  8.2  5  258.6  92  05  10.0  -69  07.7  290.7  36.2  7  257.3  99  05  10.6  -69  09.0  247.2  27.8  5  244.0  100  05  10.6  -69  03. 1  278. 1  47.7  8  244.7  105  05  10.8  -69  08.8  218.2  22.9  6  214.9  111  05  11.1  -69  05.7  213.0  15.0  6  209.8  14  SP N o .  RA  Dec.  Measured  Standard  No.  of  (1975)  (1975)  Velocity  Deviat ion  12-1  04  32.3  -66  08  218.5  26.2  13  240.7  20-5  04  49.2  -65  48  202.9  23.8  15  225. 1  29-1 5  04  56.6  -67  26  223.6  26. 1  16  245.8  30-16  04  59.7  -68  27  288.0  19.6  27  296.3  30-1 6  04  59.7  -68  27  310.3  30.8  7  296.7  30-1 6  04  59.7  -68  27  343.8  21.2  4  330.3  33-7  05  03.0  -72  21  142.8  41 .9  7  129.2  39-18  05  13.9  -69  53  227.7  20.8  16  249.8  47-1 1a  05  26.2  -70  12  235.0  29.7  17  257. 1  51-21  05  36.7  -65  35  150.2  27.2  7  172.3  51-21  05  36.7  -65  35  1 52.5  14.8  17  160.8  53-31  05  41 .5  -68  47  248.7  22.3  23  270.9  54-51  05  42.8  -70  02  276.0  30.0  16  298. 1  54-59  05  44.9  -69  04  256.0  43.2  4  278.1  60-19  05  57.6  -67  35  353.0  13.4  8  319.6  61-9  05  49. 1  -68  42  222.6  24.5  15  244.8  64-5  05  57. 1  -71  55  335.9  40.6  4  302.5  64-5  05  57. 1  -71  55  358.6  33.2  6  325.2  69-1 7  06  08.9  -67  58  330.8  25.0  8  297.4  Lines  Adopted Veloc i  -  15  RADIAL  BMB  Bar  VELOCITIES  OF  SMALL  MAGELLANIC  CLOUD CARBON  No.  STARS  RA  Dec.  Measured  Standard  of  No.  (1950)  (1950)  Veloc i t y  Deviation  8  0 46.6  -73  29.5  158.8  29.1  2  1 55.6  8  0 46.6  -73  29.5  144.6  19.2  5  141 .4  8  0 46.6  -73  29.5  138.2  42.5  5  133.8  9  0 46.8  -73  36.0  53.3  35.1  5  48.9  1 1  0 47.0  -73  30.9  1 56. 1  21.4  6  152.9  1 1  0 47.0  -73  30.9  133.5  20.4  5  129. 1  20  0 47.4  -73  25. 1  233.5  50.2  4  229. 1  23  0 47.6  -73  24.7  164. 1  46.4  4  160.9  23  0 47.6  -73  24.7  181.0  28.6  8  176.6  30  0 47.8  -73  34.2  126.5  39.2  5  123.3  30  0 47.8  -73  34.2  116.0  28.8  13  M 1 .6  31  0 47.8  -73  25.0  86.5  24.7  6  83.3  31  0 47.8  -73  25.0  116.0  22.7  8  31  0 47.8  -73  25.0  105.6  24.5  10  101.2  34  0 47.8  -73  33.2  168.6  38.3  10  164.2  35  0 47.9  -73  39. 1  90.4  36. 1  4  86.0  35  0 47.9  -73  39. 1  1 13.9  29.9  3  109.5  39  0 48. 1  -73  29. 1  1 43.9  35.1  6  139.5  40  0 48.3  -73  29.8  93. 1  30.6  5  89.9  40  0 48.3  -73  29.8  112.0  23.2  4  107.6  41  0 48.4  -73  22.9  133.5  10.5  5  1 29. 1  47  0 48.6  -73  39. 1  178.9  33.2  5  175.7  62  0 49.5  -73  28.5  118.2  19.5  6  113.8  Lines  Adopted Veloc i  '  111.6  65  0 49.7  -73  39.4  163.4  20.0  5  160  80  0 50.7  -73  38.2  177.0  28.5  5  172  81  0 50.7  -73  30.6  79.3  39.3  4  76  17  CHAPTER ROTATION  The LMC,  first  based  resulted no  OF  upon  in rotation  of  for  details  these  text.  of  I t was  rotation II  must  of be  stars  in  the  galaxy is as  were  of  own  our After  kinematical and  BMB  to  1979),  separate  of  no  of  own  the  galaxy,  discovering  that  manner  the  than  i t was  decided  to  k i n e m a t i c a l group  These  two  groups,  of  stars.  carbon  be  be  actual  stars  as  in  the  systematic  described in  Table  the  of  galaxy  and  of  disk  the  systematic of the The  galaxy  i s comprised  rotation  of  the  SP  stars  remaining that  objects treat  stars the  i n our the  i n a l l of with  own  plane LMC,  found  the  WORC  stars  galaxy  to  different  from  carbon  our  the  also  carbon  following  other  in  In  in a  taken  SP  SP  the  was  acted  almost  preferred  objects.  division  those  participates  objects  i n any  to  effects.  which  group  above  rotational  stars  P o p u l a t i o n II  along  could The  the  by the  explained later  investigate  at  of  found  realizing  P o p u l a t i o n II  rest  stars  systematic  predominantly  the  that  Those  group  disk  effects  found  from  the  groups:  show  that  then  for  available,  rotational  curves  to  carbon  of  to  the  c a t a l o g u e s , and  analogous al  not  galaxy,  shows  comprised  exist.  found  that  stars  rotation  will  Population I objects.  which  in  sample  STARS  curve  carbon  stars  two  rotation  of  carbon  curves  into  rotation  I t was  the  CARBON  exhibited  respectable  stars,  BY  level.  t h e r e f o r e found  rotation  totally  that  SP  rotation  i n the  our  sample  remaining  separated  that In  curves  stars,  carbon  participate  total  the  the  DESCRIBED  generating a  significant  carbon  generated  AS  at  the  separating  sample  LMC  attempt  statistically  simply  THE  III  were  (Richer et  stars  as  a  analyses.  groups  of  radial  18  velocity Weiss  indicators  (1977), The  were  first  ascension  taken then  step  and  abscissa  incremented  from  by  The two  important  same in  manner  the sky. This  objects  relative  rotation  curves  t o one  another  each  data  set. This  the  rotation  an  and  X-Y  another  on  dynamically  interesting  the  the right  of  t o one  these  o f t h e LMC  areas  the  as  i n the another  for  allowed  by  V I I , had  coordinates  position  in turn  given  This  degrees  t h e map  relative  between  the v e l o c i t i e s  the  and  II through  Secondly,  comparison  to  studied.  the  the a c t u a l coverage  right  of the p o s i t i o n .  accurate which  the  system  multiplying  in Figures  calculated.  allowed  curves  declination  appeared  in  to indicate  i n such  objects  resulted  t o be  of  i n increments  t o one  and  object  coordinate  Primarily  relative  these  employed  points  shown  functions.  that  each  f o r a l l of the objects  maps,  the objects  to convert  X-Y  by  measured  Feitzinger  rotation.  of  of the d e c l i n a t i o n  origin,  resulting  positioned  found  coordinates,  some c h o s e n  In t h i s degrees  were  the cosine  i n X-Y  coordinates  in  of  for galactic  a n a l y s i s was  system.  increments  ascension resulted  analyzed  declination  i n a n X-Y  ordinate  the catalogue  in this  coordinates was  from  the  accurate  maps  were  achieved  by  results  of  individual the bar  data  of  the  as  this  LMC. The was  X-Y  the  rotation which  maps w e r e  approximate curves  was  to  be  on  t h e X-Y  centred  a t RA=5h30m, D e c = - 6 9 ° 0 0 ' ,  centre  of  however,  were  l o c a t e d a t RA=5h20m  the dynamical maps  centre  coverage  centred  about  , Dec=-68°48'  o f t h e LMC  i n d i c a t e s the p o s t i o n  of  the survey.  the which  (Feast,1964). of the Radio  Radio  The  Centre  i s considered The  RC  Centre  label of the  F i g . II. x-Y map s h o w i n g t h e s u r f a c e c o v e r a g e o f WORC ' and BMB c a r b o n s t a r s i n t h e LMC. THe a p p r o x i m a t e l o c a t i o n o f the B a r i s o u t l i n e d .  e J f * * " S the s u r f a c e coverage o f S a n d u l e a k - P h i l i p c a r b o n s t a r s i n t h e LMC. The a p p r o x i m a t e l o c a t i o n of the Bar i s o u t l i n e d . i  S  1  1  1  X  Y  m  a  p  6  h  o  w  i  n  T. „*-« I g l F  e  ou?lined^  X  "  Y  m  a  p s h o w i n  a  S t h e s u r f a c e c o v e r a g e o f HII  ^  r  o  x  i  m  a  t  e  location  of  t h e  Bar  is  5-i 4-  Stars in the LMC  32  H  d H  N  -i  5  1-  6tars in'the outlined. F  -r  1  1  -r  2 1 0 -1 -2 RA*cos(dec) in Degrees  4  mc  s  h  "^3  ~  -4  i  -5  1  -6  S ? s u r f a c e coverage of luminous approximate l o c a t i o n o f the Bar i s o  w  i  n  t h  clusters'in outlined.  1  rh^Lr^?°  WlnS  t  h  e  s  u  r  f  approximate  a  coverage o f s t e l l a r l o c a t i o n of the Bar i s c  e  Fig.  V I I . X-Y  o 01f t? h eh ^ B aSrL if s a  n  Ula  map  !-, J ln  showing he  outlined.  L  M  C  '  T  the s u r f a c e h  e  a  coverage of  PP^ximate  location  25  LMC. In  order  to  investigate  different  models  available  velocity  different the  LMC  data  of objects  the dynamical initial  the  line  i n t h e LMC  of sight  quantities  were  surrounding of  this  of  t h e LMC  made  that  of  this  axial  a t an a n g l e  values  adopted  different presented  in  values by  galaxy. by  however  o f t h e LMC  distance  from  of the disk  as determined that  orbital  the Radio  of  a  to  velocity  HII  If  ring  the  this  galaxy  These  derived  values A l l of  from  those  of  is  were t h e  have  (1972).  orientation  are these  values  the  major  .  does  which  of  axis  these  different  from HII  t h e major  authors and  these  of the galaxy the  of  Vaucoleurs  and  of  ring  of sight.  Other  by F e a s t  Centre,  this  accurate i n  Feast(l964)  i n the plane  are not s u b s t a n t i a l l y  the inclination  Assuming  de  distance  upon  Both  of north.  two c o n s t a n t s  and  orbital  examined.  t o b e 0.89 w i t h  thesis.  f o r these  with  t o be v e r y  implies the plane  this  i n which  the  based  the  f o r the inclination  o f 27° t o our l i n e  Freeman  was t h a t  flattening  t o be c i r c u l a r  inclined  with  t h e manner  were  two  o f t h e LMC, a n d t h e l o c a t i o n a n d  was m e a s u r e d  flattening  LMC,  hypothesised.A l l  linearly  values  s t r u c t u r e o r i e n t e d a t 171° e a s t  axial  axis  about  previously  The o b s e r v e d  observed  for  axis  derived  HII i s assumed  values  were  the  and compared  proved  sets  of the disk  of the major  were  increased  later  model  orientation  made  of  o f t h e LMC. A m o d e l  t o the data  to this  observations.  model  assumption  Necessary  reduced  hypothesis  centre  correspondance  rotation  rotation  was t h e n  r o t a t e d . The f i r s t  simple its  galactic  p r e d i c t i o n s each  velocity from  of  the  increase was  found  linearly to  be  with the  26  dynamical velocity the  c e n t r e o f t h e LMC b y F e a s t ( 1 9 6 4 ) , will  major  Also,  axis  the  linearly proof  observed  of this  clusters, manner. major  i f this  stars  Within  from  objects At  value  this  point  of carbon  stars  were came  from in  a  this  problem  stars  was c a l c u l a t e d  to this a  curves  statistical  If  axis.  axis.  or decrease  The  geometrical  reduced  east  stellar  i n the following  i n degrees  case  sets of  nebulae,  to the individual  mean,  note  along data  was c h o s e n  of north. This six different  i nthis very  sample.  small  one s m a l l  mean  the  points  t o be  the  resulted in populations  i t should than  therotation  theorbital  However,  since employ curve  as  that  other  each  star  would  give  circumvent  for this  f o r a l lthe this  West  a l l t h e BMB  i n t h e LMC. T o  However,  the  to  and p o s i t i o n  be n o t e d  t h e WORC  t h e BMB B a r  of a rotation  employed  generated.  b e made a b o u t  earlier,  field,  region  velocity and  determined  should  A s was s t a t e d  thecalculation  weight  calculate  major  increase  planetary  f o r these  a special  stars.  undue  better  the  I.  i n each  o f 171°  graphs  included  individually  rotation  Centre  axis  perpendicularto  i n t h e LMC, t h e s i x d a t a  stars,  radial  i n t h e LMC.  sample  stars  major  set, thedistance  The major  vs position  along  HII r e g i o n s were  data  whose  will  i n Appendix  t h eRadio  determined  velocity  of the  was t r u e  and  point  velocity  SP c a r b o n  each  calculated.  earlier  of  the length  stars,  axis  radial  i spresented  see  WORC c a r b o n  f o r a l lo b j e c t s  o c c u r s a t t h e same  along  To  was  b e t h e same  theobserved  group of  carbon  star  one p o i n t  was a  i t svelocity  velocities  was  employed  much to  curve.  velocity  of objects  i n t h e LMC d o e s  increase  27  linearly  with  show  linear  a  orbital  correlation  distance  along  squares  f i t was  each  group  located least  more  these  points  points  and  line  gradient  In  for  these  in  Table  the  systemic  a l l than  Radio  III.  cases  The  final  Radio  linear  least  squares  points  is  approached  as  coefficient  approaches  1.0.  table  another  correlated. deviations gaussian were  The the  data  fit.  A  of  distribution.  set An  found  was  than  The  be  indicates removed  (1972).  given  i s given as  coefficient  of  for a  the  data  correlation  given  in  this  the  data  set  how  many  standard  from  e x p l a n a t i o n o f how  velocity  interpreted  of the  coefficient  i n Topping  in  points  r, c o e f f i c i e n t  value  well  remaining  the error  correlation  how  velocity  of data  correlation  the normal  linear  occurred  analysis  can  of  points  the  discrepant  of t h i s  the absolute  coefficient  data  less  least  data  made  and  graph  this  t h e number  was  t  were  If  change  perfect  The  linear  f i tto the  velocity  was  measure  t  d e r i v e d c a n be  set  highly  result  f o r t h e LMC.  for  there  better  the  Centre  a  should  velocity  vs p o s i t i o n  set.  however  velocity  given  was  t o be a  radial  set  d e v i a t i o n s from  data  and  The  velocity each  to the  ineach  for this,  sets  standard  five  quantities.  test  to render  Centre  observed  some d a t a  considered  removed  less  and  fitted  To  points  to the v e l o c i t y  three  were  were  was  between  applied  than  points.  removed  the data  the major a x i s .  o f o b j e c t s . In  squares  data  radius,  a  totally  these  was  random,  coefficients  28  Table I I I S o l i d Body R o t a t i o n Curve Parameters Object  SP  Velocity  Radio Centre  Correlation  Gradient  Veloc i t y  Coefficient  (km/sec/deg)  (km/sec)  6.1±7.7  260.6±17.5  0.21  0.90  -10.4±2.2  274.5±11.5  -0.61  4.64  -11  -6±1.8  276.313.8  -0.80  7.04  -12.7±3.5  266.4±5.7  -0.65  4.73  -15.2±1.2  275.811.9  -0.50  12.5  Regions -16.4±0.8  270.8+1.2  -0.90  19.8  Stars  WORC S t a r s  Coefficient  Planetary Nebulae Stellar Clusters Stars in the HII  LMC  The  parameters  found  s o l i d body r o t a t i o n curves inclusive.  Of  this  gradients  a  As the remaining  only  the  statistically  given  measured on the sky and  the t a b l e were d e r i v e d from the  shown in F i g u r e s  sample,  r o t a t i o n a l motion at velocity  in  VIII  SP  through  s t a r s d i d not show  significant  level.  simple gradient  any  not  in the plane of the  data s e t s d i d have  a  galaxy.  linear  correlation  linear and  was  devised to  small systematic v a r i a t i o n s in each data set from a  point along the velocity  The  are the v e l o c i t y g r a d i e n t s that were  between v e l o c i t y and p o s i t i o n , the f o l l o w i n g t e s t was uncover  XIII  correlation. intercept, major  Using  the  calculated  a mean l i n e a r v e l o c i t y  axis  was  calculated.  v e l o c i t y d i f f e r e n c e s were then p l a c e d i n  bins  f o r every  This  then s u b t r a c t e d from the observed  velocity data  calculated  v e l o c i t y . These 2  degrees  wide  F i g . V I I I . R a d i a l v e l o c i t y v s . p e r p e n d i c u l a r d i s t a n c e a l o n g the m a j o r a x i s , a t I ? l e a s t o f n o r t h , f o r WORC c a r b o n s t a r s . The p l o t t e d l i n e a r l e a s t s q u a r e s f i t t o t h e d a t a i s d e s c r i b e d i n T a b l e I I I . The o r i g i n i s l o c a t e d a t t h e R a d i o C e n t r e o f t h e LMC. The d a t a p o i n t f o r t h e mean p o s i t i o n o f t h e BMB B a r West f i e l d i s i n d i c a t e d by an i n s c r i b e d x.  malor a x i s l ?hP i H 5 Table III i ' T a b l e i n . The d  T  1  n  f "ty v s . p e r p e n d i c u l a r  v  ! 91°  t  7  e  f  1  a  r  l  a  6  lo  s  a  origin  t  S  0  t l  f  d i s t a n c e a l o n g the S a n d u l e a k - P h i l i p carbon s t a r s f ^ a i s described i n l o c a t e d a t t h e R a d i o C e n t r e o f t h e LMC n  q  s  o  U  r  t  a  »  h  r  e  s  f  f  o  i  r  t  t  0  t  h  e  d  420 400 380 360 3  4  _HJI  r  Regions  1  1  ,  ,  ,  1  —  0  •  •5  3  2  0  -2 3 0 0 > 280 "o 2 6 0  '~a  o 240 220 •200 180 160 140  cm  P.  -  —  n  1  -5  -4  i  i  -2  1  -1  Degrees Along at  n  I f V n  1 7 1 ^ ! ;  — n  ' 0.0  the  Major  3  4  Axis  Radial v e l o c i t y v s . p e r p e n d i c u l a r d i s t a n c e a l o n g the m a i o r a x i s  420 400 380 360 340 320 o CD >  o D  300 280 260 240 220 •200 180 160 140 -5  -4  ~3  -2  Degrees at  ni^i!"  -1  0.0  Along the  2  3  Major  Axis  1  4  5  R a d i a l v e l o c i t y v s . p e r p e n d i c u l a r d i s t a n c e a l o n g t h e manor a x i s  420 400  1  !  ,  _Stellar  Clusters  !  ~l  1  1  >  1—  380 360 •  >s •5 2 0 3  4  0  3  -2  300  > "5  280 260  oj  '~o  a  a  n  -  •  a  n  n  nn  240  %  220  •  n  D  200  -  n  -  n  -  • a  180 160  i  1  140  J  !—  i  1  ,  1  I  0.0  Degrees axis  ^t'm^P^fS  £ £ a r e ? f i t to  e  l  ° , i  i  Sft2°^  S ^ ^ r f X thl  V  Along the t  l  V S  ' P  e  i  P  e  n  d  i  Major c  ^ar  5  Axis  d i s t a n c e a l o n g the major  f o r s t e l l a r c l u s t e r s . The p l o t t e d l i n e a r  iSc^ ^^ 5  in Table I H  •  The  i  s  least  h e a t e d at CO  420 400 380 360 >N  3  4  "Planetary Nebulae  0  -2 3 0 0 CD  > 280 o 260 o 240 220 •200 180 160 140  -5  -4  -3  -2  Degrees  -1  0.0  Along ihe  1  2  Major  3  4  5  Axis  F i g . X I I I . R a d i a l v e l o c i t y v s . p e r p e n d i c u l a r d i s t a n c e a l o n g the major a x i s , a t 171 e a s t o f n o r t h , f o r p l a n e t a r y n e b u l a e . The p l o t t e d l i n e a r l e a s t squares f i t to the d a t a i s d e s c r i b e d i n T a b l e I I I . The o r i g i n i s l o c a t e d a t the Radio Centre o f the LMC.  35  every  0.5  degrees  deviations  along  of the v e l o c i t y  calculated.  In  the  nebulae,  stars  observed  i n t h e mean  of  a l l the  inclusive. rotation  between in  which good  that  initial  sign  was  a  simple  given  east  also  curves  for  north.  These  carbon rather  stars  the  less  to  rotation  rotation  failed at  to  a  SP s t a r s  are  are oriented  XVIII  of  imply not  some  body,  systematic  such  mean  half  o f one  statistically  that  randomly  the plane  in  the  i n that b i n . velocities, was  a  very  galaxy. orbital  parameters  velocity  lead  t h e SP  major  other  to  the  stars  axis.  rotation  show  Further than  171°  curves  that  significant level.  XX,  axes  i n the plane  standard  l e d to the c a l c u l a t i o n of  produce  a t major  flat  linear velocities  a t an a n g l e  XIX and  as a  difference  f o r t h e LMC  this  axis  was  XIV through  previously,  at  planetary  plots  linear  These  As s t a t e d  are Figures  results  curve  then  structure  observed  of t h i s of a  III.  a major  the  were  difference  the  than  curve  assumption  rotation  assuming  of t h i s  solid  however,  f i t  i n Table  investigation  examples  than  standard  stars,  T h e mean  indicative  for the rotation  rotation  bin  S shaped  i n Figures  and  v e l o c i t i e s of the objects  linear  of systematic  exhibited  subtle  always  linear  conclusions.  of north  each  v e l o c i t i e s and c a l c u l a t e d  r a d i a l distance  parameters  in  plots.  be  other  of the observed  a  a  a l l cases  bin  approximation  following no  In  implies  versus  could  T h e mean  t h e WORC c a r b o n  a r e shown  nature  data  The  the  S shape  a  indicated  of  difference  the observed  deviation This  This  curve.  each  case  sets  axis.  differences  and HII r e g i o n s ,  data  of  rotation  the major  which  show  of 60° and of the  of the disk halo  of  Two  rotation  120° e a s t  orbits  of  of SP  o f t h e LMC b u t the  LMC.  More  50  8 40 c  CD  30 CD Q  20  ±-!  10  u CD >  15 TJ  D  0.0 -10 -20  rr - 3 0 c a  CD  -40 -50  -4  -3  -1  -2 Degrees  s t a r s ^ ' ^ M n ? !  f  !?  r  e  Q.o  Along the n  ?  6  ^  e  t  W  e  e  n  t  h  e  2  1  m  e  Major a  n  r  a  d  i  a  Axis velocity  l  3 of WORC  carbon  m L o ^ i n ^ g . vmi i i^ asT a ^ i M ^ * * ? ^ects\ythe me a r° f u n c t i o n of d i s t a n c e a l o n g t h e major a x i s . t  h  S  e  R  a  b  n  cn  rr c o  OJ  -30 -40 -50 -4  -3  -2 Degrees  -1  .  0.0  1  Along the Major  i  2  Axis  i  3  4  F i g . XV. The d i f f e r e n c e between t h e mean r a d i a l v e l o c i t y o f HII r e g i o n s i n 2 b i n s and t h e v e l o c i t y p r e d i c t e d f o r t h e s e o b j e c t s by t h e l i n e a r l e a s t squares f i t shown i n F i g . X as a f u n c t i o n o f d i s t a n c e a l o n g t h e major a x i s .  -4  -3  -2 Degrees  -1  0.0  Along the  1 Major  2  3  4  Axis  F i g . XVI. The d i f f e r e n c e between t h e mean r a d i a l v e l o c i t y o f luminous s t a r s i n 2 b i n s and the v e l o c i t y p r e d i c t e d f o r t h e s e o b j e c t s by the l i n e a r l e a s t squares f i t shown i n F i g . XI as a f u n c t i o n o f d i s t a n c e a l o n g the major axis.  -3  - 2  1  o.O  -1  2  Degrees Along t h e Major  cluster!'if? \?  J^  Axis  3  tween the mean radial velocity of stellar Sear lit sho^^n S m ™ ! " * ? " | ° o b j e c t s by S shown m Fig. XII as a function of distance along the major axis, :  ed i  f  ence  b e  P  e  d  i  C  t  d  £  rt  h  e  s  e  to  -4  -3  -2 Degrees  -1  0.0  Along the  1 Major  2  3  4  Axis  F i g . XVIII. The difference between the mean r a d i a l v e l o c i t y of planetary nebulae i n 2 bins and the v e l o c i t y predicted f o r these objects by the l i n e a r f i t shown i n Fig. XIII as a function o f distance along the major axis.  420400-  S a n d u l e a k - P h i l i p C a r b o n Stars  380360340-| 320-  '"2 o  ^a> 0  A  300280 • 2  5  0  •  240-J  1  220200• ,  180160140 120  4  -6  -5  -4  " 3 - 2 - 1 0  1  2  3  Degrees Along the Major Axis  ma1o/a i X  X  ?Je  X I s  Sc'.  «;  fin° \ \ * ia  6  0  e  a  8  t  °  Ve  f  OC±t  n  °  v s  r  t  h  '  f  °  Perpendicular r  distance along  Sanduleak-Phi]ip  S C  arbon  the  stars  420-  Sanduleak-Philip Carbon Stars  400380360340-  >.  'o o ty  > ~o o or  320-  A  300-  A  280-  A A  260240-  A  220-  A  200180160140120—  6  n -5  1 -4  r-3  -  2  -  1  0  1  2  3  Degrees Along the Major Axis  majo/axis^t^Llr'nf^  5  6  1  in  t h e LMC!  f  n  °  r  It' 1*^™^™^ t  h  '  f  °  r S a n d  d i s t a n c e along the u l e a k - P h i l i p carbon s t a r s  43  simply,  this  kinematic  spectroscopic concludes to  that  be f o u n d In  only  results  in  radius  the linear  observed  t h e mass, M a  net  net force  central  , interior force  1979)  the  that  i s  to the  other  of  particle.  centripetal  objects  c a n be e m p l o y e d i s  spherically  orbit  between  a  symmetric.  field  i n which  test  particle  For circular  orbits,  force;  GMm/r =mv /r 2  This was  thesis  found  proportional  for  spherically  symmetric  proportional constant  to  at a l l  Employing orbits, were  the  derived  values  corelation  tangential  velocity  that; (2)  3  which  the  the galaxy  of  mass  distributioni s  circular  h a s a mass  orbits  density  i s  which i s  radii.  equation  (1)  constants  radius  of Table  in  the  implies  and the v e l o c i t y  to calculate  within  The  galaxy  radius,  derived  used  column  a  that  which Mocr  Therefore,  (1)  2  observationally to radius,  which  and a r e expected  gravitational force  on t h e t e s t  balances  a l  relationship  for  model  distribution  a  et  galaxy.  to explain  t h e mass  the photometric and  II i n nature  i n t h e LMC, t h e s i m p l e s t  i n which  exerts this  attempt  of a  with  (Richer  are Population  v e l o c i t y and  observed  This  they  agrees  o f SP s t a r s  i n the halo  an  orbital  one  analysis  study  and of  f o r t h e mass  assumption  the five  the total  given  the  mass  linear  for  i n the fourth  of  circular  rotation  the  column  LMC  contained  of Table  o f t h e LMC a r e l i s t e d  in  curves  the  V. The third  V.  simplicity i n Table  of this  model  IV between  i s indicated  v e l o c i t y gradient  by a f a s c i n a t i n g along  t h e major  44  axis  f o r a group  objects the is  followed  same a  of  o f age  older  spherically the  non-circular proportional  to  deviate  mass  the  radial  the  velocities  apogalactum  are  purely  apogalactum greater where  i t has a  amount  slower  orbital  objects  as  of objects  found  i n Table  whose  and range  more  This  with  will  velocities further  increases.  IV agrees  This  with  Lynden-Bell(1964) of e c c e n t r i c i t y  from  than  these  spends  a  that  older  i s greater  than  objects  the  larger  circular  centre  of o r b i t s  i n t e r p r e t a t i o n of the findings  and  p r o b a b i l i t y of  the local  eccentricity  two  apogalactum,  the dynamical  the e a r l i e r  and  orbit,  at  i n a greater less  orbital  of  the  object  therefore  result  of the  of perigalactum  eccentric  a  inversely  perigalactum  ratio  of the r a d i i  of f i n d i n g an  the average  group  Eggen,  The  the  (i.e.  following  the centre  at  a  force,  quantity  is  from  objects  v e l o c i t y and  velocity at radii  galaxy  ratio  the chance  of i t stime.  finding  the  of the o r b i t . be  of  Since  f o r any o b j e c t  distance  gradient  a central  velocity  be  t o which the  circular. exerts  If a l l  would  velocity  i s a conserved  tangential,  i s the inverse  will  distribution  tangential  As  velocities  from  indicates that  orbit,  that  i n d i c a t i o n of the degree  of any o b j e c t  This  objects.  the v e l o c i t y gradient  The o b s e r v a t i o n  objects  momentum  L=rXmv=constant).  and the age of those  orbits,  i s an  symmetric  angular  galaxy.  circular  for a l l objects.  function  orbits  of objects  of  in a  constants Sandage,  follow  f o r younger  of  orbits  objects.  45  Table Velocity  Gradient  Object  IV  v s . Age  o f t h e LMC  Object  Velocity Gradient  Age  (km/sec/deg) HII  Regions  Luminous Stellar  Stars Clusters  Planetary  Nebulae  WORC C a r b o n  To  obtain  a  Stars  i n the plane  velocity  gradient  linear versus  36.1±1.8  6.0  33.5±2.6  7.0  28.0±7.7  8.0  25.6±4.0  9.5  22.9±4.8  9.2  r e l a t i o n s h i p between  gradient  least  squares  the logarithm  the object  o f t h e LMC  divided  (log(years))  (which  age and  i s the  by t h e i n c l i n a t i o n  f i t was  applied  of the object  i t s velocity  observed  angle  o f t h e LMC)  to the v e l o c i t y  age.  This  radial a  gradient  resulted  in  the  relationship; S=57.7-3.58T where in  S  i s the velocity  km/sec/deg As  rough  a  and T  f  first  for  insight  into  however  i s a disk  thickness The  the  with  velocities  type  that  be  density  field  that  as a  of g i v i n g  linearly  with  age. provides  some  The  LMC  improvement  as a disk function  that  radial  of of  i n the constant  radius.  results  objects  in  circular  distance  a  gives  eccentricity.  t h e LMC  distribution  expressed  and a l s o  and so t h e next  changes  axis  symmetry  mass  orbital  model  capable  increase  spherical  of  to  the major  of the object's  galactic  galaxy  a density  radial  gravitational  total  effects  would  along  i s the logarithm  approximation,  estimate  calculations  gradient  (3)  i s  a  orbital given  46  by;  c =(2fl ,V G) Va -r 2  cr i s t h e a r e a l  where cutoff plane this  occurs  and  relating  density,  (Sobrino,  distribution  orbital  z  a  angular  (4)  z  i s the radius  Ti i s t h e a n g u l a r  of the galaxy density  mass  2  velocity  1982; Sweet,  over  the disk  velocity  to  of o b j e c t s  1983).  results the  a t which  mass  i n the  Integration  i n an  total  of  expression  mass  of  the  galaxy. M=(4a A2)/(37tG)  (5)  3  To  estimate  t h e mass  to  obtain  values  f o r a and A .  as  the linear  diameter  diameter  of 460').  velocity  data  as  great  as  Employing  values  from  in  distribution, is  most  circular  this  disk  and  though  explained  model  from  increases in  therefore  conservation  an  a  mass that  of  the given  energy,  i s at  least  centre  o f t h e LMC.  the  of Table  disk  was  and the  derived  symmetric  mass  V.  circular  orbits.  objects  mass  i s a minimum  value.  It  follow This  i s  the g r a v i t a t i o n a l p o t e n t i a l of  density  of  upon  LMC  the youngest  orbit,  as  cutoff  only  monotdnically  potential  WORC  gradients  i s based  angular  the  spherically  by d e r i v i n g  eccentric  the  the dynamical  column  o r b i t s and the d e r i v e d  easily  objects  of  the derived  likely  most  potential  case  t h e mass  of  o f 7 kpc  t o an  f i t of  that  necessary  a value  squares  velocity  i n the f i f t h  gives  coresponds  k p c , t h e mass  the various  the  (this  least  however  o f a=4.6  are listed  As  linear  (4.6 kpc) from  a value  calculated  The  i t i s therefore  Allen(l982)  o f t h e LMC  indicates 5°  o f t h e LMC  distribution.  as  radius  the o r b i t a l the  object  any o b j e c t  The  derived  increases.  radius will  increases  will  change  change. its  For  By  distance  47  from and  the centre therefore  orbital object case  and  eccentric  a  orbit  stars  decrease  limits  toward  to the true  i f t h e LMC  galaxy,  an  model  increasingly Table  object  galaxy This lower  will  will values that  should  be  inclination  angle  of the in  the an  spend  more  weight  the  for orbits the  orbits  the  derived  viewed  The v e l o c i t y g r a d i e n t s  of the v e l o c i t y gradient i s a t an  as  in  following  and t h e r e f o r e  o f t h e LMC  value.  manner  IV i n d i c a t e s  eccentric  of the disk  are the values  the galaxy  Any  increase  p o t e n t i a l energy  at apogalactum.  are l i k e l y  lower  of  decrease  decrease.  disk-shaped  eccentricity.  f o r t h e mass  table  will  i t s v e l o c i t y . I n t h e same  velocities  values  this  will  likewise  in this  gradients  carbons  i t s p o t e n t i a l energy  s p h e r i c a l l y symmetric  increasing  of  will  increase  at slower  velocity of  i t s velocity  radius  of  time  of the galaxy  as  shown i n  i n the of 27°.  plane  48  Table Mass Object  of  the  Large  Velocity  V  Magellanic  Spherical  Gradient  Mass  (km/sec/deg)  (Mo,e=0)  Cloud  Contained  Disk  Radius  Mass  (kpc)  (Mo,e=0)  HI I Regions Stars  -36.1  7.5X10  9  2.7  14.8X10  9  -33.5  6.4X10  9  2.7  12.7X10  9  -28.0  4.5X10  9  2.7  8.9X10  9  -25.6  3.7X10  9  3.6  7.4X10  9  -22.9  14.0X10  9  4.6  6.0X10  9  Stellar Clusters Planetary Nebulae WORC  Stars  These are  calculations  i n good  1981).  The  because  agreement  spherical  they  easily  be  of  carbon  the  was of  cover  seen  from stars  spherically 14.0X10  based that  upon the  Mo  9  These that  was  has  a  results  orbital  with  mass  X-Y  were  greater maps.  a  were  velocities  9  the  LMC.  on  mass the  This the  estimate  of  which  that  i s indeed  the  manner  however,  A l l the  there  from  data  i n which was  the  LMC is  implies  Mo. the  initial  s e t s employed  LMC.  can  orbits  however,  with  the  larger  distribution  mass  model  which (Allen,  is  assuming  LMC  accurate  values  stars  of  LMC  increase linearly  of  earlier,  limit  a l l derived  centre  noted  the  disk-shaped  6.0X10  dynamical this  extent  and  more  in a  of  f o r the  carbon  Therefore,  lower  derived. A  mass  from  circular  orbits  estimates  p r e v i o u s l y determined  a much the  mass  derived  symmetric  circular  LMC  produce  some  the  LMC  assumption  distance  rotates.  indication  that  from  the  indicate As  was  the  LMC  49  might  have  next  most  a  rotation likely  investigate generated  this for  maps w e r e  major  axis,  angle  0  model  the  through  the  each  If should  the  other  is  a  an  angle  than  flat  solid  Radio  Centre, i n the  velocity  exhibit of  of  the  the  the  LMC  relationship  of  angle  of  of  was  this  were the  was  groups.  from  the  the  of  this  then  plotted  point.  Figures  analysis.  flat,  the  data  points  form;  v=A-Bcos9 where and if  A  i s the  9  i s the  the  data  Fourier was  order  of  with  a  planetary  fitted first  terms the  higher  curve.  order  nebulae,  carbon  stars  and  order  dominated.  little  or  curve.  The  none  of  The  results  object of  a  to  of  stars  and  the of  the  fits  regions.  the  LMC.  To  third  WORC In  terms  the  curve  with a l l  The  relative  other  of  to  a  flat well  carbon  stars,  case  the  of  than  objects a  as  a  reasonably  higher  these  see  order  rotation  points  the  that  rotation  adequate  fitted  indicative to  be  a  of  t h e r e f o r e employed  were  clusters,  motion  flat  data  were  indicated  the  curve,  If a  was  the  HII  of  i n magnitude.  that  curve  plane  should  terms  objects  This  data. f i t  order  velocity  rotation  negligible  stellar  i s the  i n the  the  f i t  (6)  B  flat  sine  the  of  velocity,  order  being  goodness  lowest  the  signs  was a  of  the  rotation  of  showed  series  magnitude test  angle  present,  higher  systemic  the  LMC,  geometry  corresponding  results  map  north  plane  s e t . The  I. T h i s  To  stellar  of  The  curve.  velocity  east  i n the  data  body.  rotation vs  calculating  i n Appendix  rotation  follow a  by  object  radial XXVI  was  six previously investigated  generated  is explained  against XXI  possibility,  about  for  that  candidate  the  These  curve  flat  objects are  SP  first  possessed rotation given  in  420-j 400-  WORC Carbon Stars  380360340-  oci  320300-  >  280-  '•6  260-  cro  240220200180160 140-  60  90  120  150  180  210  T  1  24 0  2 70  Degrees About the Radio Centre  1 300  1  330  1  360  f o r WORC C a r b o n S t a r s . 0 d e g r e e s c o r r e s p o n d s t o t h e major axis which ,, s i t u a t e d a t 25" e a s t of n o r t h on t h e s k y . The p l o t t e d sinusoid the best first order f i t to the data described in Table V I . anu is CP O  420-j  4oo-  Sanduleak-Philip Carbon Stars  380360340320A  300-  A  280-  A A  260-  A A  240-  A  A  A*  A  220200180 160-  A  140120—  ,  ,  A  Degrees About the Radio Centre  LMC i"'i.i3i!;.KIl:i ip '2isii;st:?; 1  ,  y  o d: r 9  Q  in  «  h  7  ^^rsr  420-i  HII Regions  400380360340320-  o  300280-  g  260-  TJ  240-  o  220200180160-  1404  ~T—  30  I  60  120 150 18 0  90  210 24 0  2 70  300  330  360  Degrees About the Radio Centre LMC VoV H H R e q t which i s sUuated It Sinusoid i s t h e best described i nTable VI? 9  o  ^  s  ^  angle  l< .1,?%"lAVS'ST*' first  order e  r  M  t  l  t  t  o  of t h e ^ % t  1°  ^  h  e  ^ d  m  T  h  e  ata  a  '  o  r  »*»  P «d and i s l o t t  cn  o _o  o  150  180  i 270  210 240  1  Degrees About the Radio Centre  S"di;j.::n^^a: ?iMi  l ™ '-'"ars: s i t u a t e d at 3° east of north on the. best f i r s t order i t to the VI c  o  t  h  e  ,,  Bthe  a  t  a  a"d  piane  °  f  th  ~  ^ ' is ' P ? s i n u s o i d is is d e s c r i b e d in Table T  d  1  m a ; i o r l o t  a  e d  x  1  300 330 360  i  s  w  h  i  c  h  420-n  Stellar Clusters  400380360340-  oci  320300-  >  280-  O cn  A A A A  A  260-  A  i  240220-  A  A^  200180160140 ~30  60  90  120  150  18 0  210 24 0  2 70  300  330  Degrees About the Radio Centre  which  is  itt «.^'i; =29. .f:? :rnS?t {:*ra r  r  0  r  r  s  ^  h  e  m  a  j  o  r  a x i s  360  plotted s i n u s o i d i s the best d e s c r i b e d in Table V I .  ftrst  order  fit 1  t  to t h ^ H 0  t  h  e  d  a  t  „ >  T  a  a  n  d  h  e  s  cn cn  56  Table  VI below.  T a b l e VI Flat  Rotation  Object  Curve  Parameters  f o r t h e LMC  Systemic  Rotational  Veloc ity  Veloc ity  (km/sec)  (km/sec)  277.9±15  48.7±32  25°130°  269.6±11  30.1±19  24°130°  278.2±8  33.3134  3°+20°  274.6±5  30.2112  5°115°  Angle  of  Major (East  the  Axis  of North)  WORC Stars Planetary Nebulae Stars HII Regions  In points for  a l l t h e above along  the  rotation An sets  HII  previously  i s  60%  The carbon  higher  with  star's  any  combination  real  than  d i s p e r s i o n of the data  was t h e same  case  of  or  worse  than  a linearly  increasing  stars  the  thestars  rotational  along  show  of  four  these  a velocity  planetary  nebulae nebulae  and HII regions  velocity  kinematical  property  t h e major  , stars or rotational  so well  I t i s i n fact  o f t h e LMC  of t h e group axis.  From  of  data  of rotation  i s so d i s c r e p a n t  reason.  o f coverage  kinematic  gradient  velocity  for theplanetary  that  of theextent  and the real  velocity  curve  of the rotation  agrees  WORC c a r b o n  set  sine  discussed  r e g i o n s . The f a c t  to  thevelocity  curve. analysis  velocity  due  the fitted  i sintriguing.  which  cases  and the i s not due t o a  each  data  of objects; i t s  t h e X-Y maps  i t  i s  57  seen  that  although the planetary  gradient  than  degrees  outward  LMC.  stars  The  the stars from  nebulae  or HII r e g i o n s , the Radio  and HII  regions  the  a l o n g any g i v e n a n g l e ,  gradient from  i s  compensated  the dynamical  similar the  planetary  velocity  stars  nebulae.  star  that  t h e WORC c a r b o n than  This  f o r t h e more stars  the other  study  motion  in  objects  increase  dynamical  from  the  that  effect  about  appear  steep  velocity  are further  that  in  HII regions,  and  the  scatter  because  t o have  a  in  centre. although  object,  carbon  C e n t r e . The d i s t a n c e gradient  away  resulted  f o r any o t h e r  shallow  of the  outwards  the dynamical  i s higher  the Radio  3  more  and the r e s u l t higher  i s  rotational  objects.  therefore LMC  than  coverage  less  explains  angle  almost  extend  f o r the stars,  velocity  i s less  further  compensates  velocity  each  rotational  than  by o b j e c t s  also  velocity  C e n t r e . When a v e r a g i n g  the  It i s this  extend  only  the Radio  for  It  at  gradient  a r e found  from  velocities  observed  carbon  the  centre.  rotational  velocities The  degrees  smaller  in their  however  2  a  they  Centre  approximately velocities  have  i s  in direct  concludes one  that  i n which  proportion  c e n t r e o f t h e LMC.  the best  the o r b i t a l  description  of  velocities  of  t o the distance  from  the  58  CHAPTER  RADIAL  VELOCITY  IV  D I S P E R S I O N S IN THE  L A R G E AND  SMALL  MAGELLANIC  CLOUDS  The  previous  LMC.  Superimposed  the  individual  group  under  interest  as  dispersion on  motion  (Eggen  were  see  known  as  of  1962).  possible was  also  I t was  i n the  This  scatter  of  of  to  well  of that  velocity  This  study  their  was  space  determine  that  correlated  with  therefore  LMC  quite  increasing well  with  the rotation curves  objects  dispersion  older  of o r b i t  observed  scenario  gradient  age.  was  velocity dispersion.  age agrees  older  i t  was  has found  increasing  components  the  of i n t e r e s t to  followed  this  general  well.  This object  and  galaxy  , Sandage  were  comprising  velocity dispersion  an  i n the  however,  the objects  have  a l l three  motions  motions  i n o u r own  , Lyden-Bell  i f the objects  rule  of  radial  study  objects  eccentricity  increasing  This  f o r which  systematic  systematic  motions  previous older  examined  these  random  a  stars  increasing  upon  examination.  progressively  based  chapter  was would  are  used  also  expected  appear  of the data  as  a  orbital  observed  decrease  in this  study  sample  group.  to increase  with  on t h e r o t a t i o n c u r v e s  points  eccentricity  i n the r a d i a l  as  in  with  velocity  progressively The  velocity  increasing a s an  object  increase  in  velocity direction for  objects. This  rotation  general curves  trend  was  by means  observed  i n the l i n e a r l y  of measuring  the standard  increasing deviation in  59  radial in  velocity  the  same  velocity XXIX.  The  be  a  was  as  higher  and  expected the  many  late-type  B  tend  t o have  of  two  of  velocity  gradient  velocity  dispersion  this  that  of  of  a  of  involved  in  the  found  comparable  dispersion based  on  nebulae found  these  velocity  measured, of  as  t o be  and  value  A  i t  would  these  orbits  but  sample  very  axis.  The  curve  sample  young  of  the  as  t o be  quite  small  the  the  The  theory  velocity  as  clusters. This  the  radial  stars.  with  the  result  with  and  in  would  increasing  age,  compared  might  be  a  small  number  of  planetaries  a  measure  of  the v e l o c i t y  true  22  smaller  thesis.  stars this  with  i n t h e LMC. a  LMC  late-type  were  sample  previous of  the  supergiants  of  discrepant  stellar  not  in  peculiar  they  young  radial  dispersion,  B  rotation  out  through  of  the main  older  the  objects.  in this  dispersion  or  to  planetaries,  employed and  stars  of p l a n e t a r i e s 25  a  much  appear  sample  of  a  was  increasing  due  dispersion  and  along  t h i s group appeared  effect  well  since  relatively a  also  the carbon  statistical  as  eccentric  sample  XXIV  inclusion  stars  less  t h e mean  velocity  supergiants  actions  velocity dispersion  dispersion  the  carried  stars  the v e l o c i t y d i s p e r s i o n  of  nebulae  from  radial  supergiants,  opposing  was  in Figures  generated  peculiar  This  to generate  resulted  by  and  curve.  used  expected  0  gradient  to  curve  increase  velocity  of  and  to  would  planetary  was  caused  The  objects,  these  rotation  plots  than  likely  sample.  while  manner  rotation  supergiants, this  the  difference  exhibited this  along  study  objects  Feast  km/sec  for  This  value  sample  I f more be  by  of  than  the  35  planetaries  is truly  as  velocity  however  the  interest  (1968)  planetary could  t o see  low  as  was  be  i f the  both  of  > Q  10  o.o CO  -4  -3  -2 Degrees  -1  Along  0.0 the  1  Major  2  3  4  Axis  F i g . XXVII. S t a n d a r d d e v i a t i o n i n r a d i a l v e l o c i t y about the f i t t e d l i n e a r v e l o c i t y o f WORC carbon s t a r s v s . d i s t a n c e a l o n g the major a x i s o f the LMC.  O  "4  -3  -2 Degrees  -1 Along  0.0  1  2  the Major  3  Axis  velocity'of^l'reeiSfvf linear or mi regions vs. distance*?along the° m^ ajor axis o^ted f the LMC. u^xLy  Vel  Cit  about the  CTi  ~  4  -3  -2  -1  Degrees  0.0  Along  the  1 Major  2  3  4  Axis  vPloHt5".? f ^ r a d i a l v e l o c i t y about t h e f i t t e d l i n e a r v e l o c i t y o f luminous s t a r s v s . d i s t a n c e a l o n g t h e major a x i s o f t h e LMC (  X ,  S t a n d a r d  d  e  v  i  a  t  i  o  n  ~  4  -3  -2  Degrees  -1  Along  0.0  1  2  the Major  3  Axis  velocity * my 0f^tenS or stellardcIus^ clusters vs. distance along the major axis 1of* " t*he LMC. about the £ i t t e d  -4  -3  -2 Degrees  -1 Along  0.0  the  1 Major  2  3  Axis  F i g . XXXI. Standard d e v i a t i o n i n r a d i a l v e l o c i t y about the f i t t e d lin< v e l o c i t y o f planetary nebulae vs. distance along the major a x i s o f the LMC  65  these  samples Another  the  implied. cause  differing  these  objects  of  degrees  planetary  deviations  objects,  however,  velocities  of  velocity  dispersion  indicated  larger  and  25  were 5  by  of  of  the  HII  a l l determined  with  deviations  about  It  HII  by  in  velocities  A l l of  the  deviations  be  km/sec.  the  correctly  the  simply  velocities  km/sec.  of  which  might  regions  other  data  determined  planetary  and  sets  mean  possible  and  plots  other  the  is therefore  these  the  the  the  is  large  due  to  velocities  of  objects. In  employing  dispersions  for  the a  contributions  dynamically been  standard  exhibited  standard  The  approximately  15  to  nebulae  velocity dispersions is  all  determined.  had  between  nebulae  these  of  discrepancies  accuracy  the  standard  the  of  been  and  the  observed  have  regions  that  the  out  quantitative rotation  group to  For  this  on  a  values  curves  of  the  disruptive  ignored.  carried  rotation  objects  reason  as the  qualitative the  would  the  bar  or  be  level.  due of  the  analysis  To  suspect  that  to  such  LMC  have  was  attempt  dispersion  highly  velocity  remembered  arm  previous  yield  derive  dispersion  velocity  only  to  i t must  velocity  bodies  for  curves  only  to  derive  from  these  or  erroneous  values. To manner,  examine  the  rotation  curves,  over  The  approach  i s to  adequate  statistics  enough  for  unaffected  by  large  or  velocities proper  a  velocity dispersion  extent chose  systematic  any of  in a  other  the  more method  galaxy,  an  area  yet  small  in  which  must  be  the  galaxy  enough  v e l o c i t y .changes  quantitative samples  abandoned.  that  the  due  to  large area  is  general  66  rotation bodies  of the galaxy  as a  The the  BMB  b a r o r arm  LMC  Bar  were  determined  area.  These  those  a velocity in this For  obtained stars  from  Bar  a  determined  the  velocity of  field  17  such  field,  in  internal  i n a mean  stars  from  fulfill  the  velocities  found  same  in  in  this  manner  determining  velocity  km/sec  taken  radial  the  employed  o f 27.9  field,  which  carbon  corrected  sample  than  radial  one  carbon  km/sec  26  for  radial  velocity was  for this and  a  radial  stars.  o f 79 c a r b o n  velocities  dispersion 133.8  i n t h e SMC,  different  total  more  all  velocity  t h e 70  resulted  Bar  fields  Bar West  of  were  star  velocities  This  along  of  226.3  the  24  as the  km/sec carbon  field.  for  with  such  24  dispersion  the  determined  for  star  curve.  a n d t h e SMC  I n t h e LMC  velocities  carbon  rotation  stars  field  c a t a l o g u e , a r e two  requirements.  motions  of the galaxy.  West  above  with  or streaming  used field.  velocities  This  stars  were  sample  found.  For  determined,  was those  a mean o f  i n the c a l c u l a t i o n The  velocity  result  was  dispersion  of  a mean  of  43.6  simply  the  km/sec. The standard of  more  caused  There  by  distribution  both  cases  inadequate sampling  dispersions  values  was  sampling  existed was  the  the  distribution  This  could  have  and  were  the  case  i f  would  this  have been  of v e l o c i t i e s radial  possibility  non-gaussian  The  non-gaussian.  of the f i e l d  for  were  velocities.  gaussian distribution  calculated also  velocity  of the r a d i a l  in  complete  confirm a  above  quoted  deviations  velocities  been  to  above  even  and  velocity that  i f  a  of  improve  the  dispersions.  the r a d i a l total  interest  velocity  sample  of  67  velocities derived  was  values  comparison the  above  exact  radial  solid  yielded  a  until  the  the  were  sample  values  should  radial  dispersions  to  magnitude  to  objects  with  the  body  rotation  This  employed  i n no  radial  also  employed  above  still  space way  of  the  valid  can  be  cases  be  for  increased  considered  carbon  stars  as  in  these  explanations The  velocity to  first  be  dispersion  magnitude  in a l l  larger  then  would radial  indicate much  more  Stated  more  LMC.  a  On  30  Bar  West  field  of  the  carbon  that  both  methods  km/sec  for  the  curves  that  dispersion  derived  dispersions  of  the  dynamics  in dispersion  ways,  the  velocity could  would  be  for  a  be  equal  in  set  of  two  be  for  any  expected  velocity the  of  two the  these  Blanco LMC  two  s i m p l e s t and  curve  The  SMC  in  the  fields  and  SMC.  fields  could  most  probable  a  assumption  that  galaxy  of  magnitude  to  change  dispersion  than  the  upon  field  motions  randomized simply,  of  the  discussed.  directions.  that  rotation  found  rotation  e x p l a n a t i o n i s based  velocity  dispersion  LMC  dispersion  I t was  the  the  dispersions  compare  i n many  will  of  field.  difference  interpreted  that  velocity  small  the  curve.  veloctiy  The  velocity  approximately  indicated  the  dispersion  radial  of  give  in a  Although  were  of  dispersion  velocity  value  dispersion.  The  either  fields.  star's  be  but  f o r the  compared  were  In  the  calculated  The was  for  purposes  values  star  obtained.  of  their  of  the  galaxy  to  observed  i n the  SMC  the  carbon  stars  counterparts  stars  in  galaxy. would  i n the  in hotter  the  equal  velocity  from  is kinematically  f o r carbon  was  the  SMC  the than ,  SMC LMC. the this  68  would  appear  than  was  the  a  much  observed  larger  for a  dispersion  rotation  curve  i n the of  radial  carbon  direction  stars  found  in  LMC. A  difference  galaxies in  as  in kinematic  is likely  velocity  dispersion  stars  studies  random  in direction  radial  velocities  is  mounting  the  SMC  1970 in  have  orbits  as  moderately velocity  a  participate  much  greater  the  galaxy.  than  in a  Under  for stars  The  sense  velocity  increased LMC.  LMC  and  greater  are  disk i t  SMC  had  dispersion of  the  i n the  that  possible  most  would  SMC  there  stars  that  (Feast  carbon  stars also  e x p l a n a t i o n of  these  plane  a  same  fields.  probably  of  the  galaxy  have  that  the  galaxy  is  plane  of  observed  at  the  radial  velocity  field.  dispersions the  then  two  probable  increasing  fields,  their  therefore  o b j e c t s which  comparable  of  not  SMC.  i n the  an  carbon  curve  perpendicular to  give  two  the  and  between  is  The  carbon  likely  conditions,  observed  than  difference  ability  In  two  definitely  rotation  second  observed  would  for these  inclination  the  direction  these  dispersion  radial  to  the  rotation  of  in directions  inclination  dimensional  plane  orbits,  increasing  the  the  the  were  curve.  i s most  in this  stars  eccentric  by  defined  It  in dispersion carbon  that  objects other  1973).  these  galaxies.  shown  rotation  well  led  two  orbits  clearly  from  fairly  dispersion  If  was  between  e x p l a n a t i o n of  these  had  to define a  reasoning  these  partial  LMC  confined to  difference  Since  the  Weedman  also  This the  has  , Smith SMC  in  a  between  evidence  also  the  only  temperature  i n the  difference be  the  plane  of  the  SMC  inclination  angle  of  the  SMC  in  interpreted as  compared  results  three  in  the as  to  an the  that  69  galaxy the  being  velocity  than  seen  more  dispersion  perpendicular  velocity  the  caused  simply  fields.  U n f o r t u n a t e l y , the  only  have  comparable  dispersions  space  velocities  of  most  unlikely  carbon  stars  motion  studies.  The  are  combination  of  contributions the  bar  or  from  bimodal  Hindmann's SMC  i n an  objects bimodal would for the the  axis end  at  radial  any larger  sample  the  velocity  velocity carbon  distribution  two  fields.  ever  be  met  It as  is  these  for  proper  in  radial  objects,  is  likely  other  possibilities such  other  as  as  radial  due  to  were  way  the  SMC.  streaming  observed This  and  in  showed  the  along  Bar  of  the  motions  of  in  a  dispersion  might  f o r the no  the  distribution  velocity  measured  velocities.  in  resulted  bimodal  This effect  employed  motions  velocities the  a as  interpreted  observing  this  of  well  anomalies  (1970)  of  In  as  streaming  local  Feast  dispersion  in radial  dimensional  light  Bar  stars  three  fields  in  galaxy.  of  these  candidates  increased radial  Bar  two  fields,  distribution.  greatly  i n the  radial of  of  the  of  two  distribution  ends  be  these  sources  SMC  then  difference  to  the  radial  the  configuration.  in a  field  of  for the  on  both  result  bimodal  field  due  will  galaxy  in  angle  that  of  above  lesser  the  would  i f  the  in these  suitable  from  two  motions  gravitational observed  the  of  fields  confirm  condition  between  imformation  to  reveals  difference  i s to measure  not  view  inclination  way  interpretation  dispersions  kinematic  this  on  plane  The two  in  stars  definitely  true  velocity  a l l the  edge  i n the  these  difference  that  This  plane.  between  the  on.  i s greater  to  dispersion by  edge  explain SMC  evidence  T h i s might  have  but of  a  been  70  due  to  the  inadequate orientation  distribution of  carbon  forwarded fields case  sampling  the  of v e l o c i t i e s . stars  by  of  the  i s necessary  and  field  field  further  i t may  case  a model  sampling  t o c o n f i r m or deny  stars.  or  concealed  In e i t h e r  d i d not warrant  Feast  of carbon  of  such  this based  of these  simply a  be  bimodal  present upon  this  sample  those  and  that  ideas  adjacent  s p e c u l a t i o n s i n the  71  CHAPTER V CONCLUSIONS This carbon  thesis  stars  properties The the  carbon  first  stars  carbon that  studied  own g a l a x y .  stars  were  stars.  This  similar  300  stars  rotation  taken  from  carbon  stars  t h e WORC a n d S P c a t a l o g u e s  with  the  number  galaxy.  This  was  totally  sampled  several  field.  This holds  LMC  surveys  great  (and also  of this  large  stars  face  made  the  SMC)  sample  these  I carbon and  found  t o be  e t a l 1981) a n d  t h e WORC c a t a l o g u e .  each  list  approximately i sa small  present  in  b y t h e BMB c a t a l o g u e  diameter  fields  70 c a r b o n  for outlining in  stars i n  photometry  a r ea l s o  stars  approximately  promise  that  that  o f t h e LMC, t h i s  clear  while  stars  Population  (Cohen  from  of carbon  23 m i n u t e  a n d t h e SMC a n d f o u n d  carbon  through  Although  over  ,  t h e WORC c a t a l o g u e d i d  galactic  Population I objects  point  different  t o Population II carbon  i n t h e sample  stars  quite  rotation  of  included  carbon  listed in  d i d . T h e i m p l i c a t i o n was  confirmed  BMB  of thetotal  the  systematic  source  like  was  analysis.  to galactic  These  below.  stars  i n t h e LMC i t was f o u n d  fraction  LMC  no  analagous  kinematically  spectroscopic  carbon  kinematically  was a g o o d  division  Clouds.  arelisted  was t h a t  t h e WORC c a t a l o g u e  As those  systematic  Magellanic  i n t h e WORC a n d BMB c a t a l o g u e s . T h e S P  showed  from  kinematical properties of  implications  t o be  listed  many  Small  noted  appeared  kinematically  exhibit  were  property  stars  stars  and  of their  t h e SP c a t a l o g u e  were our  a n d some  those  uncovered  i n theLarge  SP c a t a l o g u e  from  has  great  of carbon  which  both  stars  through  the  i n each  the kinematics  detail  stars.  in  this  of  future  72  The with the  carbon  other  stars  stellar  manner  in  velocities  of  that  groups,  which these  with  distance  from  the  It  also  found  body  as  velocities  rotation curves  objects an  were  in  increasing  age.  findings  in  our  (1962).  In  an  object  age  rotation  curves  was  along  and  employed  to  assumption minimum  the  velocity  a  to  the  mass  of  the  circular for  Employing  the  a  the  rotation curves  insight  into  also  gained.  velocity  the As  was  disperson  minimum  of  and  of  a  group  this  star  mass for  BMB  of  earlier  and  Sandage  solid  generate  the  were  exhibited  velocity  gradient  objects  age.  body  this  rotation  survey  the  these  curve  was  also  LMC.  Applying  objects  led  to  the a  Mo.  9  velocity  fields  stated, of  older  approximate  to  found  the  for  as  with  LMC,  employed  in  solid  r e l a t i o n s h i p between  the  the  the  objects  favourably  that  velocity dispersion previously  was  interpreted  those  Lynden-Bell  orbital the  of  in  of  6.0X10  linear  distance  was  stars  velocities  disk  This  numbers  found  the  radial  linearly  of  sample.  ,  The  carbon  of  increase  steep  objects  logarithm  positions  LMC  less  quantify  also  about  interpretation  became  agreed  Eggen  the  along  the  v e l o c i t y gradient  data  1975).  i t was  best  the  gradient  for  determine  of  by to  (Tayler  Firstly,  eccentricity  galaxy  gradient  with  galaxy  hypothesis  obtained  proportional The  This  and  IV  this the  thesis,  centre.  the  for  this  interesting facts  the  in  that  attempt  were  Table  for  two  implied  objects  orbital  own  lifetimes  in  of  in  rotated.  dynamical  employed  increase  LMC  objects  orbital  employed  revealed  the  that  was  were  of  in  objects  the  these  theory  versus  two  LMC  and  galaxies  predicted  should  radial  increase  SMC, was  that  the  as  the  73  age  of  thesis  those could  however field  objects  neither  found  was  objects  defined  dispersion  along  than in  of  steeper  inclination The  radial that  the  velocity  of  was  this  would  ends  was  not  observed  flat.  Further  confirm field  was  or  of carbon  indicate  both  deny  dispersion  of  curve  several  over  of the  the  star  SMC  dispersion  was  This  less  difference This  generated  thesis by  the  to our l i n e increase  t o our l i n e with  velocity  only  the r a d i a l  LMC  would  orbits  to  LMC.  that  t h e LMC  these  velocity  subject  factors.  was  that  radial  i n t h e SMC.  stars radial  streaming  of the  of  the  sight  greatest  dispersion  would  in a direction  but the r a d i a l  i f  bimodal  of the  this radial  nature.  taken  from  velocity  motions  o f t h e b a r o f t h e SMC.  sampling  of a  by  higher  f o r a bimodal  from  West  be  parallel  galaxy.  sample  examined  field  SMC  of the carbon  velocity  SMC  Bar  i n the  by p r e s e n t i n g  the higher  data  field  dispersion  caused  The  o f t h e BMB  revealed  of  of the  was  the  inclinaton  This  the plane  It  the face  fields  the  dispersion.  to  across  in this  hypothesis.  quantity  dispersion  velocity by  implied  a global  caused  velocity  higher  orientation  was  BMB  likely  that  employed  of the r o t a t i o n  This  of the Bar  was  base  dispersion  o f t h e B a r West  proposes  sight.  this  position the  the dispersion dispersion  stars  with  dispersion  nor deny  the length  of carbon  Comparison  data  t h e same a s t h e v e l o c i t y  f o r t h e LMC.  variations  The  the v e l o c i t y  approximately  stars  velocity  confirm  that  carbon  minor  increased.  bimodal  velocity  If streaming  be  distribution  required  distribution motions  as  directions  d i s t r i b u t i o n was  would  velocity  i n the  distribution  i n opposing  The  field  the f i e l d  in  very to  in this the  bar  74  of  the  SMC  distribution, by  Kormendy  motions  indicators  Large that  and this  carbon  Clouds.  Small thesis  stars  evolution  the  of  will  through  help  and  necessary  o b j e c t s have  found  would  conclusion,  velocity I  this  (1981),  are  In  were  for the the  ability  to  Magellanic future new  kinematics  that  for  and  of  outline  in  the  a  in  as  velocity  upon  such  bar  system. stars  these  old  as  fine  detail.  into Large  the and  the  radial  Population  kinematics  upon  models  streaming  the  s t u d i e s based insights  radial  improve  carbon  promising  Clouds  a  predict  stability  future very  yield  confirm  others,  looks  and  to  such  It  of is  the hoped  kinematics  kinematics Small  of and  Magellanic  75  A p p e n d i x I_ Geometrical  The  Predictions  two r o t a t i o n a l m o d e l s  of Radial  proposed  upon  the following  that  thedisk  o f t h e LMC.was a t h i n ,  all  objects  were  Linear  distances  closely  were  For  purely  less  distance  derived  dynamical 68.8°,  centre  by  of  north.  the  WORC a n d S P s t a r s  of sight  were  two  assumed  and the o r b i t s of  were  of the disk.  approximated angular  very  distances  were  epochs  adopted. at  axis  Feast  RA=5h20m,  1975 a n d  the  used  had negligable  maximum  effect  than  of  to  east  thesis,  positions  i n epoch  less  Dec=-  a t 27°  i n this  a l l other  the  found t h e  o f t h e LMC i s a t 1 7 1 °  of theobjects  i s  o f t h e LMC  o f t h e LMC i s i n c l i n e d  epoch  as  of thedisk  located  difference  positions  the  disk  thelargest  (1964)  and t h e major  1950. T h i s  t h e WORC  (Smart  Feast  For thepositions  epoch  between  since  to theplane  line  on  of thedisk  a r e based  i t was  and i n theplane  o f t h e LMC t o b e  t h e normal  thesis  than 6 ° .  the  were  flat  theorientation and position  values  i nthis  Geometrically  circular  i n theplane  by angular  measured  assumptions.  Velocity  effect  precession  5' f o r a n y WORC  object  1977).  Under formed  as  assigned  t h eabove follows.  positions  assumptions Objects  the  in  i n the following  the  geometrical plane  models  of thegalaxy  were were  manner;  x'=-rsin0 y=rcos9 where the  x',y',r galaxy  and 6 a r e a l l q u a n t i t i e s measured and  0 i smeasured  in  counter-clockwise  the  plane  of  from  t h e +ve y  76  axis is  as  is illustrated  r o t a t e d by  position  of  the  the  I f the  i n F i g . XXXII.  inclination  objects  i n the  plane  of  the  the  angle  i  about  plane  of  the  sky  i s given  of  the  galaxy  galaxy  y-axis,  the  by;  x=-rsin9cosi y=rcos9 z=-rsin8sini What  is  axis.  If  the  major  plane  of  the  sky,  given  now  observed  as  axis the  the  major  i s at  new  an  axis  angle  0„ e a s t  of  c o o r d i n a t e s as  seen  of  on  i s the  north the  on  ythe  sky  are  by;  X=-rsin9cosicos0-rcos9sin0  o  Y=-rsin9cosisin0>rcos9cos0„  Z=-rsin9sini The by  X  and  is  (ra,dec)  individual purely to  coordinates coincide with  (RA-ra)*cos(dec-DEC)  (RA,DEC) and  Y  the  position  i s the  the  right  the  centre  ascension  in nature, observed  (dec-DEC)  of  o b j e c t . Assuming  angular  predict  and  stellar  motion the  radial  position  as  respectively, of  rotation  and  i n the  where  of  the  disk  declination  of  the  plane  Z component  given  can  of be  the  galaxy  is  differentiated  velocity. rift  Z=-rsimcos9gY  Linear  Orbital  For in  the  a  Velocity  linear  plane  of  vs.  velocity  the  LMC,  Radius R e l a t i o n s h i p . vs.  the  following  sini=const. The  observed  radial  velocities Radial  radius relationship quantities  for are  ^=const. should  be  of  Velocity=y*const.  the  form;  objects  constant;  77 Fig.  XXXII  Geometry  of Disk  Models.  V  the  78  This  implies  linearly the  that  the  observed  p r o p o r t i o n a l to the distance  velocity  along  the  should  be  axis  of  major  galaxy.  Flat  Rotation For  Curve  a galaxy  with  a  flat  rotation  sini=const. Therefore  the observed  radial  Radial In  radial  order  r §=const. d  r  velocity  relationship  tan9=tan(0-0,)/cosi equation  its  9  was  position.  adjusting  0 until O  employed The a best  should  be  of the  form;  Velocity=cos9*const.  to investigate this  This  curve;  where  to relate  adopted cos0  an  i t c a n be  shown;  tan0=-X/Y  object's  X-Y  position  to  f i t to the data  was  obtained  by  f i t of v e l o c i t y  v s . 9 was  found.  79  Bibliography  Aaronson,  M. , M o u l d ,  J . , 1980, Ap. J . , 240, 804.  A b e l l , C O . , 1975, E x p l o r a t i o n o f t h e U n i v e r s e Holt, Rinehart and Winston.  3rd ed.,  A l l e n , C.W., 1981, A s t r o p h y s i c a l Q u a n t i t i e s 3rd ed., U n i v e r s i t y o f London, The A t h l o n e P r e s s . Ardeberg,  A., M a u r i c e ,  E . , 1979, A s t r o n .  Astrophys.,  B l a n c o , B.M., B l a n c o , V.M., M c C a r t h y , 1978, N a t u r e 27J_, 6 3 8 .  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