UBC Theses and Dissertations

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UBC Theses and Dissertations

A 21 cm. line study of the Taurus Molecular Complex Klatt, Calvin Glenn 1986

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1  CM  LINE  STUDY  OF  THE  TAURUS  MOLECULAR COMPLEX  by CALVIN  A  THESIS THE  SUBMITTED  GLENN  IN  REQUIREMENTS MASTER  OF  KLATT  PARTIAL FOR  THE  APPLIED  FULFILMENT DEGREE  OF  SCIENCE  in THE  F A C U L T Y OF  GRADUATE  STUDIES  PHYSICS  We  accept to  THE  this  the  thesis  required  UNIVERSITY  OF  Calvin  Glenn  conforming  standard  BRITISH  August  ©  as  COLUMBIA  1986  K l a t t ,  1986  OF  In  presenting  requirements  this for  an  B r i t i s h  Columbia,  freely  available  that  permission  scholarly  I  agree for  purposes or  understood  that gain  in  advanced  for  Department  f i n a n c i a l  thesis  by  degree  that  the  reference  extensive may his  copying  s h a l l  p a r t i a l  not  be or  be  and  August  1986  study.  I  this  granted  by  the  allowed  of  make  further  Head  of It  thesis my  of it  agree >  thesis  this  without  the  University  representatives.  publication  Columbia  of  shall  of  PHYSICS  Date:  The  copying  permission.  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook Place Vancouver, Canada V6T 1W5  the  Library  her or  at  fulfilment  for my is for  written  Abstract The in  the  large  Taurus  observations 1985.  made  by  have  Complex  us  at  been  Kleiner  and  and  c r o s s - c o r r e l a t i o n  (1)  The  cold  atomic  extremely  well  defined  pc,  as  was  (2)  found  The  21  uncorrelated. degree high  of  conclusions  for cm  Arecibo  Dickman  p r i n c i p a l  been  self  at  1  C0  3  absorption  determined  Observatory  with  in  from October  previously  FCRAO.  drawn  from  analysis  hydrogen  cm  21  a  two-dimensional  are:  in  the  condensation  Taurus  scale  Complex  length  of  has 14  CO.  and  Previous  correlation  of  has  compared  The auto  an  by  distribution  Molecular  Results  observed  scale  CO c o l u m n thinking if  the  of  anticorrelation  distributed  in  shells  around  would  HI  degree  densities  and if  the  i  i  have  are  predicted  CO w e r e  the  well  atomic  molecular  essentially high  mixed,  hydrogen  gas.  a  or  was  a  Table I. II. III.  IV. V.  Contents  Introduction  1  Physical  6  Considerations  Observations  and  Data  Reduction  12  A.  Observations  12  B.  Data  14  Auto  and  Results A.  B. VI.  of  Reduction Cross-Correlation and  Analysis  23  Discussion  28  Results  28  1 .  Maps  28  2.  Correlation  Surfaces  Discussion  ~  34 40  Conclusions  46  BIBLIOGRAPHY  48  • • *  111  L i s t of F i g u r e s  Figure  1  8  Figure  2  18  Figure  3  29  Figure  4  30  Figure  5  31  Figure  6  32  Figure  7  35  Figure  8  36  Figure  9  37  Figure  10  38  Figure  11  41  Figure  12  41  Figure  13  42  Figure  14  42  iv  Acknowledgements I  would  like  his  guidance  his  f i n a n c i a l I  a  and  would  diary,  my  education  to  supportive  of  friendship  I  supervisor,  throughout  W.L.H.  this  Shuter,  project  and  for for  support. like  Mother  F i n a l l y ,  my  assistance  also  she  thank  gave  for  over  value  thank  her  Marcus  help,  and  Aurelius  Dr.  S.  for  David  keeping  for  the •  have  been  me.  thanks me  to  to  the  the  very  many  last  fine  two  highly.  v  people  years,  and  who  whose  Let u s b e g i n f r o m Z e u s , w h o m we m o r t a l s never leave unnamed. F u l l of Zeus are a l l streets, a l l meetingplaces of men, f u l l are s e a s a n d h a r b o u r s ; e v e r y w a y we s t a n d i n need of Z e u s . We a r e e v e n h i s o f f s p r i n g ; h e , in his kindness to man, p o i n t s out t h i n g s of good omen, r o u s e s the p e o p l e to labour, c a l l i n g to their minds the needs of d a i l y l i f e , t e l l s them when t h e s o i l is best for the labour of the ox and for the pick, a n d when t h e seasons are propitious for planting trees and a l l manner of s e e d s . F o r he i t was who fixed the s i g n s in the heaven, and set apart the c o n s t e l l a t i o n s , and he who, looking to the year, determined which of the s t a r s were best f i t t e d t o mark the seasons for men, so t h a t t h i n g s might grow u n f a i l i n g l y . For this cause men e v e r worship him, f i r s t and l a s t . H a i l , 0 Father, Great Wonder, great b l e s s i n g to mankind, h a i l to thyself and to thy elder l i n e . H a i l , ye M u s e s , most g r a c i o u s a l l ; and for me w h o p r e s u m e t o t e l l of the stars, so far as I rightly may, g u i d e ye a l l my song. ARATUS,  Phaenomena  vi  I. L i t t l e (GMC's) came  were  the  galaxy, was  more  realization and  of  its  that  i n t e r s t e l l a r  masses  upper  limit  on  the  the  (M©).  the  of  star  overall  s p i r a l which  time  appear  as  their  lesser  from  which  masses  how  they  is  form,  refers  to  known  ranging of  our  that  it  in  the  due  to  to  stars  putting  arise  in  clouds  from  these  an  clouds  GMC's  are  also  of  regulates a  seem  1 0  entities Solar  6  leads  stars  are the  to  to  with  an  formed, rate  and  substantial  especially  they  to  s  clouds  play  unstudied  particular  regions  in  the  component  are  molecular  1 0  single  role  respect  cluster  and  in to  with  associated.  went  p r i n c i p a l  from  these  what  which  their  largest  sizes  and  They  evidently  dark  the  structure,  quantities the  are  different  waves  because  much  clouds  galactic  are  only  implies,  it  gas  ionized  lifetimes,  thought  in  Previously,  or  ('young'  bodies  gas  hydrogen  form,  clouds  these  molecular  the  short  were  now  formation.  Molecular long  of  stars  understanding  of  density they  with  An  frequently  type  but  of  of  formation.  atomic  very  age)  molecular  understanding how  their  galaxy,  Masses  imply  molecular  birthplaces.  Giant in  extent  a l l  in  giant  discovery  star  Young  hydrogen,  true  in  was  ago  the  the  role  flux.  great  atomic  With of  medium  radiation  decade  v i r t u a l l y  whose  of  a  unknown.  believed  high  than  INTRODUCTION  found  clouds  1  (unnoticed)  composition sky. is  As  l i k e l y  made  their  molecular  neutral  for  such  a  them  name hydrogen.  hydrogen  condensed,  atoms and  In (HI)  2  Helium.  Very  important,  constituents  exist  found  cold  in  the  ingredient, are  of  for  dust  importance,  is  the  dark  grains,  believed  constitute  The  dust  size  which the  and  they  re-emit  grains  do  not  of in  appearance  about  to 1%  be of  composition visual  the  hinder  and  other  molecules  GMC's.  the  absorbers  complex  of  of  s i l i c a t e s ,  effective  many  amounts  environs  and  grain  small  well:  dense  great  responsible These  as  but  A  makes  the  infrared  of  them  radio  which  carbon  by  mass.  very radiation,  Fortunately,  or  dust  clouds.  clouds  untraviolet  infrared.  of  composed the  been  f i n a l  grains of  have  however,  frequency  radiation. It  was  observations (with were  only  with  into  the  technological observable  Infrared stars  as  to  be  in  extension  infrared  sources  the  newly  dusty  the  of  recent the  clouds  star  galactic This  within  an  process (within  formation,  2  giant as  molecular  dark  previously clouds. from  closest star  formation.  kpc)  seem  i l l u s t r a t i n g  to  their  unobserved stars  gas,  and  astronomers A l l  show  clouds  areas.  These  cold  thing  regions  are their have  nearby  evidence  ongoing  role  of in  drama.  study  r e l a t i o n s h i p  mm-wavelength  metamorphosed  to  astronomical  than  dark,  the  molecular  rather reveal  constitutes  of  that  today  observation watching  and  advancement)  observations  imbedded  believed  the  aims  between  individual  to the  increase  our  molecular  cloud.  A  understanding  and  previous  atomic  of  hydrogen  observational  the  3  program, the  conducted  University  K l e i n e r ,  Taurus  the  the  identical  grid  Simple insight  1985, H  atomic to  content  the the  mixing  of  these  however,  is  the  aim,  (auto  cross-correlation)  the  v e l o c i t y  methods data  was  or  uses  comparison allows  us  in  the  H  same  2  set  of  with  measure  cloud  for  some  trends  These  as  between a  present data.  The  is  necessary  for  maps  and  autocorrelation  surfaces,  and  and  of  function  observations  atomic  two  function  the  hydrogen  in  s t a t i s t i c a l  autocorrelation and  The  methods  for  c r o s s - c o r r e l a t e  an  components.  average  i t s e l f ,  atomic  on  provide  s t a t i s t i c a l  mentioned, on  of  involves  correlation  dimensional study  w i l l  structure.  degree  data  two  look  density  mean  one  to  mapping  work.  cloud  of  or  grids  of to  the  The  the  identical  column  of  offset.  employed  study of  measure  sets,  vector  and  use  this  of  structure  work  in  maps  two  1985,  involved  present  two  Dickman  velocity  molecular  of  the  and  hydrogen of  Robert  Kleiner,  The  that  and  I,II,III)  density  p r i n c i p a l and  (see  complex.  observation  into  Kleiner  papers  column  2  molecular  observing  Stephen  Massachusetts  Dickman,  (indirectly) the  of  by  molecular  use  also  hydrogen  data. The proved  molecular  to  v e l o c i t y  be data  meaningful secondary  of  hydrogen  some  observations  interest.  The  not  demonstrate  any  peaks,  but  that  column  peak  (the  s e l f - c o r r e l a t i o n  primary  peak  at  the  peak  zero  to  this  autocorrelation  did  of  prior  is  of  s t a t i s t i c a l l y  the  offset)  work  on  density  data  d i d .  large the  column  density  A  4  autocorrelation  surface  of  approximately  as  a  mean  content  more  size  the  Taurus  s l i g h t l y  interesting the  in  structure  of  of  expected  appears, This  result  column nor to  nor  does is  anticorrelation be  found  molecular across  the  f i e l d ,  was  d i r e c t i o n !  The  suggesting The  structures:  common  HI  to  single  was  distance  be  regarded  molecular  hydrogen  is  the  the  two  cloud  of to  have  as  large  as  well,  but  in  the  to  be  one  2  the  two  was  atomic opposite and  the  explanation.  the  the  of  H !  gradient  The  has  the  2  The  rotation.  in  H  surprise  of  appear  the  correlation  region. a  neither  around  greater  the  maps:  appear  displays  strong  at  more  structure  a  sizes  density,  even  shell  same  physical  of  scale  column  2  even  density  between  neither  maps  components  at  hydrogen  appearance  suggested  H  This  HI  proved  column  peaks  Perhaps  length  two  It  can  c r o s s - c o r r e l a t i o n  rotation  common  a n a l y s i s .  with  rotate  of  scale  and  within  the  the  indicative  a  the  the  no  observed  different  the  by  sets,  s i g n i f i c a n t l y to  have  out  was  axes  of  neutral  velocity  found  projected  peak  difference  evident.  hydrogen  the  hydrogen  same,  in  that  elements  The  the  data  a  hydrogen  secondary  the  two  borne  density  neutral  orientation.  of  the  in  velocity  than  light  different.  two  the  same  remarkably the  the  produced  the  secondary  dumpiness  of  greater  approximately  at  complex.  Both  autocorrelations  observed  This  of  observations  interesting.  only  pc.  scale  of  Our  14  was  two  data  suggests  been  sets that  unveiled  scale  length  by  which a  have  process the  discovered  in  5  the  H  2  i n i t i a l  column  formation  hydrogen. length" out  by  density  by the  This the  of  the  authors  of of  that  it  molecular  suggestion,  appearance  observations.  data  referred the  H  2  similar  was  a  remnant  cloud to  study, scale  from  as  a  of  the  neutral,  " f o s s i l  appears lengths  to in  scale be  our  borne  II. The  recent  PHYSICAL CONSIDERATIONS  extension  millimeter  wavelength  a b i l i t y  observe  to  the  temperatures  not  d i r e c t l y  observation in  the  clouds'  redio gas.  been  c o l l i s i o n s  CO  or  line  other  ratio  of  approximately  CO  column  is  seems  the  CO  is  H  the these  One  CO,  of  be  with  the  gas  method  is  (in  H  is  of molecules  observable with  more  At  gas  2  at  the  rotational  (much  emit  i t s e l f .  trace  coextensive  excited  and  the  clouds,  the  which  molecules  2  cold  indirect  to  are  strong  and and  to  with  study  structure  their  s p i n - f l i p  transition  the  observed  f i r s t  and  one  H  2  energy)  common  mm-wavelength  to 1  hence  of  3  one  a  infer  and  more  to  than  spectral  neutral  C 0 ,  the  6  most  d e n s i t i e s .  and  the  to  measuring  of  J=1  families  to  content.  radio  J=0  with  our  hydrogen  hence  column  2  Two  l i k e l y  believed  d i s t r i b u t i o n  molecular  hydrogen  of  2  increase of  H  between  1  is  and  thermal  observe.  C O  i n t e r s t e l l a r  remains  clouds,  to  in  easy  neutral  densities  t r a n s i t i o n  formation  observing  was  the  and  dark  exist  attempts  and  column  2  in  observable,  thicker  This  H  allows  r e l a t i v e l y are  o p t i c a l l y  to  uniform  believed  l e v e l s ,  exist  CO  densities  energy  cm  an  constituent)  be  the  and  with  of  developed.  composition  of  us  into  radiation. The  The  but  astronomy  provided  structure  CO m o l e c u l e s  by  any  the  has  c h a r a c t e r i s t i c  wavelengths These  radio  region  observable, has  of  1  2  of  CO  C 0  line  saturate.  understanding clouds The at  through  hyperfine  1420.4  frequency  of  MHz  spectral  important.  This  or  21  line line  7  can  be  the  warm  as  observed HI  exists  seen  in  in  gas  in  which  and/or  absorption  background  estimate  projected  face  Figure  1  situation  as  K,  the  l i k e l y  element. warm  where  we  and If  is  structure cold  easily  present  substantial, us  with  the  i d e n t i f i a b l e ,  Our  a  w i l l  but  simple  have  motion, results  a  program  across  the  the  radiation is  the  f i r s t  21  cm  emission  amounts on  the  rotation  of  along  e f f e c t s .  from  cloud,  energy  line  2.7  line  cold  absorb  compact  of  in  a  is the  line  The  region  of  cold  narrow. are  foreground the  generally  material  free  exists  absorption  from  between  feature  w i l l  the be  shown. of  profusion  picture  line  spectral  thermal  quite  sources  as  varying  contents  from  observer,  the  impinges  and  brighter)  complex.  bang, is  galactic  (hence  i l l u s t r a t e s  background  knowledge a  big  then  The  background  and  the  HI,  generally  hydrogen  continuum  hydrogen  l i n e .  l i t t l e  A  background  d i f f e r e n t i a l  and  cloud  from  consequently  the  it.  page  is  by  Cold  observational  molecular  following  neutral  feature  spectral  neutral  radiation  turbulent  cm  21  emitted  galaxy.  warmer  of  Taurus  the  from  densities  which  of  gas,  the  sky,  clouds,  this  this  by  molecular  in  the  broadened  the  use  the  to  spectral  absorption  we  remnant  cold  sight,  is  interpret  This  the  narrow  on  sources,  structure.  It  in  throughout  radiation  which  of  Added  HI  exists  of  column  direction  around  sources.  self-absorption to  every  of  molecular of  the  clouds  information principal  has  is not  mechanisms  provided  Figure  1:  21cm  Self  /Absorption  9  involved greatly and  in in  their size  roughly  clear  that  determined  goal  of  be  this of a  one  It  is  provides  us  terms  the  The  and  with  supernova  blast  interactions, objects.  Internal  gravitational embedded  stars  r e s t r i c t i n g various their yet  ways  to  relative  the  clouds,  which  a  hoped  which  clouds  density  processes also c o l l a p s i n g nearby  importances  such  wave  the a  density,  is  well  and  understood  galactic  cloud-cloud  a  major  gas  and  with  with  radiation  magnetic  many  cloud  shapes  molecular  weight  mean  from  f i e l d s  p r o c e s s e s combine  overall  other  role,  many  what  t i d a l  interactions,  clouds,  at  of  structure.  in  observed,  picture  is  undetermined. It  in  range  their as  the  the  the  clouds.  large  interactions  in  can  functions,  to  things  play  clouds  understood  govern  winds,  (gravitational)  the  be  common  such  s t e l l a r  produce  can  that  average  metre-stick,  experience  involve  These  a l l  our  A  towards  autocorrelation  processes  expanding  view  which  environment  c o l l a p s e .  is  with  complex  heating,  forces  It  underlying  waves,  and  knotty.  the  look  measurements  ray  and  at  to  velocity  perturbations  small  is  that  External  some  substantially.  be  internal  of  vary  d i f f e r  to  and  structure,  extended  h i s t o r i e s  complexes  structure,  molecular  cosmic  of  by  external  forces,  others  cloud  metre-stick  physical  giant  These  complexity  large  common  density  of  their  research  measured.  column  in  individual  have  obtaining  and  s p h e r i c a l , the  dumpiness  evolution.  temperature,  s e l f - g r a v i t a t i o n a l  as  but of  10  i n s t a b i l i t i e s by  the  Jeans  purposes, clearly  a  by  factors to  of  expected  of  are  now  and  motions  is  also  are  forms  expected  if  than out  that of  the  species  CO  H  HI  two  mean  column  scale  hydrogen  H  2  .  The  arise  common are  the  spectral  components.  many,  in  rates. lowers  the  if  gas  these  which  motions  cold  components that  the  for  observing  condensations  were  higher  were  within  program  produced the  the  two cloud.  w i l l  be  a  Inspection  of  the  maps  w i l l  these  hydrogen;  example,  d i s t r i b u t i o n s . velocity  HI  of  neutral  molecular  temperature  results  widths  unpredictable.  distribution  and  line  line  of  suggested  this  the  so  Turbulent  various  heating,  s t a t i s t i c a l of  c r i t e r i o n  c r i t e r i o n  display  around  same  densities  sizes  from  inherently  been  two  are  formation  feature  the  ray  of  this  the  motion.  hydrogen  the  our  clouds  into  which  halo  cosmic  of  star  Alternatively,  result  comparison  and  has  rough  have  clear  informative. of  by  2  It  of  for  governed  rate.  how  neutral  the  should  One fair  a  the  of  a  unclear  mixed.  hydrogen  be  observed  observed  thermal  to  expressed,  is  s e l f - g r a v i t a t i o n ) ,  processes  accepted such  be  threshold  application  clouds  to  This  Many  formation  cold  unattributable  can  than  with  other  are  clouds  simple  complications  observations  It  medium. and  other  star  Further  clouds,  a  length.  c o n f l i c t  Incorporation the  Jeans  unstable  as  in  c r i t e r i o n ,  as  (ignoring fact,  arise  alone  provide within  w i l l  be  measures  each  of  the  11  The a  evolution  smooth  while  process.  successful  possibly regions  which of  environment  star  giant  s t a b i l i t y ,  molecular forces  formation  further  might  also  giant  Internal  triggering  interplay  their  of  have  plays and  a  disrupt  disturbs  c o l l a p s e ,  otherwise  molecular  clouds  large  their  clouds  role  rates  of  star  their their  star  not  areas,  possibly  and  clearly  formation,  large  c o l l a p s e d .  in  is  dispersing The  violent  galactic structure,  formation.  III.  A.  in  this  approximately +27°  (/II  work  was  centred  =  172,  irregular  patchy  at =  bll  the  -14).  dark  REDUCTION  pc  (see  contain  10  M©  of  molecular For  study  Kleiner  determinations centroid  fixed  Chapter  complex  at  E l i a s ,  a  =  a  is  a  distance  1978),  material,  and  of  this  with  of  1  3  the  and  4h  30m,  large  most  6  =  region  of  believed of  was  of  to  H  1  3  CO  made  hydrogen  done  in  2  molecular  (1985)  molecular  This  CO  cloud's  Dickman  transition  ratio  the  to  hydrogen  by  and  hydrogen  indirect column  observing  employing  clouds  of  this  density  the  an  J=1  and  to  0  expected  type  (see  II).  The neutral  of  velocity.  rotational  This  complex,  form.  the  portion,  6  molecular  coordinates  clouds  140  about  Taurus  (1950)  approximately  in  DATA  OBSERVATIONS  Studied  of  O B S E R V A T I O N S AND  present hydrogen  hyperfine  study (HI)  focusses in  (spin-flip)  this  on  the  cloud,  transition  at  structure  and  of  employs  1420.4  MHz  the  the  (X=21  cm)  in  s e l f - a b s o r p t i o n . Our several  choice reasons.  s u f f i c i e n t l y emission  of  the  The  cloud  displaced  from  of  complicated  of  extended  warm  Taurus  cloud  is  from  conveniently  the  background  structure,  objects.  Also,  complex  galactic  sources  necessary the  12  to  for  relative  was  for  located  plane be  made  for  the  relatively  absorption proximity  HI free  studies  13  ( d i s t a n c e d that  l i t t l e  high  spatial  to  be  HII  free  data  of It  respect  was  is  for  this the  complex  material  effects  similar  cloud, final  is  very  complicates  obtained.  disruptive  complex  simple  seems  towards  to  the  generally  the  plane  lie  This  The College  and  the  reason  important  the  study,  This  complex  of  stars  0  reasons  that  for  our  choice  seems  embedded  Kleiner  a v a i l a b i l i t y  and  also  or  in  and  of  their  of  the  a  our  was  arcmin)  information  tip  angle If  axis,  the then  of  of  of  a  dusty  about gas  a  to  a l l  of  cloud  region  60°  can  with  be  assumed  correction  (l/cos0)=2  applied  this  Observatory  beamwidth  low  the  CO  of  study.  intervals much  antenna  smearing  Arecibo  which  observations  beamwidth and  the  for  should  scale  be  lengths  a n a l y s i s .  had  as  a  an  Massachusetts,  positions  The  is  Astronomy  that  at  sky.  this  observations  of  at  the  CO  necessary  i n t e r v a l ,  of  the  operation  required  sun  in  University  l i e  foreshortening  correction  Radio  (15  to  along  geometric  obtained  1/4°  Taurus  complex.  extending  of  the  studied  The  used.  the  resolution  constitutes  Taurus  to  of  foreground  regions.  Dickman  pc)  40  To  used  in  smaller beam  between  observatory,  made  (FCRAO) at  only be  were  the  made  2.7  at  than  the  neighboring  Five  by  the  wavelength It  was  exact  sample  FCRAO  sidelobes  located  mm  the  correctly the  the  operated  arcsec.  48  at  same  at  work,  the  we  sampling  so  as  to  avoid  points.  near  Arecibo,  Puerto  14  R i c o was  1  ,  the  thus  largest  an  wavelength arcmin,  appropriate of  21  cm,  and  the  purposes .  radio for  less  than  sidelobes  the  were  at  limited  from  its  having  for  our  work,  because  the  " v i s i b l e "  d i f f i c u l t y  conveniently  within  pointing a  fixed  telescope  our  beamwidth  The  2  resulting  dish  choice  the  s u f f i c i e n t l y  interval, our  single  this  15  arcmin  our  of  this was  source  for  At  a  is  ^4  sampling  satisfactory  range  sky  world,  telescope  reflector, of  the  observations.  of  a  in  the  level  for  telescope, not  a  being Arecibo  telescope. In  October  1985,  rectangular  grid  p a r a l l e l  declination)  a=4h CO  to  30m,  (41  1271  8=+27°.  observations.  p a r a l l e l  This Power  channel  autocorrelation  of  kHz  4.88  (0.515  km/sec).  seconds, The  B.  with  system  DATA  (1.03  spectra  to  right  an  intervals  were  and  signal  a  channel  times to  temperature  varied  noise was  grid  with  60  by  centred to  obtained  spectrometer,  observed  ascension  identical  spectra  were  a  that  between  ratios  in  a  of  (1950)  of  channel  spacing  the 504  width  2.44  20  every  a  31 at  using  in  and  kHz 7  spectra.  K.  REDUCTION  the  observatory,  cm  Vancouver  2  is  cm  1/4°  Integration  noise  21  1  at  km/sec)  large  The  The with The  21  power  for  spectra and  were  brought  reduction  on  a  recorded to  the  Sperry  on  UBC  magnetic Physics  tape  at  department,  microcomputer.  Arecibo Observatory i s o p e r a t e d by C o r n e l l University, f u n d s p r o v i d e d by the NSF. 21 c m " F l a t f e e d " was u s e d f o r these observations.  15  Calibration  was  done  coordinates  /II  =  intensity survey .  of  approximately, Greater  190°,  this  Zenith  3  angle with  accuracy  s i g n i f i c a n t  errors  to  measure  The density observed  background radiation regions was of  of  in  the  of  +  thus  the  f i r s t - o r d e r  polynomial  of  the  curve  this  less in  as  much  were  to  estimate  f i r s t  in  background fit  to  point  in  continuum  absorption this  through  selected  the  the  background the  below.  column  necessary  throughout  5%.  procedure  discussed  each  step  than  more  at  the  the  this  f i t t i n g  reduction  above  with  only  necessary  depth,  The  non-line  done  from  of  Williams  values  receiver),  spectrum.  be  the  data  velocity  was  K  to  and  were  because  temperatures  each  removal a  It  (2.7  f e l t  comparison  Weaver  errors  absorption  centroid  line  on  not  involved  the  g r i d .  the  observations  and  corrections  reduction  objectives and  in  0 ° ,  estimated  was  data  repeated =  bll  source  preliminary  used  through  procedure subtraction  portions  of  the  data. Absorption within  the  v e l o c i t y proved  features, The lines  in  spectra  velocity  range  to  of  contain as  we  most  are  studied  range  the  0  v i r t u a l l y  would  of  obtained  to  were  8  components a l l  limited  to  km/sec,  the  of  cloud.  of  this the  those  expected This  range  self-absorption  expect.  satisfactory  studies  The Berkeley 1973.  3  features  this on  method  type the  low-lattitude  is  of the  estimating ON/OFF  method,  in  which  and  it  in  absorbing  cloud  survey  neutral  of  background  off  hydrogen,  a  16  region the  s u f f i c i e n t l y  background  subtracted, spectra. because  One  interpolation, has  an  line  of  as  advantage  structure.  underestimates yielding  no  instance. can  to  be  that  the  to  the  well  i n t e l l e c t u a l l y  at  the  that  three  cm  Our  Gaussians.  higher-order  than  or Two  to  Both  of  a  absorbing  regions  few  must,  f i r s t  in  an  any  the  these  two  the  it  in  easily  as be  structure  resemblance  cubic  of  adequate  astrophysics  remained;  methods  multiple)  can  complex  combination  masked  for  regions  appears  l i t t l e  comparison  about  or  absorbed  more  methods  method  spectrum,  However,  bore  This  (single  glance  simple  and  a  introductory  spectra  line  temperatures,  on  f i t s  much  of  severely  top  the  object.  techniques  1981.  radiation  with  study  of  assumptions  also  f l a t  are  *For a f u l l d i s c u s s i o n and L e v i n s o n and Brown, 1980.  our  al,  other  polynomial  interpolators.  of  s a t i s f y i n g .  observed  Gaussian,  our  et  at  spectra  observatory  textbook. simple  21  for  Batrla,  Gaussian  technique,  unavailable  straight  for  then absorption  satisfactory  makes  of  the  is  it  variation  are  methods  spectra,  This  spectra  extended  background  Alternatively,  l i t t l e  of  extent  unfortunately  masked.  shown  by  is  estimate  is  less  these  in It  of  far  absorption  made  as  however,  used  two  excellent  studies  resort  there  These  considerable  Absorption  estimation".  an  method,  the  necessity,  that  radiation.  yielding  This of  close  make  of the  two  to  a  or  masked  s p l i n e  5  few  methods,  see  A cubic spline i s composed of c u b i c segments between pairs of data p o i n t s . A c o n t i n u i t y c o n d i t i o n between segments is imposed over the f i r s t three derivatives. Refer to Schultz, 1973, for a f u l l discussion. 5  17  assumptions  about  the  emission  structure  and  are  easily  implemented. Our to  choice  exhibit  with  (this  is As  in  a  with  any  spectrum cloud).  was  to  and  an  while  be  effort  Signs  a  of  be  the  should  domain  arrived  of  cutting affected  great at.  off the  error.  A  a  number  spline  the  masked spline,  page  shows  fit  of  the  made  the  of  by  chief the  the  absorbing  s i g n i f i c a n t l y  selected  the  d i f f i c u l t i e s  the  region  affected  were  of  f i t s ,  interactively,  smallest  region  possible  absorption  region  which  unaffected  by  the  as  the  l o c a l  minima  or  local  absorption.  existence maxima  in  the  away  peak.  the  spectra  performed with at  a  in  k H z to  widened  happy  were the -  fit the  medium  1  smoothed  Fourier  Hamming  0.205  attempts  smoothing  the  cubic  spline  things  that  than  lengths,  such  emission  was  a  provided  mask  over  are  noted  excessive  created  to  multiplication  IV)  adversely while  be  the  region  Masks  fit  fit  Smoothing by  Chapter  a  region  central  f i t t i n g .  For  (empirically)  poor  interpolated  .  over  following  with  method,  (the  made  maintaining to  It  was  6  the  l i k e l y  region  the  small  less  absorption).  selections  f i t s  unknown,  on  is  masked  over  selection  masked  curve  appeared  from  the  which  desirable  centre  strong  arose.  Different  different  grid  the  were  2  estimation  in  in  was  Figure  the  implementation  spline,  derivatives  r e l a t i v e l y  d i f f i c u l t y  6  third  from  curves  structure  admirably.  spectrum  cubic  structure  smooth true  zero  performed the  As  whose  its  the  unwanted  polynomial. region,  was  window  .  Too over  function  l i t t l e the  absorption  was,  prior  to  transform  however,  (see  smoothing  absorption, feature easily  and  18 F i g u r e 2: S p l i n e F i t t o the Spectrum a t t h e Map (a=4h 30m,  Centre  6=+27°)  Velocity  (km/sec)  Tbb S u b t r a c t e d Masked Region: Approximately 0 t o 6 km/sec  19  It often only  should  d i f f i c u l t showed  emission  each  no  flattened  with  two  of  were  interpolation  techniques  inhomogeneity  of  velocity A  of  the  discussion  Chapter  a  of  few  of  occasions,  obvious (four)  the  were  was  to set  to  sum the  of  also  for  grid  centroid  over  spectra  in  having  and to  the  that  value  may  be  the of  unknown  this  at  seen  due  the  seen,  that  for  these  of  the  moving  decided  assign  of  densities  d i f f i c u l t  It  absorptions  were  unattainable,  implications  the  spectra centroid  these  mean was  the  and  domain  spikes of  was  spectrometer  channels  transform  and  the  data  d i f f i c u l t y  particular  Single  entire  as  were  seen.  cloud,  v e l o c i t i e s  complex.  side  be  Column  values  be  the  absorption  taken  proved  would  smaller  to  Taurus  were  regions  most  the  mean  v e l o c i t i e s . found  in  V.  Another in  the  method  of  Centroid  absorption  on  minimum  seen.  velocity  absorptions.  advantageous  regions  the  were  absorption  Frequently  regions  this  while  significant  the  local  clumps  exhibiting  two  no  v e l o c i t i e s ,  region,  that  determine.  with  overlapping  points  the  as  l i n e ,  different  noted  to  up  Spectra when  be  transform  amplitude  had of  irreparable, of  were  its  then  its and  at  of to  in  the  the  was  appear  scaled was  column used.  failed  on  Fourier  spectra).  be  errors,  observatory.  channels  mean  neighbors  hardware  unfortunately  neighbors the  of the  made  spectrometer  spectra  velocity  result  failures  repairs  the  a  spectrometer  (poor  in  as  in  used.  A  as number  amplitude Only  density The  one  and  small  20  number  of  d i f f i c u l t  errors  of  no  have  these Once  shape and  great  centroid  made,  unabsorbed  line  (observed)  absorbed  temperature background this r  =  density  1.823  Centroid  *  to  at  b y  7  unnecesary  background  calculate Tu  some  as  to  the  and  then  as  the  as  density  (estimated)  the  Tbb  line  column  frequency,  Tspin  gas,  (»2.7"K),  given  felt  the  define  absorbing  values  10  *  1 8  are  Tl  as  the  spin the  o p t i c a l  cosmic depth  at  :  setting clear  these a  since  in  /  given  Jr*dV  by:  (/cm ),  dV  2  c a l c u l a t e d ,  where  in  km/sec  p o s s i b l e ,  in  the  (J(Tu-Tl)*dV)  the  is  value  does  frequently  to  Tspin  temperature  It  *  c a l c u l a t i o n s ,  value  that  spectrum,  then  manner:  (/(Tu-Tl)*V*dV) In  are  Tspin  v e l o c i t i e s  following =  is  of  temperature,  radiation  was  large  ln((Tu-Tspin+Tbb)/(T1-Tspin+Tbb))  Column  V  the  frequency  =  CD  of  we  temperature  potentially  again.  remains If  the  it  estimate  it  v e l o c i t y .  and  made  acceptable  been  makes  concern,  observations an  has  spectra  spin  less  within  appear  our  the  or  temperature  effect  of  decreasing  'Refer  to  Spitzer,  1976.  equal  ceases  that  occurs. the  assumption of to  absorption  line  observations,  radiation  chief  temperature  than  absorption  not  the  at  the the  cloud.  It  is  on  any  given  Tspin=Tl+Tbb.  no  common  Saturation  difference  in  lowest  region  saturation  as  was  has  minimum  would  between  occurred  the  have most  the dense  21  and  least  dense  c o r r e l a t i o n s Values =*14+2.7  K  setting  the  single  regions,  in of  column Tspin  upwards. HI  value.  density  were  A  spin  the  temperature.  quite  spin  accurate  in  K,  and  the  regions,  column  density  values,  column  density  values  thus  from  In  light of  of  the  the  data  values  was  into  the  column  to 8  +1  CO  each  a f t e r  each  the  2  C 0  excitation  is  to  l i k e l y  range  The the  In  of  obvious 1271  the  correlation  a  overestimating  the  enhancing  to  absorption.  of  of  in  assigned  most  range).  points  is  column  features  a r i s i n g  the  about of  the  analysis paper  e f f o r t  to  s e n s i t i v i t y  to  test  through  a  one  bit  value  is  in  of  number . 8  to the  common  radio  losses  in  signal  to  Wemreb,  - 1 ,  and  mean. of  the  errors  data  (SNRj by  in  density  subtraction  wirtten  discussion  an  uncertainty  involved  correlation  early  the  than  cloud  choice  lowering  at  1  less made  the  effect  test  negative  used  the  Tspin  was  been  of  This  to  spectrometers  one-bit  the  dynamic  techniques  made.  d e n s i t i e s  0 n e - b i t  has  regions  s i g n i f i c a n t  data,  autocorrelation  setting  from  the  temperature  had  thus  that  value  i n c o r r e c t l y  and  vary  assumption  hence  (the  decrease  data.  reduction  column  and  estimating  v a r i a t i o n ,  t h i s  This  would  throughout  this  choice  avoided,; without  density  the  in  this  to  indicate  coldest  warmer  d i f f i c u l t y  seen  temperature  is  turn,  v a r i a t i o n s .  thus  Observations =*10  in  simplifying  temperature HI  which,  in  (2/TT) 1963.  drop *  individual  introducing setting  error  each  of  done  by  This  was  each  p o s i t i v e  and  s e n s i t i v i t y , noise  of  this  the  value the  data  autocorrelation  astronomy,  =  the  Following  the  this  much  etc.  resulting  S N R  a  n  a  ^  has  For  0  g ) ,  been  a from refer  to  22  had  to  be  one-bit true  reset  correlation  data,  largely  with  9  See  the  unchanged.  s i g n i f i c a n t data,  to  even  results with  Chapter  c a l c u l a t i o n s .  IV  zero gave  mean  prior  remarkably  secondary In  l i g h t  were  to  peaks  of  its  unavoidably  for  a  similar and  t h i s ,  obtainable  discussion  we from  large  of  a u t o c o r r e l a t i o n results  overall are  .  This  to  the  structure  confident  our  9  that  absorption  errors.  correlation  function  I V . A U T O AND C R O S S - C O R R E L A T I O N A N A L Y S I S Correlation analyses bring t o light trends simple  observation.  a r e methods g e n e r a l l y used t o  1 0  i n data  which a r e not apparent  from  They a r e an attempt t o q u a n t i f y  s t a t i s t i c a l sense such trends.  ina  I n o u r work t h e c o r r e l a t i o n s  g i v e a m e a s u r e o f mean, l a r g e s c a l e s t r u c t u r a l parameters. The autocorrelation  cloud  function i s a measure of t h e  mean d e g r e e o f c o r r e l a t i o n b e t w e e n a l l p a i r s o f p o i n t s single data vector  s e tas a function of their spatial  ina  separation,  offset or lag. The c r o s s - c o r r e l a t i o n function i s a  m e a s u r e o f t h e mean d e g r e e o f c o r r e l a t i o n b e t w e e n t w o d a t a sets as a function of lag. In t h i s work t h e d i s c r e t e forms o f t h e t w o - d i m e n s i o n a l auto and cross-correlation functions two  dimensional  autocorrelation  a r e employed, where t h e  function  (ACF)o f F(x,y) i s  given by: FACF(T,,T ) 2  = (Ni*N /ni/n )* 2  a  Z,Z,F(x,y)*F(X+T,,y+T ) 2  2 Z F (x,y) 2  1  and  2  t h e two dimensional  cross correlation function  (XCF) o f  F(x,y) and G(x,y) i s given by: XCF(T ,T ) 1  2  = (Ni*N  2  / ni/n )« Z Z , F ( x , y ) * G ( x + r , y + r ) 1  2  1  5  /FACF(0,0)VGACF(0,0) One  can see that as l a gincreases  points the  t h e number o f  overlapping  i n o u r d i s c r e t e ACF ( o rXCF) drops o f f l i n e a r l y , and  f i r s t terms above, t h e r a t i o s o f t o t a l data p a i r s t o  data p a i r s a t the given  l a g , have been introduced  to correct  f o r t h i s . T h i s amounts t o i n t r o d u c i n g a r e c t a n g u l a r window S e e R.N. B r a c e w e l l ' s w e l l - k n o w n t e x t f o r a d i s c u s s i o n o f c o r r e l a t i o n techniques and s p e c t r a l analysis (1978). 1 0  23  24  function  in  two  dimensions,  c o r r e l a t i o n  functions.  linear  off  drop  becomes points XCFs  of  (at  large  It  is  to  "unbiased"  the  through  the  as  off  For  purpose,  f u n c t i o n  1  a p p l i c a t i o n H ( T ,  , r  2  region,  the  + 0.46*cos(7r  * r  2  function  is  similar  bias  employed  in  the  c a l c u l a t i n g  Wiener-Kinchine of  spectrum.  Fourier  function from  the  number  a  noise  of  of  the  the  data ACF  or  in  two-dimensional  spectral  r e l a t i v e l y of  in  response  l a g s ,  large  Hamming is  a n a l y s i s ,  f l a t  small  the  function  lag  and region.  window  given  for  our  taking  1  See  Bracewell,  1  2  Use  was  of  in  effect  of  1978 the  or  to  can  which  be  "intermediate"  thus the  complex and  Stanley,  e f f i c i e n t  the  the is  Fourier  the  power  provide  us  with  taking  u s e d  1  2  and  c a l c u l a t i n g  the  inverse  compared  1975.  Fast  the  autocorrelation  transform,  then  was  of  that  function  methods  method  made  states  calculate the  the  K l e i n e r .  use  spectrum This  )*  m a x ) )  transform  power  1  2  m a x )  1  autocorrelation  transform.  made  that  edge  apply  region  * T , / r  / T  ACFs,  i n d i r e c t l y  through  this  Fourier  the  to  is  of  lags).  edges  This  work  theorem,  transform  c a p a b i l i t y  the  effect  follows:  This  In  or  the  ) = (0.54 + 0.46*cos(7r  (0.54  a  the  two-dimensional  selected.  as  as  used  having  near  points  at  to  the  another  negative  commonly  data,  quickly  was  1  or  high  desirable is  central  dropping this  very  positive  function,  data  s i g n i f i c a n t  is  therefore  "unbiasing"  Unfortunately,  more and  window  to  overlapping  gradually decreases  or  Fourier  Transform  with  25  ACFs  calculated  observed. enormous due as  to  through  as  savings  set  Kleiner  the  well  doubling  and  sizes  powers  fixing  array  not  of  great  Kleiner,  set  to  mean  a  also  done  e t c . ) .  a  "Parzen  side  effects large  and  divided  the  square  respective the It  ACFs),  two is  ACF  also  f i e l d  were  large  gradients  which  are  helpful  to  (cont'd) discussion Processing 1  2  peak to  of  found  two,  a l l  the  as  are  the  spike  roots values  by  that  arrays time  each  (zero  f a c i l i t a t e  the  by  of lag  (contour  Fourier in  both  multiplication  and  1985.  The  widening  of  lag. d i r e c t l y ,  the  and  two  values  contour  data  correlation  Kleiner,  zero  each  analysis  lowering at  the  transforms  calculated of  of  in  followed  discussed  were  correlation  performed  significance  is  to  object  have  have  are  level  of  the  comparison  p i c t u r e s .  observed,  the  of  was  savings  padding  easier  dimensional  smoothing  s e l f - c o r r e l a t i o n  with  was  s e l f - c o r r e l a t i o n  by  we  zero  Smoothing  declination  Cross-correlations  time  but  to  f a c i l i t a t e  one  taper",  of  prior  zero.  F i l t e r i n g  ascension  to  difference  import.  of to  successive  with  routines,  the  of  was  right  that  necessity  by  by  suggests FFT  done  domain  significant  of  was  drawing,  no  use  were  was  and  (1985)  As  images  the  d i r e c t l y  these  most mask of  that  notably the  this  in  lower  study.  gradients  gradients  across  v e l o c i t y .  The  level In  many  removed.  algorithm in performing of t h i s a l g o r i t h m refer by S t a n l e y , 1975.  In  the  effect  correlations cases, order  it to  was do  the transforms. For to D i g i t a l Signal  a  of  26  t h i s ,  a  best  prior  to  fit  setting  Some  of  functions.  The  functions  is  occurs  perfectly central  It  should  making  about  as  also  equal  purely with  is be  and  with  regions  on  that  of  a l l  by  the  that  This  c r o s s - c o r r e l a t i o n  a l l at  general  autocorrelation  zero any  lag.  data  c l e a r l y  the  data  functions  and  set  zero  with  mean  zero  functions  are  symmetric  appear  a  zero  l e v e l .  would  at  single  peaks  as  Autocorrelation  appear  repetitive  secondary  would  as  a  central  wavelength function  spaced  not. delta  of  a  peak  spacing.  with  at  mean,  correlation  white  noise  why  functions.  to  negative  is  explains  c r o s s - c o r r e l a t i o n setting  This  are  a  a  set  functions  peaks of  data  c r o s s - c o r r e l a t i o n  function  large  of  of  autocorrelation  of  the  and  peak  fact  p o s i t i v e  while  repetitive  give  made auto  i t s e l f .  evident  surrounded  would  be  feature  the  from  c o r r e l a t i o n .  c r o s s - c o r r e l a t i o n  Cross-correlation disk  of  noted  o r i g i n ,  equally  now  striking  Autocorrelation function  and  dimensional  result  F i n a l l y ,  the  mean  s e l f - c o r r e l a t i o n  a  peak  subtracted  should  two  most  the  auto  appear.  the  was  zero  correlated  no  creates  to  discussion  appearance  peak  plane  a  simple  integer  wavelengths. In measure data.  many of  cases  the  However  has  been  lost  the  smoothing  unfortunate,  the  width in due  of  much to  width mean  of a  large  This  scale  the  central  structural following  minimum  procedure. but  the  of  central loss  of  peak  can  components work  this  width  being  information  correlations  are  of  be  a  the  information fixed is  unaffected,  by  the  study  of  which  is  our  objective.  V.  A.  RESULTS  1.  MAPS Figures  under  study.  hence  H )  Dickman.  Figure  The  and  correct, As  In  as  the  regions,  be  zero  HI  column  of  the  negate  feared map  to  regions  zero  the  of  column  clear  that  as  the  of  do  no  data  these  map  the  maps  are  column  physically  and  a  are  result in  28  not of  map  These  c i r c l e d  seem  to  in that  the  would and  velocity  appear thus  on  the  falsely  function.  clearly  These  outlined  smoothing,  agreement.  add  overall  autocorrelation are  the  reasonably  the  valleys,  of  suggests  not  regions  density as  from  are  maps  was  velocity  density two  velocity  v e l o c i t i e s  h i l l s  column  and  actual  obtained.  density,  structure  that  Kleiner  indicated.  not  regions  (and  hydrogen  levels  could  The  contribute  neutral  contour  by  region  scaled  information  interpolating  interpolated-  was  the  C 0  3  not  regions  of  was  the  the  are  are  method  It  3  of 1  provided  Figure  6,  the  there  Inspection  map.  of  provided  and  maps,  5.  nor  in  obtained  map  kindly  data 4  maps  contour  data  the  Figure  structure,  the  DISCUSSION  e a r l i e r ,  having  successful.  a  units  discussed  velocity  is  Figures  AND  are  levels  velocity  with  6  density  d e n s i t i e s ,  density  3  contour  a r b i t r a r i l y .  where  through  column  2  column  3  RESULTS  but  it  on is  29 Figure  3:  Molecular  50m  46m  Hydrogen  42m  38m  34m  Column  4 H 30m  Density  26m  22m  Map  18m  14m  10m  ,;-.Gl,.  30  30  E  2 9  H  :r :x- ::  G  R E E S D E C L I N A T I 0 N  •:• .Oft  28  •  ...... 27 •  :i:-a  : "••.0.4  :::  29  :  28  pi- j J07. >  • ;jOtt V :  ;:  h 27  £7/" p i ......  :  pr.  26  25  26  ',.07; ...i0T--. 25  1:;' r "../p4 S :  24  24  50m  46m 42m 38m 34m RIGHT ASCENSION  4 H 30m  26m  CONTOURS AT:  22m  .01 .04 .07 .1  18m  14m  10m  30  Figure  Neutral  4:  50m 46m  Hydrogen  42m  38m  Column Density  4H 34m 30m 26m  Map  22m  18m  14m 10m  30 A AO29  A  10-  :  >6  :  •20 • 28 27'  30.:  26  20.  25 1; 24  20  50 50m  46m 42m 38m 34m RIGHT ASCENSION  4H 30m  26m  CONTOURS AT:  22m  18m  14m  ,„ 0 *10 /(cm ) 10 20 30 40 50 60 70 80 90 100 ,B  2  10m  31  F i g u r e 5: R e g i o n s  50m  46m  o f Z e r o Column  42m  38m  4 34m  Density  H 30m  26m  22m  18m  14m  10m  30  r 29  28  h- 27  26  r  25  24  4 50m  46m  42m  38m  RIGHT ASCENSION  34m  H 30m  26m  22m  18m  14m  10m  32  Figure  6:  Neutral  Hydrogen  Velocity  4 50m  ->  D E G R E E S  30  A  29  A-  •  42m  38m  •  1  1  H 30m l  26m  22m  i  18m  i  .3..:  i  14m  10m  i  i 30  2,,.-  29  : 4 :  28  27-  I  26  28  r-  27  h  26  Y  25  h  24  \ . 3  3  •3.  N  A T I O  34m  •2-  D E C L  46m  Map  25  .•••'5i  N  24 H  :  4 50m  46m  42m  38m  RIGHT ASCENSION  34m  H 30m  26m  CONTOURS AT:  22m  1 2 3  4 5  18m  km/sec  14m  10m  33  Comparison (Figures the  3  two  the  right.  and  of  The are  many  quite  across  the  lower  magnitude It  3  was  a  The  neutral  objects  is  due  2  to  to  the  region.  in  a  than  velocity  map  the  km/sec  of  of  shown  as  the no  (Figure being the gradient  velocity  at  the  right.  The  same  of  to  rotating the  w i l l  slower  be  of  complex. in  the  make  rates the  lower an  it  observed  which  the  that  elongated  be  v e l o c i t y in  gradient  the  to  much  appears the  to  hydrogen.  on  upper  a  in  also  there  the  v e l o c i t y  neither  at  is  in  velocity  the  rotation,  but  right) that  2  of  a  of  left  region  km/sec at  as  d i r e c t i o n .  appears  Galactic  is  +5  gradient  that  +5  amounts  the  is  in  concentrated  molecular  in  gas  rotation  rotate,  upper  of the  H  bottom  there  the  maps  appears  Superimposed  velocity  then,  Note  the  demonstrative  the  of  from  Clearly  opposite  of  cloud  strongly  around  pockets  the  from  v e l o c i t i e s  Furthermore  ranged  greater  H  gas  the  substantial  map.  display  in  is  with  km/sec  hydrogen,  observed).  a v a i l a b l e .  running  the  indication  km/sec No  +1  suggested  in  3  of  portion  2  evident  also  km/sec  1  a  appear  v e l o c i t i e s  H  HI  within  d i r e c t i o n .  rotations  structure  hydrogen  but  clear  opposite  that  ,  was  different  the  separate  and  1  remarkably  discontinuous,  v e l o c i t i e s  2  of of  complex  l e f t  hydrogen  region  halo  the  and  component  l e f t  components of  molecular  structure  the  a  The  HI  neutral  motion  H  of  lower  evidence  6)  The  neutral  shows  elongated  centre  l e f t  4)  the  components.  roughly upper  and  of  H  2  l e f t  average  such  (1/5  of  gas to  (H +9  of  HI. this  data  was  not  made  4  2  34  2.  CORRELATION  SURFACES  Autocorrelation shown  in  the  shown  in  Figures  10  shows  maps  the  density  of 7,  function, Kleiner,  7,  is  the  1985,  towards  very  low, on  it  present  near  lag  a  2  and  data  functions  HI  are  Figure  column  slight  of  H  140  8,  2  ,  upper  other lag  right  or  by  4.2 to  HI  an  and scale  The  lower  the  secondary  This  lower  the This  or  l e f t  of  is  peaks  or  secondary  These  peaks  secondary  from  between these  the  present  ( - 3 . 8 ° , + 1.7° )  degrees  lengths  from  the 10  are  and peaks  central and  14  secondary  pc  at  peaks  0.055.  column  near  peak  5.7  largest  extended  located  but  s l i g h t l y  by  Kleiner,  and  ( - 2 ° , + 4 . 3 ° ) .  about  the  of  presented  resulting  discussed  (+3.8° , - 1 . 7 ° )  pc.  of  (0.065). pc.  that  differences  the  Two  peak  for  to  ( R A , D E C ) = ( + 5 . 3 ° , + 1 . 8 ° )  level  ( - 4 . 8 ° , - 2 . 5 ° ) .  autocorrelation  lag  secondary  13  H  the  pages.  near  shows  about  following  the  for  These  largest  function,  peak  of  identical  plateau,  between  Figure  the  the  5.  density  A  corresponding  a  column  2  ( + 2 ° , - 4 . 3 ° )  distance  found  on  and  the  near  located  reaches  9  calculated  with  ( - 5 . 3 ° , - 1 . 8 ° ) . also  H  with  extending  peak,  and  essentially  process.  are  8,  3,4,  c r o s s - c o r r e l a t i o n  smoothing  located  Figures  were  data.  Figure  but  functions  density twisting lag  peak  of  plateau,  ( + 4 . 8 ° , + 2 . 5 ° )  appears  level  autocorrelation  less  the  with or  significant  plateau  corresponds  to  is a  a  than  higher, scale  that as  length  is of  35 Figure  7:  -10  -10  Molecular  -  8  -8  -  6  -6  -  Hydrogen  4  -4  -  2  -2  LAG IN RIGHT ASCENSION  NOTE:  S o l i d  Contours  Column  0  Density  ACF  2  4  6  8  10  0 2 (DEGREES)  4  6  8  10  Indicate  CONTOURS AT:  Positive  .045 .015 -.015 -.045  Correlation  36 Figure  NOTE:  8:  Neutral  S o l i d  Hydrogen  Contours  Column  Indicate  Density  Positive  ACF  Correlation  37 F i g u r e 9:  N e u t r a l Hydrogen V e l o c i t y ACF  NOTE: S o l i d Contours I n d i c a t e P o s i t i v e C o r r e l a t i o n  Figure  10:  XCF  of  Column  NOTE:  S o l i d  Neutral  and  Molecular  Hydrogen  Densities  Contours  Indicate  Positive  Correlation  39  Figure shows  a  9,  plateau  secondary evident  near  peak  lag  had  to  with  be  the  results this  ( - 4 . 3 ° , - 0 . 7 ° ) right  peak  the  the  in  the  H  2  direction  peak  ( - 6 . 1  of  16  0  i s ,  having  no  however,  , - 2 . 7 ° )  p c . The low  significance large  into  regions  density Figure i s  the  extended  This  data 10.  of  level  of  question,  this  plateau no  plateau  data  which  peaks  obtained  to  the  lag  upper  holds,  results  the  either  the  the  single with  (<0.04) of  a  main  from  low  and  nor does  map c o r r e l a t i n g  quite in  interesting  near  resembles  hydrogen one a r e  c r o s s - c o r r e l a t e d  peak  longer  map a n d l i k e l y  but  were  The most  single  symmetry  neutral  absent  means  time  time)  i s  Monte  Carlo  were  in  that  A l l peaks  correlations  In  or  function,  this  compared  column  autocorrelations.  adequate  to  column  e x i s t ) .  Clearly  due  secondary  i t s  function  secondary  density  different  length  the  shown  (note  of  structure. to  of  a  , + 2 . 7 ° )  c a l l s  and the  peak  structure large  0  scale  a n d HI  2  of  central  in  autocorrelation  interpolated. H  lower  a  light  The  feature  ( + 6 . 1  to  in  velocity  An i s o l a t e d  (<0.04)  especially  HI  extending  peak.  corresponding this  the  our  s t a t i s t i c a l  estimating  observed. constraints  the  the  of  in  use of  the  significance  One method, (both  analysis  which  of  was n o t  programming  two d i m e n s i o n a l  i s  time  Fourier  an  the implemented  and  running  transforms  to  do  a n a l y s i s . absence  obtained  along  of  these,  selected  one dimensional directions  to  power  better  spectra i l l u s t r a t e  40  the  c o r r e l a t i o n  are  normalized  and  HI  in  lengths power  v e l o c i t y  the  autocorrelation Figure  11  of  largest  peak  in  pc,  which  extends  spectrum  of  length  of  12  Figure located  this  in  ( 3 . 8 ° , - 1 . 7 ° ) ) .  axis  pc.  near  again,  highest  No  represents  In  each  were  of  is  very  the  observed  approximately  is  is  an in  HI  13  column  map  in  and  14  density  centre  the  and  respective  the  of  to  be  a  the  scale  shows  highest  seen  scale  The  length  a  along the  the  of  power  (near scale  this  a x i s .  secondary  peak  power  14  of  structure  peak to  the  The  length  plateau  12  through 8.  to  ( 5 . 3 ° , 1 . 8 ° ) ) .  corresponds  Figure a  (near  Figure  axis  an in  to  axis  through  Figure a  scale  pc,  is  peak at  a  and  this  9.  The  length  the  secondary  peak  peak of  power  is  pc,  and  16  at  a  dominant.  autocorrelation at  7  corresponding  dominant.  represents  peak  DISCUSSION  peaks  next  peak  to  ( 6 . 1 ° , 2 . 7 ° )  B.  12,  the  represents  the  plateau  corresponding  this  Figure  through  peak  frequency  and  2  spectrum  d i r e c t i o n .  frequency  near  H  11,  through  representative  corresponding  located  axes  power  ( 4 . 8 ° , 2 . 5 ° )  14  the  secondary  of  frequency  Figure  of  spectrum  this  The  13  the  peak  l i k e l y  an  chief  shows  secondary  21  along  Figures  function.  largest  about  spectra  data  d i r e c t i o n  quoted.  approximately same  functions, the  distance.  same  secondary  orientation,  Autocorrelation  peaks and  analysis  at of  41 F i g u r e 11: Power Spectrum o f M o l e c u l a r Hydrogen Column D e n s i t y  A t an angle o f +17.5°  from c o n s t a n t  declination.  Frequency  (0.1875 deg" ) 1  F i g u r e 12: Power Spectrum o f M o l e c u l a r Hydrogen Column D e n s i t y  At an angle o f -25° from c o n s t a n t  0 il 0  1  J  II"  2  -IH"- -iHll  3  4  Ulllll 5  declination.  ill. 6 Frequency  ...... 7  8  Mill..  .Illlllllll  9  (0.1875degl) _  10  Figure  At  13: Power S p e c t r u m o f N e u t r a l H y d r o g e n Column  an a n g l e  o f +26°  from constant  5  declination.  6  7  Frequency  Figure  At  14: Power S p e c t r u m o f N e u t r a l  an a n g l e  o f +22°  from c o n s t a n t  Density  8  9  (0.1875 deg ) -1  Hydrogen  declination.  Velocity  43  v i s u a l  extinction  was  performed  and  14  pc,  repeated  with  strongly  was  an  are  along  be  24,  for  28  that  line  of  like  the  sight,  from  1  ,  S e e  32  of  HI  the  Lynds  scale  of  1  orientation.  in  the  9  in  three  appearance  i n s t a b i l i t y of  of  The  peak  different  an  catalogue "  lengths  recorrelation  history  of  60°  remaining  complex  when  it  a  gas.  an  well  those now  the  Lynds,  is  a  look  onset  of  1962,  the  plane  of  is  l i k e l y  the  foreshortening  sky,  of  wavelengths  are  clearly  (1973) one  in  This  can  and  thus  (l/cost9) = 2  of  recorrelation  7  our  some  to  observed  estimate  gravitational  Catalog  of  scale  of  for  the  HI  compact  length  by  the  in  the  region  obtained  physical  in  phenomena  far  Taurus.  i n s t a b i l i t i e s  used  pc  with  autocorrelation  a l l  scale  in  7  accounted  to  pc  agreement  a  relatively  studied  at  in  which  be  applied  The  not  dimensional  represent  being  tool  the  isolated,  gravitational  model  to  complex  pc.  Baker in  Taurus  observed  complex.  may  shall  the  analysis  not  Taurus  removed  which  in  lengths  Baker's  study  Jeans  pc  signature  Our  and  warm  Baker's  context  observed  substantially  axis  observed  of  fact  We  =0 4  geometrical  scale  was  analysis  at  an  observations  length  a  the  approximate  above,  applied.  These the  a  discussed  now  of  period  correction  should  with  from  homogeneous.  extended a  region  same  sets  suggests  more As  the  data  early  the  Kleiner  occurance  independent  from  by  in  scale in  lengths  warm  masses  HI (or  i n s t a b i l i t y  Dark  Nebulae.  in  gas.  the The  densities)  occurs.  This  44  very  simple  model  assumes  v e l o c i t y ,  and  equations  simplify  (  V  for pT  -  2  1/C  which =  A  =  2  At  k  a  2  C  the  a  2  For  Disturbances  We  w i l l  approximate Taurus / c m HI  3  ,  region,  This scale  value  1  5  =  S e e  is  pages  Deeming Mestel,  3  p  of  seen  is  a  s o l u t i o n ,  which  k ,  is  T  the  given  by  . w i l l  y  at  value,  grow  with  g r a v i t a t i o n a l  stable  simple in  is  believed  K,  very  p  416,  1965.  is  kT  and  length  time,  c o l l a p s e .  o s c i l l a t i o n s ,  treatment t y p i c a l  to  have  reasonable  wavelength  general  mass  (1984),  k  /  H  are  observed  a  0  fluctuation  This  onset  this  stable  (4/3)7rX  :  5  with  the  case  s t a b l e .  in  Jeans  marginally  0  Jeans  lengths The  Mj  a  of  4irGMP m  Jeans  T=80  =  1  relation  grow.  k>kj  use  complex and  density  value  the  marginally  p,  )  0  imaginary  for  hydrodynamic  e q u a t i o n  47rGp /C  i n i t i a l  .  0  not  to  The  zero  cot))  =  2 S  density,  f i e l d .  wave  d i s p e r s i o n  CJ i s  corresponding  k=kj  -  w i l l  0  k<kj,  +  2  c r i t i c a l  4TTGP /C  =  the  wave  4TTGP  -  2 S  to  / 3 t  e x p ( i ( k « r  CJ = 0,  2  2  magnetic  plane  disturbance k j  9  2  s a t i s f y i n g CJ  zero  constant  the  HI  of  mass  gas,  and  is  of  28  with  Taurus  the  gas  values  (Xj)  is  estimate  formed.  agreement  in  to  of  which  Taking  n =l5  for pc  a is  the  the  0  t y p i c a l  warm  obtained.  autocorrelation  complex.  a  given  out  an  spherical  region  of  by  .  417 for  of a  Astrophysics  f u l l  d i s c u s s i o n  II  by of  Bowers  this  and  model,  or  see  45  For  n =15  with  / c m  0  the  our  inconsistent precursor,  notion  In  a  are the  of  of  10" M©,  6  a  somewhat  do  not  such  It  conceivable,  however,  that  wavelength,  and  d i f f i c u l t y  remains  wavelength  has  moving  in  would  a  spacing  collapse  understanding  remained at  at  in  different  the  a  cloud  at how  of  v e l o c i t i e s ,  HI  is  the  f o s s i l with  the are  unstable about  the  as  warm  be  structures  this  with  to  this  inconsistent  which  begin  in  l o n g - l i v e d ,  in  would  appear  that  i n s t a b i l i t y ,  is  consistent  presumably  i n s t a b i l i t y  of  M®,  regions.  demonstrating  notion  appears  10  lengths  Jeans-type  very  of  x  unstable  scale  from  3.5  Jeans  condensations  clumps  to  mass  number  far  structure  out  complex a  with  we  comes  observed  fact,  unstable.  Jeans  this  amongst  While  density  ,  estimated  dispersed  case.  3  a  same  single spacing.  A  f o s s i l  the  seperate  shown  in  Figure  6.  VI. This neutral  work  and  has  complex.  HI  and  column  HI  shell  H  2  around  observed.  The  be  rotating  an  average  of  This  scale  length  i n s t a b i l i t y precursor The cloud for  the  the  time  for to  of  a  length  the  in  The  use  investigated  density  scale  with  of  and  structure.  two  molecular scale  The  of  be  single  were  four  the an  the  two  component  to  v e l o c i t i e s HI. uncovered  data  28  by  pc  sets  scale  of  the  to  a  cloud.  Jeans  correspond  to  This  length a  of  warm  The  in  the  c h a r a c t e r i s t i c  structure to and  present  is  travel  time  l i k e l y a  about  single  is  d i f f i c u l t  to  l o n g - l i v e d ,  " f o s s i l " ,  scale  complex.  dimensional to  the  large  length  Myr), a  2  in  cloud.  for.  (^30  Taurus  found  of a  may  condensation  notion  present of  and  correlated  length  the  each  corresponds  a  of  H  of  approximately  constituents  gas,  such  an  suggests  accounted  persistance for  HI  present  easily  reconcile  cloud  warm  the  not  correlation  a l l  the  those  primarily  length  to  with  Taurus  neither  mixing gas  the  found  with  each  of  the  were  structure  in  of  region  show  than  cloud  approximately  presence  is  higher the  comparison  significant  observed  scale  common  nor  the  d i r e c t i o n s ,  a n a l y s i s ,  length  of  structures  in  of  differences  maps  gas  2  km/sec  trends  recorrelation  i n s t a b i l i t y  H  opposite  s t a t i s t i c a l  analysed.  density  means  constituents  Significant  the  4  two  hydrogen  velocity  in  Average the  provided  molecular  molecular  CONCLUSIONS  correlation  useful drawback  46  for to  techniques  studies such  of  was  molecular  analysis  is  the  47  absence  of  a  simple,  significance The work  by  of  correlation  techniques Kleiner  similar,  similar,  In  prove  in  much  cloud  be  scale  length  observed  such  clouds  or  is  it  may  property cloud. the  of  In  a l l  addition  Taurus  techniques of  the  (or  on  smaller  did  much as  about  much large  complex  this,  complex  revealing  work  to  other  about scale  is  the  scales.  and  could be  be  prove  a  small  structure.  of  other,  learned  It  if  remains  common  a  to  the  Taurus to  study  correlation  studies  scale  to  physical  feasible  using  Such  previous  studied.  unique. is  the  study  peculiar  objects)  the  the  could  the  if  of  work  in  Unfortunately, seen  Taurus  this  useful  particular  molecular  measure  features.  developed  could  objects.  second,  quantitative  are  structure  capable as  this  BIBLIOGRAPHY  Baker,  P . L . , Astronomy  Batrla,  W., Wilson,  L . , Scientific  202,  R . N . , The  McGraw-Hill,  E l i a s ,  J . H . , The  p.  Kleiner,  Astrophysi  cal  1984  p.  Kleiner,  466,  1985  p.  Levinson, 242,  479,  R . L . , The  of  857, 1978.  Massachusetts,  Astrophysi  cal  Journal,  Ast rophysi  cal  Journal,  Ast rophysi  cal  Journal,  II).  R . L . , The  (Paper  F . H . and Brown, p.  Applications,  I).  (Paper  1985  Its  224, P.  Journal,  R . L . , The  S . C . , and Dickman,  295,  Jones and  II,  and  University  (Paper  S . C . , and Dickman,  295,  Lynds,  255,  and  84, 1982.  cs  Transform 1978.  S . C . , and Dickman,  286,  rophysi  New Y o r k ,  Kleiner, S . C . ,P h . D . T h e s i s , 1985.  Kleiner,  J . , Astronomy  246, p.  Ast  Fourier  327, 1976.  1981.  American,  Bowers, R. a n d Deeming, T . , B a r t l e t t , Boston, 1984.  Bracewell,  5_0, p .  Astrophysics,  T . L . and Rahe,  96, p.  Ast rophysics, B l i t z ,  and  III).  R . 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