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UBC Theses and Dissertations

A Study of the 21-cm line in the solar neighborhood Venugopal, Virinchipuram R. 1969

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A STUDY OP THE 21™cm LINE IN THE SOLAR NEIGHBOURHOOD by  VIRINCHIPURAM R. VENUGOPAL M.A., U n i v e r s i t y o f Madras, 1956 M.A., U n i v e r s i t y o f C a l i f o r n i a , 1965  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF , DOCTOR OF PHILOSOPHY i n the Department of PHYSICS  We accept t h i s t h e s i s as conforming required  THE  to the  standard  UNIVERSITY OF BRITISH COLUMBIA May, 1969  In p r e s e n t i n g an the  thesis  advanced degree at Library  I further for  this  shall  the  his  of  this  written  f u l f i l m e n t of  University  of  make i t f r e e l y  agree that  permission  s c h o l a r l y p u r p o s e s may  by  in p a r t i a l  representatives.  be  available for for extensive  g r a n t e d by  gain  permission.  of  7* The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  the  It i s understood  thes,is f o r f i n a n c i a l  Department  British  Columbia  shall  requirements  Columbia,  Head o f my  be  I agree  r e f e r e n c e and copying of  that  not  the  that  Study.  this  thesis  Department  copying or  for  or  publication  allowed without  my  ABSTRACT  Title  of Thesis:  .Supervisor:  A STUDY OF THE 21-cm LINE IN THE SOLAR NEIGHBOURHOOD  '.  DR. V/. L . H. SHUTER  A s u r v e y o f 21-cm l i n e e m i s s i o n a t p o i n t s spaced o v e r t h e e n t i r e  sky v i s i b l e from F e n t i c t o n ,  equally British  Columbia, has been made, and t h e p r o f i l e s o b t a i n e d a t t h e i n t e r m e d i a t e g a l a c t i c l a t i t u d e s have been used t o determine s e v e r a l o f t h e p r o p e r t i e s o f t h e d i s t r i b u t i o n o f the gas i n the s o l a r neighbourhood and t o study t h e dynamics  o f the gas  i n c l u d i n g the d e t e r m i n a t i o n o f s o l a r motion v / i t h r e s p e c t t o gas, t h e d i s t r i b u t i o n o f random v e l o c i t i e s .and the d e p a r t u r e o f gas v e l o c i t i e s from c i r c u l a r  motion.  ii  TABLE OF CONTENTS PAGE ABSTRACT  v  ACKNOWLEDGEMENTS  vi  INTRODUCTION  •  PHYSICS OF THE 21- Cm. LINE  1. ...10  EQUIPMENT AND OBSERVATIONS  19  ANALYSIS AND INTERPRETATION  23  DEPARTURE FROM CIRCULAR MOTION  39  SUMMARY OF RESULTS AND CONCLUSIONS  1+3  BIBLIOGRAPHY  kS  «  iii  LIST OP TABLES  Table I.  P 6 a  The c l a s s i f i c a t i o n of S t e l l a r p o p u l a t i o n s  U-9  e  iv  LIST OF FIGURES  Figure  page  1.  S t r u c t u r e of the Galaxy  50  2.  M e r i d i a n S e c t i o n of the Galaxy through the Sun  51  3.  An i d e a l i z e d p i c t u r e o f the s p i r a l P a t t e r n o f 52  the Galaxy S t r a t i f i e d model r e p r e s e n t a t i o n of the Galaxy i n the s o l a r neighbourhood 5.  P l o t of o p t i c a l depth  (*£ ) a g a i n s t cosec b f o r the  Northern G a l a o t i c Hemisphere 6.  7.  53  5k  P l o t o f o p t i c a l depth (X ) a g a i n s t cosec b f o r the Southern G a l a c t i c Hemisphere  55  T y p i c a l 21-cm. l i n e p r o f i l e s  5&  a) In the d i r e c t i o n of the G a l a c t i c c e n t r e •0 o o  b) At b = 0  t  •£ 15 c*~oL:t20  •i  ACKNOWLEDGEMENTS I wish suggesting provided  t o e x p r e s s my g r a t e f u l  t o me  investigation  t o Dr.W.L.H. S h u t e r f o r  and f o r t h e guidance  the f a c i l i t i e s Penticton,  thanks  a r e due t o D r . J . A . G a i t  f o r making  a t t h e Dominion Radio A s t r o p h y s i c a l  spectrometer,  Observatory ,  t o D r . C . H . C o s t a i n a n d Dr..R.S. R o g e r f o r discussions.  i s a p l e a s u r e t o acknowledge t h e a s s i s t a n c e  members o f b o t h  the t e c h n i c a l  F i n a n c i a l a i d from form  available  t o D r . P . E . A r g y l e f o r p e r m i t t i n g t h e u s e o f t h e 100  a s s i s t a n c e w i t h computer programming and h e l p f u l It  and a d v i c e  d u r i n g the course o f t h i s r e s e a r c h .  My s i n c e r e  channel  this  thanks  o f Graduate  and o f f i c e  the U n i v e r s i t y  Assistantship  staff  g i v e n by a l l t h e  o f the Observatory.  of B r i t i s h  Columbia  i s also appreciated.  i n the  1 INTRODUCTION P r e d i c t i o n and d i s c o v e r y o f 2 1 - c m l i n e , r a d i a t i o n ; The most abundant  element i n the u n i v e r s e i s hydrogen.  I t i s the b u i l d i n g m a t e r i a l of the s t a r s and g a l a x i e s . u n t i l about e i g h t e e n years ago astronomers had not  Yet,  succeeded  i n measuring the n e u t r a l hydrogen content o f the i n t e r s t e l l a r medium of our Galaxy. n e u t r a l hydrogen frequency range.  T h i s was because  i n i t s unexcited state  does not emit any r a d i a t i o n i n the v i s i b l e But today the 21-cm  i s a very important t o o l  r a d i o frequency r a d i a t i o n  t o the astronomer.  on the i n v e s t i g a t i o n s o f Jansky  During a c o l l o q u i u m  (37, 38) and of Reber  (56, 57)  organised by the Nederlandse Astronomen Glub i n I9kk Van de H u l s t (3k)  p r e d i c t e d that I f a hydrogen atom was i n i t s u n e x c i t e d or ' 2 ground s t a t e , d e s i g n a t e d by 1 s*g, the magnetic f i e l d of the proton and e l e c t r o n c o u l d change from p a r a l l e l t o a n t i - p a r a l l e l o r i e n t a t i o n s and a s p e c t r a l l i n e should be emitted at a frequency of lu.20 MHz  and that there appeared to be a good chance of de-  t e c t i n g t h i s t r a n s i t i o n from the v a s t but s p a r s e l y n e u t r a l hydrogen content of the Galaxy.  distributed  Shklovsky (61) on the  b a s i s o f the t r a n s i t i o n p r o b a b i l i t y between h y p e r f i n e components of the ground s t a t e o f hydrogen atom showed that t h i s l i n e s h o u l d have been d e t e c t a b l e i n the g a l a c t i c r a d i o even with the equipment  a v a i l a b l e a t the time.  at Harvard U n i v e r s i t y by the d e t e c t i o n of the 21-cm T h i s d e t e c t i o n was  a few weeks by M u l l e r and Oort (kl)  spectrum  Subsequently  the d i s c o v e r y was made i n 1951 by Ewen and P u r c e l l  g a l a c t i c atomic hydrogen.  spectral  (23 ( a ) ( b ) ) line  from  confirmed w i t h i n  i n L e i d e n and by C h r i s t i a n s e n  2 and Hindman (53)  i n Sydney.  T h i s d i s c o v e r y was  only because t h i s happened t o be the f i r s t  e x c i t i n g not  s p e c t r a l l i n e to be  d i s c o v e r e d i n s o l a r or cosmic r a d i o waves but a l s o because i t opened up a new  field  r e s e a r c h - 21-cm  of astronomical  Astronomy - with p o s s i b i l i t i e s of g r e a t l y extending ledge  of the Galaxy and  t i a l d i s c o v e r y i n 1951  the u n i v e r s e .  line  our know-  In f a c t , s i n c e the  ini-  hydrogen l i n e i n v e s t i g a t i o n s have account-  ed f o r c o n s i d e r a b l e p a r t of the e f f o r t i n r a d i o astronomy. 21-cm  l i n e of n e u t r a l hydrogen was  the o n l y s p e c t r a l l i n e  ed i n cosmic r a d i o waves u n t i l 1963,  when the r a d i o  spectrum at a wave l e n g t h near 18-cm  of the OH  cal  i n i n t e r s t e l l a r space was  The observ-  frequency  (hydroxyl)  radi-  d e t e c t e d by the M.I.T. r a d i o a s t r o -  nomy group u s i n g the 8I4. f t . p a r a b o l i c antenna o f the M i l l s t o n e Hill  Observatory  of L i n c o l n LaboratoryC7o)Sinee  l i n e s - the recombination helium  corresponding  l i n e s - of e x c i t e d atomic hydrogen  to t r a n s i t i o n s i n v o l v i n g h i g h  quantum numbers have been detected The in  I96I4. many s p e c t r a l  i n HII  and  principal  regions.  d i s c o v e r y of t h i s s p e c t r a l l i n e of atomic hydrogen  the ground s t a t e l e d to numerous s t u d i e s of g a l a c t i c s t r u c t u r e ,  p h y s i c s of the i n t e r s t e l l a r medium and hydrogen d i s t r i b u t i o n i n nearby e x t e r n a l g a l a x i e s .  As a necessary  background the c u r r e n t  knowledge of the g a l a c t i c system i s b r i e f l y reviewed General  composition The  here.  of the G a l a c t i c system;  s t r u c t u r e of the M i l k y way  Galaxy) i s shown i n f i g . 1,  and  Galaxy  (or simply,  the  the space d i s t r i b u t i o n of the  p r i n c i p a l o b j e c t s i n the Galaxy i s s c h e m a t i c a l l y i l l u s t r a t e d i n fig.  2,  which r e p r e s e n t s  through the sun.  a meridian  c r o s s s e c t i o n of the Galaxy  I t i s a v a s t wheel shaped system of some  3 hundred b i l l i o n Kiloparsecs. flattened  s t a r s w i t h a diameter that probably exceeds  The mass of the Galaxy i s about 10*° M  shape of the Galaxy i s a consequence  Q  .  30  The  of i t s r o t a t i o n *  The sun, about 10 K i l o p a r s e c s from the c e n t r e out to the r i m , moves a t a speed o f about 250 KMS"^" to complete i t s o r b i t a l r e v o l u t i o n about the g a l a o t i c c e n t r e i n about 200 m i l l i o n y e a r s . At the c e n t r e of the Galaxy, the n u c l e u s , the s t a r s are somewhat c l o s e r t o g e t h e r than they are i n the s o l a r  neighbourhood.  E x t e n d i n g outward from the nucleus and winding through the d i s k of the Galaxy are the s p i r a l arms.  The s p i r a l arms c o n s i s t of  v a s t c l o u d s of gas and cosmic dust - the so c a l l e d medium.  interstellar  I t i s i n the i n t e r s t e l l a r gas and dust clouds of the  s p i r a l arms t h a t s t a r f o r m a t i o n i s b e l i e v e d t o be s t i l l place.  The  sun i s b e l i e v e d to be l o c a t e d i n the l o c a l  taking arm.  In a d d i t i o n t o the i n d i v i d u a l s t a r s and c l o u d s of i n t e r s t e l l a r matter the Galaxy c o n t a i n s many s t a r c l u s t e r s . common are the 'open' or ' g a l a c t i c  1  The most  c l u s t e r s which are l o c a t e d i n  the main d i s k of the Galaxy and are u s u a l l y i n or near s p i r a l arms. Besides the open c l u s t e r s there are over a hundred ters.  These are s c a t t e r e d i n a r o u g h l y s p h e r i c a l  about the Galaxy.  globular  distribution  They form more or l e s s s p h e r i c a l  •corona' s u r r o u n d i n g the main body of the Galaxy.  clus-  'halo' or Mrs. Hogg  (33)  l i s t s p o s i t i o n s , d e s c r i p t i o n s and d i s t a n c e s of the 5li+ g a l a c t i c c l u s t e r s and 119 g l o b u l a r  clusters.  The i n t e r s t e l l a r c l o u d s and the 0 and B type s t a r s , hot super g i a n t s t a r s r e c e n t l y born from them and forming a very t h i n g a l a c t i c l a y e r only 1/100 'extreme  as t h i c k as i t s diameter, comprise  population I objects'.  In a d d i t i o n to the g l o b u l a r  c l u s t e r s the RR Lyrae  s t a r s t h a t are m e t a l poor and extreme sub-  dwarfs have a n e a r l y s p h e r i c a l d i s t r i b u t i o n around the g a l a c t i c centre.  T h i s c l a s s i s c a l l e d the 'halo p o p u l a t i o n I I ' . The  motion of the o b j e c t s b e l o n g i n g in  a way c o r r e s p o n d i n g  the o b j e c t s b e l o n g i n g  t o these  extreme c l a s s e s d i f f e r  to t h e i r difference i n d i s t r i b u t i o n . t o p o p u l a t i o n I move i n almost  While  circular  o r b i t s around the g a l a c t i c c e n t r e the h a l o p o p u l a t i o n I I s t a r s t r a v e l i n elongated the g a l a c t i c p l a n e .  o r b i t s t h a t are o f t e n s t r o n g l y i n c l i n e d t o Some p r o p e r t i e s o f s t e l l a r p o p u l a t i o n s are  l i s t e d i n Table 1. The  youngest s t a r s are those  t r i b u t i o n and motions s t i l l they were born.  The f i r s t  o f p o p u l a t i o n I whose d i s -  i n d i c a t e the s p i r a l arms i n which r e l i a b l e determinations  o f the g a l a c t i c  s p i r a l s t r u c t u r e based on the d i s t r i b u t i o n o f BIX r e g i o n s ing  emitt-  the H°c l i n e and a l s o on the d i s t r i b u t i o n o f 0 a s s o c i a t i o n s i n  the neighbourhood o f the sun was made by Morgan and h i s (u,5, I4.6) a t the Yerkes Observatory (Fig.  3).  colleagues  o f the U n i v e r s i t y o f Chicago.  I t has a l s o been n o t i c e d from s t u d i e s o f the d i s t r i -  b u t i o n of g a l a c t i c c l u s t e r s , Cepheid v a r i a b l e s and B s t a r s of d i f f e r e n t ages o n l y the o b j e c t s younger than about 20 m i l l i o n years are d i s t i n c t l y c o n c e n t r a t e d  i n the arms.  They are s t i l l  near thei r b i r t h p l a c e s wherWthey condensed from the gas; t h e i r o l d e r c o u n t e r p a r t s have had time to wander. the s p i r a l arms are fundamentally  T h i s suggests that  p a t t e r n s o f gas r a t h e r than  stars. I t has been r e c o g n i z e d  t h a t l i g h t from the s t a r s i s not  o n l y reddened and weakened by the i n t e r s t e l l a r gas and dust d u r i n g i t s passage through space, but i t i s a l s o p o l a r i z e d (31# 3 2 ) .  T h i s p o l a r i z a t i o n suggests t h a t something must be  causing  alignment o f the i n t e r s t e l l a r  the r e d d e n i n g . The  grains responsible f o r  The g a l a c t i c magnetic f i e l d i s an obvious  choice.  a s s o c i a t i o n o f a magnetic f i e l d with the Galaxy i s a l s o  suggested by the phenomenon of g a l a c t i c cosmic r a y s , the g a l a c t i c nonthermal r a d i a t i o n and the maintenance o f the g a l a c t i c  spiral  arms. Previous^ 21-cm l i n e s t u d i e s and some important  results:  With the breakthrough t h a t came In g a l a c t i c astronomy i n 1951 by the d i s c o v e r y o f the 21-cm l i n e i n emission  of n e u t r a l  hydrogen much v a l u a b l e i n f o r m a t i o n has accumulated i n extending our knowledge o f the p r o p e r t i e s o f the gas oomponent o f the i n t e r s t e l l a r medium i n the s o l a r neighbourhood as w e l l as the o v e r a l l l a r g e s c a l e s t r u c t u r e o f our Galaxy.  These a r e b r i e f l y reviewed  i n the f o l l o w i n g paragraphs. G a l a c t i c c o n d i t i o n s i n the s o l a r neighbourhood: Basic information has  been o b t a i n e d  l i n e a t 21-cm. (35)  on the d e n s i t y of i n t e r s t e l l a r matter  from the i n t e n s i t y o f the hydrogen  The data obtained  emission  by Van de H u l s t , M u l l e r and Oort  i n d i c a t e a mean d e n s i t y of 0.7 n e u t r a l H-atom/cm* i n the s o l a r  neighbourhood.  Since the 21-cm l i n e may be more n e a r l y  saturated  than has been assumed, and s i n c e the i o n i z e d H-atoms w i l l the mean d e n s i t y s l i g h t l y , the t o t a l mean i n t e r s t e l l a r  increase  gas dens-  i t y i s taken as e q u i v a l e n t t o 1 H-atom/cm*, near the g a l a c t i c plane.  T h i s value accounts f o r only 20$ o f the mass d e n s i t y i n  the g e n e r a l v i c i n i t y of the sun c a l c u l a t e d by Oort  (50, 51)•  About k®% o f the d e n s i t y i s accounted f o r by s t a r s of known type. Roughly molecular  remains u n e x p l a i n e d .  The i n v i s i b l e mass may be  hydrogen and (or) very f a i n t s t a r s .  6 The Lilley  r a t i o of dust to n e u t r a l hydrogen has been shown by  (1±1) to be r o u g h l y constant over l a r g e r e g i o n s but  proportionality f a i l s  the  (8,28), when s m a l l e r r e g i o n s are examined.  Recent work by H e i l e s (27)  has  i n dust clouds i n which 21-cm  shown t h a t OH emission i s expected l i n e e m i s s i o n i s not observed.  The  k i n e t i c temperature of HI i n d i c a t e d by s a t u r a t i o n i n t e n s i t i e s of the 21-cm  l i n e i s 125°  to be a harmonic mean temperature weighted by d e n s i t y . lower  temperatures  (13»11*»55»58,62).  (39)  K which has been p o i n t e d out by Kann Much  have been n o t i c e d i n i n d i v i d u a l gas clouds . The  c e r t a i n at p r e s e n t .  temperature of H I ! r e g i o n s i s v e r y  The  o p t i c a l methods y i e l d a k i n e t i c  a t u r e of 10,000°K, whereas r a d i o recombination  untemper-  l i n e methods g i v e  temperatures around 5000° K. The light  o b s e r v a t i o n s of the angles of p o l a r i z a t i o n of  suggest  t h a t the l i n e s of magnetic f o r c e i n the  solar  neighbourhood are p r e f e r e n t i a l l y o r i e n t e d a l o n g a s p i r a l (31,  32).  The  g e n e r a l p r o p e r t i e s of the gas i n the  star  arm  solar  neighbourhood have been o b t a i n e d from o b s e r v a t i o n s at 21-cm n e u t r a l hydrogen a t i n t e r m e d i a t e l a t i t u d e s . were from the three e x t e n s i v e surveys the M i l k y Way  strip.  Sydney surveys predominantly plane.  The  Carnegie  The  earlier  survey of E r i c k s o n et a l and  of McGee et a l showed that hydrogen d e n s i t y i s h o r i z o n t a l l y s t r a t i f i e d , p a r a l l e l to the  b u t i o n of hydrogen i s a s s o c i a t e d with d i f f e r e n t i a l  6 KmS~^  galactic distri-  galactic  t h a t hydrogen i s f l o w i n g away from the sun at about  i n the d i r e c t i o n s of the g a l a c t i c c e n t r e and a n t i c e n t r e  i n low and medium l a t i t u d e s and i s streaming below.  results  (15,21,22,^3,144) away from  A l s o these surveys have shown t h a t the v e l o c i t y  r o t a t i o n and  of  i n from above and  In c o n s i d e r i n g the v e l o c i t y f i e l d  i n the neighbourhood  of the^ sun the i r r e g u l a r i t i e s i n the d i s t r i b u t i o n o f i n t e r s t e l l a r matter a r e u s u a l l y d e s c r i b e d by the random cloud p i c t u r e with  the cloud about 10 Pc i n diameter with a d e n s i t y o f about 10  atoms/cijl and 8 such clouds p e r K i l o p a r s e c . cloud v e l o c i t i e s i s exponential (1,14.8,65).  Some authors  model and adopting fluctuations.  The d i s t r i b u t i o n o f  with a d i s p e r s i o n o f 7 KmS"  1,  (17,18) suggest abandoning the cloud  a model o f a continuous medium with  Holies  density  (26) h i g h r e s o l u t i o n o b s e r v a t i o n s  1  agree with the •standard  do n o t  c l o u d model'.  R e s u l t s p e r t a i n i n g t o l a r g e s c a l e s t r u c t u r e o f the Galaxy: I t was mentioned above t h a t Morgan and h i s a s s o c i a t e s d e l i n e a t e d by o p t i c a l means the s p i r a l arms i n the s o l a r n e i g h bourhood.  They c o u l d e x p l o r e  only a s m a l l f r a c t i o n o f the Galaxy  because o f the s t r o n g i n t e r s t e l l a r e x t i n c t i o n o f o p t i c a l r a d i a t i o n by the dark o b s c u r i n g m a t t e r that e x i s t s i n the plane o f the M i l k y Way,  The observed g a l a c t i c o b s c u r a t i o n  i s caused by s m a l l p a r t -  i c l e s which a r e b e l i e v e d t o be needle shaped*. The s i z e o f these s m a l l p a r t i c l e s i s very much l e s s than 21-cm, the wave l e n g t h o f r a d i a t i o n emitted by g a l a c t i c n e u t r a l hydrogen, and t h e r e f o r e the p a r t i c l e s have n e g l i g i b l e b l o c k i n g power f o r such r a d i a t i o n .  So,  t h i s 21-cm l i n e r a d i a t i o n from g a l a c t i c atomic hydrogen has been utilized  t o penetrate  the f a r reaches o f the Galaxy and i n d i c a t e  the d i s t r i b u t i o n o f n e u t r a l hydrogen.  Since  the i n t e r s t e l l a r  medium i s c l o s e l y a s s o c i a t e d w i t h extreme P o p u l a t i o n these surveys give a f a i r r e p r e s e n t a t i o n  I stars  of the P o p u l a t i o n  X  s t r u c t u r e o f the Galaxy and have confirmed the s p i r a l nature of the Galaxy.  The s p i r a l p a t t e r n o f the Galaxy was s u c c e s s f u l l y  mapped i n the 21-cm (52).  lia  Galaxy  l i n e surveys of the Netherlands  and A u s t r a -  In s p i t e of t h i s advance i n the knowledge about our  t h a t i t i s a s p i r a l nebula the i d e a s o f the dynamics of  the Galaxy need improvement.  One  o f the very c o n f u s i n g f a c t s i s  t h a t the r o t a t i o n curves o b t a i n e d f o r the n o r t h e r n and hemispheres do not agree i n d e t a i l and map  shows an asymmetry  the g a l a c t i c  between the two h a l v e s .  southern  structure  In o r d e r to  r e c o n c i l e the data of the two hemispheres K e r r (I4.O) i n v e s t i g a t e d the p o s s i b i l i t y of an outward motion equal to 7 KmS"^  o f the  l o c a l standard of r e s t .  suggested  Another  by K e r r on the assumption on a l a r g e s c a l e was from  p o s s i b i l i t y t h a t was  t h a t the Galaxy i s c i r c u l a r l y  symmetric  a g e n e r a l outward motion of the gas away  the g a l a c t i c oentre throughout  the Galaxy.  The  spiral  ern, worked out i n t h i s b a s i s becomes more symmetrical. s t u d i e s have not g e n e r a l l y supported l o c a l standard of r e s t .  Braes  (10)  patt-  But  other  the i d e a of the motion of the tried  to f i n d the  expansion  motion suggested by K e r r , but reached a n e g a t i v e c o n c l u s i o n , and he  concluded  t h a t h i s d a t a p r o v i d e d n e i t h e r proof nor a d e n i a l  of the expansion  law proposed  by K e r r .  The i n v e s t i g a t i o n o f  Weaver (69) p o i n t s out t h a t there are l o c a l i z e d and r a t h e r p e c u l i ar r a d i a l motions,  but  they are d i s t r i b u t e d i n a haphazard  and  clumsy way  over the g a l a c t i c p l a n e .  and  (67) of the s o l a r motion with r e s p e c t to hydrogen has  Shuter  An i n v e s t i g a t i o n by Venugopal  shown t h a t i n the s o l a r neighbourhood t h e r e i s no t i v e motion between s t a r s and gas.  systematic r e l a -  Thus i t i s c l e a r t h a t the  d e v i a t i o n between the r o t a t i o n curves f o r the n o r t h e r n and ern s i d e s i s due  t o l a r g e s c a l e d e v i a t i o n s from  south-  c i r c u l a r motion  9  and  t h a t a smoothly v a r y i n g c i r c u l a r o r b i t model of g a l a c t i c  r o t a t i o n can no longer be used, and t h a t the o v e r - a l l p i c t u r e of gas d i s t r i b u t i o n and motions i s a complex one. Other i n t e r e s t i n g f a c t s  t h a t have come out o f the 21-cm  l i n e s t u d i e s are the 3 Kpc expanding arm, the h i g h clouds i n the i n t e r m e d i a t e  l a t i t u d e s and the c l o u d s a t great  d i s t a n c e s from the plane which suggest  streams o f gas f l o w i n g  toward us from a d i r e c t i o n o f about 1 3 0 ° g a l a c t i c 21-cm  line  studies provide  the Galaxy.  velocity  longitude.  i n f o r m a t i o n on the magnetic f i e l d o f  The p o s s i b i l i t y o f u s i n g the 21-cm h y p e r f i n e  struct-  ure f o r measuring the very weak i n t e r s t e l l a r magnetic f i e l d s by u t i l i s i n g the Zeeman E f f e c t was suggested by B o l t o n and W i l d (9).  The r e s u l t s were n o t c o n c l u s i v e u n t i l v e r y r e c e n t l y when  Verschuur  ( 6 8 ) made a s u c c e s s f u l attempt a t the N a t i o n a l Radio  Astronomy Observatory  and found the e x i s t e n c e o f a f i e l d  o f 20  m i c r o gauss i n a c l o u d i n the Perseus arm and o f the order o f one microgauss f o r a c l o u d i n Orion arm. day  Smith  (6I4.) from F a r a -  r o t a t i o n measurements of P u l s a r CP0950 deduced v e r y  small  fields i n i t s direction. It  should a l s o be mentioned t h a t 21-cm l i n e r e s e a r c h has  been a p p l i e d f o r s t u d y i n g hydrogen d i s t r i b u t i o n i n e x t e r n a l g a l a x l e s , f o r the d e t e r m i n a t i o n ing  o f d i s t a n c e s t o r a d i o sources  includ-  quasars and p u l s a r s and f o r the measurement o f the d e n s i t y o f  the i n t e r g a l a c t i c medium.  10 PHYSICS OF THE 21-Cm. L I N E O r i g i n of the l i n e : In a r e l a t i v e l y narrow f r e q u e n c y II4.2O.J+ MHz. ( A = 21 Cm.) r a d i a t i o n r e c e i v e d from that  origin  frequency tion  by B a r r e t t  of the radio  (3). A b r i e f d e s c r i p spectral  and m o l e c u l a r  line i s  s y s t e m s t h e e l e c t r o n s and n u c l e i  t a k e up o n l y t h o s e m o t i o n s a n d o r i e n t a t i o n s  discrete  set of internal  bound s y s t e m t h e e n e r g y  e n e r g i e s - the energy i s 'quantized' .  that y i e l d levels.  Similarly,  1  a n g u l a r momenta a s s o c i a t e d w i t h  a  In a  the various  the e l e c t r o n s , nucleus  or both  quantized. The  a n g u l a r momenta n e c e s s a r y  s t a t e s o f a n atom a r e : 1) t h e t o t a l momentum  ,  3) t h e t o t a l nuclear  2) t h e t o t a l  electronic  s p i n momentum I  momentum F r : I 4 - J the  The d e t a i l s  below. In atomic  are  T h i s i s due t o t h e  o f the f o r m a t i o n o f the n e u t r a l hydrogen  given  i s double  li4.2O.i4. MHz r a d i a t i o n a n d o t h e r g a l a c t i c  l i n e s a r e reviewed  about  frequency  a t y p i c a l r e g i o n o f the Galaxy  p r o p e r t i e s o f t h e h y d r o g e n atom.  of this  centred  o f the r a d i o  o f adjacent p o r t i o n s o f the spectrum.  inherent  can  the i n t e n s i t y  interval  total  orbital  •  to specify  electronic  electronic  the energy  orbital  s p i n momentum  a n g u l a r momentum , and 5) t h e t o t a l  angular 5  'L+'S* , k) the atomic  angular  From quantum m e c h a n i c s i t i s known  a n g u l a r momentum L  i n v o l v i n g only the azimuthal o f the a d d i t i o n  ,  that  i s g i v e n b y an e x p r e s s i o n  quantum number  The  resultant  may  assume one o f s e v e r a l p o s s i b l e v a l u e s .  ^  , viz  o f two a n g u l a r momentum v e c t o r s Thus f o r a g i v e n  11 value o f L and 3 the p o s s i b l e v a l u e s o f J are L+S, L.+ S - l , L+ S-2, of  |L-S|.  In a s i m i l a r manner the p o s s i b l e values  P can be obtained. Energy l e v e l s i n atoms a r i s e from e l e c t r i c and magnetic  i n t e r a c t i o n s o f the atomic e l e c t r o n s amongst themselves and with the n u c l e u s .  The most important  o f these  interactions  from the standpoint o f Radio Astronomy i s t h a t between the magnetic moment o f the e l e c t r o n and the magnetic moment o f the n u c l e u s , that i s "the h y p e r f i n e energy". of  The e l e c t r o n , because  i t s i n h e r e n t p r o p e r t i e s and because o f i t s motion about the  nucleus, produces a magnetic f i e l d a t the n u c l e u s .  This creates  d i f f e r e n t e n e r g i e s o f the system f o r v a r i o u s o r i e n t a t i o n s o f the n u c l e a r magnetic moment with r e s p e c t t o t h i s f i e l d .  This i n t e r -  a c t i o n always occurs i n atomic system when n e i t h e r the n u c l e a r angular momentum"?  n o r the t o t a l e l e c t r o n i c angular momentum  — *  J  i s zero. 'i  . •  I f the i n t e r n a l energy o f the atom without  • • • •  •".  sion of hyperfine e f f e c t s i s E  0  inclu-  , the t o t a l i n t e r n a l energy  becomes E  ±  Eo"*- M E  ~  E  o — /**! •  where the magnetic i n t e r a c t i o n energy  H  j -  -  -  i s the n e g a t i v e o f the  v e c t o r dot product o f the n u c l e a r magnetic moment j^x magnetic f i e l d due t o the e l e c t r o n •  1  and the  For a hydrogen-like  atom the h y p e r f i n e magnetic i n t e r a c t i o n energy can be expressed in  terms of the quantum numbers F , I , J and L and the p h y s i c a l  c o n s t a n t s by ( 5 , o ) :  "1  where ^ istic  i s the n u c l e a r 'g' f a c t o r which i s c h a r a c t e r -  of a p a r t i c u l a r n u c l e u s and may be p o s i t i v e or  negative^  and  m  mass o f e l e c t r o n  M  mass o f n u c l e u s  oc  f i n e s t r u c t u r e constant =  R  Rydberg constant  Z  i o n i c charge  n  the e f f e c t i v e quantum number o f the hydrogenlike  ^  T  T  e  .  -  = jyL"l£u cl?  7'ZJ73X\0 /.o?737X lo c™' 6  =  level.  T h i s e q u a t i o n r e p r e s e n t s the energy of i n t e r a c t i o n between the magnetic f i e l d o f the e l e c t r o n and the n u c l e a r magnetic moment.  When the n u c l e a r s p i n momentum i s zero —* c o r r e s p o n d i n g t o ' f*"L ~^ /^ X"°>< F - T and goes t o z e r o . However, f o r a g i v e n I and J n o t z e r o , v a r i o u s v a l u e s o f P —>  X  N  —»  are p o s s i b l e c o r r e s p o n d i n g t o d i f f e r e n t o r i e n t a t i o n s o f J —t  r e l a t i v e t o I and the equation y i e l d s d i f f e r e n t v a l u e s of the energy f o r the d i f f e r e n t  orientations.  The t r a n s i t i o n frequency  l)  o f r a d i a t i o n emitted  (or absorbed) i s given by the w e l l known Bohr c o n d i t i o n :  where E  f  and E^^ are the e n e r g i e s o f the f i n a l and i n i t i a l  s t a t e s o f the atom r e s p e c t i v e l y .  T h i s equation a l l o w s the  p r e d i c t i o n of the t r a n s i t i o n f r e q u e n c i e s i f the e n e r g i e s of  13 the  s t a t e s and s e l e c t i o n r u l e s are known.  The atomic h y p e r f i n e  energies of hydrogen are g i v e n by e q u a t i o n 2 above and the selection rule for hyperfine transitions i s A F jumps F=.o t o F=.0 f o r b i d d e n . equivalent to a The state  spin  The 1 — • 0  — ± . 1 , 0 with  t r a n s i t i o n i s then  flip.  frequency o f the t r a n s i t i o n from a s t a t e P + l t o a  F i s given by  From t h i s e x p r e s s i o n the t r a n s i t i o n frequency f o r the hydrogen h y p e r f i n e l e v e l s can be  predicted.  I t i s w e l l known that 1  the ground s t a t e of hydrogen  2.  Sy^ , s p l i t s i n t o two very c l o s e l e v e l s on account of i t s  hyperfine structure,  due t o the mutual i n t e r a c t i o n between the  i n t r i n s i c magnetic, moments o f the p r o t o n and the e l e c t r o n ( y ^ T h e X 1  Sy^  L ~ 0,  s t a t e o f atomic hydrogen i s c h a r a c t e r i z e d S — 3g and J = !},'•  The p o s s i b l e  by n = l ,  v a l u e s o f F are 1 and 0.  This t r a n s i t i o n c a l l e d 'a ' s p i n . f l i p , ' - r e s u l t s i n theielectron, spin f l i p p i n g from a p o s i t i o n p a r a l l e l t o the n u c l e a r s p i n i n the F—1 The  l e v e l t o an a n t i - p a r a l l e l p o s i t i o n i n the F = 0  t r a n s i t i o n occurs between s t a t e s h a v i n g the same L.quantum  number i . e . j The  level.  0 and i s t h e r e f o r e  a magnetic d i p o l e  transition.  l a t e s t value f o r the frequency o f the t r a n s i t i o n i n f r e e  space, a t zero magnetic f i e l d and zero a b s o l u t e temperature i s 114.20,^05, 751.78601: 0.00lj.6HZ. G O . Transition The  probability; p r o b a b i l i t y f o r a spontaneous 1—» 0  given by the E i n s t e i n  A:Coefficient:  transition i s  Ik  A  = a.s5xio"s~' - - - - - - «  -  l 0  ^  €  where /&  i s the Bohr magneton = —  The mean l i f e  —  time of the ' e x c i t e d ' hydrogen  •  ,  lk  gen i n s t a t e F = l ) i s X , s J . - 3 . 5 x 10 0  The reasons f o r such a l o n g l i f e the  line  -20  i 0.92732X10  (since A >e< V  forbidden t r a n s i t i o n  of the hydro-  s e c . o r 11 m i l l i o n y e a r s .  time a r e the low frequency o f  ) and the f a c t  nn  (i.e.  -1.  e r g gauss  that i t comes from a  ( t r a n s i t i o n p r o b a b i l i t i e s f o r magnetic  d i p o l e r a d i a t i o n are of the order o f 10^ times as s m a l l as those f o r e l e c t r i c d i p o l e r a d i a t i o n r e g a r d l e s s o f frequency). The n a t u r a l h a l f w i d t h o f t h i s Sx 1 0 " ^  Hz  •» .  l i n e has the minute value  i n the i n t e r s t e l l a r medium the b a s i c  elemen-  t a r y p r o c e s s e s d e t e r m i n i n g the p o p u l a t i o n o f the h y p e r f i n e l e v e l s are c o l l i s i o n s o f the f i r s t sions o f the f i r s t  and second k i n d s .  In c o l l i -  k i n d a change o f K i n e t i c energy of t r a n s l a -  t i o n i n t o e x c i t a t i o n energy takes p l a c e by c o l l i s i o n .  Collisions  of  the second k i n d i n c l u d e n o t only the exact r e v e r s e o f c o l l i s i o n s  of  the f i r s t  k i n d b u t a l s o a l l o t h e r p r o c e s s e s i n which an atom  or molecule g i v e s up e x c i t a t i o n energy by c o l l i d i n g with another partner.  In e q u i l i b r i u m the number of c o l l i s i o n s of the f i r s t  k i n d per u n i t volume and time e q u a l s the number of c o l l i s i o n s o f the  second k i n d .  Then the p o p u l a t i o n o f the two h y p e r f i n e  1 and 0 "will be g i v e n by Boltzmann's  formula:  2 ^ = 1 ^ where g j  and g  Q  ,  a r e the s t a t i s t i c a l w e i g h t s o f the s u b l e v e l s  given by g= 2 P - » - 1 and T It  levels  s  i s known as the ' s p i n  temperature'.  should not be simply assumed t h a t the s p i n temperature T^ i s  15 equal t o the k i n e t i c temperature T ^ o f the atoms. Field  (Sk)  and F i e l d  (2k)  P u r c e l l and  mcde a c a r e f u l a n a l y s i s o f the v a r i o u s  processes which are competing* t o e s t a b l i s h the r e l a t i v e  popula-  t i o n s of the energy l e v e l s f o r the hydrogen l i n e from i n t e r s t e l l a r space and found  that c o l l i s i o n s are the dominant f a c t o r  in  c o n t r o l l i n g the s p i n s t a t e s and t h e r e f o r e the s p i n temperature  is  e f f e c t i v e l y equal t o the K i n e t i c  temperature.  E q u a t i o n 6 can be r e w r i t t e n a  s  —  ^ * *. T  Further  because the energy d i f f e r e n c e between the two s u b l e v e l s i s so s m a l l ft j~  i s s m a l l (0.0661 K) and the e x p o n e n t i a l above i s  c l o s e t o u n i t y f o r a l l reasonable v a l u e s o f >Xi_ ^ rvo ' to  3.  Since the i n i t i a l  .  Therefore^  s t a t e o f the t r a n s i t i o n g i v i n g  the 21-cm. l i n e i s maintained  rise  i n e q u i l i b r i u m by c o l l i s i o n s  the energy emitted i n t h i s l i n e depends on the i n t e r n a l energy of  the i n t e r s t e l l a r gas which means t h a t the monochromatic  g a l a c t i c r a d i o emission i s thermal. Although  the E i n s t e i n A c o e f f i c i e n t i s very s m a l l f o r  t h i s t r a n s i t i o n and most o f the t r a n s i t i o n s from the upper to the lower s t a t e are r a d i a t i o n - l e s s as a r e s u l t o f c o l l i s i o n s of  the second k i n d , y e t because o f the v a s t number o f hydrogen  atoms i n the g a l a c t i c d i s k the hydrogen l i n e from the i n t e r s t e l l a r medium c o u l d be d e t e c t e d . The  f o r m a t i o n o f Emission and A b s o r p t i o n  lines:  E q u a t i o n of T r a n s f e r f o r the 21-cm. l i n e : Let  us f i r s t  c o n s i d e r the t r a n s f e r o f r a d i a t i o n  any l i n e o f s i g h t p a s s i n g through  along  some assembly of atoms.  Let  the volume c o e f f i c i e n t s o f a b s o r p t i o n and emission i n the frequency  element  ( ~y)^ }) •j-cL'i) ) at the p o i n t i n the l i n e o f  16 s i g h t at d i s t a n c e S from the observer be K respectively.  Then the s p e c i f i c  ( l ) ) and J  i n t e n s i t y , I ( i) ) dU)  the r a d i a t i o n at any p o i n t i s g i v e n by the equation  ^£>L  of t r a n s f e r :  7  s o l u t i o n to t h i s can be obtained from an elementary a n a l y s i s .  Since the i n t e n s i t y at any p o i n t S and  a given d i r e c t i o n  f r o m ^ h e emission at a l l p o i n t s beyond S, reduced Q. o we  , of  -JL*) -kooica) -  cts  The  (  by the  results factor  to allow f o r the a b s o r p t i o n by the i n t e r v e n i n g matter  can w r i t e  A XO>)  = \ JOI) e °  0L6  S  o  f o r the i n t e n s i t y of the emergent r a d i a t i o n . s i t y i s u s u a l l y expressed T^OO  The  observed  i n terms of the b r i g h t n e s s  which i s g i v e n by the Rayleigh**Jeans T O>j=XCff^  inten-  temperature  formula:  b  Here ' i l ' i s the Boltzmann's  constant.  The r a t i o of the emission and a b s o r p t i o n c o e f f i c i e n t s can w r i t t e n as f o l l o w s by the P l a n c k - K i r c h h o f f '  = ~rkr  Cor)  Jw=  be  law: ^ T . K  W)  10  where T r e f e r s to the s p i n temperature which i s equal to the kinetic  temperature  T h e r e f o r e , we  obtain  * where T O O  here. oo  4  j, °  - \ K O ) c U ' i s the o p t i c a l depth and  J  n  o  T'OO  i s the  o p t i c a l depth of the whole Galaxy i n a g i v e n d i r e c t i o n . k i n e t i c temperature of the whole Galaxy i s constant,  then  I f the  17  =TO-e ' )  T t»  T h i s i s the g e n e r a l r e l a t i o n f o r an emission The  presence  o f continuous  Absorption l i n e  iz  r C5,)  b  line.  spectrum:  formation:  T h i s means t h a t we should i n t r o d u c e the continuous r p t i o n and e m i s s i o n c o e f f i c i e n t s K|(>>)and J) Now  abso-  f o r the continuum.  the e q u a t i o n o f t r a n s f e r becomes:  = JCV))-r-JiC^-lj<^)-t-K Cv)]lC5')--/3 l  As b e f o r e we g e t :  T  oo  = f^jxf \jW  B  +310)]  »v  e*f>{-j  [ K W + M ^ *  o ^ o and f o r the r e g i o n i n the continuum adjacent t o the r a d i o l i n e , J  where T O O  8111(1  k(v|)are equal t o zero,  T  ^  J l , OO e x f > y k , C » ) ^ j «u — -1«-  fc  The  14.  galaxy can be c o n s i d e r e d t r a n s p a r e n t f o r decimetre  r a d i o waves  i n the continuum; so, e q u a t i o n 15 becomes 2.  oo  A l s o , i n the r e g i o n o f the 21-cm. l i n e  K. O0.)^>  | C^) •  So e q u a t i o n II4. can be w r i t t e n a s :  o  U s i n g equations 12 and 16 i n 17 we have  ----17  T (?) - T Ij - exj, C-Tfr))! + | <ext>(-tW)). b  b  /3  18 The d i f f e r e n c e  i n b r i g h t n e s s temperature  between d i f f e r e n t p o i n t s  on the l i n e p r o f i l e and the continuum w i l l be equal t o :  AT = T £/ - o»f, c - r  -T f}- <«*K-rc*>)>] ----/<? b  to be o f the same o r d e r . I t i s e v i d e n t from the above that the r e l a t i v e s i z e o f T  and T^ determine  whether there w i l l r e s u l t an emission l i n e , no  l i n e o r an a b s o r p t i o n l i n e . I f hydrogen a b s o r p t i o n i s observed by d i r e c t i n g the antenna to a continuum source of s m a l l angular  diameter:  whereTOO*  -Q_g  8  th® effective  o p a c i t y spread over  beam angle and TgGtythat P  a r t  c o n f i n e d to - T L  S  , the  , the source  solid  angle.  The observed p r o f i l e i s g i v e n by  A T '0i>) - A T 7 J ) - 7 A 0 - 6 where A T C " ^ )  — ~ 0  —  g.'^^)  From the observables AT(^>)) A T  C  * 3 }  ZX  I s the expected p r o f i l e . 8  1  which i s of v e r y great a s t r o n o m i c a l  1  1  (  5  we can ' g e t T ^ ^  interest.  A b s o r p t i o n measurements p r o v i d e a technique f o r studyi n g i n d i v i d u a l hydrogen c l o u d s , f o r the angular diameter radio stars  of the  i s t y p i c a l l y a few minutes o f a r c so t h a t only a  narrow p e n c i l of r a y s j o i n s the source to the e a r t h , and the few clouds through which t h i s p e n c i l c u t s can u s u a l l y i n depth by t h e i r d i f f e r i n g D-oppler s h i f t s .  be aeperated  19  EQUIPMENT AND  OBSERVATIONS  A survey of n e u t r a l hydrogen of the whole sky from P e n t i c t o n has  visible  been undertaken i n o r d e r to o b t a i n a  catalogue  of p r o f i l e s spaced 5°arc apart i n the sky w i t h the p o i n t s surveyed  given i n the new  the completion  system of g a l a c t i c c o - o r d i n a t e s .  On  of the survey p a r t of the c o l l e c t e d data was  to determine s e v e r a l of the p r o p e r t i e s o f the nearby gas,  used  to  d e s c r i b e the s p a t i a l d i s t r i b u t i o n of random v e l o c i t i e s of n e u t r a l hydrogen i n the s o l a r neighbourhood f o r which there was ious information.  T h i s p r o j e c t forms the  A l s o , an a n a l y s i s of the departures  prev-  s u b j e c t of Chapter  IV.  of the v e l o c i t i e s of nearby  gas from c i r c u l a r motion i s presented ent chapter  no  i n chapter  V.  In the  a b r i e f d e s c r i p t i o n of the equipment used and  pres-  the  o b s e r v a t i o n s made i s g i v e n . The and  observations  September 1967,  line f a c i l i t i e s tory, Penticton w i t h a new  u s i n g the 2 5 . 6 metre p a r a b o l o i d and  filter  The at  spectrometer  and  constructed  a h a l f power  21-cm. i s e q u a t o r i a l l y mounted, and  A=  are p o s s i b l e .  Any  observed d i r e c t l y , and  cated by  designed  25*6 metre antenna which has  l o c a t i o n i s f a r enough south o  can be  the 21-cm.  =  100 channel  beam width of 3 6 '  ation -30  i n August  (J4.2) of the Dominion Radio A s t r o p h y s i c a l Observao o (longitude —119 37' W, l a t i t u d e I4.9 19' N)  by Dr. P.E.Argyle.  its  d e s c r i b e d here were obtained  that observations  p a r t of the  down to d e c l i n -  sky v i s i b l e at the  The  site  the t e l e s c o p e p o s i t i o n i s i n d i -  synchronous r e p e a t e r s r e a d i n g d e c l i n a t i o n , r i g h t  s i o n and hour angle.  at  telescope can.track  r a d i o frequency  ascen-  i n hour angle  the s i d e r e a l r a t e .  The  p r e a m p l i f i e r i s an  ron beam parametric  a m p l i f i e r (Adler tube ) s i m i l a r to the  at electone  20 d e s c r i b e d by A d l e r , Hrbek and Wade ( 2 ) , and i s operated i n the nondegenerate mode f o r h y d r o g e n - l i n e  s t u d i e s with the s p e c t r o -  meter. The hundred channel r a d i o frequency around a commercially filter width.  produced  system c o n t a i n s 100  '"contiguous  crystal filters,  The band edges of adjacent f i l t e r s  t o t a l band width of the system i s 1 MHz. designed that the frequency  spectrometer  is built  comb f i l t e r " .  This  each of 10 KHz.  band  c o i n c i d e , so t h a t the The  filters  are  so  components of s i g n a l not passed by a  f i l t e r are r e f l e c t e d so t h a t they are a v a i l a b l e as i n p u t s i g n a l to  other f i l t e r s ;  i n o t h e r words, the f i l t e r s  do not a c t as s h o r t  c i r c u i t s to f r e q u e n c i e s they do not t r a n s m i t . i s made i n f r o n t o f the contiguous f i l t e r ,  A l l amplification  thus a v o i d i n g the pro-  blem of m a i n t a i n i n g u n i f o r m g a i n i n one hundred independent amplifiers.  The c e n t r e frequency  the l a s t i n t e r m e d i a t e frequency  of the hydrogen r e c e i v e r .  standard i n t e g r a t i o n time used i n the spectrometer Two  i s 60  MHz.,  The  seconds.  banks of i n t e g r a t i n g c a p a c i t o r s are used so t h a t one bank can  be used while the other i s b e i n g charged. is  i s 10.7  of the spectrometer  l o s t d u r i n g read out  •  Thus no o b s e r v i n g  time  Read out of a bank of c a p a c i t o r s i s done  with a 'binary read out t r e e ' of r e e d  switches.  The  resultant  v o l t a g e s are read by a d i g i t a l v o l t m e t e r which then commands the card punch to r e c o r d the 3 d i g i t number j u s t produced. are punched on f o u r IBM  c a r d s , w i t h the f i r s t  These  data  columns of each  card  b e i n g used f o r s e r i a l number or some i d e n t i f i c a t i o n . The o v e r - a l l o system n o i s e temperature was about 250 K. o The p r o f i l e s were obtained a t p o s i t i o n s 5 ar«c apart a l o n g o c i r c l e s of l a t i t u d e a t i n t e r v a l s of 5 • The l o n g i t u d e i n t e r v a l  21 corresponding  t o t h e l e n g t h A S ( = 5°  ) of a circle  o was c a l c u l a t e d f r o m t h e r e l a t i o n the n e a r e s t expressed (7)«  degree.  i n t h e new s t a n d a r d  In a l l , o v e r  sky  visible  prepared for  from  Berkeley the  Penticton.  profile  velocities  of rest  system o f g a l a c t i c  The b r i g h t n e s s  X =  c o v e r i n g the e n t i r e  207°,  i s being calibration  observations 4  - -15°  o f the f o r which  a s 6 2 ° K.  o f h y d r o g e n g a s were r e f e r r e d t o t h e l o c a l  ( l . s . r . ) which r e q u i r e d that the observed  o f Hydrogen i n the v i c i n i t y  (67) t h a t i n t h e v i c i n i t y  radial  produced by the e a r t h ' s  o r b i t a l motion and f o r t h e m o t i o n o f t h e sun w i t h  shown  co-ordinates.  temperature  v e l o c i t i e s be c o r r e c t e d f o r D o p p l e r s h i f t s  mean v e l o c i t y  (b) a r e  of profiles  from repeated at  p e a k i n t e n s i t y was t a k e n  standard  and r o u n d e d o f f t o  ( 1 ) and l a t i t u d e  The c a t a l o g u e  was o b t a i n e d  calibration  The  Cbftb  1200 p r o f i l e s were o b t a i n e d ,  f o rpublication.  the p r o f i l e s  AS  A4> = — r  The l o n g i t u d e  of latitude  respect  o f the sun.  o f the sun there  t o the  I t has been  i s no a p p r e c i a b l e  d i f f e r e n t i a l m o t i o n b e t w e e n t h e n e u t r a l h y d r o g e n and t h e s t a r s ; so in  the r e d u c t i o n o f the observed  velocities  to l . s . r .  i n this sur-  _ vey  the standard  i-Q  s o l a r motion  tr 56°.2, B ® ^ - f - 2 3 . 2 ° ,  -1  (19) d e f i n e d by o © ~  K=  0.0 KmS  1  20.0 KmS ,  was u s e d .  In the c o r r -  e c t i o n f o r the o r b i t a l motion  o f the e a r t h the e c c e n t r i c i t y ( e ) ,  the mean l o n g i t u d e o f p e r i g e e  ( P )  tic  ( £ ) and t h e mean l o n g i t u d e  these tory  are calculated using  o f the e c l i p -  o f t h e s u n ( L ) a r e i n v o l v e d , and  the expressions  Supplement t o t h e Ephemeris The  , the o b l i q u i t y  profile s of brightness  given  i n the Explana-  (1961). temperature versus  radial  velo-  c i t y were a u t o m a t i c a l l y p l o t t e d a t t h e U n i v e r s i t y o f B r i t i s h Columbia  computer c e n t r e .  The o o - o r d i n a t e s  t o which each  profile  22  refers  were i n d i c a t e d  i n the top r i g h t hand c o r n e r .  The data from the p r o f i l e s of the i n t e r m e d i a t e l a t i t u d e zones were used f o r the f o l l o w i n g s t u d i e s of hydrogen i n the s o l a r vicinity: i)  Kinetic  temperature?,  i i ) d i s t r i b u t i o n of random motions  and i i i ) departures of v e l o c i t i e s from c i r c u l a r motion. are  d e s c r i b e d i n the next two c h a p t e r s *  These  23 ANALYSIS AND T h i s p r o j e c t was being ties  able  to d e s c r i b e the  no  It this to  undertaken with  of n e u t r a l hydrogen  t h e r e was  previous  spatial  i n the  soon became c l e a r  solar  a mean d i s t a n c e and  The found that  t o be the  solar  the p r o c e d u r e  reference the  v i c i n i t y o f the  ved  radial  standard the  local  velocities  solar  standard  city the  velocity  Thi3  from local  o f HYDROGEN i n t h e assumption i m p l i c i t  for  was (67)  s o l a r motion  determination undertaken  of  sola  earlier,  here.  standard  the mean v e l o c i t y  f o r the e a r t h ' s  ,of g a l a c t i c  assigned  21-cm. p r o f i l e s  This i s achieved  the  Galaxy  that  Observations:  with  of r e s t .  of  profiles.  standard  determined  motion(19)-  so  to n e u t r a l hydrogen  used.  r e s p e c t to the  sun.  l o c a l hydrogen i n the radial  observed  adopted i s d e s c r i b e d b r i e f l y  frame t r a v e l l i n g  respect  distribution  c o u l d be  t o n e u t r a l h y d r o g e n was  with  veloci-  motion with  t h a t the  velocity  respect  c o u l d be  Radial velocities specified,  solar  obey a s i m p l e m o d e l ,  of each of our  S o l a r M o t i o n f r o m 21-cm. l i n e  mally  the  s u f f i c i e n t l y c l o s e to the  respect  o f random  .  neighbourhood  value  objective of  neighbourhood, f o r which  the r e q u i r e m e n t  motion with  standard  motion with  distribution  of  hence r a d i a l  the h y d r o g e n e m i s s i o n  principal  t h a t the main p r e r e q u i s i t e s f o r  s t u d y were a d e t e r m i n a t i o n  h y d r o g e n i n the  the  solar  information  n e u t r a l h y d r o g e n and  and  INTERPRETATION  by  would  v i c i n i t y of i n the  of the s t a r s i n  the  sun  for  the  respect  to  21-cm. l i n e  studies  of  wish t o s p e c i f y  th  respect  sun,  and  ob3er  with  normally  hydrogen with  (12),  c o r r e c t i n g the  o f the  B e c a u s e i n the one  of r e s t  o r b i t a l motion,  velocity  are nor  one  above p r o c e d u r e  to  t h e mean  must  (73)  veio  recognize  that  there i s  2k no  systematic  d i f f e r e n t i a l m o t i o n between  and  stars.  In our i n v e s t i g a t i o n s  the  d i f f e r e n t i a l motion  by m e a s u r i n g hydrogen. method the  i s similar  commonly u s e d i n o p t i c a l  cation of  o f t h e sun w i t h r e s p e c t  technique used  s o l a r motion  from  i s required  respect  because  measured and  may  be  t o the  f o r d e t e r m i n a t i o n of  i n t h e 21-cm. l i n e c a s e  i s not usually  stars  t o the n e a r b y  in principle  astronomy  observed r a d i a l v e l o c i t y  t o the Sun  hydrogen  s t e l l a r r a d i a l v e l o c i t i e s , but  the o b s e r v e d h y d r o g e n The  have i n e f f e c t  between t h e n e a r b y h y d r o g e n  the v e l o c i t y  The  we  the nearby  a modifi-  the  distance  known.  of nearby hydrogen  r e p r e s e n t e d by  gas  with  the f a m i l i a r e q u a t i o n  ( 6 6 a-)  V  n  -  K  _SoC*s&©C0s£ccrS(^-L )~S $^&©S^& 0  -fwhere  'K'  respect tic  i s a c o n s t a n t term,  t o t h e mean v e l i c i t y  co-ordinates  radial  velocity  observed  o f hydrogen,,  2,3 o f the sun w i t h ,, B  0  o f the observed hydrogen  CoS^Qr  resulting  The  > represents  Si«.xtr  t h e gas  s i n 3,l> since  0  last  t  are the  galac-  -Ir  the  being independent  are  g a s ; and  the c o n t r i b u t i o n  about  the g a l a c t i c  S i n c e 'r,' (  the  1  ?  and h e n c e  on axis,  o f the distance  o b s e r v e d i s n o t w e l l - known;, , t h e o b s e r v a t i o n s to l o n g i t u d e s  to  rotation  o f the v e r t i c a l ^ d i s t a n c e plane.  A  term i n the  from d i f f e r e n t i a l g a l a c t i c  gas f r o m t h e g a l a c t i c  restricted  the  Sg, i s t h e s p e e d  simple h y p o t h e s i s of c i r c u l a r motion  t h i s motion  to  5^xL  Oort constant f o r r a d i a l v e l o c i t y .  above e q u a t i o n , / \  the  Ooi^ir  c o - o r d i n a t e s o f t h e apex o f s o l a r m o t i o n , yy,^ L  heliocentric the  An.  o  were  0 ° , 9 0 ° , 1 8 0 ° and 2 7 0 ° , f o r w h i c h  t h e term/^GosH-SCtii&fc v a n i s h e s .  Further,  t h e above e q u a t i o n i s o n l y v a l i d f o r ' r ' "small' compared  distance  from t h e  sun t o t h e g a l a c t i c  centre,  the o b s e r v a -  to  25  tions were confined to intermediate latitudes where, due to the thinness of the galactic disk the condition i 3 f u l f i l l e d . Two independent p r o f i l e s at each of the following 22 positions were obtained and used i n the analysis.  Co-ordinates of the p r o f i l e s used i n the analysis  1  b  0°  +20°,  +25°,  +30°,  +35°,  +k0°,  +U5°.  90°  -20°,  -25°,  -30°,  - 3 5 ° , -1+0°,  -1,5°.  180°  -20°, -25°,  -30°,  - 3 5 ° , -1+0°,  _I*5°.  270°  +30°,  +k0°,  +1*5°.  +35°,  Radial v e l o c i t y T averaged over brightness temperature for each p r o f i l e defined as  \7 = f V u ( v ) c t v / r ^ with the l i m i t s of integration V-^ aryl V  2  u  taken as the v e l o c i t y  values at which the 21-cm. brightness^ temperature T^_ (V)  was 10%  of i t s maximum value, was determined with an'accuracy of  •£ 0 . 3  -1  KmS  *  ''  . These v e l o c i t i e s were referred to t he sun using tables ( 3 0 ) ,  and the r e s u l t i n g r a d i a l v e l o c i t i e s , elements of solar motion S  Q  '', L  0  w e r e used to obtain the  ' , B  Q  , and K  by means of a  least squares solution of the equation  '  ,  —  5 G - S ^ W 6>©5uyv ir-  --[  The elements of solar motkon'relative/to neutral hydrogen obtained in,.this i n v e s t i g a t i o n , with their probable errors, are  26 SQ  —  2 1 . 1 -+:  L  -  14-9°.2 ± 8°.9  -  2k°.l  B  Q  Q  K  -  ±  1 . 3 KmS*  1  13°.7  -0.8 ±  0 . 7 KmS*  1  T h e r e i s no s i g n i f i c a n t d i f f e r e n c e between our r e s u l t s and the standard s o l a r motion given below f o r comparison: ~=z  20.0  B  -  23°.2  K  s  0 . 0 KmS  S  &  0  KmS"  1  -1  Thus our r e s u l t s i n d i c a t e t h a t i n the v i c i n i t y o f t h e sun there, i s no a p p r e c i a b l e  d i f f e r e n t i a l motion between the n e u t r a l  hydrogen and the s t a r s , and a l s o that no s i g n i f i c a n t introduced  i n 21-cm. l i n e work by u s i n g  to c o r r e c t observed r a d i a l v e l o c i t i e s  errors are  the standard s o l a r m o t i o n  t o the l o c a l standard o f r e s t .  Besides the d e t e r m i n a t i o n o f the s o l a r motion with r e s p e c t to n e u t r a l hydrogen we r e q u i r e  f o r our a n a l y s i s o f random motions  that the hydrogen d i s t r i b u t i o n i n the s o l a r v i c i n i t y be capable o f b e i n g described Murray  r e a s o n a b l y w e l l by a simple model.  McGee and  (b,3) concluded from t h e i r low r e s o l u t i o n sky survey of  n e u t r a l hydrogen t h a t the l o c a l d i s t r i b u t i o n i s s u b s t a n t i a l l y horizontally stratified  i n d e n s i t y , with a number o f concentra-  t i o n s o f gas embedded i n i t . We, t h e r e f o r e ,  t e n t a t i v e l y adopt t h e  model t h a t the hydrogen d e n s i t y i s a f u n c t i o n o n l y  of Z ,  distance  to t h e c e n t r a l  from the sun i n a d i r e c t i o n p e r p e n d i c u l a r  plane o f the g a l a c t i c d i s k .  the  T h i s model can be t e s t e d i n a simple  27 way.  Referring  parallel and Z Q  t o f i g u r e l±,  we  suppose t h a t  t o t h e c e n t r a l p l a n e o f t h e G a l a x y G, respectively  f r o m S , the p o s i t i o n  p o i n t s a t w h i c h the a v e r a g e h y d r o g e n vicinity  o f the sun.  density  as r e q u i r e d  depth 1 T  0  and  assume Z  ( -z.  'r»  Z  the p r e s e n c e o f 21-cm. l i n e  we  cosec b  0  include  i s half  and  and  the o p t i c a l  the k i n e t i c  o f t h e gas  temperature  is  i n the d i r e c t i o n  the o p t i c a l  depth  C  r  -r'  to each element.  From t h e above e q u a t i o n we  C60JL-  r  -  r  .  ,  obtain  o  optical  G r f e c Lr  optical  adopted)  temperature  T|  C  follows:  a l o n g a r a y , the  o f any r a y i s g i v e n by  o f i s o t h e r m a l homogeneous gas o f t e m p e r a t u r e ness  in  T^_ o b s e r v e d a l o n g  i s o b t a i n e d as  A d d i n g a l l the e l e m e n t a r y c o n t r i b u t i o n s brightness  i n the  write  line  depth X "  D  To a l l o w f o r  of the Galaxy  the  and  Z  the g a l a c t i c h a l o ( o r  r e l a t i o n between the b r i g h t n e s s temperature at l a t i t u d e b  p'  through  stratified  cosec b.  Q  The  of s i g h t  that  ) c o r r e s p o n d s t o an  emission from  a c o n s t a n t term  distances  c o r r e s p o n d s t o an  c  the i n a d e q u a c y o f t h e s i m p l e p i c t u r e may  and  I f the gas i s h o r i z o n t a l l y and we  p l a n e s P and  o f the sun, pass  density  , t h e n the m o d e l r e q u i r e s T T ~ X  depth  for  two  -hX  For a thick T^ and  optical  layer thick-  28 T h e r e f o r e from  (26) and (29)  T Therefore, the  =.  i f t h e gas d e n s i t y  correct  - % cc&c (r -t-Tn  Iky^^  i s horizontally  c h o i c e o f T^ i s made, a p l o t  3o  stratified  o f t vs cosec b based  on t h e o b s e r v e d -6-o^Al^is e x p e c t e d t o b e a s t r a i g h t effect If  T  k  o f an i n c o r r e c t i s chosen  c h o i c e o f T^ c a n e a s i l y be  too h i g h the p l o t  t u d e s where t h e o p t i c a l  line.  The  predicted.  w o u l d c u r v e down a t l o w  d e p t h becomes a p p r e c i a b l e ;  T^ were t o o l o w t h e p l o t  and i f  lati-  similarly, i f  would c u r v e upward a t low g a l a c t i c  lati-  tudes. In profile  this  analysis  i n the l a t i t u d e  t h e peak b r i g h t n e s s temperature  r a n g e + 10° t o •+- J4.O was o b t a i n e d and t h e 0  mean b r i g h t n e s s t e m p e r a t u r e  around  t u d e was d e t e r m i n e d  v a r i a t i o n s with g a l a c t i c  were a v e r a g e d  so t h a t  over.  o f each  each  circle  of galactic  lati-  longitude  U s i n g t h e s e mean v a l u e s o f T^_, v a l u e s o f T  were c a l c u l a t e d f o r assumed v a l u e s o f T of X  and  II4.O K, and g r a p h s  ern  and s o u t h e r n g a l a c t i c h e m i s p h e r e s  0  o f 80° K, 100° K, 120° K,  k  v s c o s e c b were p l o t t e d separately.  f o r the n o r t h -  These  plots are  shown i n F i g u r e s 5 a n d 6 . It kinetic  i s seen t h a t  temperature  best f i t t i n g around  a linear  o f 120° K.  straight  line  A least  i s obtained for a  squares s o l u t i o n  was t h e n made f o r v a r i o u s  f o r the  temperatures  120° K, i . e . , f o r 110°, 120°, 130°, and II4.O K, and t h e 0  c o r r e s p o n d i n g v a l u e s o f t o and of  relationship  , "£  2>  0  and T H w h i c h  were f o u n d .  That  combination  gave t h e minimum r e s i d u a l  - LuU-^O-e .  )\  3/  29 (where n i s the number o f T^, values considered i n each p l o t ) was taken as the best r e p r e s e n t a t i v e values of T , T a n d f k  D  •  w  R e suIts and D i s c u s s i o n : The f o l l o w i n g v a l u e s were o b t a i n e d : Northern g a l a c t i c hemisphere  T  k  —  Southern  T  k  _  g a l a c t i c hemisphere  120°K, 1 2 0  o  *T := 0.07,TT ^0.05. 0  H=  0  K #  . 8,T --0.01. 0  H  Mean values with t h e i r estimated e r r o r s a r e : T  120°  -jr 1 5 °  0.08  ±  0.01  -r-0.03  ±  0.01  -  k  <TT o  T The value of T^ ~  H  120°  with the u s u a l l y adopted  K  K obtained i n t h i s study i s i n agreement Leiden value  (71)•  The o p t i c a l depth from the sun to the h a l f d e n s i t y p o i n t s of the g a l a c t i c d i s k i s T o r : 0 . 0 8 , f u r t h e r i n the next  and t h i s value i s c o n s i d e r e d  section.  The n e g a t i v e value f o r T" ( =. — 0 . 0 3 ) H  suggests  there i s  no a p p r e c i a b l e n e u t r a l hydrogen emission from a d i s t r i b u t i o n with s p h e r i c a l symmetry about the sun, and can be accounted assuming t h a t the value of X  0  immediately  f o r by  above the sun i s s l i g h t -  l y l e s s than the average vallue at p o i n t s around the 3 u n . r e s u l t appears to be i n accordance of s t a r s near the sun  (20).  This  with the g e n e r a l d i s t r i b u t i o n  Since the value of T  w  was  derived  by a v e r a g i n g over a l l g a l a c t i c l o n g i t u d e s , i t i s not p o s s i b l e from t h i s r e s u l t to comment on whether n e u t r a l hydrogen emission from  the g a l a c t i c h a l o has been observed,  although t h i s could  be deduced by f u r t h e r a n a l y s i s of our b a s i c data.  30 D i s t r i b u t i o n o f Random Motions (a)  Technique and A n a l y s i s In order t o i n v e s t i g a t e  the d i s t r i b u t i o n o f random  motions i n nearby hydrogen "gas the axes o f the v e l o c i t y e l l i p s o i d and t h e i r d i r e c t i o n s were determined a c c o r d i n g to the f o l l o w i n g procedure. The b r i g h t n e s s temperatures, T. , of each p r o f i l e were converted to o p t i c a l depth v a l u e s , X derived  above, and the r e l a t i o n T = .  • using T  —  k  120°K  In T ^ / ^ - T ) . From the f e  p r o f i l e s o f c v s r a d i a l v e l o c i t y V, the mean v e l o c i t y "V ^ •'  (with the l i m i t s o f i n t e g r a t i o n V, and V  P  ta$en as the v e l o c i t y  v a l u e s at which the 21 cm. b r i g h t n e s s temperature T ( V ) was b  10$ o f i t s maximum v a l u e ) were c a l c u l a t e d Our aim i n t h i s study i s I n i t i a l l y dispersion  can be d e r i v e d  from  °~Z^t)  34-  i n e q u a t i o n ( 3 3 ) i s obtained from t h e  p r o f i l e s , end c r ^ , ^ dispersion  This  - ^Xx —C°^t ^ ^l^aJL*  where or -, d e f i n e d ¥a  to determine the  i n each o f the hydrogen p r o f i l e s a t t r i b u t a b l e to  random motion and t u r b u l e n c e o". r the r e l a t i o n  ^  f o r each p r o f i l e .  t  h  e  r  m  &  1  and o j -  n a t  a r e r e s p e c t i v e l y the  produced by d i f f e r e n t i a l g a l a c t i c r o t a t i o n , by  thermal broadening, and by the instrument pass band. We c o n s i d e r now the d e r i v a t i o n  o f the l a t t e r  3 quantities.  31  A c c o r d i n g t o the theory of d i f f e r e n t i a l g a l a c t i c  rotation  the mean r a d i a l v e l o c i t y i s given as ^obs-  A  r  S  i  n  2  1  c  o  s  2  ° " " ^p t  (  35*  )  f o r s m a l l h e l i o c e n t r i c d i s t a n c e s , where r i s the mean d i s t a n c e of the e m i t t i n g hydrogen, A i s the Oort'constant v e l o c i t y and "V  for radial  i s the mean value o f the p e c u l i a r r a d i a l  The mean d i s t a n c e i s r — o  velocity.  cosec b, where z^ i s the mean h e i g h t o c  of the e m i t t i n g hydrogen from the plane c o n t a i n i n g the sun. Therefore V . „ —  Az„ S i n 21 cosec b cos b  3&  2  O  ODS  where the term Vp i s b e i n g d i s r e g a r d e d f o r the mement.  Thus  value A z from a l l the p r o f i l e s was c a l c u l a t e d . With t h i s from each p r o f i l e a value o f A x was o b t a i n e d , and the mean o  e  value Az~" the t h e o r e t i c a l mean v e l o c i t y that the gas should o have i n each d i r e c t i o n o f o b s e r v a t i o n was computed from V  t n  "Z. A z  s i n 21 cosec b cos b 2  Q  —-37  Then a l i n e a r r e l a t i o n s h i p V ^ — * C V ^ - v was c o n s i d e r e d , 0  g  n  p  and  the v a l u e of <K found  f o r which  e a s i l y be shown t h a t the constant peculiar velocities V , V tends  to z e r o .  the value A z  Q  X.v  was a minimum.  i n d i c a t e s the nature  I t may of the  I f 0(-=r 1 the mean of a l l the values  I f o< d e v i a t e s from 1 the mean i s non-zero, and  must be c o r r e c t e d to<<Az  o  to a l l o w f o r the b i a s  so i n t r o d u c e d . To estimate  the v e l o c i t y d i s p e r s i o n produced by d i f f e r -  e n t i a l g a l a c t i c r o t a t i o n i t i s necessary  to make an assumption  about the manner i n which the hydrogen d e n s i t y v a r i e s with z.  32 Two simple models were c o n s i d e r e d :  the f i r s t being a uniform  d e n s i t y d i s k , and the second one i n which the hydrogen falls  o f f e x p o n e n t i a l l y w i t h z.  The second model was  density adopted,  s i n c e i t appeared to conform more c l o s e l y w i t h the p r o f i l e s . i s e a s i l y shown t h a t i n the case  r (v) where V ~ ° C V height z . Q  f c n  = r  _ -V/V  38  (o) e  corresponds t o the v e l o c i t y  at the s c a l e  Then the d i s p e r s i o n o f each p r o f i l e due t o g a l a c t i c  r o t a t i o n cr— . f o r t h i s d e n s i t y d i s t r i b u t i o n was c a l c u l a t e d rot  2  rot  _  k  from  2_2  - « C Vth ' The thermal broadening < = ^  T  It  w nerinal  » s e v a l u a t e d assuming  120°K, and the instrument broadening o ^  l g t  was a l s o d e r i v e d .  The v a l u e s o f o ~ were then used to d e r i v e the v e l o c i t y r e l l i p s o i d , a d i s p e r s i o n e l l i p s o i d with three unequal axes, a c c o r d i n g t o the procedure d e s c r i b e d by Trumpler and Weaver F i r s t the s i x second o r d e r c e n t r a l moments,f^-^^t e l l i p s o i d a l d i s t r i b u t i o n were determined by the l e a s t  (66b)  of  t  n  3  9  squares  method from the f o l l o w i n g e q u a t i o n of c o n d i t i o n  ^ f o f o / ^ o i  where the d i r e c t i o n c o s i n e s ^ ^ »  /33  —  C 0 5 o< OcnS %  =  Sin*  -  5tri %  C<* *  J  2  y  "^33  a  r  e  -  6  i  v  e  n  b  y  K  °  e  33 Prom the f^^*^ 1. ^ axes ^ X , )  QlljJ  J  >  so determined the squares o f the s e m i p r i n c i p a l 2. e l l i p s o i d were found o  f  t  n  e v  e  l  o  c  i  t  T  as the three r o o t s o f the c u b i c e q u a t i o n  f*~  200 ~*  (J^)  no  in CjL^~*  110  M-020 - C I . )  -o  5  -4-1  101  The to  2j  9  /^002-CE) * 2  d i r e c t i o n cosines  4, "mj n|Of >  J  the a x i s  corresponding  were determined from  1,3,00  u,  = ±  A | j (  °'  ,aoo)  -+.(A«Jlo)  -- 1,101)  ^  3^  Here  1  and A  , i s the c o f a c t o r o f the term c o n t a i n i n g LL, 1 ijk ' 1  J  . K  The d i r e c t i o n c o s i n e s o f the axes c o r r e s p o n d i n g t o a  n  d  a  r  e  obtained by changing the s u b s c r i p t i n the  above from 1 t o 2 and 3« _ ^obs  a n d , r  p total  p r o f i l e s at intermediate and  w  e  r  e  ' obtained f o r a sample o f $0  g a l a c t i c l a t i t u d e s between •+; 1 5 °  + hS° and c o v e r i n g 360° i n l o n g i t u d e , and the v e l o c i t y  e l l i p s o i d was d e r i v e d as d e s c r i b e d above.  (b)  Results The d e r i v e d mean value o f A z  : Q  i . e . A z = 2 . 5 3 KmS . -1  Q  The value of c< r e q u i r e d t o minimize the sum o f the squares of  the r e s i d u a l s  £v  2  s £(y  - °CV )  2  o b s  From the c o r r e c t e d valueoc A z A ^ 15 KmS"  1  Kpc"  1  th  is  °C=0.5.  1,26 KmS" , and assuming 1  Q  =  we o b t a i n f o r the s c a l e t h i c k n e s s o f the  galaxy i n the s o l a r neighbourhood:  35 E  Therefore  Q  = 1.26/15  =:  0.081+ k p c .  the t o t a l t h i c k n e s s  o f the g a l a c t i c  disk  m e a s u r e d b e t w e e n p o i n t s where/the h y d r o g e n d e n s i t y  i s one  that  pc.  a t t h e p o s i t i o n oof t h e s u n i s a*  In  3 (b) a b o v e we  obtained  H  Q  Zz  —  Q  o r 168  0.08  half  corresponding to  "z  so i n t h e s o l a r n e i g h b o u r h o o d t h e o p t i c a l d e p t h f o r t h e 21-cm.  can  be e s t i m a t e d  t o be  0.95/kpc.  The a x e s o f t h e v e l o c i t y  ellipsoid  -I  11^ n l±' *5 Kr^S  r 3 •=  7-2  E|/  f<^s  ^  1-51  and  their directions are:  36  Discussion From this analysis the mean dispersion i s equal to 6.5 KmS"^" which i s i n good agreement with other determinations. The dynamical theory of the s t e l l a r system i n a steady state developed by Lindblad and Oort (63) shows that the d i r e c t ion  of the longer axis of the v e l o c i t y e l l i p s o i d i n the g a l a c t i c  plane ( i . e . the vertex) 3hould coincide with the anticentre JL s. 180° and 0?.  centre l i n e , i . e . axis correspondinp- to i s towards  The d i r e c t i o n of this  i n the present analysis of thi s axis  =: 239°.2 which i s p a r a l l e l to that of the  magnetic f i e l d l i n e s i n the neighbourhood of the sun (36). Thi3 coincidence i n the directions suggests the random gas motions are either strongly influenced by the l o c a l magnetic f i e l d or that both the gas motion and the f i e l d are influenced i n the same way by some other perturbation. The Lindblad-Oort theory also requires that the t h i r d axis of the e l l i p s o i d which should point toward the pole of the Milky Way be equal i n length to the longer axis i n the plane, and the r a t i o of the two axes which l i e i n the plane In our analysis we obtain and  the r a t i o f E 3 / 5 1 \ 2  6.7 KmS* and 51 ^ - 7.8 KmS ", 1  -1  1.51.  The agreement between our observations of these quantiti and the predictions of the Lindblad-Oort theory i s good, but i t i s not clear whether i t should be expected i f the Lindblad-Oort theory were reformulated to take account of the e f f e c t s of the l o c a l magnetic f i e l d , so that further t h e o r e t i c a l analysis seems desirable.  37  I t i s a l s o of i n t e r e s t to compare the v e l o c i t y e l l i p s o i d elements f o r the gas (1+9). They  with t h o s e f o r B s t a r s given by Nordstrom  are  = It  I  -z. Z ^ L  tr  -54?3  =  should be noted that the v e l o c i t y d i s p e r s i o n of B. s t a r s  i s appreciably  g r e a t e r t h a n t h a t of n e u t r a l hydrogen gas,  f o r l a t e type s t a r s the d i s p e r s i o n i s even g r e a t e r  and  than that  for B stars. We  suggest a s i m i l a r p r o g r e s s i o n  longitude.  The  longitude  a p p l i e s f o r the  of the v e r t e x f o r B s t a r s  vertex  (  = 266?3)  i s about 27° f u r t h e r from the a n t i c e n t r e than that f o r the  ras.  /) For the  l a t e r type s t a r s the v e r t e x  However, the v e r t e x  longitude  direction is  f o r B s t a r s i s not w e l l  s i n c e the axes X-  ^ and  X^,  n e a r l y e q u a l and  there  seems to be  of the v e l o c i t y e l l i p s o i d  f o r the We vations,  defined, are  Bearing  suggest, a f t e r c o n s i d e r a t i o n of  a v a i l a b l e data f o r B s t a r s (16), that the v e r t e x towards  200  very  some d i f f i c u l t y i n d e c i d i n g  which of these axes corresponds to the v e r t e x . u n c e r t a i n t i e s i n mind we  o  these the  direction i s  2 2 0 ° , midway between that f o r the gas  and  that  l a t e r type s t a r s . therefore  suggest, as an e x p l a n a t i o n  of the  obser-  that the v e r t e x d i r e c t i o n of a l l c l a s s e s of s t a r s  are  .  38  found to be towards l o n g i t u d e s suggested by theory,  greater  by theory.  -  180°  that these s t a r s were formed from gas with  maximum random motions a l i g n e d w i t h gradually relaxed  I  thaia  ^  towards the d i r e c t i o n  —  21+0° and hove *^ -  1 8 0 ° required  During t h i s r e l a x a t i o n process themagnitude o f the  random v e l o c i t i e s has i n c r e a s e d  progressively.  39  DEPARTURE FROM CIRCULAR MOTION  Although i t i s c l e a r t h a t the gas motions  are predomin-  a n t l y c i r c u l a r i n most p a r t s of the Galaxy i t has a l s o been n o t i c e d that important d e v i a t i o n s from p e r f e c t c i r c u l a r  motion  do e x i s t i n the o v e r - a l l v e l o c i t y f i e l d o f the Galaxy.  Hence  an i n v e s t i g a t i o n o f the departure o f the gas motion from the c i r c u l a r motion a c c o r d i n g to the O o r t - L i n d b l a d theory of g a l a c t i c r o t a t i o n was undertaken  t o see i f our data c o u l d  suggest any s y s t e m a t i c departure from c i r c u l a r  motion.  In the l a s t chapter i t has been mentioned  Y^^"-0^ ^  -V  of OC found f o r which  Xy2*  rel>'ion ship  that a l i n e a r  was c o n s i d e r e d and that the value was a minimum.  The constant o<  i n d i c a t e s the nature of the p e c u l i a r v e l o c i t i e s Vj, <K -  1, the mean o f a l l values V  from 1 the mean i s non-zero to  ot AZ  uals  0  and the v a l u e A Z  V  c  a  n  D  e  u  3  e  <  *  I f oC d e v i a t e s  must be c o r r e c t e d Then the r e s i d -  to study the departures from  motion.  A p l o t o f the r e s i d u a l s last  D  to a l l o w f o r the b i a s so i n t r o d u c e d . — °C Vth,~  circular  tends t o zero.  . If  V  obtained i n the a n a l y s i s of  chapter a g a i n s t the l o n g i t u d e (1) f o r each l a t i t u d e (b)  seemed t o suggest a s i g n i f i c a n t cos 21 v a r i a t i o n .  A cos 21  v a r i a t i o n of the r e s i d u a l s suggests a p o s s i b i l i t y of the e x i s t ence of r a d i a l motion  i n our Galaxy.  In f a c t , there i s observ-  a t i o n a l evidence both f o r our own (59, kO) and f o r e x t e r n a l galaxies  (11) t h a t r a d i a l motions  e x i s t i n r e g i o n s with dimen-  s i o n s of a few K i l o p a r s e c s and t h a t the c i r c u l a r and r a d i a l motions may n o t be axisymmetric.  H e n c e a n attempt has been made  to  see i f any s y s t e m a t i c  r a d i a l m o t i o n c o u l d be d e t e c t e d f r o m o u r  data. Trumpler derived  expressions  to  the l o c a l  of  galactic  rotation  Vn.  K  velocity  resulting  f o r t h e sol,ar  constant Since  In latitudes  4-jf)  CtAXl  fcb  t o the sun and A i s t h e u s u a l  model r s z c o s e c b,  layer  o  i n the northern  intermediate  ( 1 5 ° t o I4.O ) c o v e r i n g 360°JL>) l o n g i t u d e and 119 p r o f i l e s 0  intermediate  latitudes  r a n g e 0 ° t o 2 3 0 ° were made u s e o f . was d e t e r m i n e d  determine  effect  The e x p r e s s i o n f o r t h e  t C  a n a l y s i s 168 p r o f i l e s  the southern  profile  t h e combined  respect  a n d C and D a r e O o r t - l i k e c o n s t a n t s .  i n the s t r a t i f i e d  this  with  vicinity i s :  LASlnZl  Co^b  (60) have  of stars  from  and r a d i a l m o t i o n .  >L i s t h e d i s t a n c e o f t h e s t a r  where  in  of rest  velocity  -  ( 6 6 c ) and R u b i n a n d B u r l e y  f o r the r a d i a l  standard  differential  Oort  and Weaver  and a l e a s t  the constants  Z  covering the longitude  The mean v e l o c i t y squares  solution  o f each  was made t o  C and D a s s u m i n g t h e v a l u e  of 1 5 . 0  o* KmS  -1  Kpc""  1  f o r t h e Oort  constant  made f o r t h e n o r t h e r n p r o f i l e s and  t h e combined p r o f i l e s  A.  (168),  (287) w i t h  No. o f Profiles  Separate  s o l u t i o n s were  the southern  p r o f i l e s (119)  the f o l l o w i n g Z Kpc  C KmS  results:  1  .  D Kpc  Northern  Profiles  '168:  0.120  7.2  -2.I4.  Southern  Profiles  (119  0.095  10.8  8.9  287  0.109  8.5  1.8  All  Profiles  kl These r e s u l t s expression  can a l s o  be e x p r e s s e d b y means o f t h e f o l l o w i n g  (66c):  - 2 Grfee D Cots" b  K  2  D  where A, =s<\J/\ +c ~ x  1  a  n  ^ tan 2 h = — .  case o f a r a d i a l m o t i o n combined the  radial velocity  longitude  T h i s means t h a t i n t h e  with a r o t a t i o n a l motion: (1)  f o r m u l a c o n t a i n s a term independent o f the  ( 2 ) the double s i n e v a r i a t i o n  a d i f f e r e n t phase;  E x p r e s s i n g our previous r e s u l t s three cases y i e l d  V*. = c  u  o  c  of r a d i a l v e l o c i t y has  the l o n g i t u d e a t which the f i r s t  i s n o t the l o n g i t u d e o f the g a l a c t i c  the  + A,) +13 - - - - - 4 5  jAi'SlnZ  w  ( l - s O °  ).  i n t h i s form w i t h a phase  shift  respectively:  b  c * H i > 7 S c w ; t (l+i&<Q  D i s c u s s i o n : V*. - O * / C o 3 o , o b Analyses  centre  term v a n i s h e s  Cci^b[[7-3Sun2,(l+l^)  1  KwxS '  c a r r i e d out o b y H e n d e r s o n ( 2 9 ) f o r t h e l o n g i t u d e r a n g e 16 t o 230 f o r l a t i t u d e o o | 10 | and b y G r a h l e t a l ( 2 5 ) f o r l a t i t u d e -p 3 0 . Their results are:  similar  i-flic^s  -  t o t h e above h a v e b e e n  o  ,  2  r  o  b J l 5 s i n 2 ( 1 + 1+..9)-0.9]k*£ 2 r' o . G r a h l e t a l ( | % 3 ) : V ^ - s 0.230 c o s e c b c o s b | l 5 s i n 2(1+- 16.5 ) - 6 . l \ K ^ S  Henderson (19^7) :  =  0.076 c o s e c b c o s  E q u a t i o n I4.3 was d e v e l o p e d f o r t h e c a s e where t h e gas m o t i o n in addition  t o the normally  assumed c i r c u l a r v e l o c i t y , h a s a  component.  A formal interpretation  radial  on t h i s b a s i s would s u g g e s t  a r a d i a l component o f m o t i o n t o w a r d s t h e g a l a c t i c  centre  o f 3k  KmS  1+2 from Henderson's data, 1 1 3 KmS -1  and 97KmS  from our d a t a .  -1  from the data of G r a h l et a l ,  T h i s i n t e r p r e t a t i o n would l e a d  to expect a v e l o c i t y d i f f e r e n c e of about 1 3 0 KmS  -1  one  between the  n o r t h e r n and southern r o t a t i o n curves of the Galaxy, whereas the -1  observed d i f f e r e n c e i s c e r t a i n l y l e s s than 20 KmS  •  -1  i f we assume the average v e l o c i t y d i f f e r e n c e i s lOKmS c a l c u l a t e d phase s h i f t determined We  i n equation o o a value f o r TV of 1 3 ± i*..6«  In f a c t , the  K>3 » whereas we have  p  t h e r e f o r e conclude that the phase s h i f t and departures  from c i r c u l a r motion observed are not a r e s u l t of l a r g e organized motion  i n the Galaxy, but a l o c a l e f f e c t .  analyses f o r 0 and B s t a r s  scale  Since s i m i l a r  (60) show much s m a l l e r d e p a r t u r e s , we  look f o r an e x p l a n a t i o n i n terms of f o r c e s which a f f e c t the gas but not the s t a r s *  An obvious candidate i s the l o c a l  magnetic  f i e l d , and we would view the phase s h i f t as a s h e a r i n g e f f e c t produced by the l o c a l magnetic  field.  1+3  SUMMARY OF RESULTS AND CONCLUSIONS Neutral hydrogen l i n e p r o f i l e s obtained at intermediate galactic latitudes have been used to 1) determine the k i n e t i c temperature of nearby g a s ; i i ) determine the solar motion with respect to t h i s gas;  i i i ) derive the v e l o c i t y e l l i p s o i d describing  the random  motions of the gas; and i v ) study departures of the gas v e l o c i t i e s from c i r c u l a r motion. i ) The k i n e t i c temperature of hydrogen obtained on the assumpo t i o n of h o r i z o n t a l s t r a t i f i c a t i o n i n density i s 120  K  i i ) The elements of solar motion r e l a t i v e to neutral hydrogen with t h e i r probable errors are : So = % M ± 1 . 3 k . m ^  L  0  = 4 ^ ± 9 ° - %  6 © = +^7±I2>°.7>  i i i ) The axes of the v e l o c i t y e l l i p s o i d describing  the d i s t -  r i b u t i o n of random motions of the gas and t h e i r directions are: £ , = 6.7 KmS 1+.5 KmS "*  £ -s 7.8 KmS  -1  -  n  1  -(x) =  o 239.2  I-  160.3  I-  3  Mean dispersion  >l-  yj  0  269.0  QL$+  o *V-*35.3  A  £z-ll+.9 «  0  &c-1+9.8  CZ f 3  and: i v ) The observed mean v e l o c i t i e s of the gas at intermediate g a l a c t i c l a t i t u d e s may be represented by the expression:  following  kk On  the b a s i s o f the above r e s u l t s the f o l l o w i n g  conclusions  are drawn: i ) That i n the v i c i n i t y of the sun there i s no a p p r e c i a b l e d i f f e r e n t i a l motion between the n e u t r a l hydrogen and the stars; i i a ) That the v e r t e x d i r e c t i o n o f the v e l o c i t y e l l i p s o i d i s found to be c l o s e l y a l i g n e d with the l o c a l magnetic f i e l d , ing  support-  the view t h a t the random motion i s i n f l u e n c e d by the  field; i i b ) That the v e r t e x  d i r e c t i o n s o f a l l c l a s s e s of s t a r s are found o to be towards l o n g i t u d e s g r e a t e r than 180 ; that these s t a r s were formed from gas with maximum random motions n  0  a l i g n e d with-c= 21+0 0  and have g r a d u a l l y r e l a x e d  •t = 180 , and that d u r i n g nitude  towards  0  the r e l a x a t i o n process the mag-  of the random v e l o c i t i e s has i n c r e a s e d  progressively  . and i i i ) That the phase s h i f t and departures from c i r c u l a r motion observed are n o t a r e s u l t o f l a r g e s c a l e organized  motion  i n the Galaxy, but a l o c a l e f f e c t caused probably by the l o c a l magnetic  field*  i+5 BIBLIOGRAPHY  1.  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J . , 72, 21,  (1967)  (1968)  The Galaxy and the M a g e l l a n i c Clouds (IAU  70.  775  531+  Symp. No. 20) 92  Weinreb, S., B a r r e t t , A.H., Meeks, M.L. and Henry, J . C , Nature,  71.  Westerhout, G.,  B.A.N.,  72.  W i l d , J.P., Ap. J . ,  73.  W o l t j e r , L.  lli,  200, 829  1 J , 201 206  (1963)  (1957)  (1952)  S t a r s and S t e l l a r Systems Chicago Press)  ( U n i v e r s i t y of  V , 571  (1965)  (I96I4.)  if9  Table I . THE CLASSIFICATION OF STELLAR POPULATIONS AT THE VATICAN CONFERENCE  1957.  (Ref: Blaauw, A., S t a r s and S t e l l a r Systems. U n i v e r s i t y o f Chicago p r e s s , V, (1)  <|z|> Mean d i s t a n c e from plane  (2)  <JZI>  Mean v e l o c i t y the g a l a c t i c  (3)  Zv  a  l\Uh»  1965)  component p e r p e n d i c u l a r to plane.  I n t e r s t e l l a r abundance o f elements h e a v i e r than Helium.  T A B L E I Population I I [ InfcermecTIa'te" Halo Pop. I I Pop. I I Subdwarfs  ;Stars o f gala-i j c t i c nucleus  High-velocity stars with z velocities > 30 km/sec  Planetary nebulae  RR Lyrae s t a r s Long p e r i o d with periods variables with periods l o n g e r than O.I4. days <250 days and s p e c t r a l types e a r l i e r than M5®  2000 75  _ 1  h . e.  Strong stars  RR Lyrae star£ with periods \ <0.l4. days  Strong?  Smooth  Smooth  Smooth?  0.003 9  T o t a l mass (10 O )  6 16  6.0 to 5.0  1.5 hi  to  Supergiants  I  Cepheids  I  120 8  160 10  100 Little  Little  0.02  0.01  j  i  1  j T T a u r i star^j j G a l a c t i c clu-i j - s t e r s of ! j Trumpler's class I  17  Strong  Young s t a r s associated w i t h the pre-sent s p i r a l I structure  !  Weak-line stars  Strong  Gas  s  I4.00  700 25  line  Me dwarfs  Novae  Extreme Pop. I  A-type s t a r s  25?  o,  Age (10 y e a r s )  Population I Older Pop. I  Globular clusters  <izi> (parsecs) <1ZI> (Km S ) A x i a l r a t i o of spheroidal distribution Concentration toward c e n t e r Distribution  Disk Population  5-0j  Patchy arms  0.1  spiral ^ o.03 n  to  5  1.5  j  Extremely Pat•chy s  < 0.1  50  Figure 1 .  STRUCTURE OF THE GALAXY  (Source: A t l a s o f the U n i v e r s e , Thomas Nelson & Sons L t d . 1 9 6 1 )  51  F i g u r e 2. MERIDIAN SECTION OF THE GALAXY THROUGH THE SUN (Ref: Blaauw,A., S t a r s and S t e l l a r  Systems,  U n i v e r s i t y o f Chicago P r e s s , V ,  /  i+l+O, 1965)  OtofeuUr Ctvtt*r* . . . . - - * ' RR^rattSV*  z hp*  Z  [kps 6  oS>»  Long per. •  • ISO  .  /  gOKM  Globul.rclufttlrt RRL»r« A S V S I  11  10  6 R(kps)  52  F i g u r e 3- AN IDEALIZED PICTURE OF THE SPIRAL PATTERN Shaded areas o u t l i n e  OF THE GALAXY.  the arms formed by the O - A s s o c i a t i o n s  Longitudes r e f e r t o the New G a l a c t i c  Coordinate System  FIG. 3 .  53  s  F i g u r e I+. STRATIFIED MODEL REPRESENTATION OF THE GALAXY IN THE SOLAR NEIGHBOURHOOD.  FIG;. 4 .  F i g u r e 5. PLOT OF OPTICAL DEPTH {Z) AGAINST COSEC b FOR NORTHERN GALACTIC HEMISPHERE.  Fi  Gi.  5.  bS  F i g u r e b. PLOT OF OPTICAL DEPTH ( t ) AGAINST COSEC b FOR SOUTHERN GALACTIC HEMISPHERE.  T"  J  I  !  I  2.  3  t  4  .  L  5  56  F i g u r e 7.  TYPICAL 21-cjn. LINE PROFILES. a) In the d i r e c t i o n of the G a l a c t i c o o o b) At b - 0 ~t 15 ^ ± 20 J  centre.  >^w»»nt|n»p>ii»» )  10. 0 .  15. 0 .  J L 20. 0.  vs. r~  i  25. 0 .  30. 0.  ***tr^ i  35. 0 .  40. 0 .  p  1"  45. 0 .  |" >l)»llUW<''* *ti|fCI»W>*»-ll W  -120.  -80.  -HO.  --00.  HO.  WsA CK~  80.  >  120.  i  L60.  110.15.  115.15.  120.15.  125.15.  130,15.  I'  ^ ^ D W Q OH-  1—^P>>«<1 tl>l||t»l|>>>»|Ot>t'»Ml l>IUYtlHl»ll'<>IH'llt"ljY"»Mlim»n< » >  |  )  >  j  135.15.  ^Mf» *l'»>^«l**»ll»IIJl>K >  r t ,  ™ g  j—^TtMl^»|^oyiHIDIMOcHlMl >y''l>>*ll>»>«»ll>»«Hnil|i»>Kt>'»>PW> l  i  140.15.  145.15.  150.15.  ^MMjMEKMHE'MortlljmftMltllr  120.  -80.  -10.  1  -0.  **»»»t»MI>>Hy "It'll'>»>HMW^t»Hft»WMH't>>f»»»»>M>«M>H  ,40.  80.  120.  [  160.  2  85. -15.  i  •o  90. -15.  95. -15.  •a a  100.-15.  105.-15.  •o a  i •O  110.-15.  115.-15.  i  •o  20.  -BO.  -10.  -0.  40.  80.  120.  120.-15.  •a a  125.-15.  •a  160.  200  75. 20.  80. 20.  | S*»H*ni>>ni|»mHllhW»l>|,i>MMIlVH>l  85. 20.  90. 20,  I'l'iiitiiiiii'in '|' i " ' " * * ^  | ^ ^ % r * i " n >»W  i <ti '1 "" * " " »f' I » "* **" h  95. 20.  100.20.  105.20.  110.20.  115.20.  •120.  -80.  -10.  -0.  80. -20.  I  85. -20.  90, -20.  95. -20.  100.-20.  i  105.-20. •  110. -20..  115.-20.  120.-20.  •120.  -BO.  -10.  -0.  40.  80.  120.  160.  2.  

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