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Studies of the 21-cm line in dense dust clouds Mahoney, Michael Joseph 1971

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STUDIES OF THE 21-cm LINE IN DENSE DUST CLOUDS  by  MICHAEL JOSEPH MAHONEY B.Sc,  U n i v e r s i t y - o f B r i t i s h Columbia, 1968  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS  We a c c e p t t h i s  t h e s i s as conforming t o the  required  standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1971  In presenting this thesis in partial fulfilment of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t f r e e l y available f o r reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.  It i s understood that copying or publication  of this thesis f o r f i n a n c i a l gain shall not be allowed without my written  permission.  Department of  PHYSICS  The University of B r i t i s h Columbia Vancouver 8, Canada  Date  SEPTEMBER '  i • »•• 11 • i -  i  1'9>'0  i ••^•fiiEa£»>w" 1  "  -ii-  ABSTRACT  U s i n g the 26 m p a r a b o l o i d a t the Dominion Radio A s t r o p h y s i c a l Observatory,  s u f f i c i e n t 21-cm l i n e d a t a have  been o b t a i n e d on t h i r t e e n dense d u s t c l o u d s t o g i v e a measure o f the s i g n i f i c a n c e o f an excess o r a d e f i c i t  i n the hydrogen  e m i s s i o n from these o b j e c t s , as compared w i t h nearby  surround-  i n g r e g i o n s o f the sky. The a n a l y s i s o f these d a t a  indicates  t h a t f o u r o f these c l o u d s show s i g n i f i c a n t d e c r e a s e s  i n the  hydrogen e m i s s i o n . I f the w i d t h s  o f these d e f i c i t s a r e t o be i n t e r p r e t e d  as thermal broadening w i t h i n a s i n g l e c l o u d , k i n e t i c  temper-  a t u r e s o b t a i n e d a r e f a r i n excess o f those i n d i c a t e d by normal OH e m i s s i o n from these same o b j e c t s .  I f the OH and  H a r e i n thermodynamic e q u i l i b r i u m and the c h e m i c a l abundances are normal, i t i s thought  t h a t the d e f i c i t s a r e due t o the  hydrogen b e i n g i n m o l e c u l a r form.  However, measurements o f  h i g h e r s p a t i a l and v e l o c i t y r e s o l u t i o n a r e needed t o r u l e out the p o s s i b i l i t y o f a c o l d a b s o r b i n g c l o u d .  -iii-  TABLE OF CONTENTS  Chapter 1  Chapter 2  Chapter 3  INTRODUCTION  Page  1-1)  H i s t o r i c a l Background  1  1-2)  Is the Hydrogen Atomic o r M o l e c u l a r ?  2  1-3)  The P r e s e n t Work  5  1- 4)  The Problem o f I n t e r p r e t a t i o n  6  GENERAL THEORY 2- 1)  D e f i n i t i o n o f Symbols  8  2-2)  Temperature and Thermodynamic E q u i l i b r i u m  2-3)  The E q u a t i o n o f T r a n s f e r  2-4)  The O p t i c a l Depth a t 21-cm, T ,  14  2-5)  The I n t e r p r e t a t i o n o f L i n e Widths  19  2-6)  The V i s u a l O p t i c a l Depth, rv  21  2-7)  What i f T  2- 8)  The C o l d A b s o r b i n g C l o u d  8 11  2  ZI  ..  I s Not P r o p o r t i o n a l t o T ? v  23 25  EQUIPMENT AND OBSERVATIONS 3- 1)  The Apparatus  29  3-2)  Which Dense Dust Clouds Do You Observe?  30  3-3)  Method  of Observation  32  3-4)  Method  of C a l i b r a t i o n  34  -iv-  TABLE  Chapter  4  Appendix A Bibliography  OF  DATA A N A L Y S I S ,  CONTENTS  (cont'd)  R E S U L T S , AND  CONCLUSIONS  Page  4-1)  The Computer Programs  38  4-2)  The Sources  46  4-3)  The R e s u l t s  46  4-4)  Interpretation of Results  47  4-5)  Comparison  of Results with  4-6)  Concluding  Remarks  A  Analyzed  L I S T I N G OF COMPUTER  Other  Work  50 51  PROGRAMS  54 •  *••  7  7  -V-  LIST OF TABLES  Table  Title  Page  TABLE I  P r o p e r t i e s o f a T y p i c a l Dust Cloud  1  TABLE I I  A L i s t o f Symbols and T h e i r D e f i n i t i o n s  8  TABLE I I I  A L i s t o f Dust Clouds S u i t a b l e f o r Observation  31  TABLE IV  A L i s t o f Observed Sources  32  TABLE V  The 21-cm L i n e C a l i b r a t i o n Standards  34  TABLE VI  A L i s t o f D e r i v e d Dust Cloud Parameters  46  -vi-  LIST OF FIGURES  Figure  Title  Page o f T*, Versus T„  FIGURE 1  The P o s s i b l e Behaviour  FIGURE 2  A B l o c k Diagram o f the R e c e i v i n g Equipment  7  29  FIGURE 3  The Method o f R e f e r e n c i n g on a Dust C l o u d  FIGURE 4  The Average D i f f e r e n c e and Expected F l u c t u a t i o n f o r Object 1  46  The Average D i f f e r e n c e and Expected F l u c t u a t i o n f o r O b j e c t 38  46  The Average D i f f e r e n c e and Expected F l u c t u a t i o n f o r O b j e c t 32  46  The Average D i f f e r e n c e and Expected F l u c t u a t i o n f o r O b j e c t 15  46  FIGURE 5 FIGURE 6  FIGURE 7  .... 32  -vii-  ACKNOWLEDGEMENTS  I would f i r s t  l i k e t o acknowledge the a s s i s t a n c e o f  my t h e s i s s u p e r v i s o r , Dr. W.L.H. Shuter, not o n l y f o r h i s e n l i g h t e n i n g d i s c u s s i o n s and encouragement, but a l s o f o r his  patience  throughout t h i s work.  Next, I would l i k e t o thank my c o l l e a g u e s , Dr. W i l l i a m McCutcheon, f o r h e l p w i t h  the r e c e i v i n g equipment, Mr. R.A.  P e r l e y , f o r s t i m u l a t i n g "over the w a l l " d i s c u s s i o n s and i n s u l t s , and my numerous f r i e n d s and enemies who made the p r e p a r a t i o n o f t h i s t h e s i s an e n j o y a b l e Finally,  endeavour.  I thank the s t a f f o f the Dominion Radio  A s t r o p h y s i c a l O b s e r v a t o r y f o r the use o f t h e i r f a c i l i t i e s and experience, financial  and the N a t i o n a l Research C o u n c i l o f Canada f o r  assistance.  -1Chapter 1 INTRODUCTION  1-1)  in  Historical  Background  Regions o f sky d e v o i d o f s t a r s were f i r s t c a t a l o g u e d 1 1919 by the American astronomer B a r n a r d , and more r e c e n t l y , 2  by Lynds.  I t was  at f i r s t  thought that these dark patches  were i n f a c t c a v i t i e s i n the g e n e r a l s t a r f i e l d ; however, a study o f Barnard's c a t a l o g u e q u i c k l y showed t h a t these dark o b j e c t s were d i s t r i b u t e d c h i e f l y i n the neighbourhood o f the g a l a c t i c p l a n e , making i t more p l a u s i b l e t o t h i n k o f them as t r u e dark masses o r nebulae, r a t h e r than l o n g tubes through the  g a l a c t i c plane which were d e v o i d o f s t a r s .  Soon, l a r g e -  s c a l e photographs o f these o b j e c t s , p r o j e c t e d a g a i n s t a luminous background,  showed them t o be t r u e d a r k nebulae  w i t h a wide range o f s i z e s and o p a c i t i e s . a b s o r p t i o n was  By assuming  that  r e s p o n s i b l e f o r the d i f f e r e n c e s i n s t a r counts  on and nearby these nebulae, astronomers were then a b l e t o e s t i m a t e t h e i r d i s t a n c e s , depths and o p a c i t i e s . of  The t e c h n i q u e s  r a d i o astronomy have y i e l d e d a d d i t i o n a l i n f o r m a t i o n on  masses and c o m p o s i t i o n , n o t a b l y through measurements o f the  21-cm  l i n e o f atomic hydrogen, and even more r e c e n t l y ,  3-6 through measurements o f the m o l e c u l a r s p e c t r a l l i n e s o f OH 7 and H 2 C O . The p r o p e r t i e s o f a t y p i c a l dark c l o u d have been summarized are  i n TABLE I .  Most o f the parameters l i s t e d 8  taken from a review paper by H e i l e s .  there  -21-2)  I s the Hydrogen Atomic o r M o l e c u l a r ? D e s p i t e a l l we know about these dark dust c l o u d s , one  matter  is still  undecided  - whether o r not the dark d u s t c l o u d s  c o n t a i n m o l e c u l a r hydrogen.  T h i s problem a r i s e s because  i s a homonuclear d i a t o m i c molecule  ^  and as such i t s r o t a t i o n a l -  v i b r a t i o n a l and pure r o t a t i o n a l t r a n s i t i o n s a r e o n l y a l l o w e d , l e a d i n g t o a v e r y weak o p t i c a l and near  quadrapole-  infrared  spectrum, which i s u n d e t e c t a b l e from the e a r t h ' s s u r f a c e because o f atmospheric  o p a c i t y and the p r e s e n t l a c k o f  astrophysical infrared  spectrometers.  The Lyman and Werner  e l e c t r o n i c band t r a n s i t i o n s a r e d i p o l e - a l l o w e d , however, but because these bands occur i n the u l t r a v i o l e t , absorbed  by the e a r t h ' s atmosphere.  they a r e a l s o  The o n l y d e t e c t i o n o f 9/ 1 0  H2 t o date has been by r o c k e t - b o r n e  instrumentation,  i V /  and  t h e s e i n d i c a t e a low f r e e space abundance o f m o l e c u l a r hydrogen. Because H2 has no f i n e o r h y p e r f i n e s t r u c t u r e i n i t s ground s t a t e , r a d i o frequency l i n e s do n o t e x i s t .  More r e c e n t l y ,  G u l l and H a r w i t ^ f a i l e d t o d e t e c t n e a r - i n f r a r e d e m i s s i o n which  12 had been p r e d i c t e d t o e x i s t  i n dark c l o u d s near  ultraviolet  s t a r s , as a r e s u l t o f the s o f t e n i n g o f the u l t r a v i o l e t by  radiation  the m o l e c u l a r hydrogen supposed t o e x i s t i n dark c l o u d s . B a r r e d from a d i r e c t measurement o f H , astronomers 2  have used b o t h 21-cm l i n e d a t a , t h e o r e t i c a l c a l c u l a t i o n s , and a T h i s i s not i n c o n s i s t e n t w i t h a h i g h H where the H i s shielded. 0  2  abundance i n dust  clouds  -3o t h e r i n f e r e n c e s t o support e x i s t e n c e o r non-existence dark dust  t h e i r c o n t e n t i o n s f o r the of molecular  hydrogen w i t h i n  clouds. 13  The e a r l i e s t  21-cm l i n e measurements o f L i l l e y  indicated  a g e n e r a l c o r r e l a t i o n between gas and dust over l a r g e r e g i o n s 14 15 o f the sky, as d i d the work o f G a r z o l i and Varsavsky. However, more r e c e n t measurements o f W e s s e l i u s  *  and S a n c i s i  i n d i c a t e t h a t a g e n e r a l c o r r e l a t i o n between gas and d u s t i n the i n t e r s t e l l a r medium does not e x i s t .  Unfortunately  this  work o n l y t e l l s us about l a r g e areas o f the sky and n o t i n d i v i d u a l dark nebulae, where the r i d d l e o f atomic molecular  hydrogen r e a l l y  versus  exists.  17 Heiles  was the f i r s t  i n d i v i d u a l dust c l o u d s .  t o study a l a r g e sample o f  From measurements o f the 21-cm  line  on and nearby f o r t y - e i g h t dark d u s t c l o u d s , he was a b l e t o conclude  t h a t one c l o u d showed a s i g n i f i c a n t excess  two c l o u d s showed s i g n i f i c a n t d e f i c i t s .  while  T h i s work however  n e g l e c t e d t o d e f i n e what was meant by the words "nearby" and " s i g n i f i c a n t " , and w i t h o n l y two r e f e r e n c e p o s i t i o n s f o r each c l o u d , i t i s indeed excesses  s u r p r i s i n g t h a t no more than  three  o r d e f i c i t s were found, as t y p i c a l hydrogen g r a d i e n t s  i n the i n t e r s t e l l a r medium can produce v e r y l a r g e d i f f e r e n c e s between a d j a c e n t beam p o s i t i o n s ^ * c e r t a i n l y much l a r g e r than Heiles s e n s i t i v i t y o f 7°K b r i g h t n e s s b see next page 1  temperature.  -4-  The most d e t a i l e d 21-cm the two-dimensional astronomers,  l i n e work on dark dust c l o u d s a r e  maps o f these o b j e c t s by the Dutch  S a n c i s i and W e s s e l i u s ^ ' ^ b u t  these maps have been made o f o n l y a few  unfortunately  o b j e c t s and do  g i v e a f a i r i n d i c a t i o n of what might be expected  not  for a large  sample o f dark dust c l o u d s . B e s i d e s these 21-cm  l i n e measurements and  their implications  ( t o be d i s c u s s e d l a t e r ) t h e o r e t i c a l c a l c u l a t i o n s by  Hollenback,  Werner and S a l p e t e r ^ i n d i c a t e t h a t f o r " 'standard c l o u d s ' w i t h •*^10/cm  and T y ^ O . l ,  the f r a c t i o n a l abundance o f m o l e c u l a r  _3 hydrogen i s 10  w h i l e i n denser and more opaque c l o u d s ( i n  p a r t i c u l a r , dark nebulae w i t h more than one magnitude of v i s u a l e x t i n c t i o n ) the hydrogen should be mainly form."  91  Verschuur^  has argued  t h a t the m i s s i n g  mass o f the g a l a x y i s H£, whereas Cheung e t a l  22  i n molecular gravitational have  suggested  b I f we l e t Nt?.,^) be the column d e n s i t y o f atomic hydrogen a t an a r b i t r a r y p o i n t on the sky and l e t the p o i n t (o,o) be a t the c e n t e r o f a dense dust c l o u d , then on d o i n g a T a y l o r s e r i e s expansion about t h i s p o i n t , we f i n d t h a t :  Ni*,p = N(o,o) + Ot x -f Hi «. + £AL  z N *u+rN l  <d+... (1-1)  where a l l the d e r i v a t i v e s are e v a l u a t e d a t the c l o u d c e n t e r . I t i s then easy t o show t h a t the average d i f f e r e n c e p r o f i l e between the c l o u d c e n t e r p o s i t i o n and f o u r nearby r e f e r e n c e p o s i t i o n s a d i s t a n c e X away to the n o r t h , south, e a s t and west i s :  £{  <£M-  .4-  rN] + ...  (1-2)  Thus the second and h i g h e r o r d e r , n o n - l i n e a r , g r a d i e n t s can e a s i l y produce a d i f f e r e n c e p r o f i l e , depending on t h e i r s i g n and magnitude.  -5-  that  i s necessary f o r the observed h i g h r a t e o f c o l l i s i o n -  a l e x c i t a t i o n o f NH^.  On the o t h e r hand, hydrogen  self-  a b s o r p t i o n measurements^-28 hydrogen a b s o r p t i o n by continuum 29 30 31 s o u r c e s , » and e m i s s i o n from h i g h l a t i t u d e c l o u d s indicate t h a t dark c l o u d s may be v e r y c o l d , and t h i s would e a s i l y e x p l a i n any d e f i c i e n c i e s i n the 21-cm l i n e e m i s s i o n , i f i t were c o n s i s t e n t w i t h o t h e r types o f measurements.  1-3)  The P r e s e n t Work The p r e s e n t work c o n s i s t e d o f 21-cm l i n e  measurements  on dark dust c l o u d s and w e l l - d e f i n e d r e f e r e n c e p o s i t i o n s . A l t h o u g h maps c o u l d not be produced each c l o u d observed  as i n the Dutch work,  had between f o u r and e i g h t r e f e r e n c e  p o s i t i o n s as compared t o o n l y two i n H e i l e s ' work. s p a t i a l r e s o l u t i o n o f 36 arcmin and the v e l o c i t y o f 2.12 Km/sec. used  Both the  resolution  i n the p r e s e n t work were the same as i n  the Dutch measurements.  The s e n s i t i v i t y o b t a i n e d here was  about seven times H e i l e s , but not as many c l o u d s were 1  The most important  surveyed.  i n n o v a t i o n o f the p r e s e n t work, however, i s  t h a t the d e t e c t e d excesses o r d e f i c i t s have been g i v e n a tical  s i g n i f i c a n c e i n terms o f what might be expected i f  n o n - l i n e a r hydrogen g r a d i e n t s e x i s t e d i n the i n t e r s t e l l a r r e g i o n s s u r r o u n d i n g the dark dust c l o u d s , as they most c e r t a i n l y do.  also  statis-  -6-  1-4)  The Problem o f I n t e r p r e t a t i o n Once i t has been e s t a b l i s h e d whether or not dark d u s t  c l o u d s show s i g n i f i c a n t excesses or d e f i c i t s e m i s s i o n , the problem a l l means.  The  still  i n t h e i r hydrogen  e x i s t s o f i n t e r p r e t i n g what i t  t h r e e cases which must be c o n s i d e r e d are  l i s t e d below, and f o r each case, s e v e r a l p o s s i b l e e x p l a n a t i o n s exist. Case 1.  No  s i g n i f i c a n t excess or d e f i c i t  I n t h i s case a t l e a s t two a)  exists.  i n t e r p r e t a t i o n s are  The excesses o r d e f i c i t s may  e x i s t , but a r e not  s i g n i f i c a n t compared t o the background b)  The  possible:  fluctuations.  gas t o d u s t d e n s i t y r a t i o i s c o n s t a n t over the  c l o u d and  i t s s u r r o u n d i n g s , l e a d i n g t o no  observable excess or d e f i c i t . Case 2.  A  s i g n i f i c a n t excess  exists.  A g a i n two p o s s i b i l i t i e s a)  exist:  I f the c l o u d s are i n f a c t m o l e c u l a r , d i s s o c i a t i o n by low energy  cosmic r a y s on the r i m o f a c l o u d  c o u l d enhance the e m i s s i o n from the  atomic  32 hydrogen t h e r e . b)  I f the c l o u d i s i n h y d r o s t a t i c e q u i l i b r i u m w i t h its  s u r r o u n d i n g s , an excess would  appear.  -7-  Case 3.  A significant deficit  exists.  Several interpretations are again possible: a)  A "genuine" hole e x i s t s i n the atomic hydrogen distribution.  b)  A h o l e e x i s t s because the atomic hydrogen i s i n f a c t molecular.  c)  The c l o u d c o n t a i n s atomic hydrogen which i s c o o l e r than the background hydrogen and hence absorbs the r a d i a t i o n from t h i s hydrogen, p r o d u c i n g an apparent d e f i c i t .  These t h r e e cases have been summarized be d e a l t w i t h i n more d e t a i l l a t e r on.  i n FIGURE 1. and w i l l I t i s the aim o f the  p r e s e n t work t o r e s o l v e these p o s s i b i l i t i e s by u s i n g a s u f f i c i e n t l y l a r g e sample o f d u s t c l o u d s , so t h a t  trends  towards any o f the three cases can be s t a t i s t i c a l l y  estab-  l i s h e d , and the s i g n i f i c a n c e o f e x c e s s e s o r d e f i c i t s i n terms o f n o n - l i n e a r hydrogen g r a d i e n t s r e s o l v e d .  -8Chapter 2 GENERAL THEORY  2-1)  Definition The  Any  symbols  further  origins  o f Symbols used i n t h i s t h e s i s  are l i s t e d  i n TABLE I I .  knowledge needed c o n c e r n i n g t h e i r meanings o r  can be found i n S p i t z e r ' s book, D i f f u s e M a t t e r i n  33  Space. 2-2)  Temperature  and Thermodynamic E q u i l i b r i u m  As the concepts o f temperature and thermodynamic e q u i l i b r i u m , and the consequences figure  of their d e f i n i t i o n s ,  will  v e r y i n t i m a t e l y i n the d i s c u s s i o n t h a t f o l l o w s , i t i s  important we c l e a r l y e s t a b l i s h  what we mean by them.  I f a gas i s i n thermodynamic e q u i l i b r i u m , i t behaves as a b l a c k body, w i t h the p a r t i c l e e n e r g i e s e q u a l l y among the i n t e r n a l  and k i n e t i c degrees o f freedom.  distributed F o r such  a gas, c h a r a c t e r i z e d by i t s temperature T, a number o f statements c a n be made. . A)  The d i s t r i b u t i o n  c of p a r t i c l e v e l o c i t i e s i s Maxwellian:  <=P<iO A* 1 / _ a i _ J  e  A  B)  dv  (2-1)  The d i s t r i b u t i o n o f p a r t i c l e s among t h e i r i n t e r n a l  energy  s t a t e s i s Boltzmannian: M*(XA)  nf(t*.)= C)  The d i s t r i b u t i o n of  ionization  c Without  C~  £ a  1  M T  (2-2)  o f p a r t i c l e s among t h e i r v a r i o u s stages  i s g i v e n by the Saha e q u a t i o n :  loss of generality,it  mean v e l o c i t v vpm'QHOC  WO  has been assumed t h a t the  oKni I  -ni <-.^  „^  „  j __. .  -9-  *.*{XA-H)= H * ( X A ) D)  (2-3)  The d i s t r i b u t i o n o f photon e n e r g i e s I s P l a n c k i a n : BV (T)  The  TVH fe.  -=. ZATJ  2  1  (2-4)  d e f i n i t i o n s o f the symbols used here and elsewhere appear  i n TABLE I I ; the a s t e r i s k r e f e r s t o the p o p u l a t i o n s i n thermodynamic e q u i l i b r i u m ( T . E . ) . d e r i v e d from statistical  first  The e q u a t i o n s  themselves can be  p r i n c i p l e s by u s i n g the methods o f  mechanics.  A gas i n T.E. the r a d i a t i o n f i e l d this d i f f i c u l t y ,  c a n c a r r y no n e t r a d i a t i o n f l u x , because o f a b l a c k body i s i s o t r o p i c .  s i n c e we w i l l be i n t e r e s t e d  o f r a d i a t i o n through  To a v o i d  i n the t r a n s f e r  a d a r k dust c l o u d , we make the a p p r o x i -  mation o f " l o c a l thermodynamic e q u i l i b r i u m " ( L . T . E . ) , i n which we assume the v a l i d i t y o f e q u a t i o n s  (2-1) through (2-4)  by a l l o w i n g the temperature T t o v a r y s p a t i a l l y and t e m p o r a l l y , i f necessary.  I n t h i s way, we can ensure  the t r a n s f e r o f  r a d i a t i o n through a dark d u s t c l o u d . Is L.T.E. a good approximation?  The answer i s f o r t u n -  a t e l y yes, because i n the case o f d a r k d u s t c l o u d s , i t i s the p r o c e s s o f c o l l i s i o n a l e x c i t a t i o n which predominates over p h o t o - e x c i t a t i o n , and consequently r e l a t i v e p o p u l a t i o n s o f the s t a t e s . extreme c a s e s , the incoming upset  t h i s balance.  determines the  I n a l l but the most  photon f l u x would do l i t t l e t o  F o r g e n e r a l i t y , however, we s h a l l go one  step f u r t h e r , and assume o n l y t h a t the l e v e l p o p u l a t i o n s a r e  -10-  c o n s t a n t i n time.  To t h i s end, we  d e f i n e the " e q u i v a l e n t  thermodynamic system" i n which the temperature T e q u a l s a c t u a l k i n e t i c temperature T^, a c t u a l v a l u e , and  the e l e c t r o n d e n s i t y e q u a l s i t s  the d e n s i t y o f p a r t i c l e s i n stage  i o n i z a t i o n , H*"(XA-+I) , e q u a l s the a c t u a l v a l u e The  d e n s i t y o f p a r t i c l e s i n the  KLj*(X/i) and  j,^  (r+1)  l e v e l of e x c i t a t i o n  however, need not equal the a c t u a l v a l u e rtj (XA.) , "^-factor":  W i t h t h i s degree o f g e n e r a l i z a t i o n , the Boltzmann and equations  s t i l l hold —  a t l e a s t f o r the degree o f  f o r which the e q u i v a l e n t thermodynamic system was s h a l l a l s o p r e s e r v e the s i m p l i c i t y o f e q u a t i o n  the temperature a t which the observed  intensity I v  Saha  ionization defined.  (2-4)  d e f i n i n g the e q u i v a l e n t b l a c k body or b r i g h t n e s s a  of  H(XA.+ I.) .  the r e l a t i o n s h i p between them d e f i n e s the  "fb , s  the  We  by  temperature,  specific  e q u a l s t h a t g i v e n by e q u a t i o n  (2-4), with  similar  d e f i n i t i o n s f o r the b r i g h t n e s s temperature,  ~T , of the  radiation  i n c i d e n t upon the dark d u s t c l o u d , and e r a t u r e , T~ , o f the c l o u d i t s e l f .  the b r i g h t n e s s temp-  This l a t t e r  c  is  0  temperature  j u s t the temperature which c h a r a c t e r i z e s the  o f the p a r t i c l e  s t a t e s , and  i s sometimes r e f e r r e d to as  s p i n or e x c i t a t i o n temperature, i n hydrogen c l o u d s , ( a n d  populations  / . s  F i e l d has  shown  that  the case a p p l i e s even more s t r o n g l y  i n the dense dust c l o u d s ) t h i s p o p u l a t i o n , except extreme c a s e s , i s e n t i r e l y determined consequently  the  i n the most  by c o l l i s i o n s ,  and  the e x c i t a t i o n temperature i s e q u a l to the  -li-  the  k i n e t i c temperature o f the gas.  The k i n e t i c temperature,  on the o t h e r hand, i s the temperature which c h a r a c t e r i z e s the Maxwellian v e l o c i t y d i s t r i b u t i o n , e q u a t i o n (2-1) a l s o .  so t h a t we can r e c o v e r  I n the case o f dense d u s t c l o u d s then,  even w i t h the perhaps unwarranted g e n e r a l i z a t i o n t o an e q u i v a l e n t thermodynamic system, we can s t i l l of  r e c o v e r the use  e q u a t i o n s (2-1) through ( 2 - 4 ) .  2-3)  The E q u a t i o n o f T r a n s f e r In  order to i n t e r p r e t  the 21-cm l i n e d a t a which has  been r e c e i v e d by a r a d i o t e l e s c o p e from beam p o s i t i o n s on and s u r r o u n d i n g dark d u s t c l o u d s , we must s o l v e the e q u a t i o n o f r a d i a t i v e t r a n s f e r f o r the passage o f t h i s r a d i a t i o n through the  i n t e r s t e l l a r medium, and i n p a r t i c u l a r , through a dense  dust  cloud. To t h i s end, we d e f i n e the s p e c i f i c  of  a radiation field  so t h a t  I JvJ^alflcLt v  those photons, whose f r e q u e n c y l i e s about i / ,  intensity  I  v  -  l (!L,&>t) v  i s the energy o f  i n the i n t e r v a l  and whose d i r e c t i o n i s w i t h i n the s o l i d a n g l e dco  about K_, which p a s s e s , i n a time i n t e r v a l ^ ,  through the  a r e a dft , which i s l o c a t e d a t p o s i t i o n A , and i s p e r p e n d i c u l a r to  the photon d i r e c t i o n K.  -12-  Changes In I  due to i n t e r a c t i o n s w i t h matter a r e d e s c r i b e d  v  by the e q u a t i o n o f t r a n s f e r , which i s d e r i v e d by c o n s i d e r i n g the f l o w o f energy i n and out o f the ends o f a c y l i n d e r o f l e n g t h JU. I<  da/  W i t h i n t h i s c y l i n d e r , both e m i s s i o n and a b s o r p t i o n o f r a d i a t i o n a r e p o s s i b l e , so we d e f i n e the e m i s s i o n c o e f f i c i e n t <jv  and the a b s o r p t i o n c o e f f i c i e n t  and K I v  v  dVd-v Jij dt  K.  v  so t h a t  y  dVdutdt  v  a r e r e s p e c t i v e l y the energy e m i t t e d by a  volume element dV i n the i n t e r v a l s  and dt , and the  energy absorbed from a beam o f s p e c i f i c i n t e n s i t y Tv> i the same i n t e r v a l s .  n  The energy l o s t from the beam i n p a s s i n g  through the volume dV i s (IV(/L-+CU)  - I^CA))  di)doo  olfl dt  and  t h i s must e q u a l the energy e m i t t e d by the volume dV, namely j  v  dYdudco  dt,  minus the energy absorbed, K.y I  v  JYdvdu  dt  y  that i s : (l2)Ut-d*)-Ij)U))ciudujd/ldt  Or  AL>  = jjdVdzidcJdt  -Kv  -  I„  cU  -Kj> I„  -+•  JVdiJdoodt  (2-6) 1  I f we d e f i n e the o p t i c a l depth, T  vt  a l o n g the photon path,  which has been assumed t o be a s t r a i g h t l i n e , by the e x p r e s s i o n *  dt r  v  = KV  (2-7  v  -13-  and  consider  the r a d i a t i o n r e c e i v e d from a dark dust  t o t a l o p t i c a l depth C  with  r  Vt  on the  then e q u a t i o n I„  We  now  incident radiation intensity  s i d e o f the c l o u d away from the  DfiRK  =  (2-6)  may  l (o)  DUST  be  +  (2-8)  e ^ ' ^ d ^  thermodynamic  t h a t the v a r i a t i o n dI /cU, , o f the v  T h i s being I  In s t r i c t T.E.  the case,  CONSTANT  —  v  equation  —  i t would be  (2-6)  (2-9)  8 )(T)=j, ,f Kjj s i n c e i  2  the P l a n c k f u n c t i o n .  , defined  c  chapter.  I n t e g r a t i o n of equation r  e- *  I -~Iv«>) v  Using  considered  gives:  assume t h a t t h i s i s the case h e r e , where the  used, i s c l o u d temperature T  specific  f*>/&ii  true that  s p e c i f i c i n t e n s i t y i s g i v e n by now  v  OBSERVER  CLOUD  i n t e n s i t y through the c l o u d i s s m a l l enough to be to v a n i s h .  l (o)  observer,  assume t h a t the above c l o u d i s i n l o c a l  e q u i l i b r i u m , but  of  integrated to give:  e'^  v  cloud  +  (2-8)  We  the shall  temperature  i n s e c t i o n 2 of  this  results in:  B^C-TdKi- e-'S  (2-10)  the e a r l i e r d e f i n i t i o n s o f the observed, i n c i d e n t and  cloud brightness  temperatures and Bi)  where we  ( T )  -  a l s o the  Zjt  have expanded the e x p o n e n t i a l  \\vJwX because  h*)/kT « 1  o f i n t e r e s t here, e q u a t i o n  approximation:  M.T  to f i r s t  order  f o r the temperatures and  (2-10) f i n a l l y y i e l d s :  in  frequencies  -14-  7; where the of the  =  first  r e s e n t s the  r  0  term on  incident  + 77 (1 - e"^)  c- >  T  the  energy by  e m i s s i o n and  r i g h t r e p r e s e n t s the  the  c l o u d , and  the  self-absorption  by  temperatures used i n e q u a t i o n (2-11) are observed q u a n t i t i e s , upon the  provided  the  cloud.  The  easily related  o f the  i n t h i s case, the  absorption  second term r e p -  i s known.  transition probabilities  b e i n g observed —  (2-iD  to  however depends  particular  1420.4 MHz  line  transition  2 between the  two  h y p e r f i n e s t a t e s of the  1  ground l e v e l  of  atomic hydrogen. 2-4)  The As  Optical  p o i n t e d out  depth a t 21-cm ities,  XI  i n the  .  p r e v i o u s paragraph, the  depends upon the E i n s t e i n  t h a t i s , on  d e f i n e d as  21-cm, T  Depth a t  the  the  transition  spontaneous t r a n s i t i o n  probability  per  t r a n s i t i o n from atomic l e v e l k  unit  transitions  the  probabilities  respectively,  In what f o l l o w s , we of the k and  21-cm  per  time of a  spontaneous  to atomic l e v e l ^ , and  to the  unit radiation  and  t r i p l e t , and  the Bfk  ,  upwards  energy d e n s i t y , Ujj.  w i l l l i m i t o u r s e l v e s to a  F=l  on  f o r induced downwards and  l i n e of atomic hydrogen, so t h a t the  j> w i l l r e f e r  probabil-  probability  induced (or s t i m u l a t e d ) t r a n s i t i o n p r o b a b i l i t i e s B^jd e f i n e d as  optical  F=0  discussion  subscripts  singlet  -15-  d hyperfine l e v e l s .  Thus we w i l l be concerned w i t h the  ition probabilities  Pi  lo  w i l l r e f e r t o the 21-cm will  indicate  /0  and  line.  Furthermore,  F-0 s t a t e s  v,  Bo\, and the frequency  0  n (HI) and  n (Hl)  t  0  the number o f atomic hydrogen atoms per  volume i n the F=-1 and Although  B  ?  trans-  unit  respectively.  the t o t a l e m i s s i o n over the 21-cm  line  naturally  has n o t h i n g to do w i t h the a b s o r p t i o n i n t h i s l i n e , i t i s s t i l l n e c e s s a r y f o r us t o c a l c u l a t e  the t o t a l e m i s s i o n i n o r d e r t o  e s t a b l i s h a r e l a t i o n s h i p between the E i n s t e i n t r a n s i t i o n p r o b a b i l i t i e s , which w i l l be needed i n c a l c u l a t i n g  T .• a  S i n c e spontaneous e m i s s i o n can o c c u r i n any d i r e c t i o n , the t o t a l energy  radiated  spontaneously per u n i t volume p e r  u n i t s o l i d angle i s : (2-12) that  i s , j u s t the p r o d u c t o f the number o f atoms capable o f  r a d i a t i n g per u n i t volume, the p r o b a b i l i t y t h a t and the energy e m i t t e d by each photon, angle t h a t  radiate,  a l l d i v i d e d by the  the r a d i a t i o n i s e m i t t e d i n t o .  t o t a l energy absorbed  they  S i m i l a r i l y , the  i n the l i n e per u n i t s o l i d angle  u n i t volume p e r u n i t time may  solid  be c a l c u l a t e d ,  but s i n c e  per the  photons e m i t t e d by induced e m i s s i o n are t r a v e l l i n g i n the same d i r e c t i o n as the s t i m u l a t i n g  photons,  and have the same  frequency, the r a t e o f energy a b s o r p t i o n must be c a l c u l a t e d  d  F, the t o t a l s p i n a n g u l a r momentum, i s the sum S + I , o f the e l e c t r o n and p r o t o n s p i n s , which are both e q u a l t o k ( i n units o f £ ) .  as  -16-  the d i f f e r e n c e between the r a t e s f o r induced induced  emission.  a b s o r p t i o n and  Assuming I „ i s r e l a t i v e l y c o n s t a n t  l i n e and u s i n g the f a c t t h a t Uv = I„/c,  the t o t a l  over the  absorption  o f r a d i a t i o n by an atom i s then the i n t e g r a l o f K v 1 ^ over the l i n e , o r  lv\  K Jv  =  V  k z)o, (  Q  OL  - fl, (Hi)  Bjli; JO  (2-13)  I f we now c a l c u l a t e the p o p u l a t i o n d e n s i t y o f e m i t t i n g atoms, ^ ( X / J , i n terms o f fiefl.C X/t+i), by means o f e q u a t i o n s  (2-2),  (2-3) and ( 2 - 5 ) , and then equate fi (XA+.) t o ft*(X/i+i) i n the e q u i v a l e n t thermodynamic system, we o b t a i n :  **(X ) = 1^ A  ^le  e"  EAfc/teT  ne VKXAH-,)  f*+i fe F o r hydrogen atoms i n the upper h y p e r f i n e l e v e l 1K(X>I)  =  H(XA+I)-  (A=l  >  t  n  e  n ^ b e r d e n s i t y o f protons, and  s i n c e i o n i z e d hydrogen has no e x c i t e d s t a t e s .  Je.*i)  v  =  ,  unity,  Making  these  (2-14), and s u b s t i t u t i n g f o r ft,(Hi) i n  changes i n e q u a t i o n  (2-13), we o b t a i n : j j, dv v  -  However, by e q u a t i o n  hi  y,i k -iJot A io rie. rip e ~  g < / / /  * ~  (2-15)  T  (2-9), the r i g h t hand s i d e s o f equations  (2-13) and (2-15) must be e q u a l when 1 ^ = Bp(T). it  v  1  n., (HI) the p o p u l a t i o n d e n s i t y o f the t r i p l e t s t a t e ,  the p a r t i t i o n f u n c t i o n f o r protons, which e q u a l s  equation  (2-14)  From  this,  follows that:  e T h i s assumes the z e r o o f energy corresponds electron at rest.  to a free  -17Th i s f i n a l l y e s t a b l i s h e s the r e l a t i o n s h i p we needed between the E i n s t e i n t r a n s i t i o n  probabilities.  In o r d e r t o d e r i v e the o p t i c a l depth a t 21-cm, we d e f i n e the i n t e g r a t e d atomic ^ whereby,  the atomic  now  c r o s s - s e c t i o n by the e q u a t i o n :  = J xlv  (2-17)  absorption cross section, i s defined  by the r e l a t i o n s h i p : rij A,  v  I f we  s p e c i f y ^ - 0 , the f-0  the l a s t  =  K  (2-18)  v  s u b l e v e l o f hydrogen, and combine  two d e f i n i t i o n s , we g e t : A  = _X—  n (Hl)J  fK  (2-19)  v  0  However, J Hv d-v i s g i v e n f o r the 21-cm  l i n e by e q u a t i o n  (2-13),  therefore,  A  =  k iJo, Bo. f 1 _  rijjjjj)  C  B \  TUCHI) BO,/  U s i n g our d e r i v e d r e l a t i o n s h i p between the E i n s t e i n probabilities of equations  U i  transition  ( e q u a t i o n ( 2 - 1 6 ) ) , t o g e t h e r w i t h the d e f i n i t i o n s (2-2) and ( 2 - 5 ) , we f i n a l l y o b t a i n :  A where A  (2-20)  lo  =  -4. ( 1 - f  - «'* ^ M  e  T  (2  . ) 21  the v a l u e of yd u n c o r r e c t e d f o r induced e m i s s i o n , i s  g i v e n by: y&u. = We  are now  the 21-cm  h iJo, Bo C  (2-22)  i n a p o s i t i o n t o c a l c u l a t e the o p t i c a l depth f o r line, T  a{  . From the d e f i n i t i o n f o r the o p t i c a l  depth ( e q u a t i o n ( 2 - 7 ) ) , we have:  -18-  n: lv) u  ~\<LXv  K,  =j  JL<V - j n (HI)4,v  v  d*  0  =  To remove the f r e q u e n c y dependence o f t (v)  we  AI  perform an i n t e g r a t i o n which we  s e c t i o n 2 o f t h i s c h a p t e r we  ribution  of p a r t i c l e s ,  (2-23)  V  must  now  avoided doing e a r l i e r i n d e r i v -  i n g an e x p r e s s i o n f o r the i n t e g r a t e d atomic In  NO(HI)A  cross-section.  showed t h a t the v e l o c i t y  i n t h i s case hydrogen  atoms,  dist-  was  Maxwellian, that i s ,  where 7 7 denotes  the k i n e t i c  temperature  assume the o n l y s i g n i f i c a n t  l i n e broadening i s due  s h i f t s between the d i f f e r e n t at and  the f r e q u e n c y Va, , then  o f the gas.  hydrogen  to D o p p l e r  atoms e m i t t i n g  v - Do, (l+v-/c).  I f we  radiation  S i n c e 7l(.V)diJ  dv = (voi /c) cfr, i t immediately f o l l o w s from e q u a t i o n  t h a t the a b s o r p t i o n p r o f i l e w i l l have a l i n e 7T(2J) -  c  \\_  m  Vo, j) J.TZ ,  _  - cPcirtdW(2-1)  shape  e  (2-24)  Consequently, xtz, =  xt- Tl{iy)  So t h a t from e q u a t i o n s (2-23) and f o r the o p t i c a l  depth a t  f i n a l l y obtain  21-cm  Tj, (v) = where A  (2-25), we  (2-25)  No (Hi) A, TC(v)  i s o f course g i v e n by e q u a t i o n (2-21).  t h a t the r a t i o  (2-26) We  now  assume  (>, / £ ) i n t h i s e q u a t i o n i s v e r y c l o s e t o u n i t y , 0  as w i l l be the case due  t o the f r e q u e n t c o l l i s i o n s i n dense  -19dust c l o u d s , and expand the e x p o n e n t i a l , so t h a t on s u b s t i t -  (2-26),  uting into equation  =  we  find:  No(HI)^  h Vos  u  Bo,  TC(v)  = (J—JLSL-B.,O)  hi (Hi)  -  HCHl)  5". 49 "10"  1+  (2-27)  Ti where a l l the c o n s t a n t s , except f\ , a r e e a s i l y l0  f\  t0  c a n be found  from a s t r a i g h t f o r w a r d , b u t l e n g t h l y ,  quantum mechanical perturbation  evaluated.  c a l c u l a t i o n i n v o l v i n g time dependent  theory.  I t i s a l s o u s e f u l t o know the i n t e g r a t e d column d e n s i t y o f hydrogen atoms.  To t h i s end, we assume t h a t the l i n e i s  u n s a t u r a t e d , so t h a t T , i s s m a l l .  Equation  z  be expanded t o f i r s t  (2-11)  may then  o r d e r i n T , t o g i v e T - To* CI-T:^ +• Ti r»», b  a  which, when the background i s s u b t r a c t e d , y i e l d s :  Tx, =-T /Tl  (2-28)  b  But  i n T.E.,7I  (2-28)  = 7«  i n equation  , so t h a t on s u b s t i t u t i o n o f e q u a t i o n  (2-27)  N(hil)  and i n t e g r a t i n g , we g e t :  = 1.83 >10 J l l 18  (v) dv  (2-29)  where V- i s measured i n Km/sec. 2-5)  The I n t e r p r e t a t i o n o f L i n e Widths One o f the most important  q u e s t i o n s we s h a l l be a s k i n g  o u r s e l v e s , i n t r y i n g t o d e c i d e whether a dense dust c l o u d  -20contains molecular  o r atomic hydrogen, i s : "What i s the  temperature o f the c l o u d ? " can be e s t i m a t e d  I t t u r n s out t h a t t h i s parameter  i n s e v e r a l ways - one o f which i s from the  width o f an observed  line profile.  Equation  (2-24) f o r a  line profile i s :  TTcv) = C_  AL_£L_  e  (2-24)  T h e r e f o r e , a t one h a l f the peak v a l u e o f 7T(z>)  f  lLr2  c A! /YI  =  where 1)^ i s the frequency i t s peak v a l u e .  e  (2-30)  a t which the p r o f i l e a t t a i n s one h a l f  I f we rearrange e q u a t i o n  the f u l l width a t h a l f i n t e n s i t y , AVT A2JL_  =  we have  T  (2-30) and d e f i n e  by the e x p r e s s i o n :  Z ( ^ - ^ i )  (2-31)  we o b t a i n : AV  L  =  Z(^]^[(JUZ)  ZkH'  (2-31a)  from which i t f o l l o w s t h a t the k i n e t i c temperature o f the a b s o r b i n g gas r e s p o n s i b l e f o r the p r o f i l e i s :  where  A l \ _ i s measured i n KHz o r Tn  =  Z1.(P ( LV-jf  where A^L. i s measured i n Km/sec.  (2-32)  -212-6)  V i s u a l O p t i c a l Depth, Xy  The  In s e c t i o n depth a t 21-cm d e n s i t y and  2-4  and  we  d e r i v e d an e x p r e s s i o n f o r the  found out  temperature.  how  i t depends upon the  S i n c e we  namely t h e i r v i s u a l o p t i c a l depth T , v  i t i s worthwhile, f o r the  r  simply  /9y  visual extinction,  properties,  their visual  and  see  extinc-  interpretation, how  i t is  related  ( i n magnitudes), i s d e f i n e d  as: flv  where Fv c l o u d and  -Z.5T ley  m  ( Fv/FvCo))  (2-33)  v i s u a l f l u x r e c e i v e d from a s t a r behind  F (o)  i s the v i s u a l f l u x t h a t would have been  v  c l o u d not  i n t e g r a l of the  integrated  =  i s the  r e c e i v e d , were the  over the  I ^ i s g i v e n by  present.  Now  s o l i d a n g l e subtended by to  Because o f the  insignificant contribution  or e m i s s i o n by  the  Fy i s j u s t star,  s t a r , where  e^'^dri to  c l o u d g r a i n s w i t h i n the  ^ J I„(o) C** d«> =  I (o) v  I  v  (2-8) from  scattering  s t e l l a r image,  second term i n t h i s e q u a t i o n .  u  the  the  be:  T  = §l Jw  flux  from the  y  = I.co) e- * + J j £ g \  n e g l e c t the  the  specific intensity I ,  e q u a t i o n (2-8)  U  may  the  Ct\.  The  the  or  purposes o f  to d e r i v e a s i m i l a r e x p r e s s i o n f o r TV to  column  r e a l l y o n l y know of  e x i s t e n c e o f dark dust c l o u d s through t h e i r v i s u a l  t i o n /9v,  optical  Therefore,  \du)  we  -22-  and =• j  F (o) v  so t h a t e q u a t i o n  l Cd)\dui v  (2-33) may be r e - w r i t t e n : Pis, =  where we have assumed uniform  ljj(o) cL) =  -ZSUj e.' ^  l.o&lotv  x  iB  (2-34)  t h a t the v i s u a l o p t i c a l depth Tv i s  over the s o l i d angle subtended by the s t a r .  g r a i n s are r e s p o n s i b l e f o r the e x t i n c t i o n , we may  Since  use  equation  (2-26) t o w r i t e : Tv  =  NG xiv  (2-35)  where NG i s the column d e n s i t y o f a b s o r b i n g  g r a i n s and  i s the atomic a b s o r p t i o n c r o s s s e c t i o n a t v i s u a l The g e o m e t r i c a l  frequencies.  c r o s s - s e c t i o n o f a s p h e r i c a l g r a i n i s TCO. , so  t h a t i f we d e f i n e  2,  the e x t i n c t i o n e f f i c i e n c y f a c t o r , Q  T  by the  expression xlv = then e q u a t i o n  TT a  z  Q  (2-35) and (2-34) may Ty  TT a  =  a  (2-36) be w r i t t e n :  Q NG  (2-37)  or /?v Now,  =  3.41 a * Q  N  (2-38)  s  the average hydrogen gas d e n s i t y and dust d e n s i t y  a column o f l e n g t h  and u n i t c r o s s  ^  H  -  along  s e c t i o n are r e s p e c t i v e l y ,  N ( H I ) WH/JL  (2-39)  and, ^ where m  ri  =  N  G  £ KO? ^> /i  i s the mass o f hydrogen and  6  p  G  (2-40)  i s the i n t e r n a l g r a i n  -23-  I f we assume a=3«lo" cm, Q-Z.O and ^  density.  = Lgm cm",  5  3  G  (2-39) and ( 2 - 4 0 ) ,  then, on t a k i n g the r a t i o o f equations we o b t a i n , -  N(HI) or on u s i n g e q u a t i o n  * 10 ° < p „ / p ) N  (2-41)  L  6  G  (2-38)  N(HI)  =  10  C p H / p ) #v  1 9  (2-42)  G  T h i s e q u a t i o n shows c l e a r l y t h a t i f the r a t i o o f mass d e n s i t i e s o f hydrogen gas t o g r a i n s i s c o n s t a n t , then /V(HI), the column d e n s i t y o f hydrogen gas, i n c r e a s e s l i n e a r l y w i t h /? , the v i s u a l v  extinction. o f f\ . y  T h i s i s what i s n o r m a l l y observed  Note t h a t by u s i n g e q u a t i o n s  l a s t e q u a t i o n c a n be expressed  f o r small values  (2-27) and ( 2 - 3 4 ) , the  i n terms of the o p t i c a l depths  and T v a s :  T2.1  Z  = USb*10  u  Since  s  ffW  (pH/pfi)  T„  (2-43)  N(Hi) and /?y a r e the commonly measured a s t r o p h y s i c a l  q u a n t i t i e s , we w i l l n o r m a l l y use e q u a t i o n ( 2 - 4 3 ) . t o be observed  here  i s that  Tn and T y a r e a l s o  The p o i n t  linearly  p r o p o r t i o n a l t o each o t h e r so t h a t whether we t a l k o f a p l o t of  N (HI) v e r s u s f\y, o r Tzt v e r s u s T V , we are speaking  about  the same t h i n g . 2-7)  What i f T | i s Not P r o p o r t i o n a l t o Ty? t  In the l a s t  s e c t i o n we saw t h a t  t o £ ) p r o v i d e d t h a t the r a t i o (*5"H/^G) v  N(HI) was p r o p o r t i o n a l w  a  s  constant.  I f , however,  the mean d e n s i t y o f atomic hydrogen decreases as we move  -24towards the center of a cloud, while the v i s u a l e x t i n c t i o n continues to increase, then a plot of downwards f o r high /9v•  Nihil) versus flv w i l l turn  This corresponds to a " d e f i c i t " i n  the atomic hydrogen d i s t r i b u t i o n and could be caused by an anomolous gas to dust r a t i o within the cloud, by the hydrogen being converted to molecular form or by a cold absorbing cloud.  More w i l l be said about these p o s s i b i l i t i e s l a t e r . I f on the other hand, a p l o t of  N(H1) versus f\y increases  upwards as / ) increases, corresponding to an "excess" i n the v  atomic hydrogen d i s t r i b u t i o n , then some other explanation must be sought.  The p o s s i b i l i t y of low energy cosmic ray  d i s s o c i a t i o n of the molecular hydrogen supposed to e x i s t i n 31  dense clouds has been considered by two authors, one more explanation e x i s t s ^ .  but at least  I f the cloud i s In hydrostatic  equilibrium with i t s surroundings, there w i l l be no pressure gradient across the outer edge of the cloud, implying that the pressure i s a constant there. we also know that  ?-  rt(M)k~ . r  l  However, by the equation of state The combination of these  f a c t s together with the assumption  two  that the temperature i s  r e l a t i v e l y constant i n the l i n e of sight through the cloud leads to the r e s u l t that /V (^1^= constant. (2-6) we found that  H  Z{  °c A / W ) / " ^ .  leads to the r e s u l t that  Tt/°c  But i n section  Substitution f o r  A/(XT) .  then  Therefore, a p l o t of  f The expulsion of dust grains from the cloud to increase the r a t i o (pr\/f ) does not seem reasonable. G  -25-  T*/ v e r s u s  2-8)  i n c r e a s e q u a d r a t i c a l l y . (see FIGURE 1 )  will  The C o l d A b s o r b i n g One remaining  Cloud  r e s u l t which i s needed b e f o r e we d i s c u s s  the o b s e r v a t i o n s , i s how t o i n t e r p r e t d e f i c i t s Consider  i n terms o f a  c o l d absorbing  cloud.  a c o l d dense d u s t c l o u d o f  temperature Tc  and o p t i c a l depth T , i n f r o n t o f a normal c  r e g i o n o f hydrogen e m i s s i o n ,  perhaps a s p i r a l arm o f the  galaxy.  f  8«CKGROUND  .  When the antenna beam i s p o i n t e d on the c o l d c l o u d , (2-11)  t e l l s us t h a t the observed b r i g h t n e s s rc  -rb «,») while  =  temperature i s :  c  c  T0 (\-e ') er* + T d- e'" )  on a nearby p o i n t the observed b r i g h t n e s s T*>fO =  equation  To  (2-44)  temperature i s :  (l-e^')  A f t e r we average the observed b r i g h t n e s s temperature on and o f f the c l o u d p o s i t i o n , the average observed  profiles deficit  w i l l be: AT", = = where t h e bars  T^ron) -Tfe(tf-ff) rc  (Tc - T ( j - e - ) ) ( I - cT ) T o  0  i n d i c a t e the average v a l u e s .  concerned o n l y w i t h e x p l a i n i n g d e f i c i t s absorbing  cloud, A T , < 0 .  (2-45) S i n c e we a r e  i n terms o f a c o l d  But we a l s o know t h a t o < ( 1 - e " ) < 1, Tc  -26hence:  AT  > ( Tc-Tod-e"^)) = (Tc -T C*ff))  b  which on rearrangement a l l o w s on the c l o u d b r i g h t n e s s  T  (2-46)  b  ^ AT  t  us t o p l a c e on upper  limit  temperature Tc b  +T <ofl) b  ~ T<orv>  (2-47)  b  t h a t i s , the c l o u d temperature i s n e c e s s a r i l y always l e s s than the mean observed b r i g h t n e s s Similarily, the  temperature on the c l o u d .  we can c a l c u l a t e a lower l i m i t  second term i n e q u a t i o n  (2-44).  T (o^ > To ( l - e b  s i n c e T (l - e~ )  ) e~  Tc  i s always p o s i t i v e .  Xc  c  T  _Xa  This  c  t o T by n e g l e c t i n g c  gives:  = T <otn e b  _ , C c  Therefore,  £ J-TL I Tb (off) ) \ Tb (.on) J  (2-48)  Some f e e l i n g f o r what the upper l i m i t on T must be,can be c  obtained  by c o n s i d e r i n g e q u a t i o n  t h e r e , even one degree b r i g h t n e s s  (2-45).  Ift  c  were too l a r g e  temperature d i f f e r e n c e s  between the on and o f f c l o u d p o s i t i o n s would be e a s i l y detected, At  and t h i s does not appear t o be the intermediate  and h i g h e r  the hydrogen i s more l i k e l y something l i k e a c o l d spot  case.  g a l a c t i c l a t i t u d e s however,  t o be l o c a l . i n a large  I n t h i s case we have  cloud.  OBSCftVER  I f we n e g l e c t  the background e m i s s i o n  then e q u a t i o n  (2-44) g i v e s :  on the c l o u d p o s i t i o n ,  -27-  T n) = Tc ( I -  e'^)  b(0  (2-49)  so t h a t T In  >, T  t  b  (on)  (2-50)  t h i s case the observed b r i g h t n e s s temperature  r e p r e s e n t s not an upper l i m i t as b e f o r e , but a  on the c l o u d lower l i m i t  the c l o u d b r i g h t n e s s temperature, T". . A t nearby p o s i t i o n s the sky, the observed b r i g h t n e s s temperature w i l l T ^*ff) b  = To(\  to  on  be:  - e' )  (2-51)  Zo  By assuming a v a l u e o f 125°K as an average v a l u e f o r the o f f c l o u d b r i g h t n e s s temperature, To » Furthermore, we  shall  w  e  c  a  n  then c a l c u l a t e  To.  assume t h a t the amount o f hydrogen  in  the c o l d spot i s g r e a t e r than o r e q u a l t o the amount a t nearby p o s i t i o n s , s i n c e a l a c k o f HI a t the c o l d spot i s i n i t s e l f a l r e a d y a good enough r e a s o n t o expect a d e f i c i t emission there.  i n the  hydrogen  From e q u a t i o n (2-27), we know t h a t A/(Hl)«cT"T ,  therefore Tc But we  c  and  >/ ~Yo Xo  have a l r e a d y e s t i m a t e d To  (2-52) and T  Tc  T. c  To so t h a t e q u a t i o n s  (2-49) r e p r e s e n t two e q u a t i o n s i n two unknowns T h i s e n a b l e s us to c a l c u l a t e on upper  and a lower l i m i t The  and  (2-52)  to  limit  T. c  two models j u s t c o n s i d e r e d g i v e q u i t e v a r i a b l e  to Tc  -28-  r e s u l t s f o r the parameters  T  c  and tc\ the r e a l case i s most  l i k e l y t o be a messy combination o f the two.  However, they  do a l l o w us t o p l a c e upper and lower l i m i t s on the c l o u d b r i g h t n e s s temperature Tl, optical  depth, T . c  and a lower l i m i t on the c l o u d  -29Chapter 3 EQUIPMENT AND  3-1)  OBSERVATIONS  The Apparatus The d a t a a n a l y z e d i n t h i s t h e s i s was o b t a i n e d d u r i n g  two weeks o f August  1970, u s i n g the 26 meter p a r a b o l o i d o f  the Dominion Radio A s t r o p h y s i c a l O b s e r v a t o r y near P e n t i c t o n , B. C.  The r a d i a t i o n c o l l e c t e d and f o c u s s e d by the p a r a b o l o i d  was f e d by a horn i n t o an uncooled p a r a m e t r i c a m p l i f i e r . (See FIGURE 2)  After this f i r s t  s i g n a l passed through a s o l i d  stage o f a m p l i f i c a t i o n , the  s t a t e pre-amp, f o l l o w e d by a  tunable band-pass f i l t e r and mixer pre-amp. heterodyned  The l a t t e r  unit  the r e c e i v e d 1420.4 MHz s i g n a l dcwn t o a 35 MHz  i n t e r m e d i a t e frequency ( I . F . ) s i g n a l , which was sent, by c a b l e from the f o c u s t o the back end i n the c o n t r o l room.  Here the  I.F. s i g n a l was a m p l i f i e d , f i l t e r e d and mixed a g a i n , t h i s w i t h a 45.7 MHz  s i g n a l t o produce a 10.7 MHz  frequency o f the f i l t e r  spectrometer.  time  s i g n a l - the c e n t e r  An automatic g a i n c o n t r o l  (A.G.C.) l o o p over t h i s s e c t i o n o f the r e c e i v e r ensured  that  a c o n s t a n t s i g n a l l e v e l was b e i n g f e d i n t o the spectrometer, which c o n s i s t e d o f 100 c o n t i g u o u s 10K.H  Z  ectors.  crystal filters  and d e t -  The two banks o f 100 i n t e g r a t i n g c i r c u i t s on the out-  put o f the spectrometer, r e f e r r e d t o as banks A and B i n the remainder  o f t h i s t h e s i s , were scanned  a l t e r n a t e l y every  60 seconds, and the 100 analogue v o l t a g e s d i g i t i z e d and dumped i n t o a PDP-9 o n - l i n e computer, from which a paper tape and  -30written output was obtained, a f t e r the designated number of spectrometer cycles had been made.  The radio frequency  l o c a l o s c i l l a t o r (L.O.) signal used to produce the I.F. i n the f i r s t stage of mixing was generated by phase locking a backward wave o s c i l l a t o r (B.W.O.) to the signal produced  by  a frequency synthesizer. A l s o , a plasma noise tube c a l i b r a t i o n could be coupled into the front end v i a a 20 db attenuator, or the paramp switched between the feed and a termination at ambient temperature 3-2)  - a "hot", signal reference l e v e l .  Which Dense Dust Clouds Do You Observe? In deciding which dense dust clouds to observe, a  number of considerations have to be taken into account. F i r s t , the clouds should have sizes comparable to the 36 arcmin h a l f power beam width of the telescope, to ensure that the reference positions are o f f the cloud and yet near enough so that the e f f e c t s due to non-linear hydrogen gradients do not become important.  N a t u r a l l y i t would be d e s i r a b l e i f  there were no other clouds nearby. Second, the clouds should be as opaque as possible, because i f any non-linear e f f e c t i n the r e l a t i o n s h i p between I'xi and T  v  i s to occur, we expect i t at the largest v i s u a l  extinctions. Third, the clouds should have a g a l a c t i c l a t i t u d e such that  \  10°. This should ensure that the observations  -31-  are b e i n g made s u f f i c i e n t l y f a r o f f the g a l a c t i c plane f l u c t u a t i o n s i n the hydrogen  that  e m i s s i o n t h e r e should not drown  out any observed excesses or d e f i c i t s . F o u r t h , the c l o u d s should, i f p o s s i b l e , be w i t h some o t h e r s p e c t r a l l i n e s ,  associated  such as those of OH  or H 2 C O .  I f an observed excess or d e f i c i t o c c u r r e d a t the same v e l o c i t y ^ as one o f these l i n e s ,  then because we  f e e l c e r t a i n t h a t these  l i n e s o r i g i n a t e i n dense r e g i o n s o f space, i t seems v e r y l i k e l y t h a t an observed d e f i c i t o r excess o c c u r r i n g a t n e a r l y the same v e l o c i t y a l s o comes from the same dense r e g i o n , s i n c e a t h i g h l a t i t u d e s there are o n l y one or two of  i n the l i n e  sight. In TABLE I I I a r e l i s t e d the o b j e c t s which  most o f these c r i t e r i a .  O b j e c t s 1-23  satisfied  are sources i n the  Cudaback - H e i l e s survey o f dark c l o u d s f o r 1667 MHz  OH  4 radiation  which i n f a c t d i d show t h i s l i n e .  Heiles'  o f f o r t y - e i g h t dark c l o u d s f o r anamolous hydrogen i n c l u d e d l e s s than h a l f o f these.  The  survey  emission  f o l l o w i n g group  of  o b j e c t s from 24 - 31 are sources i n H e i l e s * dark c l o u d survey which e i t h e r showed d e f i c i t s or were b o r d e r l i n e c a s e s . f i n a l group  The  of o b j e c t s are dark c l o u d s from the Lynds Catalogue  g A l l v e l o c i t i e s i n t h i s t h e s i s are w i t h r e s p e c t to the s t a n d a r d o f r e s t (L.S.R.), d e f i n e d as the c e n t r o i d o f f o r the l o c a l group o f s t a r s . 5  local motion  -32-  h a v i n g the l a r g e s t v i s u a l e x t i n c t i o n (5 o r 6 ) , a r e a s o f the o r d e r o f the h a l f power beam width o f the antenna, a h i g h galactic latitude from o t h e r c l o u d s .  (  /A />/^°), x  and which a r e s e p a r a t e d  A l l o f these dark c l o u d s were then l o c a t e d  on the Palomar Sky P r i n t s and checked r e f e r e n c e r e g i o n s c o u l d be found.  t o make sure  suitable  I n t h i s p r o c e s s , a few  a d d i t i o n a l sources were found and added t o the l i s t .  3-3)  Method o f O b s e r v a t i o n In a l l the work to be d e s c r i b e d here, the L.O. was changed  f o r each o b s e r v a t i o n so t h a t the spectrometer was c e n t e r e d a l t e r n a t e l y on 1420.600 MHz and 1420.570 MHz. t h a t the c r y s t a l f i l t e r s  i n the spectrometer  o f lOKHz, t h i s means t h a t two i d e n t i c a l  I f we  recall  have a bandwidth  spectra, s h i f t e d with  r e s p e c t to each o t h e r by t h r e e c h a n n e l s , were o b t a i n e d a t each position.  The r e a s o n f o r d o i n g t h i s was t h a t the spectrometer  had about a dozen bad channels, shifted profiles, was bad d a t a .  so t h a t by comparing the  i t c o u l d be d e c i d e d what was good and what  Two d i s t i n c t  types o f 21-cm o b s e r v a t i o n s were  made: A)  F u l l P r o f i l e Observations:  D u r i n g the f i r s t week o f  o b s e r v a t i o n s 21-cm l i n e p r o f i l e s were o b t a i n e d f o r the sources i n TABLE IV, and the i n d i c a t e d r e f e r e n c e p o s i t i o n s .  The  t y p i c a l p o s i t i o n i n g o f the antenna beam i s i l l u s t r a t e d i n FIGURE 3.  The r e f e r e n c e p o s i t i o n s were g e n e r a l l y chosen t o  -33be 40 arcmin away i n d e c l i n a t i o n , o r 3.5 minutes i n r i g h t ascension, o f secant  although  f o r high d e c l i n a t i o n clouds, a c o r r e c t i o n  ( d e c l i n a t i o n ) had t o be a p p l i e d t o the e a s t and  west r e f e r e n c e p o s i t i o n s t o a v o i d o v e r l a p o f the antenna beam positions.  The c l o u d r e f e r e n c e p o s i t i o n p r o f i l e s w i l l be  r e f e r r e d t o as n o r t h  (N), south  ( S ) , east  (E) and west (W).  In a d d i t i o n , r e f e r e n c e p r o f i l e s were a l s o o b t a i n e d northeast  (NE), southeast  i n the  ( S E ) , northwest (NW) and south-  west (SW) p o s i t i o n s o f some c l o u d s .  A source  (SRC) o r c l o u d  p r o f i l e was o b t a i n e d b e f o r e and a f t e r the c l o u d  reference  p o s i t i o n s were observed, as a c o n s i s t e n c y check, and then a calibration,  t o be d e s c r i b e d l a t e r , was made.  F o r a l l o f these  measurements, a two minute i n t e g r a t i o n was made f i r s t r e l e v a n t p o s i t i o n , and then w i t h  the paramp switched  "hot"  load f o r a signal reference  level.  these  s i g n a l s d i v i d e d by the r e f e r e n c e  on the t o the  The d i f f e r e n c e o f  s i g n a l was then c a l c u l a t -  ed by the computer. B)  Difference P r o f i l e Observations:  reference  Because the " h o t "  l o a d i n t r o d u c e s an e x t r a 300°K o f n o i s e t o the  r e c e i v e r n o i s e o f t y p i c a l l y 150°K and because there was some doubt as t o whether i t was s a t u r a t i n g one o f the IF a m p l i f i e r s , i t was d e c i d e d  t o re-observe  as many  sources  as p o s s i b l e , b u t t h i s time u s i n g the o f f c l o u d p o s i t i o n s as s i g n a l r e f e r e n c e l e v e l s i n s t e a d o f the " h o t " l o a d .  This  -34-  would generate d i f f e r e n c e p r o f i l e s immediately, but l i m i t the amount of i n t e r p r e t a t i o n p o s s i b l e .  slightly  A g a i n the  measurements c o n s i s t e d of 2 minute c y c l e s on the c l o u d and c l o u d r e f e r e n c e p o s i t i o n s , but i n the case o f the runs, the n o r t h g a l a c t i c p o l e was level, very  s i n c e the hydrogen  calibration  used as a s i g n a l r e f e r e n c e  e m i s s i o n from t h i s d i r e c t i o n i s  small. A summary o f the sources observed by e i t h e r of these  means and TABLE IV.  the c l o u d r e f e r e n c e p o s i t i o n s used appears i n An "X"  the column was  i n d i c a t e s t h a t the p o s i t i o n a t the head of  observed once;  i f an "X"  a l s o appears  " > 1 " column, they were observed more than 3-4)  once.  Method o f C a l i b r a t i o n Two  A)  i n the  methods of data c a l i b r a t i o n were p o s s i b l e :  Primary C a l i b r a t i o n :  A t the time the o b s e r v a t i o n s were  36 b e i n g made, W i l l i a m s  had  j u s t proposed  i n t e r n a t i o n a l standards f o r 21-cm listed  f o u r r e g i o n s as  observations.  They a r e  i n TABLE V w i t h t h e i r LSR v e l o c i t i e s and peak b r i g h t n e s s  temperatures, T  b  .  Three o f these r e g i o n s had been p r e v i o u s l y  used by the I n t e r n a t i o n a l A s t r o n o m i c a l U n i o n as standards and i t was  d e c i d e d to adopt  them i n t h i s work.  Assuming t h a t  the  s i g n a l response o f the r e c e i v e r i s l i n e a r over the range  of  s i g n a l l e v e l s b e i n g c o n s i d e r e d here, a simple comparison  of  the d i g i t a l output from a c l o u d o b s e r v a t i o n to the same output from one o f the standard r e g i o n s immediately e s t a b l i s h e s the  -35-  b r i g h t n e s s temperature s c a l e t o be used.  Because o f the time  i n v o l v e d i n d r i v i n g the t e l e s c o p e t o one o f these p o s i t i o n s a f t e r o b s e r v i n g each c l o u d , t h i s type o f c a l i b r a t i o n c o u l d o n l y be made a c o u p l e o f times a day.  However, over the  e n t i r e o b s e r v i n g p e r i o d enough d a t a was  o b t a i n e d t o determine  what c a l i b r a t i o n s h o u l d be used w i t h a p a r t i c u l a r g a i n , which was observed.  receiver  measured a f t e r each c l o u d p o s i t i o n had  been  These were t h e r e f o r e used as the primary c a l i b r a t i o n  and are a c c u r a t e to b e t t e r than i2°K,  i f we  take W i l l i a m s '  v a l u e s as d e f i n i t i v e . B)  Secondary C a l i b r a t i o n :  In the case o f c a l i b r a t i o n s  i n v o l v i n g the plasma n o i s e tube, m a t t e r s a r e n ' t q u i t e  so  s t r a i g h t f o r w a r d , because what the r e c e i v e r measures i s the antenna temperature X. , not the b r i g h t n e s s temperature o f the source, 7^  .  The antenna temperature  L i s the temperature to  which a r e s i s t a n c e matched t o the f r o n t end o f a r e c e i v e r would have t o be r a i s e d i n o r d e r t o supply the same n o i s e power as the observed s o u r c e . from a source, W, s h i p , W=  kTB,  S i n c e the n o i s e power r e c e i v e d  i s g i v e n by the f a m i l i a r N y q u i s t r e l a t i o n -  where B i s the bandwidth o f the r e c e i v e r , i t  f o l l o w s t h a t the antenna temperature c h a r a c t e r i z e s the power r e c e i v e d by a p a r t i c u l a r antenna, and w i l l v a r y from t e l e s c o p e t o t e l e s c o p e , because they have d i f f e r e n t beamwidths, r a d i a t i o n  h W i l l i a m s had t o take a l l t h i s i n t o account i n c a l c u l a t i n g the b r i g h t n e s s temperatures o f h i s proposed standard r e g i o n s .  -36-  s p i l l a g e , e t c . The b r i g h t n e s s t e m p e r a t u r e , X >  on the o t h e r  hand, c h a r a c t e r i z e s the i n t e n s i t y o f the r e c e i v e d  radiation,  because o f i t s d e f i n i t i o n i n terms o f the b l a c k body spectrum — it  i s t h e o r e t i c a l l y the same f o r a l l  telescopes.  F o r purposes  o f comparison a l o n e , a l l measurements should t h e r e f o r e be made i n terms o f the b r i g h t n e s s temperature a t a p a r t i c u l a r wavelength. 37 I t can be shown , a f t e r going through a l i t t l e theory, t h a t  and  a r e r e l a t e d by the e x p r e s s i o n  T  b  = TL/->\  where t\ i s the e f f i c i e n c y o f the t e l e s c o p e . trivial  antenna  E t a i s not exactly  t o c a l c u l a t e and f o r the purposes o f the p r e s e n t  work i s assumed t o be 0.76.  Furthermore, the n o i s e tube,  a f t e r i t i s coupled i n t o the r e c e i v e r , i s assumed t o r e p r e s e n t an antenna temperature o f X  (NT) - 100* I0°K.  The n o i s e tube  was f i r e d a f t e r each c l o u d was observed both t o check the r e c e i v e r g a i n and n o i s e temperature, and t o serve as a secondary method o f c a l i b r a t i o n . fired,  When the n o i s e tube was  i t appeared t o s a t u r a t e the r e c e i v e r ; t h i s however  c o u l d be c o r r e c t e d f o r and the r e s u l t s agreed v e r y w e l l w i t h the c a l i b r a t i o n s u s i n g the 21-cm l i n e standard c a l i b r a t i o n sources.  The most important use o f the n o i s e tube  calibration  however, was i n the c a l c u l a t i o n o f g a i n c o r r e c t i o n s or "fudge f a c t o r s " f o r the 200 d i f f e r e n t spectrometer output d e t e c t o r s and i n t e g r a t o r s , ( s e e Chapter I V , s e c t i o n 4-1) s i n c e each  -37-  c h a n n e l had a d i f f e r e n t different  outputs  gain  and w o u l d  therefore  f o r t h e same b r o a d b a n d  input.  have  -38Chapter  IV  DATA ANALYSIS,RESULTS, AND  4-1)  The Computer Programs The  raw  21-cm  l i n e d a t a , t o g e t h e r w i t h the  p r o f i l e s , were a l l brought IBM  CONCLUSIONS  360/67 computer.  calibration  to U.B.C. to be a n a l y z e d on  the  Since the d a t a a n a l y s i s programs were  w r i t t e n i n FORTRAN, w i t h what i s hoped t o be a s u f f i c i e n t number o f comment statements, explanatory.  they should be q u i t e s e l f -  For the purposes  o f completeness,  the programs  appear by name below, i n the o r d e r i n which they were w i t h a few comments on t h e i r use. programs appears A) P.T.C.  used,  A complete l i s t i n g of the  i n Appendix A.  The Computer C e n t e r f i r s t  c o p i e s the raw  data,  which i s s t o r e d i n b i n a r y on an 8 - t r a c k paper tape, onto a magnetic tape i n h e x i d e c i m a l .  T h i s i s done o f f - l i n e .  magnetic tape i s then read by the IBM P.T.C. executed.  360 and  the program  I t simply t r a n s l a t e s the b i n a r y data  d e c i m a l and w r i t e s i t i n t o a d a t a f i l e ,  The  normally  into  another  magnetic tape, i f a l o t o f d a t a i s to be s t o r e d . B)  FUDGE FACTOR  Mr. R.A.  T h i s program i s b a s i c a l l y one developed  P e r l e y and  by  the need f o r i t s use i s w e l l d e s c r i b e d  38 elsewhere. spectrometer  What i t b o i l s down t o i s t h a t a l t h o u g h a g i v e n channel output  i n c r e a s e s l i n e a r l y w i t h the l e v e l  of the i n p u t s i g n a l ,  they do not a l l g i v e the same output  f o r the same i n p u t .  T h i s program used  the broadband n o i s e  -39-  tube c a l i b r a t i o n runs t o c a l c u l a t e c o r r e c t i o n s o r "fudge f a c t o r s " f o r t h i s channel to channel g a i n v a r i a b i l i t y , and these i n t u r n can be used t o c o r r e c t the raw 21-cm l i n e d a t a . C)  NOISE  In t h i s program, the n o i s e tube c a l i b r a t i o n s a r e  used a g a i n , but t h i s time f o r t h e i r o r i g i n a l i n t e n t i o n , i s , as a secondary c a l i b r a t i o n o f the d a t a . the g a i n v a r i a t i o n s and removing  After  that  correcting  the bad channels due t o  f a u l t y r e e d s w i t c h e s , the program then c a l c u l a t e s an average n o i s e s i g n a l l e v e l , c o r r e s p o n d i n g t o a b r i g h t n e s s temperature o o f 135 ± 13 K, and a g i v e n r e c e i v e r g a i n . square  Next, the r o o t mean  (RMS) d e v i a t i o n from t h i s mean l e v e l i s c a l c u l a t e d ,  but i n p r a c t i c e i t was found t o be much l a r g e r than the expected RMS n o i s e . non-flat baseline.  T h i s was d e c i d e d t o be a r e s u l t o f a Consequently, the L i b r a r y s u b r o u t i n e OLQF  i s used t o f i t a l e a s t  squares p o l y n o m i a l to the b a s e l i n e ,  to remove the c u r v a t u r e .  This resulted  i n very reasonable  v a l u e s f o r the RMS n o i s e , which t o g e t h e r w i t h the o t h e r RMS n o i s e e s t i m a t e and the mean n o i s e s i g n a l l e v e l , a r e then p r i n t e d o u t by the computer. D)  TEMP CAL  I n t h i s program, the primary  c a l i b r a t i o n s f o r the d a t a a r e determined. standard c a l i b r a t i o n p r o f i l e s a r e f i r s t  temperature The 21-cm l i n e  divided  into  c h a r a c t e r i z e d by a d i f f e r e n t b r i g h t n e s s temperature.  groups The  A and B banks o f d a t a a r e then s u c c e s s i v e l y c o r r e c t e d f o r  -40g a i n v a r i a b i l i t y , by u s i n g the fudge bad  f a c t o r s ; removed o f  channels, by a v e r a g i n g between the channels on e i t h e r  side  i o f the bad c h a n n e l ; and c o r r e c t e d f o r b a s e l i n e c u r v a t u r e by u s i n g OLQF.  T h i s done, the peak output i s determined  the b r i g h t n e s s temperatures  o f W i l l i a m s are used  and  to c a l c u l a t e  the number o f spectrometer output u n i t s per degree  Kelvin  b r i g h t n e s s temperature,  f o r a g i v e n r e c e i v e r g a i n . The c a l .o i b r a t i o n s are t y p i c a l l y o f the o r d e r 16.0/ K, and the A and o  B banks g e n e r a l l y agreed E)  DEFZERCAL  to w i t h i n ± 0 . 1  In doing a l e a s t  /K.  squares f i t t o remove a base-  l i n e c u r v e , i t i s n e c e s s a r y t o b l a n k out any p r o f i l e i t doesn't  i n t e r f e r e w i t h the b a s e l i n e f i t .  t h e r e f o r e determines which channels reads i n the fudge  The  so t h a t  program  to blank out and  then  f a c t o r s which were c a l c u l a t e d from n o i s e  tube c a l i b r a t i o n s made a t the same time as the o b s e r v a t i o n s being analyzed.  As  i n TEMP CAL,  the g a i n v a r i a t i o n s  and  bad channels are removed, and then a s u b r o u t i n e MYOLQF, to i I t should be noted here t h a t these bad c h a n n e l s , which are the r e s u l t o f f a u l t y r e e d switches on the spectrometer output p r o d u c i n g anomolously h i g h or low r e a d i n g s , s h o u l d they o c c u r i n one o f the channels bounded by some 21-cm l i n e f e a t u r e , cannot then be removed by a simple a v e r a g i n g p r o c e s s . In t h i s case, i t i s n e c e s s a r y t o compare the d a t a a t the two f r e q u e n c i e s so t h a t , p r o v i d e d the bad channels are not s e p a r a t e d from each o t h e r by 30KHz ( o r three c h a n n e l s ) , - the amount by which the p r o f i l e s are s h i f t e d - then an unambiguous v a l u e can be determined f o r the bad c h a n n e l . T h i s u n f o r t u n a t e l y was not always the case, so t h a t some of the d a t a had to be r e j e c t e d . j T h i s wasn't n e c e s s a r y i n a n a l y z i n g the n o i s e tube c a l i b r a t i o n s as the plasma n o i s e tube p r e s e n t s f e a t u r e l e s s broadband n o i s e t o the spectrometer.  -41-  be d e s c r i b e d l a t e r ,  i s used to remove the b a s e l i n e c u r v a t u r e .  T h i s done, the data was F)  DIFFCALC  c a l i b r a t e d and  punched out on  cards.  T h i s i s a simple program which takes the  p r o f i l e o b s e r v a t i o n s and  full  c a l c u l a t e s d i f f e r e n c e p r o f i l e s between  the c l o u d (or source) p o s i t i o n s , and  the nearby r e f e r e n c e  positions. G)  ADEFPLOT  T h i s program c a l c u l a t e s and  p l o t s , with  the L.S.R.  v e l o c i t y as a b s i c c a , the average d i f f e r e n c e p r o f i l e between the source  and  f l u c t u a t i o n due SRC  the r e f e r e n c e p o s i t i o n s , and a l s o the to n o n - l i n e a r hydrogen g r a d i e n t s .  to r e p r e s e n t the on-cloud  bearings  to r e p r e s e n t  hydrogen p r o f i l e , and  expected  I f we  use  the compass  the d i f f e r e n t r e f e r e n c e p o s i t i o n hydrogen  p r o f i l e s , which are g e n e r a l l y a beamwidth away, then i n the case where o n l y f o u r r e f e r e n c e p o s i t i o n s are used, the d i f f e r e n c e p r o f i l e s a r e : (SRC-N), (SRC-S), (SRC-E) and and  (SRC-W),  the average d i f f e r e n c e p r o f i l e i s simply: flMECfiGe. PIFF£H£NC£  -  ±^ (SRC- N)  +  T h i s p a r t has been s t r a i g h t f o r w a r d ; how the expected  f l u c t u a t i o n due  ( S R C - S ) _+ ( S * C - E )  then are we  w  (Sf?C-wj(4-l)  to c a l c u l a t e  to n o n - l i n e a r hydrogen g r a d i e n t s ?  I n the s k e t c h a t the l e f t , N(HL)  +  t o see  i t i s clear  t h a t i f the hydrogen g r a d i e n t s  are l i n e a r i n going from e a s t to west and n o r t h to south,  then the d i f f e r e n c e  c  E N  >  w  s  i n the hydrogen content a t the c l o u d center i s :  -42-  and i t vanishes.  I f , on the other hand, the gradients are  non-linear, t h i s need not be the case, as the sketch at the r i g h t NCW) illustrates.  We therefore define  the expected f l u c t u a t i o n by the expression:  E  EXPECTED FLUCTUATION = _L  j  =i-[^j-(^J  (SKC-  rJ) +  (SfcC-S)  -  M  -  (SRC-E)  (4-2)  (SfcC-W)j  where the l a s t expression gives the expected f l u c t u a t i o n i n terms of the difference p r o f i l e s , and the factor of one-half has been introduced so that the RMS noise away from p r o f i l e p o s i t i o n i s the same as i n the case of an average d i f f e r e n c e plot.  This i s j u s t i f i e d since we are adding or subtracting  the same number of random noise p r o f i l e s i n e i t h e r case.  This  i s e a s i l y generalized to the case of eight reference positions to give: (4-3)  AVERAGE DIFFERENCE =  EXPECTED FLUCTUATION = J - f £  (  S R C  ^"  i.'M.s,fc  R E F  i ) "*" £ (SRC-REFOJ  ( 4-4)  t»W,8  where REFj, r e f e r s to each of the eight reference p o s i t i o n s , that i s , REF, i s important  = N, R£Fi= S ,  K E F ^ E ,  Rer^=W,  R£Fffl$  and so on. I t  to note here that with only two p r o f i l e s to deter-  mine a gradient, i t i s impossible to t e l l i n what sense i t i s non-linear, or whether two non-linear gradients happen to  -43c o i n c i d e on the c l o u d p o s i t i o n .  I f more time had been  a v a i l a b l e , i t would have been p o s s i b l e t o take r e f e r e n c e p r o f i l e s f u r t h e r o u t and then f i t a second  or higher order  k gradient (1-2)  .  Had t h i s been the case, we c o u l d then use e q u a t i o n  t o c a l c u l a t e how much o f an observed excess o r d e f i c i t  was due t o second  o r h i g h e r o r d e r hydrogen g r a d i e n t s , and  f i n a l l y be l e f t w i t h the problem o f h a v i n g t o e x p l a i n a n y t h i n g l e f t over.  F o r the time b e i n g , however, we must use our  d e f i n i t i o n o f the expected H)  LSR  f l u c t u a t i o n t o determine  this.  T h i s program i s b a s i c a l l y a h i g h p r e c i s i o n v e r s i o n  39 of  the McRae and Westerhout " L o c a l Standard  of Rest Tables",  but b e s i d e s adding p r e c i s i o n , the program a l s o takes account  the e a r t h ! s r o t a t i o n .  into  A f t e r r e a d i n g i n the r e l e v a n t  p r e c e s s i o n a l c o n s t a n t s and the time o f the o b s e r v a t i o n , i n c l u d i n g the J u l i a n Day, ( a l l o f which can be o b t a i n e d  from  the American Ephemeris and N a u t i c a l Almanac), the program then uses the s u b r o u t i n e EPOCH, i n ASTROPAK, t o p r e c e s s both the s o l a r apex and the source p o s i t i o n t o the time o f observation.  T h i s done, the e q u a t o r i a l components o f the  s o l a r apex motion and the t o t a l LSR v e l o c i t y , (which  i s comp-  uted by the s u b r o u t i n e LSRVEL, a l s o i n ASTROPAK), a r e c a l c u l a t e d , f o l l o w e d by the LSR v e l o c i t y i n the d i r e c t i o n o f the p r e c e s s e d source p o s i t i o n . k T h i s however c o u l d be c o m p l i c a t e d by the f a c t t h a t the hydrogen g r a d i e n t s might occur on a s m a l l s c a l e , i n which c a s e we would need h i g h e r s p a t i a l r e s o l u t i o n t o c o r r e c t l y determine what they a r e .  -44-  I) to  ASTROPAK  T h i s i s a c o l l e c t i o n o f s u b r o u t i n e s which tend  be used v e r y o f t e n i n a s t r o p h y s i c a l c a l c u l a t i o n s , and  such are perhaps the most u s e f u l p a r t o f t h i s 1.  EPOCH  T h i s s u b r o u t i n e uses two  l i s t e d below, namely NINLIN and  FK,  other  as  listing.  subroutines  i n o r d e r t o s o l v e the non-  l i n e a r p r e c e s s i o n a l equations oi. -  S  Ao  -  S  0  + M  +  +  N  sti^i  hi A<rOs^ c  (4-5)  (^^X^^c^±So^j  (  (  4  where e v e r y t h i n g i s measured i n seconds of time,  -  6  the nought  refers  to the i n i t i a l , e p o c h , C i s the number of r a d i a n s  second  o f time, oi and* &  are the r i g h t a s c e n s i o n and  per  declination,  and M and N are the p r e c e s s i o n a l c o n s t a n t s . (a)  NINLIN  T h i s s u b r o u t i n e i s a double  precision  v e r s i o n o f the L i b r a r y s u b r o u t i n e NONLIN, and i s used t o s o l v e the n o n - l i n e a r p r e c e s s i o n a l e q u a t i o n s . The  s u b r o u t i n e XKMAX i s w i t h i n NINLIN, and  consequence (b)  FK  2.  LSRVEL  i s of  no  here.  T h i s s u b r o u t i n e i s r e q u i r e d by NINLIN  c o n t a i n s the p r e c e s s i o n a l e q u a t i o n s  and P a c i f i c Standard  and  in explicit  In t h i s s u b r o u t i n e , the J u l i a n Day  form.  (JULDAY)  Time (HRPST, MINPST) are r e a d , and  the e q u a t o r i a l components of the t o t a l LSR YLSR and ZLSR) c a l c u l a t e d .  The  )  velocity  then  (XLSR,  s u b r o u t i n e c o n s i s t s of three  -45parts: the  the f i r s t  c a l c u l a t e s the e q u a t o r i a l components o f  e a r t h ' s r o t a t i o n " ; the second c a l c u l a t e s the e q u a t o r i a l 1  components o f the e a r t h ' s o r b i t a l v e l o c i t y ; and the t h i r d reads i n the e q u a t o r i a l components o f the sun's towards 3.  the s o l a r apex,through  SUNVEL  motion  a l a b e l l e d common statement.  T h i s s u b r o u t i n e i s used t o c a l c u l a t e the  e q u a t o r i a l components o f the motion towards  the s o l a r apex.  T h i s i s done i n the main program and then read i n t o the s u b r o u t i n e LSRVEL through a l a b e l l e d common statement t o a v o i d h a v i n g t o re-do the c a l c u l a t i o n each time LSRVEL i s c a l l e d . 4.  FROMTO  T h i s s u b r o u t i n e i s used t o c o n v e r t between d i f -  f e r e n t u n i t s o f a n g u l a r measure; the procedure t o be f o l l o w e d i s e x p l a i n e d i n the comment statements a t the b e g i n n i n g o f the  program. 5.  MYOLQF  T h i s s u b r o u t i n e i s b a s i c a l l y the L i b r a r y  s u b r o u t i n e OLQF, b u t i s d i f f e r e n t i n t h a t i t a v o i d s the long v a r i a b l e l i s t  o f t h a t program.  i t reads i n the f i r s t , the  fits,  l e s s one, channel t o be blanked ( N ) ,  t o t a l number o f channels t o be blanked (M), and the raw  data points (Y). best f i r s t , fit  Useful f o r baseline  From t h i s i n f o r m a t i o n , i t c a l c u l a t e s the  second o r t h i r d o r d e r p o l y n o m i a l l e a s t  squares  t o the unblanked raw d a t a , and r e t u r n s i t through the  v a r i a b l e Y f o r each channel number X. m As i t stands, t h i s c a l c u l a t i o n i s true f o r observations made a t D.R.A.O., b u t i s e a s i l y changed t o another observ a t o r y as e x p l a i n e d i n the program.  -46-  4-2)  The  Sources A n a l y z e d  I f we  consider  nearby o b j e c t p o s i t i o n s i n TABLE IV  to b e l o n g to a s i n g l e c l o u d , then there are o n l y f o u r d i s t i n c t clouds  f o r which data was  six  34,  (12,  20,  29,  33,  obtained.  t o a l l o w a proper e s t i m a t e  t u a t i o n , and follows.  hence are not  Five a d d i t i o n a l clouds  This l e f t  these, spread  positions could  o f the expected  not  fluc-  i n c l u d e d i n the d i s c u s s i o n t h a t  be abandoned because the bad for.  Of  (22,23,39)) were s u f f i c i e n t l y  out o b j e c t s t h a t enough nearby r e f e r e n c e be o b t a i n e d  twenty-  (21, 27,  28,  31,  37)  channels c o u l d not be  t h i r t e e n o b j e c t s f o r which the f u l l  had  to  corrected analysis  c o u l d be made.  4-3)  The  Results  The  d a t a from these t h i r t e e n c l o u d s were a n a l y z e d  preceeding  programs and  by  the  the r e l e v a n t a s t r o p h y s i c a l parameters  determined from the average d i f f e r e n c e and  expected f l u c t u a t i o n  p l o t s , f o u r examples of which appear i n FIGURES 4 - 7 .  The  parameters themselves are l i s t e d i n TABLE V I , about which a few  comments are i n o r d e r .  observed excess or d e f i c i t . to the a v e r a g i n g  V SR L  I  The  s  t  n  e  L.S.R. v e l o c i t y of  error i n this quantity  o f the r e f e r e n c e  w h i l e an a d d i t i o n a l e r r o r of i 0.8  the due  positions i s i0.4Km/sec, Km/sec a r i s e s i n d e t e r -  mining the v e l o c i t y from the graphs.  AV  w i d t h a t h a l f i n t e n s i t y i n Km/sec and  a l s o c a r r i e s an e r r o r  L  i s the f u l l  feature  -47-  o f ±-0.80 Km/sec.  In the next column, i s the column d e n s i t y 19  o f atomic hydrogen N(HI), by e q u a t i o n (2-29).  The  taken from the expected i n d i c a t e s how  i n u n i t s o f 10  AT  cm  , as  determined  i n d i c a t e d e r r o r i s the same q u a n t i t y fluctuation profile.  s i g n i f i c a n t an excess or d e f i c i t  always l a r g e r than the e r r o r due tion.  -2  It  immediately  i s , and i s  t o the temperature  calibra-  i s the e s t i m a t e d depth of an excess or d e f i c i t i n  o K b r i g h t n e s s temperature,  and  i s a c c u r a t e to b e t t e r  than  o ± 2 K.  In the f i n a l column are comments, c o n s i s t i n g  chiefly  o f the v e l o c i t i e s of the normal OH e m i s s i o n f e a t u r e s i n the same d i r e c t i o n and column d e n s i t i e s o f atomic hydrogen which H e i l e s determined  i n h i s survey.  Of the t h i r t e e n o b j e c t s a n a l y z e d , seven d i d not show any  s i g n i f i c a n t excess or d e f i c i t compared t o the c a l c u l a t e d  f l u c t u a t i o n s i n the s u r r o u n d i n g hydrogen; f o u r showed n i f i c a n t d e f i c i t s ; and two 4-4)  showed m a r g i n a l  sig-  excesses.  I n t e r p r e t a t i o n of R e s u l t s B e f o r e any attempt  i s made a t u n d e r s t a n d i n g the  results  o f TABLE V I , i t i s important t o r e a l i z e t h a t the dense d u s t clouds l i s t e d  there r e p r e s e n t , a c c o r d i n g to the c r i t e r i a  we  e s t a b l i s h e d e a r l i e r , n e a r l y a l l the o b j e c t s worth o b s e r v i n g . I t should not be a t a l l s u r p r i s i n g t h a t the work done by Dutch on L134 #15,  (Object #1)  and  the Taurus  the  dust c l o u d s ( O b j e c t s  16, 17, 25, 26) should be i n c l u d e d i n t h i s l i s t .  The  -48-  r e a s o n i s simple - these are two v e r y opaque, h i g h  latitude  o b j e c t s and there j u s t are not any o t h e r s as good.  Whether  or  not i t i s f a i r t o c o n s i d e r them as p r o t o t y p e s i s a q u e s t i o n  which i s open t o d i s c u s s i o n . most l i k e l y have t o conclude  However, i f we  will  t h a t dense dust c l o u d s , as a  whole, do not show s i g n i f i c a n t excesses hydrogen e m i s s i o n .  do not, we  S i n c e t h i s case  or d e f i c i t s i n t h e i r  i s e a s i l y explained i n  terms o f a c o n s t a n t gas t o dust d e n s i t y r a t i o or f l u c t u a t i o n s due  t o n o n - l i n e a r hydrogen g r a d i e n t s , and r e a l l y t e l l s  us  no  more than we a l r e a d y know about the i n t e r s t e l l a r medium, we w i l l by-pass i t , and c o n s i d e r L134 to  be i n d i c a t i v e of the behaviour  I f we  first  the Taurus c l o u d s  o f i d e a l dust c l o u d s .  the c a l c u l a t i o n s t h a t f o l l o w , average i n TABLE VI are b e i n g  and  In  v a l u e s of the parameters  used.  c o n s i d e r the l i n e w i d t h , we  f i n d a mean  v a l u e o f 3.6Km/sec f o r the f u l l w i d t h a t h a l f - i n t e n s i t y . A c c o r d i n g t o e q u a t i o n (2-32), t h i s i m p l i e s an upper l i m i t  to  o the k i n e t i c temperature to  o f 56 K.  The  q u e s t i o n then a r i s e s as  whether or not t h i s i s c o n s i s t e n t w i t h o t h e r  temperature  determinations. I f we  c o n s i d e r the case o f a c o l d a b s o r b i n g c l o u d ,  h a v i n g a mean background b r i g h t n e s s temperature o and an average  d e f i c i t o f 7.7 K,  T ^ ( o f f ) — 47°K  then a c c o r d i n g t o the  l e a d i n g to e q u a t i o n (2-47), the c l o u d temperature l i m i t o f Tc ^ 39°K and an o p t i c a l depth of T c ^  theory  has an upper  in(47/39) -  0.18.  -49-  On hot  the other hand, the model of a c o l d c l o u d embedded i n a sheet  o f temperature T  0  7;=125 K and 0  use equations  and  o p t i c a l depth T , i f we  (2-50),(2-51) and  us to a r r i v e a t the c o n c l u s i o n s r e a l case, likely  these  i f i n f a c t we  some u n w i e l d l y  (2-52),  Tc >/ 39°K and  enables  T >1.5. c  are d e a l i n g w i t h c o l d c l o u d s ,  conglomeration  of these  two  The i s most  results.  All  o t h e r c o n s i d e r a t i o n s a s i d e , i t would appear t h a t  two  methods f o r d e t e r m i n i n g  reasonably  c o n s i s t e n t , and  e x p l a i n e v e r y t h i n g we at  assume  0  l e a s t two  the c l o u d temperature  t h a t a c o l d c l o u d model w i l l do  have d i s c u s s e d  o b j e c t i o n s can be made.  c l o u d s produce excesses?  And  the  so f a r . The  As  first  second i s how  i s how  be handled by cases dissociation.  two  o b j e c t i o n s go,  do c o l d  i s i t possible  e x c i t a t i o n temperatures of l e s s than 10  f a r as the f i r s t  to  Unfortunately,  to r a t i o n a l i z e these k i n e t i c or c l o u d temperatures w i t h observed OH  are  the  K?  the f i r s t  might  of h y d r o s t a t i c e q u i l i b r i u m or cosmic r a y  However, we  are d e a l i n g w i t h c o l d  absorbing  atomic hydrogen c l o u d s , so the l a t t e r argument does not  really  n H e i l e s r a i s e s yet a t h i r d o b j e c t i o n by s a y i n g t h a t i f we assume t h a t we can d e t e c t a f e a t u r e of say 2 K b r i g h t n e s s temperature, and i f the background continuum a t 21-cm i s 4°K, then an o b j e c t would be u n d e t e c t a b l e i n e m i s s i o n o n l y i f i t s e x c i t a t i o n temperature were l e s s than 6°K. He then goes on to say t h a t i f t h i s were the case, the e m i s s i o n l i n e would be s a t u r a t e d and produce a s t r i k i n g a b s o r p t i o n f e a t u r e a g a i n s t the background hydrogen. However, he completely i g n o r e s t h i s same background hydrogen by u s i n g the continuum r a d i a t i o n to estimate the e x c i t a t i o n temperature i n the c l o u d .  -50-  h o l d , s i n c e i t assumes abundant amounts o f m o l e c u l a r I t i s c l e a r the problem as we  are now  hydrogen.  i s not g e t t i n g any l e s s c o m p l i c a t e d  r e q u i r i n g the c l o u d to be c o l d enough to  absorb and a t the same time, have excess e m i s s i o n . second problem,  The  t h a t o f r e s o l v i n g the OH e x c i t a t i o n temp-  e r a t u r e s o f l e s s than 10°K w i t h the much h i g h e r k i n e t i c temperatures, i s a l s o one which  i s not e a s i l y handled, as i t  i n v o l v e s the e q u i l i b r i u m  time s c a l e s f o r the f o r m a t i o n o f the  c l o u d s and the OH,  i n t u r n i n v o l v e s a number o f d i f f e r e n t  which  c o l l i s i o n c r o s s - s e c t i o n r a t e s , and  so on.  s a i d about t h i s here, as i t i s a complete  4-5)  Comparison  No more w i l l  be  subject i n i t s e l f .  o f R e s u l t s w i t h Other Work  As mentioned  i n the f i r s t  c h a p t e r , the o n l y d e t a i l e d work  done on dense d u s t c l o u d s has been by the Dutch  astronomers,  S a n c i s i and W e s s e l i u s .  on  (Object #1)  One  o f t h e i r papers was  and the o t h e r on the Taurus Dust Clouds o f  which O b j e c t s 15, 16, 17, 25 and comprise a p a r t . 21-cm  L134  26 i n the p r e s e n t work  By superimposing our antenna beam on  their  l i n e maps o f the b r i g h t n e s s temperature as a f u n c t i o n o f  and  , t h e i r observed decrease o f 7.5°K on L134  ponded t o an average Similarily,  corres-  d e f i c i t o f 4.2°K - the v a l u e found here.  the r e s u l t s on the Taurus complex c o u l d be  compared; they agreed w e l l i n a l l r e s p e c t s , except t h a t the Dutch found an e x t r a d e f i c i t at-*-2 Km/sec.  T h e i r measurements,  however, were made a t a s l i g h t l y d i f f e r e n t l a t i t u d e . comparison w i t h H e i l e s  1  r e s u l t s i s not as good.  A  -51-  To b e g i n w i t h , H e i l e s p l a c e d an upper l i m i t of 3.3 cm  x  on the column d e n s i t y o f the n e u t r a l hydrogen d e f i c i t i n  the d i r e c t i o n o f L134;  t h i s i s almost a f a c t o r o f two  than the d e f i c i t observed o f H e i l e s ' two  here and  of the p r e s e n t work, but  he p l a c e d on a nearby o b j e c t ( O b j e c t #15) of magnitude.  less  i n the Dutch work.  observed d e f i c i t s does agree w i t h the  o b t a i n e d on O b j e c t #26  One  deficit  the  limits  i s o f f by an  I t seems t h a t h i s poor s e n s i t i v i t y may  cause o f these and o t h e r d i s p a r i t i e s . i s o n , H e i l e s ' observed  order be  the  For the sake of compar  d e f i c i t s or l i m i t s are i n c l u d e d i n  TABLE V I .  4-6)  C o n c l u d i n g Remarks I t i s c l e a r from the range o f r e s u l t s o b t a i n e d  t h a t the q u e s t i o n o f the behaviour  here  o f atomic hydrogen on  or near dark dust c l o u d s i s not a simple one Had  10  t o answer.  most o f the c l o u d s a n a l y z e d shown a s i n g l e type of  behaviour,  statements  of a s t a t i s t i c a l nature might have  been made. Only measurements on more c l o u d s w i l l r e s o l v e t h i s problem. The  f a c t t h a t n e a r l y h a l f these o b j e c t s show no  n i f i c a n t excesses or d e f i c i t s might perhaps be s i g n i f i c a n t , but i t i s f e l t requirements  sig-  termed  t h a t two p r e s e n t l y l a c k i n g  need to be made r e g a r d i n g the measurements of  e m i s s i o n on and nearby dense dust c l o u d s .  -52-  A)  The  first  i s measurements o f h i g h e r v e l o c i t y  quency) r e s o l u t i o n . to  Only i n t h i s way  will  (or f r e -  i t be p o s s i b l e  determine whether or not the f u l l widths a t h a l f i n t e n s i t y  are c o r r e c t , o r whether they are r e s o l u t i o n l i m i t e d . former t u r n s out  to be the case,  I f the  then the o n l y apparent way  r e c o n c i l i n g the h i g h v e l o c i t y d i s p e r s i o n w i t h  the low  temperatures i s to say e i t h e r t h a t i t i s not due  of  kinetic  entirely  to  thermal motions o f the e m i t t i n g atoms, meaning t h a t l a r g e s c a l e t u r b u l e n c e s , e t c . must be  considered,  or t h a t the w i d t h  i s a r e s u l t o f the f a c t t h a t there are no atoms e m i t t i n g r a d i a t i o n near the L.S.R. v e l o c i t y o f the c l o u d , is  no atomic hydrogen - e i t h e r i t has become m o l e c u l a r  composition  w i t h i n the c l o u d i s anomalous.  k i n e t i c temperatures w i l l be  i n d i c a t e d , and  then v e r y  in this  t h e r e would be no o b j e c t i o n t o the c o l d c l o u d o f d e f i c i t s , although  i t i s not c l e a r t h a t the  for  reason  t h a t o t h e r m o l e c u l e s are  second i s measurements o f h i g h e r  In t h i s way,  low  case,  possibility  hydrogen c l o u d would be excluded,  The  the  explanation  of a molecular the simple  or  If i n fact i t  t u r n s out t h a t the f e a t u r e s are smoothed out,  B)  t h a t i s , there  even i f  found.  spatial resolution.  the problem o f s m a l l s c a l e hydrogen g r a d i e n t s  c o u l d be p r o p e r l y handled. i a t e l y presents  itself,  the more d i f f i c u l t  Unfortunately,  a problem immed-  f o r the h i g h e r our r e s o l u t i o n becomes,  i t i s to t e l l whether we  are l o o k i n g a t  a dark dust c l o u d , or a h o l e between some s t a r s . e s p e c i a l l y the case a t h i g h g a l a c t i c l a t i t u d e s .  This i s The  only  -53-  p o s s i b l e s o l u t i o n t o t h i s dilemma i s h i g h s c a l e maps o f the b r i g h t n e s s temperature velocity. and  i n two dimension  at a  particular  I n t h i s way, i t may be p o s s i b l e t o i s o l a t e  study t h e i r t h r e e - d i m e n s i o n a l  clouds  structure.  Dark dust c l o u d s , and more g e n e r a l l y , the i n t e r s t e l l a r medium, a r e not as simple as they a r e sometimes thought t o be, b u t perhaps these types o f measurements may h e l p us r e s o l v e the problem o f whether dense dust c l o u d s c o n t a i n m o l e c u l a r o r atomic  hydrogen.  -54-  Appendix A A LISTING OF COMPUTER PROGRAMS  - srs C  M A I N PROGRAMS USED  Q  *r '» *>" V -J* :  '1^  *>* 'r'  -r -v- V ' r 'i '* V V V 'r s  :  IN >* :  0ARK '»*  DUST  '»' 'I  1  "I*  ^1*  -»"•  CLOUD *!* '<*•  -v*  'I*  DAT A -r  -Y^  ANALYSIS  V  ->*  V  V *>* *!'  -I" ^* '! v -! 'I:  ;  -A -! *,S V V ;  :  . V :  C  c c C C  . PTC — PROGRAM TO CCNVERT PAPER T A P F TO MAG TAPE AND PUT C N F I L D I M E N S I O N A (.100) C PAPER T A P E S ARE F I R S T RF AD ONTO MAG TAPE IN H E X A D E C I M A L RY THE C COMPUTER C E N T E R . AT THE END OF T H I S TAP F THEY P u l THE Mu>=n P v C 512 IN H E X A D E C I M A L , 2 5 6 I S PUT AT THE END OF THE I N D I V I D U A L TAPES C AS THEY . A R E . RE AD IN . M= 1 M E A N S . R E A D BANK A D A T A , >< •' = 2 » 0 A N K R IC = 1 2 8 1.1. ... M=0 ....... 1 M=M + 1 C THE REST OF THF PROGRAM JUST READS A S C I I CHARACTERS AND C G E N E R A T E S THE C O R R E S P O N D I N G D E C I M A L N U M B E R S . E V E R Y T H I N G E L S E C IS IGNORED _..„ . _ DO 8 J = l , 1 0 0 2.MULT= 1 K=0 I FR AC=0 NU=0 3 C A L L PT..A.P.E.(..I...L.. I=1ABS(I ) IF( I .EQ.,5.12 )_..GG TO. 20 I = LOR( I, IC ) IF( IFRAC.EQ.1) GO TO 7 C 128=LEADER/TRAILER 1 3 3 - L F 141=CR 160=SPACE 1 7 3 = 174=. IF..(. I . E Q . 1 2 . 8 )... GO TO. 3 I F d . E Q . 1 3 8 ) GO TO 3 . IF ( I . EO . 1.4.1 ) GO TO 3 I F ( I . E 0 . 1 6 0 ) GO TO 3 I F ( 1 . E O . 173) GO TO 4 I F d . E Q . 1 7 4 ) GO TO 5 GO. TO .6... ...... 4  5  MULT =  -1  GO TO 3 IFRAC=1 GO TO 3 NQ=N0*10+(1-176) K =K +1 I F ( K . G T . 2 C ) GO TO 20 GO TO 3 R= 1 - 1 7 6 R N'T = NO 4-R / 1 0 . RNO=RNO*MULT A(J)=RNO WRITE THE NEXT ICO NUMBERS INTO A F I L E ON D E V I C E 8 WRITE (8 , 10 ) ( A ( J ), J = 1, ICO ) FORMAT( IGF 7 . 1 ) IF GANK B DATA HAS B E E N READ ( M = 2 ) , D I S C A R D THE REST OF THE I N F O R M A T I O N ON THE T A P E I F I M . L T . 2 ) GO TO 1 CAL L PT AP E( I ) I = IAhS ( I ) I F THE END CF A TAPE HAS BEEN REACHED ( 1 = 2 5 6 ) , RUT ALL TH[ T A P E S H A V E N ' T ft E EN READ (1 = 5 1 2 ) , READ TF: [• _NE X T T A P R :  6  7 8 C 10 C C 9 C C  20  c c c c c  ~  c  I F ( I . E G . 5 1 2 ) GO TG IF( I . N E . 2 5 6 ) GO TO GO TO 11 STOP . . END  20 9  FUDGE FACTOR — PROGRAM TO C A L C U L A T E C O R R E C T I O N F A C T O R S FOR THE G A I N V A R I A B I L I T Y OF THE I N D I V I D U A L S P E C T R O M E T E R CHAMNALS D I MENS 1 ON X( 10 0) , Y( 100) , YF ( 100) , Y O U 00) , WT (1 00 ) , F (100 ) Al , F ( ] OC ) D I M E N S I O N S ( 11 ) , S I GM A ( 1 0 ) . A ( 1 0 ), B { 10 ) . P ( 1 I ) . A ?F ( 1 0 n) , B( 1 1 f-n DlMENS ICN C ( 1 0 0 ) , D < 1 0 0 ) , E ( 1 0 0 ) , G ( 1 0 0 ) , H ( 1 0 0 ) , G ( 1 0 0 ) .. .. D I M E N S I O N B 2 F ( ICC) ... L O G I C A L LK c. . .. . READ I N THE CHANNEL NUMBERS (1 TO 1 0 0 ) R E A C ( 5 , 50) ( X( 1 ), 1=1, 1 0 0 ) READ IN THE WEIGHTS A S S I G N E S TO T HF D I F F E R E N T CHANNEl S c ACCORDING TO T H E I R R E L I A B I L I T Y c R E A C ( 5 , 70) (WT( I ) , 1=1 , 1 0 0 ) .. . DO 10 1 = 1 , 1 0 0 A 1F ( 1 ) = 0..C A2F ( I ) = 0 . 0 B1F(I)=0.0 10 B 2 F ( I ) = 0. 0 c ,I.N_ WHA.T_F_G.LL.OW.S.f A AN0 Q R E F E R . TO. BANKS A AND. B OF THE S P E C T R O M E T E R O U T P U T , ! AND 2 REFER TO THE TWO F R E Q U F N C I E S AT c WHICH O B S E R V A T I O N S WERE MA D E . . . . THE.. SUMS B E I N G MADE 'ARE FO c C A L C U L A T I N G A V E R A G E FUDGE FACTORS FOR BANKS A AND B AT THE c D I F F E R E N T F R E Q U E N C I E S 1 AND 2 . c DATA PUT IN THE ORDER A , B FOR ONE F R E Q U E N C Y FOR ALL THE DATA c AND. A , ...B FOR THE S E C O N D . PR EGU ENCY . FOR ALL THE DATA. c ._ DO 99 I N = 1 , 6 2 RE. AC ( 8., .60. J ( Y( I ) , 1 = 1 , 10 0 ) K=2 M= 100 L K= .TRUE. NWT = 1 USE THE L I B R A R Y R O U T I N E OL OF TO REMOVE THE B A S E L I N E AND C A L C U L A T E THE BEST F I T YF TO THE DATA Y . c ... C A L L G L Q1 - (K , M , X , Y , Y F , Y 0 , W T , N W T , S , S I G M A , A , B , S S , L K , P ) N= K +1 DO 22 1 = 1 , 1 0 0 C A L C U L A T E THE FUDGE F A C T O R S , F(I) c F( I ) = YF< I ) / Y ( I ) I F ( I N / 2 * 2 . N F . IN) Q( I )=F( I) 22 I F ( I N / 2 * 2 . N E . I M ) G C TO 23 IF( IN.1 T . 31) GO TO 29 DO 32 1 = 1 , 1 0 0 C A L C U L A T E D I F F E R E N C E OF FUDGE FACTORS FOR RANKS A AMD H c H ( I )=Q( 1 )- F( I ) B2F ( I ) = 02 F ( I ).+ F ( I ) 32 GO TO 2 4 DO 33 1 = 1 , I C O 29 H ( I )=0 ( I ) - F ( 1 ) 3 IF( I ) = B 1 F ( 1 ) + F( I ) 33 GO TC 2 4 23 WRITE ( 6 , 2 5) IF( IN . L T . 3 1 ) GO TO 28 00 30 1 = 1, 100  -St-  30  -  —  ••  A 2 F ( I I =A2F( I )+F( I ) GO TO 27 .. . . ... 28 DO 31 1 =1 , 1 0 0 31 . A 1F ( I ) = A 1F ( I ) + f ( I ) GO TO 2 7 WRI T F ( 6 , 2 6 ) 24 27 WRITE(9,501) FORMAT(7 2X) 501 WRI T E ( 9 , 5 0 2 ) ( F ( I) ,1=1 , 1 0 0 ) 502 FORMAT ( 1 0 F 7 . 3 ) . WRITE (6 , 5 0 0 ) (F ( I ), 1=1 , 100 ) I F ( 1 N / 2 * ? . E 0 . I N ) WRI TF (6 . 5 0 3 ) ( H ( I ) , I =1 . 1 0 0 ) 5U3 FOR MAI ( / 10 ( 10 F 1 0 . 3 / ) ) 25 . FORMAT ( ' I V , / / . 5 0 X ,« * * * B A N K A * * . * ' ) 26 F (j R M A T ( / / 5 0 X , « * * * 6 A N K B * * * ' ) 50 FOR MAT (1.0. F.6 .1 ) 60 FORMAT(10F7.1) 70 FORMAT ( 1.0F5. 1 ) 200 FORMAT(//1X,I5,5X,11E11.3) 3.0 C. .... FORMA.T (./.'.SUM .OF SQUARES I S ' , E 1 5 . 5 ) . 350 FORMAT ( / 4 9 X , ' Y - A X I S D I F F E R E N C E S FROM B E S T F I T ' ) FORMAT < /l 0F10. 1 ) 400 450 F O R M A T { / 5 6 X , ' F U D G E FACTORS A R E ' ) 500 FORMAT (/ 1 0 F 1 0 . 3 ) 550 FORMAT ( ' 1 ' , / / 3 0 X , ' * * * I N I T I A L BANK A FUDGE F A C T O R S * * * ' ) 60 0 FORMAT ( . / / 3 0 X , . . ' * * * F INAL ..BANK. A. .FUDGE. FAC T O R S * * * ' > FORMAT(»1« , / / 3 0 X , ' * * * IN IT I AL BANK B FUDGE FACTOR S * * * ' ) 6 50 700 . F O R M A J i / . / 3 0 X , ' * * * F I N AL BANK P. FUDGE. F A C T O R S * * * ' ) 99 CONTINUE DO 9 0 0 1 = 1 , 1 0 0 A1F( I )=A1F( I ) / 1 5 A 2 F ( I ) = A2 F{ I )/ 16 B1F ( I ) =81 F ( I ) / 15 B2F.(. I ) = B 2 F ( I.) / 16 900 C OUTPUT THE A V E R A G E D FUDGE FACTORS WP I TE ( 6 , 5 5 0 ) W R1 T E ( 6 , 5 0 0 ) ( A 1F ( I ) , I = 1, 10 0 ) WRITE(6,6()0 ) WRI TE( 6 , 5 0 0 ) ( A 2 F ( I ) ,1=1 , 1 0 0 ) W R I T E . ( 6 , 6 50 ) W R I T E ( 6 , 5 0 0 ) ( B 1 F (I ) ,1 = 1 , 1 0 0 ) WRITF(6,700) W R I T E ( 6 , 5 0 0 ) ( B 2 F ( I ), 1 = 1 , 1 0 0 ) ... WRI TE ( 9 , 5 0 1 ) W R I T E ( 9 , 5 0 2 ) (A 1F( I ) , I = 1 , 1 0 0 ) WRITE(9,501) W R I T E ( 9 , 5 C 2 ) ( B 1 F ( I ) ,1=1 , 1 0 0 ) WRITE(9,5G1) W R I T E ( 9 , 5 0 2 ) ( A 2 F ( I ), 1 = 1 , 1 0 0 ) WRITE(9,501) WRIT E ( 9 , 5 02 ) (B 2 F( I ),I = 1 , 1 0 0 ) DO 901 1=1 , 1 0 0 C( I )=A I F ( I ) - A 2 F ( I) 0 ( I ) = B1 F ( I ) - R 2 F ( I ) E( I ) = A 1 F ( I ) - B l F ( I) G( I )=A2F( I J - B 2 F ( I ) 901 WR I T E ( 6 , 5 0 4 ) ( C ( I ) , I = 1, 1 00 ) , ( D ( I ) , I =1, 1 ( 0 ) , ( E ( I ) , I =1 ,1 00) , ( G ( I ) , I #1 , 1 0 0 ) 504 F O R M A T ( 4 ( / / 10( 10F 1 0 . 3 / ) ) ) DO 6 0 1 1 = 1, 100 -  •  •  -  601  A IF ( I ) A 11- ( I ) =! 1 5 . + A 2 F ( I ) * 1 6 . ) / 3 1 . B1F(I) = (L>1F(I)*15.+B2F(1)*16.)/31. WRI TE ( 9 , 5 0 1 ) WRITE(9,502) (A1F(I),1=1,100) WRITE(9,50 1 ) WRI TF ( 9 , 5fi? )  602  603  ( B l F f I ) . I =1 .1 00 )  WRITE(6,602) FORMAT('1',//30X,'OVERALL A V E R A G E BANK WRI T E ( 6 , 5 0 0 ) ( A 1 F ( I ) ,I=1 ,100) W R I T E ! 6 , 6 03) FORMAT('I',//30X,'OVERALL AVERAGE BANK WRI TF( 6. 5 0 0 ) (R 1 F( I ) .1 =1 .1 00) STOP END -. -  A FUDGE F A C T O R S ' )  B FUDGE F A C T O R S ' )  C  .  c c c c  c  N O I S E — PROGRAM TO C A L C U I A T F THF MEAN N O I S E 1 n / F I AND TTS . . S. D I S P E R S I O N FROM THE N O I S E TUBE C A L I B R A T I O N P R O F I L E S DI MENS ION. A (l.CO ) , B U O O ) , FA( 100 ), FB( 1 0 0 ) D I M E N S I O N X ( 1 0 0 ) , Y ( 1 0 0 ) , Y F ( 1 ( 0) , Y D ( 1 0 0 ) ,WT ( 1 0 0 ) , S (4 ) , S I GMA(3 ) , A O ( tl ) , BO. (3 ) , P. ( 4 ) _ L O G I C A L LK 1 K= . FAl SF . K=0 .... NWT = 0 . . ___ _ . . M=100 . READ . I N T H E A V E R A G E PUDGE FACTOR V A L U E S ( F A , F B ) READ(5,14) (FA ( I ) , I = 1 , 1 0 0 ) , ( F B ( I ) I = 1 , 1 0 0 ) FORM AT ( 10 F7 . 3 ) DO 18 1 = 1 , 1 0 0 X( 1 )=J _ K = K +1 READ IN...BANK A... OF ...A N O I S E RUN R E A D ( 8,3) ( A( I ) ,1=1 , 1 0 0 ) FORMAT(10F7 .3) REMOVE THE E R R A T I C CHANNELS IN BANK A .... DO 16 .1 = 1 , 100 „ _ A( I )=A( I » * F A ( I ) .... A( 25) = 0 . 5 * ( A ( 2 4 ) + A ( 2 6 ) ) A(30)=0.5*(A(29)+A(31)) A ( 4 4 ) = 0 . 5 * ( A ( 4 3 ) +A(45 ) ) A ( 5 1) = ( 2 . / 3 . ) * A < 5 0 ) + ( A ( 5 3 ) / 3 . ) A ( 5 2 ) = ( A ( 5 0 ) / 3 . ) +( 2 . / 3 . ) *A ( 53) 1. A ( 8 1 ) = 0 . 5 * ( A ( 8 0 )+A(82 ) ) C A L C U L A T E THE A V E R A G E V A L U E OF THE BANK A NOISE S I G N A L , AV G A SUM=0.0 DO 5 1 = 1 , 100 Y( I ) = A( I ) SUM = SUM + A ( I ) AVGA=SUM/1UG.0 SUM=0. DO 4 1 = 1, 100 Sl)M=SUM+ ( A ( I ) - A V G A ) CONTINUE C A L C U L A T E THE D I S P E R S I O N N E G L E C T I N G THE B A S E L I N E , A N O T Z ANOIZ=SQRT(SUM/99.) K0=3 USE L I B R A R Y S U B R O U T I N E G L Q F TO REMOVE B A S E L I N E AND C A L C U L A T E PROPER D I S P E R S I G N , A N D ! S E f  14 18 15 C . 3 C 16  c  5  4 C  C C  - i f 9 -  6  f  _X C 17  . C.  _8  7 _C  C _.C  ...11  C C 12  20 C C C _C C C  CAL L OL. (JF ( K C ^ S X , Y , Y F , Y Q , WT,NWT, S , S 1GMA , AO ,3 0 , S S , LK , P ) ANOISfc' = S O R T ( S S / 9 9 . ) W R I T F ( 6 , 6 ) AV G A , A N O IZ , A N 0 I $ E F O R M A T ( 5 X ' BANK A : * , ' A V E R A G E CAL = ' , F 7 . 1, 5 X» ' R M S N O I S E = • , F 7 , 5X,F7.1) R FAG IN PAN K B OF A NOT S F RUN R E A D ( 8 , 3) ( b i 1 ) t 1 = 1 ,100 ) REMOVE. THE E R R A T I C C H A N N E L S I N BANK B DO 17 1 = 1 , ICO B d )=B(I ) * F B ( I ) . . . B( 1 2 ) = G . 5 * ( P ( 1 1 ) + B ( 13) ) B ( 3 M = 0.5*< B(33 ) +E(35 ) ) B ( 3 6 ) = 0 . 5 * ( B ( 3 5 ) + B ( 3 7)) B(4l >=0.5*(B(40)+B(42) ) B ( 4 6 ) = 0 . 8 * B { 4 > : > ) + 0 . 2 * 8 ( 50 ) B( 4 7 ) = 0 . . 4 * B ( 4 5 ) + C . 6 * B ( 50) B(48)=G.6*6(45 )+0.4*8(50 ) B ( 4 9 ) = 0 . 2 * B ( 4 5 ) +C. 8 * B ( 50) B(59)=0.5*(B(58)+B(60) ) C A L C U L A T E THE A V E R A G E V A L U E . OF T H E . BANK E NO IS E SI GN AL , A VGR SUM=0. DO 8. 1 = 1, 10.0 Y(I)=3(I) SUM-SL1M+P ( I ) A V G B = S U M / 100 . SUM=0.. DO 7 1 = 1 , ICO SUM=S.UM+( B( I ) - A V G B ) * * 2 __ CONTINUE C A L C U L A T E THE D I S P E R S I O N N E G L E C T I N G THE P A S F L I N E , B N O I Z BNOIZ=SQRT ( S U M / 9 9 . ) K0=3 USE L I B R A R Y S U B R O U T I N E OLQF TO REMOVE B A S E L I N F AND C A L C U L A T E . PROPER D I S P E R S . I O N , BNO I SE C A L L OL C F ( K C , M , X , Y , Y F , Y C , W T , N W T , S , S I G M A , A O , S C , S S , L K, P) BNOISE=SQRT(SS/99. ) WRIT E ( 6 , 1 1 ) AV G 6» BNO I Z , B N O IS E FORMAT ( 5X , '.BANK 3. .:. ' ,.' AVERAGE C A L = ' , F7 . 1, 5X , ' RMS N O I S E = ' , F 7 . it, 5 X , F7 . 1/ ) AVGA=0. 5* (AVGA+AVGB) _ ANOIZ= 0 . 5 * { A N 6 I Z +BNO I Z ) A N 0 I S E = 0 . 5 * ( A N O I S E + GNO IS E ) P R I N T OUT THE A V E R A G E N O I S E TUBE C A L I B R A T I O N L E V E L AND ITS DISPERSION WRITE(6,12 ) AVGA,ANOIZ,ANOISE FORMA T( 5 X , ' A VE RAGE C A L , BANKS A AND B = ' » F 7 . 1 , 5 X , ' A V E R A G E N O I S E //BANKS A AND B = ',F7.1,5X,F7.1//> IF(K.LE.3C) GO TO 15 STOP END  .  T  TEMP CAL — PROGRAM TO C A L C U L A T E THE NUMBER OF U N I T S PER DEGREE K E L V I N B R I G H T N E S S T E M P E R A T U R E DATA FROM THE 2 1 - C M . L I N E STANDARD C A L I B R A T I O N DI MENS ICN A ( 1.00 ) , B ( 100 ) , FA ( 100 ) , F B ( 100 ) DI MENS ION X( 100) , Y ( 100) , Y F ( 100) , Y D { 1 0 0 ) , W T ( 1 0 0 ) H ) , B C ( 3 ) , P (4 ) L O G I C A L LK  SPECTROMETER QDTP! BY A N A L Y Z I N G THE PROFILES , S ( 4 ) , S TCMA(3 ) , A O (  — 6,0-  c  .  14 15 C C C C  30 C  .  3 C  c  16  ;_  C  4 5 33 34  C C  42 43 C 44 6  NWT =0 LK=.FALSE. K=0 READ I N THE A V E R A G E FUDGE FACTORS R E A D ( 5 , 1 4 ) (FA<I ) , 1 = 1 , 1 0 0 ) , ( F B ( I » , 1 = 1 , 1 0 0 ) FORMAT ( 1 OF 7 . 3) K=K+1 READ I N THE P E A K B R I G H T N E S S T E M P E R A T U R E OF T H E RELEVANT C A L I B R A T I O N P R O F I L E AND M, THE NUMBER OF C H A N N E L S WHICH ARE NOT B L A N K E D IN T F E GLQF L E A S T SQUARES F I T TO THE B A S E L I N E T H I S PART OF PROGRAM MLST BE CHANGED FOR D I F F E R E N T OBSERVATIONS I F ( K . l . E . 1 6 ) 1R=51 . 0 I F ( ( K . G T . 1 6 ) . A N D . ( K . L E . 2 0 ) ) TR=99. I F ( K . G T . 2 C ) TB=72. I F ( K . L E . 1 6 ) GO TO 30 .. I F ( ( K . C T . 1 6 ) . A N D . ( K . L E . 2 0 ) ) GO TO 31 I F ( K . G T . 2 0 ) GO TO 30 M=6 5 READ I N BANK A FCR 13 AT A WITH CHANNELS 6 1 TO 95 B L A N K E D . . READ( 8, 3). ( A( I ) , 1 = 1 , 1 0 0 ) FORMAT ( 1 0 F 7 . 3 ) ... .. C O R R E C T . C H A N N E L G A I N S . BY U S I N G FUDGE F A C T O R S , AND REMOVE BAD C H A N N E L S IN BANK A DO 16 1 = 1 . 1 0 0 A ( I ) =A ( I ) * FA ( I ) A(.25)=0.5*.(.A(2.4).+A( 26) ) A(30)=0.5*(A(29)+A(31 ) ) . A ( 4 4 ) = 0 . 5 * ( A( 4 3 . . + A ( 45) ) A ( 5 1 ) = ( 2 . / 3 . ) A ( 50 ) + ( A ( 5 3 ) / 3 . ) A ( 5 2) = ( A ( 50 ) / 3 . ) + (2 . / 3 . ) * A ( 53 ) A(81)=0.5*(A(80)+A(82)) D E T E R M I N E W.HAT . .CHANNEL THE P E A K . . OUT PUT OCCURS, IN AMA X = 0 . DO 5 1 = 1 , 10 0 I F ( A ( I ) . G T . A M A X ) GO TO 4 GO TO 5 AMAX = A( I ) AI = I CONTINUE DO 3 3 1 = 1 , 6 0 X( I )=I Y(I)=A(I) DO 34 1 = 6 1, M . X( I ) =1 + 3.5 __ Y< I ) = A( 1 + 3 5 ) K0=3 C A L L 0 L. OF ( K 0 , M , X , Y , Y F , YD , W T, NWT, S , S I GMA., AO , BO , SS , L K , P ) C A L C U L A T E THF: B A S E L I N F BELOW THE PEAK ACCORDING TO THE ORDER OF THE PC LY NOMIAL F I T I F ( K O . E 0 . 3 ) GC TC 4 3 I F ( K O . E 0 . 2 ) GO TO 4 2 BAS EA.= P (1 ) +P ( 2 . ) * A l . GO TO 4 4 B AS E A= P ( 1 ) + ( P ( 2 ) +P ( 3 ) * A I ) * A I GO TO 4 4 BASEA=P(1)+(P(2)+(P(3)+P(4)*AI)*AI)*AI C A L C U L A T E T H E . P E A K OF THE BANK A SPECTRUM PEAKA=AMAX-BASEA WRI TT( 6 , 6 ) A MA X , AI , K C , B A S E A , P E A K A FORMAT ( 5X , • BANK A : S ' A M A X = ' , F 7. 1, 5 X , ' A I = « , F 5 . 1 , 5 X , • K.!l =  — (ol-  #» 5X, ' B ASE A = ,1-7.1 » 5 X , ' P E A K A = » , F 7 . 1 ) REPEAT FROM S T A T E M E N T S 30 TO 6 FOR BANK B R E A D ( 8 , 3 ) ( B ( I ) ,1=1 , 1 0 0 ) DO 17 1 = 1 , 1 0 0 . . . B ( I. ) = B ( I ) * F B ( I ) B( 1 2 ) = 0 . 5 * ( R ( H ) + B ( 1 3 ) ) B( 34 ) = 0 . 5 * ( B( 3 3 ) + B ( 3 5 ) ) B ( 3 6 ) = 0 . 5 * ( B ( 3 5 ) +B(37) ) B(4 1 ) = 0 . 5 * ( B ( 4 C ) + B ( 4 2 ) ) B ( 4 6 ) = 0 . 8 * B ( 4 5 ) + 0 . 2 * B ( 50) B(47)=0.4*B(45 )+0.6*0(50 ) B ( 4 8 ) = Q . 6 * B ( 4 5 ) + 0 . 4 * B ( 50) B(49) = 0 . 2 * B(45 )+0.8* B(50 ) B( 5 9 ) = C . . 5 * ( B( 5.8)+B ( 6 0 ) ) BMAX=0 . DO. 8 1 = 1., 10.0 I F ( B ( I ) . G T . B M A X ) GO TO 7 GO TO 8 BMAX=B(I) R I= 1 „_ ___ CONTINUE DO 53 I = 1 , 6 0 X{ I ) = I Y ( I ) = B( I ) DO 54 1=6 1 , M X( I.) = I + 3 5 Y(I)=B(I+35) KG = 3 .. C A L L GL Q F ( K O » M , X , Y , Y F » YD,WT,NWT » S » S I G M A , A O , B O , S S » LK » P ) I F ( K O . E Q . 3 ) GO TO 6 3 IF ( KO. E Q . 2) GO TG 6 2 B A S E B = P ( 1 ).+ P( 2.) * B I GO TO 6 4 Q A S E B = P ( 1 ) + ( P ( 2 ) + P ( 3 ) * 8 l ).*RI. GO TO 6 4 B AS F B= P (1 ) + ( P ( 2 ) + ( P ( 3 ) +P ( 4 ) * B I ) * B I ) * B I P E A KB = B MA X - B A S E B WR I T E ( 6 , 1.1 ) . BM AX , B I., KO , B A S E B , P.E A KB F O R M A T ( 5 X , BANK B : ' , ' B M A X = • , F7 . 1, 5 X , ' A I = ' , F 5 . 1 , 5 X , •KO = ' , ! # , 5 X , « R A S E . B = ' , F 7 . 1 , 5X , '. PE A KB = ' ,.F 7 .1 / ) PEAKA=PEAKA/TB PEAKB=PE.AKB/TB PEAK.= ( P E A K A + P E A K 8 ) / 2 . W R I T E ( 6 , 12.) P E A K A , P E A K S , PEAK FORMAT ( 5 X , ' N U M B E R OF U N I T S PFR DEGREE K E L V I N , BANK A , BANK B, AN # T H E I R AVERAGE V A L U E = • , 5 X , 3 ( F 6 . 1 , 5 X ) / / ) I F ( K . L T . 4 9 ) GO TO 15 GO TO 2 0 REPEAT FROM S T A T E M E N T S 30 TO 12 FOR DATA WITH C H A N N E L S 5 "TG 65 B L A N K E D OUT IN THE OLOF L E A S T SQUARES F I T M=4 0 READ(3,3) (A(I),1=1,100) DO 18 1 = 1 , 1 0 0 A ( 1 ) =A ( I ) * F A ( I ) A(25) =0 . 5 * ( A ( 2 4 ) + A ( 2 6 ) ) A(30)=0.5*(A(29)+A(31 ) ) A(44)=0.5*(A(43)+A(45)) A ( 5 1 )= ( 2 . / 3 . )* A ( 50 ) + ( A ( 5 3 ) / 3 . ) A( 5 2) = ( A ( 5 0 ) / 3 . ) + ( 2 . / 3 . ) * A ( 5 3 ) A( 81 ) = 0 . 5 * ( A( 8 0 ) + A ( 82) ) 1  C 17  7 8  53 54  62 6 3 64  11 .._  12  C C 31  18  1  -<u-  24  AMAX = 0 . DO 13 1 = 1 , 1 0 0 IF ( A( I ) . G T . A M A X ) GO TO 13 AHA X=A( I )  AT= r  GO TO 24  CONTINUC DO 7 3 1 = 1 , 5 X ( I )=I Y( I ) =A ( I ) . 73 DO 74 1=6, M X(T1=1+60 74 Y(I)=A(I+60) . K0=3 CALL OLQF(KG,M,X,Y,YF,YD,WT,NWT,S,SIGMA,AO,80,SS,LK,P) I.F( K 0 . E Q . . 3 ) G O . TO 83 ... I F I K 0 . E Q . 2 ) GO TO 8 2 RAS1 A = P ( 1 ) + P ( 2 ) * A 1 GO TO 84 82 . BASE A= P ( 1) + ( P ( 2 ) +P (.3.).* A I )* A I GO TO 8 4 B A S E A = P ( 1 ) + ( P ( 2 ) + { P ( 3 ) + P ( 4) * A I ) * A I ) * A I 8.3 . 84 PE AKA=A M A X - B AS E A WRITE(6,6)'AMAX,AI,K0,PASEA,PEAKA R E A D ( 8 , 3) ( 8 ( I ) , I = 1 , 10 0 ) DO 1 9 .1=1 ,1 0 0 _. 19 B(I)=B( I)*FB( I ) _.. B ( 1 2 ) = 0 . 5 * ( B.( .1 1 )+B( 13) ) B(34)=0.5*(B(33 ) +B(35) ) Bl36)=0.5*(B(35)+B(37)) B(4l 1 =0.5*1B(40)+B(42) ) B ( 4 6 ) =.0..8*.B.(45).+ 0 . 2 * , B ( 5 0 ) B( 4 7 ) = 0 . 4 * B ( 4 5 ) + 0 . 6 * B ( 5 0 ) B ( 4 8 ) = 0 . 6 * 8 ( 4 5 _ ) + 0 . 4 * B ( 50 ) B(49)=0.2*B{45)+C.8*B(50) B ( 5 9 1 = 0 , 5 * ( B ( 5 8 1+B(60) ) BMAX=0. . DO 2 8 I =1 ,..10.0 I F( B( I ) . G T . BMAX ) GO TO 27 GO TO 2 8 27 BMAX=B(I) BI= I 28 CONTINUE DO 9 3 1 = 1 , 5 X(I ) = I 93 Y( I ) =B( I ) DO 94 1=6,M X ( I ) = 1+60 94 Y(I)=B(I+60) K0= 3 CAL L OLQF ( K O , M , X , Y , Y F , Y D, W T ,.NWT , S , S I GMA, AO , RO, SS , L K , P 1 I F ( K u . E Q . 3 ) GO TO 1 0 3 I F ( K 0 . E Q . 2 ) GO TO 10 2 BASER=P(1)+P(2)*BI GO TO 104 B AS E B= P ( 1 ) + ( P ( 2 ) +P ( 3 )* B 1 ) * B I 102 GO TO 104 B A S E B = P ( 1 > + ( P ( 2) + ( P ( 3 ) + P ( 4 ) * B I ) * B I )*R1 10 3 104 PEAKB= B.MAX-BAS t B WRI TF < 6 , 1 1 ) BMAX , B l , K O , B A S F B , P E A K B 13  PEAK A= P F A K A / T B PEAKB=PEAK8/TB PEAK=(PEAKA+PEAKB)/2. WRITE ( 6 , 1 2 ) P E A K / S P E A K B , P E A K I F ( K. L E . 4 7 ) GO TO 15 STOP END  O E F Z E R C A L — PROGRAM TO ZERO AND C A L I B R A T E 2 1 - C M L I N E PROF I L L S PI MENS I ON X ( I OO) , S ( 1 PO) . T ( 1 00 ) , F A ( 1 0 0 ) t FP, ( I 0 Q ) . FF A ( I 0 0 ), F F R( 1 (.;"• ) L=0 N + 1. TS.. THE. F I R S T . CHANNEL B L A N K E D . I N THE OL QF B A S E L I N E F I T M I S THE TOTAL NUMBER OF C O N S E C U T I V E C H A N N E L S TO BE B L A N K E D N=40 . M=50 K= 0 L=L +1 DO .4 4. 1 = 1 , 1.00 . ; FF A ( I ) = 0 . C FIB ( I ) = 0 . 0 CAL = NUMBER OF U N I T S PER DEGREE K E L V I N B R I G H T N E S S TEMPERATURE R F A O < 5 , 2 0 ) GAL FORMAT ( F7 . 1 ) KF = 0 _ _ _ KF = KF+ 1 REAL ( 5 , 1 ) FOR M A T ( 7 2 X ) READ I N THE BANK A AND 0 FUDGE F A C T O R S (F A , F 9) FOR THE P ART ICULA SET OF O B S E R V A T I O N S B E I N G A N A L Y Z E D AND C A L C U L A T E AVERAGE V A L U E S RE AD ( 5 , 2 ) ...(FA ( I ) , 1 = 1 , 1 0 0 ) FORMAT(10F7.3) READ ( 5 , 1 ) . ... READ(5,2) ( F B ( I ) ,1 = 1 , 1 0 0 ) DO 3 1 = 1 , 1 0 0 F F A ( I ) = FF A( I )+ FA ( I ) FFB ( I ) = F F B (.1.) +FB.( I ) _ CONTINUE I F ( ( L . E Q . 1 ) . A N C . ( K F . EQ . 2 ) ) GO TO 4 2 IF((L.EC.2).AND.(KF.EQ.2)) GO TO 4 2 I F ( ( L • E Q . 3 ) . A N D . ( K F . E Q . 2 ) ) GO TO 42 GO TO 41 DO 4 3 1 = 1 , 1 0 0 F A ( I )= F F A ( I J / K F FB( I ) = FFB( I ) / K F CONTINUE . K=K +1 READ(8,7) (S( I ) , 1 = 1 , 1 0 0 ) FORMAT( 1 0 F 7 . 1) I F ( M O D ( K , 2 ) . EQ . 0 ) GO TO 6 U S E . F U D G E F A C T O R S TC CORRECT CHANNEL GAINS AND THEN AVERAGE OUT BAD C H A N N A L S I N BANK A DO 5 1 = 1 , 10 0 S(I)=S(I)*FA<I) S ( 1 ) = S ( 2) S (4 )=0 . 5 * (S (3 ) +S (5 ) ) S( 25) = 0 . 5*( S( 2 4 ) + S( 2 6 ) ) S ( 30 ) = 0 . 5 * ( S( 2 9 ) + S( 3 1) ) S < 4 4 ) = 0 . 5 * ( S ( 4 3 )+S(45) )  C 12 13 C C 6 8  .  14 51  52  '  "  c  53  c  21  S ( 5 1) = ( 2 . / 3 . > * S < 5 G ) + ( S ( 5 3 ) / 3 . ) S(52) = ( S ( 5 0 ) / 3 . } + ( 2 . / 3 . ) * S ( 5 3 ) S ( 8 1 ) = 0 . 5 * ( S ( 8 0 ) + S ( 8 2) ) S(83) = 0.5*1S(82)+S(84) ) C A L L MY OL QF ( K , N , X , S ) STORE TOE ZEROED BANK A DATA IN T ( I ) DO 13 1 = 1 , 1 0 0 T(I)=S(I) GO TO 4 USE FUDGE FACTORS TO CORRECT CHANNEL G A I N S AND THEN AVERAGE OUT BAD C H A N N E L S I N BANK B Of; 8 1 = 1 . 1 0 0 S <I )=S( I ) * F B ( I ) S(1)=S(2) S(4) =0 . 5 * ( S ( 3 ) + S ( 5 ) ) 5 ( 1 2 1 = 0 . 5 * ( S . ( 11 ) + S ( 1 3 ) ) S( 34) = 0 . 5 * ( S ( 3 3 ) + S ( 3 5 ) ) S ( 3 6 ) = 0 . 5 * ( S( 3 5 ) +S( 3 7 ) ) S ( 4 1 ) = 0 . 5 * ( S ( 4 0 ) +S(42 ) ) S..( 4 6 ) = 0 . 8*S.( 4 5 ) + 0 . 2 * S ( 50) S(47)=0.4*S(45 )+0.6*S(50 ) S ( 4 8) = 0 . 6 * S.( 4 5 ) + C 4 * S ( 5 0 ) S(49)=0.2*S(45)+0.8*S(50) S(5 9 ) = 0 . 5 * ( S ( 5 8 ) +S(60 ) ) S( 8 1 ) = 0 . 5 * ( S( 8 0 ) + S( 82) ) C A L L MYOLQF ( M , N , X , S ). .... ._ . .. _ . _ WRITE(6,51) FOR M A T ( • 1 »., 5 X , ' B A N K A , UNCAI. I RR A TED ' ) W R I T E ( 6 , 7 ) ( T ( I ) , 1 = 1 , 100 ) WRI T E ( 6 , 5 2 ) FORM A T ( / 5 X , ' BANK B , U N O A L I E R A T E D ' ) W R I T E ( 6 , 7 ) ( S( I ) , 1=1 , 1 0 0 ) AVERAGE THE ZEROED BANK A AND B DATA AND C A L I B R A T E DO 15 1 = 1 , 1 0 0 S(1 ) = 0 . 5 * ( S ( I)+T( I ) ) / C A L WRITE(6,53) FORM AT ( / 5 X , ' A V E R A G E OF A AND ^ C A L I B R A T E D ) WRI TF. ( 6 , 7 ) . ( S ( I ) , 1 = 1 , 1 00.) WRITE(9, 1 ) WRITE ( 9.,.7.) ( S ( I ) , 1 = 1 , 1 0 0 ) D E T E R M I N E C H A N N E L S TO BE BLANKED OUT IN THE OTHER SOURCE P O S I T I O N I F ( K . E 0 . 1 2 ) N=4 0 I F ( K . E Q . 1 2 ) M=45 IF ( K . E Q... 3 0.) N = 4.C _____ ' I F ( K . E Q . 3 0 ) M=4 5 I F ( K . E Q . 3 3 ) N=30 I F ( K . E Q . 3 8 ) M=45 IF(K. . E 0 . 3 6 ) GO TO 16 I F ( K . E Q . 5 0 ) N=40 I F ( K . E 0 . 5 0 ) M=6 5 I F ( K . E Q . 5 0 ) GO TO 16 I F ( K . E Q . 6 6 ) GO TO 21 GO TO 4 STOP END 1  c C C C C  D I F F C A L C — PROGRAM TO C A L C U L A T E FUI. 1 P R O F I L E n A T A  DIFFERENCE  PROFILES  FROM  -  1 C C 2 3 5 C C C 8 IC 12 __ 11 C C  16 C C 14 C C 15 9  C 21  LS-  I) I ME NS I ON S ( IOO) ,R ( 1 0 0 ) , A( IOC ) , B ( 100 ) , LK 10 0 ) J = 0. . K=0 J = J+1 DC 4 1 = 1 , 1 0 0 S ( I 1=0 . 0 K = K+1 READ(5,1) FORMAT < 72X ) R E A D . I N THE. K SOURCE P O S I T I O N T A P E S FOR A P ART ICULA i O B S E R V I N G F R E Q U E N C Y , AND STORE I N SU) RE A O ( 5 , 2 ) (A( I ) t 1 = 1 , 100 ) FORMAT(10F7.1) READ ( 5 , 3 ). INDEX FORMAT ( II ) DO. .5 I = 1 , 1 0 0 S ( I ) = S ( I ) +A ( I ) IF I N D E X = 0 , MORE OF THE SAME DATA IS TO FOLLOW IF INDEX= A N Y T H I N G E L S E , S T A R T R E A D I N G RANK B DATA AT THE I P . U N O E X . EG..0 ) GO. TO 6 C A L C U L A T E THE AVERAGE SOURCE P O S I T I O N P R O F I L E DO 8 1 = 1, IC C . S ( 1 ) =S ( I ) / K L=0 DO 12 1 = 1 , 1 0 0 R ( I )=G . 0 L = LU R E A D ! 5 , 1) READ I N THE L R E F E R E N C E T A P E S FOR A P A R T I C U L A R O B S E R V I N G FREQUENCY AND PQSIT I C N , AND STORE IN R( I ) R EAD ( 5 , 2 ) (B< I ) , 1 = 1, 100) READ ( 5_,_3 ) . I N D E X DO 16 1 = 1 , 100 R( I ) = R ( I ) + B (I ) IF I N D E X = 0 , MORE OF THE SAME DATA IS TO FOLLOW 1F( I N D E X . E Q . O ) GO TO 11 C A L C U L A T E TFE AVERAGE R E F E R E N C E P O S I T I O N P R O F I L E DO 14 1 = 1 , 1 0 0 R{ I )=R ( I ) / L CLOUD C A L C U L A T E THE D I F F E R E N C E P R O F I L E D U ) FOR A P A R T I C U L A R AND R E F E R E N C E P O S I T I O N DO 15 1 = 1 , 1 0 0 D( I )=S( I )-R ( 1 ) WRI TE ( 6 , 9 ) FORMAT( ' 1 ' 1 W R I T E ( 6 , 2 ) ( S ( I 1 , 1=1, 100 1 WRITE ( 6 , 1 ) WR I T F ( 6 , 2 ) (R( I ) , 1 = 1, 1 00) WRITE(6,1 ) W R I T F ( 6 , 2 ) (D( I) , 1 = 1 , 1 0 0 ) W R I T E ( 9, 1 ) W R I T E ( 9 , 2 ) (D( I ) , 1 = 1 , 100 ) IF INDE X = 1 , R E A D IN THE NEXT R E F E R E N C E P O S I T I O N T A P E S I F ( INDEX . E(0 . 1 ) GO TO 10 I F I N D E X = 2 , G 0 ONTO THE NEXT SOURCE P O S I T I O N OR FREQUENCY I F ( I N D E X . F Q . 2 ) GO TC 7 IF INDEX= A N Y T H I N G E L S E , S T O P STOP END  -66. C C  C  A D I T P L O T  C  F L U C T U A T I O N  - -  D I M E N S I O N  MENS  0 1  D I M E  .  2 8  O S R R A Y  N S I O N  ( 5 1 5 ) ,  T O P X ( 2 )  D O R R  , T O P Y ( 2  D A T  D S , S M I N , D V , V M I  A  P L O T  A V E R A G E  D I F F E R E N C E  A M D  E X P E C T E D  A ( 1 0 0 ) , B ( 1 0 0 ) , 0 P ( 1 0 3 ) , 0 M ( 1 0 3 ) , 0 ( 1 0 3 ) , D S U M ( 1 0 3 )  I O N  T O P X / 2 . C , 3 . 0 / , T O P  L  .  T O  D A T A  C A L L  C  P R O G R A M  A Y ( 5 1 5 ) , V A R R  ) » P C T Y ( 2  ,DO  A Y ( 5 1 5 ) , V ( 1 0 3 )  )  Y / 2 * 1 0 . 0 / , B O T Y / 2 * 0 . 0 /  N / 3 . 0 , - 9 . 0 , 3 0  . 0 , -  1 8 0 . 0 /  P L O T S  E M = 0  R E A D  I N  R E A D !  5 , 2 8 )  F O R M D O  AT. (  I  O F  S I N GL F  D A Y  P L O T S  T O  B E  M A D E  K M A X  D  K. = l , K  1 3  R E A D (  N U M B E R  M A X  5 , 1 ) _ N P . » O B J E CT . D A T E  1  F O R M A T  C  V L S R  ( 1 2 , 2 F 3 . 0  .  .  .  .  )  N H = N P / 2  c  ,  =  L S R  C O R R =  V E L O C I T Y  . C A L I O R A T I O N  F O R M  C  O F  O B S E R V A T I O N F A C T O R , ,  I F  N E C E S S A R Y  A T ( F 8 . 4., F 4 . . 2 )  R E A D D O  D A T E  VLSR.CORR  R E A D ( 5 , 2 ) 2  O N  C O R P . E C T I O N  I N  6  T H E  S O U R C E S  A D D E D  T O G E T H E R  F I R S T ,  T H E N  T H E  O T H E R S  I = 1 , 1 0 3  D P ( I ) = 0 . 0 6  0 M (  I ) = 0 . 0  D O  3  L = 1 , N P  R E A C ( 4  5 , 4 )  F O R M A T ( 7 2  _ X )  R E A 0 ( 5 , 5 )  ( A ( I  F O R M A T ( 1 0  5  ) . 1 = 1. 1 0 0 )  F T . 1 )  R E A D ( 5 , 4 ) R E A D ( 5 , 5 )  { B ( 1 ) ,1 = 1 , 1 0 0 )  ,D.( 1 ) = B ( 1 ) D ( 2 ) = B ( 2 ) D( D O .  7  D (  3 ) = B ( 3 ) . 7  J = 4 , 1 0 0  J ) = 0 . 5 = M A ( J - 3 ) + P ( J ) )  _  ...  D ( 1 0 1 ) = A ( 5 8 ) D ( 1 0 2 ) = A ( 9 9 ) D (  1 0 3 ) = A < I O C )  I F ( L . G T . N H )  DO ...  _..  8  .  8  T O  9  D P ( J ) = D P ( J ) +.DJ J ) G O  T O  3  9  D O  1 0  J=l  1 0  D M (  J ) = D M (  3  G O  j=l,103  C O N T  , 1 0 3 J ) + D ( J )  I N U F  C C J R R = C O R R / N P D D M A C  X = 0 . 0  C A L C U L A T E D O  1 1  D S U M ( 0 0 C  2 4  I  I F ( I  A V E R A G E  D I F F E R E N C E  ) = ( D P ( I ) + D M ( I ) ) * C O R  A B S ( D  T H E D I F (  W R I T E ( 0 , 2 4 F O R M A T (  W P. I T E ( 6  , 4 )  E X P E C T E D  F L U C T U A T I O N  M A X I M U M  R  ) * C O R R T E M P E R A T U R E  I ) ) . G T . AB S ( 0 D M A X ) )  )  • 1 ' )  W R I T E ( 6 , 5 )  A N D  , 1 0 3 .  ) = ( D P ( I ) - D M ( I )  C A L C U L A T E I F (  1 1  I = 1  ( D S UM ( I  ) , F = 1 , 1 0 3 )  T O  B E  P L O T T E D  D D M A X = D O I F (  I )  If ( 1 ( 3  -67W R I T E ! 6 , 5) ( D I M E ! I ) ,1 = 1, 103) W R I T E ( 6 , 2 7 ) DDMAX 27 F 0 R M A T ( F 7. 1 ) IF(DDMAX.LT .0.0) GO TO 25 DO 26 1 = 1 , 1 0 3 26 DP I F ! 1 ) = - D D I F ( I 1 C S C A L E DATA FOR P L O T T I N G 25 VZEP0=-147.128+VLSR DO 12 1 = 1 , 1 0 3 V ( I ) =1.0 . - (V ZEPO+ 1*2 . 1 2 - V M IN ) / D V D SUM(I ) = (DSUM( I ) - S M I N ) / D S + 1 . 0 12 DP 1F( I ) = (DP I F ( I ) - S M I N ) / p S - 1. 0 NEND=K*10 3 . . . NSTART=(K-1)*103 . DO 14 1 = 1 , 1 C 3 V A R R A Y ( I+ NST ART ) = V ( I ) D S R R A Y ! I+ M S T A R T ) =DSLM( 1 ) 14 DDRRAY( I+NSTART )=DD IF( I ) GO TO 3 0 . .16. „ .. C O N T I N U E . C A L L AX IS (0 . 0 , 10 . 0 , IH , + 1 , 2 . 0 , 0 . 0 , - 6 . 0 , 3 . 0 ) C A L L L I N.F,! TOPX , T G P Y , 2 , 1 ) C A L L A X I S ! 3 . 0 , 1 0 . 0 , IH ,+ 1 , 2 . 0 , 0 . 0 , - 3 . 0 , 3 . 0 ) C A L L SYMBOL (0 . 6 , 1 0 . 2 8 , 0 . 1 4 , 31HBP IGHTNESS TEMPERATURE ( 2 3 . C,M),Q.' #31) C A L L S Y M B O L ! 1 . 3 , 9 . 0 , 0 . 1.4 , 2CHE XP EC TED FL UC T UA TI ON , 2 7.0. 0 , 2 0 ) C A L L S Y M B O L ( 3 . 3 , 9 . 0 , 0 . 1 4 , 1 8 HAVERAGE D I F F E R E N C E , 270 . 0 , 18) CAL L SYMBOL ( 5 . 0 , 9 . 0 , 0 . 2 8 , 1 3 H 0 B J E C T . NUMBE P. ,2 7 0 . 0 , 1 3 ) CALL NUMBER!5.0,5.50,0.28,OBJECT,270.0,-1) I F ! L E M . E Q . 1 ) GO TO 17 CALL. SYMBOL. ( 5 . 0 , 4 . 7 , 0 . 1 4 , 1 2 H A U G . ,1970,270.0,12) C A L L . NU M B E R ( 5 . 0 , 4 . 1..,.0.. 1 4 , D A T E, 2.7 0 . 0 ,.-. 1) 17 CALL A X 1 S ( O . C , 1 0 . 0 , 2 1 H L S R VELOCITY {KM/SEC),-21,10.0,270.0,VMIM,i: fi )  32 15 30 13 18  20 19  22  „  CALL A X I S ( 0 . 0 , 0 . 0 , i n ,-1,2.0,0.0,-6.0,3.0) CALL L I N E ( T O P X , B O T Y , 2 , 1 ) CALL A X I S ( 3 . 0 , 0 . 0 , I H ,-1,2.0,0.0,-3.0,3.0) C A L L . SYMBOL ( 0 . 6 , - . 0 . 42 , 0 . 14 , 3 1HBR I G H T N E S S T E M P E R A T U R E #31 ) IF ( L E M , E.G. 1 ) GO TO 1 8 DO 32 1 = 1 , 1 0 3 C A L L SYMBCL ( D S U M ( I ) , V ( I ) , 0 . 0 7 , 2 , 270 . 0 , - 1 ) DO 15 1 = 1 , 1 0 3 C A L L SYMBOL<DD I F ( I ) , V ( I) , 0 . 0 7 , 2 , 9 0 . 0 , - 1 ) I F ! K . E Q . K M A X ) GO TO 99 CALL PLOT!7.0,O.C,-3) I F ( K . N E .KMAX ) GO TO 13 L FM=1 GO TO 16 CONTINUE CALL S Y M B C L ( 5 . 0 , 4 . 7 , 0 . 1 4 , 8 H A L L DAYS,270.0,8) DO 19 1 = 3 , 1 0 3 DO 20 J = 1 , K M A X K=I+(J-l)*j03 C A L L SYMBOL ! DORR AY( K) , V A R R A Y ( K ) , 0 . 0 7 , - l H . , 0 . 0 , 1 ) CONTINUE DO 21 1 = 1 , 1 0 3 DO 22 J=1 , K MA X K=l+{J-l)*103 C A L L SYMBOL ( D S R R A Y ( K 1 , V A R R A Y ( K ) , 0 . C 7 ,3 H . ,0 .0 , 1 1  (21.  CM),0.0  - (t>e>21 99  CONTINU F C A L L PL (IT NO S TO P END  C  c c c c c c  _  ...  LSR — PROGRAM TO P R E C E S S A SOURCE AND THE SOLAR A P E X , AND THEN C A L C U L A T E . THE V E L O C I T Y OF THE L . S . R . WITH RESPECT TO THE. SOURCE READ P R E C E S S I O N A L C O N S T A N T S FOR THE SOURCE AND SOLAR APEX 0.0 M MON / S A P F X / X S A «Y S A , 7 S A D I M E N S I O N X ( 2 ) , Y ( 2) REALMS J U L DAY R E A L* 4 M , N » M S A , N S A INTEGER YEAR»DAY, HR ... ISING=1 1=5 J=6 K=30 . . 9 WRITE(J,27) FORMAT L M . ' ) 27 WRITE!J,10) F O R M A T . I X , • ENTER P R E C E S S I O N A L CONST A N T S , M A N D , N , FOR YEAR OF O B S 10 ERVATION FOR SOURCE AND SOLAR A P E X ' , / l X , ' M = S X X X . X X X N= SXXX.XXX #.SA = SXXX . X X X . NS A= SXXX . X X X • ) M=61.469 N=26.722 MSA=215.109 MSA = 9 3 . 53 7 WRITE(J,11) M,N,MSA,NSA FORMAT (3.X , F 3 . 3 , 5 X , F8 . 3 , 7 X , F8 . 3 , 7 X , F 8 . 3 ) 11 READ THE TIME OF OB SE R VA TI ON ( J U L I A N DAY AND DAY ARE THOSE AT c G R E E N W H I C H , H E N C E , IF H R ( P S T ) I S . G R E A T E R THAN 16 AT PE NT IC TON » THE c P E N T I C T O N J U L I A N DAY AND CAY MUST BE I N C R E A S E D BY ONE DAY c 23 WRI TF ( J , 1.2 ) 12. FORMAT ( I X , ' ENT ER J U L I A N CAY , YEAR , MONTH, DAY , AND HR ( P ST ) OF O B S E P V . #TI ON S / 1 X.,.* J U L I A N...DA Y. YEAR MONTH DAY ..HR M IN ( PS T ) ' , / 1 X, ' X y tfXXXX.X YYYY MM DD HH MM ) REAG\( I , 13) J Ul DAY ,.Y F AR , MONTH , DAY , H R , MI N 13 F O R M A T ( I X , F 9 . 1 , 5 X , 1 4 , 3 X , I 2 , 5 X , I 2 , 4 X , 1 2 , 3 X , I 2) W R I T E ( J , 1 3 ) JUL 0 A Y , Y E A R , M O N T H , D A Y , H R , M I N C C A L C U L A T I O N OF P R E C E S S I O N A L CONSTANTS FOR DAY OF O B S E R V A T I O N S 24... . HR= HR+8 _ „ I F ( H R . G E . 2 4 ) HR = H R - 2 4 FAC TOR = ( ( M O N T H - 1 . ) +( { D A Y - 1. ) + . H R + M I N / 6 G . ) / 2 4 . ) / 3 0 . 5 ) / 1 2 . CM=3.0734*FACT0R CN=1.3361*FACTOR M=M+CM N=N+CN MSA=MSA+CM NSA=NSA+CN P R E C E S S P O S I T I O N OF SOLAR APEX FROM 1 9 0 0 . 0 TO DATE OF OBSERVATION C Y(1)=64800. Y(2)=7200. C A L L FR GMT 0 ( 4 1 , S R , I H R , M I N T , SECT , S D , 1, 1 , 1 . , 1. , Y( 1) , ).. , 1 . , 1. , 1. ) C A L L F R OM Ti.) ( 4 2 , SR , 1 , 1 ,1 . , SD , I D EG , MI N A , S E C A , 1 . , Y ( 2 ) , 1 . , 1 . , 1 . , 1 . ) W RIT E ( J , 16) FORMAT (1 X , • EPOCH 1 9 0 0 . 0 AND CURRENT P O S I T I O N OF SOLAR APi-X A P R : ' . 16 # 1 X , ' R A = SHH MM S S . S DFC=SDD MM S S . S ' ) 1  -69W R I T E ( J , 1 5  )  S R ,  I H R , M I N T , S E C T , S D ,  I D E G , M I N A ,  S E C A  N U M S I G = 8 M A X I T = 2 0 C A L L  E P O C H ( M S A , N S A , Y , N U M S I G , M A X  C A L L  F R 0 M T 0 ( 4 1  C A L L  F R O M T O ( 4 2 , S R  W R I T E !  J , 1 5 )  , S R , I H R , MI  C A L CU L AT WRI  1 7  , 1, 1, 1. , S D .  I C N  )  ,1 . , 1 . ,Y  IP E G . M I N A . S E C A  S R , I H R , M I N T , S E C T , S D ,  I F ( I S I N G . E Q . C ) C  I T , I S ING  N T , S E C T , S D , 1 ,1  , 1.  IP E G , M I N A, S E  ( 1 ) , 1 . , 1 . , 1 . , 1 . )  , Y ( 2)  ,1  . , 1 . . 1 . , 1 . )  CA  W R I T E ( J , 2 5 )  OF  E Q U A T O R I A L  C O M P O N E N T S  OF  S O L A R  A P E X  M O T I C N  TE ( J , 1 7 )  F O R M A T ! I X , ' E Q U A T O R I A L  C O M P O N E N T S  C A L L  7_ S A )  S U N V E L  (Y , XS  W R 1 T E ( J , 1 8 ) 1 8  F O R M A T  C  C A L C U L A T I C N  A . Y S A ,  OF  S O L A R  A P E X  M O T I O N  A R E : ' )  X S A , Y S A , Z S A  ( I X , « X S A  =  OF  ' , F 8 . 4 , 5 X , ' Y S A .  E Q U A T O R I A L  =  ' ,F 8 . 4  C O M P O N E N T S  OF  ,5 X , ' Z SA T H E  •=  T O T A L  « , F 8 . 4 ) L S R  V E L O C I T Y  W R I T E ( J , 1 9 ) 1 9  F O R M A T {  I X , ' E Q U A T O R  H R P S T = F L O A T ( H R  I A L  C O M P O N E N T S  OF  THE  T O T A L  L S R  V E L O C I T Y  A P E : '  )  M I N P S T = F L C A T ( M I N ) C A L L  L S R V E L  ( J U L DAY  W R I T E ( J , 2 0 ) .20  F O R M A T ! . I X  X L S R  , HR.P S T , M I . N P . S . T , X L S R » Y L S R  , Z L S R  )  .  , Y L S R , Z L S R  ,« X L S R  =  \ , F.8....4 , 5 X , ' Y L S R  =  ' ,F 8 . 4  , 5 X , • Z L S R  =  •  , F 8 . * )  W R I T E ! J , 1 4 ) 1 4  F O R M A T # 0 N '  .. _C  ( I X , ' E N T F R  , / 1 X ,  READ..1 N R E A D ! I ,  1 5  'RA=  P R O C E S S  C F  D E C  S O U R C E  = SOD  A N D  MM  C A L C U L A T E  P R E C E S S E D  P O S T  S S . S ' )  .. S 0 U P - C E..; F O P , .._T.HE. A P P R O P R I A T E  E P O C H  , 1 2 , 1 3 , 0 6 . ? ) )  S R ,  I H R , M I N T , S E C T , S D ,  P O S I T I O N  F R O M T O (  C A L L  S S . S  S R , I H R . M I N T , S E C T , S D , I D E G , M I N A , S E C A  F O R M A T ( 2 ( 4 X , A 1  C A L L  MM  . P C S . I T . I C . N.. 0 F 1 5 )  W R I T E ( J , 1 5 ) C  P O S I T I O N  S H H  OF  S O U R C E  F R C M  1 4 ,S R » I H R , M I N T , S E C T ,  . F R G M T O ! 2.4 , S R  ,1  , 1 , 1 . , S D ,  I D E G , M I N A , S E C A 1 9 5 0 . 0  T O  D A T E  O F  O B S E R V A T I O N S  S D , 1 , 1 , 1 . , 1. , X ( 1) , 1 . , 1 . , 1 .  I D E G t  M I N A,. S . E C A , 1 . , X ( 2 ) , 1 . , 1 . ,  , 1 . )  1 . , 1. )  N U M S I G - = 8 MAX  I T = 2 0  C A L L  E P O C H ! M , N , X , N U M S  C A L L  F R O M T O ( 4 1 , S R , I H R , M I M T , S E C  C A L L  F R C M T 0 ( 4 2 , S H , 1 ,  WRI  TE ( J , 1 5 )  SR  F O R  M A T ( ' N O  C  C A L C U L A T I O N R A D C 0 N = 7  I T ,  1, 1 . , S D ,  I S I N G ) T , S D , 1 , 1 , 1 . , 1 . , X ( 1 ) , 1 . , 1 . ,1 . , 1 . )  I D E G , M I N A , S E C A , 1 . , X !  , I H R , M I N T , S E C T , S.D.,. I D E G  I F ! I S I N G . E Q . C ) 2 5  I G , M A X  2 ) , 1 . , 1 . , I . ,1.  )  , MI N A , S E C A  W R I T E ! J , 2 5 )  C O N V E R G E N C E ' OF  L S R  )  V E L O C I T Y  OF  O B S E R V E D  OF  T H E  S O U R C E  . 2 7 2 2 1 E - 0 5  D E C = X ( 2 ) * R A D C 0 N R A = X (  1 ) *R  ADC.ON.  X S R C = X L S R * C O S  ( D E O *  Y S R C = Y L S R * C O S <  D E C )  COS  (R A  * S I N (  )  R A )  Z S R C = Z L S R * S I N ( D E C ) V L S  R = X S R C + Y S R C +  W R I T P ! J , 2 1 ) 2 1  F O R M A T  { I X , ' T H E  * F 8 . 4 / ) GO 2 6  TO  S T O P E N D  9  Z S R C  V L S R L S R  V E L O C I T Y  O B S E R V E D  S O U R C E  WA S :  VI. SP  =  '  -7-0-  c c c c c c c c c c ...  .  .  $  *  *  *  *  *  *  *  *  *  *  *  A STROP A. K - -  if. *  *  *  SUBROUTINES  *  *  *  *  *  *  *  USEFUL  *  *  *  *  *  *  #  *  *  *  *  *:  *  *  *  *  #  *  I N AST ROPHY S I C AL  *  *  *  *  *  *  *  *  *  *  *  ;V *  :'• X- *  *  CALCULATIONS  * * £ * * * * * * * * * * * s> * * * * * * * * * * # * * * * * * * * * * * * * * * * # * * * * * * * * * * * * * * * * * * * * *  *  EPOCH — . S U B R O U T I N E TO P R E C E S S A SOURCE P O S I T I O N SUBROUTINE E P O C H ( M , N , X , N U M S I G , M A X I T , I S 1 N G ) THE P R E C E S S I O N A L C O N S T A N T S M , N , D E T E R M I N E THE P E R I O D OVER W H I C H THE P R E C E S S I O N I S T C BE MA(3E DIMENSION IPO!NT(3,3),ISUB(3),X(2) REALMS Y ( 2) , C 0 E(3» 3 ) , T EM P( 3 ) » P AR T ( 3 ) , A D , DO RE A L*4 M, N _ DOUBLE P R E C I S I O N D B L E COMMON A O , D O t R E A L M , R E A L N ... REAL M = M REALN=N Y(1) = DBLE(X(1) ) Y(.2.)=DBLE.(X (2..).) AO = Y( 1 ) 00=_Y (2..) CALL N I N L I N ( 3 , M A X I T , N U M S I G , I S ING,Y, I POINT, I S U B , C O E , T E M P , P A R T ) X( 1 ) = S N G L ( Y( 1) J X(2)=SNGL(Y(2)) ... RETURN... END  0  c c c  N 1 N L I N — S U B R O U T I N E TO SOLVE THE N O N - L I N E A R P R E C E S S I O N EQUATIONS SUB ROUT I N E . . NI NL. I N { N 1, MAX IT , NUM S I G , S I NG , X , I PO .1 N T , I SUB , COB , TE M P , P A U)  c c  . . . T H I S S U B R O U T I N E I S . A DOUBLE PR EC I.S I ON VER S I G N OF T H E . L I B R A R Y PROGRAM N u N L I N D I M E N S I O N I PCI N T ( N . 1 , M l ) , I S U B ( N l ) DOUBLE P R E C I S I O N CABS R E A L * 8. X( NI.) , C O E . ( N l ,..N1..). , TEMPI Ml ) , PART.(N1 ) » P EL C O N , F A C T O R , F, H, HOL D RE AL * 8 F P L U S , D E R M A X , TE ST INTEGER CGNVGE, T A L L Y , SING  c  L.  N = N1 CGNVGE SING = R EL CON  - 1 = 1 1 = 1C.**(-NUMSIG)  r  c  c 210 C  DO 3 5 0  M = l , M A X IT  DO 210 J=1,N . .1 POINT (1 , J )  =.. J  DO. 300. K.= l.,..N IF (K . G T . 1) C A L L X K M A X ( K , N 1 , X , I S U B , C O E , IPO INT ) C A L L F K ( N , X , F , K) FACTOR = .001 r  L 220  TALLY  =  0  =  1 POI NT( K , I )  r  DO 2 30  I=K, I TEMP  N  1000 1002 1003 5 55 1001 2 30 _  HOLD = X(ITEMP) H = FACTOR*HOLD IF ( H . E Q . 0 . ) H = .001 X ( I TEMP) = HOLD + H IF (K . G T . 1) C A L L XKMAX(K , N l , X , I S U B , C C E , I P G I MT ) C A L L F K ( N i X , FPL U S , K ) CONT I NUB P A R T ( I TEMP) = (FP.LUS - F J / H X( I TEMP ) = HOLD I F ( LABS ( P ART { .1 T E MP ) ) . EQ . 0 . ) GO TO 5 5 5 IF< DABS< F / P A R T U TEMP) ) . L E . 1 0 * * 2 0 ) GO TO 1001 TALLY=TALLY + 1 CONTINUE CONTINUE  r  I F  ...C. 240  £ 2 50  C 260 27C  ( T A L L Y .1 E . ( N-K ) ) GO T 0 .24 0 FACTOR = F A C T 0 R * 1 0 . I F ( F A C T O R . G T . . 5 ) GO TO 3 7 0 GO TO 2 2 0 __ - _ _ ... IF (K , L T . N) GO TO 2 5 0 I F ( DABS (.PART ( I.TF MP) ) . E Q . O . I . GO TO . 3 7 0 C 0 E ( K , N + 1 ) = 0. K MAX = ITEMP GO TO 2 9 0 KMAX = I P O I N T ( K . K ) D E R M A X = D A G S ( PART ( KM AX ). ).. KPLUS = K + 1 DO 270 I = K P L U S , N JSUB = I P O I N T ( K , I ) TE S T=DAB S ( PART. ( J SUB).,) IF (TEST , L T . D E R M A X ) GO TO 2 6 0 DERM A X . =. T E S T 1 P O I N T ( K P L U S , I) = KM" A X K MAX = J S U B GO TO 2 7 0 IPO INT CONTINUE  ( K P L U S , I)  =  JSUB  C  IF(DABS(PART(KMAX)) . E Q . 0 . ) I S U B ( K ) = KMAX COE .( K , N+1 )..=.. . 0 .  GO TO  370  C DO 2 8 0  2 80 C 290 300 _C  J = KPLUS ,N JSUB = IPOINT(KPLUS,J) C O F ( K , J S U B ) = -t-'ARTt J S U B ) / P A R T ( K M A X ) C0E(K,N+1) = C0E(K,N+1) + PAPT(JSUB)*X(JSUB) CONTINUE  C 0 E ( K , N + 1) CONTINUE  IF IF  (N (M  X(KMAX) . G T . 1) . E Q . 1)  =  ( C 0 E ( K , N + 1)  [ = C0E(N,N+1) C A L L XKMA.X(N, GO TO 3 30  Ml,  -  F ) / P A R T ( K M A X)  X,  1SUB,  CCE,  +  IPOINT)  C DO 310 I=1,N I F ( LA P.S ( ( TEMP( I ) - X (  I ) ) /X( I ) ) .GT.RELCON)  X(KMAX)  GO TO 32 0  -7Z3 1 0  r  C O N T INUF:  C O N V G E I F . ( C O N V G E  3  GCi  TO  DO  3 4 0  =  C O N V G E  . G T .  .3)  +  GO  1  T O  3 6 0  3 0  c 3 2 0 3 3 0  C O N V G E  3 4 0 3 5 0  =  1  1 = 1 , N T E M P (  I>  =  =  M  X ( I )  C O N T I N U E GO  TO  3 8 0  GO  TO  3 8 0 .....  0 MAX  3 6 0  I T  r 3 7 0  S I N G  rL 3 8 0  =  0  R E T U R N END  .  C  - -  S U B R O U T I N E .. D I M E N S I O N R E A L * 8  X K M A X  ( K , N 1 , X , I S U B , C U E , I P 0 1  •  •  ( N 1 ,,N 1.) , 1 S U B { N 1 )  IP C INT  C 0 E ( N 1  -  N T )  , N 1 ) , X ( N l  )  C N „  D O  =  M l  KM .  =  K M A X  K ..=  1 0 0  ......  -  I  =  =  X  1 1 0  2 -  .1 )  0 .  IP O I N T ( K M , J )  X ( K M A X )  1 0 0 r  +  J = K M , N J S U B  ._  1  IS U B (K M  X { K M A X ) DO  -  1 1 . 0 . 1 - 2 ,.K  (K M A X  =  )  X ( . K M A X ) ..+.  .=. X ( K M A X  CGE.(KM.-1  , J S U B ) * X ( J S U B )  ). . + . C O E ( K M - 1 , N + 1 )  R E T U R N END  c c C  _  __c  F K  S U B R O U T I N E  S U B R O U T I N E  R E Q U I R E D  c  T H I S  C  N I N L I N  K N O W  R E A L * 8  X ( L ) , B , C , Y , A O , D O  S U B R O U T I N E  C O N T A I N S  W H E N  A  T H E  S O L U T I O N  D S I N , D C  D O U B L E  P R E C I S I O N  COM  AO , DO , R E A LM ,R E A L N  MON  B Y  N I N L I N  F K ( L , X , Y , K ) E Q U A T I O N S H A S  B E E N  T O  B E  S O L V E D  A N D  L E T S  F O U N D  O S , D T A N  B= (X (1 )+ A C ) * 3 .6 3 6 1 0 5 D-(. 5 G O 10  T G  ( 1 0 , 2 0 ) , K  C = ( X ( 2 ) + 0 0 Y = - X ( 1  )* 3 . 6 3 £ 1 0  ) +A C + R E A L M + R E  5 0 - 0 5 A L N * D S  I N ( 3 ) * D T A N ( C  )  R E T UP. N 2 0  Y = - X ( 2 )+ D 0 + R E A L N 1 ' C C 0 S (  B )  R E T U R N END C  c c c c  L S R  - -  T O T A L  S U B R O U T I N E L S R  SUB R O U T I N E  T O  C A L C U L A T E  T H E  E Q U A T O R I A L  C OM P O N E N T S  V E L U C I T Y L S R V E L ( J U L D A Y , H R P S T , M I N P S T , X L S R  , Y L S R ,  7  L S P )  OF  T H E  -73COM MON / RE A L * 8 R E A 1. * 8 R E A L*4 DOUBLE _C C C 1  1 . C A L C U L A T I C N OF E Q U A T O R I A L COMPONENTS OF E A R T H ' S R O T A T I O N CONVERT PST TO U N I V E R S A L TIME. HRUT = H R P S T + 5 . I F ( HRUT . G B . 2 4 . ) h R U T = H R U T - 2 4 . ... Ml NUT=M.INPST . FCD= (HRUT+M I N P S T / 6 0 . ) / ? 4 . FJD=JULDAY+FCU AT START..OF, J U L I A N DAY 2 4 4 0 3 6 Q . 5 ,MAY 19 , 1 9 6 9 , O H R U T , H . A . OF F I R S T POINT OF A R I E S IS 1 5 H R 4 5 M I N 5 6 . 9 9 M S E C , W H I L E L O N G I T U D E OF P E N TIC T C IS. +7HR5.8.MIN28 . . 5 3 S . E C . HENCE S I D F R 1 A L TIME AT P EN T I C TON IS 7 H R 4 7 M I N 2 8 . 4 4 S E C = C . 3 2 4 6 3 5 S I O E R I A L DAYS JD=244C 360 . 5 F SD = 0 . 3 2 4 6 3 5 C A L C U L A T E NUMBER OF SI DERI A.L ..DAYS... SI NCE MAY 19 , 196 9 . N S D M F J D - J D ) * 1 .C C2 7 3 8 NF SD=D MOD ( N S D , 1 . D + 00.1 S IDTIM = SMGL(FSD+NFSD) S IDTIM=AMGO(SIDTIM, 1. ) ST=SIDTIM*6.2831E53 CALCUL A T.E. MAX I MUM VELOG 1 TY FROM KNOWN PERI CD. OF E A R T H ' S POTAT ION VMAX=0.465 V P E N T = V M A X * C O S ( L A T I TUDE OF PENT I CT CN ) VPENT=0.2933195 VPENT=0 . 3 2 4 HENCE E QUI TOR IAL COMPONENTS A R E : XER = V P E N T * S IN( ST ) _ YER = VPE N T * C O S ( S T > ZER=0.0  C  C C C C  C  _.C. C  C  C C _C C C C. C _C C  _C_ C C C C  S A P EX / X S A , Y S A , 7 SA J U L D A Y , FCC , F JO , JD , NS D , NFS D, F S D , DAYS , T 1, T 2 » T 3» [) L R A D C C N , T , L , P , 0 , E , DI F , VB AR , A , VEC),E L , X E C , Y E 0 , Z E 0 MINPST. P R E C . I S 1 C N D M O D , B B L E , D S I N , D C O S , D S Q R T , DTAN  .  2 . C A L C U L A T I C N OF E Q U A T O R I A L COMPONENTS OF E A R T H ' S O R B I T A L VF1. OC I D E T E R M I N E NUMBER OF J U L I A N DAYS S I N C E 1 9 0 0 . 0 DAYS = F J D - 2 4 1.5020 . C C A L C U L A T E E C C E N T R I CI TY ( E ) , O B L I Q U I T Y OF EC L I P T IC ( 0 ), M E A N I.0NG1TUJ (L), L O N G I T U D E OF P E R I G E E ( P ) , FROM FORMULAS G I V E N IN THE [XPI.ANAT S U P P L E M E N T TO THE ASTRONOMICAL EP HEM E R I S , WHERE: D A Y S=T I ME MEASURED I.N E P H E M E R I S DAYS S I N C E . 1 9 0 0 . 0 T1= TIM E MEASURED IN J U L I A N C E N T U R I E S OF 3 6 5 2 5 DAYS S I N C E 1 9 0 0 . 0 T l = DAYS/36525 T2=T1**2 T3=T1*T2 RA0CCN=0 . 0 1 7 4 5 3?. 92 5 1 9 9 4 3 T=FJD-24 36204. 5 L=(0.9856C9*T+280.14275)*RADCON P = { 281 . 22 08 3 +4 . 7 0 6 8 4 D - 0 5 * Ei AYS + 4 . 5 3 D - 0 4 * T 2 + 3 . OD- 06 *T 3 ) *R A DC ON 0 = ( 2 3 . 4 5 2 2 9 H - 0 . 0 1 3 0 1 2 5 * T 1 - 1 . 6 4 0 — 0 6 * T2 + 5 . 03 U-Q7 * T 3 1 R A DC ON E=0.01675104-4.18D-05*T1-1.260-07*T2 DIF=L-P C A L C U L A T E V E L O C I T Y COMPONENTS OF E A R T H ' S O R B I T A L V E L O C I T Y IN E Q U A T O R I A L C O O R D I N A T E S , U S I N G EQUATIONS G I V E N BY MCRAE ANO WESTERHOUT,WHERE: V BAR=M EAN ANGULAR V E L O C I T Y OF EARTH A = S E M I - M A J O R A X I S OF E A R T H ' S ORBIT VBAR=1.99C987D-C7 A = 1 4 . 9 6 7 4 0+0 7  -74V E O = V B A R * A / D S Q R T ( 1 . 0 0 + 0 0 - 0 * * 2 ) E L = L  +2  . 0 * E * C S  X E Q = V E 0 *  I N ( U I F  )+ 1 . 2 5 * E * * 2 * D S I N ( 2 . G * D I  (D S I N ( E L )+ E * O S I N ( P )  Y E O = - V E 0 * ( L ) C O S { E L ) + E * 0 C 0 S ( Z E 0=Y  E 0 * DT  AN  ( 0  F )  )  P)  ) * D C O S ( 0 )  )  C C  3 .  C  L O C A L  C A L C U L A T I O N G R O U P  C  T H I S  C  X S A = V S * C U S . (  C  C F  E Q U A T O R I A L  T O W A R D S  P 0 S 1 T 1 C N  S H O U L D  C O M P O N E N T S  S O L A R  B E  A P E X :  P R E C E S S E D  OF  S U N ' S  A = 2 7 0 . 0 ,  F R O M  M O T I O N  0 = 3 0 . 0 ,  I N  T H E  V S = 2 0 . 0  1 9 0 0 . 0  A ) f t C O S ( D )  Y S A = V S * S I N ( A ) * C O S ( D )  C  Z SA = V S * S IN ( D )  C  C U R R E N T  V A L U E S  FOR  C C  T H E  X S A , Y S A , Z S A . .  THE  C O M B I N E D  E Q U I  ..  T O R I  R E A D  I N  T H R O U G H  L A B E L L F D  C O M M O N  . . . . . . . .  A L  C G M P C N E N T S  OF  M O T I O N S  1 ,  2 ,  AND  3  A R E ;  XL S R = S N G L { X E O + X S A + X E P ) Y L S R = S N G L ( Y E O + Y S A + Y E R ) ZLSK. = S N G L  ( Z E O + Z  S A )  R E T U R N END  _  _  C ...C  c C  S U N V E L  C  S U N ' S  ...  —  S U B R O U T I N E  S U B R O U T I N E .  C A L C U L A T E  SUN V E L ( X , X S A  D I M E N S I O N R A D C 0 N  T H E  E Q U A T O R I A L  C O M P O N E N T S  OF  TL-  ,Y S A ,Z S A )  X ( 2 )  = 7 . 2.7.22 I E - C 5  V S = 2 0  .0  A = X ( 1 ) * D = X (  TO  M O T I O N  R A D C 0 N  2 ) * R A DC  VCOSC=.COS.(  ON  D ) * V S  X S A = C G S ( A ) * V C O S D Y S A = VC 0 SO * S I M ( A ) Z S A = V S * S I N ( D ) RE T U R N E N D . C  c c C  ;  F R O M T O  —  S U B R O U T  S U B R O U T I N E  I N E  F R O N T 0 (  y/HR S T , S E C S A , D E G ...C C  A  TWO  D I G I T  C O N V E R T  I N T E G E R  F R O M  C  1= H O U R S , M I N U T E S  AND  S E C O N D S  C  OF  6 = S E C 0 N 0 S N  CAT  B L K / 1 H .  , 3 = R AD  A P C  OF  R E A L A  IO N  I A N S  ,7 = P E G R  U N I T S OF  A N D  N E G / I H - /  M= I / 1 0 GO  TO  { 1 ,2 ,3 ,4 ,5 ,6 ,7 ,8  I F ( S H . E Q . N E G )  2  TO  S E C = - S E C  ( 1 1 , 1 2 , 1 3 , 1 4 ,15  , 1 6  , 1 7 , 1 8 ) , N  S E C = I D E G * 2 4 0 . + M I N A * 4 . + S E C A / 1 5 . I F ( S D . E Q . N E G ) GO  3  ) , M  S E C = I H R » 3 6 0 C . + M I NT*6.Q. + S E C T  GO  TO  S E C = - S E C  ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6  S E C = R A 0 * 1  3 7 5 0 . 9 9  I D E G,M  A N G U L A R  M E A S U i - i  IN A , S E C A , R A D , S E C  , 1 7  , 1 8 )  ,N  I S  R E A D , .  S E C G N C ,  ,2 = D E G R E E S , M I O F  E B S ,8 = R F V G L U T  N = M G 0 ( 1 , 1 0 )  1  T H E  R . A .  ,4= S E C O N D S  E G / ,  D I F F E R E N T  E C T , S D ,  B E T W E E N . . 1 . 1 . A N D . ..R.8  T H E  DEC L INAT  B E T W E E N  S T ,  ,R E V )  I N D I C A T E S  C  D I G I T  SA  TO  I , S H , I H R , M I N T , S  WHERE.. T H E  N U T E S  TP-'E , 5 = H O U R S  I GNS  T O  OF  T H E  F I R S T  U N I T S . . AND  S E C G N C -  T I M E ,  4 5 6 7 8 11  21  12  22  13 .  _  14 15 16 _ 17 18  C C  C C C  c c c  30  GC TD (11,12,13,14,15,10,17,18),N SEC=SECST GO TG (11 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N SEC=HRST*360G. GO TO ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N SEC=SECSA/15. GO TO ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N SEC=DEGSA*24G. GO TO ( 1 J , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N SEC=REV*e-6400. GO TG ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N SH = R LK I F ( S E C . G T . 0 . 0 ) GO TG 21 SEC=.-S EC ... SH = NEG .. I HR= I NT ( . S E C / 3 6 C O . ) SEOAMCCM S E C , 3 6 0 0 . ) MINT=INT(SEC/60.) S EC T = A M O D ( S E C , 6 0 . ) .. ...RETURN „. SD=BLK IE- ( SEC . G T . 0 . 0) GO. TO. 2 2... S E C = - S EC SD=NEG IDEG= I N K SEC / 2 4 0 . ) S EC=AMGD (.S r C , 2 4 0 . ) _ MI NA = I NT ( S E C / 4 . ) SEC A= AMODJ. S EC., 4 . ) * 1 5 . . RETURN RAD=SEC*7.27221E-05 RETURN SECS.T--SEC _ RE TURN HRST=SE C / 3 6 0 C . RETURN SEC S A = S E C * ' 1 5 . RETURN DECSA=S E C / 2 4 0 . RETURN REV=SEC/86400. RETURN END •• -  -•-  -—  -  -  MYOLOF — S U B R O U T I N E ViHICH READS A BAD B A S E L I N E D P R O E I L E AND RETURNS A BEST L E A S T SQUARES F I T T E D P R O F I L E S U BROU T I N E MY OL Q F ( M , N , X , Y ) N + 1 . I S THE F I R S T CHANNEL B L A N K E D IN THE OLQF B A S E L I N E F IT M IS THE TOTAL NUMBER OF C O N S E C U T I V E C H A N N E L S TO BE BLA NKE n X I S THE CHANNEL NUMBER, Y A C C E P T S P R O F I L E AND R E T U R N S BEST F I T DIMENSION X(100),Y(100),YI(100),YF(1C0),YD(100),WT(100) , S (4 ) , F (4 ) #S1GMA(3),A(3),E(3) L O G I C A L l.K DATA L K , N W T / . F A L S E . , 0 / 0 0 30 1 = 1 , Ni X( I ) =1 Y I ( I )=Y( I ) L=100-M N 1 = N+ 1  -u-  _  DO 31 I = N 1 , M X { I ) =1 + L 31 YI ( I) = Y( I+ L ) K=3 OLQF F I T S THE BEST H I R S T , S E C O N D OR T H I R D ORDER POLYNOMIAL TO C THE B A S E L I N E ON E I T H E R SIDF OF THE P R O F I L E , WHICH HAS R F F N C B L A N K E D O U T . IT USES T H I S P O L Y N O M I A L TO C A L C U L A T E THE P R O F I L E C I N THE B L A N K E D R E G I O N AND RETURNS TO THE C A L L I N G PROGRAM C CALL O L Q F ( K , M , X , Y I , Y F , Y D , W T , N W T , S , S I G M A , A , B , S S , L K , P ) W R I T E ( 6 , 3 9 ) K , SS , ( P ( I ) , I = 1 , 4 ) 39 F0RMAT(3X,«K = • , I 2 , 5 X , ' S S = ' , E 1 2 . 5 , 5X , ' P (1 ) = • , E l 2 . 5 , 5X , ' P ( 2 > H ' . F I 2 . 5 , 5 X , MM 3 ) = • . E 1 2 . 5 . 5X . ' P ( 4) = ' . E 1 2 . 5 ) IFMK.EQ.3) GO TO 33 . . I F I K . E Q . 2 ) GO TO 32 DO 34 1 = 1 ,1 OO X( I )= I 34 Y F ( I )=P ( 1 )+P (2 ) * X ( 1 ) GO TO 3 5 DO 36 1 = 1 , 1 0 0 22 X ( I )=I 36 YF ( I ) = P ( 1 ) + ( P ( 2 ) + P ( 3 ) * X ( I) ) * X ( I ) GO. TP 3 5 DO 3 7 1 = 1 , 100 33 X( I ) =I 37 YF{I) =P ( l ) + (P(2)+(P<3)+P(4)*X(I))*X(m*X(I) DO . 38 1 = 1 , 1.00 _ 35. Y d )=Y( I ) - Y F ( I ) 38 RETURN END C C  c *  FATAL  FORTRAN  ERROR :  F N D - O F - F I I F FNGOUNTFRFD ON R FAD RROR CCCURED ON UNIT 5 R.ROR RETURN  SIG  0P F RAT I 0M _  -77BIBLIOGRAPHY  1.  Barnard, E.E.  2.  Lynds, B.T.  3.  Heiles,  4.  Cudaback, D.D. and H e i l e s ,  5.  Heiles,  6.  H e i l e s , C.E.  7.  Palmer P., Zuckerman, B., B u h l , D., Snyder, L.E., Ap.J., 156, L147.  8.  Heiles,  9.  C a r r u t h e r s , G.R.  1967, A p . J . ( L e t t e r s ) , 148, L141.  10.  C a r r u t h e r s , G.R.  1970, Space S c i . Rev., 10, 459.  11.  G u l l , T.R. and H a r w i t t , M.O.  12.  Gould, R . J . and H a r w i t t , M.  13.  L i l l e y , A.E.  14.  G a r z o l i , S.L. and V a r s a v s k y , C M .  1966, Ap.J., 145, 79.  15.  G a r z o l i , S.L. and V a r s a v s k y , C M .  1970, Ap.J., 160, 75.  16.  W e s s e l i u s , P.R. and S a n c i s i , R. A s t r o p h y s . , 11, 246.  17.  Heiles,  18.  S a n c i s i , R.  19.  S a n c i s i , R. and W e s s e l i u s , P.R. A s t r o p h y s . , 7, 341.  20.  H o l l e n b a c k , D.J., Werner, M.W., 1971, Ap.J., 163, 165.  21.  V e r s c h u u r , G.L.  C.E.  C.E.  C.E.  Carl  1919, Ap.J., 49, 1 and 360.  1962, A p . J . S u p p l . , F, 1. 1968, Ap.J., 151, 919. C,  1969, A p . J . ( L e t t e r s ) , 155, L21.  1969, Ap.J., 157, 123. 1970, Ap.J., 160, 51. 1969,  1971, Ann.Rev.Astron. Ap., 9, 293.  1971, Ap.J., 168, 15. 1963, Ap.J., 137, 694.  1955, Ap.J., 121, 559.  1971, A s t r o n . and  1969, Ap.J., 156, 493. (Pre-print)  1970 ( P r i v a t e  1970, A s t r o n . and  and S a l p e t e r , E.E.  communication  to Hollenback et a l )  -78-  22.  Cheung, A.C., Rank, D.M., Townes, C.H., Thornton, D . J . and Welch, W.J. 1968 Phys. Rev. L e t t e r s , 21, 1701.  23.  Heeschen,  24.  D a v i e s , R.  25.  Radhakrishnan, V.  26.  Locke, J . L . , G a i t , J.A., C o s t a i n , C.H.  27.  D'Odorico, S., S a n c i s i , R., Simonson I I I , S.C. 1969, A s t r o n . A s t r o p h y s . , 1, 131.  28.  R i e g e l , K.W.,  29.  C l a r k , B.G.  30.  C l a r k , B.G., Radhakrishnan, V., W i l s o n , R.W.  31.  V e r s c h u u r , G.L.  32.  Solomon, P.M. and Werner, M.W.  33.  S p i t z e r , L. J r .  34.  F i e l d , G.B.  35.  Van de H u l s t , H . C , M u l l e r , C A . , O o r t , J.H. 1954 B.A.I.N. 12, 117.  36.  W i l l i a m s , D.R.W.  37.  Kraus, J.D.  38.  P e r l e y , R.A. 1970, Master's T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia.  39.  MacRae, D., Westerhout, G. Publications.  D.S.  1955, Ap.J., 121, 565.  1956, M.N.R.A.S., 116, 443. 1960, P.A.S.P., 72, 296.  J e n n i n g s , M.C.  1964, Ap.J. 139, 1066.  1969, Ap.J., 157, 563.  1965, Ap.J., 142, 1398. 1962, Ap.J. 135,  1969, A s t r o p h y s . L e t t e r s , 4, 85. 1971, Ap.J. 165, 41.  1968, D i f f u s e M a t t e r i n Space,  Interscience  1958, P r o c . I.R.E., 46, 240  1970. ( P r i v a t e Communication)  1966, Radio Astronomy, M c G r a w - H i l l .  1956, Lund O b s e r v a t o r y  TABLE I  A m R rt +  a  H  P r o p e r t i e s o f T y p i c a l Dust  n  2n  3  H i  3  0  c  N (Hl)t2 N(Hj  a  Tgas Tgrains Gravity  2  2  - 1 0  Q  M  10 mag ^ 0 # 7 pc ^2000 cm" 5168 cm-3 "-0.12 cm' "0.06 o i ^8 x 10 cm" ~4 x 1 0 cm-3  i>  H c  a  Clouds  ~10°K PE/K6Z  ~10°K *2 ~200 pc m o M®  TABLE I I :  A L i s t of Symbols and  Their  Definitions  0. flfcj  Radius o f d u s t g r a i n (cm) E i n s t e i n p r o b a b i l i t y f o r downwards spontaneous transitions ( s e c ) f>v V i s u a l e x t i n c t i o n , i n magnitudes New g a l a c t i c l a t i t u d e B„0-> .... P l a n c k b l a c k body spectrum f o r i n t e n s i t y of r a d i a t i o n i n thermodynamic e q u i l i b r i u m (ergs cm" Hz" ster" ) &jk E i n s t e i n p r o b a b i l i t y c o e f f i c i e n t f o r induced radiative transitions (erg' cm ) c V e l o c i t y of l i g h t , 2.998 x 1 0 cm sec' df\ D i f f e r e n t i a l element of a r e a (cm ) ch D i f f e r e n t i a l l i n e element a l o n g the l i n e of sight (cm) eta D i f f e r e n t i a l s o l i d angle ( s t e r a d i a n s ) f t . . . . . . . P a r t i t i o n f u n c t i o n f o r atom i n stage of i o n ization ft P a r t i t i o n function for free electron G Subscript r e f e r r i n g to grains <JAJ S t a t i s t i c a l weight of l e v e l ^ , f o r atom i n stage o f i o n i z a t i o n A, k...... P l a n c k c o n s t a n t , 6.625 x 10" e r g sec H N e u t r a l hydrogen atom I S p e c i f i c i n t e n s i t y of r a d i a t i o n a t frequency >v ju E m i s s i v i t y of matter per cm at frequencyv j S u b s c r i p t f o r lower l e v e l i n atomic t r a n s i t i o n M. Boltzmann c o n s t a n t , 1.380 x 10'^ e r g "K" . Also, s u b s c r i p t f o r upper l e v e l i n atomic t r a n s i t i o n New g a l a c t i c l o n g i t u d e 1 Path length (cm) m Mass of e l e c t r o n , 9.12 x lO" gm. Mass of atomic hydrogen, 1.67 x 10" gm. M T o t a l mass M© S o l a r mass, 1.992 x 10 gm. rt' D e n s i t y of p a r t i c l e s per u n i t volume (cm ) "rtjO^).... D e n s i t y of p a r t i c l e s of element X i n stage A . of i o n i z a t i o n , l e v e l ^ of e x c i t a t i o n ( c m ) 7iOW.... P a r t i c l e d e n s i t y of atoms of element X i n stage A o f i o n i z a t i o n (cm" ) n(X) P a r t i c l e d e n s i t y o f X i n a l l stages of i o n i z a t i o n (cm" ) N Number o f p a r t i c l e s i n a column of u n i t c r o s s s e c t i o n a l o n g the l i n e of s i g h t (cm" ) Nj(X/J... . Number of p a r t i c l e s of element X i n stage of i o n i z a t i o n A , l e v e l j. of e x c i t a t i o n i n the l i n e o f s i g h t (cm-*0 1  1  1  1  1  3  10  A  1  v  5  1  z0  53  - 3  3  3  1  ^  E f f i c i e n c y f a c t o r f o r e x t i n c t i o n by  solid  particles  TABLE I I cont'd R. A yd Av  Radius o f a c l o u d (cm) Position vector I n t e g r a t e d v a l u e o f xt*, Atomic a b s o r p t i o n c r o s s - s e c t i o n f o r r a d i a t i o n a t a frequency v (cm ) I n t e g r a t e d v a l u e o f A V , u n c o r r e c t e d f o r induced emission Time ( s e c ) Temperature (°K) Antenna temperature (°K) B r i g h t n e s s temperature (°K) C l o u d temperature (°K) K i n e t i c temperature (°K) Background b r i g h t n e s s temperature (°K) S p i n temperature R a d i a t i o n energy d e n s i t y p e r u n i t f r e q u e n c y i n t e r v a l (ergs cm" H z ) F u l l w i d t h a t h a l f i n t e n s i t y (Km Sec" ) z  t T fl Tb TL \ T T Uj, 0  %  3  AV  L  £ Ji K  v  ^ M v °fi^Avr  p. Kiv)o\?>  t Tit Tv to  _ i  1  R i g h t a s c e n s i o n i n h o u r s , minutes and seconds D e c l i n a t i o n i n degrees, arcminutes and arcseconds Wave v e c t o r ( c m ) _ A b s o r p t i o n c o e f f i c i e n t p e r cm o f r a d i a t i o n o f frequency v Wavelength (cm) F u l l w i d t h a t h a l f i n t e n s i t y (KHz) Frequency ( s e c ) P r o b a b i l i t y of finding p a r t i c l e of v e l o c i t y v i n the i n t e r v a l df-about -v. Mass d e n s i t y (gm cm" ) P r o b a b i l i t y o f f i n d i n g photon o f f r e q u e n c y ^ i n the i n t e r v a l dv about u O p t i c a l depth O p t i c a l depth a t a wavelength o f 21-cm V i s u a l o p t i c a l depth Background o p t i c a l depth. -1  - 1  3  TABLE I I I  A L i s t of Dust Clouds Suitable f o r Observation  OBJECT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40  Si 19Jo)  15 18 18 18 18 18 18 18 20 22 2 3 4 4 4 4 4 5 6 5 5 16 16 4 4 4 5 16 4 16 16 16 15 16 22 3 4 15 16 22  5r00 11 58 02 11 25 31 25 45 23 07 54 27 53 07 54 23 27 55 04 30 33 19 15 27 39 58 26 07 28 59 38 30 14 26 29 50 51 12 40 15 23 35 24 15 01 30 15 18 37 00 15 18 25 00 15 27 47 17 47 51 46 18 51 18 45 00 35 00 40 00 26 00 37 12 30 00 21 30  h  s  -04° 25' -18 11 -04 32 -03 43 -03 34 -03 01 00 50 02 10 43 30 74 58 75 54 31 03 28 18 29 36 24 32 24 23 25 18 26 07 10 32 3 19 -10 14 -24 30 -24 04 26 12 25 29 25 29 7 17 -19 15 28 18 -17 58 -15 18 -14 10 -03 00 -12 40 75 00 31 40 18 20 -07 00 -23 44 74 55  l  z  (195-0)  4f2 12.7 23.5 27.0 27.1 27.3 34.4 35.4 84.7 114.5 127.7 159.7 163.7 171.4 173.3 173.9 174.6 178.9 201.5 203.3 214.5 352.9 353.4 168.1 170.8 174.2 195.1 357.3 168.7 1.9 4.2 4.8 5.5 5.9 114.5 160.3 178.1 358.9  35°.8 -0.5 8.2 3.5 3.5 4.3 -0.8 0.1 -1.0 14.6 14.0 -19.6 -15.5 -10.6 -16.3 -15.9 -13.9 -6.7 0.6 -11.2 -19.9 16.7 16.9 -19.1 -17.5 -14.0 -17.0 19.9 -15.5 16.6 18.1 19.3 36.8 20.4 14.7 -18.4 -20.5 36.9  TABLE IV: A L i s t o f  OBJECT  1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40  52 06 28 19 06 33 34 37 16 45 41 18 27 23 30 15 39 47 15 44 31 00 52 18 41 15 24 51 25 31 02 47 16 35 38 17 16 26 26 14 16 45 48 30 49 03 47 29 52 24 46 11 35 27 41 19 27 13 38 19 31 16 21 51  -4 75 76 31 28 29 24 24 25 26 10 3 -10 -24 -24 26 25 25 7 -19 28 -18 -15 -14 -3 -12 75 31 18 -7 -23 75  Sources  FULL PROFILE DATA  POSITION  15 22 2 3 4 4 4 4 4 5 6 5 5 16 16 4 4 4 5 16 4 16 16 16 15 16 22 3 4 15 16 22  Observed  29 04 00 07 21 28 35 26 20 08 31 19 13 33 07 15 32 31 18 18 21 00 20 12 04 42 07 44 23 04 47 01  DIFFERENCE DATA  xxxxxxxxx  X  xxtxbdxj Ixl  xxxxxx  xxxxixj  XXX|X|X|XjX|X|X| XX XX  XXX X XX X  XXX XXX XXX X  xxxxlx xxxxx  XX PCX X X X X XX  xxxtxM xxjxl xl X Ixl  XX XX XX X  xxxlxlx  XXXX X XXX KXXl XXXX X X X  txpqxxxl  XX X xxxl X  X  xxxxxxxxx XX X  XXXX XX X  X X  X  XXX  XX  Ixx X X  X X X X  XXXX  xxxxx  TABLE V:  REGION  The 21-cm L i n e Standard C a l i b r a t i o n Sources  GALACTIC CO-ORDINATES ^ (l<)SO) Ji (I9SO) 41V42 1V91 T  S6 (not  IAU)  EQUATORIAL CO-ORDINATES  S7 IAU  132?00  -1?00  S8 IAU  207?00  -15?00  S9 IAU  356?00  -4.00  YtsR  C Km/sec.)  x  15 28^58 h  2  h  2 38 m  -2°15'  s  60" 19'  0 -45 t o -55  C  b  °K)  51 ± 4 99  jt  7  s  -l°4l'  7  72 t 5  17 48* 46  -34° 25'  6  85 ± 6  5  1.49*  s  PEAK T  >,  5 0  n  5  TABLE V I :  POSITION  OBJECT h  1 38 30 14 11 24 19 25 18 32 ( 1  /1 f  .  1 5  16 1 7  26 10 35 40  O b s e r v a t i o n a l R e s u l t s o f HI Survey i n Dense Dust Clouds  15 15 16 4 2 4 6 5 5 16 4 4 4 4 22 22 22  m  51 37 47 39 04 01 29 14 14 46 26 28 38 37 27 35 21  s  00 12 17 58 30 30 50 26 26 18 07 59 00 00 55 00 30  o  -04 -07 -17 29 75 26 10 26 26 -14 24 24 25 25 74 75 74  25 00 58 36 54 12 32 07 07 10 32 23 18 29 58 00 55  K^/sec  K m/sec  + 3.0 + 4.6  4.0 2.1  jc |0+' c m ' 9  -5.0 +1.6  COMMENTS  AT  N(HI)  Vt.SR  1  1.6 1.0  °K  4.2 3.0  L 134 VOH = + 3.0, V c o = + !•?, H l  L17-7-8, LI78tJ VOH =  + 9.0 + 4.0  3.3 7.0  -2.8 ±.1.5 +9.2 dc 7.1  3.0 6.8  K"i/set  Von = +3-0 K-n/sec H-l-SXIO^cm- 1  V O H = 5 \ 3 Km/ ec +  S  H+3.5X)o <«M.5' Km/sec l9  VOH = +?-2 Kro/sec  + 7.5  4.0  -12.1 ±- 3.8  13.0  VOH:+4-4  H-l.0x|O'9 -»em  + ?  V O H = - -7 K ^ / s e c * ^-' Km /sec H - 9 . 1 * 1 0 ' @ £ ^ Km/sec,  VOH  + 8.0  2.1  -6.1  1.6  10.5  +  9  V O H =-4.0 Km/sec , L / Z 5 /  J  T21  1. Constant gas t o dust density r a t i o . 2. E x c e s s e s o r d e f i c i t s masked by f l u c t u a t i o n s ,  1. Low energy cosmic r a y dissociation. 2. H y d r o s t a t i c e q u i l i b r i u m  2  1. A genuine " h o l e " . 2. A c o l d a b s o r b i n g c l o u d . 3. Hydrogen i s i n m o l e c u l a r form.  FIGURE 1. The P o s s i b l e Behaviour o f 1~ v e r s u s TV zt  F I G U R E 2. A FRONT  B l o c k D« Qgram  o f t h e Receiv/mg  Equipment  E N D  Feed  Parana p  First  Solid State TilMtfe  Directional  Sf«.«e  ^1*^  X  ffoise TUbe  BACK  E N D P a r a m p Controls  /O.^MHiflmp. BOUDMS Filter*  S*csru( 3t4je Mixer  fl.G.C.  SPECTROMETER  AND  COMPUTER  Fitters ivfeewiti  Oij'.tal Voltmeter  anal I«t««-f*ee  Chart  VT  J*iAAAAA-  poP-9 Computer  Papar-lapeRmdh  Pre-cunp  FIGURE 3.  The  Method o f R e f e r e n c i n g  on  a Dust  Cloud  BRIGHTNESS TEMPERATURE (21. -3.0  o.o  -3.0  CM)  o.o  r-i  a w H ar  a>  >  <  ro OJ  oo ro  o  H«  Ml Ml fl>  (0  3  o ro  & w X  T3  ro o  rt ro a  »—  1  c o  rt C  0J rt o  3 Ml o  O cr ro o  rt  1  T  BRIGHTNESS TEMPERATURE (21. CM)  -6.0  BRIGHTNESS TEMPERATURE (21 -3.0  0.0  r3.0  CM) 0.0  3.0 I  cs a  Tl M  O  § PI  o  H  a-  > <  t oo  ro OQ  ro o  I CO " O  H-  hh Mi (D H  ro o ro  CO  a w x *o ro o rt ro a  rn' . a-  Tl  M  c  o  rt C 0) rt  r' 1  O  P Ml  m rn o —i rn a  o CD  rn x> CD rn o rn rn o rn  X ~D  cz ZD  —\  i—t  o  m  cz  c u rn  <  00  CO 5 £  .o  m o  CO  o o  o H  O cr ro o rt  Co a  1 -3.0  1  0.0  1 -3.0  1—  0.0  BRIGHTNESS TEMPERATURE (21. CM)  BRIGHTNESS  •10.0  J5pPERflTUj?£ ( 2 1  CM) o.o  5.0 l  m -v ro n —i m o o —i c: x—i>  Ul o  ro  a  i  rn TO  ZD CD  PI  ron i—i r~nn rcin rn TO  i—i Q  CO'  CD  O CD  CD  CO TO  rn  5-°  m o  CO  o ID  o o  -<  CO  o •  cn  O '  (O  n -10.0  i  1  -5.0  0.0  ~i 5.0  1  -5.0  0.0  BRIGHTNESS TEMPERATURE (21. CM)  

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