Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The preparation of a telescope for operation at millimeter wavelengths, and observations of carbon monoxide… Mahoney, Michael Joseph 1976

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1976_A1 M33_9.pdf [ 14.03MB ]
Metadata
JSON: 831-1.0084826.json
JSON-LD: 831-1.0084826-ld.json
RDF/XML (Pretty): 831-1.0084826-rdf.xml
RDF/JSON: 831-1.0084826-rdf.json
Turtle: 831-1.0084826-turtle.txt
N-Triples: 831-1.0084826-rdf-ntriples.txt
Original Record: 831-1.0084826-source.json
Full Text
831-1.0084826-fulltext.txt
Citation
831-1.0084826.ris

Full Text

THE PREPARATION OF A TELESCOPE FOR OPERATION AT MILLIMETER WAVELENGTHS, AND OBSERVATIONS OF CARBON MONOXIDE IN THE GALACTIC DUST.CLOUD LYNDS 134 by Michael Joseph Mahoney B.Sc., University of British Columbia, 1968 M.Sc, University of British Columbia, 1971 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE DEPARTMENT OF PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA Apr i l , 1976 (c) ^ M i c h a e l Joseph Mahoney, 1976 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d tha t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f y PHYSICS  The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 wesbrook Place Vancouver, Canada V6T 1W5 Date June 28, 1976 Supervisor: Dr. W. L. H. Shuter Abstract This dissertation is written in two parts. The f i r s t part discuss-es the development of a millimeter wave telescope at the University of British Columbia, and presents details on a very versatile yet cost effect-ive computer control system which has been developed for this f a c i l i t y . Also included is a comprehensive theoretical and practical treatment of the problem of aligning an equatorially mounted telescope. The second part, on the other hand, presents the results of observa-, , . , . . c 12„16„ 13„16„ , 12„18„ . tions of the J = 1 - 0 transitions of C O , C O and C 0 in the dark dust cloud Lynds 134. Analysis indicates that L134 is in fact comprised of four molecular clouds with nominal radial velocities of 0.1, 0.7, 2.7,and 4.0 km s ^ with respect to the local standard of rest, and i t is suggested that these clouds might be the result of fragmentation. The clouds at 0.7 and 2.7 km s are approximately isothermal (with an excitation temperature of ~12 K) and are shown to coincide with known HI absorption features, while the clouds at 2.7 and 4.0 km s ^ coincide with regions of maximum vis i b l e extinction, and are also the most massive of the four clouds. Ac comparison of velocities and line widths for nine molecular species at the position of the 2.7 km s ^ cloud suggests strongly that the atomic hydrogen coexists with the molecules, and does not form a shell as pre-viously thought. It is estimated that in this cloud the H/H^  abundance _3 ratio is ^7.7 x 10 and that the number density of atomic hydrogen is _3 ~11 cm . In the region of maximum vi s i b l e extinction on this cloud, the 13 16 12 18 C 0/ C 0 abundance ratio is 6.5 ± 0.9, but i t appears to be s i g n i f i -cantly larger where the visible extinction is less, perhaps due to excita-tion effects. Finally, an analysis of the spatial dependence of the line i i i widths indicates a collapse or expansion with a radial velocity dependence v oc r ; on the basis of some higher resolution CO results, and previous OH results, i t is suggested, that i t may be possible to distinguish between collapse or expansion, although better sensitivity is needed. i v T a b l e o f C o n t e n t s P a g e A b s t r a c t i i T a b l e o f C o n t e n t s i v L i s t o f T a b l e s v i i i L i s t o f F i g u r e s and I l l u s t r a t i o n s • • • • 1 i x A c k n o w l e d g e m e n t s x I n t r o d u c t i o n 1 P a r t One F r o n t i s p i e c e I: The U . B . C . M i l l i m e t e r Wave T e l e s c o p e 3 I An I n t r o d u c t i o n t o P a r t One 4 A . J u s t i f i c a t i o n f o r B u i l d i n g M i l l i m e t e r Wave T e l e s c o p e s . . . 4 B . A n O v e r v i e w o f t h e U . B . C . M i l l i m e t e r Wave T e l e s c o p e 6 C . A n O u t l i n e f o r P a r t One 8 I I A D e s c r i p t i o n o f t h e U . B . C . M i l l i m e t e r Wave T e l e s c o p e 9 A . The S i t e 9 B . The T e l e s c o p e 10 C . The R e c e i v e r s 12 I I I The Computer C o n t r o l Sys tem 18 A . I n t r o d u c t i o n 18 B. D o c u m e n t a t i o n o f t h e U . B . C . Computer C o n t r o l S y s t e m 19 C . D i s c u s s i o n o f t h e D a t a A c q u i s i t i o n Sys tem 20 D . D i s c u s s i o n o f t h e T e l e s c o p e C o n t r o l S y s t e m 25 IV T e l e s c o p e P o i n t i n g 30 A . I n t r o d u c t i o n 30 B. The T h e o r e t i c a l P o i n t i n g F u n c t i o n s 32 C . M e a s u r i n g t h e M i s a l i g n m e n t P a r a m e t e r s 35 1 . S l e w i n g e x p e r i m e n t s 35 2 . T r a c k i n g e x p e r i m e n t s 36 3 . T r a n s i t e x p e r i m e n t s 39 V P a g e D . The Measuremen t R e s u l t s 40 E . P r a c t i c a l M i s a l i g n m e n t C o r r e c t i o n s 42 V A s t r o n o m i c a l R e s u l t s 44 A . S o l a r O b s e r v a t i o n s 44 B. S p e c t r a l L i n e O b s e r v a t i o n s 45 C . C o n c l u d i n g Remarks 49 v i Page P a r t Two F r o n t i s p i e c e I I : The D a r k D u s t C l o u d , L y n d s 134 52 V I An I n t r o d u c t i o n t o P a r t Two 53 A . The C l a s s i f i c a t i o n o f D u s t C l o u d s 53 B . The F o r m a t i o n o f D u s t C l o u d s . . 55 C . O b s e r v a t i o n s o f D u s t C l o u d s 58 1 . S u r v e y s o f D u s t C l o u d s 58 2 . Maps o f D u s t C l o u d s 62 D. Why Map L y n d s 134? • 64 V I I D a t a A c q u i s i t i o n 68 A . The S i t e 68 B . The R e c e i v e r 69 C . The O b s e r v a t i o n s 71 V I I I D a t a R e d u c t i o n and A n a l y s i s 78 A . C a l i b r a t i o n 78 1 . The P r o b l e m s 78 2 . A R e v i e w o f What i s M e a s u r e d 79 3 . The C a l i b r a t i o n Me thod A d o p t e d 84 B. D a t a R e d u c t i o n 89 1 . The B a r e R e s u l t s f o r L 1 3 4 89 2 . The R e f e r e n c e S o u r c e R e s u l t s 91 C . D a t a A n a l y s i s • • • • 96 1 . The D e r i v a t i o n o f Co lumn D e n s i t i e s 96 2 . R a d i a t i o n T e m p e r a t u r e C o n t o u r s a t a F i x e d V e l o c i t y 100 3 . O t h e r A n a l y s i s 103 IX D i s c u s s i o n o f R e s u l t s and Summary 104 A . The S t r u c t u r e o f L134 104 B . The D i s t a n c e t o L134 109 C . The S i z e , D e n s i t y and Mass o f L 1 3 4 110 D . The C o m p o s i t i o n o f L 1 3 4 113 1 . C a r b o n M o n o x i d e O b s e r v a t i o n s 113 2 . HI O b s e r v a t i o n s 115 3 . R e s u l t s o f O t h e r O b s e r v a t i o n s 115 E . The D y n a m i c s and S t a b i l i t y o f L134 120 1 . P r e s s u r e E q u i l i b r i u m 120 2 . I n t e r p r e t a t i o n o f L i n e Shapes 122 3 . O r b i t a l M o t i o n 1 3 2 F . Summary and C o n c l u d i n g Remarks 135 v i i Page Bibliography 138 Appendices 142 A. The User's Manual For the U.B.C. Millimeter Wave Radio Telescope Computer Control System 143 B. An Internal Technical Report on Telescope Pointing 188 C. CO, CO and C O J = 1-0 Observations in L134 251 12 1 "3 18 D. CO, CO and C O T * Contours at Constant Velocity in L134 269 v i i i L i s t o f T a b l e s Number Page I U . B . C . R e c e i v e r S p e c i f i c a t i o n s 14 I I Summary o f R e s u l t s f o r M i s a l i g n m e n t P a r a m e t e r s 41 I I I P o s i t i v e M o l e c u l a r L i n e R e s u l t s n e a r L134 66 IV A Summary o f L 1 3 4 O b s e r v i n g P rog ram . 73 V O b s e r v a t i o n a l R e s u l t s f o r DR21 94 T I Summary o f L 1 3 4 C l o u d P a r a m e t e r s .' 112 V I I D e t a i l e d O b s e r v a t i o n a l R e s u l t s a t C e n t e r o f L134 116 i x L i s t o f F i g u r e s and I l l u s t r a t i o n s Number Page 1 A S c h e m a t i c D i a g r a m o f t h e U . B . C . CO R e c e i v e r 15 2 A S c h e m a t i c D i a g r a m o f t h e U . B . C . X mm T e l e s c o p e Computer C o n t r o l Sys tem 21 3 A S c h e m a t i c D i a g r a m o f t h e U . B . C . X mm T e l e s c o p e D r i v e C o n t r o l 26 4 E m p i r i c a l S o l a r R a d i o P o i n t i n g C u r v e s 38 5 The F i r s t L i n e D e t e c t e d a t U . B . C 46 6 N e g a t i v e R e s u l t s o f S i S L i n e S e a r c h 47 7 CO i n M17 and O r i o n 48 8 The L134 Beam P o s i t i o n s 72 9 A C o m b i n a t i o n P l o t o f L134 CO O b s e r v a t i o n s 92 13 18 10 The L 1 3 4 CO and C 0 Co lumn D e n s i t i e s 101 11 C o n s t a n t V e l o c i t y T ^ * C o n t o u r s o f t h e F o u r L134 C l o u d s 105 1 o 13 i R 12 The A v e r a g e E m i s s i o n o f CO, CO and C 0 Over t h e 2 . 7 k m / s e c C l o u d i n L 1 3 4 123 13 1 3 C 0 V e l o c i t y F u l l W i d t h i n Wing 126 13 14 CO Maximum R a d i a t i o n T e m p e r a t u r e 127 15 C o m p a r i s o n o f 250 KHz and 100 KHz P r o f i l e s 130 12 13 16 Examp le o f CO and CO 100 KHz D a t a Showing Two Components i n 2 . 7 k m / s e c C l o u d i n L134 131 X Acknow ledgemen ts A f t e r e i g h t y e a r s o f g r a d u a t e s c h o o l i t i s d i f f i c u l t t o know where t o s t a r t t h a n k i n g p e o p l e f o r t h e s u p p o r t t h e y h a v e l e n t me i n t h e c o u r s e o f e v e n t s . F rom a c a d e m i c q u a r t e r s , I must f i r s t t h a n k my t h e s i s s u p e r v i s o r D r . W . L . H . S h u t e r ; w i t h o u t h i s a v a i l a b i l i t y , o p t i m i s m and s u g g e s t i o n s , t h e e i g h t m i g h t h a v e b e e n many m o r e . And I must a l s o t h a n k my o t h e r c o l l e a g u e s i n t h e m i l l i m e t e r a s t r o n o m y g r o u p : D r . W . H . M c C u t c h e o n , D r . P . C . G r e g o r y and M r . C . C h a n ; w i t h o u t t h e i r comb ined e f f o r t s and i n s i g h t s I 'm s u r e m a t t e r s w o u l d be much l e s s f a v o u r a b l e t h a n t h e y a r e t o d a y . M r . A l e x Szabo a l s o needs r e c o g n i t i o n f o r h i s v a l u a b l e a s s i s t a n c e i n a l i g n i n g t h e m i l l i m e t e r wave t e l e s c o p e . I n c o n n e c t i o n w i t h t h e L134 o b s e r v a t i o n s , I must f i r s t t h a n k my c o l l e a g u e s D r . B i l l S h u t e r and D r . B i l l M c C u t c h e o n f o r t h e i r a s s i s t a n c e i n m a k i n g t h e o b s e r v a t i o n s and i n t e r p r e t i n g t h e r e s u l t s . F rom t h e s t a f f a t A e r o s p a c e C o r p o r a t i o n , I w i s h t o t h a n k D r . Eugene E p s t e i n f o r a r r a n g -i n g t h e o b s e r v a t i o n s , D r . B i l l W i l s o n f o r p r o v i d i n g s u c h a w o n d e r f u l r e c e i v e r , and D r . Bob D i c k m a n f o r h i s i l l u m i n a t i n g d i s c u s s i o n s r e g a r d i n g L 1 3 4 . M s . J u l i e W h i t e and M r . M i k e W r i g h t must a l s o be t h a n k e d f o r t h e i r a s s i s t a n c e w i t h t h e o b s e r v a t i o n s , o r d e r i n g H a n k ' s p i z z a s and o r -g a n i z i n g t h e L A d i n n e r c i r c u i t . N e x t I must t h a n k D r . J i l l Knapp f o r p r o v i d i n g u n p u b l i s h e d 100 KHz o b s e r v a t i o n s o f L 1 3 4 , w h i c h w e r e o b t a i n e d a t K i t t P e a k i n c o l l a -b o r a t i o n w i t h D r s . Tom K u i p e r and S t e v e K n a p p . The members o f my P h . D . C o m m i t t e e , P r o f e s s o r s M . L . H . P r y c e , F .W. D a l b y and R . A . N o d w e l l , must be t h a n k e d f o r t h e i r u n d e r s t a n d i n g over the years, since much of my time was spent on engineering rather than s c i e n t i f i c matters. And they must also be thanked for reading this thesis and pointing out many errors; those which s t i l l exist, including grammatical aberrations, are entirely my responsibility. A large number of friends not directly connected with my thesis work must also be thanked for the various roles they have played. Most notable are the Voyageurs — Balls, Baby Jake, Horse, Jake III, Tits, Dan the Man, Wild Wilf, Hamish and others — with whom I have paddled many of the rivers of Canada, and perhaps experienced some of my fondest memories. And I must thank Dan and Sandy for the many times they have rescued me from the confines of my office and taken me sailing off into the sunset ( l i t e r a l l y , not figuratively), and for the understanding they have displayed as I slogged the long hours and often neglected my friends. I thank my friends Per and Bob with whom I have sat through many meals. I thank Per for his wit and for showing the courage to do what his heart f e l t — and for sharing that with me by taking me to the mountains. I thank Bob for postponing his own work to argue about something to do with physics and often my thesis — I hope he finishes soon. I thank my old friend Rick for a l l he has done over the years — from organizing canoe trips to finding me a job. I thank Jude for teaching me about wild things, and about the North, and for having a strong commitment to understanding and dreams. x i i Finally I must thank my parents for their understanding and support over the years, my sister Karen for putting up with me for the past four months and for "womanning" the Xerox machine, my friend John for doing some of the drawings and Darlene for typing the thing. These acknowledgements could easily go on — instead, I collectively thank the many friends that I have omitted for their help. And I thank the National Research Council of Canada for their support as well as the University of British Columbia for theirs. x i i i Dedication To my parents INTRODUCTION As suggested by i t s t i t l e , this thesis may be considered to deal with two separate, but integrally related, topics; consequently, i t w i l l be divided into two parts. The f i r s t part, The Preparation of  a Telescope for Operation at Millimeter Wavelengths, w i l l be concerned with my participation i n the development at the University of Br i t i s h Columbia of a millimeter wavelength radio telescope f a c i l i t y . As might he anticipated from the t i t l e , this work was necessarily of an engineer-ing nature, although s c i e n t i f i c a l l y interesting results have come out of i t . The second part of this thesis, Observations of Carbon Mono- oxide in the Galactic Dust Cloud Lynds 134, w i l l be concerned with observations of the J = 1-0 rotational transition from three isotopic species of carbon monoxide in the dust cloud L134 (Lynds, 1962). In contrast to the f i r s t part of the dissertation, this section w i l l ad-dress essentially s c i e n t i f i c matters in the hope of gaining a better understanding of the structure, composition and thermodynamics of dust clouds within our own and other galaxies. A more detailed Introduction for both of these topics w i l l be found at the beginning of each Part. 2. Part One The Preparation of a Telescope for Operation at Millimeter Wavelengths 4. C h a p t e r I A n I n t r o d u c t i o n t o P a r t One A . J u s t i f i c a t i o n f o r B u i l d i n g M i l l i m e t e r Wave T e l e s c o p e s One does n o t h a v e t o l o o k v e r y f a r t o a p p r e c i a t e t h e r e v o l u -t i o n ou r u n d e r s t a n d i n g o f t h e i n t e r s t e l l a r medium h a s u n d e r g o n e s i n c e t h e i n t r o d u c t i o n o f t e l e s c o p e s c a p a b l e o f o b s e r v a t i o n s a t m i l l i m e t e r w a v e l e n g t h s . P r i o r t o t h e i r i n t r o d u c t i o n i n t h e l a t e 1 9 6 0 ' s , r a d i o f r e q u e n c y s p e c t r o s c o p y o f e x t r a - t e r r e s t i a l r a d i a t i o n had b e e n l i m i t e d t o o b s e r v a t i o n s o f t h e 21 cm l i n e o f a t o m i c h y d r o g e n , w h i c h had b e e n d e t e c t e d i n 1951 (Ewen and P u r c e l l , 1 9 5 1 ) , and o b s e r v a t i o n s o f t h e 18 cm t r a n s i t i o n s o f t h e h y d r o x y l r a d i c a l , w h i c h had b e e n d e t e c t e d i n 1963 CWeinreb e t a l . , 1 9 6 3 ) . B e f o r e t h i s t i m e , t h e o n l y a v a i l a b l e spec t ro-r s c o p i c means f o r s t u d y i n g t h e i n t e r s t e l l a r medium had i n v o l v e d o p t i c a l o b s e r v a t i o n s o f a b s o r p t i o n l i n e s due t o N a , C a + , C H , C H + and C N , and t h e s e w e r e n e c e s s a r i l y r e s t r i c t e d t o n e a r b y r e g i o n s o f t h e g a l a x y . W i t h t h e a d v e n t o f m i l l i m e t e r wave t e l e s c o p e s , a l l t h i s h a s c h a n g e d . I n l a t e 1 9 6 8 , t h e B e r k e l e y g roup d e t e c t e d e m i s s i o n l i n e s f r o m b o t h ammonia and w a t e r (Cheung e t a l . , 1 9 6 8 a , b ) , and by 1970 o t h e r g r o u p s had d e t e c t e d l i n e r a d i a t i o n f r o m i n t e r s t e l l a r H 2 C 0 , CO, C N , HCN, H C 3 N , C H 3 0 H and CHOOH, as w e l l as an u n i d e n t i f i e d f e a t u r e dubbed X o g e n . I n a d d i t i o n , r o c k e t u l t r a v i o l e t o b s e r v a t i o n s had s u c c e e d e d f o r t h e f i r s t t i m e i n d e t e c t i n g m o l e c u l a r h y d r o g e n ( C a r r u t h e r s , 1 9 7 0 ) , w h i c h i s t h o u g h t t o be t h e mos t abundan t c o n s t i t u e n t o f i n t e r s t e l l a r d u s t c l o u d s . S i n c e t h a t t i m e , t h e l i t a n y o f m o l e c u l a r l i n e d e t e c t i o n s h a s g rown i m p r e s s i v e l y , w i t h t h e m a j o r i t y o f t h e s e b e i n g made a t m i l l i m e t e r w a v e l e n g t h s . The 5. c u r r e n t l i s t now i n c l u d e s a t l e a s t 36 s p e c i e s o f m o l e c u l e s - e x c l u d i n g i s o t o p i c s p e c i e s - and w e l l o v e r one h u n d r e d d i f f e r e n t t r a n s i t i o n s . As r e c e i v e r s e n s i t i v i t i e s i m p r o v e , t h i s l i s t w i l l u n d o u b t a b l y g row l o n g e r . M i l l i m e t e r w a v e l e n g t h t e l e s c o p e s a r e i d e a l l y s u i t e d f o r s t u d y -i n g the i n t e r s t e l l a r medium f o r a number o f r e a s o n s . The most o b v i o u s o f t h e s e i s r e l a t e d t o t h e f a c t t h a t t h e c o n d e n s a t i o n s o r c l o u d s w h e r e m o l e c u l e s a r e t h o u g h t t o f o r m a r e c h a r a c t e r i z e d b y a gas k i n e t i c t e m -p e r a t u r e o f | K ~ 1 0 K. I n t h e a b s e n c e o f o t h e r e n e r g y s o u r c e s t h e n , o n l y t r a n s i t i o n s f r o m e n e r g y s t a t e s w h i c h c a n be p o p u l a t e d a t s u c h a l o w t e m p e r a t u r e w i l l be o b s e r v a b l e , and t h i s i m p l i e s t r a n s i t i o n f r e -q u e n c i e s V < yfeT^/&~'10^ s e c ^ o r w a v e l e n g t h s "X 1 mm. F o r t u n a t e l y t h e e a r t h . ' s a tmosphe re i s r e l a t i v e l y t r a n s p a r e n t a t t h e s e f r e q u e n c i e s , h a v i n g o n l y a few a b s o r p t i o n l i n e s due t o w a t e r v a p o u r and m o l e c u l a r o x y g e n . M i l l i m e t e r t e l e s c o p e s a l s o h a v e a n o t h e r c h a r a c t e r i s t i c w h i c h makes them i d e a l f o r s t u d y i n g t h e i n t e r s t e l l a r med ium, and t h a t i s t h e i r a n g u l a r r e s o l u t i o n . Compared t o t h e t e l e s c o p e s u s e d e a r l i e r t o s t u d y H and O H , a modes t 5 m e t e r t e l e s c o p e h a s n e a r l y a n o r d e r o f m a g n i t u d e B e t t e r r e s o l u t i o n , s i n c e a t "X - 3 mm i t s r e s o l u t i o n w o u l d be 3 a r c m i n u t e s . 6. B. A n O v e r v i e w o f t h e U . B . C . M i l l i m e t e r Wave T e l e s c o p e Funds t o b u i l d a m i l l i m e t e r wave r a d i o t e l e s c o p e a t t h e U n i -v e r s i t y o f B r i t i s h C o l u m b i a w e r e a p p l i e d f o r i n b o t h 1967 and 1 9 6 8 . I t was n o t u n t i l m i d - 1 9 7 0 however, t h a t money t o b u i l d a t e l e s c o p e was r e c e i v e d ; t h i s was p a r t o f a N e g o t i a t e d Deve lopmen t G r a n t awarded by t h e N a t i o n a l R e s e a r c h C o u n c i l o f C a n a d a t o p romo te t h e d e v e l o p m e n t o f A s t r o n o m y and L a b o r a t o r y A s t r o p h y s i c s a t U . B . C . I t was a l s o i n t e n d e d t h a t t h e U . B . C . i n s t r u m e n t w o u l d make a v a i l a b l e t o C a n a d i a n a s t r o n o m e r s a r e g i o n o f t h e e l e c t r o m a g n e t i c s p e c t r u m n o t o b s e r v a b l e w i t h o t h e r t e l e s c o p e s i n t h e c o u n t r y . By t h e t i m e t h e s e f u n d s w e r e r e c e i v e d i t s h o u l d be c l e a r f r om t h e p r e v i o u s d i s c u s s i o n t h a t m i l l i m e t e r w a v e l e n g t h a s t r o n o m y had grown a p p r e c i a b l y a n d , l i k e any new f i e l d , w o u l d i n v o l v e a l o t o f s t a t e -o f - t h e - a r t t e c h n o l o g y . N a t u r a l l y t o do c o m p e t i t i v e s c i e n c e , i t i s e s -s e n t i a l t o keep up t o t h i s t e c h n o l o g y , w h i c h , i n t h e c a s e o f m i l l i m e t e r w a v e l e n g t h w o r k , means h a v i n g t h e b e s t r e c e i v e r s . T h i s h a s b e e n a s e r i o u s h a n d i c a p t o t h e U . B . C . e f f o r t . E x a c t l y how t h i s p r o b l e m i s b e i n g r e s o l v e d w i l l be d i s c u s s e d i n more d e t a i l l a t e r o n . The d e v e l o p m e n t o f any f a c i l i t y i s s e l d o m t h e w o r k o f a s i n g l e p e r s o n and i t w o u l d be l u d i c r o u s t o t r y t o d e s c r i b e i t a s s u c h . The p e o p l e who h a v e b e e n i n v o l v e d i n t h e U . B . C . p r o j e c t f r o m i t s b e g i n n i n g i n c l u d e D r . W . L . H . S h u t e r , who h a s b e e n i n c h a r g e o f t h e w o r k and i s a l s o my t h e s i s s u p e r v i s o r , D r . W . H . M c C u t c h e o n and m y s e l f . More r e c e n t l y D r . P . C . G r e g o r y h a s j o i n e d o u r g r o u p , and M r . C P . Chan h a s w o r k e d w i t h us f o r t h e p a s t f o u r y e a r s a s an e n g i n e e r . I n a d d i t i o n , M r . P . J o e n s e n and M r . G . A n d e r s o n h a v e a l s o c o n t r i b u t e d a t d i f f e r e n t s t a g e s . 7. If I were to describe in this part of the thesis only the work in which I have contributed directly, i t would lack both unity and perspective. I w i l l therefore point out the major areas i n which I have contributed and acknowledge the work of the others, which I take the liberty to describe. During the f i r s t two years of the project, those involved did whatever tasks needed doing, as specific responsibilities were not clearly defined. During this period my major contributions were i n assembling the 112 channel f i l t e r spectrometer and packaging a vidicon tube which was subsequently used in determining the telescope pointing. During the past two to three years, Shuter, McCutcheon and Chan have concentrated their efforts on developing the various receivers, both front and back ends, while I have been individually responsible for developing the computer control system. During this time I also worked on the theoretical interpretation of solar pointing observations. This is now in quite a refined state and w i l l be discussed in Chapter IV. 8. C. An Outline for Part One The following chapter w i l l present a description of the U.B.C. telescope as a whole, including the various receivers and. the develop-ment they have undergone. In line with my major contributions, Chapter III w i l l present a description of the computer control system which has been developed, while Chapter IV w i l l discuss the problem of telescope pointing. In the f i n a l chapter of this Part, a summary of results which have been obtained with the U.B.C. telescope w i l l be presented along with, prospects for the future. 9. Chapter II A Description of the U.B.C. Millimeter Wave Telescope A. The Site A description of the U.B.C. telescope has already been given by Shuter and McCutcheon (1975). As a result, this Chapter w i l l dupli-cate their discussion only where i t i s f e l t necessary in order to make a meaningful presentation. The telescope i s located on the South end of the University of British Columbia campus, at an elevation of approximately 50 meters above sea level. Its geodetic co-ordinates are 123 13' 56" West and 49° 15' 11" North. Although other sites had been considered, the logistics that would have been involved i n trying to develop an instru-ment at any distance from the campus made them untenable. In fact, the campus site has worked very well. Weather conditions in Vancouver allow at least 3000 hours/year of useful observing time — more than local personnel would be able to use — and the zenith absorption i s not un-reasonable, varying on clear days from £ 0.25 dB at 31.4 GHz to 2.3 dB at 115 GHz. 10. B. The T e l e s c o p e The f r o n t i s p i e c e t o t h i s P a r t shows a p h o t o g r a p h o f t h e U . B . C . t e l e s c o p e a s i t a p p e a r e d i n J u n e 1 9 7 5 . The m a i n r e f l e c t o r i s a p a r a b o -l o i d o f d i a m e t e r 4 . 5 7 m e t e r s , w h i l e t h e C a s s e g r a i n s u b r e f l e c t o r i s a h y p e r b o l o i d o f d i a m e t e r 0 . 4 5 7 m e t e r s ; t h e i r s u r f a c e t o l e r a n c e s a r e 0 . 1 2 5 mm RMS and 0 . 0 2 5 mm RMS r e s p e c t i v e l y . The f o r m e r f i g u r e c o r r e s -ponds t o a ^ / 1 6 e r r o r a t 2 mm and was a c h i e v e d by h a n d - g r i n d i n g t h e s u r f a c e a f t e r i t had b e e n m a c h i n e d i n a v e r t i c a l b o r i n g m i l l . P r i o r t o t h i s , t h e r e f l e c t o r had b e e n s h a p e d f r o m a s i n g l e s h e e t o f 1 .27 cm a luminum b y s p i n n i n g i t o v e r a wooden p l u g and t h e n s t r e s s r e l i e v i n g i t w i t h t h e b a c k i n g s t r u c t u r e a t t a c h e d . The o v e r a l l w e i g h t o f t h e r e -f l e c t o r s and b a c k i n g s t r u c t u r e i s a p p r o x i m a t e l y 1400 kgm, and b o t h m i r r o r s h a v e b e e n c o a t e d w i t h a d u l l w h i t e a c r y l i c p a i n t t o e n s u r e t e m p e r a t u r e s t a b i l i z a t i o n o f t h e i r s u r f a c e s a g a i n s t s o l a r h e a t i n g . The u s e o f a C a s s e g r a i n f e e d w i t h t h i s s h o r t - f o c u s p a r a b o -l o i d ( f / D = 0 . 3 3 ) h a s t h r e e a d v a n t a g e s : i t i m p r o v e s t h e i m a g e - f o r m i n g c a p a b i l i t i e s o v e r an e q u i v a l e n t p r i m e - f o c u s i n s t r u m e n t by r e d u c i n g c o m a , i t makes t h e f r o n t - e n d r e c e i v e r more e a s i l y a c c e s s i b l e ( a t t h e same t i m e r e d u c i n g t h e m e c h a n i c a l p e r f o r m a n c e r e q u i r e d o f t h e s u b r e f l e c t o r s u p p o r t s t r u c t u r e ) , and e x c e p t a t l a r g e z e n i t h d i s t a n c e s , i t r e p l a c e s s t r a y r a d i a t i o n p i c k - u p due t o s p i l l o v e r f r o m t h e g round by t h e r e l a t i v e l y c o o l e r t h e r m a l r a d i a t i o n f r o m t h e s k y . T h i s w i l l o f c o u r s e become i n -c r e a s i n g l y i m p o r t a n t a s r e c e i v e r s e n s i t i v i t i e s a r e i m p r o v e d . The m a i n r e f l e c t o r i t s e l f i s e q u a t o r i a l l y mounted on i t s p e d e s t a l and i s b a l a n c e d by c o u n t e r w e i g h t s a t t a c h e d t o i t s b a c k i n g s t r u c -t u r e . The arms h o l d i n g t h e s e c o u n t e r w e i g h t s h a v e b e e n e m p i r i c a l l y d e -s i g n e d t o a l l o w t e l e s c o p e t r a c k i n g t o w i t h i n ± 0 . 0 1 d e g r e e s i n w i n d g u s t s up t o 36 k m / h o u r . F i n a l l y , t h e f o c u s b o x i s t h e r m a l l y i n s u l a t e d and i t s t e m p e r a -t u r e i s c o n t r o l l e d by a t h e r m o - e l e c t r i c d e v i c e . C o m m u n i c a t i o n b e t w e e n t h e f o c u s b o x i n s t r u m e n t a t i o n and t h e m a i n c o n t r o l room i s p r o v i d e d by c a b l e s w h i c h r u n down f r o m a b u l k h e a d b e h i n d t h e f o c u s b o x i n t o two l a r g e w e a t h e r p r o o f p l a s t i c t u b e s w h i c h r u n a p p r o x i m a t e l y f i f t y f e e t t o t h e c o n t r o l r o o m . The t o t a l c a b l e r u n i s abou t one h u n d r e d f e e t . D e t a i l s on t h e t e l e s c o p e d r i v e s y s t e m c a n be f o u n d i n C h a p t e r I I I , w h i l e C h a p t e r IV w i l l d i s c u s s t h e p r o b l e m o f t e l e s c o p e a l i g n m e n t . C. The Receivers The development of receivers has been essentially the work of Shuter, McCutcheon and Chan, although in the earlier stages I helped with the front end packaging, worked on the load switching system and also assembled the spectrometer. Before discussing the current U.B.C. receivers, i t may be useful to indicate briefly some of the evolution they have undergone. The high priority goal for the U.B.C. millimeter radio astro-nomy group had been to develop a 115 GHz receiver for doing CO line work. The receivers used at these high frequencies have, u n t i l recently, normally employed n-type GaAs Schottky barrier diodes as their mixing e l e m e n t t h e noise performance of these devices has improved remarkably over the past few years. As a result i t i s imperative, i f competitive work is to be done, that the best available devices be used. In the future, this requirement w i l l be partially relaxed by the fact that as noise performance improves thermal atmospheric noise w i l l become the limiting factor. The original U.B.C. receivers used the best commercially a v a i l -able diodes in a single balanced mixer configuration. Although balanced mixers require more diodes than single-ended mixers and therefore intro-duce additional diode matching d i f f i c u l t i e s , this was necessary i n order 1. These devices make use of the non-linearity of the contact potential for a planar conductor (usually gold) on a semiconductor (GaAs) to mix an observed RF signal with a local oscillator (LO) signal which is nearby in frequency. The difference frequency, or IF signal, pro-duced is subsequently amplified, detected and integrated, and in the case of spectral line observations the LO is also phase-locked so that photons arriving at a particular frequency w i l l always correspond to the same frequency in the IF. t o c a n c e l LO n o i s e , s i n c e t h e e a r l y U . B . C . I F was a t 60 M H z . F a r f r o m a d e q u a t e p e r f o r m a n c e was a c h i e v e d , h o w e v e r , s o t h a t e v e n t u a l l y t h e I F was i n c r e a s e d t o t h e c u r r e n t 340 M H z , a l t h o u g h 1 GHz had a l s o b e e n t r i e d S t i l l r e s u l t s w e r e i n a d e q u a t e : ma t ched d i o d e s w e r e d i f f i c u l t t o o b t a i n , t h e h y b r i d s f o l l o w i n g t h e m i x e r w e r e t o o l o s s y , and mos t a n n o y i n g o f a l l , l o n g d e l a y s w o u l d r e s u l t wheneve r d i o d e s had t o be s e n t away t o b e r e p a i r e d . E v e n t u a l l y we t u r n e d t o s i n g l e - e n d e d m i x e r s w i t h a 340 MHz I F , and a b i t l a t e r , b e g a n d e v e l o p i n g f a c i l i t i e s f o r r e p a i r i n g d i o d e s . A l t h o u g h m a t t e r s i m p r o v e d , i t was n o t w i t h o u t a g r e a t d e a l o f e f f o r t . We s t i l l howeve r a r e u n a b l e t o a c h i e v e r e s u l t s w i t h o u r 7 2 - 1 1 5 GHz r e c e i v e r s t h a t w o u l d a l l o w us t o be c o m p e t i t i v e w i t h o t h e r o b s e r v a t o r i e s The f i n a l c h a p t e r o f t h i s P a r t w i l l d e s c r i b e what s t e p s a r e b e i n g t a k e n t o change t h i s , as w e l l as t he r e s u l t s w h i c h h a v e b e e n a c h i e v e d . The c u r r e n t s t a t u s o f t h e U . B . C . r e c e i v e r s i s shown i n T a b l e I. I t w i l l be n o t e d t h a t w i t h t h e e x c e p t i o n o f t h e 2 8 - 3 5 GHz r e c e i v e r , t h e r e c e i v e r s may o n l y be l o a d o r p o s i t i o n s w i t c h e d . L o a d s w i t c h i n g i s a c h i e v e d b y r o t a t i n g a n amb ien t t e m p e r a t u r e a b s o r b e r i n f r o n t o f t h e f e e d h o r n a t a 52 s e c ^ r a t e , w h i l e p o s i t i o n s w i t c h i n g r e q u i r e s t h e e n t i r e a n t e n n a t o be moved s i n c e movement o f t h e s u b r e f l e c t o r i s n o t p o s s i b l e . I n t h e c a s e o f t h e 2 8 - 3 5 GHz r e c e i v e r , beam s w i t c h i n g u s i n g a f e r r i t e c i r c u l a t o r t o s w i t c h b e t w e e n two f e e d h o r n s i s a l s o a v a i l a b l e . None o f t h e r e c e i v e r s may be f r e q u e n c y s w i t c h e d . F i g u r e 1 shows a s c h e m a t i c d i a g r a m o f a t y p i c a l U . B . C . l i n e r e c e i v e r — i n t h i s c a s e t h e 115 GHz CO r e c e i v e r . I t w i l l b e n o t e d t h a t p h a s e - l o c k i n g i s a c h i e v e d i n two s t a g e s , a l t h o u g h i n t h e c a s e o f t h e 14. TaBle I: U.B.C. Receiver Specifications Frequency Range Diode Type Local Oscillator Switching T s y s ( S S B) 28 72 84.5 108.5 35 78 90.5 116.5 Si GaAS or Si GaAs GaAs BWO Klystron Klystron Klystron L, B, P L, P L, P L, P 1400 3900 7600 7600 Notes to Table: a. L = load switching B = beam switching P = position switching Multiplex to Signal Avg. Control to Signal Averag 28-35 GHz receiver only the lower stage i s used. The low frequency lock is obtained by phase locking a 26-40 GHz backward wave oscillator (BWO). This i s done by sampling some of the BWO's power through a 10 dB directional coupler and mixing i t with a high harmonic of a tunable reference crystal near 5 MHz. This mixing produces a 25 MHz IF which i s then phase detected against the f i f t h harmonic of the reference crystal to produce an error voltage for tuning the BWO helix. The high frequency lock i s then achieved by phase locking a klystron to the second, third or fourth harmonic of the phase locked BWO; the harmonic depends on the receiver. In the case of the 115 GHz receiver, the fourth harmonic of the BWO is generated i n a harmonic mixer and then mixed with a small amount of klystron power sampled by a directional coupler. This mixing produces a 60 MHz IF signal which is phase detected against a 60 MHz reference crystal to provide an error voltage for tuning the klystron reflector. The LO signal from the phase locked klystron is then coupled into the feed horn waveguide using an injection cavity and mixed in a single ended mixer. After several stages of preamplification, the mixer IF output then passes through a bandpass f i l t e r centered at 340 MHz C±65 MHz). This i n turn i s followed by a variable attenuator, several more preamplifiers (27 dB gain each), and then a voltage controlled attenuator (VCA), which in the automatic gain control (AGC) mode, con-trols the IF level to the spectrometer. The VCA i s followed by more amplification stages, and then the IF signal i s s p l i t two ways. The f i r s t path is through a coupling transformer to a wide-band detector which is either DC coupled to a total power amplifier and c h a r t r e c o r d e r , o r AC c o u p l e d t o a s w i t c h e d power a m p l i f i e r . I n t h e l a t t e r c a s e , t h e s i g n a l i s s y n c h r o n o u s l y d e t e c t e d a g a i n s t a r e f e r e n c e wave fo rm p r o d u c e d by t h e s w i t c h e d l o a d i n f r o n t o f t h e f e e d and t h e n f i n a l l y i s d i s p l a y e d on a c h a r t r e c o r d e r . The s e c o n d p a t h f o r t h e I F s i g n a l i s t o t h e 112 c h a n n e l f i l t e r s p e c t r o m e t e r . The l a t t e r c o n s i s t s o f 16 p r i n t e d c i r c u i t b o a r d s , e a c h c o n t a i n i n g s e v e n c h a n n e l s c e n t e r e d a t 19 MHz and 1 MHz w i d e . E a c h o f t h e s e s e v e n - c h a n n e l s r e c e i v e s a n I F s i g n a l 16 MHz w i d e . T h e s e a r e d e -r i v e d by m i x i n g t h e 340 MHz f i r s t I F s i g n a l w i t h s e v e n r e f e r e n c e o s c i l l a -t o r s w h i c h e x t r a c t s e v e n c o n t i g u o u s 16 MHz w i d e s e c t i o n s o f t h e p a s s b a n d . E a c h o f t h e 16 p r i n t e d c i r c u i t b o a r d s t h e n h a s a f i n a l o s c i l l a t o r w h i c h e x t r a c t s a d i f f e r e n t 1 MHz p o r t i o n o f t h e s e v e n 16 MHz w i d e I F s i g n a l s p r e s e n t e d t o i t . Thus 7 x 16 = 1 1 2 c h a n n e l s a r e f o r m e d , e a c h w i t h i t s own d e t e c t o r , a m p l i f i e r , f u l l - w a v e p h a s e d e t e c t o r and i n t e -g r a t o r . E v e r y 10 s e c o n d s t h e o u t p u t o f t h e s e i n t e g r a t o r s i s m u l t i -p l e x e d i n t o a s i g n a l a v e r a g e r f o r l o n g e r t e r m i n t e g r a t i o n . I n a d d i t i o n , e v e r y 10 s e c o n d s t h e p h a s e o f t h e r e f e r e n c e s i g n a l s f o r t h e f u l l - w a v e d e t e c t o r s , and a l s o t h e s e n s e o f t h e s i g n a l a v e r a g e r i n p u t s , i s r e v e r s e d t o remove l o n g t e r m d r i f t e f f e c t s i n t h e i n t e g r a t o r and a m p l i f i e r s f o l l o w i n g t h e f u l l - w a v e d e t e c t o r s . D e t a i l s on how s i g n a l s c a n be m a n i p u l a t e d a f t e r i n t e g r a t i o n i n t h e s i g n a l a v e r a g e , and m a t t e r s r e l a t e d t o c a l i b r a t i o n , compu te r c o n -t r o l o f o b s e r v a t i o n s and so on w i l l b e d i s c u s s e d i n t h e f o l l o w i n g C h a p t e r . Chapter III The Computer Control System A. Introduction This chapter w i l l be an extension of the previous one in that i t w i l l complete the discussion of the U.B.C. telescope hardware by presenting details of the telescope control and data acquisition systems. The computer control system developed to handle these functions has been thoroughly documented in four internal technical reports which comprise over 450 pages. These w i l l be brie f l y summarized in the following sec-tion. Then, in the f i n a l two sections of this chapter, we w i l l present discussions of the data acquisition and telescope control systems. In these discussions, we w i l l avoid material which has been handled i n the internal reports, although some duplication w i l l occur in the interest of producing a coherent picture. 19. B. Documentation of the U.B.C. Computer Control System The U.B.C. computer control system has been comprehensively described in the four internal technical reports (Mahoney, 1975, 1976b,c,d) which we l i s t below: The U.B.C. Millimeter Wave Telescope Computer Control System Part I: A Description for Primates Part II: A Description for Man the Wise Part III: A Description for Homo Neanderthalensis Part IV: An Assembly Language Listing Part I of this series i s an approximately 50 page user's manual which, describes at a very elementary level how an observer can use Tele-type commands to control the telescope, manipulate the data i t receives and perform miscellaneous astrophysical calculations. It has no pre-requisites and is included in Appendix A of this thesis to i l l u s t r a t e the tasks which can be executed. Part II i s an approximately 200 page technical description of the ideas and techniques which were used in developing the control system software. Although of a technical nature and requiring a number of pre-requisites to f a c i l i t a t e i t s reading, considerable effort was made to make i t i n t e l l i g i b l e to novices. Part III i s a very terse summary of the command language and is intended for quick reference purposes. Finally, Part IV provides a more than 200 page assembly language l i s t i n g of the control system. It has been thoroughly documented, and when combined with Parts I and II should allow modifications to be easily made. 20 . C . Discussion of the Data Acquisition System Before discussing the data acquisition system, we must f i r s t present an overview of the computer control system as a whole. This i s done schematically in Figure 2. The most obvious comment that can be made regarding this system i s that i t lacks many of the peripherals found at other observatories. Despite this fact, the control system performs a wide range of operations, and i t does so in a very cost ef-fective manner. Excluding the cost of software development and the cost of devices which, with l i t t l e modification, would be expected to appear at an observatory without computer control, the cost of implementing the U.B.C. computer system was approximately twenty thousand dollars. This i s surprisingly low in contrast to what other systems are known to cost. As shown in Figure 1, the automation system is built around a Nova 1200 minicomputer containing 24 K bytes (= 8 bits) of core memory, a central processor unit (CPU) and device 10 interfaces. Connected to the latter by means of an 10 bus are a send-receive Teletype, a high speed paper tape reader and a high speed paper tape punch. The 10 bus has also been extended to a general purpose interface which allows computer access to the telescope drive circuits, a sidereal clock, and a 1024 channel d i g i t a l signal averager. The latter device i s also inter-faced to an oscilloscope and a high speed point plotter. A l l of these devices are controlled either directly or indirectly by user initiated Teletype keyboard commands, and these w i l l be discussed shortly. During observations, analog signals from either the 112 channel spectral line or single channel continuum receivers are digitized and SCHEMATIC DIAGRAM OF U.B.C. nun WAVELENGTH RADIO TELESCOPE COMPUTER CONTROL SYSTEM Single or Multi-channel Backend Point Plotter 1024 Channel Signal Averager Nova 1200 12K 16b-word Core Memory Interfaces Teletype Output Paper Tape Punch Hour Angle and Declination to Comparator Drive Control Levels to RCU Teletype Input Paper Tape Reader Hour Angle and Declination from Digital Display Threshold and othe Levels from RCU Figure 2. 22. integrated in the signal averager's memory. Normally there i s enough unused memory here to allow room for data manipulation and analysis without calling on computer memory, which is at a premium. If desired, however, a computer image of any portion of the averager's memory can be generated to protect raw data from inadvertent errors during analysis. Although the signal averager does have manual control capability, data reduction and analysis using user Teletype commands are much more versa-t i l e ; these are now discussed. As indicated i n the previous section, Appendix A contains the user's manual written for the U.B.C. computer control system, so we w i l l only briefly summarize i t s features here. User commands, which consist of one or more words or numbers concatenated together, may be given in three ways: by using the Teletype keyboard, by reading a program tape on the low speed Teletype reader, or by executing a stack program. The latter Is simply a sequence of one or more command strings which are written into a stack i n the computer's memory and then executed i n a manner determined by a number of single letter control commands typed by the user. In this way a particular observing routine may be either typed or read in from paper tape and then repeated automatically as dictated by the control commands. If an observing sequence i s to be altered, the stack program may be l e f t and returned to as required. The commands themselves allow a great deal of f l e x i b i l i t y in format; the same instruction can be represented by a single letter or an entire sentence, depending on the user's preference. In addition, syntax errors or i l l e g a l commands are always appropriately tagged and any amount of command string editing i s allowed. Finally, when co-23. ordinates and similar information are requested, a number of formats are permitted and these are always formatted meaningfully - not simply as numbers separated by colons as i s often the case. Commands may be given to perform one of three types of functions: to manipulate data, to control the telescope or to perform miscellaneous astrophysical calculations. Commands i n the data manipulation category, in conjunction with the analog Cor point-wise digital) display of the signal averager's memory on an oscilloscope, allow the user to control and monitor the flow of data during i t s acquisition, analysis and out-put. Data can be output at any stage on either the Teletypewriter, the high, speed paper tape punch or the point plotter, or i t can be input for further analysis on the Teletypereader or the high speed paper tape reader. The commands available for data manipulation include those which add, subtract, s h i f t , scale or delete arbitrary ranges of data, those which modify individual or groups of data points and those which test noise levels, remove baseline curvature and calibrate data for output. The latter program uses information about the zenith attenuation which i t obtains from an automatic zenith attenuation calibration program to be described in the following section. Before closing this section, we should point out that s t r i c t l y speaking, the receiver i s not under computer control. This applies not only to the front end, but to the back end as well. In other words, user commands cannot be used to start an integration cycle. This pre-sents no serious, d i f f i c u l t y since, pushing a button is no more trouble than typing an instruction, but i t does have the effect of decentraliz-ing different aspects of the observing procedures. Perhaps in time this w i l l be changed. In the meantime however i t means that the computer is relatively unused, since i t isn't involved in handling interrupts which would occur i f the data acquisition were f u l l y automated. 25. D . D i s c u s s i o n o f t h e T e l e s c o p e C o n t r o l Sys tem The m a i n components o f t h e t e l e s c o p e c o n t r o l c i r c u i t r y a r e shown i n F i g u r e 3 . N o t e t h a t t h e o f f - p a g e c o n n e c t o r s i n t h i s f i g u r e a r e c o n t i n u e d i n F i g u r e 2 and a r e r e l a t e d t o c o n t r o l and d a t a l i n e s b e -tween t h e compu te r on t h e one h a n d , and t h e remo te c o n t r o l u n i t (RCU) and d i g i t a l c o m p a r a t o r on t h e o t h e r . The l a t t e r d e v i c e i s t h e c e n t r a l component o f t h e a u t o m a t i o n c i r c u i t r y . I t compares t h e a c t u a l t e l e s c o p e h o u r a n g l e and d e c l i n a t i o n w i t h t h o s e g e n e r a t e d by t h e compu te r s o f t -w a r e a n d , i f d i f f e r e n c e s g r e a t e r t h a n a 36 a r c s e c t h r e s h o l d e x i s t , t h e h a r d w i r e d c o n t r o l l o g i c p r o d u c e s a p p r o p r i a t e e r r o r s i g n a l s t o move t h e t e l e s c o p e w i t h i n t h e t h r e s h o l d l e v e l . When t h i s o c c u r s , t h e CPU i s 2. n o t i f i e d v i a an i n t e r r u p t " and t h e n e x t p h a s e o f t e l e s c o p e c o n t r o l c a n b e g i n . T h i s method o f c o n t r o l t h e r e f o r e f r e e s t h e compu te r t o p e r f o r m o t h e r u s e r t a s k s b e t w e e n d r i v e commands. The a u t o m a t i o n s y s t e m i s o f c o u r s e b a c k e d up by a m a n u a l c o n t r o l s y s t e m and i n e i t h e r o f t h e s e modes o f o p e r a t i o n , a u t o m a t i c t r a c k i n g a t t h e s i d e r e a l o r s o l a r r a t e s i s e a s i l y i n i t i a t e d . A s a m a t t e r o f e x p e d i e n c e , h o u r a n g l e i n s t e a d o f r i g h t a s c e n s i o n was u s e d as t h e a z i m u t h a l c o - o r d i n a t e , b u t a s a r e s u l t a s i d e r e a l c l o c k h a s a l s o b e e n i n t e r f a c e d . T e l e s c o p e c o n t r o l commands a l l o w t h e u s e r t o i n i t i a t e a l a r g e number o f o p e r a t i o n s w h i c h r a n g e f r o m s i m p l y s t o w i n g t h e t e l e s c o p e t o t r a c k i n g a v a r i a b l e p o s i t i o n s o u r c e s u c h a s t h e s u n o r a c o m e t . S o u r c e 2. T h i s i n t e r r u p t i s c u r r e n t l y s o f t w a r e d i s a b l e d s i n c e t h e demands on t h e c o m p u t e r ' s t i m e a r e s o m i n o r t h a t u s i n g t h e i n t e r r u p t i s u n n e c e s s a r y . The c h a n g e s n e c e s s a r y t o r e - e n a b l e i t a r e d e s c r i b e d e l s e w h e r e (Mahoney, 1 9 7 6 c ) . SCHEMATIC DIAGRAM OF U.B.C. mm WAVELENTH RADIO TELESCOPE DRIVE CONTROL positions are entered i n either galactic or equatorial co-ordinates, and are automatically precessed i f necessary. In addition, arbitrary off-source positions may be specified for position switching or i n i t i a t i n g d r i f t scans, and the user i s also free to specify the length of time a given observation i s to take. Also i n the telescope control category are commands which allow the user to st a r t aiming or tracking the telescope at any time, as well as update the telescope position for variable p o s i t i o n sources. In addition, there are a number of program flags which the user i s able to set or clear, the most noteworthy of these being the re f r a c t i o n and pointing f l a g s . If the ref r a c t i o n f l a g i s set, drive commands w i l l automatically take into account the radio frequency r e f r a c t i o n due to the earth's atmosphere, while i f the pointing f l a g i s set, corrections due to the imperfect alignment of the telescope are automatically made. If the user wishes to have a record of what these corrections are at any time, as wel l as a l i s t i n g of other parameters including the date, time and telescope position i n various co-ordinate systems, then the status command i s used. A l t e r n a t i v e l y , there i s an interrupt button which w i l l cause the same information to be typed. Two other very useful commands are available. The f i r s t i s used for making semi-automatic telescope pointing measurements (and w i l l be discussed i n the next chapter), while the second i s used to measure the zenith attenuation i n the signal band. The l a t t e r program i s noteworthy as i t actually measures the zenith attenuation at the source being observed, not the zenith. Furthermore, i t reduces the amount of telescope movement required to make the measurement. This doubling the effective air mass the telescope looks through and then noting what effect this has on the sky noise with respect to an ambient temperature load. Therefore, at large zenith distances when frequent calibrations are important, the telescope need not be moved very far, while at smaller zenith distances when the telescope must be moved further to double the air mass i t sees, frequent calibration i s nor-mally not necessary. If we assume for lack of better information, that the receiver gain is equal in both sidebands, and that the difference of the zenith attenuation in the signal and image bands can be reason-ably determined (and that i t doesn't depend c r i t i c a l l y on normal ob-serving weather conditions), then i t can be shown (Mahoney 1976a) that the signal band zenith attenuation i s given by: is a consequence of the fact that the method employed involves simply (1) where A is the air mass at which the zenith attenuation must be determined; i t is equal to secant(zenith distance), i s g s " 1 , with X 5 and Tj, being the zenith attenuations in the signal and image bands respectively, i s the ambient or load temperature, is the atmosphere temperature, and A. Is the r a t i o of the load minus sky temperatures at air masses of A and ZA , that i s : A (Ti -Ts(A))/(Tt-T8ttA>) "7^ ( £ " T a » . ) being the observed sky temperature as as determined from a total power record appropriately calibrated. As described in Appendix A, the program to determine T 3 using this tech-nique is semi-automatic. The measured value of i s then made av a i l -able to the data calibration program to correct observed signal inten-3. s i t i e s for atmospheric absorption *. Before leaving this chapter, we discuss one f i n a l category of commands — these are the commands to perform miscellaneous calcula-tions. Included in this category are commands to convert between galactic, equatorial and horizon co-ordinate systems, a command to calculate and check the sidereal time, commands to precess source posi-tions between arbitrary epochs and calculate local standard of rest velocities, and so on. Also included here are the commands which are used to read, write, l i s t , edit and punch the stack programs discussed earlier. 3. In the second part of this thesis we discuss another approach to the data calibration problem which makes no assumptions regarding the relative side band gains or the signal and image band zenith attenua-tions. It however is not yet feasible for the U.B.C. telescope. Chapter IV Telescope Pointing A. Introduction Clearly as the size of a telescope's beam decreases, the effect of various structural imperfections w i l l become increasingly important. This i s a particularly serious concern at millimeter wavelengths since the paucity of strong sources makes i t d i f f i c u l t to know where a telescope i s really pointing u n t i l after a long inte-gration has been made. As receiver sensitivities continue to improve, this d i f f i c u l t y w i l l be partially alleviated, however there w i l l always remain the basic problem of how to account for mechanical defects which cannot be permanently removed. These defects cause the true telescope hour angle and declination to diffe r from their analog or d i g i t a l readout values, and in general w i l l be a function of both these co-ordinates . The author has written a comprehensive internal technical report, The Derivation and Analysis of Theoretical Pointing Functions  for an Equatorially Mounted Telescope, discussing this problem, and i t i s included as Appendix B of this thesis. It should be pointed out that appendices D and E of this report have not been included here. There are two reasons for this: the f i r s t i s that they involve a lengthy l i s t i n g and discussion of various computer programs which have been written to analyse the U.B.C. pointing data, and i t was fe l t that they would not contribute much i n proportion to their size. The second, and perhaps most important reason f or excluding these appendices, i s that they are not e n t i r e l y the author's work. The bulk of the recent pointing measurements made at U.B.C, and t h e i r a n a l y s i s , has been through the e f f o r t s of Mr. Alexander Szabo whom the author supervised on a direc t e d studies course i n astronomy. In the remainder of t h i s chapter, we summarize the theory, measurements and r e s u l t s obtained f o r the U.B.C. telescope. More complete d e t a i l s may be found i n Appendix B. 32. B. The Theoretical Pointing Functions It i s shown in Appendix B that i f we use T and D to repre-sent the hour angle and declination of a source as displayed on a tele-scope's d i g i t a l or analog readouts, and t and & to represent the source's apparent hour angle and declination as seen from the earth's surface, then: T s - f l ^ttL^HA^fit'-ry\ti^fi S'\ - &Abc(&'-r]/4>W-t'+'¥c<ra't') (2) and 0- «+ &-riA^t'+Y 0<rt>t' (3) where the Greek letters represent the following misalignments: Y and ^ describe the orientation of the telescope pole with respect to the North. Celestial Pole; , the non-orthogonality of the declination axis to the polar axis; |3 , the non-orthogonality of the radio beam to the declination axis, and f i n a l l y , 0 and CC , the hour angle and declination encoder biases, respectively. In terms of a source's true position ( t , S) and the latitude L- of the telescope, the apparent position i s given by: and (5) where 7T , C and p r e p r e s e n t p a r a l l a x , s a g and r e f r a c t i o n c o n s t a n t s , r e s p e c t i v e l y . N o t e t h a t i n t h i s c a l c u l a t i o n i t was assumed t h a t t e l e -s c o p e s a g ( t h a t i s , sag o f t h e s u b r e f l e c t o r ) o c c u r s i n a v e r t i c a l p l a n e t h r o u g h t h e z e n i t h . W i t h t h i s a p p r o x i m a t i o n , w h i c h a p p e a r s t o g i v e r e a s o n a b l e . r e s u l t s , i t was m a t h e m a t i c a l l y c o n v e n i e n t t o i n c l u d e s a g w i t h p a r a l l a x and r e f r a c t i o n a s t h e y a l s o o c c u r i n a z e n i t h v e r t i c a l p l a n e . t h e f o l l o w i n g o b s e r v a t i o n s : f i r s t , e q u a t i o n s (2) and (3) c o n t a i n s e c o n d o r d e r t e r m s i n s e v e r a l o f t h e m i s a l i g n m e n t p a r a m e t e r s . A t p o s i t i o n s where p o i n t i n g measu remen ts o r o b s e r v a t i o n s a r e l i k e l y t o be made, t h e s e t e rms may be n e g l e c t e d . S e c o n d , t h e s e m i - a u t o m a t i c p o i n t i n g measurement p r o g r a m w h i c h h a s b e e n w r i t t e n f o r t h e U . B . C . t e l e s c o p e t a k e s i n t o a c c o u n t t h e e f f e c t s o f p a r a l l a x and r e f r a c t i o n , w h i l e d u r i n g o b s e r v a t i o n s t h e s e e f f e c t s a r e h a n d l e d i n d e p e n d e n t l y o f t h e p o i n t i n g c o r r e c t i o n s . T h i r d , f o r t h e p u r p o s e o f d o i n g l e a s t s q u a r e s f i t s t o e m p i r i c a l p o i n t i n g c u r v e s , o r f o r c o r r e c t i n g s o u r c e c o - o r d i n a t e s d u r i n g o b s e r v a t i o n s , i t i s c o n v e n i e n t t o d e f i n e t h e c o r r e c t e d p o i n t i n g f u n c t i o n s : B e f o r e d o i n g a f i n a l d e v e l o p m e n t o f t h e s e e q u a t i o n s we make (6) where t c and represent the true source hour angle "t and declina-tion & corrected for the effects of parallax and refraction. In terms of the previous equations, we may then write: At c = ~9 + (CCff&L ALrtlt-p)/W,& + (YAJLKt+Tycc&t+f)tw & (7) and A<SC - <X +<r(c^t AwSc^L-ar<b£s<wL)+¥crt (8) With these equations at our disposal, we are now in a position to make measurements to determine values for "ty , 7? , OL , |3 » ¥ , B and CT by performing least squares f i t s to empirically determined pointing curves for and Depending on whether t or $ is used as the independent variable, either tracking or transit measurements w i l l be made. In the following subsection we also show that a third kind of experiment — a slewing experiment — w i l l also allow us to independently determine the polar axis misalignment parameters f and ^ . The l a t t er parameters, incidentally, are the only structural misalignments which, with effort, can be permanently removed. In general, however, small ..... residuals w i l l remain and must be accounted for. Once the misalignment parameters are determined equations (7) and (8) may be used to make real time corrections during observa-tions. This i s described in section D of this chapter. C. Measuring the Misalignment Parameters As suggested in the previous section, there are essentially three kinds of pointing experiments which can be performed; these involve either slewing, tracking or transit measurements and they are discussed at length in Appendix B. No one kind of measurement alone w i l l allow a l l the misalignment parameters to be determined, and in general different experimental techniques may be used in conjunction with a given type of experiment. 1. Slewing experiments. Slewing experiments have been used at U.B.C. to determine the polar axis misalignment parameters Y' and ; they proceed as follows: a small optical telescope with a camera attached is rigidly mounted on the main reflector of the radio telescope and then the radio telescope is oriented so that the North Celestial Pole (NCP) i s within the camera's f i e l d of view. A timed exposure is then begun, which, since the telescope is fixed, w i l l result in stars exposing arcs on the film. Since the U.B.C. telescope is of high enough latitude that differen-t i a l refraction over the camera's f i e l d of view is n e g l i g i b l e t h e s e arcs define the position of the refracted NCP and hence, after a simple refraction correction, the true NCP. The position of the telescope pole is next found by quickly slewing the telescope through a large angle and halting. By noting where on the film the star tracks end and then begin, the position of the telescope (that i s , the pole about which the telescope moves) is defined. The timing information plus the position of one known star, say Polaris, f i n a l l y determines an hour angle and declination scale from which values for "iff and >^  can be found after the refraction of the NCP has been taken into account. The simple experiment just described works well, but i t can be refined to produce results limited only by the telescope readout accuracy. Furthermore, i t can produce them in a much shorter period of time once the ground work has been done. It proceeds as follows: i f the positions of the brighter stars in the neighbourhood of the NCP are known, then the relative positions of any three of these stars defines the refracted NCP, and the more stars the better. Therefore, instead of taking a long exposure as described above, we take exposures only long enough to define the position of the stars and then slew on to another position, and so on. Successive positions for the refracted NCP (defined by three or more stars) w i l l then appear to move about the telescope pole because the telescope i s being rotated. Finally, any three positions for the NCP (corrected for refraction) determines a separate position for the telescope pole, which, because more data is being used, results in a more accurate answer. The analysis however is tedious without a large computer. The main advantage of slewing experiments is that they are much faster than either tracking or transit experiments, and they not only the determination of the other misalignment parameters, but also allows the polar axis to be aligned without going through the tedium of a tracking or transit experiment. This is indeed fortunate since the polar axis alignment is the most c r i t i c a l of a l l and in general requires several attempts at alignment before acceptable results are obtained. 2. Tracking experiments. Tracking experiments have been made at U.B.C. using both radio and video techniques. To date, radio measurements have used only the sun as a source; they proceed as follows: provide an independent determination of and This f a c i l i t a t e s f i r s t the mean readout declination i s found by doing a d r i f t scan i n declination and noting on a total power chart recorder when the rising and f a l l i n g limbs occur. This procedure is then repeated i n hour angle, afterwhich, the apparent position i s calculated using an ephe-meris and accounting for the effects of parallax and refraction. The pointing curves for At C and A<£C are then found by repeating these measurements through the course of the day. Clearly this i s a tedious procedure and as a result, the process i s now automated. The observer need only press a computer interrupt button at the appropriate times and values for and A Or are automatically generated. Typical pointing curves measured in this way are shown in Figure 4. The video technique on the other hand makes use of the optical telescope used in conjunction with the slewing experiment described above. This time however a high sensitivity vidicon tube i s mounted behind the optical telescope and is monitored in the control room. Solar observations may of course be made, but the real forte of the technique i s that i t allows observations of sources outside the range ±23° declination. This is particularly important for the transit experiments described below. Again, the automatic pointing measurement program can be used, and furthermore, by using a stack program (see Appendix A) to control the movement of the telescope between a number of sources, the observer may simply s i t back and push a button as stars successively appear on the monitor. In this way empirical pointing curves can be obtained at a wide range of declinations simultaneously. 0-12 008 + A6 004 + (Deg.) -4. -0-04 j -0-08-• At c -0-12 + (Deg.) -0-16 -4 EMPIRICAL RADIO POINTING CURVES -* 4 * 4 * 4 4 * 4 4 4 4 ' 4 4* A A * A A 'l i A A A A A A ^ A A A A 1 A A A A • • - 3 -2 -1 0 1 HOUR ANGLE ( Hours ) 4 4 " 4 4 4 4 4 4 < 4 • 4 Mean Solar Date Declination u • • March 5 -5,6 4 4 March 4 -6.0 • • March 3 -6.4 A A March 2 -6.8 - 3 -2 -1 HOUR ANGLE ( Hours ) Before proceeding further, i t should be pointed out that tracking experiments alone cannot determine the misalignment parameters cp , B and |3 uniquely. It should also be noted that the parameters (X. , |3 a n d 0~ w i l l in general be different depending on how they are mea-sured. The reason i s of course that the radio and optical beams are not parallel, and in addition sag w i l l be less important i n the opti-cal case i f the optical telescope i s properly mounted. 3, Transit experiments. Transit experiments are the natural complement of tracking experiments. Indeed, there need be no difference for i f tracking experiments are made at a sufficient number of declina-tions and the measurements are always made at the same hour angles, then a transit experiment may be easily simulated. The important difference however, as w i l l be seen by examining equations (7) and (8), i s that a transit experiment allows the parameters C , 0 and |3 to be determined, and i f y and are known, <p and Oi may be found as well. The solar tracking experiment data has i n fact been used to simulate transit experiments, although the declination coverage i s not good. D . The Measurement R e s u l t s I n T a b l e I I we summar i ze t h e r e s u l t s o f v a r i o u s m i s a l i g n -ment p a r a m e t e r d e t e r m i n a t i o n s . T h o s e i n co lumns (2) and (3) r e p r e s e n t t h e r e s u l t s o f h a v i n g p e r f o r m e d a s i m u l t a n e o u s l e a s t s q u a r e s f i t t o a l l t h e p o i n t i n g c u r v e s ( s u c h as t h o s e i n F i g u r e 4) f o r o p t i c a l and r a d i o measurements r e s p e c t i v e l y . I t w i l l be n o t e d t h a t e x c e p t f o r t h e beam dependen t p a r a m e t e r s ( & and (3 ) and t h e s a g p a r a m e t e r ((7") t h e r a d i o and o p t i c a l , r e s u l t s a g r e e q u i t e w e l l . T h i s i s t o be e x p e c t e d s i n c e » ^? » *P a n c * ^ s h o u l d b e i n d e p e n d e n t o f t h e measurement t e c h n i -q u e ; i n t h e w o r s t s i t u a t i o n , t h e y s h o u l d n o t d i s a g r e e by more t h a n t h e r e a d o u t a c c u r a c y . I n f a c t , t h e o n l y p a r a m e t e r w h i c h a p p e a r s t o b e o u t o f l i n e i s *P and i n t h i s c a s e t h e d i f f e r e n c e p r o b a b l y r e f l e c t s t h e f a c t t h a t t h e r a d i o p o i n t i n g c u r v e s u s e d t o d e r i v e t h e s e r e s u l t s o n l y samp led a d e c l i n a t i o n r a n g e o f ±23 d e g r e e s . I n co lumn (4) o f T a b l e I I we l i s t t h e b e s t c u r r e n t r a d i o m i s -a l i g n m e n t p a r a m e t e r d e t e r m i n a t i o n s . T h e s e w e r e f o u n d a f t e r t h e c o l u m n (3) r a d i o r e s u l t s f o l l o w i n g a p o l a r a x i s a d j u s t m e n t . I t w i l l be n o t e d t h a t b o t h "ty and Y[ h a v e b e e n s i g n i f i c a n t l y i m p r o v e d as a r e s u l t o f t h i s . A s a f i n a l r e m a r k , we m e n t i o n t h a t a l l o f t h e s e r e s u l t s , when u s e d t o c a l c u l a t e t h e p o i n t i n g f u n c t i o n s , a r e c a p a b l e o f r e p r o d u c i n g any o f t h e c u r v e s f r o m w h i c h t h e y w e r e d e r i v e d w i t h a mean e r r o r no g r e a t e r t h a n t h e a c c u r a c y o f t h e t e l e s c o p e r e a d o u t s . Table II: Summary of Results for Misalignment Parameters Parameter (Meaning) C D Optical 3 (2) Radio 3 (3) Standard^* (4) a (Declination encoder bias) -.022° .093° .007° (Non-orthogonality of beam) .023 -.120 .066 * (Non-orthogonality of declination axis) -.091 -.039 -.085 e (Hour angle encoder bias) .245 .252 .242 (Polar axis meridian t i l t ) .143 .142 -.034 (Polar axis east-west t i l t ) .014 -.013 -.002 a (Sag) .047 .071 .041 Notes to the table: a. These results were obtained during the same period of time and a l l parameters except a,8 and a should be the same. See the text for a discussion. b. This column presents the most recently determined radio misalign-ment parameters, following an adjustment of the polar axis in January 1976. 42. E. Practical Misalignment Corrections Of the seven misalignment parameters we have been discussing, only the polar axis misalignments Iff and TJ may be permanently re-moved. The procedure is described in Appendix B, where i t w i l l be noted that Y and -TJ are both linearly related to adjustments which are made to the polar axis mounting bushings. From the results pre-sented i n Table III i t is clear that these misalignments are nearly removed. At present, the polar axis i s s t i l l leaning 0.034° away from the NCP in a direction opposite the local meridian. The remaining misalignments we must learn to li v e with as they are structurally fixed or vary depending on the receiver being used. The simplest method of handling these parameters, together with the polar axis residuals, i s with the computer. To this end, an ob-server may set a pointing flag which requests values for the various misalignment parameters and then automatically removes the appropriate corrections whenever a telescope drive i s made. Similar corrections are made independently for parallax and refraction. Two other features are worth noting. The f i r s t i s that i f for some reason an observer wishes to use empirical pointing curves to aim the telescope, he may do this by f i r s t making a polynomial f i t to the empirical curve. With the polynomial coefficients determined, an optional software feature i s then used to calculate polynomial point-ing corrections instead of the functional ones given by equations (7) and C8). In general, a polynomial f i t to an empirical curve w i l l be better than the corresponding functional f i t . Unfortunately, however, empirical curves do not exist for every declination at which observa-tions may be required. The second feature worth noting is that i t is also possible to generate arbitrary functional or polynomial pointing curves simply by typing the appropriate misalignment parameters or polynomial co-efficients. C h a p t e r V A s t r o n o m i c a l R e s u l t s A . S o l a r O b s e r v a t i o n s The s u n was t h e f i r s t a s t r o n o m i c a l s o u r c e t o be d e t e c t e d w i t h t h e U . B . C . t e l e s c o p e . T h i s o c c u r r e d i n F e b r u a r y 1972 a t a f r e -quency o f 40 G H z . L a t e r t h a t y e a r , S h u t e r and M c C u t c h e o n ( 1 9 7 2 ) , made an a t t e m p t t o d e t e c t a t 9 . 6 mm s o l a r o s c i l l a t i o n s w h i c h had b e e n n o t e d b o t h a t 3 . 3 mm and i n t h e v i s i b l e t o o c c u r w i t h a p e r i o d o f 5 m i n u t e s . They w e r e a b l e t o p u t an u p p e r l i m i t o f ^ 0 . 7 K e l v i n , o r .016% o f t h e s u n ' s i n t e n s i t y a t 9 . 6 mm, on t h e s e o s c i l l a t i o n s , and p o i n t e d ou t t h e i m p o r t a n c e o f r e m o v i n g a t m o s p h e r i c e f f e c t s when m a k i n g t h i s k i n d o f m e a s u r e m e n t . L a t e r , J o e n s e n e t a l . (1974) d e v e l o p e d a new method f o r i n -v e s t i g a t i n g t h e b r i g h t n e s s d i s t r i b u t i o n o f t h e s o l a r l i m b a t m i l l i -m e t e r w a v e l e n g t h s . T h e i r t e c h n i q u e i n v o l v e d c o m p a r i n g t h e l u n a r l i m b a t t h e r m a l f i r s t o r t h i r d q u a r t e r (when i t was assumed t o be n e u t r a l ) , w i t h t h e s o l a r l i m b , and d o e s n o t r e q u i r e a d e c o n v o l u t i o n . M e a s u r e -men ts a t 8 8 . 3 GHz i n d i c a t e d t h a t l i m b b r i g h t e n i n g i s ^ 1.6% o f t h e s u n ' s t o t a l power a t t h i s w a v e l e n g t h , w h i l e l i m b d a r k e n i n g i s ^ 1 . 2 % . I was n o t i n v o l v e d i n e i t h e r o f t h e a b o v e p r o g r a m s . B. S p e c t r a l L i n e O b s e r v a t i o n s I n t h e p r o c e s s o f a t t e m p t i n g t o g e t a c o m p e t i t i v e s p e c t r a l l i n e r e c e i v e r on t h e a i r , o b s e r v a t i o n s we re made o f s e v e r a l m o l e c u l a r s p e c i e s . I n F i g u r e 5 i s shown ou r f i r s t l i n e d e t e c t i o n . T h i s m a r g i n a l d e t e c t i o n o f t h e 1 1 5 . 2 7 1 GHz J = 1-0 t r a n s i t i o n o f CO i n O r i o n o c c u r -r e d i n May 1 9 7 3 . I n 1 9 7 4 , t h e 2 8 . 9 7 5 GHz J ^ _ K + = 3 1 2 ~ 3 1 3 t r a n s i t l o n o f IL^CO was d e t e c t e d i n Sg r A , w h i l e a l i t t l e l a t e r t h a t y e a r t h e 8 8 . 6 GHz J". = 1-0 t r a n s i t i o n o f HCN was d e t e c t e d i n O r i o n . A l l t h e s e l i n e s had b e e n d e t e c t e d p r e v i o u s l y . I n M a r c h 1974 we w e r e a b l e t o p u t a t h r e e s i g m a u p p e r l i m i t o f 0 . 2 K e l v i n , on t h e JK = 1 Q - ° I t r a n s i t i o n o f SO i n O r i o n a t 3 0 . 0 0 1 G H z . To o u r k n o w l e d g e t h i s t r a n s i t i o n h a s n o t y e t been d e t e c t e d i n t h e i n t e r s t e l l a r med ium. I n J u n e 1 9 7 5 , a s e a r c h was made f o r t h e J - 4 - 3 CV = 0 and V = 1) t r a n s i t i o n s o f S i S a t 7 2 . 6 1 8 GHz and 7 2 . 2 6 5 GHz r e s p e c t i v e l y . T h r e e s i g m a l i m i t s o f ~ 1 K e l v i n a n t e n n a t e m p e r a t u t e we re p l a c e d on b o t h t h e s e t r a n s i t i o n s i n O r i o n and on t h e V =* 0 t r a n s i t i o n i n IRC+10216, The n u l l r e s u l t s a r e shown i n F i g u r e 6 . I t was l a t e r r e p o r t e d ( M o r r i s e t a l . , 1975) t h a t t h e J = 6 - 5 and J~- 5 -4 t r a n s i t i o n s b f S i S had b e e n d e t e c t e d . I n t h e f a l l o f 1975 an e f f o r t was made t o o b s e r v e CO i n a number o f g a l a c t i c H I I r e g i o n s and e m i s s i o n n e b u l a e . Two o f t h e r e -s u l t i n g p r o f i l e s a r e shown i n F i g u r e 7 . C o m p a r i n g t h e O r i o n p r o f i l e w i t h t h e one p r e s e n t e d i n F i g u r e 5 shows c l e a r l y t h a t p r o g r e s s h a s B e e n made . H o w e v e r , i f t h e i n t e g r a t i o n t i m e i s n o t e d , as w e l l a s t h e f a c t t h a t 1 MHz f i l t e r s w e r e u s e d t o o b t a i n t h e s e r e s u l t s , i t w i l l be o b v i o u s t h a t a l a r g e improvemen t i s needed b e f o r e c o m p e t i t i v e r e s u l t s c a n be o b t a i n e d . T B C K ) 4 0 20 , 2 C r 6 0 I N O R I O N M A Y 4 , 1973 4 0 M I N . I N T E G R A T I O N J « 1 — 0 1 J L 1 1 1 1 1 +26.1 +20.9 +15.7 +10.5 +5.3 +0.1 -5.1 V L S R ( K M / S E C ) -10.3 Figure 5. The F i r s t Spectral Line Detection at U.B.C. - p -O N • I r 0 SILICON MONOSULPHIDE (SIS) -53 .4 - 8 5 . 0 v • 0 J - 4 - 3 (4.0 HRS) ORION v - I J « 4 ^ 3 (5.5 HRS) J. + 8.56 +70.5 VELOCITY (KM/SEC) IRC +10216 v • 0 J « 4-*3 (3.8 HRS) -23.0 +39.0 VELOCITY ( K M / S E C ) 48. V L S R ^km/sec) - 3 2 . 6 +9.0 +48.0 V L S R (km/sec) Figure 7. 49. C . C o n c l u d i n g Remarks I t h a s b e e n r e a l i z e d f o r some t i m e t h a t r e c e i v e r s e n s i t i v i t y h a s p r e v e n t e d t h e U . B . C . m i l l i m e t e r wave g r o u p f r o m d o i n g c o m p e t i t i v e a s t r o n o m y . An a d d i t i o n a l d i f f i c u l t y howeve r h a s b e e n t h a t i n many c a s e s 1 MHz s p e c t r a l r e s o l u t i o n i s n ' t s u f f i c i e n t t o r e s o l v e s p e c t r a l l i n e s f r o m many i n t e r e s t i n g m i l l i m e t e r l i n e s o u r c e s . B o t h t h e s e d i f f i c u l t i e s a r e b e i n g r e m o v e d . F i r s t , f u n d s we re g r a n t e d by t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada t o have a c o o l e d r e c e i v e r b u i l t . T h i s i s now b e i n g done and s h o u l d b e c o m p l e t e by J a n u a r y 1 9 7 7 . The r e c e i v e r b e i n g b u i l t i s a S c h o t t k y b a r r i e r m i x e r e s s e n t i a l l y t h e same a s t h o s e we a r e c u r r e n t l y u s i n g , e x c e p t t h a t e v e r y t h i n g i s c o o l e d t o 20 K e l v i n . A l t h o u g h t h e u s e o f J o s e p h s o n m i x e r s had b e e n c o n s i d e r e d , and p r o m i s e d t o be b e t t e r , t h e y a r e a s y e t u n t e s t e d d e v i c e s and we h a v e t a k e n a c o n s e r v a t i v e p o s i t i o n . I t i s e x p e c t e d t h a t when t h e new r e c e i v e r a r r i v e s o u r s i n g l e s i d e band s y s t e m n o i s e t e m p e r a t u r e w i l l be a p p r o x i m a t e l y 400 K. T h e r e f o r e , e v e n i f r e c e i v e r s e n s i t i v i t i e s i m p r o v e much o v e r t h i s , t h e n e t r e s u l t on i n t e g r a t i o n t i m e s when t h e a t m o s p h e r e i s t a k e n i n t o a c c o u n t w i l l n o t be s i g n i f i c a n t l y c h a n g e d . We t h e r e f o r e e x p e c t t o be i n a v e r y c o m p e t i -t i v e p o s i t i o n . . The p r o b l e m o f o b t a i n i n g b e t t e r s p e c t r a l r e s o l u t i o n i s a l s o b e i n g w o r k e d on and s e v e r a l a l t e r n a t i v e s h a v e b e e n c o n s i d e r e d . I n i t i a l l y p l a n s had b e e n t o b u i l d a d i g i t a l a u t o - c o r r e l a t i o n s p e c t r o m e t e r , and i n f a c t , a f o u r c h a n n e l p r o t o - t y p e was a c t u a l l y b u i l t and c l o c k e d a t 200 MHz — t h a t i s , t h e N y q u i s t r a t e f o r a 100 MHz b a n d w i d t h . W i t h f u n d s n o t available, i t was decided to wait and see how electro-optical devices developed. Finally, however, plans are now going ahead with a 64 channel, 250 KHz resolution f i l t e r spectrometer, which wil l be operated in parallel with the existing one. When i t became apparent that I would be unable to obtain useful astronomical results for at least another year with the U.B.C. telescope, i t was decided to apply for observing time elsewhere. The results of having done this are described in the second part of this thesis. My main objective in this part has been to describe my participation in the development of the U.B.C. instrument, and perhaps point out some new approaches to some old problems. 51. Part Two Observations of Carbon Monoxide in the Galactic Dust Cloud Lynds 134 52 Chapter VI Introduction to Part Two A. The Classification of Dust Clouds Dust clouds, or dark nebulae as they are often called, represent regions of the sky where vi s i b l e radiation is absorbed or scattered by interstellar dust or grains. This material has been studied by both optical and infrared techniques, and with the advent of radio frequency observations, particularly at millimeter wavelengths, i t has also been possible to study the thermodynamics, structure and composition of the gas associated with this dust, and therefore the I interstellar medium in general. The gas component i s i n fact about one hundred times more massive than the dust. Observationally dust clouds are not represented by a single set of properties, but rather are classified in a size sequence which is thought in some way to represent an evolutionary sequence. The names which astronomers use to describe this sequence, however, i s by no means uniform; thus dense dust clouds, dark dust clouds, extended obscured regions, black clouds, cloudlets, large globules, small globules, giant clouds, dark nebulae, as well as several proper names, are used to describe various morphological phases, in some cases the same, in the evolution of the interstellar medium to form stars. To be visible in the general star f i e l d , dust clouds must be nearer than ~1 Kpc, and at higher galactic latitudes, they must also be reasonably large (diameter ^10'). As seen from the earth, t h e mos t e x t e n d e d o f t h e s e o b j e c t s f o r m m a j o r comp lexes a l o n g t h e g a l a c t i c p l a n e ( B o k , 1937) w h i c h h a v e an a v e r a g e v i s i b l e e x t i n c t i o n Ay ~ l m . W i t h i n t h e s e c o m p l e x e s a r e r e g i o n s o f l m t o 5 m e x t i n c t i o n and abou t 10 s q u a r e d e g r e e s i n s i z e , s u c h as t h o s e i n T a u r u s and O p h i u c h u s w h i c h h a v e had t h e i r e x t i n c t i o n s a c c u r a t e l y measu red by Bok ( 1 9 5 6 ) . I n a d d i t i o n , t h e r e a r e i s o l a t e d r e g i o n s , n o r m a l l y r e -f e r r e d t o as d a r k d u s t c l o u d s , o f s e v e r a l a r c m i n u t e s t o a few d e g r e e s i n s i z e w h i c h have e x t i n c t i o n s o f > 5 m . The s m a l l e r o f t h e s e a r e t h e l a r g e g l o b u l e s d i s c u s s e d by Bok and R e i l l y ( 1 9 4 7 ) , w h i l e t h e s m a l l g l o b u l e s t h e s e a u t h o r s d i s c u s s a r e l e s s t h a n a few a r c m i n u t e s i n e x -t e n t and t h e r e f o r e a r e o n l y s e e n p r o j e c t e d a g a i n s t b r i g h t e m i s s i o n n e b u l a e . T h e s e s m a l l g l o b u l e s a r e t h o u g h t t o p l a y an i m p o r t a n t r o l e i n s t a r f o r m a t i o n , p e r h a p s f o r m i n g p r o t o - s t a r s . The v a r i o u s c a t e g o r i e s d e s c r i b e d above a r e o b v i o u s l y i l l -d e f i n e d , and i t i s p o s s i b l e t h a t t h e r e i s a c o n t i n u u m o f s i z e s and e x t i n c t i o n s . The o b j e c t s we s h a l l be c o n c e r n e d w i t h h e r e a r e t h e d a r k d u s t c l o u d s o r l a r g e j g l o b u l e s . B. The Formation of Dust Clouds The formation of stars from the general interstellar medium presents a poorly understood and challenging problem for astronomers to explain. In the process densities must change by some twenty-four 3 3 orders of magnitude — from typically 1 atom/cm to 1 gram/cm — and i t seems certain that at some stage dust clouds must play a role in this scenario. In the following few paragraphs we outline very superficially what this role is thought to be, but i t must be remembered that there are a large number of uncertainties. The ideas presented here are essentially those reviewed by Larson (1973). For typical interstellar conditions, i t i s easy to show that the c r i t i c a l Jeans mass for gravitational collapse i s approximately 10 -10 I ^ \ Q . Under these circumstances, assuming rotation and magnetic fields are not important, the gravita-tional binding energy of a cloud w i l l exceed i t s thermal energy and i t w i l l therefore collapse. Besides a pure gravitation collapse, i t is also conceivable that thermal i n s t a b i l i t i e s caused by radiation or cosmic ray heating,or Rayleigh-Taylor i n s t a b i l i t i e s caused by a density difference between two interacting clouds, w i l l also lead to collapse. Excluding dark dust clouds and denser objects, most interstellar clouds however w i l l not satisfy the Jeans criterion; either the mass or the density of these diffuse clouds must be increased. 4. yU. is the mean mass per particle and the other constants and variables have their normal meanings. In the currently popular spiral density-wave theory of Shu et a l . (1972) the shock front accompanying the density-wave can iso-thermally compress the gas and reduce the Jeans mass to ~ 100 !^\Q . Even then however i t is s t i l l necessary to explain how stars of normal stellar mass might eventually form from these s t i l l very massive clouds. Larson has pointed out that despite the various geometries and in s t a b i l i t i e s one might consider, the qualitative features of a collapse are essentially the same. The cloud w i l l collapse nonhomo-logously about a rapidly condensing core''*, which i t s e l f ends up con-taining a smaller and smaller fraction of the cloud's total mass. The bulk of the mass, which forms a sort of cocoon around the condensed central core, w i l l continue to collapse on a longer time scale. A l -i though a roughly spherical isothermally collapsing cloud w i l l not frag-ment in the absence of rotation, i t seems possible that an elongated object w i l l when i t s density increases sufficiently to satisfy Jeans criterion over a fraction of i t s length. Since dust clouds are seldom found to be spherical objects, this may be an important result, and i t w i l l in fact be assisted by rotation. In the above discussion, we suggested that clouds collapse 2 -3 isothermally. Clouds less dense than 10 cm are relatively transparent X-rays and cosmic rays and are therefore characterized by a temperature reflecting an energy balance between these heating sources - as well as 5. The nonhomologous collapse is a result of the fact that the free f a l l time (Spitzer, 1968): = ( 3 7 T / 3 2 . G f » ) i / 2 is shorter, the denser the central region. This result also holds for i n i t i a l l y uniform clouds since in this case a rarefaction wave propagates inward on a time scale small compared to tf 57. the thermal energy due to g r a v i t a t i o n a l collapse — and cooling r e s u l t i n g from fine structure transitions i n C + and other ions which are excited By I n e l a s t i c c o l l i s i o n s with c h i e f l y H and H^. The equilibrium tempera-ture at this density i s 20 - 60 K, depending on the effectiveness of the 2 -3 + various coolants. As the density increases above 10 cm , C cooling beco-es more e f f i c i e n t and the temperature continues to drop. At the same time, heating due to radiation and cosmic rays becomes less important, since the clouds st a r t becoming opaque to these heating sources. This of course also prevents photo-ionization of carbon, so that at a density 3 - 3 of ~10 cm the important heating process i s compression; cooling, on the other hand, i s provided by i n e l a s t i c c o l l i s i o n s between gas mole-cules and dust grains, which radiate i n the infrared. Under these c i r -cumstances, the temperature does not vary much from ^ 10 K for densities - m U -3 up to 10 cm 5 8 . C . O b s e r v a t i o n s o f D u s t C l o u d s B e c a u s e d u s t c l o u d s a r e g e n e r a l l y c h a r a c t e r i z e d by e x c i t a t i o n t e m p e r a t u r e s much l o w e r t h a n t h o s e f o u n d n e a r H I I r e g i o n s and i n f r a r e d s o u r c e s , t h e i r m o l e c u l a r l i n e r a d i a t i o n i s u s u a l l y more d i f f i c u l t t o d e t e c t . N e v e r t h e l e s s i t i s i m p o r t a n t t o o b s e r v e t h e s e o b j e c t s b e c a u s e o f t h e c l u e s t h e y m i g h t g i v e us r e g a r d i n g s t a r f o r m a t i o n . I n t h i s s e c t i o n , we b r i e f l y summar i ze t h e r e s u l t s o f a number o f s u r v e y s made s p e c i f i c a l l y o f d u s t c l o u d s ; we w i l l n o t however d i s c u s s t h e r e s u l t s , o f more g e n e r a l s u r v e y s . I n a d d i t i o n t o t h e s u r v e y w o r k , w h i c h u s u a l l y i n v o l v e s o b s e r v i n g a s i n g l e p o s i t i o n on a number o f c l o u d s , we w i l l a l s o m e n t i o n i n s t a n c e s i n w h i c h d u s t c l o u d s h a v e b e e n mapped , as t h i s p r o -v i d e s v a l u a b l e i n f o r m a t i o n | r e g a r d i n g t h e i r e x c i t a t i o n p r o c e s s e s and i d y n a m i c s . 1 . S u r v e y s o f D u s t C l o u d s , a ) A t o m i c h y d r o g e n . S u r v e y s a t t e m p t i n g t o d e t e c t 21 cm l i n e e m i s s i o n d e f i c i t s i n d a r k d u s t c l o u d s , b e c a u s e t h e h y d r o g e n m i g h t be e i t h e r c o l d o r m o l e c u l a r i n t h e s e o b j e c t s , h a v e b e e n made b y H e i l e s ( 1 9 6 9 ) , Mahoney 0.972) and Knapp ( 1 9 7 2 ) . Of t h e s e s u r v e y s , K n a p p ' s o b s e r v a t i o n s o f some 96 c l o u d s was t h e mos t c o m p r e h e n s i v e and emp loyed t h e b e s t v e l o c i t y r e s o l u t i o n ( ~ 0 . 3 4 k m / s e c ) . On t h e b a s i s o f h e r r e s u l t s , Knapp c o n -c l u d e d t h a t a p p r o x i m a t e l y one t h i r d o f t h e 96 c l o u d s had d e f i n i t e s e l f -a h s o r p t i o n f e a t u r e s , t h a t s e l f - a b s o r p t i o n i s more l i k e l y i f t h e v i s u a l e x t i n c t i o n i s > 3 m ( s i n c e p r e s u m a b l y t h e c l o u d . i s t h e n c o l d e r ) , and t h a t t h e e x c i t a t i o n t e m p e r a t u r e s we re i n t h e r a n g e 16 - 40 K . S i n c e o b s e r v e d OH e x c i t a t i o n t e m p e r a t u r e s i n d a r k d u s t c l o u d s a r e t y p i c a l l y 5 - 10 K , w h i l e t h o s e o f H^CO a r e a l w a y s < 3 K , Knapp was l e d t o i i s u g g e s t t h a t t h e H I was o u t s i d e t h e c l o u d w h i l e t h e m o l e c u l e s w e r e w i t h i n — a r e s u l t c o n s i s t e n t w i t h t h e i d e a t h a t h y d r o g e n w i t h i n d e n s e c l o u d s w o u l d b e p r o t e c t e d f r o m p h o t o - and c o s m i c r a y d i s s o c i a -t i o n , and w o u l d t h e r e f o r e be m o l e c u l a r . b) H y d r o x y l . The f i r s t m o l e c u l a r r a d i a t i o n t o be o b s e r v e d f r o m d u s t c l o u d s was t h e 18 cm / \ - d o u b l e t t r a n s i t i o n s o f OH ( H e i l e s , 1 9 6 8 ) . S h o r t l y t h e r e a f t e r , C u d a b a c k and H e i l e s (1969) o b s e r v e d b o t h OH e m i s -s i o n and a b s o r p t i o n f e a t u r e s i n 20 o f 79 c l o u d s t h e y s u r v e y e d . M o r e r e c e n t s u r v e y s o f h i g h e r s e n s i t i v i t y h a v e d e t e c t e d OH much more f r e -q u e n t l y ( T u r n e r and H e i l e s , 1 9 7 1 ; C r u t c h e r , 1973) and e x c i t a t i o n t e m p e r a t u r e s i n t h e r a n g e 5 - 10 K seem i n d i c a t e d . c ) F o r m a l d e h y d e . S u r v e y s o f b o t h t h e 6 cnv 1.^.-1 r o t a t i o n a l t r a n s i -t i o n o f H 2 C 0 ( P a l m e r e t a l . , 1 9 6 9 ; H e i l e s , 1 9 7 3 ; D i e t e r , 1973) and t h e 2 cm ^i2~^ll r o t a t i ° n a l t r a n s i t i o n ( E v a n s , 1973) have a l s o b e e n made. I n a l l c a s e s o n l y a b s o r p t i o n , a p p a r e n t l y o f t h e 2 .7 K b a c k g r o u n d r a d i a -t i o n , i s s e e n and e x c i t a t i o n t e m p e r a t u r e s d e r i v e d by s t u d y i n g t h e h y p e r f i n e s t r u c t u r e i n d i c a t e v a l u e s n o t much b e l o w 2 . 7 K . A l t h o u g h t h e r e does n o t a p p e a r t o be any abundance d i f f e r e n c e s b e t w e e n I^CO and H i n d u s t c l o u d s compared t o o t h e r s o u r c e s ( D i e t e r , 1 9 7 3 ) , t h e l i n e w i d t h s o f H2CO i n d u s t c l o u d s a r e v e r y n a r r o w ; n a r r o w e r f o r examp le t h a n OH l i n e s i n t h e same s o u r c e s . B e c a u s e k i n e t i c t e m p e r a t u r e s i n d u s t c l o u d s a r e g e n e r a l l y t h o u g h t t o be 2 . 7 K , i t a p p e a r s t h a t t h e f o r m a l d e h y d e must be r e f r i g e r a t e d by some n o n - t h e r m a l p r o c e s s mos t l i k e l y i n v o l v i n g c o l l i s i o n a l p u m p i n g . d) C a r b o n M o n o x i d e . B e c a u s e o f i t s l o w d i p o l e moment, CO i s e a s i l y t h e r m a l i z e d and t h e r e f o r e o b s e r v e d i n d a r k d u s t c l o u d s by means o f i t s 13 l o w e s t r o t a t i o n a l t r a n s i t i o n s . I n a d d i t i o n , t h e i s o t o p i c s p e c i e s CO i s a l s o q u i t e v i s i b l e . F o l l o w i n g an i n i t i a l 12 c l o u d s u r v e y by P e n z i a s e t a l . ( 1 9 7 2 ) , M i l m a n e t a l . (1975) and more r e c e n t l y D i c k m a n (1975b) 12 have made more e x t e n s i v e o b s e r v a t i o n s . D i c k m a n f o r examp le saw CO 13 i n 63 o f 64 c l o u d s and CO i n 52 o f 55 c l o u d s . On t h e b a s i s o f h i s 12 r e s u l t s , he c o n c l u d e d t h a t t h e CO l i n e must be s a t u r a t e d and t h e r e f -o r e c h a r a c t e r i z e d b y an e x c i t a t i o n t e m p e r a t u r e | x e q u a l t o t h e k i n e t i c t e m p e r a t u r e "T^  o f gas w i t h i n t h e s e c l o u d s — t h e a v e r a g e v a l u e b e i n g 9 . 6 K. I n r e l a t e d w o r k , D i c k m a n (1975a) a l s o f o u n d t h a t t h e co lumn 13 d e n s i t y o f t h e n o r m a l l y o p t i c a l l y t h i n CO l i n e was c o r r e l a t e d w i t h Ay t h e v i s u a l e x t i n c t i o n , i f l m < A y < 1 0 m . S i n c e A y i s a l s o c o r -r e l a t e d w i t h t h e m o l e c u l a r h y d r o g e n co lumn d e n s i t y N ( H 2 ) , h e was a b l e t o show t h a t : N ( H 2 ) = ( 4 . 6 ± 2 . 6 ) x 1 0 5 N ( 1 3 C O ) (9) 13 t h a t i s , t h e CO co lumn d e n s i t y c a n be u s e d as a s u r r o g a t e f o r d e t e r -m i n i n g t h e m o l e c u l a r h y d r o g e n co lumn d e n s i t y . We e m p h a s i z e h e r e t h a t 13 N ( CO) i s t h e co lumn d e n s i t y d e r i v e d a s s u m i n g L T E ; we s h a l l p u r s u e t h i s p o i n t when we u s e D i c k m a n ' s r e s u l t . e) Ammonia . I n 1 9 7 3 , Cheung e t a l . (1973) d e t e c t e d t h e 2 3 . 7 GHz ( 1 , 1 ) i n v e r s i o n t r a n s i t i o n o f NH^ i n 4 o f 10 d u s t c l o u d s t h e y s u r v e y e d , w h i l e t h e ( 2 , 2 ) t r a n s i t i o n was n o t d e t e c t e d . The f a i l u r e t o d e t e c t t h e ( 2 , 2 ) t r a n s i t i o n a l l o w e d an u p p e r l i m i t o f 25 K t o be p l a c e d on t h e k i n e t i c t e m p e r a t u r e i n two o f t h e s o u r c e s , and t h i s u p p e r l i m i t i n t u r n a l l o w e d 3 -3 a l o w e r l i m i t o f 3 x 10 cm t o be p l a c e d on t h e m o l e c u l a r h y d r o g e n co lumn d e n s i t y , a r e s u l t c o n s i s t e n t w i t h CO o b s e r v a t i o n s . f ) M e t h y l i d y n e . O b s e r v a t i o n s (Rydbeck e t a l . , 1 9 7 3 ; R y d b e c k e t a l . , 1 9 7 5 ; Zucke rman and T u r n e r , 1975) o f t h e 9 cm A - d o u b l e t t r a n s i t i o n s o f CH h a v e b e e n p a r t i c u l a r l y i n t e r e s t i n g s i n c e CH had e l u d e d r a d i o d e t e c t i o n f o r some t i m e ( d e s p i t e t h e f a c t t h a t i t i s one o f t h e t h r e e m o l e c u l e s known o p t i c a l l y ) and b e c a u s e i t p l a y s an i m p o r t a n t r o l e i n many m o l e c u l e f o r m a t i o n t h e o r i e s . O b s e r v a t i o n a l l y CH a p p e a r s t o b e s t r o n g e s t i n r e g i o n s e x p e c t e d t o c o n t a i n m o l e c u l a r h y d r o g e n , i n p a r t i -c u l a r d a r k c l o u d s , b u t o v e r a l l i t s h a r e s t h e r a t h e r u b i q u i t o u s d i s t r i -b u t i o n o f OH, I^CO and C O , d e s p i t e t h e f a c t t h a t i t i s a v e r y weak l i n e and t h o u g h t t o b e o p t i c a l l y t h i n e v e r y w h e r e . The o b s e r v e d CH l i n e s a p p e a r n a r r o w l i k e H 2 C 0 and p r o b a b l y h a v e t h e same d i s t r i b u t i o n . The f a c t t h a t CH a p p e a r s r e l a t e d t o H 2 s u p p o r t s t h e f o r m a t i o n t h e o r y o f B l a c k and D a l g a r n o (1973) t h a t i t i s f o rmed by t h e r a d i a t i v e a s s o -c i a t i o n o f C + w i t h H 2 ( o r 2 H 2 i n two s t e p s ) f o l l o w e d by d i s s o c i a t i v e r e c o m b i n a t i o n . g) C a r b o n M o n o s u l p h i d e . R e c e n t l y , M a r t i n and B a r r e t t (1975) h a v e s u r v e y e d d a r k c l o u d s f o r t h e \T = 1-0 and 2 - 1 t r a n s i t i o n s o f C S . B e -c a u s e CS h a s a l a r g e d i p o l e moment ( n e a r l y 2 Debye) i t r e q u i r e s p a r t i -c u l a r l y h i g h H 2 d e n s i t i e s t o be t h e r m a l i z e d , and t h e r e f o r e i s u s e f u l l i k e HCN f o r mapp ing d e n s e r e g i o n s . F rom t h e i r o b s e r v a t i o n s o f d a r k 4 -3 c l o u d s , a d e n s i t y 7\ ( H 2 ) > 10 cm i s i n f e r r e d w h i l e t h e abundance —8 —9 r a t i o o f C S / H 2 i s 10 - 10 . The d e r i v e d e x c i t a t i o n t e m p e r a t u r e s a r e i n t h e r a n g e 2 . 9 - 7 . 0 K . 2 . Maps o f D u s t C l o u d s . A l t h o u g h s u r v e y s p r o v i d e u s e f u l s t a t i s t i c s , a s i n g l e a n t e n n a p o s i t i o n on a c l o u d p r o v i d e s v e r y l i t t l e i n f o r m a t i o n r e g a r d i n g t h e g r o s s p r o p e r t i e s o f t h e c l o u d . By c o m p a r i s o n W i t h t h e s u r v e y w o r k d o n e , v e r y l i t t l e mapp ing o f d u s t c l o u d s h a s b e e n d o n e . S o u r c e s s u c h a s S g r B2 o r O r i o n , and p e r h a p s a h a n d f u l o f o t h e r i n t e r e s t i n g s o u r c e s a s s o c i a t e d w i t h i n f r a r e d o b j e c t s , H I I r e g i o n s , n e b u l o s i t y and t h e l i k e , h a v e b e e n mapped t o v a r y i n g d e g r e e s , b u t i s o -l a t e d d u s t c l o u d s h a v e b e e n a l m o s t c o m p l e t e l y n e g l e c t e d . S i n c e mapp ing i s a t e d i o u s a f f a i r , e s p e c i a l l y f o r weak l i n e s , i t i s n o t a t a l l s u r -p r i s i n g t h a t what w o r k h a s b e e n done h a s u t i l i z e d H I o r CO o b s e r v a t i o n s , a) A t o m i c h y d r o g e n . A t a w a v e l e n g t h o f 21 cm, s i n g l e d i s h o b s e r v a t i o n s do n o t r e a l l y h a v e t h e a n g u l a r r e s o l u t i o n t o make m e a n i n g f u l c o m p a r i s o n s w i t h m i l l i m e t e r w a v e l e n g t h r e s u l t s . R e c e n t l y h o w e v e r , C h u (1975) h a s o b t a i n e d i n t e r f e r o m e t e r o b s e r v a t i o n s o f t h r e e d a r k d u s t c l o u d s , one o f w h i c h was L 1 3 4 . B o t h L134 and a s e c o n d c l o u d , L 1 4 9 5 , showed a b s o r p t i o n f e a t u r e s and Chu was a b l e t o a r g u e t h a t t h e a b s o r b i n g gas was c o o l e r 19 20 - 2 t h a n 20 K w i t h a c o l u m n d e n s i t y b e t w e e n 10 and 10 cm . T h i s was 2 3 10 t o 10 t i m e s s m a l l e r t h a n v a l u e s b a s e d on t h e known v i s u a l e x t i n c -t i o n s and an assumed c o r r e l a t i o n b e t w e e n e x t i n c t i o n and t h e a t o m i c 2 1 - 2 h y d r o g e n c o l u m n d e n s i t y ( N ( H I ) ^ 2 x 10 Ay cm ) . The l a t t e r r e -s u l t however was b a s e d on o b s e r v a t i o n s o f gas and d u s t i n t h e d i r e c t i o n o f g l o b u l a r c l u s t e r s (Knapp e t a l . , 1973) and t h e r e f o r e a p p l i e s t o t h e g e n e r a l more d i f f u s e i n t e r s t e l l a r med ium. I n f a c t , Knapp (1972) h a s 19 shown t h a t f o r d e n s e d u s t c l o u d s , t h e r e l a t i o n s h i p : N ( H I ) ~ 6*10 Ay _2 cm , i s more a p p r o p r i a t e . P r e s u m a b l y t h i s r e f l e c t s t h e f a c t t h a t i n d e n s e c l o u d s , t h e h y d r o g e n i s m o l e c u l a r . A s i m i l a r d i s t i n c t i o n howeve r does n o t seem t o a p p l y t o OH, a c o n c l u s i o n w h i c h seems t o i m p l y t h a t OH i s s e e n i n d u s t c l o u d s n o t b e c a u s e i t i s o v e r a b u n d a n t i n t h e s e o b -j e c t s , b u t s i m p l y b e c a u s e t h e y a r e d e n s e r , b) C a r b o n M o n o x i d e . To ou r k n o w l e d g e , t h e o n l y s o u r c e s w h i c h h a v e b e e n mapped i n CO a r e c l o u d s a s s o c i a t e d w i t h r e g i o n s of a c t i v e s t a r f o r m a t i o n . T h e s e i n c l u d e t h e O r i o n m o l e c u l a r c l o u d ( s e e f o r e x a m p l e , P h i l l i p s e t a l . , 1 9 7 5 ) , L 1 6 3 0 (M i lman e t a l . , 1 9 7 5 ) , NGC 5367 (Van T i l l e t a l . , 1 9 7 5 ) , t h e c l o u d n e a r p O p h i u c h i ( E n c r e n a z e t a l . , 1 9 7 5 ) , RCrA ( L o r e n , 1975) and NGC 1333 ( L o r e n , 1 9 7 6 ) . I t was t h e r e f o r e d e c i d e d t o f i n d an i s o l a t e d d a r k d u s t c l o u d , o r l a r g e g l o b u l e , w i t h no o b v i o u s r e l a t e d n e b u l o s i t y o r a d v a n c e d s t a r f o r m a t i o n p r e s e n t , w h i c h m i g h t s e r v e a s a p r o t o t y p e f o r d a r k c l o u d s b e f o r e t h e i r e v o l u t i o n h a s become t o o a d v a n c e d . Once a c l o u d h a s become t o o e v o l v e d , i t s e m i s s i o n i s i n v a r i a b l y d o m i n a t e d b y h e a t i n g p r o c e s s e s r e l a t e d t o n e a r b y o r embedded c o n t i n u u m s o u r c e s . What we w o u l d l i k e t o s t u d y i s o b j e c t s whe re t h i s i s n o t y e t t h e c a s e . 6 4 . D . Why Map L y n d s 134? I n t h e p r e v i o u s s e c t i o n , we i n d i c a t e d t h e n e e d t o map i s o l a t e d d u s t c l o u d s a s a means o f s t u d y i n g t h e i r s t r u c t u r e , c o m p o s i t i o n and t he rmodynamics i n a way w h i c h w o u l d be i n d e p e n d e n t o f e f f e c t s w h i c h n e a r b y o b j e c t s m i g h t h a v e . I f we w e r e t o l i s t a f ew c h a r a c t e r i s t i c s a p o t e n t i a l c l o u d t o be mapped m i g h t h a v e , t h e y w o u l d be t h e f o l l o w i n g : (1) i t mus t be a n a p p a r e n t l y i s o l a t e d o b j e c t away f r o m t h e g a l a c t i c p l a n e , s o t h a t c o n f u s i o n i n r a d i a l v e l o c i t i e s w i l l n o t r e s u l t ; (2) i t must have some v e r y opaque r e g i o n s so t h a t m o l e c u l e s r e q u i r i n g h i g h d e n s i t i e s t o be t h e r m a l i z e d m i g h t be o b s e r v a b l e ; C3) i t must n o t be so e x t e n d e d t h a t mapp ing w i t h a beam o f s e v e r a l a r c m i n u t e s d i a m e t e r w o u l d r e q u i r e a n u n r e a s o n a b l e l e n g t h o f t i m e ; and (4) i t must be a known s o u r c e o f m o l e c u l a r l i n e r a d i a t i o n , i n c l u d i n g d e n s i t y s e n s i t i v e s p e c i e s . (5) F i n a l l y , c l o u d s w h i c h h a v e b e e n mapped i n o t h e r m o l e c u l a r s p e c i e s o r a t o m i c h y d r o g e n w o u l d p r o v i d e a d d i t i o n a l p o s s i b i l i t i e s f o r i n t e r p r e t a t i o n . I f we w e r e t o l o o k t h r o u g h t h e L y n d s c a t a l o g u e ( L y n d s , 1962) o f d a r k n e b u l a e , we w o u l d f i n d many d a r k d u s t c l o u d s w h i c h s a t i s f y t h e f i r s t t h r e e r e q u i r e m e n t s ; t h e f o u r t h r e q u i r e m e n t howeve r n a r r o w s m a t t e r s down c o n s i d e r a b l y s i n c e t h e most f r e q u e n t l y o b s e r v e d d u s t c l o u d s a r e t h o s e w h i c h H e i l e s (1968) f i r s t d e t e c t e d OH e m i s s i o n f r o m , and l a t e r c r u d e l y mapped b o t h i n OH ( H e i l e s , 1970) and H 2 C 0 ( H e i l e s , 1 9 7 3 ) . I f we impose a f i n a l r e q u i r e m e n t t h a t a n H I map h a s b e e n made , we a r e l i m i t e d t o a s i n g l e c l o u d , L 1 3 4 . A l t h o u g h H e i l e s ' o r i g i n a l m o t i v a t i o n f o r o b s e r v i n g L 1 3 4 had been t h a t i t was above t h e h o r i z o n when t h e o t h e r s o u r c e s h e o b s e r v e d were n o t , t h e c u r r e n t m o t i v a t i o n c e r t a i n l y i s d i f f e r e n t . A s p o i n t e d ou t by Chu ( 1 9 7 5 ) , L134 i s a r a t h e r p r i v i l e g e d d a r k d u s t c l o u d , f o r w i t h b 1 1 = 3 5 . 8 ° , i t i s one o f o n l y 13 o b j e c t s w i t h lb11] > 2 6 . 2 ° i n t h e L y n d s c a t a l o g u e o f 1802 d a r k n e b u l a e . I n a d d i t i o n , i f we r e a l i z e t h a t L y n d s a s s i g n e d s e p a r a t e numbers t o o b j e c t s i n t h e same r e g i o n w i t h d i s t i n c t b o u n d a r i e s o r d i f f e r e n t o p a c i t i e s , we may make t h e a d d i t i o n a l comment t h a t L 1 3 4 and i t s n e a r b y c l o u d s f o r m one o f o n l y f i v e g r o u p s o f d a r k d u s t c l o u d s w i t h l b 1 1 ! > 2 6 . 2 ° . L 1 3 4 h a s b e e n mapped i n a t o m i c h y d r o g e n b y S a n c i s i (1971) , who n o t e d a d e f i c i t a t 0 . 5 k m / s e c i n h i s s i n g l e d i s h o b s e r v a t i o n s . Mahoney (1972) o n t h e o t h e r hand n o t e d a b r o a d d e f i c i t w i t h r e s p e c t to t h e s u r r o u n d i n g h y d r o g e n a t + 3 . 0 k m / s e c . B o t h H e i l e s (1969) and Knapp (1972) however f a i l e d t o d e t e c t s e l f - a b s o r p t i o n f e a t u r e s , p e r h a p s b e c a u s e o f t h e i r method o f o b s e r v i n g , w h i c h i n c l u d e d o n l y a s i n g l e r e -f e r e n c e p o s i t i o n . I n any e v e n t , t h e r e i s no l o n g e r any d o u b t a b o u t t h e r e a l i t y o f t h e H I d e f i c i t s , s i n c e Chu (1975) h a s made i n t e r f e r o -m e t e r o b s e r v a t i o n s o f L134 w h i c h r e s o l v e ou t t h e b a c k g r o u n d HI and show two d i s t i n c t a b s o r p t i o n f e a t u r e s a t 0 . 7 and 2 . 7 k m / s e c . I n a d d i t i o n t o t h e s e 21 cm r e s u l t s , L 1 3 4 h a s b e e n o b s e r v e d t o 12 13 e m i t r a d i a t i o n f r o m OH a t 18 cm, ^ C O a t 6 cm, CO a t 2 . 6 mm, CO a t 2 . 7 mm, CS a t 6 . 1 and 3 . 1 mm, CH a t 9 cm and Xogen a t 3 . 4 mm. The r e s u l t s o f t h e s e o b s e r v a t i o n s a r e summar i zed i n T a b l e I I I , w h i c h f o r Table III. Positive Molecular Line Results near L134 0H a' b H2COC 1 2C0 d' e 1 3 C 0 d ' e CS(6.1mm)f CS(3.1mm)f NH3S CH h Xogen1 L134 AT .35 -.36 7.0 3.0 1.0 0.15 0.15 V 3.02 2.3 3.7 3.0 .... 2.8 3.0 2.0 AV 0.4 0.6 2.3 1.9 0.7 1.1 0.8 L169 AT 0.06 -.14 5.2 1.8 V 2.3 9.8 1.9 1.6 AV 2.1 0.5 1.4 1.7 L183/L1841 AT 0.19 -.14 7.0 2.2 v 0.32 0.15k V 2.1 2.0 2.9 3.3 2.5 2.7 AV 1.4 1.3 0.9 1.3 1.0 0.8 L1778/L1780 AT -.20 3.7 V 3.1 3.4 AV 0.4 1.1 • Notes to the table: a. Heiles, 1968 b. Heiles, 1969 c. Heiles, 1973 d. Milman et a l . 1975 e. Dickman, 1975 f. Martin and Barrett, 1975 g. Cheung et a l . , 1973 h. Rydbeck et a l . , 1975 i . Snyder and Buhl, 1971 j . This result reflects the unknown rest frequency for Xogen k. These results are listed as L134N. In fact, the source i s L183 1. L183 and L184 are the same source i n Lynds (1962) catalogue of dark nebulae. ON ON c o m p l e t e n e s s a l s o i n c l u d e s r e s u l t s f o r L 1 6 9 , L 1 8 3 / L 1 8 4 , and L 1 7 7 8 / L 1 7 8 0 . The l a t t e r a r e L y n d s c l o u d s w h i c h a r e w i t h i n a f e w d e g r e e s o f L134 and t h e y a r e i n c l u d e d h e r e s i n c e i t seems l i k e l y t h a t w h a t e v e r p r o c e s s gave r i s e t o L 1 3 4 ' s h i g h l a t i t u d e must a l s o h a v e g i v e n r i s e t o t h e s e o b j e c t s . A f i n a l r e m a r k r e g a r d i n g T a b l e III i s t h a t A T i s n o r m a l l y t h e o b s e r v e d a n t e n n a t e m p e r a t u r e i n K e l v i n , V i s t h e v e l o c i t y w i t h r e s p e c t t o t h e l o c a l s t a n d a r d o f r e s t i n k m / s e c , and fiV i s t h e l i n e f u l l w i d t h a t h a l f i n t e n s i t y i n k m / s e c . F u r t h e r d i s c u s s i o n o f t h e r e s u l t s p r e s e n t e d i n t h i s t a b l e w i l l be g i v e n i n C h a p t e r IX. From t h e above d i s c u s s i o n , i t i s c l e a r t h a t L y n d s 134 has b e e n a p a r t i c u l a r l y p r o f i t a b l e s o u r c e t o o b s e r v e . B e c a u s e o f t h i s and t h e f a c t t h a t i t a p p e a r s t o be p r o t o t y p i c o f d a r k d u s t c l o u d s o r l a r g e g l o b u l e s , i t was d e c i d e d t o map i t by o b s e r v i n g t h e J = 1-0 12 13 18 t r a n s i t i o n o f C O , CO and C 0 . The r e s u l t s o f t h e s e o b s e r v a t i o n s a r e p r e s e n t e d i n t h e f o l l o w i n g c h a p t e r s . Chapter VII Data Acquisition A. The Site The observations of L134 which we describe here were obtained during the period November 5-16, 1975, using the 4.6 meter paraboloid at the Aerospace Corporation^", E l Segundo, California. The telescope is located at a longitude of 118° 22' 28.05" West and a latitude of 33° 54' 52.56" North, and is at an elevation of 38 meters above sea level. During the period of the observations L134 was generally ob-servable for about seven hours a day starting at approximately 09:00:00 Pacific Standard Time. Although the start was hampered on occasion by morning fog, observing conditions overall were excellent, with typical mean zenith attenuations being 0.52 and 1.52 dB at 110 and 115 GHz, respectively. 6. The Aerospace spectral line radio astronomy program i s supported jointly by National Science Foundation Grant MPS 73-04554 and the Aerospace Company Programs for Research and Investigation. B. The R e c e i v e r T h e r e a r e a number o f d i f f e r e n c e s w h i c h e x i s t b e t w e e n t h e A e r o s p a c e CO r e c e i v e r and t h e one w h i c h was d e s c r i b e d i n t h e f i r s t P a r t o f t h i s t h e s i s . The mos t n o t e w o r t h y a r e i t s p h a s e l o c k s y s t e m and i t s f r e q u e n c y s w i t c h i n g c a p a b i l i t y . The LO k l y s t r o n i s p h a s e l o c k e d b y m i x i n g a s m a l l f r a c t i o n o f i t s o u t p u t power w i t h a h i g h h a r m o n i c o f a 2 GHz p h a s e l o c k o s c i l l a -t o r , w h i c h i t s e l f i s l o c k e d t o a 100 MHz f r e q u e n c y s y n t h e s i z e r . T h i s m i x i n g p r o d u c e s a 425 MHz I F w h i c h i s s y n c h r o n o u s l y d e t e c t e d a g a i n s t a r e f e r e n c e o s c i l l a t o r n e a r 425 MHz t o p r o v i d e an e r r o r v o l t a g e f o r t u n i n g t h e k l y s t r o n r e f l e c t o r . When a f r e q u e n c y s w i t c h e d s y s t e m i s u s e d h o w e v e r , t h e 425 MHz I F i s a l t e r n a t e l y s w i t c h e d b e t w e e n two r e -f e r e n c e o s c i l l a t o r s n e a r 425 M H z , w i t h t h e l i n e w i t h i n t h e r e c e i v e r band p a s s d u r i n g one h a l f c y c l e , and o u t s i d e i t d u r i n g t h e o t h e r . F o r n a r r o w l i n e s o r a s u f f i c i e n t l y w i d e band p a s s , h o w e v e r , t h e r e -f e r e n c e o s c i l l a t o r s c a n be a r r a n g e d so t h a t f o r b o t h t h e s i g n a l and r e f e r e n c e h a l f c y c l e s t h e l i n e i s w i t h i n t h e r e c e i v e r b a n d p a s s , b u t d i s p l a c e d i n f r e q u e n c y . S i n c e t h e two h a l f c y c l e s a r e s u b t r a c t e d , t h e l i n e h a s o p p o s i t e s e n s e i n e a c h h a l f o f t h e b a n d p a s s , b u t on " f o l d i n g " ( t h a t i s , s h i f t i n g , i n v e r t i n g and a v e r a g i n g ) t h e o b s e r v e d s p e c t r u m , a f a c t o r o f i n s i g n a l t o n o i s e i s g a i n e d o v e r t h e s i t u a -t i o n when t h e l i n e does n o t a p p e a r d u r i n g t h e r e f e r e n c e h a l f c y c l e . O t h e r p o i n t s to n o t e about , t h e A e r o s p a c e f r o n t - e n d a r e t h a t t h e f i r s t I F a m p l i f i e r i s a 1 .39 GHz p a r a m p , and t h a t t h e k l y s t r o n and m i x e r t u n i n g i s done r e m o t e l y f r o m t h e c o n t r o l room u s i n g s e r v o s . The A e r o s p a c e b a c k - e n d on t h e o t h e r hand i s u n d e r c o m p u t e r c o n t r o l and u t i l i z e s two 64 c h a n n e l f i l t e r s p e c t r o m e t e r s i n p a r a l l e l — one o f 1 MHz r e s o l u t i o n and t h e o t h e r o f 250 KHz r e s o l u t i o n . The s p e c t r o m e t e r o u t p u t i s i n t e g r a t e d i n a Nova 800 Compu te r and c a n be d i s p l a y e d on a v i s u a l d i s p l a y u n i t . The command l a n g u a g e u s e d i s t h e FORTH l a n g u a g e d e v e l o p e d f o r N . R . A . O . a t K i t t P e a k (Moore and R a t h e r , 1 9 7 3 ) , b u t i t i s n o t u s e d t o c o n t r o l t h e t e l e s c o p e . T h i s i s done u s i n g a s e p a r a t e compu te r w h i c h a c c e p t s s o u r c e c o - o r d i n a t e s e n t e r e d v i a thumbwheels and t h e n a u t o m a t i c a l l y makes p o i n t i n g c o r r e c t i o n s f o r r e f r a c t i o n due t o t h e e a r t h ' s a tmosphe re and f o r t i l t due t o t h e d i f f e r e n t i a l t h e r m a l e x p a n s i o n o f t h e b u i l d i n g on w h i c h t h e t e l e s c o p e i s m o u n t e d . The p o i n t i n g a c c u r a c y o f t h e A e r o s p a c e t e l e s c o p e i s n o m i n a l l y ± 10 a r c s e c o n d s and t h i s was c o n f i r m e d s e v e r a l t i m e s d u r i n g t h e c u r r e n t work by m a k i n g o b s e r v a t i o n s o f t h e s u n . 71. C . The O b s e r v a t i o n s I n F i g u r e 8 a r e shown t h e p o s i t i o n s a t w h i c h CO o b s e r v a t i o n s o f L134 w e r e made. The numbers i n t h i s f i g u r e a r e c e n t e r e d a t t h e 2 . 5 ' beam p o s i t i o n s and i n g e n e r a l a r e l o c a t e d a t t h e v e r t i c e s o f a n u n f i l l e d 4 ' g r i d c e n t e r e d abou t a n o m i n a l c e n t e r p o s i t i o n f o r L134 o f : a ( 1 9 5 0 ) : 1 5 h 5 1 m 0 0 s 5 ( 1 9 5 0 ) : - 0 4 ° 3 0 ' 0 0 s T h i s c e n t e r p o s i t i o n i s u s e d f o r a l l f i g u r e s p r e s e n t e d i n t h i s t h e s i s . The numbers t h e m s e l v e s h a v e no s i g n i f i c a n c e b e y o n d t h e f a c t t h a t t h e y we re c h o s e n t o f a c i l i t a t e t h e a n a l y s i s ; t h e y do n o t r e p r e s e n t t h e s e -12 quence o f t h e o b s e r v a t i o n s . CO was o b s e r v e d a t a l l t h e s e p o s i t i o n s ; 13 18 CO, a t p o s i t i o n s numbered l e s s t h a n o r e q u a l t o 3 5 , and C 0 a t p o s i t i o n s numbered l e s s t h a n o r e q u a l t o 1 7 . A summary o f t h e a c t u a l o b s e r v i n g p r o g r a m i s p r e s e n t e d i n T a b l e l V . A l l t h e o b s e r v a t i o n s p r e s e n t e d h e r e , w i t h t h e e x c e p t i o n o f t h o s e f o r November 6 , 1 9 7 5 , w e r e made w i t h t h e l i n e i n t h e u p p e r s i d e 13 band (USB) o f t h e r e c e i v e r . On November 6 , CO was o b s e r v e d i n t h e l o w e r s i d e band (LSB) s i n c e i t was t h o u g h t t h a t t h e k l y s t r o n u s e d m i g h t o t h e r w i s e b e o u t s i d e i t s p r a c t i c a l t u n i n g r a n g e . T h i s s u b s e -q u e n t l y t u r n e d ou t n o t t o be t h e c a s e . The v a l u e s o f T i n d i c a t e d i n T a b l e IV r e p r e s e n t t h e mean z e n i t h a t t e n u a t i o n ( i n n e p e r s ) as d e t e r m i n e d by t h e A e r o s p a c e t e l e s c o p e " t i p p i n g " p r o c e d u r e f o r m e a s u r i n g t h i s v a r i a b l e . I t was n o r m a l l y measu red a t t h e b e g i n n i n g and end o f e a c h d a y ' s o b s e r v a t i o n s , and u n d e r n o r m a l c i r c u m s t a n c e s w o u l d h a v e b e e n u s e d i n t h e s u b s e q u e n t d a t a c a l i -72. ° l -5 1.0 0.5 0.0 -0.5 -1.0 -1.5 1 1 L Y N D S I 1 3 4 BEAM P O S I T I O N S 20 3 4 19 35 31 7 17 3 2 40 36 13 6 2 - 41 2 3 2 2 21 8 1 9 10 2 4 2 5 3 9 3 7 11 3 12 4 2 14 3 8 4 15 16 2 8 5 2 7 2 9 18 2 6 30 I l— 3 3 I i - i 1.5 1.0 0.5 0.0 -0.5 -1.0 RIGHT A S C E N S I O N (MIN) (4) tVJ co o a r cn b i ro r Figure 8. 73. Table IV. Summary of the L134 Observing Program. DATE(1975) ISOTOPE3 T(nepers) POSITIONS OBSERVEDk Nov. 5 12 .44 - .355 1 - 10, 18 - 25 Nov. 6 13 .28 1 - 4, 6 - 10, 18, 20, 21, 23, 25 Nov. 7 18 .245 1, 4, 10 Nov. 8 18 .24 - .20 1, 3, 8, 9 Nov. 9 18 .18 - .155 1, 2, 6, 7 Nov. 10 18 .345 - .21 1, 2, 11, 12 Nov. 11 18 .15 - .105 3, 13, 14, 16 Nov, 12 18 .105 - .095 5, 15, 16, 17 Nov. 13 13 .113 - .105 2 - 5, 11 - 18 Nov. 14 13 .12 - .125 1, 6 - 10, 19 - 24, 26 - 30 Nov. 15 13 .147 1, 22, 27, 30 - 35 12 .30 - .36 1, 12, 15, 16, 26, 27, 30, 3 Nov. 16 12 .34 - .505 2 - 6, 8 - 9, 11, 13, 14, 17 23, 28, 29, 31, 32, 34 - 42 Notes to the Table: 12 a. 12 means CO 13 13 means CO 18 18 means C 0 b. See Figure 8 for position locations 74. b r a t i o n t o a c c o u n t f o r t h e a b s o r p t i o n due t o t h e e a r t h ' s a t m o s p h e r e . The a v a i l a b l e c u r v e s f o r d e t e r m i n i n g f f r o m t h e " t i p p i n g " measu remen ts however a p p l i e d t o a n o t h e r r e c e i v e r w h i c h had a 1090 MHz f i r s t I F ; t h e y do no t seem t o a p p l y t o t h e 1390 MHz I F w h i c h we u s e d . Our c a l i b r a t i o n p r o c e d u r e i s d e s c r i b e d i n t h e f o l l o w i n g c h a p t e r . The r e m a i n i n g co lumns i n T a b l e IV enumera te t h e i s o t o p e s o b -s e r v e d on a g i v e n day and t h e p o s i t i o n s a t w h i c h t h e y w e r e o b s e r v e d . The p o s i t i o n numbers a r e t h o s e o f F i g u r e 8 . D u r i n g t h e c o u r s e o f t h e o b s e r v a t i o n s D o p p l e r s h i f t s due t o t h e e a r t h ' s o r b i t a l and r o t a t i o n a l m o t i o n w e r e removed by m a n u a l l y t u n i n g t h e 100 MHz f r e q u e n c y s y n t h e s i z e r so t h a t t h e l i n e a l w a y s a p p e a r e d a t a v e l o c i t y o f +3 k m / s e c w i t h r e s p e c t t o t h e l o c a l s t a n d a r d o f r e s t . 12 F o r t h e November 5 CO o b s e r v a t i o n s h o w e v e r , t h e s e t u n i n g c o r r e c t i o n s we re no t a v a i l a b l e s o t h a t t h e d a t a was l a t e r s h i f t e d d u r i n g i t s a n a -l y s i s . T h i s i s a l s o d i s c u s s e d i n t h e f o l l o w i n g c h a p t e r . 12 W i t h a few e x c e p t i o n s , t h e CO r e s u l t s a t e a c h p o s i t i o n g e n e r a l l y i n v o l v e one 15 m i n u t e o r two 10 m i n u t e i n t e g r a t i o n s ; t h e 13 18 CO r e s u l t s , two 15 m i n u t e i n t e g r a t i o n s ; and t h e C 0 r e s u l t s , f o u r t o s i x 20 m i n u t e i n t e g r a t i o n s . T h i s r e s u l t e d i n a t y p i c a l s i g n a l t o p e a k - t o - p e a k n o i s e r a t i o o f a b o u t s i x a t t h e s t r o n g e r l i n e p o s i t i o n s . No t a l l o f t h e s e s h o r t i n t e g r a t i o n s ( o r s c a n s ) w e r e n e c e s s a r i l y o b -t a i n e d on t h e same d a y , b u t t h o s e t h a t w e r e , w e r e u s u a l l y a v e r a g e d t o -g e t h e r u s i n g an o n - l i n e d a t a r e d u c t i o n p r o g r a m . T h i s was done t o r e -duce t h e amount o f d a t a w h i c h w o u l d h a v e t o b e h a n d l e d i n t h e s u b s e -quen t a n a l y s i s . I n a d d i t i o n , i t s h o u l d be p o i n t e d ou t t h a t b e c a u s e f r e q u e n c y s w i t c h i n g w i t h i n t h e s p e c t r o m e t e r b a n d p a s s was u s e d t o o b t a i n a l l t h e L134 r e s u l t s , u s e was made o f a n o t h e r o n - l i n e p r o g r a m t o f o l d ( t h a t i s , s h i f t , i n v e r t and a v e r a g e ) t h e i n d i v i d u a l s c a n s . B a s e l i n e s l o p e s w e r e a l s o removed ( t o f i r s t o r d e r ) a t t h i s t i m e . To c h e c k f o r p o s s i b l e r e c e i v e r g a i n v a r i a t i o n s f r o m day t o d a y , o r t o o b t a i n b e t t e r s i g n a l t o n o i s e , a few L134 p o s i t i o n s w e r e o b s e r v e d more f r e q u e n t l y t h a n i n d i c a t e d a b o v e . I n a d d i t i o n , DR21 was o b s e r v e d a t t h e end o f e a c h d a y ' s o b s e r v a t i o n s , and on some o c c a s i o n s , W51 as w e l l . O r i o n A r e s u l t s w e r e a l s o b o r r o w e d f r o m o t h e r o b s e r v e r s s i n c e i t was n o t v i s i b l e d u r i n g ou r a l l o t t e d t i m e . The p u r p o s e f o r o b t a i n i n g t h e s e a d d i t i o n a l r e s u l t s was t o h a v e some means o f c o m p a r i n g our t e m p e r a t u r e s c a l e w i t h t h a t o f o t h e r o b s e r v e r s . Of t h e s e t h r e e r e f e r e n c e s o u r c e s , DR21 was o b s e r v e d mos t f r e q u e n t l y and a l w a y s w i t h a v e r y h i g h s i g n a l t o n o i s e . I n f a c t t h e r e p e a t a b i l i t y o f t h e DR21 o b s e r v a t i o n s p r o v i d e s a v e r y good c h e c k on t h e r e c e i v e r g a i n s t a b i l i t y and t h e v a l i d i t y o f ou r f i n a l c a l i b r a t i o n . T h i s i s d i s c u s s e d f u r t h e r i n t h e f o l l o w i n g C h a p t e r . The f i n a l p o i n t w h i c h mus t b e d i s c u s s e d i s ou r c a l i b r a t i o n o f a n t e n n a t e m p e r a t u r e s . The t e c h n i q u e u s e d was t h e " s t a n d a r d " c h o p p e r w h e e l method d e s c r i b e d by P e n z i a s and B u r r u s ( 1 9 7 3 ) , w h i c h i n v o l v e s r o t a t i n g an amb ien t t e m p e r a t u r e a b s o r b e r i n f r o n t o f t h e f e e d . I n t h i s w a y , t h e s y n c h r o n o u s l y d e t e c t e d o u t p u t b e t w e e n t h e a b s o r b e r and t h e s k y p r o v i d e s i n t e n s i t y / t e m p e r a t u r e c a l i b r a t i o n f a c t o r — p r o v i d e d t he t e m p e r a t u r e i s known. F o r r e a s o n s w h i c h w i l l be d i s c u s s e d s h o r t l y , t h e t e m p e r a t u r e d i f f e r e n c e was h e l d c o n s t a n t d u r i n g o b s e r v a t i o n s and then corrected after the fact. In general these calibrations were made whenever a change in the receiver total power was noted. This would result either from changes in the sky temperature or from receiver gain variations; the former would occur at large air masses or during changing weather conditions, while the latter resulted on occasion from heating of the f i r s t IF parametric amplifier. In either of these situations, calibrations would be made after each scan. In regard to the calibration, we mention a f i n a l point as i t bears on the discussion i n the following chapter,and this i s that when-ever a calibration was performed, the data acquisition system also c a l -culated a value for the system temperature T S » defined by the relation: TS = ^ 5 - TL do) In this expression, S represents the signal level looking at the sky; [_ , the level looking at the ambient temperature load; and JE. > a receiver zero level. The brackets indicate that an average i s made over 64 spectrometer channels, while Tj^  i s the value for the calibra-tion temperature (that i s , the load minus sky temperature) which i s held constant during observations. Now i f we consider a double side band receiver with gains Gs and Gj, in the signal and image bands respectively, and assume that the mechanisms responsible for an aper-ture efficiency different from unity re-radiate at the ambient temperature "Tj , then i t is easy to show that: S - Z * and where and (12) ~n<nj<v is the double side band (DSB) system noise, Ta, is the atmospheric temperature, TTg is the signal band zenith attenuation, T i is the image band zenith attenuation, A is the number of air masses the telescope "sees"; i t is equal to A&c(£) , where i. i s the zenith distance. Using these results, equation (10) becomes (on dropping the average): (13) where we have introduced the notation T" = ( T i + ts)/2- for the mean zenith attenuation, for the relative side band zenith attenuations and for the relative sideband receiver gains. This result w i l l be of considerable importance in the following chapter. Chapter VIII Data Reduction and Analysis A. Calibration In this section we discuss the problems, theory and practi-c a l i t i e s of calibrating a temperature scale for millimeter wave observa-tions. We do this because the methods used here are not conventional, and yet are shown to produce very reliable results. The method i s particularly applicable to source mapping observations. 1. The Problems. The calibration of radio astronomical ob-servations i s normally a two step process: f i r s t , an observed signal intensity i s converted to an antenna temperature, , by assuming the Rayleigh-Jeans approximation and comparing the observed signal to a calibration source of known temperature. The second step i s to correct for atmospheric losses, antenna losses and a number of convolution effects to determine the true source brightness (or equivalent black body) temperature. At millimeter wavelengths, and in particular for the J" = 1-0 CO observations with which we shall be concerned here, a number of d i f f i c u l t i e s arise. F i r s t , the determination of is hampered since i t i s nor-mally calibrated using the chopper wheel technique mentioned earlier for which the calibration temperature is not fixed. It i s therefore common to f i x the calibration temperature during observations and then correct afterwards when the behaviour of the calibration tempera-ture has been determined. T h i s however r e q u i r e s ' t h a t t h e s i d e b a n d g a i n s and z e n i t h a t t e n u a t i o n s be known when i n f a c t mos t c u r r e n t l y u s e d m i l l i m e t e r r e -c e i v e r s c a n n o t d i s c r i m i n a t e b e t w e e n t h e two r e c e i v e r s i d e b a n d s . A s a r e s u l t , t h e r e i s no c o n v e n i e n t way t o measu re s e p a r a t e l y t h e g a i n s i n t h e s i g n a l and image b a n d s . I n a d d i t i o n , a number o f a t m o s p h e r i c w a t e r v a p o u r and o x y g e n a b s o r p t i o n l i n e s c a u s e t h e z e n i t h a t t e n u a t i o n t o v a r y s i g n i f i c a n t l y be tween t h e image and s i g n a l s i d e b a n d s — and 12 o f t e n i n a n o n - l i n e a r manne r . M o r e s p e c i f i c a l l y , t h e 115 GHz CO l i n e i s on t h e s t e e p l y r i s i n g s i d e o f a n a t m o s p h e r i c o x y g e n l i n e and t h i s c a u s e s t h e s i g n a l z e n i t h a t t e n u a t i o n T$ t o be s i g n i f i c a n t l y d i f f e r e n t f r o m t h a t i n t h e image b a n d , X i . . ( T h i s however i s n o t as 13 18 s e r i o u s a p r o b l e m f o r t h e ~ 1 1 0 GHz CO and C 0 l i n e s w h i c h a r e i n t h e more s l o w l y v a r y i n g w i n g o f t h i s a b s o r p t i o n l i n e . ) The p r o b l e m however i s n o t t h a t Tg and 1*1 a r e d i f f e r e n t , b u t r a t h e r how t o measure t hem. P r e s u m a b l y t h i s c a n be done w i t h a s u f f i c i e n t l y l o w IF t h a t t h e z e n i t h a t t e n u a t i o n d o e s n o t v a r y much b e t w e e n t h e u p p e r and l o w e r s i d e b a n d s , b u t t h e more common p r a c t i c e i s t o a c k n o w l e d g e t h e f a c t t h a t " t i p p i n g " e x p e r i m e n t s u s e d t o measu re t h e z e n i t h a t t e n u a t i o n d e t e r m i n e o n l y a n a v e r a g e a t t e n u a t i o n TT be tween t h e two s i d e b a n d s , w h i c h , i f a r e l a t i o n s h i p be tween X j and Xj , i s known o r a s s u m e d , d e t e r m i n e s t h e s i g n a l a t t e n u a t i o n . A s w i l l be d i s c u s s e d b e l o w , a d i f f e r e n t a p p r o a c h was r e q u i r e d t o s e p a r a t e t$ and TTi f o r t h e L134 o b s e r v a t i o n s . 2 . A R e v i e w o f What i s M e a s u r e d . B e f o r e d i s c u s s i n g o u r a p p r o a c h t o t h e c a l i b r a t i o n p r o b l e m , we f i r s t r e c a l l a f ew s i m p l e r e -s u l t s w h i c h w i l l f a c i l i t a t e t h i s and l a t e r d i s c u s s i o n s . I f we c o n s i d e r a simple model in which a cloud of optical depth T is bathed in iso-tropic continuum radiation characterized by a specific intensity I_, then i t is easy to show that the transfer of line radiation through this cloud w i l l be described by a specific intensity: i L = i x ( i - e- T ) + i c tx (IA) where ix' = ( e W A T x - 1 ) " 1 C (15) is the Planck function — characterized by a temperature I ^ — which describes the equivalent black body intensity of the line photons. (In this development, a l l variables are assumed to be functions of the frequency U , while the constants have their usual meanings.) During our observations, a nearby portion of the frequency spectrum devoid of spectral features (and therefore characterized by the specific intensity !.£,), w a s synchronously subtracted from I L , so that the quantity effectively observed was: A I * ^ i L - I C = ( l X - I c ) ( i - e - T ) ( 1 6 ) The measured quantity however is not A I } since has been altered by atmospheric losses ( O 5 )» the forward beam coupling efficiency ( T^j. )» antenna losses ( ), and f i n a l l y , receiver gain ( Gs ), and spectral response ( 7 ^ ) . Therefore the measured specific intensity i s : w h i c h , by means o f t h e R a y l e i g h J e a n s r e l a t i o n s h i p : (18) may be a s s i g n e d a r a d i a t i o n o r R a y l e i g h - J e a n s t e m p e r a t u r e <X< — p r o v i d e d t h e i n t e n s i t y s c a l e i s c a l i b r a t e d a g a i n s t a r e f e r e n c e s o u r c e o f known r a d i a t i o n t e m p e r a t u r e . Now t h e r a d i a t i o n t e m p e r a t u r e c o r r e s p o n d i n g t o i s j u s t t h e a n t e n n a ' t e m p e r a t u r e w h i l e t h a t a s s i g n e d t o AX i s T"A , w h i c h i s known v a r i o u s l y a s t h e c o r r e c t e d a n t e n n a t e m p e r a t u r e o r t h e e x c e s s r a d i a t i o n t e m p e r a t u r e ^ " . U s i n g t h e s e d e f i n i t i o n s e q u a t i o n (17) may b e 8 w r i t t e n . TA* - TA e ^ / G . , , ^JLVf^A (19) w h i l e u s i n g t h e R a y l e i g h - J e a n s r e l a t i o n , e q u a t i o n (16) may be w r i t t e n : T a * - ( J * - J c ) ( i - e" 1 ) (20) I n t h i s r e s u l t , w h i c h we w i l l need l a t e r , J~ x and <JC r e f e r t o t h e R a y l e i g h - J e a n s • t e m p e r a t u r e s c o r r e s p o n d i n g t o t h e t r u e s o u r c e e x c i t a t i o n and c o n t i n u u m t e m p e r a t u r e s and ~TQ r e s p e c t i v e l y , w h i c h a r e u s e d i n 7 . T h i s name d e r i v e s f r o m t h e f a c t t h a t A I * i s t h e e x c e s s e m i s s i o n o f t h e l i n e r a d i a t i o n o v e r t h e c o n t i n u u m r a d i a t i o n . 8 . Some a u t h o r s e x c l u d e a n d / o r 7^ , f r o m t h i s d e f i n i t i o n . e q u a t i o n (15) t o f i x t h e e q u i v a l e n t b l a c k body s p e c i f i c i n t e n s i t i e s Ix and 1^ • I n w r i t i n g e q u a t i o n (19) we have assumed t h a t "T^  h a s b e e n c a l i b r a t e d . A s p o i n t e d ou t e a r l i e r h o w e v e r , t h i s i s d i f f i c u l t t o do d u r i n g o b s e r v a t i o n s s i n c e , f o r c h o p p e r w h e e l c a l i b r a t i o n s , t h e c a l i b r a t i o n t e m p e r a t u r e c h a n g e s . The n o r m a l p r o c e d u r e t h e r e f o r e i s t o s e t i t t o a f i x e d v a l u e , s a y t h e a m b i e n t o r l o a d t e m p e r a t u r e , and t h e n make a c o r r e c t i o n l a t e r . I f t h i s i s d o n e , t h e n t h e m e a s u r e d a n t e n n a t e m p e r a t u r e i s : where L and S r e p r e s e n t t h e s i g n a l i n t e n s i t y o f t h e l o a d and s k y , r e s p e c t i v e l y , d u r i n g a g i v e n c h o p p e r w h e e l c a l i b r a t i o n . I t i s t h e n t o be remembered , t h a t once t h e l o a d m i n u s s k y t e m p e r a t u r e ~^~t~& ( t h a t i s , t h e c a l i b r a t i o n t e m p e r a t u r e ) h a s b e e n d e t e r m i n e d , T " A mus t be s c a l e d by (Xx.-A> ) • E q u a t i o n (19) may t h e n be c a s t i n t h e f o r m : T* _ TA h7.„ e T ' A j ( 2 2 ) If V*. I G5 ty Ti / S i n c e we s h a l l assume Tjj and 7 ^ t o b e known , a l l t h a t r e m a i n s i s t o e v a l u a t e t h e q u a n t i t y i n c u r l y b r a c k e t s i n e q u a t i o n ( 2 2 ) . I f we u s e e q u a t i o n s (11) and (12) o f t h e p r e v i o u s c h a p t e r , T j , ^ c a n be w r i t t e n : = Gs^{T t-*-Ta(e-c^-l)} + Gi^{T^T . (e - i : i A - l )} (23) s u b j e c t t o t h e c o n d i t i o n G$ + Gl 9 1 • T h e r e f o r e , i f we u s e t h e same d e f i n i t i o n s we u s e d e a r l i e r f o r t h e mean z e n i t h a t t e n u a t i o n ) , t h e r e l a t i v e s i d e b a n d z e n i t h a t t e n u a t i o n (c(~ti./ts), and t h e r e l a t i v e s i d e b a n d g a i n (j3 = Gi /Gs )> e q u a t i o n (22) may be 9 . w r x t t e n : (24) The p u r p o s e f o r w r i t i n g t h i s e x p r e s s i o n i n te rms o f T i s o f c o u r s e t h a t o n l y t h e mean z e n i t h a t t e n u a t i o n c a n b e c o n v e n i e n t l y f o u n d i n " t i p p i n g " m e a s u r e m e n t s . T h e r e i s now t h e d i f f i c u l t y howeve r t h a t cX and 3^ a r e unknown. T h i s p r o b l e m i s n o r m a l l y a v o i d e d by a s s u m i n g t h a t t h e r e l a t i v e g a i n i n t h e two s i d e bands i s u n i t y ( t h a t i s , |S = 1) and by a d o p t i n g a v a l u e f o r t h e r e l a t i v e z e n i t h a t t e n u a t i o n , 0( Once t h i s h a s b e e n done e q u a t i o n (24) i s o f t e n u s e d t o e m p i r i c a l l y d e -t e r m i n e b e s t f i t v a l u e s f o r Tj. and T^ by f i t t i n g o b s e r v a t i o n s o f a " s t a n d a r d " s o u r c e s u c h a s O r i o n A . A l t h o u g h t h i s p r o c e d u r e h a s b e e n u s e d i n t h e p a s t a t A e r o s p a c e , i t had n o t y e t b e e n c a r r i e d o u t f o r t h e I F w h i c h we u s e d i n ou r o b s e r v a t i o n s . . A s a r e s u l t , some o t h e r method had t o be d e v e l o p e d f o r c a l i b r a t i n g t h e L134 o b s e r v a t i o n s . I t w i l l be b a s e d on e q u a t i o n (24) b u t w i l l make no a s s u m p t i o n s r e g a r d i n g & and 3^ . I n s t e a d , we w i l l s i m p l y r e q u i r e t h a t v a l u e s be u s e d w h i c h make \ f o r 9 . I t s h o u l d be e m p h a s i z e d t h a t t h i s r e s u l t assumes t h a t t h e c a l i b r a t i o n t e m p e r a t u r e w a s s e t e q u a l t o "Tj_ d u r i n g t h e o b s e r v a t i o n s ; i f i t w a s n ' t , 7^ i n t h e d e n o m i n a t o r o f e q u a t i o n (24) must be c h a n g e d . 84. for a given p o s i t i o n independent of the a i r mass A- This i s an ob-vious p h y s i c a l requirement. 3. The C a l i b r a t i o n Method Adopted. Because " t i p p i n g " measure-ments used to determine the mean zenith attenuation T were generally made only at the beginning and end of each day's observations, i t was decided not to use equation (24) d i r e c t l y to c a l i b r a t e the data. This was done since a change i n T might go unnoticed and lead to erroneous r e s u l t s . Instead, use was made of the system noise T 5 which was c a l c u l a t e d by the data a c q u i s i t i o n system at the end of each chopper wheel c a l i b r a t i o n (see end of Chapter V I I ) . Since c a l i b r a t i o n s were frequent and because T S contains a contribution due to sky noise, i t seemed reasonable that T"S might somehow be used to follow the behaviour of , since T J a f f e c t s the sky noise"^". I f the natural logarithm of T~5 i s p l o t t e d against the a i r mass A , i t i s a simple matter to show, using equation (13) of Chapter VII, that the slope T<p of such a graph i s given by: L(.+P) ( i L p L ) + e ' Y ^ + p e~ r*X A ( 2 5 ) 10. This of course assumes that other parameters don't change through-out the observations as w e l l . where , and the other parameters have their previous meanings. It i s clear that i f the expression i n curly brackets does not vary much as a function of A , T.^ w i l l be proportional T . This was in fact found to be the case when each day' s system noise data was fitt e d to find Tj and then plotted against the values of T determined from the "tipping" measurements. As a result, we can be quite confident that X and the other parameters didn't vary significantly in the course of a day'sobservations"'"''"', and that the values provide a reliable measure of the mean zenith attenuation. To check i f this conclusion was reasonable, the expression in curly brackets i n equation (25) was evaluated by assuming values for oi , p , TT and T^Ji while allowing A to vary between 1 and 3. It was found that changes of greater than 25% with respect to the value for A = 2 were uncommon, and occurred only for unreasonable choices of parameters. In addition, by noting the proportionality constant ob-tained when To. was plotted against T (from the "tipping" measurements) , i t was possible to obtain plausible values for C( and |3 . In this way, i t was found that for CO ^ 3 Xj, f while for CO and C 0, T s > Tj, — both of which are reasonable and consistent with upper side band observations. Somewhat surprising, but not unexpected, was the fact that the signal band gain needed to interpret the Tj vs. T 11. It w i l l be noted in Table V that T i n fact varied between the be-ginning and end of some day's observations, but in these cases, separate f i t s could be made to two portions of the T determinations. 86. b e h a v i o u r was a t l e a s t f i v e t i m e s t h e image band g a i n . A l t h o u g h i t was no t o u r p u r p o s e t o d e t e r m i n e Oi and 3^ , i t i s w o r t h p o i n t i n g o u t t h a t more d e t a i l e d o b s e r v a t i o n s o f t h i s k i n d u s i n g l e a s t s q u a r e s f i t t e c h n i q u e s m i g h t be a v e r y u s e f u l way f o r d e t e r m i n i n g , » G$ and Gl . O t h e r w i s e , s p e c i a l measurement t e c h n i q u e s a r e r e q u i r e d w h i c h a r e n o r m a l l y n o t a v a i l a b l e . H a v i n g e s t a b l i s h e d t h a t may b e u s e d a s a s u r r o g a t e f o r X , t h e n e x t s t e p i s t o c a l i b r a t e t h e d a t a . To do t h i s we c a s t e q u a t i o n (25) i n t h e f o r m : (26) (27) where W i s a c o n s t a n t w h i c h h a s y e t t o be d e t e r m i n e d . I t i s n o t a t a l l o b v i o u s t h a t a s i n g l e v a l u e f o r OJ c a n b e f o u n d w h i c h w i l l r e p r o d u c e t h e b e h a v i o u r o f t h e e x p r e s s i o n on t h e r i g h t hand s i d e o f e q u a t i o n ( 2 7 ) ; t h e j u s t i f i c a t i o n f o r d o i n g t h i s w i l l b e d i s c u s s e d s h o r t l y . Now i f a p a r t i c u l a r p o s i t i o n on t h e s k y i s o b s e r v e d a t d i f -- r *" f e r e n t a i r m a s s e s , t he v a l u e o f I ^ w h i c h i s c a l c u l a t e d u s i n g e q u a t i o n (26) mus t be c o n s t a n t . T a k i n g l o g a r i t h m s , we t h e r e f o r e r e q u i r e t h a t f o r a g i v e n p o s i t i o n : 87, o r (28) I f we now p l o t o b s e r v a t i o n a l r e s u l t s f o r Mf\. ~T~?\ a t a g i v e n p o s i t i o n a g a i n s t Tj A we c a n d e t e r m i n e t h e p r o p o r t i o n a l i t y c o n s t a n t cO r e q u i r e d t o c a l i -b r a t e t h e d a t a . T h i s was done f o r a number o f p o s i t i o n s u s i n g t h e 1 2 C 0 and 1 3 C 0 d a t a and i t was f o u n d t h a t f o r 1 2 C 0 , U) = + 0 . 3 5 ± 0 . 3 0 , 13 w h i l e f o r C O , LO = +0 .45 ± 0 . 3 1 , where t h e e r r o r s r e p r e s e n t maximum p o s s i b l e d e v i a t i o n s . A l t h o u g h l a r g e , t h e e r r o r s r e f l e c t m a i n l y t h e 13 p e a k - t o - p e a k n o i s e i n the d a t a . F o r e x a m p l e , f o r t h e CO d a t a , p e a k -t o - p e a k n o i s e was ~ 0 . 7 5 K , w h i c h r e s u l t s i n an a p p r o x i m a t e l y ± 0 . 1 e r r o r i n . I t was n o t p o s s i b l e t o d e t e r m i n e LO f o r C"*"^0 o b s e r -v a t i o n s s i n c e i n s u f f i c i e n t d a t a o f u s e f u l s i g n a l t o n o i s e was a v a i l a b l e t o f i n d t h e ^ J - A dependence o f J^T^ . We t h e r e f o r e assumed i t t o 13 e q u a l t h e r e s u l t f o r CO. Of c o u r s e i t i s a l s o p o s s i b l e t h a t t h e l a r g e e r r o r s may r e -f l e c t t h e f a c t t h a t i t i s n o t p o s s i b l e t o f i n d a u n i q u e v a l u e f o r CO w h i c h s a t i s f i e s e q u a t i o n ( 2 7 ) . T h i s p o s s i b i l i t y was d i s c o u n t e d by e v a l u a t i n g t h e r i g h t hand s i d e o f e q u a t i o n (27) f o r t h e v a l u e s o f cX , |3 and T t h o u g h t t o t y p i f y ou r o b s e r v a t i o n s on t h e b a s i s o f t h e vs . T> a n a l y s i s d i s c u s s e d e a r l i e r . When t h i s was done i t was f o u n d t h a t t o f i r s t o r d e r t h e l o g a r i t h m o f t h e r i g h t hand s i d e o f e q u a t i o n (27) d o e s v a r y l i n e a r l y w i t h t ^ A J t h u s j u s t i f y i n g o u r u s e o f LO a s a p r o p o r -t i o n a l i t y f a c t o r . The p r o o f o f t h e p r o c e d u r e however i s t h a t i t l e a d s t o c o n s i s t e n t r e s u l t s . A s w i l l be s e e n i n t h e f o l l o w i n g s e c t i o n , i t d o e s . I t s h o u l d be p o i n t e d o u t t h a t b e f o r e t h i s t e c h n i q u e was d e v e l o p e d , two other "standard" methods had been attempted which f a i l e d to lead to consistent r e s u l t s . In summary then, the steps leading to equation (26) were the following: (a) The noise temperature T S provided by the data acqu i s i t i o n system was used to determine a factor Tj, , which, i t was shown, i s propor-t i o n a l to the mean zenith attenuation T . (b) Observations at the same source position for dif f e r e n t a i r masses were then used to determine a factor 60 which, i t was shown, could be used i n a term Q « to correct for both atmospheric absorption and also the fact that the c a l i b r a t i o n temperature, which was fixed during data a c q u i s i t i o n , actually decreases with increasing a i r mass. This decrease i s a function of the side band zenith attenuations and r e l a t i v e side band gains, and our pres-c r i p t i o n takes both these into account. B. D a t a R e d u c t i o n 1 . The B a r e R e s u l t s f o r L 1 3 4 . B e f o r e t h e o b s e r v e d a n t e n n a t e m p e r a t u r e s c o u l d b e c a l i b r a t e d u s i n g t h e p r e s c r i p t i o n j u s t d e s c r i b e d , a number o f p r e l i m i n a r y d a t a r e d u c t i o n s t e p s w e r e r e q u i r e d . M o s t o f t h e s e s t e p s , as w e l l a s t h e d a t a a n a l y s i s d e s c r i b e d i n r e m a i n d e r o f t h i s t h e s i s , we re p e r f o r m e d u s i n g a n IBM 370 a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a Computer C e n t e r . The f i r s t s t e p i n t h e d a t a r e d u c t i o n was t o i n v e r t t h e v e l o c i t y 13 (o r f r e q u e n c y ) s c a l e f o r t h e November 6 CO o b s e r v a t i o n s , w h i c h w e r e made u s i n g t h e L S B o f t h e r e c e i v e r . A l l o t h e r r e s u l t s had b e e n o b t a i n e d u s i n g t h e U S B . The s e c o n d s t e p was t o remove any r e s i d u a l b a s e l i n e c u r v a t u r e , s l o p e o r b i a s . T h i s was done u s i n g a l e a s t s q u a r e s f i t p r o g r a m w i t h a n o p t i o n t o f i t up t o a t h i r d o r d e r p o l y n o m i a l t o t h e b a s e l i n e . I n g e n e r a l , h o w e v e r , o n l y l i n e a r f i t s w e r e r e q u i r e d s i n c e t h e b a s e l i n e s o b t a i n e d by f r e q u e n c y s w i t c h i n g w e r e r e m a r k a b l y f l a t . D u r i n g t h e f i t t i n g , a r e c o r d was a l s o made o f t h e RMS n o i s e f o r e a c h p r o f i l e as t h i s w o u l d be needed when o b s e r v a t i o n s f o r t h e same s o u r c e p o s i t i o n , o b t a i n e d on d i f f e r e n t d a y s , we re a v e r a g e d t o g e t h e r . B e f o r e a v e r a g i n g t h e d a t a h o w e v e r , i t was f i r s t n e c e s s a r y t o c a l i b r a t e i t . T h i s was done u s i n g e q u a t i o n ( 2 6 ) : w i t h t h e f o r w a r d beam c o u p l i n g e f f i c i e n c y .^f = 0 . 7 5 and r e c e i v e r s p e c t r a l 13 18 r e s p o n s e = 1 . 0 . F o r t h e CO and C 0 , may be s i g n i f i c a n t l y different from unity and recognition of t h i s fact must be made i n sub-sequent interpretation of l i n e widths. As remarked i n Chapter VII, an on-line program was used to average together contiguous scans at the same source position. Since i n some cases t h i s might have involved integrations as long as two hours (during which time the a i r mass might vary s i g n i f i c a n t l y ) , the value of the term correcting for atmospheric absorption was evaluated numerically; that i s , we calculated: Q LO T j A A CtryS ur^t CcrdL + AimSA^-L where t i and are the i n i t i a l and f i n a l values of the hour angle for each contiguous integration period, $ i s the source declination, and L i s the telescope l a t i t u d e . Such a calculation was performed for each source position observed and for each day of the observing session. On applying t h i s correction to Tj\ along with ~FJJ and Tfy, x ^ The f i n a l step then was to average together the calibrated data for each source position observed. This was done by weighting each p r o f i l e to be averaged inversely as the square of i t s RMS noise and then appropriately normalizing the average. A d i f f i c u l t y however 12 arose i n the case of the November 5 CO observations since on that day continual correction for the change i n earth's motion with respect to the l o c a l standard of rest was not made. As a resu l t the apparent position of the l i n e shifted by as much as two channels (1 .3 km/sec) during the course of the day. This gave rise to the problem of how to average together observations centered at different velocities. Since without detailed knowledge of the line shape i t is impossible to proceed, we assume a Gaussian line profile and investigate what affect linear 12 interpolation has on the peak intensity. If i t is assumed that CO has a f u l l width at half maximum of ^ 2 channels ( ^  1.3 km/sec), then i t can be shown that the maximum smoothing caused by averaging displaced profiles using linear interpolation i s ^ 15%. It i s therefore com-12 parable to peak-to-peak noise for the CO observations. Since however 12 many of the November 5 CO observations were either not averaged with other day's data or i f averaged, were displaced by an integral number of channels, this smoothing caused by averaging only affects 12 2 of the 42 positions observed for CO. These were positions 8 and 9 in Figure 8 of the previous chapter. T - Ik In Appendix C we present profiles of 1 ^ as a function of the LSR velocity for the 17 positions at which a l l three CO isotopes were observed. The co-ordinates indicated in the upper right hand corner of these figures represent the displacement in Right Ascension (in minutes) and Declination (in arcminutes) with respect to the nominal center position for L134. Figure 9, on the other hand, presents the same information, i n much more condensed form, for a l l the positions we observed. 2. The Reference Source Results. The analysis of the obser-vations obtained for the reference sources proceeded in a manner com-pletely analogous to that for L134. The only distinction was that the values of C O , which were used to correct for the effects of atmospheric 92. O < g r-< _l O UJ Q 32r 28 24 20 16 12 8 4 0 - 4 - 8 -12 -16 -20 -24 - 2 8 --32 ' LYNDS 134 CARBON MONOXIDE COORDINATES AT MAP CENTER--a (1950) = 15 H 51 M 0 0 S 8 (1950) = -4° 30' 00" J = l - 0 i i ^ J b C f '~^\s\r ^Jj^ZZ: ^ d^^Z. * — ^ — * " T ^ c ^ — ^ -6 0 6 12 V LSR (KM/SEC) xJLc^  Oc^X; CO ISOTOPE SEQUENCE .5 1.0 0.5 0.0 -0.5 RIGHT ASCENSION (MIN) -1.0 -1.5 Figure 9. absorption, were those derived using the L134 data. Therefore, i f the same results are obtained from day to day, we can be quite sure that our calibration method is at least consistent. In Table V , we summarize our DR21 observations for the position: a(1950): 20 h 37™ 13 s 6(1950): +42° 10' 00" Column (2) of this table i s included to indicate whether or not folding was used. Folded data have effectively only 32 250 KHz channels and theoretically the RMS noise is lower by a factor of ^2 for the same integration time. In column (3) are presented the maximum corrected antenna temperatures observed and i t is clear that the various obser-vations of a given isotope agree well within peak-to-peak noise. The RMS noise appears in column (4). Also included is the weighted mean T' ¥c A for each of the isotopes, together with i t s RMS noise. Having established the consistency of our results, the f i n a l step is to prove that their magnitudes are correct. The most commonly used reference source for CO observations is Orion A, but unfortunately i t could not be observed during our allotted time. We were however able to use results of others for Orion A which were obtained later in the day. Following the same reduction steps as for DR21, we find that I ^  (Orion A) = 70.02 K which is i n perfect agreement is the currently accepted value of 70 K. It should be emphasized that i n order to obtain this result, no ad hoc assumptions were required as is usually the case. It was a natural result of the physical constraints we put on our data. 9 4 -Table V: Observational Results for DR21 Isotope C D Number of Channels^ (2) T A* (MAX) CKelvin) (3) RMS Noise (Kelvin) (4) 12^18 32 C O 2. 25 0. 26 1. 78 0. 18 1. 81 0. 22 1. 98 0. 20 1. 78 0. 23 1. 91 a 0. 10 13 16„ 64 C O 11. 54 0. 75 10. 61 0. 60 10. 97 a 0. 47 32 10. 93 0. 37 11. 07 0. 40 10. 99 a 0. 27 12„16„ 64 C O 27. 52 0. 56 25. 51 0. 69 29. 92 1. 32 25. 65 a 0. 41 Notes to the table a. These are the mean values found by weighting the results inversely as the square of the RMS noise. b. 32 channels indicates frequency switching within the passband was 12 used. Because the CO line i s so broad this could not be done. The f i n a l q u e s t i o n w h i c h m i g h t be a s k e d i s w h e t h e r o r no t o u r DR21 r e s u l t s a g r e e w i t h o t h e r o b s e r v a t i o n s . The o n l y c a s e we know o f 12 13 18 i n w h i c h C O , CO and C 0 we re a l l o b s e r v e d i n DR21 i s t h e e a r l y wo rk o f P e n z i a s e t a l . ( 1 9 7 1 ) . A l t h o u g h t h e s e a u t h o r s q u o t e a n t e n n a t e m p e r a t u r e s and g i v e no i n d i c a t i o n o f t h e i r s e n s i t i v i t y , i t i s s t i l l p o s s i b l e t o make a c r u d e c o m p a r i s o n s i n c e t h e y a l s o o b s e r v e d O r i o n A . I f we s c a l e t h e i r DR21 a n t e n n a t e m p e r a t u r e s a s s u m i n g l A ( O r i A) » 70 K , we 'A f i n d : T A ^ ( 1 2 C 0 ) = 3 3 . 5 K , T ^ ( 1 3 C O ) = 1 2 . 3 K and T A * ( C 1 8 0 ) = 4 . 1 K . From t h e i r p r o f i l e s we e s t i m a t e t h e p e a k - t o - p e a k n o i s e f o r t h e 13 18 CO and C 0 r e s u l t s t o be 2 K. and 1 .5 K r e s p e c t i v e l y . Thus t h e r e i s some d e g r e e o f agreement a l t h o u g h t h e r e seems t o be l i t t l e d o u b t t h a t ou r r e s u l t s a r e more r e l i a b l e . I n f a c t , ou r r e s u l t f o r DR21 t h a t -r~# 12 l ^ ( CO) = 2 5 . 7 ± 0 . 9 K i s i n e x c e l l e n t agreement w i t h c u r r e n t b e s t e s t i m a t e s f o r t h i s p a r a m e t e r ( W i l s o n , 1 9 7 5 ) . F i n a l l y , i t m i g h t be w o r t h 13 18 n o t i n g t h a t o u r o b s e r v e d i n t e n s i t y r a t i o f o r CO/C 0 o f 5 . 7 5 i s i n e x c e l l e n t ag reement w i t h t h e t e r r e s t r i a l r a t i o o f 5 . 6 , w h i l e t h e r e s u l t s o f P e n z i a s e t a l . w o u l d l e a d us t o a v a l u e o f 3 . 0 . T h i s p r o b a b l y r e f l e c t s 18 . ^ t h e n o i s e i n t h e i r C 0 r e s u l t f o r w h i c h 1^ i s a p p a r e n t l y o v e r e s t i m a t e d . I n c o n c l u s i o n t h e n , t h e r e seems t o be v e r y good r e a s o n s f o r t r u s t i n g ou r c a l i b r a t i o n m e t h o d . I t p r o d u c e s c o n s i s t e n t r e s u l t s , i t T - * 12 y i e l d s 1^( CO) v a l u e s f o r DR21 and O r i A i n p e r f e c t ag reement w i t h c u r r e n t b e s t e s t i m a t e s , w i t h o u t any ad hoc a s s u m p t i o n s , and i t r e s u l t s 13 18 i n a CO/C 0 abundance r a t i o i n DR21 i n ag reemen t w i t h t h e t e r r e s t r i a l v a l u e . 96. C . D a t a A n a l y s i s I n t h i s s e c t i o n we d i s c u s s t h e m a j o r ways i n w h i c h t h e c a l i b r a t e d I ^ p r o f i l e s f o r L134 we re a n a l y z e d . M i n o r c a l c u l a t i o n s and a d i s c u s -s i o n o f t h e r e s u l t s d e r i v e d h e r e w i l l be p r e s e n t e d i n C h a p t e r I X . 1 . D e r i v a t i o n o f Co lumn D e n s i t i e s . I t h a s b e e n shown by s e v e r a l a u t h o r s ( s e e f o r e x a m p l e , L o r e n , 1975) t h a t i n t e r m s o f t h e e x c i t a t i o n t e m p e r a t u r e "T^  and t h e o p t i c a l d e p t h T o f a J = 1-0 r o t a t i o n a l t r a n s i t i o n , t h e i n t e g r a t e d co l umn d e n s i t y o f m o l e c u l e s i n t h e l i n e o f s i g h t i s g i v e n b y : •jZv dv (30) w h e r e , f o r p u r e r o t a t i o n a l t r a n s i t i o n s , t h e p a r t i t i o n f u n c t i o n c a n be e x p r e s s e d a s : Q(TX) = J T ( Z J > | ) j ^ ( - J ( J + O A V z t e T x ) T=0 (31) I n t h e s e e q u a t i o n s , V i s t h e f r e q u e n c y o f t h e J = 1-0 r o t -a t i o n a l t r a n s i t i o n , JA. i s t h e d i p o l e moment o f t h e m o l e c u l e s , J" i s t h e r o t a t i o n a l quantum number and t h e o t h e r c o n s t a n t s h a v e t h e i r u s u a l m e a n i n g s . I t i s t h e r e f o r e c l e a r t h a t t o d e r i v e a co lumn d e n s i t y , we must know Tj[ and f v • I t w i l l a l s o be n o t e d t h a t t h e co l umn d e n s i t y i s p r o p o r t i o n a l t o t h e i n t e g r a t e d o p t i c a l d e p t h , s o t h a t i n some s e n s e , t h e s t r e n g t h o f a l i n e w o u l d b e e x p e c t e d t o r e f l e c t i t s c o l u m n d e n s i t y . I n t h e c a s e o f ou r L 1 3 4 CO o b s e r v a t i o n s however t h e r e l a t i v e 12 13 s t r e n g t h o f t h e CO and CO l i n e s i s t y p i c a l l y a b o u t 2 , w h i l e t h e N a r e ; terrestrialabundance ratios would lead us to expect a value lik e 89. 12 It therefore seems certain that CO is heavily saturated. Assuming this to be the case, we must have t / ^ l so that equation (20) may be written : T A*(l2) = J x 0 2 ) ~ J c( ' l2) (32) If we then use the Planck and Rayleigh-Jeans relations (equations (15) and (18)), we find: (33) where V(\Z) = 115.271 x 10 9 sec 1 i s the line frequency andJc02)= 0.891 K is the Rayleigh-Jeans temperature corresponding to a 2.8 K black body 12 T at the frequency V(|2.) . Because the CO J = 1-0 line i s heavily saturated and since the only reasonable excitation process inside dust clouds involves collisions with chiefly H 2, i t is very l i k e l y that this transition has been thermalized at or near the kinetic temperature of the gas, hence T X (12.) = T K . The effect of photon trapping for such a highly saturated line would not alter this conclusion. 12 Having found the excitation temperature for CO we are now at a loss to find i t s optical depth, and therefore i t s column density. 13 18 For CO and C 0 however, progress can be made i f we make the appro-12. In the remainder of this thesis, we adopt the notation that 12, 13 or 18 in brackets fallowing an observable refer to values for the isotopic species CO, 13 C 0 and C18Q respectively. 98. p r i a t e a s s u m p t i o n s r e g a r d i n g t h e i r e x c i t a t i o n t e m p e r a t u r e . I f we 13 c o n s i d e r f i r s t t h e CO m o l e c u l e s , e q u a t i o n (20) may be r e - a r r a n g e d t o g i v e : T 0 3 ) = X* / Jx(l5) - JcQ3) \ [ J x ( l 3 ) " Jc(l») - T A * C » 3 ) / (34) S i n c e we know V (15) and c a n assume 0 . 9 4 2 K , t h e o n l y r e m a i n i n g unknown i s iXx lj3) , t h e R a y l e i g h - J e a n s e q u i v a l e n t o f t h e e x c i t a t i o n t e m p e r a t u r e Tx ('^ ) • T ^ e b e s t we c a n do i n t h i s c a s e i s t o assume e i t h e r u p p e r o r l o w e r l i m i t s f o r Tx 03) and t h e n , u s i n g e q u a t i o n ( 3 4 ) , d e r i v e e i t h e r l o w e r o r u p p e r l i m i t s , r e s p e c t i v e l y , f o r T(l3). A s l o w e r l i m i t s t o , we h a v e t r i e d Tc(l3) = 2.8 K and T x 0 3 ) - T ^ ( I 3 ) + J c (13) , b u t i n b o t h c a s e s t h e v a l u e s o f T 03) f o u n d we re l a r g e enough t h a t t h e l i n e w o u l d h a v e b e e n s a t u r a t e d 12 a n d , a s i n t h e c a s e o f CO, no f u r t h e r i n t e r p r e t a t i o n w o u l d h a v e b e e n p o s s i b l e . A s a r e s u l t , l o w e r l i m i t s f o r T x 03) w e r e n o t p u r s u e d any f u r t h e r . The most o b v i o u s u p p e r l i m i t f o r Tx (13) i s t h e k i n e t i c t e m p e r a t u r e T~K o f t h e g a s , o r e q u i v a l e n t l y , T * ( l £ ) . The l i m i t a t i o n s o f t h i s a s s u m p t i o n , w h i c h i s e q u i v a l e n t t o a s s u m i n g l o c a l t h e r m o d y n a m i c e q u i l i b r i u m ( L T E ) , h a v e b e e n d i s c u s s e d e l s e w h e r e . D i c k m a n (1975b) f o r e x a m p l e , h a s p o i n t e d ou t t h a t f o r c o n d i t i o n s t h o u g h t t o r e p r e s e n t d u s t c l o u d s , t h e a s s u m p t i o n o f LTE may l e a d t o u n d e r e s t i m a t e s o f N ( '3 ) by as much as a f a c t o r o f t w o . T h i s c o n c l u s i o n was r e a c h e d on t h e b a s i s 13 o f s e v e r a l m o d e l s he c o n s i d e r e d i n w h i c h i t was f o u n d t h a t t h e CO was s u b t h e r m a l ( T^ (»3) < T|< ) . W i t h t h e s e l i m i t a t i o n s i n m i n d , we r e -99. w r i t e e q u a t i o n (30) a s : N ( i 3 ) 4 o. L389 * 10 1 5( Q.(T*(\z)) ,]fr v03Wv A»<* 1 ->e^(-^(i3)ATx(i2))J (35) I n w r i t i n g t h i s we assume t h a t t h e o p t i c a l d e p t h i n t e g r a l i s e v a l u a t e d n u m e r i c a l l y u s i n g e q u a t i o n (34) w i t h J*x (13) = J*x (12.) and t h a t t h e v e l o c i t y i s e x p r e s s e d i n k m / s e c . I n t h i s way we make no a s s u m p t i o n s r e g a r d i n g t h e l i n e s h a p e , w h i c h i s o f t e n assumed t o b e G a u s s i a n ; s i m p l e G a u s s i a n l i n e s h a p e s a r e n o t u s u a l l y s e e n . S e v e r a l a d d i t i o n a l p o i n t s a r e w o r t h n o t i n g : (a) I n e v a l u a t i n g t he n u m e r i c a l c o n s t a n t i n e q u a t i o n (35) we u s e d /<- = 0 . 1 1 2 D f o r CO ( B u r r u s , 1 9 5 8 ) . I t h a s b e e n n o t i c e d t h a t many a u t h o r s u s e J*- = 0 . 1 0 D , w h i c h c o u l d l e a d t o a 24% e r r o r i n t h e d e r i v e d co l umn d e n s i t i e s . (b) I n e v a l u a t i n g t h e p a r t i t i o n f u n c t i o n Q ("He), we do n o t make t h e u s u a l a s s u m p t i o n t h a t , s i n c e i t was f o u n d f o r t h e e x c i t a t i o n t e m p e r a t u r e s e x p e c t e d i n d a r k d u s t c l o u d s , and i n p a r t i c u l a r L 1 3 4 , t h i s c a n l e a d t o 10% e r r o r s . I n s t e a d we n u m e r i c a l l y e v a l u a t e d Q . u s i n g e q u a t i o n (31) f o r J B 0 t o J = 5 ; t h i s was f o u n d t o g i v e a c c u r a t e r e s u l t s f o r 0 K £ T x 4 16 K . (c ) F i n a l l y , i t i s w o r t h comment ing t h a t a l t h o u g h a s s u m i n g L T E may r e s u l t i n a l a r g e u n d e r e s t i m a t e o f T 0 3 ) t t h e u n d e r e s t i m a t e o f N (13) i s n o t as g r e a t , s i n c e t h e t e rm i n c u r l y b r a c k e t s i n e q u a t i o n (35) i s o v e r e s t i m a t e d when"T"x i s o v e r e s t i m a t e d . T h i s 100. term therefore counteracts the underestimate of T ( & ) y although underestimates i n Ai(l3) as high as a f a c t o r of two can s t i l l r e s u l t . 13 18 The above discussion f o r CO can also be applied to C 0 although i n t h i s case assuming LTE probably does not a f f e c t the de-rive d number for N 0 8 ) . The lower l i m i t s f o r I\l(l3) and N (18) which were obtained by assuming T><(I2) — "Tjc.(l3) - T ^ O © ) - T K , num-e r i c a l l y i n t e g r a t i n g the o p t i c a l depth p r o f i l e s and evaluating equation (35) are shown i n Figure 10 superimposed on the red Palomar Sky Survey p r i n t . Each c i r c l e i s the s i z e of the antenna beam and i s centered 13 18 at the pos i t i o n s where eit h e r CO or C 0 was observed. The upper number i s the lower l i m i t to I\](I3) i n units of 1 0 + ^ cm 2 , while the lower number, i f present, i s i n the same u n i t s . 2. Radiation Temperature Contours at a Fixed V e l o c i t y . Although L134 has an apparently simple structure on both the red and the blue Palomar Sky Survey p r i n t s , the obvious double p r o f i l e s seen 12 i n the CO emission suggested i t might be worth i n v e s t i g a t i n g t h i s structure further. To t h i s end, excess r a d i a t i o n temperature contours were drawn f o r each v e l o c i t y at which CO emission was seen. This was done f o r each of the isotopes we observed, and involved e s s e n t i a l l y two steps. The f i r s t was to arrange the I A data f o r a p a r t i c u l a r LSR v e l o c i t y and isotope i n t o a two dimensional array corresponding to the gri d p o s i t i o n s i n L134 where each was observed. Before contours could be drawn however, i t was necessary to use i n t e r p o l a t i o n techniques 101. — n : n •. ;i . i — T f — — L Y N D S 1 3 4 - : ' ^ Y -^ • • • • • • • > ' • •• • RIGHT A S C E N S I O N (MIN) Upper number is N ( , 3 C O ) ( l O * 1 5 c m " 2 ) Lower number is N ( C , 8 0 ) ( l O + , 5 c m " " 2 ) Figure 10. 102. t o g e n e r a t e a t h r e e d i m e n s i o n a l s u r f a c e t h r o u g h t h e d a t a p o i n t s so t h a t e a c h a r r a y e l e m e n t w o u l d h a v e a v a l u e . T h i s was done b y d i v i d i n g t h e t h r e e s p a c e a r o u n d e a c h a r r a y p o i n t i n t o o c t a n t s and t h e n s e t t i n g t h e v a l u e o f t h a t p o i n t t o t h e a v e r a g e o f t h e e i g h t s u r r o u n d i n g p o i n t s w e i g h t e d i n v e r s e l y as t h e s q u a r e o f t h e i r d i s t a n c e f r o m t h e a r r a y p o i n t unde r c o n s i d e r a t i o n . I f more t h a n f o u r o c t a n t s w e r e f o u n d emp ty , a f l a g was s e t w h i c h i n t h e s u b s e q u e n t c o n t o u r i n g w o u l d s u p p r e s s c o n t o u r d r a w i n g a t t h a t p o i n t . I n t h i s way a 33 by 25 e l e m e n t a r r a y o f T A v a l u e s a n d / o r f l a g s was g e n e r a t e d f o r e a c h v e l o c i t y and i s o t o p e . The s e c o n d s t e p t h e n was t o draw c o n t o u r s t h r o u g h t h e r e g u l a r „ - . ^ a r r a y o f I A v a l u e s o r f l a g s . T h i s was done f o r a g i v e n c o n t o u r by f i n d i n g two a r r a y p o i n t s b e t w e e n w h i c h t h e c h o s e n c o n t o u r v a l u e l a y . The l a r g e r o f t h e s e was c h o s e n as a r e f e r e n c e p o i n t , and t o g e t h e r w i t h t he o t h e r p o i n t — as w e l l a s two o t h e r s — was u s e d t o f o r m a s q u a r e . The s q u a r e was t h e n d i v i d e d i n t o f o u r e q u a l t r i a n g l e s , w i t h t h e common v e r t e x b e i n g a s s i g n e d t h e a v e r a g e I A v a l u e o f t h e f o u r c o r n e r p o i n t s . The c o n t o u r l i n e was t h e n d rawn by l i n e a r i n t e r p o l a t i o n t h r o u g h t h e a p p r o p r i a t e t r i a n g l e , a new r e f e r e n c e p o i n t c h o s e n and so o n . We w i l l n o t p u r s u e t h e f i n e r d e t a i l s o f t h e t e c h n i q u e any f u r t h e r h e r e . The r e s u l t s o f h a v i n g done t h i s f o r e a c h o f t h e i s o t o p e s and f o r e a c h v e l o c i t y whe re e m i s s i o n was f o u n d h a v e b e e n c o l l e c t e d t o g e t h e r i n A p p e n d i x D . The c o n t o u r u n i t s u s e d t h e r e r e p r e s e n t t h e 12 t y p i c a l p e a k - t o - p e a k n o i s e o f t h e d a t a . I t w i l l be n o t e d t h a t CO 13 shows much more s t r u c t u r e t h a n CO w h i c h i n t u r n shows more t h a n 18 C 0 , a l t h o u g h t h i s r e m a r k n e e d s some q u a l i f i c a t i o n . A s w i l l be d i s -c u s s e d i n t h e f o l l o w i n g c h a p t e r , i t a p p e a r s t h a t L 1 3 4 i s composed o f a t l e a s t f o u r s e p a r a t e c l o u d s a t LSR v e l o c i t i e s o f 0 . 1 , 0 . 7 , 2 . 7 and 12 4 . 0 k m / s e c . A l l f o u r o f t h e s e show up i n t h e CO c o n t o u r s , w h i l e 13 o n l y t h e 2 , 7 and 4 . 0 k m / s e c c l o u d s a p p e a r i n t h e CO c o n t o u r s . T h i s i s m i s l e a d i n g however as i t i s p a r t i a l l y an a r t i f a c t o f t h e g r i d g e n e r a t i o n p r o c e s s ( d i s c u s s e d above) i n w h i c h a g r i d p o i n t was s u p p r e s s e d i f i t had l e s s t h a n f o u r n e a r e s t n e i g h b o u r s . I f i n f a c t t h e o r i g i n a l d a t a f o r t h e g r i d g e n e r a t i o n p r o g r a m a r e i n s p e c t e d , t h e r e i s c e r t a i n l y 13 e v i d e n c e f o r t h e 0 . 7 k m / s e c CO c l o u d , a l t h o u g h i t i s much w e a k e r t h a n t h e 2 . 7 k m / s e c c l o u d . T h i s c a n a l s o be s e e n b y l o o k i n g a t t h e p o s i t i o n s ( - . 2 5 , - 4 ) , ( - . 2 5 , 0) and ( - . 5 , 0) i n F i g u r e 9 , o r t h e l a r g e r s c a l e d a t a f o r t h e f i r s t two o f t h e s e p o i n t s i n A p p e n d i x C . 13 F i n a l l y , i t s h o u l d be r e m a r k e d t h a t we do n o t h a v e CO o b s e r v a t i o n s 18 a t t he p o s i t i o n o f t h e 0 . 1 k m / s e c c l o u d , n o r C 0 o b s e r v a t i o n s a t t h e p o s i t i o n s o f t h e 0 . 1 , 0 . 7 and 4 . 0 k m / s e c c l o u d s ; t h e r e f o r e , we c a n n o t comment 12 on them. On t h e b a s i s o f t h e CO r e s u l t s howeve r t h e 0 . 7 a n d 2 . 7 k m / s e c c l o u d s a r e c e r t a i n l y t h e most p r o m i n e n t . 3 . O t h e r A n a l y s i s . I n a d d i t i o n t o t h e a n a l y s i s a l r e a d y d i s c u s s e d , s e v e r a l o t h e r c a l c u l a t i o n s w e r e p e r f o r m e d . F o r e x a m p l e , c o n t o u r i n g was p e r f o r m e d f o r maximum and minimum v e l o c i t i e s , maximum r a d i a t i o n t e m p e r a t u r e s , l i n e w i d t h s , and so o n . T h e s e r e s u l t s , t o g e t h e r w i t h o t h e r l e s s l e n g t h y c a l c u l a t i o n s , w i l l be d i s c u s s e d i n t h e f o l l o w i n g c h a p t e r as t h e y o c c u r . 104. CHAPTER I X D i s c u s s i o n o f R e s u l t s and Summary A . The S t r u c t u r e o f L 1 3 4 On t h e P a l o m a r Sky S u r v e y p r i n t s , L134 h a s an a p p a r e n t l y s i m p l e s t r u c t u r e and an a n g u l a r s i z e o n l y s l i g h t l y l a r g e r t h a n t h e s u n o r t h e moon. R e c e n t l y h o w e v e r , T u c k e r e t a l . (1976) h a v e u s e d s t a r c o u n t s t o show t h a t L 1 3 4 m i g h t i n f a c t be composed o f two s e p a r a t e r e g i o n s w i t h Ay > 7 m . The l a r g e s t o f t h e s e r e g i o n s i s a p p r o x i m a t e l y 7 ' by 2 0 ' and i s e l o n g a t e d i n a N o r t h - S o u t h d i r e c t i o n j u s t West o f ou r n o m i n a l c e n t e r p o s i t i o n , w h i l e t h e o t h e r i s a p p r o x i m a t e l y 4 ' by 6 ' and l i e s abou t 1 6 ' S o u t h - E a s t o f o u r c e n t e r p o s i t i o n . I n C h a p t e r V I we r e m a r k e d t h a t Chu (1975) had s e e n two a b s o r p -t i o n f e a t u r e s i n h i s H I i n t e r f e r o m e t e r d a t a . I t i s t h e r e f o r e n a t u r a l t o wonder w h e t h e r o r n o t t h e s e c o r r e l a t e i n p o s i t i o n w i t h t h e two r e g i o n s o f h i g h o b s c u r a t i o n m e n t i o n e d a b o v e . Somewhat s u r p r i s i n g l y , we f i n d t h a t o n l y t h e H I f e a t u r e a t 2 . 7 k m / s e c shows s u c h a c o r r e l a t i o n , and i t c o r r e l a t e s w i t h t h e l a r g e s t o f t h e o b s c u r e d r e g i o n s . C h u ' s 0 . 7 k m / s e c HI a b s o r p t i o n f e a t u r e , h o w e v e r , d e f i n i t e l y l i e s t o t h e N o r t h o f t h e o t h e r r e g i o n o f h i g h o b s c u r a t i o n . On t h e b a s i s o f ou r r e s u l t s p r e s e n t e d a t t h e end o f t h e l a s t c h a p t e r , we may be i n a b e t t e r p o s i t i o n t o u n d e r s t a n d t h i s d i f f e r e n c e , f o r i t a p p e a r s t h a t L134 c o n s i s t s o f a t l e a s t f o u r c l o u d s . These a r e i l l u s t r a t e d i n F i g u r e 11 u s i n g t h e c o n s t a n t v e l o c i t y c o n t o u r s f r o m A p p e n d i x D w h i c h b e s t d e l i n e a t e t h e m . I n t h e s u b s e q u e n t d i s c u s s i o n we s h a l l r e f e r t o t h e s e c l o u d s by t h e i r n o m i n a l LSR v e l o c i t i e s o f 0 . 1 , 0 . 7 , 105. Figure 11 106. 2 .7 and 4 . 0 k m / s e c , r e s p e c t i v e l y . I t w i l l b e n o t e d t h a t t h e 0 . 7 and 2 . 7 k m / s e c c l o u d s h a v e d a s h e d c o n t o u r s d rawn o v e r t h e m . T h e s e r e p r e s e n t C h u ' s two HI a b s o r p t i o n f e a -t u r e s and i t i s c l e a r t h a t t h e y c o r r e l a t e v e r y w e l l w i t h t h e CO e m i s s i o n b o t h i n p o s i t i o n and v e l o c i t y . T h i s a r g u e s s t r o n g l y i n f a v o u r o f t h e c o e x i s t e n c e o f H and CO, and i s c o n t r a r y t o t h e o p i n i o n ( m e n t i o n e d i n t h e I n t r o d u c t i o n t o t h i s P a r t ) t h a t t h e a t o m i c h y d r o g e n f o r m s a s h e l l a r o u n d d u s t c l o u d s . T h i s c o n c l u s i o n however was b a s e d on t h e f a c t t h a t t h e e x c i t a t i o n t e m p e r a t u r e s d e r i v e d f r o m K n a p p ' s (1972) s i n g l e d i s h o b s e r v a t i o n s o f H I i n d u s t c l o u d s w e r e c o n s i d e r a b l y above t h e e x c i t a t i o n t e m p e r a t u r e d e r i v e d f r o m m o l e c u l a r o b s e r v a t i o n s . K n a p p ' s r e s u l t s however r e p r e s e n t e d u p p e r l i m i t s t o Tx , so t h a t T* < 1 6 - 4 0 K ; C h u ' s i n t e r f e r o m e t e r r e s u l t s , on t h e o t h e r h a n d , i m p l y ~TK < 20 K , w h i c h i s i n agreement w i t h m o l e c u l a r r e s u l t s . We s h a l l r e t u r n t o t h i s p r o b l e m s h o r t l y . We have a l r e a d y m e n t i o n e d t h a t C h u ' s 2 . 7 k m / s e c a b s o r p t i o n f e a t u r e c o r r e l a t e d w e l l w i t h t h e l a r g e s t r e g i o n o f h i g h o b s c u r a t i o n i n L 1 3 4 , w h i l e h i s 0 . 7 k m / s e c a b s o r p t i o n f e a t u r e d i d n o t c o r r e l a t e w i t h t h e s m a l l e r r e g i o n o f h i g h o b s c u r a t i o n . The mos t o b v i o u s q u e s t i o n t o a s k n e x t i s w h e t h e r any o f t h e CO c l o u d s show a c o r r e l a t i o n w i t h t h e s e r e g i o n s . From what h a s a l r e a d y b e e n s a i d i t i s c l e a r t h a t t h e 2 . 7 k m / s e c CO c l o u d c o r r e l a t e s w i t h b o t h H I a b s o r p t i o n and h i g h o b s c u r a t i o n , w h i l e t h e 0 .7 k m / s e c CO c l o u d c o r r e l a t e s w i t h o n l y H I a b s o r p t i o n . We now add t h e a d d i t i o n a l r e s u l t s t h a t o u r 4 .0 k m / s e c CO c l o u d c o r r e l a t e s p e r f e c t l y w i t h t h e s m a l l e r o f t h e h i g h e x t i n c t i o n r e g i o n s , w h i l e o u r 0 . 1 k m / s e c CO c l o u d h a s no a p p a r e n t h y d r o g e n o r o p t i c a l c o u n t e r p a r t s . I t s h o u l d be p o i n t e d o u t , h o w e v e r , t h a t t h e r e i s d e f i n i t e l y e v i d e n c e f o r t h e 4 . 0 k m / s e c c l o u d i n C h u ' s HI d a t a , and i t s h o u l d c e r t a i n l y be l o o k e d a t more c l o s e l y . I t w i l l be n o t e d on c a s u a l i n s p e c t i o n o f F i g u r e 9 a t t h e p o s i -12 t i o n s o f t h e 0 .7 and 2 . 7 k m / s e c c l o u d s t h a t t h e maximum CO e m i s s i o n i s a p p r o x i m a t e l y i s o t h e r m a l and h a s t h e same i n t e n s i t y . I n f a c t , w h e r e 12 t h e s e c l o u d s o v e r l a p , we s e e t h e o b v i o u s CO d o u b l e f e a t u r e s . The c l o u d s a t 0 . 1 and 4 . 0 k m / s e c however a r e l e s s o b v i o u s as t h e y a r e b l e n d e d w i t h t h e p r o m i n e n t 0 . 7 and 2 . 7 k m / s e c c l o u d s , and w o u l d n o t be s e e n u n l e s s c o n s t a n t v e l o c i t y c o n t o u r s we re d rawn as i n F i g u r e 11 and A p p e n d i x D . 13 The 4 . 0 k m / s e c c l o u d i n f a c t shows up c l e a r l y i n CO, w h i l e t h e 0 . 7 k m / s e c c l o u d does n o t a p p e a r a t a l l . A s r e m a r k e d a t t h e end o f t h e l a s t c h a p t e r , t h i s i s r e l a t e d t o i n s u f f i c i e n t s a m p l i n g n e a r t h e 0 . 7 k m / s e c c l o u d . I t c a n i n f a c t be s e e n i n t h r e e o f t h e i n d i v i d u a l p r o f i l e s , b u t t h e l i n e i s w e a k . 12 The c l o u d a t 0 . 1 k m / s e c was o n l y o b s e r v e d i n C O , b u t we c a n b e r e a s o n a b l y s u r e o f i t s i d e n t i f i c a t i o n . The l i n e s i n t h i s r e g i o n a p p e a r b r o a d e r on t h e i r l o w v e l o c i t y s i d e , and when d o u b l e f e a t u r e d , t h e l o w v e l o c i t y f e a t u r e a p p e a r s t h e s t r o n g e s t . I n f a c t , i n one i n s t a n c e o n l y t he l o w v e l o c i t y f e a t u r e i s s e e n ( s e e F i g u r e 9 ) . 18 F i n a l l y , we n o t e t h a t a l t h o u g h C 0 was mapped on o n l y t h e 2 .7 k m / s e c c l o u d , t h e e x t e n t o f i t s e m i s s i o n c o r r e l a t e s v e r y w e l l w i t h t h e l a r g e s t r e g i o n w i t h A ^ > 7™; we w o u l d t h e r e f o r e h a v e e x p e c t e d t o 13 s e e i t on t h e 4 . 0 k m / s e c c l o u d as w e l l had i t b e e n mapped t h e r e . CO on t h e o t h e r hand a p p e a r s t o h a v e a d i s t r i b u t i o n c o m p a r a b l e t o t h e o b -v i o u s b o u n d a r i e s o f L134 on t h e P a l o m a r Sky S u r v e y b l u e p r i n t , w h i l e 108. "CO e x t e n d s t o t h e A y = l m c o n t o u r o f K u t n e r e t a l . ( 1 9 7 6 ) . S t r u c t u r a l l y t h e n , L134 a p p e a r s t o be c o m p r i s e d o f f o u r CO c l o u d s : two o f t h e s e c o r r e l a t e w i t h t h e r e g i o n s o f maximum v i s i b l e e x t i n c t i o n , one c o r r e l a t e s w i t h b o t h v i s i b l e e x t i n c t i o n and HI a b s o r p t i o n , one c o r r e l a t e s o n l y w i t h H I a b s o r p t i o n and f i n a l l y , one has no o p t i c a l o r known HI c o u n t e r p a r t . I n f a c t , L134 may a c t u a l l y have more s t r u c t u r e . We make t h i s s t a t e m e n t s i n c e Knapp e t a l . (1976) 12 13 have made o b s e r v a t i o n s o f b o t h CO and CO i n a N o r t h - S o u t h s t r i p abou t 0 . 5 m i n u t e s E a s t o f ou r n o m i n a l c e n t e r p o s i t i o n , b u t w i t h a p p r o x i -m a t e l y two and a h a l f t i m e s b e t t e r s p e c t r a l and a n g u l a r r e s o l u t i o n . A l t h o u g h t h e m a j o r f e a t u r e s o f t h e i r d a t a a g r e e v e r y w e l l w i t h o u r r e -s u l t s , t h e r e i s c e r t a i n l y much e v i d e n c e f o r s m a l l e r s c a l e s t r u c t u r e t h a n we have o b s e r v e d . T h e i r l i n e s a r e v e r y a s y m m e t r i c w i t h some s h o w i n g s e v e r a l f e a t u r e s and some a p p e a r i n g f l a t - t o p p e d . We w i l l d i s c u s s t h i s d a t a l a t e r . We do n o t w i s h t o o v e r i n t e r p r e t o u r r e s u l t s , b u t i n v i e w o f o u r d i s c u s s i o n i n t h e i n t r o d u c t i o n and t h e mass e s t i m a t e s w h i c h we d e r i v e s h o r t l y , i t i s t e m p t i n g t o s u g g e s t t h a t we a r e a c t u a l l y s e e i n g t h e f r a g m e n t a t i o n o f wha t was i n i t i a l l y a s i n g l e c l o u d . T h i s c o n c l u s i o n w i l l i n f a c t be s u p p o r t e d by o u r s u b s e q u e n t d i s c u s s i o n and i s t h e f i r s t i n s t a n c e we know o f i n w h i c h a n i s o l a t e d d a r k d u s t c l o u d h a s b e e n shown t o be f r a g m e n t i n g . T h i s p r o c e s s a t p r e s e n t seems t o be t h e o n l y f e a s i b l e way i n w h i c h s t a r s o f r e a s o n a b l e masses c a n f o r m . B. The D i s t a n c e t o L134 We h a v e a l r e a d y r e m a r k e d on t h e u n i q u e p o s i t i o n w h i c h L 1 3 4 and i t s n e a r b y c l o u d s h o l d i n t h e d i s t r i b u t i o n o f d a r k n e b u l a e . B e f o r e we c a n s a y a n y t h i n g f u r t h e r h o w e v e r , we must f i r s t d e r i v e a d i s t a n c e f o r t h e s e o b j e c t s . Chu (1975) h a s p r e s e n t e d a t h o r o u g h d i s c u s s i o n o f t h i s p r o b l e m . He f i r s t a r g u e s t h a t L134 i s a s s o c i a t e d w i t h t h e l a r g e S c o r p i u s - O p h i u c h u s c o m p l e x , s i n c e i t seems more t h a n c o i n c i d e n t a l t h a t a l l t h e known h i g h l a t i t u d e d a r k n e b u l a e a r e e i t h e r i n t h e d i r e c t i o n o f t h i s c o m p l e x o r t h e O r i o n - T a u r u s - P e r s e u s c o m p l e x — t h e two most p r o m i n e n t H I c o m p l e x e s i n ou r g a l a x y . B a s e d on t h i s and o t h e r r e s u l t s , Chu c o n c l u d e s t h a t L134 must be n e a r e r t h a n 170 p c . To f i n d a l o w e r l i m i t , on t h e o t h e r h a n d , Chu was a b l e t o a r g u e t h a t a GO f o r e g r o u n d s t a r HD141269 mus t be f u r t h e r away t h a n 50 p c . I n t h i s wo rk we a d o p t a d i s t a n c e t o L 1 3 4 o f 150 pc s i n c e C h u ' s u p p e r l i m i t o f 170 p c , i f we assume t h e h a l f - t h i c k n e s s o f t h e g a l a c t i c p l a n e i s 100 p c , l e a v e s no b a c k g r o u n d HI t o be a b s o r b e d . 1 1 0 . C . The S i z e , D e n s i t y and Mass o f L134 S i n c e i s by f a r t h e most m a s s i v e component o f d u s t c l o u d s , we may u s e D i c k m a n ' s r e l a t i o n s h i p be tween N 0 3 ) and N(H2) ( s e e e q u a t i o n ( 9 ) ) t o d e r i v e t h e co lumn d e n s i t i e s i n L 1 3 4 , and h e n c e t h e number d e n s i t y and t h e m a s s . L 1 3 4 h a s b e e n shown t o c o m p r i s e f o u r c l o u d s , h o w e v e r , so we must c o n s i d e r t h e s e s e p a r a t e l y . We f i r s t d e t e r m i n e t h e a v e r a g e v a l u e o f N 03) i n e a c h c l o u d ' s c o r e . E q u a t i o n (9) c a n t h e n be u s e d t o d e t e r m i n e N ( H j ) , and f i n a l l y , t h e number d e n s i t y n and mass c a n be f o u n d f r o m : ^ ( H 2 ) ~ N ( H 2 ) / 2 R (36) and (37) where jX =• 2 . 3 3 i s t h e mean " m o l e c u l a r " w e i g h t o f t h e c l o u d p a r t i c l e s ( assum ing an a p p r o p r i a t e m i x o f h y d r o g e n and h e l i u m ( F i e l d , 1 9 7 3 ) ) , i s t h e mass o f a t o m i c h y d r o g e n , and R i s t h e c l o u d r a d i u s t o h a l f i n t e n s i t y . A n a p p r o x i m a t e r e s u l t i s i n d i c a t e d f o r n ( H 2 ) s i n c e , i f R i s u n d e r e s t i m a t e d , n ( H 2 ) i s o v e r e s t i m a t e d . T h i s however assumes n . ( H j ) i s u n i f o r m and i f i t i s n ' t , i t w i l l be u n d e r e s t i m a t e d . A l o w e r l i m i t i s i n d i c a t e d f o r t h e mass s i m p l y b e c a u s e we h a v e u s e d a l o w e r l i m i t f o r R t o f i n d i t . The mass o f t h e 4 . 0 k m / s e c c l o u d however c o u l d be f u r t h e r u n d e r e s t i m a t e d s i n c e 1 3 . ' T h i s c o u l d n o t be done f o r t h e 0 . 1 k m / s e c c l o u d s i n c e i t was n o t o b s e r v e d i n 1 3 C 0 . i t s l i n e i s s t r o n g l y b l e n d e d w i t h t h e l i n e f r o m t h e 2 . 7 k m / s e c c l o u d and we h a v e been c o n s e r v a t i v e i n e s t i m a t i n g M (13) f o r i t . The v a r i o u s p a r a m e t e r s u s e d , and t h e r e s u l t s d e r i v e d , a r e summar ized i n T a b l e V I . A d d i t i o n a l r e s u l t s p r e s e n t e d t h e r e w i l l be ex p l a i n e d s h o r t l y . F i n a l l y , we p o i n t ou t t h a t b e c a u s e t h e 0 . 7 and 4 . 0 13 k m / s e c c l o u d s we re i n c o m p l e t e l y o b s e r v e d i n CO, t h e r e s u l t s f o r t h e s c l o u d s s h o u l d n o t be t a k e n t o o s e r i o u s l y , a l t h o u g h t h e l o w e r l i m i t s a r e p r o b a b l y r e a s o n a b l e . T a b l e V I : Summary o f L 1 3 4 C l o u d P a r a m e t e r s 3 C l o u d V e l o c i t y R a d i u s ^ c R a d i u s N ( 1 3 )d • n ( H 2 ) Mass N ( H I ) e N ( H I ) / N ( H 2 ) ( k m / s e c ) ( ' ) ( pc ) (x 1 0 1 5 c n f 2 ) ( c m " 3 ) (M 0 ) (x 1 0 1 9 c m " 2 ) (x 1 0 ~ 3 ) 0 . 1 3 . 0 f 0 . 1 3 f 0 . 7 3 . 3 0 . 1 4 1.3 700 0 . 4 . 2 5 4.4 2 . 7 1 1 . 0 0 . 4 8 8 . 6 1400 34 3 . 0 7 .7 4 . 0 4 . 0 0 . 1 7 7 . 0 3100 7 .0 N o t e s t o t h e t a b l e : a . A l l r e s u l t s r e p r e s e n t l o w e r l i m i t s e x c e p t t h e LSR v e l o c i t y . b . D e t e r m i n e d f r o m N(13 ) h a l f i n t e n s i t y c o n t o u r . c . Assumes d i s t a n c e t o L134 i s 150 p c . d . A v e r a g e v a l u e i n c o r e o f c l o u d . e . D e r i v e d f r o m C h u ' s H I a b s o r p t i o n p r o f i l e s . 12 13 f . B a s e d on C O , n o t CO o b s e r v a t i o n s . D. The Composition of L134 113. 1. Carbon Monoxide Observations. Using the column density results presented in Figure 10 of the previous chapter, i t is possible to derive a value for the ratio of N03)/N(I8) in L134. This was done for each position 18 at which C 0 was detected above twice peak-to-peak noise and the average value was found to be 6.5 ± 0.9. Dickman (1975b) has pointed out, however, that assuming LTE (that is,T"x03)= Tx(l2)-~Tj^) can result in an underestimate for N(I3) by as much as a factor of two for typical dust cloud conditions. If we take this into account, we then find N(i3)/M(i$)= 6.5 (+8.3,-0.9). Since 18 C 0 is optically thin, may be somewhat overestimated because of the overestimate for T x , but we have ignored this effect. If we now assume 16 18 that the 0/ 0 abundance ratio i s t e r r e s t r i a l , that is 489, we find that 12 13 the C/ C abundance ratio must be in the range 33 - 87. It is worth 18 remarking, however, that 0 is expected to be only a secondary or tertiary product of nucleosynthesis (Wannier et a l . , 1975), and i f anything, the 16 18 ratio 0/ 0 would be expected to decrease below the t e r r e s t r i a l value. 12 1 3 Thus, the range we indicated above for the C/ C ratio in L134 can only decrease. It should also be remarked that the ratio indicated above for N(^")/fvJ(i8)really applies to the most obscured portion of the 2.7 km/sec cloud. In the outer regions, this ratio is significantly larger ( ~19 ± 12) and may reflect the fact that radiative rather than c o l l i s i o n a l processes are important in the less dense regions, thus allowing the excitation temperature to exceed the kinetic temperature. 2. HI Observations. We now derive an H/^ abundance ratio based 12 13 on our CO and CO results, and Ghu's 21 cm results. Without a know-ledge of the gas knetic temperature, Chu was unable to derive a value for N(HI) > although by model f i t t i n g he was able to argue that 0 K ^ T K ^ 20 K. We c o n s i d e r f i r s t t h e 2 .7 k m / s e c c l o u d . F o r t h i s c l o u d , Chu measu red b o t h a s e l f - r e v e r s e d H I e m i s s i o n p r o f i l e u s i n g s i n g l e d i s h o b s e r v a t i o n s ( 2 0 ' b e a m ) , and an HI a b s o r p t i o n p r o f i l e u s i n g i n t e r f e r o m e t e r o b s e r v a t i o n s ( 7 ' s y n t h e s i z e d b e a m ) ; he a l s o showed t h a t t h e s e r e s u l t s we re c o m p a t i b l e . A t h i s beam p o s i t i o n (oC(1950) : 1 5 h 5 1 m 0 6 S , £ ( 1 9 5 0 ) : - 4 ° 3 1 ' 3 6 " ) , we f i n d an a v e r a g e 1 2 C 0 e x c i t a t i o n t e m p e r a t u r e ~Ix= 1 2 . 2 ± 1.2 K , w h i c h f o r r e a s o n s m e n t i o n e d e a r l i e r , we adop t as t h e k i n e t i c t e m p e r a t u r e o f t h e g a s . N6<i) w a s t h e n f o u n d by n u m e r i c a l l y i n t e g r a t i n g : ' N ( H I ) = i.SZ'3 x i p 1 8 T x C ^ - " 2 (3 T x - T B J / i n e w h e r e , i n t h e i n t e g r a l o v e r t h e o p t i c a l d e p t h o f t h e 21 cm l i n e , Tg i s t h e b r i g h t n e s s t e m p e r a t u r e o f t h e i n t e r f e r o m e t e r a b s o r p t i o n p r o f i l e and T g i s t h e b a c k g r o u n d e m i s s i o n b r i g h t n e s s t e m p e r a t u r e . On e v a l u a t i n g t h i s i n t e g r a l , we f i n d : N ( H I ) = ( 3 . 0 ± 0 . 3 ) x 10 19 - 2 cm To d e t e r m i n e H(HZ), we f i r s t f i n d t h e a v e r a g e v a l u e o f N(l3) o v e r C h u ' s 7 ' beam p o s i t i o n ; when t h i s i s combined w i t h D i c k m a n ' s r e s u l t . we o b t a i n : N(H2)= ( 3 . 9 ± 2 . 8 ) x 1 0 2 1 c m " 2 . Thus t h e r a t i o o f H / H 2 i s g i v e n b y : ' ' , x a It l i«L ^ (7.7 * 5.5)* I o . A l o w e r l i m i t i s i n d i c a t e d s i n c e f o r e g r o u n d h y d r o g e n e m i s s i o n c o u l d l e a d t o an u n d e r e s t i m a t e o f M(HI). A s i m i l a r c a l c u l a t i o n was a l s o c a r r i e d ou t f o r t h e 0 .7 k m / s e c 13 c l o u d a l t h o u g h t h e r e we re s e v e r a l u n c e r t a i n t i e s r e g a r d i n g b o t h t h e CO o b s e r v a t i o n s and t h e H I a b s o r p t i o n . I n any c a s e , t h e d e r i v e d v a l u e w a s : i n agreement w i t h ou r p r e v i o u s r e s u l t . 115. B o t h t h e s e r e s u l t s h a v e b e e n i n c l u d e d i n T a b l e V I w i t h t h e o t h e r L134 p a r a m e t e r s . U s i n g t h e s e r e s u l t s , we c o n c l u d e t h a t t h e a t o m i c h y d r o g e n number d e n s i t y , 71 (HI) » i s abou t 3 cm i n t h e 0 . 7 k m / s e c c l o u d , and 11 cm i n t h e 2 . 7 k m / s e c c l o u d . A l t h o u g h t h i s i s i n a g r e e -ment w i t h o t h e r o b s e r v a t i o n a l r e s u l t s , w h i c h i n d i c a t e t h a t YX(Hl)ilO cm ( H e i l e s , 1 9 7 1 ) , i t d i s a g r e e s w i t h t h e t h e o r e t i c a l r e s u l t s w h i c h p r e d i c t , f o r a c o s m i c r a y i o n i z a t i o n r a t e o f ^ = 4 x 10 s e c , t h a t (HI) = 50 c m " 3 f o r M. ( H +Z Hj.) >100 c m " 3 ( H o l l e n b a c k e t a l . , 1 9 7 1 ; So lomon and W e r n e r , 1 9 7 1 ) . A l t h o u g h i t m i g h t h a v e b e e n a r g u e d on t h e b a s i s o f t h i s r e s u l t t h a t c o s m i c r a y s a r e somehow p r e v e n t e d f r o m e n t e r i n g d u s t c l o u d s , p e r h a p s b e i n g a b s o r b e d a t t h e p e r i p h e r y t o f o r m a s h e l l o f H I , t h i s p o s s i b i l i t y seems e x c l u d e d by ou r e a r l i e r d e t e r m i n a t i o n t h a t H I d o e s n o t f o r m a s h e l l as p r e v i o u s l y t h o u g h t . G l a s s g o l d (1976) h a s s u g g e s t e d t h a t ou r r e s u l t m i g h t i n f a c t be u s e d t o d e r i v e a new, s m a l l e r v a l u e f o r t h e p r i m a r y c o s m i c r a y i o n i z a t i o n r a t e Cp • ^ e n o t p u r s u e t h i s p o s s i b i l i t y h e r e . 3 . R e s u l t s o f O t h e r O b s e r v a t i o n s . I n T a b l e V I I we summar i ze a l l t h e known c a s e s i n w h i c h p o s i t i v e l i n e d e t e c t i o n s h a v e b e e n made on L134 u s i n g beam p o s i t i o n s w h i c h i n c l u d e ou r n o m i n a l c e n t e r p o s i t i o n . Co lumns ( 5 ) , (6) and (7) o f t h i s t a b l e w a r r a n t f u r t h e r d i s c u s s i o n . I t i s r e a d i l y a p p a r e n t f r o m c o l u m n (5) t h a t t h e LSR v e l o c i t i e s o f a l l l i n e r a d i a t i o n d e t e c t e d i n L134 a g r e e w e l l w i t h i n t h e e r r o r s , and t h i s a r g u e s s t r o n g l y i n f a v o u r o f t h e c o e x i s t e n c e o f H ? ^ ^ C O , OH, C S , CH and CO w i t h i n t h e 2 . 7 k m / s e c c l o u d o f L 1 3 4 . The o n l y e x c e p t i o n i s Xogen ( H C 0 + ?) and t h i s s i m p l y r e f l e c t s t h e f a c t t h a t t h e r e s t f r e q u e n c y i s unknown. S i n c e B u h l and S n y d e r (1970) assumed a r e s t f r e q u e n c y o f Table VII: Detailed Observational Results at Center of L134. Molecule (1) Transition (2) HPBW (') (3) A (Kelvin) (4) V LSR (km/sec) (5) AV (km/sec) (6) . AV b c (km/sec) (7) T K (Kelvin) (8) Reference (9) 1 2 c o J = 1-0 2.5 8.3 2.70 ± .33 1.66a 12 Present work 1 3 c o J = 1-0 2.6 4.3 2.70 ± .33 0.73a 0.72 <12 Present work c 1 8 o J = 1-0 2.6 1.0 2.70 ± .33 0.66a 0.65 <12 Present work OH 2 3 T T 3 / 2 , J 2 15 0.348 3.00 ± .01 0.58 0.55 Heiles, 1968 CH 2 TT, , J = H 15 0.15 2.70 ± .10 0.8 0.77 Rydbeck et al.,1975 CS J = 1-0 2.3 1.0 2.80 ± .30 0.63a 0.62 >4.5e Martin and Barrett, 1975 CS J = 2-1 1.1 0.15 3.00 ± 0.15 1.06a 1.05 >3.0e Martin and Barrett, 1975 Xogen 1.2 5 C (8) d 0.85a (0.85) Buhl and Synder,1970 H2CO Jk-k+ = 1ir 110 8 2.80 ± .01 0.35 1.69 Heiles, 1973 H \ -3 7 -20 2.80 ± .03 1.11 0.82 <20 Chu, 1975 Notes to the Table: a. Corrected for instrumental broadening. h, AV corrected for thermal broadening assuming T K = 12K. c. This i s T., not T * A A d. This result reflects the unknown rest frequency for Xogen. e. Assumes optically thick line. 89.190 GHz b a s e d on LSR v e l o c i t i e s i n o t h e r s o u r c e s , we may u s e t h e i r d e r i v e d LSR v e l o c i t y o f 8 k m / s e c f o r L134 t o d e r i v e a more a c c u r a t e r e s t f r e q u e n c y . T h e v e l o c i t y we a d o p t i s (2.89 ± 0.22) k m / s e c , w h i c h i s t h e w e i g h t e d mean v a l u e d e r i v e d f r o m t h e r e s u l t s i n T a b l e V I I . The r e s t f r e q u e n c y f o r Xogen i s t h e n : V 0 (Xogen) = 8 9 . 1 8 8 4 8 ± 0 . 0 0 0 0 5 GHz I f i n f a c t X o g e n i s H C 0 + , a s o r i g i n a l l y s u g g e s t e d by K l e m p e r e r ( 1 9 7 0 ) , t h e n t h e c a l c u l a t e d f r e q u e n c y f o r t h e J= 1-0 t r a n s i t i o n i s 8 9 . 2 4 6 G H z . The 58 MHz d i f f e r e n c e , a l t h o u g h l a r g e , i s n o t i n c o n s i s t e n t w i t h Xogen b e i n g H C 0 + , s i n c e t h e t h e o r e t i c a l c a l c u l a t i o n i s n o t e x p e c t e d t o b e v e r y p r e c i s e . We now d i s c u s s ' t h e v e l o c i t y f u l l w i d t h s a t h a l f i n t e n s i t y w h i c h h a v e b e e n summar i zed i n co lumn (6) o f T a b l e V I I . A l l o f t h e m i l l i m e t e r wave r e s u l t s p r e s e n t e d h e r e h a v e b e e n c o r r e c t e d f o r i n s t r u m e n t a l b r o a d e n i n g and i n a d d i t i o n , t h e r e s u l t s p r e s e n t e d i n co l umn (7) h a v e been c o r r e c t e d f o r t h e r m a l D o p p l e r b r o a d e n i n g as w e l l , by a s s u m i n g a k i n e t i c t e m p e r a t u r e = 12 K . (The l a t t e r e f f e c t i s o n l y s i g n i f i c a n t 12 f o r a t o m i c h y d r o g e n . ) We h a v e n o t i n c l u d e d t h e CO and ^ C O r e s u l t s i n c o l u m n (7) s i n c e t h e y seem t o w a r r a n t s p e c i a l c o n s i d e r a t i o n , one b e i n g t o o b r o a d and t he o t h e r , t o o n a r r o w i , I n a d d i t i o n , i t s h o u l d be p o i n t e d ou t t h a t a l t h o u g h we h a v e i n c l u d e d C S , t h e J = 2 - 1 l i n e i s v e r y weak and t h e J = 1-0 i s v e r y n o i s y ; i t t h e r e f o r e d e t r a c t s f r o m ou r r e s u l t . I n any e v e n t , t h e mean v a l u e f o r A V C f o u n d f r o m c o l u m n (7) i s 0 . 7 5 + 0 . 1 6 k m / s e c , w h i c h a g a i n s p e a k s v e r y s t r o n g l y f o r t h e 1 4 . ' A v e r y r e c e n t l a b o r a t o r y measurement (Woods, 1976) h a s f o u n d t h e r e s t f r e q u e n c y f o r H C 0 + t o be 8 9 . 1 8 8 5 1 G H z , i n e x c e l l e n t ag reement w i t h ou r r e s u l t f o r X o g e n . I t t h e r e f o r e a p p e a r s t h a t Xogen i s HC0+. 118. c o e x i s t e n c e o f t h e s e s p e c i e s . Had t h e CS and Xogen r e s u l t s b e e n e x -c l u d e d , we w o u l d h a v e f o u n d AVC = 0 . 7 0 ± 0 . 1 1 k m / s e c . We now c o n s i d e r t h e s p e c i e s t h a t w e r e n ' t i n c l u d e d i n t h i s sum, 12 12 name ly CO and ^ C O . The l a r g e l i n e w i d t h f o r CO c a n be e x p l a i n e d e a s i l y i n te rms o f a s a t u r a t e d J = 1-0 t r a n s i t i o n ; i n f a c t , t h e r a t i o AVU2)/AV(I3) = 2 . 3 i s i n good agreement w i t h t h e v a l u e 2 . 2 p r e d i c t e d by L i s z t e t a l . (1974) f o r t u r b u l e n t b r o a d e n i n g i n a homo-geneous i s o t h e r m a l med ium, a s s u m i n g r e a s o n a b l e v a l u e s f o r T('3)and a t e r r e s t r i a l i s o t o p e r a t e s . We s h a l l r e t u r n t o t h i s p o i n t i n t h e f o l l o w i n g s e c t i o n . The s m a l l h a l f w i d t h o f ^ C O , on t h e o t h e r h a n d , i s n o t u n e x p e c t e d s i n c e i t i s a p p a r e n t l y an a n t i - m a s e r . T h i s i s a l s o c o n s i s t e n t w i t h ou r comments i n t h e i n t r o d u c t i o n t h a t t h e l i n e w i d t h s o f ^ C O a r e n o r m a l l y o b s e r v e d t o be n a r r o w e r t h a n t h o s e o f OH i n d u s t c l o u d s , and t h a t , w h i l e t h e d i s t r i b u t i o n o f OH i s u b i q u i t o u s , ^ C O seems t o r e q u i r e h i g h H 2 d e n s i t i e s t o be s e e n , p r e s u m a b l y s i n c e i t i s b e i n g r e f r i g e r a t e d b y a c o l l i s i o n a l pumping m e c h a n i s m . B e f o r e c l o s i n g t h i s s e c t i o n we s h a l l make a few g e n e r a l comments . F i r s t , a l t h o u g h we d i d n o t i n c l u d e NH^ i n t h e above d i s c u s s i o n , i t h a s been o b s e r v e d i n L 1 8 3 , a d u s t c l o u d n o r t h o f L134 ( w h i c h f o r some r e a s o n i s o f t e n r e f e r r e d t o as L 1 3 4 N ) . Had we i n c l u d e d i t , o u r r e m a r k s w o u l d n o t have b e e n a l t e r e d , s i n c e t h e o b s e r v e d l i n e w i d t h f o r ammonia i n L 1 8 3 i s 1 .0 ± 0 . 2 k m / s e c . S e c o n d , we f o l l o w up a r e m a r k made by T u r n e r (1974) t h a t o n l y s i m p l e m o l e c u l e s and r a d i c a l s a r e s e e n i n d a r k d u s t c l o u d s . T h i s i s n o t s i m p l y a s e l e c t i o n e f f e c t s i n c e a t t e m p t s have b e e n made t o d e t e c t H C 3 N ( T u r n e r , 1 9 7 1 ) . a n d C H 3 0 H ( B a r r e t t e t a l . , 1 9 7 1 ) , as w e l l as t h e s i m p l e r s p e c i e s HCN ( S y n d e r and B u h l , 1971) and H^O ( T u r n e r e t a l . , 1 9 7 0 ) . I t m i g h t be p o s s i b l e however t o a r g u e t h a t t h i s r e f l e c t s a l a c k o f s e n s i t i v i t y , s i n c e n e i t h e r CS n o r NH^ we re d e t e c t e d i n e a r l y s u r v e y s . F u r t h e r m o r e , HCN may h a v e b e e n d e t e c t e d ( D i c k m a n , 1975c ) and i t d o e s n ' t seem l i k e l y t h a t ^ 0 , e v e n i f i t was p r e s e n t i n d a r k c l o u d s , w o u l d be s u f f i c i e n t l y ou t o f e q u i l i b r i u m w i t h t h e 2 . 7 K b a c k g r o u n d t h a t i t w o u l d b e o b s e r v a b l e ; t h e n o r m a l l y o b s e r v e d J " k _ ) c + = 5 2 _, _ 6-^6 t r a n s i t i o n i s some 450 cm above t h e g r o u n d r o t a t i o n a l s t a t e (Rank e t a l . , 1 9 7 1 ) . I n any c a s e , i t may be w o r t h s t u d y i n g what comp lex m o l e c u l e s c a n be fo rmed i f o n l y H , H 2 , H 2 C 0 , C O , C H , NH^ and CS a r e a v a i l a b l e t o w o r k w i t h . F o r e x a m p l e , comp lex m o l e c u l e s m i g h t b e f o r m e d on d u s t g r a i n s and o n l y be r e l e a s e d and e x c i t e d a t more a d v a n c e d s t a g e s o f c l o u d c o l l a p s e and s t a r f o r m a t i o n . -120. E . The Dynam ics and S t a b i l i t y o f L134 I n t h i s s e c t i o n we i n v e s t i g a t e t h e v a r i o u s d y n a m i c a l m o d e l s w h i c h m i g h t be u s e d t o i n t e r p r e t o u r o b s e r v a t i o n s o f L 1 3 4 . Beyond s i m p l e p r e s s u r e e q u i l i b r i u m a rguments we s h a l l a l s o c o n s i d e r v a r i o u s t u r b u l e n t and r a d i a l m o t i o n m o d e l s . I t does n o t a p p e a r howeve r t h a t t h e s p e c t r a l r e s o l u t i o n o f ou r d a t a w i l l e n a b l e a d e f i n i t i v e answer t o be made w i t h r e g a r d t o i n t e r p r e t i n g t h e l i n e s h a p e s . 1 . P r e s s u r e E q u i l i b r i u m . We c o n s i d e r f i r s t t h e s t a b i l i t y o f L 1 3 4 i n te rms o f i t s s u r r o u n d i n g s . The mos t n a i v e a p p r o a c h we c a n t a k e i s t o c a l c u l a t e t h e J e a n s m a s s . U s i n g o u r d e r i v e d p a r a m e t e r s f o r t h e 2 . 7 k m / s e c c l o u d , we f i n d t h a t M J ' - I O M O J w h e r e a s t h e o b s e r v e d mass i s > 34 M g . Thus we w o u l d e x p e c t t h i s mos t m a s s i v e component o f L134 t o h e c o l l a p s i n g . The d i f f i c u l t y h e r e , h o w e v e r , i s t h a t i f t u r b u l e n c e p l a y s a r o l e , t h e " e f f e c t i v e " t e m p e r a t u r e may b e c o n s i d e r a b l y l a r g e r t h a n t h e k i n e t i c t e m p e r a t u r e u s e d t o d e r i v e t h e above r e s u l t . We t h e r e -f o r e c o n s i d e r p r e s s u r e e q u i l i b r i u m and u s e S p i t z e r ' s (1968) r e s u l t t h a t : where p0 i s t h e e x t e r n a l p r e s s u r e on t he c l o u d and t h e o t h e r p a r a m e t e r s h a v e t h e i r p r e v i o u s m e a n i n g s . The f i r s t t e rm on t h e r i g h t hand s i d e o f t h i s e q u a t i o n r e p r e s e n t s t h e t h e r m a l p r e s s u r e o f t h e c l o u d , w h i l e t h e . m a g n e t i c f i e l d s and r o t a t i o n , w h i c h w o u l d c o n t r i b u t e as p o s i t i v e i n t e r n a l p r e s s u r e t e r m s . To e v a l u a t e p© we assume t h e gas p r e s s u r e a t t h e (39) second t e r m r e p r e s e n t s t h e g r a v i t a t i o n a l p r e s s u r e ; we have i g n o r e d b o t h 1 2 1 . - 1 2 2 g a l a c t i c m i d - p l a n e i s 1 .3 x 10 d y n e s / c m and t h a t i t f a l l s o f f as , whe re H (= 100 p c ) i s t h e h a l f - w i d t h o f t h e g a l a c t i c d i s k , and 2 i s t h e h e i g h t above t h e m i d - p l a n e . F o r L134 a t an assumed d i s t a n c e o f 150 p c and /r1 = 3 5 . 8 ° , we f i n d £ ~ 8 8 p c , so t h a t p G = 0 . 6 x 1 0 - 1 2 2 d y n e s / c m . F o r t h e 2 . 7 k m / s e c c l o u d , u s i n g t h e p a r a m e t e r s i n T a b l e V I and a s s u m i n g T = 12 K and JA. - 2 . 3 3 , we f i n d t h a t t h e e x t e r n a l p r e s s u r e and g r a v i t y e x c e e d t h e i n t e r n a l p r e s s u r e so t h e c l o u d w i l l c o l l a p s e . T h i s r e s u l t may be p r e m a t u r e h o w e v e r , s i n c e i f t h e o b s e r v e d l i n e w i d t h s a r e due t o t u r b u l e n c e r a t h e r t h a n r a d i a l m o t i o n s , t h e t u r b u l e n c e w i l l a l s o c o n t r i b u t e t o t h e i n t e r n a l p r e s s u r e . I n f a c t , t h e t h e r m a l p r e s s u r e w i l l be n e g l i g i b l e i n c o m p a r i s o n i f t h i s i s t h e c a s e . To c h e c k what e f f e c t t h i s m i g h t h a v e on t h e s t a b i l i t y o f t h e 2 . 7 k m / s e c c l o u d , we c o n v e r t t h e mean v e l o c i t y h a l f w i d t h f r o m T a b l e V I I t o a r a d i a l v e l o c i t y d i s p e r s i o n and t h e n u s e i t t o r e p l a c e t h e f a c t o r (JtT^rr]Hjn,) ± n equa t j ( 3 9 ) . The r i g h t hand s i d e o f e q u a t i o n (39) t h e n e q u a l s 0 . 9 x 10" 2 d y n e s / c m , w h i c h , i s 50% g r e a t e r t h a n t h e e x t e r n a l p r e s s u r e p 0 ; as a r e s u l t , t h e c l o u d w i l l e x p a n d . T h i s w i l l o f c o u r s e a l s o be a s s i s t e d by m a g n e t i c and c e n t r i f u g a l p r e s s u r e . I t t h e r e f o r e a p p e a r s t h a t , i f t h e o b s e r v e d l i n e s h a p e s a r e due t o t u r b u l e n t b r o a d e n i n g , L134 must be e x -p a n d i n g . A r e t h e l i n e s h a p e s i n f a c t due t o t u r b u l e n c e ? B e f o r e a t t e m p t -i n g t o answer t h i s q u e s t i o n we f i r s t p o i n t ou t t h a t i t i s p o s s i b l e t o a v o i d e x p a n s i o n o f L134 and s t i l l assume t u r b u l e n c e i f we change i t s d i s t a n c e , t h e r e a s o n b e i n g t h a t t h e t h e r m a l p r e s s u r e s c a l e s a s t h e r e c i p r o -c a l o f t h e r a d i u s , R , w h i l e t h e d e r i v e d g r a v i t a t i o n a l p r e s s u r e i s i n d e p e n -den t o f R . T h e r e f o r e i f L134 we re f u r t h e r away t h a n 150 p c — o u r u p p e r l i m i t i s 170 p c — we c o u l d s t i l l have t u r b u l e n t l i n e s h a p e s and : i o n , - 1 2 122. n o t have L134 e x p a n d i n g . The n e c e s s a r y d i s t a n c e w o u l d b e ^ 163 p c , b u t t h e u n c e r t a i n t i e s i n t h i s d e r i v a t i o n a r e l a r g e . 2 . I n t e r p r e t a t i o n o f L i n e S h a p e s . We now a d d r e s s t h e p r o b l e m o f what ou r o b s e r v e d l i n e s h a p e s mean i n te rms o f t h e d y n a m i c s o f L 1 3 4 . 12 13 18 I n F i g u r e 12 we show p l o t s o f t h e a v e r a g e CO, CO and C 0 e m i s s i o n o v e r t h e 2 . 7 k m / s e c c l o u d as d e f i n e d b y t h e HI a b s o r p t i o n h a l f i n t e n s i t y c o n t o u r . I t was f r o m t h e s e p l o t s t h a t we d e r i v e d t h e l i n e w i d t h s p r e -s e n t e d i n T a b l e V I I . A s was i n d i c a t e d e a r l i e r , t h e r a t i o A V ( I Z ) / A V 0 3 ) was f o u n d t o be 2 . 3 — a r e s u l t c o n s i s t e n t w i t h a G a u s s i a n d i s t r i b u t i o n o f o p t i c a l d e p t h , and h e n c e t u r b u l e n t l i n e b r o a d e n i n g . But f r o m what h a s j u s t been s a i d , L134 w o u l d t h e n most l i k e l y be e x p a n d i n g . A l t h o u g h t h i s i n i t s e l f i s n o t t h e o r e t i c a l l y o b j e c t i o n a b l e , i t i s more s a t i s f y i n g t o t h i n k t h a t c l o u d s condense i n t o s t a r s — e v e n i f one c l o u d i s a t e r r i b l e s a m p l e ! I n f a c t , t h e samp le i s l a r g e r t h a n t h i s . D i c k m a n ( 1 9 7 5 b ) , on t h e b a s i s o f h i s o b s e r v a t i o n s o f 64 d a r k d u s t c l o u d s , a r g u e s a g a i n s t b o t h m i c r o - and m a c r o - t u r b u l e n c e . M i c r o - t u r b u l e n c e i s e x c l u d e d s i n c e i t i s d i f f i c u l t t o c o n c e i v e o f an e n e r g y s o u r c e w h i c h w o u l d s u s t a i n t h e m i c r o - t u r b u l e n c e o v e r t h e l i f e t i m e o f t h e c l o u d , w h i l e m a c r o - t u r b u l e n c e r e q u i r e s a s c a l e l e n g t h o f 0 . 1 - 1 .0 pc and s h o u l d t h e r e f o r e be o b s e r v a b l e . M a c r o - t u r b u l e n c e may i n f a c t h a v e b e e n o b s e r v e d i n t h e O r i o n M o l e c u l a r C l o u d ( P h i l l i p s e t a l . , 1 9 7 4 ) , b u t h a s n o t been s e e n i n any d a r k d u s t c l o u d s . We a r e t h e r e f o r e l e f t t o c o n s i d e r s t r e a m i n g o r r a d i a l m o t i o n s . I f t h e a p p r o x i m a t i o n i s made t h a t t h e l i n e - o f - s i g h t f l o w v e l o c i t y i n a d a r k d u s t c l o u d i s l a r g e compared t o t h e c h a r a c t e r i s t i c t h e r m a l o r m i c r o -t u r b u l e n t v e l o c i t i e s , t h e t r a n s f e r o f l i n e r a d i a t i o n w i t h i n t h e c l o u d 124, becomes a l o c a l p r o b l e m i n w h i c h t h e " t r a p p i n g " o f l i n e p h o t o n s may p l a y an i m p o r t a n t r o l e . The s o l u t i o n t o t h i s p r o b l e m f o r v a r i o u s c l o u d g e o -m e t r i e s h a s been c o n s i d e r e d by s e v e r a l a u t h o r s ( S c o v i l l e and S o l o m o n , 1 9 7 4 ; G o l d r e i c h and Kwan , 1 9 7 4 , de J o n g e t a l . , 1975) b a s e d on t h e e a r l i e r wo rk o f S o b o l e v ( 1 9 6 0 ) , C a s t o r (1970) and L u c y (1971) f o r e x p a n d i n g s t e l l a r e n v e l o p e s . The i n i t i a l m o t i v a t i o n f o r a d o p t i n g s u c h m o d e l s had b e e n t o 12 f i n d a means f o r e x p l a i n i n g t h e s i m i l a r i t y o f l i n e s h a p e s f o u n d f o r CO 13 12 and CO, a l t h o u g h t h e CO was t h o u g h t t o be s a t u r a t e d . I n a s i m p l e t u r b u l e n t c l o u d m o d e l , t h e l i n e s h a p e s w o u l d h a v e b e e n e x p e c t e d t o be d i f f e r e n t s i n c e e a c h i s o t o p i c s p e c i e s w o u l d be o b s e r v e d f r o m d i f f e r e n t r e g i o n s o f t h e c l o u d . By s t u d y i n g t h e b e h a v i o u r o f l i n e s h a p e s a c r o s s a c l o u d i t i s p o s s i b l e t o g e t some f e e l i n g f o r t h e k i n d o f m o t i o n w h i c h i s b e i n g o b s e r v e d . I n F i g u r e 13 we show t h e b e h a v i o u r o f t h e v e l o c i t y f u l l w i d t h i n t h e l i n e 13 12 w i n g s f o r o u r CO o b s e r v a t i o n s i n L 1 3 4 . The CO r e s u l t s a r e s i m i l a r on t he w e s t e r n s i d e o f L 1 3 4 , w h i c h i s d o m i n a t e d by t h e 2 . 7 k m / s e c c l o u d , bu t a r e c o m p l i c a t e d i n t h e e a s t by t h e p r e s e n c e o f t h e o t h e r c l o u d s . B e -c a u s e o f t h e a p p a r e n t c i r c u l a r symmetry and c o i n c i d e n c e w i t h t h e 2 . 7 k m / s e c c o n s t a n t v e l o c i t y c o n t o u r o f F i g u r e 1 1 , we m i g h t be l e d t o b e l i e v e t h a t t h e 2 .7 k m / s e c c l o u d i n L134 i s u n d e r g o i n g some s o r t o f r a d i a l m o t i o n . B e f o r e m a k i n g t h i s a s s u m p t i o n h o w e v e r , we must f i r s t c o n s i d e r t h e c a s e f o r t u r b u l e n c e . I f we s u p p o s e t h a t t h e o p t i c a l d e p t h t t h r o u g h t h e c e n t e r o f t h e c l o u d i s l a r g e and t h a t t h e m o t i o n i s t u r b u l e n t , t h e n t h e r e i s no r e a s o n a p r i o r i t o e x p e c t t h e maximum l i n e w i d t h s o r r a d i a t i o n t e m p e r a t u r e 125. to occur at the cloud center, as i s apparent i n Figures 13 and 14. Only the near cloud surface would be observable and one region would be no different from another. If on the other hand T(|3) through the cloud center i s small, we would expect the observed line strength to f a l l off 2 ^  as (1 - ( "X./R ) ) 2, where 7C is the projected distance from the cloud center, and R is the cloud radius. As can be seen by examining Figure 14, the maximum radiation temperature contours f a l l off almost linearly with (~x-/R ). It therefore seems plausible that we might be dealing with radial motion, although i t is not clear that radial motion can account 12 13 for the observed ratio of the CO to CO line widths mentioned earlier. We shall return to this point shortly. Assuming the motion i s radial, we now attempt to determine i t s behaviour, that i s , we wish to determine a relationship of the form, V U ) = V U / R ) * (40) where V i s the radial velocity at the surface of a spherical cloud, A/ is the radial distance from the cloud center and (X is the as yet un-known power law dependence. Now for a given exponent cX i t is a simple matter to show that the f u l l width i n the line wings AV^ is given by: (X < O (41) (42) o 1.5 1.0 _ J 0.5 I 0.0 I -0.5 -1.0 _ l -1 L Y N D S 1 3 4 1 3 C ] 6 0 VELOCITY FULL WIDTH ]N WINGS CONTOUR UNIT (KM/SEC) 1.00 \ _j j — j 1 — i . O 0 . 5 0 . 0 - 0 . 5 RIGHT ASCENSION (MIN) 1.5 - 1 . 0 Figure 13. 1.0 0.5 0.0 -0.5 -1.0 -J 1 1 I I L Y N D S 1 3 4 1 3 C 1 6 0 MAXIMUM RADIATION TEMPERATURE CONTOURS CONTOUR UNIT (KELVIN) 0.75 Figure 14. 1 2 8 . where R and V , as b e f o r e , r e p r e s e n t t h e r a d i u s and s u r f a c e v e l o c i t y , and X i s t h e p r o j e c t e d r a d i u s . On a n a l y z i n g t h e b e h a v i o u r o f AVyv a s a f u n c t i o n o f X. f o r s e v e r a l r a y s i n F i g u r e 1 3 , away f r o m t h e d i r e c t i o n s o f t h e 0 . 1 , 0 . 7 and 4 . 0 k m / s e c c l o u d s , we c a n i m m e d i a t e l y e x c l u d e a l l m o d e l s w i t h tX ^  o. P h y s i c a l l y t h i s i s s a t i s f y i n g s i n c e i t e x c l u d e s d e n s i t y p r o f i l e s i n c l o u d s w h i c h i n c r e a s e w i t h ( A-/R ) . I n p a r t i c u l a r i t e x c l u d e s t h e u n i f o r m d e n s i t y , p r e s s u r e - f r e e c o l l a p s e m o d e l o f G o l d -r e i c h and Kwan (1974). The b e s t power l a w t o f i t t o o u r d a t a a p p e a r s t o be one w i t h = T h i s i s t h e same dependence w h i c h L o r e n (1975) f o u n d f o r t h e c l o u d s a r o u n d R CrA and L k H ^ 1 9 8 , and i s c o n s i s t e n t w i t h t h e a s y m p t o t i c s i m i l a r i t y s o l u t i o n s o f L a r s o n ( 1 9 7 2 ) , w h i c h assume t h e f o r m V"(A) ^ (A/R) z away f r o m t h e edge o f t h e c l o u d . I n f a c t , o u r o b s e r v a t i o n s do n o t f o l l o w a s t r i c t l y (x . /R. ' ) * dependence n e a r t h e c l o u d edge bu t v a r y more l i k e X a C x / R ) , s o t h i s i s a l s o a c c e p t a b l e . What i s n o t c l e a r however i s t h e i m p o r t a n c e o f t h e c e n t r a l h e a t s o u r c e s u c h as L o r e n h a s o b s e r v e d . A l t h o u g h L 1 3 4 h a s no v i s i b l e c e n t r a l s o u r c e , i t w o u l d be v e r y i n t e r e s t i n g t o f i n d o u t i f i t h a s a n a s s o c i a t e d i n f r a r e d s o u r c e . I t i s w o r t h n o t i n g (as has b e e n p o i n t e d ou t by L o r e n (1975)) t h a t f o r c o l l a p s e o r e x p a n s i o n m o d e l s w i t h (X < 0 — w h i c h L134 seems t o s a t i s f y — t h e r a d i a t i v e t r a n s f e r p r o b l e m i s no l o n g e r a l o c a l p r o b l e m ; i t how-, e v e r s t i l l a w a i t s t h e o r e t i c a l t r e a t m e n t . I t w i l l be i n t e r e s t i n g t o f i n d ou t w h e t h e r o r n o t s u c h a m o d e l c a n a c c o u n t f o r t h e l i n e w i d t h r a t i o s we have o b s e r v e d ; t h e s e c u r r e n t l y s a t i s f y o n l y t h e t u r b u l e n t m o d e l . B e f o r e l e a v i n g t h e p r o b l e m o f i n t e r p r e t i n g t h e l i n e s h a p e s i n t e rms o f a dynam ic c l o u d m o d e l , we w i l l now b r i e f l y d i s c u s s some u n p u b l i s h e d 129, 12 13 o b s e r v a t i o n s by Knapp e t a l . (1976) o f CO and CO i n L 1 3 4 ; t h e s e w e r e o b t a i n e d u s i n g t h e K i t t P e a k 3 6 ' m i l l i m e t e r wave t e l e s c o p e and a s p e c t r o -m e t e r o f 100 KHz r e s o l u t i o n — o u r r e s o l u t i o n was 250 K H z . A s p o i n t e d ou t e a r l i e r , t h e s e r e s u l t s we re o b t a i n e d on a N o r t h S o u t h s t r i p a b o u t 0 . 5 m i n u t e s E a s t o f o u r n o m i n a l c e n t e r p o s i t i o n . To show t h a t t h e g e n e r a l f e a t u r e s o f t h e 100 KHz and 250 KHz d a t a a g r e e , we p l o t i n F i g u r e 12 15 t h e c o r r e s p o n d i n g CO d a t a f o r t h e p o s i t i o n o f o u r d e e p e s t d o u b l e f e a t u r e d p r o f i l e ; t h e y a r e s c a l e d t o t h e same a m p l i t u d e a t 2 . 1 k m / s e c . I t i s c l e a r t h a t t h e agreement i s g o o d . The 100 KHz d a t a , h o w e v e r , g e n e r a l l y shows much more s t r u c t u r e t h a n i n t h i s e x a m p l e . T h i s i s i l l u s -12 13 t r a t e d i n F i g u r e 1 6 , w h i c h p r e s e n t s t h e 100 KHz CO and CO d a t a f o r a p o s i t i o n a p p r o x i m a t e l y c o r r e s p o n d i n g t o ou r p o s i t i o n 37 o r ( + 0 . 5 ™ , - 4 ' ) . 12 13 I t w i l l be n o t e d h e r e t h a t t h e 2 .7 k m / s e c f e a t u r e i n b o t h t h e CO and CO d a t a a p p e a r s t o be s p l i t i n t o two components — as s u g g e s t e d by t h e d a s h e d p r o f i l e s — and t h a t t h e s e have u n e q u a l a m p l i t u d e s . The r e l a t i v e a m p l i t u d e s , a l t h o u g h t h e o r e t i c a l l y i n t e r e s t i n g as we w i l l m e n t i o n b e l o w , a r e p r o b a b l y n o t s i g n i f i c a n t i n v i e w o f t h e n o i s e ; t h e same m i g h t a l s o have b e e n s a i d o f t h e two components t h e m s e l v e s i f t h e y d i d n ' t o c c u r a s f r e q u e n t l y as t h e y d o . T h i s s p l i t t i n g i s a l s o s u g g e s t e d i n OH o b s e r v a t i o n s ( H e i l e s , 1 9 6 9 b ) d e s p i t e t h e f a c t t h a t beam s m o o t h i n g may be i m p o r t a n t i n t h i s c a s e . We f e e l t h a t t h e two components a r e r e a l , and p o s s i b l y r e p r e -s e n t t h e two l i n e - o f - s i g h t components o f a r a d i a l c o l l a p s e o r e x p a n s i o n . -I As p o i n t e d ou t by L o r e n ( 1 9 7 5 ) , a r a d i a l c o l l a p s e p r o c e e d i n g as (A./R) w o u l d n o t be e x p e c t e d t o show a c e n t r a l l y r e v e r s e d p r o f i l e f o r a l i n e - o f -s i g h t p a s s i n g t h r o u g h a c l o u d c e n t e r , s i n c e gas a c c u m u l a t i n g i n t h e c l o u d c o r e f r om d i r e c t i o n s a p p r o x i m a t e l y n o r m a l t o t h e l i n e - o f - s i g h t w o u l d r a d i a t e a t t h e LSR v e l o c i t y o f t h e c l o u d . F u r t h e r o u t , h o w e v e r , t h i s i s Figure 16. 132. n o t t h e c a s e ; i n s t e a d , s i n c e we a r e a s s u m i n g oC<0, e a c h p a r t o f t h e e m i t t e d l i n e p r o f i l e w i l l r e c e i v e r a d i a t i o n f r om two r e g i o n s o f t h e c l o u d . Whether o r n o t t h e s e r e g i o n s a r e a t t h e same t e m p e r a t u r e — as s u g g e s t e d by ou r r e s u l t s — o r a t d i f f e r e n t t e m p e r a t u r e s — as s u g g e s t e d by L a r s o n ' s t h e o r e t i c a l m o d e l i n w h i c h IK."0 ( a / R ) 2 — a d i f f e r e n c e i n t h e s t r e n g t h of t h e two components w i l l o c c u r . I f we assume f o r examp le t h a t t h e c l o u d i s c o l l a p s i n g and c o n s i d e r an i s o t h e r m a l m o d e l , t h e n we w o u l d e x p e c t t h e h i g h v e l o c i t y ( o r r e d s h i f t e d ) component t o be s t r o n g e r t h a n t h e l ow v e l o c i t y ( o r b l u e s h i f t e d ) componen t , s i n c e t h e l a t t e r w o u l d be p a r t i a l l y a b s o r b e d by t h e n e a r e r h i g h v e l o c i t y g a s . I f on t h e o t h e r hand we c o n s i d e r L a r s o n ' s c o l l a p s e m o d e l i n w h i c h t h e t e m p e r a t u r e d e c r e a s e s w i t h r a d i u s , t h e o p p o s i t e w o u l d be t r u e , s i n c e c o l d h i g h v e l o -c i t y gas and h o t l o w v e l o c i t y gas w o u l d d o m i n a t e t h e e m i s s i o n p r o f i l e . I n t h e c a s e o f e x p a n s i o n , a l l t h e s t a t e m e n t s made above w o u l d have t o be r e v e r s e d , t h u s i t may be p o s s i b l e t o d i s t i n g u i s h b e t w e e n c o l l a p s e o r e x p a n s i o n i f t h e t e m p e r a t u r e d i s t r i b u t i o n i s known . A s a l -r e a d y r e m a r k e d , ou r d a t a s u g g e s t t h a t t h e 2 .7 k m / s e c c l o u d i s i s o t h e r m a l ; 13 t h e CO p r o f i l e i n F i g u r e 16 t h e r e f o r e m i g h t l e a d u s t o e x p e c t c o n t r a c -t i o n ^ T h i s c o n c l u s i o n i s p r o b a b l y p r e m a t u r e , h o w e v e r , s i n c e t h e s i g n a l -t o - n o i s e f o r t h i s d a t a i s n o t g o o d . I t i s w o r t h r e m a r k i n g t h a t L a r s o n ' s T J ^ C A / R ) 2 dependence may no t c o n t r a d i c t t h e f a c t t h a t we s e e a n e a r l y i s o t h e r m a l c l o u d , f o r (a) when L a r s o n c o n s i d e r s a more r e a l i s t i c o p a c i t y l a w , t h e dependence o f t h e t e m p e r a t u r e on r a d i u s becomes l e s s s t e e p , and (b) t h e ( A / R ) 2 dependence w h i c h L a r s o n f i n d s , a p p l i e s s t r i c t l y i n The CO p r o f i l e i n F i g u r e 1 6 , a l t h o u g h i t h a s p e a k s o f o p p o s i t e s e n s e , i s c l e a r l y b l e n d e d w i t h t h e 0 .7 k m / s e c c l o u d and i s a l s o s a t u r a t e d . I t i s t h e r e f o r e more d i f f i c u l t t o i n t e r p r e t . t h e c o r e r e g i o n , and may n o t a p p l y f o r t h e o u t e r r e g i o n s w h i c h we o b s e r v e . A d e t a i l e d c o m p a r i s o n i s n o t p o s s i b l e , h o w e v e r , s i n c e L a r s o n h a s n o t c a l c u l a t e d m o d e l s w i t h masses g r e a t e r t h a n 10 Mo- I f t h e q u e s t i o n o f c o l l a p s e o r e x p a n s i o n i s t o be s e t t l e d , i t i s c l e a r t h a t h i g h r e s o l u t i o n o b s e r v a t i o n s o f good s i g n a l - t o - n o i s e a r e n e e d e d , b u t i n a d d i t i o n t h e o r e t -i c a l c a l c u l a t i o n s f o r m o d e l s o f h i g h e r m a s s , as w e l l as a s o l u t i o n o f t h e n o n - l o c a l r a d i a t i v e t r a n s f e r p r o b l e m , a r e a l s o r e q u i r e d . 3 . Bound O r b i t a l M o t i o n . The f i n a l d y n a m i c a l p r o b l e m we d i s c u s s i s t h e p o s s i b i l i t y t h a t t h e c l o u d s c o m p r i s i n g L134 m i g h t be i n bound o r b i t a l m o t i o n about e a c h o t h e r . S i n c e f o r a b i n a r y s y s t e m , t h e r e l a t i v e o r b i t a l v e l o c i t y i s g i v e n b y : V~ - (G M T IOS)/7~ , where M T i s t h e t o t a l mass o f t h e s y s t e m , and CX , t h e m u t u a l s e p a r a t i o n o f t h e c o m p o n e n t s , i t i s a s i m p l e m a t t e r t o show, u s i n g t h e m a s s e s i n T a b l e V I and a p r o j e c t e d s e p a r -a t i o n o f 1 7 ' f o r t h e 2 .7 and 4.0 k m / s e c c l o u d s , t h a t bound o r b i t a l m o t i o n i s p o s s i b l e o n l y i f V"<0.49 k m / s e c . S i n c e t h e o b s e r v e d r e l a t i v e v e l o c i t y i s 1 .3 k m / s e c and CL c a n o n l y b e i n c r e a s e d , we c o n c l u d e t h a t t h e s e c l o u d s c a n n o t be i n bound o r b i t a l m o t i o n . I n c r e a s i n g t h e t o t a l mass o f t h e s y s -tem c o u l d s a v e u s , bu t i t w o u l d h a v e t o be i n c r e a s e d by a f a c t o r o f more t h a n 7 and t h i s seems u n l i k e l y . F u r t h e r m o r e , any o t h e r c o m b i n a t i o n s o f c l o u d s l e a d t o even l e s s l i k e l y s i t u a t i o n s . We t h e r e f o r e c o n c l u d e t h a t none o f t h e c l o u d s c o m p r i s i n g L134 c a n be i n o r b i t a l m o t i o n . F i n a l l y , we remark t h a t , s i n c e t h e e s c a p e v e l o c i t y o f two g r a v i t a t i n g b o d i e s i s s i m p l y t i m e s t h e i r r e l a t i v e v e l o c i t y when t h e y a r e i n bound o r b i t s , th i c l o u d s c o m p r i s i n g L134 a r e n o t g r a v i t a t i o n a l l y bound t o e a c h o t h e r i f i n f a c t t h e r e l a t i v e v e l o c i t y o f t h e c l o u d s r e p r e s e n t s a s e p a r a t i o n . T h i s o f c o u r s e i s r e q u i r e d f o r f r a g m e n t a t i o n , b u t i s a l s o c o n s i s t e n t w i t h t h e f a c t t h a t t h e o b s e r v e d s e p a r a t i o n of t h e components a g r e e s w i t h t h e s e p a r a t i o n 134. w h i c h w o u l d be p r e d i c t e d a s s u m i n g t h e o b s e r v e d r e l a t i v e v e l o c i t i e s and a c h a r a c t e r i s t i c l i f e t i m e o f 10^ y e a r s . I t i s i n t e r e s t i n g t o s p e c u l a t e w h e t h e r t h e f o u r c l o u d s n e a r L134 a r e a l s o u n b o u n d , and w h e t h e r o r n o t a l l t h e s e o b j e c t s t h e m s e l v e s may a t some t i m e h a v e b e e n p r o j e c t e d f r o m t h e S c o r p i u s - O p h i u c h u s comp lex as t h e r e s u l t o f some s o r t o f f r a g m e n t a t i o n p r o c e s s . On t h e b a s i s o f d i f f e r e n t i a l g a l a c t i c r o t a t i o n , we w o u l d e x p e c t L134 t o be m o v i n g away f r o m t h e l o c a l s t a n d a r d o f r e s t a t ~ 0 . 4 k m / s e c . I t i s t h e r e f o r e p o s s i b l e t h a t t h e most m a s s i v e component o f L134 i s i n f a c t m o v i n g away f r o m t h e g a l a c t i c p l a n e . 135. F. Summary and Concluding Remarks In the preceeding pages we have presented the analysis and inter-1 2 13 1 8 pretation of CO, CO and C 0 observations of an isolated galactic dark dust cloud L134. We have shown that L134 is comprised of four molecular clouds, and that the separation of these clouds is consistent with the idea that they are fragments of an i n i t i a l l y larger single cloud. This result has not been demonstrated before, yet i s crucial to current ideas regarding star formation. In addition, we have presented three pieces of evidence which suggest strongly that atomic hydrogen and molecules coexist in dark clouds: (a) they agree in position, (b) they agree in radial velocity, and (c) they have virtu a l l y the same line shapes. We have also suggested that the simple molecules seen in dark clouds — CO, CH, OH, CS, NH3, H2CO and HCO+ — together with atomic and molecular hydrogen, may play an important role in the formation of the more complex molecules which are seen in presumably more evolved sources. Finally, we have considered at length the possible dynamics of the most massive cloud comprising L 1 3 4 . Although our observations lacked the spectral resolution to rule out turbulence, we have argued that they are consistent with a radial collapse or expansion. We also presented preliminary observations of higher spectral resolution (but poor sensit-ivity) which possibly support this idea, and suggested that i t may allow a distinction to be made between collapse or expansion i f sufficient sensitivity is attained. The velocity dependence which we observe is consistent with the Itoc ( A / R ) 2 relationship predicted by the collapse theory of Larson. 136. T h e r e a r e many p o s s i b l e o b s e r v a t i o n s we c a n s u g g e s t w h i c h w o u l d h e l p c l e a r up many o f t h e u n c e r t a i n t i e s we h a v e r a i s e d . 13 (a) I t i s i m p e r a t i v e t h a t h i g h e r r e s o l u t i o n o b s e r v a t i o n s o f CO w i t h _ i good s i g n a l - t o - n o i s e be o b t a i n e d i n o r d e r t o t e s t t h e V~ °C ( A / f t ) Z v e l o c i t y l aw we s u g g e s t e d m i g h t a p p l y t o L 1 3 4 . I n a d d i t i o n , t h e s e o b s e r v a t i o n s may be a b l e t o d i s t i n g u i s h be tween c o l l a p s e o r e x p a n s i o n . (b) I t i s i m p o r t a n t t h a t t h e n o n - l o c a l r a d i a t i v e t r a n s f e r p r o b l e m be s o l v e d f o r v e l o c i t y l a w s w i t h oC<C,0; t h e l i n e s h a p e s d e r i v e d f r o m 12 13 s u c h m o d e l s s h o u l d be a b l e t o a c c o u n t f o r a CO t o CO l i n e w i d t h r a t i o o f ~ 2 . 2 . ( c l I t w o u l d be u s e f u l t o r e - e x a m i n e t h e H I i n t e r f e r o m e t e r d a t a o f Chu (1975) t o l o o k f o r an a b s o r p t i o n f e a t u r e on t h e h i g h l y o b s c u r e d 4 . 0 k m / s e c CO c l o u d . (d) I t i s i m p o r t a n t t h a t L134 be examined u s i n g i n f r a r e d t e c h n i q u e s t o l o o k f o r p o s s i b l e c o n t i n u u m s o u r c e s , as t h i s h a s a n i m p o r t a n t b e a r i n g on t h e t h e o r e t i c a l m o d e l s . (e) L134 s h o u l d be mapped i n o t h e r m o l e c u l a r s p e c i e s , and t h i s w i l l be a i d e d t o some e x t e n t by what i s a l r e a d y known . F o r e x a m p l e , CS and NH^ w i l l most l i k e l y be f o u n d o n l y i n t h e most o b s c u r e d r e g i o n s , and p e r h a p s HCN m i g h t a l s o be d e t e c t e d t h e r e . ( f ) I t i s a l s o i m p o r t a n t t o l o o k a t o t h e r i s o l a t e d d u s t c l o u d s and map them i n v a r i o u s m o l e c u l a r s p e c i e s . T h i s w o u l d be g r e a t l y a i d e d b y more a c c u r a t e s t a r c o u n t s on s u c h o b j e c t s . I n a d d i t i o n i t w o u l d be u s e f u l t o h a v e i n f r a r e d o b s e r v a t i o n s o f more d a r k c l o u d s , as w e l l as more HI i n t e r f e r o m e t e r r e s u l t s . The r e m a i n i n g two c l o u d s examined by Chu (1975) m i g h t be a good p l a c e t o s t a r t . The HI r e s u l t s a r e i m p o r t a n t t o u n d e r s t a n d i n g t h e H 2 d i s s o c i a t i o n mechan isms i n d a r k clouds, since the currently predicted abundances of atomic hydrogen appear to be much too high, (g) Finally, i t is important to theoretically investigate possible models for expanding clouds, as this might shed some light on the interpreta tion of line shapes, and allow a distinction to be made between the contraction or expansion of clouds. It i s hoped that in the preceeding pages we have brought to light a better understanding of the role dark dust clouds play in the evolution of the interstellar medium, and what their properties are. Since we have studied only a single cloud, i t is important that more observations be made of similar clouds so that the generality of our suggestions and results might be tested. 138. BIBLIOGRAPHY 1 . Anonymous . 2 . B a r r e t t , A . H . M a r t i n , R . A . , M e y e r s , P . C . S c h w a r t z , P . R . (1972) A p . J . 1 7 8 , L 2 3 . 3 . B l a c k , J.H. and D a l g a r n o , A . (1973) A p . L e t t e r s 1 5 , 7 9 . 4 . Bok., B , J . (1937) The D i s t r i b u t i o n o f t h e S t a r s i n S p a c e , U n i v e r s i t y o f C h i c a g o P r e s s . 5 . B o k , B . J . and R e i l l y , E . F . (1947) A p . J . 1 0 5 , 2 5 5 . 6 . B o k , B . J . (1956) A s t r o n . J . , 61_, 3 0 9 . 7 . B u h l , D . and S n y d e r , L . E . (1970) N a t u r e 2 2 8 , 2 6 7 . 8 . B u r r u s , C A . C1958) J . Chem. P h y s . 2 8 , 4 2 7 . 9 . C a r r u t h e r s , G . R . (1970) A p . J . , 1 6 1 , L 8 1 . 1 0 . C a s t o r , J . I . (1970) M o n . N a t . R . A s t r . S o c . 1 4 9 , 1 1 1 . 1 1 . C h e u n g , A . C . , R a n k , D . M . , T o w n e s , C . H . , T h o r n t o n , D . C . and W e l c h , W . J . ( 1968a ) P h y s . R e v . L e t t . 2 1 , 1 7 0 1 . 1 2 . . ( 1 9 6 8 b ) N a t u r e 2 2 1 , 6 2 6 . 1 3 . C h e u n g , A . C . , C h u i , M . F . , M a t s a k i s , D . , T o w n e s , C . H . , Y n g v e s s o n , K . S . (1973) A p . J . 1 8 6 , L 7 3 . 1 4 . C h u , K . W . (1975) P h . D . D i s s e r t a t i o n , C a l i f o r n i a I n s t i t u t e o f T e c h n o l o g y . 1 5 . C r u t c h e r , R . M . (1973) A p . J . 1 8 5 , 8 5 7 . 1 6 . C u d a b a c k , D . D . and H e i l e z C . (1969) A p . J . 1 5 5 , L 2 1 . 1 7 . D i e t e r , N . H . (1973) A p . J . 1 8 3 , 449. 1 8 . D i c k m a n , R . L . ( 1 9 7 5 a ) , P h . D . D i s s e r t a t i o n , C o l u m b i a U n i v e r s i t y . 1 9 . D i c k m a n , R . L . (1975b) A p . J . 2 0 2 , 5 0 . 2 0 . D i c k m a n , R . L . ( 1975c ) P r i v a t e c o m m u n i c a t i o n . 2 1 . E n c r e n a z , P . J . , F a l g a r o n e , E . , L u c a s , R . (1975) A s t r o n . A s t r o p h y s . 4 4 , 7 3 . 22. Evans, N. (1973) Ph.D. Dissertation, University of California (Berkeley). 23. Ewen, H.I. and Purcell, E.M. (1951) Nature, 168, 356. 24. Field, G.B, (1973) Molecules in the Galactic Environment, Wiley, Eds, Gordon and Snyder. 25. Glassgold, A.E. (1976) Private communication. 26. Goldreich, P. and Kwan, J. (1974) Ap. J. 189, 441. 27. Heiles, C.E. (1968) Ap. J. 151, 919. 2 8 • . 0.969a) Ap. J. 157, 123. 29. (1969b) Ap. J. 156, 489. 30. . (1970) Ap. J. 160, 51. 31. . (1971) Ann. Rev. Astron. Ap. 9_, 293. 32. . (1973) Ap. J. 183, 441. 33. Hollenback, D.J., Werner, M.W., Salpeter, E.E. (1971) Ap. J. 163, 165. . 34. Joensen, P., McCutcheon, W.H. and Shuter, W.L.H. (1974) Solar Physics 39, 309. 35. de Jong, T., Chu, S., Dalgarno, A. (1975) Ap. J. 199, 69. 36. Klemperer, W. (1970) Nature 227, 1230. 37. Knapp, G.R. (1972) Ph.D. Dissertation, U. of Maryland. 38. Knapp, G.R., Kerr, F.J., Rose, W.K. (1973) Ap. Letters 14, 187. 39. Knapp, G.R., Kuiper, T. and Knapp, S. (1976) Private communication. 40. Larson, R.B. (1972) MNRAS, 157, 121. 41. . (1973) Ann. Rev. Astron. Ap. 11, 219. 42. Liszt, H.S., Wilson, R.W., Penzias, A.A., Jefferts, K.B., Wannier, P.G. and Solomon, P.M. (1974) Ap. J. 190, 557. 43. Loren, R.B. (1975) Ph.D. Dissertation, U. of Texas (Austin). 44. Loren, Robert B., (1976) Ap. J. (preprint). 45. Lucy, L.B. (1971) Ap. J. 163, 95. 1 4 0 . 4 6 . L y n d s , B . T . (1962) A p . J . S u p p l . S e r i e s , V o l . V I I , 64_, 1 . 4 7 . M a h o n e y , M . J . (1972) A s t r o p h y s . L e t t . 1_2, 4 3 . 4 8 . ' 0-975) I n t e r n a l T e c h n i c a l R e p o r t o f R a d i o A s t r o n o m y G r o u p , U . B . C . The U . B . C . M i l l i m e t e r Wave T e l e s c o p e Computer C o n t r o l  S y s t e m , P a r t I. 4 9 . 0.976a) I n t e r n a l T e c h n i c a l R e p o r t o f R a d i o A s t r o n o m y G r o u p , U . B . C . The D e r i v a t i o n and A n a l y s i s o f T h e o r e t i c a l P o i n t i n g  F u n c t i o n s f o r an E q u a t o r i a l l y Moun ted T e l e s c o p e . 5 0 . ' (1976b) I n t e r n a l T e c h n i c a l R e p o r t o f R a d i o A s t r o n o m y G r o u p , U . B . C . The U . B . C . M i l l i m e t e r Wave R a d i o T e l e s c o p e Compu te r  C o n t r o l S y s t e m , P a r t I I . 5 1 . . (1976c) 0 p . c i t . P a r t I I I 5 2 . . (1976d) o p . c i t . P a r t IV 5 3 . M a r t i n , R . N . and B a r r e t t , A . H . (1975) A p . J . 2 0 2 , L 8 3 . 5 4 . O i l m a n , A . S . , K n a p p , G . R . , K e r r , F . J . , K n a p p , S . L . (1975) A s t r o n . J . 8 0 , 9 3 . 5 5 . M i l m a n , A . S . , K n a p p , G . R . , K n a p p , S . L . , W i l s o n , W . J . (1975) A s t r o n . J . 80_, 1 0 1 . 5 6 . M o o r e , C H . and R a t h e r , E . D . (1973) P r o c . I . E . E . E . 6 1 , 1 3 4 6 . 5 7 . M o r r i s , M . , Z u c k e r m a n , B . , P a l m e r , P . , T u r n e r , B . E . (1973) A p . J . 1 8 6 , 5 0 1 . 5 8 . M o r r i s , M . , G i l m o r e , W . , P a l m e r , P . , T u r n e r , B . E . , Z u c k e r m a n , B . . (1975) A p . J . 1 9 9 , L 4 7 . 5 9 . P a l m e r , P . , Z u c k e r m a n , B . , B u h l , D . , S n y d e r , L . E . (1969) A p . J . 1 5 6 , L 1 4 7 . 6 0 . P e n z i a s , A . A . , J e f f e r t s , K . B . , and W i l s o n , R.W. (1971) A p . J . 1 6 5 , 2 2 9 . 61. P e n z i a s , A . A . , S o l o m o n , P . M . , J e f f e r t s , K . B . , W i l s o n , R .W. (1972) A p . J . 1 7 4 , L43- . 6 2 . P e n z i a s , A . A . and B u r r u s , C A . (1973) A n n . R e v . A s t r o n . A p . 1 1 , 5 1 . 6 3 . P h i l l i p s , T . G . , J e f f e r t s , K . B . , W a n n i e r , P . G . and A d e , P . A . R . 0-9.74) A p . J . 1 9 1 , L 3 1 . 6~4. Rank., D . M . , Townes , C H . , and W e l c h , W . J . (1971) S c i e n c e 1 7 4 , 1 0 8 3 . 141. 6 5 . R y d b e c k , O . E . H . , E l l d e r , J . and I r v i n e , W.M. (1973) N a t u r e , 2 4 6 , 4 6 6 . 6 6 . R y d b e c k , O . E . H . , K o l l b e r g , E . , H j a l m a r s o n , A . , Sume, A . , E l l d e r , J . , and I r v i n e , W.M. (1975) R e s e a r c h R e p o r t N o . 1 2 0 , C h a l m e r s U n i v e r s i t y o f T e c h n o l o g y , Sweden. 6 7 . S a n c i s i , R . (1971) A s t r o n . A s t r o p h y s . 1 2 , 3 2 3 . 6 8 . S c o v i l l e , N . Z . and S o l o m o n , P . M . (1974) A p . J . 1 8 7 , L 6 7 . 6 9 . S h u , E . H . , M i l i o n e , V . , G e b e l , W . , Y u a n , C , G o l d s m i t h , D.W. , R o b e r t s , W.D . (1972) A p . J . 1 7 3 , 5 5 7 . 7 0 , S h u t e r , W . L . H . and M c C u t c h e o n , W . H . (1973) N a t u r e 2 4 1 , 1 4 0 . 7 1 . S h u t e r , W . L . H . and M c C u t c h e o n , W . H . (1975) R . A . S . C . J o u r . , 68_, 3 0 1 . 7 2 . S n y d e r , L . E . and B u h l , D . (1971) A p . J . 1 6 3 , L 4 7 . 7 3 . S o b o l e v , V . V . ( 1 9 6 0 ) , M o v i n g E n v e l o p e s o f S t a r s ( C a m b r i d g e : H a r v a r d U n i v e r s i t y P r e s s ) . 7 4 . S o l o m o n , P . M . and W e r n e r , M.W. (1971) A p . J . 1 6 5 , 4 1 . 7 5 . S p i t z e r , L . J r . (1968) D i f f u s e M a t t e r i n S p a c e , I n t e r s c i e n c e P u b l i s h e r s . 7 6 . T u r n e r , B . E . (1971) A p . J . 1 6 3 , L 3 5 . 7 7 . T u r n e r , B . E . , B u h l , D . , C h u r c h w e l l , E . B . , M e z g e r , P . G . , S n y d e r , L . E . (1970) A s t r o n . A p . 4., 1 6 5 . 7 8 . T u r n e r , B . E . and H e i l e s , C E . (1971) A p . J . 1 7 0 , 4 5 3 . 7 9 . T u r n e r , B . E . , Z u c k e r m a n , B . , P a l m e r , P . , M o r r i s , M . (1973) A p . J . 1 8 6 , 1 2 3 . 8 0 . T u r n e r , B . E . (1974) G a l a c t i c and E x t r a - G a l a c t i c R a d i o A s t r o n o m y G . L . V e r s c h u u r and K . I . K e l l e r m a n , E d s . ( S p r i n g e r - V e r l a g ) , p . 2 0 5 . 8 1 . Van T i l l , H . , L o r e n , R . , D a v i s , J . (1975) A p . J . 1 9 8 , . 2 3 5 . 8 2 . W a n n i e r , P . G . , P e n z i a s , A . A . , L i n k e , R . A . and W i l s o n , R.W. (1975) S u b m i t t e d t o A p . J . 8 3 . W e i n r e b , D . , B a r r e t t , A . H . , M e e k s , M . L . , and H e n r y , J . C (1963) N a t u r e 2 0 0 , 8 2 9 . 8 4 . W i l s o n , W . J . (1975) P r i v a t e c o m m u n i c a t i o n . 8 5 . Woods, R. C . (1976) P r i v a t e c o m m u n i c a t i o n . 8 6 . Z u c k e r m a n , B . , and T u r n e r , B . E . (1975) A p . J . 1 9 7 , 1 2 3 . 142. Appendix A: The User's Manual for the U.B.C. Millimeter Wave Radio Telescope Computer Control System 143. THE U.B.C. MILLIMETER WAVELENGTH RADIO TELESCOPE COMPUTER CONTROL SYSTEM PART I : A DESCRIPTION FOR PRIMATES M. J. MAHONEY REV. 02 (April 1976) 144 . CONTENTS PAGE A . G e n e r a l O v e r v i e w A - l B . P r o g r a m L o a d i n g and S t a r t i n g B - l C . G e n e r a l Command S t r i n g S t r u c t u r e and O t h e r U s e r I n p u t C - l D. Mode M D - l D.1 G e n e r a l Comments D - l D .2 Submodes and M o d i f i e r s D - l D. 3 Mode M E x a m p l e s D-5 E . Mode D E - l E . l G e n e r a l Comments E - l E . 2 Submodes and M o d i f i e r s E - 2 E . 3 Mode D E x a m p l e s E-7 F . Mode T F - l F . l G e n e r a l Comments F - l F . 2 Submodes P r e f i x e d t o A i m T e l e s c o p e F - l F . 3 Submodes P r e f i x e d t o A i m o r T r a c k T e l e s c o p e F - 2 F . 4 Submodes P r e f i x e d t o E n a b l e o r D i s a b l e P r o g r a m F l a g s F - 4 F . 5 Submodes W i t h o u t P r e f i x e s F - 7 F . 6 Mode T E x a m p l e s F - 1 0 G . S p e c i a l Commands and Sys tem C a p a b i l i t i e s G - l G . l S t a r t i n g A d d r e s s e s G - l G . 2 C o n t r o l Commands G-2 G . 3 S t a c k P r o g r a m s G - 3 A p p e n d i x : Homo N e a n d e r t h a l e n s i s A-1 145. The U.B.C. Millimeter Radio Telescope Computer Control System  Part I : A Description for Primates The following discussion should enable primates, and those further along on Darwin's evolutionary tree, to use a computer control system developed for the U.B.C. mm-radio telescope. For information not found here, the user is referred to Part II :  A Description for Man The Wise, and i f that doesn't resolve his queries, he is invited to interrogate the author. A. General Overview Once the system programs have been loaded and started (see Section B below), a particular calculation or control function is initiated by typing a command string (CS) on the teletype. The CS provides the essential interface between the user and the equipment, and has been developed so as to be easily remembered and as forgiving as possible in the event of errors. These command strings f a l l into one of three MODES of operation: MODE T for telescope control commands MODE D for data handling commands, and MODE M for miscellaneous commands. The latter is essentially a "catch-all" for calculations or operations which don't l i e logically in either of the other two MODES. The practical distinction between the MODES is not so much in what they do, but rather in the form of the command strings which are allowed within each. For this reason, the legal commands within each MODE will be discussed separately below, with differences pointed out to avoid confusion. '9 B-1 146. B. Program Loading and Starting For most minicomputers, several loaders are needed in order to bring a system into core; three are used to load the U.B.C. control system and we describe them briefly. 1. The Bootstrap Loader is toggled in using the Nova front panel console switches. Thirteen instructions are deposited from locations 127757 to 127773, and are needed to read the Absolute Binary Loader into core. 2. The Absolute Binary Loader is brought into core from the high speed paper tape reader (PTR) by setting the address 127770 in the console data switches, and then depressing RESET and START. It can be used to load any.absolute binary tape by starting i t at address 127777. The system programs, however, are written in a relocatable binary format and must therefore be loaded using the Relocatable Binary Loader. 3. The Relocatable Binary Loader is written in absolute binary code and is loaded from the PTR using the Absolute Binary Loader. Once i t has been loaded, i t types: "SAFE= " to ask the user to specify how much memory should be protected in high core during program loading. Normally a sufficiently large number would be typed so as to protect the Absolute Binary and Bootstrap Loaders,but under present circum-stances, the control system requires a l l the core that is available ( that is 12 K ). Therefore, a response of 21 is given; this protects only the Bootstrap Loader so that usually system loading w i l l begin at step 2 above. After 21 is typed, the (carriage) RETURN key is struck. The Relocatable Binary Loader responds by typing an asterisk, and then the system tapes DEUS(RB), SUBRS(RB) and FPI(RB) are loaded as illustrated below:''"* SAFE= 21 ; protect the Bootstrap Loader *2 ; type 2 to load DEUS(RB) -*2 ; type 2 to load SUBRS(RB) *2 ; type 2 to load FPI(RB) *8 ; i n i t i a l i z e the system At the present time there is insufficient core to allow the optional system tapes DEBUG III, UTILITY(RB)..and OBSER(RB) to be loaded without a special compilation, (see Part II of this series ) B-2 The " 8 " i n r e s p o n s e t o t h e f i n a l a s t e r i s k s h u f f l e s t h e l o a d e d r e l o c a t a b l e t a p e s i n t o l o w c o r e and t h e s t a r t s t h e c o n t r o l s y s t e m up when t h e c o n s o l e CONTINUE k e y i s d e p r e s s e d . The s y s t e m f i r s t i n i t i a l i z e s i t s e l f and t h e n r e q u e s t s t h e c u r r e n t d a t e t o be e n t e r e d i . e . e x e c u t e s t h e CS * M / D / / ( s e e s e c t i o n s D . 2 . a and D . 3 . a b e l o w ) , a f t e r w h i c h o t h e r u s e r command s t r i n g s may be g i v e n . The f o l l o w i n g r e p r e s e n t s t h e T e l e t y p e p r i n t o u t when t h e "m in imum" s y s t e m i s l o a d e d on May 1 5 , 1 9 7 5 : SAFE = 21 *2 *2 *£ *8 SYSTEM INITIALIZED TYPE THE DATE IN THE FORMAT YYYY/MM/DD 1974/05 /15 A f t e r w h i c h u s e r command s t r i n g s may be e n t e r e d . To s t a r t s y s t e m w i t h o u t l o a d i n g s y s t e m t a p e s , a s s u m i n g t h e s y s t e m i s a l r e a d y i n c o r e , s e e S e c t i o n G . l . C-1 148. C. General Command String Structure and Other User Input A user command string (CS) always starts with a program typed asterisk (*) and i s followed by a string of up to 144 letters, numbers, spaces, slashes and commas combined' according to well-defined syntax rules. Words, which comprise the basic elements of the command language and which may be abbreviated to their f i r s t letter, are used to represent the MODES, SUBMODES and MODIFIERS discussed below. Hope-fu l l y they represent the operations performed in a logical and easily remembered manner. Numbers, on the other hand, are used whenever a SUBMODE or MODIFIER requires numerical input. To separate or delimit the words and numbers, slashes (/) or commas (,) are used. The slash, which for convenience may be produced by depressing the ESC key, always precedes SUBMODES and MODIFIERS, that i s , words (or letters), whereas the comma, with the exception, discussed in Section D.l, always precedes numerical input. Command strings are terminated by a double ESC (//); this begins the execution of the CS and detection of any syntax errors. Up to this point, any number of CS characters may be deleted and/or changed by depressing the RUBOUT key once for each deletion. This w i l l cause each character erased to be typed by the Teletype. In the event that a syntax error is s t i l l present after • execution has begun, an appropriate error message w i l l be typed and a new CS requested. Spaces may be entered anywhere in a CS and have no effect at execution time. " The legal responses to the asterisk i n i t i a t i n g a CS are: M, D, or T, which select the Miscellaneous, Data Handling and Telescope Control Modes respectively, or a number which indicates a starting address (see Section G). A MODE response is always followed by an ESC (/), after which any legal SUBMODE within the chosen MODE may be typed to specify the calculation or control function to be performed. In addition, MODIFIERS may also be included; these are numbers and/or words specifying to the SUBMODE further information regarding what i s to be done. Syntax peculiarities of the different MODES w i l l be discussed in Sections D.l, E . l , and F . l below. C-2 149. After the execution of a CS has begun, the user must i n many cases specify times, positions, distances or other numerical factors to the control program. The input of each of these numbers follows one of fi v e input formats and i s always terminated by a break character^*, which i s any character other than an integer, a plus (+) or minus (-) sign, a decimal point (.),. an E, a SPACE, a (carriage) RETURN, a NULL or a RUBOUT. As long as a legal break character i s used, the proper formatting w i l l always r e s u l t , but i t i s suggested that the ESC key always be used. Break characters are not typed and RUBOUTS may not be given after a break character to make corrections. Using the abbreviations PST for P a c i f i c Standard Time, ST for Sidereal Time, HA for Hour Angle, RA for Right Ascension, DEC f o r D e c l i n a t i o n , L I I f o r G a l a c t i c Longitude and BII f o r G a l a c t i c L a t i t u d e , the standard formats f o r input are: 1. PST and ST XX:YY:ZZ.Z 2 . L I I , BII, HA, RA and DEC sXXX.XXXD 3. HA and RA sXXH YYM ZZ.ZS 4. DEC sXXD YY» ZZ.Z" 5. Numerical factors sXXXX.XXXEsYY where X, Y and Z are integers, and s i s a plus or minus sign, which i s optional for positive numbers. The only time the decimal point i s compulsory i s when the HA, RA or DEC are to be read on format 2 instead of 3 or 4; otherwise, i t may be excluded f o r any whole number input. Exponentiation of numerical factors i s also optional, but must be preceded by an E i f used and up to seven d i g i t s may be given for any mantissa even i f exponentiation i s not used. I f the carriage RETURN i s used, i t produces a carriage return and l i n e feed, but has no effect on the program input. S i m i l a r i l y the SPACE key produces only a space and has no other program function. NULLS and l i n e feeds (LF) are ignored and the RUBOUT may be used to correct errors j u s t as i t does during CS input. 1. In the CS input, the delimiters or MODIFIERS served as break characters. 150. The following Sections discuss the SUBMODES and MODIFIERS within each MODE,along with some general comments on the MODES and some specific examples of CS useage. It should be re-iterated here that although (for convenience) the SUBMODES and MODIFIERS discussed in the following text are abbreviated to their i n i t i a l letter, any word or phrase starting with the same letter may be used. In the brief introduction of each SUBMODE, the underlined word or words are indicative of what the SUBMODE or MODIFIER letter discussed actually stands for. For example, on page D-l, SUBMODE description a) has the word "date" underlined to indicate what SUBMODE D stands for in MODE M. Also, i t should be pointed out that in the examples any user input, normally a number string, is also underlined. Part III.of this series, A Description for Homo Neanderthalensis, summarizes for easy reference a l l the SUBMODES and MODIFIERS allowed by the system, together with other useful information. D-l 151. D. Mode M D.l General Comments A l l MODE M SUBMODES may be strung together or concatenated, and in addition, may be preceded by an integer specifying the number of times the CS is to be repeated; this i s the only instance in which a number is not preceded by a comma. The examples below should make clear the CS syntax. D.2 Submod es and Mod i f ier s a) To read an active date ' SUBMODE: D COMMENT: If "D" is encountered in a MODE M CS, the control program w i l l request a date to be typed in. The last date read in w i l l be referred to as the active date, since i t is the one used i n any subsequent calculations. After reading the active date, the SUBMODE calculates the Julian Day for use in other SUBMODES. For this reason, the active date must be the current c i v i l date when MODE T commands are to be used; otherwise, any date for which a calculation i s to be performed may be used. Since many SUBMODES require the Julian Day in their calculations, this command should normally be the f i r s t one given when starting up and i t is automatically requested when the system is loaded. If the user requires the Julian Day, i t can be obtained by using the CS: *T/STATUS// (see Section F .2.g). b) To calculate the sidereal time SUBMODE: S COMMENT: If "S" is encountered in a MODE M CS, the control program w i l l request a Pacific Standard Time (PST) to be typed in; the i t w i l l calculate for the active date, the corresponding sidereal time (ST). c) To compare the clock and calculated sidereal times . SUBMODE: C COMMENT: After performing the SUBMODE S input and output (I/O), this SUBMODE types: "THE CLOCK SIDEREAL TIME WAS" and halts the computer. The user then depresses the CONTINUE switch on D-2 1 5 2 . t h e Nova c o n s o l e a t t h e PST f o r w h i c h t h e s i d e r e a l t i m e was c a l c u l a t e d and t h e c l o c k s i d e r e a l t i m e a t t h a t i n s t a n t i s t y p e d . (The PST t h a t i s t y p e d i n s h o u l d be a b o u t a h a l f m i n u t e i n a d v a n c e o f t h e PST a t t h e t i m e t h e CS i s t y p e d , t o a l l o w t i m e f o r t h e SUBMODE S I / O . ) d) To c o n v e r t f r o m G a l a c t i c t o E q u a t o r i a l c o - o r d i n a t e s o r f r o m E q u a t o r i a l t o G a l a c t i c c o - o r d i n a t e s SUBMODES: G , E COMMENTS: I f " G " i s e n c o u n t e r e d i n a MODE M C S , t h e g a l a c t i c c o - o r d i n a t e s (1 , b ^ ) a r e r e a d i n and c o n v e r t e d t o e q u a t o r i a l c o - o r d i n a t e s ( a , 8 ) . I f " E " i s e n c o u n t e r e d , t h e c o n v e r s i o n i s f r o m e q u a t o r i a l t o g a l a c t i c c o o r d i n a t e s . e) To c a l c u l a t e t h e l o c a l s t a n d a r d o f r e s t v e l o c i t y SUBMODE: V COMMENT: I f " V " i s e n c o u n t e r e d i n a MODE M C S , e q u a t o r i a l c o - o r d i n a t e s a r e r e a d i n and t h e i r l o c a l s t a n d a r d o f r e s t (LSR) v e l o c i t y i s c a l c u l a t e d and t y p e d . f ) To p r e c e s s e q u a t o r i a l c o - o r d i n a t e s SUBMODE: P MODIF IER: A COMMENT: I f " P " i s e n c o u n t e r e d i n a MODE M C S , 1 9 5 0 . 0 e q u a t o r i a l c o - o r d i n a t e s a r e r e a d i n and p r e c e s s e d t o t h e a c t i v e d a t e . I f " P " i s f o l l o w e d b y t h e MODIFIER " A " , t h e e q u a t o r i a l c o - o r d i n a t e s f o r an a r b i t r a r y e p o c h ( s i n c e 1 9 0 0 . 0 ) a r e r e a d i n and p r e c e s s e d by t h e number o f y e a r s s p e c i f i e d i n d e c i m a l f o r m a t by t h e u s e r . I f SUBMODE P i s f o l l o w e d by SUBMODE V , t h e LSR v e l o c i t y o f t h e p r e c e s s e d p o s i t i o n i s c a l c u l a t e d as w e l l . To p r e c e s s c o - o r d i n a t e s w h i l e o b s e r v i n g , s e e S e c t i o n F b e l o w . g) To c a l c u l a t e a t m o s p h e r i c r e f r a c t i o n SUBMODE: R COMMENT: I f " R " i s e n c o u n t e r e d i n a MODE M C S , a n hou r a n g l e and d e c l i n a t i o n a r e r e a d i n . The c o r r e s p o n d i n g r e f r a c t e d p o s i t i o n i s t h e n c a l c u l a t e d i n d e c i m a l d e g r e e f o r m a t t o g e t h e r w i t h t h e c o r r e c t i o n s w h i c h mus t be added t o t h e i n p u t p o s i t i o n t o g e t D-3 1 5 3 . t h e r e f r a c t e d p o s i t i o n . F o r r e f r a c t i o n c o r r e c t i o n s w h i l e o b s e r v i n g , see S e c t i o n F b e l o w . h) To c a l c u l a t e t h e s y s t e m t e m p e r a t u r e SUBMODE: T COMMENT: I f " T " ; i s e n c o u n t e r e d i n a MODE M C S , t h e a m b i e n t t e m p e r a t u r e ( i n d e g r e e s C e l s i u s ) i s r e q u e s t e d t o g e t h e r w i t h t h e number o f d e c i b e l s c o r r e s p o n d i n g t o a H o t - C o l d m e a s u r e m e n t . The d o u b l e s i d e b a n d s y s t e m t e m p e r a t u r e i s t h e n c a l c u l a t e d and t y p e d . i ) To c a l c u l a t e t h e h o r i z o n c o - o r d i n a t e s o f a p o i n t SUBMODE: H ' COMMENT: I f " H " i s e n c o u n t e r e d i s a MODE M C S , a n hou r a n g l e and d e c l i n a t i o n a r e r e a d and c o n v e r t e d t o t h e a z i m u t h and z e n i t h d i s t a n c e f o r a n o b s e r v a t o r y a t t h e l a t i t u d e most r e c e n t l y e n -a b l e d . The d e f a u l t l a t i t u d e i s 4 9 . 2 5 3 d e g r e e s N o r t h , ( s e e S e c t i o n F . 4 ) j ) To e x e c u t e a s p e c i a l u s e r ' s p r o g r a m SUBMODE: U COMMENT: I f " U " i s e n c o u n t e r e d i n a MODE M C S , c o n t r o l i s t r a n s f e r r e d t o a s p e c i a l u s e r ' s p rog ram c a l l e d OBSER. T h i s p r o g r a m i s r e l o c a t a b l e and must be l o a d e d w i t h t h e s y s t e m t a p e s i f i t i s u s e d . When w r i t i n g a s p e c i a l o b s e r v i n g p r o g r a m , t h e u s e r o f c o u r s e h a s a c c e s s t o t h e s y s t e m s u b r o u t i n e s , b u t t h e s e mus t b e d e c l a r e d a s e i t h e r n o r m a l o r d i s p l a c e m e n t e x t e r n a l s . W r i t i n g s u c h p rog rams w i l l n o r m a l l y be beyond t h e g r a s p o f t h e c a s u a l u s e r s i n c e i t r e q u i r e s a t h o r o u g h u n d e r s t a n d i n g o f t h e c o n t r o l s y s t e m s t r u c t u r e a s w e l l a s a s s e m b l y l a n g u a g e , ( s e e P a r t I I o f t h i s s e r i e s ) k ) To w r i t e , l i s t o r y a n k s t a c k p r o g r a m s SUBMODES: W, L , Y COMMENTS: I f "W" i s e n c o u n t e r e d i s a MODE M C S , a s t a c k p rog ram may be w r i t t e n . T h e s e a r e d e s c r i b e d more c o m p l e t e l y i n S e c t i o n G . When p r o g r a m s a r e b e i n g w r i t t e n , t h e RUBOUT k e y may b e u s e d t o e r a s e any number o f c h a r a c t e r s , and t h e s e a r e echoed as t h e y a r e e r a s e d . The c a r r i a g e RETURN i s u s e d t o s t a r t new l i n e s , and t h e EOT (CTRL D) k e y i s u s e d t o t e r m i n a t e t h e s t a c k p rog ram w r i t i n g , a t w h i c h t i m e , t h e u s e r i s a s k e d w h e t h e r o r n o t a t a p e s h o u l d be p u n c h e d . I f a t a p e i s r e q u i r e d , t h e punch s h o u l d be s w i t c h e d on and a " Y " t y p e d . No l e a d e r o r t r a i l e r t a p e i s punched by t h e p r o g r a m . D-4 154. If "L" i s encountered i n a MODE M CS, the current stack program i s l i s t e d . During the l i s t i n g , control commands are written on separate lines and a new l i n e i s generated whenever a double ESC i s encountered. If "YM i s encountered i n a MODE M CS, a stack program i s yanked i n on the high speed paper tape reader. A l l program tapes must be terminated by an EOT (CTRL D). This i s automatically taken care of i f SUBMODE W i s used to write them. D-5 155. D. 3 Mode M Examples Since MODE M involves a considerable amount of Teletype printout, the i n i t i a l examples given below w i l l demonstrate the expected program output and user input for each of the SUBMODES. For brevity, subsequent examples w i l l give only the command string. It i s assumed that the system tapes have been loaded. The examples given below, less the introductory comments, appear as they would on the Teletype printout, and and any underlined text indicates user typed input. a) If the active date is to be changed to May 17, 1974, use: *M/DAT£// TYPE THE DATE IN THE FORMAT YYYY/MM/DD 1974/05/17 b) To calculate the sidereal time at 23 minutes 20 seconds past 8 AM on May 17,1974, use: *M/SIDEREAL TIME// TYPE PST IN FORMAT HH:MM:SS 08:23:20 SIDEREAL TIME IS 23:50:19 c) To compare the clock and calculated sidereal times at 30 minutes past 8 AM (PST) on May 17,1974, use: *M/COMPARE CLOCKS// TYPE PST I N . F O R M A T HH:MM:SS 08:30:00 SIDEREAL TIME IS 23:57:00 THE CLOCK SIDEREAL TIME WAS 23:57:00 After the computer halts, the user waits u n t i l 08:30:00 PST and depresses the CONTINUE switch on the Nova console. d) To convert the Galactic co-ordinates ( l 1 1 : 0.0, b 1 1 : 0.0) to Equatorial co-ordinates, use: *M/GALACTIC TO EQUATORIAL CONVERSION// LII: +000.000 BII: 4-000.000 = RA: 17H 42M 26S DEC: -28D 55' 00" e) To convert the Equatorial co-ordinates of the previous example to Galactic co-ordinates, use: *M/EQUATORIAL TO GALACTIC CONVERSION// RA: 17H 42M 26S DEC: -28D 55' 00" = L I I : +359.999 B I I : +.001 D-6 156. f) To precess the equatorial co-ordinate of the previous example from 1950.0 to May 17,1974, use: •M/PRECESS// I RA: 17H 42M 26S DEC: -28D 55' 00" P RA: 17H 43M 58S DEC: -28D 55* 35" g) To precess the Solar Apex (RA:270.0, DEC:+30.0) from 1900.0 to 1958.0, use: *M/PRECESS/ARBITRARY NUMBER OF YEARS// I RA: +270.000D DEC: +30.0000 TYPE NUMBER OF YEARS THE POSITION IS TO BE PRECESSED P RA: 18H 02M 13S DEC: +30D 00' 05" 58.000 or, using astronomical format: *M/P/A// I RA: 18H 00M 00S DEC: + 30D 00* 00" TYPE NUMBER OF YEARS THE POSITION IS TO BE PRECESSED P RA: 18H 02M 13S DEC: +30D 00* 05" 58.000 *M/VELOCITY// h) To calculate the velocity of a source at (RA: 17H 43M 58S, DEC:-28D 55' 35") with respect to the LSR on May 17, 1974 at the current sidereal time, use: RA: 17H 43M 58S DEC: -28D 55* 35" VLSR IS •24.982 KM/SEC Note that this could have been obtained by using "V" as a MODIFIER in example D.3.f, that i s , by giving the command string: *M/PRECESS/VELOCITY// i) To calculate the refraction of a source at (HA:+15.0, DEC:+29.0), use: •M/REFRACT// HA: +15.000D, R HA: DEC: +14.996D, DEC: +29.000D +29.006D* DHA: -.003D*DDEC: + .006D j) To calculate the system temperature using the difference of Hot and Cold load measurements (in decibels),use the CS: *M/TEMPERATURE// TYPE AMBIENT CELSIUS TEMPERATURE 15* HOT-COLD IN DB*S 0.23 SYSTEM TEMPERATURE IS +3805.353 DEGREES KELVIN < DSB) The user types the ambient temperature in degrees Celsius as well as the Hot-Cold level in dB's. D-7 1 5 7 . k ) The f o l l o w i n g examp le r e a d s a p a p e r t a p e c o n t a i n i n g a p r o g r a m t o w r i t e 32 memory l o c a t i o n s f r o m t h e t h i r d q u a r t e r o f t h e F T . I t t h e n l i s t s t h i s p r o g r a m , w h i c h i s s t o r e d i n a s t a c k i n memory. The e x e c u t i o n o f t h e s e s t a c k p rog rams w i l l be d i s c u s s e d i n S e c t i o n G b e l o w . •M/YANK A STACK PROGRAM/LI ST// IF TAPE IS MOUNTED AND TERMINATED WITH EOT* HIT A KEY STACK PROGRAM LISTING tH D/INPUT,561,592/WRITE// END OF PROGRAM I t s h o u l d a l s o be n o t e d t h a t w r i t i n g s t a c k p rog rams i s no d i f f e r e n t t h a n t y p i n g o r d i n a r y C S ' s , o t h e r t h a n t h a t t h e y must be t e r m i n a t e d by an EOT. 1) To c a l c u l a t e t h e LSR v e l o c i t y o f a c e r t a i n g a l a c t i c c o - o r d i n a t e o n 14 s u c c e s s i v e d a y s , g i v e : *M/14D/G/V// m) To p r e c e s s s e v e n e q u a t o r i a l c o - o r d i n a t e s f r o m 1 9 5 0 . 0 t o 1 9 7 4 . 0 , g i v e : * M / D A T E / / ; t o r e a d i n t h e a c t i v e d a t e ; 1 9 7 4 / 0 1 / 0 1 , f o l l o w e d b y : * M / 7 P R E C E S S / / A l t e r n a t i v e l y , u s e : *M /7PRECESS/ARBITRARY NUMBER OF Y E A R S / / ; and p r e c e s s f o r 24 y e a r s . n) To c a l c u l a t e t h e a t m o s p h e r i c r e f r a c t i o n a t 101 p o s i t i o n s , g i v e : * M / 1 0 1 R E F R A C T I O N S / / E-l 158. E. Mode D E. 1. General Comments MODE D command strings may be formed by concatenating SUBMODES just as in MODE M; the repetition f a c i l i t y , however, does not exist. A few other points should be observed: the Nova and shall be referred to as the ps eudo-memory. At f i r s t glance this may seem redundant, but i t provides a means of protecting data in the FT from being inadvertently destroyed during manipulation. The price paid for this protection is that an additional SUBMODE command, I or 0, must be specified on data output and input respectively. That i s , when data is to be output from the FT, i t must f i r s t be brought into the Nova by giving an I command, and then output. A similar situation exists when data is to be input from an external device into the FT -- i t must f i r s t be read into the Nova and then sent to the FT by an 0 command. b) A l l SUBMODES other than the shifting command T, and the I/O commands, I, 0, P, W and Y, operate on the FT memory exclusively. c) Until somehaxdware changes are made, the following restrictions are placed on the size of numbers which can be manipulated in MODE D; a) An image of the Fabri-tek (FT) memory exists in In SUBMODES: 0, Y, Z, L, Q, M, A, S, T, C and X -2 1 5 < N < 2 1 2-1 or -32,768 < N < + 4,095 In SUBMODES: I, P and W, 1 or -32,768 < N 1 +32,767 That i s , input and manipulation commands use only 12 bits for positive numbers and 16 bits for negative numbers, whereas output commands use 16 bits for both. E-2 159. If FT console switches are used for manipulation, 18 bits are used, but care should be taken to reduce the number of significant bits to 16 before an output command; i f the data is to be read back in at some future time, only 12 significant bits should be output, as that is a l l that can be read into the FT as a positive number. d) For a l l the SUBMODES in MODE D, one or two memory ranges (MR), or pseudo-memory ranges (PMR), must be specified. SUBMODES A, S, T and C require two, while the others require only one. Each MR consists of two integer strings preceeded by commas. The usage should be clear from the examples in Section E.3. If a SUBMODE does not specify any memory range(s) or pseudo-memory range(s), the last one(s) specified with a previous SUBMODE, even i f in another command string, is(are) assumed. (SUBMODES requiring two memory ranges are to have their f i r s t MR identified with the single MR used by the SUBMODES requiring only one). If this is confusing, i t too should be made clear in the examples below. E.2 Submodes arid Modifiers a) To input or output data between Nova and Fabri-tek SUBMODES: I, 0 COMMENT: If " I " is encountered in a MODE D CS, i t reads the Fabri-tek MR specified (or previously specified), into the corresponding Nova PMR. SUBMODE "0" performs the opposite function. Since data must be in the Nova before i t can be written on paper tape or on the teletype, SUBMODE I is used to bring i t there. However, i t could be used simply to protect raw data while i t is being analyzed in case the user inadvertently destroys what is in the FT. Should this happen, SUBMODE 0 could then be used to write the raw data back into the FT. This SUBMODE is also used to write data read in on paper tape by SUBMODE Y into the FT. E-3 160. b) To yank (or read) a paper tape SUBMODE: Y COMMENT: If "Y" is encountered in a MODE D CS, i t reads (or yanks) a paper tape into the Nova PMR specified (or last specified). (The PTR must be switched to the RUN position). If the paper tape is longer than the range specified, the PTR stops after reading the specified amount of data; i f i t is too short, the entire tape is read into the f i r s t pseudo-memory locations of the specified range. c) To punch a paper tape SUBMODE: P COMMENT: If "P" is encountered in a MODE D CS, i t punches the specified PMR onto paper tape. The paper tape punch (PTP) must have been switched ON, and the user is responsible for punching leader and t r a i l e r tape before and after the command is encountered. d) To write data on teletype SUBMODE: W COMMENT: If "W" is encountered in a MODE D CS, the specified Nova PMR is written on the teletype. e) To do a zero order, linear or quadratic least squares f i t , with options to blank part of MR or display result SUBMODES: Z, L, Q MODIFIERS: D ; B COMMENT: If "Z", "L" or "Q" is encountered in a MODE D CS, a zero order, linear, or quadratic least squares f i t , respectively, is done to the specified FT memory range. The f i t parameters AO, Al, and A2, the mean, MU, and the standard deviation, SIGMA, defined by the following expressions: E-4 161. y i ( f i t ) = AO + A l X i + A2 X? n MU = C I y i ( f i t ) - y i ) / (n - m + 1) i=m SIGMA = ( I ( y i ( f i t ) - y i ) 2 / (n - m) ) h i=m where: (m,n) i s the MR to be f i t t e d X i i s a FT address i n (m,n) y i i s the data i n l o c a t i o n X i , and y i ( f i t ) i s the l e a s t squares f i t to y i , are then typed on the Teletype. I f a part (u,v) of the f i t range (m,n) i s to be excluded (or blanked) from the f i t , t h i s i s specified by the MODIFIER B, and i f the f i t i s to be displayed on the oscilloscope, the MODIFIER D i s used. I f a memory range i s not specified with the MODIFIER D, the range (m, n) i s assumed. f) To k i l l (or clear) a portion of memory SUBMODE: K COMMENT: I f "K" i s encountered i n a MODE D CS, the specified FT memory range i s deleted. g) To multiply (or scale) a portion of memory SUBMODE: M COMMENT: I f "M" i s encountered i n a MODE D CS, a range m u l t i p l i e r i s requested, which must be a positive or negative integer or decimal number, and the specified FT memory range i s multiplied by thi s number. Care should be taken with decimal numbers, since scaled numbers are converted to integers before they are written back into the FT memory. h) To exchange FT memory contents for teletype data SUBMODE: E E-5 1 6 2 . COMMENT: If "-" is encountered in a MODE D CS, individual locations or portions the FT memory may be modified from the teletype. If a colon (:) is encountered after the f i r s t number is typed, this is interpreted to mean that individual locations are to be modified, with the address preceding the colon and the contents of that address following. Address: contents pairs w i l l be entered until a double ESC is encountered. If, on the other hand, a colon is not given after the f i r s t number is typed, this is taken to mean that the FT memory range specified is to be altered, and a sequence of numbers w i l l be read in to f i l l that-range. If the complete memory range is not to be modified, a double ESC can again be used to terminate the input. If at any time during SUBMODE E, the (carriage) RETURN key is depressed, a carriage return and line feed w i l l be produced. i) To add, subtract and transfer arbitrary memory ranges SUBMODES: A, S, T COMMENT: If one of these SUBMODES is encountered in a MODE D CS, they must be followed by two specified memory ranges, or these must have been previously specified. SUBMODE A adds the f i r s t memory range to the second; SUBMODE S subtracts the f i r s t from the second; and SUBMODE T simply transfers the f i r s t to the second. In a l l these SUBMODES, the two ranges must be of identical length, or an error message w i l l be given. Furthermore, the SUBMODE A and S memory ranges may not overlap, but the SUBMODE T ranges may, which makes i t useful for shifting data. SUBMODES A and S destroy the data in the second range and leave the f i r s t unaltered, whereas SUBMODE T deletes the f i r s t . (Of a l l the manipulation SUBMODES in MODE D, T is the only one which uses the Nova pseudo-memory. This has the advantage of saving the f i r s t memory range, which is deleted, but the user must be careful not to overwrite data which is being protected in pseudo-memory in the corresponding range). E-6 163. j) To calibrate data, with option for functional calibration SUBMODE: C MODIFIER: F COMMENT: If "C" is encountered in a MODE D CS,two MR's are required just as in SUBMODES A, S, and T. The f i r s t MR contains the data to be calibrated (e.g. an on-source minus off-source) and the second, the calibrating data (e.g. sky noise). In addition, a calibration factor is requested (e.g. temperature of sky noise). Each address in the f i r s t MR is then divided by the corresponding address in the second MR and multiplied by the calibration factor. For example, i f the calibration factor is the calibration data strength in millidegrees, then the f i r s t MR w i l l end up containing the data calibrated in millidegrees antenna temperature below the atmosphere. Again, care should be taken with calibration factors to avoid losing significance when the calibrated data is "integerized" to be written back into the FT. If SUBMODE "C" is followed by the MODIFIER "F", the data i s calibrated using as a calibration factor the function: 2T + T a{exp(x G -T i)A - 1} + 2(T1-Ta){exp(T_A) - 1} where: A (=secant(Zenith Distance)) is the air mass, T is the atmospheric cl temperature, T-, i s the load temperature and T and T. the attenuation in X S I nepers in the signal and image bands respectively. T &, T^, T G and are provided by the zenith attenuation calibration program in MODE T and the MODIFIER F cannot be used unless this calibration is performed. Assuming i t is used, the data is calibrated in antenna temperature (in millidegrees) above the atmosphere, that i s , T . E-7 164. E . 3 Mode D Examp les A s i n t h e MODE M e x a m p l e s , t h e s e examp les a r e t o be i n t e r p r e t e d a s r e p r e s e n t i n g wha t a c t u a l l y a p p e a r s on t h e t e l e t y p e p r i n t o u t , l e s s o f c o u r s e t h e comments w h i c h d e s c r i b e what i s b e i n g d o n e . T h i s means t h a t d a t a m a n i p u l a t e d i n one examp le a p p e a r s m a n i p u l a t e d i n s u b s e q u e n t e x a m p l e s and t h a t memory ( o r pseudo-memory ) r a n g e s d e f i n e d i n one examp le a r e t h e same i n s u b s e q u e n t examp les u n l e s s r e d e f i n e d i n a n o t h e r C S . a ) To r e a d 100 numbers f r o m p a p e r t a p e i n t o t h e FT MR ( 1 , 1 0 0 ) , g i v e : • D / Y A N K * 1 * 1 0 0 / O U T P U T / / b) To do a s e c o n d o r d e r ( q u a d r a t i c ) l e a s t s q u a r e s f i t t o t h e d a t a i n t h e MR ( 1 , 1 0 0 ) , l e a v i n g l o c a t i o n s ( 4 0 , 6 0 ) ou t o f t h e f i t and w r i t i n g t h e r e s u l t i n t o t h e MR ( 5 0 1 , 6 0 0 ) , g i v e : • D / Q U A D R A T I C F I T * 1 * 1 0 0 / B L A N K * 40* 6 0 / D I S P L A Y * 5 0 1 * 6 0 0 / / A0= + 3 1.440 * A 1 = - 8 . 2 7 0 * A 2 = + . 0 7 1 * M U = - 571 . 0 9 5 * S I G M A = + 1 2 5 . 2 2 2 o r • D / Q / B * 4 0 * 6 0 / D * 5 0 1 * 6 0 0 / / A0= +31 . 4 4 0 * A 1 = - 8 . 2 7 0 * A 2 = + . 0 7 1 * M U = - 571 . 0 9 5 * S I G M A = + 1 2 5 . 2 2 2 s i n c e t h e i n i t i a l MR was g i v e n i n examp le a ) . c ) To s c a l e d a t a i n t h e MR ( 5 0 1 , 6 0 0 ) by a f a c t o r o f 2 . 5 and o u t p u t t h e r e s u l t on p a p e r t a p e and t h e T e l e t y p e , g i v e : • D / M U L T I P L Y / I N P U T / P U N C H / W R I T E / / RANGE M U L T I P L I E R I S 2 . 5 0 0 - 0 0 4 4 7 - 0 0 4 2 0 - 0 0 4 0 5 - 0 0 3 8 7 - 0 0 3 6 5 - 0 0 3 5 0 - 0 0 3 3 0 - 0 0 3 1 2 e t c e t e r a . The r a n g e m u l t i p l i e r i s r e q u e s t e d p r i o r t o p u n c h i n g . and t y p i n g , w h i c h o c c u r s f r o m t h e Nova pseudo -memory , h e n c e t h e p r e s e n c e o f SUBMODE I t o g e t i t t h e r e . d) Suppose t h a t a s o u r c e h a s b e e n o b s e r v e d and t h e o n - s o u r c e m i n u s o f f - s o u r c e d a t a o c c u p i e s t h e MR ( 1 , 1 1 2 ) . I f t h i s E-8 1 6 5 . d a t a i s now t o b e c a l i b r a t e d and t h e s k y n o i s e r u n i s t o occupy t h e same MR, t h e o r i g i n a l d a t a i s t h e n t r a n s f e r r e d t o some unused MR, s a y ( 2 0 1 , 3 1 2 ) , b y : •D/TRANSFER,1,112.201.312// The s k y n o i s e r u n i s now made . Suppose i t s n o i s e t e m p e r a t u r e i s 112 K . The o r i g i n a l d a t a c o u l d t h e n be c a l i b r a t e d i n m i l l i d e g r e e s b y g i v i n g t h e C S : •D/CALIBRATE,201,312,1,112// CALIBRATION FACTOR IS 112000.0 Had t h e c a l i b r a t i o n f a c t o r b e e n 1 1 2 . 0 , t h e d a t a w o u l d h a v e been c a l i b r a t e d i n d e g r e e s , b u t b e c a u s e t h e c a l i b r a t i o n r e s u l t i s " i n t e g e r i z e d " b e f o r e b e i n g w r i t t e n b a c k i n t o t h e F T , s i g n i f i c a n c e w o u l d h a v e b e e n l o s t f o r s i g n a l s l e s s t h a n o r o f t h e o r d e r o f a d e g r e e i n s t r e n g t h . e ) Wi th , t h e c a l i b r a t e d r e s u l t now i n MR ( 2 0 1 , 3 1 2 ) , s u p p o s e t h a t l o c a t i o n s 251 and 262 a r e t o be changed t o c o n t a i n 101 and 103 r e s p e c t i v e l y , t h a t MR ( 3 0 1 , 3 1 2 ) i s t o b e d e l e t e d , and t h a t t h e MR ( 2 0 1 , 3 0 0 ) i s t o be punched on t a p e . To do t h i s g i v e : •D/EXCHANGE/KILL,301,312/INPUT,201,300/PUNCH//  251t101 262t103 f ) Suppose t h a t t h e mean and s t a n d a r d d e v i a t i o n o f 15 numbers i s t o be c a l c u l a t e d . The numbers a r e r e a d i n d i r e c t l y by SUBMODE E i n t o some f r e e FT MR, s a y ( 9 0 1 , 9 1 5 ) , and a z e r o o r d e r l e a s t s q u a r e s f i t d o n e . F o r e x a m p l e : •D/EXCHANGE,901,915/2ERQ ORDER FIT// 91 93 87 85 81 95 92 82 83 88 94 84 90 86 89 A0= +S8.000,A1= , +.000,A2= +.000,MU= +88.000,SIGMA= +4.472 g) Suppose d a t a i n t h e MR ( 2 0 1 , 3 0 0 ) i s t o b e added t o t h e MR ( 3 0 1 , 4 0 0 ) and s u b t r a c t e d f r o m t h e MR ( 4 0 1 , 5 0 0 ) . T h i s i s a c c o m p l i s h e d by t h e C S : •D/ADD,201,300,301,400/SUBTRACT,201,300,401,500// o r *r>/Ann.gpn . i w c i . s c i t . 4 0 0 / S U B T R A C T , 4 0 1 , 5 0 0 / ; / 166. which is equivalent to the f i r s t CS, but uses a RUBOUT to correct the accidentally typed slash. F-1 167. F. Mode T F.l General Comments As in MODES M and D, SUBMODES may also be concatenated in MODE T, although doing so is not recommended. An essential difference between MODE T and the other MODES is that the SUBMODES in MODE T are prefixed by words (or letters) which describe a particular function to be performed. These prefixes are: AIM (abbreviated A) or TRACK (abbreviated T) to specify aiming or tracking of the telescope at the position requested by a particular SUBMODE, and ENABLE (abbreviated E) or DISABLE (abbreviated D) to enable or disable a number of program flags. These prefixes "will be explained in more detail below. In addition i t should be noted that SUBMODES 0 and W described below use syntax that differs slightly from the usual. F.2 Submodes Prefixed to Aim the Telescope The following SUBMODES can only be used to aim the telescope to a number of predefined positions, and must be preceded by the prefix to AIM. a) To aim telescope to calibrate the zenith attenuation-. SUBMODE: C COMMENT: If "C" i s encountered in a MODE T CS prefixed to AIM, the program f i r s t requests values for the ambient (or load) temperature T.. (in Kelvins), the atmospheric temperature T (in Kelvins), X cl and the difference between the zenith attenuation in the signal and image bands, T - T . (in decibels). It then asks i f T should be measured or i f s i s the user simply wants to force a value. If is to be measured, the program saves the current RA and DEC of the telescope and slews to a position which effectively doubles the number of air masses the telescope must look through, thus changing the sky temperature T . The telescope s stays at this position u n t i l the Nova console CONTINUE key is depressed, at which time i t returns to the original RA and DEC and starts tracking again. This done, the program requests values for T^-T_(A) and T^-T g(2A), where T_(A) and T_(2A) are the sky temperatures (determined from the chart recorder.) before' and after the air mass A is doubled; i t then calculates 168. the zenith attenuation i n the s i g n a l band, T . If a measurement i s not s to be made, the user i s asked to specify a value for T . The values of T , T , x T . , and T determined here are necessary i n the MODE D CS x a s x s which does f u n c t i o n a l data c a l i b r a t i o n , namely *D/CAL/F// (see Section E.2.J). b) To aim telescope to the Stow p o s i t i o n SUBMODE: S COMMENT: If "S" i s encountered i n a MODE T CS prefixed to AIM, the telescope i s driven to the p o s i t i o n HA:',0.0, DEC: 90.0 and stopped. c) To aim telescope to the Zenith SUBMODE: Z COMMENT: If "Z" i s encountered i n a MODE T CS prefixed telescope i s driven to the p o s i t i o n HA: 0.0, DEC: 49.253 and d) To aim telescope to the ground facing West SUBMODE: W COMMENT: If "W" i s encountered i n a MODE T CS prefixed to AIM, the telescope i s driven to the p o s i t i o n HA: +90.0, DEC:-27.6 and stopped. F.3 Submodes Prefixed to Aim or Track the Telescope The following SUBMODES can be prefixed e i t h e r to AIM or TRACK the telescope at a p a r t i c u l a r p o s i t i o n . A l l these SUBMODES must be preceded by the p r e f i x AIM or TRACK, except SUBMODES 0 (to Offset) and U (to Update, the telescope p o s i t i o n ) . In these two instances, the program w i l l default to whatever the telescope was doing at the time of the command(i.e. either aiming or tracking) i f a p r e f i x i s not s p e c i f i e d . In ad d i t i o n i t should be noted that the prefixes to AIM or TRACK may be used without any SUBMODES at a l l to cause the telescope to AIM or TRACK at i t s current p o s i t i o n . to AIM, the stopped. 169. a) To aim or track a variable position, either the Moon or some other source SUBMODE:, V MODIFIERS: M, 0 COMMENTS: If "V" i s encountered in a MODE T CS prefixed to AIM or TRACK, a variable position is read in. This includes sources such as the sun, moon, planets and comets. If the f i r s t MODIFIER is M, the Moon is assumed; i f i t is 0 or unspecified, a source other than the Moon i s assumed. In the f i r s t case, the program requests the Moon's RA and DEC, and their hourly variation for the current Ephemeris interval in the American Ephemeris and Nautical Almanae (AENA); i t then corrects the geocentric position to a geodetic one, and slews to the calculated position.' In a l l other cases, the program f i r s t requests the distance to the source in Astronomical Units (AU) for use i n the geocentric to geodetic conversion; i t then carries on as for the previous case, with the exception that the variations given for the RA and DEC are for the current 24 hour Ephemeris interval, not a 1 hour interval. b) To aim or track a Galactic co-ordinate, with options to precess and calculate the LSR velocity SUBMODE: G MODIFIERS: F(A), V COMMENT: If "G" is encountered in a MODE T CS prefixed II II to AIM or TRACK, a galactic position (1 , b ) is requested, converted to equatorial co-ordinates, and then the telescope driven there. The MODIFIERS have the same functions they do as SUBMODES in MODE M ( see Section D.2.e and f ) , with the precessed position being the one driven to i f precession i s requested. c) To aim or track an equatorial co-ordinate (RA and DEC), with options to precess and calculate the LSR velocity SUBMODE: R MODIFIERS: P(A), V COMMENT: If "R" is encountered is a MODE T CS prefixed to AIM or TRACK, an equatorial position (RA and DEC) is requested and driven to. The MODIFIERS have the same functions they do as SUBMODES in MODE M (see Sections D.2.e and f).with the precessed position being the one driven to i f precession i s requested. 170. d) To aim or track an HA and DEC SUBMODE: H COMMENT: If "H" is encountered in a MODE T CS prefixed to AIM or TRACK, and HA and DEC are requested and then driven to. e) To update the current telescope position SUBMODE.: U COMMENT: If "U" is encountered in a MODE T CS prefixed to AIM or TRACK (or not prefixed at a l l , the default being the current aim or track status), the operation performed depends on the SUBMODE used to input the last command position. If SUBMODE "V" was used, the geodetic position for the current Ephemeris time i s calculated and the telescope driven there. If either SUBMODE G, R, or H was used, the telescope i s returned to the relevant input position from wherever i t currently happens to be. This i s useful when the telescope is tracking sporadically or i f i t has been driven away from the input position. If the refraction flag i s set (see F.4.c below), SUBMODE H must be used to aim, and G and R to track. f) To aim or track a position offset to the north, south, east or west of the last position that was input SUBMODE: 0 MODIFIERS: N, S, E, W COMMENTS: If "0" i s encountered in a MODE T CS prefixed to AIM or TRACK (or not prefixed at a l l , the default being the current aim or track status), the telescope w i l l be driven by a specified offset with respect to a previously read in fixed or variable position. The; MODIFIERS N, S, E, and W move the telescope North, South, East and West respectively. One or two MODIFIERS (or directions) may be specified. They are preceded by an integer giving the number of hundreths of degrees the telescope i s to be moved, with the MODIFIER being used as the break  character terminating the numerical input. As usual, integers are preceded by commas in the command string. F.4 Submodes Prefixed to Enable or Disable Program Flags Program flags are labelled memory locations, the contents of which determine what decisions a program w i l l make regarding i t s flow at execution time. Often i t is advantageous for a user to be able to set and clear (enable and disable) these flags at w i l l . As a result, a few user F-5 171. accessible flags concerned cheifly with the telescope drive program, have been included in MODE T. To f a c i l i t a t e the discussion below, the names of these flags (as they appear in the software) and their various states are summarized below. CONTROL FUNCTION  FLAG NAME State- 1 State= 0 State=-1 AORT Track telescope Aim telescope N.A. HORR Use RA and DEC Use HA and DEC N.A. RFLAG Include refraction Ignore refraction N.A. PFLAG Pointing function Ignore pointing Pointing polynomial ECHO Echo user input Don't echo input N.A. It w i l l be noted below that the aim or track flag, AORT, has a SUBMODE corresponding to each of i t s states; as a result, enabling one state i s equivalent to disabling the other. That i s , the CS: *T/ENABLE/AIMING// i s equivalent to the CS: *T/DISABLE/TRACKING//. This would also have been the case for the HORR flag which t e l l s the program whether i t should be using an HA and DEC or a RA and DEC, but the problem arises that i f "H" i s used to indicate an HA and DEC while "R" i s used to indicate an RA and DEC, then we are at a loss for what to use for the refraction flag. In view of this d i f f i c u l t y and to be as consistent as possible with other parts of the command language, i t was decided to use "R" for the refraction flag so that i f HORR is to be set to enable tracking an RA and DEC, for example, then the CS: *T/DISABLE/HA AND DEC// must be used. The CS: *T/ENABLE/RA AND DEC// would set RFLAG SO much for being long-winded. a) To enable or disable the telescope drive program SUBMODE: D COMMENT: If "D" is encountered in a MODE T CS prefixed to enable or disable a program f l a g , r a i l things w i l l be as "usual" i f this flag is enabled. If however i t is disabled user control of the telescope is effectively removed, although MODE T I/O w i l l be as "usual". This feature is useful when testing MODE T programs as i t avoids having to wait for the telescope to move between commands. It is also useful i f the user wants access to some of the MODE T printout without having to move the telescope. The perceptive reader w i l l note that this flag was not given a name in the above table. The reason is that i t is not a flag in the sense that the others are ? but rather i t is a result of dynamic programming. 172. b) To enable or disable telescope aiming or tracking SUBMODES: A, T COMMENTS: If "A" or "T" i s encountered in a MODE T CS prefixed to be enabled or disabled, their effect is as follows: i f aiming is enabled or tracking is disabled, the telescope w i l l aim when next driven; i f on the other hand aiming is disabled and tracking is enabled, the telescope w i l l track when next driven. This feature is really redundant and almost unnecessary, but was included for the benefit of people who don't like to read manuals and try to invent their own way of doing things. What has just been described might represent one of their attempts, and i t would work! c) To enable or disable refraction SUBMODE: R COMMENT: If "R" i s encountered in a MODE T CS prefixed to be enabled or disabled, i t s effects are as follows: i f enabled, an input position w i l l be" corrected for refraction before the telescope is driven to i t ; i f disabled, the input position i s driven to (assuming of course no other corrections are made). It should be pointed out that i f refraction i s enabled, the telescope must be tracking a galactic or equatorial co-ordinate, or aiming at an HA and DEC. A l i t t l e reflection w i l l reveal the need for these restrictions; any other useage w i l l result in an error message being typed. Since there is no Teletype printout associated with this flag, the CS: *T/STATUS// may be used to verify that indeed the input position has been refracted. d) To enable or disable an HA and DEC SUBMODE: H COMMENT: If "H" is encountered in a MODE T CS prefixed to be enabled or disabled, i t s effect is as follows: i f disabled, the HORR flag is set and a RA and DEC used in the next drive command; i f enabled, the HORR flag i s cleared and an HA and DEC is used in the next drive command. Followed by an update then, this SUBMODE can be used to alternate between an (HA and DEC) and a (RA and DEC) position. e) To enable or disable polynomial or functional pointing SUBMODES: P, F COMMENTS: If "P" or "F" is encountered in a MODE T CS 173, F-7 prefixed to be enabled or disabled, the effect is as follows: i f enabled, "P" or "F" w i l l result in any input positions being corrected for telescope misalignment using polynomial or functional (theoretical) respectively, before the telescope i s driven. The polynomial coefficients or functional misalignment parameters are requested by the program. If on the other hand tipti Q r np i i a r e d i s a b l e d , no pointing corrections are made to the input position. f) To enable or disable Teletype character echoing SUBMODE: E COMMENT: If "E" i s encountered in a MODE T CS prefixed to be enabled or disabled, i t s effect i s as follows: i f "E" i s enabled, normal Teletype printout occurs; i f "E" is disabled, user input is not typed. This may be useful under stack operation i f there is a lot of lengthly print-out which i t would be useful to suppress. g) To enable or disable a latitude for use by the system '[ SUBMODE: L COMMENT: If "L" is encountered in a MODE T CS prefixed to be enabled or disabled, the user is requested to enter a telescope latitude for use in refraction, LSR velocity, parallax and other calculations. The default latitude is 49.253 degrees North. As for the DRIVE command above, a flag i s not associated with this command either. F.5 Submodes Without Prefixes The SUBMODES listed below are the only MODE T SUBMODES for which prefixes are not essential. Not included are SUBMODES 0 and U for which the prefixes to AIM or TRACK are optional. These were discussed i n Section F.3 above. a) To l i s t the current status SUBMODE: S COMMENT: If "S" is encountered in a MODE T CS, the following information is typed by the Teletype: the month, day, year, PST, Julian Day, Sidereal time, and the d i g i t a l readout RA, HA and DEC. This i s followed by any pointing or refraction corrections which have been made and a statement of the true telescope RA and DEC, HA and DEC, and Azimuth(A) and Zenith Distance(Z). This information is also available by ini t i a t i n g a clock interrupt, provided a pointing measurement i s not being made (see Section F.5.c). F-8 . -174, b) To have the computer wait a specified number of hours, minutes and seconds before executing the next CS SUBMODE: W MODIFIERS: H, M, S COMMENTS: If "W" is encountered in a MODE T CS, the computer waits the specified length of time before accepting another CS. The total wait time is designated by integers preceding one or two of the above MODIFIERS, which indicate hours, minutes and seconds respectively. As i n SUBMODE 0 (see Section F.3.f), the MODIFIERS are used as break characters to terminate the numerical input and the integers must be preceded by commas in the CS. c) To execute a pointing program, either to measure pointing or restart a measurement or to calculate a pointing polynomial or function. SUBMODE: P MODIFIERS: M(M, 0), R, P, F COMMENTS: If "P" is encountered in a MODE T CS, i t s effect is determined by the MODIFIER which follows i t . The MODIFIER M is used to specify that a pointing measurement is to be made. It is followed by M or 0 to specify the Moon or some Other source as the pointing reference, with 0 being the default i f neither i s specified. The user input is identical to that for tracking a variable position source (see Section F.3.a), with the exception that the current di g i t a l readout offsets are requested as well. For convenience, these may as well be set to zero. Assuming that the sun is being used as the reference source, although the procedure would be similar for any other source, the pointing measurement is made as follows: With the telescope tracking near the sun's center, the telescope is driven approximately one degree South of the sun and then allowed to move North at the slowest possible rate. Using the a predecided level on the chart recorder as a reference, the clock inter-rupt switch is depressed as the chart recorder level rises on the southern limb and then again as i t f a l l s on the northern limb. The telescope is next returned to the center of the sun, and then moved to a fixed position approx-imately one degree West of the sun. Again the interrupt switch is depressed as the chart recorder rises on the western limb and f a l l s on the eastern limb. Depressing the switch a f i f t h time results in the relevant pointing information being typed. To perform another measurement using the same source as a reference, the MODIFIER R is used. F-9. 1 75. The MODIFIERS P and F allow the user to c a l c u l a t e polynomial and f u n c t i o n a l ( t h e o r e t i c a l ) pointing curves. In the f i r s t case, up to a f i f t h order polynomial i s calculated a f t e r the user s p e c i f i e s (or guesses) the polynomial c o e f f i c i e n t s f o r the HA pointing curve (HO to H5) and the DEC pointing curve (DO to D5). In the second case, the source d e c l i n a t i o n i s requested as w e l l as the s i x misalignment parameters f o r the t h e o r e t i c a l pointing curve c a l c u l a t i o n . The meaning or s i g n i f i c a n c e of the various c o e f f i c i e n t s and parameters i s beyond the scope of the present d i s c u s s i o n and no attempt w i l l be made to explain-• them. The net r e s u l t of either of these c a l c u l a t i o n s i s that values f o r the HA and DEC pointing curves w i l l w i l l be printed f o r one hour i n t e r v a l s over the HA range ±, s i x hours. For the casual observer, MODIFIERS F and P w i l l only be use f u l to check that proper pointing curves are being used. For the non-casual observer, they have a d d i t i o n a l uses. F-10 176. F.6 Mode T Examples As in the case of MODE M, MODE T involves a certain amount of user-Teletype dialogue, which hopefully the following examples w i l l i l l u s t r a t e . In any event, what is required of the user should be obvious either from the SUBMODE descriptions or from the actual Teletype printout. Note that whenever an HA, RA or DEC is input i t may be entered in either "astronomical" format or decimal degree format, as illustrated i n the f i r s t example below. a) To slew the telescope to (HA: 15.0, DEC:+10.0) and then AIM, use: •T/AIM/HA AND DEC// HAt 01 H 00M 00S DEC:+10D 00* 00" or •T/A/H// •HAt +1 5.000D DEC:+10.000D b) To offset the telescope 0.25 degrees North and 1.00 degrees West of this position, use: •T/OFFSET*25NORTH*100WEST// Note that since the telescope was already aiming, the AIM prefix was not necessary (cf. example g) below). c) Suppose a comet 100 AU's distant at (RA: 10H 11M 12S, DEC:+10D 40' 00") is to be tracked and i t has negligible RA and DEC variations, then use the CS: *T/TRACK/VARIABLE POSITION SOURCE// TYPE DISTANCE TO SOURCE IN ASTRONOMICAL UNITS 100.00 FOR CURRENT EPHEMERIS INTERVAL IN AENA* TYPE SRC POSITION AND VARIATIONS RA: 10H 11M 12S* VRA:0.000* DEC:+10D 40' 000"* VDEC:0.000 THE GEOCENTRIC CO-ORDINATES ARE: RA:10H U M 11S* DEC: + 10D 39* 59" THE GEODETIC CO-ORDINATES ARE: RA: 10H U M U S , DEC: + 10D 39' 59" However, since the source position variations were assumed negligible, i t could equally well have been tracked by giving the CS: F - l l 1 7 7 . fcT/TRACK/RA AND DEC// RA: 10H 11M 12S DEC:+10D 40' 00" Had t h e comet b e e n n e a r e r t h a n 1 A U , t h e l a t t e r CS w o u l d n o t h a v e worked s i n c e i t d o e s n ' t p e r f o r m t h e g e o c e n t r i c t o g e o d e t i c c o n v e r s i o n w h i c h i s n e c e s s a r y f o r n e a r b y o b j e c t s . Two o t h e r p o i n t s a r e a l s o w o r t h m e n t i o n i n g . F i r s t , i n o r d e r t o i n c l u d e r e f r a c t i o n and p o i n t i n g c o r r e c t i o n s , t h e C S ' s : * T / E N A B L E / R E F R A C T I O N / / and *T /ENABLE/POLYNOMIAL POINTING CORRECTIONS/ / o r *T /ENABLE/FUNCTIONAL POINTING CORRECTIONS/ / (o r t h e i r e q u i v a l e n t s ) w o u l d have had t o b e e n g i v e n b e f o r e e i t h e r o f t h e above e x a m p l e s . T h i s p o i n t a p p l i e s o f c o u r s e t o any o f t h e A IM o r TRACK d r i v e commands. S e c o n d , i f f o r some r e a s o n t h e u s e r had wanted t o know t h e g e o d e t i c p o s i t i o n o f t h e c o m e t , b u t d i d n ' t wan t t o move t h e t e l e s c o p e , t h e C S : * T / D I S A B L E / D R I V E / / w o u l d have a l l o w e d t h i s . c h a n g i n g , and b) i t w a s n ' t n e a r enough to p r o d u c e any p a r a l l a x p r o b l e m s . I n t h e n e x t examp le i n w h i c h t h e Moon i s t o be o b s e r v e d , b o t h t h e s e e f f e c t s a r e i m p o r t a n t . d) To t r a c k t h e moon on May 1 7 , 1974 be tween 18 and 19 h o u r s E p h e m e r i s t i m e ( 10 and 11 AM P S T ) , a s s u m i n g t h e c u r r e n t d a t e has b e e n e n t e r e d e i t h e r d u r i n g p rog ram l o a d i n g o r u s i n g t h e C S : * M / D A T E / / , t h e n g i v e t h e C S : •T/TRACK/VARIABLE SOURCE/MOON// FOR CURRENT EPHEMERIS INTERVAL IN AENA, TYPE SRC POSITION AND VARIATIONS RA: 00H 08M 51.IS, VRA: 1 19.367, DEC:+06D 28' 43.1", VDEC:723.63 THE GEOCENTRIC CO-ORDINATES ARE: RA:00H 09M 46S, DEC:+06D 34' 16" THE GEODETIC CO-ORDINATES ARE: RA;00H 08M 40S, DEC:+05D 55* 16" I f t h e g e o d e t i c c o - o r d i n a t e b e i n g t r a c k e d i s to be u p d a t e d b e t w e e n 10 and 11 A M , g i v e : *T/UPDATE// THE GEOCENTRIC CO-ORDINATES ARE: RA:00H 09M 52S, DEC:+06D 34' ST-THE GEODETIC CO-ORDINATES ARE: RA:00H 08M 44S, DEC:+05D 5 5 ' 53" F-12 178. Note that there is no user input in SUBMODE "U". It is also worth noting that had refraction or pointing been included, as suggested i n the previous example, the printout would have been no different. Only the printout during a system status command is affected by these flags, (see examples h) and g) below) e) Suppose that the Galactic Center (1950.0 co-ordinates ( l 1 1 : 0.0, b 1 1 : 0.0)) is to be tracked on May 17, 1974 and that this date has been entered either during system loading or using the CS: *M/DATE//, then give the CS: *T/TRACK/GALACTIC POSITION// L I I : 000.000 BII: 000.000 RA: 17H 42M 26S DEC:-28D 55' 00" P RA: 17H 43M 58S DEC: ^ 28D 55' 35" f) To do a d r i f t scan through the source i n the last example from a position 0.25 degrees to the North and 1.00 degrees to the West of the input position, give: *T/AIM/0FFSET,25NORTH,»100WEST// To return to the input position after the d r i f t scan and start tracking again, use the CS: *T/TRACK/OFFSET,0NORTH//. g) To l i s t the current telescope position and other parameters, use the CS: *T/STATUS// ON MAY 17,1974 AT PST: 20:13:36 THE LOCAL JULIAN DATE IS 2442184.5 THE SIDEREAL TIME IS 11:42:32 AND THE DISPLAYED TELESCOPE POSITION IS: HA: +49.010D, DEC: +39.340D MISALIGNMENT CORRECTIONS MADE WERE DHA: +.000, DDEC: +.000D REFRACTION CORRECTIONS MADE WERE DHA: -.013, DDEC: +.006D THIS CORRESPONDS TO A CORRECTED DISPLAYED POSITION OF: RA: 08H 26M 27S, DEC:+39D 20* 00" HA: +49.023D, DEC: +39.333D A: +272.887D, 2: +35.781D COMMENT: Note that prior to this CS the refraction flag had been enabled since refraction corrections are included i n the printout. F-13 i 179. h) Suppose that the telescope i s now moved to another position where a polynomial pointing correction, i n addition to the refraction correction, i s to be made. To do this, we f i r s t use the CS: *T/ENABLE/POLYNOMIAL FITTING// MISALIGNMENT PARAMETERS ARE: H0: - .21 4 HI : +. 13E-2 H2: -4 .6E-6 H3: 2. 3J>7 .44: 0. H5: 0. D0: -.106 Dl : -2.1E-3 D2: 4. 1E-5 D3: 1 .1 E-8 D4: 0. D5: 0. which t e l l s the drive program the various empirically determined polynomial pointing coefficients. The telescope is then driven to the source position ( say, (RA: 7H 5M 4 6 S , DEC:+23D 02' 31")) using a CS something like: *T/T/R//, at which time we produce a clock interrupt. The following printout would occur: CLOCK INTERRUPT. ON MAY 17,1974 AT PST: 20:43:47 THE LOCAL JULIAN DATE IS 2442184.5 THE SIDEREAL TIME IS 12:12:48 AND THE DISPLAYED TELESCOPE POSITION IS: HA: +76.999D, DEC: +23.010D MISALIGNMENT CORRECTIONS MADE WERE DHA: +.265, DDEC: -.057D REFRACTION CORRECTIONS MADE WERE DHA: -.027, DDEC: +.025D THIS CORRESPONDS TO A CORRECTED DISPLAYED POSITION OF: RA: 07H 05M 46S, DEC:+23D 02' 31" HA: +76.761D, DEC: +23.041D A: +276.106D, Z: +64.273D COMMENT: Note that now misalignment corrections as well as refrac-tion corrections occur in the printout, and that the corrected displayed position equals the input position. If i t was thought that the telescope was not tracking properly, the CS: *T/UPDATE// would move i t back to the position read using SUBMODE "R", but would produce no printout. Contrast this with what happened in example d) above, where the update was used after a SUBMODE "V" posi-tion had been the last one entered. F-14 180. i) Suppose that the sun is to be used to determine empirical pointing curves and that the current date has been made the active date (July 4, 1975 in the following example). To perform this pointing measurement, the user f i r s t enters the sun's position and variations for July 4,1975, followed by the di g i t a l readout offsets, as illustrated below: *T/POINTING/MEASUff£// TYPE DISTANCE TO SOURCE IN ASTRONOMICAL UNITS 1.0 FOR CURRENT EPHEMERIS INTERVAL IN AENA* TYPE SRC POSITION AND VARIATIONS RA: 06H 49M 40.94S* VRA:247.46* DEC:22D 56* 59.8", VDEC: -305.9 TYPE OFFSET FOR HA: 0.000D, DEC: 0.000D * Note that by default a source other than the moon was assumed. The user then depresses the clock interrupt switch to record the positions of the southern and northern limbs, followed by a similar procedure for the western and eastern limbs, as described earlier i n Section F.5.C Depressing the interrupt switch a f i f t h time causes the following output: AT ST 09:13:54* WITH OFFSETS FOR HA: +.000D* DEC: +.3Q0D READOUT POSITION WAS RA: 06H 53M 54S* HA: +35.000D, DEC: +23 .0850 GEODETIC POSITION IS RA: 06H 53M 34S, HA: +35.085D, DEC: + 2 2 . 8 6 8 D REFRACTED POSITION IS HA: +35.076D, DEC: + 2 2 . 8 7 9 D THEREFORE* POINTING ERRORS ARE DTC; +.076D* DDC: +.2CJ5D To restart the pointing measurement program, use the following CS: T/POINTING/RESTART// j) Suppose that as a result of the pointing curve measure-ments the user thinks he can make a good guess at the six misalignment parameters for a functional (as opposed to polynomial) pointing curve. The pointing curve could then be calculated as illustrated below: F-15 181. *T/PO IN TING/FUNCTION CALCULATION// MISALIGNMENT PARAMETER GUESSES ARE: ALPHA: 0.007 B E T A : 0.066 P S I : -0.034 E T A : r0.002 PHI: -0.085 T H E T A : 0.242 SIGMA: 0.041 TYPE SOURCE DEC: -6.00D, INCLUDE REFRACTION (Y OR N ) ? N HA(HRS) DTC(DEG) DDC(DEG) -5.999 +179.670 -.025 -4.999 -.328 -.035 -3.999 -.325 - .044 -2.999 -.320 - .051 -1 .999 -.314 -.056 - .999 -.307 -.059 + .000 -.299 - . 060 +1 . 000 -.291 -.058 +2.000 -.283 - .054 +3.000 -.277 -.043 +4.000 -.272 - . 040 +5.000 -.269 -.031 +6.000 -180.268 -.02 1 Note that i f a polynomial had been calculated, the user input would have been similar to that of example h) above which was used to enable polynomial misalignment correct-ions. By the same token, i f functional rather than polynomial pointing corrections had been enabled, the user input would have been similar to that just given. k) If the telescope is to be stowed, only a CS need be typed, as for example: *T/AIM/STOW//. The same applies to aiming to the ground or to the zenith. 1) If the computer i s to be halted for a certain length of time between the execution of successive CSs, the WAIT command can be used. For example, to wait 5 minutes and 10 seconds the CS: *T/WAIT,5 MINUTES,10 SECONDS// might be used. G - l G C o n t r o l Commands and O t h e r Sys tem C a p a b i l i t i e s 1 8 2 . G . 1 S t a r t i n g A d d r e s s e s The o n l y s t a r t i n g a d d r e s s (SA) w h i c h c o n c e r n s t h e c a s u a l u s e r i s SA 0 0 0 0 0 2 . To s t a r t t h e c o n t r o l s y s t e m a f t e r t h e compute r power has been o f f , i t i s n o t n e c e s s a r y t o r e l o a d t h e e n t i r e s y s t e m . One s i m p l y t u r n s t h e POWER ON, p u t s 000002 i n t h e c o n s o l e d a t a s w i t c h e s , and d e p r e s s e s t h e RESET and START s w i t c h e s on t h e Nova c o n s o l e . U n l i k e when t h e s y s t e m i s l o a d e d , t h e c u r r e n t d a t e w i l l n o t be r e q u e s t e d , so t h a t t h e C S : * M / D A T E / / s h o u l d be g i v e n b e f o r e a n y t h i n g e l s e , t o make s u r e t h e d a t e i s a v a i l a b l e f o r p rog rams t h a t m i g h t need i t . So much f o r c a s u a l u s e r s . I t s h o u l d a l s o be n o t e d t h a t i n a d d i t i o n t o SA 000002 a number o f o t h e r S A ' s a r e a v a i l a b l e . T h e s e a r e : STARTING ADDRESS FUNCTION 000002 To i n i t i a l i z e and s t a r t t h e c o n t r o l s y s t e m 000003 To r e s t a r t t h e c o n t r o l s y s t e m 000004 To e n t e r DEBUG I I I 000005 To e n t e r a s p e c i a l F l o a t i n g P o i n t Debugger 000006 To p e r f o r m a D e c i m a l t o F l o a t i n g P o i n t c o n v e r s i o n 000007 To e n t e r a M o d i f i e d DEBUG I p rog ram T h e s e o t h e r p r o g r a m s , w h i c h a r e d e s c r i b e d i n P a r t I I o f t h i s s e r i e s , A DESCRIPTION FOR MAN THE WISE , a r e c o n c e r n e d w i t h p rog ram d e b u g g i n g , and as a r e s u l t a r e beyond t h e s c o p e o f t h i s m a n u a l . I t s h o u l d be p o i n t e d o u t , however , t h a t i f t h e y a r e t o be u s e d , t h e y must be l o a d e d w i t h t h e r e s t o f t h e c o n t r o l s y s t e m ; DEBUG I I I i s on a DGC t a p e by i t s e l f , w h i l e t h e r e m a i n i n g t h r e e p rog rams a r e i n c l u d e d on U T I L I T Y ( R B ) . A t t h e p r e s e n t t i m e none o f t h e s e t a p e s c a n be l o a d e d w i t h t h e c o n t r o l s y s t e m w i t h o u t c a u s i n g a memory o v e r f l o w . The way t o a v o i d t h i s d i f f i c u l t y i s t o c o m p i l e o n l y a p a r t i a l c o n t r o l s y s t e m , i . e . l e a v e ou t MODE D o r MODE T . We r e t u r n now t o a d i s c u s s i o n o f t h e f i r s t two S A ' s . SA 000002 i s t h e n o r m a l s y s t e m s t a r t i n g a d d r e s s ; t h e o n l y d i f f e r e n c e be tween i t and SA 000003 i s t h a t SA 000002 i n i t i a l i z e s any f l a g s o r d y n a m i c a l l l y programmed l o c a t i o n s w h i c h m i g h t h a v e b e e n changed d u r i n g e x e c u t i o n f r o m G-2 their "normal" values. If, for example, there is a power failure while the high speed punch is being used, the control system's "put character" routine would have been using the punch instead of the Teletype; therefore, when the system is restarted, i t must be i n i t i a l i z e d to use the Teletype instead of the punch with the "put character" routine, otherwise, the user would be carrying on a conversation with the punch! This is just one example, there are many more — some of them very subtle. For the non-casual user, i t should also be pointed out that once the system i s running, i t i s not necessary to put a SA i n the Nova data switches to start one of the other programs. Typing the SA (without leading zeros) followed by an ESC works just as well. For example, i f DEGUG III is to be entered, typing "4ESC" would get you there. G.2 Control Commands Control commands, which are produced by depressing the CTRL key at the same time another key is depressed,^ serve a number of useful functions, most of which are concerned with the operation of stack programs. The following Table summarizes the available control commands and their functions, most of which should become obvious i n the next Section. CONTROL COMMAND FUNCTION CTRL A CTRL B CTRL C CTRL D CTRL H CTRL N CTRL Q CTRL R CTRL Snnn CTRL X Advance stack pointer to next CTRL H or CTRL B Ring Teletype b e l l twice and halt execution Continue execution after CTRL H or CTRL B Must appear at end of stack programs (also EOT) Halt program execution Enter stack program at location of stack pointer Quit execution and i n i t i a l i z e system Reset stack pointer and begin executing stack program Skip stack pointer past next nnn stack characters Exit from stack execution. Use Teletype for input. .1) Control commands have various abbreviations. For example, depressing the CTRL key and the key marked D might be represented as CTRL D, fD, or EOT. G-3 184. Of these commands, CTRL A, CTRL D, CTRL N, CTRL R, CTRL S and CTRL X are used only i n conjunction with the execution of stack programs; the others may be used i n other circumstances. In any event, t h e i r useage should be r e l a t i v e l y obvious. I t should be pointed out however that i f either CTRL H or CTRL B i s encountered, they must always be followed by another c o n t r o l command; anything else w i l l r e s u l t i n a question mark being typed. G.3 Stack Programs In Section D we discussed yanking, l i s t i n g and w r i t i n g stack programs, but we didn't say what stack programs were. A stack program i s e s s e n t i a l l y a stack of i n s t r u c t i o n s stored i n memory, which are executed i n a sequence determined by the manner i n which the user uses c o n t r o l commands to manipulate a stack pointer. Other than the addition of con t r o l commands,the ins t r u c t i o n s stored i n a stack program are the same as those used i n ordinary command s t r i n g s ; but stack programs have the advantage that they can contain many command str i n g s (the number being r e s t r i c t e d only by the amount of unused core i n memory), and the order of execution of these CS's can be varied by typing only si n g l e c o n t r o l commands? without ever having to type the CSs. To begin the execution of a stack program, the c o n t r o l command CTRL R i s used; t h i s moves the stack pointer to the top of the stack program and begins execution from that point. The commands CTRL H and CTRL B are used to h a l t program execution at various points within the stack; otherwise, continuous c y c l i n g through the stack would occur. To continue execution a f t e r h a l t i n g , CTRL C or CTRL A are used. CTRL A advances the stack pointer to the next CTRL H or CTRL B without executing any of the intermediate i n s t r u c t i o n s . CTRL C, on the other hand, j u s t continues stack execution from wherever the l a s t h a l t occurred. Besides using CTRL A, i n s t r u c t i o n s may also be skipped by using CTRL S, which i s followed by a number specifying the number of stack characters to be skipped. If no number i s given, a s i n g l e skip i s assumed. As with the execution of ordinary CSs, stack programs w i l l often require some' sort of user input. I f t h i s input doesn't change, i t may be included i n the stack program following the CS which requires i t . A simple r u l e of thumb i s to remember that the sequence of user input i s exactly as i t would be had the CS a c t u a l l y been typed. If, however, the user input does change, or i s undetermined when the stack program i s written, CTRL X 1 8 5 . may be used to automatically exit from the stack to accept Teletype input. To continue stack execution after accepting this input, CTRL N i s used. It should be pointed out that the Teletype printout for stack execution i s no different than had the CSs actually been typed, except that more control characters are encountered. These are echoed as an upward arrow followed by the letter name of the keyboard key used to produce it,and a space. As the stack pointer is moved down through the program stack i t eventually encounters the mandatory EOT which must terminate a l l stack programs. This causes the pointer to be repositioned at the top of the stack and to start working i t s way down again, thus allowing the stack program to be repeated. It should be mentioned that repeated operations may also be executed by using a paper tape loop i n the Teletype reader. This method, be-sides being'messy, noisy and unreliable, is also much less powerful than stack programming. Its use is therefore discouraged. By way of i l l u s t r a t i o n , suppose that a stack program has been written using a CS something l i k e : *M/WRITE A STACK PROGRAM//, which then punched the program on paper tape. The paper tape is then loaded into the program stack and listed as follows: *M/YANK/LI ST// IF TAPE IS MOUNTED AND TERMINATED WITH EOT, HIT A KEY STACK PROGRAM LISTING tH *' D/A,49,80,561,592/S,305,336,561,592/(3,561,592// t H D/A,561,592,817,843/I/K,0,767/W,561,592// rS 12 »H D/K,0,767// END OF PROGRAM The program illustrated calculates the difference between an on-source and an off-source line measurement(stored in the f i r s t and. second quarters of the FT) and puts the result i n the third quarter. It then performs a Quadratic least squares f i t on this data to determine the RMS noise level as a test for acceptability. G-5 186. If the data is acceptable, CTRL C is depressed and the data i s added to the fourth quarter, the f i r s t three quarters are erased, and the on-source minus off-source data i s typed. The program then skips the next twelve stack characters, which effectively brings the stack pointer to the top of the stack again, where execution is halted by the presence of a CTRL H. If however the data is unacceptable, CTRL A is depressed,which causes the stack pointer to skip to the next CTRL H. Typing CTRL C after this.halt then allows the stack program to erase the f i r s t three quarters of bad data, afterwhich the stack pointer is moved to the top of the program stack and halts. The following might represent typical user-stack program dialogue. *tR tH tjC_D/A,49,80,561,592/S,305,336,561,592/0,561,592// A0= +18.536,A1= -.008,A2= -.000,MU= +10.004,SIGMA= +14.708 *tH _C_D/A,561,592,817,848/1/K,0,767/W,561,592// -00006 -00006 -00004 -00004 -00004 -00004 -00006 -00004 -00004 -00006 -00034 -00006 -00002 -00004 -00004 -00004 -00004 -00004 -00004 -00004 -00004 -00004 -00006 -00004 -00004 -00004 -00004 -00006 -00004 -00004 -00004 -00006 *tS 12tH t_Q_D/A,49,80,561,592/S,305,336,561,592/0,561,592// A0= +.000,A1= +.000,A2= +.000,MU= +.000,SIGMA= +.000 *tH tA tH tf__D/K, 0,767// *tH 1C_D/A,49,80,561,592/S,305,336,561,592/9,561,592// A0= +.000,A1= .+.000,A2= +.000,MU= +.000,SIGMA= +.000 *tH ?????t'X T/AIM/ZENITH// Stack execution is started using CTRL R; the i n i t i a l CTRL H is encountered and the system halts. After an on-source and an off-source measurement is made, CTRL C is depressed, which causes the stack program to execute to the next CTRL H. Since the noise level was found acceptable, CTRL C was depressed. This caused the data to be added to the fourth quarter and then written out on the Teletype. Twelve instructions were then automatically skipped and a CTRL H read, which halted the system. After another on-source and off-source measurement, the CTRL C combination was again depressed, but this time the data was found unacceptable (there was none!). Consequently, CTRL A was depressed to advance the stack pointer to the next halt, where a CTRL C was used to allow the stack program to clear the f i r s t three quarters i n readiness for another measurement. Before the measurement could be started, however, some primate decided to depress CTRL D again, causing a least squares f i t to be performed on an empty third quarter. In desperation, this fool madly starts striking anything but a control command, thus causing the chain of question marks to be typed. Eventually CTRL X i s struck, causing an exit from 187 the program stack. A CS could then be typed to drive the telescope to the zenith The following represents an example of a stack program used to position switch the telescope and collect data. Fi r s t , read stack program and l i s t i t : *M/YANK A STACK PROGRAM/LIST IT// I F TAPE IS MOUNTED AND TERMINATED WITH EOT, HIT A KEY STACK PROGRAM LISTING T/OFFSET,0 NORTH/WAIT,5 MINUTES// D/TRANSFER ONSOURCE,49,80,561,592// T/OFFSET,100 NORTH/WAIT,5 MINUTES// D/SUBTRACT OFFSOURCE AND DO/QUADRATIC FIT TO,561,592/BLANK,571,577// tB D/ADD RESULT TO SUM,561,592,817,848/LNPUT/KILL,0,767/WRITE,561,592// t S 12 tH D/KILL,j2f,767// END OF PROGRAM To enter source position, for example an RA and DEC, use: *T/TRACK/RA AND DEC/PRECESS TO CURRENT EPOCH// RA: 17H 42M 26S DEC:^28D 55» 2 ( 0 " P RA: 17H 43M 58S DEC:-28D 55' 35" And i f refraction and pointing corrections are to be automatically made, use something like: *T/ENABLE/REFRACTION// *T/ENABLE/POLYNOMIAL POINTING CORRECTIONS// The last command would be followed by a l i s t of polynomial coefficients. To begin execution of the stack program, type tR. Appendix B: An Internal Technical Report on Telescope Pointing The Derivation and Analysis of Theoretical Pointing Functions For an Equatorially Mounted Telescope by M.J. MAHONEY Department of Physics and Institute of Astronomy and Space Science University of British Columbia Vancouver, B.C., Canada 190. Abstract In terms of a number of misalignment parameters describing the imperfections of a practical equatorially mounted telescope located on the earth's surface, theoretical pointing functions are derived to predict a source's observed position in terms of i t s true cele s t i a l position. In addition, three kinds of experiments are described by which the misalignment parameters can be determined; these have involved the introduction of several novel techniques. Finally, a discussion i s presented on how the various misalignments can be corrected or accounted for, with explicit reference being made to the U.B.C. millimeter wave-length radio telescope. TABLE OF CONTENTS PAGE A . INTRODUCTION 1 B . DERIVATION OF THE POINTING FUNCTIONS 4 1 . The e f f e c t s o f s t r u c t u r a l and e n c o d e r m i s a l i g n m e n t s 4 2 . The e f f e c t s o f p a r a l l a x , r e f r a c t i o n and s a g -*-3 3 . C o m b i n i n g t h e s e e f f e c t s t o f i n d p o i n t i n g f u n c t i o n s 15 4 . F u r t h e r c o n s i d e r a t i o n s r e g a r d i n g p o i n t i n g f u n c t i o n s 16 5 . C o m p a r i s o n w i t h o t h e r r e s u l t s 20 C . DETERMINATION OF THE MISALIGNMENT PARAMETERS 24 1 . S l e w i n g e x p e r i m e n t s 24 2 . T r a c k i n g e x p e r i m e n t s 27 3 . T r a n s i t e x p e r i m e n t s 28 4 . Summary o f i n s t r u m e n t a l t e c h n i q u e s 20 a) P h o t o g r a p h i c t e c h n i q u e s 30 b ) R a d i o t e c h n i q u e s ^1 c ) V i d e o t e c h n i q u e s 3 4 D. POINTING CORRECTIONS MADE FOR THE UBC Xmm TELESCOPE 3 5 3 S 1. A l i g n m e n t o f t h e p o l a r a x i s 2 . P o i n t i n g c o r r e c t i o n s made d u r i n g o b s e r v a t i o n s 3** a) M a n u a l c o n t r o l mode ^ b ) Compute r c o n t r o l mode E . CONCLUDING REMARKS 4 3 APPENDICES 46 A . D e r i v a t i o n o f e x p r e s s i o n s f o r p a r a l l a x , r e f r a c t i o n and s a g . . B . D e r i v a t i o n o f c o e f f i c i e n t s f o r p o l y n o m i a l and f u n c t i o n a l l e a s t s q u a r e s f i t s t o t h e p o i n t i n g f u n c t i o n s C . C o n v e n t i o n s u s e d w i t h m a t r i x r o t a t i o n s D. Computer p rog rams u s e d t o a n a l y z e e m p i r i c a l r e s u l t s ->9 E . P o i n t i n g measu remen ts made f o r t h e UBC Xmm t e l e s c o p e BIBLIOGRAPHY 1. 192. A. INTRODUCTION There are several ways to approach the problem of telescope misalignment. If the telescope under consideration i s easily capable of observing a large number of sources, then empirical "pointing curves" may be obtained and used in the subsequent observations of other weaker sources. These w i l l describe, as a function of hour angle, how struc-tural imperfections cause the hour angle and declination displayed on the position encoder readouts to differ from the true source values. In general, however, these curves w i l l depend c r i t i c a l l y on declination, so that both good declination and hour angle coverage are required. In the case of millimeter wavelength radio telescopes — for which our results are ultimately intended — current receiver sensitivities and the lack of strong continuum sources restri c t the available declina-tion coverage to that provided by solar system sources. This d i f f i c u l t y can be partially circumvented i f an optical telescope i s mounted with i t s beam parallel to the ele c t r i c a l axes of the radio telescope, for then v i s i b l e stars can be observed to find empirical pointing curves. The d i f f i c u l t y s t i l l remains, however, that even i f the optical and radio beams can be aligned at one position, they w i l l not be aligned at a l l positions, as the radio beam w i l l be subject to sag. Furthermore, i t would be advantageous to know how to correct for such things as polar axis misalignments, since these corrections can be made. As a result, an analytic pointing theory i s required which can predict how structural misalignments w i l l manifest themselves and what, i f possible, can be done to correct for them. 2. 193. Although astronomers have traditionally used spherical t r i -gonometry to describe relationships between objects on the c e l e s t i a l sphere, this technique can become very cumbersome for studying tele-scope misalignments unless approximate methods are used. In the pre-sent work, this d i f f i c u l t y i s avoided by using rotation matrices. Con-ceptually this approach appears much more direct,and approximations need only be introduced in order to obtain explicit solutions; other-wise, numerical techniques may be used to obtain exact solutions. Since for our purposes the numerical approach would be too time-consuming for the kind of real time manner in which pointing corrections are expected to be made, we w i l l be forced to obtain explicit solutions. Therefore, approximations w i l l be needed, but not to the degree required i f spherical trigonometry were used; and our approach has the distinct advantage of being able to provide more accurate solutions i f they are required. The remainder of this paper i s developed as follows. In the following section, we derive explicit expressions for the hour angle and declination pointing functions, At and A6 respectively. These functions provide the analytic expressions needed to perform a least squares analysis of the empirical pointing curves, so that the various misalignment para-meters can be determined. The calculation of these pointing functions is divided into two parts: f i r s t we calculate the effect of structural and synchro misalignments on the apparent source position, that i s , the position a source occupies on the celes t i a l sphere when parallax, re-fraction and telescope sag"*" are taken into account. Then we calculate The reason for including sag with parallax and refraction i s one of mathematical convenience only and w i l l be discussed later. 3. 194. the relationship between the apparent source position and the true source position, that i s , the position a source would have i f i t were observed by a perfectly aligned r i g i d telescope at the center of the earth, with both the earth and i t s atmosphere removed. The results of these two calculations are then combined to give the analytic expressions for At and A S , and these in turn are extended to forms which w i l l be useful in the subsequent analysis. Finally, a comparison i s made with the results found by other groups. In section C, we discuss different kinds of experiments which in principle can be used to solve for the various misalignment parameters. This discussion i s then followed by a brief summary of the actual techniques which have been used. More details can be found in Appendix E, where the results are presented. The next section, Section D, presents a summary of practical considerations and methods used in correcting for the misalignments of the UBC millimeter wavelength radio telescope. This includes alignment of the polar axis, the discussion of " d i g i t a l offsets" and the use of the control system programs in order to obtain automatic pointing corrections. In addition to the Appendices already mentioned are: Appendix A, where simple expressions for parallax, refraction and tele-scope sag are derived, so they can be used in Section B, Appendix B, which derives expressions for the coefficients occuring i n the functional and polynomial least squares f i t s and shows how they are 4. 195. related to the misalignment parameters, Appendix D, which provides a l i s t i n g and description of the various IBM 370 programs used i n different phases of the pointing analysis, and Appendix C, which provides a review of matrix properties and sign con-ventions which are used in the pointing function derivation. B. DERIVATION OF THE POINTING FUNCTIONS As already mentioned in the INTRODUCTION, the derivation of the pointing functions w i l l involve two steps: f i r s t we w i l l calculate the effect of telescope misalignments on the apparent source position, and then we w i l l calculate the relationship between the apparent source position and the true source position. Combining these two results leads to expressions for the pointing functions. These expressions are then further developed to f a c i l i t a t e later analysis. The section ends with a comparison of our results and those found by other groups. 1. EFFECT OF STRUCTURAL AND ENCODER MISALIGNMENTS. These misalignments result from four factors: (a) the polar axis of the telescope i s not aligned with the North Celestial Pole, (b) the declination axis i s in turn not orthogonal to the telescope's polar axis, (c) the telescope's beam is not orthogonal to the declination axis, and (d) the hour angle and declination position encoders, whether synchro transmitters or d i g i t a l encoders, w i l l be biased since they can measure only relative angles. 5. 196. In addition, telescopes which have a receiver or s u b r e f l e c t o r mounted away from the main r e f l e c t o r are also subject to a sag mis-alignment. Since i t w i l l be assumed that the sag i s proportional to the g r a v i t a t i o n a l torque exerted on the support structure, and there-fore that i t occurs i n a v e r t i c a l plane through the zenith, t h i s struc-t u r a l e f f e c t (for reasons of mathematical convenience) w i l l be included with those of r e f r a c t i o n and p a r a l l a x , which also occur i n the zenith v e r t i c a l plane. I t i s these e f f e c t s which cause the apparent source p o s i t i o n , as observed from the surface of the earth, to d i f f e r from the true source p o s i t i o n . They w i l l be discussed i n the following subsection. To determine the e f f e c t of s t r u c t u r a l and encoder misalignments, 2 we proceed as follows . Consider a geodetic co-ordinate system, C , the o r i g i n of which i s located at the p o s i t i o n of the telescope on the earth's surface, with i t s Y-Z plane l y i n g i n the zenith meridian plane such that the p o s i t i o n of source i n t h i s system i s (t',6') where t' i s the source's 3 apparent hour angle and 6 ' i t s apparent d e c l i n a t i o n . With respect to t h i s co-ordinate system, the polar axis of the telescope can be described as being aligned with the Z-axis of another co-ordinate system, P, as i l l u s t r a t e d i n FIGURE 1. Before reading t h i s d e r i v a t i o n , i t may be u s e f u l to examine the summary of matrix properties, and conventions used, that i s provided i n appendix C. This i s equivalent to saying that the apparent and true p o s i t i o n of a source i s i d e n t i c a l at the zenith. 6. 197. FIGURE 1. The source's position in P can be obtained as a rotation R,(X ,) about ty c the axis X , , followed by a rotation R (Y_) about the axis Y_,, or as a c' J n P P rotation R n^-i about Y^,, followed by a rotation R^(X_) about X_,. How-ever i t is easy to show that in the limit where ty and ri may be treated as infinitesimal rotations (so that second order terms may be neglected) that R.R = E R. = R, . Although this assumption need not be made in ty n n ty i>r\ & * the formulation of the problem, i t is however necessary in order to obtain explicit analytic expressions for At and AS, the hour angle and declina-tion pointing functions. If more accurate results are required and the time involved in finding numerical solutions i s no consideration, then the assumption of infinitesimal rotations may be easily dropped. In our case, however, time i s a consideration and we w i l l therefore assume infinitesimal rotations to be acceptable. Having specified the position of the polar axis with respect to C', we can now specify the position of the declination axis with respect to P as a rotation R, about Y followed by a rotation R. about Z as 7. 198. illustrated in FIGURE 2. The rotation R, describes the orientation of the declination axis above a plane perpendicular to the polar axis (i.e. Zp) and the rotation RQ takes into account the hour angle encoder bias. Again, o because of our assumption of infinitesimal rotations, we may write: V e = ReR<|> = R<f>e* D FIGURE 2. Finally, we must describe the orientation of the telescope beam with respect to the declination axis. The arguments are exactly as for the declination axis and we obtain E R. = RaR = R „ where Rn a 8 8 a aB 3 describes the orientation of the beam above a plane perpendicular to the declination axis (i.e. X^) and R^  takes into account the declination axis encoder bias. This i s illustrated in FIGURE 3, where the Y„ i s attached to the telescope beam. D FIGURE 3. 8. 199, A l l we have done so far i s describe a number of structural misalignments; we have done nothing to relate these to what happens when the telescope i s driven to some apparent source position (t',6 1) in C We w i l l now do that. Suppose for the moment that a l l the structural misalignment parameters vanish and that the co-ordinate system , B has i t Y-axis aligned with the source at (t',6'). The position of the source i n B i s : f0\ 1 Jwhere, without loss of generality, we are considering the source to l i e on a unit sphere. Now B may be aligned with C by a rotation R^ , about the X-axis of B, followed by a rotation R^.} about the polar axis of B, so that after these rotations: R;U.V(II <« gives the X,Y and Z components of the source in B (or C ) . Alternatively, we could have performed these rotations in the opposite order, but i n this case, the rotation about the polar axis i s seen in C' through a similarity transformation: R_l R.,, since the Z-axis of B isn't aligned with o t o that of C when the transformations are made this way around. As a result, the source position in S becomes: * 8 . < R J ! Ki ( i ) <2> which i s of course equivalent to Equation (1). Now suppose that the misalignment parameters do not vanish. How w i l l the source position i n C be affected? Clearly the apparent 9. 200. position ( t ' , 6 ' ) w i l l be changed to some new position (T,D) as a result of the misalignments. Starting again with the beam aligned with the source, we must determine which rotations T about the actual telescope polar axis and D about the actual telescope declination axis w i l l bring the co-ordinate system B again into align-ment with C'. When this i s done, we may insi s t that the X, Y and Z com- ponents of the source's position i n C' be the same whether the telescope  is aligned or not. If the beam is aligned to the source, then the source position in D i s : R l ( 1 ) , which after a CW rotation about the actual telescope 0 declination axis becomes: RpR - y^y * taking into account the declination axis misalignment and hour angle encoder bias, the source's position in P i s : R~' R_, R~l (l\ . If this i s followed by a CCW rotation^, T, about the *9 ^ a*\o) _ / 0 \ telescope polar axis, we obtain: R^1 R^ -jj R - (•*-)• w n i c' 1> when P is aligned . On equating this with the X, Y, and Z components obtained when there were no misalignments, we get: where we have freely substituted identities to il l u s t r a t e how the problem would appear i f we had chosen to solve i t using similarity transformations. CW for negative hour angles, but we have assumed, without loss of generality, that both T and D are positive. 10. 201. The f i r s t bracket gives the similarity transformation for the misaligned polar axis rotation in C ; the second, the similarity transformation for the misaligned declination axis rotation i n C' and the third, the position of the misaligned beam in C i f the beam is pointing at the source. A l l that we require i s that the effect of the rotations as seen i n C under similarity transformations be such as to align B with C . This i s as-sured by insisting that the components of the source position in C , after the similarity transformations, be the same as those produced by the rota-tions described by Equation (1) which aligned B with C' in the absence of misalignments. p l i c i t l y for T and D (in terms of the other parameters) because of com-plications introduced by the polar axis misalignment. This was avoided by multiplying i t through by R to get: which gives the position of the source in P, the polar axis co-ordinate system. We now define: As i t stands Equation (3) appears very d i f f i c u l t to solve ex-(5) (6) where x i s a Z-axis rotation and y an X-axis rotation. This w i l l enable us to solve Equation (5) for T and D in terms of x and y, while Equation (6) can be solved for x and y in terms of t' and 6' and then substituted into 11. X\ 202, the solution of Equation (5) to get the f i n a l result for T and D in terms of t' and 6 ' . On substituting Equation (9) into Equation (5), we obtain: *? V Ij) - V %e - D \l (j) We now use relations (1) through (6) of Appendix C to obtain, in explicit matrix form", 'cos x sin x 0\ / l 0 0 A /0V -sin x cos x O l i o cos y - sin y J I 1 0 0 1/ \0 sin y cos y / \0, / c o s T sin T 0\ / l Q -<fr\ / l 0 0 \ / l 0 °\ / 0 > (-sin T cos T 0 If 9 1 0 JI 0 cos D - sin D I (-B 1 a J ( 1 \ 0 0 1/\<J> 0 1/ \0 s i n D cos D/ \ 0 -a 1/ \0/ which leads to: sin x cos y = sin T (cos D + a sin D) + cos T (B + 0 cos D - <f> sin D) (7) cos x cos y = cos T (cos D + a sin D) - sin T (8 + 8 cos D - tp sin D) (8) sin y = sin D - a cos D (9) Equation (9) immediately gives: sin y = sin (D - a) or D = a + y (10) 12. 203, Furthermore, the ratio of Equations (7) and (8) gives: t a n x - sin T cos (D - a) + cos T (g + 8 cos D - <j> sin D) cos T cos (D - a) - sin T (g + 8 cos D - <f> sin D) = tan I T + (T + ( 3 + 8 cos D - <|) sin D)\ cos (D - a) / which on using Equation (1) and retaining only f i r s t order terms results in: T = y - 8 - 3 sec x + <j> tan x (11) Following a similar procedure, Equation (6) leads to: y = <5' - (n sin t' - ty cos t') (12) and x = tan •I / sin t' + n tan 6 ' \ I cos t' - ty tan 6 ' y (13) On substituting these results into Equations (10) and (11) we obtain: „ -I / s i n t 1 + TI tan 6 ' \ „ . . , , , = t a n [cos t' - ty tan 6 ' ) ~ 6 s e c ^ " n sm t' + ^ cos t') + ()> tan ( 6 ' - n sin t' + ty cos t') - 8 (14) and D = 6 * - n sin t* + ty cos t' + a (15) 13. 204. which on simplification to f i r s t order in the misalignment parameters, become: T = t' + (n COS t' + ip sin t' + <J>)tan 6' - 3 sec 6* (16) and D = 6' - n sin t 1 + Tp cos t' + a (17) 2. THE EFFECTS OF PARALLAX, REFRACTION AND SAG. The apparent source posi-tion (t', 6') that we have been dealing with so far is the position seen in a geodetic co-ordinate system attached to the telescope; this must now be related to the true source position (t, 5) which i s the position of a source as seen from a geocentric co-ordinate system C at the center of the celestial sphere. The geodetic position of a source differs from i t s geo-centric position by two well-known effects: refraction and parallax. Both of these occur in a vertical plane through the zenith and are therefore a function of the zenith distance of a, source. As mentioned earlier, sag . is also assumed to occur in this plane and as a result, i t w i l l be included with the s t r i c t l y geocentric-to-geodetic effects of refraction and parallax. This i s done simply for mathematical convenience, since i t could equally well have been included with the other structural effects. It i s shown in Appendix A that the sum total of parallax, sag, and refraction effects can be expressed as: X = ir sin Z + a sin Z + p tan Z (18) 1 4 . 2 0 5 . where Z = c o s 1 ( c o s t c o s 6 c o s L + s i n 6 s i n L ) (19) i s t h e z e n i t h d i s t a n c e o f t h e s o u r c e b e i n g o b s e r v e d , and t h e c o n s t a n t s IT, CT and p a r e 1 t h e p a r a l l a x , s a g and r e f r a c t i o n c o n s t a n t s , r e s p e c t i v e l y . E x p r e s s i o n s f o r t h e s e c a n b e f o u n d i n A p p e n d i x A , Now X h a s b e e n d e f i n e d so t h a t X > 0 means t h a t t h e n e t e f f e c t , o f p a r a l l a x , s a g and r e f r a c t i o n i s t o i n c r e a s e - t h e a p p a r e n t z e n i t h d i s t a n c e o f a s o u r c e . W i t h t h i s c o n v e n t i o n and NCP ZENITH TRUE SOURCE" ( t , 6 ) \ ^ ^ APPARENT SOURCE (t',6') FIGURE 4 . r e f e r e n c e to ' FIGURE 4 , i t i s e a s y t o show t h a t : and t ' = t + X s i n co s e c <5 6 1 = 6 - X c o s co •'-•> (20) (21) where f r om s p h e r i c a l t r i g o n o m e t r y we h a v e t h a t : s i n co = s i n t cos L / s i n Z (22) 15. 206. and c o s to = ( c o s <5 s i n L - c o s ..t s i n S c o s L) / s i n Z (23) and t h e f a c t o r s e c 6 i n t h e e x p r e s s i o n f o r t ' a c c o u n t s f o r t h e f a c t t h a t d e c l i n a t i o n c i r c l e s a r e n o t g e o d e s i e s ( i . e . g r e a t c i r c l e s ) . I t i s w o r t h p o i n t i n g o u t f o r r e f e r e n c e t h a t : < 0 f o r t < 0 < 0 f o r c o s t > t a n L/tan <5 s i n to and c o s oo > 0 f o r t > 0 - • ' . . ' > 0 f o r c o s t < tan L/tan 6 and t h a t i n g e n e r a l : p < 0 s i n c e r e f r a c t i o n r e d u c e s t h e z e n i t h d i s t a n c e and w h i l e TT > 0 s i n c e p a r a l l a x i n c r e a s e s t h e zeA j . t h d i s t a n c e a > 0 i f t h e z e n i t h d i s t a n c e o f t h e s u b r e f l e c t o r i n c r e a s e s , s i n c e t h i s w i l l r a i s e t h e beam, c a u s i n g t h e e f f e c t i v e Z t o i n c r e a s e . •a < 0 i f t h e z e n i t h d i s t a n c e o f t h e s u b r e f l e c t o r d e c r e a s e s , s i n c e t h i s w i l l l o w e r t h e beam, c a u s i n g t h e e f f e c t i v e Z t o d e c r e a s e On t h e b a s i s o f t h e a rgumen ts p r e s e n t e d ; i n A p p e n d i x A , we e x p e c t a > 0 . 3 . COMBINING THESE EFFECTS TO FIND POINTING.FUNCTIONS. Now t h e a p p r o x i -m a t i o n u s e d i n g o i n g f r o m E q u a t i o n s (14) and (15) t o E q u a t i o n s (16) and (17) c a n g e n e r a l l y be e x p e c t e d t o be q u i t e good f o r d e c l i n a t i o n s < 8 0 ° ; t h e r e f o r e , i f we s u b s t i t u t e E q u a t i o n s (20) and (21) i n t o t h e l a t t e r , we a r r i v e a t t h e f o l l o w i n g e x p r e s s i o n s : At = T - t = ('x s i n w-B) sec 6 + (n cos t +> s i n t + <j>)tan 5 - 9 (24) and AS = D - <5 = -X cos to - n s i n t + ip cos t + a (25) which may be considered to be the d e f i n i t i o n of the hour angle and d e c l i n a -t i o n pointing functions r e s p e c t i v e l y . These give the corrections which must be added to a true source p o s i t i o n i n order to obtain the correspond-ing encoder readout p o s i t i o n . I f we use Equations (18), (22) and (23) to eliminate X'sin a) arid X cos to, we f i n a l l y obtain: At = { [ ( i r+c) + p(cos t cos <5 cos L + s i n 6 s i n L) s i n t cos L - 3} sec 6 • + (ip s i n t + n cos t + <f>)tan 6 - 6 (26) and A6 = [(TT+O") + p(cos t cos 6 cos L + s i n <5 s i n L) x(cos t s i n 6 cos L - cos 5 s i n L) + (ip cos t - n s i n t) + a (27) If more accurate r e s u l t s than these are required, then they can be obtained from Equations (14) and (15) by following the same steps as above. 4. FURTHER CONSIDERATIONS REGARDING POINTING FUNCTIONS. Before pursuing the matter of measuring the various misalignment parameters, i t w i l l be useful to put the pointing function expressions (26) and (27) i n a form more consistent with^the a n a l y s i s to be made. These1 r e s u l t from the f o l -lowing considerations. The f i r s t , i s that i n the subsequent measurements i t w i l l be assumed that both pa r a l l a x and r e f r a c t i o n can be accurately accounted f o r . In f a c t , the automatic pointing measurement programs used with the U.B.C. 17. 208, millimeter wavelength radio telescope routinely calculate these corrections using the expressions derived in Appendix A for parallax and refraction. That i s , the measured quantities are: At = At - [TT + p(cos t cos 6 cos L + sin 6 sin L)-. 1 ] s i n t cos L sec 5 (28) and A6c = AS - [IT + p (cos t cos' 5 cos L + sin 5 sin L) x (cos t sin 5 cos L - cos 5 sin L) (29) = AS - TT(COS t sin S cos L - cos 5 sin L) + p (cos t tan 8 - tan L.\ cos t + tan S tan L J where At £ and AS£ represent the encoder minus true source hour angle and de-clination differences corrected for parallax and refraction. Note that ex-cept for solar system objects, the parallax term w i l l vanish; in particular, TT -> 0 for stellar work. The second consideration is that, although the various misalign-ment parameters may in principle be determined using solely radio measure-ments, the sparcity of strong sources at millimeter wavelengths makes i t useful to supplement radio measurements with optical measurements. For this purpose, an optical telescope is r i g i d l y mounted on the main reflector of the radio telescope. It w i l l be subject to the same polar axis, declination axis and hour angle encoder errors as the radio telescope, but w i l l differ by the parameter, a, used to describe the declination encoder bias, and the parameter, 8, used to describe the orientation of the optical beam with respect to a plane perpendicular.to the declination axes of the radio telescope 18. 209. (In the following discussion, the optical parameters w i l l always be written <XQ and g^, while the radio parameters w i l l appear as a_, and 8 i i f a distinction i s to be made.) A fi n a l point to be noted i s that provided the optical telescope i s r i g i d l y mounted, the sag term w i l l vanish in equations used to describe optical measurements. With these points taken into account, Equations (28) and (29) appear in the following forms, For Radio Measurements: At c = a cos L sin t sec 6 - 8 sec 6 + (ip sin t + n cos t + <f>)tan 5 -A6 c = a(cos t sin 6 cos L - cos 6 sin L) + ip cos t - n. sin t + a_. (30) For Optical Measurements: At = -g Q sec 6 + (ip sin t + n cos t + <j>)tan 5 - 9 (31) A6 c = i(» cos t - n • sin t + When analyzing empirical pointing curves, these equations need to be rearranged, but instead of working with two sets of equations, we w i l l drop the subscripts, and remember that i f optical measurements are involved, a = 0 , a a^^ and 8 -> 8 n, while in the radio case a' •> a and 8 ^ 8 . With this understanding, u r r we write: At = a cos L sin t sec 6 - 6 sec 6 + sin t + n cos t + (j))tan 6 - 9 (32) • c and 19. 210. A6 = a (cos t sin <5 cos L - cos 6 sin L) + ty cos t - TI sin t + a (33) c Now, as w i l l be seen in Section C, measurements w i l l either be made at a fixed declination or a fixed hour angle; this corresponds to,-.-tracking and transit experiments respectively. For the purpose of analyzing the empirical pointing curves, i t w i l l be useful to separate the independent variable from Equations (32) and (33) for these two cases. For Tracking Experiments, with the hour angle t.as the independent variable and the declination 6 held constant, we write: At £(t) = (-G-8 sec 6 + (j> tan 5)+(a cos L sec <5 + ty tan 6)sin t + (n tan 5)cos t (34) A6 c(t) = (a-a sin L cos <5)+(-n)sin t + (cr cos L sin 6 + ty) cos t (35) For Transit Experiments, with the declination 5 as the independent variable and the hour angle t held constant, we write: A tc ( S ) =•' (-0)+(a cos L sin. t-6)sec 6 + (ty sin t + n cos t + <\>)tan. <S (36) A6c(5) = (a+ty cos t - n sin t) + (a cos L cos t)sin 6 + (-a sin L)cos 6 (37) It w i l l be the subject of the following section to show how these equations, together with various measurement techniques, can be used to determine the various misalignment parameters. 20. 211. 5. COMPARISON WITH OTHER RESULTS. The calculations described in this report were performed because, to the author's knowledge, no published accounts had appeared in the active literature. Subsequently i t was discovered that Drake at Harvard (5) and Davis and Cogdell at Texas (4) had performed variations on these calculations, but neither was published. Since the techniques and nomenclature used here had become sufficiently ingrained to make adopting either of the other results unreasonable, and since the present calculations were tailored for the U.B.C. millimeter wavelength radio telescope (without affecting their generality), i t was decided to present a complete derivation and analysis in this report. As an aid to those who may be familiar with either the Harvard or Texas results, TABLE 1 i s included to establish nomenclature and make comparisons where they exist. In addition, i t w i l l be useful to point out differences between our calculations and those of the Harvard and Texas groups. (a) Harvard Calculation: This calculation was made almost two decades ago in conjunction with the building of the 60 foot Agassiz telescope which was designed to operate near 21 centimeters. Because i t was performed using spherical trigonmetry, the results are not as general as those presented here, although the present results, on expansion to f i r s t order in the misalignment parameters, can be shown to be the same. The major d i f f i c u l t y with these results, however, is the fact that the subsequent analysis was for a 30 arcminute beam at a frequency where there are many strong sources and this i s completely inadequate in the present circumstances. •21. (b) Texas C a l c u l a t i o n : T h i s c a l c u l a t i o n was p e r f o r m e d f o r a r a d i o t e l e -s c o p e v e r y s i m i l a r t o t h e one a t U . B . C . and i n f a c t , u s e d t h e same t e c h n i q u e o f m a t r i x r o t a t i o n s t o d e t e r m i n e t h e p o i n t i n g f u n c t i o n s . As a r e s u l t , t h e y a r e a l m o s t d i r e c t l y a p p l i c a b l e . Two m i n o r p o i n t s m i g h t be made. The f i r s t i s t h a t i n t h e p r e s e n t c a l c u l a t i o n s , t h e p a r a m e t e r s ty. and ri ( used t o d e s c r i b e t h e p o l a r a x i s m i s a l i g n m e n t ) a r e d i r e c t l y r e l a t e d t o c o r r e c t i o n s w h i c h must be a p p l i e d t o t h e p o l a r a x i s . T h i s i s n ' t t h e c a s e f o r t h e c o r r e s p o n d i n g T e x a s p a r a m e t e r s a l t h o u g h t h e t r a n s f o r m a t i o n i s a s i m p l e o n e . The s e c o n d p o i n t i s t h a t when u s e d i n t h e f o r m o f E q u a t i o n s (14) and ( 1 5 ) , t h e p o i n t i n g c u r v e s d e r i v e d h e r e do i n f a c t t a k e i n t o a c c o u n t many o f t h e s e c o n d o r d e r e f f e c t s due t o p o l a r a x i s m i s a l i g n -m e n t . T h e s e w i l l be t h e mos t i m p o r t a n t s e c o n d o r d e r e f f e c t s and a r e needed a t h i g h d e c l i n a t i o n s when b e t t e r t h a n a r c m i n u t e a c c u r a c y i s i . - -r e q u i r e d . The p r e s e n t c a l c u l a t i o n i g n o r e d h i g h e r t h a n f i r s t o r d e r . t e rms o n l y a s l o n g a s t h e y w e r e needed t o o b t a i n e x p l i c i t a n a l y t i c e x p r e s s i o n s f o r A t and A<5. The a p p r o x i m a t i o n s f o l l o w i n g E q u a t i o n s (14) and (15) w e r e n o t a l l n e c e s s a r y , b u t d i d r e s u l t i n some s i m p l i f i c a t i o n . F o r t h e d e t e r m i n a t i o n o f t h e m i s a l i g n m e n t p a r a m e t e r s , t h i s d e g r e e o f a p p r o x i m a t i o n i s j u s t i f i e d s i n c e t h e h o u r a n g l e s and d e c l i n a t i o n s o v e r w h i c h measuremen ts a r e . made c a n be c o n t r o l l e d . D u r i n g p r a c t i c a l o b s e r v a t i o n s , measuremen ts may be needed a t l a r g e h o u r a n g l e s o r . d e c l i n a t i o n s i n w h i c h c a s e E q u a t i o n s (14) and (15) w i l l p r o v i d e p a r t i a l s e c o n d o r d e r a c c u r a c y . I t d o e s n ' t seem p o s s i b l e t h a t E q u a t i o n (3) c a n be s o l v e d t o any h i g h e r o r d e r i n t h e m i s a l i g n m e n t p a r a m e t e r s w i t h o u t 22. doing so numerically. As already mentioned, this would be too time consuming to be of any practical use during observations. Both these comments pertained to the derivation of pointing functions alone. It w i l l turn out that several novel approaches have been introduced into our analysis as well. 23. 214. TABLE 1. TABLE OF APPROXIMATE CORRESPONDENCES BETWEEN UBC SYMBOLS AND THOSE USED IN THE HARVARD AND TEXAS CALCULATIONS UBC PARAMETER UBC SYMBOL HARVARD EQUIVALENT TEXAS EQUIVALENT Source hour angle t t t Source declination S 6 6 Encoder hour angle T t^ P Encoder declination D 6 D Polar axis offsets ty AA = - n sec L <j> = -tan 1 ( n / i J > ) Acj) = ty e = (ty2+r\2Y2 Declination axis offset <J> C = <j> r = -<J> Beam offset (Radio) 3 B = 8 L_^ = 8 •. r r JVL r (Optical) 8 0 L. = 8 Q Hour angle encoder bias 8 A-AA sin L = 8 b = -8 Declination encoder bias (Radio) a_, D = - a r K R f= a r (Optical) aQ . - K Q = a Q Refraction constant p n ^  1-p R(E) ='-p tan Z Parallax constant TT P = - T T Z = TT sin Z Sag constant a E(t ,<5) ,F(t ,<5) S Zenith distance or ele- Z — E vation Telescope latitude L L — Angle NCP-SRC-ZENITH oo - V = -u> • Refraction + Parallax + x - v = Z+S(E)-R(E) Sag X a) R(E) = (l+r)RQ(E), where R Q ( E ) is the calculated optical refraction b) The term -AA sin L occurs since this calculation measure hour angle with respect to a great c i r c l e through the zenith and we measure i t with respect to a great c i r c l e through the local meridian at the equator. c) S(E) = S cos (E) = a sin (Z) , Z = TT/2 - E 24. 215. C. DETERMINATION OF THE MISALIGNMENT PARAMETERS In the previous section we derived theoretical expressions to describe the effects of various mechanical defects on the pointing of an equatorially mounted telescope, this calculation also included the ef-fects of parallax and refraction. We must now describe techniques which w i l l allow us to determine what these defects are. As already suggested, this w i l l involve the use of tracking and transit experiments, but in addition a third category of experiment w i l l be employed, namely slewing experiments. Each of these three types of experiments w i l l allow certain of the seven misalignment parameters — a ,3 ,<j> ,9 ,ty ,r\ and a — to be deter-mined, with some of the parameters being found in several ways. 1. SLEWING EXPERIMENTS. To the author's knowledge these experiments have not been described elsewhere, although they have at least three distinct advantages over the tracking and transit experiments: f i r s t , once the i n i t i a l ground work has been done, a complete measurement can be made in approximately 10 minutes compared to approximately 6 hours for tracking and transit measurements; second, to f i r s t order the tech-nique is independent of the encoder readout accuracy; and third, the measured parameters are uniquely determined. The main disadvantage is that only the polar axis parameters, ty and n, or the declination axis parameters <j) and 9, can be determined. The actual manner in which a slewing experiment is performed is quite flexible, but the basic idea is the following: suppose the polar axis misalignment parameters are to be measured. One then r i g i d l y attaches an optical telescope (with a camera attached) to the main reflector of a radio telescope and aims the latter so that the North Celestial Pole (NCP) 25. 216. is within the f i e l d of view of the camera. If an exposure is begun, star tracks w i l l be exposed on the film which, provided the exposure is s u f f i c -iently long, w i l l define the position of the refracted NCP. One then quickly slews the radio telescope through an hour angle roughly equal to the previous exposure time and halts, so that a new set of tracks is traced. The beginning of these tracks and the end of the previous ones can then be used to define the position of the telescope pole since during slewing the camera is rotated about the telescope pole. In general at least a half dozen sets of star tracks w i l l be seen on developing the film. If the position of at least one of these stars is identified and the time at which the slewing was begun recorded, then an hour angle scale is easily established. Since the declination of the known star fixes an elevation scale, the position of the telescope pole is determined, and is easily related to the misalignment parameters ty and n as shown in FIGURE 5. Note that i t is being assumed here that the telescope's latitude is such that differential refraction over the camera's f i e l d of view is negligible otherwise the star tracks w i l l not be circular. WEST NCP / / . • / / / STAR TRACK REFRACTED NCP TV .TELESCOPE POLE MERIDIAN FIGURE 5 26. 217. The length of time required to execute the above measurement is restricted by the length of a star track which i s required to define the center of a c i r c l e accurately.^ Clearly the entire star track isn't needed to define the position of the refracted NCP; in fact, only 3 points on i t are needed. Therefore, to speed up the measurement we halt the tele-scope only long enough to define a point and then slew onto another posi-tion and halt, and so on un t i l a semicircle is defined. Each set of points described by 3 or more stars w i l l define a position for the refracted NCP, which, because the telescope is being rotated, w i l l appear on the exposed film to move about the telescope pole. Although this method i s much faster than the long exposure method, the analysis can be very tedious unless a computer is used. This in fact has been done, and is described more completely in Appendix E. In principle, the slewing technique-can also be used to determine the declination axis misalignment parameters <j> and 6. In this case, an optical telescope and camera are mounted parallel to the radio telescope's declination axis. Then, with the radio telescope tracking, measurements It is a legitimate question to ask what sort of projection effects the non-parallelism of the NCP, the telescope pole and the optical axis w i l l have on the resulting star tracks. If we let y be the angle between the telescope pole and the NCP, and 0 the angle between the telescope pole and the optical axis, then i t i s easy to show that the eccentricity of the projected star tracks when slewing the radio telescope i s : e = R J 2 tan y ) 2 1 h I \tan (0+x)-tan (0-y) / J which is extremely small even when unreasonable values are used for y and 0. In other words i t i s safe to assume that the star tracks are circular and that the projection effects are unimportant when making the measurements described here. 27. 218. are made as for the polar axis. These measurements however require a better knowledge of the vis i b l e sky, but unlike the polar axis measure-ments are li k e l y to only be made once since declination axis misalign-ments are d i f f i c u l t to correct. It i s indeed fortunate that the most c r i t i c a l of a l l the misalignment parameters, namely those describing the polar axis misalignment, are the easiest to measure and the easiest to correct! More w i l l be said about these corrections in the following section. It should be pointed out that since these slewing experiments involve s t r i c t l y optical techniques, i t i s impossible for them to be used to define the misalignment of the radio beam — at some stage a radio measurement must be made. The two remaining types of experiments can involve either radio or optical techniques and not a l l the measure-ments described are necessary to uniquely determine the misalignment parameters. The methods one uses are very much a matter of taste or con-venience, but the slewing technique just described Is certainly one of the quickest and cleanest methods we know of for determining the polar axis misalignment. 2. TRACKING EXPERIMENTS. These experiments use the hour angle t as the independent variable and may be interpreted by using Equations (34) and (35) of Section B.4, namely: At c = (-9-8 sec 5 + <f> tan 6) + (0 cos L sec 6 + ty tan 6 ) s i n t + (ti tan 6) cos t (34) 28. 219. A6 c(t) = (a - a sin L cos 6) + (-n) sin t + (a cos L sin <5 + ip)cos t (35) When doing a tracking experiment one records as a function of hour angle the readout position of a source and then calculates the pointing curves by subtracting the apparent source position, that i s , the source position with parallax and refraction included. A linear least squares f i t to these curves using Equations (34) and (35) above then determines the misalignment parameters —almost. In fact only ty, n, a and a can be deter-mined from the six f i t coefficients since two of the coefficients are linearly dependent (the ones involving ri) and a third coefficient involves the three parameters <f>, 6 and 8, which can't be separated. It is also worth noting that i t doesn't matter whether an optical or radio measurement is made, since the coefficients involving sag can be uniquely determined anyway. The only difference i s that one givesty, n and while the other yields ty, n» a and a . The other parameters require some other type of measurement. Davis and Cogdell (4) have discussed methods for determining a, 6 -3 r t» 3 , a -a_ and an, as well as the radio refraction. Among these r u r r u u are included simultaneous radio and optical observations of the sun. For our purposes however they aren't essential so we won't pursue them fur-ther, but i t should be noted that we have assumed the radio refraction to be calculable — this point has been discussed at length in Appendix A. To determine <f>, 9 and 8 we shall use transit experiments. 3. TRANSIT EXPERIMENTS. These experiments, which f i x the hour angle and treat the declination as the independent variable, are the obvious comple-ment to tracking experiments, and may be interpreted by using Equations (36) 29. 220. and (37) of Section B.4, namely: . (36) At (6) = (-9) + (a cos L sin t - g)sec 6 + (ty sin t + n cos t + ty)tan 6 (37) A6c(6) - (a + ty cos t - r\ sin t)+(a cos L cos t)sin S + (-a sin L)cos 6 The empirical pointing curves for transit experiments are calcu-lated in a manner identical to those for tracking experiments, but clearly the paucity of strong continuum sources at millimeter wavelengths w i l l limit the usefulness of these technique in the radio regime. If visual observations are made using an optical telescope r i g i d l y mounted to the main reflector of the radio telescope and aligned so that i t s beam i s approximately parallel to the radio beam, then the parameters 9 and BQ can be found while and <j> can only be found i f ty and n are known from some other kind of measurement (e.g. slewing or tracking experiment). Assuming this to be the case, we must s t i l l determine 3 . At least three paths may be followed: i f a radio tracking experiment was performed, then g can be found from the offset term (-0 - g sec 5 + i> tan 6) in the r r At c(t) f i t , since 9 and <j> are now known; alternatively, the optical-radio solar tracking technique of Davis and Cogdell may be used to determine the difference $Q~$T and hence g^ ; or f i n a l l y , a radio transit experiment may be simulated. For example, i f solar radio pointing curves have been found for a number of declinations in the range ±23 , and i f care was taken to make the observations always at the same hour angles, the data for an ex-tended period may be rearranged to simulate a true radio transit experi-ment. This clearly i s a very on-going project, but in any event i t i s useful to determine the various parameters in as many ways as possible to 30. 221. make sure the results are consistent. The absolute minimum experimental configuration would consist of a radio tracking experiment and an optical transit experiment. 4. SUMMARY OF INSTRUMENTAL TECHNIQUES. In the above paragraphs we des-cribed the various experiments which can be performed in order to determine the parameters describing the misalignment of an equatorially mounted tele-scope. In the remainder of this section, we w i l l b r i e f l y describe the ac-tual instrumental techniques which were employed in conjunction with the U.B.C. millimeter wavelength radio telescope to measure these parameters. They may be broadly grouped into three categories, namely photographic techniques,radio techniques and video techniques. (a) Photographic Techniques. Photographic measurements were made in con-junction with slewing experiments described in Section C l above in order to determine the polar axis misalignment. The optical telescope used was a 1600 mm Questar reflector with,a 3%" aperture, to which was attached a 35 mm SLR camera body loaded with 400 ASA (Tri-X) film. In the i n i t i a l experiments, the method involving only a single slewing of the telescope was used. The film was developed and.fixed on sit e , and the negative then projected onto an approximately 14" x 22" sheet of white paper placed on a wall. Sketches were made of the exposed star tracks, which were then bisected to find the position of the telescope pole and the refracted NCP. After a refraction correction,values for ty and r\ were found which indicated an approximately one degree misalignment of the polar axis. Using the techniques described in the following section, this misalignment was 31. 222. reduced to <10'. Subsequently, the much more accurate multiple slewing technique was developed with which i t i s expected the polar axis mis-alignment w i l l be reduced to <1'. The development of this technique was i n essence the work of Alex Szabo, whom the author supervised on a directed studies course i n astronomy. A more complete description of this work appears i n Appendix E. I t should be noted that the l i m i t i n g factor i n determining the accuracy with which the polar axis can be aligned i s not one of mea-surement accuracy, but rather i t i s limited by the patience of the person making the misalignment corrections. This to some extent w i l l of course be a function of how quickly a new position for the telescope pole can be determined and hence a quick, automated technqiue i s required. (b) Radio Techniques. For most mm wavelength radio telescopes, and i n particular the U.B.C. telescope, the use of radio techniques i n determing the misalignment parameters i s r e s t r i c t e d to the sun and the moon. How-ever, as pointed out e a r l i e r , these measurements are essential i f the position of the radio beam i s to be determined and i n fact at least a radio tracking experiment must be performed. In the case of the U.B.C. telescope, t h i s process has been p a r t i a l l y automated and the d e t a i l s can be found elsewhere (6). B r i e f l y , the sun i s scanned i n declination and then hour angle, during which time an observer watches a t o t a l power chart recorder for the r i s i n g and f a l l i n g limbs. When these occur, a computer interrupt switch i s depressed, which causes the instantaneous . pointing corrections A t £ and A 6 c , and other relevant information, to be calculated and printed on a teletype console. Since these tracking 32. 223. measurements have been made for almost two years, sufficient data is in fact available to simulate transit experiments as well, and this has been done. The analysis of this data has followed several paths, the most re-cent of which are summarized in Appendix E. For completeness however, and to put the current methods of analysis into better perspective, we w i l l b r i e f l y summarize the various stages of analysis which were followed. I n i t i a l attempts to perform least squares f i t s using the theo-re t i c a l pointing functions suffered from at least two defects. F i r s t the empirical curves had "bumps" which the theoretical functions could not account for, and second, i f a f i t to the A$ c(t) empirical curve was used to determine ty and n, and then these parameters used as constants in the At c(t) f i t , i t was found that this f i t would not converge unless a term varying linearly with hour angle was added to the At^ theoretical function. Such a linear dependence on hour angle could result from a number of causes, including a faulty drive train gear arrangement or defects in the hour angle translator, an incorrect frequency for the tracking reference crystal, problems with the synchro electronics, i n -correctly calculated refraction corrections or telescope sag. By a num-ber of methods and arguments these were a l l excluded except telescope sag, so that the latter i s now included in the theoretical pointing functions. The origin of the bumps however s t i l l remains a mystery, but may be caused by a non-fixed telescope pole or a more complicated sag dependence than has been accounted for. At this time, a sag term was not included in the theoretical pointing functions. 33. 2 2 4 . I n any c a s e , s i n c e t h e r e a s o n f o r f i t t i n g t h e e m p i r i c a l p o i n t i n g c u r v e s i s n o t t o f i n d m i s a l i g n m e n t p a r a m e t e r s p e r s e , b u t r a t h e r t o f i n d p a r a m e t e r s w h i c h w i l l r e p r o d u c e t h e e m p i r i c a l c u r v e s ( s o t h a t t h e y c a n b e u s e d i n c a l c u l a t i n g r e a l - t i m e c o r r e c t i o n s t o t h e t e l e s c o p e p o i n t i n g w h i l e o b s e r v a t i o n s a r e b e i n g m a d e ) , i t was d e c i d e d t o d e v e l o p e a t e c h n i q u e w h i c h w o u l d a t l e a s t r e p r o d u c e t h e e m p i r i c a l p o i n t i n g c u r v e s w h i l e t h e o t h e r p r o b l e m was b e i n g w o r k e d o n . To t h i s e n d , t h e p o l y n o m i a l l e a s t s q u a r e s f i t t e c h n i q u e u s i n g o r t h o g o n a l p o l y n o m i a l s was d e v e l o p e d and i t r e p r o d u c e s t h e e m p i r i c a l c u r v e s v e r y w e l l . I n a d d i t i o n , u s i n g t h e e x p r e s s i o n s d e v e l o p e d i n A p p e n d i x B , i t i s a l s o p o s s i b l e t o i n t e r p r e t t h e p o l y n o m i a l c o e f f i c i e n t s i n te rms o f t h e m i s a l i g n m e n t p a r a m e t e r s ; h o w e v e r , as p o i n t e d o u t i n t h e a p p e n d i x , t h i s i n t e r p r e t a t i o n s h o u l d n o t b e t a k e n t oo l i t e r a l l y s i n c e a f t e r a l l i t i s d e r i v e d b y e x p a n d i n g t h e t h e o r e t i c a l p o i n t i n g f u n c t i o n s w h i c h t h e m s e l v e s w e r e f o u n d t o b e i n a d e q u a t e . O t h e r l i m i t a t i o n s o f t h i s t e c h n i q u e a r e d i s c u s s e d i n A p p e n d i x B . D e s p i t e t h e s e l i m i t a t i o n s — a l l o f w h i c h a r e r e l a t e d t o d e t e r m i n i n g m i s a l i g n m e n t p a r a m e t e r s — p o l y n o m i a l f i t s a r e a u s e f u l way o f p u t t i n g a n a l y t i c e x p r e s s i o n s i n t o a compu te r so t h a t r e a l - t i m e p o i n t i n g c o r r e c t i o n s c a n b e made. F u r t h e r d e t a i l s r e g a r d i n g e i t h e r f u n c t i o n a l o r p o l y n o m i a l l e a s t s q u a r e s f i t t i n g c a n b e f o u n d i n A p p e n d i c e s B , D and E . A p p e n d i x B d e s c r i b e s how t h e c o e f f i c i e n t s f o u n d i n e i t h e r a f u n c t i o n a l o r a p o l y -n o m i a l l e a s t s q u a r e s f i t c a n . b e i n t e r p r e t e d i n te rms o f t h e m i s a l i g n m e n t p a r a m e t e r s , A p p e n d i x E d i s c u s s e s t h e r e s u l t s w h i c h have b e e n o b t a i n e d t o d a t e , and i s e x p e c t e d t o be an o n - g o i n g s e c t i o n o f t h i s r e p o r t , w h i l e A p p e n d i x D d i s c u s s e s and l i s t s t h e compu te r p rog rams w h i c h h a v e b e e n 34. 225. used i n the analysis of the empirical pointing data. (c) Video Techniques. This technique i s the most re c e n t l y developed and has been used i n conjunction with both o p t i c a l tracking and o p t i c a l tran-s i t experiments, although i t would also be very u s e f u l i f simultaneous radio and o p t i c a l s o l a r observations were to be made, since i t could e a s i l y be c a r r i e d out by a s i n g l e person. For video measurements, a high s e n s i t i v i t y v i d i c o n tube, c o n s i s t i n g of a s i l i c o n diode array as the target m a t e r i a l , i s mounted behind the 3%" Questar telescope, discussed e a r l i e r , which i n turn i s r i g i d l y attached to the main r e f l e c t o r of the radio telescope. To avoid excessive torques on the o p t i c a l telescope, which would r e s u l t i n unwanted sag e f f e c t s , the v i d i c o n tube has been removed from i t s mainframe (which i s attached to the main r e f l e c t o r backing structure nearby) and i s connected to the l a t t e r by an u m b i l i c a l cable. The UHF video s i g n a l from the mainframe i s then transmitted on 75 ohm c o - a x i a l cable to a monitor i n the radio telescope c o n t r o l room. With t h i s arrangement i t i s possible to observe down to s i x t h magnitude st a r s . As a r e s u l t , a very v e r s a t i l e technique e x i s t s f o r determining a l l the misalignment parameters except those describing the radio beam of f s e t s a and 8^. T r a n s i t measurements using a stack program to dr i v e the telescope (6) can e a s i l y be performed i n an evening (instead of h a l f a year, i f solar radio techniques are used) and the d e c l i n a t i o n range i s not r e s t r i c t e d . Furthermore, once the r e l a t i v e radio and o p t i c a l beam positions are determined, t h i s method should make i t possible to monitor the telescope pointing by doing spot checks on nearby s t a r s . This could be done during night-time s p e c t r a l l i n e observations, f o r 35. 226. example, by choosing off source positions with a known relationship to an observable star. In addition, stars seen on the monitor at any point would provide a valuable check on the quality of the telescope tracking. The analyses of o p t i c a l l y measured pointing curves d i f f e r s from that used i n the radio case by the fact that sag for the o p t i c a l t e l e -scope should not be important. In addition, the beam parameters aQ and 8Q w i l l d i f f e r from the corresponding radio parameters a and 6^.. Other-wise, o p t i c a l tracking or t r a n s i t measurements are made and analyzed i n exactly the same manner as for the radio measurements discussed above. The only other point to note i s that since the radio measurements involve looking at sources which are extended with respect to the beam s i z e , four measurements are used to define the observed source position before the empirical pointing corrections are calculated by the automatic point-ing program. In the case of point sources ( i . e . s t e l l a r observations) only one measurement i s required, but since the automatic pointing pro-gram has been written to expect four measurements, the interrupt switch must be depressed four times before A t and AcS w i l l be calculated. • c c D. POINTING CORRECTIONS MADE FOR THE U.B.C. Xmm TELESCOPE 1. ALIGNMENT OF THE POLAR AXIS. Of a l l the mechanical defects found i n a p r a c t i c a l equatorially mounted radio telescope, the polar axis mis-alignment i s the easiest to permanently correct, which i s indeed fortunate, since i t so c r i t i c a l l y affects the entire alignment problem. The polar axis of the U.B.C. telescope i s mounted on three adjustable spacers, one of which i s shown i n FIGURE 6 i n cross-section. When the spacer i s f u l l y retracted, the dimension B between the polar axis turntable and the 36. 227, TURNTABLE A A T PEDESTAL FIGURE 6 } H 7. telescope pedestal is approximately 1-3/8". * The dimension A on the other hand i s what is adjusted in order to align the polar axis, and w i l l be the subject of the following discussion. The actual layout of the three spacers is shown schematically in FIGURE 7 below, as they would appear when looking from the North Celestial Pole downwards and away from the local meridian. Since the spacers l i e on a c i r c l e of NORTH EAST WEST FIGURE 7 7. This dimension i s important sinde i t limits the size of mechanical aids which can be used to relieve the compressive stress in the north-most of the three spacers when adjustments are to be made. This stress, apparently not connected with the balancing of the telescope, can be eliminated by inserting a large bolt(with a long nut) on either side of the spacer and then expanding them. 3 7 . 2 2 8 . r a d i u s R ( = 4 1 . 2 cm) and a r e a r r a n g e d a t t h e v e r t i c e s o f a n e q u i l a t e r a l t r i a n g l e — one o f w h i c h i s a imed n o r t h w a r d — i t i s e a s y t o show t h a t t h e e f f e c t i v e t u r n i n g arm when one o f t h e s p a c e r s i s a d j u s t e d i s (1 + s i n 30 )R = 1 .5 R. T h e r e f o r e , i f one o f t h e s p a c e r s i s a d j u s t e d a s m a l l amount £ , t h e p o l a r a x i s w i l l b e t i l t e d t h r o u g h a n a n g l e £ / l . 5 0 R a b o u t an a x i s j o i n i n g t h e r e m a i n i n g two s p a c e r s . I t i s now e a s y t o d e s c r i b e v a r i o u s a d j u s t m e n t s w h i c h w i l l c o r r e c t f o r t h e p o l a r a x i s m i s a l i g n -ments ip and n . ( R e c a l l t h a t t h e s e a r e d e f i n e d t o b e p o s i t i v e f o r c l o c k -w i s e r o t a t i o n s a b o u t an a x i s f a c i n g West and t h r o u g h t h e l o c a l m e r i d a n r e s p e c t i v e l y . ) I n p a r t i c u l a r , t h e m i s a l i g n m e n t ip may b e c o r r e c t e d b y an a d j u s t m e n t g = - 1 . 5 R ip, o f t h e n o r t h e r n s p a c e r , w h i l e t h e m i s a l i g n m e n t n may b e removed i f t h e e a s t e r n s p a c e r i s a d j u s t e d an amount ? E = 1 .5 R c o t 30 n, and t h e w e s t e r n s p a c e r , an amount "£L. = T h r e e comments s h o u l d b e made a b o u t t h e s e r e s u l t s : 1 . They a r e n o t u n i q u e , b u t a r e p r o b a b l y t h e mos t c o n v e n i e n t , a d -j u s t m e n t t o make . 2 . I f g > 0 , t h e s p a c e r mus t b e e x p a n d e d . 3 . When t h e a d j u s t m e n t s above a r e made w i t h t h e p r o p e r s i g n c o n v e n t i o n f o r Tp and n , t h e y c a u s e t h e m i s a l i g n m e n t s t o b e r e m o v e d . S u b s t i t u t i n g n u m e r i c a l v a l u e s , we t h e n f i n d , f o r ip and n m e a s u r e d i n d e g r e e s , t h a t : ? N = - 1 0 . 7 9 ip mm = 0 . 4 2 4 8 ip i n c h e s £ = 6 . 2 2 7 n mm = 0 . 2 4 5 2 n i n c h e s ? W = From t h i s i t i s o b v i o u s t h a t t h e a d j u s t m e n t s made w i l l b e v e r y s m a l l . F o r e x a m p l e , i f n ,=. - 1 a r c m i n = - 0 . 0 1 6 7 d e g r e e s t h e n £ ^ = - £ g = 0 . 1 0 4 mm = 0 . 0 0 4 1 i n c h e s . A l t h o u g h v e r n i e r c a l i p e r s a r e u s e d w h i c h c a n m e a s u r e changes 38. 229. to 0.001 inches, the circumstances in which they are used necessarily imply that adjustments to this accuracy w i l l become a t r i a l and error process. This was the basis for our earlier remark that the ultimate accuracy achieved would depend both on the patience of the person making the adjustments and on how quickly a new pole position can be determined after an adjustment has been made. 2. POINTING CORRECTIONS DURING OBSERVATIONS. Besides the polar axis misalignment just discussed, i t is possible to correct the synchro mis-alignments <f> and a as well by introducing constant offsets into the di g i t a l readouts. The declination axis misalignment 0 and the beam misalignment 6 , however, in addition to sag CT and any polar axis residual misalignments must s t i l l be removed. It w i l l therefore be convenient to remove a l l the misalignments in one step — as a non-constant offset — and be done with i t . The manner in which this i s carried through w i l l depend on whether the telescope is being used in a manual control or computer control mode. Before discussing these two modes, we w i l l b r i e f l y describe the essentials of the U.B.C. telescope drive control circuitry, which is drawn in a very simplified and schematic manner in FIGURE 8. Computer Displays Displays FIGURE 8 39. 230. In the manual mode of operation, the operator controls function switches on two drive control units which cause the telescope to move as required. Synchro transmitters on the declination and polar axes relay the telescope position to analog receivers which are coupled to d i g i t a l readout units. These display a position (T,D) to which the offsets At_ and A6Q have already been added; that i s , the effect of a positive offset is to increase the displayed co-ordinate. In the computer mode of operation, the position (T,D) is also relayed to a d i g i t a l comparator, which compares this position with that requested by a computer, and then produces appropriate error voltages for the two drive control units. Note that the right ascension is never displayed, and must either be calculated manually or accessed through the computer. The reason for this is discussed elsewhere,(7). a) Manual Control Mode. In this mode of operation, in order to f a c i l i t a t e right ascension checks since the telescope tracking is not perfect, i t i s desirable to have the true source hour angle and declination displayed on the d i g i t a l readouts. This can be done as follows. We f i r s t -note that in general the displayed telescope position (T,D) w i l l differ from the true telescope position (t,6) because of the effects of parallax,refraction,sag and the various mechanical misalignments. Therefore, to have the readouts display the true source position, we require that: t = T + At 0 and <5 = D + A60 where Atg and A6grepresent the di g i t a l offsets. This result follows since the effect of a positive offset is to increase the displayed position. However, by equations (24) and (25) we know that: 40. 231. At = T - t and A6 = D - 6. We may therefore conclude that At 0 = -At and A6Q = -A6. This means that when observing in the manual control mode,corrections corresponding to the negative of the pointing functions must be added as d i g i t a l offsets. It i s worth briefly summarizing which values should be used for At and AS, since sign conventions have changed over the past few years. Early pointing curves defined quantities AHA = a(observed) - a(true) = Q HA(true) - HA(observed) and ADEC = 6(true) - 6(observed). In some cases refraction would be removed from these curves and sometimes i t wouldn't, but the main point i s that these definitions are no longer consistent with the current definitions for At and A6 since these are now defined as the difference between the observed and true hour angles and declinations respectively. Therefore care should be taken when analyzing data obtained before December 1975. In the case of pointing measurements made after this time, no d i f f i c u l t i e s should arise since pointing measurements are now made using the automated program,which measures At and A6 , the observed minus true co-ordinates, corrected c c for parallax and refraction. These are related to the quantities At and A<5 needed for the manual offsets described above by the expressions: At = At + (TT + p sec Z) sin Z sin to sec <5 a is the right ascension and HA is the hour angle. 41. 232. and AS = AS' + (TT + p sec Z) sin Z cos u) where the f i n a l terms in these two equations are defined in equations (28) and (29) and earlier, and take into account the effects of refraction and parallax, which have been removed from the empirical curves At and AS . c c Since parallax w i l l be negligible for a l l but solar or lunar work and these sources are generally only observed during pointing measurements, we w i l l exclude parallax from the following discussion. (If i t i s needed i t can be accommodated in the computer control mode discussed below.) Refraction on the other hand must be accounted for and can be calculated at any posi-tion using non-real time software described by Mahoney (6). This soft-ware calculates quantities DHA and DDEC which must be added to the true source hour angle, t, and declination, S, in order to get the refracted position. In terms of these quantities we then have: -At = -At + DHA c and -AS « -AS + DDEC c as the appropriate pointing corrections to make when using the telescope in the manual control mode. The values used for At £ and AS £ may be either from the empirical curves themselves or from analytic curves ca l -culated using either the known misalignment parameters or polynomial coefficients (6). Obviously this i s a f a i r l y involved, i f not confusing way of proceeding. 42. 233. (b) Computer Control Mode: In this mode of operation a l l the thinking is taken out of observing, but because the offsets are introduced by the computer — the offsets on the d i g i t a l readouts should be set to zero — the hour angle and declination displayed by the d i g i t a l readouts w i l l not be the true source position as was the case i n the manual mode. The method for operating under computer control has been described by Mahoney (6) and w i l l be summarized only b r i e f l y here. The effects of sag and the other mechanical defects are removed by appropriately en- ? abling a pointing flag. The program then requests either misalignment parameters or polynomial coefficients and automatically removes the appropriate pointing function each time a drive command is given. If refraction i s to be removed as well, then the refraction flag must be set; parallax, on the other hand, can only be removed for sources being sought using the variable position source drive commands, which require an ephemeris to be entered by the operator. Since offsets are not entered directly into the d i g i t a l read-outs in the computer control mode, the readouts w i l l not display the true source position. As a result, some confidence is required in the telescope tracking capability before this mode can be used. If however the true source position is required, i t can be obtained either by re-questing the telescope status, or by using a clock interrupt; the latter of course assumes that a pointing measurement i s not being made at the time. 43. 234. E. CONCLUDING REMARKS In the foregoing pages and in the appendices we have considered a number of aspects involved in accurately aligning an equatorially mounted radio telescope or involved in accounting for misalignments which can't be physically corrected. On the basis of the theoretical pointing func-tions derived in Section B, we were able to describe in Section C a num-ber of experiments which in principle could be performed in order to determine what the various misalignments were. It was seen that many of these experiments were redundant in determining what the misalignment parameters are, and that the optimum method of proceeding would be approxi-mately as follows: 1. Determine the polar axis misalignment using the slewing experiment of Section C l combined with the photographic technique of Section C.4.a. A program for reducing these results can be found in Appendix D and the method for removing the polar axis misalignments was described in Section D.l. 2. With the polar axis aligned as well as possible,a radio tracking ex-periment using the sun is performed as described in Sections C.2 and C.4.b. and again analyzed using the programs given in Appendix D. This w i l l result i n values for a_, and 0 , as well as ty and n, which hopefully by this time are small. A value i s also determined for the expression (-0 - 6^ sec 6 + <j> tan 6) which w i l l yield a number for 8 once i> and 0 are determined. r 3. To determine c|> and 0, a stellar transit experiment i s performed using the video technique of Section C.4.c. On analysis using the programs in Appendix D, values for a, 0 and 8 n are found, and since 44. 235. ty and n are known from either a slewing or tracking experiment, values can be found for <j) and a as well. This the leads to a o value for so that a l l the misalignment parameters — , a^, 8_,, 8 Q , ty, n, <j>, 6 and o — are determined. It should be pointed out that although we have assumed impli-c i t l y in the foregoing discussion that the optical beam w i l l not sag i f the optical telescope i s properly mounted, experience indicates that i t does. This leads to no new d i f f i c u l t i e s however since the foregoing discussion can easily be generalized to distinguish between radio and optical sag; no additional measurements are required. 4. Other experiments may of course be performed to check the consistency of these results. In particular, i f data is available at a sufficient number of declinations, tracking experiments may be used to simulate transit experiments, or conversely, i f data is available at a sufficient number of hour angles, transit experiments may be used to simulate tracking experiments. In this respect, i t is also worth pointing out that step 3 above need not be performed e x p l i c i t l y . If tracking measurements have been made at a number of declinations, these results may be fit t e d simultaneously to determine a l l the misalignment parameters. This in fact gives a better overall result, and the method has been described in Appendix D. With the values for the misalignment parameters determined, the methods of Section D.2 may then be used to remove the effects of these misalignments when observations are being made. This brings us the complete circ u i t . 45. 236. Before concluding, however, a few words of caution should be mentioned. The f i r s t has to do with the polar axis. From the analysis performed to date, i t appears that e i t h e r the polar axis i s non-fixed or that the e f f e c t s of sag are more complicated that the simple theory presented. I t i s a simple matter to make a l l the misalignment parameters a function of hour angle and d e c l i n a t i o n , and even time, but th i s would unnecessarily complicate the theory and make the analysis v i r t u a l l y impossible. The other extreme, however, of pointing the telescope using only empirical curves i s equally untenable. We must therefore s t r i k e the proper balance between these two extremes — which may take some time and e f f o r t . The second point which needs mentioning and which we have ignored so f a r i s that of i n t r i n s i c l i m i t a t i o n s placed on the ultimate pointing accuracy by the equipment i t s e l f . Ostensibly, these factors include blacklash (± .05°) and d i g i t a l readout r e p e a t a b i l i t y (± .03°). Although these are factory performance f i g u r e s , i n a c t u a l p r a c t i c e i t i s found that the telescope performs w e l l within these s p e c i f i c a t i o n s . These figures however must be remembered when i n t e r p r e t i n g the r e s u l t s of a pointing measurement or an actu a l observation. I t i s conceivable that the performance of the d i g i t a l readouts could be improved by i n -creasing the r e s o l u t i o n to .001°, but t h i s w i l l take time. The e f f e c t of backlash can to some extent be a l l e v i a t e d by approaching sources i n a systematic manner, for example, from lower d e c l i n a t i o n s and greater hour angles, and t h i s i s recommended. Many of these d i f f i c u l t i e s and also those r e s t r i c t i n g radio pointing measurements w i l l be greatly improved with better receiver s e n s i t i v i t y . 4 6 . 237 , APPENDIX A ; D e r i v a t i o n o f R e f r a c t i o n , P a r a l l a x and Sag E x p r e s s i o n s . 1 . REFRACTION. F o r t h e p u r p o s e o f d e r i v i n g an e x p r e s s i o n f o r r e f r a c t i o n , c o n s i d e r FIGURE A . l , w h i c h i l l u s t r a t e s a p l a n e wave e n t e r i n g t h e a t m o s p h e r e a t an a n g l e Z w i t h r e s p e c t t o t h e l o c a l z e n i t h . A b o v e t h e a t m o s p h e r e t h e r e -f r a c t i v e i n d e x i s n , w h i l e b e l o w , i t o i s n . Now by u s i n g S n e l l ' s Law on a p a r a l l e l a t m o s p h e r e we h a v e : F IGURE A . l r\ s i n Z = n s i n Z o r = n ( s i n Z + X_, c o s Z) where we have l e t = Z + X__. T h i s a p p r o x i m a t i o n r e s u l t s i n a <1% e r r o r f o r ^ 2 d e g r e e s , w h i c h w i l l c e r t a i n l y be s a t i s f i e d . I n a d d i t i o n , i t s h o u l d be n o t e d t h a t t h e p l a n e p a r a l l e l a p p r o x i m a t i o n i s g e n e r a l l y v a l i d f o r Z 5 70 d e g r e e s . We t h e r e f o r e h a v e t h a t : A . l . t a n Z = p t a n Z Now, t h e r e f r a c t i v e i n d e x n o f t h e a t m o s p h e r e i s g i v e n b y ( s e e b e l o w ) n a 1 + ( 7 7 . 6 P 3 . 7 3 x 1 0 5 e ) 1 0 "6 where P = i s t h e p a r t i a l p r e s s u r e o f d r y a i r i n m i l l i b a r s 3. T =: i s t h e t e m p e r a t u r e i n K e l v i n s e = i s t h e p a r t i a l p r e s s u r e o f w a t e r v a p o u r i n m i l l i b a r s 47. Using P = 1022 millibars a T = 289.2 K and e = 5.7 millibars and letting n = 1, we get: A.2 n - n p = = -2.98 x 10 4 radians - 1.0 arcmin. The expression used above for the index of refraction warrents some justi f i c a t i o n . It i s based on calculations of Smith and Weintraub(l) and has been found by Shimabukuro(2) to be ac-curate to 15 arcseconds at 3.3 mm for zenith distances <70°. Com-paring our result for p with the corresponding optical value p Q c a l -culated for the same atmospheric conditions (using an accurately known expression given by Blanco and McCuskey(3)) we find that: p/p = 1.04 o That i s , the millimeter refraction i s larger by 4%. Observationally this difference can be confirmed by attaching an optical telescope to the radio telescope and then simultaneously determining the radio and optical positions of the sun. Differences other than radio sag w i l l reflect refraction differences. Shimabukuro in fact has done this and confirmed our expression for the refractive index. Davis and Cogdell (4) however find the 4.3 mm refraction to be 21% + 100% less than the optical refraction, but their data has considerable 48. 239. scatter as indicated by the error. Because of these uncertainities, we w i l l assume Equation A.2 to satisfy our needs. If an actual measurement of p is required, the polar and declination sun scan techniques described by Doves and Cogdell may be used. These techniques also lead to values for cr, (a - a ) and (g - g n ), but are not essential for determining r o r 0 these parameters. 2. PARALLAX. To derive an express which illustrates a great c i r c l e through the zenith oriented towards a source. Z is the source's geo-centric distance while Z i s i t s P geodetic zenith distance. If we let Z = Z + X i t i s clear that P P A.3 X = (—-) sin Z = TT sin Z p Rs where we have defined the parallax constant TT by A. 4 TT = R /Rs, R being the earth's radius and Rs the source distance. for parallax, consider FIGURE A.2 Figure A.2 4 9 . 240. Zenith To Source 3. SAG. To a r r i v e at an expression for sag, consider the r e f l e c t o r i l l u s -trated i n FIGURE A.3, with a f o c a l length -f. Because of the symmetry, the system c o n s i s t i n g of the sub-r e f l e c t o r and spars w i l l have a center of g r a v i t y located on the l i n e from the center of the main r e f l e c t o r to the source, at a distance \i-f from the main r e f l e c t o r , where u < 1. The torque x, exerted on the subreflector-spar system i s then Subreflector Spar Main R e f l e c t o r Figure A.3 x = \i-f F s i n Z Assuming the system behaves as a simple e l a s t i c body, and the center of gr a v i t y moves through an angle y » then s T' = -k X , i s the restoring torque, k being the e l a s t i c t o r s i o n constant. In equilibrium, T + T' = 0 , therefore: A. 5 x s i n Z = a s i n Z s k where A. 6 a = \ij F/k 50. 241. defines the sag constant. This picture must be expected to be good only as an approximation since obviously the spar orientation w i l l affect the distribution of forces and therefore the amount of sag to be expected in a given direction, regardless of what Z i s . Note that we normally expect a to be > 0. This means the beam w i l l be at a smaller Z than i f sag weren't present, requiring an increased effective Z to align on the source. 4. ACCUMULATED TERMS. If we collect these terms for zenith distance variation, we find x» the sum total of parallax, sag and refraction terms, that i s , X X p + x s + x r or A.7 X (ir + a + p sec Z) sin Z where TT R /R s a 4 F/k and P (n n-n)/n . 51. 242. Appendix B: Derivation of Coefficients for Polynomial and Functional Least Squares F i t s to the Pointing Functions. When analyzing the results of a tracking or transit experiment; i t is necessary to know how to interpret the least squares f i t coeffi-cients of an empirical pointing curve in terms of the misalignment parameters. By a functional f i t we mean that the theoretical pointing functions are f i t to the empirical pointing curves; therefore we have only to isolate the coefficients of terms involving the independent variable. This has already been done in Section B.4 since Equations (34) and (35) describing the hour angle and declination pointing func-tions for a tracking experiment (corrected the effects of parallax and refraction) may be written: At c(t) = HQ + sin t + H 2 cos t (B.l) and A6 c(t) = D Q + D 1 sin t + T>2 cos t (B.2) where the coefficients HQ, H ^ , I^, DQ, D^  and are independent of t but may depend on 6,.which is constant for a given tracking experiment. Similarly, Equations (36) and (37) for a transit experiment may be written: At (6) = H ' + H , ' sec <5 + H ' tan 6 c 0 1 2 and A6 (5) = D ' + D' sin 6 + D ' cos 6 c 0 1 2 (B.3) (B.4) 5 2 . 2 4 3 . w h e r e , i n t h i s c a s e , H Q ' » H ^ , I ^ 1 , D Q " , D ^ ' and a r e i n d e p e n d e n t o f 6 , b u t may depend on t . By i n s p e c t i o n w i t h E q u a t i o n s (34) t o (37) we may w r i t e down what t h e s e c o e f f i c i e n t s a r e . T h i s has b e e n done i n TABLE B . l . U n d e r some c i r c u m s t a n c e s ( d i s c u s s e d i n t h e t e x t ) , i t may b e u s e f u l t o p e r f o r m a p o l y n o m i a l r a t h e r t h a n a f u n c t i o n a l l e a s t s q u a r e s f i t t o t h e e m p i r i c a l p o i n t i n g c u r v e s . To a r r i v e a t t h e c o e f f i c i e n t s o f a p o l y n o m i a l f i t i n te rms o f t h e m i s a l i g n m e n t p a r a m e t e r s , we s u b s t i t u t e t h e e x p a n s i o n s : x I < 00 x | < 0 0 x | < 2 x | < -i n t o E q u a t i o n s ( B . l ) t o ( B . 4 ) a b o v e . On c o l l e c t i n g te rms f o r e q u a l powers o f t h e i n d e p e n d e n t v a r i a b l e , we o b t a i n t h e r e s u l t s summar i zed i n TABLE B . 2 f o r t h e f i r s t s i x te rms i n t h e e x p a n s i o n . S e v e r a l p o i n t s o f c a u t i o n a r e w o r t h n o t i n g when p o l y n o m i a l l e a s t s q u a r e s f i t s a r e t o b e made. The f i r s t i s t h a t p o l y n o m i a l f i t s i n t r o d u c e a t r u n c a t i o n e r r o r i n t o t h e u l t i m a t e v a l u e s d e r i v e d f o r t h e m i s a l i g n m e n t p a r a m e t e r s . A l t h o u g h t h i s e r r o r c a n be r e d u c e d b y i n -c r e a s i n g t h e o r d e r o f t h e f i t , t h i s l e a d s t o a s e c o n d d i f f i c u l t y — n a m e l y , t h a t p o l y n o m i a l f i t s o f o r d e r n > 4 become v e r y good a t f o l l o w -i n g s m a l l v a r i a t i o n s i n t h e r a t h e r n o i s y e m p i r i c a l c u r v e s t h e y a r e and 3 s 7 x ° . x J x , s m x = x - 3 T + 5 T - y f - + - X 2 _ X 4 X 6 _ c o s x = ! _ _ + _ _ _ + . x 3 , 2 x 5 . 1 7 x 7 , t a n x = x + — + — + — + . , x 2 5 x 4 6 1 x 6 , s e c x = 1 + — + 24- + 7 2 0 - + 53. 244. TABLE B.l Coefficients for Functional Least Squares F i t A. Tracking experiment At (t) = H-+H. sin t + H_ cos t C U i -. A6 ( c t) = D o + D i s i n t + D2 c o s t H o H l H2 - 0 - 6 sec 6 + <j) tan 6 cr cos L sec 6 + ip tan 6 n tan 6 D o D l D2 i i a-cr sin L cos 6 -n a cos L sin 6 + ty B. Transit experiment At (6) c - v +v sec 6 + H2* tan 6 A6 c (6) = D Q« +D * sin 6 + D2' tan 6 V -0 D ' 0 a + ty cos t - n sin t V a cos L sin t - 6 D l ' a cos L cos t V ip sin t + n cos t + <J> D2' -o sin L 54. 245. TABLE B.2 Coefficients for Polynomial Least Squares F i t A. Tracking experiment At c(t) = E v n AS (t) - y d t n c n h o <f> tan S-8 sec 6-0+n tan 6 d o a+$-cr sin L cos 6+cr cos L sin 6 h l cr cos L sec S+ty tan 6 d l n h2 - n tan 8/2 d2 -(iJH-cr cos L sin 6)/2 h3 -(cr cos L sec &+ty tan 6)/6 d3 n/6 h4 ri tan 6/24 d4 (IJJ+CT cos L sin <5)/24 h5 ( a cos L sec 6+ty tan <5)/120 d5 -n/120 Transit experiment A<S (6) = E cl ' 6 n c n V cr cos L sin t-B-9 d ' o I{J cos t-n sin t + a—CT sin L V ty sin t + n cos t + <J> V a cos L cos t V (CT COS L sin t-6)/2 •V (CT sin L)/2 V (ty sin t + n cos t + cp) /3 V -(cr cos L cos t)/6 V (cr cos L sin t-B)(5/24) -(cr sin L)/24 V (ty sin t+ n cos t+<j>)(2/15) V (cr cos L cos t)/120 55. 246. being used to f i t . This results i n the higher order coefficients be-coming misleadingly large and leads to inconsistent values for the derived misalignment parameters. Therefore, when polynomial f i t s are being made — unless they are simply to reproduce an empirical pointing curve — no higher order terms should be used than are necessary to produce approximately 5% accuracy over the hour angle or declination range being f i t . As an aid for estimating the truncation error in a low order polynomial f i t FIGURE B.l is included. Generally speaking tracking experiments are subject to only sine and cosine truncation errors while transit experiments are affected by secant and tangent truncation errors as well. Therefore a tracking experiment f i t using a third order polynomial w i l l involve a <5% truncation error i f |t| < 53°, while similar accuracy could be obtained for a transit experiment only i f |S| < 41°. 56. 247. 10 20 30 40 50 60 70 ARGUMENT OF FUNCTION (Degrees) Figure B.l Truncation Error in Polynomial Expansi 57. 248. APPENDIX C: Conventions Used with Matrix Rotations. In Section B.2 we use the following convention. Clockwise (CW) rotations of a co-ordinate system are assumed to be positive. In the case of the misalignment parameters, this w i l l correspond to a value which i s greater than zero. Counterclockwise (CCW) rotations on the other hand w i l l be negative. In general a CW rotation of angle y w i l l be denoted R^  and may or may not be followed by a bracketed quantity indicating the axis (X,Y or Z) about which the rotation i s made. We can therefore write: 1 0 0 \ / cos y 0 sin y\ /cos y -sin y 0 Rni(X) =( 0 cos y -sin y j;R (Y) =[ 0 1 0 J; R (Z) = ( sin y cos y 0 J (E.l) 0 sin y cos y / ^ \-sin y 0 cos y / ^ \0 0 1 If the rotation angle y can be treated as an infinitesimal, then to f i r s t order in y we may write: 1 0 o \ / 1 0 y\ / l -y 0 R (X) =10 1 -y J- R(Y) =[ 0 1 0 l, R(Z) =[y 1 0 | (E.2) 0 • u 1 / y \-y 0 . 1 / V \0 0 1 Furthermore, i f v represents another infinitesimal rotation then to f i r s t order in both y and v: R^(X) Rv (Y) = Rv (Y) R^  (X) £ R^ (X,Y) R (X) Rv (Z) = Rv (Z) R^  (X) £ R^v (X,Z) (E.l) and R (Y) R (Z) = R (Z) R (Y) = R (Y,Z) y v v y vy 58. Since the matrices (E.l) are orthogonal, i t follows that the inverse and transpose are equal; as a result, i f is a CW rotation, then the inverse R 1 = R is a CCW rotation, and is easily obtained as y -u the transpose of R^ . Generalizing this, we can easily show that the in-— T T verse of R is R 1 = R =R , where R is the transpose of R yv yv -y,-v yv yv yv With this result, the transformations between the various co-ordinate systems described in Section B.2 may be schematically i l -lustrated as: c» July P_!£ D _ae* •< -« -< R T 1 -•• i G R~1 tyr\ <j>9 ct6 One other t r i v i a l point is worth mentioning as an aid to remem-bering which rotations are which. If the misalignments of Section B.2 are remembered in the combinations (ty,r\), (<j),6) and (a,8), then the para-meter ending in "ETA" always comes second and describes a rotation about either the Y or Z axis. That i s , the parameters describe either (X,Y), (X,Z) or (Y,Z) rotations with the "ETA" parameter indicating the second, such that the order X before Y, Y before Z is maintained. If this i s confusing, ignore i t . 250. BIBLIOGRAPHY 1. S m i t h , E . K . and W e i n t r a u b , S . P r o c . I . R . E . 4 1 , 1035 ( 1 9 5 3 ) . 2 . S h i m a b u k u r o , F . I . I . E . E . E . T r a n s a c t i o n s , A P - 1 4 , 228 ( 1 9 6 6 ) . 3 . B l a n c o , V . M . and M c C u s k e y , S .W. B a s i c P h y s i c s o f t h e S o l a r S y s t e m A d d i s o n - W e s l e y ( 1 9 6 1 ) . 4 . D a v i s , J . H . and C o g d e l l , J . R . N . A . S . A . T e c h n i c a l Memorandum N G L - 0 0 6 - 6 9 - 3 ( 1 9 6 9 ) . 5 . D r a k e , F . D . P h . D . T h e s i s , H a r v a r d U n i v e r s i t y ( 1 9 5 8 ) . 6 . M a h o n e y , M . J . The U . B . C . M i l l i m e t e r R a d i o T e l e s c o p e Compu te r C o n t r o l S y s t e m . P a r t I: A D e s c r i p t i o n f o r P r i m a t e s , U n i v e r s i t y o f B r i t i s h C o l u m b i a ( 1 9 7 5 ) . 7 . M a h o n e y , M . J . , P h . D . D i s s e r t a t i o n , U n i v e r s i t y o f B r i t i s h C o l u m b i a ( 1 9 7 6 ) . Appendix C: CO, CO and C O J= 1-0 Observations in L134 In this appendix we present plots of the excess radiation temperature T^*, as a function of the LSR velocity, for those positions 12 13 18 in L134 where CO, CO and C 0 have been observed. Positions at 12 12 13 which only CO, or CO and CO were observed are not included. The method of data reduction i s described in Chapter VIII and the num-bers i n the upper right hand corner of each figure represent the off-sets in right ascension (in minutes) and in declination (in arcminutes) with respect to our nominal center position: a(1950): 15 h 51 m 00 s £(1950): -4° 30' 00" The results for positions not shown here may be found in Figure 9 of Chapter VIII. L 1 3 4 ( + 0 . 0 0 . + 0 0 ) J I 1 —I ! 1 1 : 1 1 1 9.0 -6.0 -3.0 0.0 3.0 6.0 9.0 12.0 15. LSR VELOCITY (KM/SECi L 1 3 4 ( - 0 . 2 1 . + 0 4 ) J I 1 • 1 r 1 1 — i 1 1 9.0 -6.0 -3.0 0.0 3.0 6.0 9.0 12.0 15. LSR VELOCITY (KM/SEC) L 1 3 4 Cni .00 . -08)J L 1 3 4 ( + 0 . 0 0 . - 1 2 ) J I 1 1 r : 1 1 1 1 1 9.0 -6.0 -3.0 0.0 3.0 6.0 9.0 12.0 15.0 LSR VELOCITY (KM/SEC) L 1 3 4 (+0.00.+08)J l r- 1 — 1 1 1 1 1 1 -9.0 -6.0 -3.0 0.0 3.0 6.0 9.0 12.0 15. LSR VELOCITY (KM/SEC) L I 3 4 ( -0.50.+00)J I 1 1 1 1 1 : 1 ' l 1 -9.0 -6.0 -3.0 0.0 3.0 6.0 9.0 12.0 15. LSR VELOCITY (KM/SEC) L 1 3 4 ( + 0 . 2 5 . - 0 4 ) J -9.0 -6.0 -3.0 3.0 3.0 6.0 9.0 12.0 15.0 LSR VELOCITY (KM/SEC) L 1 3 4 ( - 0 . 2 5 . - 0 4 ) J I 1 1 1 — 1 1 1 1 ; 1 9.0 -6.0 -3.0 0.0 3.0 6.0 9.0 12.0 15.0 LSR VELOCITY (KM/SEC) L 1 3 4 1 + 0 . 2 5 . + 0 4 ) J i r - 1 r - 1 1 1 1 1 -9.0 -6.0 -3.0 0.0 3.0 6.0 9.0 12.0 15. LSR VELOCITY (KM/SEC) L 1 3 4 ( - 0 . 2 5 . - 0 8 ) J I 1 1 1 1 1 1 1 i -9.0 -6.0 -3.0 0.0 3.0 6.0 9.0 12.0 15.0 LSR VELOCITY (KM/SEC) 269. 1 o 13 18 Appendix D: CO, CO and C 0 T^* Contours at Constant Velocity in L134. In this appendix we present T * contours at constant LSR velocity for the J = 1-0 transition of CO, CO and C O in L134. The method of reduction is described i n Chapter VIII. In these figures we specify the isotope, the LSR velocity and the contour unit. The latter was chosen to represent the peak-to-peak noise for the data concerned. 13 As pointed out in the text, CO does show increased emission 12 at the position of the CO 0.7 km/sec cloud, however, i t was not con-toured because of Insufficient observations. 270. R1. .5 L.O 0.5 0.0 - 0 . 5 -1 .0 - 1 . 5 1 1 L_ I I L_u) ro L Y N D S 1 3 4 1 2 C 1 6 0 LSR VELOCITY (KM/SEC) -0.58 CONTOUR UNIT (KELVIN) 1.50 a o ^ h i i cn o i •ro 1.5 1.0 0.5 0.0 - 0 . 5 -1 .0 .-i.g r u c T r t m f i i j i T n . i i o RIGHT ASCENSION (MIN) 271. • 1.5 1.0 0.5 0.0 -0.5 -1.0 •1.5 L Y N D S 1 3 4 , 2 C 1 6 0 LSR. VELOCITY (KM/SEC) 0.07 CONTOUR UNIT (KELVIN) 1.50 n 1 1 1— 1.0 0.5 0.0 -0.5 RIGHT ASCENSION (MIN) 1.5 -1.0 272. o 1.5 ru. cn 1.0 0.5 0.0 _] I l _ -0.5 - 1 . 0 •1.5 rvi o CD. C J ct: CE o r— cr J Q LU i a a CO •—i. i 7 ^ CN rn. L Y N D S 1 3 4 1 2 C 1 6 0 L S R V E L O C I T Y ( K M / S E C ) 0 . 7 2 CONTOUR UNIT ( K E L V I N ) 1 . 5 0 n • 1 1 1— 1.0 0.5 0.0 -0.5 RIGHT A S C E N S I O N (MIN) 1.5 -1.0 -1 1.5 1.0 0.5 0.0 -0.5 -1.0 L Y N D S 1 3 4 1 2 C 1 6 0 LSR VELOCITY (KM/SEC) CONTOUR UNIT (KELVIN) 1.37 1.50 -1 1.5 1.0 0.5 0.0 -0 .5 -1.0 -1 RIGHT ASCENSION (MIN) 274. • 1.5 XT. U3. •to" CE CL UJ 1 a o LO •—1. I O 7 ^ CM rn. 1.0 _ L _ 0.5 0.0 -0.5 -1 .0 -1.5 L Y N D S 1 3 4 1 2 C 1 6 0 LSR VELOCITY (KM/SEC) 2.02 CONTOUR UNIT (KELVIN) 1.50 1.5 - 1 1 1 ~ 1 — 1.0 0.5 0.0 -0.5 RIGHT RSCENSION (MIN) - 1 . 0 -1 1.5 1.0 0.5 0.0 -0.5 -3.0 -3 -I 1 1 1 1 J L L Y N D S 1 3 4 1 2 C 1 6 0 LSR VELOCITY (KM/SEC) 2.67 CONTOUR UNIT (KELVIN) 1.50 _l 1 1 1 1 1— 1.5 1.0 0.5 0.0 -0.5 -1.0 RIGHT ASCENSION (MIN) 1.5 1.0 0.5 0.0 -0.5 -1.0 L Y N D S 1 3 4 1 2 C 1 6 0 L S R V E L O C I T Y ( K M / S E C ) 3 . 3 2 CONTOUR UNIT ( K E L V I N ) 1 . 5 0 1 1 1 1 — 1.0 0.5 0.0 -0 .5 RIGHT A S C E N S I O N (MIN) 1.5 •1.0 277. • 1.5 1.0 0.5 0.0 -0.5 -1.0 •1.5 co ru L Y N D S 1 3 4 , 2 C 1 S 0 LSR VELOCITY (KM/SEC) 3.97 CONTOUR UNIT (KELVIN) 1.50 ro • cn • Co o rt 7 _ 1 o i CO I • I — • cn a i • ro o ~l 1 1 1 1.0 0.5 0.0 -0.5 RIGHT ASCENSION (MIN) i CO 1.5 -3.0 -1. «=>1.5 1.0 0.5 0.0 -0.5 -1.0 -1 f M . L Y N D S 1 3 4 1 3 C 1 6 Q s- l LSR VELOCITY (KM/SEC) 1.29 CONTOUR UNIT (KELVIN) 0.75 fM O ID. ' O C J CC CC i—i I— C E I—I _ l a UJ i a a LO •—i. i Oi -i a ? i 1 1 1 r 1.5 1.0 0.5 0.0 -0.5 -1.0 -1 RIGHT ASCENSION (MIN) 279. 1.0 0 . 5 0 . 0 - 0 . 5 - 1 . 0 —I 1 I I I •1 .5 LO TO a ro a L Y N D S 1 3 4 • 1 3 C 1 6 0 L S R V E L O C I T Y ( K M / S E C ) 1 . 9 7 CONTOUR UNIT ( K E L V I N ) 0 . 7 5 cn o .CO o a I ' CD I Ol a i • ro ~1 1 1 1 1.0 0 . 5 0 . 0 - 0 . 5 RIGHT A S C E N S I O N (MIN) i ' CO 1.5 •1.0 ° 1.5 l.D 0.5 o — - a o C C C E O o •—i I— C E l o UJ i o o LO* • — I . I i 0.0 -0.5 L Y N D S 1 3 4 1 3 C 1 6 0 L S R V E L O C I T Y ( K M / S E C ) 2 . 6 5 CONTOUR UNIT ( K E L V I N ) 0 . 7 5 1.5 i i I—" 1— 1.0 0.5 0.0 -0.5 RIGHT A S C E N S I O N (MIN) ° 1 . 5 1.0 0.5 0.0 -0.5 -1 .0 -1 L Y N D S 1 3 4 1 3 C I 6 0 LSR VELOCITY (KM/SEC) CONTOUR UNIT (KELVIN) 3.33 0.75 - | 1 ; 1 | 1.0 0.5 0.0 - 0 . 5 RIGHT ASCENSION (MIN) 1.5 -1.0 -1 •i 282. o 1.5 f M . m 1.0 0.5 0.0 _J -0.5 -1.0 -1.5 c o ' r o a r u L Y N D S 1 3 4 1 3 C I S 0 L S R V E L O C I T Y ( K M / S E C ) 4 . 0 1 C O N T O U R U N I T C K E L V I N ) 0 . 7 5 r o Q LO . - a O cm CE •cn a cn o 0 ° CE LU i a a LO • — I . i a o i co a i • i - . o i fM. I I r o • p . fM rn. i i 1.5 n I 1 1— 1.0 0.5 0.0 -0.5 R I G H T A S C E N S I O N ( M I N ) -3.0 - i 283. Q l . 5 i .D 0.5 0.0 -0.5 -1.0 -1.5 L Y N D S 1 3 4 1 2 C 1 8 0 LSR VELOCITY (KM/SEC) CONTOUR UNIT (KELVIN) 2 . 6 5 0 . 3 0 _1 1 — 1 1 — 1.0 0.5 0.0 -0.5 RIGHT ASCENSION (MIN) 1.5 •1.0 -1 1.5 1.0 0 . 5 0 . 0 - 0 . 5 - 1 . 0 -1 I I I L : I _ L Y N D S 1 3 4 1 2 G 1 8 0 LSR VELOCITY (KM/SEC) 3.33 CONTOUR UNIT (KELVIN) 0.30 1 r 1 r 1 1.5 1.0 0 . 5 0 . 0 - 0 . 5 - 1 . 0 - i RIGHT ASCENSION (MIN) 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0084826/manifest

Comment

Related Items