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

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STUDIES OF THE 21-cm LINE IN DENSE DUST CLOUDS by MICHAEL JOSEPH MAHONEY B.Sc , U n i v e r s i t y - o f B r i t i s h Columbia, 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1971 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of PHYSICS The University of British Columbia Vancouver 8, Canada Date SEPTEMBER 1'9>'0 ' i • »•• 11 • i - i i • • ^ • f i i E a £ » > w " 1 - " - i i -ABSTRACT Using the 26 m paraboloid at the Dominion Radio Astrophysical Observatory, s u f f i c i e n t 21-cm l i n e data have been obtained on t h i r t e e n dense dust clouds to give a measure of the si g n i f i c a n c e of an excess or a d e f i c i t i n the hydrogen emission from these objects, as compared with nearby surround-ing regions of the sky. The analysis of these data indicates that four of these clouds show s i g n i f i c a n t decreases i n the hydrogen emission. I f the widths of these d e f i c i t s are to be interpreted as thermal broadening within a single cloud, k i n e t i c temper-atures obtained are f a r i n excess of those indicated by normal OH emission from these same objects. I f the OH and H are i n thermodynamic equilibrium and the chemical abundances are normal, i t i s thought that the d e f i c i t s are due to the hydrogen being i n molecular form. However, measurements of higher s p a t i a l and v e l o c i t y r e s o l u t i o n are needed to rul e out the p o s s i b i l i t y of a cold absorbing cloud. - i i i -TABLE OF CONTENTS Chapter 1 INTRODUCTION Page 1-1) H i s t o r i c a l Background 1 1-2) Is the Hydrogen Atomic or Molecular? 2 1-3) The Present Work 5 1- 4) The Problem of Interpretation 6 Chapter 2 GENERAL THEORY 2- 1) D e f i n i t i o n of Symbols 8 2-2) Temperature and Thermodynamic Equilibrium .. 8 2-3) The Equation of Transfer 11 2-4) The O p t i c a l Depth at 21-cm, T2, 14 2-5) The Interpretation of Line Widths 19 2-6) The V i s u a l O p t i c a l Depth, rv 21 2-7) What i f TZI Is Not Proportional to T v? 23 2- 8) The Cold Absorbing Cloud 25 Chapter 3 EQUIPMENT AND OBSERVATIONS 3- 1) The Apparatus 29 3-2) Which Dense Dust Clouds Do You Observe? 30 3-3) Method of Observation 32 3-4) Method of C a l i b r a t i o n 34 - i v -T A B L E OF C O N T E N T S ( c o n t ' d ) C h a p t e r 4 DATA ANALYSIS, RESULTS, AND CONCLUSIONS Page 4-1) The Computer P r o g r a m s 38 4-2) The S o u r c e s A n a l y z e d 46 4-3) The R e s u l t s 46 4-4) I n t e r p r e t a t i o n o f R e s u l t s 47 4-5) C o m p a r i s o n o f R e s u l t s w i t h O t h e r Work 50 4-6) C o n c l u d i n g Remarks 51 A p p e n d i x A A L I S T I N G OF COMPUTER PROGRAMS 54 B i b l i o g r a p h y • *•• 7 7 -V-LIST OF TABLES Table T i t l e Page TABLE I Properties of a Typ i c a l Dust Cloud 1 TABLE II A L i s t of Symbols and Their D e f i n i t i o n s 8 TABLE III A L i s t of Dust Clouds Suitable f o r Observation 31 TABLE IV A L i s t of Observed Sources 32 TABLE V The 21-cm Line C a l i b r a t i o n Standards 34 TABLE VI A L i s t of Derived Dust Cloud Parameters 46 - v i -LIST OF FIGURES Figure T i t l e Page FIGURE 1 The Pos s i b l e Behaviour of T*, Versus T„ 7 FIGURE 2 A Block Diagram of the Receiving Equipment 29 FIGURE 3 The Method of Referencing on a Dust Cloud .... 32 FIGURE 4 The Average Difference and Expected Fluctuation f o r Object 1 46 FIGURE 5 The Average Difference and Expected Fluctuation f o r Object 38 46 FIGURE 6 The Average Difference and Expected Fluctuation f o r Object 32 46 FIGURE 7 The Average Difference and Expected F l u c t u a t i o n for Object 15 46 - v i i -ACKNOWLEDGEMENTS I would f i r s t l i k e to acknowledge the assistance of my thesis supervisor, Dr. W.L.H. Shuter, not only for h i s enlightening discussions and encouragement, but also f o r h i s patience throughout t h i s work. Next, I would l i k e to thank my colleagues, Dr. William McCutcheon, f o r help with the re c e i v i n g equipment, Mr. R.A. Perley, f o r stimulating "over the w a l l " discussions and i n s u l t s , and my numerous fr i e n d s and enemies who made the preparation of t h i s thesis an enjoyable endeavour. F i n a l l y , I thank the s t a f f of the Dominion Radio Astr o p h y s i c a l Observatory f o r the use of t h e i r f a c i l i t i e s and experience, and the National Research Council of Canada fo r f i n a n c i a l assistance. -1-Chapter 1 INTRODUCTION 1-1) H i s t o r i c a l Background Regions of sky devoid of stars were f i r s t catalogued 1 i n 1919 by the American astronomer Barnard, and more recently, 2 by Lynds. I t was at f i r s t thought that these dark patches were i n fa c t c a v i t i e s i n the general star f i e l d ; however, a study of Barnard's catalogue quickly showed that these dark objects were d i s t r i b u t e d c h i e f l y i n the neighbourhood of the g a l a c t i c plane, making i t more p l a u s i b l e to think of them as true dark masses or nebulae, rather than long tubes through the g a l a c t i c plane which were devoid of stars. Soon, large-scale photographs of these objects, projected against a luminous background, showed them to be true dark nebulae with a wide range of sizes and o p a c i t i e s . By assuming that absorption was responsible f o r the differences i n star counts on and nearby these nebulae, astronomers were then able to estimate t h e i r distances, depths and o p a c i t i e s . The techniques of radio astronomy have yielded a d d i t i o n a l information on masses and composition, notably through measurements of the 21-cm l i n e of atomic hydrogen, and even more recently, 3-6 through measurements of the molecular spectral l i n e s of OH 7 and H 2 C O . The properties of a t y p i c a l dark cloud have been summarized i n TABLE I. Most of the parameters l i s t e d there 8 are taken from a review paper by H e i l e s . -2-1-2) Is the Hydrogen Atomic or Molecular? Despite a l l we know about these dark dust clouds, one matter i s s t i l l undecided - whether or not the dark dust clouds contain molecular hydrogen. This problem a r i s e s because ^ i s a homonuclear diatomic molecule and as such i t s r o t a t i o n a l -v i b r a t i o n a l and pure r o t a t i o n a l t r a n s i t i o n s are only quadrapole-allowed, leading to a very weak o p t i c a l and near i n f r a r e d spectrum, which i s undetectable from the earth's surface because of atmospheric opacity and the present lack of ast r o p h y s i c a l i n f r a r e d spectrometers. The Lyman and Werner e l e c t r o n i c band t r a n s i t i o n s are dipole-allowed, however, but because these bands occur i n the u l t r a v i o l e t , they are also absorbed by the earth's atmosphere. The only detection of 9/ 1 0 H2 to date has been by rocket-borne instrumentation, i V / and these indicate a low free space abundance of molecular hydrogen. Because H2 has no f i n e or hyperfine structure i n i t s ground s t a t e , radio frequency l i n e s do not e x i s t . More recently, G u l l and H a r w i t ^ f a i l e d to detect near-infrared emission which 12 had been predicted to e x i s t i n dark clouds near u l t r a v i o l e t s t a r s , as a r e s u l t of the softening of the u l t r a v i o l e t r a d i a t i o n by the molecular hydrogen supposed to e x i s t i n dark clouds. Barred from a d i r e c t measurement of H 2, astronomers have used both 21-cm l i n e data, t h e o r e t i c a l c a l c u l a t i o n s , and a T h i s i s not inconsistent with a high H 2 abundance i n dust clouds where the H 0 i s shielded. -3-other inferences to support t h e i r contentions f o r the existence or non-existence of molecular hydrogen within dark dust clouds. 1 3 The e a r l i e s t 21-cm l i n e measurements of L i l l e y indicated a general c o r r e l a t i o n between gas and dust over large regions 14 15 of the sky, as d i d the work of G a r z o l i and Varsavsky. * However, more recent measurements of Wesselius and S a n c i s i indicate that a general c o r r e l a t i o n between gas and dust i n the i n t e r s t e l l a r medium does not e x i s t . Unfortunately t h i s work only t e l l s us about large areas of the sky and not i n d i v i d u a l dark nebulae, where the r i d d l e of atomic versus molecular hydrogen r e a l l y e x i s t s . 17 Heiles was the f i r s t to study a large sample of i n d i v i d u a l dust clouds. From measurements of the 21-cm l i n e on and nearby f o r t y - e i g h t dark dust clouds, he was able to conclude that one cloud showed a s i g n i f i c a n t excess while two clouds showed s i g n i f i c a n t d e f i c i t s . This work however neglected to define what was meant by the words "nearby" and " s i g n i f i c a n t " , and with only two reference positions f o r each cloud, i t i s indeed s u r p r i s i n g that no more than three excesses or d e f i c i t s were found, as t y p i c a l hydrogen gradients i n the i n t e r s t e l l a r medium can produce very large differences between adjacent beam positions^* c e r t a i n l y much larger than H e i l e s 1 s e n s i t i v i t y of 7°K brightness temperature. b see next page -4-The most d e t a i l e d 21-cm l i n e work on dark dust clouds are the two-dimensional maps of these objects by the Dutch astronomers, S a n c i s i and W e s s e l i u s ^ ' ^ b u t unfortunately these maps have been made of only a few objects and do not give a f a i r i n d i c a t i o n of what might be expected f o r a large sample of dark dust clouds. Besides these 21-cm l i n e measurements and t h e i r implications (to be discussed l a t e r ) t h e o r e t i c a l c a l c u l a t i o n s by Hollenback, Werner and S a l p e t e r ^ i n d i c a t e that f o r " 'standard clouds' with •*^10/cm and T y ^ O . l , the f r a c t i o n a l abundance of molecular _3 hydrogen i s 10 while i n denser and more opaque clouds ( i n p a r t i c u l a r , dark nebulae with more than one magnitude of v i s u a l e x t inction) the hydrogen should be mainly i n molecular 91 form." Verschuur^ has argued that the missing g r a v i t a t i o n a l 22 mass of the galaxy i s H£, whereas Cheung et a l have suggested b I f we l e t Nt?.,^) be the column density of atomic hydrogen at an a r b i t r a r y point on the sky and l e t the point (o,o) be at the center of a dense dust cloud, then on doing a Taylor ser i e s expansion about t h i s point, we f i n d that: Ni*,p = N(o,o) + Ot x -f Hi «. + £AL zlN *u+rN <d+... (1-1) where a l l the d e r i v a t i v e s are evaluated at the cloud center. I t i s then easy to show that the average difference p r o f i l e between the cloud center p o s i t i o n and four nearby reference positions a distance X away to the north, south, east and west i s : £{ <£M- .4- rN] + ... (1-2) Thus the second and higher order, non-linear, gradients can e a s i l y produce a diff e r e n c e p r o f i l e , depending on t h e i r sign and magnitude. -5-that i s necessary f o r the observed high rate of c o l l i s i o n -a l e x c i t a t i o n of NH^. On the other hand, hydrogen s e l f -absorption measurements^-28 hydrogen absorption by continuum 29 30 31 sources, » and emission from high l a t i t u d e clouds indicate that dark clouds may be very cold, and t h i s would e a s i l y explain any d e f i c i e n c i e s i n the 21-cm l i n e emission, i f i t were consistent with other types of measurements. 1-3) The Present Work The present work consisted of 21-cm l i n e measurements on dark dust clouds and well-defined reference p o s i t i o n s . Although maps could not be produced as i n the Dutch work, each cloud observed had between four and eight reference positions as compared to only two i n H e i l e s ' work. Both the s p a t i a l r e s o l u t i o n of 36 arcmin and the v e l o c i t y r e s o l u t i o n of 2.12 Km/sec. used i n the present work were the same as i n the Dutch measurements. The s e n s i t i v i t y obtained here was also about seven times H e i l e s 1 , but not as many clouds were surveyed. The most important innovation of the present work, however, i s that the detected excesses or d e f i c i t s have been given a s t a t i s -t i c a l s i g n i f i c a n c e i n terms of what might be expected i f non-linear hydrogen gradients existed i n the i n t e r s t e l l a r regions surrounding the dark dust clouds, as they most c e r t a i n l y do. -6-1-4) The Problem of Interpretation Once i t has been established whether or not dark dust clouds show s i g n i f i c a n t excesses or d e f i c i t s i n t h e i r hydrogen emission, the problem s t i l l e x i s t s of i n t e r p r e t i n g what i t a l l means. The three cases which must be considered are l i s t e d below, and f o r each case, several possible explanations e x i s t . Case 1. No s i g n i f i c a n t excess or d e f i c i t e x i s t s . In t h i s case at l e a s t two i n t e r p r e t a t i o n s are possible: a) The excesses or d e f i c i t s may e x i s t , but are not s i g n i f i c a n t compared to the background f l u c t u a t i o n s . b) The gas to dust density r a t i o i s constant over the cloud and i t s surroundings, leading to no observable excess or d e f i c i t . Case 2. A s i g n i f i c a n t excess e x i s t s . Again two p o s s i b i l i t i e s e x i s t : a) I f the clouds are i n f a c t molecular, d i s s o c i a t i o n by low energy cosmic rays on the rim of a cloud could enhance the emission from the atomic 32 hydrogen there. b) I f the cloud i s i n hydrostatic equilibrium with i t s surroundings, an excess would appear. -7-Case 3. A s i g n i f i c a n t d e f i c i t e x i s t s . Several in t e r p r e t a t i o n s are again possible: a) A "genuine" hole e x i s t s i n the atomic hydrogen d i s t r i b u t i o n . b) A hole e x i s t s because the atomic hydrogen i s i n fa c t molecular. c) The cloud contains atomic hydrogen which i s cooler than the background hydrogen and hence absorbs the r a d i a t i o n from t h i s hydrogen, producing an apparent d e f i c i t . These three cases have been summarized i n FIGURE 1. and w i l l be dealt with i n more d e t a i l l a t e r on. I t i s the aim of the present work to resolve these p o s s i b i l i t i e s by using a s u f f i c i e n t l y large sample of dust clouds, so that trends towards any of the three cases can be s t a t i s t i c a l l y estab-l i s h e d , and the s i g n i f i c a n c e of excesses or d e f i c i t s i n terms of non-linear hydrogen gradients resolved. -8-Chapter 2 GENERAL THEORY 2-1) D e f i n i t i o n of Symbols The symbols used i n t h i s thesis are l i s t e d i n TABLE I I . Any further knowledge needed concerning t h e i r meanings or ori g i n s can be found i n Spitzer's book, Diffuse Matter i n 33 Space. 2-2) Temperature and Thermodynamic Equilibrium As the concepts of temperature and thermodynamic equilibrium, and the consequences of t h e i r d e f i n i t i o n s , w i l l figure very intimately i n the discussion that follows, i t i s important we c l e a r l y e s t a b l i s h what we mean by them. I f a gas i s i n thermodynamic equilibrium, i t behaves as a black body, with the p a r t i c l e energies equally d i s t r i b u t e d among the i n t e r n a l and k i n e t i c degrees of freedom. For such a gas, characterized by i t s temperature T, a number of statements can be made. . c A) The d i s t r i b u t i o n of p a r t i c l e v e l o c i t i e s i s Maxwellian: <=P<iO A* A 1/_ai _J e dv (2-1) B) The d i s t r i b u t i o n of p a r t i c l e s among t h e i r i n t e r n a l energy states i s Boltzmannian: nf(t*.)= M * ( X A ) C ~ £ a1 M T (2-2) C) The d i s t r i b u t i o n of p a r t i c l e s among t h e i r various stages of i o n i z a t i o n i s given by the Saha equation: c Without loss of g e n e r a l i t y , i t has been assumed that the mean v e l o c i t v vpm'QHOC WO oKni I -ni <-.^  „^ „ j __. . -9-*.*{XA-H)= H * (XA ) TVH fe. (2-3) D) The d i s t r i b u t i o n of photon energies Is Planckian: BV(T) -=. ZATJ2 1 (2-4) The d e f i n i t i o n s of the symbols used here and elsewhere appear i n TABLE I I ; the a s t e r i s k r e f e r s to the populations i n thermo-dynamic equilibrium (T.E.). The equations themselves can be derived from f i r s t p r i n c i p l e s by using the methods of s t a t i s t i c a l mechanics. A gas i n T.E. can carry no net r a d i a t i o n f l u x , because the r a d i a t i o n f i e l d of a black body i s i s o t r o p i c . To avoid t h i s d i f f i c u l t y , since we w i l l be interested i n the transfer of r a d i a t i o n through a dark dust cloud, we make the approxi-mation of " l o c a l thermodynamic equilibrium" (L.T.E.), i n which we assume the v a l i d i t y of equations (2-1) through (2-4) by allowing the temperature T to vary s p a t i a l l y and temporally, i f necessary. In t h i s way, we can ensure the transfer of r a d i a t i o n through a dark dust cloud. Is L.T.E. a good approximation? The answer i s fortun-a t e l y yes, because i n the case of dark dust clouds, i t i s the process of c o l l i s i o n a l e x c i t a t i o n which predominates over photo-excitation, and consequently determines the r e l a t i v e populations of the states. In a l l but the most extreme cases, the incoming photon f l u x would do l i t t l e to upset t h i s balance. For generality, however, we s h a l l go one step further, and assume only that the l e v e l populations are -10-constant i n time. To t h i s end, we define the "equivalent thermodynamic system" i n which the temperature T equals the actual k i n e t i c temperature T^, the e l e c t r o n density equals i t s actual value, and the density of p a r t i c l e s i n stage (r+1) of i o n i z a t i o n , H*"(XA-+I) , equals the actual value H(XA.+ I.) . The density of p a r t i c l e s i n the j,^ l e v e l of e x c i t a t i o n KLj*(X/i) however, need not equal the actual value rtj (XA.) , and the r e l a t i o n s h i p between them defines the " ^ - f a c t o r " : With t h i s degree of generalization, the Boltzmann and Saha equations s t i l l hold — at l e a s t for the degree of i o n i z a t i o n f o r which the equivalent thermodynamic system was defined. We s h a l l a l so preserve the s i m p l i c i t y of equation (2-4) by def i n i n g the equivalent black body or brightness temperature, "fb , a s the temperature at which the observed s p e c i f i c i n t e n s i t y Iv equals that given by equation (2-4), with s i m i l a r d e f i n i t i o n s f o r the brightness temperature, ~T0 , of the r a d i a t i o n incident upon the dark dust cloud, and the brightness temp-erature, T~c , of the cloud i t s e l f . This l a t t e r temperature i s just the temperature which characterizes the populations of the p a r t i c l e states, and i s sometimes r e f e r r e d to as the spin or e x c i t a t i o n temperature, /s . F i e l d has shown that i n hydrogen clouds,(and the case applies even more strongly i n the dense dust clouds)this population, except i n the most extreme cases, i s e n t i r e l y determined by c o l l i s i o n s , and consequently the e x c i t a t i o n temperature i s equal to the - l i -the k i n e t i c temperature of the gas. The k i n e t i c temperature, on the other hand, i s the temperature which characterizes the Maxwellian v e l o c i t y d i s t r i b u t i o n , so that we can recover equation (2-1) also. In the case of dense dust clouds then, even with the perhaps unwarranted g e n e r a l i z a t i o n to an equivalent thermodynamic system, we can s t i l l recover the use of equations (2-1) through (2-4). 2-3) The Equation of Transfer In order to i n t e r p r e t the 21-cm l i n e data which has been received by a radio telescope from beam positions on and surrounding dark dust clouds, we must solve the equation of r a d i a t i v e t r a n s f e r f o r the passage of t h i s r a d i a t i o n through the i n t e r s t e l l a r medium, and i n p a r t i c u l a r , through a dense dust cloud. To t h i s end, we define the s p e c i f i c i n t e n s i t y Iv - lv(!L,&>t) of a r a d i a t i o n f i e l d so that I v J v J ^ a l f l c L t i s the energy of those photons, whose frequency l i e s i n the i n t e r v a l about i / , and whose d i r e c t i o n i s wit h i n the s o l i d angle dco about K_, which passes, i n a time i n t e r v a l ^ , through the area dft , which i s located at p o s i t i o n A , and i s perpendicular to the photon d i r e c t i o n K. -12-Changes In Iv due to int e r a c t i o n s with matter are described by the equation of transfer, which i s derived by considering the flow of energy i n and out of the ends of a cy l i n d e r of length JU. I< da/ Within t h i s c y l i n d e r , both emission and absorption of rad-i a t i o n are possible, so we define the emission c o e f f i c i e n t <jv and the absorption c o e f f i c i e n t K.v so that yv dVdutdt and Kv Iv dVd-v Jij dt are r e s p e c t i v e l y the energy emitted by a volume element dV i n the i n t e r v a l s and dt , and the energy absorbed from a beam of s p e c i f i c i n t e n s i t y Tv> i - n the same i n t e r v a l s . The energy l o s t from the beam i n passing through the volume dV i s (IV(/L-+CU) - I^CA)) di)doo olfl dt and t h i s must equal the energy emitted by the volume dV, namely jv dYdudco dt, minus the energy absorbed, K.y I v JYdvdu dt y that i s : (l2)Ut-d*)-Ij)U))ciudujd/ldt = jjdVdzidcJdt -Kj> I„ JVdiJdoodt Or AL> - -Kv I„ -+• (2-6) cU 1 I f we define the o p t i c a l depth, Tvt along the photon path, which has been assumed to be a str a i g h t l i n e , by the expression* dt rv = KV (2-7 v -13-and consider the r a d i a t i o n received from a dark dust cloud of t o t a l o p t i c a l depth rCVt with incident r a d i a t i o n i n t e n s i t y lv(o) on the side of the cloud away from the observer, OBSERVER DfiRK D U S T CLOUD then equation (2-6) may be integrated to give: I„ = lv(o) e'^ + e ^ ' ^ d ^ (2-8) We now assume that the above cloud i s i n l o c a l thermodynamic equilibrium, but that the v a r i a t i o n dIv/cU, , of the s p e c i f i c i n t e n s i t y through the cloud i s small enough to be considered to vanish. This being the case, equation (2-6) gives: Iv — CONSTANT — f*>/&ii (2-9) In s t r i c t T.E. i t would be true that 8i)(T)=j,2,f Kjj since the s p e c i f i c i n t e n s i t y i s given by the Planck function. We s h a l l now assume that t h i s i s the case here, where the temperature used, i s cloud temperature Tc , defined i n section 2 of t h i s chapter. Integration of equation (2-8) r e s u l t s i n : Iv-~Iv«>) e-r* + B^C-TdKi- e-'S (2-10) Using the e a r l i e r d e f i n i t i o n s of the observed, incident and cloud brightness temperatures and also the approximation: Bi) ( T ) - Zjt M.T where we have expanded the exponential to f i r s t order i n \\vJwX because h*)/kT « 1 f o r the temperatures and frequencies of i n t e r e s t here, equation (2-10) f i n a l l y y i e l d s : -14-7; = T0 c-r> + 77 (1 - e"^) (2 - iD where the f i r s t term on the r i g h t represents the absorption of the incident energy by the cloud, and the second term rep-resents the emission and self-absorption by the cloud. The temperatures used i n equation (2-11) are e a s i l y r e l a t e d to observed quantities, provided i s known. however depends upon the t r a n s i t i o n p r o b a b i l i t i e s of the p a r t i c u l a r l i n e being observed — i n t h i s case, the 1420.4 MHz t r a n s i t i o n 2 between the two hyperfine states of the 1 ground l e v e l of atomic hydrogen. 2-4) The O p t i c a l Depth at 21-cm, TXI . As pointed out i n the previous paragraph, the o p t i c a l depth at 21-cm depends upon the E i n s t e i n t r a n s i t i o n probabil-i t i e s , that i s , on the spontaneous t r a n s i t i o n p r o b a b i l i t y defined as the p r o b a b i l i t y per unit time of a spontaneous t r a n s i t i o n from atomic l e v e l k to atomic l e v e l ^ , and on the induced (or stimulated) t r a n s i t i o n p r o b a b i l i t i e s B^j- and Bfk , defined as the p r o b a b i l i t i e s for induced downwards and upwards t r a n s i t i o n s r e s p e c t i v e l y , per unit r a d i a t i o n energy density, Ujj. In what follows, we w i l l l i m i t ourselves to a discussion of the 21-cm l i n e of atomic hydrogen, so that the subscripts k and j> w i l l r e f e r to the F= l t r i p l e t , and F=0 s i n g l e t -15-d hyperfine l e v e l s . Thus we w i l l be concerned with the trans-i t i o n p r o b a b i l i t i e s Pilo ? B/0 and Bo\, and the frequency v0, w i l l r e f e r to the 21-cm l i n e . Furthermore, nt (HI) and n 0 ( H l ) w i l l i n d icate the number of atomic hydrogen atoms per unit Although the t o t a l emission over the 21-cm l i n e n a t u r a l l y has nothing to do with the absorption i n t h i s l i n e , i t i s s t i l l necessary f o r us to c a l c u l a t e the t o t a l emission i n order to e s t a b l i s h a r e l a t i o n s h i p between the E i n s t e i n t r a n s i t i o n p r o b a b i l i t i e s , which w i l l be needed i n c a l c u l a t i n g Ta.• Since spontaneous emission can occur i n any d i r e c t i o n , the t o t a l energy radiated spontaneously per unit volume per unit s o l i d angle i s : that i s , just the product of the number of atoms capable of r a d i a t i n g per unit volume, the p r o b a b i l i t y that they radiate, and the energy emitted by each photon, a l l divided by the s o l i d angle that the r a d i a t i o n i s emitted i n t o . S i m i l a r i l y , the t o t a l energy absorbed i n the l i n e per unit s o l i d angle per unit volume per unit time may be calculated, but since the photons emitted by induced emission are t r a v e l l i n g i n the same d i r e c t i o n as the stimulating photons, and have the same frequency, the rate of energy absorption must be calculated as volume i n the F=-1 and F-0 states r e s p e c t i v e l y . (2-12) d F, the t o t a l spin angular momentum, i s the sum S + I , of the e l e c t r o n and proton spins, which are both equal to k ( i n u n i t s o f £ ) . -16-the d i f f e r e n c e between the rates f o r induced absorption and induced emission. Assuming I„ i s r e l a t i v e l y constant over the l i n e and using the f a c t that Uv = I„/c, the t o t a l absorption of r a d i a t i o n by an atom i s then the i n t e g r a l of Kv 1^ over the l i n e , or lv\ KV Jv = k z)o, ( QOL - fl, (Hi) Bjli; JO (2-13) If we now c a l c u l a t e the population density of emitting atoms, ^ ( X / J , i n terms of fie fl. C X/t+i), by means of equations (2-2), (2-3) and (2-5), and then equate fi (XA+.) to ft*(X/i+i) i n the equivalent thermodynamic system, we obtain: **(XA) = 1^ ^ l e e " E A f c / t e T ne VKXAH-,) (2-14) f*+i fe v For hydrogen atoms i n the upper hyperfine l e v e l (A=l 1 Je.*i)v 1K(X>I) = n., (HI) the population density of the t r i p l e t state, H(XA+I)- > t n e n ^ b e r density of protons, and = , the p a r t i t i o n function for protons, which equals unity, since ionized hydrogen has no excited states. Making these changes i n equation (2-14), and s u b s t i t u t i n g f o r ft,(Hi) i n equation (2-13), we obtain: j j,v dv - hi y,i k -iJot A io rie. rip e~ g < / / /* T~ (2-15) However, by equation (2-9), the r i g h t hand sides of equations (2-13) and (2-15) must be equal when 1^= Bp(T). From t h i s , i t follows that: e This assumes the zero of energy corresponds to a free e l e c t r o n at r e s t . -17-Th i s f i n a l l y establishes the r e l a t i o n s h i p we needed between the E i n s t e i n t r a n s i t i o n p r o b a b i l i t i e s . In order to derive the o p t i c a l depth at 21-cm, we now define the integrated atomic cross-section by the equation: ^ = J xlv (2-17) whereby, the atomic absorption cross section, i s defined by the r e l a t i o n s h i p : rij A,v = Kv (2-18) I f we specify ^ - 0 , the f-0 sublevel of hydrogen, and combine the l a s t two d e f i n i t i o n s , we get: A = _X— f Kv (2-19) n0(Hl)J However, J Hv d-v i s given f o r the 21-cm l i n e by equation (2-13), therefore, A = k iJo, Bo. f 1 _ rijjjjj) Blo\ (2-20) C TUCHI) BO,/ Using our derived r e l a t i o n s h i p between the E i n s t e i n t r a n s i t i o n p r o b a b i l i t i e s (equation (2-16)), together with the d e f i n i t i o n s of equations (2-2) and (2-5), we f i n a l l y obtain: A = -4. ( 1 - f e-M«'*T^ (2.21) where A U i the value of yd uncorrected f o r induced emission, i s given by: y&u. = h iJo, Bo (2-22) C We are now i n a p o s i t i o n to calc u l a t e the o p t i c a l depth f o r the 21-cm l i n e , Ta{ . From the d e f i n i t i o n for the o p t i c a l depth (equation (2-7)), we have: -18-n:ulv) ~\<LXv =j K,v JL<V - j n0(HI)4,v d* = NO(HI)AV (2-23) To remove the frequency dependence of tAI(v) we must now perform an i n t e g r a t i o n which we avoided doing e a r l i e r i n deriv-ing an expression f o r the integrated atomic cross-section. In section 2 of t h i s chapter we showed that the v e l o c i t y d i s t -r i b u t i o n of p a r t i c l e s , i n t h i s case hydrogen atoms, was Maxwellian, that i s , where 7 7 denotes the k i n e t i c temperature of the gas. If we assume the only s i g n i f i c a n t l i n e broadening i s due to Doppler s h i f t s between the d i f f e r e n t hydrogen atoms emitting r a d i a t i o n at the frequency Va, , then v - Do, (l+v-/c). Since 7l(.V)diJ - cPcirtdW-and dv = (voi /c) cfr, i t immediately follows from equation (2-1) that the absorption p r o f i l e w i l l have a l i n e shape Vo, j) J.TZ , 7T(2J) - c \\_ m _ e (2-24) Consequently, xtz, = xt- Tl{iy) (2-25) So that from equations (2-23) and (2-25), we f i n a l l y obtain f o r the o p t i c a l depth at 21-cm Tj, (v) = No (Hi) A, TC(v) (2-26) where A i s of course given by equation (2-21). We now assume that the r a t i o (>, /£ 0) i n t h i s equation i s very close to unity, as w i l l be the case due to the frequent c o l l i s i o n s i n dense -19-dust clouds, and expand the exponential, so that on su b s t i t -uting into equation (2-26), we f i n d : = No(HI)^u h Vos Bo, TC(v) = (J—JLSL-B.,O) hi (Hi) - 5". 49 "10"1+ HCHl) (2-27) Ti where a l l the constants, except f\l0 , are e a s i l y evaluated. f\t0 can be found from a straightforward, but lengthly, quantum mechanical c a l c u l a t i o n i n v o l v i n g time dependent perturbation theory. I t i s also useful to know the integrated column density of hydrogen atoms. To t h i s end, we assume that the l i n e i s unsaturated, so that T z, i s small. Equation (2-11) may then be expanded to f i r s t order i n T a, to give Tb - To* CI-T:^ +• Ti r»», which, when the background i s subtracted, y i e l d s : Tx, =-Tb /Tl (2-28) But i n T.E.,7I = 7« , so that on s u b s t i t u t i o n of equation (2-28) i n equation (2-27) and integ r a t i n g , we get: N(hil) = 1.83 >1018 J l l (v) dv (2-29) where V- i s measured i n Km/sec. 2-5) The Interpretation of Line Widths One of the most important questions we s h a l l be asking ourselves, i n t r y i n g to decide whether a dense dust cloud -20-contains molecular or atomic hydrogen, i s : "What i s the temperature of the cloud?" I t turns out that t h i s parameter can be estimated i n several ways - one of which i s from the width of an observed l i n e p r o f i l e . Equation (2-24) f o r a l i n e p r o f i l e i s : TTcv) = C_ AL_£L_ e (2-24) Therefore, at one h a l f the peak value of 7T(z>)f we have l L r 2 = c A! /YI e (2-30) where 1)^ i s the frequency at which the p r o f i l e a t t a i n s one h a l f i t s peak value. I f we rearrange equation (2-30) and define the f u l l width at h a l f i n t e n s i t y , AVT T by the expression: A2JL_ = Z ( ^ - ^ i ) (2-31) we obtain: AVL = Z(^]^[(JUZ) ZkH' (2-31a) from which i t follows that the k i n e t i c temperature of the absorbing gas responsible f o r the p r o f i l e i s : where A l\_is measured i n KHz or Tn = Z1.(P ( LV-jf (2-32) where A^L. i s measured i n Km/sec. -21-2-6) The V i s u a l O p t i c a l Depth, Xy In section 2-4 we derived an expression f o r the o p t i c a l depth at 21-cm and found out how i t depends upon the column density and temperature. Since we r e a l l y only know of the existence of dark dust clouds through t h e i r v i s u a l properties, namely t h e i r v i s u a l o p t i c a l depth T v, or t h e i r v i s u a l extinc-t i o n /9v, i t i s worthwhile, f o r the purposes of i n t e r p r e t a t i o n , to derive a s i m i l a r expression f o r TV and see how i t i s r e l a t e d to rCt\. The v i s u a l e x t i n c t i o n , /9y ( i n magnitudes), i s defined simply as: flv = -Z.5T leym ( Fv/FvCo)) (2-33) where Fv i s the v i s u a l f l u x received from a star behind the cloud and Fv(o) i s the v i s u a l f l u x that would have been received, were the cloud not present. Now the f l u x Fy i s just the i n t e g r a l of the s p e c i f i c i n t e n s i t y I y , from the star, integrated over the s o l i d angle subtended by the star, where I ^ i s given by equation (2-8) to be: U = I.co) e-T* + Jj£ g \ e^'^dri (2-8) Because of the i n s i g n i f i c a n t contribution to Iv from sca t t e r i n g or emission by the cloud grains within the s t e l l a r image, we may neglect the second term i n t h i s equation. Therefore, = §luJw ^ J I„(o) C** d«> = Iv(o) \du) -22-and Fv(o) =• j ljj(o) cL) = lvCd)\dui so that equation (2-33) may be re-written: Pis, = -ZSUjiBe.'x^ l.o&lotv (2-34) where we have assumed that the v i s u a l o p t i c a l depth Tv i s uniform over the s o l i d angle subtended by the star. Since grains are responsible f o r the e x t i n c t i o n , we may use equation (2-26) to write: Tv = NG xiv (2-35) where NG i s the column density of absorbing grains and i s the atomic absorption cross section at v i s u a l frequencies. The geometrical cross-section of a spherical grain i s TCO.2,, so that i f we define the e x t i n c t i o n e f f i c i e n c y f a c t o r , Q T by the expression xlv = TT az Q (2-36) then equation (2-35) and (2-34) may be written: Ty = TT a a Q NG (2-37) or /?v = 3.41 a*Q N s (2-38) Now, the average hydrogen gas density and dust density along a column of length and unit cross section are r e s p e c t i v e l y , ^ H - N(HI) WH/JL (2-39) and, ^ = N G £ KO? ^>6/i (2-40) where mri i s the mass of hydrogen and pG i s the i n t e r n a l grain -23-density. I f we assume a=3«lo"5cm, Q-Z.O and ^G = Lgm cm"3, then, on taking the r a t i o of equations (2-39) and (2-40), we obtain, N(HI) - * 10L° < p „ / p 6 ) N G (2-41) or on using equation (2-38) N(HI) = 1 0 1 9 C p H / p G ) #v (2-42) This equation shows c l e a r l y that i f the r a t i o of mass de n s i t i e s of hydrogen gas to grains i s constant, then /V(HI), the column density of hydrogen gas, increases l i n e a r l y with /? v, the v i s u a l e x t i n c t i o n . This i s what i s normally observed f o r small values of f\y. Note that by using equations (2-27) and (2-34), the l a s t equation can be expressed i n terms of the o p t i c a l depths T2.1 and T v as: Zu = USb*10s (pH/pfi) ffW T „ (2-43) Since N(Hi) and /?y are the commonly measured ast r o p h y s i c a l q u a n t i t i e s , we w i l l normally use equation (2-43). The point to be observed here i s that Tn and T y are also l i n e a r l y proportional to each other so that whether we t a l k of a plot of N (HI) versus f\y, or Tzt versus T V , we are speaking about the same thing. 2-7) What i f T t | i s Not Proportional to Ty? In the l a s t section we saw that N(HI) was proportional to £) v provided that the r a t i o (*5"H/^ G) w a s constant. I f , however, the mean density of atomic hydrogen decreases as we move -24-towards the center of a cloud, while the visual extinction continues to increase, then a plot of Nihil) versus flv w i l l turn downwards for high /9v• This corresponds to a " d e f i c i t " in the atomic hydrogen distribution and could be caused by an anomolous gas to dust ratio within the cloud, by the hydrogen being converted to molecular form or by a cold absorbing cloud. More w i l l be said about these p o s s i b i l i t i e s later. If on the other hand, a plot of N(H1) versus f\y increases upwards as /) v increases, corresponding to an "excess" in the atomic hydrogen distribution, then some other explanation must be sought. The possibility of low energy cosmic ray dissociation of the molecular hydrogen supposed to exist in 31 dense clouds has been considered by two authors, but at least one more explanation exists^. If the cloud i s In hydrostatic equilibrium with i t s surroundings, there w i l l be no pressure gradient across the outer edge of the cloud, implying that the pressure is a constant there. However, by the equation of state we also know that ?- rt(M)k~rl. The combination of these two facts together with the assumption that the temperature is relatively constant in the line of sight through the cloud leads to the result that /V(^1^= constant. But in section (2-6) we found that HZ{ °c A / W ) / " ^ . Substitution for then leads to the result that Tt/°c A/(XT) . Therefore, a plot of f The expulsion of dust grains from the cloud to increase the ratio (pr\/fG) does not seem reasonable. -25-T*/ versus w i l l increase q u a d r a t i c a l l y . (see FIGURE 1) 2-8) The Cold Absorbing Cloud One remaining r e s u l t which i s needed before we discuss the observations, i s how to i n t e r p r e t d e f i c i t s i n terms of a cold absorbing cloud. Consider a cold dense dust cloud of temperature Tc and o p t i c a l depth T c, i n front of a normal region of hydrogen emission, perhaps a s p i r a l arm of the galaxy. f 8 « C K -. GROUND When the antenna beam i s pointed on the cold cloud, equation (2 - 11 ) t e l l s us that the observed brightness temperature i s : -rb«,») = T0(\-erc') er*c + T d- e'"c) (2-44) while on a nearby point the observed brightness temperature i s : T*>fO = To ( l - e ^ ' ) A f t e r we average the observed brightness temperature p r o f i l e s on and o f f the cloud p o s i t i o n , the average observed d e f i c i t w i l l be: AT", = T^ron) -Tfe(tf-ff) = (Tc - T 0 ( j - e - T o ) ) ( I - cTrc) (2-45) where the bars indicate the average values. Since we are concerned only with explaining d e f i c i t s i n terms of a cold absorbing cloud, A T , < 0 . But we also know that o < (1-e" T c) < 1, -26-hence: ATb > ( Tc-Tod-e"^)) = (Tc -T bC*ff)) (2-46) which on rearrangement allows us to place on upper l i m i t on the cloud brightness temperature Tc T t ^ A T b +Tb<ofl) ~ Tb<orv> (2-47) that i s , the cloud temperature i s nec e s s a r i l y always l e s s than the mean observed brightness temperature on the cloud. S i m i l a r i l y , we can c a l c u l a t e a lower l i m i t to T c by neglecting the second term i n equation (2-44). This gives: T b (o^ > To ( l - e _ X a ) e~ T c = Tb<otn e _ , C c since Tc (l - e~Xc) i s always p o s i t i v e . Therefore, T c £ J-TL I Tb (off) ) (2-48) \ Tb (.on) J Some f e e l i n g f o r what the upper l i m i t on T c must be,can be obtained by considering equation (2-45). I f t c were too large there, even one degree brightness temperature differences between the on and o f f cloud positions would be e a s i l y detected, and t h i s does not appear to be the case. At intermediate and higher g a l a c t i c l a t i t u d e s however, the hydrogen i s more l i k e l y to be l o c a l . In t h i s case we have something l i k e a cold spot i n a large cloud. OBSCftVER I f we neglect the background emission on the cloud p o s i t i o n , then equation (2-44) gives: -27-Tb(0n) = Tc ( I - e ' ^ ) (2-49) so that Tt >, Tb (on) (2-50) In t h i s case the observed brightness temperature on the cloud represents not an upper l i m i t as before, but a lower l i m i t to the cloud brightness temperature, T". . At nearby positions on the sky, the observed brightness temperature w i l l be: T b^*ff) = To(\ - e'Zo) (2-51) By assuming a value of 125°K as an average value f o r the o f f -cloud brightness temperature, To » w e c a n then c a l c u l a t e To. Furthermore, we s h a l l assume that the amount of hydrogen i n the cold spot i s greater than or equal to the amount at nearby pos i t i o n s , since a lack of HI at the cold spot i s i n i t s e l f already a good enough reason to expect a d e f i c i t i n the hydrogen emission there. From equation (2-27), we know that A/(Hl)«cT"T , therefore Tc T c >/ ~Yo Xo (2-52) But we have already estimated To and To so that equations (2-52) and (2-49) represent two equations i n two unknowns T c and Tc. This enables us to c a l c u l a t e on upper l i m i t to Tc and a lower l i m i t to Tc. The two models just considered give quite v a r i a b l e -28-r e s u l t s for the parameters Tc and tc\ the r e a l case i s most l i k e l y to be a messy combination of the two. However, they do allow us to place upper and lower l i m i t s on the cloud brightness temperature Tl, and a lower l i m i t on the cloud o p t i c a l depth, T c . -29-Chapter 3 EQUIPMENT AND OBSERVATIONS 3-1) The Apparatus The data analyzed i n t h i s thesis was obtained during two weeks of August 1970, using the 26 meter paraboloid of the Dominion Radio As t r o p h y s i c a l Observatory near Penticton, B. C. The r a d i a t i o n c o l l e c t e d and focussed by the paraboloid was fed by a horn into an uncooled parametric a m p l i f i e r . (See FIGURE 2) A f t e r t h i s f i r s t stage of a m p l i f i c a t i o n , the signa l passed through a s o l i d state pre-amp, followed by a tunable band-pass f i l t e r and mixer pre-amp. The l a t t e r unit heterodyned the received 1420.4 MHz s i g n a l dcwn to a 35 MHz intermediate frequency (I.F.) s i g n a l , which was sent, by cable from the focus to the back end i n the co n t r o l room. Here the I.F. sig n a l was amplified, f i l t e r e d and mixed again, t h i s time with a 45.7 MHz sign a l to produce a 10.7 MHz signal - the center frequency of the f i l t e r spectrometer. An automatic gain control (A.G.C.) loop over t h i s section of the receiver ensured that a constant sig n a l l e v e l was being fed into the spectrometer, which consisted of 100 contiguous 10K.HZ c r y s t a l f i l t e r s and det-ectors. The two banks of 100 integra t i n g c i r c u i t s on the out-put of the spectrometer, r e f e r r e d to as banks A and B i n the remainder of th i s t h e s i s , were scanned a l t e r n a t e l y every 60 seconds, and the 100 analogue voltages d i g i t i z e d and dumped into a PDP-9 on-line computer, from which a paper tape and -30-written output was obtained, after the designated number of spectrometer cycles had been made. The radio frequency local o s c i l l a t o r (L.O.) signal used to produce the I.F. in the f i r s t stage of mixing was generated by phase locking a backward wave oscillator (B.W.O.) to the signal produced by a frequency synthesizer. Also, a plasma noise tube calibration could be coupled into the front end via a 20 db attenuator, or the paramp switched between the feed and a termination at ambient temperature - a "hot", signal reference le v e l . 3-2) Which Dense Dust Clouds Do You Observe? In deciding which dense dust clouds to observe, a number of considerations have to be taken into account. F i r s t , the clouds should have sizes comparable to the 36 arcmin half power beam width of the telescope, to ensure that the reference positions are off the cloud and yet near enough so that the effects due to non-linear hydrogen gradients do not become important. Naturally i t would be desirable i f there were no other clouds nearby. Second, the clouds should be as opaque as possible, because i f any non-linear effect in the relationship between I'xi and T v i s to occur, we expect i t at the largest visual extinctions. Third, the clouds should have a galactic latitude such that \ 10°. This should ensure that the observations -31-are being made s u f f i c i e n t l y f a r o f f the g a l a c t i c plane that f l u c t u a t i o n s i n the hydrogen emission there should not drown out any observed excesses or d e f i c i t s . Fourth, the clouds should, i f possible, be associated with some other spectral l i n e s , such as those of OH or H 2 C O . I f an observed excess or d e f i c i t occurred at the same v e l o c i t y ^ as one of these l i n e s , then because we f e e l c e r t a i n that these l i n e s originate i n dense regions of space, i t seems very l i k e l y that an observed d e f i c i t or excess occurring at nearly the same v e l o c i t y a lso comes from the same dense region, since at high l a t i t u d e s there are only one or two i n the l i n e of sight. In TABLE III are l i s t e d the objects which s a t i s f i e d most of these c r i t e r i a . Objects 1-23 are sources i n the Cudaback - Heiles survey of dark clouds f o r 1667 MHz OH 4 r a d i a t i o n which i n f a c t d i d show t h i s l i n e . H e iles' survey of f o r t y - e i g h t dark clouds f o r anamolous hydrogen emission included l e s s than h a l f of these. The following group of objects from 24 - 31 are sources i n Heiles* dark cloud survey which e i t h e r showed d e f i c i t s or were borderline cases. The f i n a l group of objects are dark clouds from the Lynds Catalogue g A l l v e l o c i t i e s i n t h i s thesis are with respect to the l o c a l standard of r e s t (L.S.R.), defined as the centroid of motion f o r the l o c a l group of st a r s . 5 -32-having the largest v i s u a l e x t i n c t i o n (5 or 6), areas of the order of the h a l f power beam width of the antenna, a high g a l a c t i c l a t i t u d e ( /Ax/>/^°), and which are separated from other clouds. A l l of these dark clouds were then located on the Palomar Sky P r i n t s and checked to make sure suitable reference regions could be found. In t h i s process, a few a d d i t i o n a l sources were found and added to the l i s t . 3-3) Method of Observation In a l l the work to be described here, the L.O. was changed f o r each observation so that the spectrometer was centered a l t e r n a t e l y on 1420.600 MHz and 1420.570 MHz. I f we r e c a l l that the c r y s t a l f i l t e r s i n the spectrometer have a bandwidth of lOKHz, t h i s means that two i d e n t i c a l spectra, s h i f t e d with respect to each other by three channels, were obtained at each p o s i t i o n . The reason f o r doing t h i s was that the spectrometer had about a dozen bad channels, so that by comparing the s h i f t e d p r o f i l e s , i t could be decided what was good and what was bad data. Two d i s t i n c t types of 21-cm observations were made: A) F u l l P r o f i l e Observations: During the f i r s t week of observations 21-cm l i n e p r o f i l e s were obtained f o r the sources i n TABLE IV, and the indicated reference positions. The t y p i c a l p o s i t i o n i n g of the antenna beam i s i l l u s t r a t e d i n FIGURE 3. The reference positions were generally chosen to -33-be 40 arcmin away i n d e c l i n a t i o n , or 3.5 minutes i n r i g h t ascension, although for high d e c l i n a t i o n clouds, a c o r r e c t i o n of secant (declination) had to be applied to the east and west reference positions to avoid overlap of the antenna beam posi t i o n s . The cloud reference p o s i t i o n p r o f i l e s w i l l be referred to as north (N), south (S), east (E) and west (W). In addition, reference p r o f i l e s were also obtained i n the northeast (NE), southeast (SE), northwest (NW) and south-west (SW) positions of some clouds. A source (SRC) or cloud p r o f i l e was obtained before and a f t e r the cloud reference positions were observed, as a consistency check, and then a c a l i b r a t i o n , to be described l a t e r , was made. For a l l of these measurements, a two minute i n t e g r a t i o n was made f i r s t on the relevant p o s i t i o n , and then with the paramp switched to the "hot" load f o r a signal reference l e v e l . The difference of these signals divided by the reference signal was then c a l c u l a t -ed by the computer. B) Difference P r o f i l e Observations: Because the "hot" reference load introduces an extra 300°K of noise to the receiver noise of t y p i c a l l y 150°K and because there was some doubt as to whether i t was saturating one of the IF a m p l i f i e r s , i t was decided to re-observe as many sources as possible, but t h i s time using the o f f cloud positions as signa l reference l e v e l s instead of the "hot" load. This -34-would generate difference p r o f i l e s immediately, but s l i g h t l y l i m i t the amount of i n t e r p r e t a t i o n possible. Again the measurements consisted of 2 minute cycles on the cloud and cloud reference positions, but i n the case of the c a l i b r a t i o n runs, the north g a l a c t i c pole was used as a sig n a l reference l e v e l , since the hydrogen emission from t h i s d i r e c t i o n i s very small. A summary of the sources observed by e i t h e r of these means and the cloud reference positions used appears i n TABLE IV. An "X" indicates that the p o s i t i o n at the head of the column was observed once; i f an "X" also appears i n the ">1" column, they were observed more than once. 3-4) Method of C a l i b r a t i o n Two methods of data c a l i b r a t i o n were possible: A) Primary C a l i b r a t i o n : At the time the observations were 36 being made, Williams had just proposed four regions as i n t e r n a t i o n a l standards f o r 21-cm observations. They are l i s t e d i n TABLE V with t h e i r LSR v e l o c i t i e s and peak brightness temperatures, T b . Three of these regions had been previously used by the International Astronomical Union as standards and i t was decided to adopt them i n th i s work. Assuming that the sign a l response of the receiver i s l i n e a r over the range of signal l e v e l s being considered here, a simple comparison of the d i g i t a l output from a cloud observation to the same output from one of the standard regions immediately establishes the -35-brightness temperature scale to be used. Because of the time involved i n d r i v i n g the telescope to one of these positions a f t e r observing each cloud, t h i s type of c a l i b r a t i o n could only be made a couple of times a day. However, over the enti r e observing period enough data was obtained to determine what c a l i b r a t i o n should be used with a p a r t i c u l a r receiver gain, which was measured a f t e r each cloud p o s i t i o n had been observed. These were therefore used as the primary c a l i b r a t i o n and are accurate to better than i2°K, i f we take Williams' values as d e f i n i t i v e . B) Secondary C a l i b r a t i o n : In the case of c a l i b r a t i o n s involving the plasma noise tube, matters aren't quite so straightforward, because what the re c e i v e r measures i s the antenna temperature X. , not the brightness temperature of the source, 7^ . The antenna temperature L i s the temperature to which a resistance matched to the front end of a re c e i v e r would have to be r a i s e d i n order to supply the same noise power as the observed source. Since the noise power received from a source, W, i s given by the f a m i l i a r Nyquist r e l a t i o n -ship, W= kTB, where B i s the bandwidth of the rec e i v e r , i t follows that the antenna temperature characterizes the power  received by a p a r t i c u l a r antenna, and w i l l vary from telescope to telescope, because they have d i f f e r e n t beamwidths, r a d i a t i o n h Williams had to take a l l t h i s into account i n c a l c u l a t i n g the brightness temperatures of h i s proposed standard regions. -36-s p i l l a g e , etc. The brightness temperature,X> on the other hand, characterizes the i n t e n s i t y of the received r a d i a t i o n , because of i t s d e f i n i t i o n i n terms of the black body spectrum — i t i s t h e o r e t i c a l l y the same f o r a l l telescopes. For purposes of comparison alone, a l l measurements should therefore be made i n terms of the brightness temperature at a p a r t i c u l a r wavelength. 37 I t can be shown , a f t e r going through a l i t t l e antenna theory, that and are related by the expression T b = TL/->\ where t\ i s the e f f i c i e n c y of the telescope. Eta i s not exactly t r i v i a l to calculate and f o r the purposes of the present work i s assumed to be 0.76. Furthermore, the noise tube, a f t e r i t i s coupled into the receiver, i s assumed to represent an antenna temperature of X (NT) - 100* I0°K. The noise tube was f i r e d a f t e r each cloud was observed both to check the receiver gain and noise temperature, and to serve as a secondary method of c a l i b r a t i o n . When the noise tube was f i r e d , i t appeared to saturate the rec e i v e r ; t h i s however could be corrected f o r and the r e s u l t s agreed very w e l l with the c a l i b r a t i o n s using the 21-cm l i n e standard c a l i b r a t i o n sources. The most important use of the noise tube c a l i b r a t i o n however, was i n the c a l c u l a t i o n of gain corrections or "fudge factors" f o r the 200 d i f f e r e n t spectrometer output detectors and integrators,(see Chapter IV , section 4-1) since each -37-channel had a d i f f e r e n t g a i n and would t h e r e f o r e have d i f f e r e n t outputs f o r the same broadband i n p u t . -38-Chapter IV DATA ANALYSIS,RESULTS, AND CONCLUSIONS 4-1) The Computer Programs The raw 21-cm l i n e data, together with the c a l i b r a t i o n p r o f i l e s , were a l l brought to U.B.C. to be analyzed on the IBM 360/67 computer. Since the data analysis programs were written i n FORTRAN, with what i s hoped to be a s u f f i c i e n t number of comment statements, they should be quite s e l f -explanatory. For the purposes of completeness, the programs appear by name below, i n the order i n which they were used, with a few comments on t h e i r use. A complete l i s t i n g of the programs appears i n Appendix A. A) P.T.C. The Computer Center f i r s t copies the raw data, which i s stored i n binary on an 8-track paper tape, onto a magnetic tape i n hexidecimal. This i s done o f f - l i n e . The magnetic tape i s then read by the IBM 360 and the program P.T.C. executed. I t simply translates the binary data into decimal and writes i t into a data f i l e , normally another magnetic tape, i f a l o t of data i s to be stored. B) FUDGE FACTOR This program i s b a s i c a l l y one developed by Mr. R.A. Perley and the need f o r i t s use i s well described 38 elsewhere. What i t b o i l s down to i s that although a given spectrometer channel output increases l i n e a r l y with the l e v e l of the input s i g n a l , they do not a l l give the same output f o r the same input. This program used the broadband noise -39-tube c a l i b r a t i o n runs to calculate corrections or "fudge f a c t o r s " for thi s channel to channel gain v a r i a b i l i t y , and these i n turn can be used to correct the raw 21-cm l i n e data. C) NOISE In t h i s program, the noise tube c a l i b r a t i o n s are used again, but t h i s time for t h e i r o r i g i n a l i n t e n t i o n , that i s , as a secondary c a l i b r a t i o n of the data. A f t e r correcting the gain v a r i a t i o n s and removing the bad channels due to f a u l t y reed switches, the program then calculates an average noise si g n a l l e v e l , corresponding to a brightness temperature o of 135 ± 13 K, and a given receiver gain. Next, the root mean square (RMS) deviation from th i s mean l e v e l i s calculat e d , but i n practice i t was found to be much larger than the expected RMS noise. This was decided to be a r e s u l t of a non-flat baseline. Consequently, the Libr a r y subroutine OLQF i s used to f i t a l e a s t squares polynomial to the baseline, to remove the curvature. This resulted i n very reasonable values f o r the RMS noise, which together with the other RMS noise estimate and the mean noise s i g n a l l e v e l , are then printed out by the computer. D) TEMP CAL In t h i s program, the primary temperature c a l i b r a t i o n s f o r the data are determined. The 21-cm l i n e standard c a l i b r a t i o n p r o f i l e s are f i r s t divided into groups characterized by a d i f f e r e n t brightness temperature. The A and B banks of data are then successively corrected f o r -40-gain v a r i a b i l i t y , by using the fudge f a c t o r s ; removed of bad channels, by averaging between the channels on e i t h e r side i of the bad channel; and corrected f o r baseline curvature by using OLQF. This done, the peak output i s determined and the brightness temperatures of Williams are used to calculate the number of spectrometer output units per degree K e l v i n brightness temperature, for a given receiver gain. The c a l -.o i b r a t i o n s are t y p i c a l l y of the order 16.0/ K, and the A and o B banks generally agreed to within ± 0 . 1 /K. E) DEFZERCAL In doing a l e a s t squares f i t to remove a base-l i n e curve, i t i s necessary to blank out any p r o f i l e so that i t doesn't i n t e r f e r e with the baseline f i t . The program therefore determines which channels to blank out and then reads i n the fudge fac t o r s which were calculated from noise tube c a l i b r a t i o n s made at the same time as the observations being analyzed. As i n TEMP CAL, the gain v a r i a t i o n s and bad channels are removed, and then a subroutine MYOLQF, to i I t should be noted here that these bad channels, which are the r e s u l t of f a u l t y reed switches on the spectrometer out-put producing anomolously high or low readings, should they occur i n one of the channels bounded by some 21-cm l i n e feature, cannot then be removed by a simple averaging process. In t h i s case, i t i s necessary to compare the data at the two frequencies so that, provided the bad channels are not separated from each other by 30KHz (or three channels), - the amount by which the p r o f i l e s are s h i f t e d - then an unambiguous value can be determined f o r the bad channel. This unfortunately was not always the case, so that some of the data had to be rejected. j This wasn't necessary i n analyzing the noise tube c a l i b r a -tions as the plasma noise tube presents featureless broad-band noise to the spectrometer. -41-be described l a t e r , i s used to remove the baseline curvature. This done, the data was c a l i b r a t e d and punched out on cards. F) DIFFCALC This i s a simple program which takes the f u l l p r o f i l e observations and calculates difference p r o f i l e s between the cloud (or source) p o s i t i o n s , and the nearby reference pos i t i o n s . G) ADEFPLOT This program calculates and p l o t s , with the L.S.R. v e l o c i t y as absicca, the average diff e r e n c e p r o f i l e between the source and the reference p o s i t i o n s , and also the expected f l u c t u a t i o n due to non-linear hydrogen gradients. I f we use SRC to represent the on-cloud hydrogen p r o f i l e , and the compass bearings to represent the d i f f e r e n t reference p o s i t i o n hydrogen p r o f i l e s , which are generally a beamwidth away, then i n the case where only four reference positions are used, the difference p r o f i l e s are: (SRC-N), (SRC-S), (SRC-E) and (SRC-W), and the average diff e r e n c e p r o f i l e i s simply: flMECfiGe. PIFF£H£NC£ - ±^ (SRC- N) + ( S R C - S ) _+ ( S * C - E ) + (Sf?C-wj(4-l) This part has been straightforward; how then are we to calculate the expected f l u c t u a t i o n due to non-linear hydrogen gradients? In the sketch at the l e f t , i t i s c l e a r w N(HL) to see that i f the hydrogen gradients are l i n e a r i n going from east to west and north to south, then the difference c i n the hydrogen content at the cloud E N > w s center i s : -42-and i t vanishes. If, on the other hand, the gradients are non-linear, this need not be the case, as the sketch at the right NCW) ill u s t r a t e s . We therefore define the expected fluctuation by the expression: EXPECTED FLUCTUATION = i - [ ^ j - ( ^ J = _L j ( SKC - rJ) + ( S f c C - S ) - (SRC-E) - (SfcC-W)j E M (4-2) where the last expression gives the expected fluctuation in terms of the difference profiles, and the factor of one-half has been introduced so that the RMS noise away from profile position i s the same as in the case of an average difference plot. This i s ju s t i f i e d since we are adding or subtracting the same number of random noise profiles in either case. This is easily generalized to the case of eight reference positions to give: AVERAGE DIFFERENCE = EXPECTED FLUCTUATION = J - f £ ( S R C ^ " R E F i ) "*" £ (SRC-REFOJ ( i.'M.s,fc t »W , 8 (4-3) 4-4) where REFj, refers to each of the eight reference positions, that i s , REF, = N, R£Fi= S , K E F ^ E , Rer^=W, R£Fffl$ and so on. It is important to note here that with only two profiles to deter-mine a gradient, i t i s impossible to t e l l i n what sense i t is non-linear, or whether two non-linear gradients happen to -43-coincide on the cloud p o s i t i o n . I f more time had been a v a i l a b l e , i t would have been possible to take reference p r o f i l e s further out and then f i t a second or higher order k gradient . Had t h i s been the case, we could then use equation (1 -2 ) to calcu l a t e how much of an observed excess or d e f i c i t was due to second or higher order hydrogen gradients, and f i n a l l y be l e f t with the problem of having to explain anything l e f t over. For the time being, however, we must use our d e f i n i t i o n of the expected f l u c t u a t i o n to determine t h i s . H) LSR This program i s b a s i c a l l y a high p r e c i s i o n v e r s i o n 39 of the McRae and Westerhout "Local Standard of Rest Tables", but besides adding p r e c i s i o n , the program also takes into account the earth!s r o t a t i o n . A f t e r reading i n the relevant precessional constants and the time of the observation, includ i n g the J u l i a n Day, ( a l l of which can be obtained from the American Ephemeris and Nautical Almanac), the program then uses the subroutine EPOCH, i n ASTROPAK, to precess both the solar apex and the source p o s i t i o n to the time of observation. This done, the equatorial components of the solar apex motion and the t o t a l LSR v e l o c i t y , (which i s comp-uted by the subroutine LSRVEL, also i n ASTROPAK), are c a l c u l -ated, followed by the LSR v e l o c i t y i n the d i r e c t i o n of the precessed source p o s i t i o n . k This however could be complicated by the fac t that the hydrogen gradients might occur on a small s c a l e , i n which case we would need higher s p a t i a l r e s o l u t i o n to c o r r e c t l y determine what they are. -44-I) ASTROPAK This i s a c o l l e c t i o n of subroutines which tend to be used very often i n astrophysical c a l c u l a t i o n s , and as such are perhaps the most useful part of t h i s l i s t i n g . 1. EPOCH This subroutine uses two other subroutines l i s t e d below, namely NINLIN and FK, i n order to solve the non-l i n e a r precessional equations oi. - Ao + M + N sti^i (^^X^^c^±So^j ( 4 - 5 ) S - S0 + hi A<rOs^ c ( ( 4 - 6 ) where everything i s measured i n seconds of time, the nought r e f e r s to the i n i t i a l , e p o c h , C i s the number of radians per second of time, oi and* & are the r i g h t ascension and d e c l i n a t i o n , and M and N are the precessional constants. (a) NINLIN This subroutine i s a double precision version of the L i b r a r y subroutine NONLIN, and i s used to solve the non-linear precessional equations. The subroutine XKMAX i s within NINLIN, and i s of no consequence here. (b) FK This subroutine i s required by NINLIN and contains the precessional equations i n e x p l i c i t form. 2. LSRVEL In t h i s subroutine, the J u l i a n Day (JULDAY) and P a c i f i c Standard Time (HRPST, MINPST) are read, and then the equatorial components of the t o t a l LSR v e l o c i t y (XLSR, YLSR and ZLSR) ca l c u l a t e d . The subroutine consists of three - 45 -parts: the f i r s t c a l c u l ates the equatorial components of the earth's rotation" 1; the second ca l c u l a t e s the equatorial components of the earth's o r b i t a l v e l o c i t y ; and the t h i r d reads i n the equatorial components of the sun's motion towards the solar apex,through a l a b e l l e d common statement. 3. SUNVEL This subroutine i s used to cal c u l a t e the equatorial components of the motion towards the solar apex. This i s done i n the main program and then read into the subroutine LSRVEL through a l a b e l l e d common statement to avoid having to re-do the c a l c u l a t i o n each time LSRVEL i s c a l l e d . 4. FROMTO This subroutine i s used to convert between d i f -ferent units of angular measure; the procedure to be followed i s explained i n the comment statements at the beginning of the program. 5. MYOLQF This subroutine i s b a s i c a l l y the Libr a r y subroutine OLQF, but i s d i f f e r e n t i n that i t avoids the long v a r i a b l e l i s t of that program. Useful f o r baseline f i t s , i t reads i n the f i r s t , l e s s one, channel to be blanked (N), the t o t a l number of channels to be blanked (M), and the raw data points (Y). From t h i s information, i t calculates the best f i r s t , second or t h i r d order polynomial l e a s t squares f i t to the unblanked raw data, and returns i t through the variable Y for each channel number X. m As i t stands, t h i s c a l c u l a t i o n i s true f o r observations made at D.R.A.O., but i s e a s i l y changed to another obser-vatory as explained i n the program. -46-4-2) The Sources Analyzed If we consider nearby object positions i n TABLE IV to belong to a single cloud, then there are only twenty-four d i s t i n c t clouds for which data was obtained. Of these, six (12, 20, 29, 33, 34, (22,23,39)) were s u f f i c i e n t l y spread out objects that enough nearby reference positions could not be obtained to allow a proper estimate of the expected f l u c -tuation, and hence are not included i n the discussion that follows. Five a d d i t i o n a l clouds (21, 27, 28, 31, 37) had to be abandoned because the bad channels could not be corrected f o r . This l e f t t h i r t e e n objects for which the f u l l a n a l y sis could be made. 4-3) The Results The data from these t h i r t e e n clouds were analyzed by the preceeding programs and the relevant astrophysical parameters determined from the average difference and expected f l u c t u a t i o n p l o t s , four examples of which appear i n FIGURES 4 - 7 . The parameters themselves are l i s t e d i n TABLE VI, about which a few comments are i n order. VLSR I s t n e L.S.R. v e l o c i t y of the observed excess or d e f i c i t . The error i n t h i s quantity due to the averaging of the reference positions i s i0.4Km/sec, while an a d d i t i o n a l error of i 0.8 Km/sec a r i s e s i n deter-mining the v e l o c i t y from the graphs. AV L i s the f u l l feature width at h a l f i n t e n s i t y i n Km/sec and also c a r r i e s an error -47-of ±-0.80 Km/sec. In the next column, i s the column density 19 -2 of atomic hydrogen N(HI), i n units of 10 cm , as determined by equation (2-29). The indicated error i s the same quantity taken from the expected f l u c t u a t i o n p r o f i l e . I t immediately indicates how s i g n i f i c a n t an excess or d e f i c i t i s , and i s always larger than the error due to the temperature c a l i b r a -t i o n . A T i s the estimated depth of an excess or d e f i c i t i n o K brightness temperature, and i s accurate to better than o ± 2 K. In the f i n a l column are comments, con s i s t i n g c h i e f l y of the v e l o c i t i e s of the normal OH emission features i n the same d i r e c t i o n and column d e n s i t i e s of atomic hydrogen which Heiles determined i n his survey. Of the t h i r t e e n objects analyzed, seven did not show any s i g n i f i c a n t excess or d e f i c i t compared to the calcu l a t e d f l u c t u a t i o n s i n the surrounding hydrogen; four showed s i g -n i f i c a n t d e f i c i t s ; and two showed marginal excesses. 4-4) Interpretation of Results Before any attempt i s made at understanding the r e s u l t s of TABLE VI, i t i s important to r e a l i z e that the dense dust clouds l i s t e d there represent, according to the c r i t e r i a we established e a r l i e r , nearly a l l the objects worth observing. I t should not be at a l l s u r p r i s i n g that the work done by the Dutch on L134 (Object #1) and the Taurus dust clouds (Objects #15, 16, 17, 25, 26) should be included i n t h i s l i s t . The -48-reason i s simple - these are two very opaque, high l a t i t u d e objects and there just are not any others as good. Whether or not i t i s f a i r to consider them as prototypes i s a question which i s open to discussion. However, i f we do not, we w i l l most l i k e l y have to conclude that dense dust clouds, as a whole, do not show s i g n i f i c a n t excesses or d e f i c i t s i n t h e i r hydrogen emission. Since t h i s case i s e a s i l y explained i n terms of a constant gas to dust density r a t i o or f l u c t u a t i o n s due to non-linear hydrogen gradients, and r e a l l y t e l l s us no more than we already know about the i n t e r s t e l l a r medium, we w i l l by-pass i t , and consider L134 and the Taurus clouds to be i n d i c a t i v e of the behaviour of i d e a l dust clouds. In the c a l c u l a t i o n s that follow, average values of the parameters i n TABLE VI are being used. I f we f i r s t consider the l i n e width, we f i n d a mean value of 3.6Km/sec f o r the f u l l width at h a l f - i n t e n s i t y . According to equation (2-32), t h i s implies an upper l i m i t to o the k i n e t i c temperature of 56 K. The question then a r i s e s as to whether or not t h i s i s consistent with other temperature determinations. If we consider the case of a cold absorbing cloud, having a mean background brightness temperature T ^ ( o f f ) — 47°K o and an average d e f i c i t of 7.7 K, then according to the theory leading to equation (2-47), the cloud temperature has an upper l i m i t of Tc ^ 39°K and an o p t i c a l depth of Tc ^ in(47/39) - 0.18. -49-On the other hand, the model of a cold cloud embedded i n a hot sheet of temperature T0 and o p t i c a l depth T0 , i f we assume 7;=1250K and use equations (2-50),(2-51) and (2-52), enables us to a r r i v e at the conclusions Tc >/ 39°K and T c>1.5. The r e a l case, i f i n f a c t we are dealing with cold clouds, i s most l i k e l y some unwieldly conglomeration of these two r e s u l t s . A l l other considerations aside, i t would appear that these two methods for determining the cloud temperature are reasonably consistent, and that a cold cloud model w i l l do to explain everything we have discussed so f a r . Unfortunately, at l e a s t two objections can be made. The f i r s t i s how do cold clouds produce excesses? And the second i s how i s i t possible to r a t i o n a l i z e these k i n e t i c or cloud temperatures with the observed OH e x c i t a t i o n temperatures of l e s s than 10 K? As f a r as the f i r s t two objections go, the f i r s t might be handled by cases of hydrostatic equilibrium or cosmic ray d i s s o c i a t i o n . However, we are dealing with cold absorbing atomic hydrogen clouds, so the l a t t e r argument does not r e a l l y n Heiles r a i s e s yet a t h i r d objection by saying that i f we assume that we can detect a feature of say 2 K brightness temperature, and i f the background continuum at 21-cm i s 4°K, then an object would be undetectable i n emission only i f i t s e x c i t a t i o n temperature were les s than 6°K. He then goes on to say that i f t h i s were the case, the emission l i n e would be saturated and produce a s t r i k i n g absorption feature against the background hydrogen. However, he completely ignores t h i s same background hydrogen by using the continuum r a d i a t i o n to estimate the e x c i t a t i o n temperature i n the cloud. -50-hold, since i t assumes abundant amounts of molecular hydrogen. It i s c l e a r the problem i s not getting any le s s complicated as we are now requiring the cloud to be cold enough to absorb and at the same time, have excess emission. The second problem, that of r e s o l v i n g the OH e x c i t a t i o n temp-eratures of l e s s than 10°K with the much higher k i n e t i c temperatures, i s also one which i s not e a s i l y handled, as i t involves the equilibrium time scales f o r the formation of the clouds and the OH, which i n turn involves a number of d i f f e r e n t c o l l i s i o n cross-section rates, and so on. No more w i l l be said about t h i s here, as i t i s a complete subject i n i t s e l f . 4-5) Comparison of Results with Other Work As mentioned i n the f i r s t chapter, the only d e t a i l e d work done on dense dust clouds has been by the Dutch astronomers, Sa n c i s i and Wesselius. One of t h e i r papers was on L134 (Object #1) and the other on the Taurus Dust Clouds of which Objects 15, 16, 17, 25 and 26 i n the present work comprise a part. By superimposing our antenna beam on t h e i r 21-cm l i n e maps of the brightness temperature as a function of and , t h e i r observed decrease of 7.5°K on L134 corres-ponded to an average d e f i c i t of 4.2°K - the value found here. S i m i l a r i l y , the r e s u l t s on the Taurus complex could be compared; they agreed well i n a l l respects, except that the Dutch found an extra d e f i c i t at-*-2 Km/sec. Their measurements, however, were made at a s l i g h t l y d i f f e r e n t l a t i t u d e . A comparison with H e i l e s 1 r e s u l t s i s not as good. -51-To begin with, Heiles placed an upper l i m i t of 3.3 x 10 cm on the column density of the neutral hydrogen d e f i c i t i n the d i r e c t i o n of L134; t h i s i s almost a fa c t o r of two less than the d e f i c i t observed here and i n the Dutch work. One of Heiles' two observed d e f i c i t s does agree with the d e f i c i t obtained on Object #26 of the present work, but the l i m i t s he placed on a nearby object (Object #15) i s o f f by an order of magnitude. It seems that h i s poor s e n s i t i v i t y may be the cause of these and other d i s p a r i t i e s . For the sake of compar ison, Heiles' observed d e f i c i t s or l i m i t s are included i n TABLE VI. 4-6) Concluding Remarks I t i s c l e a r from the range of r e s u l t s obtained here that the question of the behaviour of atomic hydrogen on or near dark dust clouds i s not a simple one to answer. Had most of the clouds analyzed shown a single type of behaviour, statements of a s t a t i s t i c a l nature might have been made. Only measurements on more clouds w i l l resolve t h i s problem. The f a c t that nearly h a l f these objects show no s i g -n i f i c a n t excesses or d e f i c i t s might perhaps be termed s i g n i f i c a n t , but i t i s f e l t that two presently lacking requirements need to be made regarding the measurements of emission on and nearby dense dust clouds. -52-A) The f i r s t i s measurements of higher v e l o c i t y (or f r e -quency) r e s o l u t i o n . Only i n t h i s way w i l l i t be possible to determine whether or not the f u l l widths at h a l f i n t e n s i t y are correct, or whether they are r e s o l u t i o n l i m i t e d . I f the former turns out to be the case, then the only apparent way of r e c o n c i l i n g the high v e l o c i t y dispersion with the low k i n e t i c temperatures i s to say e i t h e r that i t i s not due e n t i r e l y to thermal motions of the emitting atoms, meaning that large scale turbulences,etc. must be considered, or that the width i s a r e s u l t of the f a c t that there are no atoms emitting r a d i a t i o n near the L.S.R. v e l o c i t y of the cloud, that i s , there i s no atomic hydrogen - e i t h e r i t has become molecular or the composition within the cloud i s anomalous. If i n f a c t i t turns out that the features are smoothed out, then very low k i n e t i c temperatures w i l l be indicated, and i n t h i s case, there would be no objection to the cold cloud explanation of d e f i c i t s , although i t i s not c l e a r that the p o s s i b i l i t y of a molecular hydrogen cloud would be excluded, even i f fo r the simple reason that other molecules are found. B) The second i s measurements of higher s p a t i a l r e s o l u t i o n . In t h i s way, the problem of small scale hydrogen gradients could be properly handled. Unfortunately, a problem immed-i a t e l y presents i t s e l f , for the higher our r e s o l u t i o n becomes, the more d i f f i c u l t i t i s to t e l l whether we are looking at a dark dust cloud, or a hole between some star s . This i s e s p e c i a l l y the case at high g a l a c t i c l a t i t u d e s . The only -53-possible so l u t i o n to thi s dilemma i s high scale maps of the brightness temperature i n two dimension at a p a r t i c u l a r v e l o c i t y . In t h i s way, i t may be possible to i s o l a t e clouds and study t h e i r three-dimensional structure. Dark dust clouds, and more generally, the i n t e r s t e l l a r medium, are not as simple as they are sometimes thought to be, but perhaps these types of measurements may help us resolve the problem of whether dense dust clouds contain molecular or atomic hydrogen. -54-Appendix A A LISTING OF COMPUTER PROGRAMS - srs -C MAIN PROGRAMS USED IN 0ARK DUST CLOUD D A T A A N A L Y S I S Q *r '» : *>" V -J* '1^  *>* 'r' -r -v- V ' r 'i s '* : V V V 'r :>* '»* '»' 'I1 "I* ^1* -»"• *!* '<*• -v* 'I* -r -Y^  V ->* V V *>* *!' -I" ^* '! : v -!; 'I- -A -! ; *,S V V : . : V ^* C c c C . C PTC — PROGRAM TO CCNVERT PAPER TAPF TO MAG TAPE AND PUT C N F I L D IMENSION A (.100) C PAPER TAPES ARE F I R S T RF AD ONTO MAG TAPE IN HEXADECIMAL RY THE C COMPUTER C E N T E R . AT THE END OF T H I S TAP F THEY P u l THE Mu>=n P v  C 512 IN H E X A D E C I M A L , 2 5 6 I S PUT AT THE END OF THE I N D I V I D U A L TAPES C AS THEY . ARE. RE AD IN . M= 1 M E A N S . R E A D BANK A D A T A , >•'< = 2 »0 A N K R IC = 1 2 8 1.1. ... M=0 ....... 1 M=M + 1 C THE REST OF THF PROGRAM JUST READS A S C I I CHARACTERS AND  GENERATES THE CORRESPONDING DECIMAL NUMBERS. E V E R Y T H I N G ELSE IS IGNORED _..„ . _ DO 8 J = l , 1 0 0 2 .MULT= 1 K=0 I F R A C = 0  NU=0 3 C A L L PT..A.P.E.(..I...L.. I=1ABS(I ) IF( I .EQ.,5.12 )_..GG TO. 20 I = LOR( I, IC ) I F ( I F R A C . E Q . 1 ) GO TO 7  C 1 2 8 = L E A D E R / T R A I L E R 1 3 3 - L F 141=CR 160=SPACE 1 7 3 = - 1 7 4 = . IF..(. I . E Q . 1 2 . 8 )... GO TO. 3 I F d . E Q . 1 3 8 ) GO TO 3 . IF ( I . EO . 1.4.1 ) GO TO 3 I F ( I .E 0 . 1 6 0 ) GO TO 3 I F ( 1 . E O . 173) GO TO 4  I F d . E Q . 1 7 4 ) GO TO 5 GO. TO .6... ...... 4 M U L T = - 1 GO TO 3 5 IFRAC=1 GO TO 3 :  6 N Q = N 0 * 1 0 + ( 1 - 1 7 6 ) K = K + 1 I F ( K . G T . 2 C ) GO TO 20 GO TO 3 7 R= 1-176 R N'T = NO 4-R / 1 0 .  RNO=RNO*MULT 8 A(J )=RNO C WRITE THE NEXT ICO NUMBERS INTO A F I L E ON D E V I C E 8 WRITE (8 , 10 ) ( A ( J ), J = 1, ICO ) 10 FORMAT( IGF 7 . 1 ) C IF GANK B DATA HAS BEEN READ ( M = 2 ) , D ISCARD THE REST OF THE C INFORMATION ON THE T A P E I F I M . L T . 2 ) GO TO 1 9 CAL L PT AP E( I ) I = IAhS ( I ) C IF THE END CF A TAPE HAS BEEN REACHED ( 1 = 2 5 6 ) , RUT ALL TH[ C TAPES H A V E N ' T ft E EN READ (1 = 5 1 2 ) , READ TF: [• _NE X T T A P R C C IF ( I . E G . 5 1 2 ) GO TG 20 IF( I .NE . 2 5 6 ) GO TO 9 GO TO 11 20 STOP . . c END c c c FUDGE FACTOR — PROGRAM TO C A L C U L A T E CORRECTION FACTORS FOR THE c GAIN V A R I A B I L I T Y OF THE I N D I V I D U A L SPECTROMETER CHAMNALS D I MENS 1 ON X( 10 0) , Y( 100) , YF ( 100) , Y O U 00) , WT (1 00 ) , F (100 ) , Al F ( ] OC ) D IMENSION S ( 11 ) , S I GM A ( 1 0 ) . A ( 1 0 ), B { 10 ) . P ( 1 I ) . A ?F ( 1 0 n) , B 1 f-(  n D lMENS ICN C ( 1 0 0 ) , D < 1 0 0 ) , E ( 1 0 0 ) , G ( 1 0 0 ) , H ( 1 0 0 ) , G ( 1 0 0 ) .. .. D IMENSION B2F( ICC) ... L O G I C A L LK c. . .. . READ I N THE CHANNEL NUMBERS (1 TO 100 ) R E A C ( 5 , 50) ( X( 1 ) , 1=1, 100 ) c READ IN THE WEIGHTS A S S I G N E S TO T HF D I F F E R E N T CHANNEl S c ACCORDING TO THEIR R E L I A B I L I T Y R E A C ( 5 , 70) (WT( I ) , 1=1 , 1 0 0 ) .. . DO 10 1 = 1 , 1 0 0 A 1F ( 1 ) = 0..C A2F ( I ) = 0 . 0 B 1 F ( I ) = 0 . 0 10 B 2 F ( I ) = 0. 0 c ,I.N_ WHA.T_F_G.LL.OW.S.f A AN0 Q REFER . TO. BANKS A AND. B OF THE c SPECTROMETER O U T P U T , ! AND 2 REFER TO THE TWO F R E Q U F N C I E S AT c WHICH O B S E R V A T I O N S WERE MA DE. . . . THE.. SUMS BEING MADE 'ARE FO c C A L C U L A T I N G AVERAGE FUDGE FACTORS FOR BANKS A AND B AT THE c D I F F E R E N T F R E Q U E N C I E S 1 AND 2 . c DATA PUT IN THE ORDER A , B FOR ONE FREQUENCY FOR ALL THE DATA c ._ AND. A , ...B FOR THE SECOND. PR EGU ENCY . FOR ALL THE DATA. DO 99 I N = 1 , 6 2 RE. AC ( 8., .60. J ( Y( I ) , 1 = 1 , 10 0 ) K=2 M= 100 L K = . T R U E . NWT = 1 ~ c USE THE L I B R A R Y ROUTINE OL OF TO REMOVE THE B A S E L I N E AND c ... C A L C U L A T E THE BEST F I T YF TO THE DATA Y . C A L L G L Q1 - (K , M , X , Y , Y F,Y 0 , W T , N W T , S , S I G M A , A , B , S S , L K , P ) N = K + 1 DO 22 1 = 1 , 1 0 0 c C A L C U L A T E THE FUDGE F A C T O R S , F ( I ) F( I ) = YF< I ) / Y ( I ) 22 IF ( I N / 2 * 2 . N F . IN) Q( I )=F( I) I F ( I N / 2 * 2 . N E . I M ) G C TO 23 IF( IN.1 T . 31) GO TO 29 DO 32 1 = 1 , 1 0 0 c C A L C U L A T E D I F F E R E N C E OF FUDGE FACTORS FOR RANKS A AMD H H ( I ) = Q ( 1 ) - F ( I ) 32 B2F ( I ) = 02 F ( I ).+ F ( I ) GO TO 2 4 29 DO 33 1 = 1 , I C O H ( I ) = 0 ( I ) - F ( 1 ) 33 3 IF( I )=B1F( 1 ) + F( I ) GO TC 2 4 23 WRITE ( 6 , 2 5) IF( IN . L T . 3 1 ) GO TO 28 00 30 1 = 1, 100  - S t -3 0 A2F( I I =A2F( I )+F( I ) GO TO 27 .. . . ... 28 DO 31 1 =1 , 1 0 0 31 . A 1F ( I ) = A 1F ( I ) + f ( I ) GO TO 2 7 24 WRI TF (6 , 2 6 ) 27 W R I T E ( 9 , 5 0 1 ) 501 FORMAT(7 2X) WRI T E ( 9 , 502) ( F ( I) ,1=1 , 1 0 0 ) 502 FORMAT ( 1 0 F 7 . 3 ) . WRITE (6 , 5 0 0 ) (F ( I ), 1=1 , 100 ) IF ( 1 N / 2 * ? . E 0 . I N ) WRI TF (6 . 5 0 3 ) ( H ( I ) , I =1 . 1 0 0 ) 5U3 FOR MAI ( / 10 ( 10 F 1 0 . 3 / ) ) 25 . FORMAT ( ' I V , / / . 5 0 X ,« * * * B A N K A * * . * ' ) 26 F (j R M A T ( / / 5 0 X , « * * *6ANK B * * * ' ) 50 FOR MAT (1.0. F.6 .1 ) 60 F O R M A T ( 1 0 F 7 . 1 ) 70 FORMAT ( 1.0F5. 1 ) 200 F O R M A T ( / / 1 X , I 5 , 5 X , 1 1 E 1 1 . 3 ) 3.0 C. .... FORMA.T (./.'.SUM .OF SQUARES I S ' , E 1 5 . 5 ) . 350 FORMAT ( / 4 9 X , ' Y - A X I S D I F F E R E N C E S FROM BEST F I T ' ) 400 FORMAT < / l 0 F 1 0 . 1 ) 4 5 0 F O R M A T { / 5 6 X , ' F U D G E FACTORS A R E ' ) 500 FORMAT (/ 10F10 . 3 ) 550 FORMAT ( ' 1 ' , / / 3 0 X , ' * * * I N I T I A L BANK A FUDGE F A C T O R S * * * ' ) 60 0 FORMAT ( . / / 3 0 X , . . ' * * * F INAL ..BANK. A. .FUDGE. FAC T O R S * * * ' > 6 50 FORMAT(»1« , / / 3 0 X , ' * * * IN IT I AL BANK B FUDGE FACTOR S * * * ' ) 700 . F O R M A J i / . / 3 0 X , ' * * *F I N AL BANK P. FUDGE. F A C T O R S * * * ' ) 99 CONTINUE DO 900 1 = 1 , 1 0 0 A 1 F ( I )=A1F( I ) / 1 5 A 2 F ( I ) = A2 F{ I ) / 16 B1F ( I ) =81 F ( I ) / 15 9 0 0 B2F.(. I ) = B2F ( I.) / 16 C OUTPUT THE AVERAGED FUDGE FACTORS WP I TE ( 6 , 550 ) W R1 T E ( 6 , 5 0 0 ) ( A 1F ( I ) , I = 1, 10 0 ) W R I T E ( 6 , 6 ( ) 0 ) WRI TE( 6 , 5 0 0 ) ( A 2 F ( I ) ,1=1 , 1 0 0 ) - — •• - • WRITE. (6 , 6 50 ) WRITE(6 , 5 0 0 ) (B1F (I ) ,1 = 1 , 100) W R I T F ( 6 , 7 0 0 ) • -W R I T E ( 6 , 5 0 0 ) ( B 2 F ( I ), 1=1, 100) ... WRI TE ( 9 , 5 0 1 ) W R I T E ( 9 , 502 ) (A 1F( I ) , I=1 , 1 0 0 ) W R I T E ( 9 , 5 0 1 ) W R I T E ( 9 , 5 C 2 ) ( B 1 F ( I ) ,1=1 , 1 0 0 ) W R I T E ( 9 , 5 G 1 ) W R I T E ( 9 , 5 0 2 ) ( A 2 F ( I ), 1 = 1 , 1 0 0 ) W R I T E ( 9 , 5 0 1 ) WRIT E ( 9 , 5 02 ) (B 2 F( I ),I = 1 , 100) DO 901 1=1 , 1 0 0 C( I )=A IF ( I ) - A 2 F ( I) 0 ( I ) = B1 F ( I ) - R 2 F ( I ) E( I )=A1F( I ) - B l F ( I) 901 G( I )=A2F( I J - B 2 F ( I ) WR I T E ( 6 , 5 0 4 ) (C( I ) , I = 1, 1 00 ) , ( D ( I ) , I = 1, 1 ( 0 ) , ( E ( I ) , I =1 ,1 00) , ( G ( I ) , I #1 , 1 0 0 ) 504 FORMAT(4( / / 10( 10F 1 0 . 3 / ) ) ) DO 601 1 = 1, 100 A IF ( I ) A 11- ( I ) =! 15 .+A2F ( I ) * 1 6 . ) / 3 1 . 601 B 1 F ( I ) = ( L > 1 F ( I ) * 1 5 . + B 2 F ( 1 ) * 1 6 . ) / 3 1 . WRI TE ( 9 , 5 0 1 ) W R I T E ( 9 , 5 0 2 ) ( A 1 F ( I ) , 1 = 1 , 1 0 0 ) W R I T E ( 9 , 5 0 1 ) WRI TF ( 9 , 5fi? ) ( B l F f I ) . I =1 .1 00 ) W R I T E ( 6 , 6 0 2 ) 602 F O R M A T ( ' 1 ' , / / 3 0 X , ' O V E R A L L AVERAGE BANK A FUDGE F A C T O R S ' WRI T E ( 6 , 500) ( A 1 F ( I ) , I=1 , 1 0 0 ) W R I T E ! 6 , 6 03 ) ) 603 F O R M A T ( ' I ' , / / 3 0 X , ' O V E R A L L AVERAGE BANK B FUDGE F A C T O R S ' WRI TF( 6 . 5 00) (R 1 F( I ) .1 =1 .1 00) ) STOP C . c c END - . -c NOISE — PROGRAM TO C A L C U I A T F THF MEAN NOISE 1 n /F I AND TTS . . S . c D I S P E R S I O N FROM THE NOISE TUBE C A L I B R A T I O N P R O F I L E S DI MENS ION. A (l.CO ) , B U O O ) , FA( 100 ), FB( 100) D IMENSION X ( 1 0 0 ) , Y ( 1 0 0 ) , Y F ( 1 ( 0) , Y D ( 1 0 0 ) ,WT (100 ) , S (4 ) , S I GMA(3 ) , A O ( tl ) , BO. (3 ) , P. ( 4 ) _ L O G I C A L LK 1 K= . FAl SF . K=0 .... NWT = 0 . . ___ _ . . M=100 c . READ . IN THE AVERAGE PUDGE FACTOR VALUES ( F A , F B ) R E A D ( 5 , 1 4 ) (FA ( I ) , I = 1 , 1 0 0 ) , ( FB ( I ) f I = 1 , 100) 14 FORM AT ( 10 F7 . 3 ) DO 18 1 = 1 , 1 0 0 18 X( 1 )=J _ 15 K = K +1 C . READ IN...BANK A... OF ...A N O I S E RUN R E A D ( 8 , 3 ) ( A( I ) ,1=1 , 1 0 0 ) 3 F O R M A T ( 1 0 F 7 . 3 ) C REMOVE THE E R R A T I C CHANNELS IN BANK A .... DO 16 .1 = 1 , 100 „ _ 16 A( I )=A( I »*FA( I ) .... A( 25) = 0 . 5 * ( A ( 2 4 ) + A ( 2 6 ) ) A ( 3 0 ) = 0 . 5 * ( A ( 2 9 ) + A ( 3 1 ) ) A ( 4 4 ) = 0 . 5 * ( A ( 4 3 ) +A(45 ) ) A ( 5 1) = ( 2 . / 3 . ) * A < 5 0 ) + ( A ( 5 3 ) / 3 . ) A ( 5 2 ) = ( A ( 5 0 ) / 3 . ) +( 2 . / 3 . ) *A ( 53) 1. A ( 8 1 ) = 0 . 5 * ( A ( 8 0 )+A(82 ) ) c C A L C U L A T E THE AVERAGE VALUE OF THE BANK A NOISE S I G N A L , AV G A SUM=0.0 DO 5 1 = 1 , 100 Y( I ) = A( I ) 5 SUM = SUM + A ( I ) A V G A = S U M / 1 U G . 0 SUM=0. DO 4 1 = 1, 100 Sl)M=SUM+ ( A ( I ) - A V G A )  4 CONTINUE C C A L C U L A T E THE D I S P E R S I O N N E G L E C T I N G THE B A S E L I N E , A N O T Z A N O I Z = S Q R T ( S U M / 9 9 . ) K0=3 C USE L I B R A R Y SUBROUTINE GLQF TO REMOVE B A S E L I N E AND C A L C U L A T E C PROPER D I S P E R S I G N , A N D ! S E - i f 9 -CAL L OL. (JF ( K C ^ S X , Y , Y F , YQ, WT,NWT, S , S 1GMA , AO ,3 0 , S S , LK , P ) ANOISfc' = S O R T ( S S / 9 9 . ) WR I T F ( 6 , 6 ) AV GA,ANO IZ , A N 0 I$E 6 F O R M A T ( 5 X f ' BANK A : * , ' A V E R A G E CAL = ' , F 7 . 1, 5 X» 'RMS NOISE = • , F 7 , 5 X , F 7 . 1 ) _X R FAG IN PAN K B OF A NOT S F RUN  R E A D ( 8 , 3) ( b i 1 ) t 1 = 1 , 1 0 0 ) C REMOVE. THE E R R A T I C CHANNELS IN BANK B DO 17 1 = 1 , ICO 17 B d )=B( I ) * F B ( I ) . . . B( 1 2 ) = G . 5 * ( P ( 11)+B( 13) ) B ( 3 M = 0 . 5 * < B ( 3 3 ) +E(35 ) )  B ( 3 6 ) = 0 . 5 * ( B ( 3 5 ) + B ( 3 7 ) ) B ( 4 l > = 0 . 5 * ( B ( 4 0 ) + B ( 4 2 ) ) B(46)=0.8*B{4>:> ) + 0 . 2 * 8 ( 50 ) B( 4 7 ) = 0 . . 4 * B ( 45) + C. 6 * B ( 50) B ( 4 8 ) = G . 6 * 6 ( 4 5 ) + 0 . 4 * 8 ( 5 0 ) B ( 4 9 ) = 0 . 2 *B ( 45) +C. 8 *B ( 50)  B ( 5 9 ) = 0 . 5 * ( B ( 5 8 ) + B ( 6 0 ) ) . C. C A L C U L A T E THE AVERAGE VALUE. OF THE. BANK E NO IS E SI GN AL , A VGR SUM=0. DO 8. 1 = 1, 10.0 Y ( I ) = 3 ( I ) _8 SUM-SL1M+P ( I )  AVGB=SUM/ 100 . SUM=0.. DO 7 1 = 1 , ICO SUM=S.UM+( B( I ) -AVGB ) * * 2 __ 7 CONTINUE _C C A L C U L A T E THE D I S P E R S I O N N E G L E C T I N G THE P A S F L I N E , B N O I Z  BNOIZ=SQRT ( S U M / 9 9 . ) K0=3 C USE L I B R A R Y SUBROUTINE OLQF TO REMOVE B A S E L I N F AND C A L C U L A T E _.C . . PROPER D I S P E R S . I O N , BNO I SE C A L L OL C F ( K C , M , X , Y , Y F , Y C , W T , N W T , S , S I G M A , A O , S C , S S , L K, P) B N O I S E = S Q R T ( S S / 9 9 . )  WRIT E ( 6 , 1 1 ) AV G 6» BNO I Z ,BNO IS E ...11 FORMAT ( 5X , ' .BANK 3. . : . ' ,.' AVERAGE CAL = ' , F7 . 1, 5X , ' RMS NOISE = ' , F 7 . it, 5 X , F7 . 1/ ) AVGA=0. 5* (AVGA+AVGB) _ ANOIZ= 0 . 5 * { A N 6 I Z +BNO I Z ) AN0 ISE = 0 . 5 * ( A N O I S E + GNO IS E )  C P R I N T OUT THE AVERAGE NOISE TUBE C A L I B R A T I O N L E V E L AND C ITS D I S P E R S I O N W R I T E ( 6 , 1 2 ) A V G A , A N O I Z , A N O I S E 12 FORMA T( 5 X , ' A VE RAGE C A L , BANKS A AND B = ' » F 7 . 1 , 5 X , ' A V E R A G E N O I S E T / /BANKS A AND B = ' , F 7 . 1 , 5 X , F 7 . 1 / / > I F ( K . L E . 3 C ) GO TO 15  20 STOP END C C C _C TEMP CAL — PROGRAM TO C A L C U L A T E THE NUMBER OF SPECTROMETER QDTP! C UNITS PER DEGREE K E L V I N BRIGHTNESS TEMPERATURE BY A N A L Y Z I N G THE C DATA FROM THE 2 1 - C M . L I N E STANDARD C A L I B R A T I O N P R O F I L E S DI MENS ICN A ( 1.00 ) ,B ( 100 ) , FA ( 100 ) , FB( 100 ) DI MENS ION X( 100) , Y ( 100) , Y F ( 100) , Y D { 1 0 0 ) , W T ( 1 0 0 ) , S(4 ) , S TCMA(3 ) ,AO( H ) , B C ( 3 ) , P (4 ) LOGICAL LK — 6,0-NWT =0 L K = . F A L S E . K = 0 c READ IN THE AVERAGE FUDGE FACTORS R E A D ( 5 , 1 4 ) (FA<I ) , 1 = 1 , 1 0 0 ) , ( F B ( I » , 1 = 1 , 1 0 0 ) 14 FORMAT ( 1 OF 7 . 3) 15 K = K + 1 . C READ IN THE PEAK B R I G H T N E S S TEMPERATURE OF THE RELEVANT C C A L I B R A T I O N P R O F I L E AND M, THE NUMBER OF CHANNELS WHICH ARE C NOT BLANKED IN TFE GLQF LEAST SQUARES FIT TO THE B A S E L I N E C TH IS PART OF PROGRAM MLST BE CHANGED FOR D I F F E R E N T OBSERVATIONS I F ( K.l. E . 1 6 ) 1R=51 . 0 I F ( ( K . G T . 1 6 ) . A N D . ( K . L E . 2 0 ) ) T R = 9 9 . I F ( K . G T . 2 C ) T B = 7 2 . I F ( K . L E . 1 6 ) GO TO 30 .. I F ( (K . C T . 1 6 ) . A N D . ( K . L E . 2 0 ) ) GO TO 31 I F ( K . G T . 2 0 ) GO TO 30 30 M=6 5 C READ I N BANK A FCR 13 AT A WITH CHANNELS 61 TO 95 BLANKED . . READ( 8, 3). ( A( I ) , 1 = 1 , 100) 3 FORMAT ( 10F7 . 3 ) . C ... .. CORRECT. CHANNEL G A I N S . BY USING FUDGE F A C T O R S , AND c REMOVE BAD CHANNELS IN BANK A DO 16 1=1 .100 16 A ( I ) = A ( I ) * F A ( I ) A(.25)=0.5*.( .A(2.4).+A( 26) ) A ( 3 0 ) = 0 . 5 * ( A ( 2 9 ) + A ( 3 1 ) ) . A ( 4 4 ) = 0 . 5*( A( 43 . . + A ( 45) ) A ( 5 1 ) = ( 2 . / 3 . ) A ( 50 ) + ( A ( 5 3 ) / 3 . ) A ( 5 2) = ( A ( 50 ) / 3 . ) + (2 . / 3 . ) * A ( 53 ) A ( 8 1 ) = 0 . 5 * ( A ( 8 0 ) + A ( 8 2 ) ) ;_ C DETERMINE W.HAT . .CHANNEL THE PEAK. . OUT PUT OCCURS, IN AMA X=0. DO 5 1=1, 10 0 I F ( A ( I ) .GT .AMAX) GO TO 4 GO TO 5 4 AMAX = A( I ) A I = I 5 CONTINUE DO 33 1=1 ,60 X( I )=I 3 3 Y ( I ) = A ( I ) DO 34 1 = 6 1, M . X( I ) =1 + 3.5 __ 34 Y< I ) = A( 1 + 35) K0=3 C A L L 0 L. OF ( K 0 , M , X , Y , Y F , YD , W T, NWT, S , S I GMA., AO , BO , SS , L K , P ) C C A L C U L A T E THF: B A S E L I N F BELOW THE PEAK ACCORDING TO THE ORDER C OF THE PC LY NOMIAL F IT I F ( KO. E 0 . 3 ) GC TC 43 I F ( K O . E 0 . 2 ) GO TO 4 2 BAS EA.= P (1 ) +P (2.)* A l . GO TO 44 42 B AS E A= P ( 1 ) + ( P ( 2 ) +P ( 3 ) * A I ) * A I GO TO 44 43 B A S E A = P ( 1 ) + ( P ( 2 ) + ( P ( 3 ) + P ( 4 ) * A I ) * A I ) * A I C C A L C U L A T E T H E . P E A K OF THE BANK A SPECTRUM 44 P E A K A = A M A X - B A S E A WRI TT( 6 , 6 ) A MA X , AI , K C , B A S E A , P E A K A 6 FORMAT ( 5X , • BANK A : S ' A M A X = ' , F 7. 1, 5 X , ' A I = « , F 5 . 1 , 5 X , • K.!l = — (ol-# » 5 X , ' B A S E A = 1 ,1-7.1 » 5 X , ' P E A K A = » , F 7 . 1 ) C REPEAT FROM STATEMENTS 30 TO 6 FOR BANK B R E A D ( 8 , 3 ) ( B ( I ) ,1=1 , 1 0 0 ) DO 17 1 = 1 , 1 0 0 . . . 17 B ( I. ) = B ( I ) * F B ( I ) B( 1 2 ) = 0 . 5 * ( R ( H ) + B ( 1 3 ) )  B( 34 )=0 . 5*( B( 33)+B( 35) ) B ( 3 6 ) = 0 . 5 * ( B ( 3 5 ) +B(37 ) ) B ( 4 1 ) = 0 . 5 * ( B ( 4 C ) + B ( 4 2 ) ) B ( 4 6 ) = 0 . 8 * B ( 4 5 ) + 0 . 2 * B ( 50) B ( 4 7 ) = 0 . 4 * B ( 4 5 ) + 0 . 6 * 0 ( 5 0 ) B ( 4 8 ) = Q . 6 * B ( 4 5 ) + 0 . 4 * B ( 50)  B ( 4 9 ) = 0 . 2 * B ( 4 5 ) + 0 . 8 * B ( 5 0 ) B( 59) = C. .5* ( B( 5.8)+B ( 60) ) BMAX=0 . DO. 8 1 = 1., 10.0 I F ( B ( I ) . G T . B M A X ) GO TO 7 GO TO 8  7 B M A X = B ( I ) R I = 1 „ _ ___ 8 CONTINUE DO 53 I = 1 , 6 0 X{ I ) = I 53 Y ( I ) = B( I )  DO 54 1=6 1,M X( I.) = I + 3 5 54 Y ( I ) = B ( I + 3 5 ) KG = 3 .. C A L L GL QF(KO » M , X , Y , Y F » YD,WT,NWT » S » S IG M A , A O , B O , S S » LK » P ) I F ( K O . E Q . 3 ) GO TO 6 3  IF ( KO. EQ. 2) GO TG 62 BASEB=P( 1 ).+ P( 2.) *B I GO TO 6 4 62 Q A S E B = P ( 1 ) + ( P ( 2 ) + P ( 3 ) * 8 l ).*RI. GO TO 6 4 6 3 B AS F B= P (1 ) + ( P ( 2 ) + ( P ( 3 ) +P ( 4 ) * B I ) * B I ) *B I  64 P E A KB = B MA X - B A S E B WR I T E ( 6 , 1.1 ) . BM AX , B I., KO , B A S E B , P.E A KB 11 F O R M A T ( 5 X , 1 BANK B : ' , ' B M A X = • , F7 . 1, 5 X , ' A I = ' , F 5 . 1 , 5 X , •KO = ' , ! .._ #,5X,«RASE.B = ' , F 7 . 1 , 5X , '. PE A KB = ' ,.F 7 .1 / ) P E A K A = P E A K A / T B PEAKB=PE.AKB /TB  PEAK.= ( PEAKA + P E A K 8 ) / 2 . W R I T E ( 6 , 12.) P E A K A , P E A K S , PEAK 12 FORMAT (5X , ' N U M B E R OF U N I T S PFR DEGREE K E L V I N , BANK A , BANK B, AN # THEIR AVERAGE VALUE = • , 5 X , 3 ( F 6 . 1 , 5 X ) / / ) I F ( K . L T . 4 9 ) GO TO 15 GO TO 2 0  C REPEAT FROM STATEMENTS 30 TO 12 FOR DATA WITH CHANNELS 5 "TG 65 C BLANKED OUT IN THE OLOF LEAST SQUARES F I T 3 1 M=4 0 R E A D ( 3 , 3 ) ( A ( I ) , 1 = 1 , 1 0 0 ) DO 18 1=1 ,100 18 A ( 1 ) =A ( I ) *F A ( I )  A ( 2 5 ) = 0 . 5 * ( A ( 2 4 ) + A ( 2 6 ) ) A ( 3 0 ) = 0 . 5 * ( A ( 2 9 ) + A ( 3 1 ) ) A ( 4 4 ) = 0 . 5 * ( A ( 4 3 ) + A ( 4 5 ) ) A ( 5 1 ) = ( 2 . / 3 . ) * A ( 5 0 ) + ( A ( 5 3 ) / 3 . ) A( 5 2) = ( A ( 5 0 ) / 3 . ) + ( 2 . / 3 . ) * A ( 5 3 ) A( 81 ) = 0 . 5 * ( A( 80)+A( 82) ) -<u-AMAX = 0 . DO 13 1 = 1 , 1 0 0 IF ( A( I ) . G T . A M A X ) GO TO 24 GO TO 13 24 AHA X=A( I ) A T = r 13 CONTINUC DO 7 3 1=1 ,5 X ( I ) = I 73 Y ( I ) = A ( I ) . DO 74 1=6, M X(T1=1+60 7 4 Y ( I ) = A ( I + 6 0 ) . K0=3 CALL O L Q F ( K G , M , X , Y , Y F , Y D , W T , N W T , S , S I G M A , A O , 8 0 , S S , L K , P ) I.F( K 0 . E Q . . 3 ) G O . TO 83 . . . I F I K 0 . E Q . 2 ) GO TO 8 2 RAS1 A = P ( 1 ) + P (2 ) *A1  GO TO 84 82 . BASE A= P ( 1) + ( P ( 2 ) +P (.3.).* A I )* A I GO TO 8 4 8.3 . B A S E A = P ( 1 ) + ( P ( 2 ) + { P ( 3 ) + P ( 4) * A I ) * A I ) * A I 84 PE AKA=A MAX-B AS E A W R I T E ( 6 , 6 ) ' A M A X , A I , K 0 , P A S E A , P E A K A R E A D ( 8 , 3) ( 8 ( I ) , I = 1 , 10 0 ) DO 1 9 .1=1 ,1 00 _. 19 B ( I ) = B ( I ) * F B ( I ) _.. B ( 1 2 ) = 0 . 5 * ( B.( .1 1 )+B( 13) ) B ( 3 4 ) = 0 . 5 * ( B ( 3 3 ) + B ( 3 5 ) ) B l 3 6 ) = 0 . 5 * ( B ( 3 5 ) + B ( 3 7 ) ) B ( 4 l 1 = 0 . 5 * 1 B ( 4 0 ) + B ( 4 2 ) ) B ( 4 6 ) =.0..8*.B.(45).+ 0 . 2 * , B ( 5 0 ) B( 4 7 ) = 0 . 4 * B ( 4 5 ) + 0 . 6 *B( 50) B ( 4 8 ) = 0 . 6 * 8 (45_)+0 .4*B( 50 ) B ( 4 9 ) = 0 . 2 * B { 4 5 ) + C . 8 * B ( 5 0 ) B ( 5 9 1 = 0 , 5 * ( B ( 5 8 1+B(60) ) BMAX=0. . DO 2 8 I =1 ,..10.0 I F( B( I ) .GT . BMAX ) GO TO 27 GO TO 2 8 27 B M A X = B ( I ) B I = I 28 CONTINUE DO 9 3 1=1 ,5 X ( I ) = I 9 3 Y ( I ) = B ( I ) DO 94 1=6,M X ( I ) = 1+60 94 Y ( I ) = B ( I + 6 0 ) K0= 3 CAL L OLQF ( KO,M , X , Y , Y F , Y D, W T ,.NWT , S , S I GMA, AO , RO, SS , L K , P 1 I F ( K u . E Q . 3 ) GO TO 103 I F ( K 0 . E Q . 2 ) GO TO 10 2 B A S E R = P ( 1 ) + P ( 2 ) * B I GO TO 104 102 B AS E B= P ( 1 ) + ( P ( 2 ) +P ( 3 )* B 1 ) * B I GO TO 104 10 3 BASEB=P( 1 > + (P( 2) + (P ( 3)+P( 4 ) * B I ) *BI )*R1 104 PEAKB= B.MAX-BAS t B WRI TF < 6 , 1 1 ) BMAX , B l , K O , B A S F B , P E A K B PEAK A= P F A K A / T B P E A K B = P E A K 8 / T B P E A K = ( P E A K A + P E A K B ) / 2 . WRITE ( 6 , 12) P E A K / S P E A K B , P E A K I F ( K. L E . 4 7 ) GO TO 15 STOP  END OEFZERCAL — PROGRAM TO ZERO AND C A L I B R A T E 21 -CM L I N E PROF I L L S PI MENS I ON X ( I OO) , S ( 1 PO) . T ( 1 00 ) , F A (100 ) t FP, ( I 0 Q ) . FF A ( I 0 0 ), F F R( 1 (.;"• ) L = 0 N + 1. TS.. THE. F I R S T . CHANNEL B L A N K E D . I N THE OL QF B A S E L I N E FIT M IS THE TOTAL NUMBER OF CONSECUTIVE CHANNELS TO BE BLANKED N=40 . M = 5 0 K = 0  L = L + 1 DO .4 4. 1 = 1 , 1.00 . ; FF A ( I ) =0 . C F I B ( I ) = 0 . 0 CAL = NUMBER OF UNITS PER DEGREE K E L V I N BRIGHTNESS TEMPERATURE R F A O < 5 , 2 0 ) GAL  FORMAT ( F7 . 1 ) KF = 0 _ _ _ KF = KF+ 1 REAL ( 5 , 1 ) FOR MAT(72X ) READ IN THE BANK A AND 0 FUDGE FACTORS (F A , F 9) FOR THE P ART ICULA SET OF OBSERVATIONS B E I N G ANALYZED AND C A L C U L A T E AVERAGE VALUES RE AD ( 5 ,2 ) ...(FA ( I ) , 1 = 1 , 1 0 0 ) F O R M A T ( 1 0 F 7 .3) READ ( 5 , 1 ) . ... R E A D ( 5 , 2 ) ( F B ( I ) ,1 = 1 , 1 0 0 ) DO 3 1 = 1 , 1 0 0  F F A ( I ) = FF A( I )+ FA ( I ) FFB ( I ) =FFB (.1.) +FB.( I ) _ CONTINUE I F ( ( L . E Q . 1 ) . A N C . (KF . EQ . 2 ) ) GO TO 4 2 I F ( ( L . E C . 2 ) . A N D . ( K F . E Q . 2 ) ) GO TO 42 I F ( ( L • E Q . 3 ) . A N D . ( K F .EQ . 2 ) ) GO TO 42  GO TO 41 DO 4 3 1 = 1 , 1 0 0 FA( I )= FFA( I J /K F FB( I ) = F F B ( I ) / K F CONTINUE . K=K +1  R E A D ( 8 , 7 ) (S( I ) , 1 = 1 , 1 0 0 ) FORMAT( 1 0 F 7 . 1) I F ( M O D ( K , 2 ) . EQ .0 ) GO TO 6 U S E . F U D G E FACTORS TC CORRECT CHANNEL GAINS AND THEN AVERAGE OUT BAD CHANNALS I N BANK A DO 5 1 = 1, 10 0  S ( I ) = S ( I ) * F A < I ) S ( 1 ) = S ( 2) S (4 )=0 . 5 * (S (3 ) +S (5 ) ) S( 25) =0. 5*( S( 24) + S( 26) ) S ( 30 ) = 0 . 5 * ( S( 2 9 ) + S( 3 1) ) S < 4 4 ) = 0 . 5 * ( S ( 4 3 ) + S ( 4 5 ) ) S ( 5 1) = ( 2 . / 3 . > * S < 5 G ) + ( S ( 5 3 ) / 3 . ) S ( 5 2 ) = ( S ( 5 0 ) / 3 . } + ( 2 . / 3 . ) * S ( 5 3 ) S ( 8 1 ) = 0 . 5 * ( S ( 8 0 ) + S ( 8 2) ) S ( 8 3 ) = 0 . 5 * 1 S ( 8 2 ) + S ( 8 4 ) ) C A L L MY OL QF ( K , N , X , S ) C STORE TOE ZEROED BANK A DATA IN T ( I ) 12 DO 13 1 = 1 , 1 0 0 13 T ( I ) = S ( I ) GO TO 4 C USE FUDGE FACTORS TO CORRECT CHANNEL GAINS AND THEN AVERAGE C OUT BAD CHANNELS IN BANK B 6 Of; 8 1 = 1 . 1 0 0 8 S <I )=S( I ) * F B ( I ) S ( 1 ) = S ( 2 ) S ( 4 ) = 0 . 5 * ( S ( 3 ) + S ( 5 ) ) . 5 ( 1 2 1=0.5 * (S . ( 11 ) + S ( 1 3 ) ) S( 34) =0 . 5*( S ( 3 3 ) + S ( 3 5 ) ) S ( 3 6 ) = 0 . 5 * ( S( 35) +S( 37) ) S ( 4 1 ) = 0 . 5 * ( S ( 4 0 ) +S(42 ) ) S..( 46) = 0 . 8*S.( 45 ) + 0 . 2 * S ( 50) S ( 4 7 ) = 0 . 4 * S ( 4 5 ) + 0 . 6 * S ( 5 0 ) S ( 4 8) = 0 . 6 * S.( 45 ) + C 4 * S ( 5 0 ) S ( 4 9 ) = 0 . 2 * S ( 4 5 ) + 0 . 8 * S ( 5 0 ) S (5 9 ) = 0 . 5 * ( S ( 5 8 ) +S(60 ) ) S( 81 ) = 0 . 5 * ( S( 80) + S( 82) ) C A L L MYOLQF (M, N, X , S ). .... ._ . .. ._ _ 14 W R I T E ( 6 , 5 1 ) 51 FOR M A T ( • 1 »., 5 X , ' B A N K A , UNCAI. I RR A TED ' ) W R I T E ( 6 , 7 ) (T( I ) , 1=1, 100 ) WRI T E ( 6 , 5 2 ) 52 FORM A T ( / 5 X , ' BANK B , U N O A L I E R A T E D ' ) W R I T E ( 6 , 7 ) ( S( I ) , 1=1 , 1 0 0 ) ' " c AVERAGE THE ZEROED BANK A AND B DATA AND C A L I B R A T E DO 15 1 = 1 , 1 0 0 S(1 ) = 0 . 5 * ( S ( I )+T ( I ) ) / C A L W R I T E ( 6 , 5 3 ) 53 FORM AT ( / 5 X , ' A V E R A G E OF A AND ^ C A L I B R A T E D 1 ) WRI TF. ( 6 , 7 ) . ( S ( I ) , 1=1 ,1 00.) W R I T E ( 9 , 1 ) WRITE ( 9.,.7.) ( S ( I ) , 1=1, 1 0 0 ) c DETERMINE CHANNELS TO BE BLANKED OUT IN THE OTHER SOURCE P O S I T I O N I F ( K . E 0 . 1 2 ) N=4 0 I F ( K . E Q . 1 2 ) M=45 IF ( K. E Q... 3 0.) N = 4.C _____ ' I F ( K . E Q . 3 0 ) M=4 5 I F ( K . E Q . 3 3 ) N=30 I F ( K . E Q . 3 8 ) M=45 IF(K. . E 0 . 3 6 ) GO TO 16 I F ( K . E Q . 5 0 ) N=40 I F ( K . E 0 . 5 0 ) M=6 5 I F ( K . E Q . 5 0 ) GO TO 16 I F ( K . E Q . 6 6 ) GO TO 21 GO TO 4 21 STOP END c C C C D I F F C A L C — PROGRAM TO C A L C U L A T E D I F F E R E N C E P R O F I L E S FROM C FUI. 1 P R O F I L E n A T A - LS-1 C C I) I ME NS I ON S ( IOO) ,R (100 ) , A( IOC ) , B ( 100 ) , LK 10 0 ) J = 0. . K=0 J = J+1 DC 4 1 = 1 , 1 0 0 S ( I 1=0 .0 K = K+1 R E A D ( 5 , 1 ) FORMAT < 72X ) R E A D . I N THE. K SOURCE P O S I T I O N TAPES FOR A P ART ICULA i O B S E R V I N G F R E Q U E N C Y , AND STORE IN S U ) RE A O ( 5 , 2 ) (A( I ) t 1 = 1 , 100 )  2 F O R M A T ( 1 0 F 7 . 1 ) READ ( 5 , 3 ). INDEX 3 FORMAT ( II ) DO. .5 I = 1 , 1 0 0 5 S ( I ) = S ( I ) +A ( I ) C IF INDEX=0 , MORE OF THE SAME DATA IS TO FOLLOW C IF INDEX= ANYTHING E L S E , S T A R T READING RANK B DATA AT THE I P . U N O E X . EG..0 ) GO. TO 6 C C A L C U L A T E THE AVERAGE SOURCE P O S I T I O N P R O F I L E DO 8 1 = 1, IC C . 8 S ( 1 ) =S ( I ) / K IC L=0  DO 12 1 = 1 , 1 0 0 12 __ R ( I )=G .0 1 1 L = L U R E A D ! 5 , 1) C READ IN THE L C FREQUENCY AND R E F E R E N C E PQSIT I C N , TAPES FOR AND STORE A P A R T I C U L A R IN R( I )  OBSERVING 16 C R EAD ( 5 , 2 ) (B< I ) , 1 = 1, 100) READ ( 5_,_3 ) . I N D E X DO 16 1 = 1 , 100 R( I ) = R ( I ) + B (I ) IF INDEX=0, MORE OF THE SAME 1F( I N D E X . E Q . O ) GO TO 11 DATA IS TO FOLLOW C C A L C U L A T E TFE DO 14 1=1 ,100 14 R{ I )=R ( I ) / L C C A L C U L A T E THE C AND R E F E R E N C E DO 15 1 = 1 , 1 0 0 AVERAGE REFERENCE P O S I T I O N P R O F I L E D I F F E R E N C E P O S I T I O N P R O F I L E D U ) FOR A P A R T I C U L A R CLOUD 15 D( I )=S( I ) -R ( 1 ) WRI TE ( 6 , 9 ) 9 FORMAT( ' 1 ' 1 W R I T E ( 6 , 2 ) (S( I 1 , 1=1, 100 1 WRITE ( 6 , 1 ) WR ITF( 6 , 2 ) (R( I ) , 1 = 1, 1 00) C 21 W R I T E ( 6 , 1 ) W R I T F ( 6 , 2 ) (D( I) , 1 = 1 , 1 0 0 ) W R I T E ( 9 , 1 ) W R I T E ( 9 , 2 ) (D( I ) , 1 = 1 , 100 ) IF INDE X=1 ,READ IN THE NEXT I F ( INDEX . E(0 . 1 ) GO TO 10 REFERENCE P O S I T I O N TAPES IF I N D E X = 2 , G 0 ONTO THE NEXT SOURCE P O S I T I O N OR FREQUENCY I F ( I N D E X . F Q . 2 ) GO TC 7 IF INDEX= ANYTHING E L S E , S T O P STOP END - 6 6 . -C C C C A D I T P L O T - - P R O G R A M T O P L O T A V E R A G E D I F F E R E N C E A M D E X P E C T E D F L U C T U A T I O N D I M E N S I O N A ( 1 0 0 ) , B ( 1 0 0 ) , 0 P ( 1 0 3 ) , 0 M ( 1 0 3 ) , 0 ( 1 0 3 ) , D S U M ( 1 0 3 ) ,DO If ( 1 ( 3 0 1 MENS I O N O S R R A Y ( 5 1 5 ) , D O R R A Y ( 5 1 5 ) , V A R R A Y ( 5 1 5 ) , V ( 1 0 3 ) C D I M E N S I O N T O P X ( 2 ) , T O P Y ( 2 ) » P C T Y ( 2 ) D A T A T O P X / 2 . C , 3 . 0 / , T O P Y / 2 * 1 0 . 0 / , B O T Y / 2 * 0 . 0 / D A T A D S , S M I N , D V , V M I N / 3 . 0 , - 9 . 0 , 3 0 . 0 , - 1 8 0 . 0 / C A L L P L O T S L E M = 0 R E A D I N N U M B E R O F S I N G L F D A Y P L O T S T O B E M A D E . 2 8 1 R E A D ! 5 , 2 8 ) K M A X . F O R M A T . ( I D D O 1 3 K. = l , K M A X R E A D ( 5 , 1 ) _ N P . » O B J E C T . D A T E . . . . F O R M A T ( 1 2 , 2 F 3 . 0 ) N H = N P / 2 C c 2 C V L S R = L S R V E L O C I T Y O N D A T E O F O B S E R V A T I O N , C O R R = . C A L I O R A T I O N C O R P . E C T I O N F A C T O R , , I F N E C E S S A R Y R E A D ( 5 , 2 ) V L S R . C O R R F O R M A T ( F 8 . 4 . , F 4 . . 2 ) R E A D I N T H E S O U R C E S A D D E D T O G E T H E R F I R S T , T H E N T H E O T H E R S D O 6 I = 1 , 1 0 3 6 4 D P ( I ) = 0 . 0 0 M ( I ) = 0 . 0 D O 3 L = 1 , N P R E A C ( 5 , 4 ) _ F O R M A T ( 7 2 X ) R E A 0 ( 5 , 5 ) ( A ( I ) . 1 = 1 . 1 0 0 ) 5 F O R M A T ( 1 0 F T . 1 ) R E A D ( 5 , 4 ) R E A D ( 5 , 5 ) { B ( 1 ) , 1 = 1 , 1 0 0 ) ,D. ( 1 ) = B ( 1 ) D ( 2 ) = B ( 2 ) D ( 3 ) = B ( 3 ) . 7 D O . 7 J = 4 , 1 0 0 D ( J ) = 0 . 5 = M A ( J - 3 ) + P ( J ) ) _ ... D ( 1 0 1 ) = A ( 5 8 ) D ( 1 0 2 ) = A ( 9 9 ) D ( 1 0 3 ) = A < I O C ) I F ( L . G T . N H ) G O T O 9 . . . _.. 8 9 1 0 3 D O 8 j = l , 1 0 3 . D P ( J ) = D P ( J ) + . D J J ) G O T O 3 D O 1 0 J = l , 1 0 3 D M ( J ) = D M ( J ) + D ( J ) C O N T I N U F C C C J R R = C O R R / N P D D M A X = 0 . 0 C A L C U L A T E A V E R A G E D I F F E R E N C E A N D E X P E C T E D F L U C T U A T I O N D O 1 1 I = 1 , 1 0 3 . D S U M ( I ) = ( D P ( I ) + D M ( I ) ) * C O R R 0 0 I F ( I ) = ( D P ( I ) - D M ( I ) ) * C O R R C 1 1 2 4 C A L C U L A T E T H E M A X I M U M T E M P E R A T U R E T O B E P L O T T E D I F ( A B S ( D D I F ( I ) ) . G T . A B S ( 0 D M A X ) ) D D M A X = D O I F ( I ) W R I T E ( 0 , 2 4 ) F O R M A T ( • 1 ' ) W R I T E ( 6 , 5 ) ( D S U M ( I ) , F = 1 , 1 0 3 ) W P. I T E ( 6 , 4 )  -67-WRITE ! 6 , 5) ( D I M E ! I ) ,1 = 1, 103) W R I T E ( 6 , 2 7 ) DDMAX 2 7 F 0 R M A T ( F 7 . 1 ) I F ( D D M A X . L T . 0 . 0 ) GO TO 25 DO 26 1 = 1 , 1 0 3 2 6 DP I F ! 1 ) = - D D IF ( I 1  C S C A L E DATA FOR P L O T T I N G 25 V Z E P 0 = - 1 4 7 . 1 2 8 + V L S R DO 12 1 = 1 , 1 0 3 V ( I ) =1.0 . - (V ZEPO+ 1*2 . 12 -VM IN ) /DV D SUM(I ) = (DSUM( I ) - S M I N ) / D S +1 .0 12 DP 1F( I ) = (DP I F ( I ) - S M I N ) / p S - 1 . 0  NEND=K*10 3 . . . N S T A R T = ( K - 1 ) * 1 0 3 . DO 14 1 = 1 , 1 C 3 VARRAY( I+ NST ART ) = V ( I ) D S R R A Y ! I+ M START) =DSLM( 1 ) 14 DDRRAY( I+NSTART )=DD IF( I )  GO TO 3 0 . .16. „ .. CONTINUE. CALL AX IS (0 . 0 , 10 . 0 , IH , + 1 , 2 . 0 , 0 . 0 , - 6 . 0 , 3 . 0 ) C A L L L I N.F,! TOPX ,TGPY , 2 , 1 ) C A L L A X I S ! 3 . 0 , 1 0 . 0 , IH ,+ 1 , 2 . 0 , 0 . 0 , - 3 . 0 , 3 . 0 ) CALL SYMBOL (0 . 6 , 1 0 . 2 8 , 0 . 1 4 , 31HBP IGHTNESS TEMPERATURE ( 2 3 . C , M ) , Q . ' #31) CALL S Y M B O L ! 1 . 3 , 9 . 0 , 0 . 1.4 , 2CHE XP EC TED FL UC T UA TI ON , 2 7.0. 0 , 2 0 ) C A L L S Y M B O L ( 3 . 3 , 9 . 0 , 0 . 1 4 , 1 8 HAVERAGE D I F F E R E N C E , 270 . 0 , 18) CAL L SYMBOL ( 5 . 0 , 9 . 0 , 0 . 2 8 , 1 3H0BJEC T . NUMBE P. ,2 7 0 . 0 , 1 3 ) C A L L N U M B E R ! 5 . 0 , 5 . 5 0 , 0 . 2 8 , O B J E C T , 2 7 0 . 0 , - 1 ) I F ! L E M . E Q . 1 ) GO TO 17  CALL. SYMBOL. ( 5 . 0 , 4 . 7 , 0 . 1 4 , 12HAUG. , 1 9 7 0 , 2 7 0 . 0 , 1 2 ) C A L L . NU M B E R ( 5 .0 , 4 . 1..,.0.. 1 4 , D A T E, 2.7 0 .0 ,.-. 1) 17 CALL A X 1 S ( O . C , 1 0 . 0 , 2 1 H L S R V E L O C I T Y { K M / S E C ) , - 2 1 , 1 0 . 0 , 2 7 0 . 0 , V M I M , i : fi ) „ C A L L A X I S ( 0 . 0 , 0 . 0 , i n , - 1 , 2 . 0 , 0 . 0 , - 6 . 0 , 3 . 0 ) CALL L I N E ( T O P X , B O T Y , 2 , 1 )  C A L L A X I S ( 3 . 0 , 0 . 0 , I H , - 1 , 2 . 0 , 0 . 0 , - 3 . 0 , 3 . 0 ) CALL . SYMBOL ( 0 . 6 , - . 0 . 42 , 0 . 14 , 3 1HBR IGHTNESS TEMPERATURE ( 2 1 . C M ) , 0 . 0 #31 ) IF ( L E M , E.G. 1 ) GO TO 1 8 DO 32 1 = 1 , 1 0 3 32 C A L L SYMBCL (DSUM(I ) , V ( I ) ,0 . 0 7 , 2 , 270 . 0 , - 1 )  DO 15 1 = 1 , 1 0 3 15 CALL SYMBOL<DD I F ( I ) ,V( I ) , 0 . 0 7 , 2 , 9 0 . 0 , - 1 ) I F ! K . E Q . K M A X ) GO TO 99 C A L L P L O T ! 7 . 0 , O . C , - 3 ) 30 I F ( K . N E .KMAX ) GO TO 13 L F M = 1  GO TO 16 13 CONTINUE 18 C A L L S Y M B C L ( 5 . 0 , 4 . 7 , 0 . 1 4 , 8 H A L L D A Y S , 2 7 0 . 0 , 8 ) DO 19 1 = 3 , 1 0 3 DO 20 J = 1 , K M A X K = I + ( J - l ) * j 0 3  20 C A L L SYMBOL ! DORR AY( K) , V A R R A Y ( K ) , 0 . 0 7 , - l H . , 0 . 0 , 1 ) 19 CONTINUE DO 21 1 = 1 , 1 0 3 DO 22 J=1 ,K MA X K = l + { J - l ) * 1 0 3 22 CALL SYMBOL ( D S R R A Y ( K 1 , V A R R A Y ( K ) , 0 . C 7 ,3 H . ,0 .0 , 1 1 - (t>e>-21 CONTINU F 99 C A L L PL (IT NO S TO P C c END c c c LSR — PROGRAM TO P R E C E S S A SOURCE AND THE SOLAR A P E X , AND THEN c CALCULATE. THE V E L O C I T Y OF THE L . S . R . WITH RESPECT TO THE. SOURCE c READ P R E C E S S I O N A L CONSTANTS FOR THE SOURCE AND SOLAR APEX 0.0 M MON / S A P F X / X S A «Y S A , 7 S A D IMENSION X ( 2 ) , Y ( 2) REALMS JUL DAY R E A L* 4 M , N » M S A , N S A INTEGER YEAR»DAY, HR . . . ISING=1 1=5 J=6 K=30 . . 9 W R I T E ( J , 2 7 ) 27 FORMAT L M . ' ) W R I T E ! J , 1 0 ) 1 0 FORMAT. I X , • ENTER P R E C E S S I O N A L CONST ANTS,M A N D , N , FOR YEAR OF O B S -ERVATION FOR SOURCE AND SOLAR A P E X ' , / l X , ' M = S X X X . X X X N = S X X X . X X X #.SA = SXXX . X X X . NS A= SXXX .XXX • ) M = 6 1 . 4 6 9 N = 2 6 . 7 2 2 M S A = 2 1 5 . 1 0 9 MSA = 9 3 . 53 7 W R I T E ( J , 1 1 ) M , N , M S A , N S A _ 11 FORMAT (3.X , F 3 . 3 , 5 X , F8 . 3 , 7 X , F8 . 3 , 7 X , F 8 . 3 ) c READ THE TIME OF OB SE R VA TI ON ( J U L I A N DAY AND DAY ARE THOSE AT ... c G R E E N W H I C H , H E N C E , IF H R ( P S T ) I S . G R E A T E R THAN 16 AT PE NT IC TON » THE c P E N T I C T O N J U L I A N DAY AND CAY MUST BE INCREASED BY ONE DAY 23 WRI TF ( J , 1.2 ) 12. FORMAT ( I X , ' ENT ER J U L I A N CAY , YEAR , MONTH, DAY , AND HR ( P ST ) OF OBSEPV . #TI ON S / 1 X.,.* JUL I A N...DA Y. YEAR MONTH DAY ..HR M IN ( PS T ) ' , / 1 X, ' X y tfXXXX.X YYYY MM DD HH MM 1 ) REAG\( I , 13) J Ul DAY ,.Y F AR , MONTH , DAY , H R , MI N 13 F O R M A T ( I X , F 9 . 1 , 5 X , 1 4 , 3 X , I 2 , 5 X , I 2 , 4 X , 1 2 , 3 X , I 2) W R I T E ( J , 1 3 ) JUL 0 A Y , Y E A R , M O N T H , D A Y , H R , M I N C C A L C U L A T I O N OF P R E C E S S I O N A L CONSTANTS FOR DAY OF OBSERVATIONS 24... . HR= HR+8 _ „ I F ( H R . G E . 2 4 ) HR = H R - 2 4 FAC TOR = ( ( M O N T H - 1 . ) +( { D A Y - 1. ) + . H R + M I N / 6 G . ) / 2 4 . ) / 3 0 . 5 ) / 1 2 . C M = 3 . 0 7 3 4 * F A C T 0 R C N = 1 . 3 3 6 1 * F A C T O R M=M+CM N=N+CN MSA=MSA+CM NSA=NSA+CN C PRECESS P O S I T I O N OF SOLAR APEX FROM 1 9 0 0 . 0 TO DATE OF OBSERVATION Y ( 1 ) = 6 4 8 0 0 . Y ( 2 ) = 7 2 0 0 . C A L L FR GMT 0 (41 ,SR , IHR , MINT, SECT , S D , 1, 1 , 1 . , 1. , Y( 1) , ).. , 1 . , 1. , 1. ) C A L L F R OM Ti.) ( 4 2 , SR , 1 , 1 ,1 . , SD , I D EG , MI N A , S E C A , 1 . , Y ( 2 ) , 1 . , 1 . , 1 . , 1 . ) W RIT E ( J , 16 ) 1 6 FORMAT (1 X , • EPOCH 1900 . 0 AND CURRENT POSIT ION OF SOLAR APi-X A P R : ' . # 1 X , ' R A = SHH MM S S . S DFC=SDD MM S S . S ' ) -69-W R I T E ( J , 1 5 ) S R , I H R , M I N T , S E C T , S D , I D E G , M I N A , S E C A N U M S I G = 8 M A X I T = 2 0 C A L L E P O C H ( M S A , N S A , Y , N U M S I G , M A X I T , I S I N G ) C A L L F R 0 M T 0 ( 4 1 , S R , I H R , M I N T , S E C T , S D , 1 , 1 , 1 . , 1 . , Y ( 1 ) , 1 . , 1 . , 1 . , 1 . ) C A L L F R O M T O ( 4 2 , S R , 1 , 1 , 1 . , S D . I P E G . M I N A . S E C A , 1. , Y ( 2 ) ,1 . , 1 . . 1 . , 1 . ) W R I T E ! J , 1 5 ) S R , I H R , M I N T , S E C T , S D , I P E G , M I N A , S E C A I F ( I S I N G . E Q . C ) W R I T E ( J , 2 5 ) C C A L C U L A T I C N O F E Q U A T O R I A L C O M P O N E N T S O F S O L A R A P E X M O T I C N W R I T E ( J , 1 7 ) 1 7 F O R M A T ! I X , ' E Q U A T O R I A L C O M P O N E N T S O F S O L A R A P E X M O T I O N A R E : ' ) C A L L S U N V E L ( Y , X S A . Y S A , 7_ S A )  W R 1 T E ( J , 1 8 ) X S A , Y S A , Z S A 1 8 F O R M A T ( I X , « X S A = ' , F 8 . 4 , 5 X , ' Y S A . = ' , F 8 . 4 , 5 X , ' Z S A •= « , F 8 . 4 ) C C A L C U L A T I C N O F E Q U A T O R I A L C O M P O N E N T S O F T H E T O T A L L S R V E L O C I T Y W R I T E ( J , 1 9 ) 1 9 F O R M A T { I X , ' E Q U A T O R I A L C O M P O N E N T S O F T H E T O T A L L S R V E L O C I T Y A P E : ' H R P S T = F L O A T ( H R )  M I N P S T = F L C A T ( M I N ) C A L L L S R V E L ( J U L D A Y , HR.P S T , M I . N P . S . T , X L S R » Y L S R , Z L S R ) . W R I T E ( J , 2 0 ) X L S R , Y L S R , Z L S R .20 F O R M A T ! . I X , « X L S R = \ , F.8....4 , 5 X , ' Y L S R = ' , F 8 . 4 , 5 X , • Z L S R = • , F 8 . * ) W R I T E ! J , 1 4 ) 1 4 F O R M A T ( I X , ' E N T F R P O S I T I O N C F S O U R C E A N D C A L C U L A T E P R E C E S S E D P O S T # 0 N ' , / 1 X , ' R A = S H H M M S S . S D E C = S O D M M S S . S ' ) .. _C R E A D . . 1 N . P C S . I T . I C . N.. 0 F .. S 0 UP- C E..; F O P , .._T.HE. A P P R O P R I A T E E P O C H R E A D ! I , 1 5 ) S R , I H R . M I N T , S E C T , S D , I D E G , M I N A , S E C A 1 5 F O R M A T ( 2 ( 4 X , A 1 , 1 2 , 1 3 , 0 6 . ? ) ) W R I T E ( J , 1 5 ) S R , I H R , M I N T , S E C T , S D , I D E G , M I N A , S E C A C P R O C E S S P O S I T I O N O F S O U R C E F R C M 1 9 5 0 . 0 T O D A T E O F O B S E R V A T I O N S C A L L F R O M T O ( 1 4 , S R » I H R , M I N T , S E C T , S D , 1 , 1 , 1 . , 1 . , X ( 1 ) , 1 . , 1 . , 1 . , 1 . ) C A L L . F R G M T O ! 2.4 , S R , 1 , 1 , 1 . , S D , I D E G t M I N A,. S . E C A , 1 . , X ( 2 ) , 1 . , 1 . , 1 . , 1 . ) N U M S I G - = 8 M A X I T = 2 0 C A L L E P O C H ! M , N , X , N U M S I G , M A X I T , I S I N G ) C A L L F R O M T O ( 4 1 , S R , I H R , M I M T , S E C T , S D , 1 , 1 , 1 . , 1 . , X ( 1 ) , 1 . , 1 . ,1 . , 1 . )  C A L L F R C M T 0 ( 4 2 , S H , 1 , 1 , 1 . , S D , I D E G , M I N A , S E C A , 1 . , X ! 2 ) , 1 . , 1 . , I . ,1. ) W R I T E ( J , 1 5 ) S R , I H R , M I N T , S E C T , S.D.,. I D E G , M I N A , S E C A I F ! I S I N G . E Q . C ) W R I T E ! J , 2 5 ) 2 5 F O R M A T ( ' N O C O N V E R G E N C E ' ) C C A L C U L A T I O N O F L S R V E L O C I T Y O F O B S E R V E D S O U R C E R A D C 0 N = 7 . 2 7 2 2 1 E - 0 5  D E C = X ( 2 ) * R A D C 0 N R A = X ( 1 ) * R A D C . O N . X S R C = X L S R * C O S ( D E O * C O S ( R A ) Y S R C = Y L S R * C O S < D E C ) * S I N ( R A ) Z S R C = Z L S R * S I N ( D E C ) V L S R = X S R C + Y S R C + Z S R C W R I T P ! J , 2 1 ) V L S R 2 1 F O R M A T { I X , ' T H E L S R V E L O C I T Y O F T H E O B S E R V E D S O U R C E WA S : V I . S P = ' * F 8 . 4 / ) G O T O 9 2 6 S T O P E N D -7-0-c c c c c c $ * * * * * * * * * * * if. * * * * * * * * * * * * * * * * # * * * * * : * * * * # * * * * * * * * * * * * ;V * :'• X- * * A STROP A. K - - SUBROUTINES USEFUL I N AST ROPHY S I C AL CALCULAT IONS * * £ * * * * * * * * * * * s> * * * * * * * * * * # * * * * * * * * * * * * * * * * # * * * * * * * * * * * * * * * * * * * * * * c c c c EPOCH — . SUBROUTINE TO P R E C E S S A SOURCE P O S I T I O N SUBROUTINE E P O C H ( M , N , X , N U M S I G , M A X I T , I S 1 N G ) THE P R E C E S S I O N A L CONSTANTS M , N , DETERMINE THE PERIOD OVER W H I C H THE P R E C E S S I O N IS T C BE MA(3E D IMENSION I P O ! N T ( 3 , 3 ) , I S U B ( 3 ) , X ( 2 ) REALMS Y ( 2) ,C 0 E(3» 3 ) , T EM P( 3 ) » P AR T ( 3 ) ,AD , DO ... . RE A L*4 M, N _ DOUBLE P R E C I S I O N DBLE COMMON AO, D O t R E A L M , REALN ... REAL M = M REALN=N Y ( 1 ) = D B L E ( X ( 1 ) ) Y(.2.)=DBLE.(X (2..).) AO = Y( 1 ) . 00=_Y (2..) C A L L N I N L I N ( 3 , M A X I T , N U M S I G , I S I N G , Y , I P O I N T , I S U B , C O E , T E M P , P A R T ) X( 1 )=SNGL( Y( 1) J 0 c c X ( 2 ) = S N G L ( Y ( 2 ) ) ... RETURN... END c c c N 1 N L I N — SUBROUTINE TO SOLVE THE N O N - L I N E A R P R E C E S S I O N EQUATIONS SUB ROUT INE. . NI NL. I N { N 1, MAX IT , NUM S I G , S I NG , X , I PO .1 N T , I SUB , COB , TE M P , P A h U) . . .THIS SUBROUTINE I S . A DOUBLE PR EC I.S I ON VER SIGN OF THE. L I B R A R Y PROGRAM N u N L I N DIMENSION I PCI N T ( N . 1 , M l ) , I S U B ( N l ) c DOUBLE P R E C I S I O N CABS R E A L * 8. X( NI.) , C O E . ( N l ,..N1..). , TEMPI Ml ) , PART.(N1 ) » P EL CON, FACTOR, F, H, HOL D RE AL * 8 F P L U S , DERMAX, TE ST INTEGER C G N V G E , T A L L Y , S I N G L. N = N 1 - 1 r CGNVGE = 1 S ING = 1 R EL CON = 1 C . * * ( - N U M S I G ) c c DO 350 M = l , M A X IT 210 C DO 210 J = 1 , N . .1 POINT (1 , J ) =.. J DO. 300. K.= l.,..N IF (K . G T . 1) CALL X K M A X ( K , N 1 , X , I S U B , C O E , IPO INT ) CALL F K ( N , X , F , K) r FACTOR = . 0 0 1 L 220 r T A L L Y = 0 DO 2 30 I = K , N I TEMP = 1 POI NT( K , I ) HOLD = X ( I T E M P ) H = FACTOR*HOLD IF ( H . EQ. 0 . ) H = . 0 0 1 X ( I TEMP) = HOLD + H IF (K . G T . 1) C A L L XKMAX(K , N l , X , I S U B , C C E , I P G I MT ) C A L L F K ( N i X , FPL U S , K) 1000 CONT I NUB 1002 P A R T ( I TEMP) = (FP.LUS - F J / H X( I TEMP ) = HOLD 1003 I F ( LABS ( P ART { .1 T E MP ) ) . EQ . 0 . ) GO TO 555 IF< DABS< F / P A R T U TEMP) ) . L E . 1 0 * * 2 0 ) GO TO 1001 5 55 T A L L Y = T A L L Y + 1 1001 CONTINUE 2 30 _ r CONTINUE I F ( T A L L Y .1 E . ( N-K ) ) GO T 0 .24 0 FACTOR = F A C T 0 R * 1 0 . I F ( F A C T O R . G T . . 5 ) GO TO 370 GO TO 2 2 0 ...C. __ - _ _ ... 240 IF (K , LT . N) GO TO 250 I F ( DABS (.PART ( I.TF MP) ) . EQ.O . I . GO TO .370 C 0 E ( K , N + 1 ) = 0 . K MAX = ITEMP  GO TO 2 90 £ 2 50 KMAX = I P O I N T ( K . K ) DERMAX=DAGS ( PART ( KM AX ). ).. K P L U S = K + 1 DO 270 I = K P L U S , N  J S U B = I P O I N T ( K , I ) TE S T=DAB S ( PART. ( J SUB).,) IF (TEST , L T . D E R MA X ) GO TO 260 DERM AX. =. TEST 1 POINT ( K P L U S , I) = KM" A X K MAX = J S U B  GO TO 270 C 260 IPO INT ( K P L U S , I ) = J S U B 27C CONTINUE C I F ( D A B S ( P A R T ( K M A X ) ) . E Q . 0 . ) GO TO 370  I S U B ( K ) = KMAX COE .( K , N+1 )..=.. .0 . C DO 280 J = KPLUS , N JSUB = I P O I N T ( K P L U S , J ) C O F ( K , J S U B ) = -t - 'ARTt JSUB ) / P A R T ( K M A X )  C 0 E ( K , N + 1 ) = C 0 E ( K , N + 1 ) + P A P T ( J S U B ) * X ( J S U B ) 2 80 CONTINUE C 290 C 0 E ( K , N + 1) = ( C 0 E ( K , N + 1) - F ) / P A R T ( K M A X) + X (KMAX) 300 CONTINUE _C [ X ( K M A X ) = C 0 E ( N , N + 1 ) IF (N . G T . 1) C A L L XKMA.X(N, M l , X , 1 S U B , C C E , I P O I N T ) IF (M . E Q . 1) GO TO 3 30 C DO 310 I=1 , N IF( LA P.S ( ( TEMP( I ) - X ( I ) ) / X ( I ) ) . G T . R E L C O N ) GO TO 32 0 -7Z-3 1 0 r C O N T I N U F : c C O N V G E = C O N V G E + 1 I F . ( C O N V G E . G T . .3) G O T O 3 6 0 G C i T O 3 3 0 3 2 0 3 3 0 3 4 0 3 5 0 0 C O N V G E = 1 D O 3 4 0 1 = 1 , N T E M P ( I > = X ( I ) C O N T I N U E G O T O 3 8 0 3 6 0 r M A X I T = M G O T O 3 8 0 ..... 3 7 0 r S I N G = 0 L 3 8 0 R E T U R N . C C E N D S U B R O U T I N E X K M A X ( K , N 1 , X , I S U B , C U E , I P 0 1 N T ) .. D I M E N S I O N I P C I N T ( N 1 ,,N 1.) , 1 S U B { N 1 ) R E A L * 8 C 0 E ( N 1 , N 1 ) , X ( N l ) - - - • • N = M l - 1 „ D O 1 1 . 0 . 1 - 2 ,.K K M = K - I + 2 . K M A X ..= I S U B ( K M - . 1 ) X { K M A X ) = 0 . D O 1 0 0 J = K M , N ._ 1 0 0 r J S U B = I P O I N T ( K M , J ) X ( K M A X ) = X ( . K M A X ) ..+. C G E . ( K M . - 1 , J S U B ) * X ( J S U B ) ...... 1 1 0 X ( K M A X ) .=. X ( K M A X ) . . + . C O E ( K M - 1 , N + 1 ) R E T U R N E N D c c C _ __c c F K S U B R O U T I N E R E Q U I R E D B Y N I N L I N S U B R O U T I N E F K ( L , X , Y , K ) T H I S S U B R O U T I N E C O N T A I N S T H E E Q U A T I O N S T O B E S O L V E D A N D L E T S C N I N L I N K N O W W H E N A S O L U T I O N H A S B E E N F O U N D R E A L * 8 X ( L ) , B , C , Y , A O , D O D O U B L E P R E C I S I O N D S I N , D C O S , D T A N C O M M O N A O , D O , R E A L M , R E A L N B = ( X ( 1 ) + A C ) * 3 . 6 3 6 1 0 5 D - ( . 5 G O T G ( 1 0 , 2 0 ) , K 1 0 2 0 C = ( X ( 2 ) + 0 0 ) * 3 . 6 3 £ 1 0 5 0 - 0 5 Y = - X ( 1 ) + A C + R E A L M + R E A L N * D S I N ( 3 ) * D T A N ( C ) R E T UP. N Y = - X ( 2 ) + D 0 + R E A L N 1 ' C C 0 S ( B ) R E T U R N E N D C c c c c L S R - - S U B R O U T I N E T O C A L C U L A T E T H E E Q U A T O R I A L C O T O T A L L S R V E L U C I T Y S U B R O U T I N E L S R V E L ( J U L D A Y , H R P S T , M I N P S T , X L S R , Y L S R , M P O N E N T S O F T H E 7 L S P ) -73-COM MON / S A P EX / X S A , Y S A , 7 SA RE A L*8 JULDAY , FCC , F JO , JD , NS D , NFS D, F S D , DAYS , T 1, T 2 » T 3» [) L R E A 1. * 8 R A D C C N , T , L , P , 0 , E , DI F , VB AR , A , VEC),E L , X E C , Y E 0 , Z E 0 R E A L*4 M INPST. DOUBLE PREC. IS1CN D M O D , B B L E , D S I N , D C O S , D S Q R T , DTAN _C C 1 . C A L C U L A T I C N OF EQUATORIAL COMPONENTS OF E A R T H ' S ROTATION C CONVERT PST TO U N I V E R S A L T I M E . 1 HRUT = H R P S T + 5 . I F ( HRUT . G B . 2 4 . ) hRUT=HRUT-24 . . . . C Ml NUT=M.INPST . FCD= (HRUT+M I N P S T / 6 0 . ) / ? 4 .  FJD=JULDAY+FCU C AT START..OF, J U L I A N DAY 2 4 4 0 3 6 Q . 5 ,MAY 19 , 1 9 6 9 , O H R U T , H . A . OF FIRST C POINT OF ARIES IS 1 5 H R 4 5 M I N 5 6 . 9 9 M S E C , W H I L E LONGITUDE OF P E N TIC T C N C IS. +7HR5.8.MIN28 . .53S.EC. HENCE S I D F R 1 A L TIME AT P EN T I C TON IS C 7 H R 4 7 M I N 2 8 . 44SEC = C. 3 2 4 6 3 5 S I O E R I A L DAYS JD=244C 360 . 5  F SD = 0 . 3 2 4 6 3 5 C C A L C U L A T E NUMBER OF SI DERI A.L ..DAYS... SI NCE MAY 19 , 196 9 . N S D M F J D - J D ) * 1 .C C2 738 NF SD=D MOD ( N S D , 1 . D + 00.1 S IDTIM = SMGL(FSD+NFSD) S I D T I M = A M G O ( S I D T I M , 1 . )  S T = S I D T I M * 6 . 2 8 3 1 E 5 3 _.C. CALCUL A T.E. MAX I MUM VELOG 1 TY FROM KNOWN PERI CD. OF E A R T H ' S POTAT ION V M A X = 0 . 4 6 5 C V P E N T = V M A X * C O S ( L A T I TUDE OF PENT I CT CN ) V P E N T = 0 . 2 9 3 3 1 9 5 VPENT=0 . 3 2 4  C HENCE E QUI TOR IAL COMPONENTS A R E : XER = V P E N T * S IN( ST ) _ YER = VPE N T * C O S ( S T > C Z E R = 0 . 0 C _C 2 . C A L C U L A T I C N OF EQUATORIAL COMPONENTS OF E A R T H ' S ORBITAL VF1. OC I C DETERMINE NUMBER OF J U L I A N DAYS S I N C E 1 9 0 0 . 0 DAYS = F J D - 2 4 1.5020 .C C C A L C U L A T E ECCENTRI CI TY ( E ) , O B L I Q U I T Y OF EC L I P T IC ( 0 ), M E A N I.0NG1TUJ C. ( L ) , LONGITUDE OF P E R I G E E ( P ) , FROM FORMULAS G I V E N IN THE [XPI.ANAT C SUPPLEMENT TO THE ASTRONOMICAL EP HEM E R I S , WHERE: _C D A Y S=T I ME MEASURED I.N EPHEMERIS DAYS S I N C E . 1900 . 0  C T1= TIM E MEASURED IN J U L I A N C E N T U R I E S OF 3 6 5 2 5 DAYS S I N C E 1 9 0 0 . 0 T l = D A Y S / 3 6 5 2 5 T 2 = T 1 * * 2 T3=T1*T2 RA0CCN=0 . 0 1 7 4 5 3?. 92 5 1 994 3 T = F J D - 2 4 3 6 2 0 4 . 5  L = ( 0 . 9 8 5 6 C 9 * T + 2 8 0 . 1 4 2 7 5 ) * R A D C O N P = { 281 . 22 08 3 +4 . 7 0 6 8 4 D-05 * Ei AYS + 4 . 5 3 D - 0 4 * T 2 + 3 . OD- 06 *T 3 ) *R A DC ON 0 = ( 2 3 . 4 5 2 2 9 H - 0 . 0 1 3 0 1 2 5 * T 1 - 1 . 6 40—06* T2 + 5 . 03 U-Q7 * T 3 1 R A DC ON E = 0 . 0 1 6 7 5 1 0 4 - 4 . 1 8 D - 0 5 * T 1 - 1 . 2 6 0 - 0 7 * T 2 D I F = L - P _C_ C A L C U L A T E V E L O C I T Y COMPONENTS OF E A R T H ' S ORBITAL V E L O C I T Y IN C EQUATORIAL C O O R D I N A T E S , U S I N G EQUATIONS GIVEN BY MCRAE ANO C . WESTERHOUT,WHERE: C V BAR=M EAN ANGULAR V E L O C I T Y OF EARTH C A = S E M I - M A J O R A X I S OF E A R T H ' S ORBIT V B A R = 1 . 9 9 C 9 8 7 D - C 7 A = 1 4 . 9 6 7 4 0+0 7 -74-V E O = V B A R * A / D S Q R T ( 1 . 0 0 + 0 0 - 0 * * 2 ) E L = L + 2 . 0 * E * C S I N ( U I F ) + 1 . 2 5 * E * * 2 * D S I N ( 2 . G * D I F ) X E Q = V E 0 * ( D S I N ( E L ) + E * O S I N ( P ) ) Y E O = - V E 0 * ( L ) C O S { E L ) + E * 0 C 0 S ( P ) ) * D C O S ( 0 ) Z E 0 = Y E 0 * D T A N ( 0 ) C C 3 . C A L C U L A T I O N C F E Q U A T O R I A L C O M P O N E N T S O F S U N ' S M O T I O N I N T H E C L O C A L G R O U P T O W A R D S T H E S O L A R A P E X : A = 2 7 0 . 0 , 0 = 3 0 . 0 , V S = 2 0 . 0 C T H I S P 0 S 1 T 1 C N S H O U L D B E P R E C E S S E D F R O M 1 9 0 0 . 0 C X S A = V S * C U S . ( A ) f t C O S ( D ) C Y S A = V S * S I N ( A ) * C O S ( D ) C Z S A = V S * S I N ( D )  C C U R R E N T V A L U E S F O R X S A , Y S A , Z S A R E A D I N T H R O U G H L A B E L L F D C O M M O N C . . .. . . . . . . . . C T H E C O M B I N E D E Q U I T O R I A L C G M P C N E N T S O F M O T I O N S 1 , 2 , A N D 3 A R E ; X L S R = S N G L { X E O + X S A + X E P ) Y L S R = S N G L ( Y E O + Y S A + Y E R ) Z L S K . = S N G L ( Z E O + Z S A )  R E T U R N E N D _ _ C ...C c C S U N V E L — S U B R O U T I N E T O C A L C U L A T E T H E E Q U A T O R I A L C O M P O N E N T S O F TL-C S U N ' S M O T I O N ... S U B R O U T I N E . S U N V E L ( X , X S A , Y S A , Z S A ) D I M E N S I O N X ( 2 ) R A D C 0 N = 7 . 2 . 7 . 2 2 I E - C 5 V S = 2 0 . 0 A = X ( 1 ) * R A D C 0 N  D = X ( 2 ) * R A D C O N V C O S C = . C O S . ( D ) * V S X S A = C G S ( A ) * V C O S D Y S A = V C 0 S O * S I M ( A ) Z S A = V S * S I N ( D ) R E T U R N  E N D . C c c ;  C F R O M T O — S U B R O U T I N E T O C O N V E R T B E T W E E N D I F F E R E N T A N G U L A R M E A S U i - i S U B R O U T I N E F R O N T 0 ( I , S H , I H R , M I N T , S E C T , S D , I D E G , M I N A , S E C A , R A D , S E C S T , y/HR S T , S E C S A , D E G S A , R E V ) ...C A T W O D I G I T I N T E G E R B E T W E E N . .1.1. A N D . ..R.8 I S R E A D , . W H E R E . . T H E F I R S T C D I G I T I N D I C A T E S T H E F R O M U N I T S A N D T H E S E C G N C , T H E T O U N I T S . . C 1 = H O U R S , M I N U T E S A N D S E C O N D S O F R . A . , 2 = D E G R E E S , M I N U T E S A N D S E C G N C -C O F D E C L I N A T I O N , 3 = R A D I A N S , 4 = S E C O N D S O F T P - ' E , 5 = H O U R S O F T I M E , C 6 = S E C 0 N 0 S O F A P C ,7 = P E G R E B S , 8 = R F V G L U T I G N S R E A L N E G C A T A B L K / 1 H . / , N E G / I H - / N = M G 0 ( 1 , 1 0 ) M= I / 1 0 G O T O { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ) , M 1 S E C = I H R » 3 6 0 C . + M I N T * 6 . Q . + S E C T  I F ( S H . E Q . N E G ) S E C = - S E C G O T O ( 1 1 , 1 2 , 1 3 , 1 4 ,15 , 1 6 , 1 7 , 1 8 ) , N 2 S E C = I D E G * 2 4 0 . + M I N A * 4 . + S E C A / 1 5 . I F ( S D . E Q . N E G ) S E C = - S E C G O T O ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N 3 S E C = R A 0 * 1 3 7 5 0 . 9 9  GC TD ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 0 , 1 7 , 1 8 ) , N 4 SEC=SECST GO TG (11 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N 5 S E C = H R S T * 3 6 0 G . GO TO ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N 6 S E C = S E C S A / 1 5 . GO TO ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N 7 S E C = D E G S A * 2 4 G . GO TO (1J , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N 8 SEC=REV* e -6400 . GO TG ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 ) , N 1 1 SH = R LK I F ( S E C . G T . 0 . 0 ) GO TG 21 SEC=.-S EC ... SH = NEG 21 .. I HR= I NT ( . S E C / 3 6 C O . ) S E O A M C C M S E C , 3 6 0 0 . ) M I N T = I N T ( S E C / 6 0 . ) S EC T = A M O D ( S E C , 6 0 . ) .. . . .RETURN „. 12 SD=BLK IE- ( SEC .GT . 0 . 0) GO. TO. 2 2... S E C = - S EC SD=NEG 22 IDEG= I N K SEC / 2 4 0 . ) S EC=AMGD (.S rC , 240 . ) _ MI NA = I NT ( S E C / 4 . ) SEC A= AMODJ. S EC., 4 . ) * 1 5 . . RETURN 13 R A D = S E C * 7 . 2 7 2 2 1 E - 0 5 RETURN . _ 14 SECS.T--SEC _ RE TURN 15 HRST=SE C / 3 6 0 C . RETURN 16 SEC S A = S E C * ' 1 5 . RETURN _ 17 DECSA=S E C / 2 4 0 . RETURN 18 R E V = S E C / 8 6 4 0 0 . RETURN END C C C • • - -•- -— - -C MYOLOF — SUBROUTINE ViHICH READS A BAD B A S E L I N E D PROEIL E AND C RETURNS A BEST L E A S T SQUARES F I T T E D P R O F I L E S U BROU T I N E MY OL Q F ( M , N , X , Y ) c N + 1 . I S THE F I R S T CHANNEL BLANKED IN THE OLQF B A S E L I N E F IT c M IS THE TOTAL NUMBER OF CONSECUTIVE CHANNELS TO BE BLA NKE n c X I S THE CHANNEL NUMBER, Y ACCEPTS P R O F I L E AND RETURNS BEST F IT D IMENSION X ( 1 0 0 ) , Y ( 1 0 0 ) , Y I ( 1 0 0 ) , Y F ( 1 C 0 ) , Y D ( 1 0 0 ) , W T ( 1 0 0 ) , S ( 4 ) , F ( 4 ) # S 1 G M A ( 3 ) , A ( 3 ) , E ( 3 ) LOGICAL l.K DATA L K , N W T / . F A L S E . , 0 / 00 30 1 = 1 , Ni X( I ) =1 30 Y I ( I )=Y( I ) L = 1 0 0 - M N 1 = N+ 1 -u-DO 31 I=N1,M X { I ) =1 + L 31 YI ( I) = Y( I+ L ) K=3 C OLQF F I T S THE BEST H I R S T , S E C O N D OR THIRD ORDER POLYNOMIAL TO C THE B A S E L I N E ON EITHER SIDF OF THE P R O F I L E , WHICH HAS RFFN C BLANKED O U T . IT USES T H I S POLYNOMIAL TO C A L C U L A T E THE P R O F I L E C IN THE BLANKED REGION AND RETURNS TO THE C A L L I N G PROGRAM CALL O L Q F ( K , M , X , Y I , Y F , Y D , W T , N W T , S , S I G M A , A , B , S S , L K , P ) W R I T E ( 6 , 3 9 ) K, SS , ( P ( I ) , I = 1 , 4 ) 39 F0RMAT(3X,«K = • , I 2 , 5 X , ' S S = ' , E 1 2 . 5 , 5X , ' P (1 ) = • , E l 2 .5 , 5X , ' P ( 2 > H ' . F I 2 . 5 , 5 X , MM 3) = • . E 1 2 . 5 . 5X . ' P ( 4) = ' . E 1 2 . 5 ) I F M K . E Q . 3 ) GO TO 33 . . I F I K . E Q . 2 ) GO TO 32 DO 34 1 = 1 ,1 OO X( I )= I 34 Y F ( I )=P ( 1 )+P (2 ) *X( 1 ) GO TO 3 5 22 DO 36 1 = 1 , 1 0 0 X ( I ) = I 36 YF ( I ) = P ( 1 ) + ( P ( 2 ) + P ( 3 )*X ( I) ) * X ( I ) GO. TP 35 33 DO 3 7 1 = 1 , 100 X ( I ) = I 37 Y F { I ) = P ( l ) + ( P ( 2 ) + ( P < 3 ) + P ( 4 ) * X ( I ) ) * X ( m * X ( I ) _ 35 . DO . 38 1 = 1 , 1.00 _ 3 8 Y d )=Y( I ) - Y F ( I ) RETURN C END C c * F A T A L FORTRAN ERROR : F N D - O F - F I I F FNGOUNTFRFD ON R FAD 0 P F R A T I 0 M RROR CCCURED ON UNIT 5 R.ROR RETURN _ S I G -77-BIBLIOGRAPHY 1. Barnard, E.E. 1919, Ap.J., 49, 1 and 360. 2. Lynds, B.T. 1962, Ap.J. Suppl., F, 1. 3. He i l e s , C.E. 1968, Ap.J., 151, 919. 4. Cudaback, D.D. and Heiles, C , 1969, Ap.J. ( L e t t e r s ) , 155, L21. 5. Hei l e s , C.E. 1969, Ap.J., 157, 123. 6. He i l e s , C.E. 1970, Ap.J., 160, 51. 7. Palmer P., Zuckerman, B., Buhl, D., Snyder, L.E., 1969, Ap.J., 156, L147. 8. He i l e s , C.E. 1971, Ann.Rev.Astron. Ap., 9, 293. 9. Carruthers, G.R. 1967, Ap.J. ( L e t t e r s ) , 148, L141. 10. Carruthers, G.R. 1970, Space S c i . Rev., 10, 459. 11. G u l l , T.R. and Harwitt, M.O. 1971, Ap.J., 168, 15. 12. Gould, R.J. and Harwitt, M. 1963, Ap.J., 137, 694. 13. L i l l e y , A.E. 1955, Ap.J., 121, 559. 14. G a r z o l i , S.L. and Varsavsky, CM. 1966, Ap.J., 145, 79. 15. 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Clark, B.G., Radhakrishnan, V., Wilson, R.W. 1962, Ap.J. 135, 31. Verschuur, G.L. 1969, Astrophys. L e t t e r s , 4, 85. 32. Solomon, P.M. and Werner, M.W. 1971, Ap.J. 165, 41. 33. S p i t z e r , L. J r . 1968, Diffuse Matter i n Space, Interscience 34. F i e l d , G.B. 1958, Proc. I.R.E., 46, 240 35. Van de Hulst, H.C, Muller, CA., Oort, J.H. 1954 B.A.I.N. 12, 117. 36. Williams, D.R.W. 1970. (Private Communication) 37. Kraus, J.D. 1966, Radio Astronomy, McGraw-Hill. 38. Perley, R.A. 1970, Master's Thesis, U n i v e r s i t y of B r i t i s h Columbia. 39. MacRae, D., Westerhout, G. 1956, Lund Observatory Pub l i c a t i o n s . TABLE I Properties of T y p i c a l Dust Clouds A m i> 10 mag R ^ 0 # 7 pc rtH + 2 n H i ^2000 cm"3 a H c 5168 cm-3 a 0 "-0.12 cm'3 n c "0.06 o i N (Hl)t2 N(Hj ^8 x 10 cm"2 aQ ~4 x 1 0 - 1 0 cm-3 Tgas ~10°K Tgrains ~10°K Gravity PE/K6Z *2 2 ~200 pc M m o M® TABLE II : A L i s t of Symbols and Their D e f i n i t i o n s 0. Radius of dust grain (cm) flfcj E i n s t e i n p r o b a b i l i t y f o r downwards spontaneous t r a n s i t i o n s ( s e c 1 ) f>v V i s u a l e x t i n c t i o n , i n magnitudes New g a l a c t i c l a t i t u d e B„0-> .... Planck black body spectrum fo r i n t e n s i t y of rad-i a t i o n i n thermodynamic equilibrium (ergs cm"1 Hz" 1 ster" 1) &jk E i n s t e i n p r o b a b i l i t y c o e f f i c i e n t f o r induced r a d i a t i v e t r a n s i t i o n s (erg' 1cm 3) c V e l o c i t y of l i g h t , 2.998 x 10 1 0 cm sec' A df\ D i f f e r e n t i a l element of area (cm 1) ch D i f f e r e n t i a l l i n e element along the l i n e of sight (cm) eta D i f f e r e n t i a l s o l i d angle (steradians) f t . . . . . . . P a r t i t i o n function f o r atom i n stage of ion-i z a t i o n ft P a r t i t i o n function f o r free e l e c t r o n G Subscript r e f e r r i n g to grains <JAJ S t a t i s t i c a l weight of l e v e l ^ , f o r atom i n stage of i o n i z a t i o n A, k...... Planck constant, 6.625 x 10" erg sec H Neutral hydrogen atom I v S p e c i f i c i n t e n s i t y of r a d i a t i o n at frequency >v ju E m i s s i v i t y of matter per cm5 at frequencyv j Subscript f o r lower l e v e l i n atomic t r a n s i t i o n M. Boltzmann constant, 1.380 x 10'^ erg "K"1. Also, subscript f o r upper l e v e l i n atomic t r a n s i t i o n New g a l a c t i c longitude 1 Path length (cm) m Mass of e l e c t r o n , 9.12 x lO"z0gm. Mass of atomic hydrogen, 1.67 x 10" gm. M T o t a l mass M© Solar mass, 1.992 x 10 5 3 gm. rt' Density of p a r t i c l e s per unit volume (cm ) "rtjO^ ).... Density of p a r t i c l e s of element X i n stage A . of i o n i z a t i o n , l e v e l ^ of e x c i t a t i o n (cm - 3) 7iOW.... P a r t i c l e density of atoms of element X i n stage A of i o n i z a t i o n (cm" 3) n(X) P a r t i c l e density of X i n a l l stages of i o n i z a t i o n (cm"3) N Number of p a r t i c l e s i n a column of unit cross section along the l i n e of sight (cm" 1) Nj(X/J... . Number of p a r t i c l e s of element X i n stage of i o n i z a t i o n A, l e v e l j. of e x c i t a t i o n i n the l i n e of sight (cm-*0 ^ E f f i c i e n c y factor f o r e x t i n c t i o n by s o l i d p a r t i c l e s TABLE II cont'd R. Radius of a cloud (cm) A P o s i t i o n vector yd Integrated value of xt*, Av Atomic absorption cross-section for r a d i a t i o n at a frequency v (cm z) Integrated value of A V , uncorrected f o r induced emission t Time (sec) T Temperature (°K) fl Antenna temperature (°K) Tb Brightness temperature (°K) TL Cloud temperature (°K) \ K i n e t i c temperature (°K) T0 Background brightness temperature (°K) T% Spin temperature Uj, Radiation energy density per unit frequency i n t e r v a l (ergs cm"3 Hz _ i ) AVL F u l l width at h a l f i n t e n s i t y (Km Sec" 1 ) Right ascension i n hours, minutes and seconds £ D e c l i n a t i o n i n degrees, arcminutes and arcseconds Ji Wave vector (cm - 1) _ Kv Absorption c o e f f i c i e n t per cm of r a d i a t i o n of frequency v ^ Wavelength (cm) M F u l l width at h a l f i n t e n s i t y (KHz) v Frequency ( s e c - 1 ) °fi^Avr P r o b a b i l i t y of f i n d i n g p a r t i c l e of v e l o c i t y v i n the i n t e r v a l df-about -v. p. Mass density (gm cm"3) Kiv)o\?> P r o b a b i l i t y of f i n d i n g photon of frequency^ i n the i n t e r v a l dv about u t O p t i c a l depth Ti t O p t i c a l depth at a wavelength of 21-cm Tv V i s u a l o p t i c a l depth to Background o p t i c a l depth. TABLE III A L i s t of Dust Clouds Suitable for Observation OBJECT Si 19Jo) l z (195-0) 1 15 h5r00 s -04° 25' 4f2 35°.8 2 18 11 58 -18 11 12.7 -0.5 3 18 02 11 -04 32 23.5 8.2 4 18 25 31 -03 43 27.0 3.5 5 18 25 45 -03 34 27.1 3.5 6 18 23 07 -03 01 27.3 4.3 7 18 54 27 00 50 34.4 -0.8 8 18 53 07 02 10 35.4 0.1 9 20 54 23 43 30 84.7 -1.0 10 22 27 55 74 58 114.5 14.6 11 2 04 30 75 54 127.7 14.0 12 3 33 19 31 03 159.7 -19.6 13 4 15 27 28 18 163.7 -15.5 14 4 39 58 29 36 171.4 -10.6 15 4 26 07 24 32 173.3 -16.3 16 4 28 59 24 23 173.9 -15.9 17 4 38 30 25 18 174.6 -13.9 18 5 14 26 26 07 178.9 -6.7 19 6 29 50 10 32 201.5 0.6 20 5 51 12 3 19 203.3 -11.2 21 5 40 15 -10 14 214.5 -19.9 22 16 23 35 -24 30 352.9 16.7 23 16 24 15 -24 04 353.4 16.9 24 4 01 30 26 12 168.1 -19.1 25 4 15 18 25 29 170.8 -17.5 26 4 37 00 25 29 174.2 -14.0 27 5 15 18 7 17 195.1 -17.0 28 16 25 00 -19 15 357.3 19.9 29 4 15 27 28 18 168.7 -15.5 30 16 47 17 -17 58 1.9 16.6 31 16 47 51 -15 18 4.2 18.1 32 16 46 18 -14 10 4.8 19.3 33 15 51 18 -03 00 5.5 36.8 34 16 45 00 -12 40 5.9 20.4 35 22 35 00 75 00 114.5 14.7 36 3 40 00 31 40 160.3 -18.4 37 4 26 00 18 20 178.1 -20.5 38 15 37 12 -07 00 358.9 36.9 39 16 30 00 -23 44 40 22 21 30 74 55 TABLE IV: A L i s t o f Observed Sources OBJECT POSITION FULL PROFILE DATA DIFFERENCE DATA 1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 15 52 06 22 28 19 2 06 33 34 37 16 45 41 18 27 23 30 15 39 47 15 44 31 00 52 18 41 15 16 24 51 16 25 31 02 47 16 35 38 17 16 26 16 26 14 4 16 45 16 48 30 16 49 03 16 47 29 15 52 24 16 46 11 22 35 27 3 41 19 4 27 13 15 38 19 16 31 16 22 21 51 3 4 4 4 4 4 5 6 5 5 4 4 4 5 -4 29 75 04 76 00 31 07 28 21 29 28 24 35 24 26 25 20 26 08 10 31 3 19 -10 13 -24 33 -24 07 26 15 25 32 25 31 7 18 -19 18 28 21 -18 00 -15 20 -14 12 -3 04 -12 42 75 07 31 44 18 23 -7 04 -23 47 75 01 X xxtxbdxj Ixl XXX X XX X xxxxixj XXX XXX XXX x x x x l x x x x x x X XX PCX X XX X X X XX x x x t x M X xxjxl xl Ixl X X XX XX xxxlxlx XXXX XX XX X Ixx X XXX X KXXl XXXX X X X X X txpqxxxl X X XX x x x l X X x x x x x x x x x x x x x x x X XXX|X|X|XjX|X|X| XX XX x x x x x x x x x XXXX XX X X X XXX X x x x x x XXXX TABLE V: The 21-cm Line Standard C a l i b r a t i o n Sources REGION GALACTIC CO-ORDINATES EQUATORIAL CO-ORDINATES YtsR PEAK T b JiT (I9SO) ^x(l<)SO) C Km/sec.) C ° K ) S6 (not IAU) 1V91 41V42 15 h28^58 s -2°15' 0 51 ± 4 S7 IAU 132?00 -1?00 2 h 2m 38s 60" 19' -45 to -55 99 j t 7 S8 IAU 207?00 -15?00 5 1 . 4 9 * 5 0 s -l°4l' 7 72 t 5 S9 IAU 356?00 -4.00 17>,48*n465 -34° 25' 6 85 ± 6 TABLE VI: Observational Results of HI Survey i n Dense Dust Clouds OBJECT POSITION Vt.SR N(HI) A T COMMENTS h m s o K^/ sec K m/sec jc |0+'9 c m ' 1 ° K 1 15 51 00 -04 25 + 3.0 4.0 -5.0 1.6 4.2 L 134 VOH = + 3.0, V H l co = + !•?, 38 15 37 12 -07 00 + 4.6 2.1 +1.6 1.0 3.0 L17-7-8, LI78tJ 30 16 47 17 -17 58 14 4 39 58 29 36 V O H = K"i/set 11 2 04 30 75 54 Von = +3-0 K-n/sec 24 4 01 30 26 12 + 9.0 3.3 -2.8 ±. 1.5 3.0 H-l-SXIO^cm-1-19 6 29 50 10 32 + 4.0 7.0 +9.2 dc 7.1 6.8 V O H = +5\3 Km/Sec 25 5 14 26 26 07 H+3.5X)o l 9<«M.5' Km/sec 18 5 14 26 26 07 VOH = +?-2 Kro/sec 32 16 46 18 -14 10 ( 1 5 4 26 07 24 32 + 7.5 4.0 -12.1 ±- 3.8 13.0 V O H : + 4 - 4 H-l.0x|O'9em-»-1 16 4 28 59 24 23 V O H = +-?-7 K^/sec / 1 7 4 38 00 25 18 V O H * +^-' Km /sec 1 26 4 37 00 25 29 + 8.0 2.1 -6.1 1.6 10.5 H - 9 . 1 * 1 0 ' 9 @ £ ^ Km/sec, f 10 22 27 55 74 58 V O H =-4.0 Km/sec , L /Z5/ 35 22 35 00 75 00 . 40 22 21 30 74 55 J T2 1. Low energy cosmic ray d i s s o c i a t i o n . 2. Hydrostatic equilibrium 1 1. Constant gas to dust density r a t i o . 2. Excesses or d e f i c i t s masked by fluctuations, 1. A genuine "hole". 2. A cold absorbing cloud. 3. Hydrogen i s i n molecular form. FIGURE 1. The Possible Behaviour of 1~zt versus TV F I G U R E 2. A B l o c k D« Qgram o f the Receiv/mg E q u i p m e n t F R O N T E N D Feed D i r e c t i o n a l ffoise TUbe Parana p Solid State B A C K E N D TilMtfe First Sf«.«e ^ 1 * ^ Pre-cunp X P a r a m p Controls BOUDMS Filter* /O.^MHiflmp. fl.G.C. S*csru( 3t4je M i x e r S P E C T R O M E T E R AND C O M P U T E R Fitters ivfeewiti VT J*iAAAAA-Oij'.tal Voltmeter anal I«t««-f*ee Chart poP-9 C o m p u t e r Papar-lapeRmdh FIGURE 3. The Method of R e f e r e n c i n g on a Dust C l o u d BRIGHTNESS TEMPERATURE (21. CM) -3.0 o.o -3.0 o.o r-i a w H ar a> > < ro OJ oo ro o H« M l M l fl> (0 3 o ro & w X T3 ro o rt ro a »—1 c o rt C 0J rt o 3 M l o O cr ro o rt 1 T BRIGHTNESS TEMPERATURE (21. CM) Tl M O § PI H a-> < ro OQ ro o H-hh Mi (D H ro o ro a w x *o ro o rt ro a T l M c o rt C 0) rt r1' O P Ml o H O cr ro o rt Co -6.0 c s a o to o I CO " O C O < rn' . a-5 £ .o C O m o o o a BRIGHTNESS TEMPERATURE (21 -3.0 0.0 r3.0 CM) 0.0 m X ~D rn o —i rn a cz ZD —\ i—t o rn x> CD rn o rn rn o rn 3.0 I o CD m c z cu rn 0 0 CO 1 1 1 1— -3.0 0.0 -3.0 0.0 BRIGHTNESS TEMPERATURE (21. CM) •10.0 B R I G H T N E S S J5pPERflTUj?£ (21 CM) o.o Ul o ro a i C O ' CD CO TO 5-° CO m o o o CO o • cn O ' (O m -v rn o —i m o o —i c: x> —i i — i Q rn TO ZD CD rn o i — i ~n rn TO rn ci rn 5.0 l O CD P I CD rn o ID -< n i 1 1 -10.0 -5.0 0.0 -5.0 0.0 BRIGHTNESS TEMPERATURE (21. CM) ~i 5.0 

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