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The CO distribution around 1=30°, b=0° Szabo, Alexander 1980

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THE CO DISTRIBUTION AROUND 1=30°, b=0° by ALEXANDER SZABO B. Sc., The U n i v e r s i t y of B r i t i s h Columbia, 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1980 © Alexander Szabo In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I further agree that permission for extensive copying of th i s thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my writ ten permission. Department of P h y s i c s The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date March 20, 1980 6 i i A b s t r a c t The 4.6m m i l l i m e t e r wave t e l e s c o p e at the U n i v e r s i t y of B r i t i s h Columbia has been used t o map a re g i o n 1/2° i n diameter centered on 1=30°, b=0° i n the J=1->0 t r a n s i t i o n of * 2C**0. This study o f the i n n e r edge of the g a l a c t i c molecular r i n g has r e v e a l e d two w e l l d e f i n e d g i a n t molecular c l o u d s with diameters o f approximately 30 pc and masses i n the order of 5 x 10 s M©..In a d d i t i o n our a n a l y s i s i n d i c a t e s t h a t a s u b s t a n t i a l f r a c t i o n , amounting t o approximately 30%, of the i n t e g r a t e d CO i n t e n s i t y comes from a f e a t u r e c o v e r i n g the e n t i r e f i e l d observed. We have a l s o found a complex of fou r c l o u d s whose l i n e w i d t h s are a f a c t o r of two g r e a t e r than those of the standard g i a n t molecular clouds. The nature of these c l o u d s i s a t present u n c e r t a i n . The number o f clouds detected i n our survey g i v e s as 5000 the t o t a l number of g i a n t molecular clouds i n the galaxy._ S u p e r v i s o r : D r . W . L . H . S h u t e r Table of Contents page A b s t r a c t . . . . i i L i s t Of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i v L i s t Of F i g u r e s ............................................. y Acknowledgements . . v i 1. INTRODUCTION . ...1 2..DATA ACQUISITION 3 2.1 Equipment ............................................. 3 2.2 Observing Sequence 5 2.3 C a l i b r a t i o n 8 2.4 P r e l i m i n a r y P r o c e s s i n g ...............................11 3. DATA ANALYSIS ....14 3.1 R e p r e s e n t a t i o n .......................................14 3.2 Model F i t t i n g ........................................ 17 3.3 R e s u l t s 18 4. CONCLUSION 27 B i b l i o g r a p h y 29 i v L i s t o f Tables page 1. Summary Of Observing Program 9 2. Cloud Parameters Derived From Model F i t t i n g 22 3. A s t r o p h y s i c a l Parameters Of Clouds 2 And 3 .............. 25 V L i s t o f F i g u r e s page 1. View Of The Galaxy Showing The Molecular Ring And The P o s i t i o n Of Our Map ......................................2 2. Schematic Diagram Of The UBC 80-120 GHz Cooled Receiver ..4 3. Diagram Of The Beam P o s i t i o n s Observed ................... 6 4. Spectrum At The Reference P o s i t i o n ......................12 5. Ordered S p e c t r a P l o t Of The Observed Data ............... 15 6. P l o t s I l l u s t r a t i n g The R e s u l t s Of Model F i t t i n g .,.,,.,,.19 v i Acknowledgements I thank my t h e s i s s u p e r v i s o r , Dr. W.L.H. Shuter, f o r h i s a v a i l a b i l i t y , s u ggestions and encouragement over the l a s t two years. I thank the other members of the m i l l i m e t e r astronomy group: Dr. W.H.. McCutcheon and Mr. C. Chan f o r t h e i r c o n t r i b u t i o n t o t h i s p r o j e c t . F i n a l l y , I thank the Computing Center f o r t h e i r h elp with the numerical c a l c u l a t i o n s . 1 1. INTRODUCTION U n t i l r e c e n t l y astronomers s t u d y i n g the l a r g e s c a l e s t r u c t u r e o f the galaxy were l i m i t e d to the d e t e c t i o n of r a d i o waves from i n t e r s t e l l a r hydrogen atoms at a wavelength of 21 cm. Improvements i n r e c e i v e r technology have made i t p o s s i b l e to complement t h i s work with s t u d i e s of the d i s t r i b u t i o n of molecular m a t e r i a l i n the galaxy by the d e t e c t i o n of r a d i o waves from i n t e r s t e l l a r carbon monoxide (CO) molecules a t a wavelength of 2 . 6 mm. P r e v i o u s s t u d i e s of CO i n the g a l a c t i c plane (Gordon and Burton 1 9 7 9 ) have determined t h a t the molecular component of the i n t e r s t e l l a r gas forms a vast r i n g of c o l d s t a r - f o r m i n g c l o u d s . These s t u d i e s were l i m i t e d i n t h a t they were under sampled (beam p o s i t i o n s spaced at i n t e r v a l s l a r g e r than the beam width) and the surveys were one dimensional (beam p o s i t i o n s at 1 = 1 0 + n&l, b=0°) and thus i n f o r m a t i o n on i n d i v i d u a l c l o u d s was i n f e r r e d with some d i f f i c u l t y . In order to o b t a i n b e t t e r i n f o r m a t i o n on the nature and s i z e d i s t r i b u t i o n of i n d i v i d u a l clouds, a well sampled survey i n a two dimensional g r i d i s necessary. The study presented here r e p r e s e n t s one of the f i r s t attempts to do t h i s . F i g u r e 1 shows the l o c a t i o n of our survey on a d e p i c t i o n of the Galaxy.. We decided t o c e n t e r our survey at 1=30°, b=0° because t h i s was an area of e s p e c i a l l y strong CO emission. In chapter 2 , Data A c q u i s i t i o n , we d i s c u s s the methods used t o o b t a i n the data. This should prove u s e f u l to others i n v o l v e d i n m i l l i m e t e r mapping p r o j e c t s . In chapter 3, Data A n a l y s i s , we present the data and our i n t e r p r e t a t i o n of i t s s i g n i f i c a n c e . . T h e main p o i n t s are summarised i n the C o n c l u s i o n (chapter 4 ) . FIGURE 1 : View of the Milky-way galaxy from the no r t h g a l a c t i c pole showing the m o l e c u l a r r i n g and the l o c a t i o n o f our survey i n the g a l a c t i c plane. The m o l e c u l a r r i n g i s b e l i e v e d t o have i t s maximum d e n s i t y j u s t o u t s i d e the t a n g e n t i a l p o i n t a t 1 = 3 0 ° . 3 Is. DATA ACQUISITION 2.1 Equipment The o b s e r v a t i o n s of 1=30°, b=0° which we d e s c r i b e here were obt a i n e d u s i n g the 4.6m m i l l i m e t e r wave t e l e s c o p e at the U n i v e r s i t y of B r i t i s h Columbia (Shuter and McCutcheon 1974, Mahoney 1976). The t e l e s c o p e i s l o c a t e d at l a t i t u d e 49° 15* 11" N, l o n g i t u d e 123° 13« 56" W, a t an e l e v a t i o n o f 50 meters. At 115 GHz the p a r a b o l o i d has an e f f e c t i v e beam width of 0.04 degrees which ccmpares with the t e l e s c o p e p o i n t i n g accuracy of ±0.0 2 degrees. F i g u r e 2 shows a schematic diagram of the r e c e i v e r . At 115 GHz the system noise temperature was 900 k e l v i n (SSB). The s p e c t r a were obtained using a 112 channel f i l t e r spectrometer. Each channel was one MHz wide. The spectrometer degraded the t h e o r e t i c a l noise f i g u r e by a f a c t o r o f 2.5. The s p e c t r a were manipulated, a f t e r i n t e g r a t i o n i n a d i g i t a l s i g n a l averager, by a NOVA 1200 minicomputer. F I G U R E 2 : S c h e m a t i c d i a g r a m o f t h e U B C 80-120 G H z c o o l e d r e c e i v e r CHOPPER SENSOR CHOPPER MOTOR / 20 K D E W A R PARAMETRIC DH LO COUPLER AMPLIFIERS HARMONIC MIXER KLYSTRON LO ERROR VOLTAGE FREQUENCY METER 60 MHz I F ERROR VOLTAGE SYNCH-RONIZER R E F 6o MHz "UPPER PHASE LOCK" SIGNAL #1 #2 I SOL 1st I F MIXER ? AMP IS0I TUNABLE X T A L i ^ 5X ~5 MHz LO kkXO MHz 2nd MIXER HARMONIC MIXER B W 0 U X LO HARMONIC GENERATOR 2nd IF AMP PHASE SHIFTER ~25 MHz REF SYNCH-RONIZER riF ~ 25 MHz " LOWER PHASE LOCK" CHOPPER CONTROLS an. GAIN MODULATOR DRIVER RADIO-METER SPECTRO-METER CHART *RECORDER SIGNAL AVERAGER 5 2.2 Observing Sequence F i g u r e 3 shows the beam p o s i t i o n s i n our survey as they would appear on the sky. The spacing between adjacent beam p o s i t i o n s i s 0.05 degrees. The 89 beam p o s i t i o n s i n our map f a l l i n s i d e an area the s i z e of the Moon (as seen from the E a r t h ) . For convienence the team p o s i t i o n s were d i v i d e d i n t o f o u r groups (quarters) and d i f f e r e n t o b s e r v i n g methods were used t o o b t a i n the s p e c t r a i n each group. The s p e c t r a f o r the f i r s t q u a r t e r were o b t a i n e d by a l t e r n a t i n g between ON source (S) 'scans' and OFF source (E) or r e f e r e n c e 'scans'. The term scan used i n t h i s paper r e f e r s to o b t a i n i n g a spectrum by i n t e g r a t i n g on a s i n g l e f i x e d beam p o s i t i o n . Unless otherwise noted scan i n t e g r a t i o n times were 320 seconds. The purpose of o b t a i n i n g r e f e r e n c e scans i s to s u b t r a c t out the c o n t r i b u t i o n of the sky t o the s p e c t r a . Each spectrum i n the f i r s t q u a rter was the sum of fou r c o n s e c u t i v e ON source minus OFF source p a i r s . We w i l l r e p r e s e n t t h i s as f o l l o w s l 1 i 1 i 1 i 1 S E S R S R S R Each n i g h t s p e c t r a were o b t a i n e d at f i v e map p o s i t i o n s one of which was always the c e n t e r p o s i t i o n . The common spectrum was used to check the accuracy o f our r e l a t i v e c a l i b r a t i o n . S i nce one t h i r d of the observinq time i s spent moving the t e l e s c o p e from one map p o s i t i o n t o another and of the remaining time one h a l f i s spent on the OFF source p o s i t i o n i t was f e l t t h a t the mapping e f f i c i e n c y c ould be improved by adopting a d i f f e r e n t o b s e r v i n g sequence. For the second quarter scan 6 BEAM / \ 3 S © 0 © S C A L E 0.10 d e g . 2HHK2 3)(T)(3-1J(3 3 3 2 3 2 3 2 I 2 3 COORDINATES OF MAP C E N T E R : o < ( l 9 5 0 ) = 18H 43.5M S ( l 9 5 0 ) = - 2 ° 40' ©@® \ \ 4 T 4 2 1 1 K 3 ?H2 1 r / / F I G U R E 3 s D i a g r a m o f t h e beam p o s i t i o n s o b s e r v e d . T h e map beam p o s i t i o n s h a v e b e e n d i v i d e d i n t o f o u r g r o u p s l a b e l e d 1 , 2 , 3, 4. 7 i n t e g r a t i o n times were i n c r e a s e d to 640 seconds to cut i n h a l f the number of t e l e s c o p e moves. A l s o the scans were o b t a i n e d i n such a way t h a t one OFF source scan c o u l d be shared by two ON source scans, thus c u t t i n g i n h a l f the number of r e f e r e n c e scans. How t h i s was achieved can best be i l l u s t r a t e d as f o l l o w s i 1 i 1 i 1 R S| S| R S,^ H Ft . _ . . _ 1 i 1 1 1 ) where S. , S 2, S 3 # ... are d i f f e r e n t beam p o s i t i o n s . Beam p o s i t i o n s using the same R were r e l a t i v e l y f a r apart to minimize the c o r r e l a t e d noise i n t r o d u c e d by smoothing ( e x p l a i n e d l a t e r ) . N o t i ce t h a t t e l e s c o p e moves are a l s o saved because adjacent ON source p o s i t i o n s are the same. The net a f f e c t was t h a t we could .J now spend twice as' much time ON source per n i g h t than b e f o r e . T h i s improvement was not however without a p r i c e . . On some n i g h t s the sky would change r a p i d l y enough to make sky c o r r e c t i o n d i f f i c u l t with long scan times. Thus spectrum b a s e l i n e s were i n general worse than before with s h o r t scans. Also i t was d i s c o v e r e d t h a t by doing a l l the o b s e r v a t i o n s f o r a s i n g l e map p o s i t i o n at one time r e l a t i v e c a l i b r a t i o n would be d i f f i c u l t . Taking t h e s e . t h i n g s i n t o account the s p e c t r a f o r the t h i r d and f o u r t h q u a r t e r s were ob t a i n e d using 320 second i n t e g r a t i o n times and the observing sequence 1 1 i 1 1 1 S| B S-j R S j j R . . . I 1 1 1 1 1 where as before a l l the S, , S z, S 3, ... are d i f f e r e n t and p a i r s 8 Sj , Sj using the same E are r e l a t i v e l y f a r apart t o minimize the e f f e c t s o f c o r r e l a t e d n o i s e . The same map p o s i t i o n s , i n a d i f f e r e n t order, would he observed again on ot h e r n i g h t s . In t a b l e 1 we summarize the dates, p o s i t i o n s and o b s e r v i n g sequences used t o o b t a i n the s p e c t r a . Also i n c l u d e d i s an i n d i c a t i o n o f the atmospheric transparency on each n i g h t . 2.3 C a l i b r a t i o n The c a l i b r a t i o n of r a d i o a s t r o n o m i c a l s p e c t r a l l i n e o b s e r v a t i o n s at m i l l i m e t e r wavelengths i s normally a two step pr o c e s s . F i r s t , an observed s i g n a l i n t e n s i t y i s converted to an antenna temperature, T^, by assuming the Bayleigh-Jeans approximation and comparing the observed spectrum to a c a l i b r a t i o n spectrum of known temperature. I n p r a c t i c e t h i s was accomplished by s w i t c h i n g o f f the g a i n modulator and o b t a i n i n g a c a l i b r a t i o n spectrum of the synchronously detected output between the chopper wheel absorber at ambient temperature, T f l r 1 B , and the sky. The sky temperature, T S K y , was measured by comparison t o the c h a r t r e c o r d e r l e v e l s of a l i q u i d n i t r o g e n temperature absorber and an ambient temperature absorber placed i n f r o n t o f the feed a t the s t a r t of the observing s e s s i o n . 9 TABLE J. SUMMARY OF OBSERVING PROGRAM Date (197 8) f - — May 19 20 21 25 30-31 Map P o s i t i o n s Observed + + -| f i r s t q u a r t e r Observing Sequence (S-R) 7? <b> T (nepers) 45 42 33 40 40 31- 1 J u n e l - 2 2- 3 3- 4 4- 5 second quarter (a) R S S R . 39 . 38 .43 .45 H R r e f e r e n c e d E R R . 39 17- 18 18- 19 19- 20 20- 21 22-23 t h i r d and f o u r t h q u a r t e r s S R S . 57 34-.44 42-.50 52-.59 .51 +-26- 27 27- 28 28- 29 poor q u a l i t y s p e c t r a redone S R S . 55 .48 37-.49 (a) Each scan was 640 seconds l o n g f o r t h i s observing sequence whereas each scan was 320 seconds long f o r a l l the other methods. T h i s i s the atmospheric transparency (see 2.3 C a l i b r a t i o n ) . 1 0 The second s t e p i s t o c o r r e c t Tfl f o r atmospheric l o s s e s ( e-Ts sec Z j a n < j antenna l o s s e s (r\ ) to determine the t r u e source b r i g h t n e s s temperature, Tft l . The standard r e s u l t f o r a plane p a r a l l e l atmosphere i s T^ = Tft *\ e - T s S € c 2 In the above formula z i s the z e n i t h angle of the source and Ts i s the z e n i t h a t t e n u a t i o n i n the s i g n a l band, which i s r e l a t e d t o the z e n i t h a t t e n u a t i o n i n the image band, T- , and the average a t t e n u a t i o n , T , as f o l l o w s 7" = ( T S • T, ) / 2 Assuming the standard formula T can be c a l c u l a t e d given the known q u a n t i t i e s T S K > / , T f t^ Q and z. From o b s e r v a t i o n of Orion A and M17 SW, adopting peak b r i g h t n e s s temperatures of 7 0 K and 4 0 K r e s p e c t i v e l y , we determined t h a t = 1 . 7 5 T and = 0 . 4 5 f o r CO o b s e r v a t i o n s with our 4 . 7 5 GHz IF and t e l e s c o p e d i s h . The equations and b r i g h t n e s s temperatures used above can be found i n a paper by O l i c h and Haas ( 1 9 7 6 ) . 1 At m i l l i m e t e r wavelengths t h i s q u a n t i t y i s normally r e f e r e d to as t h e excess r a d i a t i o n temperature because i t i s i n f a c t the excess emission of the l i n e r a d i a t i o n over the continuum r a d i a t i o n of the cosmic background. 11 2.4 P r e l i m i n a r y P r o c e s s i n g A f t e r the e n t i r e observing program was completed we began t o prepare t h e data f o r a n a l y s i s . The f i r s t s t e p was t o c o l l e c t and average t o g e t h e r a l l the s p e c t r a a t the same map p o s i t i o n . The average was weighted a c c o r d i n g to the square o f the c a l i b r a t i o n c onstant used to c o n v e r t T R to T^ f o r each spectrum. Thus ? C 2 x ( i t h spectrum) Average Spectrum = — !  T C.z where c . = ^ e , r s s e c z J I i t h spectrum To c o r r e c t f o r any CO e m i s s i o n i n the r e f e r e n c e p o s i t i o n , R (3° west of map c e n t e r ) , we 'referenced* t h i s p o s i t i o n t o two other p o s i t i o n s , R1 (8° west of map center) and B2 (7.5° west, 2° n o r t h o f map c e n t e r ) . Based on the d i f f e r e n c e s R-R1, R1-R2 and R2-R we adopted the spectrum shown i n f i g u r e 4 as the CO em i s s i o n i n the r e f e r e n c e p o s i t i o n . The second s t e p was to add t h i s spectrum to each of the map p o s i t i o n average s p e c t r a 2 . The t h i r d step was t o c o r r e c t the spectrum b a s e l i n e s by removing a second order polynomial f i t t o those p a r t s of the 2 T h i s i s a mistake! The noi s e p r o f i l e of f i g u r e 4 can be seen i n most of the s p e c t r a shown i n f i g u r e . 5. A l l of the r e f e r e n c e spectrum except f o r the r e g i o n around channel 79 should have been s e t t o zero before adding t o the data s p e c t r a . . T A (K) 10 f 0 4 ^ 100 v e l o c i t y f r e q u e n c y SPECTROMETER CHANNEL NUMBER -10 1 F I G U R E k t S p e c t r u m a t t h e r e f e r e n c e p o s i t i o n ( l o c a t e d 3 d e g r e e s w e s t o f map c e n t e r ) . T h e s p e c t r u m h a s b e e n s m o o t h e d i n f r e q u e n c y b y t h e t r i a n g u l a r f u n c t i o n d e s c r i b e d i n t h e t e x t . T h e r e i s a 5«5K s i g n a l p e a k i n g i n c h a n n e l n u m b e r 79 w h i c h c o r r e s p o n d s t o a n LSR v e l o c i t y o f 9.3 k m / s . 13 spectrum thought t o have no s i g n a l ( i , e . t h e : f i r s t 2 8 and the l a s t 28 ch a n n e l s ) . T h i s a l s o allowed us to c a l c u l a t e <y = { ( 2 sz + Y. sz ) / 56 3 V 2 where v i s the channel number and S i s the s i g n a l i n channel v. We adopted C as the r o o t mean square (EMS) d e v i a t i o n f o r the spectrum. The f i n a l step was to smooth the data to improve the s i g n a l to n o i s e r a t i o . . In frequency the data was smoothed by the t r i a n g u l a r weighting f u n c t i o n S v (smoothed) = ( Sv_, + 2 S v + S v + l ) / 4 S p a t i a l l y t h e s p e c t r a were smoothed by a two dimensional g a u s s i a n weighting f u n c t i o n of FWHM 0 . 0 8 degrees and f u r t h e r weighted by the squares of the RMS d e v i a t i o n O * c a l c u l a t e d e a r l i e r S y ( s p a t i a l l y smoothed) = 2 q v 2 G C U o C - c O 2 • ( S ' - S ) 2 W 2 ] > D ( o ( , S # v ) = the "observed" data where the index o( % r e f e r s to the map p o s i t i o n o f the spectrum and G(x) = e - a x l ; G ( 0 . 0 4 ) = 1/2.. 14 Is. DATA ANALYSIS 3 . 1 B e p r e s e n t a t i o n Our next problem was to f i n d a meaningful way of d i s p l a y i n g the d a t a . We f i r s t t r i e d contour p l o t s at f i x e d v e l o c i t i e s . These proved to be d i f f i c u l t t o i n t e r p r e t s i n c e about 50 o f them were r e q u i r e d t o cover the range of p o s s i b l e v e l o c i t i e s . What we needed was a method of compressing our data i n t o a one page ' p i c t u r e * . We attempted t o do t h i s by using c o l o r f o r the v e l o c i t y dimension and the i n t e n s i t y of the c o l o r f o r the temperature dimension (Srllen 1 9 7 6 , H e i l e s and J e n k i n s 1 9 7 6 ) . Since the OBC Computing Center d i d not have the c o l o r g r a p h i c s f a c i l i t i e s r e q u i r e d , we d evised a process using black and white calcomp p l o t s and c o l o r f i l t e r s t o produce the c o l o r p i c t u r e s . A f t e r t h r e e months of e f f o r t we gave up the c o l o r p i c t u r e making. In sh o r t the method f a i l e d because the human eye does not allow a simple s e p a r a t i o n of c o l o r and c o l o r i n t e n s i t y . A f t e r t h i s we t r i e d s e v e r a l d i f f e r e n t ordered contour and s p e c t r a p l o t s f i n a l l y d e c i d i n g on the r e l a t i v e l y common format shown i n f i g u r e 5. F i g u r e 5 shows c l e a r l y the q u a l i t y of our spectra but i t i s d i f f i c u l t t o see how f e a t u r e s on d i f f e r e n t s p e c t r a c o r r e l a t e . Contour p l o t s showed t h i s c o r r e l a t i o n q u i t e c l e a r l y but of course only a t one v e l o c i t y . I t became apparent t h a t we would never c l e a r l y 'see' the CO d i s t r i b u t i o n i n our data d i s p l a y s . 1 5 F I G U R E 5 • O r d e r e d s p e c t r a p l o t o f t h e o b s e r v e d d a t a w h i c h h a s b e e n s m o o t h e d t o a v e l o c i t y r e s o l u t i o n o f 5 - 2 k m / s and a n a n g u l a r r e s o l u t i o n o f 0 . 0 8 d e g . T h e c e n t e r o f e a c h s q u a r e r e p r e s e n t s t h e c o o r d i n a t e o b s e r v e d . GALACTIC PLANE (1*30° b«0°) CO J - l - 0 coordinates at map center: a (1950.0)« 18 H 43.5 M 5 (1950.0)—2° 40' S h+ 12 h + 6 h 0 -A. - 6 \.rJ\_ 4 J U v 4 J L^U —4. d J L —dJ dJl^AJ — 12 udj ^ U l . M . . ) UdJuA ^ d j I . J U UdJUd. l-Jl.) d^JUdJ - 1 , - d J U * l -dJUdJ - A -1 - d .rVl, UdJ l-vyj TA(K) r. , l 0 100 10 0 V L S R(km/s) + .8 M +.4 -I I I 1_ 0.0 -.4 L_ -.8 M j i F I G U R E 5 17 3 . 2 Model F i t t i n g To determine what s o r t of CO c l o u d d i s t r i b u t i o n s made up our map we d i d some model f i t t i n g . We assumed t h a t a s i n g l e g i a n t molecular c l o u d produced a temperature p r o f i l e given by - 6 S[ (o<0-c*)2 + ($„-$) 2 ] - G,(v 0-v)z T(o( . % ,v ) = T c e where ol , & and v are the c o o r d i n a t e s i n the map and T c , Gs , Gr i ^0, S « , f vo a r e the s i x parameters which d e s c r i b e the cl o u d . The s i m p l i f y i n g assumption t h a t the temperature due to two clouds Tj and Tj at id, %> ,v ) equals the sum of the i n d i v i d u a l temperatures , Tj id , % r V ) + Tj (o( , % ,v ) was a l s o made. The model f i t t i n g c o n s i s t e d of minimizing E = Z [ D ( d , S , ? ) - 2 T, {o< , S ,v ) ) 2 with r e s p e c t to the s i x parameters TQ , G s, Gr , o(D, S 0 , \ i n each of the T j . T h i s i s a n o n l i n e a r problem and as f a r as we know has no gen e r a l or unique s o l u t i o n . . We proceeded by guessing a s o l u t i o n based on v i s u a l i n s p e c t i o n of the v a r i o u s p l o t s obtained b e f o r e . Our i n i t i a l guess c o n s i s t e d o f 12 clouds or 7 2 parameters f o r the v e l o c i t y range 6 1 - 1 1 3 km/s. We used the Computing Center r o u t i n e DFNMIN t o n u m e r i c a l l y improve the s o l u t i o n . A f t e r a few hundred 18 i t e r a t i o n s two of the clouds disappeared i n t o the noise so we removed them from the s o l u t i o n and continued i t e r a t i n g u n t i l convergence with the remaining 10 c l o u d s . The r e s u l t s of t h i s f i t t i n g procedure are i l l u s t r a t e d i n f i g u r e 6 and the 6 optimized parameters f o r each of the 10 c l o u d s are given i n t a b l e 2. F i g u r e 6(a) shows the data, D (o( , $ , v ) , and f i g u r e 6(b) shows the model, !^T, ( c ( , $ , v ) . The q u a l i t y of the f i t may be judged from the s i z e of the r e s i d u a l s , f i g u r e 6 ( c ) , which are comparable with the noise i n f i g u r e 5. For one cl o u d (cloud 2) q u i t e good e s t i m a t e s of the parameters were obtained from v i s u a l i n s p e c t i o n of the ordered contour and s p e c t r a p l o t s and these d i d not change s i g n i f i c a n t l y from the f i n a l v a l u e s o b t a i n e d from the f i t . 3.3 R e s u l t s The r e s u l t s of our a n a l y s i s have been p u b l i s h e d (Szabo, Shuter and McCutcheon 1980) and can be summarized i n the f o l l o w i n g way. The CO f i e l d shows three p r i n c i p a l f e a t u r e s : (1) an extended f e a t u r e c o v e r i n g the e n t i r e f i e l d observed (cloud 1 i n t a b l e 2) shown i n f i g u r e 6 ( d ) ; (2) two 'normal* g i a n t molecular c l o u d s (clouds 2 and 3) shown i n f i g u r e 6(e) and (f) ; (3) a blend of 4 clouds with very broad s p e c t r a l l i n e s a l l of which have almost the same c e n t r a l v e l o c i t y (clouds 4,5,6,7) shown i n f i g u r e 6 ( g ) . In a d d i t i o n to the above there are three r e s i d u a l minor c l o u d s (clouds 8,9,10) shown i n f i g u r e 6 ( h ) . We d i s c u s s these f e a t u r e s i n t u r n . 19 F I G U R E 6 : P l o t s i l l u s t r a t i n g t h e r e s u l t s o f m o d e l f i t t i n g . a ) T h e o b s e r v e d d a t a , D(e<, J% , b e t w e e n t h e v e l o c i t i e s 61 a n d 113 k m / s i n f i g u r e 5 i s r e p r o d u c e d . b) T h e c o m p u t e d s p e c t r a f o u n d f r o m t h e sum o f t h e c o n t r i b u t i o n s o f c l o u d s 1 t h r o u g h 1 0 , ^ T j « S , v ) • c ) T h e r e s i d u a l s o b t a i n e d b y s u b t r a c t i n g t h e sum o f t h e c o n t r i b u t i o n s i n t h e m o d e l (b ) f r o m t h e d a t a ( a ) . d) T h e e x t e n d e d f e a t u r e . T h i s i s " c l o u d " 1 i n T a b l e 2 . e & f ) T h e g i a n t m o l e c u l a r c l o u d s 2 a n d 3 i n T a b l e 2 . g) T h e b r o a d s p e c t r a l l i n e c l o u d s . T h i s i s t h e sum o f t h e c o n t r i b u t i o n s o f c l o u d s 4, 5t 6 a n d 7. h) T h e " m i n o r " c l o u d s , s o d e s i g n a t e d b e c a u s e t h e y o n l y c o n t r i b u t e 10% t o t h e t o t a l i n t e g r a t e d C O , w h e r e a s t h e e x t e n d e d f e a t u r e , t h e g i a n t m o l e c u l a r c l o u d s a n d t h e b r o a d s p e c t r a l l i n e c l o u d s e a c h c o n t r i b u t e a b o u t J0%. T h i s i s t h e sum o f t h e c o n t r i b u t i o n s o f c l o u d s 8 , 9 a n d 1 0 . 20 SCALE -0 .1* BEAM L-^k-^k-^ L 3 LZJ ld»fl t£fl t£3 Lri U i^ l-A k-^l k^ N k-^i k ^ I ^ k ^ L ^ k ^ k ^ k ^ k ^ [ ^ L ^ l ^ l ^ i ^ k ^ k ^ k ^ k ^ l ^ l ^ | ^ | ^ k - ^ k ^ k ^ k ^ L ^ L ~ j l ^ k ^ k ^ k ^ k ^ k ^ k ^ l ^ L ^ l^ /N l/^ N l-^ N U/\ k A k A k A k-A k ^ I——n! L~J b ^ ^ b ^ k ^ k / ^ k A k ^ k ^ k ^ L — ] ^ U ^ b ^ k ^ l ^ ^ k ^ k ^ l ^ l ^ l ^ U ^ k ^ k ^ k ^ k ^ k ^ k ^ k ^ k ^ t ^ L ^ d ^ l ^ i ^ k ^ L ^ k T ^ L ^ L ^ J k ^ k ^ b ^ l ^ k ^ k ^ k ^ j k ^ J k — j t ^ t ^ k ^ l ^ k ^ k ^ k ^ k ^ L ^ j hA k^ N k^i k^) k-^M U-M fc3 t 3 L 3 \dl k3 L 3 kr3 L 3 k^k^Nk-^ ( a ) ^ b ( b ) a ^  ** ^ L J U J L J \ A\ A\ A L_-JL_JI )( JL^L_JL-J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J u u u u u u u u u L ^ L ^ L J L J L J L J L J L J L J I—JI—)l )I )I—Jl^  )t Jl^  J[ )L -J l ^ l ^ l ^ L ^ L ^ L ^ L ^ L J L J L J L J i;—)L Jl J( 31 Jl—jr^  3LOI JL_-JL_ -J I ^ L ^ L ^ L ^ L ^ L d L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L ^ L ^ I ^ U ^ L J L J L J L J L J L J L J !—JL—)L—)'—11—JLJLJI 1LJ L ^ U ^ L J L J L J L J L J L J L J L_JL—JL—11—11 )! J! J[ J L J • [ ^ [ ^ L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L J L_J L J l_J [_J L - J L J L J L J L J L J (c) (d) T ; ( K ) 'I n 1 °6I 113 V L S R(km/$) F I G U R E 6 \ 2 1 SCALE BEAM L_)L_)l_l 1 II JI II 11 II 11 1 L ^ L ^ L ^ L ^ L J L _ J L _ J L _ ) L _ J U U U U U U I U U U U U L_JL_JI l ! ^ L ^ L ^ L ^ L ^ L J l - _ J L _ J _ J | 1 L ^ L ^ L J ^ L ^ L ^ J L ^ ) L J [ 1 I ^ L ^ L ^ i L ^ L ^ L ^ I _ d L J L - J I ^ L _ J L _ J L J L r J L ^ l L J L _ J L _ ] I II II II JLJI II 1 (e) I II ] L J LsJ LoJ L^J LoJ I II )( I I - 1 I - 1 U J 1 ^ 1 L ^ 1 I - J I 11 il II _ I U 11^11^11,^11^1 j I 11 II ) I 11-11-11^11^11.^11^1 L ^ L ^ L ^ L ^ L ^ U J L c J L ^ J L - J L c J I I' ! L _ J L _ J L _ J I ^ L ^ L ^ J 1 ^ J L ^ J L—! L—!!—-I I — I I — 11^ 11—.11—J L—1 t~J l^-J l - J I—1L -J L -J L -J L -J L -J k-J U-vl U-J L -J L -J 1^ -J L -J (g) T » 'o°L 61 VLSR L_JLJL_I U J L J L J I )l )| )| 1 L ^ l ^ l ^ l ^ L ^ L ^ I ^ L J L J L ^ U ^ L ^ L z J L ^ L J L J L J I ^ 1 L ^ L ^ L z v l l ^ L ^ I ^ L - J L _ J I 11 II 1 L ^ L ^ L ^ L ^ L ^ L ^ ! ^ L ^ I ^ I _ J L J L ^ I ^ I ^ I ^ L = J U J I II )l II )I 1 L ^ I ^ I ^ I ^ L ^ L ^ L J L J L J L ^ L ^ L ^ L J L ^ L J L J L J L J I )l II )[ )l II JI—) ( f ) L^J L_J L J L J L J U J L J L J L J L J L J L J L J I ] U 1 U J U J L J L J L J L J L . 1 L 1 U 1U 1U .IU J L J L J L JL 1L 1L 1L 1 U 1 U 1 U 1 U 1 L 1 L 1 U 1 L 1 I . 1L 1L 1 u u u u u u u u u u u U IU 1L 1L 1L 1L IL 1L 1L 1 U J I ^ I ^ L ^ L J L _ ) L _ I L _ J | ) L _ ) L J L J L J L J L_J L J L _ J L _ J L _ J (h) 113 (km/s) F I G U R E 6 c o n t . 22 TABLE 2 CLOUD PARAMETERS DERIVED FROM MODEL FITTING Cloud (a) A $ C e n t r a l V e l o c i t y Diameter| V e l o c i t y Width FWHM T FWHM | (min) (arcmin) (km/s) (km/s) (K) (deg) | (b) I | I I I 1 | — I | 103.5 13.0 | 9.9-3. 8| - I 2 I -0. 12 | -2.4 | 100.1 12.0 | 11.8 I 0.20 | 3 I 0.40 | 2.7 | 91.5 14.6 I 7.5 | 0.23 | 4 I -0.30 | -18.6 | 85.3 29.6 I 8.7 | 0.29 | 5 | 0.68 | -10.8 | 84.0 43.6 | 5.5 | 0.18 | 6 I -0. 30 | 14.1 | 84.0 21.4 | 6.8 | 0.23 | 7 | -0.70 | 0.6 I 83.4 18.8 | 5.9 | 0.23 | 8 | 0. 10 | 14.4 | 105.3 | 11.4 | 5.2 | 0.32 | 9 I 1. 12 I 2.4 | 75. 1 12.0 I 5.5 | 0.40 | 10 | -0. 14 I -0.6 | 67.8 8.8 | 3.5 | 0.39 | ; __! _ _ j (a) These o f f s e t s r e f e r to the c e n t r a l c o o r d i n a t e o( (1950) = 18h 43. 47m S (1950) = -2° 39.8« (b) Extended c l o u d . The parameters which are not meaningful have been l e f t blank. The temperature i n c r e a s e s with d e c r e a s i n g l a t i t u d e . 23 (1) The extended f e a t u r e - f i g u r e 6 ( d ) : T h i s f e a t u r e extends over our e n t i r e map, with the temperature i n c r e a s i n g i n the d i r e c t i o n of d e c r e a s i n g g a l a c t i c l a t i t u d e . T h i s temperature g r a d i e n t i s perhaps due to the f a c t t h a t t h e midplane of the CO d i s t r i b u t i o n i s d i s p l a c e d below the c o n v e n t i o n a l plane a t t h i s l o n g i t u d e . We have estimated the smoothed out molecular hydrogen number d e n s i t y due to t h i s f e a t u r e as n^=4 c m - 3 (see notes to t a b l e 3) S i n c e t h i s f e a t u r e accounts f o r about 1/3 of a l l the CO observed i n our f i e l d , the t o t a l molecular hydrogen number d e n s i t y i s i n the range 4<n^a<12 cm - 3. Because there must be condensations where n^^ i s at l e a s t two orders of magnitude h i g h e r i n order to c o l l i s i o n a l l y e x c i t e the 1 2 C 0 (Zuckerman and Palmer 1974), i t f o l l o w s t h a t the medium must be clumpy. Thus one i n t e r p r e t a t i o n i s that there i s a clumpy, widespread sheet of CO on the i n n e r edge o f the molecular r i n g , but we cannot t e l l how f a r i t extends from our l i m i t e d o b s e r v a t i o n s . Osing the g a l a c t i c r o t a t i o n curve given by Burton and Gordon (1978), the v e l o c i t y given i n t a b l e 2 i s approximately the t a n g e n t i a l v e l o c i t y at t h i s l o n g i t u d e . T h i s suggests as another i n t e r p r e t a t i o n t h at perhaps t h i s f e a t u r e i s a blend of s e v e r a l c l o u d s around the s u b c e n t r a l p o i n t where the r a d i a l v e l o c i t y g r a d i e n t of the m a t e r i a l i s a minimum. Johansson, Hjalmarson and Rydbeck (1978) have observed a s i m i l a r f e a t u r e i n the t r a n s i t i o n 2TTy » J=1/2 of CH. T h e i r l a t i t u d e - v e l o c i t y p l o t at 1=30° shows a f e a t u r e at ~102 km/s which peaks i n i n t e n s i t y at b=-0.25°. 24 (2) The g i a n t molecular c l o u d s - f i g u r e 6(e) and (f) : The d i s t a n c e s t o these c l o u d s were determined u s i n g the r o t a t i o n curve from Burton and Gordon (1978), and are given i n t a b l e 3. Because of the ambiguity of d i s t a n c e s determined from a l l v e l o c i t i e s except the t a n g e n t i a l v e l o c i t y , both v a l u e s are given. Also l i s t e d i n t a h l e 3 are the diameters and masses f o r these two c l o u d s . The range of diameters, 27-42 pc, i s i n good agreement with values found by Solomon, Sanders and S c o v i l l e (1978) but does not agree with those deduced by Burton and Gordon (1978). Notice t h a t the v i r i a l mass i s i n a l l cases l a r g e r than the i 3 C 0 number d e n s i t y mass._ T h i s i s another example of the "missing mass" problem which plagues other areas of Astronomy as w e l l . The range of number d e n s i t y masses, (1.5-3.5) x 10 s M©, agrees w e l l with both observed and p r e d i c t e d values f o r g i a n t molecular c l o u d s . (3) The broad s p e c t r a l l i n e clouds - f i g u r e 6(g) : These c l o u d s , with a mean r a d i a l v e l o c i t y of 84 km/s appear to blend to form one i r r e g u l a r l y shaped c l o u d . T h e i r d i s t i n g u i s h i n g f e a t u r e i s t h e i r broad l i n e w i d t h s , the average o f which i s a f a c t o r of 2 g r e a t e r than the average f o r c l o u d s 2 and 3. F u r t h e r o b s e r v a t i o n s are r e q u i r e d t o gain i n s i g h t i n t o the nature and d i s t r i b u t i o n of these broad l i n e c l o u d s . . Our survey has sampled approximately 1/500 of the g a l a c t i c molecular r i n g . In t h i s volume we have detected 10 'clouds'. Since most of the 'clouds' i n the galaxy are expected to be i n the molecular r i n g , we conclude t h a t t h e r e are a t o t a l of 5000 •clo u d s ' i n the galaxy. (Loosely t r a n s l a t e 'clouds' to g i a n t 25 TABLE 3 ASTEOPHISICAL PARAMETERS FOR CLOUDS 2 AND 3 1 c i o u a | Distance | Diameter 1 (kpc) | (pc) (a) 1 N(i3CO) | Mass | (x10s M0) | (b) I V i r i a l | Mass | (x10s Mg,) | \ — _} j !_ 1 1 2 | 7.8 | 27 | 9.3 | 32 ! 2.2 I 3. 1 J 5.7 I 6. 8 | I 3 | 6.9 | 28 | 10.4 | 42 I * 1 1.5 I 3. 5 | 8.5 | 12.9 | (a) T h i s i s the * 3C0 number d e n s i t y mass. We have assumed that the i z c o p r o f i l e i s s a t u r a t e d , T^ ( 1 2 C 0 ) / T ^ ( * 3C0) = 3 and LTE i s v a l i d . A l s o we have assumed N (h^_) = 4.6x10 s N(* 3C0) and t h a t the mean molecular weight m = 2.33. For the d e t a i l s of t h i s c a l c u l a t i o n see McCutcheon and Gregory (1978). (b) T h i s i s the v i r i a l mass f i r s t i n t r o d u c e d by Solomon (1979). Assuming the c l o u d i s s t a b l e and under no e x t e r n a l pressure the v i r i a l theorem s t a t e s t h a t the sum of twice the k i n e t i c energy, 3MV2 (V = h a l f v e l o c i t y width i n t a b l e 2 ) , p l u s the p o t e n t i a l energy, - 3 G M 2 / 5 R , equals zero. Thus V i r i a l Mass = 5 R V 2 / G 26 molecular clouds.) T h i s agrees w e l l with Solomon, Sanders and S c o v i l l e (1978) who quote the t o t a l number of g i a n t molecular c l o u d s as 4000 and i s two orders of magnitude s m a l l e r from the number given by Burton and Gordon (1978) who d e r i v e t h e i r number based on an i n d i r e c t s t a t i s t i c a l model of t h e i r one dimensional under sampled data. The t o t a l mass of the 'clouds' i n the g a l a c t i c molecular r i n g comprises about 1% of the t o t a l mass of the g a l a x y . 27 ib. CONCLUSION Data g u a l i t y and observing time can be optimized s i g n i f i c a n t l y i n mapping p r o j e c t s by us i n g the o b s e r v i n g sequence i 1 i 1 i 1 Sj R S^ S^ R S |^  S^ R S^ . . « t 1 i_ l i i R e l a t i v e c a l i b r a t i o n problems are e l i m i n a t e d by c o l l e c t i n g spectra at as many d i f f e r e n t map p o s i t i o n s p o s s i b l e every n i g h t , or put another way, any map p o s i t i o n spectrum i s b u i l t up from sp e c t r a c o l l e c t e d on many d i f f e r e n t n i g h t s . C o n t i n u i t y problems are e l i m i n a t e d by sampling 'between map p o s i t i o n s ' . What t h i s means i s never sample tKe same map p o s i t i o n t w i c e , r a t h e r o f f s e t the second sample h a l f way t o the adjacent map p o s i t i o n . . Great care should be taken i n the methods used to analyse data. We have found t h a t r e s u l t s can vary widely as a f u n c t i o n of the data r e p r e s e n t a t i o n and m o d e l l i n g . N e v e r t h e l e s s we are moderately c o n f i d e n t of the f o l l o w i n g c o n c l u s i o n s : -Ten c l o u d s have been detected i n our CO o b s e r v a t i o n s o f a r e g i o n 1/2° i n diameter i m p l y i n g a t o t a l number of 5000 clouds i n the g a l a c t i c molecular r i n g . -Two o f these clouds are well d e f i n e d g i a n t molecular clouds with masses of the order of 5 x 10 s M 0 and diameters of about .30 pc. -Another 'cloud' i n more l i k e a sheet of CO c o v e r i n g the e n t i r e f i e l d and i s perhaps a blend of s e v e r a l c l o u d s around the s u b c e n t r a l p o i n t . -A blend o f f o u r clouds have l i n e w i d t h s which are a f a c t o r o f 28 two l a r g e r than those f o r the w e l l - d e f i n e d g i a n t molecular clouds. We were unable t o study the d e t a i l e d shapes of these clouds, which was one o f our i n i t i a l aims, because o f the high degree of i n t r i n s i c blending o f our data. F u r t h e r i n v e s t i g a t i o n s i n l a r g e r f i e l d s and a t d i f f e r e n t l o n g i t u d e s seems d e s i r a b l e . Perhaps o b s e r v a t i o n s a degree or so o f f the g a l a c t i c plane would d e l i n e a t e the i n d i v i d u a l clouds b e t t e r . Observations of the same f i e l d i n l 3 C 0 would probably produce b e t t e r d e f i n i t i o n of the clouds, would enable t h e i r masses to be "estimated more a c c u r a t e l y , and would probably allow one t o decide whether our extended f e a t u r e i s a continuous medium or a blend of c l o u d s . 29 B i b l i o g r a p h y A l l e n , R.J. 1976, Sky and Telescope 52, 334.. Burton, W.B. , and Gordon, M.A. 1978, Astron. . Astrophys. . 63, 7. Gordon, M.A. , and Burton, W.B. May 1979, S c i e n t i f i c American 240 , 54. H e i l e s , C., and Je n k i n s , E.B. 1976, Astron. Astrophys,,46, 333. Mahoney, M.J. 1976, Ph. D. D i s s e r t a t i o n , U n i v e r s i t y of B r i t i s h Columbia. McCutcheon, W.H., and Gregory, P.C. 1978, Le c t u r e notes to Physics 570 (unpublished*) . Johansson, L.E.B. , Hjalmarson, A., and Rydbeck..0.E. H. . 1978, paper presented a t the I.A-U-. Symposium 84, Large Scale  Charact e r i s t i c s of the Galaxy ( e d i t o r W.B,.Burton), C o l l e g e Park, Maryland. Solomon, P.M. 1979, paper presented a t the I.A.U. Symposium 87, I n t e r s t e l l a r Molecules ( e d i t o r B. H. Andrew), Mt. Tremblant, Quebec.. Solomon, P.M., Sanders, D.B., and S c o v i l l e , N.Z.. 1978, paper presented at the I.A.U. Symposium 84, Large Scale  C h a r a c t e r i s t i c s o f the Galaxy ( e d i t o r W.B., Burton), C o l l e g e Park, Maryland. Shuter, W.L.H., and McCutcheon, W.H. 1974, Royal Astron. Soc. Canada Jour. 68, 301. Szabo, A., Shuter, W.L.H., and McCutcheon, W.H. Jan. 1980, Ap.. J . 30 O l i c h , B.L. , and Haas, B. W. 1976, Ap. . J . Suppl. 30, 247. Zuckerman, B., and Palmer, P. 1974, Annual Beview of Astronomy and A s t r o p h y s i c s ( e d i t o r G.B. Burbidge), Vol 12, 285. 

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