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A study of the distribution of atomic hydrogen in the Andromeda nebula by means of an interference spectrometer Argyle, Percy Edward 1964

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A STUDY OF THE DISTRIBUTION OF ATOMIC HYDROGEN IN THE ANDROMEDA NEBULA BY MEANS OF AN INTERFERENCE SPECTROMETER by PERCY EDWARD ARGYLE B.A., The U n i v e r s i t y of B r i t i s h . Columbia,. 1948 M.A., The U n i v e r s i t y of B r i t i s h Columbia, 1950  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of PHYSICS  We accept t h i s t h e s i s as conforming t o the required standard  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , I964  In the  r e q u i r e m e n t s f o r an  British  mission  for reference  for extensive  p u r p o s e s may  be  advanced  of  w i t h o u t my  written  Department o f  and  by  It  this thesis  in partial  d e g r e e at  the  study.  the  I further  Head o f my  i s understood  Physics Columbia,.  1964  fulfilment  of  University  of  s h a l l make i t f r e e l y  this thesis  permission,.  2. A p r i l  the  Library  agree for  that  or  c o p y i n g or  shall  not  per-  scholarly  Department  that  for f i n a n c i a l gain  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada, Date  that  copying of  granted  representatives*  cation  this thesis  Columbia, I agree  available  his  presenting  be  by publi-  allowed  The U n i v e r s i t y o f B r i t i s h  Columbia  FACULTY OF GRADUATE STUDIES  PROGRAMME OF THE FINAL ORAL EXAMINATION FOR  THE DEGREE OF  DOCTOR OF PHILOSOPHY  of  PERCY EDWARD ARGYLE  A., The U n i v e r s i t y o f B r i t i s h Columbia, 1948 A., The U n i v e r s i t y o f B r i t i s h Columbia, 1950  FRIDAY, MAY 8, 1964, a t 10:00 A.M. IN ROOM 301, HENNINGS BUILDING ( PHYSICS)  COMMITTEE IN CHARGE Chairman:  F.H. Soward  F.K. Bowers R.E.. Burgess J.R.H. Dempster  E x t e r n a l Examiner: Mount W i l s o n and Palomar  R. Howard G.B. Walker J.B. Warren  M. Schmidt Observatories  A.STUDY OF THE DISTRIBUTION OF ATOMIC HYDROGEN IN THE ANDROMEDA NEBULA BY MEANS OF AN INTERFERENCE SPECTROMETER ABSTRACT The i n c r e a s i n g importance o f narrow-band r a d i a t i o n s i s t r a c e d i n the r e c e n t h i s t o r y o f r a d i o astronomy. The need f o r m u l t i - c h a n n e l spectrometers t o observe these r a d i a t i o n s i s s t r e s s e d . The t f h e o r e t i c a l b a s i s of s p e c t r a l a n a l y s i s i s g i v e n w i t h ^ p a r t i c u l a r emphasis on a u t o c o r r e l a t i o n or i n t e r f e r e n c e methods. A twenty-channel r a d i o - f r e q u e n c y spectrometer designed on i n t e r f e r e n c e p r i n c i p l e s has been c o n s t r u c t e d and found t o perform i n accordance w i t h i t s theory of o p e r a t i o n . When used i n c o n j u n c t i o n w i t h a 25-metre t e l e s c o p e and a hydrogen r e c e i v e r the spectrometer i s capable o f p r o d u c i n g low-noise wideband s p e c t r a a t h i g h speed. The spectrometer output was r e c o r d e d on punched c a r d s , and subsequent data p r o c e s s i n g was by d i g i t a l methods. A l a r g e a r e a i n c l u d i n g the p o s i t i o n o f the s p i r a l g a l a x y M31 was surveyed w i t h the h e l p o f the s p e c t r o meter. One hundred and f o r t y - t h r e e independent s p e c t r a of the 21-cm r a d i a t i o n of atomic hydrogen were o b t a i n e d and a r e a n a l y z e d i n terms o f a r e a , v e l o c i t y , and shape. The major a x i s o f the nebula i s found t o extend about 2.5° e i t h e r s i d e o f the c e n t r e , i n agreement w i t h the work o f van de H u l s t , Raimond, and van Woerden (1957). The l e n g t h o f the minor a x i s , a f t e r c o r r e c t i o n f o r the e f f e c t o f the antenna beamwidth, i s o n l y 40', a r e s u l t which i n d i c a t e s a r e d u c t i o n i n the i n c l i n a t i o n ( o f the plane of the g a l a x y t o the l i n e o f s i g h t ) from 14.5° to 8.2°. T h i s lower v a l u e leads t o an upward r e v i s i o n of the o p t i c a l a x i a l r a t i o ( o f g a l a c t i c t h i c k n e s s t o g a l a c t i c diameter) to 0.2, w h i l e m a i n t a i n i n g a low r a t i o (0.07, Schmidt, 1957) f o r the d i s t r i b u t i o n o f atomic hydrogen. A.high a x i a l r a t i o would c l e a r the way f o r a r e i n t e r p r e t a t i o n o f the o p t i c a l v e l o c i t i e s o f e m i s s i o n nebulae i n M31 ( M a y a l l , 1950), which have so f a r appeared t o be i n v i o l e n t c o n t r a d i c t i o n t o the r a d i o v e l o c i t i e s (van de H u l s t et a l , 1957). I t i s suggested that many o f these e m i s s i o n o b j e c t s may l i e some d i s t a n c e from the plane o f the g a l a x y .  The p o s i t i o n a n g l e of M31, as r e v e a l e d by the s p e c t r o meter o b s e r v a t i o n s i s d i s t i n c t l y l e s s than the 38° established optically. A new v a l u e of 33° i s proposed and i t i s suggested that the former v a l u e can be accounted f o r i n terms of an i n c r e a s e d a x i a l r a t i o and the observed asymmetries i n the l i g h t d i s t r i b u t i o n . The v e l o c i t y of the c e n t r e of g r a v i t y of M31 has been o b t a i n e d by summation of a l l 143 s p e c t r a . The r e s u l t , -295.6 +0.4 km/sec w i t h r e s p e c t to the l o c a l s t a n d a r d of r e s t , i s i n complete agreement w i t h that found by van de H u l s t ( i b i d ) . R a d i a l motions of a few km/sec a r e p o s s i b l e i n the outer p a r t s of M31 but t h e i r presence has not been e s t a b l i s h e d . Many of the s p e c t r a have m u l t i p l e peaks, which may be i n t e r p r e t e d i n terms of s p i r a l s t r u c t u r e . The v e l o c i t i e s of c e r t a i n concent r a t i o n s of atomic hydrogen are measurable but t h e i r p o s i t i o n s a r e not r e s o l v e d by the antenna beam.  GRADUATE STUDIES F i e l d of Study:  Physics  E l e c t r o m a g n e t i c Theory E l e c t r o n i c Instruments Waves P h y s i c a l Systems  Related  G.B. F.K. J.C. R.E.  .Walker.. Bowers Savage Burgess  Studies:  F u n c t i o n s of a complex v a r i a b l e Theory of Measurements E l e c t r o m a g n e t i c Theory Theory of R e l a t i v i t y Wave Mechanics Nuclear P h y s i c s Electronics Cosmic Rays  R.D. James A.M. Crooker G.L. P i c k a r d W. Opechowski G.M. V o l k o f f K.C. Mann A. van der Z i e l J.B. Warren  SCIENTIFIC PUBLICATIONS - P . E . ARGYLE The a n g u l a r c o r r e l a t i o n of a n n i h i l a t i o n r a d i a t i o n . Can. J o u r . Phys., 29, 32, 1951; co-author: J.B.Warren. A method of measuring gamma-ray a b s o r p t i o n coefficients. Can.Jour.Phys., 29, 83, 1951; co-authors: G.M. G r i f f i t h s and J.B. Warren. The e f f e c t i v e quantum e f f i c i e n c y i n a s t r o n o m i c a l spectroscopy. Jour.R.A.S.C<, 49, 19, 1955. Note on magnitude s c a l e s .  Pub.A.S.P., 68, 63,  1956.  The s t e l l a r photometer o f the Dominion A s t r o p h y s i c a l Observatory. Pub.D.A.O., 10, 305, 1957. The i n t e g r a t i n g exposure meter of the Dominion A s t r o p h y s i c a l Observatory. Pub.D.A.O., 10, 323, 1957; co-author: J.B. Warren. Sputnik I.  J o u r . B r i t . I n t e r p l a n . S o c . , 16, 309,  Use of c o l l i s i o n r a d a r f o r m e t e o r i t e avoidance. B r i t . I n t e r p l a n . S o c . , 16, 1958.  1958. Jour.  Design of s t e p r o c k e t s . J o u r . B r i t . I n t e r p l a n . S o c . , 17, 1959. The automatic Observatory.  g u i d e r o f the Dominion A s t r o p h y s i c a l Pub.D.A.O., 11, 201, 1960.  A portable p h o t o e l e c t r i c detector of f l y i n g insects. Can. E n t o m o l o g i s t , 92, 728, 1960; co-author: J . Chapman. TECHNICAL PUBLICATION - P.E. ARGYLE A s o l a r cooker.  Sun at work, 8, 8,  1963.  iii ABSTRACT The i n c r e a s i n g importance of narrow-band r a d i a t i o n s i s traced i n the recent h i s t o r y of radio astronomy. f o r multi-channel spectrometers i s stressed.  The need  to observe these r a d i a t i o n s  The t h e o r e t i c a l b a s i s of s p e c t r a l a n a l y s i s  i s given with p a r t i c u l a r emphasis on a u t o c o r r e l a t i o n or i n t e r f e r e n c e methods. A twenty-channel radio-frequency spectrometer designed on i n t e r f e r e n c e p r i n c i p l e s has been constructed and found to perform i n accordance w i t h i t s theory of operation. When used i n conjunction w i t h a 25-metre telescope and a hydrogen r e c e i v e r the spectrometer i s capable of low-noise wideband spectra at high speed.  producing  The spectrometer  output was recorded on punched cards* and subsequent data processing was by d i g i t a l methods. A l a r g e area i n c l u d i n g the p o s i t i o n of the s p i r a l galaxy M31 was  surveyed with the help of the  spectrometer.  One hundred and f o r t y - t h r e e independent spectra of the 21-cm  r a d i a t i o n of atomic hydrogen were obtained and  analyzed i n terms of area, v e l o c i t y , and shape.  are  The major  a x i s of the nebula i s found to extend about 295 e i t h e r side of the centre, i n agreement w i t h the work of van de H u l s t , Raimond, and van Woerden (1957).  The length of the  minor a x i s , a f t e r c o r r e c t i o n f o r the e f f e c t of the antenna beamwidth, i s only ZfO , a r e s u l t which i n d i c a t e s a reduction T  iv i n the i n c l i n a t i o n (of the plane of the galaxy to the l i n e of s i g h t ) from 1 4 ? 5 t o 8 ? 2 . This lower value leads t o an upward r e v i s i o n o f the o p t i c a l a x i a l r a t i o (of g a l a c t i c thickness t o g a l a c t i c diameter) t o 0 . 2 , while maintaining a low r a t i o ( 0 . 0 7 , Schmidt, 1957) atomic hydrogen.  f o r the d i s t r i b u t i o n of  A high a x i a l r a t i o would c l e a r the way  f o r a r e i n t e r p r e t a t i o n o f the o p t i c a l v e l o c i t i e s o f emiss i o n nebulae i n M31 (Mayall, 1 9 5 0 ) , which have so f a r appeared to be i n v i o l e n t c o n t r a d i c t i o n t o the r a d i o v e l o c i t i e s (van de Hulst et a l , 1 9 5 7 ) .  I t i s suggested that  many o f these emission objects may l i e some distance from the plane of the galaxy. The p o s i t i o n angle o f M31, as revealed by the spectrometer observations, i s d i s t i n c t l y l e s s than the 38° established o p t i c a l l y .  A new value o f 3 3 ° i s proposed and  i t i s suggested that the former value can be accounted f o r i n terms of an increased a x i a l r a t i o and the observed asymmetries i n the l i g h t d i s t r i b u t i o n . The v e l o c i t y o f the centre o f g r a v i t y of M31 has been obtained by summation o f a l l 143 s p e c t r a .  The r e s u l t ,  - 2 9 5 ' 6 ^ 0 . 4 km/sec w i t h respect t o the l o c a l standard of  r e s t , i s i n complete agreement w i t h that found by van de Hulst ( i b i d ) .  R a d i a l motions o f a few km/sec are p o s s i b l e  i n the outer parts o f M31 but t h e i r presence has not been established.  Many o f the spectra have m u l t i p l e peaks,  V  which may be i n t e r p r e t e d i n terms of s p i r a l structure° The v e l o c i t i e s of c e r t a i n concentrations  o f atomic hydro-  gen are measurable but t h e i r p o s i t i o n s are not resolved by the antenna beam.  ACKNOWLEDGEMENTS  The author wishes t o express h i s thanks to the Observatories Branch o f the Department o f Mines and Technical Surveys f o r f i n a n c i a l a i d and educational l e a v e , and to the Dominion Radio A s t r o p h y s i c a l Observatory f o r the p r i v i l e g e o f using the radio telescope i n h i s researches. Thanks are also extended to Dr. J . B. Warren f o r h i s i n t e r e s t and h e l p f u l advice on many phases o f the work. Acknowledgement i s also made t o Dr. J . A. Gait and colleagues a t the Dominion Radio A s t r o p h y s i c a l Observatory f o r many h e l p f u l d i s c u s s i o n s .  Dr. C. H. Costain  i s thanked f o r suggesting the survey o f M31. The author i s indebted to h i s w i f e , June, f o r proofreading and f o r t y p i n g the master p l a t e s .  VI  TABLE OF CONTENTS Page I  II  III  INTRODUCTION a)  Early History  1  b)  Wartime Developments  4  c)  The Emission L i n e of Atomic Hydrogen  5  d)  Detection o f the Hydrogen Line  6  e)  Spectrum L i n e s other than Hydrogen  11  INTERFERENCE SPECTROMETRY a)  Optical Origins  12  b)  Spectrum A n a l y s i s  13  c)  M u l t i - f i l t e r Spectrometry  17  d)  A Heterodyne System  19  e)  Interference Spectrometry  20  f)  The P r a c t i c a l Theory  23  g)  C i r c u i t Element D e f i c i e n c i e s  27  h)  Compensation f o r Equipment D e f i c i e n c i e s  29  TECHNICAL DESIGN a)  b)  The Radio Telescope of the Dominion Radio A s t r o p h y s i c a l Observatory  36  The Interference Spectrometer  41  vii Page IV  V  .PERFORMANCE OF THE SPECTROMETER. a)  C i r c u i t Element Tests  50  b)  The R e s i d u a l C o e f f i c i e n t s  52  c)  S t a b i l i t y , Noise, and L i n e a r i t y  53  d)  The Instrument Functions  55  e)  Apodization  57  f)  The Gibbs E f f e c t  59  g)  The Low Frequency L i m i t  60  h)  The High Frequency L i m i t  60  i)  F o l d i n g o f the Spectrum  62  j)  Area o f A p p l i c a t i o n  64  A SURVEY OF THE ANDROMEDA NEBULA a)  Introduction  65  b)  The Radio Emission from M31  72  c)  Spectrometer Observations of M31  75  d)  Reduction of the Observations  77  e)  I n t e r p r e t a t i o n o f the Spectra  80  i)  80  ii)  General Remarks The D i s t r i b u t i o n o f the Atomic Hydrogen  iii)  82  The Minor Axis D i s t r i b u t i o n and the Aspect Ratio  84  v i i i Page  iv)  The A x i a l  85  Ratio  v)  The P o s i t i o n  Angle  87  vi)  The L o c a t i o n  o f the H I I Regions  90  vii)  The R o t a t i o n  Law  91  viii)  Fine  Structure  o f t h e Hydrogen 92  Distribution ix)  VI  The V e l o c i t y  o f the Centre o f Gravity  x)  Radial Motions  xi)  Other Galaxies  95 96  i n the Observing Field  98  CONCLUSIONS a)  The I n t e r f e r e n c e  Spectrometer  b)  The Andromeda N e b u l a  100 101  APPENDIX  103  BIBLIOGRAPHY  111  ix LIST OF ILLUSTRATIONS Figure  Following Page  The Great Nebula i n Andromeda (Mount Wilson and Palomar Observatories Photograph)  Frontispiece  1  The response matrix of the spectrometer  33  2  The i n v e r t e d response m a t r i x  34  3  The response f u n c t i o n f o r n - 7, and i t s i n v e r t  35  4  The response f u n c t i o n f o r n = 1 6 , and i t s i n v e r t  35  5  The radio telescope of the Dominion Radio A s t r o p h y s i c a l Observatory (Dominion Observatory Photograph)  36  6  The i l l u m i n a t i o n p a t t e r n f o r the 25-metre paraboloid  36  7  The p o l a r diagram f o r the radio telescope  36  8  Block diagram of the i n t e r f e r e n c e spectrometer  41  9  Schematic c i r c u i t f o r the band-pass f i l t e r  42  10  The a t t e n u a t i o n curve of the band-pass f i l t e r  42  11  Schematic diagram of the mixer  42  12  Schematic diagram of the video power a m p l i f i e r  42  13  Schematic diagram of the reference generator  43  14  Schematic diagram of the delay l i n e  44  15  Delay vs frequency f o r the delay l i n e  44  16  The a t t e n u a t i o n of the delay l i n e  44  17  Schematic diagram of a c o r r e l a t o r  44  18  Schematic diagram of the automatic gain c o n t r o l amplifier  46  19  Schematic diagram of the storage system  47  X Figure  Following  20  Schematic  21  Response f u n c t i o n s  22  Comparison o f a response f u n c t i o n truncated Fourier representation  diagram o f the rotary f o r n = 10  sampler  a n d n = 20 with i t s  Page 48 55 56  23  Instrument function  for m  = 15  57  24  Instrument function  f o r OIQ = 25  57  25  A response function  a n d i t s hammed i n v e r t  58  26  A response function  a n d i t s hammed i n v e r t  58  27  Hammed mo =  Q  instrument functions  f o r mQ  = 15 a n d  25  58  29  The G i b b s f u n c t i o n s  59  30  The c o n v o l v e d s e n s i t i v i t y f u n c t i o n  60  31  The o b s e r v i n g  field  f o r M31  75  32  Rectification  o f a spectrum  78  33  T h e s p e c t r a l map o f M31  79  34  C o n t o u r map o f a t o m i c h y d r o g e n  £2  35  The d i s t r i b u t i o n major a x i s The d i s t r i b u t i o n minor  for m  58  Hammed  36  instrument functions  = 3 a n d mo = 4 4  28  0  o f atomic hydrogen  along the 83  o f atomic hydrogen  along the 84  axis  37  Inclination  and t h e a x i a l  86  38  Mean r a d i a l  velocities  i n M31  88  39  Peak r a d i a l  velocities  i n M31  88  40  Empirical  41  Complex s p e c t r a  i n M31 a n d t h e G a l a x y  92  42  Peak v e l o c i t i e s  along t h e major  94  ratio  91  r o t a t i o n curve  axis  xi Figure  Following  43  F o u r i e r a n a l y s i s o f response f u n c t i o n s  Page 105  44  Inversion o f the A matrix  105  45  C a l c u l a t i o n o f the i n v e r t e d response functions  105  46  C a l c u l a t i o n o f the instrument  105  47  C a l c u l a t i o n of the power spectra  106  48  Reduction o f power spectra  106  functions  TABLES Table 1  Spectra i n M31  82  2  The p o s i t i o n angle o f M31  89  3  The r a d i a l v e l o c i t y o f M31  96  1 I  a)  INTRODUCTION  Early History The f i r s t attempt t o detect radio waves from beyond the  earth's atmosphere i s u s u a l l y a t t r i b u t e d t o S i r O l i v e r Lodge (Haddock, 1958; Piddington, I 9 6 I ) who t r i e d to observe long wave emission from the sun.  But Smith ( i 9 6 0 ) c r e d i t s Thomas  A.Edison with an e a r l i e r experiment d i r e c t e d t o the same end. These and a l l other such endeavours were unsuccessful, f o r the f i r s t observations of e x t r a - t e r r e s t r i a l radio waves were made by accident. In 1931 Jansky (1932) c a r r i e d out a study of the i n t e n s i t y and azimuthal d i r e c t i o n of o r i g i n of the " s t a t i c " which i n t e r f e r e d w i t h long distance radio communications, and found that the envelope of the minima i n noise power had a d i u r n a l periodicity.  These observations, made with a r o t a r y broadside  antenna on a wave length of 1 4 . 6 metres, suggested that the sun was the cause of the h i s s - t y p e noise that p e r s i s t e d when a l l thunderstorm a c t i v i t y had abated.  However, continued ob-  s e r v a t i o n with the same equipment (Jansky, 1 9 3 3 a ) brought out the c r u c i a l f a c t that the slow v a r i a t i o n o f i n t e n s i t y already noted had a period o f one s i d e r e a l day. Thus i t was establ i s h e d immediately  not only that the source of the underlying  r a d i a t i o n was e x t r a - t e r r e s t r i a l , but also that i t was l o c a t e d at a distance l a r g e compared with the diameter of the earth's orbit.  I n other words, the s i g n a l s were of cosmic o r i g i n .  2  The r i g h t ascension of the radio source was e a s i l y shown to be about 1 8  h  00 . m  Jansky ( 1 9 3 3 b ) analysed the  shape of the d a i l y azimuth vs time curves and showed that the d e c l i n a t i o n of the source must be about -10°.  He sug-  gested that the radio waves were coming from the centre of # the galaxy. 1935)  A f u r t h e r a n a l y s i s o f the records (Jansky,  showed t h a t , while the g a l a c t i c centre was the most  powerful r a d i a t o r , the region o f the a n t i - c e n t r e showed enhanced emission too.  Some energy could be detected a l l  along the M i l k y Way. The mechanism responsible f o r the generation o f the g a l a c t i c noise remained obscure.  Jansky ( i b i d . ) was unduly im-  pressed by the acoustic s i m i l a r i t y of the r e c t i f i e d r e c e i v e r output to thermal n o i s e , and suggested a thermal o r i g i n f o r the g a l a c t i c emission.  Observations at the s l i g h t l y . l o n g e r  wave length o f 1 6 . 7 metres y i e l d e d a 0.5 db increase i n r e ceived power (Jansky, 1937)•  I f a thermal mechanism ( f o r ex-  ample, r a d i a t i o n by electrons i n a hot plasma) were responsib l e f o r the emission of the observed r a d i a t i o n i t would be expected that the i n t e n s i t y would decrease with i n c r e a s i n g wave l e n g t h .  The observed increase of i n t e n s i t y with wave  l e n g t h i n d i c a t e d a non-thermal o r i g i n of the r a d i a t i o n , but t h i s point went unnoticed. Jansky s d i s c o v e r i e s were widely p u b l i c i z e d i n both the T  # The centre of the galaxy i s at r i g h t ascension 17h 42m, declination - 2 9 ° .  3 t e c h n i c a l and popular press but, unaccountably, no profess i o n a l i n t e r e s t i n the subject became evident u n t i l a f t e r the Second World War.  Whether the p r o f e s s i o n a l astronomer might  p r o f i t a b l y have pursued Jansky*s lead i s not an academic quest i o n , f o r the gap between Jansky*s work, and subsequent development o f the subject by Hey and others a f t e r the war was l a r g e l y f i l l e d by the experiments of Grote Reber, a radio amateur of Wheaton, I l l i n o i s . ^ Reber, at h i s own expense, and i n h i s own back-yard, b u i l t the world's f i r s t radio t e l e s c o p e , a f u l l y steerable 10-metre p a r a b o l o i d a l " d i s h " .  Homemade r e c e i v e r s were used,  f i r s t at 3300 Mc.i then at 910 Mc. detected at e i t h e r frequency.  No g a l a c t i c r a d i a t i o n was  By 1938 Reber had decided t o  s a c r i f i c e antenna r e s o l u t i o n i n favour o f the higher s e n s i t i v i t y to be obtained at lower frequency.  He b u i l t a 160 Mc.  r e c e i v e r and by the summer of 1939 had detected the M i l k y Way and confirmed Jansky»s conclusions about the d i s t r i b u t i o n of the r a d i a t i o n (Reber, 1940). Reber's r e s u l t s , when considered i n conjunction w i t h Jansky*s, showed c l e a r l y that the s p e c t r a l slope of the cosmic noise was i n v e r s e to that expected f o r a thermal source, such as a cloud of i o n i z e d gas, and he was unable t o o f f e r an adequate theory of the o r i g i n of the r a d i a t i o n .  Succes-  s i v e improvements i n the 160 Mc. r e c e i v e r made i t worthwhile § See Reber, ( 1 9 5 8 ) f o r a.?charming account o f h i s e a r l y experiments i n radio astronomy.  4  to survey the whole sky (Reber, 1 9 4 2 ) .  Reber»s contour maps  ( 1 9 4 4 ) of the power l e v e l s i n the northern sky o u t l i n e d the  M i l k y Way and i n d i c a t e d enhanced emission from regions i n the c o n s t e l l a t i o n s o f Cygnus, Cassiopeia and Canis Major. The sun, although quiescent, was e a s i l y detected with t h i s equipment. b)  Wartime Developments Meanwhile, Hey, ( 1 9 4 6 a ) working w i t h 5-metre wartime  radar i n England, had preceded Reber i n d e t e c t i n g the sun, but was unable t o p u b l i s h h i s r e s u l t s u n t i l a f t e r the war. Using the.same 5-metre equipment, with an antenna beamwidth o f 6 ° , Hey, Parsons, and P h i l l i p s ( 1 9 4 6 a )  confirmed  Reber*s discovery o f the r a d i a t i o n from Cygnus and l a t e r ( 1 9 4 6 b ) made the important  f i n d i n g that the Cygnus source  was o f very small angular d i a m e t e r — l e s s than 2 ° .  Subse-  quently Bolton and Stanley ( 1 9 4 8 ) , employing t h e i r now f a mous " c l i f f i n t e r f e r o m e t e r " reduced the upper l i m i t on the angular s i z e of the Cygnus source t o 8 » ; Ryle and Smith, ( 1 9 4 8 ) detected  an even more intense source i n Cassiopeia,  with an angular diameter l e s s than 6 * j and Bolton ( 1 9 4 8 ) l i s t e d a t o t a l o f s i x "point sources", none o f which could be i d e n t i f i e d with any known o b j e c t . A t h i r d discovery made by Hey was that meteors produced h e a v i l y i o n i z e d t r a i l s i n the upper atmosphere, and could be  5  u s e f u l l y observed with 5-metre radar equipment* (Hey> 1 9 4 7 a and 1 9 4 7 b ) .  With Hey's p u b l i c a t i o n s the importance of the  new study begun by Jansky and Reber had become c l e a r . Thenceforth the subject advanced at i n c r e a s i n g speed and only the h i g h l i g h t s relevant to;, the present t h e s i s w i l l be mentioned here. c)  The Emission Line of Atomic Hydrogen The works of Jansky, Reber, and Hey showed that a l l  three types of e m i t t i n g object t i l l then observed (the M i l k y Way,  the sun, and the d i s c r e t e sources) radiated a  band of energy many octaves broad.  L i t t l e was known about  the spectra of the r a d i a t i o n s but c e r t a i n l y narrow l i n e s , i n e i t h e r emission o r absorption, were n e i t h e r observed nor expected.  Then, i n 1944> at the suggestion of J.H.Oort, a  t h e o r e t i c a l search f o r a spectrum l i n e was made by van Hulst ( 1 9 5 7 ) *  de  This search culminated i n van de Hulst's  proposal that i t might be p o s s i b l e to detect a g a l a c t i c emission l i n e at 1420 Mc.  (a wave length of 21 cm)  arising  from the hyperfine s p l i t t i n g of the ground l e v e l of atomic hydrogen. In the absence of a magnetic f i e l d the ground l e v e l of the hydrogen atom i s s p l i t i n t o two s t a t e s characterized only by d i f f e r e n t values of F, the t o t a l s p i n angular momentum quantum number.  In the more energetic of the two  s t a t e s the e l e c t r o n and proton spins are p a r a l l e l , so a t r a n s i t i o n from F = 1 to F = 0 i s accompanied by  emission  6  # of a quantum h ^ Q .  O r d i n a r i l y , hyperfine t r a n s i t i o n s are  forbidden, s i n c e the o r b i t a l quantum number L does not change. But i n the present case there i s an extremely low p r o b a b i l i t y that magnetic d i p o l e r a d i a t i o n may occur.  This f i e l d ,  now  thoroughly i n v e s t i g a t e d , was f i r s t entered experimentally by Nafe, Nelson, and Rabi (1947)» who obtained ^ )  = 1 0  1 4 2 0 . 4 Mc.  by  a magnetic resonance technique. d)  D e t e c t i o n of the Hydrogen Line Van de H u l s t s estimate t h a t atomic hydrogen should be T  detectable i n the galaxy was confirmed by Ewen and P u r c e l l (1951).  Although t h e i r antenna c o n s i s t e d of a small horn with  a 1 2 ° beam-width the emission l i n e was e a s i l y detected and  was  found to be D o p p l e r - s h i f t e d the amount expected from a cons i d e r a t i o n of t e r r e s t r i a l and s o l a r motions. This momentous discovery of a spectrum l i n e i n the radio region was q u i c k l y v e r i f i e d by M u l l e r and Oort ( 1 9 5 1 ) and by C h r i s t i a n s e n and Hindman (Pawsey, 1 9 5 1 ) . The f i r s t survey of the galaxy to be made at 1420 was that of C h r i s t i a n s e n and Hindman ( 1 9 5 2 ) . the e n t i r e southern sky at i n t e r v a l s of 5° i  Mc.  They sampled n  r i g h t ascen-  s i o n and 1 ° to 2° i n d e c l i n a t i o n , with a beam-width of 2°» For each p o s i t i o n they obtained a p r o f i l e of the hydrogen Comprehensive accounts of the e x c i t a t i o n of the 21-cm l i n e of hydrogen under c o n d i t i o n s of pertinence to radio a s t r o n omy can be found i n Shklovsky ( i 9 6 0 ) and F i e l d (1958).  7  line.  Their r e s u l t s showed that the d i s t r i b u t i o n of atomic  hydrogen emission was appreciably d i f f e r e n t from that of the continuum r a d i a t i o n .  I n p a r t i c u l a r , they found a lower i n -  t e n s i t y of monochromatic r a d i a t i o n at the centre than at other d i r e c t i o n s i n the galaxy.  This f a c t i s accounted f o r by the  g r e a t e r o p t i c a l depth toward the centre. In d i r e c t i o n s other than along 0° and 180°  g a l a c t i c l o n g i t u d e the Doppler s h i f t s  a r i s i n g from d i f f e r e n t i a l g a l a c t i c r o t a t i o n prevent occurrence  the  of high o p a c i t y i n the atomic hydrogen.  This p r e l i m i n a r y survey of the sky also showed a "spur" of enhanced emission on the isophote chart at longitude 150?* This i s a region i n the sky i n which i t i s not p o s s i b l e to see e x t e r n a l g a l a x i e s because of absorption of l i g h t by dust i n our galaxy.  Thus the long suspected a s s o c i a t i o n of dust  with hydrogen was demonstrated. Another valuable r e s u l t of the survey was the d e t e c t i o n of d i s t i n c t s p i r a l arms i n the galaxy.  In d i r e c t i o n s such  that the l i n e of s i g h t of the radio telescope cut across  two  arms, the hydrogen p r o f i l e was s p l i t i n t o two components at d i f f e r e n t frequencies, representing the d i f f e r e n t r a d i a l v e l o c i t i e s of the gas i n the two arms. The f i r s t radio spectrometry  of e x t r a - g a l a c t i c objects  was done by Kerr, Hindman, and Robinson (1954).  They ob-  served the Large and Small Magellanic Clouds, a p a i r of nearby s a t e l l i t e g a l a x i e s , by a scanning technique i n which  the r o t a t i o n of the earth c a r r i e d the f i x e d 1.5 beam across the Clouds.  A f t e r each scan the a l t i t u d e of the beam was  changed and another scan made.  A f t e r the e n t i r e area of i n -  t e r e s t had been swept i n t h i s manner the received frequency was a l t e r e d and the scanning repeated.  Thus a f o u r dimen-  s i o n a l " p i c t u r e " of the Clouds was made ( i n r i g h t ascension, d e c l i n a t i o n , i n t e n s i t y , and frequency).  The r e s u l t s showed  that the Clouds r o t a t e d ; t h a t t h e i r r a d i o s i z e g r e a t l y exceeded t h e i r o p t i c a l s i z e ; and that t h e i r radio brightnesses were n e a r l y equal.  I t was also p o s s i b l e to deduce from the  observations, by c a l c u l a t i o n from theory, the t o t a l mass of n e u t r a l hydrogen i n each Cloud. The great success of these two e a r l y p r o j e c t s , one gal a c t i c , one e x t r a - g a l a c t i c , showed the power of the new rneth od to handle problems which had not y i e l d e d to the most sop h i s t i c a t e d attacks by methods of o p t i c a l astronomy.  That  radio astronomy would complement o p t i c a l astronomy i n a very s i g n i f i c a n t way was now  clear.  A second survey of the d i s t r i b u t i o n of hydrogen i n the galaxy was begun by van de H u l s t , M u l l e r , and Oort (1954). They observed the spectrum of atomic hydrogen a l l  around  the plane of the galaxy (except, of course, f o r t h a t i n t e r v a l of g a l a c t i c l o n g i t u d e that i s not a c c e s s i b l e at middle north l a t i t u d e s ) .  Using a model of g a l a c t i c r o t a t i o n based  on o p t i c a l l y derived parameters they c a l c u l a t e d the d i s tance of the gas responsible f o r the observed emission.  Thi  9  c a l c u l a t i o n gave unambiguous answers o n l y f o r the o u t e r p a r t s o f the galaxy ( i . e . those p a r t s more remote from the c e n t r e than i s the s u n ) . galaxy was  The d i s t r i b u t i o n o f gas i n the i n n e r p a r t s o f the  worked out by Kwee, M u l l e r , and Westerhout  another method.  F i n a l l y , Oort, K e r r , and Westerhout  (1954) by (1958)  combined the southern hemisphere o b s e r v a t i o n s w i t h the northern^ i n a contour map throughout  showing the d i s t r i b u t i o n o f atomic  hydrogen  a l l Of the g a l a c t i c plane except f o r two r e g i o n s —  one near l o n g i t u d e 0°» where h i g h o p a c i t y r e s t r i c t e d the  range  o f o b s e r v a t i o n s , and another near 180°* where the r a d i a l component  o f g a l a c t i c r o t a t i o n became s m a l l e r than the random  motions o f the gas c l o u d s . The c h i e f c o n c l u s i o n s supported by t h i s combined a t t a c k on g a l a c t i c s t r u c t u r e and r o t a t i o n were that 1)  The o p t i c a l l y d e r i v e d parameters  of galactic  rotation  are c o n s i s t e n t w i t h the r a d i o r e s u l t s i n the sense t h a t a p l a u s i b l e p i c t u r e of the galaxy emerges from the a n a l y s i s employing  both.  2)  The r o t a t i o n o f the galaxy i s c i r c u l a r l y  3)  Our g a l a x y i s o f s p i r a l t y p e . Another important a p p l i c a t i o n o f hydrogen  symmetric.  line  studies  has been to the r e l a t i o n s h i p between gas and dust i n g a l a c t i c nebulae, a l r e a d y r e f e r r e d t o .  Lilley  (1955) s t u d i e d the  n e b u l o s i t y i n the Taurus-Orion r e g i o n and determined t h a t the mass o f n e u t r a l hydrogen  exceeds t h a t o f the dust by a f a c t o r  10  of 100o  The t o t a l mass o f atomic hydrogen i n the nebula i s  about 20,000 times the s o l a r mass* I t was suggested by V i t k e v i t c h (1952) that i t might be p o s s i b l e t o determine the distance t o a g a l a c t i c radio source by observation o f the 21-cm l i n e o f hydrogen i n absorption* The method i s e s p e c i a l l y a p p l i c a b l e i n those cases where a "hot"  radio source o f small angular extent i s seen through one  or more o f the s p i r a l arms o f the galaxy. Hagen, L i l l e y , and McClain (1955) made t h i s type o f o b s e r v a t i o n . They showed that the powerful source, Cassiopeia A i s located beyond two s p i r a l arms and i s t h e r e f o r e about 3 , 0 0 0 parsecs away from the sun. Although t h i s r e s u l t d i f f e r e d v i o l e n t l y from the o p t i c a l estimate o f 300 parsecs (Baade and Minkowski, 1953)» the ' l a r g e r f i g u r e i s thought t o be c o r r e c t . Of the many absorption studies on radio sources that have been made one deserves s p e c i a l mention.  Williams and Davies  (1954) showed that the famous Cygnus A source e x h i b i t e d abs o r p t i o n f e a t u r e s corresponding t o a l l known masses o f hydrogen i n i t s d i r e c t i o n i n the galaxy.  Thus the suspected e x t r a -  g a l a c t i c nature o f t h i s remarkable source was confirmed. Since 1955 research based on observation o f the 21-cm l i n e i n the spectrum o f atomic hydrogen has accelerated g r e a t l y and w i l l not be described f u r t h e r i n t h i s b r i e f sketch o f the o r i g i n s and e a r l y growth o f spectrometry i n radio  astronomy.  More recent researches i n t h i s f i e l d w i l l be r e f e r r e d t o as  11  they become r e l e v a n t t o the present t h e s i s . e)  Spectrum L i n e s other than Hydrogen U n t i l very r e c e n t l y the 21-cm l i n e o f atomic hydrogen has  been the only one observed i n r a d i o astronomy.  Searches f o r  the 3 2 7 Mc. deuterium counterpart to the hydrogen l i n e have been u n f r u i t f u l .  V/einreb ( 1 9 6 2 ) places the upper l i m i t t o the  deuterium-hydrogen r a t i o below that found on e a r t h . Late i n 1963 a p a i r o f l i n e s a s c r i b a b l e t o the f i n e s t r u c t u r e o f OH were discovered by V/einreb, B a r r e t t , Meeks and Henry ( 1 9 6 3 ) near the t h e o r e t i c a l l y expected r e s t frequenc i e s o f 1665oO and 1667oO Mc. (Townes, 1 9 5 7 ) .  The l i n e s were  detected i n absorption against Cassiopeia A and were about 2°K i n depth.  Although much weaker than the 21-cm l i n e o f hydrogen,  the OH p a i r should be observable i n a v a r i e t y o f circumstances. I t i s i n t e r e s t i n g to note t h a t , o f 54 l i n e s "of i n t e r e s t , to r a d i o astronomy" discussed by Townes ( i b i d . ) i n 1 9 5 5 * the OH p a i r was mentioned s p e c i a l l y as being " s u s c e p t i b l e t o d e t e c t i o n by r a d i o t e l e s c o p e s " . E a r l i e r Shklovsky'(1949)  had included  the OH p a i r i n a s h o r t e r l i s t of. i n t e r e s t i n g l i n e s 0  I t seems  reasonable t o hope that s t i l l other l i n e s w i l l appear t o f u r t h e r e n r i c h the f i e l d o f astronomical radio spectrometry.  12 II a)  INTERFERENCE SPECTROMETRY  Optical Origins The p r i n c i p l e s of i n t e r f e r e n c e spectrometry were known  to Michelson (1892) and used by him to i n v e s t i g a t e the hyperfine s t r u c t u r e of many l i n e s i n the spectra of gases and hot m e t a l l i c vapours.  E s s e n t i a l l y , h i s method was to  measure the way.fringe v i s i b i l i t y depended on path d i f f e r ence, when a source of l i g h t was viewed through a M i c h e l son i n t e r f e r o m e t e r , and to take the F o u r i e r transform of the v i s i b i l i t y f u n c t i o n to o b t a i n the source spectrum. More r e c e n t l y o p t i c a l s p e c t r o s c o p i s t s have r e f i n e d both the theory and the p r a c t i c e of i n t e r f e r e n c e methods and app l i e d them to i n f r a r e d studies (Jacquinot, 1958).  However,  i t i s s c a r c e l y p r o f i t a b l e to pursue these developments here, f o r they are not relevant to radio spectroscopy i n i t s present form.  For example, the c h i e f advantage of the o p t i c a l  i n t e r f e r e n c e spectrometer over the conventional spectrograph l i e s i n the acceptance by the former of a l a r g e aperture, wide-angle beam of l i g h t from a source, such as the night sky ( A l l a r d , 1958; Connes and Gush, 1959), or a Raman tube (Dupeyrat, 1958), that i s both extended and f e e b l e .  But an  e l e c t r i c a l c i r c u i t i s zero dimensional, i n that the s i g n a l i n i t occurs at a p o i n t , and i s without s p a t i a l extension. Hence the concept of " l i g h t grasp" does not have a counterpart i n c i r c u i t theory.  13  • Whilej  with  t h e advent  of thelaser,  wave p h y s i c s  have become u n i f i e d  and  relative  importance o f focussing,  the  field  natural,  of optics therefore,  and radio  i ntheory,  b)  Spectrum  The tection, obtain X(t)  theory.  Analysis  output  o f a radio  i sa time varying  for theinterval  bution  astronomy voltage  X(t).  be completely  t h e random p r o c e s s  zero,  The problem i s t o o f a record o f  t = 0 t o t = T.^  only  i t s  determined b y t h e ensemble  ages and t h e ensemble a u t o c o v a r i a n c e s . that  receiver, before de-  X a r i s e s f r o m a random G a u s s i a n p r o c e s s will  I t i s  interference  t h e power s p e c t r u m o f X b y a n a l y s i s  If  etc., i n  different.  the radio  spectrometer i n terms o f c i r c u i t  and micro-  the practical  amplifying,  arequite  t o describe  optical  I f we a s s u m e  distriaverfurther  i s s t a t i o n a r y and t h e average i s  the autocovariance  C(s)  remains.  I t i s  (1 and  i t completely  characterizes  t h enoise  under t h e given  assumptions " T h i s problem i s d e a l t w i t h b y Blackman and Tukey (1958). R e l a t e d m a t e r i a l c a n be found i n V a n d e r Z i e l (1954), J e n n i s o n (1961), a n d - W a i n s t e i n and Zubakov (1962). ##Small d e p a r t u r e s f r o m t h e s e c o n d i t i o n s , p a r t i c u l a r l y t h e s t a t i o n a r i t y a s s u m p t i o n , may o c c u r i n p r a c t i c a l e q u i p m e n t , b u t t h e y do n o t i n v a l i d a t e t h e p r e s e n t d e v e l o p m e n t .  Now defined  the t o be  transform.  P(f)  The tained on  spectral density  average value  That  l  ±m  =  of  and  the  square of  is  i t s Fourier  2 X(t)  exp  (-i2 7 t f t )  dt  (2  -T/2  that  the  X ( t - s ) , and (which are  that  the  identical  multiplication  convolution  get  and  = 4  C(s)  the  cos  C(s) (1)  product  of  are  an  can  is a of  under the  right side  a form of  and  integral in  the  P(f)  signal X(t)  fT/2  s u m p t i o n ) o c c u r on  we  the  is 1  noting  transforms  pair,  of  r e l a t i o n s h i p between P ( f )  by  X(t)  the  P(f)  (2).  now  ob-  convolution  their  Fourier  stationarity  as-  Therefore,  since  operational  Wiener-Khinchin  be  transform-  theorem;  2 7 L f s ds  (3  '0 Reversing  (3)  C(0)  and  putting  P(f)  z  s =  0  gives  (4  df  Jo Putting  s  = 0 in  (1)  Lim  C^-  C(0) =  i.e.  1 T  The  right side  the  total  J  of  yields  x2  0  (5)  p o w e r , P.  (  t}  dt  i s the  (5 mean s q u a r e v a l u e  Therefore  of  X,  15  OO p  =  P(f)  Any o f t h e t h r e e f o r m u l a s as t h e b a s i s the  last  One ture  (6)  be  used  Of t h e t h r e e , and w i l l  t o be o f fundamental  concerns the concept o f a spectrum. when a p h y s i c a l l y  satisfy  density  may  c o n s i d e r e d t h e most fundamental  reason f o r regarding  spectrum  o r (6)  be  first.  precisely to  ( 2 ) , (3)»  o f a method f o r d e t e r m i n i n g P ( f ) ,  can be  discussed  (6  df  measurable (6)  an e x p r e s s i o n such as  o f P. P(f).  integration  Formula  (6)  In fact,  quantity  t h a t we  shows how  m e a s u r e ?.\, t h e t o t a l  i t i s  P i s known  speak o f the  t o measure t h e  I t i s only necessary to r e s t r i c t t o the neighborhood  na-  spectral  t h e range  of  o f s o m e f r e q u e n c y \j, a n d  power i n t h e r e s t r i c t e d  interval:  (7  This  c a n b e d o n e f o r a n y f r e q u e n c y ^0 b y p a s s i n g t h e e n -  ergy through a f i l t e r If  the transfer  integral  having a narrow  function  of the f i l t e r  pass-band i s Y^ ( f )  c e n t r e d o n -\). t h e power  becomes  2 F\  =  P(f)Y ^ f )  df  /  Y)(f)  df  16 where  t h e second  integral  i sintroduced t o normalize t h e  expression. If ,„.*0  n filters  areavailable  n  intensity garded  cy  having  \)2>  p a s s - b a n d s a t f r e q u e n c i e s *0]_,  n estimates  c a n be o b t a i n e d .  This  P-|_, ?2>  ••• ? n ° ^  s e t o f estimates  as t h emeasured spectrum, P ( f ) b e i n g  spectral may b e r e -  t h eideal  When i t i s p o s s i b l e t o v a r y  thecharacteristic  o f thef i l t e r  ( 8 )becomes  continuously,  spectrum.  frequen-  the convolution  integral  PN)  and,  = J -P(f)  o f K e r r , Hindman  as  o f t h eM a g e l l a n i c  Clouds.  a function o f telescope  shifting  each  (1954)  already  source—that  referred t o .  t h etuning o f t h e r e c e i v e r step-wise  Equation of  o f measuring t h e  hydrogen i nan astronomical  and Robinson  (9)  frequency  scan.  made t h e i r g a l a c t i c  During  a scan  after  t h eobvious  o f t h etelescope  P^ w a s m e a s u r e d  alternative step-wise  V a n de H u l s t , M u l l e r and Oort survey  each  position.  represents  t h ep o s i t i o n  (9  df  o fP ( f ) .  (8) u n d e r l i e s o n e m e t h o d  spectrum o f atomic  They s h i f t e d  |lW,-s)-f)  q  a s b e f o r e , PCs)) i s a n e s t i m a t e Equation  scan  df / J  YWA)-f)  o  i nt h i s way.  method after (1954)  17 The t w o m e t h o d s  are i n principle  equivalent but the for-  mer has t h e advantage o f n o t r e q u i r i n g ously  c)  driving  either  the telescope or the receiver  Multi-filter  Spectrometry  Both  methods  of these  same s h o r t c o m i n g — t h a t spectral method have  energy  filter  to  the signal  of  P^„  This  usual,  each  dividing  circuit  by t h e antenna.  signal  In  from  However,  chromatic  t h e power  requirement  a broad-band  method.  values  I f , as i s  the input signal  before  In the radio region of  presents  no d i f f i c u l t y ,  i s the high level  single-channel radio  spectrum  of unit  i s then  them a l l  i tdoes n o t t r a n s m i t ,i t  to amplify greatly  t o the spectrometer  signal  I f we  can connect  the "multi-filter"  absorbs  the ideal  the f i r s t  difficulty.  order t o estimate t h e degree t o which  proximates  of the  and power d e t e c t o r s , i n s t e a d o f a  i t amongst t h e n f i l t e r s .  signal  from t h e  and measure s i m u l t a n e o u s l y t h e n  i s called  this  suffer  tuning,  only a fraction  f e e d i n g o n e d e t e c t o r , we  filter  spectrum  trum  filters  be necessary  input  utilize  c a n be m o d i f i e d t o overcome t h i s  tunable  the  o f spectrometry  they  collected  n separate  will  equipment f o r c o n t i n u -  as t h e output  receiver.  t h e s e t P^j a p -  we l e t P ( f ) i n ( 9 ) b e a m o n o -  power, & ( f - f ) . 0  The measured  spec-  _  (10  and  I(-Y f ) i s called 5  0  the "instrument  function"  of the  18 spectrometer.  I t s e f f e c t i s to "smear" each s p e c t r a l element  of P ( f ) over a region defined by I(«0,f ). o  The instrument f u n c t i o n has an "equivalent width" W  0  defined by „ ,00  w W) = P  co  2  / l W , f )  df  '0  /  Jo  1  i M . f )  2  df.  (11  The equivalent width i s measured i n cycles per second of bandwidth and i s sometimes c a l l e d the " r e s o l u t i o n " o f the spectrometer because s p e c t r a l features separated i n frequency by l e s s than W  are u s u a l l y not apparent i n P(•)).  The F o u r i e r transform o f 1 ( f ) i s c a l l e d the "impulse response?" D ( s ) :  1 ( f ) cos 2/~fs d f .  (12  0  The impulse response u s u a l l y decays t o i n s i g n i f i c a n t magnitude f o r s exceeding some value s . I n the frequency domain t h i s Q  means that s p e c t r a l f l u c t u a t i o n s having a period l e s s than l/s  0  can be ignored.  But a f u n c t i o n c o n t a i n i n g a s h o r t e s t  F o u r i e r period p must be sampled every ^p i f there i s t o be no l o s s of i n f o r m a t i o n . Therefore the optimum s e p a r a t i o n , A f , of the f i l t e r s d e f i n i n g P^ should be  Af = l/2s  0  (13  19 In  practice  i t i s common t o h a v e W  -. 1 . 5 / s ,  e  s  o  0  (13)  becomes  Af and  t h e number o f f i l t e r s  region  from  (14  e  required t o analyze  c o n d i t i o n (15)  = 3(f  - fi)/W  2  i ssatisfied  e  spectrum  d e l i n e a t e d b y t h e s e t P^ w i l l  the  spectrum  P(*0)  o n (9)»  for  required t o determine  Assuming t h a t each s p e c t r a l b y t h e two systems,  economy i n o b s e r v i n g t i m e .  A Heterodyne Equation  P(f),  (2) suggests  o r an approximation  integrands  a  t h e former  provides an  A m u l t i - f i l t e r spectro(1959)«  System  f r e q u e n c i e s 'v-p ^ 2 > the  method  element i s i n t e g r a t e d  m e t e r h a s b e e n d e s c r i b e d b y McGee a n d M u r r a y d)  scanning  The o u t s t a n d i n g d i f f e r e n c e b e t w e e n t h e two  t h e same t i m e  n-fold  system  be equivalent t o  measured by t h e frequency  methods i s i n t h e o b s e r v i n g t i m e spectrum.  (15  .  by a m u l t i - f i l t e r  the  based  the spectral  f-^ t o f 2 i s  n If  W /3,  =  a third to i t .  ••• "^n  c  a  n  f o r n estimates  P  r  method o f d e t e r m i n i n g A set o f n oscillators  o  v  ide  t h e second  factor i n  o fP ( f ) :  T  2 X(t)  at  exp(-i2rc<s)t) d t  (16  20 Equation  (16) d i f f e r s from (2) i n the important respect  that the l i m i t s i g n has been dropped.  A s u i t a b l e choice of  T w i l l define the r e s o l u t i o n of each measure as does s  i n the  0  m u l t i - f i l t e r system. This method i s under c o n s i d e r a t i o n by the author as an a l t e r n a t i v e to the i n t e r f e r e n c e method.  In p r a c t i c e the i n t e -  g r a t i o n time T would be determined by a low-frequency of bandwidth 1/T.  filter  The f i l t e r output would then be r e c t i f i e d  to y i e l d P^j. A p o s s i b l e advantage of t h i s heterodyning system over the m u l t i - f i l t e r system i s t h a t i t s f i l t e r r e quirements can be met by a set of n i d e n t i c a l f i l t e r s .  If  the o s c i l l a t o r s were simple c r y s t a l - c o n t r o l l e d types they should present no d i f f i c u l t i e s .  This method w i l l not be  d e a l t w i t h f u r t h e r here. e)  I n t e r f e r e n c e Spectrometry A f o u r t h method of spectrometry can be based on equations  (1) and ( 3 ) o In t h i s method> c a l l e d " i n t e r f e r e n c e spectrometry" the s i g n a l X ( t ) i s caused to i n t e r f e r e w i t h a delayed v e r s i o n of i t s e l f , X(t-s)«  That i s , X ( t ) and X ( t - s ) are added at the  input to a d e t e c t i o n system whose output i s p r o p o r t i o n a l the product o f the two s i g n a l s .  to  The mean value of the product  i s the delayed a u t o c o r r e l a t i o n c o e f f i c i e n t C ( s ) . The power spectrum of X ( t ) can then be obtained by t a k i n g the F o u r i e r transform of C ( s ) .  21 (I960) o u t l i n e d t h e m e t h o d a n d s u g g e s t e d i t s u s e f o r  Blum observing  t h e hydrogen l i n e ;  Weinreb the  b u t he d i d n o t g i v e  (1961) d e s c r i b e d  Van Vleck  a "digital  (1943)>  relation  x  that  autocorrelation function of  and Y ( t ) i s t h e random s q u a r e wave p r o d u c e d b y h e a v y  clipping  of X(t).  Weinreb  constructed  i t (1962) i n a n u n s u c c e s s f u l  terium  line.  radiometer The  Subsequently  relation  factor  7C/2c  ceiver  increases  At  K  does n o t a t t a i n t h e The u s e o f  i n c r e a s e s t h e rms f l u c t u a t i o n s b y t h e  The D i c k e  (1946) s w i t c h i n f r o n t o f h i s r e -  t h e f l u c t u a t i o n s a f u r t h e r f a c t o r o f 2, n o t  times  over  that  Thus o b s e r v i n g  f o r an i d e a l  a meeting held  i n connection  with  Astrophysical Observatory  suggested  that X(t)  could  sequently  processed  a t slower  However, i t i s e a s i l y  be r e c o r d e d  spectrometer.  the opening o f t h e i n i 9 6 0 H. G u s h  on video  speed by d i g i t a l  shown t h a t  time i s  instrument.  (1963) g i v e s a n a n a l y s i s o f t h i s t y p e o f  Dominion Radio  t h e deu-  I963).  f o r a spectrometer.  possible switch losses.  multiplied  device  and  t h e OH p a i r w i t h t h e  (Weinreb, B a r r e t t , Meeks, and Henry,  Van Vleck  Clarke  attempt t o detect  h i g h l y s u c c e s s f u l Weinreb  counting  t h e radiometer  he d i s c o v e r e d  maximum p o s s i b l e s e n s i t i v i t y the  which states  based on  y  where C„(s) i s t h e n o r m a l i z e d  used  radiometer"  = sin(TL C ( s ) / 2 )  C (s)  X(t),  any d e t a i l s .  tape  and sub-  computer.  computing c o s t s would be  excessive  f o rthis  method.  Ryle  d e m a n d s made o n t h e d i g i t a l be  avoided  directly.  i f an analog  computer by Gush's p r o p o s a l  rate  o f computing  from  (3) w o u l d be r e a s o n a b l y  were l o n g t i m e  required to calculate  t h a t an i d e a l  w o u l d h a v e t h e same e f f i c i e n c y  multi-filter  system.  system  because t h e former,  erally, yield is  concerned,  tral  intensity  which, would  imposed  as a  comparable  to a flat  system  spectrum  noise level  filter  analyzed.  value i n spec-  This  special  s h o u l d be o f g r e a t (tS 1 ° K )  of several  gen-  and would  time-averaged  features of low intensity  upon a r e c e i v e r  a  devices  represent only the variations  a c r o s s t h e band b e i n g  inter-  than  interferometric  as f a r as t h e i r  behavior of the interference where s p e c t r a l  interference  greater stability  like  would be u n r e s p o n s i v e  outputs  spectrum  I t was h o p e d t h a t a p r a c t i c a l exhibit  the  small.  arguments i n d i c a t e d  d e v i c e would  C(s)  averages  a power  spectrometer  ference  could  t e c h n i q u e were d e v i s e d t o y i e l d  I f the coefficients  Simple  p o i n t e d out t h a t t h e heavy  value  are super-  hundred  de-  grees .  Accordingly ference and  i t was d e c i d e d  spectrometer  to test  to build  a 20-channel  the feasibility  t o d i s c o v e r i f any unexpected  of the idea,  problems would  Experience  gained  would  p r o v i d e an e s t i m a t e o f t h e c o s t and  $  also  Private  i n constructing  communication.  inter-  and u s i n g t h e  arise. spectrometer  servicing  23 problems l i k e l y channel f)  t o be a s s o c i a t e d w i t h  The p r o p o s e d  to  100-  system,,  The P r a c t i c a l  obtain  a contemplated  C(s) from  transform  Theory method o f i n t e r f e r e n c e s p e c t r o m e t r y  (1) b y m e a n s o f a n a n a l o g  t o t h e power  computer programmed tions  imply  three  tical  apparatus.  s p e c t r u m b y means o f a (3).  according to  conditions that  However,  then  digital these  equaprac-  These a r e :  That the range o f i n t e g r a t i o n  2)  That  3)  That the range o f s i s i n f i n i t e .  be d i s c r e t e  and  c a n n o t b e met b y a n y  1)  Therefore,  device  i s to  s i s continuous,  s i n c e T must be and f i n i t e ,  we  i n (1)  i s infinite,  and  finite,  and t h e v a l u e s  recast equations  (1)  of s  and  (3)  must as  follows:  (17 N  where N i s t h e number set  (18  of values  of apodizing coefficients The  simply grand.  restricted  a limited Recalling  o f s; h = s  t o be  m a x  /N,  and D  n  i s a  assigned.  range o f t h e i n t e g r a l  i n (17)  implies  observation of the quantity i n the t h a t X ( t ) i s a random G a u s s i a n  inte-  signal  24 characterized by a t o t a l power X , we g e t , f o r the mean square f l u c t u a t i o n i n C , the well-known r e s u l t g  (AC )  2  S  = 2X (BT)-2  (19  2  where B i s the bandwidth accepted by the spectrometer. Since any f i n i t e estimate of a random v a r i a b l e w i l l be subject to s t a t i s t i c a l f l u c t u a t i o n s we are prepared t o accept f o r t h i s (or any other) device the l i m i t a t i o n t o p r e c i s i o n given by (19). The r e s t r i c t e d range o f s need not be i n t e r p r e t e d as a l i m i t on the i n t e g r a l i n (3). Instead, the integrand can be m u l t i p l i e d by a "box-car" f u n c t i o n D ( s ) , having the d e f i n i tion D(s) = 1 = 0  when 0 <  ~ max otherwise. s  (20  Thus the F o u r i e r transform nature of (3) i s preserved i n the new equation,  p'(f) = JcC(s)  D(s) exp(-i27Lfs) ds  (21  which t r a n s f o r m s t o PMf)  = P(f) *  K f )  (22  25  where 1 ( f ) i s the F o u r i e r transform of D(s), and the s t a r i n d i c a t e s convolution. 1 ( f ) w i l l be recognized as the instrument  function i n -  troduced i n ( 1 0 ) , and D(s) as the impulse response f u n c t i o n . I f D(s) i s defined by (20) i t s F o u r i e r transform i s  1 ( f ) = 2s max (sin 2 7 t f s  r a a x  )/(2 J^fs  m a x  )  (23  and each s p e c t r a l element of P ( f ) i s rendered as a smear of shape 1 ( f ) i n the modified spectrum P * ( f ) . While i t i s true that a l l spectrometers must have an instrument  f u n c t i o n o f f i n i t e width, i t must be admitted  that  the f u n c t i o n (23) i s e s p e c i a l l y unsuited to most s p e c t r a l analysis.  However, i t w i l l be shown l a t e r that c e r t a i n of  the objectionable features of 1 ( f ) may be avoided by a r e d e f i n i t i o n of D ( s ) . The consequences of the d i s c r e t e nature o f t h e values of s are quite innocuous i f a simple precaution regarding input bandwidth i s observed.  To determine the e f f e c t of using the  sura (18) instead o f the i n t e g r a l (21) we use a Dirac  comb t o  w r i t e (18) i n the form: C O  P(f) = 4  C(s) D(s) hBh(s) cos 2JT-fs ds  (24  where B, (s) i s a p e r o i d i c Dirac f u n c t i o n of step h, defined  26  by B (s) n  =  0»  s  / nb-*  n  i n t e g e r or zero;  a n  /°nh+h/2 Bu(s) ds = 1. -h/2 J nh-r  and  n  The F o u r i e r transform of B ( s ) i s 1/h B - j y ( f ) and i t s h  h  convolution with 1 ( f ) w i l l reconstruct the instrument f u n c t i o n i n steps of 1/h along the f a x i s .  That i s ,  O O  K f ) = 2s ax m  V £  max( o -k/h) 2Ks (f-f -k/h)  s i n  Q  2 K s  f _ f  m a x  ™  o  In other words, the window on the spectrum i s unchanged i n shape from t h a t f o r continuous s, but i t i s repeated 1/h  along the f a x i s to i n f i n i t y .  every  Hence s p e c t r a l energy at  frequencies f + l / h , f + 2 / h , ..„ f +k/h, ... comes through Q  Q  0  the window as i f i t were at frequency f . 0  This " a l i e n a t i n g "  of frequencies from one "order," k, of the spectrum i n t o others i s a f a m i l i a r phenomenon whenever a wave i s s p e c i f i e d by a d i s c r e t e set of numbers.  Other examples occur i n the  a n a l y s i s of continuous records by means of d i s c r e t e samples along the time a x i s ; grating;  i n the theory of the d i f f r a c t i o n  i n antenna theory, e t c .  The remedy f o r t h i s d i f f i c u l t y i s to exclude a l l orders but one by i n s e r t i n g a r e c t a n g u l a r f i l t e r having f p p U  (k+l)/h and f ] _  o w e r  a e r  - k/h i n f r o n t of the spectrometer.  It i s  2?  usual to work i n the zero order. " 77  This a n a l y s i s o f the operation o f a r e a l i z a b l e spectrometer i n d i c a t e s that three precautions must be observed i n i t s use; 1)  Observations o f a spectrum must be prolonged (or repeated) u n t i l a s a t i s f a c t o r i l y low l e v e l o f ( A C ) 2 i s reached.  2)  A form o f the f u n c t i o n D(s) must be chosen that best meets the needs o f a p a r t i c u l a r measurement.  3)  The spectrometer must be protected by a f i l t e r passing j u s t the desired order o f the spectrum.  g)  C i r c u i t Element D e f i c i e n c i e s Only one important change i n the o r i g i n a l s e l e c t i o n o f  b a s i c parameters o f the spectrometer was made during construction.  This was t o double the number o f channels from  10 t o 2 0 .  I t i s worthwhile e x p l a i n i n g why t h i s change was  made because i t b r i n g s up the important problem o f how t o c o r r e c t f o r i n e v i t a b l e equipment d e f i c i e n c i e s which cause departures from i d e a l  performance.  The delay l i n e required f o r the spectrometer was b u i l t according t o the design formulas o f Shea (1929).  I n order  ^ I f , as i n t h i s work, a l l transforms are made i n cosines only, the c a l c u l a t e d spectrum w i l l always be an even funct i o n o f the frequency. Hence, the usable bandwidth i s but h a l f an order, f o r example, from f - 0 t o f = l / 2 h .  28  to improve constancy of delay with respect to frequency number of sections was chosen w e l l above the l i n e having the required bandwidth and delay.  minimum  the  for a  Also the  p h y s i c a l s i z e of the c o i l s was made l a r g e to ensure a high Q and low l i n e l o s s e s .  But when the l i n e was b u i l t  and  t e s t e d i t was found that the t o t a l delay depended on  frequen-  cy to a degree incompatible with the theory of operation of the spectrometer} i f nearly i d e a l performance was to be expected o However a c a r e f u l comparison of the t e s t r e s u l t s with the theory showed that the l i n e was i n f a c t w e l l constructed} and that s a t i s f a c t o r y performance was not to be expected i n any l i n e that could reasonably be b u i l t . Furthermore} i t was now c l e a r that the frequency  de-  pendence of the attenuation of the l i n e , although again t h i s was c o n s i s t e n t w i t h the t h e o r y spectrometer  }  was such as to depress the  performance to a merely q u a l i t a t i v e approxima-  t i o n of the i d e a l .  I f the whole i d e a was not to be aban-  doned i t would be necessary to develop a method of reducing the r e s u l t s that contained the p o s s i b i l i t y of compensating f o r i n e v i t a b l e equipment d e f i c i e n c i e s . At the time no such compensation was known. to be expected i n the outputs of the spectrometer sequently be subjected to a F o u r i e r transform, and XTOuld  The errors would sub-: this  i n v a l i d a t e any simple t e r m i n a l c o r r e c t i o n of the r e -  s u l t i n g power spectrum.  However, a method of dealing with  the problem eration  was  found,  and  o f needs i n the  parameters. then the  I f an  this  matter  might  be  bandwidth•instead  o f one,  This  increase the  and  make i t u s e f u l  large  bandwidth  of  l e d to a  constancy  imperfect delay l i n e  present l i n e  change would  success  and  and  reconsid-  of delay  was  permissible,  e m p l o y e d w i t h a two twenty scope  taps  instead  of the  megacycle of  ten.  spectrometer  i n astronomical applications moderate r e s o l u t i o n  line  where  a  were the main  re-  quirements .  h)  Compensation f o r Equipment Ideally,  form  the  the interference  to  correlation The  coefficient  apparatus  20h,  with h  C(s)  - C  n  and  f o r delay  s = nh.  The  and  C(s)  i s the delayed  auto-  s.  provides twenty  = £ microsecond,  since  (26  = X(t) X(t-s)  where X ( t ) i s the i n p u t s i g n a l  By  spectrometer i s designed  function C(s)  channel  Deficiencies  delays h  s  2h,  ...  i t i s convenient to  parameter  n  may  be  nh,  ...  write  called  the  number.  the i n v e r s e form  X(t) X(t-s) =  of the Wiener-Khinchin  JO  'P(f) cos  2/Li's d f  theorem  (27  30 therefore (28  'P(f) cos 2 7Hfnh d f  where f£ i s the bandwidth. The power spectrum i s recovered by F o u r i e r transform of the C : n  (29  n=l  The s u b s t i t u t i o n o f the summation f o r the usual i n t e g r a t i o n , and the dropping o f the constant term have been discussed above. Although (28) does not represent the processes occurr i n g i n the spectrometer as d i r e c t l y as (26) i t i s u s e f u l because i t introduces the concept o f the "comb f i l t e r " , cos 23lfs, which m u l t i p l i e s P ( f ) everywhere before i n t e g r a t i o n .  That  t h i s comb f i l t e r e x i s t s can be t e s t e d by adding a small monochromatic s i g n a l o f frequency f  Q  and power w t o the broadband  power spectrum P ( f ) and measuring the response, C ( f K n  = w  X  = w cos  6 ( f - f ) cos 27tfs df 0  2Kf s n  0  31  Taking w as the u n i t of power, and p u t t i n g s = nh, C (f) n  C (f)  = cos 2 K f n h .  (30  i s the comb f i l t e r which, i d e a l l y , has the shape of a  n  cosineo  But, owing to imperfections i n the apparatus, the  a c t u a l curves obtained, C ^ ( f ) , d i f f e r somewhat from the C (f)o n  An a c t u a l case, f o r n = 7 i s i l l u s t r a t e d i n the  upper curve of f i g u r e 3° Consequently the c o r r e l a t i o n c o e f f i c i e n t s obtained from the apparatus are also modified by equipment imperfect i o n s and i n p r a c t i c e we get, not the t r u e C  n  but pseudo-  c o r r e l a t i o n c o e f f i c i e n t s Cn> according to  (31  where CJUf) resembles cos 2 7 t f s , but i s not i d e n t i c a l to i t . The C ( f ) may be c a l l e d pseudocosine f u n c t i o n s . n  A method  i s required f o r g e t t i n g the true power spectrum from the observed C  n  Obviously the pseudocosines do not c o n s t i t u t e an o r thogonal s e t , but, as w i l l be shown, they are d i s t i n c t , and complete at l e a s t to the twentieth harmonic.  Therefore  they are capable of representing a r b i t r a r y functions w i t h i n the  same mild r e s t r i c t i o n s that apply to r e g u l a r F o u r i e r  analysis.  There w i l l be the complication t h a t , instead of  numbers, the c o e f f i c i e n t s w i l l be f u n c t i o n s , but i t turns out t h a t the f u n c t i o n s can be combined with the cosines and there i s no a d d i t i o n a l burden on computation of the F o u r i e r transforms. Expanding the C ( f ) i n F o u r i e r s e r i e s : n  cA(f) : I a k=l  (32  , cos 27Lkfh  n , I <  where a  n,k  =  f  JJ  2  2  c  n( ) f  27tkfh df  c o s  (33  (Since the apparatus i s n e a r l y i d e a l the C (f)» as already n  noted, resemble the C (f)„ coefficients a  This means that the F o u r i e r  ^ are small unless n = K, and very small  when n i s very d i f f e r e n t from k.) Truncating (32) and s u b s t i t u t i n g i t i n (31) y i e l d s  f •' f 2 f  Cn =  ^° P ( f ) X a_ k=l  JO  cos 2 K k f h df  v  (34  or ,  C  - 20 lo  2L kSl JO  =  n  rf /»f  P(f) a  cos 2K.kfh d f  n v n , K  But the general term i n (35) i s  X  "f 2  Q  p  (  f  )a  n,k  c o s  2 J t k f h  d f  =  a  n,k C  k  (35  by comparison w i t h (28). Therefore t  C  n  2 0  =  Z  a ,k k ' C  ( 3 6  n  Thus we have the observed c o e f f i c i e n t s i n terms of the ideal coefficients. The matrix equation corresponding to (36) i s  (37  or C~* = (A) ~C where (A) i s the matrix of the a  (38  , . n,k  The nature of the a c t u a l response matrix f o r the spectrometer i s i l l u s t r a t e d i n f i g u r e 1.  The rows, which repre-  sent the pseudocosines> are d i s t i n c t .  The completeness of  the pseudocosines i s seen i n the strong diagonal elements. S o l v i n g (38) f o r C gives  1  I  I 5  I 10  Figure  k  I 15  I  The response m a t r i x of the spectrometer.  L. 20  34  C = (A)" C 1  f  Denoting the elements of (A)  by b  n j k  20  C  =  n  JI  b , n  k  c£.  (39  The i n v e r t e d matrix i s i l l u s t r a t e d i n f i g u r e 2 . Although we now have the C  needed to c a l c u l a t e P ( f ) by  n  means of the F o u r i e r transform ( 2 9 ) , we must not y i e l d to t h i s temptation.  w i l l , be produced a t the rate o f 20 per  The  minute and the d i r e c t use of ( 3 9 ) would e n t a i l the summation of 20 products every 3 seconds.  Instead, ( 3 9 ) i s s u b s t i t u t e d  into ( 2 9 ) : 20  20  S  = 2N Z.  P ( f )  1C"™J_  n~"_L  b  n,k k C  c o s  2  ^  n  Interchanging the summations and t a k i n g C  f  (40  h  outside the  k  summation not i n v o l v i n g k: 20 P  (  f  >  =  W  k  ? i  20 C  i  „?! V k  c  o  s  2  *  n  f  h  '  (41  Now l e t 20 b  n=.  n,k  c o s  27T_nfh  =  Fk(f).  (42  The F (^)» which may be c a l l e d i n v e r t e d response funck  t i o n s , depend only on the shape of the comb f i l t e r s , C ^ ( f ) , from which the b  n ) k  were obtained by i n v e r s i o n of the matrix  Figure  2  The i n v e r t e d response matrix.  35  of the F o u r i e r components, &  njk  > of the C ^ ( f ) .  Thus the  F ^ ( f ) are constant functions of the apparatus and may ulated f o r computer use.  be tab-  This t a b u l a t i o n requires no more  computer storage than would a t a b u l a t i o n of cosines f o r an i d e a l spectrometer. S u b s t i t u t i n g (42)  i n t o (41)  y i e l d s f i n a l l y the F o u r i e r  transform 1 JP P ( f ) = 2N £ °k F ( f ) k=l  (43  k  Comparing (43)  with (29)  i t i s seen t h a t , i n order to  t  use the observed C  n  i n l i e u of the i d e a l C »  i t i s only nec-  n  essary to s u b s t i t u t e F ( f ) f o r cos 2 TCnfh i n  (29)»  n  T y p i c a l examples of response functions C ( f ) and t h e i r n  corresponding i n v e r t e d response functions F ( f ) are n  t r a t e d i n f i g u r e s 3 and  4.  illus-  A response f u n c t i o n and i t s i n v e r t .  A response f u n c t i o n and i t s i n v e r t .  36  III a)  TECHNICAL DESIGN  The Radio Telescope o f the Dominion Radio Astrop h y s i c a l Observatory The radio telescope o f the Dominion Radio  Astrophys-  i c a l Observatory i s a 25-metre p a r a b o l o i d a l reflector,, The paraboloid i s e q u a t o r i a l l y mounted and can be pointed to any part o f the sky. A general view of the telescope i s shown i n f i g u r e 5 . The r e f l e c t o r i s fed by a small horn mounted at the focus on three d i e l e c t r i c spars extending outward from the surface of the d i s h .  The i l l u m i n a t i o n of the paraboloid  i s s t r o n g l y tapered from the centre to the periphery i n o r der t o reduce the amplitude of the side lobes of the p o l a r diagram of the antenna.  Another advantage of t a p e r i n g the  i l l u m i n a t i o n i s the reduction o f " s p i l l - o v e r " — t h a t p o r t i o n of the r a d i a t i o n from the horn which i s d i r e c t e d outward at such l a r g e angles from the o p t i c a l a x i s that i t misses the paraboloid.  Most of the s p i l l - o v e r normally s t r i k e s the  earth i n the neighbourhood of the telescope.  The i l l u m i n a -  t i o n p a t t e r n f o r the telescope i s shown i n f i g u r e 6 , and the r e s u l t i n g p o l a r diagram i s given i n f i g u r e 7»  Other de-  t a i l s of the telescope are described i n the appendix. When used at a wave l e n g t h o f 21 cm the telescope has a beam-xcldth (between h a l f power p o i n t s ) of 36'of a r c .  Thus  the area o f the sky i n t e r c e p t e d by the beam i s about h square  -80°  -60°  -80°  -60°  -40°  -40°  -20°  0  -20°  0  Figure  e  20°  40°  60°  „ 20° 0  40°  60°  80°  80°  6  The i l l u m i n a t i o n pattern f o r the 25-metre paraboloid.  /  80-  /  %  /  60-  /  p  /  r  /  40-  /  •—  '  i  -40'  -30'  "  1  20-  i  i -20'  1  1  -10'  1  0 Figure  i  i  „  10'  i l l  \ i_.  20'  7  The polar diagram f o r the radio telescope.  J  3 0'  1 ^^"1  ^J 40'  degree.  The t o t a l sky area v i s i b l e from a l a t i t u d e of 50°  i s about 3 0 , 0 0 0 square degrees.  Therefore the r a t i o o f beam  area t o sky area i s about 10~->.  I n t h i s sense the telescope  i s a r e l a t i v e l y f i n e probe. The accuracy of p o i n t i n g o f the telescope i s about one minute of a r c , so the p o s i t i o n o f the instrument  can be  read o f f the d i a l s on the c o n t r o l panel and used without correction.  The telescope can be moved r a p i d l y to any r e -  quired p o s i t i o n , or i t can be d r i v e n slowly f o r the purpose of scanning across a region of i n t e r e s t .  A sidereal drive i s  a v a i l a b l e f o r t r a c k i n g any c e l e s t i a l object beyond the s o l a r system. A commonly used method of scanning a p o r t i o n of the sky i n v o l v e s s e t t i n g the telescope j u s t to the west o f the r e gion t o be observed.  The r o t a t i o n o f the earth then c a r r i e s  the telescope beam along the desired scanning path.  Fortun-  a t e l y the dwell time o f the beam on a point (about 2 to itminutes, depending on the d e c l i n a t i o n ) i s a s u i t a b l e one from the point o f view of s i g n a l i n t e g r a t i o n . The record o f telescope output obtained i n t h i s way i s c a l l e d a " d r i f t curve". The s i g n a l r e f l e c t e d i n t o the horn by the paraboloid i s picked up by a quarter wave probe and l e d by c o a x i a l cable t o a low-loss f e r r i t e device which f u n c t i o n s as a Dicke switch. The switch i s d r i v e n at 97 cycles per second and connects the  p r e a m p l i f i e r input terminals a l t e r n a t e l y t o the horn and to a comparison dummy l o a d .  The load i s r e f r i g e r a t e d w i t h l i q u i d  oxygen to improve the balance o f noise power between the two inputs t o the s w i t c h . The p r e a m p l i f i e r i s a parametric e l e c t r o n beam tube of the type developed by Adler (1959)> and operates at a noise temperature o f about 125°K. from ground s p i l l - o v e r .  The horn picks up about 3 0 °  K  I n a d d i t i o n t o these noise sources,  c i r c u i t and mixer l o s s e s account f o r another 25°K, b r i n g i n g the o v e r a l l system temperature to about 180°K.  I f the Adler  tube i s operated i n a non-degenerate mode, and i f the wanted s i g n a l appears i n only one o f the two input bands t h i s system temperature must be doubled to 360°K, and doubled again to 720°K i f the Dicke switch i s o p e r a t i n g . A balanced c r y s t a l mixer i s used, and the intermediate frequency i s 35 mc.  A stagger-tuned 35 mc a m p l i f i e r provides  50 db g a i n at a band-width o f 6 Mc.  This a m p l i f i e r , the mix-  e r , the A d l e r tube and the f e r r i t e switch are a l l l o c a t e d at the focus o f the paraboloid where they are housed i n a tempe r a t u r e - c o n t r o l l e d can. The output o f the 35 mc a m p l i f i e r i s l e d away by a coa x i a l cable , t e r m i n a t i n g at the hydrogen r e c e i v e r i n the cont r o l room o f the l a b o r a t o r y b u i l d i n g . the r e c e i v e r w i l l be mentioned here.  Only three features o f The f i r s t l o c a l o s c i l -  l a t o r frequency i s v a r i a b l e over a wide range to permit obs e r v a t i o n o f the D o p p l e r - s h i f t e d hydrogen l i n e ; the r e c e i v e r  39  uses double conversion t o a second intermediate frequency o f 1 0 . 7 M c ; a set o f s i x 1 0 . 7 Mc. band-pass f i l t e r s provides a choice of bandwidths from 2 kc t o 6 Mc. To o b t a i n the spectrum o f the hydrogen r a d i a t i o n the telescope i s f i r s t set t o the co-ordinates o f the region o r object t o be studied} and the telescope d r i v e i s set t o the sidereal rate.  The r e c e i v e r i s tuned, by adjustment o f the  l o c a l o s c i l l a t o r , t o one end o f the desired frequency  range.  The l o c a l o s c i l l a t o r frequency sweep i s turned on and adj u s t e d to an appropriate rate o f change o f frequency. s e l e c t i o n i s made o f one o f the band-pass f i l t e r s .  A  Finally  the 1 0 . 7 Mc. output, which i s r e c t i f i e d i n synchronism with the Dicke s w i t c h , i s recorded w i t h an appropriate time constant on a s t r i p - c h a r t recorder.  The hydrogen spectrum i s  then recorded a u t o m a t i c a l l y as a p l o t o f received power vs frequency. In p a r a l l e l w i t h the recorder i s a d i g i t a l voltmeter and IBM card punch.  Receiver output i s i n t e g r a t e d f o r 3 0  seconds and punched as a t h r e e - d i g i t f i e l d . of t h i s equipment i s f u l l y  The operation  automatic.  Routine c a l i b r a t i o n o f the output i s made by t u r n i n g on a discharge lamp o f known noise temperature.  The lamp  i s coupled l o o s e l y t o the horn s i d e o f the Dicke switch. From time t o time the lamp i s standardized against a cert a i n region o f the sky which, by i n t e r n a t i o n a l agreement, i s regarded t o be at a temperature o f 100°K.  40 Frequency determination i s by frequency counting o f a subharmonic o f the l o c a l o s c i l l a t o r frequency, and i s accurate t o 1 part i n 1 0 . 7  In a t y p i c a l observation o f g a l a c t i c hydrogen a frequency range o f 1.0 Mc. w i l l be swept at a r a t e o f one h a l f per second per hour.  megacycle  I f a bandwidth o f 10 kc i s chosen the  dwell time per u n i t bandwidth resolved w i l l be j u s t over one minute.  T o t a l time f o r observing one spectrum w i l l be two  hours. In order t o u t i l i z e the lower o f the two noise temperat u r e s mentioned above, the Adler tube i s operated i n a degenerate mode so that the s p e c t r a l element under observation occurs i n both bands.  The Adler tube pump frequency i s swept  at twice the sweep rate o f the l o c a l o s c i l l a t o r frequency i n order t o keep the two bands c o i n c i d e n t .  The s e n s i t i v i t y o f  the system, A T , i s  A T : T (Bt)'^ 0  where T  0  i s the system temperature, B i s the bandwidth, and  t i s the dwell time.  For the example considered here AT=0.4°K»  Throughout much o f the area o f the g a l a c t i c plane peak hydrogen temperatures i n the range 10° t o 100°K are observed. E v i d e n t l y the s e n s i t i v i t y c a l c u l a t e d above i s adequate f o r a wide range o f s t u d i e s outside the regions o f most intense radiation.  The hydrogen r a d i a t i o n received from e x t r a - g a l a c t i c  objects ( i . e . from other g a l a x i e s ) w i l l be l e s s intense f o r two reasons:  1 ) The d i s t a n t galaxy w i l l not f i l l the antenna  beam, o r , i n f a v o r a b l e cases, the s t r o n g l y e m i t t i n g p o r t i o n s of the galaxy w i l l not f i l l the beam;  and 2) r o t a t i o n , t u r -  bulence and other motions not r e s o l v e d by the antenna beam w i l l broaden and depress the observed  spectrum.  For example, the Andromeda nebula, the nearest t y p i c a l e x t e r n a l galaxy, although r e a d i l y resolved by the 3 6 ' beam of a 25m t e l e s c o p e , does not y i e l d s p e c t r a l i n t e n s i t i e s i n excess o f 7°K.  The 5 0 t h nearest galaxy, not yet observed at  21 cm, i s not expected t o have a peak i n t e n s i t y as high as 0.1°K.  C l e a r l y , improvements i n both beam r e s o l u t i o n and  spectrometer e f f i c i e n c y are much needed i f a s i g n i f i c a n t l y l a r g e number of g a l a x i e s are to be studied through t h e i r hydrogen emissions.  I t i s t o the p o s s i b i l i t y of improving  spectrometer e f f i c i e n c y that the present work i s d i r e c t e d . b)  The I n t e r f e r e n c e Spectrometer The p l a n f o r the spectrometer i s shown i n b l o c k form i n  figure 8.  The s i g n a l X ( t ) i s taken from the i . f . a m p l i f i e r  of the hydrogen r e c e i v e r at a frequency o f 1 0 . 7 Mc. and a bandwidth of 6 Mc.  I n order t o f a c i l i t a t e conveyance o f the  s i g n a l t o the spectrometer the i . f . a m p l i f i e r i s tapped at a 50-ohm impedance l e v e l and connection i s made by means of 30 f e e t of c o a x i a l c a b l e .  TELESCOPE HYDROGEN RECEIVER  10-7 mc. BAND-PASS FILTER  VIDEO AMPLIFIER  MIXER  SWITCHED SIGNAL  DELAY LINE  400 CPS REFERENCE GENERATOR UNSWITCHED SIGNAL  CORRELATORS  AGC AMPLIFIER  CAPACITY STORAGE BANKS  ROTARY SELECTOR  SIGNAL  DISCHARGE CONTROL  500MV BIAS  READ COMMAND  DIGITAL VOLTMETER  DIGITAL OUTPUT, PUNCH COMMAND  PUNCH COUPLER  Figure  J STRIP-CHART MONITOR  CARD PUNCH  8  Block diagram of the i n t e r f e r e n c e spectrometer.  42 The f i r s t element of the spectrometer i s , n e c e s s a r i l y , the band-pass f i l t e r .  I t s pass-band i s nominally r e c t a n g u l a r and  of width 1.8 Mc.  The f i l t e r i s a 6-section "constant k" type  and i s housed i n a r i g i d brass box w i t h soldered compartment shields.  The schematic c i r c u i t of the f i l t e r i s shown i n  f i g u r e 9> and the a t t e n u a t i o n curve i s given i n f i g u r e 10. The f u n c t i o n of the f i l t e r i s to prevent the overlapping of d i f f e r e n t orders of the spectrum.  Since the 9.84 Mc.  local  o s c i l l a t o r frequency of the spectrometer mixer l i e s w i t h i n the frequency band of the output from the hydrogen  receiver  i t would produce both p o s i t i v e and negative f r e q u e n c i e s . Hence p r e - f i l t e r i n g i s required to prevent f o l d i n g of the spectrum. The mixer c i r c u i t i s shown i n f i g u r e 11.  The balanced  form i s required to reduce l o c a l o s c i l l a t o r feed-through to an acceptable l e v e l .  The l o c a l o s c i l l a t o r frequency i s c r y s -  t a l c o n t r o l l e d and the c r y s t a l i s t h e r m a l l y s t a b i l i z e d i n an oven.  A conventional video a m p l i f i e r i s incorporated i n t o  the mixer c h a s s i s . A l a r g e video s i g n a l voltage i s needed i f r e c t i f i c a t i o n i n the c o r r e l a t o r s i s to be e f f i c i e n t .  But the delay l i n e  impedance must be low to minimize the loading e f f e c t of i t s many t a p s , so a considerable amount of power i s required at video frequencies. The necessary power i s generated i n the video power a m p l i f i e r (see f i g u r e 12), which has two  identical  OUTPUT  INPUT  @—vw-  22 -|r  22 -II-  22  -Ir-  22 -II-  22 -Ir-  22  -II-  700 190  95  190  190  190  190  >  78  5- 25 •96^ /77  0-98^H  0-98/iH  0-98/iH  0-98/xH  Figure  0-98/iH  9  Schematic c i r c u i t f o r the band-pass f i l t e r ,  I-96/aH  J  Figure  10  The attenuation curve of the band-pass f i l t e r .  L  Figure  II.  Schematic diagram of the mixer.  5763  Figure  12  Schematic diagram of the video power a m p l i f i e r .  43 output s e c t i o n s .  One s e c t i o n feeds the delay l i n e through a  400 c y c l e per second phase s w i t c h ; the other s u p p l i e s the s i g n a l at both p o l a r i t i e s to the twenty-one c o r r e l a t o r s . S p e c i a l wide-band f e r r i t e core transformers provide low impedance outputs. The phase switch does not appear i n the theory o f the spectrometer.  I t s f u n c t i o n i s simply to chop the input so  that the low l e v e l dc s i g n a l s from the r e c t i f i e r s i n the corr e l a t o r s can be a m p l i f i e d by ac techniques.  Subsequent t o  a m p l i f i c a t i o n the 400-cycle s i g n a l s are synchronously r e c t i f i e d and c o n s t i t u t e the outputs of the c o r r e l a t o r s .  In fact  the phase switch i s of great p r a c t i c a l importance i n the spectrometer.  I t s use cancels out d i f f e r e n c e s i n e f f i c i e n c y  of the r e c t i f i e r s ? avoids the problem of dc l e v e l d r i f t s , and renders innocuous even l a r g e spurious s i g n a l s such as power frequency r i p p l e . The s w i t c h i n g voltage f o r the diode r i n g s i s obtained from the reference generator shown i n f i g u r e 13 • The 400 cps square wave i s derived from an 8 0 0 cps o s c i l l a t o r by countdown through a scale of two.  This technique of frequency  d i v i s i o n ensures that a l t e r n a t e halves o f the reference s i g n a l have i d e n t i c a l d u r a t i o n s . A v a r i a b l e phase delay to one side of the generator i s obtained by means o f a monostable flip-flop.  This phase adjustment i s necessary to compensate  f o r phase s h i f t s i n the f i l t e r s i n the c o r r e l a t o r s .  The low  SCALE  DELAY UN I VIBRATOR  OF 2  800  ~  SCALE OF 2  C L O C K  100  5.6 K 33K  2 7 K  K 100  10  K  URE SWITCH  470  470 K 30 K  4 0 0 ~  O U T  3 3 0 K  3 9 K >  IM  470 K  ^  T.OI  • 2 5 0 V  B  T O  D  O  t.OI  .01  IM  IM  —  O - *  H E A T E R S E  6AQ5  470 K  4 0 0 ~ O U T  roi IM  K T  6AQ5  A 470 K  C  4 7 0  K  ISO  4 7 0 150  POWER AMPLIFIER  Figure 13 • Schematic diagram of the reference  I™  POWER  generator*  AMPLIFIER  K  :  44 impedance switches r e q u i r e a considerable d r i v i n g power, which i s supplied by the p a i r s of 6AQ5 s i n push-pull. T  The delay l i n e i s a conventional L-C type (Shea,  1929)  i n which mutual coupling between the sections i s used to improve the performance.  The f o r t y s e c t i o n s are mounted i n  three rows i n a standard c h a s s i s .  The rows are shielded but  the sections i n each row are decoupled only by the a l t e r n a t e l y v e r t i c a l and h o r i z o n t a l mounting of the c o i l s . f e c t s are detectable but are not s e r i o u s .  Row  end ef-  The c i r c u i t of the  delay l i n e i s shown i n f i g u r e 14. The c o i l s were p r e c i s i o n wound, and the capacitors were c a r e f u l l y s e l e c t e d from a l a r g e number of standard u n i t s . The capacity at each tap i s adjustable and the cables l e a d i n g from the taps to the c o r r e l a t o r s are a l l of i d e n t i c a l capacity.  The l i n e was t e s t e d i n the usual ways both with a s i g n a l  generator and a pulse generator.  The frequency dependence of  the delay and of the attenuation of the l i n e are shown i n f i g u r e s 15 and 16.  The dashed l i n e i n the f i g u r e s i n d i c a t e s  f upper f o r the spectrometer. c  The l i n e was terminated i n i t s  c h a r a c t e r i s t i c impedance to avoid r e f l e c t i o n s . Figure 17 shows the schematic diagram of a c o r r e l a t o r . The f u n c t i o n of the 21 c o r r e l a t o r s i s to provide output voltages p r o p o r t i o n a l to the lagged products X ( t ) • X ( t - s ) . This end i s achieved i n each c o r r e l a t o r by t a k i n g the time average of the d i f f e r e n c e between the square of the sum  of  78  78  21-5  78  62  62  19^  I  0 ' 200  "25  225  200  25  2Cf  200  '25  225  121-5  o, 200  '25 21-5-  Inductance values are in Figure  14  Schematic diagram o f the delay l i n e .  Capacity values are in pf.  3.0  Delay vs frequency f o r the delay l i n e ,  Figure 16 The attenuation of the delay l i n e  ADDERS  DETECTORS IK  Figure 17.  I FILTERS  DIFFERENCE AMPLIFIER  TOOI  Schematic diagram o f a c o r r e l a t o r .  r  AMPLIFIER  SYNCHRONOUS DETECTOR  250 VOLT O  45  the prompt and delayed s i g n a l s and the square of the d i f f e r e n c e between the two s i g n a l s .  Denoting a F o u r i e r component of the  prompt s i g n a l by P and i t s delayed form by D, the sum P+D i s formed by the upper p a i r of cathode f o l l o w e r s i n f i g u r e 17> and the d i f f e r e n c e , P-D, by the lower p a i r .  The detectors  produce the squares of these two q u a n t i t i e s , and the f i l t e r s f o l l o w i n g the detectors provide averages over a time of about 1ms.  That i s , the f i l t e r e d outputs of the detectors are  (P+D) and (P-D) . 2  2  These averaged voltages are d i f f e r e n c e d  i n the f o l l o w i n g d i f f e r e n t i a l  amplifier.  (P-D) - (P-D) 2  2  Since  = 4 PD = 4 C ( s )  the a m p l i f i e r output i s the c o r r e l a t i o n c o e f f i c i e n t at 400 cps.  modulated  A f t e r f u r t h e r low frequency a m p l i f i c a t i o n the  modulation i s r e c t i f i e d by the diode r i n g synchronous detect o r and the dc s i g n a l i s passed to the 10 uF c a p a c i t o r f o r averaging over a 60-second  period.  This c i r c u i t i s not the most s o p h i s t i c a t e d that could be used.  The a d d i t i o n of another stage to the 400 cycle ampli-  f i e r would permit the use of a l a r g e r measure of negative feedback.  A constant current output stage would make p o s s i -  b l e true averaging i n the storage c a p a c i t o r .  Tuning of the  a m p l i f i e r would improve the spurious s i g n a l r e j e c t i o n , a l though the r e j e c t i o n of the synchronous d e t e c t o r i s so very good that t h i s advantage may be i l l u s o r y .  Furthermore, a  l o s s of i n f o r m a t i o n i s i n c u r r e d i f a tuned a m p l i f i e r i s used,  46  as the harmonic content of the 4 0 0 - c y c l e "square" wave i s no longer passed to the detector.  However, the c h i e f reason f o r  using minimum c i r c u i t r y was to determine, i n t h i s  prototype  design, the l e a s t complex arrangement that would be s a t i s f a c t o r y i f incorporated i n t o the much bigger system that i s contemplated.  S i m p l i c i t y i s regarded as an important  feature,  e s p e c i a l l y i n a u n i t , such as the c o r r e l a t o r , that may  be  d u p l i c a t e d a hundred times. The output of the f i r s t c o r r e l a t o r i s C(0) and i s theref o r e p r o p o r t i o n a l to the t o t a l power i n the video s i g n a l . S t r i c t l y speaking, C(0) should be included i n the set of coe f f i c i e n t s from which the F o u r i e r transform i s made , because the t o t a l power l e v e l i s properly a feature of the spectrum— sometimes an important  feature.  However, i n a l l but excep-  t i o n a l circumstances the t o t a l power emerging from the hydrogen r e c e i v e r i s merely a measure of r e c e i v e r n o i s e .  There-  f o r e i t was decided to use C(0) as a sensing voltage f o r an automatic gain c o n t r o l a m p l i f i e r (see f i g u r e 18).  The  AGC  output c o n t r o l s the gain i n the hydrogen r e c e i v e r second i . f . amplifier.  Consequently C(0) i s a constant and i t would be  p o i n t l e s s to i n c l u d e i t i n the F o u r i e r transform. l e s s , C(0) i s recorded  Neverthe-  i n case of f u t u r e need.  The c o r r e l a t o r outputs are stored i n one of the  two  c a p a c i t o r banks during the f i r s t minute of observation.  Then  the stored c o e f f i c i e n t s are read out of that bank while the  TOTAL POWER INPUT  A.G.C. AMPLIFIER Figure  18  47 c o e f f i c i e n t s f o r the f o l l o w i n g minute are charging the a l t e r nate bank o f c a p a c i t o r s . Thus no observing time i s l o s t during readout.  Figure 19 shows the c i r c u i t o f the storage ca-  pacitors. The time constant o f the charging c i r c u i t i s 1 0 0 seconds and t h e r e f o r e the storage e f f i c i e n c y i s  E = 1/T  f o r T=60 seconds. The "memory" o f the storage i s imperfect, the t r a c e of remote events being slowly l o s t through the f i n i t e charging resistance.  Thus the mean age o f the data represented by the  c a p a c i t o r v o l t a g e , which i s sampled once per minute, i s not 30 seconds, but a s l i g h t l y smaller v a l u e .  E x a c t l y , the mean  age i s  I n most work the 3 second d i f f e r e n c e between the exact age and i t s 30 second approximation would be i n c o n s e q u e n t i a l . However, i n observations made by d r i f t scanning the 3 seconds would appear as an e r r o r i n the r i g h t ascension co-ordinate of the observed r e g i o n , and might be detectable i n those  ROTARY SAMPLER  21 POINT CONNECTORS TO ROTARY SAMPLER B A  B o Figure 19.  Schematic diagram of the storage system,  48  cases i n which the s i g n a l to noise r a t i o was very high.  In  the work reported here t h i s c o r r e c t i o n was not necessary. Sampling o f the c a p a c i t o r voltages i s done by means of a motor-driven 3-deck r o t a r y s w i t c h .  Although there are only  21 c a p a c i t o r s t o be read, a 2 4 - p o s i t i o n switch i s used.  The  e x t r a p o s i t i o n s provide c i r c u i t s t o discharge the bank that has j u s t been read, and to switch the c o r r e l a t o r inputs t o their alternate position.  Two o f the three switch decks are  used i n the readout process-and  the t h i r d deck serves the  dual f u n c t i o n of switching the f r o n t panel channel  indicator  lamps, and e n e r g i z i n g the read command pulse generator that a c t i v a t e s the d i g i t a l voltmeter.  The r o t a r y sampler diagram  i s given i n f i g u r e 2 0 . The d i g i t a l voltmeter i s a s i n g l e range, t h r e e - f i g u r e device capable o f reading p o s i t i v e voltages only.  I t s range  i s 0 to 0 . 9 9 9 * and when used with the i n t e r f e r e n c e spectrometer i t i s biased to about one-half v o l t so that negative c o e f f i c i e n t s can be recorded.  Neither the l a c k of response  to negative voltages nor the i n a b i l i t y to change ranges i s a drawback as i t i s d e s i r a b l e to avoid the need t o record a. s i g n o r a decimal on the punched cards.  However, a f o u r t h  decimal place would be d e s i r a b l e , as the e f f e c t i v e range o f the present instrument i s only - 500 mv i n steps of 1 mv. -This r e s t r i c t e d dynamic range i s i n s u f f i c i e n t t o record both the l a r g e s t outputs and the f l u c t u a t i o n s due t o  u^u • INPUT FROM CORRELATOR  TO CAPACITOR "B"BANK  TO CAPACITOR "A" BANK  ,, y r—? ?  n-n  21 20  2 1  +250V. 0  TO STORAGE DECK -300V. C A F 0 9 9 9  I20K  B  IOM  -4V. OUTER DECK 2K —»^20  nC  21  A  A  Ok  2  B  TO DIGITAL VOLTMETER  /77 2K  V  _V' ,/  f  ^  + 4V.  IOOKJ  r  NE-2  100 K •vw—  BANK INDICATORS  IK  +I2V.  - W r CAPACITOR SANK CHANGE-OVER RELAY  CAPACITOR - O — — •  TO STORAGE! DECK  DISCHARGE  RELAY  1—  SHAFT  L  2703  ao±  56K  .2D COCSJ NE-2 5I0K  READ PULSE OUTPUT 25K PULSE •05 AMR CONTROL  <gHl-*  DELAY  FRONT PANEL CHANNEL INDICATORS  CONTROL  250K J.IO  I5K  SCALE OF TWO  SCHMIDT TRIGGER II3V 601V 6 6 SIDEREAL FREQUENCY  Figure  20  The rotary sampler  49  receiver noise.  As the equipment i s c u r r e n t l y used f l u c t u a -  t i o n s are about 1 mv and a s l i g h t amount of information may be l o s t by t r u n c a t i o n of the reading at the t h i r d place. The card punch operates on command from the d i g i t a l voltmeter.  I t i s programmed to record the 21 c o r r e l a t i o n  c o e f f i c i e n t s i n 3 - d i g i t f i e l d s on one card.  Each card also  accommodates the r i g h t ascension and d e c l i n a t i o n of the observation, and the date.  These l a t t e r f i e l d s are punched  a u t o m a t i c a l l y by standard observatory equipment. of the punch i s one card per m i n u t e — t h a t  The output  i s , one complete  set of c o r r e l a t i o n c o e f f i c i e n t s f o r each minute of operation.  50  IV a)  PERFORMANCE OF THE SPECTROMETER  C i r c u i t Element Tests Each major element of the spectrometer was tested and  adjusted as i t was b u i l t .  A f t e r the complete spectrometer  was assembled, f u r t h e r t e s t s and adjustments were made t o overcome the unwanted i n t e r a c t i o n s between elements.  These  included the e f f e c t s of s l i g h t impedance mismatches, of feedback, of heat generation, and of delay l i n e l o a d i n g . The f i r s t element of the spectrometer i s the band-pass filter.  I t s adjustment was accomplished by tuning each  s e c t i o n independently of the others, and then trimming the t e r m i n a l impedances.  The r e s u l t i n g pass-band was nominally  r e c t a n g u l a r , and adequately f r e e of r i p p l e .  The pass-band  of the f i l t e r i s shown i n f i g u r e 1 0 . The mixer was tested c a r e f u l l y f o r harmonic  distortion,  p a r t i c u l a r l y i n the lower h a l f of i t s frequency range  Sec-  c  ond harmonic d i s t o r t i o n , f o r i n s t a n c e , would lead to an ambig u i t y , f o r a strong s i g n a l i n the lower p a r t of the band would create a "ghost" at twice the s i g n a l frequency.  No  s i g n i f i c a n t amount of d i s t o r t i o n was found, except f o r very strong s i g n a l s , f a r above the design l e v e l .  The response o f  the mixer was very f l a t t o the design l i m i t of 2 Mc. The video a m p l i f i e r output showed some d i s t o r t i o n when operated at the rather high s i g n a l l e v e l required of i t .  51  However, t h i s d i s t o r t i o n was confined to the upper end o f the frequency range where i t was not troublesome.  At the high end  of the video band odd harmonic d i s t o r t i o n i n the push-pull stages leads t o spurious s i g n a l s at frequencies too high t o pass through the delay l i n e .  Examination o f the delay l i n e  output showed i t t o be s a t i s f a c t o r i l y low i n d i s t o r t i o n at a l l frequencies. The delay l i n e performance was only f a i r , c h i e f l y as a r e s u l t o f the d e c i s i o n to use i t up t o twice i t s design f r e quency.  However, i t s response was f r e e of sharp i r r e g u l a r i -  t i e s and the mathematical procedure for.compensation  was  a v a i l a b l e , so i t was adjusted c a r e f u l l y , and used. The c o r r e l a t o r s were t e s t e d f o r t h e i r d e t e c t i o n law f o r small s i g n a l s i n the presence of n o i s e , and were found t o be quadratic t o the l i m i t of accuracy of measurement.  The audio  a m p l i f i e r output was adequately f r e e o f r i p p l e and noise. The storage capacitors and t h e i r charging r e s i s t o r s were c a r e f u l l y s e l e c t e d f o r s t a b i l i t y and e q u a l i t y o f time constants.  The c a p a c i t o r s use low leakage, low soakage mylar  f i l m d i e l e c t r i c , and the r e s i s t o r s are the deposited carbon type. The readout equipment i s mostly mechanical and, apart from the f a i l u r e of an inexpensive motor, which was replaced by a b e t t e r type, has operated w e l l .  E q u a l i t y of charging  52  times f o r the two banks of c a p a c i t o r s i s ensured by the use o f a binary s c a l e r t o d i v i d e the once per minute impulse from the switch shaft t o once per two minutes f o r the bank change-over relay. A l l o f the above apparatus except the storage banks and the readout deck are housed i n a 7-foot v e r t i c a l cabinet.  The  storage and readout chassis are mounted on an open rack, and produced r e l a y contact i n t e r f e r e n c e with other equipment i n the l a b o r a t o r y u n t i l the offending contacts were damped with R-C f i l t e r s . The numerous unavoidably long cables between the hydrogen r e c e i v e r , the spectrometer,  and the d i g i t a l voltmeter formed  ground loops which c a r r i e d a c e r t a i n amount o f 60-cycle current.  As a r e s u l t the s i g n a l l i n e t o the voltmeter c a r r i e d  about 5 mv of r i p p l e .  A l s o , the operation o f the card punch  caused f a l s e t r i g g e r i n g o f the voltmeter, which i n t u r n operated the card punch.  These d i f f i c u l t i e s were overcome by  f l o a t i n g the input t o the d i g i t a l voltmeter and making grounds through a 5-ohm r e s i s t o r . b)  The Residual C o e f f i c i e n t s When the completed spectrometer  was f i r s t tested with a  nominally f l a t input spectrum the c o r r e l a t o r output voltages, as read from the storage c a p a c i t o r s , were seen t o be nearly zero, as expected, but with an important exception.  The f i r s t  53 c o e f f i c i e n t , C]_, was r a t h e r l a r g e , and i n v e s t i g a t i o n showed that i t arose from the l a c k o f very low frequency response i n the system  0  To remedy the s i t u a t i o n by redesigning a l l o f  the equipment which depended on the use o f video transformers seemed unnecessary, and i n s t e a d , the gain o f the audio amplif i e r i n the f i r s t c o r r e l a t o r was reduced by a f a c t o r o f f o u r . This change prevented the observed overloading o f the synchronous detector and brought the value o f C]_ "on s c a l e . " S t i l l , there was considerable range i n the r e s i d u a l values o f the c o e f f i c i e n t s observed with a " f l a t " noise i n p u t , so a s e t of z e r o - s h i f t potentiometers was added to the output c i r c u i t s so that a l l c o e f f i c i e n t s could, a r b i t r a r i l y , be made zero i n the presence o f an input spectrum known to contain no hydrogen emission. Mathematically, the zero s h i f t s make no d i f f e r e n c e , as the spectrometer i s always used d i f f e r e n t i a l l y , but t h e i r use i s a great p r a c t i c a l a i d t o t e s t i n g .  For example, i f  the c o e f f i c i e n t s , as t r a c e d on the s t r i p - c h a r t monitor, are i n i t i a l l y a l l zero i t i s easy to observe any d r i f t i n t h e i r values that may occur over a period o f time. c)  S t a b i l i t y , Noise, and L i n e a r i t y With the i n s t a l l a t i o n o f the zero s h i f t potentiometers  the i n t e r f e r e n c e spectrometer was complete and ready f o r overall testing.  F i r s t to be checked was the long term  s t a b i l i t y o f the c o e f f i c i e n t s under constant i n p u t .  After  54 an adequate period o f warm-up the s t a b i l i t y was found t o be e x c e l l e n t — a b o u t 0.2°K per hour.  An exception was C]_, whose  value d r i f t e d s e v e r a l times f a s t e r , probably as a r e s u l t o f gain d r i f t i n the audio a m p l i f i e r . of  The l a r g e u n s h i f t e d value  would make i t more s u s c e p t i b l e to a m p l i f i e r d r i f t than  are the other c o e f f i c i e n t s . The minute t o minute f l u c t u a t i o n , o r n o i s e , i n the coe f f i c i e n t s — l e s s than 2 mv—corresponded t o about 0.10°K, the t h e o r e t i c a l l y expected amount.  A very small d i f f e r e n c e  (about 0.10°K) was found between the c o e f f i c i e n t s stored i n the two c a p a c i t o r banks.  Apparently the time constants o f  the charging paths were not a l l i d e n t i c a l . . I n work r e q u i r i n g the u l t i m a t e i n s e n s i t i v i t y i t would be necessary t o a r range observations so that d i f f e r e n t i a l values always came from comparisons o f each bank w i t h i t s e l f , o r from the averages o f the two banks. The l i n e a r i t y : o f the spectrometer was tested i n two ways. F i r s t , a monochromatic s i g n a l from a l a b o r a t o r y generator was i n j e c t e d over the noise spectrum from the hydrogen r e c e i v e r . (For t h i s t e s t the Dicke switch was f i x e d i n the dummy load position.)  I t was found that the d i f f e r e n t i a l c o e f f i c i e n t s  r e s u l t i n g from the i n j e c t e d s i g n a l were p r o p o r t i o n a l t o the power l e v e l o f the s i g n a l , and t h a t t h i s was t r u e f o r any frequency i n the bandwidth o f the spectrometer.  Next, the  spectrometer was fed w i t h two s i g n a l generators at once,  55 operating at d i f f e r e n t frequencies? and the r e s u l t i n g c o e f f i c i e n t s were compared w i t h those obtained from each i n j e c t e d s i g n a l s e p a r a t e l y . W i t h i n noise and d r i f t l i m i t s the c o e f f i c i e n t s r e s u l t i n g from the simultaneous p a i r of s i g n a l s were equal to the a l g e b r a i c sums of the corresponding c o e f f i c i e n t s f o r the s i g n a l s c o n s e c u t i v e l y . d)  The Instrument Functions The f i n a l , and c r u c i a l , t e s t of the spectrometer was the  determination of the instrument f u n c t i o n s . I f the instrument f u n c t i o n s c l o s e l y approximated the t h e o r e t i c a l l y expected forms, the spectrometer would be ready f o r use.  Ideally,  these f u n c t i o n s would be determined by sweeping a constant amplitude monochromatic s i g n a l through the spectrometer band and measuring C^(f) f o r a l l n and f .  But a s u f f i c i e n t l y pre-  c i s e sweeper was not a v a i l a b l e and i n s t e a d the t e s t was made at 50 e q u a l l y spaced values of f .  A w e l l regulated s i g n a l  generator was used, and the frequency i n each case was set accurately by use of a p r e c i s i o n frequency counter. The t e s t y i e l d e d 50 values of C  n  f o r each of the 20  values of n=s/h provided by the delay l i n e . was s p e c i f i e d by 50 p o i n t s .  Thus each Cn(f)  For the lower values of n the  s p e c i f i c a t i o n was more than adequate, but f o r n=20 there were only 5 p o i n t s per " c y c l e " of the curve. the case f o r n=10 and n=20.  Figure 21  illustrates  Even i n the l a t t e r example the  curve i s w e l l defined i n regard to i t s F o u r i e r components up  i  20  i 40  I  f  i 60  % of  I  range I 80  Figure 21 Response functions f o r n = 10 and n - 20.  I  I  100  56  to the maximum of 10 c y c l e s across the band, and higher components are not used i n the response matrix anyway. 50 values of  That the  s u f f i c i e n t i s i l l u s t r a t e d by f i g u r e 2 2 ,  a r e  i n which GJ>Q[f) (upper curve) and i t s truncated F o u r i e r repr e s e n t a t i o n (lower curve) are both p l o t t e d . For purposes of computation i t i s convenient to i n t r o duce a numerical frequency s c a l e , m, defined by m = 50f/f since f  = lOOfh,  u p p e r  = l / 2 h . The frequency range of the spectrometer  i s then from m=l to m=50. now b e t t e r designated C  n > m  The measured f u n c t i o n s C^(f) are .  The F o u r i e r c o e f f i c i e n t s  a  n j l c  can then be found from a s i m i l a r l y modified form o f equation (33).  That i s  jl  n,k  m=l  C*  The square m a t r i x of the a b j . n j  c  nm  '  cos JCmk/50.  (44  ^ was i n v e r t e d to y i e l d the  Then the i n v e r t e d response functions were formed from  equation (42) i n the form 20  vK,m  F  m  = 2_1] _b n , K  cos  n  ^0  (45  The computer programs f o r these and other operations pert a i n i n g t o i n t e r f e r e n c e spectroscopy are given i n the appendix.  I t i s worth noting that the F^  m  are to be formed from  57  the columns o f the b  n  ^ and not the rows.  This circumstance  a r i s e s from the interchange o f summation indexes between equations ( 4 0 ) and (41.) >• and i s an i n s i d i o u s one, as the mat r i x i s n e a r l y symmetrical about i t s d i a g o n a l . F i n a l l y , instrument f u n c t i o n s were computed by F o u r i e r transform o f the C . a c c o r d i n g t o equation ( 4 3 ) i n the form n m  T  ni,mo  JP =  G  t  n,m F 0  n j m  (46  (In the computations any constant f a c t o r s were dropped as they a f f e c t only the temperature c a l i b r a t i o n o f the spectrometer, and t h i s must, i n the end be done e m p i r i c a l l y by observation o f i n t e r n a t i o n a l sky standards w i t h the complete equipment—hydrogen r e c e i v e r plus spectrometer,)  Instru-  ment functions, f o r m =15 and m «25 are shown i n f i g u r e s 23 0  and 24<>  0  I t i s seen that they peak very a c c u r a t e l y at the  1 5 t h and 2 5 t h frequencies they represent, and that they have l a r g e secondary maxima which d i m i n i s h only s l o w l y with d i s tance from the c e n t r a l maximum.  This behavior was p r e d i c t e d  by ( 2 3 ) and i s the r e s u l t o f the choice o f D(s) made i n ( 2 0 ) . e)  Apodization V i r t u a l e l i m i n a t i o n o f the side-lobes o f the instrument  functions can be achieved by using an apodized impulse r e sponse f u n c t i o n , instead o f ( 2 0 ) .  Of the many such func-  t i o n s t o be found i n the l i t e r a t u r e , the "hamming" f u n c t i o n  Figure 23 Instrument f u n c t i o n f o r m = 1 5 • Q  Figure 24 Instrument f u n c t i o n f o r m = 2 5 . Q  58  discussed by Blackman and Tukey ( 1 9 5 8 ) has been adopted. I t s use leads to great reduction o f the side-lobes and only moderate broadening o f the main maximum.  The hamming func-  t i o n i s defined by D  k  = 0 . 5 4 + 0 . 4 6 cos(TC, k / k  m a x  (47  )  Normally} apodized instrument f u n c t i o n s are created by a p o d i z a t i o n o f the C > but i t i s not proper to apply the n  apodization function D nature o f the l a t t e r .  n  t o the  because of the composite  Instead an apodized set o f i n v e r t e d  response functions i s formed by apodizing the b (45)•  n j k  used i n  This gives F  k,m  • =  20 Z; n , k n b  D  c  o  s  n=l  *™/50  (48  where the prime i n d i c a t e s a p o d i z a t i o n . Examples o f response and hammed i n v e r t e d response f u n c t i o n s are shown together f o r various n i n f i g u r e s 25 and 2 6 . I t i s seen that the i n v e r t e d functions tend to be l a r g e where the response i s small} and v i c e versa. instrument functions f o r various m  Q  Hammed  are shown i n f i g u r e s 27  and 2 8 . Except at extreme values o f f the instrument t i o n s are o f acceptable form.  func-  Each f u n c t i o n peaks a t the  c o r r e c t frequency, and has good symmetry. The side-lobes o f the unapodized functions have diminished adequately, and the equivalent width has expanded the expected amount.  Figure  25  A response f u n c t i o n and i t s hammed i n v e r t .  •  f  •  20  •  %  of  »  40  I  J  range 60 Figure  1  1  80  26  A response f u n c t i o n and i t s hammed i n v e r t .  L  1  100  Figure  28  Hammed instrument f u n c t i o n s f o r mQ= 3 and m = kk* 0  59  f)  The Gibbs E f f e c t I t w i l l be noticed that the peak heights are not inde-  pendent of m, but t h i s r e s u l t i s expected.  I t i s a conse-  quence of employing only cosines i n the F o u r i e r transforms, and may be c a l l e d a Gibbs e f f e c t (Jennison, 1 9 6 1 ) . i d e a l equipment the height of the maximum of the  For instrument  f u n c t i o n w i l l be p r o p o r t i o n a l to .  20 £  cos^( 7Cnm/50),  n=l  and therefore w i l l o s c i l l a t e s l i g h t l y across the band, assuming double values at the ends. f e c t f o r the i d e a l case.  Figure 29a shows the ef-  The Gibbs e f f e c t does not repres-  ent a f l u c t u a t i o n i n s e n s i t i v i t y , f o r the equivalent width of the response i s i n v e r s e l y p r o p o r t i o n a l to peak h e i g h t . Thus the i n t e g r a l of the instrument f u n c t i o n , which determines the s e n s i t i v i t y , i s constant across the s p e c t r a l range. The expected Gibbs e f f e c t f o r the a c t u a l equipment was found by  forming 20 G  m  =  A,  t  C  k,m  and i s p l o t t e d i n f i g u r e 2 9 b .  F  k,m  (49  A comparison of the i n s t r u -  ment f u n c t i o n peak heights of f i g u r e s 27 and 28 with the corresponding Gibbs value of f i g u r e 29b i s perfunctory, as the i d e n t i t y i s mathematical.  I n the p r a c t i c a l case the equivalent  widths are not p r e c i s e l y r e c i p r o c a l to the peak heights  and  2  ol 2  f 20  %  of  range 40  60  Figure 2 9 The Gibbs f u n c t i o n s .  80  100  60  therefore there i s a v a r i a t i o n o f s e n s i t i v i t y with frequency. However, the v a r i a t i o n i s f a s t compared to the width o f the x  instrument f u n c t i o n s , and w i l l not be evident during normal use of the spectrometer,,  The s e n s i t i v i t y , convolved with  the instrument f u n c t i o n s , i s p l o t t e d i n f i g u r e 3 0 . g)  The Low Frequency L i m i t Another anomaly i n the behavior o f the instrument func-  t i o n s i s the sharply curved " t a i l " at the low frequency end of each function,,  The magnitude o f t h i s e f f e c t f l u c t u a t e s  r a p i d l y w i t h t e s t frequency, assuming both signs i n quick succession.  L i k e the v a r i a t i o n of s e n s i t i v i t y w i t h frequency  t h i s e f f e c t dies away upon convolution with a t y p i c a l i n s t r u ment f u n c t i o n .  Any r e s i d u a l e f f e c t can be ignored, as i t i s  not expected t h a t the extreme low frequency end o f the spectrum, w i l l be u s e f u l i n any case.  The response matrix tends  towards a s i n g u l a r i t y at zero frequency because o f the l a c k of dc response i n the spectrometer.  As a consequence, the  i n i t i a l values of the i n v e r t e d response f u n c t i o n s are very h i g h , and they degrade the s i g n a l - t o - n o i s e r a t i o at the l e f t end o f the spectrum.  Therefore i t w i l l be general  p r a c t i c e t o s a c r i f i c e the f i r s t three p o i n t s i n every spectrum to safeguard the v a l i d i t y of the r e s u l t s . h)  The High Frequency L i m i t A more s e r i o u s defect i n the instrument f u n c t i o n s i s  the p e r s i s t e n t "step" which always appears between the 4 0 t h  I05i I 00 95  80  (A C  60  o  10  O) CC  ~  o  4 0  0)  20  20  %  40 60 of bandwidth Figure  The  30  convolved s e n s i t i v i t y f u n c t i o n .  80  00  61  and 5 0 t h t e s t frequencies. I t s o r i g i n i s unknown.  I t can be  speculated that more than 50 values of f should have been used to s p e c i f y the higher order response functions,. but the matter has not been i n v e s t i g a t e d .  I t i s f e l t to be more  l i k e l y that the t r u n c a t i o n of the F o u r i e r s e r i e s between equations (32) and (34) may be a f a c t o r .  This t r u n c a t i o n  seems to be an unavoidable part of the compensation procedure that i s used, as the response matrix cannot be i n v e r t e d unless i t i s a square.  That the t r u n c a t i o n might be  impor-  tant can be surmised from the f a c t t h a t , f o r the 2 0 t h r e sponse f u n c t i o n , the lowest component to be l o s t , the i s probably as l a r g e as the 1 9 t h , ligible.  21st,  and i s t h e r e f o r e not neg-  Upon i n v e r s i o n of the matrix the e f f e c t of the  missing component w i l l be f e l t , though to reduced throughout the e n t i r e matrix.  degree,  Undoubtedly more s o p h i s t i -  cated compensations could be introduced, but there i s a p r a c t i c a l l i m i t to the complexity of manipulations that are actually useful. In order to minimize the d i s t o r t i o n of the spectrum caused by the high frequency s t e p , a simple t e r m i n a l correct i o n procedure has been adopted.  I t c o n s i s t s of the a d d i t i o n  to the r i g h t hand s i d e of each spectrum of an amount, prop o r t i o n a l to the area of the s p e c t r a l p r o f i l e , that i s j u s t s u f f i c i e n t to s t r a i g h t e n the base l i n e of the instrument functions.  Since a l l instrument f u n c t i o n s have, r e l a t i v e to  t h e i r areas, the same magnitude of step i n the same part of  62  the spectrum, and since the spectrometer i s l i n e a r , the procedure i s sound.  An example o f a spectrum, before and a f t e r  t h i s c o r r e c t i o n , i s shown i n f i g u r e 3 2 a .  The o r i g i n a l spec-  trum i s unacceptable prima f a c i e because i t i m p l i e s e i t h e r an i n e x p l i c a b l y l a r g e slope to the base l i n e o r a region of absorption very l a r g e .  Base l i n e slopes can occur, but they are never Absorption i s also a known phenomenon, but there  i s no p h y s i c a l evidence f o r any i n the i l l u s t r a t e d case. F i n a l l y , the corrected spectrum agrees w i t h one obtained by the conventional method of frequency scanning (dashed curve in figure 3 2 b ) . i)  F o l d i n g of the Spectrum The spectrometer also possesses an inconvenient response  feature which, although not revealed by the t e s t procedure, may a p p r o p r i a t e l y be considered here.  I t concerns the e f f e c t  of the compensation procedure on the f o l d i n g o f the spectrum about i t s upper frequency l i m i t . The i d e a l spectrometer i s protected from images by a rectangular f i l t e r having f  = / max° 1  u  p  p  e  r  f i l t e r w i l l have a f i n i t e slope at f  2s  u  p  p  e  r  A  realizable  and w i l l e i t h e r ,  a) permit f o l d i n g of a c e r t a i n region of the spectrum above l/2s  m a x  o r , b) exclude from the spectrum a c e r t a i n region  below l '/ 2 s max, depending on the exact value of f upper , ,. 11rir  or  In  e i t h e r case the extreme upper part of the spectrum w i l l be unusable because i t i s e i t h e r absent o r contaminated. I t  63 was o r i g i n a l l y decided to make f p U  p e r  = l/2s  e x a c t l y , so  m a x  that the b i t of the spectrum that i s weakened by f i l t e r a t tenuation i s also the b i t that i s contaminated.  A further  advantage of the idea was that the reduced s p e c t r a l i n t e n s i t y near the upper l i m i t would be strengthened by the a d d i t i o n of folded energy, and therefore the f l a t n e s s of the noise background could be maintained nearly p e r f e c t l y to the l i m i t . However, the compensation procedure discussed i n 11(h) s p o i l s t h i s concept, as i t automatically restores to f u l l value the attenuated spectrum near the l i m i t .  Now,  because  of the f i n i t e slope of the f i l t e r edge, energy j u s t above the  l i m i t i s folded i n j u s t below, and i t too i s augmented  by the compensation.  Consequently the spectrometer s e n s i t i v -  i t y r i s e s sharply to double the normal value at the high frequency end of the spectrum.  A s i n g l e spectrum, per se,  o f f e r s no way of c o r r e c t i n g f o r f o l d i n g , because any v a l i d procedure requires a knowledge of the form of the spectrum beyond the l i m i t , and t h i s can only be determined by another measurement.  But i f the e x t r a information i s a v a i l a b l e ,  u n f o l d i n g i s p o s s i b l e , and perhaps worthwhile. In the p r o j ect  described below i t was sometimes found necessary, i n  order to span the s p e c t r a l range of i n t e r e s t , to s h i f t the centre frequency of the spectrometer by j u s t one bandwidth and re-observe the spectrum.  I n these cases the s p e c t r a l  i n f o r m a t i o n necessary to the u n f o l d i n g of the contaminated region at the upper end of the f i r s t spectrum i s found at  64 the lower end of the second spectrum.  The l a t t e r region i s  i t s e l f not a scene of f o l d i n g because the absence of response below 100 kc interposes a generously wide gap between the observed spectrum and i t s image i n the negative frequency region. The d e t a i l s of the method used to unfold contaminated spectra are given i n the appendix.  The a p p l i c a t i o n of t h i s  procedure degrades somewhat the s i g n a l - t o - n o i s e r a t i o i n that part of the spectrum r e q u i r i n g c o r r e c t i o n , but i t extends the s p e c t r a l range i n t o a region that would otherwise be l o s t o  The v a l i d i t y of the c o r r e c t i o n process was  veri-  f i e d by comparing the r e s u l t i n g spectrum with one obtained by conventional frequency scanning, j)  Area of A p p l i c a t i o n With the development of the above i n t e r p r e t a t i o n s of  the imperfections i n the instrument f u n c t i o n s , and acceptance of the associated c o r r e c t i v e procedures, the i n t e r f e r ence spectrometer was considered ready f o r use. that i t i s not a p r e c i s i o n spectrometer.  I t i s clear  The 0.1°K  noise  l e v e l has no meaning f o r intense s p e c t r a that have been s t r o n g l y corrected f o r defects i n performance.  But i n the  study of f a i n t s p e c t r a with broad features the high speed and low noise of the i n t e r f e r e n c e spectrometer make i t a u s e f u l t o o l i n astronomical radio spectrometry.  Its appli-  c a t i o n to a survey of the atomic hydrogen i n the s p i r a l galaxy M31 i s described next.  65 A  V  a)  SURVEY  OF THE ANDROMEDA NEBULA  Introduction The great s p i r a l nebula i n the c o n s t e l l a t i o n of Androm-  eda i s l i s t e d i n Messier's as number 31• erffrr  rr  catalogue of nebulous objects  The l a r g e r "New  numbers i t 2 2 4 .  General Catalogue" of Drey-  The p o s i t i o n of i t s centre i s r i g h t  ascension • 0* 4 1 0 » d e c l i n a t i o n 4 1 . 0 1  m  (1950  co-ordinates).  M31 was known to p r e - t e l e s c o p i c viewers of the heavens as a hazy patch of l i g h t v i s i b l e i n the northern autumn sky on c l e a r moonless n i g h t s .  Of course, i t s true nature was  unknown to them, and indeed, to l a t e r astronomers who studi e d i t with the a i d of l a r g e t e l e s c o p e s . Even the r a p i d l y developing techniques of t e l e s c o p i c photography were f o r h a l f a century unable to s e t t l e the r i s i n g controversy concerning the l o c a t i o n of t h i s and other l i k e s p i r a l s t r u c tures.  Some astronomers, without any r e a l evidence, pos-  t u l a t e d that M31 was one of many remote " i s l a n d u n i v e r s e s " that populated the vast reaches of space beyond our own galaxy of s t a r s .  Hubble (1936) proved they were r i g h t when  he discerned, i n M31, s t a r s of a f a m i l i a r type, whose i n t r i n s i c brightness was known.  T h e i r extremely low apparent  # Charles Messier, a French comet hunter, prepared h i s catalogue around 1780 to help to d i s t i n g u i s h new comets from the permanent hazy patches that dot the sky. J. L. E. Dreyer of Armagh Observatory.  66  brightness placed them two m i l l i o n l i g h t years away—a d i s tance twenty times the diameter of the M i l k y  Way.  Most of the e x t e r n a l galaxies-~hundreds of thousands have been photographed~-show considerable symmetry of shape and are approximately e l l i p t i c a l i n o u t l i n e . a t h i r d have d i s c e r n i b l e s p i r a l s t r u c t u r e .  Of these, about Many of the r e -  mainder are a c t u a l l y e l l i p s o i d a l , but the s p i r a l s are rather f l a t and d i s c  shaped.  I t i s thought that the dynamics of the s p i r a l s i s simp l e r than that of the o t h e r s , but even the f l a t systems have not y i e l d e d to a n a l y s i s , e i t h e r experimental of t h e o r e t i c a l . P o s t u l a t e s outnumber f a c t s , and progress c o n s i s t s mostly of the r e j e c t i o n of o l d guesses about the s t r u c t u r e and i n t e r nal  motions of g a l a x i e s . A wide-angle photograph by a l a r g e telescope w i l l shov;  numerous g a l a x i e s a f t e r one hour of exposure. p l a t e s sometimes show more g a l a x i e s than s t a r s .  Long exposure The l a t t e r  are foreground o b j e c t s , and, apart from t h e i r u t i l i t y as brightness standards, t h e i r presence merely confuses the view of e x t r a - g a l a c t i c space.  Galaxy counts, p l o t t e d against  b r i g h t n e s s , show that space, i n the l a r g e , i s uniformly populated to enormous d i s t a n c e s .  P l o t t e d against p o s i t i o n i n  the sky, they show that g a l a x i e s c l u s t e r i n twos, i n hundreds, and i n tens of thousands.  One 4 8 - i n c h Palomar  Schmidt  p l a t e c a r r i e s more than 5 0 , 0 0 0 images of remote g a l a x i e s .  67 But although these counts are of great interest to the cosmolo g i s t they throw l i t t l e l i g h t on the nature o f g a l a x i e s . Narrow angle photographs o f the nearer s p i r a l g a l a x i e s present the astronomer with m a g n i f i c e n t l y d e t a i l e d views o f t h e i r luminous p a r t s .  Unfortunately the morphology of a  galaxy, as displayed i n a photograph, f a i l s t o reveal even the  d i s t r i b u t i o n of i t s mass, l e t alone d e t a i l s o f i t s com-  p o s i t i o n o r i t s motion.  The simple system o f morphological  c l a s s i f i c a t i o n of g a l a x i e s , introduced by Hubble, has been elaborated u n t i l , de Vaueouleurs admits ( M c V i t t i e , I 9 6 I ) , about 100 subtypes are needed to accommodate as much as 95% of the observed forms.  Vorontsov-Velyaminov ( i b i d . ) claims  that "morphological types . 6 . from the Palomar a t l a s cannot be r e c o n c i l e d with the e x i s t i n g c l a s s i f i c a t i o n s . " An important c o n t r i b u t i o n of the d i r e c t photograph has been- to the establishment of a distance s c a l e .  I f numerous  photographs of a nearby galaxy have been taken at s u i t a b l e i n t e r v a l s of time, they can be searched f o r v a r i a b l e s t a r s . The nature of the l i g h t curve of a v a r i a b l e — i t s period* amplitude, and degree o f symmetry—is o f t e n such as t o make reasonably c e r t a i n the type of s t a r i n v o l v e d .  I f i t i sa  Cepheid v a r i a b l e o r a nova i t can be ascribed an absolute magnitude.  The distance to the galaxy, and hence i t s diam-  e t e r , f o l l o w r e a d i l y from the apparent brightness o f the variable.  A f t e r s e v e r a l g a l a x i e s have been studied i n t h i s  way a r e l a t i o n between the appearance, brightness and angular diameter of g a l a x i e s , on the one hand, and t h e i r distance on the other, can be found.  Subsequently.the r e l a t i o n can be  used to e s t a b l i s h the distance of g a l a x i e s of a given appearance, e t c . , i n cases where there i s no hope of d e t e c t i n g individual stars.  Thus the distance s c a l e i s extended to  regions i n which the well-known red s h i f t begins to be an e f f e c t i v e c r i t e r i o n of remoteness. The f a i l u r e o f spectacular photographs to r e v e a l much about g a l a x i e s requires explanation. ficulties.  There are s e v e r a l d i f -  F i r s t , the photograph does not show whether the  l i g h t from the galaxy i s emitted by s t a r s of by gas clouds. Second, i t does not show what f r a c t i o n of the i n t e r s t e l l a r gas i s un-ionized, and therefore non-luminous.  Third, i t  does not r e v e a l whether the s t a r s are predominantly g i a n t s or dwarfs.  F i n a l l y , i t gives l i t t l e information on the  amount of l i g h t - a b s o r b i n g dust unless i t i s present i n excessive amounts.  These d i f f i c u l t i e s make i t useless to  equate the brightness d i s t r i b u t i o n to the mass d i s t r i b u t i o n . I f most s p i r a l g a l a x i e s were a l i k e , f a c t s gleaned from a photograph of a s p e c i a l c a s e — f o r example, where a companion galaxy i s p r o v i d i n g a g r a v i t a t i o n a l p e r t u r b a t i o n — c o u l d then be applied to other s p e c i a l cases where other f a c t s were available.  But the v a r i e t y i s g r e a t , and each galaxy i s i n  some way unique; o f t e n i t turns out to be unique i n the parameter that i s most e a s i l y measured.  69 Spectrographic i n v e s t i g a t i o n o f a galaxy provides i n f o r mation not obtainable from photographs.  However, the method  i s a l l but c r i p p l e d by the e x c e s s i v e l y low surface b r i g h t ness o f a l l p a r t s but the nucleus o f a galaxy, and t h i s cond i t i o n a p p l i e s w i t h almost equal force t o nearby o b j e c t s . Consequently,  the vast majority o f nebular spectrograms have .  been exposed only to l i g h t from the n u c l e i .  The spectrum  seldom reveals much about the composition of the g a l a c t i c nucleus because i t i s a composite spectrum i n which the emissions from s t a r s o f various types, and gas clouds o f d i f f e r e n t composition and e x c i t a t i o n are mixed and then b l u r r e d by d i f f e r e n t i a l Doppler e f f e c t s .  Often only the  approximate mean Doppler s h i f t can be extracted from the spectrogram.  I t i s , nevertheless, an important item o f  information. The space between g a l a x i e s seems to be f r e e o f absorbing m a t e r i a l ( F i e l d , 1959> 1 9 6 2 ) , therefore the mean surface brightness o f a nearby galaxy i s no greater than that o f a very remote one of the same type.  However, there are o f t e n  patches o r knots o f enhanced surface brightness detectable throughout a galaxy o f l a r g e angular s i z e .  I n such cases i t  i s p o s s i b l e to o b t a i n spectrograms o f the emission from mater i a l a t various distances from the centre o f a galaxy, a l b e i t at the cost o f many nights o f observing with the l a r g e s t equipment.  Such measures have been made f o r a score o f  points i n M31 ( M a y a l l , 1 9 5 0 ) .  They give a d i f f e r e n t i a l  70  v e l o c i t y , between the two ends of the galaxy, of about 500 km/sec.  Thus the r o t a t i o n of the galaxy, so u r g e n t l y demanded  by g r a v i t a t i o n a l theory, i s confirmed.  However, the low pre-  c i s i o n and poor d i s t r i b u t i o n of the measures leaves the quest i o n of the r o t a t i o n law, and hence the mass d i s t r i b u t i o n , l a r g e l y open. An e f f e c t i v e method of observing g a l a x i e s t h a t are not too c l o s e i s that of l o n g - s l i t spectroscopy.  In t h i s method  the g a l a c t i c image i s focussed on an e x t r a long entrance s l i t , f i t t e d to a s p e c i a l spectrograph.  Spectra obtained  i n t h i s way can be measured f o r r a d i a l v e l o c i t y along a l i n e through the galaxy.  Usually the s l i t i s oriented along the  major a x i s and i n favorable cases i t i s p o s s i b l e to deduce an approximate r o t a t i o n law, and to estimate a t o t a l mass. Sometimes p a r t i c u l a r items of i n f o r m a t i o n r e l a t i n g to asymmet r i e s , r a d i a l motions, e t c . , are a v a i l a b l e .  Results based  on t h i s method have been reported by the Burbidges i n a long s e r i e s of papers i n the A s t r o p h y s i c a l J o u r n a l .  Numerous  references to t h i s s e r i e s can be found i n Burbidge,(1962 ). Observations of the d i s c of our own galaxy are beset by additional d i f f i c u l t i e s .  I n t e r s t e l l a r dust absorbs a l a r g e  f r a c t i o n o f the l i g h t from d i s t a n t o b j e c t s .  The dust i s  concentrated i n the g a l a c t i c plane, where i t i s l e a s t welcome, and i t l i m i t s o p t i c a l observation to a f r a c t i o n of a g a l a c t i c r a d i u s . Worse, the presence of unpredictable  71 amounts of absorption i n various d i r e c t i o n s v i t i a t e s a l l d i s tance scales and makes d i f f i c u l t or impossible the correct i n t e r p r e t a t i o n of the few observations of remote objects that have been made.  In the region w i t h i n 5>000 l i g h t years  of the sun i t i s easy to o b t a i n spectra of i n d i v i d u a l s t a r s and of b r i g h t gas clouds.  Absorption by dust i s g e n e r a l l y  s m a l l , and distance scales are u s e f u l , i f approximate. Photography i s easy, and proper motions (across the l i n e of s i g h t ) can be obtained from c a r e f u l l y taken p l a t e s .  This  i s the region of most of the i n v e s t i g a t i o n s of astronomy and a s t r o p h y s i c s .  However, i t comprises only 1% of the area  of the g a l a c t i c d i s c and can s c a r c e l y be regarded as t y p i c a l of i t . Radio observations of almost a l l parts of our galaxy are p o s s i b l e , and have been made. But here again the l a c k of an independent distance s c a l e l i m i t s the s e c u r i t y of any i n t e r p r e t a t i o n s placed on the data.  I t i s a b s o l u t e l y essen-  t i a l to know the p o s i t i o n of the m a t e r i a l detected by a telescope i f the observation i s to be of value i n the s o l u t i o n of problems of g a l a c t i c s t r u c t u r e . However, no  new  b a s i s f o r a distance scale i s i n s i g h t , and so observations of an e x t e r n a l galaxy, where p o s i t i o n s i n the d i s c can be determined with no s i g n i f i c a n t e r r o r to i n v a l i d a t e i n t e r p r e t a t i o n s , i s a most a t t r a c t i v e a l t e r n a t i v e route to  new  knowledge of g a l a c t i c s t r u c t u r e . Present radio telescopes have s u f f i c i e n t angular r e s o l u t i o n to begin such s t u d i e s ,  72 and i t can s a f e l y be assumed that l a r g e r instruments  will  continue the work i n the f u t u r e . M31  i s n e i t h e r the c l o s e s t , the b r i g h t e s t , nor the l a r g -  est i n apparent s i z e , of the g a l a x i e s about us.  The Large  and Small Magellanic Clouds occupy a l a r g e r part of the sky and have higher surface b r i g h t n e s s .  However, they are both  i r r e g u l a r g a l a x i e s , and although t h e i r study i s of great i n t e r e s t and value, i t i s u n l i k e l y that i t w i l l throw much l i g h t on the s t r u c t u r e and dynamics of the more t y p i c a l , regular galaxies.  Their l o c a t i o n at -70° d e c l i n a t i o n  makes i t necessary to study them from the southern hemisphere. M31, at 40° north d e c l i n a t i o n , r i s e s high i n the northern sky and remains above the horizon 17 hours per day.  Its  angular extent, the greatest of any s p i r a l , i s 160* by 40* on o p t i c a l photographs, and i t s radio diameters at the hydrogen frequency are nearly twice as great.  The t i l t of i t s  plane of r o t a t i o n to the l i n e of s i g h t i s about 14°--little enough that measured r a d i a l v e l o c i t i e s may  reach 97% of the  r o t a t i o n a l values; great enough that even i t s smaller apparent dimension can be resolved by radio telescopes of moderate s i z e .  To the northern observer M31 o f f e r s a unique  opportunity f o r study. b)  The Radio Emission from M31 The continuum emission of M31 has been studied exten-  s i v e l y at J o d r e l l Bank.  Brown and Hazard (1959) observed  73 the galaxy at 158 and 237 Mc. and found that the radio diamet e r was about three times the o p t i c a l .  I t was also noted  that the r a d i o shape o f M31 was nearly c i r c u l a r .  This f a c t  was i n t e r p r e t e d to i n d i c a t e the presence o f a "corona" around the galaxy.  Subsequently Large, Mathewson, and Haslam (1959)  reobserved M31 at 408 Mc. and obtained s i m i l a r , but more detailed results.  The coronal emission was regarded as a r i s -  ing from the synchrotron mechanism, and the d i s t r i b u t i o n o f the emission about the minor a x i s suggested that the magnetic f i e l d i n the corona was ordered. The most extensive published work on the r a d i a t i o n o f atomic hydrogen from M31 i s that done by van de H u l s t , Raimond, and van Woerden ( 1 9 5 7 ) .  They obtained spectra at  twenty p o i n t s spaced 15* apart along the major a x i s o f the nebula.  Each point was observed at f i x e d frequency f o r  t h i r t y minutes.  A comparison f i e l d outside the nebula was  observed i n the same way. About 10 hours o f observation y i e l d e d values o f temperature spectrum.  f o r 1 0 frequencies i n one  Peak temperatures were between 6 ° and 7°K, and  mean e r r o r s o f 0.25°K were claimed. Observation o f atomic hydrogen i n the north-east part of M31, where r a d i a l v e l o c i t i e s are n e a r l y zero, was hampered by the presence o f g a l a c t i c hydrogen i n the foreground. Attempts t o c o r r e c t f o r t h i s contamination by making compari s o n observations o f the foreground m a t e r i a l adjacent to M31 were only p a r t l y s u c c e s s f u l .  The spectrum taken at the centre of M31 showed a c e n t r a l peak>and wide symmetrical wings.  The wide wings were not  unexpected, as the antenna (beamwidth = 0?6) would accept some r a d i a t i o n from points s u f f i c i e n t l y removed from the nucleus to; be i n rapid r o t a t i o n .  Spectra taken near the ex-  t r e m i t i e s of the major a x i s showed narrow, s l i g h t l y skewed l i n e s , d i s p l a c e d more than 200 km/sec e i t h e r s i d e of the central velocity.  At intermediate p o s i t i o n s along the a x i s  the l i n e p r o f i l e s were somewhat i r r e g u l a r i n shape.  In  regions near the centre the l i n e s were without c l e a r l y d i s t i n g u i s h a b l e maxima. In order to i n t e r p r e t the spectra i n terms of g a l a c t i c s t r u c t u r e and r o t a t i o n i t was necessary to make s e v e r a l assumptions.  Of these the two most important were that the  mass d i s t r i b u t i o n was c i r c u l a r l y symmetric and that the motions were p e r f e c t l y c i r c u l a r .  The a n a l y s i s showed that  the v e l o c i t y of r o t a t i o n f e l l slowly from a maximum of 278 km/sec at 096 from the centre to 221 km/sec at 2?5. W i t h i n 0?75  o f  t 5 a e  centre the v e l o c i t y estimate was a c t u a l l y only  an i n t e r p o l a t i o n between measures f o r the outer p a r t s . Agreement of the r a d i a l v e l o c i t i e s with o p t i c a l data was very poor, discrepancies as high as 170 km/sec being encountered.  The density d i s t r i b u t i o n determined from the areas  under the l i n e p r o f i l e s showed pronounced peaks 1° e i t h e r side of the centre, i n d i c a t i n g a mass d e f i c i e n c y near the centre.  The mass of atomic hydrogen i n the system was found  75 to be 0 . 2 5  X 10" " s o l a r masses—about 1  0  1%  of the t o t a l mass  of the galaxy. An anomaly i n the form of an excess of radi a t i o n at - 2 2 4 km/sec was found i n the north-east part of the  system, but no explanation f o r i t was found.  This im-  portant work by the astronomical group at Dwingeloo w i l l be r e f e r r e d to repeatedly as the Dutch work. c)  Spectrometer Observations of M31 With completion of t e s t i n g of the i n t e r f e r e n c e spectro-  meter i t was decided to repeat the work of the Dutch astronomers, and extend the i n v e s t i g a t i o n to the e n t i r e area of M 3 1 . The s p e c t r a l r e s o l u t i o n and the s e n s i t i v i t y of the new spectrometer \TOuld be b e t t e r than that of the Dutch equipment. The speed would be v a s t l y g r e a t e r .  In f a c t , t h i r t e e n times  as many s p e c t r a were obtained i n one tenth of the telescope time. The plan of observations, which was c a r r i e d out i n 3 " n i g h t s " (2 pm to 3 am), was to observe a rectangular region about M 3 1 , as o u t l i n e d i n f i g u r e 3 1 .  The rectangle was  chosen  l a r g e enough to ensure that observations made near i t s p e r i phery would be f r e e of r a d i a t i o n from the nebula.  The extent  of the region expected to show emission was deduced from a knowledge of the Dutch work along the major a x i s , and the assumption that the minor diameter of the nebula would be one f o u r t h the major. the  The l a r g e e l l i p s e i n f i g u r e 31 shows  radio s i z e of M31, the small e l l i p s e represents the op-  t i c a l image, and the c i r c l e i n d i c a t e s the s i z e of the antenna  t  1  1 50  m  1  1  R.A.  40 Figure  I  L_  30  m  31  The observing f i e l d f o r M31.  m  76  beam t o half-power p o i n t s . Observations were begun with a d e c l i n a t i o n scan at +38°. The scan was made by p o i n t i n g the telescope to a p o s i t i o n at the south-west edge o f the r e c t a n g u l a r region and l e t t i n g earth r o t a t i o n carry the nebula through the beam o f the antenna.  C o r r e l a t i o n c o e f f i c i e n t s from the i n t e r f e r e n c e spec-  trometer were recorded on a punched card once per minute. Thus s p e c t r a were obtained f o r each minute o f r i g h t ascens i o n along the chosen p a r a l l e l o f d e c l i n a t i o n .  The 368 mean  p o s i t i o n s at which observations were made, along 26 p a r a l l e l s of d e c l i n a t i o n , are i n d i c a t e d by the dots i n f i g u r e 31• Each scan was made f o u r times, and each spectrum was obtained from the average o f the f o u r sets o f c o r r e l a t i o n c o e f f i c i e n t s . The angular s e p a r a t i o n o f the p o i n t s i s 12* i n r i g h t ascens i o n and 1 5 i n d e c l i n a t i o n . T  The f i r s t two sets and the l a s t  two sets of c o r r e l a t i o n c o e f f i c i e n t s obtained on each scan were intended as references f o r the computation o f the i n t e r mediate spectra.  I n other words, the spectrometer was em-  ployed d i f f e r e n t i a l l y . The bandwidth o f the spectrometer i s 1.325 M c , or about 360 km/sec at 1420 Mc.  This range i s i n s u f f i c i e n t t o observe  a l l the atomic hydrogen i n M31, which has an o v e r a l l d i s p e r s i o n o f 450 km/sec.  Therefore i t was necessary t o observe  the south-west part o f M31 with a centre frequency o f 1422.7125 Mc. and the north-east part w i t h a centre f r e quency o f 1420.9970 Mc.  The c e n t r a l parts o f the nebula  77 (scans 11 to 15 i n c l u s i v e ) were observed twice> f i r s t w i t h one and then the other of these two centre frequencies. The two " h a l f - s p e c t r a " obtained f o r each observation point were j o i n e d i n the reduction procedure to form a s i n g l e wide band spectrum, d)  Reduction o f the Observations The raw data consisted o f 1792 punched cards, o f which  496 were comparison observations on the sky near M31.  The  1296 "galaxy" cards were averaged i n sets o f 4 and the d i f ferences between the averages and the appropriate "sky" cards were F o u r i e r transformed by d i g i t a l computer. The F o r t r a n program i s given i n the appendix.  The computer out-  put comprised 324 s p e c t r a , i n c l u d i n g 120 " h a l f - s p e c t r a " taken near the centre of M31.  The l a t t e r were combined i n  p a i r s to make 60 wide-band spectra o f the c e n t r a l regions. Of the 264 complete s p e c t r a obtained, 143 showed a measurable amount o f hydrogen emission. Reduction o f the observed s p e c t r a i n v o l v e s s e v e r a l operations.  For each spectrum, the f i r s t step to be performed  i s the establishment of the base l i n e .  I t i s a well-known  f a c t that there i s no e n t i r e l y o b j e c t i v e method o f drawing i n a base l i n e f o r a s p e c t r a l p r o f i l e .  However, i t i s us-  u a l l y p o s s i b l e t o make a s a t i s f a c t o r y judgment regarding the base l i n e p o s i t i o n , i f a l l r e l e v a n t a p r i o r i i n f o r m a t i o n i s taken i n t o account.  When an emission l i n e i s expected the  78 base l i n e i s f i t t e d t o the lower parts of the spectrum, unl e s s there i s a c l e a r i n d i c a t i o n that other features are present. A f t e r the base l i n e i s drawn the area under the p r o f i l e i s measured.  This area i s used only to determine the mag-  nitude of the step c o r r e c t i o n required a t the high frequency end o f the spectrum.  The nature o f t h i s c o r r e c t i o n was  discussed i n s e c t i o n I V ( h ) .  A f t e r the c o r r e c t i o n has been  made the base l i n e i s s h i f t e d s l i g h t l y to i t s f i n a l p o s i t i o n . In the few cases i n which u n f o l d i n g o f the end o f the spectrum was necessary i t was done i n the way described i n section IV(i). I f the nebular spectrum was overlapped by t h a t o f g a l a c t i c hydrogen an attempt was made t o separate the two by a comparison with the f i r s t and l a s t spectra o f the scan, which were f r e e o f nebular f e a t u r e s . The f i n a l step i n the r e c t i f i c a t i o n of each spectrum was t o set t o zero the i n t e n s i t i e s at a l l frequencies outside the p r o f i l e , and t o c a l c u l a t e f i n a l p r o f i l e i n t e n s i t i e s by s u b t r a c t i o n o f the corresponding base l i n e values.  Fig-  ure 3 2 a i l l u s t r a t e s a p r i m i t i v e spectrum with i t s step corr e c t i o n and f i n a l base l i n e .  Figure 32b shows the same  spectrum a f t e r r e c t i f i c a t i o n ( s o l i d l i n e ) . The temperature s c a l e used i n the reductions was der i v e d during the e a r l y stages of t e s t i n g of the spectro-  5  °K  4 T 3  V  /'  2  1  1  \\ \\  1  |  0  b 1  1 1 1J  /(/ -300  1 V  c  1 -200 Figure  1 Km/Sec  \  \ l  32  R e c t i f i c a t i o n of a spectrum.  -100  1  79 meter.  At that time some observations of intense emissions  from the plane of the Galaxy were made, and the r e s u l t s compared w i t h frequency scans obtained i n the conventional way, and c a l i b r a t e d w i t h the standard temperature source.  However,  the G a l a c t i c observations y i e l d e d peak temperatures i n excess of 100°K and i t was thought prudent to check the c a l i b r a t i o n at much lower i n t e n s i t i e s , even though s i g n a l generator t e s t s had i n d i c a t e d that the spectrometer response was accurately linear.  F o r t h i s check, use was made of the frequency scans  of selected p o i n t s i n M 3 1 , which were taken to confirm the v a l i d i t y o f the c o r r e c t i o n procedures described above. I t was found that there was no s i g n i f i c a n t d i f f e r e n c e between the p r d f i l e areas of the s p e c t r a obtained i n the two ways, and t h e r e f o r e the o l d temperature c a l i b r a t i o n was r e t a i n e d . One o f these scans i s shown by the dashed l i n e i n f i g u r e 32b.  The frequency-scan spectrum i s of lower height and  greater width than the one produced by the spectrometer because the nearest a v a i l a b l e bandwidth f o r frequencj* scan-  ning was somewhat greater than that of the instrument funct i o n o f the spectrometer. The e n t i r e set of 143 r e c t i f i e d s p e c t r a i s displayed i n f i g u r e 33»  The foot o f the v e r t i c a l l i n e i n each spec-  trum represents zero v e l o c i t y w i t h respect t o the centre of M31.  The bar at the top o f the l i n e i n d i c a t e s 4°K. The  v e l o c i t y s c a l e f o r the s p e c t r a i s such that adjacent v e r t i c a l l i n e s are separated by 615 km/sec.  S p e c t r a l peaks t o  AA-  a_1 A.  m  35  -300  V  0 Km/Sec  300  The Instrument Function  JA  R.A.  1 k  40'  /I  K  1  L  43  c  A  1 hx  AI  A. AA^  /I ,  A  4  k  2 • - 6 0 0  - 3 0 0  0 V,  300  600  Km/Stc  A_L  a  l l 11  La  A  1A  U  Al_  /I  \ /\ . / \.  ,  V\  A  m  A  JA  .All  La  45  A  JL  AL  AA_\1  JL  A  U 1  LA  H i S P E C T R A in  M3I  L  L, L 42  4  i DEC.  i 41° Figure  3 3  40*  39  s  80 the r i g h t o f the v e r t i c a l f i d u c i a r y f o r that spectrum have a positive velocity.  The s p e c t r a l range observed i s i n d i c a t e d  by the l e n g t h of the base l i n e , except f o r s p e c t r a near the centre o f the d i s p l a y , where the observed range was i n excess o f 615 km/sec.  The e q u a t o r i a l co-ordinates o f the  observation i n t e r s e c t at -15 km/sec, near the foot o f each v e r t i c a l mark.  I t should be noted t h a t north i s to the l e f t  i n f i g u r e 33 • e)  I n t e r p r e t a t i o n o f the Spectra i)  General Remarks To f a c i l i t a t e i n t e r p r e t a t i o n o f the great q u a n t i t y o f  data embodied i n the s p e c t r a i t i s convenient to c h a r a c t e r i z e each spectrum i n terms o f i t s i n t e g r a l (the area under the p r o f i l e ) and i t s f i r s t moment (the mean frequency). The area, expressed as the product o f temperature i n degrees K e l v i n and the bandwidth i n kc, i s p r o p o r t i o n a l to the power received by the antenna beam.  Assuming a constant s p i n  temperature f o r the atomic hydrogen throughout the extent of M31, the p r o f i l e area becomes a measure o f the amount o f atomic hydrogen intercepted by the beam. The mean frequency, through the Doppler e f f e c t , represents the mean r a d i a l v e l o c i t y o f the e m i t t i n g m a t e r i a l .  I n t h i s d i s c u s s i o n the area  i n °K>kc w i l l be used without conversion i n t o d e n s i t y o f hydrogen. ^ _ 77  The mean v e l o c i t y w i l l be subjected to numerous  An e x p l i c i t formula f o r conversion i s given i n the appendix.  81  corrections.  F i r s t , f o l l o w i n g van de H u l s t , Raimond, and van  Woerden (1957)> the observed v e l o c i t y , V to the " l o c a l standard of r e s t . "  0 D S  , w i l l be reduced  This reduction removes the  e f f e c t s o f the o r b i t a l motion o f the earth and the p e c u l i a r motion o f the sun.  The r e s u l t , V ] _ , i s obtained most e a s i l y sr  by use of the t a b l e o f McRae and Westerhout (1956).^ V Q , the v e l o c i t y with respect t o the centre o f M31, tained by subtracting  the mean v e l o c i t y of M31.  Then i s ob-  The l a t t e r  i s t e n t a t i v e l y taken to be that found by the Dutch astronomers, -296 km/sec.  F i n a l l y , but again, t e n t a t i v e l y , V , i s 1  m u l t i p l i e d by 1.03 f o r the i n c l i n a t i o n e f f e c t .  The r e s u l t ,  V , i s the r a d i a l v e l o c i t y that would be measured i f the i n c l i n a t i o n , i , o f the plane o f r o t a t i o n of M31 to the l i n e of sight were 0° instead of the accepted value o f 14?5« V  c  The  used here i s thus d i r e c t l y comparable w i t h v e l o c i t i e s i n  the Dutch model o f M31. The  shapes of the spectra are also of i n t e r e s t , but i t  i s not easy t o characterize  the shape i n a mathematical way  that i s h e l p f u l , although some use w i l l be made o f the vel o c i t i e s of the peak, o r peaks, i n each spectrum. quently the d i s c u s s i o n  Conse-  of p r o f i l e shapes w i l l be l a r g e l y  qualitative. #  " I d e a l l y , v e l o c i t i e s o f e x t r a g a l a c t i c objects would be reduced to the r e s t frame o f the Galaxy (Hindman et a l , 1963) but the motion of the sun i n t h a t frame i s not known w i t h i n 50 km/sec.  82 The b a s i c parameters f o r each spectrum are l i s t e d i n Table 1.  Columns (1) and (2) give the mean p o s i t i o n o f the  observation i n 1963.9 co-ordinates; column (3)» the area i n °K'kc; column (4)» the equivalent width i n km/sec; columns (5)> (6), and (7)> the mean v e l o c i t i e s as observed, as r e duced t o the l o c a l standard o f r e s t , and as reduced t o M31 and corrected f o r the i n c l i n a t i o n e f f e c t , r e s p e c t i v e l y ; column (8) gives the v e l o c i t y o f the highest peak o f the s p e c t r a l p r o f i l e , completely reduced and corrected as i n column ( 7 ) . ii)  The D i s t r i b u t i o n o f the Atomic Hydrogen  A contour map o f the d i s t r i b u t i o n o f atomic hydrogen i n M31 has been made from the i n f o r m a t i o n i n the f i r s t three columns o f Table 1, and i s shown i n f i g u r e 34 • The contour o o i n t e r v a l s are 5 X 10^ K k c except near the periphery where 4  o  the 2.5 X 10  contour has been added, and i n the c e n t r a l o  plateaus where 32«5 10 #  contours have been i n s e r t e d .  The  contour p o s i t i o n s were determined by reading from two sets of graphs.  I n one s e t , area was p l o t t e d vs d e c l i n a t i o n f o r  each o f the values o f R.A. at which observations were made. In the other, area was p l o t t e d against R.A. f o r f i x e d declinations.  The curves were drawn so as t o pass smoothly  through every p o i n t , and each curve was extrapolated t o zero area beyond the p o s i t i o n o f the f a i n t e s t recognizable spectrum.  Thus the zero contour does not represent an  TABLE (1).  (2)  (3)  (4)  Dec.  R.A.  Area-  Width  0  39°00  J  33 34 ? 36  (8)  Y,obs lsr "c "p K'kc (km/sec) (km/sec) (km/sec) (km/sec) (km/sec) -508.1 -512.8 -513.8 -515.1  -218.5 -223.3 -224.3 -225.7  -219.5 -226.2 -225.2 -222.4  32 33 34 f 36 37 38  211.3 336.8 426.7 501.9 392.4 130.9 88.6  87.5 64.9 68.8 72.4 80.8 77.8 104.1  -503.3 -505.6 -506.3 -496.4 -503.2 -489.3 -486.9  -512.9 -515.2 -515.9 -506.0 -512.8 -498.9 -496.5  -223.4 -225.8 -226.5 -216.3 -223.3 -209.O -206.5  -217.4 -225.6 •~ 2 24.3 -219.9 -218.7 -213 *4 -251.2  32 33 34  146.3 567.9 915.9 1030.6 760.3 508.7 234.9 161.3  52.9 74.2 71.4 76.5 77.4 88.9 123.7 114.9  -498.7 -499.6 -496.4 -497.2 -495.0 -487.3 -457.7 -430.8  -508.3 -509.2 -506.0 -506.8 -504.6 -496.9 -467.3 -440.4  -218.7 -219.6 -216.3 -217.1 -214.9 -206.9 -176.4 -148.7  -220.4 -222.2 -220.0 -219.9 -219.5 -213.4 -168.5 -189.7  55.3 212.9 557.3 977.6 1344.0 1424.1 1011.6 821.0 368.3 266.6  49.0 102.1 72.1 75.6 85.5 106.8 116.6 159.1 141.3 207.3  -499.5 -487.4 -498.2 -499.3 -497.6 -498.3 -491.5 -489.7 -474.8  -509.1 -497.0 -507.8 -508.9 -507.2 -507.9 -501.1 -496.0 -499.3 -484.4  -219.5 -207.0 -218.2 -219.3 -217.5 -218.3 -211.3 -206.0 -209.4 -194.1  149.2 452.6 800.7 1411.1 1743.9 2060.2 1625.9 1228.6 710.3 317.0  104.1 99.6 96.6 112.8 118.2 130.4 125.0 146.3 193.7 162.1  -479.1 -498.2 -491.3 -495.0 -498.3 -500.6 -497.8 -490.0 -454.4 -494.3  -488.7 -507.8 -500.9 -504.6 -507.9 -510.2 -507.4 -499.6 -464.O -503.9  -198.5 -218.2 -211.0 -214.9 -218.3 -220.6 -217.7 -209.7 -173.0 -214.1  -220.7 -224.3 -220.9 -220.1 - 223.2 -223.3 -225.2 -235=0 -237.3 -224.5 -216.9 -216.5 -219.8 -226.0 -233.3 -241.2 -240.8 -239.1 -236.5 -257.4  I 36 Z 38 39 3  31 32 33 34 35 36 Z 38 39 40 3  40 00  (7)  -498.5 -503.2 -504.2 -505.5  3  39 45  (6)  68.9 68.5 64.9 73.7  3  39 30  (5)  210.3 231.2 202.9 208.3  3  39 15  1  32 33 34  I 36 37 38 39 40 41 3  ra  -L.86.4  TABLE  1  (Continued) (7)  (3)  (2)  (3)  (4)  Dec.  R.A.  Area  Width  40°15 34 35 36 37 38 39 40 41 40 30 34 35 36 37 38 39 40 41 42  517.9 1009.3 1793.9 2431.9 2495.3 2742.3 1513.0 696.6  148.3 139.0 141.0 130.0 133.5 205.6 229.3 224.2  -478.9 -489.7 -494.8 -503.0 -501.5 -471.1 -452.2 -421.0  -483.5 -499.3 -504.4 -512.6 -511.1 -480.7 -461.8 -430.6  -198.3 -209.4 -214.7 -223.1 -221.6 -190.2 -170.8 -133.6  -176.3 -229.3 --242.2 -241.7 -242.9 -240.5 -244.5 —144«4  499.9 347.5 1591.3 2593.2 2996.3 3132.9 2206.2 1113.0 407.3  139.6 208.1 135.5 201.3 191.1 234.1 244.9 174.8 95.8  -459.7 -466.8 -473.7 -475.7 -477.1 -457.2 -437.3 -392.0 -361.2  -469.3 -476.4 -483.3 -485.3 -486.7 -466.8 -446.9 -401.6 -370.8  -178.5 -I85.8 -192.9 -195.0 -196.4 -175.9 -155.4 -108.8 - 77.0  40 45  36 37 33 39 40 41 42 43 44  493.7 955.7 2004.0 3034.2 3333.3 3665.I 2409.7 1370.0 1243.7 193.6  228.1 237.8 250.6 263.9 257.4 241.7 197.0 215.9 203.7 30.3  -445.8 -447.2 -431.9 —424.8 -407.5 -380.8 -358.3 -347.8 -324.7 -285.7  -455.4 -456.8 -441.5 -434*4 -417.1 -390.4 -367.9 -357.4 -334.3 -295.3  -I64.2 -I65.6 -149.9 -142.6 -124.7 -107.2 - 39.4 0.7  -178.4 -249.6 -242.7 -241.6 -241.5 -240.9 -136.3 - 73.0 - 65.O -120.0 -123.5 -123.3 -113.8 - 66.3 - 59.4 -• 62.4 •- 45.6 - 49.2 7.1  41 00 36 37 33 39 40 41 42 43 44 45  134.9 351.6 1450.3 2496.9 3033.0 2946.9 2590.5 1502.2 1107.4 577^1  123.6 122.0 171.5 228.7 236.3 253.1 229.7 188.6 241.1 153.6  -404.9 -366.9 -360.5 -339.9 -315.3 -298.O -277.9 -2' 8.2 -246.3 -234.5  -414.5 -376.5 -370.1 -349.5 -324.9 -307.6 -237.5 -257.8 -255.9 -244*1  -122.1 - 82.9 - 76.3 - 55°1 - 29.8 - 11.9 8.8 39-3 41.3 53.5  -108.5 - 73.2 - 57*7 - 47.7 - 39.4 - 34.6 5.6 29.9 50.4 56.5  t  ra  3  5  (5)  (6)  (1)  V. V, obs Isr "c 'p °K»kc (km/sec) (km/sec) (km/sec) (km/sec) (km/sec) V  4  ""*  O  a &  TABLE  1  (Continued)  (1)  (2)  (3)  Dec,  I. A.  Area  Width  158.6 893.4 1935.2 2290.1 3000.4 2190.5 2275.8 1460.6 574.2 359.3 88.1  77.1 184.9 203.2 202.1 244.6 220.3 232.2 222.3 197.6 207.7 96.0  -339.7 -332.0 -322.8 -277.7 -251.2 -233.7 -194.4 -I9O.3 -169.7 -156.5 -171.4  -349.3 -341.6 -332.4 -287.3 -260.8 -243.3 -204.0 -199.9 -179.3 -166.1 -181.0  - 54.9 - 47.0 - 37.5 9.0 36.3 54.3 94.8 99.0 120.2 133.8 118.5  U°15  T  37 38 39 40 41 42 43 44 45 46 47  m  (4)  (5)  (6)  (3)  (7)  V V obs P Isr c °K«kc (km/sec) (km/sec) (kin/sec) (km/sec) (km/sec  -  46.7 42.5 37.1 21.1 45.4 53.6 75.7 90.8 82.9 83.3 84«8  41 30  38 39 40 41 42 43 44 45 46 47  475.4 1090.0 1691.4 2431.8 2983.8 3367.2 2685.3 1709.3 875.7 263.7  141.7 180.1 182.7 233.7 244.9 240.1 225.1 213.4 227.7 141.6  -252.3 -243.7 -218.4 -203.5 -160.5 -137.4 -123.9 -II3.5 -133.2 -168.6  -261.9 -253.3 -228.0 -2I3.I -170.1 -147.0 -133.5 -123.1 -142.8 -178.2  35.1 44.0 70.0 85.4 129.7 153.4 167.4 178.1 157.8 121.3  27.8 36.1 50.8 69.3 106.4 220.1 235.5 233.4 115.6 110.5  41 45  39 40 41 42 43 44 45 46 47 48  741.6 1093.7 2008.1 3332.7 3501.5 3565.0 2683.8 1589.9 884.7 342.5  I84.1 191.8 218.3 217.2 159.8 151.2 151.4 157.9 190.6 191.6  -194.5 -176.7 -141.8 -123.4 - 93.8 - 86.5 - 85.0 - 86.4 -103.5 -122.9  -204.1 -186.3 -151.4 -133.0 -103.4 - 96.1 - 94.6 - 96.0 -113.1 -132.5  94.7 113.0 148.9 167.9 198.4 205.9 207.4 206.0 I88.4 I69.4  77.3 99.0 127.8 229.5 236.6 242.9 243.7 249.9 231.3 125.2  42 00  39 40 41 42 43 44 45 46 47 48  275.9 540.2 1062.0 1851.1 2501.3 2795.4 2500.8 1728.5 916.8 507.4  I64.4 185.0 208.6 171.1 136.7 112.2 106.7 110.7 126.5 154.2  -I63.2  -172.8 -181.4 -133.3 -112.4 - 93.0 - 81.3 - 78.4 - 80.3 - 86.1 -114.3  126.9 118.0 167.6 I89.I 209.1 221.1 224.1 222.2 216.2 187.2  58.9 146.8 55.3 234.6 242.2 242.3 243.8 241.1 243.1 219.4  -171.8  -123.7 -102.8 - 33.4 - 71.7 - 68.8 - 70.7 - 76.5 -104.7  TABLE (1)  Dec.  42°15  t  1  (2)  (3)  (4)  R.A.  Area  . Width  40 41 42 43 44 45 46 47 48  m  (Concluded) (6)  (5)  (7)  lsr obs c °K.kc (km/sec) (km/sec) (km/sec) (km/sec) V  V  v  (8) V, P  297.7 278.8 823.1 1192.8 1949.7 2152.8 1894.4 1249.3 751.5  158.1 115.3 176.3 147.1 117.7 110.7 107.5 IO9.4 125.6  -142.2 -147.3 - 93.7 - 91.1 - 71.7 - 72.2 - 68.5 - 71.7 - 73.2  -151.8 -156.9 -IO3.3 -100.7 - 81.3 - 81.8 - 78.1 - 8I.3 - 82.8  148.5 143.3 198.5 201.2 221.1 220.6 224.4 221.1 219.6  129.4 164.0 250.1 241.8 241.7 236.7 235.8 233.5 227.7  4 2 30  42 43 44 45 46 47 48 49  149.7 387.5 545.4 953.4 914.0 677.6 628.6 260.6  94.6 104.8 78.7 85.6 99.9 79.3 121.3 74.6  -  97.0 73.3 64.1 65.9 74.9 69.3 84.I 68.8  -106.6 - 82.9 - 73.7 - 75.5 - 84.5 - 78.9 - 93.7 - 78.4  : 195.1 219.5 229.0 227.1 217.8 223.6 208.4 224.1  206.2 235.7 236.3 238.1 233.0 231.6 232.5 228.2  42 45  44 45 46 47 48 49  134.5 184.3 439.7 253.3 175.2 244«3  81.3 64.8 99.2 90.3 89.6 103.5  -115.7 - 51.6 - 64.9 - 67.O - 78.1 - 78.3  -125.3 - 61.2 - 74.5 - 76.6 - 87.7 - 87.9  175.8 241.8 228.1 226.0 214.5 214.3  192.9 241.1 247.0 237.5 232.4 234.8  43 0 0  46 47 48  245.6  II4.9 109.7 109.4  - 61.1 - 61.7 - 78.5  - 70.7 - 71.3 - 88.1  232.1 231.4 214.1  266.2 248 • 4 239.5  324.O 252.3  Figure  34  83  observation, but the e x t r a p o l a t i o n i s very s h o r t .  Furthermore,  an extensive region outside o f the zero contour was observed and was found not t o contain a measurable amount o f hydrogen. The major and minor axes o f the p r o j e c t i o n o f the nebula on the sky, as determined o p t i c a l l y , are drawn i n . The p o s i t i o n angle o f the major a x i s i s 3 8 ° from the north-south l i n e . A conspicuous f e a t u r e o f the hydrogen d i s t r i b u t i o n i s the presence o f two peaks near the centre o f the nebula. There i s a d e f i c i e n c y o f hydrogen at the centre i t s e l f , a f a c t discovered i n the Dutch survey.  However, the hydrogen  d i s t r i b u t i o n along the major a x i s determined from the cont o u r map and p l o t t e d i n f i g u r e 35 disagrees w i t h the c i t e d work i n p l a c i n g the minimum t o the north-east o f centre. The Dutch curve shows a more shallow minimum about 2 5 ' to the south-west o f centre.  I t i s d i f f i c u l t t o account f o r  t h i s discrepancy, as i t i s l a r g e r than the e r r o r s thought to be associated w i t h the two works.  I n defence o f the  present r e s u l t I t i s pointed out t h a t the contour l i n e s def i n i n g the peaks depend on areas c a l c u l a t e d from about 20 spectra.  On the other hand the Dutch spectra may contain  significant errors.  Some repeat observations made by them  d i f f e r e d by 20% from the o r i g i n a l measures, and they express concern l e s t systematic e r r o r s enter "with measurements so near the l i m i t s o f what i s f e a s i b l e . "  Therefore  the d i s t r i b u t i o n obtained here i s t e n t a t i v e l y accepted as substantially  correct.  40  Figure  35  The d i s t r i b u t i o n of atomic hydrogen along the major a x i s .  Another, but l e s s important, d i f f e r e n c e concerns the excess of r a d i a t i o n i n the north-east part of M31 at km/sec reported by the Dutch.  -224  A c a r e f u l examination of the  relevant spectra obtained i n t h i s survey f a i l e d to show such an excess.  Otherwise there i s general agreement between the  form of the spectra obtained near the major a x i s i n t h i s work and those observed by the Dutch.  A close comparison i s  d i f f i c u l t because none of the present spectra were taken prec i s e l y on the major a x i s .  The length of the radio nebula i s  s u b s t a n t i a l l y the same i n both cases, 5°15'  and 6°.  The  l a r g e r Dutch f i g u r e depends on the acceptance of r a t h e r unconvincing spectra at the ends of the major a x i s . iii)  The Minor Axis D i s t r i b u t i o n and the Aspect Ratio  The hydrogen d i s t r i b u t i o n along the minor a x i s of M31 i s shown i n f i g u r e 36. sided.  I t i s unexpectedly  narrow and  The h a l f - w i d t h of the d i s t r i b u t i o n i s 55  the antenna beamwidth by l e s s than 50%, width must be much l e s s than 55'>  T  steepand exceeds  Therefore the true  and can be estimated by  s e t t i n g up a s e r i e s of p l a u s i b l e model d i s t r i b u t i o n s and conv o l v i n g each w i t h the antenna p o l a r diagram.  Several models  were so convolved, and i t was found that a nearly square d i s t r i b u t i o n w i t h a t o t a l width of 40* y i e l d e d a close approximation to the curve of f i g u r e 36. l e n g t h of M31 i s 315 . T  Now the observed  The t r u e length w i l l be s l i g h t l y  l e s s because of instrumental e f f e c t s .  S u b t r a c t i n g one  Figure  36  The d i s t r i b u t i o n of atomic hydrogen along the minor a x i s .  85 antenna beamwidth, 36*» from the above f i g u r e leads to an estimated t r u e length of 279'.  Thus the r a t i o of the length  of the minor a x i s to that of the major i s r = 40/279 =  0.143  where r i s the radio aspect r a t i o .  But the o p t i c a l aspect  r a t i o , pi i s p = iv)  0.25.  The A x i a l Ratio  According to the f i r s t of the two above equations i n c l i n a t i o n of M31 value i s 14°5»  the  i s sin"^-r = 8°2, whereas the o p t i c a l  I t i s not necessary to conclude that the  plane of the d i s t r i b u t i o n of atomic hydrogen i n M31  is tilted  6°3 with respect to the s t a r s and hot gas, f o r an a l t e r n a t i v e explanation i s a v a i l a b l e . Two  assumptions are made:  First,  that the d i s c of atomic hydrogen i s very t h i n , so that the i n c l i n a t i o n derived from the c a l c u l a t e d value of r i s the t r u e one.  This i s a very reasonable  assumption, as the  " f l a t " o p t i c a l component of M31 i s estimated to have a true a x i a l r a t i o (thickness to diameter) of 0.042 (de Vaucouleurs, 1958).  I n our own galaxy the atomic hydrogen i s known to  e x i s t i n an even t h i n n e r l a y e r (Oort, Kerr, and Westerhout, 1958).  Second, the o p t i c a l l y e m i t t i n g mass of M31  i s as-  sumed to have a spheroidal d i s t r i b u t i o n , or, at l e a s t , a spheroidal envelope.  This i s a commonly made assumption  86 (Burbidge et a l , 1959; Schmidt, 1957) and i m p l i e s only that the galaxy, i f seen at 0° i n c l i n a t i o n would appear as an e l l i p s e i n the Z-X plane, as shown i n f i g u r e 37, instead of as a s t r a i g h t l i n e . In the f i g u r e , 0E i s the l i n e of sight t o the observer and i i s the i n c l i n a t i o n . t i o n o f the galaxy.  The Z-axis i s the a x i s o f r o t a -  The thickness o f the galaxy i s b and  the length (or diameter) i s taken, without l o s s of g e n e r a l i t y , to be u n i t y .  Then the apparent radio and o p t i c a l widths  are represented by r and p as b e f o r e .  I t i s e a s i l y shown  that  I n s e r t i n g the values o f r and p given above we get b = 0.207 . This value o f b means that the o p t i c a l nebula has a thickness equal to about 1/5 of i t s diameter.  Thus the  l e n g t h o f the apparent minor a x i s o f the o p t i c a l image r e f l e c t s the t h i c k n e s s of the galaxy as much as i t does the departure of the i n c l i n a t i o n from 0°. Wyse and Mayall (1942) reported a mean value o f 0.08 f o r the a x i a l r a t i o o f Sb type s p i r a l s seen on edge, but t h i s e a r l y work was based on the observation o f only 5 galaxies.  Determining the' type of edge-on g a l a x i e s i s also  Figure  37  I n c l i n a t i o n and the a x i a l  ratio.  very d i f f i c u l t .  On the other hand, Schmidt (1957) c a l c u l a t e s  an a x i a l r a t i o of 0.24 f o r M31 on the b a s i s of Baade's e s t i mate of i f o r the s p i r a l arms (12?3)» and Redman and S h i r l e y ^ f i g u r e f o r the whole nebula (19?25).  Although he  o f f e r s no c r i t i c i s m of e i t h e r value of i , he r e j e c t s the implied a x i a l r a t i o as "improbable."  Burbidge (1959) adopts  0.20 f o r the a x i a l r a t i o of NGC 1068, an Sb s p i r a l galaxy. There would seem to be no b a s i s f o r the a p r i o r i r e j e c t i o n of the a x i a l r a t i o computed here. I t i s not easy to determine the accuracy of the radio value of i , f o r the d i s t r i b u t i o n of atomic hydrogen i n M31 i s not c i r c u l a r l y symmetric.  I n f a c t , the widest part of  the contour map of f i g u r e 34 i s not along the minor a x i s , but at a place considerably removed from i t .  Thus the pre-  c i s e s i g n i f i c a n c e of the radio aspect r a t i o r i s not c e r t a i n . Nevertheless, there seems to be good reason t o b e l i e v e that M31 i s considerably t h i c k e r and l e s s i n c l i n e d than so f a r thought, and that i t might be worthwhile to re-examine the o p t i c a l data i n l i g h t of these r e s u l t s . v)  The P o s i t i o n Angle Another f e a t u r e o f the radio nebula that i s v i s i b l e on  the area contour map i s the f a i l u r e of the long axis of the d i s t r i b u t i o n to coincide w i t h that of the o p t i c a l galaxy. This discrepancy i s conspicuous at the south-west end of the hydrogen map, and i s also present t o a s m a l l e r degree at the  88 north-est end. A l i n e drawn through the " i s l a n d s " o f high hydrogen content l i k e w i s e d i s p l a y s a major a x i s p o s i t i o n angle that i s s m a l l e r than the o p t i c a l . A complementary c r i t e r i o n o f p o s i t i o n angle i s the d i r e c t i o n o f the minor a x i s , which can be i n f e r r e d from the contour l i n e s o f low speed on the v e l o c i t y maps. have been prepared.  Two maps  F o r the f i r s t , the mean v e l o c i t y w i t h  respect to the centre o f M31, V  c  i n Table 1, has been graphed  against both co-ordinates, as was done f o r areas.  Then a  contour map o f constant v e l o c i t y l i n e s has been drawn on the b a s i s o f readings from the graphs.  Figure 38 shows the mean  v e l o c i t y contours and f i g u r e 39 the contours o f constant peak v e l o c i t y , V  p  from Table 1.  The low speed contours  again suggest a p o s i t i o n angle s m a l l e r than the o p t i c a l value.  The high speed patches at the e x t r e m i t i e s o f both  v e l o c i t y maps can be joined to e s t a b l i s h the d i r e c t i o n o f the major axis i n another way. F i n a l l y , the l a r g e areas on both sides o f centre that have a speed greater than 210 km/sec can be used to estimate the p o s i t i o n angle, 0, o f the a x i s . None o f these i n d i c a t i o n s that the radio a x i s i s d i s placed from the o p t i c a l i s by i t s e l f overwhelmingly convinc i n g , but taken together, the s e v e r a l pieces o f evidence are  impressive. T h e i r c o l l e c t i v e strength l i e s p a r t l y i n  the f a c t that there i s agreement that the angle o f the  Figure 38  Figure 39  8  9  radio a x i s i s l e s s than 3 8 ° , (the accepted o p t i c a l value) and p a r t l y i n the v a r i e t y and independence o f the measures t h a t u n d e r l i e them.  Each c r i t e r i o n that has been c i t e d de-  pends on measures o f many s p e c t r a . Both area and v e l o c i t y measurements are i n v o l v e d . Spectra from a l l p a r t s o f the nebula are u t i l i z e d .  Table 2 l i s t s the r e s u l t s o f 16 deter-  minations o f the tangent o f the p o s i t i o n angle.  Each e s t i -  mate was obtained by f i t t i n g a s t r a i g h t l i n e "by eye" to the relevant f e a t u r e o f one of the maps, and measuring the tangent o f i t s p o s i t i o n angle.  The mean value o f the tangents  leads to an angle o f 31°2 ± 0 ? 8 mean e r r o r .  The d i f f e r e n c e  from the accepted value i s 6?8. However, i t i s probable that the d i f f e r e n c e between the two axes i s overestimated by t h i s not e n t i r e l y o b j e c t i v e technique o f u t i l i z i n g a l l features favorable to the hypothe s i s at hand.  Therefore, as a rough estimate o f the d i f f e r -  ence between the p o s i t i o n angles o f the radio and o p t i c a l nebulae, a f i g u r e o f 5° ± 2° i s adopted.  E q u i v a l e n t l y , the  d i r e c t i o n o f the major a x i s o f the radio nebula i s 33° ± 2°. That M31 has two p o s i t i o n angles, one o p t i c a l and one r a d i o , i s no more t o be accepted than the hypothesis that i t has two i n c l i n a t i o n s .  I n e i t h e r case the i m p l i c a t i o n  would be that two i n t e r s e c t i n g d i s c s o f m a t e r i a l c o e x i s t i n one galaxy, yet somehow maintain t h e i r i n t e g r i t y i n the face of g r a v i t a t i o n a l i n t e r a c t i o n s between them.  I t Is  more reasonable t o suppose that one o r both o f the measures  THE POSITION ANGLE OF M31 Tan 0  Method Area Contours SW NE Peak regions  0.67 .62 .72  Mean V e l o c i t y Contours Extremities -80 km/sec l i n e -40 km/sec l i n e 0 km/sec l i n e 40 km/sec l i n e 80 km/sec l i n e  .61 .56 .60 .63 .52 .62  Peak V e l o c i t y Contours Extremities 230 km/sec i s l a n d s -80 km/sec l i n e -40 km/sec l i n e 0 km/sec l i n e 40 km/sec l i n e 80 km/sec l i n e  .55 .63 .67 .59 .60 .63 .49  Average Tan 6 = 0.607 ±0.011 0 = 31°2 ±0°9  TABLE  2  90  of the p o s i t i o n angle are i n a c c u r a t e , and that the d i s t r i b u t i o n of atomic hydrogen i s coplanar with t h a t of the s t a r s . I t seems p o s s i b l e that the question of the p o s i t i o n angle of M31> l i k e that of the i n c l i n a t i o n , i s connected with the interpretation  of the o p t i c a l image.  I f M31 i s as t h i c k as  suggested here, the o p t i c a l estimate of the p o s i t i o n  angle  could e a s i l y be s h i f t e d 5° by f a i l u r e to recognize that c e r t a i n areas of e m i t t i n g m a t e r i a l may be f a r from the plane of r o t a t i o n . vi)  The L o c a t i o n of the H I I Regions  The Dutch survey, as already s t a t e d , showed very poor agreement between the o p t i c a l v e l o c i t i e s of H I I regions observed by Mayall and the v e l o c i t i e s r o t a t i o n curve.  defined by the radio  Some of the o p t i c a l p o i n t s l a y more than  100 km/sec o f f the radio curve, and i n t e r n a l  disagreements  amongst the o p t i c a l data ranged up to 165 km/sec.  The  r e s p o n s i b i l i t y f o r t h i s s i t u a t i o n would seem to l i e w i t h the Dutch authors, who have reduced M a y a l l s v e l o c i t i e s to T  the major a x i s by a c o r r e c t i o n formula that t a c i t l y assumes that M31 i s f l a t , or at l e a s t t h a t Mayall*s p o i n t s of obs e r v a t i o n were a l l i n the plane of the nebula.  I f , as  now  seems l i k e l y , many of the H I I regions observed by Mayall were some distance from the plane, the disagreement can be understood.  In f a c t , the radio and o p t i c a l v e l o c i t i e s can  be r e c o n c i l e d by s h i f t i n g the H I I regions o f f the plane  91 by q u i t e moderate amounts.  In the most discordant case shown  i n f i g u r e 12 of the Dutch paper the required s h i f t w i l l be 0 . 0 5 to 0 . 0 6 of a g a l a c t i c r a d i u s .  In the average case, l e s s  than h a l f of t h i s displacement w i l l  suffice.  An opportunity now a r i s e s f o r the i n v e s t i g a t i o n of M31 as a t h i c k galaxy.  F i r s t , the values of i n c l i n a t i o n and  p o s i t i o n angle from the radio survey are accepted.  Then  the r o t a t i o n law, based on observation of atomic hydrogen, i s adopted f o r the plane.  F i n a l l y , o p t i c a l observations of  r a d i a l v e l o c i t y are f o r c e d i n t o concordance with the radio data by i n c l u s i o n of a t h i c k n e s s , or Z-axis term i n the v e l o c i t y reduction formula.  In t h i s way a l l three c o - o r d i -  nates are obtainable f o r H I I regions, novae, and other objects b r i g h t enough to y i e l d o p t i c a l v e l o c i t i e s .  These  p o s s i b i l i t i e s are being i n v e s t i g a t e d f u r t h e r . vii)  The R o t a t i o n Law  An e m p i r i c a l r o t a t i o n curve f o r the atomic hydrogen i n M31 has been prepared from the mean v e l o c i t y contour map t a k i n g readings along the o p t i c a l major a x i s .  by  This curve,  shown i n f i g u r e 4 0 , bears a close resemblance to the r o t a t i o n curve published i n the Dutch paper.  A d e t a i l e d compar-  i s o n of the two curves i s not f e a s i b l e , as the former represents a convolution of the antenna p a t t e r n over the mass and v e l o c i t y d i s t r i b u t i o n s , whereas the l a t t e r i s the r e s u l t of an attempt to unfold the convolved raw data.  However,  E m p i r i c a l r o t a t i o n curve  92 there should be c l o s e agreement concerning the v e l o c i t y i n the outer parts of M 3 1 , f o r , as can be seen on the v e l o c i t y map,  there are l a r g e regions of n e a r l y uniform motion where  beamwidth smear should have l i t t l e e f f e c t on the observed velocity.  In f a c t , the two r o t a t i o n curves i n t e r s e c t i n the  centres of the regions of uniform v e l o c i t y .  I t i s concluded  that the Dutch r o t a t i o n law and mass, d i s t r i b u t i o n f o r M31 are accurate and can be Improved upon only by observation of the nebula w i t h a l a r g e r telescope and reduction of the data on the b a s i s of a more complex model.  A few such measure-  ments have been made w i t h a 92m d i s h (Burke, Turner,  and  Tuve, 1 9 6 3 ) , and c o r r e c t i o n s to the r o t a t i o n curve are suggested. viii)  Fine S t r u c t u r e of the Hydrogen D i s t r i b u t i o n  Many of the s p e c t r a obtained i n t h i s survey show cons i d e r a b l e complexity.  Some have two peaks, others have  t h r e e , and i n a few cases i t would appear that the s p e c t r a l r e s o l u t i o n o f 35 km/sec i s i n s u f f i c i e n t to separate the many components that are present.  Consider a multiple-peaked  spectrum such as that l o c a t e d at R.A.  = 39 > Dec. = 40°30* m  i n f i g u r e 33 and reproduced on a l a r g e r s c a l e i n f i g u r e 41a. The peak v e l o c i t i e s are -241, -138, and -69 km/sec.  At  l e a s t two explanations can be o f f e r e d to account f o r t h i s s p l i t t i n g of the s p e c t r a l p r o f i l e .  One i s that the hydrogen  mass i s smoothly d i s t r i b u t e d throughout the region sensed  5 -  0)  k.  o  w0)  Q- o _  E *  I " 0 -350  -300  -250 V  -200 -150 km/sec  c  -100  -50  0  160  120  b  o  £ 80  a |40  CO  t-  0  -160  1  -120  I  1—  1  i  I  -60 Velocity  -i  0  Figure  1  1  1  60 km/sec  1  1  r s . i  120  41  Complex speotra i n M31 and the Galaxy.  i  i,  180  93 by the antenna beam, but that the hydrogen v e l o c i t y i s m u l t i valued i n that area.  But to suppose that three broad clouds  of gas, with v e l o c i t i e s d i f f e r i n g by 172 km/sec, can coexist at o r near one point i s to abandon the g a l a c t i c motions to chaos.  Instead, i t i s suggested that i t i s the density of  the hydrogen that i s multivalued, and that the v e l o c i t y f u n c t i o n i s smooth across the antenna beam.  Thus the r e l a -  t i v e weakness of the s p e c t r a l energy observed at c e r t a i n v e l o c i t i e s i m p l i e s only that the gas density i n that part of the beam where those v e l o c i t i e s are expected i s lower than normal.  I n other words, the hydrogen density o s c i l l a t e s  sharply with p o s i t i o n throughout the d i s c of the nebula. These abrupt f l u c t u a t i o n s are not d i s c e r n i b l e on the hydrogen contour map ( f i g u r e 34) because they are too rapid to be resolved by the antenna beam.  The rate of change of r a d i a l  v e l o c i t y along the major a x i s of M31 can reach a value of 14 km/sec/minute of arc.  Even higher values o f the v e l o c i t y  gradient are p o s s i b l e o f f the major a x i s because of the foreshortening e f f e c t of the i n c l i n a t i o n of the galaxy. Hence the s p e c t r a l r e s o l u t i o n o f 35 km/sec corresponds to an angular r e s o l u t i o n o f about 3 % one-twelfth o f a beamwidth. Unfortunately, i t i s not p o s s i b l e to u t i l i z e t h i s "spectro-geometric"  r e s o l u t i o n to solve uniquely f o r the  mass d i s t r i b u t i o n , because the g a l a c t i c d i s c i s two-dimens i o n a l and a given v e l o c i t y i s expected along a l i n e .  The  l i n e can be i d e n t i f i e d , but not the p o s i t i o n on i t — a t l e a s t  94 not more c l o s e l y than permitted by the antenna beamwidth. Nevertheless* the shapes of the spectra are a source of i n formation, and may suggest ideas to those who are f a m i l i a r with the o p t i c a l features of M31.  An obvious  interpretation  i s that the observed peaks correspond to concentrations of atomic hydrogen i n s p i r a l arms i n t h i s e x t e r n a l galaxy, as such peaks do i n spectra taken of the hydrogen emissions i n our own  galaxy.  This i n t e r p r e t a t i o n i s supported by the spectrum shown i n f i g u r e 41b.  This spectrum i s the sum of two spectra taken  from the catalogue of M u l l e r and Westerhout (1957)> and  has  been composed to simulate an e x t e r n a l observation of part of our own galaxy.  For t h i s purpose two s p e c t r a representing  observations of the M i l k y Way were chosen.  on opposite sides of the sun  Thus the composite spectrum simulates an ex-  t e r n a l observation of the atomic hydrogen along a narrow s t r i p through the plane of our galaxy.  I t i s seen that the  v e l o c i t y spread of the three peaks i s s i m i l a r to that i n the spectrum of M31  i n f i g u r e 41a.  The s p e c t r a l r e s o l u t i o n  and peak temperature are v a s t l y d i f f e r e n t i n the two  cases,  but t h i s Is to be expected, i n view of the enormous s i z e of the antenna beam at the distance of  M31.  Here the p r o f i l e shapes are e x p l o i t e d only through ures 39 and 42.  The f i r s t , already c i t e d , i s a contour  of the peak v e l o c i t i e s .  figmap  (The v e l o c i t y of the highest peak  Peak v e l o c i t i e s along the major a x i s .  95 was taken from each spectrum.)  I t d i f f e r s i n conspicuous  ways from the mean v e l o c i t y map.. Most s t r i k i n g are the d i s c o n t i n u i t i e s to be seen 0?5 t o the north-east and 0°6 to the south-west o f the centre.  The second f i g u r e , i n which peak  v e l o c i t i e s along the major a x i s , as read from the map, are p l o t t e d against distance from the centre, i s not to be r e garded as a r o t a t i o n curve.  I t merely i l l u s t r a t e s the main  features o f the contour map i n an a l t e r n a t i v e way. The d i s c o n t i n u i t i e s (which have been smoothed f o r convenience i n p l o t t i n g the contour map) are taken to s i g n i f y minima i n hydrogen d e n s i t y at the i n d i c a t e d v e l o c i t y (160 km/sec) and p o s i t i o n s (0°5 and 0°6 from the minor a x i s ) .  These two  s p e c i f i c a t i o n s i n t e r s e c t at f o u r p o i n t s , i n p a i r s , about ±10  1  and ±11* r e s p e c t i v e l y from the major a x i s .  But t h i s  method of determining p o s i t i o n s by the i n t e r s e c t i o n o f the antenna beam with the expected two-dimensional v e l o c i t y contours i n the d i s c of the galaxy would require e l a b o r a t i o n to be u s e f u l , and probably would not be worth the e f f o r t . ix)  The V e l o c i t y o f the Centre o f G r a v i t y  The r a d i a l v e l o c i t y o f the centre o f g r a v i t y o f M31 has been determined by o p t i c a l observations at the L i c k and Mt. Wilson observatories (Humason, M a y a l l , and Sandage, 1956) and the mean v e l o c i t y , reduced to the l o c a l standard of r e s t by van de H u l s t , i s -274 km/sec.  The mean value  obtained by the Dutch group at Dwingeloo from the radio observations along the major a x i s i s -296 km/sec.  96 The discordance i s not l a r g e , and the exact value i s perhaps not of great s i g n i f i c a n c e , so there i s l i t t l e need f o r a more accurate value than the second one quoted above. Nevertheless i t was decided to compute the v e l o c i t y using the  e n t i r e set of data obtained with the i n t e r f e r e n c e spec-  trometer.  Each of the 143 mean v e l o c i t i e s was weighted i n  p r o p o r t i o n to the area of i t s corresponding spectrum, and a weighted mean was c a l c u l a t e d .  This method a p p l i e s the def-  i n i t i o n of c e n t r e - o f - g r a v i t y v e l o c i t y and involves no assumpt i o n s about the d i s t r i b u t i o n of the hydrogen, or the nature of the r o t a t i o n .  I t would be i n t e r e s t i n g i f the r e s u l t  d i f f e r e d from the major a x i s value determined at Dwingeloo. However, the new v e l o c i t y d i f f e r s so l i t t l e that perhaps i t s only value i s t o emphasize the p r e c i s i o n with which i t i s o f t e n p o s s i b l e to measure r a d i a l v e l o c i t i e s at radio wavelengths.  A probable e r r o r was c a l c u l a t e d from the noise  temperature of the spectrometer.  The r e s u l t has been round-  ed upward, doubled, and quoted i n Table 3> which l i s t s the f o u r determinations mentioned x)  above.  Radial Motions In the d i s c u s s i o n of the i n c l i n a t i o n of M31 i n e ( i i i )  i t was t a c i t l y assumed that a l l motions were c i r c u l a r . However, there i s some reason to b e l i e v e that r a d i a l components occur t o o .  That such i s the case i n the Galaxy was  e s t a b l i s h e d by Rougoor and Oort (I960), who observed an outward f l o w of 53 km/sec i n the gas at 3 kpc from the  THE RADIAL VELOCITY OF M31  Source  Velocity (km/sec)  Probable error (km/sec)  Mt. Wilson  -262  20  Lick  -286  30  Dwingeloo  -296  3  Penticton  -295.6  0.4  TABLE  3  centre*  Kerr (1962) made a d e t a i l e d comparison between the  Leiden and Sydney 21-cm  surveys of the two halves of the  Galaxy and found an asymmetry i n the s p i r a l patterns that could be removed by p o s t u l a t i n g an outward f l o w of gas at a v e l o c i t y depending on the i n v e r s e square of the distance from the centre of the Galaxy.  His law f i t t e d the v e l o c i t y  to the f i g u r e of Rougoor and Oort (I960) near the centre and gave a v e l o c i t y of 7 km/sec f o r the region of the Sun. Subsequently i t was found by Locke, G a i t , and Costain (1964) that the Sun i s moving outward at 2.8 km/sec w i t h respect to the gas i n the a n t i c e n t r e region, i n agreement with Kerr»s model.  R a d i a l motions i n external g a l a x i e s are  o f t e n detected o p t i c a l l y (Burbidge, Burbidge, and Prendergast, 1959)> but u s u a l l y only the nuclear region i s b r i g h t enough to be observed. I f departures from c i r c u l a r motions e x i s t i n M31 they should be most e a s i l y detected along the minor a x i s , where the hypothesis of c i r c u l a r motion would p r e d i c t zero r a d i a l velocities.  Thus the exact l o c a t i o n of the minor a x i s be-  comes a matter of importance, and i t i s e s s e n t i a l to have an estimate of i t s p o s i t i o n that does not depend on the hypothesis of p e r f e c t l y c i r c u l a r motions.  Accordingly, the  f i g u r e s i n Table 2 were d i v i d e d i n t o two c l a s s e s , those depending on the p o s i t i o n of the major a x i s , and those der i v e d from the slope of the contours of low v e l o c i t y .  From  the former, the p o s i t i o n angle of the major a x i s i s 32°20 , T  9$ whereas the angle complementary v e l o c i t y contours i s 30°35 « f  t o the average slope of the  In other words, the v e l o c i t y  contours are i n c l i n e d to the minor axis by the d i f f e r e n c e between these two angles:  1°45 . T  Assuming, f o r the moment,  that t h i s d i f f e r e n c e i s s i g n i f i c a n t , i t can be deduced that there i s a r a d i a l motion, i n c r e a s i n g with r a d i u s , that reaches about 4 km/sec at the periphery of M31.  Burke,  Turner, and. Tuve (1963) place an upper l i m i t of 2 km/sec on r a d i a l motion i n M31, but t h i s f i g u r e p e r t a i n s to a point only 10 from the centre. f  I f the motion considered here i s  r e a l , and i f the south-following side of M31 i s the nearer, an outflow of gas i s o c c u r r i n g .  More observations w i l l be  required t o e s t a b l i s h the existence of r a d i a l motion. xi)  Other Galaxies i n the Observing F i e l d  The region of the sky that was observed i n t h i s survey of M3'l also includes two other nearby g a l a x i e s .  They are  M32 (NGC 221) and NGC 205, the conspicuous companions to M31 i n the photograph ( f r o n t i s p i e c e ) .  M32 i s the c i r c u l a r  object at the lower l e f t edge of M31j NGC 205 i s the l a r g e r , but f a i n t e r , image above M31. Neither galaxy i s expected t o emit s t r o n g l y at 21 cm because they are both e l l i p t i c a l and are therefore r e l a t i v e l y devoid of i n t e r s t e l l a r gas.  I t i s nevertheless of i n -  t e r e s t to determine upper l i m i t s to the atomic hydrogen content of both of these g a l a x i e s — o f M32 because i t i s the  99  b r i g h t e s t of a l l the e l l i p t i c a l s j  and o f NGC 205 because i t  i s a p e c u l i a r e l l i p t i c a l , containing dust, and therefore probably also gas. Accordingly, spectra taken i n the v i c i n i t i e s o f the two g a l a x i e s were examined f o r emission at the appropriately Doppler-shifted frequencies. e i t h e r galaxy was found.  No emission a t t r i b u t a b l e to  I n the case of M32 the temperature  at -210 km/sec, the v e l o c i t y o f the galaxy i n the l o c a l standard o f r e s t , was 0.0°K.  A safe estimate of the upper  l i m i t t o the antenna temperature that could go undetected i n the spectrum would be about 0.3°K.  This r e s u l t i s con-  s i s t e n t with that o f Davies, Gottesman, Reddish, and Verschuur (1963) who surveyed several g a l a x i e s f o r atomic hydrogen with the 75 m paraboloid at J o d r e l l Bank.  They  found an upper l i m i t of 0.3°K brightness temperature f o r M32. The search f o r atomic hydrogen i n NGC 205 i s made d i f f i c u l t by the presence of r a d i a t i o n from M31 at -234 km/sec, the v e l o c i t y o f the smaller galaxy.  The b r i g h t -  ness temperature o f M31 at the p o s i t i o n and v e l o c i t y of NGC 205 i s about 1.2°K and consequently i t i s not p o s s i b l e to deduce a u s e f u l upper l i m i t t o the c o n t r i b u t i o n from the  e l l i p t i c a l galaxy.  100  VI a)  CONCLUSIONS  The I n t e r f e r e n c e Spectrometer The i n t e r f e r e n c e spectrometer performs i n accordance  w i t h the theory presented i n S e c t i o n I I .  The noise l e v e l  i s near the t h e o r e t i c a l l i m i t , and s t a b i l i t y * except f o r b a s e - l i n e d r i f t , i s good.  The compensation procedure de-  s c r i b e d i n S e c t i o n I l h appears to be v a l i d , although not exact.  I n view o f the l a r g e departures from the i d e a l o f  some equipment parameters, p a r t i c u l a r l y those of the delay l i n e , i t i s g r a t i f y i n g that such high accuracy was achieved. Although there are some disadvantages t o the i n t e r f e r ence method i t seems probable t h a t these could be overcome by f u r t h e r development o f the equipment, and by m o d i f i c a t i o n of the observational technique.  F o r example, a b e t t e r  delay l i n e i s c e r t a i n l y p o s s i b l e , and i t s use would  improve  the o v e r a l l accuracy by l i g h t e n i n g the burden on the compensation procedure.  A considerable r e d u c t i o n i n computing  time could be achieved by making prolonged observations, instead o f repeating s h o r t e r ones as was done i n the p r o j ect reported here. The p r a c t i c a l employment of the spectrometer has thrown some l i g h t on the questions o f bandwidth and r e s o l u t i o n required f o r e x t r a g a l a c t i c s t u d i e s .  I t i s evident  that i t would be worthwhile to employ 100 channels to d e f i n e  101 a bandwidth of 4 Mc. with a r e s o l u t i o n of 40 kc.  Even  sharper r e s o l u t i o n would no doubt be an advantage i n a spectrometer used w i t h a l a r g e r t e l e s c o p e . b)  The Andromeda Nebula Observation of the atomic hydrogen i n M31 w i t h the  i n t e r f e r e n c e spectrometer has confirmed and extended the work of van de H u l s t , Raimond, and van Woerden.  The minor  a x i s of the nebula i s found to be unexpectedly s h o r t , and i f the d i s t r i b u t i o n of atomic hydrogen i s c i r c u l a r , or nearly so, t h i s r e s u l t leads to a r e v i s i o n of the i n c l i n a t i o n to about 8°, compared to the o p t i c a l value of 14°. A f u r t h e r consequence of t h i s s h i f t would be to increase the t r u e a x i a l r a t i o of M31 to 0.2.  I f an a x i a l r a t i o  t h i s l a r g e can be confirmed i t would f a c i l i t a t e the task of r e c o n c i l i n g the c u r r e n t l y divergent H I I v e l o c i t i e s with those of H I . The p o s i t i o n angle of M31 i s d e f i n i t e l y l e s s than 3 8 . 0  An accurate value i s s t i l l not a v a i l a b l e , but the present evidence from the observation of the atomic hydrogen would f a v o r a p o s i t i o n angle of 33° '±2°. Some evidence of the concentration of atomic hydrogen i n c e r t a i n regions, probably s p i r a l arms, i s seen i n the multi-peaked spectra obtained i n v a r i o u s p a r t s of M31. R a d i a l motions of about 4 km/sec may occur i n the outer  102 p a r t s of the nebula, but the evidence f o r them i s only marginally significant. The c e n t r e - o f - g r a v i t y v e l o c i t y of M31 would seem to be very w e l l e s t a b l i s h e d at -295.6 ±0.4 km/sec.  This r e s u l t  does not depend on any hypothesis concerning the i n t e r n a l motions i n M31*  as a l l the atomic hydrogen was  observed.  I t i s evident t h a t many s e c r e t s of g a l a c t i c s t r u c t u r e and dynamics remain hidden i n t h i s great s p i r a l , which should r i c h l y repay f u r t h e r study by a l a r g e r r a d i o t e l e scope and a spectrometer of increased r e s o l u t i o n .  103  APPENDIX a)  The Radio Telescope o f the D.R.A.O. The radio telescope i s located i n an uninhabited  v a l l e y about 20 km south of P e n t i c t o n , B r i t i s h Columbia.  The area i s s u b s t a n t i a l l y f r e e o f e l e c t r i c a l i n -  terference i n the VHF and UHF regions of the radio spectrum. The 25 m paraboloid has a f o c a l length of 7*4 Thus the f o c a l r a t i o i s 0.3.  m.  The r e f l e c t i n g surface of  expanded aluminum mesh i s p a r a b o l o i d a l to w i t h i n 1 cm. The d i s h i s e q u a t o r i a l l y mounted on a s t e e l tower which has been coated w i t h h i g h - r e f l e c t i v i t y paint to prevent l o s s of alignment by d i f f e r e n t i a l s o l a r heating.  The  tower i s b o l t e d t o a massive r e i n f o r c e d concrete foundation. The d i s h i s fed by a stepped-waveguide horn, which i s f l a r e d i n the E-plane to improve the c i r c u l a r i t y of the antenna beam.  The s i g n a l from the horn i s passed through  a Dicke switch to an electron-beam parametric a m p l i f i e r of the Adler type.  Although the noise temperature of an  Adler tube i s f a r higher than t h a t of a maser, there are many considerations that make the Adler tube an a t t r a c t i v e device f o r use i n radio astronomy.  Chief amongst  104  these are the a b i l i t y of the A d l e r tube to operate at normal temperatures, i t s low c o s t , l i g h t weight, and ready availability.  The tube i s capable of p r o v i d i n g 23 db gain  at the hydrogen frequency, and t h i s gain can be made h i g h l y stable. (80  F i n a l l y , the Adler tube i s a broad-band a m p l i f i e r  Mc.) The output from the Adler tube i s converted to 35  and a m p l i f i e d i n a r e c e i v e r of conventional design. f e a t u r e of the r e c e i v e r i s of i n t e r e s t — t h e keyed g a i n c o n t r o l system.  Mc. One  automatic  This system derives a c o n t r o l voltage  from the r e c e i v e r output during the h a l f c y c l e that the comparison load i s connected to the r e c e i v e r i n p u t .  A suit-  able time constant i n the c o n t r o l c i r c u i t holds the r e c e i v e r g a i n constant during the other h a l f c y c l e .  Thus the r e -  c e i v e r gain i s independent of the magnitude of the antenna signal. b)  The Computer Programs Most of the data processing associated w i t h the use  o f the i n t e r f e r e n c e spectrometer was done on an IBM d i g i t a l computer.  1620  The computer was programmed i n F o r t r a n  2, an improved " f o r m u l a - t r a n s l a t i o n " language.  The s i x  most important programs used w i t h the i n t e r f e r e n c e spectrometer are given below.  1C5  1)  F o u r i e r A n a l y s i s o f the Response Functions The a n a l y s i s of the response f u n c t i o n s of the spectro-  meter was made by means o f the program shown i n f i g u r e 43 • The response f u n c t i o n s C n , obtained by the t e s t m  procedure  o u t l i n e d i n S e c t i o n IV(d) are read i n t o the computer under the name RESP. FC.  The F o u r i e r c o e f f i c i e n t s , a ^ ^ , are c a l l e d  The response o f the spectrometer t o an input of noise  only was measured four times.  These responses are c a l l e d  DUMMYS. The set A i s a t a b l e o f cosines manufactured by the computer. 2)  Output o f the program i s a l i s t o f FC (the a ^ ) « n  I n v e r s i o n o f the A M a t r i x This program u t i l i z e s the output o f the previous pro-  gram, FC, which i s read i n as FCA.  The FCA matrix i s aug-  mented by a u n i t matrix on i t s r i g h t hand s i d e .  After  i n v e r s i o n , the r i g h t hand s i d e becomes b ,k» and i s read n  out as FCA. 3)  C a l c u l a t i o n o f the Inverted Response Functions The b ^ matrix from program 2 i s read i n as FCI, n  along w i t h the hamming f u n c t i o n , HAMM. The hammed i n v e r t e d  t  response f u n c t i o n s , Fn,m are read out as RESPI. 4) The Instrument Functions The instrument f u n c t i o n s are c a l c u l a t e d from the r e sponse f u n c t i o n s Cn,m» formerly c a l l e d RESP.  Here the C*s  ID NUMBER - 2 1 c o P R I N T E D FOk E . ARGYLF  ON  S E P . 2b  AT  10 HR,  47.U  MIN,  FOkTRAN~ 2 C O M P I L E . C POUR IE k A N A L Y S I S OF RESPONSE F U N C T I O N S DIMENSION DUMMYS(2G,4) ,DUMMY(2C) , k F S P ( 2 C , 5 0 ) , F C ( 2 C , 2 C ) ,A( ICC) 6 READ 1 ,RESP,DUMMYS 1 FORMAT( IUX , 2 G F 3 . 5 ) C L E T UUMM Y = AV ER AG E OF THE DUMMYS DO fa J = 1,20 DUMMY! J ) - . 0 DO  V 8 C 5 C  lb C  lb 7 2 17 5 U  VAK=1,4  DUMMY (J J-DUMMY(J) +DUMMYS(J , K ) DUMM Y( J ) «=. 2b *DUMMY ( J ) PUNCH b MAKE HEADINGS F O R M A T { / 5 Z X f I b h h O U R I F R A N A L Y S I S / / 5 b X , V H C U M P O N E N T / 1 3X,1 H i b X • 1H26X , t 1H3bX » lH4bX , I H b b X , I H O b X , 1 H 7 b X , 1 H b o X , 1 h V b X , 2H10/3X ,2HC H) MAKE C O S I N E T A B L E DO l b M"= I , 1 GO B-M A(M)=LOS(.Cb2b3*B) DO F O U k l E R A N A L Y S I S DO 6 1=1,20 DO 17 K * 1 , 2 C FC ( I »K ) * .0 M-C DO 2 J - l , b C M«=M + K IF (M-1C0 17 ,7 , l b M»=M-10C CONTINUE F C ( I , K ) « = F C ( I , K ) + ( R F S P ( I , J ) -DUMMY (I ) ) * A ( M ) F C ( I , K ) « . C b * F C ( I ,K ) PUNCH 4, I, ( F C ( I ,K) ,K= I ,20) FORMAT { I b , b X , 10F7 , 4 / l O X , 1 0 P 7 . i i ) GO  TO b  END  Figure 43. Fourier a n a l y s i s of response f u n c t i o n s .  ID NUMBER P R I N T E D FUR  2103 E . ARGYLE  ON  i>EP. 2b  FORTRAN 2 C O M P I L E . C GE NF RATE UNIT MATRIX DIMENSIUN FCA(20,40) 2b READ 1 b, ( < FC A( I , K ) ,K= 1 , 20 ) , I = I ,20 ) 1 FORMAT ( 1CX, 1CF7 1QX , I 0 h 7 . U ) DO 11 I - 1 t 20 DO 12 K = 21 ,U0 IF ( 2C + I -K ) )5, 14 , IIS 13 FCA( I, K) - .0 GO TO 12 14 FCAl I, K) - I . 12 CONTINUE 1l CONT INUE C INVERT MATRIX DO  22  2b 24 25 2 1 27 26  21  1=1,20  RAT 1 0 = 1 . / F C A ( 1 , 1 ) NF=20+ I IP-I +1 DO 22 K=IP,NF FCA( I , K ) = F C A ( I ,K ) *RAT I 0 DO 25 K= I ,20 IF ( I - K ) 2 b ,25,2b RATI 0 = F C A I K , I) DO 2 4 L = I P , N F F C A ( K , L ) = F C A ( K , L ) - F C A ( I ,L ) *RAT 1 0 CONTINUE CONTINUE DO 2 7 k = l , 2 G PUNCH 20 , K , ( F C A l K,L) ,L = 2 1 , 4 0 ) FORMAT ( I b , S x , 10H7 .4/1CX , 1 C E 7 . 4 ) GO TO 2b END  Figure 44. I n v e r s i o n of the A matrix.  A'l 12  HR.  l b . 3 MIN.  C  CALCULATION  INVFRTFD  RFSPONSF  niwpNSTON  F C I { ? n ? 0 ) .RFSPT(5 0).a  OI^FNSTO^  0HAMM(?0)  PFAO 100  9  t  RFAD 110  HAMMFD.  n^°)  HA>W(?G)  100  100 110  FORMAT(5OH? PUNCH RFAD  110 120  FOOMAT(?0H? PUNCH RFAD  40»HAMM  FORMATt14X.?0F3.^)  39  READ  31  FORMAT(10X.10F7.4/10X.10F7.4) PUMCH  )  120  40  130  FUNCTIONS*  FOPMAK50H2 PUNCH  120  OF  31»FCI  1^0  FORMAT(1 HO) 00  26  M=l»100  R =M 26  A(M)=COSF(,062R3*R) DO  33  I=l»20  00  59  J=l»20  Figure 45.  C a l c u l a t i o n of the i n v e r t e d response f u n c t i o n s .  59  FCI<I»J)=FCI(I•J)»HAMM<J) no  3 ? <=i»50  PFSPI(K)e.O M=0  DO 3 ? J = l » 2 0 MnM+K IF(M-100)37»37»3R  37  CONTINUF  3?  RFSPI (K)=RFSPI ( K J + F C I ( I • J ) * A(M)  33 PUNCH 34  34»I»RESPI  FORMAT(1H2»I5»4X»10F7.3/]H2»9X»10F7.3/1H2»9X»10F7«3/1H?»9X»10F7. 11H2.9X.10F7.3) GO  TO  39  FND  Figure 45 (continued).  C  41 40  59 60 5 10 84 90 81 46 48 9 47 8 6 11 7  INSTRUMENT F U N C T I O N S DIMENSION RESPI(20.50).POWER(50).DUMMYS(20*4)»DUMMY<20)»C(20) DIMENSION DHAMM(20)»R{50) READ 4 1 . < ( R E S P I < I . J ) » J = 1 . 5 0 ) . I = 1 . 2 0 ) FORMAT(10X»10F7«4) READ 4 0 , ( ( D U M M Y S t I . J ) » I » 1 * 2 G ) . J = 1 . 4 ) FORMAT(14X.20F3.3> DO 5 9 J « l » 2 0 DUMMY( J ) = • 0 DO 5 9 K = l»4 D U M M Y ( J ) * D U M M Y ( J ) + DUMMYS<J.K) DO 6 0 J « l » 2 0 D U M M Y ( J ) « D U M M Y ( J ) * 0 # 25 DO 5 M=1.50 R(M)«.0 PUNCH 10 FORMAT(///30X»20HINSTRUMENT FUNCTIONS) DO 6 L = l » 5 0 READ 4 0 . C DO 9 0 I«l»20 DHAMM(I) (C(I)-DUMMY(I)) DO 4 8 J = l » 5 0 POWER(J)-.0 DO 4 6 I=l»20 POWER(J)=POWER(J)+DHAMM(I)*RESPl(I.J) CONTINUE PUNCH 9. L FORMAT ( / / / 1 0 X . I 2 ) PUNCH 47.POWER FORMAT(/(10X»10F7-3)) DO 8 M = l » 5 0 R(M)=R(M)+POWER(M) CONTINUE PUNCH 11 FORMAT ( / / / 2 7 X . 2 7 HSUM OF INSTRUMENT F U N C T I O N S ) PUNCH 7.R FORMAT ( / / / ( 1 0 X . 1 0 F 7 . 1 ) ) STOP END s  Figure 46. C a l c u l a t i o n o f the instrument f u n c t i o n s .  106 are read i n , not as a matrix, but one row at a time, a f t e r each computation, and are c a l l e d simply G. The I ,m m  c a l l e d POWER and c o n s t i t u t e the program output.  a  r  e  0  R i s the  sum o f the I's and i s p r o p o r t i o n a l t o the s p e c t r a l s e n s i tivity. 5)  The Power Spectra The program f o r the computation o f power s p e c t r a i s  s i m i l a r to the previous one f o r instrument f u n c t i o n s . Here the input i s GALAXY and SKY, from which are taken the averages G and S. The output i s POWER. The sum o f the  squares  of the ordinates i n each spectrum (SUMSQ) i s computed and p r i n t e d w i t h each spectrum.  This sum i s u s e f u l as an i n d i -  c a t o r o f the amount o f emission i n a spectrum, but i s not of q u a n t i t a t i v e value because o f the p o s s i b i l i t y o f a basel i n e slope. 6)  Reduction o f Power Spectra The r e c t i f i c a t i o n o f s p e c t r a , as stated i n the t e x t ,  is a p a r t l y s u b j e c t i v e procedure, and t h e r e f o r e cannot be programmed i n i t s e n t i r e t y f o r computer processing. However, the d i g i t a l computer can provide valuable a i d , once a base l i n e has been chosen f o r the spectrum. The input data i n c l u d e s POWER from the previous program, here abbreviated t o P, and numerous other items which are l i s t e d below f o r the sake o f c l a r i t y .  C C C  C O M P I L A T I O N OF 27 DECEMBER 1963 POWER SPECTRUM OF M 3 1 , P . E , ARGYLE , DRAO » PENT ICTON SCANS 1 1 A » 12A. 1 3 A » 1 4 A . 15A oDIMENS ION S K Y ( 2 0 » 8 ) » S ( 2 0 ) • G A L A X Y ( 2 0 * 4 ) » G ( 2 0 ) • 1POWER(50),RESPI <20»50) READ 4 1 . ( ( R E S P I ( I » J ) t J = l » 5 J ) » I = l » 2 0 ) 41 FORMAT (10X»UF7.4) DO 35 L = l » 1 4 READ 4 C ( ( S K Y ( I » J ) » I = 1 * 2 0 ) » J = 1 » 8 ) 40 FORMAT <14X»20F3.3) DO 59 J = l » 2 0 S(J)=.0 DO 59 K = l » 8 59 S < J ) = S < J ) + S K Y ( J » K ) DO 35 M = l » 6 READ 4 0 , ( ( G A L A X Y ( I » J ) t I = l » 2 0 ) . J = l » 4 ) DO 79 J = l » 2 0 G(J)=.0 DO 79 K = l » 4 79 G(J)=G(J)+GALAXY(J,K) DO 80 J = l » 2 0 80 G ( J ) = ( 2 . * G ( J ) ) - S ( J ) PUNCH 4 7 » G 47 FORMAT ( / ( 1 0 X . 1 0 F 7 . 3 ) > DO 46 J = 1 » 5 J POWER(J)=.0 DO 46 I = l » 2 0 46 POWER(J)=POWER(J)+G(I)*RESPI(I*J) PUNCH 4 7 » POWER SUMSQ =.0 DO 33 J = 4 » 5 Q 33 SUMSU = SUMSO+ P O W E R ( J ) * * 2 35 PUNCH 3 4 » S U M S Q 34 FORMAT (/17H SUM OF SQUARES = , F 9 . 3 ) STOP END  Figure 4 7 .  C a l c u l a t i o n o f the power s p e c t r a .  C C C  I  3 II 5  6  7  8  C O M P I L A T I O N OF 30 JANUARY 1 9 6 4 R E D U C T I O N OF POWER S P E C T R A OF M31 SCANS 15 TO 21 INCLUSIVE DIMENSION P ( 5 0 ) » T < 5 0 ) » B A ( 5 0 ) 4 READ 2,NO, I R A , A t B , K» L» M» N READ I f P FORMAT ( 1 0 X . 1 C F 7 . 3 ) 2 FORMAT ( 4 X , 1 2 , 1 3 , 2 F 7 . 3 , 4 1 3 ) AM=M AN=N I=M+1 C=.02*(B-A) DO 3 J = 1, 5 0 A=A+C BA(J)=A DO 11 I Z = 1,50 T ( I Z ) = .0 DO 5 J = KtL T<J)=P(J)-BA(J) PUNCH 1 6 » NO, IRA PUNCH 1, T 16 FORMAT ( 1 0 X , 8HSCAN N 0 . » I2» 1 H / , I2» / ) SUM = .0 DO 6 J = K » L SUM = S U M + T U ) AREA = 1 4 6 . * SUM SUMSQ = ,0 DO 7 J « K , L SUMSQ x SUMSQ • T ( J ) * * 2 RMS = 4.* S Q R T F ( . 0 2 1 2 8 * SUMSQ) WIDTH = 3 6 . 5 * SUM * * 2/SUMSQ WIDTHE = . 2 1 0 7 4 * WIDTH TEMP = AREA/WIDTH V = .0 DO 8 J = K,L Z = J V = V + Z * T(J) VEL = 7 . 7 0 1 * V/SUM - 3 1 7 . 4 2 IF ( T ( N ) - T ( M ) ) 1 2 , 1 3 , 14 14 P V E L = 3 . 8 5 0 * ( A M + A N + ( T ( N ) - T ( M ) ) / ( T ( I ) - T ( M ) > J - 3 1 7 . 4 2 GO TO 15 12 P V E L = 3 . 8 5 0 * ( A M + A N + ( T ( N ) - T ( M ) ) / ( T ( I ) - T ( N ) ) ) - 3 1 7 . 4 2 GO TO 15 13 P V E L = AM + 1. 15 C O N T I N U E PUNCH 10 10 FORMAT (/11X.10H AREA K <C,3X,6H RMS K , 1 X , 9H WIDTH K C , 11X,9H WIDTH KM, 3X, 7H TEMP K , 1 X , 9H V E L O C I T Y , I X . 9H PEAK V E L ) PUNCH 9, A R E A , R M S » WIDTH, WIDTHE, T E M P » V E L , P V E L 9 FORMAT ( 5 X , F 1 5 . 3 , 6 F 1 0 . 3 / / / / ) GO TO 4 END  Figure 48.  Reduction o f power s p e c t r a .  107 Purpose  Item  Name  Scan number  Identification  NO  Right Ascension  Identification  IRA  Base l i n e height at m=0  A and B are used t o e s t a b l i s h the p o s i t i o n  A  Base l i n e height at m=50 Beginning of p r o f i l e End of p r o f i l e A frequency, m=M, j u s t below that of the peak of the s p e c t r a l p r o f i l e A frequency, m=N, above the peak  just  and slope of the base l i n e B To s t a r t r e c t i f i c a t i o n  K  To end r e c t i f i c a t i o n  L M  M and N are used t o c a l c u l a t e the peak v e l o c i t y by a t r i a n g u l a r approximation  N  S p e c t r a l temperature  Output  T  Area under p r o f i l e  Output  AREA  Rms value of spectrum  Output  RMS  Equivalent width i n kc  Output  WIDTH  Equivalent width i n km/sec  Output  WIDTHE  Mean temperature  Output  TEMP  Mean v e l o c i t y  Output  VEL  Peak  Output  PVEL  c)  velocity  C o r r e c t i o n of Folded Spectra I f the input power spectrum i s P ( f ) the t o t a l s p e c t r a l  i n t e n s i t y , P ( f ) , w i l l be augmented by f o l d i n g of energy T  from the next order of the spectrum. P (f) T  = P ( f ) W(f) + P ( 2 f  u  That i s ,  - f ) W(2f - f ) u  (1  108 where W(f) i s the square of the modulus of the t r a n s f e r funct i o n of the bandpass f i l t e r , f : i s the upper frequency of u  the s p e c t r a l order, and 0 < f <.f .  However, the e f f e c t i v e  u  i n t e n s i t y i s always normalized procedure. P  e f f  to W = 1 by the compensation  That i s ,  ( f ) = P (f)/W(f)  (2  T  = P(f) + P ( 2 f  u  - f ) ¥(2f - f)/W(f)  (3  u  The t r u e i n t e n s i t y i s t h e r e f o r e P(f) = P  e f f  ( f ) - P(2f  u  - f ) W(2f - f)/W(f)  (4  u  The observed i n t e n s i t y , P b ^ ) » * 0  s  s  always the e f f e c -  t i v e i n t e n s i t y convolved with the instrument f u n c t i o n s , l(<0,f).  Convolving both sides of ( 4 ) w i t h l ( - 0 , f ) :  P(f)*lW,f) = -[p(2f  u  P  e f f  (f)*lW,f)  - f ) W(2f -f)/W(f)] * l W , f )  (5  u  Let a second spectrum be taken with centre frequency one s p e c t r a l range above that of the f i r s t P(2f  u  spectrum.  Then  - f ) # l W , f ) i s , except f o r a r e v e r s a l of the f r e -  quency s c a l e , the observed i n t e n s i t y i n the second spectrum. In the spectra of M31 the i n t e n s i t y i s seen to be a very slowly v a r y i n g f u n c t i o n of f compared to W(2f I t i s also slowly varying compared to l ( 0 , f ) . P(2f  u  u  - f)/W(f). Therefore  - f ) i t s e l f i s taken to be slowly v a r y i n g .  t h i s assumption P ( 2 f  u  With  - f ) i n (5) may be replaced by the  109 constant P ( f ) > which i n t u r n i s replaced by the known conm  stant Pobs^m)' where f  m  i s the frequency at which the value  of W(2f - f)/W(f) i s 0.5, and in i s the numerical frequency u  index, m = 50 f / f . u  For the bandpass f i l t e r , m = 50.5, ^  u n i t i n t o the second s p e c t r a l range. Equation (5) can now be w r i t t e n P(f)*I(v,f) = P  ( f ) * - l W , f ) - P bs 50.5 ( f  e f f  )  0  [w(2f  - f)/W(f)-*lM,f)]  u  (6  A l l the q u a n t i t i e s on the r i g h t are known, and the quantity on the l e f t i s the power that would have been observed i n the absence of f o l d i n g .  For convenience i n com-  p u t a t i o n equation (6) i s w r i t t e n Pc<f) = Pobs< ) - o b f  P  S  ( f  50.5»  W  ( 7  where P ( f ) i s the corrected spectrum, and W i s a t a b u l a c  t i o n of the l a s t convolution i n ( 6 ) , and i s given below:  m 50 49 48 47 46 45 44 43 42 41  0.32 .31 .26 .20 .15 .09 .06 .02 .01 .00  110 d)  Area o f S p e c t r a l P r o f i l e and Hydrogen Density I t i s shown by F i e l d (1958) t h a t , provided the s p i n  temperature  of atomic hydrogen i s much greater than  I^Q/IC,  the 21-cm emission from o p t i c a l l y t h i n clouds i s independent o f the temperature.  A value of 125°K i s u s u a l l y adopted  f o r the temperature  i n the galaxy (van de H u l s t , M u l l e r and  Oort, 1954) whereas  h \ ) A == 0.068°K. 10  Thus emission i s  e a s i l y i n t e r p r e t e d i n terms o f the s u p e r f i c i a l d e n s i t y o f atomic hydrogen i f there i s not too much s e l f a b s o r p t i o n . 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