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Area photometry with a multi-diode array Mochnacki, Stefan Wladyslaw 1977

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AB El PHOTOMETRY .9ITH A MULTI-DIODE ARRAY by STEFAN HLABYSLAW MOCHNACKI B. Sc. (Hons.) , University of Canterbury (N.Z.), 1970 B.Sc, University of Canterbury (N.Z.), 1971 A THESIS SUBMITTED IN PARTIAL FULF ILLMENT OF THE REQOIR EMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Geophysics and Astronomy) He accept t h i s t h e s i s as conforming to the reguired standard THE UNIVERSITY OF BRITISH COLUMBIA October 1977 Stefan Wladyslaw Mochnacki, 1977. In presenting th i s thes i s in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ib ra ry sha l l make it f r e e l y ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l i ca t i on of th is thes i s fo r f i nanc i a l gain sha l l not be allowed without my writ ten permiss ion. Stefan Wladyslaw Mochnacki Department of ASTRONOMY and GEOPHYSICS^ The Un ivers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date 3 NOV. 1977. i ABSTRACT An area photometer u s i n g a RETICON RA50x50 m u l t i - d i o d e a r r a y as the d e t e c t o r has been developed and used to observe the c e n t r a l r e g i o n s of s t e l l a r systems. Computer programmes have been w r i t t e n t o handle the r e c o r d i n g of data and the sub-seguent a n a l y s i s o f images. A s e g u e n t i a l image p r o c e s s i n g language c a l l e d FIRM was developed f o r use with an IBM 370 under MTS. A t h e o r e t i c a l a n a l y s i s of the response of diode a r r a y s to Gaussian s t a r images shows that the l i g h t from a s t a r can be i n t e g r a t e d i f the s e e i n g diameter i s g r e a t e r than 2.0 times the diode c e n t r e to c e n t r e spacing. A l i a s i n g a t a l l f r e g u e n c i e s i s i n s i g n i f i c a n t f o r any s e e i n g diameter g r e a t e r than about 2.5 diode s p a c i n g s . Technigues f o r a v o i d i n g a l i a s i n g are d i s c u s s e d . Images of an area approximately 40" x 40" i n the c e n t r e of the Sb galaxy NGC 4736(=M94) have been ob t a i n e d through b l u e , v i s u a l and r e d f i l t e r s . S u b t r a c t i o n of a simple, c i r c u -l a r l y symmetric model with King core r a d i u s 6".0 ± 0".5 r e v e a l s a s m a l l , b a r - l i k e c e n t r a l s t r u c t u r e about 20" a c r o s s . T h i s c e n t r a l s t r u c t u r e i s a l i g n e d p e r p e n d i c u l a r l y to the major a x i s of the galaxy and melds i n t o p r e v i o u s l y photographed s p i r a l s t r u c t u r e . A b r i g h t p o i n t - l i k e nucleus i s a l s o seen, but i t does not stand out i n the c o l o u r maps. ft sharp c o l o u r g r a d i e n t e x i s t s at 10" r a d i u s . The reddest areas of the c e n t r a l r e g i o n c o i n c i d e roughly with patches of negative r e s i -duals after model subtraction. A simple dynamical model i s constructed for the inner region of NGC 4736, and i t i s proposed that two s p i r a l systems ex i s t i n t h i s galaxy, one inside the other with the inner system rotating more rapidly i f i t i s a two-armed s p i r a l . This model may also apply to other galaxies. A central mass to blue luminosity r a t i o of 2.4 to 3.6 i s obtained f o r a range of model parameters. Observations of the X-ray emitting globular c l u s t e r NGC 7078 (=1115) reveal a number of red giants within 15" of the centre. A map of b-^ -r instrumental colour shows that the nuclear cusp appears to be only a l i t t l e redder than the main unresolved "background" population of the c l u s t e r , but the poor seeing does not allow resolution of the cusp within 2" of the c l u s t e r centre. The colour map confirms published spectroscopic r e s u l t s . There i s very l i t t l e r a d i a l colour variation when centred c i r c u l a r apertures are simulated. i i i TABLE OF CONTENTS 1. INTRODUCTION 1 1.1 The Observation of Extended Systems. ............ 1 1.2 S t r u c t u r e Of G l o b u l a r C l u s t e r s 2 1.3 S t r u c t u r e of G a l a x i e s 6 1.4 The Programme. 18 2. INSTRUMENT DEVELOPMENT 20 2.1 Choice of D e t e c t o r . 20 2.2 System Design. 27 2.3 Operating Software. 33 2.4 System Performance. 36 2.5 O p t i c a l F i l t e r s . . . . 4 3 3. DATA ANALYSIS THEORY AND METHODS 46 3.1 General Concepts For Diode Arrays. ..,46 3.2 T h e o r e t i c a l A n a l y s i s Of Array S p a t i a l Freguency Response. 47 3.3 Technigues For Avoi d i n g A l i a s i n g . . ............... 59 3.4 P r i n c i p l e s Of Data Reduction. 65 3.5 FIRM : An Image Pro c e s s i n g Code 68 4. THE SPIRAL GALAXY NGC 4736{=M94) 74 4.1 Background. 74 4.2 NGC 4736: The Obs e r v a t i o n s . 78 4.3 NGC 4736: A n a l y s i s o f Observations 94 4.4 NGC 4736: H a l f t o n e R e s i d u a l Maps 114 4.5 NGC 4736: Ratio And Colour Maps ...120 4.6 NGC 4736: Simple Models ..130 i v 4.7 NGC 4736: S p i r a l Patterns And Resonance Phenomena. .........................................................144 4.8 NGC 4736: Discussion. ..153 4.9 NGC 4736: Conclusions 158 5. THE GLOBULAR CLUSTER NGC 7078 ... 159 5.1 Background 159 5.2 NGC 7078: The Observations .........161 5.3 NGC 7078: Scale and Orientation ...168 5.4 NGC 7078: Approximate Photometric C a l i b r a t i o n ....170 5.5 NGC 7078: Centred Aperture Photometry. .......... 174 5.6 NGC 7078: Seeing Analysis And Colour Maps 179 5.7 NGC 7078: Discussion and Conclusions. ...........184 6. SUMMARY AND CONCLUSIONS ..186 6.1 Conclusions. .............186 6.2 Problems for Future Work. ......189 REFERENCES . .. 194 APPENDIX I : FIRM Manual. ....206 APPENDIX II : Data Tapes. 252 V LIST OF TABLES I. Advantages And Disadvantages Of HETICON Array. . 2 5 II. Dynamic Dark Subtraction Code. ................. 36 I I I . Area Photometer Performance Characteristics. ...... 37 IV. Broad-band Optical F i l t e r s . ..................... 44 V. Aliased And Unaliased GRF 56 VI. Operations Performed Using FIRM . 69 VII. Elements And Properties Of NGC 4736. ........... 75 VIII. Log of Observations for NGC 4736. .. 79 IX. Comparison of Integrated Magnitudes. ........... 84 X. Blue Surface Brightness Contours 96 XI. Visual Surface Brightness Contours. 97 XII. Red Surface Brightness Contours. ............... 98 XIII. Calibrated V Surface Brightness vs Radius. ... 99 XIV. Nuclear Positions. .......127 XV. Parameters For Models Of NGC 4736. .......141 XVI. Mass To Luminosity Ratios. .......143 XVII. Radii Of V i s i b l e And Radio Features. ....145 XVIII. Main Disk Model Resonance Parameters. .......... 147 XIX. Inner Disk Model Resonance Parameters. .........152 XX. Log Of Observations For NGC 7 078. .............. 162 XXI. Centred C i r c u l a r Aperture Measures. ............ 175 XXII. C i r c u l a r Aperture Magnitudes And Colours. ......177 XXIII. Published Centred Aperture Photometry .....178 XXIV. Posit i o n a l Registration Corrections. ........... 181 v i LIST OF FIGURES 1. Schematic C i r c u i t Of Detector. 27 2. Schematic Diagram Of Area Photometer. 28 3. Internal Layout Of Camera Housing. 31 4. Recording Of Data On Tape. 34 5. Optical F i l t e r Passbands. , .......45 6. Detector Sampling Configuration. .................. 50 7. Effect Of Seeing Diameter 55 8. E f f e c t Of Image Displacement. 57 9. Effect Of Bead Space. 59 10. Raster Scanning To Reduce A l i a s i n g . ............... 63 11. Relationship of Orientations. 83 12. Gaussian Plots Of Star Images. ..86 13. Typical Noise Histogram. 87 14. NGC 4736; Blue Isophotal Contours. 89 15. NGC 4736: Visual Isophotal Contours 90 16. NGC 4736: Red Isophotal Contours. 91 17. NGC 4736: Composite Of B, V, R ...92 18. NGC 4736: Smoothed Composite Outer Contours. ...... 94 19. NGC 4736: Log I vs Log R : Red . 95 20. NGC 4736: Red F i l t e r : Log I vs R° .....101 21. NGC 4736: Blue I-* vs R« ....105 22. NGC 4736: Visual: I~* vs R* ..106 23. NGC 4736: Red: I ~ 2 vs R* 107 24. Hubble P l o t : i - o . s vs R : Red F i l t e r . ........... 109 25. Blue Minus Simple King Model. .....................110 v i i 26. visual Minus Simple King Model. ...................111 27. Red Minus Simple King Model. .....112 28. Composite Of Residuals Using King Model ...113 29. Red Minus Simple King Model: Dot-density Plot. ....115 30. Red And Blue Minus King Models: Halftones. 116 31. Red Minus Generalized Hubble Model. ..........118 32. B,V,R Minus Generalized Hubble Models. 119 33. NGC 4736: Blue Image Divided By Model. .....121 34. NGC 4736: Visual Image Divided By Model. .......... 122 35. NGC 4736: Red Image Divided By Model. 123 36. NGC 4736: Colour Map: b-v. ....124 37. NGC 4736: Colour Map: v-r. ...............125 38. NGC 4736: Colour Map: b-r. .....126 39. Colours And Residuals Along "bar". ......129 40. Colours And Residuals Perpendicular To "bar" 130 4 1. NGC 4736: F u l l Rotation Curve And Models .137 42. NGC 4736: Rotation Curve And Models To 80". .......138 43. NGC 4736:Rotation Curve To 32" And Models. ........139 44. Model Angular V e l o c i t i e s For NGC 4736. ............ 148 45. Inner Model Angular V e l o c i t i e s . ................... 153 46. NGC 7078: Blue Image Contour Map ....165 47. NGC 7078: visu a l Image Contour Map. 166 48. NGC 7078: Red Image Contour Map. ...167 49. Orientation Of RET ICON Camera. , .....169 50. S t e l l a r Image Intensity Curves. ................... 171 51. NGC 7078: B-r Colour Bap, 182 52. Line Scans Across Colour Map. ..............183 ACKNOWLEDGEMENT T h i s has been a long p r o j e c t , and many people have c o n t r i b u t e d to i t s completion. I wholeheartedly thank Dr. Gordon Walker, who has i n s p i r e d and s u p e r v i s e d t h i s work, g e n t l y g u i d i n g me past r a t h e r numerous p i t f a l l s d u r i n g my tenure as a graduate student at OBC. His f r i e n d s h i p and pa t i e n c e g r e a t l y c o n t r i b u t e d to making t h i s time pleasant and, I t r u s t , f r u i t f u l . T h i s p r o j e c t would not have been p o s s i b l e without the work of our e l e c t r o n i c s engineers Vern Buchholz, Dave Lane-- S r i g h t and B a r c l a y Isherwood. D i e t e r s c h r e i b e r worked beyond the c a l l of duty i n the f a b r i c a t i o n o f mechanical components. Dr. Jason Auman's p e r s i s t e n t and thought-provoking q u e s t i o n s motivated Chapter 3. Drs. C h r i s P r i t c h e t and John Kormendy i n the course of d i s c u s s i o n s taught me much about g a l a x i e s , while Drs. Tad O l r y c h , Greg Fahlman and Paul Sommerville c l e a r e d away the mists of freguency space. Drs. John Glaspey and Ingemar Olson i n t r o d u c e d me to minicomputer programming and I thank them f o r the use of some s u b r o u t i n e s . Alfonso Condal w i l l i n g l y shared some t e l e s c o p e time and a s s i s t e d with the o b s e r v a t i o n s . Dr. Brent T u l l y made i t p o s s i b l e f o r me to observe with him at Mauna Kea, and I thank the I n s t i t u t e f o r Astronomy at the University of Hawaii for making t h e i r f a c i l i t i e s avai-lab l e . I am very grateful to the Dominion Astrophysical Observatory, V i c t o r i a , for extensive use of their f a c i l i t i e s . I o f f e r no thanks to the weather, which f l i n g s r a i n and snow whenever I touch a telescope. Special thanks go to Dr. John Gait and a l l the s t a f f at the Dominion Badio Astrophysical Observatory, Penticton, for assistance with graphics. The outstanding service of the UBC Computing Centre i s g r a t e f u l l y acknowledged. I thank the University of B r i t i s h Columbia, and Dr. Walter Gage in p a r t i c u l a r , for the tenure of a University Fellowship. Last, but not l e a s t , I thank my wife Kathy for her encouragement and support under t r y i n g conditions., To her I dedicate t h i s thesis. X To Kathy 1 CHAPTER 1 INTRODUCTION 1. 1 The Observation of Extended Systems. Astronomical objects such as gaseous nebulae, ga l a c t i c and globular star c l u s t e r s , galaxies and cl u s t e r s of galaxies can be studied largely from two points of view: (i) The physical conditions and constitu t i o n of the diffe r e n t components of extended objects can be deduced by analysing the radiation from these objects. Examples of such studies are photometry and spectroscopy for abundance analysis and population synthesis. X-ray , in f r a - r e d and radio obser-vations to deduce the physical nature of components, area photometry for s t r u c t u r a l mapping and so f o r t h . ( i i ) The dynamics of the components of extended objects can be studied to deduce the d i s t r i b u t i o n of matter and the inte r a c t i o n of the components within the object. Motions i n extended objects are usually observed by measuring only r a d i a l v e l o c i t i e s , although i t i s possible to measure tangential (proper) motions in some nearby objects such as the Hyades clu s t e r and the Crab Nebula to obtain a complete kinematic description. The constitution and the dynamics•• of extended systems are in fact very closely intertwined. In p a r t i c u l a r I s h a l l 2 consider objects in which the d i s t r i b u t i o n and nature of luminous matter i s powerfully governed by large-scale dynamics involving very many components. These objects are globular c l u s t e r s and galaxies. Globular c l u s t e r s are s e l f - g r a v i t a t i n g ensembles of 10* to 10 7 stars o r b i t i n g i n the halos of galaxies, which i n turn contain a t o t a l of up to 10 1 3 s t a r s . I s h a l l ask the following guestion : can the projected two-dimensional brightness d i s t r i b u t i o n s i n galaxies and globular c l u s t e r s be observed and used to understand t h e i r dynamics, and vice versa? IJLZ Structure Of Globular Clusters. Of the estimated 190±30 globular c l u s t e r s in our Galaxy (Harris 1976), over 100 have been studied i n greater or lesser d e t a i l (see Peterson and King 1975, Peterson 1976 f o r summaries). The d i s t r i b u t i o n of stars has been obtained by counting i n d i v i d u a l resolved stars on plates (King et aJU 1968; Illingworth and Illingworth 1976; Peterson 1976) and by photoelectric area photometry (King 1963, 1966b; Illingworth and Illingworth 1976; Chun 1976). King (1962) derived an empirical r e l a t i o n s h i p f o r the surface brightness of globular clusters . For large t i d a l radius , t h i s gives I f r ) oc r ~ 2 , analogous to Hubble* s surface brightness law for galaxies. The masses of a number of globular c l u s t e r s have been 3 inferred from observations of v e l o c i t y dispersions (Illingworth and Illingworth 1974 and references therein). A vast l i t e r a t u r e on the photometry of i n d i v i d u a l stars i n globular c l u s t e r s e x i s t s , but i s largely outside the scope of t h i s work. The. c o l l e c t i o n of new data in the past ten years has coincided with the development of a much more thorough t h e o r e t i c a l understanding of globular c l u s t e r dynamics. I t was long understood that most globular c l u s t e r s are relaxed or brought in t o near eguilibrium by two-body interactions (e.g. Chandrasekhar 1942) and that some stars are expelled or "evaporate" (Spitzer and Harm 1958). However, i t was not u n t i l the seminal work of Michie (1963 a,b) and King (1965, 1966a) that the space d i s t r i b u t i o n of stars for a globular c l u s t e r model was computed allowing for a cut-off in the velo-c i t y d i s t r i b u t i o n due to stars having escaped. Such a cut-off i s observed in the form of a f i n i t e radius of the c l u s t e r ; t h i s radius i s sometimes c a l l e d the " t i d a l radius" because i t i s caused by the i n t e r a c t i o n between the potential f i e l d s of the c l u s t e r and of the Galaxy as the cluster o r b i t s the within the halo of the Galaxy (von Hoerner 1957, with correction by King 1962). I f there were no c u t - o f f , and the v e l o c i t y d i s t r i b u t i o n were i s o t r o p i c a l l y Gaussian, the i n f i n i t e i s o -thermal sphere would r e s u l t (Chandrasekhar 1942), with I(r)«cr- 1 f o r large r. Spitzer and Harm (1958) and King (1965) solved the Fokker-Planck equation to obtain the velo-4 c i t y d i s t r i b u t i o n , and King (1966a) then solved Poisson*s eguation to derive the corresponding s p a t i a l d i s t r i b u t i o n of stars within the c l u s t e r . This showed that a much steeper decrease of surface brightness was to be expected, depending on the t i d a l radius. Da Costa and Freeman (1976) have extended King's theory to allow for a r e a l i s t i c d i s t r i b u t i o n of s t e l l a r masses with f u l l e q uipartition of energy, whereas the e a r l i e r models assumed that the stars a l l had egual masses, or eguivalently had energy proportional to mass. This allowed a t o t a l luminosity function to be estimated for a well-observed c l u s t e r such as S3, with a better f i t to the surface brightness p r o f i l e . The surprising discovery of X-ray emission from f i v e globular clusters (Giacconi et a l . . 1974; Clark, JUarkert and L i , 1975) has led to a search for unusual features i n these c l u s t e r s . It has been suggested that massive black holes may exi s t near th e i r centres (e.g. Bahcall and Ostriker 1975). k number of t h e o r e t i c a l studies have been undertaken to consider the e f f e c t s such an object would have upon the s p a t i a l d i s t r i -bution of stars at the centre of a globular cluster or e l l i p -t i c a l galaxy (Wolfe and Burbidge 1970, Peebles 1972, Huntley and Saslaw 1975, Frank and Bees 1976, Bahcall and HoIf 1976). The most recent studies suggest that a central cusp in the density d i s t r i b u t i o n should occur, with a power law variation n(r) °C " . A higher v e l o c i t y dispersion i n the cusp i s also predicted. The work of Frank and Bees (1976) indicates 5 an observable angular extent of about one arc second f o r a thousand-solar-mass black hole at the centre of a t y p i c a l globular c l u s t e r . Electronographic observations by Newell et a l . (1976) suggest that such an object exists i n the nucleus of the X-ray globular 1315 (NGC 7078) , and these authors have further developed the t h e o r e t i c a l model of Da Costa and Freeman (1976) to compute the e f f e c t s of the central object upon the entire c l u s t e r . A number of models have been proposed for the source of X-rays in globular c l u s t e r s . There are two main problems ; (i) Formation of a collapsed object, ( i i ) Accumulation of matter to be accreted by the collapsed object. The object i s probably not a "simple" binary containing a collapsed component (Clark 1975), but rather a more massive object such as a black hole of 100 to 1000 solar masses (Silk and Arons 1975, Bahcall and Ostriker 1975). Coalescense of stars in the nucleus may be important ( H i l l s and Day 1976). The discovery of giant X-ray pulses from sources, some of which may be associated with the X-ray globulars, has further complicated the s i t u a t i o n ( see Bahcall and Ostriker 1976 and references therein). The problem of globular clusters r e t a i n i n g s u f f i c i e n t gas to f a l l onto a condensed object within a globular c l u s t e r has most recently been reviewed by Frank and G i s l e r (1976), who suggest that passage through a hot gaseous g a l a c t i c halo 6 sweeps out the gas from a l l but a group of a few globular c l u s t e r s which includes the X-ray globulars. The problem of X-ray emission from globular c l u s t e r s i s s t i l l the subject of uncertainty and controversy. C l e a r l y , more observations of d i f f e r e n t kinds are needed. Multi-cclour observations of 1315 (NGC 7078) have been made using the HE TIC ON area photometer and w i l l be discussed in Chapter 5 . 1.3 Structure of Galaxies. The structure of galaxies i s much more complex than that of globular c l u s t e r s . The e s s e n t i a l difference i s that whereas globular c l u s t e r s are relaxed by two-body interactions, stars i n galaxies are much more widely spaced and close encounters between i n d i v i d u a l stars are extremely rare (except perhaps i n the most central regions ) . There-fore galaxies cannot be relaxed by two-body interactions. This i s c a l l e d the "fundamental paradox of c l a s s i c a l dynamics" by Ogorodnikov (1965, p. 119) or t ,Zwicky ,s Paradox" by Lynden-Bell (1967). It i s therefore surprising that a globular c l u s t e r model for the surface brightness d i s t r i b u t i o n can f i t a galaxy (King 1966a). Lynden-Bell (1967) has resolved t h i s paradox by invoking the mechanism of violent relaxation. As an e l l i p t i c a l galaxy i s formed, the smooth gr a v i t a t i o n a l f i e l d due to the ensemble of already formed stars changes, thus changing the t o t a l energies of the s t a r s . 7 The violent collapse process leads to a Maxwellian d i s t r i - . bution of energy, but with temperature proportional to part-i c l e mass, i . e . no eq u i p a r t i t i o n of energy between stars takes place. Lynden-Bell*s model f i t s nicely into the galaxy formation theory of Gott and Thuan (1976), who postulate that i f s t e l l a r formation i s largely complete at the point of maxi-mum collapse of a protogalaxy, an e l l i p t i c a l galaxy i s formed. This depends on the i n i t i a l conditions of protogalaxy form-ation and collapse. The Gott and Thuan (1976) model of galaxy formation seems to be a very interesting compromise of the debate between Larson(1975) and Gott(1975), supporting, respectively, collapse with d i s s i p a t i o n and collapse ( or in fa11) without d i s s i p a t i o n . The Gott-Thuan model has the following features: (i) Protogalaxies are formed from density perturbations, which pick up angular momentum from t i d a l interactions with other protogalaxies about the time of maximum expansion (Peebles 1969) . ( i i ) More dense perturbations collapse more rapidly. The higher density leads to even more rapid star formation, which i s e s s e n t i a l l y complete by the time of maximum collapse. An e l l i p t i c a l galaxy i s formed. ( i i i ) Less dense density perturbations collapse more slowly with even slower star formation. The clouds of gas l e f t over at the point of maximum collapse c o l l i d e with dis s i p a t i o n of energy and eventually form a disk. The 8 stars formed early i n the collapse form the bulge, or halo, and the r a t i o of the mass of the s t e l l a r spheroidal halo to that of the disk i s determined by the r a t i o of the mass of stars to that of the gas at the point of maximum collapse, (iv) The t i d a l interaction of protogalaxies leads to a s i m i l a r i n i t i a l d i s t r i b u t i o n of angular momentum among protogal-axies of e l l i p t i c a l and s p i r a l galaxies. „ It can be seen that t h i s picture of galaxy formation explains naturally the existence of two components i n galaxies: a spheroidal halo or bulge, and a disk. In e l l i p t -i c a l s the disk i s absent or i n s i g n i f i c a n t , although Larson(1975) considers that disks made up of metal-enriched stars may be important inside some e l l i p t i c a l s . Observationally, disk and spheroidal components have ch a r a c t e r i s t i c s common to nearly a l l galaxies. De Vaucou-leurs(1959) found that the spheroidal component of s p i r a l s has the same empirical surface brightness law as e l l i p t i c a l s : while the outer disk has: (2) King (1966a) showed t h a t de Vaucouleurs* law c l o s e l y resembles h i s t h e o r e t i c a l model with l o g i f t ( r t /zc ) - 2.2 , 9 where r^ = t i d a l radius, r c = core radius. This i s the model which King showed to be appropriate for the e l l i p t i c a l galaxy NGC 3379. I t should be noted that no account has been taken of the "lens" or non-exponential disk seen i n some galaxies by Freeman (1975) and Koraendy (1976). No account has been taken of the t h e o r e t i c a l i n s t a b i l i t y of "cold" disk systems i n the absence of a massive halo (Peebles and Ostriker 1973), a problem of great importance i n current g a l a c t i c research. Surface brightness measurements do not necessarily correspond to the d i s t r i b u t i o n of mass because the mass-to-light r a t i o i s a p r i o r i unknown., I t i s here that kinematic observations become very important, and i t i s also here that serious p i t f a l l s occur. Rotation curves , which correspond to measurements of r a d i a l v e l o c i t y along the (apparent) major axes of galaxies, should i n p r i n c i p l e allow the determination of the run of density i n rotating axisymmetric systems. The use of rotation curves to deduce the structure of external galaxies was pioneered by Burbidge et a l . (1959) and Brandt (1960) using both o p t i c a l and 21-centimetre r a d i a l v e l o c i t y observations. The multiple-spheroid models of Burbidge et a L - (1959), inspired by work on our own Galaxy by, for example, Schmidt (1956), were superseded by the spheroid-disk models of Toomre (1963) which have a r e l a t i v e l y simple a n a l y t i c a l form. 10 Some of the models used for f i t t i n g to r a d i a l v e l o c i t y curves have been rather devoid of physical content and lack even an empirical basis. At the same time the observations have been too "noisy" and incomplete to r e l i a b l y apply a true inversion technigue. A number of the e a r l i e r a n a l y t i c a l models were reviewed by Perek (1962). I t was not u n t i l Freeman's (1970) notable work on the disks of s p i r a l galaxies that a model with an empirical basis was formulated for dynamical studies: the disk with an exponential surface density law. Spheroid and exponential disk models have been used by Nordsieck (1973a, b) , Barner et a l . (1973), Emerson and Baldwin (1973), Rots (1975) , Yoshizawa and Sakamatsu (1975) and Monnet and Simien (1977). A large amount of work has been done using a com-bination of Toomre's (1963) disk model and the Burbidge et i l i i (1959) model f o r the spheroid, including the very important work on density waves (Shu et a L - 1971; Roberts et-a l A 1975 and references therein). Unfortunately, the rotation curve i n disks often reaches a maximum, or turnover, at about the l i m i t of observations, leading to a large extrapolation for the outer unobserved region i f a Toomre model i s used (see Roberts 1975, Baldwin 1975). This extrapolation, combined with observations of low accuracy, led to the suggestion that the mass-to-luminosity r a t i o r i s e s sharply i n the outer regions of s p i r a l galaxies., This guestion has been c a r e f u l l y examined by Warner et a l . (1973), 11 Emerson and Baldwin (1973) and Baldwin (1975), who f i n d l i t t l e evidence for the mass-to-luminosity r a t i o varying by much in the disks of H31 (NGC 224} and H33 (NGC 598) . However, more recent observations extending to further r a d i i show that i n some galaxies at l e a s t there r e a l l y appears to be no turnover of the rotation curve, i n d i c a t i n g a large amount of unseen matter at large r a d i i (Roberts 1975; Krumm and salpeter 1977). Freeman (1970) pointed out that the B-V colour index shows l i t t l e v a r i a t i o n in the inter-arm regions of disks, and therefore concluded that the mass to blue l i g h t r a t i o does not change much across the disks of s p i r a l s . This has been strongly supported by the detailed photometry of six late s p i r a l galaxies by Schweizer (1976). It i s well known that element abundances in both the spheroidal and disk components show a r a d i a l v a r i a t i o n in most galaxies (see van den Bergh 1975 f o r a review), and this could have some e f f e c t on the mass to luminosity r a t i o s . Likewise the r a t i o of gas to stars changes r a d i a l l y i n the disks of galaxies such as M33 (Warner et alj, 1973) . Nevertheless, as a st a r t i n g point i n t h i s work i t w i l l be assumed that the mass to luminosity r a t i o i s constant in the disk (excluding the arms which contain a very young, very luminous population in addition to the older disk population), How does the mass to luminosity r a t i o of disks vary from galaxy to galaxy? The data are s t i l l very uncertain. Nordsieck (1973b) found that M/L decreased for l a t e r , bluer 12 galaxies, but t h i s included the arm population. Schweizer (1976) found that the disk colours f e l l i n a narrow range between B-V = +0.7 (typical of old g a l a c t i c c l u s t e r s ) and B-V = +0.9 (typical of giant e l l i p t i c a l galaxies ). Freeman's (1970) remarkable result of a very narrow range of extrapolated c e n t r a l blue surface brightnesses for disks { B(0) ••= 21.65 ± 0.30 s.d.) would tend to suggest that the central surface density also has a small range. Freeman's resul t may be largely coincidental and only apparent due to superposition of the spheroid on the disk (Kormendy 1976). I s h a l l t e n t a t i v e l y accept Freeman's r e s u l t s since galaxies with l i t t l e spheroidal contribution s t i l l display the exponential disk. What can be said about the mass-to-luminosity r a t i o s of spheroidal components? Two p r i n c i p a l approaches have been used so far to deduce the masses and hence mass-to -luminosity r a t i o s of e l l i p t i c a l galaxies and the bulges of s p i r a l s : population synthesis by f i t t i n g models to spectral scanner observations, and application of the v i r i a l theorem to measurements of the v e l o c i t y dispersion. Optical rotation curves have also been used, and the l i m i t a t i o n s of t h i s method w i l l be discussed l a t e r . Recent applications of population synthesis methods (Faber 1971; O'Connell 1974, 1976; Pritchet 1975; Williams 1976; Turnrose 1976) demonstrate the great d i f f i c u l t y in determining the mass to luminosity r a t i o from spectrum scans over a limited range of wavelenths: the l i g h t 13 i s dominated by giants while the mass i s dominated by dwarfs. This should not be a problem for v e l o c i t y dispersion measurements, since the less massive stars should have the same ve l o c i t y dispersion as the more massive ones except i n the very densest nuclear regions of some galaxies (Lynden-Bell 1967). However, i t i s known that velocity dispersions at the centre of a galaxy may not be representative of the galaxy as a whole (Poveda 1958, Poveda et ajU 1960, Morton and Chevalier 1972, Aarseth and Saslaw 1972)., i l l s o n (1975) has shown that using a more sophisticated model for e l l i p t i c a l galaxies, a sharp decrease of the v e l o c i t y dispersion with distance away from the nucleus i s to be expected and that e l l i p t i c a l galaxy masses may have been overestimated by a factor of three. Using a simpler model, Ruiz and Schwarz-s c h i l d (1976) obtain a sim i l a r r e s u l t for the bulges of s p i r a l galaxies. Observations of th i s effect are s t i l l inconclusive, since the surface brightness drops off so rapidly away from the nucleus i n spheroidal systems. Rotation curves f o r M94(=NGC 4736) (Chincarini and walker 1967), NGC 3115 (Williams 1975) and NGC 4697 (Bertola and Cappacioli 1975) have been measured without a s i g n i f i c a n t change i n vel o c i t y dispersion being noted. Faber and Jackson (1976) fi n d a higher v e l o c i t y dispersion i n the nuclei of NGC 3115 and possibly i n H31 than i n the outer parts of these galaxies, but t h i s may be due to the existence of a dynamically independent nucleus (Light et a l . , 1974, Ruiz 1976). The existence of multi-component spheroidal systems i s espe c i a l l y important for 14 some barred systems (de Vaucouleurs 1974). The formation cf a dynamically separate nucleus composed of normal s t a r s may be due to the t i d a l d i s r u p t i o n and accumulation of g l o b u l a r c l u s t e r s with s m a l l i n i t i a l p e r i g a l a c t i c a {Tremaine, O s t r i k e r and S p i t z e r 1975; Tremaine 1976a,b). Despite these d i f f i c u l t i e s , and the problems of d e r i v i n g v e l o c i t y d i s p e r s i o n s from broadened composite s p e c t r a l l i n e s , a p p l i c a t i o n o f F o u r i e r transform technigues has allowed the sy s t e m a t i c d e t e r m i n a t i o n of masses and mass t o l u m i n o s i t y r a t i o s of the n u c l e a r r e g i o n s of a r e p r e s e n t a t i v e sample of g a l a x i e s (Faber and Jackson 1976; Sargent et al.. 1977; Wi l l i a m s 1977). These authors f i n d t h a t the l u m i n o s i t y L i s p r o p o r t i o n a l to the v e l o c i t y d i s p e r s i o n t o the f o u r t h power:-Faber and Jackson (1976) f i n d some evidence f o r a r e l a t i o n s h i p : but Sargent et a l . (1977) argue t h a t r e l a t i o n (3) i m p l i e s t h a t a l l e l l i p t i c a l s have the same mean mass-to-luminosity r a t i o . W i l l i a m s (1977) f i n d s mass to l u m i n o s i t y r a t i o s ranging from 1 to 15 , with s i m i l a r ranges f o r s p i r a l s and e l l i p t i c a l s . The r e s u l t s t o date, t h e r e f o r e , are s t i l l r a t h e r rough concerning the mean v a l u e s of mass to l u m i n o s i t y r a t i o (3) 15 for spheroidal systems, and very l i t t l e indeed i s known for the variation of H/L with radius, except that there are serious discrepancies between r e s u l t s from the galaxies themselves and from double and multiple (Turner 1976, Williams 1977). The use of rotation curves could i n p r i n c i p l e allow the deduction of the d i s t r i b u t i o n of density as a function of radius i n a rotating spheroidal system (Burbidge et a l . -: 1959). &s noted e a r l i e r , t h i s can work well using r a d i a l v e l o c i t y observations of neutral and ionized hydrogen i n the disks of s p i r a l galaxies. However, there i s a serious problem when one attempts to use the s t e l l a r absorption l i n e r a d i a l v e l o c i t i e s in a spheroidal system. In a disk system, the tangential ( or o r b i t a l ) velocity dominates, since the velo-c i t y dispersion i s guite low and the o r b i t a l velocity i s high, i . e . the disk i s " c o l d " . In a spheroidal system, however, the r a d i a l motions are dominant, and hence the mean , or stream, v e l o c i t y of stars near a point i s less than the c i r c u l a r o r b i t a l v e l o c i t y for that point. This has been made very clear by Ruiz and Schwarzschild (1976). I t i s therefore, necessary to f i t a detailed model computed using technigues such as those of Prendergast and Tomer (1970), Wilson (1975) , Hunter (1975,1977), and Ruiz and Schwarzschild (1976). The mean rotation curve derived from s t e l l a r motions cannot be used as the c i r c u l a r o r b i t a l rotation curve. In f a c t , the concept of "pressure support" of Burbidge et a l . (1959) as 16 outlined by Burbidge (1975) may apply more to stars than to the gas except i n the very nucleus i t s e l f , since most of the gas in a rotating galaxy should be i n a disk and rotating i n a roughly c i r c u l a r path unless there i s an outward motion of possibly explosive o r i g i n (see, for example , Sanders and Bania 1976). P e l l e t (1976) has observed a large difference between the absorption and emission l i n e rotation curves for M31. Unfortunately, there i s usually l i t t l e gas, e s p e c i a l l y neutral hydrogen, i n the inner regions of any but the l a t e s t Hubble types (Sc, Scd and I r r I ; see Faber and Gallagher (1976) for review and references ) and u n t i l very recently radio observations of HI were of poor angular r e s o l u t i o n . Therefore there i s l i t t l e r e l i a b l e r o t a t i o n a l v e l o c i t y data on the inner regions of galaxies i n general. Fabry-Perot mapping of emission-line v e l o c i t i e s provides one way of approaching the problem (Tully 1972, 1974a,b,c) , but the discrepancies between the HI measurements of the rotation curve of H31 and previous measurements using o p t i c a l emission l i n e s (Emerson and Baldwin 1973) suggest that great caution must be used when attempting to derive a c i r c u l a r velocity curve from an observed rotation curve. T i d a l i n t e r a c t i o n s are a further complication. There i s a further caveat. Even when constructing a sophisticated model along the l i n e s of Wilson (1975), i t i s usually necessary to assume a form f o r the function s t a t i s t i -c a l l y describing the motions of the stars, c a l l e d the phase 17 d i s t r i b u t i o n f u n c t i o n . The a c t u a l motions depend c r i t i c a l l y on the process through which the galaxy was formed {Lynden-Bell 1967). I t i s w e l l known that most forms adopted f o r the phase f u n c t i o n have d e f i c i e n c e s . Hunter (1975) has d e v i s e d a method f o r o b t a i n i n g a phase d i s t r i b u t i o n once the mass d i s t r i b u t i o n i s known. But i n order to know the mass d i s t r i b u t i o n from the observed r o t a t i o n curve u s i n g methods such as those of Wilson (1975) and Ruiz and s c h w a r z s c h i l d (1976) i t i s necessary t o assume a form f o r the phase d i s t r i b u t i o n f u n c t i o n . The argument becomes c i r c u l a r . What other means are a v a i l a b l e t o deduce the d i s t r i b u t i o n of mass i n a galaxy? Can area photometry and hydrogen gas r o t a t i o n curves be combined with simple mass d i s t r i b u t i o n models to produce a reasonable d e s c r i p t i o n of g a l a x i e s ? The images of s p i r a l g a l a x i e s c o n t a i n much more i n f o r m a t i o n than images of e l l i p t i c a l g a l a x i e s a t any wavelength. ; T h i s i s due t o the presence of the f l a t d i s k . Not only does the d i s k allow the i n c l i n a t i o n to be determined i n a d d i t i o n to a more p r e c i s e d etermination of the mass d i s t r i b u t i o n , but i t i s a l s o the s i t e of c o l l e c t i v e motions which produce s p i r a l s t r u c t u r e and continued s t a r f o r m a t i o n . The most developed model f o r s p i r a l s t r u c t u r e invokes d e n s i t y waves propagating r a d i a l l y i n the s t e l l a r and gaseous d i s k to generate a g u a s i - s t a t i o n a r y s p i r a l s t r u c t u r e r o t a t i n g r i g i d l y with constant angular v e l o c i t y , (see Wielen 1974, Roberts 1974, and L i n 1975 f o r recent r e v i e w s ) . 18 The density-wave theory of s p i r a l structure has been applied to observations of galaxies, and models have been obtained for a number of s p i r a l galaxies (Shu et a l . 1971, Roberts et a l ^ 1975 and references therein). A c r u c i a l feature of the density wave theory i s the occurrence of resonant o r b i t s c a l l e d LJndbiad resonances. In p a r t i c u l a r , the inner Linblad resonance may give r i s e to a "dispersion r i n g " which could cause observable e f f e c t s such as o p t i c a l l i n e emission and radio continuum emission. The consistency of density-wave phenomena with the mass d i s t r i b u t i o n i n dynamical models of galaxies can be tested by combining area photometry with other observations. JLs-i* The Programme. A number of galaxies and globular clu s t e r s were chosen for observation of t h e i r nuclear regions. The i n t e n s i t y and colour maps of these objects were to a s s i s t i n the further understanding of some of the problems of the dynamics and structure of s t e l l a r systems as outlined in t h i s chapter. Two objects, one galaxy and one globular c l u s t e r , were chosen for detailed study. The guality of the observations and the importance of the problems they r a i s e are the p r i n c i p a l motivations f o r the work presented here . A camera using a multi-diode array as the detector was 19 constructed to carry out t h i s programme. The design, construction and development of the RETICQN camera w i l l be described i n Chapter 2. In Chapter 3, I s h a l l discuss t h e o r e t i c a l l y the s p a t i a l freguency c h a r a c t e r i s t i c s of multi-diode detectors, with special emphasis on the problem of a l i a s i n g . Data reduction and analysis technigues w i l l also be presented. Observations of the Sb galaxy NGC 4736(=M94) w i l l be presented in Chapter 4, and a simple model w i l l be described. In Chapter 5, I s h a l l b r i e f l y discuss observations of the globular cluster NGC 7078(=815), while Chapter 6 w i l l summarize the r e s u l t s and outline a plan for future work. Appendix I i s a manual for using the author*s image pro-cessing language FIRM , and Appendix II l i s t s the objects observed using the RETICCN camera, together with the locations of data on l i b r a r y tapes. 20 CHAPTER 2 INSTRUMENT DEVELOPMENT 2_j__1 choice of Detector. Images of extended astronomical objects have t r a d i t i o n -a l l y been recorded on photographic plates, from which photo-metric information i s obtained by using microdensitometers. Unfortunately, photographic techniques are not very s a t i s -factory when a very wide range of brightness l e v e l s has to be recorded over a small area, such as i n the image of a ga l a c t i c nucleus. The dynamic range and s p a t i a l c h a r a c t e r i s t i c s of photographic emulsions are well known (see, for example. Dainty and Shaw 1974)., An in t e r e s t i n g attempt by Worden{1974) to obtain seeing-iimited resolution colour maps for NGC 5194 (=H51) showed that accuracies i n colour index of only 10.2 magnitudes were possible without smoothing or averaging of microdensity data., The quantum e f f i c i e n c y of conventional photographic emulsions i s rather low, les s than 1X. Long exposures are often needed, and the s e n s i t i v i t y drops as exposure time increases. This i s c a l l e d r e c i p r o c i t y f a i l u r e . Recent advances, such as hydrogen hypefsensitization, can increase s e n s i t i v i t y by up to twenty times by eliminating r e c i p r o c i t y f a i l u r e (Babcock et alj. 1974), while new fine-grained emul-sions such as the Kodak I l l a - J increase the inforiaation 21 storage capacity of photographic plates. Electronography as opposed to d i r e c t photography has been applied to galaxies (e.g. Abies and Abies 1972), but both the observation and reduction processes are extremely laborious. Automated d i g i t a l microdensitometers such as the PDS allow new problems to be tackled using modern photographic and e l e c t r o -nographic technigues. The outer regions of galaxies have been successfully studied photographically (e.g. Kormendy 1976), but the nuclear regions are much less accessible due to the low dynamic range and low photometric accuracy of photographic emulsions at high angular resolution. Panoramic detectors have been developed to overcome some of these problems. A major goal of t h i s work was to develop an el e c t r o n i c camera to study the nuclear regions of galaxies and globular c l u s t e r s at high angular resolution and with high photometric accuracy. At the time t h i s project was begun (1972), a number of workers were using low l i g h t l e v e l t e l e -v i s i o n cameras f o r two dimensional photometry (Livingston 1973, Glaspey and Salker 1973 and references therein). These cameras generally used electron reading beam signal generating tubes as detectors, e.g. orthocon, isocon, vidicon, SEC-vidicon, etc. A p a r t i c u l a r l y productive system was the Princeton SEC-Vidicon camera (Zucchino and Lowrance 1971; Low-rance, zucchino and Williams 1974), which has been success-f u l l y used for area photometry of galaxies (Crane 1973,1S75). Experience with t h i s and other systems indicates that serious 22 li m i t a t i o n s on accuracy are imposed by using an electron beam to read out the s i g n a l from the photodetecting element of the camera tube., For example, t h i s presented serious problems i n c a l i b r a t i n g the Celescope experiment on the o r b i t i n g s a t e l l i t e 0A0-2 (Nozawa and Davis 1971). (i) Baster scan fluctuations or " j i t t e r " . The exact position of a picture element i s uncertain because the electron beam i s affected by voltage fluctuations, magnetic f i e l d s , beam bending due to picture highlights, etc. The geometric i n s t a b i l i t y of electron-beam readout devices l i m i t s the photometric accuracy. ( i i ) Limited dynamic range. Camera tubes using electron emission from a photo-cathode surface often have a li m i t e d dynamic ^ange, which can be compensated for by freguent scanning and averaging of the s i g n a l . This i s not the case for the s i l i c o n diode vidicon, which does have a large dynamic range. ( i i i ) Limited resolution and oversampling. The electron beam has a f i n i t e cross-section, and therefore adjacent picture elements overlap., A s i t u a t i o n c a l l e d over-sampling usually r e s u l t s and introduces photometric uncertainty (Devinney, F i s c h e l and Klinglesmith 1975; Fischel 1976). In some tubes, such as the isocon, the res u l t i n g picture element (or "pixel") i s physically very large, with considerable overlap between elements (Buchholz 1972). Strong signals often lead to charge spreading and even poorer r e s o l u t i o n . The e l e c t r i c 23 f i e l d s of strong highlights i n the target can also bend the electron beam, causing geometrical d i s t o r t i o n s and hence photometric errors. (iv) Hon-linear response. In addition to a low dynamic range, many of the electron-beam readout tubes have a non-linear response which has to be c a r e f u l l y calibrated (Crane 1973). (v) Beam-discharge l a g . The photocathode or target of t e l e -v i s i o n cameras i n many cases i s not completely discharged by a single sweep of the electron beam, thus leaving a "memory" of the s i g n a l . Special scans are required between the taking of images to remove lag. (vi) Threshold e f f e c t s . Very low signals i n many cases are not f u l l y detected. This reguires "preflashing" as part of a preparation cycle to set up a baseline above which the response i s reasonably l i n e a r . This baseline i s d i f f i c u l t to measure. (vii) Large bulk and d i f f i c u l t cooling,. Most panoramic detectors have to be cooled to reduce the dark s i g n a l . The large bulk and large photocathode area of some detectors require very elaborate cooling equipment (e.g. Goldberg 1973). Temperature s t a b i l i t y i s d i f f i c u l t to achieve. ( v i i i ) Poor red response.. Most camera tubes have a low quantum e f f i c i e n c y in the red and infra-red. The s i l i c o n diode vidicon and integrated s i l i c o n diode arrays over-come this deficiency. 24 (ix) Mechanical and photoelectric f r a g i l i t y . The vacuum-tube structure of conventional television-type detectors often can rather e a s i l y be broken. Internal elements can become loose, making the tube "microphonic". Exposure to daylight w i l l ruin most tubes which employ amplification by electron emission, acceleration or bombardment. S i l i c o n diode vidicons and arrays do not have t h i s problem. The BETICON RA50x50 integrated diode array (IDA) was chosen to be incorporated in t o an area photometer. : I t embodied proven technology and the instrumentation development group at UBC was already working with one dimensional BETICON arrays. The advantages and disadvantages of the BETICON array are l i s t e d i n Table I . A good review of the use of integ-rated diode arrays in astronomy has been published by L i v i n g -ston (1976), while Heckler (1975) has given a d e t a i l e d review of t h e i r p r i n c i p l e s of operation. .. The BETICON uses s i l i c o n p-n junction photodiodes oper-ating i n a photon f l u x integrating mode (weckler 1967)., The diodes are i n i t i a l l y charged, at a reverse potential of about 5 volts. Incident photons generate charge c a r r i e r s which dis-charge the diodes at a rate proportional to the photon f l u x . Further discharging i s caused by thermal leakage. The diode i s re-charged at the end of the integration period, and the amount of charge reguired measures the integrated photon f l u x . 25 BLE I . Advantages and disadvantages of RETICON RA50x50 compared with electron beam readout tubes and other so l i d - s t a t e detectors (cf. Livingston 1976). Advantages Large charge storage capacity and dynamic range. Geometric s t a b i l i t y and uniformity. Smallness of sensor elements. Compact size of whole detector. Easily cooled and recycled. Low driving voltages: detector can be handled in daylight. No threshold. Excellent l i n e a r i t y of response. Low dark current when cooled to dry ice or l i g u i d N z temperatures. Very high guantum e f f i c i e n c y , e s p e c i a l l y in the red and i n f r a - r e d . Wide spectral useful response (4000-10,000A°). Low cross-talk between elements. Uniform diode response. Blue response higher than CCD and CID devices. Disadvantages High video l i n e capacity leading to high read-out noise. Small number of sensor elements. Opague masking by conductors leading to "dead spaces" between diodes. Loss of near infra-red response at low temperatures . ( < - 1 0 Q O C ) Low u l t r a - v i o l e t response compared with photo-electric devices. 26 The BET ICON uses a double- FET "AND11 gate as a switch with each diode i n the array. Each photodiode i s sequentially re-charged through a single video l i n e by being i n d i v i d u a l l y switched one at a time into the video l i n e , as shown in Figure 1 (see White 1976b). The charge pulse from each photodiode i s amplified and d i g i t i z e d using external c i r c u i t r y . The main sources of noise i n IDA detectors such as the BETICON have been summarized by White(1976a, b). These are Johnson-Hyguist or "kTC" noise, shot noise, and the preamp-l i f i e r noise current. Because the RA50x50 has a high video l i n e capacitance (100 to 20 0 pF), the preamplifier noise current i s the p r i n c i p a l source of noise in the system. The lowest noise to be expected i s eguivalent to about 2000 electrons or "charge c a r r i e r s " per diode per readout. 2 a 2 System Design. The design of the two-dimensional BETICON camera system followed the proven pr i n c i p l e s of the image isocon and l i n e a r BETICON systems developed at UBC ( Buchholz et a l . 1973, Walker et a l ^ 1974, Walker et a L 1976). The detector elec t r o n i c s were developed by V.Buchholz, the d i g i t a l e lectronics by D.Lane-Wright and B.Isherwocd, and the mech-anical and o p t i c a l parts by the author. The computer software was developed by the author, with some subroutines written by B.I.Olson and J.W.Glaspey. The system i s i l l u s t r a t e d in block HORIZONTAL SHIFT REGISTER LINE STRRT DflTfl CLOCK ^ END OF LINE LINE CLOCK FRAME START VERTICAL SHIFT REGISTER COMMON (TO EVERY CELL) *—1 VIDEO (TO EVERY CELL) END OF FRAME 1. Schematic C i r c u i t of RETICON two-dimensional diode array (after White 1976b, and WecKler, RETICON Corp.) On T e l e s c o p e — - ^ f flCold Box Detector Filter Amp Driving & Control Mag. Tape Q O INTERDATAI 7/16 or Model 4 Front Panel Sample & Hold ADC 4 _ 1 Control & Formatting 4 Clock FIGURE 2. Schematic Diagram of Area Photometer. CO 29 diagram form in Figure 2. Detector Housing and Cooling. A standard Products for Research photomultiplier cold-box (PE-200-RF) was adapted to house the RETICON RA50x5 0. A cooling mixture of methanol and carbon-dioxide "dry i c e " keeps the i n t e r i o r of the cold-box at a temperature of -76° Celsius at sea l e v e l . At the al t i t u d e of Mauna Kea, 1205 metres, the cooling s l u r r y maintains a temperature of about -82°C. A heavy plug of epoxy doped with alumina was used to f i l l the space normally occupied by the photomultiplier. This plug was made so as to minimize e l e c t r i c a l conduction and to maximize thermal conduction and thermal capacity. This was needed to minimize capacitative couplings and to maximize the tempera-ture s t a b i l i t y of the detector. Experience with the l i n e a r arrays had shown that the alumina-doped epoxy s a t i s f i e d these requirements. The alumina was mixed i n t o the epoxy prior to hardening, i n the proportions of 55% alumina, 34% epoxy resin and 11% hardener, by weight. The epoxy used was "Power-Bond A", pro-duced by In d u s t r i a l Formulators of Canada. The alumina was dehydrated by applying strong heat to the powdered alumina before mixing i t into the r e s i n . A f a i r l y coarse grade of alumina was used to make the mixing easy. The socket seating for the detector was fabricated at the 30 same time, with sixteen p a r a l l e l conductors from the detector seat to the rear of the plug also cemented i n the plug. The video l i n e was shielded by using a t h i n coaxial cable and extra Teflon i n s u l a t i o n . The amplifier and integrator were b u i l t into a compartment at the back of the cold-box, i n the space normally occupied by the dynode r e s i s t o r chain of a photo-electric photometer. The sample and hold, the 12-bit analog-to-digital converter (ADC) and some driving c i r c u i t s were mounted i n a container bolted to the side of the cold-box. Figure 3 shows the i n t e r n a l layout of the camera housing. ; Before use, the camera must be flushed with dry nitrogen to prevent moisture condensation a f t e r dry ice i s added to the methanol i n the coolant compartment. Rubber ring seals were i n s t a l l e d at the front and back of the camera. A p l a s t i c tube c a r r i e s the incoming dry nitrogen to the front of the camera; the nitrogen then flows back through other tubes and holes to an exit pressure r e l i e f valve at the rear. Flushing for a half hour before cooling down has always proved adequate, and no f r o s t i n g problems have been known to occur. A double-pane guartz window i s mounted i n front of the RETICON , with a standard 3 watt heatinq c o i l on the front to prevent condensation. A simple f i l t e r s l i d e arrangement bolts to the front of the cold-box, and the whole camera i s belted or screwed onto an adapter or o f f s e t guider, depending on the telescope on which i t i s being used. The OBC o f f s e t guider i s C O O L A N T UHMlim H E A T E R E P O X Y a ALUMINA-n , 1 9 r - - - _ _ _ ^ CONDUCTORS TO AMP., DRIVERS N, 'finmmtrn J^-. ! ->- :^ •r)rrs'jirrjrr •RETICON flC> -4—t% I I T H E R M O -P A N E W I N D O W 3. I n t e r n a l Layout of Camera Housing (to s c a l e ) . 32 used for setting the camera onto objects as well as f o r guiding. Camera Control. The UBC BETICON BA50x50 camera i s controlled by a hard--wired unit which generates the clock and driv i n g pulses and the exposure time (Walker et a l . -. 1974). The scanning rate i s 2KHz, so that an i n t e r v a l of 1.25 seconds i s needed to read out the array. The control unit also has power supplies for the various voltages needed by the detector and associated c i r c u i t r y . The reverse bias voltage for resetting the photo-diodes i s supplied by four rechargeable nickel-cadmium c e l l s mounted at the side of the cold-box i t s e l f . Data Acquisition. The control unit also formats the s e r i a l output from the 12-bit ADC into 16-bit p a r a l l e l form., Words of 16 b i t s per detector element are read i n t o the core memory of an INTEBDATA minicomputer v i a a direct memory access interface. The mini-computer has a passive r o l e , accepting data under the control of the control unit. Once the f u l l 2500 elements of an image have been read into core, the minicomputer records the data on 9-track magnetic tape and performs elementary on-line process-ing and display functions. The image i s displayed i n a dot-density format on an oscilloscope. Before a meaningful image can be displayed, the fixed pattern must be subtracted. 33 The fixed pattern i s the fixed set of baseline signals which are caused by couplings between conductors in the camera and i n the detector i t s e l f . 2.3 Operating Software. Data acguisition i s performed by an INTERDATA Model 4 or an INTERDATA 7/16 minicomputer. Since either of the minicom-puters was sometimes unavailable, programmes were written and developed for both., The 7/16 has 16K bytes of core memory, allowing two images of 5000 bytes each to be stored i n the core memory simultaneously. One of the images i s a fixed pattern or dark measurement, which i s subtracted from sub-sequent images in the other area of core. The r e s u l t i s displayed on an oscilloscope. Programmes written by the author were cross-assembled using a FORTRAN code produced by R.D.Russell f o r the IBM 360 or 370 operating under the Michi-gan Terminal System (MTS). The assembled machine-language programmes were loaded in t o the INTERDATA minicomputers via the same magnetic tape unit as used for recording the data. The Model 4 has only 8K bytes of core, allowing only one image to be stored i n core at a time. Starting with an idea found in the tape handler for BOSS, an I NTERDATA operating system, I developed a technique whereby the fixed pattern or dark subtraction can be performed by reading data from the tape i n single bytes. As the tape moves ahead at normal 34 T a p e % . j DARK [ j O B J E C T j j DRRK ; STRRT WRITE DflTfl I 1 BACKSPACE J j RERD DK SKIP WRITE DK BflCKSPRCE ] RERD I SUBTRACT SKIP L BflCKSPRCE i j * STRRT I W R I T E N E W D K I STOP STOP flGnfiE Recording of Model H. Small sequence at new dark or fixed pattern, Data on Tape Using the INTERDATA lower l e f t i s for recording a 35 reading speed, i n t e r v a l s of time between the reading of bytes from the tape are occupied by calculations and manipulations, allowing the subtraction of the fixed pattern. Figure 4 shows the sequence of tape operations needed to write an image as one record on the tape. Table II shows an -INTE.RD.4Tft Assembler l i s t i n g of the dynamic dark subtraction section of the Model 4 programme. I t should be noted that the "dynamic subtraction" technique reguires a l l interrupts to be disabled while the tape drive i s moving. A s i m i l a r technique has been used on the 7/16 for byte by byte v e r i f i c a t i o n of data a f t e r writing onto tape. The 7/16 programme i s based on the Model 4 code, but i s simpler because i t does not require an elaborate technique for subtracting the fix e d pattern. Completion of a v i s u a l display unit and keyboard has permitted subsequent workers to add many useful i n t e r a c t i v e features to the observing programme. 2 A4"System Performance^ The performance of the RETICON area photometer was eval-uated from data taken during observing runs, and more detailed analyses are given i n Chapters 4 and 5. some c h a r a c t e r i s t i c s are summarized i n Table III . i These and other c h a r a c t e r i s t i c s are discussed below: i i i S e n s i t i v i t y : Using the " c i r c u l a r aperture" r e s u l t s from Chapters 4 and 5, s e n s i t i v i t i e s through the V passband were 36 TABLE II . Dark subtraction code for INTERDATA Model 4. * * * INTERDATA MODEL 4 CODE RETICON AREA PHOTOMETER. ********* SECTION OF OBSERVING PROGRAMME : SOBTRACTION OF DARK. ***** SET OP REGISTERS FOR ********* LHI R6,MTR LHI R12,BYTE2 LHI R13,ARRAY LHI R13,X»0002* SHR R13,R14 SET UP REGISTERS BEFORE LHI R8,MTDAT LHI R9,X«0001« LHR R10,R13 AHR R10/R9 READ S IGNORE THE 4 0 BAL LHI OC SSR BTC RDR BXLE XHR DYNAMIC READING AND MTR BYTE2 * * EXIT TAPE CARRY SSR BTCR 1DR STH SLHL AHR LH SSR BTCR RDR OHR SHR CLHR BTCR FROM STH DYNAMIC SUBTRACTION OF DARK. ADRS.OF 1ST BYTE LOOP. ADRS.OF 2ND BYTE LOOP. A DRS. OF ARRAY, AND COUNTER. HALFWORD ADDRESS INCREMENT = 2. ALLOW FOR,EXTRA HALFWORD. SKIPPING THE 40-BYTE LABEL. ******* LOAD ADDRESS OF LABEL IN CORE. LOAD BYTE ADDRESS INCREMENT. LOAD END HW. ADDRESS OF LABEL. INCREMENT TO GIVE END BYTE ADDRS. LABEL BYTES. ************************* CALL "WAIT" TO STOP TAPE DRIVE. LOAD END ADDRESS OF ARRAY. START TAPE READING MOTION. STILL BUSY OR READING A BYTE ? BRANCH BACK IF YES. READ A BYTE. LOOP BACK IF STILL IN LABEL. ZERO REGISTER (8) . SUBTRACTION OF DARK CURRENT. ********** STILL BUSY READING ? LOOP BACK IF STILL BUSY. READ FIRST BYTE OF A HALFWORD. STORE PREVIOUSLY COMBINED HALF WORD. SHIFT FIRST BYTE LEFT BY 8 BITS. INCREMENT ADDRESS COUNTER BY 2. LOAD DARK CURRENT VALUE INTO REG STILL BUSY READING ? LOOP BACK IF YES. READ THE SECOND BYTE OF HALFWORD. COMBINE FIST AND SECOND BYTES. SUBTRACT DARK CURRENT VALUE. COMPARE COUNTER WITH FINAL ADDRESS BRANCH TO "MTR" IF COUNTER LOW. LOOP ******************************************* R8,0{R13) STORE FINAL HALF WORD IN ARRAY. R15,WAIT R15,ENDHW MT,R EAD MT,STAT 8,*-2 MT,R7 R8,*-8 R8,R8 MT,STAT 8,R6 MT,R7 B 8 , 0 ( R 1 3 ) R7,8 R13,R14 R10,0 (R13) MT,STAT 8,R12 MT,R8 R8,R7 R8#R 10 R13,R15 8,R6 13 DRIVE WILL STOP BY ITSELF NOW. ********************** ON WITH OTHER PROCESSING. ************************** 37 TABLE III . Performance c h a r a c t e r i s t i c s of BETICON area photometer. Ch ar a c t e r i s t i c S i t e Numerical Value Total S e n s i t i v i t y i n V Passband for V=0 object. Random Noise Baseline f l u c t u a t i o n Average Dark Signal Maximum Dark Signal Fraction of Diodes with Dark > 2 x average. Saturation Signal (approx.) Saturation Charge per Diode 1 } MKO DAO MKO DAO MKO DAO DAO DAO DAO 8x10 7units/min. 2x10 7units/min. ±1.8units(s.d.) ±1. 8units (s.d.) ±3units(p.p.) ±1unit (p.p.) 0.3 units/min. 5.2 units/min. 3 % 1000 units 5 x 10' electrons 1. Manufacturer*s s p e c i f i c a t i o n s . MKO: 2.2 Metre Cassegrain. DAO: 1.8 Metre Broken Cassegrain. 38 obtained by comparison with published observations. Allowing for the d i f f e r e n t telescope sizes, the camera was about 2.5 times more se n s i t i v e on the 2.2 metre telescope at Mauna Kea than on the 1.8 metre telescope at V i c t o r i a . This difference was due partly to the arrangement and poor coating of the ter-t i a r y mirror i n the 1.8 metre telescope, and partly to the difference i n atmospheric extinction. Otherwise, the s e n s i t i v i t y difference i s hard to explain. ( i i ) Noise: The random diode to diode noise was 1.8 ADC units, or approximately 8000 electrons. A major contributor was d i g i t i z a t i o n b i t noise, since the analogue sig n a l was observed to have a lower noise. An attempt to increase the gain without increasing the noise was unsuccessful at the time of the observations undertaken for t h i s work. The problem was corrected l a t e r . The random noise i s defined as the root mean sguare (r.m.s.) of the difference between two dark integ-rations of egual duration with average (baseline) d r i f t being f i r s t l y removed. The noise for a single frame would therefore be 1/7? of t h i s , but would not be very meaningful because the fixed pattern always must be subtracted. The maximum possible s i g n a l to noise r a t i o at half saturation i s therefore about 250, where only the random noise remaining after subtraction of a fixed pattern integration i s considered. The formal detective quantum e f f i c i e n c y , DQE, of the detector can be written as, 39 where: £ = {sensitive area} / {total area} = 0.5, ^ = guantum e f f i c i e n c y = 0.8(max.), <MTF> = an average value of the MTF, such that <MTF>—2 i s the e f f e c t i v e number of diodes i n a seeing image, P = incident photon f l u x , N = noise introduced by charge extraction and am p l i f i -cation. For a star image with a diameter of 2 diode units, I assume <HTF>=0.--5. With N=8000 electrons, DQE = 0.06%, 0,6%, 1.5%, and 2.9% f o r P= 10*, 10 7, 2. 5X10 7 and 5x10? photons respectively. With =0.4 and <MTF>=0.5, half saturation corresponds to 2.5x107 photons from a seeing-broadened point source incident upon the surface of the detector. For a continuous d i s t r i b u t i o n rather than a star image, we have e f f e c t i v e l y <MTF>=1.0 and at. half saturation DQE=5.4%. The DQE at half saturation could be as high as 30% i f the noise N were reduced to about 2000 electrons, The present DQE i s rather low because of the high 40 read-out and d i g i t i z a t i o n noise. By comparison, the OBC Isocon system has a detective guantum e f f i c i e n c y of about 5% at 4100A°, and a s i l i c o n diode vidicon has been operated at a DQE of 1 to 2% (Buchholz &t aj^. 1973). However, the BETICON has much higher dynamic range and red response than the Isocon, and i t i s geometrically and photometrically more stable than the Vidicon. These and other c h a r a c t e r i s t i c s are not f u l l y included in the DQE figure of merit discussed here, ( i i i ) Stability, of the Baseline; The average fixed pattern fluctuated while the random diode to diode noise d i s t r i b u t i o n remained constant. The baseline uncertainty between success-ive exposures was ±3 ADC units at Hauna Kea, ±1 unit at V i c t o r i a . Over periods of hours the baseline d r i f t e d by a few units i n a non-uniform manner. The difference between two fixed-pattern exposures taken far apart sometimes looks l i k e a grid of v e r t i c a l bars. I t i s important to take fixed-pattern exposures freguently, or immediately af t e r long exposures. Because the baseline fluctuation i s of the same order of magnitude as the random noise, not much i s to be gained from averaging a number of fixed-pattern integrations. It was found that for integrations of l e s s than one min-ute, the fixed pattern d i f f e r e d from longer fixed pattern integrations, indicating a s e t t l i n g time of about one minute. Thus observations of more than one minute exposure time reguired a one minute fixed pattern integration, while short observations of l e s s than one minute reguired corresponding 41 fixed-pattern integrations of the same duration, (iv) Bark current: A discussion of the measurements w i l l be given in chapter 5.. At an indicated detector temperature of -76°C, the average dark current was 0.3 ADC units per minute, or about 25 charge c a r r i e r s per second. About 3% of the diodes were "hot", having a dark s i g n a l rate of between 0.6 and 5.2 instrumental (ADC) units per minute. For integrations of a half hour or le s s , the dark current rate was found to be constant within the l i m i t s of s i n g l e measurements. This l i n e a r i t y i s not expected for longer integrations or larger dark current rates (Heckler 1967, Dravins 1975). <v) L i n e a r i t y : S i l i c o n diodes are known to have a very l i n e a r dependance of sig n a l charge with respect to l i g h t i ntensity over a wide range when used i n the integrating mode (Heckler 1967). One-dimensional BETICON arrays have generally been found to have a l i n e a r i t y of better than 1% up to the satur-ation l e v e l (Horlick and Codding 1973, Hog and Hiskott 1974, Buchholz 1974, Dravins 1975) , and even to within 0.255J (Campbell 1977). The system developed for t h i s work uses s i g -nal amplification and d i g i t i z a t i o n c i r c u i t r y very s i m i l a r to that used by Buchholz (1974), while the manufacturer s p e c i f i e s the same l i n e a r i t y c h a r a c t e r i s t i c s for the BA50x50 as for the l i n e a r arrays. I therefore assume that the device i s l i n e a r within the errors of measurement. The "circular-aperture" r e s u l t s of Chapter 4, i n p a r t i c u l a r , support this conclusion., H2 F l a t f i e l d • response: The large scale (edge to centre, or edge to edge) va r i a t i o n within the f l a t f i e l d c a l i b r a t i o n exposures was up to ±10% of the average s i g n a l . This depended on the telescope, the vignetting ( i f any), etc. The small scale (diode to diode) variation of about ±3%, which was greater than the random noise. This meant that the f l a t f i e l d c a l i b r a t i o n had to be applied diode by diode without smoothing or running averages. The dusk or dawn sky was generally used as the f l a t f i e l d . The short time during which the sky was of suitable brightness l i m i t e d the number of exposures which could be summed to obtain an averaged f l a t f i e l d c a l i b r a t i o n through each f i l t e r . (vii) S patial freguency response: The s p a t i a l frequency c h a r a c t e r i s t i c s of the detector w i l l be given a f u l l theoret-i c a l discussion i n Chapter 3. The exact diode s e n s i t i v i t y p r o f i l e i s not very important for the f a i r l y poor seeing of the observations reported i n t h i s work. A detailed laboratory study using a laser or other narrow beam of l i g h t has been carried out by Geary (1976) for a l i n e a r BETICON , but has not been attempted here. Star images are used to obtain the t o t a l transfer function or seeing p r o f i l e , which includes i n s t r u -mental e f f e c t s . Observations at coarser plate scales show that charge spread or "blooming" i s found only when charge saturation of diodes occurs. "Lag" or charge persistence after readout i s also found only when saturation occurs. Geary (1976) reported that at wavelengths beyond 9000A an increase of the point spread function was to be found i n RETICON detectors. This i s not important here since only the B, V and R passbands have been used. The diode s e n s i t i v i t y p r o f i l e becomes wider because at very low temperatures s i l i c o n becomes more transparent, excessively so at long wavelengths. 2^ .5 Optical F i l t e r s . Broad-band absorption f i l t e r s were chosen to reproduce as clo s e l y as possible the Johnson OBVRI passbands (Johnson 1965)., The BVR combinations are l i s t e d i n table IV . The manufacturers* curves were combined and compared with the curves published by Johnson, and the glasses were selected accordingly. The f i l t e r passband curves, including the RETICON response, are shown in Figure 5, together with the curves of Johnson (1965). The results of t h i s work are i n s u f f i c i e n t to show whether the f i l t e r combination used here i s superior to that chosen by de Lara et a l . (1977) for a s i l i c o n diode photometer. More ca l i b r a t e d work with s i l i c o n diode photometers i s needed to decide on the best choice of f i l t e r s to approximate the Johnson system. An important prob-lem i s the presence of small red-leaks i n the B and V passbands with the f i l t e r s used here. .The leaks are d i f f i c u l t to eliminate using standard absorption glasses without i n t r o -ducing a large amount of absorption within the desired passband. The wide sp e c t r a l response of s i l i c o n diodes makes t h i s a worse problem than i n conventional photometry. TABLE I? . Broad-band o p t i c a l f i l t e r s . Pass- CS or KG Glass Thickness Band No. m. m. eff A CS-5-61 5562 4400 1100 V CS-3-70 3384 CS-4-97 9788 4 5 5550 1050 CS-2-73 2434 KG-3 3 2 6600 1400 1. F i l t e r transmission and detector response. (Based on manufacturers 1 data). E f f e c t i v e wavelength i s middle of half-maxima points. Pass-band i s wavelength i n t e r -val between half-maxima points. Wavelength in Microns. ZIG-URE 5« Optical f i l t e r passbands, combininq manufacturers* data for f i l t e r transmission and RETTCON response. Relative transmission plotted (s o l i d l i n e ) . Broken l i n e represents standard curves of Johnson (1965). 46 CHAPTER .3 DATA ANALYSIS THEORY AND METHODS 3«L1 General Concepts For Diode Arrays. •-In addition to having greater geometrical s t a b i l i t y than electron-beam readout detectors, the s o l i d - s t a t e diode arrays such as the RETICON RA50x50 have much more discrete and better defined sampling elements. The spreading of the electron beam and other e f f e c t s i n conventional t e l e v i s i o n cameras l i s t e d i n Chapter 2 lead to an overlapping of sampling i n t e r v a l s r e s u l t i n g i n "oversampling" (Fischel 1976). In devices such as the RETICON series of self-scanned arrays, there i s much less spreading, and the overlap of sampling elements i s complementary, i . e . the t o t a l charge extracted i s proportional to the t o t a l incident l i g h t (Geary 1975). The two-dimensional arrangement of the RA50x50 reguires op-ague metal conductors to l i e alongside the s i l i c o n diodes, thus obscuring portions of the s i l i c o n substrate. This feature i s also shared by the front-illuminated charge-coupled devices such as the F a i r c h i l d CCD211 (F a i r c h i l d Corp. 1S76), but can be eliminated using the back-illuminated arrangement which, however, involves d i f f i c u l t fabrication methods ( A n t c l i f f e 1975). While detailed laboratory measurements and c a l i b r a t i o n of the device would be most desirable, such a study i s beyond the scope of t h i s work. Geary (1975), Buchholz et a l . (1974) and Campbell (1976), among others, have found RETiCON devices to be l i n e a r to better than 1% oyer t h e i r working range. Geary (1976) has measured the s p a t i a l s e n s i t i v i t y p r o f i l e (or data window) of i n d i v i d u a l diodes in linear arrays, finding agreement with the manufacturer's 's s p e c i f i c a t i o n s except at low temperatures {near l i q u i d nitrogen) and at wavelengths greater than 9000 Angstroms. A t h e o r e t i c a l study i s outlined in the next section, suggesting ways of reducing errors i n the taking of observations. 3..2 Theoretical Analysis Of Array. Spatial Frequency Response. . The i n d i v i d u a l diodes of the RETICON RA5 0x50 are arranged in a sguare matrix, with separations of 4 mils (101.6 microns) between diodes in the X and Y dimensions., Approximately 50% of the t o t a l area i s obscured by metal conductors. We s h a l l assume for our theoretical model a centre-to-centre separation distance D, with each diode having a rectangular sensitive area a by b, with Without loss of generality, the s e n s i t i v i t y i s assumed to be 100% i n the l i v e area and 0 over the dead area. In two dimensions, the in d i v i d u a l diode aperture can be represented by (7) 48 where IT i s the box-car function (Bracewe.ll 1959, p.243). The in d i v i d u a l diode aperture function i s the data wiudgw i n t h i s sampling problem. I f the i n d i v i d u a l diode "aperture function" cannot be represented by a simple box-car, but rather has a truncated pyramid shape, the higher freguency response w i l l be more attenuated since extra "sine" terms w i l l be involved in the product i n eguation 20. Thus the rectangular "box-car*1 i s probably a worst-case representation of the data window. Most technical papers on television-type detectors employ the concepts of the square-wave amplitude response (SwAR), sinc-wave response, or point-spread function (PSF) to describe the s p a t i a l modulation transfer function (MTF). However, i n astronomy resolution i s normally limited by seeing or an o p t i c a l instrumental function. We shal}. use a Gaussian representation for the seeing or o p t i c a l p r o f i l e , and observa-tions described in Chapters 4 and 5 confirm the f i r s t - o r d e r accuracy of t h i s approximation. The d e s i r a b i l i t y of using a Gaussian instrumental function for t h i s type of analysis has been pointed out by Anger et a l . (1973), who treated a very similar problem involving a scanning auroral photometer. Se define A as the diameter of the isophote for an i n t e n s i t y which i s 1/e times the c e n t r a l intensity of the seeing p r o f i l e 49 (or star image), which i s represented by where (c,d) i s the position of the centre of the star image, as indicated in Figure 6. a l l features i n an image prior to detection are convolved with the c i r c u l a r l y symmetric normalized seeing function, A(~,j) = A *r\:r[*x*$)] •  <1°> The s i g n a l f(x,y) obtained from each diode can be thought of as the cross-correlation of the star image and the i n d i v i d u a l diode function d(x,y), the cross-correlation being sampled at discrete egui-spaced points which can be represented by an i n f i n i t e two-dimensional Dirac comb, which i s the product of two orthogonal one-dimensional Dirac combs, *LLJ(?,f)= LLl(f)LLj(t) . The e f f e c t s of having a f i n i t e array w i l l be discussed l a t e r . The s i g n a l (x,y) obtained by observing a Gaussian star image as given by eguation (10) can therefore be written as : h*.z)-\\^-*>Y!s)<(r^Y*$>$) (12> Now since the functions d(x,y) and i(x,y) are symmetric in x and y about th e i r centres, we can replace the cross-correlation i n t e g r a l by the convolution i n t e g r a l ; -5> A ( x , y ) (<£— A —H X ty IP P »e— a TT(x,y) 2 2 X • • • • • • • • • • • • olDfe— UJ (x, y) A * * A fi* Detector sampling configuration, showing Gaussian star image, diode sampling window and diode array arrangement. 51 <13) (14) which now has the same form as the expression used by Fi s c h e l (1976) . We need to obtain the s p a t i a l frequency response function as a function of seeing disk s i z e A and diode spacing D, given the diode aperture dimensions (a,b) and " s t a r " position (c,d). Applying the standard theorems (Bracewell, 1959, p. 244) , eguation 14 i s Fourier transformed to where D (u,v) i s the transform of the diode aperture function, and I(u,v) i s the transform of the seeing p r o f i l e or s t e l l a r image. We write, The convolution with the shah symbol l U l ( ] ) ^ D v j i n the (u,v), or freguency, plane i s a r e p l i c a t i o n and l o c a l summation which i s the mathematical form of a l i a s i n g . Equation (15) can be (15) so that 52 w r i t t e n as <18) v V U ' J? / Without l o s s of g e n e r a l i t y , l e t us assume the value of the se e i n g p r o f i l e i s u n i t y , i . e . /. .„ r Then R(u,v) can be expanded as Jo . £<kjK? £ ~ ' ? 7 7 ' / + < !'' ,'yj '^Z^c ^*t.c [-^^ ^ {20} where s i n c ( x ) = s i n f?rx) / (irx) . The f i n i t e s i z e L by L of the d e t e c t o r can be expressed as a l a r g e box-car f u n c t i o n i n two dimensions m u l t i p l y i n g the sample, so t h a t the sample can be w r i t t e n as The f i n i t e l ength sample f L ( x , y ) transforms t o . 53 ^ L • /Q^^[Lo^ y<U^C [LXT^ J . (22) Since L >> D, the sine functions are very sharp and the con-volution i n frequency space w i l l not appreciably broaden the Fourier transform. The f i n i t e s i z e e f f e c t w i l l be neglected from now on. In general, F(u,v) as defined i n eguation (18) i s a complex function. The t o t a l modulation transfer function (HTF) of the system, including both the seeing or o p t i c a l p r o f i l e and the detector geometry, can be c a l l e d the Gaussian response function (GRF) and can be written as, This includes the a l i a s i n g contribution. Indeed, the a l i a s i n g contribution £F(u,v) at a point (u,v) i n the freguency plane can be computed from. (24) and so, J k R F ( V ) . J>MI , ( 2 5 ) L J Uo.o) 54 How can we determine when i t i s possible to do accurate photometry of a star observed with a diode array detector? No w , \ ( ( c P ( 0 yOj =• fi>t^)d^du } (26) i . e . the zero-freguency value of the transform of the sample i s egual to the t o t a l i n t e g r a l of the sample. However, a l i a s i n g introduces errors into f(x,y), so a simple summation of the sample value f(x, , yj ) nay not give a true measure of the t o t a l i n t e n s i t y i n a s t e l l a r image. The value of £GBF(0,0) provides a measure of the accuracy with which the flux from a star may be determined, so that £GBF (0,0) can be c a l l e d the photometric error. At higher freguencies, £ G 8 F ( U , V ) gives the a l i a s i n g error at (u,v). This w i l l usually be worst at the Nyguist freguencies 1/(2D) » a number of examples have been computed. Figure 7 shows the behaviour of GBF(u,o) for a=0.9, b=0.6, D=1.0 and several values of seeing diameter .&. Table v l i s t s a corresponding set of values at the zero and Nyguist freguencies, with a comparison of the modulus of the unaliased Fourier transform B(u,v) with the aliased value |F(u,v) |. How does the GRF depend on the p o s i t i o n of the star image? Figure 8 shows a set of curves of GBF (u,v) for various displacements of the star image with respect to the Spatial Frequency FIGURE 7. E f f e c t of d i f f e r e n t s e e i n g diameters On Gaussian response f u n c t i o n ( t o t a l MTF) . TABLE v .' Aliased and unaliased Gaussian response functions ( t o t a l MTF), with a=0.9, b=0.6, c=d=0., D=1.0. .. SSfiSE numbers in each l i n e pair are R(u,v) (unaliased). Lower numbers are F(u,v), including a l i a s i n g for k,m=-1,0,1 Total s i g n a l loss due to 54% l i v e area r a t i o included. Seeing Spatial Freguency (u,v) A/D (0.,0.) (0.5,0.0) (0.,0.5) (0.5,0.5) 0.5 0.5400 0.3234 0.3973 0.2379 0.9324 0.9551 0.9048 0.9268 1.0 0. 5400 0.2036 0.2 501 0.0943 0.5971 0.4415 0.5098 0. 3770 1.5 0.0942 0.1157 0.0202 0.5426 0.1891 0.2316 0.0807 2.0 0.5400 0.0320 0.0393 0.0023 0.5400 0.0640 0.0786 0. 00 93 2. 5 0.5400 0.0080 0.009 8 0.0001 0.5400 0.0160 0.0196 0.0006 3.0 0. 5400 0.0015 0.0018 0.0000 0.5400 0.0029 0.0036 0.0000 4.0 0.5400 0.0000 0. 0. 0.5400 0.0000 0. 0. 0-0 0-5 Spatial Frequency IIlzUH a« E f f e c t of s t a r image displacement on Gaussian response f u n c t i o n ( t o t a l M T F ) . Dashed l i n e r e p r e s e n t s a l i a s i n g c o n t r i b u t i o n to zero-displacement case. 58 centre of a diode. We see that for A=1.0 the GRF varies only at the high frequency end. For A/D > 2.5, the e f f e c t s are almost i n s i g n i f i c a n t . I t i s also very i n t e r e s t i n g that for A>2.0, the diode spacing rather than the dead area i s the dominant parameter i n determining the GRF. Figure 9 shows that at very low freguencies there i s l i t t l e difference between the Fourier transforms R(u #v) fo r l i v e areas covering 15? and 100% respectively of the detector's surface. This re s u l t follows an a y t i c a l l y and was also tested using the simulated star image computed by invoking the instruction STAR in the FIRM code. Different displacements (c, d) of the star image gave s i m i l a r r e s u l t s . 3.3 Technigues For Avoiding Aliasing. As demonstrated in section 3.2, "photometry" of 1% or better accuracy i s possible i f the r a t i o of seeing disk diameter to diode centfe-to-centre spacing i s greater than or egual to 2.0 ., Geometrical d i s t o r t i o n s at a l l freguencies below the Nyguist are e s s e n t i a l l y absent for A/D > 2.5. These c r i t e r i a are almost independent of the r a t i o of " l i v e " detector area to "dead" area. Thus, i f one can match the diode spacing, the telescope plate scale and the l o c a l seeing properly so that the above c r i t e r i a are met, there i s no need to be concerned by a l i a s i n g . For example, the 1.8 metre FiGtjRE 9. E f f e c t of Read Space on Gaussian response f u n c t i o n ( t o t a l KTF).~ Curves correspond to 1 0 0 % and ^% f r a c t i o n a l s e n s i t i v e a r e a , f o r y, a = 1 . 0 and a = 0 . 1 r e s p e c t i v e l y . *° 60 r e f l e c t o r at the D.A.O., V i c t o r i a has a Cassegrain plate scale of 6 arc seconds per millimetre, corresponding to approximately 0.6 arc seconds per BETICON diode. The " l i m i t i n g " seeing i s therefore 1.2 arc seconds, a sharpness rarely achieved at t h i s s i t e . If the seeing i s better than the l i m i t i n g seeing, problems w i l l follow i f one attempts to observe an object which i n t r i n s i c a l l y has high s p a t i a l freguency features. I f A/D < 2.0 and s t a r - l i k e features are observed, meaningful area photometry can only be obtained by " p r e - f i l t e r i n g " the image before i t impinges upon the detector. In optics t h i s i s c a l l e d apodization and can be achieved by s u i t a b l e design of aspheric lenses, mirrors, or s l i t s (Blackman and Tukey, 1959; p. 100). It i s obvious that a Gaussian or s i m i l a r apodizing function can simulate seeing and s a t i s f y the a l i a s i n g c r i t e r i o n . However, t h i s i s l i k e l y to be an expensive method, so therefore other technigues should be examined. An obvious candidate i s de-focussiing of the image. A crude representation of de-focussing i s the c i r c u l a r box-car function TH) (r) , which has a simple Hankel transform: where r = J|X2+ y 2' i s the r a d i a l coordinate, a i s the radius of the c i r c u l a r box-car function and g = /Ju2+v2* i s the r a d i a l freguency. The function J ( (x) i s the Bessel function of order 1. The unaliased t r a n s f e r function becomes: 61 {28} where P = 2a i s the diameter of the defocussing function, and the volume of the function i s unity . Calculations of the t o t a l FITF (or GRF) involving c i r c u l a r defocussing showed that even for P/D = 5 the best possible photometric accuracy was no better than 1%. The conclusion i s that defocussing i s an inadeguate p r e f i l t e r i n g method especially i f a central obscuration i s present. However, i t does sharply reduce a l i a s i n g i f A/D << 1.0, and may in some cases be necessary. Some of the problems can be overcome using sguare apertures or b a f f l e s i n the collimated beam. For example, a sguare aperture can be placed over the front of the telescope , with a sguare baffle over the rear of the secondary, such that the defocussed image w i l l be a sguare with a sguare hole at the centre. To f u l l y eliminate a l i a s i n g at zero freguency, the size of the defocussed image of a point source must be an i n t e g r a l multiple of the diode spacing, as must be the siz e of the sguare hole at i t s centre. This i s not an e f f i c i e n t technigue, as well as being somewhat unpract-i c a l for large telescopes. The d e s i r a b i l i t y of a sguare convolving function suggests the following method. A very promising technigue i s scanning the image across the detector i n some c a r e f u l l y controlled manner. An example of t h i s i s the electron beam scanning method used by Beaver et 62 a i i (1972). In the o p t i c a l case, the image can be scanned in two dimensions using r e f r a c t i n g plates as in the scheme i l l u s t r a t e d i n Figure 10. Such a system has not been constructed, but i t s p r i n c i p l e s need to be discussed. The aim of scanning i s to simulate a box-car convolving f i l t e r by having each point of the image spend an egual time on the sensitive f r a c t i o n of the detector. This i s accomplished by moving the image i n a raster pattern as shown in Figure 10. F i l t e r s other than the box-car are possible but are much more d i f f i c u l t to r e a l i s e . The same e f f e c t can be produced by scanning the telescope i t s e l f in a raster pattern. Care must be taken that the scan i s uniform and that the telescope does not dwell at the turning points. The i n e r t i a of a large telescoe makes such a uniform raster d i f f i c u l t to achieve. The size of the raster should be an exact multiple of the diode spacing D, so that the equal-time condition holds. This condition can be understood i n the s p a t i a l freguency domain as the requirement that the zeroes of the convolving function be made to f a l l at a l l i n t e g r a l frequencies. An attempt was made to perform computer-controlled 10 arc second square raster scans with the 2.2 metre telescope of the Mauna Kea Observatory, but equipment problems prevented the use of the method durinq observations. This technigue i s worth further tests with more r e l i a b l e eguipment. Alternative 63 I I£UR£ 1 0 . Raster Scanninq to reduce a l i a s i n g . Proposed system would use two t i l t i n q r e f r a c t i n g p l a t e s to make every p o i n t of image execute a r a s t e r over the d e t e c t o r . 64 techniques would involve moving the detector but not the telescope, or moving the secondary mirror. Both these tech-niques would introduce p a r t i c u l a r problems, and would reguire new and very precise hardware. The scanning procedure can be mathematically represented by {29) where n i s an integer. This transforms to, . 1*^7) ^ l ^ i ^ ^ j j • <30) The net e f f e c t of apodization by scanning i s to make a rectangular "boxcar" diode function more triangular i n the MTF or GRF, or "pyramidal", thus reducing the side lobes of i t s transform and therefore reducing the a l i a s i n g . At i n t e g r a l s p a t i a l freguencies zeroes are introduced, thus eliminating a l i a s i n g at zero freguency. Small-scale s e n s i t i v i t y i r r e g u l a r i t i e s , within each diode are also smoothed out, even i f there i s no dead space between diodes. The gain of reduced alassing must be balanced against the s l i g h t loss of resolu-tion caused by p r e - f i l t e r i n g or apodization. In the future, a l i a s i n g may not be a serious problem. 65 Back-illuminated" CCD*s, for example, have l i t t l e dead space between detector elements. Apodization techniques may never-theless be desirable for reducing inherent a l i a s i n g by c o n t r o l l i n g the instrumental p r o f i l e . (Inherent a l i a s i n g i s defined as the a l i a s i n g at higher s p a t i a l freguencies due to the shape of the diode response function, even without "dead spaces"). One obvious application i s the determination of star positions with high accuracy, as in astrometry. The r e s u l t s of Chapters 4 and 5 show that star positions could be determined to within 0.01D, unless limited by geometrical i r r e g u l a r i t i e s in the diode array. Signals are recorded on magnetic tape as outlined i n Chapter 2 A "frame" can be an object observation, a sky measurement, a dark current, a f l a t f i e l d or a short dark current measurement used as a "f i x e d pattern". The raw observations need to have the fixed pattern, dark and sky contributions subracted. The remainder i s then divided by the s i m i l a r l y reduced observation of a f l a t f i e l d . These are standard procedures of area photometry and have been described by Crane (1975). In mathematical form, for the i j - t h diode. d,. i s the dark current contribution for the same integration 3.4 P r i n c i p l e s Of Data Reduction. (31) where r...- i s the raw measurement, s,.- i s the sky contribution. 66 i n t e r v a l , p,-- i s the fixed pattern and f,•• i s the " f l a t f i e l d " i n t e n s i t y . The quantities s;j- , d,y, and f,- do not contain a fixed-pattern contribution. For short exposure times, i t i s possible to combine the dark, sky and fixed pattern into a single integration g,-^  such that, sr,', - - ^ V 7 fa— (32) J'J When the exposure time for the measurement r i s long, i t i s i n e f f i c i e n t to take as long to measure the sky background, since an average over a l l the diodes can be computed: whence (33) f / 'J <r*i - A - per <s> . ,3.) This cannot be applied to the subtraction of the dark current, which varies non-uniformly from diode to diode. The " f i e l d - f l a t t e n i n g " values f.< are suitably normalised, *<i " <V> J ( 3 5 ) where f are the i n t e n s i t i e s derived by observing a f l a t f i e l d such as the dusk or dawn sky, with the corresponding fixed pattern and dark contribution subtracted. The frame reduced via equations 31, 32 or 34 contains the 67 i n t e n s i t y d i s t r i b u t i o n of an image with some noise added. The noise performance of the RETICON area photometer has been described i n Chapter 2, and shows an approximately Gaussian d i s t r i b u t i o n of deviations from the mean under normal conditions. Standard signal processing technigues i n two dimensions can be applied to reduce the noise. While optimal Wiener f i l t e r i n g i s desirable (e.g. Arp and Lorre 1976), a simple c i r c u l a r Gaussian f i l t e r i s used in t h i s work. In some cases no f i l t e r i n g i s needed because the signal to noise r a t i o i s s u f f i c i e n t . The f i l t e r i n g procedure involves transforming the picture using a Fast Fourier Transform (FFT) routine, multiplying the transform by the transform of the f i l t e r and performing the inverse transform. A simple conical con-volution f i l t e r applied in the r e a l domain gives s i m i l a r r e s u l t s i n an egual or longer computation time. The FFT tech-nigue i s preferable because the image can also be moved simultaneously using the s h i f t theorem (Bracewell, 1959, p.244). Colour index or r a t i o maps are computed by re g i s t e r i n g two images and dividing. Model intensity d i s t r i b u t i o n s can be computed and subtracted to map the residuals. Simple operations and manipulations of picture data can be combined f o r sophisticated analysis of the data, for which a general and powerful computer code i s needed. 68 Ja.5 FIRM i An Ima_ge Processing Code. A number of astronomical picture-processing codes have been developed, such as the HIT code "HPS" {McCord et a l . , 1975), the Cal' Tech-JPL code "VICAR" (see Arp and Lorre, 1976 ), the K i t t Peak system (Wells 1975),and others (see: K l i n g l e -smith 1975; Nieuwenhuijzen 1975). A l l such codes depend on the hardware and software available at the i n s t i t u t i o n s where they were developed, so i t was decided to develop a seguential modular processing language for the f a c i l i t i e s at the Oniversity of B r i t i s h Columbia . This code i s c a l l e d FIRM (for Fortran Interactive Record Manipulation), and i s set up for the IBM 370/168 running under the Michigan Terminal System (MTS) with v i r t u a l memory. I t can be used either i n batch or in t e r a c t i v e mode, but the economics and turnaround speed at U.B.C. make the batch mode more a t t r a c t i v e . . Table VI l i s t s the operations performed by FIRM. A f u l l description of the code and i t s usage i s given i n Appendix I. The most important operations i n the f i n a l processing of reduced data are PLOT, FT, SECTION, ELLIPSE and STAR. The other operations such as ADD, DIV, etc, are elementary. The PLOT command causes a contour map to be generated using a modified version of UBC CNTOUR. The area and centroid of every closed contour are computed, and printed i f the e f f e c t i v e radius i s above some pre-defined lower l i m i t (usually 0.5 diode spacing units). The e f f e c t i v e radius r of 69 TABLE VI . Operations performed using FIRM , a FORTRAN Interactive Record Manipulation Language. Operation APERTURE ADD AI AVERAGE COLUMN DIVIDE EL LIPS E END EXAMINE AVERAGE LABELS HIST CATLG FT GRAPH INT LABEL LOAD MAG MI Function Integrate over a sguare aperture i n the f i e l d of view. Add two images. Add constant to each element of an image., Read from tape and average two or more raw images. Specify which columns "dead" or " l i v e " . Divide an image by another. Generate a model e l l i p s o i d a l d i s t r i -bution or generate a c i r c u l a r aperture. End processing and exit to MTS. Print averages and extreme values, print l a b e l s , plot a histogram, or print the output f i l e catalogue. Smoothing and/or s h i f t i n g via the FFT. Graph the value at each element of one picture versus the value of each corres-ponding element of a second picture. Convert magnitudes to i n t e n s i t y . , Label a picture already i n core memory. Read a raw data record from magnetic tape and load into core. Convert i n t e n s i t y into magnitudes. Multiply each element of picture by constant. Hove an image into a dif f e r e n t array i n core. Six arrays are available. Optionally, r e g i s t r a t i o n of images i s performed using b i - l i n e a r interpolation. Multiply two images. Plot a CALCOMP or printer contour map of an image. Prin t closed contour centroids and areas. Print the contents of an image array using the l i n e printer. , Read back a reduced image from the output tape. Define dead or l i v e rows. Plot a graph of the cross-section of an image along a straight l i n e or along an e l l i p t i c a l locus. (Synonym for MOVE ) Convolve a picture with a conical f i l t e r i n g p r o f i l e . Compute a Gaussian "star image" in t e n s i t y d i s t r i b u t i o n . Subtract an image from another image. Print a 10x10 matrix of numbers corresponding to a 50x50 image averaged in 5x5 blocks. Hrite an image as a record on the output tape. Enter l a b e l into catalogue. An operation to be defined by the user. 71 each contour i s defined as, (36) as done by de Vaucouleurs and Freeman (1972), where A i s the area of the contour. The centroids of the contours of sharp features in an image are used to fi n d the movement necessary to register the image with another image so that r a t i o or difference maps can be computed. This detailed technigue i s used here rather than the global cross-correlation technigue more commonly used by other workers (e.g F i s c h e l 1976 ). The b i - l i n e a r i n t e r p o l a t i o n optionally used for image r e g i s t r a t i o n with the MOVE or SHIFT in s t r u c t i o n s i s probably i n f e r i o r to the Fourier s h i f t theorem used when FT i s invoked, unless very sharp spikes are present in the data. The Fourier method involves multiplying every element of the discrete Fourier transform (DFT) by a phase factor. where ( A x , A y ) i s the desired image movement i n the (x,y) plane and (u^ ,vK ) are the s p a t i a l freguencies (m/N, n/N) of the elements of the discrete Fourier transform. F i l t e r i n g i s equivalent to convolving with a Gaussian of e f f e c t i v e diameter A i n real space s p e c i f i e d by the user i n the FT ins t r u c t i o n . This involves multiplying each element of the DFT by 72 (38) The a l t e r n a t i v e smoothing instruction i s SMOOTH, which uses a two-dimensional convolving f i l t e r corresponding to a cone with fixed base diameter 4.0 i n the r e a l domain, D.23<?7 i.o 0.14 2? o.5 0.5 (39) This can be compared with the sguare convolving function used by Davis (1975). In both FT and SMOOTH i t i s assumed that the cuter boundaries of the image are the outermost " l i v e " rows or columns and that the intensity d i s t r i b u t i o n beyond a boundary i s a r e f l e c t i o n of the d i s t r i b u t i o n inside the boundary. when smoothing i s used, some bias occurs near the edges, but at least no information external to the observations i s introduced. The command SECTION uses simple b i - l i n e a r interpolation to plot the i n t e n s i t i e s along a straight l i n e or e l l i p t i c a l locus in the image plane, while the instructions ELLIPSE and STAR produce various model d i s t r i b u t i o n s which can be compared with or subtracted from reduced images. An e l l i p t i c a l 73 d i s t r i b u t i o n can be computed with a simple King, " g e n e r a l i z e d " Hubble, de Vaucouleurs or e x p o n e n t i a l r a d i a l dependence. A c i r c u l a r uniform d i s t r i b u t i o n can a l s o be computed f o r use as a m u l t i p l i c a t i v e " i n t e g r a t e d photometry " a p e r t u r e . S t e l l a r images are assumed t o be Gaussian, although a more p r e c i s e extended p r o f i l e such as t h a t measured by Kormendy (1973) w i l l be needed f o r work with d e t e c t o r s more s e n s i t i v e than the RETICON RA50X50 . S t e l l a r or extended i n t e n s i t y d i s t r i b u t i o n s a r e i n t e g r a t e d u s i n g t h e i n s t r u c t i o n s APERTURE or EXAMINE AVERAGE The command APERTURE uses a sguare aperture of s p e c i f i e d s i z e , with the c e n t r e being a u t o m a t i c a l l y placed a t the c e n t r o i d of the observed image. The a p e r t u r e produced by ELLIPSE must be l o c a t e d by the user, m u l t i p l i e d by the observed image and i n t e g r a t e d v i a the EXAMINE AVERAGE i n s t r u c t i o n . 74 CHAPTER 4 THE SPIRAL GALAXY NGC 4736 (=M94) 4 AJ Background. The galaxy NGC 4736 i s c l a s s i f i e d as Sb in the Hubble scheme (Humason, Mayall and Sandage, 1956), and (R)sA(r)ab i n the de yaucouleurs scheme { de Vaucouleurs 1963). Other c l a s s i f i c a t i o n s are l i s t e d by de Vaucouleurs and de Vaucou-leurs (1964). The p r i n c i p a l data for t h i s galaxy are l i s t e d in Table VII . Photographs of this galaxy reveal a structure which i s regular but very complex. The descriptions given by sandage (1961), Chincarini and Walker (1967), Lynds (1974), van der Kruit (1974,1976) and Bosma, van der Hulst and Sul l i v a n (1977) indicate the following o p t i c a l structure: (a) A prominent nucleus of 3 to 4 arc seconds diameter, (b) A very bright central region of about 16 arc seconds radius , with s p i r a l structure extending from about 7 arc seconds to one minute of arc. This inner s p i r a l structure i s defined by dust lanes. (c) At a radius of 30 to 60 arc seconds, a r i n g of bright H11 regions embedded within f a i n t e r diffuse emissions. (d) Between 60 and 180 arc seconds radius, the main disk of the galaxy, f i l l e d with a tight and broken s p i r a l structure. 75 TABLE VII . Elements and properties of NGC 4736 o^{1950) 12h 48.6m CD S (1950) 410 23' (D Galactic longitude 123.3° (D Galactic l a t i t u d e 76.0° (D Hubble type Sb (1) De Vaucouleurs type (R)SA(r)ab (D DDO type Sb-pec.II; ( 1 > Morgan type D-S g CD Photographic magnitude mPj 8.91 (2) Colour B-V 0.76 (2) Face-on diameter D(0) 6.76' C D System v e l o c i t y V(sys) 314±1 km s" 1 (3) Distance 6±2 Mpc (4) Inclination 35+10° (<*) Position angle of l i n e of nodes 122±3° (4) Source References 1. de Vaucouleurs 2. de Vaucouleurs, and de Vaucouleurs (1964). Corwin and Bollinger (1977) . 3. van der Kruit (1976). 4. Schomraer and Sull i v a n {1976). 76 (e) A zone of very low surface brightness between 200 and 260 arc seconds radius. (f) A f a i n t external ri n g , starting at 26 0 arc seconds from the centre. Hecent work shows that t h i s galaxy i s a most int e r e s t i n g "laboratory" f o r galaxy dynamics. There exists a t r i p l e radio source centred at the nucleus, with the two outer lobes coin-ciding with the emission ring (van der Kruit 1971). These sources have a non-thermal spectrum (de Bruyn 1977). Photo-metry by Sirakin (1967) shows d i s t i n c t l y bluer colours i n the emission ri n g , indicating a young s t e l l a r population there. Pritchet (1975, 1977) obtained polarization Fourier spectro-meter scans using a 20 arc second aperture over the nuclear region, and he also found there a s i g n i f i c a n t young star contribution after applying population synthesis technigues. A good o p t i c a l rotation curve has been obtained by Chin-c a r i n i and Walker (1967), who found that both the absorption and emission l i n e s were sharp and that there was no difference between the v e l o c i t i e s of the absorption and the emission l i n e s , unlike the centre of M31 (Pellet 1976). Van der Kruit (1974, 1976) has obtained numerous spectrograms at d i f f e r e n t position angles and has measured the extent and the r a d i a l v e l o c i t i e s of the emission l i n e s associated with the inner ri n g . The outer structure of t h i s galaxy and i t s HI rotation curve strongly suggest that the inner emission ring should be 77 near the i n n e r L i n d b l a d resonance, while the gap between the main d i s k and the outer r i n g probably corresponds to the c o r o t a t i o n r a d i u s (Schommer and S u l l i v a n 1976). Van der K r u i t 1 s r e s u l t s f o r the i n n e r r i n g , however, are not completely c o n s i s t e n t with c o n v e n t i o n a l models of a d i s p e r s i o n r i n g at the i n n e r L i n d b l a d resonance ( van der K r u i t 1974,1976). I t i s most l i k e l y , from van der K r u i t ' s exhaustive s t u d i e s , that an e x c e s s i v e outward expansion e x i s t s i n the inner r i n g , the excess being most pronounced at the e a s t and west e x t r e m i t i e s of the r i n g . The extent of the r i n g i s a l s o q u i t e i n t e r e s t i n g , with an apparent i n n e r boundary at about 30 ar c seconds r a d i u s and a sharp outer boundary a t about 60 ar c seconds r a d i u s . The Hoc emission appears t o be d i f f u s e , with HII r e g i o n s embedded i n i t . I t should be noted t h a t C h i n c a r i n i and Walker (1967) found emission l i n e s r i g h t i n t o the nucleus, a p o s s i b i l i t y not discounted by van der K r u i t (1976) . One p o s s i b l e model f o r the d i s c r e p a n t v e l o c i t i e s i n the emission r i n g i s that the r i n g i s the r e s u l t of an e x p l o s i o n i n the nucleus (van der K r u i t 1974). k t h e o r e t i c a l model has been computed by Sanders and Bania (1976), and i t appears to be g u i t e s u c c e s s f u l i n e x p l a i n i n g the ongoing s t a r f o r m a t i o n , the n o n - c i r c u l a r motions, and the non-thermal r a d i o emission. The most important o b s e r v a t i o n a l t e s t f o r the Sanders-Bania model i s a p a i r of d i p s i n the r o t a t i o n curve, but such dips are not confirmed by the most r e c e n t o b s e r v a t i o n s of van der 78 Kruit (1976). An even more curious phenomenon perhaps i s the existence of s p i r a l structure within the inner emission r i n g . This structure appears to be defined by dust lanes, and con-ventional photographs reveal s p i r a l structure extending to within 7 arc seconds of the centre (Chincarini and Walker 1967). Since i n addition t h i s galaxy has an unusually high surface brightness i n the bulge region (Simkin 1967; Pr i t c h e t , personal communication) , it. was chosen for observation at Hauna Kea Observatory i n March and A p r i l , 1976, using the RETICON area photometer, 4.2 NGC 0 7 3 6 ; The Observations. The RETICON area photometer was mounted at the Cassegrain focus of the 2.2 metre telescope of the Hauna Kea Observatory. Three exposures, each of 5 minutes, were taken , one each through blue, v i s u a l and red f i l t e r s . A corresponding three exposures were taken of the sky background and a further three exposures of f i v e minutes each were taken through a p o l a r i z i n g element devised by R. Wolstencroft. A vis u a l double star, HR4708, was used to c a l i b r a t e the plate scale on the detector and the orientation of the instrument. An exposure of the evening sky was used as the f l a t f i e l d c a l i b r a t i o n . The relevant observations, together with t h e i r record numbers on my permanent f i l e tapes, are l i s t e d i n Table VIII . The data TABLE V I I I . Log of observations for NGC 4736. Permanent Object F i l t e r Exp. Time at end Rec. No. Time (O.T.) F i l e ~ l 3 — ——————— ™————— ————— T 9 7 6~iarch~ 6 Dusk Sky None 5m 5h 13m 7 Dark -t i 5h 24m 35 Sky B i i 11 h 38m 36 NGC4736 B i i 11h 48m 37 tt V i i 11h 52m 38 Sky V n 12h 00m 39 n B i i 12h 05m 40 NGC4 736 R i i 1.2h 16m 41 Pol 1 i i 12h 37m 42 « Pol 2 i t 12h 44m 4 3 ii Pol 3 i i 12h 52 m 44 Sky Pol 3 i i 12h 58m 45 Sky Pol 1 i i 13h 06m 46 n Pol 2 •t 13h 12m 62 Faint Star B 1m 14h 12m 63 if n V i i 14h 13m 64 i i i i R ti 14h 15m 65 tt i i — i i F i l e 38 — __——— March 31 16 2-166 HR4708A+B B 10s . 12h 25m 167-172 II V it 12h 27m 173-17 8 n R i i 12h 28m 179-181 Dark -i i 12h 29m 80 are encoded on duplicate labelled l i b r a r y tapes stored i n the permanent magnetic tape rack of the Computer Centre at U.B.C. The f i l e and record numbers given i n Table VIII w i l l allow the l i s t e d data to be located on these tapes as reguired. Appendix II l i s t s the contents of the l i b r a r y tapes. Owing to d i f f i c u l t i e s with the equipment, only a sinqle unsaturated f i l t e r - l e s s exposure, of the sky at dusk, i s available as a f l a t - f i e l d c a l i b r a t i o n image. The orientation and angular scale of the detector and telescope combination was simply calibrated by using a suitable well-observed v i s u a l double star. I assume that both the scale and orientation are constant over the detector meaning that the plate transformation i s assumed to be li n e a r , and that the diodes are regularly spaced and aligned as specified by the RETICON Corporation., The double system HR4708 was used to c a l i b r a t e the scale and orientation of the observations of NGC 4736. Landolt (1969) has published photometry for t h i s system. Due to an excessively pessimistic estimate of the response of the system before the f i r s t observing run on the 2.2 metre telescope, HR 4708A saturated the diodes near the centre of i t s seeing disk even with the shortest possible exposure time, thus precluding i t s use for magnitude or colour c a l i b r a t i o n . , Varying degrees of saturation between the blue, visual and red exposures do not lead to s i g n i f i c a n t l y d i f f e r e n t scales or orientations of 81 the images. Since a s e r i e s of exposures on stars i n Praesepe were s i m i l a r l y saturated, i t has not been possible to t i e the instrumental measurements into the standard Johnson UBVRI system. Observations with the RETICON area photometer at V i c t o r i a and Vancouver reported i n Chapter 5, however, indicate that the following d i f f e r e n t i a l s probably apply: <=. i.t 1.-2 where b,v, and r are the magnitudes in the instrumental blue, visu a l and red passbands. The positions of HR 4708 A and B i n each exposure have been determined by averaging the centroids of contours for each star image. Only contours with r a d i i between 1.0 and 2.0 diode units were used for the averaging. , The scales for each of the three f i l t e r s did not d i f f e r by more than 0.6% from each other, and did not lead to serious r e g i s t r a t i o n errors over the area of the detector when images were registered using a s t a r - l i k e feature near the centre of the detector. The average spacing between HR 4708 A and B was 22.49±0.05 (std. devn.) diode units, with position angle of 67.9+0.1 deg-rees i n the instrumental system. The weighted average of the 82 measurements l i s t e d by Aitken (1932) for ADS 8531 gives a separation of 20".04±0.36 (std. devn.), at a position angle of 336.7+0.1 degrees i n the c e l e s t i a l coordinate system. This puts North i n the d i r e c t i o n of increasing X, East i n the direction of Y. Figure 11 shows the relationship between the instrumental orientation and the c e l e s t i a l coordinate system. The "plate" scale i s 0".89±0.02 (std. devn. ) per diode (diodes are spaced at 4 mils or 101.6 microns). The absolute i n t e n s i t y c a l i b r a t i o n i n the v passband i s obtained by comparison with the aperture photometry of Chincarini and walker (1967). Using the plate scale of 0.89 arc sec./diode, synthetic c i r c u l a r apertures were computed corresponding to the three smallest centred apertures used by Chincarini and Walker. A numerical integration of the s i g n a l within each aperture was performed, and the t o t a l s converted to magnitude measure. Table IX summarises the data necessary to c a l i b r a t e the reduced form of record F13R37 from i n s t r u -mental v magnitudes to Johnson V magnitudes. The consistency of the differences v-V i n Table IX i s very encouraging, considering the errors which can be introduced by uricertainity i n the plate scale and by assuming V= v. Table XIII for the v i s u a l f i l t e r data contains a column giving isophotal surface brightnesses in V magnitudes per sguare arc second. The seeing has been estimated from observations of a 83 ZIGURE 11. R e l a t i o n s h i p o f o r i e n t a t i o n s between camera and sky. C o o r d i n a t e s X, Y are a l i g n e d with diode a r r a y . 84 TABLE IX . Comparison of integrated c i r c u l a r aperture v i s u a l magnitudes in the instrumental system with photometry by Chin c a r i n i and Walker (1967) = C*W. The c a l i b r a t i o n applies to exposure F13R37 of NGC 4736. Corrected for sky background and f l a t f i e l d . Aperture C+W This Work Difference Diameter V v v-V 11" 10.85 -10.60 -21.45 17" . 10.28 -11.18 -21.46 28" 9.70 -11.72 -21.42 Average Difference <v-V> = -21.44±0.02(s.d.) Add 21.44 to convert from instrumental magnitudes to V magnitudes. Subtract further 0.25 magnitudes to convert from V magnitudes per diode to V magnitudes per sguare arc second ("). 85 f a i n t star on the same night, although at a higher airmass and with a shorter exposure (1 minute) than for NGC 4736. Figure 12 shows the natural log of the contour i n t e n s i t i e s versus the sguare of the corresponding e f f e c t i v e r a d i i . The residual "semi-stellar nucleus" i s also plotted (to be discussed l a t e r ) . E f f e c t i v e seeing diameters (to 1/e of central intensity) arc 3".7 (blue) 2".9 (v i s u a l ) , 3".2 (red), and 3".6 (polaroid) . Longer exposures can be expected to give worse seeing figures. The e f f e c t i v e seeing diameters include the effect of imperfect focussing and telescope guiding errors. Both the focussing and guiding controls were troublesome during t h i s observing run on the 2.2 metre telescope. The noise i n the observations was evaluated by sub-tracting the visual sky exposure from the red exposure. The histogram of the difference i s plotted i n Figure 13. after subtraction of the mean, the difference pattern was sguared and averaged to find the r.m.s. deviation, which was 1.75 instrumental units. This corresponds to the r.m.s. diode-to-diode noise within each exposure aft e r subtraction of the sky (including the fixed pattern and dark current). A histogram of the f l a t f i e l d c a l i b r a t i n g image minus a strongly smoothed version of the same f l a t f i e l d exposure yielded a wider and di f f e r e n t d i s t r i b u t i o n , with r.m.s. deviation of 2.?5 instrumental units. I conclude that the f l a t f i e l d c a l i b r a t i n g pattern has s i g n i f i c a n t diode-to-diode variations greater than the random noise of 86 fl^HRE 12. Star images in B, V and R f i l t e r s p l o t t e d on Gaussian s c a l e . " R e s i d u a l n u c l e u s " of NGC 4736 i n c l u d e d f o r comparison. 6 7 5 ***** 6 0 0 5 2 5 0 5 0 375 300 2 2 5 150 75 * * * * * * * * * * * * * * • * ******* 0 * *. 10.0 •10.0 - 8 .0 - 6 . 0 -a.O -2.0 0.0 2.0 4.0 POPULATION OF HISTOGRAM B I N S PRINTED BELOW 0 0 5 12 55 1*6 259 6U0 i»6« 3 8 3 189 71 21 BED S K I - V I S SKT 6.0 8.0 ELGURB 13. T y p i c a l Noise Histogram. P l o t of d i f f e r e n c e s between elements. flean has been s u b t r a c t e d . oo 88 the observations. I t i s , therefore, i n v a l i d to smooth the f l a t f i e l d image before dividing the observed images by the f l a t f i e l d c a l i b r a t i n g image. Soise measurements using the same method for d i f f e r e n t times of the night of 1976 March 29/30 a l l had an r.m.s. deviation about the mean of the difference between two dark exposures of between 1.75 and 2.0 instrumental units. However the mean of the difference between two successive dark exposures of the same duration showed a fl u c t u a t i o n of up to ±3 instrumental units. Thus there was a general baseline d r i f t from exposure to exposure, i n addition to the diode-to-diode scatter within each exposure. Image regions of lower sig n a l have correspondingly lower s i g n a l to noise r a t i o , l imited by the diode-to -diode scatter and the baseline d r i f t . The brightest regions w i l l be l i m i t e d to the sign a l to noise r a t i o of the f l a t f i e l d c a l i b r a t i n g image. Neglecting the baseline d r i f t in t h i s case, the s i g n a l to r.m.s. noise r a t i o of the single f l a t f i e l d c a l i b r a t i n g image was 60 (using 1.8 instrumental units as the r.m.s. diode-to-diode s c a t t e r ) . This i s the highest s i g n a l to noise r a t i o possible f o r a single picture element of the observations of NGC 4736. The surface brightness maps reduced for sky, dark current and f l a t f i e l d c o r r e c t i o n in the instrumental f i l t e r system are presented as isophotal contours i n Figures 14, 15 and 16. Figure 17 i s a composite formed by registering the blue and 89 EIGURS NGC 4736: Blue isophotal contours. Peak marked by 'X'. Closed contours l i s t e d in Table X. North i s to the right (X), East i s down (Y) . (See Fi g . 11). 90 flGURE 15. NGC 4736: V i s u a l i s o p h o t a l contours. Closed contours l i s t e d i n T a b l e XI. North i s to the r i q h t (X), East i s down (Y) . (See F i q . 1 1 ) . 91 5.0 _] 10.0 _ l 15.0 _1 20.0 25.0 _ J 30.0 _ l 35.0 _J 40.0 _ l 45.0 _ l 5?-a NGC 4736t RED t 5 MIN. o p-i o KH I i 1 1 1 1 1 1 1 h" 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 X 0I0DE NO. EI£URE 16. NGC 4736: Red i s o p h o t a l contours. Closed contours centred or. nucleus l i s t e d i n Table XII. North i s to the r i g h t (X), E a s t i s down ( 7 ) . (See F i g . 11). ZIGURE 1 7 . NGC 4 7 3 6 : Composite of B , V , R, isophotal contours. North i s to the right ( X ) , East i s down ( Y ) . (See Fig. 1 1 ) . 93 red images to the position of the v i s u a l image, and performing a direct summation. Figure 18 shows the outer contours of the composite image smoothed to show the shapes of the contours. The f i r s t information needed to probe the inner structure of NGC 4736 i s a "law" to represent the r a d i a l variation of surface brightness. a model-independent approach i s one used by de Vaucouleurs and Freeman (1972) and by ables and ables (1972), whereby the area ft of each contour i s computed and a corresponding eguivalent radius r derived, so that; i n t e n s i t y "law" independent of e l l i p t i c i t y and other d i s t o r t i o n s , but not independent of i n t e r n a l absorption. Figure 19 shows the variation of log,.I versus Ej* , in the instrumental system red f i l t e r . Tables X , XI , and XII give values of I and r* i n each f i l t e r . The contours are the same as in Figures 14, 15 and 16. Table XIII gives V surface brightnesses c a l i b r a t e d using the c a l i b r a t i o n i n Table IX. Further insight may be gained by plotting I versus r using specialized scales. For example, Kormendy (1976) has used de vaucouleurs* model very e f f e c t i v e l y by p l o t t i n g log I versus r ° , 2 s . The plot should be l i n e a r i f de Vaucouleurs* 4^3 NGC 4736; analysis of Observations (41) The plot of i n t e n s i t y I versus radius r£ then gives an 94 18. Outer contours of smoothed composite of B, V, R. North i s to the r i g h t (X), East i s down (Y) . (See F i g . 11) . - 0 - 2 - 0 . 0 CL2 0T4 oTs TB M l 1 2 LOG RflDIUS(SEC) 1 , 2 M94 : RED FILTER : M.K.O. 88-INCH 19. NGC 47.36: Log ( i n t e n s i t y ) versus l o g ( r a d i u s ) , red f i l t e r . TABLE X . Blue surface brightness contours for NGC 4736. A l l units are in the instrumental system. Surface Effect ive Brightness Badius "T8775 0.708 177.6 1.025 167.8 1.324 157. 9 1.613 148. 1 1.907 138.2 2.209 128.3 2.553 118.5 2.941 108.6 3.359 98.8 3.789 88.9 4.39 2 79.0 5. 131 69.2 6.013 59.3 6.853 49.5 8.100 39.6 9.860 29.7 12.391 19.9 16.281 Centroid x y 25.62 26.42 25.56 26.46 25.50 26.52 25.45 26.54 25.40 26.54 25.39 26.56 25.40 26.61 25.41 26.60 25.43 26.57 25.45 26.56 25.53 26.56 25.69 26.42 25.95 26.32 26.09 26. 29 26.34 26.35 26.56 26.29 26.20 25.20 25.34 24. 48 TABLE XI . Visual surface brightness contours for NGC 4736. A l l units are i n the instrumental system., Surface E f f e c t i v e Centroid Brightness Radius X y 290.4 0.573 26.20 26.18 279.8 0.763 26.23 26.14 269.2 0.940 26.25 26. 17 258.6 1.108 26.27 26. 19 248.0 1.274 26.27 26.20 237. 4 1.446 26.27 26.22 2 26.9 1.63 6 26.26 26. 25 216.3 1.841 26.25 26.29 205.7 2.077 26.23 26.33 195. 1 2.323 26.19 26.36 184.5 2.596 26.13 26. 36 173.9 2.878 26.08 26.33 163.3 3. 176 26.04 26. 33 152.7 3.53 2 26.08 26.33 142. 1 3.918 26. 14 26.28 131.5 4.34 5 26.25 26.22 120.9 4.835 26.34 26. 14 1 10.3 5.461 26.52 26,04 99.7 6.135 26.49 25.97 89.2 6.74 1 26.59 25.99 78.6 7.413 26.71 26.01 68.0 8.34 1 26.69 26.09 57.4 9.649 26.82 26.07 36.2 13.324 26.40 25.01 25.6 16.383 25.45 24.79 98 TABLE XII . Bed surface brightness contours for NGC 4736. A l l units are in the instrumental system. Surface E f f e c t i v e Centroid Brightness Radius x ' y 541. 1 0.757 28.50 28.84 522.2 0.994 28.51 28.94 503.2 1.170 28.53 28.96 484.2 1.34 4 28.56 28.98 465.3 1.515 28.58 29.00 446.3 1.685 28.61 29.02 427.3 1.86 9 28.65 29.04 408. 4 2.075 28.65 29.06 389.4 2.292 28.63 29.06 370.4 2.524 28.58 29.06 351.4 2.772 28.51 29.05 332. 5 3.058 28.49 29.04 313.5 3.389 28.52 29.03 294.5 3.725 28.56 29.01 275.6 4.089 28.57 28.99 256.6 4. 485 28.56 28.96 237.6 4.918 28.61 28.93 218.7 5.390 28.71 28.93 199.7 5.906 28.79 28.92 180.7 6.547 28.93 28.93 161.8 7. 187 29.00 28.93 142.8 7.865 29.07 28.95 123.8 8.779 29.03 28.91 104. 8 10.089 29.06 28.75 85.9 11.628 28.98 28.48 66.9 13.564 28.74 28. 12 47.9 16.582 28.06 27.96 TABLE XIII . Calibrated 7 surface brightness, versus e f f e c t i v e radius for NGC 4736. Errors are calculated from f l a t f i e l d and baseline uncertainties. Radius(arcsec) V (mag a r c s e c - 2 ) 0.51 15.03±0.03 0.68 15. 07 0.84 15. 12 0.99 15. 16 1. 13 15. 20 1.28 15.25 1.46 15. 30 1.64 15.35 1.85 15. 41 2.07 15. 46 2.31 15. 53 2.56 15. 59 2.83 15.66 3.14 15.73 3.49 15. 81 3.87 15. 89 4.30 15. 98 4.86 16.08 5.46 16.19±0.04 6.00 16. 31 6.60 16. 45 7.42 16.6110.05 8.59 16. 79 10.08 17.01+0.06 11. 86 17.2910.09 14.58 17.67±0.12 100 law holds. Figure 20 shows that i n the innermost region the plot i s not l i n e a r , and that the observations do not extend out f a r enough f o r a straight l i n e to be drawn through a s i g n i f i c a n t range of values. Some of the curvature i s due to seeing, and i t cannot be said whether de Vaucouleurs* empirical law holds for NGC 4736 or not. I t should be r e c a l l e d that t h i s law does appear to hold over the entire bulge of J531 (de Vaucouleurs 1975), a galaxy with many s i m i l a r i t i e s to NGC 4736. It i s obvious that the contour area technigue gives very smooth surface brightness curves. Experiments show that i f the pictures are smoothed using a convolution f i l t e r prior to computation of the contours, the same surface brightness curves are obtained, except i n the innermost two or three seconds of arc where smoothing degrades the resolution of the "semi-stellar" nucleus. I t can be seen from the maps that the contours are somewhat non-circular and are not aligned with the major axis or l i n e of nodes of the galaxy as a whole. The major axis of the system i s taken to be at position angle 122±3 degrees (Schommer and Sullivan 1976). Bosnia, . van der Hulst and S u l l i v a n (1977) discuss the apparent change with radius of the position angle of the l i n e of nodes of NGC 4736. In addition, a difference of about 15° was observed by them between the apparent minor axis of the o p t i c a l body and the kinematical minor axis derived from HI observations. DE VAUCOULEURS 1.25 1.4 1.55 J I L 0.8 M94 0.95 i 1 r 1.1 1.25 1.4 RADIUS(SEC)M(0.25) RED FILTER : M.K.O. 88-INCH FIGURE 20. NGC 4736: Log ( i n t e n s i t y ) versus (ra dius) 0 • 2 5 , red f i l t e r . De Vaucouleurs' law i s l i n e a r i n t h i s diagram. 102 Figure 18 shows that the major axes of some contours may be roughly perpendicular to the major axis of the system. While i t i s possible to f i t e l l i p s e s to the contours to derive the e l l i p t i c i t y and position angle of each contour such an approach has not been carried out here because there are more physically meaningful ways of treating the data. E l l i p s e f i t t i n g has been done for M31 (Peterson, Ford and Eubin 1977), and the SBO galaxy NGC 2950 (Crane 1975). The rather face-on aspect of NGC 4736 and the known presence of dust in i t s central regions suggest that f i t t i n g e l l i p s e s to contours may y i e l d confusing r e s u l t s . The King Model: I have chosen a simple model which can be used to discuss both the photometry and the dynamics of this galaxy. For the central bulge, a simple empirical model i s . as developed by King (1962) for globular c l u s t e r s , where 1(0) i s the central surface brightness and r e i s the core radius, at which I (r t ) = I(0)/2 . A spherical system which has a surface brightness described by eguation 42 has a density law corresponding to, assuming that the mass-to luminosity r a t i o M/L i s constant, an assumption to which I s h a l l return l a t e r . The c e n t r a l surface > 103 brightness and the central density are then related by (44) l(p) = 2(0(6) <rc . As a s t a r t i n g point, t h i s model has many useful features. In the l i m i t for large r, i t tends to Bubble's inverse sguare surface brightness law for e l l i p t i c a l galaxies (Hubble 1930). For small r a d i i , i t c l o s e l y follows the isothermal model. Eguation (43) gives a good f i t out to 10 isothermal scale lengths, where the scale length <=*^  i s given by, .•>- y/t. = I — L klT Cr J where v 2 i s the mean sguare velocity dispersion i n the l i n e of sight. Since King (19 66b) has shown that -Tc = 3.0 o< { a 6 ) t h i s means that the run of density i n the isothermal model and eguation (43) agree very c l o s e l y for r ^ 3r c . The agreement of eguation (42) with King's isothermal cut-off models and with de Vaucouleurs*s empirical model extends to greater r a d i i (King 1966b). Empirically, there i s f a i r l y good evidence to assume ^(r)°c: r - 3 for the bulges of s p i r a l galaxies. Oort and Plaut (1975) have shown such a r e l a t i o n s h i p to hold for RR Lyrae variables i n the Galaxy, with an a x i a l r a t i o of the spheroidal system between 0.8 and 1 ( i . e . nearly s p h e r i c a l ) . This can be taken to be s i m i l a r to 104 the run of the t o t a l bulge and halo density (Schmidt 1976). Since NGC 4736 i s probably similar to the Galaxy, and r e c a l l i n g that the e l l i p t i c i t y of the inner surface brightness contours i s small and that the major axes are not along the l i n e of nodes, I assume a c i r c u l a r l y symmetrical surface brightness law as given by eguation (42). A l l the l i g h t at the centre i s assumed to come from the bulge system. After f i t t i n g to the observed surface brightness versus e f f e c t i v e radius for the inner region, the model i s subtracted point by point from the observed image to obtain a map of residuals. The f i t t i n g was done by plotting 1/1 versus ( r * ) 2 so that a l i n e a r eguation obtains, ) I I ~L-— — _ J - 4- 1 - . nT . <47) I(V> *(?) ICO) ^ The intercept i s egual to 1/1(0) and the slope eguals 1/{I(0)r 2} . This graphical procedure was demonstrated by King (1962, Fig. 4). Figures 21, 22 and 23 show I " 1 versus r 2 in the blue, vi s u a l and red f i l t e r s , using the data of Tables X, XI and XII. The dip for small r a d i i below the linear extrapolation of the upper part of the curve i s due to the so-called "semi-stellar nucleus", which i s not predicted by King's theory. I therefore do not use t h i s portion i n determining 1(0) and r 4 . The red contours and the contours of a composite image „ „ E „ M KING(INNER) g O . O 2 5 . 0 5 0 . 0 75 .0 100.0 125.0 150.0 175.0 20tt£fl • i 1 1 1 r 0 . 0 2 5 . 0 50 .0 75 .0 100.0 RADIUS (SEC) M2 M 9 4 : BLUE : M.K.O. 8 8 - I N C H ZIQ.HSE 2 1 . NGC 4736: ( I n t e n s i t y ) - * King's law i s l i n e a r i n t h i s diagram. v e r s u s ( r a d i u s ) 2 , blue f i l t e r . KING(INNER) 75.0 100.0 J L 0.0 25.0 M94 : VISUAL FILTER : M.K.O. 88-INCH 50.0 75.0 100.0 RADIUS (SEC)M2 200?0 FIGURE 22. NGC 4736: ( I n t e n s i t y ) - * versus ( r a d i u s ) 2 , v i s u a l f i l t e r . o cn KINGUNNER) 7 5 . 0 100.0 125.0 150.0 175.0 J I I I L 1 1 1 1 :—i r 50.0 7 5 . 0 100.0 125.0 . 150.0 175.0 2 0 0 . 0 RADIUS (SEC) M2 M94 : RED FILTER : M.K.Q. 88-INCH FIGURE 23. NGC 4736: ( I n t e n s i t y ) - * versus ( r a d i u s ) 2 , red f i l t e r . -»• _ a 108 (made up from summing the registered forms of the blue, vi s u a l and red images ) give a core radius of 6.7±Q.4 (est. error) diode units. At 0.89+0.02 arc seconds per diode, t h i s corres-ponds to r = 6."0±0.*?5.. The central i n t e n s i t i e s 1(0) were estimated graphically, and the c i r c u l a r simple King d i s t r i b u t i o n s were computed and subtracted from each image. The contours of the residuals are depicted i n Figures 24 to 28. A Generalized Hubble Model Another empirical model for spheroidal systems i s due to Hubble (1930), I GO I (r) = (48) which can be compared more c l e a r l y with the simple King relationship i f one writes, 1 W = i + / ( I ) + & & I(P) { I - 2(5)] j ^ r-<KO. . (50) This law more nearly attempts to account f o r the central cusp or nucleus, while the surface brightness of the outer parts of the system follows an inverse sguare law I(r) ©C r - 2 , as does the King law. Note that Hubble*s parameter "a" i s the radius at which the surface brightness I(r) has dropped to one 2o.o « gHUBBLE PLOT J : L T 4.0 6 . 0 8.0 RADIUS(SEC) M94 : RED FILTER : M.K.O. 88-INCH IIGURE 24. NGC 4736 : ( T n t e n s i t y ) - 0 • 5 versus (radius), red f i l t e r . Hubble's surface brightness law for galaxies i s l i n e a r i n t h i s diagram. 110 I!I£U£E 25. Blue minus simple King model. Equal i n t e n s i t y increments between c o n t o u r s . Image s h i f t e d i n t o r e g i s t r a t i o n with V i m a g e . Peaks marked by 'X', minima are i n s i d e tick-marked contours. C e n t r a l contours l e f t u n p l o t t e d f o r c l a r i t y . North i s to the r i g h t (X), East i s down (Y) . (See F i g . 11). 111 112 H 1 1 1 1 1 1 1 I I T m 0 0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 X DIODE NO. 0 £ U R E 27. Red minus simple King model. Notation as f o r F i g . 25. Image s h i f t e d i n t o r e g i s t r a t i o n with V image. 113 28. Composite of r e s i d u a l s from simple King model. Notation same as for F i g u r e s 25-27. 1 14 quarter of i t s central value I{0). Eguation (49) can be written i n the form, J% Jm °-JTCO) ' (51) so that plotting 1/,/l (r)' versus r should give a straight l i n e of the Hubble law holds. Figure 24 i l l u s t r a t e s such a plot for the red contours of NGC 4736. I t would appear that the nuclear surface brightness i s over-estimated by the Hubble law. A generalized Hubble law can be written as, = ' *• c 1 ! ) * &r ' <52) where c i s some constant. Least-sguares f i t s were made to the data in Tables X to XII to evaluate I{0),a and Cj for each image. Circularly-symmetric models of the surface brightness computed using eguation (5 2) were subtracted from each image. These residual maps are discussed i n the next section. H±.H NGC 4736i Halftone Residual Haps. The residual maps obtained by subtracting simple c i r c u l a r King and generalized Hubble models from images of NGC 4736 have also been reproduced using the graphics f a c i l i t i e s of the Dominion Radio Astrophysical Observatory, Penticton. Figure 29 shows an e l e c t r o s t a t i c printer dot-density plot of the red image minus a simple King model. The same data i s shown in Figure 30, using a Raytheon half-tone p l o t t e r , together with 1 1 5 FIGURE 2 q - Red iwage minus simple King model: p l o t (Versatec e l e c t r o s t a t i c p r i n t e r p l o t t e r : l e v e l s p l o t t e d ) . d o t - d e n s i t y 8 i n t e n s i t y 116 1 1 S FIGURE 30. NGC 4736 Minus Simple King Model. 1. Red minus modelrlow c o n t r a s t . 1s. Image 1 smoothed. 2. Red minus model: hiqh c o n t r a s t . 2s. Image 2 smoothed. 3. Blue minus model, smoothed. 4. Blue minus model, smoothed, lower c u t - o f f . UStei Approximately 1/4 i n c h band around edges i s redundant. O r i e n t a t i o n r o t a t e d by 180° from contour maps. 117 blue data. Smoothed and unsmoothed versions are shown with the e f f e c t of d i f f e r e n t contrast factors. ft high-resolution Raytheon plot of the red image minus a generalized Hubble model i s shown in Figure 31. Lower resolution unsmoothed r e s i d u a l maps are shown i n Figure 32, using d i f f e r e n t contrast f a c t o r s . The contrast i s set to 100 leve l s of gray with s p e c i f i e d minimum white and maximum (black) l e v e l s . In a l l these r e s i d u a l maps, a bar l i k e structure of about 20 arc seconds length i s evident, orientated at a position angle of roughly 30 degrees. The r e s i d u a l "nucleus" i s plotted on a Gaussian scale i n Figure 12. The straight l i n e f i t gives a Gaussian 1/e diameter of 5.0 arc seconds for the composite map of residuals, corrected for the s l i g h t broadening introduced by smoothing. This compares with the 2.9 to 3.7 arc second seeing disk for the shorter one minute star exposures of a star. Since the seeing may have been worse for the longer exposure, and also since the residual nucleus has a rather Gaussian surface brightness d i s t r i b u t i o n , the nucleus cannot be said to be d e f i n i t e l y resolved. The integrated V magnitude of the residual nucleus can be estimated by summing the excess in the central region, and by applying the c a l i b r a t i o n of Table IX. This gives V (nucleus) •= 13.3. For a distance modulus of 28.9 (corres-118 119 FIGURE 32. NGC 4736 minus g e n e r a l i z e d Hubble model. 1,2: Blue - model: two c o n t r a s t s . 3,4: V i s u a l - model: two c o n t r a s t s . 5,6: Red - model: two c o n t r a s t s . Note! Approximately 1/4 redundant. O r i e n t a t i o n contour maps. inch band r o t a t e d around edges i s by 180° from 120 ponding to a distance of 6 Mpc), the absolute V magnitude i s approximately -15.6. In comparison. Light, Danielson and Schwarzschild (1974) obtain Mv = -12.0 f o r the nucleus of M31. JLL5 NGC 4736! Ratio. I M Colour MMH±.~ The residual maps presented i n Sections 4.4 and 4.5 correspond to l i n e a r intensity differences between the observed and computed surface brightness d i s t r i b u t i o n s . Since there i s a very wide range of surface brightness i n each image of the nuclear region of NGC 4736, i t i s also i n t e r e s t i n g to see the r a t i o of the observed and computed d i s t r i b u t i o n s . Figures 33, 34 and 35 show the blue, v i s u a l and red images divided by the corresponding simple King models. The ends of the bar-like structure are most strongly accentuated, as i s the arm-like feature i n the North-East guadrant. The colour maps are shown in Figures 36, 37 and 38. The b, v, and r images were smoothed using a Gaussian of 2.5 diodes diameter. The position of the nucleus l i s t e d i n Table XIV , was determined from the contour centroids for each image by averaging the positions of contours with r a d i i between 1 and 2 diode units. The blue and red images were brought into r e g i s t r a t i o n with the visu a l image by using the FIRM Fourier transform i n s t r u c t i o n FT and applying the s h i f t theorem. Small perturbations of less than 0.1 diode spacings to the image r e g i s t r a t i o n do not r a d i c a l l y change the colour maps. ZIGIEI 33. NGC 4736: Blue d i v i d e d by simple King model. Peaks marked by ' X', l o c a l minima i n s i d e t i c k e d contours. Contours separated by 5%. 122 FIGURE 34. NGC 4736: V i s u a l d i v i d e d by simple King model. Peaks marked by 'X', l o c a l minima i n s i d e t i c k e d contours. Contours separated by 5/5. 123 FIGURE 35. NGC 4736: Red d i v i d e d by simple King model. Peaks marked by 'X', l o c a l minima i n s i d e t i c k e d contours. Contours separated by 5%. 124 1 1 r 20.0 25.0 30.0 X DIODE Nl3. FIGURE 36. NGC 4736: B - V c o l o u r map. I n s t r u m e n t a l system. Contours separated by 0.05 magnitudes. Highest l e v e l (reddest) marked by shading, second h i g h e s t by broken l i n e on low s i d e of contour, t h i r d h i g h e s t by dotted l i n e , f o u r t h highest by t i c k marks. S i g n a l to n o i s e r a t i o lower near edges, h i g h e s t near nucleus. 125 EIGUBI 37. NGC 4736: V - R c o l o u r map., Ins t r u m e n t a l system. contours separated by 0.05 magnitudes. Highest l e v e l (reddest.) marked by shading, second h i g h e s t by broken l i n e on low s i d e of contour, t h i r d h i g h e s t by dotted l i n e , f o u r t h h i g h e s t by t i c k marks. S i g n a l to noi s e r a t i o lower near edges, highest near nucleus. 126 ,0.0 5.0 1 r 20.0 25.0 30.0 X DIODE NO. 35.0 I 40.0 T 45.0 50.0 IIGDRE 38. NGC 4736: B - R c o l o u r map. I n s t r u m e n t a l system. Contours separated by 0.05 magnitudes. Highest l e v e l (reddest) marked by shading, second h i g h e s t by broken l i n e on low s i d e of contour, t h i r d h i g h e s t by dotted l i n e , f o u r t h h i g h e s t by t i c k marks. S i g n a l to n o i s e r a t i o lower near edges, h i g h e s t near nucleus. TABLE XIV . Nuclear p o s i t i o n s f o r NGC 4736 de r i v e d from smoothed images ( A= 2.5 d i o d e s ) . E r r o r s are standard d e v i a t i o n s . Becord F i l t e r 127 F13R36 b 25.44+0.02 26.54±0.01 F13B37 v 26.21±0,02 26.26+0.02 F13B40 r 28.58*0. 01 29.02±0.01 128 The most s t r i k i n g features of the colour maps are a strong r a d i a l colour gradient at about JJ} to JM5 arc seconds radius, with a f l a t t e n i n g out within that radius, while the nucleus does not stand out at a l l i n the colour map. The negative residual areas are actually the reddest areas, especially the patch in the south-east guadrant. These re s u l t s w i l l be discussed i n the next section. Simulated l i n e scans computed using the SECTION command in FISH are presented f o r two orientations; 3 0 degrees and 120 degrees true position angle, passing through the nucleus. Figures 39 and 4 0 show the variation of the residuals and the colours approximately along the "bar" ( 3 0 degrees) and perpen-dicular to i t (120 degrees). i U i NGC 4736J. SimjpJLe Models. The bar-like structure and s p i r a l arm-like features reported here blend smoothly in t o the features photographed by Chincarini and Walker(1967). Although a complete survey with a larger panoramic detector i s obviously reguired, the r e s u l t s to date allow some i n t e r e s t i n g ideas to be considered. I assume that the d i s t r i b u t i o n of matter i n a s p i r a l galaxy such as NGC 4 7 3 6 can be represented by two dynamical components: a spheroidal bulge and a f l a t , thin disk. I also assume that the density ^fr) i n the bulge component can be represented by eguation ( 4 3 ) , 129 "1 1 1 1 1 1 1 1 f -32.0 -24.0 -36.0 -8.0 0.0 8.0 16.0 24.0 32.0 D I S T . IN P I X E L U N I T S ZI^UfiE 39. Colours and r e s i d u a l s along b a r - l i k e s t r u c t u r e (true p o s i t i o n angle 30°). Re s i d u a l s s c a l e d by average b r i g h t n e s s i n each f i l t e r b e f o r e model s u b t r a c t e d . I n s t r u -mental c o l o u r s i n hundredths o f a magnitude, o f f s e t by one magnitude. 130 D I S T . IN P I X E L U N I T S IIOURE UO. Colours and r e s i d u a l s p e r p e n d i c u l a r t o b a r - l i k e s t r u c t u r e (scan a t true p o s i t i o n anqle 120°). R e s i d u a l s s c a l e d by average b r i g h t n e s s i n each f i l t e r before model s u b t r a c t e d . I n s t r u m e n t a l c o l o u r s i n hundredths of a magnitude, o f f s e t by one magnitude. 131 (53) where r f i i s the core r a d i u s . The use of t h i s s p h e r i c a l l y symmetrical d i s t r i b u t i o n has been j u s t i f i e d i n s e c t i o n 4.3. Perek (1962) d e s c r i b e s methods f o r o b t a i n i n g f o r c e laws from simple a n a l y t i c a l s p h e r o i d a l d e n s i t y d i s t r i b u t i o n s . a f o r c e law has been d e r i v e d f o r the f l a t t e n e d form , but the s p h e r i c a l approximation w i l l be r e t a i n e d here. I assume an e x p o n e n t i a l d i s t r i b u t i o n of s u r f a c e d e n s i t y yU(r) i n the d i s k , yWW - f*te) *y)(-*<r) y (54) where aC-i = a^ i s the d i s k s c a l e l e n g t h . The p r o p e r t i e s of such a d i s k have been d i s c u s s e d by Freeman (1970). I t s e x i s t e n c e i s supported by photometry (e.g. Schweizer 1976), but i t has been s e r i o u s l y questioned by Kormendy (1976), who suggests t h a t the e x p o n e n t i a l behaviour of s u r f a c e b r i g h t n e s s may be an i l l u s i o n caused by the s u p e r p o s i t i o n of the outer bulge on the o p t i c a l image. While i t may be more accurate t o use the de Vaucouleurs s u r f a c e b r i g h t n e s s law and i t s d e n s i t y d i s t r i b u t i o n together with an e x p o n e n t i a l d i s k (e.g. Monnet and Simien, 1977), or to use King*s i s o t h e r m a l c l u s t e r models with an e x p o n e n t i a l d i s k (e.g. Yoshizawa and Wakamatsu, 1975), I use the s i m p l e r model expressed by equations 53 and 54. The photometry presented i n t h i s chapter suggests t h a t f o r the innermost r e g i o n s t h i s simple model may be g u i t e a c c u r a t e . I n e g l e c t the c e n t r a l cusp or nucleus, s i n c e i t s 132 t o t a l contribution, even within a small radius, i s quite small. Starting with f i r s t p r i n c i p l e s , following the clear summary of Yoshizawa and Hakamatsu (1975), the c i r c u l a r o r b i t a l velocity (r) can be written as where r i s the radius, Ff and F^  are the forces at r due to the spheroidal and disk components respectively. Thus, (56) where G>f and are the components of c i r c u l a r o r b i t a l velocity due to the spheroid and disk respectively. The spheroidal component has a simple force law, C AW r 1 " (57) (58) Thus, using the density law of eguation 53 , we have. For the disk component, Freeman (1970) has shown that ©;Cr)= TkjuM^ ( I. Jr. - I, JC,) y 1 5 9 1 where I ,K ,1 ,K are modified Bessel functions evaluated atr / ^ 2 ^ ) . Dimensionless squared v e l o c i t i e s can be defined, 133 v 1 / ^ - £*te' + Ji+ I ' M * _ '— r=7- j <60) Thus, (62) This eguation can be re-written after defining two constants. k - £ fe. — ^ ( 6 3 ) where. ( 6 4 ) a n d , y ^ J - ( /- ^) + JKA(0)) . (65) The parameter k a i s the r a t i o of scale lengths, and i s the r a t i o of the projected c e n t r a l spheroid density to the t o t a l projected central density. 1 3 4 Thus eguation (62) can be written as 2w L aj. (ju,io) - y ^ / b j ) . (66) The model depends on the two dimensionless parameters k & , k and the physical scale length r c or a^ . . This i s i n agreement with the idea that there are two fundamental gal a c t i c parameters, one of which i s scaled by a physical dimension (Roberts, Roberts and Shu 1975). The d e f i n i t i o n s used here are s i m i l a r to those of Yoshizawa and Wakamatsu (1975) and Monnet and Simien (1977), except that these authors use the de Vaucouleurs e f f e c t i v e radius rather than the King core radius. Since the simple bulge model given by eguation 53 does not have a f i n i t e mass when integrated to i n f i n i t e radius, t o t a l mass concepts are not used here. (the exponential disk, of course, has a f i n i t e mass, Ji* *nfju/(t>)C(j ). This leaves open the p o s s i b i l i t y of a massive outer spheroidal halo , which does not a f f e c t the inner rotation curve. On the other hand, a non-exponential disk in the outer regions could a f f e c t dynamics closer to the centre, a point well made by Mestel (1963) and often not understood. If i t i s assumed that the mass to luminosity r a t i o s of the bulge and of the disk do not change with radius, photo-135 metry can give the mass d i s t r i b u t i o n . On the other hand, i f i t i s assumed that the rotation curve obtained from r a d i a l v e l o c i t y measurements represents the true c i r c u l a r o r b i t a l v e l o c i t i e s in the system the mass d i s t r i b u t i o n can be inferred from the rotation curve, the photometric and dynamical r e s u l t s can then be compared. There i s no published photometry of NGC 4736 which extends out well into the disk, and only the inner bulge has been observed using the RETICON camera. To obtain a "photo-metric" model, I use the observations reported here to determine the core radius {section 4.4), and adjust the density r a t i o k^. and the disk scale length a</ to reproduce the outer HI rotation curve published by Schommer and Sul l i v a n (1976). I then compare the theoretical inner rotation curved derived from t h i s model with the rotation curves of Chincarini and Walker (1967) and van der Kruit (1976). Since a^ i s at present unknown but may be available from new observations currently being reduced by other workers (schommer and Sullivan 1976, van der Kruit 1976), the model derived here i s only an approximate one, and a detailed least sguares f i t i s not attempted. Sim i l a r l y the outer bulge i s not well observed, although there i s published l i n e scan photometry by Simkin (1967). The inner r e s u l t s are extrapolated outwards i n the present work. F i r s t l y , a model was constructed using the photo-metrically-derived bulge core radius r £ = 6".0 ± 0".5 . The 136 f i t t i n g procedure was by eye, which was g u i t e s e n s i t i v e i n t h i s case s i n c e the shape of the r o t a t i o n curve f o r an Sb galaxy v a r i e s s t r o n g l y with r e s p e c t t o the bulge to d i s k s c a l e l e n g t h r a t i o and the d e n s i t y r a t i o (see, f o r example, Yoshizawa and Wakamatsu 1975, and Roberts and Rots 1973). Secondly, a model was c o n s t r u c t e d by f i t t i n g to the e n t i r e r o t a t i o n curve. The d y n a m i c a l l y - d e r i v e d core r a d i u s , assuming t h a t the d e n s i t y law of eguation 53 i s a good approximation, i s about 8 seconds of a r c . Models f o r r c = 6 , 8 and 10 a r c seconds are shown i n F i g u r e s 41, 42 and 43, at t h r e e d i f f e r e n t s c a l e s . The o b s e r v a t i o n a l p o i n t s of the r o t a t i o n curve are taken from the graphs of Schommer and S u l l i v a n (1976) and van der K r u i t (1976), based on the obser-v a t i o n s of these authors and those of C h i n c a r i n i and Walker (1967) and Bosma, van der H u l s t and S u l l i v a n (1977). For the model with r {=6", a reasonable f i t i s obtained a t r a d i i l a r g e r than 12", but the i n n e r r o t a t i o n curve i s not as w e l l p r e d i c t e d . E i t h e r the observed i n n e r r o t a t i o n curve does not represent the t r u e c i r c u l a r o r b i t a l v e l o c i t y , or the mass to l u m i n o s i t y r a t i o v a r i e s i n the i n n e r r e g i o n s of NGC 4736. The model f o r r c =8" g i v e s a c l o s e r f i t at s m a l l r and i s g u i t e good a t a l l r a d i i . The model f o r r c =10" f i t s w e l l a t s m a l l r a d i i but has a n e g a t i v e s l o p e f o r r=40", whereas the r a d i o o b s e r v a t i o n s show a negative s l o p e beginning a t r=240". I t i s i n t e r e s t i n g t h a t the t h e o r e t i c a l r o t a t i o n curves are higher than the o b s e r v a t i o n s around 300" r a d i u s . , The o in ro _j ! ! j 1 1 : 1 1 j 0.0 50.0 100.0 150.0 ?00.0 250.0 300.0 350.0 400.0 RADIUS(SEC). II^DRE 41. NGC 4736: F u l l r o t a t i o n curve and models. C i r c l e d p o i n t s are HI measurements, from graphs of Schommer and S u l l i v a n (1976) and van der K r u i t (1976). . 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 RADIUS(SEC) ZIGURE 42. NGC 4736: Rotation curve and models to 80". Ci r c l e d points are HI measurements, from graphs of Schoramer and Sull i v a n (1976) and van der Kruit (1976). Rf lD IUS (SEC) FIGURE 43. NGC 4736: Rotation curve and models to 32". Spectrographs measurements as plotted by van der Kruit (1976). 140 parameters of a l l three models are l i s t e d are l i s t e d i n Table XV . The bulge to t o t a l mass r a t i o s should not be taken too seriously, since the model has been enormously extrapolated. The value of the disk scale length a^ i s uncertain since i t has been inferred using the model and not measured d i r e c t l y . Bearing i n mind the d i f f i c u l t y of measuring the true c i r c u l a r rotation curve close to the nucleus, and that the HI observations are more accurate than the emission-line measurements (Schommer and Sullivan 1976), the model with r c = 6" i s acceptable, although rc = 8" gives a better f i t for distances less than 10" from the nucleus. Given the s i m p l i c i t y of the spherical bulge and exponential disk model used here, the consistency between the photometric surface brightness d i s t r i b u t i o n and the rotation curve i s reasonably good. Mass to luminosity r a t i o s were computed using the models in Table XV and the photmetry of Chincarini and Halker (1S67). The i n t e g r a l of the surface brightness law of eguation (42) i s given by, L[R) = 1(D) TT rc x JL (67) where L(fi) i s the luminosity enclosed within an aperture of radius B. Assuming that the disk contribution to the ce n t r a l luminosity and projected density i s n e g l i g i b l e , the ce n t r a l surface brightness 1(0) can be found given L (B), E and r c . From t h i s , the c e n t r a l mass to blue luminosity r a t i o M/L. i s 141 TABLE XV . Parameters f o r models of NSC 4736. Parameter Model I I I I I Core radius r e (arcsec) Central projected density r a t i o k^. Disk scale length a^ (arcsec) Central surface density ju (0) (M o Pc - 2 ) Central disk density JUjiiO) (Mope-*) . Central bulge density j>, (0) (Mepc-3) Mass inside 10Kpc <Klo ( M Mass inside 25Kpc (Mp) (*) Total disk mass Bulge mass /Total mass (inside 10 Kpc) Bulge mass / Total mass (inside 25 Kpc) (*) 6. 0 0. 975 100 8.0 0.97 100 10.0 0.97 100 2.48x10* 1.83x10* 1.53x10* 6. 19x10* 5. 50x102 4.60x102 67.0 37.0 24. 8 4.8x10*0 4.8x1010 4.9x10^0 5. 8x10*0 5. 9x10*0 6.1x10*0 3.5x10»o 3.1x10^0 3.6x10*o 0.38 0.39 0. 46 0. 48 0.55 0.57 (*) : Extrapolation of density model, 142 given by, J <68) where (0) i s the projected central surface density. Mass to luminosity r a t i o s obtained using eguations (67) and 68) with models I, II and I I I are presented i n Table XVI . The s l i g h t l y lower r a t i o for Model I with the smallest aperture {compared with the value derived from the larger apertures ) shows the e f f e c t of the nuclear "cusp". The "serai-stellar" nucleus contributes about 1.0% of the l i g h t through the smallest aperture used by Chincarini and Walker {1967). Bosma, van der Hulst and Sulli v a n (1977) fi n d a t o t a l mass of 5.3x10*0 M within a radius of 9.6kpc, and a t o t a l mass to luminosity r a t i o M/Lj = 2.5 .. The dynamical model of Nordsieck (1973) was used. The t o t a l mass to luminosity r a t i o i s very si m i l a r to the nuclear mass to luminosity r a t i o found i n t h i s work. This would suggest that the bulk of the l i g h t in the galaxy comes from a population with a mass to luminosity r a t i o which i s roughly the same throughout the galaxy. TABLE XVI . Mass to blue luminosity ratios using models from Table XV and photometry of Chincarini and Walker (1967) . Units are M (sun)/Lj (sun). i — — : — i — — — :—"—~ ~ : _" ': _ : .. . .: . , — — — r — —ra JApertureJ Model \ jradius | I II III J I 5.5" | 3. 3 2.7 2.4 1 | 8.5" | 3.6 3.2 2.9 | I 14.0" | 3.6 3.5 3.5 I 144 4.7 NGC 4736: S p i r a l P a t t e r n s And Jesonance Phenomena. -The r a d i i of f e a t u r e s d e s c r i b e d i n s e c t i o n 4.1 are l i s t e d i n Table XVII . Some of these f e a t u r e s have been i d e n t i f i e d by v a r i o u s authors as evidence o f L i n d b l a d resonances (e.g. L i n d b l a d 1974, Schommer and S u l l i v a n 1976). In p a r t i c u l a r , the f e a t u r e s around 60 arc seconds r a d i u s a r e thought t o be a s s o c i a t e d with an i n n e r L i n d b l a d resonance at B=B ,•„,.«„.• where _Q(R) - * M = _ Q R , 6 9 ) The angular v e l o c i t y o f the s t a r s i n c i r c u l a r o r b i t s i s while the ang u l a r v e l o c i t y o f the two-armed s p i r a l p a t t e r n i s . The g u a n t i t y i s the e p i c y c l i c freguency, which i s the r a t e a t which a perturbed s t a r w i l l o s c i l l a t e about i t s mean c i r c u l a r o r b i t a l path (see l i e l e n 1974 f o r a l u c i d review). The e p i c y c l i c frequency i s given by ' . , J- dSL) ' + 212. -C£) < ( 7 0 ) and i s c a l c u l a t e d by simple numerical d i f f e r e n t i a t i o n . The outer edge of the main v i s i b l e d i s k i s a l s o the inn e r boundary of the l o w - l u m i n o s i t y "gap". I t i s thought t o be near the c o r o t a t i o n r a d i u s R t , at which. 145 TABLE XVII . Radii of V i s i b l e and Radio Features Adopted f o r NGC 4736. Feature Radius Source Outer edge of central "intense region". Ends of small "bar". Inner edge of observable HII emission. Outer edge of bright radio continuum inner disk. Peak of HI surface density. outer edge of HII emission r i n g . Outer edge of o p t i c a l "second zone". Outer edge of main v i s i b l e disk ("third zone") Inner edge of outer v i s i b l e r i n g . Outermost published HI r a d i a l v e l o c i t y . 16" 17" 37" 50" 4 0-6 0" 58" 60" 200" 260" 360" ( D *This Work 12) (3) (2) ( D ( D (1) (3) * Corrected for i n c l i n a t i o n 1=35°. 1. Sandage (1961) . 2. van der Kruit (1976). 3. Bosma et a l . (1977) 4. de Bruyn (?977) . 146 Sl(Rc) = SI f (71) S p i r a l structure i s not seen outside t h i s radius, but there i s a f a i n t outer r i n g (Sandage 1961). The outer Lindblad resonance i s thought to be in or beyond th i s outer ring (Schcmmer and S u l l i v a n , 1976). At the outer Lindblad resonance radius R=R o u t e y» , se have I t has been shown by Barbanis (1970) that density-wave s p i r a l arms should not propagate beyond the co-rotation radius. Contopoulos (1974) has demonstrated that only a bar may exist i n s i d e the inner Lindblad resonance radius. In NGC 4736, s p i r a l arms indeed are not seen outside the assumed corotation radius of about 200", but there i s a s p i r a l pattern defined by dust lanes within the inner 60" ring (Chincarini and Walker 1967). The present work discloses a bar-like inner structure extending to a de-projected radius of 17" (assuming that the bar-like structure l i e s in the plane of the d i s k ) . Adopting R = 200", the Lindblad resonances have been computed for Models I, II and I I I , and are l i s t e d i n Table XVIII . The angular v e l o c i t i e s Si. , JCJ--k/x and SL*kji. are shown in Figure.44. A s p i r a l pattern angular speed of 29 km s _ 1 kpc - 1 i s found for Rc = 200", using a scale of 30 4-TABLE XVIII . Main Disk Model Resonance Parameters. 147 Parameter Model = I II III SS Pattern Speed (km s - 1 k p c - 1 ) . Inner Lindblad Resonance (arcsec). Corotation Radius (arcsec). Outer Lindblad Resonance (arcsec) 29+1* 29 62 300 64 200** 200 299 29 68 200 296 33 66 210 270** * : Corresponds to V,<4. = 175±5 km s ~ 1 . ** : Adopted. SS : Model of Schommer and Sullivan (1976). FIGURE 44. Model angular v e l o c i t i e s for NGC 4736. Pattern velocity for model with r =6" shown. 149 parsecs per arc second. For each model , the inner Lindblad resonance i s well defined and l i e s between 60 and 70 arc seconds. also l i s t e d in Table XVIII i s the empirical model of Schommer and Sullivan {1976}. Their resonance r a d i i were derived from the e p i c y c l i c frequency which they computed d i r e c t l y by applying equation 7 0 to a polynomial f i t t e d to the rotation curve observations. agreement with the present work i s qood. 1 1 w°.zSp_iral Model.,, How can the s p i r a l dust pattern and the small bar inside the inner Lindblad resonance be explained? I s h a l l propose a model which involves a separate s p i r a l pattern inside the inner Lindblad resonance of the main s p i r a l of NGC 4736. This inner s p i r a l has a hiqher angular speed than the main s p i r a l . In addition to NGC 4736, several other galaxies have d i s t i n c t inner patterns. The barred s p i r a l NGC 4314 (SBa(s)pec) has a very d i s t i n c t l i t t l e two-armed s p i r a l well inside i t s main bar (Sandage 1961, Matsuda and Nelson 1977). The early barred systems NGC 1291 and 1236, c l a s s i f i e d by de Vaucouleurs as (R)SB(s)0/a, have small bars inside t h e i r main bars (de Vaucouleurs 1974). The existence of inner patterns or sub-structures may be a f a i r l y common phenomenon. I f these inner sub-structures are to obey the same rules as are thought to govern the p r i n c i p a l s p i r a l structure, th e i r pattern speeds 150 must be higher than or egual to the l o c a l value of J l - K / I . I assume that a non-axisymmetric disturbance of the g r a v i t a t i o n a l p o t e n t i a l i n the central bulge gives r i s e to a s p i r a l pattern which i s probably a gaseous s p i r a l rather than a true s t e l l a r density wave. Of course, the idea of c e n t r a l bars generating the s p i r a l patterns i n SA galaxies i s not new (e.g. Lindblad 1956, 1959, 1974; Holmberg 1958; siokin 1970; Marochnik and Suchkov 1974), but i t i s only recently that hydrodynamical ca l c u l a t i o n s have been carried out using a r e a l i s t i c mass model. Sanders and Huntley (1976) have shown that a s l i g h t oval deformation of the g r a v i t a t i o n a l potential in a galaxy can generate t r a i l i n g gas s p i r a l waves. Sorensen, Matsuda and Fujimoto (1976) have demonstrated a s i m i l a r e f f e c t for a b a r - l i k e , r a p i d l y - r o t a t i n g strong g r a v i t a t i o n a l deformation. Shock waves and non-circular gas motions are predicted by both models. An attempt to explain the p r i n c i p a l large-scale s p i r a l system in galaxies has met with limited success (flatsuda and Nelson 1977). However, I now assume that a rapidly rotating central deformation could possibly lead to a corresponding small s p i r a l pattern i n the disk inside the inner Lindblad resonance of the main s p i r a l system. I t i s beyond the scope of this work to carry out a f u l l hydrodynamical ca l c u l a t i o n to test t h i s hypothesis, but a check on i t s consistency can be obtained from area photmetry and the mass model. 151 assuming that the ends of the small central "bar" correspond to the inner resonance of the inner s p i r a l , the parameters l i s t e d in Table XIX are obtained. The corresponding angular v e l o c i t y diagram i s shown i n Figure 45. Aa_§ NGC 4736: Discussion.. The model adopted in the previous section involves two s p i r a l patterns, one inside the other, rotating at different angular speeds. The two s p i r a l s each have the i r own p a r t i c l e resonances, which are deduced by combining a model for the mass d i s t r i b u t i o n with some assumptions derived from o p t i c a l images. It can be seen from Figure 45 that adopting a d i f f e r e n t inner Lindblad resonance radius for the inner s p i r a l w i l l not greatly change the conclusions. The mass model with r = 6" gives a more consistent set of resonance r a d i i f o r both the main s p i r a l system and for the postulated inner system. This i s e s p e c i a l l y true for the phenomena around 60" radius, the position of which has been l e f t as a free parameter to be determined from the models themselves. The inner s p i r a l which st a r t s at the ends of the small bar has corotation near the inner Lindblad resonance radius of the main s p i r a l system. The bar-driven gas s p i r a l models of Sanders and Huntley (1976) and Sorensen, Hatsuda and Fujimoto (1976) have s p i r a l arms extending beyond the corotation radius 152 TABLE XIX . Inner Disk Model Resonance Parameters, Parameter Model = I II III Pattern speed (km s _ 1 kpc - 1) . Inner Lindblad Resonance (arcsec) 102 17 87 17 74 17 (*) Corotation radius (arcsec). 58 70 84 Outer Lindblad Resonance (arcsec) 99 117 123 Adopted from area photometry, corrected for i n c l i n a t i o n 1=35°. FiGUFJ 15. Inner model angular v e l o c i t i e s f o r NGC 4736.. Model p a t t e r n speeds shown. 154 to the outer L i n d b l a d resonance of the model. I f such a model i s t r u e f o r the inn e r s p i r a l system, the i n n e r system's outer p a r t s would l i e i n the main system i t s e l f . There i s l i t t l e p u b l i s h e d data on t h e s t r u c t u r e of the s p i r a l arms i n the main d i s k . I t i s known that the main s p i r a l system appears to be very broken and t i g h t l y wound (Sandage 1961; van der K r u i t 1974). Schommer and S u l l i v a n (1976) r e f e r t o unpublished s u r -f a c e photometry r e v e a l i n g a f a i n t but d i s t i n c t two-armed s p i r a l i n the main d i s k . The broken s t r u c t u r e of the s p i r a l i n the main d i s k may be p a r t l y due to i n t e r f e r e n c e between the i n n e r gas s p i r a l and the main s p i r a l . The main s p i r a l presumably i s evidence of a s t e l l a r d e n s i t y wave. According to the two s p i r a l model, the d i f f u s e H emission and enhanced s t a r formation i s caused by the shocks experienced by gas moving i n a d i s k w i t h i n the bulge of NGC 4736. The very high s u r f a c e b r i g h t n e s s and r a t h e r low mass to l u m i n o s i t y r a t i o i n the c e n t r a l r e g i o n s would a l s o be caused by t h i s s p i r a l a c t i v i t y . The r a d i o continuum emission s t u d i e d by van der K r u i t (1971) and de Bruyn (1977), and the somewhat anomalous gas v e l o c i t i e s o b t a i n e d by van der K r u i t (1974, 1976) can q u a l i t a t i v e l y be a s s o c i a t e d with the i n n e r s p i r a l , e s p e c i a l l y as there may be complex i n t e r a c t i o n s between the two s p i r a l systems at about 60 a r c seconds r a d i u s . I t i s very d i f f i c u l t a t present to decide whether the sm a l l c e n t r a l "bar 1 1 i s r e a l l y a bar composed of s t a r s or whether i t i s the p o r t i o n of the inn e r s p i r a l which l i e s 155 i n s i d e i t s i n n e r L i n d b l a d resonance. The presence of dust complicates the i n t e r p r e t a t i o n of o p t i c a l images. Thus one cannot at present decide whether the i n n e r s p i r a l p a t t e r n i s caused by a s t r o n g b a r - l i k e p e r t u r b a t i o n or by a s l i g h t o v a l non-axisymmetry of the bulge mass d i s t r i b u t i o n . I s the observed "bar" the cause or an e f f e c t of the i n n e r s p i r a l system? Some N-body c a l c u l a t i o n s have demonstrated the formation of bars i n the c e n t r a l r e g i o n s of g a l a x i e s ( H i l l e r 1972, Hohl 1972, Quirk 1972). These r e s u l t s are i n t e r p r e t e d by Contopoulos (1971) to mean t h a t the s h o r t b a r s a t the c e n t r e do not produce s p i r a l s themselves, but evolve due t o i n s t a b i l i t i e s . O s t r i k e r and Peebles (1973) f i n d t h a t a massive halo i s needed to prevent such i n s t a b i l i t i e s , and i n the case of NGC 4736 the c e n t r a l d i s k i s indeed i n s i d e a massive bulge. T a b l e XV shows t h a t the bulge c o n t a i n s between 38% and 57% of the t o t a l mass, with about 4 5% being the most l i k e l y f i g u r e . As noted before, these f i g u r e s are not well determined. Hohl (1976) showed that a c e n t r a l l y c o n c e n t r a t e d c o r e - h a l o system ( i . e . "bulge") must c o n t a i n 60% or more of the t o t a l mass i n order to s t a b i l i z e the d i s k a g a i n s t the formation of a bar, while a uniform d e n s i t y h a l o need only c o n t a i n 40% of the t o t a l mass. Thus NGC 4736 does not appear t o s a t i s f y the O s t r i k e r - P e e b l e s s t a b i l i t y c r i t e r i o n , although the d i s k - t o - b u l g e r a t i o i s c l o s e enough t o suggest a marginal case. The paradox of s t a b l e d i s k s i n g a l a x i e s with an 156 apparently small bulge has led to the suggestion of massive outer halos in s p i r a l galaxies. Since the rotation curve of NGC 4736 appears to have a d i s t i n c t "turnover", with a decrease of c i r c u l a r velocity at large r a d i i , i t i s less l i k e l y that there e x i s t s an extensive outer halo of the type postulated by Ostriker, Peebles and Yahil (1974). Is a ce n t r a l bar-like or oval d i s t o r t i o n caused by the bar instab-i l i t y , or i s i t caused by the more subtle s p i r a l resonance effects considered by, among others, Contopoulos (1970, 1975), and Mertzanides (1976) ? The bar-like or oval d i s t o r t i o n i s probably not due to the "disk-heating e f f e c t " as discussed by Ostriker and Peebles, but rather may be caused by the more subtle s p i r a l resonance e f f e c t s considered by Contopoulos (1970, 1975). The semi-stellar nucleus may i t s e l f be caused by the non-axisymmetry of the central bulge. Matsuda and Nelson (1977) have suggested that shocks experienced by gas moving through g a l a c t i c bars may lead to the loss of angular momentum by the gas and i t s eventual i n f a l l into the nucleus. However, the globular c l u s t e r accretion model of Tremaine, Ostriker and Spitzer (1975) provides another a t t r a c t i v e explanation for the formation of g a l a c t i c nuclei. Implications of the Model. Inner s p i r a l s and bars may exist in galaxies other than those mentioned i n section 4.7. Holmberg (1958) has suggested that a l l s p i r a l galaxies contain a b a r - l i k e d i s t o r t i o n i n 157 th e i r central regions. »hen the inner Lindblad resonance for the main s p i r a l pattern i s at a large radius, an inner pattern could e x i s t . Several of the galaxies studied by Roberts, Roberts and Shu (1975) have main pattern inner resonances at r a d i i greater that 2 kiloparsecs, e.g. M31, M81 and our own galaxy. High c e n t r a l mass concentration (hence early Hubble type ) and low pattern speeds lead to large resonance r a d i i . The galaxy NGC 4736 i s guite s i m i l a r to M31 and to our own galaxy, with s i m i l a r structure and s i m i l a r rotation curve, and i t i s possible that inner bar-like d i s t o r t i o n s also e x i s t i n the l a t t e r two galaxies. There i s a variation with respect to radius of e l l i p t i c i t y and position angle for the isophotes of M31 (Peterson, Ford and Rubin 1977), and f a i n t dust s p i r a l structure i s observed to within 6" of the nucleus (Johnson and Hanna 1972). Anomalous gas motions exist i n the central bulge (Rubin and Ford 1971). Similar phenomena have been found i n M81 (Goad 1976). Peculiar v e l o c i t i e s i n the c e n t r a l regions of our own galaxy have been known for a long time, and a bar has been suggested as the cause(Johnson 1957, Lindblad 1959, Cohen and Davies 1976) . Matsuda and Nelson (1977) have suggested that an inner bar could provide the driving force for the main s p i r a l system in our galaxy. However, such a bar would have to rotate at the same angular speed as the main pattern. Roberts, Roberts and Shu (1975) found a pattern speed SLP of 13.5 Km s _ 1 Kpc - 1 for the Galaxy, whereas the strong perturbation model of 158 Sorensen, Matsuda and Fujimoto (1976) requires a much higher pattern speed. flatsuda and Nelson (1977) do, however, propose the a l t e r n a t i v e idea that the inner bar does not co-rotate with the main s p i r a l pattern. The high non-circular v e l o c i t i e s found inside 3 kpc by Cohen and Davies (1976) suggest that a rapidly rotating pattern or density perturbation e x i s t s i n the centre of our galaxy. iLi.9 NGC 4736: Conclusions The disclosure of a bar-like central structure and the construction of dynamical models from area photometry strongly suggest that a double s p i r a l pattern exists i n NGC 4736. This model can q u a l i t a t i v e l y be associated with the emission and the s l i q h t l y anomalous v e l o c i t i e s observed in t h i s galaxy. The explosion models of van der Kruit (1974) and Sanders and Bania (1976) are therefore not as necessary to explain these anomalies. Similar conclusions may apply to other galaxies such as M31, H81 and our own galaxy. 159 CHAPTER 5 THE GLOBULAR CLUSTER NGC 7078 5.1 Background The bright, high-latitude globular cluster NGC 7078 (=M 15) i s notable because i t s centre l i e s within one arc minute of an X-ray source (Giacconi et a l . 1974; Clark, Markert and L i 1975), and because i t has an unusual central excess, or "cusp", of surface brightness (King 1975). Stars have been counted d i r e c t l y to within 0.45 arc minutes radius of the centre by King et a l A , (196 8) and to within 0.12 arc minutes by Bahcall, Bahcall and weistrop(1975). Leroy, Aurier and Lagues (1976) have taken a series of standard and electronographic plates i n exceptionally good seeing (0.7"), and within a f i e l d of 25" x 25" they have measured the positions and V magnitudes of 120 stars down to V=18, which contribute 30 percent of the t o t a l l i g h t in that f i e l d . They f i n d a d i s t i n c t unresolved concentration at the centre with a radius of about 2". Integrated aperture photometry has been published for apertures of 0.093 to 0.905 arc minutes radius (King 1966b). Integrated surface brightness p r o f i l e s have been obtained from electronographic plates by Kron and Papiashvili(1967) and by Newell, da Costa and Norris (1976). The l a t t e r group has also obtained UBV integrated colours (Newell, private communi-160 cation), showing that the cusp i s not s i g n i f i c a n t l y bluer than the unresolved population of the cluster. High-resolution blue and red plates of the nuclear region are being reduced by Feibelman (1977) , who suggests a high central concentration of red giants. Illingworth and King{1977) have proposed that a central "black hole" i s not needed, and that a modest number of 1.5 to 2.0 solar mass objects (such as old neutron stars) would be s u f f i c i e n t to produce the observed central cusp. These objects are more massive than the probable present red giant mass of 0.8 solar masses, and would long ago have migrated to the centre of the clu s t e r (Spitzer 1969). H i l l s and Day(1976) have calculated that NGC 7078 may have experienced about 1500 c o l l i s i o n s between i t s main seguence stars, one of the highest such numbers for t h e i r sample of globular clusters (the median value i s 92 c o l l i s i o n s per c l u s t e r ) . NGC 7078 has a f a i r l y short relaxation time of about 10 8 years , and a high escape velocity..of about HQ km s~ 1 (Peterson and King 1975). In the l i g h t of ideas discussed i n the f i r s t chapter regarding the p o s s i b i l i t y of unusual phenomena in the cores of "X-ray" globular c l u s t e r s , the central region of NGC 7078 was observed using the BETICON area photometer mounted at the Cassegrain focus of the 1.8 metre telescope of the Dominion ftstrophysical Observatory. 161 5.2 NGC 7078: The Observations The observations l i s t e d i n Table XX were taken on two unusually good nights at V i c t o r i a , sharing time with a.Condal. Since l i t t l e time was available for my observations, and because photometric conditions and good seeing are rare at V i c t o r i a , the observations were made in a d i f f e r e n t i a l mode, in the same fashion as the observations at Mauna Kea. The second night (1976 September 16) was d e f i n i t e l y superior, and only the observations from the second night were analysed in d e t a i l . Since the exposures were of d i f f e r e n t durations, care had to be taken with subtraction of the dark current. The average dark current was about 0.3 instrumental units per diode per minute, but a few diodes, about 3 percent, had dark currents of between 0.6 and 5.2 units per diode per minute. Summing over a selection of these "hot" diodes showed that up to the half-hour exposure time used here the dark current was very accurately a l i n e a r function of the exposure time. A composite dark current corresponding to an e f f e c t i v e integ-ra t i o n time of 59 minutes was computed by summing the 31 min-ute, 20 minute and 11 minute dark currents, each minus a one minute integration. The l i n e a r i t y of dark current versus time allows the dark current for any exposure time during the same night to be computed by a simple scaling. This requires the assumption that the dark current rate did not vary s i g n i f -162 TABLE XX . Log of Observations for NGC 7078 (=M15), taken using the 1.8m r e f l e c t o r of the Dominion Astrophysical Observatory, V i c t o r i a . Permanent Object F i l t e r Exp. Time at End FileSfiecord Time (U.T.) F i l e 30 1976 Sept.15 records 140 NGC7078 V 5m 8h 17m 141 Dk - 1m 8h 19m 142 NGC7078 V 10m 8h 32m 143 Dk - 1m 8h 36m 144 NGC7078 r 10m 8h 52m 145 Dk - 1m 8h 54m 146 Dk - 1m 8h 55m 148 Dk - Im 8h 56m 150 Sky r 1m 8h 57m 152 Sky V 1m 8h 59m 154 Sky V 1m 9h 00m 156 Dk - 1m 9h 0 3m 276 Dk - 5m 12h ; 47m 278 (2) 288 Dk , , 1m. 12h i 54m 310 Flat F i e l d r 1m 13 h i 21m 312 Flat F i e l d V 1m 13h . 24m 313 Dk - 1m 13h i 25m 314 Fl a t F i e l d b Im 13h i 27m 360 Dk - 11m 14h i 53m 362(2) 366 Dk 1m 15h 02m f i l e 31 1976 Sept. 226(2) 232 HD172323 r 20s 4h 20m 233(1) 235 Dk - 20s 4h 22m 23 8(2) 246 HD172323 V 20 s 4h 26m 248 Dk - 20 s 4h 27m 250(2) 260 HD172323 b 20s 4h 30m 26 2 HD172323 b 1m 4h 31m 263 Dk - 1m 4h 34m 264 (2) 266 Dk - 20s 4h 3 5m 350 NGC7078 r 20m 7h 4 1m 352(2) 356 NGC7078 r 1m 7h 44m 358 NGC7 078 r 6m 7h 50m 360 (2) 362 NGC7078 r 1m 7h 52m 363 Dk - 1m 7h 53m 364 NGC7078 b 20m 8h 16m 366 (2) 368 NGC7078 b Im 8h 18m 369 Dk - Im 8h 21m 370 NGC7078 V 11m 8h 35m 372(2) 376 NGC7 078 V 1m 8h 38m 377 Dk - 1m 8h 40m 163 F i l e 32 1976 Sept. 16 42 Sky r 6m 12h 14m 44 (2) 48 Sky r 1m 12h 17m 50 Sky V 6m 12h 25m 52(2)56 Sky V 1m 12h 28m 58 Sky b 6m 12h 36m 60 (2) 64 Sky b 1m 12h 39 m 66 Dk - 6m 12h 46 m 68 (2)72 Dk - Im 12h 49m 74 Dk - 6m 12h 55m 76 (2)80 Dk - 1m 12h 58m 92 Flat F i e l d b 1m 13h 22m 93 Dk - 1m 13h 24m 94 Flat F i e l d r 1m 13h 26 m 95 Dk - 1m 13b 28m 96 Flat F i e l d V 1m 13h 29 ra 97 Dk - 1m 13h 31m 116 Dk - 6m 14h 14m 117 Dk 1m 14h 15m 118 11m 14h 26m 120 (1) 123 Dk - 1m 14h 30m 124 Dk - 20 m 14h 50m 126 (2) 138 Dk - 1m 14h 56m 140 Dk 31m 15h 28m 142 Dk - 1m 15h 29m 144(1) 148 Dk - 1m 15h 34m Notation i ( j ) k : Records i , i + j , i+2j,....... to k. The INTERDAT& Model 4 was used for data recording. . 164 i c a n t l y during the n i g h t . Although long dark c u r r e n t s were not measured a t the beginning of the night, the l i n e a r i t y of the measurements spread over t h r e e hours towards the end of the night of September 16 (U.T.) suggests that the dark c u r r e n t r a t e was s t a b l e . In a d d i t i o n , h a l f - h o u r exposures taken by A.Condal of p l a n e t a r y nebulae throughout the same night (Sept.16) showed t h a t the dark c u r r e n t r a t e was very s t a b l e , and t h a t the "hot" diodes were always adeguately c o r r e c t e d f o r . The temperature i n s i d e the cold-box was checked from time t o time and was not seen to vary from some po i n t between -75° and -76° C e l s i u s . The sky background measurements were made j u s t a f t e r the beginning of a s t r o n o m i c a l dawn, and so may be somewhat e x c e s s i v e . However, the dominant source of e r r o r was the b a s e l i n e f l u c t u a t i o n . The s c a l e d observed per diode sky b r i g h t n e s s e s were s t i l l very low: 2.3+1.4, 3.0±0.7, 1.6±0.4 i n s t r u m e n t a l u n i t s r e s p e c t i v e l y f o r the b l u e (20m), v i s u a l (11m) and r e d (6m) exposures. The e r r o r s were computed from the r.m.s. f l u c t u a t i o n of the b a s e l i n e records F32R68-72 and F32R76-80. The sky b r i g h t n e s s values were not much l a r g e r than the peak-to-peak b a s e l i n e f l u c t u a t i o n , even with the moon up and dawn coming. The reduced images of NGC 7078 are presented as i s o p h o t a l contours i n F i g u r e s 46, 47 and 48. 165 EIP .UHE 4 6 . N G C 7 0 7 8 : Blue image contour map. 166 FIGURE 47. NGC 7078: V i s u a l image contour map. 167 168 5 i l NGC 7 078: Scale and Orlentat ion The lack of very compact {30" x 30") calibr a t e d star f i e l d s required the choice of suitably spaced, well measured f a i n t v i s u a l doubles., In p r i n c i p l e , observinq a sel e c t i o n of such doubles and f a i n t sinqle standards i n photometric cond-i t i o n s could qive a f u l l photometric t i e - i n as well as a c a l i b r a t i o n of the plate scale and detector orientation. The time available allowed observations of only one double, HD 17 2323 (= ADS 11503), l i s t e d i n Table XX . Astrcmetry l i s t e d by Aitken(1932) qives a mean separation of 19.83±0.15 arc seconds, at a position anqle of 25.0±1.1 deqrees {errors are standard deviations). Averaginq over the 1 minute blue and 20 second vis u a l and red exposures of HD172323 qives a separation of 31.94+0.03 diode units, at a position anqle of -73.8+0.1 deqrees i n the instrumental system. This y i e l d s a plate scale of 0.621+-.005 arc seconds per diode, with the orientations as in Fiqure 49. It should be noted that the KETICON data qives more consistent spacinqs and orientations than the published visual micrometry. 169 HOUSE 49. O r i e n t a t i o n of RETICON camera on D.A.O. . 1.8 metre t e l e s c o p e . 170 5._4 NGC 7078: Approximate Photometric C a l i b r a t i o n Photometry f o r t h i s double has been published by Roman(1955) and by Eggen (1963). , Only Eggen has a separate magnitude and colour f o r each component: V = 8.08, 10.70, and B-V = 0.58, 1.10, f o r components A and B respectively. Isophotal contours were computed for the s t e l l a r seeing images. The contour i n t e n s i t i e s are plotted versus e f f e c t i v e radius in Figure 50 using Gaussian scales. The Gaussians defined by the l i n e a r portions of the curves in Figure 50 were used to compute the observed magnitude differences between HD-172323 A and B, using the relationship for integrated i n t e n s i t y , The intercepts of Figure 50 are egual to log i{0,0) and the slopes correspond to -1.737/A2, where A i s the seeing disk diameter defined by the isophote f o r 1/e of the central inten-s i t y i ( 0 , 0 ) . The commonly used seeing d e f i n i t i o n of F u l l Width at Half-Maximum (FWHM) corresponds to A multiplied by 4 ~ l n (0.5)' = 0. 8325546. The short exposures for HD172323 gave A= 2.65, 2.67 and 2.33 arc seconds for the b, v, and r f i l t e r s respectively. Estimating s t e l l a r magnitudes by f i t t i n g Gaussians to the seeing disks gave differences between the components <fv= 2.68, f(b-v) = 0.27 and £(v-r)= 0.28. Osing the FIRM sguare 50., S t e l l a r image i n t e n s i t y carves. 172 aperture i n s t r u c t i o n a PEBTUBE , with a 15 x 15 diode maximum aperture, the following were obtained: Sv- 2.74, J"(b-v) -0.09 to 0 .62 (very uncertain due to the proximity to th edge of the f i e l d of component ft and the faintness of component B in the blue exposures), and <f(v-r) = 0.34 . Extensive obser-vations would be needed to establish the photometric v a l i d i t y of the two methods. Eggen's data correspond to /V= 2 . 6 2 , X(B-V) = 0 .52 (in the sense of star B - star a ) . While the agreement between Sv and /v i s reasonable, more data was needed to obtain even a rough c a l i b r a t i o n . To obtain an approximate colour c a l i b r a t i o n of the BETI-CON camera, observations were undertaken using the 30cm Casse-grain r e f l e c t o r of the Department of Geophysics and astronomy, at OBC. observations were taken on three nights of unusual c l a r i t y (for Vancouver, that is) , but only one night could be described as being p o t e n t i a l l y photometric. Subsequent reduc-tions showed that the transparency or the response varied widely but slowly, allowing some colour measurements to be used. Single stars were chosen from the Arizona-Tonantzintla Catalogue of bright stars i n OBVRI (I r i a r t e et a l . - 1965) . Since the plate scale on the 30cm telescope was about 5 arc seconds per diode, the stars were defocussed to an apparent diameter of about 10 diodes. a d i r e c t summation of intensity was performed to obtain a measure of s t e l l a r magnitude, the outer regions of the f i e l d being used to measure the sky back-173 ground. This i s i n contrast to the Gaussian f i t t i n g method for star images at high magnification. The reductions were performed using a variety of assumed plausible extinction c o e f f i c i e n t s . Although the zero-points of the transformations could not be accurately evaluated, the scale factors did not vary greatly for different sets of extinction c o e f f i c i e n t s . Formally, where the errors are estimated from the variations of the c o e f f i c i e n t s using di f f e r e n t extinction c o e f f i c i e n t s . Allowing for the fact that a different telescope was used for the observations of NGC 7078, I take the following approximate transformations, u i. o £-i.l (75) 174 The zero-points can be evaluated by comparison with c i r c -ular aperture photometry of NGC 7078 (King 1966b) . There i s l i t t l e knowledge of the colour dependence of V, but the res u l t s f o r HD172323, which has components of rather d i f f e r e n t colours, suggest that i t may not be large. 5^5 NGC 7078: Centred Aperture Photometrx± U n t i l the advent of panoramic detectors, photometry of the integrated l i g h t through apertures of di f f e r e n t sizes centred on the nucleus, or by using a small aperture and making spot measurements of diff e r e n t parts of the c l u s t e r . NGC 7078 has been observed in either or both these ways by Kron and Mayall(1960), King(1966b), van den Bergh(1967) and Chun(1976). The observations of King(1966b) are the only available data taken through apertures small enough to f i t into the f i e l d of view of the RETICON camera on the 1.8 metre telescope. Synthetic c i r c u l a r apertures were computed using the ELLIPSE ins t r u c t i o n of FIRM i n the aperture mode ( M0DE=A ). The integrated s i g n a l , scaled down, i s l i s t e d i n Table XXI . Apertures corresponding to King's two smallest apertures are included. The errors quoted are those for an uncertainty of ±1 unit i n the baseline l e v e l of each exposure, and are most serious for the larq e r apertures. Each aperture was centred at the apparent position of the nucleus i n each exposure, t h i s 175 TABLE XXI . Centred c i r c u l a r aperture measures of NGC 7078. Aperture b v r Baseline d i a . " {20 min) (11 min) (6 min) error 5.0 4.28 2.57 5.24 0.02 7.5 8.32 5.00 9.85 0.05 10.0 13.06 7.86 15.34 0.09 11.16* 15.58 9.32 18.30 0. 11 12.5 18.50 11.13 21.74 0.14 15.0 24.37 14.67 28.81 0.19 17.5 30.38 18.41 36.02 0.28 20.0 36.35 22. 13 42.91 0.36 21.60* 40. 13 24. 43 47. 19 0.42 22.5 42.20 25.73 49.60 0.46 25.0 47.98 29.29: 56.21 0.56 : Apertures corresponding to those of King(1966b). :Aperture touches edge of f i e l d . Integrated i n t e n s i t i e s have been divided by 2256 (number of l i v e diodes). Errors correspond to ±1 unit baseline error per diode. 176 p o s i t i o n having an u n c e r t a i n t y o f about 0 . 3 diode u n i t s d i s t a n c e . I n s t r u m e n t a l c o l o u r s and magnitudes are l i s t e d i n Table XXII , with no c o r r e c t i o n s f o r exposure time or e x t i n c t i o n s i n c e the photometry r e p o r t e d here i s d i f f e r e n t i a l . Each i n d i v i d u a l B and V exposure can be c a l i b r a t e d d i r e c t l y using the r e l e v a n t o b s e r v a t i o n s of King (1966b), l i s t e d i n Table XXIII . Using the t r a n s f o r m a t i o n e g u a t i o n , B - V = K. + K (^)  { ? 6 ) with Kj = 1.1 and averaging King»s r e s u l t s , we get Kft = 1.27 f o r the data i n Table X X I I I . The immediate r e s u l t of these measurements i s t h a t centred a p e r t u r e s do not show any s i g n i f i c a n t i n t e g r a t e d c o l o u r v a r i a t i o n s f o r d i f f e r e n t a p e r t u r e diameters. The s l i g h t c e n t r a l reddening i n (b-r) i s probably due t o the b e t t e r s e e i n g i n the r exposure. T h i s e f f e c t must be c o r r e c t e d f o r before c o l o u r maps i n two dimensions can be com-puted, and i s the s u b j e c t of the next s e c t i o n . 177 TABLE XXII . C i r c u l a r aperture instrumental magnitudes and colours for NGC 7078. Scaling as for Table XXI. Aperture v b-v b-r dia. " 5.0 -1.03±0.01 -0.55±0.01 0.22±0.01 7. 5 -1.75 -0.55 0.18 10.0 -2.24 -0.55 0.18 11.16 -2.42 -0.56 0. 18 12. 5 -2.62 -0.55 0.18 15. 0 -2.92±0.013 -0.55±0.02 0.18±0.015 17.5 -3. 16 -0.54 0.19 20.0 -3.36 -0.54 .0. 18 21.60 -3.47 -0.54 0.18 22. 5 -3.53 -0.54 0.18 25.0 -3. 67:±0.02 -0.54:±0.03 0.17+0.02 TABLE XXIII . Published centred aperture photometry of inner region of NGC 7078 {from King 1966b). Errors are mean errors. Aperture V B-V Dia. " 11. 16 21.60 9.90+0. 12 8.94±0.08 0.64±0.05 0.68±0.03 179 5 ..6 NGC 70782 Seeing Analysis And Colour Maps In order to form a colour map or r a t i o map from two images, i t i s necessary that: (1) the images be in geometrical r e g i s t r a t i o n , and, (2) the combined seeing and instrumental p r o f i l e s be the same for each image. An attempt was made to use the s p a t i a l power spectra of the images to determine the seeing, but the r e s u l t s were inconclusive. A much simpler method was to use the FIRM ins t r u c t i o n SECTION i n l i n e mode { HODE=L ) to plot the inten-s i t y along a l i n e passing through a given point at a s p e c i f i e d orientation in the image. The e f f e c t i v e diameter of star images was obtained by manually measuring the p r o f i l e s . The b exposure was found to have a 1/e seeing diameter of 4.0". The v seeing was 3.1" (in a roughly North-South d i r e c t i o n perpen-dicular to the East-West d i s t o r t i o n ) , and the r seeing was 3. 2". The red image therefore had to be smoothed so that i t s seeing could be degraded to that of the blue image. The diameter of the convolving Gaussian was 2.4", or 3.9 diode spacing units. The b and v images were brought into r e g i s t r a t i o n with the r image by computing the positions of a set of eight stars 180 i n each image, and f i n d i n g the mean displacement of these s t a r s r e l a t i v e to t h e i r p o s i t i o n s i n the r image. The displacements of the b and v images were c o r r e c t e d f o r using the F o u r i e r transform s h i f t theorem. A high-pass s p a t i a l f i l t e r was s i m u l a t e d by c o n v o l v i n g each image with a Gaussian of e f f e c t i v e " s e e i n g " diameter A= 6 diodes, and s u b t r a c t i n g the s t r o n g l y smoothed image from a l i g h t l y smoothed image (A= 1.5 d i o d e s ) . Only sharp f e a t u r e s such as s t a r images were r e -t a i n e d , while the u n d e r l y i n g d i s t r i b u t i o n of l i g h t was removed. The p o s i t i o n s o f the r e s i d u a l s t a r images were ob-t a i n e d by computing the c e n t r o i d s of t h e i r i s o p h o t a l c o n t o u r s . The r e g i s t r a t i o n c o r r e c t i o n s are l i s t e d i n Table XXIV . An a l t e r n a t i v e r e g i s t r a t i o n technique i s to compute the c o r r e l a t i o n f u n c t i o n between two images, i t e r a t i n g u n t i l a displacement i s found which maximizes the c o r r e l a t i o n (Arp and L o r r e 1976). However, t h i s i s somewhat time-consuming, where-as the c o n t o u r - c e n t r o i d method i s guick and g i v e s very c o n s i s -t e n t p o s i t i o n s f o r images of i s o l a t e d s t a r s such as the com-ponents of wide doubles. The presence of an u n d e r l y i n g s u r -f a c e b r i g h t n e s s and the crowding of s t a r images a l t e r s the contour p o s i t i o n s , even a f t e r high-pass f i l t e r i n g . T h i s i n t r o d u c e s a s c a t t e r which appears as the standard d e v i a t i o n i n Table XXIV . F i g u r e 51 i s the map of b-r i n the i n s t r u m e n t a l system. L i n e scans using the.SECTION command are shown i n F i g u r e 52 f o r two d i f f e r e n t o r i e n t a t i o n s , one o f which (l?5*p) avoids TABLE XXIV . P o s i t i o n a l r e g i s t r a t i o n corrections for images of NGC 7078. Record F i l t e r x y F31B364 b 0.43±0. 31 -0.12+0.14 F31B370 v -3.67±0.2U -0.25*0.20 F31R358 r 0. 0. Errors are standard deviations. Eight s t e l l a r images (including nucleus) used i n each picture. Blue and v i s u a l images registered with red image. 182 FIGURE 51. NGC 7078: Instrumental Magnitude d i f f e r e n c e between smoothed nucleus. B - R images. c o l o u r map. •X' marks 183 i o 193.8* -32.0 -24.0 -16.0 -B.0 0.0 8.0 16.0 24.0 32.0 DJST. IN PIXEL UNlfS ZISUSE 52. L i n e scans a c r o s s c o l o u r map f o r two d i f f e r e n t p o s i t i o n angles. Dotted l i n e i s f o r magnitude d i f f e r e n c e between smoothed images as p l o t t e d i n F i g . 51. S o l i d l i n e f o r unsmoothed images. 184 bright stars as much as possible. The blue image was convolved with a Gaussian of 2.0 diodes e f f e c t i v e diameter, and the red image was convolved with a Gaussian of 4.35 diodes diameter. The e f f e c t i v e seeing was therefore about 6.7 diodes. To obtain a colour-magnitude diagram f o r even the bright-est stars in t h i s object, much better seeing and photometric c a l i b r a t i o n s are reguired. An analysis of the star images to extract more information about the makeup of the core region of NGC 7078 has therefore not been attempted. 5.7 NGC 7078:. Discussion and Conclusions,. The colour map and sections of Section 5.6 show that most of the bright stars i n the f i e l d of view are red, and that the nuclear region appears to be s l i g h t l y redder but not as red as the brightest red giants. Whereas c i r c u l a r aperture photo-metry shows no average r a d i a l colour gradient, a f u l l two-dim-ensional display shows d i s t i n c t colour v a r i a t i o n s , with the underlying unresolved s t e l l a r population being much bluer than the red giants and s l i g h t l y bluer than the nuclear region. However, the poor seeing, about 4 seconds, i s such that i t i s impossible to t e l l whether the s l i g h t l y redder nucleus i s due to i n d i v i d u a l red giants of moderate luminosity or to a redder underlying population of lower luminosity stars toward the centre. Leroy, Auriere and Lagues (1976), with much better 185 s e e i n g , f i n d a p a i r o f i n t e n s i t y maxima i n the unresolved nuc-l e a r r e g i o n . They choose one of these peaks as the c l u s t e r c e n t r e . There may t h e r e f o r e be a moderately luminous s t a r w i t h i n 1" of of the " t r u e " c l u s t e r c e n t r e , and the c o l o u r d i s t r i b u t i o n obtained i n t h i s work may be a f f e c t e d by i t . However, i t i s apparent t h a t at the r e s o l u t i o n and bandpasses of the o b s e r v a t i o n s r e p o r t e d here, no r a d i c a l l y unusual c o l o u r index v a r i a t i o n i s to be found i n the n u c l e a r r e g i o n of NGC 7078. T h i s i s c o n s i s t e n t with the s p e c t r o s c o p i c o b s e r v a t i o n s of Newell, da Costa and N o r r i s (1976) . The red exposure i n p a r t i c u l a r shows the importance o f s e p a r a t i n g out the red g i a n t s from the l e s s luminous under-l y i n g p o p u l a t i o n i f a b e t t e r understanding of the d e n s i t y d i s t r i b u t i o n i s to.be obtained. . Red and i n f r a r e d . i m a g e s taken using the RETICON camera or with charge-coupled d e v i c e s are extremely v a l u a b l e i n i d e n t i f y i n g r e d g i a n t s . Given much b e t t e r s e e i n g , h o r i z o n t a l branch s t a r s s h o u l d a l s o be i d e n t i -f i a b l e through a blue f i l t e r . The present work demonstrates the e f f e c t i v e n e s s of the RETICON camera as a t o o l f o r e x p l o r -i n g the c e n t r a l r e g i o n s of g l o b u l a r c l u s t e r s . Standard photo-g r a p h i c and photometric t e c h n i g u e s are very d i f f i c u l t t o use f o r such work. 186 CHAPTER 6 SUMMARY AND CONCLUSIONS 6.1 Conclusions. In t h i s thesis, I have described the development of a multi-diode array area photometer, and i t s application to an investigation of the c e n t r a l regions of the dynamically i n t e r -esting galaxy NGC 4736 and the X-ray emitting globular c l u s t e r NGC 7078. The RETICON camera has a rather high e f f e c t i v e noise figure of about 8000 electrons. New charge-coupled devices may have e f f e c t i v e noise figures of 100 electrons or l e s s , giving about 5 magnitudes improvement in s e n s i t i v i t y . However, the superior performance of the RETICON at high signal levels may continue to make useful the camera developed here. Charge-coupled devices have problems of "blooming" and incomplete charge transfer at high charge l e v e l s . A detailed analysis of CCD detection of s t e l l a r images i s needed to make a guantitative comparison with the RETICON camera. A t h e o r e t i c a l analysis has shown that for a seeing diameter A > 2.5, (defined at 1/e of 1(0) ), a l i a s i n g i s of no consequence at any s p a t i a l freguency.photometry of stars i s feasible for A > 2.0 diode spacings., Analysis of double-star observations shows that r e l a t i v e p o s i t i o n a l accuracies of astrometric standard are possible with this instrument. 187 provided that there are no serious geometric i r r e g u l a r i t i e s i n the diode array. Area photometry of NGC 4736 showed that the surface brightness has an inverse sguare dependence on radius. The simple empirical King law, o r i g i n a l l y obtained for the cores of globular clusters (King 1962), was found to give a good approximation for the surface brightness, with a probably un-resolved central peak deviating from i t . Subtraction of c i r c u l a r l y symmetric d i s t r i b u t i o n s of i n t e n s i t y reveals a small central bar-like structure, the ends of which meld into the inner s p i r a l structure photographed by Chincarini and Walker (1967); Simple bulge and disk models strongly suggest that two s p i r a l systems exist i n NGC 4736, one inside the ether, with the inside system rotating perhaps two or three times as r a p i d l y as the outer or main s p i r a l pattern. This involves the assumption that both s p i r a l s are two-armed s p i r a l s . Colour maps show that beyond 10 arc seconds there i s a strong decrease of colour index with decrease of radius. Inside the central region, the reddest areas are not at the nucleus but rather in the areas where the differences between the observed and calculated.surface brightnesses are the most negative. This probably i s caused by dust. I t appears that dust also defines the inner s p i r a l structure on photographs. This fact and the symmetry of the bar-like structure found i n t h i s work strongly suggest a systematic o r i g i n for the inner 188 s t r u c t u r e . A c e n t r a l mass to l u m i n o s i t y r a t i o of 2.4 to 3.6 was o b t a i n e d , which i s very s i m i l a r t o t h e value of 2.5 found f o r the whole galaxy by Bosma, van der Hulst and S u l l i v a n (1977). Images of the X-ray e m i t t i n g g l o b u l a r c l u s t e r NGC 7078 were recorded i n t o o poor a s e e i n g t o allow r e s o l u t i o n of the c e n t r a l cusp. An a n a l y s i s of a c o l o u r map o f the c l u s t e r showed that there e x i s t s p a t i a l c o l o u r d i f f e r e n c e s , mostly a s s o c i a t e d with red g i a n t s , and t h a t these c o l o u r d i f f e r e n c e s are not r e v e a l e d by c e n t r e d c i r c u l a r aperture photometry. { A s i m i l a r e f f e c t was noted f o r the galaxy NGC 4736, i n which there probably e x i s t young s t a r s and dust p a t c h e s ) . B e t t e r r e s o l u t i o n i s needed to f u l l y separate the e f f e c t s of the r e l a t i v e l y few luminous s t a r s from the " u n d e r l y i n g background" of much more numerous lower l u m i n o s i t y s t a r s . The area photo-metry supports the c o n c l u s i o n s based on spectroscopy of Newell, da Costa and N o r r i s (1976) t h a t t h e r e i s no r a d i c a l d i f f e r e n c e between the cusp and the " u n d e r l y i n g " p o p u l a t i o n . 189 6.2 Problems for Future lork.. , The RETICON camera should be compared i n d e t a i l with cameras which employ charge-coupled devices (CCD's). Is the RETICON camera s t i l l superior despite i t s high noise l e v e l for the observation of g a l a c t i c nuclei, globular c l u s t e r s and s t e l l a r positions ? This comparison needs more res u l t s from CCD cameras. The image processing code FI8H should be extended to carry out the following: (i) f i t e l l i p s e s , including quadrupole terms, to contours using least squares Fourier s e r i e s f i t t i n g , i n the manner of Crane (197 5) , ( i i ) produce output i n a form suitable for the new CGMTAL graphics system to be i n s t a l l e d at OBC, ( i i i ) r e g i s t e r images by co r r e l a t i o n of complete images, (iv) accomodate images from larger arrays, (v) assemble macros ( i . e . subroutines) i n the FIRH language. The INTERDATA observing programmes have already been modified by C. Pritchet to include input and output v i a a visual display unit. A most useful addition, involving extended-precision arithmetic, would be to compute a sharpness c r i t e r i o n for focussing the telescope. Muller and Buffington (1974) have shown that the sum of sguares, 2? T... i s the J most sui t a b l e quantity to define focussing i n real-time. Allowinq for transparency fluctuations, a normalized c r i t e r i o n would be: 190 (77) The most exciting prospects are suggested by the re s u l t s for the galaxy NGC 4736. The combination of area photometry with rotation curves from o p t i c a l and radio spectroscopy opens up many p o s s i b i l i t i e s . Not only does area photometry measure projected emissivity and, hopefully, density, but also i t can reveal features which photographic methods do not show e a s i l y . The information content i s azimuthal as well as r a d i a l . The importance of t h i s has been demonstrated e f f e c t i v e l y by Schweizer (1976). The model f o r the nuclear region of NGC 4736 strongly suggests that s i m i l a r structures may exist i n galaxies which are morphologically and dynamically s i m i l a r to NGC 4736, e.g. H31, M81 and our own Galaxy. I t would be most int e r e s t i n g to observe a number of galaxies to see whether they contain structure inside the radius where t h e i r inner Lindblad reso-nance i s thought to l i e . Data has been obtained for NGC 5194 ( = M51) and NGC 4258, although not of as good qua l i t y as the data for NGC 4736. This and the polarimetry of NGC 4736 should be reduced in the near future. It i s also very important that a whole galaxy be 191 observed, not just the inner region. It i s most important that some understanding of the run of mass to luminosity r a t i o within galaxies be gained. Photometry over a much larger region of NGC 4736 and other galaxies i s needed. The vexing guestion of g a l a c t i c halos could be resolved i f much better knowledge of the d i s t r i b u t i o n of matter i n the disks of galaxies could be obtained. While the r e s u l t s of area photometry suggest that mass to luminosity r a t i o s do not vary by much in the inter-arm regions of s p i r a l galaxies (Schweizer 1976), rotation curve data suggests the opposite (Roberts 1975), at lea s t in the outer regions. The high red s e n s i t i v i t y of s i l i c o n diode based devices should be very useful i n observing the outer reaches of galaxies, since i t has been suggested that an outer halo may consist largely of red dwarfs. Low noise and low magnification are reguired. Diode array and CCD detectors used at low magnification may also have a cosmological application: the measurement of the isophotal diameters of galaxies. An f/0.8 lens in front of the RETICON has been t r i e d by R.B.Tully and t h i s author, but various problems prevented useful data from being obtained. Great care has to be taken to avoid scattering through multiple r e f l e c t i o n s and refractions when using such a strongly convergent lens with a multi-diode array. A halo around sharp images was found with the f/0.8 arrangement. The idea of the two-spiral model needs to be investigated 192 t h e o r e t i c a l l y . ft hydrodynamical r a t h e r than p a r t i c l e kine-matic model i s needed. The work of Sanders and Huntley (1976) and of Sorensen, Matsuda and Fujimoto (197 6) r e p r e s e n t s the s t a r t i n g p o i n t f o r more e x t e n s i v e hydrodynamical c a l c u l a t i o n s . The problem of i n t e r a c t i o n between the i n n e r p a t t e r n and the main d i s k i s probably extremely d i f f i c u l t t o t r e a t t h e o r e t i -c a l l y , but i t c o u l d be a s s o c i a t e d with the problem o f the energy source f o r d r i v i n g or t r i g g e r i n g the main s p i r a l p a t t e r n . A p o s s i b i l i t y which has not been explored i n t h i s t h e s i s i s that of s p i r a l s i n v o l v i n g one, three or f o u r arms. One-armed s p i r a l s may be c o n t r a - r o t a t i n g , with a negative p a t t e r n angular v e l o c i t y . T h i s i s because the inner L i n d b l a d resonance freguency f o r one-armed s p i r a l s i s _ i l — \C , which i s negative. The s t r u c t u r e of s p h e r o i d a l systems such as e l l i p t i c a l g a l a x i e s and the bulges o f s p i r a l g a l a x i e s w i l l be b e t t e r understood once h i g h l y accurate s u r f a c e b r i g h t n e s s and c o l o u r maps are a v a i l a b l e . Development of models and techniques along the l i n e s of the work of Wilson (1975) and Hunter (1975) could allow a determination of the phase d i s t r i b u t i o n f u n c t i o n as w e l l as the d e n s i t y d i s t r i b u t i o n . T h i s i n t u r n should shed l i g h t on the formation and r e l a x a t i o n processes of q a l a x i e s . Kinq (1975) and Wilson (1975) have shown t h a t present knowledqe i s inadequate to e x p l a i n the r a d i a l v a r i a t i o n o f i s o p h o t a l e l l i p t i c i t y i n e l l i p t i c a l q a l a x i e s . ft combined t h e o r e t i c a l and o b s e r v a t i o n a l a t t a c k i s most d e s i r a b l e . 193 Work on globular c l u s t e r s using the BETICON camera i s already being undertaken by others. Multi-colour imaging of c l u s t e r cores may reveal evidence of a c e n t r a l massive object, the effects of s t e l l a r c o l l i s i o n s and coalescence, or the presence of close binaries which would accumulate at the centre. These topics were reviewed i n Chapter 1. Good seeing i s e s s e n t i a l i f the central regions are to be resolved. 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A Manual By S.H.Mochnacki Dept. of Geophysics and Astronomy, Oniversity of B r i t i s h Columbia. A Reduction Programme For Data For The BETICON RA50x50 Two-dimensional Camera. For IBM 370/168 Under MTS. October 1977. 207 FIRM: Fortran Interactive Record Manipulation. Purpose: A programme to process data from a 50 x 50 two-di-mensional image detector, using a simple language to specify the records to be reduced and the operations to be performed. It can be used either i n batch mode or i n t e r a c t i v e l y , but the hard output from batch mode i s more valuable i n certain cases. How to Use: 1 . Mount the necessary tapes. The tapes are optional (e.g. a t h e o r e t i c a l model may be the purpose of a FIRM run), and either input, output or both tapes can be used. In completeness: $MOUNT input tape rack no., *IN* SIZE =5040 V0L=label output tape rack no., *ODT* SIZE=20000 { V0.L= lab e l RING=IN } SENDFILE $C0NTR0L *IN* POSH =*2* N.B. The ICONTROL command i s e s s e n t i a l - i f the input tape i s being used. 20 8 2. Run Command; $RUN SM71:FIRM 2= [status f i l e ] 3=*IN* 4=*00T* {5=commands 6= print f i l e } Followed by source cards in the FIRM language. At the end of the deck (or terminal commands) , we have: END $ENDFILE Run parameters: 2=[ status f i l e } : s p e c i f i e s name of an MTS l i n e f i l e contain-ing the labels of the records on the output tape. The f i l e i s organized as follows; l i n e no. contents 1.000 la b e l for f i r s t record on output tape. 1.500 la b e l for t h i s f i l e and tape. 2.000 la b e l for second record. 3.000 " " t h i r d " (etc) (etc). 1-iILs. S e e Tape Procedures about setting up t h i s f i l e . 3=*IN* ;input tape "pseudo device name". =*DUHMY* i f not using a raw data input tape. Always mount *IN* with RING=OUT (i.e. never specify RING=IN ). 4=*OUT* :output tape "pseudo device mame". 209 =*DUMMY* i f no reduced output to be retrieved frcm or written on the "out" tape. 5= COMMANDS : input commands to FIRM (defaults to *S00RCE* ) 6= p r i n t f i l e : printed output from FIRM (defaults to *SINK* } 9=PLOTFILE :name of plot output f i l e for UBC plotting routines (see UBC PLOT ). This can be a temporary f i l e , e.g. -PLOTF . In such a case, the following must be placed before SSIGNOFF i f the plots are wanted: $RUN PLOT:Q PAR=-PLOTF Notes: 1. , The output status f i l e ( FORTRAN unit 2) i s used to keep track of the number of records on the output tape. The output tape i s automatically positioned using the data stored i n the output status f i l e , while a new record number f o r the output record i s automatically allocated by FIRM , and returned to the user. ft complete l i s t i n g of record labels i s automatically printed at the end of any FIRM run involving the output tape. 2. The output tape *OUT* can be mounted with RING=IN i f WRITE i s to be used, and RING=0UT i f RETRIEVE but not WRITE i s being used. 210 FIRM conventions in t h i s description: 1. Notation in description: (a) f } : brackets around parameter or str i n g means that each enclosed parameter i s optional and has a default value, usually 0.0 or 1.0 i f a re a l number, and 1 or 6 i f an array index, or the current value i f a f i l e index ( in LOAD, AVERAGE etc.). (b) [ ] : one of the enclosed parameter names or values must be included. (c) PAR=XX : such parameters can be i n any order, except M0DE= , which must be f i r s t i n a l i s t i f reguired. 2. Operands for i n t e r n a l operations; Operations of the form; OPER IA, IB mean that array IB operates upon IA and the r e s u l t i s stored in array IA, e.g. ADD IA,IB means that array IB i s added to array IA, the r e s u l t being stored i n array IA. 2 1 1 Delimiters and lengths: (i) Operation code. The operation code (e.g. LOAD, RETRIEVE, LABEL ) can have up to 8 characters, but only the f i r s t two characters are necessary and s i g n i f i c a n t (e.g. LO, RE, LA ). Blank i n the f i r s t column causes the card to be ignored. ( i i ) Array, s p e c i f i c a t i o n ^ There are six (6) storage or " r e g i s t e r " arrays i n core memory, l a b e l l e d 1 to 6. The array operands always follow the operation code unless not needed. The array operands always follow the operation code unless not needed. The array numbers must be sepa-rated from the operation code and from each other by a blank, a comma or both. ( i i i ) parameters; Parameters must be separated by a blank, or a comma. Parameters of the HODE=NAME type must be f i r s t in the parameter l i s t following the regis t e r array s p e c i f i c a t i o n . , Parameters of the PAB=XX type can be in any order, and are optional or mandatory as spe c i f i e d in the command descriptions. The egual 2 1 2 signs are optional, and can be replaced by a blank or comma, e.g.: PLOT 2,NCONT=20,MIN=2.0 can be written as: PL 2 HI 2 NC 20 Note that the decimal point i s optional in such cases i f there i s no decimal f r a c t i o n . N^Bj. A f a i r l y verbose and punctuated s t y l e i s recommended since i t allows for errors to be detected more e a s i l y and i s better practice a l t o -gether. The more verbose form of the example above makes more sense to the user. (i v) Minimum requirements: The underlined portions of character strings are the minimum requirements for the str i n g to be recognized by FIRM , e.g. LOAD 5,FILE 9 RECORD 10 can be as terse as: LO 5, F 9 R 10 Mis-spellings outside the minimum (significant) range do not matter, so long as the maximum s t r i n g s i z e i s not exceeded and the delimiters : blank • *, do l l a r •$*, egual *=* and comma are not used. 213 Genera1 Examjle RFS CARD SSIGNON MYID T=20 PAGES=99 PASSWORD SflOUNT RD0678 *IN* VOL=P04071 RF0010 *OUT* SIZE=20000 RING=IN SENDFILE $CONTROL *.IN* POSN=*2* $R0N SM71:FIRM 2=TPSTATUS 3=*IN* 4=*OUT* 9=-PLOTF ROW 1,0 2,0 50,0 COL 1,0 50,0 LOAD 1,FILE 10 REC 20 AVERAGE 2,REC 21,25 SUBTRACT 1,2 LABEL 1,*NGC 1000:RED:5 MIN:15 OCT' VIEW 1, 10. EXAMINE AVERAGE 1 PLOT 1,NCONT=20,MIN=5.0 WRITE 1 PRINT 1 END SENDFILE $RUN PLOT:Q PAB=-FLOTF SSIGNOFF Notes 1. This example assumes that the input tape i s labelled (see UBC TAPE ), with volume l a b e l P04071. 2. The output tape i n t h i s case i s unlabelledand on the "f l o a t i n g rack." at the Computer Centre. , 3. The f i l e SM71-FIRN contains the contour and Fourier transform routines. 214 Tap_e procedures and settinrj uja. The FORTRAN programme FIRM handles raw data from the OBC RETICON RA50X50 area photometer plus a set of instructions i n the FIRM language as input, with output on a variety of devices: l i n e printer, p l o t t e r , magnetic tape and disk-resident direct-access MTS l i n e f i l e . Reduced data can be retrieved from the output tape using FIRM i t s e l f for further processing. However, certain procedures must be carried out before t h i s processing can be done. < 1) . Raw data tap_e copying: A l l observations (which i n general w i l l be on several tapes) should f i r s t be copied onto a single " l i b r a r y " tape, which should i t s e l f be immediately duplicated so that there i s a back-up tape with the same observations on i t . The o r i g i n a l tape should only be re-used after the copying procedure has been proven to be complete and successful. Checking can be done using the OBC routines TAPEDOMP or TAPESNIFF, or a user-written routine. The tape copying i s done using OBC TAPECOPY., 215 Example SMOUNT RF0001 *T1* SIZE=5040 HODE=800 BF0002 *T2* SIZE=5040 MODE=800 BD0678 *LIB* SIZE=5040 VOL=P04071 RING=IN $ENDFILE $CONTROL *IIB* P0SN=*25* SCONTBOL *T1* POSN=*2* $RUN *TAPECOPY 0=*T1* 1=*LIB* PAB=BECORDS=251,NOBEW $BDN *TAPECOPY 0=*T2* 1=*LIB* PAB=FILES=1 , BEC0BDS= 109, NOREti $CONTROL *LIB* WTM 2 Explanation : The case above i s for two raw data tapes mounted on pseudo-devices *T1* and *T2*; the tape on *T1* has an end-of-fi l e marker (filemark) at the beginning of the tape, followed by 251 records (each of 50 40 bytes maximum length). The second tape, on *T2*, has a filemark at the beginning followed by 109 records. The l i b r a r y tape on *LIB*, has 24 f i l e s already written on i t . Pr i o r to the copying operation the tape i s positioned at the beginning of the 25-th f i l e . The 251 records of *T1* are written as the 25-th f i l e on the l i b r a r y tape, and the contents of *T2* as the 26-th f i l e . The filemark at the beginning of *T2* serves as the tape-mark between the 25-th and 26-th f i l e s on *T1*. 2 1 6 (2). , Setting up the output tape status fi l e . . Example SCREATE TPSTATOS $GET TPSTATOS 1.0, 1.5, 0 0 TPSTATOS: FIRM OOTPOT TAPE STATUS $CREATE BACKOP $C0PY FROM TPSTATOS TO BACKOP Explanation: Lines 1.0 and 1.5 at least must exist i n TPSTATOS prior to using the WRITE in s t r u c t i o n in FIRM . A f i l e (here c a l l e d BACKOP) and a backup tape should be set up and p e r i o d i c a l l y updated as TPSTATOS and the output tape data expand. Every time a new record i s written on the output tape using FIRM , a l i n e i s added to TPSTATOS . In the "general example" near the beginning of t h i s appendix the following l i n e would be added to TPSTATOS : 20xxxx 0 1__3_10NGC1000:RED:5 MIN:15 OCT J "new" record number =line number i n TPSTATOS The format i s 214, 413, 14A2 where an array of twenty (20) halfwords i s used as output for a single l i n e of TPSTATUS. Line 1.5 contains two integers i n format 214, followed by up to 40 characters for the user's own l a b e l l i n g , e.g. 50 0TPSTAT0S: FIRM OOTPOT TAPE ON RF 0010 means that there are 50 records on the user's output tape 217 which i s mounted from rack RF0010. The integer "0" indicates the tape i s "open", i . e . Can be written onto. I f t h i s integer i s set to 1, the operation WRITE w i l l be in h i b i t e d . Jojte : Lines in the output tape status f i l e can be changed using UBC EDIT or UBC NEWEDIT. 218 Operations performed using FIRM Operation Function APERTURE Integrate over a sguare aperture in the f i e l d of view. ADD Add two images. AI Add constant to each element of an image. AVERAGE Read from tape and average two or more raw images, COLUMN Specify which columns "dead" or " l i v e " . DIVIDE Divide an image by another. ELLIPSE Generate a model e l l i p s o i d a l d i s t r i -bution or generate a c i r c u l a r aperture. END End processing and exit to MTS. EXAMINE AVERAGE Print averages and extreme values, LABELS pr i n t l a b e l s , HIST plot a histogram, or CATLG print the output f i l e catalogue. FT Smoothing and/or s h i f t i n g via the FFT. GRAPH Graph the value at each element of one picture versus the value of each corres-ponding element of a second picture. INT Convert magnitudes to i n t e n s i t y . LABEL Label a picture already i n core memory. LOAD Read a raw data record from magnetic tape and load i n t o core. MAG Convert int e n s i t y into magnitudes. MI Multiply each element of picture by constant. 219 Move an image into a d i f f e r e n t array in core. Six arrays are available. Optionally, r e g i s t r a t i o n of images i s performed using b i - l i n e a r i n t e r p o l a t i o n . Multiply two images. Plot a CALCOHP or printer contour map of an image. Print closed contour centroids and areas. Print the contents of an image array using the l i n e printer. Read back a reduced image from the output tape. Define dead or l i v e rows. Plot a graph of the cross-section of an image along a straight l i n e or along an e l l i p t i c a l locus. (Synonym f o r MOVE ) Convolve a picture with a conical f i l t e r i n g p r o f i l e . Compute a Gaussian "star image" i n t e n s i t y d i s t r i b u t i o n . Subtract an image from another image. Print a 10x10 matrix of numbers corresponding to a 50x50 image averaged in 5x5 blocks. Write an image as a record on the output tape. Enter label into catalogue. An operation to be defined by the user. 220 Summary of FIRM Operations Input/Output LOAD IA, [FILE II} RECORD I I WRITE IA RETRIEVE IA, REC I I AVE IA, {FILE II} REC I I , J J {, KK} VIEW IA, {X.X} APERTURE IA, NSIZE=II PRINT IA, (X. X} PLOT IA,[NCONT=II, INC=X.X], {MIN=X.X,MAX=X.X} GRAPH IB,IA {MINY=X.X,MINX=Y. Y} EXAMINE [ LABELS, AVERAGES, HIST, CATLG ] (IA IB} SECTION IA, MODE=[L,E,ED], {X0=X. X, Y0 = X. X , A=X.X,EPS=X,X,B=I, DELTA=X.X,GAMMA=X.X} Internal o p e r a t i o n s and manipulations. MOVE IA,IB {X1=X.X, Y1=X.X, X2=X.X, Y2=X.X, DX=X.X, DY=X. X} LABEL IA, f Characters * ADD IA,IB AI IA,X.X SOB IA,IB DIV IA,IB MOLT IA,IB 2 2 1 MI IA,X.X MAG I A , {X.X} INT i a ROW I,K I,K ... APE i a , N=II FT IA, {INV=±II, ASEE=X.X, DX=X.X, DY=X.X} COI I,K I,K ... SMOOTH IA SHIFT ... { same as MOVE), Model d i s t r i b u t i o n s . STAR IA,MODE=[ NEW, ADD], X0=X.X, Y0=X.X, DIA=X.X, I INT=X.X,I0=X. X] {$} ELLIPSE I A, MODEL=[ KING, GEN,DEVAU,XPO ~\ , XO=X.X, YO-X.X, {EPS = X.X,DELTA=X.X,} A=X.X,B=X.X, {C=X.X,GAHMA=X.X} [$} Termination. END 222 ADD P££toty._p.e:. ADD IA,IB Action:. Add image i n array IB to image i n array IA, element by element. The r e s u l t i s stored in array IA. Examples: ADD 3,1 AD 3,1 223 AI Prototype;. AI IA, X.Xf,NOISE} Action: Add "immediate" constant X.X to every element of image i n array I A. I f * NOISE' i s sp e c i f i e d , a normal d i s t r i b u t i o n simulated noise, with mean value -zero, i s added. The RMS or sigma value i s then X.X. Examples: AI 2, 5.6 AI 3, -100. AI 4, 3.0 NOISE Note: This instruction i s also used to subtract a constant. 224 APERTURE Prototype: APERTURE IA,NSIZE=II Action: To use the 2-D detector as a single-channel photometer with a square aperture NSIZE x NSIZE p i x e l s i n area. The square "aperture" i s centred on the centroid of the inte n s i t y d i s t r i b u t i o n with values greater than 10% of the maximum value in the array. The area outside the aperture i s used as a background (sky), to be scaled and subtracted from the sum of i n t e n s i t i e s i n the aperture. The aperture i s clipped and scaled appropriately i f too near an edge. N.B. 1 < NSIZE < 50, with NSIZE od,cl , for the RETICON RA50x50. Examples: APE 2,N=21 225 A V E R A G E Prototype: AVERAGE IA, {FILE NN} REC I I , J J (, KK} action:. average raw data r e c o r d s I I t o J J i n f i l e NN, with i n c r e -ment KK between r e c o r d s , i n the same sense as the FORTRAN DO i n s t r u c t i o n : DO ... I=II,JJ,KK {The d e f a u l t of KK i s 1; NN d e f a u l t s t o t h e c u r r e n t l y a c t i v e i n p u t raw data f i l e , d e c l a r e d i n an e a r l i e r AVERAGE or LOAD). The r e s u l t o f the averaging i s s t o r e d i n a r r a y IA., Examples; AVE 1, FILE 5 REC 10, 20, 2 AVE 3, REC 6,10 226 COLUMN and ROW Prototype: COLUMN I1,K 12,K ... ROW J1,K 32,K . . . Action^ Columns In or rows Jn are " k i l l e d " (K=0) or "brought back to l i f e " (K=1). A l l rows and columns are " l i v e " at the start of the computer run, and t h e i r status can be changed during processing. Examples! ROW 1,0 2,0 50,0 COL 1,0 50,0 HOW 2,1 COL 2,0 3,0 4,0 50,1 Notex This instruction i s needed to exclude faulty rows and columns, and to allow for c l i p p i n g around the borders when image r e g i s t r a t i o n i s performed. 227 DIVIDE Prototype: DIVIDE IA,IB-Ac tion:. Divide image i n array IA by image i n array IB. The resul t i s stored in array IA. Elements divided by zero are set to zero, and a warning message i s printed. Examples: DIV 2,3 228 ELLIPSE Prot o t y p e : ELLIPSE IA,MODEL=[K,G,D,X,A ], (X0=X. X,YO=X.X,EPS=X. X , DELT A= X. X,A=X. X,B=X. X,C=X. X,GAMMA=X.X} Act ion 2. Compute s u r f a c e b r i g h t n e s s d i s t r i b u t i o n with e l l i p t i c a l isopho t e s : P =' (X0,Y0) = c e n t r e of d i s t r i b u t i o n . = DELTA = p o s i t i o n angle of major a x i s EPS = e l l i p t i c i t y of i s o p h o t e s = 1 - b/a A,B,C,GAMMA = parameters f o r model d i s t r i b u t i o n s . The MODEL parameter must come f i r s t i n the l i s t . O iDELTA C o o r d i n a t e System 229 Examp_les2 ELL 1,M=A X0=25.8,Y0=30. 1 A=10.0 $ This produces a c i r c u l a r aperture. The *$* can be used to terminate the l i s t , but should not be necessary unless most of the card i s f i l l e d up. MODEL parameter: K : A simple King model i s computed: K1-where a = semi-major axis of e l l i p s e . G A generalized Hubble-law model i s computed: A ( 4 8a. 4 Cc*?- 4 CxftHn*) oi3 D : A de Vaucouleurs model i s computed: X : An exponential model i s computed: A : A c i r c u l a r aperture i s computed: I(x,y) '= 1.0 i f ^xz+y2" $ A, = 0. I f , fx2*y2 ' > A. 230 EXAMINE Prototype: gXAMINE [ AVER AGES, LABELS, HIST, CATLG] £11} {JJ} Action:. P r i n t : AVERAGES : averages, maxima and minima, or, LABELS : array l a b e l s , or, HIST : a histogram or histograms, or, CATLG : l i s t the output tape status f i l e , f or arrays II to J J i n c l u s i v e . A l l arrays are included i f no array index at a l l s p e c i f i e d . Only II sp e c i f i e d i f a si n g l e array i s to be considered. Examples: EX AVE 1 3 EX AVE EX HIST 4 EX LABELS 231 FT Prototype; f l IA, {INV=±I, ASEE=X.X, DX=X.X, DY=X.X, SIGMA^X.X} Action: Transform array IA using the discrete Fourier transform routine F0UR2 (see UBC FOUBT ) . I f INV > -1 (default = 0) , f i l t e r using Gaussian with eguivalent "seeing" diameter ASEE (in diode spacing u n i t s ) . I f ; -6 < INV < -2, a 50 x 50 subset of the absolute values of the 64 x 64 discrete Fourier transform i s stored in array JINVJ prior to f i l t e r i n g . The 32 by 32 subset with one corner at the f i r s t element i s the sguare root of the power spectrum of the image. The transform i s inverted back into real space and stored in array IA. I f SIGMA i s s p e c i f i e d , Wiener f i l t e r i n g i s performed, with a Gaussian instrumental p r o f i l e of diameter ASEE and noise l e v e l SIGMA. Examples:. FT 2, ASEE=2.7, DX=-3.6, DY=1.1 Note: the crude Wiener f i l t e r i n g option has not been very successful. More development i s needed. 232 GRAPH GRAPH IY,IX {MIII=X.X,MINX=X.X} Action: Plot a scatter diagram of the values of elements i n array IY versus the values of corresponding elements i n IY. Parameters: MI NY = (optional) minimum value of elements i n array IY to be included. MINX = (optional) minimum value of elements in array IX to be plotted. Examples: GRAPH 2,3 MINY=20.0, MINX=100. Caution^ Choose minima so that the plotting time w i l l not be excessive due to too many points being included. Beware of holes being d r i l l e d by the plotter pen ! 2 3 3 INT Prototype; INT IA Action; The image in array IA i s converted from magnitude measure to intensity measure. A warning i s printed i f the image has not been previously converted to magnitude measure. Examples; INT 5 234 LABEL Prototype: LABEL IA,» characters * Action,: Array IA i s lab e l l e d with up to 28 characters (excluding apostrophes). Examples: LABEL 2,*NGC 5914: RED: 5 MIN.1 Note: Or i g i n a l record number and f i l e number are preserved i n the header of the label (see ins t r u c t i o n LOAD for a description). The apostrophes must be used i f there are blanks in the label 235 LOAD LOAD I A,-(PILE 1} BECOBD J Actionz Record J i n f i l e I of tape (FORTRAN u n i t 3) i s loaded (read) i n t o a r r a y IA. Examples: LOAD 2,FILE 11 RECORD 29 LO 2, F 11 R 3 T h i s causes r e c o r d 29 i n f i l e 11 t o be loaded i n t o a r r a y 2. The f i l e i s on the input (tape) u n i t 3, with 5040 bytes of data per r e c o r d , c o n s i s t i n g of the f o l l o w i n g : 6 halfword i n t e g e r s , 28 c h a r a c t e r s of l a b e l l i n g i n f o r m a t i o n , and 2500 halfword (2 byte) i n t e g e r s of raw data from the RETICON system: NREC = no. Of r e c o r d i n f i l e . (NEWREC) = (unused) : space f o r output record number. (command) = (unused on 7/16) : command b i t s . OBJECT = o b j e c t index (set d u r i n g o b s e r v a t i o n ) . FILTER = f i l t e r (set durin g o b s e r v a t i o n ) . ( f i l e no.) = (unused) f i l e no. s i n c e s t a r t of obse r v i n g . 236 (LIBEL) = (unused) : characters for l a b e l , set using FIRM . 28 bytes. ARRAY = data array. 2500 halfwords. LOAD 2,REC 29 Same as f i r s t example, but FILE assumed to be the current f i l e -number, set previously using LOAD or AVE. 237 MAG MAG I A, {X.X} Action: Convert image in array IA to magnitude measure, using the eguation: ni(x,y) = -2.51og I(x,y) The optional parameter X.X i s the minimum allowed value for the i n t e n s i t y . The default minimum i s 0.001. I n t e n s i t i e s below the minimum are converted to zero magnitude. I n t e n s i t i e s should be scaled or of f s e t before using t h i s i n s t r u c t i o n i f very small or negative values are present. ExampJ.es.: MAG 2 Notex T n e t h i r d integer of the six lab e l integers for array IA i s set to 1 to serve as a f l a g . 238 MI Prototype: MI IA, X.X Action: Multiply image in array IA by constant X.X. Examples: MI 3, 10.5 MI 3, 0.995 Note^ there i s no corresponding divide by constant i n s t r u c t i o n , therefore multiply by the r e c i p r o c a l . 239 MOVE Prototype: MOVE IA,IB { Xj = X. X, Yt=X. X,X2=X. X, Y2=X. X } or MOVE IA,IB DX=X. X, DY=X. X Action: Move data in array IB into array IA without destroying contents of array IB. I f the parameters in curly brackets are spe c i f i e d , the picture i s moved by in t e r p o l a t i o n , so that old reference point (X1,Y1) corresponds to the new reference point (X2,Y2) . Alternatively one can specify DX, DY where: DX = X2 - X1 DY = Y2 - Y1 ( SHIFT and MOVE are equivalent). •Examples: MOVE 4,2 SHIFT 4,2 MOVE 4,2 DX=0.32,DY=5.1 MOVE 4,2 X1=20.01,X2=20.33,Y1=24.9,Y2=30. Note: The Fourier Transform command FT can be used to move an image using the S h i f t Theorem. In comparison, MOVE/SHIFT uses b i l i n e a r interpolation. The Fourier method should normally be used unless there are very sharp "spikes' 1 i n the image due to "hot" diodes, etc. 240 MULTIPLY Prototype:. MULTIPLY I A, IB a c t i o n : Multiply image i n array IA by image in array IB.? Store result i n array IA. Examples! MULT 3, 2 241 PLOT Prototype: PLOT IA,fNCONT=I,INC=X. X] { , MIN-X . X , £A£=X. X} Action: To produce a contour plot of the image i n array IA. The parameters are as follows: NCONT = number of contour l e v e l s . INC = increment between contour l e v e l s . MIN = minimum contour l e v e l to be plotted MAX = maximum contour l e v e l to be plotted. Examples! PLOT 5,NCONT=20,MIN=10.0 PL 5 NC=20 MIN=10 PLOT 2,INC=10.0 NAX=120. PLOT 1,NCONT=30, MAX=120., MIN=10. Notes: If INC i s s p e c i f i e d , the contours are not- lab e l l e d ( i . e . use INC as a non-labelling option). If MIN, MAX, INC or any combination of them not s p e c i f i e d , the corresponding values are automatically computed using the minimum, maximum values found i n the array. The intensity increment between contours i s computed using these values and NCGNT i f INC not s p e c i f i e d . N..B..:. Negative values are not permitted for contour l e v e l s . Offset or multiply appropriately before p l o t t i n g , or specify the MIN option. 242 PRINT Prototype: PRINT IA {, X.X} Action: The 50 x 50 image i s printed out as four consecutive pages on the l i n e printer, each page consisting of a 25 x 25 guadrant of the image. The order i s : top l e f t , bottom l e f t , top r i g h t , bottom r i g h t . The o r i g i n a l record number (if any) i s printed along the border, with an asterisk on each l i n e . Each element i s i n format 15. Each element i s multiplied by a scale factor X.X for printing out. The scale factor allows small numbers to be scaled up, and vice versa, before rounding to integer form. If omitted or zero, the default value of 1.0 i s assumed. Elements rounded to zero appear as blanks. Examples: PRINT 5, 10.0 PR 5 PR 5 100 PR 2 0.00 1 243 RETRIEVE £E°tot XP_§.! RETRIEVE IA,RECORD I Action:. Record I on the output tape { FORTRAN unit 4) i s retrieved (read) and loaded into array IA. The la b e l s i n the tape status f i l e and on the tape are printed out. Examples; RETRIEVE 2,RECORD 50 RE 2,REC 50 RETR 2,R 50 244 ROW S e e i n s t r u c t i o n COLOMN. 245 SECTION Prototype: SECTION IA ,HODE=[L # E ,ED ]# f X0=X.X,Y0=X. X,A=X. X,B=X,DELTA=X.X,EPS=X.X,GAHMA=X.X } Action: MODE=L Produce graph of values along a straight l i n e i n c l i n e d at DELTA (in degrees) to the v e r t i c a l axis i . e . a cross-sec-tion plot, passing through the point X0,YO. Parameter B defines the type of pl o t . MODE=E Produce graph of values as a function of polar angle along an e l l i p s e centred at X 0 , Y 0 , with e l l i p t i c i t y EPS= 1 - b/a, and orientation DELTA . The semi-major axis i s A pix e l units long. MODELED Same as MODE=E, except that the polar angle i s defined i n a disk i n c l i n e d at GAMMA degrees. 0 ° i s face-on. EPS need not be s p e c i f i e d , since the locus i n the image plane i s the projection of a c i r c l e in the plane of the disk. 246 O Y Y iDELTA C o o r d i n a t e D e f i n i t i o n P l o t types i n MODE=L 1 B = 0 B = 1 B = 2 B = 3 B = 4 B = 5 ( d e f a u l t : data i n array IA i s p l o t t e d d i r e c t l y a q a i n s t d i s t a n c e along the l i n e . King p l o t (1/1 vs r 2 ) Hubble p l o t (1/SQHT(I) ys r) de Vaucouleurs p l o t ( l o g / B I ys r'ft ) Gaussian p l o t ( l o g e I y s r 2 ) l o g - l o q p l o t (log,„ I ys l o q |r|) Exam^les^ SECTION 1,MODE=L,X0=25.5,Y0=33.1, B=3,DELTA=31.0 SECTION 2,M0DE=E X0=25.5,Y0=33.1 , A=10.0,DELTA=31.0 EPS=0.35 SECTION 2, MODE=ED X0=25.5, Y0=33.1, A=10.0 DELTA=31.0 GAHMA=60. 247 SMOOTH Prototype: SMOOTH IA Action: Smooth image in array IA using a conical convolving f i l t e r of base diameter 4.0 diode units. , Examples: SM 2 Notex The Gaussian smoothing f i l t e r i n the in s t r u c t i o n FT has a variable e f f e c t i v e diameter ASEE, and should normally be used rather than SMOOTH . See Chapter 3 of thesis f o r f i l t e r d e f i n i t i o n . 248 STAR £E2£oty,p_e.: STAR IA,||ODE=[|IEH,aDD],X0=X.X,Y0=X. X, [INT=X.X,10=X.X],DIA=X.X Action: Compute a Gaussian c i r c u l a r star image at position (X0,Y0), with diameter CIA and integrated i n t e n s i t y INT or cent r a l i n t e n s i t y 10. The MODE parameter s p e c i f i e s whether the array IA i s to be zeroed (NEW) or not (ADD) prior to computing the star image. The eguation i s : I(x,y) = I0*exp{-4(x2+y2)/DIA2} Examples: STAR 2,M0DE=ADD X0=26.8 Y0=29.2 10=930.0 DIA=3.5 ST 3 M=N X0=30.1 INT=2500. DIA=4.0 Y0=5,5 249 SUBTRACT Prototype; SUBTRACT IA,IB A c t i o n : Subtract image i n array IB from image in array IA. Result stored in array IA. Examples; SUB 1,4 250 VIEW Prototype: VIEW IA {,X.X} A c t i o n : The 50x50 image in array IA i s averaged into 5x5 sub-blocks and printed as a 10x10 matrix. Dead rows and columns are not included in the averaging process. The aver-ages are multiplied by X.X before being printed as rounded integers. I f omitted, the default value of X.X i s 1.0. Examples; VIEW 2,100. VI 2, 100 VIEW 5 251 WRITE P r o t o t j ^ e i WRITE Ia Action: Write contents of array II , with i t s l a b e l , as the next record on the output tape { FORTRAN unit 4) . The l a b e l , including the new output record number, i s also written into the MTS l i n e f i l e used as the status f i l e for the output tape. { The status f i l e i s FORTRAN unit 2). The output tape i s automatically positioned by FIRM using the output record counter i n l i n e 1.5 of the tape status f i l e . The MTS line-number of the new l i n e i s the same as the new record number, and the output record counter i n l i n e 1.5 i s incremented by 1. { See section on tape procedures and setting up). The written record can be subseguently read back into core using the i n s t r u c t i o n RETRIEVE Examples^ WRITE 3 APPENDIX II . . . DATA TAPES Raw Data Tapes RD0678 7OL=P01O11 primary tape RD0677 VOL=P04071 backup duplicate Output Tapes RD0906 VOL=P06287 primary tape RB0908 VOL=P05469 backup RD0907 VOL=P06263 H15(NGC7078) output RB0909 VOL=P05466 programmes (SM71) These are permanent rack numbers f o r tapes at the Computing Centre at OBC. Summary of Data Tape Contents on Next Page 253 Summary of - Data Tape Contents l e Date Telescope Objects Observed. 1975 1 Null F i l e : Tape Mark. 2 May 9 12" M87 M63 M13 Stars M57 3 Jun27 72" Star Sky Dark current 4 Jun28 72" Stars Sky 5 Nov 3 72" Observing Programme 6 II « M31 Stars : Noisy 7 n it N2392 fl31 Stars : Noisy 1976 8 Feb24 24" Praesepe N2 403 N2903 N4472 M51 9 Feb28 II N4472 M101 10 Mar 6 n S87 Star N3556 N4472 N3992 11 Mar 8 n Star Praesepe N2903 12 n II N4472 13 Mar29 88" Praesepe Stars (satd.) M94 M51 14 Apr 1 II HB4708 N4258 15 n n Star M51 M13 N6441 16 w ti Darks 17 Apr 2 « Stars M51 N5195 : f/0.8 18 Apr 3 • i 927 consecutive 20sec darks. 19 May 1 H Dk S Fl a t F i e l d 20 May 6 24" Darks 21 II it Star N5824 N644 1 22 May 7 « Stars 23 II II Stars 24 May 7 tt Stars N5824 N6266 N6441 N6624 N6715 25 H n Darks 26 May 8 n N5824 Stars N6093 28 n n N6864 Stars 29 M it Darks 30 Sep14 72" N7027 M15 N7662 M31 31 Sep 15 ti HD172323 N7027 M15 N7662 32 n ii N7662 Sky F.F. 33 Oct 16 12" Defocussed Bright Stars 34 it tt it II it 35 II tt it it it 36 Oct17 n ti n « 37 Oct 18 it II ti i i 38 Mar30 88" Praesepe stars M87 HR4708 M51 

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