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Aolp : an automatic object location program Scharein, Robert Glenn 1984

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AOLP : AN AUTOMATIC OBJECT LOCATION PROGRAM by ROBERT GLENN SCHAREIN B.Sc. (Hon), U n i v e r s i t y of Manitoba, 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Geophysics and Astronomy) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1984 © Robert Glenn S c h a r e i n , 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department ,of (j^op hyji (.5 CL^<4 ^SWO^OW.^ The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date DE-6 (.3/81) Abstract T h i s t h e s i s d e s c r i b e s the f i r s t i n c a r n a t i o n of an automated photometry program AOLP, acronym f o r Automatic Object L o c a t i o n Program. T h i s program i s designed to search through an image and to f i n d , c atalogue, and ( e v e n t u a l l y ) c l a s s i f y a l l o b j e c t s found. The primary aim i s f o r use i n a f a i n t galaxy survey. The program has a l s o proven u s e f u l i n other areas, such as photometry of g l o b u l a r c l u s t e r s and r e l a t i v e l y nearby, b r i g h t g a l a x i e s . i i Table of Contents Chapter Page A b s t r a c t i i L i s t of Tables i v L i s t of F i g u r e s v Acknowledgements v i i I. I n t r o d u c t i o n 1 A. F a i n t Galaxy Counting 1 B. Moment I n v a r i a n t s i n Astronomy 8 I I . Hardware and Software D e s c p r i p t i o n 13 A. The I 2 S Image Processor 13 B. The Automatic Object L o c a t i o n Program 17 I I I . A p p l i c a t i o n to A r t i f i c i a l F i e l d s 20 A. E f f e c t of Shape 21 IV. Mixed Star and Galaxy F i e l d s 25 V. Photometric A p p l i c a t i o n s 29 A. G l o b u l a r C l u s t e r s 32 M92 32 M13 36 B. G a l a x i e s 39 Colours and Magnitudes of Compact Group g a l a x i e s 39 Luminosity P r o f i l e s of Compact Group G a l a x i e s 41 VI. C o n c l u s i o n 67 B i b l i o g r a p h y 68 i i i L i s t of Tables I A n a l y t i c a l Values f o r Moment I n v a r i e n t s 22 II C a l i b r a t i o n S t a r s i n M92 31 III Colours and Magnitudes of Compact Group G a l a x i e s 40 i v L i s t of Figures 1 F a i n t galaxy counts 4 2 Data path i n 1 2S 14 3 R v i . C 2 f o r gaussians 23 4 C„ v s . C 2 f o r gaussians 23 5 C 2 vs. magnitude f o r E9 f i e l d • 26 6 R vs. C 2 f o r E9 f i e l d 27 7 R v s . C 2 f o r E9 f i e l d 27 8 C„ vs. C 2 f o r E9 f i e l d 28 9 C 2 vs. magnitude f o r M92 34 10 R v s . C 2 f o r M92 35 11 C„ v s . C 2 f o r M92 35 12 B v s . B-R CM diagram f o r M92 37 13 V vs. B-V CM diagram f o r M92 37 14 B vs. B-R CM diagram for M13 38 15 V v s . B-V CM diagram f o r M1 3 38 16 Luminosity p r o f i l e s f o r galaxy HCG73a 43 17 Luminosity p r o f i l e s f o r galaxy HCG73b 44 18 Luminosity p r o f i l e s f o r galaxy HCG73c 45 19 Luminosity p r o f i l e s f o r galaxy HCG73d.. 46 20 Luminosity p r o f i l e s f o r galaxy HCG76a 47 21 Luminosity p r o f i l e s f o r galaxy HCG76b 48 22 Luminosity p r o f i l e s f o r galaxy HCG76b... 49 23 Luminosity p r o f i l e s f o r galaxy HCG76c 50 24 Luminosity p r o f i l e s f o r galaxy HCG76c 51 25 Luminosity p r o f i l e s f o r galaxy HCG76d 52 v 26 ' Luminosity p r o f i l e s f o r galaxy HCG76e 53 27 Luminosity p r o f i l e s f o r galaxy HCG76f 54 28 Luminosity p r o f i l e s for galaxy HCG88a 55 29 Luminosity p r o f i l e s for galaxy HCG88b 56 30 Luminosity p r o f i l e s f o r galaxy HCG88c 57 31 Luminosity p r o f i l e s f o r galaxy HCG88d 58 32 Luminosity p r o f i l e s f o r galaxy HCG92a 59 33 Luminosity p r o f i l e s f o r galaxy HCG92bd 60 34 Luminosity p r o f i l e s f o r galaxy HCG92c 61 35 Luminosity p r o f i l e s for galaxy HCG92e 62 36 Luminosity p r o f i l e s f o r galaxy HCG97a 63 37 Luminosity p r o f i l e s f o r galaxy HCG97a 64 38 Luminosity p r o f i l e s f o r galaxy HCG97b 65 39 Luminosity p r o f i l e s f o r galaxy HCG97c 66 v i Acknowledgements I would l i k e to thank my a d v i s o r , Dr. Greg Fahlman f o r suggesting t h i s p r o j e c t and p r o v i d i n g help when needed. His p a t i e n c e and encouragement were most welcome. I would a l s o l i k e to thank Dr. Paul Hickson f o r access to h i s CCD images of compact groups and g l o b u l a r c l u s t e r s . To my f r i e n d s and c o l l e g u e s i n the Astronomy Dept, I o f f e r my g r a t i t u d e . I'd e s p e c i a l l y l i k e to thank John N i c o l , f o r always p r o v i d i n g c h e e r f u l a s s i s t a n c e with a myriad of computer problems. For a l l my dear f r i e n d s in Winnipeg and Calgary, thanks f o r standing behind me when the going got rough. To my very c l o s e f r i e n d s i n Vancouver (and those who have l e f t ) , I owe a great d e a l . Thank-you for a l l that you have shown me over the past three y e a r s . To my brother Don, h i s wife Debbie and t h e i r daughter who was born as t h i s t h e s i s was being completed I extend my love. And most of a l l I would l i k e to thank my parents, my mother with her joyous, wonderful f r e e - f l o w i n g s p i r i t , who has been a r e a l gem a l l these years; and my f a t h e r , that most b r i l l i a n t man who taught me the love of nature, wherever he may be. v i i I. Introduction A. Faint Galaxy Counting Two important and as of yet, unanswered q u e s t i o n s i n cosmology are: 1) Is the u n i v e r s e r e a l l y homogeneous? and 2) E x a c t l y how do g a l a x i e s evolve? To answer these q u e s t i o n s r e q u i r e s that we look f a r enough out i n the u n i v e r s e so that we are w e l l w i t h i n the uniform Hubble flow, and f a r enough back in time so that we can see g a l a x i e s over a s i g n i f i c a n t f r a c t i o n of t h e i r l i f e t i m e s . Thus we are i n the realm of the very f a i n t g a l a x i e s (B > 22) where, due to the l a r g e numbers i t may become necessary to have an automated means of c o u n t i n g and measuring the g a l a c t i c images. I t i s f o r t h i s purpose that the program AOLP (Automatic Object L o c a t i o n Program) has been developed. I t w i l l become p o s s i b l e with equipment p r e s e n t l y being b u i l t at the U n i v e r s i t y of B r i t i s h Columbia to o b t a i n a complete sample of f a i n t g a l a x i e s down to magnitude 25 together with r e d s h i f t i n f o r m a t i o n f o r s e v e r a l r e g i o n s of the sky. Such a sample w i l l g r e a t l y enhance our c u r r e n t understanding of these q u e s t i o n s . I t i s u s e f u l then to examine what i n f o r m a t i o n we c o u l d expect to f i n d from f a i n t galaxy counts and a l s o to see what o t h e r s have done in t h i s a r ea. F a i n t galaxy counts appear to be r e l a t i v e l y i n s e n s i t i v e to d i f f e r e n t values of the Hubble constant H0 and the d e c e l e r a t i o n parameter q0 for a s p e c i f i c c o s m o l o g i c a l model. The reason f o r t h i s i s , as shown by T i n s l e y (1977,1980), 1 2 that number-magnitude r e l a t i o n s f o r d i f f e r e n t models are im p e r c e p t i b l y d i f f e r e n t ( i g n o r i n g e v o l u t i o n ) at c o n c e i v a b l y a t t a i n a b l e magnitudes. Once we i n c l u d e g a l a c t i c e v o l u t i o n , the i n t e r p r e t a t i o n of galaxy counts i s com p l i c a t e d by many unknown parameters. A l s o , the d i s t i n c t i o n between d i f f e r e n t types of g a l a x i e s i s g e n e r a l l y not a v a i l a b l e at f a i n t magnitudes. The observed d i f f e r e n t i a l count i s t h e r e f o r e a sum over the expected number N (m) f o r each c l a s s of galaxy. The number of g a l a x i e s of a given type i n an i n t e r v a l Am of apparent magnitude i s given by, N (m) Am = J N (m, z) dl ogz Am where Zy = "formation" r e d s h i f t (when s t a r formation s t a r t e d ) N = (number of ga l a x i e s ) / m a g n i t u d e / u n i t logz = W(z) n0 *(M0) here W(z) =-4-nRlr 2 r7 \/(l-kr2) dr d I ogz i s the comoving volume/unit logz i n a Robertson-Walker cosmology with the standard metric ds2 = c 2 d t 2 - R2(t)[dr2/(1-kr2) + r2dd2 + r2si n28d<b2 ] n0 = present space d e n s i t y f o r g a l a x i e s of a given type. and $(M0)= l o c a l l u m i n o s i t y f u n c t i o n = f r a c t i o n of g a l a x i e s i n an u n i t i n t e r v a l of ab s o l u t e magnitude M, that would g i v e apparent magnitude 3 m at r e d s h i f t z The apparent and a b s o l u t e magnitudes are of course r e l a t e d by m = M + 51 og(dl/10 pc) which i n v o l v e s the l u m i n o s i t y d i s t a n c e . T h i s d i s t a n c e i s a f u n c t i o n of z, H0, and q0. We have two a b s o l u t e magnitudes M and M0 which d i f f e r only because of the K - c o r r e c t i o n 1 and e v o l u t i o n . U n f o r t u n a t e l y , present l u m i n o s i t y f u n c t i o n s are poo r l y known as i s the r e l a t i v e frequency of g a l a x i e s of d i f f e r e n t t ypes. A l s o , the n o r m a l i z a t i o n d e n s i t y n0 i s u n c e r t a i n because l o c a l l y the u n i v e r s e i s q u i t e inhomogeneous. The c o l o u r s (important f o r the K - c o r r e c t i o n ) and a b s o l u t e magnitudes of the g a l a x i e s at d i f f e r e n t epochs i s determined by the s t a r formation r a t e (SFR), another p o o r l y known q u a n t i t y which we can a l s o expect to evolve over time. S e v e r a l groups have attempted f a i n t galaxy counts: Karachentsev and Kopylov (1979), Tyson and J a r v i s (1979), Peterson et al. (1979) and Rron (1980). The paper by Kron i s a good summary of the d i f f e r e n t techniques and r e s u l t s of each observer. F i q u r e 1 shows that t h e r e i s c o n s i d e r a b l e d i s c r e p a n c y between the d i f f e r e n t groups. Kron e x p l a i n s that 1The c o r r e c t i o n needed because g a l a c t i c s p e c t r a are not f l a t . An o b s e r v a t i o n made in a given passband corresponds to a d i f f e r e n t passband i n the re s t frame of the galaxy. Therefore an e x t r a c o r r e c t i o n i s needed. O Kron 4- Tyson and Jarvis —• Peterson et al. A Karachentsev and Kopylov FC U J i i i i i i 20 21 22 23 24 J Magnitude Figure 1: F a i n t galaxy counts as measured by d i f f e r e n t o b s e r v e r s . M o d i f i e d from K r o n d 9 8 0 ) . t h i s i s l a r g e l y due to the markedly d i f f e r e n t techniques used. Out of the four groups, Karachentsev and Kopylov were the only ones to do the galaxy counts by eye. The other three groups used a computer automated technique with data d i g i t i z e d from p l a t e s . The problem with t h i s i s that i t r e q u i r e s a r e l i a b l e c l a s s i f i c a t i o n scheme to d i s t i g u i s h g a l a x i e s from non-galaxies, i . e . s t a r s , flaws, s purious images e t c . . In general t h i s i s a n o n - t r i v i a l problem i n p a t t e r n r e c o g n i t i o n , an area where the e y e - b r a i n combination i s unbeatable. On the other hand, as Kron p o i n t s out, i t i s e a s i e r to model s e l e c t i o n by machine than by eye. Also, the eye i s su b j e c t to other problems, such as f a t i g u e and p e r s o n a l b i a s . There i s a l s o the problem of c a l i b r a t i n g the eye. The l i m i t i n g f l u x to which the eye i s s e n s i t i v e depends upon the shape and c o n c e n t r a t i o n of the o b j e c t s s t u d i e d . 3 2.5 o 5 Another f a c t o r i s the remarkable tendency f o r the eye to see s t r u c t u r e s where none e x i s t . T h i s e f f e c t has shown up i n the author's own experiments with a r t i f i c i a l o b j e c t s f o r use i n t e s t i n g AOLP. For example, gaussians appeared to be made of two components, a concentrated core and a f a i n t e r outer envelope. The apparent r a d i u s of the core i s a f u n c t i o n of the b r i g h t n e s s of the d i s p l a y . I t seems that the e y e - b r a i n i n s i s t s on d e f i n i n g boundaries that may have no p h y s i c a l r e a l i t y . Indeed, even more s t r i k i n g f e a t u r e s sometimes showed up. In the experiments with gaussians, s e v e r a l people remarked at how much some of them looked l i k e g a l a x i e s , complete with s p i r a l arms! C l e a r l y , even without the p s y c h o l o g i c a l f a c t o r s , machine c o u n t i n g may s t i l l be p r e f e r r e d simply because of the enormous" task of scanning l a r g e amounts of data by eye. The other three groups each used d i f f e r e n t c l a s s i f i c a t i o n schemes for t h e i r automatic c o u n t i n g . Peterson et al. used a magnitude v s . g r a d i e n t comparison. They found that s t a r s had a much steeper g r a d i e n t at a given magnitude than d i d g a l a x i e s , a r e s u l t that f o l l o w s from s t a r images being e s s e n t i a l l y p o i n t o b j e c t s and hence the s m a l l e s t p o s s i b l e images for t h e i r b r i g h t n e s s . On t h e i r magnitude-gradient p l o t s , s t a r s separate n e a t l y from g a l a x i e s (the i n i t i a l c l a s s i f i c a t i o n being by eye). Kron used a negative power of the r a d i u s weighted with the i n t e n s i t y d i s t r i b u t i o n as a d i s t i n g u i s h i n g f a c t o r . Tyson and J a r v i s used a much more e l a b o r a t e technique. They c a l c u l a t e d 6 f o r each o b j e c t ( i n a d d i t i o n to i t s magnitude) v a r i o u s shape parameters c a l l e d moment i n v a r i a n t s (to be d i s c u s s e d l a t e r ) and parameters d e s c r i b i n g the peak d e n s i t y and the degree of resemblance to a s t e l l a r p r o f i l e . They then took these parameters and performed a c l u s t e r a n a l y s i s i n a m u l t i - d i m e n s i o n a l hyperspace. As a r e s u l t of the d i f f e r e n t c l a s s i f i c a t i o n systems used by each groups we might expect that there would be some di s c r e p a n c y between t h e i r r e s u l t s , s i n c e some o b j e c t s that would be c l a s s i f i e d by one a l g o r i t h m as a galaxy might not be c l a s s i f i e d as such by a d i f f e r e n t a l g o r i t h m . It i s not c l e a r how much of the discrepancy i s caused by t h i s f a c t o r . Each group a l s o used d i f f e r e n t techniques f o r determining the magnitudes of the found g a l a x i e s . Both Peterson et al. and Tyson and J a r v i s used an i s o p h o t a l measurement technique. Peterson et al. set the isophote l e v e l to be 2.5% above the sky l e v e l . Tyson and J a r v i s d e f i n e d a region at an isophote l e v e l about 2% above the sky and then grew the ob j e c t region to 1.2X t h i s a r e a . They then l e f t a guard re g i o n around the o b j e c t , o u t s i d e of which they determine the sky b r i g h t n e s s . Kron used a technique based on assumptions on how the l i g h t growth curve behaves as a f u n c t i o n of r a d i u s . T h i s allowed him to measure a constant f r a c t i o n of the l i g h t from a given o b j e c t , independent of the b r i g h t n e s s at the l i m i t i n g r a d i u s . In some ways t h i s i s p r e f e r r a b l e to the i s o p h o t a l approach because the f r a c t i o n of l i g h t measured w i t h i n a set isophote i s an i n c r e a s i n g 7 f u n c t i o n of the b r i g h t n e s s of a g a l a c t i c image. As a r e s u l t g a l a x i e s measured by Kron would tend to be s y s t e m a t i c a l l y b r i g h t e r . T h i s might account f o r the l a r g e r numbers counted by him at f a i n t magnitudes. So f a r a l l observers have attempted galaxy counts with broadband f i l t e r s . While t h i s can c o n s t r a i n g a l a c t i c e v o l u t i o n s c e n a r i o s , i t would be much more u s e f u l to o b t a i n r e d s h i f t d i s t r i b u t i o n s i n a d d i t i o n to magnitude d i s t r i b u t i o n s . As has been mentioned such a survey w i l l become p o s s i b l e with equipment designed by Paul Hickson and being b u i l t at the U n i v e r s i t y of B r i t i s h Columbia. The instrument i s a photon counting CCD i n c o n j u n c t i o n with 60 narrow band (100A) f i l t e r s spaced evenly from 4000A to 8000A. I t w i l l allow a low r e s o l u t i o n spectrum to be obtained f o r each o b j e c t down to magnitude 25 i n a f i e l d of 40 a r c m i n 2 . T h i s w i l l allow the r e d s h i f t of each o b j e c t to be obtained i f a prominate s p e c t r a l l i n e can be i s o l a t e d . T h i s survey w i l l r e q u i r e a convenient and r e l i a b l e technique of reducing the data. In p a r t i c u l a r i t w i l l r e q u i r e an automated o b j e c t f i n d i n g r o u t i n e because of the enormous amount of data per f i e l d . A l s o the o b j e c t s on each of the 60 f i e l d s must be matched up i n order to a r r i v e at the s p e c t r a . An approach f o l l o w i n g the moment i n v a r i a n t method of Tyson and J a r v i s has be chosen, although the technique w i l l be g r e a t l y m o d i f i e d c o n s i d e r i n g the s p e c i a l i z e d nature of the data that w i l l be obtained. 8 B. Moment Invariants in Astronomy In the f i e l d of image a n a l y s i s one i s concerned with f i n d i n g a q u a n t i t a t i v e d e s c r i p t i o n of o b j e c t shapes. One approach to t h i s problem i s to use i n t e n s i t y weighted moments. Suppose we have an ob j e c t d e f i n e d by a continuous i n t e n s i t y d i s t r i b u t i o n g(x,y) i n the x-y p l a n e . We can d e f i n e the moments of the d i s t r i b u t i o n to be, ma0  = $ * s(x,y) xa dxdy These moments i n p r i n c i p l e c o n t a i n a l l the i n f o r m a t i o n about the image, s i n c e given a complete set of one can r e c o n s t r u c t g(x,y). These moments are o b v i o u s l y dependent on the coo r d i n a t e system and are not i n v a r i a n t w i t h respect to p o s i t i o n . More u s e f u l are the c e n t r a l moments, cap = ! ! g(x,y) (x-x0)a (y-y0)® dxdy which have t h i s p r o p e r t y . Here x0 and y0 are the c o o r d i n a t e s of the c e n t r o i d d e f i n e d by x0=myo/mOQ and y0=m0./m00. From these c e n t r a l moments i t i s p o s s i b l e to d e f i n e what are known as moment invariants. These q u a n t i t i e s are i n v a r i a n t with r e s p e c t to p o s i t i o n r o t a t i o n and s c a l e changes. The theory of moment i n v a r i a n t s was f i r s t e l a b o r a t e d by Hu (1962) who d e r i v e d the f i r s t seven moment i n v a r i a n t s up to and i n c l u d i n g t h i r d order moments. The work of J. A . Tyson and J . F. J a r v i s of B e l l L a b o r a t o r i e s has alre a d y been mentioned with regard to t h e i r f a i n t galaxy 9 survey. They pioneered the technique of u s i n g moment i n v a r i a n t s to i d e n t i f y a s t r o n o m i c a l o b j e c t s . In a s e r i e s of papers (Tyson and J a r v i s 1979, J a r v i s and Tyson 1979, J a r v i s and Tyson 1981) they d e s c r i b e d t h e i r program FOCAS ( F a i n t Object C l a s s i f i c a t i o n and A n a l y s i s System). Tyson and J a r v i s used three moment i n v a r i a n t s f o r t h e i r c l a s s i f i c a t i o n procedure. The f i r s t of these i s a t o t a l second moment, C2 = ( c 20 + c 02 ) / c 00 Another i s the t o t a l f o u r t h moment, C n = ( c n 0 + 2c 2 2 + c 0 n ) / c 0 0 The t h i r d i n v a r i a n t i s an out-of-roundness parameter, R = [ ( c20 ~ c02 )2 + 4 c 2 , ] 0 ' 5 / C o o " These q u a n t i t i e s are r e a l l y only i n v a r i a n t i n the case where the c e n t r a l moments are d e f i n e d by i n t e g r a l s over continuous f u n c t i o n s . In the d i s c r e t e case found i n d i g i t a l image a n a l y s i s t h i s no longer holds t r u e . E r r o r s appear when we r e p l a c e the i n t e g r a l s by summations and the f u n t i o n g(x,y) by some a p p r o p r i a t e average over a r e c t a n g l u l a r r e g i o n (see Wiejak 1983 f o r a d i s c u s s i o n of t h i s problem). The corresp o n d i n g e r r o r i n troduced by making these approximations can be q u i t e l a r g e , e s p e c i a l l y i f the f u n c t i o n g(x.y) v a r i e s r a p i d l y over a p i x e l width (as i s the 1 0 si t u a t i o n for fa i n t , tiny galaxy images). For example, the quantity R often assumes rather large values, even for round objects in which case R should be i d e n t i c a l l y zero. Despite t h i s problem, considerable information can be gathered by using moment invariants along with other d i s t i q u i s h i n g features. Tyson and Ja r v i s also used parameters descibing the average peak density of the object and the convolution of an ideal star image around the object centroid. They then proceeded to c l a s s i f y the objects into the three catagories — stars, galaxies and noise. This was performed in two steps, the f i r s t being i n t e r a c t i v e . This was to divide the C 2 vs. magnitude and peak density v s . magnitude plots into three regions corresponding to the above catagories. An automatic procedure was then used to refine the c l a s s i f i c a t i o n , making use of a l l the parameters calculated for each object. To do thi s they used a technique similar to that of the 1S0DATA algorithm described by B a l l and Hall (1967). ISODATA (acronym for /terative Self-Organizing Data Analysis Technique (A)) i s a method of organizing data into clusters in a way dependent on the structure of the data i t s e l f . Tyson and Jar v i s claim considerable r e l i a b i l i t y for t h i s technique and they f i n d that the galaxy counts are repeatable with 95% confidence by comparing re s u l t s from two di f f e r e n t plates of the same region of the sky. Another interesting application of moment invariants reported by Valdes, Tyson and Jarvis (1983) was to search 11 for l a r g e s c a l e d e v i a t i o n s from g l o b a l homogeniety. T h i s was done u s i n g the same data base that Tyson and J a r v i s used f o r t h e i r f a i n t galaxy survey. They looked f o r c o s m o l o g i c a l d i s t o r t i o n e f f e c t s i n a d d i t i o n to that expected i n normal models. 2 The idea was to see i f there was a p r e f e r r e d d i r e c t i o n of alignment f o r g a l a c t i c images. Since each galaxy found i n the survey has moments computed f o r i t , i t i s p o s s i b l e to d e f i n e an e f f e c t i v e e l l i p t i c i t y f o r each object given by, e = [ ( c20 - c02 )2 + 4 c 2 , ] 0 ' 5 / ( c02 + c20 ). I t should be noted that t h i s q u a n t i t y i s j u s t R/C 2 so t h i s parameter can be c a l c u l a t e d from r e s u l t s a l r e a d y o b t a i n e d . They then averaged these e l l i p t i c i t i e s over a l a r g e number of g a l a x i e s . For randomly o r i e n t a t e d g a l a x i e s i n an homogeneous, i s o t r o p i c u n i verse we would expect t h a t such an average would equal zero. A n o n - n u l l r e s u l t would be expected i n an inhomogeneous u n i v e r s e , and the amount of e l l i p t i c i t y observed ( f o r a s i n g l e i n t r i n s i c a l l y s p h e r i c a l o b j e c t or an average over many o b j e c t s ) i s given by, e = C(a,8)r2 + 0(r3). where r i s the angular s i z e d i s t a n c e and C(a,b) i s a 2That i s , the i n c r e a s e of apparent angular diameter with d i stance. 12 f u n c t i o n of the Weyl conformal c u r v a t u r e t e n s o r , 3 and of the d i r e c t i o n i n the sky a, 6. They found that the net g l o b a l e l l i p t i c i t y was i n s i g n i f i c a n t and w e l l w i t h i n the e r r o r l i m i t s of a n u l l r e s u l t . They a l s o searched f o r c o r r e l a t i o n s over a l a r g e angular s c a l e by p l o t t i n g the average e l l i p t i c i t i e s f o r each of the 35 f i e l d s on a c h a r t and examining them f o r any tendency to l i n e up. T h i s a l s o gave a n u l l r e s u l t . T h e r e f o r e i t seems that the standard model i s safe f o r the time being. 3 T h i s tensor i s the t r a c e l e s s part of the Riemann tensor. It i s zero f o r standard cosmology. The Weyl tensor i s r e l a t e d to the n u l l cone s t r u c t u r e of a space-time and i s t h e r e f o r e important f o r any o p t i c a l e f f e c t s i n cosmology. II. Hardware and Software Descpription A. The I 2S Image Processor The Laboratory f o r Astronomical Image Reduction or LAIR c o n t a i n s a I 2 S Model 70 image processor and a DEC PDP-11/23 minicomputer" together with a s s o c i a t e d d i s k d r i v e s , tape d r i v e s etc.. The PDP-11/I 2S work on a master/slave r e l a t i o n s h i p , the PDP-11 c o n t r o l i n g the I 2 S v i a FORTRAN c a l l a b l e s u b r o u t i n e s . The I 2 S c o n t a i n s one megabyte of RAM which i s d i v i d e d i n t o four 512 X 512 X 8 - b i t images. These can be d i s p l a y e d on a high r e s o l u t i o n c o l o u r g r a p h i c s monitor. In a d d i t i o n to the a b i l i t y to merely d i s p l a y images, the I 2 S a l s o has very powerful f e a t u r e s f o r the i n t e r a c t i v e enhancement of images. T h i s can be accomplished by a " p i p e l i n e " type of c o n f i g u r a t i o n (see f i g u r e 2 ). There are three p i p e l i n e s , one f o r each of the primary c o l o u r s red, green and b l u e . Before the data c o n t a i n e d i n the r e f r e s h memories i s d i s p l a y e d , v a r i o u s t r a n s f o r m a t i o n s are a p p l i e d to i t , the f i r s t being the s c r o l l , zoom and s p l i t screen f u n c t i o n s . These are hardware r o u t i n e s to s h i f t one image with respect to another, zoom-in on an image (accomplished by p i x e l d u p l i c a t i o n ) or to show d i f f e r e n t images on separate p a r t s of the screen. A f t e r t h i s stage are the LUTs (or look-up t a b l e s ) . These LUTs are 8 - b i t i n / 9 - b i t out look-up t a b l e s . There i s one f o r each "Recently upgraded to a VAX 11/750 1 3 1 4 .. i « - o Figure 2: Diagram of d a t a p a t h i n I 2 S . From the I2s Product Description manual (international Imaging Systems) 15 r e f r e s h memory and f o r each c o l o u r p i p e l i n e making a t o t a l of twelve LUTs ( i n the present c o n f i g u r a t i o n ) . Each one may be loaded with an a r b i t r a r y t ransform and each LUT can be s e l e c t i v e l y turned on or o f f . A f t e r the LUT stage the data i s passed i n t o an adder a r r a y , which does a two's compliment a d d i t i o n of a l l the a c t i v e LUTs f o r th a t c o l o u r . A f t e r t h i s the data i s passed through the OFM (or output f u n c t i o n memory) which i s a 10-bit i n / 1 0 - b i t out look-up t a b l e . The output of each OFM i s passed to a d i g i t a l to analogue c o n v e r t e r which generates the s i g n a l l e v e l s f o r each primary c o l o u r (R,G,B). The dual c o n f i g u r a t i o n of LUT-OFM makes p o s s i b l e many t r a n s f o r m a t i o n s on images such as m u l t i p l i c a t i o n and d i v i s i o n . For example, a m u l t i p l i c a t i o n can be performed by l o a d i n g the LUTs with l o g a r i t h m i c transforms. The adder a r r a y then adds the l o g a r i t h i m s of the images. If the data i s then passed through an OFM c o n t a i n i n g an e x p o n e n t i a l f u n c t i o n , the product of the two images w i l l be c o n t a i n e d at the output. I t i s important to r e a l i z e that these o p e r a t i o n s are done on the whole image every r e f r e s h c y c l e of the screen (1/30*^ sec.) A l s o the data i n the r e f r e s h memories i n not a l t e r e d i n any way. The above mentioned f e a t u r e s of the I 2 S make i t a u s e f u l d e v i c e . However, i t s r e a l power becomes e v i d e n t with the a d d i t i o n of the Feedback-ALU loop and the videometer. The Feedback-ALU loop i s a device t h a t can be used to feedback the output of the OFMs back i n t o the r e f r e s h memories. The OFM output can e i t h e r be fed back d i r e c t l y or 16 v a r i o u s a r i t h m e t i c or l o g i c a l f u n c t i o n s can be performed on the data as i t passes through the ALU. Some of these are s t r a i g h t f o r w a r d and are o f t e n used, whereas others are rat h e r obscure and have no immediately obvious use. The videometer enables the user to perform histograms on the image or any- subset of the image. The histo g r a m i s performed w i t h i n two screen r e f r e s h times. T h i s i s a powerful f e a t u r e , i t i s an e f f i c i e n t way of i n t e g r a t i n g areas of the screen i n very l i t t l e time. A l s o the histogram i s performed on the output of the OFM s e l e c t e d and t h e r e f o r e a f t e r a l l the LUT-OFM t r a n f o r m a t i o n s have been performed. Of course a histogram can be performed on the data i n the r e f r e s h memories simply by l o a d i n g the LUTs and OFMs w i t h one-to-one l i n e a r tranforms. The histogram i n f o r m a t i o n can a l s o be used f o r o p e r a t i o n s such as histogram e q u a l i z a t i o n or h y p e r b o l i z a t i o n . In a d d i t i o n to the r e f r e s h memories, the I 2 S a l s o c o n t a i n s a 512 X 512 X 4- b i t g r a p h i c s memory p l a n e . T h i s can be used to p l o t graphs, annotate the screen or to mark the l o c a t i o n s of o b j e c t s . I t i s a l s o u s e f u l i n d e f i n i n g what i s known as the re g i o n of i n t e r e s t (or ROI). The ROI can be d e f i n e d to be any subset of the screen. I t i s u s e f u l because d i f f e r e n t ALU f u n c t i o n s can be performed i n s i d e and o u t s i d e of the ROI. 1 7 B. The Automatic Object Location Program The Automatic Object L o c a t i o n Program or AOLP i s a program designed to "search through an image frame, l o c a t e o b j e c t s and c a l c u l a t e v a r i o u s parameters f o r each o b j e c t found. Here an o b j e c t i s d e f i n e d as a contiguous set of p i x e l s above some preset t h r e s h o l d l e v e l . The parameters c a l c u l a t e d are the t o t a l i n t e n s i t y , the l o c a t i o n of the c e n t r o i d , and the moment i n v a r i a n t s C 2, C„, and R. These q u a n t i t i e s are then w r i t t e n onto a f i l e f o r f u t h e r p r o c e s s i n g . AOLP e x i s t s i n s e v e r a l v e r s i o n s , some of which are designed f o r s p e c i a l purposes, such as i n c r e a s e d speed. These v e r s i o n s omit c a l c u l a t i n g the moment i n v a r i a n t s . T h i s can i n c r e a s e the execution speed by as much as a f a c t o r of f o u r . The v e r s i o n d e s c r i b e d h e r e i n does not a c t u a l l y e x i s t as a s i n g l e e n t i t y . Due to l i m i t e d memory space on the PDP-11 not a l l of the f u n c t i o n s are a v a i l a b l e i n a s i n g l e program. AOLP i s or g a n i z e d i n the form of a command language and can only execute i n i t s present form i n an i n t e r a c t i v e enviroment. I t i n c l u d e s some b a s i c commands to a l t e r the d i s p l a y e d image and other commands which are d i r e c t l y 18 r e l a t e d to the o p e r a t i o n of the f i n d i n g p r o c e s s . These commands a r e : - THRESH Upon e n t e r i n g the THRESH command, the program asks the user to chose between two o p e r a t i n g modes: — single and multiple mode. M u l t i p l e mode i s used when one i s i n t e r e s t e d i n c a t a l o g u i n g a l l o b j e c t s on the screen. Any p i x e l i n the image plane above the t h r e s h o l d i s marked i n the ROI plan e . S i n g l e mode allo w s the user to s p e c i f y i n d i v i d u a l o b j e c t s to be marked i n the ROI plane. S i n g l e mode i s used e i t h e r when only one l a r g e o b j e c t (such as a galaxy) needs to be marked or when we "grow" a p r e v i o u s l y d e f i n e d t h r e s h o l d plane down to a lower t h r e s h o l d l e v e l . T h i s second a p p l i c a t i o n of s i n g l e mode i s u s e f u l for a v o i d i n g n o i s e p i x e l s being d e f i n e d as o b j e c t s . A f t e r s e t t i n g the mode the program prompts the user to input the t h r e s h o l d l e v e l . T h i s can e i t h e r be entered manually or by i n d i c a t i n g the i s o p h o t a l l e v e l v i a the c u r s o r . - FIND T h i s command causes the program to scan through the image l i n e by l i n e , l o o k i n g f o r marked p i x e l s i n the ROI plan e . As soon as a marked p i x e l i s detected, c o n t r o l passes a subroutine which determines the border of the o b j e c t . Once a c l o s e d r e g i o n i s d e f i n e d , another subroutine i s c a l l e d which c a l c u l a t e s the t o t a l i n t e n s i t y , c e n t r o i d , number of p i x e l s , and the moment i n v a r i a n t s f o r the o b j e c t . These numbers are 19 then w r i t t e n out i n t o a f i l e . - I SOPHOT T h i s command i s used f o r a u t o m a t i c a l l y d e t e r m i n i n g many i s o p h o t a l i n t e n s i t i e s f o r a s i n g l e o b j e c t . Upon e n t e r i n g the command the program asks the user f o r an i n i t i a l i sophote, a step s i z e (both i n ADC u n i t s ) and the number of l e v e l s d e s i r e d . A f t e r t h i s the user i s i n s t r u c t e d to mark one or more s t a r t i n g p i x e l s to be used as "seeds" to grow a region out to the s e l e c t e d isophote. The growing process i s performed by the ALU-feedback loop using the hardware s c r o l l f e a t u r e . The region i s grown u n t i l a l l contiguous p i x e l s l e s s than the given isophote are i n c l u d e d i n the ROI. At t h i s p o i n t , the videometer i s used to c a l c u l a t e the o b j e c t histogram. The t o t a l i n t e n s i t y i s then c a l c u l a t e d and the value w r i t t e n out to a f i l e . Note that t h i s v e r s i o n does not c a l c u l a t e the moment i n v a r i a n t s . I t s power l i e s i n the a b i l i t y to c a l c u l a t e many d i f f e r e n t i s o p h o t a l i n t e n s i t i e s i n a small f r a c t i o n ( f o r c e r t a i n a p p l i c a t i o n s as l i t t l e as 1/100f ^ ) of the time taken by the e q u i v a l e n t THRESH-FIND r o u t i n e s . T h i s i s the only r o u t i n e in AOLP that r e a l l y uses the advanced f e a t u r e s of the I 2 S . I t i s an e f f e c t i v e way of a r r i v i n g at l u m i n o s i t y p r o f i l e s f o r g a l a x i e s . I I I . A p p l i c a t i o n to A r t i f i c i a l F i e l d s In order to t e s t the r e l i a b i l i t y of the AOLP i t i s d e s i r a b l e to t e s t i t on a number of a r t i f i c i a l f i e l d s . T h i s can be done to determine the e f f e c t on the moment i n v a r i a n t s on such t h i n g s as shape, q u a n t i z a t i o n s c a l e , n o i s e and degree of merging. T h i s study i s only i n i t s p r e l i m i n a r y stage. F u r t h e r developments w i l l be made once the department's VAX can be f u l l y u t i l i z e d . The only shapes s t u d i e d were gaussians with v a r i o u s shapes. While i t i s p o s s i b l e to d e r i v e the moment i n v a r i a n t s a n a l y t i c a l l y , i t i s u s e f u l to do a s i m u l a t i o n because of s e v e r a l f a c t o r s r e l a t e d to the q u a n t i z a t i o n of the image. As has a l r e a d y been mentioned the moment i n v a r i a n t s are no longer t r u l y i n v a r i a n t when the t y p i c a l s i z e of o b j e c t s are on the order of a few p i x e l s . There i s a l s o an e f f e c t due to the f i n i t e number of ADC u n i t s f o r each o b j e c t . Both of these e f f e c t s tend to cause s c a t t e r about the a n a l y t i c a l value or i n some cases remove i t e n t i r e l y away from the a n a l y t i c a l v a l u e . The t e s t images were c r e a t e d by g e n e r a t i n g r e a l numbers at random a c c o r d i n g to some d e n s i t y f u n c t i o n . The r e a l numbers were then "binned" i n t o p i x e l s . In t h i s way, images c o u l d be generated by a process that c l o s e l y approximates the p h y s i c a l s i t u a t i o n . Each ob j e c t was generated with random c e n t e r i n g w i t h i n a p i x e l and i n the case of non-round o b j e c t s , with random o r i e n t a t i o n . 20 21 A. E f f e c t of Shape The t e s t o b j e c t s s t u d i e d were gaussians, with v a r i a t i o n s such as d i f f e r e n t values of sigma, i n t e n s i t y , and e l l i p t i c i t y . For an a r b i t r a r y gaussian with d e n s i t y f u n c t i o n g(x,y)=G exp(-ax2-bx2) we have, Ca/3 = ma/3 = $ exp(-ax2) xa dx j exp(-by2) y^ dy From the above i t i s easy to eval u a t e the moment i n v a r i a n t s in terms of a and b, C 2 = ( a " 1 + b-' ) / 2 C„ = 3/4a2 + l/2ab + 3/4b2 and R = | l/2a - l/2b .| I f i n s t e a d we express these i n terms of the standard d e v i a t i o n by s u b s t i t u t i n g a = l/2a2x and b=l/2a2^ we have, C 2 = a2 + a2 * x y C, = 3a" + 2a2o2 + 3a" ^ x x y y and R = I a2 - a2 I 1 x y 1 The above c a l c u l a t i o n , although f o r o b j e c t s symmetric about the x and y axes, i s of course true f o r gaussians of a r b i t r a r y o r i e n t a t i o n s i n c e these q u a n t i t i e s are r o t a t i o n a l l y i n v a r i a n t . In g e n e r a l , i f we denote the standard d e v i a t i o n along the major a x i s of a r o t a t e d 22 gaussian by o, and the standard deviation along the perpendicular axis by po (p<1.0) then we fi n d , C 2 = a2 ( 1 + p 2 ) C„ = ofl ( 3 + 3p 2 + 3p 4 ) and R = a2 ( 1 - p 2 ) Plots of R v s . C 2 for various values of o and p are shown in figure 3, along with a n a l y t i c a l values for the moment invariants in table I. Table I: An a l y t i c a l Values for Moment Invarients a P c 2 C 4 R 3.0 1 .0 18.0 648.0 0.0 2.5 1 .0 12.5 312.5 0.0 2.0 1 .0 8.0 128.0 0.0 1 .5 1 .0 4.5 40.5 0.0 1 .0 1 .0 2.0 8.0 0.0 3.0 0.8 14.8 446.3 3.2 3.0 0.6 12.2 332. 1 5.8 3.0 0.4 10.4 275.4 7.6 2.5 0.4 7.3 132.8 5.3 2.0 0.4 4.6 54.4 3.4 1.5 0.4 2.6 17.2 1 .9 1.0 0.4 1 .2 3.4 0.8 8.4 4 2 1 0.4 a=3.0 a-=2.5 .*0 o=2.0 0.0 2 ? „ a=1 .5 a=1 .0 V1 n ^ 0- w o °9P A 1 o o o o 10 20 23 200 100 50 20 10 5 2 1.3 Figure 3: S c a t t e r p l o t of R vs. C 2 f o r gaussians of va r i o u s shapes. + IT c. I • J i _ 1_ 10 20 Figure 4: S c a t t e r p l o t of C„ vs. C2 f o r gaussians of v a r i o u s shapes. 24 A l l the data shown here are f o r o b j e c t s of the same i n t e n s i t y (800 ADC u n i t s ) . Objects at s m a l l e r i n t e n s i t i e s were t r i e d . The only e f f e c t i s to i n c r e a s e s c a t t e r . The f i g u r e shows that the value R i s s t r o n g l y e f f e c t e d by the q u a n t i z a t i o n s c a l e . The p l o t of C 4 vs. C 2 shown i n f i g u r e 4 shows a remarkably s t r a i g h t l i n e . T h i s i s expected f o r gaussians because f o r a f i x e d value of p, C„ i s p r o p o r t i o n a l to C 2 squared. For o b j e c t s with more s t r u c t u r e we can expect that more i n f o r m a t i o n w i l l be present at high e r moments and the Ci, parameter w i l l prove to be more u s e f u l . IV. Mixed Star and Galaxy F i e l d s AOLP was designed to search through images c o n t a i n i n g a l a r g e number of f a i n t g a l a x i e s and s t a r s . U n f o r t u n a t e l y , due to a lack of a p p r o p r i a t e data, i t has only been t r i e d on one such f i e l d . The f i e l d i s the i s l o c a t e d i n the Harvard E9 f i e l d (Graham, 1982). The 300 second exposure ( i n the V-band) was taken by Greg Fahlman and Harvey R i c h e r at CTIO. The f i e l d i s unspec t a c u l a r when examined by eye on the ESO southern sky survey, c o n t a i n i n g only a few obvious g a l a x i e s and s e v e r a l d o u b t f u l o b j e c t s . The CCD frame on the other hand shows a very l a r g e number of g a l a x i e s , some as b r i g h t as magnitude 14. U n f o r t u n a t e l y the f i e l d e x h i b i t e s c o n s i d e r a b l e f r i n g i n g i n V which caused problems with AOLP. The program would dete c t some of the b r i g h t e r f r i n g e s as o b j e c t s . The l i s t c o n t a i n s 124 o b j e c t s of which only 12 were c l a s s i f i e d as s t a r s and 51 as g a l a x i e s . The r e s t were c l a s s i f i e d as noise and i n c l u d e d o b j e c t s such as f r i n g e s , CCD flaws and s a t u r a t e d o b j e c t s . T h i s c l a s s i f i c a t i o n was done i n t e r a c t i v e l y by eye and i s t h e r e f o r e s u b j e c t to c o n s i d e r a b l e p e r s o n a l i n t e r p r e t a t i o n as to what i s a galaxy and what i s not. G e n e r a l l y only those o b j e c t s whose nature was evident were c l a s s i f i e d as s t a r s or g a l a x i e s . D o u b t f u l o b j e c t s were c l a s s i f i e d as n o i s e . A s c a t t e r p l o t of C 2 v s . magnitude f o r t h i s f i e l d i s shown i n f i q u r e 5. While not too c o n v i n c i n g , i t can be seen that the s t a r s appear to l i e along a s t r a i g h t l i n e at the lower l i m i t of the s c a t t e r p l o t . G a l a x i e s occupy a wide region above the s t a r s . T h i s i s 25 26 1000 500 200 100 50 20 10 T 1 r 1 1 1 r 1 T T — -i T " i 1 i r-0.5 _ a • o n a o e? i f ° o „ ° ° 9 " ° o ^ fti " o % < o o c . J I ,, I L stars Q galaxies D other 22 21 20 19 IB 17 16 15 V M a g n i t u d e : E9 F i e l d 14 Figure 5: P l o t of C 2 vs. V-magnitude for the E9 f i e l d . to be expected and t h i s general pattern agrees with r e s u l t s found by Tyson and J a r v i s f or s i m i l a r p l o t s . Objects c l a s s i f i e d as "other" are predominantly at low magnitudes, r e f l e c t i n g the d i f f i c u l t y of dec i d i n g an obj e c t s c l a s s when i t i s f a i n t . Also of worth noting are the various shape-shape diagrams. Shown in f i g u r e 6 and 7 are s c a t t e r p l o t s of R vs. C 2. The two f i g u r e s are i d e n t i c a l except that the second one omits objects f a i n t e r than magnitude 20.5. There i s l i t t l e that one can deduce from these diagrams, except a s l i g h t tendency for s t a r s to c l u s t e r in the lower l e f t corner. Also, the s t a r s seem to be on the lower l i m i t of the p l o t , a r e s u l t i n d i c a t i n g that for objects of a given s i z e ( C 2 ) , 20 10 5 2 1 0.5 0.2 0.1 0.05 n ro n • o 1 o " 0.00 (P -o o o ° n o D o . r o 8 0 I n ~ arP 0 * D 8 o -r t 1 1 0.5 J__l..l_l-J L . 5 10 20 C. -y- stars O galaxies Q other 50 100 200 500 1000 50 20 10 5 2 1 0.5 0.2 0.1 0.05 0.02 0.00 Figure 6: P l o t of R vs. C 2 for the E9 f i e l d . , r-.--^„,-_ r^,_,^ ..r ...T , ( , , g r | T 0.5 o o o"8 cn 00 4- o • o o o 0 0 ft , o J 1 1 10 20 c„ 50 100 200 500 1000 Figure 7: Pl o t of R vs. C 2 for the E9 f i e l d o m i t t i n g objects with V<20.5 28 50000 20000 10000 5000 2000 1000 500 200 100 50 20 10 5 0.5 i I: 0.5 Ol J I l _ l I I l _ J _ ' • • • ' ! T" - i— stars O galaxies Q other _ J I L I 5 10 20 50 100 200 500 1000 C . Figure 8: P l o t of C„ vs. C 2 for the E9 f i e l d . s t a r s are g e n e r a l l y the roundest objects (smallest R ) . The C„ vs. C 2 p l o t in f i g u r e 8 shows the s t r a i g h t l i n e found e a r l i e r for the a r t i f i c i a l o b j e c t s . One wonders how much extra information can be gathered from using C„ as a c l a s s i f i c a t i o n parameter i f i t always c o r r e l a t e s so we l l with C 2. It seems a l i t t l e premature, based on these r e s u l t s , to say that i t i s p o s s i b l e to a c c u r a t e l y separate s t a r s from g a l a x i e s . While there i s some degree of sep a r a t i o n , i t seems to be n o t i c a b l e only when presented with a galaxy-star c l a s s i f i c a t i o n already made (i.e. by eye). We w i l l have to wait f or more and better data before any d e t a i l e d study of automatic g a l a x y - s t a r d i s c r i m i n a t i o n can be undertaken. V. Photometric Applications AOLP was a l s o used to do photometry i n a p p l i c a t i o n s i t wasn't s p e c i f i c a l l y designed f o r . T h i s i s the photometry of g l o b u l a r c l u s t e r s and ( r e l a t i v e l y ) nearby g a l a x i e s with l a r g e (and t h e r e f o r e no need f o r the moment i n v a r i a n t s f o r c l a s s i f i c a t i o n process) images. The data d i s c u s s e d here were obtained with the RCA-CCD d e t e c t o r at the prime focus of the Canada - France - Hawaii - Telescope on Mauna Kea. T h i s d e v i c e i s used i n c o n j u n c t i o n with a f i l t e r and s h u t t e r system. 5 The CCD has 320 rows and 512 columns of which only 316X498 are a c t i v e . Each p i x e l i s 30 microns square, corresponding to 0.418 arc-seconds per p i x e l at prime f o c u s . 6 For a d e t a i l e d d e s c r i p t i o n of the CCD c o n s u l t Walker et al. (1984). The data were obtained i n two sepa r a t e observing s e s s i o n s : During the summer of 1983 by Paul Hickson and Greg Fahlman, and durin g the summer of 1984 by Paul Hickson and the author. The observing s e s s i o n s were p r i m a r i l y to gather data f o r Paul Hickson's on-going survey of compact groups of g a l a x i e s (Hickson, 1982). The data from the f i r s t t r i p were reduced d i f f e r e n t l y from the second. At t h a t time the CCD had a r a p i d l y f l u c t u a t i n g b i a s s i g n a l . Because of t h i s there was no way to measure the zero p o i n t of the d e v i c e p r i o r to 5The FOCAS ( F a i n t Object Camera And Spectrograph) system, not to be confused with Tyson and J a r v i s ' s program of the same name, designed by Paul Hickson of U.B.C. and d e s c r i b e d in Hickson (1984). 6 T h i s was a c t u a l l y measured from the images d i r e c t l y . 29 3 0 the exposure. This f l o a t i n g bias was f i r s t removed from each frame by examining a 10X11 p i x e l area of overscanned p i x e l s . The mean of t h i s area was used as the b i a s l e v e l and subtracted from each frame p r i o r to futher p r o c e s s i n g . In a d d i t i o n to program o b j e c t s , a number of dark f i e l d (with the shutter closed) and f l a t f i e l d (a region of the sky devoid of obj e c t s down to 23rd magnitude) exposures were taken. The dark f i e l d s were then averaged and the average removed from each program object and f l a t f i e l d . The f l a t f i e l d s were averaged (one set for each colour passband), normalized, to a mean of one, cleaned by s e t t i n g p i x e l s f a r t h e r than three standard d e v i a t i o n s from the mean equal to the mean, and then used to f l a t - f i e l d the program ob j e c t s by d i v i s i o n . The data from the other observing session were reduced s i m i l a r l y except that the bias l e v e l on the CCD was much more s t a b l e . This allowed bias exposures to be taken (exposures of zero l e n g t h ) . The mean of the b i a s frames was subtracted from a l l the other frames. This part of the data reduction was done on the U n i v e r s i t y ' s Amdahl 470 V-8 computer using SUPERTOODEE, a general purpose image a n a l y s i s program i n i t i a l l y developed by Greg Fahlman and modified e x t e n s i v e l y by John N i c o l . In order to c a l i b r a t e the photometry to a standard photometric system (Kron-Cousins), s e v e r a l exposures of a f i e l d i n M92 c o n t a i n i n g standard s t a r s were taken. The f i e l d i s the number IX f i e l d (Sandage 1966). This f i e l d i s located about 5.7 arc-minutes north of the centre. The s t a r s used 31 Table I I : C a l i b r a t i o n S t a r s i n M92 Star V B-V V-R B' R' IX 18 16 .310 -0.085 -0.03 1 6 .308 16. 308 IX-9 16 .090 0.540 0.32 1 6 .519 16. 688 IX-25 1 5 .915 0.565 0.38 16 .399 15. 507 IX-26 16 .425 -0.075 0.02 16 .352 16. 402 IX-100 16 .910 1.215 0.73 1 7 .920 16. 219 f o r the c a l i b r a t i o n were numbers 8, 9, 25, 26 and 100. T h e i r i n s t r u m e n t a l magnitudes were measured on the I 2 S u s i n g a program ( w r i t t e n by Dennis Crab t r e e , now on s t a f f at CFH) that s i m u l a t e s aperture photometry. An a p e r t u r e with a r a d i u s of s i x p i x e l s (2.5 a r c - s e c ) was used, separated by a four p i x e l wide guard r e g i o n . A four p i x e l wide annulus o u t s i d e the guard region was used to measure the sky b r i g h t n e s s . The program took i n t o account the q u a n t i z a t i o n s c a l e of the images and i n t e r p o l a t e d f o r f r a c t i o n a l p i x e l s . T h i s allowed the i n s t r u m e n t a l magnitudes to be d e f i n e d as, B' = - 2. 51 ogi0(ADCU in B) + 28.14 and /?' = - 2. 51 ogio(ADCU i n R) + 27.80 The c o n s t a n t s i n the above were chosen such that s t a r #26 (which has B-R^0. 0) would have B=B' and R=R'. These c o n s t a n t s are f a i r l y a r b i t r a r y and disappear once the f i n a l c o r r e c t i o n s are made. 32 By p l o t t i n g B-B' vs. B'-R' ( i n s t r u m e n t a l c o l o u r ) f o r each s t a r and f i n d i n g the best l i n e through the r e s u l t i n g p o i n t s we can f i n d the c o r r e c t e d magnitudes as a f u n c t i o n of the i n s t r u m e n t a l magnitude and c o l o u r , B = B} + 0. 096(B' - R') and s i m i l a r l y f o r R, R = R' + 0. 044(B' - R}) + 0. 02 These c o r r e c t i o n s were used f o r a l l the data from the f i r s t o b s e r v i n g s e s s i o n , t h i s i n c l u d e s the data f o r the compact group g a l a x i e s and one of the M92 f i e l d s . S i m i l a r c o r r e c t i o n s were made f o r the data from the other s e s s i o n . The magnitudes shown are standard magnitudes i n the Kron-Cousins system. A. Globular Clusters M92 Exposures of M92 were taken on both observing s e s s i o n s . Only B and R images were obtained on the f i r s t s e s s i o n and B, V, and R on the second. A f t e r the p r e l i m i n a r y r e d u c t i o n photometry was done on each frame u s i n g AOLP. A t y p i c a l procedure was to set the t h r e s h o l d to the sky l e v e l p l u s three standard d e v i a t i o n s with the m u l t i p l e mode of the THRESH command, and then to grow the marked o b j e c t s down to 33 the sky + 2o l e v e l . A l l o b j e c t s were then found and c a t a l o g u e d . The ob j e c t i n t e n s i t y , c e n t r o i d and moment i n v a r i a n t s were a l l used in the subsequent a n a l y s i s . One problem in doing t h i s s o r t of photometry on crowded f i e l d s t y p i c a l l y found in g l o b u l a r c l u s t e r s i n the amount of con f u s i o n r e s u l t i n g from merged o b j e c t s . In order to understand what e f f e c t merging had on the moment i n v a r i a n t s , the R f i e l d was examined by eye. Objects were c l a s s i f i e d i n t o three groups - stars, merged stars, and noise. The r e s u l t s are shown i n f i g u r e 9. The s e p a r a t i o n of s t e l l a r o b j e c t s from n o n - s t e l l a r ones can be c l e a r l y seen. S t a r s occupy the lower edge of the s c a t t e r p l o t . T h i s r e s u l t i s of course expected, as al r e a d y p o i n t e d out, because s t a r s are the most c e n t r a l l y c o n c e n t r a t e d o b j e c t s f o r t h e i r magnitude. T h i s p l o t does not show any c l e a r d i s t i n c t i o n between merged s t a r s and " o t h e r s " . C l e a r l y some other parameters must be used to separate a s t r o n o m i c a l o b j e c t s from o b j e c t s such as CCD f l a w s . I t i s i n t e r e s t i n g to note that the s t a r s l i e along a s t r a i g h t l i n e . T h i s r e s u l t i s somewhat unexpected, s i n c e a l l s t a r s are i n t r i n s i c a l l y of the same shape and not a f u n c t i o n of the n o r m a l i z a t i o n {i.e. magnitude) we would expect that they a l l have the same C 2 v a l u e s . A probable e x p l a n a t i o n f o r t h i s e f f e c t i s that AOLP measures o b j e c t s w i t h i n a given isophote. Therefore b r i g h t e r o b j e c t s would have a gr e a t e r f r a c t i o n of t h e i r l i g h t above t h i s isophote and would extend f a r t h e r than f a i n t o b j e c t s . Hence the e f f e c t i v e s i z e of the object {=*C2) would depend on i t s 34 100 50 20 10 to o 5 2 0.5 23 22 21 20 19 18 17 16 15 14 Instr. R Magnitude : M92 Figure 9 : Scatter p l o t of C 2 v j , R magnitude for objects in M92. magnitude. A f i n a l d e t a i l to no t i c e i n the diagram i s the increased s c a t t e r at f a i n t e r magnitudes. This i s a r e s u l t both of the r e a l increase in the percentage of p h y s i c a l noise for f a i n t e r objects and a l s o that the q u a n t i z a t i o n e r r o r s are l a r g e s t at t h i s range of magnitudes. Also worth examining i s the R vs. C 2 p l o t shown in f i g u r e 10. In t h i s p l o t the s t a r s are con f i n e d to an almost c i r c u l a r region. There are a few n o n - s t e l l a r o b j e c t s w i t h i n t h i s region and a l a r g e r number of s t a r s outside i t , but ge n e r a l l y most st a r s l i e below the l i n e R=*1 and C 2-3. Indeed t h i s separation was used to throw out o b j e c t s p r i o r to producing colour-magnitude diagrams. ~ i — i — i — i — i — m — i — i — i — i — i — i — i — i — i — r • V „ • V V o * wi a _ v - v a * „ a + **•* •* ^ ++,•%.+ ••>*-*• a Figure 10: Scatter p l o t of R vs. C 2 for objects in M92. 50000 r 20000 -10000 -5000 L 1000 -500 L 0.5 2 5 10 20 50 100 Figure 11: Scatter p l o t of C« vs. C 2 for objects in M92. 36 The p l o t of C 4 vs. C 2 shown i n f i g u r e 11 proves to more i n t e r e s t i n g than i t was e a r l i e r . S t a r s l i e on an extremely narrow l i n e , and there i s a l s o c o n s i d e r a b l e d e v i a t i o n from t h i s l i n e f o r n o n - s t e l l a r o b j e c t s . Two colour-magnitude diagrams are show here. F i g u r e 12 shows a J? vs. B-R diagram obtained with data from the f i r s t o bserving s e s s i o n . A V vs. B-V diagram i s shown i n f i g u r e 13 with data from the second s e s s i o n . M13 Exposures of M13 were taken only on the second observing s e s s i o n . The f i e l d surveyed i s l o c a t e d f i v e arc-minutes d i r e c t l y north of the c e n t e r . Shown i n f i g u r e s 14 and 15 are B vs. B-R and V vs. B-V diagrams. T h i s approach i n determining colour-magnitude diagrams i s probably not the best one a v a i l a b l e , although i t does y i e l d i n t e r e s t i n g r e s u l t s . A b e t t e r technique i s to f i t s t e l l a r p r o f i l e s to the o b j e c t s i n the f i e l d . T h i s a l l o w s merged o b j e c t s to be i n c l u d e d i n the survey. In the approach taken here, merged o b j e c t s are d e l i b e r a t e l y avoided. 37 16 17 18 19 m 20 21 22 h 23 • * \ ^ + •H- + , + + 4+ + + • • 24 0.5 16 h 17 r 18 h 1.0 1.5 2.0 B - R : M92 Figure 12: C o l o u r magnitude d i a g r a m of M92 from f i r s t o b s e r v i n g s e s s i o n . i "i 1 — i I I T I I I 2.5 19 20 21 22 23 -0.4 0.0 + + + 4-. +"7+ + •V* 4* 0.4 1.6 0.8 1.2 B - V : M92 Figure 13: C o l o u r magnitude d i a g r a m of M92 from second o b s e r v i n g s e s s i o n . 2.0 19 r 20 r 21 r 22 23 1.2 1.6 B - R : M13 2.0 2.4 Figure Ml 3. 14: Colour magnitude diagram of i _ + i i i i i i - + *• - + + + A + -4-4- 4. 4. * + -ft* • • + + ** f 4- * * ** + i 4. • *-\ j. \* * 1 * * 4+ 4* + *+ * + + + 4 -1 1 1 1 1 1 18 19 20 21 22 0.4 0.8 1.6 1.2 B - V : M13 Figure 15: Colour magnitude diagram of Ml 3. 39 B. Galaxies AOLP was a l s o used determine the magnitudes and c o l o u r s of g a l a x i e s i n Hickson's compact group c a t a l o g u e . The data was obtained during the summer of 1983 o b s e r v i n g s e s s i o n . Exposures were made in red and blue l i g h t f o r each f i e l d . The photometry was done using the ISOPHOT command in AOLP. The i s o p h o t a l i n t e n s i t y was measured at each isophote from 255 ( i n ADC u n i t s ) down to j u s t above the sky. T h i s allowed the i n t e n s i t y p r o f i l e s to be determined i n a d d i t i o n to c o l o u r s and magnitudes for each galaxy. Colours and Magnitudes of Compact Group galaxies The c o l o u r s and magnitudes for the s e l e c t e d g a l a x i e s are shown in Table I I I . In order to determine the c o l o u r s , the two images taken through the R and B f i l t e r s had to be matched up. A number of a l t e r n a t i v e s were c o n s i d e r e d . One p o s s i b i l i t y was to d e f i n e an area by a given isophote on one image, a l i g n the images c a r e f u l l y and measure the i n t e n s i t y w i t h i n the corresponding region on the other image (note i t i s not n e c e s s a r i l y an i s o p h o t e ) . T h i s method does not f i t n a t u r a l l y i n t o the type of output generated by AOLP. The ISOPHOT command g i v e s the i n t e n s i t y w i t h i n the isophote and the area of the isophote ( i n p i x e l s ) . The technique used was to match up each measurement in one c o l o u r ( i n t h i s case blue, but the choice i s a r b i t r a r y ) with the measurement i n the other c o l o u r that c o n t a i n e d the same number of p i x e l s ( i n t e r p o l a t i n g i f n e c e s s a r y ) . A p o t e n t i a l disadvantage of 40 Table I II; Colours and Magnitudes of Compact Group Galaxies Galaxy -•23.5 (B-R) 2 3 5 &2«.0 (B-R) 2 a o Comments 73a 14.74 1.17 14.43 1.14 s p i r a l 73b 17.76 2.30 17.47 2.26 s p i r a l f 73c 17.22 1 .69 17.14 1 .69 le n t i c 73d 19.11 2.44 18.94 2.43 s p i r a l f 76a 16.11 1 .79 16.05 1 .78 spi r a l 76b 15.47 1 .58 15.33 1 .57 e l l i p 76c 1 5.70 1 .66 15.53 1 .65 e l l i p 76d 16.16 1 .60 15.97 1 .56 e l l i p 76e 17.73 1 .54 17.55 1 .54 s p i r a l 88a 14.38 1 .53 1 4.29 1 .53 s p i r a l 88b 14.51 1 .53 1 4.39 1 .52 spi r a l 88c 1 5.56 1.11 15.37 1.11 spi r a l 88d 15.87 0.78 ***** **** spi r a l 92a 13.53 1 .08 ***** **** spi r a l 92bd 14.08 1 .65 13.96 1 .65 spi r a l 92c 15.44 1 .82 14.74 1 .62 s p i r a l 92e 15.46 * * * * ***** **** ellip t -97a 14.74 1 .65 14.59 1 .65 e l l i p 97b 16.12 1 .57 16.01 1 .58 spi r a l 97c 15.26 1 .45 15.17 1 .45 lent ic t Blue photometry probably in error $ Bright star subtracted this method i s that the same region might not be measured on each image, eventhough they are of the same size area. This effect would generally be s i g n i f i c a n t only in the inner region of a galaxy where the colour along a given isophote 41 might not be constant. For measurements i n the outer regions of a galaxy, where the co l o u r i s f a i r l y uniform around an isophote, t h i s technique i s r e l i a b l e . The r e s u l t s quoted i n the t a b l e are f o r t h i s case. Luminosity P r o f i l e s of Compact Group Galaxies The ISOPHOT command i s very u s e f u l f o r determining l u m i n o s i t y p r o f i l e s of g a l a x i e s . The method used here i s somewhat d i f f e r e n t from usual techniques of a r r i v i n g at lu m i n o s i t y p r o f i l e s , but i s p o t e n t i a l l y as u s e f u l . Luminosity p r o f i l e s are u s u a l l y determined from r a d i a l c u t s , e i t h e r along the minor or major a x i s or at some angle to i t . Aperture photometry i s a l s o used with c i r c u l a r a p e r t u r e s or e l l i p t i c a l a p e r t u r e s t a i l o r e d to f i t a given g a l a x y . A l l of these methods s u f f e r from the problem that they are not g e n e r a l . R a d i a l cuts c o n t a i n i n f o r m a t i o n only from one par t of the galaxy. With aperture photometry i t i s d i f f i c u l t to accommodate p e c u l i a r i t i e s i n i n d i v i d u a l galaxy shapes. I t i s worthwhile to develop an approach that i s holistic i n the sense that i t d e s c r i b e s the e n t i r e galaxy, and general i n that i t can be a p p l i e d to a l l g a l a x i e s i n a c o n s i s t e n t manner. We d e f i n e here the effective radius of an isophote to be re=\/(A/n) where A i s the area w i t h i n the i s o p h o t e . For an e l l i p s e of e l l i p t i c i t y e t h i s corresponds to a r a d i a l cut at an angle 4>=arccos {(1 - e)'05} to the major a x i s . For d i s r u p t e d g a l a x i e s there i s no such correspondence between the e f f e c t i v e radius and a r a d i a l c u t . These g a l a x i e s o f t e n 42 have no c l e a r l y d e f i n e d major a x i s and the e f f e c t i v e r a d i u s seems to be the most meaningful r a d i a l parameter. Many of the g a l a x i e s s t u d i e d here are of t h i s type. F o l l o w i n g are the d i f f e r e n t i a l and i n t e g r a t e d l u m i n o s i t y p r o f i l e s for 2. of the compact group g a l a x i e s . Magnitude i s p l o t t e d as a f u n c t i o n of r f o r each galaxy, and a l s o as a f u n c t i o n of r e ° ' 2 S f o r e l l i p t i c a l g a l a x i e s . The magnitudes shown are instrumental blue magnitudes. 43 2 0 I 1 1 1 1 1 1 1 -2 5 i i i i i i i I 0.0 5 10 15 2 0 2 5 3 0 3 5 Eff. Radius (arc-sec) : HCG73a 14- I 1 1 1 1 1 r 0.0 5 10 15 2 0 2 5 3 0 3 5 Eff. Radius (arc-sec) : HCG73a Figure 16: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG73a. Open faced Sc s p i r a l . 44 21 0.0 5 10 15 Eff. Radius (arc-sec) : HCG73b 0.0 5 10 15 Eff. Radius (arc-sec) : HCG73b Figure 17: D i f f e r e n t i a l and i n t e g r a t e d magnitude p r o f i l e s f o r galaxy HCG73b. S p i r a l galaxy. The blue photometry i s probably in e r r o r . Figure 18: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG73c. Lenticular galaxy. 46 T 1 1 1 1 1 1 1 1 1 0.0 2 4 6 8 10 Eff. Radius (arc-sec) : HCG73d i 1 1 i i i i i i i I 0.0 2 4 6 8 10 Eff. Radius (arc-sec) : HCG73d Figure 19: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG73d. S p i r a l galaxy. Photometry probably in error. 47 0.0 18 r 0.0 5 10 15 Eff. Radius (arc-sec) : HCG76a 5 10 15 Eff. Radius (arc-sec) : HCG76a Figure 20: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG76a. S p i r a l galaxy. J I L 0.0 5 10 15 20 25 30 Eff. Radius (arc-sec) : HCG76b i 1 1 1 1 1 1 0.0 5 10 15 20 25 30 Eff. Radius (arc-sec) : HCG76b Figure 21: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG76b. E l l i p t i c a l galaxy. cd S 15 16 17 1.0 1.5 2.0 2.5 (Eff. Rad.)* 5 (arc-sec)" 2 5 : HCG76b Figure 22: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG76b. E l l i p t i c a l galaxy. •4-3 d CO S OJ 16 17 0.0 Eff. 5 10 15 Radius (arc-sec) : HCG76c Figure 23: magnitude E l l i p t i c a l 20 D i f f e r e n t i a l p r o f i l e s f o r galaxy. and i n t e g r a t e d galaxy HCG76c. 1 1.5 2 2.5 (Eff. Rad)"86 (arc-sec)"* : HCG76c i - 1 1 1 • — i i I I i i i i 1 1 1 1.5 2 2.5 (Eff. Rad)* 8 (arc-sec)"* : HCG76c Figure 24: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG76c. E l l i p t i c a l galaxy. 20 Eff. Radius (arc-sec) : HCG76d Figure 25: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG76d. E l l i p t i c a l galaxy. Sharp jump in p r o f i l e due to presence of bright st a r . 5 3 l i I I I I I i i I I 0.0 2 4 6 8 10 Eff. Radius (arc-sec) : HCG76e Figure 26: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG76e. S p i r a l galaxy. CD -*-> ti S 18 19 20 0.0 2 4 6 8 10 Eff. Radius (arc-sec) : HCG76f 12 Figure 27: D i f f e r e n t i a l magnitude p r o f i l e s for Lenticular galaxy. and integrated galaxy HCG76f. 55 I i i i i 1 1 1 0.0 5 10 15 20 25 30 35 Eff. Radius (arc-sec) : HCG88a Figure 28: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG88a. S p i r a l galaxy. 56 . I 1 1 i i i i I 0.0 5 10 15 20 25 30 35 Eff. Radius (arc-sec) : HCG88b 14 I 1 1 1 1 1 1 . 1 15 -i-j fl ca «! 16 fl 0.0 5 10 15 20 25 30 35 Eff. Radius (arc-sec) : HCG88b Figure 29: D i f f e r e n t i a l and in t e g r a t e d magnitude p r o f i l e s f or galaxy HCG88b. S p i r a l galaxy. 57 0.0 5 10 15 20 25 30 Eff. Radius (arc-sec) : HCG88c T 1 1 1 r j i i i L ° 0 5 10 15 20 25 30 Eff. Radius (arc-sec) : HCG88c Figure 30: D i f f e r e n t i a l and i n t e g r a t e d magnitude p r o f i l e s f o r galaxy HCG88c. S p i r a l galaxy. 58 Figure 31: D i f f e r e n t i a l and integrated^ magnitude p r o f i l e s for galaxy HCG88d. S p i r a l galaxy. 59 20 I 1 1 1 1 1 1 1 24 I 1 1 1 1 1 1 1 0.0 5 10 15 20 25 30 35 Eff. Radius (arc-sec) : HCG92a 13 I i 1 1 1 1 r 22 1 1 i i i i i I 0.0 5 10 15 20 25 30 35 Eff. Radius (arc-sec) : HCG92a Figure 32: D i f f e r e n t i a l and i n t e g r a t e d magnitude p r o f i l e s f o r galaxy HCG92a. S p i r a l galaxy. B r i g h t e s t . member in Stephen's Q u i n t e t . Galaxy with d i s c r e p e n t r e d s h i f t . Sharp jump i n p r o f i l e due to presence of b r i g h t s t a r . 20 | 1 1 1 1 1 r 0.0 5 10 15 20 25 30 35 Eff. Radius (arc-sec) : HCG92bd I r 1 1 1 1 i I <u 14 •d +-> -•-< a aj SS si C ~ 15 I i I i i i i l 0.0 5 10 15 20 25 30 35 Eff. Radius (arc-sec) : HCG92bd Figure 33: D i f f e r e n t i a l and i n t e g r a t e d magnitude p r o f i l e s f o r galaxy HCG92bd. P a i r of i n t e r a c t i n g s p i r a l g a l a x i e s i n Stephen's Q u i n t e t . 61 20 0.0 5 10 15 20 25 30 Eff. Radius (arc-sec) : HCG92c J L 0.0 5 10 15 20 25 30 Eff. Radius (arc-sec) : HCG92c Figure 34: D i f f e r e n t i a l and integrated magnitude p r o f i l e s for galaxy HCG92c. S p i r a l galaxy in Stephen's Quintet. Eff. Radius (arc-sec) : HCG92e CD c cd 3 S CD 14 15 16 0.0 5 10 15 20 Eff. Radius (arc-sec) : HCG92e 25 Figure 35: D i f f e r e n t i a l and i n t e g r a t e d magnitude p r o f i l e s f o r galaxy HCG92e. E l l i p t i c a l galaxy i n Stephen's Q u i n t e t . The sharp jump in the p r o f i l e i s due the presence of a b r i g h t s t a r . 63 I 1 1 I I i i I 0.0 5 10 15 20 25 30 35 Eff. R a d i u s ( a r c - s e c ) : HCG97a 0.0 5 10 15 20 25 30 35 Eff. R a d i u s ( a r c - s e c ) : HCG97a Figure 36: D i f f e r e n t i a l and in t e g r a t e d magnitude p r o f i l e s for galaxy HCG97a. E l l i p t i c a l galaxy. I I I I I I I 1.0 1.5 2.0 2.5 ( E f f . R a d . ) * 6 ( a r c - s e c ) * * : HCG97a Figure 37: D i f f e r e n t i a l and i n t e g r a t e d magnitude p r o f i l e s f o r galaxy HCG97a. E l l i p t i c a l galaxy. 0.0 5 10 15 Eff. Radius (arc-sec) : HCG97b 20 Figure 38 magnitude galaxy. D i f f e r e n t i a l and p r o f i l e s f o r galaxy i n t e g r a t e d HCG97b. S p i r a l 15 cd s OJ 16 0.0 5 10 15 20 Eff. Radius (arc-sec) : HCG97c Figure 39: D i f f e r e n t i a l and i n t e g r a t e d magnitude p r o f i l e s f o r galaxy HCG97c. L e n t i c u l a r galaxy. VI. Conclusion The f i r s t stages of AOLP have shown i t to be useful in a number of d i f f e r e n t applications. It is a r e l i a b l e method of obtaining colour-magnitude diagrams for globular clusters although i t is probably not the best approach. Luminosity p r o f i l e s of galaxies are quickly and e f f i c i e n t l y determined with the program. More research s t i l l needs to be done in the application to mixed star and galaxy f i e l d s . This w i l l have to wait u n t i l the proper data base can be assembled. The i n i t i a l work with moment invarients looks promising, the technique proved helpful in discriminating stars from other objects when applied to the globular cluster f i e l d s . 67 

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