The evolution of galaxies in the Hubble Deep Fields

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in the Hubble Deep Fields

by

S tep h en D onald Je rn iy G w yn

B.Sc. McGill University 1990 M.Sc. University of Victoria 1995

A Dissertation Subm itted in Partial Fulfillrnent of the Requirements for the Degree of

Do c t o r o f Ph i l o s o p h y

in the Department o f Physics and Astronomy

We accept this thesis as conforming to the required standard.

Dr. F. D. A. H iirtwick. Supervisor (D ep a rtm en t o f P hysics & A stro n o m y)

Dr. C. ./. P ritchet, D epartm ental M em b er (D ep a rtm en t o f P hysics & Astronomy^

Dr. D. C r a m p ^ c ^ D w a r tm e n ta l M e m b er (H erzberg In s titu te o f .Astrophysics)

|G. B ^ I o . O u tsid e M em b er (D ep a rtm en t o f C h em istrv)

'

D Ï T s / T T / ^ y ^ t e i ^ a/ E.xaminer (H erzberg In s titu te o f .Astrophysics)

© Stephen Donald .lermy Gwyn. 2001.

U niversity o f Victoria.

.All rig h ts reserved. This d is s e r ta tio n m a y n o t be reprodaced in whole o r in p a rt, by p h o to co p yin g o r o th e r m ea n s, w ith o u t th e p e r m is s io n o f the au th or.

Abstract

T h is th esis is a stu d y of several a sp ec ts of th e evo lu tio n of galaxies using p h o to m e tric redshifts in th e H ubble Deep Fields (H D F 's). T h e p h o to m e tric redshift m e th o d is used in th e H D F 's dow n to a m a g n itu d e lim it of / = 28. T h e large sam p le a n d th e u n p reced en ted d e p th o f th e H ubble Deep Fields allow one to tra c e th e evolution of several p ro p e rtie s of galaxies from c = 5 to th e p resent in a s ta tis tic a l m an n er. T h is thesis stu d ies four such iispects:

1. T h e c lu ste rin g of galaxies is exam ined. W hen th e redshift d istrib u tio n s o f th e H D F -N o rth an d th e H D F -S o u th are co m p ared , one finds a sig­ nificantly g re a te r n u m b er of galaxies a ro u n d ;= 0 .5 . T h is suggests th e presence of a s tru c tu re (a very weak c lu ste r o r a very stro n g g roup) in th e H D F -X o rth .

2. T h e s ta r form ation ra te d e n sity (S F R D ) is d e te rm in e d by m easu rin g th e U V -lum inosity density. A fter c o rre c tin g for d u st e x tin c tio n , th e s ta r fo rm atio n ra te is found to decrease ex p o n e n tially w ith tim e w ith an e-folding perio d of a b o u t 4 G yr.

3. T h e difference betw een th e th e ra te of declines of th e B b an d galaxy n u m b e r d ensity a n d th e lu m in o sity d en sities are used to exam ine th e m erging h isto ry of th e U niverse. W hile th e to ta l B b a n d lu m inosity d e n sity of th e U niverse decreases o nly slig h tly w ith tim e since z = 5. th e n u m b er d e n sity of galaxies d ro p s co n sid e rab ly m ore. O n average, a p resen t day g alax y is th e p ro d u c t o f ~ 3 p ro g en ito rs.

4. T h e m orphology o f galaxies is qu an tified using a "lum piness" p a ra m ­ e ter. I , w hich m easures th e nu m b er o f local m ax im a in th e im age of a galaxy. R est-fram e D b a n d im ages are m ade of b o th H D F 's by A.-correcting each pixel of each galaxy in th e fram es using th e p h o to ­ m etric red sh ifts o f th e p aren t galaxies. It is found th a t L increases w ith increasing a b so lu te brightness a n d increasing red sh ift. a lb e it only slightly.

E.xaminers:

Dr. F. D. A. Héirtnick. Supervisor (Department o f Phvsics & Astronomv)

Dr. C. ./. Pritchet. Departmental Member (Department o f Physics & Astronomy)

---rtmental Member (Herzberg Institute o f .\strophysics) Dr. D.

Outside Member (Department o f Chemistry)

Abstract

ii

Contents

iv

List of Tables

vil

List of Figures

viii

Acknowledgments

x

1 Introduction

1

2 The Hubble Deep Fields

8

2.1 D escription of th e H ubble D eep Fields ... 8

2.2 D e t e c t i o n ... 12

2.3 P h o t o m e t r y ... 16

2.4 T h e s a m p l e ... 21

3 Photom etric Redshifts

28

3.1 b rie f histo ry of p h o to m e tric r e d s h i f t s ... 29

3.1.1 D irect shift m e a s u r e m e n t... 29 3.1.2 C olour-colour d i a g r a m s ...30 3.1.3 L inear r e g r e s s i o n ... 33 3.1.4 T em p late f i t t i n g ... 34 3.1.5 V a r i a t i o n s ... 35 3.2 T h e te m p la te fittin g tech n iq u e in g e n e r a l ...36

3.2.1 P lio to m e try to s p e c tra l energy d i s t r i b u t i o n s ... 37

3.2.2 T h e te m p la te s p e c t r a ... 40

3.2.3 C o m p a rin g th e te m p la te s to th e S E D 's ...4.5

3.3 T h e te m p la te fittin g technique as used in th is t h e s i s ... 47

3.4 R e s u l t s ... .53

4 Clustering

57

4.1 M o tiv a tio n ... 58

4.2 M ethod ... 62

4.3 R e s u l t s ... 63

5

Star Formation Rates

69

5.1 T h e l / l ’a m e t h o d ... 70 5.2 T h e SW M L m eth o d ... 71 5.3 T h e ^ - c o r r e c t i o n s ... 73 5.4 C o m p a rin g m eth o d s a n d f i e l d s ... 77 5.5 Surface b r ig h t n e s s ... 79 5.6 E d d in g to n correctio n s ... 86 5.7 L um inosity f u n c t i o n s ... 91 5.8 L um inosity d e n s i t y ... 95 5.9 T h e effects of d u st ... 104 5.10 S ta r fo rm a tio n rate s ... 109

6

Merging

118

6.1 T h e V/Vmax s t a t i s t i c ... 120

6.2 B b a n d lu m in o sity a n d lu m inosity density f u n c t i o n s ... 125

6.3 I n t e r p r e t a t i o n ...131

7 Morphologies

147

7.1 T h e I p a r a m e t e r ... 147 7.2 R est B im a g e s ...152 7.3 R e s u l t s ... 156

8 Conclusion

164

8.1 S u m m a ry ...164 8.2 F u tu re w o r k ... 166 8.2.1 G alax ies a t 1 < z < 2 ...166 8.2.2 D u st a t high r e d s h i f t ... 167

8.2.4 Im proved sp e c tra l t e m p l a t e s ... IG9

2.1 List of o b s e r v a t io n s ... 12

3.1 F ilte r p r o p e r t i e s ... 39

5.1 M edian E { B - T ) for various sam ples ... 107

5.2 Conversion of L '\' d e n sitv to S F R ... 110

2.1 F ilte rs used in th e H D F 's ... 10

2.2 S e g m en ta tio n im ages in different b a n d s ... L5 2.3 N u m b er counts in all b a n d s ...22

2.4 I b a n d n um ber c o u n t s ... 23

2.5 P h o to m e tric c o m p l e t e n e s s ... 25

2.6 Surface brightness c o m p l e te n e s s ...27

3.1 In te rg ala ctic a b so rp tio n ... 44

3.2 S p e c tra l t e m p l a t e s ... 49

3.3 i ' d ro p o u ts ... 51

3.4 com parison o f p h o to m e tric a n d sp ectro sco p ic red sh ifts . . . 54

3.5 P h o to m e tric redshift d istrib u tio n s for th e H D FX a n d H D FS . 56 4.1 R elative nu m b er co u n ts for th e H ubble Deep F i e l d s ...59

4.2 / b a n d light in th e H D FX a n d H D F S ... 61 4.3 C o rrela tio n f u n c t i o n s ... 65 4.4 F our galaxy f r a g m e n t s ...68 5.1 L inearly in te rp o la te d Ar-corrections ... 76 5.2 N o rth vs. S outh. 1/1 ^ vs. S W M L ... 78 5.3 1 /1 ‘a vs. SW M L. a v e r a g e s ...80

5.4 T h e effects of surface brig h tn ess on c,„ax ...82

5.5 T h e effects of surface b rightness on th e lu m in o sity functions . 84 5.6 B iv ariate brightness d i s t r i b u t i o n ... 87

5.7 T h e effects of ob serv atio n al e r r o r s ... 90

5.8 R em oving th e E d d in g to n b i a s ...92

5.9 L u m inosity functions for th e H ubble Deep F i e ld s ...94

5.10 T h e effects o f cosm ologj' on lu m in o sity f u n c t i o n s ... 96

5.11 T h e irrelevance of th e effects of c o s m o l o g j- ...97

5.12 T h e lum inosity d e n sity functio n s ... 98

5.13 T h e lum inosity d e n sity a t 1625A ... 100

5.14 T h e lum inosity d en sity a t 2000A 101 5.15 T h e lum inosity d en sity a t 2500A ...102

5.16 T h e lum inosity d en sity a t 2 8 0 0 .\ 103 5.17 E [ B - V ) AS a function of t y p e ... 108

5.18 E volution of the S F R o f th e U n i v e r s e ... I l l 5.19 T h e effects o f cosmolog\- on th e S F R D ... 114

5.20 S ta r form ation fis a fu n ctio n of t i m e ... 117

6.1 for s u b -s a m p le s ... 124

6.2 T h e B hand lum inosity f u n c t i o n s ...126

6.3 T h e B b an d lum inosity d en sity f u n c t i o n s ...127

6.4 T h e evolution o f B b a n d nu m b er d e n s i t y ... 129

6.5 T h e evolution o f B b an d lu m inosity density ...130

6.6 T h e processes of galaxy e v o l u t i o n ...132

6.7 m in im ization of e v o lu tio n a ry p a ra m ete rs ...141

6.8 A m odel for th e evolution o f B b an d num ber d e n s i t y ... 142

6.9 R elative im p o rta n c e of different ev o lutionary e f f e c t s ...144

6.10 M erger f r e q u e n c y ... 146

7.1 L um p finding a n d grouping ...151

7.2 G alaxy nu m b er co u n ts sp lit by L ...153

7.3 A section of th e rest B im age of th e H D F X ... 157

7.4 T h e lum piness of galaxies vs. redshift for / < 2 5 ...158

7.5 T h e lum piness of galaxies vs. a p p a re n t I m a g n i t u d e ...160

7.6 T h e lum piness of galaxies vs. ab so lu te B m a g n i t u d e ...161

M any th a n k s are d u e to my fellow g ra d u a te s tu d e n ts , ptust a n d present, for m any useful conversations, occasionally on th e s u b je c t of astronom y. K a th le e n . Mike. .lam es. E ric. Dave. .James (th e o th e r one). Luc an d D avid, it's been fun. T h e sam e goes for Senor H udson a n d M ad am e Lewis.

It w ould be im possible to u n d e re stim ate th e im p o rta n c e of coffee or te q u ila in th e p re p a ra tio n of this thesis. I would also like to th a n k my muses. M essrs. B u ffett. W aits. .Jagger. P alm er. K iiopfier a n d Ms. .A.nderson for m ak in g my office a b e a ra b le place to work.

T h a n k s are d u e to .\o rm a Dowler who pro o f-read th is thesis (easier to rea d th a n "Ulysses" ) for th e m odest fee of a few pecan pies.

I w ould like to th a n k His M ajesty. King R o b e rt th e B ald, fo u rth K ing of th e Island o f R edonda. for nam ing m e his .\s tro n o m e r Royal.

T h is research has m ade use of d a ta o b ta in e d from th e C a n a d a France H aw aii Telescope (C F H T ). which is o p e ra te d by th e N a tio n a l R esearch C oun­ cil o f C a n a d a , th e C e n tre N atio n al de la R echerche S cientifique o f F rance and th e U n iversity of Hawaii.

Finally. I would especially like to th a n k m y su p e rv iso r. Dr. H artw ick. W ith o u t his financial s u p p o rt an d th e in n u m erab le discussions in w hich he su p p lie d gu id an ce, advice a n d an unfailing pen. th is th esis w ould have been im possible. His p atien ce d u rin g th e p a st 11(!) years has been ad m irab le.

Introduction

In th e beginning, acco rd in g to th e s ta n d a rd m odel of g alax y fo rm ation th ro u g h hierarchical clu sterin g , th e U niverse is filled w ith an alm o st perfectly sm o o th d is trib u tio n o f d a rk m a tte r a n d a c o m p a rativ ely sm all am o u n t of baryonic gets. U nder th e influence o f gravity, th is d a rk m a tte r collapses in to filam ents w hich in tu rn collapse o n to large clum ps o f d a rk m a tte r halos. T h e gas cools o n to these halos, form ing disks. In th e disks, th e gas is tra n sfo rm ed in to s ta rs . As long as th ere is a su p p ly of gas. s ta r fo rm a tio n continues a n d th e g alax y will co n tain young, blue sta rs. W hen th e gas is d ep leted, blown o u t by supernovae, or s trip p e d by in te rac tio n s w ith o th e r galaxies, no m ore s ta rs can form : th e ste lla r p o p u la tio n ages. H ot blue s ta r s have relativ ely sh o rt life spans: w hen th ey die. th e y leave beh in d a p o p u la tio n of longer-lived cool red sta rs. T h e cool s ta rs are fain ter th a n th e hot sta rs: the galaxies fade as th ey age. T h e d a rk m a tte r halos, a n d th e g alaxies inside th em , can u n ­ dergo m ergers. If th e m erger is betw een two galaxies o f different m asses, th e sm a lle r galax y will be a b so rb e d by th e larg e r galaxy, which will undergo a b u rst of s ta r fo rm a tio n as its gas is p e rtu rb e d . If th e m erger is betw een two

galaxies of roughly equal m ass, b o th will be d isru p te d a n d will reform into a n e llip tica l galaxy. T h is ellip tical galaxy can th en a c c re te o th er, sm aller galaxies, becom ing a bulge in th e centre o f disk galaxy.

T h e H ubble D eep F ields a re the d eepest o p tic a l im ages of th e sky yet o b ta in e d . O bserved w ith H ubble Space Telescope w ith w eek-long exposures, th e y pro b e th e U niverse to th e point w here th e U niverse was only a te n th its present age. B ecause th e observations were m ade from space, b eyond the d is to rtin g effects of th e a tm o sp h e re , th e q u a lity of th e im ages of th e galaxies is e x tra o rd in a ry . T h u s, th e H ubble Deep F ields are th e ideal places in which to s tu d y th e ev o lu tio n of galaxies.

T h e H ubble Deep Fields (H D F 's) a re so deep in fact th a t m o st of the galaxies are to o faint to be observed sp ectroscopically w ith c u rre n t telescopes. O nly th e b rig h te st 10% of th e galaxies have spectro sco p ic redshifts. To learn m ore a b o u t th e rem a in in g 90% . one m ust use p h o to m e tric redshifts. Indeed, th e H D F 's a n d p h o to m e tric redshifts seem m ade for each o th er. W h ile the H ubble Deep F ields co n ta in galaxies at red sh ifts of : = 5. m ost of these galaxies c a n n o t be observed spectroscopically. Hence, p h o to m e tric redshifts a re needed to s tu d y th e H ubble Deep Fields. O n th e o th e r hand, for p h o to ­ m e tric red sh ifts to be feasible, one needs an im aging su rv ey in a t least four pass ban d s. F u rth e r, for p h o to m e tric red shifts to be useful, th is su rv ey m ust ne largely u n s tu d ie d spectroscopically. T h e H D F 's m eet b o th these c rite ria . T h is thesis is a s tu d y of g ala x y evolution in th e H ubble D eep F ields using p h o to m e tric redshifts.

R a th e r th a n o b serv in g narrow s p e c tra l features o f g a la x y s p e c tra , such as lines, th e p h o to m e tric red sh ift technique c o n c e n tra te s on b ro ad features.

such as th e 4000À break and th e overall sh a p e o f a s p e c tru m . In th is m eth o d , th e p h o to m e try of observed galaxies is co n verted into low resolution sp e c tra l energ)' d istrib u tio n s (S E D 's). R edshifts are d e te rm in e d by co m p arin g these S E D 's to red shifted te m p la te galax y sp e c tra .

T h e chief ad v antage of using th e p h o to m e tric redshift technique is speed. In spectroscopy, th e light from th e gahrxy is s e p a ra te d into narrow w avelength bins a few a n g stro m s across. Each bin th e n receives only a sm all fractio n of th e to ta l light from the galaxy. Hence, to achieve a sufficiently high signal-to- noise ra tio in each bin. long in te g ra tio n tim es a re required. For ph o to m etry , however th e bins are m uch larger, typically I0 0 0 .\ wide. It recpiires only a sh o rt exp o su re tim e to reach th e sam e sig n al-to-noise ratio . For very faint o b jec ts, th e exposure tim es required for sp ectro sco p ic o b servation rap id ly becom e p ro h ib itiv e. It is possible to m eiisure p h o to m e tric redshifts in the H ubble D eep Field down to 1s t = 28.^ It w ould tak e years to o b ta in spec­ troscopic redshifts for th e sam e galaxies using Keck, cu rre n tly th e largest telescope in th e world.

T h e m ain d isadvantage of using p h o to m e tric red sh ifts is th a t th e y are less precise. T h e u n certain ties of sp ectro sco p ically m easu red red sh ifts are on th e o rd e r of A c=±O.O OI. w hile p h o to m e tric redshift u n c e rtain tie s are ty p ic a lly A c = ± 0 .1 . For s tu d y in g in d iv id u al galaxies, th is level of u n c e rta in ty is g enerally too large. For d e te rm in in g p ro p ertie s of large n um bers of galaxies in a s ta tis tic a l m anner, however, th is u n c e rta in ty is q u ite accep tab le.

Tor simplicity, L's t-Bs tMs t and 1s t will be used to denote magnitudes in the F.300W. F450W. F606W and F814W bands respectively. The ST zero-point system is used unless otherwise specified.

To m easure p h o to m e tric red sh ifts for galaxies, one m ust first o b ta in pho­ to m e try for th o se galaxies. In p a rtic u la r, a c c u ra te colours m ust be d e te r­ m ined. C h a p te r 2 describes th e d e te c tio n an d p h o to m e try o f galaxies in the H D F im ages. .A. sam p le o f 1694 galaxies, co m p lete dow n to I g r = '-8 is g en erated .

C h a p te r 3 gives a h isto ry of the various p h o to m e tric red sh ift techniques used in th e p a st a n d describes in d e ta il th e p h o to m e tric red sh ift technique used in th is thesis. .Applying th is technique to th e p h o to m e tric sam ple, we o b ta in a c a ta lo g of galaxies w ith positions, colours an d red shifts. T his sam p le is th e n used to stu d y th e evolution from r = 5 to c = 0 of four p ro p e rtie s of galaxies: clu ste rin g , s ta r fo rm atio n rates, m erging a n d m orphologies.

T he c lu ste rin g of galaxies d epends on how th e d a rk m a tte r halos are clu stered, w hich in tu rn s dep en d s on th e d e ta ils of how th e halos form and evolve. C h a p te r 4 discusses th e clu sterin g of galaxies as m easu red by th e two- p o in t p ro je c te d s p a tia l c o rre la tio n function. Different h ierarchical m odels m ake different p red ictio n s a b o u t th e evolution of th e clu ste rin g of galaxies as a fu nction o f red sh ift. .Although th e solid angle su b te n d e d by the H ubble D eep Fields is so m ew h at to o sm all to give very s trin g e n t c o n s tra in ts on these m odels, th e difference in nu m b er counts an d c lu ste rin g from N o rth to S o u th allows one to say so m e th in g m ore definite a b o u t th e v a ria tio n s in sp a tia l den sities of galaxies.

In th e last few years, th ere has been g reat in te rest in th e evolution o f th e global s ta r fo rm a tio n rate . S ta r fo rm atio n ra te d e n sity (S F R D ) m easures th e m ass of s ta rs c re a te d p e r tim e interval p e r u n it volum e o f space, in u n its of M ^ y r" ^ M p c “ '^. In general, th e s ta r fo rm atio n is considered to have been m ore

ra p id in th e p a st. T h e exact d e ta ils of its ev o lu tio n w ith red sh ift. however, a re th e su b je c t of d e b a te , .\lth o u g h m ost a stro n o m e rs believe th a t, a t low red sh ift, th e s ta r fo rm atio n ra te den sity is ste a d ily increasing w ith redshift from c = 0 to c = 1. th e re is som e discussion as to th e e x act ra te (Lilly et

a i . 1996: Cow ie et a i . 1999. are rep re sen ta tiv e of th e two o p in ions). . \ t high

red sh ift. som e (M ad au et al.. 1996. for exam ple) hold th a t th e S F R D peaks a t a ro u n d : ~ 1.5 an d declines a t higher redshift. w hile o th e rs (S teidel et al..

1999) m a in ta in it rem ains relatively c o n sta n t. c o m p lic a tin g facto r is th e presence of du st in galaxies, which can cause th e S F R D to be u n d e re s tim a te d by a fa c to r o f five. N um erous surveys a t different redshifts. using different tech niques have been used to m easure th e S F R D o f th e U niverse. Som e of these surveys acco u n t for d u s t a n d som e of which do not. C h a p te r 5 presents m ea su rem e n ts of th e s ta r fo rm a tio n ra te d e n sity over th e e n tire red sh ift range from c = 0 to c = 4.5 using a single technique a n d ac co u n tin g for d u st.

C h a p te r 6 in v estigates th e m erger h isto ry of galaxies. It is clear th a t som e, if n ot m ost galaxies have undergone m ergers in th e p a st. T h e qu estio n is: how m an y m ergers? O ne a p p ro ach to answ er th is q u e stio n is to look a t galax ies a n d d e te rm in e w h at fraction are c u rre n tly underg o in g m ergers. O ne can look for galaxies th a t are clearly u n d erg o in g m ergers (d isru p te d m orphologies, tid a l tails) or look for galaxies th a t are close to each o th e r in space, a n d will likely m erge in the n e a r fu tu re . P a tto n (1999) looked a t close p a irs in th e C X O C l ■ (Yee et al.. 1996) an d C X 0 C 2 (Vee et a i . 2000) surveys a n d d e te rm in e d th e m erger ra te as a function of redshift o u t to r = 0.5. A n o th e r ap p ro a c h is look a t th e n u m b er of galaxies a t som e

Cosniolog}-p oint in th e Cosniolog}-p a st a n d c o m Cosniolog}-p are it to th e n u m b er of galaxies a t th e Cosniolog}-p resent. S im plistically. if th ere is a large nu m b er o f m ergers, th ere will be significant d ro p in th e n u m b er of galaxies. A lthough th e re are a nu m b er of co m p lic a tin g factors, this a p p ro a c h can be used to d e te rm in e th e overall m erger ra te .

W hen one looks a t th e galaxies in th e H ubble Deep Fields, one sees a n u m b er of w ell-form ed sp ira l an d reg u la r ellip tical galaxies. However, one's eye is caught by th e large n um ber of galaxies w ith very d is tu rb e d m orpholo­ gies. th e so-called " tra in wrecks” and o th e r p ecu liar o b jects. W h en observed spectroscopically, these galaxies are often found to be a t high red sh ift. T h e re ­ fore. th e naive conclusion is th a t higher redshift galaxies have increasingly irreg u lar m orphologies. T h e m orphology of galaxies in th e H ubble Deep Field N o rth was stu d ie d by .\b ra h a m et al. (1996) using q u a n tita tiv e m ea­ sures of m orpholog}' as well cis visual classifications. .A braham 's m easure of asym m etry. .4. is d e te rm in e d by ro ta tin g th e im age of a galaxy by 180’ a n d s u b tra c tin g th e ro ta te d im age from th e o rig in al. .4 is defined as h a lf th e ra­ tio o f th e a b so lu te value o f th e to ta l flux in th e se lf-su b tra c te d im age to th e to ta l flux in th e original im age. His m easure of c e n tra l c o n c en tra tio n . C is th e inverse ra tio of th e flux w ithin an o u te r ellip tical a p e rtu re (w hose rad iu s is d e te rm in e d from th e intensity-w eighted seco n d -o rd er im age m o m en ts) a n d th e flux w ith in an in n er elliptical a p e rtu re (w hose rad iu s is 0.3 th a t of th e o u te r). W hile these p a ra m e te rs can be m easu red dow n to 1s t = ‘-4 in th e H ubble D eep F ield, fa in te r galaxies c a n n o t be so classified. Low ering th e signal-to-noise ra tio of th e im ages of galaxies drives th e asym m etr}' to .4 = 0 a n d causes th e c e n tral c o n c en tra tio n m ea su rem e n ts to be in d istin g u ish a b le from th e seeing disk. C h a p te r 7 in tro d u c es a n o th e r q u a n tita tiv e m easure

o f morphology-. L. w hich m easures th e "lum piness" o f g alax y im ages, which ca n be m easu red to fain ter m agnitudes. T h e evo lu tio n o f I w ith redshift is tra c e d .

The Hubble Deep Fields

T h is c h a p te r describes th e m eth o d s used for d e te c tio n a n d p h o to m e try of galaxies in th e H ubble Deep Fields, an d th e d efinition of th e galaxy sam p le th a t will be used for th e rem a in d e r of th is thesis.

2.1

Description of the Hubble Deep Fields

T h e H ubble Deep Fields form th e o b se rv a tio n a l basis for th is thesis. T h e H ubble D eep Field N o rth (H D F X ) was observed in D ecem ber 1995 using th e W ide Field P la n e ta ry C a m e ra (W F P C ) on th e H ubble Space T elescope. It is c e n tred a t R ight .-Vscension 12*'3G"'49!4. D eclination +G2°12'58"00 in J2000.0 c o o rd in a te s. T h e field was chosen to be a typical "blank" bit of sky. T h e H ubble Deep F ield S o u th (H D F S) was observed in S e p te m b e r/O c to b e r 1998. In ste a d of an a rb itra ry p o in tin g , th e a re a of th e sky in th e vicin ity o f th e q u a s a r .12233-GOG was observed. Several H ST in stru m e n ts were used. T h e S pace Telescope Im aging S p e c tro g ra p h (ST IS) was po in ted d ire c tly a t th e q u a s a r w hile th e W F P C a n d th e N ear In fra re d C a m e ra an d M u lti-O b je c t

S p e c tro g ra p h (N IC M O S) were observed in p arallel on nearb y areas of th e sky. T h e H D FS W F P C field is centred a t 22''32'"56f22. -62°33'02'.'69 (.12000.0).

B o th fields were im aged in four H ST filters: F300W . F4.50W. F606W a n d F 814W . T h e F300W lies a b o u t .300.A. to th e blue of th e .Johnson U b a n d . T h e o th e r th ree filters are roughly equivalent to th e B R I bandpasses respectively. For sim plicity, th e F300W . F4.50W. F60GW a n d F814W filters will be referred to as th e U B R I filters in this thesis. T h e responses of these filters are show n in F igure 2.1. T h e four im ages of each field are registered to very high accuracy: ~ 0.1 pixels.

T h e H ubble Deep Fields have been im aged a t m any o th e r w avelengths from X -ray to radio. Indeed, th e H D FX in p a rtic u la r is pro b ab ly th e m ost carefully s tu d ie d p a rt of th e sky. It has been im aged in X -rays, th e L '\’- o p tic a l. in fra re d , su b -m m . a n d radio bands. O f p o te n tia l in terest for pho­ to m e tric red sh ift purposes are th e n e a r in frared im ages. U n fo rtu n ately , the two sp ace-b ased XTCMOS im ages are not publicly available except its HST archival im ages, which require a degree of fu rth e r processing before th ey can be used. .A.Iso. th e im ages e ith e r do not cover th e e n tire field (T hom pson

et a i . 1999) or are too shallow (D ickinson. 2000). T h e sam e can be said

of th e g ro u n d -b a se d im ages (Hogg et a i . 1997: D ickinson et al.. 1998: Hogg

et a i . 1999). F u rth er, in order to c o m p u te c o n sisten t p h o to m e try for b o th

lower reso lu tio n in frared im ages an d th e hig h er resolution o p tical im ages, it w ould be necessary to deg rad e th e seeing of th e late r. T h e H ubble D eep Field S o u th h as also been im aged in o th e r bands (d a C o sta et al.. 1998). However th e only im ag in g d a ta com m on to b o th th e H D FX a n d H D FS of identical ban d p a sse s a n d d e p th is th e U B R I im aging. T herefore, th e present analysis

F300W

F450W

F606W

F814W

c 0.8

u £

g 0.6

L (0 (U M

C 0.4

CL M 0) CH

0.2

0.0

2000

4000

6000

8000

10000

X(Angstrom s)

will be confined to ju s t th e U B R I d a ta from HST.

N ot having in frared d a ta , w hile slig h tly vexing, is no g re a t loss. In frared d a ta is b o th a help an d a h in d ra n c e w hen m easu rin g p h o to m e tric redshifts. O n th e plus side, it does e x te n d th e w avelength coverage of BED. O n th e m inus side, sp e c tra l te m p la te s for th e rest fram e in frared are ra re a n d not reliable. In a blind te st of p h o to m e tric redshifts organized by Hogg et al. ( 1998). th e inclusion of in frared d a ta Wcis not found to im prove th e accu racy o f th e p h o to m e tric red sh ifts significantly.

T h e H D F X a n d th e H D FS are b o th freely available electro n ically a t h t t p : / / www. s t s c i . e d u / f t p / s c i e n c e / h d f / a r c h i v e / m o s a i c s . h tm l a n d h t t p : / / www. s t s c i . e d u / f t p / s c i e n c e / h d f s o u t h / r e d u c _ w f p c 2 . h tm l respec­ tively. T h e im ages are available as m osaics of th e th re e W ide Field im ages plus th e sm a lle r P la n e ta ry C a m e ra im age. T h e num erous im ages th a t m ake th e final m osaic were com bined w ith th e "drizzle" a lg o rith m (F ru c h te r & H ook. 1998); th e final pixels are 0.03985 arcseconds on a side. T h e m osaics m easu re 4096 x 4096 pixels for th e H D F X a n d 4096 x 4600 pixels for th e H D F S . T h e im ages as d is trib u te d are s k y -su b tra c te d . T h e y are scaled in in te n sity to 1 electro n p er second: th a t is to say. th ey are scaled as if the to ta l exp o su re had been one second. To re tu rn them to th e o riginal scale, th e im ages were m u ltip lie d by th e e x p o su re tim es given in T able 2.1 w hich also lists th e S T m a g n itu d e zeropoint for each image.

T able 2.1: List o f o b s e n ’a tio n s Field F ilte r E x p osure T im e S T m a g n itu d e zeropoint H D FX F300W 153700 19.47 H D FX F450W 120600 21.52 H D FX F606W 109050 23.21 H D FX F814W 123600 22.90 HD FS F30ÜW 140185 19.45 HD FS F450W 100950 21.53 H D FS F606W 81275 23.21 HD FS F814W 100300 22.91

2.2

Detection

T h e S E .\tra c to r package (B e rtin & .■X.riiouts. 1996) was used to d e te c t the galaxies in th e im ages an d to set up se g m e n ta tio n m aps. T his package c a n n o t be praised loudly enough. It is easy to d o w nload a n d in sta ll on any L’NTX (or sim ilar) sy stem . It takes up little disk space. It is easy to use: p a ra m e te rs can be fed to it via default files, com m and-specific files or on th e co m m an d line. It is q u ite fast. It is very well d o c u m e n ted . Its m ain defect is its nam e, w hich is sh o rt for Source E x tra c to r : searching for d o c u m e n ta tio n for th e package usually leads to web sites w hose co n te n ts have little to do w ith astronom y.

W h en searching for galaxies. S E x tra c to r first convolves th e im age in q u e stio n w ith a sm all filter th a t can be specified by th e user. For th is work

th e d efau lt filter:

I 2 _I

2 ₄ 2

1 2 I

was used. C onvolving like th is im proves th e signal-to-noi.se ra tio for de­ tectio n . S E x tra c to r th e n scans th e convolved im age, looking for a c e rtain n u m b er of c o n tig u o u s pixels above a c e rta in th resh o ld . In th is case, th e d e­ tec tio n th re sh o ld was set to 3 tim es th e s ta n d a rd d e v ia tio n of th e background a n d th e n u m b er of pixels was 5. T h is 3-sigm a d ete c tio n lim it works o u t to a surface b rig h tn e ss th resh o ld of 26.40 m ag n itu d e s p e r sq u a re arcsecond in

1s t- S E x tra c to r th e n assigns all pixels contiguous to th e o b jec t.

T h e next ste p is to deblend th e galaxies. T h is is w here S E x tra c to r really shines. For each o b je c t it d ete c ts, it sp lits th e brightness profile into a nu m b er of levels, from th e p e a k flux dow n to th e d ete c tio n th resh o ld . S E x tra c to r th en searches dow nw ards th ro u g h th e th resh o ld s looking for se co n d ary peaks in th e 2-dim ensional brig h tn ess d istrib u tio n . If it finds any. it htis to m ake a decision w h e th e r to sp lit th e o b jec t in two or m ore su b -o b jects. T h e decision to split or not is m ad e using th e following criteria: (A ) Is th e ra tio o f to ta l brig h tn ess in th e pro sp ectiv e su b -o b je c t to th e to ta l brig h tn ess o f th e original o b ject g re a te r th a n a c e rta in c o n tra s t p a ra m e te r? (B) Is c o n d itio n (A) tru e for a t least one m ore su b -o b je c t (p o ten tially , th e rest of th e o b je c t)? If b o th (A) a n d (B) are tru e , th en th e o b je c t is sp lit. C ontiguous pixels below the c u rre n t th re sh o ld a re reassigned to th e a p p ro p ria te su b -o b je c t.

T h e relevant p a ra m e te rs for th is m u lti-th re sh o ld in g are th e n u m b er of levels (in th is case. 32) the way in which th e different levels are spaced (in th is case, e x p o n e n tially ) an d th e c o n tra st p a ra m e te r (in th is case. 0.005).

B e rtin &: A rn o u ts, (1996) recom m end these values as b eing the m ost useful in general. In fact, th e exact values are not c ritic a l. C han g in g th e num ber of su b -th resh o ld s by a factor of 2 e ith e r way does not m ake a noticeable difference in th e se g m e n tatio n im age: n e ith e r does changing th e c o n tra st p a ra m e te r by 30%.

T h is a u to m a tic s p littin g works rem ark ab ly well. O nly in the largest, b rig h te st a n d lum piest (Sc types a n d later) galaxies does it fail. Even in these relativ ely difficult objects, it only fails occasionally. T hese relatively few cases are q u ite obvious a n d are easily co rrected by h an d . To be on the safe side, all th e galaxies in the sam p le were carefully scru tin ized individually by eye to see if any had been sp lit w hen th ey should have been m erged or m erged w hen th ey should have been split.

S E x tra c to r produces a c a ta lo g w ith x a n d tj p o sitio n s and photom etry. It also pro d u ces a se g m e n tatio n im age. T h is F IT S im age is th e sam e size as th e o riginal im age. It has zeros everyw here t h a t th e original im age had b lan k sky. W ith in th e bounds of each o b je c t (its "segm ent"), th e pixels have a value equal to th e ID nu m b er c o rresp o n d in g to th e relevant o b jec t in th e cata lo g . For an uncrow ded o b je c t, this will be all th e pixels above the iso p h o ta l th re sh o ld . For a crow ded o b jec t, th e segm ent will be all th e pixels above th e iso p h o ta l th re sh o ld th a t were not assigned to a n o th e r o b ject d u rin g th e d e b le n d in g p rocedure. T h e se g m e n tatio n im age m akes it possible to see w hich pixels were assigned to w hich ob ject. T h is is a very in te restin g and useful d iag n o stic in its own right, b u t has o th e r uses for fu rth e r p h o to m e try as will be discussed in th e next section. For a n exam ple o f a se g m en tatio n im age, see F ig u re 2.2.

-/ b an d _ . •

*

f * % • B band • .I f f # % T'

# #

• ■

mm

. • # . # » * w % > ^ * •

F ig u re 2.2: S e g m en ta tio n im ages in different bands. T h e u p p e r p anels show a su b sectio n of th e H D F N in b o th th e / a n d B b a n d s (left a n d right re­ spectiv ely ). T h e lower p anels show th e se g m e n ta tio n im age p ro d u ce d by S E x tra c to r for th e sam e su b sectio n . D ifferent shades of grey are used to d istin g u ish different o b je c ts. N’o te th e s u b s ta n tia l differences in th e segm en­ ta tio n im age from b a n d to b an d .

B ecause of th e dithering^ d u rin g the o b se rv a tio n s, som e sections of th e H D F im ages have s u b s ta n tia lly lower e x p o su re tim es th a n th e bulk of the im age. T hese sections are located a ro u n d th e edges of th e im ages. Because o f th e increase in noise, th ere are m any sp u rio u s d e te c tio n s in these aretis. T h e re is also th e occitsional leg itim ate d e te c tio n , u su ally a relativ ely bright o b je c t. R a th e r th a n try to so rt th e sp u rio u s from th e le g itim a te o b jec ts, the edges of th e im ages were m asked off. .\11 o b je c ts whose c en tres lay w ithin th e nuisked off areiis were rejected.

2.3

Photom etry

T h e re a re several m eth o d s for doing g alax y p h o to m e try . T h e m e th o d s re­ sem ble each o th e r in as m uch as they all have som e a lg o rith m or rule to decide w hich pixels of a galaxy im age a re a sso c ia te d w ith th e galaxy, and th e n su m th e light from these pixels to p ro d u ce a m a g n itu d e . T h e pixels are all given equal w eight, unlike m any techniques used in s te lla r ph o to m etry . T h e m e th o d s differ m ainly by th e way in w hich th e pixels a sso c ia te d w ith th e o b je c t a re chosen:

• F ixed a p e rtu re p h o to m e try : T h is is by far th e sim p lest m eth o d . .\11 th e pixels w ith in a c e rta in circu lar rad iu s a re used. O f course, not all galaxies a re th e sam e size, so fixed a p e rtu re p h o to m e try will m easure a different fractio n of th e to ta l light from each galaxy. If th e a p e rtu re ra d iu s is to o sm all w ith respect to th e size o f th e galaxy, som e unknow n

‘Dithering: small shifts in the pointing of the telescope to ensure that objects do not always fall on the same pixels of the detector.

light from th e galaxy will be lost, m aking it im possible mocisure to ta l m ag n itu d es. If th e a p e rtu re is to o large, a fair a m o u n t of sky will be included, d eg rad in g th e signal-to-noise ra tio o f th e ph o to m etry .

• A u to m a tic a p e rtu re (K ron) p h o to m e try : O ne can m atch th e size of th e a p e rtu re to th e size of th e galaxy. T h e size o f th e galaxy, ry. is m easured using th e K ron a lg o rith m (K ron. 1980):

r, = 1 9 /

C2.1,

O ne can th en use a c irc u la r a p e rtu re of radius Arri. w ith k som e con­ s ta n t. generally 2 or an elliptical a p e rtu re w ith prin cip al axes (kr^ an d

k r i / e (where e is th e ellip ticity of th e gahuxy) to do th e ph o to m etry .

O ne can m easure a c c u ra te to ta l m ag n itu d e s w ith th is m ethod.

• Isophotal p h o to m e try : In th is m eth o d , th e a p e rtu re is not circu lar, nor an y regular g eo m etric sh ape. It is th e set of all pixels asso ciated w ith a galaxy whose brightness is g re a te r th a n som e th resh o ld . T h e light from each a n d every pixel likely to c o n trib u te s u b s ta n tia lly to th e to ta l is included. Conversely, no (or a t Iccist verv" few) pixels c o n ta in in g only sky are included.

• C o rrected iso p h o tal photometn,*: S tra ig h t iso p h o tal p h o to m e try m isses a fraction of th e light from each galaxy. It d ep en d s on th e surface brig h tn ess of th e galaxy; th e fra c tio n o f light m issed is larger for fain ter galaxies. However a co rrectio n facto r, q. can be c o m p u ted (to second

order) follow ing M addox et al. (1990);

A/ - 1 - 0.1961 - 0.7512 (2.2)

w here .4 is th e a re a w ith in th e isophote. t is th e Isophotal th re sh o ld . a n d /,so is th e flux w ith in th e isophote.

S E x tra c to r can c o m p u te p h o to m e try via all these m eth o d s. It also can c o m p u te a "best" m a g n itu d e (know n, a p tly enough, its MAG_BEST in S E x ­ tra c to r term inology’) w hich is e ith e r a co rrected iso p h o tal m ag n itu d e (in th e case w here a g alax y m ay be su b je c te d to crow ding) or a K ron m a g n itu d e (w hen crow ding is n o t a problem ). T his "best" m a g n itu d e is a ro b u st to ta l m ag n itu d e.

T h e q u estio n is: w hich m eth o d of doing galaxy p h o to m e try is b est for th e problem a t h a n d ? W hen m easuring p h o to m e tric red sh ifts. g e ttin g reli­ able colours is key: sy ste m a tic erro rs in th e colours sh o u ld be m inim ized. T h e exact sam e p o rtio n o f th e sky should be m easured in all bands. For this purpose, sm all fixed a p e rtu re s are ideal. O n th e o th e r h a n d , th e p h o to m e ­ try is also used for g e n e ra tin g lum inosity functions a n d A:-corrections. For th is, a c c u ra te to ta l m ag n itu d e s are necessary. T h is is p a rtic u la rly tru e for th e / b a n d , since it is in th a t b and the final g alax y sam p le will be defined. Sm all fixed a p e rtu re m ag n itu d e s do not give goo d to ta l m ag n itu d e s. Isopho­ ta l m a g n itu d e s a re s u b je c t to (1 4- r ) ' surface brig h tn ess d im m in g effects which m akes m ea su rin g lum inosity functions by th e l/Vmax m eth o d cjuite com p licated .

O ne can. in p rinciple, m easure to ta l m ag n itu d e s by th e co rrected isopho­ ta l m e th o d o r th e K ron m e th o d in all ban d s. However, th e isophotes an d

K ron rad ii in som e ban d s m ay be con sid erab ly different th a n in o th ers. T h is can be clearly seen when c o m p a rin g th e im age a n d se g m e n tatio n m ap o f th e

B b an d im age to th eir c o u n te rp a rts in I as show n in F igure 2.2. B ecause

of these differences, th e colours m ay not be m eiisured on e x a ctly th e sam e p a rts o f th e sky. w hich could lead to in a c c u ra te colours.

T h e best com prom ise is to:

• d e te rm in e th e iso p h o te in th e I ban d .

• do p h o to m e try in all b a n d s th ro u g h th e / isophote

• d e te rm in e to ta l m ag n itu d e s in th e I b a n d by th e co rrected iso p h o tal m e th o d or th e K ron m e th o d (S E x tra c to r's MAG_BEST)

• correct the photom etry in all bands by the difference for the / band between MAG_BEST and the isophotal photometry.

T h is p ro ced u re h a s m any ad v an tag es. T h e colours are m easured consistently, th ro u g h identical — if irreg u larly sh a p ed — a p e rtu re s: hence th ey are ap ­ p ro p ria te for p h o to m e tric redshifts. T h e m a g n itu d e s are to ta l m ag n itu d e s, a p p ro p ria te for sam p le selection a n d th e m easu rem en t of lu m in o sity func­ tions. T h e co rrectio n from iso p h o tal to to ta l m a g n itu d e s is sm all, ty pically less th a n 0.1 m ag. T h e only d isa d v a n tag e is th a t th e I isophotes are usually larger th a n isophotes in o th e r bands. T h is m eans th a t m ore sky pixels are included in th e o th e r b an d s, in creasing th e noise. However, th e increase in ran d o m erro rs is m ore th a n offset by th e decrease in sy ste m atic errors.

S E x tra c to r. a lth o u g h a d m ira b le in m any respects, has one sh o rtc o m ­ ing: it c a n n o t process m any im ages sim ultaneously. T his m akes m u lti-co lo u r

p h o to m e try following th e m e th o d d escribed above a b it p ro b le m atic . To th is end. a new program '- was w ritte n . It perform s p h o to m e try on all four im ­ ages sim ultaneously, th ro u g h identical a p e rtu re s. It takes as in p u t d a ta th e o b je c t c a ta lo g a n d th e se g m e n ta tio n im age p roduced by S E x tra c to r. as well iis all four U B R I d a ta im ages. For each o b ject in th e c atalo g , th e p ro g ra m first d e te rm in e s which segm ent to use based on th e x a n d y c o o rd in a te s from th e cata lo g . N ext, th e p ro g ra m sum s all th e flux in th a t segm ent in each o f th e four bands. (Since th e se g m e n tatio n im age reflects b o th th e isophotes an d th e d e b len d in g d e scrib ed in the previous section th is is effectively "de­ blended isophotal" p h o to m e try .) T h is to ta l flux in each b a n d is co n verted into a m a g n itu d e in th e usual way: m a g n itu d e = - 2 . 5 lo g (F lu x ). T h e m ag ­ n itu d e is co rrected for th e zero-point a n d the exp o su re tim e. T h e m a g n itu d e in each b an d is fu rth e r c o rrected by th e difference betw een th e iso p h o tal m a g n itu d e an d th e to ta l (MAG_BEST) m a g n itu d e in th e I b a n d . Since th e im ages are sk y -s u b tra c te d as p a rt of th e H ST pipeline, no co rre c tio n for sky background is m ade. T h is m e th o d is m ade easier by th e fact th e H D F im ages in each b an d are reg istered to very high accuracy.

T h e u n c e rta in ty in th e to ta l flux. CTf. is c a lc u la te d as follows:

ctf

=

\/F +

(

2

.

3

)

w here F is th e to ta l flux in th e a p e rtu re , an d Up,x is th e n u m b er of pixels in th e a p e rtu re . T h e variance in th e sky. is c a lc u la te d once p er im age. It is m easured in 20 o r so b lan k sections of th e skv. each of w hich is -50 x .50

•for those interested in such details, the program was written in FORTR.A..\. using the FITSIO libraries

pixels. T h e u n c e rta in ty in th e co rresp o n d in g m a g n itu d e , cr^. is given by:

= 2.5 log (2.4)

T h e m e th o d described above was a p p lie d to th e H ubble Deep Fields. T h e resu lts are show n in Figures 2.3 a n d 2.4. F ig u re 2.3 shows th e num ber co u n ts in all four bands. F igure 2.4 shows th e n u m b er counts in th e I band sp lit by field. N’o te th e difference in th e n u m b er co u n ts betw een th e HD F N o rth a n d th e H D F S outh. T h is difference will be e x am in ed m ore closely in C h a p te r 4.

2.4

The sample

H aving m easu red p h o to m e try for th e galaxies, th e next ste p is to c o n stru c t a w ell-defined sam p le of galaxies. P h o to m e tric red sh ifts will be calc u la te d for th e galaxies in th is sam ple. T herefore all th e galaxies m ust be observed in a t least 3 b ands. T hese p h o to m e tric red sh ifts will be used to g e n erate lu m in o sity fu n ctio n s. V/Vmax s ta tis tic s a n d th e like. Ideally, th e n , th e sam ple m u st be c o m p lete dow n to a m ag n itu d e lim it, w ith little or no c o n stra in ts from surface b rig htness. T h e m ag n itu d e lim it th a t was chosen is 1s t < 28. 7 = 2 8 in th e S T sy stem is equivalent to 7 = 2 7 .2 in th e .\B system a n d 7= 26.8 in t h e \ e g a sy stem .

F ig u re 2.5 shows 7 b a n d nu m b er co u n ts for a v ariety of c rite ria . T he heavy solid line show s th e to ta l counts. T h e light lines show th e 7 counts for th e set o f galaxies d e te c te d in all bands (dashed) in a t least th e B . R a n d 7 b a n d s (d o tte d ) a n d ju s t th e R a n d 7 b a n d s (solid). All galaxies d e te c te d in

ST ST u 100

10

■ST ^

100

- J - U

10

22

24

26

28

30 22

24

26

28

m a g n itu d e

m a g n itu d e

30

F igure 2.3: T o ta l nu m b er counts for th e H D F X a n d H D FS in th e U B R I b ands. T h e solid lines show th e to ta l n u m b er counts. T h e dash ed lines show th e nu m b er co u n ts for o b jec ts w ith / < 28. T h e m a g n itu d e scale is th e S T svstem for all bands.

100

-■ H D FN o H D F S 73

c

3 O Ü

10

-- < > < > < > 1 -Î 1 ? ,

o r

22

24

26

IgT m a g n itu d e

28

F ig u re 2.4: f b a n d n um ber counts for th e H D F N (solid points) a n d the H D FS (open p o in ts). T he erro r b ars reflect Poisson s ta tis tic s in each bin. T h e d a sh ed v e rtica l line shows th e cu to ff for th e sam ple.

I a re also d ete cted in R dow n to = 29: th e light solid line a n d th e heavy solid line are d istin g u ish a b le only in th e two fain test bins. O ne also sees from th e figure th a t all b u t l7c of th e galaxies b rig h te r th a n 1s t < 28 are d e te c te d

in a t least th re e b ands. All (w ith one ex ception) o f the sm all fra c tio n t h a t do n o t have B d e te c tio n s can reliably assigned redshifts of : > 3.5 based on th e lower lim its of th eir B - R colours: t h a t is to say. they are B -d ro p o u ts . A larg er fraction of gahixies are not d e te c te d in U. T h is is p a rtia lly b e cau se th e U im age is not as deep as th e B R I im ages. However, a n o th e r fra c tio n of th e galaxies w ith no U d e te c tio n s a re bona fide high redshift f '-d r o p o u ts . In e ith e r ciise. p h o to m e tric red sh ifts can be m easu red for the e n tire sam ple.

T h e next ste p is to show t h a t th e sa m p le is com plete, th a t is to say. t h a t th e re is no significant p o p u la tio n galaxies dow n to the lim itin g m a g n itu d e th a t are m issed by th e d e te c tio n a lg o rith m . For th is, sim u latio n s were used. .A sub -sectio n co n ta in in g no b o rd er effects or large bright galaxies was c u t o u t of th e / im age of th e H D FX . G alax ies were th en added a t ra n d o m to th is im age. T hese sim u late d galaxies h ad e x p o n e n tial profiles w ith various to ta l m ag n itu d e s Lot an d c e n tral surface b rig htnesses. ^ / . S e ttin g th e p a ra m e te rs e x a c tly as in th e original e x tra c tio n cis d e scrib ed above. S E x tra c to r was ru n on th e im age w ith e x tra galaxies. T h e fra c tio n of a rtificial galaxies recovered gives th e com pleteness as a fu nction c e n tra l surface brig h tn ess a n d to ta l m a g n itu d e . In each tria l. 10 galaxies were a d d e d to the im age. For each c o m b in a tio n o f Lot a n d /Vf. LOO tria ls were m ade. T h e test was done a t 0.1 m a g n itu d e intervals of Rot a n d

T h e resu lts are show n in F igure 2.6. T h e d o ts show the to ta l I m a g n itu d e a n d peak surface b rig h tn ess o f all th e g alaxies d e te c te d in th e H ubble D eep

1000

Total I

I and R

I and BR

I and UBR

M —I

c

3

o

Ü

u 100

o E 3 C

22

24

26

28

30

Ig- (m a g n itu d e s )

F ig u re 2.5: P h o to m e tric com pleteness lim its. T h e lig h t lines show th e / n u m b er c o u n ts in cluding only those galaxies w hich were d e te c te d in o th e r b an d s. T h e d a sh ed line shows th e / counts for galaxies d e te c te d in all bands. T h e d o tte d line shows th e / counts for galaxies d e te c te d in a t least th e B R I bands. T h e light solid line shows th e I c o u n ts for g alaxies d e te c te d in at least th e R I b an d s. T h e h e a \y solid line shows th e to ta l I b a n d n um ber co u n ts, regardless of w h eth er those galaxies were d e te c te d in o th e r bands: it can only be d istin g u ish e d from th e / plus R co u n ts in th e two fain test bins. T h e v ertical line shows th e Ls t = - 8 cutoff of th e sam ple.

Fields. T h e labeled lines in d ic a te th e 90% . 70%. 50%. 30% an d 10% com ­ pleteness lim its of the sam ple. T h e co m p leten ess reOects two things: F irst, th ere is th e chance of recovering a faint g a la x y from th e noise. If a galaxy has e ith e r a low surface brightness or a faint to ta l m ag n itu d e , it will be m issed. In p a rtic u la r, if its peak surface b rig h tn e ss is below th e d e te c tio n th resh o ld of 26.4 m ag a r c s e c '- . it will alw ays be m issed. Second, th ere are th e effects of crow ding. Even b rig h t galaxies can be m issed if th ey are su p erim p o sed on o th e r o b jec ts. T h is occurs roughly 2% of th e tim e. .A.s can be soon from F igure 2.6. th e vast m ajo rity of th e observed o b je c ts w ith 1s t > '-8 lie in an

a re a th a t is a t least 90% com plete. Four o b je c ts lie n ear b u t slightly above th e 90% c o n to u r line. It can be seen from F ig u re 2.6 (an d will be fu rth e r show n in C h a p . 5) th a t surface b rig h tn e ss effects play only a m inor role.

c o m p le t e n e s s

aiir ^

Itot (m a g n itu d e s )

F ig u re 2.6: Surface b rig h tn ess com pleteness lim its. T h e d o ts show th e to ta l

I m a g n itu d e a n d peak surface b rightness of all th e galaxies d e te c te d in th e

H ubble D eep Fields. T h e labeled lines in d ic a te th e various com pleteness lim its o f th e sam ple. T h e vertical line shows th e m a g n itu d e cu t for th e sam ple.

Photometric Redshifts

T h is c h a p te r first exam ines th e p h o to m e tric redshift technique from a h isto r­ ical p e rsp ectiv e, w ith a brief d e scrip tio n o f every m eth o d used so far. For th is thesis, tlie te m p la te fitting m eth o d of p h o to m e tric redshifts was used: th e re ­ fore th is tech n iq u e is described in m uch g re a te r d e ta il. T h e H ubble Deep F ields p resent a challange for p h o to m e tric red shifts. T h e redshift ran g e is very large. ,A.t high redshift. th e te m p la te s m ust be e x ten d ed fu rth e r in to th e U \ th a n o b servations have been m ade locally. F u rth e r, a lth o u g h th e B R I im ages are of com parable d e p th , th e i ' im age is som ew hat shallow er. It is im p o rta n t to d istinguish betw een genuine i ' d r o p o u t/L y m a n b reak galaxies a n d n e a re r galaxies th a t are in trin sica lly faint in th e C band. T h e m odifica­ tio n s to th e basic technique th a t are needed to a p p ly it to th e H ubble D eep Field d a ta are discussed. Finally, th e m e th o d is a p p lied to th e sam ple defined in th e previous ch ap ter, a n d th e p h o to m e tric red sh ift d istrib u tio n dow n to

1

s t = 28 is presented.

3.1

A brief history of photometric redshifts

T h e concept of p h o to m e tric red sh ifts is not new: it was first developed by B aum (1937: 1962). B u t w ith th e advent of th e H ubble Deep Field (W illiam s

et a i . 1996). th ere has been a recent revival in interest in p h o to m e tric red­

shifts. Indeed, th ere have been m ore papers dealin g w ith p h o to m e tric red­ sh ifts since 1996 (G w yn & H a rt wick. 1996: L a n z e tta et al.. 1996: .M obasher

et a i . 1996: Sawicki et al.. 1997: Cowie et a i . 1996: M a d au et al.. 1996:

S u b b a R a o et al.. 1996: Pellô et al.. 1996: S teidel et a i . 1996a: S teidel et a i . 1996b: Belloni & R oser. 1996: B enitez. 1999: B ru n n e r et a i . 1997: C onnolly

et al.. 1997: F urusaw a et a i . 1999: G iallongo et a i . 1998: H udson et al.. 1998:

Hogg et al.. 1998; Liu & G reen. 1998: W ang et al.. 1998. a m o n g o th ers) th a n in th e previous 33 years (B au m . 1962: Koo. 1983: Ellis et al.. 1983: Loh & S pillar. 1986b: Loh & S pillar. 1986a: M acL aren et al.. 1988: Ri.xon et a i . 1991: C onnolly et al.. 1993a). R ecently an en tire conference (W eym ann et

a i . 1999) has been devoted to p h o to m e tric redshifts. so m e th in g t h a t would

have been u n h e a rd of five years ago.

T h is section will o u tlin e a b rie f history of p h o to m e tric red sh ifts. T he list of p a p e rs reviewed here is not exhaustive: however, it does cover all of the techniques so far developed.

3.1.1

Direct shift measurement

B aum was th e first to propose (1937) and th en develop (1962) a technique for m easu rin g red sh ifts p h o to m etrically . He used a p h o to ele ctric p h o to m e ­ te r a n d 9 b an d p asses s p a n n in g th e sp e c tru m from 3730À to 9873A . W ith

th is sy stem he observed th e sp e c tra l energy d is trib u tio n (SED ) of 6 b rig h t e llip tica l galaxies in th e \'ir g o clu ster. He th e n observed 3 e llip tica l galaxies in a n o th e r c lu ste r (C10925+2044. also know n as .\b e ll 0801). By p lo ttin g th e average SE D of th e \'irg o galaxies an d th e average SE D of th e C10925 g alaxies on th e sam e g rap h using a lo g arith m ic w avelength scale, he was ab le to m ea su re th e displacem ent betw een th e two energ>- d istrib u tio n s , and hence th e red sh ift of th e second cluster. His red sh ift value of c = 0.19 agreed closely w ith th e known spectroscopic value o f : = 0.192. so he ex te n d e d his tech n iq u e to a h andful of clu sters of th en unknow n redshifts o u t to m axim um red sh ift of : = 0.46. He then derived a very rough value o f Do- B a u m 's tech ­ nique was fairly a c cu ra te , but because of its d ep en d en ce on a large 4 000.\ b rea k s p e c tra l feature, it could only work on ellip tical galaxies.

3.1.2

Colour-colour diagrams

K oo (1985) followed a different ap p ro ach . F irs t, he used p h o to g ra p h ic p late s in ste a d o f a p h o to m e te r, m aking it possible to m easure p h o to m e tric redshifts for a large n u m b er of galaxies sim ultaneously. Second, in ste a d of using 9 filters he used only 4; C . I F X ( = C B j R p I s ) - T h ird , in ste a d of using an e m p irical s p e c tra l energ>- d istrib u tio n , he used th e th e o re tic a l B ruzual (1983. am o n g o th ers) no-evolution m odels for all g a la x y types.

T h e m ost im p o rta n t difference, however, was th e way th e colours were used. In ste a d o f converting th e p h o to m e tric colours into a kind of low resolu­ tio n s p e c tru m , he converted th e B ruzual te m p la te s into colours, a n d p lo tte d lines of c o n s ta n t redshift a n d varying s p e c tra l ty p e, know n as iso-z lines, on a co lo u r-co lo u r d iag ra m . F in d in g th a t th e m o st n o rm a l colour-colour d iag ra m s

(e.g. L - ./ versus J — F an d J — F versus F — .V) were d e g e n era te in a range of redshifts. he invented w iiat he called colour-shape diaijrams. T h e

shape m easu red w h eth er th e SE D tu rn e d up o r dow n a t b o th ends, th a t is.

w h e th e r th e sp e c tru m was bowl s h a p e d or hu m p ed . .-\.nother way to p u t it is th a t th e colour m easured th e first d e riv a tiv e w ith respect to w avelength of th e sp e c tru m and the sh ap e m easu red th e second derivative. For colour he used e ith e r 2U — I F ox U + J — F — .V. b o th of which sp a n a large wave­ len g th range. For sh a p e, he used e ith e r - U + 2.1 - F or - F -f-./ -r F - .V. Follow ing th is m eth o d to m etisure th e redshift of a galaxy. Koo c a lc u la te d th e colour an d th e sh ap e from th e i ' . J F X m a g n itu d e s a n d p lo tte d th em on th e colour-shape d iag ra m . T h e red sh ift of th e galaxy was th en found by finding th e iso-z line closest to th e p o in t rep resen tin g th e galaxy. Koo te ste d th is m e th o d on a sam p le of 100 g alaxies w ith known sp ectroscopic red sh ifts ranging from : = .025 to : = .700.

T h is m eth o d is sim ila r to th a t used by Pellô et al. (1996) an d M iralles. Pellô & Le Borgne (1996). T h e y used th e B R L I K colours of galaxies to d e te rm in e " p e rm itte d redshifts" in th e following m anner: T h e colours of g alaxies are p lo tte d as a function o f redshift from th e B ruzual & C h a rio t (1993) m odels. Each available co lo u r (w ith its asso ciated u n c e rta in ty ) of a galax y defines a " p e rm itte d " red sh ift range on th e co rresp o n d in g colour- redshift d iag ra m . T h e in te rse c tio n o f th e p e rm itte d redshift ranges for all th e colours determ in es th e red sh ift. T h is a m o u n ts to a colour-colour-colour- colour d ia g ra m (4 d im ensions in ste a d o f 2). T h is m e th o d was used by Pellô et

al. (1996) to discover a clu ste r of g alax ies a t c ~ .75 by looking for an excess

M iralles et al. (1996) used th e m eth o d to d e te rm in e th e redshift d istrib u tio n o f th e H ubble Deep Field.

T h e "u ltra -v io le t d ro p o u t" techniques of S teidel et al. (1996b: 1996a) a n d M ad au et al. (1996) are sim ilar if sim pler. .\11 galaxy s p e c tra have a large L ym an break; sh o rtw ard of 9 1 2 .\. th e co n tin u u m d ro p s d ram a tic ally . W h en th is break is redshifted into an d p a st th e C filter, th e U flux is g rea tly reduced or non-ex isten t, resulting in very red u ltra -v io le t colours.

In th e u ltra -v io le t d ro p o u t techniques, an exact redshift of a gahuxy is not d e te rm in e d . R a th e r, th e redshift is d e te rm in e d to be in th e redshift range w here th e L ym an break is in o r ju s t p a st th e C filter. Since U filters ty p ically have a ce n tral w avelength of 3 o 0 0 .\. th is works o u t to a redshift o f : ~ 2.5. In p rac tic a l term s, redshifted te m p la te galaxy s p e c tra are used to d e te rm in e a locus on a colour-colour plot w here m ost galaxies lie in a p a rtic u la r redshift range. T hose galaxies whose m easured colours lie w ith in th e locus are deem ed to be in th a t redshift range. Clearly, th is m e th o d is a lot sim p ler th a n th a t of Pellô et al. (1996) as only two colours are considered. It is also a lot less precise since th e redshift is not stro n g ly c o n stra in e d . For b o th these reasons it is best su ited for p re-selecting galaxies a t high redshift for sp ectro sco p ic study. S teidel et al. (1996b) did e x actly th is using th e f ’.v.

G. a n d V, filters to preselect o b jec ts for spectroscopy. M adau et al. (1996)

a p p lie d th is technique to th e H ubble Deep Field using th e F 300W . F450W . F 606W a n d F814W filters. T h e technique was e x ten d ed to hig h er redshifts by using F 450W d ro p o u ts to find galaxies of redshifts : ~ 4. By d e te c tin g th ese d ro p o u ts, it was possible to place c o n s tra in ts on th e s ta r fo rm atio n ra te a n d m e ta l p ro d u ctio n a t high redshifts.