Evolution of Elliptical Galaxies

Teresa Lym Kroeker

A thesis submitted in conformity with the requirements for the Degree of Doctor of Philosophy Graduate Department of Astmnomy University of To~onto

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Abstract In the first part of this thesis early-type galaxies in Arp groups are examined to determine if any recent mergers have occurred. No unusud rotation curves are found to indicate a merger event in the four out of eleven eady-type galaxies with suftiùent signal-to-noise ratio. Minor axis rotation is another sign of peculiar kinematics and it too is not detected in the four galaxies with strong rotation and for which the slit positions are aligned along the major and minor axes. The average velocity dispersion of this sample of Arp gd&e~ is 7 * 4% lower than other early-type galaxies, but otherwise these galaxies appear to be indistinguishable fiom normal galaxies. The lack of strong emission lines indicates that these galaxies have not undergone recent star formation wit h the exception of two galaxies which are currently interacting with other members of their group. There is no strong evidence in these Arp groups of recent mergers. These results are in agreement with other authors who find that the occurrence of recent major merger events in compact groups is rare. The Fundamental Plane is a superior tool to either the Faber-Jackson or luminosity- size relation for the study of the luminosity and mass-telight ratio evolution of early-type galaxies in clusters. Surface brightness selection effects will cause the Faber-Jackson relation to underestimate the liiminosity evolution. These selection effects are clearly demonstrated for the cluster Abell 2390. Sudace brightness selection efFects will &O affect the results derived fkom the luminosity-size relation but to a lesser degree. The Fundamental Plane analysis is insensitive to surface brightness selection dects and t herefore produces reliable results. Comparing the Fundamental Planes of the Coma cluster, a nearby cluster, and Abell 2390, a distant cluster, we hdthe evolution in luminosity is AMB(AB) = -0.54 f 0.11. The mass-telight ratios increase by 20?::% between Abell 2390 (z = 0.23) and Coma (z = 0.023). This weak evolution in mas-to-light ratio favours high formation redshifts for early-type galaxies in clusters. These results are consistent with those found by other authors. The results of this thesis support the formation of early-type galaxies at redshifts greater than 2, and seems to rule out any sigdicant formation at redshifts less than 1. 1 wish to thank my supervisor, Dr. Ray Carlberg, for suggesting the subject of this thesis, his guidance and encouragement. Thanks are &O due to Dr. Chris Pritchet, Dr. David Schade, Dr. Howard Yee for providing both data and assistance in data reduction techniques. I wodd also Iike to thank the members of my PhD Oral Examination Committee for their helpful comments on this manuscript. There are many people with which I had useful discussions (and who were willing to answer the many questions 1 had) about science, computers, and more general topics that 1would also like to thank: Felipe Barrientos, Dr. James Brown, Dr. Charles Dyer, Dr. Pierre Gravel, Dr. Sylvie Landry, Dr. Huan Lin, Sandra Scott, and ail my past and present student colleagues. Very special thanks are due to Dr. John Harper for his support and encouragement. Without his help and understanding I would not have completed thiç thesis. I would also like to thank my family for their support and understanding. This research has been supported by scholarships from the Department of Astron- omy, University of Toronto and by the Natural Sciences and Engineering Research Council of Canada. Contents

Abstract i

Acknowledgement s ii

List of Tables v

List of Figures vii

1 Introduction 1 1.1 GalaxyTypes ...... 2 1.2 Galaxy Formation and Environment ...... 3 1.3 Mergers and Interactions ...... 4 1.4 Formation and Evolution of Early-Type Galaxies ...... 5 1.5 Mergers and Arp Galaxies ...... 9 1.6 The -damental Plane of Coma and Abel1 2390 ...... 10 1.7 Outline of Thesis ...... 13

2 Fourier Quotient and Bayesian Methods 14 2.1 Fourier Quotient Method (ff) ...... 17 2.2 Bayesian Method (spec) ...... 19 2.3 Comparisonofffandspec ...... 21

3 Arp Galaxies 25 3.1 Data and Initial Reductions ...... 27 3.1.1 Observations ...... 27 3.1.2 Reductions ...... 29 3.1.3 Background Subtraction ...... 34 3.2 Tests of the Fourier Quotient Program ...... 35 3.2.1 TestswithSimulatedData ...... 35 3.2.2 Tests with Templates ...... 46 3.2.3 Tests with Broadened Templates ...... 51 3.2.4 Tests with Actual Data ...... 56 3.3 Kinernatics ...... 64 3.4 Line Emission ...... 75 3.5 Faber-Jackson Relation ...... 77 3.6 Summary ...... 79

4 Velocity Dispersions of Distant Galaxies 82 4.1 Observations ...... 83 4.2 Data ...... 85 4.2.1 GaIaxy Spectra ...... 85 4.2.2 Template Spectra ...... 89 4.3 Tests with Simulated Data ...... 97 4.3.1 Creation of Test Data ...... 97 4.3.2 No Noise Tests ...... 97 4.3.3 Noise Tests ...... 100 4.3.4 Mismatched Spectra Tests ...... 109 4.3.5 Tests with broadened spectra ...... 116 4.3.6 Summary ...... 118 4.4 Analysis using the Bayesian Method ...... 119 4.5 Analysis using the Fourier Quotient Method ...... 135 4.6 Discussion ...... 145

5 Fundamental Plane of Abell2390 148 5.1 Photometry ...... 150 5.1.1 Coma ...... 150

List of Tables

2.1 Cornparison of ff and spec velocities ...... 22 2.2 Cornparison of ff and spec velocity dispersions ...... 23

3.1 Environment of the Arp Galaxies ...... 28 3.2 Exposure information for the Arp Galaxies ...... 30 3.3 Exposure information for the Stellar Templates ...... 31 3.4 Cornparison of non zero velocity tests (variable intenal widths) .... 40 3.5 Cornparison of non zero velociw tests (single inted widths) ..... 44 3.6 Comparison of noise tests with zero noise tests (single interval widths). 45 3.7 The mean velocity of each star fkom all of the templates ...... 48 3.8 The mean velocity dispersion of each star relative to ail templates ... 49 3.9 The mean line strength of each star £rom dl of the templates ..... 50 3.10 Ranks of the velocity dispersion and line strength of the templates . . 51 3.11 Central Velocity Dispersions of the Arp Galaxies ...... 60 3.12 Summary of resdts for the Arp Galaxies ...... 74

Preliminary redshift estimates. magnitudes. and wavelength bits . . 86 Sbline wavelengths ...... 87 Skylines ...... 91 Template lines with FWHM < 1.5A ...... 93 Template lines with FWHM < 1.2A ...... 93 Fourier Quotient Test Results (No Noise) ...... 98 Spec Test Results (No Noise) ...... 99 Test results for input velocity dispersion of 250 km& ...... 104 4.9 Cornparison with galaxy S/N ratios ...... 108 4.10 Mismatched Spectra Parameters ...... 110 4.11 Redshifts for the templates for each galaxy ...... 121 4.12 Results fiom spec for shifted template spectra ...... 121 4.13 Results fiom ff for shifted template spectra ...... 122 4.14 Results fiom spec for both unbroadened templates (wsO and MO) . . 123 4.15 Results fiom spec for unbroadened and broadened ws templates ... 134 4.16 Results from ff using the unbroadened ws template ...... 136 4.17 Results hom ff for both unbroadened templates (wsO and nsO) .... 137 4.18 Results from ff for unbroadened and broadened ws templates ..... 138 4.19 Results fiom the medium boxcar broadened ws template for both ff andspec...... 147

5.1 Coma Data: EKpticaJs ...... 151 5.2 Coma Data: Lenticulars and Others ...... 152 5.3 MOS Imaging Data of Abe11 2390 ...... 153 5.4 HST Imagirrg Data of Abell2390 ...... 154 5.5 HST/MOShagingData ...... 155 5.6 JFKComaData ...... 157 5.7 Morphological types ...... 158 5 -8 Luminosiw-Size Relation Results ...... 162 5.9 Faber-Jackson Relation Results ...... 166 5.10 Fundamental Plane Fitting Results (3; 4 aperture) ...... 169 5.11 Fundamental Plane Fitting Results (re/4aperture) ...... 170 5.12 logr, Residuals (3?4 aperture) ...... 171 5.13 log r. Residualç (re/4 aperture) ...... 172 5.14 hindamental Plane Fitting Results For Abell2390 ...... 179 5.15 Am = -2.5A log (1). for various datasets ...... 192 5.16 Am = -2.5A log (I)=for various datasets...... 193 5. 17 Mass-to-Light Ratio Increases ...... 198

vii List of Figures

3.1 Images of Arp galaxies 105. 106. 123. 136. 165. and 167 hom SkyView. 32 3.2 Images of Aip galaxies 174. 228. 315. 316. and 327 fkom SkyView... 33 3.3 Fourier Quotient plots with no noise. no sky lines and a sky line ... 38 3.4 FourierQuotientplotsfortest lOO(noskylinesandaskyline) ... 41 3.5 Fourier Quotient plots for test 500 (no sky lines and a sky line) ... 42 3.6 Fourier Quotient plots for tests 1000 - 5000 (no sky lines) ...... 43 3.7 Measured and input velocities of broadened test spectra ...... 53 3.8 Measured and input velocity dispersions of broadened test spectra . 54 3.9 Cornparison of the errors for different intenml widths ...... 57 3.10 Cornparison of the results from different template stars ...... 59 3.11 Cornparison of the results £kom different initial velocities...... 62 3.12 Rotation cwes for Arp 106 and Arp 123 ...... 65 3.13 Rotation curves for Arp 136 and Arp 165 ...... 66 3.14 Rotation curves for Arp 167 and cornpanion ...... 67 3.15 Rotation curves for Arp 174 and Arp 315 ...... 68 3.16 Rotation curves for Arp 316 and Arp 327 ...... 69 3.17 Cornparison of observed rotation curve of A136a to models ...... 71 3.18 Faber-Jackson relation for Arp galaxies ...... 78

4.1 Finding chart for the galaxies in Abell2390 ...... 84 4.2 Galaxy Spectra for Abell2390 ...... 88 4.3 Skylines 6300A and 6363a in background spectra ...... 90

4.4 Template (#2 Ori) Spectra ...... 92 4.5 Profiles of the template Gaussian convolved with boxcars ...... 94 4.6 Profiles of the template Gaussian convolved with boxcars ...... 95 4.7 Norrnaüzed test spectra with varying amounts of noise ...... 101 4.8 Normilized gdqspectra for galaxies 1-9 ...... 102 4.9 Normalized galaxy spectra for galaxies 10-13 ...... 103 4.10 c~~~~/-vs oinwt (spec) wïth noise ...... 106

4.11 o~~~/o~~~~~vs 0-t (ff) with noise ...... 107 4.12 Shapes ofthemod~gfunctionfi ...... 110 4.13 The original template spectnun...... 112 4.14 This is mismatched spectrum 1 ...... 113 4.15 This is mismatched spectnim 2 ...... 114 4.16 This is mismatched spectnim 3 ...... 115 4.17 spec results for galaxy 1 (unbroadened ns template) ...... 124 4.18 spec results for galaxy 1 (unbroadened ws template) ...... 125 4.19 spec results for galaxy 1 (Gaussian broadened ws template) ..... 126 4.20 spec resuIts for galaxy I (boxcar broadened ws template) ...... 127 4.21 spec results for galaxy 2 (boxcar broadened ws template) ...... 128 4.22 spec results for galaxy 4 (boxcar broadened ws template) ...... 128 4.23 spec results for galaxy 5 (boxcar broadened ws template) ...... 129 4.24 spec results for galaxy 6 (boxcar broadened ws template) ...... 129 4.25 spec results for galaxy 7 (boxcar broadened ws template) ...... 130 4.26 spec results for gdaxy 8 (boxcar broadened ws template) ...... 130 4.27 spec results for galaxy 9 (boxcar broadened ws template) ...... 131 4.28 spec results for galaxy 10 (boxcar broadened ws template) ...... 131 4.29 spec results for galaxy 11 (boxcar broadened ws template) ...... 132 4.30 spec results for galaxy 12 (boxcar broadened ws template) ...... 132 4.31 spec results for galaxy 13 (boxcar broadened ws template) ...... 133 4.32 Velocity dispersion as a function of ki, ...... 139 4.33 ff fit and residuals for galq 1 (unbroadened ns template) ...... 140 4.34 ff fit for galaxy 1 (unbroadened ws template) ...... 141 4.35 ff fit for galaxy 1 (Gaussian broadened ws template) ...... 141 4.36 ff fit for galaxies 1 to 4 (boxcar broadened ws template) ...... 142 4.37 ff fit for galaxies 5 to 9 (boxcar broadened ws template) ...... 143 4.38 ff fit for galaxies 10 to 13 (boxcar broadened ws template) ...... 144 4.39 Cornparison of ff and spec velocity dispersions ...... 146

5.1 Cornparison of hindamentd Plane parameters ...... 158 5.2 logr, vs log (I)...... 159 5.3 The luminosity-size relation for Abel1 2390 and Coma ...... 163 5.4 Faber-Jackson relation for Abe112390 and Coma ...... 165 5.5 FP plots for JFK and our Coma data (all data. our E M) ...... 173 5.6 FP plots for JFK and our Coma data (E data. our E fit) ...... 174 5.7 FP plots for JFK and our Coma data (E data. JFK7sE fit) ...... 175 5.8 FP plots for JFK and our Coma data (cornmon data. ouE fit) ... 176 5.9 FP plots for JFK and our Coma data (common E data. our E fit) . . 177 5.10 FP plots for Coma and AbeU 2390 (E data. our E fit) ...... 180 5.11 FP plots for Coma and Abell2390 (E data. JFK's E fit) ...... 181 5.12 FP plots for Coma and Abell2390 (E data. our E- fit) ...... 182 5.13 FP plots for Local Cluster ...... 185 5.14 FP plots for Distant Cluster ...... 187 5.15 Luminosity-Size relation for a local cluster ...... 188 5.16 Luminosity-Size relation for a distant cluster ...... 188 5.17 Faber-Jackson relation for a local cluster ...... 189 5.18 Faber- Jackson relation for a distant cluster ...... 189 5.19 MIL versus r;'-'/~d+"/fi(E) ...... 195 5.20 MIL versus r;'-'/j%? +a/fl (E-) ...... 196 5.21 AlogM/Lversus z ...... 200 Chapter 1

Introduction

Galaxy mergers are thought to play a major role in the formation of elliptical galaxies. When and how often these mergers occur is important to our understanding of the evolution of elliptical galaxies since the formation epoch of eUiptical galaxies is tied quite closely with the role that mergers play. There are two zxtreme theories for the formation of elliptical galaxies. If, on the one hand, elliptical galaxies formed from the collapse of large gas clouds and evolved paçsively (Field 1975), then mergers would not play a large part in their evolution. At the other extreme it has been suggested by Toomre (1977) that all elliptical galaxies are formed by the mergers of spiral gala~ies.~If this is the case then elliptical galaxies were formed after spiral galuies. Determining the formation epoch and leaming more about galaxy mergers will aid in our understanding of the evolution of elliptical galaxies. In the first part of this thesis, signs of recent mergers are sought in early-type galaxies in Arp groups. In the second part, the Fundamental Plane of a distant cluster (Abell2390) is compared to that of a nearby and therefore older cluster (Coma) and from this cornparison constraints on the formation epoch will be determined.

'These two theories are not exclusive and both methods of formation could take place. 1.1 Galaxy Types

Early-type galaxies consist of elliptical and lenticular (or SO/SAO/SBO) galaxies. El- liptical galaxies have no prominent disk, large random veIocities, and no significant current star formation. They range in size from dwarf elliptical galaxies to giant cluster galaxies with luminosities that vary by up to a factor of 107. Most elliptical galaxies contain little or no gas and dust, and are relatively featureless. Their contours of constant surface brightness, isophotes, are ellipses which vaxy from round to an axial ratio of 0.3. Ellipticd galaxies are further classified into disky and boxy ellipticals (e.g. Kormendy & Bender 1996). Disky elliptical galaxies have disky isophotes (which are pointed at either end of the ellipse), average to low luminosity, rapid rotation, an isotropic stellar velocity distribution, an oblate spheroidal shape (Bender 1988a; Ni- eto, Capaccioli, & Held 1988), are coreless, and have weak radio and X-ray emission (Bender et al. 1989). The shape of the isophotes may indicate an embedded disk. Boxy elliptical galaxies have boxy isophotes (box shaped), high luminosity, including those galaxies with little or no rotation, an anisotropic stellar velocity distribution, a triaxial shape, and cuspy cores2 (Kormendy et al. 1996). Those with perfectly ellipticd isophotes are considered to be intermediate (Kormendy & Bender 1996). CD galaxies, a subclass of elliptical galaxies, are very massive galacies found at the centers of galaxy clusters and have extended halos. Lenticular galaxies are disk galaxies with no gas, dust, or spiral arms. They have a prominent disk and spheroidal component or bulge and possibly a bar. Lenticular galaxies are often referred to as SO galaxies and the presence (absence) of a bar may be noted by the designation SB0 (SAO). The stellar content of early-type galaxies is mostly old Population II starç. Some nearby early-type galaxies show evidence of recent star formation (e.g. Rose 1985). Late-type galaxies consist of spiral and irregdar galaxies. Spiral galaxies have a disk of young Popdation 1 stars. The spiral amis of these galaxies ~syin their tightness of spiral winding and there may or rnay not be a bar present. The relative intensity of the spheroid of Population II stars varies with how tightly the spiral arms

2At smali r the surface brightness varies as r7,with O < 7 < 0.25. are wound. Most irregular galaxies are low-luminosity gas-rich galzxïes with young stars and W regions.

1.2 Galaxy Formation and Environment

The distribution of galaxy types in different environments offers us a due as to how galaxies were formed and their subsequent evolution. Dressler et al. (1994) found that only 25% of the galaxies in the field and in small groups are early-type gda;Kies. In clusters of galaxies, this value increases to 60% and near the centers of rich clusters almost all (80%) of the galaxies are early-type galaxies. Galaxy formation and evolution theories must be able to explain this population dependence on the environment. Two simple formation mechanisms are briefly discussed below to illustrate how the difEerent types of galaxies can be formed and how the population dependence on environment can be achieved. Star formation rates are important in determining the type of galaxy in the collapse theory of galaxy formation (Larson & Tinsley 1978). If star formation occurs quiddy as the protogalactic cloud collapses an elliptical galaxy is formed. If, on the other hand, the protogalactic cloud collapses before forming stars a disk galaxy results. Initial asymmetnes in the cloud cause it to rotate and conservation of angular momentum results in a collapse that is preferentially in one direction. Lower densities in the field environment could be responsible for the slower collapse of the protogalactic gas cloud, giving rise to the higher numbers of late-type galaxies. In hierarchical-clustering models srnall clouds collapse first and then merge to form larger structures, such as galaxies and groups and clusters of galaxies. Hierarchical- clustering is the method of galaxy formation in Cold Dark Matter models. One possible scenario is that spheroidal systems (globular clusters, dwarf galaxies, bulges of disk galaxies, ellipticd galaxies and dark matter halos) formed first from the pri- mordial density fluctuations. Infalling gas later formed the disks of galaxies and irregular galaxies. In high density regions all the gas is used up in the initial creation of early-type galaxies. In lower density regions late-type galaxies are predominant. CIEAPTER 1- INTRODUCTION 1.3 Mergers and Interactions

We see interactions and mergers of both nearby and more distant galaxies and these events most likely occurred more oRen in the past. Later mergers of galaxies could be signiiicant in the evolution of galaxies regardles of the formation scenario and the significance of mergers in the early history of galaxies is dependent on the formation mechanism. Bames & Hemquist (1992) have reviewed the subject of interacting galaxies and brief mention will be made of some of the signs of interactions and mergers that they discuss in more detail. Bridges can be found "connecting" large disk galaxies and their smder companions. Interacting disk galaxies often have tidal tails and have been modelled succes~yby Mnous authors. Head-on and nearly head-on collisions are thought to have created cartwheel and some ring galzccies. Elliptical galaxies on the other hand do not show such spectacular signs of interactions. The environment in which elliptical galaxies are commonly found is probably responsible for this. Encounters in rich cbters are fast due to the high relative motions of the galaxies and may produce extended halos, distorted and off centered isophotes, and peculiar kinematics. Dumbbell galaxies found at the centers of rich clusters are thought to be the central galaxies of two rich clusters which are merging (Demaine 1990). Dynamical fkiction is responsible for the eventual rnerger of a satellite galaxy with its larger companion. Shells, ripples, plumes, boxy isophotes, and X-shaped structures are common photometric signatures that have been hypoth- esized to be due to the accretion of a smaller companion onto an early-type gaiaxy. Polar rings in SO galaxies which appear to be kinematically distinct could be due to either the accretion of a gas-rich small companion or due to the capture of material from a passing galaxy. Mergers and interactions can in some cases induce star formation since star formation has been detected in some interacting pairs of galaxies. Infrared luminous starbursting galaxies with large amounts of gas in their nuclei have been detected by the IRAS survey. There are indications that some of the active galactic nuclei of Seyfert galaxies (late-type galaxies) are caused by mergers. There is also indirect evidence for mergers being responsible for activity in quasars. Elliptical CHAPTER 1. INTRODUCTION 5 galaxies with strong radio ernission appear to be the product of recent mergers. N-body simulations have been used by many authors to study the consequences of various types of interactions of different types of galaxies. Holmberg (1941) was the first to use such a method with an optical analog cornputer and modelled the tidal interaction of two disk galaxies. Many of the signs of interactions that are seen in galaxies have been modelled, for example, tidal tails and bridges of spiral galaxies (e.g. Toomre & Toomre 1972), sheh in elliptical galaxies (e.g. Hernquist & Quim 1988), and X structures in SO galaxies (e.g. Mihos et al. 1995). Numerical simulations by Balcells & Quinn(1990) showed that a counter-rotating core can be produced fiom the merger of a satellite elliptical galaxy and its larger parent galaxy if the orbit of the merger is retrograde with respect to the rotation of the primary elliptical galaxy. This mechanism for producing counter-rotating cores was first proposed by Komdy (1984). Barnes & Hemquist (1991) used a hybrid N-body gasdynamics code to show that the tidal interactions of two disk galaxies can induce the formation of a central bar as well as a counter-rotating disk of gas and stars. The rnerging of two disk galaxies as suggested by Toomre (1977) has difncdties as a method for the formation of elliptical galaxies. Carlberg (1986) showed that the high phase-space densities of elliptical galaxy cores cannot be created £rom pure stellar mergers of two lower phase-space density disk galaxies. Bekki & Shioya's (1997) numerical simulations of the mergers of gas-rich disk galaxies illustrate a possible scenario for the formation of dkky and boxy ellipticd galaxies. Disky elliptical galaxies form if the gas consumed by star formation is gradual and boxy elliptical galaxies fonn if the depletion of gas is rapid.

1.4 Formation and Evolution of Early-Type Galaxies

There are many questions one can ask about the formation and evolution of ellipticd galaxies. When did elliptical galaxies form? How long did the formation process CEAPTER 1. INTRODUCTION 6

take? Did all elliptical galaxies form at the same tirne? Are elliptical galaxies in clusters and in the field the sarne? Do boxy and disky ellipticals share the same history? How did CD galaxies acquire their extended halos? Are different formation or evolutionary processes at work that are dependent on the environment? How important are mergers to the formation and evolution of elliptical galaxies? Stellar population models (e-g. Larson & Tinsley 1978; Bmzual& Charlot 1993; Worthey 1994) have played a large role in attempts to determine the ages of early-type galaxies. The observed properties of galaxies (broad-band colors and spectral indices) are compared to mode1 predictions assuming a initial mass function, metallicity, and age. Models can be created for a single burst of star formation or one can add smaller bursts to an older stellar population. There are several complications when applying these models to observations. SrnaIl recent bursts of star formation look similar to laxger older bursts (Worthey & Ottaviani 1997). Unfortunately differences in age and metallicity are also hard to distinguish (Worthey 1994). Two stellar populations wiU have the same colors and nearly identical line indices (for most indices) if the ratio

of the percentage changes in age and metallicity (2)is Aage/AZ ri: 312. An old, metal-poor stellar population can appear to be similar to a younger, more metal- rich stellar population. Another complication is that age estimates fiom synthesis models fiom different authors with the same metallicity and initial mass function can vary up to f35% (Charlot, Worthey, & Bressan 1996). Even though these problems exist, using these models with these limitations in mind can put limits on the ages of stellar populations. Worthey (1996b) finds that the spread in ages of early-type galaxies is significant. Note that these ages are either the true formation age andior indicative of recent starbursts. In Worthey's sample of field and cluster early-type galaxies no cluster elliptical galaxies are found with ages less than 3 Gyr. There are also other differences between cluster and field galaxies that have been detected, for example, field elliptical galaxies have a larger spread in colors than duster galaxies

(Sandage & Vismathan 1978). The detection of galaxies at high redshifts (Z > 3, e.g. Steidel et al. 1996) indicates that at least sorne galaxies formed early. Are these high redshift galaxies representative of the galaxies we see locally? Giavalisco, Steidel, CWTER1. INTRODUCTION

& Macchetio's (1996) analysis of HST images indicates that these young gdaxies may be the progenitors of present day luminous galaxies. Sawicki & Yee (1998) constmcted broadband optical and IR spectral energy distributions of 17 Lyman break gal&es (z > 2) and conclude that the large amounts of dust that they found around these galaxies has led to underestimates of the star formations rates and overestimates of the galaxy masses. They also conclude that these objects are either the progenitom of dwarf galaxies or the building blocks of present day luminous galaxies. Bender, Ziegler, & Bruzual (1996) fmd a srnall amount of passive evolution in the steIIar populations of elliptical galaxies from their cornparison of the velocity dispersions and Mg2 absorption line strengths between z = 0.37 and local galaxies. They conclude that the bdk of the stars must have formed before a redshift of 2. Bender (1996) concludes that more that half of luminous (boxy) elliptical galaxies have peculiar core kinematics when taking projection effects into account, where peculiar core kinematics include counter-rotating cores, minor axis rotation, and peculiar velocity fields. These peculiar cores are generally long lived and therefore are not necessarily indicative of a recent merger event, but do suggest that merging has played a part in the galaxy's history. Another possible explanation for some of the unusual cores that does not involve merging is the projection of a triaxial figure (e-g. Statler 1994). Dissipationless merging of a compact elliptical or SO has been suggested as a possible mechanism for the formation of peculiar cores (Kormendy 1984; Balcells & Quinn 1990). Bender & Surma (1992) favour merging events that include gas-rich spiral galaxies, a gas-rich spiral galaxy and an elliptical galaxy, or compact goups, and hierarchical merging of partidy gaseous objects. Accretion of gas-rich companions will not produce the observed large central cores and the merger of a compact elliptical will not result in large rotation velocities and enhanced metallicities also found in these cores (Bender, Burstein, & Faber 1992). Schweizer & Seitzer (1992) studied 69 early-type galaxies (mostly) in the field and groups in an attempt to date merger events. They compared the UBV colors of these galaxies with their fine structure (ripples, plumes, ta&, twists, X structure, and boxy isophotes) and found that galaxies with more fine structure were bluer. The CWTER 1. INTRODUCTION 8

galaxies that showed no fine structure have a mean heuristic merger age of 8 Gyrs and those with the most fine structure have a mean age of 4.6 Gyrs (based on a two burst model). They also concluded that the small scatter in the color-magnitude diagram is consistent with these galaxies fomiing or having a major merger event within 113 to 213 of the age of the Universe (or z - 0.3 to 1.1 for Ho = 50 km s-' Mpc-' and qo = 0.5). Bower, Lucey, & Ellis (1992) from their analysis of early-type galaxies

in the Virgo and Coma clusters find an earlier formation epoch, i > 2 (qo = 0.5). Ellis et al. (1997) found that the scatter in the colors of elliptical galaxies in clusters at z cz 0.5 is srnall. They conclude that the stars of these elliptical galaxies formed

early (t > 3) and that the galaxies are evolving passively. There appears to be a growing amount of evidence that suggests that cluster elliptical galames are older than field elliptical galaxies. Kaufhann (1996) has even suggested that bright field elliptical galaxies are intrinsicdy different fiom cluster elliptical galaxies, they have undergone recent merging and star formation and would eventually grow new disks and tuni back into spiral galaxies. The rnorphology-density relation for clusters of galaxies evolves with redshift (Dressler et ai. 1997). Dressler et al. found that in simüar density environments, elliptical galaxies in clusters at z - 0.5 are overabundant by a factor of 1.5 compared with local clusters. Spiral galaxies are also overabundant by a factor of 2, but SO galaxies are underabundant by a factor of 2-3. Ellis (1998) suggests that two types of SO galaxies (van den Bergh 1990) could explah the evolution in morphology of SO and spiral galaxies. Luminous SO galaxies were probably formed by similar processes that created elliptical galaxies, since they have sirnilar properties (Ellis et al. 1997). Less luminous SO gaIaies, on the other hand, may have been transformed from spiral galaxies by merging and dynamical friction. Tidal stripping by Iarge CDgalaxies has been used to explain the large extensive halos found around these galaxies. The self-gravity of a smaller nearby galaxy is unable to hold itself together in the presence of the tidal forces created by the CD gala- Tidal stripping in the dense cores of present epoch clusters is difncult due to the large velociw dispersions of the galaxies in clusters and likely occurred before the clusters formed fiom smaller groups of galaxies (Merrïtt 1984). Other theories for the formation of CD halos include galactic cannibalism (the merging of satellite galaxies that corne too close to a giant galaxy), and coohg flows (intracluster gas cooling and accreting on the giant gdaxy). From their study of the galaxy luminosity funetions of clusters L6pez-Cruz et al. (1997) propose that a large fiaction of the dwarf galaxies were disrupted early in the evolution of the cluster and these stars formed the CD'Shalo. Garijo, Athanassoula, & Garcia-Gbmez (1997) used N-body simulations to study the formation of CDgalaxies and found that the central object of their clusters grew by two methods, galactic cannibalism and tidal stripping, with the importance of each method dependent on the initial conditions.

1.5 Mergers and Arp Galaxies

An environment where one may expect to find the remnants of galaxy mergers is in groups of galaxies where there are signs of current interactions. Arp (1966) compiled an atlas of peculiar galaxies of which many are classed as cuwent interactions, for example, those systems with bridges and tails; and remnants of o previow interaction, for example, those with shells. For this study galaxies were selected fkom this atlas that appear normal but rnight have minor distortions A kinematically distinct core subpopulation, young stars, or nuclear activity in these galaxies would suggest a previous merger. In this study the main focus will be searching for kinematic signatures of a merger but evidence of a recent starburst will also be sought. Examination of the kinematics of early-type galaxies in Arp groups has not been done previously. Other authors have studied the kinematics of specific early-type galaxies and samples in compact groups and clusters. F'ranx & Illingworth (1988), Jedrzejewski & Schechter (1988), and Bender (1988b) aIl found peculiar cores (couter- and co-rotating cores) in elliptical galaxies, and more peculiar cores have been found since these were discovered. Zepf & Whitmore (1993) found that the velocity dispersions of elliptical galaxies in compact groups are 20% lower than for other elliptical galaxies but these authors did not study the detailed kinematics of the galaxies. Longo et alh (1994) study of the galaxies in Hickson group No. 90 showed that two of the four galaxies have signs of a strong interaction. The velocity dispersion profiles of brightest cluster galaxies are similar to those of bright elliptical galaxies (Fisher, Illingworth, & Franx 1995), and these authors also found that most of their galaxies show no significant rotation, with one of the thirteen galaxies having a counter-rotating core. They also conclude that these slowly rotating brightest ciuster galaxies in high velocity dispersion clusters are consistent with the galaxies having formed by rnergers. Kinematics of early-type galaxies in the Fornax cluster have been studied by D'Onofkio et al. (1995) and they found that hoof the 15 galaxies showed a hint of a counter-rotating core. Our study of Arp galaxies will aid in the understanding of when and how often mergers occur.

1.6 The Fundamental Plane of Coma and Abel1

Since the late 1970's it has been known that there are correlations between various parameters of elliptical galaxies. Two of the most common are the Faber-Jackson relation (Faber & Jackson 1976), which relates luminosity and velocity dispersion, and the luminosiw-size relation (Kormendy 1977). It was later discovered that if three parameters were used a tighter relationship was obtained (Djorgovski & Davis 1987; Dressler et al. 1987). The Faber-Jackson relation and the luminosity-size relation are projections of this so called Fundamental Plane. The scatter in the Faber-Jackson relation is due to mass-to-light dations. The Fundamental Plane takes into account the differences in structure and stellar mix and reduces the scatter. The three parameters most often used to create a Fundamental Plane are surface brightness, effective radius, and velocity dispersion. Color or line index has also been used in place of velocity dispersion (de Carvalho & Djorgovski 1989). The size and the velocity dispersion are essentially dynamicd parameters and are dependent on the mas of the galaxy. The surface brightness depends on the total luminosity of the galaxy. The huidamental Plane measures the average mas-to-light ratio of a group of galaxies. CHAPTER 1. INTRODUCTION Il

If it is assumed that galaxies in a cluster have formed at the same theand therefore have the same age but are slightly different due to their initial masses, then by cornparing two clusters at different redshifts the change in the mas-to-light ratio can be measur ed. The physics of the Fundamental Plane is still not well understood (Pahre & Djorgovski 1997). The basic form of the Fundamental Plane cm be derived from the virial theorem and the assumption that the mas-to-light ratio for ellipticd galaxies is constant. The trace of the tensor virial theorem is, KE = T + II = -W, where KE is the total kinetic energy, T is the kinetic energy of order motion, II is the kinetic energy of random motion, and W is the potential energy. It follows from this equation that the mass of galaxy is

where r. is the effective radius, a, is the central velocity dispersion, and c, will be a constant for galaxies that are structurdy similar. The luminosi@ is

where 1' is the surface brightness at a radius T., and ci is a constant. Rom equations (1.1) and (1.2) it follows that

If we assume that the MIL ratio is constant for a group of galaxies and that both c, and cl are constants, then the following relation is found,

(Faber et al. 1987; Bender, Burstein, & Faber 1992). In observational studies a plane is fit to the data and the coefficients of the velocity dispersion and the surface CWTER 1. INTRODUCTION 12 bnghtness are solved for ushg Miious fitting methods. The coeficient of the velocity dispersion, usually denoted as a in the above relation, is found to be lower than the predicted value of 2 and is usually between 1.0 and 1.4 (e-g. Jgrgeasen, Franx, & Kjærgaard 1996; Saglia, Bender, & Dressler 1993). The coefficient of the surface brightness, P, is &O found to merfrom the expected value (- -0.8). Several reasons why these coefficients are not in agreement with those predicted by the virial theorem are discussed by Graham & Colles (1997) and they include a systematic dation in the MIL along the Fundamental Plane, a systernatic dation in the stellar age of galaxies, broken dynamical hornology, and broken structural hornology. The reasons why this tilt in the hindamental Plane exists is not weU understood. There are indications that the Fundamental Planes of cluster and field galaxies (de Canmlho & Djorgovski 1992) and of dusters of different richnesses (e.g. Lucey et al. 1991) differ. It also appears that the Fundamental Plane may vary with redshift (van Dokkum & F'ranx 1996; Jgrgensen & Hjorth 1997; Kelson et al. 1997). Velocity dispersions of galaxies at higher redshifts have been difEcult to obtain in the past but recent studies, including this one, are able to obtain spectra of sufficient S/N ratio to determine the central velocity dispersions. By studying the Fundamental PIanes of distant and local clusters we can gain insight into the evolution of elIiptica1 galaxies. In the second part of this thesis the velocity dispersions of early-type galaxies in the cluster AbelI 2390 are rneasured for the findamental Plane analysis. Meauring velocity dispersions of distant galaxies requires special treatment since it is not pas- sible to compare the spectra of these galaxies with stars at the same redshift using the same instrumental setup. By comparing the Fundamental Planes of a distant cluster, Abell2390, and a nearby cluster, Coma, the amount of luminosity and mas- to-light ratio evolution will be determined. Projections of the Fundamental Plane will also be used to determine the lwninosity evolution. The amount of luminosity and mas-to-light evolution will be used to constrain the formation epoch of early-type gdaxies. 1.7 Outline of Thesis

Chapter 2 describes the two approaches, the Fourier Quotient method and the Bayesian method, that are used in this study to fuid the velocities and velocity dispersions of early-type galaxies. Both methods are used to determine the velocities and velocity dispersions of test spectra and these results are compared. Since the details of the analysis are different for near (Arp galaxies) and distant galaxies (Abe11 2390 galaxies) further detailed tests of these methods are presented in later chapters. Chapter 3 is devoted to the analysis of the Arp gdaxy data. The primary focus of this andysis is the search for signs of a recent merger. Extensive tests of the Fourier Quotient program which is used to determine the rotation curves and velocity dispersion profiles are summarized. For each gdaxy the rotation curves are presented dong with the results of models created to test whether or not an unusual core could be detected. Since peculiar kinematics cannot date a merger event but recent star formation cm, line emission is also discussed. Arp galaxies are compared with a ''normal" sample of galaxies using the FaberJackson relation. The determination of the velocity dispersions of the Abell 2390 gal~esusing both the Fourier Quotient and Bayesian methods is presented in Chapter 4. Applying methods to determine the velocity dispersions that were developed to study nearby galaxies to distant galaxies requires special treatment and therefore detailed tests are presented in t his chapt er. The Fundamental Plane analysis of Abell 2390 follows in Chapter 5. The ph* tometry of Coma and Abell 2390 is discussed and compared to that of other authors. The luminosity-size relation and Faber-Jackson relation of Coma and AbeU 2390 are compared to determine the amount of luminosity evolution. Difficulties with using the luminosity-size and Faber-Jackson relation to measure the luminosity relation are also discussed. The change in the luminosity and the change in the mass-telight ratio of the Abell 2390 galaxies with respect to the Coma galaxies is also determined. In the final chapter the results of both the Arp galdes and the Abell 2390 analyses are srrmmarized. Chapter 2

Fourier Quotient and Bayesian Methods

This chapter describes the two methods used in th* study to detennine the velocities and velocity dispersions of galaxies fiom their absorption-line spectra. The systemic velocity of a galaxy is determined by measuring the shift in wavelength of the galaxy's absorptions lines relative to a template or stellar spectrum. Rotation curves of galaxies can be found by obtaining long-slit spectra, which are usually centered on the galaxy core and which sample the spectnim of a galaxy at MIying radii. The velocities measured at these different radii produce a velocity profile or "rotation curve". These same absorption luies are dso Doppler broadened due to the random velocities of the stars in the galaxy dong the line of sight. The central velocity dispersion and/or velocity dispersion profile may therefore also be determined kom the galaxy spectra. Several methods have been employed to measure velocities and velocity dispersions. Among these methods are the Fourier Quotient method (e.g. Simkin 1974, Sargent et al. 1977)' the Cross Correlation method (Tonry & Davis 1979), the Fourier Fitting method (Fr=, Illingworth, & Heckman 1989), the Fourier Cor- relation method (Bender 1990b), the Direct Fitting method (Rix & White 1992), the Modified Fourier Quotient method (WinsaU & Freeman 1993), and the Bayesian method (Saha & Wiiarns 1994). The main assumption in all these methods is that CHAP!ZER 2. FOURlER QUOTIENT AND BAYESIAN METR'ODS 15 the gdaxy spectrum is the convolution of a mean stellar spectnun, which is dependent on the stellar composition of the gdaxy, and a broadening function, which may or may not be assumed to be a Gaussian. Compaxisons and studies of these different methods have been made by the above authors, Laird & Levison (1985), and others. The velocities and velocity dispersions found using these methods can vary especidy when the signal-to-noise (SIN) ratio is low (see below) and if different broadening functions are used. The use of a Gaussian broadening function has been shown to be incorrect for sorne galaxies and errors of up to 10% in the estimates of the velocity dispersion can O ccur with this assumption (Winsall & Freeman 1993). Non-Gaussian line-of-sight velocity distributions are expected in rapidly rotation systems (especially at the centers of these systems), galaxies with local velocity anisotropies, and sys- terns with a two component structure (e.g. SO galaxies) (Rix & White 1992). Two factors which can cause the observed line-of-sight velocity distribution to approach a Gaussian shape, are the integation of the velocity distributions along the iine of sight, and the spatial averaging caused by seeing and by the finite width of the slit (Rix & White 1992). One reason for assuming a Gaussian broadening hction in this study is that cornparisons will be made to other kinematic results which use the same broadening function. Another reason is that high S/N data is required if the shape of the broadening function is to be deterrnined. Schechter & Gunn (1979) created test objects horn broadened stellar spectra and analyzed these objects using mismatched templates. They found that the velocily dispersion was overestimated by up to 20% when the object was created with a G8 III spectnim and analyzed with a K2 III template. Kormendy & IUingworth (1982) also found that early-type (G8 III) template stars gave 12% lower velocity dispersions than later type (KO-K2III) stars for their sample of disk galaxies. Laird & Levison 1985 found that velocity dispersions can vary by -15% over the metallicity range of -1.0 5 [FeIH] 5 0.5. The template or cornparison object should therefore be carefully chosen. The Ca 11 H and K lines are commonly excluded from the analysis since their presence can cause the velocity dispersion to be overestimated (Kormendy & Illingworth 1982). CHAPTER 2. FOURlER QUOTIENT AND BAYESLGN METHODS 16

The rotation cuve will not be affected by a mismatched template since the positions of lines are independent of stellar type, but the velocity dispersion may be a$ected since the intrinçic velocity dispersion and the width of the various lines d vary. Tests with different templates are presented in $3.2.2 for the Arp gaI&e, and the effects of mismatched templates for the AbelI 2390 galaxies are presented in 54.3.4. To illustrate the ciifferences that can occur using different methods, an analysis of the data presented by Nella et al. (1995) foUows. NelIa used the Cross Correlation (CC), Fourier Quotient (FQ), and Fourier Correlation Quotient (FCQ) methods to measure the velocities and velocity dispersions of 95 early-type field galaxies. Com- parison of their resdts kom the Merent methods shows that there are systematic differences when the SIN ratio' of the spectrum decreases. The mean difference between the FQ and FCQ velocity dispersions is ap~- OF~Q = -14f 46 km s-' and the mean Merence between the FQ and CC velociw dispersions is o~p- CTC~ = O f36 km s-' for the whole sample of galaxies. If the comparison is limited to those galaxies with low S/N ratios (Iess than - 50) the Merences are OFQ - OFCQ = -55 f 35 kms-' and OFQ - occ = -16 & 46 km s-l. For those galaxies with S/N ratios greater than 50 the clifferences are OFQ - OFCQ = 5 f38 km s-' and ~FQ- CTC~ = 8 & 28 km s-'. The FCQ method on average gives higher velocity dispersions than the FQ method if the S/N ratio is low. The CC method also gives slightly higher velocity dispersions than the FQ method. If the S/N ratio is high the results fkom d three methods are similar. The important point from this comparison is that different methods can produce bi- ased results if the SIN ratio is low. These differences may be due in part to the fact that the FCQ methods allows for non-Gaussian broadening functions. Without tests with artificially created data it is not possible to determine which of these programs produces more accurate resuits at Iow SIN ratios. With alI methods detailed tests should be performed to determine the behavior of the programs at low SIN ratios. The Fourier Quotient method and the program used to irnplement this method are discussed in 52.1. The Bayesian method and its program are bnefly explained in

'Nella et al.% (1995) rnethod for &&ulating the S/N ratio is diseussed later in this chapter. GWTER2. F0URLE:R QUOTIENT AND BAYESIAN METHODS 17

$2.2. The results of tests of both of these program are presented in the Iast section of this chapter. More detailed tests of both programs are discussed in later chapters.

2.1 Fourier Quotient Method (ff)

The Fourier Quotient method used in this study is based on the formulation presented by Sargent et al. (1977) and is often referred to as the SSBS Fourier Quotient method. The original FORTRAN code from Kormendy was translated into C and modified to suit the needs of our data and library routines. Other modifications were also made to enhance the performance of the program. The Fourier Quotient method and the program are discussed in this section.

The gdaxy spectnun, G', is assumed to be the convoIution (O) of a mean stellar spectnim, SI, and a Gaussian broadening function, B(t,O), which is itself a function of the velocity or redshift, z, and velocity dispersion, O:

If the gdaxy and stellar (template) spectra are obsemed with the same instrumental configuration, the instrumental broadening, BI, will be identical and cancels out. In pixel or channel space (j)the observed galaxy spectrum is

where S(j) = Sf(j)0 Br is the observed stellar spectrum. The galaxy and stellar spectra are first placed on a logarithmic wavelength scale. The program, ff, then prepares the spectra by fitting and subtracting the continuum and normalizing the residual intensities to uni@ An estirnate of the systemic velocity must be provided so that the areas outside the overlap regions of gdaq and template spectra can be zeroed. The resulting spectra are filtered using a cosine bell, w(j). Night sky lines and other regions specified in either the galaxy or template spectra are replaced CWTER 2. FOURIER QUOTlENT AND BAYESW IMETHODS 18 by interpolating between the endpoints of the regions. Taking the discrete Fourier transform of equation (2.2) results in

where denotes the Fourier transform. Dividing equation (2.4) by S(k)gives equation (2) from SSBS,

where

c7 h(1+z) S = and - cAhX - AlnA ' are the velocity dispersion and the logarithmic redshift respectively (measured in channels), 7 is a measure of the relative line strengths of the galaxy and stellar spectra, AhX is channel width2, and n is the number of channels or pixels. The fiactionai uncertauity of the quotient Q(k) = G(k)/S(k)is given by equation (5) of SSBS,

where the error of the Fourier transform of the galaxy or template spectrum (equation (4) of SSBS) is estimated. By rninimizing equation (7) of SSBS,

where kup and ki, are the high and low frequency cutofb, using the Levenberg- Marquardt method for a system of non-linex equations (e.g. Press et al. 1988)

'A ln X = (In A. - in Xb)/(n- l), where A, and Ab are the wavelength limits of the spectrum. CRAPTER 2. FOURlER QUOTZENT AND BAYESIAN IMETHODS 19 estimates of the velocity, velocity dispersion, and line strength are found. The errors in these quantities are provide by the Levenberg-Marquardt subroutine and are discussed in tests presented later. Initial guesses for the velocity and velocity dispersions are needed to prepare the spectra and for the Levenberg-Marquardt subroutine. To reduce the possibility of finding a local minimum instead of the true minimum, ten attempts are made to find a solution and the best solution (the solution with the lowest x2)is chosen. The starting point for each iteration is the initial guess or best solution found thus far perturbed by a random amount up to &10%. For long-slit spectra the starting point for the next spectnun is the solution of the previous spectrum.

2.2 Bayesian Method (spec)

The Bayesian program, spec, is discussed in detail in Saha & Williams (1994, here- aRer SW). This method has several advantages over the Fourier Quotient method. The spectra do not need any preprocessing (sky subtraction, removal of tilts and S-distortion, or rebinning to Fourier space). The program does not assume that the broadening function is Gaussian and prior information about the broadening function can be input. Template mismatching is dealt with by finding the best combination of stellar spectra to use as the template. The authors also daim that this program cm deal with lower S/N ratio data. The program is written in the progrmming language CWEB and was kindly provided by Saha. This method uses Bayes' theorem,

where P(B1 A) is the probability of B assuming A is true, P(A1B) is the probability of A assuming B is true, P(B)is the probability of B, and P(A) is the probability of A. For a mode1 M with parameters w the probability distribution of the data D is P(D(w,M). For Gaussian noise this probability is

where Di is the data point, Di is the predicted valued fiom the model, and ai is the noise dispersion (equation (4) of SW). The probabüity distribution depends on the properties of the mode1 and the instrument used to gather the data. The parameters of the model w are not known and the data D are given. The probability distribution of the mode1 parameters based on model and data is

where P(w1M) is the prior probability of the parameters, and P(DI M) is essentially a normalizing factor (equation (6) of SW). The prior probability contains information about the broadening function that is known prior to collecting the data, for instance, that it is non-negative and most Iikely smooth. The broadening function can also be restricted to be Gaussian. The Metropolis algorithm is used to estimate the parameters and their uncertainties; its steps are: 1. Start with parameters w and P(wlD, M). 2. Choose a dw and calculate P(w + bw(D,M). 3. If P(w + bwlD, M) > P(wlD,M) accept bw, else accept 6w only P(w + 6wlD, M)/P(wlD, M)of the time. 4. Iterate starting at step (2). The galaxy and stelIar spectra do not require preprocessing to remove tilts, S- distortion or the sky background as this is done by the program. Information about the wavelength calibration and the spectra are also input into the program. The noise properties of the data in this raw form are the simplest and hence this is an advantage to this method. Next the program chooses which elements dong the slit to combine for the fitting of the broadening function based on their mean brightnesses. The CWTER2. FO UMER QUOllENT AND BAYESLAN LMETHODS 21 broadening functions of the inner elements are assumed to be independent, whereas the outer parts are assumed to have a common broadening function. One of the stellar templates and the Cross Correlation method are used to fhd the starting broadening function. The best-fit template, which is a combination of the steIlar spectra, is found based on this preliminzry broadening function. The parameters of the broadening hinction and their uncertainties are then estimated using the Metropolis algorithm. The program then fin& a better template with the Ïmproved broadening function and new parameters and their uncert ainties.

2.3 Cornparison of ff and spec

In this section tests are briefly described that compare the two programs ff and spec. Test spectra are created fiom a stellar template spectrum by adding Poisson noise, a velocity shift, and a velocity dispersion. The same spectrum that is used to create the test spectra is also used as the template in the analysis of both programs. Essentially these test spectra have been preprocessed and have no sky background. Since the data in this study have been preprocessed this cornparison of preprocessed data is valid for this study, but the performance of spec was not fully tested. Test spectra are created with S/N ratios of 15, 10, and 5, and all have a systemic velocity of 1000 km~-'.~A Gaussian broadening function is used to broaden the template spectra to a velocity dispersion of 200 kms-l. There are 100 test spectra at each SIN ratio, each slightly different due to the noise. The results are summarized in Tables 2.1 and 2.2. The mean velocity and velociw dispersion are listed in t hese tables for each of the S/N ratios and progams in colurnn 3. The number of results out of

3These S/N ratios are the input values to the program that creates the spectra. The measured S/N ratios are 14.3, 9.5, and 5.1 respectively, using the method described by Neiia et al. (1995). The noise is assumed to follow a Gawsian distribution and therefore the standard deviation of the noise is o = 1.25(1Azl). Therefore the nahe is equal to 1.25 CE: Il$ - Fi+1I/n, where fi is the value of intensity of the ith pixel. The signal is the mean of the intensity values. Two iterations are performed, the fist is used to detennine the mean value of [Fi - Fi+r(, the second rejects ail differences of IFi - Fi+l 1 greater than three times the mean due (and the corresponding Fi in the cddation of the signal). This is done in an attempt to eliminate contribution of the signal to the estimation of the noise. The input and measured S/N ratios agree weli with one another. CHAPTER 2. FOURIER QUOTIENT AND BAYESIAN IMETHODS 22

100 test spectra that are within a specific percentage of the input value are &O hted. The Fourier Quotient program is slightly better than the Bayesian method at a S/N ratio of 15. The meaa velocity and velocity dispersion found by ff are 1003f 16 km s-' and 205 f 17km s-', while for spec they are 1011 f 18 km s-' and 202 I 23 km s-'. When the SIN ratio decreases the Fourier Quotient program is significantly better than the Bayesian program. At a S/N ratio of 5 the ff results are very close to the input values with 94% of the velocities within 10% of the input dueof 1000 km s-', and 57% of the velocity dispersions are within 20% of 200 km s-? With the program spec these percentages decrease, only 71% of the velocities are within 10% and 31% of the velocity dispersions are within 20% of the input values. It should be noted that several modifications to the Bayesian program were made since the data are preprocessed. These changes may affect the performance of the program.

Table 2.1: Cornparison of ff and spec velocities

spec 15 1011 & 18 100 100 100 100 96 '73 40 spec 10 1012 * 26 100 100 100 100 92 53 27 spec 5 1046 f: 172 96 93 88 70 38 20 8 NOTES. Col. (2). - S/N ratio. Col. (3). - Mean velocity and standard deviation in km s-'. Col. (4). - Number of tests that converged to a solution. Cols. (5)-(10). - Number of velocities that are withx% of the input value of 1000 kms-l. CHAPTER 2. FOURlER QUOTIENT AND BAYESLAN MET-

Table 2.2: Cornparison of ff and spec velocity dispersions

ff 10 207 & 28 100 100 83 59 34 13 4 ff 5 203 & 71 100 90 57 34 19 7 4 spec 15 202 I 23 100 100 92 59 39 18 14 spec 10 208 I 40 100 98 75 41 21 9 3 sDec 5 300 & 163 96 60 30 13 7 2 2 NOTES. Col. (2). - SIN ratio. Col. (3). - Mean velocity dispersion and standard deviation in km s-l. Col. (4). - Number of tests that converged to a solution. Cols. (5)(0). - Number of velocity dispersions that are within x% of the input value of 200 kms-l.

From these tests it can be seen that spec and ff are comparable at high SIN ratios, but as the SIN ratio decreases ff is better at finding the velocities and velocity dispersions of the test spectra. Note also that these tests did not use spec to its fullest potentid since the data are preprocessed and the template is a perfect match. spec was written with the intent of fitting the data in pixel space (the original CCD data) to avoid introducing correlation in the noise. For the hst part of this study, the Arp galaxies, only the Fourier Quotient method will be used since the data are preprocessed and it is not clear that the Bayesian method will give better results. More tests with the Fourier Quotient program and the Arp data will be discussed in the next chapter. The data in the second pa.rt of this study, the Abell2390 galaxies, are also preprocessed but both programs will be used to analyze the data. More extensive tests with both program axe presented in 84.3. The results from spec in the tests discussed in this chapter are in conflict with the set of tests done iater in 54.3 for the Abell 2390 galaxies. Two different versions of the program spec are used in this study. The original program used for the set of tests in this chapter performs well at kding the input velocities and velocity dispersions. The velocity dispersions fiom tests with the version of the program used for the Abell 2390 galaxies are 92% of the input value. Several modifications were made to the program including some made by the original authors. The routine that converts CHAPTER 2. FOURIER QUOTIENT AND BAYESLAN METHODS 24 fiom pixel space to wavelength space was changed in this new version of spec to suit the Abell 2390 data. Lt is likely that in making these modifications a software bug was introduced. Many attempts were made to fix this modified version of the program, but none were successfur due to Iack of familiarity with the CWEB language and code. Hence, the results from this modified version of spec are not used in the final analysis. The Fourier Quotient program performs quite we11 at finding the input velocities and velocity dispersions in the tests in this chapter and later diapters. Chapter 3

Arp Galaxies

There are two extreme theories for the formation of ellipticd galaxies. Toomre (1977) has suggested that all elliptical galaxies and spheroids of disk galaxies are the product of mergers and are made up of stars that were previously formed in diçks. The other theory predicts that the stars in elliptical galaxies were formed during gravitational collapse of a gas cloud. In the first of these extreme theories rnergers play a crucial roles in the formation of early-type galaxies and in the second theory they do not play a role at d.In order to understand the relative importance of interactions and mergers of galaxies in the evolution of galaxies we must know how often interactions occur and how galaxies are dected by them. The rnost likely place to discover old merged disks is in a goup where mergers are currently observed. The probability that galaxies in groups (and other dense regions) were in the same environment within the dpamical time of the gronp, several billion years, is very high. Past galaxy mergers can be studied by examining galaxies that show unusual features, such as greatly disturbed structure, high star-formation rates, and nuclear activity. For this study the selected galaxies have a high probability of a recent merger but are otherwise morphologicaUy normal. The sample of galaxies consists of E and SO galaxies in Arp groups that may have minor envelope distortions (e-g. shells, 'Yaint streamers", but not tails or plumes) but show no visible signs of dust, ionized gas, or young stars. The presence of these galaxies in groups or other dense regions makes it highly probable that they were recently in the same CHAPTER 3. ARP GfiAXZES 26 environment of fkequent collisions, and hence are exceptionally likely to have been created in a merger if that is the formation process. The existence of a kinematicdy distinct core subpopulation would be a signature of a merger and the presence of young stars or nuclear activity would be a signature of a recent merger. Counter- and co-rot ating cores, musual velocity dispersion profiles, minor axis rotation, and peculiar velocity fields are ail possible signs of a merger. Counter- and CO-rotating cores are found by examining the rotation curves. Minor axis rotation can also be detected from the rotation curves provided that the slit position is aligned with the minor axis. Evidence for unusual rotation cmes, minor axis rotation, and abnormal velocity dispersion profiles will be sought in this study. Peculiar velocity fields or unusual light-of-sight velocity distributions cmbe found by examining the broadening function. Since the Fourier Quotient program assumes that the broadening function is a Gaussian and this progam is used for the andysis of the Aqgalaxy data, peculiar velocity fields cannot be detected. The presence of HP emission may indicate recent star formation. Nuclear activity would also produce line emission and both HP (4861A) and [OIII] (4959 A and 5007A) are within the observed spectral region of the Arp galaxies. The analysis and cornparison of spectra in the core region and main body of early-type galaxies dows the study of the core dynamics and stellar populations. In $3.1 the observations and initial reductions are discussed. Extensive tests of the Wurier Quotient program with simulated data, stellar templates, and actual data are presented in $3.2. Long-slit test spectra are created with a rotation curve, velocity dispersion, and/or noise. The accuracy with which the Fourier Quotient program can determine the input velocity and velocity dispersion is discussed. Tests are performed with the stellar spectra to determine which template spectra are most suited to be used as templates for the galaxy spectra. F'ther tests with actual data are needed in order to determine the best procedure for analyzhg the galaxy spectra and are also presented in this section. The results fiom the Fourier Quotient program are discussed in 53.3. The rotation curves, velocity dispersion profiles, and models created to determine whether or not unusud kinematics could be detected are presented in this section. Unusual kinematics do not date a merger since they are long lived and therefore evidence for young stmand nuclear activity wiIl be sought in line emission in 53.4. The Faber-Jackson relation for the Arp gdaxies is compared to normal galaxies in 53.5 to determine if these galaxies appear unusual. The results of this chapter are summarized in the last section (53.6).

3.1 Data and Initial Reductions

Early-type galaxies that show no signs of stxformation, ionized dust, or young stars were chosen from the Atlas of Peculiar Galaxies (Arp 1966). Galaxies that showed obvious signs of current interactions were excluded since the aim of this study is to examine morphologically normal galaxies. This sample of galaxies contains only a fkaction of those galaxies that satisfy the above criterion and the sample size in this study is limited by the available observing time. The galaxies in this study corne from a Mnety of environments ranging from a possible isolated galaxy (Arp 165), to pairs of galaxies (e.g. Arp 167 and SPI), groups of galaxies (Arp 327) and a triple within a cluster (hp105). The results of a search for galaxies within a radius of 1.0 and 0.5 Mpc (Ho = 50 kms-' Mpc-') using the NED' database (Helou et al. 1991) is dispiayed in Table 3.1. The galaxies found in the NED database are not necessarily at the same redshift as the Arp galaxy studied, since velocity information is not adable for aU objects. A bias most likely exists for a larger nurnber of galaxies to be found around nearby Arp galaxies, and those galaxies that have been well studied. Most of the Arp galaxies in this study reside in smali groups.

3.1.1 Observations

Long-dit spectra were obtained at CFHT on the nights of 1990 UT February 13- 16 with the Herzberg spectrograph at the Cassegrain focus by R. G. Carlberg and

- 'The NASA/IPAC Extragdactic Database (NED) is operated by the Jet Propulsion Labora- tory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. CRAPTER 3. ARP GALAXIES

Table 3.1: Environment of the Arp Galaxies

Arp NGC/IC Vh N(l.O) N(0.5) Environment 105 NGC 3561B 8811 55 (6) 37 (6) TRIPLE in AbeIl 1185 106 NGC 4211 6744 9 (1) 3 (1) PAIR in group? 123 NGC 1889 2482 26 (1) 5 (1) PAIR in group? 136 NGC 5820 3252 20 (1) 9 (0) tripIe? 165 NGC 2418 5057 7 (0) 5 (0) isolated? 167 NGC 2672 3849 17 (1) 8 (1) PAIR, 174 NGC 3068A 6322 3 (2) 2 (1) PAIR 228 IC 162 5132 8 (1) 7 (1) group 315 NGC 2832 6869 24 (1) 16 (1) PAIR in group 316 NGC 3193 1379 96 (4) 35 (3) CROUP 327 NGC 1875 8997 5 (1) 4 (1) GROUP NOTES. Col. (1).- Arp designation. Col. (2). - NGC or IC designation. Col. (3). - Heliocentric velocity nom the RC3 Catalog. Col. (4). - The number of galaxies found within a 1.0 Mpc radius of the Arp galaxy under study from the NED database. The number of galaxy pairs, galaxy triples, and galaxy groups found within this radius is indicated in brackets. Col. (5). - The number of galaxies found within a 0.5 Mpc radius of the Arp gdaxy under study fiom the NED database. The number of galaxy pairs, galaxy triples, and galaxy groups found within this radius is indicated in brackets. Col. (6). - The 'cminimum"environment in which the galaxy resides as determined from the NED database. Redshifts for some of the nearby galaxies are unavailable and therefore it cannot be determined if these galaxies are actually part of a group. Uppercase letters indicates that this is the environment as reported by NED. Low- ercase letters indicates that the environment was determined by the author from the NED positions and redshifts. CWTER3. ARP GALAXIES 29

C. Pritchet. The wavelength coverage is fiom 4387A to 5906A with a dispersion of 1.49A per pixel. Two slit widths, 2" and 0075, were used and their respective spectral resolutions are 5.8A and 2.2A. The length of the dit is 520". The galaxies were observed at two slit positions, with two or more 900 second exposures using the SAICl CCD. The positions of the slits were chosen to include a nearby cornpanion if present and are not necessarily along the major and minor axes. Taide 3.2 contains information about the O bse~vationsfor each of the galaxies including NGC designations, exposure times, and slit positions. The seeing was typically - 1" for the obsedg run. Several ternplate stars were observed during this run and are listed in Table 3.3 along with theK exposure information and spectral mes. Figures 3.1 and 3.2 show SERGJ band images of the gdaxies. These images are fkom the Digitized Sky Survey? and were acquired using SkyView3. The images are 340" by 340" with North at the top and West to the right of the images.

3.1.2 Reductions

The CCD reductions were performed using IRAI?. The spectra were bias-subtracted, trimmed and flat fielded using dome flats. The alignment of groups of fiames along the wavelength axis is better than 0.3 pixel (30 km s-') and the alignment along the dispersion axis better than 0.6 pixels. Cosrnic rays were removed from the images and the cleaned Mages of each object with the same slit width and position were summed. The stellar spectra are found to be rotated slightly with respect to the CCD columns, that is the spectra are not aligned perfectly with the columns. The amount of rotation is determined by looking at stars fiom nights 1to 3. The average amount of rotation is 0.101 & 0.028 degrees. The stellar and galaxy images are rotated by

2Based on photographic data obtained using Oschin Schmidt Telescope on Palomar Mountain. The Palomar Obsemtory SbSurvey was funded by the National Geographic Society. The Oschin Schmidt Tdescope is operated by the California Institute of Technology and Palomar Observatory. The plates were processed into the present compressed digital format with their permission. The Digitized Sky Survey was produced at the Space Telescope Science Institute (ST ScI) under U. S. Govenunent grant NAG W-2166. 3SkyView is supported by NASA ADP grant NAS 5-32068. Table 3.2: Exposure information for the Arp Galaxies

image NGC/IC night slit (") Pos Angle exposures SIN ArplOSa NGC 3561B & A 0.75 -4.2 5 8 ArplO5b NGC 3561B ArplO6a NGC 4211 & comp Arpl06b NGC 4211 & comp ArplOGc NGC 4211 Arp123a NGC 1889 Arp123b NGC 1889 Arp136a NGC 5820 Arp136b NGC 5820 Arp136c NGC 5820 A.rp136d NGC 5820 Arp165a NGC 2418 & comp Arpl65b NGC 2418 & faint comp Arp165c NGC 2418 Arp165d NGC 2418 & comp Arp167a NGC 2672 & 2673 A.rp167b NGC 2672 Arp l74a NGC 3068A & B Arp l74b NGC 3068A Arp228a IC 162 Arp315a NGC 2832 & 2831 Arp315b NGC 2832 Arp316a NGC 3193 Arp316b NGC 3193 Arp316c NGC 3193 Arp316d NGC 3193 Arp327a NGC 1875 & comp Am327b NGC 1875 NOTES. Col. (1). - The Arp number with an added letter to distinguish the different slit positions and widths. Col. (2). - The NGC or IC number of the main galaxy and a cornpanion galaxy if present along the slit. Col. (3). - The night the observations were made. 1 = 13 February 1990, 2 = 14 February 1990, etc. Col. (4). - The dit width in arcseconds. Col. (5). - Position angle of the slit in degrees. A position angle of O degrees is south and 90 degrees is west. Col. (6). - The number of 900 second exposures summed. In a few cases partial exposures were made and are indicated as a haction. * indicates that the exposures were 1200 seconds each instead of 900 seconds. Col. (7). - The S/N ratio of the central spectrum of the summed image based on the method described by Nella et al. (1995) (see 52.3). C'rnR3. ARP GALAXIES

Table 3.3: Exposure information for the Stellar Templates

Star Spectrum Star Spectral Type Night SLit Width ( ") Exposure 053 HR3093 G8 III 1 0.75 1 064 HR3905 K2 III 1 0.75 1f 078 HR.4668 K0.5 TIIb 1 0.75 1 091 HB.4668 K0.5 IIIb 1 0.75 1 095 HR5787 G8.5 III 1 0.75 1f 122 HD19445 F2 2 0.75 1 163 SA029165 GO 2 0.75 1 175 HR.5940 K1 IV 2 0.75 1 230 HR2119 KO II 3 0.75 1 233 HD19445 F2 3 0.75 3 257 HR3905 K2 III 3 0.75 1f 284 HR5787 G8.5 III 3 2.00 2oFt 335 HR2119 KO II 4 0.75 1 336 HR.2119 KOII 4 2 .O0 30t NOTES. Cd. (1).- Spectrum designation. Col. (2). - Harvard Revised number (HR), Henry Draper Catalog (HD)number or SA0 Catalog number. Col. (3). - Spectral type fiom Bright Star Catalog, 5th Edition (for HR stars) or £rom Smithsonian Astrophysical Observatory Star Catalog (HD19445 and SA029165). Note that HD19445 is a flux standard and will not be used as a template in the aaalysis. Col. (4). - The night the observations were made. 1 = 13 February 1990, 2 = 14 February 1990, etc. Col. (5). - The slit width in arcseconds. Col. (6). - Exposure time in seconds. = 10% transmisivity of neutrd density filter. = 5% transmisivity of neutral density filter. ' = star was trailed across SM. CWTER3. ARP GALAXIEiS

O - a Arp 136

Figure 3.1: Images of Arp galaxies 105, 106, 123, 136, 165, and 167 from SkyView. Arp:

#k Arp 315

Figure 3.2: Images of Arp galaxies 174, 228, 315, 316, and 327 from Swiew. Note that Arp 174 is slightly off center. C&APTER 3. ARP GALAXlES 34

0.1 degree to correct this for this slight mis-alignment . The IRAF program Identify is used to &d the prominent lines in the Cd/Ne arc spectrum. The distortion maps appear to be constant throughout the run, therefore the entire observational run is transformed using a single map. The images are traasposed for the Fourier Quotient program. A log X scale is required for the Fourier Quotient program and a X scale for the IRAF program rvO and brightness profiles. The variation in focus perpendicular to the slit as well as dong the dit is believed to be small and therefore is not accounted for.

3.1.3 Background Subtraction

The following procedure is used to subtract the sky background from the galaxy images. One or two background regions for each image, usually chosen to be on either side of the galaxy, may be specified and then averaged. Each region is block averaged and the average of these two regions is taken. A 5th order Chebyshev polynomial is fit to this average background spectium. This smooth background curve is subtracted fkom each line or spectnun. This procedure wilI not remove the night sky lines. To identify the location of the sky lines the relative error between the smooth background and the average background is found for each pixel. If the relative error is greater than f30% the value of the pixel(s) in the galaxy spectrum is replaced by linear interpolation. Note that this method will not remove faint sky lines, but these features are smdenough that they will not have a large effect on the results especially when the signal from the galaxy is strong. 3.2 Tests of the Fourier Quotient Program

3.2.1 Tests with Simulated Data

In this section several test images are created from one of the steIlar spectra. In these tests a rotation curve, constant velocity dispersion, and/or noise are added. In all cases the template spectrum used in the analysis is the original steilar spectnun £kom which the test images are created unless otherwise specified.

Zero velocity, zero velocity dispersion, and zero noise

The spectnun of star HR 3903 (image 053) is replicated 100 times to form the test image (a simulated long-slit spectnun). DifTerent intenml widths along the spatial direction of the slit are specified that vary in width from 1row to 5 rows for a total of 28 intervals. The rows of spectra within an interval are added and the program fin& the velocity and velocity dispersion of this sum. Interval widths are set to 1 near the center of the galaxy, and increase with increasing distance from the center. This is the same procedure that would be used for real long-slit spectra with high SIN ratio near the center of the galaxy, and low S/N ratio near the periphery. The velocity amplitudes found by the Fourier Quotient program are less than IO-^ kms-' and well within the errors reported. The velocity dispersions are less than 0.04 km s-? In some cases the velocity dispersion errors reported by the Fourier Quotient program are less than the velocity dispersion, but all of the velocity dispersions are very close to zero. The measured values of the iine strength are very close to 1 as expected. The results are dependent on the number of rows added but do not vary significantly. The Fourier Quotient program is successful at hding the input values for the zero velocity, zero velocity dispersion, and zero noise test.

Zero velocity and zero noise

In this test a velocity dispersion of 100 km s-' is added to the test data by convolving the spectrum with a Gaussian. The velocities found are near zero, but not quite within the errors, -0.06 f 0.04 kms-', and vary by less than 0.003 kms-' for the CHAPTER 3. ARP GALAXlES 36

different interval widths. The velocity dispersions found are consistently lOO.28f 0.06 km s-' for the different intenml widths. The line strengths are slightly below 1 at 0.9984 f 0.0004. The low measured hestrengths are due to the introduction of velocity dispersion. A second test is performed using an input velocity dispersion of 150 km s-' . A velocity of -0.12 km s-' is consistently found with the error varying between 0.16 and 0.20 kmsSL.The velocity dispersions are consistently 150.3 f 0.2 km s-? This test confirms that increasing the velocity dispersion lowers the line strength slightly; the line strength is found to be 0.997 f 0.001. In both of tests there are some minor variations in the results for the different interval widths. The Fourier Quotient program is successful at finding the input velociw dispersion in the test with no velocity or noise added.

Zero velocity dispersion and zero noise

This test image has zero velocity dispersion, zero noise, and non-zero velocities. A rotation curve is created with the following parameters: the systernic velocity, vo = 1000 km s-', the rotation velocity, vrd = 200 km s-' and dvldy = 20 km s-' pixel-' at the center. The shifting of the spectrurn in amounts that are not a multiple of the pixel width and adding rows will cause an unintentional velocity dispersion. The velocities found are lower than the input velocities, but are within 5 kms-' and the average reported error in the velociw is 0.20 kms-'. The velocity dispersions found are between 17.5 =t 0.8 and 45.0 k 0.8 kms-' and have a mean value of 37.6 kms-'. The line strengths Vary between 0.974&0.003 and O.987f 0.001. The Fourier Quotient program fmds slightly lower velocities than the input values, but otherwise performs well at recovering the rotation curve.

Zero noise

A test image with a constant velocity dispersion of 100 kms-' and the same rotation curve as the previous test is created. This test Mage is analyzed with variable interval widths as in the other tests. The velocities found are on average 3.0 kms-' too low with a maximum clifference of 4.6 km s-'. The velocity dispersions range £rom 102 to CHAPTER3. ARP GAL-S 37

110 km sa' with an average value of 107 km s-l. The average line strength is slightly below 1 at a due of 0.983. The initial velocity or starting point specified for the Fourier Quotient program is changed fkom 800 to 850 kms-' in the next test. The velocities are within 0.01 km s-' and the velocity dispersions are within 0.05 km s-' of each other for these two tests with different starting velocities. This indicates that the Fourier Quotient program is not highly dependent on small Mnations in the starting values. More tests with respect to the starting point will be discussed

later. The test image is &O analyzed with interval widths of one and the results are consistent with the variable interval width results. In the last two tests with this image a sky line is assumed to be present. The region where the sky line is assumed to be present is masked out and interpolated by the Fourier Quotient program. Comparing with the test where no sky lines are assumed to be present, it is found that the velocities are within 0.3 km s-' of each other and the velocity dispersions are within 4 kms-l. The velocities found are again on average 3.0 kms-' lower than the input values and the mean error increases to 2.2 kms-'. The velocity dispersions are on average 7.3 kxn s-' too high and the mean error is 3.0 km s-l. Similar results are found for the tests using an initial velocity of 850 km&. The introduction of the assumed sky line has Sected the velocity dispersions more than the velocities. The real and imaginary parts of the Fourier Quotient are shown in Figure 3.3. Recd that fiom Equation (2.5) the real part of the Fourier Quotient is proportional to the exponential of the velociw dispersion term and the cosine of the velocity term. The imaginary term is proportional to the exponential of the velocity dispersion term and the sine of the velocity term. IR comparing the plots of the real and imaginary parts of Fourier quotient, for both assuming no sky lines and assuming a sky line, the introduction of the sky line increases the noise present in these plots (see Figure 3.3). The velocities reported by the Fourier Quotient program are slightly Iower than the input values and the velocity dispersions found are slightly higher. Slight changes in the starting point do not appear to affect the results. The presence of sky lines vdincrease the uncertninty in the resuits, but overd the values are consistent with CHAPTE23 3. ARP GALAXIES

s53n0-nl galaxy interval 1 s53nO.d galaxy intervol 1

s53n0 galaxy intervol 1 s53n0 galoxy intervol 1

Figure 3.3: Fourier Quotient plots for the tests with no noise assuming no sky lines and assuming a sky Iine for the first interval. The top two plots are for the test assumùig no sky lines. The bottom two plots assume that there is one sky line. The left two plots are the real part of the quotient, G(k)/S(k)versus wavenumber k. The right two plots are the imaginary part of the quotient versus wavenumber k. The fit is shown with a dashed curve. The dashed vertical Iines indicate the region of wave numbers used for the fit. Note that the quotient is no longer smooth in the bottom two plots, the test assiiming a sky line. CWTER3. ARP GALAXES the no sky line resdts.

Noise tests

In this set of tests noise is added to the same spectnun that is used in the previous test. The S/N ratio is calculated based on the method described by Nella et al. (1995) (see 82.3). Table 3.4 summarizes the resdts fiom these tests for vaxiable inted widths- The average rneasured velocity is lower than the input values for low SIN ratios. The standard deviations of the mean of the velocities are comparable to the mean error if the S/N ratio is low. The mean velocity dispersion tends to overestimate the input velocity dispersion and increases as the noise increases. As the noise increases the mean line strength decreases. If the errors in the velociw and velocity dispersions are too hi&, the values reported by the Fourier Quotient program are suspect. Figures 3.4 to 3.6 are similar to the plots of Figure 3.3 and show the effect of the mglevels of noise on the Fourier Quotient. In Figure 3.4 the real and irnaginary parts of the Fourier Quotient are plotted versus the wavenumber for the 100 test, a iow noise test. As with the no noise test assuming a sky line is present adds more noise to the Fourier Quotient (bottom plots). This is also tme for the 500 test (S/N = 11.4) but it is less noticeable (see Figure 3.5). In Figure 3.6 only the plots of the real part of the Fourier Quotient versus wavenumber axe shown for the tests 1000, 2000, 3000, and 5000 (S/N = 6.3, 2.9, 1.9, and 1.1) assuming no sky lines. As expected with the increase in noise, the Fourier Quotient program has greater difEculty in finding the correct solution. It should be noted that even though the velocities found by the program are quite close to the input values, especially in the high noise tests, this agreement is most likely due to the initial velocity guess being close to the input velocity. From a visual inspection of these plots any solution from the 5000 test and

&O the 3000 test is suspect. These plots are included to be an aid in judging the reliability of the results in low S/N ratio spectra (e.g. the Abell2390 galaxies). Recall that the template is a perfect match to the test spectra and mismatched templates will also add to the uncertainty in the results. CHAPTER 3- ARP GALAXTES

Table 3.4: Cornparison of non zero velocity tests (variable interval widths). ------test SIN Av O*. 6v Q a, ba 1 or SI O 57.1 3.02 1.08 0.22 107.3 2.3 0.3 0.983 0.005 0.002 50 49.7 3.08 1.35 0.70 107.5 2.5 0-9 0.982 0.005 0.006 100 38.1 2.74 1-58 1.33 108.2 2.1 1.8 0.980 0.009 0.011 500 11.4 4.16 5.05 6.63 115.7 7.4 8.6 0.919 0.041 0.047 1000 6.3 3.29 15.48- 13.31 119.7 13.8 17-2 0.808 0.067 0.077 2000 2.9 -7.75 22.44 28-88 115.4 46.8 47.1 0.647 0.182 0.113 3000 1.9 -22.47 71.73 56.86 143.7 77.6 80.2 0.600 0.230 0.167 5000 1.1 -23.80 160.67 177.38 192.9 109.0 207.1 0.641 0.384 0.273 - - NOTES. Col. (1). - Test name and amount of noise added in DU to the spectnun. Col. (2). - SIN ratio. Col. (3). - The mean of the Merence between the input velocity and measured velocity in km s-' . Col. (4). - The standard deviation of the mean of the ciifference between the input velocity and measured velocity in km s-? Col. (5). - The mean error of the velocity reported by the Fourier Quotient program in km s-l- Col. (6). - The mean velocity dispersion measured in km s-l. Recall t hat the input value is 100 km s-'. Col. (7). - The standard deviation of the mean velocity dispersion measured in km s-l. Col. (8). - The mean error in the velocity dispersion reported by the Fourier Quotient program in km s-'. Col. (9). - The rnean line strength as reported by the Fourier Quotient program. Col. (10). - The standard deviation of the mean line strength as reported by the Fourier Quotient program. Col. (11). - The mean error in the line strength as reported by the Fourier Quotient program. CHAPTER 3. ARP GALrnS

s53n100.nI golaxy interval 1 s53n 100.nl galaxy intervat 1

s53n100 galaxy interval 1 s53n100 galaxy interval 1

Figure 3.4: Fourier Quotient plots for the test 100 (S/N = 38.1) assuming no se lines and assuming a sky line for the first interval. The top two plots are for the test assuming no sky lines. The bottom two plots assume that there is one sky line. The left two plots are the real part of the quotient, G(k)/S(k)versus wavenumber k. The right two plots are the irnaginary part of the quotient versus wavenurnber k. The fit is shown with a dashed curve. The dashed vertical lines indicate the region of wave numbers used for the fit. Note that the quotient is no longer as smooth as in the bottom two plots, the test assuming a sky line. CHAPTER 3. ARP GALAXES

s53n500.nl galaxy interval 1 s53n500.nl galaxy interval t

~5311500galaxy interval 1 s53n500 galaxy interval t

Figure 3.5: Fourier Quotient plots for the test 500 (SIN = 11.4) assuming no slq hes and assuming a sky line for the fkst interval. The top two plots are for the test assuming no sky lines. The bottom two plots assume that there is one sky line. The left two plots are the real part of the quotient, G(k)/S(k)versus wavenumber k. The right two plots are the imaginary part of the quotient versus wavenumber k. The fit is show with a dashed cuve. The dashed vertical hes indicate the region of wave numbers used for the fit. Note that the quotient is slightly noisier in the bottom two plots, the test assuming a sky line. s53n1000.nl galaxy interval 1 s53n2000.nl galoxy interval 1 I .I

s53n3000.nl galaxy interval 1 s53n5000.nl galaxy interval 1

Figure 3.6: Fourier Quotient plots for the tests 1000, 2000, 3000, and 5000 (SIN = 6.3, 2.9, 1.9, and 1.1) assuming no sky lines for the first intenml. The real part of the quotient, G(k)/S(k)versus wavenumber k. The dashed vertical Lines indicate the region of wave nurnbers used for the fit. This is the first interval of each set of spectra. The values found for the velocity and velocity dispersion of each of the tests are: 1000 test - 817 f 12 km s-l and 133 14 km s-l; 2050 test - 824 I 21 km s-l and 110 f 31 kms-'; 3000 test - 814 f58 km s-' and 320 f 62 km s-'; 5000 test - 815 & 37 km s-' and 64 I 85 km s-' respectively. The input values are 804 and 100. The velocities found in the higher noise tests can be close to the true value since the initial guess is quite close to the true value and a local minimum may be found. C&APTER 3. ARP GALmS 44

The variable intervd widths are chosen to simulate the interval widths that might be used for a real galaxy spectnun where the intensity dong the slit drops off near the outer parts of the galaxy. Several rows will be added to produce higher SIN ratios at the outer parts of the slit, 2nd single interval widths will be chosen near the center of the galaxy. Another set of tests is performed with the same images and single intenml widths. The rdtsare presented in Table 3.5. The main merence between the variable intenml width tests and the single interval width tests is that as the S/N ratio decreases the results of the single interval tests are more inaccurate. This is to be expected since the variable interval width tests artificially increase the S/N ratio by adding spectra. For the tests where there is a si@cant amount of noise the mean error in the velocity is slightly higher than the standard deviation of the mean velocity. This is &O true of the velocity dispersion. In the highest noise tests the mean errors are very Iarge.

Table 3.5: Cornparison of non zero velociw tests (single inter4 widths).

------test S/N Av a*, dv O OU da 1 01 61 O 57.1 3.05 1.08 0.25 107.7 2.0 0.3 0.982 0.004 0.002 50 49.7 3.10 1.42 1.11 107.8 2.5 1.5 0.981 0.007 0.009 100 38.1 2.89 1.93 2.15 108.5 2.9 2.9 0.979 0.011 0.017 500 11.4 3.42 7.37 10.58 114.0 11.9 14.2 0.888 0.059 0.068 1000 6.3 1.75 18.90 21.37 116.1 24.4 29.8 0.764 0.106 0.111 2000 2.9 -7.30 48.86 52.66 132.9 74.2 84.4 0.712 0.262 0-192 3000 1.9 -18.92 117.26 124.20 152.2 109-4 230.5 0.623 0.326 0.258 5000 1.1 24.49 283.24 466.12 189.3 164.6 1074.6 0.738 0.468 0.460 NOTES.See Table 3.4 for a description of the columns.

Table 3.6 compares the results of the no noise test to the tests with noise. For each interval the velocity, velocity dispersion, and line strength of the zero noise test is subtracted fiom the noise test. The mean and standard deviation of these differences are also shown in this table. The last column contains the number of intervals for which the Fourier Quotient program failed to find a solution. As more noise is added the mean velocity and velocity dispersion found is higher than the no noise cases, and this difference increases as the noise increases. The opposite is true for the line C'TER3. ARP GALAXTES 45

strength which decreases as the noise increases. Comparison of the SIN ratios and errors of these tests with the analysis of the spectra of the galaxies in this study indicates that the errors found in the tests are a lower limit. This is to be expected since the templates are not a perfect match to the galaxies.

Table 3.6: Comparison of non zero velocity noise tests with the zero noise tests (single interval widths) . - - - test S/N Av ~AV A0 UA@ Al CAL Nhit 50 49.7 0.05 0.78 -0.1 1.4 0.000 0.006 O

NOTES. Col. (1). - Test name and amount of noise added in DU to the spectnun. Col. (2). - SIN ratio. Col. (3). - The mean of the ciifferences in the velocities of the tests with noise and without noise in km s-'. Col. (4). - The standard deviation of the mean of the Merences in velocities in km s-l. Col. (5). - The mean of the clifferences in the velocity dispersions of the tests with noise and without noise in km s-' . Col. (6). - The standard deviation of the mean of the differences in velocity dispersions in km s'l. Col. (7). - The mean of the Merences in the line strengths of the tests with noise and without noise in km s-l. Col. (8). - The standard deviation of the mean of the difFerences in line strengths. Col. (9). - The number of intervals for which the program failed to find a solution.

The Fourier Quotient program performs well at finding the velocity and velocity dispersions of test spectra. As the SIN ratio decreases there is a tendency for the measured velocity dispersion to be an overestimate of the real value. This tendency was also found by Kormendy & Illingworth (1982). The reported uncertainties agree fairly weU with the standard deviations of the velocities and velocity dispersions. Even though the program performs weU at low S/N ratios caution is advised if the spectra are too noisy (SIN < 3). 3.2.2 Tests with TempIates

The velocity, velocity dispersion, and line strength of each star are measured usbg each star as a template. This is done for the following reasons. The velocities of the stars relative to one another are needed in order to compare the results of using different template stars with the galaq spectra. It is also desirable to know if a star has an unusual amount of broadening, which can be interpreted as a velocity dispersion, since ideally the template star should be typical for its type. The relative line strengths of the stars are also compared with one another as another check of the program. Two analyses are perfonned, one assuming sky lines are present the other assuming no sky lines. The velocities of the stars are measwed relative to the star 053." The lRAF program NO is also used to determine the relative velocities of the stars. The velocity results from the Fourier Quotient program assuming no sky lines and assuming 5 sky lines, and the results fiom rvO are presented in Table 3.7. The velocities fond using the different templates are in good agreement with one another. Note that these velocities are the observed velocities and have not been corrected for the motion of the Earth and therefore spectra of the same star (e.g. 078 and 091) will have dinerent velocities. The velocities found using these methods agree quite well with each other. Excluding the spectra of the flux standard, the Fourier Quotient resdts for the rest of the template spectra are within about 1 kms-1 of each other. The rvO results do not agree quite as well, but are within 10 kms-' of the Fourier Quotient results. TabIes 3.8 and 3.9 contain similar information for the velocity dispersion and line strength, respectively for the Fourier Quotient program only. The velocity dispersions Vary more than the velocities found using the different templates (Le. > aa). The agreement of the velocity dispersions found using the Fourier Quotient program assuming sky lines and assuming no sky iines is not as good as the velocities, there are clifferences of up to 28 kms-'. Note that the amount of broadening can be

* ~otethat the velocities are measured relative to a preliminary velocity meanirement of star 053 and therdore 053's velocity is not exactly zero relative to this prelirninary measurernent. CKAPTER 3. ARP GALAXZES 47

negative when a star with a higher velocity dispersion is used to determine the velocity dispersion of a star with a lower velocity dispersion. The mean velocity dispersions of the same star fkom Merent spectra are in good agreement. The spectra 284 and 336 were taken with a 2% slit and the measured velocity dispersions of these spectra are larger than the narrow slit spectra. This is due to an increase in the instrumental broadening caused by the larger slit. The early-type stars 095 (G8.5 III), 053 (G8 III), 163 (GO) have lower velocity dispersions than the later type stars. This relationship between spectral type and velocity dispersion was also noted by Kormendy & Illingworth (1982). None of the templates has an unusual veiocity dispersion as they ad follow the general trend of increasing velocity dispersion with later spectral types. The "best" template for each galaxy will be chosen by examining the errors in the velocity dispersions reported the Fouxïer Quotient program. Ideally one would like to create a composite spectm made of difFerent template stars to simulate the difFerent stellar populations found in a galaxy. The program used in this study does not dow for multiple templates to be used as input. The line strengths found assuming sky lines and assuming no sky lines are consistent. Note that the flux standard HD19945 (spectra 122 and 233) has the lowest line strength. The agreement of the mean line strength of the dïfferent spectra of the same star is very good (within 0.01 exduding HD19945). Table 3.7: The mean velocity of each star from all of the templates.

Star Spectrum af (no lines) fff (5 lines) nt0 a CiJ Ü cii Û OU 053 0.77 0.47 0.53 0.61 0.04 0.05 064 -44.12 0.73 -44.88 0.87 -34-69 0.95 078 -151.18 1.01 -151.24 1.41 -154.15 0.94 091 -193.75 1.83 -193.73 2.08 -198.89 1-61 095 -107.31 1.06 -107.81 1.25 -107.98 1-03 122 -245.49 3.69 -239.88 3.38 -239.81 3.38 163 -89.99 1.52 -91.05 1.29 -94.09 1.16 175 -177.35 0.91 -177.47 1.28 -179.69 0.90 230 40.44 0.73 40.44 0.89 42.21 0.86 233 -216.62 2.77 -210.32 1.57 -218.98 3.45 257 -44.92 0.84 -45.85 1.17 -46.31 0.99 284 -191.26 1.16 -191.09 1.14 -194.35 1.04 335 9.80 0.85 9.45 0.96 9.33 0.86 336 -11.04 0.62 -11.49 0.64 -10.98 0.60 - - NOTES. Coi. (1). - Template imagefspectrum designation. Cols. (2) & (3). - Mean and standard deviation of the velocity found fkom all of the stars using the Fourier Quotient method and assuming no sky lines. Cols. (4) & (5). - Mean and standard deviation of the velocity found fiom dl of the stars using the Fourier Quotient method and assuming 5 sky lines. Cols. (6) & (7). - Mean and standard deviation of the velocity found from all of the stars using rvO in IRAF. CHAPTER3. ARF GALAXIES

Table 3.8: The mean velocity dispersion of each star relative to dl of the other templates.

Sta Spectnim fn (no lines) fff (5 lines) - t~ 0, a cc?

NOTES.Col. (1). - Template image/spectnun designation. Cols. (2) & (3). - Mean and standard deviation of the velocity dispersion found f?om dl of the stars using the Fourier Quotient method and assuming no sky lines. Note that the velocity dispersion is relative to the template used and can be negative if a star with a higher velocity dispersion is used to find the amount of broadening of a lower velocity dispersion star. Cols. (4) & (5). - Mean and standard deviation of the velocity dispersion found £rom aU of the stars using the Fourier Quotient method and assuming 5 sky lines. CHAPTER 3. ARP GALAXIES

Table 3.9: The mean line strength of each star from all of the ternplates.

Star Spectrum fff (no lines) fff (5 lines) ;ii Cr* 7 n*

NOTES. Col. (1). - Template image/spectrum designation. Cols. (2) & (3). - Mean and standard deviation of the line strength found £rom all of the stars using the Fourier Quotient method and assuming no sky lines. Cols. (4) & (5). - Mean and standard deviation of the line strength found from ail of the stars using the Fourier Quotient method and assuming 5 sky lines. The velocity dispersions found by each template are ranked in order to find the stars with the lowest velocity dispersion (Table 3.10). The sum of the ranks and the rank of the sum are shown for the velociw dispersions and line strengths for the Fourier Quotient tests. The three stars with the lowest velocity dispersion are 053, 095, and 163. These three stars ako have smd luie strengths in cornparison to the other stars.

Table 3.10: Ranks of the velocity dispersion and line strength of the templates.

velocity dispersion üne strength StarSpectrum Sp.Type nolines 5 lines no lines 5 lines sum rank sum rank sum rank sum rank 053 G8 III 31 2 13 1 47 4 38 3 064 K2 III 107 8.5 82 6 130 10 123 9 O78 K0.5 IIIb 55 4 106 8 79 6 89 7 091 K0.5 II& 91 7 66 5 90 7 77 6 095 (28.5 III 23 1 40 2 29 2 31 2 163 GO 43 3 43 3 13 1 13 1 175 K1 IV 119 10 109 10 104 8 104 8 230 KO II 74 6 87 7 44 3 52 4 257 K2 III 107 8.5 107 9 117 9 124 10 335 KO II 65 5 62 4 62 5 64 5

The relative velocities and velocity dispersions of the template spectra are found to agree weil with each other. These relative velocities will be used to compare the results of analyzing the galaxy spectra with different templates. Tests with the different templates and and broadened test spectra wiil be done in the next section.

3.2.3 Tests with Broadened Templates

The effects of template mismatch are further explored in this section. Ln this set of tests each nmow dit template is broadened with a veiocity dispersion of 100, 150, 200, 250, or 300 kms-'. The test spectra are also shifted so that the velocity is 100 km& relative to the original template from which the spectnun was created. No noise is added to these test spectra. Each test spectnun is analyzed using the Fourier Quotient program with each of the templates. Figure 3.7 summarizes the velocity CWTER3. ARP GALAXIES 52 results for these tests. The velocities found by the Fourier Quotient program have been nomalized to the template 053 and the ratio of this normalized velocity with the input velocity is plotted versus the input velocity dispersion. If two template images are of the same star the color of the symbol used is the same (e-g. 230 and 335). The panels are arrangecl in spectral sequence fkom left to right and top to bottom, with the earliest star (GO) in the upper left panel and the latest star (K2 III) in the lower rïght panel. The errors in the measured velocities range between 1.2 and 15.4 km s-' with a median of 4.5 km s-' for mismatched templates. If the template used to determine the velocity is the same as the one used to create the test spectrum the errors are much lower. For velocity dispersions of 200 kms-' or less the measured velocities axe within 4% of the input values. As the velocity dispersion increases so does the difference between the input and measured velocities (and the errors reported by the program). Templates with similar spectral types tend to produce better results as expected. Figure 3.8 is a plot of the ratio of the measured and input velocity dispersions versus the input velocity dispersion. The errors in the measured velocity dispersion range between 1.6 and 16.3 km s-' with a median of 5.0 km s-', if the template is a mismatch. At large values of the input velocity dispersion the rneasured velocities are within 5% of the input values. At low values the measured velocity dispersions can Vary by as much as 17% and the measwed velocity dispersion tends to overestimate the input values. This result was &O found by Schechter & Gunn (1979). When the early-type stars (053, 163, and 095) are used as templates to determine the velocity dispersion lower values are measured as compared with the results using later type stars as templates. The template stellar spectra 078 and 335 give the largest velocity dispersions at high input velocity dispersions. At low values for the input velocity dispersion templates 053, 163, and 095 give the largest measured velocity dispersion. In the tests presented in 54.3, the measured velocity dispersions agree better with the input values than the tests in this chapter, because the dispersion of the Arp spectra is 1.48~K/~ixelor 87 kms-' and a typical Abell 2390 galaxy spectnim has a dispersion of 0.?18K/~ixel or 42 km&. The higher dispersion spectra can CHAPTER 3. ARP GALAXIES 53

be broadened more precisely and the velocitg and velocity dispersions can thus be determineci more accurately.

input dispersion (km/s)

Figure 3.7: The ratio of the measured veiocity to the input velocity versus the input velocity dispersion for the test spectra created fkom the stellar templates. The velocities have been nomalized to the template 053. In each panel the results fkom a Srent set of test spectra created from the indicated ternplates are presented. Each test spednim is analyzed with all the template spectra and their results cm be distinguished with the different symbols indicated next to the template. For example, the resdts from template 163 are represented by a blue square. The results of 64 (solid lines) and 257 (dotted lines) are combined in one panel for presentation purposes. The measured velocities agree well with the input values, especially at low velocity dispersions. C-R3. ARP GALAXlES

input dispersion (km/s)

Figure 3.8: The ratio of the measured velocity dispersion to the input velocity dispersion versus the input velocity dispersion for the test spectra created from the stellar templates. In each panel the results &om a different set of test spectra created from the indicated templates are presented. Each test spectrum is analyzed with aU the template spectra and their results can be distinguished with the difïerent symbols indicated next to the template. For example, the results fiom template 163 are rep resented by a blue square. The resdts of 64 (solid lines) and 257 (dotted lines) are combined in one panel for presentation purposes. At Iow velocity dispersions the tendency for early-type stars to have lmer velocity dispersion relative to the later type stars can be seen. CKAPTER 3. ARP GALAXIES 55

From the tests in this section it can be seen that the rotation curves will not be greatly affecteci if there is a mismatch between the template and galaxy spectra. The velocities found using the different templates agree well with one another. This is to be expected since the positions of the hes do not change with spectral type. As the velocity dispersion increases the agreement between the input and measured velocities decreases as expected since the spectral lines are much broader. On the other hand, the velocity dispersions are affected more by a mismatch. This is in part due the trend that early-type stars appear to have a lower velocity dispersion than the later type stars. There is also an increase in the difference between the input and measured velocity dispersions at lower velocity dispersions which is expected since the dispersion of the spectra is low. To obtain accurate velocity dispersions the galaxy spectra should be analyzed with all of the template spectra and the results for the best match used in the final analysis. CHAPTER 3. ARP GAL-S

3.2.4 Tests with Actual Data

In this section several tests are done with actud data to determine the best way to analyze the gdaxy spectra. Since the intensity of a galaxy Mnes with radius and adjacent spectra along the slit may need to be added to increase the SIN ratio, results from different interval widths are presented and a method for choosing the interval widths is discussed. The results from different templates are compared to determine which template(s) should be used in the ha1 analysis. The sensitivity of the Fourier Quotient program to the initial velocity is also studied. Lastly, several tests with actual data are performed to determine if the sky background should be subtracted prior to analysis and the effects of interpolating sky lines.

Interval Widths

The sudace brightness ofa gdaxy decreases with radius and hence the intensity dong the slit des,therefore interval widths chosen at each radius should also vary. Near the center of the galaxy single row intervals will be used if the S/N ratio is sufnciently high and at the outer edges of the galaxy the intenml widths will be increased to 3 or 4. The width of the interval at each radius will be choseo so that the errors in the velocity and velocity dispersion are not too hi&. To determine what inted widths should be chosen the galaxy spectra are analyzed with interval widths of 1, 2, 3, and 4 and the results are compared. In Figure 3.9 the errors in the velocity, velocity dispersion, and line strength are shown as a function of radius or dit position. As expected single interval widths should ody be used near the center of the galaxy. Using plots similar to these the intervals for each galaxy are chosen to minimïze the errors and maximize the number of data points along the rotation curve.

DifEerent Templates

Ali of the nmrow-dit template spectra are used to andyze each of the high S/N ratio narrow-slit galaxy images. Figure 3.10 shows the results from the different templates for galaxy image A136a. The template 175 has the lowest errors, but otherwise does radius

radius Figure 3.9: Cornparison of the absolute errors for interval widths of 1, 2, 3, and 4 for galaxy image A136a. The upper left plot shows the velocity errors ( km s-') versus radius or position along the dit (in pixels) with the center of the galaxy at 109 pixels ( 1 pixel = 0051). The upper right plot shows the velocity dispersion ( km s-l) errors versus radius. The bottom left plot shows the errors in the line strength versus radius. The interval width is indicated by the digit after 053s in the key. Note that the errors for the larger interval widths are lower than the smaller inted widths at all radii. CWTER3- ARP GALAXlES 58

not appear to be distinguishable from the other templates. It can be seen that the rotation curves are very similar for all of the templates. The mean velocity clifference between each star and the template 053 desby at most 3.5 km se' for each intenml. The velocity dispersion profiles cliffer by small amounts (mean difference is at most 7.0 kms-') and these differences are due to the mismatch of the template and the galaxy. The line strengths show the greatest dinerences. Note that templates of the same star (e.g. 064 and 257) in general have results that are more consistent than the results of different stars. Galaxy spectra with lower SIN ratios have more variation in the rotation curves derived kom different templates. The template that gives the lowest errors in the central velocity dispersion is chosen as the "best" match (see Table 3.11). For most galaxy spectra this best match is template 175. For galaxy images A106a and A106c the "best" ternplates are 095 and 257 respectively. The S/N ratios of these images are comparatively low and this is most likely the reason for the difZerent "best" templates. Low SIN ratios are probably the reason discrepant templates for Arp 315 (175 and 230 for A315a and A315b respectively) as well. The best template for both of the Arp 123 images is 095 and since the S/N ratios are high for these spectra, this template is believed to be actually better match than the other templates. Template 175 is the best template for Arp 136, 165, 167, 174, 316, and 327. The shape of the rotation curves are not dependent on the template that is used as expected from the tests in 53.2.3. Significant differences only appear when the SIN ratio is low.

DifEerent Starting Velocities

The dependence of the results on the initial parameters used by the Fourier Quotient program is also investigated. For all of the previous tests with Mage A136a the initial velocity guess is 3443 km s-l, the velocity dispersion guess is 200 km s-', and the line strength guess is 1.0. A change in the initial velocity dispersion guess from 200 to 100 kms-1 does not dect the results si&caatly (the results are within 0.5%). A change in the initial line strength fiom 1.0 to 0.5 also does not affect the results (the results are within 0.4%). The initial velocity, on the other hand, needs to be CHAPTER 3. ARP GALAXES

radius A13Ba

Figure 3.10: Comparison of the results from different template stars. The upper two plots show the velocity ( km s-I) as a function of radius in arcseconds. The right plot shows the rotation curves offset for clarity. Starting from the bottom the templates are 053, 064, 078, 091, 095, 163, 175, 230, 257, and 335. The middle two plots show the velocity dispersion ( km s-') as a function of radius. The bottom two plots are the line strength as a function of radius. Note that the results for the velocity and velocity dispersion are almost independent of the template used and vary most where the S/N ratio is low at large radii. Table 3.11: Central Velocity Dispersions of the Arp Galaxies

Arp t emplat e 105 1751175 106 0951257 123 0951095 136 1751175 165 175/175 167 1751175 174 175/175 315 175/230 316 1751175 327 175/175 NOTES. Coi. (1). - Arp designation. Col. (2). - Best template for each narrow slit position, a and b respectively. For Arp 106 the slit positions are a and c. Col. (3). - The central velocity dispersion and error in kms-' from the best template. The central velocity dispersion is calculated by finding the average of the velocity dispersions in the inner 3 pixels (single bin data) for each nmow slit image (with quality data) and then taking the mean of these two values. For Arp 105 and 315 the binned data at the center are used since the single pixel bin results have errors that are large. Col. (4). - The mean central velocity dispersion in km s-' from a.ll templates. Col. (5). - The standard deviation of the mean of the central velocity dispersion in km s-l. CHAPTER 3. ARP GfiAXIES 61

more accurately estimated since the spectra are prepared using this initial velocity. In Figure 3.11 the results fiom the initial velocities 3043, 3143, 3243, 3343, 3443, 3543, 3643, and 3743 km s-' are shown. Note that the initial velocity should be chosen to be close to all of the values in the rotation curve. The results £rom the different initial velocity tests are consistent except for the 3743 km s-1 test. If the velocity is off by more than a few hundred kms-' the resdts found could be a local minimum instead of the true minimum. Several iterations should be done before the ha1initial velocity guess is chosen.

Sky Background and Sky Lines

To determine if it is necessary subtract the sky background and if the sky lines should be removed by interpolation, two galaxy images, A165a and A316a, are prepared in different ways and analyzed with the Fourier Quotient program. The first test with image A165a takes into account the sky hesthat are present and uses template image 163. The second test with image A165a is the same as the first but it ignores the sky lines. The Fourier Quotient plots are much noisier if the sky lines are ignored and the

velocities are on average 44 kms-' lower. The velocity dispersions are &O lower by an average of 70 kms-'. The average errors of the velocities and velocity dispersions of the test which interpolates the sky lines are 39 and 42 km s-', and for the test which ignores the sky lines the average errors are 52 and 66 km&. Note that all the intervals are averaged including those for which the S/N ratio is quite low. The best interval has errors of about 20 kms-' for both the velocity and velocity dispersion for the sky line test and are double that if the sky lines are ignored. Better results are obtained when the sky lines are interpolated than when they are ignored. The next two tests are sirnilar to the fbst two, but the sky background has been subtracted. The main difference in the background subtracted results and the un- subtracted results is the luie strength. The line strength is higher for the background subtracted data. The velocities and velocity dispersions ciiffer on average by less than 1 kmsdl. Therefore it is not necessary to subtract the sky background if the sb lines are interpolated. ARP GALAXIES

radius A138a

radius

Figure 3.11: Cornparison of the results fiom different initial velocities. The upper two plots show the velociw as a function of radius or slit position in pixels. The right plot shows the rotation curves oEset for clarity. Starting fiom the bottom the initial velocities 3043,3143,3243,3343,3443,3543,3643,and 3743 kms-l. The middle two plots show the velocity dispersion as a function of radius. The bottom two plots are the line strength as a function of radius. Note that for most of the initial velocities the results are very similar except for the highest initial velocity tests 3743 km s-' (top curve in the right hand plots) where the results are incorrect for some of the int ervals. CWTER3. ARP GALAXES 63

A different template, 095, is &O used to analyze the image A165a. The rotation curve found has the same shape, but is offset by an average of 18 kms-1 (excluding one spurious point) which is to be expected since the template velocities differ by 17 km s-'. The velocity dispersions are on average 8 km s-' higher for the 095 template. SMilar tests are done with the image A316a and template 053 and the results are consistent with the A165a tests. The difFerence in the tests which take into account the sky lines and those which ignore the sky lines is less since the gdaxy A316 is brighter and the sky lines are not as strong. In summary, the inte4 widths will be dedto take into account the changing surface brightness of the galaxy so that the errors are minimized and a maximum number of data points dong the rotation cuve is obtained. The results appear to be independent of the template used. The initial velocity needs to be accurately estirnated for the program to converge to the correct minimum and not a local minimum. The sky background does not need to be subtracted pnor to the analysis, but the program needs to know the location of the sky lines so that they may be interpolated. 3.3 Kinematics

The rotation curves and the velocity dispersion profiles for each slit width and position angle of each galaxy are found using the Fourier Quotient method. The rotation curves are shown in Figures 3.12 to 3.16 for each of the galaxies in this study except Arp 105 and Arp 228, whose SIN ratios are too low to produce reasonable rotation curves. The "best" template that is used to determine the rotation cuve is shown in the key. For two of the galaxies Arp 106 and Arp 315, the results from two different templates are shown, since the two slit positions have different "best" templates. The resdts f?om these two templates for both galaxies are very similar. Arp 136, 165, and 316 have results kom both nmow (template 175) and wide (template 336) slit spectra. No unusual velocity dispersion profiles, rotation cwes, or minor axis rotators are detected. The first step in determinhg whether or not any of the galaxies are minor axis rotators is to compare the slit positions with images of the galaxies in Arp's (1966) Atlas of Peculiar Galaxies. The five galaxies that do not have their orthogonal slit positions aligned with the major and minor axes, will be discussed first. Arp 123 does not show strong rotation along either slit direction. There appears to be rotation in Arp 167 in the second slit position. Arp 174 shows rotation along both slits, which is to be expected if the galaxy has rotation since the slits are aligned at approximately 45 degrees to the major and minor axes. No rotation curve was found for Arp 228 due to a luw SIN ratio spectrum. Arp 327 appears to show weak rotation dong the slit the second slit position. Six of the galaxies in this study have their slit positions cIosely aiigned with the major and minor axes. Of these six galaxies (Arp 105, 106, 136, 165, 315, and 316) si&cant rotation is detected in four (Arp 106, 136, 165, and 316) all along the major axis. The quality of the data for the remaining two galaxies is poor and determination of a rotation axis, if it exists, is difficult. No minor axis rotation is detected in the four galaxies that have positions aligned dong the major and minor axes and qualits' rotation curves. In order to determine whether or not it is possible to detect an unusual core CHAPTER 3. ARP GALAXZES

A106a radius (kpc) radius (kpc)

-a- 257 V, = 6628 V, = 6628

100

radius (arcsec) radius (arcsec)

radius (kpc) radius (kpc)

V, = 2409

100

radius (arcsec) radius (arcsec)

Figure 3.12: Rotation cwes for Arp 106 and Arp 123. Velocity versus radius in arcseconds and kpc (Ho = 50 kms-' Mpc-') for images A106a (upper left), A106c (upper right), A123a (lower left), and A123b (lower right). The results fkom templates 95 and 257 are shown for Arp 106. Arp 106 shows some possible rotation in the A106a image and none is seen dong the other d.Arp 123 shows virtually no rotation. CHAPTER 3. ARP GALAi(JES

radius (arcsec)

radius (kpc) radius (kpc) -5 O 5 -6 O 5 10 zoo-,--.-,---.,-zoo-'0. . . - , - - . , . - - - , - . - - , - 175 - 175 .- 4- 336 4- 336 i V, = 5013 - V, = 5013 .- %- . 1 ! i. r/i . i- 100 100 '..- !- - - .)+ L-. .. i :: y - * - h î .- -1. w

O O - c.a.

'f "'-L"-'"'--L""' -200~"~~"~"~~~""~""""" -200- -10 -5 O 6 10 -20 -10 O 10 20 radius (arcsec) radius (arcsec)

Figure 3.13: Rotation curves for Arp 136 and Arp 165. Velocity versus radius in arcseconds and kpc for images A136a and A136c (upper left), A136b and A136d (upper right), A165a and A165d (lower left), and A165b and A165c (lower right). The A136c, A136d, A165d, and A165c rotation cuves (template 336) are the wide slit images. Arp 136 shows strong rotation and a smooth rotation cunre in the A136a and A136c images. Arp 165 also shows fairly strong rotation. CIIAPTER 3- ARP GALAXlES

radius (kpc) radius (kpc) -2 O 2 4 =O-* - - . , - . - , . - . , - . . - 175 v, = 3774 .

100 - O O L-.*aJ

-2OoI'--.-'.---'.---'--'~'~-2001'..-.'-.--'...-'-.-.nI - 10 -6 O 5 10 - 10 -6 O S 10 radius (arcsec) radius (arcsec)

A167a companion radius (kpc)

-460

v, = 3774

-600

radius (arcsec)

Figure 3.14: Rotation curves for Arp 167 and companion. Velocity versus radius in arcseconds and kpc for images A167a (upper left), A167b (upper nght), and its companion (lower). Arp 167 and its companion do not show strong rotation. Note that this is the only companion in this study for which a detailed rotation curve is found. radius (kpc) radius (kpc) -2 -1 O 1 2 -2 O 2 .,..-S...,. .,--.-,----,..-.1-.--B.' - 175 - 175 V, = 6277 - V, = 6277

-4 -2 O 2 radius (arcsec) radius (arcsec)

A3 lSb radius (kpc) radius (kpc)

b n E 2:. w s O: .C. O O - c. al. > .

-200 -6 O 6 radius (arcsec)

Figure 3.15: Rotation curves for Arp 174 and Arp 315. Velociiy versus radius in arcseconds and kpc for images A174a (upper left), A174b (upper right), A315a (lower left), and A315b (lower right). Arp 174 appears to show strong rotation dong both axes but the errors are relatively large. No rotation is detected in Aip 315 but the errors are also large for this galaxy. The results fiom templates 175 and 230 are shown for Arp 315. radius (kpc) radius (kpc) -2 -1 O 1 2 I---.I--.'I-.'-I'.-1- - 175 -.r- 336 -Q- 336 11 V, = 1295 100 - voff = - LM)

f ii- i

w * O-; 2 i g -.; # - 92>

-100 -

radius (arcsec) radius (arcsec)

radius (kpc) radius (kpc) -4 -2 O 2 4 -4 -2 O 2 4 zoo,.-.,---.-..,---1 ~-.-,-.-,--.,---, - 175 - 115 V, = 9001 .

LOO - <- E 4:. w % O- - 3 - .CI O O- -aJ. i > * -LOO - -

radius (arcsec) radius (arcsec)

Figure 3.16: Rotation curves for Arp 316 and Arp 327. Velocity versus radius in arcseconds and kpc for images A316a and A316c (upper left), A316b and A316d (upper right), A327a (lower left), and A327b (lower right). The A316b and A316d rotation cunres (template 336) are the wide slit images. Gdaxy 316 shows a steep rotation curve dong the first slit position but no rotation dong the second slit position. No rotation is detected in Arp 327. several mode1 rotation curves are created and compared to those found for each of the galaxies that have detded rotation curves. The outer part of the model curve matches the observed rotation curve and the inner part may or may not have a counter- or CO-rotating core. Two counter-rotating and one CO-rotating cores are modelled using the velocity profiles the unusual cores of NGC 3608 and NGC 4494 (Jedrzejewski & Schechter 1988). The specifications of the musc-al cores are 1) a counter-rotating core with a maximum rotational velocity of 20 km s-' at a radius of - 400 pc, 2) a CO-rotating core with a maximum rotational velocity of 37kms-' at a radius of - 300 pc, and 3) a counter-rotating core with the same properties as 2). The velocity dispersion in each mode1 curve does not vaq with radius and is set to the value found at the center of the observed gdaxy. The line strength is also constant and is equal to 1. The intensity profile along the slit is assumed to be a Hubble profile and closely matches the observed profile. Two types of noise are added to the model, Poisson and Gaussian. The Gaussian noise is Wed until the errors in the velocities and velocity dispersions of the model approximate the errors found in the observations. These models are created with the template star 053, and are compared with the results of the analysis of the true galaq spectra with template star 053. Since the rotation curves of the galaxies do not vary when the analysis is performed with different templates stars, the "best" template does not need to be used to create these models. The galaxy images with the position angle that shows the largest rotation are chosen for the models. A description of each galaxy and its models follows. Graphical results are shown ody for Arp 136 to illustrate the method used to determine if a unusual core could have been detected. Arp 136: The rotation curve in galaxy image A136a is very smooth and a counter- rotating core similar to those modelled wodd have been detected if it was present. Co-rotating cores are more difEcult to detect than counter-rotating cores and for this galaxy it would be very diIricult to detect a CO-rotatingcore similar to the one modeUed. Figure 3.17 shows the observed rotation curve and the results fiom the models both before and after adding noise. CWmR3- ARP GALAXIES

Figure 3.17: Cornparison of observed rotation curve of A136a to models. The upper left rotation cuve is the observed rotation curve. The upper middle rotation curve is the base model and the upper right plot is the base model with noise added to match that of the observations. The middle row of plots are the rotation curves with the counter-, CO-, and counter-rotating cores as descnbed in the text. The bottorn plots are the above models with the same amount of noise as the observed galaxy. Note that a counter-rotating core of the modelled types would have been detected if one was present. CHAPTER 3. ARP GALAXIES

Arp 123: One counter-rotating core and one CO-rotationcore are modeIled for gdaxy image A123a. The errors are large in the outer parts of the galaxy and results beyond about 5 pixels (2.8") are uncertain. Therefore, it is most likely that only the core of the galaxy is seen and no information about the outer part of the galaxy is available. Even though the rotation curve is only of the inner part of the galaxy, the lack of rapid rotation indicates that it is unlikely that a merger of a dwarf gala~yhas recently taken place. Arp 165: Two counter-rotating cores are modeued for galaxy image A165b. A counter-rotating core of the types modeIled should have been detected if one was present . Arp 316: For galaxy image A316a it is slightly more difficdt to detect unusud cores of the type found by Jedrzejewski & Schechter (1988) since these cores would extend to radius of about 5 arcseconds. The rotation curve does not show any irregularities out to a radius at which the velocities become uncertain (at 8 arcseconds), therefore no evidence of an unusual core is detected. Note that this core has the steepest rotation curve of all of the galaxies studied. Arp 174: In galaxy image A174b it is not possible to detect an unusual core since these cores would have a small angular size (a radius of about 1" or 2 pixels). Arp 167: In galaxy image A167a only the core of the galaxy is seen in the observed rotation curve and it would be impossible to detect an unusual core if it existed. NGC 2672 and NGC 2673 have been studied by Borne et al. (1994) and Bonfanti et al. (19%). The central velocity dispersions of all three studies of this pair of galaxies agree quite weU with each other. The rotation curves and velocity dispersion profiles of the two more recent observations have smaller errors and are in agreement with our results. The position angles of the slits of these observations vary and our dit positions are closest to Borne et al. (1994). Note that Borne et al. (1994) find a weak U-shaped rotation profile in the secondary. Bonfanti et al. (1995) find a inverse U- shaped rotation curve in the primq at a position angle of 30 degrees. U-shaped and inverse U-shaped rotation curves are an indication of a tidal interaction (Borne 1990). This paV of galaxies is considered to be interacting and hence is not a merger remnant. CHAPTER 3. ARP GALAXIES 73

No unusual rotation curves are found (counter- and co-rotating cores or steep inner rotation curves in those cases where the outer part of the galaxy is too fat) out of the 4 galaxies in which the data are of reasonable quality. The velocity dispersion profiles also do not show any peculiarities. No minor axis rotation is detected in the four galaxies that show strong rotation and have a sIit aligned with the minor axis. These results are summarized in Table 3.12. Six of the eleven galaxies have been classified as peculiar. The maximum rotation velocity is listed for each of the galaxies as determined fiom the rotation curves. Note that the quality of the rotation curves varies and hence the confidence in this maximum rotational velocity also varies. These galaxies are not well studied and there is variation in the the quality of the photometry that is available. No evidence of peculiar kinernatics is detected in this sarnple of Arp galaxies. Table 3.12: Summary of results for the Arp Galaxies

Arp NGC Morph Vh Vm (6) Q 60 C? O? JSC? is? B$ 105 3561B SO": p 8811 ... O 210 36 ... n n n n 14.57

NOTES. Col. (1). - Arp designation. Col. (2). - NGC or IC designation. Col. (3). - Morphological type fiom the RC3 Catalog. p = peculiarity, : = uncertain, sp = spincile. Col. (4). - Heliocentric velocity f?om the RC3 Catalog. Col. (5). - Maximum rneasured rotational velociw in km s-'. COI. (6). - Confidence in maximum rotational velocity, O = no value, 1 = low, ... 5 = high. Col. (7). - Central velocity dispersion in km s-' . Col. (8). - Mean error in the central velocity dispersion in km s-' . Col. (9). - dvldy at the center of the galaxy in units of km s-' parsec-'. Col. (10). - 1s the core well resolved? Col. (11). - Are the data at the outer part of the galaxy of sdficient SIN ratio? Col. (12). - Codd an unusual core be detected? Col. (13). - 1s an musual core detected? Col. (14). - Corrected B-band total magnitude. Note that this magnitude is based on the photoelectric total magnitude, BT for 136, 315, 316, and 327, photographie magnitude, rn~for 165 and 228, both fiom the RC3 Catalog. For the rest of the galaxies this magnitude is based on the magnitudes given by NED, the band is not specified and is assumed to be B-band. The value for Arp 167 is from Bonfanti et ai. (1995). CHAPTER 3- ARP GALAXZES 75 3.4 Line Emission

Line indices and gradients as well as visual inspection of the spectra axe used to determine which galaxies show emission. Starburst galaxies have strong narrow emission lines (5150 kms-') with the most prominent lines being [OIII],[011], Be1 and HI. Active galactic nuclei (AGNs) are characterized by narrow (500.1000 km s-') and broad (103 - 104 km s-') emission lines. Typical normal early-type galaxies do not show emission in HP. HP (4861A) and [Om](4959A and 5007A) are within the observed spectral region and therefore emission in these Lues should be detectable if present.5 A discussion of each of the galaxies in this sample with respect to line emission follows: Arp 105: Both the primary galaxy, NGC 3561B and its companion, NGC 3561A have strong emission lines. The primary early-type galaxy shows the strongest emission in HP 4861A (equivalent width, W., = a)of all of the galaxies in this sample and also has [OIII] 5007A emission but ody in the core. The secondary spiral galaxy has strong emission in HP 4861K, [OIII]~oo~A, and also in the [NI] doublet at 5200A. The HP emission extends well out from center of this companion galaxy. Arp 105 is not a merger remnant but a pair of interacting galaxies. A.rp 106: The absorption in HP is low at the core of this gdaq indicating that there may be some HP emission, but the the spectrum is fairly noisy. Arp 167: There is some faint emission (W,, = 1.34 of [0111] 5007 A at 4959A about 2" from the core in NGC 2672, which is most likely caused by the tidal interaction between the two galaxies in this system. Recall that this system is not a merger remnant but a pair of interacting galaxies. A.rp 174: There is indication of HP emission in this galaxy from visual inspection of the spectra but it is faint. An equivalent width of 1.5A is measured using splot in IRAF. Arp 228: There are apparent strong emission features at observed wavelengths of

5Any emission detected is removed from the spectra prior to anaiysis with the Fourier Quotient program (or înterpolated) . CHAPTER 3. ARP GALAXIES 76

5356A and 5763A that correspond to rest frame mvelengths (for a velocity of 5000 kms-') of approximately 5270K and 5670& respectively. The emission at 5356A (W, < 134 extends well out from the center of the galaxy (1.5" to the south and 7.2" to the north). The extent of the emission at 5763A (W, < 10A) is less but also has the same asymmetry about the center of the galaxy. Possible emission at an observed wavelength of 5067A is also detected. This galaxy is one of those chosen for a study of shell galaxies (Thronson, Bdy, & Ha6g1989) and like many of the other shell SO galaxies in their sample this galaxy does not have unusudy high infrared emission. Since the emission lines are unidentified and the data are poor for this gdaxy it WU be not be included in the summary of the results. Al1 of the above emission lines have widths less than 500 km s-' with the narrowest line in Arp 228 (< 200 km s-'). Line emiçsion is detected in four galaxies, two of which are part of interacting systems and not merger remnants, and the HP emission in the other two galaxies is faint. CIEAPTER3. ARP GALmS 3.5 Faber- Jackson Relation

The Arp galaxy data are compared with the data used by Kormendy and Illingworth (1983), hereafter KI, to obtain their Faber-Jackson, L oc on,relation (Figure 3.18). The Arp galaq data are represented by Wed circles with the Arp number next to the data point and KI'S data are represent by x's. For both datasets black (cyan) symbols indicate the galaxies classified as elliptical (SO) galaxies. Note that the SO KI data consist of only SA0 galaxies (Le. no barred SOS) and the total magnitudes are used. The magnitudes used for the Arp galaxy data are listed in Table 3.12. NGC 1889 (Arp 123) has an unusually low velocity dispersion for the assumed B- band absolute magnitude, but it should be noted that this is one of the galaxies whose magnitude is uncertain. The reverse is true for NGC 3068A (Arp 174) whose magnitude is also uncertain. None of the other galaxies appear to have an unusual placement on the L - 0 plot. The solid black line is the KI fit to their elliptical data. The solid red line is the fit to al1 of the KI data holding the slope constant at n = 4, the value from Faber & Jackson (1976). The dashed red line is the fit to the Arp galaxy data again holding the slope constant at n = 4. The simple mean of the shifts of the Arp data relative to the KI fit with n = 4 is A log o = -3.7ft:?% at c = 200 km s-'. Rom the linear Ieast-squares fit, OLS(MB1 log o)~,the dope is found to be n = 3.0 & 0.3 for the KI sample and is shown with a solid green line. Note that the slope found using only the elliptical galaxies in the KI sample is n = 3.0 & 0.4, which is difFerent from the slope found by KI, since their linear least squares fit was most likely OLS(log o(M'). The simple mean of the shifts of the Arp galaxy data is Alogcr = -4.7f::9% and is indicated by a dashed green line. The weighted mean of the shifts7 is Alogo = -5.7?::$% (solid magenta line). Similar results are found if only the elliptical galaxies are used in the KI sample (A logo = -5.423i). The above calculations of the mean of the shifts include all of the galaxies except Arp

60rdinary least-squares with MB(AB) as the independent variable. 7Alog cr is the mean of the shifts for each galaxy and its uncertainty is the sample standard deviation multiplied by (N - 1)-Il2. This is similar to the method described by Feigelson & Babu (1992)- CHAPTER 3. ARP GALAXtES 78

228 for which no central velocity dispersion was fonnd. If galaxies Arp 123 and 174 are omitted A loga increases to -6.92% (n = 4, simple mean) -10.4fg% (n = 3, simple mean), and -9.6?:$% (n = 3, weighted mean). The Arp galaxies on average have a lower velocie dispersion than those of the KI sample but otherwise they do not appear to

Figure 3.18: Velocity dispersion (km s-l) versus absolute magnitude in the B band (Ho = 50 km s-' Mpc-l). Arp galacies are indicated by Wed ckcles with the Arp number next to the data point. Kormendy and Illingworth's (1983) data are represented by x's. For both datasets bladr symbols indicate elliptical galaxia and cyan symbols indiate SO galaxies. The solid bladc IÏne is their fit using efiptical galaxies only to the L a on relation (n = 5.4). The solid red line is the fit to dl of the KI sample with a slope of n = 4. The dashed red line is the fit to the Arp galaxies with a dope of n = 4. The solid green heis a different hear least squares fit to the KI data and the dashed green and solid magenta lines are fits to the Arp gdaxy data with the same slope (n = 3, see text for nuther details). The Arp galaxies on average tend to have a lower velocity dispersion than the KI sample but otherwise are similar. 3.6 Summary

No evidence of unusual rotation curves, unusud velocity dispersion profiles, or minor axis rotation is found in this sample of early-type galaxies. The quality of the data is sufncient to deout unusual kinematics in four of the eleven galaxies (Arp 123, 136, 165 and 316) and these galaxies do not show any dynamical evidence of a merger. Of the six galaxies that have observations approximately dong the major and minor axes, four (Aq 106, 136, 165, and 316) are major axis rotators and the SIN ratios of the remaining two galaxies (Arp 105 and 315) are insuficient to determine whether or not they are minor or major axis rotators. This lack of evidence of peculiar core kinematics in these early-type elliptical galaxies is not in codïct with the results of Bender (1990a) who found that one third of luminous (boxy) elliptical galaxies show peculiar core kinematics since our sample only contains 3 luminous elliptical galaxies. The upper limit for the number of counter-rotating cores in lumkous elliptical galaxies £rom our data is 45.9% at 84.13% (la) confidence level (Gehrels 1986), which is consistent Bender's resdt. If all of our galaxies with quality data is used the upper limit decreases to 36.9% at 84.13% confidence level, which is still consistent Bender's result. A laxger sampie size of Arp galaxies with good kinernatics is needed to draw £kmconclusions about counter-rotating cores. Based on MB magnitudes Arp 167,315, and 316 are luminous (boxy) elliptical galaxies and Arp 123 and 165 are low lurninosity (disky) elliptical galaxies. The remaining six galaxies consist of 5 SO galaxies and one SA0 galaxy. Two of the galaxies, Arp 105 and 167, are currently undergoing an interaction and shgw emission lines and are not recent merger candidates due to their current interactions. The remaining galaxies have little or no line emission and therefore do not show signs of recent star formation. From the Faber-Jackson relation individually these galaxies do not appear to be significantly difFerent kom normal galaxies, but as a coup their average velocity dispersion is 7 f 4% lower. These results agree with those of Zepf & Whitmore (1993) who found that the velocity dispersions of elliptical galaxies in compact groups are 20% lower than otlier galaxies, but they hda greater diaerence in velocity dispersions. Since the central spectra CWT'3. ARP GALAXIES are relatively normal in these galaxies and there is no evidence of peculiar cores, this strongly constrains the recent merger of a dwarf galaxy, particularly if it was gas rich. Schweizer and Seitzer (1992) in their study of the colors and fine stmcture of E and SO field and group galaxies find that the mean merger age of these galaxies is 8 Gyr (or z = 0.9 for Ho = 50 km s-l Mpc-l and go = 0.5). Field elliptical gdaxies have a Iarger spread in color than ciuster elliptical galaxies (Sandage & Visvanathan 1978). This indicates a larger spread in formation epochs Normore starbursts for the field galaxies. Zepf & Whitmore (1991) fînd that the colors of elliptical galaxies in compact groups are consistent with those in the field with only a few exceptions. One would expect that the merger rate in compact groups would be much higher than for field galaxies and therefore result in anornalous colors. Bower, Lucey, & Ellis (1992) argue that the smddispersion in the color-velocity dispersion relation indicates that elliptical galaxies are old and that they formed at z > 2. They also place an upper limit of 10% of the stellar mass on starbursts seen at z - 0.5. Rose (1985) and Bower et al. (1990) also find that ellipticals in clusters are older (by 6-7 Gyr) than field ellipticals. Caon et al. (1994) conclude from the surface brightness-radius relation that a large fraction of elliptical galaxies in compact groups appear to have had at least one major merguig event and that these mergers occurred at least 2 Gyr ago since the galaxies colors appear to be normal. Zepf & Whitmore (1993) suggest that the lower velocity dispersions of elliptical galaxies in compact groups could be due to weak tidal encounters or the accretion of a gas-rich satellite which dissipates and forms a stellar disk. The accretion of a gas-rich satellite would also explain the presence of disky isophotes, but again this accretion would have to occur early in the history of the group since the galaxy colors are normal (Caon et al. 1994). Note that our observations are extremely sensitive to changes in the core, whereas the above authors tend to measure the global properties of the galaxies. This sample of early-type gal&es cannot be disthguished from other early-type galaxies and therefore the formation process in the two samples is most likely sllnilar. One would expect that in the Arp group env-konment in which these galaxies reside a merger may have happened in the past log years. Since these galaxies do not appear to be significantly brighter than other elliptical galaxies (Figure 3.18), if a merger has occurred, then only a few percent of the total stellar mass is new stars. These results suggest that mergers that make elliptical galaJoes in clusters and groups could have taken place around a redshift of 2 or earlier and are uncornmon now. Further studies of the kinematics of early-type galaxies in groups are needed since our sample size is small. Improved photometry is required to forrn a better Faber- Jackson relation. Kinematic signatures of mergers are longer lived t han those produced by starbursts and therefore studies of both the kinematics and star formation histories would be useful in the understanding effects of mergers on the evolution of early-type galaxies. Chapter 4

Velocity Dispersions of Distant Galaxies

In this chapter the velocity dispersions of 13 early-type galaxies in the cluster Abell 2390 are found using two methods, the Fourier Quotient method and the Bayesian method. The spectnun of each of these distant galaxies will be compared to those of a nearby star to determine how much broader the galaxy absorptions lines are in corn- pa.rison to those of the star. For nearby galaxies the same instrumental setup can be used for both the galaxy and the template star. The galaxies of Abell2390 are distant and therefore their spectra are redshifted considerably. Different spectral regions for the template and the galaxy will have to be observed to obtain the same rest frame spectral region for both objects. Observing these diEerent spectral regions requires different instrumental setups (grating and slit width). The instmmentd broadening cancels when the instrumental setups are the same, but in the case of a faint distant galaxy and a bright nearby star the instrumental broadening is different. Therefore determining the velocity dispersion of a distant galaxy where different spectral regions are observed for the template and the galaxy required special considerations. These velocity dispersions will be used in the subsequent analysis chapter to form the Fundamental Plane of Abell 2390. FVst, the observations and initial reductions are discussed in 54.1. The following section (54.2) describes the data and how they are prepared for the two methods. CWTER4. VELOC'DISPERSIONS OF DISTANT GAl;AXIES 83

Extensive tests with both the Fourier Quotient and Bayesian methods with smulated data are described in 54.3. In the first set of tests the velocity dispersion of the test spectra is Miied and the performance of both programs is evaluated. To determine how well each program works with low S/N ratio data, noise is then added in the next set of tests. The effects of rnismatched galaxy and template spectra are also studied. The velocity dispersions of the galaxies are presented for both the Bayesian method and Fourier Quotient method in 54.4 and 54.5. These results are summarized and discussed in the last section (54.6).

4.1 Observations

Multislit spectra of 13 galaxies in Abell2390 were taken with the 3.6m CFHT using the SIS spectrograph and the 0600 grism on 1994 October 1-3 by Chris Pritchet and Howard Yee. Four separate exposures were made and later summed (two 5000s and two 5400s exposures). Spectra of a template star, $2 015(4 different spectral regions) were also taken during this observing run using the B600 and U900 grisms. The slit widths of the galaxy and steuar spectra are 0.8 and 0Y25 respectively. The seeing was excellent on this observing nui, 0-35, &mhg the first two exposures, 0Y66 during the third exposure, and 0.49 during the last exposure. The initial reductions of the spectra were performed by Pntchet and Yee. The cosmic-rays were first removed and then the images were bias-subtracted and trimmed. The spectra were not flat fielded since the S/N ratios of the spectra were not high enough to warrant it. Wavelength calibration of the spectra and background sky subtraction were done before summing the four exposures. A cornparison of the sky spectra shows that the wavelength and pixel scales are aligned to better than 0.5 pixels for the four exposures. The wavelength scale alignrnent is within 0.3-0.4 A. A hding chart for the galaxies in this study is presented in Figure 4.1, where each galaxy is identified by a number to its immediate North. This image is a portion of the 900 s Johnson R band image taken by the CNOC group on 1993 June 18 with the 3.6m CFHT (Yee et d. 1996). CWTER 4. VELOCITY DISPERSIONS OF DETANT GALAXIES 84

Figure 4.1: Finding chart for the galaxies in Abell2390 in this study (Yee et al. 1996)- Note that the galaxies are South of the designated number. North and East are indicated on the image.

CHAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXTES 85 4.2 Data

This section describes data and its preparation for the two programs, ff (Fourier Quotient program) and spec (Bayesian program), which requiie that the data be in difXerent forms. Both programs assume that the galaxy and stellar (or template) spectra were taken with the same instrumental setup which is not true in this case due to the redshift difference between the galaxies and the template. Therefore the instrumental broadening ciifference must be estirnated and corrected for by broadening the template spectra.

4.2.1 GaIaxy Spectra

The galaxy spectra, with 2x2 binning, ~picallyhave an obsenred wavelength range of 5780 - 6672A at a scale of 0.87A/~ixe~The spectral resolution of the galaxy spectra with a dit width of OY8 is 4.0A. The redshifts from the CNOC duster redshift survey (Yee et al. 1996) are used as initial redshifts estimates, except for 2 galaxies which do not have CNOC redshifts and a value of 0.23 is used. Table 4.1 contains the prelirninary redshift estimate, apparent Gunn T magnitude, and the observed wavelength range of the spectnun for each of the galaxies. The galaxy spectra are shown in Figure 4.2 and have the same intensity scale. The main features are HP (4861A),the Mgb tripletfF. (51774,Fe 5270A,and Fe 533~4,which have wavelengths of approximately 5975A, 6365& 6478A, and 6559A respectively, at the average redshift of the Abell 2390 galaxies. Galaxy 11, the CD,has quite strong emission lines at 5980A,6099A, 6158A,and 6395K which correspond to HP at 4861A, [OIII] at 49594 [OIII] at ~oo~A,and the [NI] doublet at ~~ooA,respectively, at a redshift of 0.23014. When the galaxy spectra are extracted fiom the original images they are linearized and in the same operation placed on a logarithmic wavelength scale. This is the required format for Ten copies of each of the galaxy spectra are stacked to form a two dimensional image. fF will assume that each of the 10 identical spectra is different and find solutions for each copy. Note that the solutions found will be slightly different due to the random starting points in the search for a solution. In fact, if the solutions CRAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXIES

Table 4.1: Preliminaty redshift estimates, magnitudes, and wavelength limits

vaiy too much, this is an indication that the SIN ratio is too low to find a reliable solution. ff can ignore specific regions in either the template or galaxy spectnim. For example, the ends of the spectrum of galaxy 1 taper off due to its position on the CCD. These ends will cause problems for the program if they are not ignored. The sky subtraction is not completely successful in eliminating the night sky line at 6300A and this line is over- or under-subtracted in all but a few spectra. Note that this is a common problem with strong night sky lines. The position and width of the residual of the night sky line are listed in Table 4.2. In some cases the preprocessing removed the sky line cornpletely so it was not necessary to mask it out (i.e. the line width is zero). The preparation of the data for the program spec is slightly different. The spectra are hearized but not placed on a logarithmic wavelength scale. Ideally one would like to input the raw spectra into spec, but it could not be determined how to convert the pixel coordinates of the data to wavelength.' Again ten copies of each spectra are combined to form a two dimensional image. spec can &O be told to ignore specific regions of the spectrum, but the spectrum must be smooth in those regions. spec

'The linearized spectra use spline cwaicients to convert fiom pixel coordinates to wavelength. If one went back to the original caiibration spectra the conversion could be done. CKAPTER 4. WLOCITY DISPERSIONS OF DISTANT GALAXIES 87

Table 4.2: Skyline wavelengths

galaxy kk, &es width 1 6299.982 6301.5 7

NOTES.Col. (2). - The central wavelength of the sky line in A as rneasured from the background spectnim. Col. (3). - The central wavelength of the residual of the sky line in A. Col. (4). - The width in pixels that is masked out. can ignore minor fiaws, but it has problems with major ones, since it uses the raw spectra to get a first estimate of the solution. The mean of the swounduig pixels is used to replace the night sky lines and the ends of galaxy 1's spectnun. CWTER4. VELOCITY DISPERSIONS OF DDISTANT GAL-S 88

5800 6000 6200 6400 6600 6800 Wavelength [angstromsl

Figure 4.2: Intensity versus wavelength for each observed galaxy in Abeii 2390. The intensity scde is the same for each gala, The galaxy is indicated by the number to the left of each spectnim. The absorption features are virtually non existent in the spectra of galaxies 3 and 6. The spectrum of galaxy 11 is daced out of order due to its strong emission lines. Note the incompleEe sky subtrakion of the [01]line at 6300A. C'TER4. VELOCITY DBPERSIONS OF DISTXIVT GAL-S

4.2.2 Template Spectra

The template star, q52 008 (KO W),was observed using two grisms 8600 and U900. The B600 data WUbe used as the template for the Abell2390 galaxies. -The stellar ternplate spectnun has a dispersion of 0.44A/~ixeland a spectral resolution of 1.3A with 8x1 binning. A twinslit mask was used to obtain the steUar spectrum with exposures times of 4 seconds each. The wavelength ranges of the upper and lower slit images (phi2origdv and phi2okvdv) are approximately 4225 to 5090A and 4890 to 5775A respectively (see Figure 4.4).

Instrumental Broadening

The galaxy spectra and the template (stellar) spectra were acquired using different instrumental setups. This is necessary because the cluster galaxies are at a high redshift and it is impossible to observe a template star at the redshift of the cluster. A nearby star is observed and then its spectrum artificidy redshifted out to the redshift of the galaxies in the cluster. The same rest fiame spectral regions of the the galaxy and template star must be observed. If the galaxy is at a low redshift the same instrumental setup is used for observing both the galaxy and the template star and hence the instrumental broadening will also be the same. This is not the case when observing galaxies at high redshifk and therefore a correction must be made for the differences in instrument al broadening . There are two main instrumental differences in the observations of the galaxies and the template star. First, the slit width used for the galaxies is 008 while for the template it is 0!'25. This difference appears to have produced a slight "boxiness" in the line profile as well as broadening it. The second difference is the grating, 0600 was used for the galaxy spectra and B600 for the template. To account for these clifferences the template spectnim WU be broadened so that the differences in the instrumental setups are negligible. The diaerence in the amount of broadening will be determined by comparing the background sky ernission lines in the galaxy spectra with the narrowest stellar absorptions lines in the template spectra. Two types of broadening functions wilI be used to broaden the template spectra: a Gaussian and a function which produces the same boq shape of the night sky Iines.

NOAO/IRAF V2.10,4EXPUR kroe qrho nray Tue 17:39:58 30-Jul-96 Sepuruk 1 on s?ep - *?8668.

1 1 I I 6300 6320 6340 6360 Wavelength tangstrornsl

Figure 4.3: Sky lines 6300A and 6363A for each of the galaxy's background spectra (bottom thirteen spectra). The first two spectra are the sum of sky lines. Note that profile of the lines is indeed boxy.

In order to determine how much the template spectra should be broadened, the widths of nmow lines of spectra in each setup will be determined. Ideally one would like to measure exactly the same spectral feature, but this is not possible with the adable data. Therefore the widths of narrow night sky emission lines in the galaxy spectra will be compared with the widths of the narrowest lines in the stellar ~pectra.~ These widths will then allow the determination of the difference in the amount of instrumental broadening between the two setups. A Gaussian is fit to the night sky emission [01]hes (6300A and 6363A) and Nd

-- - 2The illumination of the spectrograph is different for a point source and an extended source such as a gdaxy. The sky lines are assumed to be representative of the instrumental response function since the sky is an extended source and the stellar template was trailed across the slit to mimic an extended source* hes (5890A and 5896k) in the sky background of the gdaxy spectra. The averages of the central wavelengths and the widths of these lines are presented in Table 4.3. The results for each of the four prominent sky lines are contained in this table as well as the results from the combined spectra for the [01] lines. In Figure 4.3 the profiles of the [01] emission lines from the 13 background spectra and their sum (at the top) are shown. The sum of the lines is slightly broader than individual lines, which is to be expected if the central wavelength of the lines are not exactly the same. Note that the shape of the line profile is boxy. Since the [OI]lines, with an average o of 1.203 A, are stronger than the Nd lines, their shape will be used to broaden the template spectra.

Table 4.3: Sky lines

& O FWHM 6299.988 0.104 1.193 0.009 2.810 0.022 6299.982" ... 1.213 ... 2.858 ... 6363.503 0.098 1.191 0.014 2.805 0.032 6363.496" ... 1.215 ... 2.860 ... 5889.651 0.074 1.294 0.028 3.048 0.067 5895.742 0.071 1.205 0.030 2.838 0.071 NOTES. COL.(1) & (2). - The mean and error of the measured wavelength of the sky line in A. Cols. (3) & (4). - The mean and error of the rneasured cr of the fitted Gaussian in A. Cols. (5) & (6). - The mean and error of the FWHM of the fitted Gaussian in A. a Results from combining all 13 spectra.

The same method is also used to hdthe width of the narrowest lines in the stellar spectra. This is more diaicult due to the number of lines and blends that are present in the spectra. Two stellar spectra wilI be combined to form the final template spectrum for the analysis prograrns. Both the original template spectra (upper and lower slit images) and the combined template spectnim (combined) are used to find the widths of the narrowest lines. The results are presented in Tables 4.4 and 4.5. Table 4.4 contains the results fiom lines with FWHM < 1.5A and Table 4.5 fkom lines with FWHM < UA. CKAPTER 4- VELOCITY DISPERSIONS OF DISTANT GALAXIES

Iower slit

4750 5000 5250 Wavelength (angstromsl

Figure 4.4: Intensity versus wavelength for the two template spectra of q52 015.The intensiw scale is the same for each spectrum. Note the overlap region of about 200A. The offset of the two spectra is due to the twinslit maçk. CWTER4. VELOCITY DISPERSIONS OF DISTANT GALAXIES 93

Table 4.4: Template lines with FWHM < 1.5A

sample n a FWHM upper sIit 7 0.474 0.085 1.115 0.200 lower slit 11 0.407 0.090 0.958 0.212 upper+lower 18 0.440 0.083 1.035 0.195 combined 16 0.447 0.073 1.053 0.173 all 34 0.440 0.083 1.035 0.195 -- NOTES. Col. (1). - Image(~)fkom which lines were measured. Col. (2). - Number of lines averaged. Cols. (3) & (4). - Mean and error of the CT of the Gaussian profiles in A. Cols. (5) & (6). - Mean and error of the FWEIM of the Gaussian profiles in A.

Table 4.5: Template lines with FWHM c 1.2A

sample n FWHM upper slit 4 0.424 0.066 0.999 0.155 lower dit 9 0.369 0.038 0.870 0.090 upper+lower 13 0.386 0.053 0.910 0.124 cornbined 11 0.406 0.043 0.957 0.100 al1 24 0.395 0.048 0.931 0.114 NOTES.See Table 4.4 for a description of the columns.

The mean width of all the measured template lines with a FWHM < UA will be used, since the lines with FWHM > 1.2A may be blends. The narrow lines of the stellar template will be assumed to be Gaussian in shape with a (r=0.395A. The stellar template spectra are redshifted out the galaxy during the analysis and therefore the widths of the lines of the template and galaxy spectra must be cornpared at the same redshift. We will compare the line widths at zero redshift. The average redshift of our sample of galaxies in Abell2390 is 0.22939. The Gaussian profile of the sky lines will have a o = 1.203&(1+ a) = 0.9785K when deredshifted back to z = O. Therefore the template spectra will be convolved with a Gaussian with 0 = 40.97g2 - 0.3952 = 0.905A = 3.62 pixels before artificially redshifting the template spectra out to the galaxies. As previously noted the sky lines are boxy in shape and a broadening kernel that produces this shape will also be used to broaden the template spectrum. The CWTER4. VELOCITY DISPERSIONS OF DISTANT GAZIAXES 94 profiles of the two [OI]lines are very similar and are scded and averaged to form the average sky line profile. This is the shape of an unresolved narrow line at the average redshift of the galaxies, zave= 0.22939. The template line profile, a Gaussian, is also created at this redshift with 4 = 0.395 * (1 + zaut,,.)= 0.4856A. Both the sky line profile and template line profile are then biueshifted back to z = O. The next step in the procedure is to find a kernel that when convolved with the template line profile results in a profile similar to the sky line profile. The results of three boxcar kernels are shown in Figures 4.5 and 4.6. Figure 4.5 shows the results of convolving the template line profile with boxcars of width 10 and 11. Both of these profiles are similar to the sky lïne profile which is indicated by a dashed curve. A boxcar of width 10.5 produces an even better result, shown in Figure 4.6. All three boxcars are used to broaden the upper slit and lower siit template spectra to produce new template spectra for the analysis programs. These templates are referred to as bn (boxcar narrow), bm (boxcar middle), and bw (boxcar wide) which have broadening boxcar widths of 10, 10.5, and 11 respectively.

NOAO/IRAF V2,10,4EXPORT kroskerOlorien Ved 19:00:07 31-Jul-96 Separation step = 0.

Figure 4.5: Profiles of the template Gaussian convolved with boxcars of widths 10 and 11. The sky line profile is shown as a dashed cwe. Both of these profiles are similar to the sky iine profile. NOAWIRAF V2.10.4MPORT kroeker~torienVed 18:56:57 31-Jul-96 Saparation stop = 0. I I 1 I 1 I I

Vavelength (angstroisl

Figure 4.6: Profde of the template Gaussian convolved with boxcar of width 10.5 and the sky line profile (dashed cuve). This broadened profile matches very weLl with the sky line profile.

Two methods are used to combine the template spectra of $2 On. There is a region of approximately 200A of overlap between the lower slit and upper slit spectra. The kt method, denoted by ns (no shaping), scales the images so that the overlapping regions have the same mean intensity and then joins the spectra together by taking the mean value in the overlapping regions. The resulting spectnim has two smdl discontinuities in it at the beginning and end of the overlap region. The second method shapes the template spectrum simila.to the galaxy spectrum, denoted by ws (with shaping). The template spectra are normalized by dividing each spectrurn by its continuum. These flattened spectra are then combined. The shape of the continuum of each gdaxy spectra is used to scale the template spectra so they have the same shape as the galaxy spectra. Each galaxy requires a different template since each galaxy has a slightly different redshift and wavelength limits. This should solve the problem of different shapes of the spectra due to different instrumental setups. Note that different shaped spectra are only a problem with spec since it does continuum subtraction as opposed to continuum normalization with ff. CRAPTER 4. VELOCm DISPERSIONS OF DISTANT GUmS 96

From the prelllninary redshift estimates a region of the template spectnun is extracted that matches each galaxy wavelength region. The wavelength region of the template is specified to be the same region that the galaxy spectra has. Essentially the template is being redshifted out to the galaxy. For example, galaxy 1 has wavelength limits of 5895.7 to 6797.d (0.88148&xel). If the redshift of this gdaxy is 0.22801, then the rest fmewavelength limits axe 4801.0 to 5535.3A (0.717ûlA/~ixel). This section of the template spectra is extracted. The programs are told that the wavelength range of the extracted ternplate region is 5895.7 to 6797.d. Since the template is artificially redshifted out the galaxy, the velociw dispersions fond do not need to be corrected. Three types of ternplate spectra are used, unbroadened, Gaussian broadened, and boxcar broadened to determine the velociw dispersion of the galaxies. CHAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXZES 4.3 Tests with Simulated Data

In this section tests with simulated data will be presented for both the Fourier Quo- tient program, ff, and the Bayesian program, spec (see $2.1 and 52.2 for a detailed description of the methods). The method used to create the test data is described first in 54.3.1. The first set of tests does not contain any added noise and the velocity dispersion is varied to determine how well the programs wiU perform in perfect conditions (54.3.2). In the next set of tests noise is added and varied to approximate the S/N ratios in the actual galaxy spectra (54.3.3). Since the template and galaxy spectra are unlikely to be a perfect match, the third set of tests deals with mismatched spectra both with and without noise (54.3.4). Test spectra based on the broadened template spectra are analyzed with the unbroadened template in the last set of tests. The purpose of this set of tests is to aid in the understanding of the dinerences in the results of the galaxy spectra analyzed with the unbroadened and broadened template spectra (54.35).

4.3.1, Creation of Test Data

The simulated data are created fiom the unbroadened ws (with shaping) template spectrum for galaxy 1. The velocity, velocity dispersion, and mean intensity of each spectrum can be Mned. Two types of noise can be added to the spectra: Poisson noise which is dependent on the intensity of each pixel, and a Gaussian or constant noise to simulate read-out noise for example. A two dimensional image is created with each line identical to the rest if no noise is added, or slightly different from the other lines if noise has been added to the spectrum. The template spectrum used by the programs, spec and ff, is the original spectrum from which the test spectra are created (i.e., the "galaxy" and the template spectra are a perfect match).

4.3.2 No Noise Tests ki this first set of tests the accuracy to which the programs cm determine velocity dispersions is tested. No noise or velocity shift has been added, only the velocity dispersion is changed. The spectra are scaled so that the mean intensity is 1100, the approximate mean intensity of the brightest galaxy spectnun. The Fourier Quotient program, E, hds the correct velocity dispersions to within 0.595, as shown in Table 4.6. The velocity dispersions found by spec are about 93% of the input value for velocity dispersions greater than about 140 km s-' (see Table 4.7). The 68% confidence intenmls as reported by spec do not always contain the input velocity dispersion. If the input velociw dispersion is Iess than about 140 km s-' the values found can be as smaU as 86% of the input value. These results are inconsistent with the results from the actual galaxy spectra (54.4 and 54.5). The spec velocity dispersions are higher than the ff results for the actual galaxy spectra, whereas with the no-noise tests the spec resdts are lower than the ff results (and the input values) by about 7%.

Table 4.6: Fourier Quotient Test Results (No Noise)

- - NOTES. Col. (1). - Input velocity dispersion in km s-l. Cols. (2) & (3). - Measured veIociQ and error in km s-l. Cols. (4) & (5). - Measured velocity dispersion and error in km s-'. Cols. (6) & (7). - Measured line strength and error. Col. (8). - Ratio of the measured veloaty dispersion and the input velocity dispersion. CHAPTER 4. VELOCITY DlcrPEMIïXVS OF DISTANT GALAXIES

Table 4.7: Spec Test Results (No Noise)

-- - NOTES.COI. (1). - Input velocity dispersion in km s-' . Cols. (2), (3), & (4). - Lower hmit, measured value, and upper limit of the velocity in kms? q, and VE are the 68% "confidence inteITvalS". Cols. (5), (6), & (7). - Lower limit, measured value, and upper limit of the velocity dispersion in kms-'. alo and t~~ are the 68% "confidence intervals". Col. (8). - Ratio of the measured ve1ociQ dispersion and the input velocity dispersion. CWTER 4. VEZOCITY DISPERSIONS OF DISTANT GALAXlES 100

4.3.3 Noise Tests

The test spectra created in this section attempt to replicate the estimated noise in the galaxy spectra. Both the Fourier Quotient program and the Bayesian program are used to analyze the test spectra. The first set of tests discussed below has an input vebcity dispersion of 250 km s-' and in the following set of tests the velocity dispersion is varied. The test spectra have mean intensities, Io, which vary fiom 100 to 1100 and have a constant Gaussian noise of 40 added. SIN ratios are measured using the method described in 52.3 and vary fiom 1.8 to 20.2 (see Table 4.8). The data are read-out noise limited, therefore only Gaussian noise is added, otherwise Poisson noise would be added. Using the above mean intensities and Gaussian noise, test spectra are created that match quite well with the galaxy spectra. The normalized spectra (fiom fT) for the test spectra are shown in Figure 4.7 and for the galaxies they are shown in Figures 4.8 and 4.9. The galaxy and test spectra are compared visually to find the best match of the SIN ratio. The second column in Table 4.9 is the calcdated S/N ratio using the method described in 52.3. The third column is the best match in the SIN ratio (indicated by the value of 1,)based on visual comparisons of the test spectra for each galaxy spectrum. There is good agreement between the visual cornparison and the numerical cornparison using the S/N ratios (rounding down to lower SIN ratio test spectra), with 10 spectra in perfect agreement and 3 spectra within one test spectm. The only galaxy spectra that differ between the visual and numerical comparisons with the test spectra, are the spectra of galaxies 4 (higher visual), 7 (higher numerical), and 10 (higher numerical). An input velocity dispersion of 250 km s-' is used to broaden the test spectra (no velocity shift). The results of the tests are presented in Table 4.8. Ten spectra are produced for each mean intensity and are slightly différent due to the raadom noise added. The velociw dispersions found by each program are averaged. To eliminate spurious results hom spec, only those results wit h a velocity dispersion greater than 50 and line strength of less than 1.5 are averaged. Both programs have problems U galoxy intaml 1

O 500 Io00

LN tAUBLM (pixels: LN WBM(pixels)

t3 galoxy intcrval 1

O 500 1O00 LN WBDA (pixels) LN MBM(pirata)

- I:: I:: 0 LN wam500 (pixeis) Io00

Figure 4.7: Normalized test spectra with varying amounts of noise. Fkom left to right starting at the top row and contiming down Io = 100, 250, 300, 400, 500, 600, 700, 750, 1100. with finding a reasonable solution for the lowest S/N ratio test spectra (1, = 100, S/N = 1.8). The Fourier Quotient program is more successful at finding the correct velocity dispersion in the rest of the tests. The standard deviations of the mean of the ff velocity dispersions are only slightiy higher than the mean errors. This indicates that the errors reported by ff are reasonable. The standard deviations of the mean of the spec velocity dispersions are higher than the ff results indicating that the results O 500

LN UMBDA (pixels) LN LAMBOA (pixels) LN ;AUBOA (pixels)

LN MBDA (pixels) LN LAMBDA (pixels)

Figure 4.8: Normalized galaxy spectra for galaxies 1-9. These spectra can be cornpared with the test spectra in Figure 4.7. fkom ff are more consistent. The mean of 68% confidence intervals as reported by spec are smd in cornparison to the standard deviation of the mean. This implies that the confidence intends for the velocity dispersions are too small. The velocities found by ff are more accurate than those found by spec. Since no velocity shift was added, the measured velociw should be zero. The mean velocities found by ff are very close to zero, but for spec the mean velocities vary quite at bit (see the v~ and v,, columns in Table 4.8). The tme velocity is within the spec CHAPTER 4. VELOClTY DEPERSIONS OF DISTANT GALAXlES 103

t10.wü0 gaiaxy intarvol 1 :I 1.d galaxy uitsrwl 1 tl2.1sO goJazy intmvd 1

- - - I -, I...-I 1-1 ...... , - 1-, . . . . , , . &. O 500 t 000 O 500 IWO O 500 lW0 LN LAMBOA (pixels) LN W8ûA (pixels)

Figure 4.9: Normalized galaxy spectra for galaxies 10-13. These spectra can be compared with the test spectra in Figure 4.7. The emission lines of galaxy 11 have been interpolated.

confidence intervals if the mean intensity is 700 or greater. When the SIN ratio decreases, the confidence intervals do not contain zero. The mean velocity errors for £F vary fiom 14.9 kms-' (Io = 1100, S/N = 20.2) to 58.3 kms-' (1, = 250, S/N = 4.6) for the noise tests. The standard deviations of the mean of the velocity vaq from 8.6 kms-' (Io = 1100, S/N = 20.2) to 29.0 kms-' (Io= 250, S/N = 4.6). The velocity errors as reported by ff are too high by a factor of 1.86 on average. The confidence levels for the measured velocity from spec are again too small. The velocity dispersion is Mned fkom 150 to 325 kms-' for this set of tests. The spec results are shown graphically in Figure 4.10 and the ff results are shown in Figure 4.11. In these figures the ratio of the measured velocity dispersion and the input velocity dispersion is plotted versus the input velocity dispersion. Each panel represents a difFerent amount of noise specified by the mean intensity. The lower right hand panel is the test with no noise. Each point represents the mean of the results CHAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXZES 104

Table 4.8: Test results for input velocity dispersion of 250 km s-'.

10 S/N ff bcff ((5) vff % chi (10) %pet 100 1.8 ...... 60.5 65.2 70.6 76.1 -6994-1 250 4.6 254.9 60.6 67.4 -1.5 308.4 337.3 360.2 52.2 -62.9 300 5.5 254.2 52.8 57.2 -0.8 302.3 325.7 351.6 67.6 -65.6 400 7.4 253.8 41.8 44.0 -0.1 258.4 277.6 290.0 73.6 -34.5 500 9.2 253.5 34.4 35.8 0.1 231.7 240.5 249.6 39.8 10.3 600 11.0 253.3 29.1 30.2 0.2 232.8 241.2 249.8 34-7 9.3 700 12.9 253.1 25.3 26.1 0.2 230.9 238.1 245.3 32.2 3.2 750 13.8 253.0 23.7 24.5 0.2 231.1 237.2 242.5 27.0 2.7 1100 20.2 252.3 16.5 17.0 0.2 231.5 235.9 241.0 21.0 2-2 1100* 284.1 249.0 0.0 0.5 0.0 229.1 235.1 242.1 2.8 1 .O NOTES. Col. (1). - Mean intensity of the spectra. Note that all tests have a constant Gaussian noise added in the amount of 40 except for the la& test rnarked with a *. Col. (2). - S/N ratio. Col. (3). - Mean velocity dispersion in km s-' found by ff. Col. (4). - The mean enor in km s-' found by ff. Col. (5). - The standard deviation of the mean of the velocity dispersion in km s-' found by ff. Col. (6). - Mean velocify in kms-' found by ff. Cols. (7),(8), & (9). - Mean of the lower limit, measured value, and upper limit of the velocity dispersion in kms-' found by spec. oh and obi are the 68% "confidence int ends" . Col. (10). -The standard deviation of the mean of the velocity dispersion in km s-' found by spec. Col. (11). - Mean velocity in km s-' found by spec. of 10 different spectra created with the same parameters, but slightly different due to the random noise and the error bars indicate the standard deviation of the mean. The spec program wtly underestirnates the velociw dispersions in the Iowest SIN ratio test (Io = 100, SIN = 1.8). The measured velocity dispersion in the other low S/N ratio tests (250, 300, 400) is larger than the input velocity dispersion. As the SIN ratio increases the meanired velocity decreases and approaches 93% of the input value. Even though the measured velocity dispersion is less than the input velocity dispersion, the error bars are large enough and include the input velocity dispersion in the tests with added noise. The ff program also has problems with the lowest SIN ratio tests (1, = 100, S/N = CKAP?TER 4- VELOCITY DISPERSIONS OF DISTANT GALAXLE:S 105

1.8). In general the lower the input velocity dispersion and the lower the S/N ratio the higher the measured velocity dispersion. Kormendy & Illingworth (1982) aiso found that the Fourier Quotient method tends to overestimate the velocity dispersion at low S/N ratios. As the SIN ratio increases the measured velocity dispersion approaches the input value. In all of the tests with 1, 2 250 (SIN geq4.6) the input velocity dispersion is well within the ff erron. The velocity dispersions from spec and ff using the unbroadened ws template and the actual galaxy spectra are presented in Table 4.9. Cornparisons of the ff and spec test results and the results hom the galaxy spectra are made in an attempt to understand why the spec and ff results for the galaxy spectra are different. The spec velocity dispersions for the galaxy spectra are either close to or higher than the ff results. Rom the results of the tests with no noise the spec results should be lower. But once noise is added to the spectra the spec velocity dispersions increase. The spec results for an input velocity dispersion of 250 km s-' are higher than the ff results if the mean intensiw is 400 or less. The SIN ratio where this crossover appears varies with input velocity dispersion. For 8 of the 11 galaxies with sufficient S/N ratio the spec results are higher than the ff resdts and even though this is expected fkom the noise tests five of these are even higher than predicted by these tests. In summary, ff is much better at finding the input velocity dispersion than spec. If the spectra have a high SIN ratio, then one can predict what the true velocity dispersions should be when analyzing the spectra with spec (the measured value is 93% of the input velocity dispersion). It becomes more difficult to correct the velocity dispersion when the spectra are noisy. All of these tests use a perfect template, the template is used to create the spectra and also in the analysis. If there are any ciifferences between the ternplate spectmm and the galaxy spectrum, then the situation is even more complicated as will be show in the next section. CRAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXIES 106

input dispersion (km/s)

Figure 4.10: Measured velocity dispersion / input velocity dispersion versus the input velocity dispersion for various SIN ratios for the program spec. The mean intensity is indicated on each panel and a constant Gaussian noise of 40 is added to each spectnun. Each point is the average of the results of 10 different spectra (with the same parameters) and the error bars indicate the standard deviation. For the low S/N ratio tests the program spec overestimates the velocity dispersion. As the S/N ratio increases the measured value approaches 93% of the input value, which is the measured value found in the no-noise test (the Iower rïght panel). CHAPTER 4. VELOClTY DISPERSIONS OF DISTANT GALAXIES 107

.-c 1.2- --- \

V1 Lc - -, a0, ------a-y 0.8 - -- - aal 1.4,IIIiIIIiIII- II I:,;!IIII;::/IIl L - 750 1 1100.0 (no noise) 1 2 - - - - 1.2- -- - E - - -

------4- -- - 0.8 ------1711 t~!! 1111 1111 III~ 100 200 300 100 200 300 100 200 300 input dispersion (km/s)

Figure 4.11: Measured velocity dispersion / input velocity dispersion versus the input velocity dispersion for various SIN ratios for the program ff. The mem intensity is indicated on each panel and a constant Gaussian noise of 40 is added to each spectnun. Each point is the average of the results of 10 difEerent spectra (with the same parameters) and the error bars indicate the standard devîation. The program ff overestimates the velocity dispersion when the input velocity dispersion is low and/or the S/N ratio ratio is Iow. CHAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXLES 108

Table 4.9: Cornparison with galaxy SIN ratios

- -- gaiS/N Io CE ~,,a,, -CE %p,/w ex~.> / = comment 1 14.5 750 268.0 269.4 1.4 1-01 0.93 = within bit higher .-- higher wit hin .. . higher within higher just within within higher 13 10.5 500 208.7 257.2 48.5 1.23 0.94 > higher NOTES. Col. (1). - Gdaxy number. Col. (2). - SIN ratio. Col. (3). -Mean intensity of the test spectra that best matches the galaxy spectrum. Note that this match is based on visual cornparisons of the test spectra and galaxy spectrum. Col. (4). - Velocity dispersion found using ff and the unbroadened template. Col. (5). - Velocity dispersion found using spec and the unbroadened template. Col. (6). - The Werence between the spec and the ff velocity dispersions. Col. (7). - The ratio of the spec velocity dispersion to the ff velocity dispersion. Col. (8). - The expected ratio based on the tests. Note that this assumes that the template is a perfect match which it is not, therefore the spec results may be higher or lower than expected. Col. (9). - Indicates if the spec results are approximately the same (=) or sigrdi- cantly higher (>) thaa the ff results. x indicates that the spectrum is too noisy. Col. (10). - A comment about whether or not the spec results are within the expected range or higher based on the tests. 4.3.4 Mismatched Spectra Tests

It is tinlikely that our template spectrum is a perfect match to our galq spectra. In this section mismatched spectra are created and the velocity dispersion is measured with the Fourier Quotient program, ff. The Bayesian program, spec, is not used in these tests since it cannot find the exact velocity dispersion even under ideal conditions. Mismatched spectra are created by altering the template and then broadening the resdting spectra. The original spectrum is used as the template for the andysis. The template spectrum is altered by multiplying it by a sine function, which changes the relative Iine strengths but does not alter their wavelengths. The new spectrum Di can be written as follows,

where c& is the original spectnim, ai is the first order continuum (essentially a straight line), and fi = A sin 2kn(i + o)/n, where A is the amplitude, k is the number of sine waves per spectrum, O is the offset, n is the number of pixels, and i is the pixel number. Eight Merent mismatched spectra are created and their parameters are listed in Table 4.10. The shape of the modifjhg function for each of the tests is shown in Figure 4.12. The normalized spectra and a cornparison of the measured velocity dispersions to the input velocity dispersions are shown for the unaltered template in Figure 4.13 and for tests 1, 2, and 3 in Figures 4.14 to 4.16. The velocity dispersions found in the no-noise tests vary by at most 8% from the input value. These mismatched spectra simulate the effects of different spectral types and metallicities of the galaxy and template in a crude fashion. The main spectral features in the spectlum aze HP, on the Ieft side of the spectrum, the Mgb triplet, near the center, and Fe 5270Aand Fe 5335A, on the right hand side. In general, if the weaker lines at larger wavelengths (right hand side, Fe lines) are made even weaker the velocity dispersion found is an overestimate. This simulates a galaxy with a lower metallicity or earlier spectral type than the template. These results do not CRAPTER 4. VELOCITY DISPERSIONS OF DETANT GALmS 110

Table 4.10: Mismatched Spectra Parameters

test A k O a&in description O 0.5 0.5 O 0.99 strongercenter 1 0.5 1.0 O 1.05 weakernght 2 0.5 1.0 1024 0.92 stronger right 3 0.5 0.5 512 1.01 depressedcenter 4 0.5 0.5 256 1.03 weakerright 5 0.5 0.5 1536 0.95 stronger right 6 0.5 0.5 256 1.01 weaker right 7 0.5 0.5 1280 0.96 stronger right NOTES. Col. (5). - The velocity dispersion found by ff divided by the input velocity dispersion for the no-noise test. Col. (6). - Description of the relative depths of the spectral lines as compared with the original template.

Figure 4.12: Shapes of the modifying function fi. agree with those of Laird & Levison (1985), who found that if the galaxy has a lower rnetallicity ([Fe/H]) than the template, the velocity dispersion found is lower than the input velocity dispersion, but do agree with those in 53.2.3, where it was found that later spectral type templates hdhigher velocity dispersions than early spectral type templates. If the lines at longer wavelength (Fe lines) are made stronger the velocity dispersion found is an underestimate. These spectra simulate a higher metallicity or later spectral type gdaxy, which again agrees with the results of 83.2.3. Laird & Levison (1985) also found that if the metallicity of the galaxy was slightly higher than the template the velocity dispersion found is a overestimate, but if the clifference in [Fe/H] was greater than 0.5 the velocity dispersion found was smaller than the input CRAPTER 4. VELOCITY DLSPERSIONS OF DISTANT GALAXIElS value (which agrees with our results). If the central lines (Mg lines), which are the strongest, are depressed or made stronger, then the measured velocity dispersion is still close to the input value. For all of the mismatched spectra the meanired velocity dispersion increases with increasing noise. E'rom these results it can be concluded that the velocity dispersions found for the galaxies will most likeb be overestimates. CHAPTER 4. VELOCW DISPERSIONS OF DISTANT GAZIAXIES

LN LAMBDA (pixels)

L 0.8 - -- - - .,l,..,l,,, ,,,<11, ,t ,,., 100 200 300 100 200 300 100 200 300 input dispersion (km/s)

Figure 4.13: This is the original template. The upper plot is the normalized spectntm before broadening. The lower set of plots are similar to Figure 4.11. The measured velocity dispersions are an overestimate of the input velocity dispersions in the noisy spectra whereas the input velocity dispersion is found in the noiseless tests. CKAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXIES

t4 galaxy inïervol 1

, 1 l l I 1 II

LN LAMBDA (pixels)

Figure 4.14: This is mismatched spectrum 1. The upper plot is the nomalized spectrum before broadening. The lower plot is similar to Figure 4.11. The measured velocity dispersions are an overestimate of the input velocity dispersion in ail tests with and without noise. The noiseless tests find velocity dispersions 5% higher than the input values. CWTER4. VELOCITY DISPERSIONS OF DISTANT GALmS

f4 galaxy inferval 1

LN LAMBDA (pixels)

Figure 4.15: This is mismatched spectnun 2. The upper plot is the norrnalized spectrum before broadening. The lower set of plots are similar to Figure 4.11. In the tests without added noise the velocity dispersions measured are 92% of the input values. The measured velociv dispersions are higher when the spectra are noisy. CKAPTER 4. VELOCITY DISPERSIONS OF DLSTANT GALAXIES

t4 golaxy interval 1

1 b 1 1 1 I I

O 500 1 O00

LN LAMBDA (pixels)

-- 1100

- l.,. 1, 100 200 300 100 200 300 100 200 300 input dispersion (krn/s)

Figure 4.16: This is mismatched spectnirn 3. The upper plot is the normalized spectrum before broadening. The lower set of plots are similar to Figure 4.11. The noiseless tests find velocity dispersions 1%higher than the input values. The measured velocity dispersions are higher when the spectra are no@. CHAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXIES 116

4.3.5 Tests with broadened spectra

To understand the differences between the results using unbroadened and broadened template spectra, test spectra are created fkom the broadened template spectra and analyzed with the original unbroadened template spectnim. Test spectra both with and without noise are created fkom the Gaussian and three boxcar broadened templates. Both a velocity shift and velocity dispersion are added to the spectra. When both the velocity and velocity diGersion are zero, the program ff has difficulty finding a solution, but only when no noise has been added to the spectra. If the test spectrum has no added noise and is based on an unbroadened template spectnun, the velocity dispersion found by ff is within 2 km s-' of the input velocity dispersion provided the input velocity dispersion is greater than about 50 km s-'. If a broadened template spectm is used to create the test spectra, the velocity dispersions found are higher by a factor of 50 km s-' (recall that velocity dispersions are added in quadrature). If no extra velocity dispersion is added, the Gauçsian broadened test spectrum is 54.37 km s-' broader than the unbroadened template. The test spectra created fkom the narrow, medium, and wide boxcar templates have velocity dispersions of 46.78, 49.08, and 51.18 km s-' respectively relative to the unbroadened template spectrum providing no extra velocity dispersion is added. When the test spectra are broadened further with velocity dispersions ranging from 25 to 325 kms-l, the amount of extra velocity dispersion introduced by the broadened templates is consistent with the above results to within 5 kms-'. Note that when the added velocity dispersion is high the clifference between the input and rneasured velocity dispersions is smdler than expected. For example, the Gaussian broadened spectrum with an input velocity dispersion of 325 kms-' has a rneasured velocity dispersion of 325.26 kms-' relative to the unbroadened template spectm. The expected value is 329.52 kms-' since the original Gaussian broadened spectnun is 54.37 kms-' broader than the template. No noise was added to any of the above tests. The next set of tests is similar to the tests without noise and has a constant Gaussian noise of 40 added to the spectra, which have a mean intensity of 1100. These test spectra have a relatively high S/N ratio of 20. The velocity dispersions found by ff for the test spectra created from the unbroadened template are about 2-4 kms-l higher than the input velocity dispersions provided the input velocity dispersion is greater than or equal to 25 kms-'. As with the no-noise tests if a broadened template is used to create the test spectra, the velocity dispersions found are about 50 kms-l higher than the input velocity dispersions. Specifically, the Gaussian broadened spectra are 55.16 kms-' broader than the template when no extra velocity dispersion is added. The boxcar broadened spectra have a measured velocity dispersions of 47.47, 49 -80,and 51.83 km s-' relative to the unbroadened template. If the test spectra are further broadened the differences in the measured and input velocity dispersions are consistent to the above values to within 1 kms-'. Note that these results are better than the no-noise tests. In summary, the difference in the instrumental broadening for the template and galaxy setups is approximately 50 kms-'. Since dispersions are added in quadrature, this results in only a few kms-' difFerence in measured velocity dispersions when using unbroadened and broadened template spectra. It is expected that the velociw dispersions of the galaxy spectra analyzed with the broadened spectra will result in measured velocity dispersions higher by only a few km s-' relative to the results with the unbroadened template spectra. Since the shape of the boxcar broadened template spectra matches the shape of the sky lines in the galaxy spectra, one would expect that the results with this ternplate should have lower errors than the results analyzed by templates whose iine profiles are not similar. It will be seen in the next sections that this is not tme. This may be due to the fact that the spectra are noisy and any advantages of having similarly shaped profiles are lost in the noise. CWTER 4. VELOCITY DrSPEWIONS OF DISTANT GALAXIES 118

In the tests with no noise the Fourier Quotient program, ff, estimates the input velocity dispersion much better than the Bayesian program, spec, which hds a velocity dispersion of about 93% of the input value. It should be noted that several modifications were made to the original Bayesian program and these changes may be responsible for the inaccurate results. When noise is added to the test spectra ff is again better at finding the correct velocity dispersion. The addition of noise to the spectra tends to cause both programs to overestimate the velocity dispersions. If the noise is high or the input velocity dispersion is low, the velocity dispersion found by ff is higher than the input value. Mismatched spectra can produce either under or overestimates of the velocity dispersions, but for the tests performed the velocity dispersions are between 92% and 105% of the input values. Tests with broadened test spectra indicate that the results using unbroadened and broadened template spectra should &Fer by a few kms-' as expected, since the instrumental broadening for the galaxy and the template spectra differ by 50 km s-'. From the tests performed in this section it is concluded that Fourier Quotient program will give the best results. 4.4 Analysis of the Galaxy Spectra using the Bayesian Method

In this section the galaxy spectra are analyzed using the Bayesian program spec, which is described in detail in 52.2. Unbroadened, Gaussian broadened, and boxcar broadened template spectra are used to determine the central velocity dispersions of the galaxies in Abell 2390. Two types of unbroadened template spectra (see 84.2.2) are used, "with shaping" (ws) and 'ho shaping" (ns). Only the ws spectrum will be broadened since the 2 values fiom the spec results using the ws templates are lower than with the ns template. The velocity dispersions found from the different ws broadened template spectra are within 11 kms-' of the unbroadened ws template spectra dues and the redshifts are within 4 x 1od5 (12 km&). Recall that spec assumes that the template and the galaxy images are taken with the same instrumental setup. The program spec requires that the spectra have the same wavelength intervals. This is the reason for redshifting the template out to the redshift of the galaxy. Therefore, a good initial guess of the redshift is needed; preliminary redshift estimates are listed in Table 4.1. Starting with these dues an iterative process is used to find more accurate redshifts for the galaxies. The final redshift estimates fiom spec are within 5 x of the preliminary values excluding galaxies 3, 6, and 11. Note that for two of the galaxies, 3 and 6, the S/N ratio is too low and the results are incorrect. The emission lines of CD gdaxy (11) must be masked out, which does not leave very much of the spectnim, and therefore the results for this galaxy are suspect. Accurate redshifts are needed for the velocity dispersions found by spec to be valid. The redshifts, and velocity dispersions reported fiom the program spec are an average of the results of 10 identical spectra. The results are slightly different for each copy of the spectmm since spec uses a Monte Carlo method. For example, the redshifts of galaxy 1 vary by at most 0.00003 fiom the mean and the velocity dispersions by 7 km s-? Table 4.11 contains the redshifts used to prepare the template spectra for both spec and E. To test the effects of an incorrect template redshift these redshifts are CHAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXZES 120 shifted by -0.004 to 0.004 in increments of 0.001 and it is found that spec only gives consistent results if the shift is not too large (see Table 4.12). If the shift is between -0.002 and 0.001 the redshifts and velocity dispersions found are similar. The Fourier Quotient program, fF, always gives consistent results for the above shifts (see Table 4.13). ff requires that the spectra be on a log scale and spec requires that the spectra be on a linear scale. It is this Merence that causes spec to give inaccurate results if the initial redshift is incorrect. The spec results are illustrated with four different plots (see Figures 4.17 tu 4.31). The top two plots are the "rad' template and gdaxy spectra. Note that the ternplate spectrum has been rebinned and is not tdyraw, hence the absorption lines do not line up exactly in these two plots. The third plot is the continuum subtracted galaxy spectrum, scaled such that the noise dispersion per pixel is about 1. The fourth plot is the residuals after subtracting the broadened template. Figures 4.17 to 4.20 show the results for galaxy 1 with the unbroadened ns, unbroadened ws, Gaussian broadened ws, and middle boxcar broadened ws templates. The obvious difference among these figures is the plot of the raw template spectrum. The shape of the continuum in the template spectrum in Figure 4.18 clearly matches the shape of the galaxy spectnun better than in Figure 4.17. The template spectra in Figures 4.19 and 4.20 have broader lines than the ws spectra. The residuals (bottom plot) in these figures are all very similar and only by careful examination can one detect Merences. Figures 4.21 to 4.31 show the results for galaxies 2 to 13 (excluding galaxy 3) using the middle boxcar broadened ws template. Recd that the [OI]sky line at 6300A is not cornpletely subtracted in some cases and therefore this area is masked out for the analysis. CKAPTER 4. VECOCITY DISPERSIONS OF DISTANT GALAXlES 121

Table 4.11: Redshifts for the templates for each gzlaxy

Table 4.12: Results korn spec using unbroadened "shaped" template spectra (ws) va,rying the redshift of the template spectra for galaxies 2 and 4.

- - NOTES. Col. (1). - Galaxy. Col. (2). - Amount the redshift of the template diners fkom the values given in Table 4.11. Col. (3). - The 2 value as reported by spec. Cols. (4), (5), & (6). - Mean of the lower limit, measured value, and upper limit of the redshift found by spec. q, and .q,i are the 68% "confidence intervals". Cols. (7), (8), & (9). - Mean of the lower limit, measured value, and upper bitof the velocity dispersion in km s-' found by spec. q, and ahi are the 68% "confidence intervals". CHAPTER 4. VELOCITY DISPERSIONS OF DETMT GALAXIES 122

Table 4-13: Results &om ff using unbroadened "shaped" template spectra (ws) w- ing the redshift of the template spectra for galaxies 2 and 4. Table 4.14: Results from spec for both unbroadened templates (wsO and nsO)

IR Table 4.14 the results from spec using both unbroadened templates are compared. It can be seen that the shaped templates (WSO)~produce better results (the x2 value is smaller for most galaxies) than the non-shaped spectra (nsO). In dl but three cases (galaxy 5, 10, and 11) the results fkom both templates are consistent with one another (i.e. within the 68% confidence levels). The redshifts vary by at most 0.00007 (21 kms-'). The galaxies with a high S/N ratio have velocity dispersions that vary by less than 16 km s-l.

3The "On indicates that no extra shift was added to the redshiRs in Table 4.11. CHAPTER 4. WLOCITY DLSPERSIONS OF DISTANT GALAXIES

pixel

I I Y 1 I 1 I I l I I I I 6000 6200 6400 6600 6800 wavelength

Figure 4.17: spec results for galaxy 1 with the unbroadened ns (no shaping) template. The top two plots are the "raw" template and galaxy spectra. The third plot is the continuum-subtracted galaxy spectnun. The bottom plot is the residuals after subtracting the modified template. The Mg and HP lines are slightly visible in the residuals . Figure 4.18: spec results for galaxy 1 *th the unbroadened ws (with shaping) template. The top two plots are the "raw" tempiate and galaxy spectra. The third plot is the continuum-subtracted galaxy spectrum. The bottom plot is the residuals after subtracting the modified template. Note that the shape of the continuum of the template and galaxy are similar. The Mg and HP lines are slightly visible in the residuals. CHAPTER 4- VELOC'DISPERSIONS OF DLSTANT GALAXIES

1 I 1 I I I 1 I 1 1 1 I I 1 I i 1 6000 6200 6400 6600 6800 wavelength

Figure 4.19: spec results for galaxy 1 with the Gaussian broadened ws template. The top two plots are the "raw" template and galaxy spectra. The third plot is the continuum-subtracted galaxy spectrum. The bottom plot is the residuals after subtracting the modified template. The template's absorption Iines are broader than in Figure 4.18. The Mg and HP iines are slightly visible in the residuals. CWTER4. VELOCITY DISPERSIONS OF DISTmT GALAXZE3S

400 600 pixel

- - 1 I I I I I I I I I I 1 1 I 6000 6200 6400 6600 6800 wavelength

Figure 4.20: spec results for galaxy 1 with the (middle) boxcar broadened template. The top two plots are the "raw" template and galaxy spectra. The third plot is the continuum-subtracted galaxy spectrum. The bottom plot is the residuals after subtracting the modified template. The Mg and Ho lines are slightly visible in the residuals. CWTER4, VELOCITY DrSPEMIONS OF DISTANT GALAXZES 128

1 I I I I I L 6000 6200 6400 6600 wavelength

Figure 4.21: spec results for galaxy 2 with the (middle) boxcar broadened template. The top plot is the continuum-subtracted galaxy spectmm for galaxy 2. The bottom plot is the residuals after subtracting the modified template for galaxy 2. The absorption lines are still slightly visible in the residuals. Have the Mg lines been over subtracted? This would lead to an overestimate of the value of the velocity dispersion.

6000 6200 6400 6600 wavelength

Figure 4.22: spec results for galaxy 4 with the (middle) boxcar broadened template. The top plot is the continuum-subtracted galaxy spectrum for galaxy 4. The bottom plot is the residuals after subtracting the modified template for galaxy 4. HP is still slightly visible in the residuals. t 1 1' , 1 1 I t i -1 5800 6000 6200 6400 6600 wavelength

Figure 4.23: spec results for galaxy 5 with the (middle) boxcar broadened template. The top plot is the continuum-subtracted galaxy spectnun for gdaxy 5. The bottom plot is the residuals after subtracting the modified template for galaxy 5. The resuits are suspect since the galaxy spectrum is quite noisy. The HP emission was masked out before analysis.

5 O

-5

L II' 10

-5

Figure 4.24: spec results for galaxy 6 with the (middle) boxcar broadened template. The top plot is the continuum-subtracted galaxy spectnun for galaxy 6. The bottom plot is the residuals after subtracting the rnodSed ternplate for galaxy 6. A true solution was not found since the SIN ratio is too low. CKAFTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXIES

t.I I f 1 i 4 5800 6000 6200 6400 6600 wavelength

Figure 4.25: spec results for galaxy 7 with the (middle) boxcar broadened template. The top plot is the continuum-subtracted galaxy spectnim for gdaxy 7. The bottom plot is the residuals after subtracting the modified template for galaxy 7. The absorption lines are still slightly visible in the residuals.

wavelength

Figure 4.26: spec results for galaxy 8 with the (middle) boxcar broadened template. The top plot is the continuum-subtracted galaxy spectrum for galaxy 8. The bottom plot is the residuals after subtracting the modified template for galaxy 8. The results are suspect since the gdaxy spectnim is quite noisy. CHAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXES 131

- -10 -- 1 * 1 I 1 t 1 I 5800 6000 6200 6400 6600 wavelength

Figure 4.27: spec results for galaxy 9 with the (middle) boxcar broadened template. The top plot is the continuum-subtracted galaxy spectrum for galaxy 9. The bottom plot is the residuals after subtracting the modified template for galaxy 9. The absorption lines are slightly visible in the residuals.

-10 , I I 1 1 1 1 I 1 5800 6000 6200 6400 6600 wavelength

Figure 4.28: spec results for galaxy 10 with the (rniddle) boxcar broadened template. The top plot is the continuum-subtracted gdaxy spectnun for galaxy 10. The bottom plot is the residuals after subtracting the modified template for galaxy 10. The HP emission was masked out. The Mg lines are slightly visible in the residuals. CEAPTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXIES 132

5 O -5 -10 -15 5 O -5 -10 - 15 5800 6000 6200 6400 6600 wavelength

Figure 4.29: spec results for galaxy 11 with the (middle) boxcar broadened template. The top plot is the continuum-subtracted galaxy spectrum for galaxy 11. The bottom plot is the residuals after subtracting the modSed template for galaxy 11. The four strong emission lines were masked out. The results are suspect since there is only a small portion of the Mg absorption lines left. There is also an unknown absorption line at approhately 5890A (rest fiame - 4788A).

wavelength

Figure 4.30: spec results for galaxy 12 with the (middle) boxcar broadened template. The top plot is the continuurn-subtracted galaxy spectrum for galaxy 12. The bottom plot is the residuals after subtracting the modified template for galaxy 12. The results are suspect since the galaxy spectrum is quite noisy. CWTER4. V'OCITYDISPERSIONS OF DISTANT GALAXIES

wavelength

Figure 4.31: spec resdts for galaxy 13 with the (middle) boxcar broadened template. The top plot is the continuum-subtracted galaxy spectnun for galaxy 13. The bottom plot is the residuals after subtracting the modified template for galaxy 13. The results are suspect since the galaxy spectnun is fairly noisy. CEZAPTER 4, VELOCITY DEPERSIONS OF DISTANT GALAXIES

The velocity dispersions found using the unbroadened and broadened ws template spectra are presented in Table 4.15. Note that solutions for galaxies 3 and 6 are not always found and when a solution is 'Yound" it is incorrect- The velocity dispersions vary by at most 11 km s-' . It is expected that if a broader template is used the velocity dispersion found should be lower than with an unbroadened template. This is true for 8 out of 11 galaxies when using the Gaussian broadened template and for 7 out of 11 galaxies when using the medium boxcar broadened template. Only a few km s-l difference is expected which is smaller than the errors. The x2 values are very similar for the different template spectra, with the unbroadened ws template having the lowest value for 8 out of 11 galaxies.

Table 4.15: Results from spec for unbroadened and broadened ws templates

ws0 wsOg wsObn wsObm wsObw gd 0 U Chi 01 0 chi Uio 0 Ohi O obi 010 ahi 1 264 269 276 255 261 267 258 264 270 258 264 271 257 264 270 2 275 287 298 278 290 300 279 287 295 279 287 296 275 284 293 3 42 42 42 42 42 42 ...... -. .-...... 4 262 268 274 253 258 265 253 261 267 253 259 265 253 259 265 5 186 198 214 194 208 225 189 205 221 187 205 222 188 203 222 6 57 60 64 ...... -...... 7 295 304 313 284 293 303 290 297 307 291 301 309 290 297 305 8 228 234 240 220 226 231 222 228 235 221 228 235 219 226 234 9 207 213 219 204 211 217 205 212 219 206 213 221 206 213 220 10 202 207 214 195 201 206 196 202 207 197 203 209 197 204 209 11 257 267 278 250 260 270 255 263 272 255 265 275 254 263 274 12 197 205 213 194 206 216 197 206 215 198 208 216 195 207 216 13 249 257 265 244 251 259 249 257 267 248 256 264 249 256 264 NOTES. - wsO = unbroadened template results, wsOg = Gaussian-broadened template results, wsOb[nmw] = boxcar-broadened [narrow, middle, wide] template result S. CWTER4. VELOCITY DISPERSIONS OF DISTANT GALAXIES 135 4.5 Analysis of the Galaxy Spectra using the Fourier Quotient Method

In this section the Fourier Quotient program ff is used to determine the central velocity dispersions of early-type galaxies in Abell 2390. In 52.1 the ff program is discussed in detail. As with spec the galaxy spectra are analyzed with unbroadened and Gaussian- and boxcar-broadened template spectra. The velocity dispersion errors are lower for the "with shaping" (ws) template spectra than the "no shaping" (ns) template spectra for 11 out of 13 galaxies, therefore ody the ws template spectra will be broadened. The velocity dispersions fkom the broadened templates are within 15.7 km s-' of the ws template spectra and the redshifts are within 15.8 km s-'. The Fourier Quotient program requires that the data be on a logarithmic scale and that both the template and galaxy spectra have the same wavelength interval. This program was originally written assuming that the same instrumental setup is used for obtaining both the galaxy and template spectra. Initial guesses for both the velocity and velocity dispersion are needed as input to the program. Since 10 identical spectra are being analyzed the program varies the initial velocity randody for each copy of the spectnun. If the program is converging to the true minimum and not a local minimum, then the same result wiIl be found for each of the 10 spectra. As mentioned in 84.4 the ff program is not as sensitive as spec to an incorrect redshift of the template. The results for the unbroadened ws template with no shift and the average of al1 of the shifts are shown in Table 4.16. The redshift that is used to prepare the template spectnun for analysis with each galaxy spectnun is given in Table 4.11. The template redshift is also shifted by Az = f0.004 in increments of 0.001. The redshifts and velocity dispersions found with Az = O (no added shift) are in agreement with the average values for aJl the redshifts with and without added shifts. Notice that the program is able to find a "solution" for galaxies 3 and 6. It is questionable whether or not these results are valid. Table 4.17 compares the results £rom the nsO and wsO templates (both with zero CHAPTER 4. VELOCïTY DISPERSIONS OF DISTANT GALAXZE;iS 136 shift). The velocity dispersions agree to within 10 kms-1 (except for galaxies 3, 6, and 11) and the redshifts are within 0.00005 (15 km s-'). The veIocity dispersions from ail of the galaxies (even 3, 6, and 11) agree within the errors.

Table 4.16: Results fiom ff using the unbroadened ws template with wavenumber k = 10 to 200

unbroadened ws no shift unbroadened ws average gda~y z 6% O Sa z dz a 60 1 0.22791 0.00010 268.0 27.7 0.22790 0.00010 265.3 28.1 2 0.22909 0.00014 255.1 39.8 0.22909 0.00014 253.5 39.2 3 0.22963 0.00030 231.2 85.7 0.22965 0.00029 230.6 86.0 4 0.21913 0.00009 245.2 26.3 0.21913 0.00009 245.2 26.1 5 0.23741 0.00017 143.7 51.1 0.23740 0.00017 143.9 50.6 6 0.23488 0.00017 106.2 50.7 0.23489 0.00017 99.5 49.2 7 0.22444 0.00013 266.2 37.6 0.22447 0.00013 263.1 36.5 8 0.22637 0.00014 233.3 38.6 0.22637 0.00014 234.4 38.8 9 0.23020 0.00011 181.2 32.7 0.23020 0.00011 179.3 32.8 10 0.23176 0.00009 189.5 25.6 0.23176 0.00009 186.8 25.3 11 0.23076 0.00017 263.5 54.4 0.23077 0,00017 255.7 52.9 12 0.22811 0.00013 154.1 39.3 0.22811 0.00013 155.6 39.7 13 0.23124 0.00014 208.7 39.7 0.23123 0.00014 209.7 39.3

The lower (k,) and upper (k,J Iimits of the wavenumber in the fit can be varied. The lower limit has the most duence on the results. To ve* that klo = 10 is the correct choice for each galaxy ff is run with different values of kl, ranging from O to 20 in increments of 5. Figure 4.32 shows the velocity dispersion as a function of kl, for each galaxy with the medium boxcar broadened ws templates. For all of the galaxies either the velocity dispersion is independent of klo or k,, = 10 provides a good fit as seen fiom the errors in the velocity dispersion and visual inspection of the Fourier fit plots for the different values of klo. For galaxies 3 and 11 the velocity dispersion is highly dependent on kIoand these plots reinforce previous statements that the results for these galaxies are highly suspect. Figure 4.33 shows the Fourier transform data and fit for the velocity, velocity dispersion, and line strength. The top two plots are the real and imaginary parts of G(k)/S(k)versus k. The fit is shown with a dashed curve. The dashed vertical hes indicate the region in wavenumber (k = 10 to 200) used for the fit. The bottom two CWTER4. VELOCITY DISPERSIONS OF DISTANT GALAXlES 137

Table 4.17: Results from ff for both unbroadened templates (wsO and nsO) with no shift and k = 10 to 200

plots are the residuals of the upper two plots. Figures 4.36 to 4.38 show only the real part of G(k)/S(k)versus k since the redshift of the galaxy relative to the redshifted template should be zero (the imaginary part of equation (2.5) is zero). The velocity dispersions found using the broadened and unbroadened ws template spectra are presented in Table 4.18. Solutions for galaxy 6 are not found in most cases. Galaxy 3 has the largest errors and its results are unlikely to be correct. The velocity dispersions found using the broadened ws templates va.ry by at most 15.7 kms-' from the unbroadened ws template velocity dispersions (excluding galaxy 3 and Il). CHAPTER 4. VELOCITY DISPERSONS OF DISTANT GAI/AXIES 138

Table 4.18: Results from ff for unbroadened and broadened ws templates and k = 10 to 200

ws0 wsOg wsObn wsObm wsObw

The velocities found with the broadened ws templates vary by at most 15.8 km s-' fiom the unbroadened template values. The velocity dispersions found using the Gaussian broadened ws template are lower than the unbroadened template values for dl galaxies except 3 and 13. The velocity dispersions £corn the medium boxcar ws templates are lower than the unbroadened ws template values for all galaxies except 1, 3, and 13. The errors are very simila for each of the dîfFerent templates, but the Gaussian template has the lowest errors for 7 out of 12 galaxies. CWTER 4. VELOCITY DISPERSIONS OF DISTANT GALAXIES 139

Figure 4.32: Velocity dispersion as a function of klo using medium boxcar broadened ws template. The galaxy is indicated by the number in the top left corner of each panel. The velocity dispersion is the mean of 10 attempts and its error is the mean of the errors of these 10 attempts. Note that no solution is found for galaxy 6 for any of the values of ki, and no solution is found for galaxy 5 with klo = O. Similar results are found for the unbroadened ws template with the most mation in galaxy 11. For most galaxies the velocity dispersion in independent of klo. CWTER4. WLOCITY DISPERSIONS OF ZiTSTANT GALAXLES 140

tf .nsO galaxy interval 1 t 1 .nsO galaxy interval 1

tl .nsO galaxy intervol 1 il .nsO galoxy intervol 1

Figure 4.33: fF fit and residuals for galaxy 1 with the unbroadened ns (no shaping) template for klo = 10. The top two plots are the real and imaginary parts of G(k)/S(k) versus k. The fit is shown with a dashed curve. The dashed vertical lines indicate the region of wavenumbers used for the fit. The bottom two plots are the residuals of the upper two plots. CWTER4. VELOCITY DLSPERSIONS OF DISTANT GALAXIES

tl .wsO galaxy interval 1

Figure 4.34: ff fit and residuals for galaxy 1with the unbroadened ws (with shaping) template for kh = 10. The rdpart of G(k)/S(k)versus k. Note that there are noticeable Merences between this plot and that of the unbroadened ns template (Figure 4.33).

tl.wsOg galaxy iniervoi 1

Figure 4.35: ff fit for galaxy 1 with the Gaussian broadened ws template for kio = 10. The red part of G(k)/S(k)versus k. This plot is are noticeably noisier than the unbroadened template plots (Figures 4.33 and 4.34). CWTER4. VELOCITY DISPERSIONS OF DBTmT GALAXlEIS 142

tl.ws0brn galaxy interval 1 t2.wsObrn galaxy intervol 1

K K t3.wsObm golaxy interval 1 t4.wsObm goloxy interval 1

Figure 4.36: ff fit for galaxy 1 to 4 with the (middle) boxcar broadened ws template for kIo = 10. The real part of G(k)/S(k) versus k. Minor ciifferences can be seen between the two broadened tempIate plots for galaq 1 (top left). Visual inspection of these plots easily confirms that the fit that is found by ff is valid for galaxy 2 (top right). No valid solution is possible since the S/N ratio is low for galaxy 3 (bottom left). GaIaxy 4 (bottom right) has the highest SIN ratio in our sample. CKAPTER 4. VELOClTY DISPERSIONS OF DISTANT GALAXIE!S

t5.wsObm goloxy interval 1 t7.wsObm galaxy intervol 1

K t8.wsObm galaxy interval 1 t9.wsObm gaioxy iniervoi 1

Figure 4.37: ff fit for galaxy 5 to 9 with the (middle) boxcar broadened ws template for ki, = 10. The red part of G(k)/S(k)versus k. The results for galaxy 5 (top Mt) are suspect since the plot is quite noisy. No solution was found for galaxy 6. The solutions found for gdaxy 7 (top right) and 9 (bottom right) appear to be valid. The results for galaxy 8 (bottom left) are suspect since the plot is somewhat noisy. CEL4FTER 4. WLOCLTY DISPERSIONS OF DISTANT GALAXTES 144

t f O.wsObrn.200.10 gaiaxy interval 1 t 1 1 .wsObm galoxy in terval 1

ti 2.wsObm gaiaxy interval i tl3.wsObm galoxy intervcl 1

Figure 4.38: ff fit for galaxy 5 to 9 with the (middle) boxcar broadened ws template for ki, = 10. The real part of G(k)/S(k) versus k. The results are suspect since these plots are noisy for galaxy 10 (top left) , 12 (bottom left) , and 13 (bottom right). Gdaxy 11 (top right) is the CDgalaxy and the strong emission lines have been masked out. Therefore its results aie highly suspect. CRAPTER 4, VELOCITY DZSPERSIONS OF DISTANT GALAXIES 4.6 Discussion

A Fourier Quotient program, ff, and a Bayesian program, spec, are used to determine the velocity dispersions and redshifts of 13 early-type galaxies in Abell2390. The results of extensive tests with both programs indicate that ff is much better at hdhg the input velocity dispersions than spec. The tempIate star, q52 Ori was obsemed using a different instrumental configuration than that of the galaxîes. The Mer- ent instrumental setups cause different amount of instrumental broadening. This Uerence is determined by comparing sky lines in the galaxy background spectra with narrow absorption lines in the template. Rom the measured difference in the widths of these lines the template spectra can be broadened to match the instrumental broadening of the galaxy spectra. Two types of broadened spectra are created, Gaussian and boxcar. All three types of templates are used by both programs to find the velocity dispersions of the galaxies. The results are summarized in Figure 4.39 for the E (black) and the spec (red) programs. For each galaxy the results for four dinerent templates are illustrated. Note that in almost dl cases the spec results are higher than the ff results. The error bars for the spec results are much smaller than the ff results and recall that fiom the tests the spec error bars are in fact too small, whereas the error bars for the ff results are probably correct. Table 4.19 compares the results fiorn the medium boxcar broadened ws template for both E and spec. Note that for two of the galaxies the ff and spec results are very close. The spectnun of galaxy 1 has a high SIN ratio. The spectrum of galaxy 8 is noisy and therefore the very similar results might be fortuitous. Rom the tests performed in 54.3.3 it is expected that the spec velocity dispersions should be lower than the ff results, but this is not found to be the case and the reasons for this discrepancy are not weU understood. Both spec and ff overestimate the velocity dispersion when the S/N ratio is low. When this expected overestimation is taken into account, 5 galaxies stÏU have spec velocity dispersions that are higher than p&dicted by the test. Since the tests indicate that the spec program cannot find the input velocity dispersion, the ff medium boxcar broadened ws template results will be used C'R4. VELOClTY DlSPERSIONVc OF DISTANT GU-S 146 in the rest of the analysis. The medium bmcar broadened ws template is chosen Qnce its lùie profile most cclosely matches that of the sky Iines in the paiaxy spectra. 400 1 I I I I I I I I I I I I i T I

Figure 4.39: Cornparison of ff (black) and spec (rd) velocity dispersions. The galaxy number is indicated on the x-a;xis and the velocity dispersion is the y-ais. The circles are the unbroadened ns template results, the open triangles the unbroadened ws template redts, the x's the Gaussian broadened ws template results, and the füled squares are the medium baxcar broadened results. The spec results are higher for all of the galaxies except galaxies 1 and 3. Note that galaxy 3 has a very noisy spectrurn and that the velocity dispersions are incorrect for spec and most likely incorrect for ff. The results for galaxies 1 and 8 agree quite dl. CWTER4. VELOCITY DISPERSIONS OF DISTANT GALAXIES 147

Table 4.19: Results from the medium boxcar broadened ws template for both ff and spec.

------NOTES. " A valid solution was not found. The data is too noisy and therefore the resdts are very suspect. 9 The results are questionable since the data is fairly noisy. There are possible problems with the results as seen in the plots (the fit is bad or lines in residuals are strong). Chapter 5

Fundamental Plane of Abell 2390

In this chapter the evolution of the mas-to-light ratio of cluster elliptical galkes will be measured by comparing the Fundamental Planes of the distant Abell 2390 cluster (t = 0.23) and the neaxby Coma cluster (z = 0.023). If cluster formation is coeval, galaxies at higher redshifts are younger and therefore contain a larger fraction of young stars. These younger stars are more luminous relative to theK masses and therefore young galaxies have a lower mas-to-light ratio (Larson & Tinsley 1978; Worthey 1994). If these galaxies evolve passively their total luminosity will decrease and their mass-to-light ratio will increase. If elliptical galaxies formed about 15 Gyrs ago and evolved passively, the approximate expected luminosity evolution is a few tenths of a magnitude (for z = 0.23 =+ 0.023). If elliptical galaxies formed more recently their luminosity evolution will be geater since the luminosity evolution is more rapid at earlier stages. Not only can the total luminosity of a galaxy change as it evolves but the structure can dso change, especially if rnergers are important. If mergers play a significant role, then the average mass of galaxies will also change. Since we are measuring the luminosity evolution as a function of the mass-to-light ratio, this analysis is not sensitive to mass evolution. Acquiring comparable data for clusters at Werent redshifts is ficult. The more distant galaxies have a smalIer apparent size and apparent bnghtness and require higher resolution imaging and longer integation times. Publically availabie HST/WFPG2 optical images of these distant redshift clusters are becoming an im- CWTE:R5. FUNDAMENTAL PLANE OF ABELL 2390 149 portant source of data for Fundamental Plane analysis. Measuring the velocity dispersions of high redshift galaxies is also complicated as shown in the previous chapter. Again longer integation times are needed to obtain spectra of sufficient SIN ratios. To compare the properties and Fundamental Planes of the two clusters Abell 2390 and Coma two assumptions must be made, first that the clusters are coeval, and second that the galaxies within the clusters are in a similar environment such that the galaxies) fundamental properties are infiuenced in the same way. Abell 2390 is approximately 1.5 times richer than Coma (Howard Yee - private communication). The other major difference between these two clusters is that Coma is thought to be made up of two clusters that are merging (Colless & Dunn 1996). The primary goal is to measure the evolution of the mas-to-light ratio. We are also interested in the basic properties of the Fundamental Plane of Abell2390. Does the Fundamental Plane still exist at higher redshift? If it does exist, is it dinerent fiom the Fundamental Plane of a local cluster? It is expected that the younger stellar populations of the galaxies of Abell 2390 will result in brighter galaxies as compared to an older local cluster. If there have been no structural changes in the galaxies, then we should be able to detect pure luminosity evolution by comparing the Fundamental Planes of Coma and Abell2390. In the htsection (55.1) the photometry of both clusters will be discussed. It is important to establish that the photometric analysis of both clusters is consistent. 55.2 compares the photometry of Coma by Schade, Barrientos, & LbpetCruz (1997) to that of Jgrgensen, Ranx, & Kjærgaard (1995a),hereafter JFK95a. The procedure used to normalize the velocity dispersions of the two clusters to a common aperture size is briefly discussed in 55.3. The luminosity-size relation and Faber-Jackson relation are used to determine the amount of evolution in luminosity between Abell2390 and Coma ($5.4 and 55.5). The E'undamental Planes of both Abell 2390 and Coma are compared in 55.6. The dBculties associated with using projections of the hdamental Plane to measure luminosity evolution are discussed in 55.6.3. The amount of evolution in luminosity and the mass-to-light ratio is &O estimated in this section. The results of this chapter are surnmarized in the last section (55.7) . CWmR5. FIINDAMENTA PLANE OF ABELL 2390 5.1 Photometry

5.1.1 Coma

In order to measure the amount of luminosity evolution that has taken place between Abell 2390 and the present we must compare the galaxies of AbelI 2390 with a local cluster, such as the Coma cluster. In this section the photometry of both Coma and Abell 2390 are presented. Other authors have photometric data of Coma but there is no standard method for the photometric analysis. If their results for Coma are used, the slight clifFerences in the methods could lead to an incorrect estimate of the amount of evolution. Therefore it is important to base our results on photometry analyzed using the same techniques for both of these clusters. Using the Kitt Peak 0.9m telescope, on 1993 December 12 an 800 second B band exposure of the central area of the Coma Cluster was taken by Omar Lbpez- Cruz (1997). This image was andyzed by Schade (Schade, Barrientos, & Lbpez-Cruz 1997) and the procedure is described in Schade et al. (1995). Two-dimensional galaxy models were fitted to "syrnmetrired" galaxy images to determine the efFective radii and surface brightnesses. Note that one-dimensional models were used for the two CD galaxies in the cluster. Both types of models have a de Vaucouleurs (r1I4)profile. The models açsumed that the galaxies are pure elliptical galaxies (Le. no diçk component) . The model parameters for the SOS may be incorrect since up to 40% of the light can corne fkom the disk component. The photometry of the SO galaxies could be redone but for this study it is not deemed necessary since the elliptical galaxies in this sample form a well dehed Fundamental Plane (see 55.6.1) and we wish to compare elliptical galaxies in Coma with similar galaxies in Abel1 2390. The results presented here are corrected for Galactic extinction, cosmological surface brightness dimming and are also K-coaected. The difference in brightness between Coma and AbeU 23Yü galaxies wilI therefore be due to evolution only. The photometric parameters in Tables 5.1 and 5.2 are derived fkom (photometric) model parameters with Ho = 50 km s-l Mpc-' and qo = 0.5. The first column of velocity dispersions are taken fkom J~rgemen,fianx, & Kjærgaard (1995b) and have an aperture diameter of 31'4. The second set of velocity dispersions have an aperture diameter of r,/4 (see 55.3). The morphological types are from Andreon et al. (1996).

Table 5.1: Coma Data: EKpticals

D Morph. M'(AB) pBo (AB) logi, (kpc) Fit log a

NOTES.Col. (1). - Dressler number. Col. (2). - Morphological classi.&ation (Andreon et al. 1996). unE = undetermined efiptical, diE = disky elliptical, and boE = boxy elliptical. Col. (3). - Absolute magnitude in B (AB) band (no galactic extinction correction) fiom mode1 fis. Col. (4). - IntrInsic central surface brightness in B(AB) band (no galactic extinction correction) £rom model fits. Cols. (5) & (6). - 10gie and the error in logr,, where r, in kpc fiom model fits. Errors were not available for the two CDgalaxies (129 and 148). Galaxies 151 and 155 (Table 5.2) have errors less than 0.0005. Col. (7). - Quality of the photometry fits. 3 = good, 2 = fair, 1 = poor/bad. Cols. (8) & (9). - log of velocity dispersion within an aperture of diameter 3I'4 and re/4 respectively (see 85.3). Table 5.2: Coma Data: Lenticulars and Others

D Morph. M*(AB) pB,, (AB) log T, (kpc) Fit log O (3:'4) (reI4 88 SA0 -20.32 12.50 ... SA0 S.. SABO/SAO SB0 SB0 SB0 SA0 SA0 SB0 SABO/a SAO/SABO SAO/a SA0 .- SB0 SA0 SB0 SAO/SAa SB0 SA0 SAO/a SAB0 SA0 .. . SA0 SBO/SABO NOTES.See Table 5.1 for a description of the columns.

5.1.2 Abel1 2390

Abel1 2390 has both ground-based and HST observations. On 1993 June 18 the Canadian Network for Observational Cosmology (CNOC) group took a 900 second exposure in Johnson R with the 3.6m CFHT using the Multiobject Spectrograph (MOS)(Yee et al. 1996). The HST observations were made on 1994 December 10 using WFPC2 and the F814W filter (5 exposures of 2100 seconds each) and these CWTER5. FUNDMNTAL PLANE OF ABEL& 2390 153 data were obtained fiom the HST archive at the Canadian Astronomy Data Centre. The photometnc andysis of Abell2390 was also done by Schade (Schade et al. 1996, 1997). Tables 5.3 and 5.4 contain the results of the photometric analysis for the MOS and HST images respectively (Schade, private communication).

Table 5.3: MOS Imaging Data of Abell 2390

NOTES.NO MOS image data adable for Galaxies 3 and 6 due to their low luminosities. The extinction correction of 0.17 has not been applied to values in this table. Col. (2). - Absolute magnitude in B(AI3) band (no Galactic extinction correction) from model fits. Col. (3). -Intrinsic central surface bnght~essin B(Al3) band (no Galactic extinction correction) fiom model fits. Cols. (4) & (5). - logTe and the error in logr., where r, in kpc from model fits.

A combination of HST and MOS data are used for the analysis. There do not appear to be any systematic merences between the HST and MOS data. The mean Merences between the HST and MOS data for pBo(AB),MB(AB), and logr, are respectively O.13f O.84,O.lOf 0.20, and -0.05k0.16 for the eight galaxies in cornmon.' The agreement between the MOS and HST datasets is good. The HST data are of higher quality and will be used when avaikble except for galaxy 13 for which the MOS data are used. The reason for this is that galaxy 13 lies far away fiom the plane Table 5.4: HST haging Data of AbeU 2390

- -- NOTES. Galaxies 1, 2, 3 are not in the HST image. Galaxy 11, the CD,contains substructure and the fit is poor. The fits for galaxies 4 and 8 are fair (they are both edge-on SOS). The extinction correction of 0.17 has not be applied to values in this table. See Table 5.3 for description of columns. formed by the rest of the galaxies when plotting the projections of the Fundamental Plane with the HST data. It appears that the HST value for the surface brightness may be too high. Table 5.5 contains the photometric parameters used in this study. Table 5.5: HST/MOS Imabkg Data

2 -20.83 12.71 0.442 0.01 3 ...... -.- 4 -21.30 12.54 0.690 0-002 5 -20.01 13.48 0.429 0.006 6 -19.96 16.64 1.098 0.006 7 -21.13 12.58 0.509 0.003 8 -20.79 12.99 0.664 0-002 9 -21.43 13.69 0.761 0-003 10 -21.02 12.48 0.430 0-006 1 -23.37 15.04 1.419 0.01 12 -20.75 13.78 0.627 0.003 1 -20.89 13.27 0-674 0.02 * MOS data. NOTE. See Table 5.3 for description of columns. CBAPTER 5, FUNDAMENTU PLANE OF ABELL 2390 5.2 Cornparison with JFK Coma data

In this section the Coma data are compared to that of Jgrgensen, fianx, & Kjærgaard (1995a,b), hereafter JFK. It will be shown that these two datasets agree fairly weU with one another, but that there are some systematic merences, which reinforces the need to compare results analyzed in the same manner. Table 5.6 contains the JFK data used in this study. The photometric parameters from JFK95a are K-corrected, seeing corrected, and corrected for cosmologicd surface brightness dimming and extinction. The velocity dispersions are from Jgrgensen, Franx, & Kjzrgaard (1995b) and have an aperture diameter of 3Y4. The number of different morphological types in each of the datasets and the type of symbols used in the plots are listed in Table 5.7. In general our data2 are plotted through out this chapter (see for example Figures 5.2 and 5.5) with open symbols and 3FK's data with filled symbols. If one of our symbols has a red or black dot inside, it indicates that the photometnc fit is only fair or poor/bad respectively. In Figure 5.1 the Fundamental Plane parameters of galaxies common to both JFK's dataset and Schade's dataset are compared. We find that our log(1). are on average 0.05 f 0.16 lower than JFK's values and Schade's logr, are on average 0.07 f 0.13 higher. If the CD galaxies are excluded the agreement between the two datasets is very good. Schade's log (1). values are 0.02 f 0.07 higher than JFK's values and Schade's log re are also slightly higher (0.02 f0.08). The scatter in the logr. vs log (l), plot is less for Schade's data than for the JFK data when considering ody the common eiliptical galaxies (Figure 5.2). The reverse is true when all the elliptical galaxies are included. The dope of the lines are very similar considering the differences in the quantities for a given gdaxy. This is also true when plotting log r, vs the apparent magnitude, = log (P)~- 5 (log r, +0.192) - 2.5 log 27r (not shown). Schade's data are in general good agreement with JFK's data even though individual galaxies may ~iy.For the most part we will only use Our elliptical galaxies in

2~hereour data refers coliectively to Schade's photometric data and our velocity dispersion data Table 5.6: JFK Coma Data

D Morph. (P)G logr, (arcsec) log a 31 SAO/diE 22.47 0.06 1.49 0.02 2.429

NOTES.Col. (1). - Dressler number. Col. (2). -Morphological classification (Andreon et al. 1996). diE = disky elliptical, boE = boxy elliptical, unE = undefined elliptical. Cols. (3) & (4). - Mean surface brightness within r, and error. Cols. (5) & (6). - log re and its error in arcseconds. Col. (7). - log of the velocity dispersion. this study. Results will be presented for al1 elliptical galaxies and elliptical galaxies excluclhg the CDS. This is done in part because the photometric andysis is slightly different for the CDS(ID fit as opposed to a 20 fit). There are merences between the JFK data and Schade's data for the CDS (Schade's logr, values are higher than C'TER5. FUNnWNTAL PLANE OF ABEIL 2390

Table 5.7: Morphological types

Morphological types JFK Schade color symbol E (boxy, disdisky and undetermined) 18 10 black (circles) disky E/SAO 5 5 magenta (pentagons) SA0 1 10 green (squares) SB0 and SABO 3 10 blue (squares) spiral/SO 1 4 cyan (trïangles) spiral O 1 cyan (hexagons) UIZkllown O 3 yellow (pentagons) NOTES.The JFK data are plotted throughout this chapter with filled symbols and our/Schade data with open symbols. Poor and bad fits have a black dot inside the symbols. Fair fits have a red dot inside.

- mean = -0.05 I 0.16 -

1 1.5 2 2.5 3 3.5 log CI>.

Figure 5.1: Cornparison of Fundamental Plane parameters of elliptical galaxies cornmon to JFK's and Schade's dataset. In the left plot JFK's log (1). is plotted versus Schade's log(&. The straight line represents the 1:l line. Similarly the right plot compares logr,. The mean differences between Schade's values and JFK's are shown on the both of the plots. Galaxies are labeued with their Dressler numbers. The agreement between JFK's data and Schade's data is quite good. Note that there are some merences between the two CDgalaxies (129 and 148).

JFK's but since Schadels effective radii are larger, his surface brightnesses are lower) but in the logl; vs log (1). (Figure 5.2) and plots the scatter for the CDgalaxies is comparable to that of the other galacies. log ,

Figure 5.2: Io~T,vs log (I), for the JFK and Schade datasets. M ellipticd galaxies are plotted. The JFK data points (filled circles) are joined to the correspondhg Schade points (open circles) by a straight line. The least-squares fit to each dataset containing only the common galaxies is shown with solid lines for JFK's data and dashed lines for Schade's data. The rms scatter in both datasets is indicated on the plots for the cornmon galaxies and for all of the galaxies. The slope in the lines are very similar even though there are clifferences among the individual galaxies. The rms scatter is Iess for Schade's data when only the galaxies in common are considered. When all the elliptical galkes are used the JFK rms scatter is smaller. CHAPTER 5. FUNDMNTAPLANE OF ABELL 2390 5.3 Velocity Dispersions and Aperture Size

To compare the velocity dispersions of galaxies it is desirable that they have the same aperture. Jflrgensen, Franx, & Kjærgaard j1995b) have found the following relation for early-me galaxies, logg,, = log ad. + 0.04(log dds - log d,,), where

O,, is the corrected velocity dispersion for an aperture size of dm, in kpc and is the observed velocity dispersion for an aperture size of dda in kpc. The aperture of the Abell2390 galaxies is 0:'8 in one direction since this is the size of the slit. We will assume that the aperture is square and the other dimension is also 0Y8. The velocity dispersions of Coma have been normalized to an aperture diameter of 3Y4. A correction of 0.0844 in logo (for Ho = 50 kms-l Mpc-' and qo = 0.5) must be applied to our velocity dispersions of the Abel1 2390 galaxies so that they have the same aperture size as the Coma galaxies. Velocity dispersions for Coma with an aperture diameter of rJ4 are also used in this study. Schade's values of r, are used to calculate this set of velocity dispersions and will therefore mer fiom those of JFK95a even though the method is the same. Note that the 31'4 diameter velocity dispersions are used for most of the analysis. 5.4 Luminosity-Size Relation

The relationship between luminosity and size (Kormendy 1977) is often used in the study of luminosi@ evolution. One assumes that the size, the effective radius, of the gataxy does not change significantly and measures the change in 1uminosiQ t with redshift. Schade, Barrientos, & Lbpez-Cruz (1997) have found the following luminosity-size relation for local galaxies: MB (AB) = -3.33 log r, - 18.65 (Ho = 50 kms-' Mpc-'). Figure 5.3 is a plot of MB(AB) vs logr, for the elliptical galaxies in Coma (open circles) and the Abell 2390 galaxies (Iabelled asterisks). The solid black line (nearly coincident with the green line but just above it) is the above local relation and the dotted black line is the local relation shifted to fit the Abell 2390 galaxies (keeping the slope constant). The Abell 2390 line is shifted by AMB(AB) = -0.46 I 0.12 with respect to Comae3 Note that Schade et al. (1997) found AMB = -0.34 f0.20 for a sample of 10 galaxies in AbeU 2390 using HST data and the Mg - logr, relation. These two values are in agreement within the errors. The solid green line (just below the solid bladc line) is the fit to Schade's Coma elliptical galaxies keeping the slope constant at -3.33 (the intercept is -18.64). This increases the amount of brightening measured for Abell2390 slightly to AMB(A.B)= -0.48 f 0.12. A linear le&-squares fit, OLS(MB(AB) 1 log T,)~,gives the following

relation: Me(AB) = (-2.85 & 0.19) log T, - (19.02 & 0.22), which is indicated by the solid red line, and AMB (AB) = -0.41 & 0.11 for the simple mean of the shifts and AMe(AB) = -0.39 f0.04 for the weighted mean of the shifk5 Both of these values are consistent with the value found by Schade et al. (1997). Note that the datasets used in this study and the Schade et al. (1997) study are not the same. The dataset in this study includes 9 Abell2390 galaxies that were observed by HST and 3 additional galaxies for which only MOS observations are available.

3AMB(AB)is the mean of the shifts for each galaxy and its uncertainty is the sample standard deviation multiplied by (N - 1)-Il2. This is similar to the method descnbed by Feigelson & Babu (1992). 40rdinary least-squares with MB(AB) as the independent variable 5Note that the weighted mean aualysis is possible when the full calibration set is avaiiable. The uncertainty in the weighted mean is the standard deviation of the mean. These results are summarized in Table 5.8. Two different data sets are used to hdAMB (AB): the dataset with 11 galaxies contains all the galaxies except 3 and 6; the dataset with 7 galaxies also excludes 4, 5, 8, and 11 for reasons explained in 35.6. The amount of brightening found using all 11 galaxies is lower than if the subset of 7 galaxies is used. The amount of brightening that agrees best with the Schade et al. (1997) results is the one found using ali 11 galaxies.

Table 5.8: Luminosity-Size Relation Results

MR(AB) dope inter n AM n AM phot -3.33 -18.65 11 -0.46 0.12 7 -0.60 0.16 phot -3.33 -18.64 11 -0.48 0.12 7 -061 0.16 phot -2.85 -19.02 11 -0.41 0.11 7 -0.52 0.14 r)hota -2.85 -19.02 11 -0.39 0.04 7 -0.48 0.05 NOTES. Col. (1). -phot = absolute magnitudes are from the photometric analysis. a weighted mean analysis. Cols. (4) & (7). - Number of galaxies in the sample. The sample containing 11 galaxies excludes 3 and 6. The sample containing 7 galaxies excludes 3, 4, 5, 6, 8, and 11. CHAPTER 5. FUNDAIME:NTL PLANE OF ABELL 2390

1 I I I 1 i I 1 I I 1 III I 1 1 I I

Figure 5.3: The luminosity-size relation (MB(AB) vs log r, ) for Coma elliptieals (open circles) and AbeIl 2390 galaties (labellecl asterisks). The solid blad< line coincident with but just above the solid green line is the relation found by Schade et al. (lWï), Ms(AB)= -3.33 Iogr. - 18.65. The dotted black line is the line that fits the AbeIl 2390 gaiaXies (exduding g&q 6) with the same slope. The solid green Iine just below the black line is the fit to the Coma galaxies keeping the slope constant at -3.33 (shifted by 0.01). The solid red line is the least-squares fit to the Coma ellipticals (MB(AB)= -2.8510gre - 19.02). The dotted red line is the correspondhg fit to the Abell2390 galaxies. The luminosi@ evolution measured nom the luminosity-size relation is appraximately -0.46 magnitudes. CHAPTER 5. FUNDWNTAL PLANE OF ABELL 2390 5.5 Faber-Jackson Relation

The Faber-Jackson relation (Faber & Jackson 1976), ~5 cc aa, where a is usuauy between 2.5 and 4, is shown in Figure 5.4 for the elliptical galaxies in Coma and the Abeu2390 galaxies. There is a fair amount of scatter in both sets of data. The solid line is the fit to the Coma ellipticals with a = 4. The dotted line is the fit to the Abell 2390 galaxies. Most of the Abell 2390 galaxies appear to be fainter than the relation dehed by the Coma galaxies with a = 4 (AMB(AB)= 0.39 5 0.34). If a straight line is fit to the Coma sample n = 3.6 it 0.6 and the amount of dimming is iess, AMs(AB) = 0.35 I0.32 (simple mean) and AMB(AB)= 0.25 f 0.11 (weighted mean). Bender, Ziegler, & Bninial (1996) rneasured the Bband lurninosity evolution of 16 elliptical galaxies in 3 clusters at a redshift of 0.37 with the Faber-Jackson relation and found that these galaxies were 0.5 & 0.1 magnitudes brighter than local elliptical galaxies fkom the Coma and Virgo clusters (Ho = 50 km s-' ~pc-land qo = 0.5). If a simple linear relation is assumed between B-band luminosity and age, then galaxies at a redshift of 0.23 should be about 0.3 f 0.1 brighter than local galaxies. This assumption of a hear relation is valid over small redshift ranges. These results are not consistent with the luminosity-size relation results or with the expected brightening of galaxies at higher redshifts. One possibility is that the velocity dispersions are overestimated for the Abell 2390 galaxies. Extensive tests were performed on the procedure used to mesure the velocity dispersions so this is considered unlikely. The Fourier Quotient method tends to overestimate the velociw dispersion if the data are noisy, but for the majority of the galaxies it is estimated that this results in only a one or two percent overestimate. Both sets of velocity dispersions have been aperture corrected so this is not the source of the problem. Galaxies which are more centrdy concentrated (i.e. have a higher surface brightness) are more likely to have been chosen for the Abell2390 sample. This may have introduced a selection bias which is not present in the Coma sample. This surface brightness selection effect is explained in more detail in 85.6.3. If a bias exists that is related to how CHAPTER 5. FmAIME:NTAT, PLANE OF ABELL 2390 165

centrdy condensed a galaxy is, then the Fundamental Plane analysis whkh includes the effective radius will result in an improved estimate of the Iuminotity evolution.

Figure 5.4: Velocity dispersion venus absolute magnitude. Coma elIïpticals are indicated by open circles. Labelled asterisks are the Abell 2390 galaxies. The solid line is the Faber-Jackson relation, L oc a*,for the Coma elliptical galaxies (intercept 0.1445). The dotted line is the fit to the Abell2390 galaxies. The luminosity evolution rneasured from the Faber-Jackson relation and using the absolute magnitudes for the photometric analysis is 0.41 10.34. Note that even though this implies a

Table 5.9: Faber-Jackson Relation Resdts

MB(AB) a Il AM n AM phot 4.0 11 0.39 0.34 7 0.59 0.37 phot 3.6 11 0.35 0.32 7 0.53 0.33 phota 3.6 11 0.25 0.11 7 0.43 0.14 NOTES. Col. (1). - phot = absolute magnitudes are from the photometric analysis. a weighted mean analysis. Cols. (3) & (6). - Number of gdaxies in the sample. The sample containing 11 galaxies excludes 3 and 6. The sample containing 7 galaxies excludes 3, 4, 5, 6, 8, and II. CHAPTER 5. FU'NDWNTAL PLANE OF ABELL 2390 5.6 The Fundamental Plane

In this section the Fundamental Plane of Coma WUbe detennined and compared to the Fundamental Plane derived from the JFK data. Both the JFK and our datasets and subsets of each dataset are used to find the Fundamental Plane of Coma. Using the Fundamental Planes of AbeU 2390 and Coma the change in lumhosity between elliptical galaxies in AbeU 2390 and Coma wiU be determined. The Fundamental Plane is a superior method to the Faber-Jackson relation in estimating the luminosity evolution. The evolution of the mass-to-light ratio of elliptical galaxies in Coma and Abell2390 will also be estimated.

5.6.1 The Fundamental Plane of Coma

A method similar to that described by Jgrgensen, Franx, & Kjærgaard (1996, hereafter JFK96), is used to determine the findamental Plane of Coma. The hindamen- ta1 Plane can be written as

logr, = crlogo +Plog(I), +r, (5-1) where Te is the effective radius, o is the centra1 velocity dispersion, (I), is the mean surface brightness within re, and a,P, and 7 (zero point) are to be determined. The Fundamental Plane solution (a,,O, and 7)is found by minimizing the sum of the absolute residuals perpendicular to the plane,

for different values of 7.6 The enors in the parameters are calculated using the Jaddrnife Method (Efion & Stein 1981). Table 5.10 contains the results fiom fitting the Fundamental Plane to various Coma datasets. The three main datasets are the JFK data (Table 5.6), owdata with

'Uncertainties in the quantities of the individual data points are not used to calculate the Fun- damental Plane solution. CHAPTER 5. FUNnAMENTA PLANE OF BELL 2390 168

both fair and good photometry fits and our data with just the good photometry fits (Tables 5.1 and 5.2). The Fundamental Plane is determined for Mnous subsets of the datasets based on morphological type. It should be noted that for our data the photometric analysis assumed that the gaIaxies are efipticals (pure bulges) . This will contribute to the high scatter and errors when all the galaxies are used to detennine the Fundamental Plane. The results in Table 5.10 are based on corrected velocity dispersions with an aperture of diameter 3Y4. Table 5.11 contains the results for an aperture diameter of re/4. We dso find that the absolute value of both a and P on average increase when an aperture diameter of 44is used instead of 3Y4 (see JFK96). The Fundamental Plane is fust derived for aU of the galaxies regardless of morphological type. The next subset consists of ellipticd and SO galaxies (E,S(AB)O). Barred SO are excluded korn the next subset (E,SAO) since there maybe dBculties in the photornetrie analysis if bars are present. The E+ subset includes E and diE/SAO galaxies. The next two subsets contain only elliptical galaxies, E and E(-CDS). This last subset excludes the CD galaxies since a slightly different photometric analysis technique was used (a 1D fit as opposed to a 2D fit). The Fundamental Plane that we find for our Coma sample, the JFK sample, and the solution that JFK96 found for their sample of 226 E and SO galaxies in 10 clusters are in good agreement. JFK96 found a = 1.20 f 0.06 and P = -0.83 f 0.02 in the Johnson B band for cluster E and SO galiuEies. For the JFK sample of Coma galaxies we find a = 1.180 f0.015 and P = -0.837 f0.006. Cornparing only the subsets with elliptical galaxies we £ind a = 1.193 f 0.004 and P = -0.856 I0.001 for the JFK sample and a = 1.028 I0.060 and P = -0.855 f 0.028 for our sample. If the CDS are excluded from both datasets of elliptical galaxies we fbd a = 1.192 f 0.010 and P = -0.856I0.006 for the JFK sample and a = 1.119f0.381 and B= -0.801I0.065 for our sample. The values of a and fl are in good agreement when one considers that the omission of two points can change these values by up to 0.09 and 0.05 respectively (datasets containhg elliptical gaIaxies with and without the CDS). The rms scatter of the residuals in log r, is often used as a measure of the thidmess CKAPTER 5. FUNDMNTAL PLANE OF BELL 2390 169

Table 5.10: Fundamental Plane Fitting Results (3Y4 aperture)

Data Fit Types No Min a! fi 7 J - al1 28 0.632 1.180 0.015 -0.837 0.006 0.046 0.035 J - E,S(AB)O 27 0.603 1.186 0.008 -0.840 0.004 0.042 0.035 J - E,SAO 24 0.454 1.187 0.021 -0.843 0.010 0.047 0.030 J - Et 23 0.438 1.193 0.012 -0.856 0.010 0,064 0.031 J - E 18 0.253 1.193 0.004 -0.856 0.001 0,064 0.023 J - E(-CDS) 16 0.240 1.192 0.010 -0.856 0.006 0.065 0.025 S F ail 40 2.166 1.095 0-029 -0.816 0.008 0.263 0.083 S F E,S(AB)O 33 1.784 1.090 0.074 -0.825 0.011 0.286 0.087 S F E,SAO 24 1.233 1.012 0.006 -0.807 0.004 0.452 0.083 S F Et 15 0.559 1.064 0.070 -0.827 0.031 0.353 0.059 S F E 10 0.202 1.028 0.060 -0.855 0.028 0.475 0.035 S F E(-CDS) 8 0.186 1.119 0.381 -0.801 0.065 0.151 0.046 S G all 25 1.027 1.062 0.099 -0.807 0.016 0.298 0.063 S G E,S(AB)O 24 1.016 1.215 0.117 -0.813 0.015 -0.028 0.064 S G E,SAO 19 0.770 1.082 0,032 -0.785 0.019 0.214 0.061 S G E+ 13 0.389 1.037 0.131 -0.815 0.035 0.378 0.048 S G E 10 0.202 1.028 0.060 -0.855 0.028 0.475 0.035 S G E(-CDS) 8 0.186 1.119 0.381 -0.801 0.065 0.151 0.046 NOTES. Col. (1). - J = JFK Coma data set, S - our data set. Col. (2). - F = includes both fair and good photometry fits. G = only those galaxies with good photometry fits. Col. (3). - "all" inchdes all galaxies listed in Tables 5.1, 5.2 and 5.6. The "E,S(AB)On dataset contains E, SAO, SABO, and SB0 galaxies (excluding the un- knowns and spirals). The "E,SAO" dataset contains E, diE/SAO and SA0 galaxies. The "E+" dataset contains E and diE/SAO. The ''E" dataset contains only E galaxies. The "E(-CD)" dataset contains E galaxies excluding the CDS. Col. (4). - Number of galaxies in the dataset. Col. (5). - Minimum value of the sum of the absolute residuals perpendiculax to the plane, equation (5.2). Cols. (6) & (7). - a and its error. Cols. (8) & (9). - p and its error. Cols. (10) & (11). - 7 and its error. of the Fundamental Plane. The residuals in log T,, log r, - (alog n + ,6 log (I),+ r), are shown in Tables 5.12 and 5.13. The scatter in l0gî; of our Coma elliptical galaxies is 0.049 and for the JFK elliptical galaxies it is 0.040. Our dataset only contains 10 galaxies as compared to 18 for JFK so it is to be expected that our data set will have a higher larger rms error. JFK96 found the scatter in logre to be 0.084 for their Table 5.11: Fundamental Plane Fitting Results (r,/4 aperture)

Data Fit Srpes No Min a fl 7 S F al1 40 2.367 0.989 0.076 -0.860 0.016 0.595 0.090

NOTES.See Table 5.10 for description of columns. sample of cluster E and SO galacies. They also noted that Coma's F'undarnental Plane is thinner than the Fwidamental Plane for their sample of 226 cluster galaxies. They find a rms scatter of 0.042 for 28 E galaxies in Coma7, which compares well to ou value of 0.040 for 18 E galaxies in our JFK sample. The residuals are slightly higher when using the re/4 aperture for the velocity dispersions. In the next set of Figures (5.5 to 5.9) our data and the JFK data for Coma are compared. Various datasets and values of a, ,O, and 7 are used in the plots. Each set of figures has three plots. The upper two plots are edge-on views of the Fundamental Plane. The left and right plots show the Fundamental Plane along a long and short side respectively. The edge-on view 1 plot is (alogo + ,û log (I),) venus log T, and the edge-on view 2 plot is log O versus (log T, - p log (l),). The dotted lines in these two plots are the Fundamental Plane fit. The bottom plot is the face-on view of the Fundamental Plane, (alog (1). - plogo)/Jm- versus

[(a2 + p2)*log T= + log (l)=+ a log o]/d(a2 + p2)2+ a* + PZ. The dashed line is a line of constant luminosity at approximately L.. Figure 5.5 is a plot of al1 the data using the fit for our elliptical galaxies. The high scatter in Our data (open

70~JFK sample of 28 galaxies is not the same set that JFK96 used. CHAP?IER 5. FUNDAMENTAL PLANE OF ABELL 2390

Table 5-12: log r, Residuals (3.4 aperture)

Data Fit Types No nns mean sigma J - al1 28 0.0602 -0.0034 0.0598

S G E,S(AB)O 24 0.1073 0.0099 0.1024 S G E,SAO 19 0.1000 0.0142 0.0931 S G Et- 13 0.0733 -0.0069 0.0541 S GE 10 0.0493 -0.0081 0.0466 S G E(-CDS) 8 0.0577 -0.0214 0.0529 NOTES. Col. (1). - J = JFK Coma data set, S = our data set. Col. (2). -F = includes both fair and good photometry fits. G = only those galaxies with good photometry fits. Col. (3). - "alln includes all galaxies listed in Tables 5.1, 5.2 and 5.6. The "E,S(AB)On dataset contains E, SAO, SABO, and SB0 galaxies (excluding the un- knowns and spirals). The "E,SAO" dataset contains E, diE/SAO and SA0 galaxies. The "E+" dataset contains E and diE/SAO. The 'Edataset contains only E galaxies. The "E(-CD)" dataset contains E galaxies and excludes the CDS. Col. (4). - Number of galaxies in the dataset. Col. (5). - rms of the log r, residuals. Col. (6). - Mean of the logr, residuals. Col. (7). - Sigma of the mean of the logr, residuals. points) is due to the assumption that al1 of the galaxies are elliptical galaxies in the photometric analysis. Only elliptical gdlames are plotted in Figure 5.6. The elliptical galaxies of both datasets form a tight Fundamental Plane. In the edge-on view 2 plot it can be seen that most of the JFK galaxies lie above the plane that is defined by our galaxies (dashed lines). Figure 5.7 is a similar plot except the Fundamental Plane fit is for the JFK elliptical galaxies. In Figures 5.8 and 5.9 only galaxies Table 5.13: logr, Residuals (re/4aperture)

Data Fit Types No rms mean sigma S Fd 40 0.1442 0.0312 0.1398 S F E,S(AB)O 33 0.1505 0.0326 0.1462 S F E,SAO 24 0.1436 -0.0008 0.1012 S F E+ 15 0.1014 0.0071 0.0874 S FE 10 0.0562 0.0004 0.0527 S F E(-CDS) 8 0,0662 -0.0159 0.0640 S Gall 25 0.1140 0.0057 0.1066

common to both datasets are plotted and the fit to our Coma ellipticals is used. As noted before the scatter in the non-elliptical galaxies is higher for our sample (Figure 5.8). Figure 5.9 contains only the elliptical galaxies cornmon to both datasets. Even though there are differences in the individual quantities (e.g. log r,) of the two Coma datasets simila Fundamental Planes are formed. Due to differences in photometric reduction techniques, including possible zero point dserences, it would be best to use parameters derived using the same techniques. Our sample of Coma elliptical galaxies is small but it has been shown that a Fundamental Plane derived £rom this sample agrees reasonably well with that found by JFK96 and with one we derived using JFK data. CHAPTER 5- FUNDAMENDU PLANE OF ABELL 2390

log r, + 0.866 log d>,

Figure 5.5: Eiindamental Plane plots for JFK and Our Coma data. AU available data are plotted. See Table 5.7 for an exphnation of the different symbols. The dotted line in the top two edge-on plots is the Fiindamentai Plane fit. The dashed hein the bottom face-on plot is a constant lirminosity lïne for Le.Our hindamental Plane fit for elIiptical galaxies is used (a= 1.028,P = -0.855, and y = 0.475). Note that the higher scatter in our Coma data is due to an assumption in the photometric analysis. CH-APTER 5. FUNDAMENTU PLANE OF ABELL 2390

dama 0 E

(1.m log r, - 0.866 log , + 1.028 log u) / 223 Figure 5.6: Fundamental Plane plots for JFK and our Coma data. Only elliptical galaxies are plotted. See Table 5.7 for an explanation of the difFerent symbols. The dotted line in the top two edge-on plots is Fundamental Plane fit. The dashed line in the bottom face-on plot is a constant luminosity line for L,. Our Fundamental Plane fit for elliptical galaxies is used (a= 1.028, B = -0.855, and 7 = 0.475). The elliptical galaxies form a tight Fundamental Plane. Most of the JFK elliptical galaxies Lie above the hein the edge-on view 2 plot. log r, 4 0.856 log CI>,

Corna JFK Coma O E E

. .s. 'll""l"i'll' O 1 2 (2.16 log r, - 0.858 log , + 1.193 log u) / 2.61

Figure 5.7: Fundamental Plane plots for JFK and our Coma data. Only elliptical galaxies are plotted. See Table 5.7 for an explanation of the different syrnbols. The dotted iine in the top two edge-on plots is Fundamental Plane fit. The dashed line in the bottom face-on plot is a constant luminosity hefor L,. JFK's Fundamental Plane fit for elliptical galaxies is used (o! = 1.193, 0 = -0.856, and 7 = 0.064). This Fiindamental Plane solution does not fit our Coma data as well as Figure 5.6. CHAPTER 5. FUNnAmLPLANE OF ABELL 2390

2.6 3 log r, + 0.866 log CI>,

r. 8 V - ... fair fit .8 bad/poor fit 2"~"1'''q1'~*' O 1 2 (1.70 Log ri - 0.866 log CI>, e 1.028 log a) / 2.23 Figure 5.8: F'undamental Plane plots for JFK and our Coma data. Only galaicies common to both datasets are plotted. See Table 5.7 for an explanation of the different sgmbols. The dotted line in the top two edge-on plots is the hdamental Plane fit. The dashed Iine in the bottom faceon plot is a constant luminosity line for L.. Our Fbdamental Plane fit for eliipticd galacies is used (a = 1.028, ,û = -0.855, and 7 = 0.475). The edge-on view 2 plot provides the best view of the plane tu identify correspondhg points from the two datasets since the velocity dispersions are identical. Our non-ellipticd galavies increase the scatter in the Fundamental Plane. CWTER5. FUNDWNT'PLANE OF BELL 2390

2.5 3 log r, + 0.855 log 0,

JFK Coma a E

O 1 2 (1.79 log r, - 0.856 log CI>, + 1.028 log O) / 2.23

Figure 5.9: Fiindamental Plane plots for JFK and our Coma data. Only ellipticd galaxies common to both datasets are plotted. See Table 5.7 for an explanation of the cWerent symbols. The dotted line in the top two edge-on plots is the Fundamental Plane fit. The dashed line in the bottom face-on plot is a constant luminosity line for L.. Our Fundamental Plane fit for elliptical galaxies is used (a= 1.028, P = -0.855, and y = 0.475). In the edge-on view 2 plot four out of eight galaxies match host exactly with the correspondhg gdaxies in the two datasets. A tight Fundamental Plane is formed by both datasets. 5.6.2 Fundamental Plane of Abell 2390

In this section the Fundamental Plane of AbelI 2390 will be determined and compared to the Fundamentai Plane of Coma In Figures 5.10 to 5.12 the Fundamental Planes of Coma and the AbeLi 2390 galmcies are plotted for various Fundamental Plane solutions. ki Figure 5.10 our Fundamental Plane fit for elliptical galaxies of Coma is used. The Abell2390 galaxies lie below and to the right of both lines in the edge-on (upper) plots. The Abell2390 galaxies have a smaller range in absolute magnitudes than the Coma galaxies (bottom plot) and have a larger fiaction of galacies with L > A.. The JFK Fundamental Plane fit for ellipticd galaxies is used in the next plot (Figure 5.11). Again the Abell 2390 galaxies lie below and to the right of the Lines. If our hindamental Plane plot for elliptical galaxies excluding the CDS (Figure 5.12) is used the Abell 2390 galaxies rnove up with respect to the lines in the upper two plots and do not show as much evolution. An attempt is made to find the Fundamental Plane for the AbeU 2390 galaxies (a,p, and 7). The small sample size and larger eaors in the data contribute to the problem of finding a reasonable fit. It is also possible that the galaxies in Abell 2390 do not forrn a thin Fundamental Plane. The results of these attempts to find a Fundamental Plane for different subsets of the Abell2390 dataset are given in Table 5.14. The fkst dataset contains aU the galaxies except the faintest two (3 and 6) for which the SIN ratio was too low to obtain accurate photometry and velocity dispersions. The second dataset excludes the CD (11) and the two SO galaxies (4 and 8). The third data set excludes galaxies 1 and 2, for which there is only MOS photometry and the CD and SO galaxies. The data in the next two datasets are chosen based on the quality of the velocity dispersion and photometry results. In the next subset galaxy 5, 8, and 11 are all omitted due to uncertainties in the velocity dispersions derived. Galaxy 4 is omitted due to the fact that it is and edge-on SO galaxy from the last subset list in the table, as well as galaxies 5, 8, and 11. The number of data points in each of these subsets it too small to obtain a reasonable fit to the Fundamental Plane as can be seen by the widely varying results and their CHAPTER 5. FUNDAMENTAL PL- OF BELL 2390 179 large errors. The third dataset listed in this table has the smallest value for the sum of the residuals perpendicular to the plane, and the values of a and P do not disagree significantly from those from the Coma cluster when taking into account the errors.

Table 5.14: Fundamental Plane Fitting Results For Abell 2390

No Galaxies Omitted Min a P 7' 11 none 0.427 1,816 0.119 -1.025 0.054 -0.668 0.070 8 4,8,11 0.284 0.723 0.499 -0.606 0.239 0.614 0.077 6 1,2,4,8,11 0.109 1,576 0.518 -0.967 0,223 -0.313 0.046 8 5,8,11 0.355 0,747 0.770 -0.517 0-419 0.333 0.094 7 4,5,8,11 0.203 0.379 0.654 -0.620 0.221 1.490 0.054 C'TER5. FU2VDA2MENTA.L PLANE OF ABELL 2390

26 S log r, + 0,866 log a>,

O 1 2 (1.70 log r, - 0.W log (I>, + 1.028 log u) / 223 Figure 5.10: Fundamental Plane plots for Coma and Abell 2390. Only elliptical galaxies in Coma are plotted. The dotted line in the top two edge-on plots is the Fundamental Plane fit. The dashed line in the bottom face-on plot is a constant luminosity line for L.. Our hindamental Plane fit for elliptical galaxies of Coma is used (a = 1.028, P = -0.855, and 7 = 0.475). AU of the AbeU 2390 galaxies lie below and to the right of the Fundamental Plane fit indicated by the dotted line in the edge-on plots. 2.6 3 log r, + 0.856 log CI>,

1111*.1~,~8 . face-on view Abell 2390 8 8 * b E/90 t 8 - dalaxy 11 CD * 4- b. \ - Galaxies 4 and 8 90 n 0 b ,,psi.* w - 0 ',a O c. f?* 3.5 - , 6- t)\ol* Coma rO ,L2* . O E 2 ;0 + - 0 As, À 3- 'b 11. 0 L , O v . m b* . c. . m .b a 2.6 - L - d * O 8 .b Y-- , - b. .b 2111""1'14'11' O 1 2 (2.18 log r, - 0.856 log CI>, + 1.193 log O) / 2.61 Figure 5.11: findamental Plane plots for Coma and Abell 2390. Only ellipticd galaxies are plotted. The dotted line in the top two edge-on plots is the Fundamentai Plane fit. The dashed line in the bottom face-on plot is a constant luminosity line for L,. JFK's Fundamental Plane fit for elliptical galaxies of Coma is used (a= 1.193, ,û = -0.856, and 7 = 0.064). AU of the Abell2390 galaxies lie below and to the right of the Fundamental Plmefit indicated by the dotted line in the edgesn plots. CEAPTER 5. FUNDAMENTAT, PLANE OF ABEU 2390

AbeU 2300 ** E/$O ddaxy 11 CD Qalaxiecr 4 and 8 80

Corna O E

O 1 2 (1.89 Log r, - 0.601 log CI>, +- 1.llQ log u) / 2.34

Figure 5.12: Fundamental Plane plots for Coma and Abell 2390. Only elliptical galaxies are plotted. The dotted line in the top two edge-on plots is the Fundamental Plane fit. The dashed line in the bottom face-on plot is a constant luminosity line for L.. Our Fundamental Plane fit for elliptical galaxies (excluding the CDS)of Coma is used (a= 1.119, fl = -0.801, and 7 = 0.151). Abell 2390 galaxies 1 and 2 lie just above the line defining the Fundamental Plane but the rest of the Abd 2390 galaxies are below and to the right of the dotted lines. CWTER 5. FUNDAMENTAT, PLANE OF ABELL 2390

5.6.3 Projections of the Fundamental Plane

Both the luminosity-size and Faber-Jackson relations have been used to determine the evolution in luminosity of galaxies by studying clusters at various redshifts. In this section it WUbe shown that care should be taken when detennining the evolution of fwîdamental parameters from projections of the Fundamental Plane, because selection effects can influence the results of these two methods. The solution of the Fundamental Plane derived using our Coma elliptical galaxies (a = 1.028, ,û = -0.855, and y = 0.475) is used to create a theoretical grid of points that populates this plane, and hence creates a local cluster. The Fundamental Plane plots of this local cluster are illustrated in Figure 5.13. The values of logcr are calculated from the Fundamental Plane solution using values of log T. that vaqfrom O to 1.9 in steps of 0.1 (indicated by class of shape of symbol) , and values of log (I). that vary from 1.3 to 3.2 in steps of 0.1 (indicated by color). The velocity dispersion is represented by the number of vertices on the symbol. See the key in the lower right hand corner of Figure 5.13 for the range of values that each prope* of the symbol represents. The exclusion zone fkst noted by Bender (1992) is indicated by bladc squares in the centers of the symbols and a solid line. This zone, in the upper right hand corner in face-on view, is devoid of galaxies in observational hdamental Plane plots. A magnitude limit (MB(AB)< 19) is indicated with a dot-dashed line and black circles around the data points within this area. Data fainter than this magnitude limit occupy the lower left hand corner of the face-on view. The absolute magnitudes of these theoretical galaxies are calculated using the formula L = 7.215 deRz @/a) assuming b/a = 1 (Gilmore et al. 1990). A simulated distant cluster is created assuming that cr and re remain constant for each galaxy, but that (1). increases with redshift. We will assume that these galaxies are 0.54 magnitudes brighter than those in the local cluster. This is the increase in brightness that is fond between Coma and Abell2390 using the Eùndamental Plane (see 55.6.4)- The Fundamental Plane plots for this distant cluster are shown in Figure 5.14. The Fhdamental Plane fit indicated on these plots is that of the local cluster. Galaxies with log (1). > 3.2 exist only in the distant cluster. It should be noted that both this distant cluster and the local cluster have Fundamental Planes with zero thickness. Projections of these two simulated Fundamental Planes cm now be created to determine the effectiveness of using the luminosity-size and Faber-Jackson relations to study the luminosity evolution of elliptical galaxies. The luminosity-size relation for the local and distant clusters are shown in Figures 5.15 and 5-16. In both figures the luminosity-size relation found fiom the Coma galaxies using magnitudes calculated as described above is shom with a solid green line. These calculated magnitudes are used for Coma since this is the same method that is used to determine the magnitudes for the local and distant clusters. The dotted green line indicates the luminosity-size relation for the Abel1 2390 galaxies (labelled asterisks in Figure 5.16). In both of these figures it is easily seen that the Fundamental Plane is not being viewed edge on. The exclusion zone decreases the width of the band that is occupied by the Fundamental Plane in both of these figures, especially for large radii. The change of position of this band along the magnitude axis between the two clusters is the expected 0.54 magnitudes. This shift is srnall in cornparison to the width of the band. It is assumed that the exclusion zone occupies the same space in the Fundamental Plane plots of the distant and local clusters. In the luminosity-size relation plots, the position of the exclusion zone changes by - 0.3 magnitudes, which will cause the amount of brightening of the distant cluster to be underestimate by - 0.1 magnitudes. Rom the Fundamental Plane analysis for Abell2390 it was found that AMB(AB) = -0.54 f O. 11 (55.6.4) and from the luminosity-size relation AMB(AB)= -0.46 rt 0.12 (55.4), which agrees with the predicted underestimation caused by the exclusion zone. If the exclusion zone evolves with redshift (Le., it occupies a different part of the Fundamental Plane plots for dserent redshifts) the situation is more complicated. Galaxies with a range of surface brightnesses will be easily observed in a local cluster. For a distant cluster, only the galaxies with higher surface brightnesses will have reliable measurements, therefore low surface brightness galaxies will most likely be exchded kom the sample. This selection effect will cause the luminosity evolution 23 3 log r, + 0.856 log .

log m (Lms-')-

O 1 2 (1.79 log ri - 0.866 log , + 1.028 log m) / 2.23

Figure 5.13: hindamental Plane plots for a local cluster. This grid of points is created ushg our Fundamental Plane fit for efiptical galaxies (a = 1.028, /3 = -0.855, and 7 = 0.475). Each symbol has three properties: color, number of vertices, and class of shape (open, skeletd, star, fillecl). The different colors represent different values of Iog (I)., the number of vertices represent dserent values of loga, and the different types of shapes represent Werent values of logr.. Also indicated are the directions in which these three quantities increase. The exclusion zone noted by Bender (1992) is indicated with black squares inside the points and a solid black line in the face-on plot. A magnitude limit of MB(AB) < 19 is indicated by a black circle around the points and a dot-dashed he. The dotted hein the top two edge-on plots is the Fundamental Plane fit. The dashed line in the bottom faceon plot is a constant luminosity line for Le. The Abell 2390 galaxies are indicated by labelled black asterisks. to be overestirnated, since the higher surface brightness galaxies will bias the distant cluster sample. When using the luminosity-size relation to measure the luminosity evolution, one must be concerned with surface brightness selection effects. The Faber-Jackson relations for the local and distant clusters are shown in Figures 5.17 and 5.18. In both figures the Faber- Jackson relation found for the Coma galaxies (ushg calculated magnitudes) is indicated with a soüd black line. Almost no evolution is found when the fit is made to the Abell2390 galaxies. The line that indicates the Abell 2390 galaxies fit is coincident with the solid line of the Coma galaxies. Note that the position of the band changes between the local and distant clusters, and that the shift is the expected 0.54 magnitudes. For a given velocity dispersion and surface brightness, the luminosity of a galaxy increases in the distant cluster. Surface brightness selection effects can cause the amount of luminosity evolution measured by Faber-Jzckson relation to decrease and even cause the distant cluster to appear to be fainter than a local cluster. Note that the high surface brightness galaxies (green and purple) are found on the left edge of the band. A local cluster will be well sampled with respect to surface brightness, but if only high surface brightness galaxies are observed in a distant cluster, the amount of evolution measured by the Faber- Jackson relation will be too low. This selection efFect is responsible for the apparent dimming of Abell 2390 galaxies with respect similar galaxies in Coma (55.5). CH.APT'ER 5. FUlVDAMENTAL PLANE OF ABELI, 2390 187

cdge-on vlew 1 2

2-6 3 log r; + 0.866 log 0.

log , &pc? . a . . ---f S1.7 L20 529 526 62.9

log r, (WC) A A A A

- O 1 2 (1.79 log r, - 0.866 log CI>, + 1.028 log a) / 2.23

Figure 5.14: Fundamentd Plane plots for a distant duster. This grid of points was created using our Fundamental Plane fit for elliptid galaxies (a = 1.028, ,8 = -0.855, and 7 = 0.475) and assiIming that this duster is 0.54 magnitudes brighter than the local cluster. Each symbol has three properties: color, number of vertices, and class of shape (open, skeletal, star, filled). The different colors represent dinerent vaIues of log (l),, the number of vertices represent different values of logo, and the diBesent types of shapes represent different values of Iogr.. Ahindicated are the directions in which these three quantities increase. The exclusion zone first noted by Bender (1992) is indicated with black squares inside the points and a solid black line in the faceon plot. A magnitude limit of MB(AB)< 19 is indicated by a black circle around the points and a dot-dashed line. The dotted line in the top two edge-on plots is the local Fbdamentd Plane fit. The dashed line in the bottom faceon plot is a constant luminosity line for Le.The Abd 2390 galavies are indicated by labelleci black asterisks, CHAPTER 5. FU'ZVDAMEMENTAT, PLANE OF ABEU 2390

Figure 5.15: The liiminosity-size relation for a local cluster. The absolute magnitudes are dculated fiom L = 7.215d,',Rz(b/a) assuming b/a = 1. The solid green Iine is the fit to the Coma *es with a dope of -3.33. The dotted green line is the fit the AbeII 2390 galaxies keeping the elope constant at -3.33. The directions that (I)., T,, and a increase is also indicated.

Figure 5.16: The luminosity-size relation for a distant cluster. This plot is simiIar to Figure 5.15. The Abeu2390 galaxies are indicated by labelleci black asterisks. Note the change of position of the exdusion zone relative to the band of galaxies. Figure 5.17: The Faber- Jackson relation for a local chuter. The absolute magnitudes are calculated fiom L = 7.215rIe~:(b/a)assuming b/a = 1. The solid black is the fit to the Coma galacies (L o: 0"). The fit to the Abell2390 galacies is coincident with this iine. The directions that (I),, te,and o increase is also indicated.

Figure 5.18: The Faber-Jackson relation for a distant duster. This plot is similar to Figure 5.17. The Abell 2390 galaxies are indicated by labded black asterisks. Note that high surface brightness galaxies are dong the IeR edge of the band. CHAPTER 5. FUNDA2MENTL PLANE OF ABELL 2390

It has been shown in this section that both the hmhosity-size and Faber-Jackson relations are iderior to the Fwidamental Plane for measuring the luminosity evolution of elliptical galaxies in clusters. It is assumed that the galaxies evolve passively, with only their surface brightness changing with time. Even if this is not completely tme the fact that the Fundamental Plane exists at higher redshifts indicates a departure fiom pure lurninosity evolution wdi not greatly affect these conclusions. Another assumption is that the axial ratio (bla)of galaxies is unity. Weit is known that all galaxies do not have an axial ratio of 1, this assumption is made for simplicity purposes and the conclusions will not change if a different axial ratio is used for both clusters. Evolution in the axial ratio will change the position of the bands, since the calculated luminosity depends on the axial ratio. Normdy one uses photometric magnitudes and not calculated magnitudes in the luminosity-size and Faber-Jackson relations, therefore evolution in the axial ratio will not affect the amount of Iuminosity evolution measured by either of these methods. It is also assumed that Fundamental Planes of the distant and local clusters are populated in a similar manner, the exclusion zone is the same for both clusters and as mentioned above the effective radius and velocity dispersion ranges are the same. Changes in the exclusion zone WU have a greater effect on the results of the luminosi@-size relation than the Faber-Jackson relation. Since idedy one wishes to measure the shift of the Fundamental Plane, any Uitrinsic differences in the way the Ehdarnental Plane is populated will affect the perceived location of the band in the projections of the Fundamental Plane and therefore affect the amount of luminosity evolution meanired. Both the Faber-Jackson and luminosity-size relations are subject to surface brightness selection effects. Without a complete sample the Faber-Jackson relation cmot meame the luminosity evolution between two clusters. Distant clusters are most likely to be affected by surface brightness selection effects and using the Faber-Jackson relation to measure luminosi@ evolution will result in erroneousty low amounts of evolution and therefore is not recommended. The luminosity-size relation is not only affected by surface brightness selection effects but also by the exclusion zone and its possible evolution. Surface brightness selection effects will cause the luminosity-size CHAPTER 5. FUNDAAMENTU PLANE OF ABEL 2390 191 relation to overestimate the amount of Iuminosity evolution which rnay or may not offset the underestimation caused by the exclusion zone. The Fiuidamental Plane andysis is demonstrated to be insensitive to surface brightness selection effects and the exclusion zone, and it wÏU therefore give robust results in their presence, whereas the Faber-Jacbon and iuminosity-size relations can be badly in error (to the extent of implying an evolution of the wrong sign!). CsAPTER 5. FUNT)AMENTAL PLANE OF ABELXI 2390 192

5.6.4 Change in Luminosity

In this section the change in luminosity between the elliptical galaxies in Abell 2390 and Coma will be determined from the Fundamental Plane results. It is crssumed that the velocity dispersions and effective radii of the galaxies do not change over the. This would be true if the galaxies evolved passively (Le. no mergers or accretion). The clifference between the observed log (1),and its expected value based on the solutions found for the Fundamental Plane are calculated for each of the galaxies (Ag(1)) The mean of Am = -2.5A log (I), is calculated for some Fundamen- tal Plane solutions found in 85.6.2. The first colwnn in Table 5.15 indicates which Fundamental Plane fit is used. The first character denotes either the JFK (J) or our dataset (S). The second character indicates the subsample used to determine the hindamental Plane: A = all galaxies, + = E and diE/SAO galaxies, E = ellipticals, and - = ellipticals excluding the CDS. The next three columns in Table 5.15 are a, p and 7. The fifth, eighth and eleventh columns are the number of data points used. The following two columns are the mean and the sample standard deviation rnulti- plied by (N - I)-'/~ of Am = -2.5A log (I).. Three different Abell2390 datasets are used. The first dataset (containhg 11 galaxies) contains ail the galaxies except the faintest two (galaxies 3 and 6) for which the S/N ratio was too low to obtain accurate photometry. The second dataset of 8 galaxies omits the CD and the two SO galaxies. The photometry is fair for these galaxies. The third dataset (6 galaxies) omits the CD,SOS and galaxies 1 and 2 for which there is only MOS photometry.

Table 5.15: Am = -2.58 log (1),for Mous datasets. The datasets in Table 5.15 only omit galaxies based on photometry. The datasets in Table 5.16 &O take in to account the accuracy of the velocity dispersions. The first dataset contains 8 galaxies. Galaxy 5 is omitted due to low SIN ratio in the spectra. Galaxy 8 has a questionable velociw dispersion. The velocity dispersion of Galaxy 11 is also suspect since it has strong emissions lines. The photometry is fair for both gdaxies 5 and 8. The second dataset omits the above three and galaxy 4 since it is an edge-on galaxy. There are only two galaxies (7 and 9) in the third subset that have very good velocity dispersions and photometry.

Table 5.16: Am = -MA log (1). for vaxious datasets.

The average brightening varies fkom 0.30 f 0.09 to 0.63 f 0.11 magnitudes for different datasets and Fundamental Plane fits in Tables 5.15 and 5.16. Omitting the edge on SOS, the CDand galaxy 5 leaves 7 galaxies. The average brightening of these 7 galaxies using the Fundamental Plane fit from all of our Coma galaxies is 0.33 f 0.10. If ody the elliptical galaxies in Coma are used the average brightening is 0.42 I 0.10. If we exclude the cDs from the Coma ellipticals the average brightening is 0.321 0.11. The average brightening increases if the JFK Fundamental Plane fits are used. These values are in agreement with results using the lurninosity-size relation, but not with those found with the Faber-Jackson relation. CHAPTER 5. FUNDAMENTT, PLANE OF BELL 2390

5.6.5 Change in Mass-to-Light Ratio

In this section the mas-telight ratio of elliptical galaxies in Coma and Abell 2390 will be compared. The change of the MIL ratio is important in understanding how galaxies evolve. van Dokkum & Ranx (1996) found that the MIL ratio increases

by 31 f 12% (in the V band) between z = 0.391 (CL 0024) and t = 0.023 (Coma). Kelson et al. (1997) with two more clusters, Cl 1358+68 at z = 0.33 and MS 2053- 04 at z = 0.58, also find AlogM/Lv - -0.32. Preliminary results by Jflrgensen & Hjorth (1997) in the Gunn r band indicate that AlogMIL, - -0.42. Using a similar method the change in MIL ratio between AbeU 2390 and Coma is calculated. The M/L ratio is assumed to be well behaved, if the MIL ratio was not well behaved it can be seen that fiorn equation (1.3) the Fundamental Plane would not exist (Dressler et al. 1987). The follow-ing relation can be used if the galaxies are stmc- turally simila$ : MIL oc ~;'-l&?+~/fi (JFK96). In Figures 5.19 and 5.20 log MIL is plotted versus T;'-~~~*+~IB,where the masses of the galaxies are calculated from M = 502re/G;and the luminosity, L, is the B(AB) luminosity. The solid line is a fit to all of the elliptical galaxies in Coma. Two datasets for Abell 2390 are used. The fits to the dataset containing all of the Abell2390 galaxies are dotted lines, one with the same slope as the Coma galaxies and one with no constraint on the slope. The two corresponding dashed lines are for the 7 "good" Abell 2390 galaxies. Figure 5 .l9 uses the cr and 0 found for the Ftndamental Plane fit for aLI the ellipticd galaxies in Coma. Figure 5.20 uses a,P, and a line fit to the elliptical galaxies exduding the CDS in Coma. We hdthat the higher MIL ratio galaxies appear to have reached the line defined by Coma and that the lower MIL ratio galaxies are still evolving upwaxds to a higher MIL ratio as did van Dokkum & F'ranx (1996). This implies that the F'undamentd Plane of the cluster Abell2390 is different fkom that of Coma Cluster. In Table 5.17 the change in the M/L ratio between the Abell2390 datasets and Coma datasets is calculated for dSerent Fundamental Plane solutions (see columns 1, 2, 3, and 4). The fifkh column specaes the Coma data set used to find the best fit to

'Red that in equation (1.1) it is assumed that cl is a constant. cl wiii be a constant if the gdaxies have similar structure. CWTER5. FUNDAlMENTA PLANE OF ABELL 2390

log r:-17

Figure 5.19: MIL versus T;'-'/B$+~I~~.Open cirdes are Coma ellipticds and stars are Abell 2390 galaxies. The a! and P used are for the Fundamental Plane found from ail the Coma elliptical galaxies. The solid line is the fit to the eIlipticd galaxies in Coma. The dotted line which has the same slope is the fit to all 11 Abell 2390 galaxies holding the dope constant. The other dotted line is the fit to all 11 AbeU 2390 galaxies without constraint on the slope. The dashed lines are for the 7 "good" Abell 2390 galaxies. The MIL ratio increases by 18f::% (Il galaxies) or 20+:3% (7 galaxies). CHAPTER 5. FUNnANT' PLANE OF ABELL 2390

log r,0-25 DO.'

Figure 5.20: MIL versus ~;'-'/fi$+~lB. Open circles are Coma eilipticals and stars are Abell 2390 galaxies. The a and ,û used are for the Fundamental Plane found fkom the Coma &iptical galaxies excluding the CDS(the two right most open circles). The solid heis the fit for the ellipticd galaxies excluding the CDSin Coma. The dotted line with the same slope as the solid line is the fit to 411Abell2390 galaxies holding the slope constant. The other dotted line is the fit to all 11 Abell 2390 galaxies. The dashed lines are for the 7 "good" Abell 2390 galaxies. Note that the dashed and dotted lines with the same dope as the Coma galaxies lie nearly on top of one another. The MIL ratio increases by 25?::% (11 galaxies) or 24?:;% (7 gdaxies). CHAPTER 5- FUNDANTU PLANE OF ABELL 2390 197

log MIL vs r;'-'/pf +&/p. The ninth column is the number of galaxies in the Abell 2390 dataset. The mean and sigma of the clifference between the measured log MIL and calculated values based on the Coma galaxies are the tenth and eleventh columns. The percentage increase in MIL fkom Abell 2390 to Coma is the last column. The seven "good" Abell 2390 galaxies dong with the hindamental Plane solution and linear least-squares fit based on the eIliptical galaxies in Coma give a 20: :3% increase in the MIL ratio. If alI eleven galaxies are used this duedecreases only by 2%. But if the CDSare excluded fkom both the kdamental Plane and least-squares fit the MIL ratio increase is 14f:3%. If a Fundamental Plane solution that is based on a subsample which includes the CDSis used with a hear le& squares fit that does not include the CDS,then the percentage increase is much higher (13% higher). In Figure 5.21 the change in the MIL ratio is plotted as a function of redshift. The Coma points (z = 0.023), which are normalized to zero, and the Abell 2390 points (z = 0.229) are calculated for Merent Fundamental Plane fits and fits to log MIL vs r~'-'/@c?+~/B with re = 3 kpc and a = 200 km s-'. There are four sets of points offset sIightIy for cIarity and are based on the different Fundamental Plane fits. The AbeU 2390 points (from the fits to log MIL vs C'-'/B$+~/B use all of the Coma efiptical galaxies except for the S- subset which excludes the CDS)include only the 7 "good" galaxies, but it should be noted that these points are almost the same if al1 11 galaxies are included. The line is drawn through these two points is shown with the following different line types JE = solid, S- = dotted, SE = solid (red), S+ = dot-dashed. The slopes of these lines are -0.27, -0.59,-0.36, and -0.30 respectively. Results from single-burst stellar population models by Worthey (1994) are represented by shaded areas in Figure 5.21. These areas represent a range in metallicities for formation redshifts of 1 (blue), 2 (cyan), 10 (green), and oo (magenta) for the SE result. The stellar initial mas function for early-type galaxies is uncertain and these results uses a Salpeter's initial mass function. if a steeper initial mass function is used the M/L evolution will not be as rapid. Note that the relationship between log(M/L) and redshift is approximated by a straight line in the region of low redshifts. va,n Dokkum & Fra,nx's (1996) increase CWTER5. FUNDAMENTAL. PLANE OF ABELL 2390 198

Table 5.17: Mass-to-Light Ratio Increases

NOTES.Col. (1). - hndamental Plane fit: JE = JFK Ellipticals, S+ our E and diE/SAO, SE our Ellipticals. S- E galaxies excluding the CDS. Cols. (Z), (3) & (4). - a,p, and 7 of the Fundamental Plane solution. Col. (5). - Which Coma galaxies were used in the determination of the line: E = Coma ellipticals, E = Coma ellipticals exc1uding the CDS. Col. (6). - The exponent of r,. Col. (7). - The exponent of o. Col. (8). - The rrns residuals in the le&-squares fit of the Coma data. Col. (9). -The number of Abell2390 galaxies used to determine the change in MIL ratio. "11" is all of the galaxies. "7" excludes galaxies 4, 5, 8, and 11. Coi. (10). - The mean difference between the rneasured log MIL and the calculated log MIL (based on the Coma relation). Col. (11). - The sigma of Col (10). Col. (12). - The mean percentage increase in MIL fiom Abell 2390 to Coma. in the MIL ratio corresponds to a slope of -0.32 (recall that their measurement is in the V band). Kelson et al. (1997) found a slope of -0.4 in Gunn r. Worthey's (1994) population models indicate that the slope of the log MIL versus redshift relations in the B band is 5 to 13% steeper than the V band and 8 to 21% steeper in the Cousins R band depending on the metallicity. For a formation redshift of 1and for low redshifts the slope is -0.96, -0.84, and -0.79 in the B, VI Rc bands respectively (averaging over all metallicities). If a higher formation redshift (e.g. z = 4) is used the values are CHAPTER 5. FUNDAMENTAt PLANE: OF ABELL 2390 199

-0.56,-0.50, and -0.48. The values approach -0.45, -0.40, and -0.38 for a formation redshift of infinitgr. The Gunn r and Cousins R band's have approxhately the same effective wavelength so the slopes will be similar. The B(AB) band results will have the same slope as the B band, only the offset changes. Our results imply a high formation redshift assuming a single-burst of star formation and passive evolution. This is in agreement with the results of van Dokkum & Franx (1996), Jflrgensen & Hjorth (1997) and Kelson et al. (1997). The mode1 of a single-burst of star formation greatly simplifies the probable history of elliptical galaxies. Mergers and infall which cause later star formation are known to take place. Younger stellar populations have lower MIL ratios and even if a small percentage of the stellar population is recent the overall measured MIL ratio can change si&- cantly as seen in Worthey's (1994) population models. The role these events play in the evolution of ellipticd galaxies is still being investigated. It is also not clear how the dynarnical properties of the galaxies will be influenced. Another important consideration, are the elliptical galaxies that we observe at higher redshifts earlier versions of the elliptical galaxies that we observe locally? More sarnples of elliptical galaxies in clusters are being obtained by various authors (e.g. Pahre & Djorgov- ski 1997 with the Keck Telescope) and these results combined will give us a better understanding of the evolution of galaxies. C'R5. FCfNDAMENTAL PLMOF ABELL 2390 200

Figure 5.21: A logM/L versus z. There are four points at each redshift (t = 0.023 for Coma and r = 0.229 for AbeU 2390) offset slightly for clarity. The first point (open circles) in each set is based on the hiindamental Plane fit for JFK ellipticd galaxies (JE).The second and third points (skeletal and starred) are based on the Fûndamental Plane fit for our elliptical gdaxies excluding the CDS(S-) and including all elliptical galaxies (SE) respectively. The SE results are in red. The fourth points (solid circle) are based on the Fundamental Plane fit for our E and diE/SAO galaxies (S+). The Coma A log MIL values have been normalized to zero and the AbeU 2390 values are based on the fits to logM/L vs r;'-'/B$+*IB. The fits use d of the Coma elliptical galaxies arcept for the S- subset which exdudes the CDS. The linear least-squares fit to these points is shown with the following dinerent Iine types JE = solid, S- = dotted, SE = solid (rd), S+ = dobdashed. The shaded areas represent the range of dues edculated fiom singieburst wolutionary models wîth dinerent metallicities. Formation redshût of 1 is indicated with blue, 2 is cyan, 10 is green, and oo is magenta. Note that low formation redshifts appear to be dedout by these results. The photometric analysis of Coma by Schade agrees well with that of JFK95a. Even though on the whole the results are similar, it is still important to compare the photometry of galaxies in different clusters using the same analysis techniques. Both the Faber- Jackson and luminosity-size relations are projections of the Fun- damental Plane. The Faber-Jackson relation does not show the expected evolution in luminosity between the elliptical galaxies in Abel12390 and Coma (AMB(AB)= 0.39 f 0.34), but indicates that the Abell 2390 galacies are fainter than the Coma galaxies. This discrepancy is explained by a surface brightness selection effect. High surface brightness galaxies are more lücely to be chosen for the Abell 2390 sample. These galaxies populate only a portion of the band that is formed by the hdamental Plane in the L - a plot. Without a complete sample at both redshifts the Faber- Jackson relation cannot be used effectively to measure the evolution in lu mi no si^. From the luminosity-size relation we hdA Ms(AB) = -0.46 f 0.12 for ail eleven galaxies and AMB(AB)= -0.60 f 0.16 for the "good" seven galaxies in Abell 2390 with respect to similar galaxies in the Coma cluster. The luminosity-size relation is also subject to the surface brightness section effect but to a lesser degree than the Faber-Jackson relation. The presence and possible evolution of the exclusion zone will also affect the results from the luminosity-size relation. These two effects must be taken into account when using the luminosity-size relation to determine the amount of luminosity evolution between hoclusters. The Fundamental Plane is a superior method to both the Faber-Jackson and luminosity-size relation for measuring luminosity evolution, since it is not aifected by surface brightness selection effects or the exclusion zone. Elliptical galaxies in Coma form a tight Fundamental Plane and when comparing the galaxies in Abell2390 to Coma we find AMB(AB) = -0.54 f 0.11 for all eleven galaxies and AMB(AB) = -0.42 & 0.10 for the seven "good" galaxies. We find that the MIL ratio increases by 20?:$6 between AbeU 2390 (r = 0.23) and Coma (z = 0.023). This increase in the MIL ratio favours high formation redshifts for elliptical galaxies and is consistent CRAPTER 5. FUNnANTAL PLANE OF ABELL 2390 202 with the results of van Dokkum & Ranx (1996), Jgrgensen & Hjorth (1997), and

KeIson et al. (1997). We &O find possible evidence for a change in the Fundamental Plane with redshift (van Dokkum & Frm 1996). CWTER 5- FUNnANTfi PLANE OF ABELL 2390 203 5.8 Appendix

This Appendix describes the details of the conversions used to prepare the photometric data of the clusters Coma and Abell 2390 for the Fundamental Plane andysis. The values of pBo(RB) and logr, (kpc) were provided for each galaxy in the Schade datasets. To create the hdamental Plane we need to convert pBo(AB),the central surface brightness in magnitudes to (I)., the mean surface brightness within the effective radius in units of Lapc-2. The surface brightness at the effective radius (r.), p,, and the central surface brightness, p, are related by the following formula: pe = po + 8.3268. The mean surface brightness within r, is (I), = 3.6081,, where

I,is the surface brightness at T.. To convert surface brightness from magnitudes to the following formula is used log (1). = -0.4((p)), - C), where C = 27.0 for Johnson B band (JFK). Finally an extinction correction, Ec, must be zpplied. This results in the following relation log (1),= -0.4(pB,., (AB)- Ec+8.3268 - 27.0) +0.557, where Ec is 0.05 for Coma and 0.17 for Abell 2390. The logr, values for the Schade datasets have the correct units of kpc. Both the published JFK Coma surface brightnesses and effective radii need to be converted to the form used in the Fundamentai Plane. The clifference between Johnson B and B(AB) is 0.17 magnitudes, (p).(B(AB)) = (p),(Johnson B) - 0.17. The published logr, values are in arcseconds and need to be converted to kpc, logr, (kpc) = logre (arcsec) -0.192, since 1kpc = 10556 for Ho = 50 kms-l Mpc-', qo = 0.5, and z = 0.023. Chapter 6

Summary

To understand the importance mergers play in the formation of galaxies we need to determine how often, when and where they occur. Groups of galaxies where interactions are currently occurring are likely places to find the remnants of recent mergea. For this study eleven 'iiormal" early-type galaxies in Arp groups were chosen to search for dynamical signs of a merger. The kinematics of early-type gdaxies in these environments has not been well explored. Specific galaxies and groups of galaxies have been studied, but a concentrated effort in studying the kinematics of galaxies in groups where a merger was likely to have taken place has not been undertaken before. A kinematically distinct core subpopulation, such as a counter- or cerotating core, are signatures of a possible merger event. The rotation curves and velocity dispersion profiles of this sample of galaxies are examined to determine if they have distinct cores. Models of counter- and CO-rotatingcores are produced and compared to the rotation curves to determine if it is possible to detect an unusual core given the quality of the data. No unusual rotation curves are found in the four out of the eleven galaxies in which the signal-tenoise ratio is sufficient. Minor axïs rotation is also another sign of a distinct core subpopulation and no minor axis rotation is detected in this sample of galaxies. The spectra of these galaxies are ais0 examined for strong HP emission which is a signature of star formation, since a recent merger would also result in a starburst. Two of the eleven galaxies show strong HP emission, but these galaxies are members of interacting pairs and therefore cannot be considered recent mergers. None of the other galaxies show çignificant HP emission. By comparing the position of the galaxies on the luminosity versus velocity dispersion plot (Faber- Jackson relation) with other early-type galaxies it can be determined if these galaxies have an unusually high or low velocity dispersion. The galaxies of this study individually appear to be vimially indistinguishable fiom the Komendy and Illingworth (1983) sample, but the average velocity dispersion is about 7pm4% lower than their sample of normal galaxies. Zepf & Whitmore (1993) &O found that the velocity dispersions of elliptical galaxies in compact groups are less than those of other galaxies, but they found a difference of 20%. The la& of dynamical evidence for a merger, evidence of a recent starburst, and the similarity of these galaxies to other elliptical galaxies implies that if mergers play a large role in the formation of elliptical galaxies, then these mergers occmed at a much eariier epoch and the galaxies evolved passively since then. This agrees with the standard picture that is emerging that early-type galaxies in cluster and groups formed at a redshift of 2 or earlier. Due to our smd sample size, the conclusions that are reached are not strong and further studies of the kinematics of early-type galaxies in Arp groups are needed to conhthese kdings. The evolution of early-type galaxies can be studied by determinkg how combina- tions of paramet ers change with redshift . Bot h the Faber- Jackson and luminosity-size relations have been used extensively to compare different populations of early-type galaxies. The Fundamental Plane is also becoming a common tool in the study of early-type galaxies. The hndarnentd Plane is a three parameter relationship and the Faber-Jackson and luminosity-size relations are projections of this plane. The Faber-Jackson relation, luminosity-size relation, and Fundamental Planes of a near cluster, Coma (z = 0.023) and a distant cluster, Abell2390 (z = 0.229) are compared to determine the evolution in luminosity and mas-to-light ratio. The Faber-Jackson relation does not show the expected evolution in luminosity between Abell2390 and Coma (AMB(AB) = 0.39 f 0.34). A surface brightness selection effect is responsible for the Faber-Jackson relation indicating that the elliptical galaxies in the Abell 2390 cluster are fainter than those in the Coma cluster. Rom the luminosity-size relation we find AMB(AB)= -0.46 f 0.12 for all eleven galzies in Abell 2390 and AMB(AB) = -0.60 & 0.16 for the L'good'pseven galacies in Abeli 2390 with respect to simila galaxies in Coma. These values agree with AMg = -0.34 10.20 found by Schade et al. (1997) for a sample of 10 galaxies in Abell 2390 using the luminosity- size relation. Surface brightness selection effects will also affect the results from the luminosity-size relation, but will most likely cause the evoIution to be slightly overestimated. The presence of the exclusion zone causes the luminosity evolution to be underestimated. Surface brightness selection effects and the presence of the exclusion zone do not affect the Fundamental Plane andysis, therefore the results fiom the Fundamental Plane analysis are more reliable. Our sarnple of elliptical galaxies in Coma forms a well defined Fundamental Plane and compares well with that of JFK96. From the Fundamental Planes of Coma and Abeil2390 we hdAMB(AB) = -0.54f 0.11 for all eleven galaxies and AMB(AB)= -0.42~t0.10for the seven "good" galaxies. The luminosity-size relation appears to be sufncient to study the luminosity evolution of these two clusters. But to determine the MIL evolution the Fundamental Plane is needed. The MIL ratio of Coma is 2022% higher than that of AbeU 2390. If it is assumed that early-type galaxies evolve passively one can predict the change in the MIL ratio for various formation redshifts. Comparing these results with models by Worthey (1994) rules out low formation redshifts (z < 2), which agrees with the results of other authors. This single burst mode1 is a great simplification of the history of elliptical gal&es. Mergers and infd will change the global parameters of these galaxies but to what extent? Possible evidence for a change in the huidamental Plane with redshift is also detected and requires further investigation. Further studies of the Fundamental Plane are needed especially at higher redshifts to help determine the formation redshift. The role of mergers alço needs to be understood so that the M/L evolution of galacies can be modelled correctly. The la& of evidence of mergers in early-type galaxies in Arp groups and the early formation epoch hom the Fundamental Plane analysis of elliptical galaxies in Abell 2390 hply that mergers that play a significant role in the history of these galaxies occurred at a mudi earlier epoch, z > 2. The formation of eIliptical galacies from the merger of disk galaxies is possible if the disk galaxies are gas-rich and the mergers occurred at early epochs, which also implies that these disk galaxies are older than the field spiral galaxies that we see locally. Hierarchical-dustering and collapse theories of galaxy formation are also not dedout providing that the epoch of major merging events occurs early- References

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