BR Photometry of the Globular Cluster System of NGC 3115

S.J. Bickerton

A thesis submitted in the Department of Physics

in conformit?; with the requirements for

the degree of Master of Science

Queen's

Kingston. Ontario. Canada

January. 2002

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The lenticular galavy NGC 3113 sits in isolation in the constellation Sextans.

Photometric observations of the gala~ymade with the CFHlZK detector at the

Canada- France-Hawaii 3.6m telescope have provided the deepest wide field images of the galavy to date. revealing nearly its entire globular cluster system. The com- preiiensive data show an apparent multimodality in the colour distribution of NGC

31 15. This is suggestive of a complicated formation or evolutionary history and is more consistent with a hierarchical formation mode1 than with one of monolithic collapse. Globular cluster luniinosity functions (GCLFs) wre made using both B ancl R fil ters and yielded apparent turnover niagnit udes of ms =ZL-E1tO.O-I. and rnR=21.9-lf0.O-l. These yield a distance modulus of rn~- -\fB=30.0Tf 0.28 for XGC

3113 and an absolute GCLF turnover in R of .\IR=-7.99k0.10. Tests of the metallicity/colour effects on the GCLF turnover magnitude (Ashman. Conti. and Zepf.

1995) werr perfornied iising separate GCLFs for three colour groups. Observations supported the proposed systernatic trend. The radial density distribution of globular cliisters was found to be somemhat niore distendeci than the intensity of halo light.

So significant difference in object density aas found between 'blue' and 'red' cluster populations. The specific frequency ivas found to be SLv = 1.7 I:::a value typical

for an SO galiuy not in a large cluster. Acknowledgement s

1 wish to thank a number of people who have tiad a very positive influence on rny aork here at Queen's. First and foremost. 1 thank rny supervisor Dave Hanes and the Department of Physics at Queen's University. Having arrived as a geophysicist. iinfamiliar with astronomy ou took a chance in providing me the opportunity to study a new discipline. I've enjoyed my work. and I've enjoyed rny time here at

Queen's. 1 look fornard to continuing in astronomy. hlany thanks! Three friends aithin the department have on countless occassions willingly provided rnuch needed scientific and technical council. My most sincere thanks go to Kathy Perrett. Steve

Biitterworth. and Doug IIcSeil: 1 sirnply can't espress how much I've appreciated your aclvicc and assistance. For assisting me tvith al1 the bureaucratie details inher- eiit in an acadeniic program. my thanks go to llargaret Ilorris. Terry Busse. and

Janie Barr. Kithout your help L niight aell have forgotten to register. 1 also wish to thank rny parents and my sisters for their support. For every meal that nasn't eaten in front of a cornputer. I can't tliank ou enough. For yars of hockey. thank ou to virtually everyone in geologv and geophysics. The choice to pursue astronomy carne at the erpense of discontinuing my studies in geophysics. The many geolo- gists and geophysicists who invested so much of their time in my education have

continued to be supportive and have provided encouragement through every step.

To Colin Thomson. Gerhardt Pratt. John Hanes. Ron Peterson and everyone in the

Department of Geology for the past seven years. thank ou! CONTENTS

Table of Contents ...... iv

ListofTables ...... vi

... List of Figures ...... viii

1 . Introduction ...... 1

2 . Background ...... 5

2.1 Photometry. co!our . and the magnitude scale ...... 3 - 2.2 Galas? Formation ...... i

'2.3 GlobularClusters ...... 8

2.3.1 The Globular Cluster Luminosity Function ...... 10

'2.3.2 The CoIour Distribution ...... 11

2.3.3 The Colour Gradient ...... 12

2.3.4 The Radial and Angular Profiles ...... 13

2.3. The Specific Frequency ...... 13

3 . The Target: NGC 3115. the Spindle Galawy ...... 16

4 . Data Reduction ...... 18 Contents v

1 Observations ...... 18

4.2 Frame Preprocessing ...... 20

4.3 Photometry ...... 23

4.4 Estimation of recovery using artificial stars: the corripleteness func tion 25

4.5 Object Classification ...... 30

4.6 Calibrations ...... 32

4.6.1 The Aperture Correction ...... 35

4-62 Transformation to thestandardphotornetricsystem ...... 36

4.6.3 Reddening Corrections ...... 39

5 . AnalysisandResults ...... 40

.3 .1 The Colour Distribution ...... 41

5.1.1 Evaliilating the significance of the rnultimodality ...... 43

5.2 The Globular Cluster Luminosity Function ...... 53

5.2.1 The effects of rnetallicity on the GCLF peak ...... 39

5.3 Spatial distributions and relations hips ...... 63

5.3.1 The colour gradient ...... 66

3 .2 The Radial profiles ...... 67

5.3.3 The angular profiles ...... -Pia

-.- 5 .4 The Specific Frequency ...... i i

6 . Discussion and Conclusions ...... 81

6.1 llultirnodality in the colour distribution ...... 81

6.2 The GCLF and the distance to XGC 3115 ...... 82 Contents vi

6.3 The effects of rnetallicity on the GCLF turnover ...... 83

6.4 Spatial distributions and relationships ...... 84

6.4.1 The colour gradient ...... 81

6.4.2 The radial distribution ...... 85

6.4.3 The angular distribution ...... 86

6.5 The specific frequency ...... 87

6.6 Conclusions ...... 88

References ...... 91

A . The Use of sliding-keroel distributions ...... 9-4

A.1 Sornialization to a niiniber density ...... 9-1

A.? Cncertainty ...... 96

B . Supplemeatary Figures ...... 97

C. Coordinates. magnitudes and colours of the globular cluster can-

didates ...... 120 LIST OF TABLES

3.1 Physical parameters for SCC 3113 . Al1 values were retrieved from the

NASA Estragalactic Database (NED. 200 1) ...... 16

4 1 Perceritages of data culleci for both artificial and real objects ..... 34

4.2 Aperture correct ion factors ...... 36

4 .3 Calibration coefficients ...... 38

4.4 RMS resictuals for calibratioris ...... 35

5 .1 Best-fit Gaiissian pararneters for the GCLFs ...... 56

.?.2 Peaks for the GCLFs with final uncertainties ...... 56

3.3 Estimates of the GCLF peak in B ...... j9

5.4 Best-fit Gaussian parameters for the GCLFs ...... 60 - - 3.3 Distance moduli computed using separate (B-R) subgroups ...... 63

5 6 Least-squares fit radial profile parameters ...... 72 - - 3 Least-squares fit a parameters for al1 data. and (B-R) subgroups ... 7-1

6.1 Typical SN values compiled by Harris ( 1991)...... 87

C.1 Coordiriates . magnitudes and colours of the globular cluster candi-

dates (Detector 1)...... 120

vii ... List of Tables VIU

C. 2 Coordinat es. niagni t udes and colours of the globular cluster candi-

dates (Detector 2)...... 123

C.3 Coordinates. magnitudes and colours of the globular cluster candi-

dates (Detector 3)...... 126

C.4 Coordinates. magnitudes and colours of the globular cluster candi-

dates (Detector 1)...... 128 LIST OF FIGURES

Digitized sky suryey (DSS) image of SGC 3115 ...... 3

The CFH1X detector ...... 19

The passbands for the filters at CFHT ...... 19

Tlie preprocessed niosaic image of SGC 3115 ...... > 9

Schematic Aow of the photomet- algorithm ...... 24

Tlie niedian filtered niosaic image of SGC 3 113 ...... 26

Conipleteness fiinct ions for dctertor 1 ...... 29

Tlie pliotometric scatter of artificial stars iidded to detector .... 31

Th r-2 classification diagram for the itrtificinl stars for d~tector1 . . 33

The r-2 classification diagrani for t lie real data ...... 33

The cluster candidate . and background object regions for the (B-R) colour ciistribution ...... 43

The (B-R) colour distribution ...... 44

The K\I'rI models of the (B-R) colour distribution ...... 47

The independent (B-R) colour distributions for the four central detectors 49

The least-squares Gaussian fit for the (B-R) colour distribution ... 51

The .. and Zo2distributions for random unimodal data ...... 52 ii- List of Figures x

5 .7 The cluster candidates and background object regions used for the

GCLF ......

5.8 The globular cluster luminosity functions in B and R ......

5.9 The GCLFs in B and R for thrce sub-populations in (B-R) colour . .

5.10 The (Y-1) YS . (B-R) relation for 'tlilky Wq- globular clusters.....

5-11 The positions of the 'red' and 'bliie' cluster candidates......

5.12 The positions of cluster candidates from each of the K'\.I'\I subgroiips .

3.13 The (B-R) colour gradient ......

5.14 The radial coverage rorrt.ctiori......

5.15 The radial profiles ......

5.16 The radial profiles for two separate (B-R) colour groups ......

3 . lï -4 sample angular coverage correction ......

3.15 The angular profiles of halo light iiitensit......

3.19 The angular profiles of blue and red cluster candidates (RGC5 s'.O) .

3.20 The angular profiles of blue and red cluster candidates in three ranges

0fRGc ......

5.2 1 The Uonte Car10 population distribution for determining specific fre-

6.1 The colour distribut ion converted to (Y-1) for cornparison wit h Kundu

and ivhitrnore ( 1998) ......

6.2 The relationship betn-een galxq- luminosity and the shape parameter ct 86

B .1 .B.8 Completeness functions for detectors 1-8 ...... 98 List of Figures xi

B.9 - B.16 The photometric scatter for detecton 1-8 ...... 104

B. 17 - B.32 The r-' classification diagram for detectors 1-8 ...... 112 1. INTRODUCTION

Surroiinding every galas- is a soniewhat loosely defined spherical region called the halo. 111 virruaily pvery obsened galauy. this halo is inhabited bu a few dozen to a few tlioiisand compact spherical star clusters. raçh containing anywhere from 10' to

10"tars. These are the ylobular clusters.

The stiidy of globular cluster systems lias recently been enjoying a renaissance.

Although part of the cretiit for this cmbe giren to powerful new instruments capable uf slieddiiig iiew liigit oii uld questions. indications that globular clusters are likely to have formecl during the very early stages of galauy formatiori (Harris. 1991) and through galasy mergers (.Ashnian and Zepf. 1992: Schweitzer and Seitzer. 1993) have brought the field to the forefront in studies of gelasy formation and erolution.

Among the more recent developments in the field of globular cluster study is the tiiscovery that the coloiir distributions of man' systems are bimodal. This phe- nomenon can be attributed to a. corresponding bimodality in either the metallicity or the age of the cluster population. or combination of the tno. The presence of distinct sub-populations could be esplained by gala- merges (Schweitzer and Seitzer.

1993: Zepf and Ashman. 1993). or by an evolution punctuated by separate periods of cluster format ion ( Forbes. Brodie. and Grillmair. MK).

SGC 31 15 is an SO (lenticular) gal- which lies in isolation at a distance of about Figure 1.1: Digitizecl sky survey (DSS) image of NGC 3115

10 41pc. .-\ digitized sky survey (DSS)image of the gaiaxy is shown in Figure 1.1.

SGC 31 13 was recently studied by Kundu and Whitmore (1998) using 2.5 x 2.'5 images taken with the Wide Field Planetary Camera 2 (WFPCZ) on the Hubble

Space Telescope (HST).However, images for this study have been collected using the

CFH12K wide field mosaic detector at the Canada-France-Hawaii Telescope (CFHT), and provide a -. 28' x 28' view of the system. Yo comparable wide-field photometric study of SGC 31 15's globular cluster system has been performed to date.

This thesis outlines the findings of a thorough photometric study of the globular cluster system of YGC 3113 and describes the relevance of these tindings as they 1. Introduction 3 pertain to currently debated theories in the field of galavy formation. In brief. the primary objectives are:

1. To examine the colour distribution. Past research (Kundu and Whitmore.

1998: Kavelaars. 1998) hm suggested a bimodality in the colour distribution.

Wtli defield images. esaminatiou of the spatial distribution of any sub-

groups present will be possible.

2. To determine the distance to NGC 3115. Csing the globular cluster

luniinosity function as a standard caridle. the distance to SGC 3115 can he

determined.

3. To examine the effects of colour on the globular cluster luminosity

function (GCLF) turn-over. Diiring the project. a multimodality in the

rolour distril~iitionwas hund. As -4shrnan. Conti. and Zepf (1995) suggestecl

that riietallicity plqs a significant role in the position of the turn-over in the

GCLF. and colour can be an indication of metallicity. it seemed an ideal op-

portunity to test the effects of colour on the luminosity function.

4. To examine the spatial distributions and relationships of the globular

cluster system. including:

(a) the colour gradient: the trend in colour with increasing galactocen-

tric radius. T~vopredominant gal- formation models disagree on the

presence of a colour gradient. 1. Introduction 3

(b) the dope of the scale-fkee radial profile (a):a mesure of the central

concentration of the globular cluster system. and

system with respect to the semimajor ais of YGC 31 15.

5. To derive the specific frequency (SN):the cluster population normal-

ized to the luniinosity of the host galaxy -1s population scales with galavy

luniinosity. this is iisecl to compare the cluster systems of different hosts.

A bricf clisciission of relevant background information is provided in tlie Chap ter Y. the particular interest of tlie target galaxy NGC 3115 is outlinecl in detail in

Cliapter 3. and the data rediiction and processing rnethods used are presented in

Chapter 4. The results. discussion. and conclusions occupy the final chapters. 2. BACKGROUND

2.1 Photometry, colour, and the magnitude scde

As early as the era of ancient Greece. astronomers began to classify stars based on ttieir brightnessl. In a book by Claudius Ptoleniy (AD.137) the brightest stars. ahich appeared first in the evening. were given a magnitude of 1. while the faintest aere given a magnitude of 6'. Over many centuries. astronomers such as .Al Sufi

( Persia. Ioth century ). Tycho Brahe (Denniark. cent ury j. and Galileo Galilei

( Italy. Kthcentury ) measured stellar magnitudes. However. in about 1830. .John

Herschel discovrred thnt duc to the response of the eye. the magnitude scale did tiot increase linearly witli intensity Rather. it nas roughly logarithmic wit h intensity.

increasing by a factor of - 2.5 over each magnitude. .\ short time later in 1836.

the English ast ronorner Sorman Robert Pogson proposed a mathernat ical standard

for the magnitude scale nhich scaled intensity by a factor of 2.2119 per magnitude

(rather than 2.5) as this corresponded to a factor of 100 over 5 magnitudes. Adopted

alrnost immediately. his scale is sometirnes called the Pogson scale and is defined as

follows: Historicd aspects of astronomicd rneasurement arc discussed thoroughiy by Minaika and Sin- ton (1961) ' An even oIder catdog which classified stellar brightnesses on a scale of 1 to 3 was reputetiiy cornpiled by Hipparchus (129 B.C.). Llnfortunately. the work is lost. in ahich m. and I are the magnitude and intensity of the observed object. When a specific filter is used. its first Ietter is subscripted. The zeroth magnitude \vas then defined to correspond to the intensity of the star Yega (aLyrae). This is the standard zero point for al1 filters in common use.

The magnitudes just described are called apparent magnitudes as theu represent a direct observation of an object wit tioiit taking into coiisideration the distance to that object. They are typically denoted sirnply by filter rather than using the subscript

riotatiori (ie. R rather than mR).The nbsolute magnitude is tiien defined to the be

the niagriitiide an objwt ulould have were it to be observecl froni a distance of 10

parsec. It is typically denotecl using a capital JI with the filter subscripted (ie -\IR).

Clrarly. deterniining the absolute magnitude requires a knowldge of the distance to

the object. However. shoiild the object be a tell understood type of source with a

known typical absolute magnitude. rneasurement of the apparent magnitude can be

iised to calrulate the distance to the object. Classes of objects iised in this fashion

are called stundard cundles. The distance. d. (in parsecs) is determined using the

following relation.

Froni an understanding of the magnitude scale. we can develop the concept of

photometric colour. The black body energ curve iised to mode1 emission from a star 2. Background 7 is a peaked funçtion. For progressively cooler stars. this distribution shifts to longer and longer ivavelengths. Thus. by taking the ratio of the flux through two different band-pass filters. a crude measure of teniperature or colour of a star is obtained. In terms of magnitudes (see Equation 2.1 above). this ratio of fluxes simply equates to the difference of the magnitudes (apparent or absolute) as measured through the two filters. In ttiis stiidy B (blue. - 3700 - 4900 -4) and R (red. .V 6000 - 7200 -4) filters were iised. Thus the term (B-R) is a reference to colour defined in this fashion and is called a colour index. By definition. the star Vega has a colour of zero in al1 colour indices. As such. a colour index greater than O indicates that a star is redder and

couler thari \éga. nhile a negntiw colour incics inclicates a star is bluer and hotter

tlian Vega.

If a more estensiw description of photonietry is desired. please refer to BGhm

Vitense (1989). or Carroll and Ostlie (1996).

2.2 Galaxy Formation

The currently acceptecf modcl of the universe is the stundard Big Bang model in

wtiich. some 15 billion yars ago. the early universe vas extremely dense but was

espanding. Alter a few hundred thousand years. the universe contained an almost

homogenous. isotropic3 gas of electrons and protons. too hot to permit the formation

of hydrogen atoms. In thermal equilibrium aith the electrons and protons wre

photons. or radiation. With espansion came cooling. and in a cosmic instant. the

"deed. things were neither completely homogeneous. nor isotropic. It would later be the subtle inhornogeneities which would condense to form galaxies. Similady indispensible, observations of the anisotropy have provideci a duable test in the determination of various cosrnologicai parameters. 2. Background 8 electrons and protons combined to form hydrogen in an event called recombination.

Lnable to interact with the newly formed atoms. the radiation was left adrift in the expanding universe. It can be observed today in its extremely redshifted forni as the

cosrriic rnicrowave background or C'rIB.

Gradually. overdense regions began to collapse under their own gravity in aggregates wtiich would later evolve to form galasies and clusters of galaxies: the universe as ive see it todq began to take shape. The earliest model of gala-y collapse aas that of Eggen. Lynden-Bell. and Sandage (1962) (commonly called the ELS rnodel)". in which the formation process wius depictecl as a continuous. smooth process whereby each aggregate collapseci gradually. The theory wspromptecl by observations indicating a relationship betwem nietallicity and orbital eccentricity for local stars. -4

later model. ttiat of Searle and Zinii (1978). suggested an episotiic process in wtiicli

protogalactic fragments ' began early emlution iridependently and then agglomer-

ated to forni it single galaxy. Ttie crolution process does not end after formation. of

course. as fiilly formed galasies are known to be interacting and rnerging presently

(Toonire and Toonire. 197'1: Zepf and Ashrnan. 1993).

Duririg the life cycle of a star. heavy elements are created through fusion processes.

For particularly massive stars (231, ). once the fuel has run out these heavy el-

ements are scattered into space in an energetic supernova explosion. This recycled

In fact. the ELS mode1 was not proposed in any cosmological context. Rather. it aas restricted to the colIapse of a single gai-. protogaiactic fragments was the term used by Searle and Zinn. -4 popular modern version of this agglomeration model refers to Super Giant Moleculor Cloud9 (SGMC) (Harris and Pudritz, 1994). material permeares its local environment. enriching the gas clouds from which young stars are forrning. Consequently. the Iieavy element abundance or metaliicit~of a netvly forming star cluster is typically greater than that of a cluster which fornied in the less enriched environment of the past.

Globular clusters are foiind in al1 types of galaxies. both in the halo (population

II). aiid with the yoiinger. metal abundant stars in the disk/bulge (population 1).

From studies of the SIilky Way. it is unclear tvhcther metal-rich globular clusters located in spiral galaxies rotate with the disk and have properties siniilar to those of the disk stars (Harris. 1991). or are better associated with the galactic bulge (Slinniti.

1995: Cote. 1999). .Ut hough int ri~isicallybriglit , tliese popiilatioii 1 clusters tend not to I>e visible nt great distances as they are o~er~vhelrrietiby the brightiiess of the disk. Hoaever. also of interest in cstragalactiç astronomy are the population II halo clusters nhirh arc believed to move on highly ecceritric orbits about the galactic* centre (Harris. 1991). These halo globular ciiisters display a broad range in metal content as compared to other stellar populations nithin the same galwy (Harris.

1991). Esamination of colour-iriagnitude diagrams (CIID) intiicates that these are arnong the oldest stellar aggregates7: old enough. in fact. to have witnesxd the earliest moments in the birtli of the galauy. As such. the use of globular cluster systems as galasian fossils provides valuable insight into the processes of galavy

" The term metal has corne to refer to any element above Helium on the periodic table. Although it is perhaps a poor choice of terniinoIogy. it remains in common usage. .\ young steiiar population occupies a nearly linear diagonal (the main sequence) on a coIour- magnitude diagra.cn u-ith massive bright blue stars (blue giants) in the upper-teft ranging down to small faint red stars (red dn-arfs) in the lower-right. As more massive stars have shorter life spans. they are the first stars to move off the main sequence to becorne 'rd giants' near the end of their lives. Euamination of the number of stars remaining on the main sequence protides an indication of the age of the star ciuster. 2. Background 10 formation and evolution.

The fundamental aspects of globular cluster systems are briefly described below.

A more detailed discussion of globular clusters in general can be found in Harris

(2001).

2.3.1 The Globular Cluster Luminosity Fùnction

The globular cluster luminosity function (GCLF) is defined as the number of clusters per unit magnitude interval. The observed distribution results froni bot h the initial rnass spectrum (the distribution of object masses present in a system at formation) and the subsequent long-terni erosion of the globular cluster system and can be approsimated by a Gaussian:

in whicli A is a normalization factor proportional to the total cluster population. rri, is the riiean apparent magnitude. nl is the observed magnitude. and o is the dispersion (Harris. 1991). It should be noted that the log-nornial function is purely an ernpirical niatch to a real GCLF. That said. there have been no sigriificant dis- crepancies betaeen observed GCLFs and this Gaussian forma.

Hanes (1977a.b) nas the first to demonstrate the effectiveness of using the GCLF as a standard candle. although the peak of the distribution twnot reached. but had to be inferred. The GCLF has since been found to be remarkably consistent

"t should be noted that Secker (1992) found the very similar student's t - distribution to be more representative of the GCLF. 2. Background 11 in absolute magnitude from galavy to galavy and is therefore quite reliable as a standard candle in measuring distance to a host gali(Harris. 1991).

2.3.2 The Colour Distribution

The colour distribution is. in this case. the nimber of clusters per unit (B-R) colour.

The (B-V) index has traditionally been the most common index used in stellar photorrietry. and the (VI) indes is the most frequently used in globular cluster stiidies. However. as a long baseline (passbaiid separation) was desired. and the I band has ver- bright sky lewls. the (B-R) index was chosen as a compromise.

-4s the nietallicity of iln object increases. absorptioii lines in its spectriiiri be- conie niore pronounced. redticing the Rus throiigh any filter containing significant absorption featiires. The absorbed radiation is then re-radiated at lorer frequencies

increasirig flux in the corresponding filters. The net result is to artificially rdden

the object being observed. that is. to increase the measured (B-R) value. Thus the

(B-R) colour is not only dependent on the blackbody radiation curw for an object.

but also on its metal content. -4s several of the common Fraunhofer lines lie within

the B passband (H Sr I\: (Ca II). h (Ha). G (CH band). (H,). and F (HJ).(B-R)

colour is a part icularly good choice if rnetallicity sensit ivity is desired.

The colour of a globular cluster represents an integrated colour of its stellar

components. As the first stars to Iense the main sequence to become red giants

are the blue giants. O\-er time the integrated colour of a globular cluster becomes

'redder'. Hoivever. while these age effects are dominant in ounger objects < 1 Gyr,

colour differences are more indicative of metallicity in objects of age > 1 Gyr 2. Background 12

(Ashman. Conti. and Zepf. 1995). In the case of NGC 3113. the GCS can safely be assumed to be of sufficient age that colour differences are representative of metal content. As a continuous period of cluster formation would permit a gradual increase

in the iiietallicity of forming clusters (depending on the efficiency of enrichment and

recylirig arid the density of niaterial). such a formation history woiild be likely

to nianifest itself as a srnootti broad colour distribution. Conversely. an evolution

punctuated by distinct periods of cluster format ion in an environment of continuous enrichnient WOU Id produce a mu lt irnodal colour distribution.

2.3.3 The Colour Gradient

[ri the ereiit of a slow. sniootti collapse of material during galaq- formation (on a

tinie scale greater than tliat of stellar evoltition 5 10' years). one woulci expect to

see a gradual enrichnient of niaterial totvard the centre of the galauy. aiid thus a

r:orresponciing increast. in (B-R) colour or colo,ur gradient. The model of Eggen.

Lyncieri-Bell. and Sandage (1962) does suggest such a sniooth collapse on a time

srale of -- 10"ears and is thus likely to display a gradient. The protogalactic

Fragments of Searle and Zinn ( 1978) would have contributed halo cliisters of slightly

different age. but would not Iikely have distributed theni in such a way as to leave a

gradient. Consequently. the ELS model woiild be consistent with the preserice of a

colour gradient. while the absence of a gradient would support the Searle and Zinn

model. 2. Background 13

2.3.4 The Radial and Angular Profiles

The radial and angular density profiles together define the projected shape of the globular cluster systern. Radial profiles show the object density as a function of galactocentric radius. while angular profiles show the object numbers in angular bins about the centre of a galas.

Iii the case of a radial profile. cornparison wit h the corresponding distribution of halo liglit reveals shether the globular clusters are associated with the esisting

population of halo stars. or are clistributed in sonie different fashion. A signifiant cliscrepancy between t hese two distri but ions woulci be an indication t hat t hey have

~speriericeddifferent formation or evolution histories. It is not uncornmon to find

the GCS to be more distendecl thm the halo light. In siich cases, it is Iikely that the

cluster system is being observed much as it esisted ahen it or Ily formed (Harris.

1986).

Esamining radial and angul ar profiles of sub-groups of cluster candidates. sep

iiratecl based on (B- R) colour. rnakes it possible to examine the rnetal enrichment

history in the contest of spatial distribution. Differences between the colour groups

would represent changes in the structure of the cluster system as metal enrichment

\vas occurring.

2.3.5 The Specific EZequency

Considering globular clusters in a stat istical sense. the most straightfonvard statistic

nhich can be observed is the population (.y).which is simply the number of clusters 2. Background 14 inhabiting a given host galâuy. Howewr. not surprisingly, populations increase with galavy luminosity: a larger amount of material available for star formation in the halo would presumably also contribute to the forniation of globular clusters. Con- sequently. if we wish to compare p,)for different gal~ries.a normalized version of the population is required. Thiis the specific frequency (.Sb*)represents the size of the cluster population nornialized to an absolute magnitude of .\Il. = -15 (Harris and Racine. 1979).

Recalling the definition of the magnitude scale in equation 2.1. Ss can xlso bc

written iii the following wy.

where L is the liiminosity of the galuy. In t his form. the specific frequency cm be

regarded as a globiilar cluster formation efficiency (11cLaughlin. 1999) representing

the ratio of the number of clusters to the luminosity of field stars (ie. a represeritation

of the amount of collapsing gas which fornied globular clusters instead of field stars).

Due to the need for spatial and photometric completeness corrections. reliable

object identification and an accurate distance measurement to the galaxy ( to obtain

an accurate luniinosity). the specific frequency is typically considered to be valid to

\vit hin a factor of two (Harris. 1991). Despite this limitation. significant differences

still esist between galaxies. particularly between galaxies of different types. Spirals 3. Background 15 tend to have SN values less than 3. while SO and elliptical galaxies have SaVvalues evenly distributed up to 10 or even 90 for giant ellipticals (Harris. 1991. 2001).

Interestingly. dwarf ellipticals also tend to have iinusually high specific frequencies

(Durrell and Harris. 1996).

Such variation in would appear to suggest variation in the cluster formation efficiency in different galaxies. This wu called the specific freyuency prublern?

Taking into consideration variability in the gas content of different types of galasies. .\lcLaughlin (1999) established that there is no rieed to invoke varied forniation efficiencies to esplain anomalous specific frequencies.

Y Technicdy. this is the first specific frequency problem. As it is the one most commonly referred to in the literature. it is the focus of the discussion here. The second specific frequency probiem, an increase in S,v aith gaiactocentric radius. is related to it and was &O addressed by McLaughlin ( 1999). 3. THE TARGET: NGC 3115, THE SPINDLE GALAXY

The object of interest. NGC 3115. is a lenticular galauy which sits in isolation in the region of the constellation Sextans at a distance of about 10 llpc. Also called

the spindle guluxijj. it vas discovered in 1787 by William Herschel. -4s it is alrnost conipletely devoid of gas. yet has a rapiclly rotating bulge (Illingworth and Schechter.

1982). it is the ver- definition of the SO galmy type. perfectly bridging the gap

betwrn the the elliptical E-type galaxies and the spiral and barred-spiral S and

SB-type galx~ies.The physical paranieters of SGC 3113 are presented in Table 3.1.

T'rble 3.1: Physicai parritneters For NGC 3 115. AI1 values were retrieved from the NASA Extragalactic Database (NED. '2001)

Riglit Ascension (52000.0) 10~05"13.9" Declinat ion (52000.0) -07D43'01" Helio. radial velocity 720 f 5 km/s Redshift (2.40 f 0.02) x lw3 Corrected Total Slagnitude (B) -- 9.67 Classification SO-

Being in relatively close prorimity and oriented almost precisely edge-on. YGC

31 1.5 has been a popiilar target in a varietu of observations. To date. NGC 3113

has found itself to be the focus of some three dozen publications. Since early work

on the missing mas problem was performed through a study of the rotation curve

of NGC 3113 (Oort. 1940). it has been studied for a variety of reasoos. One of the

16 3. The Target: NGC 3115, the Spindle Galaxy 17 most interesting discussions of SGC 31 15 was that of Kormendy et al. (1996) who presented evidence for the presence of a 10' Ab, black hole at the heart of the galauy.

Püst pliotometric xork has involved both the halo light. and the globular cluster system. Evidence for chernical evolution in the galavy has been discovered in various studies. Differences in the Aattening of isochromes (contours of constant colour) and isopliotes (contours of constant intensity) dong the major avis of the galavy (Strom et al.. 1977). and the presence of a bimodality in the colour distribution of the halo red giant population (Elson. 1997: Iiundu aiid Khitmore. 1998) both point to a history involving nietal enrichment.

-4s yet globular cluster observations of SGC 31 13 have been somewtiat lirnited.

The earliest work was that of Strom et al. (1977) who obtained a GCLF and çorre- sponcling distance estimate by romparison to that of 1131. Research by Hanes and

Harris (1986) considered the radial distribution. The most recent work has been t hnt of Kavelaars ( 1998) who obtainecl photornetry and spectroscopy for NGC 3113.

Ynfortunately. the peak of the luminosity function 1~snot reached. liundu and

\iVhitmore(1998) obtnined excellent data iising the Hubble Space Telescope's (HST)

\Vide-Field Plaiietary caniera (KFPC?). Howewr. although full? two magnitudes

past the GCLF turnover. t heir field of vieiv aas limited to aithin a l'.O radius (5 3 kpc) of the galactic center.

In this sparse environment. NGC 3115 is unlikely to have erperienced an evo-

lut ion complicated by interactions with multiple (if any) neighbours. .As such. t his

seemingly untouched system is ideal for the study of globular cluster systems in the

contest of galavy formation. 4. DATA REDUCTION

4.1 Observations

The CCD observations of SGC 31 Ei and the associateci calibration fields were rriade on the nights of Narch 14. 1999 (Kron-Cousins R filter). and llarch 17. 1999 (Kron-

Cousins B filter) at the 3.6 ni Cariada France Hawaii Telescope (CFHT)in Hawaii.

In wrh case. the CFH1-K niosiac CCD camera. a detector composed of twelve 2048 x 4096 CCDs arranged in a niosaic to form what is effectively a 13k x Sk carnera.

\vas iised to obtain four dithereci' 480s esposures of the target. The observations.

hoeever. use only the eight central CCDs as the four outer CCDs extended I~eyond

the dinierisions of the filters. U'itli an image scale of 0."306 per pixel. the final 8k x

8k frames cover a region '28.'1 s 3.'1 (- 80 kpc s 80 kpc at a distance of -- 10 hlpc).

rentred ori SGC 31 15 (a2ooo= 10~05~14.~29.bOo0 = -704?'31."1). Seeing was 0."9

and 1."" on each night respectively. As it is occasionally necessa- to refer specifically

to a component detector of the CFH12K camera. a scheniatic of the nurnbers used

is illustrated in Figure 4.1. The passbands for the filters at CFHT are presented in

Figure 4.2.

C'nless otherwise specified. al1 image reduction and analj-sis aas completed using

- -- -- ' Dithering is a technique whereby multiple exposures are taken with siightly offset pointings. Although this complicates the process of Iater cornbining the images for improved signal-to-noise. detector defects such as dead pixels or columns can be eiiminated. 4. Data Reduction 19

Figure 4.1: The CFH12K deteetor. Spaces shown between individual deteetors are ex- aggerated here for clarity. The numbering scheme used to refer to specific detectors is shown.

Figure 4.2 The pasbands for the mters at CFHT. B and R fiiters were used in this study. Sky ernmission (jagged blark iine) and quantum efficiency of the two types of detectors (dashed and soiid hes) are also shown. 4. Data Reduction 20 the standard IR-\F2 software package developed by the National Optical hstronorny

O bservat ories (NOAO).

4.2 Rame Preprocessing

Raw data fraines began the reduction process in their original multi-extension FITS file format (NEF) in which al1 mosaic sections of an image are stored as extensions iri a single file.

An tinexposed image. after readout and analog-digital (AD)conversion will produce pisel valiies distributecl evenly about zero. To avoid negative nurnbers in a final image. a small number of digital counts are placed on the cletector prior to esposure

(in practice this is a voltage). To determine the number of counts corresponding to photoelectrons. this bias leuel must be removed. This is done in two steps. During readout . the cietector oaerclocks each row by ( usually) 32 fictional pixels carrying t lie current bias level. This contribiites 33 unphysical coliimns called the overclock region. Thc first stcp in bias renioval is the subtraction of the mean overclock level.

In this case. a gradua1 increase with row number was hanclled by siibtracting a linear approximation of the overclock region. This first step deals with franie-tdrame changes in the bis level. For the second step. to account for local 2D variability in the bias Ievel. a bzas or rem frame must be subtracted. Bias frames are estimated by taking the average (or median in this case) of several zero-length exposures. The same bias frame \vas used for each image. After the bias level was subtracted from

IR4F: image Reduction and Anaiysis Facility is distributed by the Sational Optical .4stronomy Observatories (X0.40). whicti is operated by the Association of Universities of Research in Astron- omy. Inc. (.ICR4) under cooperative agreement n-ith the Xationai Science Foundation (MF). 4. Data Reduction 21 each UEF frame. a mean twilight Aat field exposure was divided out to correct for pixel-to-pixel sensitivity variation in the camera. For a more detiled description of bias subtraction and Rat Fielding. refer to Howell (1000).

At t his point ir became apparent that the remainder of the reduction process could be greatly simplified by proceeding with each mosaic segment individually. Hence. the frames were split. Csing the IRAF tasks GEOMAP aiid GEOTMN. each of the iridividual esposutes then \vas transformed onto a true astronietric grid using the coordinates of guidestars (about 60 evenly distributed per CCD rhip) available through tlie Cnitecl States .\'ad Observatoy (CSSO). With al1 the images in a çonirrion coordinate systmi. thq were aligiied (iising the same - GO guidestars) and iriediaii-combincd to crmte final ptcprocessed images wit h iniproved signal-to-noise.

The pr~processeciR-filter image is shown in Figure 4.3.

Sear the eclges of tlie image in Figure 4.3. a brighter circiilar region can be

seen. This is a consequence of barn1 distortion: an optical phenornenon cornnion

with niany instriinients. Iniperfect corrector optics cause the plate scale (arcseconds

prr pisel) to increase near the edges of the frame. The pkels in these regions are

effectively larger t han those near the centre and collect more liglit. An image of a

square will appear somewhat rounded. t hiis the name. However. the grey-scaling

used in Figure 4.3 is niisleading as it esagerates this effect. The increase in flux in

regions affected by barrel distortion is only on the order of 34%. Sonetheless. areas

affected by barrel distortion were avoided shenever possible. 4. Data Reduction 22

Figure 4.3: The preprocessed mosaic image of NGC 3115 (R filter). It seems that the sensitivity is greater near the periphery of the kame. It is in fxt not a variation in detector sensitivity. but an optical effect known as barre2 distortion. As the display software exagentes the greyscaie somewhat in t his range, the effect appears much stronger than it is. Flux in the distorted region is higher by - 3% - 5%. Efforts were made to mid these regions of the detector. 4. Data Reduction 23

4.3 Photometry

Photometry was performed entirel? iising the DAOPHOT package in IRAF (Stet- son. 1987). In order to obtain accurate pliotonietry, it was necessary to subtract the broad gradient of diffuse gala~ylight from each image. Sleasurement of the mag-

nitude of an object requires ttiat digital counts contributed by other sources (sky

light. galavy halo light) not be included. This is most accurately done when such contributions are constant. To determine the magnitude of an object. sky levels miist

be subtracted. This aas done using a variation of the method described by Fischer

et al. (1990) in nhich the background light is modeled by applying a niedian filter

to an iniage. .\ledian filtering is a two dimensional smoothing process in which each

pisel is assigncd the metlian ~îliieof the pisels within a specified region surrounding

it. By subtracting tliis mode1 froiii the image. stellar objects are left on a Bat back-

ground IV here t heir magni t iides can niore accurately be nieasured. S Iagnit udes are

then coniputed by creating a rrioclcl for an ideal stellar profile using several bright

isolated objects in an image. The niodel. called a point-spread-function or PSF. has

n functional forni very much like that of a bivariate circular Gaussian aith somecvhat

more estended aings. This PSF is then scaled and fitted to each object detected in

the frame and the magnitude is calculated using the height of the fitted PSF. A Aon

cliart in Figure 4.4 outlines the key aspects of Fischer's algorithm.

Alt hough t his algorit hm typically employs t hree or four iterations of median filter

subtraction. it \vas found t hat additional iterat ions not only offered no improvement 4. Data Reduction 23

Find severai bright isolateci steliar objects and create a point spread function (PSF) (D.IOFIYD.PHOT.PSF) u Raw image (Preprocessed) U Find stellar objects. perform aperture photoinetryt. perforni PSF photornet- and subtract objects from the frarne (DAOFIJD.PHOT.=\LLST.4R) 1 Firid missed stellar objects in star sutitracted €rame. perform aperture photometry. perform PSF photonietry and subtract these from the frame. (DXOFISD.PHOT.PCO?;C,-\T,.4LLST-AR) 1 Ring niedicm ( 12 < radius < 13 ) the star-siibtracted frame to modcl large scde gradients md subtract this rnedian filter from the raw iniage to crcrite a median- filtered image.

Add the mean sky level (estimateci CU the mode of the rnedian filter). (R~IEDI.4S.Il1ST.4T,Ilii4RITH) +1 Finci st~llarohjpcts in the fiitered franie. perform aperture p hotometry, perform PSF photoinetry and subtract objects from the filtered frame. !D.4OFISD .PHOT..I\LLST.\R) 1 Find missed stellar objects in the fiitcred star subtracted franie. perform aperture photometry and create a list of al1 detections. (DAOFIXD.PHOT.PCOSC.4T) u Perform final psf-photonietry on the cornplete List of detections tising the median filtered images. (-1LLST.IR)

i An aperture magnitude is cornputed using dl of the flu (digital counts) contained u-ithin a specified radius of an object's center. Aperture magnitudes measured throughout this algorithm were necessexy only as input for the ALLST.4R task.

Fi,gure 4.4: Schematic flow of the photometry aigorit hm. Corresponding IIWF tasks are listed at each stage. 4. Data Reductioa 25 in recover- but also introduced a small number of false detections %t high magnitude. Tlius a single filter subtraction was used. The median filtered version of

Figure 4.3 is shown in Figure 4.5.

4.4 Estimation of recovery using artificial stars: the completeness function

In order to assess the efficiency of the detection process. stellar objects of known magnitude were added randomly to each image using the ADDSTAR taçk in IRAF's

DAOPHOT package. The photoniet ry algorit hm from the prerious section w,ls t hen

run on these artificial frames using parameters identical to those used for the pure data.

Thcoiriplet~ness function is created by dividirig the nuriiber of detected artificial

objects in a givm magnitude bin by the number of added objects in that bin. It

therefore represeiits the perceiitage detection efficiency as a function of niagnitiide.

Loiver rriagnitucles (brighter objects) are typically at a cornpleteness level of 1 (or

100% detection efficiency ) . while the completeness for higher magnitudes gradually

falls to zero. The magnitude at which the completeness function lias fallen to 0.50

is defined as the completeness limit (Harris. 1990). At this point. randorn noise

variations and photon statistics cause an object to be detected as often as it is

missed.

If an escessire number of objects are added to a given frame. the resulting increase

in object density can change the pliotornetric properties of the frame. Wth this

- Initially. it appeared multiple iterations were improving the yield. However. when the aigorithm was tested using artificial stars. no such increase in recovery was observed. These faise detections were likely spurious noise spikes mistaken by the D.4OFLYD program as faint stellar objects. 4. Data Reduction 26

Figure 4.5: The median filtered m&c image of NGC 3115 (R filter). A variability in sky levels is clearly visible. As each detector was calibrateci separately, such sensitivity variations between detectors have no infiuence on the final data. That said, the variations are almo5t purely cosmetic. The stark difference in sky level is an art&t of the display software. In fact, ciifferences are - 3 - 5%. 4. Data Reduction 27 particular data set the images were not at al1 crowded. containing 4000 to 6000 objects on each 2048~4096chip. Tests showed that "00 objects could be addecl easily to each image without significantly affecting completeness or the recovered magnitude of any one object.

Hoivever. as a successful detection reqiiires that an object be foiind in bot h the

R ancl the B filter images. an object's (B-R) colour plays an important role in detection. An object easily detected in the R filter. but very red (high (B-R) colour) is more likely to fail detection in the B filter ttian a typical object. Similady. a bright bliir object is more likely to fail detection in the R filter ttian in the B filter. To account for this dependence. when an artificial object aas adciecl to a B filter image. a corresponding object \vas added to ttie R filter image at an appropriate niagnitude.

.-\ successful artificial object detection required that both be found.

As completeness corrections were applied separately for globiilar cluster candidates and background field objects. random (B-R) ~alueswere generatecl separately for arti ficial glo biilar cliister candidates and background field objects. The random numbers were generated in Gaussian distributions to closely approximate the true

(B-R) colour distributions of ench of these groups. The means and dispersions for thesc t~voGaussian niodels were found b- fitting Gaussians to the corresponding colour distributions. T~vot iiousand objects were assigned random locations and random magnitudes between B = 19 and B = 28 and were added to the B filter

images. Each objcct ras assigned a *cluster candidate' colour and a 'field object' colour taken from the corresponding random number set, and \.as then added to a

'cluster candidate' R image and a 'field object* R image. Thus. for every artificial 1. Data Reduction 28

B image. two artificial R images were created with objects corresponding to those in the B images: one containing typical globular cluster colours. and one containing typical background field object colours. In order to reduce uncertainties for the conipleteness functions. this process nas rcpeared five times to bring the total number of artificial objects to ten thousand. in the end. completeness functions for cluster candidates and background field objects were indistiguishable.

Unfortunatel- the cornpleteness is dependent on the levels of background gai- light . Cornpleteness funct ions were t herefore corn puted separately in elli pt ical annuli centered on. and oriented along the major avis of the galaxy. Typically. niore central regions show Iower (brighter) completeness limits due to the influence of the halo light. Because these small elliptical annuli cover little area of the overall image. the. contairi relativdy few of the artificial stars. To improve the completeness uncertainties in this region. a snialler region of lOOOxlOOO pixels near the galaxy on each of the central four detector chips \vas separated out to undergo additional artificial star testing. Two hundred objects were added to each small field (approximately the sarne object density as tvas used for the whole frame) in the same fashion as described above to en tiance s tat ist ics. This was repeated ten t imes. augnient ing the

total by two thusand objects per chip. Cltimately. cornpleteness corrections were

applied to the GCLFs and the radial profiles. The completeness functions for detec-

tor chip 1 are shotvn in Figure 4.6. Those of the remaining detectors are presented

in Appendis B.

Cncertainties in the completeness function are computed using the variance for

a binomial distribution of .V trials tvith success probability p (Bolte. 1989): -1. Data Reduction 39

lnner ellipse lnner ellipse 500 c a c 800 500 < a c 800 167 cb c 267 167 c b < 267 0.8 0.8 5046 limit . . 0.6 0.6

19 20 21 22 23 24 25 26 27 19 20 21 22 23 24 25 26 27 0 magnitude R magnitude

0.8 - 0+6 -

0.4 - Ourer ellipse 0.2 - 800 c a < 2300 267 c b c 767 O 19 20 21 22 23 24 25 26 27 R magnitude

Figure 4.6: Completeness furictions for detector 1. Plots are showu for botti B and R filters. and for the inner-galmy and outer-galaxy elliptical annuli. The values a and b appearing on ttie plots refer to the semi-major and semi-minor axis lengths (in pixels) of elliptical mnuli around the galaxy. Siriiilar plots for otlicr chips are presented in Xppenciix B

which can be sliown to correspond to ttie following variance in the completeness function (f):

Artificial star tests also provide a convenient means of estimating the systematic and random photometric uncertainties by simply comparing an artificial object's detected rnagnit ude to t hat which was originally added. The magnitude difference

Ah1 = ~Idrteclrd-~loddedis plotted against LIadded to reveal any bias which may be 4. Data Reduction 30 present in the photometry algorithin. Figure 4.7 shows that AM is centred nicely on zero indicating that no systematic errors ivere introduced. and that the random errors remain sniall ( RUS i 0.1 niag ) through most of the region of interest.

4.5 Object CIassification

At the distance of NGC 3113 (approximately 10 Slpc) a typical globular cluster with half-light radius 5pc occupies - 0."- and thus cannot be resolved with seeing - l."O.

Rather. they appear as an overdensity of star-like point sources in the vicinity of the host gal~xy.Interspersed amongst the globular clusters. hoaever. are distant backgroiirid galaxies and moneously de tected noise peaks. The ALLSTAR t iisk in IRAF's DAOP HOT package at tempts to iclentify t hese undesirable contaniinants using parameters called SHARP and ROCSD ahich cruclely quaritify the peakedness iind circular syrnnietry of an object. Alt hough soniewhat successful. a more effective met hod uses the CLASSIFI' routine (Harris et al.. L99l). CLASSIFY computes tao parameters usefiil iri object identification: NI.and r-2. The A.\! paranieter is simply the ciifference between an object's aperture magnitude and its PSF magnitude.

Cnfortunately. it was found to be quite susceptible to object crowding which led to the rejection of good data. Consequently. only the r-2 parameter aas used for the final culling. It coniputes a type of radial moment for each object. and is defined as

foHows:

in nhich I, is the intensity of the jth pixel (~lthsky background subtracted), and 4. Data Reduction 31

Figure 4.7: The photometric scatter of artificiai stars added to detector 1. Plots of the scatter and RiMS scatter are shown for both R and B filtem. It appears as t hough considerably less scat ter is present in the R data near the completeness limit . However, as only typical globular cluster colours were used ( (B-R) -1.5) . an object detected in R may not be detected in B. Thus, the R data appear less scattered only because the hill depth of those images was not exploiteci in t his reduction technique. Similar plots for other chips are presented in Appendu B. 4. Data Reduction 32 r, is the radial distance of that p~uelfrom the object centre. Although the r-2 parameter also siiffered somewiiat due to image crowding? it ras possible to mitigate ttiis problem by restricting the routine to sum to a maximum radius of only 3 pixels in R filter images. or 4 pixels in B filter images. ''

The basic premise is that stellar objects have most of their intensity concentrated

riear the centre. n-hile background galaxies tend to be broader or more distended.

This differeiice causes background galaxies to have Iiigher values of r-? than would

be typical of a stellar object. Culling above a uniform threshold is therefore quite cffectiw iri wrding out non-stellar detections. Thresholds were selected to yield

>95% recoïcry of artificial stars. Plots of the r-2 vs. LItnst (instrument inagnitude)

are showri for artificial stars in Figure 4.8 while those for the real data are presented

iri Figure 4.9.

.\Lisclassification of artificial stars as non-stellar ranged between 3% and 5%.

Detector-specific \;dues for the artificial and real objects are presented in Table 4.1.

4.6 Calibra tions

To cleterniine the magnitude of an object. an ideal steliar profile (the PSF) with

an internally defined zero point \vas fitted to it. Thus. although al1 object magni-

t udes nieasured in t his way (called rnstrunrerct magnitudes) are in ternally consistent

aith one another. the! are not calibrated to the standard systeni. Two important

correct ions were required in calibrat ing the data: the aperture correction and the

transformation to the standard photometric system. In addition to these. a correc- These radii represent - 2/3 FJC'HSI for a typical stetiar object through the respective Mters. 4. Data Reductioa 33

Before cuiling (0) Before culling (R)

* 1

18 19 20 21 22 23 24 25 26 27 28 6 magnitude (inst) R magnitude (inst) Aher culling (6) Alter culling (R)

0.8 158 16 17 18 19 20 21 22 23 24 25 26 18 19 20 21 22 23 24 25 26 27 28 8 magnitude (im9 R magnttude (inst)

Figure 4.8- The r-2 classification diagram for the artificid st.us for detector 1. Siniilar plots for other chips are presented in Xppendix B. Beiore culling (BI Betore culling (R)

B magnitude (inst) R magniiude (inst) Atter culling (6) Atter culling (A)

0.8l2 2 0.8 8 18 19 20 21 22 23 24 25 26 27 28 15 16 17 10 19 20 21 22 23 24 25 26 B magnitude (inst) R magnitude (inst)

Fiyre 4.9: The r-2 classification diagram for the real data. Similar plots for other chips are presented in Xppendix B. 4. Data Reduction 34

Table 4.1: Percentages of data culled for both artificial and real objects Filter Detector Art. stars culled Real objects culled ' r-2 threshold ('% m B 1 4.7 42.0 1.99 B 01 2.8 39.8 1.99 B 3 4.1 5 1.8 1.95 B 4 4.0 54.1 2.95 - B ;l -4.4 42. 4 1.98 B 6- 4.8 42.7 1.0 B 1 3.9 49.3 1.91 B 8 4.6 46.3 1.94 R 1 3.1 52.6 1.62 R 2 3.1 69.5 1.61 R 3 2.9 54.1 1-57 R 4 3.3 68.6 1.59 - 'J - - R ;I) ,. -I 33.9 1.63 R 6- 2.3 55.4 1.64 R I 2. I 48.0 1.61 R 8 3.3 50.8 1.SC

Percentages used here represent only objects brighter than an assigneci cut-off magnitude (B = 26.0. R = 24.5) beyond which few artificial stars were detected. Note that this is not the 30% completeness limit. but approxirnately the 95% cornpleteness lirnit. 4. Data Reduction 35 tion factor is required to account for obsciiration by interstellar dust.

4.6.1 The Aperture Correction

In order to ilse the PSF fitting method to measure niagnitudes. the IRAF task

ALLSTAR reqiiires one PSF fit nitli a knowi magnitude to deteriniiie a zero point: al1 other niagnitudes are based on this. This zero-point magnitude is established when the PSF is created bu assigning the aperture magnitude of the first object in the iiiput list of bright isolated objects. As an aperture magnitude measures al1 flus tliroiigh an aperture of a specified radius. any flux outside that radius is unaccounted for. Consequent ly. an aperture rnagnit ude always overest imates t lie rnagnit ude of aii object (ie. nieasiires it to be t oo jaint) . Since a11 PSF magnitudes are based on a zero

point t akeri froni an aperture magnitude. t hcy must be corrected to account for the

Rus whirh ivas outside the original aperture5. In this case apertures were set to be

- 1 Fi\-Hl1 (Full Width Half '\lmimurn). or 1 and 6 pixels in R and B respectively.

To determine the correction term. the PHOT task ~1sused to mesure several

aperture magnitudes for each object. The apertures used began at a radius of 2

pisels. and grew by 1 pisel iip to a radius of 18 pisels. At this largest aperture. it

was apparent that virtually al1 Rus from eacli object tvas being included. Csing the

IRAF ta& APPHOT (in the PHOTCAL package). a series of gron-th curves were

çreated to show the increase in flus measured as aperture radius grew. The difference

in magnitude from the -4 and 6 p~xelradii (R and B filters) to the asymptotic limit

" It's tempting to try to circumvent this problem through use of a larger aperture. Hou-ewr. an aperture n-hich is too large introduces primarily only sky background CO the flux measurement. This adds very little srgnd and substantid noise and is thus costly in terms of signal-tenoise. In the worst case. a larger aperture ma? also include flmx from a crowding neighbour. 4. Data Reduction 36

Table 4.3: Aperture correction factors in magnitudes.

- Detector / B 1 -0.28 k 0.01 -1 -0.25 k 0.01 3 -0.2 * 0.01 4- -0.24 i 0.01 3 -0.29 k 0.01 6- -0.32 k 0.01 1 -0.27 k 0.01 8 -0.20 i 0.01 of the growtli terni is the aperture cmrection. The values obtained are listed in

Table 4.2. These were added to the instrument niagnitudes of the objects found on

the corrrspondirig detectors.

4.6.2 Zkansforrna tion to the standard photometric systern

In order to transforni the m~asuredmagnitudes to the stanclard pliotornetric system.

obserations of standard stars nith already established niagnitudes were made. The

standards used wre those defined by Landolt ( 1983. 1992).

The standard magnitude scale is defined with respect to the star Vega (a Lyrae)

which is assigned a magnitude of zero in al1 filters. In processing the data. a certain

detector efficiency is assumed: that is to Say. the zero magnitude is assigned some

reasonable number of digital units on the detector. This assumed number of digital

counts must then be corrected to be consistent with flm which would be receiveci

from kga. In practice \èga itself is not directly observed. Rather. during the

observing run several objects in a standard selected region of the sky were imaged.

There are many such regions containing objects ~itba variety of very well defined

magnitudes to be osed in place of that for Vega. The resulting correction term is a 4. Data Reduction 37 constant nhich can be added to. or subtracted from. al1 instrument magnitudes as required. It is called the zero point ofset and is denoted here as 6.

In addition to ttie zero point correction. it is necessary to correct for any non- uniform quantum efficiency over the spectruni of the detector. For example two objects of different colour (ie different black-body distributions) niay contribute t hc same Rus ttirough a given filter. but if the detector efficiency changes across the pass-band of the filter the object with niore flux in the higher efficiency region of tlie filter will be detected as being brighter. .A correction term ahich is a Function of colour is therefore also required. Ideally. the term aould incorporate polynornials in (B-R) colour. but in practice. only ttie liriear term ever contributes significantly.

The linear coefficient is called the colour coeficient and is denoted here as p.

Fiiially. one other correction miist be made to account for the tliickness of tlie at mosphere t lirough w hich the obserntions were made. This is called the extinction correction. With the zenith defined to be an airniass of 1.0, an observation niade at a zenith clistarice B rvoiild be taken through an airmass of The resuiting correction term is linear in airmass (.Y) and is denoted E.

Nominal values of 5 were provided by the observatory and values for & and Ir

tvere determined using regression to fit a line for the following equation in both B

and R filters.

"he assertion that airmass = sec(9) assumes that the cumture of the earth can be neglected. This approximation is excellent up to a zenith distance of 9 2 60" (an airmass of 2.0). A11 observations made were through airmasses Iess than 1.5. 4. Data Reduction 38

Table 4.3: Caiibrat ion coefficients

Detector

Table 4.4: RhIS residuals for calibrations Number of RAIS residuals Calibration stars R B 0.03 0.04 0.01 0.02 0.04 0.03 0.04 0.06 0.02 0.03 0.01 0.01 0.02 0.04 0.01 0.01 where .\frid is the knoan magnitude of a standard star. and rn,,,,, is the instrument magnitude of the same star through a large (radius of 18 pixels) aperture.

The final values of these parameters appear in Table 4.3. Due to the potential hazards of poor calibration. otlier researchers currently reducing data from the

CFH 1?K detector were contacted to confirni t hese values independent Iy (Kavelaars

2001. private communication). The coefficients were found to be in agreement. The

final RUS residual values for the calibration stars in each detector are presented in

Table 4.4. 4. Data Reduction 39

4.6.3 Reddening Corrections

In any obser~ation.not only is the atmosphere an obscuring factor. but also the dust tvit hin Our own Milky Way galaxy. Such scattering is dependent on the wavelength of light incident on a dust grain and affects short wavelengths more severely than longer unes. Observatioiis t hrough bluer filters like B are t herefore more strongly affected

(ie. lose a greater proportion of Rus) than those made tlirotigh redder filters like R.

This causes a systematic increase in the calculation of (B-R) making objects appear redder than they truly are. The correction is thus called the reddening correction and is denoted .As. tvhere S is the relevant filter.

As the corrections are based on optical densities of dust. t hey cannot be derived. but rather mut be determinecl t hrough observation. The most rwmt siich ass~ss- nient of reddening corrections is thof Schlegel et al. (1998). For observations in the direction of SGC 3115. .-lB = 0.205. and -AR = 0.127. 5. ANALYSIS AND RESULTS

Kith preprocessing and data reduction completed. the culled. calibrated data were transforrnecl onto a global coordinate system crntered on NGC 31 15. As the region of interest surrounding SGC 31 15 is broken over eight detectors. the aiialysis was soniewhat more complicated than would have been the case for a single detector. For

the most part. hcwerer. it aas possible to cornpiete the analysis independently for each deteetor.

.-ilriiost dlof tlie resuits preseiited are distributions of various quantiries. -4s it is

possible. when using histograms. to obtain subtly different results through shifts in

bin positions. it \vas decided in ttiis case that a format unaffected by binning changes

would be preferred. Distributions have been computed using a sliding kernel met hod.

Ariy point in a plot is the weighted sum of the data in its immediate cicinity. In this

case. the weight function (kernel) used \vas a Gaussian and the 'immediate ricinity'

was takeri to be i3a. tvhere a is the dispersion of the Gaussian kernel. Values of a

aere chosen appropriately in each case and are stated on each plot. \-dues presented

are normalized to represent the number density in order tliat the integral of the

distribution equal the total nurnber of data points used. X detailed account of the

met hod including r he evaluation of uncertainties is presented in Append~uA.

Al1 relevant information regarding the individual globular cluster candidates is 5. Aadysis and Results 41 tabulated in Appendix C. Coordinates (a20OO,and d20ao),magnitudes. and (B-R)

colours for al1 objects within a galactocentric radius of RGC = ;.'O (5 20 kpc). brighter than B=24.2. and in the colour range 1.0 < (B- R) < 1.8 are included.

5.1 The Colour Distribution

The creation of the (B-R) colour distribution was a fairly straigtit-forward process.

Al1 cluster candidates wre drawn from a large circular region centered on the galavy

(see Figure 5.1). Only objects with B<23.6 were chosen. This restriction serves two purposes. First. although the iincertainties in B and R ni- be quite reasonahle at tiigher magnitudes (50.1). the resiilting qiiadratiire uncertainty in (B-R)ciln be quite large (50.1.5). This iincertitinty is comparable to the scale of the features being soiiglit if such featiires esist: the separate peaks of a mukirnodal distribution. -4s sucli. ;i snieariiig effect beconies a prohlem i11 colotir distributions at niuch brighter

levels than would be the case in a luminosity function. Also. using only the brightest ohjects eliminates the need for a cotnpleteness correction as the magnitudes in qiiestion are at conipleteness le~elsbetter than 90%.

The inclusion of background objects in the sample of cluster candidates is in-

evitabie. To correct for the contamination introduced into the cluster sample. regions

of the image ~4 removed from the galavy were chosen to represent the background

object density (see Figure 5.1 j. The sections selected as background were on the

outer portions of al1 eight detectors. At the distance of YGC 3115 (- 10 SIpc). tliese

sections are approsimately 30 kpc from the centre of the gala?. Radial density pro-

files (presented later in Section 5.3.2) demonstrate t hat the object density beyond - 5. Andysis and Results 12

20 kpc (;.'O at this distance) is essentially constant. meaning that background levels have been reached. Although portions of the background regions are affected by the barre1 distortion discussed in Section 4.2 (a -- 3 - 5% effect)? the effect is comparable in both B and R filters. It therefore cancels out in the calculation of (B-R).

In order to subtract awiv the distribution of background field objects, it was necessary to scaie it such tliat it would correspond to the area that \vas used for the cluster candidates. Although the basic geonietry of the cluster and background regions (circles and rectangles) \vas quite simple. the presence of gaps between the detectors complicated the proccss. To correct for the area differences. JO 000 randorn coordinates nere generated for eacli detector (-LOO 000 in total). Some of these random coordinates fell into 'cliistcr candidate' regions. some fell into 'background field object' regions. and sonie fcll irito regions of the detector wliich were not iiscd. -4s tlie

density of these randoni coordinates nas constant. tlie ratio of the nimber whirti fell

into a cltister region to the niimber which fell in a background region was taken to be

eqtial to the ratio of the two areas. This was the correction factor used to scale the

background distribution to subtract it froni the distribution of cluster candidates.

Kith so niany points being used. the uncertainty in this factor was 5 0.1%. This is

far more precise than was necessa- as the variability in the density of background

objects is much greater than I0.1%. The colour distributions of cluster candidates.

background o bjects. and background-subtracted cluster candidates are presented in

Figures 5.2 (a).(b). and (c) respectivel. Al1 of these distributions were made using

a a value of 0.01s mag for the kernel function. A traditional histogram of the back-

ground subtracted distribution is presented in Figure 5.2 (d) to indicate the number Figure 5.1 : The cluster candidate. and background object regions for the (B-R)colour distribution. Ali objects within the centrai red-shaded region were used as cluster candidates. while d those in the blue-shaded regions at the periphery of the kame were used to represent the background population. Objects in the grey-shaded areas were not used. of objects involved.

5.1.1 Evalulating the signiflcance of the multimodality

The multimodality of the colour distribution is immediately apparent. To eiduate the statistical significance of t his multimodality. two tests were applied: the KNSI mixture-modeling routine descrïbed by Ashman. Bird, and Zepf (1994). and a Monte

Carlo simulation using crosscorrelation of subsamples.

The KMM tests

Slixture-modeiing is a process by which the statistical significance of clustering within a dataset is evduated. By providing the number of potential subgroups within the 5. -4nalysis and Results 34

Cluster Candidates - Uncertainty - 20.5 c B c 23.6 -

(b) 800 . Background oqects - Uncertaint'y 600 - 20 5 < B c 23.6

400 - 'se 5

0.8 0.9 t 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 B-R

Figure 5.2: The (B-R) colour distribution. From top to bottom: (a) The raw colour distribution of cluster candidates. (b) the distribution of background objects. (c) the final background-subracted colour dis t ribtit ion. and (d) the final background- subtracted distribut ion shown as a traditional histogram. The smoot hing ker- ne1 for (a). (b). and (c) used 0=0.015. 5. Aaaiysis and Resuits 45 dataset and the functional form of the subgroups (almost always Gaussian), the parameters (ie. mean. variance) which best represent that number of subgroups are determined. This nas thoroughly described in an astrononiical context by Nemec and Seriiec (1991). Hoaever. Ashman. Bird. and Zepf (199-4) popularized mixture- modeling techniques for colour distributions. The KM11 algori t hm t hey used is freely distributeci. and is now widely rrseci.

The KM'II routine fits a specified number of Gaussians to a univariate dataset and corriputes rnasirnum likelihood estimates of the nieans and variances and estimates the sigriificance of the fit over that of a single Gaussian (the nul1 hypothesis).

The routine runs using a list of data points and therefore could not be used to direct ly niodel the background-subt racted distribution. However. as the background contributes mry little structure to the colour distribution. the full list of cluster candidates was believed to be adequately representative of the final distribution. The routine can be run in honioscedastic (component distributions are forced to have the sanie covariance) or heteroscedastic (variances are left as free paraineters) modes.

.Ut hoiigh the aut hors siiggest t hat the homoscedastic algorit hni is more robiist statistically there aas no a priori reason to warrant irnposing this restriction. Thus each hypothesised modality nas tested in botli of these modes.

Several modalities (n = 3. 4. 5. and 6) were examined. AI1 hypotheses tested

(homoscedastic and heteroscedastic for al1 modalities) were evaluated to be improve- ments over the unimodal mode1 at greater than 99% confidence. Al1 of the models arriwd at by IilIII are presented in Figures 5.3 (a)-(j) Althouph the six mode

models appear quite compelling they are not in any way statistically preferred over 5. -4ndysis and Results 46 another hypothesis. The colour distribution is best regarded simply as multimodal.

The Monte Carlo simulations

In order to test the robustness of the peaks. four independent samples were created by dracving data separately frorn each of the four central detectors (see Figure 5.4.

Cnforturiately such an analysis suffers Frorn small sample statistics. Nonctheless. riiany of the peaks appear consistently iii al1 four. or in at least three of the quad- rants of' the galaxy. To determine the likelihood that a unimodal distribution would prodiice sucli consistent structure ahen subsampled. Monte Carlo simulations were used.

To mat hrmatically waliiate t lie similarity between the sub-distributions. correlations twre iiserl. Howwr. the lise of a corr~latiorito test for similarity betweri tiw furictions is niost effective when the two functions Vary about a level of zeroi. To exploit t his property. a snioot hed version of each distribution tvas subtracted from that distribution to leave fluctuations which varied about zero. Thus a distribution f (2)and the snioothed version of it. /(r).were used to create a distribution 1 (r):

Eacfi of the resulting zero-level distributions was correlated nlth each of the others.

Two distributions containing fluctuations about some positive o&et level wiii conelate to give a large positive number regardIess of whether or not the fluctuations correspond well with one another. \-ariations about a zero offset. however, will only correlate to produce a large positive p due if they are similar. Sirnilarly. variations which oppose one another will correlate to produce a large negative number. Cluster candidates (forcornpanson) Cluster canâidates (for campanson) m 800 r 1

0.8 1 1.2 1.4 16 1.8 2 B-R 3 mode test (heterosced.) 3 made test (hornosced.1 m 600

0.8 1 1.2 1.4 1.6 1.8 2 B-R

4 mode test (heterosced.) 4 mode test (homosced.) rn m

5 mode test (heterosced.) 5 mode lest (Mmosced.) m m

6 mode test (hetemsced.) 6 mode test (homasced.) m m

Fi,we 5.3: The KSlh.1 niodels of the ( B-R) colour distribution showing the heteroscedastic (left) and honioscedastic (right ) models for various modalit ies. For cornparison. the colour distribution for the cluster candidates used by the KMM algorithm is shown as the top figure on each side. 5. AaaZysis and Results 48

B-R

400 Detector 4 - Unceminty . â 20.5 c B < 23.6

0.8 0.9 1 t.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 B-R

Figure 5.4: The independent (B-R) colour distributions for the four central detectors: (a) der. 1. (b) det. 2. (c) det. 3. (ci) det. 4. The smoothing kernel for each distribution used o=0.015. 5. Analysis and Results 39

Each of t liese integrations was performed numerically using the trapezoid nile. The colour distributions were made using the sliding kernel methods described at the beginning of t his chapter wit li point spacings of l(B-R)=O.OO5 and ok,,,,i=0.015.

With four such zero-level distributions. six correlations were performed.

If similar structure is indeed present in the subsamples. t hey should ali correlate

well. The niean (KA).median (EJ. and variance (a:,) of the six KA correlation

values were used to define two correlation indices. Zui and Eu:, as follo.rvs:

In tliis rvay. the niean and niedian values of the correlations are weighted by the

variance. To obtain a high value for either of these parameters. each distribution

niiist correlate well \vit h each of the others. Althoiigti two random distributions

niight occassionally correlate ver? well to cause a significant increase in XA. the

îorresponding increase in the variance will prevent the set from obtaining high Eor

value. The values obtained for the real data are as follows: 5. Analysis adResults 50

To tcst the significance of the results obtained. Monte Car10 simulations of the alternate hypot hesis were performed. If the distribution is not multirnodal. t hen the peaks are statistical fluctuations in a unimodal distribution. Thus art ificial datasets wre created for each of the subsarnple distributions by drawing a corresponding

iiunibe? of data points frorn a random iinimodal Gaussian distribution. The random

nuniber generator (a standard algorithm from Press et al. (1986)) was configureci to

produce Gaiissian distributed (B-R) colours. To determine the mean and dispersion of the Gaiissian to be used in this unimodal modcl. a Gaussian was fitted to the

real (B-R) colour distribution iising a Slarquart-Levenberg non-linear least-squares

fitting algorithniJ. This best-fit Gaiissian is shown superimposed on the (B-R) colour

diagrain in Figure 5.5. The randomly generated datasets were kernel smoothed to

produce distributions in the same nay the real (B-R) colour distribution nas created.

The $2 and values were then calculated for the four random samples. This

was repeated for 4000 sets of four random subsamples. The distributions of %Z and

? .As background-subtracted colour distributions were used. the nurnber of data points within a distribution could not simply be counted. Rather. the nurnber was determined by integrating the distribution. This was found to be accurate to within *l data point. The SIarquardt-Levenberg aigorithm is the default fitting algorithm used by the GIjGplot software package. It is an iteratiw least squares method capable of fitting non-iinear functions of severai parameters. For a thorough discussion of the algorithm, refer to Press et ai. (1986). 5. .4naiysis and Results 51

700 I a i I 1 6ackgmund-subtracteddislnbution - Least-squares gaussian ...... -

Figure 5.5: The least-squares Gaussian fit for the (B-R) colour distribution. Raiidoui (B- R) colours were gexieraced to have a distribution with the sanie parameters (mean and dispersion) as t his bcst-fit Gaussian. - K,' outconies are presented in Figures 5.6 (a). and (b). The values obtained froni the riinctom trials wre normalizcd to the those of the real data. Thiis the real clata - are sho~v\.riivith arrows at vnliies of X,r = 1. and r;,: = 1. Values for the randoni ciatasets are seen to be evenly distributcd about zero.

The significance of the result is imniediately apparent. The sniall skew tomrd positive values is believed to be a consequence of the smoothing method used to compute the mean distribution used in Equation 5.1. Should there be any tendency for the mean to be too high. or too low. the resulting correlation would tend to be positive. However. the effect is small. and is not in a- way believed to undermine the significance of the result. -1s no four random samples were found to correlate in this fashion as aell as the real data. the statisticai significance could not be determined Figure 5.6: The Xy2. and Ee2 distributions for random unimodal data. The values have tieen normalized to those caiculated for the real data. Thus. the arrows at - rio2 = 1. 2,: = 1 indicate the positions of the values for the red data. The apparent skew toward positive values is believed to have originated during subtroction of the smoothed distribution in Equation 5.1. Xny bias level in the rernaining fluctuations would introduce a slight tendency toward positive çorrelat ion values. regardless of whet her the bias was positive or negative. .As the effect is small. it is believed that it in no way affects the conclusion that the persistent mult imodality is significant. 5. Anaiysis anci Resdts 53 specifically Suffice it to Say. the multimodality wit hin the colour distribution appears to be real. nith very high significance.

Throughout the reniainder of the analysis. whenever appropriate. the data in

these separate peaks will be examineci independentlu.

5.2 The Globular Cluster Luminosity hinction

In the GCLF analysis. cluster candidates were selected froni a srnaller region than

was used in making the (B-R) colour distribution (compare Figure 3.7 to 5.1). To

mininiize contamination in the saniple of globular clusters. the objects to be con-

sidrred cluster candidates wre selected froni within elliptical regions in the near

vicinity of the galasy. The ellipses were chosen to have eccmtricity e = 2/3 (a ratio

of major uis n to niinor aixis b of 3: 1). aiid were aligned with. and centered on.

the galas?. This particular shape ivns cliosen as it \vas qualitativelu found to be a

good approsiniation to the shape of t lie halo light. Kith completeness being greatly

influenced bu levels of halo light. regions with similar levels were analyed together

in this fashion. Two elliptical regions were chosen (defined here using the major avis

only) :

1.'72 < a < 'L!X and L'75 < a < X36,

or 5.0 kpc < a < 8.0 kpc. and 8.0 kpc < a < 23.0 kpc.

\\-hile the inner annulus aas significantly affected by leveis of galavy light. the outer

annulus was sufficiently removed for light to be at sky levels. Typically. several such

annuli sould be used to account for the variation in completeness as the background

gala? light increases near the center of the gala?. However. in t his case. the regions 5. Analysis and Resdts 54

Figure 5.7: The cluster candidate and background object regions wed for the GCLF . Clus- ter candidates were drawn from the inner (shaded rd), and outer (shaded green) eliiptcd annuli in the center of the kame. while background objects were drawn from the blue-sbaded rectangular regions on the four outer-most detectors. Objects in the remaining grey-shaded areas were not used. Each detector chip was processed independently, and completeness correct ions were applied separately to data within the two elliptical annuli. which would have been giwn this kind of special consideration were blocked by the intersecting gaps between the detectors and could not be considered at all.

To eliminate objects which were unlikely to be globular clusten. a broad (B-

R) colour culling was completed for cluster candidates, background objects. and mificial stars. Data for the Mlky Miay cluster system compiled by Harris (1996) suggest a range of 0.9 < (B-R) < 1.4 is appropriate for globular clusters. However. as the colour distribution for SGC 3113 containeci a significant number of objects at colours up to (B-R) = 1.8, and none below (B-R)= 1.0 ', the cul1 aas set to

' Globular cluster colours are quite similar between different systems. However, age and rnetai- licity Merences, or dust reddening can cause srnaii variations. A survey of the globuiar cluster systerns of 29 SO galaxies by Kundu and Whitmore (2001) found mean V-1 colours for systems 5. .4naiysis and Results 55 include the cluster colours observed in NGC 3115 and the final range used na:

1.0 < (B-R) < 1.8.

Distri but ions of rnagni tudes for cluster candidates and background objects were

made using the sliding-kernel rnethod discussed above with dispersion a~,,,,~= 0.2

niag. Siniilar distributions were then made using the artificial stars. and the corn-

pleteness fiinction nas createci by dividing the distribution of the Tound' stars by

that of the 'acideci' stars. The cornpleteness correction was applied to the data on

a point-by-point basis for each point in the distribution. Errors a, were estiniated

using the methocf suggested by Boite (1989)~:

Hrre. f is the completeness function. nobs is the number of obsen-ed objects. and

01 is the completeness iincertaiiity definecf in Equation 4.2. The luminosity func-

tions of the cluster candidates in B and R are prescnted in Figures 5.8(a) and (b).

respecti~ely. The distributions of the background objects were made in the same

fashion as tiiose of the cluster candidates and are show in Figures 5.8(c). and (d).

Sote that the regions chosen for background objects are not the sanie as those cho-

sen in the colour distribution. More central sections of the outer chips were used

to avoid selecting objects affected by barre1 distortion near the edges of the frame.

These background objects are still -25 kpc from the center of the galaxy. The back-

to range from (Y-I)=0.85 ((B-R)s 1.1) to (V-I)=l.li ((B-R)zz 1.5). Xote that these numbers do not refiect the typical range FIithin one systern, but rather are mean dues for entire cluster systems. .\fter calculating a, using Equation 5.9. the dueo, aas normaiized to the scale of the sliding kemel distribution as discussed in Appendix A. 5. Analysis and Resuits 56

Table 5.1: Best-fit Gaussian parameters for the GCLFs

Peaks for the GCLFs with final uncertainties. The stated uncertainty is the quadrature sum of: the standard error for the Gaussian fit. the mean of the RMS calibration errors for the detectors. and the mean of the aperture correct ion errors. Uncertaint ies Filter Peak Fitt ing Calibration Aperture RMS correct ion Ro 21.94 f 0.04 0.03 0.02 0.02 Bo '23.42 ;fi 0.04 0.03 0.03 0.01 ground distribution \vas scaled to correspond to a region of area equal to tliat iised for the globular cluster candidates. This scaling factor was calciilatcd using the sanie technique whicli wcas used for the background scaling of the colour distribution described in Section 5.1. The conipleteness-corrected. background-subtracted GCLFs are presented in Figures S.S(e). and (f).

.A non-linear lest squares Ilarquardt-Levenberg algorithm (Press et al.. 1986)

\vas used to compute the paranieters -4. a. and mo (see Equation 2.3) for the best-fit

Gaussians of the two final luminosity functions in B and R. Only data up to the

50% conipleteness lirnit were used in the fitting. The final fit parameters can be found in Table 5.1. and the final peak magnitudes with a summary of accumulated uncertainties are presented in Table 5.2. 5. Analvsis and Resuits 07

300 Cluster candidates - 1

Figure 5.8: The giobdar cluster luminosity hinctions in B (lefi) and R (right). Fkom top to bottom: (a. and b) the liiminosity functions of cluster candidates. (c.and d) the Iuminoaity functions of background objects (normaiized to the same area used for cluster candidates), and (e, and t) the final globular cluster luminosity function. AU smoothing kernels used a=0.2 mag. 5. Analvsis and Results 58

In order to determine the distance modulus. the absolute magnitude of the GCLF peaks in B and R are required. Cnfortunately, R peaks are not commonly reported.

Hoivever. suffiçient information exists to make a reasonable estimate of the the peak in B. Csing published GCLF turnover magnitudes in B from Ferrarese et al. (2000) and distance nioduli determined by Tonry et al. (2001) using surface brightness fluctuations (SBF). absolute magnitudes for the GCLF peak in B were calculatecl.

These were then areraged with values for the Mlky Way and 1131 (Sandage and

Taninianil. 1995) to cletermine a reasonable value for the B turnover.

Data for sis sptems were available. The B turn-over magnitudes were calibrated to absolute magnitudes by subtracting the SBF distance moduli. and the correspond- iiig unrertainties were aclded in quadrature. These sis dues averaged mith those of the llilky \\*a?. and 1131 yielded a result of .Us= -6.65. To deterrniiie the uncer-

tainty in the final value. two separate methods gave similar results. The standard deviation of the five values yielded k0.30. while the average of the uncertainties of

the five ccontributing values gave i0.26. Thus the absolute magnitude of the peak

wu tnken to bc: .Us = -6.65 k 0.29. The data usecl to cornpute this are presented

in Table 5.3.

Csirig this value of .IlB. the distance modulus for NGC 3115 is found to be: 5. Analvsis and Results 59

Table 5.3: Estimates of the GCLF peak in B.

Object GCLF turn-over in B m-M (SBF) MB (Ferrarese et d.. 2000) (Tonry et al., 2001) NGC 13'19 24.95I0.30 31.5lst0.15 -6.56i0.34 NGC 1399 XXIIO. 10 31.50&0.16 -6.91k0.19 NGC 1404 24.86k0.21 31.61k0. 19 -6.75i0.28 NGC 4472 24.ïSk0.23 31.06kO. 10 -6.28i0.25 NGC 4649 24.41~tO.18 31 .13&0. 15 -6.66M.23 XGC 4665 '25.383~0.46 31.55k0.17 -S. lïkO.49 Mlky Way f -6.90kO. 11 1131 .t -1.01 k0.20 1 -6.63k0.23 1 t From Sandage and Tmniann (1995)

Although the GCLF turn-over in R coulcl riot tw used to support tliis result. it was used in combination with estirriates of the distance niodulus for XGC 3115 to tleterniiric ari absoliitc rriagnitutle for the turn-over in R. This is included in the discussion in Chapter 6.

5.2.1 The eflects of rnetallicity on the GCLF peak

It lias beeii suggesteti that metallicity may haw a significant influence on the position of the GCLF pcak (Ashrnan. Conti. and Zepf. 1995). Thus a clearly multimodal colour distribution lends itself nicely to a test of this theo. Luminosity functions nere createcf for specific (B-R) ranges corresponding to the first (bluest) three peaks in the colour distribution. Eacli nas then fitted with a Gaussian by the same method clescribed for the full data set. The GCLFs and fitted curves are displayed in Fig- ure 5.9 and the best-fit parameters are listed in Table 3.4.

To estiniate the number of objects used in each GCLF. the distributions were integrated. The approximate numbers of objects contribiiting to each luminosity 5. Anaiysis and Results 60

Table 5.4: Best-fit Gaussian parameters for the GCLFs. The uncertaiuties in & and Bo are the quadrature sum of the standard error in the Gaussian fit. the mean RMS error for the calibrations. and the mean error for the aperture correction. Un- certainties for the other parameters listed are t lie Gaussian fitting paraueters. The values of a~ and OB were hed at 0.8 to be consistent the GCLF's made iising a11 data points. Peak I Peak 2 Peak 3 1

fiinction are listed in riie colunin headings of Table 5.4.

In ordcr to test the absolute values of the GCLF turn-ovrrs suggested by ;\shman.

Conti. and Zepf (1995). estirriates of the metallicity of each (B-R) siibgroiip had to

11c iriacfr. Lkfortiiiiatc.ly. no relation for nietallicity and (B-R) colour could bc foiind.

Howwr. Iiissler-Patig et al. (1998) obtained the followiiig relation for rnetallirity in(-1 coloiir:

To ot~tiiiiia relation betwcen (V-I) and (B-R) colour. al1 Mlky Way giobiilar rlusters froni Harris (1996)with E(B-\')

(1- - 1) = 0.090(k0.064) + 0.71 1(f0.058) . (B- R).

These were then combined to yield: 5. Anaiysis and Resuits 61

Figure 5.9: The GCLFs in B (left) and R (rîght) for three sub-populations in (B-R)colour. Rom top to bottom: (a. and b) The first (bluest) peak (1.09 < (B-R)< 1.17). (c. and d) the second peak (1.20 < (B-R)< 1.28). (e. and f) and the third peak (1.30 < (B-R)< 1.a)- Smoothing kernels used u=0.2. 5. Analysis and Results 62

B-R

Figure 5.10: The (V-1) vs. (B-R)relation for Milky Way giobular clusters. Ouly objects with E(B-V)

Csiiig this relation (Equation 5.12). estiniated nietallicities for the three 'bliiest' subgroups in the (B-R) distribution were calculateci. The final values are presented in Tb5.5 Ashman. Conti. and Zepf (1995) provided no uncertainties for t heir metallicity-specific absolute magnitudes. .4s the uncertainty in a GCLF distance modulus would be dominated by the absolute magnitude component ( typically kO.2 as conipared to k0.05 for the fit ting error in apparent turnover magnitude). uncer- t aint ies were not propagated t hrough t hese calculations.

Reviewing the resulting sis distance nioduli. the values obtained are remarkably consistent. particularly t hose in B. The proposed systematic trend with metallicity appears to agree nicely with observation. 5. Anaivsis aod Results 63

Table 5.5: Distance moduli computed using separate (B-R)subgroups. IFilter (B-R) GCLF [Fe/H] M m-M 1 (Peak value) turn-over (approx.)

5.3 Spatial distributions and relationships.

Spatial distribut ions and relationships such as colour gradients. radial density profiles. and angular profiles are typically examineci for globiilar cliister systems. In this case. in light of an apparent rnultimodality in the colour distribution. when- ewr appropriate these same distributions and relationships have been deterniined for separate colour sub-populations.

The most fundamentel illustration of the projected structure within the systern is a simple coordinate diagram. Figures 5.1 1 (a)and (b) present the object coordinates of the blue ( 1.00 < (B-R) < 1.42) and red (1.42 < (B-R) < 1.80) cluster candidates separatel. In Figures 5.12 (a)-(f)the same coordinates are shown separated into six colour-separated subpopulations. 11 1 ¶ 1 1 I 1 1 10 OZ SL O1 S O ç- 01- SL- Ot-

.f .. si- 8 e. . .m. .. . a *.@ O *. . . . . -8 - . - a *. *. .* . . .@. ... . + * a' .. 1 , .* * I . 1 1 1 1 9 * OZ ÇL DL S O E 01- ÇL- OZ- (=)ejuatwa 5. .;lnalysis and Results 65

(a) 1.00 < 8-R c 1.18 (b) t.18~0-Re1.30 Distance (kpc) Distance (kpc) -20 -15 -10 -5 O 5 10 15 20 -20 -15 -10 -5 O 5 10 15 20

Distance (arcrnin) Distance (arcmin) (c) 1.30 < 0-R < 1.42 (d) 1.42 < 8-R < 1.53 Distance (kpc) Distance (kgc) -20 -15 -10 -5 O 5 10 15 20 -20 -15 -10 -5 O 5 10 15 20

-20 0 t 1.1.1 1 1 -844-20 2 4 6 8 8-64-202468 Oislance (arcmin) Distance (arcmin)

(e) 1.53 c 8-R c 1 .M (f) 1.64 c BR c 1.80 Distance (kpc) Distance (kpc) -20 -15 -tO -5 O 5 10 15 20 -20 -15 -10 -5 O 5 10 15 20

Distance (arcmin) Distance (arcmin)

The positions of cluster candidates from each of the KMM subgroups. The 4++ synibol represents the position and orientation of NGC 3115. Rames (a)-(f)show the objects within each of the subgroups of (B-R) colour. The (B-R) range for each figure is specified in its title. 5. .;inalysis and Results 66

5.3.1 The colour gradient

A plot of colour rersus galactocentric radius is shown in Figure 5.13. It must be rioted that the radii used are projected radii. Consequently. some objects appearing at small raclii are likely to be niuch fart her froni the center of the galauy tlian t hey appear. Stiould a gradient be preserit. it ail1 be tlifficult to discern.

To atternpt to deterniine whether or not a colour gradient is present in the globiilar cluster systeni. the data aere first culled by magnitude to use the same objects which were used for tlie (B-R) colour distribution: '20.5 < B < 23.6. Ttie colour range was restrirted to values found to be typical for this system: 1.0 < (B-R) <

1.8 (the same range used in niaking the GCLF). Both the selected cluster candidates ancl tlie rejectcd objects are presented in Figure 5.13. -4s consiclerable scatter made it cliffirrilt to clisc~rnthe presence or absence of any trend aith galactocentric radius.

points at each radius wcre averagecl in bins in the tiope ttiat any trend in the data

~vouldbe bctter elticidated. Eacli point au weighted using a Gaussian based on its

distance from the center of the bin being considered. With r representing the radius

of the value being consiclrred. the weighted mean and its standard deviationGre

described as follo~vs:

"4s objects with B>23.6 were not included. a sample (as opposed to population) standard deviation was used. 5. Analysis and Results 67

The weighting function used was a Gaussian (also shown in Equation 5.13) with o~~~~~~=O.'~This value of ak,,,,~ corresponds to a characteristic kernel width of 0.'6 which is nide enough to include a sufficient number of points at each radius without being so wide tliat a trend would be aashed-out by smoothing.

It aas not possible to esplicitly eliminate contaminant background objects. Ob- jects appearing in Figure 5.13 outside the specified colour range (1.0 < (B-R) <

1.8) are almost certainly background field objects. As the (B-R) background levels shown in Figure 3.2 (b) stiggest that the density of background objects remains com- pariiblr (or decreases) within the specified colour range. contamination of the sarnple by backgrourid field objects was not believed to be a serious problem: certaiiily not in regions very near the galavy ahere clustcr derisity is rery high.

The cquation of the best-fit regression line \vas found to be:

The curve showing the weighted average. and the best-fit regression line are also shown in Figure 5.13. There is no apparent evidence of any relationship between colour and galactoçentric radius.

5.3.2 The Radial profiles

The shapes of typical radial profiles are well represented by the empiricle de \aucouleurs relation (de Vaucouleurs. 1977): a I r 1 B+st fit ri: (iiob. duster mndidarsses - B-A t 2.7(+1-6.4)~10~~,+ 1.36(+/0.03) StandardMean Dewwn sue mfttüm -..-.--.. O O O O cmusnotao~0

Figure 5.1 3: The (B-R)colour gradient. Globular cluster candidates with (20.5 < B < 23.6) were separated using a colour cd(1.0 < (B-R) < 1.8) as subgested by the colour distribution (shown as red crosses). The mean (solid rd) and ieast-squares (dashed black) lines show no evidence of a gradient. in which acc is the spatial density of globular clusters (arcmin-'). Rcc is the galactocentric radius. and ao, al, a* are fitted parameters. This relation can also be expressed in a similar semi-logarithmic fom which excludes the background a0 corn- ponent:

logocc = bi + bRGC1/4 (5.17)

Here. occ and bCare as previously defined, and bl, are fitted parameters. hlternatively. the profiles can be fitted using a scale-free log-log relation with fit ted parameters b3 and b4: 5. Anaiysis and Resufts 69

The most cornmonly compared parameter is b4 mhich is frequently referred to simply as a.

Because rieit her of the logarit hniic relations include background levels. a background lerel had to be subtracted froni al1 points before fitting Equations 5.17 and 5.18.

In total. three radial profiles were created: one which included al1 of the cluster candidates. and two using restricted colour ranges to esamine the 'bluest' (1.00 <

(B-R) < 1.4'1). and 'reddest' (1.42 < (B-R) < 1.80) objects in the (B-R) colour distribution. Profiles involving al1 cluster candidates wre fitted to al1 of the above mipirical relations. Those of the specific colour groups were evaluated using only tlie log-log relation in Equation 5.18.

Lines titted in log-log plots wre particularly sensitive to tlie level of tlir background subtraction. The fornial standard-error in the dope of a fittd line cannot incorporate this iincertainty. To address this systeniatiç error. the log-log fits were repeated iising over-. and under-subtracted data. The background Level was over- or under-subtracted by 50% of its vaIue (ie. 150% background. and 50% background were iised). The least-squares fits for each of these extremes are shorn on al1 log-log

plots. The uncertainty stated in each value of a (the dope of the log-log fit) is sep

arated into systeniatic and random error. The 'systematic' error reflects the range

of slopes obsemed for a 50% error in background level. and the *random' error is the

standard error for the least-squares fit.

Before the radial profiles could be made. it \vas necessary to make a detector

coverage correction to compensate for objects which were lost due to the gaps between 5. Anaiysis and Results 70 the detectors.

Detector coverage corrections

The use of a mosaic CCD camera. although irnproving the size of the overall field of view. leaves gaps between individual detectors. Determining the number of objects present in a given annulus reqiiires correcting the detected number of objects to account for incomplete spatial coverage.

The correctioii factor. representing the ratio of detected area to total area for ari aririulus. ws determincd using a set of randomly generated coordinates. As was the case with the photonietric cornpleteness function. the correction factor can be treated as the probability of a sucressful trial iri a binomial distributioii. A11 raridom points ivithiii ari iinnulus are considered. and a point which fdls aithin the bounds of a cletector is coiinted as a saecess. -4s this \vas the sarne rnathematical approach which was used in determining the photometric conipleteness correction, the variance is defined by Equation 4.2.

The radial detector coverage correction is presented in Figure 5.l-I. Regions where the gaps between the detectors Iiiive significantly reduced recovery are obvious near the wnter of the image (srnall RGC) and between the inner and outer detectors

(RGc 7').

It should be noted that. because magnitudes cannot be measured within a few pisels of the edge of a detector. the eflective detector area is not that of the entire

detector. However. magnitude measurernents wre possible to within 4 pixels (5 1

FWHM of r he object profile) of the edges. Taking this to be the minimum near-edge 5. Analysis and Results 71

Figure 5.14: The radial coverage correction. Recovery suffers signiticantly at low galactocentric radii, and at a distance of about 7' between the inner and outer detectors. distarice for detection on a 2000x4000 pixel detector suggests a systematic error of

50.5% was int roduced in detector coverage correct ions.

Making the radial profiles

Each point in each of the profiles aas deterrnined as follows: AI1 objects not in the desired colour range were ciilled out of the data. At each radius RGC. objects within an annulus of width - 0f.68 (ie. Rcc f 0f.34) were selected as cluster candidates7.

Conipleteness corrected GCLFs tvere made for cacli annulus. and were then numerically integrated from 21 < B < 74 using a trapezoid integration to obtain the total number of objects detected within the annulus.' Similarly. uncertainties were determined by integrating the uncertainty in the completeness corrected GCLF. As each In processing. aniiuli were chosen to have a width of 200 p~xels;large enough to contain a sufficient nurnber of objects, and small enough CO avoid including objects which were not representative of the given radius. When stated in arcminutes. this u-idth seems unnecessarily specific. In fact, it resulted from the processing parameters having ben set in pixels. Y Although the 50% completeness limit was B - 24.5 throughout most of the fraine, it was considerably lower (brighter) in the inner annuli (B - 23.5 for the inner-most annulus used here). in order to ensure that inner radii could be cornpareci CO outer radii in a meaningful way, the iimiting photometric depth (completeness conected) was set to B = 24. -4s uncertainty increases significantly for completeness corrections beond the 50% recovery limit, dues at smd Rcc are somewhat less reliable than those at large kc.but are at the same photometnc depth. 5. Anaiysis and Results 72

Table 5.6: Least-squares radial profile parameters. Equations 5.16, 5.17, and 5.18 are re- stated.

point the GCLF used is unlikely to iiave been in error by the largest amount in the same systematic way. the uncertainty in each point in the radial profile is a very conservativc estimate.

So background subtraction was perfornieci in the GCLF calculatioiis. To do so would reqiiire that a portion of the frame be Jefined as background and this would force the radial profiles to zero at the çorresponding radius. Instead. profiles were created iising al1 cluster candidates. The background ivas then set to be the best fit

(least-squares) constant in the range 8'.0 < RGC < 14l.0. Inspection of the radial profile in Figure 5.15 (a) suggests that few clusters are present in this region and a constant background dominates.

The detector coverage corrections were applied at each radius. and the total number of inferred objects was di~idedby the area of the annulus to yield the object density o~c(nrnnin-') as a function of radius. The radiai profiles using al1 cluster candidates are presented in Figures 5.15 (a).(b). and (c).and the fitted parameters are listed in Table 5.6. The log-log profiles of the two separate colour groups are presented in Figures 5.16 (a).and (b). with values of n listed in Table 5.7.

In order to compare the extent of the globular cluster system to that of the halo 5. -4nalysis and Results 73

US VS. Ra m Best fit de Vaucouleurs r funcbon - -

\ - -

Figure 5-15: The radial profiles. Object densities (oGC)are shown in the following formats: (a)occ m. Rcc (b)log(occ) vs. ~2:. and (c)log(occ) vs. log(Rcc). The halo light intensity dong the major axis of NGC 3115 (arbitrarily scaled) is aIso shown in (c) for comparisoa. 5. Anaiysis and Results 74

Figure 5.16: The radial profiles and least-squares fits for two separate (B-R)colour groups. The halo light intensity dong the major axis of NGC 31 15 (arbitrarily scaled) is also shown for cornparison.

Table 5.7: Least-squares fit a parameters for ail data and (B-R)subgroups

Colour range a Cncertainties A11 data 1.00 < (B-R) < 1.80 -1.63 I0.18 (*O.l-lsgs,*O-Odran) Blue objects 1.00 < (B-R) < 1.42 4-56k 0.21 (fO.l5,,. f0.06r.,) Red objects 1.42 < (B-R)< 1.80 -1.64 i 0.14 (fO.O8,,, O.O6,,) 5. Analysis and Results 75 light. each of the log-log plots also shows the halo light intensity dong the major axis of the galauy. The background sky aas subtracted ofT, and the halo light was scaled arbitrarily to be at the level of the first point in the radial profile. The globular clusters are apparently sornewhat more distended than the halo light.

Although the blue members of the population do appear to have a lower value of a suggesting they occupy a sornewhat more distended spatial region than the red rnembers. the values found for the blue and red objects. and for the population as a whole. are dl within uricertainty of one ariother.

5.3.3 The angular proff les

The angular profiles iwre created as a means of comparing red and blue sub-populations of cluster candidates. The two sub-populations were the same as those used in niak-

ing radial distributions. namely: 1.00~(B-R) < 1.42 (blue) and 1.-U< (B-R) < 1.80

( red) .

Ideally. angular profiles would be made in the same fashion as radial profiles: by

integrat ing completeness corrected luminosit y funct ions for each point. Hocverer. as

liiminosity functioris require different completeness corrections in different lerels of

halo light. t liis becomes estremely impract icsl. Extensive artificial star siniulations

would be required to accurately establish completeness in the narrow angular bins

near the galasy. Consequentl-. a somewhat more crude. but much simpler approach

Kas taken. The profiles were made using a sliding Gaussian kernel with o = ?O0.

The only correction applied nas a detector coverage correction. It nias created us-

ing the same method as that described for the radial profile coverage correction in 5. Andysis and Resdts 76

Figure 5.1 E A sample angular coverage correction for 3.'5 < RGC < 3.'8. Lower recovery rates can be seen at 0". 90". 180". and 270"

700 - detector detmor detector delector -3- -4 - -1- -2- 600 - - 500 - -9 = 400 - 300 - --_ -/2---- 2w--,------'-- -\ -- - *------

Figure 3-18: A1igu1.u profiles of halo ligtit intensity. The three profiles shown are the halo light iiiterisity at radii of li.4 (strorigest peaks). 2'.1. and 3l.8 (weakest peaks). The scale is the pixel intensity. and is therefore entirely arbitrary. Caps between the detector chips cm be seen cleürly. The relevent detector nirmbers (refer to Figure 4.1) are iiidicated.

section 5.32. To account for differences in object density with radius. profiles were

coverage corrected in discrete radial bins and summed. .A sample coverage correction

for the region 3.5 < Rcc < 3!5 is shown in Figure 5.17.

To compare each population to the galaxy itself. three profiles of the halo light

intensity aere made at progressivel- larger galactocentric radii. These are shown in

Figure 5.18.

Tu compare each of the subgroups in their entirety? angular profiles were made

iising al1 cluster candidates out to Rcc = S'.O. These are presented in Figure 5.19.

Each of the two colour-subgroups were then further subdivided based on galactocen- 5. Analpis and Results 77

Figure 5.1 9: The angular profiles of blue and red cluster candidates (kC5 s'.O. The halo Lght intensity at bC= ll.l is shown superimposed for cornparison. tric radius. Angular profiles for both blue and red clusters were made for inner-halo

(0'.0 < < ?.O). mid-halo (?'.O < Rcc < -l'.O). and outer-halo objects (-l'.O < l?&- < 89). These profiles are shown in Figure 5.20.

5.4 The Specific Requency

The total population of globuiar clusters is typicaiiy calculated by integrating the luminosity function up to the peak magnitude and assuming that this represents half of the population (ie. a symmetric luminosity function corrected for photometric and spatial completeness). Lnfonunately, in t his case, the gaps between detectors were significant in the vicinity of the gaiaxv. and the GCLF did not represent the entire population. However. extensive efforts were made to correct the radial profiles for both photometric completeness and detector coverage. making them the best choice 5. Analvsis and Resdts 78

Figure 5.20: The angular profiles of biue and red cluster candidates in three ranges of Rcc. Blue clusters (1.00 < (B-R)< 1.42) are on the left. and red (1.42 < (B-R) < 1.80) are on the right. F'rom top to bottom: (a),(b)inner-haio objects (@.O < kC< 2'.0): (c).(d)mid-halo objects (T.0 < hc< 4.0): and (e),(f) out-halo objects (1l.0 < kc< 8I.0). The halo light intensity at Rcc = lI.4 is shown superimposeci for cornparison in each profile. 5. Analysis and Results 79 for use in determining the population.

.-\ radial profile was constructed to be photometrically complete to the peak of the luminosity function. As the inner 0l.8 of the radial profile was missing, it was assunied to be a constant within this region. As Harris (1991) reports that the

radial profile typically becomes contant at RGC 5 2 kpc. this is not an unreasonable assuniption. At the distance of SGC 31 15. some 10 llpc. a 2 kpc separation is about

O1.l.

The de \'aucouleurs relation in Equation 5.16 was then fitted to the profile. The

best fit values were the folloming:

To determine the most probable population. a Monte Carlo approach vas used. As

t lie uncertainties stated in each parameter are standard errors. normal distributions

were generated independently for each parameter. and values were drawn raridomly

from them. The ao. ni. and a- values selected in this fashion were used in the

following int egration ( r represents Rcc) to obtain one value for the populatiori.

occ(O.S) r dr dB + lZi1: oCC(r)r (3.19)

This was repeated 1000 times to create the distribution of possible population values

based on the best fit parameters. This distribution is shown in Figure 3.21. 5. Anaiysis and Results 80

Figure 5.21: The Monte Car10 populatioii distribution showing the most probable population [for use in computing the specific frequency), and the haif-maximum

The lower and upper values were taken to be those of the hall maxima. Due to the asymrnetry of the distribution. separate positive and negative uncertainties were ctiosen. The half-population cvas found to be: .Yt = 260 1:;. With the luminosity of

SGC 31 15 being dl: = -21.2 (Harris. 1986). Equation 2.4 yields a specific frequency

1.7 '0.6 of $.y = -0.5' 6. DISCUSSION AND CONCLUSIONS

6.1 Multimodality in the colour distribution

Mixture niodeling and Monte Carlo correlation tests suggest quite strongly that the

niultimodal structure apparent iri the (B-R) colour distribution is indeed real and

not an artifact of random fluctuations. Although it could be argued that as many as six separate subgroups are present. the testing performed does not have the capacity

to confirm so bold an assertion. The colour distribution is best regarded simply as

mult imodal.

The coloiir distribution of SGC 31 15 has to this point been regarded as bimodal.

Birnodality is a very cornrnon attribute in globular cluster systems for large ellip

ticals: it is more the norm than the exception (Larsen et al.. '1001). Kundu and

Whitniore (1998) found a clear indication of bimodality using the (VI) colour in-

des. Csing the (Y-I).(B-R) relation in Equation 5.11. the (B-R) colour distribu-

tion wvas transformed to the (\'-1) index to provide a cornparison to prcvious work.

These two distributions are shown superimposed in Figure 6.1. It should be noted

that Kundu's observations were made using the \Vide Field Planetary Camera 2

(WFPC2) detector on the Hubble Space Telescope with a very narrow field of view.

SLany of the objects observed aere not present in CFH12K data as they were lost in

gaps between detectors. The two samples are thus largely independent. They appear 6. Discussion and Conclusions 82

Figure 6.1: The coloiu distribution converted to (V-1) for cornparison with Kundu and Whitmore (1998). The distribution was converted using Equation 5.11.

Kiindti's (V-1) data are shown CU a histograrri. while the convertcd fB-R) data are shown ru a kerriel snioothed distribution. to agree nicely.

Such el-idence for miiltiple rnetallicity subgroups within the globular cluster system of the galavy favours a Searle and Zinn (1978) model of galaxy formation whereby distinct protogalactic fragments (supergiant molecular clouds) agglomerated to produce what is observed today. The ELS model (Eggen. Lynden-Bell. and Sandage.

1962) does not agree with these findings.

6.2 The GCLF and the distance to NGC 3115

Csing Equation 2.2. the distance niodulus calculated (m-.LI = 30.07&0.28) cari be

converted to a distance of: 6. Discussion and Conclusions 83

This result agrees nicely with existing distance estimates. Csing the GCLF turnover. Kundu and Whitmore (1998) obtained a distance niodulus of B.8f 0.3 and corresponding distance of 9.1k1.3JIpc. However. one of the most reliable results to date has been that of Tonry et al. (1001) ivho. using the method of surface brightness

fluctuations. foiind m-SI = 29.93k0.09 to yield a distance of 9.210.1 Xlpc.

-4s it was not possible to conipare the GCLF turn-over in R to an appropriate

absolute niagnitude. it was instead used to determine a value of .UR using the distance

riioclulus of Tonry et al. (2001). This yields a result of:

The iincertainty statd here is purely a propagated error. Although the GCLF

turnover is reniarkably consistent between different systems. variability is typically

larger than the 0.10 value stated liere. This uncertainty should be considered a lower

limit .

6.3 The effects of metdlicity on the GCLF turnover

With GCLF parameters determined in both B and R for the three 'bluest peaks' in

the (B-R) colour distribution. a total of sis distance moduli tvere computed. These

are listed in Table 5.5. The SBF distance modulus m-1I = 29.93f0.09 (Tonry et

al.. 1001) was taken to be the most reliable value available for use in cornparison. 6. Discussion and Conclusions 84

Alt hough the values obtained are consistently lower than t his fiducial by 0.06-0.11 magnitudes. most are within uncertainty'.

Given that the shifts in the apparent turn-overs differ significantly from one another. and that the corresponding shifts in the absoluted turn-over magnitudes differ in precisely the opposite fashion. the metallicity corrections proposed by Ashman.

Conti. and Zepf (1993.)appear to show the correct systematic trend. The success of this test suggests that accounting for the metallicity of the system being observed could ciramatically iinprove the accuracy and precision of the GCLF as a standard candle.

In principle. a nietallicity correction could be applied on an object-by-object buis

as a part of calibration. Magnitudes calibrated in such a fashion would correspond

to a standard nietallicity.

Searly al1 of the uncertainty in GCLF distance moduli is introduced through

variability in the absolute magnitude. Any improvernent in the precision of that

value n-ould correspond to a similar improvement in the precision of GCLF distance

moduli.

6.4 Spatial distributions and relationships

6.4.1 The colour gradient

The best-fit line representing (B-R) vs. Rcc \vas found to be the following:

Only the 50.09 magnitude uncertainty of the SBF distance modulus is referred to here as no appropriate uncertainty could be assigned to the distance moduli for the (B-R)subgroups 6. Discussion and Concl usions 85

(B- R) = 2.7(&6.4) x IO-^ RGC + 1.35(+0.03). (5.15, repeated)

This suggests that no significant colour gradient is present in the halo of NGC 3115.

Hosever. noting that projected radii were used. a small gradient could easily have been ovrrwhelnied. The niodel of Searle and Zinn (1978) does not require such a feature and is supported in its absence. -4s the mode1 of Eggen. Lynden-Bell. and

Sandage (196'2) does predict that a gradient should be present it appears unlikely to be applicable to SGC 3113.

6.4.2 The radiai distribution

The radial profiles shown in Figure 5-15 are quite typical. In Figure 6.2 the ci parameter from Figure 5-15 (c) is compared to ttiat of other galauies. shown agairist absolute \' magnitude for the host galaxy (Harris. 1986).

Also quite typical is the less centrally concentrated nature of the cluster systeni as coinpareci to that of the halo light. This is particularly common in elliptical galaxies. It is likely that the cluster systeni is being observed much as it existecl when it originally formed (Harris. 1986).

Not surprisingly. values of n determined for red and blue subgroups straddle the value for the population as a whole (see Table 5.7). However. while the sornewhat shalloner dope for the blue members suggests they form a more distended group, the

uncertainties are large enough for the ~aluesto be in agreement with one another.

The difference is. nonetheless. consistent with Kundu and Whitmore (1998) who

report that the red population is somen-bat disk-like, while the blue population is 6. Discussion and Conclusions 86

Figure 6.2: The relat ionship between galaxy luminasity and the shape parameter a. Points shown were taken from Harris (1986). The best-fit Line is superimposed. less concentrated.

6.4.3 The angular distribution

Somewhat surprisingly. the blue population of cluster candidates shows significant alignment with the halo light while the red population does not. In the innermost region of SGC 3115 Kundu and Whitmore (1998) found what appeared to be a red disk population of clusten and a more spherically distributed blue halo population.

On the large scale. this does not appear to be the case. The presence of such a significant number of spherically distributed red clusters in the extremeties of the halo would seem to preclude the possibility of the monolit hic collapse format ion mechanism of Eggen, Lynden-Bell, and Sandage (1962).

One subtle point of interest in the angular protiles is that of the alignment with 6. Discussion and Conclusi011~ 87

Table 6.1: Typical S.V values compiled by Harris (1991).

GalaW Type < S.v > N Sc/Irr 0.3 5 0.2 1 Sa/Sb 1.2 k 0.2 9 E/SO (Small Groups) 2.6 k 0.5 13 E/SO (Yirgo. Fomau) 5.4 & 0.6 t 15 dE 4.8 * 1.0 4

t excludes 1187 (S.V = 14 i 3). Y1399 (SN = 12 f 4) tt excludes Fornax (S.V = 73 I 12). 1132 (Siv 0.8) the halo light. hmongst the blue population. alignment aith the major avis of NGC

3115 appears to Vary rith distance from the center of the galaxy. The innermost objects appear to be aligned sligtitly clockwise of the halo light. the rnid-halo objects appear to be aligned with the halo light. and the outermost objects appear to be aligned slightly counter-clockaise of the halo light. Although the effect is small and could easily be coincidental. it is worthy of mention.

6.5 The specific fiequency

The specific frequency derived for SGC 3115 is typical of that for Spiral and SO

galaxies. Harris (1991) conipiled a list of specific frequencies for a vxiety of Hubble

types. The mean values are show in Table 6.1'.

This large wriability betwen system would seem to suggest that dramatically

different formation efficiencies are possible for different system (Harris. 1991). Hoa-

ever. the normalization to galaxy luminosity assumes that al1 the material initially

arailable to form stars or cliisters has done so. SIcLaughlin (1999) reports that

this assumption cannot be applied universally as rnany -stems contain significant

- S-tem ~hi&were not included in the averages listed in Table 6.1 have particularly anomalous specific frequencies. 6. Discussion and Conclusions 88 amounts of matter in the form of non-luminous3 gas.

With respect to the values presented in Table 6.1 (specifically, E/SO for small groups). SGC 3 115's specific frequency of Ss = 1.' -,., is quite typical for a lenticular

(SO) galasy in isolation.

6.6 Conclusions

With respect to the four stated objectives of this research project. the folloaing can be concluded:

1. Examination of the colour distribution revealed what appears to be a

mult imodal distribut ion. This suggests a cornplicated formation history. The

galaxy formation model of Searle and Zinn (1978) is supported while that

of Eggen. Lynden-Bell. and Sandage (1962) (ELS) is inconsistent sith the

observations. This does riot disprove the ELS model. but rather indicates that

it is an unlikely formation mechanism for NGC 3115.

2. The distance to NGC 3115 \vas deterrnined and is in agreement with values

in the literature arrired at using different techniques:

Distance = 10.2 k 1.3 Upc (m- .\f = 30.07 i 0.28)

3. The effects of colour/metallicity on the GCLF turn-over proposed by

Ashman. Conti. and Zepf (1995) agree nicely aith observations of NGC 31 15.

The GCLFs shifted to higher magnitudes (fainter) when made using redder

(more metal rich) objects. The term non-luminous used here refers only to luminosity in the V passband used for normalization in deriving the specific frequency. 6. Discussion and Conclusions 89

4. The spatial distributions and relationships of the globular cluster

system were determined:

(a) no significant colour gradient was observed:

(B- R) = Z.T(i6.4) x 10-3 . RGC + 1.33(&0.03)

(b) the slope of the scale-free radial profile (a)was fouiid using al1 cluster

candidates. and also for red and bliie subgroups. Although the value for

blue clusters suggests a slight ly niore distended cluster system. al1 values

are within uncertainty of one another:

to the major avis of SGC 3115. while the red objects appear to be more

spherically distributed.

5. the specific fkequency (Sr) of NGC 3115 nas found to be typical of that for

spiral aiid lent iciilar galaxies:

Observations in agreement with the work of Ashman. Conti. and Zepf (1993) suggest that GCLF could be made more reliable as a standard candle through the use of a metallicity correction for the system being considered. The concept of a 6. Discussion and Conclusions 90 metallicity correction could even be estended to be performed on an object-by-object

basis.

Sitting in splendid isolation. SGC 3115 provides a rare viea ohsystem ivhich has evolved uninfluenced by multiple ncighboiirs. Wth the appearance of niultimodaiity

in the globular cluster colour distribution. the nest logical step is a spectroscopic

study of the cluster system. Spcctra would not only allow any contaminant field objects to be identified and removed. but would also provide true metallicities to better

determine the colour-metallicity relation and rewal any dyamical or kineniatical

relationships present within the obsened colour groups in the systern. Such a study

woulci be invaluable in elucidating the formation and evolution liistory of this unique

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Zinn. R. 1983. ApJ 293 4'24 A. THE USE OF SLIDING-KERNEL DISTRIBUTIONS

Although the methods described below are by no means rigourous. the- were found to be extremely effective in representing the distributions and t heir uncertainties and eliminated an? effects which might othenvise have been introduced through binning changes.

Init ially. the obvious solution is to iniplenient a histogram style distribution in which the bins are more closely spaced t han t heir widt h. In t his case. it is niore iiseful to cietinr the qiiantities as densities rat her t han siniple coiints (ie. cwurit.s/biniridth) .

In this rv-. the function will integrate to the total population. Cncertainties in such a technique can be lound using the sanie poisson 0value (Olbintcidth in the case of a density) which would be employed in a typical histogram.

A smoother version of a distribution can be obtained. however. through the use of a kernel-weightd bin in place of the evenly weighted (ie unweighted) boxcar bin.

The normalization of such a distribution to represent a number disity is no longer as simple as dividing by a bin width as no clearly defined bin width exists.

A. 1 Normalization to a number density

.\lthough the kernel function chosen in this case was a gaussian. the method used to determine its normalization constant is also developed for an arbitrary kernel

94 -4. The Use oL sliding-kerael distributions 95 function. Thus, defining a kernel function w! any distribution point f (xj)is the sum of the weighted contributions of .V data points and is obtained in the following

fas hion.

In order to normalize the function and deterrnine the constant -4. consider the

aniount b(r,) a single data point at r, will contribute to the distribution points x,

in its vicinity.

A nunierical integration of the contributions of a single point niust tlieri iritegrate

to 1. Thus. ta determine the normalization factor -4. let lx be the spacing between

distribution points. and Let Ar -t dx.

Applying this logic to the gaussian kernel the normalization constant is found.

Equation -4.1 can therefore be expressed as follows. A. The Use ofsliding-kernel distributions 96

In determining the uncertainty of a point in a distribution created with a sliding kernel. a simple variation of poisson statistics was used. .As the number of data values

'i falling within a given bin are uncertain by &fi,the weighted number of data value .V, are approximated to be uncertain by &a.In the case of the gaussian. both terms can then be normalized using the sanie 1/60factor. The justification for this is. of course. purely heuristic. However. in practise. the cornparison of a slidiiig gaussian distribution against a t raditional histogram reveals no dist inguishible differerices wit h respect tu uncertaintu. B. SUPPLEMENTARY FIGURES B. Supplementary Figures 98

1.2 lnner ellipse

i9 20 21 22 23 24 25 26 27 B magnitude R magnitude

1.2 7

Outer ellipse - 800

19 20 27 22 23 24 25 26 27 B magnitude

Figure B.1: Completeness functions for detector 1. Plots are shown for both B and R filters. and for the near-galaxy and outer-galaxy annuii. The values a and b appearing on the plots refer to the semi-major and senii-minor axis Iengths of elliptical annuli around the gaiaxy. B. Supplementary Figures 99

1.2 1.2 lnner ellipse Inner ellipse

6 magnitude R magnitude rn

- Outer ellipse - 800 s a c 2300 267 < b < 767

19 20 21 22 23 24 25 26 27 19 20 21 22 23 24 25 26 27 0 magnitude R magnitude

Figure B.2: Corripieteness fiinctions for detector 2. Plots are shown for both B and R tilters. and for the near-galaxy and outer-galmcy annuli. The values a and b appearirig on the plats refer to the semi-major and semi-rni~ioraxis lengths of elliptical annuli around the galaxy. B. Supplementary Figures 1 O0

12 '-& l lnner ellipse 1 lnner ellipse