Weighing dark matter in brightest cluster galaxies

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Weighing dark matter in brightest cluster

galaxies

HC Branken

22095306

Dissertation submitted in partial fulfilment of the requirements

for the degree

Magister Scientiae

in

Space Physics

at the

Potchefstroom Campus of the North-West University

Supervisor:

Dr SI Loubser

Co-supervisor:

Dr K Sheth

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Abstract

Despite being a fundamental property that tests galaxy formation models, the measurement of elliptical galaxy masses is notoriously difficult. However, constraining the mass profiles of galaxy clusters is more tractable as these objects present us with a number of independent mass probes, such as lensing, X-ray, and stellar kinematic measurements. Lensing and X-ray analyses can provide stringent mass constraints up to the virial radius, but become unfeasible within ∼ 50 kpc due to the instrumental resolution and/or substructure in the central parts of clusters. On the other hand, complementary stellar kinematics of the central, gas-poor brightest cluster galaxy (BCG) can extend over the range ∼ 1–200 kpc in favourable circumstances. The fact that BCGs lie at the bottom of the potential well of non-interacting clusters, means that the stellar dynamics are indispensable in disentangling dark matter (DM) and stellar mass of galaxy clusters on relatively small scales. In this study, spatially-resolved stellar kinematics and WFPC2/F814W (I-band) Hubble images were used to study the stellar and dark matter distributions of a sample of 18 nearby BCGs. Furthermore,

these mass distributions were analysed within one effective radius (1 a_e), which denotes the radius

in which half the total light of a galaxy is contained. This study employed the Multi Gaussian Expansion (MGE) formalism to accurately parametrise the BCG stellar mass from the original F814W images, as well as the DM profiles that were parametrised by the generalised-Navarro-Frenk-White (gNFW) formula. Secondly, a non-parametric, smoothing algorithm, known as LOESS, was employed in tandem with 3000 Monte-Carlo simulations to smooth the velocity dispersion profiles later incorporated in the Jeans analysis. Thirdly, this study iterated the Jeans Anisotropic MGE (JAM) routine—which implements the solution of the anisotropic Jeans equations—over a large, five-dimensional free-parameter space in an attempt to reproduce the BCG dispersion profiles,

and thus acquire constraints on physical quantities through a minimum χ2 statistical analysis.

Furthermore, χ2 maps were constructed to assist in understanding the structure and dependencies

in the free-parameter space. An important novelty of this study is that the anisotropy parameter, β—parametrising orbital properties of a galaxy—was left as a free parameter, and therefore not a priori assumed to be isotropic as is traditionally done in many other studies. Results from this study indicated that the best-fit, mean stellar mass-to-light ratio in the F814W filter evaluates to

hΥ_?,Ii ∼ 4 Υ,I for the sample of BCGs. The best-fit β solutions showed a strong tendency towards

mildly, radially-biased solutions (β ∼ 0.2). On the other hand, the best-fit DM inner slope (δ) solutions exhibited a bimodal distribution in which ∼ 44% of BCGs preferred shallow slopes (δ < 1), and ∼ 56% preferred cuspy slopes (δ > 1). On average for this BCG sample, stellar mass represent

∼ 73% of the total mass budget within 1 a_e, whereas DM takes up ∼ 27%. Multiwavelength

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approaches, longer stellar kinematic profiles, more generalised dynamical models, and larger BCG samples will promote progress in disentangling the stellar mass and DM distributions of clusters in future studies.

Keywords: stars : kinematics and dynamics — galaxies : BCGs, cDs, ellipticals — galaxies :

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Opsomming

Ten spyte daarvan dat massa ’n fundamentele eienskap is wat galaksievorming-modelle toets, bly die meting van elliptiese galaksie massas ’n uitdagende taak. Nietemin is die bestudering van die massa profiele van galaksieswerms meer toegangbaar aangesien onafhanklike massas deur verskil-lende metodes—byvoorbeeld swaartelense, X-straal, en stellêre kinematika analises—gemeet kan word. Swaartelense en X-straal analises verskaf voortreflike massa bepalings tot en met die viriale radius, maar word belemmer binne ∼ 50 kpc deur beperkte instrumentele resolusie en/of substruk-tuur in die sentrale gebiede van swerms. Aan die ander kant, kan aanvullende stellêre kinematika van die sentrale, gas-lose, helderste galaksie oor die gebied van ∼ 1–200 kpc strek in gunstige om-standighede. Die feit dat hierdie galaksies by die bodem geleë is van die swaartekrag potensiaal van swerms wat in ewewig is, beteken dat die stellêre dinamika uiters noodsaaklik is om die donker materie (DM) te skei van die stellêre massa in galaksieswerms op relatiewe klein skale. In hierdie studie was gebruik gemaak van stellêre kinematika en WFPC2/F814W (I -filter) Hubble beelde om die stellêre en DM massa verspreidings van ’n steekproef van 18 naby-geleë helderste galaksies te bestudeer. Bowendien, was hierdie massa verspreidings ge-analiseer binne een effektiewe radius

(1 ae), wat die radius aandui waarin die helfte van die totale lig van ’n galaksie ingesluit word.

Hi-erdie studie het die Multi-Gaussian Uitbreiding formalisme gebruik om die helderste galaskie stellêre massa akkuraat te parametriseer vanuit die oorspronklike F814W beelde, sowel as die DM profiele wat geparametriseer was deur die veralgemeende-Navarro-Frenk-White formule. Tweedens, was ’n nie-parametriese algoritme, bekend as LOESS, gebruik tesame met 3 000 Monte-Carlo simulasies om die snelheid dispersie profiele egalig te maak voordat dit gebruik was in die Jeans analise. Derdens, het hierdie studie die Jeans Anisotropiese MGE roetine—wat die oplossing van die anisotropiese Jeans vergelykings implementeer—herhaal in iterasies oor ’n groot, vyf-dimensionele vry-parameter ruimte in ’n poging om die helderste galaksie dispersie profiele te reproduseer, en dus grense op

fisiese kwantiteite te verkry deur middel van ’n minimum χ2 statistiese analise. Bowendien was

χ2 kaarte geskep om die struktuur en afhanklikhede in die vry-parameter ruimte te bestudeer.

’n Belangrike eienskap van hierdie studie is dat die anisotropiese parameter, β—wat die orbitale eienskappe van ’n galaksie parametriseer—as ’n vry parameter gelaat was, en dus nie a priori aan-geneem dat dit isotropies is nie, soos dit dikwels in ander studies hanteer word. Resultate van hierdie studie het aangedui dat die beste-passing, gemiddelde stellêre massa-tot-lig verhouding in

die F814W filter gelyk is aan hΥ_?,Ii ∼ 4 Υ,I. Die beste-passing β oplossings het ’n sterk neiging

na matige, radiale-partydige oplossings (β ∼ 0.2). Aan die ander kant, was die beste-passing DM binnenste gradiënt (δ) oplossings aanduidend van ’n bimodale verspreiding waarin ∼ 44% van die

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helderste galaksies vlak hellings (δ < 1) vertoon, en ∼ 56% steil hellings (δ > 1) vertoon. In gemid-delde terme vir hierdie helderste galaksie steekproef, verteenwoordig stellêre massa ∼ 73% van die

totale massa binne 1 a_e, terwyl DM ∼ 27% vervat. Multi-frekwensie benaderings, langer stellêre

kinematika profiele, meer veralgemeende dinamika modelle, en groter helderste galaksie steekproewe sal vordering kweek in die skeiding van stellêre massa en DM verspreidings van galaksieswerms in toekomstige studies.

Sleutelwoorde: stellêr : kinematika en dinamika — galaksies : helderste galaksies, cDs,

ellip-tiese galaksies — galaksies : massa verspreidings — donker materie : veralgemeende-Navarro-Frenk-White

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List of Figures

1.1 Weak and strong gravitational lensing . . . 4

1.2 The cosmic web, 2dFGRS survey, Abell2261 galaxy cluster, and Hubble tuning fork . 5

1.3 Monolithic collapse, hierarchical merging, and AGN feedback . . . 14

1.4 Aquarius and Phoenix N -body simulations . . . 20

1.5 An example of the softening of the dark matter slope when stellar kinematics of the

central BCG is incorporated in the dynamical fit . . . 21

2.1 Nuclear regions of NGC3311 and NGC2832 . . . 28

2.2 Wide Field Planetary Camera 2 field of view projected on the sky . . . 29

3.1 Three-dimensional comparison between the observed image profile and Multi-Gaussian

Expansion model of NGC3842 . . . 33

3.2 Example of MGE extracting geometrical properties of ESO444-046 . . . 33

3.3 Example of MGE sectoring the image of ESO444-046 into radial and angular bins . . 34

3.4 A comparison between the image profile and MGE model of NGC7768 along the

major axis of the BCG . . . 36

3.5 Example of a contour-plot comparison between the image and MGE model of

ESO444-046 . . . 36

3.6 Image reduction and calibration: removing padded white space and cropping the

nuclear region . . . 38

3.7 The mismatch between PC-only and WF images . . . 38

3.8 Image reduction and calibration: flagging contaminated pixels . . . 39

3.9 _{find_galaxy, sectors_photometry, and print_contours MGE output for}

the sample of 18 BCGs . . . 47

3.10 Comparison between image and MGE modelling along the major axis for the sample

of 18 BCGs . . . 52

4.1 The projection of a spherical body along the line-of-sight of an observer . . . 60

4.2 A typical example of a gNFW profile as a function of radius . . . 67

4.3 One-dimensional MGE approximations of the two most ‘extreme’ gNFW profiles used

in this study . . . 69

4.4 Example of the MGE expansion of a gNFW cumulative distribution function . . . . 71

4.5 A visualisation of the sequence of steps involved when smoothing the L09D velocity

dispersion profile of a BCG. IC1633 is used as an example in this figure . . . 78

4.6 Smoothed LOESS curves for sample of 18 BCGs . . . 81

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List of Figures (continued) viii

4.7 Ensemble of 2D χ2 maps and 1D χ2 distributions of ESO349-010 . . . 85

4.8 Ensemble of 2D χ2 maps and 1D χ2 distributions of NGC541 . . . 86

4.9 Ensemble of 2D χ2 maps and 1D χ2 distributions of NGC3842 . . . 87

4.10 Marginalised 1D χ2 distributions for sample of 18 BCGs where each independent variable {δ, β, r_s, σ0, Υ?,I} is considered on a separate axis system . . . 88

4.11 The distributions of the best-fit free parameters of the sample of 18 BCGs where each independent variable {δ, β, r_s, σ0, Υ?,I} is considered on a separate axis system . . . . 89

4.12 Minimum χ2 JAM fits, σJAM(R), to the LOESS dispersion profiles, σLOESS(R), of the sample of 18 BCGs . . . 95

4.13 Individual plots of the stellar, dark matter, and black hole mass profiles extrapolated out to one effective radius for the sample of 18 BCGs . . . 102

4.14 Mass profiles for sample of 18 BCGs, grouped into four categories: ρ_?(r), ρDM(r), M?(≤ r) and MDM(r) . . . 103

4.15 Distributions of the mass CDF profiles evaluated at one effective radius . . . 104

4.16 Example of the full ensemble of results per BCG . . . 108

5.1 Sensitivity of the Jeans solution on different black-hole masses . . . 111

5.2 2D log χ2(Υ?,I, β) maps generated when different black-hole masses are fed into JAM 112 5.3 Sensitivity of the Jeans solution on different dispersion radial extents . . . 114

5.4 2D log χ2(Υ?,I, β) maps generated when the dispersion profile is truncated at four different radial cut-offs . . . 115

6.1 The rising dispersion profiles of the Newman et al. (2013a) sample of seven BCGs . . 121

A.1 Spatially-resolved kinematics, as derived by L09D, of the sample of 18 BCGs . . . . 137

B.1 ESO349-010 results . . . 139 B.2 ESO444-046 results . . . 140 B.3 IC1633 results . . . 141 B.4 MCG-02-12-039 results . . . 142 B.5 NGC541 results . . . 143 B.6 NGC1399 results . . . 144 B.7 NGC2832 results . . . 145 B.8 NGC3842 results . . . 146 B.9 NGC4839 results . . . 147 B.10 NGC4874 results . . . 148 B.11 NGC6173 results . . . 149 B.12 NGC7647 results . . . 150 B.13 NGC7649 results . . . 151 B.14 NGC7720 results . . . 152 B.15 NGC7768 results . . . 153 B.16 UGC579 results . . . 154 B.17 UGC2232 results . . . 155

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List of Figures (continued) ix

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List of Tables

2.1 Basic properties of the sample of the 18 BCGs, including: BCG & host-cluster names,

photometric redshift, RA & Dec, Hubble observation rootname, effective radius,

dis-tance, pixelsize, and exposure time . . . 30

3.1 Table giving the following MGE-related output for the sample of 18 BCGs: average

ellipticity, position angle, and total I-band luminosity in the PC region . . . 53

3.2 MGE solutions, {I_i0, σ_i0, q_i0}, for the sample of 18 BCGs . . . 56

4.1 Free parameter ranges, step intervals, and total samples associated with β and Υ_?,I . 65

4.2 Free parameter ranges, step intervals, and total samples associated with the gNFW

parametersδ, log rs,kpc, log σ0,km/s . . . 67

4.3 Free parameter ranges, step intervals, and total samples for the free parameters

β, Υ_?,I, log rs,kpc, log σ0,km/s, δ . . . 73

4.4 Table giving information for the sample of 18 BCGs that are of interest in the JAM

routine. This includes: Maximum radial extent of the velocity dispersion profile,

black hole mass, distance, and pixelsize . . . 74

4.5 Table containing the JAM output for the sample of 18 BCGs, which includes the

best-fit free parameter solutions, and minimum χ2 values . . . 90

4.6 The stellar, dark matter, and dynamical mass of the sample of 18 BCGs evaluated

at one effective radius . . . 104

5.1 Table giving the best-fit free parameters,β, Υ?,I, log χ2Min , of all the regimes applied

to UGC10143 in Chapter 5 . . . 116

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Glossary

Acronyms

AGN active galactic nucleus

BBN Big Bang nucleosynthesis

BCG brightest cluster galaxy

BH black hole

CBE collisionless Boltzmann equation

CCD charge coupled device

CDF cumulative distribution function

CDM cold dark matter

CI confidence interval

CMB cosmic microwave background

CR cosmic ray

DF distribution function

DM dark matter

DR8 Data Release 8

dSph dwarf spheroidal

EPS evolutionary population synthesis

ETG early-type galaxy

FJ Faber-Jackson

FOV field of view

FP fundamental plane

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Glossary (continued) xii

GC globular cluster

gNFW generalised Navarro-Frenk-White

HDM hot dark matter

HLA Hubble Legacy Archive

HR Hertzsprung-Russel

HST Hubble Space Telescope

ICL intra-cluster light

ICM intra-cluster medium

IFU integral field unit

IMF initial mass function

IR infrared

IRAF Image Reduction and Analysis Facility

JAM Jeans Anisotropic MGE

JE Jeans equation

l.o.s. line-of-sight

LHC Large Hadron Collider

LINER low-ionisation nuclear emission-line region

LOSVD line-of-sight velocity distribution

LRG luminous red galaxy

LTG late-type galaxy

MA major axis

MAD mass-anisotropy degeneracy

MC Monte-Carlo

MGE Multi Gaussian Expansion

NFW Navarro-Frenk-White

NIR near-infrared

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Glossary (continued) xiii

PA position angle

PC Planetary Camera

PD percentage deviation

PN planetary nebula

PSF point spread function

SAM semi-analytic model

SED spectral energy distribution

SF star formation

SFH star formation history

SIDM self interacting dark matter

SMBH supermassive black hole

SN supernova

SPS stellar population synthesis

SSP simple stellar population

STScI Space Telescope Science Institute

SZ Sunyaev-Zel’dovich

WDM warm dark matter

WF Wide Field

WF/PC1 Wide Field Planetary Camera 1

WFC3 Wide Field Camera 3

WFPC2 Wide Field Planetary Camera 2

WHT William-Herschel Telescope

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Your throne, O God,

is forever and ever:

The scepter of Your kingdom

is a righteous scepter.

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Chapter 1 Introduction

1.1 Preface

Mass is one of the most fundamental properties of galaxies as they evolve through time (Courteau et al. 2014, and references therein). Approximately ∼ 26% (see §1.4.3) of the mass-energy budget of the Universe consists of ‘invisible’, elusive material that cannot be observed directly, and is commonly referred to as dark matter (hereafter DM). This elusive matter is ‘dark’ because it does not emit light, nor does it interact with the electromagnetic force. It is hypothesised that DM consists of weakly interacting particles that only interact through gravity and the weak force (e.g. Frenk & White 2012; Armendariz-Picon & Neelakanta 2014). Although DM is invisible to the entire electromagnetic spectrum, it can still be traced through its gravitational effects, such as the flat/rising rotation curves of spiral galaxies, and the bending of background light in a process known as gravitational lensing (figure 1.1). On the other hand, ∼ 5% (see §1.4.3) of the mass-energy budget of the Universe consists of matter we are more acquainted with, and is known as baryonic material. This ‘ordinary matter’ consists of atomic nuclei composed of protons and neutrons, and is the basic building block of a rich variety of astronomical sources, which includes: stars, excited gas clouds, planets, black holes (BHs), neutron stars, brown dwarfs, cool molecular clouds, etc.

Both computer simulations (e.g. Boylan-Kolchin et al. 2009) and large-field surveys (Coil 2013, and references therein) converge towards the observation that DM has settled into a webbed, filamentary network of DM haloes (figures 1.2.A & 1.2.B). A DM halo can be pictured as a large cocoon of DM that envelopes any type of galaxy, extends far beyond the optical images of galaxies, and dominates the total mass budget of galaxies by a large margin. Given enough time after the Big Bang for baryonic material to condense and form stars and galaxies, eventually swarms of hundreds to thousands of galaxies begin collapse through the gravitational interactions of their DM haloes, and consequently form gravitationally-bound systems known as galaxy clusters. For the great majority of galaxy clusters, a ‘dominant’ galaxy is anchored at the centre, whose luminosity also outshines the other galaxies (figure 1.2.C). The uniqueness of these central galaxies puts them in a class of their own (see §1.2), and are defined as brightest cluster galaxies (BCGs). Additionally, clusters also contain other galaxies spanning a wide range of luminosities and morphologies (e.g. Martel

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Section 1.1. Preface 2

et al. 2014), including low-luminosity dwarf galaxies, spiral galaxies, barred spiral galaxies, elliptical galaxies, and lenticular (S0) galaxies (see figure 1.2.D and corresponding caption for definitions of these galaxy types).

Broadly speaking, baryonic matter dominates at the centre of a galaxy cluster where the BCG

typically resides; DM becomes gravitationally dominant at the 1_{outskirts of BCGs and further}

beyond (e.g. Newman 2013; Courteau et al. 2014). Moreover, a robust, testable prediction of

cosmological simulations is the so-called Navarro-Frenk-White (NFW) profile that describes the DM distribution as a function of radius in DM haloes (Navarro et al. 1996, 1997). The

small-scale prediction of the NFW profile, i.e. ρ_NFW ∝ r−1 as r → 0, is however a hotly debated issue

because some observational studies (Sand et al. 2002, 2004, 2008; Newman et al. 2009, 2011, 2013a,b, discussed in §1.5) suggest that the inner DM slope is shallower than the NFW profile.

Mapping the stellar mass and DM of elliptical galaxies in general as a function of radius is a notori-ously difficult task rife with many unwanted degeneracies (Courteau et al. 2014). Constraining the detailed mass profiles of galaxy clusters is however more tractable due to the variety of independent mass probes specifically available for galaxy clusters (Newman 2013, and references therein). In particular, independent mass profiles can be constructed for galaxy clusters from weak lensing (e.g. Clowe et al. 2000; Paulin-Henriksson et al. 2007; Holhjem et al. 2009), strong lensing (e.g. Shapiro & Iliev 2000; Shu et al. 2008; Kawamata et al. 2016), X-ray (e.g. Gitti et al. 2007; Sanderson & Ponman 2010; Donahue et al. 2014), and/or stellar kinematic measurements (e.g. Newman et al. 2013a), where each regime is limited to a specific range in radius.

Weak lensing (figure 1.1.A)—causing apparent ellipticity distortions in galaxies lying behind and to the side of a galaxy cluster—allows one to reconstruct the mass distribution statistically up to

the 2virial radius, but does not have the resolution to constrain mass profiles within ∼ 100 kpc.

Strong lensing (figure 1.1.B)—producing multiple images, arcs and/or rings of background galaxy in the central regions of massive clusters—provides projected mass distributions typically in the

range of ∼ 30–200 kpc. X-ray spectroscopy is used to measure the temperature profile, Tg(r), of

the hot plasma dispersed in intracluster space, whereas the plasma density profile, ng(r), is inferred

from X-ray surface brightness measurements. Assuming that hydrostatic equilibrium holds for the cluster (i.e. pressure and gravity balance each other) the enclosed mass profile M (≤ r) can be

determined from T_g(r) and ng(r). Due to typical X-ray instrumental resolutions, and/or residual

substructure at the centres of clusters (figure 1.3.C), X-ray measurements are limited to radii larger than ∼ 50 kpc, and can typically extend out to ∼ 500 kpc. Lastly, from long exposures on large telescopes, the stellar kinematics of the central, gas-poor BCG can be mapped out from ∼ 1 kpc to ∼ 200 kpc. The stellar kinematics effectively probes the deep gravitational potential well at the centre of the cluster, thus providing strong constraints on the total mass distribution at small radii within the cluster.

1

This observation is related to competing baryon-DM interactions that take place during galaxy formation, which is admittedly also not fully understood at present. Three mechanisms, in particular, are often brought up in the literature, and are known as (i) adiabatic contraction, (ii) dynamical friction, and (iii) AGN-feedback. A brief discussion on these mechanisms are supplied in the three bullets starting on p. 125.

2_{The radius at which the mass density is 200 × ρ}

crit, where ρcritis the critical density required to keep the Universe

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Clearly, the stellar kinematics component is complementary to the other mass probes in the sense that it provides mass constraints at small radii where the lensing resolution is significantly degraded and X-ray measurements are typically obscured by substructure (see the ‘cooling flow’ discussion in §1.3.3). More significantly, standalone lensing and X-ray measurements are unable to separate the DM component from the baryonic component at small radii. However, when implemented in conjunction with stellar kinematics, stringent constraints can be placed on the relative contributions of DM and stellar mass (Mellier et al. 1993; Miralda-Escude 1995).

This study is concerned with constraining the stellar mass and DM profiles of a sample of BCGs through modelling their stellar kinematics with the spherical Jeans equations. The Jeans equations describe the the motion of an ensemble of stars subject to a gravitational field, Φ (r), generated by the mass distribution of the BCG (Jeans 1915; Binney & Tremaine 1987; Diakogiannis et al. 2014). From measurements of the line-of-sight (l.o.s.) stellar kinematics and the surface brightness profile of a BCG, the Jeans equations can be invoked to constrain the BCG mass profile.

The structure of the rest of Chapter 1 is as follows: §1.2 gives an overview of BCGs and the unique properties associated with them. This is followed by §1.3 which discusses the formation mechanisms of BCGs, where particular attention is given to monolithic collapse, cooling flows and hierarchical merging. §1.4 introduces some important concepts of DM, and explains how observational evidence

(since 1922) has led to the current 1ΛCDM paradigm. Important to note in §1.4 is the discussion

dealing with current discrepancies between observations and ΛCDM predictions on sub-galactic scales, as it forms part of the scientific motivation of this study. §1.5 highlights the methodology and most important findings of previous studies in which the stellar mass and DM of galaxy clusters were disentangled. Lastly, the scientific motivation and structure of this dissertation is supplied in §1.6.

1_{The ΛCDM paradigm is the standard model of the Big Bang cosmology. In this model, the Universe predominantly}

consists of a cosmological constant, Λ, that is associated with dark, vacuum energy causing the accelerated expansion of the Universe, and cold dark matter, abbreviated as CDM. See §1.4.3 for a more detailed discussion of the ΛCDM paradigm.

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A

B

Figure 1.1.— (A): Weak gravitational lensing in which an intrinsically circular source (zgalaxy≈ 1) appears

elliptical to the observer (zobserver= 0) as a result of the foreground lens (zlens ≈ 0.3–0.5) weakly deflecting the

source’s light rays. In reality though, it is impossible to detect weak lensing in a single source. (B): The ‘Cosmic Horseshoe’ is a strong lensing system in which a star-forming galaxy (z ∼ 2.379) is (nearly) perfectly aligned behind

the massive lens galaxy LRG 3-757 (z ∼ 0.444), thereby forming a ∼ 300◦ Einstein ring as the light rays of the

star-forming galaxy are strongly deflected in the warped space-time fabric surrounding LRG 3-757 (Belokurov et al. 2007). Other phenomena common in strong lensing include multiple imaging and arc structures. A Image Credit: Jason D. Rhodes (Jet Propulsion Laboratory), http://www.euclid.caltech.edu/page/weak_lensing. B Image Credit: ESA/Hubble, https://www.spacetelescope.org/images/potw1151a/.

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A

B

C

D

Figure 1.2.— (A): The large-scale DM distribution in the Universe as produced by the Millennium Simulation Project. The central, bright ‘knot’ represents the most massive DM halo. (B): The large-scale galaxy distribution

as a function of redshift and right-ascension, projected through 3◦in declination. This thick 3◦slice contains 63 000

galaxies from the 2dFGRS survey (two-degree Field Galaxy Redshift Survey performed with a two-degree field fibre spectrograph). Images A and B support the scenario in which large-scale structure in the Universe grew through gravitational instability. (C): Example of a galaxy cluster (Abell2261) with a central, massive and luminous BCG that possesses a diffuse, extended stellar envelope. (D): Typical representation of the Hubble tuning fork. The E0, E4 & E7 images on the left represent elliptical galaxies with progressively increasing ellipticity (i.e. the number 0 corresponds to perfectly spherical, and 7 to highly elliptical). The top and bottom prongs of the tuning fork represent spiral and barred-spiral galaxies respectively. Type-a galaxies have tightly wound spiral arms and large central bulges, whereas type-c galaxies are loosely wound with small central bulges. The S0 galaxy (sometimes referred to as lenticular galaxies) is an ‘intermediate’-type galaxy between ellipticals and spirals. An S0 galaxy has a central bulge and a (flat) stellar disk without any spiral arms. Irregular (Irr) type galaxies have (asymmetric) chaotic structures, and are thought to be the by-product of uneven gravitational forces exerted on structured galaxies, or the by-product of colliding galaxies: a dwarf galaxy is a typical example of an Irr-type galaxy. Hubble (1936) thought that E-type galaxies were the first to assemble in the Universe, and later evolve into S(B)-type galaxies. This is not the case since it is impossible for a pressure-supported elliptical galaxy to spontaneously transform into a rotating spiral galaxy. Despite the fact that Hubble was wrong in his theory of galaxy evolution, astronomers still use his terminology in which ellipticals are referred to as early-type galaxies (ETGs) and spirals as late-type galaxies (LTGs). The Hubble tuning fork provides a useful way to classify galaxy morphology, but does not contain any physical significance. Within this framework, BCGs can be pictured as extremely massive, and luminous

E-type galaxies. A Image Credit: The Millennium Simulation Project, http://wwwmpa.mpa-garching.mpg.de/

galform/virgo/millennium/#slices, Springel et al. (2005). B Image Credit: Anglo-Australian Observatory, The 2dF Galaxy Redshift Survey, http://www.2dfgrs.net/. C Image Credit: NASA, ESA, CLASH team, http:

//www.nasa.gov/mission_pages/hubble/science/a2261-bcg.html, Postman et al. (2012b). D Image Credit:

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Section 1.2. Brightest cluster galaxies 6

1.2 Brightest cluster galaxies

BCGs are some of the most massive and most luminous galaxies in the Universe, and are usually located at the centres of galaxy clusters. Their privileged locations are substantiated by their close proximity to the X-ray emission peak of bright X-ray clusters (e.g. Bildfell et al. 2008), as well as their small peculiar velocity relative to the cluster mean velocity (e.g. Lauer et al. 2014). Because

these central galaxies are of the most brightest (and most massive, ∼ 1013 M) galaxies in their

cluster, the term BCG has become synonymous with central cluster galaxy. However, for a very small fraction of clusters, the BCG might not necessarily be the brightest galaxy in the cluster. Nonetheless, it suffices to denote a BCG as the ‘dominant’ galaxy at the centre of the cluster for the purposes of this study.

At small redshifts, BCGs exhibit a small scatter in their luminosities. This enabled researchers in the past to use BCGs as ‘standard candles’ to measure cosmological distances, originally done to extend the range of the Hubble redshift-distance law (Sandage 1972; Gunn & Oke 1975; Hoessel & Schneider 1985; Postman & Lauer 1995).

What usually makes the distinction between BCGs and normal elliptical galaxies visually obvious, however, is that most BCGs possess extensive stellar envelopes (in figure 1.2.C the stellar halo of the BCG is identified from the diffuse light surrounding the nuclear region of the BCG). These stellar

envelopes cause an excess of light over the r1/4 _{de Vaucouleurs (1948) law at large radii (Matthews}

et al. 1964; Oemler 1973, 1976; Schombert 1986, 1987, 1988; Gonzalez et al. 2005; Seigar et al. 2007),

which is also a unique property of 1‘cD galaxies’. These cD envelope structures have low surface

brightness and large spatial extents (Zibetti et al. 2005).

1.2.1 Why brightest cluster galaxies are special

Some of the most fundamental properties of galaxies include their size, luminosity and (central stel-lar) velocity dispersion (e.g. Taranu et al. 2015). Faber & Jackson (1976) discovered that the velocity

dispersion and luminosity of elliptical galaxies follow the scaling relation L ∝ σ4. In the following

year, Kormendy (1977) connected the size (2half-light radius, R_e, to be more precise) of ellipticals

with their surface brightness, µ. If µ is more specifically defined as the mean surface brightness

within R_e, then the Kormendy relation is expressed as µ = −2.5 log (L_/_R2

e). The fundamental plane

(FP) effectively combines the Faber-Jackson (FJ) and Kormendy relations into one proportionality,

R ∝ σaµb, which describes the three-dimensional scaling relation between size, velocity dispersion,

and luminosity (where µ is interchangeable with L) of elliptical galaxies (Djorgovski & Davis 1987; Dressler et al. 1987). Based on observations in the optical passband, it has been consistently found that a = 1–1.5 and b = 0.25–0.35 (Taranu et al. 2015).

In contrast, BCGs deviate from the FJ and Kormendy relations with lower velocity dispersions and larger sizes respectively than predicted (von der Linden et al. 2007, hereafter vdL07; Ruszkowski

1

All BCGs can also be regarded as cD galaxies, which are simply defined as supergiant, massive, elliptical galaxies

with large, diffuse haloes of stars causing an excess of light over the r1/4 _{de Vaucouleurs (1948) law at large radii.}

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Section 1.3. Formation mechanisms of brightest cluster galaxies 7

& Springel 2009, hereafter RS09). According to vdL07, the observed differences may be a result of enhanced DM fraction due to the typical position of the BCG near the cluster core. More importantly, these differences also point to a unique evolutionary history of BCGs that differs from the evolution of normal ETGs (RS09).

Stellar population studies indicate that BCGs have similar mean stellar ages and 1_{metallicities to}

normal ellipticals of the same mass (e.g. Pipino et al. 2011). However, BCGs have enhanced2[α_/_Fe_]

ratios, which can be interpreted as BCG star formation (SF) ocurring over a shorter time-scale (vdL07; Loubser et al. 2008). In addition, BCGs are also more likely to host radio-loud active galactic nuclei (AGNs) than other galaxies of the same mass (see §1.3.3). The feedback mechanism of radio-loud AGN (discussed in §1.3.3) can possibly account for SF being shut down at an earlier stage during the evolution of BCGs (vdL07).

It has also been shown that the dispersion about the mean luminosity of a population of BCGs is significantly smaller than would be the case if BCGs were simply the brightest galaxies extracted

from a standard 3luminosity function (Tremaine & Richstone 1977; Loh & Strauss 2006; Ascaso

et al. 2008; Lin et al. 2010). In other words, the narrowness of the BCG luminosity distribution does not extend to other types of galaxies.

Due to their privileged location at the bottom of potential wells, BCGs are exposed to a large number of events, such as dynamical interactions with satellite galaxies, that shape their properties (e.g. Martizzi et al. 2014). Therefore, the evolution of BCGs is also closely linked with that of their host clusters (e.g. Ascaso et al. 2011). As such, BCGs are important probes of the development of large-scale structures in the Universe.

1.3 Formation mechanisms of brightest cluster galaxies

Plausible BCG formation mechanisms have been proposed in an attempt to explain the unique properties of BCGs. In the following, the (i) monolithic collapse, (ii) hierarchical merging and (iii) cooling flow mechanisms are discussed. In §1.3.2, both the modelling and observational aspects of hierarchical merging are considered.

1_{Often defined in terms of the iron content of a star: [}Fe_/_H_{] = log (}Fe_/_H_{) − log (}Fe/H) where Fe and H are mass

fractions. Alternatively, the following definition may be used which captures the entire ‘metallic’ content of a star:

Z =P

i>Hes mi

M = 1 − X − Y , where M is the stellar mass, and X & Y are the Hydrogen and Helium mass fractions

of the star respectively.

2

α denotes all the ‘α-process’ elements, which consist of an integer multiple of 4 nucleons. Typical examples are the

chemical elements O, Mg, Si, Ca and Ti. In many works, the notation [α_/_Fe_{] is defined as the average of [}Mg_/_Fe_],

[Si_/_Fe_{], [}Ca_/_Fe_{], and [}Ti_/_Fe_].

3_{In this particular case, an analytic function describing the distribution of galaxies (in a galaxy cluster) as a function}

of luminosity. The Schechter function is typically used to characterise the luminosity function (Schechter 1976):

ϕ (L) dL = ϕ∗(L_/_L∗₎α_{exp (}− L_/_L∗_{) d (}L_/_L∗_{), where ϕ}∗_{is a normalisation factor, L}∗_{a characteristic luminosity, α the}

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1.3.1 Monolithic collapse

In the monolithic collapse model, all elliptical galaxies are believed to have formed from the collapse of primordial gas clouds in the early Universe, followed by rapid massive starbursts during which nearly all of the available gas was converted into stars (e.g. Larson 1974; Matteucci & Tornambe 1987; Pipino & Matteucci 2004). Stellar winds, generated by supernovae (SNe) outbursts, carried any residual gas out of the galaxy, therefore inhibiting further SF.

In this model, all galaxies evolved as ‘isolated’ entities and completed their growth by z ∼ 3. Once assembled, these galaxies are expected to evolve passively and undergo very little or no structural evolution. Merritt (1983) further claims that after galaxy clusters have collapsed, any merger events between cluster galaxies are inhibited due to their supposedly high velocities. In this framework, all elliptical galaxies are largely ‘red and dead’ systems due to the absence of SF since z ∼ 3 (e.g. Pipino et al. 2009).

At present, this model is recognised as overly-simplistic that lacks many features of the ΛCDM paradigm established after 1983 (see §1.4.3). van Dokkum et al. (2008), for example, who studied the size evolution of ETGs, completely ruled out the monolithic collapse model and also stated that elliptical galaxies must evolve significantly after z ∼ 2.3 through dry mergers as predicted from hierarchical models (see §1.3.2).

1.3.2 Hierarchical merging

As the name implies, in the hierarchical merging model all structures are built in a bottom-top fashion, i.e. larger structures are formed through the gravitational interactions (such as merging and accretion) of smaller progenitors (e.g. Laporte et al. 2012). As such, the order in which cosmic structures emerge in the hierarchical model, as a function of time after the Big Bang, is typically as follows: gas clouds, star clusters, galaxies, galaxy groups, galaxy clusters, and finally, galaxy superclusters. Similarly, DM haloes continuously assemble by a series of mergers of smaller haloes until the present epoch. Hierarchical merging is rooted in the ‘nurture argument’, which claims that the evolution of galaxies is strongly influenced by their environment. This is in contrast with the ‘nature argument’ of the monolithic collapse model (§1.3.1), which states that the properties of present-day galaxies are predetermined by the initial conditions in the early Universe, after which they evolve as relatively ‘isolated’ entities (compare figures 1.3.A & 1.3.B).

The scenario in which BCGs assemble through hierarchical merging in an evolving spatial network of DM haloes is well established at present (e.g. Zhang et al. 2016). Secondly, most of the contemporary models of galaxy formation are based on the model of the hierarchical merging of DM haloes (Oliva-Altamirano et al. 2014). In what follows, the growth and formation of BCGs, within the framework of the hierarchical model, are discussed.

After the Big Bang, clouds of DM cooled down and collapsed to form the structures in which baryonic gas can sink in and give birth to SF (Peebles 1969; Doroshkevich 1970; White 1984). The broad consensus is that BCGs can be traced back to the rarest density peaks to collapse at very high

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redshift (Martizzi et al. 2012; Burke & Collins 2013). Indeed, the variations that are detected in the cosmic microwave background (CMB) radiation suggests that the density distribution in the early universe was ‘lumpy’. Following gas condensation and star formation, small galaxies are formed in the DM haloes (Renzini 2006; Bai et al. 2014). These low-mass progenitors serve as building blocks in subsequent mergers that lead to more massive structures.

Important to note is that in the earlier (high-redshift) epochs—during which stars and galaxies were still in their infant stages and thus also far from completing their growth and passively evolving thereafter—conditions were not met for outflows to take place in the form of SNe winds and AGN outbursts. As a result, the gas content of these galaxies remained mostly intact within their host

galaxies, and hence were not driven out. Therefore, at intermediate and high redshifts, z & 2,

merger events between DM haloes involved a lot of gas (so-called ‘wet’ mergers) and possibly led to massive starbursts (Tacconi et al. 2010; Jimmy et al. 2013).

Major merger events are likely to occur in galaxy group environments due to their small velocity dispersion which increases the probability (or cross-section) for interactions (RS09; Laporte et al. 2012). This enhances the formation of a massive central galaxy, therefore making galaxy groups attractive birthplaces of future BCGs. In subsequent DM halo merging, the central galaxy of the most massive halo sinks to the bottom of the potential well and becomes the central galaxy of the new cluster (e.g. Kauffmann et al. 1993), whereas the other galaxies become satellite galaxies.

After a sufficient amount of merger events, a galaxy cluster is eventually formed which contains hundreds to thousands of satellite galaxies. Furthermore, merger events in the redshift range from z = 2 to z = 0 become increasingly gas-poor (so-called ‘dissipationless’ or ‘dry’ mergers) as feedback processes start to play a significant role, and hence remove gas from galaxies (Naab et al. 2006; Hopkins et al. 2009).

Once a galaxy cluster has formed, the stage is set for the subsequent growth of the central galaxy via ‘galactic cannabalism’. In galactic cannabalism, also known as minor merger events, the central galaxy gradually engulfs the stellar material of the surrounding companion galaxies. The stripped stellar material is primarily deposited on the outskirts of the central galaxy, thereby helping it grow in size and mass. Galactic cannabalism was originally invoked by White (1976), Ostriker & Hausman (1977), and Hausman & Ostriker (1978) in order to explain the massive sizes and luminosities of BCGs. According to Zhao et al. (2015), the central galaxies in clusters are likely to start out as massive elliptical galaxies, which through subsequent galactic cannabalism were later transformed into cD galaxies. This phenomenon also fits well in the ΛCDM framework where structure grows hierarchically (Laporte et al. 2013).

In summary, the formation of BCGs can be described as a two-phase process (Oser et al. 2010):

Firstly, during the earlier epochs of the Universe, z _{& 2, wet mergers and gas condensation led}

to vigorous star formation that gave rise to small, low-mass progenitor galaxies. Therefore most of the stellar mass of BCGs are formed at very high redshifts in separate galaxy entities (e.g.

Webb et al. 2015). Secondly, during z _{. 3, the BCG slowly acquires its identity through the}

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et al. 2014). These merger events are expected to be dissipationless due to feedback processes that become important at lower redshifts, which deplete galaxies of their gaseous contents. The old stellar populations observed in low-redshift BCGs substantiates the fact that the majority of SF has been halted in these systems for a long period of time (see the discussion on residual SF in nearby BCGs in §1.3.3). Finally, once the BCG spends the majority of its time in increasingly denser regions, its envelope gets expanded by galactic cannabalism (RS09; Lauer et al. 2014).

A popular avenue for exploring BCG evolution is cosmological N -body simulations. Broadly

speak-ing, an N -body code consists of two components: (i) the 1gravitational force-field is computed for

a specific configuration of N particles (where each N particle represents a DM halo), and (ii) the subsequent movement of the particles in the given force field is computed. In each iteration of an N -body simulation, both components are executed to ensure the particle trajectories evolve in a self-consistent manner (Bagla & Padmanabhan 1997). These N -body simulations are carried out to create mock galaxy clusters with readily-identifiable, bright, central galaxies. These mock BCGs are then compared with observed BCGs to test the fidelity of models describing BCG evolution and structure formation (Bellstedt et al. 2016).

The study of Dubinski (1998) was a notable landmark in the development of structure formation theory. In Dubinski (1998), it was shown that when a population of disk galaxies falls in a collapsing cluster, a bright, central elliptical galaxy is naturally produced, whose surface brightness and velocity dispersion profiles are similar to those of observed BCGs. This also proved that the origin of BCGs are intimately related to the collapse and formation of the cluster itself. As time progressed, the resolution and volume of cosmological simulations increased dramatically (e.g. Rudick et al. 2006 and RS09 that were inspired by Dubinski 1998).

While N -body simulations describe mass assembly and the evolution of DM haloes in great detail, they only have limited success. That is, pure N -body simulations do not address the details of baryonic physics in connection with galaxy evolution, such as star formation, supermassive black holes (SMBHs), and energetic feedback processes (Pipino et al. 2009; Ragone-Figueroa et al. 2013; Oliva-Altamirano et al. 2014; Zhang et al. 2016). Hence, N -body simulations cannot uniquely predict baryonic properties, such as neutral Hydrogen distribution, galaxy morphology, and stellar and gas content of galaxies (Ragone-Figueroa et al. 2013; Vogelsberger et al. 2013). Semi-analytic models (SAMs) (e.g. Croton et al. 2006; De Lucia & Blaizot 2007; Tonini et al. 2012) partly alleviate this problem in that they are a combination of N -body simulations and baryonic physics modelled at the scale of the entire galaxy, and hence have course resolutions. In the review by Mutch et al. (2013), for example, it was noted that in order to reproduce galaxy evolution over cosmic time, some physical parameters in their SAM had to be adjusted to extreme values that were unjustified by current observations.

A full understanding of all these competing processes requires hydrodynamical cosmological

sim-ulations (e.g. the 2Illustris project) which incorporate computational fluid dynamics to treat the

1_{Various algorithms exist in the literature that approximate the gravitational field in order to reduce the computational}

expenses. Examples include tree algorithms (e.g. Barnes & Hut 1986), particle-mesh algorithms (e.g. White et al. 1983), and hybrids of the tree and particle-mesh algorithms (e.g. Springel 2005).

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evolution of the gaseous components in the Universe. This allows complex interactions of baryonic components to be treated at much smaller scales, therefore yielding a much more self-consistent and powerfully predictive calculation. These are however far more challenging and computationally expensive than N -body simulations (Schaller et al. 2015).

Hierarchical simulations versus observations: important highlights

One of the highest benchmarks of complete, quantitative simulations of BCG formation is provided by De Lucia & Blaizot (2007, hereafter DLB07). The DLB07 SAM predicts that during the early epochs of the Universe, gas clouds collapsed which resulted in rapid star formation. DLB07 approx-imates that 50% of the stellar component of BCGs is formed by z ∼ 5, and approximately 80% by z ∼ 3 in separate, progenitor galaxies. At a redshift of z = 1, BCGs only have ∼ 20–30% of their stellar mass assembled.

In the second phase of the DLB07 model, BCGs assemble most of their stellar mass via dissipa-tionless mergers since z = 1, therefore approximately quadrupling their stellar mass over this time period. In other words, the DLB07 model implies that most of the stars in nearby BCGs were not formed in situ, but accreted from pre-existing progenitors via gas-poor mergers. At redshift z = 0, the BCGs of this theoretical model only contain old stellar populations, and are therefore ‘red and dead’. This is attributed to the DLB07 model which assumes a very efficient form of AGN feedback in the second phase of BCG formation, which inhibits further SF (in light of §1.3.3, however, the AGN feedback of DLB07 is likely over-efficient).

On the other hand, many observational studies have also been performed to probe the evolution of BCGs over cosmic time. However, the conclusions reached by these studies are sometimes con-tradictory. For example, Aragon-Salamanca et al. (1998) inferred drastic stellar mass growth by a factor of ∼ 4–5 for BCGs since z ∼ 1. Burke et al. (2000), using a sample of X-ray selected clusters spanning the same redshift range, found substantially less growth. This discrepancy was attributed to selection bias in the study of Aragon-Salamanca et al. (1998), a conclusion supported by Nelson et al. (2002). At the other extreme, Whiley et al. (2008), Collins et al. (2009), and Stott et al. (2008, 2010, 2011) found little, if any, evolutionary changes in BCGs since z ∼ 1. According to Lid-man et al. (2012), these studies apparently suffered from selection bias in the sense that the BCGs selected at high redshift were more massive than the likely progenitors of BCGs in the low-redshift comparison samples. In light of these vexing discrepancies, a long-standing issue was whether the DLB07 model overestimated the stellar mass growth since z ∼ 1.

Some convergence between the modelling predictions of hierarchical merging and observations has emerged in more recent years. In the model of Tonini et al. (2012), BCGs experience a factor of ∼ 2–3 growth in their stellar mass since z ∼ 1.6, and also show signs of SF activity down to low redshifts, a feature which has indeed been observed for some BCGs (§1.3.3). This stands in close agreement with Laporte et al. (2013) who predicts the same growth factor for z ∼ 2 BCGs and reinforces the scenario where BCGs mainly assemble mass through dissipationless mergers without substantial, additional SF after z ∼ 2.

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On the observational side, Lidman et al. (2012), for example, inferred a growth factor of ∼ 1.8 since z ∼ 1, and concluded that SF rates at z < 1 are generally too low to result in significant buildup

of mass. Furthermore, Lidman et al. (2012) attributes the mass assembly of BCGs (during z _{. 1)}

primarily to dry mergers (see also Bai et al. 2014; Liu et al. 2015; Shankar et al. 2015; Webb et al. 2015; Zhao et al. 2015).

The finer details of stellar mass assembly, however, remains unclear. In the study of Lin et al. (2013), it was noted that while there is a strong match between model predictions and observations

for 0.5 < z < 1.5, they start to diverge for z _{. 0.5. That is, while the model BCGs continue to}

grow below z = 0.5, the growth observed in BCGs appears to stall. Therefore, the epoch of z < 0.5 is a very important time to examine the mass assembly history of BCGs. Observational studies

focusing on BCG mass growth for z _{. 0.5 include Inagaki et al. (2015), Oliva-Altamirano et al.}

(2014) and Bellstedt et al. (2016); these studies are broadly consistent with the notion that BCGs rapidly acquired their stellar mass at higher redshifts, but appears to be slowing down at lower

redshifts (z < 0.5).

It should also be kept in mind, however, that the comparison between observations and models, in BCG evolutionary studies, is not trivial. It can also be argued that, at low redshifts, the continual accretion of satellite galaxies adds mass to the outskirts of the galaxy, far beyond the observable regions and thus not taken into account in observational studies (e.g. Whiley et al. 2008). Further-more, differences between model growth rates and observations can potentially be alleviated if the stripped material from companion galaxies ends up in the diffuse intra-cluster light (ICL) (Burke & Collins 2013), which consists of unbounded stars dispersed in intracluster space (e.g. Zhang et al. 2016).

Although the most important salient points of BCG evolution are firmly established, we still lack a detailed picture of BCG evolution at present. The conditions that arise in cluster environments which allow various mechanisms to be efficient, as well as the redshift epochs during which these mechanisms are pivotal in shaping the properties of BCGs, are not completely understood yet (Ascaso et al. 2014).

1.3.3 Cooling flows, star formation, and AGN feedback

Nearby BCGs are usually thought to be passively evolving, ‘red and dead’ systems whose SF has been completely halted since z ∼ 2. However, there is compelling evidence that some low-redshift BCGs exhibit recent SF within the last Gyr (e.g. Mittal et al. 2015). This includes optical emission-line nebulae (e.g. O’Dea et al. 2010), blue BCG cores with near-ultraviolet (NUV) enhancement

(as observed by 1GALEX), that cannot be explained by an old, evolved stellar population such as

horizontal-branch stars (Pipino et al. 2009). Furthermore, the radial extent of the blue BCG cores eliminates the possibility that point-like sources, such as AGN, are the underlying cause (Bildfell et al. 2008; Pipino et al. 2009).

The majority of baryonic material in galaxy clusters exists in the form of a hot plasma known as the 1

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intra-cluster medium (ICM) (e.g. Prasad et al. 2015). Cool-core clusters are galaxy clusters in which

the intra-cluster gas has a high enough density (or equivalently, a low entropy K0 6 30 keV cm2,

Voit et al. 2008) such that the radiative cooling timescale of the intra-cluster gas is typically less than a Gyr, and therefore also shorter than the age of the galaxy cluster itself. Furthermore, a low-entropy gas implies that the corresponding gas cooling rate is relatively large (e.g. Hoffer et al. 2012; Loubser 2014), thus giving rise to highly-peaked X-ray surface brightness profiles.

Because the X-ray gas in cool-core clusters has ample time to cool down, one would naively expect large flows of cooling material towards the centres of these cool-core clusters (i.e. where BCGs typically reside). With this line of reasoning, also known as the classical cooling-flow model, Fabian

(1994) predicted that these cooling flows should lead to SF rates of the order of 300 < M <˙

1 000 M_/_yr_{. However,} 1_{Chandra and} 2_{XMM-Newton observations revealed a lack of widespread}

Fe lines expected from X-ray gas cooling below 1–2 keV in cool-core clusters (e.g. Böhringer et al. 2002; Peterson et al. 2001, 2003; Peterson & Fabian 2006; McNamara & Nulsen 2007). This proved that there is significantly less cooling material at the centres of cool-core clusters than expected from the classical cooling-flow model. The preceding mismatch between theoretical predictions and observations has become known as the cooling-flow problem.

In order to reconcile the theory with the observed rates of SF in cool-core clusters, some non-gravitational heating mechanism that ‘rectifies’ the excessive cooling rate needs to be invoked (e.g. Bildfell et al. 2008). At present, AGN feedback (largely inspired by Booth & Schaye 2009) is established as the leading mechanism that prevents the X-ray gas from cooling at catastrophic rates. Hlavacek-Larrondo et al. (2013), for example, defines AGN feedback as the interplay between

the accretion of cooling material onto a SMBH (MBH> 106Maccording to Booth & Schaye 2009)

and the release of energy through radiation and outflows.

The most recent numerical simulations (e.g. Gaspari et al. 2012; Donahue et al. 2015; Prasad et al. 2015; Voit et al. 2015; Loubser et al. 2016a) of AGN feedback all point to the following qualitative, cyclical pattern in cool-core clusters: Firstly, when the cooling time of the X-ray gas is less than ten

times the free-fall time (tc_/_tff _{< 10), the gas condensates and precipitates towards the cluster centre,}

causing a large accretion rate of cooling material onto the SMBH. The enhanced accretion rate onto the SMBH is followed by strong (bipolar) jetted outflows of relativistic plasma from the AGN.

As a result of this AGN feedback, the ICM is overheated such that tc_/_tff _{> 10. Therefore, further}

condensation is suppressed and the accretion rate onto the SMBH falls. Eventually, the whole cycle

is restarted when the X-ray gas slowly starts to cool and condensate again. In summary, iftc_/_tff _{< 10,}

the cold gas feeds local SF and BH accretion, with AGN feedback serving as a rectifier that shuts down cooling, and allows the cycle to refresh (Voit et al. 2015).

Some of the strongest evidence for AGN feedback are the observations of radio and X-ray cavities in galaxy clusters (Martizzi et al. 2012), which are created as the X-ray gas is being pushed aside by the jetted AGN outflows (Hlavacek-Larrondo et al. 2013). These cavities are detectable as regions of reduced surface brightness in the X-ray images (see figure 1.3.C). Furthermore, simulation studies

1_{http://chandra.si.edu/}

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prove that AGN feedback is necessary to reduce the overall formation of stars at low redshifts (e.g. Ragone-Figueroa et al. 2013; Martizzi et al. 2014). In other words, when AGN feedback is excluded, the simulated elliptical galaxies are too massive (and hence over-luminous) with excessive emission in the blue part of the spectrum due to the over-abundance of young stars.

From an optically-selected sample from the1_{SDSS, Liu et al. (2012) found that the SF rates in BCGs}

are not necessarily low, although it is simultaneously not high enough to contribute significantly to the stellar mass of BCGs by more than 1% (the reader is however also referred to the very puzzling case of McDonald et al. 2012). To conclude, AGN feedback does not completely shut off SF in most BCGs, but only reduces the magnitude of the cooling flow that leads to the residual SF rates of the

order of 10–100 M_/_yr_{, as observed in many BCGs.}

A B

C

Figure 1.3.— (A & B): Simple representations of the monolithic collapse (A) and hierarchical merging (B) models of galaxy formation and evolution. In A a galaxy evolves as an isolated entity, whereas in B the gravitational interactions between progenitor systems shape the properties of the descendant galaxy. (C): X-ray Chandra image of NGC5813 showing pairs of cavities (regions of reduced X-ray surface brightness) caused by AGN feedback. A & B Image Credit: Figure 1 of Ellis et al. (2000). C Image Credit: Figure 1 of Randall et al. (2011).

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Section 1.4. Dark matter 15

1.4 Dark matter

1.4.1 Brief historic overview of dark matter and cosmology

The very first deduction of a missing-mass component dates as far back as 1922 when Kapteyn stud-ied the motions of stars perpendicular to the Galactic plane. By comparing the dynamically-derived total mass with the luminous mass, Kapteyn noticed a discrepancy between the two estimates. In 1932, Oort performed a similar study on the Milky Way disk, and found that the local mass density exceeded that derived from the stars. Oort however cautioned that the luminous mass could have been underestimated due to the crude star counts available at that time.

This ‘missing-mass’ anomaly became much more pronounced in 1933 when Zwicky measured the radial velocities of eight galaxies in the Coma cluster, which yielded a velocity dispersion of σ =

1019 ± 360 km s−1. By applying the virial theorem, based on the assumption that Coma is a

gravitationally-relaxed cluster, Zwicky derived a dynamical mass for Coma that is approximately

400 times greater than the stellar mass. Therefore, the cluster galaxies would ‘fly apart’ in a

crossing time of ∼ 2 Gyr if they were not ‘settled’ in a potential well generated by a large amount of unseen mass. A dynamical study of the Virgo cluster, done by Smith (1936), pointed to the same verdict.

Another major inconsistency arose when Babcock (1939) derived the rotation curve (which maps the rotational velocities of stars in a galaxy as a function of radius) of M31 from spectroscopy out to

1000. By balancing gravitational and centripetal effects experienced by a star, the circular velocity

of a star located at a radial distance r from the centre of the galaxy is given by v (r) =pGM (≤ r)_/_r_,

where M (≤ r) denotes the total mass contained within a sphere of radius r. If stars account for the

majority of the galaxy’s mass, the rotation curve is predicted to have the shape v ∝ r−1/2 _{for large}

radii where M (≤ r) should be constant. Instead, Babcock found a rotation curve that ‘flattens out’ for large radii, implying that M (≤ r) should increase despite the drastic decline in luminosity output.

Rubin et al. (1980)—studying a sample 21 1_{Sc galaxies spanning a wide range of radii, masses and}

luminosities—made the remarkable discovery that for all 21 Sc galaxies, the expected Keplerian ve-locity decrease in the rotation curves was definitely absent. In fact, most rotation curves were found to be rising slowly even at the farthest radial bin, whereas the remainder of rotation curves remain flat. It is therefore clear that a rising-rotation curve is common to a wide range of disk galaxies, and not just unique to M31. More importantly, the observations of Rubin et al. (1980) unambiguously proved that galaxy mass is not centrally condensed, and that a significant amount of non-luminous matter must be located beyond the optical image of a galaxy. Moreover, Dressler (1979) measured rising velocity dispersion profiles for some cD galaxies (which are pressure supported as opposed to

rotationally supported), which similarly suggest a rising (dynamical) mass-to-light ratio (M_/_L_{) for}

elliptical-type galaxies.

From a theoretical viewpoint, Ostriker & Peebles (1973) recognised the need for DM to explain the

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dynamical stability of thin disk galaxies. White (1977) further argued that the ‘missing mass’ in Coma cannot be attributed to individual galaxies, since the resulting dynamical friction would lead to a much higher degree of mass segregation than observed today. These considerations, amongst others, culminated to the hierarchical gravitational collapse model, hypothesised in 1978 by White & Rees which formed the basis for the galaxy formation scenario. This theory states that DM haloes provide the gravitational wells in which baryonic matter can ‘sink’, cool and condense to form the luminous galaxies we observe today.

Independent studies carried out by Wagoner (1973) and Rogerson & York (1973) derived a baryonic

matter density of 1Ωb ∼ 0.01. This followed from the Big Bang nucleosynthesis (BBN) model and

measurements of interstellar Deuterium (which is destroyed within stars). Contemporary obser-vational evidence (Ostriker et al. 1974), however, favoured a cosmological mean matter density of

Ωm ∼ 0.2, therefore implying that the majority of matter is non-baryonic.

Prospective dark-matter candidates were subsequently classified into three families: Hot, Warm and Cold Dark Matter (HDM, WDM, and CDM respectively). These names reflect the typical velocities of the candidate particle at the epoch of recombination (e.g. Bond et al. 1980). Light neutrinos are the prototype for HDM, as they maintain relativistic speeds until ‘late’ times. Gravitino’s and sterile neutrinos are popular candidates in the WDM category. On the other hand, CDM candidates are very massive, weakly interacting particles with negligible thermal velocities in the early universe, which only interact via the weak and gravitational forces (e.g. the WIMP thermal relic or axion particle: Peebles 1982 and Blumenthal et al. 1984).

The idea that dark matter is non-baryonic received much attention when Lubimov et al. measured the mass of a neutrino particle (also the HDM prototype), of ∼ 30 eV, in 1980. Therefore N -body simulations had to be done to test whether HDM reproduces the ‘cosmic web structure’ we see today (e.g. figure 1.2.B). The latter was initially benchmarked by the CfA redshift-survey (Davis & Peebles 1983) that provided the first, representative picture of the cosmic web. Simulations performed by White et al. (1983) revealed that HDM leads to galaxies clustering on a much larger scale than permitted by CfA observations. More specifically, in the HDM scenario, superclusters form first, whereas smaller objects develop via fragmentation. Therefore, HDM, along with the anti-hierarchical, top-bottom galaxy formation coupled to it, was dismissed.

A good match to the cosmic-web structure was first yielded in 1985 when Davis et al. performed N -body simulations of a CDM universe, which encouraged further exploration in the CDM direc-tion. CDM further implies that galaxy formation proceeds in the hierarchical fashion where galaxies collapse to form galaxy clusters and superclusters (and not vice versa). Moreover, in the 1980’s, a ‘flat’ universe was considered a natural outcome of the cosmic inflation theory set forth by Guth (1981) and Linde (1982), however a cosmological constant (i.e. negative pressure leading to expan-sion) was deferred, and hence an Einstein-de Sitter (SCDM) model became the main driving force for a decade.

2_{COBE measurements of the CMB placed further constraints on cosmological parameters, however}

1_Ω

b∼ 0.01 implies that baryons form ∼ 1% of mass-energy budget of the universe.

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a degeneracy persisted between the spatial curvature and expansion history of the universe. The

transition to the1ΛCDM model was finally made when supernova data (Riess et al. 1998; Perlmutter

et al. 1999) revealed an accelerated expansion in the universe, and when2_{balloon-borne experiments}

(de Bernardis et al. 2000; Hanany et al. 2000), measuring fluctuations in the CMB spectrum,

demonstrated that the universe is ‘flat’. Higher sensitivity and resolution of the 3WMAP-satellite

measurements of the CMB (Spergel et al. 2003) convincingly excluded many alternatives to the

ΛCDM model. COBE and WMAP are forerunners of the the 4Planck mission, a 3rd-generation

satellite, which currently provides the most accurate estimates of the baryon and dark matter densities.

1.4.2 An epilogue on dark matter

The present impetus in dark-matter research consists of numerical simulations that explore predic-tions of the ΛCDM model with increasing resolution and precision (e.g. figure 1.2.A). In tandem with these computational efforts is a wealth of observational techniques (gravitational lensing, ve-locity dispersion measurements, X-ray observations, redshift surveys, etc.) that probe the detailed structure of DM haloes. Mention should also be made of detection experiments ‘searching’ for DM either directly, or indirectly through the decay or annihilation radiation of favoured DM candi-dates (e.g. Graham & Rajendran 2011; Jaeckel & Redondo 2013). It is also possible that the Large Hadron Collider (LHC) may reveal particle-physics evidence for the existence of DM (e.g. Feng et al. 2006; Grajek 2009). Other exotic DM candidates have also been proposed to reconcile remaining discrepancies between simulations and observations (see §1.4.3), of which the self interacting dark matter (SIDM) candidate (Spergel & Steinhardt 2000) is quite notable. In any case, it would be interesting to see what new discoveries will be made in the next decade in the quest of constraining the properties of DM. For a much more extensive review of DM and cosmic structure, the reader is referred to, e.g., Frenk & White (2012).

1.4.3 The ΛCDM paradigm

The evidence for a ΛCDM cosmological paradigm has become compelling over the years (§1.4; Springel et al. 2006; Frenk & White 2012). In the aftermath of the ‘golden age of cosmology’, the geometry of the Universe (flat universe experiencing accelerated expansion) as well as the initial conditions for the formation of all cosmic structures (cosmic inflation) have been validated experimentally through detailed measurements of the temperature fluctuations in the CMB radiation and through extensive surveys of cosmic large-scale structure. The exact microphysics of DM, however, still awaits experimental confirmation.

Some important cosmological constraints, also of some interest in this study, involves the

dis-tribution of the matter-energy budget amongst baryons, CDM, and dark energy. As reported

1_{See footnote 1 on p. 3.}

2

BOOMERanG and MAXIMA balloon-borne experiments.

3_{Wilkinson Microwave Anisotropy Probe. http://map.gsfc.nasa.gov/}

4

Weighing dark matter in brightest cluster galaxies