tw1979_final_report_ref_correct

Astrophysics Group, School of Physics, University of Bristol c©ESO 2015May 13, 2015

Hunting for satellites of the most massive galaxy clusters

Thomas Wigg

H. H. Wills Physics Laboratory, University of Bristol, Tyndall Ave, Bristol BS8 1TL, UK.e-mail: [email protected]

ABSTRACT

Galaxy clusters accrete the majority of their mass through mergers with comparable mass satellite clusters, but theselower mass satellites are often dicult to identify from their X-ray signal alone, especially at higher redshifts. Satelliteclusters were searched for in the vicinity of a sample of 11 X-ray detected clusters from the XMM-XXL cluster survey inthe redshift range 0.5 < z < 0.9 found in the overlap region of the VIPERS and CFHTLS-W1 galaxy catalogues. Twoselection techniques were used to create subsets of galaxies from the two catalogues likely to be part of the conrmedclusters and any surrounding structure, and potential satellites were identied by looking for overdensities in thecombination of these selections. Sources from the XXL catalogue thought to originate from the satellites were selectedand mass estimates calculated based on their X-ray ux. The validity of any identied systems was then investigatedthrough comparison with similar systems from the Millennium Simulations and an additional mass estimate calculatedbased on the stellar ux of each satellite and its more massive companion. Using light cones from the MillenniumSimulations the occurrence rate of cluster systems detected with apparent satellites and the number of these associatedsatellites around each cluster were compared to expected rates predicted by the computer models. One conrmedand ve potential satellites around four of the XXL clusters were identied, all of which have estimated masses andseparations from their companion cluster deemed reasonable. The rate of clusters with companion satellites and thenumber of satellites per cluster were both greater in simulations than real observations but this was attributed tolimitations of the catalogues used, issues identifying weaker galactic overdensities and ambiguity in selecting satellitesin the simulations. No single piece of evidence suggests the satellite candidates found are not true clusters, but follow-upobservations are required to conrm their presence.

Key words. Galaxies: clusters: general - galaxies: clusters: intracluster medium - galaxies: distances and redshifts -X-rays: galaxies: clusters - cosmology: dark matter.

1. Introduction

Only in recent years have attempts to reconcile observationsof the universe with a single model for the architecture ofthe universe, and the growth of structure within it, beensuccessful. This is termed the concordance model and re-quires a at geometry of the observable universe, implyingthat the total energy density is close to the critical densityrequired for the universe to become closed. As it is under-stood today, the universe is composed mainly of two domi-nant components: non-baryonic dark matter and a form ofdark energy, where the gravity of the former is responsiblefor structure formation and the latter is responsible for theaccelerated expansion of the universe. The mean density ofbaryonic matter corresponds to around only 15% of the to-tal matter in the universe (Voit 2005) and this matter isonly observable because it has been drawn into the deeppotential wells created by concentrations of dark matter,where a small fraction has condensed into stars and galax-ies.

Clusters of galaxies are important in testing the under-lying cosmological model, as according to the concordancemodel they are the largest and most recent gravitationally-relaxed objects to form (as structure grows hierarchically)and they trace the large-scale distribution of matter in theuniverse. Structure formation is driven by gravity and in

the early universe regions where a uctuation caused thedensity to slightly exceed the mean density became gravi-tationally bound. These regions eventually decoupled fromexpansion and collapsed upon themselves, entering a stateof virial equilibrium where the mean speeds of the compo-nent particles are approximately half of the escape veloc-ity (Voit 2005). Density perturbations in the concordancemodel have greater amplitudes on smaller length scales anddue to this small, sub-galactic objects decoupled rst, col-lapsed and virialised. The scale of the virialisation increaseduntil clusters of galaxies, with masses between 1013 and 1015

times that of the Sun (1013M−1015M) were formed: thisis termed hierarchical clustering. Press and Schechter de-veloped an analytic formalism for this process of structureformation in their landmark 1974 paper (Press & Schechter1974).

With improvements to equipment over the past fewdecades, the catalogue of known clusters is continuouslyincreasing and with it more information is being garneredfrom observations of clusters than ever before. This, coupledwith recent advances in computational technology, meansthe ability to develop models via simulations and semi-analytic techniques and subsequently test said models withobservations has become an imperative reality.

However, technical limitations still pose an issue in clus-ter detection: X-ray cluster surveys suer from inherently

of 17


low count rates and poor signal-to-noise, meaning detec-tion of lower mass clusters becomes increasingly dicultat greater redshifts, whilst cluster identication from opti-cal galaxy surveys suers from signicant projection eects.Clusters accrete the majority of their mass through merg-ers with comparable mass satellite clusters which are drawninto the potential well of their more massive companion(Lidman et al. 2013). Looking back into the early universe,when few clusters were fully-formed, many clusters shouldbe present with satellites in their vicinity, but due to thelimitations of current observatories it is rarely possible toidentify these lower mass satellite clusters around the moremassive clusters detected on the sky; this issue provides themotivation for this project.

Using photometric techniques to select galaxies fromthe CFHTLS-W1 catalogue likely to belong to the larger-scale structure around detected clusters from the XMM-XXL cluster survey and using redshift information fromthe spectroscopic VIPERS galaxy catalogue, overdensitiesin the number of these galaxies in the vicinity of massiveclusters are identied, indicative of the satellites one ex-pects to see. Potential X-ray sources from the full XXLcatalogue thought to originate from the satellites are thenidentied and from this mass estimates of the potential clus-ters are calculated. A variety of techniques are then used tocheck whether the cluster systems identied seem reason-able, notably utilising data from the Millennium Simula-tions to investigate satellite characteristics and occurrencerates.

This paper is split into four further sections: Section 2covers the observable properties of clusters (2.1) and de-scribes the processes by which they grow (2.2), along witha collation of cluster catalogues and growth curves producedusing the Millennium Simulations which comprises the rstwork of this paper (2.3). Section 3 describes the hunt forthe satellites of massive clusters conducted by making selec-tions of structure in spectroscopic (3.1) and photometric(3.2) galaxy catalogues and the combination of these tech-niques to identify overdensities in these galaxies indicativeof clustering (3.3). Section 3 continues with attempts toidentify X-ray signals from the potential satellites and fromthese make an estimate of their mass (3.4) and concludeswith eorts to determine the validity of the potential clustersystems discovered using the Millennium Simulations andcomparisons between the masses calculated from the X-rayux of potential cluster sources and estimated from the ra-tio of stellar mass between the satellites and their massivecompanion (3.5). Section 4 discusses the sources of pos-sible uncertainty (4.1), the signicance of the discoveredsystems (4.2) and the future of satellite detection with ref-erence to the scheduled eROSITA observatory (4.3), withsection 5 summarising the project.

Throughout this paper, a at cold dark matter cosmol-ogy with ΩΛ = 0.70 , Ωm = 0.30 and H0 = 70km-1Mpc-1 isassumed.

2. Background and preliminary work

2.1. Observable properties of galaxy clusters

In order to select clusters (or groups) of galaxies from theobserved galaxy distribution, one must dene some selec-tion criteria. In 1958, Abell selected 1,682 galaxy clustersfrom the Palomar Sky Survey (Abell 1958) according to

two selection criteria: the rst put a constraint on the min-imum density of the cluster and the second required thatthe cluster contained a sucient amount of galaxies. Thesewere termed the compactness and richness criterion respec-tively. Abell also classied a cluster as regular if its galaxydistribution was roughly circularly symmetric and irregularotherwise.

Stars make up only a small fraction of the total bary-onic mass of a cluster, with substantially more containedin hot gas which emits in the X-ray and is visible in themicrowave through the Sunyaev-Zel'dovich eect, allowingcluster detection in these frequency ranges as well as theoptical. The baryonic mass of stars and hot gas in a clus-ter only makes up approximately one eighth of the totalmass (Allen et al. 2002), which means gravitational lensingis also an extremely useful probe of massive structures likeclusters.

2.1.1. Optical

Charles Messier and William Herschel (Messier 1781; Her-schel 1785) were among the rst to identify concentrationsof galaxies using optical observations; they observed galax-ies in the Virgo and Coma clusters. Optical techniques haveimproved over the past two centuries, culminating in thedenitive cluster catalogues of George Abell and collabo-rators (Abell 1958; Abell et al. 1989). Abell's cataloguescontain most of the known nearby galaxy clusters and arethe basis for much of our modern understanding of clusters.

Optical observations are useful as the cluster luminos-ity scales with cluster mass, generally adhering to the lumi-nosity distribution proposed by Schechter (1976), with thenumber of galaxies in luminosity range dL about L propor-tional to L−αexp(−L/L∗), with α ∼ 1 (e.g. Balogh et al.2001). This relationship is important as it is often moreuseful to compare cluster masses, which dictate many ofthe physical processes in the cluster, rather than clusterluminosities.

Once a cluster has been optically identied, obtainingthe radial velocities vr of the cluster galaxies helps deter-mine the cluster mass. As the velocity distribution of a re-laxed cluster is expected to be approximately Gaussian invelocity space, cluster candidates can be conrmed if theirvelocities fall within a chosen number of standard devia-tions of the mean dispersion, dependent on the stringencyof the cluster member selection. Zwicky (1933, 1937) wasthe rst to measure the one-dimensional velocity dispersionσ1D of a cluster, nding σ1D ∼ 700kms-1 for the Coma clus-ter. This provided some of the rst evidence for the presenceof dark matter in the universe, as the inferred mass fromthis velocity dispersion along with his estimated cluster ra-dius required substantially more mass than was observed instars.

In his 1937 paper, Zwicky also proposed that clustermasses could be measured through the gravitational lensingof background galaxies. The technique did not become prac-tical for another sixty years but is now one of the primarymethods for measuring cluster mass. Chwolson in 1924 andEinstein in 1936 were the rst to propose that, if a back-ground star were precisely aligned with a massive object,the gravitational eect of this mass would deect the pathof the star's photons resulting in a circular ring of light, cen-tred on the deector (Chwolson 1924; Einstein 1936). Mea-suring the weak-lensing distortion of any single galaxy is

of 17

Thomas Wigg 2015 | Hunting for satellites of the most massive galaxy clusters

nearly impossible, but the mass of a cluster can be inferredby looking at the distortion of an entire eld - this techniqueis demonstrated in Bartelmann & Schneider (1999).

2.1.2. X-ray

With only around one tenth of the universe's baryons re-siding in stars in galaxies, there is a signicant amountof matter located in intergalactic space. These inter-galactic baryons are generally very dicult to observe,but when compressed by the deep gravitational potentialwells of clusters, the intracluster gas is heated to X-rayemitting temperatures, releasing photons through thermalbremsstrahlung. This gas, which corresponds to approxi-mately 15% of the cluster mass, has a temperature whichcorrelates to the depth of the potential well and from thisthe total mass of the galaxy cluster can be calculated - thephysics of this is described in Sarazin (1988). It was follow-ing the detection of the ionised iron line FeXXVI by theAriel-V satellite (Mitchell et al. 1976) that the usefulnessof X-ray emission of the intracluster medium (ICM) as aprobe of the gravitational potential within the cluster (andtherefore the gravitating mass) was realised. The calcula-tion for this is presented by Fabricant, Lecar and Gorenstein(Fabricant et al. 1980).

Galaxy clusters are identied from the X-ray signal oftheir ICM through a reduction pipeline - an algorithm se-lects source candidates based on whether their characteris-tics are indicative of cluster emission. However, with the in-herently low count rates and signal-to-noise associated withcluster detection, at greater distances it becomes increas-ingly dicult to identify the extended sources of galaxycluster ICM amidst a universe of X-ray bright point sourcessuch as active galactic nuclei (AGN). Cluster X-ray lumi-nosity scales with mass (Piaretti et al. 2010), leading tolower mass clusters being biased against at higher redshift,as they are the rst to fall below either the ux limit orpipeline conrmation limit for a given survey.

2.1.3. Microwave (Sunyaev-Zel'dovich eect)

The hot intracluster medium can also be observed throughits eect on the cosmic microwave background (CMB).The CMB itself has a nearly perfect blackbody spectrum(Mather et al. 1990) and soon after the discovery of thisbackground radiation it was theorised that the spectrumwould be distorted by Compton upscattering of the CMBphotons by the intergalactic gas (Weymann 1965, 1966).Sunyaev & Zel'dovich (1970, 1972) predicted that the CMBphotons would indeed be upscattered to higher energy bythe ICM and this eect is now known as the Sunyaev-Zel'dovich (S-Z) eect.

Birkinshaw (1991) demonstrated some of the rst S-Zdetections of clusters, but these were marginal. However,in the following decade, many clusters were detected withhigh signicance (Birkinshaw 1999; Carlstrom et al. 2000).Several S-Z surveys, including the South Pole Telescope(SPT, Carlstrom et al. 2009) survey, the Atacama Cos-mology Telescope (ACT, Fowler et al. 2007), and Planck(Tauber et al. 2010), are actively ongoing, providing therst S-Z-selected cluster catalogues (e.g. Vanderlinde et al.2010; Menanteau et al. 2010).

Using S-Z techniques to identify clusters is advantageousas, due to the fact that the observed photons are from theCMB, they are redshift-independent. However, X-ray ob-servations of S-Z-detected clusters are still important formany reasons. The X-ray properties allow a better calibra-tion of the S-Z signal and yield the calibration of the scalingrelations needed for cosmological studies with S-Z-selectedcluster samples. X-ray observations also allow the testing ofthe selection function of S-Z surveys and verication of newS-Z cluster candidates. Furthermore, they are essential forstatistical analyses of the S-Z data (Piaretti et al. 2010).

2.2. Growth of clusters

Due to the hierarchical nature of structure growth and theself-similarity of galaxy clusters, growth of structure onvastly dierent scales occurs in much the same way. Mergersnot only appear to be the dominant channel for mass growthof a galaxy or cluster's dark matter halo but also the stellarmass growth, both directly through galaxy-galaxy mergersand through the accretion of potentially star-forming gas(Fakhouri et al. 2010; Lidman et al. 2013). Lidman et al.(2013) dene a major merger as 0.25 < µ∗ < 1, where µ∗ isthe mass ratio between the satellite and its more massivecompanion. If the orbital energy is suciently low, close en-counters between two systems can lead to a merger. How-ever, galaxies in clusters are unlikely to merge as their en-counter speed is generally much larger than their internalvelocity dispersion (Mo et al. 2010). There is one importantexception: through dynamical friction, galaxies lose energyand momentum which causes them to `sink' towards thecentre of the potential well. Provided the dynamical fric-tion time is suciently short, the galaxy will eventuallyreach the cluster centre and merge with the central galaxyresiding there. This process is called galactic cannibalism.

2.2.1. Satellite clusters

According to self-similarity, satellite clusters are bona declusters which appear structurally identical to the mostmassive clusters they are bound to (Neumann & Arnaud2001), albeit consisting of fewer galaxies and of lower mass.Due to the nature of merger-based growth, satellite clustersmust be present in the vicinity of some massive clusters,especially in earlier periods of cosmic history when few, ifany, galaxy clusters had cleared the surrounding universeof dust and smaller clusters to become fully-formed. Clus-ter systems in the process of merging have been observedand detailed in numerous papers (Hagino et al. 2015; Katoet al. 2015; Storm et al. 2015; Zhang et al. 2015 to list buta few of the most recent), though little investigation hasbeen performed into the presence of discrete satellites, stillindependent from the massive clusters to which they willeventually infall.

This is due to the fact that the emission from a lowermass satellite will likely be considerably smaller than thatobserved from its more massive companion. In the case ofthe emission from the satellite's ICM, the X-ray ux ob-served is a function of its mass (Piaretti et al. 2010), mean-ing that for more distant clusters, where the cluster emis-sion itself is near the ux limit of the observations whichdetect it, the X-ray signal from any satellite clusters will

of 17


likely fall below the threshold to be conrmed as clustersof their own volition.

Detection of these satellites is important, not only toconrm theoretical models detailing the growth of clusters,but also to plot the large-scale structure, of which clustersare intrinsic components in forming the laments and voidswhich trace the largest arrangement of matter in the uni-verse.

2.2.2. Simulations

N-body simulations representing the dark matter haloesof galaxies and clusters, occasionally combined with semi-analytic descriptions, have been increasingly used over thepast two decades to investigate the hierarchical forma-tion of large-scale structure in the universe (e.g. Navarroet al. 1997; De Lucia & Blaizot 2007; McBride et al. 2009;Fakhouri et al. 2010; Laporte et al. 2013). Only recently,however, have the theoretical expectations and observationsof cluster growth come into excellent agreement (Laporteet al. 2013).

Fakhouri et al. (2010) utilise the Millennium (Springelet al. 2005) and Millennium-II (Boylan-Kolchin et al. 2009)to construct merger trees of dark matter haloes and quan-tify their merger rates and mass growth rates from betweenz = 0 and z = 15 for over ve orders of magnitude in thedescendant halo mass (1010M . M0 . 1015M). TheMillennium-II simulation has the same number of particlesbut 125 times better mass resolution and the new data baseprovides 7.5×106 dark matter haloes (each containing morethan 1000 simulation particles) between redshift 0 and 15,adding to the 11.3 × 106 haloes (between z = 0 and z = 6)from the Millennium simulation.

To compute the total mass growth rate of a halo ofgiven mas M0 at time t, Fakhouri et al. (2010) follow themain branch of its merger tree and set M = (M0 −M1)/t,where M0 is the descendant mass at time t and M1 is themass of its most massive progenitor at time t − ∆t. Theplot showing the mean value of M as a function of z, takenfrom Fakhouri et al. (2010), can be seen in Fig. 1. Theynd the mass accretion rates shown in Fig. 1 to be well tby equations (8) and (9) of McBride et al. (2009) with onlythe coecients needing minor adjustments. They nd thatthe updated t, shown by the dashed lines in Fig. 1, for themean growth rates of haloes of mass M at redshift z canbe written

⟨M⟩mean

= 46.1Myr−1

(M

1012M

)1.1

×(1 + 1.11z)√

Ωm(1 + z)3 + ΩΛ (1)

2.3. Collation of cluster catalogues and analyses of clustermass growth

The work of Piaretti et al. (2010) sought to homogenise,to an overdensity of 5001, many previous ROSAT All Sky1 Cluster limits are dicult to dene, so in order to make clusterproperties comparable the region with an edge corresponding toa certain overdensity, where the density of matter is a givenfactor times the critical density, is normally used.

Fig. 1. Fakhouri et al. (2010) - Mean mass accretion rate ofdark matter on to haloes as a function of redshift from the twoMillennium simulations (solid curves). Halo masses ranging from1010 to > 1014M are plotted. The dashed curves show theaccurate t provided by Equation (1). The right-hand side ofthe vertical axis labels the mean accretion rate of baryons, Mb,assuming a cosmological baryon-to-dark matter ratio of 1/6.

Survey-based (NORAS, REFLEX, BCS, SGP, NEP, MACSand CIZA) and serendipitous (160SD, 400SD, SHARC,WARPS and EMSS) cluster catalogues into a single Meta-Catalogue of X-ray Clusters of galaxies: the MCXC. TheMCXC comprises of 1743 clusters, with redshift z, stan-dardised 0.1 − 2.4 keV band luminosity L500, total massM500 and radius R500 provided. Being the largest catalogue,all subsequent catalogues were homogenised to be compa-rable to the MCXC according to Piaretti et al. (2010).

In addition to the clusters contained in the MCXC,clusters from the XMM-XXL (Pierre et al. 2011), XMM-LSS (Clerc et al. 2014) and XMM-XCS (Mehrtens et al.2012) - all X-ray surveys utilising the XMM-Newton tele-scope - were also added to the catalogue. In order to ho-mogenise the surveys with the MCXC, it was necessary totransform the luminosities into the correct (0.1 − 2.4 keV)band, as the LSS and XXL catalogues were published in the0.5 − 2.0 keV band and the XCS catalogue in the bolomet-ric (0.01 − 100 keV) band. To do this, a correction factor,which is simply the ratio between the uxes in each band,is required. This factor is X-ray temperature and redshiftdependent, and a table of the correction factors was gen-erated using the APEC emission spectrum in xspec. Anabundance of 0.3 was used.

As well as the mentioned X-ray clusters, two S-Z-selected catalogues - the all sky Planck-SZ (Planck Collab-oration 2013) and 720deg2 South Pole Telescope SPT-SZ(Reichardt et al. 2012) - were also included. The Planckcatalogue contains 861 conrmed clusters, with 178 con-rmed as new clusters, mostly through follow-up observa-tions whilst the SPT catalogue consists 158 optically orinfrared conrmed clusters, with 117 new discoveries. Both

of 17


the Planck and SPT luminosities were already in the correctband to be included in this catalogue.

To ensure the masses in the four catalogues used arecomparable, equation (2) of Piaretti et al. (2010) was usedto covert the L500 of the XMM-LSS and XMM-XCS tocluster masses M500. This equation reads

h(z)−7/3

(L500

1044ergs−1

)= C

(M500

3 × 1014M

)α(2)

where log(C) = 0.274, α = 1.64 and h(z) is the ratio ofthe Hubble constant at redshift z to its present value, H0

i.e. h(z)2 = Ωm(1 + z)3 + ΩΛ. Note that this is an exampleof an X-ray scaling relation; references with a more exten-sive derivation (e.g. Giodini et al. 2013) and papers tacklingscaling relations in the optical and microwave bands (Cza-kon et al. 2014) are readily available.

After considering the work of Fakhouri et al. (2010), itwas decided that obtaining a form of equation (1) whichgives the change in mass ∆M of a given cluster of mass Mbetween the look-back times t1 and t2, corresponding to aredshift change of z(t1) to z(t2), would be useful. Beforenumerical integration was necessary, the simplest form ofthis equation can be written

∆M = −z(t2)∫z(t1)

√ΩΛ

Ω0

[(1 + 1.11z)

(z + 1)

√Ωm(z + 1)3 + ΩΛ

Ω0(z + 1)3 + ΩΛ

]dz

(3)

Fig. 2 shows the distribution of the MCXC, XMM-XXL,XMM-LSS, XMM-XCS, Planck-SZ and SPT-SZ clusters ona plot of mass against redshift. Equation (3) was numeri-cally integrated over all M(z) and z using the trapeziumrule to produce contour plot beneath the cluster points onFig. 2, where a line of constant colour traces the likely masshistory of a cluster based on the work of Fakhouri et al.(2010).

It is clear from this that at intermediate redshifts, fewclusters have been detected with masses < 1014M. Thisdoes not correlate to the actual existence of lower massclusters however, and is simply a comment on the technicallimitations of current detection techniques. As mentioned,it is for this reason that is has not yet been possible todetect many low mass satellites around massive clusters -a problem discussed in the following section and addressedin the remainder of this paper.

3. Hunting for satellite clusters

The nature of hierarchical clustering insists that at higherredshift (z > 0.5), where clusters are rarely fully-formed,more massive clusters be surrounded by lower mass satellitegroups and clusters which will eventually merge with thehost. The statement by Lidman et al. (2013) and Fakhouriet al. (2010) that major mergers provide the dominant chan-nel of mass growth of massive clusters means that satel-lite clusters of comparable (but lower) mass to the hostshould be present around clusters in the early universe.Self-similarity requires these be clusters of their own vo-lition, with a present ICM and associated X-ray emission.

As discussed earlier, unidentied satellite clusters are in-trinsically too low a mass to be conrmed from their X-raysignal alone (see 2.1.2). In this paper, potential satelliteswere identied by searching for overdensities in the numberof observed galaxies around conrmed clusters.

Determining the spatial distribution of objects in theUniverse when observing from our xed position on Earthis inherently dicult: without some form of additional in-formation, the three-dimension cosmos exists only as a two-dimensional projection on our sky. Because of this, somemeans of determining or inferring the three-dimensional dis-tribution of galaxies is necessary to identify clustering. Twomethods for identifying this clustering were used in this in-vestigation. The rst relies on using the spectroscopicallydetermined redshifts of a sample of galaxies to plot theirtrue spatial distribution. The second involves using pho-tometric data from a dierent sample of galaxies to makerelevant colour cuts about a cluster's red sequence to iso-late galaxies that were likely formed at the same epoch asthe cluster. Both of these techniques are described in moredetail in the subsequent subsections.

It is advantageous to combine these techniques in or-der identify satellites which fall below the selection thresh-old of any one observational technique, and as such theareas surveyed using each method must necessarily over-lap. This hugely restricts the available data, as only ar-eas of sky with deep-eld X-ray, spectroscopic galaxy andphotometric galaxy data are usable. One such overlap be-tween the the VIMOS Public Extragalactic Redshift Survey(VIPERS), Canada-France-Hawaii Telescope Legacy Sur-vey (CFHTLS) and the XXL-North cluster catalogue isutilised in this paper.

The XXL Extragalactic Survey (Pierre et al. 2011;Pierre & XXL Consortium 2014) is a recent X-ray clustersurvey utilising the XMM-Newton observatory. It contains336 likely clusters (188 of which are are very good clustercandidates) with 0 < z < 2.24 split between two survey ar-eas. The Northern catalogue utilised in this investigation iscentred on the CFHTLS-W1 area (RA: 2h23m, Dec: -4 deg30') and covers an area of 25deg2. A total of 26,555 X-raysources were detected in the Northern eld of the XXL sur-vey. Galaxy clusters demonstrate the largest X-ray sourceextent, or core radius, as the emission from the ICM is dif-fuse. Likely clusters are classied from this extent and thecorresponding likelihood of that being the true extension,with a lower limit on both set to dene very good class 1(C1) cluster candidates and possible class 2 clusters (C2).A minimum extension of 15 arcseconds is imposed for bothC1 and C2 sources, with lower likelihood limits of 5 and 33dening the two classes respectively (Pacaud et al. 2006).

The rst VIPERS public data release (PDR-1; Garilliet al. 2014), comprises 57,204 spectroscopic measurementsof galaxies with iAB < 22.5 and 0.5 < z < 1.2. This in-vestigation uses the catalogue of 30,523 galaxies from theincomplete W1 eld (centred at RA: 02h26m00.0s, Dec: -04deg 30'00), with a surveyed area of 7.932deg2 at the timeof the rst data release. Objects chosen for spectroscopicfollow-up to be included in VIPERS were selected from theCFHTLS-Wide catalogue.

CFHTLS (Hudelot et al. 2012) is the combination ofa large fraction (∼50%) of Canada and France's darkand grey telescope time from mid-2003 to early 2009 andcomprises two components: CFHTLS-Deep and CFHTLS-Wide, with the latter being comprised of 4 contiguous in-

of 17


∆ XMM-XCS ∇ XMM-LSS XXL MCXC + SPT-SZ × PCCS-SZ

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

z

1

10

100

1000

M500(z

) [

10

12 s

ola

r m

ass

es]

1

10

102

103

M0 /

[1

012 s

ola

r m

ass

es]

Fig. 2. Plot of mass M500/1012M against redshift z showing the clusters collated from the MCXC, XMM-XXL, XMM-LSS,

XMM-XCS, Planck-SZ and SPT-SZ catalogues. The contour plot below shows the likely mass accretion of a cluster, with lines ofconstant colour representing how the mass M(z) of a cluster of mass M0 today has changed since z = 2.

dependent patches covering a total area of ∼155deg2. TheCFHTLS-W1 area selected for this investigation is reducedto contain the 1,034,605 objects for which 3.6µm and 4.5µmband magnitudes are available. This is due to the nature ofthe photometric cuts made in this investigation, describedin detail in 3.2.

The VIPERS area is the smallest of the three surveyareas used and consequently is the limiting area for thisproject. Within this area, the 11 XXL clusters (of which 6are C1) with 0.5 < z < 0.9 were selected for investigation,with this restriction necessary due the fact that the densityof VIPERS galaxies drops to an unusable level at redshiftsgreater than this.

3.1. Isolating structure using spectroscopic redshifts

If the redshifts of a sample of galaxies are known, it al-lows the unique opportunity of plotting the precise three-dimensional distribution of these galaxies in space, with aredshift directly correlating to a spatial distance away fromEarth. This method provides the most direct way of identi-fying clusters of galaxies, with overdensities in the distribu-tion resulting from the true grouping of galaxies in space,rather than being inferred from a selection proxy (as withthe photometric technique used in 3.2).

For each of the selected clusters, an initial redshift cutin the VIPERS catalogue of ±0.1 about the cluster red-shift in a square area of 0.25deg2, when possible centredon the cluster, was made with a view to identify any ex-tended structure. For clusters where galactic overdensities

were obvious, a manual selection of the structure was madeto produce a subset of galaxies that appear to belong tothe same, larger-scale structure as the conrmed XXL clus-ter. For clusters where no obvious galactic clustering waspresent, a cut in redshift of ±0.02 was made about the clus-ter - this range was chosen as, for the clusters where galacticoverdensities were identiable in the redshift-RA plane, anyobservable structure was contained in this cut.

An example of a selection of obvious structure can beseen in the spatial distribution of galaxies shown in Fig. 3,with evident clustering around n0286, a class 1 cluster fromthe XXL-N catalogue. Whilst the selection was made man-ually, the validity of this method is supported by the his-togram: the selection of galaxies made is contained within astrong, single peak in the distribution, suggesting that themajority of the galaxies selected are in fact part of the largerstructure the cluster occupies. Of the 11 clusters examined,6 were situated in regions of galactic overdensity such thatis was possible to select its likely containing structure.

3.2. Identifying likely clustering using photometric techniques

All rich galaxy clusters contain a population of passivelyevolving, early-type elliptical galaxies which show a stronglinear relationship between their colour and magnitude.This relation, termed the red sequence, demonstrates an in-credibly low scatter and appears extremely homogeneous,both within clusters and between them (Bower et al. 1992).The stellar population which makes up the red sequenceappears to be formed at high redshift (z > 2) (Gladders

of 17


32.0 32.1 32.2 32.3 32.40.65

0.70

0.75

0.80

0.85 XXL cluster (n0286) Selected subset Excluded galaxies

z

RA (Deg)0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84

0

5

10

15

Cou

nt

z

Selected subset Excluded galaxies

Fig. 3. Left: spatial distribution of VIPERS galaxies (blue and orange) in the RA-z plane within a Dec. cut of ±0.25deg aboutC1 XXL cluster n0286 (black circle). Orange points show the manually selected subset of galaxies assumed to be part of thelarge-scale structure in which n0286 is present. Right: Distribution of VIPERS galaxies in redshift contained within a 0.25deg2

square annulus in RA and Dec. about the position of the C1 XXL cluster n0286. The manually selected subset of galaxies aboutthe cluster is shown.

& Yee 2000), which is to be expected in cold-dark-matterdominated scenarios of hierarchical structure formation, aspresent-day clusters are associated with the most extremeinitial overdensities, which were the rst to collapse.

Other than their homogeneity, there are many otherobservational reasons that make the red sequence an at-tractive target for cluster identication. Elliptical galaxiescan be morphologically selected with a high level of con-dence due to their core-dominated compact brightness pro-les (Abraham et al. 1994; Gladders et al. 1998). In addi-tion to this, elliptical galaxies have been shown to dominatethe bright end of the cluster luminosity function (Sandageet al. 1985; Barger et al. 1998), meaning in ux limitedsurveys they are the most readily observed. Cluster ellip-ticals are also brighter at greater redshift (Schade et al.1997; van Dokkum et al. 1998), which is to be expected ofstellar populations which are passively evolving. Accordingto the morphology-density relation (Dressler et al. 1997),the radial distribution of elliptical galaxies in regular, cen-trally concentrated clusters is also more compact than othermorphological types, providing a higher contrast againstthe background. Even in irregular clusters with no well de-ned centre, ellipticals still trace the densest cluster regionsas the morphology-density relation holds true, albeit withlesser signicance (Dressler et al. 1997).

The Cluster Red Sequence (CRS) method of cluster de-tection is described in detail by Gladders & Yee (2000),and identies clusters computationally as an overdensity ofgalaxies on the sky, which correlates to an overdensity inthe colour-magnitude plane consistent with a red sequenceof early-type galaxies. The CRS method is practically un-aected by projection eects for two reasons: the rst isthat as cluster ellipticals are the oldest stellar populationsin the universe, they are as red or redder than any othergalaxies at a given redshift. The second utilises the factthat, with properly chosen optical lters (straddling the4000Å break), the cluster red sequence has been shown to

be as red or redder than any other galaxies at a given red-shift and all lower redshifts - a fact which means the CRSmethod does not accumulate signicant foreground noise,with background contamination also being minimised asstructures at higher redshift will generally be most signi-cant at yet redder colours. Gladders & Yee (2000) also notethat a cluster's red sequence can be used as a remarkablyprecise redshift indicator, given a coherent enough popula-tion of early-type galaxies.

The consequences of the previous statements mean thatany clusters that were formed at the same point in cos-mic history (i.e. at the same redshift) should demonstratea unique red sequence, which means that a cluster and anypotential satellite clusters at approximately the same red-shift should show a very similar red sequence. This is themotivation for the photometric technique of satellite clusteridentication used in this section of the paper: by identify-ing the red sequence of a conrmed XXL cluster and reduc-ing the CFHTLS-W1 catalogue by making a restriction incolour corresponding to the cluster's red sequence, it shouldbe possible to identify surrounding structure, despite therebeing no direct redshift information available. Gladders &Yee (2000) states that the passively evolving, early-typegalaxies which make up the red sequence are present out toa redshift of at least 1.3, which means this method is validfor all clusters chosen for this investigation.

It was thought that the most rigorous way to create asubset of galaxies from the CFHTLS-W1 catalogue, fromwhich to attempt to identify a red sequence, would beachieved by calculating the virial radius of the XXL clus-ter in question and selecting all galaxies which fall withinthe angular region of sky corresponding to this radius. Forthe purposes of this investigation, it was assumed that thevirial radius can be approximated to the radius which cor-responds to an overdensity of 200 times the critical density,R200 (Kravtsov 2013). In order to calculate R200 of the XXLclusters, it was rst necessary to convert the given masses

of 17


(which are to an overdensity of 500,M500) to an overdensityof 200 (M200); the details of this conversion can be found inHu & Kravtsov (2003). Assuming the cluster is sphericallydistributed, the equation for the required radius,

R200 =

(3M200

800πρc

) 13

(4)

where is ρc is the critical density, can be derived.The angular separation on the sky corresponding to each

cluster's virial radius was then calculated given the clus-ter's redshift (Wright 2006), and from this is was possibleto create a subset of galaxies for each cluster which fallwithin the projected virial radius. The colour (rAB − iAB)against i-band magnitude (iAB) was plotted for each of thegalaxies in each subset, but attempts to identify any red se-quence in this data were futile: there was simply too muchnoise. This is due to the fact that selecting all the galax-ies within a projection of the virial radius on the sky willinclude huge numbers of foreground and background galax-ies, with largely dierent colours and magnitudes, whichwill pollute the true red sequence of the cluster. Progresswas made by utilising the earlier statement that, accordingto the morphology-density relation, the early-type galaxiesresponsible for the red sequence occupy the densest clus-ter region(s). Assuming the clusters we are investigatingare centrally concentrated, the early-type galaxies shouldinhabit the central core of the cluster. Using this informa-tion, a circular region corresponding to a projection of 30%of the virial radius of the cluster on the sky was insteadused to select the subset of galaxies from which attemptsto identify the the red sequence would be made, under theassumption that this would greatly increase the proportionof galaxies in each selection which are true cluster ellipti-cals.

This selection technique proved much more eective,with possible red sequences identied for 8 of the 11 clus-ters. To make a selection of galaxies using the identied redsequence, a cut of (rAB− iAB)RS±0.1 about the estimatedcentre of the red sequence was taken, and all galaxies out-side of this colour cut excluded. It was considered that thismethod of selection assumes a perfectly horizontal red se-quence, but this was deemed acceptable for two reasons.Firstly, in Gladders & Yee (2000) it is shown that the slopeof the red sequence for sequence colours of rAB− iAB < 1.5is very shallow and as all the clusters for which red se-quences were identied had sequence colours which fall be-low this value, a horizontal approximation was consideredvalid. The second is a comment on the quality of the data- because of the inevitable projection eects suered evenwith a reduced selection annulus, the red sequences still re-mained tricky to identify and any attempts to determinethe slope of the sequence were unsuccessful.

Fig. 4 shows the galaxies selected from within the pro-jection of 30% of the virial radius of cluster n0286. Note thata magnitude cut of iAB < 23 has been made to remove anyfaint background galaxies that are unlikely to be part ofthe cluster or its surrounding structure. The red sequencecan be identied with some condence as a line of higherdensity in the colour-magnitude plane, with a restrictionin colour containing the red sequence shown. Fig. 5 showsthis selection in context with the other galaxies containedin the 0.25deg2 area surrounding n0286. The nal selectionof galaxies made using a magnitude cut of iAB < 23 and

restriction in colour of 1.25 < rAB − iAB < 1.45 is shownand it is evident that this technique signicantly reducesthe population of galaxies being investigated.

19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8 RS selection Galaxies within 30% VR

r - i

i

Fig. 4. Galaxies from the CFHTLS-W1 catalogue selected fromwithin the projection of 30% of the virial radius of XXL clustern0286 on the sky, with a magnitude cut of iAB < 23 performed.Orange points show the selected red sequence, contained in acut of 1.25 < rAB − iAB < 1.45.

16 18 20 22 24 260.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2 0.25deg2 galaxies Galaxies in 30% VR RS members Colour/mag. cut

r - i

i

Fig. 5. Galaxies from the CFHTLS-W1 catalogue in a 0.25deg2

area around XXL cluster n0286. Dark grey points show a subsetof these galaxies in a selection with a magnitude restriction ofiAB < 23 and colour restriction of 1.25 < rAB−iAB < 1.45. Theselection of galaxies made from within the projection of 30% ofthe virial radius of n0286 on the sky, along with the identiedred sequence both shown in Fig. 4, are also displayed.

As mentioned, by making a cut in colour about a clus-ter's red sequence, it was hoped that it would be possible toisolate not only the population of early-type galaxies fromwithin the cluster, but also any populations of passivelyevolving ellipticals contained in the cores of nearby clusterstructures, as these must have formed at the same time asthe cluster's red sequence members.

of 17


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

0.0

0.5

1.0

1.5

2.0

1.2 1.4

0.0

0.5 0.25deg2 galaxies RS members Double colour/mag. cut

3.6

m -

4.5

m

r - i

Fig. 6. Galaxies from the CFHTLS-W1 catalogue in a 0.25deg2

area around XXL cluster n0286. Dark grey points show a subsetof these galaxies in a selection with a magnitude restriction ofiAB < 23 and a double restriction in colour of 1.25 < rAB −iAB < 1.45 and −0.2 < 3.6µmAB − 4.5µmAB < 0.2. The subsetof galaxies selected to be the cluster's red sequence is also shown.The area of interest is shown for clarity.

However, it is likely that a number of foreground andbackground eld galaxies, which happen to have colourswithin the relatively broad range of (rAB−iAB)RS±0.1, willenter the selection and pollute the data. To further isolategalaxies which are part of the cluster and any surroundingstructure, an additional cut in colour in the 3.6µm - 4.5µmband was made to isolate galaxies with a similar spectralenergy distribution as the red sequence members.

Fig. 6 shows how this selection was performed by plot-ting the colour of the identied red sequence galaxies in the3.6µm - 4.5µm band against the colour in the rAB − iABband and identifying any corresponding grouping in the for-mer; a range of 0.4 in the 3.6µm - 4.5µm band was used tomake a second restriction in colour. This range often didnot include all galaxies from the original selection, whichsuggests those galaxies are not truly part of the cluster'spopulation of early-type galaxies as the red sequence shouldbe a ubiquitous presence in all colour bands (Gladders &Yee 2000). The 0.4 cut was chosen as it was the range overwhich any obvious grouping in the 3.6µm - 4.5µm band ex-isted. Whilst this is a more generous restriction than theone used in the original red sequence selection, this wasdeemed necessary as identifying any sort of central valuefor the sequence in the second band was impossible withsuch a limited number of galaxies. As such, with a smallerband, it is possible that true sequence galaxies may be ex-cluded, reducing the quality of the data. It is clear from Fig.6 however, the eectiveness of the double colour restrictionin reducing the number of galaxies being investigated.

Applying this selection method to all clusters for whicha red sequence was identiable produced a subset of galax-ies within a 0.25deg2 area around each cluster which havea similar spectral energy distribution to those selected asearly-type galaxies from the XXL cluster. The advantagesof this selection are twofold for identifying satellite clusters:in the case of passively evolving galaxies such as these, they

were very likely to have formed at the same cosmic epochand therefore exist at the same redshift as the cluster and,as is the nature of galaxies of this morphological type, theyare likely to inhabit the central regions of nearby clusters.The validity of this method was supported by the fact that,for all clusters for which a red sequence was identiable, astrong overdensity in the number of galaxies in each selec-tion was present at the locations of the clusters in the XXLcatalogue, dened by their respective X-ray sources, sug-gesting that the restrictions imposed are in fact selectinggalaxies which are part of the cluster structure.

3.3. Combining spectroscopic and photometric cuts toidentify cluster systems

Fig. 7 shows how the combination of both subsets of galax-ies from the VIPERS (3.1) and CFHTLS-W1 (3.2) cata-logues can be combined to plot the number density of galax-ies as a two-dimensional histogram of the sky to identifyany clustering. Note that to avoid any double counts re-sulting from galaxies contained in both the CFHTLS-W1and VIPERS catalogues, a matching algorithm was usedto remove any duplicates. For the scale of clustering neces-sary to be gravitationally bound and considered a satellitecluster of its own volition, clustering in the subsets selectedusing both methods would likely be evident, and for thisreason combining the two selection methods is advanta-geous: any clustering found in both selections will show asa strong overdensity, whilst any clustering in an individualcatalogue not present in the other, which is therefore un-likely to correspond to a massive cluster, will not appear soevidently. It is worth noting that, as there is no direct red-shift information available for the CFHTLS-W1 catalogue,any clustering has been inferred by proxy and condencein its existence must be cautious. The combination of bothtechniques has the additional advantage that, should clus-tering in the VIPERS catalogue be present at a locationof clustering in the CFHTLS-W1 galaxies, this adds cre-dence to assumption that the clustering is present and atthe redshift of the XXL cluster being investigated.

As is to be expected, for all of the clusters for which ared sequence was identiable in the CFHTLS-W1 galaxiesand apparent structure selectable in the VIPERS catalogue,strong overdensities in the number of galaxies were presentat the locations of the clusters from the XXL catalogue.Fig. 8 shows the four of these clusters which also demon-strated overdensities in the number of galaxies on the skyin the proximity of, but separate from, the XXL clusterlocation following the selections made in accordance with3.1 and 3.2. These nearby overdensities are indicative ofclustering, but two questions need to be answered beforethey can be dened as bone de satellites of the four C1XXL clusters shown. The rst asks whether the overdensi-ties correspond to a true clustering of galaxies in space orwhether the grouping on the sky is a coincidental result ofthe galaxy selections made. The second asks whether thecharacteristics of the identied cluster are reasonable andin accordance with current theoretical understanding of thegrowth of clusters. Both of these questions are discussed indetail in subsequent subsections.

of 17


31.9 32.0 32.1 32.2 32.3 32.4

-4.7

-4.6

-4.5

-4.4

-4.3 CFHTLS-W1 galaxies VIPERS galaxies Cluster (n0286)

Dec

(Deg

)

RA (Deg)31.9 32.0 32.1 32.2 32.3 32.4

-4.7

-4.6

-4.5

-4.4

-4.3

RA (deg)

Dec

(deg

)

0

1

2

3

4

5

6

7

8

9

10Count

Fig. 7. Left: Distribution of galaxies on the sky in a 0.25deg2 area around class 1 XXL cluster, n0286 from the CFHTLS-W1and VIPERS catalogues following selections made according to 3.2 and 3.1 respectively. CFHTLS-W1 galaxies are subject to amagnitude restriction of iAB < 23 and a double restriction in colour of 1.25 < rAB−iAB < 1.45 and −0.2 < 3.6µmAB−4.5µmAB <0.2. The subset of VIPERS galaxies was constructed using a manual selection of structure. Right: Number density on the sky ofthe selected galaxies using a square bin of 0.025deg.

3.4. Identifying potential satellite cluster X-ray sources

As discussed earlier, self-similarity dictates that the satelliteclusters this report attempts to identify must be composedin structurally the same way as the massive XXL clustersin question. This means ∼15% of their mass must be con-tained in the hot, X-ray emitting intracluster medium. Aspreviously explained, likely clusters were conrmed fromthe XXL source catalog based on a lower limit exclusionin both source extension and extension likelihood and themost massive clusters in the redshift range we are investi-gating have source characteristics such that they are iden-tied as class 1 XXL clusters. Identifying clusters in thisway has its limitations however, as in order for a clustersource to be extended the cluster must not only have alarge physical size but also a signal well above ux limitfor the observations. With both radius and X-ray ux di-rectly correlated to the mass of the cluster, it is clear thatlower mass clusters - such as the satellites of massive clus-ters being searched for in this investigation - will unlikelydemonstrate X-ray signals good enough to be conrmed asclusters from X-ray observations alone. X-ray sources fromthe ICM of the most massive satellites should still be de-tectable though, and with the locations of potential satel-lites determined from the overdensities observed in 3.3, itshould be possible to identify any X-ray sources in the vicin-ity of these galactic overdensities with a view to estimatethe mass of the satellites from their X-ray ux.

By plotting the full XXL X-ray source catalogue inthe RA-Dec plane, it was possible to identify sources inthe vicinity of the potential satellites for three of the fourclusters around which strong galactic overdensities werepresent. For each cluster, a selection of any sources in, orvery close to, the identied potential satellites were taken.The extent of the selected sources in arcseconds was plot-ted against their respective extension likelihoods and thesources with properties most resembling clusters (those

with the greatest extent and extension likelihood) were se-lected as the most promising candidates for ICM signal.Fig. 9 shows the position of these sources relative to the C1and C2 XXL clusters, along with all the sources in the XXLcatalogue. In the case of the apparently diuse satellite nearcluster n0286, three potential sources were identied. It canbe suggested from inspection of Fig. 7 that the overdensitynear cluster n0286 can be split into at least two indepen-dent potential satellites. X-ray sources 1 and 2 are locatedin the vicinity of the upper overdensity, whilst source 3 islocated in the lower.

Assuming the sources are located the same distanceaway from Earth as the host cluster, the cluster redshiftfrom the XXL catalogue can be used to calculate the lu-minosity distance to the potential satellites (Wright 2006).From this the X-ray luminosity L500 can be calculated fromthe X-ray ux of the selected sources. Using equation (2) itis then possible to deduce the mass of the satellite clusterfrom which the source is assumed to originate. The calcu-lated masses M500 of the potential satellite X-ray sourcesidentied earlier are shown and discussed in 3.5.1.

3.5. Investigating the validity of potential cluster systems

Now that potential satellite clusters have been identiedfrom galactic overdensities and the masses of said clustersestimated from the ux of X-ray sources in their vicinity, itis important to check whether the systems discovered arephysically valid. Investigations using the Millennium Simu-lations were used to determine whether the mass and sepa-ration of the potential satellites is reasonable and to verifywhether the observed occurrence rates of massive satellitesare in line with simulated predictions, whilst a method ofmass estimation using stellar ux ratios was used as a self-consistency check to determine whether the X-ray sourcesare likely to originate from the assumed satellite clusters.

of 17


35.6 35.7 35.8 35.9 36.0

-4.6

-4.5

-4.4

-4.3

-4.2

Count

RA (deg)

Dec

(deg

)

0

2

4

6

8

10

12

14

16

18

d

z=0.6308; d ~ 6.23Mpc

35.4 35.5 35.6 35.7 35.8 35.9-5.2

-5.1

-5.0

-4.9

-4.8

-4.7Count

RA (deg)

Dec

(deg

)

0

1

2

3

4

5

6

7

d

z=0.8327; d ~ 5.04Mpc

31.9 32.0 32.1 32.2 32.3 32.4

-4.7

-4.6

-4.5

-4.4

-4.3

d

RA (deg)

Dec

(deg

)

0

1

2

3

4

5

6

7

8

9

10Countz=0.7556; d ~ 3.31Mpc

30.8 30.9 31.0 31.1 31.2

-5.2

-5.1

-5.0

-4.9

-4.8

Count

RA (deg)

Dec

(deg

)

0

1

2

3

4

5

6

7

8

9

d

z=0.5202; d ~ 4.60Mpc

Fig. 8. Number density on the sky of a selection of galaxies from the CFHTLS-W1 and VIPERS catalogue in a 0.25deg2 areaaround four selected XXL clusters, chosen using the techniques described in 3.1 and 3.2. Clockwise from top left, the XXLclusters shown are n0019, n0064, n0260, n0286. The locations of the X-ray sources from the XXL catalogue corresponding to eachcluster are circled in white and the distance d between each cluster and the nearest overdensity are shown for scale, with the valuenoted at the top left of each plot. A square bin of 0.025deg was used.

3.5.1. Mass and separation of satellites from the MillenniumSimulations

The Millennium I and Millennium II Simulations are N-body simulations which plot the movement and growth ofdark matter haloes at discrete redshift snapshots from theearly universe through to the present day (0 < z < 15).The masses of the clusters are inferred from their halo massand the history of each halo and its constituent parts arerecorded. To check whether the estimated satellite massesand the separations from their host cluster are reasonable,the ve nearest mass haloes at the nearest redshift snapshot(this was within zcluster ± 0.15 in all cases) were taken andthe mass and separation of the most massive satellite clusterrecorded. Tab. 1 summarises these results and compares

them to the observed mass and separation of the satellitesdetermined in previous sections.

In almost all cases does the estimated satellite mass fallwithin the predicted range and in cases where they do not,the observed characteristics are extremely close to those de-termined from the Millennium Simulations. In the case ofthe separations, all satellites fall well within the discoveredrange and within one standard deviation of the mean. Dueto the fact that only the ve nearest mass clusters weretaken from the simulations, the results shown here are byno means extensive enough to disregard the X-ray sourcesfor which the satellite mass does not fall within the deter-mined range; in the case of n0064, the estimated satellitemass is only slightly greater than the upper limit on therange from the simulations. Considering n0286, compari-son to the range deduced from the simulations must be

of 17


Table 1. Comparison of observationally determined satellite (sat.) masses and separations (sep.) with those determined from theMillennium Simulations. Potential satellite masses were estimated from the X-ray ux of sources assumed, but not conrmed, tohave originated from the satellite's ICM. For cluster n0286, the satellite masses from top to bottom were calculated from X-raysources 1, 2 and 3 respectively.

10-3

10-2

10-1

100

101

102

103

10-4 10-3 10-2 10-1 100 101 102 103 104

XXL sources C2 clusters C1 clusters

Satellite sources n0064 n0260 n02861

n02862

n02863

Extension Likelihood

Exte

nt (a

rcse

c)

Fig. 9. X-ray sources from the full XXL catalogue with sourcescorresponding to class 1 (blue) and class 2 (red) clusters indi-cated. A solid line at an extent of 15 arcseconds denes a lowerlimit for both cluster classes, with a solid line at an extensionlikelihood of 5 and dashed line at 33 establish the limits forC2 and C1 clusters respectively. X-ray sources located in thevicinity of the galactic overdensities corresponding to potentialsatellite clusters identied in 3.3 are shown.

cautious as we are certainly considering at least the secondmost massive satellite and potentially the third, depend-ing on whether the galactic overdensity corresponds to twoor three discrete satellites. Given more time, a mean andrange of characteristics for the second and third most mas-sive satellites of the Millennium Simulation clusters wouldalso be investigated and compared to those implied fromobservation.

3.5.2. Estimating the satellite mass from stellar ux

In general, redshift information is not readily available fromX-ray pointings alone, with optical follow-up often neededto determine the redshift of a cluster with any condence.Yu et al. (2011), among others, have investigated the pos-sibility of determining the redshift spectroscopically usingthe ubiquitous Fe-line complex in the X-ray spectrum ofa cluster's ICM signal. To reliably determine a redshift inthis manner, higher resolution and longer pointings thanare generally available are necessary. For this reason, noredshift information is available for the potential satellitesources discussed earlier, meaning it cannot be condentlyasserted that the signal truly originates from the ICM ofthe potential satellite. With the additional galaxy uxesin the 3.6µm and 4.5µm bands that the CFHTLS-W1 cat-alogue provides, the total galactic ux of the cluster andsatellite in each of the two bands can be determined. Es-kew et al. (2012) provide the following relation between thetotal 3.6µm and 4.5µm uxes in Jy (F3.6 and F4.5 respec-tively) and the total stellar mass of the cluster M∗,

M∗ = 105.65F 2.853.6 F−1.85

4.5

(D

0.05

)2

M (5)

where D is the luminosity distance to the cluster in Mpc.Given the quoted masses of the conrmed clusters from

the XXL catalogue and by assuming that the ratio of stel-lar mass to total mass of a cluster is constant, it is possibleto reach a mass estimate of the satellite based on galacticemission alone. By comparing this mass estimate with thatdeduced from the identied X-ray sources provides an ef-fective, albeit far from rigorous, consistency check for thevalidity of the calculated X-ray mass of the satellites: if theratio of the inferred X-ray mass to 3.6µm/4.5µm mass isfar from unity, this would suggest the satellite's ICM is notresponsible for the X-ray signal.

To determine the galaxies to include within the selectionfor the clusters and their satellites, it seemed most appro-

of 17


Table 2. Comparison of the satellite masses estimated from theX-ray ux of the XXL sources thought to originate in the satel-lite and the masses estimated from a calculation of their stellarmass based on their 3.6µm and 4.5µm ux - the ratio shown isbetween the latter and former mass estimates respectively. Forcluster n0286, the satellite masses from top to bottom corre-spond to X-ray sources 1, 2 and 3 respectively.

priate to use the virial radii. The virial radii of the satel-lites were calculated according to the method described in3.2 using the masses inferred from the potential satelliteX-ray sources; this again serves as an additional check forself-consistency. Using these calculated radii along with thevirial radii of the XXL clusters determined earlier, a se-lection of all the galaxies, already subject to the relevantphotometric cuts, inside the virial radius of each cluster andits satellites was made. In the case of the satellites, the po-sition of the X-ray source used to calculate its virial radiuswas used as the cluster centre. Following this, the total uxin both the 3.6µm and 4.5µm bands, calculated by summingthe individual ux from each of the galaxies, was used todetermine the stellar mass of the galaxies in the selectionfor each cluster and their satellites using equation (5). Anestimate of the total satellite mass, based on the satellite'sand its host cluster's stellar mass was then calculated usingthe ratio method described earlier.

Tab. 2 shows the resulting total mass estimates for thesatellites based on the X-ray ux of the sources thoughtto originate from the satellite's ICM and the stellar massratios independently, along with a ratio of these values forcomparison.

The fact that the resulting ratios do not fall close tounity appears unfortunate for the continued assumptionthat the satellites' ICM is responsible for the X-ray sourcesused to calculate an estimate for their mass. However, dueto the sheer number of points at which error on the massestimate based on the stellar mass can be accumulatedthroughout the calculations and conversions, a result of thismass estimate being ∼ 9% to ∼ 321% of the mass calcu-lated from the X-ray signal may actually be an encouragingresult. Again, this section of the investigation should nothope to conrm with any certainty that the X-ray sourcesselected do come from the satellite cluster, but instead iden-tify any sources for which the X-ray mass estimate and themass calculated from the 3.6µm and 4.5µm uxes dier bysuch an extreme amount that the source can be rejected; inthis case none of them appears too unreasonable to excludeat this point.

3.5.3. Expected observed satellite occurrence rates from theMillennium Simulations

The previous subsections have been useful in determiningwhether the properties of the potential satellite clustersdiscovered are reasonable. It is also of interest conrmingwhether the occurrence rate of massive clusters and theirsatellites detected is to be expected in the universe as it iscurrently understood. Again, the Millennium Simulationsprovide a unique opportunity to investigate the number ofthese massive clusters with satellite companions that areactually present in a universe modelled to represent ours.

Following the simulation of the growth of dark matterhaloes, twenty-four 1deg2 light cones representing a viewof the sky from redshift 0 were produced and individualgalaxies were `painted' onto each halo in each cone us-ing computer models of cluster structure. These provide aunique opportunity of exploring a simulated universe froma xed viewpoint, such as observations of the real universeare made from Earth.

For each of eight light cones chosen at random a redshiftrestriction of 0.5 < z < 0.9 was made and a subset of anygalaxies located in a containing cluster with a central virialmass of greater than 1014M was created. This limit waschosen as the massive clusters chosen from the XXL surveyaround which potential satellites were identied were of amass of this order of magnitude or greater. Once these mostmassive clusters were identied, a further subset of galaxieswith central virial mass greater than 1013M contained in a0.25deg2 square area of `sky' within a redshift cut of ±0.02about the cluster centre was taken. An area of this sizewas chosen as it corresponds directly to the area abouteach XXL cluster within which satellites were searched forwhilst this redshift range was selected as any identiablestructure from the spectroscopic selections made in 3.1was contained within this cut. A cuto mass of 1013Mwas used as this was the order of the lower limit on thecluster mass estimated from the X-ray sources thought tooriginate from the potential satellites. The RA-Dec planefor each subset was then plotted and the number of satelliteclusters around each > 1014M cluster were recorded.

Tab. 3 shows a summary of the results from the sampleof eight light cones. This part of the investigation enabledtwo important insights: rst a test of the rate of detection ofmassive clusters from the XXL survey and second a check ofwhether the number of satellites identied in this report isreasonable. On the rst count, a total of 36 clusters of mass> 1014M were identied, corresponding to a mean numberof 5 massive clusters per square degree, in the stated red-shift range of 0.5 < z < 0.9. Compare this to the 11 XXLclusters in the ∼8deg2 overlap with the VIPERS region andit is clear there is a discrepancy between the number pre-dicted by the simulations and what is actually observed.This suggests that the cluster catalogue produced by XXLis not extensive, even for the most massive end of the clus-ter population, for which their X-ray signal should be mosteasily classied. This also supports the assertion that thereare still many unclassied cluster signals in the XXL sourcecatalogue, which was the assumption used when selectingpotential satellite X-ray signals. On the question of the fre-quency of satellite systems, it quickly became apparent thatthe number of satellites per cluster in the simulations farexceeded that which we observed on the sky, with a meannumber of 5 satellites per cluster found across the eight

of 17


Table 3. The total and average number per square degree ofmassive (> 1014M) clusters from a sample of eight 1deg2 lightcones produced from the Millennium Simulations. The averagenumber of satellite (> 1013M) clusters observed in a 0.25deg2

area of `sky' about each massive cluster is also shown.

cones. With 1 conrmed (see 4.2) and 5 likely satellitesidentied around 4 of the 11 XXL clusters investigated, theresults from the simulations may seem irreconcilably dier-ent. However, when identifying potential satellites, only thegreatest overdensity around each XXL cluster was investi-gated. Looking back to Fig. 8, it is clear there is more thanone area of overdensity present in the vicinity of most of theclusters, each of which could correspond to an additionalsatellite cluster. This highlights an issue in the method andsuggests that it would advantageous to return to each of thechosen clusters and investigate these further overdensitiesin the same way as the potential satellites identied in orderto more eectively compare the rate of satellite occurrencewith observation. This does not, however, account for thefact that around every one of the 36 massive clusters in thesimulations was there at least one satellite. Of the clustersfor which it was possible to identify a red sequence and com-bine this selection with the VIPERS subset, of which therewere 6, 4 showed apparent satellites in their vicinity. Whilstthis rate is markedly lower than the simulations, with sucha small sample size of XXL clusters it is dicult to makeany further comment of whether the simulations and ob-servations truly contradict. Note this section includes thecount of the C2 (n0211) satellite found in the vicinity of C1cluster n0219, discussed in 4.2 for more accurate compar-ison between the observations and simulations.

4. Discussion

4.1. Sources of uncertainty and potential improvements

The nature of this project means that areas of potential er-ror incursion are numerous. With regard to the galaxy cat-alogues used, the area of sky surveyed is not continuous foreither catalogue, with the VIPERS region split into manydistinct rectangular regions with signicant gaps between.This means there are times when combining selections thatan area of interest falls in or near a gap in the VIPERSrange. The sampling rate for neither survey is complete,with the sampling rate of the VIPERS catalogue uctuat-ing around a redshift-variable value of ∼ 40% (Guzzo et al.2014). Both of these factors mean that the view of sky inves-tigated, whilst still very useful in the search for structure,is incomplete and as such there is the potential for unseensystems.

Despite this, the redshift information provided by theVIPERS catalogue is incredibly precise and provides oneof the most useful tools in the search for cluster sys-tems: it is not only possible to identify clustering in thethree-dimensional distribution of VIPERS galaxies, but to

conrm the presence of true galactic overdensities in theCFHTLS-W1 catalogue which are only inferred by selec-tion.

When making selections in the CFHTLS-W1 catalogueby locating the red sequence, a horizontal cut in colour wasmade. This was discussed earlier, with a comment made onthe diculty of identifying the red sequence, let alone itsslope, when any selection of cluster members was inherentlypolluted by eld galaxies. Gladders & Yee (2000) use theCRS (cluster red sequence) algorithm to identify the red se-quence computationally. It would be interesting to attemptthe identication of the red sequences of the XXL clustersinvestigated in this paper in the CFHTLS-W1 catalogueusing the CRS algorithm. If successful, it would provide amore rigorous method of identication and would allow se-lections to be made about the slope of the sequence, thoughthe ratio of sequence galaxies to eld galaxies in the clusterregion may prove problematic.

The nature of binning galaxies when combining theCFHTLS-W1 and VIPERS selections means that, shoulda satellite cluster straddle the border between two or morebins, it will appear less overdense than if the cluster werecentral in a bin, meaning the potential for missed identi-cation of true satellites was present. Another issue facedwas the fact that x-y binning has the eect of smoothing thedata along those principal axes. This means that identifyingwhether larger satellites are truly extended or in fact multi-ple discrete clusters and locating any lamentary structureis inherently dicult. The eect of this was minimised byplotting the number density of galaxies using a variety ofbin sizes and identifying overdensities in each case.

When attempting to identify X-ray sources originatingfrom the potential satellites, the obvious issue is that with-out any redshift information about the source, there is noway of knowing whether it is truly the signal from the clus-ter's ICM or a chance projection along the line of sight. Themasses estimated from the sources seem encouraging, butthe majority of the sources in the region of sky investigatedare in an X-ray ux range that would produce a reason-able estimated cluster mass using equation 2. For this rea-son, calculating an estimate for the mass is more useful inidentifying sources which are obviously too bright to orig-inate from a cluster and can therefore be excluded. How-ever, when considering the position of the potential satellitesources in the extent-extension likelihood plane (see Fig. 9),their proximity to the conrmation threshold, especially inthe case of the three sources identied for n0286, suggeststhey are extended sources and is further evidence in sup-port of the assumption they are cluster signals. It is worthnoting however, the uncertainty in X-ray-based cluster de-tection; with such a wide variety of X-ray sources in theuniverse, many of which displaying emission similar to thatof a cluster, conrmation through other detection methodsis often required to classify a cluster with condence. TheXXL sources identied as class 2 clusters have a ∼50% pos-sibility of in fact originating from an AGN (Pierre & XXLConsortium 2014).

The ability to compare the characteristics of the po-tential satellites with the properties of similar cluster sys-tems from the Millennium Simulations is advantageous, butthe small sample size means that excluding any anomaloussystems would only have been possible should the satellitemass estimate and/or separation from its massive compan-ion have fallen well outside the range recorded from the sim-

of 17


ulations; in the case of all systems investigated, the proper-ties of the potential satellites fall in or very near this rangeand are therefore deemed reasonable. Given more time, amore extensive list of similar systems from the simulationswould have been created such that any anomalous observa-tions could be more easily identied.

Estimating the satellite mass using the mass ratios cal-culated from the stellar ux was intended to provide a usefulself-consistency check for the selected potential satellite X-ray sources and whilst, again, it allows the identication ofany sources which are obviously too bright, inherent awsin the method mean that error is inccured at almost everystep. As mentioned, the sampling rate for the CFHTLS-W1catalogue is not complete, and further to this, only galaxiesfor which 3.6 and 4.5 micron uxes are recorded were avail-able. In the case of the ratio method used, this will onlyleave the satellite mass estimate unaected if the ratio ofgalaxies for which 3.6/4.5 micron data is available to thetotal number of galaxies is identical for the satellite and itsmassive companion: an assumption which will inevitablyincur a varying amount of error for each of the identiedsystems. The same is true when considering the photomet-ric restrictions made in 3.1: the ratio is only consistentprovided the proportion of the number and ux of galax-ies selected between the satellite and conrmed cluster isindicative of the true ratio of these quantities. The eectof background counts of eld galaxies projected along theline of sight when selecting cluster members was also ne-glected, which will cause an over-estimation of the satellitemass. It would be more rigorous to determine and subtractan average background ux from the total stellar ux ofthe clusters before calculating their mass. However, withthe other sources of error incurred and the relatively lowbackground galaxy count, this will be of negligible eect.

When determining the number of massive clusters andcompanion satellites from the Millennium Simulation lightcones, deciding clusters to include in each count posed an is-sue. When using the simulations the information about eachgalaxy's containing structure, and the mass of the clusterof which it is a member, is readily available; this is evi-dently not the case for real observations. For this reason,only satellites in the simulations with galaxy densities inexcess of around ve per square arcminute were counted,corresponding to the lower limit of the bin density seen forthe potential satellites identied. Despite this, this makesno correction for the fact that the Millennium Simulationsare an extensive galaxy population, not subject to any ofthe survey sampling rates or selections made from the cata-logues in this investigation. This goes some way to explain-ing the increased number of massive clusters with compan-ion satellites recorded from the simulations. This nal partof the investigation would be improved by making appro-priate corrections for the selection eects intrinsic of realobservations.

4.2. Conrming potential satellites and a comment onmethod

This investigation aimed to identify satellite clusters ofmore massive, X-ray detected clusters; has this aim beenfullled? The project combined many techniques for dis-covering satellites and determining the validity of the po-tential cluster systems identied, none of which alone isenough to conrm the presence of the satellites discovered.

Many of the satellite properties determined are also subjectto large potential error or operate under bold assumptionand are therefore of use only to exclude obviously anoma-lous systems. However, with all the information providedby these techniques, it can be stated that no single piece ofevidence contradicts the claim that 5 satellite clusters havebeen discovered around 3 conrmed XXL clusters, and thecombination of all of the determined properties and com-parison with simulated expectations alludes to the true ex-istence of the potential systems identied. This is especiallytrue for cluster n0286, whose three identied satellites allhave potential X-ray sources with extent above and exten-sion likelihood very close to the XXL cluster conrmationthreshold. In order to conrm with any certainty the pres-ence of these satellites, longer X-ray pointings or follow-upobservations to determine the velocity dispersions of themember galaxies are required.

A nal comment on the method of galaxy selection isprovided by the cluster system in Fig. 10. The subset ofCFHTLS-W1 galaxies shown was selected as usual by iden-tifying the red sequence of the class 1 XXL cluster n0219,which has a mass of M500 = 12.8× 1013M located at red-shift z = 0.6265. When the corresponding double colourcut was made, a strong overdensity at the location of class2 XXL cluster n0211, with a mass ofM500 = 7.56×1013Mat redshift z = 0.6090, a distance of ∼ 6.44Mpc from n0219was identied. A selection of VIPERS galaxies in redshiftwas made with a slightly larger range to encompass bothclusters and their likely surrounding structure, with strongoverdensities apparent at the positions of the two clustersalso. Returning to the Millennium Simulations, identifyingthe ve nearest mass haloes to that of n0219 and recordingthe mass and separation of the most massive satellite, thecluster system shown in Fig. 10 is of reasonable propertiesto suggest that the two clusters will eventually undergo amerger. At the very least, it can be said that this system isexactly of the type this investigation has been attemptingto identify. This supports the fact that the satellite systemsbeing searched for do exist and that it is the technical lim-itations of the observations that restrict their discovery -cluster n0211 happens to have source characteristics suchthat it can be identied from the X-ray signal of its ICMalone. More encouragingly though, it also supports the va-lidity of the red sequence method, not only to identify thecluster itself, but also any surrounding satellites formed atthe same cosmic epoch.

4.3. Future

With such a limited area of sky as was available for thisinvestigation, attempting any sort of statistics regardingoccurrence rates and characteristic properties of satellitesystems is dicult: only 11 XXL clusters in the redshiftrange were examined and of these only 3 (4 includingn0219) show evidence of likely companion satellites. Theextended ROentgen Survey with an Imaging Telescope Ar-ray (eROSITA) is a revolutionary new observatory due tolaunch in 2016, designed to probe the entire X-ray sky withunprecedented spectral and angular resolution out to red-shifts z > 1: mapping in the soft band (0.5-2keV) will betwenty times more sensitive than the ROSAT all-sky surveywhilst in the hard band (2-10keV) it will provide the rstever true imaging survey of the sky at that energy (Merloniet al. 2012). The mission has many goals, most relevant of

of 17


37.0 37.1 37.2 37.3 37.4 37.5

-4.9

-4.8

-4.7

-4.6

-4.5

Count

RA (deg)

Dec

(deg

)

0

2

4

6

8

10

12

14

16z1=0.6265, z2=0.6090; d ~ 6.44Mpc

d

Fig. 10. Number density on the sky of a selection of galaxiesfrom the CFHTLS-W1 and VIPERS catalogues in a 0.25deg2

area around around XXL clusters n0219 (class 1; left) and n0211(class 2; right). The selections were made according to 3.1 and3.2 using n0219 as the reference cluster. The locations of theX-ray sources from the XXL catalogue corresponding to eachcluster are circled in white and the distance d between the twoclusters is shown for scale, corresponding to a physical separa-tion of ∼ 6.44Mpc. A square bin of 0.025deg was used.

which is the predicted identication of ∼ 105 new galaxyclusters.

The all-sky nature of eROSITA's planned survey hasmany distinct advantages. With the entire sky surveyed toa depth comparable to XXL, the geometry of large-scalestructure in the universe will be accurately determined andwith the predicted discovery of so many new clusters, pro-ducing rigorous statistics about the distribution of matterand its containing systems will, for the rst time, become apossible reality. With over 40,000deg2 of sky mapped (com-pared to the ∼ 8deg2of this investigation), eROSITA willalso nd intrinsically rare objects. With its improved reso-lution, eROSITA will also be able to better identify clustersignals from the population of AGN and other X-ray sourcesin the universe. For these reasons, eROSITA will allow therst real possibility of comparing the large-scale distribu-tion of matter in the universe with modelled predictionssuch as those provided by the Millennium Simulations.

eROSITA should not only detect many systems like thatof n0219/n0211 shown in Fig. 10, but also clusters whosesatellites currently fall below the detection threshold of cur-rent observations. This will allow some insight into the dis-tribution of mass around larger clusters and also allow cal-culations of the percentage of mass contained in observablecluster satellites to be made. The method of satellite iden-tication developed in this investigation will not be maderedundant however, as utilising a combination of techniquessuch as in this paper will prove valuable in situations whena single observational technique is insucient to conrmthe presence of a cluster. However, it is a time-consumingmethod which requires good coverage in both optical pho-tometric and spectroscopic galaxy, and deep eld X-ray ob-servations. With minor improvements made according to

the issues identied, the techniques described in this papershould still provide an eective means of satellite clusteridentication when X-ray observations alone are insucientto conrm their existence, but in the case of combining itwith data from the eROSITA observatory, it will likely haveto be restricted to points of interest as applying this tech-nique to the whole sky is not practically valid.

5. Summary

The project utilised a sample of 11 clusters from the XMM-XXL cluster survey in the redshift range 0.5 < z < 0.9found in the overlap region of the VIPERS and CFHTLS-W1 galaxy catalogues. Using the spectroscopic redshift in-formation of the VIPERS catalogue and photometric dataof the CFHTLS-W1 catalogue to create a subset of galaxiesabout each cluster likely to be part of the conrmed clusteror any surrounding undetected clusters, potential satelliteswere identied by looking for overdensities in the numberof galaxies when combining these selections. Sources fromthe full XXL catalogue thought to originate from any satel-lites were selected and mass estimates calculated based ontheir X-ray ux. The validity of any identied systems wasthen investigated through comparison with similar systemsfrom the Millennium Simulations and an additional massestimate calculated based on the stellar ux of each satel-lite and its more massive companion - the latter also actingas a check of self-consistency of the satellites' potential X-ray sources. Finally, using light cones from the MillenniumSimulations the occurrence rate of cluster systems detectedwith apparent satellites and the number of these associatedsatellites around each cluster was compared to expectedrates predicted by the computer models.

In total, 5 potential satellites around 3 of the XXL clus-ters in addition to a C2 satellite of a more massive C1cluster were identied, all of which have masses and sep-arations from their companion cluster deemed reasonablefollowing comparison with the simulations. The masses es-timated from the stellar ux were subject to large errorsand as such provided little use other than to identify anyextremely anomalous properties, of which there appeared tobe none. Finally, the rate of clusters with companion satel-lites and the number of satellites per cluster both appearedmuch greater in the simulations than real observations -this was attributed to the incomplete sampling rate of thegalaxy surveys used, the diuse nature of satellites in thesimulation and selection eects intrinsic of the techniquesemployed. Follow-up observations would be required to con-rm the presence of the potential satellites, as this was notpossible with the information gathered in this investigationalone; though no single piece of evidence suggests the satel-lite candidates found are not true clusters.

Little rigorous statistical insight has been possible withsuch a small sample size, however the launch of the all-skyeROSITA X-ray observatory should provide a more thansucient population of galaxy clusters to investigate andallow truly eective comparison between simulation andobservation.

Acknowledgements. I would like to thank my partner, J. IderChitham, for his continuous input to the project, along with ProfM. Bremer, Dr B. Maughan, Miss K. Husband and Dr M. Taylor forguidance throughout the duration of the investigation.

of 17


References

Abell, G. O. 1958, Astrophys. J. Suppl. Ser., 3, 211Abell, G. O., Corwin, Harold G., J., & Olowin, R. P. 1989, Astrophys.

J. Suppl. Ser., 70, 1Abraham, R. G., Valdes, F., Yee, H. K. C., & van den Bergh, S. 1994,

Astrophys. J., 432, 75Allen, S. W., Schmidt, R. W., & Fabian, A. C. 2002, Mon. Not. R.

Astron. Soc., 334, L11Balogh, M. L., Christlein, D., Zabludo, A. I., & Zaritsky, D. 2001,

Astrophys. J., 557, 117Barger, A. J., Aragon-Salamanca, A., Smail, I., et al. 1998, Astrophys.

J., 501, 522Bartelmann, M. & Schneider, P. 1999 [arXiv:9912508]Birkinshaw, M. 1991, Phys. Cosmol.Birkinshaw, M. 1999, Phys. Rep., 310, 97Bower, R., Lucey, J., & Ellis, R. 1992, Mon. Not. R. Astron. Soc., 254Boylan-Kolchin, M., Springel, V., White, S. D. M., Jenkins, A., &

Lemson, G. 2009, Mon. Not. R. Astron. Soc., 398, 1150Carlstrom, J. E., Ade, P. A. R., Aird, K. A., et al. 2009

[arXiv:0907.4445]Carlstrom, J. E., Joy, M. K., Grego, L., et al. 2000, Phys. Scr., T85,

148Chwolson, O. 1924, Astron. Nachrichten, 221Clerc, N., Adami, C., Lieu, M., et al. 2014, Mon. Not. R. Astron. Soc.,

21, 1Czakon, N., Donahue, M., Medezinski, E., CLASH, & Bolocam. 2014,

Am. Astron. Soc.De Lucia, G. & Blaizot, J. 2007, Mon. Not. R. Astron. Soc., 375, 2Dressler, A., Oemler, Â Augustus, J., Couch, W., et al. 1997, Astro-

phys. J., 490, 577Einstein, A. 1936, Science, 84, 506Eskew, M. R., Zaritsky, D. F., & Meidt, S. E. 2012, Astron. J., 143,

139Fabricant, D., Lecar, M., & Gorenstein, P. 1980, Astrophys. J., 241,

552Fakhouri, O., Ma, C.-P., & Boylan-Kolchin, M. 2010, Mon. Not. R.

Astron. Soc., 406, 2267Fowler, J. W., Niemack, M. D., Dicker, S. R., et al. 2007, Appl. Opt.,

46, 3444Garilli, B., Guzzo, L., Scodeggio, M., et al. 2014, Astron. Astrophys.,

562, A23Giodini, S., Lovisari, L., Pointecouteau, E., et al. 2013, Space Sci.

Rev., 177, 247Gladders, M. D., Lopez-Cruz, O., Yee, H. K. C., & Kodama, T. 1998,

Astrophys. J., 501, 571Gladders, M. D. & Yee, H. K. C. 2000, Astron. J., 120, 2148Guzzo, L., Scodeggio, M., Garilli, B., et al. 2014, Astron. Astrophys.,

566, A108Hagino, K., Stawarz, L., Siemiginowska, A., et al. 2015, eprint

arXiv:1503.07244Herschel, W. 1785, Philos. Trans. R. Soc. London, 75, 213Hu, W. & Kravtsov, A. V. 2003, Astrophys. J., 584, 702Hudelot, P., Cuillandre, J.-C., Withington, K., et al. 2012, VizieR

On-line Data Cat. II/317. Orig. Publ. 2012yCat.2317....0HKato, Y., Nakazawa, K., Gu, L., et al. 2015, eprint arXiv:1504.02708Kravtsov, A. V. 2013, Astrophys. J., 764, 5Laporte, C. F. P., White, S. D. M., Naab, T., & Gao, L. 2013, Mon.

Not. R. Astron. Soc., 435, 901Lidman, C., Iacobuta, G., Bauer, A. E., et al. 2013, Mon. Not. R.

Astron. Soc., 433, 825Mather, J. C., Cheng, E. S., Eplee, R. E., J., et al. 1990, Astrophys.

J., 354, L37McBride, J., Fakhouri, O., & Ma, C.-P. 2009, Mon. Not. R. Astron.

Soc., 398, 1858Mehrtens, N., Romer, A. K., Hilton, M., et al. 2012, Mon. Not. R.

Astron. Soc., 423, 1024Menanteau, F., González, J., Juin, J.-B., et al. 2010, Astrophys. J.,

723, 1523Merloni, A., Predehl, P., Becker, W., et al. 2012, eprint

arXiv:1209.3114, 84Messier, C. 1781, Connoissance des Temps 1784, 227Mitchell, R., Culhane, J., Davison, P., & Ives, J. 1976, Mon. Not. R.

Astron. Soc., 175Mo, H., van den Bosch, F., & White, S. 2010, Galaxy Formation and

Evolution (Cambridge: Cambridge University Press)Navarro, J., Frenk, C., White, S., et al. 1997, Astrophys. J., 490, 493Neumann, D. M. & Arnaud, M. 2001, Astron. Astrophys., 373, L33Pacaud, F., Pierre, M., Refregier, A., et al. 2006, Mon. Not. R. Astron.

Soc., 372, 578

Pierre, M., Pacaud, F., Juin, J. B., et al. 2011, Mon. Not. R. Astron.Soc., 414, 1732

Pierre, M. & XXL Consortium. 2014, X-ray Universe 2014Piaretti, R., Arnaud, M., Pratt, G. W., Pointecouteau, E., & Melin,

J.-B. B. 2010, Astron. Astrophys., 534, 17Planck Collaboration. 2013, eprint arXiv:1303.5089, 42Press, W. H. & Schechter, P. 1974, Astrophys. J., 187, 425Reichardt, C. L., Stalder, B., Bleem, L. E., et al. 2012, 22Sandage, A., Binggeli, B., & Tammann, G. A. 1985, Astron. J., 90,

1759Sarazin, C. L. 1988, X-ray emission from clusters of galaxies (Cam-

bridge: Cambridge Astrophysics Series, Cambridge UniversityPress)

Schade, D., Barrientos, L. F., & López-Cruz, O. 1997, Astrophys. J.,477, L17

Schechter, P. 1976, Astrophys. J., 203, 297Springel, V., White, S. D. M., Jenkins, A., et al. 2005, Nature, 435,

629Storm, E., Jeltema, T. E., & Rudnick, L. 2015, Mon. Not. R. Astron.

Soc., 448, 2495Sunyaev, R. A. & Zel'dovich, Y. B. 1970, Astrophys. Space Sci., 7Sunyaev, R. A. & Zel'dovich, Y. B. 1972, Comments Astrophys. Sp.

Phys., 4Tauber, J. A., Mandolesi, N., Puget, J.-L., et al. 2010, Astron. Astro-

phys., 520, A1van Dokkum, P. G., Franx, M., Kelson, D. D., & Illingworth, G. D.

1998, Astrophys. J., 504, L17Vanderlinde, K., Crawford, T. M., de Haan, T., et al. 2010, Astrophys.

J., 722, 19Voit, G. 2005, Rev. Mod. Phys., 77, 207Weymann, R. 1965, Phys. Fluids, 8, 2112Weymann, R. 1966, Astrophys. J., 145, 560Wright, E. 2006, Publ. Astron. Soc. Pacic, 118, 1711Yu, H., Tozzi, P., Borgani, S., Rosati, P., & Zhu, Z.-H. 2011, Astron.

Astrophys., 529, A65Zhang, B., David, L., Jones, C., et al. 2015, eprint arXiv:1503.07694Zwicky, F. 1933, Helv. Phys. Acta, 6, 110Zwicky, F. 1937, Astrophys. J., 86, 217

of 17

tw1979_final_report_ref_correct

Documents

xxl clusters

rate of clusters

conrmed clusters

true clusters

clusters cosmology

companion satellites

number of satellites

apparent satellites