X-ray versus infrared selection of distant galaxy clusters: A case study using the XMM-LSS and SpARCS cluster samples
J. P. Willis, M. E. Ramos-Ceja, A. Muzzin, F. Pacaud, H. K. C. Yee, G. Wilson
MMon. Not. R. Astron. Soc. , 1–22 (2002) Printed 19 April 2018 (MN L A TEX style file v2.2)
X-ray versus infrared selection of distant galaxy clusters: Acase study using the XMM-LSS and SpARCS clustersamples
J. P. Willis (cid:63) , M. E. Ramos-Ceja , A. Muzzin , F. Pacaud , H. K. C. Yee , G. Wilson Department of Physics and Astronomy, University of Victoria, 3800 Finnerty Road, Victoria, BC, V8P 5C2, Canada Argelander-Institut f¨ur Astronomie (AIfA), Universit¨at Bonn, Auf dem H¨ugel 71. D-53121 Bonn, Germany Department of Physics and Astronomy, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3 Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario M5S 3H4, Canada Department of Physics and Astronomy, University of California-Riverside, 900 University Avenue, Riverside, CA 92521, USA
Accepted 2018 April 13. Received 2018 April 13; in original form 2017 June 2
ABSTRACT
We present a comparison of two samples of z > . Key words:
X-rays: galaxies: clusters.
A galaxy cluster is a massive physical structure dominatedby a dark matter halo, an intra-cluster medium (ICM) con-sisting of a hot atmosphere of baryonic gas, and a popu-lation of member galaxies. Furthermore, each of the abovemass components is in approximate virial equilibrium withthe total gravitational potential.Galaxy clusters represent the most massive structuresin the Universe to have achieved this state at the presentepoch – with the most extreme examples of such clusters pre-senting virial masses in excess of 10 M (cid:12) (McDonald et al. (cid:63) E-mail: [email protected] (JPW)
M/M (cid:12) = 13 . −
14 (e.g. Sarazin 1986).Galaxy clusters are identified by various observationaltechniques: overdensity searches identify the statistical ex-cess of projected cluster member galaxies in relation to the c (cid:13) a r X i v : . [ a s t r o - ph . C O ] A p r J. P. Willis et al. “background” of non-cluster galaxies along the line-of-sight(e.g. Postman et al. 1996; Gladders & Yee 2000; Rykoff et al.2014); X-ray searches identify the integrated emission fromoptically thin bremsstrahlung emission arising from the hotICM (e.g. Gioia et al. 1990; B¨ohringer et al. 2001; Clercet al. 2012); Weak lensing searches identify the integratedshear signal introduced into the shapes of background galax-ies by the effect of the cluster mass on local spacetime (e.g.Miyazaki et al. 2002; Wittman et al. 2006; Gavazzi & Soucail2007); and Sunyaev-Zeld’ovich (SZ) searches identify the ap-parent decrement in the brightness of the cosmic microwavebackground (CMB) caused by the inverse Compton scatter-ing of CMB photons by energetic electrons in the ICM (e.g.Staniszewski et al. 2009; Marriage et al. 2011; Reichardtet al. 2013).Each of these observational techniques is sensitive toa distinct physical component of galaxy clusters: Overden-sity searches are sensitive to the integrated star formationhistory of the cluster; X-ray searches to the projection ofthe square of the free electron density in the ICM (with aweak dependence upon the ICM temperature); Weak lensingsearches to the total projected cluster mass; and SZ searchesto the thermal pressure of the free ICM electrons (with smallrelativistic corrections for the hottest systems).The question which concerns this paper is how do thephysical properties of cluster samples differ depending uponthe observational technique used to identify them? Suchknowledge is important because it a) permits a consistentcomparison between results generated for different clustersamples (e.g. Gilbank et al. 2004; Barkhouse et al. 2006;Rozo & Rykoff 2014; Rossetti et al. 2017) and b) provides ameans to relate the results generated for a particular clustersample to the “true” cluster population (e.g. Borgani et al.2001; Mantz et al. 2008; Rozo et al. 2010; Planck Collabo-ration et al. 2014; Jimeno et al. 2017).At redshifts z < . z <
1. Once again, Donahue et al. noted that the relative fractionof optical clusters lacking an X-ray counterpart could beexplained by a steep scaling relationship between X-ray andoptical cluster luminosity, i.e. L X ∝ L − opt . In addition, both studies concluded that the majority of the X-ray clusterslacking an optical counterpart could be attributed to themaximum and minimum effective redshift limitations of theoptical cluster selection criteria.This paper is motivated by the interest in applying asimilar comparison to samples of distant galaxy clusters,in this case compiled using data at X-ray and mid-infrared(MIR) wavelengths. This motivation is in part due to the in-creased potential for cluster-scale astrophysics to influencethe observed properties of such clusters and their galaxypopulations, e.g. recent star formation (Bayliss et al. 2014;Hayashi et al. 2011; Brodwin et al. 2013; Nantais et al. 2016,2017), mergers (Nastasi et al. 2011; Lotz et al. 2013), or AGNactivity (Galametz et al. 2009; Martini et al. 2013; Ehlertet al. 2015; Alberts et al. 2016). However, because such dis-tant clusters are typically identified at low significance insurvey quality data (and thus might be prone to consider-able scattering effects on mass-observable relations) we donot compare cluster catalogues compiled at different wave-bands via their scaling relations. Instead we apply multipletechniques to determine the extent to which each sampleexhibits different physical properties and relate those prop-erties to cluster evolutionary state (e.g. star formation andmerger histories).The structure of the paper is as follows: In Section 2 wedescribe each distant cluster sample. In Section 3 we describethe available data common to each sample and in Section 4we use this data to measure fixed aperture brightness valuesof individual clusters. We present the results of this anal-ysis in Section 5 and draw appropriate conclusions in Sec-tion 6. Where necessary we assume a Friedmann-Lemˆaitre-Robertson-Walker cosmological model described by the pa-rameters Ω M = 0 .
3, Ω Λ = 0 . H = 70kms − Mpc − . The distant X-ray selected galaxy clusters studied in this pa-per are taken from Willis et al. (2013). This paper presenteda sample of 20 galaxy clusters at z > . detectionlikelihood > , extensionlikelihood > , extension > (cid:48)(cid:48) and as C2if they satisfied extensionlikelihood > , extension > (cid:48)(cid:48) (see Pacaud et al. 2006 for further details). In addition,sources were classified as distant clusters if they either pos-sess a known spectroscopic redshift z > . z < .
8. Ten band photometry ( ugrizY JK [3 . µ m][4 . µ m])for these latter systems was employed to derive photomet-ric redshifts for bright galaxies deemed to be associatedwith each extended X-ray source. Candidate clusters wereretained in the distant sample if they displayed an over-density of galaxies consistent with a single location in pho-tometric redshift space at z phot > .
8. Of these 20 clus-ters, 18 lie within the common footprint of the XMM-LSS/SWIRE/CFHTLS-W1 surveys and were retained foranalysis. c (cid:13)000
8. Of these 20 clus-ters, 18 lie within the common footprint of the XMM-LSS/SWIRE/CFHTLS-W1 surveys and were retained foranalysis. c (cid:13)000 , 1–22 -ray vs. IR selection of distant galaxy clusters The MIR selected distant clusters studied in this paper aretaken from the Spitzer Adaptation of the Red SequenceCluster survey (SpARCS; Muzzin et al. 2009; Wilson et al.2009). Candidate clusters are identified with significant over-densities in the multiple dimensional space defined by skyposition, z (cid:48) − . µ m colour, and 3.6 µ m brightness. Two cen-troid estimates are provided for each cluster: the first is thesky position of the brightest cluster galaxy (BCG) deter-mined from its location on the cluster red sequence. Thesecond estimate is referred to as the barycentre position andis based upon the mean sky position of all candidate clustermembers identified by the red sequence method. We employboth centroid measures in this paper and comment explicitlyon how each produces different results. Finally, in additionto the candidate cluster sky position, we also retain the clus-ter photometric redshift estimate based upon the location ofthe cluster red sequence in z (cid:48) − . µ m colour.The SpARCS catalogue located within SWIRE fieldcontains 218 candidate galaxy clusters within the redshiftinterval 0 . < z < .
7. These correspond to clusters satisfy-ing a richness cut of N red >
6, where N red is the number ofbackground-subtracted red-sequence galaxies brighter than M ∗ ( z ) + 1. The value of M ∗ ( z ) is computed from a pas-sive stellar population evolution model formed at z f = 4(Muzzin et al. 2008). Red-sequence galaxies are defined asthose within ± .
15 magnitudes of the best-fitting z (cid:48) − . N red > z > . z < . ∼
15% at z ∼ z > . (cid:48) of each other on the sky this isnot a significant issue. However, in these cases we applieda selection to the SpARCS catalogue to accept the clustergenerating the higher signal-to-noise ratio (SNR) detectionalong the line of sight. These considerations resulted in asample of 92 clusters for analysis. An initial means of assessing the commonality of objectsappearing in each sample is to match the catalogue posi-tions using a fixed tolerance (e.g. Oguri et al. 2017). Weperformed such a test using a tolerance of 60 (cid:48)(cid:48) (having con- firmed that this arbitrary threshold does not exclude clustersclose to, yet exceeding, this value). The results of the match-ing procedure are summarised in Table 1 and indicate that11/12 XMM-LSS clusters at 0 . < z < . z > . . < z < . z = 1 . z > . z > . (cid:48)(cid:48) to a source in the full XMM-LSScatalogue, rising to 50/92 within a 60 (cid:48)(cid:48) matching radius. Themajority of X-ray sources contributing to these matches arelow-SNR sources of marginally significant extent (C3) in ad-dition to low-SNR point sources (which include unresolvedextended sources). However, if we restrict the matching anal-ysis solely to 12 X-ray bright SpARCS clusters (see Section5.1 for details of X-ray aperture flux measurement), whereone would expect a match to the X-ray source catalogue tooccur, we find 6/12 and 11/12 matches within 30 and 60 (cid:48)(cid:48) respectively. Of these, 3 and 4 respectively are associatedwith C1 or C2 sources.Relaxing the restriction on morphological type of X-ray source to which the SpARCS clusters are matched gen-erates a larger fraction of matched objects. This indicatesthat X-ray sources classified as C1 or C2 within the XMM-LSS survey form a restricted subset of a larger population ofgravitationally-bound structures as traced by the SpARCS z > . z > . c (cid:13) , 1–22 J. P. Willis et al.
Table 1.
Matching results between the XMM-LSS and SpARCS z > . (cid:48)(cid:48) tolerance. Where N red (cid:54)
6, this indicates a match obtained with a cluster lying below the richness cut appliedto the SpARCS sample used for analysis in this paper. The X-ray mass values correspond to M c are taken from Willis et al. (2013)and are computed by applying appropriate scaling relations to the measured X-ray flux and redshift. As discussed in Willis et al. (2013)such mass estimates vary considerably with the assumed scaling relation model and should be take as indicative, as opposed to exact,values.ID Cluster name XLSSC Class Spec. XMM-LSS SpARCS Match N red X-ray massconfirmed redshift z phot ( × M (cid:12) )01 XLSS J022400.4-032529 32 C2 Y 0.803 0.98 BC 11.5 1 . +0 . − .
02 XLSS J022233.8-045803 66 C2 Y 0.833 0.92 BC 8.5 1 . +0 . − .
03 XLSSU J021832.0-050105 64 C2 Y 0.875 0.98 BC 16.5 1 . +0 . − .
04 XLSSU J021524.1-034332 67 C1 Y 1.003 1.08 BC 15.8 2 . +0 . − .
05 XLSS J022253.6-032828 48 C1 Y 1.005 1.13 BC 6.1 1 . +0 . − .
07 XLSS J022404.1-041330 29 C1 Y 1.050 1.10 BC 11.9 2 . +0 . − .
08 XLSS J022709.2-041800 5 C1 Y 1.053 1.18 ∗ BC 10.3 1 . +0 . − .
09 XLSS J022303.3-043621 46 C2 Y 1.213 1.4 ∗ BC 9.2 0 . +0 . − .
12 XLSSU J021547.7-045027 78 C1 Y 0.953 1.06 BC 4.8 1 . +0 . − .
13 XLSSU J021859.5-034608 C2 Y 0.979 1.06 BC 5.8 1 . +0 . − .
14 XLSS J022059.0-043921 C2 1 . +0 . − . . +0 . − .
15 XLSS J022252.3-041647 C2 1 . +0 . − . N/A NM – 0 . +0 . − .
16 XLSSU J021712.1-041059 C2 1 . +0 . − . N/A NM – 0 . +0 . − .
17 XLSSU J021700.3-034747 C2 1 . +0 . − . N/A NM – 0 . +0 . − .
18 XLSSU J022005.5-050824 C2 1 . +0 . − . N/A NM – 1 . +0 . − .
20 XLSS J022418.7-043959 C2 1 . +0 . − . . +0 . − .
21 XLSSU J021744.1-034536 122 C1 Y 1.98 N/A NM – 1 . +0 . − .
22 XLSS J022554.5-045058 C2 2 . +0 . − . N/A NM – 0 . +0 . − . Note: In the two cases marked by an asterisk each has a z ∼ . (cid:48)(cid:48) matching radius and at similar redshifts. X-ray data are obtained from the XMM-LSS survey. Thesurvey has imaged a 11.1 square degree area centered onR.A. = 2 h m , Dec. = − ◦ (cid:48) with a mosaic of 93 overlap-ping XMM-Newton pointings (Chiappetti et al. 2013). Eachpointing displays a typical exposure time of 10 ks and cor-responds to a single observation with the EPIC detectors(MOS1, MOS2 and PN) in full frame imaging mode, span-ning a field of view of roughly 30 (cid:48) diameter. The effective fluxlimit for extended sources identified by the C1/C2 surfacebrightness selection threshold is ∼ × − ergs s − cm − . Approximately 9 square degrees of the XMM-LSS regionhas been imaged by the Spitzer space telescope as partof the SWIRE extragalactic survey (Lonsdale et al. 2003).The Spitzer/SWIRE data used in this paper are describedin Chiappetti et al. (2013). In particular, we make use ofthe IRAC channel 1 data corresponding to a photomet-ric bandpass located at 3.6 µ m. Fluxes for extended sourceswere measured within the so-called aperture 2 and are ex- This aperture corresponds to a 1 . (cid:48)(cid:48) pressed in AB magnitudes employing the relation [3 .
6] =23 . − . ν / µ Jy).
In addition to the X-ray and MIR data described abovewe also used optical u ∗ g (cid:48) r (cid:48) i (cid:48) z (cid:48) photometry obtained fromthe Canada France Hawaii Telescope Legacy Survey W1field (CFHTLS-W1; Gwyn 2012). Photometry was com-puted within an aperture based upon the Kron (1980) radiusand quoted on the AB magnitude system. Optical photome-try was identified for all sources within the Spitzer MIR cat-alogue described above. Two independent multi-band cata-logues were produced using SExtractor in two-image modewith either the r (cid:48) - or z (cid:48) -band image used as the detectionband in each case. The construction of separate r (cid:48) - and z (cid:48) -selected later permitted a self-consistent examination of theeffects of the colour selection of high-redshift cluster galaxiesusing either r (cid:48) − . µ m or z (cid:48) − . µ m colours. Optical sourceswere matched to MIR sources when they are located within apositional tolerance of < (cid:48)(cid:48) with the brightest optical sourceselected in the case of multiple matches. In the case where amatching optical source was not found, the computed colourof the Spitzer source represents a lower limit based uponthe completeness of the optical catalogue in the appropriate measure. See Section 4.11.2 of the IRAC instrument handbook or http://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/iracinstrumenthandbook/29/ c (cid:13)000
In addition to the X-ray and MIR data described abovewe also used optical u ∗ g (cid:48) r (cid:48) i (cid:48) z (cid:48) photometry obtained fromthe Canada France Hawaii Telescope Legacy Survey W1field (CFHTLS-W1; Gwyn 2012). Photometry was com-puted within an aperture based upon the Kron (1980) radiusand quoted on the AB magnitude system. Optical photome-try was identified for all sources within the Spitzer MIR cat-alogue described above. Two independent multi-band cata-logues were produced using SExtractor in two-image modewith either the r (cid:48) - or z (cid:48) -band image used as the detectionband in each case. The construction of separate r (cid:48) - and z (cid:48) -selected later permitted a self-consistent examination of theeffects of the colour selection of high-redshift cluster galaxiesusing either r (cid:48) − . µ m or z (cid:48) − . µ m colours. Optical sourceswere matched to MIR sources when they are located within apositional tolerance of < (cid:48)(cid:48) with the brightest optical sourceselected in the case of multiple matches. In the case where amatching optical source was not found, the computed colourof the Spitzer source represents a lower limit based uponthe completeness of the optical catalogue in the appropriate measure. See Section 4.11.2 of the IRAC instrument handbook or http://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/iracinstrumenthandbook/29/ c (cid:13)000 , 1–22 -ray vs. IR selection of distant galaxy clusters Figure 1.
An example of star/galaxy separation applied to aparticular r (cid:48) -band image of the CFHTLS data set (“Field A”).The red points indicate sources identified as stars. Star-galaxyseparation is performed for sources satisfying aper(1) <
22 AB.No separation is performed fainter than this threshold. band. Finally, star-galaxy separation was performed uponthe matched catalogue in the appropriate optical detectionband using the distribution of sources on the plane definedby aper(1)-aper(3) versus aper(1) where aper( n ) is themagnitude measured in an aperture of diameter equal to n arcseconds (these quantities represent measures of sourceextent and brightness respectively; Figure 1). Given the two cluster samples described above and a com-mon X-ray, optical and MIR data set, it is possible to mea-sure X-ray and MIR brightness measures for all clusters em-ploying a simple, consistent approach.The cluster signal in each waveband was measured ina circular aperture of fixed radius equal to 1 (cid:48) centered onthe X-ray position for XMM-LSS clusters and either theBCG or the barycentre position for SpARCS clusters. Thisapproach was selected to measure the cluster signal in as ro-bust a manner as possible and using the fewest assumptionsregarding the properties of individual clusters. For example,this approach requires only the sky position of each clus-ter and thus lends itself well to comparing cluster samplesdrawn from a variety of selection approaches.Application of a circular aperture is the simplest re-sponse to the lack of data on the shapes of distant clusters.Furthermore, application of a fixed angular radius offers anumber of advantages: the background applied to correct the line-of-sight signal from each cluster is uniform across thesample. As the line-of-sight signal from each cluster is oftenbackground dominated, this generates consistent and com-parable uncertainties across the sample of measurements.In addition, although one could choose to apply an aper-ture of fixed physical radius in the rest frame of each clusterit should be noted that, over the redshift interval 0 . < z < ±
5% about the fiducialredshift z = 1. The X-ray brightness measurement from a galaxy cluster issensitive to the emission from gravitationally confined gas atthe virial temperature of the cluster gravitational potential.The X-ray brightness of a cluster is primarily a measure ofthe (square of) the baryonic gas mass with a slowly varyingdependence upon the cluster gas temperature.We implemented a Bayesian approach for calculatingX-ray aperture photometry. The method is an adaptationfrom the approach taken by van Dyk et al. (2001) and Parket al. (2006). In the following we explain our procedure.Net source counts are computed from independentsource and background apertures areas. Sky areas associ-ated with non-extended source detections (i.e. non-C1 orC2) were masked from this process to remove any possiblecontribution from X-ray Active Galactic Nuclei (AGN). Weassume that C counts are measured in a source aperture ofarea A s , and B counts are measured in a background aper-ture of area A b . The observed counts are generated via aPoisson process, i.e., C ∼ Poisson( f ( s + b )) , (1) B ∼ Poisson( rgb ) , (2)where C is given by the sum of counts due to the source, s ,and the background, b . The symbols f = 1 /T s and g = 1 /T b are factors that convert the net counts to count-rates giventhe average exposure time in A s and A b . The quantity r isan area correction factor given by r = A b /A s . We determine s from its posterior probability density marginalized overthe background, p ( s | CB ) = (cid:90) d b p ( sb | CB ) . (3)Via Bayes’ theorem, the joint posterior probability of s and b can be rewritten as p ( sb | CB ) = p ( s ) p ( b ) p ( C | sb ) p ( B | b ) (cid:82) (cid:82) d b d s p ( s ) p ( b ) p ( C | sb ) p ( B | b ) . (4) p ( C | sb ) and p ( B | b ) are Poisson distributions, and p ( s ) and p ( b ) are generalized γ -priors. Further details in the final an-alytical derivation of p ( s | CB ) can be found in Appendix A2of Park et al. (2006). In our work we assume non-informativepriors, given as the result p ( s | CB ) = A − × B, (5)where A = (cid:34) C (cid:88) j =0 j + 1)Γ( C − j + 1) Γ( C + B + 1 − j )( f + gr ) C + B +1 − j Γ(1 + j ) f j (cid:35) (6) c (cid:13) , 1–22 J. P. Willis et al. and B = C (cid:88) j =0 j + 1)Γ( C − j + 1) Γ( C + B + 1 − j )( f + gr ) C + B +1 − j s j e − fs . (7)The value of s is obtained from the mode of p ( s | CB ) distri-bution, and the confidence levels are determined by numer-ically integrating p ( s | CB ) until the desired confidence levelis reached. In this way, if the mode of p ( s | CB ) is equal to 0,one can still provide upper limit for s .We applied the above approach to the clusters in thesample to obtain their X-ray aperture photometry. Aper-tures of 1 (cid:48) radius are used and are located on the clustercentroid. We have two ways to obtain the background countsdepending on the cluster position in the XMM pointing: • If the cluster centroid is close ( < (cid:48) ) to the pointing cen-ter, the background aperture is defined as an annulus cen-tered on the cluster position. The annulus has a width of 1 (cid:48) ,and is 1 (cid:48) away from the source aperture to avoid contami-nation from the cluster. • If the cluster centroid is far ( > (cid:48) ) from the pointing cen-ter, the background aperture is an annulus encompassing thecluster aperture and at similar off-axis angle. A quadrant of45 degrees (centered on the cluster) is excluded from thebackground measurement to avoid residual cluster contam-ination.This approach accounts for the radial variation of theXMM background. The procedure is applied separately toeach XXM-Newton EPIC detector, obtaining three differ-ent count-rate posterior probability density distributions foreach cluster. We then convert each count-rate distributioninto a flux posterior probability density, p ( f ), through anenergy conversion factor (ECF). This factor is calculated us-ing XSPEC (Arnaud 1996) and an
APEC emission model with z = 1, T = 2 keV, N H = 2 . × cm , Ab = 0 .
3, andstandard on-axis EPIC response matrices. The ECF scalesthe flux of the three EPIC detectors to a common sensitiv-ity. The final flux posterior probability density, p ( f X ), for agiven cluster is obtained by multiplying the individual fluxdistributions of the different EPIC detectors: p ( f X ) = (cid:89) i =1 p ( f i ) , (8)where i refers to the three EPIC detectors. The final X-rayflux is obtained from the mode of p ( f X ), together with itscorresponding 68% confidence levels. The Spitzer MIR brightness measurement for a galaxy clus-ter is computed as the summed stellar 3.6 µ m brightness ofindividual galaxies identified as cluster members. To deter-mine membership we applied a colour cut to the optical-MIRsource catalogue to identify candidate z > . z > . r (cid:48) − . µ m > . z (cid:48) − . µ m > .
3. The MIR fluxes of those galaxies thatsatisfy these colour cuts and lie within 1 (cid:48) of the cluster cen-troid are then summed to provide a two separate 3 . µ m flux measurements per cluster. Much of the analysis in the subse-quent sections was repeated using aperture fluxes and lumi-nosities computing using either the r (cid:48) − . µ m and z (cid:48) − . µ mcuts. However, at this point we note that all of the analy-sis which follows generated similar results and conclusionsirrespective of which colour cut was considered. The use oftwo colour cuts therefore provided useful a consistency checkbut, in the interests of brevity, we only present results de-rived using the r (cid:48) − . µ m colour cut.Each aperture measurement was corrected for unasso-ciated galaxies along the line of sight employing a sampleof 5000 randomly placed 1 (cid:48) apertures located within thecommon survey footprint and using the same photomet-ric thresholds as applied to the cluster samples. Althoughmost non-cluster galaxies will lie in the foreground of adistant cluster, for simplicity we refer to these randomlyplaced apertures as “the background”. We rejected back-ground apertures which lay within 2 (cid:48) of any SpARCS clusterto retain a sample of 4667 apertures for analysis. The distri-bution of background aperture flux measurements was mod-elled as a Gaussian function modified by a shallow powerlaw to describe a slight skewness of the observed distribu-tion toward higher background values. The source flux ineach cluster aperture was then computed as the maximumvalue of the posterior distribution of the cluster apertureflux (source plus background) minus the background modelwith the prior that the source flux s (cid:62)
0. The error on eachcluster flux measurement is computed from the interval ofthe above posterior distribution per cluster which contains68% of the distribution.
Figure 2 compares the cluster 3.6 µ m summed aperture fluxto the X-ray aperture flux measured for 18 XMM-LSS and92 SpARCS z > . r (cid:48) − . µ m > . c (cid:13)000
Figure 2 compares the cluster 3.6 µ m summed aperture fluxto the X-ray aperture flux measured for 18 XMM-LSS and92 SpARCS z > . r (cid:48) − . µ m > . c (cid:13)000 , 1–22 -ray vs. IR selection of distant galaxy clusters Figure 2.
A comparison of X-ray and MIR 1 (cid:48) aperture brightness values for XMM-LSS (blue squares) and SpARCS (black squares)clusters. This comparison uses the r − . µ m > . f X = −
16 for clarity. The solid triangles indicate the fluxes measured for the stacked clustersamples (see Section 5.5); red indicates SpARCS and blue indicates XMM-LSS clusters. Right: Comparison by luminosity. SpARCSclusters with zero measured X-ray luminosity are marked at log L X = − . In the following sections we compare the physical prop-erties of the XMM-LSS sample to three sub-samples basedupon the distribution of the SpARCS clusters on the X-ray/MIR plane displayed in Figure 2 – the aim being todetermine if each sub-sample displays quantifiable physicaldifferences. We define X-ray bright MIR selected clusters asthose displaying f X (cid:62) . × − ergs s − cm − . We furthersplit X-ray faint ( f X < . × − ergs s − cm − ) MIR se-lected clusters into those which are MIR bright ( f . µ m (cid:62) µ Jy) and faint ( f . µ m < µ Jy). These thresholds aredefined arbitrarily yet identify the broad trends present inthe above diagrams, the most important of which appearsto be that a significant fraction of the brightest SpARCSscluster, whether defined by MIR flux or luminosity, appeardeficient in X-ray emission. Though defined in this mannerit is important to note that the conclusions presented in thispaper are relatively insensitive to the exact choice of thresh-old values applied. The final numbers of clusters present ineach sample are as follows: XMM-LSS, 18; SpARCS X-raybright, 12; SpARCS X-ray faint, MIR bright, 10; SpARCSX-ray faint, MIR faint, 70.There exists the concern that the X-ray faint, MIRbright sub-sample of SpARCS clusters could be due to in-trinsically X-ray faint, MIR faint clusters boosted by highlocal background values that are under-subtracted by themodal value of the global background applied in Section4.2. To investigate this issue we computed local backgrounds about each SpARCS cluster using a circular annulus at afixed radial distance from the cluster centroid. Applying abackground annulus with inner and outer radii respectively5 and 6 arcminutes from each cluster centroid generated aset of background values distributed symmetrically aboutthe global background computed in Section 4.2 with no evi-dence of clusters with high MIR aperture flux measurementsdisplaying enhanced local background values. Identificationof X-ray faint, MIR bright clusters in Figure 2 is thereforenot influenced by the application of a global backgroundcorrection to MIR cluster aperture fluxes.It is furthermore unlikely that the non-cluster mask-ing procedure applied to the computation of X-ray aper-ture fluxes results in the exclusion of bona-fide cluster fluxfrom the aperture measurement. As mentioned previously,XMM-LSS pipeline detections corresponding to non-C1/C2sources were masked from the aperture measurement. An al-ternative masking procedure was tested, this time excludingsource areas corresponding only to point sources classifiedas P1 (high significance, low extension), with little or noqualitative difference in the results presented above.We also compare the X-ray and MIR brightness mea-sures of each cluster sample in terms of their luminosity us-ing the measured redshift for each cluster and the assumedcosmological model to convert the measured aperture flux ineither the X-ray or IRAC1 band respectively to a rest-frame[0.5-2] keV X-ray and K -band stellar luminosity. c (cid:13) , 1–22 J. P. Willis et al.
In addition to the luminosity distance to each source,the correction to luminosity requires the application of a k -correction. For the X-ray brightness this correction is com-puted using the same T = 2 keV plasma model used toconvert count rates to flux. In the MIR we employ a k -correction derived from a 1 Gyr, solar metallicity burst ofstar formation which evolves passively from a formation red-shift z f = 10.This model is taken from Willis et al. (2013)and matches the red sequence evolution of the XMM-LSSdistant cluster sample. Furthermore, as demonstrated byvan der Burg et al. (2014), the stellar mass in SpARCS dis-tant clusters is dominated by M ∗ galaxies located on thered sequence. The evolving spectrum was realised using theGALAXEV 2003 stellar population synthesis code (Bruzual& Charlot 2003).Computing the MIR luminosity of a galaxy clusterwithin a spatial aperture effectively involves integrating thecluster galaxy luminosity function (LF) down to a sensitiv-ity limit which itself may be expected to be a function ofredshift. In order to determine whether this is likely to bean important bias in the aperture luminosity values com-puted for this paper we performed the following analysis:taking the 3.6 µ m flux limit of the optical-MIR catalogueas 3.7 µ Jy we computed the corresponding K -band lumi-nosity of a galaxy with this flux over the redshift interval0 . < z < . K -band clustergalaxy LF presented by De Propris et al. (2007). The rela-tive change in the value of this integral over a function ofredshift indicates the expected effect on the measured aper-ture luminosity values. This LF correction factor varies withrespect to a fiducial value at z = 1 by ±
5% over the inter-val 0 . < z < . z = 1 . L X (cid:62) . × ergs s − cm − . We fur-ther split X-ray faint ( L X < . × ergs s − cm − )MIR selected clusters into those which are IR luminous( L K (cid:62) . × L (cid:12) ) and faint ( L K < . × L (cid:12) ). Thefinal numbers of clusters present in each sample are as fol-lows: XMM-LSS, 18; SpARCS X-ray bright, 17; SpARCSX-ray faint, IR bright, 16; SpARCS X-ray faint, IR faint,59. The is considerable overlap between cluster sub-samplesdefined by flux and luminosity. For example of the 12 highflux SpARCS clusters defined using the BCG position, 11are present in the luminosity defined sample. Of the 10 X-ray faint, MIR bright clusters defined by flux, 7 are presentin the corresponding luminosity defined sample.Figure 3 shows the cumulative fraction distribution inpositional offset (BCG-barycentre position) and redshift ofeach cluster sub-sample selected either on the basis of aper-ture flux or aperture luminosity measurements. A number oftrends are apparent, notably that the X-ray faint, MIR faint Figure 3.
The cumulative fraction distribution in both off-set (BCG-barycentre position) and redshift of each cluster sub-sample: XMM-LSS (blue), X-ray bright SpARCS (green), X-rayfaint MIR faint SpARCS (red), X-ray faint, MIR bright (black).Panels: a) offset distribution of cluster sub-samples selected on thebasis of aperture flux measurements, b) redshift distribution ofcluster sub-samples selected on the aperture flux measurements.Panels c) and d) follow panels a) and b) for cluster sub-samplesselected on the basis of aperture luminosity measurements. Theblack dashed line in panel (a) indicates the BCG-barycentre offsetdistribution expected from a 22 (cid:48)(cid:48)
1D Gaussian random error inthe barycentre centroid values (see Section 5.2 for more details). cluster sub-sample is composed of distant, i.e. higher red-shift, intrinsically luminous clusters when selected by aper-ture flux and nearby, i.e. lower redshift, intrinsically faintclusters when selected by luminosity. In each case the sub-sample of X-ray faint, MIR bright clusters, whether selectedby flux or luminosity, displays a distribution of position off-sets between the BCG and barycentre position dominatedby higher values than other cluster sub-samples. Further-more, this conclusion holds whether the selection of X-rayfaint, MIR bright clusters is performed using either r (cid:48) − . z (cid:48) − . The average MIR angular surface brightness distributionwithin each cluster sub-sample was computed using the re-lation c (cid:13) , 1–22 -ray vs. IR selection of distant galaxy clusters µ ( r i ) = N (cid:80) i =1 f . µm,i πr N , (9)where f . µ m ,i and r i are respectively the 3.6 µ m flux andangular separation from the appropriate cluster centroid ofa list of N galaxies within each cluster sub-sample orderedby increasing r i . Once again, the X-ray centroid is used asthe reference position for XMM-LSS clusters and the BCGposition is used for SpARCS. Note that to avoid infinite val-ues of central surface brightness in the case where the BCGposition is used we apply a softening radius to Equation 9of the form r N = r N + r S with r S equal to 1 . (cid:48)(cid:48)
8. We also notethat the above cumulative formalism generates qualitativelythe same results as a differential approach which computesthe surface brightness in radial bins about each cluster cen-tre yet avoids an arbitrary choice of radial bins. The surfacebrightness expressed in terms of rest-frame K -band lumi-nosity per unit area can also be computed in a straightfor-ward manner by replacing the flux of each colour-selectedcandidate cluster galaxy along the line-of-sight with the lu-minosity computed with the appropriate distance modulusand k -correction discussed in Section 5.1. Figure 4 displaysthe resulting surface flux and luminosity profiles for eachcluster sub-sample. Taken together, the figures indicate thatboth X-ray selected and either X-ray bright or MIR-brightcolour-selected clusters display similar projected distribu-tions of galaxy light respectively about either the X-ray orBCG location. X-ray faint, MIR-faint SpARCS clusters dis-play similar profiles yet with lower normalisation. Note thatthis procedure does not account for the background of non-cluster galaxies along the line-of-sight. However, each dis-tribution tends to an asymptotic background value at largeradius. In the left panel of Figure 4 one notes that all distantcluster projected surface brightness distributions are clearlydifferent from the average distribution of background galax-ies within a 1 arcminute radius aperture.We repeated the above analysis using the barycentre po-sition of each SpARCS cluster instead of the BCG location.The results are plotted in Figure 5 and indicate that eachsub-sample of SpARCS clusters displays a central deficit oflight compared to the analysis using the BCG location.We investigated whether this apparent deficit was dueto large errors in the barycentre centroid values relative tothe BCG positions measured for the SpARCS clusters. Suchcentroid errors, based upon the average position of candidatecluster members, are a persistent feature of galaxy overden-sity cluster finding algorithms (e.g. Lin, Mohr & Stanford2004; Rozo & Rykoff 2014; Oguri et al. 2017). We restrictedour analysis to the SpARCS X-ray bright clusters assum-ing that these represent bona-fide clusters where the BCGlocation is close to the true centroid of each cluster. We ap-plied a random Gaussian offset to the measured BCG rightascension and declination of each cluster and recomputedthe stacked surface brightness profile as described above.We repeated this process N times to generate an ensembleof surface brightness distributions at each specified offset(Figure 6).The results indicate that the SpARCS X-ray brightbarycentre surface brightness distribution is consistent withthat generated employing BCG positions convolved with a1D centroid error in R.A. and dec. of σ = 15 (cid:48)(cid:48) , corresponding to an error of 22 (cid:48)(cid:48) in radius. Figure 3 (panel (a)) indicatesthat this error model describes a large component, thoughnot all, of the observed distribution of BCG-barycentre off-set values for the SpARCS X-ray bright (and X-ray faint,MIR faint) sub-samples.The X-ray faint, MIR bright SpARCS clusters display adistribution of centroid offsets in excess of this centroid errormodel and likely indicates an additional, intrinsic offset dis-tribution. In studies at lower redshifts, large positional off-sets between the BCG location and other measures of clustercentroid (e.g. X-ray location or average member galaxy loca-tion) are often taken as an indicator of a cluster displayingthe effects of incomplete virial relaxation (e.g. Sanderson,Edge & Smith 2009; Lavoie et al. 2016).It may be that the location of X-ray faint, MIR brightSpARCS clusters on the X-ray versus MIR aperture bright-ness diagrams shown in Section 5.1 is explained by such dis-turbance/virialisation arguments. However, further evidencemust be considered before reaching a conclusion, namelyperforming a visual assessment of individual clusters in eachsub-sample and considering stacked, two-dimensional X-rayimages of each sub-sample. It is sensible to determine whether the trends in radial sur-face brightness presented in Section 5.2 are supported by avisual assessment of individual clusters in each sub-sample.Figures 7, 8, 9 and 10 display Spitzer/IRAC 3.6 µ m images ofclusters drawn from the XMM-LSS, SpARCS X-ray bright,SpARCS X-ray faint, MIR bright and SpARCS X-ray faint,MIR faint samples respectively.Although a visual assessment can only deliver qualita-tive information, it is clear that the images of clusters in eachsub-sample support the surface brightness trends presentedin Section 5.2 with both the XMM-LSS and SpARCS clus-ters appearing as centrally concentrated systems of galaxies.The sub-sample of SpARCS X-ray faint, MIR faintclusters presents a range of appearances, largely consistentwith their low MIR aperture fluxes. There is some evidencefor central concentrations of galaxies in the 3.6 µ m images.However, there are also numerous examples, particularly athigher redshift, of images sparsely populated by galaxieswhere no conclusive statement can be made on the basisof visual inspection. The creation of stacked colour magnitude diagrams foreach cluster sub-sample provides an opportunity to assesswhether each represents a population of galaxies drawn froma narrow range of star formation histories. In particular thepresence, location and width of the characteristic cluster redsequence provides measure of the average evolved galaxypopulation within each cluster sub-sample.Photometry corresponding to 3.6 µ m magnitudes and r (cid:48) − . µ m colours for galaxies located within 1 (cid:48) of each clus-ter centroid were obtained. Photometry for different clustersin each sub-sample were each transformed from the cata-logue redshift of each cluster to a common reference of z = 1by applying an appropriate k − and distance modulus cor-rection as discussed in Section 5.1. c (cid:13) , 1–22 J. P. Willis et al.
Figure 4.
The cumulative angular MIR surface brightness distribution of each cluster sub-sample: XMM-LSS (blue), X-ray brightSpARCS (green), X-ray faint MIR faint SpARCS (red), X-ray faint, MIR bright (black). Left panel: Surface brightness computedusing flux. The black dashed line indicates the average cumulative surface brightness distribution computed from 100 randomly placedapertures. Right panel: Surface brightness computed using luminosity. Note that no background is displayed in this panel as it is notpossible to apply a conversion between flux and luminosity given the unknown redshift distribution of the background galaxies.
Figure 5.
The cumulative angular MIR surface brightness distribution of each cluster sub-sample: XMM-LSS (blue), X-ray brightSpARCS (green), X-ray faint MIR faint SpARCS (red), X-ray faint, MIR bright (black). Centroids for SpARCS clusters employ thebarycentre position. Note that the axis scale employed in this figures is the same as Figure 4. c (cid:13) , 1–22 -ray vs. IR selection of distant galaxy clusters Figure 6.
A detailed comparison of the cumulative surfacebrightness distributions of the SpARCS X-ray bright clusters em-ploying BCG (dark green) and barycentre (light green) centroidvalues. The set of grey lines indicate 50 simulations of the stackedsurface brightness calculation in which a random Gaussian offsetof σ = 15 (cid:48)(cid:48) is applied to each cluster BCG R.A. and dec. centroidprior to stacking. Figure 11 isolates the red sequence distribution by col-lapsing the colour-magnitude plane along the 3.6 µ m mag-nitude axis to create a colour histogram for each clustersub-sample. All sources displaying a redshift-corrected mag-nitude [3 . µ m] <
21 AB are co-added following this method.Despite the changing normalisation of each sub-sample asone proceeds from XMM-LSS clusters to SpARCS X-raybright and finally to SpARCS X-ray faint, MIR faint clustersit is clear that each displays a similar red sequence distribu-tion, i.e. each contains a red galaxy population of approxi-mately similar absolute age and scatter.The comparison indicates that the typical number of redsequence galaxies located in XMM-LSS clusters is compara-ble to that found in the X-ray faint, MIR faint sub-sampleof SpARCS clusters, echoing earlier comparisons betweendistant X-ray and IR-selected clusters (Foltz et al. 2015).SpARCS clusters labelled as X-ray bright and X-ray faint,MIR bright each display more populous red sequence distri-butions, marginally in the case of X-ray bright systems moresignificantly for X-ray faint, MIR bright clusters (thoughomitted for clarity, the typical Poisson error for each datapoint in Figure 11 is approximately 0.25-0.3).
The creation of stacked X-ray images for each cluster sub-sample permits the average X-ray emission properties ofeach to be discussed. Furthermore, the low noise propertiesof stacked images in particular permits a sensitive test of theaverage emission from the SpARCS X-ray faint sub-samplesto be investigated.We examine stacked images of the cluster sub-samples using the data from the XMM-LSS survey. In brief, for eachsub-sample and for each EPIC detector we follow this pro-cedure:(i) Extract a 2 (cid:48) radius EPIC image and correspondingexposure map for each cluster in the [0.5-2] keV band.(ii) Create a background map for each field by fitting atwo component model to source masked EPIC images. Inthis way, the effects of spatial variation in the backgroundare taken into account.(iii) Mask out all point sources in each image, exposureand background maps. Point source locations are obtainedfrom the XMM-LSS pipeline.(iv) Sum each of the EPIC images to produce a stackedimage. Also sum each of the individual exposure and back-ground maps. In this step, the MOS exposure maps areweighted according to the MOS/PN response ratio. The rel-ative sensitivity of the MOS and PN detectors is calculatedwith
XSPEC using standard on-axis PN and MOS responsematrices.The final count-rate image is obtained by subtracting thestacked background map from the stacked photon image anddividing by the stacked exposure map. Figures 12 and 13shows the final images for each sub-sample stacked by eitherflux or luminosity. As a test of our flux stacking procedurewe also analyzed a set of 100 randomly selected positionsfrom the XMM-LSS region in an identical way as the realcluster positions. Luminosity stacks are created from fluxstacks employing an energy conversion factor based uponthe mean redshift of each sub-sample.Highly significant X-ray emission is seen in both theXMM-LSS and X-ray bright SpARCS sub-samples whencompared to the image created by combining 100 randomlocations. Weaker emission is also detected in the stackedimage corresponding to the X-ray faint, MIR bright sub-sample. It is apparent that the spatial distribution of X-ray emission in the SpARCS sub-samples is associated moreclosely with the cluster BCG position compared to thebarycentre position. This is indicated visually in the stacksfor the X-ray bright and X-ray faint, MIR bright sub-samplewhere more compact, centrally-peaked X-ray emission isgenerated when stacking on the BCG position. The stackedimage for the X-ray faint, MIR faint SpARCS sub-sampledisplays only marginal X-ray emission in excess of ran-dom when stacking on the BCG position – a result consis-tent with the low overall aperture X-ray flux measurementsfor this sub-sample. Stacking in luminosity largely confirmsthese trends yet with additional substructure present inthe stacked images. This is attributed to individual distantsources in each sub-sample for which a large correction isobtained when converting pixel values from count rate toluminosity.The visual trends noted in the stacked images are rein-forced by inspection of the angular X-ray surface brightnessdistributions in each cluster sub-sample shown in Figures14 and 15. The results confirm that the X-ray emission ineach SpARCS sub-sample is consistent with being centred onthe BCG and that the X-ray faint, MIR bright sub-sampledisplays weak yet significant extended X-ray emission. Thesurface brightness distributions computed using barycentrecentroids are suppressed relative to those computed using c (cid:13) , 1–22 J. P. Willis et al.
Figure 7.
Spitzer/IRAC 3.6 µ m images of each cluster in the XMM-LSS sample. The white circle in each image displays the 1 (cid:48) circularaperture applied to each cluster. Each image is oriented north up and east left. the BCG centroids in a manner consistent with a barycen-tre centroid error as discussed in Section 5.2.When interpreting the stacked X-ray emission from eachsub-sample, care must be taken to ensure that the resultingsignal is dominated by extended ICM emission instead of theemission from weak AGN (strong AGN, i.e. those identifiedin individual exposures, having been masked prior to stack-ing). The stacked surface brightness distribution of each SpARCS sub-sample is compared to a scaled point spreadfunction (PSF) appropriate to the combined XMM detec-tors. Focussing on the BCG centroid stacks, panels c/d/e ofFigures 14 and 15 indicate that extended X-ray emission ispresent in all three sub-samples. Following Anderson, Breg-man & Dai (2013), we compute the X-ray hardness ratioas c (cid:13) , 1–22 -ray vs. IR selection of distant galaxy clusters Figure 8.
Spitzer/IRAC 3.6 µ m images of each cluster in the SpARCS X-ray bright sub-sample. The white circle in each image displaysthe 1 (cid:48) circular aperture applied to each cluster and is centered on the BCG position. The BCG and barycentre positions of each clusterare indicated respectively by the cross and the circle. Each image is oriented north up and east left. HR = H − SH + S , (10)within the central 15 (cid:48)(cid:48) of each stack using the [0.5-2] keVand [2-10] keV intervals as the soft and hard band respec-tively. The results are plotted in Figure 16 and are comparedto two, simple spectral models which respectively representredshifted thermal ICM and non-thermal AGN emission (seecaption for more details).Given the simplicity of the model comparison it is per-haps appropriate only to comment that the XMM-LSS clus-ters, in addition to the SpARCS X-ray bright and X-rayfaint, MIR bright sub-samples show little evidence for AGNcontamination on the basis of hardness ratio. The hardnessratio for the stacked SpARCS X-ray faint, MIR faint sub-sample is nominally consistent with the simple AGN emis-sion model presented here, albeit with large errors. How-ever, the emission morphology in the stacked SpARCS X-ray faint, MIR faint sample is clearly extended, leaving thequestion of the fraction of BCGs in these clusters that hostweak AGN relatively unconstrained. Webb et al. (2015) re- port that 7/125 or 6% of SpARCS BCGs hosting bright24 µ m sources – the majority of which occurring at z (cid:38) < z < . k -correction usedto convert between X-ray flux and luminosity (Section 5.1)remains reasonable.Aperture flux and luminosity measurements were com-puted for the stacked X-ray images and comparable MIRaperture measurements were were computed for each clus-ter sub-sample. Figure 17 displays the posterior probabilitydistributions (PPDs) of each of the aperture fluxes and lu-minosities measured from each stacked image. Stacked aper-ture measures are plotted in Figure 2 and indicate significant c (cid:13) , 1–22 J. P. Willis et al.
Figure 9.
Spitzer/IRAC 3.6 µ m images of each cluster in the SpARCS X-ray faint, MIR bright sub-sample. The white circle in eachimage displays the 1 (cid:48) circular aperture applied to each cluster and is centered on the BCG position. The BCG and barycentre positionsof each cluster are indicated respectively by the cross and the circle. Each image is oriented north up and east left. detections for each sub-sample. Values corresponding to thestacked Xray flux/luminosity represent the mode of the PPDand the error bars indicate the confidence interval enclosing68% of the distribution. In particular, a significant (thoughfaint) X-ray detection is obtained for the X-ray faint, MIRbright stack. The comparison of the properties of the XMM-LSS andSpARCS distant cluster samples has revealed that X-raybright clusters, whether detected using X-ray or optical-MIRmethods, display very similar MIR and X-ray surface bright-ness distributions. We note however, that there is tenta-tive evidence that such X-ray bright clusters detected usingoptical-MIR methods display numerically larger populationsof red sequence galaxies than X-ray selected counterparts, anobservation consistent with SpARCS selection based uponthe presence of an identifiable red sequence.There are further physical differences between cluster samples detected using each method. Within the optical-MIR selected SpARCS sample we have identified three sub-samples of clusters based upon their X-ray and MIR aper-ture flux measurements. In particular, the sub-sample of X-ray faint, MIR bright SpARCS clusters display the same red-shift distribution as X-ray bright SpARCS clusters yet show,on-average, higher values of the BCG-barycentre distance.In the literature, larger values of BGC-cluster centroid off-set have been demonstrated to be strongly correlated withmore shallow X-ray surface brightness profiles (e.g. Sander-son, Edge & Smith 2009; Mantz et al. 2015).Interpreting greater values of the BCG-centroid dis-tance as an indicator of dynamical disturbance in a clustermight provide an explanation of their relatively low X-raycompared to stellar emission, e.g. if the X-ray emitting gashas been disturbed by a recent merger, reducing the X-raysurface brightness as a result (e.g. Eckert, Molendi & Pal-tani 2011; Barnes et al. 2017). An alternative explanation isthat the X-ray faint, MIR bright cluster sub-sample is as-sociated with secular mass assembly in massive structureswhereby a compact, low-mass, virialised core is surrounded c (cid:13)000
Spitzer/IRAC 3.6 µ m images of each cluster in the SpARCS X-ray faint, MIR bright sub-sample. The white circle in eachimage displays the 1 (cid:48) circular aperture applied to each cluster and is centered on the BCG position. The BCG and barycentre positionsof each cluster are indicated respectively by the cross and the circle. Each image is oriented north up and east left. detections for each sub-sample. Values corresponding to thestacked Xray flux/luminosity represent the mode of the PPDand the error bars indicate the confidence interval enclosing68% of the distribution. In particular, a significant (thoughfaint) X-ray detection is obtained for the X-ray faint, MIRbright stack. The comparison of the properties of the XMM-LSS andSpARCS distant cluster samples has revealed that X-raybright clusters, whether detected using X-ray or optical-MIRmethods, display very similar MIR and X-ray surface bright-ness distributions. We note however, that there is tenta-tive evidence that such X-ray bright clusters detected usingoptical-MIR methods display numerically larger populationsof red sequence galaxies than X-ray selected counterparts, anobservation consistent with SpARCS selection based uponthe presence of an identifiable red sequence.There are further physical differences between cluster samples detected using each method. Within the optical-MIR selected SpARCS sample we have identified three sub-samples of clusters based upon their X-ray and MIR aper-ture flux measurements. In particular, the sub-sample of X-ray faint, MIR bright SpARCS clusters display the same red-shift distribution as X-ray bright SpARCS clusters yet show,on-average, higher values of the BCG-barycentre distance.In the literature, larger values of BGC-cluster centroid off-set have been demonstrated to be strongly correlated withmore shallow X-ray surface brightness profiles (e.g. Sander-son, Edge & Smith 2009; Mantz et al. 2015).Interpreting greater values of the BCG-centroid dis-tance as an indicator of dynamical disturbance in a clustermight provide an explanation of their relatively low X-raycompared to stellar emission, e.g. if the X-ray emitting gashas been disturbed by a recent merger, reducing the X-raysurface brightness as a result (e.g. Eckert, Molendi & Pal-tani 2011; Barnes et al. 2017). An alternative explanation isthat the X-ray faint, MIR bright cluster sub-sample is as-sociated with secular mass assembly in massive structureswhereby a compact, low-mass, virialised core is surrounded c (cid:13)000 , 1–22 -ray vs. IR selection of distant galaxy clusters Figure 10.
Spitzer/IRAC 3.6 µ m images of a subset of clusters from the SpARCS X-ray faint, MIR faint sub-sample. The top, middleand bottom rows show typical clusters at low, middle and high redshift within this sub-sample. The white circle in each image displaysthe 1 (cid:48) circular aperture applied to each cluster and is centered on the BCG position. The BCG and barycentre positions of each clusterare indicated respectively by the cross and the circle. Each image is oriented north up and east left. by an envelope of accreting material (c.f. Figure 1 of Mul-drew, Hatch & Cooke 2015). The location of the BCG canbe perturbed but, overall, the mass accretion is on-going andcontinuous as opposed to associated with large, stochasticmerger events. Note that this statement regarding the dy-namical state of optical-MIR selected clusters does not ig-nore the observation that X-ray selected clusters also displaya range of relaxation states (e.g. Sanderson, Edge & Smith2009; Lavoie et al. 2016). However, the departures from re-laxation are slight compared to that observed in the presentSpARCS sample.A contrasting argument, that such X-ray faint, MIRbright systems represent projected large-scale structure vari-ations along the line-of-sight, as opposed to bound systemsdisplaying incomplete virialisation, requires a rate of con-tamination in marked disagreement with previously deter-mined rates of false detection in such systems (Gladders& Yee 2000) and with the successful results of spectro-scopic follow-up campaigns employing these clusters (e.g. Muzzin et al. 2012). Of the z > . > µ Jy, 8/10 are X-ray faint. Thecorresponding value for clusters with aperture luminosities L K > . × L (cid:12) is 8/16.The analysis presented in this paper shares many sim-ilarities with that of Rossetti et al. (2017) who compareclusters selected from the Planck SZ catalogue with X-rayselected clusters from the MAssive Cluster Survey (MACS;Ebeling et al. 2010). Rossetti et al. (2017) demonstrate thatthe X-ray cool-core fraction of SZ detected clusters is signifi-cantly lower than that determined for X-ray selected clustersand claim that this result can be explained in large part asdue to the relative detectability of clusters of varying sur-face brightness properties in each sample. Interestingly, theyalso detect a population of shallow surface brightness profile(NCC) SZ “bright” clusters that are undetected in MACSyet possess X-ray luminosities based upon an extrapolated L X − Y relation that nominally place them within the MACS c (cid:13) , 1–22 J. P. Willis et al.
Figure 11.
Average r (cid:48) − . µ m colour histogram for clustersin each sub-sample: XMM-LSS (blue), X-ray bright SpARCS(green), X-ray faint, MIR faint SpARCS (red), X-ray faint, MIRbright (black). The dashed black line shows the scaled colour his-togram generated by placing 100 1 (cid:48) apertures at random withinthe survey area and extracting all sources satisfying the distantgalaxy colour cut. Only sources satisfying [3 . µ m] <
21 whencorrected to z = 1 are displayed. No k - or distance modulus cor-rections are applied to the randomly collected source photometry. selection criteria (Figure 9 of Rossetti et al. 2017), i.e. X-rayunder luminous for their SZ-determined mass.X-ray emission in the X-ray faint, MIR bright sub-sample of SpARCS clusters is clearly present and associatedwith the location of the BCG in each cluster. Figures 14and 15 indicate that the stacked X-ray surface brightnessdistribution in these clusters is similar in shape to X-raybright clusters yet offset to lower overall normalisation. Thiswould appear to support the assertion that X-ray faint, MIRbright SpARCS clusters represent bona-fide clusters where alow-mass, virialised core surrounded by an extended, boundenvelope of material.This conclusion is also supported by the observationthat all samples of clusters considered in this paper displayidentifiable red sequence galaxy populations, thus confirm-ing that we are observing real galaxy overdensities of com-mon age and star formation history as opposed to chanceprojections. If low mass groups are indeed the sites of pre-processing to create such red sequence populations (e.g. Li,Yee & Ellingson 2009) then these structures, accreting ontoX-ray faint, MIR bright SpARCS clusters may be respon- sible for the high values of MIR aperture fluxes and lu-minosities observed in these systems. In addition, there istentative evidence that the red sequence population of X-ray selected clusters is marginally smaller than the red se-quence in optical-MIR selected clusters of comparable X-raybrightness (c.f. Donahue et al. 2002). However, the precisionachievable in this current study does not permit more thana tentative statement.It should also be noted that all of the above conclusionsare based upon the average properties of sub-samples of clus-ters and thus any information of the distribution of relax-ation states of optical-MIR selected clusters is not available.What we can say however, based upon the distribution ofclusters in the X-ray versus MIR aperture flux plane, is thateach SpARCS sub-sample is not isolated from any other; in-stead each is drawn from a continuous range of propertiesformed by the overall SpARCS sample and each is identifiedusing sensible, yet essentially arbitrary, cuts.Furthermore, if the X-ray faint, MIR bright sub-sampleof clusters is indeed associated with either ongoing mass as-sembly onto a virialised core or disruption from a recent ma-jor merger, then the X-ray surface brightness profiles of suchclusters would be expected to change significantly as theyevolve to a more relaxed state. The surface brightness pro-file determines the detectability of faint clusters and there-fore modelling of X-ray cluster surface brightness profiles (orequivalently the astrophysics underlying the surface bright-ness profile) is a key factor in computing an accurate clusterselection function. This point extends beyond the inclusionof an explicit surface brightness expression for clusters in theselection modelling (e.g. Pacaud et al. 2006) to a descriptionthat includes a distribution of surface brightness propertiesinformed by the dynamical state of the cluster population.Cluster mass assembly state therefore represents an impor-tant source of astrophysical uncertainty, particularly in theapplication of X-ray selected cluster samples to cosmologi-cal analyses employing cluster number counts (e.g. Borganiet al. 2001; Mantz et al. 2008).If the dynamical state of galaxy clusters is indeed caus-ing surface brightness driven incompleteness in observationsof galaxy clusters, how should such observations be recon-ciled with the aim of using galaxy clusters as a probe of thecosmological model? For cosmological applications, one typ-ically compares the observed sample to the true populationas provided by either a numerical model or simulations.Focussing on the relationship between mass growth ingalaxy clusters and their observability as a function of wave-length, if the X-ray under luminous structures identified inthis paper are collapsing filaments, would they pass appliedfriends-of-friends or spherical overdensity criteria to qual-ify as a halo and therefore contribute to the mass function(e.g. Watson et al. 2013)? If yes, then X-ray selection func-tions might require an additional incompleteness term (e.g.a sub-population of X-ray dark haloes in the scaling relationmodel). If no, then optical-IR samples might require an addi-tional contamination term (e.g. to represent the selection ofbound yet unvirialised structures). If X-ray under luminousclusters instead represent recent mergers that have not yetreached equilibrium, one might consider whether deblend-ing methods are consistent between observations and sim-ulations. Would numerical simulations identify one or two c (cid:13)000
21 whencorrected to z = 1 are displayed. No k - or distance modulus cor-rections are applied to the randomly collected source photometry. selection criteria (Figure 9 of Rossetti et al. 2017), i.e. X-rayunder luminous for their SZ-determined mass.X-ray emission in the X-ray faint, MIR bright sub-sample of SpARCS clusters is clearly present and associatedwith the location of the BCG in each cluster. Figures 14and 15 indicate that the stacked X-ray surface brightnessdistribution in these clusters is similar in shape to X-raybright clusters yet offset to lower overall normalisation. Thiswould appear to support the assertion that X-ray faint, MIRbright SpARCS clusters represent bona-fide clusters where alow-mass, virialised core surrounded by an extended, boundenvelope of material.This conclusion is also supported by the observationthat all samples of clusters considered in this paper displayidentifiable red sequence galaxy populations, thus confirm-ing that we are observing real galaxy overdensities of com-mon age and star formation history as opposed to chanceprojections. If low mass groups are indeed the sites of pre-processing to create such red sequence populations (e.g. Li,Yee & Ellingson 2009) then these structures, accreting ontoX-ray faint, MIR bright SpARCS clusters may be respon- sible for the high values of MIR aperture fluxes and lu-minosities observed in these systems. In addition, there istentative evidence that the red sequence population of X-ray selected clusters is marginally smaller than the red se-quence in optical-MIR selected clusters of comparable X-raybrightness (c.f. Donahue et al. 2002). However, the precisionachievable in this current study does not permit more thana tentative statement.It should also be noted that all of the above conclusionsare based upon the average properties of sub-samples of clus-ters and thus any information of the distribution of relax-ation states of optical-MIR selected clusters is not available.What we can say however, based upon the distribution ofclusters in the X-ray versus MIR aperture flux plane, is thateach SpARCS sub-sample is not isolated from any other; in-stead each is drawn from a continuous range of propertiesformed by the overall SpARCS sample and each is identifiedusing sensible, yet essentially arbitrary, cuts.Furthermore, if the X-ray faint, MIR bright sub-sampleof clusters is indeed associated with either ongoing mass as-sembly onto a virialised core or disruption from a recent ma-jor merger, then the X-ray surface brightness profiles of suchclusters would be expected to change significantly as theyevolve to a more relaxed state. The surface brightness pro-file determines the detectability of faint clusters and there-fore modelling of X-ray cluster surface brightness profiles (orequivalently the astrophysics underlying the surface bright-ness profile) is a key factor in computing an accurate clusterselection function. This point extends beyond the inclusionof an explicit surface brightness expression for clusters in theselection modelling (e.g. Pacaud et al. 2006) to a descriptionthat includes a distribution of surface brightness propertiesinformed by the dynamical state of the cluster population.Cluster mass assembly state therefore represents an impor-tant source of astrophysical uncertainty, particularly in theapplication of X-ray selected cluster samples to cosmologi-cal analyses employing cluster number counts (e.g. Borganiet al. 2001; Mantz et al. 2008).If the dynamical state of galaxy clusters is indeed caus-ing surface brightness driven incompleteness in observationsof galaxy clusters, how should such observations be recon-ciled with the aim of using galaxy clusters as a probe of thecosmological model? For cosmological applications, one typ-ically compares the observed sample to the true populationas provided by either a numerical model or simulations.Focussing on the relationship between mass growth ingalaxy clusters and their observability as a function of wave-length, if the X-ray under luminous structures identified inthis paper are collapsing filaments, would they pass appliedfriends-of-friends or spherical overdensity criteria to qual-ify as a halo and therefore contribute to the mass function(e.g. Watson et al. 2013)? If yes, then X-ray selection func-tions might require an additional incompleteness term (e.g.a sub-population of X-ray dark haloes in the scaling relationmodel). If no, then optical-IR samples might require an addi-tional contamination term (e.g. to represent the selection ofbound yet unvirialised structures). If X-ray under luminousclusters instead represent recent mergers that have not yetreached equilibrium, one might consider whether deblend-ing methods are consistent between observations and sim-ulations. Would numerical simulations identify one or two c (cid:13)000 , 1–22 -ray vs. IR selection of distant galaxy clusters Figure 12.
Stacked X-ray flux images for each cluster sub-sample. Each image is smoothed with a Gaussian kernel of sigma equal tothree pixels. The scale bar indicates the flux per pixel in units of ergs s − cm − . Panels: a) XMM-LSS clusters, b) Stack of 100 randompositions, c,d,e) SpARCS clusters stacked on the catalogue barycentre position, c) X-ray bright, d) X-ray faint, MIR bright, e) X-rayfaint, MIR faint, f,g,h) SpARCS clusters stacked on the catalogue BCG position, f) X-ray bright, g) X-ray faint, MIR bright, h) X-rayfaint, MIR faint. The blue circle in each panel represents the 1 (cid:48) radius aperture used to measure individual cluster X-ray fluxes. halos? Would X-ray image analysis do so, for example, weredeeper data available?A related question is whether this X-ray under lumi-nous population is represented within scaling relation mod-els. Do such systems represent simply the low-end of thelog-normal distribution derived from analysis of X-ray sam-ples, or are they instead a population so far relatively un-detected by X-ray selected cluster studies? If they are un-detected, this would support the idea that X-ray scaling re-lations should be derived from cluster samples selected atother wavelengths e.g. Andreon et al. (2016). In closing, it is clear that any survey for galaxy clustersprovides only a partial view of the true population of virialstructures above a given mass threshold. However, compar-isons of cluster samples compiled at multiple wavelengths,such as performed in this paper and others, provide a meansto reveal the nature and extent of any bias. Ultimately, andpossibly with recourse to simulated clusters samples incor-porating both cosmological and gas physics (e.g. McCarthyet al. 2017; Barnes et al. 2017), the effects of such bias canbe corrected for and an impartial view obtained of the for- c (cid:13) , 1–22 J. P. Willis et al.
Figure 13.
Stacked X-ray luminosity images for each cluster sub-sample. The caption information is the same as for Figure 12 with theexception that the scale bar indicates the luminosity per pixel in units of 10 ergs s − . mation of large scale structure and the evolution of galaxiestherein. ACKNOWLEDGMENTS
The authors would like to thank the anonymous referee fortheir comments that resulted in many improvements in thepaper. The authors further wish to thank Dr. Irene PintosCastro for checking our XMM-SpARCS matching results.MERC acknowledges support by the Bonn-Cologne Gradu-ate School of Physics and Astronomy (BCGS) and the Ger-man Aerospace Agency (DLR) with funds from the Min-istry of Economy and Technology (BMWi) through grant 50 OR 1608. G.W. acknowledges financial support for this workfrom NSF grant AST-1517863 and from NASA through pro-grams GO-13306, GO- 13677, GO-13747 & GO-13845/14327from the Space Telescope Science Institute, which is oper-ated by AURA, Inc., under NASA contract NAS 5-26555,and grant number 80NSSC17K0019 issued through the As-trophysics Data Analysis Program (ADAP).
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