Issue 
A&A
Volume 577, May 2015



Article Number  A19  
Number of page(s)  15  
Section  Cosmology (including clusters of galaxies)  
DOI  https://doi.org/10.1051/00046361/201425460  
Published online  24 April 2015 
Online material
Appendix A: Selection effects in GCLASS
Fig. A.1
Black solid line: Tinker et al. (2008) cumulative mass function at z = 1 for WMAP7 cosmology. Black dotted lines: Tinker et al. (2008) cumulative mass functions at z = 0.86 and z = 1.34, which are the redshift limits within which the GCLASS clusters are selected. Red dashed line: cumulative mass function of the ten GCLASS clusters, normalised by the total volume of SpARCS. 

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Given the significant evolution that is observed between the GCLASS sample and the lowz descendant sample, we have to consider the possibility that this inferred evolution is caused by the way these samples are selected. Since it is impossible to select a cluster sample based on halo mass, different selection methods (Xray, SZ, or galaxy selections) potentially result in a biased sample of clusters.
The GCLASS sample consists of ten clusters drawn from the 42 degree Spitzer Adaptation of the Redsequence Cluster Survey (SpARCS; Muzzin et al. 2009; Wilson et al. 2009; Demarco et al. 2010). Clusters in SpARCS were detected using the redsequence detection method developed by Gladders & Yee (2000), and expanded on in Muzzin et al. (2008). In summary, this detection method was applied to the optical+InfraRed data in SpARCS, so that the z′ − 3.6 μm colour was used to detect clusters at redshifts z> 0.8 after convolving the galaxy number density maps with an exponential kernel (see Gladders & Yee 2000, Eq. (3)). Richnesses were measured in fixed apertures with a radius of 500 kpc, after which the richest systems were considered for followup photometry and spectroscopy. Muzzin et al. (2012) describe how this GCLASS followup sample was drawn from the richest systems after optimising the redshift baseline and ensuring a spread in RA for observational convenience. The fixed aperture of 500 kpc makes the richness selection independent on concentration. However, in principle it is possible that richness and concentration are correlated quantities, such that a richness selection indirectly biases our sample towards high/low concentrations.
The statistics in the GCLASS sample are insufficient to study a possible trend between richness and concentration at z ~ 1, but we proceed to test a potential bias in the selection of GCLASS by comparing the dynamical masses of the GCLASS sample to the Tinker et al. (2008) cumulative halo mass function based on a WMAP7 cosmology, which we show in Fig. A.1.
Fig. A.2
Black solid line: GCLASS ensemble average stellar mass concentration with a Gaussian probability distribution around c = 7.12. Also shown are the lognormal concentration distribution for clusters with the same mass and redshift as the GCLASS sample for the relaxed haloes in Duffy et al. (2008) (blue dotted line), and their full sample (red dashed line). 

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Given the effective area of 41.9 square degrees we estimate the effective volume of the SpARCS survey (from which GCLASS was selected) in the redshift slice 0.86 <z< 1.34 and normalise the cumulative number density of the GCLASS clusters over this volume. At the highmass end of the distribution we expect Poisson scatter, and there is scatter in the massrichness relation to be considered. The ten GCLASS systems are therefore not necessarily the most massive ones. Based on this comparison, we estimate that in GCLASS we probe around 10% of the clusters in the SpARCS volume around the median mass of the GCLASS sample (M_{200} ≃ 10^{14.3}M_{⊙}).
We consider the possibility that the clusters probed by GCLASS are the 10% with the highest concentrations in the simulation. Figure A.2 shows the GCLASS ensemble average stellar mass concentration with a Gaussian probability distribution around c = 7.12. The Duffy et al. (2008) lognormal concentration distribution for clustersized haloes in Nbody simulations are also shown, both for their relaxed and full sample (haloes were categorised based on the distance between the most bound particle and the centre of mass in the simulation). The relaxed sample has a slightly higher concentration of c = 3.30 compared to c = 2.84 for the full sample, but has a smaller scatter (σ(log_{10}c) = 0.11 dex versus 0.15 dex for the full sample). Where the Duffy et al. (2008) distributions overlap with the GCLASS probability distribution, these two distributions are similar.
We perform a simple test in which we randomly sample 100 concentrations from the Duffy et al. (2008) relations. We do this for 1000 different realisations and each time average the ten most concentrated ones. In only 3% of the realisations we do find a larger average than the measured concentration from GCLASS (), taking account also of the error on this measured concentration. Therefore, even under the most conservative assumption that a richness selection is completely biased towards the most concentrated galaxy clusters, there is only a 3% probability that we measure an average concentration for GCLASS of . Moreover, as we argued in vdB14, the measured concentration of c ≃ 7.12 is a lower limit if we include uncertainties arising from offsets between the BCGs and the “true” cluster centres. Given these arguments, it is unlikely that both the observed evolution since z ~ 1, and the difference between the predictions from Nbody simulations and observations at this redshift, are only an effect of the way the GCLASS sample is selected.
© ESO, 2015
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