Issue 
A&A
Volume 558, October 2013



Article Number  A1  
Number of page(s)  22  
Section  Cosmology (including clusters of galaxies)  
DOI  https://doi.org/10.1051/00046361/201321955  
Published online  26 September 2013 
Online material
Appendix A: The effects of different cluster membership definitions
The determinations of M(r) and β(r) described in Sects. 3 and 4 are based, at least in part, on the sample of cluster members defined by the P+G procedure (see Sect. 2.1). Here we examine how a different cluster membership definition affects our results. For this, we here consider the membership definition obtained with the Clean method instead of the P+G method. The two methods use very different approaches for the identification of cluster members, as described in Sect. 2.1.
In Table A.1 we list the fractional differences and associated 1σ uncertainties of the r_{200},r_{2} and r_{ν} determinations obtained by using the two samples of cluster members identified with the P+G and the Clean methods. The effects of changing the method of membership selection are marginal, as all changes are within 1σ.
Effects of changing the member selection method (Clean vs. P+G).
The r_{200} estimates are all slightly increased when adopting the Clean method instead of the P+G method, and this happens because of the 8 galaxies with high absolute values of v_{rf} near the cluster center selected as members by the Clean method but not by the P+G method (see Fig. 2). Since 7 of these 8 galaxies are passive, the effects of the different membership selection are stronger on the quantities derived using only passive galaxies.
The inclusion of these 8 galaxies in the sample of cluster members causes a higher velocity dispersion estimate near the center, and therefore a steeper σ_{los} profile. To accommodate for the steeper σ_{los} profile near the center, the MAMPOSSt analysis forces more concentrated mass profiles, with 20–25% smaller r_{2} estimates. However, given the large uncertainties on the r_{2} estimates these changes are far from being significant. The Caustic M(r) estimate is less affected, because i) it is only partially based on the membership selection within the virial radius, and ii) it uses all galaxies (and not only members) also beyond the virial radius.
The r_{ν} estimates depend very little on which membership selection is chosen, because i) they are based not only on the sample of spectroscopic members but also on the sample of z_{p}selected members; and ii) the inclusion of the 8 additional members near the center has a smaller impact on n(R) than it has on σ_{los}(R).
Given the marginal changes in the MAMPOSSt and Caustic estimates of r_{200} and r_{2}, using the Cleanbased membership determination instead of the P+Gbased one, we still find consistency between the M(r) obtained via the MAMPOSSt and Caustic method and that of U12. As a consequence, we would still adopt the M(r) of U12 within r_{200,U} and the Caustic M(r) at larger radii, and the resulting M(r) would be almost identical to the one we adopted using the P+G membership determination (Sect. 3.3).
Fig. A.1
Difference of the β(r) determined using the Clean and P+G samples of members. The solid (white), dashed (red), and dashdotted (cyan) curves are for all, passive, and SF galaxies, respectively. 1σ intervals on the differences are shown as shaded regions, with 45, 0, and 90 degrees orientation of the (gray, orange, blue) shading for all, passive, and SF galaxies, respectively. 

Open with DEXTER 
The β(r) profiles resulting from the inversion of the Jeans equation are marginally affected mostly because of the steepening of the σ_{los} profile. Given that the adopted M(r) is almost unchanged with respect to the case of P+G membership selection, the steepening of σ_{los}(R) near the center must be compensated by an increased radial anisotropy. This concerns mostly the passive galaxies. The differences between the β(r) obtained using the Cleanbased sample of members and those obtained using the P+Gbased sample of members are consistent with zero within 1σ for all cluster populations and at all radii (see Fig. A.1).
We conclude that our results do not change significantly if we use the Clean instead of the P+G method for membership selection.
Appendix B: Comparison with other cluster mass estimates from the literature
We here compare our results to those obtained by Foëx et al. (2012) and Ebeling et al. (2009). In both cases their data were of insufficiently quality to constrain both r_{200} and r_{2}, so we only compare the r_{200} values.
The weak lensing r_{200} estimate of Foëx et al. (2012), Mpc, is in good agreement with our estimate.
Ebeling et al. (2009) have estimated the cluster mass in three ways; i) by strong lensing; ii) by an hydrostatic equilibrium analysis of the Xray emitting intracluster medium; and iii) by the virial theorem. Their strong lensing mass estimate, 1.12 × 10^{14}M_{⊙} within 0.12 Mpc from the cluster center, is in agreement with our determinations. By applying a scaling relation to the cluster Xray temperature Ebeling et al. (2009) obtain an approximate value of r_{200}, 2.3 ± 0.1 Mpc, in disagreement with our estimate. They then estimate the cluster mass within this radius using an isothermal β model profile, 1.7 ± 1 × 10^{15} M_{⊙}. This M_{200} estimate corresponds to a r_{200} estimate of 2.1 Mpc, different from their initial estimate, but still above our best estimate. Had they iterated their Eq. (5) they would have obtained a concordant pair of r_{200},M_{200} estimates with a final value of r_{200} of 2.03 Mpc, closer to our best estimate.
The virial theorem mass estimate of Ebeling et al. (2009) is instead grossly discrepant with any other estimate discussed so far. This appears to be due to a combination of causes.
First, their membership selection is too simplistic since it does not take into account the radial position of galaxies. As a consequence, they obtain a much larger velocity dispersion estimate than we do, 1581 km s^{1} (compare to the values in Table 1). Their large estimate is also due to the fact that σ_{los} is decreasing with R (see Fig. 3) and their spectroscopic sample does not reach r_{200,U}. Other causes that lead Ebeling et al. (2009) to overestimate the cluster mass using the virial theorem are the neglect of the surfacepressure term (The & White 1986), and the use of a spatially incomplete sample in the estimate of the projected harmonic mean radius (see Biviano et al. 2006).
© ESO, 2013
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