Free Access
Volume 558, October 2013
Article Number A1
Number of page(s) 22
Section Cosmology (including clusters of galaxies)
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 r200,r-2 and rν 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.

Table A.1

Effects of changing the member selection method (Clean vs. P+G).

The r200 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 vrf 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 σlos profile. To accommodate for the steeper σlos 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 rν 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 zp-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 σlos(R).

Given the marginal changes in the MAMPOSSt and Caustic estimates of r200 and r-2, using the Clean-based membership determination instead of the P+G-based 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 r200,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).

thumbnail Fig. A.1

Difference of the β(r) determined using the Clean and P+G samples of members. The solid (white), dashed (red), and dash-dotted (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 σlos profile. Given that the adopted M(r) is almost unchanged with respect to the case of P+G membership selection, the steepening of σlos(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 Clean-based sample of members and those obtained using the P+G-based 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 r200 and r-2, so we only compare the r200 values.

The weak lensing r200 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 X-ray emitting intra-cluster medium; and iii) by the virial theorem. Their strong lensing mass estimate, 1.12 × 1014M within 0.12 Mpc from the cluster center, is in agreement with our determinations. By applying a scaling relation to the cluster X-ray temperature Ebeling et al. (2009) obtain an approximate value of r200, 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 × 1015  M. This M200 estimate corresponds to a r200 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 r200,M200 estimates with a final value of r200 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 σlos is decreasing with R (see Fig. 3) and their spectroscopic sample does not reach r200,U. Other causes that lead Ebeling et al. (2009) to overestimate the cluster mass using the virial theorem are the neglect of the surface-pressure 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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