The ESO Nearby Abell Cluster Survey. XII. The Mass and Mass‐to‐Light Ratio Profiles of Rich Clusters

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Abstract
We determine the mass profile of an ensemble cluster built from 3056 galaxies in 59 nearby clusters observed in the ESO Nearby Abell Cluster Survey. The mass profile is derived from the distribution and kinematics of the early-type (elliptical and S0) galaxies only, with projected distances from the centers of their clusters ≤1.5r200. These galaxies are most likely to meet the conditions for the application of the Jeans equation, since they are the oldest cluster population and are thus quite likely to be in dynamical equilibrium with the cluster potential. In addition, the assumption that the early-type galaxies have isotropic orbits is supported by the shape of their velocity distribution. For galaxies of other types (the brightest elliptical galaxies, with MR ≤ -22 + 5 log h, and the early and late spirals) these assumptions are much less likely to be satisfied. For the determination of the mass profile we also exclude early-type galaxies in subclusters. Application of the Jeans equation yields a nonparametric estimate of the cumulative mass profile M(<r), which has a logarithmic slope of -2.4 ± 0.4 in the density profile at r200 (approximately the virial radius). We compare our result with several analytical models from the literature and estimate their best-fit parameters from a comparison of observed and predicted velocity-dispersion profiles. We obtain acceptable solutions for all models (NFW, Moore et al., softened isothermal sphere [SIS], and Burkert). Our data do not provide compelling evidence for the existence of a core; as a matter of fact, the best-fitting core models have core-radii well below 100 h-1 kpc. The upper limit that we put on the size of the core-radius provides a constraint for the scattering cross section of dark matter particles. The total-mass density appears to be traced remarkably well by the luminosity density of the early-type galaxies. On the contrary, the luminosity density of the brightest elliptical galaxies increases faster toward the center than the mass density, while the luminosity density profiles of the early and late spirals are somewhat flatter than the mass density profile.
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