The entire virial radius of the fossil cluster RXJ 1159 + 5531. II. Dark matter and baryon fraction

In this second paper on the entire virial region of the relaxed fossil cluster RXJ 1159+5531, we present a hydrostatic analysis of the azimuthally averaged hot intracluster medium (ICM) using the results of Su et al. For a model consisting of ICM, stellar mass from the central galaxy (BCG), and an NFW dark matter (DM) halo, we obtain a good description of the projected radial profiles of ICM emissivity and temperature that yield precise constraints on the total mass profile. The BCG stellar mass component is clearly detected with a K-band stellar mass-to-light ratio, $M_{\star }/L_K=0.61\pm 0.11M_{\odot }/L_{\odot }$, consistent with stellar population synthesis models for a Milky Way initial mass function. We obtain a halo concentration, $c_{200}=8.4\pm 1.0$, and virial mass, $M_{200}=(7.9\pm 0.6)\times {10}^{13}{M}_{\odot }$. For its mass, the inferred concentration is larger than most relaxed halos produced in cosmological simulations with Planck parameters, consistent with RXJ 1159+5531 forming earlier than the general halo population. The baryon fraction at r ₂₀₀, $f_{b,200}=0.134\pm 0.007$, is slightly below the Planck value (0.155) for the universe. However, when we take into account the additional stellar baryons associated with non-central galaxies and the uncertain intracluster light (ICL), $f_{b,200}$ increases by $\approx 0.015$, consistent with the cosmic value and therefore no significant baryon loss from the system. The total mass profile is nearly a power law over a large radial range (∼0.2–10 R _e), where the corresponding density slope α obeys the $\alpha -R_e$ scaling relation for massive early-type galaxies. Performing our analysis in the context of MOND still requires a large DM fraction ($85.0\%\pm 2.5\%$ at r = 100 kpc) similar to that obtained using the standard Newtonian approach. The detection of a plausible stellar BCG mass component distinct from the NFW DM halo in the total gravitational potential suggests that $\sim {10}^{14}{M}_{\odot }$ represents the mass scale above which dissipation is unimportant in the formation of the central regions of galaxy clusters.