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In this second paper on the entire virial region of the relaxed fossilcluster RXJ1159+5531, we present a hydrostatic analysis of the hot intraclustermedium (ICM). For a model consisting of ICM, stellar mass from the centralgalaxy (BCG), and an NFW dark matter (DM) halo, we obtain good descriptions ofthe projected radial profiles of ICM emissivity and temperature. The BCGstellar mass is clearly detected with M_star/L_K = 0.61 +/- 0.11 solar,consistent with stellar population synthesis models for a Milky-Way IMF. Weobtain a halo concentration, c_200 =8.4 +/- 1.0, and virial mass, M_200 = 7.9+/- 0.6 x 10^13 M_sun. For its mass, the inferred concentration is larger thanmost relaxed halos produced in cosmological simulations with Planck parameters,consistent with RXJ1159+5531 forming earlier than the general halo population.The baryon fraction at r_200, f_b,200 = 0.134 +/- 0.007, is slightly below thePlanck value (0.155) for the universe. When we account for the stellar baryonsassociated with non-central galaxies and the uncertain intracluster light,f_b,200 increases by ~0.015, consistent with the cosmic value. Performing ouranalysis in the context of MOND still requires a large DM fraction (85.0% +/-2.5% at r=100 kpc) similar to that obtained using the standard Newtonianapproach. The detection of a plausible stellar BCG mass component distinct fromthe NFW DM halo in the total gravitational potential suggests that ~10^14 M_sunrepresents the mass scale above which dissipation is unimportant in theformation of the central regions of galaxy clusters. (Abridged)

The Entire Virial Radius of the Fossil Cluster RXJ1159+5531: II. Dark Matter and Baryon Fraction