CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of the z=0.44 galaxy cluster MACS 1206.2-0847

We use an unprecedented data-set of about 600 redshifts for cluster members, obtained as part of a VLT/VIMOS large programme, to constrain the mass profile of the z=0.44 cluster MACS J1206.2-0847 over the radial range 0-5 Mpc (0-2.5 virial radii) using the MAMPOSSt and Caustic methods. We then add external constraints from our previous gravitational lensing analysis. We invert the Jeans equation to obtain the velocity-anisotropy profiles of cluster members. With the mass-density and velocity-anisotropy profiles we then obtain the first determination of a cluster pseudo-phase-space density profile. The kinematics and lensing determinations of the cluster mass profile are in excellent agreement. This is very well fitted by a NFW model with mass M200=(1.4 +- 0.2) 10^15 Msun and concentration c200=6 +- 1, only slightly higher than theoretical expectations. Other mass profile models also provide acceptable fits to our data, of (slightly) lower (Burkert, Hernquist, and Softened Isothermal Sphere) or comparable (Einasto) quality than NFW. The velocity anisotropy profiles of the passive and star-forming cluster members are similar, close to isotropic near the center and increasingly radial outside. Passive cluster members follow extremely well the theoretical expectations for the pseudo-phase-space density profile and the relation between the slope of the mass-density profile and the velocity anisotropy. Star-forming cluster members show marginal deviations from theoretical expectations. This is the most accurate determination of a cluster mass profile out to a radius of 5 Mpc, and the only determination of the velocity-anisotropy and pseudo-phase-space density profiles of both passive and star-forming galaxies for an individual cluster [abridged]