Mass, velocity anisotropy, and pseudo phase-space density profiles of Abell 2142

Abstract

Aim: We aim to compute the mass and velocity anisotropy profiles of Abell 2142 and, from there, the pseudo phase--space density profile $Q(r)$ and the density slope - velocity anisotropy $\beta - \gamma$ relation, and then to compare them with theoretical expectations. Methods: The mass profiles were obtained by using three techniques based on member galaxy kinematics, namely the caustic method, the method of Dispersion - Kurtosis, and MAMPOSSt. Through the inversion of the Jeans equation, it was possible to compute the velocity anisotropy profiles. Results: The mass profiles, as well as the virial values of mass and radius, computed with the different techniques agree with one another and with the estimates coming from X-ray and weak lensing studies. A concordance mass profile is obtained by averaging the lensing, X-ray, and kinematics determinations. The cluster mass profile is well fitted by an NFW profile with $c=4.0 \pm 0.5$. The population of red and blue galaxies appear to have a different velocity anisotropy configuration, since red galaxies are almost isotropic, while blue galaxies are radially anisotropic, with a weak dependence on radius. The $Q(r)$ profile for the red galaxy population agrees with the theoretical results found in cosmological simulations, suggesting that any bias, relative to the dark matter particles, in velocity dispersion of the red component is independent of radius. The $\beta - \gamma$ relation for red galaxies matches the theoretical relation only in the inner region. The deviations might be due to the use of galaxies as tracers of the gravitational potential, unlike the non--collisional tracer used in the theoretical relation.