  We consider the solid or hexatic non-equilibrium phases of an interacting
two-dimensional system of Active Brownian Particles at high density and
investigate numerically and theoretically the properties of the velocity
distribution function and the associated kinetic temperature. We obtain
approximate analytical predictions for the shape of the velocity distribution
and find a transition from a Mexican-hat-like to a Gaussian-like distribution
as the persistence time of the active force changes from the small to the large
persistence regime. Through a detailed numerical and theoretical analysis of
the single-particle velocity variance, we report an exact analytical expression
for the kinetic temperature of dense spherical self-propelled particles that
holds also in the non-equilibrium regimes with large persistence times and
discuss its range of validity.
