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We consider the solid or hexatic non-equilibrium phases of an interactingtwo-dimensional system of Active Brownian Particles at high density andinvestigate numerically and theoretically the properties of the velocitydistribution function and the associated kinetic temperature. We obtainapproximate analytical predictions for the shape of the velocity distributionand find a transition from a Mexican-hat-like to a Gaussian-like distributionas the persistence time of the active force changes from the small to the largepersistence regime. Through a detailed numerical and theoretical analysis ofthe single-particle velocity variance, we report an exact analytical expressionfor the kinetic temperature of dense spherical self-propelled particles thatholds also in the non-equilibrium regimes with large persistence times anddiscuss its range of validity.

Active Matter at high density: velocity distribution and kinetic temperature