Granular rough sphere in a low-density thermal bath

We study the stationary state of a rough granular sphere immersed in a thermal bath composed of point particles. When the centre of mass of the sphere is fixed the stationary angular velocity distribution is shown to be Gaussian with an effective temperature lower than that of the bath. For a freely moving rough sphere coupled to the thermostat via inelastic collisions we find a condition under which the joint distribution of the translational and rotational velocities is a product of Gaussian distributions with the same effective temperature. In this rather unexpected case we derive a formula for the stationary energy flow from the thermostat to the sphere in accordance with the Fourier law.