  We study here the steady state attained in a granular gas of inelastic rough
spheres that is subject to a spatially uniform random volume force. The
stochastic force has the form of the so-called white noise and acts by adding
impulse to the particle translational velocities. We work out an analytical
solution of the corresponding velocity distribution function from a Sonine
polynomial expansion that displays energy non-equipartition between the
translational and rotational modes, translational and rotational kurtoses, and
translational-rotational velocity correlations. By comparison with a numerical
solution of the Boltzmann kinetic equation (by means of the Direct Simulation
Monte Carlo method) we show that our analytical solution provides a good
description that is quantitatively very accurate in certain ranges of
inelasticity and roughness. We also find three important features that make the
forced granular gas steady state very different from the homogeneous cooling
state (attained by an unforced granular gas). First, the marginal velocity
distributions are always close to a Maxwellian. Second, there is a continuous
transition to the purely smooth limit (where the effects of particle rotations
are ignored). And third, the angular translational-rotational velocity
correlations show a preference for a quasiperpendicular mutual orientation
(which is called "lifted-tennis-ball" behavior).
