Vertical distribution of temperature and density in a planetary ring

We model temperature and density profiles for a dilute planetary ring, base d on the hydrodynamic balance equations for momentum and energy of granular flows. Within our approximation the ring consists of inelastic smooth sphe res of unique size and mass, while the fluxes of mass, momentum and energy are linear functions of the gradients of density, velocity and temperature. The resulting system of coupled differential equations leads to temperatur e and density profiles, which we compare to the results of a triaxial kinet ic approach to the dynamics of a planetary ring. We find that both approach es agree fairly well in the elastic limit. Further, we carry out event driv en N-particle simulations of a ring, subject to the conditions of the theor etical model. The simulated profiles are then compared to the theoretical o nes: for the density a good agreement is found for both theoretical approac hes, but the simulated temperature profiles increase monotonically with ver tical distance whereas the theoretical profiles always have a turnover at s ome distance from the mid plane. This disagreement is likely to be connecte d to the vertical dependence of the velocity ellipsoid, which is not taken into account in the theoretical treatments.