Density structures in perturbed thin cold discs

Abstract

We investigate the action of gravitational perturbers in thin cold astrophysical discs. The model includes viscous diffusion of the disc matter and gravitational scattering by the perturber as two counteracting processes. Two types of density structures are found, depending on the mass of the perturbing body and on the amount of momentum transport in the disc. A gap around the whole circumference of the disc is opened if the perturber is more massive than a certain threshold. Alternatively, a local S-shaped density modulation is generated that we call a ‘propeller’. We derive an analytic solution of the S-shaped density patterns using Green functions of the stationary problem. We find that the large-scale appearance of propellers does not depend on the details of the scattering process but mainly on the effective strength of the gravity perturbations ‐ namely the amplitudes of the Green functions. The crucial disc parameter is the kinematic viscosity describing the transport properties of the disc material. The solution provides the characteristic spatial extensions of the structures depending on the mass of the perturber and the viscosity of the disc. Furthermore, we propose a new criterion for the threshold mass of the perturber needed to open a gap. The results are applied to dense planetary rings perturbed by an embedded moonlet, and to gas‐dust discs around a protostar perturbed by a protoplanet. Concerning the rings of Saturn there is the chance to verify our findings with the high-resolution experiments of the Cassini spacecraft, which arrives at Saturn in 2004.