The nonlinear evolution of a single mode of the magnetic shearing instability

Abstract

We simulate in one dimension the magnetic shearing instability for a vertical magnetic field penetrating a Keplerian accretion disc. An initial equilibrium state is perturbed by adding a single eigenmode of the shearing instability and the subsequent evolution is followed into the nonlinear regime. Assuming that the perturbation is the most rapidly growing eigenmode, the linear theory remains applicable until the magnetic pressure perturbation is strong enough to induce significant deviations from the original density. If the initial perturbation is not the fastest growing mode, the faster growing modes will appear after some time.