Rossby Wave Instability of Thin Accretion Disks. III. Nonlinear Simulations

Abstract

We study the nonlinear evolution of the Rossby wave instability in thin disks using global two-dimensional hydrodynamic simulations. The detailed linear theory of this nonaxisymmetric instability was developed earlier by Lovelace et al. and Li et al., who found that the instability can be excited when there is an extremum in the radial profile of an entropy-modified version of potential vorticity. The key questions we are addressing in this paper are the following: (1) What happens when the instability becomes nonlinear? Specifically, does it lead to vortex formation? (2) What is the detailed behavior of a vortex? (3) Can the instability sustain itself and can the vortex last a long time? Among various initial equilibria that we have examined, we generally find that there are three stages of the disk evolution: (1) The exponential growth of the initial small amplitude perturbations. This is in excellent agreement with the linear theory; (2) The production of large-scale vortices and their interactions with the background flow, including shocks. Significant accretion is observed owing to these vortices. (3) The coupling of Rossby waves/vortices with global spiral waves, which facilitates further accretion throughout the whole disk. Even after more than 20 revolutions at the radius of vortices, we find that the disk maintains a state that is populated with vortices, shocks, spiral waves/shocks, all of which transport angular momentum outward. We elucidate the physics at each stage and show that there is an efficient outward angular momentum transport in stages (2) and (3) over most parts of the disk, with an equivalent Shakura-Sunyaev angular momentum transport parameter α in the range from 10-4 to 10-2. By carefully analyzing the flow structure around a vortex, we show why such vortices prove to be almost ideal "units" in transporting angular momentum outward, namely by positively correlating the radial and azimuthal velocity components. In converting the gravitational energy to the internal energy, we find some special cases in which entropy can remain the same while angular momentum is transported. This is different from the classical α-disk model, which results in the maximum dissipation (or entropy production). The dependence of the transport efficiency on various physical parameters are examined and effects of radiative cooling are briefly discussed as well. We conclude that Rossby wave/vortex instability is an efficient, purely hydrodynamic mechanism for angular momentum transport in thin disks, and may find important applications in many astrophysical systems.