Rossby wave instability of thin accretion disks. II. Detailed linear theory

In an earlier work we identified a global, nonaxisymmetric instability associated with the presence of an extreme in the radial profile of the key function L(r) drop (Sigma Omega/k(2))S-2/Gamma in a thin, inviscid, nonmagnetized accretion disk. Here Sigma(r) is the surface mass density of the disk, Omega(r) is the angular rotation rate, S(r) is the specific entropy, Gamma is the adiabatic index, and kappa(r) is the radial epicyclic frequency. The dispersion relation of the instability was shown to be similar to that of Rossby waves in planetary atmospheres. In this paper, we present the detailed linear theory of this Rossby wave instability and show that it exists for a wider range of conditions, specifically, for the case where there is a jump over some range of r in Sigma(r) or in the pressure P(r). We elucidate the physical mechanism of this instability and its dependence on various parameters, including the magnitude of the bump or jump, the azimuthal mode number, and the sound speed in the disk. We find a large parameter range where the disk is stable to axisymmetric perturbations but unstable to the nonaxisymmetric Rossby waves. We find that growth rates of the Rossby wave instability can be high, similar to 0.2 Omega(K) for relative small jumps or bumps. We discuss possible conditions which can lead to this instability and the consequences of the instability.