1999/07/20 by Hui Li, H. Li, J. M. Finn +4 · 4 citations
Earth and Planetary Sciences · Physics and Astronomy · #Astro and Planetary Science #Astrophysics and Star Formation Studies #High-pressure geophysics and materials #astro-ph
paper · pdf · doi:10.1086/308693
Use emulapj style, 14 pages, 12 figures, submitted to ApJ
arxiv created 1999/07/20 · openalex publication_date 2000/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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 ( r ) ≡ (ΣΩ/κ 2 ) S 2/Γ in a thin, inviscid, nonmagnetized accretion disk. Here Σ( r ) is the surface mass density of the disk, Ω( r ) is the angular rotation rate, S ( r ) is the specific entropy, Γ is the adiabatic index, and κ( 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 Σ( 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, ~0.2Ω K for relative small jumps or bumps. We discuss possible conditions which can lead to this instability and the consequences of the instability.