The stability of accretion tori. I - Long-wavelength modes of slender tori
Abstract
The principal branch of the dispersion relation of a slender torus is considered, and it is shown that the long-wavelength unstable modes of the two-dimensionally incompressible ribbon are coupled edge waves. Height-averaged fluid equations are used to estimate the growth rate as a function of q, n, and beta, and the governing equation for linear modes is reduced from a partial to an ordinary differential equation. Two-dimensional modes when n = 1/2 are solved, and the underlying physical mechanism of the instability modes of Papaloizou and Pringle (1985) is identified. The presence of corotation resonance is reflected by a singularity in the differential equation of the height-integrated system whenever there is a nonzero gradient of vorticity per unit surface density, and regions of parameter space are identified where both principal modes decay. For the special case q = 2, n = 0, the system is found to be unstable.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- July 1986
- DOI:
- 10.1093/mnras/221.2.339
- Bibcode:
- 1986MNRAS.221..339G
- Keywords:
-
- Accretion Disks;
- Astrophysics;
- Dynamic Stability;
- Toruses;
- Corotation;
- Incompressible Flow;
- Inviscid Flow;
- Isentropic Processes;
- Modal Response;
- Perturbation Theory;
- Astrophysics