The stability of accretion tori. IV - Fission and fragmentation of slender, self-gravitating annuli

Abstract

Results on the dynamical evolution of 2D, geometrically slender, differentially rotating, self-gravitating annuli orbiting around a central mass are presented. The equilibrium of a 2D compressible, self-gravitating annulus of arbitrary radial width is discussed, and the equilibrium structure of an n = 1 annulus in the 'slender' approximation is solved. Linear stability analysis of the equilibrium solutions is performed, and results corresponding to constant specific angular momentum annuli are presented. Numerical, fully nonlinear, hydrodynamical model evolutions of some slender annuli are described, and the linear and nonlinear results are compared. An interpretation of the physics of the instabilities is presented.