Stability criteria for gaseous selfgravitating disks
Abstract
The stability of spiral perturbations with an arbitrary degree of winding in gaseous astrophysical disks is studied. Simple stability criteria are obtained for localized perturbations. These criteria are formulated in terms of Toomre's stability parameter Q, which, by definition, is equal to unity at the stability boundary of radial perturbations. It turns out that to stabilize arbitrary perturbations requires that Q be greater than some critical value Q_c, where Q_c is considerably greater than unity; i.e., one can say that the perturbations that break the initial axial symmetry of the disk are less stable than the radial perturbations. It is shown that Q_c is only a function of the parameter that determines the extent to which the disk rotation is differential, but it does not depend on the model that is used. In particular, for a plane rotation curve, Q_c is a universal constant (Q_c = square root(3)), both for an infinitely thin disk within a massive halo and for a disk of finite thickness with an arbitrary adiabatic index.
 Publication:

Astronomy Letters
 Pub Date:
 July 1997
 Bibcode:
 1997AstL...23..483P