Local stability of self-gravitating fluid disks made of two components in relative motion

Abstract

Context. We consider a simple self-gravitating disk, made of two fluid components characterized by different effective thermal speeds and interacting with one another only through gravity; two-component models of this type have often been considered in order to estimate the impact of the cold interstellar medium on gravitational instabilities in star-dominated galaxy disks. Aims. This simple model allows us to produce a unified description of instabilities in non-viscous self-gravitating disks, some originating from Jeans collapse, and others from the relative motion between the two components. In particular, the model suggests that the small streaming velocity between the two components associated with the so-called asymmetric drift may be the origin of instability for suitable non-axisymmetric perturbations. Methods. The result is obtained by examining the properties of a local, linear dispersion relation for tightly wound density waves in such two-component model. The parameters characterizing the equilibrium model and the related dispersion relation allow us to recover as natural limits the cases, known in the literature, in which the relative drift between the two components is ignored. Results. Dynamically, the instability is similar to (although gentler than) that known to affect counter-rotating disks. However, in contrast to the instability induced by counter-rotation, which is a relatively rare phenomenon, the mechanism discussed in this paper is likely to be rather common in nature. Conclusions. We briefly indicate some consequences of the instability on the evolution of galaxy disks and possible applications to other astrophysical systems, in particular to protostellar disks and accretion disks.