Nonlocal density wave theory for gravitational instability of protoplanetary disks without sharp boundaries

Abstract

The stability of a self‐gravitating infinitesimally thin gaseous disk rotating around a central mass is studied. Our global linear analysis concerns marginal stability, i.e. it yields the critical temperature for the onset of instability for any given ratio of the disk mass to the central mass. Both axisymmetric and low‐m nonaxisymmetric excitations are analysed. When the fractional disk mass increases, the symmetry character of the instability changes from rings (m = 0) to one‐armed trailing spirals (m = 1). The distribution of the surface density along the spiral arms is not uniform, but describes a sequence of maxima that might be identified with forming planets. The number of the mass concentrations decreases with increasing fractional disk mass. We also obtain solutions in the form of global nonaxisymmetric vortices, which are, however, never excited.

Hydrodynamic stability in accretion disks under the combined influence of shear and density stratification

“…The main shortcoming in our presentation is the short-wave assumption ( 22) under which all the above considerations are only valid. Without this assumption, Fourier modes are no longer solutions of the linearized equations and we have to switch to much more complicated mathematics involving integral equations (see Rüdiger & Kitchatinov 2000). We prefer to present numerical simulations for the stability of (isothermal) density-stratified Keplerian disks under the influence of finite disturbances.…”