On the mechanism of self gravitating Rossby interfacial waves in proto-stellar accretion discs

TL;DR

This paper investigates how self-gravity influences Rossby-like edge waves at density interfaces in proto-stellar discs, revealing conditions for stability and the effects of self-gravity and stratification on wave dynamics.

Contribution

It provides a detailed analysis of self-gravity's role in the stability and propagation of edge waves in proto-stellar discs, including effects of Boussinesq and non-Boussinesq dynamics.

Findings

Self-gravity stabilizes certain wave modes regardless of stratification.

Instability occurs only when pressure gradient opposes density jump.

Self-gravity affects vorticity production and wave propagation characteristics.

Abstract

The dynamical response of edge waves under the influence of self-gravity is examined in an idealized two-dimensional model of a proto-stellar disc, characterized in steady state as a rotating vertically infinite cylinder of fluid with constant density except for a single density interface at some radius r0. The fluid in basic state is prescribed to rotate with a Keplerian profile $\Omega_k(r)\sim r^{-3/2}$ modified by some additional azimuthal sheared flow. A linear analysis shows that there are two azimuthally propagating edge waves, kin to the familiar Rossby waves and surface gravity waves in terrestrial studies, which move opposite to one another with respect to the local basic state rotation rate at the interface. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified) where self-gravity acts as a wave stabilizer irrespective of the stratification of the system. The propagation properties of the waves are discussed in detail in the language of vorticity edge waves. The roles of both Boussinesq and non-Boussinesq effects upon the stability and propagation of these waves with and without the inclusion of self-gravity are then quantified. The dynamics involved with self-gravity non- Boussinesq effect is shown to be a source of vorticity production where there is a jump in the basic state density, in addition, self-gravity also alters the dynamics via the radial main pressure gradient, which is a Boussinesq effect . Further applications of these mechanical insights are presented in the conclusion including the ways in which multiple density jumps or gaps may or may not be stable.