Rayleigh Adjustment of Narrow Barriers in Protoplanetary Discs

TL;DR

This paper investigates the stability of sharp density features in protoplanetary discs, proposing that Rayleigh-unstable features should be smoothed out by turbulence to maintain disc stability.

Contribution

It introduces the concept of Rayleigh adjustment, a process for diffusing unstable density features in viscous disc models to ensure stability.

Findings

Density features near the vertical scale height may be Rayleigh unstable.

Stability depends on thermodynamics and vertical structure of the disc.

Rayleigh adjustment leads to quasi-continuous smoothing of unstable features.

Abstract

Sharp density features in protoplanetary discs, for instance at the edge of a magnetically dead zone, have recently been proposed as effective barriers to slow down or even stop the problematically fast migration of planetary cores into their central star. Density features on a radial scale approaching the disc vertical scale height might not exist, however, since they could be Rayleigh (or more generally Solberg-Hoiland) unstable. Stability must be checked explicitly in one-dimensional viscous accretion disc models because these instabilities are artificially eliminated in the process of reducing the full set of axisymmetric equations. The disc thermodynamics, via the entropy stratification, and its vertical structure also influence stability when sharp density features are present. We propose the concept of Rayleigh adjustment for viscous disc models: any density feature that violates Rayleigh stability (or its generalization) should be diffused radially by hydrodynamical turbulence on a dynamical time-scale, approaching marginal stability in a quasi-continuous manner.