The reflex instability: exponential growth of a large-scale $m=1$ mode in astrophysical discs

TL;DR

This paper discovers a linear, global $m=1$ mode instability in astrophysical gas discs that causes exponential growth in star-barycenter displacement, potentially affecting disc evolution and planet formation.

Contribution

It identifies and characterizes a new reflex instability in gas discs, demonstrating its dependence on star reflex motion and its potential significance in astrophysical contexts.

Findings

The instability exhibits exponential growth in simulations across various codes.

Disappearance of the instability when star reflex motion is excluded.

Growth timescale decreases with increasing disc mass, reaching a few hundred orbits.

Abstract

We report the finding of a linear, non-axisymmetric, global instability in gas discs around stars, which may be relevant to other astrophysical discs. It takes the form of an $m=1$ mode that grows in the disc density distribution while the star-barycentre distance rises exponentially with a characteristic timescale that is orders of magnitude longer than the orbital period. We present results of hydrodynamical simulations with various codes and numerical methods, using either barycentric or stellocentric reference frames, with or without the disc's self gravity: all simulations consistently show an unstable mode growing exponentially. The instability disappears if, and only if, the reflex motion of the star due to the disc's asymmetry is not taken into account in the simulations. For this reason we refer to this instability as the reflex instability. We identify a feedback loop as a possible origin, whereby the acceleration of the star excites the eccentricity of the disc, yielding an $m=1$ mode in the density distribution which, in turn, pulls the star. The growth timescale of the instability decreases with increasing disc mass and is a few hundred orbits for disc-to-star mass ratios of a few percent. If truly physical, and not due to a numerical artifact that would be common to all the codes we have employed, the reflex instability could have a dramatic impact on protoplanetary discs evolution and planetary formation.