Hydrodynamic instability in eccentric astrophysical discs

TL;DR

This paper investigates the hydrodynamic instabilities in eccentric astrophysical discs, revealing their tendency to generate turbulence and affect disc evolution through a combination of analytical and numerical methods.

Contribution

It provides a comprehensive analysis of the linear stability of eccentric discs, including analytical explanations for small eccentricities and the identification of parametric excitation of inertial waves.

Findings

Eccentric discs are generally unstable to small-scale inertial waves.

Vertical oscillations play a crucial role in disc stability.

Instabilities can lead to turbulence, affecting disc eccentricity and mixing.

Abstract

Eccentric Keplerian discs are believed to be unstable to three-dimensional hydrodynamical instabilities driven by the time-dependence of fluid properties around an orbit. These instabilities could lead to small-scale turbulence, and ultimately modify the global disc properties. We use a local model of an eccentric disc, derived in a companion paper, to compute the nonlinear vertical ("breathing mode") oscillations of the disc. We then analyse their linear stability to locally axisymmetric disturbances for any disc eccentricity and eccentricity gradient using a numerical Floquet method. In the limit of small departures from a circular reference orbit, the instability of an isothermal disc is explained analytically. We also study analytically the small-scale instability of an eccentric neutrally stratified polytropic disc with any polytropic index using a WKB approximation. We find that eccentric discs are generically unstable to the parametric excitation of small-scale inertial waves. The nonlinear evolution of these instabilities should be studied in numerical simulations, where we expect them to lead to a decay of the disc eccentricity and eccentricity gradient as well as to induce additional transport and mixing. Our results highlight that it is essential to consider the three-dimensional structure of eccentric discs, and their resulting vertical oscillatory flows, in order to correctly capture their evolution.