Nonlinear hydrodynamical evolution of eccentric Keplerian discs in two dimensions: validation of secular theory

TL;DR

This study uses 2D hydrodynamical simulations to validate and extend secular theory for eccentric Keplerian discs, revealing nonlinear effects and long-term eccentricity persistence relevant to astrophysical phenomena.

Contribution

It derives a nonlinear secular theory explaining eccentricity precession faster than linear predictions and validates it with simulations, highlighting effects in highly eccentric discs.

Findings

Linear theory accurately predicts small eccentricity disc behavior.

Nonlinear effects cause faster retrograde precession in larger eccentricities.

Eccentricity remains long-lived despite weak damping mechanisms.

Abstract

We perform global two-dimensional hydrodynamical simulations of Keplerian discs with free eccentricity over thousands of orbital periods. Our aim is to determine the validity of secular theory in describing the evolution of eccentric discs, and to explore their nonlinear evolution for moderate eccentricities. Linear secular theory is found to correctly predict the structure and precession rates of discs with small eccentricities. However, discs with larger eccentricities (and eccentricity gradients) are observed to precess faster (retrograde relative to the orbital motion), at a rate that depends on their eccentricities (and eccentricity gradients). We derive analytically a nonlinear secular theory for eccentric gas discs, which explains this result as a modification of the pressure forces whenever eccentric orbits in a disc nearly intersect. This effect could be particularly important for highly eccentric discs produced in tidal disruption events, or for narrow gaseous rings; it might also play a role in causing some of the variability in superhump binary systems. In two dimensions, the eccentricity of a moderately eccentric disc is long-lived and persists throughout the duration of our simulations. Eccentric modes are however weakly damped by their interaction with non-axisymmetric spiral density waves (driven by the Papaloizou-Pringle instability, which occurs in our idealised setup with solid walls), as well as numerical diffusion.