Nonlinear r-modes in neutron stars: A hydrodynamical limitation on r-mode amplitudes

TL;DR

This paper identifies a nonlinear hydrodynamic coupling mechanism that limits the amplitude of r-modes in neutron stars, showing that the instability is only valid for small amplitudes below approximately 0.01.

Contribution

It reveals the specific three-mode coupling responsible for catastrophic decay of large amplitude r-modes in neutron stars.

Findings

The coupling strength is sufficient to limit r-mode amplitudes to below 10^{-2}.

The decay mechanism involves particular fluid mode interactions.

The usual r-mode instability picture applies only at small amplitudes.

Abstract

Previously we found that large amplitude $r$-modes could decay catastrophically due to nonlinear hydrodynamic effects. In this paper we found the particular coupling mechanism responsible for this catastrophic decay, and identified the fluid modes involved. We find that for a neutron star described by a polytropic equation of state with polytropic index $\Gamma=2$, the coupling strength of the particular three-mode interaction causing the decay is strong enough that the usual picture of the $r$-mode instability with a flow pattern dominated by that of an $r$-mode can only be valid for the dimensionless $r$-mode amplitude less than $O(10^{-2})$.