Convective stability analysis of massive neutron stars formed in binary mergers

TL;DR

This study uses general-relativistic simulations to analyze the convective stability and mode characteristics of massive neutron stars formed after binary mergers, finding no large-scale convective instability and questioning the physical origin of certain observed modes.

Contribution

It introduces a new stability criterion for hot, differentially rotating relativistic stars and applies it to post-merger neutron stars, providing insights into their convective stability and mode excitation.

Findings

No evidence of large-scale convective instability in massive NSs.

Rotational effects enhance local stability against convection.

Observed m=1 mode growth may be due to numerical artifacts.

Abstract

We perform fully general-relativistic hydrodynamics simulations of binary neutron star mergers over $100\,\rm ms$ post-merger to investigate the dynamics of remnant massive neutron stars (NSs). Our focus is mainly on the analysis of convective stability and mode characteristics of the massive NSs. We derive stability criteria for hot, differentially rotating relativistic stars that account for both buoyant and rotational restoring forces, and apply them for the first time to the post-merger massive NSs. Our results show no evidence of large-scale convective instability, as both angle-averaged specific entropy and specific angular momentum increase outward within the massive NSs. Rotational effects significantly enhance stability for local regions that would be otherwise unstable by the Schwarzschild criterion. Additionally, our mode analysis of matter fields and gravitational waves reveals no excitation of observable inertial modes after the damping of quadrupolar $f$-modes in the massive NSs, contrasting with previous studies. As in many previous works, we observe the excitation of an $m=1$ one-armed mode. However, we also find that the growth of the $m=1$ mode amplitude after the merger may correlate strongly with the violation of linear momentum conservation, indicating that we cannot reject the possibility that the excitation of the one-armed mode has a numerical origin.