On the stability and maximum mass of differentially rotating relativistic stars

TL;DR

This paper investigates the stability and maximum mass of differentially rotating relativistic stars, establishing a stability criterion and universal relations that allow estimating the maximum mass supported by differential rotation.

Contribution

It introduces a stability criterion for differentially rotating neutron stars and derives quasi-universal relations to estimate their maximum mass based on nonrotating star models.

Findings

A stability criterion similar to uniform rotation applies to differential rotation.

Quasi-universal relations enable estimation of maximum mass supported by differential rotation.

Maximum mass can be approximated as about 1.54 times the nonrotating maximum mass.

Abstract

The stability properties of rotating relativistic stars against prompt gravitational collapse to a black hole are rather well understood for uniformly rotating models. This is not the case for differentially rotating neutron stars, which are expected to be produced in catastrophic events such as the merger of binary system of neutron stars or the collapse of a massive stellar core. We consider sequences of differentially rotating equilibrium models using the $j$-constant law and by combining them with their dynamical evolution, we show that a sufficient stability criterion for differentially rotating neutron stars exists similar to the one of their uniformly rotating counterparts. Namely: along a sequence of constant angular momentum, a dynamical instability sets in for central rest-mass densities slightly below the one of the equilibrium solution at the turning point. In addition, following Breu & Rezzolla (2016), we show that "quasi-universal" relations can be found when calculating the turning-point mass. In turn, this allows us to compute the maximum mass allowed by differential rotation, $M_{\rm max,dr}$, in terms of the maximum mass of the nonrotating configuration, $M_{_{\rm TOV}}$, finding that $M_{\rm max, dr} \simeq \left(1.54 \pm 0.05\right) M_{_{\rm TOV}}$ for all the equations of state we have considered.