Universal relations for differentially rotating relativistic stars at the threshold to collapse

TL;DR

This paper discovers universal relations in differentially rotating relativistic stars at the collapse threshold, which are largely independent of the degree of differential rotation and applicable across various equations of state.

Contribution

It extends the known universal relations for uniformly rotating stars to differentially rotating models, providing a computationally efficient way to estimate collapse conditions.

Findings

Universal relations hold for differentially rotating models with high accuracy.

Relations are insensitive to the degree of differential rotation.

Applicable across multiple equations of state.

Abstract

A binary neutron star merger produces a rapidly and differentially rotating compact remnant whose lifespan heavily affects the electromagnetic and gravitational emissions. Its stability depends on both the equation of state (EOS) and the rotation law and it is usually investigated through numerical simulations. Nevertheless, by means of a sufficient criterion for secular instability, equilibrium sequences can be used as a computationally inexpensive way to estimate the onset of dynamical instability, which, in general, is close to the secular one. This method works well for uniform rotation and relies on the location of turning points: stellar models that are stationary points in a sequence of equilibrium solutions with constant rest mass or angular momentum. Here, we investigate differentially rotating models (using a large number of equations of state and different rotation laws) and find that several universal relations between properly scaled gravitational mass, rest mass and angular momentum of the turning-point models that are valid for uniform rotation, are insensitive to the degree of differential rotation, to high accuracy.