Equilibrium sequences of differentially rotating stars with post-merger-like rotational profiles

TL;DR

This paper introduces new equilibrium models of differentially rotating relativistic stars with profiles inspired by binary neutron star merger remnants, comparing different rotation laws and assessing approximation accuracy.

Contribution

It presents a new rotation law for relativistic stars, enabling models that match merger remnant profiles while maintaining quasi-spherical shapes.

Findings

The new rotation law has minimal impact on mass but affects radius.

Models can replicate merger remnant rotational profiles and axis ratios.

The IWM-CFC approximation remains sufficiently accurate for these models.

Abstract

We present equilibrium sequences of rotating relativistic stars, constructed with a new rotation law that was proposed by Uryu et al. (2017). We choose rotational parameters motivated by simulations of binary neutron star merger remnants, but otherwise adopt a cold, relativistic N=1 polytropic EOS, in order to perform a detailed comparison to published equilibrium sequences that used the Komatsu, Eriguchi and Hachisu (1989) rotation law. We find a small influence of the choice of rotation law on the mass of the equilibrium models and a somewhat larger influence on their radius. The versatility of the new rotation law allows us to construct models that have a similar rotational profile and axis ratio as observed for merger remnants, while at the same time being quasi-spherical. More specifically, we construct equilibrium sequence variations with different degrees of differential rotation and identify type A and type C solutions, similar to the corresponding types in the classification of Ansorg, Gondek-Rosinska and Villain (2009). While our models are highly accurate solutions of the fully general relativistic structure equations, we demonstrate that for models relevant to merger remnants the IWM-CFC approximation still maintains an acceptable accuracy.