On the Solution Space of Differentially Rotating Neutron Stars in General Relativity

TL;DR

This paper uses a high-precision spectral code to explore the diverse solution space of differentially rotating neutron stars in general relativity, revealing new configurations and transitions relevant for astrophysics.

Contribution

It introduces detailed analysis of the solution space, including new spheroidal configurations and the transition to toroidal bodies, expanding understanding beyond previous numerical limitations.

Findings

Sequences terminate at mass-shedding limits for weak differential rotation.

Moderate to strong differential rotation leads to a transition to toroidal configurations.

Various new spheroidal configurations were identified in the solution space.

Abstract

A highly accurate, multi-domain spectral code is used in order to construct sequences of general relativistic, differentially rotating neutron stars in axisymmetry and stationarity. For bodies with a spheroidal topology and a homogeneous or an N=1 polytropic equation of state, we investigate the solution space corresponding to broad ranges of degree of differential rotation and stellar densities. In particular, starting from static and spherical configurations, we analyse the changes of the corresponding surface shapes as the rate of rotation is increased. For a sufficiently weak degree of differential rotation, the sequences terminate at a mass-shedding limit, while for moderate and strong rates of differential rotation, they exhibit a continuous parametric transition to a regime of toroidal fluid bodies. In this article, we concentrate on the appearance of this transition, analyse in detail its occurrence and show its relevance for the calculation of astrophysical sequences. Moreover, we find that the solution space contains various types of spheroidal configurations, which were not considered in previous work, mainly due to numerical limitations.