Differentially-rotating neutron star models with a parametrized rotation profile

TL;DR

This paper investigates how different rotation laws affect the equilibrium and maximum mass of relativistic, differentially-rotating neutron stars, introducing a new generalized rotation law that aligns with simulation data.

Contribution

It introduces a new parametrized rotation law for neutron stars and demonstrates its ability to reproduce angular velocity profiles from binary neutron star merger simulations.

Findings

Maximum mass is sensitive to the rotation law and differential rotation degree.

Equilibrium sequences do not reach T/|W| values above 0.14, indicating stability limits.

The new rotation law effectively models angular velocity profiles from simulations.

Abstract

We analyze the impact of the choice rotation law on equilibrium sequences of relativistic differentially-rotating neutron stars in axisymmetry. The maximum allowed mass for each model is strongly affected by the distribution of angular velocity along the radial direction and by the consequent degree of differential rotation. In order to study the wide parameter space implied by the choice of rotation law, we introduce a functional form that generalizes the so called "j-const. law" adopted in all previous work. Using this new rotation law we reproduce the angular velocity profile of differentially-rotating remnants from the coalescence of binary neutron stars in various 3-dimensional dynamical simulations. We compute equilibrium sequences of differentially rotating stars with a polytropic equation of state starting from the spherically symmetric static case. By analyzing the sequences at constant ratio, T/|W|, of rotational kinetic energy to gravitational binding energy, we find that the parameters that best describe the binary neutron star remnants cannot produce equilibrium configurations with values of T/|W| that exceed 0.14, the criterion for the onset of the secular instability.