Low-mass neutron stars: universal relations, the nuclear symmetry energy and gravitational radiation

TL;DR

This paper investigates low-mass neutron stars, extending empirical relations to include rotation and tidal effects, and explores how these can constrain nuclear symmetry energy parameters through electromagnetic and gravitational-wave observations.

Contribution

It extends existing models of neutron star properties to account for rotation and tidal deformation, providing new fitting formulas for observational constraints.

Findings

Derived fits for moment of inertia, quadrupole moment, and Love numbers as functions of nuclear parameters.

Extended empirical relations to slowly rotating and tidally deformed neutron stars.

Potential to constrain nuclear symmetry energy parameters through astrophysical observations.

Abstract

The lowest neutron star masses currently measured are in the range $1.0-1.1~M_\odot$, but these measurement have either large uncertainties or refer to isolated neutron stars. The recent claim of a precisely measured mass $M/M_{\odot} = 1.174 \pm 0.004$ by Martinez et al [Astrophys. J. 812, 143 (2015)] in a double neutron star system suggests that low-mass neutron stars may be an interesting target for gravitational-wave detectors. Furthermore, Sotani et al [PTEP 2014, 051E01 (2014)] recently found empirical formulas relating the mass and surface redshift of nonrotating neutron stars to the star's central density and to the parameter $\eta\equiv (K_0 L^2)^{1/3}$, where $K_0$ is the incompressibility of symmetric nuclear matter and $L$ is the slope of the symmetry energy at saturation density. Motivated by these considerations, we extend the work by Sotani et al to slowly rotating and tidally deformed neutron stars. We compute the moment of inertia, quadrupole moment, quadrupole ellipticity, tidal and rotational Love number and apsidal constant of slowly rotating neutron stars by integrating the Hartle-Thorne equations at second order in rotation, and we fit all of these quantities as functions of $\eta$ and of the central density. These fits may be used to constrain $\eta$, either via observations of binary pulsars in the electromagnetic spectrum, or via near-future observations of inspiralling compact binaries in the gravitational-wave spectrum.