Quadrupole moments of rotating neutron stars and strange stars

TL;DR

This paper investigates the quadrupole moments of rotating neutron and strange stars using the Hartle-Thorne method, revealing uniformity in the $QM/J^2$ parameter across equations of state and proposing a potential observational distinction between star types.

Contribution

It provides a comprehensive analysis of quadrupole moments for neutron and strange stars across various equations of state, highlighting a nearly universal relation for neutron stars and a method to differentiate star types.

Findings

$QM/J^2$ approaches 1 for Kerr black holes at high mass.

Neutron stars show nearly universal $QM/J^2$ vs. compactness relation.

Strange stars exhibit distinct $QM/J^2$ behavior, enabling differentiation.

Abstract

We present results for models of neutron stars and strange stars constructed using the Hartle-Thorne slow-rotation method with a wide range of equations of state, focusing on the values obtained for the angular momentum $J$ and the quadrupole moment $Q$, when the gravitational mass $M$ and the rotational frequency $\Omega$ are specified. Building on previous work, which showed surprising uniformity in the behaviour of the moment of inertia for neutron-star models constructed with widely-different equations of state, we find similar uniformity for the quadrupole moment. These two quantities, together with the mass, are fundamental for determining the vacuum space-time outside neutron stars. We study particularly the dimensionless combination of parameters $QM/J^2$ (using units for which $c=G=1$). This quantity goes to 1 in the case of a Kerr-metric black hole and deviations away from 1 then characterize the difference between neutron-star and black-hole space-times. It is found that $QM/J^2$ for both neutron stars and strange stars decreases with increasing mass, for a given equation of state, reaching a value of around 2 (or even less) for maximum-mass models, meaning that their external space-time is then rather well approximated by the Kerr metric. If $QM/J^2$ is plotter against compactness $R/2M$ (where $R$ is the radius), it is found that the relationship is nearly unique for neutron-star models, independent of the equation of state, while it is significantly different for strange stars. This gives a new way of possibly distinguishing between them.