Relations Between Neutron-Star Parameters in the Hartle-Thorne Approximation

TL;DR

This paper derives analytic and empirical relations connecting key neutron star parameters within the Hartle-Thorne approximation, aiding observational modeling and parameter estimation.

Contribution

It provides new analytic formulas and empirical relations linking neutron star surface ellipticity, compactness, spin, and quadrupole moment, simplifying observational analysis.

Findings

Analytic expressions match numerical results within a few percent.

Empirical relations effectively connect compactness, spin, and quadrupole moment.

Simplifies modeling of neutron star observations for mass, radius, and equation of state.

Abstract

Using stellar structure calculations in the Hartle-Thorne approximation, we derive analytic expressions connecting the ellipticity of the stellar surface to the compactness, the spin angular momentum, and the quadrupole moment of the spacetime. We also obtain empirical relations between the compactness, the spin angular momentum, and the spacetime quadrupole. Our formulae reproduce the results of numerical calculations to within a few percent and help reduce the number of parameters necessary to model the observational appearance of moderately spinning neutron stars. This is sufficient for comparing theoretical spectroscopic and timing models to observations that aim to measure the masses and radii of neutron stars and to determine the equation of state prevailing in their interiors.