Highly-accurate neutron star modeling in the Hartle-Thorne Approximation

TL;DR

This paper extends the Hartle-Thorne approximation to seventh order in spin for neutron star modeling, providing precise analytical solutions for gravitational fields and multipole moments crucial for interpreting future astrophysical observations.

Contribution

It develops high-order perturbation equations and exact solutions for slowly-rotating neutron stars, enhancing the accuracy of gravitational field models up to seventh order in spin.

Findings

Derived analytical solutions for exterior metric at each spin order

Calculated multipole moments up to seventh order in spin

Enabled precise modeling of neutron star observables for future data

Abstract

Future X-ray missions, such as NICER and LOFT, together with gravitational-wave observations from ground-based detectors, will provide new insights into neutron stars. Interpreting accurate observations in the future will require accurate models of their gravitational fields. In this first paper of a two-part series, we construct the perturbation equations for slowly-rotating, isolated, and unmagnetized neutron stars, extending the Hartle-Thorne approximation to seventh order in a slow-rotation expansion. We obtain exact, closed-form, analytical solutions for the exterior metric at each order in spin. From these solutions, we derive expressions for the mass and mass-current scalar multipole moments, $M_{\ell}$ and $S_{\ell}$, respectively, up to seventh order in spin frequency, using two distinct methods. This high-order expansion allows us to calculate second-, fourth-, and sixth-order relative spin corrections to the observed mass and moment of inertia; second- and fourth-order relative spin corrections to the quadrupole and octopole moments; second-order relative spin corrections to the hexadecapole and dotriacontapole moments; and leading-order-in-spin expressions for the hexacontatetrapole and hectoicosaoctapole moments. Going to seventh order in the spin-frequency approximation will enable very precise calculations of X-ray pulse profiles, as well as the I-Love-Q and three-hair relations for slowly-rotating neutron stars. These results will be valuable for breaking parameter degeneracies in future multimessenger observations.