Improved Universality in the Neutron Star Three-Hair Relations

TL;DR

This paper explores new normalization methods for neutron star multipole moments to enhance the universality of their relations, which could improve astrophysical modeling of pulsars.

Contribution

It identifies optimal normalizations for multipole moments that strengthen equation-of-state universality in neutron star relations, advancing previous findings.

Findings

Stronger universality achieved with new normalizations

Optimal normalization minimizes equation-of-state dependence

Results applicable to modeling pulsar X-ray signals

Abstract

No-hair like relations between the multipole moments of the exterior gravitational field of neutron stars have recently been found to be approximately independent of the star's internal structure. This approximate, equation-of-state universality arises after one adimensionalizes the multipole moments appropriately, which then begs the question of whether there are better ways to adimensionalize the moments to obtain stronger universality. We here investigate this question in detail by considering slowly-rotating neutron stars both in the non-relativistic limit and in full General Relativity. We find that there exist normalizations that lead to stronger equation-of-state universality in the relations among the moment of inertia and the quadrupole, octopole and hexadecapole moments of neutron stars. We determine the optimal normalization that minimizes the equation-of-state dependence in these relations. The results found here may have applications in the modeling of X-ray pulses and atomic line profiles from millisecond pulsars with NICER and LOFT.