Toward Realistic and Practical No-Hair Relations for Neutron Stars in the Non-Relativistic Limit

TL;DR

This paper extends the understanding of no-hair relations for neutron stars in the Newtonian limit, demonstrating their universality for realistic equations of state and deriving analytical relations with high accuracy.

Contribution

It shows that universal relations hold for realistic neutron star equations of state and provides analytical formulas that closely match semi-analytic results.

Findings

Universality of no-hair relations extends to realistic equations of state.

Analytical relations reproduce semi-analytic results within 1%.

Linear-order perturbation sometimes vanishes, indicating deeper universality.

Abstract

The gravitational properties of astrophysical objects depend sensitively on their internal structure. In Newtonian theory, the gravitational potential of a rotating star can be fully described by an infinite number of multipole moments of its mass distribution. Recently, this infinite number of moments for uniformly-rotating stars were shown semi-analytically to be expressible in terms of just the first three: the mass, the spin, and the quadrupole moment of the star. The relations between the various lower multipole moments were additionally shown to depend weakly on the equation of state, when considering neutron stars and assuming single polytropic equations of state. Here we extend this result in two ways. First, we show that the universality also holds for realistic equations of state, thus relaxing the need to use single polytropes. Second, we derive purely analytical universal relations by perturbing the equations of structure about an $n=0$ polytrope that reproduce semi-analytic results to $\mathcal{O}(1\%)$. We also find that the linear-order perturbation vanishes in some cases, which provides further evidence and a deeper understanding of the universality.