Effect of the crust on neutron star empirical relations

TL;DR

This study investigates how the neutron star crust's equation of state influences key astrophysical relations and constraints, finding that the crust's impact is generally small but significant in certain mass-dependent relations.

Contribution

It introduces model-independent, thermodynamically consistent equations of state for neutron star matter, analyzing the crust's effect on empirical relations and observational constraints.

Findings

Crust effects on most relations are below 2%.

The relation between tidal deformability and radius becomes crust-independent for massive stars.

The crust influences the correlation between effective tidal deformability and binary neutron star radius by about 14%.

Abstract

We analyze how the crust equation of state affects several neutron star properties and how it impacts on possible constraints inferred from astrophysical observations. Using three distinct crusts, we generate three sets of model-independent equations of state describing stellar matter from a Taylor expansion around saturation density. The equations of state are thermodynamically consistent, causal, and compatible with astrophysical observations. The relations between the tidal deformability $\Lambda$ and compactness $C$, Love number $k_2$ and radius of neutron star with mass $M$ are studied, and the effect of the crust equation of state on these relations analyzed. In most of the relations, the impact of the crust equation of state is not larger that 2\%. If, however, a fixed neutron star mass is considered, the relation between the tidal deformability and the radius depends on the crust. We have found that the relation $\Lambda_{M_i} = \alpha R_{M_i}^{\beta}$ becomes almost exact and crust independent for massive neutron stars. It is shown that it is possible to determine the tidal deformability of an 1.4$M_\odot$ star from the GW179817 effective tidal deformability $\tilde\Lambda$ with an accuracy of at least $\approx 10\%$. A high correlation between $\tilde\Lambda$ and the radius of the most massive star of the neutron star binary was confirmed, however, it was demonstrated that the crust has an effect of $\approx 14\%$ on this relation. We have found that the relation $\Lambda_1/\Lambda_2=q^a$ depends on $M_{\text{chirp}}$ as $a\sim \sqrt{M_{\text{chirp}}}$.