# Probing crustal structures from neutron star compactness

## TL;DR

This paper investigates neutron star crust and pasta phase thicknesses across various EOS parameters, deriving formulas linking these thicknesses to stellar compactness and nuclear matter properties, enabling constraints on crust structure via compactness.

## Contribution

The study provides new fitting formulas relating crust and pasta phase thicknesses to neutron star compactness and nuclear matter parameters, aiding in constraining crust properties.

## Key findings

- Crust and spherical nuclei phase thicknesses strongly depend on compactness.
- Both crust and spherical nuclei phase thicknesses show weak dependence on EOS parameters.
- Formulas enable constraining crust structure through compactness measurements.

## Abstract

With various sets of the parameters that characterize the equation of state (EOS) of nuclear matter, we systematically examine the thickness of a neutron star crust and of the pasta phases contained therein. Then, with respect to the thickness of the phase of spherical nuclei, the thickness of the cylindrical phase, and the crust thickness, we successfully derive fitting formulas that express the ratio of each thickness to the star's radius as a function of the star's compactness, the incompressibility of symmetric nuclear matter, and the density dependence of the symmetry energy. In particular, we find that the thickness of the phase of spherical nuclei has such a strong dependence on the stellar compactness as the crust thickness, but both of them show a much weaker dependence on the EOS parameters. Thus, via determination of the compactness, the thickness of the phase of spherical nuclei as well as the crust thickness can be constrained reasonably, even if the EOS parameters remain to be well-determined.