# Consistent Skyrme parametrizations constrained by GW170817

## TL;DR

This paper evaluates Skyrme parametrizations consistent with nuclear constraints against gravitational wave data from GW170817, finding they accurately predict neutron star radii, tidal deformabilities, and support the universal I-Love relation.

## Contribution

It introduces a set of consistent Skyrme parametrizations that align with nuclear matter constraints and gravitational wave observations, enhancing neutron star modeling accuracy.

## Key findings

- CSkP predict neutron star radii between 11.86 km and 12.55 km.
- CSkP results are compatible with LIGO/Virgo tidal deformability bounds.
- A correlation between tidal deformability and radius is established.

## Abstract

The high-density behavior of the stellar matter composed of nucleons and leptons under $\beta$~equilibrium and charge neutrality conditions is studied with the Skyrme parametrizations shown to be consistent (CSkP) with the nuclear matter, pure neutron matter, symmetry energy and its derivatives in a set of $11$ constraints [Dutra {\it et al.}, Phys. Rev. C 85, 035201 (2012)]. The predictions of these parametrizations on the tidal deformabilities related to the GW170817 event are also examined. The CSkP that produce massive neutron stars give a range of $11.86~\mbox{km} \leqslant R_{1.4} \leqslant 12.55~\mbox{km}$ for the canonical star radius, in agreement with other theoretical predictions. It is shown that the CSkP are compatible with the region of masses and radii obtained from the analysis of recent data from LIGO and Virgo Collaboration (LVC). A correlation between dimensionless tidal deformability and radius of the canonical star is found, namely, $\Lambda_{1.4} \approx 3.16\times10^{-6}R_{1.4}^{7.35}$, with results for the CSkP compatible with the recent range of $\Lambda_{1.4}=190_{-120}^{+390}$ from LVC. An analysis of the $\Lambda_1\times\Lambda_2$ graph shows that all the CSkP are compatible with the recent bounds obtained by LVC. Finally, the universal correlation between the moment of inertia and the deformability of a neutron star, named as the \mbox{$I$-Love} relation, is verified for the CSkP, that are also shown to be consistent with the prediction for the moment of inertia of the \mbox{PSR J0737-3039} primary component pulsar.