Stability of Neutron Stars with Dark Matter Core Using Three Crustal Types and the Impact on Mass-Radius Relations

TL;DR

This study examines how dark matter influences neutron star structure and mass-radius relations, revealing that dark matter softens the EoS and reduces star mass, while crust types significantly affect the star's radius.

Contribution

It introduces a model incorporating dark matter into neutron star equations of state and analyzes the impact of different crust types on mass-radius relations.

Findings

Dark matter softens the EoS, lowering maximum neutron star mass.

Crust types significantly increase the star's radius at fixed dark matter parameters.

Dark matter reduces the overall mass of neutron stars.

Abstract

We investigate the effects of dark matter (DM) on the nuclear equation of state (EoS) and neutron star structure, in the relativistic mean field theory, both in the absence and presence of a crust. The $\sigma-\omega$ model is modified by adding a WIMP-DM component, which interacts with nucleonic matter through the Higgs portal. This model agrees well with previous studies which utilized either a more complicated nuclear model or higher-order terms of the Higgs potential, in that DM softens the EoS, resulting in stars with lower maximum masses. However, instabilities corresponding to negative pressure values in the low-energy density regime of the DM-admixed EoS are present, and this effect becomes more prominent as we increase the DM Fermi momentum. We resolve this by confining DM in the star's core. The regions of instability were replaced by three types of crust: first by the Friedman-Pandharipande-Skyrme (FPS), Skyrme-Lyon (SLy) and BSk19 EoS from the Brussels-Montreal Group, which can be represented by analytical approximations. For a fixed value of the DM Fermi momentum $p_F^{DM}$, the DM-admixed neutron star does not have significant changes in its mass with the addition of the crusts. However, the entire mass-radius relation of the neutron star is significantly affected, with an observed increase in the radius of the star corresponding to the mass. The effect of DM is to reduce the mass of the star, while the crust does not affect the radius significantly, as the value of the $p_F^{DM}$ increases.