General relativistic study of $f$-mode oscillations in neutron stars with gravitationally bound dark matter

TL;DR

This paper investigates how gravitationally bound dark matter affects neutron star oscillations, revealing modifications in mode frequencies and damping times, and connects these effects with gravitational wave observations within a full general relativity framework.

Contribution

It introduces a detailed model of dark matter distribution in neutron stars and analyzes its impact on nonradial oscillation modes using full general relativity, including universal relations and observational constraints.

Findings

Dark matter distribution alters $f$-mode frequencies and damping times.

Enhanced coupling between matter and spacetime perturbations due to dark matter.

Derived observational bounds on dark matter effects from GW170817 data.

Abstract

A comprehensive investigation of nonradial oscillations in neutron star (NS) admixed with gravitationally bounded dark matter (DM) is carried out within the framework of full general relativity. The relativistic mean field (RMF) formalism is employed to illustrate the hadronic equation of state (EOS), while a physically motivated, gravitationally captured, non-uniform fermionic Higgs-portal DM component is incorporated to model DM-admixed NS. The DM distribution is characterized by two free parameters: $\alpha M_\chi$, an effective scaling factor that combines the DM concentration and the DM candidate mass, and $\beta$, a steepness index controlling the DM density distribution. The quasi normal mode (QNM) characteristics such as fundamental ($f$) mode frequency and its corresponding gravitational-wave (GW) damping time ($\tau$) is calculated for DM-admixed NS by solving the general relativistic perturbed equations involving axial as well as polar modes. The study demonstrates how the inclusion of DM distribution modifies the $f$-mode frequency and enhances the damping rate, reflecting a stronger coupling between matter and spacetime perturbations. Considering DM effects, the correlation analysis among DM model parameters, NS observables and QNM characteristics also carried out. Analytic fits for the $f-C-\tau$ and $f-\Lambda -\tau$ relations are constructed and calibrated for DM-admixed NS models. Building upon asteroseismic universal relations (URs), multimessenger constraint from the GW170817 event is employed by mapping the tidal deformability $\Lambda_{1.4}$ into the $(f_{1.4},\tau_{1.4})$ space, thereby providing observational bounds on the oscillation properties of canonical DM-admixed NS model.