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

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: $αM_χ$, an effective control parameter that combines the DM concentration and the DM candidate mass, and $β$, a steepness parameter 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 ($τ$) 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 $f-C-τ$ and $f-Λ-τ$ 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 $Λ_{1.4}$ into the $(f_{1.4},τ_{1.4})$ space, thereby providing observational bounds on the oscillation properties of canonical DM-admixed NS model.