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

Pinku Routaray

TL;DR

This paper investigates nonradial $f$-mode oscillations in neutron stars admixed with gravitationally bound dark matter using full general relativity. The authors adopt a single-fluid, Higgs-portal DM model with a physically motivated non-uniform DM density described by two parameters, $\alpha M_χ$ and $β$, embedded into a relativistic mean-field hadronic EOS, and solve the TOV equations together with GR perturbations to obtain complex QNM frequencies via the Zerilli formalism. They derive analytic fits for the $f$-mode frequency versus compactness and tidal deformability ($f$-$C$-$τ$ and $f$-$Λ$-$τ$ relations), and examine correlations and universal relations (URs) in the presence of DM, including a GW170817-driven constraint on the canonical NS oscillation properties. The results show that DM softens the EOS, lowering the maximum mass and radius while increasing the $f$-mode frequency and decreasing the damping time; URs largely survive DM admixture, enabling DM–NS properties to be constrained by future multimessenger observations. Overall, the study provides a framework to connect microscopic DM parameters to macroscopic NS observables and GW signals, highlighting how asteroseismology can help bound Higgs-portal DM scenarios in light of GW 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: $αM_χ$, an effective scaling factor that combines the DM concentration and the DM candidate mass, and $β$, 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 ($τ$) 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.

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

TL;DR

This paper investigates nonradial -mode oscillations in neutron stars admixed with gravitationally bound dark matter using full general relativity. The authors adopt a single-fluid, Higgs-portal DM model with a physically motivated non-uniform DM density described by two parameters, and , embedded into a relativistic mean-field hadronic EOS, and solve the TOV equations together with GR perturbations to obtain complex QNM frequencies via the Zerilli formalism. They derive analytic fits for the -mode frequency versus compactness and tidal deformability (-- and -- relations), and examine correlations and universal relations (URs) in the presence of DM, including a GW170817-driven constraint on the canonical NS oscillation properties. The results show that DM softens the EOS, lowering the maximum mass and radius while increasing the -mode frequency and decreasing the damping time; URs largely survive DM admixture, enabling DM–NS properties to be constrained by future multimessenger observations. Overall, the study provides a framework to connect microscopic DM parameters to macroscopic NS observables and GW signals, highlighting how asteroseismology can help bound Higgs-portal DM scenarios in light of GW 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: , an effective scaling factor that combines the DM concentration and the DM candidate mass, and , a steepness index controlling the DM density distribution. The quasi normal mode (QNM) characteristics such as fundamental () mode frequency and its corresponding gravitational-wave (GW) damping time () 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 -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 and 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 into the space, thereby providing observational bounds on the oscillation properties of canonical DM-admixed NS model.

Paper Structure

This paper contains 17 sections, 31 equations, 12 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Formalism
  3. Equation of State of Dark Matter Admixed Neutron Star
  4. Hydrostatic Equilibrium
  5. Quasinormal Modes
  6. Results And Discussions
  7. Mass-radius relations
  8. Dark matter effects on Quasinormal modes
  9. Correlation Study
  10. Universal relations in DM-admixed NS asteroseismology
  11. $\bar{\omega}-C$ relation
  12. $\bar{\omega}-\Lambda$ relation
  13. Summary and Conclusion
  14. Hadronic equation of state
  15. Equations to solve the non-radial Quasinormal modes
  16. ...and 2 more sections

Figures (12)

  • Figure 1: The mass-radius relation of DM-admixed NS is shown. Different choices of $\alpha M_\chi$ parameter are compared at different steepness parameter in different panels; $\beta=1$ (a), $\beta=2$ (b) and $\beta=4$ (c). The $1\sigma$ and $2\sigma$ mass-radius constraints from PSR J0030+0451 Riley_2019 and PSR J0740+6620 Riley_2021 are used. Also, the $50\%$ and $90\%$ confidence intervals from the LIGO-Virgo analysis for binary NS components of the GW170817 event are imposed Abbott_2017.
  • Figure 2: The maximum DM mass fraction is plotted with $\alpha M_\chi$ at different $\beta$,
  • Figure 3: The $f$-mode frequency (left panel) and damping time (right panel) are plotted with mass of the DM-admixed NS.
  • Figure 4: Same as Fig. \ref{['fig:fd_m']}, but with tidal deformability.
  • Figure 5: Panel (a): The $f$-mode frequency is shown for $1.0 \ M_\odot$, $1.2 \ M_\odot$, and $1.4 \ M_\odot$ DM-admixed NS models as a function of $\alpha M_\chi$ at fixed $\beta$. Panel (b): Same as panel (a), but for the damping time.
  • ...and 7 more figures