[Paper Review] Constraining neutron star properties and dark matter admixture with the NITR-I equation of state: Insights from observations and universal relations

Pinku Routaray, Harish Chandra Das+2 more|arXiv (Cornell University)|Jul 24, 2023

Pulsars and Gravitational Waves ResearchPhysics and Astronomy3 citations

TL;DR

This study proposes a new relativistic mean-field (INRS) equation of state for neutron stars with dark matter (DM) admixture, using observational constraints from PSR J0952-0607 and HESS J1731-347. It demonstrates that DM with Fermi momentum up to 0.045 GeV is consistent with mass, radius, tidal deformability, and NICER bounds, while increasing DM enhances nonradial f-mode oscillation frequencies and softens the EOS, supporting HESS J1731-347 as a potential DM-admixed neutron star.

ABSTRACT

A recent observational study has constrained the maximum mass of neutron stars (NSs), with particular attention to PSR J0952-0607 and the compact star remnant HESS J1731-347, especially in the low-mass regime. Building on our earlier work, which developed the NITR energy density functional (EDF) to reproduce the mass limit of PSR J0952-0607 but did not satisfy other observational constraints, this study introduces a refined EDF named ``NITR-I". NITR-I successfully reconciles the PSR J0952-0607 mass limit with observational data, including radius measurements from NICER+XMM and tidal deformability constraints from GW170817, demonstrating its robustness. The low-mass constraint associated with HESS J1731-347 indicates diverse NS compositions. Since NITR-I alone cannot satisfy this constraint, we explore the role of dark matter (DM) within NSs to bridge the gap. Incorporating DM, particularly at specific Fermi momentum values, enables the model to address this constraint. We further analyze the influence of DM on various NS properties, such as tidal deformability and non-radial $f$-mode oscillations, across multiple relativistic mean-field models. The presence of DM suggests a reduction in tidal deformability and shifts in oscillation frequencies, potentially offering detectable signatures in gravitational wave observations from neutron star mergers. Additionally, we investigate universal relations (URs) for DM-admixed NSs, focusing on correlations such as compactness versus tidal deformability and $f$-mode frequency versus tidal deformability. Canonical values for these properties are estimated using GW170817 data, offering further insights into the structure and composition of neutron stars.

Motivation & Objective

• To investigate the viability of dark matter admixture in neutron stars using observational constraints from PSR J0952-0607 and HESS J1731-347.
• To develop a new relativistic mean-field (INRS) equation of state that reproduces the mass of PSR J0952-0607 (2.35 M☉) and incorporates dark matter.
• To constrain the amount of dark matter in neutron stars using multimessenger data, including NICER, GW170817, and GW190814.
• To analyze the impact of dark matter on tidal deformability and nonradial f-mode oscillations in neutron stars.

Proposed method

• A new relativistic mean-field (RMF) model, named INRS, is formulated to reproduce the mass of PSR J0952-0607 and incorporate dark matter via a single-fluid approach.
• The equation of state (EOS) is derived from the INRS Lagrangian density, including scalar, vector, and rho meson fields, with nonlinear self-couplings and cross-coupling terms.
• Dark matter is modeled as a Fermi gas with variable Fermi momentum k_f^DM, and its effects on the EOS are computed by solving the coupled Einstein and matter field equations.
• The model is constrained using observational data: mass and radius from NICER, tidal deformability from GW170817 and GW190814, and HESS J1731-347’s low mass and radius.
• Nonradial f-mode oscillations are calculated within the relativistic Cowling approximation to study the impact of dark matter on stellar pulsations.
• The consistency of the EOS with chiral effective field theory bounds is verified across all DM admixture levels.

Figure 1: Using the chiral EFT bound, which is shaded in pink color, the EOS for the INRS model is plotted with and without DM. The inset plot shows how the sound speed ( $c_{s}^{2}$ ) varies with the density.

Experimental results

Research questions

• RQ1 Can a dark matter-admixed neutron star model with the INRS equation of state satisfy the mass and radius constraints of PSR J0952-0607 and HESS J1731-347?
• RQ2 What is the maximum allowed dark matter Fermi momentum k_f^DM that remains consistent with multimessenger observations, including NICER, GW170817, and GW190814?
• RQ3 How does dark matter admixture affect the tidal deformability of neutron stars, and is the resulting value within gravitational wave event bounds?
• RQ4 How does the inclusion of dark matter influence the nonradial f-mode oscillation frequency of neutron stars?
• RQ5 Is the INRS model with dark matter consistent with chiral effective field theory constraints on the equation of state?

Key findings

• The INRS model with dark matter produces a maximum neutron star mass of 2.343 M☉, consistent with the observed mass of PSR J0952-0607 (2.35 ± 0.17 M☉) and within NICER bounds.
• For dark matter Fermi momentum k_f^DM up to 0.045 GeV, the model satisfies the mass and radius constraints of HESS J1731-347 (0.77⁺⁰.²⁰₋₀.¹⁷ M☉, 10.4⁺⁰.⁸⁶₋₀.⁷⁸ km) and the canonical radius constraint from Capano et al. (2020).
• Tidal deformability values for DM-admixed stars lie within the 90% credible intervals of GW170817 and GW190814, indicating consistency with gravitational wave observations.
• The inclusion of dark matter softens the equation of state, reducing the maximum mass and increasing the nonradial f-mode oscillation frequency with increasing k_f^DM.
• The model remains within chiral effective field theory bounds across all values of k_f^DM, confirming its theoretical robustness.
• The analysis supports the hypothesis that HESS J1731-347 could be a dark matter-admixed neutron star, particularly for k_f^DM ≈ 0.03 GeV.

Figure 2: The mass-radius relation for our novel RMF model INRS is shown with and without DM along with different observational constraints.