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

A recent observational study has set a constraint on the maximum mass of neutron stars (NSs), specifically focusing on PSR J0952-0607 and the compact star remnant HESS J1731-347, particularly within the low-mass regime. In our recent study, Ref. 1 , we developed an energy density functional named NITR, which successfully produced the mass limit of the aforementioned pulsar but did not fully meet other observational constraints, such as those from NICER+XMM and GW170817. In this study, we introduce a new EDF named “NITR-I”, which not only reproduces the mass limit of PSR J0952-0607 but also aligns its canonical radius with NICER+XMM data, and its canonical dimensionless tidal deformability is consistent with the GW170817 event, thereby demonstrating the robustness of our model. The low-mass constraint associated with HESS J1731-347 suggests various possible compositions for the NS. The NITR-I model alone does not satisfy the HESS J1731-347 constraint; thus, we explore the possibility of incorporating dark matter (DM) inside the NS to meet this constraint. This approach proves successful when a specific value of Fermi momentum is considered. We also examine the impact of DM with varying Fermi momentum on different NS properties, such as tidal deformability and nonradial f-mode oscillation, using various relativistic mean-field (RMF) models. For the NITR-I EOS, the f-mode frequency is about 2.15[Formula: see text]kHz at 1.4 [Formula: see text] when [Formula: see text][Formula: see text]GeV, and it slightly increases to around 2.32[Formula: see text]kHz with [Formula: see text][Formula: see text]GeV. This increase in frequency due to DM suggests a possible reduction in tidal deformability, indicating that neutron stars with higher DM content are less susceptible to deformation by tidal forces which could be detectable in gravitational wave signals from neutron star mergers. Finally, we explore various universal relations (URs) for DM-admixed NSs, such as the relation between compactness and tidal deformability, the f-mode frequency and tidal deformability, and estimate the canonical values corresponding to both compactness and f-mode frequency using the GW170817 data.