Impact of dark matter distribution on neutron star properties

We investigate the structural and observable impacts of dark matter (DM) on neutron stars (NSs) using a combined equation of state that integrates the relativistic mean-field (RMF) model for baryonic matter with a variable density profile for DM, incorporating DM-baryon interactions mediated by the Higgs field. Employing three RMF parameter sets (NL3, BigApple, and IOPB-I) for baryonic matter, we analyze mass-radius relations, maximum mass, and tidal deformability, focusing on DM density scaling ($\ensuremath{\alpha}$) and steepness ($\ensuremath{\beta}$) parameters. Our findings reveal that increased DM concentration significantly enhances NS compactness, shifting mass-radius profiles and reducing tidal deformability. The DM influence strongly depends on the steepness of the DM density profile, where high $\ensuremath{\beta}$ values lead to strongly confined DM within the NS core, resulting in more compact and less deformable configurations. Observational constraints from PSR $\mathrm{J}0740+6620$ and GW170817 impose consistent structural limits on DM fractions across different equations of state models, narrowing the allowable parameter space for DM and linking specific combinations of $\ensuremath{\alpha}{M}_{\ensuremath{\chi}}$ (${M}_{\ensuremath{\chi}}$ being the mass of dark matter particle) and $\ensuremath{\beta}$ values to viable NS structures. This study highlights the interplay among DM concentration, nuclear stiffness, and observational data in shaping NS structure, offering insights into future constraints on DM in high-density astrophysical environments.