Imprints of Higgs-portal fermionic dark matter on neutron-star tidal deformability and the mass-radius slope

Abstract

We investigate the structure of neutron stars (NSs) admixed with fermionic dark matter (DM) using three density-dependent relativistic mean-field (DDRMF) functionals (DDME, DDB, and GDFM) for $\beta$-equilibrated nucleonic matter. Modeling DM as the lightest neutralino interacting via Higgs exchange, we treat the DM Fermi momentum $k_F^{\rm DM}$ as a control parameter in the range $0.02$-$0.06$ GeV. We solve the coupled mean-field and Tolman-Oppenheimer-Volkoff equations to obtain the mass-radius relation, maximum mass $M_{\rm max}$, radial sound speed profile $c_s^2$, and tidal deformability $\Lambda$. In all models, DM softens the equation of state, systematically reducing $M_{\rm max}$, the radius $R_{1.4}$ (at $1.4M_{\odot}$), and the tidal deformability $\Lambda_{1.4}$ (at $1.4M_{\odot}$) as $k_F^{\rm DM}$ increases. Consequently, the $2 M_\odot$ pulsar limit and NICER data place a model-dependent upper limit on the DM content, while the GW170817 tidal bound requires a minimal DM content for the stiffest functional. Using a recent Bayesian inference of the DDRMF equation of state as the nucleonic reference band, we evaluate if this DM imprint can be distinguished from nucleonic uncertainties using only measureable quantities. Analyzing the tidal deformability $\Lambda$ and mass-radius slope $dR/dM$ at fixed mass, we find that $\Lambda$ is a sharp discriminator: at $1.4 M_\odot$ and $k_F^{\rm DM}=0.06$ GeV, the DM-induced reduction of $\Lambda$ reaches $\simeq 8$ times the nucleonic $1\sigma$ width (model-independently $7.5$-$7.8\sigma$). The DM track leaves the nucleonic $1\sigma$ band for $k_F^{\rm DM}\gtrsim0.03$-$0.04$ GeV, whereas $dR/dM$ becomes diagnostic only for the heavier ($1.8$-$2.0 M_\odot$) branch.