Constraining the mass of fermionic dark matter from its feeble interaction with hadronic matter via dark mediators in neutron stars

Considering ten well-known relativistic mean field models, we invoke feeble interaction between hadronic matter and fermionic dark matter (DM) $\chi$ via new physics scalar ($\varphi$) and vector ($\xi$) mediators in neutron star core, thereby forming DM admixed neutron stars (DMANSs). The chosen masses of the DM fermion ($m_{\chi }$) and the mediators ($m_{\varphi }$ and $m_{\xi }$) are consistent with the self-interaction constraint from bullet cluster while their respective couplings ($y_{\varphi }$ and $y_{\xi }$) are also constrained by the present day relic abundance. Assuming that both $\varphi$ and $\xi$ contribute equally to the relic abundance, we compute the equation of state of the DMANSs and consequently their structural properties. We found that for a particular (constant) DM density, the presence of lighter DM results in more massive DMANSs with larger radius. In the light of the various recent constraints like those from the massive pulsar PSR $J0740+6620$, the gravitational wave (GW170817) data and the results of NICER experiments for PSR $J0030+0451$ and PSR $J0740+6620$, we provide a bound on $m_{\chi }$ within the framework of the present work as $m_{\chi }\approx (0.1-30)\mathrm{GeV}$ for a wide range of fixed DM Fermi momenta $k_F^{\chi }=(0.01-0.06)\mathrm{GeV}$. In the case of the hadronic models that yield larger radii corresponding to the low mass neutron stars in the no-DM scenario, interaction with comparatively heavier DM fermion is necessary in order to ensure that the DMANSs obtained with such models satisfy the radius constraints from both GW170817 and NICER data for PSR $J0030+0451$.