Bayesian analysis of density profile of light dark matter elucidating the properties of dark matter admixed neutron stars in the presence of hyperons

Abstract: We study the impact of symmetry energy ($S$), hyperons, and dark matter (DM) on structural and oscillatory properties of neutron stars (NSs). Uncertainty from hadronic equation of state for NSs is considered with 15 relativistic mean field models having slope parameter ($L_0$) of $S$ in range $40-120$ MeV. DM admixed NSs (DMANSs) are described with feeble interaction between light DM fermions ($χ$) with hadronic matter in the presence of hyperons via scalar ($η$) and vector ($ξ$) dark mediators. The masses $m_χ$, $m_η$ and $m_ξ$ are related by self-interaction constraints from bullet cluster. DM self-interaction couplings are related to $m_χ$ by relic density constraint. The DM density is taken as an exponential function of baryon density with a free parameter $α$. Uncertainty from DM model is incorporated by exploring the dependence on $m_χ$ and $α$. Several DM search experiments have almost ruled out the existence of massive DM ($\gtrsim$ GeV). Lately, pursuit for sub-GeV DM has attracted significant attention. Therefore, we consider $m_χ<$ 1 GeV and $α\leq$ 0.1 such that the contribution of DM to the total mass of the DMANSs is $<10\%$. Comparing our results with various astrophysical constraints, we find that the HESS J1731-347 and GW170817 data are very important in determining the presence of light DM in NSs in moderate amount, relevant in the range $L_0\lesssim$ 58 MeV. Employing models of DMANSs that satisfy several observational data, we infer with Bayesian analysis, the likely ranges of $m_χ$ and $α$ are almost independent of the underlying hadronic model within 40 MeV $\lesssim$ $L_0$ $<$ 58 MeV. In the absence of DM and with the most probable values of $m_χ$ and $α$ obtained from the Bayesian inference, we calculate the frequencies of non-radial $f$- and $p_1$-modes oscillation of NSs/DMANSs.