Dark matter admixed neutron star properties in the light of X-ray pulse profile observations

The distribution of the dark matter (DM) in DM-admixed-neutron stars (DANSs) is supposed to be either a dense dark core or an extended dark halo, which is subject to the DM fraction of DANS ($f_{\chi}$) and the DM properties, such as the mass ($m_{\chi}$) and the strength of the self-interaction ($y$). In this paper, we perform an in-depth analysis of the formation criterion for dark core/dark halo and point out that the relative distribution of these two components is essentially determined by the ratio of the central enthalpy of the DM component to that of the baryonic matter component inside DANSs. For the critical case where the radii of DM and baryonic matter are the same, we further derive an analytical formula to describe the dependence of $f^{\rm crit}_{\chi}$ on $m_{\chi}$ and $y$ for given DANS mass. The relative distribution of the two components in DANSs can lead to different observational effects. We here focus on the modification of the pulsar pulse profile due to the extra light-bending effect in the case of a dark-halo existence and conduct the first investigation of the dark-halo effects on the pulse profile. We find that the peak flux deviation is strongly dependent on the ratio of the halo mass to the radius of the DM component. Lastly, we perform Bayesian parameter estimation on the DM particle properties based on the recent X-ray observations of PSR J0030+0451 and PSR J0740+6620 by the Neutron Star Interior Composition Explorer.