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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 issubject to the DM fraction of DANS ($f_{\chi}$) and the DM properties, such asthe mass ($m_{\chi}$) and the strength of the self-interaction ($y$). In thispaper, we perform an in-depth analysis of the formation criterion for darkcore/dark halo and point out that the relative distribution of these twocomponents is essentially determined by the ratio of the central enthalpy ofthe DM component to that of the baryonic matter component inside DANSs. For thecritical case where the radii of DM and baryonic matter are the same, wefurther derive an analytical formula to describe the dependence of $f^{\rmcrit}_{\chi}$ on $m_{\chi}$ and $y$ for given DANS mass. The relativedistribution of the two components in DANSs can lead to different observationaleffects. We here focus on the modification of the pulsar pulse profile due tothe extra light-bending effect in the case of a dark-halo existence and conductthe first investigation of the dark-halo effects on the pulse profile. We findthat the peak flux deviation is strongly dependent on the ratio of the halomass to the radius of the DM component. Lastly, we perform Bayesian parameterestimation on the DM particle properties based on the recent X-ray observationsof PSR J0030+0451 and PSR J0740+6620 by the Neutron Star Interior CompositionExplorer.

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