Estimating the dark matter halo velocity and surface temperature of some known pulsars due to dark matter capture

Considering four known pulsars J1906+0746, J1933-6211, J2043+1711 and the Vela pulsar, we study the scenario of dark matter (DM) capture in neutron stars (NSs). For the purpose we choose four well-known relativistic mean field models to obtain the radius corresponding to the observed mass of these pulsars and consequently the scattering cross-section of DM with the different particles of the $\beta$ stable NS matter. The estimated DM-electron scattering cross-section in this work is stringent compared to the current direct detection experimental probe. We then compute the lower limit on the halo velocity of DM for the four pulsars from the knowledge of the upper limit on effective temperature of the individual pulsars. We also extend our work to calculate the value of the effective temperature with the different models using the fitted values of the halo velocity of DM of the four pulsars with respect to their distances from the galactic center. Our findings are consistent with the analysis of the observed data.