Cooling of dark-matter Admixed Neutron Stars with density-dependent Equation of State.

We propose a dark-matter (DM) admixed density-dependent equation of state where the fermioinc DM interacts with the nucleons via Higgs portal. Presence of DM can hardly influence the particle distribution inside neutron star (NS) but can significantly affect the structure as well as equation of state (EOS) of NS. Introduction of DM inside NS softens the equation of state. We explored the effect of variation of DM mass and DM fermi momentum on the NS EOS. Moreover, DM-Higgs coupling is constrained using dark matter direct detection experiments. Then, we studied cooling of normal NSs using APR and DD2 EOSs and DM admixed NSs using dark-matter modified DD2 with varying DM mass and fermi momentum. We have done our analysis by considering different NS masses. Also DM mass and DM fermi momentum are varied for fixed NS mass and DM-Higgs coupling. We calculated the variations of luminosity and temperature of NS with time for all EOSs considered in our work and then compared our calculations with the observed astronomical cooling data of three pulsars namely PSR B0656+14, Geminga and PSR B1055-52. It is found that APR EOS agrees well with the pulsar data for lighter and medium mass NSs but cooling is very fast for heavier NS. For DM admixed DD2 EOS, we found that in case of medium and heavier mass NSs, all chosen DM masses and fermi momenta agree well with the observational data but for lower mass NSs, all DM fermi momenta and high DM masses barely agree with the observations. Furthermore, only lower DM mass agrees with observations in case of lighter NSs. Cooling becomes faster as compared to normal NSs in case of increasing DM mass and fermi momenta. It is infered from the calculations that if low mass super cold NSs are observed in future that may support the fact that heavier WIMP can be present inside neutron stars.