Neutron Stars (NSs) are born as hot, lepton-rich objects that evolve according to the standard paradigm through subsequent stages where they radiate the excess of energy by emitting, first, neutrinos and, later on, photons. Current descriptions based on Standard Model calculations cannot fully explain all the existing cooling data series for the dozens of objects that have been reported. In this work, we consider the intriguing possibility that cooling NSs could be actually admixed with a fraction of light dark matter (LDM), χ. We focus on a particular case study assuming a generic light candidate with mass that undergoes self-annihilating reactions through pseudoscalar mediators producing neutrinos in the final state. We include one additional feature, allowing thermal conduction from LDM while inside the dark core. By performing simulations of the temperature evolution in the NS, we find that cooling patterns could be distorted by the presence of LDM and discuss these results in light of their observability.
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