Freeze-in dark matter in neutron stars

Every neutron star is born in the process of core-collapse supernova explosion that, for a brief moment, reproduces conditions of the early Universe with temperatures $T\sim O(30\rm\,MeV)$. We calculate the production of Dark Matter $\chi$ from the SM particles in such events, SM $\to\chi\bar\chi$, for the freeze-in range of couplings, $\alpha_{\rm FI} \sim O(10^{-26})$, finding that $O(10^{-6})$ $\chi$'s per nucleon is produced. The strong gravitational potential well of the neutron star retains a substantial fraction of these particles that will eventually undergo the reverse process of energy injection, $\chi\bar\chi\to$ SM. This may lead to the abnormal energy injection creating observable signatures such as late-time heating of the neutron stars. To demonstrate the power of this method, we construct a set of simple dark matter models coupled to lepton currents, and show that neutron stars provide unique constraints on parameter space that otherwise cannot be accessed by other means, probing effectively the scattering cross sections with the SM in the ballpark of $\sigma_{\chi\,\rm SM} \propto O(10^{-70})\,\rm cm^2$.