Old neutron stars as probes of isospin-violating dark matter

Isospin-violating dark matter (IVDM), which couples differently with protons and neutrons, provides a promising mechanism to ameliorate the tension among recent direct detection experiments. Assuming DM is non-interacting bosonic asymmetric IVDM, we investigate how the existence of old neutron stars limits the DM-proton scattering cross-section $\sigma_{\rm p}$, especially the effects of the isospin violating DM-nucleon interactions and the symmetry energy in the equation of state of isospin asymmetric nuclear matter. Our calculations are completely based on general relativity and especially the structure of neutron stars is obtained by solving the Tolman-Oppenheimer-Volkoff equations with nuclear matter equation of state constrained by terrestrial experiments. We find that, by considering the more realistic neutron star model rather than a simple uniform neutron sphere as usual, the $\sigma_{\rm p}$ bounds from old neutron stars can be varied by more than an order of magnitude depending on the specific values of the DM neutron-to-proton coupling ratio $f_{\rm n}/f_{\rm p}$, and they can be further varied by more than a factor of two depending on the density dependence of the symmetry energy. In particular, we demonstrate that the observed nearby isolated old neutron star PSR B1257+12 can set a very strong limit on $\sigma_{\rm p}$ for low-mass DM particles ($ \le 20 \, {\rm GeV}$) that reaches a sensitivity beyond the current best limits from direct detection experiments and disfavors the DM interpretation of previously-reported positive experimental results, including the IVDM.