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.
