  Pseudo-Nambu-Goldstone dark matter connected to Standard Model fermion
through the Higgs portal has the property that its direct detection vanishes in
the zero momentum transfer limit due to a cancellation mechanism. This feature
helps the Pseudo-Nambu-Goldstone dark matter to escape the stringent
constraints from direct detection experiments. In this paper we explore new
constraints on parameter space of non-zero momentum transfer from the direct
detection experiments, and also from the neutron star temperature via the dark
matter reheating mechanism.
