Possible maximum mass of dark matter existing in compact stars based on the self-interacting fermionic model

The dark matter admixed neutron stars (DANSs) are studied using the two-fluid TOV equations separately, in which the normal matter (NM) and dark matter (DM) are simulated by the relativistic mean field theory and self-interacting fermionic model, respectively. A universal relationship M-D(max) = (0.269 m (f)/m (I) + 0.627)(1 GeV/m (f))M-2(circle dot) is suggested, where M-D(max) is the maximum mass of DM existing in DANSs, m (f) is the particle mass of DM ranging from 5 GeV to 1 TeV, m (I) is the interaction mass scale with the value 300 GeV (0.1 GeV) for weak (strong) interaction DM model. This simple formula connects directly the microcosmic nature of DM particle with its macrocosmic mass existing in DANSs. Meanwhile, such a formula exhibits that the existence of NM has little effect on M-D(max). It is found that the ratio of radius of DM in DANSs over M-D(max) is a constant with the value about 12 km/M-circle dot (7 km/M-circle dot) for weak (strong) interaction DM cases. According to the calculated results, only for the strong interaction DM cases with m (f) = 5 to 10 GeV and central energy density epsilon (D) > 10(3) MeV/fm(3), DM has obvious effect on the mass of compact star. Compared with the energy density of DM in the Milky Way galaxy, similar to 10(-36) MeV/fm(3), the existence of DM might hardly affect the mass of compact stars in the Milky Way galaxy.