The maximum mass of dark matter existing in compact stars based on the
  self-interacting fermionic model
  By assuming that only gravitation acts between dark matter (DM) and normal
matter (NM), we studied DM admixed neutron stars (DANSs) using the two-fluid
TOV equations. The NM and DM of compact stars are simulated by the relativistic
mean field (RMF) theory and non-self-annihilating self-interacting fermionic
model, respectively. The effects of the particle mass of fermionic DM $m_f$ and
the interaction strength parameter $y$ on the properties of DANSs are
investigated in detail. $m_f$ and $y$ are considered as the free parameters due
to the lack of information about the particle nature of DM so far. For a DANS,
we suggest a simple universal relationship $M_D^{\max}=(0.267 y
+0.627-3.21\frac{M_N}{\M_{\odot}})( \frac{1\GeV}{{m_f}})^2 \M_{\odot}$ for
$y>100$, where $M_D^{\max}$ is the maximum mass of DM existing in DANSs and
$M_N$ is the mass of the neutron star without DM. For free fermion DM model
($y$=0), the relationship becomes $
M_D^{\max}=(0.627-0.027\frac{M_N^2}{\M_{\odot}^2}) ( \frac{1\GeV}{{m_f}})^2
\M_{\odot}$. The radius of DM $R_D$ shows a linear relationship with
$M_D^{\max}$ in DANSs, namely $R_D=(7.02 \frac{M_D^{\max}}{
\M_{\odot}}+1.36)$~km. These conclusions are independent of the different NM
EOSs from RMF theory. Such a kind of universal relationship connecting the
nature of DM particle and mass of stars might shed light on the constraining
the nature of the DM by indirect method.
