Gravitational wave asteroseismology of dark matter hadronic stars

The influence of the dark matter mass ($M_{\chi }$) and the Fermi momentum ($k_F^{\mathrm{DM}}$) on the $f_0$-mode oscillation frequency, damping time parameter, and tidal deformability of hadronic stars are studied by employing a numerical integration of hydrostatic equilibrium, nonradial oscillation, and tidal deformability equations. The matter inside the hadronic stars follows the NL3* equation of state. We obtain that the influence of $M_{\chi }$ and $k_F^{\mathrm{DM}}$ is observed in the $f_0$-mode, damping tome parameter, and tidal deformability. Finally, the correlation between the tidal deformability of the GW170817 event with $M_{\chi }$ and $k_F^{\mathrm{DM}}$ are also investigated.