Radial Oscillations of Strange Quark Stars Admixed with Dark Matter

We investigate the equilibrium structure and radial oscillations of strange quark stars admixed with fermionic dark matter. For strange quark matter, we employ a stiff equation of state from a color-superconductivity improved bag model. For dark matter, we adopt the cold free Fermi gas model. We rederive and numerically solve the radial oscillation equations of two-fluid stars based on general relativity, in which the dark matter and strange quark matter couple through gravity and oscillate with the same frequency. Our results show that the stellar maximum mass and radius are reduced by inclusion of dark matter. As to the fundamental mode of the radial oscillations, the frequency f0 is also reduced comparing to pure strange stars, and f02 reaches the zero point at the maximum stellar mass with dM/dϵq,c=0. Therefore, the stability criteria f02>0 and dM/dϵq,c>0 are consistent in our dark matter-mixed strange quark stars with a fixed fraction of dark matter. We also find a discontinuity of f0 as functions of the stellar mass, in contrast to the continuous function in pure strange stars. And it is also accompanied with discontinuity of the oscillation amplitudes as well as a discontinuous in-phase-to-out-phase transition between oscillations of dark matter and strange quark matter.