Nonradial oscillations of quark stars

Recently, it has been reported that a candidate for a quark star may have been observed. In this article, we pay attention to quark stars with radiation radii in the reported range. We calculate nonradial oscillations of $f$-, $w$- and $w_{\mathrm{I}\mathrm{I}}$-modes. Then, we find that the dependence of the $f$-mode quasi-normal frequency on the bag constant and stellar radiation radius is very strong and different from that of the lowest $w_{\mathrm{I}\mathrm{I}}$-mode quasi-normal frequency. Furthermore we deduce a new empirical formula between the $f$-mode frequency of gravitational waves and the parameter of the equation of state for quark stars. The observation of gravitational waves both of the $f$-mode and of the lowest $w_{\mathrm{I}\mathrm{I}}$-mode would provide a powerful probe for the equation of state of quark matter and the properties of quark stars.