Identifying the QCD Phase Transitions via the Gravitational Wave Frequency from Supernova Explosion

We investigate the non-radial oscillations of newly born neutron stars (NSs) and strange quark stars (SQSs). This is done with the relativistic nuclear field theory with hyperon degrees of freedom employed to describe the equation of state for the stellar matter in NSs, and with both the MIT bag model and the Nambu--Jona-Lasinio model adopted to construct the configurations of the SQSs. We find that the gravitational-mode ($g$-mode) eigenfrequencies of newly born SQSs are significantly lower than those of NSs, which is independent of models implemented to describe the equation of state for the strange quark matter. Meanwhile, the eigenfrequencies of the other modes of non-radial oscillations, e.g., fundamental ($f$)- and pressure ($p$)-modes, are much larger than those of the $g$-mode, and is related to the stiffness of the equation of states (EoSs). In the light of the first direct observation of gravitational waves, it is promising to employ the gravitational waves to identify the QCD phase transition in high density strong interaction matter.