Sound velocity in dense stellar matter with strangeness and compact stars.

The phase state in the intermediate density range of dense matter ($\sim1-10$ times of nuclear saturation density) is both intriguing and unclear, and could have important observable effects in the present gravitational wave era of neutron stars. Since the matter density in neutron stars is in the nonperturbative interaction region, the sound velocity is expected to approach the conformal limit ($c_s/c=1/\sqrt{3}$) at high densities, and it should also fulfill the causality limit ($c_s/c<1$). However, its detailed behavior remains a hot topic of debate. We explore the general properties of the sound velocity and the adiabatic index in hybrid stars, as well as in neutron stars and quark stars. For this purpose, the bag model, the perturbation model, the equivparticle model, and the quasiparticle model are employed for the quark phase. One representative effective field theory model is used for the hardon phase. Various conditions are employed for hadron-quark phase transition and we employ an interface tension in a preferred range of $1-50~\rm MeV/fm^2$. The results are compared with various ab-initio calculations. We find a characteristic behavior of dynamical rescaling of the bag constant on the sound velocity in quark matter, which resembles that of quark deconfinement phase transition at $\sim3-7$ times of nuclear saturation density. And it leads to a much compact star with similar mass. We also propose a new class of quark star equation of states attributing the feature. The quark star equation of state model, as well as the in-medium scaling of the bag parameter in our calculation can be tested by future high-precision radius measurements of pulsar-like objects.