Sound velocity in dense stellar matter with strangeness and compact stars

The phase state of dense matter in the intermediate density range ($\sim$1-10 times the nuclear saturation density) is both intriguing and unclear and could have important observable effects in the present gravitational wave era of neutron stars. As the matter density increases in compact stars, the sound velocity is expected to approach the conformal limit ($c_s/c=1/\sqrt{3}$) at high densities and should also fulfill the causality limit ($c_s/c<1$). However, its detailed behavior remains a hot topic of debate. It was suggested that the sound velocity of dense matter could be an important indicator for a deconfinement phase transition, where a particular shape might be expected for its density dependence. In this work, we explore the general properties of the sound velocity and the adiabatic index of dense matter in hybrid stars, as well as in neutron stars and quark stars. Various conditions are employed for hadron-quark phase transition with varying interface tension. We find that the expected behavior of the sound velocity can also be achieved by the nonperturbative properties of the quark phase, in addition to a deconfinement phase transition. And it leads to a more compact star with a similar mass. We then propose a new class of quark star equation of states, which could be tested by future high-precision radius measurements of pulsar-like objects.