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

Sound velocity in dense stellar matter with strangeness and compact stars