A corresponding-state approach to quark-cluster matter

The state of super-dense matter is essential for us to understand the nature of pulsars;however,nonperturbative quantum chromodynamics makes it very difficult to make direct calculations of the state of cold matter at realistic baryon number densities inside compact stars.Nevertheless,from an observational point of view,it is conjectured that pulsars could be made up of quark clusters since the strong coupling between quarks might render the quarks to be grouped in clusters.In this paper,we attempt to find an equation of state of condensed quark-cluster matter in a phenomenological way.Supposing that the quark-clusters could be analogized to inert gases,we apply here the corresponding-state approach to derive the equation of state of quark-cluster matter,as was similarly demonstrated for nuclear and neutron-star matter in the 1970s.According to the calculations that we have presented,the quark-cluster stars,which are composed of quark-cluster matter,could have a high maximum mass that is consistent with observations and,in turn,further observations of pulsar mass could also place a constraint on the properties of quark-cluster matter.We will also briefly discuss the melting heat during the solid-liquid phase conversion and its related astrophysical consequences.