Phenomenological QCD equations of state for neutron star mergers, a talk presented at CPOD17

We delineate the properties of dense QCD matter through equations of state constrained by the neutron star observations. The two solar mass constraint, the radius constraint of 11-13 km, and the causality constraint on the speed of sound, are used to develop the picture of hadron-quark continuity in which hadronic matter continuously transforms into quark matter. A unified equation of state at zero temperature and beta-equilibrium is constructed by a phenomenological interpolation between nuclear and quark matter equations of state. For applications to supernovae and neutron star mergers, the unified equation of state is perturbed by temperature corrections.