Abstract
The properties of dense QCD matter are delineated through the construction of equations of state which should be consistent with the low and high density limits of QCD, nuclear laboratory experiments, and the neutron star observations. These constraints, together with the causality condition of the sound velocity, are used to develop the picture of hadron-quark continuity in which hadronic matter continuously transforms into quark matter (modulo small 1st order phase transitions). The resultant unified equation of state at zero temperature and $\beta$-equilibrium, which we call Quark-Hadron-Crossover (QHC19), is consistent with the measured properties of neutron stars as well as the microphysics known for the hadron phenomenology. In particular to $\sim 10n_0$ ($n_0$: saturation density) the gluons remain as non-perturbative as in vacuum and the strangeness can be as abundant as up- and down-quarks at the core of two-solar mass neutron stars. Within our modeling the maximum mass is found less than $\simeq 2.35$ times solar mass and the baryon density at the core ranges in $\sim 5$-8$n_0$.
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