Phenomenological neutron star equations of state. 3-window modeling of QCD matter

We discuss the 3-window modeling of cold, dense QCD matter equations of state at density relevant to neutron star properties. At low baryon density, n_B s (n_s: nuclear saturation density), we utilize purely hadronic equations of state that are constrained by empirical observations at density n_B ∝ n_s and neutron star radii. At high density, n_B >or similar 5n_s, we use the percolated quark matter equations of state which must be very stiff to pass the two-solar mass constraints. The intermediate domain at 2 B/n_s s² ≤ 1. The characteristics of the 3-window equation of state are compared with those of conventional hybrid and self-bound quark matters. Using a schematic quark model for the percolated domain, it is argued that the two-solar mass constraint requires the model parameters to be as large as their vacuum values, indicating that the gluon dynamics remains strongly non-perturbative to n_B ∝ 10n_s. The hyperon puzzle is also briefly discussed in light of quark descriptions. (orig.)