Phenomenological neutron star equations of state

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, $n_{B}\lesssim 2n_{s}$ ($n_{s}$: nuclear saturation density), we utilize purely hadronic equations of state that are constrained by empirical observations at density $ n_B\sim n_s$ and neutron star radii. At high density, $n_{B}\gtrsim 5n_{s}$, 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 $2\lesssim n_{B}/n_{s} \lesssim 5$ is described as neither purely hadronic nor percolated quark matter, and the equations of state are inferred by interpolating hadronic and percolated quark matter equations of state. Possible forms of the interpolation are severely restricted by the condition on the (square of) speed of sound, $ 0\le c_{s}^{2} \le 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}\sim 10n_{s}$. The hyperon puzzle is also briefly discussed in light of quark descriptions