  We delineate the properties of QCD matter at baryon density n_B=1-10n_0 (n_0:
nuclear saturation density), through the construction of neutron star equations
of state that satisfy the neutron star mass-radius constraints as well as
physical conditions on the speed of sound. The QCD matter is described in the
3-window modeling: at n_B < 2n_0 purely nuclear matter; at n_B > 5n_0
percolated quark matter; and at 2n_0 < n_B < 5n_0 matter intermediate between
these two which are constructed by interpolation. Using a schematic quark model
with effective interactions inspired from hadron and nuclear physics, we
analyze the strength of interactions necessary to describe observed neutron
star properties. Our finding is that the interactions should remain as strong
as in the QCD vacuum, indicating that gluons at n_B =1-10 n_0 remain
non-perturbative even after quark matter formation.
