Phenomenological QCD equations of state for massive neutron stars

We construct an equation of state for massive neutron stars based on QCD phenomenology, with special attention to the behavior at density larger than twice of saturation density. Our primary purpose is to delineate the relevant ingredients of equations of state that simultaneously have the required stiffness and satisfy constraints from thermodynamics and causality. We construct the equations of state based on the 3-window description: at low density, we use the APR equation of state; at high density we use the NJL model with supplemental vector and diquark interactions that are inferred from the hadron spectroscopy and nuclear physics; at intermediate density we interpolate the low and high density equations of state. Our 3-window approach allows us to consider a class of equations of state which have been implicitly omitted in the conventional hybrid construction.