Compact Stars, Heavy Ion Collisions, and Possible Lessons For QCD at Finite Densities

Large neutron star masses as the recently measured $1.97\pm 0.04$ M${}_{\odot }$ for PSR J1614-2230 provide a valuable lower limit on the stiffness of the equation of state of dense, nuclear and quark matter. Complementary, the analysis of the elliptic flow in heavy ion collisions suggests an upper limit on the EoS stiffness. We illustrate how this dichotomy permits to constrain parameters of effective EoS models which otherwise could not be derived unambiguously from first principles.