Differential Elliptic Flow in 2 - 6 AGeV Au+Au Collisions: A New Constraint for the Nuclear Equation of State

Proton elliptic flow is studied as a function of impact-parameter $b$, for two transverse momentum cuts in 2 - 6 AGeV Au + Au collisions. The elliptic flow shows an essentially linear dependence on b (for $1.5 < b < 8$ fm) with a negative slope at 2 AGeV, a positive slope at 6 AGeV and a near zero slope at 4 AGeV. These dependencies serve as an important constraint for discriminating between various equations of state (EOS) for high density nuclear matter, and they provide important insights on the interplay between collision geometry and the expansion dynamics. Extensive comparisons of the measured and calculated differential flows provide further evidence for a softening of the EOS between 2 and 6 GeV/nucleon.