Elliptic Flow: Transition from Out-of-Plane to In-Plane Emission in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Au</mml:mi><mml:mspace/><mml:mo>+</mml:mo><mml:mspace/><mml:mi mathvariant="normal">Au</mml:mi></mml:math>Collisions

We have measured the proton elliptic flow excitation function for the $\mathrm{Au}+\mathrm{Au}$ system spanning the beam energy range $(2--8)A\mathrm{GeV}$. The excitation function shows a transition from negative to positive elliptic flow at a beam energy, ${E}_{\mathrm{tr}}\ensuremath{\sim}4A\mathrm{GeV}$. Detailed comparisons with calculations from a relativistic Boltzmann equation are presented. The comparisons suggest a softening of the nuclear equation of state from a stiff form ( $K\ensuremath{\sim}380\mathrm{MeV}$) at low beam energies ( ${E}_{\mathrm{beam}}\ensuremath{\le}2A\mathrm{GeV}$) to a softer form ( $K\ensuremath{\sim}210\mathrm{MeV}$) at higher energies ( ${E}_{\mathrm{beam}}\ensuremath{\ge}4A\mathrm{GeV}$) where the calculated baryon density $\ensuremath{\rho}\ensuremath{\sim}4{\ensuremath{\rho}}_{0}$.