Viscosity and the equation of state in high energy heavy-ion reactions

Abstract

Viscous hydrodynamic calculations of high energy heavy-ion collisions (Nb-Nb and Au-Au) from 200 to 800 MeV/nucleon are presented. The resulting baryon rapidity distributions, the in-plane transverse momentum transfer (bounce-off), and the azimuthal dependence of the midrapidity particles (off-plane squeeze out) compare well with Plastic Ball data. We find that the considered observables are sensitive both to the nuclear equation of state and to the nuclear shear viscosity \ensuremath{\eta}. Transverse momentum distributions indicate a high shear viscosity (\ensuremath{\eta}\ensuremath{\approxeq}60 MeV/${\mathrm{fm}}^{2}$ c) in the compression zone, in agreement with nuclear matter estimates. The bulk viscosity \ensuremath{\zeta} influences only the entropy production during the expansion stage; collective observables like flow and dN/dY do not depend strongly on \ensuremath{\zeta}. The recently observed off-plane (\ensuremath{\varphi}=90\ifmmode^\circ\else\textdegree\fi{}) squeeze-out, which is found in the triple-differential rapidity distribution, exhibits the strongest sensitivity to the nuclear equation of state. It is demonstrated that for very central collisions, b=1 fm, the squeeze-out is visible even in the double-differential cross section. This is experimentally accessible by studying azimuthally symmetric events, as confirmed recently by data of the European 4\ensuremath{\pi} detector collaboration at Gesellchaft f\"ur Schwerionforschung Darmstadt.