Causal viscous hydrodynamics in 2 + 1 dimensions for relativistic heavy-ion collisions

Abstract

We explore the effects of shear viscosity on the hydrodynamic evolution and final hadron spectra of Cu + Cu collisions at ultrarelativistic collision energies, using the newly developed (2 + 1)-dimensional viscous hydrodynamic code VISH2+1. Based on the causal Israel-Stewart formalism, this code describes the transverse evolution of longitudinally boost-invariant systems without azimuthal symmetry around the beam direction. Shear viscosity is shown to decelerate the longitudinal and accelerate the transverse hydrodynamic expansion. For fixed initial conditions, this leads to a longer quark-gluon plasma (QGP) lifetime, larger radial flow in the final state, and flatter transverse momentum spectra for the emitted hadrons compared to ideal fluid dynamic simulations. We find that the elliptic flow coefficient ${v}_{2}$ is particularly sensitive to shear viscosity: even the lowest value allowed by the AdS/CFT conjecture $\ensuremath{\eta}/s\ensuremath{\geqslant}1/4\ensuremath{\pi}$ suppresses ${v}_{2}$ enough to have significant consequences for the phenomenology of heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC). A comparison between our numerical results and earlier analytic estimates of viscous effects within a blast-wave model parametrization of the expanding fireball at freeze-out reveals that the full dynamical theory leads to much tighter constraints for the specific shear viscosity $\ensuremath{\eta}/s$, thereby supporting the notion that the quark-gluon plasma created at RHIC exhibits almost ``perfect fluidity.''