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

TL;DR

This paper investigates how shear viscosity influences the evolution and particle spectra in relativistic heavy-ion collisions using a new (2+1)-dimensional viscous hydrodynamic model, revealing significant effects on flow and spectra.

Contribution

It introduces a causal viscous hydrodynamic code VISH2+1 for 2+1D simulations, providing detailed insights into shear viscosity effects on QGP evolution and observables.

Findings

Shear viscosity slows longitudinal expansion and speeds up transverse flow.

Viscosity increases the QGP lifetime and flattens hadron spectra.

Elliptic flow v_2 is highly sensitive to shear viscosity, constraining eta/s.

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, eta/s=1/4pi, suppresses v_2 enough to have significant consequences for the phenomenology of heavy-ion collisions at the Relativistic Heavy Ion Collider. 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 eta/s, thereby supporting the notion that the quark-gluon plasma created at RHIC exhibits almost ``perfect fluidity''.