Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?

Relativistic viscous hydrodynamic fits to Brookhaven Relativistic Heavy Ion Collider data on the centrality dependence of multiplicity, transverse, and elliptic flow for $\sqrt{s}=200\mathrm{GeV}$ $\mathrm{Au}+\mathrm{Au}$ collisions are presented. For standard (Glauber-type) initial conditions, while data on the integrated elliptic flow coefficient $v_2$ are consistent with a ratio of viscosity over entropy density up to $\eta /s\simeq 0.16$, data on minimum bias $v_2$ seem to favor a much smaller viscosity over entropy ratio, below the bound from the anti–de Sitter conformal field theory conjecture. Some caveats on this result are discussed.

Figure 1

Correlation function $f(k,\tau ,{\tau }_0=1\mathrm{fm}/c)$ as a function of momentum $k$, measured for our hydrodynamics code on a ${64}^2$ lattice with a lattice spacing of $1{\mathrm{GeV}}^{-1}$ (symbols), compared to the “analytic” result from the linearized Eq. (2) (lines). The good overall agreement indicates the code is solving Eq. (2) correctly in the linear regime (see 16 for details).

Figure 2

Total multiplicity $dN/dy$ and mean momentum for ${\pi }^{+}$, ${\pi }^{-}$, $K^{+}$, $K^{-}$, $p$, and $\overline{p}$ from PHENIX [40] for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200\mathrm{GeV}$, compared to our hydrodynamic model for various viscosity ratios $\eta /s$.

Figure 3

PHOBOS [41] data on $p_T$ integrated $v_2$ and STAR [30] data on minimum bias $v_2$, for charged particles in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200\mathrm{GeV}$, compared to our hydrodynamic model for various viscosity ratios $\eta /s$. Error bars for PHOBOS data show 90% confidence level systematic errors, while for STAR only statistical errors are shown.