Centrality dependence of elliptic flow, the hydrodynamic limit, and the viscosity of hot QCD

Abstract

We show that the centrality and system-size dependence of elliptic flow measured at RHIC are fully described by a simple model based on eccentricity scaling and incomplete thermalization. We argue that the elliptic flow is at least 25% below the (ideal) "hydrodynamic limit", even for the most central Au-Au collisions. This lack of perfect equilibration allows for estimates of the effective parton cross section in the Quark-Gluon Plasma and of its viscosity to entropy density ratio. We also show how the initial conditions affect the transport coefficients and thermodynamic quantities extracted from the data, in particular the viscosity and the speed of sound.

Entropy production in high-energy heavy-ion collisions and the correlation of shear viscosity and thermalization time

“…Their magnitude matches approximately predictions based on ideal Euler (inviscid) hydrodynamics 1 [2]. More precisely, the transverse momentum and centrality dependence of the azimuthally asymmetric flow, v 2 , requires a shear viscosity to entropy density ratio as low as η/s ≤ 0.2 [4,5,6,7]; this is much lower than perturbative extrapolations to temperatures T ≃ 200 MeV [8]. However, it is comparable to recent results for SU(3) pure gauge theory from the lattice [9], and to the conjectured lower bound for strongly coupled systems η/s ≥ 1/(4π) [10].…”

“…6, the minimal τ 0 compatible with both η/s ≥ 1/(4π) and ∆S/S ini = 10% is about 1.2 fm/c. If η/s ≃ 0.1 − 0.2, as deduced from the centrality dependence of elliptic flow at RHIC [6], then τ 0 ≃ 1.5 fm/c. In Fig.…”

Shear and bulk viscosities of the gluon plasma in a quasiparticle description

“…Based on unitarity arguments [45][46][47], the dimensionless specific shear viscosity (i.e., the ratio of shear viscosity to entropy density s) was recently conjectured to be bound from below by (η/s) KSS h/(4π ) (Kovtun-Son-Starinets bound). The comparison of causal viscous hydrodynamic calculations with data on low-momentum elliptic flow spectra measured at RHIC showed that η/s should be close to this lower bound [13,20,21,31,33,48]. Nevertheless, some other results seem to indicate that the KSS bound might be violated for the QGP at RHIC [20,31,36].…”

“…Although the results of these calculations depend crucially on the employed freeze-out prescription as well as the assumed initial conditions [11][12][13][14][15][16][17][18], the success of ideal hydrodynamics suggested, at most, small dissipative effects in the medium produced at RHIC [19][20][21]. This observation led to the interpretation that the produced quark-gluon plasma (QGP) behaves as a strongly coupled fluid rather than a weakly interacting gas [22][23][24].…”

Toward a deeper understanding of how experiments constrain the underlying physics of heavy-ion collisions

“…where the parameter f wn describes the weighting between two other parameterized forms, wn which is the wounded nucleon form [7], and sat , which describes a form more in line with some ideas of saturation, similarly to [8].…”