Huichao Song

200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid

A new robust method to extract the specific shear viscosity (η/s)(QGP) of a quark-gluon plasma (QGP) at temperatures T(c) < T ≲ 2T(c) from the centrality dependence of the eccentricity-scaled elliptic flow v2/ε measured in ultrarelativistic heavy-ion collisions is presented. Coupling viscous fluid dynamics for the QGP with a microscopic transport model for hadronic freeze-out we find for 200 A GeV Au + Au collisions that v2/ε is a universal function of multiplicity density (1/S)(dN(ch)/dy) that depends only on the viscosity but not on the model used for computing the initial fireball eccentricity ε. Comparing with measurements we find 1<4π(η/s)(QGP) < 2.5 where the uncertainty range is dominated by model uncertainties for the values of ε used to normalize the measured v2.

Suppression of elliptic flow in a minimally viscous quark-gluon plasma

The success of the hydrodynamic model in describing the bulk of hadron production in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC) [1] has led to a paradigmatic shift in our view of the quark-gluon plasma (QGP): Instead of behaving like a gas of weakly interacting quarks and gluons [2], as naively expected on the basis of asymptotic freedom in QCD, its collective properties rather reflect those of a “perfect liquid” with (almost) vanishing viscosity. However, due to quantum mechanical uncertainty no fluid can have exactly zero viscosity [3], and recent work [4] on strongly coupled gauge field theories, based on techniques exploiting the AdS/CFT correspondence, suggests an absolute lower limit for the ratio of shear viscosity η to entropy density s: η/s ≥ ~/4π. This raises the interesting question how close to this limit the actual value of the shear viscosity of the QGP created at RHIC is. Answering this question requires hydrodynamic simulations for relativistic viscous fluids in which the ratio η/s enters as a parameter. To study the anisotropic (“elliptic”) collective flow in non-central heavy-ion collisions, from which limits on η/s can be extracted [5], requires a code that evolves the hydrodynamic fields at least in the two dimensions transverse to the heavy-ion beam. In this Letter we present our first results from such simulations [6]; a longer paper with a discussion of all technical details of our approach is in preparation [7].

Multiplicity scaling in ideal and viscous hydrodynamics

Using numerical results from ideal and viscous relativistic hydrodynamic simulations with three different equations of state, for Au+Au and Cu+Cu collisions at different centralities and initial energy densities, we explore the dependence of the eccentricity-scaled elliptic flow, v{sub 2}/{epsilon}, and the produced entropy fraction, {delta}S/S{sub 0}, on the final charged hadron multiplicity density dN{sub ch}/dy per unit transverse overlap area S,(1/S)dN{sub ch}/dy. The viscous hydrodynamic simulations are performed with two different versions of the Israel-Stewart kinetic evolution equations, and in each case we investigate the dependence of the physical observables on the kinetic relaxation time. We find approximate scaling of v{sub 2}/{epsilon} and {delta}S/S{sub 0} with (1/S)dN{sub ch}/dy, with scaling functions that depend on the EOS and, in particular, on the value of the specific shear viscosity {eta}/s. Small scaling violations are seen even in ideal hydrodynamics, caused by a breaking of the scale invariance of ideal fluid dynamics by the freeze-out condition. Viscous hydrodynamics shows somewhat larger scale-breaking effects that increase with increasing {eta}/s and decreasing system size and initial energy density. We propose to use precision studies of these scaling violations to help constrain the shear viscosity {eta}/s of the quark-gluon plasma created in relativistic heavy ion collisions.

Radial and elliptic flow in Pb + Pb collisions at energies available at the CERN Large Hadron Collider from viscous hydrodynamics

A comprehensive viscous hydrodynamic fit of spectra and elliptic flow for charged hadrons and identified pions and protons from Au+Au collisions of all centralities measured at the Relativistic Heavy Ion Collider is performed and used as the basis for predicting the analogous observables for Pb+Pb collisions at the Large Hadron Collider at sqrt(s)=2.76 and 5.5 A TeV. Comparison with recent measurements of the elliptic flow of charged hadrons by the ALICE experiment shows that the model slightly over-predicts the data if the same (constant) specific shear viscosity eta/s is assumed at both collision energies. In spite of differences in our assumptions for the equation of state, the freeze-out temperature, the chemical composition at freeze-out, and the starting time for the hydrodynamic evolution, our results agree remarkably well with those of Luzum [M. Luzum, Phys. Rev. C 83, 044911 (2011)], indicating robustness of the hydrodynamic model extrapolations. Future measurements of the centrality and transverse momentum dependence of spectra and elliptic flow for identified hadrons predicted here will further test the model and shed light on possible variations of the quark-gluon transport coefficients between RHIC and LHC energies.

Extracting the QGP viscosity from RHIC data—a status report from viscous hydrodynamics

We report recent progress on causal viscous hydrodynamics for relativistic heavy-ion collisions. For fixed specific shear viscosity η/s, uncertainties in the elliptic flow arising from initial conditions, equation of state, bulk viscosity and numerical viscosity, and the treatment of the highly viscous hadronic stage and freeze-out procedure are analysed. A comparison of current viscous hydrodynamic results with experimental data yields a robust upper limit .

The iEBE-VISHNU code package for relativistic heavy-ion collisions

The iEBE-VISHNU code package performs event-by-event simulations for relativistic heavy-ion collisions using a hybrid approach based on (2+1)-dimensional viscous hydrodynamics coupled to a hadronic cascade model. We present the detailed model implementation, accompanied by some numerical code tests for the package. iEBE-VISHNU forms the core of a general theoretical framework for model-data comparisons through large scale Monte-Carlo simulations. A numerical interface between the hydrodynamically evolving medium and thermal photon radiation is also discussed. This interface is more generally designed for calculations of all kinds of rare probes that are coupled to the temperature and flow velocity evolution of the bulk medium, such as jet energy loss and heavy quark diffusion.

Dissipative hydrodynamics for viscous relativistic fluids

Explicit equations are given for describing the space-time evolution of nonideal (viscous) relativistic fluids undergoing boost-invariant longitudinal and arbitrary transverse expansion. The equations are derived from the second-order Israel-Stewart approach which ensures causal evolution. Both azimuthally symmetric (1+1)dimensional and nonsymmetric (2+1)-dimensional transverse expansion are discussed. The latter provides the formal basis for the hydrodynamic computation of elliptic flow in relativistic heavy ion collisions including dissipative effects.

Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach

A hybrid transport approach for the bulk evolution of viscous QCD matter produced in ultrarelativistic heavy-ion collisions is presented. The expansion of the dense deconfined phase of the reaction is modeled with viscous hydrodynamics while the dilute late hadron gas stage is described microscopically by the Boltzmann equation. The advantages of such a hybrid approach lie in the improved capability of handling large dissipative corrections in the late dilute phase of the reaction, including a realistic treatment of the non-equilibrium hadronic chemistry and kinetic freeze-out. By varying the switching temperature at which the hydrodynamic output is converted to particles for further propagation with the Boltzmann cascade we test the ability of the macroscopic hydrodynamic approach to emulate the microscopic evolution during the hadronic stage and extract the temperature dependence of the effective shear viscosity of the hadron resonance gas produced in the collision. We find that the extracted values depend on the prior hydrodynamic history and hence do not represent fundamental transport properties of the hadron resonance gas. We conclude that viscous fluid dynamics does not provide a faithful description of hadron resonance gas dynamics with predictive power, and that both components of the hybrid approach are needed for a quantitative description of the fireball expansion and its freeze-out.

Interplay of shear and bulk viscosity in generating flow in heavy-ion collisions

We perform viscous hydrodynamic calculations in 2+1 dimensions to investigate the influence of bulk viscosity on the viscous suppression of elliptic flow in noncentral heavy-ion collisions at Relativistic Heavy Ion Collider energies. Bulk and shear viscous effects on the evolution of radial and elliptic flow are studied with different model assumptions for the transport coefficients. We find that the temperature dependence of the relaxation time for the bulk viscous pressure, especially its critical slowing-down near the quark-hadron phase transition at T{sub c}, partially offsets effects from the strong growth of the bulk viscosity itself near T{sub c} and that even small values of the specific shear viscosity eta/s of the fireball matter can be extracted without large uncertainties from poorly controlled bulk viscous effects.

Hadron spectra and elliptic flow for 200 A GeV Au + Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade

It is shown that the recently developed hybrid code VISHNU, which couples a relativistic viscous fluid dynamical description of the quark-gluon plasma (QGP) with a microscopic Boltzmann cascade for the late hadronic rescattering stage, yields an excellent description of charged and identified hadron spectra and elliptic flow measured in 200 A GeV Au+Au collisions at the Relativistic Heavy-Ion Collider (RHIC). Using initial conditions that incorporate event-by-event fluctuations in the initial shape and orientation of the collision fireball and values {eta}/s for the specific shear viscosity of the quark-gluon plasma that were recently extracted from the measured centrality dependence of the eccentricity-scaled, p{sub T}-integrated charged hadron elliptic flow v{sub 2,ch}/{epsilon}, we obtain universally good agreement between theory and experiment for the p{sub T} spectra and differential elliptic flow v{sub 2}(p{sub T}) for both pions and protons at all collision centralities.