The problem of early thermalization of matter produced in relativistic heavy-ion collisions at RHIC is discussed in the framework of a hybrid model that consists of the transverse-hydrodynamics stage followed by the standard perfect-fluid hydrodynamics stage and freeze-out. The two hydrodynamic regimes are connected with the help of Landau matching conditions. A satisfactory description of the soft hadronic observables is achieved. This indicates that the early-thermalization problem and also the HBT puzzle may be to large extent circumvented.
Triple-gluon elastic scatterings are briefly reviewed since the scatterings explain the early thermalization puzzle in Au-Au collisions at RHIC energies. A numerical solution of the transport equation with the triple-gluon elastic scatterings demonstrates gluon momentum isotropy achieved at a time of the order of 0.65 fm/c. Triple-gluon scatterings lead to a short thermalization time of gluon matter.
I argue that measurements of Au+Au collisions at 20, 130 and 200 GeV of the centrality dependence of the mean p_t together with p_t and net-charge fluctuations reflect the approach to local thermal equilibrium.
Elliptic flow at RHIC is computed event-by-event with NeXSPheRIO. Reasonable agreement with experimental results on $v_2(η)$ is obtained. Various effects are studied as well: reconstruction of impact parameter direction, freeze out temperature, equation of state (with or without crossover), emission mecanism.
The large elliptic flow observed in Au-Au collisions at RHIC is often put forward as a compelling evidence for the formation of a strongly-interacting quark-gluon plasma. The main argument is that the measured elliptic flow is as large as the value given by fluid-dynamics models that assume complete thermalization. It is argued that this claim may not be justified, since a detailed examination of experimental data rather suggests that the system created is not fully equilibrated at the time when anisotropic flow develops.
The centrality dependence of dynamic fluctuations of the transverse momentum and the net charge can signal the approach to local thermal equilibrium in nuclear collisions. I explore this signal by comparing transport-theory calculations to STAR and PHENIX data at a range of energies. In particular, I find that this model can describe PHENIX data on the dependence of fluctuations on the transverse momentum range in which they are measured.
We address the problem if the early thermalization and HBT puzzles in relativistic heavy-ion collisions may be solved by the assumption that the early dynamics of the produced matter is locally anisotropic. The hybrid model describing the purely transverse hydrodynamic evolution followed by the perfect-fluid hydrodynamic stage is constructed. The transition from the transverse to perfect-fluid hydrodynamics is described by the Landau matching conditions applied at a fixed proper time. The global fit to the RHIC data reproduces the soft hadronic observables (the pion, kaon, and the proton spect…
Ideal hydroynamics provides an excellent description of all aspects of the single-particle spectra of all hadrons with transverse momenta below about 1.5-2 GeV/c at RHIC. This is shown to require rapid local thermalization at a time scale below 1 fm/c and at energy densities which exceed the critical value for color deconfinement by an order of magnitude. The only known thermalized state at such energy densities is the quark-gluon plasma (QGP). The rapid thermalization indicates that the QGP is a strongly interacting liquid rather than the weakly interacting gas of quarks and gluons that was p…
The early thermalization and HBT puzzles in relativistic heavy-ion collisions studied at RHIC are shortly reviewed. The results of recent hydrodynamic calculations that shed light on these two intriguing issues are presented. In particular, the role of the elliptic flow as a signature of early thermalization is critically examined.
We consider the evolution of a parton system which is formed in the central region just after a relativistic heavy ion collision. The parton consist of mostly gluons, minijets, which are produced by elastic scattering between constituent partons of the colliding nuclei. We assume the system can be described by a semi-classical Boltzmann transport equation, which we solve by means of the test particle Monte-Carlo method including retardation. The partons proliferate via secondary radiative $gg \to ggg$ processes until the thermalization is reached for some assumptions. The extended system is th…
The implications of parton rearrangement processes on the dynamics of ultra-relativistic heavy-ion collisions have been investigated. A microscopic transport approach, namely the quark gluon string model (QGSM) which has been extended for a locally density-dependent partonic rearrangement and fusion procedure served as the tool for this investigations. The model emulates effectively the dynamics of a strongly coupled quark plasma and final hadronic interactions. Main QGSM results on anisotropic flow components v1 and v2 at top RHIC energy are compiled. Predictions for the pseudorapidity depend…
We use a hydrodynamical model to describe the evolution of the collision system at collision energies sqrt{s}=130 and 200 GeV. At lower sqrt{s}=130 GeV energy we compare the results obtained assuming fast or slow thermalization (thermalization times tau_0=0.6 and 4.1 fm/c, respectively) and show that slow thermalization fails to reproduce the observed anisotropy of particle distribution. At sqrt{s}=200 GeV collision energy our results show anisotropies similar to those observed at sqrt{s}=130 GeV.
I discuss how the initial conditions for QGP-production in ultrarelativistic heavy ion collisions at the LHC and RHIC can be computed from perturbative QCD.
We investigate how thermalization of gluons depends on the initial conditions assumed in ultrarelativistic heavy ion collisions at RHIC. The study is based on simulations employing the pQCD inspired parton cascade solving the Boltzmann equation for gluons. We consider independently produced minijets with $p_T > p_0=1.3 \sim 2.0$ GeV and a color glass condensate as possible initial conditions for the freed gluons. It turns out that full kinetic equilibrium is achieved slightly sooner in denser system and its timescale tends to saturate. Compared with the kinetic equilibration we find a stronger…
We find that collective flow model which can successfully analyze charged particle distributions at AGS and lower SPS (less than 20Gev/n). but fails to analyze that of at RHIC. The tails of distribution of charged particle at RHIC has a jump from the collective flow model calculation as the energy increases. Thermalization Component Model is presented based on collective flow to study the multiplicity distributions at RHIC in this paper. It is realized that the region of phase space of collective flow can reflect that of thermalization region. By comparing the contributions of particle product…
The hydrodynamical models used to describe the evolution of heavy-ion collisions are briefly reviewed and their results compared with recent RHIC data.
The current status of the application of hydrodynamics to ultrarelativistic heavy ion collisions is reviewed. We elaborate on the arguments for strong transverse flow and rapid thermalization and discuss future applications and trends in hydrodynamics.
Three-gluon to three-gluon scatterings lead to rapid thermalization of gluon matter created in central Au-Au collisions at RHIC energies. Thermalization of quark matter is studied from three-quark to three-quark scatterings.
The hydrodynamic model is used to describe the single-particle spectra and elliptic flow of hadrons at RHIC and to predict the emission angle dependence of HBT correlations at RHIC and LHC energies.
The pseudorapidity dependence of elliptic flow in Au+Au collisions at 130 $A$ GeV is studied within a full three-dimensional hydrodynamic model in the light-cone coordinate. First, we prepare two initial conditions in the hydrodynamic model for analyzing elliptic flow. Both initial conditions lead to reasonable agreement with single particle spectra in central and semi-central collisions. Next, by using these hydrodynamic simulations, we compare elliptic flow as a function of pseudorapidity with experimental data recently measured by the PHOBOS Collaboration. Our results are in agreement with …
A hydrodynamic model coupled to the statistical hadronization code Therminator is used to study a set of observables in the soft sector at RHIC. A satisfactory description of the pT-spectra and elliptic flow is obtained, similarly to other hydrodynamic models. With the Gaussian initial conditions the transverse femtoscopic radii are also reproduced, providing a possible solution of the RHIC HBT puzzle.
The framework of anisotropic hydrodynamics is used in 3+1 dimensions to analyze behavior of matter produced in ultra-relativistic heavy-ion collisions. The model predictions for the hadronic transverse-momentum spectra, directed and elliptic flows, and the HBT radii are presented. We show that the effects of the initial anisotropy of pressure may be compensated by appropriate adjustment of the initial energy density. In this way, the final hadronic observables become insensitive to the early stage dynamics and the early thermalization puzzle may be circumvented.
We review the apparently hydrodynamic behaviour of low transverse momentum particles (p_T < 1.5 GeV/c) produced in central and semicentral (b < 7 fm) heavy ion collisions at RHIC. We investigate the impact parameter dependence of various observables, elaborating on radial and elliptic flow and particle multiplicities. We also discuss possible ambiguities in the initialization of the hydrodynamic system and present observables that should allow for their resolution.
A brief overview of the current status of hydrodynamic concepts applied to ultra relativistic heavy-ion collisions is presented. Special emphasis is placed on future prospects for extracting the thermodynamic properties and the bulk features of the created medium from experimental observations.
In an earlier work (arXiv:0808.0953) we established that causal Israel-Stewart viscous hydrodynamics is only accurate in RHIC applications at very low shear viscosities 4 pi eta_s / s < ~ 1.5-2. We show here that the region of applicability is significantly reduced if bulk viscosity plays a role in the dynamics.
The dynamical scaling behavior of hydrodynamic and non-hydrodynamic moments of the distribution function is studied using third-order Chapman-Enskog hydrodynamics and anisotropic hydrodynamics for systems undergoing Bjorken and Gubser expansions, where exact solutions of the Boltzmann equation in Relaxation Time Approximation (RTA) are available for comparison. While dimensionless quantities like normalized shear, pressure anisotropy and normalized entropy show at late times universal scaling relations with small (large) Knudsen number for Bjorken (Gubser) flows, dimensionful quantities like t…
I review the successes and limitations of the ideal fluid dynamic model in describing hadron emission spectra from Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC).
In the flat space, non-spherical shells collapse to give globular cluster after many oscillations. We show that in anti de sitter space, they form black holes in one dynamical time. We propose that this is the mechanism of early thermalization in strong quark-gluon plasma in gravity dual. This is traced back to the a remarkable property of AdS : the period in radial motion is amplitude independent in spite of the NON-linearity of the equation of motion. We investigate the interaction effect numerically and observe the same qualitative behavior for the attractive forces. For repulsive interacti…
Hydrodynamic behavior and the associated discussions of viscosity at RHIC has inspired a r enaissance in modeling viscous hydrodynamics. An explanation of Israel-Stewart hydrodynamics is presented here, with an emphasis on the tangible benefits compared to Navier Stokes.
It is argued that the use of the initial Gaussian energy density profile for hydrodynamics leads to much better uniform description of the RHIC heavy-ion data than the use of the standard initial condition obtained from the Glauber model. With the modified Gaussian initial conditions we successfully reproduce the transverse-momentum spectra, v2, and the pionic HBT radii (including their azimuthal dependence). The emerging consistent picture of hadron production hints that a solution of the long standing RHIC HBT puzzle has been found.
Current status of dynamical modeling of relativistic heavy ion collisions and hydrodynamic description of the quark gluon plasma is reported. We find the hadronic rescattering effect plays an important role in interpretation of mass splitting pattern in the differential elliptic flow data observed at RHIC. To demonstrate this, we predict the elliptic flow parameter for phi mesons to directly observe the flow just after hadronisation. We also discuss recent applications of outputs from hydrodynamic calculations to J/psi suppression, thermal photon radiation and heavy quark diffusion.
We discuss the present collective flow signals for the phase transition to quark-gluon plasma (QGP) and the collective flow as a barometer for the equation of state (EoS). A study of Mach shocks induced by fast partonic jets propagating through the QGP is given. We predict a significant deformation of Mach shocks in central Au+Au collisions at RHIC and LHC energies as compared to the case of jet propagation in a static medium. Results of a hydrodynamical study of jet energy loss are presented.
It is argued that the observation of anisotropic azimuthal distribution of final state particles alone is insufficient to show whether the formed matter at RHIC behaves like hydrodynamic flow. Examining the intrinsic interaction (or correlation) of the formed matter should provide more definite judgement. To the end, a spatial-dependent azimuthal multiplicity-correlation pattern is suggested. It shows clearly in the pattern that there are two kinds of interactions at the early stage of Au + Au collisions at $\sqnn=200$ GeV generated by RQMD with hadron re-scattering and AMPT with string meltin…
We show that a consistent hydrodynamic description of soft-hadronic one- and two-particle observables (the HBT radii) studied in the relativistic heavy-ion collisions at RHIC may be obtained if one uses the Gaussian energy density profile as the initial condition. The transverse-momentum spectra, the elliptic flow coefficient $v_2$, and the pionic azimuthally sensitive HBT radii are successfully reproduced, which hints that the long standing HBT puzzle has been solved.
We report recent progress on causal viscous hydrodynamics for relativistic heavy ion collisions. For fixed specific shear viscosity eta/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 eta/s < 5/(4pi).
We compare elliptic flow evolution from ideal hydrodynamics and covariant parton transport theory, and show that, for conditions expected at RHIC, dissipation significantly reduces elliptic flow even for extreme parton cross sections and/or densities sigma_gg * dN/dη(b=0) ~ 45 mb * 1000. The difference between transport and hydrodynamic elliptic flow is established rather early during the evolution of the system, but the buildup of elliptic flow is surprisingly insensitive to the choice of the initial (formation or thermalization) time in both models.
We can establish a new picture, the perfect fluid sQGP core and the dissipative hadronic corona, of the space-time evolution of produced matter in relativistic heavy ion collisions at RHIC. It is also shown that the picture works well also in the forward rapidity region through an analysis based on a new class of the hydro-kinetic model and that this is a manifestation of rapid increase of entropy density in the vicinity of QCD critical temperature, namely deconfinement.
The bulk of the hot and dense matter created at RHIC behaves like an almost ideal fluid. I present the evidence for this and also discuss what we can learn about the transport properties of the quark-gluon plasma (QGP) from the gradual breakdown of ideal fluid dynamic behavior at large transverse momenta, lower beam energies, larger impact parameters, and forward rapidities.
A hybrid parameterization including contributions of hydrodynamics and of expectations from the spectral shape observed in p+p collisions is introduced. This parameterization can successfully describe identified hadron spectra over a wide range of $p_{T}$ in Au+Au reactions at $\sqrt{s_{NN}}$ = 200 GeV for all centralities. The parameters of the hydrodynamic source compare reasonably well to other attempts to describe the spectra. The description is obtained using one universal suppression factor of the hard scattering component independent of $p_{T}$ and hadron species. For the fit results ob…
The pseudo-rapidity dependence of the elliptic flow at various excitation energies measured by the PHOBOS Collaboration in Au+Au collisions at RHIC is one of the surprising results that has not been explained before in terms of hydrodynamical models. Here we show that these data are in agreement with theoretical predictions based on perfect fluid hydrodynamics. We also show that these PHOBOS data satisfy the universal scaling relation predicted by the Buda-Lund hydrodynamical model, based on exact solutions of perfect fluid hydrodynamics.
A hydrodynamic + cascade model of relativistic heavy ion collisions is presented and compared to available hadronic data from the SPS to RHIC. The model consistently reproduces the radial and elliptic flow data for different particles, collision energies, and impact parameters. Three ingredients are essential to the success: (a) a reasonable EOS exhibiting the hard and soft features of the QCD phase transition, (b) thermal hadronization at the phase boundary, and (c) subsequent hadronic rescattering. Some features of the RHIC data are readily explained: (i) the observed elliptic flow and its d…
I review recent progress in thermalization in heavy-ion collisions, with particular emphasis on hydrodynamic attractor, and also report recent progress in hydrodynamic fluctuations.
Using the (2+1)-dimensional ultrarelativistic viscous hydrodynamics+hadron cascade, VISHNU, hybrid model, we study the $p_{\rm T}$-spectra and elliptic flow of $Λ$, $Ξ$, and $Ω$ in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV. Comparing our model results with the data measurements, we find that the VISHNU model gives general descriptions of the measurements of these strange and multi-strange hadrons at several centrality classes at RHIC and LHC. Mass ordering of elliptic flow $v_{2}$ among $π$, $K$, $p$, $Λ$, $Ξ$, and $Ω$ are further investiga…
The charged particles produced in nucleus-nucleus collisions are divided into two parts. One is from the hot and dense matter created in collisions. The other is from leading particles. The hot and dense matter is assumed to expand according to unified hydrodynamics and freezes out into charged particles from a space-like hypersurface with a fixed proper time of Tau_FO.The leading particles are conventionally taken as the particles which inherit the quantum numbers of colliding nucleons and carry off most of incident energy. The rapidity distributions of the charged particles from these two pa…
Thermalization of quark matter and antiquark matter is studied with quark-quark-antiquark as well as quark-antiquark-antiquark elastic scatterings. Squared amplitudes of qqqbar to qqqbar and qqbarqbar to qqbarqbar at order alpha_s^4 are derived in perturbative QCD. Solved by a new technique, solutions of transport equations with the squared amplitudes indicate that the scatterings qqqbar to qqqbar and qqbarqbar to qqbarqbar shorten the thermalization time of quark matter and antiquark matter. It is emphasized that three-parton and other multi-parton scatterings become important at the high par…
We present hydrodynamic predictions for the charged pion HBT radii for a range of initial conditions covering those presumably reached in Pb+Pb collisions at the LHC. We study central (b=0) and semi-central (b=7fm) collisions and show the expected increase of the HBT radii and their azimuthal oscillations. The predicted trends in the oscillation amplitudes reflect a change of the final source shape from out-of-plane to in-plane deformation as the initial entropy density is increased.
In this article, we briefly review recent progress on hydrodynamic modeling and its implementations to relativistic heavy-ion collisions at RHIC and the LHC. The related topics include: 1) initial state fluctuations, final state correlations and event-by-event hydrodynamics, 2) extracting the QGP shear viscosity from flow data, 3) flow and hydrodynamics in 5.02 A TeV p+Pb collisions.
It is argued that the consistent description of the transverse-momentum spectra, elliptic flow, and the HBT radii in the relativistic heavy-ion collisions studied at RHIC may be obtained within the hydrodynamic model if one uses the Gaussian profile for the initial energy density in the transverse plane. Moreover, we show that the results obtained in the scenario with an early start of hydrodynamics (at the proper time tau0 = 0.25 fm) are practically equivalent to the results obtained in the model where the hydrodynamics is preceded by the free-streaming stage of partons (in the proper time in…
Hydrodynamical modeling of heavy ion collisions at RHIC suggests that the quark-gluon plasma (QGP) "thermalizes" in a remarkably short time scale, about 0.6 fm/c. We argue that this should be viewed as indicating fast isotropization, but not necessarily complete thermalization, of the non-equilibrium QGP. Non-Abelian plasma instabilities can drive local isotropization of an anisotropic QGP on a time scale which is faster than ordinary perturbative scattering processes. As a result, we argue that theoretical expectations based on weak coupling analysis are not necessarily in conflict with hydro…
We review the basic concepts of perturbative quantum chromodynamics (QCD) and relativistic hydrodynamics, and their applications to hadron production in high energy nuclear collisions. We discuss results from the Relativistic Heavy Ion Collider (RHIC) in light of these theoretical approaches. Perturbative QCD and hydrodynamics together explain a large amount of experimental data gathered during the first decade of RHIC running, although some questions remain open. We focus primarily on practical aspects of the calculations, covering basic topics like perturbation theory, initial state nuclear …
The hydrodynamic model for the expansion of the fireball in relativistic heavy-ion collisions is presented. Calculations using relativistic hydrodynamics of a fluid with small viscosity yield a satisfactory description of the experimental data on the particle spectra, the elliptic flow or the interferometry radii.
We describe the propagation of charm quarks in the quark-gluon plasma (QGP) by means of a Boltzmann transport approach. Non-perturbative interaction between heavy quarks and light quarks have been taken into account through a quasi-particle approach in which light partons are dressed with thermal masses tuned to lQCD thermodynamics. Such a model is able to describe the main feature of the non-perturbative dynamics: the enhancement of the interaction strength near $T_c$. We show that the resulting charm in-medium evolution is able to correctly predict simultaneously the nuclear suppression fact…
Initial conditions for quark-gluon plasma formation at $τ=0.1\fm$ are considered in lowest order perturbative QCD. Chemical composition, thermalization of the formed semihard quark-gluon system and especially implications of the new HERA parton distributions with the enhancement at small $x$ are studied. The plasma at $τ=0.1\fm$ is shown to be strongly gluon dominated both at RHIC and LHC, and a possibility for rapid thermalization of gluons at LHC is pointed out. Uncertainties in the calculations, particularly shadowing corrections to the parton distributions, are discussed. Free streaming an…
Transverse mass spectra of pions and protons measured in central collisions of heavy ions at the SPS and at RHIC are compared to a hydrodynamic parameterization. While the chemical temperature needed at RHIC is significantly higher compared to SPS, the spectra may be described using kinetic freeze-out parameters which are similar for both beam energies. At RHIC either the temperature or the flow velocity is higher, but the data provide no unambiguous proof for much stronger transverse flow. The contribution of such hydrodynamic emission at high transverse momenta is investigated in detail. It …
Anisotropic transverse flow is studied in Pb+Pb and Au+Au collisions at SPS and RHIC energies. The centrality and transverse momentum dependence at midrapidity of the elliptic flow coefficient v_2 is calculated in the hydrodynamic and low density limits. Hydrodynamics is found to agree well with the RHIC data for semicentral collisions up to transverse momenta of 1-1.5 GeV/c, but it considerably overestimates the measured elliptic flow at SPS energies. The low density limit LDL is inconsistent with the measured magnitude of v_2 at RHIC energies and with the shape of its p_t-dependence at both …
In this talk I will describe various features of time dependent dynamics of strongly coupled plasma from the perspective of the AdS/CFT correspondence. I will take as an example boost invariant plasma flow and concentrate on the properties of hydrodynamic expansion, thermalization versus hydrodynamization and some features of nonequilibrium behaviour.
Scattering of particles produced in Au+Au collisions at RHIC can wrestle the system into a state near local thermal equilibrium. I illustrate how measurements of the centrality dependence of the mean transverse momentum and its fluctuations can exhibit this thermalization.
Gauge/gravity duality has provided unprecedented opportunities to study dynamics in certain strongly coupled gauge theories. This review aims to highlight several applications to heavy ion collisions including far-from-equilibrium dynamics, hydrodynamics and jet energy loss at strong coupling.
Pre-thermal flow plays an important role in the final state evolution of heavy ion collisions at RHIC. We show that flow has universal features for a wide range of models. This significantly reduces the uncertainty in initializing hydrodynamic models at RHIC.
In this proceedings contribution, we review 3+1d quasiparticle anisotropic hydrodynamics (aHydroQP). Then, we show some recent phenomenological comparisons between the aHydroQP model and some experimental results. We show comparisons between aHydroQP and Pb-Pb 2.76 TeV collisions from the ALICE collaboration and Au-Au 200 GeV collisions from RHIC experiments. We show that the quasiparticle anisotropic hydrodynamics model is able to describe the experimental results for Pb-Pb and Au-Au collisions quite well for many observables such as the spectra, multiplicity, elliptic flow, and HBT radii in …
A known class of analytic, exact, accelerating solutions of prefect relativistic hydrodynamics with longitudinal acceleration is utilized to describe results on the pseudorapidity distributions for different collision systems. These results include $dN/dη$ measured in p+p, Cu+Cu, Au+Au, and Pb+Pb collisions at RHIC and LHC, in a broad centrality range. Going beyond the traditional Bjorken model, from the accelerating hydrodynamic description we determine the initial energy density and other thermodynamic quantities in those collisions.
