Hydrodynamic Description of Heavy Ion Collisions

We give a short review of hydrodynamic models at heavy ion collisions from the point of view of initial conditions, an equation of states (EoS) and freezeout process. Then we show our latest results of a combined fully three-dimensional macroscopic/microscopic transport approach. In this model for the early, dense, deconfined stage relativistic 3D-hydrodynamics of the reaction and a microscopic nonequilibrium model for the later hadronic stage where the equilibrium assumptions are not valid anymore are employed. Within this approach we study the dynamics of hot, bulk QCD matter, which is being created in ultra-relativistic heavy ion collisions at RHIC. 1. Hydrodynamic Models at RHIC The first five years of RHIC operations at √ sNN = 130 GeV and √ sNN = 200 GeV have yielded a vast amount of interesting and sometimes surprising results. There exists mounting evidence that RHIC has created a hot and dense state of deconfined QCD matter with properties similar to that of an ideal fluid [1, 2] – this state of matter has been termed the strongly interacting Quark-Gluon-Plasma (sQGP). One of the evidence is the success of ideal hydrodynamic models in various physical observables. Especially, for the first time, in elliptic flow the hydrodynamic limit shows good agreement with the experimental data at RHIC, though at AGS and SPS hydrodynamic models give larger value as compared to experimental data. The sophisticated 3D ideal hydrodynamic calculations, however, reveal that many of experimental data have not yet been fully evaluated or understood [5]. For example, elliptic flow at forward and backward rapidity ‡ and at peripheral collisions is overestimated by ideal hydrodynamical models. The Hanbury-Brown Twiss (HBT) puzzle is not completely understood from the point of view of hydrodynamics. These distinctions between hydrodynamic calculation and experimental data suggest that the ideal hydrodynamic picture is not applicable to all physical observables even in low transverse momentum region. At present our main interest in hydrodynamic models is the following: How perfect the sQGP is? ‡ Brazil group shows improved results of v2 at forward/backward rapidity by using event-by-event fluctuated initial conditions [3]. Hydrodynamic Description of Heavy Ion Collisions 2 Here, first, we shall give a short review of hydrodynamic models at heavy ion collisions. In addition to a numerical procedure for solving the relativistic hydrodynamic equation, hydrodynamic models are characterized by initial conditions, EoSs and freezeout process. The necessity of input of initial conditions for hydrodynamic models is one of the largest limitations of them. Because an initial condition is not be able to determined in the framework of hydrodynamic model itself, usually a parametrization of energy density and baryon number density based on Glauber type is used and parameters in it are determined by comparison with experimental data [4, 5, 11]. Recently there are some studies in which more basic approaches, Color Glass Condensate (CGC) [6], pQCD + saturation model [7] are used for construction of initial conditions. The most important advantage of hydrodynamic models is that it directly incorporates an EoS as input and thus is so far the only dynamical model in which a phase transition can explicitly be incorporated. In the ideal fluid approximation – and once an initial condition has been specified – the EoS is the only input to the equations of motion and relates directly to properties of the matter under consideration. In this sense a hydrodynamic model is a bridge between QCD theory and experimental data and indispensable to describe heavy ion physics. However in usual practical hydrodynamic simulations, an EoS with 1st order phase transition (Bag model) is used. In fact, there are few studies on effect of order of QCD phase transition on physical observables [8]. Conventional hydrodynamic calculations need to assume a freezeout temperature at which the hydrodynamic evolution is terminated and a transition from the zero mean-free-path approximation of a hydrodynamic approach to the infinite mean-freepath of free streaming particles takes place. The freezeout temperature usually is a free parameter which can be fitted to measured hadron spectra. There are several approaches for dealing with freezeout process: chemical equilibrium [4, 8], partial chemical equilibrium [5], continuous emission model [9] and construction of a hybrid model of a hydro + cascade model [10, 11, 12]. In Tab. 1 several hydrodynamic models are listed from the viewpoint of initial conditions and freezeout processes, because almost the same EoS with strong 1st order phase transition is used. Reference [4] presents the first calculation which shows the remarkable agreement with experimental data for both of PT spectra and v2 at RHIC. However it turns out that the assumption of single freezeout temperature where chemical freezeout and kinetic freezeout occur at the same time fails in reproducing hadron ratios correctly. To obtain correct proton PT spectra, we need to renormalize the PT spectra using the p to π ratio at the critical temperature. In addition, recently, Hirano and Gyullasy point out that the good agreement of elliptic flow with experimental data may accidentally happen. Hirano and Kolb et al. propose that the introduction of two kinds of freezeout processes, chemical freezeout and kinetic freezeout to hydrodynamic models. In this model, normalization of the PT spectra for each particle are obtained correctly [5], but to get better agreement with experiments in elliptic flow additional initial transverse flow is needed. At present, the combination of Gluaber type and a Hydrodynamic Description of Heavy Ion Collisions 3 cascade model gives us the most promising result for both of PT spectra and v2. Hirano et al. perform calculations using CGC for initial condition and a cascade model for freezeout process, which suggests that viscosity is not negligible even at early stage of the expansion. In the next section we show our latest results [11] based on the full 3D hydrodynamic approach [13] with the microscopic Ultra-relativistic QuantumMolecular-Dynamics (UrQMD) model [14]. Table 1. Hydrodynamic models at RHIC. Reference Initial Conditions Freezeout Process [4] Glauber type chemical equilibrium [5] Glauber type partial chemical equilibrium [10, 11] Glauber type cascade model [15] CGC partial chemical equilibrium [12] CGC cascade model 2. Hydro+UrQMD Model We calculate hadron distribution at switching temperature from the 3D hydrodynamic model using Cooper-Frye formula [16] and produce initial conditions for UrQMD model by Monte Carlo from it. Such hybrid macro/micro transport calculations are to date the most successful approaches for describing the soft physics at RHIC. The biggest advantage of the hydrodynamic description is that it directly incorporates an EoS as input one of its largest limitations is that it requires thermalized initial conditions and one is not able to do an ab-initio calculation. Figure 1 shows a schematic sketch of the full 3D hydrodynamic model + UrQMD. After heavy ion collisions, first, hydrodynamic expansion starts. We introduce one more parameter, switching temperature from hydrodynamic picture to hadron base event generator, UrQMD. This switching temperature should be just below the critical temperature. Here it is set to 160 MeV. t fm C T T SW EoS:1st order phae transition Cooper−Frye formula Monte Carlo interactions final state Full 3D Hydrodynamics UrQMD hadronization Figure 1. Schematic sketch of 3D hydro+UrQMDmodel. Tc(= 160 MeV) and TSW(= 150) MeV are critical temperature and switching temperature from hydrodynamics to UrQMD model, respectively. Hydrodynamic Description of Heavy Ion Collisions 4 Figure 2 shows the PT spectra of π , K and p at √ sNN = 200 GeV central collisions. The most compelling feature is that the hydro+micro approach is capable of accounting for the proper normalization of the spectra for all hadron species without any additional correction as is performed in the pure hydrodynamic model. The introduction of a realistic freezeout process provides therefore a natural solution to the problem of separating chemical and kinetic freeze-out in a pure hydrodynamic approach. In Fig. 3 centrality dependence of PT spectra of π + is shown. The impact parameter for each centrality is determined simply by the collision geometry. The separation between model results and experiment appears at lower transverse momentum in peripheral collisions compared to central collisions, just as in the pure hydrodynamic calculation. The 3D hydro + micro model does not provide any improvement for this behavior, since the hard physics high PT contribution to the spectra occurs at early reaction times before the system has reached the QGP phase and is therefore neither included in the pure 3D hydrodynamic calculation nor in the hydro+micro approach. PT (GeV) 10 10 10 10 1 10 10 10 1/ (2 ) P T d N /d P T d y (G eV -2 ) Figure 2. PT spectra for π , K and p at central collisions with PHENIX data [17]. PT (GeV) 10 10 10 10 10 1 10 10 10 1/ (2 ) P T d N /d P T d y (G eV -2 ) Figure 3. Centrality dependence of PT spectra of π + with PHENIX data [17]. The PT spectra at 10–15 %, 15–20% and 20–30 % are divided by 5, 25 and 200, respectively. Figure 4 shows the centrality dependence of the pseudorapidity distribution of charged hadrons compared to PHOBOS data [18]. Solid circles stand for model results and open circles denote data taken by the PHOBOS collaboration [18]. The impact parameters are set to b = 2.4, 4.5, 6.3, 7.9 fm for 0-6 %, 6-15 %, 15-25 % and 2535 % centralities, respectively. Our results are consistent with experimental data over a wide pseudorapidity region. There is no distinct difference between 3-D ideal hydrodynamic model and the hydro + UrQMD model in the centrality dependence of the psuedorapidity distribution, indicating that the shape of psuedorapidity distribution is insensitive to the detailed microscopic reaction dynamics of the hadronic final state Hydrodynamic Description of Heavy Ion Collisions 5 [11]. In Fig. 5 we analyze the PT spectra of multistrange particles. Our results show good agreement with experimental data for Λ, Ξ, Ω for centralities 0–5 %. In this calculation the additional procedure for normalization is not needed (Fig. 6). Recent experimental results suggest that at thermal freezeout multistrange baryons exhibit less transverse flow and a higher temperature closer to the chemical freezeout temperature compared to nonor single-strange baryons [19, 20]. This behavior can be understood in terms of the flavor dependence of the hadronic cross section, which decreases with increasing strangeness content of the hadron. The reduced cross section of multi-strange baryons leads to a decoupling from the hadronic medium at an earlier stage of the reaction, allowing them to provide information on the properties of the hadronizing QGP less distorted by hadronic final state interactions 0 200 400 600 80