Using ideal relativistic hydrodynamics in 2+1 dimensions, we study the collision energy dependence of radial and elliptic flow, of the emitted hadron spectra, and of the transverse momentum dependence of several hadronic particle ratios, covering the range from Alternating Gradient Synchrotron (AGS) to Large Hadron Collider (LHC) energies. These calculations establish an ideal fluid dynamic baseline that can be used to assess non-equilibrium features manifest in future LHC heavy-ion experiments. Contrary to earlier suggestions we find that a saturation and even decrease of the differential elliptic flow v_2(p_T) with increasing collision energy cannot be unambiguously associated with the QCD phase transition.
The rather complete data set of hadron yields from central Si + A collisions at the Brookhaven AGS is used to test whether the system at freeze-out is in thermal and hadro-chemical equilibrium. Rapidity and transverse momentum distributions are discussed with regards to the information they provide on hydrodynamic flow.
The recent results on anisotropic flow in ultrarelativistic nuclear collisions along with recent methodical developments and achievements in the understanding of the phenomena, are reviewed. The emphasis is given to the elliptic flow results.
Entropy production in the initial compression stage of relativistic heavy-ion collisions from AGS to SPS energies is calculated within a three-fluid hydrodynamical model. The entropy per participating net baryon is found to increase smoothly and does not exhibit a jump or a plateau as in the 1-dimensional one-fluid shock model. Therefore, the excess of pions per participating net baryon in nucleus-nucleus collisions as compared to proton-proton reactions also increases smoothly with beam energy.
Within hydrodynamics we study the effects of the initial spatial anisotropy in non-central heavy-ion collisions on the momentum distributions of the emitted hadrons. We show that the elliptic flow measured at midrapidity in 158 A GeV/c Pb+Pb collisions can be quantitatively reproduced by hydrodynamic expansion, indicating early thermalization in the collision. We predict the excitation functions of the 2nd and 4th harmonic flow coefficients from AGS to LHC energies and discuss their sensitivity to the quark-hadron phase transition.
Using the relativistic transport model (ART), we predict the energy dependence of the stopping power, maximum baryon and energy densities, the population of resonance matter as well as the strength of the transverse and radial flow for central Au+Au reactions at beam momentum from 2 to 12 GeV/c available at Brookhaven's AGS. The maximum baryon and energy densities are further compared to the predictions of relativistic hydrodynamics assuming the formation of shock waves. We also discuss the Fermi-Landau scaling of the pion multiplicity in these reactions.
We analyze the baryon sideward and elliptic flow from SIS (0.25 $\sim$ 2 A GeV) to AGS (2 $\sim 11.0A$GeV) energies for Au + Au collisions in the relativistic transport model RBUU that includes all baryon resonances up to a mass of 2 GeV as well as string degrees of freedom for the higher mass continuum. There are two factors which dominantly determine the baryon flow at these energies: the momentum dependence of the scalar and vector potentials and the resonance-string degrees of freedom. We fix the explicit momentum dependence of the nucleon-meson couplings within the NL3 parameter set by th…
We study the proton sideward and elliptic differential flow for Au+Au collisions at AGS energies (2 -- 8 A cdot GeV) in a microscopic relativistic transport model that includes all baryon resonances up to a mass of 2 GeV as well as string degrees of freedom for the higher hadronic excitations. In order to explore the sensitivity of the various differential flows to the nuclear equation of state (EoS) we use three different parameterizations of the scalar- and vector mean-fields, i.e. NL2 (soft), NL23 (medium) and NL3 (hard), with their momentum dependence fitted to the experimental Schrodinger…
We apply the parton recombination approach to study the energy dependence of the elliptic flow, v_2 in heavy ion collisions from AGS to LHC energies. The relevant input quantities ($T, μ_B, η_T$) at the various center of mass energies are obtained from fits to the available data. The model yields a good description of the integrated v_2 data for charged particles at midrapidity from AGS to RHIC energies. In stark contrast to the current expectations, we observe a decrease of the integrated v_2 values above the highest RHIC energy. Thus, we predict a decrease of v_2 at LHC energies compared to …
Transverse-mass spectra in Au+Au and Pb+Pb collisions in incident energy range from 2A to 160A GeV are analyzed within the model of 3-fluid dynamics. It is shown that dynamical description of freeze-out, accepted in this model, naturally explains the incident energy behavior of inverse-slope parameters of these spectra observed in experiment. Simultaneous reproduction of the inverse-slopes of all considered particles (protons, pions and kaons) suggests that these particles belong to the same hydrodynamic flow at the instant of their freeze-out.
Collective flows in heavy-ion collisions from AGS ($(2-11)A$ GeV) to SPS ($(40,158)A$ GeV) energies are investigated in a nonequilibrium transport model with nuclear mean-field (MF). Sideward $<p_x>$, directed $v_1$, and elliptic flows $v_2$ are systematically studied with different assumptions on the nuclear equation of state (EOS). We find that momentum dependence in the nuclear MF is important for the understanding of the proton collective flows at AGS and SPS energies. Calculated results with momentum dependent MF qualitatively reproduce the experimental data of proton sideward, directed, …
Using a relativistic hadron transport model, we investigate the utility of the elliptic flow excitation function as a probe for the stiffness of nuclear matter and for the onset of a possible quark-gluon-plasma (QGP) phase-transition at AGS energies 1 < E_Beam < 11 AGeV. The excitation function shows a strong dependence on the nuclear equation of state, and exhibits characteristic signatures which could signal the onset of a phase transition to the QGP.
Hydrodynamics is applied to describe the dynamics of relativistic heavy-ion collisions. The focus of the present study is the influence of a possible (phase) transition to the quark-gluon plasma in the nuclear matter equation of state on collective observables, such as the lifetime of the system and the transverse directed flow of matter. It is shown that such a transition leads to a softening of the equation of state, and consequently to a time-delayed expansion which is in principle observable via two-particle correlation functions. Moreover, the delayed expansion leads to a local minimum in…
The centrality dependence of elliptic flow and how it is related to the physics of expansion of the system created in high energy nuclear collisions is discussed. Since in the hydro limit the centrality dependence of elliptic flow is mostly defined by the elliptic anisotropy of the overlapping region of the colliding nuclei, and in the low density limit by the product of the elliptic anisotropy and the multiplicity, we argue that the centrality dependence of elliptic flow should be a good indicator of the degree of equilibration reached in the reaction. Then we analyze experimental data obtain…
Ideal hydrodynamic simulations are performed to compute the evolution with collision energy of hadron spectra and elliptic flow between AGS and LHC energies. We argue that viscous effects should decrease with increasing energy, improving the applicability of ideal fluid dynamics at higher energies. We show that the increasing radial flow at higher energies pushes the elliptic flow to larger transverse momenta, leading to a peaking and subsequent decrease of the elliptic flow at fixed p_T with increasing collision energy, independent of whether or not there is a phase transition in the equation…
Collective transverse flow in heavy-ion collisions at incident energies E_{lab} = (1 -160)A GeV is analyzed within the model of 3-fluid dynamics (3FD). Simulations are performed with purely hadronic equation of state (EoS). At the AGS energies the flow turns out to be sensitive to the stopping power of nuclear matter rather than only to the stiffness of the EoS. When the stopping power is fixed to reproduce other observables, the flow data favor more and more soft EoS with the incident energy rise, which can be associated with ``a transition from hadronic to string matter'' reported in the Had…
We study the time scale for pressure equilibration in heavy ion collisions at AGS energies within the three-fluid hydrodynamical model and a microscopic cascade model (UrQMD). We find that kinetic equilibrium is reached in both models after a time of 5 fm/c (center-of-mass time). Thus, observables which are sensitive to the early stage of the reaction differ considerably from the expectations within the instant thermalization scenario (one-fluid hydrodynamical model).
We present a new direct simulation Monte-Carlo method for solving the relativistic Boltzmann equation. We solve numerically the 2-dimensional Boltzmann equation using this new algorithm. We find that elliptic flow from this transport calculation smoothly converges towards the value from ideal hydrodynamics as the number of collisions per particle increases, as expected on general theoretical grounds, but in contrast with previous transport calculations.
We use a hydrodynamic model to study the space-time evolution transverse to the beam direction in ultrarelativistic heavy-ion collisions with nonzero impact parameters. We focus on the influence of early pressure on the development of radial and elliptic flow. We show that at high energies elliptic flow is generated only during the initial stages of the expansion while radial flow continues to grow until freeze-out. Quantitative comparisons with SPS data from semiperipheral Pb+Pb collisions suggest the applicability of hydrodynamical concepts already $\approx$ 1 fm/c after impact.
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 extracte…
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 is a manifestation of deconfinement.
The azimuthal anisotropies of the collective transverse flow of charged hadrons are investigated in a wide range of heavy-ion collision energies within the microscopic Parton-Hadron-String Dynamics (PHSD) transport approach which incorporates explicit partonic degrees-of-freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD as well as the dynamical hadronization and hadronic collision dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow $v_2$ of charged hadrons with collision ene…
The transverse momentum dependence of elliptic flow of pions calculated in a full (3+1)d Boltzmann approach with an intermediate hydrodynamic stage for heavy ion reactions for CERN-SPS energies is discussed in the context of the experimental data. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to larger elliptic flow. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data. Within this i…
In a hydrodynamic model, we have studied $J/ψ$ suppression and elliptic flow in Au+Au collisions at RHIC energy $\sqrt{s}$=200 GeV. At the initial time, $J/ψ$'s are randomly distributed in the fluid. As the fluid evolve in time, the free streaming $J/ψ$'s are dissolved if the local fluid temperature exceeds a melting temperature $T_{J/ψ}$. Sequential melting of charmonium states ($χ_c$, $ψ\prime$ and $J/ψ$), with melting temperatures $T_{χ_c}=T_{ψ\prime} \approx 1.2T_c$, $T_{J/ψ} \approx2T_c$ and feed-down fraction $F\approx 0.3$, is consistent with the PHENIX data on $J/ψ$ suppression and nea…
To describe ultrarelativistic heavy-ion collisions we construct a three-fluid hydrodynamical model. In contrast to one-fluid hydrodynamics, it accounts for the finite stopping power of nuclear matter, i.e. for nonequilibrium effects in the early stage of the reaction. Within this model, we study baryon dynamics in the BNL-AGS energy range. For the system Au+Au we find that kinetic equilibrium between projectile and target nucleons is established only after a time $t_{CM}^{eq}\approx 5~fm/c\simeq 2R_{Au}/γ_{CM}$. Observables which are sensitive to the early stage of the collision (like e.g. nuc…
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.
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…
A model for energy, pressure and flow velocity distributions at the beginning of relativistic heavy ion collisions is presented, which can be used as initial condition for hydrodynamical calculations. The results show that QGP forms a tilted disk, such that the direction of the largest pressure gradient stays in the reaction plane, but deviates from both the beam and the usual transverse flow directions. Such initial condition may lead to the creation of "antiflow" or "third flow component".
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.
It has been discovered in recent heavy-ion experiments that elliptic and triangular flow of direct photons are underpredicted by most hydrodynamic models. I discuss possible enhancement mechanisms based on late chemical equilibration of the QGP and in-medium modification of parton distributions. Numerical hydrodynamic analyses indicate that they suppress early photon emission and visibly enhance thermal photon elliptic flow.
Available data on heavy-ion collisions at AGS and SPS energies are analyzed using a 3-fluid dynamical model within a purely hadronic scenario. We investigate the problems met in reproducing these data within this scheme. In particular, we try to indicate those data which could point towards the occurrence of a phase transition into the quark-gluon phase. We also discuss the success of the model in reproducing the transverse-mass spectra of various hadrons. We argue that the simultaneous reproduction of the inverse-slope parameters of all considered particles may imply that these particles belo…
We briefly discuss the recent developments in causal dissipative hydrodynamic for relativistic heavy ion collisions. Phenomenological estimate of QGP viscosity over entropy ratio from several experimental data, e.g. STAR's $ϕ$ meson data, centrality dependence of elliptic flow, universal scaling elliptic flow etc. are discussed. QGP viscosity, extracted from hydrodynamical model analysis can have very large systematic uncertainty due to uncertain initial conditions.
Viscous hydrodynamics gives a satisfactory description of the transverse momentum spectra, of the elliptic and triangular flow, and of the femtoscopic correlations for particles produced in relativistic heavy-ion collisions. On general grounds, a similar collective behavior has been predicted for proton-lead (p-Pb) collisions at the LHC. We present results of the hydrodynamics calculation of the elliptic and triangular flow in p-Pb. We discuss the mass dependence of flow coefficients and of the average transverse momentum for identified particles.
I review the recent progress in measuring elliptic flow in heavy ion collisions. These measurements show clearly how hydrodynamics starts to develop as the system size is increased from peripheral to central collisions. During this transition, the momentum range described by hydrodynamics increases as the system progresses from a kinetic to a hydrodynamic regime. Many of the systematic deviations from ideal hydrodynamics are reproduced effortlessly once the shear viscosity is included. In order to extract the shear viscosity from the data, kinetic theory can be used to determine which aspects …
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.
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 and satisfy the universal scaling relation predicted by the Buda-Lund hydrodynamical model, based on exact solutions of perfect fluid hydrodynamics. We also show a theoretical prediction on the rapidity and transverse momentum scaling of the HBT radii measured in heavy ion …
We compare microscopic transport model calculations to recent data on the directed and elliptic flow of various hadrons in 2 - 10 A GeV Au+Au and Pb (158 A GeV) Pb collisions. For the Au+Au excitation function a transition from the squeeze-out to an in-plane enhanced emission is consistently described with mean field potentials corresponding to one incompressibility. For the Pb (158 A GeV) Pb system the elliptic flow prefers in-plane emission both for protons and pions, the directed flow of protons is opposite to that of the pions, which exhibit anti-flow. Strong directed transverse flow is pr…
Effect of shear viscosity on elliptic flow is studied in causal dissipative hydrodynamics in 2+1 dimensions. Elliptic flow is reduced in viscous dynamics. Causal evolution of minimally viscous fluid ($η/s$=0.08), can explain the PHENIX data on elliptic flow in 16-23% Au+Au collisions up to $p_T\approx$3.6 GeV. In contrast, ideal hydrodynamics, can explain the same data only up to $p_T\approx$1.5 GeV. $p_T$ spectra of identified particles are also better explained in minimally viscous fluid than in ideal dynamics. However, saturation of elliptic flow at large $p_T$ is not reproduced.
This study presents generalization of the Landau hydrodynamic solution for multiparticle production applied to non-central relativistic heavy ion collisions. Obtained results shows longitudinal scaling of elliptic flow $v_2$ as a function of rapidity shifted by beam rapidity ($y-y_{beam}$) for different energies ($\sqrt{s_{NN}}=62.4$ GeV and 200 GeV) and for different systems (Au-Au and Cu-Cu). It is argued, that the elliptic flow and its longitudinal scaling is due to the initial transverse energy density distribution and initial longitudinal thickness effect.
The experimentally measured elliptic ($v_{2}$) and hexadecapole ($v_{4}$) flow of charged particles as a function of transverse momentum ($p_{T}$) at midrapidity in Pb-Pb collisions at $\sqrt{s_{\mathrm NN}}$ = 2.76 TeV are compared with the relativistic viscous hydrodynamic model simulations. The simulations are carried out for two different initial energy density profiles obtained from (i) Glauber model, and (ii) Color Glass Condensate (CGC) model. Comparison to experimental data for 10-20% to 40-50% centrality, shows that a centrality dependent shear viscosity to entropy density ($η/s$) rat…
We present an event-by-event hydrodynamical framework which takes into account the initial density fluctuations arising from a Monte Carlo Glauber model. The elliptic flow is calculated with the event plane method and a one-to-one comparison with the measured event plane $v_2$ is made. Both the centrality- and $p_T$-dependence of the $v_2$ are remarkably well reproduced. We also find that the participant plane is a quite good approximation for the event plane.
We present results for the elliptic and triangular flow coefficients in Au+Au collisions at root-s=200 AGeV using event-by-event (3+1)D viscous hydrodynamic simulations. We study the effect of initial state fluctuations and finite viscosities on the flow coefficients v_2 and v_3 as functions of transverse momentum and pseudo-rapidity. Fluctuations are essential to reproduce the measured centrality dependence of elliptic flow. We argue that simultaneous measurements of v_2 and v_3 can determine eta/s more precisely.
We develop an event-by-event ideal hydrodynamical framework where initial state density fluctuations are present and where we use a similar flow-analysis method as in the experiments to make a one-to-one $v_2$ comparison with the measured data. Our studies also show that the participant plane is quite a good approximation for the event plane.
Bulk viscosity suppresses elliptic flow v_2, as does shear viscosity. It can thus not be neglected when extracting the shear viscosity from elliptic flow data. We here explore uncertainties in the bulk viscous contribution to viscous v_2 suppression that arise from presently uncontrolled uncertainties in the initial value of the bulk viscous pressure and its microscopic relaxation time.
The centrality dependence of the charged multiplicity, transverse energy, and elliptic flow coefficient is studied in a hydrodynamic model, using a variety of different initializations which model the initial energy or entropy production process as a hard or soft process, respectively. While the charged multiplicity depends strongly on the chosen initialization, the p_t-integrated elliptic flow for charged particles as a function of charged particle multiplicity and the p_t-differential elliptic flow for charged particles in minimum bias events turn out to be almost independent of the initial …
In an ideal hydrodynamic model, with an equation of state where the confinement-deconfinement transition is a cross-over at $T_{co}=196 MeV$, we have simulated $\sqrt{s}$=200 GeV Au+Au collisions. Simultaneous description of the experimental charged particle's $p_T$ spectra and elliptic flow require that in central (0-10%) Au+Au collisions, initial energy density scales with the binary collision number density. In less central collisions, experimental data demand scaling with the participant density. Simulation studies also indicate that in central collisions viscous effects are minimal.
Looking for the underlying hydrodynamic mechanisms determining the elliptic flow we show that for an expanding relativistic perfect fluid the transverse flow may derive from a solvable hydrodynamic potential, if the entropy is transversally conserved and the corresponding expansion "quasi-stationary", that is mainly governed by the temperature cooling. Exact solutions for the velocity flow coefficients $v_2$ and the temperature dependence of the spatial and momentum anisotropy are obtained and shown to be in agreement with the elliptic flow features of heavy-ion collisions.
We develop a framework for event-by-event ideal hydrodynamics to study the differential elliptic flow which is measured at different centralities in Au+Au collisions at Relativistic Heavy Ion Collider (RHIC). Fluctuating initial energy density profiles, which here are the event-by-event analogues of the eWN profiles, are created using a Monte Carlo Glauber model. Using the same event plane method for obtaining $v_2$ as in the data analysis, we can reproduce both the measured centrality dependence and the $p_T$ shape of charged-particle elliptic flow up to $p_T\sim2$~GeV. We also consider the r…
Taking into account of entropy generation during evolution of a viscous fluid, we have estimated inverse Knudsen number, ideal hydrodynamic limit for elliptic flow and QGP viscosity to entropy ratio in $\sqrt{s}$=62 and 200 GeV Cu+Cu/Au+Au collisions. Viscosity to entropy ratio is estimated as $η/s=0.17\pm 0.10\pm 0.20$, the first error is statistical, the second one is systematic. In a central Au+Au collision, inverse Knudsen number is $\approx 2.80\pm 1.63$, which presumably small for complete equilibration. In peripheral collisions it is even less. Ideal hydrodynamic limit for elliptic flow…
In this dissertation I introduce relativistic heavy ion collisions and describe theoretical approaches to understanding them--in particular, viscous hydrodynamic simulations and investigations of final state interactions. The successful ideal hydrodynamic models of the collisions at the Relativistic Heavy Ion Collider (RHIC) were extended by performing viscous hydrodynamic simulations. This was done by making use of the recently derived full conformally invariant second order relativistic viscous hydrodynamic equations. Results for multiplicity, radial flow and elliptic flow in sqrt{s_NN}=200 …
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 …
The effect of hadronic rescattering on the elliptic flow has been investigated by the Cooper-Frye hadronization model from hydrodynamic evolution following by the afterburner hadronic rescattering model for 200 GeV/c Au + Au at 20-40% centrality. It is found that the hadronic rescattering can suppress elliptic flow $v_2$ in momentum space especially in lower transverse momentum region. In addition, the hadronic rescattering effects on transverse momentum spectra and anisotropy coordinate space of hadrons are studied.
We study effects of eccentricity fluctuations on the elliptic flow coefficient v_2 at mid-rapidity in both Au+Au and Cu+Cu collisions at sqrt{s_NN}=200 GeV by using a hybrid model that combines ideal hydrodynamics for space-time evolution of the quark gluon plasma phase and a hadronic transport model for the hadronic matter. For initial conditions in hydrodynamic simulations, both the Glauber model and the color glass condensate model are employed to demonstrate the effect of initial eccentricity fluctuations originating from the nucleon position inside a colliding nucleus. The effect of eccen…
In the Israel-Stewart's theory of second order hydrodynamics, we have simulated $\sqrt{s}$=2.76 TeV Pb+Pb collisions. ALICE data for the centrality dependence of charged particles multiplicity, $p_T$ spectra in 0-5% collisions, centrality dependence of integrated and differential elliptic flow are analysed. Analysis indicate that while ALICE data on charged particles multiplicity or $p_T$ spectra do not demand any viscosity, viscosity is demanded by the elliptic flow data. From a simulataneous fit to all the data sets, viscosity to entropy ratio in $\sqrt{s}_{NN}$=2.76 TeV Pb+Pb collisions is …
Based on the (3+1)-dimensional hydrodynamic model, the space-time evolution of hot and dense nuclear matter produced in non-central relativistic heavy-ion collisions is discussed. The elliptic flow parameter v_2 is obtained by Fourier analysis of the azimuthal distribution of pions and protons which are emitted from the freeze-out hypersurface. As a function of rapidity, the pion and proton elliptic flow parameters both have a peak at midrapidity.
In this work we simulate a viscous hydrodynamical model of non-central Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance. The model fluid equations were proposed by Öttinger and Grmela \cite{OG}. Freezeout is signaled when the viscous corrections become large relative to the ideal terms. Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated. When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest. However, when these corrections are included,…
The elliptic flows of thermal di-electrons are investigated within a (2+1)-dimension event-by-event hydrodynamic model for Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. The fluctuating initial conditions are given by the Monte Carlo Glauber model. We find in our event-by-event calculation rather weak correlation between the dilepton emission angles and the event plane angles of charged hadrons. We observe strong fluctuation effects in dilepton elliptic flows when using the event plane angles of dileptons at specific invariant mass $M$. The correlation between the dilepton event plane angle and …
I calculate the first correction to the thermal distribution function of an expanding gas due to shear viscosity. With this modified distribution function I estimate viscous corrections to spectra, elliptic flow, and HBT radii in hydrodynamic simulations of heavy ion collisions using the blast wave model. For reasonable values of the shear viscosity, viscous corrections become of order one when the transverse momentum of the particle is larger than 1.7 GeV. This places a bound on the $p_{T}$ range accessible to hydrodynamics for this observable. Shear corrections to elliptic flow cause $v_{2}(…
Simple, self-similar, elliptic solutions of non-relativistic fireball hydrodynamics are presented, generalizing earlier results for spherically symmetric fireballs with Hubble flows and homogeneous temperature profiles. The transition from one dimensional to three dimensional expansions is investigated in an efficient manner.
At Large Hadron Collider energy, the expected large multiplicities suggests the presence of collective behavior even in pp collisions. A hydrodynamical approach has been applied to estimate the expected elliptic flow measured by the azimuthal asymmetry parameter $v_2$, in pp collisions at $\surd$s = 14 TeV. $v_2$ of $π^-$ is found to be strongly dependent on the parton density profile inside a proton [e.g., surface diffuseness parameter ($ξ$)]. For $ξ$ = 0.105, $v_2$ is found to be positive while at $ξ$ = 0.25, $v_2$ is close to zero and approaches negative values at large $p_t$. The impact pa…
Using the (2+1)-dimensional viscous hydrodynamic code VISH2+1, we present systematic studies of the dependence of pion and proton transverse momentum spectra and their elliptic flow in 200 A GeV Au+Au collisions on the parameters of the hydrodynamic model (thermalization time, initial entropy density distribution, decoupling temperature, equation of state, and specific shear viscosity eta/s). We identify a tension between the slope of the proton spectra, which (within hydrodynamic simulations that assume a constant shear viscosity to entropy density ratio) prefer larger eta/s values, and the s…
