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.
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.
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.
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.
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…
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.
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…
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 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 …
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.
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…
We study the elliptic flow $v_2$ of multi-strange hadrons such as the $ϕ$, $Ξ$ and $Ω$ as a function of transverse momentum in the recombination and fragmentation model and compare to a standard hydrodynamic calculation. We find that the measurement of $v_2$ for the $ϕ$ and $Ω$ will allow for the unambiguous distinction between parton recombination and statistical hadro-chemistry to be the dominant process in hadronization at intermediate transverse momenta.
We investigate the effect of early chemical freeze-out on radial and elliptic flow by using a fully three dimensional hydrodynamic model. We find that the time evolution of temperature and the thermal freeze-out temperature dependence of average radial flow are different from the results by using a conventional hydrodynamic model in which chemical equilibrium is always assumed. We also analyse the p_t spectrum and v_2(p_t) at the RHIC energy and consistently reproduce experimental data by choosing the thermal freeze-out temperature T_th = 140 MeV.
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 …
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.
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…
It is shown that a simultaneous comparison of both elliptic and triangular flow from (2+1)-dimensional viscous fluid dynamics with recent measurements in Pb+Pb collisions at the Large Hadron Collider (LHC) favors a small specific shear viscosity (eta/s)_QGP approximately equal to 1/(4pi) for the quark-gluon plasma. Using this viscosity value, the relative magnitude of the elliptic and triangular flow is well described with Monte-Carlo Glauber (MC-Glauber) initial conditions while Monte-Carlo Kharzeev-Levin-Nardi (MC-KLN) initial conditions require twice as large viscosity to reproduce the elli…
I compare the first viscous hydrodynamic prediction for integrated elliptic flow in Pb-Pb collisions at the LHC with the first data released by the ALICE collaboration. These new data are found to be consistent with hydrodynamic extrapolations of RHIC data with no change in medium parameters (e.g., average viscosity). I also discuss how, in general, a precise comparison of data to theoretical calculations requires an understanding of some subtleties of the measurement -- most notably the cut on transverse momentum of the particles used and the differing sensitivities to flow fluctuations and n…
Anomalous hydrodynamics is a low-energy effective theory that captures effects of quantum anomalies. We develop a numerical code of anomalous hydrodynamics and apply it to dynamics of heavy-ion collisions, where anomalous transports are expected to occur. This is the first attempt to perform fully non-linear numerical simulations of anomalous hydrodynamics. We discuss implications of the simulations for possible experimental observations of anomalous transport effects. From analyses of the charge-dependent elliptic flow parameters ($v_2^\pm$) as a function of the net charge asymmetry $A_\pm$, …
The elliptic flow excitation function calculated in a full (3+1)d hybrid Boltzmann approach with an intermediate hydrodynamic stage for heavy ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. In this study, we employ a hadron gas equation of state to investigate the differences in the dynamics and viscosity effects. The specific event-by-event setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and transport simulations. At higher SPS energ…
The agreement of elliptic flow data at RHIC at central rapidity with the hydrodynamic model has led to the conclusion of very rapid thermalization. This conclusion is based on the intuitive argument that hydrodynamics, which assumes instantaneous local thermalization, produces the largest possible elliptic flow values and that the data seem to saturate this limit. We here investigate the question whether incompletely thermalized viscous systems may actually produce more elliptic flow than ideal hydrodynamics. Motivated by the extremely fast primordial longitudinal expansion of the reaction zon…
We calculate the elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV in relativistic viscous hydrodynamics. The recent data of the ALICE Collaboration on the elliptic flow as function of the centrality can be very well described using the hydrodynamic expansion of a fluid with a small shear viscosity eta/s=0.08. The elliptic flow as function of the transverse momentum shows systematic deviations from a hydrodynamic behavior in the small momenta region pt<800MeV. It indicates that a non-negligible contribution of non-thermalized particles from jet fragmentation is present.
Elliptic flow of direct photons in relativistic heavy ion collisions is believed to be dominated by contribution from thermal radiation of quark gluon plasma up to $p_T$ $\sim 5$ GeV/$c$, although other sources start outshining the thermal contribution at already smaller values of $p_T$ in the direct photon spectrum. The elliptic flow of thermal photons from ideal hydrodynamics considering a smooth initial density distribution under-predicts the PHENIX direct photon data from 200A GeV Au+Au collisions at RHIC by a large margin in the range $1 < p_T < 5$ GeV/$c$. However, a significant enhancem…
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 coll…
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 ell…
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.
We consider a holographic dual of hydrodynamics of N=4 SYM plasma that undergoes non-isotropic three-dimensional expansion relevant to RHIC fireball. Our model is a natural extension of the Bjorken's one-dimensional expansion, and it describes an elliptic flow whose v2 and eccentricity are given in terms of anisotropy parameters. Holographic renormalization shows that absence of conformal anomaly in the SYM theory constrains our local rest frame to be a Kasner spacetime. We show that the Kasner spcetime provides a simple description of the anisotropically expanding fluid within a well-controle…
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.
Using the newly developed hybrid model VISHNU which connects viscous hydrodynamics with a hadron cascade model, we study the differential and integrated elliptic flow v_2 at different centrality bins for 200 A GeV Au+Au collisions and 2.76 A TeV Pb+Pb collisions. We find that the average Quark Gluon Plasma (QGP) specific shear viscosity eta/s slightly increases from Relativistic Heavy Ion Collider (RHIC) to Large Hadron Collider (LHC) energies. However, a further study assuming different temperature dependencies for (eta/s)_QGP shows that one cannot uniquely constrain the form of (eta/s)_QGP(T…
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…
We investigate the effect of early chemical freeze-out on radial flow, elliptic flow and HBT radii by using a fully three dimensional hydrodynamic model. When we take account of the early chemical freeze-out, the space-time evolution of temperature in the hadron phase is considerably different from the conventional model in which chemical equilibrium is always assumed. As a result, we find that radial and elliptic flows are suppressed and that the lifetime and the spatial size of the fluid are reduced. We analyze the p_t spectrum, the differential elliptic flow, and the HBT radii at the RHIC e…
We study the charm quark elliptic flow ($v_{2}$) in heavy ion as well as small system collisions by tracking the evolution history of quarks of different flavors within a multi-phase transport model. The charm quark $v_{2}$ is studied as a function of the number of collisions the charm quark suffers with other quarks and then compared to the $v_{2}$ of lighter quarks. We find that the common escape mechanism is at work for both the charm and light quark $v_{2}$. However, contrary to the naive expectation, the hydrodynamics-type flow is found to contribute more to the final state charm $v_{2}$ …
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…
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.
We use the Boltzmann equation in the relaxation time approximation to study the expansion of a dilute Fermi gas at unitarity. We focus, in particular, on the approach to the hydrodynamic limit. Our main finding are: i) In the regime that has been studied experimentally hydrodynamic effects beyond the Navier-Stokes approximation are small, ii) mean field corrections to the Boltzmann equation are not important, iii) experimental data imply that freezeout occurs very late, that means that the relaxation time remains smaller than the expansion time during the entire evolution of the system, iv) th…
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 t…
Centrality dependence of charged particles multiplicity, transverse momentum spectra, integrated and differential elliptic flow, in $\sqrt{s}_{NN}$=200 GeV Au+Au collisions are analyzed using event by event ideal hydrodynamics. Monte-Carlo Glauber model of initial condition, constrained to reproduce experimental charged particle's multiplicity in 0-10% Au+Au collisions, reasonably well reproduces all the experimental observables, e.g. centrality dependence of charged particles multiplicity, integrated and differential elliptic flow. Model predictions for higher flow harmonics, $v_3$, $v_4$ how…
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…
We study the effect of anisotropic escape mechanism on elliptic flow in relativistic heavy-ion collisions. We use Glauber model to generate initial conditions and ignore hydrodynamic expansion in the transverse direction. We employ Beer-Lambert law to allow for the transmittance of produced hadrons in the medium and calculate the anisotropy generated due to the suppression of particles traversing through the medium. In order to separate non-flow contribution due to surface bias effects, we ignore hydrodynamic expansion in the transverse direction and consider purely longitudinal boost-invarian…
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".
The invariant mass spectrum and the elliptic flow of lepton pairs produced in relativistic heavy-ion collisions at RHIC are studied with viscous hydrodynamics. The effects of viscous corrections on dilepton observables are explored. The lepton pairs originating from charm quarks evolving in the viscous background are seen to be a good probe of quark energy loss and gain, as quantified by the dilepton spectrum and by the dilepton elliptic flow.
Recent development of a hydrodynamic model is discussed by putting an emphasis on realistic treatment of the early and late stages in relativistic heavy ion collisions. The model, which incorporates a hydrodynamic description of the quark-gluon plasma with a kinetic approach of hadron cascades, is applied to analysis of elliptic flow data at the Relativistic Heavy Ion Collider energy. It is predicted that the elliptic flow parameter based on the hybrid model increases with the collision energy up to the Large Hadron Collider energy.
We present some exact solutions of relativistic second-order hydrodynamic equations in theories with conformal symmetry. Starting from a spherically expanding solution in ideal hydrodynamics, we take into account general conformal second-order corrections, and construct, for the first time, fully analytical axisymmetric exact solutions including the case with nonzero vorticity. These solutions are time-reversible despite having a nonvanishing shear stress tensor and provide a useful quantitative measure of the second-order effects in relativistic hydrodynamics.
We exactly solve the one-dimensional boost-invariant Boltzmann equation in the relaxation time approximation for arbitrary shear viscosity. The results are compared with the predictions of viscous and anisotropic hydrodynamics. Studying different non-equilibrium cases and comparing the exact kinetic-theory results to the second-order viscous hydrodynamics results we find that recent formulations of second-order viscous hydrodynamics agree better with the exact solution than the standard Israel-Stewart approach. Additionally, we find that, given the appropriate connection between the kinetic an…
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.
A new set of equations for relativistic viscous hydrodynamics that captures both weak-coupling and strong-coupling physics to second order in gradients has been developed recently. We apply this framework to bulk physics at RHIC, both for standard (Glauber-type) as well as for Color-Glass-Condensate initial conditions and show that the results do not depend strongly on the values for the second-order transport coefficients. Results for multiplicity, radial flow and elliptic flow are presented and we quote the ratio of viscosity over entropy density for which our hydrodynamic model is consisten…
In this paper we present the details of our previous work on exact solutions in second-order conformal hydrodynamics together with a number of new solutions found by mapping Minkowski space onto various curved spacetimes such as anti-de Sitter space and hyperbolic space. We analytically show how the solutions of ideal hydrodynamics are modified by the second-order effects including vorticity. We also find novel boost-invariant exact solutions which exist only in second-order hydrodynamics and have an unusual dependence on the proper time.
The effects of initial state fluctuations on elliptic flow are investigated within a (3+1)d Boltzmann + hydrodynamics transport approach. The spatial eccentricity ($ε_{\rm RP}$ and $ε_{\rm part}$) is calculated for initial conditions generated by a hadronic transport approach (UrQMD). Elliptic flow results as a function of impact parameter, beam energy and transverse momentum for two different equations of state and for averaged initial conditions or a full event-by-event setup are presented. These investigations allow the conclusion that in mid-central ($b=5-9$ fm) heavy ion collisions the fi…
The mass splitting of elliptic anisotropy ($v_2$) at low transverse momentum is considered as a hallmark of hydrodynamic collective flow. We investigate a multiphase transport (AMPT) model where the $v_2$ is mainly generated by an anisotropic escape mechanism, not of the hydrodynamic flow nature, and where mass splitting is also observed. We demonstrate that the $v_2$ mass splitting in AMPT is small right after hadronization (especially when resonance decays are included); the mass splitting mainly comes from hadronic rescatterings, even though their contribution to the overall charged hadron …
Single particle spectra as well as elliptic flow in Cu+Cu collisions at $\sqrt{s_{NN}}=200$ GeV are investigated within a hadronic cascade model and an ideal hydrodynamic model. Pseudorapidity distribution and transverse momentum spectra for charged hadrons are surprisingly comparable between these two models. However, a large deviation is predicted for the elliptic flow. The forthcoming experimental data will clarify the transport and thermalization aspects of matter produced in Cu+Cu collisions.
It is commonly believed that azimuthal anisotropies in relativistic heavy ion collisions are generated by hydrodynamic evolution of the strongly interacting quark-gluon plasma. Here we use transport models to study how azimuthal anisotropies depend on the number of collisions that each parton suffers. We find that the majority of $v_2$ comes from the anisotropic escape of partons, not from the parton collective flow, for semi-central Au+Au collisions at 200A GeV. As expected, the fraction of $v_2$ from the anisotropic particle escape is even higher for smaller systems such as d+Au. Our transpo…
We study the collision energy dependence of elliptic flow v_2 and triangular flow v_3 in Au+Au collisions within the energy range sqrt(s_{NN}) = 5-200 GeV, utilizing a transport + hydrodynamics hybrid model. The transport part is described by the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) approach, combined with an intermediate (3+1)-dimensional ideal hydrodynamical evolution phase using a chiral model equation of state. We find the decrease of v_2 produced by hydrodynamics at lower collision energies partially compensated by the transport dynamics. This does not apply to v_3, which …
