Ulrich Heinz, Stephen M. H. Wong
We study to what extent the measured elliptic flow at RHIC constrains viscous deviations from ideal hydrodynamics. We solve a toy model where only transverse momenta are thermalized while the system undergoes longitudinal free-streaming. We show that RHIC data exclude such a model and thus require fast 3-dimensional thermalization.
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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.
The hydrodynamic description of transversally thermalized matter, possibly formed at the early stages of ultra-relativistic heavy-ion collisions, is developed. The formalism is based on the thermodynamically consistent approach with all thermodynamic variables referring to two-dimensional objects, the so-called transverse clusters, which are identified with the particles having the same rapidity. The resulting hydrodynamic equations for a single cluster have the form of the two-dimensional hydrodynamic equations of the perfect fluid. Since the clusters do not perform any work in the longitudin…
In this letter, we study the pion momentum distribution of a coherent source and investigate the influences of coherent emission on the pion transverse-momentum ($p_T$) spectrum and elliptic anisotropy. With a partially coherent source, constructed by a conventional viscous hydrodynamics model (chaotic part) and a parameterized expanding coherent source model, we reproduce the pion $p_T$ spectrum and elliptic anisotropy coefficient $v_2(p_T)$ in the peripheral Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. It is found that the influences of coherent emission on the pion $p_T$ spectrum and $v_2(…
Charged particles $p_T$ spectra and elliptic flow in 0-60% Au+Au collisions at RHIC are analyzed in a hydrodynamic model with hot, hadronic resonance gas in the initial state. Physically conceivable hadronic resonance gas, thermalized in the time scale $τ_i$=1 fm, at a (central) temperature $T_i$=220 MeV, with viscosity to entropy ratio $η/s$=0.24, reasonably well explains $p_T$ spectra in all the collision centralities. Centrality dependence of elliptic flow however demands continual increase of viscosity to entropy ratio with centrality.
We investigate the elliptic and the triangular flow of heavy mesons in ultrarelativistic heavy-ion collisions at RHIC and the LHC. The dynamics of heavy quarks is coupled to the locally thermalized and fluid dynamically evolving quark-gluon plasma. The elliptic flow of $D$ mesons and the centrality dependence measured at the LHC is well reproduced for purely collisional and bremsstrahlung interactions. Due to the event-by-event fluctuating initial conditions from the EPOS2 model, the $D$ meson triangular flow is predicted to be nonzero at $\sqrt{s}=200$ GeV and $\sqrt{s}=2.76$ TeV. We study th…
The scaling properties of elliptic flow of hadrons produced in ultrarelativistic heavy-ion collisions are investigated at low transverse momenta, $p_T\lsim 2$\,GeV. Utilizing empirical parameterizations of a thermalized fireball with collective-flow fields, Resonance Recombination Model (RRM) is employed to describe hadronization via quark coalescence at the hadronization transition. We reconfirm that RRM converts equilibrium quark distribution functions into equilibrated hadron spectra including the effects of space-momentum correlations on elliptic flow. This provides the basis for a control…
The separation of the source created in ultrarelativistic heavy-ion collisions into a thermalized dense core and an outer mantle consisting of independent nucleon-nucleon collisions is discussed. Evidence for such a two component picture is found in transverse mass spectra of kaon, protons and antiprotons produced in Au-Au collisions at 200GeV. Estimates of the sizes of the thermal and direct sources are compared to models separating the interaction zone into a core and a corona, according to the density of participants or to the number of collisions. Consequences for the modeling of the dynam…
We argue that RHIC data, in particular those on the anisotropic flow coefficients v_2 and v_4, suggest that the matter produced in the early stages of nucleus-nucleus collisions is incompletely thermalized. We interpret the parameter (1/S)(dN/dy), where S is the transverse area of the collision zone and dN/dy the multiplicity density, as an indicator of the number of collisions per particle at the time when elliptic flow is established, and hence as a measure of the degree of equilibration. This number serves as a control parameter which can be varied experimentally by changing the system size…
We calculate the transverse momentum and invariant mass dependence of elliptic flow of thermal dileptons for Au+Au collisions at the Relativistic Heavy Ion Collider. The system is described using hydrodynamics, with the assumption of formation of a thermalized quark-gluon plasma at some early time, followed by cooling through expansion, hadronization and decoupling. Dileptons are emitted throughout the expansion history: by annihilation of quarks and anti-quarks inthe early quark-gluon plasma stage and through a set of hadronic reactions during the late hadronic stage. The resulting differenti…
Hadron spectra and elliptic flow in high-energy heavy-ion collisions are studied within a (3+1)D ideal hydrodynamic model with fluctuating initial conditions given by the AMPT Monte Carlo model. Results from event-by-event simulations are compared with experimental data at both RHIC and LHC energies. Fluctuations in the initial energy density come from not only the number of coherent soft interactions of overlapping nucleons but also incoherent semi-hard parton scatterings in each binary nucleon collision. Mini-jets from semi-hard parton scatterings are assumed to be locally thermalized throug…
We predict the transverse momentum (pT) dependence of elliptic flow of thermal photons for Au+Au collisions at the Relativistic Heavy Ion Collider. We model the system hydrodynamically, assuming formation of a thermalized quark-gluon plasma at some early time, followed by cooling through expansion, hadronization and decoupling. Photons are emitted throughout the expansion history. Contrary to hadron elliptic flow, which hydrodynamics predicts to increase monotonically with pT, the elliptic flow of thermal photons is predicted to first rise and then fall again as pT increases. Photon elliptic f…
In this article we report on our results about the computation of the elliptic flow of the quark-gluon-plasma produced in relativistic heavy ion collisions, simulating the expansion of the fireball by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear viscosity to entropy density ratio $η/s$. Our main goal is to put emphasis on the role of a saturation scale in the initial gluon spectrum, which makes the initial distribution far from a thermalized one. We find that the presence of the saturation scale reduces the efficiency in building-up th…
Hadron spectra and elliptic flow in relativistic heavy-ion collisions are studied in event-by-event (3+1)D ideal hydrodynamic simulations with fluctuating initial conditions given by the AMPT Monte Carlo model. Both the coherent soft gluon production from wounded nucleons and incoherent mini-jet production in semi-hard parton scatterings are considered. These partons take part in parton cascade and are assumed to be locally thermalized. They provide the fluctuating initial conditions for hydrodynamic simulations with a Gaussian smearing. Effects of both transverse and longitudinal fluctuations…
The large values and the constituent-quark-number (NCQ) scaling of the elliptic flow of low-$p_T$ $D$ mesons imply that charm quarks, initially produced through hard processes, might be partially thermalized through the strong interactions with the quark-gluon plasma (QGP) in high-energy heavy-ion collisions. To quantify the degree of thermalization of low-$p_T$ charm quarks, we compare the $D^0$ meson spectra and elliptic flow from a hydrodynamic model to the experimental data as well as transport model simulations. We use an effective charm chemical potential at the freeze-out temperature to…
We assume that the early evolution of matter produced in relativistic heavy-ion collisions is described by the transverse hydrodynamics. In this approach only transverse degrees of freedom are thermalized, while the longitudinal motion is described by free streaming. When the energy density of the system drops to a certain value, the system becomes isotropic (locally, in the momentum space) and freezes out. The sudden isotropization transition is described with the help of the Landau matching conditions, and the freeze-out is modeled with THERMINATOR. Within this scenario one is able to reprod…
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 …
We will show how both elliptic and radial flow generated during the first fm/c at RHIC can be expressed in a form which is quasi-independent of the state of matter and depends only on the initial energy density profile. Descriptions based on partons or classical fields, thermalized or highly anisotropic, all lead to the same collective velocity given a few easily satisfied conditions. This significantly narrows the uncertainty for initializing hydrodynamic prescriptions.
The production of ground-state and excited bottomonia in ultrarelativistic heavy-ion collisions is investigated within a kinetic-rate equation approach including regeneration. We augment our previous calculations by an improved treatment of medium effects, with temperature-dependent binding energies and pertinent reaction rates, $B$-meson resonance states in the equilibrium limit near the hadronization temperature, and a lattice-QCD based equation of state for the bulk medium. In addition to the centrality dependence of the bottomonium yields we compute their transverse-momentum ($p_T$) spectr…
We interpret the scaling of the corrected elliptic flow parameter w.r.t. the corrected multiplicity, observed to hold in heavy ion collisions for a wide variety of energies and system sizes. We use dimensional analysis and power-counting arguments to place constraints on the changes of initial conditions in systems with different center of mass energy $\sqrt{s}$. Specifically, we show that a large class of changes in the (initial) equation of state, mean free path, and longitudinal geometry over the observed $\sqrt{s}$ are likely to spoil the scaling in $v_2$ observed experimentally. We theref…
Recent analyses of several isospin effects in heavy-ion reactions have allowed us to constrain the density dependence of nuclear symmetry energy at sub-saturation densities within a narrow range. Combined with constraints on the Equation of State (EOS) of symmetric nuclear matter obtained previously from analyzing the elliptic flow in relativistic heavy-ion collisions, the EOS of neutron-rich nuclear matter is thus partially constrained. Here we report effects of the partially constrained EOS of neutron-rich nuclear matter on the mass-radius correlation, moment of inertia, elliptical deformati…
The influence of resonance decays on the elliptic flows of stable hadrons is studied in the quark coalescence model. Although difference between the elliptic flow of pions from resonance decays, except the rho meson, and that of directly produced pions is appreciable, those for other stable hadrons are small. Since there are more pions from the decays of rho mesons than from other resonances, including resonance decays can only account partially the deviation of final pion elliptic flow from the observed scaling of hadron elliptic flows, i.e., the hadron elliptic flow per quark is the same at …
Combining the hydrodynamic equations for the QGP evolution and the transport equation for the primordially produced $J/ψ$ in the QGP, we investigate the $J/ψ$ transverse momentum distribution as well as its suppression in the $\sqrt{s}$=17.3A GeV Pb-Pb collisions at SPS and $\sqrt{s}$=200A GeV Au-Au collisions at RHIC. The two sets of equations are connected by the $J/ψ$ anomalous suppression induced by its inelastic scattering with gluons in the QGP. The calculated centrality dependence of $J/ψ$ suppression and average transverse momentum square agree well with the SPS data. From the comparis…
Within a transport model coupled with a microscopic coalescence model, the directed and elliptic flows of protons and deuterons as well as their scalling properties are studied in the centrality of 20-30% Au+Au collisions at $\sqrt{s_{\rm NN}}=2.4$ GeV. It is found that the flows as well as their scaling properties simulated with the isospin- and momentum-dependent nuclear mean field with an incompressibility $K_{0}=230$ MeV fit fairly the HADES data, while those simulated with the commonly used momentum-independent nuclear mean field with an incompressibility $K_{0}=380$ MeV can only fit part…
I present a theory-guided review of RHIC data, arguing that they provide strong evidence for formation of a thermalized quark-gluon plasma at RHIC. Strong radial flow reflects high thermal pressure in the reaction zone. Large elliptic flow proves that the pressure builds up quickly and the system thermalizes on a very short time scale of less than 1 fm/c. The observed hadron yields are consistent with statistical hadron formation from a quark-gluon plasma, followed by immediate chemical decoupling due to strong radial expansion. The observed suppression of jets appears to confirm the predicted…
As a new observable for heavy flavor correlations the momentum imbalance $A_D$ of D mesons is proposed. It is defined analogously to the jet momentum imbalance $A_J$ of fully reconstructed jets. However, since D mesons are flavor tagged particles, no jet reconstruction is necessary. $A_D$ quantifies the influence of the medium created in heavy-ion collisions on correlated charm pairs. We present results with the partonic transport model Boltzmann Approach to MultiParton Scatterings (BAMPS), which describes well the nuclear modification factor and elliptic flow of all heavy flavor particles at …
We perform viscous hydrodynamic calculations in 2+1 dimensions to investigate the influence of bulk viscosity on the viscous suppression of elliptic flow in non-central heavy-ion collisions at RHIC energies. Bulk and shear viscous effects on the evolution of radial and elliptic flow are studied with different model assumptions for the transport coefficients. We find that the temperature dependence of the relaxation time for the bulk viscous pressure, especially its critical slowing down near the quark-hadron phase transition at T_c, partially offsets effects from the strong growth of the bulk …
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