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 consistent with experimental data. For Color-Glass-Condensate initial conditions, early thermalization does not seem to be required in order for hydrodynamics to describe charged hadron elliptic flow.
The charged-particle's final state spectrum is derived from an analytic perturbative solution for the relativistic viscous hydrodynamics. By taking into account the longitudinal acceleration effect in relativistic viscous hydrodynamics, the pseudorapidity spectrum describes well the nucleus-nucleus colliding systems at RHIC and LHC. Based on both the extracted longitudinal acceleration parameters $λ^{*}$ and a phenomenological description of the $λ^{*}$, the charged-particle's pseudorapidity distributions for $\sqrt{s_{NN}}$ = 5.44 TeV Xe+Xe collisions are computed from the final state express…
We investigate the form of the viscous correction to the equilibrium distribution function in the context of a Cooper-Frye freeze out prescription for viscous hydrodynamic simulations of relativistic heavy ion collisions. The standard quadratic ansatz used by all groups for the case of shear viscosity is found to be disfavored by experimental data for v4/(v2)^2 at the Relativistic Heavy Ion Collider, and is unlikely to be correct for the hadron resonance gas present at freeze out. Instead, data for v2(pt) along with v4/(v2)^2 favor a momentum dependence between linear and quadratic.
We compute v4/(v2)^2 in ideal and viscous hydrodynamics. We investigate its sensitivity to details of the hydrodynamic model and compare the results to experimental data from RHIC. Whereas v2 has a significant sensitivity only to initial eccentricity and viscosity while being insensitive to freeze out temperature, we find that v4/(v2)^2 is quite insensitive to initial eccentricity. On the other hand, it can still be sensitive to shear viscosity in addition to freeze out temperature, although viscous effects do not universally increase v4/(v2)^2 as originally predicted. Consistent with data, we…
A state-of-the-art 3+1 dimensional cascade + viscous hydro + cascade model vHLLE+UrQMD has been applied to heavy ion collisions in RHIC Beam Energy Scan range $\sqrt{s_{\rm NN}}=7.7\dots 200$ GeV. Based on comparison to available experimental data it was estimated that an effective value of shear viscosity over entropy density ratio $η/s$ in hydrodynamic stage has to decrease from $η/s=0.2$ to $0.08$ as collision energy increases from $\sqrt{s_{\rm NN}} = 7.7$ to $39$ GeV, and to stay at $η/s=0.08$ for $39\le\sqrt{s_{\rm NN}}\le200$ GeV. In this work we show how an equation of state with first…
In this proceeding, we briefly describe the viscous hydrodynamics + hadron cascade hybrid model VISHNU for relativistic heavy ion collisions and report the current status on extracting the QGP viscosity from elliptic flow data.
Using ideal and viscous hydrodynamics, the ratio of azimuthal moments v4/(v2)^2 is calculated for pions, protons, and kaons in sqrt{s}=200 A*GeV Au+Au collisions. For any value of viscosity here is little dependence on particle species. Ideal hydrodynamics and data show a flat curve as a function of pt. Adding viscosity in the standard way destroys this flatness. However, it can be restored by replacing the standard quadratic ansatz for delta f (the viscous correction to the distribution function at freeze-out) with a weaker momentum dependence.
In an earlier work (arXiv:0808.0953) we established that causal Israel-Stewart viscous hydrodynamics is only accurate in RHIC applications at very low shear viscosities 4 pi eta_s / s < ~ 1.5-2. We show here that the region of applicability is significantly reduced if bulk viscosity plays a role in the dynamics.
We report recent progress on causal viscous hydrodynamics for relativistic heavy ion collisions. For fixed specific shear viscosity eta/s, uncertainties in the elliptic flow arising from initial conditions, equation of state, bulk viscosity and numerical viscosity, and the treatment of the highly viscous hadronic stage and freeze-out procedure are analysed. A comparison of current viscous hydrodynamic results with experimental data yields a robust upper limit eta/s < 5/(4pi).
Firstly, we give a short review about the hydrodynamic model and its application to the elliptic flow phenomena in relativistic heavy ion collisions. Secondly, we show the first approach to construct a unified model for the description of the dynamics in relativistic heavy ion collisions.
Fluid dynamical description of elementary particle collisions has a long history dating back to the works of Landau and Fermi. Nevertheless, it is during the last 10-15 years when fluid dynamics has become the standard tool to describe the evolution of matter created in ultrarelativistic heavy ion collisions. In this review I briefly describe the hydrodynamical models, what we have learned when analyzing the RHIC and LHC data using these models, and what the latest developments and challenges are.
In this article, we briefly review recent progress on hydrodynamic modeling and its implementations to relativistic heavy-ion collisions at RHIC and the LHC. The related topics include: 1) initial state fluctuations, final state correlations and event-by-event hydrodynamics, 2) extracting the QGP shear viscosity from flow data, 3) flow and hydrodynamics in 5.02 A TeV p+Pb collisions.
We present a fully three-dimensional initial state model for relativistic heavy-ion collisions at RHIC Beam Energy Scan (BES) collision energies. The initial energy and net baryon density profiles are produced based on a classical string deceleration model. The baryon stopping and fluctuations during this early stage of the collision are investigated by studying the net baryon rapidity distribution and longitudinal decorrelation of the transverse geometry.
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.
The hydrodynamic model for the expansion of the fireball in relativistic heavy-ion collisions is presented. Calculations using relativistic hydrodynamics of a fluid with small viscosity yield a satisfactory description of the experimental data on the particle spectra, the elliptic flow or the interferometry radii.
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 hydrodynamic approach to relativistic heavy ion collisions, hadrons with nonzero spin, produced out of the hydrodynamic medium, can acquire polarization via spin-vorticity thermodynamic coupling mechanism. The hydrodynamical quantity steering the polarization is the thermal vorticity, that is minus the antisymmetric part of the gradient of four-temperature field. Based on this mechanism there have been several calculations in hydrodynamic and non-hydrodynamic models for non-central heavy ion collisions in the RHIC Beam Energy Scan energy range, showing that the amount of polarization of pro…
Correlations of different azimuthal flow harmonics $v_n$ and symmetry planes $Ψ_n$ can add constraints to theoretical models, and probe aspects of the system that are independent of the traditional single-harmonic measurements. Using NeXSPheRIO, a hydrodynamical model which has accurately reproduced a large set of single-harmonic correlations at RHIC, we make predictions of these new observables for 200 A GeV Au+Au Collisions, providing an important baseline for comparison to correlations of flow harmonics, which contain non-trivial information about the initial state. We also point out how to…
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 investigate hydrodynamic evolution of the quark gluon plasma for the colour glass condensate type initial conditions. We solve full second-order viscous hydrodynamic equations in the longitudinal direction to find that non-boost invariant expansion leads to visible deformation on the initial rapidity distribution. The results indicate that hydrodynamic evolution with viscosity plays an important role in determining parameters for the initial distributions.
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.
In the RHIC Beam Energy Scan program, gold nuclei are collided with different collision energies in the range from few to 62.4 GeV. The goals of the program are to explore the onset of QGP creation, locate the critical point of QCD and study dense baryon matter. We report on the first application of Monte Carlo Glauber (GLISSANDO2) and T$_{\rm R}$ENTo $p=0$ initial states extended to 3D for event-by-event viscous fluid dynamic (vHLLE) with hadronic cascade modelling of Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=27$ and 62.4 GeV, which is the upper region of RHIC BES energies. The initial states…
The hydrodynamical models used to describe the evolution of heavy-ion collisions are briefly reviewed and their results compared with recent RHIC data.
In this proceedings contribution, we review 3+1d quasiparticle anisotropic hydrodynamics (aHydroQP). Then, we show some recent phenomenological comparisons between the aHydroQP model and some experimental results. We show comparisons between aHydroQP and Pb-Pb 2.76 TeV collisions from the ALICE collaboration and Au-Au 200 GeV collisions from RHIC experiments. We show that the quasiparticle anisotropic hydrodynamics model is able to describe the experimental results for Pb-Pb and Au-Au collisions quite well for many observables such as the spectra, multiplicity, elliptic flow, and HBT radii in …
A known class of analytic, exact, accelerating solutions of prefect relativistic hydrodynamics with longitudinal acceleration is utilized to describe results on the pseudorapidity distributions for different collision systems. These results include $dN/dη$ measured in p+p, Cu+Cu, Au+Au, and Pb+Pb collisions at RHIC and LHC, in a broad centrality range. Going beyond the traditional Bjorken model, from the accelerating hydrodynamic description we determine the initial energy density and other thermodynamic quantities in those collisions.
This is a comment to hep-th/0703243. The paper determined the relaxation time tau_pi of the shear viscous stress for the N=4 SYM from AdS/CFT correspondence. The purpose of this comment is to point out that the value of tau_pi is 3 times larger than their result if one takes into account an additional term in the hydrodynamic equation.
We investigate the phenomenology of freely expanding fluids, with different material properties, evolving through the Israel-Stewart (IS) causal viscous hydrodynamics, and compare our results with those obtained in the relativistic Eckart-Landau-Navier-Stokes (ELNS) acausal viscous hydrodynamics. Through the analysis of scaling invariants we give a definition of thermalization time which can be self-consistently determined in viscous hydrodynamics. Next we construct the solutions for one-dimensional boost-invariant flows. Expansion of viscous fluids is slower than that of one-dimensional ideal…
The current status of the application of hydrodynamics to ultrarelativistic heavy ion collisions is reviewed. We elaborate on the arguments for strong transverse flow and rapid thermalization and discuss future applications and trends in hydrodynamics.
A new formulation of second-order viscous hydrodynamics, based on an expansion around a locally anisotropic momentum distribution, is presented. It generalizes the previously developed formalism of anisotropic hydrodynamics (aHydro) to include a complete set of dissipative currents for which equations of motion are derived by solving the Boltzmann equation in the 14-moment approximation. By solving the vaHydro equations for a transversally homogeneous, longitudinally boost-invariant system ((0+1)-dimensional expansion) and comparing with the exact solution of the Boltzmann equation in relaxati…
The hydrodynamic model is used to describe the single-particle spectra and elliptic flow of hadrons at RHIC and to predict the emission angle dependence of HBT correlations at RHIC and LHC energies.
We investigate the role of the initial condition used for the hydrodynamic evolution of the system formed in ultra-relativistic heavy-ion collisions and find that an appropriate choice motivated by the models of early-stage dynamics, specifically a simple two-dimensional Gaussian profile, leads to a uniform description of soft observables measured in the Relativistic Heavy-Ion Collider (RHIC). In particular, the transverse-momentum spectra, the elliptic-flow, and the Hanbury-Brown--Twiss correlation radii, including the ratio R_out/R_side as well as the dependence of the radii on the azimuthal…
We compute the particle multiplicities and transverse energies at central and nearly central AA collisions at RHIC and LHC. The initial state is computed from perturbative QCD supplemented by the conjecture of saturation of produced partons. The expansion stage is described in terms of hydrodynamics assuming longitudinal boost invariance and azimuthal symmetry. Transverse flow effects, a realistic list of hadrons and resonance decays are included. Comparison with the data of the multiplicities at $\sqrt s=56$ AGeV and 130 AGeV from RHIC is done and predictions for the full RHIC energy and LHC …
Hadron spectra in Au+Au collisions at RHIC are calculated by hydrodynamics with initial conditions from the Color Glass Condensate (CGC). Minijet components with parton energy loss in medium are also taken into account by using parton density obtained from hydrodynamical simulations. We found that CGC provides a good initial condition for hydrodynamics in Au+Au collisions at RHIC.
A hydrodynamic model coupled to the statistical hadronization code Therminator is used to study a set of observables in the soft sector at RHIC. A satisfactory description of the pT-spectra and elliptic flow is obtained, similarly to other hydrodynamic models. With the Gaussian initial conditions the transverse femtoscopic radii are also reproduced, providing a possible solution of the RHIC HBT puzzle.
We review the apparently hydrodynamic behaviour of low transverse momentum particles (p_T < 1.5 GeV/c) produced in central and semicentral (b < 7 fm) heavy ion collisions at RHIC. We investigate the impact parameter dependence of various observables, elaborating on radial and elliptic flow and particle multiplicities. We also discuss possible ambiguities in the initialization of the hydrodynamic system and present observables that should allow for their resolution.
A brief overview of the current status of hydrodynamic concepts applied to ultra relativistic heavy-ion collisions is presented. Special emphasis is placed on future prospects for extracting the thermodynamic properties and the bulk features of the created medium from experimental observations.
We report part of our recent work on viscous hydrodynamics with consistent phase space distribution $f(x,\p)$ for freeze out. We develop the gradient expansion formalism based on kinetic theory, and with the constraints from the comparison between hydrodynamics and kinetic theory, viscous corrections to $f(x,\p)$ can be consistently determined order by order. Then with the obtained $f(x,\p)$, second order viscous hydrodynamical calculations are carried out for elliptic flow $v_2$.
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…
Hydrodynamic simulations are used to make predictions for the integrated elliptic flow coefficient v_2 in sqrt(s)=5.5 TeV lead-lead and sqrt(s)=14 TeV proton-proton collisions at the LHC. We predict a 10% increase in v_2 from RHIC to Pb+Pb at LHC, and v_2 ~ 0 in p+p collisions unless eta/s < 0.08.
We present a systematic hydrodynamic study of the evolution of hadron spectra and their azimuthal anisotropy from the lowest collision energy studied at the Relativistic Heavy Ion Collider (RHIC), sqrt(s) = 7.7 A GeV, to the highest energy reachable at the Large Hadron Collider (LHC), sqrt(s) = 5500 A GeV. The energy dependence of the flow observables are quantitatively studied for both the Monte-Carlo Glauber and Monte-Carlo Kharzeev-Levin-Nardi (MC-KLN) models. For MC-Glauber model initial conditions with η/s = 0.08, the differential charged hadron elliptic flow v_2^{ch}(p_T, sqrt(s)) is fou…
We show that by requiring positivity of the longitudinal pressure it is possible to constrain the initial conditions one can use in 2nd-order viscous hydrodynamical simulations of ultrarelativistic heavy-ion collisions. We demonstrate this explicitly for 0+1 dimensional viscous hydrodynamics and discuss how the constraint extends to higher dimensions. Additionally, we present an analytic approximation to the solution of 0+1 dimensional 2nd-order viscous hydrodynamical evolution equations appropriate to describe the evolution of matter in an ultrarelativistic heavy-ion collision.
The relativistic hydrodynamic model is applied to describe the expansion of the dense matter formed in relativistic heavy-ion collisions. The hydrodynamic expansion of the fluid, supplemented with the statistical emission of hadrons at freeze-out gives a satisfactory description of the observables for particles emitted with soft momenta. Experimental data for the transverse momentum spectra, elliptic flow and interferometry radii give constraints on the properties of the fluid, its equation of state and viscosity coefficients. The role of the fluctuations of the initial profile of the energy d…
I review the successes and limitations of the ideal fluid dynamic model in describing hadron emission spectra from Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC).
The drag and diffusion coefficients are studied within the framework of Fokker-Planck dynamics for the case of a charm quark propagating in an expanding quark-gluon plasma. The space-time evolution of the nuclear matter created in the relativistic heavy-ion collision is modelled using MUSIC, a 3+1 D relativistic viscous hydrodynamic approach. The effect of viscous corrections to the heavy quark transport coefficients is explored by considering scattering processes with thermal quarks and gluons in the medium. It is observed that the momentum diffusion of the heavy quarks is sensitive to the sh…
We calculate open heavy-flavor (HF) transport in relativistic heavy-ion collisions by applying a strong-coupling treatment in both macro- and microscopic dynamics (hydrodynamics and non-perturbative diffusion interactions). The hydrodynamic medium evolution is quantitatively constrained by bulk and multi-strange hadron spectra and elliptic flow. The heavy quark (HQ) transport coefficient is evaluated from a non-perturbative $T$-matrix approach in the Quark-Gluon Plasma (QGP) which, close to the critical temperature, leads to resonance formation and feeds into the recombination of heavy quarks …
Hydrodynamic behavior and the associated discussions of viscosity at RHIC has inspired a r enaissance in modeling viscous hydrodynamics. An explanation of Israel-Stewart hydrodynamics is presented here, with an emphasis on the tangible benefits compared to Navier Stokes.
The interplay between shear and bulk viscosities on the flow harmonics, $v_n$'s, at RHIC is investigated using the newly developed relativistic 2+1 hydrodynamical code v-USPhydro that includes bulk and shear viscosity effects both in the hydrodynamic evolution and also at freeze-out. While shear viscosity is known to attenuate the flow harmonics, we find that the inclusion of bulk viscosity decreases the shear viscosity-induced suppression of the flow harmonics bringing them closer to their values in ideal hydrodynamical calculations. Depending on the value of the bulk viscosity to entropy den…
Event-by-event viscous hydrodynamics is combined with heavy quark energy loss models to compute heavy flavor flow cumulants $v_2\{2\}$, $v_3\{2\}$, and $v_2\{4\}$ as well as the nuclear modification factors of $D^0$ and $B^0$ mesons in PbPb collisions at 2.76 TeV. Our results indicate that bottom quarks can flow as much as charm quarks in the $p_T$ range 8--30 GeV.
It is argued that the use of the initial Gaussian energy density profile for hydrodynamics leads to much better uniform description of the RHIC heavy-ion data than the use of the standard initial condition obtained from the Glauber model. With the modified Gaussian initial conditions we successfully reproduce the transverse-momentum spectra, v2, and the pionic HBT radii (including their azimuthal dependence). The emerging consistent picture of hadron production hints that a solution of the long standing RHIC HBT puzzle has been found.
Current status of dynamical modeling of relativistic heavy ion collisions and hydrodynamic description of the quark gluon plasma is reported. We find the hadronic rescattering effect plays an important role in interpretation of mass splitting pattern in the differential elliptic flow data observed at RHIC. To demonstrate this, we predict the elliptic flow parameter for phi mesons to directly observe the flow just after hadronisation. We also discuss recent applications of outputs from hydrodynamic calculations to J/psi suppression, thermal photon radiation and heavy quark diffusion.
The problem of early thermalization of matter produced in relativistic heavy-ion collisions at RHIC is discussed in the framework of a hybrid model that consists of the transverse-hydrodynamics stage followed by the standard perfect-fluid hydrodynamics stage and freeze-out. The two hydrodynamic regimes are connected with the help of Landau matching conditions. A satisfactory description of the soft hadronic observables is achieved. This indicates that the early-thermalization problem and also the HBT puzzle may be to large extent circumvented.
The matter created in central p+p, p+Pb and Pb+Pb collisions at sqrt{s}=5.02 TeV is simulated event-by-event using the superSONIC model, which combines pre-equilibrium flow, viscous hydrodynamic evolution and late-stage hadronic rescatterings. Employing a generalization of the Monte Carlo Glauber model where each nucleon possesses three constituent quarks, superSONIC describes the experimentally measured elliptic and triangular flow at central rapidity in all systems using a single choice for the fluid parameters, such as shear and bulk viscosities. This suggests a common hydrodynamic origin o…
The pseudorapidity dependence of elliptic flow in Au+Au collisions at 130 $A$ GeV is studied within a full three-dimensional hydrodynamic model in the light-cone coordinate. First, we prepare two initial conditions in the hydrodynamic model for analyzing elliptic flow. Both initial conditions lead to reasonable agreement with single particle spectra in central and semi-central collisions. Next, by using these hydrodynamic simulations, we compare elliptic flow as a function of pseudorapidity with experimental data recently measured by the PHOBOS Collaboration. Our results are in agreement with …
The nonequilibrium evolution in a boost-invariant Bjorken flow of a hybrid viscous fluid model containing two interacting components with different viscosities, such that they represent strongly and weakly self-coupled sectors, is shown to be characterized by a hydrodynamic attractor which has an early-time behavior that is reminiscent of the so-called bottom-up thermalization scenario in heavy-ion collisions. The hydrodynamization times for the two sectors can differ strongly, with details depending on the curve realized on the two-dimensional attractor surface, which might account for differ…
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…
We present a first calculation of the dilepton yield and elliptic flow done with 3+1D viscous hydrodynamical simulations of relativistic heavy ion collisions at the top RHIC energy. A comparison with recent experimental data from the STAR collaboration is made.
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…
