Using viscous relativistic hydrodynamics we show that systematic studies of the impact parameter dependence of the eccentricity scaled elliptic flow can distinguish between different models for the calculation of the initial source eccentricity. This removes the largest present uncertainty in the extraction of the specific viscosity of the matter created in relativistic heavy-ion collisions from precise elliptic flow measurements.
We show from covariant transport theory that, for a massless ideal gas equation of state, even a small shear viscosity to entropy density ratio $η\approx s/(4 π)$ generates significant 15-30% dissipative corrections to elliptic flow for conditions expected in mid-peripheral (b = 8 fm) Au+Au collisions at $\sqrt{s_{NN}} \sim 200$ GeV at RHIC.
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.
In this contribution we present an alternative scenario for the large elliptic flow observed in relativistic heavy ion collisions. Motivated by recent results from Lattice QCD on flavor off-diagonal susceptibilities we argue that the matter right above $T_{c}$ can be described by single-particle dynamics in a repulsive single-particle potential, which in turn gives rise to elliptic flow. These ideas can be tested experimentally by measuring elliptic flow of heavy quarks, preferably via the measurement of $J/Ψ$ elliptic flow.
The correlation between the elliptic flow $v_2$ scaled by the impact parameter $b$ and the shear viscosity $η$ as well as the specific viscosity $η/s$, defined as the ratio of the shear viscosity to the entropy density $s$, is investigated for the first time in intermediate-energy heavy-ion collisions based on an isospin-dependent quantum molecular dynamic model. The elliptic flow is calculated at balance energies to exclude the geometric influence such as the blocking effect from the spectators. Our study shows that $v_{2}/b$ decreases almost linearly with increasing $η$, consistent with that…
We estimate the effects of viscosity on the phase space distribution appearing in the Cooper-Frye formula within the framework of the Grad's fourteen moment method and find that there are non-trivialities in the discussion of a multi-component system. We calculate the viscous corrections of particle spectra and elliptic flow coefficients from the distortion of the distribution using the flow and the hypersurface taken from a (3+1)-dimensional ideal hydrodynamic simulation. We see that the bulk viscosity have visible effects on particle spectra. The results suggest we should treat both shear an…
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…
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 $v_{2}(…
Bulk viscosity suppresses elliptic flow v_2, as does shear viscosity. It can thus not be neglected when extracting the shear viscosity from elliptic flow data. We here explore uncertainties in the bulk viscous contribution to viscous v_2 suppression that arise from presently uncontrolled uncertainties in the initial value of the bulk viscous pressure and its microscopic relaxation time.
We examine the evolution of quark-gluon plasma (QGP) droplets with viscous hydrodynamics and analyze the pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss (HBT) interferometry in a granular source model consisting of viscous QGP droplets. The shear viscosity of the QGP droplet speeds up and slows down the droplet evolution in the central and peripheral regions of the droplet, respectively. The effect of the bulk viscosity on the evolution is negligible. Although there are viscous effects on the droplet evolution, the pion momentum spectrum and elliptic flow change littl…
In the Israel-Stewart's theory of second order hydrodynamics, we have analysed the recent PHENIX data on charged particles elliptic flow in Au+Au collisions. PHENIX data demand more viscous fluid in peripheral collisions than in central collisions. Over a broad range of collision centrality (0-10%- 50-60%), viscosity to entropy ratio ($η/s$) varies between 0-0.17.
We investigate the influence of a temperature-dependent shear viscosity over entropy density ratio eta/s on the transverse momentum spectra and elliptic flow of hadrons in ultrarelativistic heavy-ion collisions. We find that the elliptic flow in sqrt(s_NN) = 200 GeV Au+Au collisions at RHIC is dominated by the viscosity in the hadronic phase and in the phase transition region, but largely insensitive to the viscosity of the quark-gluon plasma (QGP). At the highest LHC energy, the elliptic flow becomes sensitive to the QGP viscosity and insensitive to the hadronic viscosity.
Effects of the bulk viscosity on the elliptic flow are studied. To introduce a realistic equation of state and transport coefficients, we apply the results of the lattice QCD and hadron resonance gas calculations for these quantities. We found that the bulk viscosity acts in a non trivial manner on the elliptic flow $v_{2}$. The reduction of $v_{2}$ is more effective at low $p_{T}$ compared to the case of shear viscosity, whereas at high $p_{T}$, the situation is reversed, leading to $v_{2}$ enhancement. We argue that this is caused by the competition of the critical behaviors of the equation …
In this contribution we summarize recent progress in understanding the shear viscosity of strongly correlated dilute Fermi gases. We discuss predictions from kinetic theory, and show how these predictions can be tested using recent experimental data on elliptic flow. We find agreement between theory and experiments in the high temperature regime $T\gg T_F$, where $T_F$ is the the temperature where quantum degeneracy effects become important. In the low temperature regime, $T\sim T_F$, the strongest constraints on the shear viscosity come from experimental studies of the damping of collective m…
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…
The elliptic flow $v_2$ and the ratio of the shear viscosity over the entropy density, $η/s$, of gluon matter are calculated from the perturbative QCD (pQCD) based parton cascade Boltzmann approach of multiparton scatterings. For Au+Au collisions at $\sqrt{s}=200$A GeV the gluon plasma generates large $v_2$ values measured at the BNL Relativistic Heavy Ion Collider. Standard pQCD yields $η/s\approx 0.08-0.15$ as small as the lower bound found from the anti-de Sitter/conformal field theory conjecture.
Within a covariant parton cascade, we discuss the impact of both finite shear viscosity $η$ and freeze-out dynamics on the elliptic flow generated at RHIC. We find that the enhancement of $η/s$ in the cross-over region of the QGP phase transition cannot be neglected in order to extract the information from the QGP phase. We also point out that the elliptic flow $v_2(p_T)$ for a fluid at $η/s \sim 0.1-0.2$ is consistent with the one needed by quark number scaling drawing a nice consistency between the nearly perfect fluid property of QGP and the coalescence process.
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 …
We explore the influence of a temperature-dependent shear viscosity over entropy density ratio $η/s$ on the azimuthal anisotropies v_2 and v_4 of hadrons at various rapidities. We find that in Au+Au collisions at full RHIC energy, $\sqrt{s_{NN}}=200$ GeV, the flow anisotropies are dominated by hadronic viscosity at all rapidities, whereas in Pb+Pb collisions at the LHC energy, $\sqrt{s_{NN}}=2760$ GeV, the flow coefficients are affected by the viscosity both in the plasma and hadronic phases at midrapidity, but the further away from midrapidity, the more dominant the hadronic viscosity is. We …
In this talk, 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 $η/s$. We emphasize the role of saturation in the initial gluon spectrum modelling the shattering of the color glass condensate, causing the initial distribution to be out of equilibrium. We find that the saturation reduces the efficiency in building-up the elli…
Elliptic flow measurements at RHIC suggest that quark gluon plasma flows with very little viscosity compared to weak coupling expectations, challenging theorists to explain why this fluid is so nearly ``perfect''. It is therefore vital to find quantitative experimental information on the viscosity of the plasma. We propose that measurements of transverse momentum fluctuations can be used to determine the shear viscosity. We use current data to estimate the viscosity-to-entropy ratio in the range from 0.08 to 0.3, and discuss how future measurements can reduce this uncertainty.
We study the effects of bulk viscosity on p_T spectra and elliptic flow in heavy ion collisions at RHIC. We argue that direct effect of the bulk viscosity on the evolution of the velocity field is small, but corrections to the freezeout distributions can be significant. These effects are dominated by chemical non-equilibration in the hadronic phase. We show that a non-zero bulk viscosity in the range $ζ/s \lsim 0.05$ improves the description of spectra and flow at RHIC.
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 …
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…
A new framework for evaluating hydrodynamic models of relativistic heavy ion collisions has been developed. This framework, a Comprehesive Heavy Ion Model Evaluation and Reporting Algorithm (CHIMERA) has been implemented by augmenting UVH 2+1D viscous hydrodynamic model with eccentricity fluctuations, pre-equilibrium flow, and the Ultra-relativistic Quantum Molecular Dynamic (UrQMD) hadronic cascade. A range of initial temperatures and shear viscosity to entropy ratios were evaluated for four initial profiles, $N_{part}$ and $N_{coll}$ scaling with and without pre-equilibrium flow. The model r…
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).
Within a parton cascade approach we investigate the scaling of the differential elliptic flow $v_2(p_T)$ with eccentricity $ε_x$ and system size and its sensitivity to finite shear viscosity. We present calculations for shear viscosity to entropy density ratio $η/s$ in the range from $1/4π$ up to $1/π$, finding that the $v_2$ saturation value varies by about a factor 2. Scaling of $v_2(p_T)/ε_x$ is seen also for finite $η/s$ which indicates that it does not prove a perfect hydrodynamical behavior, but is compatible with a plasma at finite $η/s$. Introducing a suitable freeze-out condition, we …
We investigate fluid-to-particle conversion using the usual Cooper-Frye approach but with more general local equilibrium distributions than the Boltzmann or Bose/Fermi distributions typically used. Even though we study ideal fluids (i.e., shear stress and bulk pressure are zero everywhere), we find a suppression of elliptic flow (v2) at high transverse momenta (pT>1.5 GeV/c), relative to results obtained with the traditional Boltzmann distributions. The non-viscous suppression shows qualitatively similar features to the well-known shear viscous suppression of v2; for example, it increases with…
We predict how differential elliptic flow v2(pT) changes from RHIC to LHC collision energies (Pb+Pb at 5.5 TeV/nucleon), ASSUMING that the quark-gluon system created has a ``minimal'' shear viscosity eta/s = 1/(4*pi) at both RHIC and the LHC.
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.
We study the influence of a temperature-dependent shear viscosity over entropy density ratio $η/s$, different shear relaxation times $τ_π$, as well as different initial conditions on the transverse momentum spectra of charged hadrons and identified particles. We investigate the azimuthal flow asymmetries as a function of both collision energy and centrality. The elliptic flow coefficient turns out to be dominated by the hadronic viscosity at RHIC energies. Only at higher collision energies the impact of the viscosity in the QGP phase is visible in the flow asymmetries. Nevertheless, the shear …
I compute the first viscous correction to the thermal distribution function. With this correction, I calculate the effect of viscosity on spectra, elliptic flow, and HBT radii. Indicating the breakdown of hydrodynamics, viscous corrections become of order one for $p_{T}\sim 1.5$ GeV. Viscous corrections to HBT radii are particularly large and reduce the outward and longitudinal radii. This reduction is a direct consequence of the reduction in longitudinal pressure.
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 …
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 compute the time evolution of elliptic flow in non-central relativistic heavy-ion collisions, using a (2+1)-dimensional code with longitudinal boost-invariance to simulate viscous fluid dynamics in the causal Israel-Stewart formulation. We show that even ``minimal'' shear viscosity eta/s=hbar/(4pi) leads to a large reduction of elliptic flow compared to ideal fluid dynamics, raising questions about the interpretation of recent experimental data from the Relativistic Heavy Ion Collider.
With the new viscous hydrodynamic + hadron cascade hybrid code VISHNU, a rather precise (O(25%)) extraction of the QGP shear viscosity (eta/s)_QGP from heavy-ion elliptic flow data is possible if the initial eccentricity of the collision fireball is known with <5% accuracy. At this point, eccentricities from initial state models differ by up to 20%, leading to an O(100%) uncertainty for (eta/s)_QGP. It is shown that a simultaneous comparison of elliptic and triangular flow, v_2 and v_3, puts strong constraints on initial state models and can largely eliminate the present uncertainty in (eta/s)…
In 2+1 dimension, we have simulated the hydrodynamic evolution of QGP fluid with dissipation due to shear viscosity. Comparison of evolution of ideal and viscous fluid, both initialised under the same conditions e.g. same equilibration time, energy density and velocity profile, reveal that the dissipative fluid evolves slowly, cooling at a slower rate. Cooling get still slower for higher viscosity. The fluid velocities on the otherhand evolve faster in a dissipative fluid than in an ideal fluid. The transverse expansion is also enhanced in dissipative evolution. For the same decoupling tempera…
We study the effects of bulk viscosity on pT spectra and elliptic flow in heavy ion collisions. For this purpose we compute the dissipative correction df to the single particle distribution functions in leading-log QCD, and in several simplified models. We consider, in particular, the relaxation time approximation and a kinetic model for the hadron resonance gas. We implement these distribution functions in a hydrodynamic simulation of Au + Au collisions at RHIC. We find significant corrections due to bulk viscosity in hadron pT spectra and the differential elliptic flow parameter v2(pT). Thes…
The $\mathrm{n^{th}}$-order linear flow coefficients $\mathrm{v^L_n \, (n=2,3,4,5)}$, and the corresponding nonlinear mode-coupled ($\mathrm{mc}$) coefficients $\mathrm{v^{mc}_{4,(2,2)}}$, $\mathrm{v^{mc}_{5,(2,3)}}$, $\mathrm{v^{mc}_{6,(3,3)}}$ and $\mathrm{v^{mc}_{6,(2,2,2)}}$, are studied for Pb+Pb collisions at $\sqrt{s_{_{\rm NN}}} = 2.76$ TeV. Both sets of coefficients indicate a common acoustic scaling pattern of exponential viscous modulation, with a rate proportional to the square of the harmonic numbers and the mean transverse momenta (respectively), and inversely proportional to the…
In heavy ion collisions, event-by-event fluctuations in participating nucleon positions can lead to triangular flow. With fluctuating initial conditions, flow coefficients will also fluctuate. In a hydrodynamic model, we study the fluctuations in elliptic and triangular flow, due to fluctuating initial conditions. Both elliptic and triangular flow fluctuates strongly, triangular flow more strongly than the elliptic flow. Strong fluctuations greatly reduce the sensitivity of elliptic and triangular flow to viscosity.
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…
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 effects of the shear and bulk viscosities in the hadronic phase on the expansion of the fireball and on the particle production in relativistic heavy ion collisions. Comparing simulation with or without viscosity in the hadronic matter we find that elliptic flow observables strongly dependent on dissipative effects in the late stage. On the other hand, interferometry radii are sensitive, through the early transverse flow, on the value of the viscosity at high temperatures. We present first calculations including the effects of bulk viscosity in the hadronic phase and in the hadron…
In the Israel-Stewart's theory of dissipative hydrodynamics, we study the scaling properties elliptic flow in Au+Au collisions. Initial energy density of the fluid was fixed to reproduce STAR data on $ϕ$ meson multiplicity in 0-5% Au+Au collisions, such that irrespective of fluid viscosity, entropy at the freeze-out is similar in ideal or in viscous evolution. Initial eccentricity or constituent quark number scaling is only approximate in ideal or minimally viscous ($η/s=1/4π$) fluid. Eccentricity scaling become nearly exact in more viscous fluid ($η/s \geq$0.12). However, in more viscous flui…
In this paper, we present a fully analytical description of the early-stage formation of elliptic flow in relativistic viscous hydrodynamics. We first construct an elliptic deformation of Gubser flow which is a boost invariant solution of the Navier-Stokes equation with a nontrivial transverse profile. We then analytically calculate the momentum anisotropy of the flow as a function of time and discuss the connection with the empirical formula by Bhalerao {\it et al.} regarding the viscosity dependence of elliptic flow.
The eddy viscosity for a turbulent compressible fluid with a relativistic equation of state is derived. Compressibility allows for sound modes, but the eddy viscosity in the shear mode is found to be the same as for incompressible fluids. For two space dimensions (which is the relevant case for the dynamics of relativistic heavy-ion collisions) the eddy viscosity in the shear mode is negative, reducing the effective viscosity below its microscopic value. This could explain the tiny viscosity found at RHIC. Implications for the experimentally accessible elliptic flow coefficient at the LHC are …
Using the (2+1)-dimensional viscous hydrodynamic code VISH2+1 with a temperature dependent specific shear viscosity (eta/s)(T), we present a detailed study of the influence of a large hadronic shear viscosity and its corresponding relaxation time tau_pi on the transverse momentum spectra and elliptic flow of hadrons produced in 200 A GeV Au+Au collisions. Although theory, in principle, predicts a well-defined relation T*tau_pi = kappa(T)*(eta/s)(T), the precise form of kappa(T) for the matter created in relativistic heavy-ion collisions is not known. For the popular choice kappa=3 the hadron s…
Relativistic viscous hydrodynamic fits to RHIC data on the centrality dependence of multiplicity, transverse and elliptic flow for sqrt{s}=200 GeV Au+Au collisions are presented. For Glauber-type initial conditions, while data on integrated v_2 is consistent with a ratio of viscosity over entropy density up to eta/s=0.16, data on minimum bias v_2 seems to favor a much smaller viscosity over entropy ratio, below the bound from the AdS/CFT conjecture. Some caveats on this result are discussed.
The shear ($η$) and bulk ($ζ$) viscosities are calculated in a quasiparticle relaxation time approximation for a hadron matter described within the relativistic mean-field based model with scaled hadron masses and couplings. Comparison with results of other models is presented. We demonstrate that a small value of the shear viscosity to entropy density ratio required for explaining a large elliptic flow observed at RHIC may be reached in the hadron phase. Large values of the bulk viscosity are noted in case of the baryon enriched matter.
In a hydrodynamic model, with fluctuating initial conditions, the correlation between triangular flow and initial spatial triangularity is studied. The triangular flow, even in ideal fluid, is only weakly correlated with the initial triangularity. The correlation is largely reduced in viscous fluid. Elliptic flow on the other hand appears to be strongly correlated with initial eccentricity. Weak correlation between triangular flow and initial triangularity indicate that a part of triangular flow is unrelated to initial triangularity. Triangularity acquired during the fluid evolution also contr…
We calculate the yield and elliptic flow of mid-rapidity dileptons emitted from the quark-gluon plasma generated in Pb-Pb collisions at LHC. We use relativistic anisotropic hydrodynamics for the 3+1 dimensional evolution of the quark-gluon plasma and convolve this with the momentum-anisotropic local rest frame production rate for dileptons. The effects of momentum anisotropy of the quark distribution functions, viscosity to entropy density ratio, centrality of the collisions, and initial momentum anisotropy on the results are investigated and discussed.
The quark gluon plasma produced in ultra-relativistic heavy-ion collisions exhibits remarkable features. It behaves like a nearly perfect liquid with a small shear viscosity to entropy density ratio and leads to the quenching of highly energetic particles. We show that both effects can be understood for the first time within one common framework. Employing the parton cascade Boltzmann Approach to Multi-Parton Scatterings (BAMPS), the microscopic interactions and the space-time evolution of the quark gluon plasma are calculated by solving the relativistic Boltzmann equation. Based on cross sect…
This work reports on investigations of the effects on the evolution of viscous hydrodynamics and on the flow coefficients of thermal dileptons, originating from a temperature-dependent specific shear viscosity $η/s (T)$ at temperatures beyond 180 MeV formed at the Relativistic Heavy-Ion Collider (RHIC). We show that the elliptic flow of thermal dileptons can resolve the magnitude of $η/s$ at the high temperatures, where partonic degrees of freedom become relevant, whereas discriminating between different specific functional forms will likely not be possible at RHIC using this observable.
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 specific shear viscosity (eta/s)_QGP of a Quark-Gluon-Plasma (QGP) at temperatures T_c < T < 2T_c is extracted from the centrality dependence of the eccentricity-scaled elliptic flow measured in ultra-relativistic heavy-ion collisions. Coupling viscous fluid dynamics for the QGP with a microscopic transport model for hadronic freeze-out we find that the eccentricity-scaled elliptic flow is a universal function of charged multiplicity per unit overlap area, (1/S)(dN_ch/dy), that depends only on the viscosity but not on the model used for computing the initial fireball eccentricity. Comparin…
We study entropy production in the early stage of high-energy heavy-ion collisions due to shear viscosity. We employ the second-order theory of Israel-Stewart with two different stress relaxation times, as appropriate for strong coupling or for a Boltzmann gas, respectively, and compare the hydrodynamic evolution. Based on present knowledge of initial particle production, we argue that entropy production is tightly constrained. We derive new limits on the shear viscosity to entropy density ratio $η/s$, independent from elliptic flow effects, and determine the corresponding Reynolds number. Fur…
