Radoslaw Ryblewski

Boost-Invariant (2+1)-Dimensional Anisotropic Hydrodynamics

We present results of the application of the anisotropic hydrodynamics (aHydro) framework to (2+1)-dimensional boost-invariant systems. The necessary aHydro dynamical equations are derived by taking moments of the Boltzmann equation using a momentum-space anisotropic one-particle distribution function. We present a derivation of the necessary equations and then proceed to numerical solutions of the resulting partial differential equations using both realistic smooth Glauber initial conditions and fluctuating Monte Carlo Glauber initial conditions. For this purpose we have developed two numerical implementations: one that is based on straightforward integration of the resulting partial differential equations supplemented by a two-dimensional weighted Lax-Friedrichs smoothing in the case of fluctuating initial conditions and another that is based on the application of the Kurganov-Tadmor central scheme. For our final results we compute the collective flow of the matter via the laboratory-frame energy-momentum tensor eccentricity as a function of the assumed shear viscosity-to-entropy ratio, proper time, and impact parameter.

Testing viscous and anisotropic hydrodynamics in an exactly solvable case

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 and anisotropic hydrodynamics relaxation times, anisotropic hydrodynamics provides a very good approximation to the exact relaxation time approximation solution.

Anisotropic Hydrodynamics for Rapidly Expanding Systems

Abstract We exactly solve the relaxation-time approximation Boltzmann equation for a system which is transversely homogeneous and undergoing boost-invariant longitudinal expansion. We compare the resulting exact numerical solution with approximate solutions available in the anisotropic hydrodynamics and second order viscous hydrodynamics frameworks. In all cases studied, we find that the anisotropic hydrodynamics framework is a better approximation to the exact solution than traditional viscous hydrodynamical approaches.

Highly-anisotropic hydrodynamics in 3+1 space-time dimensions

Recently formulated model of highly-anisotropic and strongly dissipative hydrodynamics is used in 3+1 dimensions to study behavior of matter produced in ultra-relativistic heavy-ion collisions. We search for possible effects of the initial high anisotropy of pressure on the final soft-hadronic observables. We find that by appropriate adjustment of the initial energy density and/or the initial pseudorapidity distributions, the effects of the initial anisotropy of pressure may be easily compensated and the final hadronic observables become insensitive to early dynamics. Our results indicate that the early thermalization assumption is not necessary to describe hadronic data, in particular, to reproduce the measured elliptic flow v_2. The complete thermalization of matter (local equilibration) may take place only at the times of about 1-2 fm/c, in agreement with the results of microscopic models.

Non-boost-invariant motion of dissipative and highly anisotropic fluid

The recently formulated framework of anisotropic and dissipative hydrodynamics (ADHYDRO) is used to describe non-boost-invariant motion of the fluid created at the early stages of heavy-ion collisions. Very strong initial asymmetries of pressure are reduced by the entropy production processes. By the appropriate choice of the form of the entropy source we can describe isotropization times of about 1 fm, which agrees with the common expectations that already at such times the perfect-fluid hydrodynamics may be applied. Our previous results are generalized by including the realistic equation of state as the limit of the isotropization processes.

Bulk viscous evolution within anisotropic hydrodynamics

Abstract We derive a system of moment-based dynamical equations that describe the 1+1d space-timeevolution of a cylindrically symmetric massive gas undergoing boost-invariant longitudinal expan-sion. Extending previous work, we introduce an explicit degree of freedom associated with thebulk pressure of the system. The resulting form generalizes the ellipsoidal one-particle distributionfunction appropriate for massless particles to massive particles. Using this generalized form, weobtain a system of partial di erential equations that can be solved numerically. In order to assessthe performance of this scheme, we compare the resulting anisotropic hydrodynamics solutionswith the exact solution of the 0+1d Boltzmann equation in the relaxation time approximation.We nd that the inclusion of the bulk degree of freedom improves agreement between anisotropichydrodynamics and the exact solution for a massive gas. PACS numbers: 12.38.Mh, 24.10.Nz, 25.75.-q, 51.10.+y, 52.27.NyKeywords: Relativistic heavy-ion collisions, Relativistic hydrodynamics, Relativistic transport, Boltzmannequation

Exact solution of the (0+1)-dimensional Boltzmann equation for a massive gas

We solve the one-dimensional boost-invariant kinetic equation for a relativistic massive system with the collision term treated in the relaxation time approximation. The result is an exact integral equation which can be solved numerically by the method of iteration to arbitrary precision. We compare predictions for the shear and bulk viscosities of a massive system with those obtained from the exact solution. Finally, we compare the time evolution of the bulk pressure obtained from our exact solution with results obtained from the dynamical equations of second-order viscous hydrodynamics.

Bottomonia suppression in 2.76 TeV Pb-Pb collisions

The relativistic heavy-ion collision experiments being carried out at Brookhaven National Laboratory’s Relativistic Heavy Ion Collider (RHIC) and CERN’s Large Hadron Collider (LHC) study the behavior of matter at extreme temperatures and densities. The goal of these experiments is to generate a deconned state of nuclear

(3+1)D Quasiparticle Anisotropic Hydrodynamics for Ultrarelativistic Heavy-Ion Collisions

We present the first comparisons of experimental data with phenomenological results from (3+1)D quasiparticle anisotropic hydrodynamics (aHydroQP). We compare particle spectra, average transverse momentum, and elliptic flow. The dynamical equations used for the hydrodynamic stage utilize aHydroQP, which naturally includes both shear and bulk viscous effects. The (3+1)D aHydroQP evolution obtained is self-consistently converted to hadrons using anisotropic Cooper-Frye freeze-out. Hadron production and decays are modeled using a customized version of therminator 2. In this first study, we utilized smooth Glauber-type initial conditions and a single effective freeze-out temperature T_{FO}=130  MeV with all hadronic species in full chemical equilibrium. With this rather simple setup, we find a very good description of many heavy-ion observables.

Leading-order anisotropic hydrodynamics for central collisions

We use leading-order anisotropic hydrodynamics to study an azimuthally-symmetric boost-invariant quark-gluon plasma. We impose a realistic lattice-based equation of state and perform self-consistent anisotropic freeze-out to hadronic degrees of freedom. We then compare our results for the full spatiotemporal evolution of the quark-gluon plasma and its subsequent freeze-out to results obtained using 1+1d Israel-Stewart second-order viscous hydrodynamics. We find that for small shear viscosities, 4 pi eta/s ~ 1, the two methods agree well for nucleus-nucleus collisions, however, for large shear viscosity to entropy density ratios or proton-nucleus collisions we find important corrections to the Israel-Stewart results for the final particle spectra and the total number of charged particles. Finally, we demonstrate that the total number of charged particles produced is a monotonically increasing function of 4 pi eta/s in Israel-Stewart viscous hydrodynamics whereas in anisotropic hydrodynamics it has a maximum at 4 pi eta/s ~ 10. For all 4 pi eta/s > 0, we find that for Pb-Pb collisions Israel-Stewart viscous hydrodynamics predicts more dissipative particle production than anisotropic hydrodynamics.