(3+1)-dimensional anisotropic fluid dynamics with a lattice QCD equation of state

Abstract

Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections non-perturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade description of the final collision stage. We present a new dissipative hydrodynamic formulation for non-conformal fluids where both of these effects are treated nonperturbatively. The evolution equations are derived from the Boltzmann equation in the 14-moment approximation, using an expansion around an anisotropic leading-order distribution function with two momentum-space deformation parameters, accounting for the longitudinal and transverse pressures. To obtain their evolution we impose generalized Landau matching conditions for the longitudinal and transverse pressures. We describe an approximate anisotropic equation of state that relates the anisotropy parameters with the macroscopic pressures. Residual shear stresses are smaller and are treated perturbatively, as in standard second-order dissipative fluid dynamics. The resulting optimized viscous anisotropic hydrodynamic evolution equations are derived in 3+1 dimensions and tested in a (0+1)-dimensional Bjorken expansion, using a state-of-the-art lattice equation of state. Comparisons with other viscous hydrodynamical frameworks are presented.

arXiv comment27 pages, 7 figures

References in corpus (63)

• Collective flow and viscosity in relativistic heavy-ion collisions
• The equation of state in (2+1)-flavor QCD
• The QCD equation of state with dynamical quarks
• Hydrodynamic Modeling of Heavy-Ion Collisions
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Fluctuating Glasma initial conditions and flow in heavy ion collisions
• Event-by-event anisotropic flow in heavy-ion collisions from combined Yang-Mills and viscous fluid dynamics
• 3+1D hydrodynamic simulation of relativistic heavy-ion collisions
• Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma medium
• Collective Modes of an Anisotropic Quark-Gluon Plasma
• First Results from Pb+Pb collisions at the LHC
• On the Strongly-Interacting Low-Viscosity Matter Created in Relativistic Nuclear Collisions
• A calculation of the bulk viscosity in SU(3) gluodynamics
• Effective Kinetic Theory for High Temperature Gauge Theories
• The importance of the bulk viscosity of QCD in ultrarelativistic heavy-ion collisions
• Universal properties of bulk viscosity near the QCD phase transition
• The production of photons in relativistic heavy-ion collisions
• Dissipative Dynamics of Highly Anisotropic Systems
• Slowing Out of Equilibrium Near the QCD Critical Point
• The Bulk Viscosity of High-Temperature QCD
• Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
• Radial and elliptic flow in Pb+Pb collisions at the Large Hadron Collider from viscous hydrodynamic
• One fluid to rule them all: viscous hydrodynamic description of event-by-event central p+p, p+Pb and Pb+Pb collisions at $\sqrt{s}=5.02$ TeV
• Pressure isotropization in high energy heavy ion collisions
• Results from the Relativistic Heavy Ion Collider
• Bulk viscosity of QCD matter near the critical temperature
• Transport Coefficients of Bulk Viscous Pressure in the 14-moment approximation
• Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach
• Dynamical initial state model for relativistic heavy-ion collisions
• Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics
• Eccentric protons? Sensitivity of flow to system size and shape in p+p, p+Pb and Pb+Pb collisions
• Second-order (2+1)-dimensional anisotropic hydrodynamics
• Interplay of shear and bulk viscosity in generating flow in heavy-ion collisions
• Effect of bulk viscosity on Elliptic Flow near QCD phase transition
• Exploiting Intrinsic Triangular Geometry in Relativistic He3+Au Collisions to Disentangle Medium Properties
• Origins of Bulk Viscosity at RHIC
• Collectivity and electromagnetic radiation in small systems
• Hydrodynamic Predictions for Pb+Pb Collisions at 5.02 A TeV
• Effects of bulk viscosity and hadronic rescattering in heavy ion collisions at RHIC and LHC
• Bulk Viscosity and Cavitation in Boost-Invariant Hydrodynamic Expansion
• The viscosity of quark-gluon plasma at RHIC and the LHC
• Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
• 3+1d quasiparticle anisotropic hydrodynamics for ultrarelativistic heavy-ion collisions
• Particle spectra and HBT radii for simulated central nuclear collisions of C+C, Al+Al, Cu+Cu, Au+Au, and Pb+Pb from Sqrt(s)=62.4-2760 GeV
• Bulk viscous evolution within anisotropic hydrodynamics
• Projection method and new formulation of leading-order anisotropic hydrodynamics
• Viscous Hydrodynamics and the Quark Gluon Plasma
• Early collective expansion: Relativistic hydrodynamics and the transport properties of QCD matter
• Colliding shock waves and hydrodynamics in small systems
• Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of moment of the Boltzmann equation
• Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions
• Quasiparticle equation of state for anisotropic hydrodynamics
• QM2017: Status and Key open Questions in Ultra-Relativistic Heavy-Ion Physics
• Leading-order anisotropic hydrodynamics for systems with massive particles
• Anisotropic matching principle for the hydrodynamics expansion
• Anisotropic fluid dynamics for Gubser flow
• Quasiparticle second-order viscous hydrodynamics from kinetic theory
• Early thermalization, hydrodynamics and energy loss in AdS/CFT
• Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA
• Quasiparticle anisotropic hydrodynamics for central collisions
• Quark-Gluon Plasma at RHIC and the LHC: Perfect Fluid too Perfect?
• Collective flow from AA, pA to pp collisions - Toward a unified paradigm
• Characterization of the initial state and QGP medium from a combined Bayesian analysis of LHC data at 2.76 and 5.02 TeV

Cited by in corpus (18)

• The smallest fluid on earth
• The Present and Future of QCD
• Hydrodynamic attractors in heavy ion collisions: a review
• Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
• Theories of Relativistic Dissipative Fluid Dynamics
• ${}^{16}{\mathrm{O}}^{16}\mathrm{O}$ at RHIC and the LHC comparing $\alpha$ clustering vs substructure
• Studying QGP with flow: A theory overview
• On non-conformal kinetic theory and hydrodynamics for Bjorken flow
• Hydrodynamics from free-streaming to thermalization and back again
• Anisotropic hydrodynamic modeling of 200 GeV Au-Au collisions
• Modified equilibrium distributions for Cooper--Frye particlization
• Anisotropic fluid dynamical simulations of heavy-ion collisions
• Applications of emulation and Bayesian methods in heavy-ion physics
• Including off-diagonal anisotropies in anisotropic hydrodynamics
• Stability of Gluonic Systems with Multiple Soft Interactions
• Viscous hydrodynamics for nonconformal anisotropic fluids
• Far-from-equilibrium hydrodynamic simulations of ultrarelativistic nuclear collisions
• Extended applicability domain of viscous anisotropic hydrodynamics in (2+1)-D Bjorken flow with transverse expansion