Abstract
Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections nonperturbatively. 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 nonconformal 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.
Highlights
Dissipative relativistic fluid dynamics has become the workhorse for simulations of the dynamical evolution of relativistic heavy-ion collisions [1,2,3,4,5,6,7,8]
When supplemented with realistic fluctuating initial conditions, a pre-equilibrium evolution module that evolves these initial conditions into starting values for the hydrodynamic evolution, and a hadronic rescattering afterburner that describes the late microscopic kinetic evolution of the collision fireball during its dilute decoupling stage, the approach has yielded impressive quantitative precision in its description of a broad set of soft hadronic observables obtained from heavy-ion-collision experiments at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) [9,10,11,12], and it has demonstrated convincing predictive power when extending the calculations into new domains of collision energy [13,14,15,16,17] or for new collision systems [18,19,20,21,22,23]
3He + Au collisions at RHIC and p + p collisions at the LHC [20,23,24], i.e., for “small” collision systems in which the hydrodynamic model had been widely expected to break down. This finding has generated much recent work addressing two obvious questions arising from these observations: (1) What exactly are the formal criteria that ensure the applicability of relativistic dissipative fluid dynamics to small physical systems undergoing rapid collective expansion and control its eventual breakdown? How far away from local thermal equilibrium can a system be and still evolve hydrodynamically? (2) Are there alternate mechanisms at work that can mimic the phenomenological signals of hydrodynamic collective flow, especially in small collision systems, without requiring strong final-state interactions among the constituents of the fireball created in the collision that lead to some degree of approximate local thermalization?
Summary
Dissipative relativistic fluid dynamics has become the workhorse for simulations of the dynamical evolution of relativistic heavy-ion collisions [1,2,3,4,5,6,7,8]. [43,48], the evolution of these deformation parameters is optimized by determining them through generalized dynamical Landau matching conditions, similar to those fixing the evolution of the temperature and chemical potential This guarantees that the leading-order anisotropic distribution fa (around which the full distribution function is expanded in moments) fully accounts for the energy and conserved charge density, and for the longitudinal and transverse pressures (or, equivalently, the longitudinal-transverse pressure anisotropy (which is the largest shear stress component) and the bulk viscous pressure, as described above). It significantly simplifies the structure of the relaxation equations for the residual dissipative flows.
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