Abstract
We study the evolution of hydrodynamic and non-hydrodynamic moments of the distribution function using anisotropic and third-order Chapman-Enskog hydrodynamics for systems undergoing Bjorken and Gubser flows. The hydrodynamic results are compared with the exact solution of the Boltzmann equation with a collision term in relaxation time approximation. While the evolution of the hydrodynamic moments of the distribution function (i.e. of the energy momentum tensor) can be described with high accuracy by both hydrodynamic approximation schemes, their description of the evolution of the entropy of the system is much less precise. We attribute this to large contributions from non-hydrodynamic modes coupling into the entropy evolution which are not well captured by the hydrodynamic approximations. The differences between the exact solution and the hydrodynamic approximations are larger for the third-order Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which effectively resums some of the dissipative effects from anisotropic expansion to all orders in the anisotropy, and are larger for Gubser flow than for Bjorken flow. Overall, anisotropic hydrodynamics provides the most precise macroscopic description for these highly anisotropically expanding systems.
Highlights
A remarkable property of the hot and dense matter formed in ultrarelativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) is a strong collective motion which has been successfully modeled using relativistic hydrodynamics
The differences between the exact solution and the hydrodynamic approximations are larger for the third-order Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which effectively resums some of the dissipative effects from anisotropic expansion to all orders in the anisotropy, and are larger for Gubser flow than for Bjorken flow
We have considered two different formalisms for deriving macroscopic descriptions of the nonequilibrium dynamics of a system, namely, dissipative hydrodynamics using the Chapman-Enskog iterative scheme to third order and anisotropic hydrodynamics with PL matching
Summary
A remarkable property of the hot and dense matter formed in ultrarelativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) is a strong collective motion which has been successfully modeled using relativistic hydrodynamics (see Ref. [1] for a recent review). A systematic approach of obtaining viscous hydrodynamics, to any given order in gradients of the macroscopic flow velocity, is based on a Chapman-Enskog-like iterative solution of Boltzmann equation [22,23,24,25,26,27,28,29,30,31] This method was employed to derive higher order dissipative hydrodynamic equations [29]. We close with conclusions and an outlook in Sec VII
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