Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions

Abstract

We develop a macroscopic description of the space-time evolution of the energy-momentum tensor during the pre-equilibrium stage of a high-energy heavy-ion collision. Based on a weak coupling effective kinetic description of the microscopic equilibration process (\`a la ``bottom-up''), we calculate the nonequilibrium evolution of the local background energy-momentum tensor as well as the nonequilibrium linear response to transverse energy and momentum perturbations for realistic boost-invariant initial conditions for heavy-ion collisions. We demonstrate how this framework can be used on an event-by-event basis to propagate the energy-momentum tensor from far-from-equilibrium initial-state models to the time ${\ensuremath{\tau}}_{\text{hydro}}$ when the system is well described by relativistic viscous hydrodynamics. The subsequent hydrodynamic evolution becomes essentially independent of the hydrodynamic initialization time ${\ensuremath{\tau}}_{\text{hydro}}$ as long as ${\ensuremath{\tau}}_{\text{hydro}}$ is chosen in an appropriate range where both kinetic and hydrodynamic descriptions overlap. We find that for $\sqrt{{s}_{NN}}=2.76\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\text{TeV}$ central Pb-Pb collisions, the typical timescale when viscous hydrodynamics with shear viscosity over entropy ratio $\ensuremath{\eta}/s=0.16$ becomes applicable is ${\ensuremath{\tau}}_{\text{hydro}}\ensuremath{\sim}1\phantom{\rule{0.16em}{0ex}}\mathrm{fm}/\mathrm{c}$ after the collision.