CERN Accelerating science

Average transverse and longitudinal pressures, $P_T= (T^{xx}+T^{yy})/2$ and $P_L=\tau^2 T^{\eta\eta}$, of a realistic heavy ion event evolved in succession by 2+1D Yang-Mills evolution (IP-glasma model)~\cite{Schenke:2012wb,Schenke:2012fw}, QCD kinetic theory (\kompost) and relativistic viscous hydrodynamics~\cite{Schenke:2010nt,Schenke:2010rr,Paquet:2015lta}.

(a) Energy density and (b) velocity profiles in the hydrodynamic stage at time $\tau_\text{out}=2.0\,\text{fm}$, for different durations of the kinetic preequilibrium stage ($\tauekt \rightarrow \tauhydro$).

Evolution of the background energy density in kinetic theory for two values of the coupling constant $\lambda$, corresponding to a range of specific shear viscosities $\eta/s\approx 0.16{-}0.62$. Scaling the vertical axis by the ideal hydrodynamic asymptotics $e_\text{id.}=\nu_g \pi^2\TId^4/30$ and the horizontal axis by the kinetic relaxation time $\tau_\text{R}(\tau) \equiv (\eta/s)/\TId(\tau)$ reveals that the nonequilibrium evolution follows a universal attractor curve which smoothly interpolates between free streaming at early times and viscous hydrodynamics at late times.

Evolution of the transverse energy density profile calculated within the linear response framework \kompost{}, from early time $\tauekt\sim 0.1\,\text{fm/c}$ to hydrodynamization time $\tauhydro\sim 1.0\,\text{fm/c}$. The energy-momentum tensor at each point $\x$ in the transverse plane receives causal contributions from the local average background, and linearized energy and momentum perturbations propagated from $\tauekt$ to $\tauhydro$ (\Eq{eq:pert_evol}). The causal past for point $\x$ is indicated by the black cone and white circle.