From Full Stopping to Transparency in a Holographic Model of Heavy Ion Collisions

We numerically simulate planar shock wave collisions in anti–de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a crossover between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model. At high energies the receding fragments move outwards at the speed of light, with a region of negative energy density and negative longitudinal pressure trailing behind them. The rapidity distribution of the energy density at late times around midrapidity is not approximately boost invariant but Gaussian, albeit with a width that increases with the collision energy.

Figure 1

Energy and pressures for collisions of thick (top row) and thin (bottom row) shocks. The gray planes lie at the origin of the vertical axes.

Figure 2

Energy flux $S/{\rho }^4$ for collisions of thick (left) and thin (right) shocks. The dotted curves show the location of the maxima of the flux.

Figure 3

$3\Delta {\mathcal{P}}_L^{\mathrm{loc}}/{\mathcal{E}}_{\mathrm{loc}}$ for thick (left) and thin (right) shocks. The white areas indicate the vacuum regions outside the light cone. The gray areas indicate regions where hydrodynamics deviates by more than 100%. The dotted curves indicate the location of the maxima of the energy flux, as in Fig. 2.

Figure 4

Center and off-center values of $\mathcal{E}/3{\rho }^4$ (black), ${\mathcal{P}}_L/{\rho }^4$ (red), and ${\mathcal{P}}_T/{\rho }^4$ (blue) as a function of time for a collision of thick (top row) and thin (bottom row) shocks. The dotted curves show the hydrodynamic approximation.

Figure 5

Ratios ${\mathcal{P}}_L/\mathcal{E}$ (red) and ${\mathcal{P}}_T/\mathcal{E}$ (blue) at $z=0$ for thick (left) and thin (right) shocks.

Figure 6

Energy density in the local rest frame around midrapidity as a function of spacetime rapidity $\eta$ and proper time $\tau$ for thick (left) and thin (right) shocks. In the latter case we have excluded from the plot the region in which the local rest frame is not defined because $2|\mathcal{S}|>|\mathcal{E}+{\mathcal{P}}_L|$.