Relativistic Shock Waves in Viscous Gluon Matter

We solve the relativistic Riemann problem in viscous gluon matter employing a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock waves by varying the shear viscosity to entropy density ratio $\eta /s$ from zero to infinity. We show that an $\eta /s$ ratio larger than 0.2 prevents the development of well-defined shock waves on time scales typical for ultrarelativistic heavy-ion collisions. Comparisons with viscous hydrodynamic calculations confirm our findings.

Figure 1

The solution of the Riemann problem. At $t=0$, the pressure is $P_0=5.43\mathrm{GeV}{\mathrm{fm}}^{-3}$ for $z<0$ and $P_4=2.22\mathrm{GeV}{\mathrm{fm}}^{-3}$ for $z>0$. The upper panel shows the pressure and the lower panel the velocity at time $t=3.2\mathrm{fm}/c$.

Figure 2

The time evolution of the Riemann problem for $\eta /s=0.1$ and the initial condition of Fig. 1.

Figure 3

Formation time of shock waves as a function of $\eta /s$.

Figure 4

The same as Fig. 1. Results obtained from vSHASTA and BAMPS calculations are compared.