Mach cones in viscous heavy-ion collisions

The formation of Mach cones is studied in a full $(3+1)$-dimensional setup of ultrarelativistic heavy-ion collisions, considering a transverse and longitudinal expanding medium at Relativistic Heavy-Ion Collider energies. For smooth initial conditions and central collisions the jet-medium interaction is investigated using high-energy jets and various values of the ratio of shear viscosity over entropy density, $\eta /s$. For small viscosities, the formation of Mach cones is proven, whereas for larger viscosities the characteristic structures smear out and vanish eventually. The formation of a double-peak structure both in a single- and in a multiple-jet event is discussed.

Figure 1

Schematic representation of different jet paths initialized on a semicircle; see also Ref. [46]. The left-hand panel shows all possible paths, and the right-hand panel shows the reduced number of paths due to reasons of symmetry.

Figure 2

Time evolution of a Mach cone in a central heavy-ion collision. The local rest frame energy density around midrapidity $\left(|{\eta }_{\mathrm{rap}}|<0.1\right)$ is shown, overlaid by the velocity profile, indicated by scaled arrows. The results are depicted at various time steps and different values of the ratio of shear viscosity over entropy density, $\eta /s$. The jet is initialized at a fixed-angle position of ${\varphi }_{\mathrm{jet}}={180}^{\circ }$ on the semicircle with an initial momentum of $p_x=E_{\mathrm{jet}}=20$ GeV.

Figure 3

The time evolution of the jet energy extracted from BAMPS calculations shown in Fig. 2 for different values of the ratio of shear viscosity over entropy density, $\eta /s$.

Figure 4

The extracted radial flow from BAMPS calculations at $t=5$ fm$/c$ and central collisions for different values of the ratio of shear viscosity over entropy density, $\eta /s$.

Figure 5

Two-particle correlations, $dN/\left(Nd\varphi \right)$, extracted from BAMPS calculations for different values of $\eta /s$ and $p_T$ cuts. The jet is initialized at a fixed-angle position of ${\varphi }_{\mathrm{jet}}={180}^{\circ }$ on the semicircle (see Fig. 2). The results are shown for a fixed time $t=12$ fm$/c$.

Figure 6

Two-particle correlations, $dN/\left(Nd\varphi \right)$, extracted from BAMPS calculations for a fixed value of $\eta /s=0.08$ and various evolution times. The jet is initialized at a fixed-angle position of ${\varphi }_{\mathrm{jet}}={180}^{\circ }$ on the semicircle (see Fig. 2).

Figure 7

Time evolution of a Mach cone in a central heavy-ion collision. We show the local rest frame energy density within a midrapidity range of $|{\eta }_{\mathrm{rap}}|<0.1$, overlaid by the velocity profile indicated by scaled arrows. The results are depicted at various time steps and for different values of the ratio of shear viscosity over entropy density, $\eta /s$. The jet is initialized at a fixed-angle position of ${\varphi }_{\mathrm{jet}}={135}^{\circ }$ on the semicircle with an initial momentum of $p_x=E_{\mathrm{jet}}=20$ GeV.

Figure 8

Two-particle correlations, $dN/\left(Nd\varphi \right)$, extracted from BAMPS calculations for different values of $\eta /s$ and $p_T$ cuts. The jet is initialized at a fixed-angle position of ${\varphi }_{\mathrm{jet}}={135}^{\circ }$ on the semicircle (see Fig. 7). The results are shown for a fixed time $t=12$ fm$/c$.

Figure 9

Two-particle correlations, $dN/\left(Nd\varphi \right)$, extracted from BAMPS calculations for different values of $\eta /s$ and $p_T$ cuts. Here, we consider various starting positions of the jet on the semicircle. The results are shown at a fixed time of $t=12$ fm$/c$.