Longitudinal distribution of initial energy density and directed flow of charged particles in relativistic heavy-ion collisions

We study the origin of the directed flow of charged particles produced in relativistic heavy-ion collisions. Three different initial conditions, $\mathrm{Boz}\dot{\text{e}}\mathrm{k}$-Wyskiel, CCNU, and Shen-Alzhrani, of energy density distributions are coupled to the $(3+1)$-dimensional viscous hydrodynamic model CLVisc, and their effects on the development of the anisotropic medium geometry, pressure gradient, and radial flow are systematically compared. By comparison to experimental data at both the Relativistic Heavy-Ion Collider and the Large Hadron Collider, we find that the directed flow provides a unique constraint on the tilt of the initial medium profile in the plane spanned by the impact parameter and space-time rapidity. Within midrapidity, the counterclockwise tilt is shown to be a crucial source of the positive-negative force by the pressure gradient along the impact parameter $\left(x\right)$ direction at backward-forward rapidity, which drives a negative slope of the $x$ component of the medium flow velocity with respect to rapidity, and in the end the same feature of the charged particle directed flow.

Figure 1

The initial energy density on the ${\eta }_s\text{−}x$ plane at ${\tau }_0$ = 0.6 fm in 5–40% ($b$ = 6.7 fm) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV. From top to bottom panel, we present case (A) $\mathrm{Boz}\dot{\text{e}}\mathrm{k}$-Wyskiel parametrization with ${\eta }_m=2.8$, case (B) CCNU parametrization with $H_t=2.9$, and case (C) Shen-Alzhrani parametrization with $f$ = 0.15. The arrows (aqua color) sketch the counterclockwise tilted initial condition with respect to the $x=0$ axis in the ${\eta }_s\text{−}x$ plane.

Figure 2

The first-order eccentricity coefficient ${\varepsilon }_1\left({\eta }_s\right)$ at ${\tau }_0$ = 0.6 fm for 5–40% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV, compared between three different model setups.

Figure 3

The initial pressure gradient $-{\partial }_{x}P$ on the $x\text{−}y$ plane at ${\tau }_0=0.6$ fm and ${\eta }_s=2.1$ in 5–40% ($b$ = 6.7 fm) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV, compared between three different model setups.

Figure 4

Time evolution of the average pressure gradient in the $x$ direction at ${\eta }_s=-0.9$ (upper panel) and ${\eta }_s=0.9$ (lower panel) in 5–40% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV, compared between three parametrization methods of the initial condition.

Figure 5

Time evolution of the average pressure gradient in the $x$ direction at ${\eta }_s=-2.1$ (upper panel) and ${\eta }_s=2.1$ (lower panel) in 5–40% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV, compared between three parametrization methods of the initial condition.

Figure 6

Space-time rapidity dependence of the average flow velocity in the $x$ direction at different evolution times in 5–40% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV, compared between three parametrization methods of the initial condition.

Figure 7

Pseudorapidity distribution of charged particles in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV in 0–6%, 6–15%, 15–25%, and 25–35% centrality classes, compared between the CLVisc hydrodynamic calculation with three initial condition setups and the PHOBOS data [71].

Figure 8

Pseudorapidity distribution of charged particles in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV in 0–5%, 5–10%, 10–20%, and 20–30% centrality classes, compared between the CLVisc hydrodynamic calculation with three initial condition setups and the ALICE data [72].

Figure 9

Pseudorapidity dependence of the directed flow coefficient in 5–40% (upper panel) and 30–60% (lower panel) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV, compared between the CLVisc hydrodynamic calculation with three initial condition setups and the STAR data [32, 55].

Figure 10

Pseudorapidity dependence of the directed flow coefficient in 10–20% (upper panel) and 30–40% (lower panel) $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV, compared between the CLVisc hydrodynamic calculation with three initial condition setups and the ALICE data [56].