Elliptic and Triangular Flow in Event-by-Event $\mathrm{D}=3+1$ Viscous Hydrodynamics

We present results for the elliptic and triangular flow coefficients $v_2$ and $v_3$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200A\mathrm{GeV}$ using event-by-event $\mathrm{D}=3+1$ viscous hydrodynamic simulations. We study the effect of initial state fluctuations and finite viscosities on the flow coefficients $v_2$ and $v_3$ as functions of transverse momentum and pseudorapidity. Fluctuations are essential to reproduce the measured centrality dependence of elliptic flow. We argue that simultaneous measurements of $v_2$ and $v_3$ can determine $\eta /s$ more precisely.

Figure 1

Energy density distribution in the transverse plane for one event with $b=2.4\mathrm{fm}$ at the initial time (left), and after $\tau =6\mathrm{fm}/c$ for the ideal case (middle) and with $\eta /s=0.16$ (right).

Figure 2

Freeze-out surfaces for two different events (red [dark gray] and yellow [medium gray]) compared to that for the averaged initial condition (light gray).

Figure 3

Charged hadron $v_2$ for different centralities as a function of $p_T$ for averaged initial conditions (avg) and event-by-event simulations (e-b-e) using different $\eta /s$ compared to STAR [37] and PHENIX [38] data.

Figure 4

Charged hadron $v_3$ for different centralities as a function of $p_T$ for event-by-event simulations using different viscosity to entropy density ratios.

Figure 5

Charged hadron $v_2$ and $v_3$ as a function of pseudorapidity for event-by-event simulations using different viscosity to entropy density ratios.