Effects of initial-state dynamics on collective flow within a coupled transport and viscous hydrodynamic approach

We evaluate the effects of preequilibrium dynamics on observables in ultrarelativistic heavy-ion collisions. We simulate the initial nonequilibrium phase within a multiphase transport (AMPT) model, while the subsequent near-equilibrium evolution is modeled using (2+1)-dimensional relativistic viscous hydrodynamics. We match the two stages of evolution carefully by calculating the full energy-momentum tensor from AMPT and using it as input for the hydrodynamic evolution. We find that when the preequilibrium evolution is taken into account, final-state observables are insensitive to the switching time from AMPT to hydrodynamics. Unlike some earlier treatments of preequilibrium dynamics, we do not find the initial shear viscous tensor to be large. With a shear viscosity to entropy density ratio of 0.12, our model describes quantitatively a large set of experimental data on Pb+Pb collisions at the Large Hadron Collider over a wide range of centrality: differential anisotropic flow $v_n\left(p_T\right)(n=2–6)$, event-plane correlations, correlation between $v_2$ and $v_3$, and cumulant ratio $v_2\left\{4\right\}/v_2\left\{2\right\}$.

Figure 1

Time evolution of (a) the eccentricity in the reaction plane, (b) the momentum anisotropy, (c) the transverse flow velocity, and (d) various components of the shear pressure tensor ${\pi }^{mn}$ normalized by the enthalpy density. Averages over the transverse plane in (a), (c), and (d) are evaluated with a Lorentz contracted energy density as weight [15]. All quantities are averaged over events. Each panel compares four different initializations (see text). The switching time between AMPT and hydrodynamics is ${\tau }_{\mathrm{sw}}=0.4\mathrm{fm}/c$.

Figure 2

Transverse momentum spectra of charged particles from the AMPT+hydro calculations. The results are for two switching times ${\tau }_{\mathrm{sw}}=0.4$ and $0.9\mathrm{fm}/c$ and three different initial conditions. Curves for ${\tau }_{\mathrm{sw}}=0.9$ fm/c are shifted vertically in order to avoid overlapping.

Figure 3

Anisotropic flow coefficients, $v_n\left\{2\right\}\left(p_T\right)$ (for $n=2–5$, top to bottom), for charged hadrons in the AMPT+hydro calculations. (a) Initial flow and viscous tensor set to 0, and two different switching times, ${\tau }_{\mathrm{sw}}=0.4\mathrm{fm}/c$ (black dotted lines) and $0.9\mathrm{fm}/c$ (green dashed lines). (b) With initial flow and viscous tensor from AMPT. (c) Results for three initial conditions at ${\tau }_{\mathrm{sw}}=0.4\mathrm{fm}/c$.

Figure 4

Transverse momentum spectra of pions, kaons, and protons at midrapidity for two centrality ranges, $0–5\%$ and $30–40\%$ in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV in the AMPT+hydro model (solid lines) as compared to the ALICE data [68] (symbols). Model predictions of the particle spectra for Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV are shown as dashed lines.

Figure 5

Anisotropic flow of charged hadrons (top to bottom: $v_2$ to $v_6$) as a function of transverse momentum in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV in four centrality windows. Lines: AMPT+Hydro calculations; Symbols: ATLAS data [4].

Figure 6

Anisotropic flow in Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV in 4 centrality windows. Lines: AMPT+Hydro calculations; Symbols: ALICE data for $v_2$, $v_3$, and $v_4$ [74].

Figure 7

Two-plane correlations obtained in the initial-state (open squares) and final-state (open circles) as a function of the number of participants in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV in the AMPT+Hydro model as compared to the ATLAS data [76] using the scalar-product method (solid circles).

Figure 8

Same as Fig. 7, but for three-plane correlations.

Figure 9

The correlation between $v_2$ and $v_3$ for $0.5<p_T<2\mathrm{GeV}/c$ in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV in the AMPT+Hydro model (blue open circles) with $\eta /s=0.12$ as compared to the ATLAS data [83] (red solid circles). The data points (starting at bottom left) correspond to fourteen 5% centrality intervals over the centrality range 0–70 %. The inset shows ${\varepsilon }_2\text{−}{\varepsilon }_3$ correlation as a function of centrality in the model calculations.

Figure 10

The centrality dependence of the ratio $v_2\left\{4\right\}/v_2\left\{2\right\}$ for the elliptic flow obtained from two-and four-particle cumulant method in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV in the AMPT+Hydro model (blue open circles) with $\eta /s=0.12$ as compared to the ATLAS data [84] (red solid circles). Also shown is the ratio ${\varepsilon }_2\left\{4\right\}/{\varepsilon }_2\left\{2\right\}$ for the eccentricities in the model calculations (green open squares).