Anisotropic flow and flow fluctuations for Au + Au at $\sqrt{s_{NN}}=200$ GeV in a multiphase transport model

Anisotropic flow coefficients and their fluctuations are investigated for Au + Au collisions at center-of-mass energy $\sqrt{s_{NN}}$ = 200 GeV by using a multiphase transport model with string melting scenario. Experimental results of azimuthal anisotropies by means of the two- and four-particle cumulants are generally well reproduced by the model including both parton cascade and hadronic rescatterings. Event-by-event treatments of the harmonic flow coefficients $v_n$ (for $n=2$, 3, and 4) are performed, in which event distributions of $v_n$ for different orders are consistent with Gaussian shapes over all centrality bins. Systematic studies on centrality, transverse momentum ($p_T$), and pseudorapidity ($\eta$) dependencies of anisotropic flows and quantitative estimations of the flow fluctuations are presented. The $p_T$ and $\eta$ dependencies of absolute fluctuations for both $v_2$ and $v_3$ follow trends similar to their flow coefficients. Relative fluctuation of triangular flow $v_3$ is slightly centrality dependent, which is quite different from that of elliptic flow $v_2$. It is observed that parton cascade has a large effect on the flow fluctuations, but hadronic scatterings make little contribution to the flow fluctuations, which indicates flow fluctuations are mainly modified during partonic evolution stage.

Figure 1

Distributions of $v_n\left\{P\right\}$ [$n=2$ (a), 3 (b), 4 (c)] for different centrality bins in Au + Au collisions at 200 GeV from the AMPT simulations.

Figure 2

Flow coefficients $v_n$ [$n=2$ (a), 3 (b), 4 (c)] for all charged particles in midrapidity ($\left|\eta \right|$ $\le$ 1.0) from participant plane method and $Q$-cumulant method as a function of $\langle N_P\rangle$ in Au + Au collision at 200 GeV. Absolute flow fluctuation ${\sigma }_{v_n}\left(Q\right)$ (black dotted line) and ${\sigma }_{v_n}\left(P\right)$ (blue [gray] dotted line) are also presented, and experimental results from the STAR experiment are shown (red [gray] solid star for $v_2\left\{2\right\}$ and red [gray] solid square for $v_2\left\{4\right\}$). Experimental measurement of $v_3\left\{2\right\}$ with pseudorapidity gap applied is also shown for comparison (in the middle panel) [26].

Figure 3

Differential $v_2$ (upper six panels) and $v_3$ (lower six panels) as a function of transverse momentum for charged particles in midrapidity for six centrality bins in Au + Au collision at 200 GeV. $v_2\left\{2\right\}$, $v_2\left\{4\right\}$ are from $Q$-cumulant methods, and $v_2\left\{P\right\}$ is from participant plane method. Blacks dots with gray shadow areas show the magnitudes of absolute flow fluctuation. The open and solid star symbols represents experimental results for two-particle $v_2\left\{2\right\}$ and four-particle $v_2\left\{4\right\}$ respectively. The absolute $v_3$ fluctuation from $Q$-cumulant method $\sqrt{v_3^2\left\{2\right\}/2}$ and participant plane method ${\sigma }_{v_3}\left(P\right)$ are represented with gray solid squares and blue (gray) dotted line separately. Experimental $v_3\left\{TPC\right\}$ data (solid downward-pointing triangles), which were based on the time projection chamber (TPC) event plane method, are taken from Ref. [71] for comparison.

Figure 4

The AMPT results on $v_2$ (upper six panels) and $v_3$ (lower six panels) from $Q$-cumulant method and participant plane method as a function of pseudorapidity for six centrality bins in Au + Au collisions at 200 GeV. Experimental $v_3\left\{TPC\right\}$ data are also taken from Ref. [71].

Figure 5

The AMPT results on relative elliptic (upper panel) and triangular (lower panel) flow fluctuations as a function of transverse momentum $p_T$ at different centrality bins in Au + Au collisions at 200 GeV. Experimental $v_2$ fluctuation data are derived from Refs. [74, 75].

Figure 6

AMPT results on relative elliptic (upper panel) and triangular (lower panel) flow fluctuations as a function of pseudorapidity $\eta$ at different centrality bins in Au + Au collisions at 200 GeV.

Figure 7

The AMPT results on elliptic flow fluctuation $R_{v_2}$ as a function of $\langle N_P\rangle$ for Au + Au collision at 200 GeV, where panel (a) shows $R_{v_2}$ from AMPT simulations with parton interaction cross sections of 3 and 10 mb with final hadronic rescatterings, and panel (b) shows $R_{v_2}$ with and without hadronic scatterings. Flow fluctuations are compared to STAR and PHOBOS data [39, 40]. The PHOBOS data errors are quoted from Ref. [78].