Azimuthal anisotropy in particle distribution in a multiphase transport model

Anisotropic flow of hadronic matter is considered a sensitive tool to detect the early-stage dynamics of high-energy heavy-ion collisions. Taking the event-by-event fluctuations of the collision geometry into account, the elliptic flow parameter and the triangular flow parameter derived from the azimuthal distribution of produced hadrons are investigated within the framework of a multiphase transport (AMPT) model, at a collision energy that in near future will typically be available at the Facility for Antiproton and Ion Research. The dependence of elliptic and triangular flow parameters on initial fluctuations, on parton scattering cross sections and their mass ordering on different hadron species, and on the constituent quark number scaling are examined. The AMPT simulation cannot exactly match the elliptic flow results on Pb+Pb collision at $40A$ GeV of the NA49 experiment. The simulation results presented in this work are expected to provide us with an insight to study flow properties at high baryonic density and at moderate temperature, and with an opportunity to compare similar results available from Relativistic Heavy Ion Collider and Large Hadron Collider experiments.

Figure 1

Azimuthal angle (measured in radian) distribution of charged hadrons produced in Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 2

$p_{{}_T}$ distribution of identified charged hadrons produced in Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 3

Average $p_{{}_T}$ of inclusive charged hadrons produced in the Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV plotted against centrality.

Figure 4

Centrality dependence of ${\varepsilon }_n$ of the overlapping region of Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 5

$v_2$ as a function of ${\varepsilon }_2$ in different $N_{\mathrm{part}}$ intervals for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV with $\sigma =3$ mb.

Figure 6

$v_3$ as a function of ${\varepsilon }_3$ in different $N_{\mathrm{part}}$ intervals for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV with $\sigma =3$ mb.

Figure 7

$v_2$ and $v_3$ as functions of $p_{{}_T}$ at midrapidity for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 8

$p_{{}_T}$ dependence of $v_2$ for different centrality windows at midrapidity for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 9

$p_{{}_T}$ dependence of $v_3$ for different centrality windows at midrapidity for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 10

NA49 data on $p_{{}_T}$ dependence of $v_2$ obtained from Pb+Pb interactions at $40A$ GeV compared with AMPT simulation (both default and sring melting) for pions and protons at different partonic cross sections and at different centralities. The experimental values are shown as points, while corresponding simulations are shown by continuous curves.

Figure 11

Distributions of $v_2/\langle v_2\rangle$ and ${\varepsilon }_2/\langle {\varepsilon }_2\rangle$ for charged hadrons in Au+Au collisions at $E_{\mathrm{lab}}=30A$ GeV.

Figure 12

Distributions of $v_3/\langle v_3\rangle$ and ${\varepsilon }_3/\langle {\varepsilon }_3\rangle$ for charged hadrons in Au+Au collisions at $E_{\mathrm{lab}}=30A$ GeV.

Figure 13

Elliptical flow scaled by eccentricity against centrality for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 14

Triangular flow scaled by triangularity plotted against centrality for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 15

Elliptical flow scaled by eccentricity plotted against particle density in the transverse plane for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV. Solid lines represent best fits to the linear portion of the data.

Figure 16

$v_3/v_2$ ratio plotted as a function of $N_{\mathrm{part}}$ in different $p_T$ intervals for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV (upper panel). The same plot, but now the values of $v_3/v_2$ for a given $p_T$ interval is scaled by the corresponding ratio for the entire $p_T$ interval $(0\le p_T\le 2.0)$ GeV/$c$ (lower panel).

Figure 17

Dependence of $v_3/v_2$ on $N_{\mathrm{part}}$ in different $p_{{}_T}$ bins for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 18

Species dependence of $v_2$ (upper panel) and $v_3$ (lower panel) as a function of $p_{{}_T}$ for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.

Figure 19

$v_2$ (upper panel) and $v_3$ (lower panel) scaled by the constituent quark numbers of hadrons as a function of $K_{{}_T}/n_q$ for Au+Au collision at $E_{\mathrm{lab}}=30A$ GeV.