Evolution of transverse flow and effective temperatures in the parton phase from a multiphase transport model

I study the space-time evolution of transverse flow and effective temperatures in the dense parton phase with the string melting version of a multiphase transport model. Parameters of the model are first constrained to reproduce the bulk data on the rapidity density, $p_T$ spectrum, and elliptic flow at low $p_T$ for central and midcentral Au + Au collisions at $200A$ GeV and Pb + Pb collisions at $2760A$ GeV. I then calculate the transverse flow and effective temperatures in volume cells within mid-spacetime-rapidity $\left|\eta \right|<1/2$. I find that the effective temperatures extracted from different variables, which are all evaluated in the rest frame of a volume cell, can be very different; this indicates that the parton system in the model is not in full chemical or thermal equilibrium locally, even after averaging over many events. In particular, the effective temperatures extracted from the parton energy density or number density are often quite different from those extracted from the parton mean $p_T$ or mean energy. For these collisions in general, effective temperatures extracted from the parton energy density or number density are higher than those extracted from the parton mean $p_T$ in the inner part of the overlap volume, while the opposite occurs in the outer part of the overlap volume. I argue that this indicates that the dense parton matter in the inner part of the overlap volume is overpopulated; I also find that all cells with energy density above 1 ${\text{GeV/fm}}^3$ are overpopulated after a couple of fm/$c$.

Figure 1

AMPT-SM results for central and midcentral Au + Au collisions at $200A$ GeV and Pb + Pb collisions at $2760A$ GeV in comparison with experimental data for 0–5% and 20–30% centralities: (a) $dN/dy$ of ${\pi }^{+}$, and (b) $dN/d$y of $K^{+}$.

Figure 2

$p_T$ spectra of ${\pi }^{+}$ and $K^{+}$ at midrapidity in central collisions from AMPT-SM in comparison with experimental data for 0–5% centrality.

Figure 3

Elliptic flow $v_2\left\{\mathrm{EP}\right\}$ at midrapidity in midcentral collisions from AMPT-SM (curves without circles) in comparison with experimental data for 20–30% centrality (circles): (a) for charged pions, and (b) for charged kaons.

Figure 4

Transverse flow of partons in the cell at $x=3$ fm and $y=0$ fm and in the cell at $x=7$ fm and $y=0$ fm as functions of time in central Au + Au collisions at $200A$ GeV.

Figure 5

Flow along the $x$ direction as functions of $x$ at different times in cells within $-0.5<y<0.5$ fm in central Au + Au collisions at $200A$ GeV.

Figure 6

AMPT-SM results for partons in the rest frame of the center cell in central Au + Au collisions at $200A$ GeV: (a) time evolutions of the energy density, number density, mean $p_T$, mean transverse energy, and mean energy; and (b) time evolutions of effective temperatures extracted from different variables.

Figure 7

AMPT-SM results on effective temperatures as functions of time for the center cell in (a) Pb + Pb collisions at $2760A$ GeV, and (b) Au + Au collisions at $200A$ GeV.

Figure 8

AMPT-SM results on effective temperatures as functions of time for the cell at $x=7$ fm and $y=0$ fm in central Au + Au collisions at $200A$ GeV; the dot-dashed curve represents the flow magnitude (multiplied by 100) in the cell.

Figure 9

AMPT-SM results on effective temperatures in cells along the impact parameter at $t=0.2$ and $2.0$ fm/$c$: (a) for central Pb + Pb collisions at $2760A$ GeV, and (b) for midcentral Au + Au collisions at $200A$ GeV.

Figure 10

AMPT-SM results on effective temperatures in cells along the impact parameter for different collisions: (a) at $t=0.2$ fm/$c$, and (b) at $t=5.0$ fm/$c$.

Figure 11

Phase-space distribution of partons in the center cell in central Pb + Pb collisions at $2760A$ GeV versus momentum $p$ (solid curves) or versus $p_T$ at midrapidity (dashed curves) (a) at $t=0.2$ fm/$c$, and (b) at $t=5.0$ fm/$c$. Circles represent results from the AMPT-SM model, curves with squares represent an ideal QGP at temperature $T_{\langle p_T\rangle }$, solid and dashed curves without symbols represent an ideal QGP at temperature $T_{\epsilon }$, and dotted curves represent an ideal QGP at temperature $T_{\epsilon }$ with quantum statistics.

Figure 12

For partons within $\left|\eta \right|<1/2$ in midcentral Pb + Pb collisions at $2760A$ GeV, filled circles represent the center locations in the transverse plane for QGP cells at $t=0.2$ fm/$c$, filled squares represent overpopulated QGP cells at $t=0.2$ fm/$c$, and open triangles represent overpopulated QGP cells at $t=3.0$ fm/$c$. The circle is drawn as a reference shape.

Figure 13

Transverse areas of QGP cells ($A_{\mathrm{QGP}}$) and transverse areas of QGP cells that are overpopulated ($A_{\mathrm{over}-\mathrm{p}}$) as functions of time for different collisions.

Figure 14

Phase-space distribution of partons in the center cell in central Pb + Pb collisions at $2760A$ GeV versus momentum $p$ from AMPT-SM (a) at $t=0.2$ fm/$c$, and (b) at $t=5.0$ fm/$c$, in comparison with the corresponding nonequilibrium quantum distributions of Eq. (14) at ${\gamma }_g={\gamma }_g^{\max }$ and ${\gamma }_q=0$ and at ${\gamma }_g={\gamma }_g^{\min }$ and ${\gamma }_q=1$ and the nonequilibrium Boltzmann distribution of Eq. (16).

Figure 15

Extracted range of ${\mu }_g$, the gluon “chemical potential” parameter, in overpopulated cells along the impact parameter at $t=0.2$ and $2.0$ fm/$c$: (a) for central Pb + Pb collisions at $2760A$ GeV, and (b) for midcentral Au + Au collisions at $200A$ GeV.