Dynamical phase trajectories for relativistic nuclear collisions

Central collisions of gold nuclei are simulated by several existing models and the central net baryon density ρ and the energy density ɛ are extracted at successive times for beam kinetic energies of 5–40 GeV/nucleon. The resulting trajectories in the $(\rho ,\varepsilon )$ phase plane are discussed from the perspective of experimentally exploring the expected first-order hadronization phase transition with the planned FAIR at GSI or in a low-energy campaign at the Relativistic Heavy Ion Collider.

Figure 1

The $\rho \text{−}\varepsilon$ phase plane used for representing the extracted dynamical evolution of the central environment in Au+Au collisions. The energetically accessible region is bounded from below by the zero-temperature compressional energy density ${\varepsilon }_{T=0}(\rho )$. The hadronic freeze-out is indicated at the lower left [2]. The phase coexistence region obtained in Ref. [11] on the basis of an excluded volume is delineated by the outer contour, whereas the inner contour, which depicts a schematic boundary with a critial point, will serve as a reference for the phase trajectories.

Figure 2

The chiral hadronic SU(3) model: The energetically inaccessible region (gray area) and the phase-coexistence region (shaded area within solid boundary) are shown together with the corresponding quantities for the schematic equation of state displayed in Fig. 1. Also shown are the phase trajectories $(\rho ,\varepsilon )$ resulting from adiabatic expansions starting from counterstreaming Lorentz-contracted nuclei at the indicated beam kinetic energies $E_0$ ($A$ GeV).

Figure 3

The time evolution of the net baryon density $\rho (t)$ (left) and the total energy density $\varepsilon (t)$ (right) at the center of a head-on Au+Au collision for various bombarding energies (indicated in $A$ GeV), in the three-fluid model.

Figure 4

The phase trajectories ($\rho (t),\varepsilon (t)$) for the three-fluid collisions addressed in Fig. 3, together with the schematic reference phase boundary depicted in Fig. 1.

Figure 5

The time evolution of the central net baryon density $\rho (t)$ (left) and the corresponding phase trajectory ($\rho (t),\varepsilon (t)$) (right) at the center of a head-on Au+Au collision at various bombarding energies (indicated in $A$ GeV), in the PHSD model, together with the schematic reference phase boundary depicted in Fig. 1.

Figure 6

The time evolution of the central net baryon density $\rho (t)$ (left) and the corresponding phase trajectory ($\rho (t),\varepsilon (t)$) (right) at the center of a head-on Au+Au collision at various bombarding energies (indicated in $A$ GeV), in the URQMD model, together with the schematic reference phase boundary depicted in Fig. 1. The symbols on the curves are separated by $\Delta t=1\mathrm{fm}/c$.

Figure 7

The QGSM evolution of the central net baryon density, $\rho (t)$ (left), and the corresponding phase trajectory ($\rho (t),\varepsilon (t)$) (right) at the center of a head-on Au+Au collision at various bombarding energies (indicated in $A$ GeV), with the time increments $\Delta t$ between the symbols indicated in parentheses. Also shown is the schematic reference phase boundary depicted in Fig. 1.

Figure 8

The time evolution of the central net baryon density $\rho (t)$ (left) and the corresponding phase trajectory ($\rho (t),\varepsilon (t)$) (right) at the center of a head-on Au+Au collision at various bombarding energies (indicated in $A$ GeV), in the GIBUU model, together with the schematic phase boundary shown in Fig. 1.

Figure 9

The phase trajectories ($\rho (t),\varepsilon (t)$) at the center of a head-on Au+Au collision for various bombarding energies as obtained with the indicated models, together with the schematic phase boundary shown in Fig. 1 and the hadronic freeze-out line [2]. The symbols on the URQMD and QGSM curves are separated by the time intervals indicated in parentheses (fm/$c$).