Spinodal Amplification of Density Fluctuations in Fluid-Dynamical Simulations of Relativistic Nuclear Collisions

Extending a previously developed two-phase equation of state, we simulate head-on relativistic lead-lead collisions with fluid dynamics, augmented with a finite-range term, and study the effects of the phase structure on the evolution of the baryon density. For collision energies that bring the bulk of the system into the mechanically unstable spinodal region of the phase diagram, the density irregularities are being amplified significantly. The resulting density clumping may be exploited as a signal of the phase transition, possibly through an enhanced production of composite particles.

Figure 1

The ($\epsilon$, $\rho$) phase diagram: ${\epsilon }_{T=0}(\rho )$, the minimal $\epsilon$ for a given $\rho$ (black line); the phase-coexistence boundary (red line) ending at the critical point (c. p.), as well as the isothermal spinodal boundary where $v_T=0$ (green line) and the isentropic spinodal boundary where $v_s=0$ (blue line). Points corresponding to counterstreaming Lorentz-contracted nuclei are shown for various energies $E_{\mathrm{lab}}$, indicated in $A\mathrm{GeV}$ (circles). The two contours (dashed line) show where the points of maximum compression are concentrated in ensembles of collisions simulated with fluid dynamics for $E_{\mathrm{lab}}=2$ or $5A\mathrm{GeV}$.

Figure 2

Effect of the gradient term: For various values of the parameter $a$ in Eq. (1) is shown the interface tension ${\sigma }_T$ as a function of $T$ (upper panel) and the growth rate ${\gamma }_k$ as a function of the wave number $k$ of a disturbance, as obtained with ideal fluid dynamics (lower panel).

Figure 3

Mean time evolution of normalized density moments obtained for $E_{\mathrm{lab}}=3A\mathrm{GeV}$ with $a=0.033\mathrm{fm}$ (for which ${\sigma }_0\approx 10\mathrm{MeV}/{\mathrm{fm}}^2$), using either the two-phase equation of state (solid lines) or its one-phase partner (dashed lines).

Figure 4

Mean maximum enhancement of the normalized density moments for $N=7$ and 5 (top and bottom, respectively) as obtained for various energies by using either the two-phase equation of state (solid lines) or its one-phase Maxwell partner (dashed lines).