Chemical Freezeout in Heavy Ion Collisions

TL;DR

Heavy ion collisions progress from a quark–gluon plasma to a hadronic gas, with rapid thermal equilibration but much slower chemical equilibration. The authors construct an equation of state that enforces chemical freezeout by keeping the hadron yields fixed along an adiabatic trajectory and implement it in a hydro plus hadronic cascade framework to study SPS energies; comparisons with RQMD assess switching temperature effects. They find that the pressure–energy density relation remains largely unchanged, but the mapping between energy density and temperature is significantly altered by chemical potentials (e.g., μπ ≈ 80 MeV), affecting observables like v2. Implementing chemical freezeout yields spectra that are robust to the chosen switching temperature, though elliptic flow retains a modest sensitivity, and the inferred freezeout conditions for pions correspond to T_f ≈ 100 MeV with μπ ≈ 80 MeV. Overall, the chemically frozen EOS provides a thermodynamically consistent bridge between hydrodynamic and cascade descriptions, clarifying the late-stage hadronic evolution and its impact on observable flow and spectra.

Abstract

We construct a hadronic equation of state consistent with chemical freezeout and discuss how such an equation of state modifies the radial and elliptic flow in a hydrodynamic + hadronic cascade model of relativistic heavy ion collisions at the SPS. Incorporating chemical freezeout does not change the relation between pressure and energy density. However, it does change the relation between temperature and energy density. Consequently, when the hydrodynamic solution and freezeout are expressed in terms of energy density, chemical freezeout does not modify the hydrodynamic radial and elliptic flow velocities studied previously. Finally, we examine chemical freezeout within the hadronic cascade (RQMD). Once chemical freezeout is incorporated into the hydrodynamics, the final spectra and fireball lifetimes are insensitive to the temperature at which the switch from hydrodynamics to cascade is made. Closer inspection indicates that the pion spectrum in chemically frozen hydrodynamics is significantly cooler than in the hydro+cascade model. This difference is reflected in $v_{2}(p_{T})$. We extract the freezeout hadron density in RQMD and interpret it in thermal terms; the freezeout hadron density corresponds to a freezeout temperature of $T_{f}\approx100 $ MeV and $μ_π \approx 80 $ MeV.

Figures (10)

• Figure 1: Chemical potentials as a function of temperature at the SPS ($s/n_{B}$=42) for (a) $\pi$, $K$ and $\Lambda$ and (b) $\pi$ only. Eq. \ref{['MuFormula']} gives an approximate formula for these chemical potentials.
• Figure 2: The energy density as a function of temperature with and without chemical freezeout for the SPS ($s/n_{B}$=42).
• Figure 3: The (a) pressure, (b) sound speed squared and (c) entropy density as functions of the energy density with and without chemical freezeout at the SPS ($s/n_{B}$=42). The analogous curves at RHIC are only slightly different.
• Figure 4: The hydrodynamic solution (a) with and (b) without chemical freezeout at the SPS (PbPb, $\sqrt{s}$=17 GeV A, b=0 fm, $s/n_{B}$=42). The thick arcs show contours of constant energy density. The first contour indicates the start of the mixed phase, $e_{Q}$. The next three contours indicate energy densities corresponding to temperatures (a) T = 160, 120, 80 MeV with chemical freezeout and (b) T=163, 142 , 115 MeV without chemical freezeout, see Table \ref{['ttemperature']}. The thin lines shows contours of constant transverse fluid rapidity, $y_{T}=0.1, 0.2, \dots, 0.7$ . Walking along the thick arcs, the arc is divided into solid and dotted segments. 20% of the total entropy passing through the arc passes through each segment. $\left\langle y_{T} \right\rangle$ denotes the mean transverse rapidity (weighted with entropy) on the arc.
• Figure 5: Sensitivity of particle spectra at the SPS (PbPb, $\sqrt{s}$=17 GeV A, b=6 fm, $s/n_{B}$=42) to $T_{switch}$ with chemical freezeout, $\mu_{\pi}>0$ and without, $\mu_{\pi}=0$. The spectra are for $\pi^{-}$, $p$, and $\bar{p}$. The filled histograms are $T_{switch}=160$. The other curves are for $T_{switch}=117$.