A Hydrodynamic Description of Heavy Ion Collisions at the SPS and RHIC

TL;DR

This work develops a hydro+cascade framework to describe relativistic heavy-ion collisions across SPS to RHIC energies, using an EOS with tunable latent heat to capture both the soft and hard features of the QCD phase transition. By coupling 2D relativistic hydrodynamics to a hadronic cascade via Cooper-Frye emission, and by varying the latent-heat parameter LH, the authors reproduce radial and elliptic flow observables for multiple particle species, centralities, and energies, with LH8 providing the best global agreement. The study shows that strong early QGP pressure, followed by differential hadronic freezeout, naturally explains the RHIC-era data, including the elevated ⟨M_T⟩, the p_T-dependent elliptic flow, and the anomalous ⟨p̄⟩/π− ratios, while highlighting the importance of hadronic rescattering for final-state spectra. The results underscore the sensitivity of collective flow to the EOS and freezeout dynamics, offering a quantitative link between macroscopic fluid behavior and microscopic hadronic interactions, and point to ongoing challenges such as HBT radii to be resolved in future work.

Abstract

A hydrodynamic + cascade model of relativistic heavy ion collisions is presented and compared to available hadronic data from the SPS to RHIC. The model consistently reproduces the radial and elliptic flow data for different particles, collision energies, and impact parameters. Three ingredients are essential to the success: (a) a reasonable EOS exhibiting the hard and soft features of the QCD phase transition, (b) thermal hadronization at the phase boundary, and (c) subsequent hadronic rescattering. Some features of the RHIC data are readily explained: (i) the observed elliptic flow and its dependence on $p_{T}$ and mass, (ii) the anomalous $\bar{p}/π^{-}$ ratio for $p_{T} \approx 2.0$ GeV, (iii) the difference in the slope parameters measured by the STAR and PHENIX collaborations, and (iv) the respectively strong and weak impact parameter dependence of the $\bar{p}$ and $φ$ slope parameters. For an EOS without the hard and soft features of the QCD phase transition, the broad consistency with the data is lost.

Figures (30)

• Figure 1: The derived quantities $\epsilon$ and $R_{rms}/R_{A}$, defined by Eq. \ref{['GlauberEquRms']} and \ref{['GlauberEquEps']}, as a function of the number of participants relative to the maximum number. The axis on top of the graph shows the impact parameter b relative to $2 R_{A}$. The curves are drawn for PbPb collisions at the SPS, but depend only slightly on the colliding system and energy.
• Figure 2: The pressure ($p$) versus energy density ($e$) for different EOS. EOS LH8, LH16 and LH$\infty$ become increasingly soft and have latent heats $0.8\,\hbox{GeV/fm}^{3}$, $1.6\,\hbox{GeV/fm}^{3}$, and $\infty$. The EOS are shown along the adiabatic path for SPS initial conditions, $s/n_{B}=42$. For RHIC initial conditions, $s/n_{B}=150$, the changes are small.
• Figure 3: The left and right sides show the hydrodynamic solution at the SPS and RHIC for different EOS. The thin lines show contours of constant transverse fluid rapidity ($v_{T} = \tanh(y_{T})$) with values 0.1,0.2,...,0.7 . The thick lines show contours of constant energy density. $e_{120}$ denotes the energy density where $T=120\,\hbox{MeV}$. $e_{H}$ and $e_{Q}$ denote the energy density (for LH8) where the matter shifts from hadronic to mixed and mixed to a QGP, respectively. The shift to RQMD is made at $e_{H}$. $\langle y_{T} \rangle$ denotes the mean transverse rapidity weighted with the total entropy flowing through the energy density contours. Walking along these contours, the line is broken into segments by dashed and then solid lines. 20% of the total entropy passing through the entire arc passes through each segment.
• Figure 4:
• Figure 5: Following Kolb $et$$al.$Kolb-UU, we show the anisotropy of the stress tensor, $\epsilon_{p}$ (a measure of elliptic flow) for the EOS used in this work. The solid (dashed) curves are for RHIC (SPS). The solid (open) symbols indicate when the center of the fluid passes through a temperature of 160 MeV (120 MeV). The solid symbols are therefore representative of the switching temperature to RQMD or $e_H$ in Fig. \ref{['FSurface']}.