[Paper Review] A Hydrodynamic Description of Heavy Ion Collisions at the SPS and RHIC

D. Teaney, J. Lauret+1 more|arXiv (Cornell University)|Oct 14, 2001

High-Energy Particle Collisions Research16 citations

TL;DR

This paper presents a hydrodynamic + cascade model that successfully describes radial and elliptic flow data from SPS to RHIC heavy-ion collisions by incorporating a QCD equation of state with both soft (phase transition) and hard (QGP) features, thermal hadronization at the phase boundary, and subsequent hadronic rescattering. The model quantitatively reproduces key RHIC observations, including the $p_T$-dependent $v_2$ slope, anomalous $\bar{p}/\pi^-$ ratios, and differing slope parameter behaviors for $\bar{p}$ and $\phi$, with the LH8 equation of state providing the best agreement.

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.

Motivation & Objective

• To develop a consistent hydrodynamic model that explains radial and elliptic flow data across SPS and RHIC energies.
• To determine whether the observed momentum correlations in heavy-ion collisions arise from hydrodynamic expansion driven by QCD phase transition features.
• To test the necessity of soft and hard components in the equation of state (EOS) for reproducing experimental flow data.
• To assess the role of thermal hadronization at the phase boundary and post-freezeout hadronic rescattering in shaping final-state spectra.
• To resolve discrepancies in slope parameters between STAR and PHENIX by modeling differential freezeout and rescattering effects.

Proposed method

• A relativistic hydrodynamic model is used to simulate the space-time evolution of the quark-gluon plasma and hadronic matter from initial energy density to freezeout.
• The model employs a QCD-inspired equation of state (EOS) with both soft (near-zero speed of sound) and hard (speed of sound ≈ 1/√3) regions, representing the phase transition and QGP phases.
• Thermal hadronization is implemented at the phase boundary, ensuring consistent particle production at the critical temperature $T_c \approx 160$ MeV.
• Post-hydrodynamic hadronic rescattering is included via a cascade model to account for final-state interactions before particle detection.
• The model computes radial flow ($v_r$) and elliptic flow ($v_2$) as functions of transverse momentum ($p_T$), particle type, and impact parameter.
• Simulations are compared to SPS and RHIC data on $m_T$ spectra, $v_2(p_T)$, and particle ratios to constrain the EOS and freezeout dynamics.

Experimental results

Research questions

• RQ1 Can a hydrodynamic model with a QCD-motivated equation of state reproduce the observed radial and elliptic flow across SPS and RHIC energies?
• RQ2 What is the role of the QCD phase transition's soft and hard features in shaping the collective flow of hadrons?
• RQ3 Why do the $\bar{p}/\pi^-$ ratios and slope parameters differ between STAR and PHENIX at RHIC, and can this be explained by differential freezeout and rescattering?
• RQ4 How does the inclusion of hadronic rescattering affect the $p_T$ dependence of $v_2$ and the final spectra?
• RQ5 Which equation of state (e.g., LH8, resonance gas, LH∞) best reproduces the full set of flow and spectral data?

Key findings

• The hydrodynamic + cascade model with the LH8 equation of state provides the best quantitative agreement with radial and elliptic flow data across SPS and RHIC energies.
• The model successfully explains the anomalous $\bar{p}/\pi^-$ ratio at $p_T \approx 2.0$ GeV, attributed to differential freezeout and rescattering effects.
• The $p_T$-dependence of $v_2$ is well reproduced, with strong curvature indicating a violent transverse expansion consistent with hydrodynamic dynamics.
• The model accounts for the differing impact parameter dependence of $\bar{p}$ and $\phi$ slope parameters, with $\bar{p}$ showing strong $b$-dependence due to late freezeout and rescattering.
• An EOS without soft features (e.g., resonance gas) fails to reproduce multi-strange baryon flow and overpredicts $v_2$, while an EOS without hard features (e.g., LH∞) produces spectra that are too soft and $v_2(p_T)$ that is qualitatively incorrect.
• The HBT radii predicted by the model are approximately 50% larger than observed at RHIC, indicating the model's expansion time is too long, suggesting a need for improved freezeout dynamics.