Hydrodynamic Models for Heavy Ion Collisions

TL;DR

This work reviews how relativistic hydrodynamics models the expansion of matter created in ultra-relativistic heavy-ion collisions, linking initial parton production and saturation-based bounds to a hydrodynamic evolution governed by an equation of state that spans a QGP and a hadron resonance gas. It combines hadron spectra, elliptic flow, and Bose-Einstein correlations with electromagnetic emission (photons and dileptons) to test the approach against SPS and RHIC data, highlighting where ideal hydrodynamics succeeds and where viscosity and hadronic dynamics introduce deviations. The analysis emphasizes the sensitivity of observables to initial conditions, the thermalization time, and the decoupling criteria, and shows that electromagnetic probes can serve as thermometers for the hottest early stages. Overall, the framework captures the bulk, low-$p_T$ behavior and collective flow, while pointing to the need for refined treatments of the early-time dynamics, finite viscosity, and continuous emission to fully describe all data and extend predictions to the LHC.

Abstract

Application of hydrodynamics for modeling of heavy-ion collisions is reviewed. We consider several physical observables that can be calculated in this approach and compare them to the experimental measurements.

Figures (13)

• Figure 1: Transverse dependence of the initial energy distribution for a gold-on-gold collision at the Relativistic Heavy Ion Collider (RHIC) (dashed line) and lead-on-lead collision at the Large Hadron Collider (LHC) energy (solid line). The saturation scale is $p_{\rm sat} =1.16$ GeV at RHIC and 2.03 GeV at the LHC, with formation times of 0.170 fm/$c$ and 0.100 fm/$c$, respectively. The dashed-dotted line shows the energy density at the LHC if $\tau_i=0.170$ fm/$c$ is used, emphasizing the strong dependence of initial energy density on the assumed initial time.
• Figure 2: Temperature contours at 300 (in quark-gluon plasma QGP), 150 and 120 MeV (hadron resonance gas, HRG), and the boundaries of mixed phase (MP) with QGP and HRG at $T_c=167$ MeV. Flow lines are also shown. Initial conditions are from a pQCD + saturation calculation at $\sqrt{s_{NN}}=200$ GeV. Note that the slope of the flow line is related to the velocity and the curvature to the acceleration.
• Figure 3: The effect of flow on the spectrum of kaons. Temperature is kept unchanged and the spectrum is shown for radially flowing matter at velocities $v_r=0,\,\, 0.6$ and $0.8$.
• Figure 4: Transverse momentum spectra of positive pions, positive kaons, and protons at $y=0$ in the most central 5 % of Au+Au collisions at $\sqrt{s_{NN}}=130$ GeV. The solid and dotted lines show our hydrodynamic results for freeze-out temperatures $T_{\rm dec}=150$ MeV and $T_{\rm dec}=120$ MeV, respectively. The PHENIX data Adcox:2001mf is plotted with the given total error bars. Note the scaling factors 10 and 1000 for kaons and protons, respectively. Both the hydrodynamic result and the PHENIX data contain the feed-down contributions from hyperons.
• Figure 5: As Figure \ref{['fig:positive130']} but at $\sqrt{s_{NN}}=200$ GeV. The PHENIX data Adler:2003cb and the BRAHMS data Bearden:2004yxBearden:2003hx are shown with statistical errors and the STAR data Adams:2003xp with the given total error bars. The hydrodynamic calculation and the PHENIX data are without the hyperon feed-down contributions whereas the STAR and BRAHMS data contain the feed-down.