Hydrodynamical description of collective flow

TL;DR

This review outlines how relativistic hydrodynamics can describe collective flow in ultrarelativistic heavy-ion collisions by linking conservation laws to the equation of state and transport properties. It details the standard hydro framework, including initialization strategies, EOS choices, and freeze-out prescriptions, and analyzes how transverse flow and flow anisotropies, especially elliptic flow, arise from pressure gradients and initial geometry. The article discusses how RHIC data constrain the EOS and imply early thermalization, while highlighting model sensitivities to initial conditions, chemical vs kinetic freeze-out, and resonance decays. Overall, hydrodynamics provides a robust, if idealized, description of flow phenomena and remains essential for interpreting heavy-ion collision data, with open questions about thermalization mechanisms and detailed early-time dynamics guiding future work.

Abstract

I review how hydrodynamical flow is related to the observed flow in ultrarelativistic heavy ion collisions and how initial conditions, equation of state and freeze-out temperature affect flow in hydrodynamical models.

Figures (14)

• Figure 1: Charged particle yield per participating nucleon pair at midrapidity as a function of the number of participants for different initialization models discussed in the textKolb:2001b. All curves were normalized to $dN_{ch}/d\eta = 550$ for 5% of the most central collisions ($b=2.3$ fm.) The data are from refs.Phobos-multStar-mult.
• Figure 2: Slope parameters as a function of particle mass for (a) Pb+Pb central collisions at the SPS ($\sqrt{s}=17.2$ GeV/$A$) and (b) Au+Au central collisions at RHIC ($\sqrt{s}=130$ GeV/$A$). From ref.NuXu.
• Figure 3: Hydrodynamically calculated slope parameters as a function of particle mass in central collisions at RHIC ($\sqrt{s}=130$ GeV/$A$). In the left panel the slope parameters are from fits to spectra in two different $p_T$ intervals. In the right panel the fits are done in interval $0.1<p_T<1$ GeV/$c$ for spectra after resonance decays (w. reso), before resonance decays (therm) and for thermal spectra immediately after hadronization at $T_c=165$ MeV.
• Figure 4: Schematic representation of the collision geometry and different anisotropies of flow seen in the transverse plane. P and T denote the projectile and target nuclei, respectively. Top: directed flow in projectile rapidity region, positive (left) and negative (right). Bottom: elliptic flow, in plane (left) and out of plane (right). From ref.Ollitrault:1997.
• Figure 5: Reaction plane of a semi-central $Au+Au$ collision for impact parameter $b = 7$ fm. The density of dots is proportional to the number of participating nucleons in the overlap region. From ref.hh.