Hydrodynamic description of ultrarelativistic heavy-ion collisions

TL;DR

This review demonstrates that relativistic hydrodynamics successfully describes the bulk, strongly interacting matter created in RHIC heavy-ion collisions, from rapid thermalization to the development of collective radial and elliptic flow. By employing a hydrodynamic framework with a combined equation of state (EOS Q), Glauber-based initialization, and Cooper-Frye freeze-out, the authors show good agreement with central and semi-central Au+Au data for momentum spectra and elliptic flow up to moderate transverse momenta, implying early quark-gluon plasma formation and high energy densities. However, certain observables, notably two-particle correlations (HBT), challenge the hydrodynamic description and motivate hybrid approaches and further measurements. Overall, the work highlights the dynamical emergence of strong collective behavior in hot QCD matter and sets the stage for probing the quark-hadron transition through heavy-ion phenomenology.

Abstract

Relativistic hydrodynamics has been extensively applied to high energy heavy-ion collisions. We review hydrodynamic calculations for Au+Au collisions at RHIC energies and provide a comprehensive comparison between the model and experimental data. The model provides a very good description of all measured momentum distributions in central and semiperipheral Au+Au collisions, including the momentum anisotropies (elliptic flow) and systematic dependencies on the hadron rest masses up to transverse momenta of about 1.5--2 GeV/c. This provides impressive evidence that the bulk of the fireball matter shows efficient thermalization and behaves hydrodynamically. At higher p_t the hydrodynamic model begins to gradually break down, following an interesting pattern which we discuss. The elliptic flow anisotropy is shown to develop early in the collision and to provide important information about the early expansion stage, pointing to the formation of a highly equilibrated quark-gluon plasma at energy densities well above the deconfinement threshold. Two-particle momentum correlations provide information about the spatial structure of the fireball (size, deformation, flow) at the end of the collision. Hydrodynamic calculations of the two-particle correlation functions do not describe the data very well. Possible origins of the discrepancies are discussed but not fully resolved, and further measurements to help clarify this situation are suggested.

Figures (8)

• Figure 1: Equation of state of the Hagedorn resonance gas (EOS H), an ideal gas of massless particles (EOS I) and the Maxwellian connection of those two as discussed in the text (EOS Q). The figure shows the pressure as function or energy density at vanishing net baryon density.
• Figure 2: Left: Number of wounded nucleons and binary collisions as a function of impact parameter, for Au+Au collisions $\sqrt{s}=130\,A$ GeV ($\sigma_0=40$ mb). Right: Density of wounded nucleons and binary collisions in the center of the collision as a function of impact parameter.
• Figure 3: Density of binary collisions in the transverse plane for a Au+Au collision with impact parameter $b=7$ fm (left). Shown are contours of constant density together with the projection of the initial nuclei (dashed lines). The right plot shows the geometric eccentricity as a function of the impact parameter for the wounded nucleon and binary collision distributions.
• Figure 4: Left panel: Time evolution of the entropy density at three different points in the fireball (0, 3, and 5 fm from the center). Dashed lines indicate the expectations for pure one-dimensional and three-dimensional dilution, respectively. Right panel: Time evolution of the temperature at the same points. The plateau at $T{\,=\,}164$ MeV results from the transition of the corresponding fluid cells through the mixed phase.
• Figure 5: Left panel: Time evolution of the local expansion coefficient $\alpha = - \partial (\ln s) / \partial (\ln \tau)$ at three different fireball locations. The horizontal dashed lines indicate expectations for pure Bjorken ($\alpha =1$) and Hubble-like expansions ($\alpha = 3$). Right panel: The local expansion rate $\partial_\mu u^\mu$ multiplied by time, again compared to Bjorken and Hubble-like scaling expansions. Note that the expansion coefficient $\alpha$ decreases with radial distance from the center whereas the expansion rate shows the opposite behavior.