Elliptic flow at SPS and RHIC: from kinetic transport to hydrodynamics

Abstract

Anisotropic transverse flow is studied in Pb+Pb and Au+Au collisions at SPS and RHIC energies. The centrality and transverse momentum dependence at midrapidity of the elliptic flow coefficient v_2 is calculated in the hydrodynamic and low density limits. Hydrodynamics is found to agree well with the RHIC data for semicentral collisions up to transverse momenta of 1-1.5 GeV/c, but it considerably overestimates the measured elliptic flow at SPS energies. The low density limit LDL is inconsistent with the measured magnitude of v_2 at RHIC energies and with the shape of its p_t-dependence at both RHIC and SPS energies. The success of the hydrodynamic model points to very rapid thermalization in Au+Au collisions at RHIC and provides a serious challenge for kinetic approaches based on classical scattering of on-shell particles.

Figures (5)

• Figure 1: The number of participants $N_{\rm part}$, the initial transverse radii $R_x, R_y$, and the initial spatial deformation $\epsilon_x\equiv\delta$ for Au+Au at $\sqrt{s}=130\,A$ GeV, as functions of the scaled impact parameter $b/R$. For details see text.
• Figure 2: Elliptic flow for pions at midrapidity vs. centrality, for 158 $A$ GeV Pb+Pb collisions. Hydrodynamic calculations and results from the LDL are compared to NA49 data NA49v2NA49QM99. Numbers in brackets give $T_{\rm f}$ in MeV and the reduction from resonance decays, respectively.
• Figure 3: Centrality dependence of the elliptic flow coefficient $v_2$ for charged particles from Au+Au collisions at $\sqrt{s}= 130\,A$ GeV. The data STAR are shown with the quoted systematic error of $\pm 0.005$. For details see text.
• Figure 4: The elliptic flow of charged particles from Au+Au collisions at $\sqrt{s}=130\,A$ GeV vs. transverse momentum. Hydrodynamic calculations and predictions from the LDL are compared with the data STAR. The shape of the LDL curve reflects the weighting of different hadrons with their contribution to the charged particle spectrum; at small $p_t$ it is dominated by light pions, at high $p_t$ by heavy baryons.
• Figure 5: $p_t$-dependence of elliptic flow for pions (left) and protons (right) from Pb+Pb collisions at $\sqrt{s}=17\,A$ GeV with impact parameters $b<11$ fm. The data NA49v2 correspond to 6.5 fm $<b<$ 8 fm and are averaged over the forward rapidity interval $4<y<5$ while the hydrodynamic calculations apply to midrapidity $y=2.9$. The squares show the NA49 data after correction for azimuthal HBT correlations DBO00. For details see text.