Centrality dependence of multiplicity, transverse energy, and elliptic flow from hydrodynamics

TL;DR

This study probes how the centrality dependence of multiplicity, transverse energy, and elliptic flow arises in relativistic heavy-ion collisions within a boost-invariant hydrodynamic framework. By comparing five initialization schemes—including soft and hard scaling for energy or entropy, and a saturation model—the authors show that dN_ch/dy is highly sensitive to the initial density profile, whereas the integrated elliptic flow v2 and the differential v2(pT) for minimum-bias charged hadrons are remarkably stable against these initial conditions. The results favor a scenario with a significant hard (binary-collision) component in initial energy deposition, yet reveal a notable cancellation between changes in initial geometry and entropy production when predicting v2 observables. These findings support the hydrodynamic description at RHIC energies and provide constraints on the initial-state physics and the equation of state, while highlighting the importance of potential event-by-event fluctuations for future investigations.

Abstract

The centrality dependence of the charged multiplicity, transverse energy, and elliptic flow coefficient is studied in a hydrodynamic model, using a variety of different initializations which model the initial energy or entropy production process as a hard or soft process, respectively. While the charged multiplicity depends strongly on the chosen initialization, the p_t-integrated elliptic flow for charged particles as a function of charged particle multiplicity and the p_t-differential elliptic flow for charged particles in minimum bias events turn out to be almost independent of the initial energy density profile.

Figures (10)

• Figure 1: Number of participating ("wounded") nucleons and of binary nucleon-nucleon collisions as functions of impact parameter. This and all following figures refer to Au+Au collisions at $\sqrt{s}=130\,A$ GeV.
• Figure 2: The formation and initial thermalization time $\tau_{\rm sat}(b){\,\equiv\,}\tau_{\rm sat}(\bbox{s}{\,=\,}0;\bbox{b}){\,=\,}1/p_{\rm sat}$ in the saturation model, as a function of impact parameter $b$.
• Figure 3: Initial energy density profiles in the transverse plane for the five different initialization models described in this Section. Top: $b{\,=\,}0$. Bottom: $b{\,=\,}10$ fm. In each case two cuts in $x$-direction are shown, one for $y{\,=\,}0$ and one for $y{\,=\,}5$ fm. For the saturation model ("sat.") the profile was hydrodynamically propagated from the initial thermalization time assumed in that model to $\tau_0=0.6$ fm/$c$ where the hydrodynamic evolution was started for the other four models.
• Figure 4: Initial spatial anisotropy as a function of impact parameter, for the different initializations.
• Figure 5: Charged particle yield per participating nucleon pair at midrapidity as a function of the number of participants. All curves were normalized to $dN_{\rm ch}/dy=670$ for central ($b{\,=\,}0$) collisions (see discussion below Fig. \ref{['F3']}). The top panel gives the rapidity, the bottom panel the pseudorapidity density. The data are taken from Refs. PHOBOSPHENIXRoland.