Initial condition for hydrodynamics, partonic free streaming, and the uniform description of soft observables at RHIC

TL;DR

This work investigates the hydrodynamic evolution of the system formed in ultrarelativistic heavy-ion collisions and finds that an appropriate choice of the initial condition, specifically a simple two-dimensional Gaussian profile for the transverse energy, leads to a uniform description of soft observables measured at the relativisticheavy-ion collider.

Abstract

We investigate the role of the initial condition used for the hydrodynamic evolution of the system formed in ultra-relativistic heavy-ion collisions and find that an appropriate choice motivated by the models of early-stage dynamics, specifically a simple two-dimensional Gaussian profile, leads to a uniform description of soft observables measured in the Relativistic Heavy-Ion Collider (RHIC). In particular, the transverse-momentum spectra, the elliptic-flow, and the Hanbury-Brown--Twiss correlation radii, including the ratio R_out/R_side as well as the dependence of the radii on the azimuthal angle (azHBT), are properly described. We use the perfect-fluid hydrodynamics with a realistic equation of state based on lattice calculations and the hadronic gas at high and low temperatures, respectively. We also show that the inclusion of the partonic free-streaming in the early stage allows to delay the start of the hydrodynamical description to comfortable times of the order of 1 fm/c. Free streaming broadens the initial energy-density profile, but generates the initial transverse and elliptic flow. The data may be described equally well when the hydrodynamics is started early, or with a delay due to partonic free-streaming.

Figures (4)

• Figure 1: (Color online) The transverse-momentum spectra of pions, kaons and protons for the centrality class $c$=0-5% (the upper panel) and $c$=20-30% (the middle panel), and the transverse-momentum dependence of the elliptic flow coefficient $v_2$ for the centrality class $c$=20-40% (the lower panel). The darker (lighter) lines/bands describe the model results for the case without (with) free-streaming. The PHENIX data are taken from Refs. Adler:2003cbAdler:2003kt.
• Figure 2: (Color online) The transverse-momentum dependence of the HBT radii $R_{\rm side}$ (a), $R_{\rm out}$ (b), $R_{\rm long}$ (c), and the ratio $R_{\rm out}/R_{\rm side}$ (d) for central collisions. The darker (lighter) lines describe the results without (with) free-streaming. The STAR data are from Ref. Adams:2004yc.
• Figure 3: (Color online) Sections of the energy-density profile $\epsilon$ (gaussian-like curves) normalized to unity at the origin, and of the velocity profile $v=\sqrt{v^2_x+v^2_y}$ (curves starting at the origin), cut along the $x$ axis (solid lines) and $y$-axis (dashed lines). The initial profile is from Eq. (\ref{['profile']}) for centrality 20-40% at $\tau_0=025$ fm. The $\epsilon$ profiles are for $\tau=\tau_0=0.25$, $1$, and $2$ fm, while the velocity profiles are for $\tau=1$ and $2$ fm, all from bottom to top. We note that the flow is azimuthally asymmetric and stronger along the $x$ axis.
• Figure 4: (Color online) Study of azHBT: The quantities $R^2_{{\rm side},2}/R^2_{{\rm side},0}$ and $R^2_{{\rm out},2}/R^2_{{\rm side},0}$ from the model (bands) and experiment Adams:2003ra (points), plotted as functions of the transverse momentum of the pion pair.