Extending the hydrodynamical description of heavy-ion collisions to the "outer edge" of the fireball

Abstract

It is well known that relativistic hydrodynamics provides very good description of heavy-ion collisions at RHIC/LHC energies up to transverse momenta $p_\perp\sim 2\, \text{GeV}$. In this paper, we suggest that this description can be extended to higher $p_\perp\sim 6\, \text{GeV}$, beyond which hard collisions contribute. While most previous work focused on a part of the freezeout surface at the latest proper time (referred to in this work as the "lid"), we focus on the complementary part, to be referred as "the outer edge," where the highest transverse rapidity of flow $\kappa\sim 1.4$ is achieved. We study this surface analytically, using the Riemann rarefaction wave, and numerically, using MUSIC numerical hydrodynamic code. We also use an improved freezeout condition, where the collision rate equals the expansion rate. For central collisions, we observe good description of spectra for $\pi,K,N$ in central PbPb LHC collisions in this extended region. We further suggest that "the outer edge" has very small azimuthal asymmetry even for non-central collisions, smaller than predicted by standard hydrodynamics.