On the formation of Hubble flow in Little Bangs

A dynamical appearance of scaling solutions in the relativistic hydrodynamics applied to describe ultra-relativistic heavy-ion collisions is studied. We consider the boost-invariant cylindrically symmetric systems and the effects of the phase transition are taken into account by using a temperature dependent sound velocity inferred from the lattice simulations of QCD. We find that the transverse flow acquires the scaling form r/t within the short evolution times, 10 - 15 fm, only if the initial transverse flow originating from the pre-equilibrium collective behavior is present at the initial stage of the hydrodynamic evolution. The amount of such pre-equilibrium flow is correlated with the initial pressure gradient; larger gradients require smaller initial flow. The results of the numerical calculations support the phenomenological parameterizations used in the Blast-Wave, Buda-Lund, and Cracow models of the freeze-out process.