We discuss a recently found family of exact and analytic, finite and accelerating, [Formula: see text]-dimensional solutions of perfect fluid relativistic hydrodynamics to describe the pseudorapidity densities and longitudinal HBT-radii and to estimate the lifetime parameter and the initial energy density of the expanding fireball in Au[Formula: see text]+[Formula: see text]Au collisions at RHIC with [Formula: see text] GeV and 200 GeV colliding energies. From these exact solutions of relativistic hydrodynamics, we derive a simple and powerful formula to describe the pseudorapidity density distributions in high-energy proton–proton and heavy-ion collisions, and derive the scaling of the longitudinal HBT radius parameter as a function of the pseudorapidity density. We improve upon several oversimplifications in Bjorken’s famous initial energy density estimate, and apply our results to estimate the initial energy densities of high-energy reactions with data-driven pseudorapidity distributions. When compared to similar estimates at the LHC energies, our results indicate a surprising and nonmonotonic dependence of the initial energy density on the energy of heavy-ion collisions.
Initial energy density and gluon distribution from the glasma in heavy-ion collisions
