  We discuss a recently found family of exact and analytic, finite and
accelerating, 1+1 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+Au collisions at RHIC with $\sqrt{s_{NN}}=130$
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
non-monotonic dependence of the initial energy density on the energy of heavy
ion collisions.
