Quark-gluon-plasma evolution in scaling hydrodynamics

The relation between the rapidity density of produced particles in ultrarelativistic nuclear collisions and the maximum proper energy density ${\ensuremath{\epsilon}}_{0}$ is derived. The new scaling hydrodynamic equations of Bjorken, Kajantie, and McLerran are employed. The results exceed earlier estimates obtained with inside-outside cascade models and provide an independent estimate of ${\ensuremath{\epsilon}}_{0}$ from collision data. We also derive a lower bound on ${\ensuremath{\epsilon}}_{0}$ incorporating viscous heating and the first-order phase transition between the quark and hadronic phases. We infer that ${\ensuremath{\epsilon}}_{0}>2$ GeV/${\mathrm{fm}}^{3}$ can indeed be reached in the collision of heavy nuclei at cosmic-ray energies.