Relativistic Hydrodynamics for Heavy--Ion Collisions: Freeze--Out and Particle Spectra

We investigate freeze--out in hydrodynamic models for relativistic heavy--ion collisions. In particular, instantaneous freeze--out across a hypersurface of constant temperature (``isothermal'' freeze--out) is compared with that across a hypersurface at constant time in the center-of-momentum frame (``isochronous'' freeze--out). For one--dimensional (longitudinal) expansion the rapidity distributions are shown to differ significantly in the two scenarios, while the transverse momentum spectra are remarkably similar. We also investigate the rapidity distribution in greater detail and show that the Gaussian-like shape of this distribution commonly associated with the Landau expansion model in general emerges only if one neglects contributions from time-like parts of the isothermal freeze--out hypersurface.