  We present a new high-resolution N-body/SPH simulation of an encounter of two
gas-rich disk galaxies which closely matches the morphology and kinematics of
the interacting Antennae galaxies (NGC 4038/39). The simulation includes
radiative cooling, star formation and feedback from SNII. The large-scale
morphology and kinematics are determined by the internal structure and the
orbit of the progenitor disks. The properties of the central region, in
particular the starburst in the overlap region, only match the observations for
a very short time interval of ~20 Myr after the second encounter. This
indicates that the Antennae galaxies are in a special phase only about 40 Myr
after the second encounter and 50 Myr before their final collision. This is the
only phase in the simulation when a gas-rich overlap region between the nuclei
is forming accompanied by enhanced star formation. The star formation rate as
well as the recent star formation history in the central region agree well with
observational estimates. For the first time this new model explains the
distributed extra-nuclear star formation in the Antennae galaxies as a
consequence of the recent second encounter. The proposed model predicts that
the Antennae are in a later merger stage than the Mice (NGC 4676) and would
therefore lose their first place in the classical Toomre sequence.
