  All galaxies without a radio-loud AGN follow a tight correlation between
their global FIR and radio synchrotron luminosities, which is believed to be
ultimately the result of the formation of massive stars. Two colliding pairs of
galaxies, UGC12914/5 and UGC 813/6 deviate from this correlation and show an
excess of radio emission which in both cases originates to a large extent in a
gas bridge connecting the two galactic disks. We are aiming to clarify the
origin of the radio continuum emission from the bridge. The radio synchrotron
emission expected from the bridge regions is calculated, assuming that the
kinetic energy liberated in the predominantly gas dynamic interaction of the
respective interstellar media (ISM) has produced shock waves that efficiently
accelerate nuclei and electrons to relativistic energies. We present a model
for this acceleration and calculate the resulting radio emission, its spectral
index and the expected high-energy gamma-ray emission. It is found that the
nonthermal energy produced in the collision is large enough to explain the
radio emission from the bridge between the two galaxies. The calculated
spectral index at the present time also agrees with the observed value. The
deviation of these two interacting galaxy systems from the standard FIR-radio
correlation is consistent with the acceleration of an additional population of
electrons. This process is not related to star formation and therefore it is
expected that the systems do not follow the FIR-radio correlation. The
acceleration of relativistic electrons in shocks caused by an ISM collision, in
the same way as described here, is likely to take place in other systems as
well, as in galaxy clusters and groups or high-redshift systems.
