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.
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