Molecular clouds are expected to emit non-thermal radiation due to cosmic ray interactions in the dense magnetized gas. Such emission is amplified if a cloud is located close to an accelerator of cosmic rays and if cosmic rays can leave the accelerator and diffusively reach the cloud. We consider the situation in which a molecular cloud is located in the proximity of a supernova remnant which is accelerating cosmic rays and gradually releasing them into the interstellar medium. We calculate the multiwavelength spectrum from radio to gamma rays which emerges from the cloud as the result of cosmic ray interactions. The total energy output is dominated by the gamma ray emission, which can exceed the emission from other bands by an order of magnitude or more. This suggests that some of the unidentified TeV sources detected so far, with no obvious or very weak counterpart in other wavelengths, might be associated with clouds illuminated by cosmic rays coming from a nearby source.
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