Gamma-ray emission from molecular clouds with the Cherenkov Telescope Array and the cosmic ray spectrum in the Galaxy

In this work we calculate the diffuse emission from molecular clouds (MCs) in the Galaxy at very high energy (from hundreds of GeV to hundreds of TeV).We present the results from the analysis of the simulated emission of these sources as it will be detected by the incoming imaging Cherenkov telescope detector, the Cherenkov telescope array (CTA) and we estimate the capabilities of such measurements to constrain the cosmic ray spectrum in the cloud. Molecular clouds are regions of the Galaxy, typically a few tens of parsec in size, where the density of cold molecular gas is often orders of magnitude higher than that of the diffuse interstellar medium. The MCs high gas density enhances the gamma-ray emission produced through the hadronic channel by cosmic ray nuclei interacting with the ambient gas. The gamma-ray emission from MCs depends only upon the total mass and the distance of the cloud. Assuming to know them from radio observations, one can thus test the cosmic ray spectrum far away from the Earth, in regions of the Galaxy, where no direct measurements of the cosmic ray spectrum can be carried out. MCs serve then as cosmic ray barometers.