We analyze the processes governing cosmic-ray (CR) penetration into molecular
clouds and the resulting generation of gamma-ray emission. The density of CRs
inside a cloud is depleted at lower energies due to the self-excited MHD
turbulence. The depletion depends on the effective gas column density ("size")
of the cloud. We consider two different environments where the depletion effect
is expected to be observed. For the Central Molecular Zone, the expected range
of CR energy depletion is E≲10 GeV, leading to the depletion of
gamma-ray flux below Eγ​≈2 GeV. This effect can be important for
the interpretation of the GeV gamma-ray excess in the Galactic Center, which
has been revealed from the standard model of CR propagation (assuming the CR
spectrum inside a cloud to be equal to the interstellar spectrum). Furthermore,
recent observations of some local molecular clouds suggest the depletion of the
gamma-ray emission, indicating possible self-modulation of the penetrating
low-energy CRs.Comment: 10 pages, 5 figures, accepted for publication in Ap