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We investigate ionization and heating of gas in the dense, shieldedclumps/cores of molecular clouds bathed by an influx of energetic, chargedcosmic rays (CRs). These molecular clouds have complex structures, withsubstantial variation in their physical properties over a wide range of lengthscales. The propagation and distribution of the CRs is thus regulatedaccordingly, in particular, by the magnetic fields threaded through the cloudsand into the dense regions within. We have found that a specific heating ratereaching $10^{-26}$ erg cm$^{-3}$ s$^{-1}$ can be sustained in the denseclumps/cores for Galactic environments, and this rate increases with CR energydensity. The propagation of CRs and heating rates in some star-formingfilaments identified in IC 5146 are calculated, with the CR diffusioncoefficients in these structures determined from magnetic field fluctuationsinferred from optical and near-infrared polarizations of starlight, which ispresumably a magnetic-field tracer. Our calculations indicate that CR heatingcan vary by nearly three orders of magnitude between different filaments withina cloud due to different levels of CR penetration. The CR ionization rate amongthese filaments is similar. The equilibrium temperature that could bemaintained by CR heating alone is of order $1~{\rm K}$ in a Galacticenvironment, but this value would be higher in strongly star-formingenvironments, thus causing an increase in the Jeans mass of their molecularclouds.

Observational signatures of cosmic ray interactions in molecular clouds