Excitation of molecular hydrogen by cosmic-ray protons

Low-energy cosmic rays ($E\lesssim 1$ GeV) are responsible for the ionisation and heating of molecular clouds. While the role of supra-thermal electrons produced in the ionisation process in inducing excitation of the ambient gas (mostly molecular hydrogen) has been studied in detail, the role of primary cosmic-ray nuclei (protons and heavier nuclei) has been generally neglected. Here, we introduce, for the first time, cross sections for proton impact on H$_2$, calculated using the semi-classical implementation of the molecular convergent close-coupling method. Our findings show that proton-induced H$_2$ excitation is comparable in magnitude to that caused by electrons. We discuss the possible implications on the estimate of the cosmic-ray ionisation rate from observations in the near-infrared domain and on the cosmic-ray-induced H$_2$ ultraviolet luminescence. We also derive a new approximated analytical parameterisation of the spectrum of secondary electrons that can be easily incorporated in numerical codes.