Cosmic-ray ionisation in circumstellar discs

Galactic cosmic rays are a ubiquitous source of ionisation of the interstellar gas, competing with UV and X-ray photons as well as natural radioactivity in determining the fractional abundance of electrons, ions and charged dust grains in molecular clouds and circumstellar discs. We model the propagation of different components of Galactic cosmic rays versus the column density of the gas. Our study is focussed on the propagation at high densities, above a few g cm$^{-2}$, especially relevant for the inner regions of collapsing clouds and circumstellar discs. The propagation of primary and secondary CR particles (protons and heavier nuclei, electrons, positrons, and photons) is computed in the continuous slowing down approximation, diffusion approximation, or catastrophic approximation, by adopting a matching procedure for the different transport regimes. A choice of the proper regime depends on the nature of the dominant loss process, modelled as continuous or catastrophic. The CR ionisation rate is determined by CR protons and their secondary electrons below $approx 130$ g cm$^{-2}$ and by electron/positron pairs created by photon decay above $approx600$ g cm$^{-2}$. We show that a proper description of the particle transport is essential to compute the ionisation rate in the latter case, since the electron/positron differential fluxes depend sensitively on the fluxes of both protons and photons. Our results show that the CR ionisation rate in high-density environments, like, e.g., the inner parts of collapsing molecular clouds or the mid-plane of circumstellar discs, is larger than previously assumed. It does not decline exponentially with increasing column density, but follows a more complex behaviour due to the interplay of different processes governing the generation and propagation of secondary particles.