Cosmic-ray ionisation in circumstellar discs

Context. Galactic cosmic rays (CRs) 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. Aims. We model the propagation of various components of Galactic CRs 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. Methods. 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 various transport regimes. A choice of the proper regime depends on the nature of the dominant loss process modelled as continuous or catastrophic. Results. The CR ionisation rate is determined by CR protons and their secondary electrons below approximate to 130 g cm(-2) and by electronpositron pairs created by photon decay above approximate to 600 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 and positron differential fluxes depend sensitively on the fluxes of both protons and photons. Conclusions. Our results show that the CR ionisation rate in high-density environments, such as the inner parts of collapsing molecular clouds or the mid-plane of circumstellar discs, is higher than previously assumed. It does not decline exponentially with increasing column density, but follows a more complex behaviour because of the interplay of the different processes governing the generation and propagation of secondary particles.