Cosmic-ray ionisation in circumstellar discs

Abstract

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 ≈ 130 g cm −2 and by electronpositron pairs created by photon decay above ≈ 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.

Impact of Low-Energy Cosmic Rays on Star Formation

“…Since the pion rest mass is significant, CR protons lose a non-negligible fraction of their energy in each collision (Schlickeiser, 2002). Padovani et al (2018b) showed that CSDA works for E 25 MeV; according to Fig. 3, this corresponds to column densities N 7 × 10 22 cm −2 .…”

“…Thus, we adopt the concept of the guiding centre for CRs and consider their propagation along the local magnetic field, with coordinate s measured along the field line. We introduce the effective column density of gas traversed by a CR particle before it reaches a given point (Padovani et al, 2018b),…”

“…3 In Padovani et al (2018b), the total column density of all gaseous species was used (assuming all the hydrogen to be in molecular form), whereas N in Eq. (1) is the total column density of hydrogen atoms.…”

“…(1) is the total column density of hydrogen atoms. Therefore, N in Silsbee and Ivlev (2019) is a factor of 1.67 higher than that in Padovani et al (2018b), which is taken into account in the value of L 0 .…”

“…where σ ion p,H 2 (E) is the ionisation cross section for molecular hydrogen. For protons with energies between 10 5 eV and 5 × 10 8 eV, the ratio between L p (E) and σ ion p,H 2 (E) is nearly constant and equal to ∼ 37 eV (Cravens and Dalgarno, 1978;Padovani et al, 2018b). This fact allows us to replace the cross section in Eq.…”