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.

The ionisation fraction is a fundamental quantity for the dynamics of the interstellar gas, in particular during the earliest stages of star formation, from the collapse of a molecular cloud core to the formation of an accretion disc. Before the formation of a protostar, cosmic-ray ionisation regulates the degree of coupling between gas and magnetic field in the densest parts of a cloud core, setting the timescale of magnetic field diffusion, see e.g. [1], and controlling the amount of magnetic braking of collapsing rotating envelopes [2,3].

Previous studies on cosmic-ray propagation [4,5,6,7,8] neglected the contribution of electron-positron pairs generated by photon decay and that of relativistic protons and electrons. A group of researchers - led by the AstroFIt2 fellow Marco Padovani and including Daniele Galli of the Osservatorio Astrofisico di Arcetri - showed that, while this approximation is appropriate for diffuse and dense molecular clouds, it becomes invalid at the high values of column densities characteristic of circumstellar discs, where cosmic-ray ionisation is dominated by both relativistic and secondary particles (see Fig. 1).


Fig.1: Ionisation diagram, explaining the effect of secondary particles that are generated (directly or indirectly) by CR protons and electrons through ionisation, pion decay, bremsstrahlung (BS), and pair production (pair). The secondary particles include electrons, positrons and electrons, and photons, all contributing to the respective ionisation routes.

Padovani et al. (2018)  modelled the various components of Galactic cosmic rays versus the column density of the gas, focusing on their propagation at high densities, above a few g cm-2, relevant for circumstellar discs.
They found that the cosmic-ray ionisation rate is determined by cosmic-ray protons and their secondary electrons below 130 g cm−2 and by electron-positron pairs created by photon decay above 600 g~cm−2. They showed that the cosmic-ray 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 [9]. 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 (see Fig. 2).


Fig.2: Ionisation rate per H2 molecule due to primary and secondary cosmic-ray species plotted vs. the surface density  (bottom scale) and the column density (top scale). The black line shows the total ionisation rate. Partial contributions include ionisation due to primary CR protons and electrons (blue and red lines, respectively), ionisation due to secondary electrons created by primary cosmic rays (orange line), and ionisation due to electrons and positrons created by charged pion decay and pair production (green line). The blue dashed line shows the proton contribution calculated with the continuous slowing down approximation approach. The horizontal dashed line at 1.4 10−22 s−1 indicates the total ionisation rate set by long-lived radioactive nuclei (LLR). For comparison, the total ionisation rate per H2 molecule ([9]; grey dashed line) is shown.

The main result of this paper is the characterisation of the CR ionisation rate at high column densities that turns out to be useful for numerical simulations and chemical models in order to interpret observations of circumstellar discs.

[1] Pinto et al. (2008)
[2] Galli et al. (2006) 
[3] Li et al. (2016) 
[4] Padovani et al. (2009) 
[5] Padovani & Galli (2011)
[6] Padovani & Galli (2013) 
[7] Padovani et al. (2013) 
[8] Padovani et al. (2014) 
[9] Umebayashi & Nakano (1981) 


Marco Padovani acknowledges funding from the European Unions Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 664931.