Rigorous theory for secondary cosmic-ray ionization

TL;DR

This paper provides a rigorous theoretical calculation of secondary cosmic-ray ionization rates in molecular gas, revealing their dependence on gas column density and primary ionization rates, with implications for dense interstellar environments.

Contribution

The paper introduces a rigorous method to compute secondary ionization rates as a function of gas density, improving accuracy over previous approximations.

Findings

The ratio of secondary to primary ionization rates increases with gas column density.

The ratio can significantly exceed the commonly assumed value of 0.67.

For soft interstellar spectra, the ratio's dependence on spectral shape is minimal.

Abstract

The energy spectrum of electrons produced in molecular gas by interstellar cosmic rays (CRs) is rigorously calculated as a function of gas column density $N$ traversed by the CRs. This allows us to accurately compute the local value of the secondary ionization rate of molecular hydrogen, $\zeta_{\rm sec}(N)$, as a function of the local primary ionization rate, $\zeta_p(N)$. The ratio $\zeta_{\rm sec}/\zeta_p$ increases monotonically with $N$, and can considerably exceed the value of $\approx0.67$ commonly adopted in the literature. For sufficiently soft interstellar spectra, the dependence $\zeta_{\rm sec}/\zeta_p$ versus $N$ is practically insensitive to their particular shape and thus is a general characteristic of the secondary CR ionization in dense gas.