Impact of cosmic-ray propagation on the chemistry and ionisation fraction of dark clouds

¹ Departamento de Astronomía, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Av. Esteban Iturra s/n Barrio Universitario, Casilla 160, Concepción, Chile
² Como Lake Center for Astrophysics, DiSAT, Università degli Studi dell’Insubria, via Valleggio 11, 22100 Como, Italy
³ INAF, Osservatorio Astronomico di Bologna, Via Gobetti 93/3, 40129 Bologna, Italy
⁴ Chemistry Department, Sapienza University of Rome, P.le A. Moro, 00185 Rome, Italy
⁵ INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
⁶ Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstr. 1, 85749 Garching bei München, Germany

^★ Corresponding author: gonzajaque2016@udec.cl

Received: 3 October 2024
Accepted: 30 April 2025

Abstract

Aims. A proper modelling of the cosmic-ray ionisation rate within gas clouds is crucial to describe their chemical evolution accurately. However, this modelling is computationally demanding because it requires the propagation of cosmic rays throughout the cloud over time. We present a more efficient approach that simultaneously guarantees a reliable estimate of the cosmic-ray impact on the chemistry of prestellar cores.

Methods. We introduce a numerical framework that mimics the cosmic-ray propagation within gas clouds and applies it to magnetohydrodynamic simulations performed with the code GIZMO. It simulates the cosmic-ray attenuation by computing the effective column density of H₂ that is traversed, which is estimated using the same kernel weighting approach as employed in the simulation. The obtained cosmic-ray ionisation rate is then used in post-processing to study the chemical evolution of the clouds.

Results. We found that cosmic-ray propagation affects deuterated and non-deuterated species significantly and that it depends on the assumed cosmic-ray spectrum. We explored correlations between the electron abundance, the cosmic-ray ionisation rate, and the abundance of the most relevant ions (HCO⁺, N₂H⁺, DCO⁺, N₂D⁺, and o-H₂D⁺), with the purpose of finding simple expressions that link them. We provide an analytical formula to estimate the ionisation fraction, X(e⁻), from observable tracers and applied it to existing observations of high-mass clumps. We obtained values of about 10⁻⁸, which is in line with previous works and with expectations for dense clouds. We also provide a linear fit to calculate the cosmic-ray ionisation rate from the local H₂ density, which is to be employed in three-dimensional simulations that do not include cosmic-ray propagation.