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Abstract

Cosmic rays are a global source of ionization, and the ionization fraction represents a fundamental parameter in the interstellar medium. Ions couple to magnetic fields, and affect the chemistry and the dynamics of star-forming regions as well as planetary atmospheres. However, the cosmic ray ionization rate represents one of the bottlenecks for astrochemical models, and its determination is one of the most puzzling problems in astrophysics. While for diffuse clouds reasonable values have been provided from H₃⁺ observations, for dense clouds, due to the lack of rotational transitions, this is not possible, and estimates are strongly biased by the employed model. We present here an analytical expression, obtained from first principles, to estimate the cosmic ray ionization rate from observational quantities. The theoretical predictions are validated with high-resolution 3D numerical simulations and applied to the well-known core L1544; we obtained an estimate of ζ₂ ∼ 2–3 × 10⁻¹⁷ s⁻¹. Our results and the analytical formulae provided represent the first model-independent robust tool to probe the cosmic ray ionization rate in the densest part of star-forming regions (on spatial scales of R ≤ 0.05 pc). An error analysis is presented to give statistical relevance to our study.