Cosmic rays in molecular clouds probed by H2 rovibrational lines - Perspectives for the James Webb Space Telescope (Corrigendum)

Marco Padovani; Shmuel Bialy; Daniele Galli; Alexei V. Ivlev; Tommaso Grassi; Liam H. Scarlett; Una S. Rehill; Mark C. Zammit; Dmitry V. Fursa; Igor Bray

doi:10.1051/0004-6361/202558164e

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A&A, 704 (2025) C2

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Erratum

This article is an erratum for:
[https://doi.org/10.1051/0004-6361/202142560]

Issue		A&A Volume 704, December 2025


Article Number		C2
Number of page(s)		1
Section		Interstellar and circumstellar matter
DOI		https://doi.org/10.1051/0004-6361/202558164e
Published online		19 December 2025

A&A, 704, C2 (2025)

Cosmic rays in molecular clouds probed by H₂ rovibrational lines

Perspectives for the James Webb Space Telescope (Corrigendum)

Marco Padovani¹^★, Shmuel Bialy², Daniele Galli¹, Alexei V. Ivlev³, Tommaso Grassi³, Liam H. Scarlett⁴, Una S. Rehill⁴, Mark C. Zammit⁵, Dmitry V. Fursa⁴ and Igor Bray⁴

¹ INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
² Department of Astronomy, University of Maryland, College Park, MD 20742, USA
³ Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstr. 1, 85748 Garching, Germany
⁴ Curtin Institute for Computation and Department of Physics and Astronomy, Curtin University, Perth, Western Australia 6102, Australia
⁵ Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Key words: molecular processes / ISM: clouds / cosmic rays / infrared: ISM / errata, addenda

Erratum for: A&A, 658, A189 (2022), https://doi.org/10.1051/0004-6361/202142560

In the original publication, the contribution to the ionisation rate of secondary electrons produced by primary cosmic-ray electrons was overestimated by a factor of 2. The corrected values of the excitation rate, ζ_exc,u, and the ionisation rate, ζ_ion, as a function of H₂ column density are shown in the new version of Fig. 5 (red curves).

Because the contribution of electrons becomes less important, the ratio ζ_exc,u/ζ_ion remains constant. In particular, ζ_exc,u/ζ_ion = 1.57 and 1.78 for the transitions (v, J) = (0, 0) → (1, 0) and (0, 0) → (1, 2), respectively.

The weak dependence of this ratio on the cosmic-ray proton spectrum and column density shown in Fig. 6 of the original paper is therefore a spurious result. The conclusions of the paper are unaffected.

Fig. 5

Cosmic-ray excitation and ionisation rates. Upper panel: CR excitation rate due to secondary electrons as a function of H₂ column density for the H₂ rovibrational transitions (v, J) = (0, 0) → (1, 0) and (v, J) = (0, 0) → (1, 2) (solid and dashed lines, respectively). The black and red lines show the rates due to secondaries produced by CR protons, $e_{s e c}^{p}$ $\[e_{\mathrm{sec}}^{p}\]$ , and primary CR electrons, $e_{s e c}^{e}$ $\[e_{\mathrm{sec}}^{e}\]$ , respectively. Lower panel: CR ionisation rate from CR protons (solid black lines) and CR electrons (solid red line). All curves include the contribution to ionisation from the corresponding generation of secondary electrons. The labels on the left in both panels denote the low-energy spectral slope (parameter α in Eq. (2)). The cases α = 0.1 and α = −0.8 correspond to models ℒ and ℋ, respectively.

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Fig. 5

Cosmic-ray excitation and ionisation rates. Upper panel: CR excitation rate due to secondary electrons as a function of H₂ column density for the H₂ rovibrational transitions (v, J) = (0, 0) → (1, 0) and (v, J) = (0, 0) → (1, 2) (solid and dashed lines, respectively). The black and red lines show the rates due to secondaries produced by CR protons, $e_{s e c}^{p}$ $\[e_{\mathrm{sec}}^{p}\]$ , and primary CR electrons, $e_{s e c}^{e}$ $\[e_{\mathrm{sec}}^{e}\]$ , respectively. Lower panel: CR ionisation rate from CR protons (solid black lines) and CR electrons (solid red line). All curves include the contribution to ionisation from the corresponding generation of secondary electrons. The labels on the left in both panels denote the low-energy spectral slope (parameter α in Eq. (2)). The cases α = 0.1 and α = −0.8 correspond to models ℒ and ℋ, respectively.

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