Chemistry and ro-vibrational excitation of CH⁺ in the planetary nebula NGC 7027

¹ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
² Univ Rennes, CNRS, IPR (Institut de Physique de Rennes) – UMR 6251, 35000 Rennes, France
³ Institute of Astronomy, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
⁴ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
⁵ Instituto de Física Fundamental, IFF-CSIC, Serrano 123, 28006 Madrid, Spain
⁶ Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA
⁷ KU Leuven, Department of Chemistry, 3001 Leuven, Belgium

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

Received: 17 January 2026
Accepted: 6 April 2026

Abstract

Context. Small carbon hydride cations, such as methylidynium (CH⁺), are important in the chemistry of the interstellar medium. They participate in a network of gas-phase reactions with a range of molecular and atomic species and lead to the formation of diverse hydrocarbon products that, in turn, act as precursors to more complex carbon-chain and organic molecules.

Aims. CH⁺ is known to be a reactive ion that is quickly destroyed by H, H₂, and free electrons, which makes its excitation challenging to model because chemical formation and destruction rates should be considered along with the usual radiative and inelastic rates when solving the statistical equilibrium equations. This so-called chemical pumping or excitation effect, already evidenced in the literature, is examined here with the first set of ab initio state-resolved ro-vibrational (reactive and inelastic) collision data to model the observed CH⁺ line intensities and better constrain the physico-chemical conditions of the environment.

Methods. Multiple rotational and ro-vibrational transitions of CH⁺ detected toward the planetary nebula NGC 7027 are analyzed in this work. The chemical structure of CH⁺ in NGC 7027 was modeled with the photoionization code CLOUDY using updated formation and destruction reaction rate coefficients for CH⁺. The electron temperature and atomic and molecular gas densities were modeled as a function of position within the nebula. The nonlocal thermodynamic equilibrium analysis of the observed CH⁺ emission lines was then performed with the 1D code CLOUDY and single-zone code RADEX using an accurate and comprehensive set of spectroscopic and inelastic collisional data. In a second approach, chemical formation and destruction rate coefficients of CH⁺ were implemented in RADEX. This code was combined with a Markov chain Monte Carlo sampling (performed in the RADEX-parameter space) in order to extract the best-fit CH⁺ column density and physical conditions from the observed line fluxes.

Results. Our CLOUDY model reproduces the observed CH⁺ line fluxes to within a factor of 1.3 on average, with a maximum deviation of a factor of 3. It also suggests that the rotational and ro-vibrational CH⁺ lines originate from physically distinct regions within NGC 7027 that differ mostly in kinetic temperature. Our RADEX models show that chemical pumping significantly enhances the population of all levels above (v = 0, J = 1), with a strong increase in the ro-vibrational line intensities within the v = 2 → 1 band. A single-zone model, however, remains limited, and we strongly encourage using a full 1D model, which consistently incorporates all excitation processes, with the rate coefficients we accurately determined here.