Chemistry and ro-vibrational excitation of HeH⁺ 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 Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
⁴ KU Leuven, Department of Chemistry, 3001 Leuven, Belgium
⁵ J. Heyrovský Institute of Physical Chemistry, Academy of Sciences, Dolejškova 2155/3, 182 23 Prague 8, Czech Republic

^★ Corresponding authors; milansil93@gmail.com; alexandre.faure@univ-grenoble-alpes.fr

Received: 26 November 2024
Accepted: 21 February 2025

Abstract

Context. The helium hydride cation (HeH⁺) holds the distinction of being the first molecule to form in the metal-free Universe after the Big Bang. Following its first circumstellar detection via the pure rotational J = 1 → 0 transition in the young and dense planetary nebula NGC 7027, its presence is further confirmed by detecting the υ = 1 → 0 P(l) and P(2) ro-vibrational line emissions.

Aims. HeH⁺ belongs to the class of “reactive” ions that can be destroyed so quickly that chemical formation and destruction rates may compete with inelastic rates and should be considered when solving the statistical equilibrium equations. This so-called chemical “pumping” or “excitation” effect is investigated here for the first time in HeH⁺.

Methods. The chemical evolution of HeH⁺ in NGC 7027 is modeled with the CLOUDY photoionization code using updated reaction rate coefficients. The electron temperature and atomic-molecular densities are modeled as a function of position in the nebula. The non-local thermodynamic equilibrium (NLTE) analysis of the three observed HeH⁺ emission lines is then performed with the CLOUDY and RADEX codes using an extensive set of spectroscopic and inelastic collisional data suitable for the specific high-temperature environment of NGC 7027. In a second approach, chemical formation and destruction rates of HeH⁺ are implemented in RADEX. This code is combined with a Markov Chain Monte Carlo (MCMC) sampling (performed on the RADEX-parameters space) in order to extract the best-fit HeH⁺ column density and physical conditions from the observed line fluxes.

Results. The CLOUDY and RADEX NLTE results are found to be in good agreement, and they reproduce the observed HeH⁺ line fluxes to within a factor of 2–5, and the υ = 1 → 0 P(2)/P(l) line ratio to better than 20%. Agreement to better than a factor of 2.3 is obtained when including the reaction between He(2³S) and H as an additional source of HeH⁺ in the chemical model. The RADEX-MCMC model with chemical pumping is found to reproduce both the observed line fluxes and the line ratio to 20%. However, while the best-fit parameters agree rather well with the model predictions, the posterior distributions are poorly constrained, suggesting that additional HeH⁺ lines must be detected in NGC 7027 to better constrain the physical conditions via NLTE models. On the other hand, uncertainties in collisional (reactive and inelastic) data of HeH⁺ have been largely reduced in this work. We also show that the three observed lines are not sensitive to chemical pumping while excited “short-lived” levels are significantly overpopulated with respect to a NLTE model neglecting chemical excitation. The corresponding full-line spectrum predicted for NGC 7027 is provided.