Fluorescence Modelling and Spectroscopic Analysis of the NH2 Radical inCometary Environments

Introduction
The amidogen (NH₂) radical is a widely found species in the coma of comets. It is believed to be primarily produced through the photodissociation of ammonia (NH₃) as parent species by the solar ultraviolet radiation. The presence of ammonia in comets serves as a crucial indicator of the first molecules formed in the protosolar nebula, reflecting the primordial conditions of the early Solar System. NH₃, together with H²O, CH₄, CO and CO₂, is believed to be one of the first ices formed on the surface of dust grains in the presolar nebula (Watanabe & Kouchi 2008).

Detecting ammonia (NH3) in comets remains challenging. In the radio domain, its inversion transitions near 24 GHz have been firmly detected only in a few cases, such as comets C/1996 B2 (Hyakutake) and C/1995 O1 (Hale-Bopp) (Palmer et al. 1996; Bird et al. 1997), due to beam dilution and sensitivity limits. In the infrared, rovibrational transitions around 3 µm offer a favourable window, though atmospheric absorption and line blending with other species often interfere with clear identification. In contrast, NH₂,
the primary photodissociation product of NH₃, emits strongly in the optical range (4000–8000 Å), and is commonly used as a proxy for ammonia in cometary comae, assuming it originates solely from NH3 photolysis (Tegler & Wyckoff 1989). After formation, NH₂ radicals are excited by solar radiation and
decay via fluorescence. Fluorescence models generally assume equilibrium conditions in an optically thin coma, where collisional effects near the nucleus are negligible (Tegler & Wyckoff 1989; Kawakita et al. 2001; Kawakita & Watanabe 2002). Under these assumptions, NH₂ emission can be reliably used to
infer ammonia abundance.

Aim
In the current literature, there are relatively few studies on NH₂ fluorescence models, and these are confined to specific spectral regions at a time (Kawakita & Watanabe 2002; Kawakita & Mumma 2011), leaving gaps in the overall understanding of NH₂ fluorescence behaviour across broader ranges.
The starting point of this study is to develop a comprehensive and improved fluorescence model for NH₂, aiming to provide a unified framework for the calculation of fluorescence efficiencies (g-factors) for multiple bands, offering a more complete and consistent approach to NH₂ fluorescence analysis. 

One of the drivers behind revising the current understanding of the spectroscopic behaviour of NH₂ is the presence of numerous unidentified features in high-resolution cometary spectra (Brown et al. 1996; Cremonese et al. 2007; Cambianica et al. 2021). In particular, high-resolution spectra of comet
NEOWISE (Cambianica et al. 2021) revealed a considerable number of unidentified lines. These lines are typically confined to specific regions of the spectrum, suggesting that they may originate from the same species. Since other known radicals, such as CN and C₂, already have well-established models for line positions and fluorescence efficiency (Rousselot et al. 2000; Tanabashi et al. 2007; Schleicher 2010; Brooke et al. 2014), it is unlikely that these unidentified features belong to them. As a result, NH₂ remains a promising candidate for resolving some uncertain line assignments. A detailed re-analysis of
existing NH₂ spectroscopic data, along with a revision of the current fluorescence models, is necessary to explore this possibility.

Methods
The treatment of fluorescence equilibrium equations is based on the methodology implemented in the Python code FlorPy (Bromley et al. 2024). FlorPy is a valuable tool for solving these equations, and allows the computation of fluorescence efficiencies (g-factors) for individual transitions, if the line positions and Einstein coefficients are known.

This activity has prompted the authors to improve the spectroscopic study of the NH₂ radical by re-analising the vast but rather sparse data collection present in the literature (Hadj Bachir et al. 1999; Huet et al. 1996; Dressler & Ramsay 1959; Ross et al. 1988).
For this purpose, we will use the PGOPHER program (Western 2017), a tool widely employed for spectral fitting of many molecular species. Such comprehensive treatment of the NH2 radical will culminate in a complete set of g-factors for cometary abundance retrieval. This approach would make a significant contribution in terms of the accuracy of the g-factors calculation, though it also introduces several complications.

As a matter of fact, NH₂ is a triatomic radical with an open-shell electronic configuration (Dressler & Ramsay 1957). In its electronic ground state (X²B₁), it is bent and behaves as a regular semi-rigid asymmetric top. The first excited state exhibits a quasi-linear configuration and it features a strong vibronic coupling between the electronic angular momentum and vibrational angular momentum produced by the linear (doubly degenerate) bending motion. This coupling is labelled as Renner-Teller effect and breaks down the Born-Oppenheimer approximation, making the usual formalism for the computation of ro-vibrational energies no longer applicable (Renner 1934).

The PGOPHER tool operates within the frame of the Born-Oppenheimer approximation, i.e. by postulating a clear separation between electronic and ro-vibrational energies. Still, it can be used for problematic cases, as of NH₂, by adopting the approach of effective fits, i.e. by separating the overall spectrum in independent subbands, for which specialised Hamiltonians are able to "effectively" reproduce the observed line positions within experimental accuracy. If properly adopted, this approach can provide a set of spectroscopic parameters which, if difficult to interpret in the usual manner, do have good spectral predictive capability within the range of energies actually sampled by the analysis.

Conclusions
This work presents a new approach to the analysis of the NH₂ radical, currently under development. It focuses on its fluorescence mechanisms and the computation of g-factors for individual transitions. The development of a self-consistent model for NH₂  would significantly enhance the accuracy of abundance calculations in cometary environments and contribute to a deeper understanding of molecular spectroscopy in comets. However, this approach also presents challenges, particularly concerning the Renner-Teller effect, which will require further refinement of existing models. Despite these complications, the work is expected to improve the current understanding of NH₂ radical fluorescence mechanism in cometary comae.