# A cometary Fluorescence Model for the ν3 Vibrational Band of Cyanogen

Pierre Hardy, Philippe Rousselot, Cyril Richard, Vincent Boudon, Xavier

Landsheere, Alexandre Voute, Laurent Manceron, F. Kwabia Tchana

► To cite this version:

Pierre Hardy, Philippe Rousselot, Cyril Richard, Vincent Boudon, Xavier Landsheere, et al. A cometary Fluorescence Model for the ν3 Vibrational Band of Cyanogen. The Astrophysical Journal, 2025, 988 (1), pp.2. 10.3847/1538-4357/addf3e. hal-05004328

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# A Cometary Fluorescence Model for the $v_3$ Vibrational Band of Cyanogen

P. Hardy<fnref n="1" />,<fnref n="2" /> ID, P. Rousselot<fnref n="2" /> ID, C. Richard<fnref n="1" /> ID, V. Boudon<fnref n="1" /> ID, X. Landsheere<fnref n="3" /> ID, A. Voute<fnref n="3" />,<fnref n="4" /> ID, L. Manceron<fnref n="3" />,<fnref n="4" /> ID, and F. Kwabia Tchana<fnref n="3" /> ID

## Abstract

Cyanogen ($C_2N_2$) has been suspected for a long time to be present in comets and to contribute to the creation of the CN radical. So far no observations with ground-based facilities have managed to detect this species, but the Rosetta mission, thanks to in situ observations with the ROSINA mass spectrometer, detected this species in the coma of 67P/Churyumov-Gerasimenko. To investigate its presence from infrared spectra in other comets, we developed a fluorescence model for the $v_3$ fundamental band. From new laboratory high-resolution infrared spectra of cyanogen, we analyzed the region of the $v_3$ band of $C_2N_2$, centered around 4.63 µm (2158 cm$^{-1}$). In addition to line positions and intensities, molecular parameters for the ground and excited vibrational state were obtained. These parameters allowed us to develop a fluorescence model for cyanogen. Line-by-line excitation rates of the $v_3$ band of cyanogen in cometary comae are presented. An upper limit of the abundance of cyanogen in a spectrum of comet C/2022 E3 (ZTF) is discussed.

*Unified Astronomy Thesaurus concepts: Comets (280); Near infrared astronomy (1093); Molecular data (2259); Molecular spectroscopy (2095)*

## 1. Introduction

Among the limited number of space missions dedicated to cometary science, the Rosetta spacecraft launched in 2004 significantly enhanced the understanding of those small bodies, by conducting a 2 yr study of the comet 67P/Churyumov-Gerasimenko. One of Rosetta's instruments, the mass spectrometer ROSINA, discovered numerous chemical species in the coma that had never been observed in comets before.

One such species, cyanogen ($C_2N_2$), is a linear molecule that was previously only observed in the atmosphere of Titan by V. G. Kunde et al. (1981) before its detection on comet 67P (K. Altwegg et al. 2019). Although the CN radical is a prominent feature in cometary optical spectra, its origins (i.e., its corresponding parent species) are still poorly understood. In particular, hydrogen cyanide (HCN) has been shown not to be the only source of cometary CN (N. Hänni et al. 2020, 2021). $C_2N_2$, while being much less abundant than HCN in the coma of comet 67P (N. Hänni et al. 2021) reported $C_2N_2$/HCN= 0.0018 ± 0.0009 (1.24–1.74 au)), could still participate in the formation of CN. Its detection in 67P should be extended to other comets to better constrain its abundance in cometary environments. While the $v_5$ far-infrared band of $C_2N_2$ is already present in the HITRAN database (A. Fayt et al. 2012; I. Gordon et al. 2022), no data are available at wavenumbers greater than 310 cm$^{-1}$. In particular, one of the fundamental bands of cyanogen, centered at 2158 cm$^{-1}$ (4.63 µm), was never studied at high resolution. This band is particularly interesting to study as it is centered in the *M* infrared window, a spectral region where few atmospheric emission lines of $H_2O$ and $CO_2$ are present.

<figure><img src="image_3.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

The paper is organized as follows. After discussing experimental details (Section 2) and theoretical aspects (Section 3), we present both the results of our spectroscopic analysis in Section 4 and the development of a fluorescence model adapted to comets in Section 5. Finally, our results and an upper limit on the abundance of cyanogen in comet C/2022 E3 (ZTF) are presented in Section 6.

## 2. Experimental Details

Seven absorption spectra of cyanogen have been recorded in the range from 1800 to 3500 cm$^{-1}$ using the high-resolution Bruker IFS125HR Fourier transform spectrometer (FTS) located at the LISA facility in Créteil (France). The instrument was equipped with a silicon carbide Globar source, a KBr/Ge beamsplitter and a liquid nitrogen-cooled indium antimonide (InSb) detector. The InSb detector was used in conjunction with an optical filter, with a bandpass of 1800–3400 cm$^{-1}$, to minimize the size of the interferogram data files and also to improve the signal-to-noise ratio. The FTS was continuously evacuated below $3 \times 10^4$ hPa by a turbomolecular pump to minimize absorption by atmospheric gases. The diameter of the entrance aperture of the spectrometer was set to 1.3 mm to maximize the intensity of infrared radiation falling onto the InSb detector without saturation or loss of spectral resolution. Interferograms were recorded with an 80 kHz scanner frequency and a maximum optical path difference (MOPD) of 250 cm. According to the Bruker definition (resolution = 0.9/MOPD), this corresponds to a resolution of 0.0036 cm$^{-1}$. The spectra were obtained by Fourier transformation of the interferograms using a Mertz phase correction with a 1 cm$^{-1}$ resolution, a zero-filling factor of 2, and no apodization (boxcar option). The cyanogen ($C_2N_2$) sample was synthesized in the laboratory by progressive heating of silver cyanide (99%, Sigma-Aldrich) in a

<footnote n="1">¹ Université Bourgogne Europe, CNRS, Laboratoire Interdisciplinaire Carnot de Bourgogne ICB UMR 6303, 21000 Dijon, France</footnote>

<footnote n="2">² Université Marie et Louis Pasteur, CNRS, Institut UTINAM (UMR 6213), OSU THETA, F-25000 Besançon, France</footnote>

<footnote n="3">³ Université Paris Cité and Université Paris Est Créteil, CNRS, LISA, F-75013 Paris, France</footnote>

<footnote n="4">⁴ Synchrotron SOLEIL, Ligne AILES, L'Orme des Merisiers, St-Aubin BP48, 91192 Gif-sur-Yvette Cedex, France</footnote>

<footnote>Received 2025 April 3; revised 2025 May 14; accepted 2025 May 31; published 2025 July 10</footnote>
<table><caption>**Table 1**
Pressure of C₂N₂ (in hPa) and Number of Interferograms Averaged to Yield the Corresponding Spectrum (Number of Scans)</caption><thead><tr><th>#</th><th>C<sub>2</sub>N<sub>2</sub> Pressure (hPa)</th><th>Number of Scans</th></tr></thead><tbody><tr><td>S1</td><td>0.9968 (50)</td><td>1460</td></tr><tr><td>S2</td><td>1.3404 (67)</td><td>1310</td></tr><tr><td>S3</td><td>1.8718 (94)</td><td>1430</td></tr><tr><td>S4</td><td>2.337 (12)</td><td>1410</td></tr><tr><td>S5</td><td>2.673 (13)</td><td>1480</td></tr><tr><td>S6</td><td>3.335 (17)</td><td>1250</td></tr><tr><td>S7</td><td>4.003 (20)</td><td>1250</td></tr></tbody></table>

Note. All the spectra were recorded with an absorption optical path of 0.849 (2 m, at a stabilized room temperature of 293 ± 1 K, a resolution (equal to 0.9 divided by the maximum optical path difference) of 0.0036 cm⁻¹, and an entrance aperture diameter of the interferometer equal to 1.3 mm. The absolute uncertainty on the pressure is equal to 0.5% of the value given.

glass bulb previously evacuated:

$$2\text{Ag} - \text{CN} \xrightarrow[(-2\text{Ag})]{\Delta>350^{\circ}\text{C}} \text{NC} - \text{CN}. \quad (1)$$

About 5 g of silver cyanide powder was placed in a thoroughly cleaned, grease-free glass bulb and heated gently under high vacuum up to 200°C to eliminate atmospheric gases and adsorbed water vapor. Next, the powder was progressively heated to 300°C, where evolution of cyanogen gas slowly started to occur. The first batch, containing traces of carbon dioxide from carbonate impurities, was discarded, further heating to about 400°C completed the reaction, and cyanogen was collected in a glass trap on the vacuum line. Finally, a trap-to-trap distillation at about -70°C helped reduce possible remaining impurities (HCN, CO₂, or others). The remaining CO₂ traces were estimated from IR measurements to much less than 0.1%.

A short-path absorption cell (SPAC) made of Pyrex glass and equipped with CsBr windows was used for all the measurements. The SPAC is a White-type multipass cell with a base length of 0.20 m. In this experiment, an optical path of 0.849(2) m was used. The sample pressure in the cell was measured using calibrated MKS Baratron capacitance manometer models 627 (2.6664 hPa full scale) and 628 D (13.332 hPa full scale), characterized by a stated reading accuracy of 0.12%. Considering the uncertainty arising from small variations of the pressure during the recording (<0.35%), we estimated the measurement uncertainty on the pressure to be equal to 0.5%. All the spectra were recorded at a stabilized room temperature of 293 ± 1 K. The following procedure was used to record the spectra. A background spectrum was first collected while the cell was being continuously evacuated. It was recorded at the same resolution as the sample spectra to ensure proper removal of the H₂O or CO₂ absorption lines. The infrared gas cell was then passivated several times with the C₂N₂ sample. Finally, spectra were recorded for seven different sample pressures of cyanogen. The seven pressures chosen and the number of interferograms recorded and averaged to yield the corresponding spectra are listed in Table 1. All the sample spectra were ratioed against the empty cell background spectrum, and interpolated 4 times. The rms signal-to-noise ratio in the ratioed spectra ranged between 1200 and 1900. The spectrum was calibrated by matching the measured positions of 25 lines of residual CO₂

and H₂O observed therein to reference wavenumbers available in HITRAN (I. Gordon et al. 2022) with an rms deviation of 0.00018 cm⁻¹. The absolute accuracy of the measured C₂N₂ line positions was estimated as the square root of the sum of squares of the accuracy of the reference CO₂ and H₂O line positions in HITRAN (better than 0.0001 cm⁻¹) plus the rms deviation between the observed frequencies and values listed in HITRAN for CO₂ and H₂O, yielding in total 0.0002 cm⁻¹.

### 3. Theoretical Aspects

Cyanogen (C₂N₂) is a linear molecule belonging to the *D*<sub>∞h</sub> point group, with five fundamental vibrational modes: CN symmetric stretch (ν₁, centered at 2330.4859 cm⁻¹, with Σ<sub>g</sub> symmetry, infrared inactive), CC symmetric stretch (ν₂, centered at 845.5939 cm⁻¹, with Σ<sub>g</sub> symmetry, infrared inactive), CN asymmetric stretch (ν₃, centered at 2157.8243 cm⁻¹, with Σ<sub>u</sub> symmetry), and two doubly degenerated CCN bending modes (ν₄, centered at 502.7745 cm⁻¹, with Π<sub>g</sub> symmetry, infrared inactive; and ν₅, centered at 233.7225 cm⁻¹, with Π<sub>u</sub> symmetry). Band-center values come from the analysis of A. G. Maki (2011). Our study is focused on the ν₃ mode, centered at 2158 cm⁻¹.

The rotational energy levels are described as usual by

$$E(J) = BJ(J + 1) - DJ^2(J + 1)^2 + HJ^3(J + 1)^3 + \dots, \quad (2)$$

where *B* is the rotational constant, and *D* and *H* represent centrifugal distortion corrections. The allowed frequencies are obtained as $ν_J = ν_0 + E_u(J_u) - E_l(J_l)$, where $ν_0$ is the frequency of the pure vibrational transitions, and the subscripts *u* and *l* refer to the upper and lower vibrational levels, respectively. For non-Σ states, the interaction between rotation and angular momentum components leads to *l*-doubling, resulting in energy splitting given by

$$\Lambda(J) = qJ(J + 1) + q_D J^2(J + 1)^2 + q_H J^3(J + 1)^3 + \dots \quad (3)$$

Individual line strengths ($S_J$) can be expressed in terms of the band strength ($S_ν$, usually given in cm⁻² atm⁻¹; L. S. Rothman & L. D. G. Young 1981),

$$S_J = \varepsilon_J \frac{\nu_J}{\nu_0} L_J \frac{S_\nu}{Q_r} (e^{-hcE_l/kT})(1 - e^{-hc\nu_J/kT})(1 + A_1 m)^2. \quad (4)$$

Here, $\varepsilon_J$ represents the statistical weight, $L_J$ is the Hönl-London factor, and $Q_r$ is the rotational partition function. The last term is the first-order Herman-Wallis correction, which is equal to 1 for perfect rigid rotors and *Q* branches. This correction depends on *m*, defined as $J + 1$ for the *R* branch, and $-J$ for the *P* branch. For linear (and diatomic) molecules, the Hönl-London factors for the *P* and *R* branches of Σ-Σ transitions are simply given by (G. Herzberg 1950)

$$L_J = |m|l. \quad (5)$$

For the main isotopologue (¹⁴N¹²C¹²C¹⁴N, with an abundance of 97.08% reported in I. Gordon et al. 2022), $\varepsilon_J$ is equal to 6 for even *J* values and 3 for odd *J* values. In practice, these statistical weights lead to an intensity alternation between two consecutive lines in the spectra. The rotational partition function appearing in Equation (4) is expressed as

$$Q_R = \sum_{J=0}^{\infty} \varepsilon_J (2J + 1) e^{-hcE_l(J)/kT}, \quad (6)$$
<figure><img src="image_4.png" /><figcaption>Figure 1. Experimental high-resolution spectrum of C₂N₂ between 2120 and 2185 cm⁻¹.</figcaption></figure>

while the vibrational partition function is given by

$$Q_V = \prod_{i=1}^{5} (1 - e^{(-hc\nu_{0,i}/kT)})^{-d_i}, \quad (7)$$

where $d_i$ is the degeneracy of the fundamental band i, centered at $\nu_{0,i}$. The rotovibrational partition function ($Q$) is the product of $Q_R$ and $Q_V$. To derive the excitation rates, we followed the development presented in N. Dello Russo et al. (2001). The Einstein coefficient $A_\nu$ (in s⁻¹) for a vibrational band (J. Crovisier & T. Encrenaz 1983; J. Crovisier 1984) is defined by

$$A_\nu = \frac{3.080 \times 10^{-8} (T_\nu/300) \nu_0^2 S_\nu Q_V}{\omega}, \quad (8)$$

where $T_\nu$ is the temperature (in kelvins) at which the band strength $S_\nu$ (in cm⁻² atm⁻¹) is obtained, and $\omega$ is the band degeneracy ($\omega = 1$ for $\nu_3$). The g-factor for a fundamental band excited by a blackbody of solid angle $\Omega$ at temperature $T_b$ is then expressed (J. Crovisier & T. Encrenaz 1983):

$$g_\nu = \frac{\omega\Omega}{4\pi} A_\nu (e^{hc\nu_0/kT_b} - 1)^{-1}. \quad (9)$$

With an excitation by the Sun at 1 au, $T_b = 5770$ K and $\Omega/4\pi = 5.42 \times 10^{-6}$ (N. Dello Russo et al. 2001).

# 4. Spectroscopic Analysis

## 4.1. Positions

Using the PGOPHER software (C. M. Western 2017), we analyzed the experimental spectra of C₂N₂ from 2120 to 2185 cm⁻¹. The S2 experimental spectrum ($P = 1.3404$ (67) hPa) is represented in Figure 1.

In addition to the $\nu_3$ fundamental band, some absorption lines from hot bands are also present in the spectrum: we identified $\nu_3 + \nu_4 - \nu_4$, $\nu_3 + \nu_5 - \nu_5$, and $\nu_3 + 2\nu_5 - 2\nu_5$. Energy levels and the four transitions discussed hereafter are shown in Figure 2.

As $\nu_4$, $\nu_5$, and $2\nu_5$ are the lowest excited energy levels of C₂N₂, these hot bands are quite strong and affect the study of the fundamental band $\nu_3$, because hot bands lines are often blended with $\nu_3$ lines. In this context and because they were fairly easy to assign, we decided to include the hot bands in

<figure><img src="image_5.png" /><figcaption>Figure 2. The four vibrational bands presented in this work: $\nu_3$ - GS, $\nu_3 + \nu_5 - \nu_5$, $\nu_3 + 2\nu_5 - 2\nu_5$, and $\nu_3 + \nu_4 - \nu_4$. Symmetries are labeled for each energy level.</figcaption></figure>

this work, even though the fluorescence model described later only focuses on the fundamental band, as it is supposed to be the main component in cold environments such as the coma of a comet. We started our analysis in PGOPHER using spectroscopic parameters from A. G. Maki (2011).

For the $\nu_3$ band, 201 lines have been assigned from $J=0$ to $J=112$. A few lines have been systematically removed from the fit if they were obviously blended with other lines and decreased the quality of the fit. The average error, $d_{rms}$, is defined as

$$d_{rms} = \sqrt{\frac{\sum_i d_i^2}{n}}, \quad (10)$$

where $n$ is the number of observations, and $d_i$ is the difference in cm⁻¹ between the observed and calculated positions of line i. In our fit of the fundamental band $\nu_3$, $d_{rms} = 1.21 \times 10^{-4}$ cm⁻¹. For the hot band $\nu_3 + 2\nu_5 - 2\nu_5$, 114 lines have been assigned,
<figure><img src="image_6.png" /><figcaption>(a) Fit residuals for the ν₃ band. 190 observations, average error: 1.10 × 10⁻⁴ cm⁻¹.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(c) Fit residuals for the ν₃+ν₅−ν₅ band. 319 observations, average error: 1.53 × 10⁻⁴ cm⁻¹.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(b) Fit residuals for the ν₃ + ν₄ − ν₄ band. 234 observations, average error: 2.44 × 10⁻⁴ cm⁻¹.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(d) Fit residuals for the ν₃ + 2ν₅ − 2ν₅ band. 137 observations, average error: 2.06 × 10⁻⁴ cm⁻¹.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(e) Fit residuals for all four bands, plotted against wavenumber. 880 observations, average error: 1.83 × 10⁻⁴ cm⁻¹.</figcaption></figure>

<caption>**Figure 3.** Fit residuals for the line positions of the vibrational bands of C₂N₂ with respect to the upper-state rotational quantum number *J* and wavenumber.</caption>

from *J* = 1 to *J* = 99, with *d*<sub>rms</sub> = 2.43 × 10<sup>-4</sup> cm<sup>-1</sup>. ν<sub>3</sub> and ν<sub>3</sub> + 2ν<sub>5</sub> are both Σ<sup>+</sup><sub>u</sub> states, meaning there is no *l*-doubling observed for those two bands. This is not the case for ν<sub>3</sub> + ν<sub>4</sub> and ν<sub>3</sub> + ν<sub>5</sub>, which are respectively Π<sub>u</sub> and Π<sub>g</sub> states. As lines are blended for low *J* (because the splitting is not large enough), we did not include lines with *J* < 11 for ν<sub>3</sub> + ν<sub>5</sub> − ν<sub>5</sub> and *J* < 14 for ν<sub>3</sub> + ν<sub>4</sub> − ν<sub>4</sub> while fitting positions. The evolution of the splitting as *J* increases is illustrated in the Appendix.

For ν₃ + ν₄ − ν₄, we fitted 195 lines from *J* = 13 to *J* = 85, with *d*<sub>rms</sub> = 2.34 × 10<sup>-4</sup> cm<sup>-1</sup>. For ν₃ + ν₅ − ν₅, we fitted 323 lines from *J* = 10 to *J* = 96, with *d*<sub>rms</sub> = 1.46 × 10<sup>-4</sup> cm<sup>-1</sup>. The fit residuals for the line positions of each band discussed are represented in Figures 3(a)–(d). Residuals are plotted against the upper-level rotational quantum number *J*, to highlight potential nonzero higher terms in the polynomial expansion of the energy states. The total average error (considering the four bands together) is 1.8 × 10<sup>-4</sup> cm<sup>-1</sup>, and all the fit residuals are represented in Figure 3(e), where the *x*-axis is now the wavenumber in cm<sup>-1</sup>.

The spectroscopic parameters derived from the fit in positions are summarized in Table 2. The standard deviation is indicated in parentheses. No parentheses indicate that the value was fixed using values from A. G. Maki (2011).

## 4.2. Intensities

We restricted our intensity analysis to the ν₃ band, as the cometary fluorescence model will focus only on this band. The fit was done using the Multi-Spectrum Fitting Program (MSFP) developed by Jean Vander Auwera at Université Libre de Bruxelles. This program takes as input the spectra recorded under different conditions, the total internal partition function of the considered species, and the line lists to be fitted. We measured the intensity (in the usual HITRAN units, cm⁻¹/(molecule cm⁻²), at *T*<sub>ref</sub> = 296 K) and self-broadening coefficients (in cm⁻² atm⁻¹) of 147 lines of the ν₃ band by fitting Voigt profiles. As an example, the line *R*(53) is represented for three different pressures (S2, S3, S4) in Figure 4. We did not include lines known to be blended with absorption
<table><caption>**Table 2**

Derived Parameters from the Line Position Analysis in PGOPHER</caption><thead><tr><th></th><th>Origin<br>(cm<sup>-1</sup>)</th><th>B<br>(cm<sup>-1</sup>)</th><th>D × 10<sup>8</sup><br>(cm<sup>-1</sup>)</th><th>H × 10<sup>13</sup><br>(cm<sup>-1</sup>)</th><th>L × 10<sup>17</sup><br>(cm<sup>-1</sup>)</th><th>q × 10<sup>4</sup><br>(cm<sup>-1</sup>)</th><th>qD × 10<sup>9</sup><br>(cm<sup>-1</sup>)</th><th>qH × 10<sup>13</sup><br>(cm<sup>-1</sup>)</th><th>qL × 10<sup>17</sup><br>(cm<sup>-1</sup>)</th></tr></thead><tbody><tr><td>GS (Σ<sub>g</sub>)</td><td>0</td><td>0.1570879982(2801)</td><td>2.11469(189)</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>ν<sub>5</sub>(Π<sub>u</sub>)</td><td>233.7225<sup>a</sup></td><td>0.1576278497(3905)</td><td>2.222624(8402)</td><td>0.11146(5439)</td><td>0</td><td>-2.212580(4536)</td><td>0.4129(387)</td><td>0</td><td>0</td></tr><tr><td>2ν<sub>5</sub>(Σ<sub>g</sub>)</td><td>464.8685<sup>a</sup></td><td>0.158166967(1048)</td><td>4.20455(5699)</td><td>9.153(1175)</td><td>-1.7012(8007)</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>ν<sub>4</sub>(Π<sub>g</sub>)</td><td>502.7745<sup>a</sup></td><td>0.1574531178(2931)</td><td>2.15394(332)</td><td>0</td><td>0</td><td>-1.17900(1700)</td><td>-3.3476(8270)</td><td>5.628(1551)</td><td>-3.3370(9800)</td></tr><tr><td>ν<sub>3</sub>(Σ<sub>u</sub>)</td><td>2157.824256(34)</td><td>0.1565544657(2892)</td><td>2.101485(3062)</td><td>-0.06649(2975)</td><td>0.0300(132)</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>ν<sub>3</sub> + ν<sub>5</sub>(Π<sub>g</sub>)</td><td>2389.736280(30)</td><td>0.1570968635(3867)</td><td>2.214595(8253)</td><td>0.09869(5294)</td><td>0</td><td>-2.186458(4525)</td><td>0.3904(383)</td><td>0</td><td>0</td></tr><tr><td>ν<sub>3</sub> + 2ν<sub>5</sub>(Σ<sub>u</sub>)</td><td>2619.092571(39)</td><td>0.157638754(1055)</td><td>4.17941(5716)</td><td>9.163(1170)</td><td>-1.8518(7922)</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>ν<sub>3</sub> + ν<sub>4</sub>(Π<sub>u</sub>)</td><td>2657.530013(67)</td><td>0.1569204218(3257)</td><td>2.160948(8013)</td><td>0.3876(1410)</td><td>-0.3061(958)</td><td>-1.17655(1709)</td><td>-3.2873(8441)</td><td>5.4587(16123)</td><td>-3.192(1040)</td></tr></tbody></table>

**Notes.** GS stands for ground state. Uncertainties are indicated in parentheses, in units of the last digits. B: rotational constant; D: *J*⁴ centrifugal distortion; H: *J*⁶ centrifugal distortion; L: *J*⁸ centrifugal distortion; *q*: l-doubling constant; *qD*: *J*⁴ centrifugal distortion of *q*; *qH*: *J*⁶ centrifugal distortion of *q*; *qL*: *J*⁸ centrifugal distortion of *q*.

<footnote>a Fixed values come from A. G. Maki (2011).</footnote>
<figure><img src="image_11.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(c)</figcaption></figure>

<caption>**Figure 4.** Simulation (in red) and observation (in blue) of the $\nu_3 R(53)$ line of C$_2$N$_2$ in the S2 (a), S3 (b), and S4 (c) spectra. Residuals are shown in green for each case.</caption>

lines originating from the three hot bands discussed earlier because the measured line intensities and broadening are overestimated in those cases. From the individual measurements of $S_J$, we derived the total band strength $S_{\nu_3}$ using the intensity formula (Equation (4)): $S_{\nu_3} = 18.328 \pm 0.071 \text{ cm}^{-2} \text{ atm}^{-1}$ ($S_{\nu_3} = 18.5 \text{ cm}^{-2} \text{ atm}^{-1}$ in D. Bockelee-Morvan & J. Crovisier 1985). Contrary to individual line intensities, the band strength is expressed in cm$^{-2}$ atm$^{-1}$. The conversion between the two systems of units was done using the factors given in K. N. Rao (2012). The first term in the Herman-Wallis correction was also derived, and we found $A_1 = 53.4 \pm 6.2 \times 10^{-5}$. The intensity fit has an rms deviation equal to 6.383%. The comparison between the measured intensities and the calculated intensities is shown in the Appendix.

# 5. Development of a Cometary Fluorescence Model

## 5.1. Ground-state Population and Energy Levels

From our analysis, we first computed the energy levels $E_J$ of cyanogen in the ground state. As a parent species, it is assumed that the initial population of C$_2$N$_2$ is mainly in the ground state. This is because the temperature in the coma is very low

(typically a few tens of kelvins), and the sublimation of the parent species from the nucleus to the coma does not excite the molecules to higher vibrational states. Moreover, in a first good approximation, collisions are negligible because the coma is an optically thin environment. The initial population distribution in the ground state follows:

$$N_J = \varepsilon_J (2J + 1) e^{-hcE_J/kT}, \quad (11)$$

and the initial fractional population $f_J$ is the ratio between $N_J$ and the total partition function $Q$ at temperature $T$.

$$f_J = \frac{N_J}{Q}. \quad (12)$$

## 5.2. Branching Ratio from the Ground State to $\nu_3$

The population of the upper-state $\nu_3$ is determined using branching ratios, defined as

$$Br(J) = \frac{L_J}{2J + 1} \times (1 + A_1 m)^2, \quad (13)$$

which we develop as

$$Br(J; \Delta J = -1) = \frac{J}{2J + 1} \times (1 - A_1 J)^2, \quad (14)$$

$$Br(J; \Delta J = +1) = \frac{J + 1}{2J + 1} \times (1 + A_1(J + 1))^2. \quad (15)$$

In absorption, $\Delta J = -1$ corresponds to the P branch, while $\Delta J = +1$ corresponds to the R branch. The populated J level in the ground state is split to the J (P branch) or J + 1 (R branch) level of the $\nu_3$ excited level, following the usual selection rules for rotovibrational transitions of linear molecules:

$$\begin{aligned} \Delta\Lambda &= 0, \pm 1, \\ \Delta J &= \pm 1, \quad \text{if } \Delta\Lambda = 0, \Lambda = 0, \\ \Delta J &= 0, \pm 1 \quad \text{else.} \end{aligned} \quad (16)$$

In our case, $\nu_3$ and GS being both $\Sigma$ states, $\Delta\Lambda = 0, \Lambda = 0$, and the Q branch is forbidden. The fractional population $f_{J'}$ in the excited state J' is then

$$f_{J'} = Br(J = J' - 1; \Delta J = +1) f_{J' = J' - 1}, \quad (17)$$

$$+Br(J = J' + 1; \Delta J = -1) f_{J' = J' + 1}. \quad (18)$$

As an example, the excited $J' = 1$ level is populated from the ground states $J = 0$ and $J = 2$, and

$$f_{J'=1} = Br(J = 0; \Delta J = +1) f_{J=0}, \quad (19)$$

$$+Br(J = 2; \Delta J = -1) f_{J=2}. \quad (20)$$

Energy levels $E_J$ and fractional population of C$_2$N$_2$ in the ground state and in the $\nu_3$ excited state at $T = 50$ K are presented in Table 3. Finally, the population that falls back from the excited $J'$ level to the $J''$ level in the ground state through the R branch or P branch is

$$f_{J'',R} = Br(J'' = J'' + 1; \Delta J = -1) f_{J'' = J'' + 1}, \quad (21)$$

$$f_{J'',P} = Br(J'' = J'' - 1; \Delta J = +1) f_{J'' = J'' - 1}, \quad (22)$$

where $\Delta J$ is now defined as $J'' - J'$. This unusual choice in spectroscopy (where $\Delta J$ is normally $J' - J'')$ was made to stay consistent with Equations (14) and (15). The corresponding emission g-factors are obtained by multiplying $f_{J''}$ by
<table><caption>**Table 3**
Energy Levels and Fractional Population of C₂N₂ in the Ground State and in the ν₃ Excited State, with T = 50 K</caption><thead><tr><th rowspan="2">J/J'</th><th colspan="2">GS</th><th colspan="2">ν<sub>3</sub></th></tr><tr><th>E<sub>J</sub></th><th>f<sub>J</sub></th><th>E<sub>J'</sub></th><th>f<sub>J'</sub></th></tr></thead><tbody><tr><td>0</td><td>0.00</td><td>0.00600</td><td>2157.82</td><td>0.00297</td></tr><tr><td>1</td><td>0.31</td><td>0.00892</td><td>2158.14</td><td>0.01767</td></tr><tr><td>2</td><td>0.94</td><td>0.02921</td><td>2158.76</td><td>0.01446</td></tr><tr><td>3</td><td>1.89</td><td>0.01990</td><td>2159.70</td><td>0.03943</td></tr><tr><td>4</td><td>3.14</td><td>0.04936</td><td>2160.96</td><td>0.02446</td></tr><tr><td>5</td><td>4.71</td><td>0.02883</td><td>2162.52</td><td>0.05717</td></tr><tr><td>6</td><td>6.60</td><td>0.06455</td><td>2164.40</td><td>0.03202</td></tr><tr><td>7</td><td>8.80</td><td>0.03496</td><td>2166.59</td><td>0.06941</td></tr><tr><td>8</td><td>11.31</td><td>0.07370</td><td>2169.10</td><td>0.03662</td></tr><tr><td>9</td><td>14.14</td><td>0.03797</td><td>2171.91</td><td>0.07552</td></tr><tr><td>10</td><td>17.28</td><td>0.07668</td><td>2175.04</td><td>0.03817</td></tr><tr><td>11</td><td>20.74</td><td>0.03801</td><td>2178.49</td><td>0.07577</td></tr><tr><td>12</td><td>24.51</td><td>0.07414</td><td>2182.25</td><td>0.03699</td></tr><tr><td>13</td><td>28.59</td><td>0.03560</td><td>2186.32</td><td>0.07114</td></tr><tr><td>14</td><td>32.99</td><td>0.06738</td><td>2190.70</td><td>0.03371</td></tr><tr><td>15</td><td>37.70</td><td>0.03145</td><td>2195.40</td><td>0.06302</td></tr><tr><td>16</td><td>42.73</td><td>0.05793</td><td>2200.41</td><td>0.02907</td></tr><tr><td>17</td><td>48.07</td><td>0.02635</td><td>2205.73</td><td>0.05298</td></tr><tr><td>18</td><td>53.72</td><td>0.04734</td><td>2211.36</td><td>0.02384</td></tr><tr><td>19</td><td>59.69</td><td>0.02101</td><td>2217.31</td><td>0.04241</td></tr><tr><td>20</td><td>65.97</td><td>0.03687</td><td>2223.57</td><td>0.01864</td></tr></tbody></table>

Note: GS stands for ground state.

the g-factor of the band (defined in Equation (9)):

$$g_{J'',R} = f_{J'',R} \times g_{\nu}, \qquad (23)$$

$$g_{J'',P} = f_{J'',P} \times g_{\nu}. \qquad (24)$$

### 5.3. Excitation Rates

For the $\nu_3$ band, considering an excitation by the Sun at 1 au, $g_\nu = 5.22 \times 10^{-5}$ photons s$^{-1}$molecules$^{-1}$, a value 50% higher than the one reported in D. Bockelee-Morvan & J. Crovisier (1985), despite reporting a similar band strength. We explain this difference by an underestimation of the vibrational partition function $Q_V$ in D. Bockelee-Morvan & J. Crovisier (1985), impacting the Einstein coefficient of the band and therefore the g-factor of the band (respectively, Equations (8) and (9)). At 300 K, $Q_\nu = 1.819$ in D. Bockelee-Morvan & J. Crovisier (1985), while we have $Q_\nu = 2.703$ and A. Fayt et al. (2012) have $Q_\nu = 2.70687$. Excitation rates up to $J=20$ for $T=50$ K are presented in Table 4 and represented in Figure 5.

## 6. Investigation in Comet C/2022 E3 (ZTF)

### 6.1. Observations and Data Reduction

The Oort cloud comet C/2022 E3 (ZTF) was discovered on 2022 March 2 by the Zwicky Transient Facility (ZTF). It reached perihelion in 2023 January, at around 1.11 au, with a peak magnitude of 5 (B. T. Bolin et al. 2022). The comet was observed by JWST between 2023 February 28 and March 4, with $r_h \sim 1.3$ au and $\Delta \sim 0.9$ au (S. N. Milam et al. 2023). We investigated the JWST/NIRSPEC spectra obtained with the G395H/F290LP grating/filters configuration, covering the 2.87–5.27 µm range through the Integral Field Unit, with a $3.0 \times 3.0$ field of view with the NRSIRS2RAPID readout and

a 4-point dither (T. Böker et al. 2023). The spectra were extracted with a $1.3$ diameter. Third-level processed data were retrieved from the ESA JWST Science Archive.<fnref n="5" />

### 6.2. Search for Cyanogen

The temperature of the coma was estimated by analyzing the intensity distribution of the $\nu_3$ band of CO₂, the strongest emission feature in the spectrum. We assumed the gas to be in local thermodynamic equilibrium (LTE), and we expect the relative population levels to follow a Boltzmann law. From the HITRAN database (I. Gordon et al. 2022) and simulation of the fluorescence spectrum in PGOPHER (C. M. Western 2017), we derived $T = 56$ K. This is in agreement with the gas temperature derived from radio spectroscopy of the comet in early February by N. Biver et al. (2024), where $T = 60$ K. The $\nu_3$ band of CO₂ and the simulation are represented in Figure 6. We observe that the assumed Boltzmann distribution matches very well the cometary spectrum, confirming the LTE assumption. As CO₂ is a parent molecule with a short lifetime ($\tau = 5 \times 10^5$ s; J. Crovisier & T. Encrenaz 1983), it is more concentrated around the nucleus, and no temperature gradient is expected. The lifetime of C₂N₂ being even shorter, the LTE assumption holds for this molecule as well.

The production rate $Q$ (in molecules s⁻¹) can be expressed as

$$Q = \frac{4\pi\Delta^2F}{\tau g h c \nu f} G, \qquad (25)$$

where $\Delta$ is the geocentric distance (in meters), $F$ is the flux of the emission line (in W m⁻²), $\tau$ is the lifetime (in seconds) of the molecule, $g$ is the fluorescence efficiency (in photons per molecule s⁻¹) of the emission line, $h c \nu$ is the energy (in joules) of a photon with a wavenumber $\nu$, and $f$ is a geometric term representing the fraction of molecules sampled through the telescope aperture relative to the total number of molecules in the coma. We write $G$ for the growth factor of the considered species, which is the ratio between the terminal production rate and the nucleus-centered production rate (N. Dello Russo et al. 1998). In Equation (25), $\tau$ and $g$ both depend on the heliocentric distance ($R_h$, expressed in au). However, as $g \propto R_h^{-2}$ (see Equation (9)) and $\tau \propto R_h^2$, their product is independent of the heliocentric distance.

To quantify an upper limit for $Q(C_2N_2)$ in comet C/2022 E3 (ZTF), we used the Haser model (L. Haser 1957), which describes the distribution of chemical species in the coma. It relies on the following hypothesis:

1. The cometary nucleus is assumed to be spherical, with a radius $R_0$.

2. Parent species are isotropically ejected away from the nucleus, with a constant velocity noted $v_0$.

3. The photodissociation of parent species is given by the law

$$n = n_0 e^{-t/\tau}, \qquad (26)$$

where $n_0$ is the number of molecules at time $t=0$, and $\tau$ is the photodissociation lifetime of the corresponding molecule.

<footnote n="5">⁵ https://jwst.esac.esa.int/archive/</footnote>
<figure><img src="image_14.png" /><figcaption>**Figure 5.** Emission g-factors of C₂N₂ expressed in photons s⁻¹ molecule⁻¹ at T = 50 K. The values are the same as in Table 4.</figcaption></figure>

<table><caption>**Table 4**
Wavenumbers and Excitation Rates (g-factors, Noted as g<sub>j''</sub>) of 40 Lines with J ≤ 20 Calculated at T = 50 K and Considering a Sun Illumination at 1 au</caption><thead><tr><th>Line</th><th>Wavenumber<br>(cm<sup>-1</sup>)</th><th>g<sub>j''</sub>/10<sup>-6</sup> s<sup>-1</sup> molecule<sup>-1</sup></th><th>Line</th><th>Wavenumber<br>(cm<sup>-1</sup>)</th><th>g<sub>j''</sub>/10<sup>-6</sup> s<sup>-1</sup> molecule<sup>-1</sup></th></tr></thead><tbody><tr><td>P(20)</td><td>2151.3387</td><td>1.111</td><td>R(0)</td><td>2158.1374</td><td>0.308</td></tr><tr><td>P(19)</td><td>2151.6730</td><td>0.626</td><td>R(1)</td><td>2158.4494</td><td>0.303</td></tr><tr><td>P(18)</td><td>2152.0063</td><td>1.395</td><td>R(2)</td><td>2158.7604</td><td>0.885</td></tr><tr><td>P(17)</td><td>2152.3386</td><td>0.768</td><td>R(3)</td><td>2159.0703</td><td>0.570</td></tr><tr><td>P(16)</td><td>2152.6697</td><td>1.669</td><td>R(4)</td><td>2159.3791</td><td>1.364</td></tr><tr><td>P(15)</td><td>2152.9999</td><td>0.896</td><td>R(5)</td><td>2159.6869</td><td>0.776</td></tr><tr><td>P(14)</td><td>2153.3289</td><td>1.897</td><td>R(6)</td><td>2159.9936</td><td>1.703</td></tr><tr><td>P(13)</td><td>2153.6569</td><td>0.990</td><td>R(7)</td><td>2160.2992</td><td>0.907</td></tr><tr><td>P(12)</td><td>2153.9839</td><td>2.037</td><td>R(8)</td><td>2160.6038</td><td>1.885</td></tr><tr><td>P(11)</td><td>2154.3097</td><td>1.031</td><td>R(9)</td><td>2160.9072</td><td>0.959</td></tr><tr><td>P(10)</td><td>2154.6346</td><td>2.053</td><td>R(10)</td><td>2161.2097</td><td>1.914</td></tr><tr><td>P(9)</td><td>2154.9583</td><td>1.002</td><td>R(11)</td><td>2161.5110</td><td>0.939</td></tr><tr><td>P(8)</td><td>2155.2810</td><td>1.916</td><td>R(12)</td><td>2161.8113</td><td>1.813</td></tr><tr><td>P(7)</td><td>2155.6026</td><td>0.893</td><td>R(13)</td><td>2162.1105</td><td>0.862</td></tr><tr><td>P(6)</td><td>2155.9232</td><td>1.617</td><td>R(14)</td><td>2162.4086</td><td>1.618</td></tr><tr><td>P(5)</td><td>2156.2427</td><td>0.705</td><td>R(15)</td><td>2162.7056</td><td>0.749</td></tr><tr><td>P(4)</td><td>2156.5612</td><td>1.171</td><td>R(16)</td><td>2163.0016</td><td>1.368</td></tr><tr><td>P(3)</td><td>2156.8785</td><td>0.452</td><td>R(17)</td><td>2163.2965</td><td>0.617</td></tr><tr><td>P(2)</td><td>2157.1948</td><td>0.614</td><td>R(18)</td><td>2163.5903</td><td>1.101</td></tr><tr><td>P(1)</td><td>2157.5101</td><td>0.155</td><td>R(19)</td><td>2163.8830</td><td>0.485</td></tr></tbody></table>

**Note.** Excitation rates are expressed in photons s⁻¹ molecule⁻¹. The excitation rate of the whole ν₃ band is g<sub>ν</sub> = 5.22 × 10⁻⁵ photons s⁻¹ molecule⁻¹.

The density of parent species at a distance R > R₀ from the nucleus is given by

$$n(R) = \frac{Q}{4\pi\nu_0 R^2} \exp\left(-\frac{R-R_0}{\gamma}\right), \qquad (27)$$

where Q is the production rate of the parent species (expressed in molecules s⁻¹) and γ is the scale length, defined as γ = ν₀τ₀. The column density of molecules, N(ρ), is obtained by integrating n(R) along the line of sight:

$$N(\rho) = \frac{Q}{4\pi\nu_0} \exp\left(\frac{R_0}{\gamma}\right) \int_{-\infty}^{\infty} \frac{1}{R^2} \exp\left(-\frac{R}{\gamma}\right) dz, \qquad (28)$$

$$= \frac{Q}{2\pi\nu_0\rho} \exp\left(\frac{R_0}{\gamma}\right) \int_{0}^{\pi/2} \exp\left(-\frac{\rho}{\gamma \cos \alpha}\right) d\alpha, \qquad (29)$$

where we changed the variable of integration for α such that ρ = R cos α, and dz = ρdα/cos²α (the change of variables is illustrated in the Appendix). We write M(s) for the total number of molecules for a specific parent species observed through a circular aperture s as

$$M(s) = 2\pi \int_{R_0}^{R} \rho N(\rho) d\rho, \qquad (30)$$

where we assumed that the aperture was centered on the nucleus. R ≈ Δ × s is the physical size at the comet given the geocentric distance Δ, with s in radian. The total number of
<figure><img src="image_15.png" /><figcaption>**Figure 6.** JWST/NIRSPEC spectrum of comet C/2022 E3 (ZTF) (in black) between 2320 and 2380 cm⁻¹. A first-order background signal (due to the scattered light on the dust) has been removed, and the spectrum has then been normalized. The intensity distribution in the band enabled us to estimate the rotational temperature of CO₂ as T = 56 K. In green, a synthetic fluorescence spectrum at this rotational temperature, based on data from HITRAN (I. Gordon et al. 2022) and convolved taking into account the resolving power of JWST/NIRSPEC (R ~ 2700), is represented.</figcaption></figure>

molecules is obtained when s, R → ∞ in Equation (30):

$$M(\infty) = \frac{Q}{v_0} \exp\left(\frac{R_0}{\gamma}\right) \left(\gamma - \int_0^{R_0} \int_0^{\pi/2} \exp\left(-\frac{\rho}{\gamma \cos \alpha}\right) d\alpha d\rho\right), \quad (31)$$

$$\approx \frac{Q\gamma}{v_0}, \quad \text{since } R_0 \ll \gamma. \qquad (32)$$

For a rectangular aperture of dimensions s₁, s₂, centered on the nucleus,

$$M(s_1, s_2) = \left( 4 \int_0^{R_2} \int_0^{R_1} N(x, y) dxdy \right) - \left( 2\pi \int_0^{R_0} \rho N(\rho) d\rho \right), \quad (33)$$

where R₁ ≈ Δ × s₁, R₂ ≈ Δ × s₂. Again, as the second term is much smaller than the first one, the total number of molecules is approximately

$$M(s_1, s_2) \approx 4 \int_0^{R_2} \int_0^{R_1} N(x, y) dxdy. \quad (34)$$

The geometric factor f in the production rate's equation (Equation (25)) is then

$$f = \frac{M(s_1, s_2)}{M(\infty)}. \qquad (35)$$

This factor depends on the slit's dimensions (3.0 × 3.0), the radius R₀ of the cometary nucleus (we assumed R₀ = 2.5 km, a value compatible with a recent photometric study of C/2022 E3 (ZTF); B. Liu & X. Liu 2024), the geocentric distance Δ, the lifetime τ at the heliocentric distance Rₕ (τ = τ₁au × R²ₕ), and the ejection velocity v₀ of the parent species (we chose v₀ = 0.8 × R⁻⁰.⁵ km s⁻¹).

The photodissociation rate of C₂N₂ at 1 au (k = 3.08 × 10⁻⁵ s⁻¹) was computed by D. Bockelee-Morvan & J. Crovisier (1985), using vacuum ultraviolet spectra from J. A. Nuth & S. Glicker (1982). This leads to a photodissociation lifetime at

1 au equal to τ₁au = 3.25 × 10⁴ s, which is very close to the lifetime of acetylene (C₂H₂) at 1 au (τ₁au = 3.2 × 10⁴ s), as reported by J. Crovisier & T. Encrenaz (1983).

We simulated synthetic spectra of C₂N₂ up to J = 50 to retrieve an upper limit (at 3σ-level) in the spectrum of C/2022 E3 (ZTF). We assumed the rotational temperature of C₂N₂ was equal to the rotational temperature derived with the CO₂ ν₃ band (Tᵣ₉₄ = 56 K). We convolved the emission lines using the resolving power of JWST/NIRSPEC, choosing a Gaussian profile for the convolution. The resolution of JWST/NIRSPEC in this configuration (R ~ 2700) is too low to observe lines of C₂N₂ individually, as its rotational constant is low (B ~ 0.157 cm⁻¹). As a comparison, the much larger rotational constant of CO (B ~ 1.922 cm⁻¹; D. Rank et al. 1965) leads to a much larger separation between two consecutive lines. This is illustrated in Figure 7. We obtained Q (C₂N₂) < 6 × 10²⁵ molecules s⁻¹ (3σ), where this upper limit corresponds to the maximum production rate at which the total contribution of the C₂N₂ band remains below the 3σ noise level in the JWST/NIRSPEC spectrum. Since the 3σ noise level is calculated from regions where no emission lines are visible, it takes into account the various noise sources (coming from both the instrument itself and photon noise due to the intensity of the light scattered by the dust particles). A blend with other molecular species is unlikely—with the exception of the bright emission lines appearing in Figure 7—because no emission bands appear in the spectral range corresponding to the C₂N₂ band.

From three water lines with known g-factors at T = 60 K (summarized in Table 5; N. Dello Russo et al. 2000), we estimated the production rate of water of C/2022 E3 (ZTF) on 2023 March 1 as Q(H₂O) ~ 3 × 10²⁸ molecules s⁻¹. We assumed a usual ortho to para ratio of 3, and a growth factor of 1.8. The derived value is very close to the mean production rate of water derived by M. Combi et al. (2023; reported in J. Li et al. 2025) 1 month prior to the JWST measurements, when Rₕ = 1.162 au (postperihelion): 3.05 ± 0.06 × 10²⁸ molecules s⁻¹.

Our upper limit on the mixing ratio of cyanogen is C₂N₂/H₂O < 0.22% (3σ). This value is still higher than the abundances derived in situ in the coma of 67P (N. Hänni et al. 2021): C₂N₂/HCN = 0.18% ± 0.09%, (1.24–1.74 au), and HCN/H₂O = 0.14% ± 0.04% in 2015 May, at the same time as detection of C₂N₂ (M. Rubin et al. 2019).

## 6.3. Perspectives

The mixing ratios measured in comet 67P mentioned above correspond to a C₂N₂/H₂O ~ 3 × 10⁻⁶ for this comet. Such a ratio, if similar for other comets, would imply a minimum water production rate of about 6 × 10²⁵/3 × 10⁻⁶ ~ 2 × 10³¹ molecules s⁻¹ as the minimum water production rate to allow detection of C₂N₂ (if considering similar heliocentric and geocentric distances to the ones at the time of comet C/2022 E3 (ZTF) observations). Such a water production rate can be compared to that measured in comet C/1995 O1 Hale-Bopp of about 8.3 × 10³⁰ molecules s⁻¹ (N. Dello Russo et al. 2000), i.e., of the same order of magnitude. Such values confirm that C₂N₂ could reasonably be detected by infrared spectroscopy with ground-based facilities or infrared space observatories for some comets, if they are bright enough, for small heliocentric and geocentric distances (those at the time of observations of comet C/2022 E3 (ZTF) not being truly optimal). Additionally, advancements in telescope technology will contribute to reducing uncertainties. Instruments like METIS (Mid-Infrared ELT Imager and Spectrograph), planned for installation in 2028 on the 39 m
<figure><img src="image_16.png" /><figcaption>**Figure 7.** Top: JWST/NIRSPEC spectrum of comet C/2022 E3 (ZTF) between 2140 and 2175 cm⁻¹. Emission lines of CO (ν₁) and of H₂O are represented by alternated gray and blue lines, respectively. Bottom: synthetic spectrum of C₂N₂ (solid curve) calculated as the sum of ν₃ lines (dashed lines) up to *J* = 50 at *T* = 56 K, convoluted by the JWST/NIRSPEC resolving power (*R* ~ 2700). The ±3σ flux error envelope is represented in pink in each plot.</figcaption></figure>

<table><caption>**Table 5**

Emission Lines of Water Used to Estimate the Water Production Rate in Comet C/2022 E3 (ZTF) on 2023 March 1</caption><thead><tr><th>Band Assignment</th><th>Line Assignment</th><th>Rest Frequency (cm<sup>-1</sup>)</th><th>g-factors at 60 K (s<sup>-1</sup>)</th><th>Measured Flux (W m<sup>-2</sup>)</th><th>Q<sub>H<sub>2</sub>O</sub> (s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>100–010</td><td>1<sub>01</sub> – 1<sub>10</sub></td><td>2039.95</td><td>7.15 × 10<sup>-7</sup></td><td>2.9631(52) × 10<sup>-18</sup></td><td>2.96 × 10<sup>28</sup></td></tr><tr><td>001–010</td><td>0<sub>00</sub> – 1<sub>01</sub></td><td>2137.37</td><td>8.22 × 10<sup>-7</sup></td><td>3.6173(46) × 10<sup>-18</sup></td><td>3.00 × 10<sup>28</sup></td></tr><tr><td>001–010</td><td>1<sub>11</sub> – 1<sub>10</sub></td><td>2151.19</td><td>5.70 × 10<sup>-7</sup></td><td>2.5353(48) × 10<sup>-18</sup></td><td>3.01 × 10<sup>28</sup></td></tr></tbody></table>

**Note.** g-factors (from N. Dello Russo et al. 2000) are expressed for *R*<sub>h</sub> = 1 au, and assuming an ortho-to-para ratio of 3.

ESO Extremely Large Telescope (ELT; B. R. Brandl et al. 2018), will offer high-resolution spectroscopy (*R* ~ 100,000) in the *L/M* infrared windows. B. Brandl et al. (2010) provide a comparison of the sensitivity between JWST/NIRSPEC and METIS for the *M* band (their Figure 3). It is found that METIS should be about twice as sensitive as JWST/NIRSPEC in this band, which should facilitate the detection of C₂N₂ emission lines, mainly due to a much higher spectral resolution allowing the separation of the different lines. Such an instrument should make it possible to better understand the production rates of C₂N₂, thus offering new possibilities for probing its presence in cometary atmospheres.

## 7. Conclusions

This study presents a fluorescence model for the ν₃ vibrational band of cyanogen (C₂N₂), offering a robust tool for analyzing its spectral characteristics in cometary environments. By combining high-resolution laboratory spectra with detailed theoretical modeling, we have, for the first time, derived line-by-line excitation rates for this molecule. The analysis of the ν₃ band confirms that cyanogen's fluorescence efficiency is low; however, future bright comets observed either with JWST or ground-based facilities such as METIS

are expected to significantly improve the detection and characterization of cyanogen in cometary spectra.

Cyanogen is the second molecule studied as part of the COSMIC project (COMputation and Spectroscopy of Molecules in the Infrared for Comets), following chloromethane (CH₃Cl; P. Hardy et al. 2023). Although the ESA/Rosetta mission led to the discovery of approximately 40 new molecules, molecular databases remain incomplete, lacking data on many key species needed to analyze trace elements in cometary spectra effectively. This work highlights the importance of continued laboratory spectroscopy efforts to expand these databases and enhance our understanding of cometary chemistry, and of the origins of our solar system.

## Acknowledgments

The authors are grateful to Jean Vander Auwera from Université Libre de Bruxelles for providing the MSFP program to fit line intensities. We also thank the anonymous reviewers for their thorough and constructive feedback. The COSMIC project is financed by the EIPHI Graduate School and held by ICB and UTINAM, supported by the Conseil Régional de Bourgogne Franche-Comté and the French National Research Agency (ANR).
## Data Availability

The database supporting the results presented in this article is freely available at the VAMDC: https://vamdc.icb.cnrs.fr/download/C2N2-Dijon-Database.zip. A copy of this database has also been deposited to Zenodo: doi:10.5281/zenodo.15658824. It contains the rotational, vibrational, and total partition function, the analysis of line positions for all bands discussed in this work (summarized in a PGOPHER output file), and the intensity fitting of the $\nu_3$ lines performed using the MSFP program, as well as the calculated g-factors at various temperatures.

## Appendix

### Additional Figures

Figures 8–10 provide additional details related to the spectral analysis and modeling. Figure 8 shows measured and calculated $\nu_3$ line intensities, with selected and rejected lines and the corresponding residuals. Figure 9 presents spectral regions with increasing rotational quantum number *J*, showing band splitting and contributions from hot bands. Figure 10 defines the geometric variables used in the derivation of Equation (28).

<figure><img src="image_17.png" /></figure>

**Figure 8.** Top: comparison between measured (dots) and calculated (blue solid lines) intensities of $\nu_3$ absorption lines with respect to *m* (defined in Section 3). Black dots represent the 147 lines that were used to derive the band strength and the Herman–Wallis correction. We also represented the rejected lines in red: they correspond to lines blended with at least one line originating from a hot band. Error bars are displayed for each dot, but are too small to be seen in most of the cases. Bottom: fit residuals, expressed as the relative difference (($\text{Obs.} - \text{Cal.}$)/Cal.), showing deviations between observed and calculated intensities.
<figure><img src="image_18.png" /></figure>

(a) Comparison between the calculated and experimental spectrum in the region 2159.33-2159.56 cm⁻¹. The ν₃ + ν₅ - ν₅ R(10) lines (in green) and the ν₃ + ν₄ - ν₄ R(14) lines (in blue) are blended.

<figure><img src="image_19.png" /></figure>

(b) Comparison between the calculated and experimental spectrum in the region 2163.69-2163.92 cm⁻¹. The ν₃ + ν₅ - ν₅ R(25) lines (in green) and the ν₃ + ν₄ - ν₄ R(29) lines (in blue) are separating.

<figure><img src="image_20.png" /></figure>

(c) Comparison between the calculated and experimental spectrum in the region 2167.69-2167.92 cm⁻¹. The ν₃ + ν₅ - ν₅ R(39) lines (in green) and the ν₃ + ν₄ - ν₄ R(44) lines (in blue) are well separated.

**Figure 9.** Three regions in the *R* branch with increasing rotational quantum number *J* (in respect to each band) from (a)–(c). The splitting of ν₃ + ν₅ - ν₅ and ν₃ + ν₄ - ν₄ is getting stronger as *J* is increasing. Some absorption lines coming from hot bands not taken into account in this work can be observed while comparing the experimental spectrum (in brown) with the total simulation (in black). An arbitrary Gaussian profile and relative intensities have been chosen to calculate the spectra in PGOPHER.

<figure><img src="image_21.png" /></figure>

**Figure 10.** Variables used to derive the integral in Equation (28). ρ = R cos α, dl/R = tan dα ≈ dα, and dl/dz = cos α. This leads to dz = ρ/cos² α dα.

ORCID iDs

P. Hardy https://orcid.org/0009-0007-4824-0504

P. Rousselot https://orcid.org/0000-0001-6798-7805

C. Richard https://orcid.org/0000-0002-8882-8448

V. Boudon https://orcid.org/0000-0001-5015-6538

X. Landsheere https://orcid.org/0000-0001-8289-7795

A. Voute https://orcid.org/0000-0001-8318-0761

L. Manceron https://orcid.org/0000-0001-5033-4293

F. Kwabia Tchana https://orcid.org/0000-0002-8322-0978

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