Formation of the Methyl Cation by Photochemistry in a Protoplanetary Disk

Olivier Berné1, Marie-Aline Martin-Drumel2, Ilane Schroetter1, Javier R.
Goicoechea3, Ugo Jacovella2, Bérenger Gans2, Emmanuel Dartois2, Laurent
Coudert2, Edwin Bergin4, Felipe Alarcon4, Jan Cami5,6,7, Evelyne Roueff8, John
H. Black9, Oskar Asvany10, Emilie Habart11, Els Peeters5,6,7, Amelie Canin1,
Boris Trahin11, Christine Joblin1, Stephan Schlemmer10, Sven Thorwirth10, Jose
Cernicharo3, Maryvonne Gerin8, Alexander Tielens12,13, Marion Zannese11, Alain
Abergel11, Jeronimo Bernard-Salas14,15, Christiaan Boersma16, Emeric Bron8,
Ryan Chown5,6, Sara Cuadrado3, Daniel Dicken11, Meriem Elyajouri11, Asunción
Fuente17, Karl D. Gordon18, Lina Issa1, Olga Kannavou11, Baria Khan5, Ozan
Lacinbala27, David Languignon8, Romane Le Gal19,20, Alexandros
Maragkoudakis16, Raphael Meshaka8, Yoko Okada10, Takashi Onaka21,22, Sofia
Pasquini5, Marc W. Pound13, Massimo Robberto18, Markus Röllig23,24, Bethany
Schefter5, Thiébaut Schirmer11,25, Ameek Sidhu5,6, Benoit Tabone11, Dries Van
De Putte18, Sílvia Vicente26, Mark G. Wolfire13.

1Institut de Recherche en Astrophysique et Planétologie, Université de
Toulouse, CNRS, CNES, UPS, 9 Av. du colonel Roche, 31028 Toulouse Cedex 04,
France
2Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d’Orsay,
91405 Orsay, France
3Instituto de Física Fundamental (CSIC). Calle Serrano 121-123, 28006, Madrid,
Spain.
4Department of Astronomy, University of Michigan, 1085 South University
Avenue, Ann Arbor, MI 48109, USA
5Department of Physics & Astronomy, The University of Western Ontario, London
ON N6A 3K7, Canada
6Institute for Earth and Space Exploration, The University of Western Ontario,
London ON N6A 3K7, Canada
7Carl Sagan Center, SETI Institute, 339 Bernardo Avenue, Suite 200, Mountain
View, CA 94043, USA
8LERMA, Observatoire de Paris, PSL University, Sorbonne Université, CNRS, 5
place Janssen, 92190, Meudon Cedex, France.
9Department of Space, Earth, and Environment, Chalmers University of
Technology, Onsala Space Observatory, 43992 Onsala, Sweden.
10I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937
Köln, Germany
11Institut d’Astrophysique Spatiale, Université Paris-Saclay, CNRS, Bâtiment
121, 91405 Orsay Cedex, France
12Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The
Netherlands
13Astronomy Department, University of Maryland, College Park, MD 20742, USA
14ACRI-ST, Centre d’Etudes et de Recherche de Grasse (CERGA), 10 Av. Nicolas
Copernic, F-06130 Grasse, France
15INCLASS Common Laboratory., 10 Av. Nicolas Copernic, 06130 Grasse, France
16 NASA Ames Research Center, MS 245-6, Moffett Field, CA 94035-1000, USA
17Observatorio Astronómico Nacional (OAN,IGN), Alfonso XII, 3, E-28014 Madrid,
Spain
18Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA
19Institut de Planétologie et d’Astrophysique de Grenoble (IPAG), Université
Grenoble Alpes, CNRS, F-38000 Grenoble, France
20Institut de Radioastronomie Millimétrique (IRAM), 300 Rue de la Piscine,
F-38406 Saint-Martin d’Hères, France
21Department of Physics, Faculty of Science and Engineering, Meisei
University, 2-1-1 Hodokubo, Hino, Tokyo 191-8506, Japan
22Department of Astronomy, Graduate School of Science, The University of
Tokyo, 7-3-1 Bunkyo-ku, Tokyo 113-0033, Japan
23 Physikalischer Verein - Gesellschaft für Bildung und Wissenschaft, Robert-
Mayer-Str. 2, 60325 Frankfurt, Germany
24 Goethe-Universität, Physikalisches Institut, Frankfurt am Main, Germany
25Department of Space, Earth and Environment, Chalmers University of
Technology, Onsala Space Observatory, SE-439 92 Onsala, Sweden
26Instituto de Astrofísica e Ciências do Espaço, Tapada da Ajuda, Edifício
Leste, 2 ∘ Piso, P-1349-018 Lisboa, Portugal
27 KU Leuven Quantum Solid State Physics (QSP) Celestijnenlaan 200d - box 2414
3001 Leuven

> Forty years ago it was proposed that gas phase organic chemistry in the
> interstellar medium was initiated by the methyl cation CH3+ (?, ?, ?), but
> hitherto it has not been observed outside the Solar System (?, ?).
> Alternative routes involving processes on grain surfaces have been invoked
> (?, ?). Here we report JWST observations of CH3+ in a protoplanetary disk in
> the Orion star forming region. We find that gas-phase organic chemistry is
> activated by UV irradiation.

As part of the PDRs4All Early Release Science program on the
JWST111pdrs4all.org (?), we have obtained observations of the protoplanetary
disk d203-506 (?). This object is situated in the Orion Bar, at about 0.25 pc
from the massive, strongly UV emitting Trapezium stars which are at 414 pc
from Earth (?), inside the Orion Nebula. The disk is about 100 au in radius,
and has an estimated mass of $\sim 10M_{\rm Jup}$ (Berné et al. in prep.). The
central star of d203-506 has a estimated mass of $M_{\star}=0.2\pm
0.1M_{\odot}$ (Berné et al. in prep.), typical for stars of the Orion Nebula
Cluster (?). This star is obscured by the flared disk that is seen nearly
edge-on (?). Fig. 1 shows integrated intensity images of the d203-506 disk
(see Methods for details on JWST data reduction). This includes the emission
of vibrationally and rotationally excited H2 and CH+, and fine-structure
emission of Oxygen ([OI]) and ionized iron ([FeII]). The molecular emission
arises from a hot ($T_{\rm gas}\sim 1000\,$K) and dense
($n_{\mathrm{H}}>10^{5}$ cm-3) wind that is produced by photoevaporation from
the disk due to irradiation by far-UV photons (FUV; 6 $<$ $E$ $<$ 13.6 eV)
from the Trapezium stars (Berné et al. in prep.). The [FeII] image shows the
emission associated with a collimated jet. Some of the wind emission is co-
spatial with this jet, but overall the wind is more extended and creates a
“halo” around the disk.

The mid infrared spectrum of d203-506 was obtained using the MIRI-MRS
spectrometer onboard JWST (see Methods for details) and is shown in Fig. 2. In
the spectrum, we detect pure rotational lines of H2 [0-0 S(1) to 0-0 S(8)]
from which we derive an excitation temperature $T_{\rm ex}=923\pm 48$ K
(Methods). The straight line observed in the excitation diagram derived from
these lines (Extended Data Fig. 3) indicates that the excitation temperature
of H2 is close to the gas kinetic temperature, and thus confirms the presence
of hot molecular gas in the wind of d203-506.

In addition to identified H2 and H i emission lines (see Methods), a strong
residual emission consisting in a series of lines in the 6.5–8.0 µm range is
observed (Fig. 2). This emission, as seen in the lower middle panel of Fig. 1,
is spatially resolved and only present in d203-506. It is co-spatial with H_2
and CH+ emission, with the best spatial correlation observed with the 2.12 µm
line of vibrationally excited H2 (see Fig. 1). We conclude that the observed
features in Fig. 2 are an astrophysical signal associated with emission from
the wind of the d203-506 protoplanetary disk. We note however, that given that
the angular resolution of MIRI is at the limit to resolve the structures in
d203-506, we cannot fully exclude an emission contribution from the jet.

The 7 µm band visible in Fig. 2 is composed of a succession of narrow features
corresponding to ro-vibrational transitions of a molecular carrier. Such
insight into the detailed structure of the band is enabled by the
unprecedented high spectral resolution and high sensitivity provided by JWST
in that spectral region. The presence of these resolved structures, and their
spectral span, is compatible with a light molecular carrier. The wavelength
coincidence between the observed emission features around 7 µm (Fig. 2) and
the $\nu_{2}$ (out-of-plane bending, “umbrella” motion) and $\nu_{4}$ (in-
plane bending) bands of CH3+ (?) is striking. Besides CH3+, not a single match
has been found for a molecule that would possess its shortest wavelength
emission signature at 7 µm (see details in the Supplementary information).
Recent laboratory work on the low temperature vibrational spectroscopy of CH3+
(?) finds the vibrational bands match the observed wavelengths. Two additional
spectroscopic analyses further strengthen the CH3+ assignment. First, the
intensity pattern of successive emission lines (Fig. 3) is characteristic of
the spin statistics of a molecular carrier suggesting three equivalent non-
zero-spin atoms (e.g., hydrogen atoms), as expected for CH${}_{3}^{+}$.
Second, the observed emission spectrum can be satisfactorily simulated (see
Fig. 3) using sets of spectroscopic constants taking values within the range
of what is expected from available calculations (Refs. (?, ?) and this work,
see Table LABEL:table:fit_results) and laboratory measurements (?). A detailed
description of the spectroscopic analysis procedure is given in the Methods.
Quantum number assignments to the ro-vibrational transitions in this spectral
range will require both additional theoretical input (notably investigating
the Coriolis interaction between the two bands (?)) and laboratory
measurements, in particular at even higher resolution and ideally at cold
temperature to reduce the spectral density. The higher energy $\nu_{3}$ band
of CH${}_{3}^{+}$, situated near 3 µm, has been measured at high resolution in
the laboratory (?). Some of the expected lines from the $\nu_{3}$ band in this
spectral range are tentatively detected with NIRSpec in d203-506 (see
Supplementary Information and Extended Data Fig. 6). In summary, by
spectroscopic standards, CH3+ is the best candidate to explain the 7 µm
spectral band observed towards the d203-506 protoplanetary disk.

Table 1: Spectroscopic parameters of CH3+ in the two excited states $\nu_{2}$
and $\nu_{4}$ from experiment and theory, and comparison with constants from
our best model of the observed signatures. The ground state values ($v=0$) are
kept fixed to the experimental values determined in Ref. (?). See Table 3 for
a more complete set of parameters.

Parameter | Unit | $v_{2}=1$ |  | $v_{4}=1$
---|---|---|---|---
|  | Prediction | Model |  | Prediction | Model
$\nu$ |  cm-1 |  1372–1412a | 1391 |  |  1373–1393b | 1375
| µm | 7.289–7.082 | 7.133 |  | 7.283–7.179 | 7.273
$B$ |  cm-1 |  9.06–9.49c | 9.37 |  |  9.48–9.52c | 9.50
$C$ |  cm-1 |  4.61–4.66c | 4.66 |  |  4.55–4.65c | 4.57

a 1$\sigma$ confidence interval from the experimental values of Ref. (?) (1402
$\pm$ 10 cm-1) and Ref. (?) (1387 $\pm$ 15 cm-1).

b 1$\sigma$ confidence interval from the experimental value of Ref. (?) (1383
$\pm$ 10 cm-1)

c from Refs. (?, ?) and this work, and scaled to the ground state parameters
of Ref. (?), see Table 3

The presence of CH${}_{3}^{+}$ in d203-506 raises the question of its origin.
Carbon chemistry in these environments typically starts by the radiative
association C+ + H2 -¿ CH2+ + $h\nu$, which is a very slow process. The
alternative bimolecular reaction C+ + H2 ($v$ = 0) -¿ CH+ + H [1], is
endothermic by $\Delta E$/$k_{\mathrm{B}}$ = 4300 K (?, ?), and thus very slow
in cold ($T\sim 100$K) interstellar gas where $T$ $\ll$ $\Delta
E$/$k_{\mathrm{B}}$. However, strong external FUV radiation fields combined
with high gas densities as found in protoplanetary disks open new routes for
chemistry. The irradiated gas reaches high temperatures (near 1000 K, (?)) and
a significant fraction of the H2 molecules are radiatively pumped through
fluoresence to vibrationally excited states (?), H${}_{2}^{*}$ ($v$$>$0). This
suprathermal excitation overcomes the endothermicity of reaction [1], allowing
H${}_{2}^{*}$ to react with C+, leading to the formation of abundant CH+ (?,
?, ?). Subsequent fast and exothermic hydrogen abstraction reactions CH+
$\xrightarrow[(2)]{\rm H_{2}}$ CH${}_{2}^{+}$ $\xrightarrow[(3)]{\rm H_{2}}$
CH${}_{3}^{+}$ then efficiently lead to CH${}_{3}^{+}$. In the Methods
section, we quantitatively assess these processes using models, and show that
for a wide range of acceptable parameters, CH${}_{3}^{+}$ is formed
efficiently in FUV irradiated environments. The formed CH${}_{3}^{+}$ reacts
very slowly with H2 (through radiative association) and is mainly destroyed by
dissociative recombination with electrons, leading to CH2, CH, and C in
comparable amounts (?). CH${}_{3}^{+}$ can also be destroyed by reactions with
neutral oxygen producing HCO+ and with neutral molecules producing molecular
ions. These undergo dissociative recombination with electrons yielding complex
organic molecules. Therefore, in the presence of UV radiation, gas-phase
organic chemistry is initiated through CH${}_{3}^{+}$ (?, ?, ?).

The ongoing chemistry in d203-506 described above differs greatly from what
has been observed in disks that are not exposed to external UV irradiation
where the freeze out of H2O and CO2 control the gas composition. In such
disks, high abundances of water, HCN, CH4, C2H2, etc. are observed (?, ?),
species which are not detected in d203-506. In the last decades, the formation
of organic molecules in space has been considered to happen mostly at the
surface of grains (?, ?). The detection of CH${}_{3}^{+}$ indicates that
alternative gas-phase routes are available to activate the organic chemistry,
when UV radiation is present. Far from being anecdotal, external UV
irradiation is expected to occur during the early life of most protoplanetary
disks (?), making UV-driven organic chemistry common for the chemical
evolution of most protoplanetary disks and of the early the Solar System (?,
?). More generally, this chemistry can be active in any environment providing
sufficiently high gas density and FUV irradiation ($n_{\rm H}\gtrsim 10^{5}$
cm-3, $G_{0}\gtrsim 10^{4}$). This can include, for instance, star-forming
regions, the envelopes of planetary nebulae, the inner regions of disks around
T-Tauri stars, and the interstellar medium of star-forming galaxies near and
far. While the CH${}_{3}^{+}$ detection presented here is a promising
achievement, there are still numerous unanswered questions surrounding the
excitation, chemistry, and spectroscopic properties of this species (Methods
and Supplementary Information). These topics shall be addressed thanks to
interdisciplinary scientific efforts that incorporate the expertise of
astronomers, physicists, and spectroscopists (both laboratory and theory) in
order to fully understand the role of CH${}_{3}^{+}$ in organic chemistry in
space.

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Figure 1:  Overview of the d203-506 externally irradiated protoplanetary disk.
Integrated intensity images from NIRCam F212N filter (a), Hubble Space
Telescope [OI] (b), NIRSpec [FeII] (c), NIRSpec CH+ 1-0 $P(7)$ at 3.95 µm (d),
and MIRI MRS integrated from 7.16 to 7.20 µm assigned to CH${}_{3}^{+}$ (e).
Each panel is centered at $\alpha$=5:35:20.318 and $\delta$=-5:25:05.662 and
are $2^{\prime\prime}\times 2^{\prime\prime}$ wide. Contours of NIRCam
vibrationally excited H2 (2.12 µm band) are represented in orange, and ALMA
dust continuum emission at 344 GHz from the disk in white contours. (f,)
Sketch of the d203-506 disk, jet, and wind. We note that the low mass star is
not seen in the images because of the disk flaring. All JWST images are from
the PDRs4All program, while the Hubble image is from (?).  Figure 2:  JWST-
MRIRI spectra of d203-506. a, Spectrum on the position of d203-506 (ON, green)
and close to 203-506 (OFF, orange) over the 6-9 µm MIRI-MRS spectral range.
The OFF spectrum is dominated by emission of the Orion Nebula: The broad
features at 6.2, 7.7 and 8.6 µm are due to the emission of UV excited
polycyclic aromatic hydrocarbons (PAHs, see Chown et al. in prep. for a
detailed discussion). b, Spectrum of d203-506 after subtraction of the nebular
emission (ON $-$ OFF).  Figure 3: Comparison between the observed JWST
spectrum of d203-506 and modeled CH${}_{3}^{+}$ spectrum. a, Full spectrum. b,
Zoom on the strongest lines. The model (black curve) for the $\nu_{2}$ and
$\nu_{4}$ vibrations of CH${}_{3}^{+}$ was obtained using the constants of
Table LABEL:table:fit_results (see Methods for a more detailed description of
the simulation). A Gaussian linewidth of 0.35 cm-1, corresponding to the MIRI
MRS resolution in this range ($\frac{\lambda}{\Delta\lambda}\sim 3800$), has
been used in the simulation performed using PGOPHER (?). For clarity, the
observational spectrum has been baseline corrected using a spline function and
strong individual lines have been removed from the plot : [Ni II] at 6.63, H2
at 6.92, [Ar II] at 6.99, He I at 7.47, and H2 at 8.02 µm. The standard
deviation (1$\sigma$) of the noise level is $\sim 10$ MJy sr-1 in this range.
The observed lines are 10 to 100 times this noise level.

## Acknowledgments

OB is funded by a CNES APR program. MIRI data reduction is performed at the
French MIRI centre of expertise with the support of CNES and the ANR-labcom
INCLASS between IAS and the company ACRI-ST. Part of this work was supported
by the Programme National “Physique et Chimie du Milieu Interstellaire” (PCMI)
of CNRS/INSU with INC/INP co-funded by CEA and CNES. Quantum chemical
calculations were performed using HPC resources from the “Mésocentre”
computing center of CentraleSupélec and École Normale Supérieure Paris-Saclay
supported by CNRS and Région Île-de-France
(http://mesocentre.centralesupelec.fr/). JRG and SC thank the Spanish MCINN
for funding support under grant PID2019-106110GB-I00. JC and EP acknowledge
support from the University of Western Ontario, the Institute for Earth and
Space Exploration, the Canadian Space Agency, and the Natural Sciences and
Engineering Research Council of Canada. The Cologne spectroscopy group
acknowledges funding by the Deutsche Forschungsgemeinschaft DFG (CRC956, sub-
project B2, ID 184018867) and the ERC AdG Missions (ID: 101020583). Work by YO
and MR is carried out within the Collaborative Research Centre 956, sub-
project C1, funded by the DFG – project ID 184018867. CB is grateful for an
appointment at NASA Ames Research Center through the San José State University
Research Foundation (80NSSC22M0107). TO acknowledges support from JSPS
Bilateral Program, Grant Number 120219939.

## Author contributions

O.B. found the signal in the data and led the analysis of the data and write-
up of the article. M.A.M.D., I.S., U.J., B.G., E.D., L.C., E.B., F.A., J.C.,
E.R., J.B., O.A., C.J., S.S., S.T., J.C., M.G., A.T., T.O., M.Z. conducted the
spectroscopic analysis and participated in the write-up. M.A.M.D. created
figures 3, S4, S5. I.S. created figures 1, 2, S1, S2, S3. I.S. and O.B.
created figure S6. J.G. performed the chemical models and figures S7, S8 and
participated in the write-up. O.B., E.H., E.P. led the JWST observing program.
I.S., J.G., E.D., E.B., F.A., J.C., A.C., B.T., C.J., A.T., M.Z., A.A.,
J.B.S., C.B., E.B., R.C., S.C., D.D., M.E., A.F., K.D., L.I., O.K., B.K.,
O.L., D.L., R.L.G., A.M., R.M., Y.O., T.O., S.P., M.P., M.R., M.R., B.S.,
T.S., A.S., B.T., D.V.P., S.V. and M.W. contributed to the observing program
with JWST. I.S., A.C., R.C., A.S., B.T., F.A., D.V.P. reduced the data. E.D.,
M.A.M.D., L.C., J.G. and O.B. conducted the column density analysis. J.H.B.
wrote the section on the excitation of CH3+. M.W. and J.H.B. corrected the
English throughout the manuscript. All authors contributed to the discussions
and provided feedback on the manuscript.

## Methods

### Observations and data reduction

The JWST/MIRI Medium Resolution Spectroscopy (MRS) Integral Field Unit (IFU)
data were obtained on 2023 January 31 as part of the JWST ERS 1288 program
(PI: O. Berné, E. Habart, E. Peeters, (?)) referred to as “PDRs4All”. All four
channels and the three sub-channels were used, covering a wavelength range of
4.9–28 µm at a spectral resolution of 4000–1500 (?). The observations are
centered on RA=05h35m 20s.4749
DEC$=-05^{\circ}\,25^{\prime}\,,10^{\prime\prime}.45$ and span a mosaic of 9
pointings. The overall science exposure time is 14086.11s for the whole
mosaic. We used the FASTR1 readout mode with 4-point dithering. We reduced the
data using the JWST Data Reduction pipeline version 1.9.5. The stage 2
residual fringe correction was applied in addition to the standard fringe
correction step. A master background subtraction was applied in stage 3 of the
reduction. At the end of the data reduction, we obtained four MIRI datacubes,
one for each channel, each channel containing its three corresponding sub-
channels (short, medium and long). The details of the data reduction for MIRI-
IFU is part of a dedicated paper by the PDRs4All team (Chown et al. in
preparation).

In this paper we also use one narrow band image of the NIRSpec observations of
the same object as well as a NIRCam filter. Specifically, we use the NIRCam
F212N filter image and the NIRSpec spectral cube corresponding to the F290LP
filter which spans from $\sim 2.9$ to 5 µm. Observations were obtained with
JWST-NIRSpec (JWST-NIRCam) on 2022 September 10 and reduced using the JWST
pipeline version 1.9.4 (1.7.1) with Calibration Reference Data System (CRDS)
context file jwst_1014.pmap (jwst_0969.pmap). For the NIRCam observations, no
OFF emission was subtracted. For the NIRSpec observations, a dedicated OFF
observation was subtracted. The details of the data reduction for these two
instruments is discussed in a dedicated paper by the PDRs4All team on NIRCam
(Habart et al. in prep) and NIRSpec (Peeters et al. in prep). The details on
the observing strategy can be found in (?).

### Data analysis

In order to work with complete spectra spanning all the MIRI MRS wavelength
range of 4.9–28 µm, we first stitch the spectra of the four channels to remove
jumps between spectral orders. For each spectrum, we arbitrarily choose the
one from Channel 2 long as a reference. Shorter and longer wavelengths
(Channels 1, 3, and 4) are thus scaled accordingly. We create (with numpy) an
array of wavelengths spanning the full wavelength range, i.e. between 4.900
and 27.901 µm, with 50 000 points and a constant step . Each channel spectrum
is then interpolated onto this grid and jumps are removed by scaling each
spectral order based on the average flux in the overlap region. The integrated
intensity is conserved in this procedure, and uncertainties propagated.

The two extracted spectra shown in blue and orange in Fig. 2 are from the “ON”
and ——OFF” position, respectively. The ON (OFF) spectrum were extracted from
an ellipse (circular aperture) centered on the position $\alpha=$ 5:35:20.357
, $\delta=$ $-$5:25:05.81 ($\alpha=$ 5:35:20.370, $\delta=$ $-$5:25:04.97),
with dimension $l=0.52$”, $h=0.38$” (of radius $r=0.365$”) and a position
angle PA=+33 (0) degrees (trigonometric) with respect to North. In order to
have the emission of d203-506 we choose to subtract the nebula emission by
evaluating ON$-$OFF. The ON and OFF spectra over the full MIRI-MRS range are
shown in Extended Data Fig. 1, and the full subtracted spectrum is shown in
Extended Data Fig. 2. In Extended Data Fig. 2, some lines are negative due to
the over-subtraction of ionized emission lines which dominate in the nebula
but are absent in d203-506. Some PAH bands are seen in negative in the
ON$-$OFF spectrum; this is due to intrinsic variation of the PAH bands due to
e.g. size or ionization, and this cannot be interpreted as PAH absorption.

### Line identification

Using the ON-OFF spectrum described previously and the line list provided by
the PDRs4All ERS team (?), we identified the strong emission lines present in
the data. The main emission lines are from H i and H2 and are listed in Table
1 and 2, respectively. The H2 lines intensities presented in the latter table
are measured using a Gaussian fitting to the observed lines, and the
wavelength of the H2 transition from (?). The approach to fit the observed
lines is presented in (?). Nebular emission lines from atomic ions are also
identified and are shown in Figures 2 and 2 with black vertical lines with
their name in the attached box. In addition, a number of OH lines are also
identified between 9 and 11 µm and are shown as green vertical lines on the
same Figures. For this wavelength range we used OH wavelengths from (?) and
(?). The study of OH emission in d203-506 will be the subject of a forthcoming
paper (Zannese et al. in prep.).

From the H2 lines listed in Table 2 we derive an excitation diagram, using the
H2 Toolbox (?) developed as part of the PDRs4All project science enabling
products (see https://pdrs4all.org/seps/ and). This is a tool for fitting
temperature, column density, and ortho-to-para ratio in H2 excitation
diagrams. A one or two temperature model is assumed, and the fit finds the
excitation temperatures and column densities, and optionally ortho-to-para
ratio. The source code is available at
https://dustem.astro.umd.edu/tools.html. (?)he result of this analysis is
shown in Extended Data Fig. 3. The derived excitation temperature is $T_{\rm
ex}=923\pm 48.2K$.

### Other candidate molecules

There are no unassigned series of lines observed in the 5.2–6.2 µm range,
corresponding to C=O or C+N vibrations (Fig. 2) thus excluding most small
species containing these chemical functions as carrier of the observed 7 µm
features. At longer wavelengths (8–17 µm, see Extended Data Fig. 2), the
spectrum is devoid of strong unassigned emission lines. Many hydrocarbon
molecules, radicals, and ions (e.g., CH2, CH2+, …) possess low frequency modes
and would thus emit in that range. Instead, the lowest vibrational modes of
CH3+ lie at 7 µm. We thoroughly inspected the literature data on other
hydrocarbons and known interstellar species (both neutral and charged) for
possible matches and used local thermodynamic equilibrium (LTE) models to
predict the emission from molecules in this spectral range. The tested
molecules include—not exhaustively—H2O (and isotopologues), H2O+,
NH${}_{4}^{+}$, C2H2, CH3, HCN, SO2, all hydrocarbons present in the HITRAN
database (?), NH3, CH3OH, and CH3CN.

### Spectroscopy of the Methyl cation

CH3+ is a planar molecule belonging to the $D_{3h}$ group of symmetry. It
possesses four fundamental modes of vibration following an irreducible
representation $\Gamma=1A_{1}^{\prime}+1A_{2}^{\prime\prime}+2E^{\prime}$ (the
two $E^{\prime}$ modes are doubly degenerate). It is an oblate symmetric-top
molecule for which rotational energy levels of non-degenerate vibrational
states are described with two quantum numbers, $J$, the total-angular-momentum
quantum number excluding nuclear spin, and $K$, the projection of $\vec{N}$
(the total angular momentum excluding nuclear and electron spins) along the
principal axis of symmetry; an additional $l$ quantum number accounts for
Coriolis-coupling in degenerate vibrational states ($l=\pm 1$ in $v_{4}=1$).
The energy levels in a given vibronic state can be calculated using the energy
of the vibronic state, two rotational constants ($A=B$ and $C$), centrifugal
distortion parameters ($D_{J}$, $D_{JK}$, $D_{K}$…), and, for states of
$E^{\prime}$ symmetry, additional Coriolis-coupling and $l$-doubling
parameters ($\zeta$, $\eta_{J}$, $q$). The molecule possesses three equivalent
hydrogen atoms (fermions, $I_{\mathrm{H}}=1/2$) resulting in spin-statistical
weights of (0, 0, 4, 4, 2, 2) for the levels of the states of symmetries
($A_{1}^{\prime},A_{1}^{\prime\prime},A_{2}^{\prime},A_{2}^{\prime\prime},E^{\prime},E^{\prime\prime}$)
(?). In the following, we used the PGOPHER software (?) to simulate the
rovibrational spectrum of CH3+.

Since no experimental information is available on the $v_{2}=1$
($A_{2}^{\prime\prime}$ symmetry) and $v_{4}=1$ ($E^{\prime}$ symmetry) states
of CH3+, except the band positions (?, ?), we rely on quantum chemical
calculations to estimate the rotational constants in these excited states. We
carried out geometry optimization and anharmonic frequency analysis at the
$\omega$B97X-D/cc-pVQZ level of theory (?, ?, ?) using the Gaussian 16 suite
of electronic structure programs (?). The main results from these calculations
are reported in Table 3. The table also contains the calculated constants
reported in the literature (?, ?). Besides the rotational constants, the
quantum chemical calculations also give us insights about the transition
moments of the $\nu_{2}$ (out-of-plane bending, “umbrella” motion) and
$\nu_{4}$ (in-plane bending) bands. Our calculations predict transition
moments of 0.084 D and 0.064 D for $\nu_{2}$ and $\nu_{4}$, respectively. Such
low values have to be taken with caution as experimental values can differ
significantly, by 0.1 D or more. Nevertheless, these values are consistent
with the small values obtained by CCSD(T)/cc-pwCVTZ calculations performed in
course of the work presented in Ref. (?) (0.06 D and 0.07 D, respectively), as
well as those reported in Ref. (?) (0.049 D and 0.111 D) and Ref. (?) (0.10 D
and 0.16 D).

To assess the reliability of the spectroscopic constants derived from the
different quantum chemical calculations (both from this work and the
literature), the calculated values in $v=0$ and $v_{3}=1$ were compared to the
experimental values of the $\nu_{3}$ band. Transitions within the $\nu_{3}$
band (asymmetric stretching) observed by Crofton et al. (?) were fitted in the
present work using PGOPHER (so as to use the same model for $\nu_{3}$ and
$\nu_{2}/\nu_{4}$) leading to the spectroscopic parameters reported in Table
3. These derived parameters are in excellent agreement with those reported in
Ref. (?). They also are in very good agreement with the parameters obtained by
the anharmonic calculations from this study. These results were used to scale
the calculated constants in $v_{2}=1$ and $v_{4}=1$ according to the formula
$B_{\mathrm{scaled}\,v_{i}}=B_{\mathrm{calc}\,v_{i}}\times
B_{\mathrm{exp}\,v_{3}=1}/B_{\mathrm{calc}\,v_{3}=1}$ (and similarly for $C$).
For the rotational constants calculated in Ref. (?), since no calculated
values in $v_{3}=1$ are reported, the scaling was made using values in $v=0$.
The scaled values appear in blue in Table 3; they serve as a range of
confidence for the spectral simulations.

Despite our best efforts, no definite spectroscopic analysis of the bands
observed by JWST was achieved, i.e., we could not assign with confidence
quantum numbers to the observed transitions. Instead, we performed several
simulations by varying the rotational constants of $v_{2}=1$ and $v_{4}=1$
until qualitative agreement with the observational data was achieved. Such
qualitative agreement was assessed using the following criteria (by decreasing
order of importance): i) Q-branch line position and intensity; ii) P- and
R-branches spread and spectral line density; iii) line positions and
intensities in the P- and R-branches. In all cases, the Coriolis interaction
constants were kept fixed to the calculated values of those in $v_{3}=1$, and
so were the transition moments of the $\nu_{2}$ and $\nu_{4}$ bands. This lead
us to produce four models, I to IV (see Table 3 and Figures 4-5; model III
being the model presented in the main article), that reasonably reproduce the
astronomical data. It is worth noting, however, that the spectral density is
greater on the spectrum of d203-506 than in our simulations, which could
either reflect the presence of another species, or some discrepancies in the
rotational constants used in models I to IV. Regarding the temperature, for
all models, a rotational temperature of 400 K seems to adequately simulate the
astronomical features (i.e., the spread of the P-, Q- and R-branches). Higher
temperatures lead to P- and R-branches that spread further than what is
observed in the astronomical spectrum. While the simulations were performed
under the assumption of thermal equilibrium, astronomical excitation
conditions may differ significantly (see detailed discussion in the following
section). This is particularly relevant to the relative intensities of the
$\nu_{2}$ and $\nu_{4}$ bands, since the $v_{2}=1$ and $v_{4}=1$ vibrational
states may be populated differently in d203-506.

We have also investigated the presence of lines emanating from the $\nu_{3}$
band of CH${}_{3}^{+}$ near 3 µm in the NIRSpec data of d203-506 presented in
Berné et al.(in prep.). The $\nu_{3}$ band has been observed at high
resolution in the laboratory by Refs. (?, ?). Using the constants derived from
these observations, we computed a synthetic spectrum of the $\nu_{3}$ band at
400 K and compare it to the NIRSpec background subtracted spectrum (using the
same apertures as for MIRI, see Methods) in Extended Data Fig. 6. The
predicted lines are found to coincide with lines in the observations.

In summary, high-resolution laboratory infrared spectra of CH${}_{3}^{+}$ in
the 7 µm region are needed to identify individual transitions in the
astronomical data. First laboratory measurements at low temperatures will
initiate this process, hopefully deciphering the strong Coriolis coupling
between the degenerate $\nu_{2}$ and $\nu_{4}$ vibrations of CH${}_{3}^{+}$.
In order to support a quantitative analysis of the astronomical spectra,
laboratory works also conducted at higher temperatures are required.

### Chemistry of the Methyl cation

We modeled the chemistry in the strongly FUV–irradiated photoevaporative wind
and upper disk layers of d203-506 using the Meudon Photodissociation Region
(PDR hereafter) code (?). The code solves the FUV radiative transfer in a
medium of gas and dust (?), as well as the steady-state heating, cooling,
chemistry, and H2 ($v$, $J$) level populations as a function of depth into the
neutral disk (in mag of visual extinction $A_{V}$). Berné et al.(in prep.)
previously used this code to reproduce the H2 line intensities detected by
JWST/NIRSpec and obtained a radiation field intensity $G_{0}$ $\simeq$
4$\times$104 and a gas density $n_{\rm H}$ = $n$(H) + 2$n$(H2) $\simeq$
3.5$\times$105 cm-3 as the best-fit. We first adopt the same physical
parameters and use an extinction law suited to Orion molecular cloud (?), and
consistent with dust grains ($R_{V}$ = 5.62 and $N_{\rm H}$ / $E(B-V)$ =
1.05$\times$1022 cm-2) bigger than in standard diffuse interstellar clouds
($R_{V}$ = 3.1). This choice leads to a FUV dust extinction cross-section,
$\sigma_{\rm 1000A}$(FUV) = 1.1$\times$10-21 cm-2/H, which is in the upper
range of the cross-sections estimated by Berné et al. (in prep.) for this
object, and a factor of about two smaller than standard ISM grains. In
addition, we run models adopting ”bigger grains” (by a factor of about four),
leading to $\sigma_{\rm 1000A}$(FUV) = 7$\times$10-22 cm-2/H. This smaller FUV
cross-section is still compatible with the wind models presented by Berné et
al. (in prep.) and with the kind of dust grains expected in the upper layers
of protoplanetary disks (?).

Extended Data Fig. 7 shows the predicted density and temperature structure of
the wind and upper disk layers (upper panels) as well as the C+, CH+,
CH${}_{2}^{+}$, CH${}_{3}^{+}$, CO, and HCO+ abundance profiles (lower
panels). Figure 7a refers to models using “Orion grains” and $n_{\rm H}$ =
3.5$\times$105 cm-3 (Berné et al. in prep.). The other plots refer to models
adopting “bigger grains” and densities of 3.5$\times$105 cm-3 (Extended Data
Fig. 7b), 3.5$\times$106 cm-3 (Extended Data Fig. 7c), and 107 cm-3 (Extended
Data Fig. 7d). The latter ones are more representative of the outer layers of
a disk (?).

In all these models, reaction C+ \+ H2($v$, $J$) $\rightarrow$ CH+ $+$ H [1]
drives the formation of CH+ as soon as the H2 abundance rises. In these
conditions, high temperatures and presence of FUV-pumped vibrationally excited
H${}_{2}^{*}$, reaction [1] is much faster than the slow radiative association
reactions C+ \+ H2 $\rightarrow$ CH${}_{2}^{+}$ $+$ photon and C+ \+ H
$\rightarrow$ CH+ $+$ photon. These radiative associations produce small
amounts of CH${}_{2}^{+}$ and CH+ in cold gas ($T$ $<$ 100 K). Our models
include an H2($v$, $J$) state-dependent treatment of reaction [1] (?),
appropriate to the nonthermal populations of H${}_{2}^{*}$ in FUV-irradiated
environments. In particular, the CH+ formation rate is computed by summing
over all formation rates for each specific state of H2. Once CH+ is formed,
fast and exoergic hydrogen abstraction reactions CH+ $\xrightarrow[]{\rm
H_{2}}$ CH${}_{2}^{+}$ $\xrightarrow[]{\rm H_{2}}$ CH${}_{3}^{+}$ lead to
CH${}_{3}^{+}$. The efficiency of this chemical pipe to CH${}_{3}^{+}$ depends
on the abundance of H atoms in the gas (because they readily react with CH+;
(?)) and that of electrons (because they destroy CH${}_{2}^{+}$ and
CH${}_{3}^{+}$). Reactions with atomic hydrogen dominate CH+ destruction when
the molecular gas fraction, defined as $f_{\rm H_{2}}$ = 2$n$(H2)/$n_{\rm H}$,
is $\lesssim$ 0.5 ($f_{\rm H_{2}}$ = 1 when all hydrogen is in molecular
form). All models in Extended Data Fig. 7 predict that the CH${}_{3}^{+}$
abundance peaks close to the H /H2 transition, at $A_{V}$ $\simeq$ 1 mag,
where $T$ $\simeq$ 1000-800 K. Extended Data Fig. 8 summarizes the dominant
chemical reactions at the CH${}_{3}^{+}$ abundance peak. We note that the CH+
and CH${}_{3}^{+}$ abundance profiles roughly follow the density profile of
vibrationally excited H${}_{2}^{*}$ (dotted black curve in the upper panel of
Extended Data Fig. 7). Hence, irrespective of the exact gas density value, the
infrared H2 lines detected with JWST in d203-506 probe strongly FUV-irradiated
hot gas, where CH+ and CH${}_{3}^{+}$ efficiently form.

Our models predict $N$(CH${}_{3}^{+}$)/$N$(CH+) column density ratios of
$\simeq$ 1–15 (increasing as $n_{\rm H}$ increases). We note that the bulk
column density of these species stem from FUV-illuminated gas at $A_{V}$ $<$ 3
mag. Deeper inside, their abundances drop by orders of magnitude. Hence, both
CH+ and CH${}_{3}^{+}$ are chemical tracers of the most irradiated wind and
upper disk layers.

The local CH+ / CH${}_{3}^{+}$ abundance ratio can be analytically estimated
from the following network of gas-phase chemical reactions:

C+ \+ H2 ($v$, $J$) $\rightarrow$ CH+ $+$ H [1]

CH+ \+ H $\rightarrow$ C+ $+$ H2 [2a]

CH+ \+ H2 $\rightarrow$ CH${}_{2}^{+}$ $+$ H [2b]

CH${}_{2}^{+}$ \+ H2 $\rightarrow$ CH${}_{3}^{+}$ $+$ H [3]

CH${}_{2}^{+}$ \+ e- $\rightarrow$ products [4]

CH${}_{3}^{+}$ \+ e- $\rightarrow$ products [5]

We note that adopting the photodissociation rate of (?), CH${}_{3}^{+}$
photodissociation is expected to be much slower than dissociative
recombination with electrons even in strong UV fields. Therefore, in steady-
state one obtains:

$\frac{x({\rm CH_{3}^{+}})}{x({\rm
CH^{+}})}=\frac{k_{2b}f_{H_{2}}^{2}}{2k_{5}\,x_{e}\,(f_{H_{2}}+2x_{e}\,k_{4}/k_{3})}\simeq\frac{k_{2b}}{2k_{5}\,x_{e}}f_{{\rm
H_{2}}}$ (1)

where $x_{e}$ = $n$(e-)/$n_{\rm H}$ is the electron abundance. In the last
step we assumed that CH${}_{2}^{+}$ destruction by reactions with H2 are much
faster than dissociative recombinations with electrons at the CH${}_{3}^{+}$
abundance peak (as confirmed by the model). In our model we used the following
reaction rate coefficients: $k_{2b}$ = 1.2$\times$10-9 cm3 s-1 (?), $k_{3}$ =
1.6$\times$10-9 cm3 s-1 (?), $k_{4}$ = 6.40$\times$10-7 $(T/300)^{-0.60}$ cm3
s-1 (?), and $k_{5}$ = 6.97$\times$10-7 $(T/300)^{-0.61}$ cm3 s-1 (?). Using
representative values for the wind and upper disk layers of d203-506; $T$ =
900 K and $x_{e}$ $\simeq$ $x$(C+) $\simeq$1.4$\times$10-4, one obtains
$x$(CH${}_{3}^{+}$) / $x$(CH+) $\simeq$ 12 $f_{\rm H_{2}}$ from Eq. (1). This
analytical abundance ratio agrees with the detailed predictions of our
photochemical models. That is, the above chemical reactions dominate the
formation of CH${}_{3}^{+}$ in FUV-irradiated gas. In particular, models
predict that the CH${}_{3}^{+}$ abundance peaks at gas molecular fractions of
$f_{\rm H_{2}}$ $=$ 0.3–0.5 (pink dotted curves in Figs. 7).

Reaction [5] produces CH2, CH, and C in similar amounts (?). These are key
reactive intermediate species that trigger the chemistry of carbon species
(?). In addition, reaction O + CH${}_{3}^{+}$ $\rightarrow$ HCO+ \+ H2 (?) is
a dominant source of HCO+, and thus of CO, in these irradiated hot gas layers
( Extended Data Fig. 7 also shows the predicted HCO+ abundance profile in the
photoevaporative wind and upper disk layers). The morphology of the observed
HCO+ $J$ = 4-3 line emission (first detected by (?) and then mapped with ALMA
at high angular resolution by (Berné et al. in prep.)) resembles that of
vibrationally excited H2 and CH3+ observed with JWST (Berné et al. in prep.).
It will be difficult to explain the presence of extended HCO+ emission in
these strongly irradiated gas layers without the FUV-driven chemistry
described here and tested by the presence of CH${}_{3}^{+}$. We note that this
hot HCO+ linked to the extended H${}_{2}^{*}$ emission is different from the
HCO+ present in lower and denser layers of protoplanetary disks and formed by
standard ion-molecule chemistry (?).

Specific 2D models, better adapted to the geometry of the upper disk layers
and FUV-irradiated wind, will be needed to fully understand the density
structure and abundance distribution of the observed molecular emission with
JWST.

## Data Availability

The JWST data presented in this paper is publicly available through the MAST
online archive (http://mast.stsci.edu) using the PID 1288. The MIRI spectra
presented in Fig. 2 and Extended Data Figs. 1,2 are available in ASCII format
at https://doi.org/10.5281/zenodo.7989669. The p-Gopher files to create the
model spectra of CH3+ are available via :
https://doi.org/10.5281/zenodo.7993330.

## Code Availability

The JWST pipeline used to produce the final data produducts presented in this
article is available at https://github.com/spacetelescope/jwst. The MEUDON PDR
code is publicly available at https://ism.obspm.fr/pdr_download.html

## Author information

Supplementary Information is available for this paper.

Correspondence and requests for materials should be addressed to Olivier
Berné.

The authors declare no financial or non-financial competing interest.

## Supplementary information

### Supplementary methods

####  $\nu_{3}$ emission of CH${}_{3}^{+}$

CH${}_{3}^{+}$ has a band ($\nu_{3}$) near 3µm. This spectral range was
observed as part of the PDRs4All ERS program with the NIRSpec instrument.
These data are subject of other papers in preparation, however we present here
an analysis of these data for d203-506 in the context of the CH${}_{3}^{+}$
detection. The NIRSpec spectrum in the spectral range of the $\nu_{3}$ band is
shown in Fig. 6. The shaded region represents the $\pm 3\sigma$ error interval
of the data. This error interval has been computed as the sum of the errors
provided by the JWST pipeline and an empirical error. The empirical error is
three times the standard deviation of noise in the 3.102 to 3.126 spectral
range of NIRSpec, where no lines are present. In the same figure we show a
best fit model of the OH lines which are present in this spectral range. This
is an LTE model at a temperature of 800K. A detailed model of the OH emission
will be presented in a forthcoming paper (Zannese et al. in prep). The
objective here is not to obtain the best possible model, but rather to assess
the contribution of OH in this spectral range. The H2 lines present in the
spectral range have been fitted individually with Gaussians using the
wavelengths provided by (?). The width is set by the instrumental resolution.
The CH${}_{3}^{+}$ model used here is Model III., at a temperature of 400K.
All the models have been convolved to the spectral resolution of NIRSpec which
is 2100 in this range, and re-sampled on the NIRSpec wavelength grid. The
total model is the sum of the OH, H2 and CH${}_{3}^{+}$ models. It can be seen
in Fig. 6 that there is a good agreement between the total model and the
NIRSpec data. We note that the intensity of the detectable CH${}_{3}^{+}$
signal is comparable with the 3$\sigma$ noise of NIRSpec. Several strong lines
of CH${}_{3}^{+}$, in particular at 3.157 or 3.223 µm do appear clearly in the
data. However, at this stage, the noise level in the data is too high to
provide a definitive identification of specific lines of CH${}_{3}^{+}$ with
NIRSpec. We are currently working on obtaining a higher SNR spectrum by
improving the data reduction, and by performing additional observations.

#### Excitation of CH${}_{3}^{+}$ infrared bands

Hereafter we estimate the rates of the competing processes that might
influence the excitation and line emission of CH${}_{3}^{+}$.

COLLISIONAL EXCITATION. A vibrationally excited state of the molecule can be
excited by inelastic collisions with H or H2 with an upward rate coefficient

$q_{\ell u}=q_{0}\exp(-hc{\bar{\nu}}/kT_{k})g_{u}/g_{\ell}\;\;\;{\rm
cm}^{3}\;{\rm s}^{-1}$

where $T_{\rm k}$ is the kinetic temperature of the gas, $q_{0}$ is the
corresponding collisional quenching rate of the band $u\to\ell$, with
degeneracies $g_{u}$ and $g_{\ell}$ of the upper and lower states,
respectively. The wavenumber of the transition is ${\bar{\nu}}$. In the disk
wind, the H2 pure rotational lines, which have a critical density lower than
that of the gas density, are thermalized, hence $T_{\rm rot}(H_{2})=T_{\rm
k}\approx 900$ K. The quenching rate coefficient might be as large as
$10^{-11}$ cm3 s-1; therefore, at the gas density of the reference PDR model
shown in Fig. 7, $n_{\rm H}=3.5\times 10^{5}$ cm-3, the collisional excitation
rates of the CH${}_{3}^{+}$ $\nu_{4}$ and $\nu_{3}$ fundamental bands would be
at most $7\times 10^{-7}$ s-1 and $5\times 10^{-8}$ s-1 per ion, respectively.
For a higher density of $n_{\rm H}=10^{7}$ cm-3, these rates would be $2\times
10^{-5}$ and $1\times 10^{-6}$s-1 per ion, respectively. The spontaneous
transition probability of the $\nu_{4}$ fundamental band is calculated to be
$A=12$ s-1. This means that the vibrationally excited state of CH${}_{3}^{+}$
cannot be thermally populated at the $T_{\rm k}$ : the collisional rates are
many orders of magnitude too small, and thus $T_{\rm ex}<T_{\rm k}$.

FORMATION-PUMPING. As shown in previous sections, CH${}_{3}^{+}$ is thought to
form mainly through a sequence of exothermic ion-neutral reactions. The change
of enthalpy in the reaction

${\rm CH}_{2}^{+}+{\rm H}_{2}\to{\rm CH}_{3}^{+}+{\rm H}$

is 65.6 kJ/mol, which corresponds to 5481 cm-1. Energetically, this is
sufficient to leave the product ion in the $v_{4}=1$ (1403 cm-1) or $v_{3}=1$
(3108 cm-1) vibrationally excited states; however, this is likely to happen in
only a small fraction $f_{u}$ of the reactions. In steady state, the total
formation rate $F({\rm CH}_{3}^{+})$ in cm-3 s-1 is balanced by a total
destruction rate $n({\rm CH}_{3}^{+})D$. The principal destruction processes
in the PDR include dissociative recombination with electrons, slow radiative
association reactions with H2, reaction with atomic O to form HCO+, and
photodissociation. Photodissociation of CH${}_{3}^{+}$ was investigated
through ab initio computations (?), but there has been no recent treatment of
the process. As a result, photodissociation of CH${}_{3}^{+}$ is absent from
the Leiden database of photodissociation and photoionization of
astrophysically relevant molecules. (?) identified the electronic states of
CH${}_{3}^{+}$ that would participate in its photodissociation and found only
one 1E” state with an energy below 13.6 eV with the right symmetry. They
estimated that the oscillator strength for transitions to this state must be
small, $f\sim 10^{-3}$, implying that the photodissociation rate in the
background Galactic radiation field must be of the order of 10-11 s-1. The
reference PDR model in Fig. 7 has $G_{0}=4\times 10^{4}$, so that that the
corresponding photodissociation rate is $\sim 4\times 10^{-7}$ s-1. With
reference to the zone of the PDR model where CH${}_{3}^{+}$ is most abundant,
$n_{\rm H}=3.5\times 10^{5}$ cm-3, $T_{\rm k}=900$ K, and the electron
fraction $x_{e}\approx 10^{-4}$. Adopting the rate coefficients of (?) for
dissociative recombination, we estimate that the destruction rate of
CH${}_{3}^{+}$ by electrons is $1.3\times 10^{-5}$ s-1, which completely
dominates over reactions with H2 and O. For higher densitites - as discussed
in the previous section, this destruction process will be even more efficient.
For a given density, CH${}_{3}^{+}$ is likely to be destroyed at least 100
times faster than it can be vibrationally excited by collisions at 900 K. This
means that the excited vibrational states cannot be populated in equilibrium.
It also implies that the excitation rate by the formation process might be of
the order of $\sim 10^{-5}f_{u}$ s-1 per ion. Thus if the ion-neutral source
reaction yields $\sim 1\%$ of the product CH${}_{3}^{+}$ ions in $v_{4}=1$,
the formation process could be at least as important as collisional
excitation.

RADIATIVE EXCITATION. The rate of radiative pumping by absorption of
continuous radiation is given by

${{A_{u\ell}g_{u}/g_{\ell}}\over{\exp(hc{\bar{\nu}}/kT_{b})-1}}\;\;\;{\rm
s}^{-1}$

where $A_{u\ell}$ is the spontaneous transition probability and $T_{b}$ is the
brightness temperature of radiation at frequency $\bar{\nu}$ defined by the
Planck function

$B_{\nu}(T_{b})={{2hc{\bar{\nu}}^{3}}\over{\exp(hc{\bar{\nu}}/kT_{b})-1}}\;\;.$

As shown in Fig 2, the surface brightness of the continuum in the ON-OFF
difference spectrum is 500 MJy sr-1 ($=5\times 10^{-18}$ W m-2 Hz-1 sr-1) near
the wavelength of the $\nu_{4}$ fundamental band. This corresponds to
$T_{b}=105$ K. In the calculation of Ref. (?), this band has a transition
dipole moment of $\mu=0.165$ Debye and $g_{u}/g_{\ell}=2$, so that the
corresponding transition probability is $A=12$ s-1. If the continuum source is
roughly co-extensive with the CH${}_{3}^{+}$-emitting region, then the
molecules ”feel” the same surface brightness that we see. Thus the radiative
pumping rate in the $\nu_{4}$ band itself is of the order of $5\times 10^{-8}$
s-1 per ion. The total continuum brightness in the PDR spectrum (Fig. 2), is
10 times larger than that of the ON-OFF spectrum, which suggests that the
molecules might be exposed to an even larger radiative excitation rate. The
surface brightness in the NIRSpec spectrum of d$203-506$ is approximately 450
MJy sr-1 at 3150 cm-1 in the vicinity of the $\nu_{3}$ band, corresponding to
$T_{b}=208$ K at this frequency. For a calculated transition probability
$A=309$ s-1 (dipole transition moment 0.181 Debye from (?)), this implies a
radiative excitation rate of $1.1\times 10^{-7}$ s-1 per ion. Both estimates
of radiative excitation omit the diluted starlight from the stars that
energize the PDR.

COMPARISON. The rates of collisional excitation, hot-molecule formation, and
infrared-radiative excitation of the observed CH${}_{3}^{+}$ bands can be
comparable to order-of-magnitude in the case of a moderate density ($n_{\rm
H}=3.5\times 10^{5}$ cm-3). For higher densities ($n_{\rm H}=1\times 10^{7}$
cm-3) collisions are likely to dominate the excitation. This example
illustrates the possible non-LTE excitation mechanisms of the molecular
vibrational bands that JWST may detect in related interstellar environments.

#### Column density estimates

Because the excitation processes that lead to the observed emission of
CH${}_{3}^{+}$ remain to be determined (see previous section), it is difficult
at this stage to provide an accurate determination of the total column density
of the species. We however provide an order of magnitude estimate hereafter,
and also point to the main limiting factors in this derivation to guide future
studies.

The integration over frequency of the emission band in the JWST observations
in the 1200–1600 cm-1 range, after local baseline subtraction (spline fit on
points outside the strong bands), is of $J_{\rm tot}\sim 8\times 10^{-6}$
W/m2/sr. To get an estimate of the column density of CH3+, we operate under
the assumption that the $\nu_{2}$ and $\nu_{4}$ bands of this ion are the
major contributors to the observed features (once the strong isolated atomic
and H2 lines are removed). Using the Einstein coefficients reported in Ref.
(?) of $A(\nu_{2})=2.65$ s-1 and $A(\nu_{4})=$ 4.43 s-1, the column density in
these upper emitting states can be derived by:

$N_{\nu_{2},\nu_{4}}\approx J_{\rm
tot}\frac{4\pi}{h{\nu}\sum_{\nu_{2},\nu_{4}}A}$

i.e., $N_{\nu_{2},\nu_{4}}\sim 4.7\times 10^{10}$ cm-2. From PGOPHER models
using dipole moments values 0.084 and 0.064 D from our best model (III.) for
the vibrational modes $\nu_{2}$ and $\nu_{4}$, respectively, we derive a total
emission in the 7 µm band of $\rm 1.13\times 10^{-19}$ W/CH${}_{3}^{+}$. Thus,
under such assumptions a column density of $N_{\nu_{2},\nu_{4}}\sim 7.8\times
10^{10}$ cm-2 is estimated. These numbers must be taken with caution however,
and are provided to the reader as an order of magnitude on the column
densities for this species in this protoplanetary disk, as the line strength
are not determined experimentally yet, resulting in possible change by large
factors in the derivation. In addition, as the excitation is unlikely to be at
LTE (see previous section), the determination of $N{{}_{\rm tot}}$(CH3+), the
total column density of CH3+, cannot be safely determined by using simple
Boltzmann factors to relate $\nu_{2}$ and $\nu_{4}$ populations to the ground
state one. Within LTE approximation, this factor is given by the ratio of
states degeneracies multiplied by $\exp(-h(\nu_{i}\rightarrow 0)/kT)$. For the
considered transitions, and excitation temperatures in the $800-300$ K range,
it implies total column densities a factor of ten to thousand times the above
quoted $N_{\nu_{2},\nu_{4}}$, respectively. At 400 K at LTE, $N{{}_{\rm
tot}}$(CH3+)$\,\sim 4\times 10^{12}$ cm-2. A model including lines
spectroscopic assignment and collisional rates, when they will be determined,
is to be developed in the future to better constrain the CH3+ excitation (see
section above) and the total column densities, under the observed astronomical
conditions. Finally, an additional uncertainty in this derivation stems from
the beam dilution, as the emission from the CH3+ emitting region is likely not
spatially resolved with MIRI. Hence – put aside the spectroscopic
uncertainties describe hereabove, the determined column density value should
be considered as a lower limit. Overall, this discussion further demonstrates
the absolute need for collaborative actions coordinating astrophysicists
observations and spectroscopists dedicated laboratory astrophysics experiments
to interpret such sets of data.

## Extended Data

Figure 1: On and off spectra of d203-506 over the full MIRI-MRS spectral
range. The On-Off spectrum is also shown. Main atomic and H2 lines are
indicated.  Figure 2: On-Off spectrum of d203-506 over the full MIRI-MRS
spectral range. Main atomic and H2 lines are indicated.  Figure 3:  H2
excitation diagram derived from the line intensities in Table 2 using the H2
toolbox (?) developed within the PDRs4All team as one of their Science
Enabling Products. Error bars result from the propagation of the absolute
calibration error of MIRI, which we take from (?). Table 1: H i detected
emission lines

$\lambda$ (µm) | $E_{\rm up}$ | $A$ | Transition
---|---|---|---
(1) | (2) | (3) | (4)
5.128662 | 156225.1 |  3.6881 104 | 6–10
5.263685 | 157316.1 |  1.3121 103 | 7–18
5.379776 | 157257.1 |  1.7812 103 | 7–17
5.525190 | 157186.7 |  2.4709 103 | 7–16
5.711464 | 157101.8 |  3.51558 103 | 7–15
5.908220 | 155854.9 |  7.0652 104 | 6–9
6.291918 | 156869.4 |  7.8457 103 | 7–13
6.771993 | 156707.3 |  1.2503 104 | 7–12
7.45984 | 153419.7 |  1.0254 106 | 5–6
7.502502 | 155337.5 |  1.5609 105 | 6–8
7.508107 | 156498.9 |  2.1174 104 | 7–11
8.760068 | 156225.1 |  3.9049 104 | 7–10
9.392013 | 156869.4 |  7.8037 103 | 8–13
10.803593 | 157186.7 |  2.2679 103 | 9–16
12.387158 | 156498.9 |  2.3007 104 | 8–11
16.20909 | 156225.1 |  4.6762 104 | 8–10
19.06192 | 155337.5 |  2.272 105 | 7–8

(1) Emission line wavelength (µm); (2) upper level energy (K); (3) Einstein A
coefficient; (s-1) (4) Transition label.

Table 2: Pure rotational H2 detected emission lines in MIRI MRS wavelength
range

$\lambda$ (µm) | $T_{u}$ | $\nu$ | $A$ | Transition |  Intensity ($\times 10^{-4}$)
---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6)
5.0531 | 8677.1 | 1978.977 |  3.236 10-7 | 0-0 S(8) | 0.864
5.5111 | 7196.7 | 1814.492 |  2.001 10-7 | 0-0 S(7) | 4.367
6.1085 | 5829.8 | 1637.046 |  1.142 10-7 | 0-0 S(6) | 2.582
6.9095 | 4586.1 | 1447.280 |  5.879 10-8 | 0-0 S(5) | 12.217
8.0250 | 3474.5 | 1246.099 |  2.643 10-8 | 0-0 S(4) | 4.193
9.6649 | 2503.7 | 1034.670 |  9.836 10-9 | 0-0 S(3) | 6.468
12.278 | 1681.6 | 814.424 |  2.755 10-9 | 0-0 S(2) | 2.408
17.034 | 1015.1 | 587.032 |  4.761 10-10 | 0-0 S(1) | 1.742

(1) Emission line wavelength (µm), from (?); (2) Upper level energy (K); (3)
Transition energy (cm-1); (4) Einstein A coefficient (s-1); (5) transition
label; (6) erg s-1 cm-2 sr-1

Table 3: Spectroscopic parameters of CH3+.

|  | Experimental | Calculated∗,a |  | Models∗
---|---|---|---|---|---
|  |  |  This workb |  Ref. (?) |  Ref. (?) |  | I | II | III | IV
$v=0$ |  |  |  |  |  |  |  |
| $B$ | $9.36214(28)$ | $9.32$ | $9.415$ | $9.18$ |  | $9.36214$ | $9.36214$ | $9.36214$ | $9.36214$
| $C$ | $4.589949(35)$ | $4.59$ | $4.715$ | $4.59$ |  | $4.589949$ | $4.589949$ | $4.589949$ | $4.589949$
| $D_{J}$ | $0.0007380(36)$ | $0.00071$ | $0.000719$ |  |  | $0.0007380$ | $0.0007380$ | $0.0007380$ | $0.0007380$
| $D_{JK}$ | $-0.0013144(79)$ | $-0.00124$ | $-0.001239$ |  |  | $-0.0013144$ | $-0.0013144$ | $-0.0013144$ | $-0.0013144$
| $D_{K}$ | $0.0004552(51)$ | $0.00057$ | $0.000568$ |  |  | $0.0004552$ | $0.0004552$ | $0.0004552$ | $0.0004552$
$v_{3}=1$ |  |  |  |  |  |  |  |
| $\nu$ | $3108.3556(18)$ | $2948$ |  |  |  |  |  |  |
| $B$ | $9.27239(25)$ | $9.21$ |  | $9.00$ |  |  |  |  |
| $C$ | $4.550184(29)$ | $4.46$ |  | $4.50$ |  |  |  |  |
| $D_{J}$ | $0.0007029(30)$ |  |  |  |  |  |  |  |
| $D_{JK}$ | $-0.0012814(71)$ |  |  |  |  |  |  |  |
| $D_{K}$ | $0.0004547(47)$ |  |  |  |  |  |  |  |
| $\zeta$ | $0.110551(38)$ | $0.115$ |  |  |  |  |  |  |
| $\eta_{J}$ | $-0.0006660(80)$ |  |  |  |  |  |  |  |
| $q^{+}$ | $0.00971(17)$ |  |  |  |  |  |  |  |
$v_{2}=1$ |  |  |  |  |  |  |  |
| $\nu$ | $1372-1412$ | $1412$ | $1391,1433$ | $1383,1418$ |  | $1392.80$ | $1389.01$ | $1391.22$ | $1388.71$
| $B$ |  | $9.21\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}9.27}]$ | $9.112\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}9.06}]$ | $9.21\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}9.49}]$ |  | $9.2270$ | $9.3766$ | $9.3721$ | $9.3647$
| $C$ |  | $4.53\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}4.61}]$ | $4.758\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}4.63}]$ | $4.61\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}4.66}]$ |  | $4.6392$ | $4.6542$ | $4.6560$ | $4.6651$
| $D_{J}$ |  |  | $0.000715$ |  |  | $0.002201$ | $0.000798$ | $.000703$ | $.000703$
| $D_{JK}$ |  |  | $-0.001212$ |  |  | $-0.005267$ | $-0.00131$ | $-.00118$ | $-.00113$
| $D_{K}$ |  |  | $0.000547$ |  |  | $0.002995$ | $0.000488$ | $.000455$ | $.000455$
$v_{4}=1$ |  |  |  |  |  |  |  |
| $\nu$ | $1373-1393$ | $1331$ | $1399$ | $1385,1429$ |  | $1374.56$ | $1374.46$ | $1374.54$ | $1396.35$
| $B$ |  | $9.44\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}9.50}]$ | $9.574\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}9.52}]$ | $9.20\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}9.48}]$ |  | $9.50$ | $9.50$ | $9.5000$ | $9.5027$
| $C$ |  | $4.46\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}4.55}]$ | $4.743\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}4.62}]$ | $4.60\,[{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}4.65}]$ |  | $4.5776$ | $4.5802$ | $4.5714$ | $4.7534$
| $D_{J}$ |  |  | $0.000719$ |  |  | $0.000747$ | $0.000938$ | $.000703$ | $.000703$
| $D_{JK}$ |  |  | $-0.001240$ |  |  | $-0.00116$ | $-0.00146$ | $-.00128$ | $-.00082$
| $D_{K}$ |  |  | $0.000569$ |  |  | $0.000326$ | $0.00032$ | $.000455$ | $.000455$
| $\zeta$ |  | $0.115$ | $0.1136$ |  |  | $0.11$ | $0.11$ | $0.11$ | $0.11$
| $\eta_{J}$ |  |  |  |  |  | $-0.00063$ | $-0.00063$ | $-0.00063$ | $-0.00063$
| $q^{+}$ |  |  |  |  |  | $0.0095$ | $0.0095$ | $0.0095$ | $0.0095$
$<v_{2}=1|v_{4}=1>^{c}$ |  |  |  |  |  |  |  |
| $\zeta_{24}$ |  | $-0.66$ |  |  |  | $-0.66$ | $-0.66$ | $-0.66$ | $-0.66$
$<v_{i}=1|d_{i}|v=0>^{d}$ |  |  |  |  |  |  |  |
| $d_{2}$ |  |  | $0.084$ |  |  | $0.084$ | $0.084$ | $0.084$ | $0.084$
| $d_{3}$ |  |  | $0.102$ |  |  |  |  |  |
| $d_{4}$ |  |  | $0.064$ |  |  | $0.064$ | $0.064$ | $0.064$ | $0.064$

∗ Rotational, centrifugal distortion, and Coriolis constants in the ground
state, $v_{3}=1$, $v_{2}=1$, and $v_{4}=1$ (in cm-1), and transition moments
of the $\nu_{2}$ and $\nu_{4}$ bands. Comparison of quantum calculated values,
and those used to best model the spectrum of the d203-506 source around 1400
cm-1. a Values in brakets (in blue) are scaled according to $v_{3}=1$ results
when available, to $v=0$ otherwise

b $\omega$B97X-D/cc-pVQZ, this work

c Coriolis interaction parameter between $v_{2}=1$ and $v_{4}=1$, unitless

d Transition dipole moment of the $\nu_{i}$ fundamental bands, in Debye

Figure 4:  a, Model I, with zoom on the strongest lines (b). c, Model II, with
zoom on strongest the lines (d). For these models, the excitation temperature
is $T=400$ K, and we use a Gaussian profile of 0.35 cm-1 full-width-at-half-
maximum.

Figure 5: Model III. (a), and Model IV. (b) $T=400$ K, Gaussian profile (0.35
cm-1 full-width-at-half-maximum) Figure 6:  NIRSpec spectrum of d203-506. The
spectrum is shown in gray, the shaded regions is the $\pm$ 3 sigma error
interval of the data. This includes the error provided by the JWST pipeline,
and error $\nu_{3}$ band of CH${}_{3}^{+}$ in the NIRSpec spectrum of
d203-506. Model of the OH emission (blue), H2 emission (orange),
CH${}_{3}^{+}$ emission (green), and sum of these three (red). Beyond 3.22µm,
emission due to the wings of the Aromatic Infrared Band at 3.3 µm is seen,
affecting the baseline of the NIRSpec spectrum. The OH spectrum is computed
with an LTE model at a temperature of 800K. A detailed model of the OH
emission will be presented in a forthcoming paper (Zannese et al. in prep).
The H2 lines are fitted individually. The CH${}_{3}^{+}$ model used here is
Model III., at a temperature of 400K.  Figure 7: Photochemical model results
for d203-506 adopting $G_{0}$ = 4$\times$104 and different gas densities
($n_{\rm H}$) and dust grain properties. Upper panels: Density and gas
temperature structure as a function of visual extinction ($A_{V}$) from the
wind surface. The gray curve shows the density of vibrationally excited
H${}_{2}^{*}$($v>0$). Lower panels: Abundance profiles with respect to H
nuclei. The pink dotted curves show the molecular fraction $f_{H_{2}}$
profile. Dashed curves in model a) refer to a model with the same gas density
but $G_{0}$ lower by a factor 104.  Figure 8: Dominant CH${}_{3}^{+}$
formation and destruction reactions at the CH${}_{3}^{+}$ abundance peak
predicted by the photochemical model shown in Fig. 7. This reaction network
also leads to abundant HCO+ in FUV-irradiated gas layers where $x$(C+) $>$
$x$(CO). Red arrows show endoergic reactions when H2 is in the ground-
vibrational state $v$ = 0. These reactions become fast only in disk layers
where the gas temperature is high (several hundred K) and/or significant
vibrationally excited H${}_{2}^{*}$ ($v$ $\geq$0) exists. The formation of
CH${}_{3}^{+}$ from methane will only be relevant if very high CH4 and H+
abundances coexist in the gas.