# A photochemical model of Triton’s atmosphere with an uncertainty propagation
study ††thanks: Supplementary material related to this article is available
at: https://doi.org/10.13140/RG.2.2.12820.99203

B. Benne1,∗, M. Dobrijevic1, T. Cavalié1,2, J-C. Loison3, K. M. Hickson3

1 Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, Allée
Geoffroy Saint-Hilaire, 33615 Pessac, France
2 LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université,
Univ. Paris Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon,
France
3 Institut des Sciences Moléculaires, CNRS, Univ. Bordeaux, 351 Cours de la
Libération, 33400 Talence, France
∗E-mail adress<EMAIL_ADDRESS>

###### Abstract

Triton is the largest satellite of Neptune and probably a Kuiper Belt Object
that was captured by the planet. It has a tenuous nitrogen atmosphere similar
to the one of Pluto and may be an ocean world. The Neptunian system has only
been visited by Voyager 2 in 1989. Over the last few years, the demand for a
new mission to the Ice Giants and their systems has increased so that a
theoretical basis to prepare for such a mission is important.

We aim to develop a photochemical model of Triton’s atmosphere with an up-to-
date chemical scheme, as previous photochemical models date back to the post-
flyby years. This is done to better understand the mechanisms governing
Triton’s atmospheric chemistry and highlight the critical parameters having a
significant impact on the atmospheric composition. We also study model
uncertainties to find what chemical studies are necessary to improve the
modeling of Triton’s atmosphere.

We adapted a model of Titan’s atmosphere from Dobrijevic et al. (2016) to
Triton’s conditions. We first used Titan’s chemical scheme before updating it
to better model Triton’s atmospheric conditions. Once the nominal results were
obtained, we studied model uncertainties with a Monte-Carlo procedure,
considering the reaction rates as random variables. Then, we performed global
sensitivity analyzes to identify the reactions responsible for model
uncertainties.

With the nominal results, we determined the composition of Triton’s atmosphere
and studied the production and loss processes for the main atmospheric
species. We highlighted key chemical reactions that are the most important for
the overall chemistry. We also identified some key parameters having a
significant impact on the results. Uncertainties are large for most of the
main atmospheric species as the atmospheric temperature is very low. We
identified key uncertainty reactions that have the largest impact on the
results uncertainties. These reactions must be studied in priority in order to
improve the significance of our results by decreasing these uncertainties.

_K_ eywords Triton $\cdot$ atmosphere $\cdot$ photochemical model $\cdot$
uncertainty propagation

##  1 Introduction

Triton is the largest satellite of Neptune. Its orbit is inclined and
retrograde, suggesting that it is a former Kuiper Belt Object (KBO) that was
captured by Neptune (McKinnon et al., 1995; Agnor and Hamilton, 2006). This
belief is reinforced by the similarities observed with Pluto. Triton was
visited by Voyager 2 in August 1989, the only mission so far to have studied
the Neptunian system. The flyby allowed to observe and characterize the
surface ices, composed of N2, CO2, H2O, CH4 and CO (Brown et al., 1995; Yelle
et al., 1995), and to discover the presence of plumes of organic material and
hazes (Herbert and Sandel, 1991; Yelle et al., 1991; Krasnopolsky et al.,
1992; Yelle et al., 1995). A study of the atmosphere was performed by
occultations and the measurement of its airglow (Broadfoot et al., 1989). It
showed that the atmosphere is mainly composed of N2 and traces of CH4 were
found near the surface. The presence of atomic nitrogen and atomic hydrogen
was also deduced from these measurements. The surface pressure and temperature
were determined using the radio data of Voyager (Tyler et al., 1989) and were
found to be 16$\pm$3 $\mu$bar and 38 K respectively. It is considered that the
atmosphere is formed by sublimation of the surface ices and that it is at
vapor pressure equilibrium with those ices (Yelle et al., 1995). CO was not
detected during this mission but was observed from Earth (Lellouch et al.,
2010). A dense ionosphere was also detected with a peak concentration of
electrons of about 104 cm-3 (Tyler et al., 1989) and the thermospheric
temperature was measured as 95$\pm$5 K (Broadfoot et al., 1989). A review of
the knowledge acquired about Triton during the mission can be found in
Cruikshank et al. (1995).

The chemistry in the lower atmosphere is mainly triggered by the photolysis of
CH4 by Lyman-$\alpha$ photons coming from solar irradiation and from the
interplanetary medium (Strobel et al., 1990b; Herbert and Sandel, 1991;
Krasnopolsky et al., 1992, 1993; Krasnopolsky and Cruikshank, 1995; Strobel
and Summers, 1995; Strobel and Zhu, 2017), while at higher altitudes it is
governed by the photolysis of N2 by solar EUV radiation ($\lambda<100$ nm) and
by its interaction with energetic electrons from Neptune’s magnetosphere
(Strobel et al., 1990a; Krasnopolsky et al., 1993; Krasnopolsky and
Cruikshank, 1995; Strobel and Summers, 1995; Strobel and Zhu, 2017).

Apart from this, very little is known about Triton, as no mission has been
sent to the Neptunian system since Voyager 2. This is why the demand for a new
mission to the Ice Giants is currently growing in the community. Also, Triton
is thought to be an ocean world (such as Titan, Enceladus, Europa and
Ganymede) meaning that it may have a liquid ocean under its icy surface,
heated by obliquity tides (Rymer et al., 2021; Fletcher et al., 2020). It
makes it a high priority target to study the possibility of developing life in
the outer worlds of the Solar System (Committee on the Planetary Science and
Astrobiology Decadal Survey et al., 2022). Hence, a mission to the Neptunian
system would allow studies across a very large spectrum of disciplines. In
order to prepare such a mission, it is important to develop photochemical
models of Triton’s atmosphere, as this will give a theoretical basis to
develop the instruments and anticipate future in-situ measurements.

Due to the scarcity of data available after the Voyager flyby, few articles
about the photochemistry of Triton’s atmosphere have been published: Majeed et
al. (1990); Strobel et al. (1990b); Lyons et al. (1992); Krasnopolsky et al.
(1993); Krasnopolsky and Cruikshank (1995); Strobel and Summers (1995).
Significant improvements in the modeling of the photochemistry of Titan’s
atmosphere have been made thanks to the Cassini-Huygens data, in particular in
the determination of the chemical scheme. A lot of models of this atmosphere
were developed and refined, and are now quite robust (e.g. Dobrijevic et al.,
2016; Loison et al., 2019; Nuñez-Reyes et al., 2019a, b; Hickson et al., 2020;
Vuitton et al., 2019). They can be used as a starting point for the
development of a new photochemical model of Triton’s atmosphere since it is
composed of N2 and CH4, which happen to be also the main constituents of
Titan’s atmosphere. Recent 1D-photochemical models use thousands of chemical
reactions and consider hundreds of species including neutral and ionic
compounds. Using a more complete chemical scheme could change the vision and
the understanding of the chemical mechanisms governing Triton’s atmosphere. It
is also important to take into account ground-based observations such as those
of Lellouch et al. (2010) which measured the abundance of CO.

As the temperature of Triton’s atmosphere is particularly low (<100 K at all
altitudes), we expect to have large uncertainties with regard to the
chemistry. Indeed, reaction rates are mostly measured or calculated at room
temperature. Hence, their values may be wrong in Triton’s conditions, even if
these rates are given with an uncertainty factor which accounts for errors
within the experiments or the computations. This problem was presented in
Hébrard et al. (2009). To see the impact of these uncertainties on our
results, we used a Monte-Carlo procedure over all reaction rates, as done in
Dobrijevic and Parisot (1998); Dobrijevic et al. (2003); Hébrard et al.
(2007); Dobrijevic et al. (2010a) and following papers. Along with this study,
we also performed global sensitivity analyzes to determine which reactions had
the strongest impact on chemical uncertainties, which we call key uncertainty
reactions. The determination of these reactions indicate which reactions need
to be measured in priority by new chemical studies.

The aim of the present work was to develop a new photochemical model of
Triton’s atmosphere and determine the key uncertainty reactions that must be
studied in priority in order to reduce the uncertainties on model results. Our
atmospheric model is presented in Sect. 2, our photochemical model in Sect. 3,
our updated chemical scheme in Sect. 4, our results for the nominal chemistry
with this updated scheme in Sect. 5, our study of chemical uncertainties and
the determination of key uncertainty reactions in Sect. 6 and our conclusions
in Sect. 7.

##  2 Atmospheric model

In this section, we present all the basic inputs of our model. These inputs
are the temperature, pressure and density profiles, the altitude grid, the
boundary conditions, the diffusion coefficients and the atmospheric escape
rates. All these inputs are independent from the chemical scheme and from the
photochemical parameters.

###  2.1 Atmospheric profiles and altitude grid

With the measurement of the surface temperature, the thermospheric temperature
$T_{th}$ was inferred by using the number density of N2 and assuming
hydrostatic equilibrium. It gave $T_{th}=95\pm$ 5 K (Broadfoot et al., 1989),
but the complete temperature profile could not be determined and was the
subject of several subsequent studies (see Yelle et al., 1991; Stevens et al.,
1992; Krasnopolsky et al., 1993; Strobel and Zhu, 2017).

Due to the presence of plumes (that were observed up to 8 km above the
surface) and clouds, it is thought that the temperature gradient near the
surface is negative, indicating the presence of a troposphere (Yelle et al.,
1991, 1995). Energy is brought to the atmosphere by solar Extreme Ultraviolet
(EUV) photons and by precipitating electrons from Neptune’s magnetosphere
(Strobel et al., 1990a; Yelle et al., 1991; Stevens et al., 1992; Strobel and
Summers, 1995; Krasnopolsky and Cruikshank, 1995; Strobel and Zhu, 2017).
Energy is then transferred through the atmosphere by conduction (Yelle et al.,
1991, 1995; Strobel and Summers, 1995). Magnetospheric electrons (ME) have not
always been taken into account, some models considering the Sun and the
interplanetary radiation flux as the only energy sources, as in Lyons et al.
(1992). However, Strobel et al. (1990a); Stevens et al. (1992); Krasnopolsky
and Cruikshank (1995); Strobel and Zhu (2017) showed that they are necessary
to explain the thermospheric temperature measured by Voyager. Another critical
parameter is the abundance of CO because of its cooling capabilities (Stevens
et al., 1992; Krasnopolsky et al., 1993; Strobel and Zhu, 2017). As its
abundance was not measured by Voyager, it was adjusted to fit the measured
tangential N2 column densities (Stevens et al., 1992). Krasnopolsky et al.
(1993) tried different values of the initial abundance of CO but were unable
to constrain its value from thermal balance calculations. This abundance was
measured as (2-18)$\times 10^{-4}$ by high-resolution spectroscopic
observations in the 2.32-2.37 $\mu$m range, using the CRyogenic high-
resolution InfraRed Echelle Spectrograph (CRIRES) at the Very Large Telescope
(VLT) (Lellouch et al., 2010) and is consistent with the upper limit inferred
by Voyager data (i.e. <1% Broadfoot et al. 1989).

In a more recent paper, taking advantage of the similarities between Pluto and
Triton, Strobel and Zhu (2017) adapted the thermal model of Pluto from Zhu et
al. (2014) to Triton. The main differences between the two atmospheres are the
mole fraction of CH4 (higher on Pluto) and the energy supply from
magnetospheric electrons from Neptune’s magnetosphere. They used the abundance
of CO determined in Lellouch et al. (2010) and studied three different models
to see the impact of magnetospheric electrons on the thermal profile: two
models without magnetospheric electrons and with different CH4 abundances and
a third with magnetospheric electrons. Their conclusion was that
magnetospheric heating is necessary to retrieve N2 tangential column number
densities comparable to the measurements from Voyager 2.

In our model, we used data from their Triton-3 model, which considers
precipitations of magnetospheric electrons. Thus, we used the associated
temperature and pressure profiles. It has to be noted that this thermal
profile does not consider a troposphere as the temperature gradient is always
positive, in contrast to the work of Krasnopolsky et al. (1993), Krasnopolsky
and Cruikshank (1995), Yelle et al. (1991) and Yelle et al. (1995).

The maximum altitude for this model is 1026 km. The temperature varies between
37.8 and 90.3 K from the surface to the upper end of the atmosphere, the
pressure between 16 and 2.8$\times 10^{-8}$ $\mu$bar and the number density is
computed following the ideal gas law.

We sampled the altitude grid with $H$/5 steps, where
$H(z)=\frac{k_{\text{B}}T(z)}{\bar{m}(z)g(z)}$ is the scale height of the
atmosphere at altitude $z$ ($k_{\text{B}}$ is the Boltzmann constant, $T$,
$\bar{m}$ and $g$ are respectively the temperature, mean mass and
gravitational acceleration at altitude $z$). Using these criteria, our
altitude levels are spaced by 2 km near the surface and by 21 km near the top
of the atmosphere, giving a 96 level grid. Temperature and number density
profiles are shown in Fig. 1, along with the altitude levels.

Figure 1: (a): Initial abundance profiles of N2 (green solid line), CH4
(orange dash-dotted line) and CO (red dashed line). The CH4 abundance
decreases exponentially with a scale height of 9 km. (b): Temperature (red
dashed line) and number density (orange solid line) profiles from the Triton-3
case of Strobel and Zhu (2017) that are used as inputs in our model. The
altitudinal grid is composed of 96 levels and the total number density is
plotted with blue dots.

The electronic temperature profile is a parameter required to compute the
reaction rates of dissociative recombination reactions. As it has never been
measured, we considered that the electronic temperature is equal to the
neutral temperature at all altitudes.

###  2.2 Initial and boundary conditions

The initial abundance of a given species corresponds to the value taken at the
beginning of the program, before the photochemical calculations. To be
consistent with the use of the thermal, pressure and number density profiles
of Strobel and Zhu (2017), we also used their initial abundance of CO:
$y_{0}$(CO)=$6.0\times 10^{-4}$, which corresponds to the measurement made by
Lellouch et al. (2010). The initial abundance of CO is constant throughout the
atmosphere. The initial mole fraction of CH4 was taken equal to the
$\frac{P_{v}(\text{CH${}_{4}$})}{P}$ ratio at the surface, $P_{v}$ being the
vapor pressure and $P$ the total pressure. With the formula of Fray and
Schmitt (2009), this corresponds to $y_{0}$(CH4)=0.89$\times$10-4. Thus, the
initial abundance is 40% lower than the value of Strobel and Zhu (2017), which
is $y_{0}$(CH4)=$1.5\times 10^{-4}$.

We chose to take an exponentially decreasing profile for CH4 as the initial
condition, with a scale height of 9 km corresponding to Voyager’s observations
(Strobel et al., 1990b). Then, at all altitudes, we simply filled the rest of
the atmosphere with N2 by taking
$y_{\text{N${}_{2}$}}(z)=1-$[$y_{\text{CH${}_{4}$}}(z)$+$y_{\text{CO}}(z)$].
The initial profiles of these 3 compounds are plotted in Fig. 1.

###  2.3 Eddy diffusion coefficient

The eddy diffusion coefficient $K_{zz}$ is a critical parameter of the model.
In previous articles about the photochemistry of Triton’s atmosphere, this
coefficient was adapted to match the CH4 profile measured by Voyager 2
(Strobel et al., 1990b; Herbert and Sandel, 1991; Krasnopolsky and Cruikshank,
1995). All the profiles inferred in these studies are different, as shown in
Table 1 and Fig. 2.

Study |  $K_{zz}$($z$) [cm2.s-1] | Homopause [km]
---|---|---
Strobel et al. (1990b) | [4-8]$\times$103 | [35-47]
Herbert and Sandel (1991) | [1.2-1.6]$\times$10${}^{3}\left(\frac{\left[\text{N}_{2}\right]_{0}}{\left[\text{N}_{2}\right](z)}\right)^{0.5}$ | 35
Krasnopolsky and Cruikshank (1995) | 105 in the troposphere, 4.103 above | 35
Table 1: Comparison of the different $K_{zz}$($z$) used in previous Triton
photochemical models since the flyby of Voyager 2 in 1989.

We tested the different profiles from Table 1 and obtained the best agreement
with observations using the profile from Herbert and Sandel (1991) and thus
kept it for the rest of our work.

Figure 2: Comparison between the eddy diffusion coefficients $K_{zz}$ of
Strobel et al. (1990b) (black dotted line), Herbert and Sandel (1991) (blue
dashed line) and Krasnopolsky and Cruikshank (1995) (red dash-dotted line).
For the Strobel et al. (1990b) profile, we plotted $K_{zz}=6.0\times 10^{3}$
cm2.s-1 and for the Herbert and Sandel (1991) profile $K_{zz}=1.4\times
10^{3}\left(\frac{\left[\text{N}_{2}\right]_{0}}{\left[\text{N}_{2}\right](z)}\right)^{0.5}$
cm2.s-1, the averages of the values for the summer and winter hemispheres. The
homopause of CH4 is located at the altitude where the molecular diffusion
coefficient $D_{\text{CH${}_{4}$}}$ of this species (orange solid line) is
equal to $K_{zz}$.

###  2.4 Molecular diffusion coefficient

The other main type of diffusion in planetary atmospheres is molecular
diffusion. It is used to describe the diffusion of minor species in one or
more major species. This type of diffusion occurs when the number density of
the minor species deviates from its distribution at hydrostatic equilibrium. A
coefficient is linked to this type of diffusion and we computed it with
formulas (1) and (2) taken from Poling et al. (2001), as we considered
molecular diffusion in the two main species of Triton’s atmosphere. In this
case, one of the terms of (1) always depends on N2 as it is the most abundant
species throughout the atmosphere but the second main species varies with
altitude. The latter is noted $j_{2}$ in (1) describing the molecular
diffusion coefficient of species $i$ at altitude $z$:

$D_{i}(z)=\frac{1}{\frac{y_{\text{N${}_{2}$}}(z)}{D_{i,\text{N${}_{2}$}}(z)}+\frac{y_{j_{2}}(z)}{D_{i,j_{2}}(z)}}$
(1)

where $D_{i,j}$ is the diffusion coefficient of the minor species $i$ in a
single major species $j$ whose relative abundance is $y_{j}$. $D_{i,j}$ is
computed with:

$D_{i,j}(z)=\frac{0.00143\times
T(z)^{\frac{1}{3}}}{P(z)M_{i,j}^{\frac{1}{2}}\left[(\Sigma_{v})_{i}^{\frac{1}{3}}+(\Sigma_{v})^{\frac{1}{3}}_{j}\right]^{2}}$
(2)

where $T$ is the temperature, $P$ the pressure, $M_{i,j}=\mu_{i,j}\times 2$
with $\mu_{i,j}$ the reduced mass of species $i$ and $j$ and $\Sigma_{v}$ is
the diffusion volume.

###  2.5 Atmospheric escape

Atmospheric escape of neutral and ionized species is considered in many papers
about Triton, such as Summers and Strobel (1991) or Krasnopolsky and
Cruikshank (1995). It is thought that this mass load in Neptune’s
magnetosphere could affect Neptune’s auroras (Broadfoot et al., 1989).

In our model, we simply considered Jeans thermal escape from the top of the
atmosphere, which is at 1026 km. The flux is computed for each neutral species
$i$ following Eq. (3):

$J_{i}=n_{i}\times
v_{\text{lim${}_{i}$}}=n_{i}\times\sqrt{\frac{k_{\text{B}}\times
T(z_{\text{max}})}{2\pi m_{i}}}\times\exp{\left(-q\right)}\times(1+q)$ (3)

with $v_{\text{lim}_{i}}$ the escape velocity of species $i$ at the top of the
atmosphere, corresponding to the altitude $z_{\text{max}}$, $n_{i}$ its number
density, $m_{i}$ its mass and $k_{\text{B}}$ the Boltzmann constant.
$T(z_{\text{max}})$ is the neutral temperature at this altitude level and $q$
is computed as follows, with $R_{T}$ the radius of Triton:

$q=\frac{(R_{T}+z_{\text{max}})\times m_{i}\times
g(z_{\text{max}})}{k_{\text{B}}\times T(z_{\text{max}})}$ (4)

Unlike Krasnopolsky and Cruikshank (1995), we did not consider ion escape and
did not scale our electronic profile on this escape above 600 km.

##  3 Photochemical model

###  3.1 Baseline chemical scheme

As our model is one-dimensional, we could use a complex chemical scheme
without suffering excessively long computation times. Capitalizing on the
similarities between the major constituents of Triton’s and Titan’s
atmospheres, we used the chemical scheme of Titan’s atmosphere presented in
Dobrijevic et al. (2016) as a basis for our work. This chemical scheme was
updated in Loison et al. (2019); Nuñez-Reyes et al. (2019a, b); Hickson et al.
(2020). The number of reactions and atmospheric species used in this scheme is
presented in Table 2.

Although the initial composition of the atmospheres of Titan and Triton are
quite similar, differences have to be noted as they could have an impact on
the results. Firstly, CH4 is only a trace species on Triton, whereas its
abundance on Titan reaches 20% at the top of the atmosphere. Thus, some
reactions could be less important on Triton due to the absence of methane in
the upper atmosphere. Conversely, some reactions that do not have a great
impact on Titan could be crucial on Triton. Secondly, the temperature and
pressure are much lower on Triton, and this directly impacts the reaction
rates and the condensation of some species, such as hydrocarbons. Thus, this
initial scheme was modified after the first results were obtained, following
the methodology presented in Sect. 4.

###  3.2 Generalities about calculations

Our photochemical model solves the continuity Eq. (5) for all the considered
species $i$ at all the altitude levels. At altitude $z$, it gives:

$\frac{\partial n_{i}(z)}{\partial
t}=-\text{div}~{}\overrightarrow{\Phi_{i}}(z)+P_{i}(z)-n_{i}(z)L_{i}(z)$ (5)

where $n_{i}$ is the number density of the species $i$, $P_{i}$ is the
chemical production term in cm-3.s-1 and $L_{i}$ the chemical loss term in
s-1. $\overrightarrow{\Phi_{i}}$ is the particle vertical flux computed by:

$\begin{split}\Phi_{i}(z)=-D_{i}(z)n_{i}(z)\left[\frac{1}{y_{i}(z)}\frac{\partial
y_{i}(z)}{\partial
z}+\frac{1}{H_{i}(z)}-\frac{1}{H(z)}\right]-K_{zz}(z)n_{i}(z)\left[\frac{1}{y_{i}(z)}\frac{\partial
y_{i}(z)}{\partial z}\right]\end{split}$ (6)

where $D_{i}$ is the molecular diffusion coefficient, $K_{zz}$ the eddy
diffusion coefficient, $y_{i}$ the abundance, $H_{i}$ the scale height of
species $i$ and $H$ the atmospheric scale height. Here, thermal diffusion is
neglected.

Equation (5) is integrated over time until steady state is reached, that is
when $\frac{\Delta n_{i}(z)}{\Delta t}$ is below a given threshold. This ratio
is computed at the end of each time step. In our case, the threshold was fixed
at 10%, because such a variation was small in comparison to model result
uncertainties caused by chemical uncertainties.

To compute the abundance profiles of all the considered atmospheric species,
we operated in steps. At the start, we used an atmosphere only composed of N2,
CH4 and CO and computed the chemical rates and the actinic flux. Then, we
calculated chemical and transport terms to integrate the continuity equation
and determine the abundance profiles of all the species. When convergence was
reached, we computed again the chemical rates and the actinic flux with the
newly obtained abundance profiles and ran the integration again. This pattern
was repeated until the difference between the results of two successive steps
was weak compared to the model uncertainties. In our case, three iterations
were needed to reach steady state.

In the following, we describe each parameter that is useful to compute all the
terms of Eqs. (5) and (6).

###  3.3 Energy sources

####  3.3.1 Solar flux

Triton is 30 AU away from the Sun. Consequently, the solar flux it receives is
900 times lower than on Earth and so approximately 10 times lower than on
Titan. Despite this, the ionosphere of Triton is denser than the one of Titan.

We used different sources of data for the solar flux, allowing us to consider
different solar activity cases. For the low activity case, we used a high
resolution composite spectrum built with data from Curdt et al. (2001, 2004)
that has a resolution of 0.004 nm between 67 and 160 nm and from Thuillier et
al. (2004). This spectrum is the same as the one used in Dobrijevic et al.
(2016).

For medium and high solar activity, we used low resolution spectra with a
resolution of 1 nm. As the flyby of Triton in 1989 occurred at a maximum solar
activity, we used the corresponding low resolution file between 1 and 730 nm
in our calculations.

####  3.3.2 Magnetospheric electrons

As the solar flux seemed too weak to explain the presence of a dense
ionosphere, a second source of energy was hypothesized (Majeed et al., 1990).
The most obvious candidate was the precipitation of energetic electrons from
Neptune’s magnetosphere, as energetic electrons were observed with the Low-
Energy Charged Particles (LECP) instrument aboard Voyager 2 (Krimigis et al.,
1989).

These measurements were used in Strobel et al. (1990a) to calculate the
production rates of N${}_{2}^{+}$ and N+ in Triton’s atmosphere. They show
that without electron precipitation, the predicted electronic peak derived
using only the solar flux does not correspond to the one observed by Voyager,
as it is weaker and at a higher altitude. Adding magnetospheric electrons,
they find a more reliable profile but at an altitude lower than expected.
Thus, their ionization profile has to be moved up by two scale heights in
order to find an electronic peak that fits with the observations (Summers and
Strobel, 1991). Finally, as the incident electronic flux used for the
calculations was measured when Triton was close to Neptune’s magnetic equator,
the ionization profile has to be adapted to represent mean orbital conditions
as done in Strobel et al. (1990a); Stevens et al. (1992); Krasnopolsky and
Cruikshank (1995); Strobel and Summers (1995).

In our model, we need an electron production rate to compute the reaction
rates of the ionizations and dissociations of N2 by magnetospheric electrons.
Thus, we used the ionization profile of Strobel et al. (1990a), moved it up by
two scale heights and divided it by 6 in order to represent mean conditions,
as done in Krasnopolsky and Cruikshank (1995).

The reaction rates $k$(ME,N2) for the interaction between magnetospheric
electrons and N2 are then computed with Eq. (7).

$k(\text{ME},\text{N}_{2})=\frac{prod(z)\times br}{n_{\text{N}_{2}}(z)}$ (7)

where $prod(z)$ is the production rate of electrons at altitude $z$, $br$ is
the branching ratio of the reaction and $n_{\text{N}_{2}}(z)$ is the number
density of N2 at the altitude $z$.

We considered three different reactions between magnetospheric electrons and
N2 for which branching ratios are respectively 0.8, 0.2 and 0.6 (Fox and
Victor, 1988):

$\displaystyle\text{N}_{2}+\text{ME}$
$\displaystyle\longrightarrow\text{N}_{2}^{+}+e^{-}$
$\displaystyle\text{N}_{2}+\text{ME}$
$\displaystyle\longrightarrow\text{N}_{2}^{+}+\text{N(}^{2}\text{D)}+e^{-}$
$\displaystyle\text{N}_{2}+\text{ME}$
$\displaystyle\longrightarrow\text{N(}^{4}\text{S)}+\text{N(}^{2}\text{D)}$

####  3.3.3 Interplanetary flux

We also took into account the interplanetary radiation flux. As stated in
Strobel et al. (1990b), at Triton’s distance from the Sun, this radiation is
not negligible with a flux $F$ at Lyman-$\alpha$ (121.6 nm) of 340 R
(Broadfoot et al., 1989) (1 R = $\frac{10^{6}}{4\pi}$ photons.cm-2.s-1.sr-1),
equivalent to a 8.5$\times$107 photons.cm-2.s-1 flux, to be compared to a
3.1$\times$108 photons.cm-2.s-1 solar flux at Lyman-$\alpha$ with a maximum
solar activity. In addition, we also considered two additional interplanetary
radiation fluxes: one at Lyman-$\beta$ (102.5 nm) with a ratio
$\frac{F(Ly-\alpha)}{F(Ly-\beta)}=360$ and one at the Helium line (58.4 nm)
with a ratio $\frac{F(Ly-\alpha)}{F(Helium)}=170$, as done in Dobrijevic
(1996).

###  3.4 Condensation

As the temperature is very low in the lower atmosphere of Triton, condensation
occurs for several species. It is consistent with observations of hazes in the
lowest 30 km by Voyager 2. This haze is thought to be composed of hydrocarbons
that are the products of CH4 photolysis (Strobel et al., 1990b; Herbert and
Sandel, 1991; Krasnopolsky et al., 1992).

In our model, we used a simplified consideration of the condensation, by
fixing the abundance of the condensing species at
$y_{i}(z)=\frac{P_{v}(z)}{P(z)}-1.0\times 10^{-10}$ if the abundance of the
considered species exceeds the $\frac{P_{v}(z)}{P(z)}$ ratio.

Our formulas to compute the vapor pressure $P_{v}$ of the different species
come from different sources, the main ones being Lara et al. (1996), Fray and
Schmitt (2009), the NIST database and Haynes (2012).

It has to be noted that as the temperature near the surface of Triton is very
low, small differences in the vapor pressure formulas in the temperature range
where they are commonly measured could lead to significant differences in the
final abundance profiles, as these abundances are restricted by the
$\frac{P_{v}(z)}{P(z)}$ ratio.

##  4 Update of the chemical scheme

As said in 3.1, we expected some chemical differences to emerge between the
Titan and Triton models, forcing us to modify the initial chemical scheme. To
do this, we first performed a run under the conditions of Triton’s atmosphere.
A very important difference between the atmospheres of Triton and Titan arises
from the absence of CH4 in the higher atmosphere of Triton, which impacts the
overall chemistry. To complete our chemical network, we focused on the species
that became much more abundant in the atmosphere of Triton. This is the case
in particular for some atomic species such as N(4S), N(2D), C and C+ as
already noted before by Krasnopolsky and Cruikshank (1995). The low abundance
of CH4 in the upper atmosphere of Triton induces low abundances of
hydrocarbons and hydrocarbon radicals (in particular CH3). As a result,
association reactions with N2 become much more important, such as the C + N2
$\longrightarrow$ CNN reaction which is the main loss reaction for atomic
carbon in the new model. It is thus also necessary to include these new
species, such as CNN, and to introduce their chemical network. The high
abundance of atomic carbon associated with its low ionization energy makes
charge transfer reactions efficient. This leads to a high abundance of ionized
atomic carbon which becomes the main ion above 175 km; an important difference
to the atmosphere of Titan. Once the new reactions to be included in the
network were identified, the rate constants and branching ratios were chosen
mainly from literature searches (e.g. Husain and Kirsch (1971) for the new
critical reaction C + N2 or Anicich (2003) for the C+ reactions). When no
study existed we followed the same methodology as in our previous studies on
Titan’s chemistry (Hébrard et al., 2012; Loison et al., 2015). As some
reactions require the introduction of new species, some iterations were
necessary to converge on a nominal chemical scheme. We also took care to
compare our final network with that of Krasnopolsky and Cruikshank (1995),
allowing us to identify several important differences (see later). We also
compared our results with data derived from the Voyager 2 observations
presented in Broadfoot et al. (1989), Tyler et al. (1989), Herbert and Sandel
(1991) and with results from previous photochemical models such as
Krasnopolsky and Cruikshank (1995) and Strobel and Summers (1995). This
methodology is presented in Fig. 3.

Figure 3: Methodology used to adapt Titan’s chemical scheme to Triton.

After having modified the chemical scheme, we ended up with a nominal chemical
scheme consisting of 220 atmospheric species and 1764 reactions, as described
in Table 2. A file containing a list of all the atmospheric species and their
masses is available as supplementary material.

|  | Initial chemical
---
scheme
| Revised chemical
---
scheme
Neutral species | 99 | 131
Ionic species | 83 | 89
| Neutral-neutral
---
reactions
419 | 710
| Ion-neutral
---
reactions
468 | 582
Photodissociations | 124 | 170
Photoionizations | 25 | 32
| Dissociative
---
recombinations
236 | 264
| ME/GCR
---
reactions
6 | 6
| Total number
---
of reactions
1278 | 1764
Table 2: Comparison between the initial and updated chemical schemes. The
initial chemical scheme comes from the model of Titan’s atmosphere from
Dobrijevic et al. (2016) that we used as a basis for our work. The revised
chemical scheme is used in our actual model of Triton’s atmosphere. "ME" is
used for Magnetospheric Electrons and "GCR" for Gamma Cosmic Rays. "Neutral-
neutral reactions" regroups two-body, three-body, bimolecular and termolecular
reactions.

##  5 Nominal results with the updated chemical scheme

For the nominal model, we used the nominal values of the chemical reaction
rates, meaning that we did not consider any uncertainty in their computation.
By doing this, we only had to run the program once. As described in Sect. 3,
we did three steps before reaching steady abundance profiles. In the
following, we present the abundance profiles of the main neutral species and
of the main ions. We detail the main production and loss processes for each
important species in order to better understand the main mechanisms of
Triton’s atmospheric chemistry and why they are different to those found for
Titan. Tables containing all these reactions and plots with their reaction
rates depending on altitude are given in the supplementary material associated
with this paper. We also aim to identify the parameters that have the greatest
impact on the final abundance profiles and compare our results with
observations at the end of this section.

###  5.1 Neutral atmosphere

####  5.1.1 Main species

The most abundant neutral species are N2, N (N(4S) and N(2D)), C, CO, H, H2
and O(3P). Their abundance profiles are given in Fig. 4. N(4S) corresponds to
the ground state of atomic nitrogen and N(2D) is its first excited state. We
only consider O(3P) here as the abundance of O(1D) remains negligible.

Figure 4: Relative abundances of the main neutral species in the atmosphere of
Triton. (a): Relative abundance of N2 (green solid line), CH4 (orange solid
line with circles), CO (red dashed line), H2 (blue dash-dotted line) and H
(dark blue dotted line). (b): Relative abundances of N(4S) (black solid line),
N(2D) (black dotted line), C (gray dash-dotted line) and O(3P) (cyan dashed
line). We only give the O(3P) profile as the abundance of O(1D) is negligible.

We can observe that N2 remains the main atmospheric throughout the atmosphere.
Near the surface, CO, CH4 and H2 are the most abundant trace species. The
abundance of CH4 decreases quickly at higher altitude due to its photolysis by
Lyman-$\alpha$ radiation. Above 50 km, we see a large increase in the
abundances of atomic species N, C, O and H. N becomes the second most abundant
species and C the third.

In the following paragraphs, we detail the main production and loss processes
for each of these species in order to understand these evolutions (we precise
that the third body of all the three-body reactions is N2, thus, it is not
precised in the rest of the paper). All the reactions used in this model and
their integrated column rates are given as supplementary material.

##### N2

N2 being the main species of Triton’s atmosphere, it is used as a reservoir in
our model. Therefore, its abundance is not renormalized at each time step. It
is destroyed by photodissociation, photoionization and interaction with
magnetospheric electrons. These reactions produce atomic nitrogen N(4S) and
N(2D) and N${}_{2}^{+}$ and N+ ions. The loss rate by photointeraction is of
the order of one third of that by electrointeraction. This is consistent with
the input energy flux, the energy carried by magnetospheric electrons being
higher than the one from the solar flux. More details are given about this in
Sect. 5.1.6. The interaction with magnetospheric electrons is the second most
important loss process for N2, the first one being the three-body reaction
with C giving CNN. N2 also reacts with CH, which is a product of methane
photolysis, to produce HCNN, with a loss rate half that of the previous
reaction. Photoionization and reactions with magnetospheric electrons reach
their maximum rate in the ionosphere, at 390 and 345 km respectively, while
other loss reactions mainly occur below 200 km.

N2 is mostly produced through the CNN cycle:

N2 \+ C | $\longrightarrow$ | CNN
---|---|---
CNN + N(4S) | $\longrightarrow$ | N2 \+ CN
CN + N(4S) | $\longrightarrow$ | N2 \+ C
net N(4S) + N(4S) | $\longrightarrow$ | N2

The peak rate of these reactions occurs at 121 km. The reaction between H and
HCNN giving 1CH2 \+ N2 has an integrated production rate four times lower than
the ones of the CNN cycle but is the main production process below 50 km,
which is logical as the reaction producing HCNN reaches its maximum rate at 10
km. At altitudes higher than 250 km, dissociative recombination of N2H+ is the
main source of N2.

##### CH4

CH4 is very important for Triton’s atmospheric chemistry as its photolysis is
a source of the CH, 3CH2, 1CH2 and CH3 radicals, of H and H2. It also leads to
the production of more complex hydrocarbons. Its chemistry is triggered by
photodissociation and photoionization by Lyman-$\alpha$ radiation from the Sun
and from the interstellar medium (ISM). Photodissociation reactions account
for 71% of the total loss of CH4.

CH4 also reacts with CH to produce C2H4. This reaction contributes for 29% of
the total loss of CH4, explaining why C2H4 is the most abundant hydrocarbon in
the lower atmosphere (cf Sect. 5.1.2). These results are consistent with the
description of Strobel et al. (1990b).

All these reactions reach their maximum rate at 10 km, which corresponds to
the altitude where the atmosphere becomes optically thick at the
Lyman-$\alpha$ wavelength, as shown in Fig. 5.

Figure 5: Altitude at which the optical thickness of the atmosphere is 1
depending on the wavelength of the incident radiation. The plot is cut at 200
nm as the atmosphere is not optically thick for all wavelengths above 160 nm,
but the initial solar flux goes from 0 to 730 nm.

Almost all CH4 production comes from the three-body reaction between CH3 and
H, in agreement with Strobel et al. (1990b). This reaction accounts for 94.5%
of the integrated production and peaks at 10 km, again at the photolysis
maximum. At altitudes higher than 75 km, CH4 is produced by diverse ion-
neutral reactions, the main one being CH${}_{5}^{+}$ \+ CO $\longrightarrow$
CH4 \+ HCO+.

##### N(4S) and N(2D)

Atomic nitrogen is the second most abundant species between 155 km and the top
of the atmosphere. In our chemical scheme, we consider two distinct states of
atomic nitrogen: the ground state N(4S) and the first excited state N(2D).

N(2D) is produced through reactions between N2 and magnetospheric electrons
(32%), but also by photodissociation (12.5%) and photoionization (1%) of this
species. However, the main production process is the dissociative
recombination of N${}_{2}^{+}$ (54.5%). The production peaks of all these
reactions are located around 350 km, except for the photodissociation of N2
giving N(4S) + N(2D) whose peak is at 71 km (the other channel producing
2N(2D) peaks at 378 km).

Then, N(2D) is quenched to ground state N(4S) through collisions with CO
(75.5%), C (15%) and O(3P) (9.5%), whose loss rates are maximum at 334 km for
the former reaction and 356 km for the others. These reactions account for
47.5, 9.5 and 6% of the integrated production of N(4S) respectively. This
species is also produced by dissociative recombination of N${}_{2}^{+}$ (11%)
and dissociation of N2 by magnetospheric electrons (13%). Photodissociation of
N2 accounts for 4.5%. The CN + O(3P) $\longrightarrow$ N(4S) + CO reaction is
the main production process of N(4S) around 120 km where the production rate
of this reaction is maximum. It contributes for 2.3% of the integrated
production of N(4S).

As said in Krasnopolsky and Cruikshank (1995), the CNN cycle is an important
loss process for atomic nitrogen. In our case, it contributes for 81.5% of the
integrated loss of N(4S). Around 35 km, N(4S) also reacts with species from
methane photolysis such as H, CH3 and 3CH2, producing NH, H2CN + H and HCN + H
respectively. The rates of these reactions are at least one order of magnitude
lower than the ones of the CNN cycle.

##### H2 and H

The direct photolysis of CH4 only accounts for 38.5% of the integrated
production of H2 (considering the reactions giving directly H2 from CH4). H2
is also produced through other reactions involving products of CH4 photolysis
such as H, 3CH2 or CH3. The main one is H + 3CH2 which gives H2 \+ CH (51% of
the integrated production). Consequently, H2 is mainly produced around 10 km,
the altitude where the photolysis loss rate of CH4 is maximum.

Losses of H2 mainly occur at higher altitude, through ion-neutral reactions
with N${}_{2}^{+}$ giving N2H+ \+ H (50% of the integrated loss, maximum loss
rate at 303 km), with N+ producing NH+ \+ H (13%, maximum at 356 km), with CO+
which gives (HCO+, HOC+) + H (14%, maximum at 127 km) and with CH+ and
CH${}_{2}^{+}$ giving CH${}_{2}^{+}$ \+ H and CH${}_{3}^{+}$ \+ H respectively
(12% and 7%, maxima at 127 km). The reaction with N+ is the main loss process
above 550 km.

H is also produced directly by CH4 photolysis (43.5%) and through the reaction
CH + CH4 $\longrightarrow$ C2H4 \+ H (28%) near the methane photolysis peak.
In the ionosphere, it is mainly produced through the N${}_{2}^{+}$ \+ H2
$\longrightarrow$ N2H+ \+ H reaction and by the dissociative recombination of
the latter ion (each reaction contributes for 3.5% of the integrated
production of H).

H is mainly lost through reactions with 3CH2 (56% of the integrated loss) and
HCNN (28.5%) to produce CH + H2 and 1CH2 \+ N2, respectively. These reactions
are important in the lower atmosphere as they involve products of methane
photolysis (HCNN is produced by N2 \+ CH $\longrightarrow$ HCNN whose
production rate peaks at 10 km). H is also converted to H2 through the
following cycle:

H + C3 $\displaystyle\longrightarrow\text{ (c-C${}_{3}$H,l-C${}_{3}$H)
(1.30\%, 1.30\%)}$ (c-C3H,l-C3H) + H $\displaystyle\longrightarrow\text{
C${}_{3}$ + H${}_{2}$ (1.63\%, 1.02\%)}$

The three-body reaction H + H $\longrightarrow$ H2 is an important loss
process for H in Krasnopolsky and Cruikshank (1995) but this reaction is much
less noticeable in our case, as it contributes for only 0.025% on the
integrated loss.

##### CO

Losses of CO mostly occur in the ionosphere where it reacts with N+, which
explains the decrease of its relative abundance observed in Fig. 4. It also
photodissociates and photoionizes in the lower atmosphere, with maximum rates
reached at 181 and 127 km respectively. It has to be noted that in our model
CO absorbs solar radiation up to 163 nm, but is only photoionized by radiation
with $\lambda<89$ nm and photodissociated by radiation with
$\lambda\in[89,108[$ nm. Thus, CO absorbs radiation between 108 and 163 nm
without being dissociated. This leads to an attenuation of the solar flux at
these wavelengths, thus impacting the photolysis of hydrocarbons such as C2H2
(see Fig. 5). We should consider that CO molecules re-emit absorbed photons at
these wavelengths in every direction, thus contributing to the photolysis of
other species but this is not done in our model.

CO is mainly produced through reactions of O(3P) with CNN and CN, which
produce respectively N2 \+ CO and N(4S) + CO, the latter having a slightly
higher production rate.

##### C

We find a higher relative abundance of C than Krasnopolsky and Cruikshank
(1995) throughout the atmosphere. The peak concentration is 5.2$\times$107 cm3
at 167 km compared with $\sim$1.5$\times$107 cm3 at $\sim$130 km in the cited
article. This species is mainly produced through the reaction N(4S) + CN
$\longrightarrow$ N2 \+ C (68.5% of the integrated production of C), which is
part of the CNN cycle converting atomic nitrogen into N2. But this production
is counterbalanced by the N2 \+ C $\longrightarrow$ CNN reaction whose
integrated rate is 9% higher and contributes for 76% of the integrated loss of
C, being therefore the main loss process. The rates of these reactions are
maximum at 121 km. Various ionic reactions also produce C, such as the
dissociative recombination of CO+ (8% of the integrated production), the
radiative recombination of C+ (1.5%) or the ion-neutral reaction CO + N+
$\longrightarrow$ C + NO+ (1%).

Apart from the reaction with N2, C is lost through various reactions with ions
in the ionosphere, but these reactions are at least two orders of magnitude
less significant than the former reaction.

##### O(3P)

O(3P) is also an abundant species in our model. As in Krasnopolsky and
Cruikshank (1995), the peak concentration of O(3P) is about 108 cm-3. We
recall that we do not consider O(1D) here because its abundance is negligible
in comparison to O(3P). This species is mainly produced by dissociative
recombination of the CO+ and NO+ ions (the latter contributing approximately 8
times less than the former). These reactions are important in the ionosphere
as their peak rate is reached at 345 km. At lower altitudes, O(3P) is produced
through the reaction N(4S) + NO $\longrightarrow$ O(3P) + N2 with an
integrated rate one order of magnitude lower than for the dissociative
recombinations.

O(3P) is mainly lost through reactions with CNN and CN as discussed above and
whose maximum rates are reached at 121 km. Below this altitude, O(3P) reacts
with various species such as CH3, NH or H2CN, giving respectively (H2CO + H,
CO + H2 \+ H), NO + H and (OH + HCN, HCNO + H), but the integrated rates of
these reactions are one order of magnitude lower than those of the reactions
with CN and CNN.

####  5.1.2 Hydrocarbons and HCN

The abundances of the main hydrocarbons and of HCN are presented in Fig. 6.

Figure 6: (a): Relative abundances of the main hydrocarbons (orange solid line
with circles for CH4, solid pink line for C2H2, purple dash-dotted line for
C2H4 and brown dashed line for C2H6) and HCN (blue dotted line). (b): Relative
abundances (solid lines) compared to the ratio of the vapor pressure $P_{v}$
and the pressure $P$ (dashed lines) depending on altitude for CH4, the main
C2Hx and HCN. When the curves of the $P_{v}/P$ ratio and the abundance merge,
this means that the species is condensing, as its abundance cannot be higher
than this ratio.

In agreement with Krasnopolsky and Cruikshank (1995), the most abundant
hydrocarbon in our model is C2H4. However, it is half as abundant in their
model as in ours, with a peak concentration of 5.1$\times$106 cm-3 at 47 km
where we have 2.0$\times$107 cm-3 at 36 km. We also find that C2H6 is more
abundant than C2H2 as the peak concentration of the former is 1.9$\times$106
cm-3 at 36 km compared with 4.4$\times$105 cm-3 at 56 km for the latter. In
Krasnopolsky and Cruikshank (1995), these two species have approximately the
same peak number density (1.3$\times$106 cm-3 and 1.4$\times$106 cm-3
respectively). These differences come from the different vapor pressure
formula used in our model. In comparison, for the summer and winter
hemispheres respectively, Strobel and Summers (1995) find (2.6-1.6)$\times$107
cm-3 at (17-30) km for C2H4 and (3.3$\times$105-1.3$\times$106) cm-3 at
(100-104) km for C2H2. In addition, our HCN abundance is much lower, its peak
number density being 1.8$\times$102 cm-3 against 3$\times$106 cm-3 for
Krasnopolsky and Cruikshank (1995) (while the peak concentration of HCN is
nearly 107 cm-3 in Strobel and Summers 1995). This difference comes from the
vapor pressure of HCN that is much lower than the ones of the studied
hydrocarbons, as shown in the right-hand panel of Fig. 6, and which forces the
number density of this species to drop below 275 km. As for neutral species,
we discuss the main production and loss processes for these compounds in the
following paragraphs.

##### C2H2

C2H2 is the least abundant of the three studied C2Hx in the lower atmosphere,
as its vapor pressure is lower than those of C2H4 and C2H6. Its production
relies almost exclusively on methane photolysis as it is produced at 53.5%
through 3CH2 \+ 3CH2 $\longrightarrow$ C2H2 \+ H2 and 39% through CH3 \+ HCNN
$\longrightarrow$ C2H2 \+ H2 \+ N2. The remaining production comes from C2H4
photolysis (4.5%). The two former reactions reach their peak production rate
at 10 km whereas C2H4 photolysis peaks at 36 km.

C2H2 is mainly lost around 56 km where it reacts with C to form C3 \+ H2 and
c-C3H + H (37 and 59.5%) or is photodissociated, which gives C2H + H (2%). The
C + C2H2 $\longrightarrow$ l-C3H + H channel also exists but its integrated
rate is two orders of magnitude lower than the one of the c-C3H channel. C2H2
condenses below 60 km, as the temperature falls when approaching the surface,
as shown in Fig. 6. The integrated condensation rate of C2H2 is 1.1$\times$107
cm-2.s-1, which corresponds to a mass condensation rate of 4.6$\times$10-16
g.cm-2.s-1. This value is one order of magnitude higher than the one of
Krasnopolsky and Cruikshank (1995), which is 4$\times$10-17 g.cm-2.s-1. This
difference comes from the use of a lower vapor pressure profile and a
different chemical scheme, leading to a higher integrated production rate for
this compound compared to Krasnopolsky and Cruikshank (1995).

##### C2H4

C2H4 is the most abundant C2Hx species. Strobel et al. (1990b) stated that
C2H4 is produced through the reaction 3CH2 \+ 3CH2 $\longrightarrow$ C2H4 and
also through CH + CH4 $\longrightarrow$ C2H4 \+ H. In our case, we effectively
find that the latter is responsible for 84% of the integrated production but
the former is not taken into account, as we consider 3CH2 \+ 3CH2
$\longrightarrow$ C2H2 \+ H2. Instead, 15.5% of the production is due to the
reaction 3CH2 \+ CH3 $\longrightarrow$ C2H4 \+ H. The production rates of
these reactions are maximum at 10 km, which is consistent with the fact that
C2H4 derives from methane photolysis, which is maximum at this altitude.

C2H4 is lost by photodissociation (22.5%), yielding C2H2, C2H3, H2 and H. It
also reacts with C (9.5%) to produce C3H3 and H, but the main loss process is
the three-body reaction with H giving C2H5 (60.5%). The photodissociation peak
is located at 36 km, as the maximum rate of the three-body reaction, whereas
the reaction with C peaks at 46 km. C2H4 condenses below 40 km (Fig. 6). The
integrated condensation rate of C2H4 is 9.0$\times$107 cm-2.s-1, which
corresponds to a mass condensation rate of 4.2$\times$10-15 g.cm-2.s-1.
Krasnopolsky and Cruikshank (1995) find 4.3$\times$10-15 g.cm-2.s-1, which is
very close to our value.

##### C2H6

This species is entirely produced by a three-body reaction between two CH3
(99.98%), with a maximum production rate at 10 km, again due to methane
photolysis.

It is destroyed by photolysis (97.5%) and reaction with CN (2%) and condenses
below 40 km (Fig. 6). All these reactions reach their maximum loss rate at 36
km. The integrated condensation rate of C2H6 is 2.0$\times$107 cm-2.s-1, which
corresponds to a mass condensation rate of 1.0$\times$10-15 g.cm-2.s-1. The
value given in Krasnopolsky and Cruikshank (1995) is 8.9$\times$10-16
g.cm-2.s-1, which is slightly lower than ours. The ratio between these two
rates is nearly the same as the ratio of our integrated production rates, thus
the difference comes from the chemical scheme.

##### HCN

HCN is mostly produced through reactions involving H2CN (produced through the
reaction N(4S) + CH3 $\longrightarrow$ H2CN + H), which reacts with H and
O(3P) to give respectively HCN + H2 (47% of the integrated production) and HCN
+ OH (6.5%). But it is also produced through the following reactions involving
N(4S):

N(4S) + 3CH2 $\displaystyle\longrightarrow\text{ HCN + H (30\%)}$ N(4S) + HCNN
$\displaystyle\longrightarrow\text{ HCN + N${}_{2}$ (13.5\%)}$

The maximum rates of these reactions are reached between 31 and 51 km.

HCN is lost in the ionosphere through reactions with N(2D) giving CH and N2
(19%) and with H+ giving HNC+ and H (80.5%). These reaction rates peak at 303
km and 293 km respectively. This species condenses below 280 km (Fig. 6), so
at much higher altitude than the C2Hx species.

####  5.1.3 Radicals

As radicals were evoked during our study of key chemical reactions for the
main neutral species, we give their relative abundances in Fig. 7. 1CH2 is
completely converted to 3CH2 through collisions with N2. Therefore, its
abundance is negligible and we focus on 3CH2 in the following.

Figure 7: Relative abundances of the radicals that appeared in the key
chemical reactions of the main neutral species (solid blue line for CH, orange
dashed line for CH2, green solid line with circles for CH3, dash-dotted pink
line for CN and purple dotted line for CNN). The CH2 profile corresponds to
3CH2, as the relative abundance of 1CH2 is negligible.

In agreement with what we discussed above, the production of CH3 and 3CH2 is
maximum at 10 km as it depends on methane direct photolysis, this process
contributing for respectively 97% and 8.5% of the integrated production of
these species. The remaining production of 3CH2 comes from collisions between
1CH2 and N2 (91%). 1CH2 is also produced by direct methane photolysis (54.5%)
and through H + HCNN $\longrightarrow$ 1CH2 \+ N2 (45%), thus depending on H
which is also a photolysis product.

CH3 mainly reacts with other CH3 radicals to produce C2H6 (55.5% of the
integrated loss), but also with 3CH2 (19%) and N(4S) (13.5%), which yields
C2H4 \+ H and H2CN + H respectively. The reaction between CH3 and 3CH2
accounts for 8.5% of the integrated loss of 3CH2. The latter compound reacts
mainly with H to produce CH + H2 (80% of the integrated loss). It also reacts
with other 3CH2 radicals to form C2H2 \+ H2 (7%). All these reactions reach
their maximum rate at 10 km apart from the N(4S) + CH3 reaction whose maximum
is at 31 km.

CH is mainly produced through the 3CH2 \+ H $\longrightarrow$ CH + H2 reaction
(87%) and direct methane photolysis (12%). It is mainly lost through CH + CH4
$\longrightarrow$ C2H4 \+ H (49.5%) and CH + N2 $\longrightarrow$ HCNN (49%).
All these reactions also reach their maximum rate at 10 km.

CN and CNN are mostly produced and lost through the CNN cycle that converts
atomic nitrogen to N2, as seen above. Thus, CN is almost exclusively produced
through the reaction N(4S) + CNN $\longrightarrow$ CN + N2 (96%) and CNN
through C + N2 $\longrightarrow$ CNN (100%). CN is then mostly lost through
N(4S) + CN $\longrightarrow$ C + N2 (94%) and CNN through N(4S) + CNN
$\longrightarrow$ CN + N2 (92.5%). These reactions all reach their maximum
rate at 121 km.

In addition, CN and CNN react with O(3P) to yield CO + N(4S) and CO + N2
respectively, these reactions accounting for 6 and 5% of the integrated loss.

####  5.1.4 Heavier Cx-compounds

The most abundant C3Hx species is C3 with a peak relative abundance of
1.4$\times$10-7 at 103 km. It intervenes in a cycle converting atomic hydrogen
into molecular hydrogen, which we have discussed above. Reactions of this
cycle account for 98.25% of the integrated production of C3 and 96.28% of its
integrated loss. The integrated rates of the production reactions are slightly
higher than the ones of the loss reactions. Apart from this cycle, C3 is
produced through the reaction C + C2H2 $\longrightarrow$ C3 \+ H2 and lost by
photodissociation producing 3C2 \+ C.

Aside this species, the other neutral C3-compounds are much less abundant. For
example, the second most abundant is C3H3CN and the third is c-C3H2 with
respective peak relative abundances of 1.7$\times$10-10 at 46 km and
2.5$\times$10-11 at 181 km. C3H3CN is mostly produced through the reaction CN
+ CH3CCH $\longrightarrow$ C3H3CN + H (11% of the integrated production) and H
+ CH2C3N $\longrightarrow$ C3H3CN (79%). It is lost at 77.2% by
photodissociation, producing CH2C3N + H and C3H3 \+ CN. It also reacts with
C2H${}_{5}^{+}$ to produce CH3C3NH+ \+ C2H4 (15% of the integrated loss).
c-C3H2 is mainly produced through H + (c-C3H + l-C3H) $\longrightarrow$ c-C3H2
(72%) and dissociative recombinations of c-C3H${}_{3}^{+}$ (5.9%),
l-C3H${}_{3}^{+}$ (3.7%) and C3H${}_{5}^{+}$ (9.2%). c-C3H2 is almost
exclusively lost through a three-body reaction with H producing C3H3 (97.7% of
the integrated loss).

l-C3H${}_{3}^{+}$ is the most abundant C3Hx ion with a peak relative abundance
of 2.0$\times$10-12 at 153 km. It is mainly produced through C3H${}_{4}^{+}$
\+ H $\longrightarrow$ l-C3H${}_{3}^{+}$ \+ H2 (12.7%). It is lost by
dissociative recombination (91.5%) and reactions with C2H4 producing heavier
ions C5H${}_{5}^{+}$ and C2H${}_{7}^{+}$ (3.5% of the integrated loss for each
channel).

The second most abundant C3Hx ion is C3H${}_{5}^{+}$ with a peak relative
abundance of 7.9$\times$10-13 at 109 km. It is produced through CH4 \+
(C2H${}_{2}^{+}$, C2H${}_{3}^{+}$) $\longrightarrow$ C3H${}_{5}^{+}$ \+ (H,
H2) (10%, 83%) and C2H4 \+ (C2H${}_{4}^{+}$, C2H${}_{5}^{+}$)
$\longrightarrow$ C3H${}_{5}^{+}$ \+ (CH3, CH4) (5%, 1.5%). It is mainly lost
by reacting with H (19%), which gives C2H${}_{3}^{+}$ \+ CH3 or by
dissociative recombination (68%). It also reacts with C2H4 to produce
C5H${}_{7}^{+}$ \+ H2 (10%).

In total, eight neutral C3-compounds and eight C3H${}_{x}^{+}$ ions have a
relative abundance higher than 10-15. In the same interval, we find seven
neutral C4-compounds, the most abundant being nC4H8 with a peak abundance of
6.5$\times$10-13. We also identify six heavier ions C8H${}_{11}^{+}$,
C5H${}_{5}^{+}$, C7H${}_{7}^{+}$, C5H${}_{7}^{+}$, C5H${}_{9}^{+}$ and
C6H${}_{7}^{+}$ with peak abundances ranging from 1.6$\times$10-14 to
2.2$\times$10-15 (species are given in order of decreasing abundance).

####  5.1.5 Main ions

Using nominal chemical reaction rates, we find that the main ions of Triton’s
ionosphere are C+, N+, H+ and N${}_{2}^{+}$, as shown in Fig. 8.

Figure 8: Relative abundances of the main ions of the atmosphere of Triton.
(a): Most abundant ions, which we focus on (blue solid line with circles for
C+, orange dashed line for N+, green dash-dotted line for N${}_{2}^{+}$,
purple dotted line for H+, thin brown solid line for CO+, thin dark blue
dashed line for N2H+ and red solid line for electrons). (b): The most abundant
ions below 175 km.

The electronic number density is maximum at 334 km, which is close to the
interval (340-350) km given in Tyler et al. (1989). We can see that the
electronic number density quickly increases above 175 km, where the
concentration of C+ varies strongly. It nearly corresponds to the sharp
ionospheric cutoff around 200 km observed in Voyager’s data and shown in Tyler
et al. (1989). In Krasnopolsky and Cruikshank (1995), the main ions were C+
and N+, H+ being only the sixth most abundant ion. Another difference is that
in their model C+ and N+ abundances tend to converge after the electronic
peak, but this behavior in less pronounced in our results.

In panel (b) of Fig. 8, we present the most abundant ions below 175 km. We can
observe that the higher mass ions reach their peak relative abundance at lower
altitude than the lower mass ones, with CH${}_{3}^{+}$ being the main ion
between 175 and 125 km. Then C2H${}_{5}^{+}$, NH2CO+ and HCO+ are most
abundant between 125 and 60 km and finally C5H${}_{5}^{+}$, c-C3H${}_{3}^{+}$,
C8H${}_{11}^{+}$, C3H${}_{6}^{+}$ and NH2CO+ dominate below 60 km. This is
consistent with the fact that heavier species are abundant in the lower
atmosphere only (e.g. hydrocarbons) whereas lighter species (e.g. atomic
species as C, O and N) are dominant at higher altitudes. However, the relative
abundances of these heavy ions remain low in comparison to the lighter ions in
the upper atmosphere. Therefore, we do not focus on the lower atmosphere ions
in the rest of our study.

####  5.1.6 Photoionization and interaction with magnetospheric electrons

The photoionization reactions with the highest integrated column rates are
listed in Table 3. These reactions contribute for 99.98% of the total
photoionization integrated column rate. For the interaction with
magnetospheric electrons, the main reactions and their integrated column rates
are given in Table 4. Unsurprisingly, ionization of N2 dominates as it is the
main atmospheric species. These reactions are sources of ions N${}_{2}^{+}$,
N+ but also of atomic nitrogen. Dissociation of N2 by magnetospheric electrons
is also a source of the latter species. We note that the peak of these
reactions is located slightly above the electronic peak, which is located at
334 km.

Photoionization reaction |  | Integrated
---
colum rate
[cm-2.s-1]
| Maximum rate
---
altitude [km]
N2 \+ $h\nu\longrightarrow$ N${}_{2}^{+}$ \+ $e^{-}$ | 2.7$\times$107 | 390
N2 \+ $h\nu\longrightarrow$ N+ \+ N(2D) + $e^{-}$ | 2.2$\times$106 | 345
CO + $h\nu\longrightarrow$ CO+ \+ $e^{-}$ | 1.3$\times$106 | 127
Table 3: Photoionization reactions with the highest integrated column rates. Reaction with ME |  | Integrated
---
colum rate
[cm-2.s-1]
| Maximum
---
rate altitude
[km]
N2 \+ ME $\longrightarrow$ N${}_{2}^{+}$ \+ $e^{-}$ | 6.6$\times$107 | 345
N2 \+ ME $\longrightarrow$ N+ \+ N(2D) + $e^{-}$ | 1.6$\times$107 | 345
N2 \+ ME $\longrightarrow$ N(4S) + N(2D) + $e^{-}$ | 4.9$\times$107 | 345
Table 4: Ionization and dissociation reactions by magnetospheric electrons
(ME) and their integrated column rates.

We can see that ionization by magnetospheric electrons is more important than
photoionization. The ratio between the rates for photoionization and the rates
for magnetospheric interaction is 3/8, which is comparable to the ratio given
in Krasnopolsky and Cruikshank (1995) of 0.5.

####  5.1.7 Production and loss processes

We detail here the main production and loss processes for the main ions of the
ionosphere of Triton.

##### C+

C+ is the most abundant ionospheric ion in Strobel and Summers (1995) and
Krasnopolsky and Cruikshank (1995). Lyons et al. (1992) were the first to
consider C+ as an abundant ion after using a charge exchange reaction between
N${}_{2}^{+}$ and C. In our model, this reaction is the main source of C+,
accounting for 74.5% of the integrated production. This ion is also produced
by two other charge exchange reactions between C and N+ or CO+, with
respective contributions of 11 and 14.5%. The maximum production rate of the
reaction between C and N${}_{2}^{+}$ is located at 334 km, which corresponds
to the electronic concentration peak. The production peak for charge exchange
with N+ is located at 414 km and the one for charge exchange with CO+ at 313
km.

C+ is almost exclusively lost by radiative recombination (98%) whose rate is
maximum at 334 km also. In Krasnopolsky and Cruikshank (1995), the main
chemical process for loss of C+ is by reacting with CH4, but in our case, this
reaction has an integrated loss rate 104 times lower than the radiative
recombination reaction mentioned before. This is due to the very low number
density of CH4 at ionospheric altitudes. Moreover, we do not consider
atmospheric escape for ions, which is the main loss process in Krasnopolsky
and Cruikshank (1995). This may explain why we have a higher number density of
C+.

##### N+

N+ is the second main ion of the ionosphere, as in Krasnopolsky and Cruikshank
(1995). On the other hand, in Strobel and Summers (1995), N+ is the second
main ion between 250 and 550 km and then becomes the most abundant ion. In our
case, N+ was the main ion with the initial chemical scheme but this changed
with the updated one where the N${}_{2}^{+}$ \+ C $\longrightarrow$ N2 \+ C+
reaction was added, making C+ the main ion. In our updated chemical scheme, we
also added reactions between N+ and CO, based on Anicich (2003). These
reactions became important for N+, as they account for 87.5% of its integrated
loss. Their loss rate is maximum at 345 km, where the ionization reactions of
N2 giving N+ are maximum. N+ also reacts with H2 to produce NH+ \+ H. The loss
rate of this reaction is maximum at 356 km and accounts for 11% of the
integrated loss of N+.

The ionization of N2 by magnetospheric electrons contributes for 75% of the
integrated production of N+. Photoionization contributes for 10% and charge
exchange between N${}_{2}^{+}$ and atomic nitrogen for 15%. The first two
reactions reach the production peak at 345 km whereas the latter reaches it at
334 km.

##### N${}_{2}^{+}$

Even though N2 is the main atmospheric species and the ionization reactions
giving N${}_{2}^{+}$ have a higher branching ratio compared to the ones giving
N+, N${}_{2}^{+}$ is only the third or fourth most abundant ion of Triton’s
ionosphere depending on altitude. It is produced by photoionization and
electron impact ionization of N2 (respectively 29 and 71% of the integrated
production) but it quickly recombines with electrons to produce atomic
nitrogen (82% of the integrated loss). It also reacts with H2 to produce N2H+
(10.5%) and with C, N(4S) and CO through charge exchange reactions (7% in
total). The loss rate for dissociative recombination is maximum at 356 km,
whereas the one for charge exchange with C and N(4S) is at 334 km (293 km for
charge exchange with CO). For the reaction with H2, the maximum rate is
reached at 303 km.

##### H+

H+ is mostly produced through a charge exchange reaction between CO+ and H
whose maximum rate is reached at 293 km and accounts for 96% of the integrated
production. Photoionization of H contributes for 3% and is maximum at 146 km.

H+ is lost by radiative recombination (29% of the integrated loss) around 345
km, but mostly by reacting with HCN and HNC to produce HNC+ \+ H (45.88%),
whose rates are maximum at 293 and 264 km respectively. It also appears in
charge exchange reactions with C and C3 (4.5 and 17%) and reacts with CH4 to
produce CH${}_{3}^{+}$ \+ H2 (2.5%).

###  5.2 Key chemical reactions for the main species

We studied in the previous sections the main production and loss processes for
the main species of Triton’s atmosphere. The reactions associated to these
processes thus contribute significantly to the production or loss of these
species. We call these reactions key chemical reactions. All these reactions
are given as supplementary material. Table 5 displays the reactions that
contribute significantly to the production or loss of several of the main
atmospheric species.

Reaction | Species (production) | Species (loss)
---|---|---
CH4 \+ $h\nu$ $\longrightarrow$ CH3 \+ H | H (26%) | CH4 (27%)
CH4 \+ $h\nu$ $\longrightarrow$ 1CH2 \+ H2 | H2 (32%) | CH4 (31%)
H + 3CH2 $\longrightarrow$ CH + H2 | H2 (51%) | H (56%)
CH4 \+ CH $\longrightarrow$ C2H4 \+ H | H (28%) ; C2H4 (84%) | CH4 (29%)
H + HCNN $\longrightarrow$ 1CH2 \+ N2 | N2 (12%) | H (29%)
N2 \+ $h\nu$ $\longrightarrow$ N${}_{2}^{+}$ \+ $e^{-}$ | N${}_{2}^{+}$ (29%) ; $e^{-}$ (24%) |
N2 \+ ME $\longrightarrow$ N${}_{2}^{+}$ \+ $e^{-}$ | N${}_{2}^{+}$ (71%) ; $e^{-}$ (59%) | N2 (12%)
N2 \+ ME $\longrightarrow$ N+ \+ N(2D) + $e^{-}$ | N+ (75%) ; $e^{-}$ (15%) |
N2 \+ ME $\longrightarrow$ N(4S) + N(2D) | N(4S) (13%) ; N(2D) (24%) |
N+ \+ H2 $\longrightarrow$ H + NH+ |  | H2 (13%) ; N+ (11%)
N${}_{2}^{+}$ \+ H2 $\longrightarrow$ N2H+ \+ H |  | N2 (10%) ; H2 (50%)
N${}_{2}^{+}$ \+ $e^{-}$ $\longrightarrow$ N(4S) + N(2D) | N(4S) (11%); N(2D) (20%) | N${}_{2}^{+}$ (44%) ; $e^{-}$ (37%)
N${}_{2}^{+}$ \+ $e^{-}$ $\longrightarrow$ N(2D) + N(2D) | N(2D) (34%) | N${}_{2}^{+}$ (38%) ; $e^{-}$ (31%)
N(4S) + CN $\longrightarrow$ N2 \+ C | N2 (25%) ; C (69%) | N(4S) (40%)
N(4S) + CNN $\longrightarrow$ N2 \+ CN | N2 (25%) | N(4S) (41%)
N2\+ C $\longrightarrow$ CNN |  | N2 (27%) ; C (76%)
N(2D) + CO $\longrightarrow$ N(4S) + CO | N(4S) (47%) | N(2D) (75%)
CO+ \+ $e^{-}$ $\longrightarrow$ C + O(3P) | O(3P) (37%) |  $e^{-}$ (14%)
H+ \+ HCN $\longrightarrow$ HNC+ \+ H |  | H+ (20%) ; HCN (81%)
Table 5: Key chemical reactions for the main atmospheric species. These
reactions contribute for at least 10% of the integrated production or loss of
at least two of the main species. The contribution of the reaction to the
total integrated loss or production of a species is noted next to the species
name.

We can identify several groups of reactions in this table:

  * •

CH4 photolysis: unsurprisingly, we find that photolysis of CH4 is important,
as stated in Strobel et al. (1990b); Krasnopolsky and Cruikshank (1995);
Strobel and Summers (1995). Its products also appear in other key chemical
reactions. It triggers the chemistry in the lower atmosphere, the photolysis
peak being located at 10 km. It is a source of H, H2 and radicals.

  * •

Photoionization of N2 and reactions with magnetospheric electrons: these
reactions impact logically the number density of N2, N${}_{2}^{+}$, N+,
electrons and atomic nitrogen. These products appear in numerous reactions of
the table (as presented in the following points), thus the former reactions
are important for the atmospheric chemistry in general.

  * •

N${}_{2}^{+}$ dissociative recombinations: these reactions have a significant
impact on the electronic and N${}_{2}^{+}$ loss as these species recombine
together quickly. This gives atomic nitrogen in the ground or first excited
state.

  * •

Atomic nitrogen: several reactions involve atomic nitrogen. We can in
particular identify a cycle involving CNN that regenerates N2 from N(4S).
N(2D) is quenched to ground state N(4S) through collisions with CO, O(3P) and
C (the main channel being the one with CO).

###  5.3 Discussion

As the data available about Triton mostly come from Voyager 2, we have very
few data points to validate our results. As given in Krasnopolsky and
Cruikshank (1995), we know that the number density of N2 at 575 km is
(4$\pm$0.4)$\times$108 cm-3, that the concentration of atomic nitrogen at 400
km is (1$\pm$0.25)$\times$108 cm-3 and (5$\pm$2.5)$\times$108 cm-3 at 200 km.
Our N2 profile is in agreement with the data as we find 3.7$\times$108 cm-3 at
571 km. Likewise for the atomic nitrogen data at 400 km as we find
1.0$\times$108 cm-3 at 402 km. But our value at 200 km is slightly above the
corresponding interval, as we have 9.6 and 8.8$\times$108 cm-3 at 196 and 204
km respectively. At this level, we expect chemical uncertainties to be quite
significant, possibly explaining the departure of our nominal value from the
observed range. The peak concentration of atomic nitrogen is 2.0$\times$109
cm-3 at 80 km, which is close to values from Krasnopolsky and Cruikshank
(1995) and Strobel and Summers (1995) which are about $\sim$1$\times$109 cm-3
at $\sim$115 km.

We also have the CH4 number density profiles near the surface for the two
solar occultation points from Herbert and Sandel (1991). With the actual model
and nominal reaction rates, we are nearly in agreement with these profiles, as
shown in panel (a) of Fig. 9. The differences at low altitude are only due to
our lower CH4 abundance at the surface coming from the use of the vapor
pressure formula of Fray and Schmitt (2009). We also note that we were unable
to match the data if we used a different $K_{zz}$ profile or if we used a
solar flux not corresponding to a maximum solar activity. Therefore, these two
parameters seem to be critical for the modeling of Triton’s atmosphere. As
$K_{zz}$ impacts strongly our results, it could be important to better
determine its profile as the one we use was inferred by using the CH4 number
density near the surface only (Herbert and Sandel, 1991).

Figure 9: (a): CH4 number density profiles near the surface derived from
Voyager 2 data and presented in Herbert and Sandel (1991) (dark blue and
orange), data points from Strobel and Zhu (2017) (black dots) and result from
our model using nominal reaction rates (red), i.e. without considering any
uncertainty. (b): Comparison of the relative abundances of the main neutral
species when using a high resolution solar spectrum (solid lines) versus a low
resolution spectrum (dashed lines). These results are obtained with solar
fluxes corresponding to low solar activity.

The spectral resolution of the solar flux was found to have a non negligible
impact on the abundance profiles of CH4 as shown in the right-hand panel of
Fig. 9. Following these observations, we may need a high resolution spectrum
for high solar activity in order to obtain more representative results.

If we sum the mass condensation rates for the three C2Hx studied in this
section, we find a total mass condensation rate of 5.7$\times$10-15
g.cm-2.s-1, which fits the aerosol production rate interval of
[4-8]$\times$10-15 g.cm-2.s-1 given in Strobel and Summers (1995) for the
winter and summer hemispheres respectively.

For ions, we first examine if our electronic profile corresponds to the
profiles presented in Tyler et al. (1989) and derived from Voyager data. These
profiles are shown in Fig. 10. We can observe that our electronic peak is
located at 334 km, which is slightly lower than the altitudinal range
(340-350) km determined from Voyager measurements and given in Tyler et al.
(1989). Also, our electronic peak concentration is 1.0$\times$105 cm-3, which
is higher than the interval of (3.5$\pm$1)$\times$104 cm-3 given in
Krasnopolsky and Cruikshank (1995). We show in Sect. 6 the impact of chemical
uncertainties on the electronic profile. But as we found that reactions with
magnetospheric electrons had a large impact on the atmospheric chemistry,
these results could change significantly if we take another electronic
production profile. Also, we modified the ionization profile from Strobel et
al. (1990a) in a rather arbitrary way, following the manipulations made in
Summers and Strobel (1991) and Krasnopolsky and Cruikshank (1995). Thus,
changing these arbitrary values could also impact our results in a significant
way. In order to model the interaction between magnetospheric electrons and
Triton’s atmosphere better, we recommend using an electron transport code in
further studies.

Figure 10: Number densities of the main ions in Triton’s atmosphere. The black
triangles and dark blue circles represent the electronic profiles measured by
Voyager 2 at the two occultations points (Tyler et al., 1989).

We also recall that we considered the electronic temperature to be equal to
the neutral temperature in all the atmosphere because this parameter was not
measured by Voyager. But we observed that dissociative recombination reactions
of N${}_{2}^{+}$ were among the most important key chemical reactions for the
main species. As the rates of these reactions are computed using the
electronic temperature, having a good estimation or measurements of this
parameter seems mandatory in order to improve the confidence in our model.

In the same way, recent occultation measurements presented in Oliveira et al.
(2022) indicate that the thermal profile in the lower atmosphere could be
quite different from the profile that we use here, with a strong positive
gradient near the surface and the potential presence of a mesosphere. If
correct, this could greatly impact the profiles of condensable species such as
methane and hydrocarbons.

##  6 Chemical uncertainties

As the temperature is very low on Triton, we expect to have large
uncertainties on our abundance profiles. Indeed, chemical reaction rates are
determined experimentally or theoretically but always with an uncertainty. It
is expressed with two different factors: the temperature dependent uncertainty
factor $F_{i}(T)$ and $g_{i}$, a coefficient that is used to extrapolate
$F_{i}$ depending on temperature. The uncertainty factor is computed from Eq.
(8) (see for instance Sander et al., 2006; Hébrard et al., 2006, 2007, 2009):

$F_{i}(T)=F_{i}(300\text{K})\times\exp{\left\\{g_{i}\left[\frac{1}{T}-\frac{1}{300}\right]\right\\}}$
(8)

where $F_{i}(300\text{K})$ is the uncertainty factor at 300 K, which is
commonly given with the reaction rates, as they are mainly measured around
room temperature. This is why we expect uncertainties to be large: the
temperature on Triton being below 100 K, we use rate formulas that are in
general not known in these conditions and we extrapolate the associated
uncertainty factors, about which we have a very limited knowledge. This
generally leads to a greater uncertainty for most of the reaction rates that
subsequently propagates into the model. Thus, it is necessary to examine how
these uncertainties propagate during the calculations and their impact on the
results and thus on the number density profiles of the different species.

To study the propagation of chemical uncertainties in our model, we use a
Monte-Carlo simulation. After the model was run with nominal reaction rates,
that is without considering any uncertainty (as done in the previous section),
we compute again all the reaction rates using the uncertainty factors $F_{i}$
and $g_{i}$, considering each rate as a random variable $k_{i}$ with a log-
normal distribution centered on the nominal rate $k_{0_{i}}$ and with a
standard deviation $\log{F_{i}}$ (Hébrard et al., 2007; Dobrijevic et al.,
2008b). For two-body reactions, $k_{i}$ is obtained from Eq. (9):

$\log(k_{i})=\log(k_{0_{i}})+\varepsilon_{i}\log\left[F_{i}(T)\right]$ (9)

$\varepsilon_{i}$ is a random number with a normal distribution centered on
zero and with a standard deviation of one. With this, we have a 68.3%
probability to find $k_{i}$ in the interval
$\left[\frac{k_{0_{i}}}{F_{i}},k_{0_{i}}\times F_{i}\right]$. To avoid
considering extreme values of $k_{i}$, we only use values of $k_{i}$ computed
with $\lvert\varepsilon\rvert$ <2.

For three-body reactions the reaction rate is given by:

$k_{i}(z)=\frac{k_{0}\times[M]\times\chi+k_{r}}{1+\frac{k_{0}[M]}{k_{\infty}}}$
(10)

$[M]$ being the number density of the third body, $k_{0}$ the reaction rate
for low pressure conditions, $k_{\infty}$ the reaction rate for high pressure
conditions and $k_{r}$ the rate for recombination. $\chi$ is the uncertainty
factor of Troe which is computed with (for all three-body reactions except H +
C2H2 and H + C4H2 that have their own formulas):

$\chi=\frac{\log(0.64)}{1+\left[\log\left(\frac{k_{0}[M]}{k_{\infty}}\right)\right]^{2}}$
(11)

Thus, we have to compute an uncertainty factor for $k_{0}$, $k_{\infty}$ and
$k_{r}$ by using formula (8), with a $F(300\text{K})$ and a $g$ for each.
Then, each $k_{i}$ is recalculated using equation (9).

For photodissociation, photoionization and electron-impact
dissociation/ionization, the corresponding reaction rates do not depend on
temperature. In this case, we assume a constant uncertainty factor $F_{i}=1.2$
(which may be underestimated) for all these reactions. Reaction rates are then
computed directly with Eq. (9).

For ion-neutral and dissociative recombination reactions, branching ratios are
applied on reaction rates to express the probability that the reaction gives a
specific set of products. These branching ratios are also measured or computed
theoretically and thus have an associated uncertainty. To account for it, we
also generate for each run of the program a new branching ratio $br_{i}$,
randomly generated between
$\left[\frac{br_{0_{i}}}{F_{br_{i}}},br_{0_{i}}\times F_{br_{i}}\right]$ using
a Dirichlet uniform distribution (cf Carrasco et al. 2007), $F_{br_{i}}$ being
the uncertainty factor for the considered branching ratio and $br_{0_{i}}$ the
nominal branching ratio. The chemical reaction rate of each branch is then
multiplied by $\frac{br_{i}}{br_{0_{i}}}$.

###  6.1 Results

We performed 250 iterations of the Monte-Carlo procedure. In Fig. 11, we
present the nominal mole fraction profiles of six species alongside the 250
profiles generated by the procedure. Histograms of mole fractions at the
altitude where the associated uncertainty is maximum are also plotted. As the
reaction rates have a log-normal distribution, we would expect to find normal
distributions with reasonable standard deviations, as shown for H in Fig. 11.
But in Triton’s low temperature atmosphere, we find large uncertainties for
the majority of the studied species, meaning a high standard deviation values.
In Table 6 we give the mean abundances and the standard deviation of these
abundance distributions, expressed by an uncertainty factor $F(\bar{y_{i}})$
at the altitude where the uncertainty is maximum.

Figure 11: Abundance profiles and histograms of the logarithm of the abundance of H, O(3P), N(2D), CH4, C2H2 and C for 250 runs of the Monte-Carlo procedure. Histograms are plotted at the altitude where the uncertainty is maximum for each species (red dashed line).  Species |  | Altitude
---
[km]
$\bar{y_{i}}$ | $F(\bar{y_{i}})$
N2 | 1026 | 7.8$\times$10-1 | 1.02
CH4 | 237 | 7.6$\times$10-12 | 23.59
N(4S) | 31 | 3.0$\times$10-9 | 33.07
N(2D) | 127 | 5.5$\times$10-12 | 36.35
H2 | 903 | 1.1$\times$10-3 | 1.17
H | 0 | 1.2$\times$10-10 | 2.97
CO | 1026 | 1.0$\times$10-4 | 1.15
C | 51 | 6.9$\times$10-13 | 4.69
O(3P) | 36 | 1.4$\times$10-9 | 37.85
C2H2 | 76 | 5.6$\times$10-11 | 7.19
C2H4 | 66 | 4.0$\times$10-10 | 6.02
C2H6 | 174 | 2.0$\times$10-11 | 3.71
HCN | 1026 | 1.3$\times$10-10 | 4.35
C+ | 181 | 1.6$\times$10-10 | 3.60
N+ | 810 | 1.4$\times$10-5 | 1.68
N${}_{2}^{+}$ | 1026 | 7.4$\times$10-7 | 1.94
H+ | 196 | 5.5$\times$10-12 | 5.92
$e^{-}$ | 212 | 1.0$\times$10-8 | 3.15
Table 6: Mean abundances $\bar{y_{i}}$ and associated uncertainty factors
$F(\bar{y_{i}})$ for the main atmospheric species. These values are computed
at the altitude level where the uncertainty on the abundance of the considered
species is maximum. $F(\bar{y})$ gives the interval
$\left[\frac{\bar{y}}{F(\bar{y})},\bar{y}\times F(\bar{y})\right]$ at
1$\sigma$.

We see that very few species have a standard deviation lower than two at the
level where their uncertainty is maximum, as it is only the case for N2, H2,
CO, N+ and N${}_{2}^{+}$. The maximum uncertainty factor is obtained for O(3P)
and gives a ratio between the high and the low value of the 1-$\sigma$
interval of 1.4$\times$103. We can observe that highly reactive species such
as atomic nitrogen or CH4 also have large uncertainty factors. For the
majority of the studied species, high uncertainties emerge at the altitude
level where their mole fractions vary strongly. This can be seen for O(3P) in
Fig. 11.

By plotting the histograms of the abundances of these species at the
considered levels, we can highlight bimodalities in some of the distributions.
This subject was studied in Dobrijevic et al. (2008a) for Titan’s atmosphere.
They are due to uncertainties on reaction rates and show that two distinct
paths are explored by the model, which gives a bimodal distribution instead of
the expected unimodal one as reaction rates follow a log-normal distribution.
We call them epistemic bimodalities as they do not correspond to any real
phenomenon but are artifacts arising from the large uncertainties of some
reaction rates in Triton’s conditions (Dobrijevic et al., 2008a). As an
example, in Fig. 11 the histogram of O(3P) shows a bimodality. To cancel out
these effects, we have to find which reactions strongly impact the model
uncertainties.

###  6.2 Identifying key uncertainty reactions

In order to have more significant results, we need to reduce the chemical
uncertainties. To do this, we must identify the key uncertainty reactions.
This kind of key reaction must not be confused with the key chemical
reactions: these reactions are defined as those that have the most important
influence on the chemical scheme, whereas key uncertainty reactions are
defined as those that have the most important contribution to the overall
uncertainty on species abundances.

Thus, we have to identify these key uncertainty reactions for each species in
order to see if we can reduce the uncertainty over the abundance profiles by
improving our knowledge about these reactions. Dobrijevic et al. (2010b)
presented different methods to determine key uncertainty reactions. In our
case, we performed global sensitivity analyzes, as presented in the following.

####  6.2.1 Global sensitivity analysis

This type of analysis allows us to vary all the input factors at each run
(here the chemical reaction rates) and study the link between these input
factors and the uncertainty on the outputs, which are the abundance profiles
of the studied species obtained with the Monte-Carlo procedure. It also allows
us to conserve the non-linearity and coupling of the model, resulting from the
use of a high number of species and reactions.

To do this, we use Rank Correlation Coefficients (RCCs). As shown in Carrasco
et al. (2007), Hébrard et al. (2009), Dobrijevic et al. (2010a) and Dobrijevic
et al. (2010b), these coefficients convert a nonlinear but monotonic
relationship between the input factors and the outputs into a linear
relationship. To do so, it replaces the values of the sampled inputs and
outputs by their respective ranks (Helton et al., 2006). The outcome of this
procedure is a coefficient between -1 and 1 for each input-output couple. If
the coefficient is positive, it means that the two correlated parameters vary
in the same way. Thus, in our case, each coefficient links a reaction to the
uncertainty on the abundance profile of a particular species. Reactions with
high RCCs (in absolute value) contribute strongly to the uncertainty on the
abundance of this species and are therefore key uncertainty reactions.

We analyze RCCs in two different ways: first, we perform the analysis for each
of the main species at the altitude where their uncertainty is maximum (one
species at a time). Second, we choose some characteristic atmospheric levels
and perform an analysis over all the species at a time. Coupling the results
of these two studies allows us to determine the key uncertainty reactions of
our model.

####  6.2.2 Results for the study for one species at a time

For this study, we chose to focus on reactions that have a RCC higher than 0.2
in absolute value. We ran this sensitivity analysis for the 18 main species at
the altitude where their uncertainty is maximum, as given in Table 6.
Reactions that were found for more than one of these species are given in
Appendix A, in Table 8. We identified 35 reactions: 12 neutral-neutral
reactions, 10 ion-neutral reactions, 4 dissociative recombinations, 3
photodissociations, 3 photoionizations and 3 reactions with magnetospheric
electrons.

We also identified which reactions gave high RCC absolute values, even if they
do not necessarily appear for more than one species. These reactions are given
in Table 9 of Appendix A, with the species associated to a high RCC value. One
additional reaction appears in this table.

For the majority of these reactions, we always have a high value of $F_{i}$ or
$g_{i}$ and sometimes both. This confirms that for this study, high RCCs are
often linked to a lack of knowledge about reaction rates.

####  6.2.3 Results for the study of all species at a given altitude

We also performed the sensitivity analysis at a given altitude level and for
all the species of our model at the same time. In this case, we count the
number of times that a reaction has a RCC higher than 0.2 (in absolute value)
over the total number of species. For each level, we then rank the reactions
that appear the most and therefore contribute the most to the overall
uncertainty at this level. We chose to perform this test at seven different
levels to sample diverse altitudes: 0, 86, 220, 334, 502, 758 and 1026 km.
Reactions that appear for at least one quarter of the species of our chemical
scheme at these levels are given in Table 10 of Appendix A.

We notice that the reaction N(2D) + CO $\longrightarrow$ N(4S) + CO appears at
each studied level. We also find that the main key uncertainty reactions are
different depending on the considered altitude. In the lower atmosphere (0 and
86 km), neutral-neutral reactions are dominant. At 86 km, we highlight three
different three-body reactions. At 220 km, in the lower ionosphere, photolysis
of CH4 and CO is important. At higher levels, de-excitation of N(2D) through
collisions with CO and C are the main key uncertainty reactions. For levels
higher than 500 km, the charge exchange between N+ and C giving N$(^{4}$S) +
C+ also contributes significantly.

We also performed a complementary study focusing on the main atmospheric
species to avoid biases from species with negligible abundances. This study
highlights key uncertainty reactions that we already found in the previous
analyzes, confirming their role in the overall uncertainty.

Finally, as we did for the study with one species at a time, we listed the
reactions with high RCC values. These reactions are given in Table 11 with the
involved species at each of the seven levels studied here. Again, we find
reactions that were previously highlighted but also some new ones, in general
important for only one species at one or more levels, for example reactions
between N+ and CO that are important for the uncertainty of N+. This also
confirms that key uncertainty reactions depend on the studied altitude.

###  6.3 Discussion - uncertainties and key uncertainty reactions

By computing the RCCs in various cases, we were able to identify reactions
that were responsible for large uncertainties for a particular species or more
globally at a given level. If we look at all the results presented in Appendix
A, we see that some reactions are involved in all (or nearly all) the treated
cases. These reactions are presented in Table 7.

Reaction | Rate coefficients |  | $F_{i}(300\text{K})$
---
or F
$g_{i}$
N(2D) + CO $\longrightarrow$ N(4S) + CO | 1.9$\times$10-12 | 1.6 | 300.0
N(2D) + C $\longrightarrow$ N(4S) + C | 4.0$\times$10-12$\times\exp{\left(\frac{-259}{T(z)}\right)}$ | 3.0 | 200.0
C + N2 $\longrightarrow$ CNN |  $k_{0}$ = 3.1$\times$10-33 $\times\left(\frac{T(z)}{300}\right)^{-1.5}$ | 1.8 | 100.0
|  $k_{\infty}$ = 1.0$\times$10-11 | 10.0 | 0.0
O(3P) + CNN $\longrightarrow$ N2 \+ CO | 1.0$\times$10-10 | 3.0 | 7.0
N+ \+ C $\longrightarrow$ N(4S) + C+ | 4.0$\times$10-12 | 10.0 | 0.0
C+ \+ $e^{-}$ $\longrightarrow$ C | 4.4$\times$10-12 $\times\left(\frac{T_{e}(z)}{300}\right)^{0.61}$ | 1.6 | 0.0
N(4S) + CNN $\longrightarrow$ CN + N2 | 1.0$\times$10-10 | 3.0 | 7.0
N${}_{2}^{+}$ \+ C $\longrightarrow$ N2 \+ C+ | 1.0$\times$10-10 | 3.0 | 0.0
C + H2 $\longrightarrow$ 3CH2 |  $k_{0}$ = 7.0$\times$10-32 $\times\left(\frac{T(z)}{300}\right)^{-1.5}$ | 2.0 | 100.0
|  $k_{\infty}$ = 2.06$\times$10-11$\times\exp{\left(\frac{-57}{T(z)}\right)}$ | 3.0 | 100.0
CH4 \+ $h\nu$ $\longrightarrow$ 1CH2 \+ H2 | Photodissociation | 1.2 | -
Table 7: Main key uncertainty reactions identified through sensitivity
analyzes. These reactions are the ones that appeared the most in our
sensitivity analyzes and thus contribute the most to the model uncertainties.
$T(z)$ is the atmospheric neutral temperature at altitude $z$ and $T_{e}(z)$
the electronic temperature. $F_{i}(300K)$ is the uncertainty factor at 300 K
and its value is given in the corresponding column by non bold numbers, while
F is the global uncertainty factor that is computed with $F_{i}$ and $g_{i}$
but has a fixed value for photodissociations and reactions with ME. When F is
given, the value is in bold.

We also find that many of the reactions that were identified through the
sensitivity analyzes appeared as key chemical reactions for the main species
of the atmosphere. Thus, it appears even more important to improve our
knowledge of the kinetics of these key reactions as they have the biggest
influence on the number density profiles of the main species. Without this
supplementary knowledge at low temperature, it seems difficult to obtain a
clearer image of the composition of Triton’s atmosphere.

We also note that O(3P) appears as a reactant in key chemical reactions for
some of the main species and also in key uncertainty reactions. At the moment,
we do not consider any interplanetary dust flux. But Moses and Poppe (2017)
showed that the external flux of water in Neptune’s atmosphere is likely
coming from interplanetary dust. If true, this flux should also impact
Triton’s atmospheric chemistry, as stated in Poppe and Horányi (2018). Thus,
it will be interesting to add this dust delivery and observe its impact on the
number density profiles and also on chemical uncertainties.

In Sect. 5, we observed that the electronic number density profile was higher
than expected when comparing to observations presented in Tyler et al. (1989).
If we examine the electronic profiles of the 250 runs of the Monte-Carlo
procedure, we find that the mean number density at the electronic peak is
$\bar{y_{i}}(e^{-}_{peak})$ = 1.1$\times$105 cm-3 with an uncertainty factor
of 1.38 at 1-$\sigma$. Thus, the peak concentration of electrons found with
our model is consistently higher than the measured value of
(3.5$\pm$1)$\times$104 cm-3 (Tyler et al., 1989; Krasnopolsky and Cruikshank,
1995).

The altitude of the electronic peak also varies at each run. For 250 runs, we
find $z(e^{-}_{peak})$=(338$\pm$9) km, which matches the interval of (340-350)
km given in Krasnopolsky and Cruikshank (1995).

However the electronic production, as well as the electronic density, depends
mostly on N2 impact ionization by magnetospheric electrons. Therefore, it
depends on how the interaction between Triton’s atmosphere and Neptune’s
magnetosphere is modeled. In our case, we used the arbitrarily modified
ionization profile from Strobel et al. (1990a). Thus, the results may be
significantly affected when changing these arbitrary parameters. Moreover, the
uncertainty factors of reactions involving magnetospheric electrons is
constant and equal to 1.2. These uncertainties may be underestimated and thus
the observed difference between Voyager’s data and our results may not be
significant.

In Sect. 5, we failed to find a number density of atomic nitrogen that matches
the value given in Krasnopolsky and Cruikshank (1995) at 200 km, that is
(5$\pm$2.5)$\times$108 cm-3, when using nominal reaction rates. With 250 runs,
the number density of N is (11$\pm$4)$\times$108 cm-3 at 196 km and
(10$\pm$4)$\times$108 cm-3 at 204 km. Thus, these intervals and the one of
Krasnopolsky and Cruikshank (1995) overlap. But as for electrons, the
production of atomic nitrogen depends mostly on the interaction between
magnetospheric electrons and N2 (directly or indirectly), reactions for which
we consider a constant and probably underestimated uncertainty factor.
Therefore, the small differences observed between our results and the measured
data are not significant.

##  7 Discussion and Conclusion

Our goal was to create a 1D photochemical model of Triton’s atmosphere with an
up-to-date chemical scheme in order to determine the atmospheric composition,
the main parameters having an impact on it and also highlight which studies
are necessary in order to reduce uncertainties on model results.

To do this, we used an existing model of Titan’s atmosphere from Dobrijevic et
al. (2016) and adapted it to Triton’s conditions. We used input data from
Strobel and Zhu (2017) for our initial conditions (temperature and number
density profiles, initial abundance of CO), the eddy diffusion profile of
Herbert and Sandel (1991), took a solar flux corresponding to a maximum solar
activity, added interplanetary radiation and considered the interaction
between Triton and Neptune’s magnetosphere through reactions between N2 and
magnetospheric electrons. Considering the latter processes was crucial in
order to find nominal results for CH4 and atomic nitrogen in agreement with
the Voyager data.

We also improved our chemical scheme by comparing the results with the Voyager
data and previous articles about the photochemistry of Triton such as those by
Krasnopolsky and Cruikshank (1995) or Strobel and Summers (1995). By doing
this, we added nearly 40 atmospheric species and 500 reactions to our initial
scheme, giving a total of 220 species and 1764 reactions.

With this updated model, we studied 18 species in particular which are the
main neutral species (N2, N(4S), N(2D), CH4, CO, H2, H, C, O(3P)),
hydrocarbons (C2H2, C2H4, C2H6), nitriles (HCN) and ions (C+, N+,
N${}_{2}^{+}$, H+, electrons), highlighting their main production and loss
processes through the identification of key chemical reactions. Nitrogen
chemistry is triggered by ionization and dissociation of N2 by solar radiation
and magnetospheric electrons, while methane chemistry results from its
photolysis by Lyman-$\alpha$ radiation from the Sun and the interstellar
medium, creating radicals and hydrogen (atomic and molecular). These radicals
then react to form hydrocarbons that condense due to the very low temperature
in the lower atmosphere, the most abundant C2Hx being C2H4. Molecular hydrogen
reacts mostly with ions, while H reacts mainly with HCNN or radicals. Atomic
nitrogen produced in the N(2D) state is converted to ground state N(4S)
through collisions with CO, C and O(3P). N(4S) is then converted back to N2
through the CNN cycle. CO is depleted in the higher atmosphere by reacting
with N+ ions. N${}_{2}^{+}$ ions recombine rapidly with electrons producing
atomic nitrogen.

We find a dense ionosphere with a cutoff around 175 km, where the abundance of
C+ increases strongly. This ion is the most abundant in the majority of the
ionosphere and is produced by charge exchange reactions between N${}_{2}^{+}$,
CO+, N+ and C. The other abundant ions are N+, H+ and N${}_{2}^{+}$. Below 175
km, the main ions are heavier but their abundances are low. The electronic
peak is located at 334 km, which is consistent with Voyager data presented in
Tyler et al. (1989). Our number density profile is higher than the one given
in the latter article, even considering chemical uncertainties. However, these
results are very dependent on the modeling of the interaction between Triton’s
atmosphere and Neptune’s magnetosphere.

Using a Monte-Carlo procedure over all the chemical reaction rates, we studied
uncertainties on the abundance profiles. We performed 250 runs and found that
for the majority of species, the uncertainty factors on these profiles are
significant. This is due to our lack of knowledge about chemical reaction
rates at the very low temperatures of Triton’s atmosphere. These uncertainties
also lead to epistemic bimodalities in the abundance distributions of some
species, at the level where the associated uncertainty is maximum. We
determined the key uncertainty reactions responsible for the observed
uncertainties and bimodalities. To do this, we performed global sensitivity
analyzes using Rank Correlation Coefficients to determine correlations between
the outputs (number density profiles) and the input factors (chemical reaction
rates) of the model. We did this study for each of the 18 most abundant
species at the level where the uncertainty on their abundance is maximum, but
also for all the species of our model at different altitudes. We identified
the main key uncertainty reactions for which we absolutely need to improve our
knowledge if we want to improve the significance of the model results.
Finally, we found that a great number of key uncertainty reactions also
appeared as key chemical reactions for the main species, which confirms the
need for new studies about these reactions.

In the end, the use of an up-to-date chemical scheme allows a much deeper
comprehension of the composition and of the mechanisms governing the chemistry
of Triton’s atmosphere in comparison to the work of Krasnopolsky and
Cruikshank (1995) and Strobel and Summers (1995), while the study of the model
uncertainty is the first of its kind for Triton’s atmosphere.

However, the current model of Triton’s atmosphere can be improved in many
areas. As oxygenated species appeared in several key uncertainty reactions, we
need to study how the interplanetary water flux could impact the results of
our model. As the precipitation of magnetospheric electrons has a strong
impact on the atmospheric chemistry, having a better model which really
considers the temporal variation of the precipitation depending on the
position of Triton in Neptune’s complex magnetosphere should improve the
significance of the model results.

The chemical scheme can also be simplified in order to decrease the
computation time (cf Dobrijevic et al. 2011). This is not feasible before
obtaining the uncertainties on model results as they give an objective
criterion to verify if the results given by the reduced scheme are in
agreement with the nominal model.

## Acknowledgments

B.B, M.D and T.C. acknowledge funding from CNES. B.B, M.D, T.C and K.M.H
acknowledge funding from the “Programme National Planétologie” (PNP) of
CNRS/INSU. K.M.H. acknowledges support from the French program “Physique et
Chimie du Milieu Interstellaire” (PCMI) of the CNRS/INSU with the INC/INP co-
funded by the CEA and CNES.

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##  Appendix A Identification of key uncertainty reactions

Reaction |  | Number of
---
occurrences
| Maximum
---
RCC
$F_{i}$ | $g_{i}$
O(3P) + CNN $\longrightarrow$ CO + N2 | 6 | 0.43 | 3.0 | 7.0
C + N2 $\longrightarrow$ CNN | 6 | 0.51 | 1.8 | 10.0
|  |  | 10.0 | 0.0
|  |  | 30.0 | 0.0
N(4S) + N(4S) $\longrightarrow$ N2 | 5 | 0.42 | 2.5 | 100.0
|  |  | 2.0 | 100.0
|  |  | 1.0 | 0.0
CH4 \+ $h\nu$ $\longrightarrow$ CH3 \+ H | 4 | 0.33 | 1.2 | -
CH + CH4 $\longrightarrow$ C2H4 \+ H | 4 | 0.44 | 1.3 | 4.45
N(2D) + CO $\longrightarrow$ N(4S) + CO | 4 | 1.0 | 1.6 | 300.0
CO + $h\nu$ $\longrightarrow$ CO+ \+ $e^{-}$ | 4 | 0.34 | 1.2 | -
N(4S) + H $\longrightarrow$ NH | 3 | 0.55 | 3.16 | 100.0
|  |  | 2.0 | 100.0
|  |  | 30.0 | 0.0
H + iC4H7 $\longrightarrow$ CH3 \+ CH2CHCH2 | 3 | 0.22 | 0.0 | 0.0
|  |  | 0.0 | 0.0
|  |  | 1.0 | 0.0
C10H8 \+ $h\nu$ $\longrightarrow$ C10H${}_{8}^{+}$ \+ $e^{-}$ | 3 | 0.29 | 1.2 | -
CH${}_{3}^{+}$ \+ CH4 $\longrightarrow$ C2H${}_{5}^{+}$ \+ H2 | 3 | 0.46 | 1.4 | 0.0
CO+ \+ H2 $\longrightarrow$ HOC+ \+ H | 3 | 0.23 | 1.15 | 0.0
CO+ \+ C $\longrightarrow$ C+ \+ CO | 3 | 0.28 | 1.4 | 0.0
N+ \+ C $\longrightarrow$ N(4S) + C+ | 3 | 0.80 | 10.0 | 0.0
N2 \+ ME $\longrightarrow$ N${}_{2}^{+}$ \+ $e^{-}$ | 3 | 0.61 | 1.2 | -
CH4 \+ $h\nu$ $\longrightarrow$ 1CH2 \+ H2 | 2 | 0.28 | 1.2 | -
CH3CH2CCH + $h\nu$ $\longrightarrow$ C4H5 \+ H | 2 | 0.23 | 1.2 | -
N(2D) + C6H5C6H5 $\longrightarrow$ AROM | 2 | 0.21 | 3.0 | 0.0
N(2D) + C2H3 $\longrightarrow$ NH + C2H2 | 2 | 0.2 | 2.0 | 7.0
N(4S) + CH $\longrightarrow$ CN + H | 2 | 0.26 | 1.6 | 7.0
O(3P) + CN $\longrightarrow$ CO + N(4S) | 2 | 0.27 | 2.0 | 0.0
C + H2 $\longrightarrow$ 3CH2 | 2 | 0.30 | 2.0 | 100.0
|  |  | 3.0 | 100.0
|  |  | 1.0 | 0.0
N2 \+ $h\nu$ $\longrightarrow$ N${}_{2}^{+}$ \+ $e^{-}$ | 2 | 0.39 | 1.2 | -