Kinetic and Photochemical Disequilibrium in the Potentially Carbon-rich Atmosphere of
the Warm Jupiter WASP-69 b

Nidhi Bangera1,2 , Christiane Helling1,2 , Gloria Guilluy3 , Patricio Cubillos1,3 , Luca Fossati1 , Paolo Giacobbe3 ,
Paul Rimmer4 , and Daniel Kitzmann5,6

1 Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria; nidhirohit.bangera@oeaw.ac.at
2 Institute for Theoretical and Computational Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austria

3 INAF—Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025, Pino Torinese, Italy
4 Cavendish Laboratory, University of Cambridge, JJ Thomson Ave., Cambridge, CB3 0HE, UK

5 Space Research and Planetary Sciences, Physics Institute, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
6 Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland

Received 2024 February 6; revised 2025 January 10; accepted 2025 January 13; published 2025 February 10

Abstract

High-resolution transmission spectroscopy of the warm gas giant WASP-69 b has revealed the presence of H2O,
CO, CH4, NH3, and C2H2 in its atmosphere. This study investigates the impact of vertical diffusion and
photochemistry on its atmospheric composition, with a focus on the detected species plus HCN and CO2, to
constrain the atmospheric C/O ratio. We utilize nonequilibrium gas-phase simulations to conduct a parameter
study for vertical diffusion strength, local gas temperature, and C/O ratio. Our results indicate that a carbon-rich
atmosphere enhances CH4 and C2H2 concentrations, while NH3 undergoes chemical conversion into HCN in
carbon-rich, high-temperature environments. Consequently, HCN is abundantly produced in such atmospheres,
though its strong spectral features remain undetected in WASP-69 b. Photochemical production of HCN and C2H2

is highly sensitive to vertical diffusion strength, with weaker diffusion resulting in higher concentrations. Cross-
correlation of synthetic spectra with observed data shows that models with C/O= 2 best match observations, but
models with C/O= 0.55 and 0.9 lead to statistically equivalent fits, leaving the C/O ratio unconstrained. We
highlight the importance of accurately modeling NH3 quenching at pressures greater than 100 bars. Models for
WASP-69 b capped at 100 bars bias cross-correlation fits toward carbon-rich values. We suggest that if the
atmosphere of WASP-69 b is indeed carbon-rich with a solar metallicity, future observations should reveal the
presence of HCN.

Unified Astronomy Thesaurus concepts: Chemical kinetics (2233); Exoplanet atmospheres (487); Planetary
atmospheres (1244)

1. Introduction

The atmospheric composition of exoplanets can offer
valuable insights on planet formation processes. Previous
studies suggest that atmospheric elemental ratios, such as the
carbon-to-oxygen ratio (C/O), can help identifying the location
of gas giant exoplanets’ formation and their accretion history
within a protoplanetary disk (e.g., K. I. Öberg et al. 2011;
C. Helling et al. 2014; K. I. Öberg & E. A. Bergin 2016;
P. Mollière et al. 2022; B. Tabone et al. 2023). Whether the
planetary C/O coincides with that of its host star could depend
on the method of planet formation, with two possible scenarios:
the “inheritance” scenario, where the planet inherits its
chemical makeup from the parent molecular cloud, or the
“chemical reset” scenario, where the accreted material is reset
to its atomic state due to the ionizing irradiation from the
protostar (C. Eistrup et al. 2016, 2018).

Previously, there have been a few observations that indicate
supersolar C/O in exoplanet atmospheres (e.g., N. Madhusud-
han et al. 2011; B. R. Oppenheimer et al. 2013; A. Tsiaras et al.
2016). One example is WASP-69 b, a transiting warm giant
exoplanet with an equilibrium temperature of Teq ∼ 950 K (D.
R. Anderson et al. 2014; A. S. Bonomo et al. 2017). In their

study, G. Guilluy et al. (2022) utilized high-resolution
transmission spectroscopy to observe the atmosphere of
WASP-69 b, detecting H2O, CH4, NH3, CO, and C2H2.
G. Guilluy et al. (2022) employed radiative and thermochemi-
cal equilibrium models, incorporating disequilibrium chemistry
effects in a postprocessing step, to explore different C/O ratios
and atmospheric metallicity scenarios consistent with their
observations. Their findings suggest that atmospheric scenarios
with supersolar metallicities are unlikely for this planet.
Additionally, they propose that the observed presence of
C2H2 and the stronger detection of CH4 compared to H2O
could be better explained by an atmospheric C/O ratio greater
than 1. Among the models tested, the most favorable match to
observations was achieved by a model with solar metallicity,
C/O= 2.0, and artificially increased concentrations for NH3

and C2H2 at 10−7
–10−6. However, the high concentrations of

NH3 and C2H2 may also be explained by chemical disequili-
brium processes in the atmosphere. Therefore, disequilibrium
chemistry calculations are needed to confirm or disprove the
conclusions of G. Guilluy et al. (2022) on the presence of
disequilibrium chemistry and on the inferred C/O. In this
work, we build upon the findings of G. Guilluy et al. (2022) by
employing a novel approach that couples kinetic modeling,
which provides physically supported abundance profiles
accounting for disequilibrium chemistry, and high-resolution
transmission spectroscopy to constrain the chemical properties
of the atmosphere.

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At atmospheric pressures that can be probed by infrared
observations (10−6–1 bar), vertical-diffusion-induced quenching
and photochemistry are the two key physical processes that may
drive the atmospheric composition of an exoplanet out of
thermochemical equilibrium. In the deep atmosphere, where gas
temperatures and pressures are high, the chemistry can be assumed
to be in thermochemical equilibrium. However, at lower atmo-
spheric gas temperatures, when chemical timescales are larger than
dynamical timescales, vertical diffusion can push the chemistry out
of equilibrium (e.g., J. I. Moses 2014; C. Baxter et al. 2021;
Y. Kawashima &M. Min 2021). Molecules may thus be present in
the upper atmospheric layers with concentrations higher than in
equilibrium, suggesting that their concentrations are “quenched” in
the deep atmosphere at thermochemical equilibrium concentrations
and then transported upward in the atmosphere faster than they can
be chemically converted to the expected equilibrium species higher
up in the atmosphere. These processes are expected to be
particularly significant for planets with Teq  1300K (e.g.,
N. Madhusudhan et al. 2014; J. I. Moses 2014) such as WASP-69
b. At these temperatures, where the carbon chemistry shifts
between being CH4- and CO-dominated, while the nitrogen
chemistry shifts between being NH3- and N2-dominated (K. Lod-
ders & B. Fegley 2002; P. Woitke et al. 2018), vertical-diffusion-
induced quenching can significantly impact both the diversity of
the observed species and the strength of the observed spectral
features. M. Zamyatina et al. (2023) find that while this diffusion-
induced quenching is predicted to occur in the atmospheres of
HAT-P-11 b, HD 189733 b, HD 209458 b, and WASP-17 b, the
extent to which it affects spectra and phase curves varies from
planet to planet.

Additionally, photochemistry, i.e., the impact of the stellar
radiation on the gas composition, can influence atmospheric
composition (e.g., N. Madhusudhan 2012; J. I. Moses et al. 2013;
J. I. Moses 2014; P. Barth et al. 2021; R. Baeyens et al. 2022b).
The parent molecules transported from deep atmospheric regions
are photodissociated in upper layers producing radicals that react
to form new species. The shape of the stellar spectra, as well as
the atmospheric temperature profile and initial atmospheric
elemental composition, influence the diversity of chemical
products in the atmosphere. Lower atmospheric temperatures
produce abundant CH4 and NH3 that is beneficial for photo-
chemistry, since these species are more active photochemical
precursors than CO and N2 (J. I. Moses 2014). High atmospheric
temperatures serve to counterbalance the effect of photochemistry,
maintaining the atmospheric composition closer to what is
expected in the presence of thermochemical equilibrium.
Recently, direct evidence of photochemistry in hot gas giant
atmospheres was obtained from the JWST observations of SO2 in
the atmospheres of WASP-39 b (S.-M. Tsai et al. 2023) and
WASP-107 b (A. Dyrek et al. 2024). On WASP-69 b, it is the
detection of C2H2 that suggests that a photochemical model is
preferable to chemical equilibrium models for interpreting the
observations (e.g., J. I. Moses et al. 2011; O. Venot et al. 2012;
J. I. Moses 2014).

To investigate the impact of disequilibrium chemistry on the
atmospheric composition of WASP-69 b, we performed a
series of 1D calculations using the ARGO code (P. B. Rimmer
& C. Helling 2016), which incorporates thermochemical and
photochemical kinetics along with vertical transport processes
to model vertical atmospheric profiles. The code currently
utilizes the STAND2020 network, which includes neutral and
ion chemistry for molecules containing H, C, O, and N, with a

limited neutral chemistry for S-bearing molecules. Our study
focuses on three key parameters: atmospheric C/O ratio,
thermal structure, and strength of eddy diffusion. The atmo-
spheric C/O ratio is of particular interest, as equilibrium
modeling has suggested a carbon-rich atmosphere for WASP-
69 b, which contrasts with the C/O ratio of its host star
(D. R. Anderson et al. 2014). Additionally, we accounted for
the temperature difference of up to ∼400 K between the two
terminator regions, as expected for a planet with an equilibrium
temperature of ∼1000 K orbiting a K-type star like WASP-69 b
(C. Helling et al. 2023). The eddy diffusion coefficient was also
examined, given its role as a poorly constrained parameter that
can significantly influence atmospheric concentration predic-
tions, potentially varying by orders of magnitude (e.g.,
J. I. Moses et al. 2011; A. Arfaux & P. Lavvas 2023). Finally,
synthetic spectra generated from our models were compared to
the observations of G. Guilluy et al. (2022) to evaluate the
consistency of our findings.
This paper is structured as follows. Section 2 describes the

modeling approach used to derive the atmospheric composition
and synthetic spectra. Section 3 presents how the disequili-
brium results differ from the chemical equilibrium solution for
our base model and the results of the parameter space study for
each of the detected species (H2O, CO, CH4, C2H2, NH3), plus
HCN and CO2 that were not detected in the GIANO-B near-
infrared data. Section 4 presents the synthetic transmission
spectra in comparison to the observations of G. Guilluy et al.
(2022), together with the implications for WASP-69 b's
atmospheric C/O. Section 5 presents a discussion of the
degeneracy in the models as well as the model sensitivities to
boundary conditions. Section 6 concludes the paper.

2. Modeling Approach

We employ STAND2020 (R. Hobbs et al. 2021;
P. B. Rimmer et al. 2021), an ion–neutral photochemical
C/N/O/H+S rate network with >4000 reaction paths to
determine the local gas-phase composition in the observable
terminator regions of WASP-69 b. Leaving the required input
radiation field constant, we explore the effect of local
temperature, mixing efficiency, and C/O on the atmospheric
chemistry leading to 14 independent models described in
Table 1. The chemical models are used as input to calculate
transmission spectra, which are then cross-correlated with the

Table 1
Description of Models Corresponding to Figure 10

Model
Number C/O

Temperature–Pressure Profile
(as in Figure 1)

Kzz (as in
Figure 1)

1 0.55 TP Kzz,1

2 0.55 TP Kzz,2

3 0.55 TP Kzz,3

4 0.55 TP-100 Kzz,2

5 0.55 TP+100 Kzz,2

6 0.55 TP+200 Kzz,2

7 2 TP Kzz,1

8 2 TP Kzz,2

9 2 TP Kzz,3

10 2 TP-100 Kzz,2

11 2 TP+100 Kzz,2

12 2 TP+200 Kzz,2

13 0.9 TP Kzz,2

14 5 TP Kzz,2

2

The Astrophysical Journal, 980:147 (16pp), 2025 February 10 Bangera et al.



near-IR observations to test the conclusions of G. Guilluy et al.
(2022) employing a physically motivated model.

2.1. Chemical Kinetics Modeling

We employed the 1D photochemical diffusion code ARGO
(P. B. Rimmer & C. Helling 2016, 2019) to model the
atmospheric chemistry of WASP-69 b in thermochemical
disequilibrium. The model consists of two parts: a transport
model that considers ion–neutral and neutral–neutral reactions
and a model calculating the chemical rate constants for
photochemistry and cosmic rays. It solves the 1D continuity
equation for each gas species i,

( )n

t
P L

z
, 1i

i i
if¶

¶
= - -

¶
¶

where ni, in cm−3, is the number density of species i; Pi and Li
are the production and loss rates of species i, respectively
[cm−3 s−1]; and

z
if¶

¶
is the vertical change in flux fi [cm

−2 s−1].
The production and loss terms Pi and Li describe two-body
neutral–neutral and ion–neutral reactions, three-body neutral
reactions, dissociation reactions, radiative–association reac-
tions, and thermal ionization and recombination reactions.
Vertical transport is assumed to occur via both eddy (Kzz

[cm2 s−1]) and molecular (Dzz [cm
2 s−1]) diffusion,

( )
( ) ( )

K n

D n , 2

i
n

z i H T

dT

dz

n

z i H T

dT

dz

zz
1 1

zz
1 1

i

i

i

T

0
f =- + +

- + + a

¶
¶

¶
¶

+

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

where H0 is the atmospheric pressure scale height at vertical
height z, Hi is the atmospheric scale height for species i, T is the
temperature, and αT is the thermal diffusion coefficient
(P. M. Banks & G. Kockarts 1973; K. Zahnle et al. 2006).
The molecular diffusion coefficients in ARGO are adopted
from Chapman–Enskog theory (D. Enskog 1917; S. Chapman
& T. G. Cowling 1991). The eddy diffusion coefficients are
used as a free parameter.

2.2. Radiative Transfer with C-DISORT

In order to calculate photochemical rates, the stellar high-
energy flux received at the top of the planet’s atmosphere and
its variation throughout the atmosphere is required. For the
corresponding radiative transfer calculations, we added the
discrete ordinate radiative transfer code C-DISORT (B. Hamre
et al. 2013) to ARGO. C-DISORT is an improved C version of

the well-known DISORT code originally written in FORTRAN
(K. Stamnes et al. 1988).
C-DISORT provides the exact solution of the plane-parallel

radiative transfer equation for a given set of polar angles. In the
framework of a discrete ordinate radiative transfer scheme,
these are referred to as streams, and their number determines
the numerical accuracy of the solution. For this work, we
employ four streams, which is usually sufficient for calculating
angular-averaged quantities in scenarios without strongly
asymmetric scattering. The C-DISORT radiative transfer yields
the mean intensity as a function of atmospheric height, which is
subsequently converted into the actinic flux that is used to
calculate the corresponding photodissociation rates.

2.3. Model Setup

For the incident stellar radiation, we constructed the stellar
spectral energy distribution (SED) for WASP-69 b (Figure 9)
by mixing a PHOENIX model in the UV, optical, and infrared
(T. O. Husser et al. 2013) with a scaled solar flux in the EUV
and X-ray regimes (M. Claire et al. 2012). The solar X-ray and
ultraviolet (XUV) emission has been scaled to best match the
observed stellar X-ray luminosity (L. Nortmann et al. 2018)
and expected EUV flux (L. Fossati et al. 2023). To model the
terminator regions, we set the stellar zenith angle of the
incident stellar beam in C-DISORT to 85°. In addition to stellar
radiation, we include the effect of low-energy cosmic rays in
our simulations based on P. B. Rimmer & C. Helling (2016).
For atmospheric composition and synthetic transmission
spectrum calculations, we considered the same stellar para-
meters and planetary log(g) used by G. Guilluy et al. (2022;
Table 2).
We treated the local thermodynamic properties, element

abundances, and mixing efficiency as free parameters in our
models as described below.
(1) Temperature profile. Figure 1 illustrates the (Tgas, pgas)

profiles used as input to model WASP-69 b's atmosphere
chemistry. The base profile (orange curve) was obtained from
1D radiative-thermochemical-equilibrium calculations assum-
ing solar composition (G. Guilluy et al. 2022; P. Cubillos et al.
2024, in preparation). These radiative-equilibrium calculations
considered an atmospheric model ranging from 100 to
10−9 bars and a spectral window ranging from 0.3 to 30 μm
to cover the bulk of the stellar and planetary radiation. The
radiative transfer was computed with the PYRAT BAY code
(P. E. Cubillos & J. Blecic 2021), using the line-by-line
sampling approach over a cross-section grid with a resolving
power of 15,000. The radiative transfer routine in PYRAT
BAY uses the line-sampling approach, considering the major
sources of opacity expected in H2-dominated atmospheres: CO,

Table 2
WASP-69 b System Parameters for the Host Star and the Planet as Used by G. Guilluy et al. (2022)

Quantity Value Source

Stellar mass (Me) 0.826(29) D. R. Anderson et al. (2014)
Stellar radius (Re) 0.813(28) D. R. Anderson et al. (2014)
Stellar effective temperature (K) 4715(50) D. R. Anderson et al. (2014)
Planetary mass (MJup) 0.260(17) D. R. Anderson et al. (2014)
Planetary radius (RJup) 1.057(47) D. R. Anderson et al. (2014)
Planetary equilibrium temperature (K) 963(18) D. R. Anderson et al. (2014)
Semimajor axis (au) 0.04527 0.00054

0.00053
-
+ A. S. Bonomo et al. (2017)

Note. The numbers in parentheses are the standard uncertainty corresponding to the last digits of the quoted values.

3

The Astrophysical Journal, 980:147 (16pp), 2025 February 10 Bangera et al.



CO2, SO2, and CH4 from HITEMP (L. S. Rothman et al. 2010;
G. Li et al. 2015; R. J. Hargreaves et al. 2020); H2O, HCN,
NH3, and C2H2 from ExoMol (G. J. Harris et al. 2006, 2008;
S. N. Yurchenko et al. 2011; A. A. A. Azzam et al. 2016;
D. S. Underwood et al. 2016; O. L. Polyansky et al. 2018;
P. A. Coles et al. 2019; K. L. Chubb et al. 2020); Na and K
(A. Burrows et al. 2000); and collision-induced absorption due
to H2–H2 and H2–He (J. Borysow et al. 1988; A. Borysow &
L. Frommhold 1989; A. Borysow et al. 1989, 2001; A. Bory-
sow 2002). The large molecular line-list databases were
preprocessed with the REPACK algorithm (P. E. Cubil-
los 2017) before sampling into the opacity data. An intrinsic
heat flux of 100 K was adopted, as it is typically assumed for
Jupiter-sized planets.

To extend the pressure profile to 1000 bars, capturing deeper
regions where NH3 quenching may occur (J. I. Moses et al.
2011), we applied the hot adiabatic temperature profile from
F. Sainsbury-Martinez et al. (2019) as detailed in Equation (21)
of A. D. Schneider et al. (2022),

( ) · ( )T p
p

100 bars
100 bars

, 3ad
gasQ> =

h
⎛
⎝

⎞
⎠

where Θad is the local gas temperature of the adiabat at
100 bars and η= 1/3.56. This extended profile serves as our
base model “TP,” while additional profiles are obtained by
shifting TP by ±100 K throughout the atmosphere.

(2) Eddy diffusion coefficient (Kzz). While several studies
using 3D general circulation models have provided numerical
and theoretical estimates of the eddy diffusion coefficient Kzz

(e.g., V. Parmentier et al. 2013; T. D. Komacek et al. 2019;
A. Arfaux & P. Lavvas 2023), the parameter remains difficult
to constrain. Three different Kzz profiles are investigated here
(Figure 1). The first is a constant Kzz,1= 1010 cm2 s−1

throughout the atmosphere. The second depends on the local
gas pressure derived by V. Parmentier et al. (2013) for
HD 209458 b, [ ]K cm s .

pzz,2
5 10 2 1

8

gas
= ´ - V. Parmentier et al.

(2013) find this to be a valid parameterization for
pgas= 102K 10−6 bars. We extend the Kzz,2 profile to
10−9 bars, resulting in high Kzz(10

13
–1014 cm2 s−1) in the

upper atmosphere. The Kzz,3 profile is 10 × Kzz,2 across the
same pressure range. For pressures greater than 100 bars in all
three profiles, we set Kzz to a constant value of 1010 cm2 s−1, as

suggested by J. I. Moses et al. (2022). The various Kzz profiles
investigated here allow one to study a range of efficiencies in
eddy mixing for both the top and bottom of the atmosphere.
(3) C/O. The elemental abundances are set to solar

(M. Asplund et al. 2009). For the composition of the
atmosphere, we consider C/O= 0.55 (solar), 0.9, 2, and 5,
altering the C abundance each time. These values range from
oxygen-rich to carbon-rich and are used to probe how high a
value for C/O is required for C2H2 to be observable.
The base model utilizes the (Tgas, pgas) profile “TP” (orange

in Figure 1), the pressure-dependent eddy diffusion profile
/K p1zz,2 gas~ , and solar element abundances with an

oxygen-rich C/O= 0.55. Thirteen additional models are built
by independently varying these parameters. A summary of the
different model parameters is presented in Table 1.

2.4. Cross-correlation to Observations

The 14 nonequilibrium chemistry models computed in this
work are compared to the “full model” used in G. Guilluy et al.
(2022), where the authors conducted high-resolution transmis-
sion spectroscopy of WASP-69 b. They analyzed data from
three nights gathered with the near-infrared spectrograph
GIANO-B of the Telescopio Nazionale Galileo.
To compute the transmission spectra of WASP-69 b based

on our photochemical kinetics result, we used the PYRAT
BAY package, this time sampling the cross sections at a
resolution of R= 80,000 over a wavelength range of
0.9–2.5 μm, to be able to compare the results at a high spectral
resolution.
To maintain consistency, we employed the same data

processing methodology described in G. Guilluy et al. (2022)
starting from the residual GIANO-B spectra resulting from the
principal component analysis for telluric correction. The real
data are cross-correlated with our models by following the
same approach described in Section 3 of G. Guilluy et al.
(2022). First, we convolved each model to the GIANO-B
instrument profile (a Gaussian profile with full width at half-
maximum, FWHM, of ∼5.4 km s−1). For each night, we used
the GIANO-B orders selected in G. Guilluy et al. (2022) and
performed cross-correlation (CC) for every phase over a lag
vector corresponding to planet radial velocities (RVs) in the
range −252 km s−1� RV� 252 km s−1 in steps of 3 km s−1

Figure 1. Gas temperature–pressure (left) and eddy diffusion Kzz (right) profiles used in this work. The orange (Tgas, pgas) profile, up to 100 bars, is adapted from
G. Guilluy et al. (2022) for their analysis of WASP-69 b and extended to 1000 bars assuming a hot adiabatic temperature profile. All other (Tgas, pgas) profiles are
obtained by shifting the orange profile in steps of 100 K.

4

The Astrophysical Journal, 980:147 (16pp), 2025 February 10 Bangera et al.



(to cover all possible RVs of the planet). Subsequently, we
coadded the CC functions over the selected orders, nights, and
orbital phase after shifting them in the planet rest frame by
assuming a circular orbit (i.e., zero eccentricity). We scanned a
range of planet RV semiamplitudes 0 km s−1 �KP�
200 km s−1 in steps of 1.5 km s−1 (which includes the expected
KP, KP,theo= 127.11 1.52

1.49
-
+ km s−1; see Table 1 in G. Guilluy

et al. 2022). To quantify the confidence level of our detections,
we converted the total CC signal into signal-to-noise (S/N) by
dividing the total CC matrix by its standard deviation
(calculated by excluding the CC peak; e.g., M. Brogi et al.
2018; P. Giacobbe et al. 2021).

3. Results

3.1. Equilibrium versus Quenching versus Photochemistry

The chemical species investigated in this work are H2O, CO,
CH4, C2H2, NH3, HCN, and CO2. Of these, H2O, CO, CH4,
C2H2, and NH3 have been detected in the terminator regions of
WASP-69 b based on high-resolution transmission spectra
collected with the GIANO-B near-infrared spectrograph. Ion–
neutral chemistry has been included in our modeling with
STAND, but its impact on the aforementioned molecules is
found to be negligible. We test the hypothesis by G. Guilluy
et al. (2022) that these species can only be present
simultaneously if chemical disequilibrium processes affect
their formation and/or destruction. Since each of these
molecules may be affected to a different extent by photo-
chemistry and vertical diffusion in the atmosphere, three
different cases are studied and compared: (i) chemical
equilibrium, (ii) disequilibrium chemistry resulting from eddy
diffusion, and (iii) disequilibrium chemistry resulting from
eddy diffusion and photochemistry. The equilibrium concen-
trations (case (i)) are calculated using the GGchem code
(P. Woitke et al. 2018) using solar element abundances and
C/O= 0.55. We use the respective (Tgas, pgas) profile as our
base model as outlined in Section 2.1 for cases (ii) and (iii) with
Kzz,2. The results are shown in Figure 2.

In both cases with (ii) only diffusion and (iii) diffusion with
photochemistry, the concentrations of H2O and CO remain
close to their equilibrium values, except for pgas < 10−7 bars,
where they are depleted by photodissociation. This agreement
with equilibrium concentrations is because both species are
already the most abundant species at their quench points and
throughout the atmosphere and thus not significantly affected
by quenching. This is consistent with the results presented in
J. I. Moses et al. (2011), B. Drummond et al. (2020), and
R. Baeyens et al. (2022b). CH4, being less abundant in WASP-
69 b's atmosphere than CO at these gas temperatures, is more
significantly affected by diffusion. It is quenched at ∼0.4 bar
and photodissociated at pgas < 10−6, resulting in concentrations
up to 4 dex larger than its equilibrium concentrations in the
upper atmosphere.

NH3 concentrations depart from equilibrium and are
quenched at ∼100 bars. Similar high-pressure quenching for
NH3 has been reported by J. I. Moses et al. (2011) in the
atmosphere of HD 189733 b due to ammonia reaching the
N2–NH3 interconversion quench point at high pressures and
temperatures. We find that the quenching of NH3 results in it
having comparable concentrations to N2 on WASP-69 b. In our

model, NH3 is produced through the following scheme:

( )

( )

N H N H
N H H N H H
N H H NH NH
NH H NH H
2 NH H NH H
2H M H M

Net: N 3H 2NH . 4

2 2

2 2 2 2

2 2 2

2 2

2 2 3

2

2 2 3

+ 
+  +
+  +

+  +
+  +

+  +
+ 

Here, M is any third body. The final quench point for NH3 is at
the intermediate gas pressures of ∼1 bar. This arises because
the gas temperature profile remains relatively constant in the
pressure range between 1 and 100 bars, allowing the effective
interconversion reactions between NH3 and N2 to persist
(J. I. Moses et al. 2011). At pgas < 1 bar, the temperature
gradients become significant again (Figure 1), causing the rates
of the interconversion reactions to drop off, resulting in the
final quenching of NH3, beyond which it maintains a uniform
concentration until photochemical destruction in the upper
atmospheric layers. The impact of this quench point is more
pronounced when comparing models with different Kzz values,
as discussed in Section 3.2.6.
C2H2 follows its equilibrium profile up to ∼1 bar. At

0.01 bar < pgas < 1 bar, the disequilibrium concentrations are
up to 1 dex higher than the equilibrium concentrations, caused
by the increased concentrations of parent molecule CH4 due to
quenching. C2H2 production occurs through the following
scheme at these pressure levels:

( )

H CH CH H
CH CH C H H
C H M C H H M
C H H C H H
C H M C H H M

Net: 2CH C H 3H . 5

4 3 2

3 4 2 5 2

2 5 2 4

2 4 2 3 2

2 3 2 2

4 2 2 2

+  +
+  +
+  + +
+  +
+  + +

 +

At pgas ∼ 0.01 bar, C2H2 is quenched. Its concentration is
further enhanced by up to 7 dex in the upper atmosphere due to
the abundance of photochemically released atomic H, along
with high levels of quenched CH4. The following chemical
scheme is responsible for the production of C2H2 in the upper
atmosphere:

( )

( )

2 CH H CH H
2CH C H
C H H C H H
C H H C H H
C H H C H H
C H H C H H
3H M 6H M

Net: 2CH C H 3H . 6

4 3 2

3 2 6

2 6 2 5 2

2 5 2 4 2

2 4 2 3 2

2 3 2 2 2

2

4 2 2 2

+  +

+  +
+  +
+  +
+  +

+  +
 +

This scheme also results in the release of molecular hydrogen
in the upper (photochemically active) atmosphere. It is similar
to J. I. Moses et al. (2013) for the production of C2H2 in the
atmosphere of XO-1 b, with the exception of the step that
produces C2H4. In their scheme, the production of C2H4 is
accomplished through collision with a third body: C2H5 +

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Figure 2. Local nonequilibrium gas-phase concentrations of H2O, CO, CH4, NH3, C2H2, HCN, and CO2 for (i) thermochemical equilibrium (solid lines), (ii) vertical
diffusion but no photochemistry (dotted lines), and (iii) vertical diffusion with photochemistry (dashed lines). The input (Tgas, pgas) profile is the base model “TP” with
the eddy diffusion profile Kzz,2 and C/O = 0.55. NH3 and CH4 concentrations are increased by diffusion, which then contributes to increased concentrations of C2H2

and HCN. Note that the x-axis range differs in each subfigure.

6

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M → H + C2H4 + M, resulting in the use of two fewer H and
the production of one fewer H2 in this reaction.

Similar to C2H2, the concentration of HCN is influenced by
chemical disequilibrium in three ways. First, in the deep
atmosphere, the increased presence of parent molecules CH4

and NH3 leads to a higher chemical production of HCN. The
production scheme is then as follows:

( )

NH H NH H
NH H NH H
NH H N H
CH H CH H
N CH H CN H
H CN M HCN H
H M 2H M

Net: NH CH HCN 3H . 7

3 2 2

2 2

2

4 3 2

3 2

2

2

3 4 2

+  +
+  +
+  +
+  +

+  +
+  +

+  +
+  +

Second, HCN concentrations are quenched at pgas ∼ 1 bar.
Third, XUV radiation boosts HCN at pgas= 10−3.5

–10−8 bars
and photodissociates it at higher altitudes. At these gas
pressures, the production scheme is similar to Scheme (7),
except for the formation of NH, which happens through the
photodissociation of NH3 through NH3 → [hν] NH + 2H. In
agreement with B. Drummond et al. (2020), CO2 is found to be
depleted by a factor of ∼4 at pgas < 10−1 bars through
quenching as carbon is quenched into CH4. CO2 is depleted by
photodissociation at pgas < 10−7 bars.

3.2. The Parameter Study for Individual Molecules

3.2.1. H2O

As shown in Figure 3, at solar C/O, the strength of the eddy
diffusion parameter does not significantly affect H2O concen-
trations in the deep atmosphere. However, in the upper
atmosphere, the stronger eddy diffusion can support concen-
trations against photodissociation, whereas for the weakest
eddy diffusion probed, H2O concentrations are depleted by
>4 dex. At higher C/O, for, e.g., C/O= 2, H2O is no longer
the dominant species at its quench point; hence, the strength of
mixing significantly affects the concentrations. Here, the model
with the most efficient mixing in the deep atmosphere (Kzz,1)
quenches at higher pressures and thus at higher concentrations.
For “TP” and Kzz,2, an increase in C/O results in decreased
concentrations for H2O as there is less oxygen available to form
water once carbon sequesters the amount needed to form CO.
This change in concentrations is less notable when C/O < 1,
i.e., in an oxygen-dominated atmosphere. For C/O= 0.55, a
change in temperature does not significantly affect H2O
concentrations. At colder temperatures, there is a slight increase
in concentration as CO depletes in the atmosphere in favor of
CH4. In contrast, for C/O= 2, an increase in gas temperature
causes H2O concentrations to deplete rapidly as more oxygen is
preferentially trapped in CO.

3.2.2. CO

At a planetary equilibrium temperature of ∼950 K, the
CO–CH4 interconversion becomes crucial in WASP-69 b's
atmosphere, with CO being the preferred species at higher
temperatures. Thus, the strength of eddy diffusion does
substantially affect the concentrations of CO, as seen in
Figure 3. For a higher diffusion coefficient, CH4 is quenched at

higher concentrations, and consequentially, CO is quenched at
a lower concentration. This trend remains consistent for C/O of
both 0.55 and 2. In the upper atmosphere, a higher diffusion
strength serves to replenish concentrations against photodisso-
ciation, similarly to H2O. As C/O increases, the concentration
of CO increases until oxygen is entirely trapped in CO. A
further increase in C/O only results in higher concentrations of
CH4 and other hydrocarbons. With regard to the dependence on
the local gas temperature, high temperatures push the carbon
chemistry toward CO instead of CH4. For WASP-69 b, this
suggests that, at solar C/O, a gas temperature increase of
∼100 K in the lower atmosphere can effectively turn the bulk
of carbon from CH4 into CO. The following chemical pathway
converts CH4 to CO in the upper atmosphere:

( )

H O H H O
CH H CH H
CH O CH O H

CH O H CHO H
CHO H CO H

Net: H O CH CO 3H . 8

2
hv

4 3 2

3 2

2 2

2

2 4 2

 + +
+  +
+  +
+  +
+  +
+  +

3.2.3. CH4

Figure 4 shows the effect of the different parameters on CH4

concentrations. Conversely to CO, stronger mixing serves to
increase the concentrations of CH4 in the upper observable
atmosphere. In the upper atmosphere, CH4 is photodissociated,
resulting in higher-order hydrocarbons, and is also chemically
recycled into CO through Scheme (8). CH4 concentrations
experience a significant gain when C/O > 1. As the
equilibrium CH4 concentration is larger at the quench point
for the higher-C/O models, the quenched methane concentra-
tion is larger for these models. This larger concentration then
enhances the effectiveness of mechanisms that convert CH4 to
hydrocarbons like C2H2 (e.g., through Schemes (5) and (6)).
For solar C/O, there is a rapid depletion of CH4 concentrations
as the gas temperature increases, as the carbon chemistry shifts
toward CO. However, for higher C/O, CH4 remains the
preferred carrier of carbon due to the limited amount of oxygen
available in the atmosphere; hence, there is no strong depletion
of concentrations with increase in temperature.

3.2.4. CO2

The concentration of CO2 in the atmosphere of WASP-69 b
varies in response to the disequilibrium abundances of H2O and
CO via the following scheme:

( )

H O H H OH
CO OH CO H

Net: H O CO H CO . 9

2 2

2

2 2 2

+  +
+  +

+  +

Thus, as seen in Figure 4, for a low C/O, the reaction rate is
limited by the concentration of the less abundant CO; thus, CO2

reflects the same dependence on the eddy diffusion strength
and local gas temperature as CO. Conversely, for a high C/O,
H2O concentrations are strongly depleted; thus, the dependence
of CO2 on Kzz and gas temperature is similar to that of H2O.
CO2 is therefore also created more abundantly in an oxygen-
rich environment, as it needs to sequester the oxygen from
H2O.

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3.2.5. C2H2

The relationship between Kzz and C2H2 concentrations is
complex, with a behavior that is not uniform throughout the
atmosphere and depends on the local abundances of other species,
as illustrated in Figure 5. At higher pressures (10−2–102 bars),
C2H2 concentrations increase with stronger mixing (Kzz,1), as
C2H2 is formed through Scheme (5) by the neutral–neutral
reactions of CH4 and CH3 and thus reflects methane's dependency
on Kzz at these pressures. Conversely, in the upper atmosphere
(pgas < 10−2 bars), C2H2 concentrations decrease for higher
mixing strengths, because C2H2 formation here requires the
interaction of photochemically released H with the quenched CH4.
Stronger diffusion in the upper atmosphere works against
photochemistry, leading to a lower production of C2H2. In the
lower atmosphere (pgas > 10mbar), the dependence on Kzz is
more prominent for the solar C/O model, as CH4 concentrations
depend strongly on Kzz. In the upper atmosphere, the dependence
on Kzz C/O= 2, as C2H2 concentrations are impacted by the
strong depletion of H2O against the XUV flux for small Kzz

values. When the C/O ratio exceeds 1, the concentration of C2H2

increases significantly due to the increased efficiency of the
formation pathway through Schemes (5) and (6). This is in
agreement with the results of C. Helling et al. (2017), where the
effect of increasing the thermal stability of more complex
hydrocarbon molecules with increasing C/O ratios was demon-
strated for brown dwarfs. Similarly to CO2, there is an inversion in

the dependence on temperature for low and high C/O. At low
C/O, an increase in temperature leads to more CO production
rather than CH4, which in turn makes the production pathway of
C2H2 through CH4 less efficient. However, at high C/O, the
concentration of CH4 increases and the production pathway to
form C2H2 becomes more efficient at higher temperatures,
resulting in higher concentrations of C2H2. In all models, C2H2

is primarily lost into larger hydrocarbons such as C2H4 and C2H6,
which have similar concentrations to C2H2. D. Gasman et al.
(2022) suggest that a concentration above 1 × 10−7–1 × 10−6 is
needed to observe hydrocarbon species through the atmosphere.
This is also the requirement placed in G. Guilluy et al. (2022) for
their best-fit model. Our models show that these concentrations
are achieved at high C/O, high temperatures, and low Kzz.

3.2.6. NH3

Figure 5 presents the effect of the different parameters on
NH3 concentrations. A more efficient atmospheric gas diffusion
helps to maintain the quenched NH3 concentration up to higher
altitudes, as the fast eddy diffusion offsets the NH3 loss caused
by photodissociation (see also K. Ohno & J. J. Fortney 2023b).
NH3 quenching occurs deep in the atmosphere at
pgas ∼ 100 bars, and since the Kzz values at the model lower
boundary are identical across the profiles, no difference in NH3

concentrations is observed at these depths. At pressures of
∼1 bar, the second quench point emerges. Here the difference

Figure 3. H2O and CO concentrations for the terminator region of WASP-69 b. Top: varying eddy diffusion for TP and C/O = 0.55 and 2. Middle: varying C/O
ratios for TP and Kzz,2. Bottom: varying (Tgas, pgas) for Kzz,2 and C/O = 0.55 and 2.

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in Kzz between the profiles—approximately 1 dex—impacts
NH3 concentrations by a factor of 2. Molecules such as NH3

and N2, which do not contain carbon or oxygen, are relatively
unaffected by the C/O ratio. However, as the quenched
concentration of CH4 increases with higher C/O ratios,
processes that kinetically convert CH4 and NH3 into HCN
(Scheme (7)) become more effective for high C/O. This leads
to a lower NH3 concentration in the middle atmosphere above
the quench point for the C/O= 2.0 model as compared to the
C/O= 0.5 model. At these temperatures, nitrogen is preferen-
tially stored in NH3. For both a solar and C/O= 2 model, NH3

concentrations are depleted as temperatures increase and NH3

is converted to HCN and N2.

3.2.7. HCN

In these models, HCN is generated in the deep atmosphere
through Scheme (7). Figure 6 illustrates that for stronger
diffusion, HCN is quenched at lower concentrations in the
deeper regions of the atmosphere. Conversely, less efficient
diffusion results in higher quenched HCN concentrations since
it is quenched at higher altitudes, where NH3 and CH4

concentrations are also quenched, allowing for local chemical
production. In the upper atmosphere, a lower Kzz supports the
concentrations (until it is photochemically destroyed), because
NH3 photodissociation is not offset by diffusion. The higher
concentrations of CH4 at larger C/O result in more NH3

chemically converted to HCN for high C/O ratios. In addition,
the higher C/O also smooths out the HCN profile throughout
the atmosphere as the quenched HCN concentrations approach
those produced by photochemistry. HCN concentrations
initially rise with temperature up until the (Tgas, pgas) profile
“TP+200,” at which profile the concentration decreases. This is
because the reaction rate coefficient of HCN formation from
CH4 and NH3 increases as temperatures rise, while the
concentrations of NH3 and CH4 themselves decrease. HCN is
primarily destroyed in these models by being recycled back
into NH3 as follows:

( )

HCN M HNC M
HNC OH HNCO H
HNCO H CO NH
NH H NH H
H O H OH H

Net: HCN H O CO NH . 10

2

2 2 3

2 2

2 3

+  +
+  +
+  +

+  +
+  +

+  +

4. Comparison to Observational Data: Mid-IR Transit
Spectroscopy

Of the 14 models computed in this work, eight models
(Table 3) are found to have CC maps that peak at the expected
location (vrest∼ 0 km s−1 and KP∼ KP,theo= 127.11 1.52

1.49
-
+ km s−1),

where KP,theo refers to the expected RV semiamplitude of

Figure 4. Same as Figure 3 but for CH4 and CO2.

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WASP-69 b (see Table 3). The S/N maps for all models
computed in this work are shown in Figure 10.

The CC framework implicitly assumes that the signal
amplitude and the S/N are uniform across the considered
spectral range. Yet this assumption is only valid at a first-order
level. To delve deeper into this aspect, we transformed the CC
values into likelihood (LH) mapping values for the eight
models following the method proposed by M. Brogi &
M. R. Line (2019) and utilized by P. Giacobbe et al. (2021).
In this approach, LH is determined by considering the model's
line depth alongside the S/N order by order and spectrum by
spectrum. Consequently, identifying a peak in the LH at the
correct position within the (vrest, KP) space provides additional
confirmation of the detection. Yet the eight models are
compatible within 2σ, suggesting that they are statistically
equivalent.

This study represents one of the first applications of high-
resolution data to derive atmospheric properties based on
kinetic chemistry modeling. Among the eight models fitting the
data in CC, four exhibit C/O of 2.0, including model 9, which
yields the best fit in the LH analysis. This aligns with
G. Guilluy et al.’s (2022) findings of a carbon-rich atmosphere
(C/O= 2.0) on WASP-69 b. Conversely, the remaining four
models suggest C/O of 0.55 and 0.9, preventing a definitive
conclusion of a carbon-rich atmosphere. Furthermore, seven of

the eight models suggest an atmosphere with a temperature–
pressure profile comparable to or cooler than equilibrium
modeling predictions at the substellar point, while only one
indicates a hotter atmosphere. Finally, the observational data
used here do not conclusively constrain the shape or value of
the Kzz parameter.
Our results highlight the intrinsic degeneracy in the problem

at hand, at least within the scope of our grid of models. One of
the possible reasons for this degeneracy is that the physical and
chemical properties of planetary atmospheres are not homo-
geneous across the terminator (see Section 5.1). One possible
additional explanation is that transmission spectra generated
with different parameter combinations could appear similar.
Finally, we acknowledge that there are data analysis steps yet
to be fully understood, especially when high-resolution
observations are used to derive atmospheric properties. One
such aspect is the order selection used for the CC analysis
(G. Guilluy et al. 2022; P. Giacobbe et al. 2025, in preparation).
To address these challenges in future works, retrievals could be
applied, although this may lead to nonphysical solutions.
Nonetheless, the computation of physically motivated models
is still too slow to be applied in a retrieval framework;
therefore, it is crucial to compare the results of retrieval
analyses to those obtained from physically motivated forward
modeling.

Figure 5. Same as Figure 3 but for C2H2 and NH3.

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5. Discussion

5.1. Multidimensional Nature of Planetary Atmospheres

If the atmosphere of WASP-69 b is indeed carbon-rich, as
indicated by four out of eight models that match the
observations, the temperature variations among these models

may reflect the contrasting conditions of the morning (cooler)
and evening (warmer) terminators. These differences align with
the expected temperature gradients for a planet of this type
(C. Helling et al. 2023). As the observation is time- and space-
averaged, contributions from both regions can be expected.
Efforts to disentangle the components from the two terminators
on exoplanets have been a focus of several recent studies,
utilizing both low-resolution and high-resolution data to reveal
differing atmospheric conditions across the two regions (e.g.,
D. Ehrenreich et al. 2020; N. Espinoza & K. Jones 2021;
D. Grant & H. R. Wakeford 2023).
A notable observation is the detection of C2H2 in WASP-69

b's atmosphere, accompanied by the lack of detection of HCN.
Both molecules are commonly considered tracers of warm,
carbon-rich atmospheres (O. Venot et al. 2015; K. Ohno &
J. J. Fortney 2023a). Among our best-fit models, only model 12
—which features the highest temperature within the carbon-
rich models—shows a strong C2H2 signal. This model also
predicts a substantial HCN concentration with a spectral signal
comparable to that of C2H2 and over 10 times stronger than that
of NH3, particularly near 1.5 μm (see Figure 7). Therefore, if
C2H2 is present on WASP-69 b, we predict that HCN should
also exist at detectable levels, suggesting that future observa-
tions might reveal its signature.
Our 1D modeling does not account for 3D mixing effects

and wind jets. In tidally locked hot Jupiters, uneven heating
may result in significant temperature contrasts between the day-
and nightsides, leading to variations in atmospheric composi-
tion. Strong superrotating equatorial jets may instead homo-
genize these differences in composition (e.g., N. Madhusudhan
et al. 2016; R. Baeyens et al. 2022a). In line with the results of
R. Baeyens et al. (2024), it can be anticipated that the main
effect of horizontal chemical transport in WASP-69 b would be
to quench molecular concentrations on the evening terminator
to values typical of the hotter dayside regions and those on the
morning terminator to levels resembling the colder nightside.
Given that the equilibrium temperature of WASP-69 b,
∼950 K, puts it on the cusp of CH4–CO conversion and
NH3–N2 conversion, and that our models show that temper-
ature differences of 100–200 K through the atmosphere
significantly change the concentrations of the observed
molecules, this horizontal quenching may result in significantly
different concentration profiles for the two terminator regions.

Figure 6. Same as Figure 3 but for HCN.

Table 3
CC and LH Test Results

Model Number CC Framework LH Framework

vrest0 (km s−1) KP0 (km s−1) S/N vrest0 (km s−1) KP0 (km s−1) LHmax σ

1 0.0 105.0 3.18 2.0 138.0 5,527,572.94 1.86
3 0.0 102.0 3.21 2.0 135.0 5,527,573.63 1.44
4 0.0 100.5 46.5

72.0
-
+ 3.04 2.0 138.0 5,527,573.66 1.42

7 0.0 105.0 3.48 2.0 141.0 5,527,573.74 1.37
9 0.0 105.0 3.23 2.0 141.0 5,527,574.67 Ref.
10 0.0 102.0 3.15 2.0 141.0 5,527,574.23 0.94
12 0.0 133.5 3.35 0.0 159.0 5,527,573.83 1.30
13 0.0 102.0 48.0

75.0
-
+ 3.21 2.0 138.0 5,527,574.00 1.16

Note. From left to right: the model name, the CC result with theoretical models in the S/N framework, and the LH findings. The planet orbital semiamplitude (P0) as
well as the velocity in the planet rest frame (vrest0) of the CC and LH peak are reported. The S/N, the maximum of the LH matrix max, and the goodness of fit obtained
with the Wilks theorem on the LH-ratio test are also present. The goodness of fit of the models is shown with respect to the best model in units of standard deviations σ
(the higher the σ, the more disfavored the model).

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An additional consequence of the horizontal mixing would be
an increase in photochemical products HCN and C2H2 on the
morning terminator due to mixing of the more photochemically
active parent species CH4 and NH3 from the nightside, while
there may be fewer of these photochemical products on the
evening terminator, as demonstrated by S.-M. Tsai et al.
(2024).

5.2. Capturing NH3 Quenching

The (Tgas, pgas) profile retrieved through equilibrium
modeling in G. Guilluy et al. (2022) is constrained to a
maximum pressure of 100 bars. To evaluate the implications of
this constraint on nonequilibrium chemistry, we compare our
models with lower boundary pressures of 1000 bars to those
restricted to 100 bars.

Our models are initialized with atomic abundances at the
lower boundary, as opposed to equilibrium values, and are then
evolved until a steady state is achieved. This approach reveals
significant deviations from equilibrium concentrations for NH3

and HCN at 100 bars (Figure 8), indicating that NH3 quenching
occurs at pressures deeper than 100 bars, in agreement with the
findings of J. I. Moses et al. (2011) for HD 189733 b, where
NH3 concentrations at 100 bars are strongly influenced by the

N2–NH3 interconversion quench point at higher temperatures
and pressures.
At lower atmospheric temperatures, the kinetics pathways

favor NH3 formation. For WASP-69 b, the deeper atmospheric
layers are cooler than those of HD 189733 b. As a result, the
100 bar models overpredict NH3 concentrations relative to their
equilibrium value and produce higher NH3 concentrations than
expected for the deeper pressure models. This overestimation
also impacts the formation of HCN, amplifying its abundance.
In contrast, other key molecules such as CH4, CO, and H2O
show minimal sensitivity to the pressure boundary, as their
concentrations are largely dictated by equilibrium chemistry
even at 100 bars, and they are quenched at lower pressures,
minimizing their dependence on deeper atmospheric dynamics.
To evaluate the observational implications of these differ-

ences, we generated synthetic spectra for the 100 bar models.
The spectra consistently show stronger HCN spectral features
compared to NH3, reflecting the higher HCN concentrations
across these models. Additionally, only 3 of the 14 100 bar
models achieve robust CC fits and LHs, compared to the eight
models in the 1000 bar atmosphere models. The three good-fit
models in this case correspond to the parameters of models 7,
9, and 12 of Table 1, thus biasing the conclusions to carbon-
rich atmospheres (C/O= 2). This difference highlights the

Figure 7. Synthetic transmission spectra for model 12 with indications for the C2H2, HCN, and NH3 signal strengths.

Figure 8. Concentrations of key species for the terminator region of WASP-69 b for a model with lower boundary 100 bars vs. lower boundary 1000 bars.

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importance of accurately capturing the NH3 quenching at high
pressures.

Uncertainty in individual rate coefficients is another factor
that may influence the quenched NH3 concentrations in high-
pressure and high-temperature environments. The N2–NH3

interconversion is particularly sensitive to nonequilibrium
chemistry, and differences of over an order of magnitude in
the relevant reaction rate coefficients are reported in the
literature (e.g., J. I. Moses 2014; S.-M. Tsai et al. 2021;
R. Veillet et al. 2024). For example, J. I. Moses (2014)
demonstrates that NH3 predictions for HD 189733 b could
differ by up to an order of magnitude depending on whether the
J. I. Moses et al. (2011) or O. Venot et al. (2012) chemical
network was employed. P. B. Rimmer & C. Helling (2016)
provide a further discussion on the choice of reaction rate
coefficients for NH3 adopted in STAND and a comparison with
the J. I. Moses et al. (2011) network.

6. Summary

A parameter study of Kzz, (Tgas, pgas), and C/O ratio was
conducted with 1D photochemistry diffusion modeling to
analyze the effect of vertical mixing and photochemistry in
producing the species detected in WASP-69 b's atmosphere and
further constrain C/O. With this study, we confirm the
hypothesis of G. Guilluy et al. (2022) that the near-IR
WASP-69 b transition spectrum is more likely shaped by
chemical disequilibrium processes rather than equilibrium;
however, our exploration of 1D disequilibrium chemistry
prescriptions cannot replicate all of the spectral features
observed on WASP-69 b. Our results indicate the following.

1. CH4, NH3, C2H2, and HCN are the species most sensitive
to vertical diffusion and photochemistry in WASP-69 b.
Of the three parameters tested in this work, the local gas
temperature has the strongest impact on the concentra-
tions of these species in the terminator regions. However,
this dependency cannot be easily disentangled from that
of atmospheric C/O.

2. Highly efficient mixing in the upper atmosphere
competes with the effect of photodissociation, effectively
retaining the photochemical parent species at their
quenched concentrations and thereby reducing the
production of species like C2H2 and HCN.

3. A combination of high gas temperatures and C/O ∼ 2 is
required to produce C2H2 concentrations at the
10−7

–10−6 level in the lower atmosphere. However, at
gas pressures <10−6 bars, high concentrations of C2H2

are also photochemically produced for solar C/O.
4. The relation of C2H2 concentrations and Kzz is complex

and dependent on the local gas temperature and
composition (i.e., C/O).

5. The observational data are not sufficient to distinguish
different mixing profiles.

Metallicity has not been examined in this study as a free
parameter. However, if atmospheric metallicity were to
increase, the resulting reduction in CH4 concentrations
would cause a corresponding decrease in HCN and C2H2

concentrations due to the balance between CO and CH4

production shifting toward CO (V. Soni & K. Acharyya 2023).
J. I. Moses et al. (2013) find that although the CH4/H2O
fraction is more sensitive to C/O than to metallicity, the
individual concentrations are very sensitive to metallicity. In
terms of NH3, K. Ohno & J. J. Fortney (2023b) found that
although the quenched NH3 concentration remains constant as
atmospheric metallicity increases, the ratio of NH3 to bulk
atmospheric nitrogen abundance decreases significantly, as N
becomes locked in N2. Therefore, higher metallicity can be
expected to result in lower concentrations of CH4, HCN, C2H2,
and NH3. As outlined in G. Guilluy et al. (2022), this scenario
is disfavored by the observations.
After performing CC of the simulated transmission spectra

for the 14 models with the observed high-resolution data, 8
models were identified with the expected planetary rest-frame
velocity vrest0 = 0 km s−1 and planetary maximal RV
KP ∼ KP,theo. These models all differ in C/O and Kzz but
suggest a temperature–pressure profile consistent with the
predictions of equilibrium modeling or cooler. The difficulty in
distinguishing between models of varying (Tgas, pgas) and Kzz

might be related to the spatial and temporal averaging of the
observations. Interestingly, despite the high-C/O models
suggesting high HCN concentrations, this molecule has not
been detected in the atmosphere of WASP-69 b. The
transmission and emission spectroscopy observations of
WASP-69 b with JWST (GTO programs 1177 and 1185 and
GO program 3712) can be expected to provide more insights on
its atmospheric properties. By combining the low- and high-
resolution observations, the atmospheric properties of this
planet may be better constrained, and a better understanding
may be obtained of the kinetic processes in its deep and upper
atmosphere.

Acknowledgments

N.B. acknowledges financial support from the Austrian
Academy of Sciences. Ch.H. is part of the CHAMELEON MC
ITN EJD, which received funding from the European Union's
Horizon 2020 research and innovation program under Marie
Sklodowska-Curie grant agreement number 860470. P.C. is
funded by the Austrian Science Fund (FWF) Erwin Schroe-
dinger Fellowship, program J4595-N. G.G. and P.G. acknowl-
edge the financial contribution from PRIN MUR 2022 (project
No. 2022CERJ49) and PRIN INAF 2019. N.B. would like to
thank Patrick Barth for helpful advice regarding use of the
ARGO code and STAND network.

Appendix
Additional Figures and Tables

Figure 9 presents the input stellar flux at the top of the
atmosphere of WASP-69 b. Figure 10 shows the posterior
distribution for the S/N fitting of disequilibrium model spectra
produced in this work to the high-res data obtained by
G. Guilluy et al. (2022). In Figure 11, the LH maps for the
eight models with vrest0 = 0 km s−1 and KP ∼ KP,theo are shown.

13

The Astrophysical Journal, 980:147 (16pp), 2025 February 10 Bangera et al.



Figure 9. SED of the host star at the top of the atmosphere of WASP-69 b. The SED is constructed by mixing a PHOENIX model in the UV, optical, and infrared
(T. O. Husser et al. 2013) and a scaled solar flux in the EUV and X-ray regimes (M. Claire et al. 2012).

Figure 10. CC in the S/N of all models produced in this work to the high-resolution transmission spectroscopy of WASP-69 b conducted by G. Guilluy et al. (2022)
as a function of the planet's maximum RV (KP) and the planet's rest-frame velocity (Vrest). The inset numbers correspond to the models listed in Table 1. The CC peaks
are indicated by a red cross.

14

The Astrophysical Journal, 980:147 (16pp), 2025 February 10 Bangera et al.



ORCID iDs

Nidhi Bangera https://orcid.org/0009-0008-7545-5022
Christiane Helling https://orcid.org/0000-0002-8275-1371
Gloria Guilluy https://orcid.org/0000-0002-1259-2678
Patricio Cubillos https://orcid.org/0000-0002-1347-2600
Luca Fossati https://orcid.org/0000-0003-4426-9530
Paolo Giacobbe https://orcid.org/0000-0001-7034-7024
Paul Rimmer https://orcid.org/0000-0002-7180-081X
Daniel Kitzmann https://orcid.org/0000-0003-4269-3311

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	1. Introduction
	2. Modeling Approach
	2.1. Chemical Kinetics Modeling
	2.2. Radiative Transfer with C-DISORT
	2.3. Model Setup
	2.4. Cross-correlation to Observations

	3. Results
	3.1. Equilibrium versus Quenching versus Photochemistry
	3.2. The Parameter Study for Individual Molecules
	3.2.1. H2O
	3.2.2. CO
	3.2.3. CH4
	3.2.4. CO2
	3.2.5. C2H2
	3.2.6. NH3
	3.2.7. HCN


	4. Comparison to Observational Data: Mid-IR Transit Spectroscopy
	5. Discussion
	5.1. Multidimensional Nature of Planetary Atmospheres
	5.2. Capturing NH3 Quenching

	6. Summary
	AppendixAdditional Figures and Tables
	References