The Planetary Science Journal, 4:97 (20pp), 2023 May

https://doi.org/10.3847/PSJ/acd32f© 2023. The Author(s). Published by the American Astronomical Society.

Depletion of 13C in CO in the Atmosphere of Mars Suggested by ExoMars-TGO/
NOMAD Observations
S. Aoki1,2 , K. Shiobara3, N. Yoshida3 , L. Trompet2 , T. Yoshida3 , N. Terada3 , H. Nakagawa3 , G. Liuzzi4 ,A. C. Vandaele2 , I. R. Thomas2 , G. L. Villanueva5 , M. A. Lopez-Valverde6 , A. Brines6 , M. R. Patel7 , S. Faggi5,8
F. Daerden2 , J. T. Erwin2 , B. Ristic2 , G. Bellucci9 , J. J. Lopez-Moreno6 , H. Kurokawa10,11 , and Y. Ueno11
1,

Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 2778561, Japan; shohei.aoki@edu.k.u-tokyo.ac.jp
2
Royal Belgian Institute for Space Aeronomy, 3 Avenue Circulaire, B-1180 Brussels, Belgium
3
Tohoku University, 6-3, Aramaki Aza-Aoba, Sendai 980-8578, Japan
4
Scuola di Ingegneria, Universitá degli Studi della Basilicata, Via dell’Ateneo Lucano, 10, I-85100 Potenza, Italy
5
NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, 20771 MD, USA
6
Instituto de Astrofísica de Andalucía, Glorieta de la Astronomia, E-18008 Granada, Spain
7
School of Physical Sciences, The Open University, Milton Keynes, MK7 6AA, UK
8
American University, 4400 Massachusetts Avenue Northwest, Washington, DC 20016, USA
9Istituto Nazionale di Astroﬁsica, Via del Fosso del Cavaliere 100, I-00133 Rome, Italy
10
Department of Earth Science and Astronomy, Graduate School of Arts and Sciences, The University of Tokyo, Japan
11
Tokyo Institute of Technology, 2-12-1 Ookayama, Tokyo 152-8550, Japan
Received 2022 December 22; revised 2023 May 2; accepted 2023 May 4; published 2023 May 26

Abstract
The atmosphere of Mars is mainly composed by carbon dioxide (CO2). It has been predicted that photodissociation ofCO2 depletes 13C in carbon monoxide (CO). We present the carbon 13C/12C isotopic ratio in CO at 30–50 km altitude
from the analysis of the solar occultation measurements taken by the instrument Nadir and Occultation for Mars
Discovery on board the ExoMars Trace Gas Orbiter (ExoMars-TGO). We retrieve 12C16O, 13C16O, and 12C18O volume
mixing ratios from the spectra taken at 4112–4213 cm−1, where multiple CO isotope lines with similar intensities areavailable. The intensities of the 12C16O lines in this spectral range are particularly sensitive to temperature, thus wederive the atmospheric temperature by retrieving CO2 density with simultaneously measured spectra at 2966–2990
cm−1. The mean δ 13C value obtained from the 13C16O/12C16O ratios is −263‰, and the standard deviation andstandard error of the mean are 132‰ and 4‰, respectively. The relatively large standard deviation is due to the strong
temperature dependences in the 12C16O lines. We also examine the 13C16O/12C18O ratio, whose lines are less sensitive
to temperature. The mean δ value obtained with 12C18O instead of 12C16O is −82‰ with smaller standard deviation,
60‰. These results suggest that CO is depleted in 13C when compared to CO2 in the Martian atmosphere as measured
by the Curiosity rover. This depletion of 13C in CO is consistent with the CO2 photolysis-induced fractionation, whichmight support a CO-based photochemical origin of organics in Martian sediments.
Uniﬁed Astronomy Thesaurus concepts: Planetary atmospheres (1244)
Yoshida et al. (2023) have predicted that CO can be depleted in
13
C compared with CO2 by about −170‰ in the lower
atmosphere (below 50 km) via photolysis of CO2. A similar
depletion of 13C in CO that is probably due to photolysisinduced fractionation has in fact been observed in Earth’s
mesosphere (Beale et al. 2016).
Recently, from the measurements made by Curiosity rover,
House et al. (2022) showed that ∼3.5 billion years old
sedimentary organic carbon at Gale crater on Mars is depleted
in 13C down to about −137‰ relative to the Vienna Pee Dee
Belemnite (V-PDB). The δ 13C [‰] value is deﬁned by(R/Rs – 1) × 1000, where the reference value of the V-PDB for
the 13C/12C ratio (Rs) is 1.123 × 10−2. One possible explanation for this is that it is due to the photochemical production
and deposition of organic materials via CO fractionatedthrough the photolysis of CO2, which suggests that the earlyMartian organics were originated from CO in the early Mars
atmosphere (Lammer et al. 2020). Thus, knowledge of the
carbon isotopic ratio in CO is essential for understanding theorigin of the organic compounds on Mars.
However, there are no accurate measurements of 13C/12C in
CO available in the literature and previous observations ofcarbon isotopic ratio in the Martian atmosphere are limited to

1. Introduction
Isotopic ratios in trace gases are sensitive to short-term
process (∼days/years), such as photochemistry, sublimationcondensation, diffusion, as well as for long-term effects(∼million/billion years), such as degassing and escaping tospace (e.g., Lammer et al. 2020). The current atmosphere ofMars is mainly composed by carbon dioxide (CO2, ∼96%).
Atmospheric CO2 can be photodissociated with ultraviolet
light, but the CO2-rich atmosphere is maintained by thereaction between CO and OH to reproduce CO2 (CO + OH →CO2 + H). Schmidt et al. (2013) showed with quantum
mechanical calculations that the UV absorption cross-section of
13
CO2 is several tenths of a percent less than that of 12CO2,
which suggests that faster photolysis of 12CO2 with respect to
13
CO2 could induce an isotopic depletion of 13C relative to 12C
in CO, δ 13C (see deﬁnition below) by about −200‰ relative toinitial CO. With calculation by a one-dimensional photochemical model considering the isotopic fractionation,
Original content from this work may be used under the termsof the Creative Commons Attribution 4.0 licence. Any further
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CO2. Webster et al. (2013) showed that the C/ C in CO2 isenriched in 13C, 46 ± 4‰ with respect to V-PDB from themeasurements with Tunable Laser Spectrometer on board theCuriosity rover operating over the Gale Crater. Recent solar
occultation measurements have not shown signiﬁcant variability of this latter ratio over locations and seasons below 50
km (Liuzzi et al. 2022). Lellouch et al. (1989) suggested the13
C/12C ratio in CO is not compatible with the terrestrial value
by telescope observations in the millimeter spectral ranges.
However, these results strongly depend on the thermal proﬁlesassumed in the radiative transfer calculation. Moreover, Clancy& Muhleman (1990) pointed out that the radiative transfer
calculation performed in Lellouch et al. (1989) are incorrect.
The ExoMars Trace Gas Orbiter (TGO) has two highspectral resolution spectrometers—Nadir and Occultation forMars Discovery (NOMAD; Vandaele et al. 2018) and Atmospheric Chemistry Suite (ACS; Korablev et al. 2018)—that
carry out solar occultation measurements, which allows us toperform sensitive measurements of trace gases on Mars.
Characterizing the isotopic ratios in trace gases is one of theirmain science goals. In fact, previous studies with TGO
measurements have revealed the isotopic ratios of carbon andoxygen in CO2 from 70 to 100 km, hydrogen and oxygen inwater vapor from surface to 50 km, and chlorine in HCl in thelower atmosphere (Alday et al. 2019, 2021a, 2021b; Vandaele
et al. 2019; Liuzzi et al. 2021; Trokhimovskiy et al. 2021;
Villanueva et al. 2021, 2022). In this study, we investigate thecarbon isotopic ratio in CO from the NOMAD data set taken
between 2022 March and April. We perform the analysis bysimultaneously ﬁtting the spectra taken at four different
diffraction orders to reduce the uncertainty in the obtained
isotopic ratio. The details of the data set and analysis aredescribed in Section 2, and the observational results are shownand discussed in Section 3.
13

12synthetic spectra computed by a radiative transfer model toretrieve abundances of trace gases and aerosols along the lineof sight (see below for further details). To properly model the
spectra measured by the NOMAD SO channel, a goodknowledge of the instrumental line shape (ILS) function and
the AOTF transfer function is required. These instrumental
functions have been accurately characterized by in-ﬂight
calibration measurements (see Villanueva et al. 2022 fordetails) and implemented in the radiative transfer calculations.
Figure 1 shows the synthetic spectra for the NOMAD SO
observations with diffraction orders 186 (4180–4213 cm−1),
185 (4157–4190 cm−1), 184 (4134–4167 cm−1), and 183(4112–4145 cm−1), which demonstrates that 12C16O, 13C16O,
and 12C18O lines should be clearly visible in these spectral
ranges. The intensities of these lines as seen in the NOMAD
spectra are comparable, so that similar weighting functions
along the line of sight are ensured. However, there are somechallenges when working on the spectra taken in these
diffraction orders. The ﬁrst challenge is the fact that many
weak features due to CO lines coming from adjacent diffraction
orders appear in the spectra (see the NOMAD synthetic spectrathat separately illustrate the contributions of the main andadjacent orders, shown in Figure A1), due to the nature of the
AOTF transfer function (Villanueva et al. 2022). The second
challenge is that the intensities of the 12C16O lines are highly
sensitive to temperature. The lower-state energy of thetransition E″ parameter for the main 12C16O lines is greaterthan 1000 cm−1 (see the E″ parameters of CO lines in
diffraction orders 183–186, shown in Figure A2). Thus, a goodknowledge of the AOTF transfer function and the temperature
at the time and place of the observation is required. Villanueva
et al. (2022) performed an in-depth investigation of the AOTF
transfer function based on the in-ﬂight calibration measurements of the Sun, which allows us to improve the quality of themolecular retrievals. We constrain the temperature by retrieving it from simultaneous measurement of the CO2 band in
diffraction order 132 (2966–2990 cm−1). The errors in the
retrieved isotopic ratio due to the uncertainties in the AOTF
transfer function and temperature used in the radiative transfer
calculation are also evaluated.
The observations with the diffraction orders 185, 184, and183 have been added to the nominal operation of the NOMAD
SO channel in 2022 March. In this study, we analyzed eight
orbits taken between 2022 March and April, which simultaneously measure orders 183, 184, 185, 186, and 132. Table 1
shows the geometry information of these orbits. The measurements are performed in the northern fall season (Ls = 182°–205°) over the middle and high latitudes, except for the lastorbit measured on 2022 April 8 that was acquired over theequatorial region.
The retrieval of both temperature and CO abundances isconducted by Atmospheric Spectra Inversion Modular Utility
Tools (ASIMUT)—Asimut Lidort VLidort (ALVL) radiativetransfer and inversion code (Vandaele et al. 2006). The
temperature proﬁles are derived from CO2 density proﬁles
using the hydrostatic equilibrium equation. The CO2 density
proﬁles are retrieved from the measurements at diffraction
orders 132 (2966–2990 cm−1), which is suitable to scan the
troposphere (0–50 km). The method is described in detail in
Trompet et al. (2022a). The baseline level of the spectra is
gradually decreased toward the lower altitude, due to a highdensity of aerosols along the line of sight. In this study, no

2. Data Set and Analysis
NOMAD is a spectrometer on board ExoMars TGO that has
three spectral channels: a Solar Occultation (SO) channel
operating at 2.3–4.3 μm, a Limb Nadir and solar Occultation(LNO) channel at 2.3–3.8 μm, and an Ultraviolet and Visible
Spectrometer (UVIS) channel at 200–650 nm (Vandaele et al.
2018). In this study, the solar occultation measurements takenby the SO channel are analyzed. One of the advantages of the
NOMAD SO channel when compared to the near-infrared
spectrometers on board previous missions is its relatively highspectral resolution (λ/dλ ∼ 17,000 for the SO channel), whichis achieved by an echelle grating. The selection of the grating
diffraction orders is performed by the Acousto Optical Tunable
Filter (AOTF). Because the order selection by the AOTF is
instantaneous, the SO channel can measure ﬁve or six different
diffraction orders in ∼1 s, which provides a vertical sampling
step of less than ∼1 km. Another advantage of NOMAD is its
high signal-to-noise ratio (greater than 1000) thanks to the solar
occultation technique, which allows us to perform sensitive
searches of absorption features from the trace gases andmeasurements of their isotopic ratios.
The spectra measured through the Mars atmosphere are
divided by the reference solar spectrum to obtain transmittances. This division removes systematic instrumental effects.
The reference solar spectrum is created by extrapolation of
those recorded above the atmosphere (see Trompet et al. 2022afor details). The calculated transmittances are compared with2

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Figure 1. Synthetic spectra of the NOMAD measurements taken with diffraction order 183 (a), order 184 (b), order 185 (c), and order 186 (b) around 30 km tangent
height. The assumed vertical proﬁle of total CO volume mixing ratio is 1000 ppm (uniform) and along the line of sight. The isotopic ratios deﬁned in the
HITRAN2020 databases are assumed. The red, blue, and green curves illustrate contributions due to 12C16O, 13C16O, and 12C18O absorption lines. The origin of the Yaxis for the red, blue, and green curves have been offset to improve visibility.

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Figure 2. Examples of the NOMAD spectra measured by diffraction order 132 around 30 km tangent height (black) and the best-ﬁt synthetic spectra (red). The bottom
small panels show the differences between the observed spectra and the best-ﬁt synthetic spectra in red curves and the instrumental noise level in black.
Table 1
List of the TGO/NOMAD Orbits and Their Geometry Information Analyzed in This Study
Filename

LatitudeLongitude

Local Time

Ls

20220301_114833_1p0a_SO_A_I
20220304_063802_1p0a_SO_A_I
20220307_001142_1p0a_SO_A_E
20220307_234718_1p0a_SO_A_E
20220311_172904_1p0a_SO_A_I
20220331_214359_1p0a_SO_A_E
20220407_050322_1p0a_SO_A_E
20220408_175248_1p0a_SO_A_I

−79.4
−84.1
57.3
59.6
−83.8
80.8
79.6
1.46

61.2
154.1
−60.2
−43.8
−62.9
−73.1
−99.3
164.3

5.6
4.8
6.3
6.3
20.4
11.0
12.5
18.0

182.790184.375
185.936186.500
188.654200.493204.266
205.191

Note. Latitude, longitude, and local time given in this table are those at the tangent point of the line of sight.

retrieval is attempted when the baseline level is lower than 0.5 intransmittance. Therefore, this lower limit varies following seasonsand latitudes. Some examples of ﬁt for diffraction order 132 areprovided in Figure 2. The vertical resolution on the temperature
proﬁles is on average around 1.6 km and the uncertainty is about
5 K, which is the total error including the regularization error andthe retrieval noise error (Trompet et al. 2022a). A comparison

between the NOMAD temperature retrievals and those by theMars Climate Sounder (MCS) on board the Mars Reconnaissance
Orbiter shows that the difference is within 5 K (see Figure 2 of
Trompet et al. 2022b). Even though the number of the orbits forthe comparison is not so large (only 47 proﬁles), it suggests that if
there is a systematic bias in the temperature retrievals, whichshould be less than 5 K. The upper boundary of the temperature
4

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Figure 3. Example of spectra measured by TGO/NOMAD (black curves) in diffraction order 183 (a), order 184 (b), order 185 (c), and order 186 (d). These spectra aremeasured around 30 km tangential height on 2022 March 1st (the ﬁrst orbit shown in Table 1). The red curves show the best-ﬁt synthetic spectra. The continuum
transmittance is around 0.97, due to the extinction by the aerosols presented along the line of sight. The top small panels show the line intensities of 12C16O (red withcircular symbols), 13C16O (blue with triangle symbols), and 12C18O (green with square symbols) in the main diffraction order obtained from HITRAN2020 database.
The small bottom panels illustrate the residuals of the top panel in red and the instrumental noise level in black. The residuals are usually within the instrumental noiselevel, except for some features that come from nearby diffraction orders (these features are present due to the nature of the AOTF transfer function).

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Figure 3. (Continued.)

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Figure 4. Vertical proﬁle of the temperature proﬁles (a), volume mixing ratio of 12C16O (red with circular symbols), 13C16O (blue with square symbols), 12C18O(green with triangle symbols) (b), and δ values calculated with 13C16O/12C16O ratios (blue with square symbols) and 13C16O/12C18O ratios (green with triangle
symbols) (c). These proﬁles are retrieved from the orbit taken on 2022 March 11 (the ﬁfth orbit shown in Table 1). The results from the other orbits are shown in
Figure B1. In the panel (a), the red-solid curve, black-dotted curve, and the blue-dashed curves represent temperature proﬁles retrieved from order 132, predicted by
GEM-Mars model, and combined with retrieval and GEM-Mars model, respectively. The x-axis of the panel (b) is the total CO volume mixing ratio retrieved from
12 16
C O, 13C16O, or 12C18O lines by assuming the terrestrial isotopic ratio. In other words, the retrieved volume mixing ratios of 12C16O, 13C16O, or 12C18O are
multiplied by the terrestrial isotopic ratios (9.86544 × 10−1, 1.10836 × 10−2, and 1.97822 × 10−3, respectively). The red, blue, and green curves would beoverlapped if δ value is 0‰.

Figure 5. Vertical proﬁles (a) and histogram (b) of δ 13C values in CO obtained with 12C16O and 13C16O volume mixing ratio retrieved with original AOTF transfer
function and temperature proﬁles.

proﬁles (ztop) is controlled by the disappearance of the CO2 lines,
while the lower boundary (zbot) is controlled by the reduction of
the baseline due to the aerosols or the saturation of the CO2 lines(see Supp. information of Trompet et al. 2022a). Most of theinformation in the retrieved CO abundances come from the few
km above the tangent altitude (about 70% of the slant number
density integrated over the LOS is within 4 km from the tangent
height), thus the temperature proﬁles obtained from order 132

cover the essential altitude range. For the calculation with theradiative transfer model, since it needs a full vertical proﬁle oftemperature, we build a full proﬁle x̂ from the ground to around
120 km with the retrieved proﬁle x and a GEM-Mars proﬁle xa
simulated for the time and location of the occultation with theformula:xˆ = xa + A (x - xa)

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Figure 6. Vertical proﬁles (a) and histogram (b) of δ 13C values in CO obtained with 12C16O and 13C16O volume mixing ratio retrieved with original temperature
proﬁles and AOTF transfer function shifted by its uncertainty in the positive direction.

Figure 7. Vertical proﬁles (a) and histogram (b) of δ 13C values in CO obtained with 12C16O and 13C16O volume mixing ratio retrieved with original temperature
proﬁles and AOTF transfer function shifted by its uncertainty in the negative direction.

where A is a matrix built as:

the combination of the proﬁles. Some examples of the
combined proﬁles are provided in Figures 4 and B1.
For the retrievals of CO abundances, the same methodology
as the previous water vapor and HCl studies with the NOMAD
SO data is applied (Aoki et al. 2019, 2021, 2022). We
performed the retrievals for the measurements taken below 50
km because above this altitude the noise exceeds the depth of
the absorption features. Only CO and CO2 molecularabsorptions are considered in the radiative transfer calculation.
The absorption coefﬁcients are calculated by the line-by-line
method with the HITRAN2020 spectroscopic parameters that
correct pressure-broadening coefﬁcients for CO2 atmosphere(Gordon et al. 2022). The vertical proﬁles of pressure and CO2volume mixing ratio in the radiative transfer calculation are
obtained from the Global Environmental Multiscale Mars
(GEM-Mars) model (Daerden et al. 2019) and those of

0ij
if zi > ztop  zi < zbot⎧⎪
if zbot + 10 < zi < ztop - 10dij⎪
∣ zj - z i ∣⎪⎛ 1 - z -z ⎞boti⎪ max ⎜0,if zbot < zi < zbot + 10⎟
zi - zbot ⎟
⎜
Aij =
⎨
⎝
⎠
⎪
∣ zj - z i ∣⎛ 1 - z -z ⎞⎪topiif ztop - 10 < zi < ztop.
⎪ max ⎜0,⎟
ztop - zi ⎟
⎪
⎜
⎝
⎠
⎩

The integral of each row of A is equal to one and the triangularfunction at the bounds of the retrieved proﬁle serves to smooth8

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Figure 8. Vertical proﬁles (a) and histogram (b) of δ 13C values in CO obtained with 12C16O and 13C16O volume mixing ratio retrieved with original AOTF transfer
function and temperature proﬁles shifted by +5 K.

Figure 9. Vertical proﬁles (a) and histogram (b) of δ 13C values in CO obtained with 12C16O and 13C16O volume mixing ratio retrieved with original AOTF transfer
function and temperature proﬁles shifted by −5 K.

uncertainty of the obtained CO abundances due to the
instrumental random photon noise.
To reduce the uncertainty in the obtained isotopic ratio, we
perform the retrievals simultaneously with the spectra recordedin the four different diffraction orders: order 186 (4180–4213cm−1), order 185 (4157–4190 cm−1), order 184 (4134–4167
cm−1), and order 183 (4112–4145 cm−1). Figure 3 shows
examples of the data analysis for these four spectral ranges. The
agreements between the best-ﬁt synthetic spectra and themeasured spectra are generally good and within the instrumental random photon noise, except for a few features that are
attributed to contamination from adjacent orders.
The major sources of errors in the retrieved isotopic ratio are(1) the instrumental random photon noise, (2) uncertainty in thetemperature proﬁle assumed in the radiative transfer

temperature are obtained from the CO2 retrievals using order132. The vertical coordinate is deﬁned by height above theMars geoid (Lemoine et al. 2001). The ﬁeld of view measured
by the NOMAD SO channel is recorded on 16 detector rows,
which are split into four discrete “bins” of four rows each.
Therefore, four spectra are acquired simultaneously andreturned individually. The retrievals are processed for eachbin and every single spectrum taken at a tangential altitude byassuming a constant volume mixing ratio along the line of sight(in other words, the 12C16O, 13C16O, and 12C18O column
densities along the line of sight are retrieved). The retrieved COabundances are ﬁnally averaged on a common vertical gridwith an interval of 1 km to reduce the uncertainties fromrandom variations. The standard deviation of the retrieved COabundances within 1 km altitudes provides a realistic relative9

Type of the NOMAD Retrievals
13 16

12 16

10

C O/ C O ratios with original AOTF andtemperature
13 16
C O/12C16O ratios with AOTF function shifted
positive Direction
13 16
C O/12C16O ratios with AOTF function shifted
negative direction
13 16
C O/12C16O ratios with temperature shifted by +5 K
13 16
C O/12C16O ratios with temperature shifted by −5 K
13 16
C O/12C18O ratios with AOTF and temperature
13 16
C O/12C18O ratios with AOTF function shifted
positive direction
13 16
C O/12C18O ratios with AOTF function shifted
negative direction
13 16
C O/12C18O ratios with temperature shifted by +5 K
13 16
C O/12C18O ratios with temperature shifted by −5 K

Mean δ Values

Standard Deviation of
the MeanStandard Error of
the Mean

−263‰

132‰

4‰

−279‰

131‰

4‰

−238‰

134‰

3‰

−139‰
−375‰
−82‰
−69‰

145‰
119‰
60‰
70‰

4‰
3‰
5‰
5‰

−98‰

55‰

4‰

−88‰
−77‰

58‰
64‰

4‰
5‰

Photochemical Model (Yoshida et al. 2023)
From −165 to −117‰ (with vertical transport) and from −225 to −178‰(without vertical transport)

The Planetary Science Journal, 4:97 (20pp), 2023 May

Table 2
List of the CO Isotopic Ratios Obtained by the Analysis of the TGO/NOMAD Presented in This Paper and Calculated by the One-dimensional Photochemical Model Reported in Yoshida et al. (2023)

L

Aoki et al.

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Figure 10. Vertical proﬁles (a) and histogram (b) of δ values in CO obtained with 12C18O and 13C16O volume mixing ratio retrieved with original AOTF transfer
function and temperature proﬁles.

Figure 11. Vertical proﬁles (a) and histogram (b) of δ value in CO obtained with 18C16O and 13C16O volume mixing ratio retrieved with original temperature proﬁlesand AOTF transfer function shifted by its uncertainty in the positive direction.

calculations, and (3) uncertainty in the AOTF transfer function.
The error in the retrieved CO abundances due to instrumental
photon noise can be evaluated from the standard deviation
when the retrieved CO abundances from each spectrum areaveraged within 1 km (there are 3–12 spectra for each 1 km
interval). Based on the retrievals, the CO isotopic ratios(12C16O/13C16O, 12C18O/13C16O) are calculated for every 1
km for each orbit. The ﬁnal results are provided by theirweighted mean. The random error in the ﬁnal isotopic ratios
due to the instrumental random photon noise and temperature
uncertainty can be obtained by the standard deviation andstandard error of the mean. Meanwhile, the systematic error in
the ﬁnal isotopic ratios of CO is difﬁcult to estimate.
Uncertainty in the AOTF transfer function and a possible

systematic error in the temperature retrievals are candidates forthe sources of the systematic error in the isotopic ratios in CO.
To estimate the magnitude of these systematic errors, we
perform the retrievals with temperature proﬁles and the AOTF
transfer functions shifted by their uncertainty. Possible
systematic error in the temperature retrievals is within 5 K,
as described above, and thus we perform the retrievals withtemperature proﬁles shifted by ±5 K. The uncertainty of the
AOTF transfer function can be estimated from the standard
deviation when four parameters to characterize the AOTF
transfer function are determined by ﬁtting with second ordersof polynomial function (Figure FA1 in Villanueva et al. 2022,
see also the the AOTF transfer function for order 185 of the
NOMAD SO channel shown in Figure A3 in Appendix A).
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Figure 12. Vertical proﬁles (a) and histogram (b) of δ value in CO obtained with 18C16O and 13C16O volume mixing ratio retrieved with original temperature proﬁlesand AOTF transfer function shifted by its uncertainty in the negative direction.

Figure 13. Vertical proﬁles (a) and histogram (b) of δ values in CO obtained with 12C18O and 13C16O volume mixing ratio retrieved with original AOTF transfer
function and temperature proﬁles shifted by +5 K.

Standard deviation and standard error of the mean are 132‰
and 4‰, respectively, which represent the uncertainty in theobtained δ 13C value due to instrumental photon noise andrandom error in the retrieved temperature (note that thestandard error of the mean, which is derived by the division
between standard deviation and the square root of the numberof samples, reﬂects the uncertainty in the mean value). Apartfrom these random error sources, the uncertainty in the AOTF
transfer function and possible systematic error in the retrieved
temperature proﬁles are candidates of the systematic errors in
the retrieved δ 13C value. To estimate the magnitude of thesesystematic errors, the same retrievals are performed with either
the temperature proﬁles shifted by ±5 K or the AOTF transfer
functions shifted by their uncertainties. Figures 6 and 7 show
the vertical proﬁles and histograms of the δ 13C values retrieved

3. Results and Discussion
Figure 4 shows an example of the retrieved vertical proﬁlesof temperature, 12C16O, 13C16O, and 12C18O volume mixing
ratio, and the isotopic ratios. CO retrievals are only performed
for those altitudes where temperature retrievals from order 132
are available. The lower limits of the vertical proﬁles of 12C16O
and 13C16O are deﬁned as 30 km and 20 km, respectively,
unless the lower limit of the temperature retrievals is above
these altitudes, because the optical depth along the line of sightfor the lines reaches very high values below these altitudes.
Figure 5 shows the calculated δ 13C values based on the
retrieved 12C16O and 13C16O volume mixing ratio at each
altitude. Figure 5(a) presents the vertical proﬁles of theobtained δ 13C values and Figure 5(b) shows their histogram.
The weighted mean value of the δ 13C values is −263‰.
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The Planetary Science Journal, 4:97 (20pp), 2023 May

Aoki et al.

Figure 14. Vertical proﬁles (a) and histogram (b) of δ values in CO obtained with 12C18O and 13C16O volume mixing ratio retrieved with original AOTF transfer
function and temperature proﬁles shifted by −5 K.

AOTF transfer function shifted by their uncertainty (Figures 11
and 12) and the temperature proﬁle shifted by ±5 K
(Figures 13 and 14). Table 2 also summarizes the obtained δvalues with the original and shifted temperature proﬁles or
AOTF transfer functions. The weighted mean of the obtained δvalues can be changed by ∼15‰ due to systematic uncertainty
in the AOTF transfer function and by ∼5‰ due to a possible
systematic error in the retrieval temperature proﬁles. Thisshows that the δ values obtained with 13C16O/12C18O are muchless sensitive to temperature when compared to the δ C13 values
obtained with 13C16O/12C16O. However, by deﬁnition, the δvalues that obtained here are affected by both carbon andoxygen fractionation, and the oxygen isotopic composition of
CO in the Martian atmosphere is uncertain. Schmidt et al.
(2013) suggested that the photolysis of CO2 may theoreticallyinduce the depletion of oxygen in CO compared to CO2, up to
about −150‰. Meanwhile, oxides such as O3 and CO2 in the
Earth’s atmosphere are known to be mass independently
enriched in 17O and 18O by ∼10‰ through several fractionation processes, such as formation reactions of ozone (e.g.,Thiemens 1999). Among the fractionation processes, thephotolysis of CO2 is expected to affect the oxygen isotopic
composition of CO dominantly because it is the major sourceof CO in the Martian atmosphere. Here, assuming that theoxygen isotopic composition of CO is mainly determinedthrough the photolysis of CO2, both δ 18O and δ 13C–δ 18O in
CO are negative, as shown by Schmidt et al. (2013), leading to
the negative value of δ about −100‰. This is consistent withthe measured negative δ value by NOMAD, indicating thedepletion of not only 18O but also 13C in CO, as found from theanalysis of 13C16O/12C16O.
The calculation by one-dimensional photochemical model by
Yoshida et al. (2023) predicted that the δ 13C can be between−165‰ and −117‰ with vertical transport and between−225‰ and −178‰ without vertical transport at 30–50 km
due to the fractionation induced by the photolysis of CO2.

with the AOTF transfer function shifted by their uncertainty,
and Figures 8 and 9 present those retrieved with thetemperature proﬁles shifted by ±5 K. Table 2 summarizes
these obtained δ 13C values with original and shifted
temperature proﬁles and AOTF transfer functions. The
weighted mean values of the δ 13C values can be changed by∼20‰ due to systematic uncertainty in the AOTF transfer
function, and by ∼120‰ due to a possible systematic error in
the retrieval temperature proﬁles. Despite the relatively large
uncertainties due to temperature, the result suggests a depletionof 13C in CO.
The temperature assumed in the radiative transfer calculation
has a large impact on the obtained δ 13C. This is primary due tothe fact that the 12C16O lines are quite sensitive to temperature.
We also examine the 13C16O/12C18O ratio to obtain further
information because these lines are less sensitive to temperature. Figure 10 shows the vertical proﬁles and histogram of δvalues in CO between 20 and 50 km based on the retrieved
volume mixing ratio of 13C16O and 12C18O. The δ values thatare shown here calculated by the same equation for δ 13C
except that 12C18O is used instead of 12C16O:(13C16O 12 C18O)
d = ⎡ 13 16 12 18 Mars - 1⎤ ´ 1000‰⎢⎥⎣ ( C O C O)Earth⎦
13C ´ 10-3 + 1
d= ⎛ 18- 1⎞ ´ 1000‰,-3 + 1
O
10
d
´
⎝
⎠
⎜

⎟

(1 )

where (13C16O/12C18O)Mars is the retrieved isotopic ratio, and(13C16O/12C18O)Earth is the ratio between isotopic ratios of theterrestrial atmosphere deﬁned in HITRAN2020 database((13C16O/12C18O)Earth = 5.5899 (Gordon et al. 2022). Notethat HITRAN2020 uses V-PDB for carbon and Vienna
Standard Mean Ocean Water (V-SMOW) for oxygen as thereferences). The weighted mean of the obtained δ values is−82‰, and the standard deviation and standard error of themean are 60‰ and 5‰, respectively. Figures 11–14 show thevertical proﬁles and histogram of the δ values retrieved with the13The Planetary Science Journal, 4:97 (20pp), 2023 May

Aoki et al.

Despite its relatively large uncertainty, our analysis with the
TGO/NOMAD measurements suggests that such a depletionof 13C in CO may actually be present. As shown in Table 2, themeasurements and models agree within the error values andobserved depletion of 13C in CO is consistent with the CO2
photolysis-induced fractionation.
CO2 in the current Mars atmosphere is slightly enriched in
13
C as measured by the Curiosity rover (δ13C = 46 ± 4;
Webster et al. 2013). Analysis of the carbonates in the Allan
Hills (ALH) 84001 Martian meteorite, which formed ∼4 Ga
before present, suggests that the δ 13C value ∼4 Ga before
present was already slightly enriched in 13C, estimated to be+30 ± 10‰ (e.g., Niles et al. 2005; Halevy et al. 2011;
Shaheen et al. 2015). Compared to these values, the recent
discovery of 13C depletion in sedimentary organic carbon atGale crater (up to about −137‰; House et al. 2022) is quite
signiﬁcant. The results of the analysis with TGO/NOMAD
data presented in this study suggest that such a 13C depletion in
CO may be induced by photolysis of CO2. This is consistent
with the hypothesis that strong 13C depletion in sedimentaryorganic carbon, which is difﬁcult to explain only by currently
known biological fractionation processes such as methanotrophy (House et al. 2022), is originated by the depletion of 13C in
CO. This implies that CO might be more abundant in the earlyMars atmosphere and organics might be originated from CO
via formaldehyde by photochemical reaction (Lammer et al.
2020).

This work is supported by JSPS KAKENHI grant Nos.
22H05151, 22K03709, 22H00164, 19H00707. The NOMAD
experiment is led by the Royal Belgian Institute for Space
Aeronomy (IASB-BIRA), assisted by Co-PI teams from Spain(IAA-CSIC), Italy (INAF-IAPS), and the United Kingdom(Open University). This project acknowledges funding by the
Belgian Science Policy Ofﬁce (BELSPO), with the ﬁnancial
and contractual coordination by the ESA Prodex Ofﬁce (PEA
4000103401, 4000121493), by Spanish Ministry of Scienceand Innovation (MCIU) and by European funds under grants
PGC2018-101836-B-I00 and ESP2017-87143-R (MINECO/
FEDER), as well as by UK Space Agency through grants ST/
V005332/1, ST/V002295/1, ST/W00268X/1, and ST/
R001405/1 and Italian Space Agency through grant 2018-2HH.0. This work is supported by the Belgian Fonds de laRecherche Scientiﬁque—FNRS under grant No. 30442502(ET_HOME) and has received funing from the European
Union's Horizon 2020 research and innovation program (grant
agreement No. 101004052, RoadMap project). The IAA/CSIC
team acknowledges ﬁnancial support from the State Agency for
Research of the Spanish MCIU through the ‘Center of
Excellence Severo Ochoa’ award for the Instituto de Astrofísica
de Andalucía (SEV-2017-0709). US investigators were supported by the National Aeronautics and Space Administration.
Canadian investigators were supported by the Canadian Space
Agency. S.R. thanks BELSPO for the FED-tWIN funding (Prf2019-077 - RT MOLEXO).

4. Conclusion

Appendix A
Challenges for the Analysis of the NOMAD Spectra Taken
in Orders 183–186

We have analyzed eight orbits of the solar occultation
measurements taken by ExoMars-TGO/NOMAD to investigate 13C/12C in CO in the atmosphere of Mars. The analysis isperformed with the spectra taken with four diffraction orders.
The mean δ 13C value obtained from the retrieved 13C16O and12 16
C O volume mixing ratios is −263‰, and the standard
deviation and standard error of the mean are 132‰ and 4‰,
respectively. This value can be changed by ∼20‰ due touncertainty in the AOTF transfer function and by ∼120‰ due
to possible systematic error in the retrieved temperature
proﬁles. This large uncertainty in the obtained 13C16O/12C16O
ratio is mainly due to the strong temperature dependence in the
12 16
C O lines. Less temperature-dependent lines of 12C18O areused instead of 12C16O. The mean δ value obtained with theretrieved 13C16O and 12C18O volume mixing ratios is −82‰,
and the standard deviation and standard error of the mean are
59‰ and 4‰, respectively. This value can be changed by∼15‰ due to uncertainty in the AOTF transfer function and by∼5‰ due to possible systematic error in the retrieved
temperature proﬁles. With the assumption that 18O in CO isdepleted by about −150‰, the δ 13C value obtained by
13 16
C O/12C16O is consistent with the δ value obtained by
3 16
C O/12C18O.
Despite the fact that the uncertainties are relatively large, ourresults suggest a depletion of 13C in CO. This is consistent withthe results predicted by a one-dimensional photochemical
model (Yoshida et al. 2023), which shows that a fractionationin 13C/12C occurs in the photolysis of CO2. This result might
support the hypothesis that the atmosphere of early Mars was
CO-rich and the recently discovered depleted 13C in the organiccarbon at Gale crater (House et al. 2022) is due to fractionation
during the photolysis of CO2 (Lammer et al. 2020).

As described in the main body of the text, there are somechallenges to work on the NOMAD spectra taken in diffraction
orders 183–186. The ﬁrst challenge is the contamination of thefeatures from adjacent diffraction orders due to the nature of the
AOTF transfer function. Figure A1 separately visualizes thecontributions from the adjacent orders. As shown in theseﬁgures, many features from adjacent orders appear in measuredorders 183–186 spectra. The second challenge is the strong
temperature dependence of the 12C16O lines in the spectral
ranges of orders 183–186. Figure A2 shows the E″ parametersof 12C16O, 13C16O, and 12C18O lines at diffraction orders
183–186 obtained from HITRAN2020 database. As shown inthese ﬁgures, the values for 12C16O lines are particularly highin order 183–185. To estimate the errors in the retrieved CO
isotopic ratio due to these uncertainties, the retrievals withtemperature proﬁles or the AOTF transfer function shifted bythese uncertainties are performed. The black curve in Figure A3
shows the AOTF transfer function for order 185 calculated by
the parameters presented in Villanueva et al. (2022). The
AOTF transfer function of the NOMAD SO channel ismodeled by the combination of a sinc squared function and a
Gaussian function. There are four parameters to characterizethese functions (i.e., width of the sinc function, side-lobe factor
for the sinc function, asymmetry factor for the sinc function,and the intensity of the Gaussian function, see Villanueva et al.
2022 for details). The most sensitive parameter to the retrieved
abundances of trace gases is the last parameter, i.e., theintensity of the Gaussian function, because it changes
proportionally to the depth of the absorption features. Thus,
we evaluate the uncertainty of this parameter and create the
AOTF transfer function shifted by the uncertainty to perform
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The Planetary Science Journal, 4:97 (20pp), 2023 May

Aoki et al.

Figure A1. The contribution of the main and adjacent orders appeared in the NOMAD spectra for order 183 (a), order 184 (b), order 185 (c), and order 186 (d). The
synthetic spectra are calculated for the measurements around 30 km tangent height. The differences in color and line type represent the contribution of the different
diffraction order (the main order contribution is shown as the bold lines in red, and the adjacent orders are shown in the other colors).

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The Planetary Science Journal, 4:97 (20pp), 2023 May

Aoki et al.

Figure A2. Lower-state energy of the transition (the E″ parameters) of 12C16O (red with circular symbols), 13C16O (blue with triangle symbols), and 12C18O (green
with square symbols) lines in diffraction order 183 (a), order 184 (b), order 185 (c), and 186 (d) obtained from HITRAN2020 database.

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The Planetary Science Journal, 4:97 (20pp), 2023 May

Aoki et al.

Figure A3. The AOTF transfer function for the order 185 of the NOMAD SO channel (the black curve). The orange and light blue curves show those shifted by onesigma uncertainty in the Gaussian intensity parameter in the AOTF transfer function.

the retrievals. The evaluation of the uncertainty is performed by
calculating the standard deviation in the ﬁtting by second
orders of the polynomial function to determine this parameter(see Figure FA1 in Villanueva et al. 2022). The red and blue
curves in Figure A3 are the AOTF transfer function shifted bytheir uncertainty.

Appendix B
Vertical Proﬁles of Temperature Proﬁle, CO Volume
Mixing Ratios, and the Isotopic Ratios
In this appendix, vertical proﬁles of the temperature, volume
mixing ratio of CO isotopes, and δ values are shown as
Figure B1.

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The Planetary Science Journal, 4:97 (20pp), 2023 May

Aoki et al.

Figure B1. Same as Figure 4, but for the rest of the orbits.

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The Planetary Science Journal, 4:97 (20pp), 2023 May

Aoki et al.

Figure B1. (Continued.)

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The Planetary Science Journal, 4:97 (20pp), 2023 May

Aoki et al.

Figure B1. (Continued.)

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S. Aoki https://orcid.org/0000-0001-6727-125X
N. Yoshida https://orcid.org/0000-0001-5214-5680
L. Trompet https://orcid.org/0000-0001-6259-2054
T. Yoshida https://orcid.org/0000-0001-5214-5680
N. Terada https://orcid.org/0000-0001-5685-9736
H. Nakagawa https://orcid.org/0000-0001-8166-0171
G. Liuzzi https://orcid.org/0000-0003-3638-5750
A. C. Vandaele https://orcid.org/0000-0001-8940-9301
I. R. Thomas https://orcid.org/0000-0003-3887-6668
G. L. Villanueva https://orcid.org/0000-0002-2662-5776
M. A. Lopez-Valverde https://orcid.org/0000-00027989-4267
A. Brines https://orcid.org/0000-0002-7044-3638
M. R. Patel https://orcid.org/0000-0002-8223-3566
S. Faggi https://orcid.org/0000-0003-0194-5615
F. Daerden https://orcid.org/0000-0001-7433-1839
J. T. Erwin https://orcid.org/0000-0003-0200-3195
B. Ristic https://orcid.org/0000-0002-9635-1125
G. Bellucci https://orcid.org/0000-0003-0867-8679
J. J. Lopez-Moreno https://orcid.org/0000-0002-7946-2624
H. Kurokawa https://orcid.org/0000-0003-1965-1586
Y. Ueno https://orcid.org/0000-0002-9095-4742
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