# Strong depletion of 13C in CO induced by photolysis of CO2 in the Martian
atmosphere calculated by a photochemical model

Tatsuya Yoshida  Department of Geophysics, Graduate School of Science, Tohoku
University, Sendai, Miyagi, Japan  Shohei Aoki  Department of Complexity
Science and Engineering, Graduate School of Frontier Sciences, University of
Tokyo, Kashiwa, Chiba, Japan  Yuichiro Ueno  Department of Earth and Planetary
Sciences, Tokyo Institute of Technology, Meguro, Tokyo, Japan  Earth-Life
Science Institute (WPI-ELSI), Tokyo Institute of Technology, Meguro, Tokyo,
Japan  Japan Agency for Marine-Earth Science and Technology (JAMSTEC),
Yokosuka, Kanagawa, Japan  Naoki Terada  Department of Geophysics, Graduate
School of Science, Tohoku University, Sendai, Miyagi, Japan  Yuki Nakamura
Department of Geophysics, Graduate School of Science, Tohoku University,
Sendai, Miyagi, Japan  Kimie Shiobara  Department of Geophysics, Graduate
School of Science, Tohoku University, Sendai, Miyagi, Japan  Nao Yoshida
Department of Geophysics, Graduate School of Science, Tohoku University,
Sendai, Miyagi, Japan  Hiromu Nakagawa  Department of Geophysics, Graduate
School of Science, Tohoku University, Sendai, Miyagi, Japan  Shotaro Sakai
Department of Geophysics, Graduate School of Science, Tohoku University,
Sendai, Miyagi, Japan  Shungo Koyama  Department of Geophysics, Graduate
School of Science, Tohoku University, Sendai, Miyagi, Japan

###### Abstract

The isotopic signature of atmospheric carbon offers a unique tracer for the
history of the Martian atmosphere and the origin of organic matter on Mars.
Photolysis of CO2 is known to induce strong isotopic fractionation of carbon
between CO2 and CO. However, its effect on the carbon isotopic compositions in
the Martian atmosphere remains uncertain. Here we develop a 1-D photochemical
model considering isotopic fractionation via photolysis of CO2 to estimate the
vertical profiles of the carbon isotopic compositions of CO and CO2 in the
Martian atmosphere. We find that CO is depleted in 13C compared with CO2 at
each altitude due to the fractionation via CO2 photolysis: the minimum value
of $\delta^{13}$C in CO is about $-170$ ‰ under the standard eddy diffusion
setting. This result supports the hypothesis that fractionated atmospheric CO
is responsible for the production of the 13C-depleted organic carbon in
Martian sediments detected by Curiosity Rover through the conversion of CO
into organic materials and their deposition on the surface. The photolysis and
transport-induced fractionation of CO we report here leads to a $\sim 15$ %
decrease in the amount of inferred atmospheric loss when combined with the
present-day fractionation of the atmosphere and previous studies of carbon
escape to space. The fractionated isotopic composition of CO in the Martian
atmosphere may be observed by ExoMars Trace Gas Orbiter (TGO) and ground-based
telescopes, and escaping ion species produced by the fractionated carbon-
bearing species may be detected by Martian Moons eXploration (MMX) in the
future.

Planetary atmospheres (1244)

##  1 Introduction

Isotopic compositions of volatiles have been used to trace the history of
planetary atmospheres. The enrichment in the heavy isotopes of the atmospheric
components such as hydrogen, carbon, nitrogen, and noble gases of Mars with
respect to Earth and primitive meteorites indicates that Mars has lost a large
portion of the atmosphere by atmospheric escape processes (e.g., Owen, 1977;
Jakosky, 1991; Jakosky et al., 1994; Pepin, 1991; 1994; Hu et al., 2015;
Kurokawa et al., 2018).

The isotopic signature of carbon-bearing species offers a unique tracer for
the atmospheric evolution of Mars since CO2 is the major constituent of the
Martian atmosphere (Hu et al., 2015). Hu et al. (2015) modeled the isotopic
fractionation of carbon induced by atmospheric escape processes such as
photochemical escape and solar-wind-induced sputtering, deposition of
carbonate minerals, and volcanic outgassing to trace the evolution of the
carbon reservoir and its isotopic composition to satisfy the present-day
carbon isotopic ratio of CO2 in the atmosphere observed by the Curiosity
Rover. In their calculation, atmospheric escape, especially photochemical
escape via CO photodissociation, enriches heavy carbon (13C) in the atmosphere
efficiently, which can drive the carbon isotopic ratio to the present-day
fractionated value.

In addition to the isotopic fractionation processes considered by Hu et al.
(2015), photolysis of CO2 is expected to affect the isotopic compositions of
carbon-bearing species significantly. Schmidt et al. (2013) demonstrated that
the UV absorption cross-section of 13CO2 is several hundred per mil lower than
that of 12CO2 in the wavelength range of 138-212 nm by quantum mechanical
methodology. This suggests that the photolysis of CO2 could induce isotopic
fractionation between CO2 and carbon-bearing photochemical products such as CO
in the troposphere and stratosphere by several hundred per mil. The degree of
the fractionation is much higher than those of other known isotopic
fractionation processes. For example, condensation of carbonate minerals, one
of the other fractionation processes of carbon, enriches the carbon isotopic
ratio of carbonate precipitates only by $\sim 10$ ‰ relative to the source
atmosphere (Hu et al., 2015). However, the effect of photo-induced isotopic
fractionation on the carbon isotopic composition in the Martian atmosphere has
not been investigated quantitatively.

The photo-induced carbon isotopic fractionation in CO may be related to the
carbon isotopic composition of organic carbon in Martian sediments. It was
predicted that 13C-depleted organic materials can have been deposited on the
surface if their photochemical production via CO as an intermediate proceeded
efficiently on early Mars (Lammer et al., 2020; Stueken et al., 2020). As
expected, Curiosity Rover found that $\sim 3.5$ billion years old sedimentary
organic carbon at Gale crater is depleted in 13C by more than $\sim 100$ ‰
compared with that of the atmosphere (House et al., 2022). In response to
this, Ueno et al. (2022) has suggested that atmospheric synthesis of organic
materials from CO is a plausible mechanism to explain the presence of organic
carbon in early Martian sediments and its strong 13C depletion through the
experimental and theoretical studies of photolysis of CO2. To validate this
hypothesis, quantitative estimates of the carbon isotopic composition in CO
considering chemical kinetics and transport in the atmosphere are needed.

The photo-induced carbon isotopic fractionation in CO may also affect the
degree of isotopic fractionation by atmospheric escape. Photodissociation of
CO is the most important photochemical source of escaping carbon atoms from
Mars (Fox and Bakalian, 2001; Groeller et al., 2014; Lo et al., 2021). Here,
considering vertical transport of the fractionated CO to the upper atmosphere
near the escape region should lead to a change in the fractionation factor of
photochemical escape via CO photodissociation.

In this study, we develop a 1-D atmospheric photochemical model considering
the isotopic fractionation via photolysis of CO2 in order to quantitatively
estimate the vertical profiles of the carbon isotopic compositions of CO and
CO2. It allows us to clarify the effect of the photolysis on the isotopic
compositions. This paper is organized as follows. In Section 2, we describe
the outline of our 1-D photochemical model. In Section 3, we show the
numerical results of the atmospheric profiles. In Section 4.1, we discuss the
dependence of the isotopic composition profiles on the magnitude of the eddy
diffusion coefficient. In Section 4.2, we discuss the relationship between the
fractionated atmospheric CO and 13C-depleted organic carbon in Martian
sediments. In Section 4.3, we discuss the effect of the fractionation by the
photolysis on the degree of the fractionation through atmospheric escape. In
Section 4.4, the detectability of the calculated isotopic fractionation in CO
by the existing measurements is discussed.

##  2 Model description

We use a 1-D photochemical model developed by Nakamura et al. (2022b, c) with
some modifications to the chemical processes. It solves continuity-transport
equations that govern changes in the number density profiles of each chemical
species by numerical integration over time until the profiles settle into
steady states. As for the chemical processes, 57 chemical reactions are
considered for 17 species: 12CO2, 13CO2, 12CO, 13CO, H2O, O, O(1D), H, OH, H2,
O3, O2, HO2, H2O2, HO12CO, HO13CO, and 12CO${}_{2}^{+}$ (Table A1). Here we
refer to the chemical species and reactions considered by Chaffin et al.
(2017). We newly include minor carbon-bearing isotopologues such as 13CO2,
13CO, and HO13CO and their chemical reactions. To calculate the profiles of
photolysis rates, we adopt the solar spectrum profile in the wavelength from
0.5 to 1100 nm obtained by Woods et al. (2009) and solve the radiative
transfer by considering the absorption of the solar irradiation by chemical
species. We adopt the absorption cross-section of 12CO2 and 13CO2 at 138-212
nm provided by Schmidt et al. (2013) to estimate the isotopic fractionation
through the photolysis. For the absorption cross-sections of 12CO2 and 13CO2
in other wavelengths, we refer to Huestis and Berkowitz (2011) and references
therein. For the absorption cross-sections of the other chemical species, we
mainly refer to the JPL publication (Burkholder et al., 2015) and the MPI-
Mainz-UV-VIS Spectral Atlas of Gaseous Molecules (Keller-Rudek et al., 2013;
https://www.uv-vis-spectral-atlas-mainz.org/uvvis/). The spectral bin at
138-212 nm is 0.1 nm to resolve the difference in the photolysis rate between
12CO2 and 13CO2, and that at the other wavelengths is 1 nm. We also consider
the difference in the rate coefficients of the chemical reactions between 12CO
and 13CO: the rate coefficient of the reaction of 13CO with O (R22 in Table
A1) is 1.0074 times as large as that of 12CO (R21) (Ueno et al., 2022) and the
rate coefficients of the reactions of 13CO with OH (R52 and R54) is 0.9891
times as large as those of 12CO (R51 and R53) (Feilberg et al., 2005). In
addition, the rate coefficient of the reaction of HO13CO with O2 (R56) is
assumed to be 0.9891 times as large as that of HO12CO (R55) by referring to
the difference in the rate coefficient between R51(R53) and R52(R54). We adopt
the fixed number density profile of H2O used by Koyama et al. (2021). Here the
relative humidity below 30 km is fixed at 22 % to give 9.5 precipitable
microns of water and the H2O profile above is connected to saturation water
vapor at the altitude where the temperature is minimum; then, the same mixing
ratio is assumed above higher altitudes. The number density profile of
12CO${}_{2}^{+}$ is fixed as the standard case of Chaffin et al. (2017). The
profiles of temperature, eddy diffusion coefficient, and binary diffusion
coefficient are taken from Chaffin et al. (2017).

The lower boundary is set at the planetary surface. The number densities of
12CO2 and 13CO2 at the lower boundary are fixed at $2.10\times
10^{17}\,\mathrm{cm^{-3}}$ (Chaffin et al., 2017) and $2.46\times
10^{15}\,\mathrm{cm^{-3}}$ respectively to satisfy the carbon isotopic ratio
in CO2 measured by the Sample Analysis at Mars’ Tunable Laser Spectrometer
(SAM/TLS) on the Curiosity Rover (Webster et al., 2013). The altitude of the
upper boundary is set at 200 km. As the upper boundary condition, H and H2 are
assumed to escape to space by Jeans escape, and the O escape rate is fixed at
$1.2\times 10^{8}\,\mathrm{cm^{-2}\,s^{-1}}$ as Chaffin et al. (2017).

Figure 1: Number density profiles of each chemical species.

##  3 Results

The number density profiles of each chemical species in the steady state are
shown in Fig. 1. The calculated profiles of major isotopologues are in good
agreement with Chaffin et al. (2017) except for the slight difference in the
abundances of odd hydrogen and odd oxygen caused by the difference in the
adopted absorption cross-sections and H2O profile. Fig. 2 represents the
profiles of the carbon isotopic ratios in CO and CO2. Here the carbon isotopic
ratios are expressed by the deviation of the calculated ratio with respect to
the standard ratio in units per mil:

$\delta^{13}\mathrm{C}=\left(\frac{R}{R_{s}}-1\right)\times 1000$ (1)

where $R$ is the 13C/12C ratio and $R_{s}=1.123\times 10^{-2}$ which is the
13C/12C ratio of the Vienna Pee Dee Belemnite (VPDB). As shown in Fig. 2, CO
has lower $\delta^{13}$C than CO2 at each altitude because photolysis of CO2,
which is the main formation reaction of CO, involves the isotopic
fractionation of carbon between CO2 and CO due to the difference in the
absorption cross-section between 12CO2 and 13CO2 (Shmidt et al., 2013; Fig.
3).

Below $\sim 100$ km, $\delta^{13}$C in CO decreases as the altitude decreases:
it takes the minimum value of about $-170$ ‰ near the surface. The degree of
the isotopic fractionation is much higher than those of other fractionation
processes such as condensation of carbonate minerals (Hu et al., 2015). The
reason why $\delta^{13}$C in CO decreases with decreasing altitude is that the
wavelength of the absorbed solar irradiation is longer in the lower region
(Fig. 3(a)), where the difference in the absorption cross-section between
12CO2 and 13CO2 is large (Fig. 3(b),(c)).

The carbon isotopic ratio in CO2 below $\sim 100$ km is constant at the
surface value of $46$ ‰ which is assumed to be equal to the value measured by
SAM/TLS on Curiosity Rover. On the other hand, the average $\delta^{13}$C in
the altitude range of $70-90$ km measured by the Atmospheric Chemistry Suite
(ACS) onboard TGO is $-3\pm 37$ ‰ (Alday et al., 2021b). The reason for the
difference in the evaluated carbon isotopic ratio in CO2 between our model
(SAM/TLS) and ACS remains uncertain. Alday et al. (2021b) suggested two
scenarios to reconcile both measurements by SAM/TLS and ACS as follows. One
possible scenario requires the presence of unknown isotopic fractionation
processes between the lower and upper atmospheres of Mars: ACS measures the
carbon isotopic ratio above 70 km while the Curiosity Rover measures that on
the surface. The other relies on the impact of climatological isotopic
fractionation: the ACS measurements extend over a large range of locations,
seasons, and local times, which allows averaging over hundreds of
measurements, from which the effects of climatological fractionation are
expected to be small although the measurements made by the Curiosity Rover are
always made in the same location, at roughly the same local time.

$\delta^{13}$C in both CO and CO2 decreases as the altitude increases above
$\sim 100$ km, which corresponds to the altitude of the homopause, by the
diffusive separation resulting from the difference in the molecular mass
between isotopologues. The calculated isotopic fractionation of CO2 in the
upper region above $\sim 100$ km is consistent with the profile observed by
ACS (Alday et al., 2021b).

The dotted line in Fig. 2 represents the ratio of the photolysis rate of 13CO2
to that of 12CO2, which approximates the isotopic ratio of CO when assuming
the local photochemical equilibrium without vertical transport. The difference
between the dotted line and the solid orange line shows the effect of the
vertical transport by diffusion on the profile of the CO isotopic composition:
the vertical transport dilutes the difference in the isotopic composition
among altitudes.

Figure 2: Profiles of the carbon isotopic ratios in CO and CO2. The isotopic
ratios are expressed by the deviation of the calculated ratio with respect to
the standard ratio in units per mil:
$\delta^{13}\mathrm{C}=\left(\frac{R}{R_{s}}-1\right)\times 1000$, where $R$
is the 13C/12C ratio and $R_{s}=1.123\times 10^{-2}$. The orange solid line
and red solid line represent the carbon isotopic ratio in CO and CO2,
respectively. The dotted orange line represents the ratio of the photolysis
rate of 13CO2 to that of 12CO2, which approximates the isotopic ratio of CO
when assuming the local photochemical equilibrium without vertical transport.
Figure 3: (a) Profiles of photon flux with wavelength at each altitude. (b)
Absorption cross-sections of 12CO2 and 13CO2 with wavelength. The black and
red lines represent the absorption cross-sections of 12CO2 and 13CO2,
respectively. (c) The relative difference of absorption cross-section between
12CO2 and 13CO2:
$(\sigma_{\rm{}^{13}CO_{2}}$/$\sigma_{\rm{}^{12}CO_{2}}-1)\times 1000$ where
$\sigma_{\rm{}^{12}CO_{2}}$ and $\sigma_{\rm{}^{13}CO_{2}}$ are the absorption
cross-sections of 12CO2 and 13CO2, respectively. Here it is averaged over a
Gaussian window with FWHMs of 2.5 nm as done by Schmidt et al. (2013).

##  4 Discussion

###  4.1 Effect of change in the magnitude of eddy diffusion coefficient on
atmospheric profile

The eddy diffusion coefficient in the Martian atmosphere is estimated to be
variable with season and latitude (Yoshida et al., 2022). The change in the
eddy diffusion coefficient affects the atmospheric profile including the
isotopic composition. Fig.4 compares the profiles of the carbon isotopic
ratios of CO and CO2 under the eddy diffusion coefficient 10 times as small as
the standard setting with those under the standard setting. Below $\sim
25\,\mathrm{km}$, $\delta^{13}$C in CO becomes lower under the lower eddy
diffusion coefficient due to the suppression of the dilution of the difference
in the isotopic composition among altitudes by vertical transport. In the
upper region above $\sim 75$ km, $\delta^{13}$C in both CO and CO2 becomes
lower due to the more efficient diffusive separation through the molecular
diffusion relative to the mixing by the eddy diffusion. To the contrary, under
higher eddy diffusion coefficient, the dilution of the difference in the
isotopic composition among altitudes is enhanced, and the diffusive separation
through the molecular diffusion is suppressed.

Figure 4: (a) Profiles of the eddy diffusion coefficient and the molecular
diffusion coefficient. The solid blue line represents the profile of the eddy
diffusion coefficient under the standard setting (“Standard case”), and the
dashed blue line represents that 10 times as small as the standard setting
(“Low eddy case”). The dotted orange, red, and pink lines represent the
profiles of the molecular diffusion coefficients of O, H2, and H,
respectively. (b) Profiles of the carbon isotopic ratios in CO and CO2
depending on the magnitude of the eddy diffusion coefficient. The isotopic
ratios are expressed by the deviation of the calculated ratio with respect to
the standard ratio in units per mil:
$\delta^{13}\mathrm{C}=\left(\frac{R}{R_{s}}-1\right)\times 1000$, where $R$
is the 13C/12C ratio and $R_{s}=1.123\times 10^{-2}$. The solid lines and
dashed lines show the results under the standard eddy diffusion setting and
those under the eddy diffusion coefficient 10 times as small as the standard
setting, respectively. The orange lines and red lines represent the carbon
isotopic ratios in CO and CO2, respectively. The dotted orange line is the
same as that in Fig. 2, which represents the isotopic ratio of CO on the
assumption of the local photochemical equilibrium.

###  4.2 Relationship between the fractionated atmospheric CO and 13C-depleted
organic carbon in Martian sediments

Our results that CO is depleted in 13C support the hypothesis that
photochemical production and deposition of organic materials via CO is
responsible for producing the 13C-depleted organic carbon in Martian sediments
(Lammer et al., 2020; Stueken et al., 2020; Ueno et al., 2022). The main
organic molecule produced in an early Martian CO2-dominated atmosphere should
be formaldehyde (H2CO), which can be produced as follows (e.g., Pinto et al.,
1980):

$\mathrm{H}+\mathrm{CO}+\mathrm{M}\to\mathrm{HCO}+\mathrm{M},$ (2)
$\mathrm{HCO}+\mathrm{HCO}+\mathrm{M}\to\mathrm{H_{2}CO}+\mathrm{CO}+\mathrm{M},$
(3)

where M is the third body. Considering the production processes, the
13C-depleted isotopic composition of CO is expected to be transferred to
formaldehyde. Assuming that formaldehyde has the same isotopic composition as
CO, our results can explain the existence of organic carbon with
$\delta^{13}$C lower than $-100$ ‰ detected by Curiosity Rover. On the other
hand, this study does not suppose an early Martian atmosphere condition where
organic materials could have been produced. It is our future work to estimate
the deposition rate and isotopic composition of organic molecules such as
formaldehyde on the condition of early Mars.

###  4.3 Effect of the carbon isotopic fractionation in CO on the
fractionation through photochemical escape

The carbon isotopic fractionation between the lower atmosphere and the escape
region is expected to affect the degree of the fractionation through
atmospheric escape. In this section, we estimate the effect roughly by using
the framework of Rayleigh fractionation (Rayleigh, 1895; Hunten, 1982). As for
atmospheric escape processes, we consider only photochemical escape via CO
photodissociation, which is the dominant process for the production of
escaping carbon atoms on Mars (e.g., Fox & Bakalian, 2001; Groeller et al.,
2014; Lo et al., 2021). The relationship between the isotopic ratio and the
fractionation factor is given by

$\frac{R}{R_{0}}=\left(\frac{N_{{}^{12}\mathrm{C}}}{N_{{}^{12}\mathrm{C}}^{0}}\right)^{f-1}$
(4)

where $R$ and $R_{0}$ are the 13C/12C ratio and its initial value in the whole
atmosphere, $f$ is the fractionation factor, $N_{{}^{12}\mathrm{C}}$ and
$N_{{}^{12}\mathrm{C}}^{0}$ are the total inventory of 12C and its initial
value. Here we define the net fractionation factor as follows:

$f=f_{\mathrm{s-e}}\times f_{\mathrm{esc}}$ (5)

where $f_{\mathrm{s-e}}$ is the fractionation factor between the surface and
the escape region, which is the ratio of 13C/12C in CO at the escape region to
that in CO2 at the surface, and $f_{\mathrm{esc}}$ is the fractionation factor
by the atmospheric escape. We assume that the fractionation factor by the
photochemical escape via CO photodissociation $f_{\rm esc}$ is 0.6 referring
to Hu et al. (2015) and the altitude of the escape region is 160 km where the
production of escaping atoms typically peaks (e.g., Fox and Hać, 2009; Lo et
al., 2021). The net fractionation factor $f$ under the standard eddy diffusion
setting is 0.52. It highly depends on the magnitude of the eddy diffusion
coefficient. For example, $f=0.46\,(0.54)$ under the eddy diffusion
coefficient 10 times as small (large) as the standard setting.

Fig. 5 shows the 13C/12C ratio relative to the initial value in the whole
atmosphere as a function of the fraction of gas lost to space. The carbon
fractionation when considering the isotopic fractionation between the lower
atmosphere and the escape region proceeds more efficiently than the estimates
by Hu et al. (2015). The 13C/12C ratio of the present Martian CO2 atmosphere
is higher by a factor of about 1.07 than that of mantle-degassed CO2 derived
from the magmatic component of the SNC meteorites (Hu et al., 2015). Beginning
with an atmospheric 13C/12C ratio equal to that of mantle-degassed CO2, the
effective carbon isotopic fractionation through photochemical escape can drive
the carbon isotopic ratio to the present-day fractionated value even when the
amount lost by atmospheric escape is small compared with that evaluated by Hu
et al. (2015). On the other hand, there are various isotopic fractionation
processes such as other atmospheric escape processes like solar-wind-induced
sputtering and ion pickup, volcanic outgassing, deposition of carbonate
minerals and organic matters, and so on. It is our future work to estimate the
evolution of the carbon reservoir and its isotopic composition by considering
these processes comprehensively.

Figure 5: 13C/12C ratio relative to the initial value in the whole atmosphere
as a function of the fraction of gas lost to space for each fractionation
factor on the standard eddy diffusion coefficient setting ( “Standard case”),
the eddy diffusion coefficient 10 times as small as the standard setting (“Low
eddy case”), the eddy diffusion coefficient 10 times as large as the standard
setting (“High eddy case”), and the setting of Hu et al. (2015) (“Hu et al.,
2015”), respectively. The dotted black line represents the 13C/12C ratio of
the present Martian atmosphere relative to that of mantle-degassed CO2 derived
from the magmatic component of the SNC meteorites (Hu et al., 2015).

###  4.4 Possibility of observing the fractionated carbon isotopic composition

Even though a relatively strong depletion of 13C in CO is suggested by our
calculations, the isotopic ratio between 12CO and 13CO has not been quantified
by previous observations. Strong 12CO and 13CO lines are available in the
near-infrared spectral range at 4140-4220 cm-1, which can be used to measure
the isotopic ratio. For that, a high-resolution spectroscopy is required since
the lines of 12CO and 13CO in the spectral range are quite narrow under the
condition of the Mars atmosphere. Spectrometers onboard ExoMars Trace Gas
Orbiter (TGO), Nadir and Occultation for Mars Discovery (NOMAD; Vandaele et
al., 2018) and Atmospheric Chemistry Suite (ACS; Korablev et al., 2018), are
able to perform such a spectroscopic measurements of these spectral ranges
with relatively high spectral resolution ($R\sim$16,000-50,000). These
instruments perform solar occultation measurements, which makes it possible to
achieve high SNR (¿ 1000) and investigate vertical profiles of trace gas. In
fact, these instruments have revealed the vertical profiles of D/H and
18O/17O/16O in water vapor (Villanueva et al., 2021, 2022; Alday et al.,
2021a) and 13C/12C and 18O/17O/16O in CO2 (Alday et al., 2021b) and measuring
13C/12C in CO was listed as one of the science targets (Vandaele et al.,
2018). Fig. 6(a) shows the expected spectra of NOMAD at 26 km calculated by
Asimut radiative transfer code (Vandaele et al., 2006; Aoki et al., 2019). The
SNR of the NOMAD spectrum is typically greater than 1000 for a single
spectrum, thus the synthetic spectra shown in Fig. 6(a) demonstrate that the
strong depletion of 13C in CO suggested by our calculations can be identified
by the NOMAD observations. The other potential platform to measure 13C/12C in
CO is a high spectral resolution spectrograph installed at large ground-based
telescopes (such as IRTF/iSHELL, VLT/CRIRES+, etc.). They cannot perform solar
occultation measurements, however, the spectral resolution of these
instruments is about 2-5 times better than that of NOMAD and ACS. Fig. 6(b)
shows the expected spectra of the IRTF/iSHELL calculated by PSG radiative
transfer code (Villanueva et al., 2018). The SNR of a Mars spectrum taken by
IRTF/iSHELL binning over a few pixels (which corresponds to $\sim$1.0”) is
typically greater than 100. Given the angular diameter of Mars is greater than
10” in an optimal observation period, the global average of the retrievals can
detect the suggested depletion of 13C in CO with IRTF/iSHELL. Note that the
signal from Mars is attenuated by the absorption due to the telluric
atmosphere (shown as the black dotted curve in FIg. 6(b)), however the target
CO features are not heavily overlapped with the telluric features. Moreover,
the telluric features can be removed by modeling them with radiative transfer
calculations (e.g., see Villanueva et al., 2013).

Our results suggest that the degree of the isotopic fractionation of escaping
carbon is enhanced through vertical transport of the fractionated CO to the
upper atmosphere near the escape region (Section 4.3). Recently, the fluxes of
C+ in the Martian magnetotail have been detected by the Mars Atmospheric and
Volatile EvolutioN SupraThermal And Thermal Ion Composition (MAVEN-STATIC)
(Pickett et al., 2022). On the other hand, isotopic compositions of ions have
not been detected due to the difficulty in resolving the mass difference. The
Martian Moons eXploration (MMX) mission, which is planned by the Japan
Aerospace Exploration Agency (JAXA) targeting the two Martian moons with the
scheduled launch in 2024 (Kuramoto et al., 2022), may measure the isotopic
compositions of escaping ions. It has the mass spectrum analyzer (MSA) with
unprecedented mass resolution aboard MMX enough to measure isotope ratios of
escaping ion species such as O+ and C+ (Yokota et al., 2021; Ogohara et al.,
2022; Kuramoto et al., 2022). Such measurements can constrain the
fractionation factor by atmospheric escape and the history of the Martian
atmosphere empirically. On the other hand, it should be mentioned that if
photochemical loss of carbon as a neutral is dominant then the measurements of
the isotope ratios would only constrain the fractionation of a small fraction
of escaping carbon.

Figure 6: (a) Synthetic spectra of a solar occultation measurement by
TGO/NOMAD taken with the diffraction order 186. The calculations are performed
by Asimut radiative transfer and retrieval code (Vandaele et al., 2006). The
simulation is made for the measurement at 26 km over the northern polar region
(latitude: 82°N) at Ls=165°. The atmospheric condition is obtained from the
GEM-Mars (Daerden et al., 2019). The CO volume mixing ratio at 26 km is
assumed to be 776 ppm. The difference in color represents the assumed isotopic
ratios for the 13CO lines (Blue: $\delta^{13}$C=-400 ‰, Light blue:
$\delta^{13}$C=-200 ‰, Black: $\delta^{13}$C=0 ‰, Orange: $\delta^{13}$C=+200
‰, Red: $\delta^{13}$C=400 ‰). The rest of the strong features are due to
12CO. The upper panel shows the whole spectral range of the order 186, and the
small bottom panel is for a limited spectral range which contains both 12CO
and 13CO lines. The typical signal to noise ratio of a single NOMAD spectrum
is more than 1000, which suggests that the strong depletion of 13C presented
in this study may be observed by TGO/NOMAD. (b) Synthetic spectra of a
measurement by IRTF/iSHELL taken with the diffraction order 215 in the K3
band. The calculations are performed with online version of Planetary Spectrum
Generator (Villanueva et al., 2018). In the calculation, a typical atmospheric
condition at the Mars equatorial regions (the volume mixing ratio of CO is 700
ppm) is assumed. The bottom panel shows the features due to CO2 (the black
curve), H2O (the dark yellow curve), 12C16O (the dark green curve), 13C16O
(the purple curve), and 12C18O (the light green curve). The expected telluric
transmittance at Maunakea observatory (where IRTF telescope is located) is
exhibited as the black dotted curve. The small upper panel shows the 13C16O
lines at 4151.97 cm-1 for different isotopic ratios (Blue: $\delta^{13}$C=-400
‰, Light blue: $\delta^{13}$C=-200 ‰, Black: $\delta^{13}$C=0 ‰, Orange:
$\delta^{13}$C=+200 ‰, Red: $\delta^{13}$C=400 ‰). The typical signal to noise
ratio of a Mars spectrum taken by IRTF/iSHELL over a few pixels (which
corresponds to 0.1”) spectra of Mars observations is more than 100, which
suggests that the strong depletion of 13C presented in this study may be also
observed by IRTF/iSHELL.

##  5 Conclusion

We have developed a 1-D photochemical model considering carbon isotopic
fractionation induced by photolysis of CO2 for the Martian atmosphere.
According to our results, CO is depleted in 13C compared with CO2 at each
altitude due to the fractionation effect of photolysis. Below the homopause,
$\delta^{13}$C in CO decreases as the altitude decreases: it takes about
$-170$ ‰ near the surface under the standard eddy diffusion setting. Above the
homopouse, $\delta^{13}$C in both CO and CO2 decreases as the altitude
increases by the diffusive separation resulting from the difference in the
molecular mass between isotopologues. Our results support the hypothesis that
the fractionated atmospheric CO is responsible for the production of the
13C-depleted organic carbon in Martian sediments detected by Curiosity Rover
through the conversion of CO into organic materials and their deposition on
the surface. The isotopic fractionation of CO by the photolysis and diffusive
separation between the lower atmosphere and the escape region enhances the
degree of the fractionation through photochemical escape via CO
photodissociation. The fractionation factor considering these effects becomes
lower than that evaluated by Hu et al. (2015): it changes from 0.60 to 0.52
under the standard eddy diffusion setting. The change in the fractionation
factor may lead to a decrease in the amount lost by atmospheric escape
constrained by the evolution of the atmospheric carbon isotopic composition.
The fractionated isotopic composition of CO in the Martian atmosphere may be
observed by ExoMars Trace Gas Orbiter (TGO) and ground-based telescopes, and
escaping ion species produced by the fractionated carbon-bearing species may
be detected by Martian Moons eXploration (MMX) in the future.

Table 1: Chemical reactions No. | Reaction |  |  | Reaction rate coefficienta |  | Column rateb |
---|---|---|---|---|---|---|---
|  |  |  |  | standard case | small eddy case | large eddy case
R1 | ${}^{12}\mathrm{CO}_{2}+h\nu$ | $\to$ | ${}^{12}\mathrm{CO}+\mathrm{O}$ |  | $1.3\times 10^{12}$ | $1.2\times 10^{12}$ | $1.4\times 10^{12}$
R2 |  | $\to$ | ${}^{12}\mathrm{CO}+\mathrm{O(^{1}D)}$ |  | $2.0\times 10^{11}$ | $1.7\times 10^{11}$ | $2.1\times 10^{11}$
R3 | ${}^{13}\mathrm{CO}_{2}+h\nu$ | $\to$ | ${}^{13}\mathrm{CO}+\mathrm{O}$ |  | $1.2\times 10^{10}$ | $1.1\times 10^{10}$ | $1.2\times 10^{10}$
R4 |  | $\to$ | ${}^{13}\mathrm{CO}+\mathrm{O(^{1}D)}$ |  | $2.3\times 10^{9}$ | $1.9\times 10^{9}$ | $2.4\times 10^{9}$
R5 | $\mathrm{H_{2}O}+h\nu$ | $\to$ | $\mathrm{H}+\mathrm{OH}$ |  | $8.3\times 10^{9}$ | $8.5\times 10^{9}$ | $8.7\times 10^{9}$
R6 |  | $\to$ | $\mathrm{H}_{2}+\mathrm{O(^{1}D)}$ |  | $5.7\times 10^{3}$ | $5.7\times 10^{3}$ | $5.7\times 10^{3}$
R7 | $\mathrm{O}_{3}+h\nu$ | $\to$ | $\mathrm{O}_{2}+\mathrm{O}$ |  | $7.1\times 10^{11}$ | $5.9\times 10^{11}$ | $1.3\times 10^{11}$
R8 |  | $\to$ | $\mathrm{O}_{2}+\mathrm{O(^{1}D)}$ |  | $4.1\times 10^{12}$ | $3.4\times 10^{12}$ | $7.4\times 10^{11}$
R9 | $\mathrm{O_{2}}+h\nu$ | $\to$ | $\mathrm{O}+\mathrm{O}$ |  | $1.3\times 10^{11}$ | $1.3\times 10^{11}$ | $2.8\times 10^{10}$
R10 |  | $\to$ | $\mathrm{O}+\mathrm{O(^{1}D)}$ |  | $1.6\times 10^{10}$ | $5.7\times 10^{10}$ | $2.5\times 10^{9}$
R11 | $\mathrm{H}_{2}+h\nu$ | $\to$ | $\mathrm{H}+\mathrm{H}$ |  | $6.6\times 10^{4}$ | $6.6\times 10^{4}$ | $2.2\times 10^{5}$
R12 | $\mathrm{OH}+h\nu$ | $\to$ | $\mathrm{O}+\mathrm{H}$ |  | $9.0\times 10^{5}$ | $6.0\times 10^{5}$ | $1.0\times 10^{6}$
R13 |  | $\to$ | $\mathrm{O(^{1}D)}+\mathrm{H}$ |  | $4.4\times 10^{2}$ | $8.8\times 10^{1}$ | $4.8\times 10^{3}$
R14 | $\mathrm{HO}_{2}+h\nu$ | $\to$ | $\mathrm{OH}+\mathrm{O}$ |  | $3.9\times 10^{10}$ | $3.2\times 10^{10}$ | $3.7\times 10^{10}$
R15 | $\mathrm{H_{2}O_{2}}+h\nu$ | $\to$ | $\mathrm{OH}+\mathrm{OH}$ |  | $1.7\times 10^{11}$ | $1.4\times 10^{11}$ | $1.4\times 10^{11}$
R16 |  | $\to$ | $\mathrm{HO}_{2}+\mathrm{H}$ |  | $1.7\times 10^{10}$ | $1.4\times 10^{10}$ | $1.4\times 10^{10}$
R17 |  | $\to$ | $\mathrm{H_{2}O}+\mathrm{O(^{1}D)}$ |  | $0$ | $0$ | $0$
R18 | $\mathrm{O}+\mathrm{O}+\mathrm{M}$ | $\to$ | $\mathrm{O_{2}}+\mathrm{M}$ | $5.4\times 10^{-33}(300/T)^{3.25}$ | $2.3\times 10^{11}$ | $2.7\times 10^{11}$ | $8.2\times 10^{10}$
R19 | $\mathrm{O}+\mathrm{O_{2}}+\mathrm{{}^{12}CO_{2}}$ | $\to$ | $\mathrm{O_{3}}+\mathrm{{}^{12}CO_{2}}$ | $1.5\times 10^{-33}(300/T)^{2.4}$ | $4.9\times 10^{12}$ | $4.1\times 10^{12}$ | $9.4\times 10^{11}$
R20 | $\mathrm{O}+\mathrm{O_{3}}$ | $\to$ | $\mathrm{O_{2}}+\mathrm{O_{2}}$ | $8.0\times 10^{-12}\mathrm{exp}(-2060/T)$ | $3.7\times 10^{7}$ | $4.3\times 10^{7}$ | $7.0\times 10^{6}$
R21 | $\mathrm{O}+\mathrm{{}^{12}CO}+\mathrm{M}$ | $\to$ | $\mathrm{{}^{12}CO_{2}}+\mathrm{M}$ | $2.2\times 10^{-33}\mathrm{exp}(-1780/T)$ | $1.3\times 10^{8}$ | $8.9\times 10^{7}$ | $2.2\times 10^{8}$
R22 | $\mathrm{O}+\mathrm{{}^{13}CO}+\mathrm{M}$ | $\to$ | $\mathrm{{}^{13}CO_{2}}+\mathrm{M}$ | $1.0074\times 2.2\times 10^{-33}\mathrm{exp}(-1780/T)$ | $1.2\times 10^{6}$ | $8.3\times 10^{5}$ | $2.1\times 10^{6}$
R23 | $\mathrm{O(^{1}D)}+\mathrm{O_{2}}$ | $\to$ | $\mathrm{O}+\mathrm{O_{2}}$ | $3.2\times 10^{-11}\mathrm{exp}(70/T)$ | $2.4\times 10^{9}$ | $2.8\times 10^{9}$ | $1.0\times 10^{8}$
R24 | $\mathrm{O(^{1}D)}+\mathrm{O_{3}}$ | $\to$ | $\mathrm{O_{2}}+\mathrm{O_{2}}$ | $1.2\times 10^{-10}$ | $8.4\times 10^{4}$ | $1.5\times 10^{5}$ | $2.2\times 10^{3}$
R25 | $\mathrm{O(^{1}D)}+\mathrm{O_{3}}$ | $\to$ | $\mathrm{O}+\mathrm{O}+\mathrm{O_{2}}$ | $1.2\times 10^{-10}$ | $8.4\times 10^{4}$ | $1.5\times 10^{5}$ | $2.2\times 10^{3}$
R26 | $\mathrm{O(^{1}D)}+\mathrm{H_{2}}$ | $\to$ | $\mathrm{H}+\mathrm{OH}$ | $1.2\times 10^{-10}$ | $5.8\times 10^{7}$ | $3.3\times 10^{7}$ | $2.5\times 10^{8}$
R27 | $\mathrm{O(^{1}D)}+\mathrm{{}^{12}CO_{2}}$ | $\to$ | $\mathrm{O}+\mathrm{{}^{12}CO_{2}}$ | $7.5\times 10^{-11}\mathrm{exp}(115/T)$ | $4.3\times 10^{12}$ | $3.7\times 10^{12}$ | $9.5\times 10^{11}$
R28 | $\mathrm{O(^{1}D)}+\mathrm{H_{2}O}$ | $\to$ | $\mathrm{OH}+\mathrm{OH}$ | $1.63\times 10^{-10}\mathrm{exp}(60/T)$ | $8.5\times 10^{8}$ | $5.3\times 10^{8}$ | $1.6\times 10^{8}$
R29 | $\mathrm{H_{2}}+\mathrm{O}$ | $\to$ | $\mathrm{OH}+\mathrm{H}$ | $6.34\times 10^{-12}\mathrm{exp}(-4000/T)$ | $1.5\times 10^{6}$ | $1.1\times 10^{6}$ | $3.0\times 10^{7}$
R30 | $\mathrm{OH}+\mathrm{H_{2}}$ | $\to$ | $\mathrm{H_{2}O}+\mathrm{H}$ | $9.01\times 10^{-13}\mathrm{exp}(-1526/T)$ | $1.3\times 10^{8}$ | $1.2\times 10^{8}$ | $1.5\times 10^{9}$
R31 | $\mathrm{H}+\mathrm{H}+\mathrm{{}^{12}CO_{2}}$ | $\to$ | $\mathrm{H_{2}}+\mathrm{{}^{12}CO_{2}}$ | $1.6\times 10^{-32}(298/T)^{2.27}$ | $2.6\times 10^{5}$ | $1.9\times 10^{5}$ | $1.3\times 10^{7}$
R32 | $\mathrm{H}+\mathrm{OH}+\mathrm{{}^{12}CO_{2}}$ | $\to$ | $\mathrm{H_{2}O}+\mathrm{{}^{12}CO_{2}}$ | $1.292\times 10^{-30}(300/T)^{2}$ | $1.6\times 10^{5}$ | $9.1\times 10^{4}$ | $2.0\times 10^{6}$
R33 | $\mathrm{H}+\mathrm{HO_{2}}$ | $\to$ | $\mathrm{OH}+\mathrm{OH}$ | $7.2\times 10^{-11}$ | $7.0\times 10^{9}$ | $5.7\times 10^{9}$ | $6.6\times 10^{10}$
R34 | $\mathrm{H}+\mathrm{HO_{2}}$ | $\to$ | $\mathrm{H_{2}O}+\mathrm{O(^{1}D)}$ | $1.6\times 10^{-12}$ | $1.6\times 10^{8}$ | $1.3\times 10^{8}$ | $1.5\times 10^{9}$
R35 | $\mathrm{H}+\mathrm{HO_{2}}$ | $\to$ | $\mathrm{H_{2}}+\mathrm{O_{2}}$ | $3.45\times 10^{-12}$ | $3.4\times 10^{8}$ | $2.7\times 10^{8}$ | $3.1\times 10^{9}$
R36 | $\mathrm{H}+\mathrm{H_{2}O_{2}}$ | $\to$ | $\mathrm{HO_{2}}+\mathrm{H_{2}}$ | $2.8\times 10^{-12}\mathrm{exp}(-1890/T)$ | $4.7\times 10^{5}$ | $5.0\times 10^{5}$ | $2.3\times 10^{6}$
R37 | $\mathrm{H}+\mathrm{H_{2}O_{2}}$ | $\to$ | $\mathrm{H_{2}O}+\mathrm{OH}$ | $1.7\times 10^{-11}\mathrm{exp}(-1800/T)$ | $4.5\times 10^{6}$ | $4.8\times 10^{6}$ | $2.3\times 10^{7}$
R38 | $\mathrm{H}+\mathrm{O_{2}}+\mathrm{M}$ | $\to$ | $\mathrm{HO_{2}}+\mathrm{M}$ | $k_{0}=8.8\times 10^{-32}(300/T)^{1.3}$ | $1.6\times 10^{12}$ | $1.4\times 10^{12}$ | $1.7\times 10^{12}$
|  |  |  | $k_{\infty}=7.5\times 10^{-11}(300/T)^{-0.2}$ |  |  |
R39 | $\mathrm{H}+\mathrm{O_{3}}$ | $\to$ | $\mathrm{OH}+\mathrm{O_{2}}$ | $1.4\times 10^{-10}\mathrm{exp}(-470/T)$ | $6.8\times 10^{10}$ | $8.0\times 10^{10}$ | $7.5\times 10^{10}$
R40 | $\mathrm{O}+\mathrm{OH}$ | $\to$ | $\mathrm{O_{2}}+\mathrm{H}$ | $1.8\times 10^{-11}\mathrm{exp}(180/T)$ | $1.3\times 10^{11}$ | $8.7\times 10^{10}$ | $1.9\times 10^{11}$
|  |  |  |  a2-body: cm3s-1; 3-body: cm6s-1 |  |  bcm-2s-1 |
Table 2: Chemical reactions No. | Reaction |  |  | Reaction rate coefficienta |  | Column rateb |
---|---|---|---|---|---|---|---
|  |  |  |  | standard case | small eddy case | large eddy case
R41 | $\mathrm{O}+\mathrm{HO_{2}}$ | $\to$ | $\mathrm{OH}+\mathrm{O_{2}}$ | $3.0\times 10^{-11}\mathrm{exp}(200/T)$ | $1.2\times 10^{12}$ | $1.1\times 10^{12}$ | $1.3\times 10^{12}$
R42 | $\mathrm{O}+\mathrm{H_{2}O_{2}}$ | $\to$ | $\mathrm{OH}+\mathrm{HO_{2}}$ | $1.4\times 10^{-12}\mathrm{exp}(-2000/T)$ | $3.5\times 10^{7}$ | $3.0\times 10^{7}$ | $2.8\times 10^{7}$
R43 | $\mathrm{OH}+\mathrm{OH}$ | $\to$ | $\mathrm{H_{2}O}+\mathrm{O}$ | $1.8\times 10^{-12}$ | $4.7\times 10^{5}$ | $1.6\times 10^{5}$ | $8.8\times 10^{5}$
R44 | $\mathrm{OH}+\mathrm{OH}+\mathrm{M}$ | $\to$ | $\mathrm{H_{2}O_{2}}+\mathrm{M}$ | $k_{0}=8.97\times 10^{-31}(300/T)$ | $9.5\times 10^{3}$ | $8.1\times 10^{3}$ | $9.9\times 10^{3}$
|  |  |  | $k_{\infty}=2.6\times 10^{-11}$ |  |  |
R45 | $\mathrm{OH}+\mathrm{O_{3}}$ | $\to$ | $\mathrm{HO_{2}}+\mathrm{O_{2}}$ | $1.7\times 10^{-12}\mathrm{exp}(-940/T)$ | $3.5\times 10^{6}$ | $3.1\times 10^{6}$ | $3.8\times 10^{5}$
R46 | $\mathrm{OH}+\mathrm{HO_{2}}$ | $\to$ | $\mathrm{H_{2}O}+\mathrm{O_{2}}$ | $4.8\times 10^{-11}\mathrm{exp}(250/T)$ | $6.0\times 10^{9}$ | $5.6\times 10^{9}$ | $4.3\times 10^{9}$
R47 | $\mathrm{OH}+\mathrm{H_{2}O_{2}}$ | $\to$ | $\mathrm{H_{2}O}+\mathrm{HO_{2}}$ | $1.8\times 10^{-12}$ | $2.8\times 10^{9}$ | $3.0\times 10^{9}$ | $1.5\times 10^{9}$
R48 | $\mathrm{HO_{2}}+\mathrm{O_{3}}$ | $\to$ | $\mathrm{OH}+\mathrm{O_{2}}+\mathrm{O_{2}}$ | $1.0\times 10^{-14}\mathrm{exp}(-490/T)$ | $4.2\times 10^{8}$ | $2.5\times 10^{8}$ | $7.0\times 10^{7}$
R49 | $\mathrm{HO_{2}}+\mathrm{HO_{2}}$ | $\to$ | $\mathrm{H_{2}O_{2}}+\mathrm{O_{2}}$ | $3.0\times 10^{-13}\mathrm{exp}(460/T)$ | $1.8\times 10^{11}$ | $1.5\times 10^{11}$ | $1.5\times 10^{11}$
R50 | $\mathrm{HO_{2}}+\mathrm{HO_{2}}+\mathrm{M}$ | $\to$ | $\mathrm{H_{2}O_{2}}+\mathrm{O_{2}}+\mathrm{M}$ | $4.2\times 10^{-33}\mathrm{exp}(920/T)$ | $6.4\times 10^{9}$ | $5.6\times 10^{9}$ | $4.9\times 10^{9}$
R51 | $\mathrm{{}^{12}CO}+\mathrm{OH}+\mathrm{M}$ | $\to$ | $\mathrm{{}^{12}CO_{2}}+\mathrm{H}+\mathrm{M}$ | $k_{0}=1.5\times 10^{-13}(300/T)^{0.6}$ | $1.5\times 10^{12}$ | $1.4\times 10^{12}$ | $1.6\times 10^{12}$
|  |  |  | $k_{\infty}=2.1\times 10^{9}(300/T)^{-6.1}$ |  |  |
R52 | $\mathrm{{}^{13}CO}+\mathrm{OH}+\mathrm{M}$ | $\to$ | $\mathrm{{}^{13}CO_{2}}+\mathrm{H}+\mathrm{M}$ | $k_{0}=0.9891\times 1.5\times 10^{-13}(300/T)^{0.6}$ | $1.4\times 10^{10}$ | $1.3\times 10^{10}$ | $1.5\times 10^{10}$
|  |  |  | $k_{\infty}=0.9891\times 2.1\times 10^{9}(300/T)^{-6.1}$ |  |  |
R53 | $\mathrm{{}^{12}CO}+\mathrm{OH}+\mathrm{M}$ | $\to$ | $\mathrm{HO^{12}CO}+\mathrm{M}$ | $k_{0}=5.9\times 10^{-33}(300/T)^{1.4}$ | $1.1\times 10^{10}$ | $9.8\times 10^{9}$ | $9.3\times 10^{9}$
|  |  |  | $k_{\infty}=1.1\times 10^{-12}(300/T)^{-1.3}$ |  |  |
R54 | $\mathrm{{}^{13}CO}+\mathrm{OH}+\mathrm{M}$ | $\to$ | $\mathrm{HO^{13}CO}+\mathrm{M}$ | $k_{0}=0.9891\times 5.9\times 10^{-33}(300/T)^{1.4}$ | $9.9\times 10^{7}$ | $8.9\times 10^{7}$ | $8.7\times 10^{7}$
|  |  |  | $k_{\infty}=0.9891\times 1.1\times 10^{-12}(300/T)^{-1.3}$ |  |  |
R55 | $\mathrm{HO^{12}CO}+\mathrm{O_{2}}$ | $\to$ | $\mathrm{HO_{2}}+\mathrm{{}^{12}CO_{2}}$ | $2.0\times 10^{-12}$ | $1.1\times 10^{10}$ | $9.8\times 10^{9}$ | $9.3\times 10^{9}$
R56 | $\mathrm{HO^{13}CO}+\mathrm{O_{2}}$ | $\to$ | $\mathrm{HO_{2}}+\mathrm{{}^{13}CO_{2}}$ | $0.9891\times 2.0\times 10^{-12}$ | $9.9\times 10^{7}$ | $8.9\times 10^{7}$ | $8.7\times 10^{7a}$
R57 | $\mathrm{{}^{12}CO_{2}^{+}}+\mathrm{H_{2}}$ | $\to$ | $\mathrm{{}^{12}CO_{2}}+\mathrm{H}+\mathrm{H}$ | $8.7\times 10^{-10}$ | $1.4\times 10^{8}$ | $1.2\times 10^{8}$ | $1.4\times 10^{9}$
|  |  |  |  a2-body: cm3s-1; 3-body: cm6s-1 |  |  bcm-2s-1 |

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