# Not enough H2O2 to warm early Mars

Maxime Maurice, François Forget, Franck Lefèvre, Aurélien Stolzenbach, A.

Yassin Jaziri, Ashwin S Braude, Martin Turbet, Ehouarn Millour, Yangcheng

Luo

► To cite this version:

Maxime Maurice, François Forget, Franck Lefèvre, Aurélien Stolzenbach, A. Yassin Jaziri, et al. Not enough H2O2 to warm early Mars. Icarus, 2026, 448, pp.116914. 10.1016/j.icarus.2025.116914. hal-05486006

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Submitted on 30 Jan 2026

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Research Paper

# Not enough H₂O₂ to warm early Mars

Maxime Maurice a,*, François Forget a, Franck Lefèvre b, Aurélien Stolzenbach c, A. Yassin Jaziri b, Ashwin S. Braude d, Martin Turbet a, Ehouarn Millour a, Yangcheng Luo a

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

Keywords:

Atmospheres chemistry

Atmospheres dynamics

Mars atmosphere

Mars climate

Photochemistry

## ABSTRACT

There exists strong geomorphological, sedimentary and mineralogical evidence that Mars had an active surface hydrological cycle during the Noachian period, about 3.8 Gyr ago (Ga). However, how surface temperatures compatible with perennial liquid water could be sustained in spite of a Sun that only had 75% of its present-day brightness has remained elusive, leading to the faint young Sun paradox for Mars. Recently, the greenhouse effect of hydrogen peroxide (H₂O₂) has been proposed as a solution by Ito et al. (2020). Radiative transfer models have shown that a few ppmv of H₂O₂ in a 1 or 2 bar CO₂ atmosphere could solve the faint young Sun paradox on early Mars. In a warm and wet CO₂ atmosphere, H₂O₂ is produced by photochemistry and contributes to the stability of the CO₂ atmosphere along with the HOₓ (H, OH and HO₃⁻) catalytic cycles. Nevertheless, a thorough assessment of the viability of such a high H₂O₂ abundance is still lacking. Using 1D and 3D climate models coupled with a C-H-O photochemistry solver, we show that in the most favorable case for H₂O₂ to build up, its steady-state abundance is several orders of magnitude short from its required abundance of ~ 1 ppmv to have a significant radiative effect. Furthermore, we also show that a transient warming episode associated with massive H₂O₂ release cannot exceed 10 Martian years. We therefore rule out H₂O₂ as a warming agent for early Mars.

## 1. Introduction

The surface temperature of Mars in the late Noachian — early Hesperian (about 3.6 to 3.8 Ga) was high enough to locally sustain seasonal to year-long, surface liquid water (Rapin et al., 2023; Mondro et al., 2025) that carved valley networks (Fassett and Head, 2008; Hoke et al., 2011; Goudge et al., 2024) and formed abundant hydrated (or aqueous alteration-associated) minerals (e.g., sulfates and phyllosilicates) (Bibring et al., 2005; Murchie et al., 2009; Ehlmann et al., 2011; Carter et al., 2023). While of prime astrobiological importance (Sasselov et al., 2020), how such conditions could be achieved in spite of a Sun that had only ~ 75% of its present brightness (Gough, 1981) remains elusive (Kasting, 1991; Forget et al., 2013; Wordsworth et al., 2013; Wordsworth, 2016; Haberle et al., 2017). Although several lines of evidence suggest that Mars had a denser CO₂ atmosphere then (possibly up to 1 or 2 bar (Kite et al., 2014; Chassefière et al., 2016; Cassata, 2017; Kurokawa et al., 2018)), the resulting enhanced greenhouse effect would have been offset by the increased albedo due to Rayleigh scattering. As a result, the surface temperature should have remained several tens of K below the melting point of water

under a pure CO₂ atmosphere (Kasting, 1991; Forget et al., 2013), and additional warming mechanism are required.

Recently, Jorge et al. (2024) investigated the greenhouse potential of 15 common gases and found that HNO₃, SO₂, NH₃, C₂H₄ and H₂O₂ could induce sufficient greenhouse warming to reach a surface temperature of 273 K (the melting point of water) if present in sufficient amount. The most potent greenhouse gas able to raise early Mars surface temperature to 273 K identified by Jorge et al. (2024) is hydrogen peroxyde (H₂O₂). H₂O₂ had already been proposed by Ito et al. (2020), who noted that it has an infrared absorption window around 500 cm⁻¹ – close to the wavelength of the peak emission of a 220 to 270 K blackbody – which only marginally overlaps with CO₂ absorption windows and is coincident with CO₂'s absorption trough (15 µm and far-infrared CO₂'s collision-induced absorption bands). H₂O₂ was once proposed as an oxidative agent explaining the then apparent absence of organic molecules in the Martian soil (Hunten, 1979), though organics have since then be found (Freissinet et al., 2025). A few tens of ppbv of H₂O₂ have been detected on present-day Mars (Encrenaz et al., 2004,

<footnote>a Laboratoire de Météorologie Dynamique (LMD), IPSL, Sorbonne Université, Ecole Normale Supérieure, Ecole Polytechnique, Paris, France</footnote>

<footnote>b Laboratoire Atmosphère Milieux, Observations Spatiales (LATMOS), UVSQ, Université Paris-Saclay, Paris, France</footnote>

<footnote>c Instituto de Astrofísica de Andalucía, Granada, Spain</footnote>

<footnote>d Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA</footnote>

<footnote>* Correspondence to: Laboratoire Magma et Volcans (LMV), CNRS, Université Clermont Auvergne, Aubière, France.
E-mail address: maximemaurice@protonmail.com (M. Maurice).</footnote>
2019), and a warm and wet atmosphere on early Mars (with a stronger water cycle) should have sustained even higher abundances, as H₂O₂ is produced by odd hydrogen (H, OH and HO₂, commonly referred to as HOₓ) chemistry driven by water vapor photolysis. Both Jorge et al. (2024) and Ito et al. (2020) found that ~ 1 ppmv H₂O₂ in a 2 bar CO₂ atmosphere could raise the surface temperature above 273 K.

Ito et al. (2020) further claimed that this abundance of H₂O₂ could have been reached in early Mars' atmosphere based on the following reasoning: to maintain a CO₂-dominated atmosphere, CO₂ recombination needs to be catalyzed, because CO₂ photolysis is much faster than its restoring reaction

$$CO + O + M \rightarrow CO_2 + M, \qquad (R23)$$

which is spin-forbidden. Thus, CO₂ restoration operates instead via the oxidation of CO by OH:

$$CO + OH \rightarrow CO_2 + H, \qquad (R1)$$

requiring a source of hydroxyl radicals (McElroy and Donahue, 1972; Parkinson and Hunten, 1972). n the present-day Mars atmosphere, OH production mainly involves HOₓ and odd oxygen (O and O₃, commonly referred to as Oₓ) species ((Stock et al., 2012), P2 and P3 in Table 1), and thus ultimately depends on water photolysis from which HOₓ originate. However, other chemical pathways exist where OH is a product of H₂O₂ photodissociation ((Parkinson and Hunten, 1972), P1 in Table 1). Pathway P1 accounts for ~ 8% of CO₂ recombination on present-day Mars (Stock et al., 2012). Ito et al. (2020) proposed that, in a warm and wet early Mars atmosphere offering more favorable conditions for H₂O₂, CO₂ recombination was exclusively catalyzed by H₂O₂ photo-dissociation. Thus, in steady-state, the net photo-dissociation and recombination rates of CO₂ cancel out. Under the conservative assumption that H₂O₂ photo-dissociation is the rate-limiting reaction of the pathway, the column densities and photo-dissociation rates of both species are linked:

$$J_{CO_2} \Sigma_{CO_2} = 2 J_{H_2O_2} \Sigma_{H_2O_2}, \qquad (1)$$

where Jₓ and Σₓ are the photolysis rate and column density of species X, respectively, and the factor 2 comes from the fact that the photo-dissociation of one molecule of H₂O₂ catalyzes the recombination of two CO₂ molecules (see P1 in Table 1). From Eq. (1) applied in a 2 bar CO₂ atmosphere, Ito et al. (2020) estimated a column density of H₂O₂ of up to 5 × 10¹⁸ cm⁻² and claimed that it would have provided sufficient infrared opacity to reach a surface temperature of 273 K on early Mars.

The assumption that the photo-dissociation of H₂O₂ catalyzes 100% of CO₂ recombination in early Mars atmosphere is a strong hypothesis that needs to be tested with photochemical models. In this study, we use a C–H–O photochemical solver integrated into a 1D and 3D climate model to investigate this hypothesis and assess the upper bound of H₂O₂ abundance that can be achieved in early Mars atmosphere. We show that under the most favorable conditions, i.e., a warm and wet atmosphere, the abundance of H₂O₂ is orders of magnitude too small to induce a noticeable greenhouse warming. We also test the case of a transient event of H₂O₂ release associated with the destabilization of water ice cover with abundant H₂O₂ dissolved, and find that in this case, a very generous upper bound to the duration of a H₂O₂-induced warm climate is ~ 10 Martian years, one order of magnitude shorter than required for the duration an episode of river-forming climate (Kite, 2019). In Section 2, we describe how we set up the model to create the most favorable conditions for H₂O₂ formation, in order to estimate realistic upper bounds on H₂O₂ that could be sustained by atmospheric chemistry at temperatures above 273 K. To validate our upper bounds, in Section 3.1 we benchmark 1D results against equivalent results in 3D, because only the former can approach chemical equilibrium of long-lived species like H₂O₂. We then analyze the photochemistry in a warm and wet early Mars atmosphere in Section 3.2 and gauge

realistic upper limits for H₂O₂ in Section 3.3. In Section 3.4, we frame the abundance of the long-lived species H₂ at chemical equilibrium in order to support our results, and in Section 3.5 we assess the effect of transient H₂O₂ release. Finally, we discuss other perspectives for warming early Mars and provide final conclusions in Section 4.

## 2. Model

We use the Generic PCM (Forget et al., 2013; Wordsworth et al., 2013; Turbet and Forget, 2021) to simulate the climate of a warm and wet early Mars. As our goal is not to assess the warming effect of H₂O₂ (this has already been done by Ito et al. (2020) and Jorge et al. (2024)) but rather to constrain an upper bound for its abundance, we adopt an optimal setup for H₂O₂ build up, i.e., a one warm and wet one hat yields a surface temperature above 273 K already without accounting for the radiative effect of H₂O₂. We do so by considering a 2 bar CO₂ atmosphere receiving a solar flux reduced by 30% (to account for a faint young Sun at 3.8 Ga (Gough, 1981)), and adding a supplementary infrared opacity term amounting to the CO₂-H₂ collision-induced absorption of a 2 bar CO₂ atmosphere with 15 mol.% H₂ from Turbet et al. (2020a), as this setup has been shown to result in mean surface temperatures above 273 K by Turbet and Forget (2021). Notice that this additional opacity term is unrelated to the atmospheric composition predicted by the photochemical solver, as its goal is only to ensure warm conditions rather than having a consistent physical meaning. This alleviates the need to spin up a new simulation involving an abstract opacity source. Indeed, we do not expect the greenhouse mechanism (gray gas or CO₂-H₂ collision-induced absorption) to affect our results on H₂O₂ production. Notice that the dry convective lapse rate is also computed for a 15 wt% H₂ atmosphere in order to reproduce the thermal state of Turbet and Forget (2021). Still focusing on determining the abundance of H₂O₂ in an already warm atmosphere rather than its direct warming potential, we do not account the H₂O₂'s radiative effect (a choice that will be validated a posteriori). Water vapor is thus the only variable gas to be radiatively active (following Turbet and Forget (2021)), and originates from oceans covering the northern highlands and Hellas basin on a pre-true polar wander topography (Bouley et al., 2016) (corresponding to a global water budget of 550 m global equivalent layer). Our 3D simulations are initialized from the 136th month of the corresponding case from Turbet and Forget (2021), to which we refer the reader for more information on the climate model setup.

In addition to this setup, we use the Adaptive Semi-Implicit Scheme (ASIS) photochemical solver (Cariolle et al., 2017), implemented in the Generic PCM by Jaziri et al. (2022), to solve for the C–H–O network reported in Tables 2 and 3. This reduced network of 10 species and 40 reactions (including 12 photo-dissociation reactions) represents the C–H–O sub-network used by Zahnle et al. (2008) to study the stability of present and past Mars CO₂ atmospheres (with updated reaction rates, and without CHO and CH₂O, which we found to have minor influence on the results). The solar UV flux is calculated for the Sun at 3.8 Ga following Claire et al. (2012). The model is initialized with a pure CO₂ atmosphere and the surface water reservoirs previously mentioned, as well as the atmospheric water vapor from the spin-up simulation. We neglect atmospheric escape as well as surface deposition of any species, in particular of H₂O₂, thereby favoring its accumulation. In early Mars conditions, H₂ likely escapes, affecting the redox state of the atmosphere. However, a proper description of H₂ escape requires a model of the upper atmosphere, which is beyond the scope of this study. Furthermore, as discussed in Section 3.4, our simulations cannot reach H₂ equilibrium, so instead of assessing its exact abundance, we test various fixed abundances for it, framing its expected equilibrated value.

The photochemical system converges on a timescale prohibitively long to run 3D simulations to chemical steady-state. In order to investigate chemical equilibration, we run additional 1D simulations using the
<figure><img src="image_4.png" /><figcaption>Fig. 1. Temperature profiles of the 1D simulation (blue, after 1000 Martian years) and the 3D simulation (orange, averaged between 9 and 10 Martian years of simulation time) (a), converged water vapor abundance profiles for the 1D simulation in blue and for the 3D simulation in orange (b), and eddy mixing coefficient of the 1D simulation K<sub>zz</sub> (c). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

1D version of the Generic PCM, which is significantly faster at the cost of neglecting 3D climatic features (e.g., cloud cover). The 1D simulation uses the same radiative setup as the 3D except for the radiative effect of water and CO<sub>2</sub> clouds, which is not realistically captured in 1D and is thus ignored, and, in line with Turbet and Forget (2021), the surface relative humidity is maintained at 80%. The dynamical influence on vertical mixing is parameterized by an eddy mixing coefficient, which we empirically tune so that our 1D simulation satisfactorily reproduce the averaged vertical profile of chemical species in our 3D runs, yielding:

$$K_{zz} = \begin{cases} K_{zz,\min} & \text{if } z < 35 \text{ km} \\ K_{zz,\min} (p/p_{35 \text{ km}})^a & \text{if } z > 35 \text{ km,} \end{cases} \quad (2)$$

where K<sub>zz,min</sub> = 10<sup>4</sup> cm/s<sup>2</sup>, z is altitude (in m), p is pressure (in Pa), p<sub>35 km</sub> is the pressure at an altitude of 35 km, and a = -0.2. The converged 3D and 1D temperature and water vapor profiles, as well as the 1D eddy diffusion profile, are represented in Fig. 1. Notice that, as a time-marching model resolving processes like moist adjustment on a sub-sol time resolution, even the 1D model is limited in simulation time and cannot be run to complete chemical equilibration of the longest-lived species, namely H<sub>2</sub> (see Section 3.4).

## 3. Results

### 3.1. Approach of thermo-chemical convergence

We use a setup known to yield yearly-averaged mean surface temperatures above 273 K (Turbet and Forget, 2021). We observe a very good agreement between the 3D and 1D temperature profiles, both exhibiting surface temperatures above 273 K (see Fig. 1a). The abundance profiles of our 1D simulation after 10 Martian years evolution are also in good agreement with the averaged abundance profiles of the 3D simulation at the same time for most species (see Fig. 2). The water vapor profile exhibits a stronger cold trap in the 3D case (Fig. 1b). This is reflected in the HO<sub>x</sub> averaged profiles exhibiting an inflection around 40 km in 3D and not in 1D (Fig. 2a). HO<sub>2</sub>'s averaged profile is further altered by the diurnal cycle which is not accounted for in 1D. Fig. 3 represents the diurnal HO<sub>x</sub> cycle. At dusk, H production stalls in the upper atmosphere and atomic hydrogen is converted into HO<sub>2</sub> by reaction R25. On the other hand, HO<sub>2</sub> production in the deep atmosphere also stops, resulting in an upward increasing HO<sub>2</sub> profile at night, and a bimodal vertical distribution when integrated over the whole planet (thick green curve in Fig. 2a).

Both CO and O<sub>2</sub> profiles are enriched in the upper atmosphere and depleted in the lower atmosphere in the 3D case compared to the 1D case, which is likely due to an overestimate of the vertical mixing of these species in 1D, as they are created by photolysis at high altitude and consumed in the deep atmosphere. HO<sub>2</sub> being the main precursor of H<sub>2</sub>O<sub>2</sub> (via reactions R30 and R31), the discrepancy in its profile between 1D and 3D propagates to that of H<sub>2</sub>O<sub>2</sub>. However, 1D and 3D agree remarkably well below 50 km, where the radiative effect of H<sub>2</sub>O<sub>2</sub> should be maximal. Importantly, we see in Fig. 2c that H<sub>2</sub>O<sub>2</sub> remains largely below the ppmv level required to induce significant greenhouse warming.

At the end of 10 Martian years, although CO, O<sub>2</sub>, H<sub>2</sub>O<sub>2</sub> and H<sub>2</sub> abundances still evolve in our 3D simulation, the reaction rates are qualitatively similar to those of the converged 1D simulations after 1000 Martian years. Of note, H<sub>2</sub> still evolves at the end of the 1D simulation. Indeed, with a calculated column-integrated chemical lifetime over 3400 Martian years, H<sub>2</sub> is much longer-lived than our simulation time, which, even in 1D, is limited by the time-stepping required by a time-marching climate model. The CO and O<sub>2</sub> abundances, however, reach a quasi steady-state, stabilizing within ~ 200 Martian years around column-integrated masses of 0.65 and 0.35 kg/m<sup>2</sup>, respectively (corresponding to volume mixing ratios of 121 and 65 ppmv, respectively), close to the theoretical ratio of CO/O<sub>2</sub> = 2 dictated by the stoichiometry of CO<sub>2</sub> photo-dissociation. H<sub>2</sub>O<sub>2</sub> is further discussed in Section 3.3.

### 3.2. The role of H<sub>2</sub>O<sub>2</sub> in the atmosphere's photochemical stability

In order to identify the various chemical pathways leading to CO<sub>2</sub> restoration and assess their relative importances, we use the code PaPy (Appendix B) by Stolzenbach (2025), which implements the chemical pathway analysis algorithm from Lehmann (2004). We identify the major chemical pathways responsible for CO<sub>2</sub> production in the bulk atmosphere of the converged 1D simulation (Fig. 5 and Table 1).

We first notice that, while the integrated column of atmosphere is at chemical near steady-state (with H<sub>2</sub> slowly but steadily increasing), this is not locally true. Indeed, CO<sub>2</sub> is mainly destroyed in the upper atmosphere by photolysis, and produced in the lower atmosphere (where it is shielded from UV radiation) by CO oxidation reaction R1. This can be seen in Fig. 4 by comparing the dark blue curve (net CO<sub>2</sub> destruction) and the red curve (99.5% of the net CO<sub>2</sub> production). Thus the CO<sub>2</sub> production pathways listed in Table 1 and described below are not homogeneous in the atmosphere, but ensure a dynamical quasi-steady-state.
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Volume-mixing ratio profiles of various species: HOₓ (blue curves for H, orange for OH and green for HO₂) in panel a, CO (blue curves) and O₂ (orange curves) in panel b, and H₂O₂ (blue curves) and O₃ (orange curves) in panel c. Thick (resp. thin) solid curves represent the 3D case averaged between simulation year 9 and 10 (resp. 1D the case after 10 Martian years), and dotted curves represent the 1D case after 1000 Martian years. The blue dashed curve in panel c represents the saturation point of H₂O₂ (calculated from the final 1D temperature profile). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Time-evolution of the meridionally-averaged distributions of H (a), OH (b) and HO₂ (c) at longitude 0° over a typical day. As on present-day Mars (Lefèvre and Krasnopolsky, 2017), H dominates in the upper atmosphere during the day and HO₂ in the lower atmosphere, OH being intermediate. At night, H in the upper atmosphere turns into HO₂.</figcaption></figure>

Pathway P1 was first identified by Parkinson and Hunten (1972). It relies on H₂O₂ photolysis to produce OH radicals which then oxidize CO into CO₂ (Table 1). H₂O₂ production is due to either the bimolecular or third body-catalyzed self reaction of HO₂, the former dominating in the

upper atmosphere while the latter dominates in the deep atmosphere where pressure is higher (see Fig. 4). Pathway P1 belongs to class II of Stock et al. (2012), which involve HOₓ but no odd oxygen. We observe that the rate of H₂O₂ supply (pink and brown curves in Fig.
<figure><img src="image_7.png" /><figcaption>Fig. 4. Rates of the various reactions involved in the CO₂-restoring cycles.</figcaption></figure>

4) and photolysis control CO₂ recombination by reaction R1 (red curve in Fig. 4) below ~ 30 km, suggesting the importance of pathway P1 in the deep atmosphere. While Ito et al. (2020) assumed pathway P1 to be responsible for 100% of CO₂ production to support their calculation, we find it to account for 46.7% of it (Fig. 5). In present-day Mars atmosphere, where the pressure is too low for the termolecular branch to be efficient, P1 only accounts for 8.2% of CO₂ production (P7 in Stock et al. (2012)).

Pathway P2 was introduced by McElroy and Donahue (1972). It differs from pathway P1 in that HO₂ is the direct precursor of OH through reaction R10, without intermediate H₂O₂ (Table 1). Pathway P2 involves both HOₓ and Oₓ, and thus belongs to class I of Stock et al. (2012). Reaction R10's rate (violet curve in Fig. 4) controls CO₂ recombination (R1) rate above ~ 30 km. Of note, the atomic oxygen in P2 can originate from O(¹D) quenching, yielding the net reaction CO+O(¹D)→CO₂. P2 is the main CO₂ restoring pathway in present-day Mars atmosphere, representing more than 50% of net CO₂ production (when considering together Stock et al. (2012)'s O₂ photolysis-driven pathway P1 and transport-driven pathway P2). In our simulations, we find it to be slightly less important, representing 42.7% of the net CO₂ production (Fig. 5).

Pathway P3, in which ozone reacts with atomic hydrogen to form OH through reaction R12 is another contributor of CO₂ restoration in present-day Mars atmosphere, accounting for 7.9% of it (when considering together Stock et al. (2012)'s transport-driven pathway P5 and O₂ photolysis-driven pathway P6) (Stock et al., 2012). As for P2, P3 includes a branch relying on O(¹D) quenching. Involving O₃ and OH, P3 is also a class I pathway. Reaction R12 (cyan curve in Fig. 4), becomes a significant contributor to CO₂ recombination (R1) above 55 km. However, at this altitude, CO₂ is effectively destroyed, with a photolysis rate several orders of magnitude larger than its recombination rate. Its role in early Mars CO₂ restoration is similar to that of present-day Mars, with 8% of CO₂ production (Fig. 5).

Finally, other pathways whose total rates each account for less than 1% of CO₂ net production (like reaction R23, accounting for 0.54% of

<table><caption>**Table 1**
Relevant pathways for CO₂ restoration.</caption><thead><tr><th>Pathway</th><th>Cycle</th><th>CO<sub>2</sub> column rate (cm<sup>-2</sup>s<sup>-1</sup>)</th><th>%</th></tr></thead><tbody><tr><td>P1</td><td>H<sub>2</sub>O<sub>2</sub> + hν → 2OH<br>2 × (CO + OH → CO<sub>2</sub> + H)<br>2 × (H + O<sub>2</sub> + M → HO<sub>2</sub> + M)<br>2HO<sub>2</sub> + M → H<sub>2</sub>O<sub>2</sub> + O<sub>2</sub> + M<br><hr>O<sub>2</sub> + 2CO → 2CO<sub>2</sub></td><td>4.989 × 10<sup>14</sup></td><td>46.66</td></tr><tr><td>P2</td><td>O + HO<sub>2</sub> → OH + O<sub>2</sub><br>CO + OH → CO<sub>2</sub> + H<br>H + O<sub>2</sub> + M → HO<sub>2</sub> + M<br><hr>O + CO → CO<sub>2</sub></td><td>4.561 × 10<sup>14</sup></td><td>42.66</td></tr><tr><td>P3</td><td>O + O<sub>2</sub> + M → O<sub>3</sub> + M<br>H + O<sub>3</sub> → OH + O<sub>2</sub><br>CO + OH → CO<sub>2</sub> + H<br><hr>O + CO → CO<sub>2</sub></td><td>8.568 × 10<sup>13</sup></td><td>8.01</td></tr><tr><td>P<sub>slow</sub></td><td>Cycles &lt; 1.00%</td><td>2.883 × 10<sup>13</sup></td><td>2.67</td></tr></tbody></table>

CO₂ net production) are lumped together in the P<sub>slow</sub> quadrant of Fig. 5, adding up to 2.7% of CO₂ production.

We thus observe a decrease in the relative contribution of class I pathways to CO₂ production in a warm and wet early Mars atmosphere compared to present-day Mars, to the benefit of class II pathway P1. Nevertheless, H₂O₂ photo-dissociation-based pathway P1 accounts for less than half of the net CO₂ production. While that contradicts Ito et al. (2020)'s assumption, P1 still has a significant share in CO₂ restoration.

### 3.3. Upper bound in H₂O₂ abundance

In our quasi steady-state 1D simulation, the column density of H₂O₂ is 1.6 × 10¹⁷ cm⁻². This is about 4 times less than the value calculated by Ito et al. (2020) (8 × 10¹⁷ cm⁻²) who assumed that CO₂
<figure><img src="image_8.png" /><figcaption>Fig. 5. Contributions of the various chemical pathways in CO₂ restoration. The pathways are reported in Table 1. Class I pathways are reported in green, while class II pathways are reported in blue. Additional pathways whose rate is inferior to 1% are lumped together in P_slow, adding up to 2.3% of CO₂ production. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

restoration was exclusively catalyzed by H₂O₂ photolysis, and considered a conservative H₂O₂ photo-dissociation shielding wavelength of 227.5 nm. Making the former assumption and solving Eq. (1) using the CO₂ photo-dissociation rate and J<sub>H₂O₂</sub> from our simulation would yield an H₂O₂ column density of 1.4 × 10¹⁸ cm⁻², which is between the 8 × 10¹⁷ cm⁻² and 5 × 10¹⁸ cm⁻² calculated by Ito et al. (2020) for shielding wavelengths of 227.5 and 300 nm, respectively. This discrepancy might stem from differences in the photolysis cross sections of either CO₂ or H₂O₂, as well as a more accurate calculation of UV shielding (which is self-consistently calculated in our model) and an H₂O₂ photo-dissociation threshold wavelength of 350 nm.

The column-integrated mass of H₂O₂ we obtain corresponds to an average volume mixing ratio of 2.1 ppbv. Interestingly, this is smaller than the present-day value of ~ 10–45 ppbv (Encrenaz et al., 2019). However, atmospheric conditions (e.g., surface pressure) are so different that an insightful comparison is not straightforward to make. The actual H₂O₂ profile is represented in Fig. 2c. As mentioned above, our 1D simulation underestimates H₂O₂ in the upper atmosphere because it does not properly capture the influence of the diurnal cycle on HO₂, the main precursor of H₂O₂. However, this difference in the high atmosphere, where density is low, has a negligible impact on the column-integrated H₂O₂ abundance. Of note, we find that H₂O₂ is always at least one order of magnitude short of the saturation point. Ito et al. (2020) and Jorge et al. (2024) found that a 2 bar CO₂ atmosphere requires ~ 1 ppmv H₂O₂ to sustain a surface temperature of 273 K. Our results, representing the most favorable case for H₂O₂ to build up (a warm and wet atmosphere with no H₂O₂ condensation, rainout or surface deposition), show that H₂O₂ abundance is short by almost 3 orders of magnitude. While our simulations are “artificially” kept warm to present a favorable case, a colder atmosphere would be drier, further lowering the abundance of H₂O₂. Consequently, we rule out H₂O₂ as a viable source of heating for Noachian Mars.

### 3.4. Effect of H₂ and the redox state of the atmosphere

As mentioned above, the characteristic chemical evolution time of H₂ is too long for a coupled time-marching climate-chemical model to

converge. All other species reach a quasi steady-state. In order to assess the influence of H₂'s evolution on H₂O₂, we ran additional simulations keeping a fixed H₂ (homogeneous) abundance, thereby alleviating the issue of H₂ convergence. In order to frame a realistic equilibrated value for H₂ abundance, we tested various abundances, from 100 ppt to 1 ppm. These simulations all reach chemical equilibrium within a few hundred Martian years, the same timescale needed for the baseline simulation to reach a quasi steady-state. We observe an intuitive trend of increasing equilibrium abundances of oxidized species with decreasing H₂'s abundances, and vis-versa for reduced species. In particular, atomic hydrogen – the most reduced HOₓ – is favored by increased H₂ abundances, while HO₂ – the most oxidized HOₓ and precursor of H₂O₂ – is disfavored. As the imposed H₂ abundance is decreased, the equilibrium H₂O₂ abundance converges toward a value close the final value reached by our baseline simulation, where H₂ is free to evolve. Thus, as H₂ slowly builds up in the baseline simulation, we expect H₂O₂ to decrease, making our results a conservative estimate of H₂O₂'s abundance upper bound.

Other processes, such as serpentinization (Chassefière et al., 2016) or atmospheric escape (Batalha et al., 2015; Adams et al., 2025) can further affect the equilibrium abundance of H₂. The former is poorly constrained but will enhance the abundance of H₂, and thus decrease that of H₂O₂ as described above. Our model does not include hydrogen escape; to do so, a proper modeling of the thermosphere, including effects such as UV heating and non-local thermodynamical equilibrium radiative transfer is required, which is not available. Hydrogen escape should affect negatively H₂'s abundance, however it is not straightforward to assess whether this will decrease to lower values than investigated here, because the diffusion-limited escape of H₂ depends on the abundance of hydrogenated species at the homopause. In any case, the plateauing of H₂O₂ upon reaching the lowest H₂ abundances tested suggests that even lower values will not result in more H₂O₂.

### 3.5. Transient H₂O₂ warming

While our results clearly show that H₂O₂ of purely photochemical origin cannot build up to an abundance sufficient to be radiatively significant, a transient source of H₂O₂ yielding an anomalously high flux could provide an episodic warming mechanism. Liang et al. (2006) proposed that, during a snowball Earth event, H₂O₂ can accumulate in the ice cover, and be subsequently released into the atmosphere upon remelting. In order to test a similar scenario for Mars, we run an additional simulation restarting from our baseline 1D case, adding a high surface flux of H₂O₂, corresponding to the release associated with ice cover destabilization. We estimate this flux F<sub>H₂O₂</sub> (in m⁻²s⁻¹) as:

$$F_{H_2O_2} = \frac{d\Sigma_{\text{ice}}}{dt} \frac{N_A}{M_{H_2O}} [H_2O_2]_{\text{ice}}, \quad (3)$$

where Σ<sub>ice</sub> is the column density of water ice (in kg/m²), N<sub>A</sub> is Avogadro's number, M<sub>H₂O</sub> is the molar mass of water, and [H₂O₂]<sub>ice</sub> is the abundance of H₂O₂ in the ice (in molar mixing ratio). The first term in the right-hand-side of Eq. (3) is estimated by:

$$\frac{d\Sigma_{\text{ice}}}{dt} = \frac{F_{\text{surf}}^{\text{rad}}}{L}, \quad (4)$$

where F<sub>surf</sub><sup>rad</sup> = 33.3 W/m² is downward radiative flux at the surface of our simulation, and L = 333.55 kJ/kg is the latent heat of melting of water (we expect water to melt rather than sublimate in a thicker early Mars atmosphere). This yields a lifetime of 58 sols for 550 m-thick ice cover. The abundance of H₂O₂ in the ice is obtained by:

$$[H_2O_2]_{\text{ice}} = K_D [H_2O_2]_{\text{air}}, \quad (5)$$

where K<sub>D</sub> is the ice-air partition coefficient of H₂O₂ and [H₂O₂]<sub>air</sub> is the air molar (i.e., volume) mixing ratio within ~ 200 Martian years of H₂O₂. For the former, Conklin et al. (1993) measured a value of
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Time-series of the H₂O₂ bulk atmospheric abundance during transient H₂O₂ release events associated with a 550 m-thick ice cover destabilization. The fastest melting rate (blue curve) yields a 58 sols H₂O₂ flux of F<sub>H₂O₂</sub><sup>max</sup> = 2.76 × 10<sup>20</sup> m<sup>-2</sup>s<sup>-1</sup>. Orange, green and red curves represent 10, 100 and 1000 times lower H₂O₂ release fluxes, respectively (and correspondingly lower melting rates), and dots of corresponding color mark the end of the H₂O₂ production period. The blue shaded area depicts the H₂O₂ abundance necessary to raise the surface temperature to 273 K. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

$K_D = 10.7 \times 10^6$ in terrestrial air (we are not aware of any measurement in a Mars-like atmosphere) at the lowest temperature they investigated (-45 °C), which maximizes $K_D$. They further argued that effective uptake of H₂O₂ could be up to 5 times higher in case it is controlled by co-condensation of H₂O and H₂O₂ rather than ice-air diffusion of H₂O₂. As this corresponds to the upper bound in H₂O₂ uptake, we use $K_D = 5 \times 10.7 \times 10^6$ in order to maximize the release of H₂O₂. For [H₂O₂]air, we take the value from our simulation in the lowermost atmospheric level. Both these choices concur to yield the highest value of [H₂O₂]ice, since our simulations are already tuned to maximize [H₂O₂]air, and a colder (frozen) early Mars would yield a lower H₂O₂ abundance. Of note, we only account for an H₂O₂ influx in the chemical system, while the melting of the ice cap would likely also induce a surge of water vapor in the atmosphere.

With this setup, we run simulations restarting our baseline case with the obtained flux of H₂O₂ (F<sub>H₂O₂</sub><sup>max</sup> = 2.76 × 10<sup>20</sup> m<sup>-2</sup>s<sup>-1</sup>) during the 58 sols needed to melt the whole ice cover, after which we set F<sub>H₂O₂</sub> = 0 m<sup>-2</sup>s<sup>-1</sup> and continue the simulation (blue curve in Fig. 6). We observe a strong increase in H₂O₂ during the destabilization period of the ice cover, peaking to a maximum column-integrated volume mixing ratio of ~ 10<sup>3</sup> ppm (largely sufficient to reach 273 K) at the end of the 58 sols release period. After the end of ice melting-induced H₂O₂ release, its abundance drops, returning below 1 ppm within 4000 sols (almost 6 Martian years), indicating the duration of transient H₂O₂ warming in this case.

As this represents a probably unrealistic upper bound on H₂O₂ production, we also test cases with H₂O₂ release fluxes 10, 100 and 1000 times lower over periods of time 10, 100 and 1000 times longer, respectively. The case F<sub>H₂O₂</sub><sup>max</sup>/10 closely follows the higher H₂O₂ release case, although with some delay. It reaches a similar peak values and subsequently drops in a similar fashion, resulting in a slightly shorter total duration above 1 ppmv H₂O₂. The case F<sub>H₂O₂</sub><sup>max</sup>/100 reaches a significantly lower abundance of H₂O₂, although above 1 ppmv and thus still potentially able to warm the surface above 273 K. The duration of the resulting transient warm climate approximately corresponds to the H₂O₂ production (i.e., ice melting), which totals 5782 sols (8.6 Martian years). This correspondence is due to the duration of the release period

exceeding the chemical lifetime of H₂O₂ in early Mars' atmosphere (which remains below half a Martian year for this simulation).

Finally, F<sub>H₂O₂</sub><sup>max</sup>/1000 provide too low a flux of H₂O₂ compared to photochemical sinks, and H₂O₂ never exceeds the 1 ppmv necessary to reach 273 K. Hence, we derive an upper bound of less than 10 Martian years for the duration of a single warm (i.e., ice-melting surface temperature) climate episode of early Mars triggered by transient release of H₂O₂. It is at least one order of magnitude shorter short of the 10<sup>2</sup>-10<sup>3</sup> years minimum duration constraint for single episodes of valley network-forming warm climate suggested by Kite (2019). Of note, this upper bound does not account for the effect of H₂O₂ saturation which is ignored in our model. While further 3D simulations taking into account H₂O₂ dissolution into ice during a cold episode on early Mars and subsequent ice cover destabilization in a more realistic way are warranted to draw firm conclusions about the ability of H₂O₂ to have any warming potential, we argue that our results rule out H₂O₂ as a main warming agent of early Mars.

## 4. Conclusions

Our results clearly rule out equilibrium photochemical H₂O₂ abundances high enough to be a significant warming agent for early Mars, even in the most favorable case of an already warm and wet atmosphere. Furthermore, transient H₂O₂ release associated with ice cover destabilization can sustain H₂O₂ abundances high enough to warm early Mars to 273 K for less than 10 Martian years — and likely much less given the very generous choice of parameter values we test. Hence, our study supports focusing on other greenhouse gases (or mix thereof) (Jorge et al., 2024), or other warming mechanism which have been envisaged, such as the CO₂-H₂ collision-induced absorption (Ramirez et al., 2014; Wordsworth et al., 2017; Turbet et al., 2020a; Turbet and Forget, 2021; Adams et al., 2025) or high altitude clouds (Urata and Toon, 2013; Wordsworth et al., 2013; Ramirez and Kasting, 2017; Turbet et al., 2020b; Kite et al., 2021). Further modeling efforts, relying on comprehensive 3D climate and photochemical simulations, will be necessary to thoroughly assess these leads.
<table><caption>**Table 2**

Chemical network.</caption><thead><tr><th>Reactants</th><th>Products</th><th>Reaction rate</th><th>Reference</th></tr></thead><tbody><tr><td>CO + OH</td><td>CO<sub>2</sub> + H</td><td>R1 See Eq. (6)</td><td>Burkholder et al. (2015)</td></tr><tr><td>O('D)+O<sub>2</sub></td><td>O+O<sub>2</sub></td><td>R2 3.3 × 10<sup>-11</sup> exp (55/T)</td><td>Burkholder et al. (2015)</td></tr><tr><td>O('D)+CO</td><td>O+CO</td><td>R3 6 × 10<sup>-11</sup></td><td>Zahnle et al. (2008)</td></tr><tr><td>O('D)+CO<sub>2</sub></td><td>O+CO<sub>2</sub></td><td>R4 7.5 × 10<sup>-11</sup> exp (115/T)</td><td>Burkholder et al. (2015)</td></tr><tr><td>O+O<sub>2</sub></td><td>O<sub>2</sub>+O<sub>2</sub></td><td>R5 8 × 10<sup>-12</sup> exp (-2060/T)</td><td>Zahnle et al. (2008)</td></tr><tr><td>O('D)+H<sub>2</sub>O</td><td>OH+OH</td><td>R6 1.63 × 10<sup>-10</sup> exp (60/T)</td><td>Burkholder et al. (2015)</td></tr><tr><td>O('D)+H<sub>2</sub></td><td>OH+H</td><td>R7 1.2 × 10<sup>-10</sup></td><td>Burkholder et al. (2015)</td></tr><tr><td>O+H<sub>2</sub></td><td>OH+H</td><td>R7 1.34 × 10<sup>-15</sup> exp (-1460/T) (T/298 K)<sup>-6.52</sup></td><td>Zahnle et al. (2008)</td></tr><tr><td>O('D)+O<sub>3</sub></td><td>O<sub>2</sub>+O<sub>2</sub></td><td>R8 1.2 × 10<sup>-10</sup></td><td>Zahnle et al. (2008)</td></tr><tr><td>O('D)+O<sub>3</sub></td><td>O<sub>2</sub>+O<sub>2</sub>+O</td><td>R9 1.2 × 10<sup>-10</sup></td><td>Zahnle et al. (2008)</td></tr><tr><td>O+HO<sub>2</sub></td><td>OH+O<sub>2</sub></td><td>R10 3 × 10<sup>-11</sup> exp (200/T)</td><td>Zahnle et al. (2008)</td></tr><tr><td>O+OH</td><td>O<sub>2</sub>+H</td><td>R11 1.8 × 10<sup>-11</sup> exp (180/T)</td><td>Burkholder et al. (2015)</td></tr><tr><td>H+O<sub>3</sub></td><td>O<sub>2</sub>+OH</td><td>R12 1.4 × 10<sup>-10</sup> exp (-470/T)</td><td>Zahnle et al. (2008)</td></tr><tr><td>H+HO<sub>2</sub></td><td>OH+OH</td><td>R13 7.2 × 10<sup>-11</sup></td><td>Zahnle et al. (2008)</td></tr><tr><td>H+HO<sub>2</sub></td><td>H<sub>2</sub>+O<sub>2</sub></td><td>R14 6.9 × 10<sup>-12</sup></td><td>Zahnle et al. (2008)</td></tr><tr><td>H+HO<sub>2</sub></td><td>H<sub>2</sub>O+O</td><td>R15 1.6 × 10<sup>-12</sup></td><td>Zahnle et al. (2008)</td></tr><tr><td>OH+HO<sub>2</sub></td><td>H<sub>2</sub>O+O<sub>2</sub></td><td>R16 4.8 × 10<sup>-11</sup> exp (250/T)</td><td>Zahnle et al. (2008)</td></tr><tr><td>OH+H<sub>2</sub>O<sub>2</sub></td><td>H<sub>2</sub>O+HO<sub>2</sub></td><td>R17 2.9 × 10<sup>-12</sup> exp (-160/T)</td><td>Zahnle et al. (2008)</td></tr><tr><td>OH+H<sub>2</sub></td><td>H<sub>2</sub>O+H</td><td>R18 2.8 × 10<sup>-12</sup> exp (-1800/T)</td><td>Burkholder et al. (2015)</td></tr><tr><td>O+H<sub>2</sub>O<sub>2</sub></td><td>OH+HO<sub>2</sub></td><td>R19 1.4 × 10<sup>-12</sup> exp (-2000/T)</td><td>Zahnle et al. (2008)</td></tr><tr><td>OH+O<sub>3</sub></td><td>HO<sub>2</sub> + O<sub>2</sub></td><td>R20 1.7 × 10<sup>-12</sup> exp (-940/T)</td><td>Zahnle et al. (2008)</td></tr><tr><td>HO<sub>2</sub> + O<sub>3</sub></td><td>OH + O<sub>2</sub> + O<sub>2</sub></td><td>R21 1 × 10<sup>-14</sup> exp (-490/T)</td><td>Zahnle et al. (2008)</td></tr><tr><td>OH + OH</td><td>H<sub>2</sub>O + O</td><td>R22 1.8 × 10<sup>-12</sup></td><td>Burkholder et al. (2015)</td></tr><tr><td>CO + O + M</td><td>CO<sub>2</sub> + M</td><td>R23 2.2 × 10<sup>-33</sup> exp (-1780/T) [M]</td><td>Zahnle et al. (2008)</td></tr><tr><td>O + O + M</td><td>O<sub>2</sub> + M</td><td>R24 1.2 × 10<sup>-32</sup> (T/300 K)<sup>-2</sup> [M]</td><td>Zahnle et al. (2008)</td></tr><tr><td>H + O<sub>2</sub> + M</td><td>HO<sub>2</sub> + M</td><td>R25 See Eq. (8)</td><td>Zahnle et al. (2008)</td></tr><tr><td>O + O<sub>2</sub> + M</td><td>O<sub>3</sub> + M</td><td>R26 6.1 × 10<sup>-34</sup> (T/300 K)<sup>-2.4</sup> [M]</td><td>Burkholder et al. (2015)</td></tr><tr><td>H + OH + M</td><td>H<sub>2</sub>O + M</td><td>R27 1.7 × 10<sup>-30</sup> (T/298 K)<sup>-2</sup> [M]</td><td>Zahnle et al. (2008)</td></tr><tr><td>OH + OH + M</td><td>H<sub>2</sub>O<sub>2</sub> + M</td><td>R28 See Eq. (8)</td><td>Burkholder et al. (2015)</td></tr><tr><td>H + H + M</td><td>H<sub>2</sub> + M</td><td>R29 2.3 × 10<sup>-32</sup> (T/298 K)<sup>-0.6</sup> [M]</td><td>Zahnle et al. (2008)</td></tr><tr><td>HO<sub>2</sub> + HO<sub>2</sub></td><td>H<sub>2</sub>O<sub>2</sub> + O<sub>2</sub></td><td>R30 3 × 10<sup>-13</sup> exp (460/T)</td><td>Burkholder et al. (2015)</td></tr><tr><td>HO<sub>2</sub> + HO<sub>2</sub> + M</td><td>H<sub>2</sub>O<sub>2</sub> + O<sub>2</sub> + M</td><td>R31 2.1 × 10<sup>-33</sup> exp (920/T) [M]</td><td>Burkholder et al. (2015)</td></tr></tbody></table>

### CRediT authorship contribution statement

**Maxime Maurice:** Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing – original draft, Visualization. **François Forget:** Conceptualization, Methodology, Software, Resources, Writing – review & editing, Supervision, Project administration, Funding acquisition. **Franck Lefèvre:** Conceptualization, Methodology, Software, Writing – review & editing, Supervision. **Aurélien Stolzenbach:** Software, Validation, Formal analysis, Writing – review & editing, Visualization. **A. Yassin Jaziri:** Software, Writing – review & editing. **Martin Turbet:** Software, Writing – review & editing. **Ehouarn Millour:** Software. **Yangcheng Luo:** Writing – review & editing.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The authors thank the two anonymous reviewers for their constructive criticism and comments. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No 835275), project "Mars Through Time". Aurélien Stolzenbach acknowledges the support of project PID2021-126365NB-C21 funded by MCIN/AEI/10.13039/501100011033/ and FEDER. A. Y. Jaziri has received funding from the European Research Council (ERC) under the ERC OxyPlanets projects (grant agreement No 101053033). This study benefited from the IPSL Data and Computing Center ESPRI, which is supported by CNRS, Sorbonne Université, CNES and Ecole Polytechnique, as well as from the High-Performance Computing (HPC) resources of the HPC resources of Center Informatique National de

l'Enseignement Supérieur (CINES) under the allocation n° A01201 10391 made by Grand Equipement National de Calcul Intensif (GENCI). The simulations ran for this study totaled approximately $10^5$ CPU h, amounting to 0.2 tons of CO₂ equivalent.

## Appendix A. Photochemical network

The chemical network used in this study is presented in Table 2 and photo-dissociation reactions are given in Table 3. Specific reaction rates are given below:

$$k_{R1} = \frac{1.5 \times 10^{-13} (T/300 \text{ K})^{0.6}}{1 + \frac{1.5 \times 10^{-13} (T/300 \text{ K})^{0.6} [\text{CO}_2]}{2.1 \times 10^{-9} (T/300 \text{ K})^{0.6}}} \times 0.6 \frac{\frac{1}{1+\log\left(\frac{1.5 \times 10^{-13} (T/300 \text{ K})^{0.6} [\text{CO}_2]}{2.1 \times 10^{-9} (T/300 \text{ K})^{0.6}}\right)^2}}{1+\log\left(\frac{5.9 \times 10^{-33} (T/300 \text{ K})^{-1.4} [\text{CO}_2]}{1.1 \times 10^{-12} (T/300 \text{ K})^{-1.3}}\right)^2} \\ + \frac{5.9 \times 10^{-33} (T/300 \text{ K})^{-1.4}}{1 + \frac{5.9 \times 10^{-33} (T/300 \text{ K})^{-1.4} [\text{CO}_2]}{1.1 \times 10^{-12} (T/300 \text{ K})^{-1.3}}} \times 0.6 \frac{1}{1+\log\left(\frac{5.9 \times 10^{-33} (T/300 \text{ K})^{-1.4} [\text{CO}_2]}{1.1 \times 10^{-12} (T/300 \text{ K})^{-1.3}}\right)^2} \quad (6)$$

$$k_{R25} = \frac{5.3 \times 10^{-32} (T/298 \text{ K})^{-1.8}}{1 + \frac{5.3 \times 10^{-32} (T/298 \text{ K})^{-1.8} [\text{M}]}{9.5 \times 10^{-11} (T/298 \text{ K})^{0.4}}} \times 0.6 \frac{\frac{1}{1+\log\left(\frac{5.3 \times 10^{-32} (T/298 \text{ K})^{-1.8} [\text{M}]}{9.5 \times 10^{-11} (T/298 \text{ K})^{0.4}}\right)^2}}{1+\log\left(\frac{6.9 \times 10^{-31} (T/300 \text{ K})^{-1} [\text{M}]}{2.6 \times 10^{-11} (T/300 \text{ K})^{0.6}}\right)^2} \quad (7)$$

$$k_{R28} = \frac{6.9 \times 10^{-31} (T/300 \text{ K})^{-1}}{1 + \frac{6.9 \times 10^{-31} (T/300 \text{ K})^{-1} [\text{M}]}{2.6 \times 10^{-11} (T/300 \text{ K})^{0.6}}} \times 0.6 \frac{\frac{1}{1+\log\left(\frac{6.9 \times 10^{-31} (T/300 \text{ K})^{-1} [\text{M}]}{2.6 \times 10^{-11} (T/300 \text{ K})^{0.6}}\right)^2}}{1+\log\left(\frac{6.9 \times 10^{-31} (T/300 \text{ K})^{-1} [\text{M}]}{2.6 \times 10^{-11} (T/300 \text{ K})^{0.6}}\right)^2} \quad (8)$$

## Appendix B. PaPy, a chemical pathways analysis solver

PaPy program (Stolzenbach, 2025) is based on the Lehmann's algorithm for solving the chemical pathways analysis as described in Lehmann (2004). The main purpose of such solver is to give a description of chemical pathways representing a specific state of the
<table><caption>**Table 3**
Photo-dissociations.</caption><thead><tr><th>Reactants</th><th></th><th>Products</th><th>Reference</th></tr></thead><tbody><tr><td>O<sub>2</sub> + hν</td><td>→</td><td>O + O</td><td>R32<br>Ogawa and Ogawa (1975), Lewis et al. (1983)<br>Gibson et al. (1983), Minschwaner et al. (1992)<br>Yoshino et al. (1988), Fally et al. (2000)</td></tr><tr><td>O<sub>2</sub> + hν</td><td>→</td><td>O + O(<sup>1</sup>D)</td><td>R33<br>Ogawa and Ogawa (1975), Lewis et al. (1983)<br>Gibson et al. (1983), Minschwaner et al. (1992)<br>Yoshino et al. (1988), Fally et al. (2000)</td></tr><tr><td>O<sub>3</sub> + hν</td><td>→</td><td>O<sub>2</sub> + O</td><td>R34<br>Sander et al. (2006)</td></tr><tr><td>O<sub>3</sub> + hν</td><td>→</td><td>O<sub>2</sub> + O(<sup>1</sup>D)</td><td>R35<br>Sander et al. (2006)</td></tr><tr><td>H<sub>2</sub>O<sub>2</sub> + hν</td><td>→</td><td>OH + OH</td><td>R36<br>Schurgers and Welge (1968), DeMore et al. (1997)</td></tr><tr><td>H<sub>2</sub>O + hν</td><td>→</td><td>H + OH</td><td>R37<br>Mota et al. (2005), Chung et al. (2001)<br>Thompson et al. (1963), Parkinson and Yoshino (2003)</td></tr><tr><td>CO<sub>2</sub> + hν</td><td>→</td><td>CO + O</td><td>R38<br>Huestis and Berkowitz (2010), Starck et al. (2007)</td></tr><tr><td>CO<sub>2</sub> + hν</td><td>→</td><td>CO + O(<sup>1</sup>D)</td><td>R39<br>Huestis and Berkowitz (2010), Starck et al. (2007)</td></tr><tr><td>HO<sub>2</sub> + hν</td><td>→</td><td>OH + O</td><td>R40<br>Sander et al. (2003)</td></tr></tbody></table>

chemical species described by the kinetics rates of a given chemical system.

$$ \Delta C_i = \Delta t \sum_{j=0}^{n} k_j \qquad (9) $$

Eq. (9) describes the fundamental assumption for PaPy (Stolzenbach, 2025) algorithm first detailed in Lehmann (2004). For each chemical species present in the chemical system, its variation $\Delta C_i$ during $\Delta t$ is exactly explained by the sum of each chemical reaction j and its kinetic rate $k_j$ production of loss of the chemical species i. The general principle of PaPy is to arrange according to their lifetime each chemical species. Then, constructing chemical pathways branching existing pathways producing the given chemical species with pathways consuming it while distributing the kinetic rate of each chemical reaction involved. The process iterates with each chemical species with increasing lifetime. PaPy is able to detect sub-pathways and deal with deleted part of the kinetic rates from slow pathways as described in Lehmann (2004). PaPy keeps track of each pathways along computation, active and, contrary to Lehmann (2004) which only stores the deleted flux for each species, deleted pathways alike. This assures a conservation of kinetic rates in the order of machine error.

PaPy main inputs are the kinetic rates of each chemical reactions in the chemical system and the time averaged concentration over $\Delta t$ of each chemical species present in the chemical system. A minimum kinetic rate can be set as to avoid combinatory explosion due to the possible pathways configuration possible. The minimum kinetic rate for pathways has been set-up to 0.01 % of CO₂ equilibrium flux for the results of this study. We ran PaPy until O₂ is a branching point. It means that O(<sup>1</sup>D), OH, H, O, HO₂, O₃, H₂O₂, and O₂ were used as branching points and leaves CO, H₂ and CO₂ as long-term species. We stop the analysis before using CO as branching points since the main destruction of CO₂ is in fact a production of CO via CO₂ + hν → CO + O (R38). Hence, since the restoration pathways of CO₂ all have a net result with CO as a reactant, pursuing with CO as a branching would let us with a close to steady-state CO₂.

## Data availability

Data will be made available on request.

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