H₂O₂ induced greenhouse warming on oxidized early Mars

We have performed two benchmark tests of our simulation code, and we have confirmed that our model reproduce the numerical solutions for the dry and wet CO₂-rich atmospheres of early Mars shown in Ramirez et al. (2014).

We first compare our line-by-line model against a well-tested line-by-line model, SMART (Meadows & Crisp, 1996), for a dry, 2-bar CO₂(95%)-N₂(5%) atmosphere. With the same temperature profile shown in Figure S1 of Ramirez et al. (2014), we calculated the outgoing planetary radiation using our model. Fig. 3 shows a comparison between the SMART result and that from our model. Our model spectra agree well with the SMART spectra, although there is some difference in the wavenumber region from 800 cm^-1 to 1200 cm^-1, which is likely due to the different absorption data used in both studies. The total flux of our model is 87.2 W/m², which agrees well with that found by SMART (88.4 W/m²). Note that the calculated fluxes differ by at most 0.05 %, even if we double the resolution of the wavenumber or the number of vertical layers.

Next, we compare the surface temperatures of a wet, 2-bar CO₂(95%)-N₂(5%) atmosphere with that calculated by the one-dimensional radiative convective model Ramirez et al. (2014). Our results agrees well with those of Ramirez et al. (2014), as shown in Fig. 4, where the differences in the calculated surface temperatures are no more than 4 K. Because the results of our models agree to within 2 % of the previous studies, we have confirmed that our model is consistent with these models.

H₂O₂ is much more abundant in a wet and oxidized atmosphere, though the concentration of H₂O₂ in the current dry Martian atmosphere is about 10 ppb (Encrenaz et al., 2004). Although chemical models suggest that the concentration of H₂O₂ reaches at most 0.1 ppm in dry atmospheres (Parkinson & Hunten, 1972; Gao et al., 2015), a wet and oxidized atmosphere which is suitable for the formation of H₂O₂ would contain H₂O₂ in a concentration higher than 0.1 ppm. This is because H₂O₂ is produced through the chemical reactions of HO_x gas species such as H, OH and HO₂ which originate from H₂O. Also, the abundance of H₂O₂ would be higher in an oxidized atmosphere because such an atmosphere inhibits the regeneration of H₂O from HO_x and enhances the production of H₂O₂.

In a wet and oxidized Martian atmosphere, the photolysis of H₂O₂ is considered to be an effective pathway to regenerate CO₂ (Yung & Demore, 1999). This regeneration is necessary because CO₂ is destroyed by far-UV irradiation ($\lambda\leq$227.5 nm) from the Sun via;

Indeed CO₂ regeneration is required to maintain the CO₂ atmosphere over geological timescales. In a wet atmosphere, H₂O₂ can be sufficiently produced as an intermediate product through the following catalytic cycle:

Meanwhile, although a thick and dry CO₂-rich atmosphere is unstable (Zahnle et al., 2008), in a wet and oxidized atmosphere of early Mars, CO₂ could have been stabilized by S1 (=R2+R3+R4+R5) even if the atmosphere was thick.

We estimate the H₂O₂ abundance in a warm/wet and oxidized CO₂ atmosphere by assuming that S1 is the cycle most responsible for the regeneration of CO₂ against loses due to R1. We assume that the bulk CO₂ abundance in the atmosphere is in balance between its photo-dissociation flux (R1), and twice the H₂O₂ photo-dissociation flux (R4) that produces OH for oxidizing CO. Also, it is assumed that there is no optical shielding effect for photons with wavelengths longer than the shielded wavelength, $\lambda_{\mathrm{sh}}$, but there is complete shielding for all other UV photons to H₂O₂, for simplicity. Then, the vertical column density of H₂O₂, $\Sigma_{\mathrm{H_{2}O_{2}}}$, can be written as;

where $\hat{F_{\lambda}}$ is solar photon flux, and $\sigma_{\mathrm{diss},\lambda}$ and $\lambda_{\mathrm{th}}$ are the photo-dissociation cross section and the threshold wavelength for a photon to effectively dissociate H₂O₂, respectively. Owing to the low bonding energy of H₂O₂ ($\sim$ 50 kcal/mol $\sim$ 570 nm; Bach et al. 1996), the photo-dissociation is caused not only by UV but also by visible light photons. Therefore, H₂O₂ is not completely shielded from stellar irradiation by H₂O, O₂ and CO₂ (Yung & Demore, 1999). On the other hand, a developed O₃ layer may shield solar photons with wavelengths $\lesssim$ 300 nm, as displayed on Earth today. Here we use $\lambda_{\mathrm{sh}}=227.5$ nm and 300 nm as fiducial values of a shielded wavelength.

The dissociation cross section of H₂O₂ has been measured only for photon wavelengths in the range $\leq$ 410 nm (Kahan et al., 2012) because of the technical problem of measuring small absorption cross sections. Hence, we use $\lambda_{\mathrm{th}}=410$ nm as a fiducial value of the threshold wavelength. Note that, according to Kahan et al. (2012), the photolysis of H₂O₂ mainly occurs at photon wavelengths shorter than 350 nm. Therefore, inputing $\lambda_{\mathrm{sh}}=227.5$ nm, the measured cross section with $\lambda_{\mathrm{th}}=$ 410 nm (Lin et al., 1978; Kahan et al., 2012) and the solar spectral irradiance at 4 Ga developed by combining the observed spectrum from the Sun with those of solar-type stars at different ages (Claire et al., 2012) in Eq. (3), we find $\Sigma_{\mathrm{H_{2}O_{2}}}\sim 8\times 10^{17}$ cm^-2. When we substitute $\lambda_{\mathrm{sh}}=300$ nm into Eq. (3), we find $\Sigma_{\mathrm{H_{2}O_{2}}}\sim 5\times 10^{18}$ cm^-2. These values change only 10 % if the solar spectral irradiance at 3.5 Ga is used instead.

The column densities estimated here are significantly larger than the current typical value of $\sim 2\times 10^{15}$ cm^-2, which corresponds to 10 ppb at 6 mbar, in the present-day Martian atmosphere. These large column densities produce optical depth over wavenumbers $\nu=100$–500 cm^-1 of $\tau_{\nu}=0.003$–0.6 for $\lambda_{\mathrm{sh}}=227.5$ nm and $\tau_{\nu}=0.02$–4 for $\lambda_{\mathrm{sh}}=300$ nm, assuming a far-IR absorption cross section of H₂O₂, $\sigma_{\nu,H_{2}O_{2}}=0.04$–$8\times 10^{-19}$ cm², which is shown in Fig. 1. Thus, if the other gases such as O₃ sufficiently can reduce the photolysis of H₂O₂, then the amount of H₂O₂ in the atmosphere would be large enough to warm the planetary surface. Note that, the column density of H₂O₂ estimated by Eq. (3) is just a typical value when S1 is the cycle most responsible for the stabilization of CO₂, while this value could be increased if the self-shielding effect was taken into account in Eq. (3). This is because we impose the restriction that only the OH produced by the photolysis of H₂O₂ is used to oxidize CO via R5, but all other reactions which produce and remove OH are ignored. Also, the other process potentially affecting the concentration of H₂O₂ is discussed in Sec 4.3.

It is likely that H₂O₂ in a warm and wet atmosphere of early Mars is super-saturated because the timescale for condensation is likely longer than that for photochemical production. As described later, a timescale for condensation would be much longer than that that governing the production and photo-dissociation of H₂O₂, which was shown by Nair et al. (1994), who used a photochemical model, to be of order several hours.

The condensation time can be estimated by assuming that H₂O₂ condenses as soon as it collides with condensation nuclei, namely;

where $r$ and $N_{\mathrm{ccn}}$ are the size and concentration of the condensation nuclei, respectively, $\rho$ is the atmospheric mass density and $v_{T}$ is the thermal velocity of the gas. The timescale for condensation is longer at higher altitudes because the nuclei concentration decreases with increasing altitude. Note that, the condensation timescale is underestimated in an atmospheric region with a mean free path smaller than the size of the nuclei (i.e., a dense region) because the diffusive motion of the gas around the nuclei delays the timescale (see Lohmann et al., 2016, for the diffusive case).

Achieving sufficient warming is possible even if H₂O₂ condenses at lower altitudes due to the subsequent shorter condensation times. Fig. 7 shows the minimum H₂O₂ concentration necessary for maintaining a surface temperature of at least 273 K in a 2-bar atmosphere as a function of a condensation altitude. The condensation altitude stands for an altitude above which the H₂O₂ concentration is constant and below which all the H₂O₂ gas is virtually removed by rainout through condensation. To warm the surface environment, the required concentration of H₂O₂ needs to be about 2 ppm when the condensation altitude is no higher than about 20 km. The 2 ppm of H₂O₂ in the upper atmosphere is comparable to 1.5$\times$10¹⁹ cm^-2 which is also comparable to the H₂O₂ column density necessary to stabilize the CO₂ atmosphere (Sec 4.1).

The condensation timescale will not be significantly changed if the dilution effect of H₂O₂ in an H₂O solution is taken into account. When the temperature is above $\sim 220$ K, an H₂O–H₂O₂ solution can exist, and then the saturation vapor pressure of H₂O₂ will be lowered relative to that of pure H₂O₂ (Foley & Giguére, 1951b; Manatt & Manatt, 2004). However, the temperatures in the photosphere for photons with wavenumbers in the range $\geq$ 500 cm^-1 are lower than 220 K in thick and warm atmospheres (Fig. 5). So, it is likely that aqueous solutions would be frozen in the upper atmosphere where the concentration of H₂O₂ has the greatest influence on the surface temperature. Therefore, the dilution effect of H₂O₂ in an H₂O solution would little affect the surface temperature.

The atmospheric concentration of H₂O₂ can also be affected by several processes such as dissolution into water droplets, dry deposition and photochemical reactions with volcanic and reactive species (e.g., SO₂ and NO_x) (Vione et al., 2003).

Although H₂O₂ is a minor species with at most 3.5 ppb level in the Earth’s atmosphere, which is mainly due to the dissolution of gaseous H₂O₂ into water droplets, where SO₂ enhances the dissolution rate (Vione et al., 2003), it might not be a minor species on early Mars during the era in which the observed Mn-oxide-rich rocks at Gale crater would have precipitated out. Since the temperatures at high altitudes in the early Martian atmosphere would be so low that H₂O would freeze, its non-dissolution into water droplets would not deplete H₂O₂. Meanwhile, at lower altitude regions, H₂O₂ would dissolve into water droplets, and precipitation would remove it.

In Earth’s atmosphere, dry deposition is another removal process of atmospheric H₂O₂ at lower altitudes. Atmospheric H₂O₂ of early Mars would be vertically transported by eddy diffusion to the surface, whereby dry deposition and precipitation remove it. For the current Martian atmosphere at altitudes lower than 40 km, the scale height is $H\sim 10$ km and the vertical eddy diffusion coefficient is $K_{\mathrm{ed}}\leq 10^{7}$cm²/s (Nair et al., 1994); hence the diffusion timescale is $H^{2}/K_{\mathrm{ed}}\geq 1$ days. Since the timescale of H₂O₂ photochemical reactions is less than a day (Nair et al., 1994; Zahnle et al., 2008), the atmospheric concentration of H₂O₂ at high altitudes is likely controlled by photochemical reactions.

The actual eddy diffusion coefficient and dry deposition timescale on early Mars would depend on turbulence/large-scale-winds and the compositions/oxidations states of the surface rocks, respectively. As such, a more detailed examination requires that photochemical calculations be done alongside those of the atmospheric thermal structure, which will be the focus of a future study.

An early surface environment warmed by the greenhouse effect of H₂O₂ (Sec. 4.1) is consistent with the global, highly oxidized conditions implied by the high Mn materials found on the Martian surface by the Curiosity rover in Gale crater and by the Opportunity rover in Endeavour crater (Lanza et al., 2016; Arvidson et al., 2016).

The redox state of early Martian atmosphere is likely controlled by the escape of atmospheric components into space. In the early Martian atmosphere, UV radiation from the young Sun would have enhanced hydrogen escape and effectively oxidized the atmosphere and the surface environment. In addition to hydrogen escape, the escape of atomic carbon might also have contributed to the oxidation of the early Martian atmosphere because its escape flux would not be limited by diffusion in a CO₂-rich atmosphere (N. Terada, private communications). Further studies are required to determine the redox state of the early Martian atmosphere, which could also be affected by the supply of reduced gases (e.g., CO and H₂) through volcanic degassing, oxygen escape, and oxygen uptake through weathering of the planetary surface (Zahnle et al., 2008; Wetzel et al., 2013; Batalha et al., 2015).

It is interesting to note that H₂O₂ might be able to warm a frozen planet and melt water ice. Liang et al. (2006) demonstrated that a weak hydrological cycle coupled with photochemical reactions could give rise to a sustained production of H₂O₂ during long and severe glacial intervals. Although an icy surface has a high albedo, the surface temperature can be warmed to temperatures above 273 K by a 4 and 15 ppm levels of H₂O₂ in a 2 bar atmosphere when the planetary albedo is assumed to be $\leq$ 0.45 and $\leq$ 0.5, respectively, as demonstrated by our model.

It has also been suggested that H₂O₂ deposited on the planetary surface could be stored in the ice during the time of a global snowball episode (Liang et al., 2006). If early Mars was once a snowball, and a large amount of H₂O₂ was stored in the ice, it would be released into the atmosphere upon melting caused by any mechanism, such as meteor impacts, volcanic emissions, or obliquity changes (e.g., Wordsworth, 2016, references therein). The release of abundant H₂O₂ would cause not only a global oxidation event but also enhance greenhouse warming. If so, there might be geological evidence that oxidation and warming occurred simultaneously in the aftermath of a snowball Mars.