Entry Physics.

Particles with a diameter of less than 1 mm are too small to generate a bow shock during atmospheric entry (6), meaning that micrometeorites smaller than this do not create the shock waves or gas caps that typically form around larger particles under these conditions. The interaction between the smaller micrometeorites and the atmosphere is therefore thought to be simple, as no shock-induced chemical alteration occurs to the surrounding air during entry. Instead, the micrometeorite is simply slowed by, and may react with, the gas it encounters. Deceleration is a function of momentum exchange, and frictional heating during deceleration is what causes the micrometeorite to briefly melt and quench crystallize. The speed of the micrometeorite decreases by a factor of 1/e for each particle mass column of gas that the micrometeorite impacts, assuming all of the gas momentum is transferred to the micrometeorite. A micrometeorite’s speed would decrease to 0.37 and 0.135 of the initial speed after colliding with gas equal to 1 and 2 particle masses, respectively. Faster micrometeorites would encounter more air while molten because of their greater momentum.

The temperature of an entering micrometeorite depends on its velocity and on the ambient gas density, such thatradiated power=14·(12ρair)·v3.[1]Here, ρair is the ambient air density and v is the micrometeorite’s entry velocity. The melting temperature of Fe and its oxides is ∼1,500 °C, so the micrometeorite’s speed must be above 6 km/s at 80 km and above 9 km/s at 85 km (in the modern Earth’s atmosphere) to reach the melting point. To take up oxygen and form the mix of magnetite, wüstite, and metal observed in the Tomkins et al. (5) spherules, the micrometeorites need to be molten.

Depending on size and particle speed, most micrometeorites should contact 1 to 2 equivalent masses of air in the time that they are traveling fast enough to be heated to their melting points. A complication is that the micrometeorites are potentially evaporating some fraction of their mass during entry, and this is strongly dependent on entry angle and initial micrometeorite size. Evaporative mass loss during entry would likely decrease the number of Fe atoms that would need to be reacting with oxidants for the micrometeorite to be fully oxidized. But newly acquired oxygen may be lost as well, and so the uncertainties associated with mass loss make it difficult to constrain in our calculations without knowing more about entry angle and initial size. For this study, we assume that the micrometeorite retains most or all of the oxygen it encounters, along with its own initial mass, so oxidizing the micrometeorites is therefore a function of how much oxygen the meteorite encounters in the upper atmosphere while molten.

Tomkins et al. (5) assumed that the altitude region within which the micrometeorites were molten would be the same in the Archean as it is in the modern atmosphere (between ∼75 and 90 km, as ref. 6 specified). But the deceleration—and frictional heating—of a micrometeorite depends on the number of particles it encounters during entry. Thus, the window in which oxidation occurs is not located at a fixed altitude range, but rather at a fixed pressure range. Pressure in our model Archean atmosphere falls off more rapidly than in the modern atmosphere (SI Appendix, Fig. S1B) because of the cooler, ozone-poor stratosphere, along with the higher mean molecular weight caused by increased CO₂. Thus, the “oxidation altitude range” of 75 to 90 km for the modern atmosphere should really be redefined as an “oxidation pressure range” from ∼2.3 × 10⁻⁵ bar to ∼1.6 × 10⁻⁷ bar. The corresponding altitude of oxidation therefore varies with the CO₂ concentration and is generally lower than assumed by Tomkins et al. (5) (Table 1).

Micrometeorite Oxidation Chemistry.

In a Neoarchean atmosphere with a primarily N₂-CO₂ composition, upper atmospheric chemistry would be dominated by the reactionCO2+hv→CO+O.[2]Direct recombination of CO with O is spin forbidden, and therefore slow, so O primarily recombines with itself to form O₂:O+O+M→O2+M.[3]In terms of micrometeorite oxidation, it should not matter much whether oxygen was present as O or O₂, as the high temperature of the molten iron micrometeorites should allow all of the gaseous species interacting with them to equilibrate with each other on short timescales.

Tomkins et al. (5) considered O₂ only as a potential oxidant, assuming that the concentration of other forms of oxygen would be negligible. Their figure 4 shows calculations by Zahnle et al. (9) that appear to support this assumption. But our own photochemical model of the 2.7-Ga atmosphere indicates that both O₂ and O would be present in the stratosphere (Photochemical Calculations). The Zahnle et al. model (9, 10), which is a derivative of our model, would almost certainly yield the same result. However, those authors were focused on the lower atmosphere and simply did not include O in their figure.

It is also possible—even likely—that CO₂ itself was an oxidant for the micrometeorites. Tomkins et al. (5) argued that Fe oxidation by CO₂ would be slow, based on studies of Fe metallurgy at temperatures below 1,470 K (11, 12). But iron micrometeorites (and iron oxide) need to reach at least ∼1,770 K during entry to melt (6). Shock tube experiments above the Fe melting temperature indicate that oxidation rates of Fe to FeO by O₂ (13) and CO₂ (14) are roughly equal and are up to 3 orders of magnitude faster than reduction of FeO by CO (15). Other possible oxidation reactions include O₂ oxidation of Fe to FeO₂ (16) and CO₂ oxidation of FeO to FeCO₃ (17) at similar reaction rates. But it is worth noting that O can also reduce FeO to form O₂ in the upper mesosphere (18), albeit at much lower temperatures than the micrometeorites would experience during entry. Until experimental chemical reaction rate data are obtained for the appropriate temperature and pressure range, we cannot definitively state which oxidation and reduction reactions are likely to dominate. Nonetheless, the CO₂ oxidation pathway indicates the value such experiments would have for micrometeorite analysis—and, for now, existing data point to its potential significance for the Tomkins micrometeorites. In short, it suggests that at least one O atom from each CO₂ molecule may contribute to micrometeorite oxidation during entry. It also suggests that reduction of the newly formed Fe oxides by CO is unlikely to occur during the short time that the micrometeorite is molten and that accumulating an adequate amount of oxidant in the oxidation pressure range is more important than the ratio of oxidants to reductants.

If so, then one should consider the oxidation potential from O, O₂, and CO₂ within the oxidation pressure window. And this, in turn, makes the calculation quite simple, as nearly all O and O₂ in the upper atmosphere is derived from CO₂. O atoms are neither created nor destroyed in the atmosphere above the altitude at which they are removed by rainout of H₂O. Thus, from mass balance, it is easy to demonstrate (SI Appendix) that if O₂ concentrations are low near the surface, and if H₂O concentrations are low at the tropopause, thenf(O)+2fO2+fCO2=const.=fCO20.[4]Here, f_i is the volume mixing ratio of species i and fCO20 is the mixing ratio of CO₂ at the surface. More precisely, fCO20 is the mixing ratio of CO₂ at the base of the stratosphere; however, the difference between this value and the surface CO₂ mixing ratio is negligible. Thus, in our analysis, the key parameter is the CO₂:N₂ ratio at the surface. CO₂ oxidizes the micrometeorites, whereas both CO₂ and N₂ decelerate the meteorites. The CO₂:N₂ ratio determines whether or not they are oxidized, independent of particle size.

To make this analysis more concrete, consider the modern atmosphere, within which we know that incoming metal micrometeorites are partly to fully oxidized to form a mix of Fe_(1-x)O (wüstite), Fe₃O₄, and sometimes iron metal during entry (6). For total oxidation, this requires the addition of 1 to 1.3 O atoms per iron atom. In the modern atmosphere, this oxidation is accomplished almost exclusively by O₂. Assume for now that the particle remains molten, and hence reactive, only during its encounter with the first equivalent air mass. Because the atomic mass of Fe (∼56 amu) is just under twice the average atmospheric mass (29.6 for N₂-O₂-⁴⁰Ar), the micrometeorite should encounter about twice as many air molecules as it contains Fe atoms while it is still molten. Of these, 21% are O₂ molecules. Therefore, the ratio of O₂ molecules encountered to Fe atoms within the micrometeorite is equal to 2 × 0.21 ≅ 0.4. The ratio of O:Fe is twice that, or 0.8. This ratio is close enough to the O:Fe ratio required to form the observed oxides (as the micrometeorites contain some varying fraction of Ni instead of Fe), provided that oxidation is total and nearly 100% efficient. We can express this relationship compactly by writing(5629.6)⋅2fO2≅0.8.[5]Now, let us apply this same logic to the Neoarchean atmosphere, assuming that it consists primarily of N₂ and CO₂ within the oxidation pressure window. (Fig. 1 and SI Appendix, Fig. S2 show that this is approximately true.) The mean molecular weight of the atmosphere is thenMat≅44fCO2+28(1−fCO2).[6]Here, fCO₂ is effectively fCO20, the CO₂ mixing ratio at the ground. We use these terms interchangeably from here on. Using the identical requirement of 0.8 O atoms per Fe atom for complete oxidation then yields(56Mat)fCO2=(56fCO244 fCO2+28(1−fCO2))≥0.8or(2fCO21+(47)fCO2)≥0.8.[7]Solving for fCO₂ gives a minimum value of 0.52 needed to oxidize a micrometeorite encountering one equivalent mass of air during entry.

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Fig. 1.

Vertical profiles of major constituents mixing ratios for fCO₂ = 25%, close to our minimum estimated value. The pressure range for micrometeorite oxidation is indicated by the shaded yellow region. The modern O₂ mixing ratio is shown by the vertical dotted line. Atmosphere also contains 0.8 bar N₂.

Suppose now that the meteorite remains molten during its encounter with 2 equivalent air masses. The required CO₂ mixing ratio is lower, but not exactly by a factor of 2. The analog to Eq. 7 is(56Mat)⋅2fCO2=(56fCO244fCO2+28(1−fCO2))≥0.8or, more simply,(4fCO21+(47)fCO2)≥0.8.[8]Solving for fCO₂ in this case yields a value of 0.23. It is slightly less than half the value predicted from Eq. 7 because the mean molecular weight of the atmosphere is lower, causing the micrometeorite to encounter more air molecules as it decelerates.

Similar calculations can be performed for the case when CO₂ is not considered to be an oxidant for Fe. We do this here because it remains unclear which assumption is actually correct. In this case, CO₂ and N₂ would still be the dominant constituents in the oxidation pressure range, so M_at remains unchanged, but the fraction of oxidant is fO_oxy ≡ (fO + 2 fO₂), rather than fCO₂. Thus, if the particle remains molten during encounter with one equivalent air mass, we can write(56Mat)fOoxy=fOoxy(5644fCO2+28(1−fCO2))≥0.8or(2·fOoxy1+47fCO2)≥0.8.[9]The value of fO_oxy needed to oxidize the micrometeorites still depends on the mixing ratio of CO₂, but the relationship is more complicated, as O and O₂ are both produced, directly or indirectly, from CO₂ photolysis. Thus, a photochemical model is needed to determine this relationship. We have performed such modeling (Photochemical Calculations) and, not surprisingly, the required atmospheric CO₂ mixing ratios for micrometeorite oxidation using only O and O₂ are much higher. For a 2-air-mass oxidation event, the required value of fO_oxy in Eq. 9 is cut exactly in half, as the mean molecular mass does not change. But, as we shall see, attaining even this lower value of fO_oxy is difficult to achieve in a realistic Archean atmosphere.

Methods.

Photochemical model calculations are required if CO₂ is not included as a possible oxidant for Fe micrometeorites. For our calculations, we used a version of our 1D photochemical model developed for high-CO₂, low-O₂ atmospheres (19). Our model contains 49 chemical species involved in 221 reactions (see supporting information in ref. 20 for the full list). It extends upward from the Earth’s surface to 100 km in 1-km thick layers. Vertical mixing is parameterized as a combination of eddy and molecular diffusion, using a profile appropriate for the modern atmosphere (21). Absorption and scattering of solar radiation were calculated using a 2-stream algorithm (22), assuming a fixed solar zenith angle of 50°. The time-dependent, coupled chemistry/diffusion equations were integrated to steady state using the (fully implicit) reverse Euler method. We also calculated changes to the solar UV flux using a parameterization developed by Ribas et al. (23). Properly scaling the UV flux is essential for this analysis, as the rate of free oxygen production via CO₂ photolysis depends on this parameter. At 2.7 Ga, the Sun would have been only ∼81% as bright as today in the visible wavelength range (24, 25), but ∼50% brighter than today at far-UV wavelengths (<1,750 Å).

Calculations were performed for a 1-bar, CO₂-N₂ atmosphere with 1 to 50% CO₂, along with low concentrations of methane (below). We should note that we are solving minor-constituent diffusion equations for major species, which introduces some error in the ratio of CO₂:CO:O at high altitudes in the model atmosphere. However, this should have little effect on our results because, as discussed earlier, it is only the sum of CO₂, O₂, and O that matters, as iron reduction by CO is slow. Furthermore, the largest errors in these ratios occur close to the top of the model atmosphere, above the altitude range at which most meteorite oxidation occurs.

We assumed a simplified temperature structure that decreases from 285 K at the surface to 175 K at 9.5 km and then remains constant above that height (SI Appendix, Fig. S1A). This is consistent with predictions from 1D climate models (e.g., ref. 26), which suggest that the temperature profile of an ozone-free atmosphere should follow a moist adiabat from the surface up to the tropopause and then become roughly isothermal above that altitude. We have not attempted to keep the surface temperature consistent with the assumed CO₂ concentration and solar flux in these calculations, reasoning that upper atmospheric composition should be relatively insensitive to this parameter. We examine the implications of atmospheric composition and photochemistry on surface temperature in our climate calculations (Discussion).

An upward CH₄ flux of 3.0 × 10⁹ molecules⋅cm⁻²⋅s⁻¹ was assumed for our photochemical calculations. This is about 3% of the present CH₄ flux and well below the estimated CH₄ flux during the Archean (27). Unlike Tomkins et al. (5), we do not rely on a stratospheric temperature inversion to help build up upper atmospheric O₂, and so we avoid the regime in which fCH₄/fCO₂ > 0.1 and in which organic haze may form (28). The actual amount of CH₄ present should have little effect on micrometeorite oxidation; however, it does have implications for climate at that time, so we return to this issue in Discussion.

Data for both photochemical and climate model calculations are available on request from the corresponding author.

Results.

Vertical profiles of major atmospheric constituents for our 25% CO₂ case are shown in Fig. 1. Key reducing and oxidizing species in the upper atmosphere at different CO₂ concentrations are shown in SI Appendix, Fig. S2. Both O and O₂ are present within the micrometeorite oxidation pressure range, with O dominating in the upper part of this region and O₂ in the lower part. In all these simulations, the sum of fO + 2fO₂ (fO_oxy) is much less than fCO₂. That is because virtually all of the O and O₂ is coming from CO₂ and because CO₂ itself is relatively resistant to photolysis (CO₂ photolyzes only below ∼200 nm, where the solar UV flux is relatively low). Accumulating large amounts of O and O₂ in the stratosphere would require unrealistically low eddy mixing. Tomkins et al. (5) argued that such low mixing might result from a stratospheric temperature inversion caused by the presence of organic haze. But the eddy diffusion profile used here already accounts for this phenomenon, as it was derived for the modern stratosphere which has a temperature inversion caused by ozone.

Even with CO₂ concentrations as high as 50%, the fraction of the atmosphere within the oxidation pressure range that is composed of O and O₂ combined is less than 2% (SI Appendix, Fig. S2). Oxidizing the micrometeorites with oxygen alone (Eq. 9) requires reaching a value of fO_oxy roughly 10 times higher than this. Doing so would thus require both an extremely high CO₂ concentration and extremely low eddy mixing. It is therefore difficult, or even impossible, to oxidize the Tomkins et al. (5) micrometeorites using just O and O₂, unless O₂ was abundant throughout the atmosphere. But this possibility is ruled out by geologic data, including sulfur isotope studies, as mentioned earlier. It is much more likely that the micrometeorites were oxidized by CO₂, in which case the limits on fCO₂ derived in Micrometeorite Oxidation Chemistry remain applicable.