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There are three problems to consider. First, Gaillard et al.1 argue that the release of SO2 comes at the expense of H2S, according to:

But the extra H2 released by this reaction exactly compensates for the switch from H2S to SO2. The mixture of SO2 and H2 has the same redox potential as H2S and water2. Fortunately, what happens in their model is different. The H2S to SO2 ratio is buffered by magma, which has a fixed oxidation state, described in terms of a fixed oxygen fugacity. The relevant reaction is:

where ‘O2’ represents oxidants (mostly ferric iron) in the melt. Reaction (2) produces SO2 and H2 in equimolar proportions, in agreement with results shown in figure 2 of ref. 1. When SO2 is reduced to pyrite, FeS2, it consumes hydrogen as follows:

Because reaction (3) consumes more hydrogen per mole of SO2 than is produced by reaction (2), the net effect is to oxidize the atmosphere. Thus, this part of their proposed atmospheric oxidation mechanism appears to work, but not for the reasons they stated.

The second issue is that sulphur-containing gas fluxes are not the only ones that control O2. CO2 is crucial because some CO2 is reduced to organic carbon, CH2O, which is then buried. A mole of photosynthetic O2 is released for every mole of buried CH2O. However, O2 can be lost in atmospheric reaction with H2, so the net effect is:

The carbon isotope record suggests that 20% of outgassed CO2 is reduced and buried in this manner3,4. Holland4 quantified the effect of volcanic gases on the hydrogen budget by defining a parameter denoted f. Gases for which f > 1 can reduce 20% of the CO2 to organic matter and all of the SO2 to pyrite, leaving excess hydrogen to support an anoxic atmosphere; gases with f < 1 contain too little hydrogen to do this. Atmospheric O2 ‘wins’ over hydrogen when f drops below unity. This analysis neglects other sources of hydrogen that might have been important (for example, serpentinization of ultramafic rocks on the continents and seafloor, or precipitation of ferric iron in banded iron formations), but it is useful for analysing the volcanic gases of ref. 1.

In the model of Gaillard et al.1, the proportion of CO2 in released volcanic gases decreases by a factor of 3 when volcanoes switch from submarine to subaerial conditions because the pressure decreases from 100 bar to 1 bar. This change should tend to oppose atmospheric oxygenation, as less organic matter is buried (given a constant burial fraction), and thus less H2 is consumed. To estimate the net effect on atmospheric redox balance, we calculated f values for cases listed in the Supplementary Information of ref. 1. Gaillard et al.1 include S2 as a species, which requires us to modify Holland’s f parameter, as follows:

Here, m(i) is the mole fraction of species i in the released gases. As shown in Table 1, f is less than unity in the cases shown in Supplementary Tables 1 and 2 of Gaillard et al.1, and so would not allow a reduced atmosphere before 2.4 Gyr ago. This means that no rise of O2 is possible because the initial atmosphere is already oxidized. This could be because other hydrogen sources are neglected, as mentioned above, or because model parameters—for example, the outgassing temperature—are incorrect. In any case, the model, as presented in ref. 1, appears incapable of triggering a rise in atmospheric oxygen if Holland’s method of analysis is correct.

Table 1 f values for different cases from ref. 1

Last, Gaillard et al.1 assume that gases released from a submarine magma at 1,300 °C do not re-equilibrate with the surrounding basalts at lower temperatures as they emerge from depth; this assumption is at odds with previous work5,6. Such re-equilibration might have allowed Archaean volcanic gases to be more reduced; hence, a switch to subaerial volcanism around 2.5 Gyr ago might then result in atmospheric oxidation. But this would be a different oxidation mechanism from the one described in ref. 1. There is also a broader caveat. The reduced oxidation state of volcanic gases comes at the expense of oxidizing the source rocks; thus, erosion and subsequent reduction of the source rocks may cancel out surficial redox change in the long term.