1, increasing from ∼10−7 to ∼10−5.

Despite this relative enhancement, both cases 1 and 2 remain strongly depleted in carbon-bearing species overall.

The soot–water–rock case (case 3) differs fundamentally: its atmosphere is methane-dominated at the magma ocean interface, with major species in decreasing order of CH4, CO, H2, and H2O.

This distinct composition arises from case 3’s exceptionally high combined mole fraction of C, O, and H (∼90%), distributed as approximately 70% H, 20% O, and 10% C.

The water-rock case (case 4) has a similarly high combined C-O-H budget, but is carbon-poor in its elemental distribution (∼74% H, 26% O, <1% C), producing
an H2-dominated atmosphere with CH4, H2O, and CO as the next most abundant species.

Taken together, these results establish a clear compositional dichotomy: planets assembled from soot and water are predicted to be methane-dominated worlds, fundamentally distinct from those formed from either component alone, which retain hydrogen-dominated atmospheres.

The gas composition across all cases depends only weakly — to second order — on the accreted primordial gas fraction in the range explored (1–9%), while varying substantially between formation cases.

This robustness supports the interpretation of our results as reflecting primarily the bulk composition of the planetary building blocks rather than uncertainties in gas accretion history.
3.1.

Upper atmosphere signatures Having established how bulk core composition shapes the chemical equilibrium state at the magma ocean interface, we now trace how these deep atmospheric signatures propagate into the upper, observable atmosphere.

Figure 4 shows the full atmospheric profiles — pressure–temperature structure, vertical mixing ratios, and mean molecular weight — for the soot-bearing cases (cases 2 and 3) and the water–rock case (case 4).

We restrict attention to these three scenarios as they span the most chemically distinct outcomes identified in Section 3, and display only the dominant carbon- and oxygen-bearing species.

Refractory gases such as SiO2, Mg, and Fe are omitted as they are likely to condense before reaching the observable atmosphere.

The pressure–temperature profiles (top panel) are broadly similar across cases, with one notable exception: below ∼0.01 bar, the soot–water–rock case (case 3) develops two distinct convective regions, whereas the soot–rock case (case 2) exhibits only a single deep convective zone.

We attribute this structural difference to the higher mean molecular weight and methane-dominated composition of case 3, which alters the thermal gradient in the upper atmosphere.

Because refractory condensation is not included in our atmospheric model, however, this feature should be treated with caution and may be modified in more complete treatments.

The middle panel shows the vertical mixing ratios of the dominant carbon- and oxygen-bearing species as a function of pressure.

Under weak vertical mixing, the mixing ratios decrease substantially above ∼10−3 bar as molecules become photochemically dissociated.

In the strong-mixing regime (high Kzz), vertical transport continuously replenishes these species from depth, limiting compositional gradients to within roughly one order of magnitude and confining them primarily to the deep atmosphere between 10 and 1000 bar.

These dynamics are reflected directly in the mean molecular weight profiles (bottom panel).

Under strong mixing, the MMW remains nearly constant with pressure across all cases.

Under weak mixing, the MMW can vary by up to one order of magnitude in case 3, while changes are moderate for other cases.

The sensitivity of the MMW to mixing strength is therefore most pronounced in case 3, where photochemistry dramatically lightens the upper atmosphere.

Despite this sensitivity to vertical mixing, the fundamental chemical differences between cases identified at depth remain discernible within the pressure range Article number, page 5