follow
the
workflow
previously
described
in
Werlen et al. (2025b): The calculated atmospheric composi-
tions output from the GCE model are input to FastChem for
the initial P-T conditions representing the atmospheric con-
ditions just above the magma ocean. This output is passed
to HELIOS-K to compute gas opacities, which in turn serve
as inputs for HELIOS to derive an atmospheric P–T profile.
The P-T profile, along with the gas composition above the
magma ocean, comprising the lower boundary condition,
is input to VULCAN to compute the steady-state chemical
structure. We use the output from VULCAN to recompute the
opacities with HELIOS-K and update the P–T structure with
HELIOS. This iterative cycle between HELIOS/HELIOS-K and
VULCAN is repeated until convergence is achieved in both
the gas molar mixing ratios and the P-T profile. In VULCAN,
Article number, page 4 of CO and CO2 in both the silicate melts and the atmosphere (Figure 3).

The dominant atmospheric effect of water addition, however, is a dramatic increase in CH4 by at least four orders of magnitude (Figure 3).

The substantial hydrogen supplied by water promotes efficient methane formation (see also Steinmeyer et al. 2026).

As a consequence, carbon is preferentially stored in CH4, while much of the added oxygen is sequestered in the interior.

The net atmospheric effect of adding water is therefore an increase in C/O, despite the higher total oxygen budget.

For a lower temperature TAMOI = 2000 K than the fiducial TAMOI = 3000 K, a remarkable difference is that the water-rock case 4 shows a C/O ratio an order of magnitude lower, reaching sub-solar C/O values.

The C/O ratios of the soot-water-rock case 3 remain high (Figure 2).

The strong increase in CH4 in the water-rich cases 3 and 4 also explains their higher atmospheric metal mass fractions, which exceed 0.7 and approach unity for the soot–water–rock core (case 3).

In contrast, the water–rock case (case 4) remains distinctly below unity and only slightly exceeds values of 0.8.

Planets formed within the water ice line (cases 1 and 2) instead retain hydrogendominated envelopes, with water as the second most abundant species, resulting in atmospheric metal mass fractions below 0.3.

In all cases, the atmospheric metal mass fractions are only marginally sensitive to variations in TAMOI.

We further find pronounced differences in atmospheric mass fractions when comparing the soot–water–rock case (case 3) with the other cases.

The differences are approximately one order of magnitude.

Case 3 exhibits characteristically high atmospheric mass fractions of order 10%, whereas the less volatile-rich cases yield gas mass fractions below 1%.

For cooler interiors with TAMOI = 2000 K these contrasts become less extreme.

The differences decrease to roughly a factor of three, as cases 1, 2, and 4 reach atmospheric mass fractions between 1% and 5%.

The atmospheric mass fraction may therefore help distinguish between the two volatile-rich cases (3 and 4), and thereby constrain the role of soot in sub-Neptune interiors, though its discriminating power is temperature-dependent.

More robustly, the mean molecular weight (MMW) of the atmosphere differs markedly between cases 3 and 4: case 3 yields MMW > 17 reflecting its methane-dominated composition, while case 4 yields MMW < 7.5.

Figure 3 shows the molar mixing ratios of atmospheric species in equilibrium with the magma ocean across all four cases.

Cases 1 and 2 share the same dominant species H2-H2O-SiO in decreasing order.

The main differences between case 1 and case 2 are within the minor species: in the soot-rock case, the CH4 and CO mixing ratios are roughly two orders of magnitude higher than in the rock-only case 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.