, fOmelt
, which governs melting behaviour at high pressure, and a surface oxygen fugacity, fOsurf
, which controls near-surface outgassing and volatile speciation.

This distinction reflects an effective pressuredependence of fO2, consistent with experimental and theoretical results indicating that oxidation state may vary between deep and shallow mantle conditions.

Recent experiments by Lin et al. (2024) suggested that increasing fOmelt
depresses the solidus relative to reduced baseline measurements (Trønnes 2000; Trønnes & Frost 2002; Ishii et al. 2018).

This effect is attributed to increased Fe3+ concentrations in the melt, which act as incompatible species that lower the activities of major cation-bearing components and thermodynamically stabilize the liquid phase relative to crystalline minerals.

As a result, oxidizing conditions can significantly depress the solidus by hundreds of Kelvin across a broad pressure range highlighting the combined influence of melt composition and pressure on magma ocean stability (Shahar et al. 2021; Lin et al. 2024).

This redox-dependent shift in the melting curves influences where a planetary interior temperature profile intersects the solidus, thereby affecting the onset of crystallisation, the depth and longevity of the magma ocean, and the efficiency of volatile exchange between the interior and the growing atmosphere.

In principle, increasing fO2 should shift
melting curves to lower temperatures, allowing melting to persist to greater depths and potentially prolonging magma-ocean lifetimes, whereas more reducing conditions would be expected to favour earlier crystallisation.

In addition to the effects of oxygen fugacity, dissolved volatiles also modify mantle melting relations.

Experimental studies indicate that H2O and CO2 can significantly depress silicate melting temperatures by altering melt structure and phase relations.

In particular, water promotes hydroxylation of the silicate network (Katz et al. 2003), whereby H2O is incorporated into the melt as OH−, weakening the mineral framework and stabilizing the liquid phase.

This volatile-induced modification of melt properties lowers the solidus and can influence the thermal evolution and longevity of magma oceans (Dasgupta & Hirschmann 2007; Myhill et al. 2017; Xie et al. 2024).

However, explicitly resolving how evolving volatile contents feedback on mantle melting introduces additional complexity that lies beyond the scope of the present study.

In this work, we extended the PROTEUS simulation framework (Lichtenberg et al. 2021; Nicholls et al. 2024, 2025a,b; Nicholls 2026) to quantify the influence of redox-dependent melting relations and volatile speciation on the coupled thermal and compositional evolution of magma ocean planets.

We explicitly distinguished between the deep-mantle oxidation state, fOmelt
, which governs melting behaviour and interior cooling, and the surface oxidation state, fOsurf
, which regulates outgassing and atmospheric composition.

As a reference case, we adopted the super-Earth exoplanet GJ 1132 b, discovered by Berta-Thompson et al. (2015) using the MEarth-South telescope array.

It orbits a nearby M dwarf star at 12.04 pc, with a mass of 1.62 ± 0.55 M⊕, a radius of 1.16 ± 0.11 R⊕, and a bulk density of 6.0 ± 2.5 g cm−3, consistent with a rocky composition (Southworth et al. 2017).

Receiving approximately 19 times Earth’s insolation, it represents a benchmark target for testing magma ocean and atmospheric evolution models under strong stellar irradiation.

With Teq ≈584 K and AB = 0.19+0.12 −0.15(Xue et al. 2024), its atmospheric characterisation history includes previously claimed detections of H2O, CH4 and H2-dominated envelopes (Southworth et al. 2017; Swain et al. 2021; May et al. 2023).

More recent and higher-precision JWST observations have progressively converged toward a bare-rock interpretation (Xue et al. 2024; Bennett et al. 2025).

We selected GJ 1132 b as our reference case because it combines well-characterised planetary parameters, favourable observational accessibility, and a stringent set of atmospheric constraints that can directly test the evolutionary pathways predicted by our models.

Using this system, we investigated how variations in deep-mantle and surface redox reservoirs control mantle cooling history, solidification timescales, and volatile release.

By systematically exploring different combinations of fOmelt
and fOsurf
together with the initial hydrogen inventory (Hoceans) inherited from accretion, we aim to quantify the geophysical conditions under which redox processes may leave detectable imprints on the secondary atmospheres of super-Earth exoplanets.