Carbon solubility and liquid–liquid immiscibility in Fe–C–S ternary system up to 6 GPa: implications for the core of small planetary bodies

High-pressure, high-temperature experiments were conducted in a multi-anvil press using seven different starting compositions to investigate the phase relations of Fe-C-S liquids at pressures up to 6 GPa and temperatures up to 2000 K. Quenched samples revealed immiscible C-rich and S-rich metallic liquids at 2 and 4 GPa, manifesting as either large immiscible zones or emulsified smaller droplets. On the contrary, no immiscibility was observed at 5 or 6 GPa. At these higher pressures, the carbon solubility limit, significantly reduced by increasing sulfur content in the ternary liquid, prevents the formation of a liquid phase rich in both C and S. Our findings thus indicate that super-liquidus immiscibility in Fe-rich compositions does not occur at pressures above 5 GPa, due to the differential pressure dependence of C solubility and miscibility. The limited C solubility in S-rich liquids at higher pressures effectively suppresses immiscibility. Based on these results, terrestrial planetary bodies with fluid cores at pressures exceeding 5 GPa are unlikely to experience liquid-liquid immiscibility, even when both carbon and sulfur are abundant, as sulfur limits carbon solubility and promotes its exsolution. For the Moon, immiscibility-induced core stratification is not expected, though local emulsification could occur near the core-mantle boundary (CMB). In smaller bodies, a two-liquid Fe-C-S core may form at high temperatures, but progressive cooling may lead to graphite crystallization and the potential development of a graphitic crust. Supplementary Information: The online version contains supplementary material available at https://doi.org/10.1186/s40645-026-00846-3.