Structure and composition of Jupiter, Saturn, Uranus, and Neptune under different constraints and distortion due to rotation

ABSTRACT The radii of planets serve as significant constraints for their internal structure. Despite the complexity of planetary internal structure compared to stars, substantial advancements have been made in this field. The most critical uncertainties stem from the chemical composition and equation of state of planetary material. Using the MESA code, we construct rotating and non-rotating interior models for Jupiter and Saturn and sought to align these models to the observed radii. Rotation exerts a significant influence on their structures, distorting planetary, and stellar structures in distinct ways. Regarding gas planets’ structure, two pivotal uncertain parameters depend on a possible separation between hydrogen and helium in the protosolar disc gas due to unequal evaporation between these two gases. In an extreme scenario where only hydrogen is lost and no heavy elements or helium are lost, Jupiter and Saturn would have a core mass of zero. However, this approach fails to yield a solution for Uranus and Neptune. Instead, our models indicate that hydrogen and helium were likely lost together during the protosolar disc phase, resulting in core masses of approximately 40, 25, 14, and 12 M⊕ for Jupiter, Saturn, Neptune, and Uranus, respectively. These findings are highly compatible with the observed mass–radius relationship of exoplanets, as well as the seismic and Juno data for Jupiter’s near-surface temperature.