Equilibrium figure of Haumea and possible detection via stellar occultation

We studied the equilibrium figure of dwarf planet Haumea to determine if the observed shape is compatible with a differentiated hydrostatic body. Three groups of interior models of Haumea were assumed, all with a rocky core and a volatile-rich outer shell that may contain some porosity. A third layer located between the core and the outer shell has a density suggesting partial differentiation or the presence of a large fraction of organic matter. Using the code BALEINES, which solves for the equilibrium figures of the boundaries between layers, we show that the hydrostatic models closest to the shape derived via stellar occultation approach a state of critical rotation, which translates into a pinched shape with large deviations from an ellipsoid (up to 110 km). The previous stellar occultation and light curves cannot be used to distinguish between the ellipsoid and the pinched shape, but we predict this figure could be observable during the next stellar occultation of Haumea on May 4, 2026, if some chords are obtained in the northern or southern limbs of the shadow.