Static effects of differential rotation on Jupiter’s shape, gravity field, and interior structure

Context . Jupiter’s atmosphere has strong zonal flows and exhibits marked differential rotation. The dynamic effects of these flows on Jupiter’s gravity field and internal structure have been extensively investigated in order to interpret Juno gravity field data. However, static effects arising from differential rotation are generally ignored in interior modeling. Along with precise measurements of Jupiter’s gravity field, it is of interest to explore the static effects on Jupiter’s shape, gravity field, and interior structure. Aims . We aim to incorporate differential rotation into the fifth-order theory of figures (TOF5) to self-consistently derive planetary shapes and gravitational harmonics. Using Juno gravity field data as constraints, we further investigate the static effects of differential rotation on Jupiter’s shape, gravity field, and interior structure. Methods . We propose a simplified differential rotation model with one free parameter characterizing the intensity of differential rotation. TOF5 is extended to account for differential rotation and is subsequently integrated into Jupiter’s interior models. Results . Our analysis reveals that differential rotation systematically increases Jupiter’s oblateness, with the degree of flattening dependent on the intensity of differential rotation. Absolute values of even gravitational harmonics | J 2 n | increase with the intensity of differential rotation, and higher-order ones exhibit a more pronounced response. Constrained by the Juno gravity data, we find that differential rotation significantly alters Jupiter’s shape and interior structure compared to the results of rigid rotation. The atmospheric metallicity of Jupiter is generally reduced by differential rotation. This implies that a higher 1 bar temperature or a density deficit in part of the molecular envelope is required to interpret the Galileo atmospheric measurement. Furthermore, incorporating differential rotation allows for more heavy elements in Jupiter’s interior, which are mainly concentrated in the metallic hydrogen envelope and the diluted core region. This enrichment is accompanied by a corresponding reduction of heavy elements in the compact core and molecular atmosphere.