Understanding Saturn’s interior from the

Context. Measurements of Saturn’s gravity field by Cassini Grand Finale have been acquired with high precision. It has been demonstrated that the even gravitational harmonics J6–J10 have larger absolute values than the predictions by typical rigid-body interior models. A four-layer structure model, proposed to interpret Juno’s gravity measurements for Jupiter, has been applied to Saturn, but great attention was paid to the depth of zonal flows in order to interpret the large absolute values of J6–J10. Aims. We aim to understand the internal structure and interior composition of Saturn with a similar model for Jupiter. The additional uncertainties in Saturn’s structure and composition are investigated in detail, such as rotation periods, atmospheric helium mass fractions, and flow-induced gravity corrections. Also, we investigate the effect of equations of state for hydrogen and helium on the predictions of the core mass and heavy element abundance. Methods. In the four-layer structure model, we adjusted the heavy element abundances in the outer two envelopes and the mass of the compact core in order to reproduce Saturn’s equatorial radius as well as the Cassini Grand Finale gravity measurements corrected by the flow-induced gravity signals. Different four-layer interior models are specified in terms of the rotation period, the atmospheric helium mass fraction, and the flow-induced gravity corrections. Two different ab initio equations of state for hydrogen and helium were used in interior structure calculations. Optimized calculations were then performed to explore Saturn’s internal structure and composition. Results. It is found that the absolute values of J6–J10 tend to increase with increasing deep rotation rate and depend on the equations of state adopted in interior calculations. Saturn’s deep rotation rate and atmospheric helium mass fraction are important to determine the distribution of helium and heavy elements in the outer envelopes. We also show that the core mass and heavy element abundance in Saturn are dependent upon the deep rotation rate, the atmospheric helium mass fraction, the flow-induced gravity corrections, and the equations of state for hydrogen and helium