Models of Saturn's Interior Constructed with an Accelerated Concentric Maclaurin Spheroid Method

The Cassini spacecraft's Grand Finale orbits provided a unique opportunity to probe Saturn's gravity field and interior structure. Doppler measurements yielded unexpectedly large values for the gravity harmonics J ₆, J ₈, and J ₁₀, which cannot be matched using planetary interior models that assume uniform rotation. Instead we present a suite of models that assume the planet's interior rotates on cylinders, which allows us to match all the observed even gravity harmonics. For every interior model, the gravity field is calculated self-consistently with high precision using the Concentric Maclaurin Spheroid method. We present an acceleration technique for this method, which drastically reduces the computational cost, allows us to efficiently optimize model parameters and map out allowed parameter regions with Monte Carlo sampling, and increases the precision of the calculated J _2n gravity harmonics to match the error bars of the observations, which would be difficult without acceleration. Based on our models, Saturn is predicted to have a dense central core of ∼15-18 Earth masses and an additional 1.5-5 Earth masses of heavy elements in the envelope. Finally, we vary the rotation period in the planet's deep interior and determine the resulting oblateness, which we compare with the value from radio occultation measurements by the Voyager spacecraft. We predict a rotation period of 10:33:34 hr +55 s, which is in agreement with recent estimates derived from ring seismology.