Empirical Structure Models of Uranus and Neptune

Uranus and Neptune are still poorly understood. Their gravitational fields, rotation periods, atmosphere dynamics, and internal structures are not well determined. In this paper we present empirical structure models of Uranus and Neptune where the density profiles are represented by polytropes. By using these models, that are set to fit the planetary gravity field, we predict the higher order gravitational coefficients $J_6$ and $J_8$ for various assumed rotation periods, wind depths, and uncertainty of the low-order harmonics. We show that faster rotation and/or deep winds favour centrally concentrated density distributions. We demonstrate that an accurate determination of $J_6$ or $J_8$ with a relative uncertainty no larger than $10\%$ could constrain wind depths of Uranus and Neptune. We also confirm that the Voyager rotation periods are inconsistent with the measured shapes of Uranus and Neptune. We next demonstrate that more accurate determination of the gravity field can significantly reduce the possible range of internal structures. Finally, we suggest that an accurate measurement of the moment of inertia of Uranus and Neptune with a relative uncertainty of $\sim1\%$ and $\sim0.1\%$, could constrain their rotation periods and depths of the winds, respectively.