Lower-order zonal gravitational coefficients caused by zonal circulations inside gaseous planets: Convective flows and numerical comparison between modeling approaches

Abstract

To infer the internal equilibrium structure of a gaseous planet, especially the equation of state (EOS) and size of its inner core, requires accurate determination of lower‐order zonal gravitational coefficients. Modeling of the gravitational signature associated with deep zonal circulation depends critically upon reliable subtraction of the dynamical components from totally derived gravitational coefficients. In the era of the Juno mission and the Grand Finale phase of the Cassini mission, it is timely and necessary to revisit and examine the so‐called ‘Thermal Wind Equation (TWE)’, which has been extensively utilized to diagnose the dynamical parts of the gravitational fields measured by the two spacecrafts. TWE treats as negligible a few terms in the full equation of balance. However, the self‐gravitational anomaly of the distorted fluid, unlike oblateness effects of solid‐body rotation, is not a priori minor and thus should not be neglected in the name of approximation. Another equation, the ‘Thermal Gravitational Wind Equation (TGWE)’, includes this important additional term; we compare it with the TWE and show that physically the TGWE models a fundamentally different balance from the TWE and delivers numerical results considerably different from models based on the TWE. We conclude that the TWE balance cannot be relied upon to produce realistic convection models. Only after the TGWE balance is obtained can the relative importance of terms be assessed. The calculations we report here are based on two types of zonal circulations that are produced by realistically possible convections inside planets, instead of being constructed or assumed.