Linking Zonal Winds and Gravity: The Relative Importance of Dynamic Self Gravity

TL;DR

This paper investigates the significance of Dynamic Self Gravity (DSG) in planetary gravity measurements, showing it is a first-order effect for low degrees and should be included in models to improve accuracy.

Contribution

The study provides an analytical approach to quantify DSG's impact on gravity harmonics, demonstrating its importance for degrees l=2 to about l=10 in planetary interior modeling.

Findings

DSG significantly affects low-degree gravity harmonics (l=2 to 4).

Impact of DSG decreases with increasing harmonic degree.

Including DSG improves the accuracy of gravity-based zonal flow inferences.

Abstract

Recent precise measurements at Jupiter's and Saturn's gravity fields constrain the properties of the zonal flows in the outer envelopes of these planets. A simplified dynamic equation, sometimes called the thermal wind or thermo-gravitational wind equation, establishes a link between zonal flows and the related buoyancy perturbation, which in turn can be exploited to yield the dynamic gravity perturbation. Whether or not the action of the dynamic gravity perturbation needs to be explicitly included in this equation, an effect we call the Dynamic Self Gravity (DSG), has been a matter of intense debate. We show that, under reasonable assumptions, the equation can be solved (semi) analytically. This allows us to quantify the impact of the DSG on each gravity harmonic, practically independent of the zonal flow or the details of the planetary interior model. The impact decreases with growing spherical harmonic degree l. For degrees l=2 to about l=4, the DSG is a first order effect and should be taken into account in any attempt of inverting gravity measurements for zonal flow properties. For degrees of about l=5 to roughly l=10, the relative impact of DSG is about 10% and thus seems worthwhile to include, in particular since this comes at little extra costs with the method presented here. For yet higher degrees, is seems questionable whether gravity measurements or interior models will ever reach the required precision equivalent of the DSG impact of only a few percent of less.