Linking zonal winds and gravity: the relative importance of dynamic self-gravity

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 . For degrees = 2 to about = 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 = 5 to roughly = 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.

Theory of Figures to the Seventh Order and the Interiors of Jupiter and Saturn

“…This means that the joint interior and wind solutions are not unique, given the uncertainties we allowed for. In addition, alternative interior models which fit all the J n when combined with a wind model may be possible for different EOSs and wind models, such as the MH13 H/He EOS and wind models that account for the oblate shape (Cao & Stevenson 2017) or solve for the gravo-thermal wind equation that accounts for the dynamic self-gravity of the flow (TGWE; Kong et al 2018;Wicht et al 2020). We note that Galanti et al (2017) find that these modified wind models introduce corrections that are an order of magnitude smaller for most J n , while Dietrich et al (2021) obtain corrections of ∼60% and ∼20% for J 3 and J 5 , respectively, when including the dynamic self-gravity for polytropic models and an additional correction of ∼40% and ∼10% when accounting for Jupiter-model specific background density and gravity profiles.…”

Investigating Barotropic Zonal Flow in Jupiter's Deep Atmosphere Using Juno Gravitational Data

“…In Equation 9, the term 𝐴𝐴 ∇𝜌𝜌0 × 𝐠𝐠 ′ ef f is sometimes referred to as the dynamic self-gravity (Wicht et al, 2020;Zhang et al, 2015). In the context of studying zonal flows in a gas giant atmosphere where the background density rapidly increases with depth, the importance of this term is a subject of debate.…”

Theory of Figures to the 7th order and the interiors of Jupiter and Saturn

“…This means that the joint interior and wind solutions are not unique, given the uncertainties we allowed for. In addition, alternative interior models which fit all the J n when combined with a wind model may be possible for different equations of state and wind models, such as the MH13 H/He EOS and wind models that account for the oblate shape (Cao & Stevenson 2017) or solve for the gravo-thermal wind equation that accounts for the dynamic self-gravity of the flow (TGWE) (Kong et al 2018;Wicht et al 2020). We note that Galanti et al (2017) find that these modified wind models introduce corrections that are an order of magnitude smaller for most J n , while Dietrich et al (2021) obtain corrections of respectively ∼60% and ∼20% for J 3 and J 5 when including the dynamic self-gravity for polytropic models and an additional correction of ∼40% and ∼10% when accounting for Jupiter-model specific background density and gravity profiles.…”