The range of Jupiter's flow structures fitting the Juno asymmetric gravity measurements

The asymmetric gravity field measured by the Juno spacecraft allowed estimation of the depth of Jupiter's zonal jets, showing that the winds extend approximately $3000$ km beneath the cloud-level. This estimate was based on an analysis using a combination of all measured odd gravity harmonics $J_{3}$, $J_{5}$, $J_{7}$, and $J_{9}$, but the wind profile dependence on each of them separately has not been investigated. Furthermore, these calculations assumed the meridional profile of the cloud-level wind extends to depth. However, it is possible that the interior jet profile varies from that of the cloud-level as hinted by the Juno microwave measurement that find a smoother nadir brightness temperature profile at depth compared to the cloud-level. Here we analyze in detail the possible meridional and vertical structure of Jupiter's deep jet-streams. We find that each odd gravity harmonic constrains the flow at a different depth, with $J_{3}$ being the most dominant at depths below $3000$ km, $J_{5}$ being the most restrictive overall, and $J_{9}$ not constraining the flow at all if the other odd harmonics are within the measurement range. Interior flow profiles constructed from perturbations to the cloud-level winds allow a more extensive range of vertical wind profiles, yet when the profiles differ substantially from the cloud-level, the ability to match the gravity data reduces significantly. Overall, we find that while interior wind profiles that do not resemble the cloud-level are possible, they are statistically unlikely. However, slightly smoother profiles, which resemble the Juno's microwave radiometer temperature profile at depth, are still compatible with the gravity measurements.