Characterizing Jupiter's interior using machine learning reveals four key structures

TL;DR

This work combines a four-layer Jupiter interior model with a CMS-based neural regressor (NeuralCMS) and a self-consistent wind model to efficiently sample interior structures compatible with Juno gravity and atmospheric data. By regressing the CMS outputs for gravity moments and mass, then refining with a wind-constrained thermal wind balance, the authors identify four characteristic interior structures and demonstrate that the interior can be described by two effective parameters. The wind constraints predominantly limit the low-order gravity harmonics, while higher-order harmonics are mainly governed by interior structure, leading to a robust, reduced-dimensionality framework for giant planet interiors. The approach yields insights into the distribution of heavy elements, the extent of the dilute core, and the envelope state, and it can be adapted to other giant planets and exoplanets with similar data constraints.

Abstract

The internal structure of Jupiter is constrained by the precise gravity field measurements by NASA's Juno mission, atmospheric data from the Galileo entry probe, and Voyager radio occultations. Not only are these observations few compared to the possible interior setups and their multiple controlling parameters, but they remain challenging to reconcile. As a complex, multidimensional problem, characterizing typical structures can help simplify the modeling process. We used NeuralCMS, a deep learning model based on the accurate concentric Maclaurin spheroid (CMS) method, coupled with a fully consistent wind model to efficiently explore a wide range of interior models without prior assumptions. We then identified those consistent with the measurements and clustered the plausible combinations of parameters controlling the interior. We determine the plausible ranges of internal structures and the dynamical contributions to Jupiter's gravity field. Four typical interior structures are identified, characterized by their envelope and core properties. This reduces the dimensionality of Jupiter's interior to only two effective parameters. Within the reduced 2D phase space, we show that the most observationally constrained structures fall within one of the key structures, but they require a higher 1 bar temperature than the observed value. We provide a robust framework for characterizing giant planet interiors with consistent wind treatment, demonstrating that for Jupiter, wind constraints strongly impact the gravity harmonics while the interior parameter distribution remains largely unchanged. Importantly, we find that Jupiter's interior can be described by two effective parameters that clearly distinguish the four characteristic structures and conclude that atmospheric measurements may not fully represent the entire envelope.

Figures (8)

• Figure 1: Schematic view of Jupiter's interior model used in this study (left) and the exploration workflow (right). The model's free parameters are shown. For each step of the exploration, we state which method is being used, which observables are used to constrain the solutions, and the number of plausible models resulting from this step. The prediction errors of NeuralCMS are denoted by $\epsilon$Ziv2024.
• Figure 2: Optimized wind solutions for all models accepted by the wind criteria (Table \ref{['tab:Criteria']}). Panel a: latitudinal cloud-level wind profiles. Panel b: the radial decay function with depth. The blue profile represents the observed cloud-level wind Tollefson2017, and the dashed yellow profile indicates the mean of all decay profiles.
• Figure 3: Distribution of observables (a-g) and interior structure parameters (h-n) for plausible interior models. The gravity harmonics (a-e) are the static components, which are fitted to Juno's measurements using the wind model. Panel o shows the compact core mass determined by $r_{\rm core}$. Blue histograms correspond to models that satisfy the interior criteria ($19\,982$ models), while red histograms represent those that also meet the wind criteria (491 models). The red vertical line marks Juno's $J_{2n}$ measurements Durante2020 and derived mass Ziv2024. Black Gaussians represent the allowed range for the static gravity harmonics accounting for differential rotation ($J_{2n}^{\rm static}=J_{2n}^{\rm Juno}-\Delta J_{2n}^{\rm dynamical}$) from Miguel2022. For $J_{10}$ (e), the Juno measurement lies outside the range shown, but the black Gaussian covers the displayed values. The preferred model from Militzer2022 is shown in green lines (we show the inner edge of the He rain region compared to $P_{12}$). The gravity harmonics (a-e) distance from the red lines represents $\Delta J_{2n}$. The histogram color corresponds to Fig. \ref{['fig: Model_schematic']}.
• Figure 4: Normalized maximum variance for increasing number of clusters tested. Shown is the analysis for the full sample of plausible interior structures (thick blue), and the mean and standard deviation of the analysis for 10 randomly selected sub-samples with different sizes. The red circle marks our selection of four clusters for this analysis.
• Figure 5: Interior parameters' means (points) and standard deviations (error bars) within the four clusters, shown in different colors. Clusters 1 and 2 (red and blue) show high values of $T_{\rm 1bar}$ and $Z_{1}$, while clusters 3 and 4 (green and yellow) show lower values of these parameters. Clusters 1 and 3 feature high values of $m_{\rm dilute}$ and $r_{\rm core}$, and low values of $Z_{\rm dilute}$, whereas clusters 2 and 4 display the opposite trend. We note that the compact core mass, $M_{\rm{core}}$, was not used in the clustering analysis.