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

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Table 1

Observables used to constrain the interior models.

Criteria	Constraints
Interior	$\| J_{2}^{CMS} - J_{2}^{Juno} \| \leq 2 \times 10^{- 6}$ ${\left\| {J_2^{{\rm{CMS}}} - J_2^{{\rm{Juno}}}} \right\| \le 2 \times {{10}^{ - 6}}}$
	$\| J_{4}^{CMS} - J_{4}^{Juno} \| \leq 10^{- 6}$ ${\left\| {J_4^{{\rm{CMS}}} - J_4^{{\rm{Juno}}}} \right\| \le {{10}^{ - 6}}}$
	\|M^CMS − M^Juno\| ≤ ΔM = 0.0005 × 10²⁷ kg

Wind	$\| (Δ J_{2 n}^{sol} + J_{2 n}^{CMS}) - J_{2 n}^{Juno} \| \leq 3 σ_{2 n}^{Juno} (n = 1, \dots, 5)$ $\left\| {\left( {{\rm{\Delta }}J_{2n}^{{\rm{sol}}} + J_{2n}^{{\rm{CMS}}}} \right) - J_{2n}^{{\rm{Juno}}}} \right\| \le 3\sigma _{2n}^{{\rm{Juno}}}(n = 1, \ldots ,5)$
	$\| Δ J_{n}^{sol} - J_{n}^{Juno} \| \leq 3 σ_{n}^{Juno} (n = 3, 5, 7, 9)$ $\left\| {{\rm{\Delta }}J_n^{{\rm{sol}}} - J_n^{{\rm{Juno}}}} \right\| \le 3\sigma _n^{{\rm{Juno}}}(n = 3,5,7,9)$
	\|u^sol(θ) − u^obs(θ)\| ≤ 20 m s ⁻¹

Obs.	T_1bar ≤ 178 K
	Z₁ ≥ 0.015 ≈ Z_solar
	P₁₂ ≤ 3 Mbar

Notes. The CMS solutions are the static gravity harmonics. The Juno-measured gravity harmonics $(J_{n}^{Juno})$ $\left( {J_n^{{\rm{Juno}}}} \right)$ and their corresponding 3σ uncertainties $(3 σ_{n}^{Juno})$ $\left( {3\sigma _n^{{\rm{Juno}}}} \right)$ are taken from Durante et al. (2020). The Juno-derived mass is M^Juno = 1.8983 × 10²⁷ kg,and ΔM is the mass uncertainty due to the available range of the gravitational constant G (see Ziv et al. 2024). The observed cloud-level wind u^obs(θ) are from Tollefson et al. (2017). We consider Z_so1ar as the protosolar value from Lodders et al. (2009).

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