A rapidly time-varying equatorial jet in Jupiter's deep interior

The study investigates whether Jupiter’s deep equatorial zonal jet, previously inferred from secular variation of the magnetic field, is steady or time varying. Prior work established that an axisymmetric equatorial jet contributes strongly to Jupiter’s magnetic secular variation. Determining temporal variability is crucial: a steady flow suggests manifestation of deep convective dynamo processes, whereas variability on year-scale times would point to wave-like dynamics (e.g., torsional or Alfvénic) in the metallic hydrogen region. The purpose is to analyze expanded Juno magnetic field observations to test for temporal modulation of the jet speed and to interpret any detected periodicity in terms of plausible interior MHD waves.

• Secular variation in Jupiter’s magnetic field has been detected and linked to zonal wind advection and differential rotation (refs. 1–3,12). The Great Blue Spot at the equator is a region of concentrated field strongly affected by the equatorial jet.
• Theoretical and numerical studies anticipate strong zonal jets associated with deep convection in giant planets (refs. 4–9).
• Torsional oscillations—cylindrically symmetric, axisymmetric Alfvénic motions about the rotation axis—are known in geophysical contexts (ref. 10) and have been proposed to modulate Jupiter’s cloud-level variability on sub-decadal timescales via heat-flux modulation (ref. 15).
• MAC waves typically have much longer periods than a few years (ref. 14), making them less consistent with any short-period variability.
• Juno mission and magnetometer instrumentation provide high-precision field measurements critical for resolving secular variation and interior dynamics (refs. 11,13).

Data and modeling:

• Built a new magnetic field and flow model incorporating Juno magnetic observations from 41 data-yielding perijoves (PJ), including targeted passes over the Great Blue Spot region, extending prior 33-orbit analyses to a 42-orbit model (one pass, PJO2, had no data).
• Employed the same inversion framework as prior work at reference radius r = 0.9 R_J: spherical harmonic expansion for the magnetic field; zonal flow expanded in Legendre functions; time integration of the radial induction equation; regularized nonlinear inversion to solve for initial field coefficients and steady zonal flow profile.
• Assessed model performance via residuals along track and misfit (r.m.s. of residual vector) both globally and within a defined equatorial box around the Great Blue Spot.

Testing time variability:

• Noted that extending to 42 orbits worsened the steady-flow fit, particularly near the spot, and reduced the inferred maximum equatorial jet speed from 0.86 cm s−1 (33-orbit model) to 0.64 cm s−1 (42-orbit model), suggesting temporal changes.
• Implemented pass-by-pass velocity scale factors f_i that uniformly scale the zonal flow amplitude (profile shape fixed) for each PJ, estimating best-fit average flow speed for each pass’s time window.
• Evaluated residual reduction after applying f_i to diagnose the magnitude of temporal variability consistent with the data.
• Fitted the set of f_i values with a simple sinusoidal time variation model v(t) = C + A cos(2π t/τ + ψ) (no damping), relating f_i to the integral (time-average) over each pass epoch. Estimated [C, A, τ, ψ] by search with equal weighting across selected passes, omitting PJ01 (insensitive due to proximity to baseline epoch). Also tested robustness by omitting two outlier passes (PJ26, PJ37).

Methods details (from Methods section):

• Induction equation handled with matrices G(g) and V(v0) dependent on Elsasser integrals; solutions via iterative regularized inversion at 0.9 R_J.
• Residual r = y − f(m); misfit = sqrt((r^T r)/N).
• Velocity scaling: u_i = f_i u_0; uncertainties on f_i estimated by exploring scaling ranges yielding r.m.s. misfits within 50 nT of minimum (recognizing correlated errors and unmodeled signals).
• Periodic fit parameters found: best fit [C, A, τ, ψ] = [1.08, 1.13, 3.83 years, 2.82 rad]. Alternative fit omitting PJ26 and PJ37 yields τ ≈ 4.1 years.
• Computed misfit reductions for individual components, emphasizing B_r for interpretability; noted some passes show larger improvements in other components (e.g., B_φ for PJ24).

• Evidence for time variability: The 42-orbit steady-flow model fits worse than the earlier 33-orbit model, especially near the Great Blue Spot, despite higher-altitude later passes that should sample weaker fields. Global misfit increased to 492 nT (vs 411 nT for 33 orbits; r.m.s. observed field ≈ 282,000 nT). Within the equatorial box, misfit rose to 934 nT (vs 675 nT; r.m.s. observed field ≈ 393,000 nT). The equatorial jet’s maximum speed decreased from 0.86 cm s−1 to 0.64 cm s−1, indicating temporal change.
• Spatial-temporal residual patterns: Adjacent-in-space but separated-in-time pass pairs (e.g., PJ19 vs PJ36; PJ24 vs PJ38) show oppositely signed residuals over the spot, consistent with time-varying flow speeds.
• Pass-by-pass scaling factors: Applying per-pass velocity scale factors reduces residuals notably, especially west of the spot; within-box misfit drops to 721 nT, corresponding to a 40% variance reduction relative to the 42-orbit steady-flow solution.
• Sinusoidal time variation: A single-period, no-damping sinusoidal model fitted to the per-pass scale factors yields a best-fit period of 3.8 years (τ = 3.83 years), delivering a 24.8% variance reduction within the box relative to the 42-orbit steady-flow model. Omitting two outlier passes (PJ26, PJ37) gives a similar period of ≈4.1 years and improves the fit to most remaining passes, including targeted ones (PJ36, PJ38, PJ39, PJ41, PJ42).
• Physical interpretation: The ≈4-year period is consistent with torsional oscillations or a localized Alfvén wave rather than MAC waves (which would be much longer). Using B_perp ≈ 0.6 mT at 0.9 R_J for ±10° equatorial belt implies an Alfvén speed ~10^2 m s−1. A 4-year oscillation period implies B_perp ≈ 3 mT if interpreted as a torsional oscillation, suggesting either stronger fields at depth or small-scale fields not captured at satellite altitude. The wave may instead be a localized Alfvén wave propagating along Great Blue Spot-associated field lines, with a longer-period torsional mode potentially also present.
• Additional complexity: Two easterly passes (PJ26, PJ37) are not well explained by the single sinusoid (PJ37 requires faster flow than temporally adjacent passes; PJ26 prefers slower flow), indicating potential additional spatial and/or temporal complexity (e.g., multiple waves or damping).

The deterioration of the steady-flow fit with the expanded dataset, coupled with systematic patterns of oppositely signed residuals in spatially adjacent but temporally separated passes, indicates that Jupiter’s deep equatorial jet is not steady. Modeling the jet amplitude with a simple periodic variation accounts for a substantial fraction of the variance, identifying a characteristic period of about 4 years. This timescale strongly suggests MHD wave dynamics—either axisymmetric torsional oscillations or localized Alfvén waves—in the metallic hydrogen region rather than slow convective adjustments or MAC waves. The inferred period and required B_perp highlight that the internal magnetic field strength and structure at depths below 0.9 R_J are likely stronger and more complex than deduced from the external potential field alone. The findings open a new observational window into the interior magnetic field topology and wave dynamics, offering constraints on Jupiter’s dynamo operation. However, the poorer fit for certain passes and hints of spatial nonuniformity imply that a single undamped sinusoid is an oversimplification; multiple modes, damping, or localized waveguides (e.g., field lines associated with the Great Blue Spot) may be involved. These results align with ideas that torsional oscillations can modulate heat flux and potentially contribute to observed cloud-level variability on subdecadal timescales.

This work demonstrates that Jupiter’s deep equatorial jet exhibits a wavelike fluctuation with a period of roughly 4 years, revealed by analyzing expanded Juno magnetic field observations and modeling secular variation with a time-variable flow amplitude. The time dependence is consistent with torsional oscillations or a localized Alfvén wave in the metallic hydrogen interior, providing new constraints on the interior magnetic field strength/geometry and the planetary dynamo. The approach—pass-by-pass velocity scaling and sinusoidal fitting—reduces misfits substantially and explains key residual patterns. Future research should incorporate more realistic temporal models (multiple modes, damping), allow spatial complexity in the jet variability, assimilate additional Juno passes and complementary datasets, and develop interior field models that include deeper, stronger, and smaller-scale magnetic structures to better reconcile observed periods and amplitudes. Linking interior wave dynamics to cloud-level variability and heat-flux modulation is a promising avenue.

• The steady-flow profile shape is held fixed; only a uniform amplitude scale factor varies per pass, potentially missing spatial changes in the flow structure.
• The sinusoidal time-variation model assumes a single period and no damping; outliers (PJ26, PJ37) suggest multiple modes and/or damping may be present.
• Flow resolution is poor in the southern hemisphere south of 30°S, limiting spatial characterization there.
• The internal magnetic field below 0.9 R_J cannot be reliably estimated from external observations due to rapidly increasing electrical conductivity with depth; small-scale intense fields are geometrically attenuated at spacecraft altitude, biasing B_perp estimates low.
• Error bars on velocity scaling factors are uncertain due to correlated errors and unmodeled signals; a pragmatic criterion (within 50 nT of minimum misfit) was used.
• One perijove (PJO2) lacked data; temporal sampling is uneven and later passes cluster in time.
• Interpretation of a single equatorial fluctuation’s wavenumber is indirect; using cloud-level variability as a proxy introduces additional assumptions.