Variance-Geometry Diagnostics Identify Transition Layers in Jupiter's Equatorial Emission: A Methodological Validation

This work applies eigenvalue-based variance-geometry diagnostics to 33 years (1984–2017) of latitude-resolved brightness measurements of Jupiter’s equatorial emission, dominated by the Io plasma torus, to evaluate whether the RTLI framework can identify physically meaningful transition layers in a well-characterized planetary system. At the global level, Jupiter’s equatorial emission is strongly super-critical, with an eigenvalue ratio λₑ ≈ 8.9 and 83.5% of variance captured by the first principal component, consistent with dominance by a single coherent emission source. The empirically identified transition corridor [√e, 7/4] ≈ [1.65, 1.75] does not appear at the ensemble level, confirming that the system as a whole is structurally locked. However, when variance is examined locally using the Intrinsic Variance Ratio (IVR), a corridor-adjacent transition emerges specifically at southern equatorial latitudes (−2° to −3°), where IVR ≈ 1.58–1.63. This localized signature identifies a transition layer separating noise-dominated, stable northern emission from regions exhibiting intrinsic, marginal variability. Importantly, this transition is invisible to brightness profiles, total variance, and standard PCA diagnostics. A highly significant and temporally evolving north–south brightness asymmetry (⟨N/S⟩ ≈ 2.63, p < 10⁻¹⁰⁰) correlates with IVR structure, ruling out instrumental or geometric artifacts. Null tests using shuffled latitude data confirm that the observed corridor-adjacent structure is not a statistical artifact. These results demonstrate that variance-geometry diagnostics are sensitive to scale-dependent structural transitions within globally coherent systems. The Jupiter analysis provides methodological validation of the RTLI framework, showing that it can locate physically meaningful transition layers without relying on detailed physical modeling. This establishes variance-geometry diagnostics as a complementary tool for magnetospheric studies, comparative planetology, and archival analysis of spatially extended astrophysical systems.