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The Lost Meaning of Jupiter's High-degree Love Numbers

Idini, Benjamin and Stevenson, David J. (2022) The Lost Meaning of Jupiter's High-degree Love Numbers. Planetary Science Journal, 3 (1). Art. No. 11. ISSN 2632-3338. doi:10.3847/psj/ac4248.

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NASA's Juno mission recently reported Jupiter's high-degree (degree ℓ, azimuthal order m = 4, 2) Love number k₄₂ = 1.289 ± 0.063 (1σ), an order of magnitude above the hydrostatic k₄₂ obtained in a nonrotating Jupiter model. After numerically modeling rotation, the hydrostatic k₄₂ = 1.743 ± 0.002 is still 7σ away from the observation, raising doubts about our understanding of Jupiter's tidal response. Here, we use first-order perturbation theory to explain the hydrostatic k₄₂ result analytically. We use a simple Jupiter equation of state (n = 1 polytrope) to obtain the fractional change in k₄₂ when comparing a rotating model with a nonrotating model. Our analytical result shows that the hydrostatic k₄₂ is dominated by the tidal response at ℓ = m = 2 coupled into the spherical harmonic ℓ, m = 4, 2 by the planet's oblate figure. The ℓ = 4 normalization in k₄₂ introduces an orbital factor (a/s)² into k₄₂, where a is the satellite semimajor axis and s is Jupiter's average radius. As a result, different Galilean satellites produce a different k42. We conclude that high-degree tesseral Love numbers (ℓ > m, m ≥ 2) are dominated by lower-degree Love numbers and thus provide little additional information about interior structure, at least when they are primarily hydrostatic. Our results entail important implications for a future interpretation of the currently observed Juno k₄₂. After including the coupling from the well-understood ℓ = 2 dynamical tides (Δk₂ ≈ −4%), Jupiter's hydrostatic k₄₂ requires an unknown dynamical effect to produce a fractional correction Δk₄₂ ≈ −11% in order to fit Juno's observation within 3σ. Future work is required to explain the required Δk₄₂.

Item Type:Article
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URLURL TypeDescription
Idini, Benjamin0000-0002-2697-3893
Stevenson, David J.0000-0001-9432-7159
Additional Information:We acknowledge the support of NASA's Juno mission. We benefited from constructive discussions with James Fuller, Janosz Dewberry, and Christopher Mankovich.
Group:Division of Geological and Planetary Sciences
Funding AgencyGrant Number
Issue or Number:1
Record Number:CaltechAUTHORS:20230203-893210800.10
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119008
Deposited By: Research Services Depository
Deposited On:24 Feb 2023 20:25
Last Modified:24 Feb 2023 20:25

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