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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 Paper
Idini, Benjamin0000-0002-2697-3893
Stevenson, David J.0000-0001-9432-7159
Additional Information:© 2022. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 2021 November 2; revised 2021 November 29; accepted 2021 December 10; published 2022 January 20. We acknowledge the support of NASA's Juno mission. We benefited from constructive discussions with James Fuller, Janosz Dewberry, and Christopher Mankovich. Software: Mathematica (Wolfram 1999).
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Subject Keywords:Solar system gas giant planets; Galilean satellites; Planetary interior; Tides
Issue or Number:1
Record Number:CaltechAUTHORS:20220121-870696000
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Official Citation:Benjamin Idini and David J. Stevenson 2022 Planet. Sci. J. 3 11
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113055
Deposited By: George Porter
Deposited On:21 Jan 2022 23:42
Last Modified:21 Jan 2022 23:42

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