Analysis of Io's Tidal Response as a Function of the Properties of the Partially Molten Layer Article Swipe

MAKE IMPACT

Matteo Paris , A. Mura , F. Zambon , Antonio Genova , F. Tosi , G. Piccioni , Anastasia Consorzi , Giuseppe Mitri , R. Sordini , R. Noschese , A. Cicchetti , S. J. Bolton , Christina Plainaki , Giuseppe Sindoni · YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.5194/epsc-dps2025-886

Introduction Jupiter’s moon Io, the most volcanically active body in the Solar System [1][2], exhibits intense internal heating believed to be driven by tidal friction. While tidal dissipation is widely accepted as the primary mechanism powering this volcanic activity, the spatial distribution and depth of heating generation remain unresolved[3]. The tidal response of Io is characterized by the Love number k2 [4], where the real part describes the in-phase deformation due to Jupiter’s gravitational potential, and the imaginary part captures the delayed anelastic response associated with internal energy dissipation [5]. Methods We analyze Io’s tidal response by computing second-order Love numbers as functions of the radius at which mantle melting begins (RΦ0) and the latent heat of fusion (L) of the constituent materials. The Love number k2 is derived by solving the spheroidal oscillation equations for an initial three-layer structure (fluid core, viscoelastic mantle, and viscoelastic crust), using an adapted version of the California Planetary Geophysics Code (CPGC) [6]. Tidal dissipation is computed from radial and tangential displacements and stresses [7], and the resulting melt fraction is obtained following the approach in [8]. Viscosity, rigidity, and Andrade rheology parameters (β) are then updated based on the local melt fraction, and the mantle is discretized into 67 layers. This process is iterated until k2 converges and repeated across a range of RΦ0 and L values. The fluid core is modeled with a density of 5150 kg/m3 and a radius of 950 km. The mantle, 820 km thick with a density of 3259 kg/m3, follows Andrade rheology (α = 0.3, initial β = 10−12 Pa−1s−0.3). The overlying 50 km-thick crust shares the mantle’s density and is modeled with Maxwell rheology. Initial viscosities and rigidities are set to 1021 Pa · s and 40 GPa for the mantle, and 1025 Pa · s and 40 GPa for the crust. Two scenarios are explored: one with constant β, representing tidal heating concentrated in the deep mantle, and another with depth-dependent β, allowing dissipation to localize in the upper mantle. The agreement with the observed values of k2 [5] is verified using also the ALMA3 code [9]. ALMA3 was used to double-check whether the values we obtained with CPGC are consistent with an independent software. Results The results are presented in Figures 1-2-3. Figure 1 shows the behavior of k2 as a function of the melting radius (RΦ0) and latent heat of fusion (L), assuming a constant β throughout the mantle. Several combinations reproduce the real part of k2 (Re(k2) = 0.125 ± 0.047, [5]), while the imaginary part slightly exceeds the estimated value (Im(k2) = 0.0109 ± 0.0054) but remains within one standard deviation. Figure 2 illustrates results for a depth-dependent β. The real part of k2 remains consistent with observation over a broad range of RΦ0 and L, whereas the imaginary part lies marginally outside the 1-σ confidence interval but is within 2-σ. Figure 3 compares the trends in Im(k2): it increases with RΦ0 when β is constant, but decreases when β varies with depth. Ongoing refinements to the initial β values aim to improve agreement with the observed tidal dissipation. SummaryThe proposed methodology enables a detailed investigation of the possible configuration of Io’s mantle, by evaluating the influence of rigidity, viscosity, volumetric tidal heating rate, and melt fraction Φ, on Love Number k2 and its phase lag. Several internal structure models incorporating a partially molten mantle with Φ below the rheologically critical melt fraction (RCMF) [10] yield Re(k2) values consistent with estimates from NASA’s Juno. Assuming an initial β of 10−12, the corresponding Im(k2) values fall within the 2-σ uncertainty of observational constraints. These results highlight the importance of a sensitivity analysis of k2 with respect to the initial parameter β to better constrain Io’s interior using observational data acquired by Juno [5].Figure 1: Love number k2 as a function of melting radius (RΦ0) and latent heat of fusion (L), assuming constant β. In the first panel, the estimated value of Re(k2) from [5] (0.125 ± 0.047) is shown as a reference curve. The second panel omits the reference for Im(k2), as all computed values exceed 0.0109 but remain below 0.0163.Figure 2: Same as Figure 1 but assuming variable β. In the first panel, the estimated value of Re(k2) from [5] (0.125 ± 0.047) is shown as a reference. In the second panel, no reference is shown for Im(k2), as all values exceed 0.0163.Figure 3: Imaginary part of k2 as a function of melting radius (RΦ0) for different latent heat values (L), shown for constant (first) and variable (second) β. The trend of Im(k2) reverses between the two cases: it increases with increasing RΦ0when β is constant, and decreases when β is variable. AcknowledgmentsWe thank Agenzia Spaziale Italiana (ASI) for the support of the JIRAM contribution to the Juno mission; this work is supported by the ASI–INAF Addendum n. 2016-23-H.3-2023 to grant 2016-23 H.0.References[1] Lopes, R. M. C., and Spencer, J. R. (2007) Io after Galileo: A new view of Jupiter’s volcanic moon, Springer.[2] Lopes, R. M. C., De Kleer, K., and Keane, J. T. (2023) Io: A new view of Jupiter’s moon, Springer International Publishing.[3] Keane, J., et al. (2021) Bull. Am. Astron. Soc., 53:178.[4] Efroimsky, M., and Lainey, V. (2007) JGR: Planets, 112(E12).[5] Park, R. S., et al. (2025) Nature, 638(8049):69–73.[6] Ermakov, A., and Akiba, R. (2024) California Planetary Geophysics Code, GitHub repository.[7] Beuthe, M. (2013) Icarus, 223(1):308–329.[8] Bierson, C. J., and Nimmo, F. (2016) JGR: Planets, 121(11):2211–2224.[9] Melini, D., Saliby, C., and Spada, G. (2022) Geophys. J. Int., 231(3):1502–1517.[10] Breuer, D., Hamilton, C. W., and Khurana, K. (2022) Elements, 18(6):385–390.

Type

preprint

Language

en

Landing Page

https://doi.org/10.5194/epsc-dps2025-886

OA Status

gold

Related Works

10

OpenAlex ID

https://openalex.org/W4412120521

Raw OpenAlex JSON

OpenAlex ID

https://openalex.org/W4412120521

Canonical identifier for this work in OpenAlex

DOI

https://doi.org/10.5194/epsc-dps2025-886

Digital Object Identifier

Title

Analysis of Io's Tidal Response as a Function of the Properties of the Partially Molten Layer

Work title

Type

preprint

OpenAlex work type

Language

en

Primary language

Publication year

2025

Year of publication

Publication date

2025-07-09

Full publication date if available

Authors

Matteo Paris, A. Mura, F. Zambon, Antonio Genova, F. Tosi, G. Piccioni, Anastasia Consorzi, Giuseppe Mitri, R. Sordini, R. Noschese, A. Cicchetti, S. J. Bolton, Christina Plainaki, Giuseppe Sindoni

List of authors in order

Landing page

https://doi.org/10.5194/epsc-dps2025-886

Publisher landing page

Open access

Yes

Whether a free full text is available

OA status

gold

Open access status per OpenAlex

OA URL

https://doi.org/10.5194/epsc-dps2025-886

Direct OA link when available

Concepts

Function (biology), Layer (electronics), Chemistry, Materials science, Composite material, Cell biology, Biology

Top concepts (fields/topics) attached by OpenAlex

Cited by

0

Total citation count in OpenAlex

Related works (count)

10

Other works algorithmically related by OpenAlex

Full payload