Feedback-driven Tidal Heating in Io

Jovian tides power intense and widespread volcanism on Io, but the observed distribution of its volcanic activity is distinctly non-uniform. Decades of spacecraft and ground-based observations reveal that volcanism is concentrated at equatorial and mid-latitudes and peaks approximately 30–60° east of the sub-Jovian and anti-Jovian points [1,2,3]. Traditional tidal heating models, which treat Io as a spherically symmetric viscoelastic solid, can account for enhanced equatorial activity if they assume there is a low-viscosity asthenosphere. However, they cannot reproduce the observed eastward shift. This inability has until recently been used as evidence for a global magma ocean, but a global, shallow magma ocean can not explain Io’s observed k₂ Love number [4].

Our work demonstrates that the feedback between tidal heating and the viscoelastic properties of a partially molten asthenosphere can induce an eastward shift in the heating pattern. Tidal dissipation varies both radially and laterally, influencing local melt fractions and hence the viscosity [5,6]. Because tidal dissipation depends on viscosity, a feedback loop emerges. We show that accounting for this feedback leads to heating patterns with stable eastward shifts whose magnitude depends on the strength of the coupling between melt generation and heating. Notably, when the coupling becomes sufficiently strong, the system enters an unstable regime. In this case, the heating pattern no longer converges to a stable pattern but instead undergoes continuous eastward migration. Evidence for Io to be in this regime might be found in the distribution of active vs inactive hotspots [1,7]. If active hotspots generally lie more eastward, this could indicate a shift in peak tidal heating with time. 

We further explore the parameter space and the conditions for both the stable and unstable patterns through the use of a toy model. We find that there is an inherent stability in the system and that the coupling strength fully determines the final pattern in our current model. Our results are not particular to Io and can be applied to any tidally heated body, suggesting that the same mechanism might generally lead to asymmetrical 3D structures.

To better link our model to the observations of Io, the heat transport model needs to be improved. This will create a self-consistent model of Io’s interior evolution. The more sophisticated heat transport model, based on melt advection models [8,9], will then allow us to investigate the stability of hot spots like Loki Patera, the origin of the leading-trailing dichotomy in observed heat flux [3,10], and the time scale associated with a non-stable pattern.

 

References

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[2] Davies, A. G., Veeder, G. J., Matson, D. L., & Johnson, T. V. 2015, Icarus, 262, 67

[3] Davies, A. G., Perry, J. E., Williams, D. A., Veeder, G. J., & Nelson, D. M. 2024, The Planetary Science Journal, 5, 121

[4] Park, R., Jacobson, R., Gomez Casajus, L., et al. 2024, Nature, 1

[5] Mei, S., Bai, W., Hiraga, T., & Kohlstedt, D. L. 2002, Earth and Planetary Science Letters, 201, 491

[6] Bierson, C. J. & Nimmo, F. 2016, Journal of Geophysical Research (Planets), 121, 2211

[7] Steinke, T., van Sliedregt, D., Vilella, K., van der Wal, W., & Vermeersen, B. 2020, Journal of Geophysical Research (Planets), 125, e06521

[8] Moore, W. B. 2001, Icarus, 154, 548

[9] Spencer, D. C., Katz, R. F., & Hewitt, I. J. 2020, Journal of Geophysical Research (Planets), 125, e06443

[10] de Kleer, K. & de Pater, I. 2016, Icarus, 280, 405