Modeling the Tidal Response of Io: Coupled Viscoelastic Dissipation and Melt Distribution

Abstract:

Astronomical observations [1] and heat flow measurements [2] of Io have provided a constraint on Io’s tidal dissipation rate (k₂/Q). Induction measurements have been used to infer a partially molten region with ∼ 20% melt [3]. Here we investigate Io’s tidal response using these constraints and a model in which tidal heating and melt distribution are coupled.

Previous tidal models of Io have assumed a Maxwellian rheology [4, 5]. The Maxwell model is highly idealized which leads to estimates of Io’s mantle viscosity on order 10¹³ − 10¹⁶ Pa·s, much smaller than typical values for partially-molten rocks.

Here we build on the work of [6], with two significant differences. First, we couple tidal heating to the melt distribution model of [6], using the approach developed in [7]. Second, rather than a Maxwell rheology we adopt the more realistic Andrade model [8]. The response of partially-molten rocks under periodic and steady-state (viscous) conditions is modeled using the experimental results of [8] and [9], respectively.

Initial results yield Io mantle viscosities in excess of 10¹⁷Pa·s, compatible with experimental data, and melt fractions of up to 20%, consistent with the induction observations [3].

[1] V. Lainey et al., Nature 459.7249 (2009), pp. 957–959. [2] W. B. Moore et al., Io After Galileo: A New View of Jupiter’s Volcanic Moon. 2007, pp. 89–108. [3] K. Khurana et al., Science 332.June (2011). [4] W. B. Moore., Journal of Geophysical Research 108 (2003), pp. 1–6. [5] R. H. Tyler et al., The Astrophysical Journal Supplement Series 218.2 (2015), p. 22. [6] W. B. Moore., Icarus 154 (2001), pp. 548– 550. [7] J. H. Roberts and F. Nimmo., Icarus 194.2 (2008), pp. 675–689. [8] I. Jackson et al., Journal of Geophysical Research B: Solid Earth 109.6 (2004), pp. 1–17. [9] S. Mei et al., Earth and Planetary Science Letters 201 (2002), pp. 491–507.