Io's tidal response precludes a shallow magma ocean

Abstract

Io experiences tidal deformation as a result of its eccentric orbit around Jupiter, which provides a primary energy source for Io's continuing volcanic activity and infrared emission¹. The amount of tidal energy dissipated within Io is enormous and has been suggested to support the large-scale melting of its interior and the formation of a global subsurface magma ocean. If Io has a shallow global magma ocean, its tidal deformation would be much larger than in the case of a more rigid, mostly solid interior². Here we report the measurement of Io's tidal deformation, quantified by the gravitational tidal Love number k₂, enabled by two recent flybys of the Juno spacecraft. By combining Juno^3,4 and Galileo^5-7 Doppler data from the NASA Deep Space Network and astrometric observations, we recover Re(k₂) of 0.125 ± 0.047 (1σ) and the tidal dissipation parameter Q of 11.4 ± 3.6 (1σ). These measurements confirm that a shallow global magma ocean in Io does not exist and are consistent with Io having a mostly solid mantle². Our results indicate that tidal forces do not universally create global magma oceans, which may be prevented from forming owing to rapid melt ascent, intrusion and eruption^8,9, so even strong tidal heating-such as that expected on several known exoplanets and super-Earths¹⁰-may not guarantee the formation of magma oceans on moons or planetary bodies.

Fig. 1. The measured tidal response (Re(k₂) and |k₂|/Q) of Io compared against models without and with a magma ocean.

a, No magma ocean. Shaded green boxes are 1σ and 3σ Juno results (Methods) and shaded grey boxes are from a previous study based on astrometry. Here a three-layer Io is assumed with an elastic lid of thickness d, a partially molten mantle with an Andrade parameter β (in Pa⁻¹ s⁻ⁿ) as specified by the symbols and a liquid iron core. The second Andrade parameter is assumed to be n = 0.3. The purple star marker represents the model from Fig. 2 of ref. . b, The same as in a but for models including a magma ocean with upper mantle. Here the ocean is at a depth h and is sandwiched between two Andrade viscoelastic layers. The magma ocean is assumed to be 100 km thick. Increasing the upper-mantle thickness reduces Re(k₂), as expected; to match the Juno results, the depth h exceeds 500 km, which correlates to a deep magma ocean. Further details are given in Methods.

Fig. 2. The internal structure of Io as revealed by the present study.

Our estimate of k₂ suggests that Io does not have a shallow global magma ocean and is consistent with that expected for a mostly solid mantle (green hues), with substantial melt (yellows and oranges), overlying a liquid core (red/black). Artist rendering by Sofia Shen (JPL/Caltech).

Extended Data Fig. 1. Ground tracks of Galileo (I24, I25, I27, I32 and I33) and Juno (I57 and I58) for altitude ≤ 5,000 km of the closest approach over a colour image mosaic of Io.

The altitudes were computed relative to a spherical Io, assuming an 1,829.4-km radius. The black circles represent the closest approaches. The angles in parentheses represent the true anomaly of Io with respect to Jupiter.

Extended Data Fig. 2. Doppler residuals of Galileo (I24, I25, I27, I32 and I33) and Juno (I57 and I58) near the closest approach to Io.

The vertical black lines represent the time of the closest approach. The Doppler r.m.s. for each flyby is shown in the upper-right side of each plot. The red dashed and cyan dotted lines represent the ±1σ and ±3σ ranges of the Doppler r.m.s., respectively. Nearly all points are well within the 3σ range. The Juno Doppler data are generally about an order of magnitude more accurate than the Galileo Doppler data (note the scale of the axes).

Extended Data Fig. 3. Effect of solid core and 50-km-thick elastic lid on tidal response.

a, Effect of a solid core on the no magma ocean case. Solid and dashed lines represent cases with liquid and solid cores, respectively. The solid core case results in a lower Re(k₂) for a given mantle rheology. b, Effect of adding a 50-km-thick elastic lid to the case with a magma ocean (that is, a five-layer case). Solid and dashed lines represent cases without and with an elastic lid, respectively.

Extended Data Fig. 4. Posterior distribution of the upper mantle thickness and physical libration amplitude.

a, Posterior distribution of the upper mantle thickness for the case with a magma ocean. The upper mantle thickness h represents the depth to the top of the global magma ocean layer. The median value of h is 605 km. The vertical dashed lines indicate 5th and 95th percentiles that correspond to thicknesses of 420 km and 810 km, respectively. At a 3σ level (0.135% probability), the lower bound on the upper mantle thickness is 318 km. b, Posterior distribution of the physical libration amplitude for the cases with and without a magma ocean. The with magma ocean case represents the distribution of solutions with a magma ocean, whose depth is constrained by the observed static gravity and Love numbers. Although the two probability distributions overlap, smaller libration amplitudes are possible for the no magma ocean case, indicating that future measurements of libration could exclude the deep magma ocean case.

Extended Data Fig. 5. Corner plot showing the posterior distribution of Io’s internal structure parameters for the case with a magma ocean.

The variables are as follows: h_i are layer thicknesses, ρ_i are layer densities, δC_nm are non-hydrostatic contributions to gravity coefficients C_nm, μ_i are shear moduli, η_i are viscosities and β_i are the Andrade rheology parameters. The layers are numbered from the outermost layer inward.

Extended Data Fig. 6. Corner plot showing the posterior distribution of Io’s internal structure parameters for the case without a magma ocean.

The variables are as follows: h_i are layer thicknesses, ρ_i are layer densities, δC_nm are non-hydrostatic contributions to gravity coefficients C_nm, μ_i are shear moduli, η_i are viscosities and β_i are the Andrade rheology parameters. The layers are numbered from the outermost layer inward.

Extended Data Fig. 7. Posterior distribution of gravitational and linear libration amplitudes for the cases with and without a magma ocean.

The vertical axis shows the gravitational libration amplitude and the horizontal axis shows the libration amplitude (1σ, 2σ and 3σ regions are shown).