Primordial thermal evolution of Galilean moons in the pebble accretion framework

The four larger satellites of Jupiter, with roughly comparable mass, are termed Galilean moons. They display (i) a water fraction that increases with dis- tance to Jupiter (ranging from no-water for volcanic innermost Io, to approximately half-half ratio of water and rocks for outermost Callisto) as well as (ii) various degrees of differentiation (two end-members corresponding to the two outer moons of similar radius: highly differentiated Ganymede, including a metallic core, locus of the dynamo observed at present, and much-less differentiated Callisto possibly harboring large volumes of ice-rock mixtures). A plausible cause for these variations can be related to the formation of the moons, although their later evolution could also affect both properties.

Owing to the orbits of the four moons (compact, prograde, coplanar and nearly circular), a contemporaneous formation in a circum-jovian disk orbiting in the equatorial plane of the proto-planet is put forward, similar to the formation of planets albeit with significantly different time- and length-scales. The latter is not a minor difference: in practice, classical scenarios [1, 2] cope with the problem of too-much heating associated to large impacts as well as the migration of satellitesimals onto the proto-planet. A new paradigm for the formation of giant planets has emerged re- cently. It has been termed ’pebble accretion’ and highlights the efficiency of accretion of small particles in a context where gas drag dissipates energy as the pebble passes the protoplanet [3]. In this framework, formation of the Galilean moons is envisioned to occur naturally and contemporaneously to the growth of the giant planet. Details are nevertheless controversial: two re- cent scenarios propose either a fast [4] or a slow [5] accretion.

Here, we reproduce these two end-member scenar- ios and specifically focus on the thermal evolution of the growing moons. A simple description of the heat equation is adopted assuming a spherical sym- metry. Heat deposition by pebbles as well as radiogenic heat sources are accounted for during a 30 Myr period that encompasses the formation of all moons. We systematically investigate the influence of timing (start/duration) and consider a range for the concentra- tion in of short-lived radio-isotopes (²⁶Al,⁶⁰Fe,⁵³Mn) that reproduces the composition of LL (high enery content) and CI (low enery content) chondrites. Our results demonstrate that, whatever the scenario, the formation process involves little collisional energy, as can be expected owing to the small size of impactors. As a consequence, after 30 Myr of evolution, moons formed via pebble accretion show a small degree of differenciation or none at all. Either subsequent heat- ing via radioactive decay of long-lived isotopes or tidal heating possibly associated to the moons entrance in the Laplace resonance must be considered to explain the highly differentiated state observed at present for Ganymede. This includes the formation of the hydrosphere, the dehydration of rocks and the melting of the metallic component in order to form the moon’s core.

Interestingly, the main heat sources differ depend- ing on the scenario: in the case of slow accretion, the decay of short-lived radio-isotopes is predominant when accretion of the moons starts sufficiently early; in the case of a fast accretion, the main heat source is associated to viscous dissipation in the disk that heats up the surface of the protosatellites. In the former case, the interior might reach the melting point of water in a limited fraction of the parameter space but only in the innermost region of the moons. Conversely, in the latter case, the melting point can be reached in the outer envelope, as predicted for large moons in the classical formation scenarios [6], but to a much lesser extent. The subsequent evolutionary path leading to the differentiation observed at present for Ganymede thus necessarily involve distinct dynami- cal phenomena: Rayleigh-Taylor type instabilities of the thick rock-ice mixture into the hydrosphere [7] if accretion is slow; if accretion is rapid, a possible delay in solid-state segregation of the rock component if double-diffusive convection occurs owing to a stabilizing density gradient [8].

 

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[2] Canup, R. M., and Ward, W. R. (2009). Origin of Europa and the Galilean satellites. Europa, edited by RT Pappalardo, WB McKinnon, and K. Khurana, University of Arizona Press, Tucson, 59-83.

[3] Johansen, A., and Lambrechts, M. (2017). Forming planets via pebble accretion. Annual Review of Earth and Planetary Sciences, 45, 359-387.

[4] Ronnet,T., and Johansen,A.(2020). Formation of moon systems around giant planets-Capture and ablation of planetesimals as foundation for a pebble accretion scenario. Astronomy & Astrophysics, 633, A93.

[5] Shibaike, Y., Ormel, C. W., Ida, S., Okuzumi, S., and Sasaki, T. (2019). The Galilean Satellites Formed Slowly from Pebbles. The Astrophysical Journal, 885(1), 79.

[6] Monteux, J., Tobie, G., Choblet, G., and Le Feuvre, M. (2014). Can large icy moons accrete undifferentiated?. Icarus, 237, 377-387.

[7] Rubin, M. E., Desch, S. J., and Neveu, M. (2014). The effect of Rayleigh-Taylor instabilities on the thickness of undifferentiated crust on Kuiper Belt Objects. Icarus, 236, 122-135.

[8] O’Rourke, J. G., and Stevenson, D. J. (2014). Stability of ice/rock mixtures with application to a partially differentiated Titan. Icarus, 227, 67-77.