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1. Introduction We are interested in systems where two phases coexist: a solid phase with a high effective viscosity, and a low-viscosity liquid phase which fills the porosity of the solid phase. Two-phase systems, or "mush", are common in planetary sciences: magma extraction, Earth's inner core, icy moons... On terrestrial or icy bodies, such biphasic layers can compact under their own weight, which leads to the extraction of the liquid phase from the solid phase, and compaction of this solid phase. We present here a new model of two-phase flows with phase change (melting or freezing), and focus on 2 applications: Earth's inner core compaction: Whether the inner core crystallises dendritically or by sedimentation, it is likely that some liquid iron is trapped within the inner core, which may explain its low rigidity [1]. We extend here the studies of Sumita et al., 1996 [2] and Lasbleis et al., 2019 [3] by taking into account phase change within the inner core. Transneptunian objects (TNOs): Ices may contain antifreezes like ammonia or methanol which could depress the melting point by up to 155 K [4]. Due to their presence, the melting temperature depends on their concentration. Then it is very likely that there would not be any clear border between solid and liquid if the melting point was reached, but rather a mushy layer. Several authors have studied the thermal evolution of TNOs without these considerations (for instance [5], [6], [7]). 2. Two-phase flow model The model is based on the two-phase formalism developed by Bercovici et al., 2001 [8] for a non-reacting two-phase medium, which we generalise to allow for non-congruent phase change. This requires solving equations of conservation of mass and momentum for each phases, energy, and solute, with appropriate boundary conditions. In our model, the solid and liquid phases are assumed to be in thermodynamic equilibrium, which allows to link temperature and composition through the phase diagram. To simplify the problem, the liquidus temperature is taken to be linear (Fig. 1), which implies that the temperature in the two-phase region is a linear function of solute concentration. We further assume that the solute is considered to be totally contained in the melt (solid/liquid partition coefficient equal to 0). The set of equations is written in 1D spherical geometry. These assumptions allow us to reduce the system of equations to a system of only three equations (conservation of momentum, energy, and solute), which we solve to obtain the temperature (directly connected to composition), radial velocity of liquid (linked to velocity of solid) and porosity (the proportion of liquid). The code solves equations in a 1D sphere, which size can evolve with time, either due to accretion (TNOs during their formation), or solidification (inner core). This is taken into account thanks to an adaptive grid. The code has been developed from the code written by Lasbleis et al., 2019 [3]. 3. Preliminary results Application to Earth's inner core In the inner core, 'light elements', and in particular oxygen, act as antifreezes [9]. Within the inner core, the effect of pressure on the liquidus temperature cannot be neglected, and we thus take this factor into account in the model. The temperature-composition relation thus depends on pressure, or radius; the slope of the liquidus with respect to solute concentration is take to be constant but TL decreases with decreasing pressure and increasing radius. At the inner core boundary, the temperature is set to TL(χ0, r). Fig. 2 and Fig. 3 show the evolution of porosity and temperature in the inner core as functions of time and radius. Application to TNOs When modeling the thermal evolution and differentiation of TNOs, our code has to be associated with an external icy diffusive spherical shell. If in addition we consider the formation of a rocky core, the mush (modeled by our code) is a spherical shell around a spherical rocky core. Our model takes into account the variations with temperature of ice thermal conductivity and heat capacity, which are far better known than for iron Earth's inner conditions [10] [11]. However, the pressure effect on TL is negligible. Acknowledgements This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreements 802699 and 716429). References [1] Deguen, R. (2012). Earth and Planetary Science Letters, 333, 211-225. [2] Sumita, I., Yoshida, S., Kumazawa, M., & Hamano, Y. (1996). Geophysical Journal International, 124(2), 502-524. [3] Lasbleis, M., Kervazo, M., & Choblet, G. (2020). Geophysical Research Letters, 47(2), e2019GL085654. [4] McKinnon, W. B., Prialnik, D., Stern, S. A., & Coradini, A. (2008). The solar system beyond Neptune, 1, 213-241. [5] Bierson, C. J., Nimmo, F., & McKinnon, W. B. (2018). Icarus, 309, 207-219. [6] Desch, S. J., & Neveu, M. (2017). Icarus, 287, 175-186. [7] Malamud, U., & Prialnik, D. (2015). Icarus, 246, 21-36. [8] Bercovici, D., Ricard, Y., & Schubert, G. (2001). Journal of Geophysical Research: Solid Earth, 106(B5), 8887-8906. [9] Alfè, D., Gillan, M. J., & Price, G. D. (2002). Earth and Planetary Science Letters, 195(1-2), 91-98. [10] Klinger, J. (1980). Science, 209(4453), 271-272. [11] McCord, T. B., & Sotin, C. (2005). Journal of Geophysical Research: Planets, 110(E5).

Modeling the evolution and internal structure of large- and mid-size Trans-Neptunian objects (TNOs) is a challenging task, owing to the strong dependence on the thermophysical and structural parameters involved, which are poorly constrained. Thus the outcome of evolutionary tracks for a given object may range from fully pristine to completely differentiated and need to be further constrained by detailed observations of TNOs’ physical and chemical properties. The key question remains, whether knowing surface and bulk properties is sufficient for inferring internal properties and more ambitiously, the evolutionary course of a TNO from formation to present day. Recent models of Charon involve a complex evolution, including the formation of subsurface oceans and past cryovolcanism. This perspective should trigger the development of new comprehensive models, which—combined with new observations—should lead to significant progress in our understanding of how the whole population formed and evolved.

International audience; The transneptunian region has proven to be a valuable probe to test models of the formation and evolution of the solar system. To further advance our current knowledge of these early stages requires an increased knowledge of the physical properties of Transneptunian Objects (TNOs). Colors and albedos have been the best way so far to classify and study the surface properties of a large number TNOs. However, they only provide a limited fraction of the compositional information, required for understanding the physical and chemical processes to which these objects have been exposed since their formation. This can be better achieved by near-infrared (NIR) spectroscopy, since water ice, hydrocarbons, and nitrile compounds display diagnostic absorption bands in this wavelength range. Visible and NIR spectra taken from ground-based facilities have been observed for ∼80 objects so far, covering the full range of spectral types: from neutral to extremely red with respect to the Sun, featureless to volatile-bearing and volatile-dominated (Barkume et al., 2008; Guilbert et al., 2009; Barucci et al., 2011; Brown, 2012). The largest TNOs are bright and thus allow for detailed and reliable spectroscopy: they exhibit complex surface compositions, including water ice, methane, ammonia, and nitrogen. Smaller objects are more difficult to observe even from the largest telescopes in the world. In order to further constrain the inventory of volatiles and organics in the solar system, and understand the physical and chemical evolution of these bodies, high-quality NIR spectra of a larger sample of TNOs need to be observed. JWST/NIRSpec is expected to provide a substantial improvement in this regard, by increasing both the quality of observed spectra and the number of observed objects. In this paper, we review the current knowledge of TNO properties and provide diagnostics for using NIRSpec to constrain TNO surface compositions.