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.
<p><strong>1. Introduction</strong></p> <p>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:</p> <ul> <li> <p><strong>Earth's inner core compaction:</strong> 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 <em>et al.</em>, 1996 [2] and Lasbleis<em> et al.</em>, 2019 [3] by taking into account phase change within the inner core.&#160;</p> </li> <li> <p><strong>Transneptunian objects (TNOs):</strong> 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]).</p> </li> </ul> <p>&#160;</p> <p><strong>2. Two-phase flow model</strong></p> <p>The model is based on the two-phase formalism developed by Bercovici <em>et al.</em>, 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 (<strong>Fig. 1</strong>), 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).</p> <p><img src="data:image/png;base64, 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