New 3D thermal evolution model for icy bodies application to trans-Neptunian objects

Abstract

Context. Thermal evolution models have been developed over the years to investigate the evolution of thermal properties based on the transfer of heat fluxes or transport of gas through a porous matrix, among others. Applications of such models to trans-Neptunian objects (TNOs) and Centaurs has shown that these bodies could be strongly differentiated from the point of view of chemistry (i.e. loss of most volatile ices), as well as from physics (e.g. melting of water ice), resulting in stratified internal structures with differentiated cores and potential pristine material close to the surface. In this context, some observational results, such as the detection of crystalline water ice or volatiles, remain puzzling. Aims. In this paper, we would like to present a new fully three-dimensional thermal evolution model. With this model, we aim to improve determination of the temperature distribution inside icy bodies such as TNOs by accounting for lateral heat fluxes, which have been proven to be important for accurate simulations. We also would like to be able to account for heterogeneous boundary conditions at the surface through various albedo properties, for example, that might induce different local temperature distributions. Methods. In a departure from published modeling approaches, the heat diffusion problem and its boundary conditions are represented in terms of real spherical harmonics, increasing the numerical efficiency by roughly an order of magnitude. We then compare this new model and another 3D model recently published to illustrate the advantages and limits of the new model. We try to put some constraints on the presence of crystalline water ice at the surface of TNOs. Results. The results obtained with this new model are in excellent agreement with results obtained by different groups with various models. Small TNOs could remain primitive unless they are formed quickly (less than 2 Myr) or are debris from the disruption of larger bodies. We find that, for large objects with a thermal evolution dominated by the decay of long-lived isotopes (objects with a formation period greater than 2 to 3 Myr), the presence of crystalline water ice would require both a large radius (>300 km) and high density (>1500 kg m −3 ). In particular, objects with intermediate radii and densities would be an interesting transitory population deserving a detailed study of individual fates.

Methane, ammonia, and their irradiation products at the surface of an intermediate-size KBO?

“…We used a 3D thermal evolution model by Guilbert-Lepoutre et al (2010) that simulates the temperature of the whole object as a function of its size, density, porosity, orbit, formation delay and radiogenic elements primordial inventory ( 26 Al, 60 Fe, 53 Mn, 40 K, 232 Th, 235 U, 238 U). The bulk assumed composition is dust (77%) plus amorphous water ice (23%), the relative mass fractions being derived from the input 10% porosity.…”

“…In this table, the maximum surface temperature is computed from a thermal balance for the whole surface including different energy inputs such as: the incoming solar energy, (with A the Bond albedo, C the solar constant, d H the heliocentric distance and ξ the local zenith angle), the thermal emission εσT 4 (with ε the thermal emissivity, σ the Stefan-Boltzmann constant and T the temperature), the radial heat flux and lateral heat fluxes, considering a thermal conductivity of about 10 −2 W m −1 K −1 . This thermal balance is computed for about 50 orbits with a full 3D thermal evolution model to get the resulting temperatures (see Appendix B of Guilbert-Lepoutre et al 2010). The insulation per orbit (in J), is computed with the formula (Prialnik et al 2004)…”

“…The resulting equation is numerically solved using an implicit stable Crank Nicolson scheme. A full description of this model can be found in Guilbert-Lepoutre et al (2010). Several physical parameters have to be initialized before simulating the thermal evolution of Orcus.…”

“…at the surface and discuss the results. Finally, we use a new 3D thermal evolution model dedicated to the interiors of KBOs (Guilbert-Lepoutre et al 2010) to describe Orcus' thermal history over the age of the Solar System and the observable consequences of this history on the current surface.…”

Pre-perihelion activity of comet 67P/Churyumov-Gerasimenko

“…The temperature is determined using a numerical model of three-dimensional heat transport (Guilbert-Lepoutre et al 2011). The model solves the heat equation taking into account conduction via contacts between grains, radiation within pores, insolation, and thermal emission at the surface.…”