Numerical Model of Reduction of Apparent Thermal Inertia by Interrupted Vertical Heat-Flow

Introduction: The JAXA Hayabusa2 sample return mission investigated asteroid (162173) Ryugu via remote sensing (Tsuda et al., 2013, Watanabe et al., 2019), deployed the DLR/CNES MASCOT (Ho et al., 2021), performed an artificial impact experiment (Arakawa et al., 2020) and returned samples to Earth (Yada et al., 2022). Ryugu is a rubble-pile asteroid with similarities to aqueously altered carbonaceous chondrites, in particular CI chondrites (Kitazato et al., 2021, Hamm et al., 2022, Nakamura et al. 2022, Yokoyama et al., 2022). One of the biggest surprises was the prevalence of boulders and dm-sized pebbles on the surface and the deficiency of smaller particles (Jaumann et al., 2019, Sugita et al., 2019). Such finer particles were expected to dominate the surface based on thermal inertia estimates from telescopic infrared observations (Müller et al., 2011). The MASCOT radiometer MARA and the main spacecraft’s TIR infrared imager confirmed the thermal inertia estimates from telescopic observations despite the boulder-dominated surface (Grott et al., 2019, Okada et al., 2020). The low thermal inertia was confirmed to be an intrinsic property of the boulders themselves (Grott et al., 2019, Hamm et al., 2020, Sakatani et al., 2021, Hamm et al., 2022). More specifically, the presence of a layer of dust masking the thermophysical properties of the boulder was limited to small patches of thin dust layers, or no dust at all (Biele et al., 2019, Hamm et al., 2023). In contrast to these in-situ results, the analysis of sample fragments by lock-in thermography resulted in a much higher thermal inertia more comparable to that of meteorites samples (Ishizaki et al., 2023). In this study we attempt to reconciliate the results from spacecraft observations and laboratory analysis by expanding our thermophysical mode to incorporate horizontal fractures. This procedure has been proposed by Elder et al., 2022. We investigate if it is possible to explain the MARA observations with a fracture boulder of higher bulk thermal inertia. This work has implication on the regolith gardening on asteroids like Ryugu as weak and porous boulders would respond to impacts of micro-meteorites differently than fracture boulders with low porosity (Cambioni et al., 2021).

Methods: We start from the 1D-thermal model as used in Hamm et al., 2020. The heat conduction equation is solved for a 1D grid of N points from x₀ = 0 to x_N  . At the lower boundary condition, the flux is set to zero. The upper boundary condition is given by the energy balance. Illumination is calculated by averaging over those DEM-facets of the boulder shape model within the MARA field of view.  The emissivity of the surface reduced by thermal reradiation as described in Hamm et al., 2023. Here we modify the model such that the heat conduction equation is given by:

ρc_p ∂T/∂t = σ(T⁴(x_d,t)- T⁴(x_u,t))

For x_u <=x <= x_d, with x_d the lower edge of the fracture and x_u the upper  edge, i.e., closer to the surface.  Elsewhere on the grid the heat conduction equation is:

ρc_p ∂T/∂t = k ∂²T/∂x²

This adaption accounts for radiative transfer across a horizontal fracture that blocks the conductive heat transfer. It is valid locally within the material if the fracture is spread far enough to neglect conduction over contact points. Also, the model assumes that the fracture is wide enough to neglect heat transfer contributions by evanescent waves (Persson and Biele, 2022).

We vary the depth of the crack and vary the thermal conductivity  of the bulk material. For specific heat capacity and density we use the bulk values of the Ryugu samples as reported in Nakamura et al., 2022:  c_p = 865J/K and ρ = 1800 kg/m³. The thermal conductivity is varied such that the thermal inertia TI = (kρc_p)^0.5  varies from 300 to 1000 Jm^-2K^-1s^-1/2,(units assumed hereafter).

Preliminary Results:

Figure 1 shows preliminary results of the thermophysical model in comparison to the surface temperature observations by MARA. For reference we show the result for a simplified thermal model with no fracture and a thermal inertia of 300 (Hamm et al., 2023). A fracture placed at 1 cm depth results in a similar nighttime temperature curve even for a bulk thermal inertia of 600. At shallow fracture depth the resulting temperature curve mainly depends on the depth of the fracture rather than bulk thermal inertia. Nevertheless, the model cannot reproduce the temperature drop after local sunset. This could be due to the simplicity of our model. It could also mean that the average thermal inertia of layer observed by MARA is lower than that of the returned sample due to a selection effect caused by the destructive sampling mechanism.  

Figure 1: Surface temperature derived from the MARA 8-12 µm filter in comparison to result of the thermopysical model with various parameters. In green is the best fitting model curve for a homogenous 1D-model with no modelled fracture. In shades of orange is the model assuming a fracture at depth h and a much higher bulk thermal inertia.

Acknowledgement: This work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-No. 497966340. 

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