New theoretical results on asteroid regolith specific heat, cohesion and heat transfer,and a revisit of comet 67P surface strength
J. Biele1, M. Grott2, S. Ulamec1, J. Knollenberg2, J.-B. Vincent2
1
German Aerospace Center, DLR-RB/MUSC Cologne, Germany
2German Aerospace Center, DLR-PF, Berlin, Germany
We report and discuss on some of our recent theoretical advances on asteroid regolith specific heat cP, van der Waals-force
between regolith particles, and heat transfer in the regolith. We also report on the strength of comet surface material, includinga refined model of its size dependence and wide variability depending on the degree of “cementation” (sintering) and a reappraisal of some particularly low and high strength values for comet 67P reported earlier in the literature. Thermal andmechanical properties are correlated.
Specific heat
Surface temperature models could be impacted by the drastic decrease in cP(T) values toward low temperatures; thermalmodels generally assume lunar basalt calorimetric properties, which are not well known outside the data range 90 K to 350 K.
Indeed, ‘knowledge of specific heat variability as a function of temperature and bulk material composition remains largely
under-constrained for the need of planetary thermal modelers’[1].
In particular, the specific heat capacity of geological materials
relevant to solar system body surfaces below room temperature is
not particularly well constrained and the thermal modelingcommunity only has a limited set of adequate ready-to-use cP(T)trends for planetary surface temperature modeling. - We provide
the means to calculate synthetic cP(T) from a known bulk
composition, for almost any solar system material from 10 K to1000 K, and additionally a method to predict the specific heat curve
beyond the temperature range measured, even if the composition isnot (well) known. [2]Van-der-Waals force[3] have calculated the pull-of force due to van der Waals interaction, and due to capillary bridges, between particles with selfaffine fractal (random) roughness, which is realistic. They have shown that surface roughness, if big enough, results in aninteraction (VdW) force which is independent of the size of the particles, in contrast to the linear size dependency expected forparticles with smooth surfaces (simple JKR, DMT). For fractured rock particles a realistic surface roughness reduces the pullof force between micrometer sized particles by a factor of ∼ 100, and even more for larger particles, it is of the order of 0.1 – 1nN. This means that the dependence of cohesive strength (or tensilestrength, in N/m²) of the granular medium on particle size is due tothe increase in the number of particle-particle contacts (per unitarea) alone. A decrease in particle size only increases the number ofcontacts without changing the strength of the particle-particle
adhesive bond. The small-particle glue idea, figure 1, of [4] is agood one! This results also affects the predicted (high) porosity of
granular media in micro-gravity, since the granular Bond number isvery different now.
Figure 1. The big particles (fragments) in an asteroid could be kept together by a matrix of smaller particles. Effective yield stress of rubble
pile asteroids of order (or less than) σY ≈ 25 Pa.

Heat transfer
Thermal conductivity k of granular media and porous rocks seemed well explained by classical theories (Maxwell equations,Stefan-Boltzmann radiative transfer, contact mechanics like Hertz or JKR theory). All those classical thermal conductivity
theories operate with models from the 19th century (Maxwell, Fourier, Stefan-Boltzmann law, Hertz) and completely neglect
phonons and quantum mechanics! We are revising the underlying assumptions, and find that most are doubtful.

Figure 2 Cartoons
depicting idealized (leftand right) and realistic
contact (middle)

Rough irregular rock (silicate) particles do not form strong contacts when granular, not much phonon conduction across point
contacts, JKR not applicable at all, heat transfer by near-field evanescent EM waves at least equally important, (NFRHT)~1/R0.8-dependence. Radiative conduction is not ∝ T3 either, if grains are not well conducting (non-isothermality);different regime if void scale <= thermal wavelength λT ≈3000/T µm K (radiative transfer, dense media scattering andtransmission, Planck not valid if particle size < λT); Most assumptions on porosity dependence, in particular of krad, werewrong [5, 6]. Porous rock effective conductivity (meteorites) as function of porosity in not Maxwell „swiss cheese“, much
lower values at medium porosities  rather weakly cemented/sintered ex granular matter. Cracks, percolating and closepores, .. no theory is available! We are working both theoretically and experimentally to understand this better [7, 8].
Revisit of Comet Surface Strength
For comet 67P, we have re-analyzed the data for the apparently exceptional 67P Abydos site, where originally a lower limit ofseveral MPa for compressive strength was suggested. We use a correlation going back to Digby [9, 10] between strength,
Young’s module and thermal conductivity for weakly sintered porous media; our revised value for compressive strength is 28–690 kPa on the 5–30 cm scale, still representing the probably most competent material on the comet, potentially with a reduced
porosity compared to the average 70–80%. The size effect law [11] for quasi-brittle failures bridging the small-size asymptotic
strength (compressive or tensile) and the power law ~1/d1/2 of LEFM seems to apply for cometary and meteoritic material: thestrength of very small lab samples cannot be simply extrapolated to larger sizes!

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[10] Grott, M., et al., Nature Astronomy, 2019. 3(11): p. 971-976. [11] Bažant, Z.P., Archive of Applied Mechanics, 1999.
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