The Macroporosity of (162173) Ryugu is estimated based on the observed boulder size-frequency distribution

Biele, Jens

Grott, Matthias

Honda, C.

Kameda, S.

Michel, P.

Michikami, Tatsuhiro

Neumann, Wladimir

Sakatani, N.

Schröder, Stefan

Sugita, S.

Institute of Transport Research:Publications

MACRO-POROSITY AND GRAIN DENSITY OF C-TYPE ASTEROID (162173) RYUGU.  M. Grott1, J. Biele2, P. Michel3, S. Sugita4, S. Schröder1, N. Sakatani5, W. Neumann1, S. Kameda6, T. Michikami7, C. Honda8, 1German Aerospace Center, Berlin, Germany (Matthias.Grott@dlr.de), 2German Aerospace Center, Cologne, Ger-many, 3Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Nice, France, 4University of Tokyo, Tokyo, Japan, 5ISAS/JAXA, Sagamihara, Japan, 6Rikkyo University, Tokyo, Japan, 7Kindai University, Hiroshima, Japan, 8University of Aizu, Aizu-Wakamatsu, Japan.   Introduction:  Upon arrival of the Hayabusa2 spacecraft [1] the C-type asteroid (162173) Ryugu was found to be a spinning top-shaped rubble pile [2], whose surface is dominated by large blocks and boul-ders [3]. A regolith cover of fine particles appears to be absent [4]. Boulders on Ryugu are predominantly dark and rugged [4,5], and these boulders appear to be simi-lar to CI chondritic meteorites [5,6]. Thermal proper-ties a boulder measured in-situ indicate high intrinsic porosities [6], consistent with the overall low bulk density of the asteroid [4]. Assuming typical grain densities for carbonaceous chondrites, bulk porosities close to 50% would be expected [2]. Porosity inside rubble pile asteroid Ryugu can be separated into two contributions: the first one stems from the intrinsic porosity of rocks and boulders and is termed micro-porosity φm, whereas the second contri-bution refers to voids in between individual rocks and is termed macro-porosity φM [7]. Given the size distri-bution of particles, the  macro-porosity of the asteroid can be calculated using semi-empirical mixing models [7,8], assuming the surface distribution of boulders to be representative for the entire asteroid.  Data: Boulder size and shape distributions have been determined by [3] using data from the Hayabusa2 on-board navigation camera (ONC). Images were taken at altitudes between 20 km and 6.5 km with resolutions of up to 0.65 m/pixel, and size-frequency and shape distributions were determined in the 0.02 to 140 m size range (Figure 1). Size-frequency data was fitted using power laws, and power law indices be-tween 1.65 and 2.65 have been obtained [3], with 2.65 being the best fit for the global dataset. Furthermore, particles are generally elongated, and axis ratios for boulders >2m are close to 0.70, consistent with boulder generation by impact processes [3].  We fitted the data provided by [3] to a simple pol-ynomial, and data can be adequately represented by a second order function in log-log coordinates. Results of the fitting are shown together with the uncertainty of the data in Figure 1. It is worth noting that representing the data using a single power law for the entire size range does not adequately represent the data [3].  Modeling:  Here we compute the macro-porosity φM of Ryugu using semi-empirical mixing models [7,8] given the size-frequency distribution of observed boul-ders [3]. For poly-disperse particles, macro-porosity can be much lower than the canonical 36% for a ran-dom close packing or ~42% for a random loose pack-ing of spherical mono-sized particles [7], as smaller particles start filling the gaps between larger ones. Once φM has been computed, macro-porosity φM, mi-cro-porosity φm, and bulk porosity φB are related by  Figure 1: Cumulative size-frequency distribution of boulders observed on Ryugu. The global fit represents the data of [3], spanning the size range between 0.02 and 140 m.   𝜙𝜙𝑀𝑀 = 1 − 1 − 𝜙𝜙𝐵𝐵1 − 𝜙𝜙𝑚𝑚 (1)  where φB = 1 - ρb/ρs. Here, ρb and ρs are Ryugu’s bulk and grain density, respectively. While the bulk density of Ryugu has been estimated to be 1190 ± 20 kg/m3 [4], the boulder’s micro-porosity φm cannot currently be unambiguously constrained due to the difficulties associated with extrapolating meteorite thermal conductivities to porosities in excess of 20% [9]. However, end-member models [10,11] suggest micro-porosities φm between 28-35% and 41-55% for Ryugu’s dark and rugged boulders [6]. Here we use Monte-Carlo simulations to propagate these uncertain-ties to the uncertainty of Ryugu’s grain density ρs.   Results: Assuming minimum and maximum parti-cle sizes of 0.02 and 140 m, Ryugu’s macro-porosity φM is calculated to be 15 ± 2.5 %, and results of the Monte-Carlo simulations using 1000000 draws are 10-210-110 0 10 1 10 2 10 3Diameter [m]10 010 510 10N(>D) [km-2]Global FitData incl. Uncertainty2038.pdfAsteroid Science 2019 (LPI Contrib. No. 2189)shown in Figure 2, where a histogram of the grain density ρs is shown. Owing to the two different models used to extrapolate boulder micro-porosity, two sepa-rate peaks are obtained for the distribution of admissi-ble grain densities. Extrapolation of thermal properties using the porosity model of [11] results in lower mi-cro-porosities, and consequently, obtained grain densi-ties also have to be lower to satisfy the constraint posed by Ryugu’s bulk density. On the other hand, the extrapolation using the model of [10] results in higher micro-porosities and higher grain densities. Overall, grain densities ρs = 2002 ± 85 kg m-3 and ρs = 2672 ± 229 kg m-3 are obtained for the two different models.  Figure 2: Results of the Monte-Carlo simulations showing the histogram of grain density ρs assuming two endmember models for the micro-porosity φm [6].  Discussion: In the above analysis, we have ne-glected the influence of particle shape on the porosity. In general, particle sphericity can have a significant effect on the porosity of particle mixtures, but this effect only becomes important for sphericities of less than 0.8. For the Ryugu boulders, axis ratios b/a of close to 0.7 have been reported [3], resulting in sphe-ricities of 0.84. Therefore, particle shape can be con-sidered a second order effect here. The grain densities obtained here are much lower than typical grain densities of ordinary chondrites, which range from 3520 to 3710 kg m-3 [10], and also lower than those of most carbonaceous chondrites, which typically have grain densities in excess of 3360 kg m-3. Only the CM and CI sub-classes show lower grain densities, and ρs,CM  = 2960 ± 40 kg m-3 while ρs,CI  = 2420 kg m-3 [10]. The Tagish Lake meteorite, an ungrouped carbonaceous chondrite, exhibits similar grain densities in the range between 2430 and 2840 kg m-3 [12]. While the larger grain densities obtained here are consistent with the CM, CI, and Tagish Lake re-sults, the lower densities are inconsistent with those of known meteorite samples.  Support for extrapolating boulder porosities using the model by [10] rather than the model by [11] is provided by laboratory measurements of thermal con-ductivity at high porosities [13]. The UTPS Tagish Lake simulant [14] has a grain density of 2813 kg m-3 and a porosity of 47%, while at the same time exhibit-ing thermal conductivities similar to those obtained for Ryugu’s rugged boulders. This falls within the range predicted by the model of [11], favoring grain densities of ρs = 2672 ± 229 kg m-3. However, more laboratory measurements at high porosity are needed to confirm these results and reduce uncertainties. Results presented here assume that the size-frequency distribution observed on the surface is repre-sentative for the entire asteroid, but it has been argued that particle size sorting may take place during rubble pile re-accretion, with larger particles accreting first [15]. On the other hand, seismic shaking and the Brazil Nut Effect could lead to an overrepresentation of large particles on the surface [16]. This topic can be ad-dressed once grain density and micro-porosity have been determined from the returned samples. Summary: Rubble pile asteroid (162173) Ryugu’s boulder size-frequency distribution is consistent with a macro-porosity close to 15 ± 2.5 %, provided the ob-served surface distribution of boulders is representative for the bulk asteroid. In this case, a grain density of  ρs = 2672 ± 229 kg m-3 is best compatible with the avail-able data, consistent with a CI or CM composition. Acknowledgements: P.M. acknowledges support from CNES and from the Acad. 2 & 3 of Univ. Côte d’Azur IDEX JEDI. References: [1] Watanabe et al., Space Sci. Rev. 208, 3–16 (2017). [2]  Watanabe et al., Science, 364, 6437, 268–272 (2019). [3] Michikami et al., Icarus, 331, 179-191 (2019) [4]. Sugita et al., Science, 364, 6437 (2019). [5] Jaumann et al., Science, 365(6455):817–820 (2019). [6] Grott et al., Nature Astronomy, doi: 10.1038/s41550-019-0832-x (2019). [7] Yu and Zou, Powder and Particle Journal, 16, 68–81 (1998). [8] Zou,  Gan,  and  Yu, Chemical Engi-neering Science, 66, 220, 4711–4721 (2011). [9] Macke,  Consolmagno, and Britt, Meteorit. Planet. Sci. 46, 1842–1862 (2011). [10] Flynn et al., Chem. Erde, 78, 269-298 (2018). [11] Henke et al. A&A 589, A41 (2016). [12] Ralchenko et al., LPSC abstract #1021 (2014). [13] Hamm et al., LPSC abstract #1373 (2019). [14] Miyamoto et al., LPSC abstract #1882 (2018). [15] Britt and Consolmagno, Icarus, 152, 134-139 (2011). [16] Maurel et al., MNRAS, 464, 2866-2881 (2017).  1600 1800 2000 2200 2400 2600 2800 3000 3200 3400Grain Density s  [kg m-3]00.010.020.030.040.050.060.07Fraction of ModelsHenke et al., 2016Flynn et al., 20182038.pdfAsteroid Science 2019 (LPI Contrib. No. 2189)

Macro-Porosity and Grain Density of C-Type Asteroid (162173) Ryugu

Macro-Porosity and Grain Density of C-Type Asteroid (162173) Ryugu

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