Modeling first-order scattering processes from OSIRIS-REx color images of the rough surface of asteroid (101955) Bennu
Authors: Hasselmann Pedro Henrique , Fornasier Sonia , Barucci Maria Antonietta , Praet Alice , Clark Beth Ellen , Li Jian-Yang , Golish Dathon , N. DellaGiustina Daniella , Deshapriya Prasanna , Zou Xiao-Duan , G. Daly Mike , S. Barnouin Olivier , A. Simon Amy , S. Lauretta Dante 
Published: October 2020

Introduction: The OSIRIS-REx mission has revealed a dark, boulder-rich, apparently dust-poor surface of the B-type asteroid (101955) Bennu [1], therefore a challenge for bi-directional reflectance (rF) modeling. With an estimated geometric albedo of 4.5% [2], Bennu is darker than many comets, and its reflectance distribution is dominated by single-scattering processes. The general approach to model a dark asteroid&#8217;s bi-directional reflectance distribution is to apply the standard Hapke IMSA model and its shadowing function [3]. However, this can imprecisely describe the roughness slopes for rocky surfaces [4]. Assuming that surfaces are fully diffuse can negate a specular forward-scattering contribution from crystalline components in the regolith [7]. To achieve a more complete photometric modeling of Bennu&#8217;s scattering curve, we rely on the radiative transfer semi-numerical model of Van Ginneken et al. [8,9]. Observations: MapCam is an optical imager [10] on-board the OSIRIS-REx spacecraft, equipped with four broadband color filters (60-90 nm wide) centered at 473 (b'), 550 (v'), 698 (w') and 847 (x') nm. We analyzed images acquired during the Equatorial Station (EQ), a campaign of the Detailed Survey mission phase [11], over a full rotation of (101955) Bennu at a nadir spatial resolution of ~33 cm/px. EQ comprehended seven phase angle configurations &#945; =[7.5&#176; ,30&#176; ,45&#176; ,90&#176; ,130&#176;] .We analyzed the pixel subtended by the mission&#8217;s candidate sample collection sites, for which highly precise, laser altimeter-based digital terrain models (DTMs) were available [12,13]. These four candidate sites were called Sandpiper (latitude=-47&#176;; longitude=322&#176;), Osprey (11&#176;; 88&#176;), Nightingale ( 56&#176;; 43&#176;), and Kingfisher (11&#176;; 56&#176;). The varied latitude and longitudes provided the range of observational conditions required for our analysis.Methodology: The methodology consists of the following steps:a) NAIF SPICE kernels [14] and the DTMs are ingested into a ray-tracing code for rendering shadowed images. This allows us to discount for the effects of macroscopic shadows, leaving only the sub-facet texture to be modeled. These ancillary images provide the incidence, emergence, phase &amp; azimuth for every facet.b) We apply Van Ginneken&#8217;s model to every facet. Occlusion and shadowing as well as the retro-reflection among the reliefs are taken into account. The model has two major components: the analytical expression for the specular reflection; and the numerically-integrated diffusive reflection. At total, the model has three free parameters: &#961; (single-scattering albedo), &#963; (RMS roughness slope), and g (specular-to-diffuse ratio), plus the three more related to the scattering phase function (bi-lobe Henyey-Greenstein function: c, b1, and b2)c) Inverse problem: We run the Monte Carlo Markov Chain to sample the multi-parametric space in order to reconstruct a posteriori probability distribution of solutions for every free parameter, i.e., (&#961;, &#963;, g, b1, b2, c), from which the statistics for every solution are estimated. Results: The MCMC technique reveals some interesting aspects of Bennu's surface (Fig. 1): while the RMS roughness slope of 27+1-5 is in line with what has been obtained for other asteroids using Hapke shadowing function, we are puzzled by the indication of a non-zero specular reflection ratio from the surface (2.6+1&#8722;0.8 %). The specular reflection hints at a possible mono-crystalline component. As for the diffuse rough component, the analysis of the photometric correction of OCAMS images taken at varied phase angles (&#945;) indicates a more complex scenario. Up to &#945; = 90&#176;, the photometric correction is vastly improved by mixing two different solutions for roughness (one with low RMS &#963; and another with global RMS &#963;), a bi-modality already perceived from the MCMC a posteriori distributions. We have shown that most of Bennu's brightness variation can be explained by tuning the roughness slope statistical distribution. Finally, we report a back-scatter phase function for the phase angle range between 7.5&#176;, and 130&#176;, without any expressive spectral trend in the visible range. The MCMC inversion hints at a possible second forward-scatter lobe of at least ~0.2 width. This leads to two possible solutions for the asymmetric factor (&#958; (1) = &#8722;0.360 &#177; 0.030 and &#958;(2) = &#8722;0.444 &#177; 0.020). We also report a dark global approximate single-scattering albedo at 550 nm from the collective analysis of all site candidates of 4.64+0.08-0.09 % . The single-scattering MapCam four-band colors show a similar spectral trend to the global average OVIRS EQ3 spectrum. The four sites together provide a general description of Bennu's colors.Fig. 1. Parametric solutions after the MCMC technique for all sample sites together, and the scattering phase function (bottom row) for each MapCam filters.References:[1] Lauretta, D. et al. Met.. &amp; Plan. Scie., 50, Issue 4, 834-849, 2015.[2] DellaGiustina, D.N. et al., Nat. Astron. 3, 241-351, 2019.[3] Hapke, B. Icarus 59, 41-59,1984.[4] Shkuratov et al., JQSRT 113, 18, 2431-2456, 2012.[5] Davidsson, B. et al. Icarus 201, 335&#8211;357, 2009.[6] Labarre, S. et al. Icarus 290, 63-80, 2017.[7] Bowell, E., et al. Asteroid II, Univ. of Ariz. Press, 1989.[8] Van Ginneken, B. et al. AO 37, 130-139, 1998.[9] Goguen, J. et al. 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