DART mission ejecta plume: Modeling the reflectance through radiative transfer and geometric optics in support to LICIACube observations
Authors: Hasselmann Pedro Henrique , Bertini Ivano , Zanotti Giovanni , Rossi Alessandro , Ivanovski Stavro , Gai Igor , Deshapriya Jasinghege Don Prasanna , Mazzotta Epifani Elena , Dotto Elisabetta , Della Corte Vincenzo , Zinzi Angelo ,   LICIACube Team
Published: September 2022

&lt;p&gt;&lt;strong&gt;Introduction:&lt;/strong&gt; DART mission will be the first to undertake an orbital deflection experiment against a Near-Earth Asteroid. The smallest member of the binary Didymos-Dimorphos system will be impacted by the 660-kg spacecraft at the velocity of 6.6 km/s, leading the orbital period to change in return. The expected baseline kinetic energy is 9.7 GJ [1], about half the input energy of Deep Impact[2], and &gt;10^5 kg of mass is to be released [3].&lt;/p&gt;&lt;p&gt;The impact will produce an ejecta plume, lasting for several minutes [3], that will be observed by ASI/LICIACube camera up to about 4 m/px resolution [4,5] and phase angles ranging from 45 to 120 deg. The plume is therefore expected to be resolved during several frames and its phase function studied in order to retrieve properties such as albedo, grain size frequency distribution and optical depth. Therefore, we put forth a light scattering model that relies on previous knowledge about the Dydimos binary system composition [6] and the Deep Impact event [7].&lt;/p&gt;&lt;p&gt;&lt;strong&gt;LICIACube Observations:&lt;/strong&gt; The Light Italian Cubesat For Imaging Asteroids is a 6C Cubesat hosted by DART spacecraft. LICIACube will detach from DART spacecraft 10 days from the nominal impact date of 26&lt;sup&gt;th&lt;/sup&gt; September 2022 to start the trajectory correction to be positioned in fly-by mode. LICIACube payload holds two optical cameras, LUKE and LEIA, designed for color imaging studies [5]. At 167 sec after the impact, the Italian Cubesat will reach the closest approach and obtain the highest resolution images from the binary system.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Methodology: &lt;/strong&gt;&lt;em&gt;grain &lt;/em&gt;&lt;em&gt;size range.&lt;/em&gt; To provide support and analyze the broad grain&amp;#8217;s size distribution range expected in the plume, we relied two numerical codes covering two different size regimes: (i) The Mishchenko et al., [8,9] radiative transfer code for Mie-Lorentz scatters distribution (~0.5-80 microns size in visible range) with Percus-Yevick filling factor correction (called RTT-PM, [10]) to model the thick portion of the plume; (ii) and the Muinonen et al. [11] ray optics code for diverse particle shapes and sizes higher than 100 microns.&lt;/p&gt;&lt;p&gt;&lt;em&gt;model conditions. &lt;/em&gt;The plume boundaries are considered much similar to an atmospheric cloud, with particles sparse, many mean radii separated from each other, and the observations in far-field, removed several kilometers from the object of study. Furthermore, we imposed that the number of large particles (&gt;100 microns) is much smaller than the number of Mie-Lorenz particles, therefore limiting the interactions among the large particles, but not with the small particles. Hence, the validity regime for the radiative transfer equation is conserved. Furthermore, coherent effects, shadowing, and opposition effect mechanisms are out of the scope of our calculations and observational conditions with LICIACube.&lt;/p&gt;&lt;p&gt;&lt;em&gt;interaction.&lt;/em&gt; The interactions are only resolved between the thick cloud and the &gt;100 microns particles. In the first approach, we compute the particles hovering over the radiative transfer semi-infinite plane of the thick plume, as it gets backlit in varied distances up. In reverse, the thick plume is forward-lit by the particle scattering. In the second approach, the large particles are embedded in the thick plume up to optical depth = 5, again, the medium is considered sparse.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Preliminary Results: &lt;/strong&gt;Given that Didymos is an S-type asteroid, with visible spectra profile very similar to L/LL Chondrites [6], we selected the Itokawa sample size frequency distribution obtained by the Hayabusa mission as analog [12]. L/LL Chondrite most abundant minerals are Fayalites and Ferrosilites. However only VIS optical constants for Fayalites were recovered [13], thus we stick with it in our simulations. In Fig. 1, we present the bi-directional reflectance distribution factor (BRDF) for the layers composing the plume in our simulation: (I) thick &amp;#8220;core&amp;#8221;, multiple-scattering Mie RTT-PM; (ii) &amp;#8220;scattered small particles'', single-scattering-only Mie-Lorenz particle volumes; (iii) &amp;#8220;scattered large particles&amp;#8221;, single-scattering-only &gt;100 microns particle volumes. The BDRF can therefore vary as the volumes become less opaque, leading to less reflectiveness for middle phase angles.&lt;/p&gt;&lt;p&gt;In future developments of our modeling, we will use results from ejecta dynamics to constrain the number of particles and population for different zones and lines of sights through the plume [14, 15, 16].&lt;/p&gt;&lt;p&gt;Furthermore, the interaction of the large particles and the thick Mie particle cloud is under refinement, as we test the codes for different binning, distances and depths. Nonetheless, first tests indicate a magnification of the overall BRDF for large azimuth angles, due to coupling with the overall forward scattering behavior of the large particles.&lt;/p&gt;&lt;p&gt;&lt;img src=&quot;https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.d8ce00dfe38266773182561/sdaolpUECMynit/2202CSPE&amp;app=m&amp;a=0&amp;c=e5bab3f77dce15673a50453c455b88bf&amp;ct=x&amp;pn=gnp.elif&amp;d=1&quot; alt=&quot;&quot; width=&quot;758&quot; height=&quot;421&quot;&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Fig. 1. &lt;/strong&gt;bi-directional reflectance distribution factor for different layers of the plume,&amp;#160;separately. Fayalite&amp;#8217;s optical constants at 550 nm (Re(m)=1.6, Im(m)=5e-3) are used, together with Itokawa sample size frequency distribution (Nakamura et al., 2012). Filling factor for RTT-PM is fixed at 0.1%.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Acknowledgements:&lt;/strong&gt; This research was supported by the Italian Space Agency (ASI) within the LICIACube project (ASI-INAF agreement AC n. 2019-31-HH.0).&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References: &lt;/strong&gt;[1] Sarli et al., 2017, AAS/AIAA 17-206.[2] Groussin et al., 2010, Icarus 205, 627&amp;#8211;637.[3] Cheng et al., 2020, Icarus 352, 113989.[4] Dotto et al., 2021, PSS, Volume 199, 10518.[5] Poggiali et al., 2022, PSJ Focus Issue (submitted).[6] Ieva et al., 2022, PSJ Focus Issue (submitted).[7] A&amp;#8217;Hearn, 2006, 229th IAU Sym. ACM Proc., 33-40.[8] Mishchenko et al., 1999, JQSRT, &lt;strong&gt;63&lt;/strong&gt;, 409-432.[9] Mishchenko et al., 2015, JQSRT 156, 97-108.[10] Ito et al;, 2018, JGRE 123, 5, 1203-1220[11] Muinonen et al., 2009, JQSRT 110, 14-16, 1628-1639.[12] Metzger &amp; Britt, 2020, Icarus 350, 113904.[13] Fabian et al., 2001, A&amp;A 373, 1125&amp;#8211;1138.[14] Rossi, A. F. et al., 2022, PSJ, Focus Issue (in press).[15] Zanotti, G., and M. Lavagna, 2020, IAC 71.[16] Ivanovski et al., 2022, PSJ Focus Issue (submitted).&lt;/p&gt;