Investigation of the YORP effect on asteroid (162173) Ryugu &#8211; An application of FEM approach thermophysical model
Authors: Nakano Ryota , Hirabayashi Masatoshi 
Published: July 2021

Summary:We investigated the Yarkovsky-O&#8217;Keefe-Radzievskii-Paddack (YORP) effect [Rubincam 2000] acting on asteroid (162173) Ryugu. To accurately simulate the thermal condition on Ryugu, we employed a thermophysical model recently developed by Nakano and Hirabayashi [2021], which considers self-heating effect and scattering of radiation and solves the 3-dimensional heat equation via Finite Element Modeling (FEM) approach. Our result indicates that on 1 August 2018 TDB, the thermal torque (YORP torque) was acting in a direction that accelerates Ryugu&#8217;s spin rate.&#160;Introduction:Dynamics of small bodies among the near-Earth and main belt asteroids are controlled by secular effects due to thermal radiation forces and torques, known as the Yarkovsky and YORP effects [Rubincam 2000; Vokrouhlick&#253; and &#268;apek, 2002, Bottke et al., 2006]. Recent increase in the number of observed top-like shape objects suggests that the YORP effect is a key mechanism for their spin rates acceleration (or deceleration), which can induce mass-shedding or catastrophic disruptions [e.g., Holsapple, 2010; Hirabayashi, 2015]. Thus, modeling the Yarkovsky and YORP effects based on a proper thermophysical technique is one of the crucial steps to understand their formation and evolution mechanisms. Here, we investigate the YORP effect on asteroid (162173) Ryugu by using a thermophysical model recently developed by Nakano and Hirabayashi [2021].&#160;Thermophysical modeling of Ryugu:Unlike earlier thermophysical models which typically solve the 1-dimensional heat equation, the FEM approach thermophysical model solves the 3-dimensional heat equation. It considers the self-heating and scattering of radiation, similar to other models [e.g., Rozits and Green, 2011; Davidsson and Rickman, 2014]. The surface boundary condition includes: direct solar flux U, diffuse solar radiation flux W, direct self-heating u, and diffuse self-heating w [Davidsson and Rickman, 2014]. To efficiently describe the surface/subsurface thermal evolution, &#8220;layer&#8221; FEM shape model, where only the layers of tetrahedral meshes exist for the surface and subsurface, and the inside is left as cavity, is used. (See Nakano and Hirabayashi [2021] for more detail.)We retrieved Ryugu&#8217;s ephemeris and the sun&#8217;s position vector as seen from Ryugu on 1 August 2018 TDB, using a SPICE kernel for Ryugu. The orbital elements and physical parameters used in this investigation are listed in Table 1. The layer FEM shape model was constructed based on SFM_49k_v20180804 [Watanabe et al., 2019], but the number of facets was decreased from 49k to 4.9k. Figure 1 shows the surface temperature distribution on Ryugu obtained after 25 spins (&#8776;190 hr) at the fixed distance from the Sun. The surface temperature distribution is comparable to that observed by Hayabusa2 spacecraft [Okada et al., 2020].&#160;The YORP effect on Ryugu:Once the surface temperature is obtained, a recoil force df due to reflected solar and thermally radiated photons for each facet can be computed [Rozits and Green, 2012]. Assuming Lambert (isotropic) emission from the surface, it is given by [Vokrouhlick&#253; and &#268;apek, 2002; Rozits and Green, 2012]:where &#949; is the emissivity of the surface, &#963; is the Stefan-Boltzmann constant, T is the surface temperature, G is reflected scattered flux, c is the speed of light, and dS is the facet area. The net torque &#964; acting on Ryugu can be computed by taking a cross product of the facet position r and the recoil force df&#160;for each facet and integrating it over the whole surface:The net torque computed by the above equation can be decomposed into three meaningful YORP torque components of our interest: a spin period change component &#964;&#969;, a spin pole obliquity change component &#964;&#949;, and a precession of rotation &#964;&#968; (see e.g., Bottke et al., 2006 for the equations). Figure 2 shows the time history of YORP torque components over one Ryugu&#8217;s spin. The one-spin averaged YORP torque components are found to be:&#160;Discussion:Due to its top-like asymmetric shape, Ryugu should be susceptible to the YORP effect. Our investigation with the 3-dimensional thermophysical modeling technique clearly showed that Ryugu does experience non-negligible YORP effect. While the YORP torque components change their signs during one spin (Figure 2), the one-spin averaged values were all found to be positive. In particular, the positive &#160;implies an increase of Ryugu&#8217;s spin rate. This contradicts with the current hypothesis that Ryugu spun faster in the past and later slowed down to the current spin state [Watanabe et al., 2019]. In this investigation, however, we only explored Ryugu&#8217;s thermal condition at a particular epoch. Therefore, we cannot infer Ryugu&#8217;s secular dynamical evolution. The YORP effect may be highly sensitive to small topographic features on the surface [Statler, 2009]. The surface roughness may also affect thermal evolutions [Shimaki et al., 2020]. We plan to expand our modeling technique to investigate such effects and to further constrain the Yarkovsky and YORP effects on small bodies.&#160;Table 1. List of parameters used in this investigation&#160;Figure 1. Surface temperature distribution on 1 August 2018 TDB&#160;Figure 2. YORP torque components versus time&#160;Acknowledgments: RN and MH acknowledge support from NASA/Solar System Workings (NNH17ZDA001N/80NSSC19K0548) and Auburn University/Intramural Grant Program.&#160;References:Bottke et al. (2006) Annu. Rev. Earth Planet. Sci., 34; Davidsson and Rickman (2014), Icarus, 243; Hirabayashi (2015) MNRAS, 454; Holsapple (2001) Icarus, 154; Nakano and Hirabayashi (2021) 52nd LPSC, 1292; Okada et al. (2020) Nature, 579; Rozits and Green (2011) MNRAS, 415; Rozits and Green (2012) MNRAS, 423; Rubincam (2000) Icarus, 148; Shimaki et al. (2020) Icarus, 348; Statler (2009) Icarus, 202; Vokrouhlick&#253; and &#268;apek (2002) Icarus, 159; Watanabe et al. (2019) Science, 364