Geometric Correction for Thermal Imaging of Asteroid Ryugu 1 Observed by TIR onboard Hayabusa2 2

The thermal infrared imager (TIR) onboard the Hayabusa2 spacecraft performed thermographic 6 observations of the asteroid 162173 Ryugu (1999 JU3) from June 2018 to November 2019. In this study, 7 we performed a geometric correction for TIR images by making a one-to-one correspondence between 8 the observed areas and the surface coordinates derived from a shape model of Ryugu. The pointing 9 direction, which is an alignment direction of TIR, was adjusted by rotating the TIR frame relative to 10 the base of the Hayabusa2 frame using a least-squares ﬁt. This geometric correction allows us to 11 identify observed local areas within one pixel, which corresponds to 5 m error in a 5 km altitude 12 observation. The corrected temperature images projected onto the shape model were constructed. Hot 13 temperature regions were found at the base of Ejima Saxum and Otohime Saxum, for instance. A 14 simulation result indicates that multiple radiations from the surrounding terrains generate hot regions. 15 The estimated thermal inertia of the base of Ejima Saxum as characteristic shape area is approximately 16 300 Jm − 2 s − 0 . 5 K − 1 within the error bars of the observed temperature proﬁle. This estimation is 17 succeeded by performing the geometric correction in case that the surface topographic features are 18 greater than the spatial resolution of the pixel. However, thermal inertia estimations of smooth terrains, 19 such as the center of Urashima crater, were diﬃcult probably because of surface roughness eﬀects. Our 20 results suggest the necessity to develop a hybrid thermophysical model that implements large- and 21 small-scale surface roughness. 22 The thermal infrared imager (TIR) onboard the Hayabusa2 spacecraft performed thermographic observations of the asteroid 162173 Ryugu (1999 JU3). In this study, we performed a geometric correction for TIR images by making a one-to-one correspondence between the observed areas and the surface coordinates derived from a shape model of Ryugu. This geometric correction allows us to identify observed local areas within one pixel, which corresponds to 5 m error in a 5 km altitude observation.

Hayabusa2 is a Japanese asteroid sample return mission that rendezvoused with the asteroid 162173  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 period is 7.63 hours. Kitazato et al. (2019) suggested that the surface materials of Ryugu, observed using 31 the near-infrared spectrometer (NIRS3), are similar to thermally or shock-metamorphosed carbonaceous 32 chondrites. The optical navigation camera (ONC) onboard Hayabusa2 found several characteristic 33 features of the surface in the scale of centimeters to meters; they are large ridges, regolith deposits, 34 and cracked rocks (Sugita et al. 2019). The gravitational observation indicated that the bulk density of 35 Ryugu is 1.19 ± 0.02 gcm −3 (Watanabe et al. 2019). These results implied that the asteroid Ryugu has 36 a porous, coalesced rubble piles internal structure. 37 The thermal infrared imager (TIR) onboard the Hayabusa2 is a thermographic camera of 328 × 248 pixels 38 resolution (Okada et al. 2017). The sensor is an array of microbolometers, and one pixel has a size 39 of 37 µm. The observation wavelength is integration energy ranges from 8 to 12 µm. The field of view 40 is an angle of 12.66 • × 16.74 • , and the spatial resolution is 0.051 • /pixel. The goal of TIR is to reveal 41 the history of Ryugu, such as the thermal properties of coalesced parent bodies, orbital evolution due to 42 radiation force (Yarkovsky effect, Bottke et al. 2006), and the thermal alteration in parent bodies. In 43 particular, to obtain thermal inertia of the Ryugu surface is the primary purpose. The thermal inertia is 44 written as Γ = ρc p k, where ρ is the bulk density, k is the thermal conductivity, and c p is the specific 45 heat. 46 The observed thermal images of TIR indicated that the distribution on the brightness temperature of the 47 Ryugu surface is broadly homogeneous over the observed hemisphere. This phenomenon is considered changes drastically (e.g., bases of large boulders) was not determined.

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The observed temperatures are affected by the surface terrain larger than a pixel resolution, such as 59 bases of large boulders. Thus, the derivation for the accurate observation area of TIR is necessary to  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 determine actual surface temperature. The shape models of Ryugu were constructed by ONC observations 61 (Watanabe et al. 2019). The position and attitude of Hayabusa2 were calculated and controlled 62 by an attitude and orbit control system (AOCS) and controlled by a reaction control system (RCS) 63 (Tsuda et al. 2013). After each observation and following data reduction, the data of ONC and the 64 light detection and ranging (LIDAR) laser altimeter provided detailed trajectories that include relative 65 attitude and position between Ryugu and Hayabusa2 after observation (Matsumoto et al. 2020 In this study, we performed a geometric correction with a one-to-one correspondence between the observed 75 area and the surface coordinate addressed on the polygons of the shape model. The pointing direction of 76 TIR was adjusted to rotate the frame of images from the Hayabusa2 frame using a least-squares fit. We 77 update the alignment values of TIR and discuss the application for temperature estimation of the Ryugu 78 surface using the geometric correction, comparing the observed data with the simulated data.

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The observed data of TIR were converted from digital data to brightness temperature using a calibration product), and the higher degree products.

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The brightness temperature projection from a TIR image to a shape model of Ryugu is expressed as 118 a coordinate transformation from the pixel coordinate to the Ryugu coordinate. We consider that 119 the observed brightness temperature in a pixel is the mean temperature of the region because the 120 TIR pixel detects total radiation fluxes from a region of the Ryugu surface (e.g., 5m squares in Mid-121 Alt). Here, we assume that the observed fluxes are isotropic radiation fluxes from the Lambertian 122 surface. The brightness temperature value in an image is directly converted to that in a shape model as  The shape-to-image temperature conversion is written as well as the image-to-shape conversion to 136 iterate the temperature projection. Note that we consider a blended brightness temperature of a pixel 137 included rays from several polygons of the shape model. Thus, the reprojection is irreversible, i.e., where k is the emissivity, σ is the Boltzmann constant, s k is the area pf the polygons, φ k is the emission 142 angle to TIR direction, and k denotes the index of the polygon. The observation area for one pixel is  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 written as the sum of polygon areas, as follows: We neglect the scattering component because the intensity of the radiation flux in the is 8 to 12 µm 145 wavelengths is more than two orders of magnitude smaller than that of infrared radiation of a body with 146 about 300 K. We assume a constant emissivity each facet, and thus the re-imaged temperature τ for a 147 pixel is rewritten using Equation (1) and (2), as follows: The frame 150 transformation is described by using the Euler rotation, as follows: where R z , R y , and R x form the Euler rotation matrix in the right-handed coordinate system. The 152 matrix R z is the rotation of the TIR boresight vector, which has a bimodal path in the clockwise and 153 the counterclockwise rotations. In this study, R z is fixed as a unit matrix because TIR is a 2D imager, 154 and this parameter is not effective in minimizing the converge value of the least-squares fitting by the 155 geometric correction. Hence, Equation (4) is written, as follows: where θ x and θ y are the Euler angles. shape T (i, j) in the image pixel coordinate using the least-squares fit, as follows: 7   1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 where RSS is a residual sum of squares in temperature. The free parameters of this fitting are the Euler 163 angles of θ y and θ x in Equation (5). The fitting is performed by using the algorithms of the Levenberg-

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Marquardt and Simplex fitting method (Press et al. 2007). The fitting converged value of RSS is ideally 165 zero. However, the observed temperature at the asteroid limb increases the RSS value because the pixel 166 value at the limb includes temperatures of the Ryugu surface and space background.

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The geometric correction was performed for the observed TIR images in the early major observations.   values of TIR, which will be released in December 2020.