Opposition Observations of 162173 Ryugu: Normal Albedo Map Highlights Variations in Regolith Characteristics

On 2019 January 8, the Telescopic Optical Navigation Camera (ONC-T) on board the Hayabusa2 spacecraft observed the Cb-type asteroid 162173 Ryugu under near-opposition illumination and viewing conditions from approximately 20 km in distance. Although opposition observations have never been used for mapping purposes of a planetary body, we found three advantages for mapping under these conditions: (1) images are free of topographic shadows, (2) the reflectance is nearly independent of the orientation of the surface, and (3) spurious color artifacts that may appear near shadowed terrain are avoided. We present normal albedo maps, one for each of the seven filters (0.40–0.95 μm), using an empirical photometric correction. Global coverage of Ryugu is 99.4%. The 0.55 μm band average normal albedo is 4.06% ± 0.10%. Various spectral variations are derived from these maps. Spectral features of regions and boulders are quantified by examining the normal albedo-derived spectral slope and UV index (spectral slope from visible to ultraviolet wavelength) value. In terms of space weathering, three spectral characteristics are observed over the majority of Ryugu: (1) reddening, (2) increases in reflectance at ultraviolet wavelengths compared to visible, and (3) darkening. By contrast, the bright boulders (“type 3”) show a different trend, with wide variations in the 0.95 μm albedo and UV index. Finally, principal component analysis (PCA) comparisons with other asteroids strongly suggest that the main components of Ryugu belong to the B-Cb-type populations. The PCA feature of the fresh material on Ryugu is close to the Eulalia family.


Introduction
The asteroid explorer Hayabusa2 encountered the Cb-type asteroid 162173 Ryugu between 2018 June and 2019 November at distances of 20 km and less during reconnaissance maneuvers. During this period, the Telescopic Optical Navigation Camera (ONC-T) (Kameda et al. 2017;Suzuki et al. 2018;Sugita et al. 2019;Tatsumi et al. 2019, hereafter S19) on board Hayabusa2 observed Ryugu using seven bandpass filters ranging in wavelength from 0.40 to 0.95 μm. Ryugu is a spinning-topshaped asteroid with an equatorial radius of 502 ± 2 m and a polar-to-equatorial axis ratio of 0.872 ± 0.007 (Watanabe et al. 2019). Ryugu has a very low surface reflectance (geometric albedo at 0.55 μm = 4.0% ± 0.5%; Tatsumi et al. 2020a). Its photometric properties were examined from the ONC images acquired during the approach phase and home position ( Figure 1) prior to 2018 September. The results were used to construct global color maps for each of the ONC-T camera filter wavelengths (Tatsumi et al. 2020a).
On 2019 January 8, ONC-T observed the asteroid under near-opposition illumination and viewing conditions (phase angle <1°.7) from approximately 20 km in distance (∼2 m pixel −1 ) through one rotation period (7.6 hr). In previous missions, opposition observations were utilized for photometric studies, but they have never been used for mapping purposes. This is because observing the entire surface at these small phase angles is difficult, and variations due to topography are muted due to minimized shadows, making this geometry poor for morphological studies. However, this geometry is governed by and is very sensitive to physical properties such as porosity, grain size, and grain size distribution of the regolith (e.g., Hapke 2012). These are the regolith properties most sensitive to alteration by space weathering processes. Opposition observations have several advantages for mapping. First, images are free from topographic shadows. Second, for dark surfaces such as that of Ryugu, the reflectance is nearly independent of the surface orientation, i.e., variations in incidence and emission angles (e.g., Veverka et al. 1978). Third, spurious color artifacts that may appear near shadowed terrain when combining multiband images acquired at slightly different geometries are minimized.
When a reflectance map of a planetary surface is produced, it is standardized to a preselected illumination and viewing geometry to remove reflectance variations due to photometry, thus accenting reflectance variations due to surface physical and chemical properties. The most common geometry consists of an incidence angle of 30°, emission angle of 0°, and phase angle of 30°, which matches the geometry of most laboratory spectral measurements of minerals. However, selecting a standard geometry close to the observed geometries reduces any potential errors in photometric correction due to modeling limitations. Therefore, in this study, we chose to standardize our maps to the opposition geometry of 0°, 0°, and 0°in incidence, emission, and phase. The normal albedo of a surface was defined as the radiance factor (I/F) at the opposition geometry (e.g., Hapke 2012). Thus, the maps created in this study were normal albedo maps of the surface in all seven filters of the ONC-T.
Here, we present the normal albedo maps, one for each of the seven ONC-T filters, of Ryugu's surface as derived from these opposition observations. We examine the variability in normal albedo across Ryugu's surface, including variations in the spectral characteristics, their associations with different morphological features, regolith movement, and potential alteration processes.
In this study, the term "space weathering" is defined separately from solar heating. We use space weathering as the alteration process on the surface due to micrometeorite and solar wind ion bombardment (e.g., Housley et al. 1973;Hapke 2001). As the previous study by Morota et al. (2020) demonstrated that Ryugu underwent a temporary orbital excursion closer to the Sun than the present, it is convenient to use this definition to distinguish between the solar heating that occurred when Ryugu is closer to the Sun and the alteration process that has occurred more recently.

Optical Navigation Camera-telescopic
The ONC instrument consists of three cameras: one telescopic camera (ONC-T) and two wide-angle cameras (ONC-W1 and -W2) (Kameda et al. 2017;Suzuki et al. 2018;Tatsumi et al. 2019). The ONC-T has seven broadband filters ranging in wavelength from 0.40 to 0.95 μm and one wide panchromatic filter (wide band). Table 1 lists the effective central wavelengths of the seven broadband filters as determined by Tatsumi et al. (2019). The wideband filter was not used in the opposition observation campaign. The ONC-T is equipped with a filter wheel for changing the filters, and the CCD is common for all bandpass filters. To change filters, a small gap exists in the observation time for a set of seven-band observations. Although the time difference is small, it causes small changes in illumination and viewing geometry from image to image due to the rotation of the asteroid. According to Tatsumi et al. (2019), the signal-to-noise ratio of typical ONC-T images obtained at the standard temperature (−30°C) is approximately 200.
A full-resolution ONC image is 1024 × 1024 pixels in size (Kameda et al. 2017). The field of view (FOV) of an ONC-T image is 6°.27 with an instantaneous FOV of 22 14 (=0.1074 mrad). Therefore, in this study, the spatial resolution of Ryugu's surface is 2.1 m pixel −1 for images taken at a distance of 20 km. This resolution corresponds to a longitudinal resolution of 0°.24 pixel −1 at the equator. A detailed description of the ONC-T is provided by Kameda et al. (2017).

Operation
Before describing the global opposition observations, we first summarize the nominal spacecraft position and operations surrounding the acquisition of the opposition images. Figure 1 illustrates the Hayabusa2 spacecraft positions (Watanabe et al. 2019) during the mission's proximity phase (asteroid encounter). The Hayabusa2 team defined the "home position" (HP) as a point 20 km above the asteroid with the communications antenna facing in the sub-Earth direction. During nominal operations, the spacecraft was kept in "Box-A," a 10 × 10 × 5 km rectangular volume centered on the HP. This was done for the safety of the spacecraft. The spacecraft hovered at the HP and did not orbit around the asteroid. Because  Note. a Effective wavelength with respect to the solar spectrum (nm) (Tatsumi et al. 2019). The wideband filter is excluded from this table.
Hayabusa2 revolves around the Sun with Ryugu, Hayabusa2 always observes the day side, and the observational solar phase angle is constrained to less than 90°. The solar phase angle at HP changed with the seasons, as illustrated in Figure 2.
Although the solar phase angle values naturally dropped below a few degrees around 2018 November and December, in this period, the Sun's position was between the spacecraft and the Earth, and communication between the spacecraft and the Earth control center was not possible. During this "conjunction" period ( Figure 2), ONC science observations were not executed. Instead, near-zero phase angle observations were acquired just after the conjunction period.
On 2019 January 7, Hayabusa2 began its "Box-B" operations. Hayabusa2 moved from the HP toward a subsolar position (+X direction in Figure 1). Hayabusa2 reached the subsolar position on 2019 January 8, and ONC-T observed the asteroid in the opposition geometry from an approximately 20 km altitude over the course of more than one rotation period. The January 8th image set served as the input for this study. In this observation sequence, a seven-band image set was obtained at every 30°of the rotational phase. The final opposition image data set from this operation included 13 frames for each band, totaling 91 frames. The local solar phase angle α of the pixels within this image data set ranged from 0°.0 to approximately 1°.7. Figure 3 compares an example image from the opposition observation sequence (2019 January 8) with an image of the same surface acquired at a 19°phase angle (2019 July 12). The same face of Ryugu can be seen in both images, and the shadowing effects from topography clearly seen in the 19°p hase angle image are absent in the opposition image, thus illustrating the effects of illumination (incidence) and viewing (emission) conditions on the reflectance properties of a planetary surface.
We note that an artificial object was imaged in this opposition observation data set. In Figure 3(b), a red arrow indicates a white dot on Ryugu, a highly reflective target marker (TM; 10 cm sphere covered with retroreflective material) deployed from the spacecraft for the first four operations (Ogawa et al. 2020).

I/F and Observation Geometry
All imaging data in this study (listed in Table A1 in Appendix A.1) were converted to radiance factor (I/F) using the calibration algorithm and parameters described in Tatsumi et al. (2019) and Honda et al. (2021). The calibration also included an updated flat field (Kameda et al. 2021) and a correction for the distortion in the optics. For details on the calibration process and algorithms, see Tatsumi et al. (2019), Honda et al. (2021), and Kameda et al. (2021).
The observation geometry of each pixel was calculated using Ryugu's shape model (Watanabe et al. 2019). The shape model (3 million polygon's version by the shape model team, ID SHAPE_SPC_3M_v20190802) was used to derive the orientation of the surface facets and determine the values of the latitude, longitude, incidence (i), emission (e), and phase angles (α) for each pixel within the image. This allowed the production of image cubes that contained the following backplanes: I/F, incidence (i), emission (e), phase angle (α), longitude, and latitude. Thus, the reflectance, photometric angles (i, e, α), and geographic position information were available for each pixel within the image. The I/F and geometry information were used to examine the photometric properties and model the opposition behavior of the surface (Section 3) and to map the opposition behavior across the surface (Section 4).

Data Set
The images used in this study were converted to image cubes, as previously described. The data retrieved from the images were grouped according to band. An initial data set was retrieved from the images within each band, where all the pixels on the disk of Ryugu were within an image for which i < 70°and e < 70°were collected. This data retrieval was performed for each image within the band group, and the data extracted from each image were combined into a single data file to form the initial data set for each band. This resulted in, for example, 424,590 data points in the v band.
Once the initial data were retrieved for all images in each band group, the data were examined and binned based on i, e, and α coverage. Binning was done to make the data set for each band more manageable for modeling and to ensure that the angle space was equally weighted over all available i, e, and α combinations. The initial data set for each band was segregated into photometric angle bins of every 1°in incidence and emission angle value and every 0°.1 of phase angle value. The median value of the reflectance, incidence, emission, and phase angle values within each photometric angle bin was calculated and stored. These median values comprised the final photometric data set that was analyzed in this study. For example, in the v band, this resulted in 2999 data points evenly partitioned across the available angle coverage.

Phase Function
The radiance factor I/F is defined as the ratio of the bidirectional reflectance of a surface to that of a perfectly scattered surface illuminated in the normal (i = 0°, e = 0°, α = 0°) direction (e.g., Hapke 1981;Li et al. 2015). We denote I/F at the observation geometry (i, e, α) as ( ) l a r i e , , , , where λ is the wavelength. The "normal albedo" is defined as I/F at the zero phase angle, namely, r 0 (λ, i = e, e, 0) (Hapke 1981;Li et al. 2015). Although the solar phase angle of our opposition observations was close to zero (2°), a photometric model was still necessary to convert the observed r (λ, i, e, α) into normal albedo r 0 (λ, e, e, 0°). The original definition of the normal albedo by Hapke (1981) allowed for nonzero incidence and emission angles. However, for this study, we used i = e = 0°as a narrower definition of normal albedo.
In general, empirical photometric models of airless bodies are often expressed as follows (e.g., Shkuratov et al. 2011): where A(λ) is a quantity related to the surface albedo at wavelength λ, D(i, e, α) is a disk function describing the dependence of reflection on i and e (i.e., topography), and f(λ, α) is a phase function. We follow this model structure with simplifications for a narrow phase angle range between 0°a nd 2°. Previous studies of other airless bodies (e.g., Schröder et al. 2013Schröder et al. , 2017Hasselmann et al. 2016) show that the dependence on incidence and emission angles is negligibly small around a zero degree phase angle. Therefore, we assume an initial constant value for the disk function of ( ) a = D i e , , 1 in the phase angle range between 0°and 2°. Recently, Golish et al. (2021a) found that the dependence on i and e is also negligibly small at small phase angles for the B-type asteroid Bennu, a dark asteroid similar in albedo to Ryugu, which supports this assumption. In addition, we define f (λ, 0°) = 1. Then, Equation (1) can be simplified to where r 0 (λ) denotes the normal albedo. Figure 4 shows the observed I/F values for each of the seven bands as a function of phase angle α. The Sun-Ryugu distance at the time of observation was 1.412 au. The apparent radius of the Sun from this distance was 0°. 189. Considering the possibility that the phase curve may exhibit aberrations below this apparent angular radius of the Sun, we excluded data with solar phase angles <0.2 in this study.
These plots suggest that a linear phase function may be suitable for this narrow phase angle range. We applied a linear fit to this data set and derived the linear coefficients a 0,λ and a 1,λ , whose values are listed in Table 2. In Equation (3), a 0,λ corresponds to the average r 0 (λ) and the average phase function f avg. (λ) is described as 1,

0,
We assume that these linear coefficients are applicable to all areas on Ryugu's surface to first order. Therefore, using the coefficients listed in Table 2, the normal albedo r 0 (λ) of a pixel is converted from the observed r(λ, α) by the expression Model phase curves f (λ, α) are shown in Figure 5(a) for the lowest 2°of phase angle, i.e., in the range of the opposition effect (OE). Figure 5(b) shows that the width of the OE appears to be independent of wavelength. The OE parameters slope and amplitude are also uncorrelated for the Ryugu surface ( Figure 5(c)). It has been predicted that one of the potential contributors to the opposition effect, coherent backscatter, creates a wavelength dependence of the OE angular width (Mishchenko 1992). Thus far, it has proven impossible to verify the existence of this dependence for planetary surfaces (Schröder et al. 2018;Ciarniello et al. 2020). Therefore, the absence of a clear wavelength dependence of the OE width . Grayscale is the same as panel (a). Although the face of the asteroid is the same as that shown in panel (a), a topographic shadow does not appear in this image, and the asteroid disk appears featureless. A white dot indicated by a red arrow is a highly reflective target marker (TM; 10 cm sphere covered with retroreflective material) deployed from the spacecraft for touch-down operations. (c) Same image as that in panel (b), but the brightness is enhanced for a narrow I/F range. Because no shadow exists, albedo variation is distinguishable.
cannot be regarded as a diagnostic for the presence or absence of coherent backscatter in the regolith of Ryugu.

Dependency on Incidence and Emission Angles
After converting the image data to normal albedo, r 0 , we reexamined the normal albedo values for any remaining dependency on i and e. In Figure 6, the v-band data were converted to normal albedo r 0 using the geometry backplanes and then divided by the average r 0 . If the assumption holds that the effects of topography were negligible over the phase angle range of our data set, the ratio was expected to concentrate around unity. The results showed that the majority of the data fell within ±1% of unity. Thus, any residual dependency on the incidence or emission angle was small. Because the remaining dependency was very small over this phase angle range, we did not include a correction for i and e. Although a detailed study of this residual would be an interesting photometric study, it would not significantly contribute to the global variations in normal albedo. This study prioritizes the production and analysis of initial normal albedo maps.

Mapping Methods
Hereafter, we refer to the images converted to normal albedo (as previously discussed) as normal albedo images. We projected each pixel from both the original opposition and normal albedo images onto a simple cylindrical projection,  creating two mosaics of Ryugu's surface. The mosaic size was set to 3600 × 1800 pixels (0°. 1 pixel −1 ) for both mosaics. This size was selected to avoid the loss of spatial information from the images, as it was set higher than the spatial resolution of the observations (longitude resolution was 0°. 24 pixel −1 at the equator; see Section 2). Our assessment of the resulting normal albedo mosaic was performed using the overlapping portions between the source images. Figures 7(a) and (b) are projections of two single images acquired in sequence. These are the original opposition images, which were not converted to normal albedo. Figure 7(c) shows the ratio of the overlapping portions of the images in panels (a) and (b) by color scale. No photometric correction to normal albedo was applied to these images. Therefore, a difference in reflectance was observed at the locations where the observed phase angles of the two images were dissimilar. The difference was as high as 4%. Figure 7(d) shows the same ratio, but this was constructed with the same images after they were photometrically corrected to normal albedo. The difference between the normal albedo images was within 1%.
Using this mapping method, we produced a mosaic map for each band from the 13 frames acquired in each band during the opposition sequence. For the overlapping portion between the multiple images, the image pixel with the lowest emission angle value and with phase angle values above 0°.2 (i.e., greater than the apparent radius of the Sun, 0°.19) was selected for the mosaic. The resulting normal albedo mosaics for each band are presented as follows.

General Features
The derived v-band normal albedo map is shown in Figure 8. Because the observed brightness in the opposition condition was less affected by shadows or topographic undulations than other illumination or viewing geometries, the derived map successfully shows the albedo distribution as governed by the physical and chemical properties of the regolith. The coverage of the global area was 99.4%, which was calculated for the area with >0.1% normal albedo. As previously mentioned, opposition observations have rarely been used for mapping purposes. However, we found that this approach is useful for examining a dark, very rocky, object.
Let us examine the overall characteristics of the normal albedo maps. Figure 9  divided into patches of approximately 8 × 8 m 2 (1°square at the equator). Note that the vertical axis is shown on a log scale. The histograms show asymmetric distributions in albedo with a longer tail of materials out at brighter albedos. If darkening of the surface is caused by space weathering, then the brighter albedo materials can be explained by a shorter exposure to the space environment and were thus less weathered. With sufficient exposure time, the surface reaches a "saturation point" where it cannot darken any further. The presence of the brighter albedo tail signifies that Ryugu's surface has not reached its saturation point across the entire surface, and portions of the surface are not completely space-weathered.
This asymmetry was stronger in the short-than in the longwavelength band. Figure 9(b) shows the global average spectrum and standard deviation. Their values are listed in Table 3. The standard deviation has a clear negative correlation with the wavelength. Namely, the shorter wavelength mosaic of Ryugu has greater albedo variations than the longer-wavelength mosaic. This translates to greater spectral variability across Ryugu's surface at near-ultraviolet wavelengths than at near-infrared wavelengths. This is commensurate with what is observed in the opposition observations acquired by the Near-infrared Spectrometer 3 (NIRS3) on board Hayabusa2 (Domingue et al. 2021).
The global average of the normal albedo obtained in the v band (0.55 μm) is 0.0406 with a standard deviation of 0.0010 (Table 3). This value is consistent with the geometric albedo (disk-integrated albedo at zero phase angle) of 0.040 ± 0.005 derived by Tatsumi et al. (2020a). For the asteroid Bennu, Golish et al. (2021b) derived a median normal albedo at a similar wavelength of 0.046 ± 0.002 with a standard deviation of 0.0067 from a broadband panchromatic filter (482-808 nm). Both asteroids belong to the dark C-class group of asteroids, but Ryugu is observed to be slightly, but significantly, darker. The standard deviation of Ryugu's normal albedo is smaller than that of Bennu, suggesting Ryugu's surface is more homogeneous than Bennu's surface.

Spectral Slope and Albedo
A false-color mosaic (Figure 10(a)) created from the b-, v-, and x-band (0.48, 0.55, and 0.86 μm, respectively) normal albedo mosaics (red, green, and blue channels, respectively) highlights the spectral variability across Ryugu's surface. The variability is similar to that shown by Sugita et al. (2019) and Tatsumi et al. (2020a) from observations acquired at larger phase angles. These previous color studies (e.g., Sugita et al. 2019;Morota et al. 2020;Tatsumi et al. 2020a) reported that the general spectral slope from the b band (0.48 μm) to the x band (0.86 μm), that is, the b-x slope, exhibits the greatest regional variations on Ryugu (Figure 10(b)). The spectral slope for this figure was calculated with a 3 × 3 pixel moving average.
The b-x slope γ bx is calculated using a method similar to the spectral slope calculation used in Tatsumi et al. (2020c) from five bands, from the b band to the x band. Normalized reflectance spectra are fitted to the equation below using the least-squares method: where R(λ k ) is the normalized reflectance spectra r 0 (λ k )/ r 0 (0.55 μm), λ k is the wavelength of the band k in micrometers, and γ is the slope of the fitted line, constrained to a value of unity at 0.55 μm.
We also examined the UV index (Table 3), which is a color index to measure the UV up-/downturn of a reflectance spectrum, as defined by Tatsumi et al. (2020c). The UV index C UV is defined as is the extrapolated ul-band normalized reflectance calculated from the v-to-x slope γ vx using R(0.55-0.86 μm): When the b-x slope mosaic is compared with the false-color map in Figure 10(a), the regions exhibiting brighter and bluer colors in the false-color mosaic correlate to the regions exhibiting negative spectral slopes in the b-x slope mosaic. In contrast, dark regions tend to have positive spectral slopes. Previous studies also reported a correlation between the v-band reflectance and b-x slope. An examination of these properties using the normal albedo mosaics (Figure 11(a)) also reveals a strong correlation between the v-band normal albedo and b-x slope calculated from the normal albedo values. Figure 11 Examinations of the correlations between the v-band reflectance and b-x slope by Sugita et al. (2019) were compared with those from this study (Figure 11(b)). The examination by Sugita et al. (2019) was conducted using a reflectance factor, defined as the ratio of the bidirectional reflectance to a perfectly scattering surface illuminated at the same geometry (i, e, α), and observations acquired at the 19°p hase standardized to (i, e, α) = (30°, 0°, 30°). Recently, Tatsumi et al. (2020a) derived Hapke parameters for Ryugu's surface from a wider phase angle range. Table 4 shows the conversion factor from normal albedo to geometry (i, e, α) = (30°, 0°, 30°) based on their study. Using this conversion factor, we converted the v-band reflectance factor to normal albedo ( Figure 11(b)). Another contributor to the differences between the two studies is phase reddening (e.g., Gehrels et al. 1964). The b-x slope of Figure 11(b) was shifted −0.04 [μm −1 ] to convert from 19°phase observation to 0°phase observation, based on the phase curve of Tatsumi et al. (2020a). From a comparison of Figures 11(a) and (b), the opposition observation data displays a stronger correlation, that is, a morelinear and less-diffuse relationship. This is because of the differences in phase angle between the two studies and the role of surface roughness in the reflectance properties of a regolith.
Images of Ryugu's surface show a rocky, very rough surface (Sugita et al. 2019) such that even at 19°phase, the unevenness of Ryugu's surface is so severe that many shadows are produced, resulting in a higher dependence of reflectance on incidence and emission angle because of the shadowing of the surface by the topography. The resolution of the shape model used to provide the photometric standardization of the Sugita et al. (2019) observations was too low to account for all the variability in Ryugu's very rocky surface. Thus, reflectance variations due to topography are still present in the higher phase angle data set, creating higher variability caused by errors in photometrical correction. By contrast, for the opposition observations, the dependency on i and e was very small, as previously demonstrated, thus producing less variability in reflectance and spectral slope properties due to topography.
As previously described, the normal albedo of Ryugu's surface displays greater spectral variability at shorter nearultraviolet wavelengths than at the longer near-infrared wavelengths. Thus, the b-x slope is mainly determined by the properties at shorter wavelengths, such as the v band. This contributes to the high correlation between the b-x slope and vband normal albedo (Figure 11(a)). To investigate other more subtle spectral features, we examined spectral slope variations with p-band (0.95 μm) normal albedo values. Figure 11(c) shows the spectral slope versus p-band normal albedo. In this case, the correlation between these two spectral properties is more diffuse. In the next section, we examine variations in Ryugu's surface in further detail using these metrics.  Table 3. Error bars indicate the standard deviation within each wavelength.

Regional Spectral Variations
We further investigate the spectral properties across Ryugu by dividing Ryugu's surface into several regions and examining the relationship between normal albedo and color within and between each region.

Selection of Regions, Boulder Sites, and Terrain Sites
We divide the global map of Ryugu into 11 regions based on a combination of geomorphology, topography, and albedo ( Figure 12, Section 5.1.1) in order to investigate any statistically significant variations in the color/spectral properties of the surface correlated with these aspects of the surface. Spectra from ∼8 × 8 m size bins (=1°bin at equator) were extracted from each region for these statistical analyses.  We also selected spectra of characteristic terrain (Section 5.1.2) from each region. The intention in the selection of terrains was to insure we have a representative sample of the regolith, thus we avoided terrains visually dominated by large boulders in our selection of areas to represent the terrain of each region.
Finally, we selected a number of boulders for further examination (Section 5.1.3). We selected all boulders with an average diameter larger than 15 m and examined their shape from the image sets acquired from the 5 km altitude observation ("mid-altitude observation" at 2018 August 1, 0.5 m pixel −1 resolution). In contrast to the terrain sites, these boulder sites may potentially provide a spectrum of the mechanically unmixed end-members that comprise Ryugu's regolith (Tatsumi et al. 2020c).

Regions
A diagram of the selected regions is shown in Figure 12(a) with the corresponding geopotential map (Watanabe et al. 2019) shown in Figure 12b. We define several regions based on geomorphology. These include two fossae (troughs) in the southern hemisphere (#3 and 4 in Figure 12(a)), a relatively smooth plain in the north (#11), and the equatorial ridge (#2).
North plain and nearby boulder. A very visually smooth, unnamed plain has been observed at ∼46°.6N, ∼276°.5E ( Figure A1). We define this currently unnamed plain and the nearby dark rugged boulder as independent areas (#10 and #11 in Figure 12(a)). In this study, we refer to this plain as the "North plain." Equatorial ridge. We defined the boundaries of the equatorial ridge (Ryujin Dorsum) based on the topographic slope. Figure 12(c) shows the latitudinal dependency of the topographic slope taken from Watanabe et al. (2019). The quantiles Q1 (25% of the topographic slope value over all longitudes), Q2 (50% or the median value of the topographic slope over all longitudes), and Q3 (75% of the topographic slope value over all longitudes) at each latitude are plotted in Figure 12 c. This figure shows that the ridge region has a median slope value ranging from ∼9°to ∼16°. Using the central value of the median slope range, 12°. 5, we constructed a binary topographic image map of regions with slopes either above or below 12°.5 and defined the ridge boundary to match this binary image. The resulting equatorial ridge is shown as region #2 in Figure 12(a). Note that this defined region contains not only the top of the ridge but also the base of the ridge.
Bright areas in the north and south polar regions. The albedo maps show some very bright areas in the polar regions. We define these areas (regions #6 and #7 in Figure 12 Western bulge and eastern hemisphere. The largest regions we defined are the western bulge and the eastern hemisphere (regions #5 and #1, respectively, in Figure 12(a)). These two hemispheres are divided by the two fossae described above.  They are known to have different boulder densities (Michikami et al. 2019) and crater densities (Cho et al. submitted). The southern boundary of the western bulge boundary is constrained by the trough regions. On the other hand, because the northern boundary is not clearly delineated in Sugita et al. (2019), we defined the northern boundary as the bottom of the geopotential valley, as seen in Figure 12(b).
Otohime and Ejima Saxum. These are two large boulders identified by Sugita et al. (2019) (regions #8 and #9 in Figure 12(a)). The largest boulder (∼160 m), Otohime Saxum, is located at the south pole. This is the only type 4 boulder defined by Sugita et al. (2019). Ejima Saxum, a large 70 m-sized type 1 boulder located at (−32°. 0N, 101°.1E) was also selected as an independent area. A close-up image of the boulder is shown in Figure A3(a).

Terrain Sites
Locations of the terrain sites and sampled boulders are shown in Figure 12(d) and Figure A2. The ID of each site is also indicated in Figure A2.
Midlatitude dark terrain. Previous studies (Sugita et al. 2019;Morota et al. 2020;Tatsumi et al. 2020a) reported that the ridge is characterized by a bluer b-x slope and a brighter albedo. We select eight sites to represent midlatitude terrains relatively darker than the ridge ("T-Dark x" in Figure A2) to compare with the ridge data.
Typical ridge terrain. We selected six homogeneous albedo sites on the ridge. We label these sites as typical ridge ("T-R_Typical x" in Figure A2) terrains because this group comprises a larger area than the next group, the bright background terrains found on the ridge. Bright background ridge terrain. Takaki et al. (2020) observed wake-like structures around many large boulders on the equatorial ridge. These wake-like areas have bluer spectra than the surrounding terrain, and they are proposed to be exposed subsurface materials associated with surface flow. The false-color map (Figure 10(a)) shows some areas adjacent to large boulders on the ridge region that exhibit brighter and bluer spectra than the typical ridge surface. We select five example locations to sample this terrain type ("T-R_Bright" in Figure A2). We assume the spectra of these terrain areas may represent examples of immature material.
Tokoyo bright surface. Tokoyo fossa was defined as a separate region from the equatorial Ridge based on morphology and topography. To compare the spectral properties of Tokoyo fossa's terrain with the terrain units from the equatorial Ridge, we chose three bright sites on Tokoyo fossa, avoiding areas with large boulders.
North pole bright surface. In order to ensure that we sample as diverse a selection of terrain types as possible, we included one site within the north pole bright region.

Boulder Sites
To investigate the spectrum of the unmixed source component of Ryugu, we selected boulders that are distinguishable from a distance of 20 km (∼2 m pixel −1 resolution). Michikami et al. (2019, hereafter M19) carried out a global boulder inventory of Ryugu. We use their boulder list to select the boulders for spectral examination for this project. We set the lower limit of the average diameter D of the target boulders to 15 m. A total of 251 boulders with a D > 15 m are listed in the M19 list. The boulders examined in this study are labeled by an ID based on the size rank of their average diameter, as ranked by M19. For example, "ID17" means the 17th largest boulder from the M19 list.
Because no topographic shadows are visible in the normal albedo map, we use the "mid-altitude observation" data acquired at a 0.5 m pixel −1 resolution (5 km altitude) to visually select the interior of the boulder shape. We projected those images onto the same map projection as the normal albedo map, and the area of the boulder was identified on this mid-altitude observational map. Although the mid-altitude observational data has a high spatial resolution, the observations did not cover high latitudes. Therefore, we selected all 157 boulders that were located within the mid-and low latitudes, the area covered in the mid-altitude observations. Five of these boulders display variation in albedo (brighter/ darker) within the surface of a single boulder. Close-up images of these boulders are shown in Figure A3. This variation may provide information on the spectral trends associated with space weathering, thermal metamorphism, or boulder brecciation (C. Sugimoto et al. 2020aSugimoto et al. , in preparation, 2020b. For such boulders, we examine two sites on the boulder surface, which are labeled as "pairs" later in the analyses. Albedo difference among these two sites could be attributed to either space weathering or the deposition of ejecta from the surroundings accumulating on the flat face of a boulder. With the inclusion of these paired data sets, the number of selected boulder sites within the mid-to low latitude becomes 162 (157 boulders). The locations of these boulder sites are shown in Figure 12(d).
These boulders contain the boulder types 1-3, as defined by S19. As a more quantitative boulder classification scheme is still under development (Yumoto et al. 2020), we segregated our boulder sample using the following scheme based on the classifications from S19.
Type 1 (S19). Type 1 boulders display a dark rugged surface morphology (Sugita et al. 2019). We note that one of these type 1 boulders (Boulder ID17, D = 29.89 m; Figure A3) resides within the equatorial ridge and displays a high albedo contrast with the background terrain. We note this boulder in order to investigate the cause for this high albedo contrast.
Type 3 (S19). We include three "type 3" boulders as described by S19. These type 3 boulders are characterized by a brighter reflectance than the surrounding terrain. They display a blocky variation in albedo on the surface (Sugita et al. 2019), but their surface morphology is not rugged as type 1. These boulders correspond to IDs 101, 109, and 127 of the boulder list of M19.
In addition, we selected sites on the Otohime Saxum, the large boulder at the south pole. Therefore, the total number of boulders examined in this study is 158.
Otohime (Ot). Although we already defined a region centered on Otohime Saxum (Figure 12(a)), we also defined a set of sites to extract representative seven-band spectra of this large boulder. Because this boulder shows local albedo variation on its surface, we selected four representative sites. Table 5 summarizes the number of selected terrain sites and boulders.

Spectral Characteristics
In this section, we discuss the variations in the regional spectral properties. We especially consider the effects of space weathering and thermal metamorphism. The relationship between the albedo (or reflectance) and spectral slope (or spectral ratio) has often been used to describe the alteration of planetary surfaces due to space weathering (Moon: Lucey et al. 1998, Eros: Murchie et al. 2002, Itokawa: Hiroi et al. 2006Ishiguro et al. 2007). For five boulders, we selected two sites on the same boulder. The first site represents the albedo and texture of the majority of the boulder and the second site represents areas of higher albedo that occupy smaller portions of the boulder facets. A comparison of the spectral properties of the two sites provides information on potential space weathering alterations of these boulders. However, we note that there could be other causes for these differences, such as (1) partial dust coverings, (2) the boulder is brecciated, containing a mixture of boulder types, and (3) textural changes between the two sites.
Recent studies of various regions on Ryugu (ridge: Morota et al. 2020;pole: Tatsumi et al. 2020b; bright background at the ridge: Takaki et al. 2020) have reported spectral slope associations with fresher surfaces versus mature surfaces, such that fresher surfaces are associated with bluer spectral slopes and more mature surfaces are associated with redder slopes. Because the v-band albedo and spectral slope are inversely correlated, it is presumed that fresh material is bright and mature material is dark. However, the artificial crater experiment on Ryugu (Hayabusa2 Small Carry-on Impactor (SCI) experiment, Arakawa et al. 2020) shows that the inside of the artificial crater, assumed to be fresh material, is darker than the surrounding terrain. This conflicts with the spectral associations, so interpretations in regard to spectral space weathering trends need to be made with caution.
To distinguish between the spectra of mature and fresh surfaces, we assume that mature surfaces are more abundant, and therefore, mature surfaces should occupy a larger surface area than fresh surfaces. This assumption is based on the paucity of large, recent cratering events ) that would be needed to produce an abundant amount of fresh surfaces. For example, the formation of the Urashima crater is considered to be older than the age of the ridge formation ). The normal albedo histograms (Figure 9(a)) show that the majority of the albedo distribution is at the darker end of the albedo range with a lower abundance spread at the brighter albedo values, providing confirmation that darker albedo surfaces are more abundant. If mature surfaces are more abundant, then these albedo distributions support the correlation that the brighter surfaces are fresh and darker surfaces are mature. Another assumption we make regarding the maturity of boulders is that if a facet on a boulder surface is smooth, with sharp edges, the facet is considered to be fresh because rugged morphologies on boulder surface may be produced by intense thermal disaggregation and/or exfoliation. Figure 13 shows the relative seven-band spectra of the regions identified in Figure 12(a). These spectra are divided by the global average shown in Figure 9(b). Figure 14 shows the derived b-x slope versus p-band normal albedo plots of these regions. Figure 15 shows the UV index versus p-band plots. The average values of the derived seven-band normal albedo spectra and color indexes are listed in Table 6.

Regions
Eastern hemisphere and western bulge. Using observations acquired at 19°phase, previous studies (Sugita et al. 2019;Tatsumi et al. 2020a) reported that the western bulge has a slightly higher vband reflectance than the reflectance of the eastern hemisphere. This dichotomy is also seen in the near-infrared data analysis (Barucci et al. 2019). However, in the opposition observations, both regions indicate similar value ranges in v-band normal albedo (eastern: 4.05% ± 0.09%, western: 4.07% ± 0.07%). This relative difference in v-band reflectance with phase angle can be explained by differences in the surface roughness or the small-scale topographic properties between these two regions. A study of boulder size-frequency distributions reported that the western hemisphere of Ryugu has a smaller number of boulders (D > 5 m) than the eastern hemisphere (Michikami et al. 2019). Additionally, a study of crater size-frequency distributions revealed that the western bulge has a lower crater density than the eastern hemisphere (Cho et al. 2021). Both studies indicate that differences in surface roughness exist between the eastern and western regions, Figure 13. The seven-band relative spectra of the selected regions. They are divided by Ryugu's globally averaged spectrum (Figure 9(b)) to accent the spectral differences. Each spectrum is shown with a 0.1 offset in the vertical axis for clarity.  on the scale of 5 m or larger. The resolution of the ONC-T observations used in this study is 2.1 m pixel −1 . The surface topography on the scale of 5 m and larger will affect the reflectance properties seen in these images. However, if these hemispherical topographic or roughness differences are also present at subpixel scales (below the 2.1 m pixel −1 image resolution), the surface roughness at these scales will also affect the photometric behavior, producing reflectance differences at 19°phase angle between these two hemispheres that would not be apparent at opposition.
The standard deviations (1σ) in the spectral properties ( Table 6) for the eastern hemisphere are larger than the corresponding western bulge values. This may reflect the more numerous data points for the larger, eastern hemisphere. Within the standard deviations, the spectral properties between the eastern hemisphere and western bulge are similar.
In future work, more detailed photometric analysis with a broader range of illumination and viewing geometry data is required to test and confirm a roughness explanation for the differences between the western bulge and the eastern hemisphere.
Ridge. The data density distribution for the equatorial ridge region is similar to that of the eastern hemisphere region (Figures 14 and 15). Although the ridge predominately consists of bright areas, Figure 12(a) also shows the presence of some dark areas. Therefore, the average spectrum for the ridge region becomes similar to the globally averaged spectrum (Figure 13). The material in this region may also be a mix spectrally similar to the globally distributed material. Figure 16 shows that both the p-band albedo and b-x slope of the ridge region are loosely correlated with geopotential (correlation coefficients are 0.20 for p-band and 0.35 for b-x slope). We confirm that the top of the ridge tends to be bright and blue; however, the low correlation coefficient values suggest that there are factors other than the geopotential contributing to the concentration of bright and blue areas in the ridge region.
Tokoyo and Horai fossa. Tokoyo fossa has a relatively higher normal albedo and a bluer spectral slope than the global average ( Figure 13). The spatial distribution of the bright and blue area within the Tokoyo fossa is connected to the bright and blue areas in the ridge region (Figures 8 and Figure  10(a)). On the other hand, the Horai fossa region displays a darker and redder spectrum than observed in Tokoyo fossa (Figure 13).
North and south pole bright areas. Tatsumi et al. (2020b) report that spectrally very bright and blue regions are concentrated near both poles. Figure 13 confirms that the opposition observation data of both polar regions also display bluer (lower b-x slope) spectral properties than the eastern hemisphere spectra. In p-band normal albedo, the average albedo of the north pole region is brighter than that of the south pole region. Otohime Saxum. The average normal albedo spectrum of Otohime is slightly darker and redder than the globally averaged spectrum of Ryugu (Figure 13). Otohime has been noted to have variations in brightness and color depending on which facet of the rock is being observed (Tatsumi et al. 2020b). Such variation contributes to the relatively larger standard deviations in normal albedo for this boulder than the deviations measured for the eastern hemisphere normal albedo values ( Table 6). Ejima Saxum. The normal albedo spectrum of Ejima Saxum is slightly darker and redder than Ryugu's globally averaged spectrum However, the Ejima Saxum spectrum is similar to Otohime Saxum's spectrum (Figure 13).
North plain boulder and north plain. On this dark rugged boulder, the albedo and color indexes show similar values to Ejima Saxum (Table 6). This north plain boulder also has similar values for the b-x slope and UV index as determined for Ejima Saxum.
The average normal albedo spectrum for the north plain region is similar to the spectra for the north plain boulder (Figure 13). This suggests that the north plain boulder may have contributed to the materials in the adjacent north plain. On the other hand, the standard deviation for the north plain (e.g., vband albedo 1σ = 0.0008) is smaller than that for the north boulder (1σ = 0.0005). Because the albedo value itself is small (approximately 0.04), this standard deviation value is also small. However, because the signal-to-noise ratio within the images from which these values are measured is 200, this difference in albedo is considered to be significant (the significance is quantified by the 1σ value divided by the average albedo, 0.0008/∼0.04 = ∼0.02 and 0.0005/∼0.04 = ∼0.013 for the north plain and north boulder, respectively). This implies that the boulder surface may contain some heterogeneity in albedo, and/ or the terrain of the north plain is well mixed within the observational spatial resolution (∼2 m pixel −1 ). There are two possible interpretations of the potential boulder heterogeneity: (1) the breccia-like nature of the dark rugged boulders, as pointed out by Sugita et al. (2019) andC. Sugimoto et al. (2020a, in preparation), may reflect the heterogeneity of the source material from the parent body, and/or (2) the possibility that the degree of space weathering differs from place to place even if the starting material is the same.
The north plain may be supplied with pebbles/regolith from the north plain boulder. This plain has similar spectral features to the north plain boulder (Figures 14 and 15), but has a smaller deviation in spectral properties than the north plain boulder. It is in line with the hypothesis that the terrain is mixed and has become more homogeneous.

Terrain Sites
For the terrain sites defined on the surface, Figure 17 displays the seven-band relative spectra. These spectra are divided by the globally averaged spectrum to show and accent the relative differences. The absolute value spectra are provided in Table A.2 of the Appendix. Figure 18(a) shows the spectral slope versus albedo, and Figure 18(b) shows the UV index versus albedo properties.
Midlatitude dark terrain (T-Dark x). We confirm that this terrain type has a darker and redder spectrum than the globally averaged spectrum (Figure 17). In Figure 18, this group shows low p-band albedo values, high or red b-x slopes, and high UV indices. This high UV index value corresponds to the horizontal feature observed in the spectra between 400 to 500 nm, as seen in Figure 17.
Typical ridge (T-R_Typical x). In comparison with the T-Dark spectra, the relative spectra (Figure 17) of this terrain type are brighter at the shorter wavelengths. In the v band (0.55 μm), the average spectrum of this terrain type is brighter than the average of the T-Dark terrain by 4.4%. On the other hand, the difference in the p-band (0.95 μm) average is +1.8%.
These T-R Typical sites are relatively bluer than the T-Dark sites. Accordingly, in the spectral slope versus albedo diagram (Figure 18(a)) these terrains are distributed to the lower right from the T-Dark terrains.
Bright ridge terrains (T-R_Bright x). The relative spectra of this group of terrains display a very blue spectral slope property ( Figure 17). In comparison with the average ridge, the range in the v-band albedo is clearly higher in these bright terrains, but the difference in the p-band albedo is smaller. The bright ridge terrain spectra also show different distributions in the p band to b-x slope properties and in the p band to UV index properties from the typical ridge spectra (Figure 18). The spectral slope value is smaller (difference is ∼0.05), and the UV index trends lower than the typical ridge.
Tokoyo fossae bright terrains (T-Tokoyo x). These terrains display a brighter p-band normal albedo than the typical ridge terrains (Figure 17). Additionally, they show different spectral properties (smaller b-x slope and larger UV index, shown in Figure 18) than the bright ridge terrains.
North pole bright area (T-NP_Bright). This site is a part of the north pole bright region. This terrain displays the brightest, bluest, and lowest UV index of any of the other terrains examined.

Boulder Sites
For the sites defined on the boulders, Figure 17 displays the seven-band relative spectra (absolute spectrum divided by the globally averaged spectrum). The spectral slope (bto x-band) γ bx and UV index (C UV ), Figures 18(c) and (d), respectively, of the selected boulder sites are shown as a function of the p-band normal albedo r 0 (0.95 μm). Parts of Figures 18(c) and (d) are zoomed in Figures 18(e) and (f) to clarify the color pair data.
Dark rugged boulder on the ridge. As described earlier, the opposition observations confirm that the normal albedo of the ridge terrain is higher than the surrounding regions. Additionally, we observed the presence of a dark rugged boulder within this bright ridge region. This boulder, ID17, corresponds to a "type 1" boulder, as described by Sugita et al. (2019). The darker albedo of this boulder is in clear contrast to the surrounding background surface albedo in the ridge region.
Bright boulders. The seven-band spectra (Figure 17(e)) show that the type 3 (S19) boulders have a larger albedo variation, even at longer wavelengths, than the other boulders we examined. The b-x slopes γ bx of type 3 spectra are relatively flat (white). This characteristic is highlighted in Figures 18(c) and (d), where the type 3 boulder distribution extends to the right side of the spectral property figures.
In Figures 18(c) and (d), boulder ID238 shows similar features as a type 3, which is apparently different from the majority of the boulders. We will discuss this boulder together with type 3 in Section 5.4.
Dark/bright pairs on boulders. The spectral pair of dark/ bright areas from the same boulder ( Figure A4) is connected by lines in the spectral property diagrams shown in Figures 18(c) and (d). If these differences are caused by space weathering, then these lines suggest that space weathering changes the spectra properties of the boulder material by (1) reddening, (2) increasing the UV index, and (3) darkening or lowering the pband reflectance. Interestingly, these trends are coincident with those is seen in the Ryugu terrain spectra.
Otohime Saxum (Ot). The relative spectra of the four selected areas on Otohime Saxum are plotted in Figure 17(g). To better compare the data for this boulder, Figure 19 shows the region data versus the boulder site measurements in γ bx versus r 0 (0.95 μm) in the same plot. On this boulder, we observe that the majority of the boulder surface has a higher p-band albedo than the trend line made by Ot_Dark, Ot_Midbright, and Ot_Bright boulder areas. Because Otohime's surface does not visually display significant textural variations or evidence for clasts ( Figure A5), this spectral variation may not be caused by the different textures. This suggests that the spectral alteration of Otohime is complex and an interesting subject for future work.

Comparisons between Regions, Terrain Sites, and Boulder Sites
Origin of Type 1 boulder ID17. Figures 18(c) and (d) show that the spectral features of the ID17 boulder overlap those of the dark terrain found at midlatitude (Terrain-Dark in Figures 18(a) and (b)). This boulder belongs to the darkest albedo category on Ryugu. Figure 17 also shows that the spectra of both this boulder and the dark, midlatitude region are very similar. This suggests that both are composed of similar material and have undergone similar alteration processes (space weathering/thermal metamorphism).
What is the origin of this dark and rugged boulder on the ridge? Why is there such an albedo contrast between this boulder and its surroundings? Morota et al. (2020) describe a scenario regarding the ridge's spectral properties. They postulate that the surface of the ridge was originally red and dark, similar to the midlatitude surfaces, but was eroded due to a change in Ryugu's rotation rate, thus exposing the brighter, bluer subsurface material. Based on this scenario, we set two hypotheses for the origin of boulder ID17: (A) This boulder is ejecta or material that has migrated from the midlatitudes, or (B) this boulder is a survivor of the ridge's erosion event. To distinguish between these two hypotheses, we investigated the Figure 17. The seven-band relative spectra of the selected terrain sites. Normal albedo spectra have been divided by Ryugu's globally averaged spectrum (Figure 9(b)) to highlight the spectral differences. shape of this boulder as seen in higher-resolution ONC images ( Figure A3). These high-resolution images show that this boulder appears to be partially buried within the ridge terrains.
We first consider the case of hypothesis A. The observation that the boulder is currently buried implies that pebbles/ regolith was moved and subsequently buried the boulder during an era after the boulder was emplaced. However, this boulder is currently located on the ridge, a region of high geopotential. As proposed by Morota et al. (2020), terrain material would move from the top side of the ridge to the bottom, i.e., from a region of high geopotential to one of lower geopotential. Therefore, hypothesis A is not suitable for explaining why the root of the dark rugged boulder is buried. Alternatively, if this boulder was initially a near, subsurface boulder, the migration of material from the ridge may have partially exposed the boulder, leaving just a portion of it still buried, fitting hypothesis B.
Ridge terrain and bright background. If we assume that the typical ridge terrain and the bright background terrain originated from the same material, then Figure 18 suggests that some alteration effect, possibly a general space weathering effect (including solar wind implantation, micrometeoroid bombardments, and solar heating) altered the ridge spectra in the following ways as the surface matures: reddening of the spectral slope, increasing of the UV index, and darkening of the p-band normal albedo.
Explaining the color of Tokoyo fossa. The distribution of the spectrally bright areas in Tokoyo fossa is spatially connected to the bright and blue areas on the ridge. However, the ridge and fossa (troughs) are terrains with opposite geopotential properties (Figure 12(b)). In the case of the ridge, the brighter and bluer spectral properties of the surface in this region can be explained by the migration of the darker, overlying surface material from the high geopotential ridge to outside the ridge, as described above. However, the same mechanism does not explain the spectral properties of Tokoyo fossa, which is already at a lower geopotential than its surroundings. In contrast, the Horai fossa, another trough area, is not as spectrally bright or blue as the Tokoyo fossa, suggesting an alternate mechanism is at work to explain the Tokoyo fossa's spectral properties. We note that the Tokoyo fossa spatially extends from the ridge to Otohime Saxum at the south pole. Therefore, we propose that material may have migrated from Otohime to the Tokoyo fossa region.
However, the γ bx versus r 0 (0.95 μm) diagram in Figure 19 suggests that this hypothesis does not completely explain the spectral properties of the Tokoyo fossa. Although these regions are spatially adjacent to each other on Ryugu, their spectral properties do not completely coincide in this figure. This implies that the mechanisms responsible for the Tokoyo fossa's spectral properties may be more complex.

Comparison with Other Asteroids
Application of principal component analysis (PCA) techniques, as used by Sugita et al. (2019), is useful in comparing the spectral data of Ryugu with the abundant ground-based observational data of other asteroids. We especially focus on the comparison with C-type asteroids and try to interpret the color variation on Ryugu in the context of the vast archive of asteroid spectra data. We used the C-type asteroid spectra from the SMASS2 catalog (Bus & Binzel 2002), as used by Sugita et al. (2019). The details of the methodology are described in the Supplementary Online Material of Sugita et al. (2019). The principal components for C-type asteroids, PC1, PC2, and PC3, are correlated to the continuum slope, the characteristics of the UV drop-off, and the properties of the 0.7 um band absorption, respectively. Figures 20 and 21 show the distribution of C-type asteroids and Ryugu's surface spectra in PC1-PC2 and PC2-PC3 component spaces. The wide distribution of global Ryugu data in the PC1 component indicates a wide variety in the spectral slope. It should be noted that the trend in Ryugu's global spectral properties is well aligned with the B-Cb population in PC1-PC2 space (Figure 20). This is quite different from the correlation seen by Sugita et al. (2019). Our study may have reduced the spectral ambiguity in the short wavelength range due to the narrow range in the photometric angle values coupled with the photometric standardization to opposition. We also see a similar trend in PC2-PC3 space ( Figure 21) where the global spectral trend is aligned with the B-Cb-C populations. Sugita et al. (2019) pointed out the bimodal distribution of Ch-Cgh and B-Cb populations in the PC2-PC3 space. The global spectra obtained in this study strongly suggest that the main components of Ryugu correlate best with the B-Cb populations. The wide variety within Ryugu's spectra implies a potential relationship with these asteroid populations. The potential relationship with these asteroid types was also suggested based on ground-based observations, even the same asteroid family members show different spectral types Morate et al. 2016). Our results demonstrate the wide variety of colors that can be produced by the processes modifying asteroid surfaces after the catastrophic disruption of a parent body and its reaccumulation.
In addition, we compare Ryugu's surface spectra with the spectra of possible candidate parent bodies. Based on N-body simulations, Ryugu is shown to originate from the inner asteroid main belt (Campins et al. 2010). Polana, Eulalia, and Erigone are the parent bodies of the majority of the inner main belt families among carbonaceous, C-type, asteroids. Furthermore, Bottke et al. (2015) demonstrated possible pathways for Ryugu from the Eulalia and Polana families to its current orbit taking into account the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. They derived a ∼70% probability of Ryugu originating from the Polana family and a ∼30% probability from the Eulalia family. The young age of the Erigone family suggests a much lower probability of Ryugu coming from the Erigone family compared with the Polana and Eulalia families. The average spectrum of Ryugu is significantly different from all of these families. However, the variation in Ryugu's spectral properties certainly overlaps with those of these asteroids. Specifically, the trend in global spectral properties suggests that the bluer end-members of Ryugu's spectra are similar to the spectra of Polana and Eulalia. Erigone exhibits absorption at 0.7 μm, indicating phyllosilicates, which is not strongly detected in the Ryugu spectral data. Thus, Ryugu could be a member of the Polana or Eulalia family but less probably a member of the Erigone family. Among the various spectra on Ryugu, the features from the bright areas on the ridge (T-R_Bright) are particularly close to those of Eulalia. This suggests that the average surface of Eulalia is less processed than the average surface on Ryugu.

Evolution of Ryugu's Surface
Gray dashed circles in Figure 18 summarize the concept regarding the spectral alteration of Ryugu's surface, as derived in this study. On Ryugu, major spectral alteration results in three changes: (1) reddening, (2) increasing UV index, and (3) darkening. This trend is common for the majority of Ryugu's surface and is indicated by the area labeled "Trend A" in Figure 18. The discussion of latitudinal variation in the b-x slope by Morota et al. (2020) supports the correlation between the b-x slope and maturity, where redder material is more mature than bluer material.  The observation that the pair sites from the same boulder (Figures 18(c) and (d); Figures 18(e) and (f) zoomed)) are contained within the Trend A area suggests the sites are exposed to the same space weathering processes. On the other hand, according to the hypothesis of Morota et al. (2020), the difference between T-Dark and T-R_typical may represent a difference in past solar heating, which is also in line with Trend A. These considerations suggest that space weathering and past solar heating cannot be separated by the three spectral indices (p-band normal albedo r 0 (0.95 μm), b-x slope γ bx , and UV index C UV ) and that in both contribute to the surface alterations defined within Trend A.
As for the cause of the UV index increase, there are several possible sources. Hendrix & Vilas (2019) discuss an upturn in the UV created by the presence of nanocarbon. Hiroi et al. (2020) found that a UV upturn could be created by pulsed-laser irradiation of a meteorite sample, Meteorite Hills (MET) 00639, which is considered one of the most spectrally similar meteorites to Ryugu, suggesting space weathering. DellaGiustina et al. (2020) found UV changes in Bennu attributable to the presence of magnetite. However, from the remote sensing data analysis in this study, we cannot distinguish between these possible sources.
Differences in the physical state, such as surface roughness, are unlikely to produce the spectral changes defined by Trend A. This is because the opposition observation data used in this study are free of the shadowing effects produced by surface roughness. The effects of porosity, grain size, and grain size distribution on the spectral properties are unclear, even though these surface properties can be mildly modified by space weathering processes. The spectral trend toward a common end point, however, is similar to what is seen on the lunar surface (Lucey et al. 1998) and Eros (Murchie et al. 2002), and thus argues for a space weathering origin.
Another hypothesis to explain the spectral properties captured in Trend A is the mixing of multiple end-member materials. This possibility is not completely ruled out by these studies. However, cluster analyses by Barucci et al. (2019) show that the ONC spectra can be described by two spectral clusters at the 3σ level (where the first cluster represents 97% of the spectra) or six clusters at the 2σ level (where the first cluster represents 92% of the spectra). While the complicated distributions and interrelationships indicated in Figure 19 could also be explained, in part, by multiple end-members, this is not strongly supported in the cluster analyses.
Although the end-member hypothesis should be examined in future work, for the most part, we propose that Trend A may roughly represent both the solar heating experienced during the orbital excursion and the space weathering of the surface due to micrometeorite and solar wind ion bombardment. When we focus on the relationship among T-R_Bright, T-R_typical, and T-Dark, the spectral trends between the T-R_Bright and T-R_typical areas can be explained by space weathering, and the spectral trends between the T-R_typical and T-Dark areas can be explained by solar heating.
On the other hand, the type 3 boulders and boulder ID238 display wider p-band albedo and UV index value ranges, and their spectral properties place them outside the Trend A area (Figures 18(c) and (d)). None of the Ryugu terrain spectra place them outside of the Trend A area. Although part of the north pole bright area has a large p-band albedo, up to 0.045 (Figure 14), the b-x slope value is much lower (∼−0.20 μm −1 ) than these boulders (>∼−0.10 μm −1 ), keeping this region within the Trend A area. We label the distribution of this group with the area labeled "Trend B." The fact that the Trend B spectral properties were only detected in a very small portion (4 of 158 boulders) of the asteroid's surface is important. If the terrain sites contain pebbles with spectral properties similar to the Trend B boulders, then the spectral contribution by those pebbles are being obscured by the spectral properties of the terrain constituents.
To interpret the significance of the boulders defining spectral Trend B, an examination of the analysis of the bright boulders on Ryugu by Tatsumi et al. (2020c) is important. They used high-resolution ONC-T images (0.3 m pixel −1 ) to study 21 bright boulders. They further classified bright boulders into two spectral types, S/Q type, and C/X type. The type 3 boulder ID127 is included in their analysis as "site M6," and it was classified as a C/X type. The S/Q type is either too small or too bright (and thus saturated the detector) to be included in our data set (2019 Jan 8 observation). Because our Trend B boulders do not show a significant 1 μm absorption feature, they correspond predominantly to the C/X type defined by Tatsumi et al. (2020c). Based on the heating experiments of the hydrated carbonaceous chondrites Murchison and Ivuna (Hiroi et al. 1996a(Hiroi et al. , 1996b, Tatsumi et al. (2020c) interpreted the spectra of their C/X-type bright boulders to be the result of thermal metamorphism, and those boulders may provide samples from different parts of the parent body.
Based on the results of Tatsumi et al. (2020c), we propose that Trend B possibly represents the degree of the thermal metamorphism on the parent body. Because solar heating is also a thermal effect, the difference in directions on the diagrams (Figures 18(c) and (d)) seems inconsistent. However, this may be explained by the nonlinear and complex change of heated carbonaceous chondrites observed in laboratory experiments (Hiroi et al. 1996a(Hiroi et al. , 1996b.
Another hypothesis is that Trend B reflects innate differences in the composition. In this case, we expect that analysis of a larger set of boulders would show a spectral separation between Trend B boulders and Trend A boulders. Future analysis of the smaller boulder population is important to better examine the Trend B spectral population.

Conclusion
Using the opposition observations of Ryugu acquired by the Hayabusa2 ONC-T, we successfully derived normal albedo multiband maps of Ryugu. The surface coverage of this map is 99.4%. Although opposition observations have never been used for mapping purposes, such observations have three advantages for mapping: the images are (1) free from topographic shadows and (2) almost free from facet orientation effects, and (3) spurious color artifacts that may appear near shadowed terrain are avoided. The second point is relevant for intrinsically dark objects such as C-type asteroids, but not as relevant for bright objects due to limb-darkening effects. This approach will be useful for future missions to dark objects with very rocky surfaces.
From this map, a v-band (0.55 μm) average normal albedo is derived as 4.06% ± 0.10%. This value is consistent with the geometric albedo (disk-integrated albedo at zero phase angle) of 4.0% ± 0.5%, derived from the recent photometry study of Tatsumi et al. (2020a). Figure A1 shows the close-up of the north plain and north plain boulder explained in Section 5.1.1. Figure A2 shows the location of the selected terrain sites explained in Section 5.1.2. Figure A3 shows the close-up of dark rugged boulder ID17 explained in Section 5.2.4. Figure A4 shows the close-up images of dark/bright pairs on the five boulders explained in Section 5.2.3. Figure A5 shows the faces of Otohime saxum explained in Section 5.2.3.     The western wall of this boulder is seen in the image. Due to the large incidence angle, the top side of the boulder is in shadow.

A.2. Additional Images of the Regions and Sites
A.3. Normal Albedo Spectra of the Terrain/Boulder Sites See Table A2 for the normal albedo spectra of the terrain/ boulder sites used in Figure 17.