Nicole G Dias

Beltran N Arribas

Paulo Gordo

Tiago Sousa

João Marinho

Rui Melicio
email: ruimelicio@gmail.com

António Amorim

Patrick Michel

Neo-Mapp Team

HERA Mission LIDAR Altimeter Implementation

The Asteroid Impact & Deflection Assessment (AIDA) is a collaboration between the NASA DART mission and ESA Hera mission. The aim scope is to study the asteroid deflection through a kinetic collision. DART spacecraft will collide with Didymos-B, while ground stations monitor the orbit change. HERA spacecraft will study the post-impact scenario. The HERA spacecraft is composed by a main spacecraft and two small CubeSats. HERA will monitor the asteroid through cameras, Radar, Satellite-to-Satellite doppler tracking, LIDAR, seismometry and gravimetry. In this paper is reported the first iteration on the LIDAR ENGINEERING MODEL ALTIMETER named HELENA. HELENA is a TOF altimeter that provides time-tagged distances and velocity measurements. The LIDAR can be used for support near asteroid navigation and provides scientific information. The HELENA design comprises a microchip laser and low noise sensor. The synergies between these two technologies enable developing a compact instrument for range measurements of up to 14 km. Thermal-mechanical and radiometric simulations of the HELENA telescope are reported in this paper. The design is subjected to vibrational, static and thermal conditions, and it was possible to conclude by the results that the telescope is compliant with the random vibration levels, the static load and the operating temperatures.

Introduction

In the mid to late 1960s, the laser profiling and scanning systems were developed where the phased comparison and the pulse echo were the main measurement techniques. This technology began with the terrestrial cases and progressed to the airborne and space scenarios. In the last case, very powerful lasers have to be used to measure hundreds of kilometers, at least "100 times greater than those being measured form an airborne platform" [START_REF] Shan | Topographic laser ranging and scanning principles and processing[END_REF]. Due to the reduced rate of measurement that a great laser pulse provided, the spaceborne missions were limited at the time. NASA has been the pioneer in developing laser profilers and scanners since 1970, and the first spaceborne altimeters were integrated in the Apollo missions (Apollo 15, 16 and 17) [START_REF] Gardner | Ranging performance of satellite laser altimeters[END_REF]. Several other missions were accomplished with different aims, such as study topographies, assess canopies, measuring distances, or support spacecraft navigation, from fly by to landing operations, making LIDAR a very versatile technology.

Low mass compact spacecraft missions to asteroids is an increasing trend, including small landing spacecraft. This fact tends to drive instrument design, namely miniaturization, and flexibility, 1024 (2021) 012112 IOP Publishing doi:10.1088/1757-899X/1024/1/012112 2 maintaining its performance. New compact rangefinder technologies are therefore needed for future asteroid missions.

The AIDA mission is an effort between DART mission (NASA) and Hera mission (ESA). DART's goal is to cause and demonstrate the deflection of an asteroid using the kinetic impact, and Hera is to characterize the deflection caused by the impact. The target, called Dydimos-B, is the small object from a binary Near-Earth Asteroid (NEA), Dydimos, and so LIDAR plays an important role allowing to map the asteroid and support spacecraft navigation.

HELENA is a Time of Flight (ToF) LIDAR altimeter that measure distances from HERA spacecraft to the asteroid, providing information for a 3D topographic mapping of the asteroid, and also reports the power of the received pulse being possible to calculate the target reflectivity. Most's measure operations will be performed at 14 km to 10 km of distance, and by the end of the mission, more hazardous operations will be performed, such as Fly byes or landing operations [START_REF] Gordo | HELENA-Hera LIDAR engineering model altimeter design[END_REF][START_REF] Gordo | HERA Lidar Instrument Development[END_REF][START_REF] Gordo | Planetary altimeter for HERA development[END_REF].

This work presents the design of the optical front end of the LIDAR, its radiometric calculations, optomechanical design, and mechanical simulations [START_REF] Gordo | HELENA-Hera LIDAR engineering model altimeter design[END_REF][START_REF] Gordo | HERA Lidar Instrument Development[END_REF][START_REF] Gordo | Planetary altimeter for HERA development[END_REF]. The LIDAR design comprises a microchip laser and a low noise sensor. The synergies between these two technologies enable developing a compact instrument for range measurements of up to 14 km with low power consumption and envelope. HELENA acquisition modes can be made in BURST or SINGLE mode. In the first mode, the instrument will output measurement at a configurable periodicity (maximum 10 Hz), and in the second mode, HELENA will output only on measurement, with the value of the median of nine measurement samples [START_REF] Gordo | HELENA-Hera LIDAR engineering model altimeter design[END_REF]. HELENA will also periodically send a housekeeping packet with the equipment health information in both working modes. On the lowest power consumption mode, IDLE, only housekeeping data is available and all the front-end are switched off. The paper is structured as follows: Section 2 is about radiometric model. Section 3 presents the mechanical design. Section 4 presents the thermal-mechanical simulations. Finally, Section 5 outlines conclusions.

Radiometric model

To dimension the LIDAR, it is necessary to perform a radiometric analysis in its operational scenario. The LASER source for HELENA is currently being developed at the Faculdade de Ciências da Universidade de Lisboa (FCUL), and it is a diode-pumped, passively Q-switched Yb-Er Microchip Laser-targeting a 100 μJ pulse with a full-width half-maximum (FWHM) of 2 ns [START_REF] Gordo | HELENA-Hera LIDAR engineering model altimeter design[END_REF].

The radiometric budget allows the calculation of LIDAR front-end "received" energy as a function of emitted pulse energy taking into consideration the LIDAR specifications (e.g., LIDAR laser pulse energy, optical transmittance, optical aperture). The received pulsed energy, i.e., the relation between pulse energy sent and energy received at the Avalanche Photodiode (APD) is calculated by the LIDAR link equation given by:

𝐸𝐸 𝑟𝑟 = 𝐸𝐸 𝑡𝑡𝑟𝑟 𝜏𝜏 𝑟𝑟 𝐴𝐴 𝑟𝑟 𝑅𝑅 2 𝑟𝑟 𝑠𝑠 𝜋𝜋 𝑂𝑂 𝑣𝑣 (1)
where E r is the echo pulse energy (J), E tr is the transmitted laser-pulse energy (J), τ r is the receiver optics transmission, A r is the receiver telescope aperture area (m 2 ), r s is the target surface reflectivity (assuming Lambertian), O v is the overlap between emitter and receiver, and R is the distance from the LIDAR to the asteroid. The peak power of the receiver signal P (W) is given by:

𝑃𝑃 = 0.94•𝐸𝐸 𝑟𝑟 Δ𝑡𝑡 ( 2
)
where Δ𝑡𝑡 is the FWHM of the gaussian pulse duration. The requirements and specifications for the LIDAR radiometric calculations are given in the Table 1. The returned peak power, along with the sensor's saturation limits and minimum detectable power (considering the solar background, sensor NEP, and M=20), are presented in Figure 1.

The solar background was also considered a source of noise, and it can be mitigated by using an optical bandpass filter of 6 nm FWHM at the center of the laser wavelength.

The minimum detectable power is 4.1 nW (considering the sensor NEP and the solar radiation background). According to the simulations, the LIDAR can detect signal for the mission operational distance value of 14 km, even if the target surface has a 20 degree inclination. From the simulations, the telescope aperture and the optical bandpass filter were defined.

Mechanical design

The optical front-end optomechanics are composed of four main blocks: 1) the receiver; 2) the emitter, the 3) front-end electronics, and 4) the electronics box. The main mechanical material is AL6063-T6, and it was used in the majority of the mechanical parts. The receiver, emitter, and front-end electronics IOP Publishing doi:10.1088/1757-899X/1024/1/012112 4 are assembled on the exterior of the spacecraft (LIDAR front end), and the electronics box (LIDAR electronics) is assembled in the satellite.

The receiver consists of telescope (Cassegrain design), refractive optics, and the sensor. The primary mirror is made of zerodur and has a 100 mm diameter. The receiver telescope is considered the most critical structure, from optical, mechanical, and thermal points of view, and therefore was the main subject of the thermal-mechanical simulations. The LIDAR front end is presented in Figure 2. The emitter has a microchip laser followed by a beam expander and is assembled by the receiver's side. Both receiver and emitter are assembled on a base plate that, in turn, is assembled on the frontend electronics' enclosure. HELENA is a very compact instrument with 185 mm of length, 174 mm of width, and 320 mm of height.

Thermal-mechanical simulations

The thermal-mechanical simulations are divided into the vibrational, static, and thermal analysis. The software used to perform such studies was SolidWorks. The objective was to investigate the most critical component, the telescope, and assess the optical performance under different environmental conditions. The optical evaluation criterium was based on the optical tolerance analysis, that defined as ∓0.15 mm the maximum admissible displacement (secondary mirror to baseplate distance), and ∓0.2 mrad the maximum admissible tilt of the secondary mirror. Two studies were made, namely: One that considers the upper telescope structural components were made of AL6063-T6. Other that considers the upper telescope structural components made of Titanium, as shown in Figure 3.

Vibrational analysis

The levels for the Random Vibration environment considered was from ARIANE 6. The preprocessing, analysis and post-processing were made with SolidWorks. The finite element model presented a mesh with 15522 elements and 29115 nodes. It was only considered the first study case. The boundary conditions applied in this analysis are presented in Figure 4, where the structure is fixed at the base (Figure 4a) and a remote mass equivalent to the secondary mirror plus the other components that fix it to the crown (Figure 4b). The Power Spectral Density (PSD) is the variation of the acceleration for a given axis concerning the frequency. The results are given on the basis of a one sigma probability of the stresses to be under the maximum value, this means that the stress has a probability of 68% to be under the maximum value.

To be more accurate, the maximum stress must be multiplied by 2 or 3 for a probability of 95% and 99%, respectively. This gives for the von Mises stress, for the X-axis, a probability of 99% to be under 73.86 N/mm 2 which is considered an acceptable value.

A typical result is presented in Figure 5 and in Figure 6 for the X-axis. Figure 5 shows the von Mises stress distribution, and Figure 6 represents the total displacement felt by the telescope when subjected to the random vibration level. Axis X 1 × 10 -3 9.69 × 10 -1 Axis X 2.144 × 10 -5 25.62 Table 2 shows that the structure is well fitted for the load requested, as no member presents excessive stress, which is an indicator that deformation will not occur.

IOP Publishing doi:10.1088/1757-899X/1024/1/012112 6

Static analysis

For the static analysis, it was used a refined mesh with 235372 elements and 373785 nodes. The boundary condition applied was a fixture, shown in Figure 7, in a small area of the base, and for the load conditions, a 5G force applied in the -y-direction, and another 5G force was applied in the -zdirection, as shown in Figure 8. The von Mises stress distribution was obtained for both studies, i.e., aluminium and titanium studies, and the maximum stress for the first study was 26.72 MPa, and it was observed in the area where the fixture was applied, given a safety factor value of 8.05. For the second analysis, the maximum stress was verified in the same area with a value of 32.13 MPa, with a safety factor value of 6.70.

The secondary mirror's displacement with respect to the telescope baseplate was retrieved from the upper structure (blue line) in Figure 9. The simulations provided two types of results: secondary mirror displacement, and secondary mirror surface deformation. Both studies are presented in Figure 10, to help the comparison.

Figure 10 (a) represents the secondary mirror's displacement when applied the G forces (for the aluminium and titanium studies). Figure 10 (b) shows a comparison of the secondary mirror surface profile (i.e. before and after applied load conditions).

For the titanium study, the safety factor is lower, and regarding the deformation, the secondary mirror surface shows a slightly higher deformation, as can be seen in Figure 10 (a).

Thermal analysis

The LIDAR operational temperatures are -40℃ to +60℃. Thermal analysis of -40℃ was performed, where the reference temperature at zero strain was set to 24.85℃. Note that in this case, the optical performance is a requirement; consequently, the optical tolerance analysis must be considered. For the temperature simulations the same mechanical model, as the Static Analysis, was used. Table 3 shows the von Mises stress distribution for the different upper structural material. When applied the titanium material, the component that suffers the maximum stress, is in the fixation area. When the aluminium is the chosen material, the maximum stress is verified in the GRV, the component that supports the secondary mirror. The secondary mirror displacement results when the telescope is at the temperature of -40℃ is presented in Figure 11 (a). The mirror surface profile variation is presented in Figure 11 (b). The values of the maximum displacement are compared with the tolerance analysis.

Regarding the thermal results, when the telescope was subjected to a temperature of -40℃, it suffered a contraction of 0.1101 mm when the upper structure was made of aluminum, and a contraction of 0.09454 mm for the titanium material. These values are compliant with the optical tolerance analysis.

Conclusions

During the LIDAR operative life the structure will be subject to a diverse range of environmental conditions: vibrations, accelerations, shocks, temperature variations.

Random vibration analysis is useful to verify if the structure can endure launch loads. In HERA mission ARIANE 6 is to be the launcher. Our simulations results concluded that the structure was not subjected to excessive stress, being an indication that permanent deformation will not occur.

Regarding the thermal-mechanical analysis, it can be concluded that when the telescope is subjected to the G forces, both materials can be an option, since in both studies the safety factor is high and deformation very low. However, for the thermal simulations, the best material for the telescope's upper structure, is titanium since the maximum stress and deformations are lower.

NEO-MAPP Team

Karl Atkinson, Paula Benavidez, Jens Biele, Mélanie Drilleau, Colleen Fiaschetti, Sarah Fontaine, Alain Hérique, Martin Jutzi, Ozgur Karatekin, Julia de Leon, Javier Licandro, Naomi Murdoch, Danica Rémy, Grig Richter, Francisco da Silva Pais Cabral, Paolo Tortora, Kleomenis Tsiganis, Jean-Baptiste Vincent, George Voyatzis, Kai Wuennemann, Marco Zannoni.

Figure 1 .

 1 Figure 1. Detected peak power.

Figure 2 .

 2 Figure 2. LIDAR mechanical design. 1) the receiver; 2) the emitter, and the 3) front-end electronics.

Figure 3 .

 3 Figure 3. Upper components (simplified version).

Figure 4 .

 4 Figure 4. LIDAR structure boundary conditions: a) fixed base, b) remote mass.

Figure 5 .

 5 Figure 5. LIDAR vibration stress: X-axis.Figure 6. LIDAR vibration displacement: X-axis

Figure 6 .

 6 Figure 5. LIDAR vibration stress: X-axis.Figure 6. LIDAR vibration displacement: X-axis

Figure 7 .

 7 Figure 7. Boundary condition: Fixture.Figure 8. Boundary condition: Load.

Figure 8 .

 8 Figure 7. Boundary condition: Fixture.Figure 8. Boundary condition: Load.

Figure 9 .

 9 Figure 9. Secondary mirror upper surface.

Figure 10 .

 10 Figure 10. Static analysis: a) displacement, b) deformation.

Figure 11 .

 11 Figure 11. Negative temperature analysis: a) displacement, b) deformation.

Table 1 .

 1 LIDAR system parameters

		System parameters & mission requirements
	Symbol	Value	Description
	R	200 m to 14 km	Variation of HERA probe distance during LIDAR
			operation.
	r s	0.1	Asteroid albedo
			LIDAR Receiver specifications
	E tr	94 μJ	Transmitted laser pulse energy (after optics)
	τ r	0.91	Receiver optics transmission
		100 mm	Receiver telescope primary mirror diameter
		1.5 mrad	Receiver FOV
		Sensor responsivity Sensor @M=20, 1550 nm":230*kV/Watt
		3.2 nW	Sensor NEP
		6 nm	FWHM Spectral filter
			LIDAR emitter specifications
		1 mrad	Emitter FOV
		21 mm	Emitter aperture
		94 μJ	Transmitted laser pulse energy (after optics)
		2 ns	Laser FWHM
		29 mm	Edge distance between receiver and emitter

Table 2 .

 2 Results of the vibrational analysis: displacement and von Mises stress

	Displacement	Minimum [mm]	Maximum [mm]	von Mises Stress	Minimum [MPa]	Maximum [MPa]

Table 3 .

 3 von Mises stress results, for -40℃

		Aluminium			Titanium
	Maximum stress [MPa]	SF	Component	Maximum stress [MPa]	SF	Component
	206.9	1.04	GRV	180.1	1.19	Fixation area

Acknowledgment

The ongoing work presented in this paper was financed by national funds through FCT (Foundation for Science and Technology, I.P.) through CENTRA, project UIDB/00099/2020; funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 870377 (project NEO-MAPP); funded through Foundation for Science and Technology (FCT) under the ICT (Institute of Earth Sciences) project UIDB/04683/2020; Portuguese Funds through the Foundation for Science and Technology (FCT) under the LAETA project UIDB/50022/2020.


Chiho Sugimoto

Eri Tatsumi

Yuichiro Cho

Tomokatsu Morota

Rie Honda

Shingo Kameda

Yosuhiro Yokota

Koki Yumoto

Minami Aoki

Daniella N Dellagiustina

Tatsuhiro Michikami

Takahiro Hiroi

Deborah L Domingue

Patrick Michel

Stefan E Schröder

Tomoki Nakamura

Manabu Yamada

Naoya Sakatani

Toru Kouyama

Chikatoshi Honda

Masahiko Hayakawa

Moe Matsuoka

Hidehiko Suzuki

Kazuo Yoshioka

Kazunori Ogawa

Hirotaka Sawada

Masahiko Arakawa

Takanao Saiki

Hiroshi Imamura

Yasuhiko Takagi

Hajime Yano

Kei Shirai

Chisato Okamoto

Yuichi Tsuda

Satoru Nakazawa

Yuichi Iijima

Seiji Sugita
email: sugita@eps.s.u-tokyo.ac.jp

High-resolution observations of bright boulders on asteroid Ryugu: 1. Size frequency distribution and morphology

Keywords:

The near-Earth asteroid (1 62 17 3) Ryugu displays a Cb-type average spectrum and a very low average norma l albe do of 0.04 . Although the ma jority of boulders on Ryugu have reflectanc e spectra and albe do similar to the Ryugu average, a sm all fraction of boulders exhibit anomalously high albe do and distinc tively different spectra. A previous stud y (Tatsum i et al., 20 21 Nature As tronomy, 5, doi:https://doi.org/10 .10 38 / s415 50 -02 0-11 79 -z) based on the 2.7-km observations and a series of low-altitude (d own to 68 m) descent observations condu cted prior to the first touc hdown have shown that the spectra of these anomalous boulders can be classified into two distinc t groups corresponding to S and C type asteroids. The forme r originate most likely from an impactor that collided with Ryugu's parent body, wh ereas the latter ma y be from portions of Ryugu's parent body that experienced a different temperature history than experienced by the majority of boulder ma terials. In this stud y, we analyzed images captured after the first touc hdown to determine the quantitative properties of these bright boulders on Ryugu. We me asured the sizes of more than a thousand bright boulders and ch aracterized the morph ologic properties of the largest ones.

Introduction

Recent spacecraf t observations have shown that many small asteroids, such as Itokaw a, Ryugu, and Bennu, are rubble-pile asteroids (Fujiwa ra et al., 2006;Watanabe et al., 2019;Lauretta et al., 2019). Owing to their short collisional lifetime, they were likely formed recently (~10 8 years) from much larger parent bodies due to impactinduced catastrophic disruption (O'Brien and Greenberg, 2005;[START_REF] Bottke | The foss il ized si ze distri bution of the ma in as tero id belt[END_REF]Michel et al., 2020). These theoretical predictions are largely consistent with the properties of asteroid fa milies revealed via telescopic observations, such as parent body sizes, their spectral types, and collisional timings (Ma siero et al., 2015). However, many other important aspects of the collisional evolution of asteroids, from the catastrophic disruption of the parent bodies to the reaccumulation and/or formation of rubble-pile asteroids, are not fully understood thus fa r. More specifically, projectile types, spectral variety within the preimpact parent bodies, and brecciation processes on parent bodies, particularly for low-albedo carbonaceous chondrites (CCs), most of which are known to be breccias (e.g., [START_REF] Bischoff | Nature an d Or ig ins of Meteor itic Breccias in METEOR ITES AND THE EARL Y SO LAR SY STEM II[END_REF], are not fully understood. Understanding such specific properties of individual collision events and subsequent geologic processes requires highly detailed observations of rubble-pile asteroids.

The Hayabusa2 mission observed a C-type rubble-pile asteroid in detail (Watanabe et al., 2017). In particular, the initial observation of Ryugu using the Optical Navigation Camera telescope (ONC-T) onboard Hayabusa2 revealed that the colour of Ryugu's surfa ce is very uniform and extremely dark, and that the average spectrum is similar to aqueously altered and subsequently thermally metamorphosed carbonaceous chondrites (Sugita et al., 2019). The geometric albedo of Ryugu is 4.0% at 0.55 μm (Ta tsimi et al., 2020), one of the darkest bodies in the Solar System. Thus, anomalous materials that deviate from the average reflectance on Ryugu are expected to stand out as bright spots. Hayabusa2's initial observations at an altitude of ~20 km (image resolution of ~2.1 m/pixel) revealed the presence of bright spots (Sugita et al., 2019). Subsequently, Ta tsumi et al. (2021) discovered many bright spots based on higher-resolution (~0.29 m/pixel) images captured during the hovering operation af ter the deployment of the CNES-DLR MASCOT lander at ~2.7 km in altitude and images (7.3 mm/pixel) acquired during the MI NERVA-II hopper deployment operation down to ~68 m in altitude. With such datasets, it wa s found that the bright spots are boulders. It is noteworthy that many small depressions (i.e., mini-craters) are observed on Bennu and that their colors are either similar to the surrounding surfa ces or darker, not brighter (Ballouz et a. 2020).

Analyses of 21 bright boulders on Ryugu by Ta tsumi et al. ( 2021) revealed many of their important, distinctive properties. The main find-ings can be summarized as follows: (1) There are two spectral types: C/ X and S. [START_REF] Shal Izi | Power-la w distri butions in empiri cal da ta[END_REF] The spectra of S-type bright boulders at visible-nearinfrared wa velengths are consistent with ordinary chondrites (OCs). ( 3) The size and number density of S-type bright boulders indicate that these boulders are too large and too numerous to have been accreted on Ryugu af ter its formation to its current size and mass. Furthermore, because the mass of impactor(s) that catastrophically disrupted (CD) Ryugu's parent body would be much greater than impactors that did not, the likelihood that exogenic fragments are from CD impactor(s) is greater than non-CD impactors. Consequently, S-type bright boulders may be remnants of the impactor that catastrophically disrupted Ryugu's parent body and that contributed to the reaccumlation process that formed Ryugu (Michel et al., 2020). ( 4) The visible spectra of C-/ X-type bright boulders are consistent with heated CCs. Because of the similarity to CCs, we call these boulders C-type hereaf ter. (5) The size frequency distribution (SFD) of bright boulders is similar to that of other large (1-100 m) boulders with an average brightness similar to Ryugu's surfa ce (Michikami et al., 2019); both have a power-law distribution index of ~2. Here, it is noted that some "bright boulders" are smaller than the geology definition (i.e., rocks greater than 256 mm) of boulder. For simplicity, however, we call pebble-and cobble-size objects also "bright boulders" in this study and our companion paper 2 in accordance with the use of the term by Ta tsumi et al. (2021).

Ta tsumi et al. (2021) further characterized the properties of these bright boulders in more detail. Observations by the near-infrared spectrometer NIRS3 suggest that the S-type bright boulders have a very weak or no 2-μm absorption. This is more consistent with OCs than with the Howa rdite-Eucrite-Diogenite meteorites, even af ter considering possible contamination from background surfa ce spectra. This finding is particularly important for understanding Ryugu's collisional evolution because bright boulders found on a similarly dark rubble-pile asteroid, Bennu, were identified to contain anhydrous silicates with a 2-μm absorption features not observed in the Ryugu spectra (DellaG iustina et al., 2021). The different spectral properties of exogenic bright boulders on these rubble pile asteroids suggest that their parent bodies might have been struck by projectiles of different compositions, supporting that they experienced different collisional evolutions.

Ta tsumi et al . (2021) found that most of C-type bright boulders show spectra similar to the surfa ce of Ryugu and that a few bright boulders in this group show spectra with much stronger UV absorption and larger spectral slope. Comparison between these C-type bright boulders and heated CCs indicates that the observed colour variation of C-type bright boulders is similar in range and pattern to those of heated Murchison (CM2) and heated Ivuna (CI) meteorites.

However, other important properties of bright boulders, such as their morphologies, occurrence and distribution, or details of their colour variation, have not yet been investigated. These properties are important for understanding their origins. Furthermore, no bright boulder at higher latitudes has been found, but we underline that highresolution search for bright boulders have been conducted only at low latitudes thus fa r. Thus, the spatial distribution of bright boulders on Ryugu has not been well-constrained. Hayabusa2 conducted many other low-altitude observations covering wider areas on Ryugu than the data analyzed by Ta tsumi et al. (2021). Consequently, in this study, we conducted a series of analyses of bright boulders on Ryugu using high-resolution (< 10 cm/pixel) images captured by ONC-T at lower altitudes (< 1 km) and with wider surfa ce area coverage at higher latitudes.

High-resolution observations allow us to investigate detailed morphological properties of bright boulders to constrain their origin. Through such imagery dataset, brecciated boulders composed of fragments with different brightness were discovered on Ryugu (Sugita et al., 2019). The incorporation of bright boulders within boulders corresponding to breccia suggests that materials of different composition, including exogenic ones, have congregated and subsequently experienced cementation processes, which are difficult to produce on small rubble-pile bodies. Such incorporation rather suggests mixing through a violent enough process during/before the catastrophic disruption of Ryugu's parent body. Furthermore, to examine whether bright boulders exist only on the surfa ce of Ryugu or whether they also exist in the interior of Ryugu, we investigate images around the artificial crater created by a small carry-on impactor (SCI) onboard Hayabusa2 (Arakaw a et al., 2020).

Although high-resolution images also allow us to investigate the spectral variations within bright boulders, this is beyond the scope of this study and is explored in a separate contribution (Sugimoto et al., 2021), which is hereinaf ter referred to as Paper 2. The remainder of this paper is organized as follows. We discuss the data and analysis method in Section 2, spatial and size frequency distributions in section 3, morphological analysis results in Section 4, geological implications for the evolution of Ryugu and its parent body in Section 5, and conclusions in Section 6.

Method

To investigate the size frequency and detailed morphology of bright boulders, we used v-band images. In this section, we first discuss the vband image data reduction in Section 2.1 and then the SFD measurements in Section 2.2.

Datasets and processing

We used v-band (0.55 μm) images captured by the telescopic Optical Navigation Camera (ONC-T) onboard Hayabusa2 (Kameda et al., 2017;Sugita et al., 2019) for the size-frequency analysis and detailed morphological analysis of bright boulders. We analyzed the data used in Ta tsumi et al. (2021) as well as those obtained later in the mission. The former wa s obtained during hovering operations af ter MASCOT deployment at ~2.7 km in altitude (~0.29 m/pixel) on 3 to 4 October 2018. The latter includes two sets of high-resolution (~0.18 m/pixel) images captured at ~1.7 km in altitude during the artificial crater search scanning operations before (CRA1) and af ter (CRA2) the SCI operations (Arakaw a et al., 2020) conducted on 21 Ma rch and 25 April 2019, respectively. The latter also includes descent observation images (≥ 3.8 mm/pixel) down to ~35 m altitude. Those descent observations include images acquired during the first touchdown rehearsal (TD1-R1A), the first touchdown (TD1), as well as descent observations (DO-S01) around the second touchdown site and low descent observations (PPTD-TM 1B) around the SCI crater conducted on 15 October 2018, 21 February 2019, 8 Ma rch 2019, and 13 June 2019, respectively. It is noted that exposure times used for the PPTD -TM 1B descending sequence are about a half with respect to the other low altitude observations in order to avoid signal saturations for bright boulders seen in other low-altitude observations. For such reason, these images are particularly important for analyzing bright boulders.

For the size-frequency analysis, we analyzed images captured during TD 1-R1A, 2.7-km hovering observations, and 1.7-km scanning observations (CRA1). Although 12 images were taken during the CRA1 observations, peripheral areas of some these images are highly distorted. Thus, accurate size measurements of boulders in these images are difficult. Consequently, we decided to use only four central images from the CRA1 observations in the SFD analysis. Illumination and observation geometry wa s calculated based on the orbital and attitude information. The phase angles θ of observations during MASCOT hovering is 12.7°± 1.8°. Most of this pixel-level variation in phase angle θ results from the width (±3.1°) of field of view (FOV) of ONC-T. The standard deviation of the image-averaged phase angle is very small (0.13°) because the viewing geometry during MASCOT hovering wa s nearly constant. In contrast, the spacecraf t attitude during CRA1 and CRA2 observations wa s systematically changed for scanning a large surfa ce area on Ryugu (Arakaw a et al., 2020). The phase angle a wa s 20.3°± 6.0°for CRA1 and 26.7°± 7.1°for CRA2. The intra-image variation in θ is the same as the MASCOT hovering series, but the interimage variation in average θ is much larger (2.9°for CRA1 and 3.0°for CRA2). Because of large uncertainty in spacecraf t trajectories during the low-attitude observations (i.e., TD 1-R1A, TD 1, DO-S01, and PPTD -TM 1B), we could not derive specific illumination conditions for these datasets.

We conducted data processing, such as the removal of stray light, bias, and read-out smear, flat fielding, and I/F conversion based on the calibration data and method described in [START_REF] Suzuki | Initia l inflig ht cali br ation for Ha ya busa 2 optical na vi ga tion camera (ONC) for science observ ations of as tero id Ry ugu[END_REF] and Ta tsumi et al. (2019). Note that the updated flat fields based on the close encounter images of the asteroids (Kameda et al., 2021;Kouyama et al., 2021) were employed.

SFD of bright boulders

As ONC-T has a fixed focal length, its spatial resolution is determined by the altitude of the spacecraf t from the surfa ce of Ryugu. Thus, the measurements of bright boulders with sizes over a wide range require observations at altitudes covering a wide range. We analyzed images captured during two descent operations, 2.7-km hovering observations, and 1.7-km scanning observations: TD 1 rehearsal, low descent observation around the SCI crater, hovering operation af ter MASCOT deployment, and the artificial crater search scanning operations before/af ter the SCI operation. The SFDs obtained for the bright boulders from theses sets of observations were compared with the SFD of general bright boulders studied by Michikami et al. (2019), who measured the SFD of all the boulders including bright boulders in the images taken during the TD 1 rehearsal. As for touchdown rehearsal, we analyzed seven images captured at distances from the surfa ce ranging from 1194 to 80 m. We defined objects brighter than 1.5 times the median value of each image as bright boulders. Examples of identified bright boulders in this analysis are shown in Fig. B1. This brightness criterion (1.5 times) for bright boulders is the same as that used by Ta tsumi et al. (2021) and is higher than the average by 5σ, where σ is the standard deviation in surfa ce albedo. Assuming that bright boulders have a circular shape, the diameter D BB (in m) of a bright boulder wa s calculated from the pixel area S pix (i.e., the number of pixels that covers bright boulders) using (1) where l (m/pixel) is the pixel scale at the altitude the image wa s acquired. As errors due to the point-spread function (PSF 1.7 pix) are expected to exist, the relative error in the diameter D BB would be ≲ 66% for very small bright boulders (~3 pix in diameter) and ~20% for larger bright boulders (~10 pix in diameter). Here, the relative error in the size of a bright boulder is given by 2/(n + 2), when the linear dimension of a BB is n pixels. This is because its image size may differ from n to n + 2 pixels depending on where the edges of the BB are located with respect to the the charge-coupled device (CCD) pixel grid. Thus, relative error is 66% and 20% for n = 1 and n = 10, respectively. This level of precision is still߭ sufficient for our analysis since the SFD is examined in orders of magnitudes and discussed here. The cumulative number distribution of boulder sizes can be expressed by N(>D) ∝ D -α , where D is the diameter of the bright boulder and α is the power-law index. The boulder distribution in each image is fitted by a power law based on the maximum likelihood method with a goodness-of-fit test based on the Kolmogorov-Smirnov statistics (Clauset et al., 2009), which wa s implemented in the python library, powerlaw, by [START_REF] Alstott | Powerl aw : a Python pa ckag e for an al ys is of heav y-tail ed distri butions[END_REF].

To investigate the SFD of S-type bright boulders, we used the results of the spectral classification by Ta tsumi et al. (2021) and those in Paper 2. Some of the bright boulders observed in the v-band images captured during the 2.7-km hovering observation and 1.7-km scanning observations have been spectroscopically analyzed. The location map of these bright boulders is shown in Fig. 1, and their longitudes and latitudes are listed in Ta ble 1. Note that the sizes listed in this table are not those derived from the Eq. ( 1), but those obtained using the size estimation method described in Section 2.2 of Paper 2. The SFD of S-type bright boulders wa s obtained from the sizes calculated by Eq. (1). For the SFD of C-type bright boulders, the sizes of bright boulders other than those classified as S type were considered. Three the bright boulders (i.e., C65, C29, and C26) analyzed in this study overlap with the bright boulders (i.e., M7, M19, and M21) discovered by Ta tsumi et al. ( 2021) and the correspondence are given in Ta ble 1.

Size and spatial distributions of bright boulders

The new analysis conducted in this study revealed a number of important properties of bright boulders on Ryugu. In the following, we discuss the spatial distributions of bright boulders in Section 3.1, their SFD in Section 3.2, and their estimated volume and surfa ce area in Section 3.3.

Spatial distribution of bright boulders

The coverage areas of the 2.7-km hovering observations (~0.29 m/ pixel) and 1.7-km scanning observations (~0.18 m/pixels) are shown in Fig. 1. The observational coverage of the 2.7-km hovering images is limited to the equatorial region, but it includes all longitudes, which is useful for investigating the longitudinal distribution of bright boulders. In contrast, the 1.7-km scanning images cover higher latitudes, allowing us to examine the latitudinal distribution.

Bright boulders in the equatorial region exhibit a west/east dichotomy, which is similar to the longitudinal distribution seen in the general boulders (i.e., boulders with brightness 1.5 less than the median value of each image). Initial observations revealed that the western side of Ryugu (160°E-290°E) has a lower number density of large boulders than the eastern side (Sugita et al., 2019;Michikami et al., 2019). In the images captured during the 2.7-km hovering observations, two to three bright boulders can be observed every 30°ranging between 240°E and 150°E (240°E to 0°E and 0°to 150°E). In contrast, no or only one bright boulder can be observed in the range between 150°E and 240°W. This observation suggests that bright boulders follow the same longitudinal distribution as the general boulders. The fa ct that both bright boulders and general boulders follow a similar longitudinal SFD suggests that the two types of boulders experienced similar size sorting processes, possibly as a result of the process leading to the west/ east dichotomy formation.

The images captured during the 1.7-km scanning observations show that more bright boulders are present at lower latitudes than at higher latitudes. More specifically, 7, 35, 27, and 10 bright boulders are observed in the ranges of 90°N to 30°N, 30°N to 0°N, 0°S to 30°S, and 30°S to 60°S, respectively. Note that this apparent concentration of bright boulders in the equatorial region could be due to bias resulting from the different spatial resolution for different altitudes. The images of the high-latitude regions are distorted because of the greater tilt of the local surfa ce with respect to the line sight of the ONC-T (Fig. 1). This leads to lower spatial resolutions at higher latitudes. It is also noted that the number density of large boulders (>10 cm) in general is much greater at higher latitudes than at lower latitudes (Sugita et al., 2019;Michikami et al., 2019). Thus, it is not clear that the latitudinal distribution observed for the bright boulders is different from that of large boulders in general. We underline that more extensive analysis is needed. Nevertheless, the fa ct that bright boulders are also observed at higher latitudes is evident from our results, indicating that bright boulders are ubiquitously present on Ryugu. This suggests that bright boulders are well mixed inside Ryugu's body, which might further suggest that they were mixed before Ryugu accreted to its current mass, as proposed by Ta tsumi et al. (2021).

SFD of bright boulders

Regarding the SFD of bright boulders, two different sites on Ryugu, where high-resolution observations were conducted during the MI N-ERVA-II deployment operation and TD 1 rehearsal descents, show similar cumulative SFDs. The cumulative SFDs of bright boulders at 180°-265°E (TD1 rehearsal descents) are shown in Fig. 2a. These distributions express as: [START_REF] Shal Izi | Power-la w distri butions in empiri cal da ta[END_REF] where D is the diameter of the bright boulder and α is the power-law index. The best fit power-law indexes and their errors are listed in Ta ble 2. Their power-law indexes range from 2.2 to 3.2. However, the powerlaw index over the entire size range is much steeper than the one estimated from narrower size ranges captured by individual images acquired at different altitudes. Comparisons between our results and the power-law indexes of bright boulders at different sites, 110°-140°E (Ta tsumi et al., 2021) are shown in Fig. 3. The power-law indexes at these two sites are similar although some of them have large errors. The general agreement in power-law indexes between Ta tsumi et al. ( 2021) and this study suggests that the SFD of bright boulders might be globally uniform.

We derived the best fit power-law indexes for the entire size range, using the following method. As described in Section 2.2, we defined objects brighter than 1.5 times the median value of each image as bright boulders. Due to the PSF, however, the albedo of small bright boulders that are only two pixels across or less are contaminated by light from the surrounding surfa ce. Thus, they are not detected as bright boulders. Consequently, smaller bright boulders tend to be overlooked by our detection method. These small bright boulders need to be searched for in higher resolution images since this size of bright boulders suffer less from the "light dilution" due to the PSF effect in higher-resolution images. Thus, the SFD curves obtained with our method tend to be shallower (smaller α) than the actual distribution. However, because the PSF is fixed on the CCD pixels, not on the actual physical size, the effect of the PSF on detection probability is expected to be the same for bright boulders covering the same number of pixels at different resolutions (i.e., m/pix). Thus, comparing the SFD at the same pixel diameter obtained in images with different spatial resolutions would provide a more accurate SFD slope (i.e., α). Consequently, for the SFD derived from multiple images in Fig. 2a, the power-law indexes were calculated using data points with the same pixel size range (> 1 pixel). More specifically, we selected 6 data points (MINERVA-II deployment operation or TD 1 rehearsal descents) from a relatively small size range and 24 data points (2.7-km hovering operation) from a relatively large size range and calculated the power-law indexes obtained with any combination (144 cases) of these data points as shown (Fig. 2b). Furthermore, regional differences in SFD are considered here. The SFDs derived from images captured during the 2.7-km hovering observation are inte-grated in Fig. 2a. In contrast, we used the SFDs obtained from the individual images in this analysis. Fig. 2b shows that there is a regional difference of about 10 times between images taken during 2.7-km hovering observation at different longitudes. The power-law indexes α were calculated by selecting 144 combinations from a relatively small size range and relatively large size range. The intercepts N(>1 m) were calculated based on the obtained α. The average index and intercept were 3.0 ± 0.7 and 11.4 -2.9 +4.0 , respectively (Fig. 2c).

The best fit power-law index for the entire size range from 0.02 to 2 m in diameter is approximately 3. Furthermore, it is noted that the c For bright boulders with areas >9 pixel 2 , we estima ted their spectra by averaging the reflectanc e of the pixels within the area occu pied by the boulder for each band (M ethod A). For bright boulders with areas ≦ 9 pixel 2 , we extracted the spectra of these bright boulders using the following me thod (M ethod B). Details of me thod A and B are given in Section 2.2. in Paper 2.

power-law indices for the two different spectral types of bright boulders are very different. Using the same method described above, the best fit power-law index 1.6 ± 1.3 for S-type bright boulders observed during the 2.7-km hovering observations wa s derived from 10 combinations of 5 data points (Fig. 2d). The large error for the power law index is resulted from the small number of data points. In fa ct, the distribution of number of cases is not close to Ga ussian. However, we took 2σ as the error of the distribution, which encompasses the entire distribution obtained in the bootstrap calculation. Thus, it is likely that our error estimate is sufficiently conservative. The power-law index for Ctype bright boulders is practically the same as that for all the bright boulders. This demonstrates that the power-law index for S-type bright boulders is much shallower than the C-type bright boulders value. Although the cause for such a difference is not fully understood, it may be due to the difference in the mechanical strength of C-and S-type bright boulders. The observation that S-type bright boulders have a shallower power-law index than C-type bright boulders is consistent with the finding that S-type material (i.e., OCs) generally has a much stronger mechanical strength than C-type material (i.e., CCs) (Flynn et al., 2018). Furthermore, the number density of C-type bright boulders is much greater than that of S-type bright boulders at the smaller size range. On the other hand, at the size range larger than ~1 m in diameter, the number density is dominated by S-type bright boulders. Furthermore, lower thermal conductivities of CCs (e. g., Opeil et al., 2012) may contribute to fa st breakdown through thermal fa tigue of C-type bright boulders (e.g., [START_REF] Delbo | Therma l fa tigue as the or ig in of rego li th on sm al l as tero ids[END_REF]. However, because the ranges of thermal conductivity among CCs and OCs are greater than the difference between their average values (Opeil et al., 2012), it is difficult to determine if this thermal conductivity difference between CCs and OCs contribute to the difference between S-type and C-type bright boulders until the actual thermal conductivity of Ryugu samples have been measured.

Here, it is noted that some data points in Fig. 2a are multiple small bright clasts embedded in large boulders. Such counting is unavoidable because we automatically count regions with brightness 1.5 times the surroundings or greater. The entire boulders including multiple smaller bright clasts may be somewhat larger than the SFD shown in this figure. Thus, the SFD of bright boulders may be significantly different when the size of the entire bright boulders that contain multiple smaller bright clasts are used for the statistics. More specifically, the SFD or the power-law index for such a SFD of bright boulders that contain smaller bright clasts would have a shallower distribution than the distribution shown in Fig. 2a. Nevertheless, the general trend that S-type bright boulders are more abundant than C-type bright boulders at a larger size range will not change even af ter such a fa ctor is considered. It is also important to note that the shallow SFD of S-type bright boulders has been confirmed by the higher-resolution, 1.7-km scanning observations as shown in Fig. 2a. We found one new S-type bright boulder in the 1.7km scanning images used for the SFD analysis, whose size follows the shallow SFD defined by the S-type bright boulders in the 2.7 kmhovering observations (Fig. 2a). Thus, we decided to take this shallow power-law index (1.6 ± 1.3) for the SFD of S-type bright boulders to estimate the volume and surfa ce area of C-and S-type bright boulders in Section 3.3. Here, the error is 2σ (standard distribution) of the distribution.

Volume and surface area estima te fo r bright boulders

The SFDs of bright boulders observed on the surfa ce of Ryugu or within the larger boulders on Ryugu were used to estimate the surfa ce area and volumes of those materials. It is difficult to estimate how much more material is buried underneath other darker material on the surfa ce or within the substrate boulders. In other words, we only consider bright boulders exposed on the surfa ce. Using the SFD estimates for C-type and S-type bright boulders described in Section 3.2, we estimated both the volumes and surfa ce areas of those two types of boulders.

Using the Eq. ( 2), the incremental SFD of bright boulders can be expressed by:

(3) Assuming that boulders have the same aspect ratios as the dark boulders on Ryugu and other typical boulders on asteroids (Michikami et al. 2016, Michikami et al., 2019), the volumes and surfa ce areas of bright boulders are given by: (4)

(5)

The power-law indices α, intercepts N(>1 m), minimum size D min , and maximum size D max used to calculate the surfa ce areas and volumes are listed in Ta ble 3. Note that α = 3.005 wa s used to avoid division by zero for C-type bright boulders. Here it is noted that actual boulders on Ryugu as well as other asteroids are known to have aspect ratios different from unity. However, the departure from a sphere is very small; the volumes of general boulders on Ryugu are estimated to be about 0.65 times of a sphere with the same dimension (Michikami and Hagermann, 2021).

The analysis results indicate that S-type bright boulders have a volume of about 3.7 -2.6 +3.3 × 10 m 3 and cover a surfa ce area of 4.1 -3.2 +9.1 × 10 m 2 , while C-type bright boulders have a volume of about 2.3 -1.3 +7.3 × 10 2 m 3 and cover a surfa ce area of 3.8 -3.1 +27.3 × 10 3 m 2 . The errors presented here were estimated in the following fa shion. As discussed above in Section 3.2, we selected all the possible combinations of bright boulder abundance measurements at large diameters (~0.6 m) and those at small diameters (0.01-0.1 m). The fluctuation in boulder abundances among the different image data includes both statistical fluctuation and real spatial variation; we decided to consider both in our error estimation. Thus, our error estimates could be larger than the actual error. These volumes and surfa ce areas are much smaller than the volume and surfa ce area of the darker, general boulders.

The volume ratio of S-type bright boulders to darker boulders is only 7.1 -5.0 +6.3 × 10 -6 , while the surfa ce ratio is 1.5 -1.2 +3.2 × 10 -5 . Note here that these ratios are effectively the ratio of S-type bright boulders to the entire Ryugu. Similarly, the ratios of C-type bright boulders to darker boulders are 4.4 -2.2 +14.0 × 10 -5 in volume and 1.3 -1.1 +9.8 × 10 -3 in surfa ce area. For the diameter range 0.3 to 2 m overlapping between C-type and S-type bright boulders, the ratio of the total volume of C-type and S-type bright boulders to that of dark boulders are 1.8 -0.1 +0.3 × 10 -5 and 3.9 -3.2 +6.9 × 10 -6 , respectively. The ratio of total surfa ce area of C-type and S-type bright boulders to that of dark boulders at the same overlapping diameter range are 7.6 -1.9 +3.1 × 10 -5 and 1.1 -0.9 +3.2 × 10 -5 , respectively.

If the hypothesis that S-type bright boulders on Ryugu are exogenic, as suggested by Ta tsumi et al. ( 2021), is correct, then the mass mixing ratio of the projectile that hit the parent body of Ryugu is 7.1 -5.0 +6.3 × 10 -6 . This is important to constrain the nature of the collisional history of Ryugu's parent body. Furthermore, as shown by the small power-law index obtained above, the largest boulders account for the dominant proportion of the total mass of S-type bright boulders. In particular, the largest S-type bright boulder, M13, contributes significantly. More specifically, M13 has a semi-major and semi-minor ax is of about 2.1 ± 0.2 m and 1.2 ± 0.2 m, respectively as shown in Fig. 4. Here, we used the average of the ax es of the circumscribed and inscribed ellipses as the best fit value of the ax es of this bright boulder and half the difference as the error. Then, the volume of M13 is estimated to be 13 ± 5 m 3 , assuming that its two shorter ax es are the same as the observed minor ax is. This volume accounts for ~40% of the total volume of S-type bright boulders on Ryugu.

Similarly, the volume ratio 4.4 -2.2 +14.0 × 10 -5 of C-type bright boulders is a suitable measure for the mixing ratio of the parent body's portions that may have experienced different thermal conditions from the dark general boulders on Ryugu. This small ratio of C-type bright boulders supports the theory that the vast majority of Ryugu's materials experienced uniform degrees of thermal metamorphism on Ryugu's parent body. This also places import constraints on the evolution of Ryugu's parent body. More specifically, such a uniform thermal history over a large portion of Ryugu's parent body supports uniform heating Furthermore, the fa ct that the surfa ce area ratio of C-type bright boulders is quite large (1.3 -1.1 +9.8 × 10 -3 ) also has an important implication for understanding the very high-resolution images of Ryugu and possibly the returned samples from Ryugu to Earth. This ratio is calculated based on the size range down to only 2 cm. The SFD of bright boulders smaller than 5 cm has a rollover in the obtained data. However, this may be due to the insufficient spatial resolution of the images. Thus, the same steep SFD might extend to smaller size ranges for bright boulders, possibly down to a mm in diameter. If this wa s the case, then the ratio of C-type bright boulders could be even higher. For example, using the average estimated power-law index (3.0) for C-type bright boulders, the power-law index (1.65) for general boulders with sizes between 0.02 and 3.26 m (Michikami et al., 2019), and the size range 1 mm to 1 cm (the approximate size of the sampler horn), the surfa ce area ratio of C-type bright boulders is ~30%. Due to the error in the estimated power-law index of C-type bright boulders, this volume ratio estimation has a large error. Nevertheless, when we use the lower limit of the estimated power-law index ( 2.3) for C-type bright boulders, the surfa ce area ratio of C-type bright boulders is estimated to be as much as ≳0.4%. Thus, the odds that C-type bright boulder materials are contained in the samples captured by Hayabusa2 touchdown could be significant. In particular, the finding that some of the boulders observed on the Ryugu surfa ce by MASCOT have large bright inclusions with the size range of sub-millimeter to a few millimeters is not inconsistent with the SFD extrapolated from the C-type bright boulders in this study (Jaumann et al., 2019). The nature of such bright inclusions on dark boulders on Ryugu's surfa ce may be a very important observational constraint on the nature of Ryugu's surfa ce material. Thus, the search and examination of such potential inclusions or C-type bright materials will be of very high interest in the returned samples.

Occurrence and morphologies of bright boulders

In this section we discuss the morphologies of bright boulders mostly based on higher resolution (down to ~1 cm/pixel) observations. Morphological analysis based on high-resolution images captured at low altitudes revealed two notable characteristics of the bright boulders on Ryugu. 1) Some bright boulders have intra-boulder variation in reflectance and 2) bright boulders are also observed inside the artificial crater cavity newly formed by the SCI. These findings have important implications for the origin of bright boulders.

Some of the spatially resolved bright boulders are observed as small individual boulders (Fig. 5a andb). Reflectance profiles across these bright boulders are shown in Fig. 5c andd. The reflectance profile shown in Fig. 5c shows that the jump in reflectance at the boundaries of the boulder is much greater than the background fluctuation in reflectance on Ryugu. Specifically, the reflectance of this bright boulder is ~1.5 times brighter than that of the surrounding background and the reflectance jump between the plateau of the bright boulder and background is >4 σ bk where σ bk is the standard deviation in the background reflectance in the image. The reflectance profile shown in Fig. 5d shows a much greater jump (~60σ bk ) at the boundaries of the bright boulder and shows that this bright boulder is ~3.7 times brighter than the surrounding background. These bright boulders have C-and S-type spectra, respectively as shown in Fig. 5e.

Other bright boulders are observed as bright clasts embedded in larger substrates (Fig. 6a,b,c, and possibly d). The presence of such bright clasts embedded in general boulders is important because such morphologies indicate that these bright clasts have experienced intense mixing and agglomeration within darker fragments in Ryugu's parent body rather than having soft-landed on Ryugu in its current small size. Reflectance profiles across these bright clasts are shown in the same figures along with the boundaries of the bright area and substrate boulder. The increases in the reflectance of these intra-boulder bright clasts are also much larger (e.g., ~20σ bk in Fig. 6a) than the background fluctuation σ bk .

Furthermore, multiple bright spots are sometimes seen in a single substrate boulder (Fig. 6a,b,c, and e). The appearances observed so fa r are all consistent with bright clasts embedded in a large substrate boulder. For example, one boulder has two intra-boulder bright clasts (Fig. 6a). No apparent shadows are observed around these intra-boulder bright clasts, whereas the boundary at the base of the boulder that contains these bright spots displays a clear shadow. Meanwhile, other boulders of comparable sizes in this image also display shadows. Similarly, in Fig. 6b, another bright spot has a small extension to the right, and it does not cast a shadow on the substrate boulder. If the bright spot is topographically higher than the dark substrate boulder, shadows would be observed. Furthermore, the shadows of this bright spot and substrate boulder in the upper left are smoothly connected; there are no abrupt kinks in the shadow boundary. This observation suggests that they have a continuous surfa ce. A third bright spot is found to display a two-step increases in reflectance (Fig. 6c). Most of the area for this bright spot is approximately two times brighter than the surrounding background, but a small brighter cluster (at least approximately four times brighter than the background) is included within this area. No apparent shadows are observed around the larger bright spot or the smaller bright cluster. The left side of this boulder is darker than the surrounding terrain. However, this dark region is not a shadow but rather a region with a high solar incidence angle due to a large and sharp change in surfa ce inclination. In contrast, the right side of this boulder has a reflectance comparable to the background; the upper and lower edges of the bright spot and the right side of the boulder are smoothly connected. This smooth connection suggests that their surfa ces are continuous. Thus, the significant brightness variations on this boulder are likely due to the variations in the constituent material. We also found additional bright spots, whose morphologies support embedded structures, but not as strongly as the above cases. One such example is shown in Fig. 6d. On this boulder, the substrate boulder exhibits imbricated structures; shadows are projected to the left of a convex dark mass on this boulder. The right side of the bright boulder appears to be partially hidden by the shadow of a boulder sitting on the substrate boulder. This observation suggests that this bright spot is flat, which is consistent with an embedded structure for this bright spot.

In the four images described above, reflectance profiles suggest that the background brightness is ~1/3 of the bright spots but the CCD pixels of the brightest area are saturated. Thus, the brightest points of these boulders have a reflectance of at least ~3 times that of Ryugu's surfa ce. As described in Section 3 in Paper 2, S-type bright boulders tend to be brighter than C-types. Among relatively well-resolved bright boulders (≧ 10 pixels) studied by Ta tsumi et al . (2021) and in this study, all bright boulders with reflectance >3 times the global average of Ryugu exhibit S-types spectra. The reflectance fa ctors of C-type bright boulders range from 1.1 to 2.3 times the global average, while S-types are 1.8-4.7 times. Thus, bright clasts with such high reflectance are more likely S-types than C-types. This observation suggests that many S-type fragments, which are very likely exogenic, may be embedded in Ryugu's boulders.

To investigate such a possibility, we examined the spectra of bright clasts embedded in dark boulders. However, the images with multiple colour band observations of bright clasts are not as high in spatial resolution as the ones used for the morphological analysis presented above. The multi-colour observations of bright boulders within the substrate boulders are available in ONC dataset; shown in Fig. 6f, g, andh (bright boulders C6, S2, and C65 in Ta ble 1, respectively). Comparisons between substrate boulder and the embedded clasts indicates that these bright clasts possess colour and reflectance properties different from those of the substrates (Fig. 7). The substrates in Fig. 6f, g, andh exhibit spectra similar to the global average of Ryugu. In contrast, as described in Section 3 in Paper 2, the bright clasts, such as C65 and C6, on these substrate boulders exhibit S-type or S-type candidate spectra, respectively (Fig. 7). Both bright clasts and the substrate boulder in Fig. 6g exhibit relatively flat ul-to-v slope, which is defined by the slope between ul and v bands on ONC-T (Ta tsumi et al., 2021), but the bright spot has a slightly stronger UV-downturn.

One of the S-type bright boulders is also observed as a bright spot on a larger darker boulder (Fig. 6h). A super-resolution image composed using the same method by Lucy (1974) and Richardson (1972) based on 4 individual images of this boulder is shown in Fig. 8. In this image, the shadow of the S-type bright boulder can be observed at the west part of the boulder, suggesting that a part of the bright boulder is extended beyond the edge of the substrate boulder. The ratio of the area extending beyond the edge to that within the substrate boulder is ~1.5. This unstable configuration indicates the presence of some kind of cohesion between the bright boulder and substrate boulder. This observation strongly suggests that the substrate boulder is a polymict breccia that includes this S-type clast. This is consistent with the hypothesis that Stype bright boulders are more likely to be mixed during and/or before the catastrophic disruption of Ryugu's parent body and subsequently cemented together with other Ryugu materials rather than to have soft-landed on Ryugu af ter its formation, as suggested by Ta tsumi et al. (2021).

The SCI experiment performed by the Hayabusa2 mission provides important information on the occurrence and distribution of bright boulders. Hayabusa2 performed the first detailed examination of an artificial impact crater (i.e., SCI crater), especially on a rubble-pile asteroid, created by the SCI on April 5, 2019 (Arakaw a et al., 2020). Bright boulders are observed around and inside the SCI crater (Fig. 9). The dis-turbance of the surfa ce due to this artificial impact provided a unique opportunity to examine whether bright boulders are mechanically adhered to substrate boulders and whether bright boulders exist underneath the surfa ce layers of Ryugu. Image comparisons between before and af ter the SCI experiments indicate that a bright boulder (S2) wa s not displaced from its substrate boulder through the SCI impact, as shown in Fig. 9. Note that S1-S12 bright boulders in this figure are selected by visual inspection. The observation suggests that this bright boulder is embedded in the substrate boulder. More specifically, the substrate boulder (labeled Stable Boulder (SB) in Fig. 9) is located in the vicinity (~3 m) of the impact point and exhibited no appreciable motion (<1 pix; 1.3 m) caused by the SCI impact (Arakaw a et al., 2020). However, other similar sized boulders, such as the one labeled Mobile Boulder (MB), were significantly moved by the impact and a large volume of material wa s excavated to the north and west of the stable boulder (Arakaw a et al., 2020). Therefore, the Stable Boulder must have experienced intense disturbance by the impact. Nevertheless, this bright boulder on Stable Boulder wa s not moved by the disturbance, suggesting that this bright boulder is mechanically adhered to Stable Boulder.

Furthermore, in the high-resolution post-SCI images, bright boulders can be observed on the floor of the artificial SCI crater, suggesting that bright boulders also exist in the subsurfa ce layers of Ryugu (Fig. 9d and e). Observations of such subsurfa ce bright boulders are important for at least a couple of different reasons. First, both the crater morphology observations [START_REF] Cho | Geol og ic histor y an d crater mo rp holo gy of as tero id (162173)[END_REF] and the SCI ejecta curtain observations (Kadono et al., 2020) suggest that there may be subsurfa ce stratifications in the boulder SFD, indicating the possibility of size sorting. Such size sorting may influence the spatial distribution of bright boul- ders on Ryugu. Boulder size stratification may also be important for understanding the difference between surfa ce mass motion on Ryugu and Bennu. Bennu exhibits more localized mass motions (Walsh et al., 2019;[START_REF] Jawin | Global pa tterns of recent ma ss mo vement on as tero id (101955) Bennu[END_REF] than Ryugu, which exhibits region-scale (e.g., equatorial ridge towa rd mid-latitude geopotential lows) mass motions (Sugita et al., 2019;Morota et al., 2020). Second, it is highly unlikely that bright boulders newly excavated by the SCI experiment experienced space weathering. Thus, their spectral and albedo properties are important for understanding the intrinsic compositional properties of bright boulders on Ryugu.

However, not many spatially resolved bright boulders have been found on the SCI crater floor owing to its limited surfa ce area. Furthermore, because some filter-band images are saturated by the albedo of these bright boulders, their exact spectral properties cannot be determined with great confidence. Nevertheless, some v-band images were not saturated by these bright boulders (such as S10, S11, and S12 in Fig. 9). Thus, we were able to estimate the approximate brightness of these bright boulders. Analysis results indicate that bright boulder S10 exhibits a brightness 2.7 times the brightness of its surroundings. Because this brightness contrast is significantly greater than the other Ctype bright boulders (≤2.3 times) on Ryugu, this may have S-type spectrum or other bright substance, such as carbonates as found on Bennu (Kaplan et al., 2020). Bright boulders S11 and S12 exhibit 1.9 times the brightness of its surroundings, which are consistent with the brightness of both C-and S-type bright boulders observed thus fa r.

Furthermore, using the same method described in Section 2.2, we studied the SFD of bright boulders within the SCI crater floor (Fig. 2). The SFD of the SCI crater floor bright boulders follow the entire SFD of (2020) and Kadono et al. (2020) show that most of the material within the SCI cavity experienced only weak shock pressures (≲ 500 Pa), fragmentation of bright boulders due to the SCI impact experiment is expected to be minimal. Thus, this observation suggests that the number density of bright boulders is not greatly influenced by the possible sizesorting processes on Ryugu.

Implic ations for collisional history and brecci ation on Ryugu's parent body

The results from our morphological analyses of bright spots (boulders and clasts) also have important implications for Ryugu's collisional history. First, as discussed in Section 4, some bright spots appear as bright clasts embedded within larger substrate boulders. In particular, one of the S-type bright clasts exhibits a morphology indicating mechanical adherence to the substrate boulder. Such morphologies indicate that they have experienced mixing and agglomeration with darker fragments, which constitute the dominant fraction of the host rocks on Ryugu's parent body, rather than having soft-landed on Ryugu af ter its re-accretion. Thus, the presence of structurally embedded S-type bright boulders supports the hypothesis that these boulders were likely mixed during/before the catastrophic disruption of the parent body that created Ryugu (Ta tsumi et al., 2021).

Second, the results from our detailed analyses of bright clasts embedded in larger substrate boulders can constrain the timing and process of brecciation on Ryugu's parent body. Furthermore, S-type and C-type intra-boulder bright clasts have different types of constraints. For example, one of the intra-boulder bright clasts exhibits an S-type spectrum and lacks a 0.7-μm absorption. This observation indicates that the mafic minerals, which are rich in S-type minerals, have not been aqueously altered to serpentine. Thus, the delivery of this Stype intra-boulder bright clast material, as well as its brecciation or cementation in the surrounding dark C-type clasts, likely occurred af ter These results indicate that the cementation process on Ryugu's parent body may have continued even af ter the cessation of aqueous alteration and possible thermal metamorphism and may have taken place af ter the catastrophic disruption of the parent body (i.e., Polana or Eulalia), which is at least a billion years af ter the parent body formation (Bottke et al., 2015). Thus, the embedding of an S-type fragment in a large breccia on Ryugu suggests that the cementation process might have occurred billions of years af ter the formation of the Solar System.

If the cementation on Ryugu's parent body occurred over such a long period or over many stages of its evolution, a large number of impact fragments generated over the long history of Ryugu's parent body could cement together to generate many breccias. These could be the dominant constituent materials on Ryugu's parent body. The dominance of brecciated material may contribute to the globally low thermal inertia of Ryugu (Sugita et al., 2019;[START_REF] Grott | Lo w therma l conductivi ty boulder with high poro si ty identified on C-type as tero id (162173)[END_REF]Okada et al., 2020;Shimaki et al., 2020). Indeed, it is known that an increase in particle size from regolith to boulders typically leads to increased thermal inertia. However, the spatial distribution of thermal inertia on Ryugu does not appear to follow this typical trend; regolith and boulders exhibit practically the same thermal inertia on Ryugu. Similarly, a more unusual trend is observed on Bennu; the thermal inertias of boulders are lower than its regolith (DellaG iustina et al., 2019;Ryan et al., 2019).

Furthermore, the dominance of brecciated materials is further consistent with the properties of carbonaceous chondrites. Large fractions of dark carbonaceous chondrites (CM and CI chondrites) are known to be breccias; ~100% of CM and CI meteorites are breccias [START_REF] Bischoff | Nature an d Or ig ins of Meteor itic Breccias in METEOR ITES AND THE EARL Y SO LAR SY STEM II[END_REF]. Clasts from some chondrites show various degrees of aqueous alteration (e.g., Kerraouch, 2019). The late brecciation on Ryugu's parent body, however, raises a question regarding what process caused the cementation of clasts within breccias on Ryugu. Although the breccias within carbonaceous chondrites may form when aqueous alteration occurs in carbonaceous chondrite parent bodies (e.g., McCoy et al., 2019), the above interpretation that brecciation occurred af ter the cessation of aqueous alteration on Ryugu is inconsistent with cementation by aqueous alteration processes. Another possibility is cementation via impact melt (e.g., [START_REF] Bischoff | Nature an d Or ig ins of Meteor itic Breccias in METEOR ITES AND THE EARL Y SO LAR SY STEM II[END_REF]. Although impact melts would have played an important role in breccia formation, creating a sufficient amount of impact melt to cause adherence among a large fraction of clastic materials may not be easy to generate. This is because the volume of materials that experiences sufficiently intense shock heating to reach the melting temperatures of silicates (e.g., ~1000 °C) is much smaller than the mass of cold fragments from the catastrophic disruption of a 100-km parent body (e. g., Michel et al., 2020;Jutzi and Michel, 2020). However, precisely quantifying the volume fraction of melting that is necessary or which phase of materials is needed to melt for abundant breccia formation remains a challenge.

The key to answering this question may reside in the properties of the adhesive or cementing materials that glue together clasts within the breccia of carbonaceous chondrites. However, cementing materials in CC breccias are not well understood because of the unavoidable oxidation (i.e., rusting) of meteoritic materials af ter their fa ll to Earth. Thus, samples of Ryugu brought back by Hayabusa2 and those of Bennu returned by OSIRIS-Rex without exposing the samples to either rain or oxygen-rich air, will be suitable samples to investigate these adhesive materials. When the nature of this material that cements breccias on Ryugu is understood, then we will gain insight into the brecciation process on Ryugu's parent body.

Conclusions

We analyzed 12 high-resolution (~0.19 m/pixel), 0.55-μm images obtained during the 1.7-km scanning observations and 11 higherresolution (down to 3.8 mm/pix) images obtained during the lowaltitude descents (down to ~35 m). The analysis of more than a thou-sand bright spots (brightness ≥1.5 times the surrounding regolith and boulders) detected in our measurements yielded the following conclusions:

• Bright boulders at higher latitudes (>30°S and > 15°N) were found, indicating that bright boulders are present ubiquitously on Ryugu. This ubiquitous presence suggests that bright boulders are well mixed in the body of Ryugu, supporting the hypothesis that they are mixed before rather than af ter Ryugu's accretion.

• Bright boulders in the equatorial region exhibit a west/east dichotomy in abundance. The longitudinal pattern is the same as the dichotomic pattern found for large dark boulders by Sugita et al. (2019) andMichikami et al. (2019).

• The SFD of S-type bright boulders in the range 0.3 m to 3 m follows a power law with an exponent of 1.6 ± 1.3.

• Comparisons in SFD between S-type bright boulders and darker general boulders indicate that that the former has a volume of about 3.7 -2.6 +3.3 × 10 m 3 and surface area of 4.1 -3.2 +9.1 × 10 m 2 .

The volume ratio of the former to the latter is only 7.1 -5.0 +6.3 × 10 -6 and the surface ratio is 1.5 -1.2 +3.2 × 10 -5 .

• The SFD of C-type bright boulders from 2 cm to 2 m follows a power law with an exponent of 3.0 ± 0.7.

• Comparisons in SFDs between C-type bright boulders and general boulders indicate that that the former (diameter from 2 cm to 2 m) has a volume of about 2.3 -1.3 +7.3 × 10 2 m 3 and a surface area of 3.8 -3.1 +27.3 × 10 3 m 2 . The volume ratio of the former to the latter is 4.4 -2.2 +14.0 × 10 -5 , and the surface ratio is 1.3 -1.1 +9.8 × 10 -3 . When this power law is extrapolated to millimeter scales, which is the size range of samples that can be captured by the Hayabusa2 sampler system, the abundance of C-type bright boulder materials is estimated to be greater than 0.4%.

• For the diameter range 0.3 m to 2 m overlapping between C-type and S-type bright boulders, the ratio of the total volume of C-type and S-type bright boulders to that of dark boulders are 1.8 -0.1 +0.3 × 10 -5 and 3.9 -3.2 +6.9 × 10 -6 , respectively. The ratio of total surface area of C-type and S-type bright boulders to that of dark boulders at the same overlapping diameter range are 7.6 -1.9 +3.1 × 10 -5 and 1.1 -0.9 +3.2 × 10 -5 , respectively.

• The number density of bright boulders inside the newly made SCI crater is consistent with the outside number density to within a fa ctor of two. This confirms the assumption that the abundance of bright boulders is similar between the surface and subsurfa ce; the observed bright boulder abundance represents the bulk abundance of bright boulders on Ryugu.

• Ma ny bright clasts embedded in large substrate boulders were observed. These bright clasts include both S-type and C-type materials. Such morphologies indicate that they have experienced mixing and agglomeration with darker fragments on Ryugu's parent body rather than a soft-landing on Ryugu af ter Ryugu's accretion. This observation also suggests that the cementation process on Ryugu's parent body may have continued until af ter the cessation of aqueous alteration, thermal metamorphism, and perhaps until catastrophic disruption of the parent body, resulting in a very large number of breccias. Such breccias would have a very high porosity and may have contributed to the globally low thermal inertia observed for Ryugu.

Decl aration of Competing Interest

None.

Ac knowledgments

The authors wish to thank all members of the JAXA's Hayabusa2 team for their operational support and scientific discussions.

Fig. 1 .

 1 Fig. 1. Spatial distribution of spectroscopically analyzed bright boulders and coverage of the 2.7-km hovering observations, the 1.7-km scanning observations, and the decent observations. (a) global ma p and (b ) a close-up ma p around 1.7-km scanning observations. Yellow open circles indicate the locations of M1 -M2 1 bright boulders in Tatsum i et al. (2 02 1) and cyan open circles indicate C1-C79 bright boulders investigated in this stud y and Paper 2. The yellow boun dary indicates the area observed du ring the 2.7-km hovering observations (~0.29 m/ pixel), and the cyan boun dary indicates that of the 1.7-km scanning observations (~0.18 m/ pixel). Note that some M-series and C-series boulders overlap. Table 1 presents the details of the relationships. The areas surroun ded by ma genta and lime thick solid lines indicate the area covered by high-resolution images du ring the two decent observations: MINERVA -II release operations and TD1 rehearsal. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2 .

 2 Fig. 2. (a) The SFD of bright boulders and the bright boulders observed du ring a TD1 rehearsal (b lack circles), 2.7-km hovering observations (C-type: pink squares, S-type: blue squares), and 1.7-km scanning observations (C-type: yellow stars, S-type: green stars). Bright boulders in the SCI crater are indicated by red diamond s. General boulders stud ied by Mich ikam i et al. (2 01 9) are shown as gray circles for comparison. Dashed gray and blue lines indicate the be st fit power-law distribution for C-and S-type bright boulders with power-law index 3.0 and 1.6, respectively (the power-law indexes and intercepts are listed in Table3). Dotted gray and blue lines boun d the up per and lower limits of these power-law indices 3.0 ± 0.7 and 1.6 ± 1.3. (b ) SFDs used to obtain the be st fit power-law indices for C/S-type bright boulders. Six data points (b lack diamond s: MINERVA -II deployme nt operation, black circles: TD1 rehearsal descents) in the sm aller size range and 24 data points (p ink circles: 2.7-km hovering operations) in the larger size range were used. The be st fit power-law index for C-type bright boulders was calcu lated from all the combination (1 44 cases) of these data points. The be st fit power-law index of S-type bright boulders was derived from the SFD of S-type bright boulders observed du ring the 2.7-km hovering observation (b lue squares). (c) The distribution of the powerlaw indices of C-type bright boulders calcu lated using the 14 4 combination of data points inFig. 2b. (d ) The distribution of the power-law indices of S-type bright boulders calcu lated using the 10 combination of data points in Fig.2b. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3 .

 3 Fig. 3. Best fit power-law index for boulder distributions using close-up images captured du ring MINERVA -II deployme nt and TD1 rehearsal operations. Power-law indices and their errors for bright boulders (orange squares) identified du ring MINERVA -II deployme nt are listed in Tatsum i et al. (2 02 1) and those of bright boulders identified du ring TD1 rehearsal are listed in Table 2. Those of general boulders (b lue circles) are listed in Mich ikam i et al. (2 01 9) . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

  processes such as radiogenic heating in Ryugu's parent body as proposed by Sugita et al. (2019).

Fig. 4 .Fig. 5 .

 45 Fig. 4. (a)V-band image (hyb2 _onc_20 18 10 03 _232 50 9) of an S-type bright boulder (M 13 ) foun d by Tatsum i et al. (2 02 1) . The yellow scale bars is 2 m. (b ) The semi-ma jor and semi-minor axes of the circu mscribe d ellipse (cyan dashed line) of the bright boulder, wh ose area is defined by brightness values greater than 1.5 time s the me dian value of the background , are 2.3 and 1.4 m, respectively, and those of the inscribe d ellipse (red solid line) are 1.9 and 1.0 m, respectively. (c) Radiance factor profiles along the wh ite lines in (a). Green dashed line and solid line indicate the me dian value of the background and 1.5 time s of it, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6 .

 6 Fig. 6. Intra-boulder bright clasts. The v-band image of each bright boulder is shown in the up per panel, and the radiance factor profiles are shown in the lower panels similar to that in Fig. 5. The boun daries of the bright parts and substrate boulders are indicated with red and blue arrows in (a)-(c). The digital nu mbe rs of the brightest area in (a)-(d ) are saturated. Thus, these bright clasts are brighter than those shown in the radiance factor profiles. (a) hyb2 _on-c_20 19 03 08 _030 54 8; wh ite arrows in panel (a) indicate dark boulders with sizes comparable to that of the bright boulders in this image. (b ) hyb2 _on-c_20 19 03 08 _032 44 8, (c) hyb2 _onc_20 18 10 15 _130 70 5, (d ) hyb2 _ onc_20 19 02 21 _215 93 8, (e) hyb2 _onc_20 19 06 13 _010 04 3, (f) C6 bright boulder; hy-b2 _onc _ 20 19 03 21 _190 55 4, (g) hyb2 _onc_20 19 06 13 _020 40 4, and (h) C65 (M 7) , hyb2 _onc_20 19 03 21 _193 41 0. The blue dashed ellipses shown in (f), (g), and (h) are the areas used for the spectral me asureme nts shown in Fig. 7. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 7 .

 7 Fig. 7. Spectral comparison be tween intra-boulder bright clasts and their substrate boulders shown in Fig. 6. Black lines with squares are the spectra of the bright clasts and the blue lines with circles are the spectra of the substrate boulders: the spectra of bright boulders/spots C6, S2, and C65. Dashed gray lines are the global average spectrum of Ryugu. The gray line with triangles is the spectrum of the same boulder derived from the 7-band images captured du ring the 2.7-km hovering observations (d etails of the spectral analysis are provided in Paper 2) . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 8 .

 8 Fig. 8. Super-resolution image of C65 (M 7) bright boulder. The yellow scale bar is 1 m. The red arrow indicate the part of the bright boulder that appears to be attach ed to the substrate boulder, wh ile the blue arrow indicates that this part of bright boulder extend s out of the substrate boulder. The ratio of the areas indicated with the red and green dashed lines is ~2:3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) bright boulders measured in various observations, which are previously discussed in Section 3 (the TD 1 rehearsal, the 2.7-km hovering observations, and the 1.7-km scanning observations). Because Arakaw a et al. (2020) and Kadono et al. (2020) show that most of the material within the SCI cavity experienced only weak shock pressures (≲ 500 Pa), fragmentation of bright boulders due to the SCI impact experiment is expected to be minimal. Thus, this observation suggests that the number density of bright boulders is not greatly influenced by the possible sizesorting processes on Ryugu.

Fig. 9 .

 9 Fig. 9. Comparison of bright boulders around the SCI crater be fore and after the impact. Size bars are 1 m. The left (a-c) and right (d -f) colum n images were captured be fore and after the SCI impact experime nt, respectively. The up per and bottom images are close-up images of the center images. The Mobile Block (M B) and Stable Block (SB) are indicated with wh ite arrows. Large boulders and bright boulders #1-#7 with cyan arrows in the south of the SCI crater rema ined at the same location be fore and after the impact experime nt. In contrast, large and bright boulders #8-#9 with yellow arrows inside the SCI crater were moved or driven away from the surface. Bright boulders #10-#14 with ma genta arrows are newly observed in the floor of the SCI crater cavity. Note that some of the bright boulders, such as S4 and S6, are faint in a pre-impact image (c) and be came mu ch clearer in a postimpact image (f); (a, b) hyb2 _onc_20 19 03 08 _035 65 6, (c) hyb2 _onc_20 19 03 08 _033 74 2, (d ) hyb2 _onc_20 19 06 13 _020 22 4, (e) hyb2 _onc _ 20 19 06 13 _021 71 1, and (f) hyb2 _onc _ 20 19 06 13 _020 91 8. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) the cessation of aqueous alteration on Ryugu's parent body. The other intra-boulder bright clasts exhibit C-type spectra. As described in Section 4.2 in Paper 2, C-type bright clasts may have experienced different degrees of thermal metamorphism from dark general boulder materials

  Fig. A1. Bright boulders observed du ring CRA1 /CRA2 at ~1.7 km on March 21 and Ap ril 25 , 20 19 . Size bars are 1 m. The sizes and locations of these bright boulders (C1-C79) are given inTable 1. ◀

Table 1

 1 Bright boulders observed in CRA1 , CRA2 , DO-S01, and PPTD-TM1B operations.

	ID		La titude	Lo ngitude	Diam eter [m ]		Norm al Albedo [% ]		Spectral Type b	Si ze meas urement Method c
			[deg] a	[deg] a	D ave	#	σ D l #	σ Du #	A norm al †	σ A l †	σ Au †
	C1 C2 C3 C4 C5 C6 C7 C8 C9 C1 0 C1 1 C1 2 C1 3 C1 4 C1 5 C1 6 C1 7 C1 8 C1 9 C2 0 C2 1 C2 2 C2 3 C2 4 C2 5 C2 6 C2 7 C2 8 C2 9 C3 0 C3 1 C3 2 C3 3 C3 4 C3 5 C3 6 C3 7 C3 8 C3 9 C4 0 C4 1 C4 2 C4 3 C4 4 C4 5 C4 6 C4 7 C4 8 C4 9 C5 0 C5 1 C5 2 C5 3 C5 4 C5 5 C5 6 C5 7 C5 8 C5 9 C6 0 C6 1 C6 2 C6 3 C6 4 C6 5 C6 6	-------------------------M21 --M19 -----------------------------------M7 -	-5.1 -5.1 -16. 0 -14. 0 -24. 4 -31. 3 2. 6 -49. 4 -39. 0 -39. 7 -27. 8 -34. 1 -29. 4 -23. 4 -26. 7 -26. 7 -49. 8 -38. 5 -39. 6 -36. 1 -27. 4 -38. 3 2. 3 4. 2 -4.6 -5.6 -4.5 -3.7 -7.6 4. 5 2. 4 2. 4 16.4 14.2 5. 2 10.0 5. 2 42.0 25.3 33.8 32.9 22.5 19.8 26.9 23.4 72.4 75.3 57.5 41.4 29.6 24.0 21.5 14.6 29.0 5. 1 3. 4 -1.0 -7.2 -9.3 -3.6 -11. 2 -11. 9 -9.3 -6.1 -16. 8 -19. 9	334. 4 319. 8 329. 3 319. 0 333. 2 332. 0 286. 2 330. 2 318. 7 304. 4 296. 4 297. 8 289. 2 285. 8 286. 4 285. 6 290. 7 285. 9 284. 4 279. 5 282. 8 284. 5 310. 9 308. 1 311. 1 308. 6 306. 2 304. 6 306. 1 305. 2 304. 3 304. 0 321. 6 312. 5 316. 9 306. 1 300. 8 333. 5 341. 2 327. 2 317. 7 330. 4 331. 7 322. 9 319. 6 314. 1 300. 9 301. 8 300. 2 301. 5 303. 5 303. 2 293. 5 301. 3 294. 6 301. 7 297. 4 290. 8 292. 7 283. 3 285. 9 286. 5 282. 9 280. 3 284. 6 278. 7	0. 26 0. 43 0. 59 0. 22 1. 50 0. 35 0. 13 0. 17 1. 50 1. 50 2. 50 1. 50 0. 24 0. 60 1. 50 2. 50 1. 50 1. 50 1. 50 0. 75 0. 46 0. 75 0. 37 0. 75 0. 18 0. 75 0. 21 0. 43 0. 75 0. 75 0. 12 0. 11 0. 75 0. 75 0. 19 3. 00 2. 50 6. 5 0. 75 0. 26 0. 24 0. 21 0. 35 0. 75 1. 50 2. 50 6. 0 4. 0 0. 13 7. 50 0. 22 0. 29 3. 50 2. 50 0. 25 0. 34 1. 50 0. 52 2. 50 0. 23 0. 26 2. 50 0. 21 2. 50 0. 75 0. 23	0. 21 0. 29 0. 19 0. 17 0. 50 0. 31 0. 08 0. 11 0. 50 0. 50 0. 50 0. 50 0. 20 0. 15 0. 50 0. 50 0. 50 0. 50 0. 50 0. 25 0. 35 0. 25 0. 23 0. 25 0. 13 0. 25 0. 17 0. 29 0. 25 0. 25 0. 07 0. 07 0. 25 0. 25 0. 14 0. 50 0. 50 0. 50 0. 25 0. 21 0. 19 0. 16 0. 30 0. 25 0. 50 0. 50 0. 50 0. 50 0. 08 0. 50 0. 18 0. 24 0. 50 0. 50 0. 20 0. 24 0. 50 0. 36 0. 50 0. 17 0. 19 0. 50 0. 17 0. 50 0. 25 0. 18	0. 21 0. 22 0. 19 0. 17 0. 50 0. 31 0. 08 0. 11 0. 50 0. 50 0. 50 0. 50 0. 20 0. 15 0. 50 0. 50 0. 50 0. 50 0. 50 0. 25 0. 32 0. 25 0. 11 0. 25 0. 12 0. 25 0. 17 0. 24 0. 25 0. 25 0. 07 0. 06 0. 25 0. 25 0. 14 0. 50 0. 50 0. 50 0. 25 0. 21 0. 18 0. 16 0. 29 0. 25 0. 50 0. 50 0. 50 0. 50 0. 08 0. 50 0. 22 0. 24 0. 50 0. 50 0. 20 0. 22 0. 50 0. 30 0. 50 0. 15 0. 19 0. 50 0. 17 0. 50 0. 25 0. 18	20.5 9. 3 7. 1 9. 7 7. 4 11.4 40.7 43.3 7. 0 6. 4 6. 3 6. 4 15.0 5. 6 5. 9 6. 1 6. 6 6. 2 6. 9 5. 9 6. 5 7. 5 12.5 6. 8 14.9 7. 2 16.8 7. 6 7. 7 8. 3 33.4 23.8 7. 7 10.2 17.5 6. 8 6. 8 7. 3 7. 8 14.2 19.1 12.6 10.8 7. 1 7. 4 6. 5 6. 3 6. 1 31.9 6. 7 17.5 8. 9 6. 3 7. 7 14.9 12.4 6. 9 9. 0 6. 8 23.5 17.1 6. 8 15.7 6. 4 11.9 10.3	20.5 5. 0 1. 9 8. 0 1. 9 11.4 38.6 41.3 1. 8 1. 6 1. 6 1. 7 15.0 1. 6 1. 5 1. 6 1. 7 1. 6 1. 8 1. 6 4. 5 2. 0 6. 9 1. 8 12.9 1. 9 16.8 3. 8 2. 1 2. 3 26.0 18.8 2. 1 2. 8 16.0 1. 7 1. 7 1. 9 2. 2 13.8 17.2 10.6 8. 6 1. 9 2. 0 1. 7 1. 6 1. 6 26.1 1. 7 13.9 7. 0 1. 6 2. 0 14.9 9. 1 1. 8 4. 3 1. 8 18.7 17.1 1. 8 15.7 1. 6 3. 6 9. 3	18.0 6. 4 2. 7 7. 1 4. 6 10.1 37.5 40.3 4. 4 4. 0 3. 9 4. 0 12.9 2. 2 3. 7 3. 8 4. 2 3. 9 4. 4 3. 8 4. 5 4. 7 9. 0 4. 3 12.1 4. 6 14.5 4. 6 4. 9 5. 4 29.2 20.3 4. 9 6. 6 14.4 4. 2 4. 2 4. 6 5. 1 11.6 14.9 9. 5 7. 4 4. 5 4. 7 4. 1 4. 0 3. 9 27.6 4. 2 12.6 6. 1 3. 9 4. 8 12.7 9. 3 4. 3 5. 4 4. 3 17.6 18.6 4. 3 13.6 4. 0 8. 1 8. 0	-C C S C -C C C C C C C C C C C C C C C C C C S C C C C C C C C C C C C C C C C C C C C C C C C C -C C C C C C C C C C C C C S C	B B B B A B B B A A A A B B A A A A A A B A B A B A B B A A B B A A B A A A A B B B B A A A A A B A B B A A B B A B A B B A B A A B

(co ntinued on ne xt page)

Table 1

 1 Du# are average diam eter of bright boulders, lower error, and up per error, respectively. These were obtained using the size estima tion me thod describe d in Section 2.2 of Paper 2. † : A no rmal , σ A l , and σ Au are average norma l albe do, lower error, and up per error, respectively.

		(continued)
	ID		La titude	Lo ngitude	Diam eter [m ]		Norm al Albedo [% ]		Spectral Type b	Si ze meas urement Method c
			[deg] a	[deg] a	D ave	#	σ D l #	σ Du #	A norm al †	σ A l †	σ Au †
	C6 7 C6 8 C6 9 C7 0 C7 1 C7 2 C7 3 C7 4 C7 5 C7 6 C7 7 C7 8 C7 9 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12	-------------------------	-26. 3 -28. 5 9. 8 -0.7 1. 8 -1.9 -2.0 -6.8 24.5 -27. 4 5. 7 -29. 0 -28. 2 -3.4 5. 1 -1.0 0. 6 0. 7 1. 2 1. 2 7. 2 7. 9 5. 5 6. 0 5. 2	283. 2 273. 9 264. 0 278. 6 272. 6 278. 5 272. 5 264. 4 279. 3 275. 0 285. 6 277. 0 274. 4 295. 6 300. 3 299. 0 299. 5 299. 7 300. 0 301. 1 300. 5 301. 6 300. 4 300. 0 299. 8	0. 55 0. 75 0. 75 0. 23 0. 11 0. 75 1. 50 1. 50 0. 24 2. 50 4. 0 2. 50 2. 50 0. 22 1. 24 2. 79 0. 17 0. 60 0. 63 0. 26 0. 22 0. 39 0. 17 0. 11 0. 10	0. 17 0. 25 0. 25 0. 19 0. 06 0. 25 0. 50 0. 50 0. 19 0. 50 0. 50 0. 50 0. 50 0. 21 0. 69 1. 79 0. 11 0. 28 0. 56 0. 08 0. 49 0. 59 0. 06 0. 05 0. 06	0. 16 0. 25 0. 25 0. 19 0. 06 0. 25 0. 50 0. 50 0. 19 0. 50 0. 50 0. 50 0. 50 0. 15 0. 54 1. 35 0. 09 0. 22 0. 38 0. 07 0. 21 0. 35 0. 05 0. 04 0. 05	7. 7 6. 1 5. 4 12.7 28.8 6. 4 6. 2 6. 5 17.8 6. 7 6. 5 5. 8 5. 9 16.4 1 14.3 8 14.1 2 23.0 9 10.9 9 13.0 1 22.3 8 10.2 7 9. 59 18.2 3 13.1 9 10.7 1	3. 0 1. 6 1. 5 11.8 23.2 1. 8 1. 6 1. 8 17.8 1. 7 1. 7 1. 5 1. 5 6. 09 0. 11 0. 61 5. 06 0. 35 0. 69 0. 65 8. 51 4. 62 1. 17 1. 27 1. 31	4. 5 3. 9 3. 5 10.1 25.0 4. 2 4. 0 4. 2 19.4 4. 2 4. 1 3. 6 3. 7 7. 73 0. 11 0. 61 8. 51 0. 35 0. 69 4. 38 5. 33 4. 31 4. 25 3. 06 2. 20	C C C C C C C C C C C C C ------------	B A A B B A A A B A A A A B A A B A A B B B B B B
	# : D ave	# , σ D l

# , and σ a Error in longitud e and latitude estima ted from the resolution of the digital elevation model (SHAPE_SFM_3M _v201 80 80 4) is 0.1°.

b

The spectral type classification is given in Section 3 in Paper 2. Hyph en in this column indicates that spectral type is un classified.

Table 2

 2 Power-law index for boulder distribution from close-up images captured du ring TD1 rehearsal observation.

	Im ag e	Altitude (m)	Co unted numb er of br ig ht boulders	Power-la w index	Erro r (1σ) of power index	Brig ht boulders si ze ra nge (m)
	hyb2_onc_2018 1015_141813 _tvf_iof hyb2_onc_2018 1015_140115 _tvf_iof hyb2_onc_2018 1015_123017 _tvf_iof hyb2_onc_2018 1015_130705 _tvf_iof hyb2_onc_2018 1015_132201 _tvf_iof hyb2_onc_2018 1015_133033 _tvf_iof hyb2_onc_2018 _tvf_iof 1015_133417	1194 617 464 241 159 100 80	18 41 78 135 141 154 182	3. 18 2. 85 2. 19 2. 38 2. 80 2. 55 2. 18	1. 12 1. 27 0. 49 0. 37 0. 42 0. 37 0. 25	0. 29-0. 53 0. 16-0. 32 0. 1-0. 35 0. 07-0. 34 0. 05-0. 18 0. 03-0. 12 0. 02-0. 12

Table 3

 3 Power-law index, intercept and size range used to calcu late the surface area and volum e of C/S-type bright boulders.

		Power-la w index α ± 2σ alpha	Intercepts N (>1 m) †	Brig ht boulders si ze ra nge (m)
	C-type br ig ht boulder S-type br ig ht boulder	3. 0 ± 0. 7 1. 6 ± 1. 3	11.4 -2.9 +4.0 5. 0 -1.6 +2.3	0. 02-2 0. 3-3
	†: The up per and lower errors are from intercept N(>1 m) for steepest (α + 2σ) and shallowest (α-2σ) SFDs. Respective combinations of intercept and power-law index are used, the up per and lower estima tes for volum e and surface area of bright boulders are obtained.