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1
Asteroid Ryugu Before the
Hayabusa2 Encounter
Koji Wada1, Matthias Grott2, Patrick Michel3, Kevin J. Walsh4, Antonella M. Barucci5, Jens Biele6, Jürgen
Blum7, Carolyn M. Ernst8, Jan T. Grundmann9, Bastian Gundlach7, Axel Hagermann10, Maximilian Hamm2,
Martin Jutzi11, Myung-Jin Kim12, Ekkehard Kührt2, Lucille Le Corre13, Guy Libourel3, Roy Lichtenheldt14,
Alessandro Maturilli2, Scott R. Messenger15, Tatsuhiro Michikami16, Hideaki Miyamoto17, Stefano Mottola2,
Akiko M. Nakamura18, Thomas Müller19, Larry R. Nittler20, Kazunori Ogawa18, Tatsuaki Okada21, Ernesto
Palomba22, Naoya Sakatani21, Stefan Schröder2, Hiroki Senshu1, Driss Takir23, Michael E. Zolensky15, and
International Regolith Science Group (IRSG) in Hayabusa2 project
Corresponding Author:
Koji Wada
Planetary Exploration Research Center (PERC),
Chiba Institute of Technology (Chitech),
Tsudanuma 2-17-1, Narashino, Chiba 275-0016, Japan
Email: wada@perc.it-chiba.ac.jp
tel : +81-47-478-4744, fax : +81-47-478-0372
Affiliations:
1 Planetary Exploration Research Center (PERC), Chiba Institute of Technology, Chiba, Japan
2 DLR Institute for Planetary Research, Rutherfordstr. 2, 12489 Berlin, Germany
3 Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Lagrange Laboratory
4 Southwest Research Institute, Boulder, USA
2
5 Laboratoire d’Etudes Spatiales et d’Instrumentation en Astrophysique (LESIA), Observatoire de Paris,
PSL Research University, CNRS, Université Paris Diderot, Sorbonne Paris Cité, UPMC Université Paris
06, Sorbonne Universités, 5 Place J. Janssen, Meudon Principal Cedex 92195, France
6 DLR RB-MSC German Aerospace Center, 51147 Cologne, Germany
7 Institut für Geophysik und extraterrestrische Physik, Technische Universität Braunschweig,
Mendelssohnstr. 3, D-38106 Braunschweig, Germany
8 Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA
9 DLR German Aerospace Center, Institute of Space Systems, System Engineering and Project Office,
Robert-Hooke-Strasse 7, D-28359 Bremen, Germany
10 Department of Biological and Environmental Sciences, University of Stirling, FK9 4LA, Scotland
11 Physics Institute, University of Bern, Switzerland
12 Center for Space Situational Awareness, Korea Astronomy and Space Science Institute, 776,
Daedeokdae-ro, Yuseong-gu, Daejeon, 305-348, Republic of Korea
13 Planetary Science Institute, 1700 East Fort Lowell, Suite 106, Tucson, AZ 85719, USA
14 DLR Institute of System Dynamics and Control, Oberpfaffenhoffen, Germany
15 Robert M Walker for Space Sciences, Astromaterials Research and Exploration Science, NASA Johnson
Space Center, Houston, TX 77058, USA
16 Faculty of Engineering, Kindai University, Hiroshima Campus, 1 Takaya Umenobe, Higashi-Hiroshima,
Hiroshima 739-2116, Japan
17 Deptartment of Systems Innovation, University of Tokyo, Tokyo, Japan
18 Department of Planetology, Graduate School of Science, Kobe University, 1-1 Rokkodai, Nada-ku,
Kobe 657-8501, Japan
19 Max-Planck Institute for Extraterrestrial Physics, Garching, Germany
20 Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Rd NW,
20015, USA
21 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Japan
22 INAF, Istituto di Astrofisica e Planetologia Spaziali, via Fosso del Cavaliere, 00133 Rome, Italy
3
23 SETI Institute, 189 Bernardo Ave., Mountain View, CA 94043, USA
Abstract
Asteroid (162173) Ryugu is the target object of Hayabusa2, an asteroid exploration and sample return
mission led by Japan Aerospace Exploration Agency (JAXA). Ground-based observations indicate that
Ryugu is a C-type near-Earth asteroid with a diameter of less than 1 km, but the knowledge of its detailed
properties is still very limited. This paper summarizes our best understanding of the physical and dynamical
properties of Ryugu based on remote sensing and theoretical modeling. This information is used to
construct a design reference model of the asteroid that is used for formulation of mission operations plans
in advance of asteroid arrival. Particular attention is given to the surface properties of Ryugu that are
relevant to sample acquisition. This reference model helps readers to appropriately interpret the data that
will be directly obtained by Hayabusa2 and promotes scientific studies not only for Ryugu itself and other
small bodies but also for the Solar System evolution that small bodies shed light on.
Keywords:
Hayabusa 2, Ryugu, Asteroids, Regolith, Physical Properties
Table of Contents
1. Introduction ................................................................................................................................... 5
2. Global Properties ........................................................................................................................... 7
2.1. Measured Quantities .............................................................................................................. 7
Orbital Properties............................................................................................................ 7
Size, Shape, and Spin ...................................................................................................... 8
Phase Function .............................................................................................................. 10
Spectral Properties ........................................................................................................ 12
2.2. Derived Quantities ................................................................................................................ 14
4
Composition .................................................................................................................. 15
2.3. Predicted Quantities ............................................................................................................. 15
Satellites, Dust and the Local Environment .................................................................. 15
Boulders, Craters, and Surface Roughness ................................................................... 16
Size Frequency Distribution of Boulders ....................................................................... 17
Shapes of Boulders ....................................................................................................... 20
3. Regolith Thermophysical Properties ............................................................................................ 22
3.1. Measured Quantities ............................................................................................................ 23
Thermal Inertia and Albedo .......................................................................................... 23
3.2. Derived Quantities ................................................................................................................ 24
Thermal Conductivity .................................................................................................... 24
3.3. Predicted Properties ............................................................................................................. 27
Regolith Heat Capacity .................................................................................................. 27
Surface Temperatures, Thermal Gradients, and Thermal Fatigue ............................... 29
4. Regolith Mechanical Properties ............................................................................................ 32
4.1. Measured Quantities ........................................................................................................ 32
4.2. Derived Quantities ........................................................................................................... 32
Grain Size .................................................................................................................... 33
Grain Shape ................................................................................................................ 33
4.3. Predicted Quantities ............................................................................................................. 35
Regolith Porosity ........................................................................................................... 35
Regolith Subsurface Properties ..................................................................................... 36
5
Regolith Cohesion, Angle of Friction, Tensile Strength and Their Influence on Shear
Strength 37
Regolith Bearing Strength ............................................................................................. 41
Whole Rock Properties ................................................................................................. 41
Presence of Ponds and Their Properties ....................................................................... 41
5. Summary and Conclusions ........................................................................................................... 44
6. Acknowledgements ...................................................................................................................... 47
7. References .................................................................................................................................... 47
1. Introduction
Asteroids and comets are relicts of the early stages of solar system evolution. They contain materials
and structures which are relatively primitive compared to those composing planets and thus provide a
window into the earliest stages of planet formation. Investigation of various properties of small bodies
thus provides crucial knowledge needed to understand the origin and evolution of the solar system. The
asteroid (162173) Ryugu is a C-type near-Earth asteroid (NEA) with a diameter of less than 1 km. It is the
target of Hayabusa2, the second asteroid sample return mission led by Japan Aerospace Exploration
Agency (JAXA) (Tsuda et al. 2013). Ryugu will offer a great opportunity to understand the present status
and the evolutionary history of volatile-rich primitive materials in the solar system (Watanabe et al. 2017).
This expectation is supported by the fact that Hayabusa, the previous and first asteroid exploration and
sample return mission by JAXA, returned a lot of surprising and fruitful data from remote-sensing
observations and the returned particles of the S-type NEA (25143) Itokawa (e.g., Fujiwara et al. 2006;
Miyamoto et al. 2007; Nagao et al. 2011; Nakamura et al. 2011; Yoshikawa et al. 2015). Although small
bodies are full of treasures, only a limited number have been visited by spacecraft so far, such as asteroid
(433) Eros (e.g., Cheng 2002) and comet 67P/Churyumov-Gerasimenko (e.g., Sierks et al. 2015). C-type
(and related B-type) asteroids are considered to be the most primitive bodies in the inner solar system as
they are inferred to be relatively rich in volatile materials like water and organics. The only C-type asteroid
visited by a spacecraft so far is the main belt asteroid (253) Mathilde, but it was a flyby observation and
full global mapping images were not obtained (Thomas et al., 1999). Thus, we do not have yet any detailed
information on the most primitive types of asteroids, other than laboratory analysis of primitive
meteorites, but the specific provenance of these is unknown.
6
Hayabusa2 will arrive at Ryugu in the early summer (mid-June to beginning of July) of 2018 and stay
around Ryugu for one year and a half (Tsuda et al. 2013; Watanabe et al. 2017). In addition, the NASA
asteroid sample return mission OSIRIS-REx will arrive at a B-type asteroid (101955) Bennu (~500 m in
diameter) in August of the same year (Lauretta et al. 2017). These will be the first volatile-rich asteroids
for which we will obtain high-resolution images of nearly the whole surfaces and will provide critical insight
as to whether observed characteristics of boulders, craters, and surface roughness (in addition to other
properties discussed elsewhere in this paper) are representative of similarly sized, primitive asteroids.
Since Ryugu has never been visited before, the limited information before Hayabusa2’s arrival should
be reviewed and appropriately set out in order to guide the Hayabusa2 mission toward success. For this
purpose, the International Regolith Science Group (IRSG) was organized as a branch of the Interdisciplinary
Science Team in the Hayabusa2 project. In this paper, a product of an IRSG activity, we review the
information about Ryugu before the encounter of Hayabusa2. We focus especially on the properties of the
surface regolith layer, i.e. its global properties including surface geological features (Section 2), its
thermophysical properties (Section 3), and its mechanical properties (Section 4). The information
described in each section falls into three categories in terms of our present knowledge: the measured data
obtained so far, the properties directly derived/deduced from the present data with basic physics, and the
predicted properties. As a whole, this paper provides a reference model of Ryugu’s regolith with the
categorized data/properties. This model will be useful for Hayabusa2 operations such as landing site
selection and touch-down operations as well as for interpreting and understanding data that will be
obtained by the remote sensing observations of Hayabusa2 and by the analysis of samples returned from
the asteroid.
Hayabusa2 carries a suite of instruments for scientific observation. These include three optical
navigation cameras (ONC), consisting of a telescopic camera with seven band filters (ONC-T) and two wide
field of view cameras (ONC-W1 and -W2), a near-infrared spectrometer (NIRS3), a thermal infrared imager
(TIR), and a light detection and ranging (LIDAR) instrument. The surface of Ryugu will be investigated with
these instruments. For example, global and local mapping of topography, such as craters and boulders,
will be carried out by ONC imaging (Kameda et al. 2017). The spectroscopic properties of the surface will
be revealed by ONC-T and NIRS3 observations, e.g., for detection of hydrated minerals (Kameda et al.
2015; Iwata et al. 2017). The thermophysical properties such as the thermal inertia derived from the
surface temperature distribution will be explored by TIR observations, and these will help to estimate the
particle size and the porosity of the regolith layer (Okada et al. 2017; Arai et al. 2017; Takita et al. 2017).
LIDAR will be used for the albedo observation and dust detection around Ryugu, in addition to measuring
the distance between the Hayabusa2 spacecraft and Ryugu’s surface (Namiki et al. 2014; Mizuno et al.
2017; Yamada et al. 2017; Senshu et al. 2017). Two landers (rovers) are also carried by Hayabusa2, called
MINERVA-II and MASCOT. In particular, MASCOT, developed by the German Aerospace Centre (DLR) in
collaboration with the Centre National d’Etudes Spatiales (CNES), has several instruments for scientific
investigation on the surface (Ho et al. 2017): a camera with illumination unit (MasCam, Jaumann et al.
2017), a near- to mid-infrared spectromicroscope (MicrOmega, Bibring et al. 2017), a multi-channel
radiometer (MARA, Grott et al. 2017), and a magnetometer (MasMag, Herčík et al. 2017). The close
7
observation of the regolith surface by each of MASCOT’s instruments will provide “ground truth” of the
remote sensing data obtained by the Hayabusa2 spacecraft, such as the particle size distribution, mineral
composition, and thermal inertia. In addition to the above remote sensing data, the mechanical properties
of the regolith layer will be investigated by an impact experiment carried out with the so-called Small
Carry-on Impactor (SCI) and in-situ observation with a deployable camera (DCAM3) (Saiki et al. 2017;
Arakawa et al. 2017; Ogawa et al. 2017; Ishibashi et al. 2017; Sawada et al. 2017). If the trajectory of
MASCOT during its descent and after rebound on the surface is traceable, its analysis can also be used to
estimate the mechanical properties of the regolith layer (e.g., Thuillet et al. 2018). After the end of the
mission at Ryugu, and with the benefit of analyses of the returned samples, the reference model built in
this paper will be fully checked and refined, and our knowledge of small bodies in the solar system will be
considerably improved.
2. Global Properties
Here, the global properties of Ryugu are presented along with the best knowledge of the uncertainties
in the measurements. The described properties provide essential inputs for mission planning in advance
of Ryugu’s arrival. In particular, the design reference mission requires precise knowledge of Ryugu’s orbit
and dynamical state, size and shape, and near-surface spectral reflectance properties.
2.1. Measured Quantities
Orbital Properties
The observations used for orbit determination of Ryugu date from 1986, and include 725
measurements from the JPL-Horizons ephemerides (from 16-May-2017). The derived orbit is listed in Table
1. Ryugu’s perihelion (q) of 0.963 AU, and aphelion (Q) of 1.416 AU classify it as an Apollo-type near-Earth
object. Its Earth Minimum Orbit Intersection Distance (MOID) of 0.00111549 AU is among the smallest
values for asteroids larger than 100 m (JPL/SSD).
Numerical modeling of NEA orbital evolution indicates that Ryugu originated in the inner asteroid belt.
According to a model by Bottke et al. (2002), Ryugu is statistically most likely to have followed the ν6
secular resonance pathway from the Main Asteroid Belt (Campins et al. 2013). This pathway marks the
inner boundary of the Main Asteroid Belt at ~2.1 AU and is the most efficient way to deliver bodies into
near-Earth space, accounting for most of those that reach very Earth-like orbits characterized by low-MOID
values and low Delta-V space mission trajectories. Several models suggest that Ryugu likely originated in
the inner Main Asteroid Belt, between ~2.1-2.5 AU, and reached ν6 by inward Yarkovsky drift (Campins et
al. 2013, Walsh et al. 2013, Bottke et al. 2015).
Working from the scenario of an inner Main Belt origin for Ryugu, it is possible to seek relationships
with known asteroid families. Campins et al. (2013) suggested that the spectral taxonomy of Ryugu
prevents a solid match with known families, while Bottke et al. (2015) studied the dynamical possibilities
8
of delivery from either the New Polana or Eulalia families. This work found that Ryugu was more likely to
have originated from the ~1-Gyr old New Polana family that is centered at 2.42 AU. Surveys of these two
families in visible and near-infrared wavelengths find no significant differences between them, leaving
Ryugu’s origin uncertain (Pinilla-Alonso et al. 2016, de León et al. 2016).
Table 1: Summary of important orbital and global properties. The orbital data are taken from JPL’s SSD website (NASA’s Jet
Propulsion Laboratory Solar Systems Dynamics Group - HORIZONS at http://ssd.jpl.nasa.gov/). Rotation period is from
numerous references (Kim et al. 2013; Müller et al. 2017; Perna et al. 2017).
Eccentricity
0.190208
Semi-major axis (AU)
1.189555
Inclination (deg)
5.883556
Period (days)
473.8878
Perihelion (AU)
0.963292
Aphelion (AU)
1.415819
Rotation Period (hr)
7.6326
Size, Shape, and Spin
The reference Ryugu shape model was reconstructed from the inversion of optical and thermal infrared
data by Müller et al. (2017). Because of the small amplitude of the obtained light curves and low quality
of the optical light curves, the inversion did not lead to a unique solution for the pole, shape, and period.
Formally, there were different sets of these parameters that fit the available data equally well. However,
after a careful analysis, Müller et al. (2017) concluded that the most likely pole direction in ecliptic
coordinates is: lambda = 310-340°, beta = -40° ± 15°. The corresponding shape model is roughly spherical
with a volume-equivalent diameter of 850-880 m (see Figure 1).
9
Figure 1: Best fit shape model for Ryugu. Image taken from Müller et al. 2017.
Ryugu has a rotation period of approximately 7.63 h (Perna et al. 2017). Müller at al. (2017) provided
more possible values for the sidereal rotation period (7.6300, 7.6311, 7.6326 h) but from the analysis of
the new data from Very Large Telescope (VLT) (Perna et al. 2017) and other observatories (Kim. et al.
2016), the sidereal rotation period of 7.6326 h is preferred (Durech, pers. comm.). As shown in Figure 2,
the light curve has an asymmetric behavior with two different maxima and minima. The asymmetric trend
of the light curve is connected to either the irregular shape and/or variations in albedo.
Figure 2: Composite lightcurve of Ryugu, as observed at the Very Large Telescope of the European Southern Observatory (ESO-
VLT) on 12-Jul-2016 by Perna et al (2017). The rotational phase corresponds to a synodic period of 7.63 h. The zero phase time
corresponds to 57581.0 MJD.
10
Phase Function
As discussed in Le Corre et al. (2018), the spherical albedo and phase integral of Ryugu are useful
quantities for deriving the bolometric Bond albedo map. These quantities allow us to make temperature
prediction across the surface of this asteroid during site and landing selections events of Hayabusa2
mission. These quantities can also be useful to calculate Ryugu’s thermal inertia and constrain the
Yarkovsky effect.
Le Corre et al. (2018) used ground-based photometric data of Ryugu, which were compiled by Ishiguro
et al. (2014) and references therein, to constrain the average disk-resolved brightness across Ryugu’s
surface. The Radiance Factor (RADF) is the ratio of the bidirectional reflectance of a surface to that of a
perfectly diffuse surface illuminated at the incident angle i = 0 (Hapke 2012). Reflectance, (,e,
α
), is
directly related to
RADF
(,,) or [/](,,) as described in:
[/] (,,) = F(,,) = (,,) (1),
where i, e, and
α
being the incidence angle, the emission angle, and the phase angle, respectively. I is the
radiance and has units of W m-2 nm-1 sr-1. J = is the irradiance and has units of W m-2 nm-1.
Under the assumption that the photometric properties of the surface are well described by a Lommel-
Seeliger law, we can write:
[/] (,,) =
()
(2),
where = cos(), = cos(), =
is the Lommel-Seeliger albedo, () is the phase function, and
is the average particle single scattering albedo. We approximate the phase function with an exponential-
polynomial function of the form f() = (Takir et al. 2015), the coefficients of which,
β
,
γ
, and
δ
, are fitted to the data.
Figure 3 shows Lommel-Seeliger models that capture low and high phase angle behavior, and the
scatter in the moderate phase angle ground-based observations of Ishiguro et al. (2014). Le Corre et al.
(2018) computed models for nominal, maximum, and minimum predicted brightness of Ryugu at 550 nm
(Table 2). Although this photometric model fitted the disk-integrated data of Ryugu well, It may not be an
appropriate model for this asteroid’s disk-resolved data especially at larger phase angles (>100o) (e.g.,
Schröder et al. 2017). This Lommel-Seeliger model is a preliminary model and can be updated when the
spacecraft arrives at Ryugu.
Table 3 includes the albedo quantities of Ryugu, computed with the Lommel-Seeliger model, and the
quantities computed by Ishiguro et al. (2014). The two sets of quantities are consistent with each other.
11
Table 2: Lommel-Seeliger functions that predict [I/] (i,e,
α
) (reflectance) of Ryugu at 550 nm. is Lommel-Seeliger Albedo
and f(
α
) =. Table from Le Corre et al. (2018).
Nominal
0.027
-4.14 x 10-2
3.22 x 10-4
19.16 x 10-7
Maximum
0.030
-3.99 x 10-2
3.27 x 10-4
22.15 x 10-7
Minimum
0.024
-4.46 x 10-2
3.77 x 10-4
21.33 x 10-7
Table 3: Albedo quantities of Ryugu computed using the Lommel Seeliger model and by Ishiguro et al. (2014). pv is the geometric
albedo, q is the phase integral, and AB is the spherical Bond albedo. Table from Le Corre et al. (2018).
p
v
q
A
B
Lommel-Seeliger
0.042.
.
0.34.
.
0.014.
.
Ishiguro et al. (2014)
0.047.
.
0.32.
.
0.014.
.
Figure 3: The Reduced V magnitude of Ryugu as a function of phase angle predicted by the Lommel-Seeliger model is shown
compared with the ground-based measurements of Ishiguro et al. (2014) and references therein. Shown are the minimum
12
(red dots), maximum (blue dashes), and nominal (black solid line) models. Our minimum and maximum models do not
include the Mathilde data, however our nominal model does. Reflectance is in units of sr-1. Figure from Le Corre et al.
(2018).
Spectral Properties
Ryugu is a primitive Apollo NEA classified as a C-type asteroid. At present, there are 8 ground-based
spectroscopic observations of this asteroid, three of which extends towards the near-IR (Table 4). In nearly
all the observations, the spectrum is featureless, with a slight reddening in the IR and a slight UV drop off.
The best meteorite spectral counterpart is a heated CM chondrite or possibly a CI chondrite (Tonui et al.
2014), however this comparison is complicated by the poorly-known effects of space weathering on Ryugu.
The spectral analysis by Vilas (2008) at visible wavelengths showed a feature at 0.7 µm attributed to
the Fe2+->Fe3+ charge transfer transition in oxidized phyllosilicates. This feature has not been detected in
any other observations of Ryugu and the author suggested a spatial heterogeneity in the asteroid surface
composition, as already observed in other main-belt C-type asteroid spectra (see Rivkin et al. 2002).
The observations by Lazzaro et al. (2013) in the 0.4-0.85 µm spectral range covered 70% of Ryugu’s
surface and showed an almost uniform C-type featureless spectrum, with no direct evidence of hydration
features. Few variations have been observed at wavelengths shorter than 0.5 µm, which lie in a UV drop-
off as found in previous observations (Binzel et al 2001). The UV drop-off is a common spectral feature of
asteroids whose taxonomy is associated with carbonaceous chondrites, particularly for G and F asteroid
classes (Tholen & Barucci 1989) or Cg in the Bus-DeMeo system (Bus and Binzel 2002; DeMeo et al. 2009).
This spectral behavior was investigated and widely discussed by Hiroi et al. (1996, 2003) and Cloutis et al.
(2012). These authors noticed decreased reflectance in the UV after heating or laser bombardment
processing to simulate micrometeorite bombardment. These hypervelocity impacts cause localized
melting and the production of spherical glassy droplets. The slight UV drop-off observed in different
regions of Ryugu’s surface could thus be explained by the effect of heterogeneous processing due to space
weathering and/or episodes of substantial heating via, presumably, closer perihelion passages.
The IR observations by Abe et al. (2008) and Pinilla-Alonso et al. (2013), show a featureless/flat
spectrum and confirm that Ryugu is a C-type asteroid in line with all the other observations. A very slight
positive slope is observed. The two studies derive different slope values, which could be indicative of a
heterogeneous surface; however, the visible observations by Moskovitz et al. (2013) reported a
homogenous and flat spectrum in different observations of Ryugu, suggesting that possible
heterogeneities should be constrained to 5% of the entire asteroid surface. This work proposed that Ryugu
was best represented by a thermally altered sample of the Murchison (CM2) meteorite and by the
thermally metamorphosed CI chondrite Yamato 86029. The most recent work by Perna et al. (2017)
confirms all the previous observations with a slight UV drop off and a featureless/flat spectrum in both the
visible and near IR (Figure 4). Le Corre et al. (2018) observed Ryugu during its close fly-by of the Earth in
July 2016. Their spectrum differs from those presented in Moskovitz et al. (2013) and Perna et al. (2017),
with a stronger red spectral slope shortward of 1.6 µm. However, like previous observations, Ryugu’s
spectrum does not show any well-defined absorption bands. Le Corre et al. (2018) suggested the possible
presence of two broad absorption bands centered around 1 and 2.2 µm in their data. They proposed that
if both are present, these bands could be indicative of a CO or CV chondrite-like composition. These
13
meteorites are typically too bright to match Ryugu’s reflectance and would require darkening effects of
space weathering to provide a match to the asteroid (Le Corre et al. 2018). These authors used curve fitting
techniques to confirm that CM chondrites remain the best match. They also found two small asteroids
with very similar spectra (showing a pronounced red slope) to Ryugu: NEA (85275) 1994 LY and Mars-
crossing asteroid (316720) 1998 BE7. In addition, this work showed that the newly-observed spectrum of
Main Belt asteroid (302) Clarissa, suggested as a possible source family for Ryugu (Campins et al., 2013),
does not match their spectrum of Ryugu. It is however a closer match with the spectrum from Moskovitz
et al. (2013).
Table 4: Spectroscopic observations of asteroid Ryugu since its discovery in 2001. Spectral and compositional characteristics
are listed.
Reference
Spectral
interval
µm
Taxonomy Type
T=Tholen BD=Bus-
De Meo
Meteoritical
counterpart
Spectral Characteristics
Binzel et al.
2001
0.4-0.9
Cg (BD)
N.A.
UV drop off: Red (0.4-0.65)
µm Flat (0.65-0.9)µm
Vilas 2008
0.42-0.93
C (T)
CM2
Band at 0.7 µm Flat with
very weak band at 0.6 µm
Abe et al. 2008
0.4-2.4
C
N.A.
Flat & Featureless spectral
slope (0.85-2.2 µm) 0.89 ±
0.03 %/1000 Å
Lazzaro et al.
2013
0.4-0.85
C
N.A.
Flat & Featureless UV drop
off (<0.45 µm)
Pinilla-Alonso et
al. 2013
0.85– 2.2
C
N.A.
Featureless spectral slope
(0.85-
2.2 µm) 0.37 ±
0.28 %/1000 Å
Sugita et al.
2013
0.47-0.8
163Erigone
Family
CM (heated
Murchison)
Flat & Featureless
Moskovitz et al.
2013
0.44-0.94
C (BD)
CM (heated
Murchison) CI (Y-
86029)
Spectrally flat
Perna et al. 2017
0.35-2.15
C (BD)
heated Murchison CM
unusual/heated CI
Featureless UV drop off
(<0.45 µm) spectral slope
(0.5-0.8 µm)
14
Le Corre et al.
2018
0.8-2.4
C
CM2 carbonaceous
chondrites, Mighei
(grain size < 40 μm)
and ALH83100 (grain
size < 100 μm)
near-perfect match with
NEA (85275) 1994 LY and
Mars-crossing asteroid
(316720) 1998 BE7
Figure 4: The featureless/flatness nature of the Ryugu spectrum is evident in this series of three Vis-IR spectra. Superimposed
are the spectra of thermally altered samples of the CM carbonaceous chondrite Murchison, in red (heated at 900 °C) and in
cyan and green (heated at 1000 °C) (from Perna et al. 2017).
2.2. Derived Quantities
Determining the composition of Ryugu by remote spectroscopic observations requires accounting for
viewing geometry and modeling of the asteroid’s surface properties. Reflectance properties of asteroids
may differ from laboratory analogues due to grain size, phase angle, and space weathering (Binzel et al.
2015; Sanchez et al. 2012; Reddy et al. 2012). Laboratory spectral measurements of meteorites relevant
to Ryugu can improve the interpretation of future hyperspectral observations obtained by Hayabusa2
NIRS3 instrument by linking absorption bands to well-characterized mineralogical composition. Here, we
summarize various authors’ interpretations of their Ryugu spectra, most of which are included in Table 4
(see Le Corre et al. 2018 for a lengthy discussion of spectral interpretations of Ryugu).
15
Composition
Generally, ground-based observations of asteroid Ryugu show a featureless spectrum, with a slight
reddening in the near IR and with a slight drop off in the UV range. Based on laboratory data, the best
available meteoritic spectral analogs are, to first order, a heated CM or possibly CI chondrites. However, a
list of possible surface analogs for Ryugu should contain at least components of CM and CI meteorites (e.g.
Murchison, Orgueil, Jbilet Winselwan, Y82182, Y86029 and so on), plus a suite of serpentines, saponite,
phyllosilicates, magnetite, sulfates, sulfides, pyroxenes, and carbonates.
The extent of alteration and the spectral characteristics of 16 heated CI and CM chondrites was
investigated at the Planetary Science Laboratory (PSL) of the Institute for Planetary Research of DLR, in
Berlin, Germany. Only meteorites whose bulk modal mineralogy and H2O contents had previously been
examined were included. Near- and mid-IR reflectance spectra were collected for powdered samples of
the meteorites. The aim was to directly relate spectral features to the known properties and alteration
history of the heated CI and CM chondrites and accurately interpret the surface mineralogy of C-type
asteroids. Features in the mid-IR are particularly diagnostic of the anhydrous and hydrous silicate
mineralogy and can be used to remotely infer the extent of aqueous and thermal processing on these
primitive bodies (Tonui et al. 2014; King et al. 2016).
Laboratory measurements of reflectance spectra of a series of 23 carbonaceous chondrites belonging
to the CM and CR groups have been obtained between 0.3 to 100 µm in support of efforts to be able to
interpret and relate measurements of the surface of Ryugu. The major results are i) the presence of 0.7
and 0.9 µm features correlated to the amount of phyllosilicates (confirming previous work such as Vilas
and Sykes 1996); ii) reporting for the first time of the presence of 0.7 and 0.9 µm features in spectra of a
CR chondrites (Grosvenor Mountains 95577); these data suggest that Cgh-type asteroids (which make up
about 1/3 of the main-belt C-type asteroids) could be the parent bodies of CM but also of some CR
chondrites; iii) the presence of a goethite-like 3-µm band for some CR chondrites (Beck et al. 2018).
2.3. Predicted Quantities
Moving from derived quantities, where measured properties are used to derive new values for the
properties of Ryugu, here we use the best evidence regarding Ryugu to predict properties for which there
are no measurements of any kind. This section will often rely on knowledge gained from previous
explorations and general estimates for C-type and NEAs. Some are explained in depth, notably block sizes,
due to the importance they could have for mission operations planning regarding spacecraft safety.
Satellites, Dust and the Local Environment
There are no directly observed, or inferred, satellites at Ryugu, so this feature, along with dust floating
around the asteroid, has fallen into the “predicted” category of this work. What would drive a prediction
16
of the existence of a satellite? Satellites among NEAs are common – it is expected that 15% of the
population have satellites on relatively close orbits (Walsh and Jacobson 2015, Margot et al. 2015).
However, nearly all NEAs with satellites are very rapidly rotating, typically near the critical rotation rate of
~2.2h, and nearly all have small lightcurve amplitudes, and where available, their shapes are often found
to be “top-shapes” or nearly spherical with equatorial bulges. Given that small bodies can be spun up or
down by the Yarkovsky–O'Keefe–Radzievskii–Paddack effect (YORP), but this is highly uncertain, the
current spin rate of Ryugu certainly does not indicate that it was ever a rapid rotator in the past, but at
first glance there is no strong indication that Ryugu will have a satellite or significant floating dust.
Boulders, Craters, and Surface Roughness
Safely delivering the spacecraft to the asteroid surface and effectively obtaining a sample are mission
critical events that require careful evaluation of the asteroid surface properties. The distribution and
abundance of boulders and craters pose the greatest risk to spacecraft flight that must be carried out
autonomously. The surface roughness, or regolith grain size distribution are irrelevant to safety but critical
to the ability to successfully obtain a sample. Here we summarize spacecraft observations of asteroids that
provide useful guidance for what we can expect upon arrival to asteroid Ryugu.
Asteroid Itokawa is similar in size (535 m x 294 m x 209 m; Demura et al. 2006) to Ryugu (~ 900 m),
but significant differences in geological features are expected. Returned sample analyses confirmed that
S-type asteroid Itokawa is composed of ordinary chondrite-like material, whereas C-type asteroid Ryugu
is likely to be more volatile rich and weaker. It is already known that Itokawa and Ryugu have strikingly
differing shapes. Itokawa is highly elongated and appears to be a rubble pile composed of fragments from
the catastrophic disruption of a larger body (Michel and Richardson 2013). In contrast, Ryugu is roughly
spherical, but its evolutionary history is not yet known.
The only C-type asteroid that has been previously visited by spacecraft is the main belt asteroid
Mathilde—a significantly larger asteroid at ~53-km mean diameter (Thomas et al. 1999). The best images
obtained during the NEAR flyby of Mathilde were 160 m/pixel (Thomas et al. 1999). At this scale, Ryugu
would be only a few pixels across, so these images do not offer much insight into what to expect on Ryugu’s
surface. Several other asteroids (S-types Eros, (243) Ida, (951) Gaspra, (2867) Steins, (4179) Toutatis,
(5535) Annefrank; Q-type, (9969) Braille; M-type (21) Lutetia) and other small bodies (Phobos, Deimos,
several comets, and moons of Saturn) have been imaged by spacecraft and provide some constraints as to
what to expect from Ryugu; however, of those bodies only Eros, Phobos, Toutatis, and 67P/Churyumov-
Gerasimenko (67P) were imaged at scales sufficient to resolve small boulders, and only Eros, Phobos
(highest resolution images only available in one area), and 67P have been imaged globally. The size of Eros,
the size and celestial location of Phobos, and the cometary composition/nature of 67P all pose
complications for using these bodies as analogs to Ryugu.
At a larger scale, images of Ida and Gaspra look broadly similar to those of Eros, perhaps indicating
that Eros is representative of an S-type asteroid of its size. Aside from Itokawa, Steins (5.3-km mean
diameter) and Toutatis (3-km mean diameter) are the asteroids that have been observed by spacecraft
17
that are closest in size (both are larger) to Ryugu but have a different taxonomic type; the best global
Steins images have a ~160-m pixel scale, again insufficient to give much insight into Ryugu. The Toutatis
data are limited, but have a pixel scale of ~3 m. There is limited, very low resolution data available for
Annefrank and Braille. (4) Vesta and Ceres are so much larger than Ryugu that they do not provide very
good points of comparison for what to expect.
Size Frequency Distribution of Boulders
The cumulative size–frequency distributions (SFD) of boulders on many small bodies (where sufficient
data are available) can be fit by power laws (see Table 5). Many, though not all, of the fits to global boulder
populations have power-law exponents around -3. The exponent of the power-law fit depends on several
factors, including the geological context, the strength of the material, and possibly the size of boulders.
Power-law behavior of cumulative size–frequency distributions of terrestrial fragmented objects has also
been observed (Turcotte 1997; see also Table 1 in Pajola et al. 2015), with the examples listed in Pajola et
al. (2015) having exponents ranging from -1.89 to -3.54.
In the cases of Eros, Itokawa, and Phobos, extending the SFD power-law fit from large, tens-of-meter-
sized blocks down to small, tens-of-centimeter-sized blocks yields reasonable estimates of small block
populations (Rodgers et al. 2016, see Figure 5). However, the geological context of an area matters for the
absolute block density – if lower-resolution counts include multiple geological settings, they will not
extrapolate accurately to local areas containing only one setting (Ernst et al. 2015; Rodgers et al. 2016).
Table 5: Small bodies for which boulder counts have been made from spacecraft images. The minimum boulder sizes measured
are directly related to the best image resolution available for a given object.
Name
Mean
Diameter
(km)
Spectral
Type
Min boulder
size of
global count
(m)
Min boulder
size of
regional
count (m)
Power law
found
Data source
References
Eros
17
S
15
0.05
-3.2 as low
as -2.3
locally
NEAR
Rodgers et al. 2016;
Thomas et al. 2001
Itokawa
0.35
S
6
0.1
-3.1
-3.5
as low as -
2.2 locally
Hayabusa
Mazrouei et al. 2014;
Michikami et al. 2008;
Noviello et al. 2014;
Rodgers et al. 2016
18
Toutatis
2.9
S
n/a
10
-4.4
locally
Chang’e 2
Jiang et al. 2015;
Huang et al. 2013
Lutetia
99
M
n/a
60
-5.0
Rosetta
Küppers et al. 2012;
Sierks et al. 2011
Ida
32
S
n/a
45
n/a
Galileo
Lee et al. 1996
Phobos
22
D
n/a
5
-3.2
Viking
MGS
MEX
MRO
Ernst et al. 2015;
Rodgers et al. 2016;
Thomas et al. 2000
Deimos
12
D
n/a
~4
-3.2
Viking
S. W. Lee et al. 1986;
C. Ernst, personal
communication
Churyumov-
Gerasimenko
4
com
et
7
2
-3.6 global
local
ranges -2.2
to -4.0
Rosetta
Pajola et al. 2015;
2016
19
Figure 5: Figure taken from Rodgers et al. 2016 showing the size frequency distribution of the blocks measured on Eros, Itokawa,
Phobos and comet 67P/Churyumov-Gerasimenko (see Rodgers et al. 2016, Figure 1.).
Radar observations of some NEAs have identified large boulders on at least 14 NEAs (Benner et al.
2015), but the size of the boulders identified is limited by the resolution of the data. Toutatis provides the
only “ground truth” between radar identifications of boulders and spacecraft images of boulders—the SNR
of the radar observations was too low to positively identify boulders on Eros or Itokawa (Benner et al.
2015). Radar data can be used to measure the radar scattering properties of asteroids, which gives insight
into surface cobbles of the scale of the radar wavelength (0.035 m for Goldstone, 0.126m for Arecibo).
If there were radar data that suggest either a number of boulders or a cobble number, an average size
distribution of boulders for the asteroid could be estimated by assuming a -3 power law exponent. The
actual distribution of boulders will be influenced by factors such as their origin, and the geopotential of
Ryugu. Ponds full of cm-sized cobbles are found on Itokawa at geopotential lows, and most boulders are
located in other regions of the asteroid (Fujiwara et al. 2006; Saito et al. 2006). If this distribution is typical
of a small asteroid, Ryugu should have concentrations of finer material (ponds) near the geopotential lows,
and boulders will be found at higher geopotentials. Generally, the lowest potential for an asteroid of
Ryugu’s shape is expected to be found at or near the equator; the shape and density of the asteroid will
affect the location of these geopotential lows.
If the boulders are sourced from craters, as with Eros (Thomas et al. 2001), they are likely to be
distributed around the craters as ejecta would fall on the irregularly shaped body. On the other hand, they
may preferentially settle in the equatorial or near-equatorial regions.
20
Shapes of Boulders
The aspect ratios of boulders on Itokawa >6-m in diameter were measured by Mazrouei et al. (2014),
who found that most boulders in this size range were elongated, with b/a ratios of 0.7 (a, b, and c are
triaxial dimensions of the boulders, defined to be a≥b≥c). It was not possible to measure the third
dimension of most boulders in the Hayabusa AMICA images. Similar b/a ratios (0.62–0.68) were found by
Michikami et al. (2010). The c/a ratio was measured for 21 boulders, the mean was 0.46 (Michikami et al.
2016). A compilation of fragment dimensions from several laboratory experiments is shown in Table 6.
Although the measurements assume an ellipsoidal shape, the fragments are actually irregular in shape. It
is not known whether the aspect ratio of rocks on a C-type asteroid would be different from those seen
on Itokawa or in the strong-rock experiments of Table 6. Also unknown is the magnitude of the influence
of thermal degradation on boulder fragmentation.
Table 6: Compilation of fragment ratios b/a and c/a from several publications in the literature. Dimensions are defined to be
a≥b≥c.
Reference
Target
Projectile
Impact
Velocity
(km/s)
b/a
c/a
Fujiwara et al. 1978
Basalt
Polycarbo
nate cylinders
2.6 and 3.7
0.73
0.50
Capaccioni et al.
1986
Basalt
Concrete
Aluminum
spheres
8.8 and 9.7
0.7
0.5
Durda et al. 2015
Basalt
Aluminum
spheres
3.9-5.8
0.72 ± 0.13
0.39 ± 0.13
Michikami et al.
2016
Basalt
Nylon
spheres
1.6–7.1
0.74
0.5 (catastrophic
disruption)
0.2 (impact cratering)
Craters
Itokawa has a small number of identified impact craters, especially small ones (Hirata et al. 2009).
Given its similar size to Itokawa, Ryugu may also not exhibit many craters. Eros, Phobos, Ida, and Gaspra
all have numerous craters; on Eros, seismic shaking is suggested to have acted to erase many small (<100-
m-diameter) craters (Chapman et al. 2002; Thomas and Robinson 2005); craters of 100 m-size would be of
significant size compared to Ryugu. These observations imply that Eros has a global loose regolith as deep
21
as 100 meters (Robinson et al. 2002). Eros’s relatively flat topography (<55% of the surface is steeper than
30º) may also be explained by a thick global regolith (Zuber et al. 2000). Craters are more apparent on
Toutatis than on Itokawa (Huang et al. 2013), with different densities of craters seen on the different lobes
of the asteroid (Zou et al. 2014). As Ryugu is intermediate in size between Itokawa and Toutatis, it might
be expected to have more craters per unit area than Itokawa but fewer than Toutatis. Since the size of
regolith particles on Ryugu is expected to be similar to that on Itokawa (see Section 3.2.2), steep cratered
topography is not expected on Ryugu as well as Itokawa. However, the different composition of Ryugu
could affect the size of craters and the regolith depth and structure.
Meter-Scale Surface Roughness
Here, surface roughness at the meter-scale is described, to be distinguished from the smaller-scale
roughness that is a parameter in thermophysical model fitting routines, or roughness in terms of very fine
scale regolith grains – both are discussed in later Sections. The surface roughness of Itokawa and Eros has
been measured by rendezvous spacecraft laser altimeters. Itokawa’s two major regions, the highlands and
lowlands, have different surface roughnesses that are obvious even in the images. The roughest parts of
the asteroid correspond to those with more boulders, which correspond to regions of higher geopotential
(Barnouin-Jha et al., 2008). It is thought that finer materials may move to regions of lower geopotential
and cover up larger boulders, creating a smoother (less rough) region. These areas are thought to
correspond to areas with the thickest (fine) regolith. Over baselines of 8–50 meters, the highlands of
Itokawa are 2.3 × 0.4 m rougher than the MUSES-C regio (Barnouin-Jha et al. 2008); this difference may
correspond to the expected regolith depth in this area.
The highlands of Itokawa are at a baseline of 20 meters - rougher than Eros - and the lowlands of
Itokawa are significantly smoother than Eros (with the possible exception of Eros’ ponds) (Barnouin-Jha et
al. 2008). The surface roughness of Itokawa is not self-affine over the examined baselines (Barnouin-Jha
et al. 2008)
On Eros, the surface roughness is self-affine over two orders of magnitude of baseline (~4–200 m),
suggesting similar processes control the surface properties over these scales (Cheng et al. 2002). The
corresponding Hurst exponents lie between 0.81 and 0.91 (Cheng et al. 2002). There are regional variations
in surface roughness of Eros; smaller roughness values are found where more regolith is thought to have
accumulated, and higher values are found along crater walls and grooves (Susorney and Barnouin 2016).
There is a strong dependence of radar circular polarization ratio with asteroid class, suggesting a
relationship between roughness at the cm- to dm-scale and composition (Benner et al. 2008). However,
the mean ratios for S- and C-type NEAs are indistinguishable, perhaps indicating similar average surface
properties for these populations (Benner et al. 2008).
22
3. Regolith Thermophysical Properties
Regolith thermophysical properties govern the exchange of radiative energy between the asteroid and
its environment, and knowledge of these parameters is needed to calculate surface and subsurface
temperatures. While the surface energy balance is governed by insolation and regolith thermal inertia,
heat diffusion governs temperatures in the subsurface. Heat is conducted to the subsurface according to
=
(3)
where
ρ
is regolith density, cp is heat capacity, T is temperature, t is time, z is depth, and k is thermal
conductivity. Eq. (3) is a second order differential equation, which can be solved by prescribing two
boundary conditions: One is usually given by zero heat flux from the interior, while the other is usually
given in terms of the surface energy balance. For periodic insolation forcing, the surface energy balance
takes the convenient form
=(1)+
(4)
where is the Stefan-Boltzmann constant, is surface emissivity, A is the Bond albedo, S is total solar
radiative flux including scattered radiation, P is the period of the forcing, and =/ is depth
normalized to the skin depth =/. In Eq. (4), all material parameters have been absorbed in
the single thermal inertia parameter I, which is defined as
=
(5)
It is worth noting that Eq. (5) is only valid at the surface and provided that thermal conductivity is
constant, which is not strictly true (see below). However, thermal inertia is a convenient way to describe
the reaction of surface temperatures to insolation changes, and it is thus widely used. In addition, lack of
data usually does not allow different parameters to be disentangled, although recent studies indicate that
the radiometrically measured thermal inertia changes with heliocentric distance for an individual object
(Rozitis et al. 2017, Marsset et al. 2017). Nevertheless, temperature dependence of thermal conductivity
can have a significant influence when interpreting conductivity in terms of regolith grain size (e.g.,
Gundlach and Blum 2013; Piqueux and Christensen 2011; Sakatani et al. 2017), and thermal inertia
is therefore generally interpreted at a representative surface temperature (e.g., Müller et al. 2017;
Gundlach and Blum 2013). In addition, care must be taken when converting thermal inertia to material
parameters like thermal conductivity, since different combinations of material parameters govern the
temperature at the surface (thermal inertia) and in the subsurface (thermal diffusivity).
There is evidence for regolith layering in terms of thermal conductivity from remote sensing data of
main belt asteroids (MBA), and Harris and Drube (2016) argue that thermal inertia typically increases
significantly as a function of thermal skin depth for these bodies. This effect may be caused by the fact
23
that for slowly rotating asteroids surface temperature and thus surface thermal inertia is influenced by
deeper layers than for fast rotators, and thus for slow rotators they probe regolith material parameters to
greater depth. The observed increase of surface thermal inertia as a function of skin depth can thus be
interpreted as thermal conductivity increasing as a function of depth, and it should therefore be kept in
mind that a similar layering may be present on Ryugu.
3.1. Measured Quantities
Thermal Inertia and Albedo
Relevant thermal observations of Ryugu are summarized in Müller et al. (2017) and include: SUBARU-
COMICS, multiple N-band (Aug 2007), AKARI IRC 15/24 micron photometry (May 2007), Herschel-PACS,
70/160 micron photometry (Apr 2013), Spitzer-IRS spectrum (5-38 micron) (May 2008), Spitzer-IRAC
3.6/4.5 micron two-epoch thermal light curves (Feb/May 2013), Spitzer-IRAC 3.6/4.5 micron multiple-
epoch point-and-shoot sequence (Jan-May 2013), new data from NEOWISE at 4.6 micron (Sep 2016; J.
Masiero, priv. comm.)
A thermal inertia of 150 to 300 J m-2 s-1/2 K-1 is required to explain the available rich data set of thermal
measurements over a wide phase-angle and wavelength range. The corresponding maximum surface
temperatures are in the range ~320 to 375 K (rhelio = 1.00 - 1.41 AU for our observational thermal data
set), with Tmax ~350 K at the object's semi-major axis distance (a = 1.18 AU). The corresponding shape
model is very spherical with the volume-equivalent diameter 850-880 m (compare Sec. 2.1.2). The surface
has thermal inertia of 150-300 J m-2 s-1/2 K-1 and the roughness is small with the rms of surface slopes < 0.1,
which means the surface appears very smooth in the radiometric context (connected to a very low width-
to-depth ratio in the modelled spherical crater segments on Ryugu's surface). The reference model of
Müller et al. (2017) has the pole direction (340°, - 40°), the volume-equivalent diameter 865 m, surface
thermal inertia 200 J m-2 s-1/2 K-1, low surface roughness with rms of surface slopes 0.05, geometric V-band
albedo 0.049, infrared emissivity 0.9, and rotation period 7.63109 h (compare Sec. 2.1.1 and 2.1.2).
Geometric albedo, phase integral, as well as the spherical bond albedo have already been discussed in Sec.
2.1.3, and values presented there are compatible with estimates from thermophyiscal models, which yield
geometric V-band albedos of approximately 0.042 to 0.055. Using a phase integral of q = 0.29 + 0.684G
the bond albedo can be calculated using A = qpV. The uncertainty in G translates into an uncertainty in the
phase integral q (Bowell et al. 1989), and combined with a 5% accuracy of the q − G relation (Muinonen et
al. 2010) a bond albedo of A=0.019±0.003 for the full admissible thermal inertia and roughness range is
obtained.
24
3.2. Derived Quantities
Thermal Conductivity
Thermal conductivity of particulate media is known to be very low in a vacuum, because the weak
contacts between particles act as high thermal resistance points for heat conduction, and contributions of
heat transfer by gas are absent (e.g. Fountain and West 1970). In fact, thermal conductivity of the lunar
regolith was estimated to be less than 0.03 W m-1 K-1 even at depths below 50 cm based on the analyses
of Apollo Heat Flow Experiment data (Langseth et al. 1976; Grott et al. 2010), and much lower values are
expected at shallower depth. Accordingly, thermal conductivity of Ryugu’s surface is also expected to be
very low if it is covered by regolith or small particles.
Thermal conductivity of the top surface layer can be constrained using Eq. (5) if thermal inertia is
assumed to be known from, e.g., ground-based observations. For Ryugu, using the estimated typical value
of 200 J m-2 K-1 s-1/2 (Müller et al. 2017) and assuming a bulk density of
ρ
= 1100–1500 kg m-3 (typically 1270
kg m-3) as well as a specific heat capacity cp of 758 J kg-1 K-1 at 300 K (as an averaged temperature of daytime
on Ryugu), thermal conductivity is constrained to be 0.020 < k < 0.108 W m-1 K-1, with a most likely value
of k = 0.042 W m-1 K-1. However, it is worth pointing out again that this estimate is only valid if density,
specific heat capacity, and thermal conductivity are constant as a function depth and time, which will in
general not hold. Rather, on the actual Ryugu, these parameters may have depth-directional distributions
and will vary with time due to the diurnal temperature variations.
Thermal conductivity of regolith-like powders is a complicated function of parameters such as, e.g.,
grain size, porosity, temperature, and particle surface energy, and different models have been proposed
for this problem (e.g. Halajian and Reichmann, 1969; Hütter et al. 2008, Gundlach and Blum, 2012). Here
we use the integrated model by Sakatani et al. (2017) that was developed based on experimental studies.
Under vacuum conditions, effective thermal conductivity is given by the sum of “solid conductivity”
originating from thermal conduction through inter-particle contacts and “radiative conductivity”
originating from thermal radiation through void spaces between the particles, and it is given by
= + .
(6)
The solid part of the conductivity can be modelled as serial and parallel connections of heat paths
around the contact areas between spheres and it may be expressed as
=4
(1)
,
(7)
where is the thermal conductivity of the bulk material, is the porosity, is the coordination number,
is the radius of the contacts area between two spheres, is the radius of the grains, and is a
coefficient that represents reduction of contact heat conductance due to surface roughness on the grains;
= 1 if particles are perfectly smooth spheres, and comparison with experimental data showed that
25
1 for natural samples including spherical glass beads. The coordination number may be expressed as a
function of porosity, and according to Suzuki et al. (1980) it is given by
=2.812(1)/
(1 + ),
(8)
where = 0.07318 + 2.1933.357+ 3.194. The contact radius between two spheres
depends on the force with which the particles are pressed together as well as their elastic parameters, and
under the micro-gravity environment of Ryugu surface energy and thus van der Waals forces will
dominate the solid conductivity contribution. Contact radius may be expressed as
=
+
+3+
/
,
(9)
where is Poisson’s ratio, is Young’s modulus, is the external compressive force on the particle, and
is the surface energy (Johnson et al. 1971). is given as the compressional stress divided by the
number of grains per unit cross-sectional area, and
=2
6(1).
(10)
On planetary surfaces, the compressional stress is caused by the self-weight according to =
(1) with being the bulk density of the grain, gravitational acceleration, and depth, but
on Ryugu this contribution will be small. Overburden pressure on Ryugu is only of the order of 0.01 Pa at
a depth of 10 cm, and van der Waals forces will thus dominate. However, in total the contribution of the
solid conductivity to the total conductivity will be small for typical NEAs with thermal inertia I larger than
100 J m-2 K-1 s-1/2 when compared to the radiative contribution, and radiative conductivity will dominate.
The radiative part of the conductivity may be modeled by approximating the particle layers as multiple
infinitely-thin parallel slabs. Then, radiative conductivity may be written as
=4
2,
(11)
where is the grain surface’s thermal emissivity, is the Stefan-Boltzmann constant, is temperature,
and is the effective radiative distance between the slabs. Thus, is proportional to the geometrical
clearance or typical pore length between the grains, and in a homogeneous packing of equal-sized spheres
the geometrical pore length can be expressed in terms of grain size and porosity (Piqueux and Christensen
2009). Additionally introducing a factor to scale the geometrical length to the effective one, is given by
= 2
1/.
(12)
26
Comparison with experimental data for glass beads showed that increases with decreasing grain size,
which may be caused by a number of effects: First, the assumption of independent scatterers may break
down, or a change of the scattering characteristics may take place for particles smaller than the thermal
wavelength, resulting in more forward scattering. Further, radiative transfer may be enhanced across gaps
smaller than the thermal wavelength (Rousseau et al. 2009), or there may be bias in the experimentally
derived ksolid. The latter may be due to the fact that the temperature dependence of krad is not exactly T³
due to the coupling between solid and radiative heat transfer (Singh and Kaviany 1994), thus an
extrapolation of measured data to 0 K for determining ksolid may not be perfect.
A potential shortcoming of the above theory is that natural regolith does not consist of monodispersed
spherical particles. However, laboratory measurements of the thermal conductivity of lunar regolith
analogue material (Sakatani et al. 2018) show that measured thermal conductivity is in close agreement
with theory if the median particle size (in the volume fraction sense) is used in the above equations. This
is due to the fact that (a) the solid conduction only weakly depends on particle size and (b) the average
pore size is close to the one calculated with the median radius using Eq. (12).
Another simplifying assumption made above is the spherical particle shape, while natural regolith is
generally both non-spherical and angular. The deviation from the ideal shape can be measured by
quantities called sphericity and angularity, and both shape indicators may influence the contact radii in
the solid conduction contribution in complicated ways. However, their main contribution on thermal
conductivity is to change regolith porosity, which is sufficiently described by the median particle radius.
Thus, the current best estimate for determining is an empirical relation derived from the experimental
results of Sakatani et al. (2018) for a lunar regolith simulant, and it is given by
= 0.68 +7.6 × 10
.
(13)
In the above model, thermal conductivity of the regolith depends mainly on particle size and porosity,
and ranges for these two parameters can be estimated if thermal inertia or effective thermal conductivity
is known. Figure 6 shows a thermal inertia contour plot as a function of particle size and porosity. For
thermal inertia values of I = 150–300 J m-2 K-1 s-1/2 as derived from remote sensing observations (Müller et
al. 2017) a typical particle size for the Ryugu regolith can be estimated to be 3–30 mm, with 6–10 mm
being the most likely. In this range of thermal inertia, the radiative conductivity is dominant over the solid
conductivity, so that uncertainty of assumed parameters in the solid conductivity model, such as Young’s
modulus and surface energy, does not affect the grain size estimation. On the other hand, porosity cannot
be effectively constrained because a major part of heat flow is made by the radiative heat transfer in this
particle size range. Radiative thermal conductivity increases while the heat capacity decreases with
porosity, therefore this balance of both parameters makes thermal inertia nearly constant for various
porosities.
For a verification of the determined grain size, a comparison with the thermal model developed by
Gundlach and Blum (2013) can be made. This model is based on the same physical concept as the
27
calculations described above, however deviates in some details. Basically, these differences are: (i) the
formulation of the network heat conductivity, (ii) the description of the radiative thermal transport process,
and (iii) the irregularity parameter measured by different calibration measurements. A derivation of the
regolith grain radius based on the Gundlach and Blum (2013) formulations yields radii ranging between
1.1 and 2.5 mm (for volume filling factors between 0.1 and 0.6). Thus, both models agree rather well, with
the Gundlach and Blum (2013) model having slightly smaller sizes, which provides confidence in the grain-
size determination from thermal inertia measurements of planetary surfaces.
Figure 6: Contour plot of thermal inertia (in units of J m-2 s-1/2 K-1) as a function of particle diameter and porosity. The gray-
filled region indicates the thermal inertia range estimated for Ryugu by ground based observations (Müller et al. 2017). The
regolith parameters assumed in the calculation are = 758 J kg-1 K-1, = 300 K, = 3110 kg m-3, = 0.0021 + 1.19 W m-1
K-1, = 0.032 J m-2, = 0.25, = 78 GPa, = 1.0, = 0.12, = 0.01 m, and = 1.8 x 10-4 m s-2, respectively. and were
optimized for experimental data of lunar regolith simulant JSC-1A (Sakatani et al. 2018)
3.3. Predicted Properties
Regolith Heat Capacity
The specific heat capacity of rocks and soils at low temperatures has been studied for lunar samples
(Robie et al. 1970; Fujii and Osako 1973; Hemingway et al. 1973), and a strong temperature dependence
has been found. The suite of materials studied includes particulate material such as lunar fines and soils,
but brecciated lunar rocks as well as basalts have also been studied. A best fit to the lunar soils data is
given by Hemingway et al. (1973) and the specific heat capacity can be approximated as
=23.173 + 2.127+ 1.5009 107.369910+ 9.6552 10,
(14)
28
where cp is specific heat capacity in units of J kg-1 K-1 and T is temperature in K. This best fitting formula is
accurate to within 2 percent down to temperatures of 200 K and to within 6% down to temperatures of
90 K. At higher temperatures, the expression
=4184 (0.2029 + 0.0383 1exp 350
100 ,
(15)
by Wechsler et al. (1972) may be used (also see Ledlow et al. (1992), Stebbins et al. (1984), and Schreiner
et al. (2016)). The fit to the data is shown along with the data in Figure 7 and extends to temperatures of
up to 350 K, as appropriate for Ryugu. The extrapolation applicable at higher temperatures is shown as a
dashed line.
Measurements on lunar material are in good agreement with measurements performed by Winter and
Saari (1969) using other geological materials as well as measurements of the specific heat capacity of
meteorites performed by Yomogida and Matsui (1983) as well as Consolmagno et al. (2013). It may be
worth noting that a trend exists with respect to the iron content of the considered samples, with low iron
corresponding to high heat capacity (Yomogida and Matsui 1983). While heat capacity thus shows a strong
temperature dependence, this is only relevant if the near surface regolith layer is considered. At depths
below a few skin depths, perturbations rapidly decay such that the regolith can be assumed isothermal for
the purpose of determining its heat capacity. Evaluated at a representative average daytime surface
temperature of 300 K, a value of cp = 758 J kg-1 K-1 is obtained by evaluating Eq. 14.
29
Figure 7: Specific heat capacity of lunar samples 14163,186 (fines >1 mm, blue circles), 15301,20 (soil, red triangles), 60601,31
(soil, green squares), and 15555,159 (basalt, cyan left triangles) as a function of temperature together with the best fitting
curve (solid line) as well as an extrapolation for temperatures beyond 350 K (dashed line). Data and fit from Hemingway et al.
(1973), extrapolation from Ledlow et al. (1992).
Surface Temperatures, Thermal Gradients, and Thermal Fatigue
The thermal evolution of Ryugu is simulated by solving Eq. (3) numerically. In general the input flux at
the surface is not only the heat flux from the sun but also the sum of the heat radiation from the other
surface area (Rozitis and Greeen 2011; Davidsson and Rickman 2014; Davidsson et al. 2015). However,
Ryugu is predicted to be a round-shape body from ground-based observations. Thus hereafter, for
simplicity, it is assumed that the surface is convex and areas to be calculated do not receive heat radiation
from other areas.
It is to be noted that the thermal emissivity is not needed to be the complement of the surface albedo,
because the peak wavelength of the solar radiation is in the range of the visible light while that of the
thermal radiation from the surface of an asteroid is around or longer than 10 um. Thus the thermal
emissivity and the albedo are independent parameters. We adopt 0.019 for the albedo and 0.90 for the
emissivity of the surface of Ryugu as nominal values. Hereafter we will show the equilibrium temperature
evolution as a function of local time, which is obtained after 100 asteroid rotations at fixed solar distance
and sub-solar latitude. The difference between the equilibrium temperature distribution and a full
numerical simulation taking into account the orbit of the body around the Sun is less than a few K.
Figure 8 shows the evolution of equilibrium surface temperature as a function of local time with
constant thermal inertia (left panel, thermal inertia equal to 200 J m-2 s-1/2 K-1) but various local latitudes,
and constant local latitude (right panel, 0 degree) but various thermal inertias. In these numerical
30
simulations we adopt a solar distance of 1.2 AU and the sub-solar latitude of 0 degree (equator) for
simplicity. As shown in Figure 8, surface temperature changes with solar direction and decreases almost
linearly during night time. Both the maximum and minimum temperatures decrease with latitude for a
constant thermal inertia. The local time of the maximum temperature is achieved after noon and the
degree of phase shift relative to the noon is almost the same for each latitude. On the other hand, as
shown in the right panel of Figure 8, the local time of the maximum temperature becomes later with
thermal inertia. The phase shift is a diagnostic parameter to estimate the thermal inertia from the surface
temperature distribution obtained by the instrument TIR (Takita et al. 2017). The maximum temperature
decreases with thermal inertia and the minimum temperature increases with thermal inertia because
subsurface temperatures are kept warmer for larger thermal conductivities. It is to be noted that the total
thermal radiation from the surface must balance with solar influx in the equilibrium state. Thus the
decrease of maximum temperature is smaller than the increase of minimum temperature since the
thermal radiation is proportional to the fourth power of the temperature.
Figure 8: Surface temperature change as a function of local time for various latitudes (left) and thermal inertia (right). The
sub-solar latitude is assumed to be 0 (equator).
Figure 9 shows results similar to Figure 8, but for a spin axis tilted by 30 degrees. In this case the
duration of day and night depends on latitude. As a result the maximum temperature is not needed to be
obtained at the latitude identical to the sub-solar latitude. For the case with a thermal inertia of 1000 J m-
2 s-1/2 K-1, the maximum temperature is obtained at the latitude of 45 degrees. Despite the change of the
length of day time, the shift of the local time of peak temperature is independent of the latitude. These
results are similar to those obtained by Müller et al. (2017), who calculated maximum surface
temperatures in the range of 320 to 375 K by considering the derived object properties and heliocentric
distances of 1.00 - 1.41 AU. At the object's semi-major axis distance of 1.18 AU, Müller et al. (2017) find a
reference maximum temperature of 350 K.
31
Figure 9: Left: Similar to Figure 8, but for a case with sub-solar latitude of 30, i.e. a tilted spin axis. Left: The thermal inertia
is 200 J m-2 s-1/2 K-1. Right: Thermal inertia is 1000 J m-2 s-1/2 K-1.
Delbo et al. (2014) suggested that thermal fatigue could be the driver of regolith formation on asteroids
with perihelion distances of less than 2.5 AU, including NEAs such as Ryugu. Thermal fatigue describes the
breakdown of larger boulders due to thermal stress. The regolith is exposed to large temperature
differences between night and day time temperatures causing large temperature gradients and therefore
stress in the material leading to crack formation and propagation. Delbo et al. (2014) estimated that
thermal fatigue erodes the surfaces of NEAs like Ryugu several orders of magnitude faster than erosion
caused by micrometeoroids. Consequently, studying the temperature gradient at the surface might be
essential for understanding the evolution of the surface of Ryugu. Figure 10 represents the evolution of
the temperature gradient just beneath the surface as a function of the local time and latitude. The thermal
inertia and sub-solar latitude are assumed to be 1000 J m-2 s-1/2 K-1 and 0 degree, respectively. We adopted
a larger thermal inertia than the nominal value of Ryugu because dust creation due to the thermal fatigue
takes place at the surface of consolidated boulders or monolithic rocks. As shown in Figure 10 the
maximum temperature gradient is achieved before noon. The absolute value of thermal gradient is larger
for lower latitude. This is simply because the larger thermal spatial gradient is obtained at the time when
the maximum temporal gradient of the surface temperature is achieved. In fact, as shown in the right
panel of Figure 8, the maximum temporal gradient at the surface is achieved before noon. The maximum
thermal spatial gradient becomes larger for smaller thermal inertia. On the other hand, the negative
maximum temperature gradient is achieved at sunset. After sunset the temperature gradient becomes
smaller because the underground temperature distribution is alleviated during night time. The right hand
panel of Figure 10 is similar to the left one, but uses a spin axis tilted by 30 degrees. In this case the
maximum thermal gradient is achieved not only at the sub-solar latitude but at the sub-solar latitude and
the equator. Thus the determination of location at which the maximum temperature gradient is achieved
is not straightforward (Hamm et al. submitted). It is to be noted that the integration of thermal gradient
through a day should be zero in the equilibrium state if the thermal conductivity is independent of
temperature.
32
Figure 10: Thermal gradient just beneath the surface as a function of local time. Left: Sub-solar latitude of 0 degree. Right:
Sub-solar latitude of 30 degrees. The negative maximum of the thermal gradient is achieved at sunset while the positive
maximum of the thermal gradient is achieved just before noon.
We assumed above that the surface of Ryugu is smooth. If the roughness of the surface is taken into
account, the apparent temperature distribution changes depending on the degree of roughness (Rozitis
and Green 2011; Davidsson et al. 2014, 2015). The temperature of a slope is especially affected at dawn
and dusk. A wall of a valley observed at a low phase angle will have a much higher temperature than the
horizontal, surrounding surface. Contrarily, when observing a wall against the sun it will be much colder
than its surroundings. In addition to the case of concave areas such as craters, the absorption of radiation
could raise the temperature of the bottom area of the concavity depending on its size and shape.
Moreover, we must point out that the bond albedo of a rough surface changes with solar incident angle
(Senshu et al. in preparation). These effects need to be taken into account when analyzing the apparent
temperature distribution obtained by the Hayabusa2 TIR instrument.
4. Regolith Mechanical Properties
4.1. Measured Quantities
There are no directly measured quantities of the mechanical properties of the regolith on Ryugu, as for
any asteroid that has not been visited by a spacecraft. Therefore, the only quantities that can be
determined must be derived from current data or rely on pure assumptions.
4.2. Derived Quantities
The only quantity that can be derived from observations is the dominant grain size, based on the
measurement of the thermal inertia of the asteroid (see previous sections). The grain shape can also be
derived from the only asteroid from which regolith particles have been returned, i.e. the asteroid Itokawa.
However, we note that Itokawa belongs to the S taxonomic class, and its composition is thus very different
33
from that expected for Ryugu. This probably also means that its mechanical properties are different, and
therefore how regolith is generated on this body, as well as its properties, are likely to be different too.
But since this is the only data point that we have so far, we use it in this section.
Grain Size
As summarized in Sec. 3, a thermal inertia of 150 to 300 J m-2 s-0.5 K-1 is required to be compatible with
remote sensing observations (Müller et al. 2017). Using the model by Sakatani et al. (2016), this translates
to typical particle diameters of 3–30 mm for Ryugu, with 6–10 mm being the most likely. This is consistent
with, although slightly larger, than the results by Gundlach and Blum (2013), who obtain grain diameters
of 2.2 to 5 mm.
Grain Shape
For the grain shape as shown in Figure 11 and Figure 12, we note that the mean aspect ratios of
particles returned from the asteroid Itokawa by the Hayabusa mission, b/a and c/a (a is the longest axis, b
is the medium axis, c is the shortest axis) (Tsuchiyama et al. 2014), are 0.72 ± 0.13 and 0.44 ± 0.15,
respectively, and are similar to the mean axial ratio of fragments generated in laboratory impact
experiments (a:b:c ≈ 2:√2:1 or b/a ≈ 0.71 and c/a ≈ 0.5). Note that the bulk density of Itokawa samples is
3.4 g cm−3. The average porosity of Itokawa samples is 1.5%. We do not have any data yet for a C-type
asteroid like Ryugu.
34
Figure 11: Backscattered electron (BSE) images of asteroid Itokawa regolith grains RA-QD02-0030 (A), RA-QD02-0024 (B), RA-
QD02-0013 (C), and RA-QD02-0027 (D) from (Nakamura et al. 2011). Here, Ol: olivine, LPx: low-Ca pyroxene, Chr: chromite, Pl:
plagioclase, Tr: troilite, Tae: taenite.
35
Figure 12: The 3D external shapes of Itokawa particles. (A) Stereogram (box size 232 μm by 232 μm by 203 µm) and (B) SEM
micrograph of RA-QD02-0023.(C) Stereogram (box size, 112 μm by 112 μm by 93 µm) and (D) SEM micrograph of RA-QD02-
0042.
4.3. Predicted Quantities
Because we do not yet have any detailed image of a C-type asteroid of Ryugu’s size and any experiment
done on such a surface allowing us to understand how it responds to an external action, most of the
information regarding regolith mechanical properties of Ryugu are predictions.
Regolith Porosity
Natural regolith is typically non-spherical (measured by a quantity called sphericity) and angular
(measured by “angularity”). Together with the adhesion properties, the median grain size and the size
distribution determine the porosity.
It is well known that random packings of monosized coarse spheres have a porosity of 0.363 (dense) to
0.42 (loose packing). Adhesion increases the porosity, to the limit of 1; the decisive parameter is the
granular Bond number Bo = Fvdw/Fg, i.e. the ratio of van der Waals forces and weight acting on a grain
(Kiuchi and Nakamura 2014). If the particles are polydisperse, the porosity tends to decrease with the
width of the size distribution (the smaller particles filling up the voids of the larger particles). Finally, non-
spherical grains tend to increase the porosity compared to packings consisting of spherical grains.
36
A well-known packing theory which can be used for predictions is described in Zou et al. (2011). Here
the equation expressing the “initial porosity” as a function of grain size has to be generalized to arbitrary
gravity (instead of 1 g) and assumption has to be made on the increase of initial porosity due to shape
effects.
Ryugu has a very low gravity so that compaction by lithostatic pressure is not likely to play a role in the
upper meter or so. This is different from the Moon: the porosity of lunar regolith (as a function of depth)
is relatively well known; it is 83% on the very surface (Hapke and Sato 2016), decreases quickly to about
58% at a few cm and to about 38% at a few meter depth. Apart from the very upper surface, we see
compaction by overburden pressure at work (Schräpler et al. 2015; Omura and Nakamura 2017).
Given these considerations, a porosity of ~0.4-0.5 can be assumed for the near-surface regolith, which
corresponds to the random loose packing of slightly adhesive [relative to weight!] cm-sized irregular but
roundish particles with a size distribution.
Regolith Subsurface Properties
According to Britt and Consolmagno (2001), materials in porous asteroids may be sorted by particle
size. The large irregular pieces (and larger voids/fractures) may be located deeper inside the asteroid and
the fine particle size fractions that are observed on their surfaces are restricted to the surface regolith
zone (Figure 13). The large interior voids/fractures are preserved from infilling by the effects of friction on
the smaller size fractions. Friction tends to dominate the downward pull of gravity and prevents the fine
fractions from filtering into the interior of the asteroid and infilling the large fractures and voids. Friction
may also play a role in allowing shattered asteroids to maintain their relief features and shape by resisting
the movements of pieces within the object, in effect providing strength to non-coherent objects.
However, another mechanism, called the Brazil nut effect, may cause an opposite trend (Matsumura
et al. 2014; Maurel et al. 2017) and segregate larger particles to the surface, as seen on Itokawa. Thus,
coarse gravel (1 cm or greater) may be expected to exist on the surface overlaying fine grained material
with the fraction of fines increasing with depth. The combination of low surface acceleration and solar
radiation pressure tends to strip off fine particles that have been generated by comminution processes,
and leave lags of larger, harder to move materials. On the other hand, this material may experience
thermal fatigue that can turn them in smaller pieces. There is thus a competition between various
processes, and we are not yet in a position to understand which one is dominant or their respective
contributions to the final product. We would actually need at least one image of the surface of a C-type
asteroid of Ryugu’s size, which does not yet exist, and thus we have to wait for Hayabusa2 to provide one.
37
Figure 13: Schematic of the possible structure of rubble pile asteroids. The original reaccretion of these objects is assumed to
be particle size sorted with the largest pieces accreting first to form the core of the object and successively smaller sizes
accreting later (Michel and Richardson, 2013). The finest size fractions are generated at the surface by regolith action. These
fine particles are confined to the near-surface zone by the dominance of frictional forces (from Britt and Consolmagno 2001).
Regolith Cohesion, Angle of Friction, Tensile Strength and Their Influence on Shear
Strength
In terrestrial environments, the shear strength of regolith is driven by inter-grain frictional forces and
rotations, however both effects are largely affected by the level of gravity. Thus as gravitational forces
decrease, other forces start to govern the behaviour of granular matter. With the decrease of gravitational
forces, the importance of attractive forces like van der Waals forces rise. These attractive forces may, like
higher gravity, increase the frictional forces by holding grains together and hence increasing the normal
pressure. Thereby both frictional forces and resistance torques are increased, which in turn increase shear
strength. Taking these considerations into account, the behaviour of granular matter gets even more
complex in micro-gravity (µg). Furthermore, each particle is affected by the spin of the asteroid
(particularly if it is fast) and the resulting forces, which constantly try to separate the grains and thus break
the soil.
Cohesion, friction angles and relative density have been linked for the lunar regolith as shown in Figure
14.
38
Figure 14: Friction angle as a function of cohesion and relative density for the regolith on the Moon (same as Fig. 9.27 of Heiken
et al. 1991).
With an assumption of 50% porosity, the cohesion should be 300 Pa, and the angle of friction about 37
degrees. However, this is estimated for lunar regolith with fine grains. If Ryugu’s regolith is coarser (1 mm-
1 cm grains), then it may have lower cohesion, say 100 Pa (30% relative density) equivalent to an angle of
friction of 33 degrees. From this, we can estimate the tensile strength from the Mohr-Coulomb curve to
be 1 kPa or less (see Figure 9.26 of Heiken et al. 1991). The effect of gravity is a complicating factor, but
Kleinhans et al. (2011) have shown that if gravity decreases the static angle of repose of regolith increases.
While cohesion in regolith is best known for the influence of water bridges in terrestrial environments,
here the term cohesion covers the whole range of attractive forces. Due to the absence of water the most
important attractive forces for µg environments are van der Waals forces, electrostatic forces,
magnetostatic forces, and self-gravity (Scheeres et al. 2010; Murdoch et al. 2015). In a study comparing
the cohesive forces to gravitational forces in different levels of gravity, Scheeres et al. (2010) have shown
that cohesion might be one of the governing effects for the shear strength of granular matter in micro-
gravity. Using scaling laws, the study showed that cohesion mostly governed by van der Waals forces may
be able to be the governing force even for gravel-sized particles (~centimeter size) in Ryugu’s ambient
gravity as shown in Figure 15.
39
Figure 15: Magnitude of different forces compared to gravity as a function of particle radius (from Scheeres et al. 2010). VDW
expresses van der Waals force and S is the surface cleanness (S goes to 1 for clean surfaces). Ryugu’s ambient gravity is
estimated of the order of 0.25 milli-G.
The non-dimensional bond number can be expressed by the relation between the gravitational weight
and the cohesional forces (Scheeres et al. 2010, see Figure 16):
=
. (16)
For the expected gravitational level of Ryugu, Scheeres et al. (2010) predict bond numbers of one for gain
sizes up to 10th of cm. They also state that clumping and macroscopic cohesional behaviour will be present
even in regolith made of coarse sand portions. Other authors like Durda et al. (2012) studied the likely
behaviour of asteroid regolith using terrestrial laboratory simulants.
40
Figure 16: Bond numbers as a function of particle radius and gravitational acceleration (from Scheeres et al. 2010). Ryugu’s
ambient gravity is estimated of the order of 0.25 milli G.
As inter-grain cohesional forces act on the grain friction level, they act similarly to overburden pressure
regarding macroscopic friction and grain rolling. This may easily be shown regarding the normal and
tangential forces on grain level:
= (17)
= (+) (18)
where is the repulsive force due to contact, the total cohesion force and µ the micro-scale friction
coefficient. The effect of cohesion lowers the repulsive effect of contact forces by holding grains together,
whereas this effect does not lower the effective normal force for friction as cohesion keeps the contact in
a tense condition. Regarding this issue, the magnitude of frictional force may not only depend on the level
of gravity and the bond number, but also on the loading history. Higher loads that might have occurred in
the past will compact the material establishing a larger number of bonds at possibly larger bond areas and
thus increase the total amount of contact tension. The higher contact tension and thus micro-scale normal
forces, the higher the friction forces and hence the macro-scale shear strength.
Given the expected angle of friction as stated above and the expected grain shape, inter-grain friction
can also be expected to be higher than for most terrestrial sands. Thus the inter-grain friction angle for a
spherical surrogate particle is expected to be in the range of 40-50 deg.
41
Regolith Bearing Strength
Assuming that the shape of an interacting device with the regolith is a square or a circle, the bearing
capacity or strength of the regolith is defined as σ = 1.3 * c * Nc, where 1.3 is the shape factor
(corresponding to a square or a circle), c is the regolith cohesion, and Nc is the bearing capacity factor.
Assuming that cohesion is of the order of 100 Pa (see Sec. 4.3.5.) and that Nc is in the range 6-20 depending
on the actual angle of friction (0-33 degrees), then the bearing strength may be of the order of a few kPa
or lower.
Whole Rock Properties
We use as a reference the Master’s thesis of S. Shigaki (2016, Kobe University) for regolith with mm
size range particles (Table 7); for bigger rocks, strength scaling may apply, resulting in weaker strength
with increasing size. Note that the tensile strength measure gives similar or slightly higher values.
Table 7: Crushing strength of various materials from Shigaki (2016).
Materials
Crushing strength (MPa)
Chondrule from Allende (CV3)
7.7 ± 5.9
Chondrule from Saratov (L4)
9.4 ± 6.0
Glass bead (1 mm size)
223 ± 61
Dunite (a few mm)
13.1 ± 2.6
Basalt (a few mm)
16.9 ± 2.6
Sandstone (a few mm) *
3.4 ± 1.1
* Sandstone can be considered as an upper limit for the whole rock properties of Ryugu.
The compressive (unconfined) strength of sandstone is of the order of 50-100 MPa, while tensile strength
is of the order of a few MPa (Ahrens 1995). However, the rock porosity of Ryugu may be higher (~40%)
than the rock porosity of sandstone (~20%), and therefore the compressive and tensile strengths may be
a factor 3 lower than that of sandstone, similar to Weibern tuff (Poelchau et al. 2014). This means that we
can assume that the compressive strength could be of the order of 15-30 MPa and the tensile strength
about 1 MPa or less.
Presence of Ponds and Their Properties
For sample return missions, very flat areas among the wide variety of asteroid surfaces are the most
sought after since they are the safest places to touch down. As revealed by asteroid surfaces imaged at
the cm-scale, ponds are good candidates (Veverka et al. 2001; Robinson et al. 2001; Cheng et al. 2002;
Miyamoto et al. 2007). Since it is likely ponds are present on Ryugu’s surface, it is essential to know if there
42
is a difference between the material present in the ponds, and the material in other areas. Do our
chondrite samples help us solve this issue?
Some fine-grained cognate lithologies in chondrites (Figure 17 and Figure 18) have been inferred to be
sedimentary features indicating that they sample asteroid ponds. A cognate clast in the Vigarano CV3
chondrite, first identified by Johnson et al. (1990) appears to be a sample from such a pond, from a C-type
asteroid. The clast consists mainly of micron-sized grains of olivine, arranged into layers with varying
composition and porosity. The densest (most Fe-rich) olivine grains are in sections of layers with the
lowest bulk porosity, which appear bright in BSE images. The most remarkable aspect of the clast are
crossbeds. Zolensky et al. (2002, 2017) proposed that this clast formed by the processes of electrostatic
grain levitation and subsequent seismic shaking. They then described similar clasts in another Vigarano
sample, and in a section of Allende – all CV3 chondrites, and most recently in the LL3 chondrite NWA 8330
(Zolensky et al. 2017). These clasts consist mainly of olivine, whose compositional range is essentially
identical to the host meteorite, although there is a striking predominance of heavy, Fe-rich olivine in the
bulk clast relative to the bulk host. However, because of the compositional zoning within the pond deposit
layers, the top most surface is depleted in Fe-rich, heavier olivine. Based on these observations, samples
collected from the surfaces of ponds on Ryugu will significantly differ from the bulk asteroid by being finer-
grained, metal poor, and silicates will be Fe-poor. Note that Itokawa samples were also depleted from
typical LL chondrites by being metal depleted. Grain sizes in Ryugu regolith probably will extend down to
the micron size, as was the case for Itokawa.
This interpretation is however challenged by a recent survey of Fe-rich secondary phases in CV
chondrites (Ganino and Libourel 2017), which states that the phases constituting such similar networks of
veinlets formed in reduced conditions near the iron-magnetite redox buffer at low aSiO2 (log(aSiO2) < −1)
and moderate temperature (210–610 °C). The various lithologies in CV3 chondrites, i.e., CV3Red, CV3OxA,
CV3OxB, including those present in Figures 17 and 18, and their diverse porosity and permeability
(MacPherson and Krot 2014) are in good agreement with CV3 lithologies being variably altered crustal
pieces coming from an asteroid percolated heterogeneously via porous flow of hydrothermal fluids. These
hot, reduced and iron-rich fluids resemble pervasive, Darcy flow type, supercritical hydrothermal fluids,
and consistent with textural settings of secondary phases, as scattered patches in the CV chondrite
matrices or, when the fluid is channelized, as subtle veinlet networks. If this interpretation is correct, the
permeability/porosity/cohesiveness of the unprocessed Ryugu surface, assuming CV (or CO) chondrites
are relevant proxy, will depend on the percolation of hydrothermal fluids in the Ryugu’s parent body, and
their efficiency to precipitate secondary phases, which will in turn control the formation and evolution of
the regolith, its size distribution and the ease of its sampling (see section 3).
43
Figure 17: Back-scattered electron image of a portion of a pond deposit clast from the Vigarano CV3 chondrite. The mineralogy
of the clast is mainly olivine, with Fe-rich olivine being lighter in shade. Sedimentary beds are apparent, and light grey (Fe-
olivine-rich) layers are at the bottoms of the beds. Crossbeds are apparent.
44
Figure 18: Close-up on the clast in Figure 17, showing the bottom of one bed (upper left) with a sharp contact with the top of
the succeeding bed (lower right). The mineralogy of the clast is mainly olivine, with Fe-rich olivine being lighter in shade. The
highest concentration of light grey, Fe-rich olivine is at the bottom of the bed. Insert image at lower left is a lower mag view of
the same area, with the high mag area at the lower left of the insert. Note that the grain size extends down to the micron scale.
5. Summary and Conclusions
We have reviewed a wide range of information about the C-type, NEA (162173) Ryugu from the point
of view of describing the regolith layer of Ryugu: the global properties, the thermophysical properties, and
the mechanical properties. Each property is categorized into three types, i.e., the measured/observed, the
derived, and the predicted properties, as summarized in Table 8. This table gives a reference model of
Ryugu, especially on the surface regolith.
Table 8: Properties of Ryugu, covered and discussed in the text.
Global properties
Measure
d
Eccentricity
0.190208
Semi-major axis
1.189555
AU
Inclination
5.883556
deg
Period
473.8878
day
45
Perihelion
0.963292
AU
Aphelion
1.415819
AU
Rotation period
7.6326
hour
Pole direction in ecliptic coordinates
(lambda, beta)
(310-340,-40 +/-
15)
deg
Shape
almost spherical
Volume-equivalent diameter
850-880
m
Phase function (Lommel-Seeliger model)
see Table 2
Geometric and bond albedos
see Table 3
Spectral type
C-type, see also
Table 4
Derived
Composition (meteorite spectral
counterpart)
heated CM,
CM2, or CI
Predicted
Satellite
no
Dust around Ryugu
no or little
Boulders: power law exponent of
cumulative SFD
-3
Crater density
more than
Itokawa,
less than Toutatis
Surface roughness at meter scales
like Eros and
Itokawa
46
Origin
originated in the
inner Main Asteroid
belt, between ~2.1-
2.5 AU, and reached
the ν6
by inward
Yarkovsky drift
Regolith thermophysical properties
Measure
d
Thermal inertia
150-300,
typically 200
J m-2 s-1/2 K-1
Maximum surface temperature
320-375
K
Roughness (the rms of surface slopes)
< 0.1
Derived
Regolith thermal conductivity
0.020-0.108,
most likely 0.042
W m-1 K-1
Typical particle size in diameter
3-30
most likely 6-10
(2.2-5 by Gundlach
& Blum 2013
model)
mm
Predicted
Regolith heat capacity at 300 K
758
J kg-1 K-1
Regolith emissivity
0.9
Regolith thermal albedo
0.019
Regolith bulk density
1100-1500
kg m-3
Regolith mechanical properties
Predicted
Regolith porosity
~0.4-0.5
Regolith cohesion
100
Pa
Regolith angle of friction
33
deg
Regolith tensile strength
< 1000
Pa
47
Inter-grain friction angle
40-50
deg
Regolith bearing strength
< a few 1000
Pa
Compressive strength of rock
15-30
MPa
Tensile strength of rock
< 1
MPa
Presence of ponds
possible, there
compositions being
expected to be
significantly
different from that
of the bulk asteroid
As a whole, this paper provides a reference model of Ryugu’s regolith which should be extremely useful
both for science applications until Hayabusa2’s arrival and for Hayabusa2 operations at Ryugu. It will be
checked and refined thanks to Hayabusa2 data and further related scientific studies will be promoted
toward understanding Ryugu, other small bodies, and Solar System evolution.
6. Acknowledgements
This paper is a product of IRSG in Hayabusa2 project, JAXA.
P.M. and M. A. B. acknowledge financial support from the French space agency CNES. M.E.Z. is
supported by the NASA Emerging Worlds and Hayabusa2 Participating Scientist Programs, and the SERVII
Center for Lunar Science and Exploration.
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