Icarus 194 (2008) 137–145www.elsevier.com/locate/icarus

Near-infrared spectrophotometry of Asteroid 25143 Itokawa from NIRSon the Hayabusa spacecraft

Kohei Kitazato a,b,∗, Beth E. Clark c, Masanao Abe b, Shinsuke Abe d, Yasuhiko Takagi e,Takahiro Hiroi f, Olivier S. Barnouin-Jha g, Paul A. Abell h, Susan M. Lederer i, Faith Vilas j

a Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japanb Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan

c Physics Department, Ithaca College, 953 Danby Road, Ithaca, NY 14850, USAd Graduate School of Science and Technology, Kobe University, 1-1 Rokkodai-cho, Nada, Kobe, Hyogo 657-8501, Japan

e Toho Gakuen University, 3-11 Heiwagaoka, Meito, Nagoya, Aichi 465-8515, Japanf Department of Geological Sciences, Brown University, Providence, RI 02912, USA

g The Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20723-6099, USAh NASA, Johnson Space Center, Houston, TX 77058, USA

i Department of Physics, California State University, San Bernardino, CA 92407, USAj MMT Observatory, University of Arizona, Tucson, AZ 85721, USA

Received 18 February 2007; revised 13 August 2007

Abstract

A photometric analysis of the S-type Asteroid 25143 Itokawa is performed over multiple wavelengths ranging from 0.85 to 2.10 µm basedon disk-resolved reflectance spectra obtained with the Hayabusa near-infrared spectrometer (NIRS). We derive the global photometric propertiesof Itokawa in terms of Hapke’s photometric model. We find that Itokawa has a single-scatter albedo that is 35–40% less than that of Asteroid433 Eros. Itokawa also has a single-particle phase function that is more strongly back-scattering than that of Eros. Despite its hummocky surfacestrewn with large boulders, Itokawa exhibits an opposition effect. However, the total amplitude of the opposition surge for Itokawa was estimatedto be less than unity while Eros and other S-type asteroids have been found to have model values exceeding unity. The wavelength dependence ofthe opposition surge width reveals that coherent backscatter contributes to the opposition effect on Itokawa’s surface. The photometric roughnessof Itokawa is well constrained to a value of 26◦ ± 1◦ which is similar to Eros, suggesting that photometric roughness models the smallest surfaceroughness scale for which shadows exist.© 2007 Elsevier Inc. All rights reserved.

Keywords: Asteroid Itokawa; Photometry; Spectrophotometry

1. Introduction

The near infrared spectrometer (NIRS) instrument of theHayabusa spacecraft obtained more than 80,000 surface-re-solved reflectance spectra of the near-Earth Asteroid 25143Itokawa during the period of September 10 to December 24,2005. Spectra from 0.76 to 2.25 µm were acquired over a wide

* Corresponding author at: Institute of Space and Astronautical Science,Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Sagamihara, Kana-gawa 229-8510, Japan. Fax: +81 42 759 8457.

E-mail address: kitazato@planeta.sci.isas.jaxa.jp (K. Kitazato).

0019-1035/$ – see front matter © 2007 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2007.08.029

range of incidence and emission angles and covering phase an-gles from 0.2◦ to 38.4◦, allowing us to construct a spectropho-tometric model of the asteroid’s surface that could be used toderive physical properties of the asteroid’s surface and to cor-rect all NIRS spectra to a common viewing geometry.

Light scattering on the surface of an atmosphereless So-lar System body can provide constraints on the physical andtextural characteristics of the surface materials, such as sur-face roughness, porosity, and optical properties. Abundant disk-resolved data with different viewing geometries are essential todetermine the photometric properties accurately, which is dif-ficult to obtain from ground-based observation (Domingue and

138 K. Kitazato et al. / Icarus 194 (2008) 137–145

Fig. 1. The left panel shows the trajectory of the Hayabusa spacecraft in the HP coordinate system, where the origin is the mass center of asteroid, +Z axis is thedirection toward the Earth, +Y axis is normal to the plane given by the asteroid–Earth and asteroid–Sun vectors (roughly southward in ecliptic frame), and +X axiscompletes right-handed coordinate. The right panel shows the history of the distance to the asteroid surface, the solar phase angle, and the spatial resolution of theNIRS field-of-view between September 17 and October 16, 2005, respectively.

Hapke, 1989). Recent spacecraft flyby and rendezvous missionshave resulted in an increase in the availability of disk-resolvedphotometric data for asteroids and comets at visible to near-infrared wavelengths (e.g., Helfenstein et al., 1994, 1996; Clarket al., 1999; Li et al., 2004, 2007). The first near-infrared spec-trophotometric study describing the wavelength dependence ofphotometric properties was performed on the Asteroid 433 Erosusing Hapke’s photometric model (Clark et al., 2002).

Asteroid 25143 Itokawa is revealed by ground-based obser-vations (Binzel et al., 2001) and NIRS initial results (M. Abe etal., 2006) to be an S-type asteroid with a surface dominantlycomposed of olivine and pyroxene, similar to Eros. Close-up images of Itokawa taken by Hayabusa multiband imagingcamera (AMICA) show rough terrains that are hummocky andstrewn with angular rock fragments several meters in size, incontrast with smooth terrains that are buried in pebble-sizedparticles (Saito et al., 2006). Eros’ surface appears to be glob-ally covered with a thick layer of fine regolith, and the cm- tomm-sized pebbles embedded in the smooth areas on Itokawaare larger than the finest surface particles observed on Eros(Yano et al., 2006). The contrast in surface appearance betweenItokawa and Eros can be explained by the size difference ofthese objects, roughly 500 m and 30 km in diameter, respec-tively. Itokawa’s surface has a much smaller escape velocitythan Eros, such that a larger fraction of fine particles would belost by impacts with interplanetary projectiles (Fujiwara et al.,2006). Here we compare the photometric properties of Itokawa

with those of Eros and discuss the effects of the physical prop-erties of the surface on their photometric behavior.

NIRS was designed to map the composition and distribu-tion of minerals on the surface of Itokawa. Because Itokawahas a very irregular shape, almost all of the NIRS spectral datawere acquired under widely varying viewing geometries andlighting conditions. Before comparison with one another, theobserved spectra must be photometrically corrected to a com-mon viewing geometry using an accurate photometric function.Otherwise, photometric effects, e.g., phase reddening, could beinterpreted as spectral variations.

2. Observations

After the 2-year cruise phase, the Hayabusa spacecraft per-formed Itokawa rendezvous operations including two touch-downs for asteroid sample collection from September to earlyDecember, 2005. Fig. 1 shows a locus chart of the spacecraftand the history of the spacecraft–asteroid distance, solar phaseangle and NIRS spatial resolution from September 17 to Octo-ber 16, 2005. The trajectory of the Hayabusa spacecraft duringthe rendezvous phase can be broadly divided into the follow-ing three sub-phases according to the relative distance to theasteroid: (1) the Gate-Position phase of 20–8 km, (2) the Home-Position phase of ∼8 km, and (3) the descent and touchdownphase. During the Gate-Position phase, the spacecraft kept itsposition on the Earth–asteroid line and gradually got closer tothe asteroid using chemical thrusters for reconnaissance oper-

Hayabusa NIRS photometry of 25143 Itokawa 139

ation, so that the solar phase angle remained nearly constant.NIRS first detected the reflected sunlight from Itokawa’s sur-face on September 10. While transferring to the Home-Positionphase, the spacecraft’s path allowed a sequence of observationsof the asteroid’s surface to be made under varying lighting con-ditions and for the polar regions. Because of solar panel point-ing requirements related to spacecraft power, the spacecraft wasunable to fly at a solar phase angle larger than ∼40◦, but passedthrough the zero phase angle point between the Sun and the as-teroid on October 13. After that, touchdown on a smooth terraincalled Muses-C regio and the liftoff were performed on Novem-ber 19 and 25.

NIRS is nominally boresighted with the 0.1◦ × 0.1◦ of thefield-of-view (FOV) on the spacecraft −Z axis (+Z is thepointing direction of the solar panels and high gain antenna).In normal operation mode, NIRS made one-dimensional lati-tude scans with the target point fixed on the asteroid. Unfor-tunately, problems occurred with the second reaction wheelin early October. Thereby, the chemical thrusters were subse-quently used for attitude control and the NIRS observationalmode was shifted to two-dimensional global mapping scanswith the advantages of both asteroid spin and spacecraft nu-tation. The solar phase angle through the entire observationperiod varied from near 0◦ to 38◦. Although NIRS success-fully obtained the high resolution disk-resolved spectra in thetouchdown phase, these data are not used for this photometricanalysis because of spacecraft position and pointing uncertain-ties.

Integration times were set to within the range of 0.82 to26.21 s to prevent any detector channels from reaching satura-tion and to maximize the spatial resolution of a single spectralmeasurement within the constraint on data downlink. The spec-trometer detector consisting of a 64-channel Indium–Gallium–Arsenide (InGaAs) photodiode array maintained at a constanttemperature of 258 K during the rendezvous phase. Light pass-ing through the aperture is dispersed by a grism that is a trans-mission diffraction grating combined with a cross disperser andfalls on the linear detector arrays. NIRS carries two types ofonboard calibration targets: a halogen lamp and a light emittingdiode (LED) for periodic monitoring of the detector’s stability.From in-flight calibrations using these caltargets, no degrada-tion of the detector was found through the rendezvous opera-tion.

3. Data reduction

NIRS data are taken by stacking a number of sequentialsets of light and dark frames at a single spectral measurement.Raw analog voltages measured by the detector are converted todigital numbers (DNs) within the NIRS electronics. Dark sub-traction and data averaging are operated with onboard software,and only the mean and standard deviation of the DNs at indi-vidual channels were downloaded in instrument telemetry. DNswere then converted on the ground to reflectance units, I/F ,where I is the reflected intensity and πF is the incident solarflux. The per-channel DN-to-radiance conversion factor was de-termined in a number of tests by recording the detector response

while viewing a laboratory calibrated field with a halogen lampand a spectralon reflectance target (Abe et al., 2002).

Spectral calibration uses the measured response of each de-tector channel in a monochromator scan where the center wave-length of each channel is given by

λ = −23.56n + 2271.44 (nm),

where n is the channel number between 1 to 64. This expressionwas tested using observations of the light from the Hayabusaranging instrument (LIDAR), which was co-aligned with NIRSin the rendezvous phase (S. Abe et al., 2006, Fig. 1). The fullrange of the detector array is 751.8 to 2259.7 nm. This rangeis further limited, however, to 850 to 2100 nm due to fall-off indetector response and contamination from stray light.

To estimate the viewing geometry at each observation time,we used the most up-to-date Itokawa shape model consisting of49,152 plates (Gaskell et al., 2006). We used instrument point-ing information derived from pre-flight calibration data, thevalidity of which was confirmed by simultaneous observationsof point light source stars with AMICA. With SPICE softwaredeveloped at JPL (cf. http://naif.jpl.nasa.gov/naif/index.html),local angles of incidence i, emission e, and phase α were com-puted for each shape model plate included within the NIRSfootprint. Mean angles were calculated by weighting the aver-age with the projected area ratio of those plates within the foot-print. The pointing and trajectory uncertainties in this processare typically less than about 20% of the NIRS FOV, or roughlyequivalent to 0.02◦ of positional uncertainty along the equatoras viewed from a distance of 7–18 km.

For this photometric analysis, we selected data that fulfilledthe following criteria: (1) the ephemeredes including spacecraftposition and pointing were available and (2) the instrumentFOV was filled with a fully illuminated surface and with nospace, limb, or large shadows inside (as derived from geomet-ric calculations using ray-tracing methods). Additionally, wenarrowed down the dataset to those obtained between Septem-ber 17 and October 16 to meet the highest phase angle cov-erage while evening out the distribution in phase angle andspatial resolution. After this selection process, approximately10,000 spectra remained with spatial resolutions ranging from10 × 10 to 30 × 30 m. Fig. 2 shows the spatial coverage andobservational frequency of NIRS data selected for photometricanalysis. The dataset consists mostly of spectra obtained nearthe equatorial regions, where rough terrain strewn with several-meter-sized boulders dominates.

4. Photometric analysis

Fig. 3a shows the variation of the bidirectional reflectance,I/F of the dataset for this photometric analysis at 1.57 µm withrespect to phase angle. Here the brightness changes at the samephase angle are due to differences in incidence and emission an-gles or regional photometric variations. At small phase angles,a non-linear surge of brightness called the “opposition effect”can be seen. In Fig. 3b, the ratio of reflectance at 1.57 µm tothat at 0.95 µm is plotted as a function of phase angle, showingevidence of spectral reddening with increasing phase angle.

140 K. Kitazato et al. / Icarus 194 (2008) 137–145

Fig. 2. The observational data used for photometric analysis is projected onto the Itokawa shape model of Gaskell et al. (2006). Both western and eastern side viewsare shown. North pole direction is upward. Areas drawn in gray scale are regions lack spectral coverage.

Fig. 3. (a) The bidirectional reflectance of Itokawa at 1.57 µm, and (b) the reflectance ratio of 1.57 to 0.95 µm as a function of phase angle.

These data were fit with a Hapke photometric model (Hapke1981, 1984, 1986, 2002). Hapke’s model is based on an ap-proximate analytic solution to the radiative transfer equa-tions describing the scattering of light from particulate sur-faces and contains the following physical parameters: thesingle-scattering albedo, w; the single-particle phase function,P(α,g); the opposition effect, B(α,B0, h); and the shadowingfactor of macroscopic surface roughness, S(i, e,α, θ̄). In thismodel the bidirectional reflectance is given by

I

F= w

4π

μ0e

μ0e + μe

{[1 + B(α,B0, h)

]P(α,g)

+ H(μ0e,w)H(μe,w) − 1}S(i, e,α, θ̄),

where μ0e, μe are the effective cosines of the incidence andemission angles, respectively, that correlate with the surfaceroughness parameter θ̄ . H -functions represent the multiplescattering between the particulate media, and for this study the

improved approximation to the Ambartsumina–ChandasekharH -function was used (Hapke, 2002).

For the single-particle phase function, we adopted a singleHenyey–Greenstein function (Henyey and Greenstein, 1941)with the asymmetry factor, g, which describes the directionalscattering properties of individual particles. Use of a multi-parameter single-particle phase function would not be appropri-ate for this study due to the restriction of phase angle coverage(<38.4◦), although it enables a higher precision of fit (Hartmanand Domingue, 1998).

The opposition effect has been proposed to consist of twomechanisms, shadow-hiding and coherent backscatter (Hapke,2002). Because both mechanisms show almost similar behav-ior of brightness enhancement at low phase angles, it is difficultto distinguish quantitatively their contributions to brightness asa function of phase angle. Therefore, the contribution of thecoherent backscatter phenomenon to the opposition surge can-

Hayabusa NIRS photometry of 25143 Itokawa 141

Fig. 4. The wavelength dependence of the Hapke parameters: the single scattering albedo (top left), the asymmetry parameter (top right), the amplitude of theopposition surge (bottom left), and the opposition surge width (bottom right). For comparison, the data of Eros derived from Clark et al. (2002) are also plotted.

not presently be modeled and was treated as a bundle with theshadow-hiding opposition effect in this analysis. Hence, the twoparameters here used for opposition effect, amplitude B0 andwidth h, account for the total opposition effect caused by bothmechanisms.

The fitting routine was a least-squares method using theNelder and Mead Simplex algorithm (Buchanan and Turner,1992) that minimizes χ2 and varies free parameters simul-taneously. The parameter χ2 is defined as the sum of thesquares of the differences between the observed and modeledreflectance at each data point. The parameter optimization wasperformed in two stages. First, with the five free parameters(w,g,B0, h, θ̄ ) optimal solutions were determined using all se-lected data points for each wavelength. Since the roughnessparameter is a purely geometric parameter that should be com-pletely independent of wavelength, we averaged the roughnessvalues over the available wavelengths. Then, with the rough-ness parameter fixed at the mean value, optimal solutions forthe remaining four parameters were determined using the sameprocedure. We executed 100 runs of fitting procedures withrandomized initial values of these parameters. Measured re-flectance values have uncertainties which are the sum of ab-solute calibration uncertainties and the standard deviations ofthe stacked raw signals. To estimate the errors in our modelparameters, we computed models using the lower and upperranges of the reflectance uncertainties. Absolute calibration isthe main source of uncertainty, so our measured reflectance

values are uncertain by approximately 10% over the effectivewavelength range.

5. Results

The results of our least-squares fit of the Hapke photomet-ric function to the observed data are graphically summarized inFig. 4, where the global average values of four photometric pa-rameters (w,g,B0, h) for Itokawa at the multiple wavelengthsare shown. For comparison, the results from Eros (Clark et al.,2002) are also plotted. The value of the roughness parameter, θ̄ ,was estimated to be 26◦ ±1◦ for Itokawa, compared to 24◦ ±2◦for Eros.

The goodness of fit of the Hapke model to the observed datais shown in Figs. 5 and 6 at a representative wavelength of1.57 µm. Fig. 5 compares the observed reflectance values tothose predicted by the Hapke model. Fig. 6 shows the ratio ofthe observed to modeled reflectance values plotted against in-cidence, emission, and phase angles, and spacecraft range tothe asteroid surface. The NIRS channel-to-channel measure-ment errors of reflectances are very small, less than 1%. Con-sequently, the deviation of the ratio between the observed andmodeled reflectances falls within 10% and there is no system-atic variation of the ratio with viewing angle. Such deviationcan be considered as resulting from regional differences in sur-face brightness.

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6. Discussion

6.1. Single-particle characteristics

The single-scattering albedo is an intrinsic scattering prop-erty of a particle, determined by its size, shape and refrac-tive index. The values of single-scattering albedo estimated forItokawa’s surface are on the order of 35–40% below those ofEros within the NIRS coverage. Based on the reflectance spec-trum, Itokawa’s surface is dominated by olivine and pyroxene,and the corresponding ordinary chondrite class was estimatedto be LL5 or LL6 (M. Abe et al., 2006). Eros is most consistentwith an L6 composition (Izenberg et al., 2003).

The single-scattering albedo of the particles at any givenwavelength is determined by both the composition and the grainsize in Mie scattering (Hapke, 1993). Assuming the mean grainsizes of mixture components in the surface material are allthe same, we calculated the single-scattering albedo for indi-

Fig. 5. The goodness of fit between the observed and modeled reflectance at1.57 µm. The dashed line denotes exact agreement between the observed andmodeled values.

vidual ordinary chondrite classes (H, L, LL) as a function ofgrain size using mineral proportions compiled from the pub-lished literature (McSween et al., 1991). Fig. 7 shows profilesof single-scattering albedo for each meteorite class at 1.40 µm.The refractive indices for three minerals (olivine, orthopyrox-ene, clinopyroxene) are given as functions of the Mg number,the ratio of Mg to Mg+Fe on a molecular basis (Lucey, 1998).As for the refractive index of metal, we used that of iron esti-mated by Johnson and Christy (1974). The imaginary parts ofthe refractive indices at the closest wavelengths to 1.40 µm areadopted due to the lack of estimated values at the same wave-length. Thus, we extend the range of the fitted single-scatteringalbedo for Itokawa from 0.37 at 1.30 µm to 0.42 at 1.58 µm.Considering that the theoretical value of the single-scattering

Fig. 7. The theoretical single-scattering albedo for individual ordinary chon-drite classes as a function of mean grain size at 1.40 µm wavelength. Forthe imaginary parts of the refractive indices for olivine, orthopyroxene, andclinopyroxene given by Lucey (1998), the values estimated at 1.58, 1.30 and1.45 µm, respectively are used. Two dashed horizontal lines represent the fit-ted values of single-scattering albedo for Itokawa, 0.37 at 1.30 µm and 0.42 at1.58 µm.

Fig. 6. The ratio of the modeled to observed reflectance plotted as a function of the incidence angle (top left), the emission angle (bottom left), the phase angle (topright), and the distance of the spacecraft to the asteroid surface (bottom right).

Hayabusa NIRS photometry of 25143 Itokawa 143

albedo is obtained within that range, we find that the mean grainsize of Itokawa’s surface is more than 150 µm and the H chon-drite cannot correspond to the surface material of Itokawa. Wesuggest that the difference in single-scattering albedo betweenItokawa and Eros is due to grain size and compositional differ-ences.

The single-particle phase function describes the directionalscattering properties of the individual particles. The lower thevalue of the asymmetry factor, g, the stronger the backscatter-ing behavior of the average particle. The asymmetry factor forItokawa is about 30% lower than that of Eros, which wouldindicate that the surface materials of Itokawa have a strongerbackscattering component in the phase function. This is in ac-cordance with the results from the ground-based photometry ofLederer et al. (2007), in which the wide solar phase angle rangeof 4◦–130◦ is covered. If the internal scattering optical thick-ness is large, most of the light is scattered out of the back face ofthe particle after traveling only a short internal distance, so thatthe phase function is dominated by a back scattered component(McGuire and Hapke, 1995). Thus, the stronger backscatteringproperty for Itokawa is in reasonable agreement with the resultsfor the single-scattering albedo.

6.2. Opposition effect

In the photometric behavior of airless bodies in the SolarSystem, two major mechanisms contribute to the opposition ef-fect: shadow-hiding and coherent backscattering. The shadow-hiding opposition effect occurs when the shadow cast by oneparticle on another disappears at zero phase angle, when eachparticle hides its own shadow, causing a relatively broad surgein brightness at small phase angles (Hapke, 1986). The coher-ent backscattering opposition effect results when portions ofwaves traveling in opposite directions along the same pathswithin a scattering medium interfere constructively with eachother as they exit the medium near zero phase and cause a rela-tive peak in brightness there that is narrow (Hapke, 1990). Theshadow-hiding mechanism is wavelength independent, whereasthe coherent backscatter phenomenon is wavelength dependent.Hapke et al. (1993, 1998) demonstrated through reflectance andpolarization studies in the laboratory that lunar soils display anopposition effect due to a combination of both mechanisms.

Although the surface of Itokawa seems to be remarkablyhummocky and covered with numerous angular rock fragments,the photometric phase curve shows an opposition surge compa-rable to the regolith-covered surface of Eros. In previous photo-metric studies of S-type asteroids including Eros, the amplitudeof the opposition surge is allowed B0 to exceed the theoreticallimit of unity (Clark et al., 2002). This can adequately accountfor the total opposition effect of both shadow hiding and coher-ent backscattering. Values of B0 for Itokawa are, however, lessthan unity. In addition, we find that a wavelength dependenceof the opposition surge width exists, indicating that coherentbackscattering contributes to the opposition effect. Accordingto Hapke (1993), the narrower width of the opposition surgefor Itokawa compared to Eros could indicate a more denselypacked state of the particles. The shadow hiding opposition

Table 1Roughness parameters for the selected S-type asteroids

Object Data type θ̄ (deg) References

Itokawa Disk-resolved 26 ± 1 This studyEros Disk-resolved 24 Clark et al. (2002)

Disk-resolved 28 Li et al. (2004)Disk-integrated 36 Domingue et al. (2002)

Gaspra Disk-resolved 29 Helfenstein et al. (1994)Ida Disk-resolved 18 Helfenstein et al. (1996)Avg S-type Disk-integrated 20 Helfenstein and Veverka (1989)

effect disappears for a solid surface when the medium is com-pletely occupied by particles, as in zero porosity. Thus, the factthat Itokawa has low values of B0 could be explained by thesmall contribution of shadow hiding due to the compaction stateof the optically active portion of its surface material.

6.3. Surface roughness

The global roughness parameter, θ̄ , models the mean slopeangle within each unresolved surface patch as measured fromthe local horizon and captures the effect of unresolved shadowscast by tilted facets. In order to constrain the roughness pa-rameter, it is necessary to include disk-resolved data obtainedat a wide range of incidence and emission angles. The valuesof roughness parameter for the representative S-type asteroidsincluding Itokawa are summarized in Table 1. The estimatesgiven here are individual average values over the surface. Infact, the size and distribution of surface features such as cratersand boulders are not homogeneous on the asteroid surface.

Comparing the values of roughness parameter betweenItokawa and Eros, we find that their values are almost similar al-though not resembling in surface appearance. In addition, thereis little variability of surface roughness with spatial resolutionwithin our observation scale (Fig. 6). Shepard and Campbell(1998) determined the shadowing behavior of a wide range offractal surfaces using digital terrain model, suggesting that thescale which dominates surface shadowing is the smallest sur-face scale for which shadows exist. The similarity in the derivedvalues for θ̄ between the two bodies agrees with their hypoth-esis and indicates a possibility that S-type asteroids commonlymay have photometric roughness values ranging from 20◦ to30◦, whether or not the surface is covered with a thick regolithlayer.

6.4. Spectral changes depending on viewing geometry

We simulate spectral changes that occur with viewing angleusing the obtained parameter values. Fig. 8a shows the vari-ation of the modeled spectra when the phase angle is variedfrom 10◦ to 40◦. We find that the relative reflectances near 1and 2 µm to the spectral continuum becomes smaller by 3%and 1% respectively with increasing phase angle within 10◦to 40◦. Those relationships invert at small phase angle (<2◦).Considering that the asymmetry factor for phase function is in-dependent of wavelength, it is clear that such variations in colorratio would arise from the coherent backscattering oppositioneffect in Hapke theory.

144 K. Kitazato et al. / Icarus 194 (2008) 137–145

Fig. 8. Spectral changes due to viewing geometry are simulated using our Hapke models. (a) Phase angle variations and (b) incidence and emission angle variations.The parenthetical values represent the incidence, emission and phase angles starting from the left, respectively.

The variation in reflectance at 1 µm is larger with phase an-gle than at 2 µm, which is consistent with the profile of theopposition effect angular width as seen in Fig. 4. According toHapke (2002), the angular width of a coherent backscatteringopposition surge is proportional to wavelength and inverselyproportional to transport mean free path in the medium. Thetransport mean free path may be thought of as the mean distancea photon travels in the medium before its direction is changedby a large angle and is expressed as a function of inverse tothe mean single-scattering albedo in radiative transfer literature.Thus, theoretically the angular width of coherent backscatter-ing opposition effect should have a positive correlation withthe single-scattering albedo, which disagrees with our result.In practice, the transport mean free path is heavily weighted bythe effects of internal and surface scattering inhomogeneities inthe media of large complex particles. On the other hand, suchspectral changes cannot be easily detected with variations in in-cidence and emission angles as shown in Fig. 8b. There wouldbe a slight variation in color ratio derived from the multiplescattering in the media in such a case.

7. Conclusions

We have presented a Hapke model analysis of disk-resolvedreflectance data of the asteroid Itokawa obtained from HayabusaNIRS observations at wavelengths from 0.85 to 2.10 µm. Wefind that the Hapke photometric model can fit observations

of Itokawa’s hummocky asteroid surface as well as it fits theregolith-covered surface of Eros. Our models can be used tocorrect the NIRS data for variations caused by viewing geome-try.

From our estimates of the Hapke photometric parameters,we find that the surface materials of Itokawa have values ofsingle-scattering albedo 35–40% lower than at Eros. Itokawaalso shows more dominant backscattering than Eros. These dif-ferences can be explained by a large grain size of surface ma-terial at Itokawa. Despite its rough hummocky surface, Itokawaexhibits an opposition effect. The values of B0 for Itokawa areless than unity at all wavelengths within the NIRS coverage.This indicates that the contribution of the shadow-hiding mech-anism to the opposition surge is weaker at Itokawa than at Eros.Like Eros, a wavelength dependence of h is found for Itokawa,possibly indicating that coherent backscatter is contributing tothe opposition effect. The roughness parameter for Itokawa isestimated to be almost equal to that at Eros indicating that thesmallest surface roughness scale at which shadows exist is thescale that is effective in the modeled photometric surface rough-ness.

We examined spectral changes that occur with viewing an-gle using our Hapke models. Relative reflectances at 1 and 2 µmto spectral continuum vary with phase angle due to coherentbackscattering opposition effect, but there is almost no varia-tion in spectral profile when incidence and emission angles arevaried.

Hayabusa NIRS photometry of 25143 Itokawa 145

Acknowledgments

NIRS data acquisition was a team effort involving de-tailed and meticulous planning of spacecraft operations andinstrument sequencing. The authors are grateful to the mis-sion operations and spacecraft team of the Hayabusa projectat ISAS/JAXA for their efforts that resulted in making the mis-sion possible and successful. We also thank Nikolai Kiselev andan anonymous referee for their thoughtful reviews of this paper.K.K. acknowledges support by the Research Fellowships of theJapan Society for the Promotion of Science for Young Scien-tists.

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