Icarus 226 (2013) 663–670

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Icarus

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Lightcurve, Color and Phase Function Photometry of the OSIRIS-REx Target Asteroid (101955) Bennu q ⇑ Carl W. Hergenrother a, , Michael C. Nolan b, Richard P. Binzel c, Edward A. Cloutis d, Maria Antonietta Barucci e, Patrick Michel f, Daniel J. Scheeres g, Christian Drouet d’Aubigny a, Daniela Lazzaro h, Noemi Pinilla-Alonso i, Humberto Campins j, Javier Licandro k, Beth E. Clark l, Bashar Rizk a, Edward C. Beshore a, Dante S. Lauretta a a Lunar and Planetary Laboratory, University of Arizona, 1629 E. University Blvd., Tucson, AZ 85721, USA b Arecibo Observatory/USRA, HC3 Box 53995, Arecibo, PR 00612, USA c Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA d Department of Geography, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9, Canada e LESIA-Observatoire de Paris, CNRS, Universite Pierre et MarieCurie, Universite Paris Diderot, F – 92195 Meudon Principal Cedex, France f Lagrange Laboratory, Université Nice Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, BP 4229, 06304 Nice Cedex 4, France g Colorado Center for Astrodynamics Research, University of Colorado Boulder, 431 UCB, Boulder, CO 80309-431, USA h Observatório Nacional, COAA, Rua Gal. José Cristino 77, 20921-400 Rio de Janeiro, Brazil i Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, TN 37996, USA j Department of Physics, University of Central Florida, P.O. Box 162385, Orlando, FL 32816.2385, USA k Instituto de Astrofísica de Canarias (IAC), C/Vía Láctea s/n, 38205 La Laguna, Spain l Department of Physics, Ithaca College, Ithaca, NY 14850, USA article info abstract

Article history: The NASA OSIRIS-REx mission will retrieve a sample of the carbonaceous near-Earth Asteroid (101955) Bennu Received 1 February 2013 and return it to Earth in 2023. Photometry in the Eight Color Asteroid Survey (ECAS) filter system and John- Revised 23 May 2013 son–Cousins V and R filters were conducted during the two most recent apparitions in 2005/2006 and 2011/ Accepted 31 May 2013 2012. Lightcurve observations over the nights of September 14–17, 2005 yielded a synodic rotation period of Available online 22 June 2013 4.2905 ± 0.0065 h, which is consistent with the results of Nolan et al. (2013). ECAS color measurements made during the same nights confirm the B-type classification of Clark et al. (Clark, B.E., Binzel, R.P., Howell, E.S., Keywords: Cloutis, E.A., Ockert-Bell, M., Christensen, P., Barucci, M.A., DeMeo, F., Lauretta, D.S., Connolly, H., Soderberg, Asteroids A., Hergenrother, C., Lim, L., Emery, J., Mueller, M. [2011]. Icarus 216, 462–475). A search for the 0.7 m hydra- Asteroids, Rotation l Near-Earth objects tion feature using the method of Vilas (Vilas, F. [1994]. Icarus 111, 456–467) did not reveal its presence. Pho- Photometry tometry was obtained over a range of phase angles from 15° to 96° between 2005 and 2012. The resulting phase function slope of 0.040 magnitudes per degree is consistent with the phase slopes of other low albedo near-Earth asteroids (Belskaya, I.N., Shevchenko, V.G. [2000]. Icarus 147, 94–105). Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction organics on Earth. Their chemical and physical nature, distribution, formation, and evolution are fundamental to understanding planet Inner Solar System asteroids are the direct remnants of the ori- formation and the origin of life. Sample return from a carbona- ginal building blocks of the terrestrial planets. The presence of vol- ceous asteroid is the goal of the NASA New Frontiers-class mission atiles and complex organic compounds in primitive meteorites has OSIRIS-REx. Scheduled for launch in 2016, OSIRIS-REx will rendez- indicated that carbonaceous asteroids are a source of volatiles and vous with and collect samples from the near-Earth Asteroid

(101955) Bennu (formerly 1999 RQ36). These samples will then

q be returned to Earth for analysis in 2023 (Lauretta et al., 2010). Based on observations with the VATT: the Alice P. Lennon Telescope and the An extensive multi-wavelength campaign was conducted both Thomas J. Bannan Astrophysics Facility and on observations obtained at the Southern Astrophysical Research (SOAR) telescope, which is a joint project of the before and after the selection of Bennu as the target of OSIRIS- Ministério da Ciência, Tecnologia, e Inovação (MCTI) da República Federativa do REx. Today Bennu is one of the best-characterized near-Earth Brasil, the U.S. National Optical Astronomy Observatory (NOAO), the University of asteroids ever. The asteroid was a 15th magnitude object when dis- North Carolina at Chapel Hill (UNC), and Michigan State University (MSU). covered on September 11, 1999 by the Lincoln Laboratory Near ⇑ Corresponding author. Address: Lunar and Planetary Lab, University of Arizona, Tucson, AZ 85721, USA. Fax: +1 520 626 1973. Earth Asteroid Research (LINEAR) survey (Williams, 1999). Since E-mail address: [email protected] (C.W. Hergenrother). discovery there have been three opportunities to conduct ground-

0019-1035/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2013.05.044 664 C.W. Hergenrother et al. / Icarus 226 (2013) 663–670 and space-based observations. During the discovery 1999–2000 system used at the Kuiper 1.5-m was ‘CCD32’ while ‘CCD26’ was apparition Bennu passed within 0.015 AU of Earth and peaked in used at the VATT 1.8-m. During 2011–2012, the Mont4k was used brightness at 14th magnitude. During the 2005–2006 apparition on the Kuiper 1.5-m. The Mont4k is a Fairchild CCD486 it approached to within 0.033 AU of Earth and brightened to 16th 4096 4097 CCD with 15-lm pixels (Randall et al., 2007). The magnitude. The most recent apparition extended from mid-2011 instrument provides a FOV of 9.70 9.70 and plate scale of 0.4200/ to mid-2012 when it approached to within 0.177 AU of Earth pixel when binned 3 3. The SOAR 4.2-m and SOI instrument were resulting in a much fainter peak magnitude of 19th magnitude. used in remote queue observing mode to collect V- and R-band Bennu resides on a low delta-V orbit with respect to Earth mak- data in order to determine the V–R color index. The SOAR Optical ing it easily accessible for sample return (Binzel et al., 2004). With Imager (SOI) instrument is a mini-mosaic of two E2V 2 K 4K a semi-major axis of 1.126 AU and perihelion of 0.897 AU, its orbit CCDs covering a 5.30 5.30 field-of-view. The images were binned is classified as an Apollo-type. Currently the orbit of Bennu ap- 2 2 resulting in a plate scale of 0.15400/pixel. proaches to within 0.0027 AU (1.05 lunar distances) of Earth’s or- All data were reduced with the IRAF software package. The bit. This Minimum Orbit Intercept Distance (MOID) will steadily images were bias-subtracted and flat-fielded with twilight and decrease resulting in a cumulative Earth impact probability of or- night sky flat images using tasks in the CCDRED package. The APP- der 103 during the later decades of the 22nd century, making Ben- HOT package was used to perform aperture photometry of Bennu nu one of the most potentially hazardous known asteroids (Milani and photometric standard stars. In order to compensate for vari- et al., 2009; Chesley et al., 2012). able seeing and maximize signal-to-noise, the average FWHM Comparative analysis of visible to near-infrared reflectance was measured for each image and the photometric aperture was spectra identifies Bennu as a spectral B class asteroid with spectral set to a radius of 2 FWHM (Howell, 1989). Sky background was similarities to CI and/or CM meteorites (Clark et al., 2011). The measured with a circular ring aperture of radius 20 pixels and dynamical evidence suggests an inner Main Belt, low inclination width of 10 pixels. The sky aperture was centered on the position origin for Bennu. In particular, the Polana asteroid family, which of the measured source. is composed of B-type objects, is identified as a probable source Photometric ECAS reference stars from Tedesco et al. (1982) and (Campins et al., 2010). V- and R-band reference stars from Landolt (1992) were observed Radar observations from the Goldstone and Arecibo radio tele- at multiple airmasses on each night in order to determine the pho- scopes found Bennu to be an irregular spheroid with a mean diam- tometric zero point and extinction coefficient. Standard star obser- eter of 493 m with evidence of a single boulder and no craters vations were reduced following the same method as the Bennu down to a resolution of 7.5 m (Nolan et al., 2013). There is also observations with the same 2 FWHM photometric apertures no evidence of any satellites larger than the resolution limit. The and sky background annuli. existence of an equatorial ridge, similar to those seen on other All telescopes were tracked at the rate of the motion of the near-Earth asteroids such as (66391) 1999 KW4, suggests that Ben- asteroid. During the 2011–2012 apparition Bennu was always fain- nu may have experienced a rotationally-induced splitting event in ter than V = 19. Due to its faintness a number of 30–60 s exposures the past and could have been a binary asteroid at one point or have were co-added along the motion of the asteroid in order to increase lost material migrating to the equator (Scheeres et al., 2006; Walsh S/N on the Kuiper and VATT telescopes. et al., 2008; Jacobson and Scheeres, 2011; Walsh et al., 2012). Extensive infrared observations covering near-, mid-, and ther- 3. Results and analysis mal-infrared wavelengths find a very low albedo of 0.030–0.045 (Emery et al., 2010; Clark et al., 2011; Müller et al., 2012). Observa- 3.1. Rotation period tions from the Spitzer and Herschel space telescopes also find a thermal inertia of 600 ± 150 J m2 s0.5 K1 (Emery et al., 2010) Time-series photometry was obtained with the University of which is similar to other sub-kilometer near-Earth asteroids (Delbo Arizona Kuiper 1.5-m over four consecutive nights on 2005 Sep- and Tanga, 2009; Emery et al., 2010). tember 14–17 UT. Observations were made using multiple ECAS In this paper, we present characterization and discussion of the filters though the w (0.705 lm) filter was primarily used. Prelimin- photometric properties of Bennu at visible wavelengths including ary period determination was conducted with the Asteroid Light- determinations of rotation period, phase function, and colors in curve (ALC) software package (version 0.96) provided by P. the Eight Color Asteroids Survey (ECAS) as well as in the John- Pravec. Observations were corrected for light travel time and son–Cousins UBVRI filter systems. changes in heliocentric distance (r), geocentric distance (D), and phase angle (a). Observing circumstances are listed in Table 1. 2. Observations and data reduction 3.1.1. Period determination All lightcurve and phase function observations were obtained A 10th order Fourier series fit finds a synodic rotation period of with University of Arizona Observatories telescopes located in 4.2905 ± 0.0065 h with an amplitude of 0.16 magnitudes (Fig. 1). southeastern Arizona during the 2005–2006 and 2011–2012 appa- This result is twice the value of 2.146 h found in 1999 by Krugly ritions. Lightcurve and ECAS color photometry were acquired at the et al. (2002). The discrepancy is likely due to their not observing Kuiper 1.54-m reflector on the nights of 2005 September 14–17 UT. a total rotation period during any of the 1999 nights. As a result, Additional Harris R-band phase function photometric measure- they incorrectly arrived at a sub-multiple (P/2) of the real period. ments were obtained between 2005 and 2012 at the Vatican By comparison, three of our four nights covered a complete rota- Observatory VATT 1.8-m reflector (on 2006 April 30 and 2012 tion giving more credence to the 4.2905 h synodic period. May 15) and the Kuiper 1.54-m (all other dates). Dates and obser- Observing geometry changed sufficiently over the course of vational circumstances for the lightcurve photometry and ECAS/VR the four nights to use the phase angle bisector (PAB) approxima- color photometry are presented in Table 1. Dates and observing cir- tion to determine the difference between the synodic and sidereal cumstances for the phase angle photometry are presented in period (Harris et al., 1984; Pravec et al., 2005). The minimum dif- Table 4. ference between the synodic and sidereal period was calculated The observations from 2005 to 2006 were obtained with at 0.0071 h. The lightcurve observations by themselves were not thinned Loral 2048 2048 CCDs with 15-lm pixels. The camera sufficient to determine the direction of rotation or whether the C.W. Hergenrother et al. / Icarus 226 (2013) 663–670 665

Table 1 Lightcurve and color observational circumstances.

Year Mo (UT) Day Filters D (AU) r (AU) a (°) ECAS/Landolt standard stars Lightcurve and ECAS Color Observations at Kuiper 1.54-m telescope 2005 09 14.32–14.41 bvw 0.041 1.025 60.1 SA71-07, SA71-20 2005 09 15.31–15.50 ubvwxp 0.038 1.022 63.4 SA114-223, SA114-790 2005 09 16.33–16.47 ubvwxp 0.037 1.019 67.0 SA71-07, SA71-20 2005 09 17.32–17.50 ubvwxp 0.035 1.016 71.2 SA71-07, SA71-20 VR color observations at SOAR 4.2-m telescope 2012 05 19.18–19.29 VR 0.363 1.343 20.7 G153-41, PG1525-071A, PG1525-071B, PG1525-071D

Fig. 1. The phased lightcurve of Bennu consists of photometry taken on 2005 Fig. 2. The rotation period (in hours) is plotted against absolute magnitude (H). September 14–17 UT. The photometry is phased to the synodic rotation period of Rotation period data is from the Asteroid Lightcurve Database (LCDB) described in 4.2905 ± 0.0065 h. Warner et al. (2009). sidereal period is longer or shorter than the synodic period. Nolan can be excluded, only a tetrahedron shape (or irregular with simi- et al. (2013) determined a sidereal period of 4.29746 ± 0.002 h by lar morphology) can give a lightcurve with such number of max- comparing the lightcurves from Krugly et al. (2002) in 1999, the ima or minima. Work by Harris (2012) shows that a 3-sided lightcurves from 2005 (this work), and the radar images from shape would produce a maximum amplitude of 0.156 magnitudes 1999 and 2005 with the expected lightcurves and radar images at 0° phase angle. The observed lightcurve amplitude of 0.16 mag- based on the shape model. Adding the lightcurve derived PAB nitudes was measured at high phase angle (60–70°). Zappala et al. approximation difference in the synodic and sidereal periods (1990) showed that lightcurve amplitudes increase with phase an- (0.0071 h) to the synodic period (4.2905 h) yields a sidereal peri- gle. This implies a smaller amplitude than 0.156 magnitudes at 0° od of 4.2975 h, which closely matches the Nolan et al. (2013) phase angle. The low amplitude observed for Bennu is consistent result. with the results of Harris (2012). A good interpretation of the lightcurves can be done only if one has many lightcurves at different geometrical aspects. In this case a 3.1.2. Lightcurve analysis good shape model can be computed. More detail on the rotation The rotation periods of asteroids whose absolute magnitudes period determination and its implications for the radar-derived are in the range 13 < H < 25 are plotted in Fig. 2. Approximately shape model can be found in Nolan et al. (2013). 75% of all asteroids smaller than H = 22 are rapid rotators with rotation periods shorter than 2 h (Hergenrother and Whiteley, 2011). Many of these rapid rotators have periods on the order of 3.2. Color indices minutes. The rotation period of Bennu is compared with all aster- oid rotation periods included in the Asteroid Lightcurve Database 3.2.1. ECAS color photometry described in Warner et al. (2009) (see Fig. 2). Interestingly, the Concurrent with the rotation lightcurve data taken on 2005 rotation period of Bennu (about 4.3 h) is very close to that of the September 14–17 UT, ECAS photometry was obtained in the u carbonaceous binary whose primary has a similar size to Bennu. (0.320 lm), b (0.430 lm), v (0.545 lm), x (0.860 lm), and p Moreover, the oblate spheroidal shape of Bennu and the existence (0.955 lm) filters in addition to the w (0.705 lm) filter. Photomet- of an equatorial ridge are typical characteristics of primaries of ric variability due to rotation and change in phase angle has been small NEO binaries (e.g., Ostro et al., 2006). corrected. The resulting u–v, b–v, v–w, v–x and v–p indices are pre- A lightcurve with three maxima and three minima is in general sented in Table 2. unusual for most asteroid shapes. The triple maxima and minima Hydrated minerals on the surface of C-complex asteroids can be pairs are suggestive of a tetrahedron shape. Emery et al. (2010) identified by the presence of absorption features at 0.7 and 3.0 lm. found no evidence of albedo variations across the surface of Bennu Sloan Digital Sky Survey (SDSS) color photometry of Main Belt in Spitzer 16 and 22 lm photometric data. Since albedo variations asteroids were analyzed by Rivkin (2012) who found that 30 ± 5% 666 C.W. Hergenrother et al. / Icarus 226 (2013) 663–670 of C-complex asteroids show a 0.7 lm band. Vilas (1994) showed Table 3 that the ECAS v, w and x filter magnitudes indicate the presence Johnson–Cousins derived color index results. of the 0.7 lm feature if the following relation is found to be true. U–BB–VV–RV–I +0.16 ± 0.05 +0.64 ± 0.04 +0.36 ± 0.04 +0.69 ± 0.04 ðRw ððRx RwÞ0:4984ÞÞ=Rv > 0

Here Rv, Rw and Rx is the relative reflectance of the v, w and x filters, respectively, and a value greater than 0 denotes the presence of the band. A result of 0.01 ± 0.04 is interpreted as a non-detection of the 0.7 lm hydration feature since it was not conclusively detected within the photometric errors.

3.2.2. Johnson–Cousins UBVRI colors V- and R-band photometry conducted with the SOAR 4.2-m in May of 2012 yielded a V–R color of +0.37 ± 0.03 magnitudes. Trans- formations from the ECAS system to the Johnson–Cousins system in Howell (1995) give a V–R color of +0.35. The mean value of V– R = +0.36 ± 0.04 is from both the ECAS and SOAR VR photometry. Though Bennu was not observed in the Johnson U and B and Cousins I band, transformations from the ECAS photometric system to the Johnson–Cousins system are possible (Howell, 1995). Trans- formed Johnson–Cousins U–B, B–V, V–R and V–I indices are pre- sented in Table 3.

3.2.3. Taxonomic classification Bennu has been identified as a B-type asteroid with a bluish slope across visible wavelengths (Clark et al., 2011). Fig. 3 presents Fig. 3. The ECAS spectrophotometry (this work) is compared with visible to near-IR a comparison of the visible and IR spectra from Clark et al. (2011) spectroscopy from Clark et al. (2011). with the ECAS photometry, normalized to unity at a wavelength of 0.545 lm. Both sets of data are consistent within the error bars. The extension of measurements toward the ultra-violet allows some comparison with spectral properties characterized by the Tholen taxonomy (Tholen, 1984; Tholen and Barucci, 1989). Mod- ern CCD spectroscopy typically does not provide sensitivity for measurements below 0.45 lm; the Eight-Color Asteroid Survey (Zellner et al., 1985) extends down to 0.34 lm. While Bennu main- tains the general spectral qualities of the C-class and its various subtypes (denoted by Tholen as B, C, F), the UV turnover for Bennu is less pronounced. Two ECAS photometry datasets were retrieved from the NASA Planetary Data System (PDS) Small Body Node. Both of these PDS sets include measurements taken with the ECAS u and b filters (Whiteley, 2004; Zellner et al., 2009). Fig. 4 presents a comparison of the ECAS u–b and v–x color indices of Bennu with Main Belt asteroids from Zellner et al. (1985) and near-Earth asteroids from Whiteley (2001). The relative rarity of objects such as Bennu with no observable UV turnover at wavelengths longwards of 0.32 lm and a bluish slope between 0.545 lm and 0.860 lm is evident. The two near-Earth asteroids with the most similar spectral char- acteristics are (152679) 1998 KU2 (u–b = 0.02 and v–x = 0.03) Fig. 4. Near-Earth asteroid Bennu ECAS u–b and v–x color indices are 0.04 and and (234145) 2000 EW70 (u–b = 0.01 and v–x = 0.01), relative 0.01, respectively. Comparing Bennu’s ECAS u–b and v–x colors with those of Main to Bennu with an ECAS u–b and v–x color index of 0.04 and Belt asteroids and near-Earth asteroids observed in the ECAS system, shows the 0.01, respectively. rarity of asteroids showing a blue slope between the wavelengths of 0.320 and 0.430 lm as well as between 0.545 and 0.860 lm. The ECAS Main Belt photometry is from Zellner et al. (1985) and was obtained from the NASA Small Body Node 3.3. Phase function (SBN) of the Planetary Data System (PDS) (Zellner et al., 2009). The ECAS near-Earth asteroid photometry is from Whiteley (2001) and was also obtained from the NASA Measuring the relationship between the brightness of an aster- SBN PDS (Whiteley, 2004). oid and the observed phase angle (a) allows an estimate of the absolute magnitude (H), or brightness of the asteroid at zero phase angle is determined by normalizing the observed apparent degrees phase angle (where phase angle is defined as the Sun– magnitude of the asteroid to a heliocentric and geocentric distance asteroid–Earth angle). The relationship between brightness and of 1 AU. The phase function can be modeled a number of ways. In

Table 2 ECAS color index results.

V–R u–vb–vv–wv–xv–p

+0.36 ± 0.04 0.07 ± 0.03 0.03 ± 0.02 0.01 ± 0.02 0.01 ± 0.03 0.05 ± 0.03 C.W. Hergenrother et al. / Icarus 226 (2013) 663–670 667

angle (Fig. 5). The linear fit does not include any opposition effect, which usually occurs at phase angles of much less than 15°. Low albedo carbonaceous asteroids show shallow opposition effects of <0.3 magnitudes (Shevchenko et al., 2008; Muinonen et al., 2010). Shevchenko and Belskaya (2010) found a correlation be- tween the albedo and the magnitude of the opposition effect. Their study of 33 low albedo asteroids found that the magnitude of the opposition effect decreased with decreasing albedo. Based on their results (and Fig. 2 of Shevchenko and Belskaya (2010) in particu- lar), Bennu with an albedo of 0.030–0.045 should have an opposi- þ0:15 tion effect of 0:05 0:05 magnitudes. Assuming such an opposition þ0:05 effect for Bennu results in an Hv of 20:56 0:15. The Minor Planet Center (MPC) assumes a G value of +0.15 for most asteroids. A fit to the photometry reported here using

G = +0.15 yields an Hv of 20.73 which is consistent with the MPC value of 20.9. The discrepancy between the values for Hv is because the MPC uses all photometry submitted to them. Most of the MPC photometric data are of low precision and low accuracy due to sys- tematic and random errors (Oszkiewicz et al., 2011). Our dataset is Fig. 5. Linear phase function for Bennu phase photometry obtained between 2005 limited to the data presented in Table 4. Solving for both H and G and 2012. Observed magnitudes were converted to heliocentric magnitudes by produces values of Hv = 19.97 ± 0.26 and G = 0.12 ± 0.06. The H– normalizing each to a distance of 1 AU from the Sun and 1 AU from Earth. G system is known to have difficulty with low albedo objects such as Bennu (Shevchenko et al., 2008). Further difficulty in constrain- ing H and G with the IAU H–G system is due to the lack of photom- this paper, our observations are modeled with a simple linear least etry at low phase angles. As a result, there is no constraint on the squares fit and the IAU H–G photometric system derived by Bowell amplitude and width of the opposition effect. The Hv value from et al. (1989) for airless bodies. this system is derived from an extrapolated opposition effect that is much larger than those observed for dark objects (Shevchenko and Belskaya, 2010). Due to these limitations, the H–G fit is suspect 3.3.1. Phase function derived from Bennu data and should not be used without low phase angle observations to The dataset for Bennu consists of V-, R-, and ECAS w-band mag- constrain the opposition effect. nitude measurements made during the 2005/2006 apparition be- tween 2005 September 14 UT and 2006 June 19 UT and during the 2011/2012 apparition between 2011 September 26 UT and 3.3.2. Comparison with (253) Mathilde 2012 May 29 UT. The range of phase angles observed in 2005/ Few carbonaceous asteroids have been accurately observed 2006 range from 15.0° to 80.2° and those observed in 2011/2012 over a large range of phase angles. One of them is the Main Belt range from 17.7° to 95.6°. R-band data were transformed to V using Asteroid (253) Mathilde, images of which were obtained over a the measured V–R color index of +0.36 from this work. The ECAS w- wide range of geometries. Mathilde is a larger object than Bennu band data were transformed to V using a V–w color index of +0.30 with a mean diameter of 52.8 km versus 0.5 km (Veverka et al., derived from Howell (1995). A linear least squares fit through the 1999; Nolan et al., 2013). According to the analysis by Delbo and data produces an absolute magnitude (Hv) of 20.61 ± 0.20 and Tanga (2009), asteroids in the 50 km diameter range have lower phase slope (b) of 0.040 ± 0.003 magnitude per degree of phase thermal inertia values than those in the sub-km range. This

Table 4 Phase function observational circumstances.

Year Mo (UT) Day V(r,D,a) V(1,1,a) Filter D (AU) r (AU) a (°) 2005 09 14.40 16.22 23.10 ± 0.10 w 0.041 1.025 60.1 2005 09 15.41 16.22 23.27 ± 0.10 w 0.038 1.022 63.4 2005 09 16.40 16.26 23.38 ± 0.10 w 0.037 1.019 67.0 2005 09 17.41 16.38 23.63 ± 0.10 w 0.035 1.016 71.2 2006 01 05.52 21.54 23.72 ± 0.30 V 0.376 0.975 80.2 2006 04 30.24 19.20 21.14 ± 0.15 R 0.313 1.307 15.0 2006 05 22.27 20.49 21.79 ± 0.20 R 0.411 1.338 31.8 2006 05 26.19 20.77 21.95 ± 0.20 R 0.432 1.342 34.0 2006 06 19.19 21.97 22.49 ± 0.20 R 0.580 1.355 43.4 2011 09 26.48 20.75 24.37 ± 0.20 R 0.195 0.965 95.6 2011 11 23.52 22.16 24.27 ± 0.30 R 0.418 0.903 88.9 2012 01 19.54 22.01 23.29 ± 0.30 R 0.531 1.043 68.7 2012 01 26.53 21.85 23.10 ± 0.30 R 0.527 1.067 66.6 2012 01 27.54 21.68 22.92 ± 0.30 R 0.526 1.070 66.3 2012 02 23.51 21.96 23.24 ± 0.30 R 0.477 1.159 57.6 2012 02 24.50 21.51 22.80 ± 0.30 R 0.475 1.162 57.2 2012 03 27.49 20.71 22.33 ± 0.30 R 0.377 1.253 40.7 2012 03 28.49 20.46 22.10 ± 0.30 R 0.374 1.256 40.0 2012 04 20.40 19.48 21.33 ± 0.30 R 0.327 1.304 20.4 2012 04 21.43 19.63 21.46 ± 0.30 R 0.326 1.306 19.5 2012 05 15.23 19.89 21.53 ± 0.30 R 0.351 1.339 17.7 2012 05 16.27 19.66 21.28 ± 0.30 R 0.354 1.340 18.5 2012 05 29.16 20.31 21.63 ± 0.30 R 0.402 1.351 28.1 668 C.W. Hergenrother et al. / Icarus 226 (2013) 663–670

Table 5 Comparison of albedo vs phase slope for NEAs.

Asteroid Albedo Errors Phase slope (mag/°) Phase slope error Tax.a type Ref.b

+err err (101955) Bennu 0.03 0.01 0.01 0.040 0.003 B,F [1] (433) Eros 0.23 0 0 0.028 0.005 S [2] (1580) Betulia 0.08 0.02 0.02 0.038 0.003 C [3] (1627) Ivar 0.13 0.12 0.05 0.028 0.007 S [4] (1863) Antinous 0.10 0 0 0.030 0.004 Sq [5] (1866) Sisyphus 0.15 0 0 0.033 0.003 S [6] (1943) Anteros 0.14 0.11 0.06 0.030 0.003 S,L [4] (3103) Eger 0.39 0 0 0.027 0.006 Xe [5] (3199) Nefertiti 0.41 0.07 0.04 0.020 0.003 Sq [7] (3200) Phaethon 0.11 0 0 0.035 0.003 B,F [8] (3360) Syrinx 0.07 0 0 0.031 0.004 [7] (4015) Wilson-Harrington 0.06 0.01 0.01 0.037 0.004 C,F [9] (5381) Sekhmet 0.23 0.13 0.13 0.027 0.002 V [10] (5604) 1992 FE 0.38 0 0 0.028 0.002 V [5] (5751) Zao 0.36 0 0 0.019 0.004 X,K [6] (9856) 1991 EE 0.30 0.10 0.10 0.021 0.011 S [11] (14402) 1991 DB 0.14 0 0 0.028 0.005 M [6] (25330) 1999 KV4 0.05 0 0 0.041 0.004 B,C [6] (26760) 2001 KP41 0.06 0.04 0.04 0.033 0.006 Q [12] (33342) 1998 WT24 0.56 0.20 0.20 0.019 0.001 Xe [13] (53319) 1999 JM8 0.02 0 0 0.047 0.002 X,P [14] (68372) 2001 PM9 0.02 0.02 0.01 0.026 0.003 B [4] (142040) 2002 QE15 0.15 0.08 0.06 0.026 0.003 S,A [15] (162173) 1999 JU3 0.07 0.01 0.01 0.036 0.003 C [4,16] (164121) 2003 YT1 0.05 0.02 0.02 0.037 0.008 Sr [10]

[1] Clark et al. (2011), [2] Li et al. (2004), [3] Harris et al. (2005), [4] Mueller et al. (2011), [5] Trilling et al. (2010), [6] Delbo et al. (2003), [7] Veeder et al. (1989), [8] Harris and Lagerros (2002), [9] Licandro et al. (2009), [10] Delbo et al. (2011), [11] Harris et al. (1998), [12] Rivkin et al. (2005), [13] Harris et al. (2007), [14] Benner et al. (2002), [15] Wolters et al. (2005), [16] Campins et al. (2009). a Taxonomic types from the European Asteroid Research Node database of physical properties of NEOs. b References for albedo measurements. suggests a surface composed of finer regolith material than ex- Mount Lemmon Survey [G96] and the Siding Spring Survey [E12]). pected for Bennu. Similarities between the two objects include car- These surveys use no filter resulting in a loss of color information, bonaceous taxonomies, low albedos (Mathilde with 0.047 ± 0.005 though all of their fields are calibrated against solar-type stars. As and Bennu with 0.030 0.045), low bulk densities (Mathilde with a result, their photometry is internally consistent and is acceptable a density of 1.3 ± 0.3 g cm3 and Bennu with 0.98 ± 0.15 g cm3) for assessing the brightness changes due to phase angle. Phase and similar meteorite analogs (Yeomans et al., 1997; Veverka curves for near-Earth asteroids deviate greatly from linearity at very et al., 1999; Clark et al., 1999; Kelley et al., 2007). low and very high phase angles. For this work, we measure phase Measurements of the brightness of Mathilde obtained over a function slopes for photometry between phase angles of 15° and range of phase angles from 1.2° to 136.2° are presented in Clark et al. (1999). The Mathilde photometry is shifted fainter by 10.02 magnitudes in absolute magnitude (normalized to 1 AU from the Sun and Earth) to match the Bennu photometry. IAU H–G values for the combined data are Hv = 20.19 ± 0.06 and G = 0.08 ± 0.02 (Fig. 6). Due to the measurements at very low phase angles the opposition effect is better constrained by the H–G system but a clo- ser examination of the curve fit still shows an exaggerated opposi- tion effect solution. A visual inspection of the combined data at very low phase angles suggest a shallow opposition effect with a best fit Hv of 20.40 ± 0.05.

3.3.3. Relationship between phase function and albedo A correlation exists between the slope of the linear phase func- tion and the albedo of asteroids (Belskaya and Shevchenko, 2000; Oszkiewicz et al., 2011). Generally the phase function slope in- creases as the albedo decreases. The work of Belskaya and Shev- chenko (2000) included a set of large Main Belt asteroids. In order to determine if the albedo-phase slope correlation is valid for near-Earth asteroids that are much smaller than bright Main Belt asteroids (0.1–10 km rather than 100s of km in diameter) we pro- duced phase functions for near-Earth asteroids with accurate albedo measurements (see Table 5). Photometric data was obtained from Fig. 6. H–G phase function fit to a combination of the Bennu data presented in this paper and ground-based and NEAR photometry of (253) Mathilde from Clark et al. the Minor Planet Center. Since the data submitted to the MPC can (1999). The Mathilde photometry has been shifted fainter by 10.02 magnitudes to be of variable quality, we only used data taken by the Catalina Sky match the Bennu data. Magnitudes were normalized to heliocentric magnitudes as Survey telescopes (Catalina Sky Survey proper [MPC code 703], in Fig. 5. C.W. Hergenrother et al. / Icarus 226 (2013) 663–670 669

Grant No. NNX10AP64G issued through the Near-Earth Object Observations Program. E.A.C. thanks NSERC and the CSA for sup- port for this project. M.A.B. and P.M. thank CNES for support for this project. The OSIRIS-REx mission is funded by the NASA New Frontiers Program.

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