38 less favorable apparitions at intervals of 2.056 years (e.g., 2017 POLE AND SHAPE FOR THE NEA (436724) 2011 UW158 Sep with V ~ 20.7) will provide opportunities for additional observations with large telescope apertures for elucidating the Albino Carbognani nature of fast-spinning, rocky asteroids. Astronomical Observatory of the Aosta Valley Autonomous Region (OAVdA) Acknowledgements Lignan 39, 11020 Nus (Aosta), ITALY [email protected] Asteroid ephemeris information was provided by Caltech’s Jet Propulsion Laboratory web site: http://ssd.jpl.nasa.gov/horizons. Bruce L. Gary Calibration with SDSS magnitudes in the UCAC4 catalog was Hereford Arizona Observatory made possible through the use of the AAVSO Photometric All-Sky Hereford, Arizona, USA Survey (APASS), funded by the Robert Martin Ayers Sciences Fund. I want to record my appreciation to Dr. Arne Henden for Julian Oey initiating the APASS project; this is a sentiment I feel every Blue Mountains Observatory morning after a night’s observations as I select APASS stars for Leura, AUSTRALIA calibration. Radar images were kindly provided by the Arecibo Observatory, which is operated by SRI International under a Giorgio Baj cooperative agreement with the National Science Foundation Astronomical Station of Monteviasco (AST-1100968), and in alliance with Ana G. Méndez-Universidad Varese, ITALY Metropolitana, and the Universities Space Research Association. The Arecibo planetary radar program is supported by the National Paolo Bacci Aeronautics and Space Administration under Grant Nos. Astronomical Observatory of San Marcello Pistoiese NNX12AF24G and NNX13AQ46G issued through the Near-Earth Pistoia, ITALY Object Observations program. The “spin frequency/diameter” (Received: 2015 Oct 7) diagram (Fig. 8) is a modification of a graph at the IAU Minor Planet Center web site, which is based on data from the asteroid lightcurve database (Warner et al., 2009). The near-Earth asteroid (436724) 2011 UW158 was followed by an international team of observers on 31 References nights between 2015 Jun 17 and Sep 26. By using the standard lightcurve inversion method with the combined Belskaya, I.N., Shevchenko, V.B. (2000). “Opposition Effect of photometry data set, we obtained a unique spin axis Asteroids.” Icarus, 147, 94-105. solution with ecliptic coordinates . = 290° ± 3°, Gary, B.L. (2014). Exoplanet Observing for Amateurs, Hereford, 4 = –39° ± 2°, a sidereal period PS = 0.610752 ± AZ: Reductionist Publications. 0.000001 h, and a shape model qualitatively consistent with radar observations. Gary, B.L. (2015a). http://brucegary.net/asteroids/ Gary, B.L. (2015b). http://www.brucegary.net/UW158/ Asteroids of size D " 0.15 km generally do not have periods P # 2.2 h, a limit known as the cohesionless spin-barrier. This Gary, B.L. (2015c). http://brucegary.net/SA/ barrier can be explained by the rubble-pile structure model. According to this model, the asteroids are made up of collisional Gary, B.L. (2015d). http://www.brucegary.net/UW158/#Moon breakup fragments bound together only by mutual gravitational force (Pravec and Harris 2000). The exceptions to this “rule,” Gary, B.L. (2015e). http://www.brucegary.net/mags/#Examples called large super-fast rotators (LSFR), are very few; 2001 OE84, (335433) 2005 UW163, and 2011 XA3 are the best known Hapke, B., Denevi. B., Sato, H., Braden, S., Robson, M. (2015). examples. The presence of these objects was theorized for the first http://onlinelibrary.wiley.com/doi/10.1029/2011JE003916/full time by Holsapple (2007). His analysis shows that the cohesion necessary to bind together a rubble-pile asteroid under the spin- Pravec, P., Kusnirak, P., Sarounova, L., Harris, A.W., Binzel, R. barrier value is low, but he does not specifically propose a theory P., Rivkin, A.S. (2002). “Large Coherent Asteroid 2001 OE84”, for how cohesion could arise. These results have been confirmed Proc. Asteroids, Comets, Meteors (ACM 2002), Jul 29 – Aug 02, and enriched by subsequent theoretical studies, such as by Sànchez Tech. Univ. Berlin, Berlin, Germany (ESA SP-500). and Scheeres (2014), in which a model for the origin of the Shevchenko, V.G, (1996). “Analysis of the Asteroid Phase cohesion forces within a regolith has been proposed. The presence Dependencies of Brightness.” Lunar Planet Sci. 27, 1193. of cohesion forces begins to be important only for objects with diameter D < 10 km. So, for small bodies (0.15 km < D <10 km) Shevchenko, V.G. (1997). “Analysis of Asteroid Brightness-Phase with rubble-pile structure, the presence of even a very small Relations.” Solar System Res. 31, 219-234. amount of strength allows much more rapid spin than the simple cohesionless spin-barrier value. Warner, B.D., Harris, A.W., Pravec, P. (2009). “The Asteroid Lightcurve Database.” Icarus 202, 134-146. Updated 2015 Sept. The asteroid 2011 UW158 is a near-Earth asteroid and potentially http://www.minorplanet.info/lightcurvedatabase.html hazardous object. It was discovered on 2011 Oct 25 by the Pan- STARRS observatory at Haleakala (Hawaii, USA). A flyby with the Earth occurred on 2015 Jul 19 at a distance of 0.0164 AU, so this object also became a radar target for Goldstone and Arecibo. This asteroid, with a synodic period of about 37 minutes and an Minor Planet Bulletin 43 (2016) 39 absolute magnitude of about 19.5 (D = 240-740 m) is an example using MPO LCInvert v11.1.0.2 (Bdw Publishing), which of LSFR. This short period was first found by Bruce Gary on 2015 implements the core algorithms developed by Kaasalainen and Jun 17 (see his paper elsewhere in this issue) and independently by then converted to C language by Josef Durech. Julian Oey on Jul 1. Table I shows the instruments used while Table II lists the observing sessions that produced lightcurves used for this analysis. The photometric coverage was dense because our purpose was to determine the pole of rotation and convex shape using the standard lightcurve (LC) inversion method (Kaasalainen et al. 2001; Kaasalainen and Torppa, 2001). In most cases, it is not possible to get a reasonable solution for a pole using LC inversion with photometric observations from one apparition. It may be possible to get an initial solution if, as in the case of ours observations, the total span covers several rotations and a large range of phase angles, the synodic period is well- established, and the photometric data are of good quality. It is also Figure 1. Distribution of phase angle bisector (PAB) for 2011 helpful if the viewing aspect, as measured by the phase angle UW158. Data is from Table 2. bisector, goes through a relatively large range as well. In our case the range of observed phase angle is 62° to 109° and 109° to 20°; Period Search the amplitudes of angle bisector are LPAB = 137° and BPAB = 64° (Fig. 1). The inversion process started by finding the sidereal rotation period of the asteroid. A search in MPO LCInvert was confined to Observer Telescope CCD camera 0.6100 to 0.6115 h, a range that includes the synodic period found Bacci Ref. 0.60-m f/4 Apogee Alta 1024 in the single phased LC, with weight 0.5. However, inclusion of all Baj RC 0.25-m f/8 SBIG-ST10 observations listed in Table II leads to %2 values that are quite high. Carbognani RC 0.81-m f/7.9 FLI 1001E Gary SC 0.35-m f/10 SBIG-ST10XME After some tests, we found that by restricting observations to those Oey CDK 0.61-m f/6.8 Apogee U42 by Gary (in this way the range of the phase angle remains unchanged) and those before Aug 15 for the other observers, the %2 Table 1. Observers, telescopes and CCD camera used. values were reduced to reasonable values. Obs. yyyy/mm/dd Phase LPAB BPAB A (°) (°) (°) (mag) The search process found an isolated, deep, and flat minimum in Gary 2015/06/17 62.3 230.7 -12.9 0.50 the plot of %2 vs. sidereal period (Fig. 2). A renormalization was Gary 2015/06/20 65.7 231.9 -12.5 0.52 2 2 Oey 2015/07/01 79.0 236.4 -9.3 0.67 not necessary since reduced % ~ 1.0 (i.e., N = 24 and sum % is Oey 2015/07/02 80.3 236.8 -9.3 0.67 also ~24). The minimum appears asymmetrical, i.e. the descending Oey 2015/07/03 81.6 237.1 -8.8 0.73 branch is less steep than the ascending branch. For this reason we Oey 2015/07/06 85.8 238.1 -6.7 0.76 assumed the value of the point to the right, Oey 2015/07/08 88.9 238.6 -4.7 0.71 0.6107643 h, for the starting period in the pole search. Gary 2015/07/08 88.9 238.6 -4.7 0.70 Gary 2015/07/12 96.0 239.4 2.3 0.70 Gary 2015/07/20 109.3 269.9 50.6 0.92 Baj 2015/07/23 101.9 314.6 50.5 1.92 Bacci 2015/08/01 82.0 341.4 30.0 2.38 Carb. 2015/08/02 80.4 342.4 29.0 1.96 Gary 2015/08/03 78.9 343.3 28.1 1.95 Gary 2015/08/04 77.5 344.1 27.3 2.05 Carb. 2015/08/11 68.3 348.9 23.4 1.96 Gary 2015/08/13 65.8 350.1 22.6 1.84 Bacci 2015/08/14 64.6 350.7 22.3 1.82 Carb. 2015/08/19 58.6 353.4 20.8 1.62 Bacci 2015/08/20 57.4 353.9 20.5 1.65 Gary 2015/08/29 47.0 357.9 18.6 1.46 Baj 2015/09/05 39.1 0.5 17.3 1.27 Figure 2.