Christopher Magri, Ellen S. Howell, Michael C. Nolan, Patrick A. Taylor, Yanga R. Fernandez, Michael Mueller, Ronald J. Vervack Jr, Lance A.M. Benner, Jon D. Giorgini, Steven J. Ostro, Daniel J. Scheeres, Michael D. Hicks, Heath Rhoades, James M. Somers, Ninel M. Gaftonyuk, Vladimir V. Kouprianov, Yurij N. Krugly, Igor E. Molotov, Michael W. Busch, Jean-Luc Margot, Vladimir Benishek, Vojislava Protitch-Benishek, Adrian Galad, David Higgins, Peter Kusnirak, Donald P. Pray
Icarus 214, 210-227 (2011)
We observed near-Earth Asteroid (8567) 1996 HW1 at the Arecibo Observatory on six dates in September 2008, obtaining radar images and spectra. By combining these data with an extensive set of new lightcurves taken during 2008-2009 and with previously published lightcurves from 2005, we were able to reconstruct the object's shape and spin state. 1996 HW1 is an elongated, bifurcated object with maximum diameters of 3.8 x 1.6 x 1.5 km and a contact-binary shape. It is the most bifurcated near-Earth asteroid yet studied and one of the most elongated as well. The sidereal rotation period is 8.76243 ± 0.00004 h and the pole direction is within 5° of ecliptic longitude and latitude (281°, -31°). Radar astrometry has reduced the orbital element uncertainties by 27% relative to the a priori orbit solution that was based on a half-century of optical data. Simple dynamical arguments are used to demonstrate that this asteroid could have originated as a binary system that tidally decayed and merged.
Fig. 1. Delay-Doppler images of 1996 HW1. OC images obtained on each of the six indicated 2008 observing dates are displayed, arranged chronologically from top to bottom. Each displayed image is the sum of three consecutive runs listed in Table 1, except for the third 21 September image which is the sum of only two runs. (The final sums for 15 and 19 September have been omitted from the figure.) Images are oriented with Earth toward the top and positive Doppler to the right. Each pixel is 0.238 Hz x 0.50 us, corresponding to 0.076 km x 0.075 km at our mean subradar latitude of +9°; each image spans 14.3 Hz x 25.5 us, corresponding to 4.57 km x 3.82 km. All images are on the same grayscale in radar cross section. The asteroid rotated through about 9° during the time (~14 min) spanned by each set of three runs; the resulting smearing can be seen in the second 17 September sum. Individual runs, each one covering only 3° of rotation, were used as input to shape modeling and are shown as the "obs" images in Fig. 2.
Fig. 2. 1996 HW1 delay-Doppler images and model. Every second OC image is displayed, with the corresponding synthetic image from the model fit shown to its right, and the corresponding plane-of-sky (POS) rendering of the shape model shown to the right of the synthetic image. The actual and synthetic delay-Doppler images have the same orientation, pixel dimensions, and overall dimensions as do the images displayed in Fig. 1. Here, however, many noise pixels in the actual images have been masked out and appear black, causing the image outlines to appear irregular. The grayscales for the actual and synthetic images have the same maxima, with radar cross section values of 0.009 km^2 per pixel or more mapping to bright white. To enhance visual clarity the grayscale for the actual images has been set to deemphasize low-level noise; this has not been done for the synthetic images in order to display the weak features that could be observed in the limit of noise-free data. In the POS frames, north is up and east is to the left. Each POS frame is 5.0 km on a side, and each pixel is 0.025 km on a side. The sidereal spin vector is denoted by an arrow. POS renderings use Lambert scattering, producing somewhat stronger limb-darkening than would the best-fit radar scattering law. In each panel time increases from top to bottom and then from left to right; the end of each of the six observing dates is marked by a horizontal white line. The final images obtained on 15 and 19 September have been omitted from the figure.
Fig. 3. 1996 HW1 CW spectra and model. (a) Echo power, in units of standard deviations of the noise, is plotted vs. Doppler frequency (Hz) relative to that of hypothetical echoes from the target's center of mass. Each of the sixteen OC spectra is displayed as a solid line, with the corresponding synthetic spectrum from the model fit superimposed as a dashed line. All plots have identical axis scales, shown on the plot at lower left. The vertical bar at the origin indicates ±1 standard deviation of the noise. Each label gives the 2008 o bserving date and the CW run number on that date. All spectra are displayed at the raw frequency resolution of 0.20 Hz. (b) Plane-of-sky (POS) renderings of the shape model at or near the midpoint of the CW observations for each of the six observing dates. Each rendering's size, orientation, and adopted scattering law is the same as for the POS views in Fig. 2.
Fig. 4. 1996 HW1 lightcurves and model. The x-axis represents rotation phase, with plane-of-sky motion taken into account and the zero-phase epoch as given in the notes to Table 1. Units on the y-axis are magnitudes, although our modeling software minimized chi-square in intensity space rather than magnitude space. Each plot spans 1.50 mag. Data points for each lightcurve are displayed as crosses and the corresponding synthetic lightcurve is displayed as a solid curve. No correction for solar phase angle has been applied to the data. Each lightcurve is labeled by the observing date and, in cases of multiple lightcurves on the same date, by the photometric filter (for absolute photometry), the observatory (CHO = Carbuncle Hill, HHO = Hunters Hill), or a sequence number (for lightcurves obtained at the same observatory).
Fig. 5. Views of our best-fit 1996 HW1 model along its principal-axis directions. The rendering uses a Lambert backscattering law and has been effectively smoothed as described by Magri et al. (2007, Section 3.1.2); hence the triangular facets are not visible. Yellow-shaded regions are those that the radar never viewed or else viewed only at scattering angles greater than 60°, ensuring nonexistent o r weak contributions to the radar images and spectra. (Lightcurve observers viewed the entire surface such that both the incidence angle and the scattering angle were less than 60°, except for one tiny r egion near the north pole.)
Fig. 6. Pole-on view of 1996 HW1 showing the locations of the four synchronous orbital equilibria in the equatorial plane, overlain on a contour plot showing values of the geopotential above and on the surface of 1996 HW1. A hypothetical particle placed at any of these equilibrium points with zero speed in the co-rotating 1996 HW1 frame will experience a net zero acceleration in the co-rotating frame and, in an inertial frame, would describe a circular orbit exactly synchronous with 1996 HW1's rotation rate. For 1996 HW1 all four of these circular orbits are unstable, meaning that any particle placed in such an orbit would not remain in that orbit indefinitely. The geopotential for 1996 HW1 is the sum of the gravitational potential plus the rotational potential. The lowest point of the geopotential on the model's surface (depicted in blue) is located in the area between the components, while the highest points on the geopotential (depicted in green) occur at the ends of the asteroid.
Last update: 2011 October 04