2 Observations

Kleopatra was observed by one of us (F.M.) using the ADONIS system on October 25, 1999 from 6.7 to 7.4 h UTC (i.e. over approximately one eighth of its 5.385 hr rotational period). Observations were performed in the near infrared using the SHARPII+ camera in the Ks band ( $\lambda = 2.154~\mu$m, $\Delta\lambda = 0.323~\mu$m) and with a 35 mas/pixel scale (corresponding to 30.5 km/pixel at 1.2 AU). Wavefront sensing was performed at optical wavelengths using Kleopatra itself as the reference. The object brightness ( $m_V \sim 9.7$) and predicted angular diameter (less than 0.2 arcsec) made it an excellent target for adaptive optics observations during a night characterized by good and stable seeing conditions ($\sim$0.6 arcsec). In order to enhance the signal-to-noise ratio, each image used for the analysis is the result of adding 32 single exposures, corresponding to a total integration time of approximately 2.7 min. During the night, an image of a single star was also taken in order to obtain a point-spread function ( PSF), required to estimate the observation quality and to apply further deconvolution procedures. The Full Width at Half Maximum (FWHM) of the PSF (0.14 arcsec) and the relatively good Strehl ratio (SR= 22%) indicate that, although the AO correction is not perfect, the signal-to-noise ratio is high enough to ensure that the deconvolution is reliable. Subsequent observations were obtained in the same band and following the same procedure on December 3, 1999 from 2.1 to 2.4 UTC with lower quality and degraded resolution.

In addition to the usual MLR technique, the MISTRAL (Myopic Iterative STep-preserving Restoration ALgorithm) deconvolution technique (Conan et al. 1998, 1999), specially adapted to planetary objects, was applied. The main difference between this technique and other more "classical'' methods is the avoidance of both noise amplification and creation of sharp-edges artifacts or "ringing effects'', and better restoration of the initial photometry. However, since the actual PSF is unknown, two basic parameters representing the image noise and the object sharpness need to be optimized. The restored images however are not highly sensitive to these two parameters. On the other hand, simulations show that different shape models would produce similar restored images with two separated spots. Figure 1 displays the basic and restored images of the October run. The restored images display a well separated binary system. The two components have similar sizes and magnitudes with a measured flux ratio $F=0.81\pm 0.03$. These confirm the bimodality of the spectral signature from radar observations (Mitchell et al. 1995; Ostro et al. 2000) and the characteristic interferogram shape of the HST/FGS observations (Tanga et al. 2001). Nevertheless the resolution limit together with the pixel scale, and to a lesser extent the PSF variability, limit the accuracy of the deconvolved-image model. Simulations of our present observations show that we cannot preclude a dumbbell-shaped model.

Figure 2: Simulated and restored images for three shape models (see text) from the VLT/NAOS adaptive optics system. The first row shows the simulated pixel-sampled shape. The observed image is the result of the convolution with the instrument PSF. The last three rows give the restored image when applying the MISTRAL and MLR techniques. The restored images are presented on a linear scale. The small insets provide the residuals: deconvolved minus perfect images.

Figure 3: Same as Fig. 2 for an Hektor-type asteroid in the H band. Only the restored images using the MISTRAL procedure are shown. The last row is a display of two PSFs used for the simulation of the observations of Hektor and Kleopatra. Note the presence of several Airy rings for the brightest star.

Our estimated pole direction of $\lambda=72\hbox{$^\circ$ }$ and $\beta=23\hbox{$^\circ$ }$ for the ecliptic B1950 coordinates matches within $\pm 5\hbox{$^\circ$ }$ the observed orientation of the majority of the observations found in the literature. In the case where the two apparent lobes are well separated with a center-to-center separation of 129 km and an orbital period equal to the known rotation period, the binary system would have a total mass of $3.4\times10^{18}~$kg. The component separation being close to the Roche limit, mutual tidal distortions are expected to occur. Under the assumptions of two Roche ellipsoids of fluid in hydrostatic equilibrium and in synchronous orbit (Leone et al. 1984), the measured flux ration F, together with an assumed maximum amplitude $A=0.9\pm0.25$ (Zappalà et al. 1983), yields a density in the range of 4-5 g/cm³ (assumed to be the same for each body). Such a relatively large value for the bulk density suggests that the M-type asteroid Kleopatra contains a significant fraction of metals. This seems realistic for a rubble-pile body (i.e. of non negligible porosity) composed of differentiated material, but it does not preclude a monolithic-like body. It is moreover consistent with the asteroid surface bulk density (>3.5 g/cm³) determined by Ostro et al. (2000) and marginally consistent with the value of (3.9 g/cm³) predicted by Cellino et al. (1985). Depending on its actual nature, the non family-member asteroid Kleopatra could be the result of a catastrophic collision inducing binary fission (Hartmann 1979; Farinella et al. 1982) or the result of a more subtle collision (Leinhardt et al. 2000).