4 Discussion

The epochs at which the HST/FGS and radar data were taken differ by about two months from each other, hence the aspect angle did not significantly change between the two observing runs. The overall sizes of the radar nominal model are coherent with the HST/FGS data, but significant departures from the observations are also present in Fig. 4. It is a known characteristic of the FGS interferogram that the largest the object, the largest the flattening of the S-curve. Thus changing the scaling of the radar-derived model in one direction will change the shape of the computed interferogram. We hence have derived computed interferograms for increased sizes of the nominal 3-dimensional model along its principal axes. It appears that the goodness of fit, for both FGS axes, is somewhat increased, particularly in the last visits, when increasing the flattening of the nominal model by about 20%. This corresponds to an increase of the largest dimension parallel to the principal axis of 43 km, compatible with the uncertainty of the radar model. It would moreover result in a more elongated body in agreement with the result obtained in previous Sect. 3.2, and coherent with the stellar occultation data of Sect. 3.1.

The FGS data are limited to a single epoch and cover approximately 45 min, thus they do not test the whole structure of the radar-derived model. In addition to the nominal 3-dimensional topographic model, some parameters such as those describing the scattering of light at the surface, possible albedo variations, and the rotational phase angle have to be introduced in this analysis. However, we have verified that changing the light-scattering law or variations in its associated parameter, as well as variations in the zero rotational phase-angle of a few degrees have little effect on the interferogram shape, while albedo features must be large and important to significantly change the overall shape of the computed S-curves. Hence, reasonable errors in the above approximations should produce only second order effects on the modeled lightcurves and S-curve shapes, and cannot exclusively explain the discrepancy between the radar-derived model and these independent observations. Nevertheless, a larger and more elongated body-model could be more consistent with the occultations, the photometric and the interferometric HST/FGS results. This suggests that Kleopatra's modeled overall size and shape flattening are likely underestimated to be fully compatible with the whole set of observations available for this object. Also the accuracy in size and shape of the present model could be improved by combining all these observations and in particular the radar and FGS data.

Figure 4: Comparison between the observed HST/FGS data and the radar model. The computed interferogram (see text) is plotted (line) against the observed one for five selected visits and for both FGS axes (X on the left side, and Y on the right). The UTC (hours and decimals) of the observations are given in the small box.

Interestingly, the radar data (Ostro et al. 2000) and the adaptive optics data (Marchis et al. 1999) might be consistent with the presence of an empty gap in the middle of the asteroid, hence closer to a separated binary model. On an other hand, a simple model of a non-convex single-object consisting of two "overlapping ellipsoids'' (i.e. the shape is modeled by the union two ellipsoids whose center-to-center separation is less than the sum of the semi-major axes) provides a better fit to the HST/FGS data (Tanga et al. 2001). The latter model also better reproduces the large amplitude of the lightcurves given in Fig. 2. However, it does not completely match neither the observed stellar occultation chords, nor the detailed features of the observed lightcurves of this body. In particular the size of the medium and shortest axes of the Tanga et al. (2001) model are underestimated, while the longest axis fits inside the limits of the 1991 occultation. Other observations with the HST/FGS astrometer at different aspect angle would be needed to better constrain the shape in those directions.