Considering that the S/N ratio measured on the averaged S-curves is >10 for all the objects, with the exception of (624) Hektor, the technique of data reduction proves to be sufficient to extract relevant shape information from our data. As explained in Paper I, we recall here that, when fit residuals are as low as in the case of (63) Ausonia, the sensitivity of size estimates reach a level of 1-2 mas, at least on favorably projected directions.
The available data allow us to test the binary structure hypothesis, providing valuable information on the asteroid size. For instance the tentative binary models of Cellino et al. (1985), that would be in satisfactory agreement to observed light-curves, would give too large diameters ratio to be coherent with our HST/FGS data. Also, the inversion procedure applied here, which considered only ellipsoidal figures, provides good indication on the presence of unmodeled shape and/or brightness anomalies, as it can be seen in the cases of (15) Eunomia and (63) Ausonia.
None of the asteroids of this program appears to be a well separated or nearly-contact binary system, with components of similar size, as expected from a binary fission model. Except for (216) Kleopatra, which is best represented as two overlapping ellipsoids (hence resembling a nearly-contact binary structure), the observed asteroids turn out to be, on average, not very different from single triaxial ellipsoids, although some appreciable discrepancies with such a simple shape model are apparent in some cases, as quoted above. For instance, a better fit solution is obtained for (15) Eunomia when considering a single egg-like shaped convex body, while for (43) Ariadne, a contact-binary non-convex shape would provide a better fit to the data. Kaasalainen et al. (2002) give a convex conical shape-model of (44) Nysa that they suggest to be the signature of a contact structure whose components have different sizes. A more extensive test of such an hypothesis from the HST/FGS data will be done in a forthcoming work.
As for the absolute precision of the size measurements, those derived represent probably lowest boundary values, since we considered uniform brightness distributions. In fact, introducing an a priori limb-darkening would result in slightly larger sizes. Adopting a realistic Minnaert parameter of k=0.6 the size is approximately 3% larger. This would lead to an improved agreement with nominal IRAS results, but in cases, like (216) Kleopatra, in which the resulting shape is very far from a sphere. It is also clear, in any case, that a better determination of the most uncertain axis lengths would be needed to carry out a more detailed comparison with published size data.
In this respect, a whole shape reconstruction at the highest precision reachable by HST/FGS would offer a precious insight on the real shape of these asteroids. Unfortunately, our model-fitting inversion procedure is limited by the short available observing time. This was generally long enough to provide useful indications on the three-dimensional shape of the bodies, but it was nevertheless shorter than 10% of the rotation period. Moreover, our observations of each object were limited to a single value of the aspect angle. Obviously, more data covering different observing geometries could allow us to retrieve a more complete model of asteroid shapes at the available resolution. In particular, observations made at different aspect (and rotation) angles could be combined to eliminate the limited resolution that is possible in the determination of some of the principal axes. A further level of investigation will require us also to combine HST data with observations made by other techniques (e.g. radar observations Hudson & Ostro 1994 or light-curve inversion Kaasalainen & Torppa 2001). For instance, light-curve amplitudes can help to constrain the surface scattering parameters for a given ellipsoid. Furthermore, photometry can suggest asymmetric shapes that could justify the differences observed between primary and secondary extrema. This refinements represent, in fact, the next step in an analysis that should eventually lead to a reduction process that takes consistently into account, both photometry and HST/FGS interferograms at the same time.
The reduction of the residual uncertainties would allow us to compare the
obtained models to the equilibrium figures for fluid bodies (rubble
piles) as
suggested by Farinella et al. (1981). The available data seem to indicate
that the observed asteroids would resemble prolate spheroids (i.e. 
), which, although not being part of the Jacobi sequence, would
suggest low bulk densities. When dealing with rubble pile structures,
which are not ideal fluid bodies,
however, one should also consider the possible role of internal
friction, as suggested by Holsapple (2001), leading to
more realistic bulk-densities and macroscopic porosities.
Copyright ESO 2003