2 Observations and data reduction

   
2.1 Strategy

The ephemerides of the targets at the epochs of their observations and the observing logs are given in Table 1. The observations were carried out using the FGS astrometer ( FGS#3 for all objects, with the exception of (216) Kleopatra, observed by FGSR#1). In order to improve the signal-to-noise (S/N) ratio, the multiple scan merging strategy used by Lattanzi et al. (1997) was followed. Four to six consecutive scans were made before each re-centering; this set of target acquisition and observation is called a "visit''. Each object was observed during a whole HST "orbit'', i.e. a sequence of visits distributed all along a continuous visibility period of the asteroid as seen from HST. The position angle of the FGS axes did not change during the orbit. The FGS was used with a step delay of 0.025 s. Each sampling step was 1.0 or 1.5 mas, with a total scan duration of 160 or 120 s, respectively. Only in the case of (624) Hektor, was the sampling step 2.4 mas, and the total scan duration 150 s. In all cases, these parameters correspond to a total scan length of 2 arcsec. All observations were performed with the PUPIL filter which - although penalizing in limiting magnitude - reduce the negative effect of the spherical aberration of HST optics.

Due to the limited time-allocation, only a relatively small fraction (5-10%) of the total spin period, corresponding to the duration of each orbit, is covered by the observations. Since the main purpose of this program was the detection of nearly-contact binary systems, the asteroids were observed near their predicted light-curve maximum, approximately corresponding to the maximal apparent separation of possible components. The observations of each object were carried out at an epoch corresponding to a given value of the aspect angle $\xi$. As a consequence, the complete three-dimensional shape of the asteroids cannot be completely and unambiguously retrieved. In particular, assuming for the sake of simplicity that an object is a perfect triaxial ellipsoid with axes a>b>c observed at the epoch of the maximum light-curve, one should expect that the projected area on the sky will be an ellipse, having axes equal to a (longest apparent axis) and $\sqrt{b^2 \cos^2{\xi} + c^2 \cos^2{\xi}}$ (shortest axis), respectively. According to the value of the aspect angle $\xi$, the relative contribution of the semiaxes b and c to the corresponding shortest axis of the projected ellipse varies significantly, although one could expect a priori that a pole-on view (leading to full determination of b and complete indetermination of c) is rarely achievable in practice, whereas an aspect closer to equatorial view (corresponding to full determination of c and complete indetermination of b) is more likely. In principle, having the possibility to follow an object during a significant fraction of its rotation period would lead to a much better determination of the overall shape. In our observations, we have tried to maximize the information coming from the slow, steady change of the apparent ellipse projected by each object, although it is clear that a longer available observation time would have allowed us to carry out a much better reconstruction of the true three-dimensional shapes.

The recorded signal is an "S-shaped'' curve (usually called an "S-curve'') whose detailed shape depends upon the target size, shape, and surface brightness distribution. As explained in detail in Paper I, the "S-curve'' allows us to distinguish a close binary object, such as those searched for by this observing program. Many examples are shown in this paper (Figs. 7-14) and discussed in the text in the following Sections.

   
2.2 Data reduction

As explained in Paper I, the data over successive scans (corresponding to less than 5 mn of time) are merged to obtain a higher S/N ratio. For (624) Hektor, a smoothing of data by low-pass filtering was performed before merging. A single S-curve is thus obtained for each FGS axis and each visit. Because the targets were at a few AU distance, the data were corrected for the apparent motion of the target during the scan, produced by the displacement of the HST platform along its orbit. This correction corresponds to a re-scaling of the FGS-axis abscissa. Synthetic S-curves are subsequently calculated by convolution of a template transfer function with a shape model, taking into account a specific brightness distribution. Different template files acquired in 1998 and 1999 have been made available by the STScI. They were acquired in 1998 and 1999 and correspond to stars Upgren 69 (B-V=0.5, file f44v0702m in the calibration database) and HD 233877 (B-V=1.1, file f43p0501m), whose color indexes are close to that of a typical asteroid. No use is made of piecewise interpolated data, but the value of T(x) for any abscissa x is obtained by linear interpolation. Except for the asteroid (216) Kleopatra, the calibration data obtained in 1998 for the HD 233877 star was used for the transfer function.

Concerning single body shape models, only perfect triaxial ellipsoid shapes have been considered in this analysis. On one hand, this is justified by the purpose of finding basic information on the overall shapes of the objects, avoiding as a first step excessive and unnecessary complexity; on the other hand, the limited coverage of the rotational phase and the single aspect angle covered by the observations do not permit us to analyze much more complex models. As we will see, simple shapes are sufficient, in general, to reproduce the overall features of the observations, and to identify interesting discrepancies when present. Finally, for what concerns possible binarity, we assumed that the binary components are triaxial ellipsoids in synchronous rotation, with major axes mutually aligned and parallel spin axes, accordingly with the original idea of possible equilibrium models suggested by available light-curves (Cellino et al. 1985).