Astron. Astrophys. 338, 340-352 (1998)

3. Properties of the individual asteroids

An overview of the model parameters is provided in Table 1. The shape, the spin-vector and the HG values are the essential input parameters for the thermophysical modelling. The shape is generally described as an ellipsoidal with the axis ratios and . Only for 4 Vesta a more sophisticated shape model, based on HST results (Thomas et al. 1997), could be used. The rotation periods vary from a few hours to more than one day. The spin-vector can not always be derived unambiguously from lightcurve observations (Magnusson et al. 1989). The limited observational coverage for 10 Hygiea, 54 Alexandra, 65 Cybele and 313 Chaldaea leads to an ambiguous solution (A. Erikson, priv. communication, 1997). Müller  (1997) investigated the effects of both spin-vector solutions on the basis of ratios between observations and predicted fluxes. The parameters which produced the lowest scatter in the ratios were considered as the more realistic solution.

Table 1. Size, shape, spin-vector and magnitude input parameters. The values are based on direct measurements and lightcurve observations. The asteroids are divided into primary (top) and secondary (bottom) targets, as discussed in the text. The values in parenthesis are considered to be less reliable.

We use the IAU two-parameter magnitude system for asteroids (Bowell et al. 1989), termed also as the HG-magnitude system. H is the absolute magnitude, G is the slope parameter. Both values are used to derive radiometric diameters and albedos from observational data.

1 Ceres The H and G have been determined from several apparitions, with good coverage at small phase angles (Lagerkvist et al. 1992). The weighted mean of H from available apparitions is used here. The size and shape of Ceres have been determined from occultation observations combined with previous diameter measures and extensive photoelectric photometry (Millis et al. 1987). There exists also a lower accuracy shape model based on speckle observations (Schertl et al. 1995), which is not used here. Considering the very low amplitude of the Ceres lightcurve (Tedesco et al. 1983), less than , it is quite difficult to extract a pole position by the classical method of lightcurve inversion. We use a prograde spin vector, perpendicular to the ecliptic (, ). This is in good agreement with the conclusions of Millis et al. (1987), Spencer et al. (1989) and also with the considerations of Saint-Pe et al. (1993). Merline et. al. (1996) found indications for surface albedo variations on Ceres from HST imaging. They are not taken into account in the following.

2 Pallas The H and G values are taken from Lagerkvist et al. (1992). There exist two occultation observations (Wasserman et al. 1979; Dunham et al. 1990) and some speckle data (Drummond & Hege 1989). We adopted the most accurate value (Dunham et al. 1990). The results for the minor axis and vary significantly and do not agree within the given error bars. In order to match all lightcurve observations we accepted the and ratios and the spin-vector from a lightcurve analysis (Erikson 1998, P. Magnusson, priv communication, 1997).

3 Juno Piironen et al. (1997) presented HG-fits for Juno based on several recent apparitions and derived reliable weighted means. The asteroid cross section has been directly determined during an occultation event (Millis et al. 1981) and with speckle interferometry (Baier & Weigelt 1983). The values of the calculated largest axis agree within , but in both cases no has been determined. We put the occultation value in Table 1 in parenthesis since it is only related to an instantaneous cross section and not to a full 3-dimensional ellipsoid. The shape and spin vector are in accordance with the available lightcurve data (Erikson 1998, P. Magnusson, priv communication, 1997).

4 Vesta For Vesta we combined the HG results from Piironen et al. (1997), Lagerkvist et al. (1992) and Lagerkvist & Magnusson (1990). There are several publications about occultation measurement (Dunham 1991), speckle observations (Schertl et al. 1995; Tsvetkova et al. 1991) and a combination of different methods (Drummond et al. 1988; McCarthy et al. 1994) with a reasonable agreement in results of size and shape. From Hubble Space Telescope images it has, however, been possible to determine the spin vector and detailed shape of Vesta (Thomas et al. 1997, see also "note added in proof"). The derived detailed shape model is available from a WWW-page (Stooke 1997), and was used instead of an ellipsoid. Binzel et al. (1997) derived a relative albedo map of the Vesta surface. Since there are no absolute albedo values assigned, it is not possible to apply it in our procedure. The albedo variations will cause a different temperature distribution on the surface and correspondingly alter the flux. Since the far IR fluxes are dominated by the cross section at the time of the observation, it will only be a second order effect in our aimed wavelength range beyond .

10 Hygiea Piironen et al. (1997) derived reliable HG-values based on 3 apparitions with observations at very small phase angles. The shape and spin vector are taken from Erikson (1998) and P. Magnusson (priv. communication). For Hygiea is only a single-chord occultation with a lower limit for the diameter available (D. Dunham, 1997, priv. communication).

54 Alexandra For Alexandra we use a default value of based on its taxonomic type (Lagerkvist & Magnusson 1990). Under that assumption it was possible to calculate a mean H value from normalised magnitudes given in Belskaya et al. (1993). The shape and spin vector are taken from Belskaya et al. (1993), Erikson (1998) and P. Magnusson (priv. communication, 1997). There exists no published direct diameter value.

65 Cybele The H and G are taken from Lagerkvist & Magnusson (1990), with H as the mean value of 4 apparitions. Taylor (1981) published a low quality occultation observation of Cybele with only 3 chords over the full cross section, the value in Table 1 is therefore in parenthesis. The shape and spin vector are taken from Erikson (1998).

106 Dione For Dione we use a default value of based on its taxonomic type (Lagerkvist & Magnusson 1990). The absolute magnitude H has been calculated to (A. Erikson, priv. communication, 1998). The major axis is taken from one occultation measurement (Kristensen 1984). Since there exists no spin-vector solution we take a default spin-vector of and , and assume and to reproduce the occultation cross section and to avoid artificial lightcurve variations.

313 Chaldaea The Chaldaea H, G values as well as the shape and spin-vector are given in Erikson (1998). There exists no published direct diameter value.

532 Herculina Lagerkvist et al. (1992) derived H and G values based on four apparitions. For H we calculated the mean magnitude. The available occultation measurement produced only a 2-dimensional cross section (Bowell et al. 1978), whereas a sequence of speckle observation (Drummond et al. 1985) lead to a 3-dimensional ellipsoidal shape model. In Table 1 we included (in parenthesis) the largest axis from the speckle results. The shape and spin-vector information is in agreement with the lightcurve observations (Michalowski 1996).

© European Southern Observatory (ESO) 1998

Online publication: September 8, 1998
helpdesk.link@springer.de