2 The Themis family

Themis family is located in the outer part of the main belt with proper semi-major axis in the region from 3.06 to 3.23 AU. The orbits have relatively high eccentricities and small inclinations. The Themis family, as determined by Zappalà et al. (1995) has 550 members: four - 24 Themis, 90 Antiope, 171 Ophelia, and 268 Adorea - with a diameter greater than 100 km, ten with diameter in the range 50-100 km while the remaining are smaller than 50 km. The expected size limit of completeness for this family corresponds to 20 km (Zappalà & Cellino 1995). According to Migliorini et al. (1995), the expected number of interlopers is relatively low, even if one or two can be expected at sizes as large as 40 km.

The distributions of the proper elements in the a-e, $a-\sin(i)$ and $e-\sin(i)$planes are shown in Fig. 1, using Milani & Knezevic (1994) proper elements. In this figure the sizes of the circles are proportional to the diameter of the objects and the open circles indicate objects observed in the present work. The two stars indicate objects which might be interlopers as will be discussed in the next section. A core-halo structure, in which a dense "core'' is surrounded by a "halo'' of decreasing density, was initially described by Williams (1979, 1992). However, more recent studies do not present such a distribution but mostly a vertical dispersion at the border coincident with the 2/1 resonance. Zappalà et al. (1995) even introduce the denomination of "tribe'' for this family due to its particular space distribution.

  

Figure 1: Distribution of the Themis family in proper elements phase space: a) semi-major axis $\times$ eccentricity, b) semi-major axis $\times$ sine of inclination, and c) eccentricity $\times$ sine of inclination. The size of the circles is proportional to the diameter of the objects and the open circles indicate those observed in the present work (available on-line)

Since the pioneer work of Hirayama (1918) it has been assumed that families of asteroids are the outcome of one, or more, large impact of a body with a smaller "projectile'' leading to the complete fragmentation or to the erosion of the parent body. From a statistical point of view this hypothesis is confirmed by the clustering observed when the planetary perturbations are removed, i.e., in the proper elements phase space. In this sense Themis family is undoubtedly one of the most reliable. However, the breakup mechanism which originated any family, as well as the subsequent evolution of its fragments, still rely on a wide set of working hypotheses and initial parameters which may not be the real ones (see, for example, Farinella et al. 1982; Fujiwara 1982; Zappalà et al. 1984; Davis et al. 1985; Farinella & Davis 1992; Bottke et al. 1994; Marzari et al. 1995). Notwithstanding the limitation of these models, some hypotheses on the Themis family formation are mostly accepted: i) The parent body was completely disrupted; ii) The family is the outcome of a very energetic collision, probably unique in all the asteroid belt, with original parent body and projectile of 380 km and 190 km, respectively (Marzari et al. 1995); iii) Such a collision has a very low probability to occur over the age of the Solar System; iv) The large remnants are probably "rubble-piles'' shaped by their self-gravitation (Fujiwara 1982; Farinella et al. 1982). The mineralogical characterization of Themis family members' surfaces can, therefore, help to constrain the collisional model of its formation.