3.5 Families

The new set of synthetic proper elements is accurate enough to enable the study of the dynamical features of individual families. Such studies have been conducted in the recent past (e.g. family of Veritas; see Milani and Farinella [1994]; Milani et al. [1997]; Knezevic and Jovanovic [1997]; Nesvorný and Morbidelli [1998]; Knezevic [1999]) in the framework of dedicated projects, but now one can recognize many interesting features by simply looking at suitably prepared plots. Many of these features, so far hidden and/or smeared out by proper elements not accurate enough, became visible due to better resolution provided by new elements.

  

Figure: The region of the Koronis and Eos families. Dots stand for asteroids with good proper elements, crosses are objects with large errors in proper eccentricity and inclination; chaotic asteroids are marked with open circles - a dot inside the circle indicates stable chaos cases with satisfactory proper eccentricity and inclination, while a cross inside the circle indicates that chaotic diffusion disturbed also eccentricity and inclination.

The chaotic orbits are included in the family envelopes as projected on the ($a,\sin I$) space, for example, especially within the largest families like Koronis, Eos and Themis, but also within the small, compact ones, like Hygiea and Veritas. Mean motion resonances cross the families giving rise to chaotic diffusion, and this causes the family members to spill out from the regions occupied by the families, mostly because of diffusion in the e_p direction.. Thus, even if genuine fragments belonging to the families (possibly formed billions of years ago), they do not belong to the family cluster as they can be identified with the present orbits. Such objects are crucial for the studies of the post-formation dynamics of fragments and could be counted in the family membership. On the other hand, they should not be used for the reconstruction of the breakup relative velocity fields, not to mix chaotic diffusion with relative velocities acquired at breakup.

  

Figure: The region of the Themis and Hygiea families. Dots stand for asteroids with good proper elements, crosses are objects with large errors in proper eccentricity and inclination; chaotic asteroids are marked with open circles.

As an example we show on Figure 10 the region in the (a_p,e_p) plane where the Koronis and Eos families are located. Some alignments of chaotic objects, possible ex-members of the families, along the resonant lines is clearly visible. The spillover from Koronis family due to chaotic diffusion seems to be responsible for at least part of the so-called Prometheus surge at $\sim 2.9$ AU, while the 9:4 resonance affects Eos at $\sim 3.03$ AU, with spillover both to higher and lower eccentricities (compare with Morbidelli et al., [1995]). Another example is shown in Figure 11, where the region with 3.05<a_p<3.24 AU and $\sin I_P<0.1$ contains the Themis and Hygiea families and is crossed by several mean motion resonances. It is clear that the spillover from the Themis family can extend a long way.