The accuracy of proper orbital elements and the properties of asteroid families: Comparison with the linear theory

The accuracy and reliability of the proper orbital elements used to define asteroid families are investigated by simulating numerically the dynamical evolution of families assumed to arise from the “explosion” of a parent object. The orbits of the simulated family asteroids have then been integrated in the frame of the elliptic restricted three-body problem Sun-Jupiter-asteroid, for times of the order of the circulation periods of perihelia and nodes. By filtering out short-periodic perturbations, we have monitored the behavior of the proper eccentricities and inclinations, computed according to the linear secular perturbation theory. Significant long-period variations have been found especially for families having nonnegligible eccentricities and/or inclinations (like the Eos family), and strong disturbances due to the proximity of mean motion commensurabilities with Jupiter have been evidenced (for instance, in the case of the Themis family). These phenomena can cause a significant “noise” on the proper eccentricities and inclinations, probably affecting in some cases the derived family memberships. They can also give rise to a spurious anisotropy in the fragment ejection velocity fields computed from the dispersion in proper elements observed in each family, and this could explain the puzzling anisotropies of this kind actually found in real families by D. Brouwer (1951, Astron. J. 56, 9–32) and by V. Zappalà, P. Farinella, Z. Knežević, and P. Paolicchi (1984), Icarus 59, 261–285).