Collisional origin of the asteroid families: Mass and velocity distributions

The origin of asteroid families in terms of collisional breakup is analyzed using the data by Williams (1979, in Asteroids (T. Gehrels, Ed.), pp. 1040–1063, Univ. of Arizona Press, Tucson). The distributions of mass and relative velocity of the minor family members with respect to the largest body are derived. These ditributions are then compared with the outcomes of catastrophic impacts, predicted from theoretical arguments and observed from laboratory experiments. The general features of the mass distributions can be interpreted in terms of collisional disruption of a parent body followed by self-gravitational reaccumulation on the largest remnant; no decisive evidence for multiple reaccumulations is found. The typical ejection velocities of the family members are of the same order as those of laboratory fragments; since the definition of families is based on purely dynamical arguments, this results gives direct observational support to the collisional formation hypothesis. The transition between collisional outcomes dominated by solid-state forces and by self-gravitatation, expected to occur at diameters D ～ 100 km on the basis of rotational studies and of theoretical estimates, is clearly confirmed by the present analysis. A “morphological” classification into three broad classes (asymmetric, dispersed, and intermediate) is introduced; it is based on the distribution of mass vs relative velocity, taking also into account the parent body's (and the largest remnant's) escape velocity. Finally some results are outlined which apparently do not fit the theoretical predictions: (1) the degree of fragmentation in real families is generally lower than that observed for experimental targets and (2) when the relative velocities are computed, including also proper eccentricity and inclination differences, values higher by about a factor 4 than those derived from semiaxes differences only are found. Further studies are proposed, including more observations, better proper elements computation and classification methods, and new investigations on the physics of hypervelocity impacts.