The random walk evolution of asteroid families

The dynamical evolution of asteroid families is determined by a range of mechanisms that include: (1) catastrophic collisions, (2) changes in spin direction and (3) evolution of the semimajor axes driven by Yarkovsky radiation forces, but the timescales of these mechanisms are uncertain. Yarkovsky evolution of family asteroids in a-1/D space can result in a V-shaped distribution that can be used to estimate the age of the family. However, these age estimates assume that the asteroids in the extreme limits of the V-shape have evolved without change in mass or spin direction. Here, we explore the evolution of older families for which these simplifying assumptions may not be valid. For older families, the evolution of the semimajor axes may be more like a random walk. Consequently, the spread in the semimajor axes is very much reduced and this results in an increase in the estimated age of the family.