The Size Distributions of Asteroid Families in the SDSS Moving Object   Catalog 4
  Asteroid families, traditionally defined as clusters of objects in orbital parameter space, often have distinctive optical colors. We show that the separation of family members from background interlopers can be improved with the aid of SDSS colors as a qualifier for family membership. Based on an ~88,000 object subset of the Sloan Digital Sky Survey Moving Object Catalog 4 with available proper orbital elements, we define 37 statistically robust asteroid families with at least 100 members using a simple Gaussian distribution model in both orbital and color space. The interloper rejection rate based on colors is typically ~10% for a given orbital family definition, with four families that can be reliably isolated only with the aid of colors. About 50% of all objects in this data set belong to families, and this fraction varies from about 35% for objects brighter than an H magnitude of 13 and rises to 60% for objects fainter than this. The fraction of C-type objects in families decreases with increasing H magnitude for H > 13, while the fraction of S-type objects above this limit remains effectively constant. This suggests that S-type objects require a shorter timescale for equilibrating the background and family size distributions via collisional processing. The size distributions for 15 families display a well-defined change of slope and can be modeled as a "broken" double power-law. Such "broken" size distributions are twice as likely for S-type familes than for C-type families, and are dominated by dynamically old families. The remaining families with size distributions that can be modeled as a single power law are dominated by young families. When size distribution requires a double power-law model, the two slopes are correlated and are steeper for S-type families. 
Alex H. Parker, Zeljko Ivezic, Mario Juric, Robert H. Lupton, Michael   D. Sekora, Adam F. Kowalski