Observational Constraints on the Catastrophic Disruption Rate of Small Main Belt Asteroids

We have calculated 90% confidence limits on the steady-state rate of catastrophic disruptions of main belt asteroids in terms of the absolute magnitude at which one catastrophic disruption occurs per year (HCL) as a function of the post-disruption increase in brightness (delta m) and subsequent brightness decay rate (tau). The confidence limits were calculated using the brightest unknown main belt asteroid (V = 18.5) detected with the Pan-STARRS1 (Pan-STARRS1) telescope. We measured the Pan-STARRS1's catastrophic disruption detection efficiency over a 453-day interval using the Pan-STARRS moving object processing system (MOPS) and a simple model for the catastrophic disruption event's photometric behavior in a small aperture centered on the catastrophic disruption event. Our simplistic catastrophic disruption model suggests that delta m = 20 mag and 0.01 mag d-1 < tau < 0.1 mag d-1 which would imply that H0 = 28 -- strongly inconsistent with H0,B2005 = 23.26 +/- 0.02 predicted by Bottke et al. (2005) using purely collisional models. We postulate that the solution to the discrepancy is that > 99% of main belt catastrophic disruptions in the size range to which this study was sensitive (100 m) are not impact-generated, but are instead due to fainter rotational breakups, of which the recent discoveries of disrupted asteroids P/2013 P5 and P/2013 R3 are probable examples. We estimate that current and upcoming asteroid surveys may discover up to 10 catastrophic disruptions/year brighter than V = 18.5.