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 H0CL as a function of the post-disruption increase in brightness (Δm) and subsequent brightness decay rate (τ). 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. We then calculated the H0CL contours in the ranges from 0.5mag<Δm<20mag and 0.001magd-1<τ<10magd-1 encompassing measured values from known cratering and disruption events and our model's predictions. Our simplistic catastrophic disruption model suggests that Δm∼20mag and 0.01magd-1≲τ≲0.1magd-1 which would imply that H0≳28-strongly inconsistent with H0,B2005=23.26±0.02 predicted by Bottke et al. (Bottke, W.F., Durda, D.D., Nesvorný, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H.F. [2005]. Icarus, 179, 63-94.) using purely collisional models. However, if we assume that H0=H0,B2005 our results constrain 11.0mag≲Δm≲12.4mag, inconsistent with our simplistic impact-generated catastrophic disruption model. 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.