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 H 0 CL as a function of the post-disruption increase in brightness ( Δ m ) 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 H 0 CL contours in the ranges from 0.5 mag < Δ m < 20 mag and 0.001 mag d - 1 < τ < 10 mag d - 1 encompassing measured values from known cratering and disruption events and our model’s predictions. Our simplistic catastrophic disruption model suggests that Δ m ∼ 20 mag and 0.01 mag d - 1 ≲ τ ≲ 0.1 mag d - 1 which would imply that H 0 ≳ 28 —strongly inconsistent with H 0 , B 2005 = 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 H 0 = H 0 , B 2005 our results constrain 11.0 mag ≲ Δ m ≲ 12.4 mag , 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 .