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  as a function of the post-disruption increase in brightness (Δm) and subsequent brightness decay rate (<em style="margin: 0px; padding: 0px; border: 0px currentColor; border-image: none; text-align: justify; color: rgb(46, 46, 46); text-transform: none; line-height: 20px; text-indent: 0px; letter-spacing: normal; font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: 13px; font-variant: normal; font-weight: 100; word-spacing: -1.03px; vertical-align: baseline; white-space: normal; background-color: rgb(255, 255, 255); -webkit-text-stroke-width: 0px;">τ  </em>). 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  contours in the ranges from  and  encompassing measured values from known cratering and disruption events and our model’s predictions. Our simplistic catastrophic disruption model suggests that  and  which would imply that H<sub style="margin: 0px; padding: 0px; border: 0px currentColor; border-image: none; line-height: 0; font-size: 0.75em; font-weight: 100; vertical-align: sub;">0≳28</sub>—strongly inconsistent withH<sub style="margin: 0px; padding: 0px; border: 0px currentColor; border-image: none; line-height: 0; font-size: 0.75em; font-weight: 100; vertical-align: sub;">0,B2005=23.26±0.02</sub> 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<sub style="margin: 0px; padding: 0px; border: 0px currentColor; border-image: none; line-height: 0; font-size: 0.75em; font-weight: 100; vertical-align: sub;">0=H<sub style="margin: 0px; padding: 0px; border: 0px currentColor; border-image: none; line-height: 0; font-size: 0.75em; font-weight: 100; vertical-align: sub;">0,B2005</sub></sub> our results constrain , 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.