Anatomy of an Asteroid Break-Up: The Case of P/2013 R3

We present an analysis of new and published data on P/2013 R3, the first asteroid detected while disintegrating. Thirteen discrete components are measured in the interval between UT 2013 October 01 and 2014 February 13. We determine a mean, pair-wise velocity dispersion amongst these components of $\Delta v = 0.33\pm0.03$ m s$^{-1}$ and find that their separation times are staggered over an interval of $\sim$5 months. Dust enveloping the system has, in the first observations, a cross-section $\sim$30 km$^2$ but fades monotonically at a rate consistent with the action of radiation pressure sweeping. The individual components exhibit comet-like morphologies and also fade except where secondary fragmentation is accompanied by the release of additional dust. We find only upper limits to the radii of any embedded solid nuclei, typically $\sim$100 to 200 m (geometric albedo 0.05 assumed). Combined, the components of P/2013 R3 would form a single spherical body with radius $\lesssim$400 m, which is our best estimate of the size of the precursor object. The observations are consistent with rotational disruption of a weak (cohesive strength $\sim$50 to 100 N m$^{-2}$) parent body, $\sim$400 m in radius. Estimated radiation (YORP) spin-up times of this parent are $\lesssim$1 Myr, shorter than the collisional lifetime. If present, water ice sublimating at as little as 10$^{-3}$ kg s$^{-1}$ could generate a torque on the parent body rivaling the YORP torque. Under conservative assumptions about the frequency of similar disruptions, the inferred asteroid debris production rate is $\gtrsim$10$^3$ kg s$^{-1}$, which is at least 4% of the rate needed to maintain the Zodiacal Cloud.