Constraints on the Physical Properties of Main Belt Comet P/2013 R3 from its Breakup Event

Jewitt et al. (2014) recently reported that main belt comet P/2013 R3 experienced a breakup, probably due to rotational disruption, with its components separating on mutually hyperbolic orbits. We propose a technique for constraining physical properties of the proto-body, especially the initial spin period and cohesive strength, as a function of the body's estimated size and density. The breakup conditions are developed by combining mutual orbit dynamics of the smaller components and the failure condition of the proto-body. Given a proto-body with a bulk density ranging from 1000 kg/m3 to 1500 kg/m3 (a typical range of the bulk density of C-type asteroids), we obtain possible values of the cohesive strength (40 - 210 Pa) and the initial spin state (0.48 - 1.9 hr). From this result, we conclude that although the proto-body could have been a rubble pile, it was likely spinning beyond its gravitational binding limit and would have needed cohesive strength to hold itself together. Additional observations of P/2013 R3 will enable stronger constraints on this event, and the present technique will be able to give more precise estimates of its internal structure.