End of Life Scenarios for Rubble Pile Asteroids

Abstract:

Recent theory and observations of asteroids have shown that rubble pile bodies can have a weak level of cohesion, allowing them to spin faster than the gravitational limit, but not too fast (Sanchez & Scheeres MAPS 2014; Hirabayashi et al. ApJL 2014). However, these predicted fission spin rates are less than the maximum spin rates observed for small asteroids, implying that some of these smaller asteroids may be the monolithic components of a rubble pile, or boulders shed from these bodies in the past. 

For a rubble pile body with a given level of cohesion, its maximum spin rate is inversely proportional to the body diameter. Thus, every time a rubble pile body is split into smaller components, the resulting body can spin proportionally faster before it can shed or fission again. In contrast, the YORP effect’s spin acceleration is inversely proportional to the body diameter squared. Thus, the time it takes for the components of a fissioned body to spin up to its new fission limit is proportional to the body diameter and takes proportionally less time to achieve their next fission. If a body fissions into N components, the new effective diameters of the components will equal $N^{-1/3}$ times their initial diameter. Thus, if we assume that a fissioned component is immediately accelerated to its next fission rate, the total time for a rubble pile to completely fission is a convergent power series, and can be shown to be equal to the initial YORP time scale of the starting, initial rubble pile. This total time can be extended by an order of magnitude if a fissioned body is initially rotationally decelerated. It may also be extended if its post-fission tumbling state slows its YORP rotational acceleration.

We will present predictions for the lifetimes of small rubble pile asteroids before they are disaggregated. Direct comparisons will be made between the competing effects of YORP acceleration, dissipation of a complex rotation state back to uniform rotation, and the number of components that a body may split into. We find that, based on recent constraints placed on the $\mu Q$ values of rubble pile bodies, the relaxation time back to uniform rotation should be short compared to the time to be accelerated to its next fission spin rate. Throughout the talk the rubble pile, fast-spinning, tumbling asteroid 2008 TC3 will be used as a motivating example.