Statistical Variation in YORP Evolution due to Random Boulder Populations and their Motion

The motion of asteroids is secularly influenced by the re-radiation of thermal energy absorbed by the surface from solar radiation. This is the source of the YORP effect, which can be described as the change in spin rate and obliquity as a result of asymmetry in the surface which imparts torque on the spin pole via this re-radiative process (Vokrouhlicky, 2015). Small surface features such as boulders can have a large impact on spin rates by a lever arm mechanism which accumulates over the large timescales that YORP operates on (Statler, 2009). It is also difficult to characterize these small features due to the constant process of surface reformation of non-monolithic bodies (DeMeo, 2023). Current work approaches this problem via stochastic random walk, but the integration of knowledge from geophysical surveys can inform the uncertainty in spin dynamic models (Cheng, 2021). The work to be presented here is, first, the derivation of an analytical adjustment factor to address the uncertainty in YORP coefficients, and then simulation of randomly sampled boulder placements and densities on a reasonably standard small-body shape, such as Bennu, which will inform the bounds of uncertainty in this adjustment factor.

A Boulder Adjustment to YORP (BAY) factor is presented that will encapsulate the uncertainty from Monte Carlo simulations and characterize deviations in the dynamics resulting from surface roughness (by addition of boulders) applied to regular asteroid shape models. This factor can be expressed as an uncertainty bound on the current form of YORP coefficients which are functions of solar latitude averaged over spin periodicity. The specific model to be expanded in this work follows Scheeres’ derivation which describes a set of non-dimensional YORP coefficients that are dependent only on shape, not size (Scheeres, 2007). The BAY factor is informed by statistical Monte Carlo results that constrain the distribution of dynamic impact from possible boulder placements and additionally their evolution over time as they undergo the quasi-static process of migration via YORP spin-up/down. This boulder motion aspect addresses the coupled dynamics between surface features and spin which has led to the self-limitation of YORP cycles. This factor simplifies current approaches to address uncertainty in YORP models and allows for constrained stochastic evolution of torque and obliquity over time. As a result, predictions of asteroid dynamics will be more confident and informed by what is currently understood about small body surfaces.