Impact Excitation of a Seismic Pulse and Vibrational Normal Modes on Asteroid Bennu and Associated Slumping of Regolith

Regolith flow on top-shaped asteroids

We develop a continuum framework of regolith flow on asteroids. We focus on top-shaped asteroids that may be taken as consisting of regolith lying on a solid core. Depth-averaging is employed to model the regolith flow, and effects due to the asteroid’s rotation and its complex gravity field are retained. Angular momentum conservation is invoked to couple regolith flow to the asteroid’s changing shape and spin. This framework is first used to explore the equilibrium of regolith as a function of its friction, and the asteroid’s shape and spin rate. Next, we study regolith flow on top-shaped spinning asteroids and find conditions for the regolith’s shedding or deposition. We also discuss how the regolith’s flow and the asteroid’s spin influence each other. Finally, as an application, we propose and investigate the following evolution history of Bennu: a fast spinning Bennu was slowed down by multiple, impact-induced global landslides to its present spin state. Regolith was shed if the spin was higher than a critical rate. Once the spin rate fell below this critical value, regolith flow from higher latitudes began depositing regolith at its equator, giving Bennu its distinctive shape.

Mass Spring Models of Amorphous Solids

In this paper we analyse static properties of mass spring models (MSMs) with the focus of modelling non crystalline materials, and explore basic improvements, which can be made to MSMs with disordered point placement. Presented techniques address the problem of high variance of MSM properties which occur due to randomised nature of point distribution. The focus is placed on tuning spring parameters in a way which would compensate for local non-uniformity of point and spring density. We demonstrate that a simple force balancing algorithm can improve properties of the MSM on a global scale, while a more detailed stress distribution analysis is needed to achieve local scale improvements. Considered MSMs are three dimensional.

Excitation of Tumbling in Phobos and Deimos

Mass-spring model simulations are used to investigate past spin states of a viscoelastic Phobos and Deimos. From an initially tidally locked state, we find crossing of a spin-orbit resonance with Mars or a mean motion resonance with each other does not excite tumbling in Phobos or Deimos. However, once tumbling our simulations show that these moons can remain so for an extended period and during this time their orbital eccentricity can be substantially reduced. We attribute the tendency for simulations of an initially tumbling viscoelastic body to drop into spin-synchronous state at very low eccentricity to the insensitivity of the tumbling chaotic zone volume to eccentricity. After a tumbling body enters the spin synchronous resonance, it can exhibit long lived non-principal axis rotation and this too can prolong the period of time with enhanced tidally generated energy dissipation. The low orbital eccentricities of Phobos and Deimos could in part be due to spin excitation by nearly catastrophic impacts rather than tidal evolution following orbital resonance excitation.

Near/Far Side Asymmetry in the Tidally Heated Moon

Using viscoelastic mass spring model simulations to track heat distribution inside a tidally perturbed body, we measure the near/far side asymmetry of heating in the crust of a spin synchronous Moon in eccentric orbit about the Earth. With the young Moon within. 8 Earth radii of the Earth, we find that tidal heating per unit area in a lunar crustal shell is asymmetric due to the octupole order moment in the Earth's tidal field and is 10 to 20% higher on its near side than on its far side. Tidal heating reduces the crustal basal heat flux and the rate of magma ocean crystallization. Assuming that the local crustal growth rate depends on the local basal heat flux and the distribution of tidal heating in latitude and longitude, a heat conductivity model illustrates that a moderately asymmetric and growing lunar crust could maintain its near/far side thickness asymmetry but only while the Moon is near the Earth.

Simulations of wobble damping in viscoelastic rotators

Using a damped mass-spring model, we simulate wobble of spinning homogeneous viscoelastic ellipsoids undergoing non-principal axis rotation. Energy damping rates are measured for oblate and prolate bodies with different spin rates, spin states, viscoelastic relaxation timescales, axis ratios, and strengths. Analytical models using a quality factor by Breiter et al. (2012) and for the Maxwell rheology by Frouard & Efroimsky (2018) match our numerical measurements of the energy dissipation rate after we modify their predictions for the numerically simulated Kelvin-Voigt rheology. Simulations of nearly spherical but wobbling bodies with hard and soft cores show that the energy dissipation rate is more sensitive to the material properties in the core than near the surface.