Deterministic Model for Asteroid Thermal Evolution With Fragmentation and Reassembly Into a Gravitational Aggregate

We present a model for the thermal evolution of asteroids that experience catastrophic fragmentation and reassembly into a gravitational aggregate. The three stage model comprises the initial radiogenic heating, fragmentation and cooling, and reassembly into a porous gravitational aggregate. The heat loss during catastrophic fragmentation is largely determined by the production of small particles that equilibrate thermally with ambient space. To determine this heat loss we combine a power-law for the cumulative fragment mass distribution with analytic solutions for conductive cooling. To keep the model deterministic we fragment the parent body and reassemble the gravitational aggregate in shells ordered in decreasing volume. We use the resulting model to show that catastrophic fragmentation can lead to significant heat loss despite the short reassembly times (e.g., $\le$1 year), due to the production of many small fragments. Despite the heat loss during fragmentation, the reassembled gravitational aggregate will retain more heat than the undisturbed parent body in the long term, due to the formation of an insulating megaregolith. Applied to the H-chondrite parent body, our model can reproduce both the fast cooling rates at high temperatures and slow cooling rates at low temperature.