Size-dependent Decay of Accretion Populations

Collisional fragmentation during terrestrial planet accretion has been shown to significantly damp the orbits of the growing planets and prolong the time they take to fully accrete. N-body models of terrestrial planet accretion that include collisional fragmentation produce results that are in good agreement with the dynamical structure of the modern solar system. However, while the observable solar system offers strong constraints on the final dynamical structure of modeled systems, the number and size distribution of massive bodies in the solar system throughout the duration of terrestrial planet accretion is largely unconstrained. We show that the size-frequency distribution of bodies in the inner solar system varies throughout the early history of the solar system, resulting in size-dependent decay curves for remnant small bodies. We show that the number of planetary embryos in the solar system decreases steadily from a maximum at the start of accretion, while the number of planetesimals and smaller fragments increases rapidly to a peak as collisional fragmentation generates large amounts of debris. These smaller bodies are then gradually swept up, with some populations lingering late into the accretion process. We further hypothesize that a record of these late lingering populations, and their size-dependent decay curves, may be found in the cratering records of the most ancient surfaces in the inner solar system. In summary, we find that the total number of bodies in the terrestrial region varies over the age of the solar system, with the growth or decay rate of a population dependent on the average mass of the population. These findings challenge the viewpoint that the shape of the size-frequency distribution of bodies in the inner solar system has remained constant over the age of the solar system.