Consequences of imperfect accretion in the early giant planet instabilitymodel

Terrestrial planet formation in the solar system describes the growth of the innermost planets, including Earth. There are two competing accretion mechanisms that may be important for building these planets. The pebble accretion theory proposes rapid (<10 Myr) growth through the accretion of cm-sized objects (pebbles). If Earth grew mostly from pebbles, then this hypothesis requires a Moon-forming impact characterized as late, high angular momentum, and between nearly equal-size bodies. Alternatively, the pairwise accretion theory proposes a much longer Earth formation timescale (10–100 Myr) during which Earth is built through a series of collisions between lunar- to Mars-sized bodies. This hypothesis is consistent with the canonical Mars-sized Moon-forming impactor. The runaway growth that produces the planetary embryos in the pairwise accretion theory could have been produced by pebble accretion, so certainly, both processes could have occurred during the formation of the terrestrial planets. Thus, many hybrid scenarios combining the two theories can be imagined. Therefore, it is necessary to understand how much of a role each accretion mechanism played in the formation of the terrestrial planets.

 

This challenge can be approached by examining the history of impact debris production, transport, and storage in the main asteroid belt. Impact debris production occurs for all large impacts even relatively small ones such as those that produce the lunar and Martian meteorites, but ejecta creation is particularly voluminous during giant impacts. Indeed, at least one giant impact occurred in all terrestrial planet formation scenarios. Therefore, an investigation into the consequences of these impacts based on their frequency and strength can be conducted. For all giant impacts that occur, debris is generated, but what happens to this debris has not been considered. Spectroscopic studies of meteorites and asteroids have connected a rare set of differentiated asteroids to giant impact debris, which may make up as much as a few percent the mass of the asteroid belt. Thus, we hypothesize that some fraction of debris produced by giant impacts could currently reside in the asteroid belt. Quantifying the mass of potential debris currently in the asteroid belt provides an observational constraint on the total mass of debris produced during terrestrial planet formation.

 

In this study, we incorporate imperfect accretion into one of the leading pairwise accretion scenarios, the early instability scenario, allowing for various collision types and debris generation. The astrophysical N-body integrator SyMBA is used to track and quantify the total mass of debris that resides in the asteroid belt. After numerically evolving each simulated systems for 100 Myr, we reproduced terrestrial planet analogues similar to other simulations of the early giant planet instability scenario, and our results also agree that an orbital instability occurring between 1 and 10 Myr work best for reproducing terrestrial planet analogues. Like past work, we found that including imperfect accretion had a relatively small effect on the final accreted planets, however unlike most past work, we now focus on what happened to the debris from these impact events.

 

Every simulation of terrestrial planet formation possessed giant impacts which produced debris. These debris particles were scattered onto many different orbits including trajectories that intersected the Sun and other planets. Some were even ejected from the solar system. At the end of the 100 Myr simulation, we assessed which particles were on stable orbits in the asteroid belt. We found that 52 (32%) of simulations produced a significant overabundance of debris on stable orbits in the main asteroid belt while the remaining 110 (68%) simulations produce no debris on stable orbits in the asteroid belt. Of the simulations that had debris in the asteroid belt, ~95% had a total mass of debris that was greater than the current mass of the asteroid belt, as shown in Fig. 1. Some simulations produced as much as about 46 times more mass in debris than there is mass in the asteroid belt. The strong dichotomy between those simulations that produced a lot of debris in the asteroid belt and those that produced very little is likely due to a resolution issue. The debris particles used were each between about 4 – 0.85 times an asteroid belt mass, so these simulations struggled to resolve instances where perhaps only a small amount of debris ended up in the asteroid belt. 

Figure 1. The total mass of debris in the asteroid belt (2.2-3.5 AU) at the end of the 100 Myr simulation as a function of the total mass of debris generated throughout the entire simulation. The mass of the debris is normalized by the current mass of the asteroid belt, where 1 defines the current mass of the asteroid belt (red dashed line). The dark blue, pink, grey, and light blue points represent runs where an orbital instability was triggered at 1 Myr, 5 Myr, 10 Myr, and 50 Myr respectively. Only the simulations that generated debris in the asteroid belt are shown here.