The Kepler missions discovery of a number of circumbinary planets orbiting close (a_p < 1.1 au) to the stellar binary raises questions as to how these planets could have formed given the intense gravitational perturbations the dual stars impart on th
e disk. The gas component of circumbinary protoplanetary disks is perturbed in a similar manner to the solid, planetesimal dominated counterpart, although the mechanism by which disk eccentricity originates differs. This is the first work of a series that aims to investigate the conditions for planet formation in circumbinary protoplanetary disks. We present a number of hydrodynamical simulations that explore the response of gas disks around two observed binary systems: Kepler-16 and Kepler-34. We probe the importance of disk viscosity, aspect-ratio, inner boundary condition, initial surface density gradient, and self-gravity on the dynamical evolution of the disk, as well as its quasi steady-state profile. We find there is a strong influence of binary type on the mean disk eccentricity, e_d, leading to e_d = 0.02 - 0.08 for Kepler-16 and e_d = 0.10 - 0.15 in Kepler-34. The value of alpha-viscosity has little influence on the disk, but we find a strong increase in mean disk eccentricity with increasing aspect-ratio due to wave propagation effects. The choice of inner boundary condition only has a small effect on the surface density and eccentricity of the disk. Our primary finding is that including disk self-gravity has little impact on the evolution or final state of the disk for disks with masses less than 12.5 times that of the minimum-mass solar nebula. This finding contrasts with the results of self-gravity relevance in circumprimary disks, where its inclusion is found to be an important factor in describing the disk evolution.
Numerical simulations of the stochastic end stage of planet formation typically begin with a population of embryos and planetesimals that grow into planets by merging. We analyzed the impact parameters of collisions leading to the growth of terrestri
al planets from recent $N$-body simulations that assumed perfect merging and calculated more realistic outcomes using a new analytic collision physics model. We find that collision outcomes are diverse and span all possible regimes: hit-and-run, merging, partial accretion, partial erosion, and catastrophic disruption. The primary outcomes of giant impacts between planetary embryos are approximately evenly split between partial accretion, graze-and-merge, and hit-and-run events. To explore the cumulative effects of more realistic collision outcomes, we modeled the growth of individual planets with a Monte Carlo technique using the distribution of impact parameters from $N$-body simulations. We find that fewer planets reached masses $>0.7 M_{rm Earth}$ using the collision physics model compared to simulations that assumed every collision results in perfect merging. For final planets with masses $>0.7 M_{rm Earth}$, 60% are enriched in their core-to-mantle mass fraction by >10% compared to the initial embryo composition. Fragmentation during planet formation produces significant debris ($sim15$% of the final mass) and occurs primarily by erosion of the smaller body in partial accretion and hit-and-run events. In partial accretion events, the target body grows by preferentially accreting the iron core of the projectile and the escaping fragments are derived primarily from the silicate mantles of both bodies. Thus, the bulk composition of a planet can evolve via stochastic giant impacts.
In this paper we extend our numerical method for simulating terrestrial planet formation from Leinhardt and Richardson (2005) to include dynamical friction from the unresolved debris component. In the previous work we implemented a rubble pile planet
esimal collision model into direct N-body simulations of terrestrial planet formation. The new collision model treated both accretion and erosion of planetesimals but did not include dynamical friction from debris particles smaller than the resolution limit for the simulation. By extending our numerical model to include dynamical friction from the unresolved debris, we can simulate the dynamical effect of debris produced during collisions and can also investigate the effect of initial debris mass on terrestrial planet formation. We find that significant initial debris mass, 10% or more of the total disk mass, changes the mode of planetesimal growth. Specifically, planetesimals in this situation do not go through a runaway growth phase. Instead they grow concurrently, similar to oligarchic growth. In addition to including the dynamical friction from the unresolved debris, we have implemented particle tracking as a proxy for monitoring compositional mixing. Although there is much less mixing due to collisions and gravitational scattering when dynamical friction of the background debris is included, there is significant inward migration of the largest protoplanets in the most extreme initial conditions.
