The Effects of Gravitational Collapse on the Masses and Rotational Dynamics of Planetesimal Systems

Planetesimal growth barriers—namely radial drift, fragmentation, and bouncing—limit the pairwise growth of pebbles in the protoplanetary disk to cm-sizes, hindering planetesimal formation. Growth up to planetesimal sizes may occur beyond these barriers via the gravitational collapse of clouds of pebbles gathered by interactions with nebular gas (i.e. the streaming instability) (Youdin & Goodman 2005; Johansen et al. 2007). The abundance of Kuiper belt binaries is evidence of this formation process, as excess angular momentum leftover from the streaming instability would prevent the coalescence of the pebble cloud into a single body (Nesvorný et al. 2010, 2019, 2020; Robinson et al. 2020). Here, we examine how a collapsing cloud’s initial angular velocity and mass distributions affect the formation of planetesimal systems, with emphasis on system dynamics and multiplicity, individual planetesimal morphology, planetesimal rotation states and dynamics, and the detailed collisional history of planetesimal systems. We model the gravitational collapse process using PKDGRAV (Stadel 2001; Richardson et al. 2000)—a parallel tree gravitational N-body integrator—and its soft-sphere discrete element method, which ensures that colliding particles may stick and rest upon one another rather than merging to form a single larger spherical particle (Schwartz et al. 2012). Because we do not use an artificial inflation factor to enhance the collision rate, our particles maintain realistic densities throughout the duration of the simulation. The use of inflation factors may induce overly vigorous planetesimal growth, preventing the formation of tightly orbiting systems, and biases final systems towards binarity rather than higher number multiplicity. Our simulations form planetesimal systems composed of a single large primary and bound secondary planetesimal, multibody systems more common at higher angular velocities, and a region of debris bound to each system. Gravitational collapse is very efficient, with binary systems retaining ≥20% of the initial cloud mass. Only several of our higher angular velocity simulations form binary systems with comparable mass, while the remaining angular velocity and mass distribution simulations form systems with binary mass ratios (m₂/m₁) ranging from 10^-3 to 10^-2. All simulations formed tightly bound planetesimal systems with mild dynamics and orbital separations ranging between 10²-10³ km, independent of both angular velocity and mass distribution. Further, we find that primaries in all of our resulting systems rotate with a period of 30-50 hours, on average.