Considering Contact Forces during the Formation of Planetesimals by Gravitational Collapse: Mutual Orbits, Spin States, and Shapes
September 2025 • 2025ApJ...990..130B
Abstract • In this work, we apply a soft-sphere discrete element method (SSDEM) within the PKDGRAV N-body integrator to investigate the formation of planetesimal systems through the gravitational collapse of clouds of superparticles. Previously published numerical models have demonstrated that the gravitational collapse of pebble clouds is an efficient pathway to produce binary planetesimal systems. However, such investigations were limited by their use of a perfect-merger and inflated-radii superparticle approach, which inhibits any analysis of planetesimal shapes and spin states, precludes the formation of the tightest binary orbits, and produces significantly underdense planetesimals. The SSDEM enables superparticles to rest upon each other through mutual surface penetration and by simulating contact physics. Superparticles do not need to be inflated, and collisions are not treated as perfect mergers; we can thus track the evolution of planetesimal shapes, spins, and tight binary orbits. We demonstrate that the SSDEM is an excellent method to model the collapse process, and is capable of producing many binary planetesimal systems from a single cloud. The most massive systems often exhibit low-inclination (i ≲ 15°) and moderately eccentric (e ≲ 0.40) orbits within a tight range of semimajor axes normalized by their Hill radii (a/RHill ∼ 0.02─0.15). Conversely, less massive planetesimal systems display a wider range of eccentricities and inclinations and maintain a wider range of a/RHill (0.15 to ≥0.50). These results confirm the findings of previously published perfect-merging models while also producing novel results about planetesimal spin and shape properties. Newly formed planetesimals exhibit 10 hr rotation periods on average and can be characterized by a wide variety of shapes (spherical, oblate, top-shaped, flattened, egg-shaped, or prolate), with the most massive planetesimals primarily forming as spheres and oblate spheroids.
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