The structure of terrestrial bodies: Impact heating, corotation limits, and synestias

During accretion, terrestrial bodies attain a wide range of thermal and rotational states, which are accompanied by significant changes in physical structure (size, shape, pressure and temperature profile, etc.). However, variations in structure have been neglected in most studies of rocky planet formation and evolution. Here we present a new code, the Highly Eccentric Rotating Concentric U (potential) Layers Equilibrium Structure (HERCULES) code, that solves for the equilibrium structure of planets as a series of overlapping constant-density spheroids. Using HERCULES and a smoothed particle hydrodynamics code, we show that Earth-like bodies display a dramatic range of morphologies. For any rotating planetary body, there is a thermal limit beyond which the rotational velocity at the equator intersects the Keplerian orbital velocity. Beyond this corotation limit (CoRoL), a hot planetary body forms a structure, which we name a synestia, with a corotating inner region connected to a disk-like outer region. By analyzing calculations of giant impacts and models of planet formation, we show that typical rocky planets are substantially vaporized multiple times during accretion. For the expected angular momentum of growing planets, a large fraction of post-impact bodies will exceed the CoRoL and form synestias. The common occurrence of hot, rotating states during accretion has major implications for planet formation and the properties of the final planets. In particular, the structure of post-impact bodies influences the physical processes that control accretion, core formation, and internal evolution. Synestias also lead to new mechanisms for satellite formation. Finally, the wide variety of possible structures for terrestrial bodies also expands the mass-radius range for rocky exoplanets. Plain Language Summary During the end stage of planet formation, planets collide together and produce bodies that are partially vaporized and rapidly rotating. In this work, we developed new techniques to calculate the shape and internal pressures of hot, rotating, Earth-like planets. We find that rocky planets can have a variety of shapes and sizes. In addition, for certain combinations of thermal energy and rotation rate, a planet cannot rotate as if it were a solid body. Beyond this corotation limit, the planet has an inner region that is rotating at a single rate connected to a disk-like outer region with orbital velocities. The dynamics of this extended structure are significantly different than a normal planet, so we gave the extended structure a name: a synestia. We show that rocky planets are vaporized multiple times during their formation and are likely to form synestias. The different structures of hot, rotating planets change our understanding of multiple aspects of planet formation, including the origin of our Moon.