Spin of protoplanets generated by pebble accretion: Influences of protoplanet-induced gas flow

Abstract

Context. In the pebble accretion model, protoplanets accrete millimeter-to-centimeter-sized particles (pebbles). When a protoplanet grows, a dense gas envelope forms around it. The envelope affects accretion of pebbles and, in particular, the spin angular momentum transfer at the collision to the planet. Aims. We aim to investigate the spin state of a protoplanet during the pebble accretion influenced by the gas flow in the gravitational potential of the protoplanet and how it depends on the planetary mass, the headwind speed, the distance from the host star, and the pebble size. Methods. We performed nonisothermal three-dimensional hydrodynamical simulations in a local frame to obtain the gas flow around the planet. We then numerically integrated three-dimensional orbits of pebbles under the obtained gas flow. Finally, assuming uniform spatial distribution of incoming pebbles, we calculated net spin by summing up specific angular momentum that individual pebbles transfer to the protoplanet at impacts. Results. We find that a protoplanet with the envelope acquires prograde net spin rotation regardless of the planetary mass, the pebble size, and the headwind speed of the gas. This is because accreting pebbles are dragged by the envelope that commonly has prograde rotation. As the planetary mass or orbital radius increases, the envelope is thicker and the prograde rotation is faster, resulting in faster net prograde spin. When the dimensionless thermal mass of the planet, m = RBondi/H, where RBondi and H are the Bondi radius and the disk gas scale height, is larger than a certain critical mass (m ≳ 0.3 at 0.1 au or m ≳ 0.1 at 1 au), the spin rotation exceeds the breakup one. Conclusions. The predicted spin frequency reaches the breakup one at the planetary mass miso,rot ~ 0.1 (a/1 au)−1/2 (where a is the orbital radius), suggesting that the protoplanet cannot grow beyond miso,rot. It is consistent with the Earth’s current mass and could help the formation of the Moon with a giant impact on a fast-spinning proto-Earth.