Orbital Architecture of Planetary Systems Formed by Gravitational Scattering and Collisions

Eiichiro Kokubo, Haruka Hoshino, Yuji Matsumoto

In the standard model of solar system formation, terrestrial planets are spontaneously formed by giant impacts of protoplanets or planetary embryos after the dispersal of protoplanetary disk gas. Similar models are also proposed for forming close-in super-Earths mainly discovered by the Kepler transit observations. In the giant impact stage protoplanets collide with each other to complete planets. We investigate the orbital architecture of planetary systems formed from protoplanet systems by giant impacts using N-body simulations. We systematically change the system parameters of initial protoplanet systems, such as the total mass, mean semimajor axis, and dispersions of eccentricity and inclination, and investigate their effects on planetary systems. As system orbital architecture parameters, we calculate the mean orbital separation of two adjacent planets and the orbital eccentricity of planets in a planetary system. We find that the orbital separation and eccentricity normalized by the Hill radius are nearly independent of the total mass, mass distribution, orbital separation, and eccentricity of the initial protoplanet systems in the realistic parameter range. On the other hand, they show a positive dependence on the mean semimajor axis and the bulk density of planets. The equilibrium random eccentricity can explain this dependence. Suppose the system evolves by gravitational scattering and collisional coalescence. In that case, the equilibrium eccentricity is about the value of the two-body surface escape velocity normalized by the Keplerian velocity, which increases with the semimajor axis and bulk density of planets. We show that the orbital architecture is scaled by the equilibrium random eccentricity that includes the Hill scaling.