Formation of terrestrial planets from protoplanets. I. Statistics of basic dynamical properties

The final stage of terrestrial planet formation is known as the giant impact stage, where protoplanets collide with one another to form planets. As this process is stochastic, in order to clarify it, it is necessary to quantify it statistically. We investigate this final assemblage of terrestrial planets from protoplanets using N-body simulations. As initial conditions, we adopt the oligarchic growth model of protoplanets. We systematically change the surface density, surface density profile, and orbital separation of the initial protoplanet system, and the bulk density of protoplanets, while the initial system radial range is fixed at 0.5-1.5 AU. For each initial condition, we perform 20 runs, and from their results we derive the statistical properties of the assembled planets. For the standard disk model, typically two Earth-sized planets form in the terrestrial planet region. We show the dependences of the masses and orbital elements of planets on the initial protoplanet system parameters and give their simple empirical fits. The number of planets slowly decreases as the surface density of the initial protoplanets increases, while the masses of individual planets increase almost linearly. For a steeper surface density profile, large planets tend to form closer to the star. For the parameter ranges that we test, the basic structure of planetary systems depends only slightly on the initial distribution of protoplanets and the bulk density as long as the total mass is fixed.