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The final stage of terrestrial planet formation is known as the giant impactstage where protoplanets collide with one another to form planets. So far thisstage has been mainly investigated by N-body simulations with an assumption ofperfect accretion in which all collisions lead to accretion. However, thisassumption breaks for collisions with high velocity and/or a large impactparameter. We derive an accretion condition for protoplanet collisions in termsof impact velocity and angle and masses of colliding bodies, from the resultsof numerical collision experiments. For the first time, we adopt this realisticaccretion condition in N-body simulations of terrestrial planet formation fromprotoplanets. We compare the results with those with perfect accretion and showhow the accretion condition affects terrestrial planet formation. We find thatin the realistic accretion model, about half of collisions do not lead toaccretion. However, the final number, mass, orbital elements, and even growthtimescale of planets are barely affected by the accretion condition. For thestandard protoplanetary disk model, typically two Earth-sized planets form inthe terrestrial planet region over about 100 M years in both realistic andperfect accretion models. We also find that for the realistic accretion model,the spin angular velocity is about 30% smaller than that for the perfectaccretion model that is as large as the critical spin angular velocity forrotational instability. The spin angular velocity and obliquity obey Gaussianand isotropic distributions, respectively, independently of the accretioncondition.

Formation of Terrestrial Planets from Protoplanets under a Realistic Accretion Condition