MERGING CRITERIA FOR GIANT IMPACTS OF PROTOPLANETS

Abstract

At the final stage of terrestrial planet formation, known as the giant impact\nstage, a few tens of Mars-sized protoplanets collide with one another to form\nterrestrial planets. Almost all previous studies on the orbital and accretional\nevolution of protoplanets in this stage have been based on the assumption of\nperfect accretion, where two colliding protoplanets always merge. However,\nrecent impact simulations have shown that collisions among protoplanets are not\nalways merging events, that is, two colliding protoplanets sometimes move apart\nafter the collision (hit-and-run collision). As a first step towards studying\nthe effects of such imperfect accretion of protoplanets on terrestrial planet\nformation, we investigated the merging criteria for collisions of rocky\nprotoplanets. Using the smoothed particle hydrodynamic (SPH) method, we\nperformed more than 1000 simulations of giant impacts with various parameter\nsets, such as the mass ratio of protoplanets, $\\gamma$, the total mass of two\nprotoplanets, $M_{\\rm T}$, the impact angle, $\\theta$, and the impact velocity,\n$v_{\\rm imp}$. We investigated the critical impact velocity, $v_{\\rm cr}$, at\nthe transition between merging and hit-and-run collisions. We found that the\nnormalized critical impact velocity, $v_{\\rm cr}/v_{\\rm esc}$, depends on\n$\\gamma$ and $\\theta$, but does not depend on $M_{\\rm T}$, where $v_{\\rm esc}$\nis the two-body escape velocity. We derived a simple formula for $v_{\\rm\ncr}/v_{\\rm esc}$ as a function of $\\gamma$ and $\\theta$, and applied it to the\ngiant impact events obtained by \\textit{N}-body calculations in the previous\nstudies. We found that 40% of these events should not be merging events.\n