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[40.02] Runaway Growth and Isolation of Planetary Embryos

S. J. Weidenschilling (Planetary Science Institute), F. Marzari (Universita di Padova), D. R. Davis (Planetary Science Institute)

It is often assumed that runaway growth yields planetary embryos with the limiting mass imposed by the restricted 3-body problem. A small planetesimal can encounter a massive embryo their initial orbit separation is less than 2 \sqrt{3} Hill radii. If the embryo accretes all particles within this distance, the ``isolation mass" M_iso = 0.0021 R³ \sigma ^3/2 M_Earth , where R = heliocentric distance (AU) and \sigma = surface density (g cm^-2). However, deviations from the idealized problem can alter this outcome, e.g., collisions among small bodies, migration due to gas drag, and mutual scattering and mergers among embryos. We use a multizone accretion code to model embryo growth to 5 My in the region 0.5 - 4 AU. Parameters and processes are varied to determine effects of planetesimal size, surface density profile, fragmentation, gas drag, and tidal interactions of embryos with a gaseous disk. Although M_iso increases with R, embryos grow larger inside 2 AU due to more effective drag-induced migration of planetesimals and embryo mergers, producing bodies several times M_iso. At larger R these processes are less effective, resulting in embryo masses ~10²⁷ g nearly independent of R. The time of onset of runaway varies inversely with planetesimal size and increases with R; if initial planetesimals are 10 km in size runaway is not complete in the asteroid zone in 5 My. Fragmentation moderately decreases the final masses and spacings of embryos. The standard model of tidal migration results in rapid loss of embryos into the Sun, leaving insufficient mass to produce terrestrial planets. Either the migration rate is slower than predicted, or gas was depleted from the inner nebula on a timescale ~ 1 My. Supported by NASA PGG; computations at NCCS.

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Bulletin of the American Astronomical Society, 36 #4
© 2004. The American Astronomical Soceity.