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S. J. Weidenschilling, D. R. Davis (Planetary Science Institute)
We have used the PSI multi-zone code (1) to model accretion in a planetesimal swarm in the region of terrestrial planets and inner asteroid belt. The nominal model has 4 ME between 0.5 and 3 AU. Consistent with our earlier results, and those of Kokubo and Ida (2), we find that runaway growth ceases after producing protoplanetary embryos of a roughly uniform limiting mass (``oligarchic growth"). In our simulations, the limiting mass is ~1027 g. The timescale to reach this mass is a strong function of distance, so that embryo formation propagates outward in a ``wave" that reaches ~1.5 AU after 4 MY of model time. Growth is slower at larger distances, with the largest bodies at 3 AU only ~1024 g at that time. Even at 107 y, only a few bodies beyond 2 AU reach ~ 1026g, with most of the mass in much smaller objects. This result contrasts with analytic models (3) that predict increasing embryo mass with heliocentric distance. It is not necessary to invoke mass depletion or interference by an early-formed Jupiter to inhibit the growth of planet-sized bodies in the asteroid region. We also find that the presence of nebular gas has a strong stabilizing effect on embryo orbits; although they are too large to be directly affected by drag, they are linked by dynamical friction to the residual population of small planetesimals, which are strongly damped. Removal of the gas results in increasing eccentricities of the embryos and onset of crossing orbits with close encounters and collisions. The transition from an oligarchy of embryos to the chaotic final stage of giant impacts may have been triggered by dissipation of the solar nebula, rather than by embryos reaching a critical mass or the gradual accumulation of mutual perturbations (4).
References: (1) S. Weidenschilling et al., Icarus 128, 429 (1997); (2) I. Kokubo and S. Ida, Icarus 131, 171 (1998); (3) J. Lissauer and G. Stewart, Protostars & Planets III, 1061 (1993); (4) T. Ito and K. Tanikawa, Icarus 139, 336 (1999).