[Previous] | [Session 25] | [Next]
S. J. Weidenschilling, D. R. Davis (Planetary Science Institute)
A planetary embryo can accrete planetesimals from a restricted region of space. The Jacobi parameter sets a limit on separation of semimajor axes \Delta a for a small particle to collide with an embryo of mass M, \Delta a = 2 \sqrt 3 Hill radii; RH = a [M/M\odot]1/3. The ``isolation mass" Miso = 0.0021 \sigma 3/2 a 3 M\oplus, where the surface density is in \sigma g cm-2 and a in AU. At 1 AU in a minimum mass solar nebula with \sigma = 8 g cm-2, Miso = 0.05 M\oplus. To form Jupiter's core, Miso = 10 M\oplus requires \sigma ~10.5 g cm-2 at 5 AU, implying a disk mass several times the minimum. Conditions assumed for derivation of Miso may be violated: small bodies migrate due to gas drag, scattering by multiple embryos does not conserve the Jacobi parameter, and embryos can collide. N-body integrations (Kokubo and Ida, ApJ 581, 666) yield masses ~4-5 \times Miso. Their simulations covered a limited range of a ~ 1~AU, and used large (1000~km) bodies with enhanced cross-sections. Our multi-zone accretion code (Weidenschilling et al. 1997, Icarus 128, 429) reproduces their results. We use our code for more realistic conditions over a wider range of a, starting with km-sized bodies with no enhancement of cross-sections, and including gas drag. We compare models with R-3/2 and R-1 surface density profiles, with \sigma = 8.4 g cm-2 at 1 AU. In the range 0.5 - 4~AU, outcomes are similar for both gradients, reaching Miso in a few 104 orbital periods, and ~5 Miso (0.25 M\oplus at 1 AU) in < 106 periods. Growth does not halt at this size; 2 to 4 planets ~0.5 M\oplus form in 3 \times 106 y. The surface density index has more effect at larger distances. We ran simulations from 2-15 AU, with a ``snow line" at 4.5 AU. For \sigma \propto R-3/2, 8 embryos with masses ~1-3 M\oplus accreted between 5 and 12 AU in 5 \times 106 y. For the R-1 gradient, two bodies at 7 and 10.5 AU exceeded 10 M\oplus within 5 \times 106 y. Two cores were ejected to ~ 17 and 24 AU, producing analogs of Uranus and Neptune. Core accretion appears feasible if the solar nebula had a surface density gradient of R-1, rather than the ``standard" R-3/2.
[Previous] | [Session 25] | [Next]
Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.