Planetary Accretion: Beyond the "Isolation Mass"

Details Planetary Accretion: Beyond the "Isolation Mass" Planetary Accretion: Beyond the "Isolation Mass"

May 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003dps....35.2507w&link_type=abstract

American Astronomical Society, DPS meeting #35, #25.07; Bulletin of the American Astronomical Society, Vol. 35, p.962

Astronomy and Astrophysics

Astronomy

Scientific paper

A planetary embryo can accrete planetesimals from a restricted region of space. The Jacobi parameter sets a limit on separation of semimajor axes Δ a for a small particle to collide with an embryo of mass M, Δ a = 2 √ 3 Hill radii; RH = a [M/Msun]1/3. The ``isolation mass" Miso = 0.0021 σ 3/2 a 3 M⊕ , where the surface density is in σ g cm-2 and a in AU. At 1 AU in a minimum mass solar nebula with σ = 8 g cm-2, Miso = 0.05 M⊕ . To form Jupiter's core, Miso = 10 M⊕ requires σ ˜ 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 x 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 σ = 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⊕ at 1 AU) in < 106 periods. Growth does not halt at this size; 2 to 4 planets ˜ 0.5 M⊕ form in 3 x 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 σ R-3/2, 8 embryos with masses ˜ 1-3 M⊕ accreted between 5 and 12 AU in 5 x 106 y. For the R-1 gradient, two bodies at 7 and 10.5 AU exceeded 10 M⊕ within 5 x 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.

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