3-D numerical simulations of a growing planet with the core formation by the impact

Details 3-D numerical simulations of a growing planet with the core formation by the impact 3-D numerical simulations of a growing planet with the core formation by the impact

Dec 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011agufm.p11a1580f&link_type=abstract

American Geophysical Union, Fall Meeting 2011, abstract #P11A-1580

Statistics

Computation

[0545] Computational Geophysics / Modeling, [5430] Planetary Sciences: Solid Surface Planets / Interiors, [8125] Tectonophysics / Evolution Of The Earth, [8147] Tectonophysics / Planetary Interiors

Scientific paper

The formation of a metallic core is widely accepted as the biggest differentiation event during the final stage of the planetary formation [e.g. Stevenson, 1990]. The early Earth hypothesis also suggested that the core formation process would be an important for understanding the initial condition (both thermal and chemical) of mantle convection [Labrosse et al., 2007]. Although the formation process of metallic core is still not clear, it is clear that the different time-scale of dynamics in solid and liquid contribute to that. Here, we assume the scenario that the planetesimal impact induces a significant volume of melt which laterally spreads over the global (magma ocean) or regional area (magma pond) in the short crystallization time scale (~300yr) [Reese and Solomatov, 2006]. After the solidification of magma ocean/pond, hot metallic and silicate rich layers are created [e.g. Senshu et al., 2002]. Since the heavy metal rich material causes the gravitational instability in the viscous planet's interior, the planetary core would form with sinking the metallic material into the center. The silicate layer which floods from the magma pond, deforms as a viscous flow on the planetary surface due to the isostatic adjustment. A series of event on the core formation would have the time-scale of ~100 Mys at the maximum. In order to investigate the scenario described above, we developed the simulation code to solve the Stokes flow with the free surface under the self-gravitating field in 3-D, designed for the massively parallel/vector supercomputer system Earth Simulator 2(ES2) [Furuichi, 2011]. Expressing the free surface motion, a stick air layer, which is the low viscosity layer surrounding the planetary surface, is assumed [e.g. Furuichi et al, 2009]. An ill conditioned Stokes problem of the finite difference discretization on a staggered grid, is solved by iterative Stokes flow solver, robust to large viscosity jumps, using a strong Schur complement preconditioner and mixed precision arithmetic utilizing the double-double method. We also solve the temperature equation with shear heating effects. The viscosity is dependent on temperature, pressure and yield stress. Our simulation starts from the proto-planet with Martian size under the self-gravitating field. The core formation occurs when the planet experiences the large impact assumed with adding the mixture of silicate and metal rich materials with the buried heat to the planetary surface. This setup simplifies for the relationship between the hot excavated solid material and flooding the magma from the magma pond. The sinking metal layer in planetary interior and the post-impact rebound of planetary surface are captured with the deformable free surface with updating the gravity potential and temperature field. Depending on the state of planetary interior and condition of impactor, the core formation process might change, for example, from the low mode (overturn process by metallic layer) [e.g. Lin et al., 2011] to the high mode (sinking metallic ball) [e.g. Golabek et al., 2009] of the Rayleigh-Taylor instability. We investigate the influences of the rheological parameters and impact heating on the core formation process. In addition, the effect of the timing of impacts is discussed as a control parameter of the core formation.

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