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K. Iwasaki, H. Emori, H. Tanaka, K. Nakazawa (Tokyo Inst. of Tech., Dept. of Earth & Planetary Sci.)
We investigated the effect of the gravitational or hydrodynamical interaction with the gas disk on the orbital instability of a protoplanet system. We consider five protoplanets with the mass of 1 \times 10-7 \: Msun, which are distributed with the same separation distance, \Delta a, and their initial orbits are circular and coplanar. The gravitational interaction between a protoplanet and the gas disk is expressed as the drag force which is proportional to the random velocity of a protoplanet, while the hydrodynamical gas drag force caused by the gas disk is proportional to the square of the random velocity. Taking account of these two kinds of drag force effects respectively, we calculated numerically the orbits of the protoplanets and examined the orbital instability time under the drag force, Tinstdf. Regardless of the kind of the drag force, we found that Tinstdf is enlarged in magnitude compared with the instability time under the drag-free condition and the orbital instability does not occur substantially when \Delta a is larger than a critical separation distance, {\Delta a}crit. We obtained the relation between {\Delta a}crit and the surface density of the gas disk. Applying this relation to a protoplanet system with a typical orbital separation (i.e., \Delta a ~10 Hill radii), we found that, for the formation of terrestrial planets, in other words, the occurence of an orbital instability of the protoplanet system, the surface density of the nebular gas must decrease to about 0.1 % of the minimum mass nebula model.
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Bulletin of the American Astronomical Society, 34, #3
© 2002. The American Astronomical Society.