The Gas-Drag Effect on the Orbital Instability of a Protoplanet System

Details The Gas-Drag Effect on the Orbital Instability of a Protoplanet System The Gas-Drag Effect on the Orbital Instability of a Protoplanet System

Apr 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001pasj...53..321i&link_type=abstract

Publications of the Astronomical Society of Japan, vol.53, no. 2, p. 321-329.

Astronomy and Astrophysics

Astronomy

19

Earth, Gas-Drag Effect, Instabilities, Solar System: Formation

Scientific paper

We have investigated numerically the orbital instability of a protoplanet system while taking account of the gas-drag force due to the solar nebula. In the present work, we considered an equally spaced five-protoplanet (with the same mass of 1 × 10-7Modot) system, in which their initial orbits are coplanar and circular, and assumed that the gas-drag force is proportional to the square of the relative velocity between the gas and a protoplanet. We first re-examined and confirmed that, under a gas-free condition, log10Tinst can be approximately written as a linear function of the initial orbital separation distance, Δã0, where Tinst is the time of the orbital instability (i.e., the time of the first orbital crossing between any two protoplanets). Next, we investigated the instability time under the gas-drag effect, Tgasinst, and found that Tgasinst suddenly becomes large compared with Tinst, when Δã0 is larger than a certain critical separation distance, (Δã0)crit. Furthermore, we showed that (Δã0)crit can be described semi-analytically as a function of the gaseous density. From a function extrapolated with a density in the minimum mass nebula model, we estimated (Δã0)crit in the nebula as being about 10 Hill radius at 1 AU.

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