We have investigated numerically the orbital instability of a protoplanet system while taking account of the gasdrag force due to the solar nebula. In the present work, we considered an equally spaced five-protoplanet (with the same mass of 1 x 10-7 M⊙ ) 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 reexamined and confirmed that, under a gas-free condition, log10 Tinst 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.
- Gas-drag effect
- Solar system: formation