He-Feng Hsieh (NTHU); Ing-Guey Jiang(NTHU)
The resonant perturbations from planets are able to halt the drag-induced migration, and capture the inwardly drifting planetesimals into mean motion resonances. The equilibrium eccentricity of planetesimals in resonances, and the minimum size of planetesimal that can trigger resonance trapping, have been analyzed and formulated. However, the analytical works based on the assumption that the disk is axis-symmetric, which is violated by the asymmetric structures developed by planets. We perform long-term 2D hydrodynamic simulations to study the dynamics of planetesimals in the j:(j+1) first-order exterior resonances, and re-examine the theoretical expressions. We find the expression of equilibrium eccentricity underestimates the values for resonances with j < 5. The deviation in eccentricity is significant in particular the case of 1:2 resonance, with a factor of 30 - 40%. With the values predicted by our modified expression, we find the equilibrium eccentricity is reduced significantly in a disk with asymmetric structures. The amount of discrepancy depends on the degree of asymmetric structures. For cases of Earth-sized planets, where the disk is less disturbed, the planetesimal's eccentricity can reach to the values predicted by the modified expression. For cases of gaseous planets, however, the eccentricity can be 0.01 - 0.02 smaller in value. We also find the exact minimum size can be 10 times smaller than the theoretical value. The influences of asymmetric profiles on the eccentricity and the minimum size could affect the outcome of collisions between resonant and non-resonant planetesimals, and the amount of planetesimals migrated into the planet's feeding zone.