在原始行星盤中，微行星因氣體阻滯力而向中心的恆星遷移。若其軌道內有一行星，在此行星的重力影響下，微行星可被行星共振陷獲而停止遷移。藉由引入微行星運動方程式之高階項，我們重新推導處於平衡態下的微行星其離心率，與可被共振陷獲的微行星之最小半徑。在 j : (j + 1) 外部共振情況下， 平衡態下的微行星其離心率應較文獻值高上 10%— 40%，而最小半徑則小上約莫十倍。此預測與多體模擬軟體 REBOUND 之模擬結果相符。我們並推導出微行星離心率其增長時間。此增長時間為 j、平衡態下的微行星離心率、及微行星的史托克斯數之一函數。
此理論分析建基於此原始行星盤的氣體呈軸對稱分佈，然而行星的重力會於行星盤引起非軸對稱之結構（例如旋臂）。藉由流體軟體 FARGO3D 的幫助，我們模擬處於非軸對稱行星盤的微行星之演化，並探討非軸對稱結構對其之影響。我們發現行星盤的演化會影響並降低微行星其離心率。此乃因行星盤上之氣體會於行星外堆積，使共振軌道周圍的氣體分佈變得平緩，進而減少處於平衡態下的微行星其離心率。然而，我們亦發現若行星盤被高度擾動，即使考量行星盤之氣體演化，微行星其離心率仍較理論值低。此偏差似與非軸對稱之結構相關，但仍須進一步的討論。於最小半徑，我們發現對於特定大小下之微行星可被短暫共振陷獲，並最終因行星盤演化而逃脫共振陷獲。

We revisit the resonance trapping that the drag-induced drifting planetesimals
are halted and captured into mean motion resonances due to the gravitational force from
the inner planets.
By including the high order $e^3$ term in the equations of motion of gas drag,
we revise the analytical expressions,
which predict the equilibrium eccentricity of resonant planetesimals
and the minimum size of planetesimal that can trigger resonance trapping,
for $j:(j + 1)$ exterior resonances.
We find the equilibrium eccentricity is $10\% - 40\%$ times larger,
and the minimum size is $10$ times smaller,
for planetesimals trapped in resonances with small $j$.
The revised expressions are consistent with the \textit{N}-body simulation results
generated by the REBOUND code.
We also derive the expression of the growth time of planetesimal eccentricity.
The growth time depends on $j$, the equilibrium eccentricity,
and the Stokes number of the planetesimal.
For planetesimals with larger size,
the required growth time would be longer.

The analytical works are based on the assumption that the disk is axisymmetric.
However, the presence of planets could generate asymmetric structures (e.g., spiral arms)
so that the disk is no longer axisymmetric.
We further perform 2D hydrodynamic simulations using FARGO3D
to study the dynamics of resonant planetesimals in an asymmetric gaseous disk.
We find the eccentricity of resonant planetesimals are reduced due to the evolved density profile.
The viscous evolution causes the gas at the outer disk migrates inward
and accumulates outside the planet due to the planet's gravity,
resulting in the flatter density profile in the vicinity of resonance locations
and the smaller equilibrium eccentricity.
However, in part of the simulations where the planet is massive,
the planetesimal eccentricity is smaller than the equilibrium eccentricity
evaluated using the evolved density profile.
We find the deviation in eccentricity is more pronounced if the disk is highly disturbed,
which seems to be related to the asymmetric structures in the disk.
On the minimum size,
we find that for planetesimals in sizes of a certain range,
they can be transiently trapped into resonances,
and will eventually leave the resonance due to the disk evolution.

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