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In star clusters, close stellar encounters can strongly impact the architecture of a planetary system or even destroy it. We present a systematic study on the effects of stellar flybys on two-planet systems. When such a system experiences flybys, one or both planets can be ejected, forming free-floating planets (FFPs), captured planets (CPs) around the flyby star, and free-floating binary planets (BPs) ; the remaining single-surviving-planets (SSPs) can have their orbital radii and eccentricities greatly changed. Through numerical experiments, we calculate the formation fractions (or branching ratios) of FFPs, SSPs, CPs and BPs as a function of the pericenter distance of the flyby, and use them to derive analytical expressions for the formation rates of FFPs, SSPs, CPs and BPs in general cluster environments. We find that the production rates of FFPs and SSPs are similar (for initial planet semi-major axis ratio a₁/a₂=0. 6-0. 8), while the rate for CPs is a few times smaller. The formation fraction of BPs depends strongly on a₁/a₂ and on the planet masses. For Jupiter-mass planets, the formation fraction of BPs is always less than 1\% (for a₁/a₂=0. 8) and typically much smaller (0. 2\% for a₁/a₂ 0. 7). The fraction remains less than 1\% when considering 4M ₉ planets. Overall, when averaging over all flybys, the production rate of BPs is less than 0. 1\% of that for FFPs. We also derive the velocity distribution of FFPs produced by stellar flybys, and the orbital parameter distributions of SSPs, CPs and BPs. These results can be used in future studies of exotic planets (including FFPs) and planetary systems.
Yu et al. (Mon,) studied this question.