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The inclination distribution of circumbinary planets (CBPs) is an importantscientific issue. It is of great significance in estimating the occurrence rateof CBPs and studying their formation and evolution. Although the CBPs currentlydiscovered by the transit method are nearly coplanar, the true inclinationdistribution of CBPs is still unknown. Previous researches on CBPs mostlyregarded them as an isolated binary-planet system, without considering thebirth environment of their host binaries. It is generally believed that almostall stars are born in clusters. Therefore, it is necessary to consider theimpact of the close encounters of stars on the CBP systems. This articlediscusses how the close encounters of fly-by stars affect the inclination ofCBP. Based on extensive numerical simulations, we found that CBPs in closebinary with a spacing of about 0.2 au are almost unaffected by star fly-bys.Their orbits remain coplanar. However, when the spacing of the binary stars isgreater than 1 au, the 2-3 fly-bys of the intruding star can excite aconsiderable inclination even for the CBP near the unstable boundary of thebinary. For the planets in the outer region, a single star fly-by can excite aninclination to more than 5 degrees. Especially, CBPs in near polar orretrograde orbits can naturally form through bianry-star encounters. If closebinaries are born in open clusters, our simulations suggest that there may behigh-inclination CBPs in binaries with spacing > 1 au.

Birth environment of circumbinary planets: are there CBPs on the inclined orbits?