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

The distribution of the orbital inclination angles of circumbinary planets (CBPs) is an important scientific issue, and it is of great significance for estimating the occurrence rate of CBPs and studying their formation and evolution. Although the CBPs currently discovered by the transit method are nearly coplanar, the true distribution of the inclinations of CBPs is still unknown. Previous research on CBPs has mostly regarded them as isolated binary-planet systems, without considering the birth environment of their host binaries. It is generally believed that almost all stars are born in clusters. Therefore, it is necessary to consider the effects of the close encounters of stars on CBP systems. In this paper, we discuss how the close encounters of fly-by stars affect the inclinations of CBPs. Based on extensive numerical simulations, we have found that CBPs in a close binary with a spacing of similar to 0.2 au are almost unaffected by fly-by stars. Their orbits remain coplanar. However, when the spacing of the binary stars is greater than 1 au, two to three fly-bys of an intruding star can excite a considerable inclination, even for a CBP near the unstable boundary of the binary. For CBPs in the outer region, the fly-by of a single star can excite an inclination to more than 5 0 . In particular, CBPs in near polar or retrograde orbits can naturally form through binary-star encounters. If close binaries are born in open clusters, our simulations suggest that there may be high-inclination CBPs in binaries with a spacing > 1 au.