Hamers et al
Detection of transiting circumbinary planets is more tractable around short-period binaries, however, no such binaries were found with orbits shorter than 7 days. Short-period main sequence binaries have been suggested to form in triple systems, through a combination of secular Kozai-Lidov cycles and tidal friction (KLCTF). Here, we show that coplanar circumbinary transiting planets are unlikely to exist around short-period binaries, due to triple evolution. We use secular analysis, N-body simulations and analytic considerations as well as population synthesis models to characterize their overall properties. We find that the existence of a circumbinary planet in a triple is likely to produce one of the following outcomes. (1) Sufficiently massive planets in tight and/or coplanar orbits around the inner binary can partially or completely quench the KL evolution, `shielding' the inner binary from the secular effects of the tertiary, and not allowing the KLCTF process to take place. In this case, the inner binary will not shrink to become a short-period binary. (2) KL evolution is not quenched and it drives the planetary orbit into high eccentricities, giving rise to an unstable configuration, in which the planet is most likely ejected from the system. (3) KL evolution is not quenched, but the planet survives the KLCTF evolution and the formation of the short-period binary; the planet orbit is likely to be much wider than the currently observed inner binary orbit, and is likely to be inclined in respect to the binary orbit, as well as eccentric. These outcomes lead to two main conclusions: (1) it is unlikely to find a (massive) planet on a tight and coplanar orbit around a short-period main-sequence binary, and (2) the frequency, masses and orbits of non-coplanar circumbinary planets in short-period binaries are constrained by their secular evolution.