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Resonant locking of two planets is an expected outcome of convergent discmigration. The planets subsequently migrate together as a resonant pair. In thecontext of circumbinary planets, the disc is truncated internally by thebinary. If there were only a single planet, then this inner disc edge wouldprovide a natural parking location. However, for two planets migrating togetherin resonance there will be a tension between the inner planet stopping at thedisc edge, and the outer planet continuing to be torqued inwards. In this paperwe study this effect, showing that the outcome is a function of theplanet-planet mass ratio. Smaller outer planets tend to be parked in a stableexterior 2:1 or 3:2 resonance with the inner planet, which itself remains nearthe disc edge. Equal or larger mass outer planets tend to push the inner planetpast the disc edge and too close to the binary, causing it to be ejected orsometimes flipped to an exterior orbit. Our simulations show that this processmay explain an observed dearth of small (< 3 Earth radii) circumbinary planets,since small planets are frequently ejected or left on long-period orbits, forwhich transit detection is less likely. This may also be an efficient mechanismfor producing free-floating planets and interstellar interlopers like`Oumuamua.

Sculpting the circumbinary planet size distribution through resonant interactions with companion planets