Searching for Small Circumbinary Planets. I. The STANLEY Automated Algorithm and No New Planets in Existing Systems

No circumbinary planets have been discovered smaller than 3 R_⊕, yet planets of this small size comprise over 75% of the discoveries around single stars. The observations do not prove the nonexistence of small circumbinary planets; rather, they are much harder to find than around single stars because their transit timing variations are much larger than the transit durations. We present STANLEY, an automated algorithm to find small circumbinary planets. It employs custom methods to detrend eclipsing binary light curves and stack shallow transits of variable duration and interval using N-body integrations. Applied to the Kepler circumbinaries, we recover all known planets, including the three planets of Kepler-47, and constrain the absence of additional planets of similar or smaller size. We also show that we could have detected <3 R_⊕ planets in half of the known systems. Our work will ultimately be applied to a broad sample of eclipsing binaries to (hopefully) produce new discoveries and derive a circumbinary size distribution that can be compared to that for single stars.