Concealing Circumbinary Planets with Tidal Shrinkage
Of the 14 transiting planets that have been detected orbiting eclipsing binaries ('circumbinary planets'), none have been detected with stellar binary orbital periods shorter than 7 days, despite such binaries existing in abundance. The eccentricity-period data for stellar binaries indicates that short-period ($< 7$ day) binaries have had their orbits tidally circularized. We examine here to what extent tidal circularization and shrinkage can conceal circumbinary planets, i.e. whether planets actually exist around short-period binaries, but are not detected because their transit probabilities drop as tides shrink the binary away from the planet. We carry out a population synthesis by initializing a population of eccentric stellar binaries hosting circumbinary planets, and then circularizing and tightening the host orbits using stellar tides. To match the circumbinary transit statistics, stellar binaries must form with eccentricities $\gtrsim$ 0.2 and periods $\gtrsim$ 6 days, with circumbinary planets emplaced on exterior stable orbits before tidal circularization; moreover, tidal dissipation must be efficient enough to circularize and shrink binaries out to $\sim$6-8 days. The resultant binaries that shrink to sub-7-day periods no longer host transiting planets. However, this scenario cannot explain the formation of nearly circular, tight binaries, brought to their present sub-seven-day orbits from other processes like disk migration. Still, tidal shrinkage can introduce a bias against finding transiting circumbinary planets, and predicts a population of KIC 3853259 (AB)b analogs consisting of wide-separation, non-transiting planets orbiting tight binaries.