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Wide-field surveys for transiting planets, such as the NASA Kepler and TESSmissions, are usually conducted without knowing which stars have binarycompanions. Unresolved and unrecognized binaries give rise to systematic errorsin planet occurrence rates, including misclassified planets and mistakes incompleteness corrections. The individual errors can have different signs,making it difficult to anticipate the net effect on inferred occurrence rates.Here we use simplified models of signal-to-noise limited transit surveys to tryand clarify the situation. We derive a formula for the apparent occurrence ratedensity measured by an observer who falsely assumes all stars are single. Theformula depends on the binary fraction; the mass function of the secondarystars; and the true occurrence of planets around primaries, secondaries, andsingle stars. It also takes into account the Malmquist bias by which binariesare over-represented in flux-limited samples. Application of the formula to anidealized Kepler-like survey shows that for planets larger than 2 $R_\oplus$,the net systematic error is of order 5%. In particular, unrecognized binariesare unlikely to be the reason for the apparent discrepancies between hotJupiter occurrence rates measured in different surveys. For smaller planets theerrors are potentially larger: the occurrence of Earth-sized planets could beoverestimated by as much as 50%. We also show that whenever high-resolutionimaging reveals a transit host star to be a binary, the planet is usually morelikely to orbit the primary star than the secondary star.

Biases in Planet Occurrence Caused by Unresolved Binaries in Transit Surveys