Biases in Planet Occurrence Caused by Unresolved Binaries in Transit Surveys
Wide-field surveys for transiting planets, such as Kepler and TESS, are usually conducted without knowing which stars have binary companions. Unrecognized binaries lead to systematic errors in the inferred number of planets per star, i.e., in the occurrence rates. To gauge the amplitude and sign of the errors, we developed an analytic model of a signal-to-noise limited transit survey. This allows us to calculate the relationship between the true occurrence rate, and the apparent occurrence rate measured by an observer who falsely assumes all stars are single.
Applying our formalism to an idealized Kepler-like survey, we find that
- for Earth-sized planets, planet occurrence rates can be overestimated by as much as 50%, depending on the (unknown) true radius distribution of planets smaller than about 2 R_earth;
- for planets larger than 2 R_earth, the systematic errors associated with binarity are on the order of a few percent;
- detected planets with small apparent radii are more likely to be in binaries than detected planets with large apparent radii;
- whenever high-resolution imaging reveals a transit host star to be a binary, the planet is more likely to orbit the primary star than the secondary. However, the Kepler catalog probably does include a small population of planets around secondary stars of unresolved binaries.