Impact of binary stars on planet statistics - I. Planet occurrence rates and trends with stellar mass

Close binaries suppress the formation of circumstellar (S-type) planets and therefore significantly bias the inferred planet occurrence rates and statistical trends. After compiling various radial velocity and high-resolution imaging surveys, we determine that binaries with a < 1 au fully suppress S-type planets, binaries with a = 10 au host close planets at 15$_{-12}^{+17}$ per cent the occurrence rate of single stars, and wide binaries with a > 200 au have a negligible effect on close planet formation. We show that F = 43 ± 7 per cent of solar-type primaries in magnitude-limited samples do not host close planets due to suppression by close stellar companions. By removing spectroscopic binaries from their samples, radial velocity surveys for giant planets boost their detection rates by a factor of 1/(1-F) = 1.8 ± 0.2 compared to transiting surveys. This selection bias fully accounts for the discrepancy in hot Jupiter and close Neptune occurrence rates inferred from these two detection methods. Correcting for both planet suppression by close binaries and transit dilution by wide binaries, the occurrence rate of small planets orbiting single G-dwarfs is 2.1 ± 0.3 times larger than the rate inferred from all G-dwarfs in the Kepler survey. Additionally, about half (but not all) of the observed increase in small, short-period planets towards low-mass hosts can be explained by the corresponding decrease in the binary fraction.