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Impact of Binary Stars on Planet Statistics -- I. Planet Occurrence Rates, Trends with Stellar Mass, and Wide Companions to Hot Jupiter Hosts

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% 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% of solar-type primaries 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 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 toward low-mass hosts can be explained by the corresponding decrease in the binary fraction. Finally, we demonstrate that the apparent enhancement of wide stellar companions to hot Jupiter hosts is due to multiple selection effects. Very close binaries, brown dwarf companions, and massive planets with M_2 > 7 M_J within a < 0.2 au preferentially have metal-poor hosts and wide tertiary companions, but genuine hot Jupiters with M_p = 0.2-4 M_J that formed via core accretion instead favor metal-rich hosts and do not exhibit a statistically significant excess of wide stellar companions.