Influence of Stellar Multiplicity On Planet Formation. II. Planets Are Less Common in Multiple-Star Systems with Separations Smaller than 1500 AU

Almost half of the stellar systems in the solar neighborhood are made up of multiple stars. In multiple-star systems, planet formation is under the dynamical influence of stellar companions, and the planet occurrence rate is expected to be different from that for single stars. There have been numerous studies on the planet occurrence rate of single star systems. However, to fully understand planet formation, the planet occurrence rate in multiple-star systems needs to be addressed. In this work, we {{infer}} the planet occurrence rate in multiple-star systems by measuring the stellar multiplicity rate for planet host stars. For a sub-sample of 56 $Kepler$ planet host stars, we use adaptive optics (AO) imaging and the radial velocity (RV) technique to search for stellar companions. The combination of these two techniques results in high search completeness for stellar companions. We detect 59 visual stellar companions to 25 planet host stars with AO data. {{Three stellar companions are within 2$^{\prime\prime}$, and 27 within 6$^{\prime\prime}$. We also detect 2 possible stellar companions (KOI 5 and KOI 69) showing long-term RV acceleration.}} After correcting for a bias against planet detection in multiple-star systems due to flux contamination, we find that planet formation is suppressed in multiple-star systems with separations smaller than 1500 AU. Specifically, we find that compared to single star systems, planets in multiple-star systems occur $4.5\pm3.2$, $2.6\pm1.0$, and $1.7\pm0.5$ times less frequently when a stellar companion is present at a distance of 10, 100, and 1000 AU, respectively. This conclusion applies only to circumstellar planets; the planet occurrence rate for circumbinary planets requires further investigation.