Robo-AO Kepler Survey. IV. The Effect of Nearby Stars on 3857 Planetary Candidate Systems

We present the overall statistical results from the Robo-AO Kepler planetary candidate survey, comprising of 3857 high-angular resolution observations of planetary candidate systems with Robo-AO, an automated laser adaptive optics system. These observations reveal previously unknown nearby stars blended with the planetary candidate host stars that alter the derived planetary radii or may be the source of an astrophysical false positive transit signal. In the first three papers in the survey, we detected 440 nearby stars around 3313 planetary candidate host stars. In this paper, we present observations of 532 planetary candidate host stars, detecting 94 companions around 88 stars; 84 of these companions have not previously been observed in high resolution. We also report 50 more-widely separated companions near 715 targets previously observed by Robo-AO. We derive corrected planetary radius estimates for the 814 planetary candidates in systems with a detected nearby star. If planetary candidates are equally likely to orbit the primary or secondary star, the radius estimates for planetary candidates in systems with likely bound nearby stars increase by a factor of 1.54, on average. We find that 35 previously believed rocky planet candidates are likely not rocky due to the presence of nearby stars. From the combined data sets from the complete Robo-AO KOI survey, we find that 14.5 0.5% of planetary candidate hosts have a nearby star with 4″, while 1.2% have two nearby stars, and 0.08% have three. We find that 16% of Earth-sized, 13% of Neptune-sized, 14% of Saturn-sized, and 19% of Jupiter-sized planet candidates have detected nearby stars.