2017AJ....153..117H

We report on 176 close (<2'') stellar companions detected with high-resolution imaging near 170 hosts of Kepler Objects of Interest (KOIs). These Kepler targets were prioritized for imaging follow-up based on the presence of small planets, so most of the KOIs in these systems (176 out of 204) have nominal radii <6 R_⊕. Each KOI in our sample was observed in at least two filters with adaptive optics, speckle imaging, lucky imaging, or the Hubble Space Telescope. Multi-filter photometry provides color information on the companions, allowing us to constrain their stellar properties and assess the probability that the companions are physically bound. We find that 60%-80% of companions within 1'' are bound, and the bound fraction is >90% for companions within 0.''5; the bound fraction decreases with increasing angular separation. This picture is consistent with simulations of the binary and background stellar populations in the Kepler field. We also reassess the planet radii in these systems, converting the observed differential magnitudes to a contamination in the Kepler bandpass and calculating the planet radius correction factor, X_R = R_p(true)/R_p(single). Under the assumption that planets in bound binaries are equally likely to orbit the primary or secondary, we find a mean radius correction factor for planets in stellar multiples of X_R = 1.65. If stellar multiplicity in the Kepler field is similar to the solar neighborhood, then nearly half of all Kepler planets may have radii underestimated by an average of 65%, unless vetted using high-resolution imaging or spectroscopy.