  The Kepler light curves used to detect thousands of planetary candidates are
susceptible to dilution due to blending with previously unknown nearby stars.
With the automated laser adaptive optics instrument, Robo-AO, we have observed
620 nearby stars around 3857 planetary candidates host stars. Many of the
nearby stars, however, are not bound to the KOI. In this paper, we quantify the
association probability between each KOI and detected nearby stars through
several methods. Galactic stellar models and the observed stellar density are
used to estimate the number and properties of unbound stars. We estimate the
spectral type and distance to 145 KOIs with nearby stars using multi-band
observations from Robo-AO and Keck-AO. We find most nearby stars within 1" of a
Kepler planetary candidate are likely bound, in agreement with past studies. We
use likely bound stars as well as the precise stellar parameters from the
California Kepler Survey to search for correlations between stellar binarity
and planetary properties. No significant difference between the binarity
fraction of single and multiple planet systems is found, and planet hosting
stars follow similar binarity trends as field stars, many of which likely host
their own non-aligned planets. We find that hot Jupiters are ~4x more likely
than other planets to reside in a binary star system. We correct the radius
estimates of the planet candidates in characterized systems and find that for
likely bound systems, the estimated planetary candidate radii will increase on
average by a factor of 1.77, if either star is equally likely to host the
planet. We find that the planetary radius gap is robust to the impact of
dilution, and find an intriguing 95%-confidence discrepancy between the radius
distribution of small planets in single and binary systems.
