Most Sub-Arcsecond Companions of Kepler Exoplanet Candidate Host Stars are Gravitationally Bound

Using the known detection limits for high-resolution imaging observations and the statistical properties of true binary and line-of-sight companions, we estimate the binary fraction of {\it Kepler} exoplanet host stars. Our speckle imaging programs at the WIYN 3.5-m and Gemini North 8.1-m telescopes have observed over 600 {\it Kepler} objects of interest (KOIs) and detected 49 stellar companions within $\sim$1 arcsecond. Assuming binary stars follow a log-normal period distribution for an effective temperature range of 3,000 to 10,000 K, then the model predicts that the vast majority of detected sub-arcsecond companions are long period ($P>50$ years), gravitationally bound companions. In comparing the model predictions to the number of real detections in both observational programs, we conclude that the overall binary fraction of host stars is similar to the 40-50\% rate observed for field stars.