Friends of Hot Jupiters. IV. Stellar companions beyond 50 AU might facilitate giant planet formation, but most are unlikely to cause Kozai-Lidov migrationAuthors:Ngo et alAbstract:Stellar companions can influence the formation and evolution of planetary systems, but there are currently few observational constraints on the properties of planet-hosting binary star systems. We search for stellar companions around 77 transiting hot Jupiter systems to explore the statistical properties of this population of companions as compared to field stars of similar spectral type. After correcting for survey incompleteness, we find that 47%±7% of hot Jupiter systems have stellar companions with semi-major axes between 50-2000 AU. This is 2.9 times larger than the field star companion fraction in this separation range, with a significance of 4.4σ. In the 1-50AU range, only 3.9+4.5−2.0% of hot Jupiters host stellar companions compared to the field star value of 16.4%±0.7%, which is a 2.7σ difference. We find that the distribution of mass ratios for stellar companions to hot Jupiter systems peaks at small values and therefore differs from that of field star binaries which tend to be uniformly distributed across all mass ratios. We conclude that either wide separation stellar binaries are more favorable sites for gas giant planet formation at all separations, or that the presence of stellar companions preferentially causes the inward migration of gas giant planets that formed farther out in the disk via dynamical processes such as Kozai-Lidov oscillations. We determine that less than 20% of hot Jupiters have stellar companions capable of inducing Kozai-Lidov oscillations assuming initial semi-major axes between 1-5 AU, implying that the enhanced companion occurrence is likely correlated with environments where gas giants can form efficiently.