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Planet formation is often considered in the context of one circumstellar diskaround one star. Yet stellar binary systems are ubiquitous, and thus asubstantial fraction of all potential planets must form and evolve in morecomplex, dynamical environments. We present the results of a five-yearastrometric monitoring campaign studying 45 binary star systems that hostKepler planet candidates. The planet-forming environments in these systemswould have literally been shaped by the binary orbits that persist to thepresent day. Crucially, the mutual inclinations of star-planet orbits can onlybe addressed by a statistical sample. We describe in detail our sampleselection and Keck/NIRC2 laser guide star adaptive optics observationscollected from 2012 to 2017. We measure orbital arcs, with a typical accuracyof ~0.1 mas/yr, that test whether the binary orbits tend to be aligned with theedge-on transiting planet orbits. We rule out randomly-distributed binaryorbits at 4.7$\sigma$, and we show that low mutual inclinations are required toexplain the observed orbital arcs. If the stellar orbits have a fieldbinary-like eccentricity distribution, then the best match to our observedorbital arcs is a distribution of mutual inclinations ranging from 0-30degrees. We discuss the implications of such widespread planet-binary alignmentin the theoretical context of planet formation and circumstellar diskevolution.

Orbital Architectures of Planet-Hosting Binaries II. Low Mutual Inclinations Between Planetary and Stellar Orbits