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Understanding The Effects Of Stellar Multiplicity On The Derived Planet Radii From Transit Surveys: Implications for Kepler, K2, and TESS

We present a study on the effect of undetected stellar companions on the derived planetary radii for the Kepler Objects of Interest (KOIs). The current production of the KOI list assumes that the each KOI is a single star. Not accounting for stellar multiplicity statistically biases the planets towards smaller radii. The bias towards smaller radii depends on the properties of the companion stars and whether the planets orbit the primary or the companion stars. Defining a planetary radius correction factor $X_R$, we find that if the KOIs are assumed to be single, then, {\it on average}, the planetary radii may be underestimated by a factor of $\langle X_R \rangle \approx 1.5$. If typical radial velocity and high resolution imaging observations are performed and no companions are detected, this factor reduces to $\langle X_R \rangle \approx 1.2$. The correction factor $\langle X_R \rangle$ is dependent upon the primary star properties and ranges from $\langle X_R \rangle \approx 1.6$ for A and F stars to $\langle X_R \rangle \approx 1.2$ for K and M stars. For missions like K2 and TESS where the stars may be closer than the stars in the Kepler target sample, observational vetting (primary imaging) reduces the radius correction factor to $\langle X_R \rangle \approx 1.1$. Finally, we show that if the stellar multiplicity rates are not accounted for correctly, occurrence rate calculations for Earth-sized planets may overestimate the frequency of small planets by as much as $15-20$\%.