How Complete Are Surveys for Nearby Transiting Hot Jupiters?

Hot Jupiters are a rare and interesting outcome of planet formation. Although more than 500 hot Jupiters (HJs) are known, most of them were discovered by a heterogeneous collection of surveys with selection biases that are difficult to quantify. Currently, our best knowledge of HJ demographics around FGK stars comes from the sample of $\approx40$ objects detected by the Kepler mission, which have a well-quantified selection function. Using the Kepler results, we simulate the characteristics of the population of nearby transiting HJs. A comparison between the known sample of nearby HJs and simulated magnitude-limited samples leads to four conclusions: (1) The known sample of HJs appears to be $\approx 75\%$ complete for stars brighter than Gaia $G\leq10.5$, falling to $\lesssim 50\%$ for $G\leq12$. (2) There are probably a few undiscovered HJs with host stars brighter than $G\approx10$ located within 10$^\circ$ of the Galactic plane. (3) The period and radius distributions of HJs may differ for F-type hosts (which dominate the nearby sample) and G-type hosts (which dominate the Kepler sample). (4) To obtain a magnitude-limited sample of HJs that is larger than the Kepler sample by an order of magnitude, the limiting magnitude should be approximately $G\approx12.5$. This magnitude limit is within the range for which NASA's Transiting Exoplanet Survey Satellite (TESS) can easily detect HJs, presenting the opportunity to greatly expand our knowledge of hot Jupiter demographics.