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While cooler giant planets are often observed with non-zero eccentricities,the short-period circular orbits of hot Jupiters suggest that they lose orbitalenergy and angular momentum due to tidal interactions with their host stars.However, orbital decay has never been unambiguously observed. We use data fromGaia Data Release 2 to show that hot Jupiter host stars have a smaller Galacticvelocity dispersion than a similar population of stars without hot Jupiters.Since Galactic velocity dispersion is correlated with age, this observationimplies that the population of hot Jupiter host stars is on average youngerthan the field population. The best explanation for this inference is thattidal interactions cause hot Jupiters to inspiral while their host stars are onthe main sequence. This observation requires that the typical modified stellartidal quality factor $Q_{\ast}^{'}$ for solar-type stars be in the range$\log_{10}{Q_{\ast}^{'}} \lesssim 7$.

Hot Jupiters are Destroyed by Tides While Their Host Stars are on the Main Sequence