Most Hot Jupiters Were Cool Giant Planets for More Than 1 Gyr

Abstract

The origin of hot Jupiters is the oldest problem in exoplanet astrophysics. Hot Jupiters formed in situ or via disk migration should be in place just a few Myr after the formation of their host stars. On the other hand, hot Jupiters formed via eccentricity excitation and tidal damping as a result of planet--planet scattering or Kozai-Lidov oscillations may take 1 Gyr or more to arrive at their observed locations. We propose that the relative ages of hot Jupiters inside, near, and outside the bias-corrected peak of the observed hot Jupiter period distribution can be used to distinguish between these possibilities. Though the lack of precise and accurate age inferences for isolated hot Jupiter host stars makes this test difficult to implement, comparisons between the Galactic velocity dispersions of the hot Jupiter subpopulations enable this investigation. To transform relative age offsets into absolute age offsets, we calibrate the monotonically increasing solar neighborhood age--velocity dispersion relation using an all-sky sample of subgiants with precise ages and a metallicity distribution matched to that of hot Jupiter hosts. We find that the inside-peak and near-peak subpopulations are older than the outside-peak subpopulation, with the inside-peak subpopulation slightly older than the near-peak subpopulation. We conclude that at least 40\% but not more than 70\% of the hot Jupiter population must have formed via a late-time, peak-populating process like high-eccentricity migration that typically occurs more than 1.5 Gyr after system formation.