  Gas giant planets orbiting within 0.1 AU of their host stars, unlikely to
have formed in situ, are evidence for planetary migration. It is debated
whether the typical hot Jupiter smoothly migrated inward from its formation
location through the proto-planetary disk or was perturbed by another body onto
a highly eccentric orbit, which tidal dissipation subsequently shrank and
circularized during close stellar passages. Socrates and collaborators
predicted that the latter class of model should produce a population of
super-eccentric proto-hot Jupiters readily observable by Kepler. We find a
paucity of such planets in the Kepler sample, inconsistent with the theoretical
prediction with 96.9% confidence. Observational effects are unlikely to explain
this discrepancy. We find that the fraction of hot Jupiters with orbital period
P > 3 days produced by the star-planet Kozai mechanism does not exceed (at
two-sigma) 44%. Our results may indicate that disk migration is the dominant
channel for producing hot Jupiters with P > 3 days. Alternatively, the typical
hot Jupiter may have been perturbed to a high eccentricity by interactions with
a planetary rather than stellar companion and began tidal circularization much
interior to 1 AU after multiple scatterings. A final alternative is that tidal
circularization occurs much more rapidly early in the tidal circularization
process at high eccentricities than later in the process at low eccentricities,
contrary to current tidal theories.
