2012ApJ...750..106S

An important class of formation theories for hot Jupiters involves the excitation of extreme orbital eccentricity (e=0.99 or even larger) followed by tidal dissipation at periastron passage that eventually circularizes the planetary orbit at a period less than 10 days. In a steady state, this mechanism requires the existence of a significant population of super-eccentric (e > 0.9) migrating Jupiters with long orbital periods and periastron distances of only a few stellar radii. For these super-eccentric planets, the periastron is fixed due to conservation of orbital angular momentum and the energy dissipated per orbit is constant, implying that the rate of change in semi-major axis a is {dot}a∝a^1/2 and consequently the number distribution satisfies dN/d log a ∝a^1/2. If this formation process produces most hot Jupiters, Kepler should detect several super-eccentric migrating progenitors of hot Jupiters, allowing for a test of high-eccentricity migration scenarios.