Secular resonance sweeping of the main asteroid belt during planet migration

We calculate the eccentricity excitation of asteroids produced by the sweeping ν6 secular resonance during the epoch of planetesimal-driven giant planet migration in the early history of the solar system. We derive analytical expressions for the magnitude of the eccentricity change and its dependence on the sweep rate and on planetary parameters; the ν6 sweeping leads to either an increase or a decrease of eccentricity depending on an asteroid’s initial orbit. Based on the slowest rate of ν6 sweeping that allows a remnant asteroid belt to survive, we derive a lower limit on Saturn’s migration speed of ∼ 0.15 AU My during the era that the ν6 resonance swept through the inner asteroid belt (semimajor axis range 2.1–2.8 AU). This rate limit is for Saturn’s current eccentricity, and scales with the square of Saturn’s eccentricity; the limit on Saturn’s migration rate could be lower if Saturn’s eccentricity were lower during its migration. Applied to an ensemble of fictitious asteroids, our calculations show that a prior single-peaked distribution of asteroid eccentricities would be transformed into a double-peaked distribution due to the sweeping of the ν6. Examination of the orbital data of