SECULAR RESONANCE SWEEPING OF THE MAIN ASTEROID BELT DURING PLANET MIGRATION

We calculate the eccentricity excitation of asteroids produced by the sweeping nu(6) 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 nu(6) sweeping leads to either an increase or a decrease of eccentricity depending on an asteroid's initial orbit. Based on the slowest rate of nu(6) sweeping that allows a remnant asteroid belt to survive, we derive a lower limit on Saturn's migration speed of similar to 0.15 AU Myr(-1) during the era that the nu(6) 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 its eccentricity; the limit on Saturn's migration rate could be lower if its 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 nu(6) resonance. Examination of the orbital data of main belt asteroids reveals that the proper eccentricities of the known bright (H <= 10.8) asteroids may be consistent with a double-peaked distribution. If so, our theoretical analysis then yields two possible solutions for the migration rate of Saturn and for the dynamical states of the pre-migration asteroid belt: a dynamically cold state (single-peaked eccentricity distribution with mean of similar to 0.05) linked with Saturn'smigration speed similar to 4 AU Myr(-1) or a dynamically hot state (single-peaked eccentricity distribution with mean of similar to 0.3) linked with Saturn's migration speed similar to 0.8 AU Myr(-1).