Secular Resonance Sweeping of the Main Asteroid Belt During Planet Migration

• Published in: The Astrophysical journal 2011-05, Vol.732 (1), p.53-jQuery1323909185286='48'
• Main Authors: Minton, David A, Malhotra, Renu
• Format: Article
• Language: English
• Subjects: ASTEROIDS; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ENERGY-LEVEL TRANSITIONS; EXCITATION; MIGRATION; ORBITS; PLANETS
• ISSN: 0004-637X; 1538-4357
• DOI: 10.1088/0004-637X/732/1/53

We calculate the eccentricity excitation of asteroids produced by the sweeping Delta *n6 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 Delta *n6 sweeping leads to either an increase or a decrease of eccentricity depending on an asteroid's initial orbit. Based on the slowest rate of Delta *n6 sweeping that allows a remnant asteroid belt to survive, we derive a lower limit on Saturn's migration speed of ~0.15 AU Myr--1 during the era that the Delta *n6 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 Delta *n6 resonance. Examination of the orbital data of main belt asteroids reveals that the proper eccentricities of the known bright (H