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Tidal torques on infrequently colliding particle disks in binary systems and the truncation of the asteroid belt |
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| Authors: | FA Franklin M Lecar DNC Lin J Papaloizou |
| Institution: | 1. Institute of Astronomy, Madingley Road, Cambridge, England;2. Board of Studies in Astronomy and Astrophysics, University of California, Santa Cruz, California 95064, USA |
| Abstract: | We study numerically and analytically the conditions leading to the truncation, at the 2:1 resonance, of a disk of infrequently colliding particles surrounding the primary of a binary system. We focus on systems with small mass ratios, q, such as the Sun-Jupiter system with q = 10?3. Previous studies showed that if collisions are frequent with respect to the orbital period, truncation 3nly occurs if the Reynolds number is greater than q?2. This corresponds to particle eccentricity, e, less than of order q for a particle disk of optical depth unity. In thepresent case collisions are less frequent than orbital periods (the period of the forced eccentricity at the 2:1 resonance), and truncation occurs and (Kirkwood) gaps are produced only if e is less than some critical value which we estimate to be of order , or ～0.02 for the Sun-Jupiter case. We mention several means whereby the eccentricities may have been subsequently increased to their observed values. |
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