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D. P. O'Brien, R. Greenberg (Lunar and Planetary Lab, University of Arizona)
It has been proposed that the size distribution of main-belt asteroids may be significantly modified by the Yarkovsky effect---a size-dependent radiation force which can sweep asteroids into resonances and out of the main belt. Bell [1] suggested that this effect could deplete the population of asteroids smaller than ~10 m by at least an order of magnitude, resulting in the lack of small craters observed on Eros. Others have hypothesized that the same effect could explain the steepness of the crater distribution on Gaspra [2]. We have explicitly included Yarkovsky removal in a numerical collisional evolution model. The algorithm uses recent calculations of the expected removal rates of different sized bodies from the main belt (David Vokrouhlicky, personal communication). We find that the rate of removal of bodies from the main belt by the Yarkovsky effect may be within an order of magnitude of the rate of collisional destruction for asteroids ~10 m in diameter, and negligible for larger or smaller asteroids.
When Yarkovsky removal is incorporated into our numerical collisional evolution model, the numbers of bodies ~10 m in diameter is reduced by ~10-20%, and a wave propagates up the size distribution increasing the number of bodies ~300 m by ~10%. This `waviness' could conceivably be detected in the cratering records on asteroids. However, the uncertainties in crater counts on Ida, Gaspra, Malthide, and Eros are >10% for diameters >100 m (i. e. the craters made by impactors >10 m in diameter). Contrary to the earlier hypothesis, Yarkovsky removal of small asteroids cannot have substantially affected the overall slopes of the crater populations on these asteroids. Moreover, Yarkovsky removal cannot explain the lack of small (<10 m) craters on Eros, because the corresponding impactors (<1 m) are unaffected by the Yarkovsky effect.
[1] Bell, J. F. (2001). LPSC XXXII abstract no. 1964. [2] Hartmann, W. K. and E. V. Ryan (1996). DPS 28, abstract no. 10.35.