We study the capture and crossing probabilities into the 3:1 mean motion resonance with Jupiter for a small asteroid that migrates from the inner to the middle Main Belt under the action of the Yarkovsky effect. We use an algebraic mapping of the ave
raged planar restricted three-body problem based on the symplectic mapping of Hadjidemetriou (1993), adding the secular variations of the orbit of Jupiter and non-symplectic terms to simulate the migration. We found that, for fast migration rates, the captures occur at discrete windows of initial eccentricities whose specific locations depend on the initial resonant angles, indicating that the capture phenomenon is not probabilistic. For slow migration rates, these windows become narrower and start to accumulate at low eccentricities, generating a region of mutual overlap where the capture probability tends to 100%, in agreement with the theoretical predictions for the adiabatic regime. Our simulations allow to predict the capture probabilities in both the adiabatic and non-adiabatic cases, in good agreement with results of Gomes (1995) and Quillen (2006). We apply our model to the case of the Vesta asteroid family in the same context as Roig et al. (2008), and found results indicating that the high capture probability of Vesta family members into the 3:1 mean motion resonance is basically governed by the eccentricity of Jupiter and its secular variations.
The recent discovery of the first V-type asteroid in the middle belt, (21238) 1995WV7, located at ~2.54 AU, raises the question of whether it came from (4) Vesta or not. In this paper, we present spectroscopic observations indicating the existence of
another V-type asteroid at ~2.53 AU, (40521) 1999RL95, and we investigate the possibility that these two asteroids evolved from the Vesta family to their present orbits by drifting in semi-major axis due to the Yarkovsky effect. The main problem with this scenario is that the asteroids need to cross the 3/1 mean motion resonance with Jupiter, which is highly unstable. Combining numerical simulations of the orbital evolution, that include the Yarkovsky effect, with Monte Carlo models, we compute the probability of an asteroid of given diameter D to evolve from the Vesta family and to cross over the 3/1 resonance, reaching a stable orbit in the middle belt. Our results indicate that an asteroid like (21238) 1995WV7 has a low probability of having evolved through this mechanism due to its large size (~5 km). However, the mechanism might explain the orbit of smaller bodies like (40521) 1999RL95 (~3 km), provided that we assume that the Vesta family formed > 3.5 Gy ago. We estimate that about 10% or more of the V-type bodies with D>1 km may come from the Vesta family by crossing over the 3/1 resonance. The remaining 90% must have a different origin.
