In the following thre figures we report plots of the mean values of a, e, and i for the three simulations involving Adeona.  For real members of Adeona, variations in sigma_a covered a range of less than 2% of the initial value, 5% for members of the synthetic families integrated with SWIFT-SKEEL, and 600% for the Yarkovsky simulation.   The fact that members of the synthetic family experienced a larger dispersion in a than real members might be due to the their smaller original dispersion in a, so that it was more probable for asteroids to be scattered outwards than inwards.   If that is true, than close encounters could be playing a non negligible role in dispersing asteroid families in the immediate phases after their creation.  About the Yarkovsky integration, David Nesvorny' wrote a paragraph in the Flora's article about the qualitative difference between the semimajor axis mobility driven by the gravitational perturbations of massive asteroids and that driven by the Yarkovsky effect.   "Essentially, while semimajor axis jumps more or less randomly (but we power law with B usually larger than 0.5) due to close encounters, the Yarkovsky force affects the standard deviation of the a distribution in a more complex way.  First, the bodies start to migrate, depending on their spin axis orientations and physical properties, either outwards (if the diurnal effect dominates and the spin orientation is less than 90^o, or inwards (if the spin orientation is more than 90^o, or the seasonal effect dominates).  Before that their spin axis is re-oriented by small impactors, the migration speed and direction are fixed.  Consequently, the standard deviation computed over an ensemble of particles must linearly increase with time.   This is what we actually observe for sigma_da computed from the Yarkovsky simulations.
 
 

The most interesting result from the close encounters simulation was obtained for the case of the synthetic Gefion family:  variation in sigma_a reached a maximum value of 30% (2% for real members of Gefion, 500% for the Yarkovsky simulation).  Most of the change occurred in the first 400 Myr of the integration, and then the dispersion in a remained approximately constant.   We believe that this could be due to the smaller initial dispersion in a: once the family expand sufficiently, the chance of being scattered outward decreases, and  so the increase in sigma_a.
 

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