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The relationship between the `limiting' Yarkovsky drift speed and asteroid families' Yarkovsky V-shape

The Yarkovsky effect is an important force to consider in order to understand
 the long-term dynamics of asteroids. This non-gravitational force affects the
 orbital elements of objects revolving around a source of heat, especially
 their semi-major axes. Following the recently defined `limiting' value of the
 Yarkovsky drift speed at 7x10-5 au/Myr in Milic Zitnik (2019) (below this
 value of speed asteroids typically jump quickly across the mean motion
 resonances), we decided to investigate the relation between the asteroid
 family Yarkovsky V-shape and the `limiting' Yarkovsky drift speed of
 asteroid's semi-major axes. We have used the known scaling formula to
 calculate the Yarkovsky drift speed (Spoto et al. 2015) in order to
 determine the inner and outer `limiting' diameters (for the inner and outer
 V-shape borders) from the `limiting' Yarkovsky drift speed. The method was
 applied to 11 asteroid families of different taxonomic classes, origin type
 and age, located throughout the Main Belt. Here, we present the results of
 our calculation on relationship between asteroid families' V-shapes (crossed
 by strong and/or weak mean motion resonances) and the `limiting' diameters
 in the (a, 1=D) plane. Our main conclusion is that the `breakpoints' in
 changing V-shape of the very old asteroid families, crossed by relatively
 strong mean motion resonances on both sides very close to the parent body,
 are exactly the inverse of `limiting' diameters in the a versus 1=D plane.
 This result uncovers a novel interesting property of asteroid families'
 Yarkovsky V-shapes.