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.