Size-dependent modification of asteroid family Yarkovsky V-shapes

The thermal properties of the surfaces of asteroids determine the magnitude of the drift rate cause by the Yarkovsky force. In the general case of Main Belt asteroids, the Yarkovsky force is indirectly proportional to the thermal inertia, $\Gamma$. Following the proposed relationship between $\Gamma$ and asteroid diameter $D$, we find that asteroids' Yarkovsky drift rates might have a more complex size dependence than previous thought, leading to a curved family V-shape boundary in semi-major axis, a, vs. 1/$D$ space. This implies that asteroids are drifting faster at larger sizes than previously considered decreasing on average the known ages of asteroid families. The V-Shape curvature is determined for $>$25 families located throughout the Main Belt to quantify the Yarkovsky size-dependent drift rate. We find that there is no correlation between family age and V-shape curvature. In addition, the V-shape curvature decreases for asteroid families with larger heliocentric distances suggesting that the relationship between $\Gamma$ and $D$ is weaker in the outer MB possibly due to homogenous surface roughness among family members.