Unveiling the Yarkovsky Effect: Enhanced V-Shape Clarity in Asteroid Families via a Spin-Diameter Metric

Abstract: Asteroid families, formed from catastrophic collisions, evolve under the Yarkovsky effect, which causes orbital drift dependent on both asteroid size and spin, theoretically producing a characteristic 'V'-shape in plots of orbital separation versus asteroid properties. However, the continuous modification of asteroid spins by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect often obscures this signature, complicating its empirical detection and the disentanglement of these two fundamental forces. This study introduces a novel methodology to empirically distinguish these effects by comparing the clarity of the V-shape morphology in two distinct representations: the traditional $\text{log(P)}$ versus $\text{log(|a-ac|)}$ (spin period vs. orbital separation) and a new composite variable $\text{log(sqrt(P)/D)}$ versus $\text{log(|a-ac|)}$ (combining spin period and diameter). We analyzed 12,879 asteroids across 35 asteroid families, employing a 'Consistency Metric' (C) and a 'Steepness Coefficient' (f) to quantitatively assess the clarity and form of the V-shape in each representation. Our results demonstrate that the $\text{log(sqrt(P)/D)}$ representation consistently yields significantly clearer V-shapes across families. Specifically, while only two families exhibited a 'Well-defined' V-shape (C > 3.0) using $\text{log(P)}$, twelve families showed this clarity with $\text{log(sqrt(P)/D)}$, with the latter representation producing a V-shape more than twice as clear on average (median $\Delta \text{C}$ = 2.22). This enhanced clarity is attributed to $\text{log(sqrt(P)/D)}$ more accurately capturing the combined size and spin dependence of Yarkovsky drift, making it inherently more robust to the long-term, YORP-induced scrambling of asteroid spin states. Although a direct correlation between this differential clarity and family age was not observed, likely due to the complexities of initial conditions and compositional variations, this approach provides a powerful new empirical tool for disentangling the coupled spin and orbital evolution processes that shape asteroid families over billions of years.

Subjects:	astro-ph.EP; physics.space-ph
Cite as:	PX:2508.00063