Quantifying Spin-Dependent Yarkovsky Drift: Empirical Evidence from Asteroid Family V-Shapes

Abstract: Asteroid families gradually disperse over cosmic timescales primarily due to the Yarkovsky effect, an acceleration mechanism driven by anisotropic thermal re-emission that depends on an asteroid's size, spin, and thermophysical properties. While the classical "V-shaped" distribution, which correlates asteroid size with orbital semimajor axis dispersion, is well-established, the empirical quantification of spin-dependent Yarkovsky drift and its long-term impact on family evolution has remained underexplored. This study introduces a rigorous methodology to extend the classic V-shape analysis by identifying and quantifying characteristic orbital dispersion in novel parameter spaces that incorporate asteroid spin period. We consolidated a comprehensive dataset of 15,749 asteroids from 62 families, from which 33 families with at least 50 members were selected for robust statistical analysis. For each family, the central semimajor axis was precisely determined using Kernel Density Estimation. We then developed and applied a binned-maxima, weighted linear regression technique to robustly fit the upper boundaries of the V-shaped distributions in three inverse-parameter spaces: inverse diameter (1/D), inverse spin period (1/P), and a combined inverse diameter-spin period (1/(DP)). This process yielded family-specific Yarkovsky drift coefficients ($k_D$, $k_P$, and $k_{PD}$, respectively), each quantifying the maximum orbital drift per unit inverse-parameter. Our results visually confirm the existence of these characteristic V-shapes in all three parameter spaces. Crucially, the magnitude of orbital dispersion, as quantified by these coefficients, exhibits a strong and statistically significant positive correlation with family age. Specifically, we found Pearson correlation coefficients of $r=0.629$ ($p=8.88times10^{-5}$) for $k_D$ vs. age, $r=0.492$ ($p=0.0037$) for $k_P$ vs. age, and $r=0.618$ ($p=1.27times10^{-4}$) for $k_{PD}$ vs. age. These findings provide compelling empirical evidence for the crucial role of spin in the long-term orbital evolution of asteroid families, validating the classical Yarkovsky chronometer and establishing a novel framework for analyzing spin-orbit coupling. Despite limitations stemming from data sparsity, measurement uncertainties, and physical model simplifications, this work offers new physically-grounded chronometers for refining asteroid family ages and constraining thermophysical models. \

Subjects:	astro-ph.EP; physics.space-ph
Cite as:	PX:2508.00061