Quantifying Yarkovsky-Driven Orbital Dispersion Gradients and Proxy Efficacy in Asteroid Families

Abstract: The Yarkovsky effect, a crucial non-gravitational force, systematically disperses asteroid family members in semimajor axis, leading to characteristic V-shaped distributions. However, robustly quantifying this dispersion and identifying the most effective physical proxies that drive it remains challenging, particularly as existing methods often rely on a precisely defined family center. This study introduces the Orbital Dispersion Gradient (ODG) method, a novel approach that quantifies the rate of increase in semimajor axis standard deviation ($\sigma_a$) with respect to various Yarkovsky-sensitive proxies, thereby circumventing the need for a precise family center. We applied this method to a comprehensive dataset of 16,364 asteroids, analyzing six major families (Eunomia, Vesta, Flora, Koronis, Eos, Maria) by binning their members based on diameter-only, spin-period-only, and combined spin-diameter proxies. Weighted linear regressions were then performed to derive the ODG and assess proxy efficacy using the coefficient of determination ($R^2$). Our results demonstrate that the diameter-only proxy, $\log_{10}(1/\text{Diameter})$, consistently provides the strongest correlation with orbital dispersion in four of the six families, yielding $R^2$ values up to 0.9353 for the Maria family. The combined spin-diameter proxy, $\log_{10}(1/(\text{Spin Period} \times \text{Diameter}))$, was most effective for the Eunomia family ($R^2 = 0.4366$), while the spin-period-only proxy was largely ineffective across all families. Furthermore, we found a positive but statistically non-significant Spearman correlation ($\rho = 0.3714$, p-value = 0.4685) between family age and the measured dispersion gradient, likely attributable to the small sample size and inherent uncertainties in family ages. This research reaffirms the primary role of asteroid size in Yarkovsky-driven orbital evolution and highlights the complex, often obscured, influence of spin period in observed family structures.

Subjects:	astro-ph.EP; physics.space-ph
Cite as:	PX:2508.00059