Spin-Orbit V-Shapes in Asteroid Families: Empirical Constraints for Yarkovsky-YORP Evolution

Abstract: The long-term orbital and spin evolution of asteroid families is primarily governed by the Yarkovsky and YORP non-gravitational effects, which manifest as characteristic "V-shapes" in asteroid family distributions when plotting inverse diameter against semi-major axis. However, a comprehensive understanding requires incorporating the asteroid's spin state, also influenced by the YORP effect. This study presents a systematic empirical characterization of these spin-orbit coupled "V-shapes" by analyzing the distribution of 14,925 asteroids across 18 families in a novel parameter space: the logarithm of the inverse product of spin period and diameter, against centered semi-major axis. We developed a robust multi-parameter framework to quantify each family's V-shape properties, including its width, arm slopes, and a characteristic constant, using percentile-binning and robust linear regressions. Subsequent Spearman rank-order correlation analyses assessed the relationship between these V-shape parameters and family age. Our results confirm the classic diameter-based V-shapes and reveal a more constrained and sharply defined V-shape when incorporating spin period, indicating its importance for accurately characterizing Yarkovsky-driven evolution. Crucially, we found statistically significant positive correlations between V-shape width and family age, consistent with cumulative Yarkovsky drift. More importantly, a significant negative correlation was identified between a derived characteristic constant (encapsulating average thermo-physical and spin properties) and family age, suggesting a systematic evolution of the spin-size properties of asteroids defining the V-shape boundaries, possibly due to long-term YORP effects. Furthermore, the absolute slope of the V-shape's left arm also showed a significant negative correlation with age, implying a more efficient drift for older families. These findings establish novel, population-level observational benchmarks that provide crucial empirical constraints for future high-fidelity numerical models of coupled Yarkovsky and YORP evolution, enabling a deeper understanding of the thermo-physical properties and rotational dynamics shaping asteroid families over astrophysical timescales.

Subjects:	astro-ph.EP; physics.space-ph
Cite as:	PX:2508.00060