Exploring rotational properties and the YORP effect in asteroid families

TL;DR

The study addresses how asteroid rotational states evolve under YORP and collisional processes across asteroid families by analyzing spin periods and obliquities in a dimensionless time t = age / tau_YORP. The authors introduce t to enable cross-family comparisons, quantify two observables (f_slow and f_pol), and fit their evolution with robust piecewise models, revealing a stochastic YORP timescale about 10 times longer than the static prediction and a transition to collision-dominated spin reorientation around t ≈ 20. These findings constrain long-term rotational evolution, inform the interpretation of family ages from V-shapes, and offer a new diagnostic dimension for ages in the LSST era. Overall, the work provides population-level empirical support for stochastic YORP and highlights the evolving role of collisions in shaping spin states over Gyr timescales, with practical implications for age dating of asteroid families.

Abstract

The long-term dynamical evolution of asteroid families is governed by the interplay between orbital and rotational evolution driven by thermal forces and collision. We aim to observationally trace the rotational evolution of main-belt asteroid families over Gyr timescales. We analyzed rotational properties of 8739 asteroids with spin period measurements and 3794 asteroids with obliquity determinations across 28 asteroid families spanning ages from 14~Myrs to 3~Gyrs. We introduced a dimensionless timescale that normalizes each asteroid's family age by its classical YORP timescale, enabling direct comparison of rotational states across different evolutionary stages. We examined two key observables: the fraction of slow rotators (periods greater than or equal to 30 hours) and the polarization fraction (the degree to which asteroid spin poles align correctly with their position in the family's V-shape distribution according to the Yarkovsky theory). Evolution of both quantities were fitted to identify characteristic transition timescales. We discovered that the slow-rotator fraction increases steeply with $t$ and saturates at $f_{\rm slow} \simeq 0.25$ around a breakpoint $t_{\rm bp} \simeq 20$. This implies a stochastic YORP timescale $τ_{\rm YORP,stoc} \simeq 10\,τ_{\rm YORP}$ by comparison with rotational evolution models that include tumbling and weakened YORP torques. The polarization fraction reaches a maximum of $\simeq 0.8$ at $t \simeq 16$ and then decays toward the random limit $f_{\rm pol} \rightarrow 0.5$ for $t \gtrsim 20$, indicating an increasing dominance of collisional spin reorientation over time. The rotation properties within different asteroid families offer crucial clues to rotation evolution and can serve as a new dimension for age estimation of asteroid families with more data in the LSST era.

Figures (5)

• Figure 1: In gray, observational data from Gaia showing the period-diameter distribution for asteroids. As purple squares the distribution of the Hygeia family, and as green triangles the distribution of the Massalia family. The red dashed line is the fitted line that identifies the gap wenhan_slowrot_25. Spin period values were calculated by durech_spins_2023 and cellino_spins_2024. The ages in the legend are the weighted average ages computed from spoto_asteroid_2015.
• Figure 2: Distribution of calculated $t$ values for 8739 asteroids. The minimum $t$ is $t_{\rm min} \simeq 0.003$, while the maximum is $t_{\max} \simeq 1182.8$.
• Figure 3: Fraction of slow rotators as a function of the dimensionless time $t$. The green points are the binned collected observational data in this work. Black triangles are simulation data from wenhan_slowrot_25 model where the YORP timescale is manually increased by 10 times compared to the normal YORP timescale. The red line is the fit function in Eq. \ref{['eq:explin_fit']}. The shaded area is the 95% confidence interval of the fit. We do not show individual families because data are not sufficient for a statistical analysis.
• Figure 4: Polarization fraction as a function of the dimensionless time $t$. The green points are the binned data, the red line is the fit function in Eq. \ref{['eq:polarization_fit']}. The black triangles are the distribution of polarization fraction for the Eos family. The general trend is visible in single asteroid families. The shaded area is the 95% confidence interval of the fit.
• Figure 5: Comparison between the best breakpoint estimated from the original dataset, $t_{\rm bp}^*$ (circle marker) and the best breakpoint derived from the resampled dataset, $t_{\rm bp, err}^*$ (square marker). The breakpoints related to the slow rotators fraction (polarization fraction) are shown in blue (red). The breakpoints calculated from the resampled datasets are consistent with the original breakpoints.