The dependence of the asteroid rotation on their composition

TL;DR

This study shows that the valley separating fast and slow asteroid rotators in the period–diameter plane depends on composition, with C-complex bodies (carbonaceous) rotating at longer periods than S-complex bodies (silicate-rich) for a given diameter. By extending MP3C to include spectral classifications and applying a semi-supervised boundary-learning approach, the authors quantify two class-specific valley boundaries: $P^{*}_{\rm S} = 11.6\,{\rm h}\left(\frac{D}{1\,\rm km}\right)^{0.718}$ and $P^{*}_{\rm C} = 14.4\,{\rm h}\left(\frac{D}{1\,\rm km}\right)^{0.739}$, corresponding to $\mu Q \approx 13$ GPa for S-complex and $\approx 2$ GPa for C-complex. The results imply that compositional and structural differences—such as porosity, cohesion, and regolith properties—drive the efficiency of angular-momentum dissipation and the YORP-driven evolution, yielding a class-dependent rotational valley. These findings bridge spin-state evolution models with interior-structure diagnostics and motivate extending such analyses to broader taxonomic classes with upcoming large surveys. Overall, the paper demonstrates that spectral information is essential to interpret asteroid rotational dynamics at the population level and provides quantitative constraints on internal properties across asteroid populations.

Abstract

The rotational properties of asteroids provide critical information about not only their internal structure but also their collisional and thermal histories. Previous work has revealed a bimodal distribution of asteroid spin rates, dividing populations into fast and slow rotators, but to date this separation remains poorly understood (e.g. its dependency on composition). We investigate whether the valley separating fast and slow rotators in rotational period-diameter space depends on the composition of the asteroid, approximated by asteroids' spectral class. First, we extended the Minor Planet Physical Properties Catalogue (MP3C) to include the available spectral classes of asteroids. Then, for each asteroid we selected the best diameter, rotational period, and spectral class. Building upon a semi-supervised machine-learning method, we quantify the valley between fast and slow rotators for S- and C-complex asteroids, which are linked to ordinary and carbonaceous chondrites respectively. The method iteratively fits a linear boundary between the two populations in rotational period-diameter space to maximise their separation. We find a clear compositional dependence of the valley: for C-complex asteroids the transition occurs at longer periods than for S-complex, with P* = 14.4 D_km^0.739 (C-complex) and P* = 11.6 D_km^0.718 (S-complex), where period and diameter are given in hours and kilometres respectively. This corresponds to mu Q approximately 2 and 13 GPa, respectively, where mu is the rigidity and Q the quality factor. The dependence of the valley on spectral classes likely reflects compositional and structural differences: C-complex asteroids, being more porous and weaker, dissipate angular momentum more efficiently than stronger, more coherent S-complex asteroids. This represents quantitative evidence of class-dependent rotational valleys within asteroid populations.

Figures (6)

• Figure 1: Period-diameter distribution and the fitted valley functions for S- and C- complex asteroid.
• Figure 2: Spin-period distribution of S-complex and C-complex asteroids in 5-10 km diameter range. The local minimum in each distribution corresponds to the valley of the $P$-$D$ diagram. The minimum for C-complex asteroids (blue) occurs at longer periods than for S-complex asteroids (orange).
• Figure 3: Normalised distributions of the dimensionless offset from the fitted valley loci, $\log_{10}(P/P^{*}_{ S})$ and $\log_{10}(P/P^{*}_{ C})$, shown separately for the S-complex (orange) and the C-complex (blue). The vertical dashed line marks $\log_{10}(P/P^{*}_{ S}) = 0$ and $\log_{10}(P/P^{*}_{ C})=0$, corresponding to the valleys' centre.
• Figure 4: Period–diameter ($P-D$) distribution for S-complex and C-complex asteroids. The lines are fitted functions for the S-complex valley and C-complex valley in the synthetic datasets generated according to the diameter uncertainty.
• Figure 5: Distributions of the valley parameter $k$ and $b$ (Eq. \ref{['eq:valley_function']}) for S-complex and C-complex asteroids, derived from fits to synthetic datasets that account for diameter uncertainties. Larger values of $b$ correspond to a lower vertical position of the valley in the $P$–$D$ diagram.