The dependence of asteroid rotation on composition. A spectral class database for MP3C

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; however, this separation remains poorly understood, for example, with regard to its dependence on composition. We investigated whether the valley that separates fast and slow rotators in rotational period-diameter space depends on asteroid composition. We approximated the composition using the asteroids' spectral class. First, we extended the Minor Planet Physical Properties Catalogue (MP3C) to include the available spectral classes of asteroids. For each asteroid, we then selected the best diameter, rotational period, and spectral class. Building upon a semi-supervised machine-learning method, we quantified the valley between fast and slow rotators for S- and C-complex asteroids, which are linked to different types of meteorites: ordinary and carbonaceous chondrites, respectively. The method iteratively fits a linear boundary between the two populations in a rotational period-diameter space to maximise separation between them. 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_ ̊m km ^ 0. 739 (C-complex) and P_ = 11. 6, D_ ̊m km ^ 0. 718 (S-complex), where the period and diameter are given in hours and kilometres, respectively. This corresponds to μ Q ≃ 2 and 13 ̊m GPa, respectively, where μ is rigidity, which measures how strongly a body resists shear deformation under applied stress, and Q is the quality factor, which measures how efficiently a body dissipates mechanical energy when cyclically deformed. 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.