The dependence of the asteroid rotation on their composition

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.