Critical spin periods of sub-km-sized cohesive rubble-pile asteroids: dependences on material parameters

In this work, we employ a soft-sphere discrete element method with a cohesion implementation to model the dynamical process of sub-km-sized cohesive rubble piles under continuous spin-up. The dependences of the critical spin periods T-c on several material parameters for oblate rubble piles with different diameters were explored. Our simulations show that the interparticle cohesive force can strengthen the bodies as expected, especially for the smaller ones. The simulated results of T-c were fitted with the continuum theory developed by Holsapple, through which we find the interparticle cohesion is proportional to the best-fitting bulk cohesion and the ratio shows no dependence on the density. In addition, we find T-c decreases as the density increases in the compressive regime, while the trend reverses when transitioning to the tensile regime. Besides, though a higher friction angle can strengthen the bodies, its influence on T-c is minimized near the separation between the two regimes. Our numerical findings are generally consistent with the continuum theory, except that the latter predicts that T-c should increase as the friction angle increases in the tensile regime, which is contrary to the numerical results. This remarkable difference reminds us to take caution when applying the continuum theory to critically spinning cohesive rubble piles in the tensile regime, especially when dealing with the effect of the friction angle. Finally, we emphasize that the separation between the regimes can be specified by a characteristic period, which is only a function of density for a given shape.