Kinetic theory for rings around oblate central bodies

Abstract

We apply kinetic theory (KT) to solve for the vertical structure of an axisymmetric, self-gravitating, particulate ring around a spheroidal central body which may be either spherical or oblate. Our work improves upon the present KT models of rings by introducing a more general central body potential. We consider both dilute and dense rings. As an example for a dilute ring, we solve for the vertical structure of Saturn’s A ring including Saturn’s oblateness in our calculations. We compare our results with earlier works (Simon and Jenkins 1994) which assumed a spherical Saturn. Then, we calculate the corrections due to the oblateness on the ring stability condition obtained by them. We find that the planetary oblateness adversely affects ring stability due to the enhanced shearing. Next, we add self-gravity as an additional vertical force in dilute rings, where particle clumping is negligible, and find the combined stability boundary. Self-gravity is seen to have a stabilising effect on the ring as reported in earlier studies (Salo 1995), though, its stabilising effect is observed to be less than the destabilising effect of the oblateness of the central body, at least, for dilute rings. Then, we move to moderately dense rings. Oblateness of the central body is seen to perturb the ring properties, and, the results indicate a good qualitative comparison with DE simulations of Gupta et al., (2018). However, we note the emergence of strong self-gravity wakes in dense rings, an aspect that is usually ignored in kinetic theory for rings. Hence, we show the need for improved constitutive modelling of rings including the mesoscopic inhomogeneities in the form self-gravity wakes. Finally, we apply KT to solve for the vertical structure of Chariklo’s inner ring. Through this we estimate the 1/3 resonance torque of Chariklo that acts on the inner boundary of Chariklo’s inner ring by calculating the shear stress in the ring. Overall, our work demonstrates the structural differences of rings around minor planets like Chariklo that have highly oblate shapes.