Structure of gaps induced by retrograde satellites embedded in accretion discs

Abstract

Using 2D simulations, we investigate how a non-accreting satellite on a fixed retrograde circular orbit affects the structure of the accretion disc in which it is embedded. We vary the satellite-to-primary mass ratio $q$, the disc viscosity $\nu$, and the inner boundary conditions. A viscous criterion for gap opening is derived, which is broadly consistent with the simulations. We find a scaling relation of the gap depth with $q$ and $\nu$. Unlike the prograde case, the satellite is located at the gap's inner edge, resulting in a surface density at the satellite's orbital radius up to $20$ times higher than at the gap's minimum. As the viscosity decreases, the gap depth increases, while the radial shift of the gap and the satellite's orbital radius decreases. Gap-opening satellites may drive radial motions in the disc, producing eccentric gaps. Positioned at the gap edge, satellites experience a rapidly fluctuating environment. Migrating satellites can develop orbital eccentricities comparable to the disc's aspect ratio. In a 3D simulation with $q=0.01$, the flow velocity exhibits a notorious vertical component in the gap's inner edge. A comparison between 2D and 3D simulations reveals a slight radial offset in gap position, resulting in a lower surface density at the perturber's orbital radius in the 3D simulation.