Structure of gaps induced by retrograde satellites embedded in accretion discs

TL;DR

This study uses 2D simulations to analyze how retrograde satellites influence accretion disc structures, revealing unique gap features, the impact of viscosity, and potential for eccentric gap formation.

Contribution

It introduces a viscous criterion for gap opening by retrograde satellites and compares 2D and 3D simulation results, highlighting differences in gap structure and satellite dynamics.

Findings

Gap depth scales with satellite mass ratio and viscosity.

Retrograde satellites are located at the gap's inner edge, causing high surface density.

Lower viscosity results in deeper gaps and reduced radial shift.

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.