A close pair of orbiters embedded in a gaseous disk: the repulsive effect

We develop a theoretical framework and use two-dimensional hydrodynamical simulations to study the repulsive effect between two close orbiters embedded in an accretion disk. We consider orbiters on fixed Keplerian orbits with masses low enough to open shallow gaps. The simulations indicate that the repulsion is larger for more massive orbiters and decreases with the orbital separation and the disk's viscosity. We use two different assumptions to derive theoretical scaling relations for the repulsion. A first scenario assumes that each orbiter absorbs the angular momentum deposited in its horseshoe region by the companion's wake. A second scenario assumes that the corotation torques of the orbiters are modified because the companion changes the underlying radial gradient of the disk surface density. We find a substantial difference between the predictions of these two scenarios. The first one fails to reproduce the scaling of the repulsion with the disk viscosity and generally overestimates the strength of the repulsion. The second scenario, however, gives results that are broadly consistent with those obtained in the simulations.
Comment: 18 pages, 15 figures, accepted for publication in ApJ