Prograde and Retrograde Gas Flow around Disk-embedded Companions: Dependence on Eccentricity, Mass, and Disk Properties

We apply 3D hydrodynamical simulations to study the rotational aspect of gas flow patterns around eccentric companions embedded in an accretion disk. We sample a wide range of companion mass ratios q and disk aspect ratios h ₀, and confirm a generic transition from prograde (steady tidal interaction dominated) to retrograde (background Keplerian shear dominated) circumcompanion flow when orbital eccentricity exceeds a critical value e _t . We find e _t ∼ h ₀ for subthermal companions while e t ∼ ( q / h 0 3 ) 1 / 3 for superthermal companions, and propose an empirical formula to unify the two scenarios. Our results also suggest that e _t is insensitive to modest levels of turbulence, modeled in the form of a kinematic viscosity term. In the context of stellar-mass black holes (sBHs) embedded in active galactic nucleus (AGN) accretion disks, the bifurcation of their circumstellar disk rotation suggests the formation of a population of nearly antialigned sBHs, whose relevance to low spin gravitational wave events can be probed in more detail with future population models of sBH evolution in AGN disks, making use of our quantitative scaling for e _t ; in the context of circumplanetary disks (CPDs), our results suggest the possibility of forming retrograde satellites in situ in retrograde CPDs around eccentric planets.