Migration of Accreting Planets and Black Holes in Disks

Abstract Nascent planets are thought to lose angular momentum (AM) to the gaseous protoplanetary disk via gravitational interactions, leading to inward migration. A similar migration process also applies to stellar-mass black holes (BHs) embedded in the disks of active galactic nuclei. However, AM exchange via accretion onto the planet/BH may strongly influence the migration torque. In this study, we perform 2D global hydrodynamic simulations of an accreting planet/BH embedded in a disk, where AM exchange between the planet/BH and disk via gravity, accretion, pressure, and viscosity are considered. When accretion is turned off, we recover the linear estimate for Type I migration torque. However, for the two planet masses we investigated with our accreting simulations, we find outward migration due to the positive AM deposited onto the accreting body by the disk gas. Our simulations achieve the global steady state for the transport of mass and AM: The mass and AM fluxes are constant across the disk except for jumps ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mover accent="true"> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> ) at the planet’s location, and the jumps match the accretion rate and torque on the planet. Our findings suggest that caution is needed when applying the standard results of disk migration to accreting planets and BHs.