Torques on Low-mass Bodies in Retrograde Orbit in Gaseous Disks

Abstract

We evaluate the torque acting on a gravitational perturber on a retrograde circular orbit in the midplane of a gaseous disk. We assume that the mass of this satellite is so low it weakly disturbs the disk (type I migration). The perturber may represent the companion of a binary system with a small mass ratio. We compare the results of hydrodynamical simulations with analytic predictions. Our two-dimensional (2D) simulations indicate that the torque acting on a perturber with softening radius R soft can be accounted for by a scattering approach if R soft < 0.3H, where H is defined as the ratio between the sound speed and the angular velocity at the orbital radius of the perturber. For R soft > 0.3H, the torque may present large and persistent oscillations, but the resultant time-averaged torque decreases rapidly with increasing R soft /H, in agreement with previous analytical studies. We then focus on the torque acting on small-size perturbers embedded in full three-dimensional (3D) disks and argue that the density waves propagating at distances H from the perturber contribute significantly to the torque because they transport angular momentum. We find a good agreement between the torque found in 3D simulations and analytical estimates based on ballistic orbits. We compare the radial migration timescales of prograde versus retrograde perturbers. For a certain range of the perturber's mass and aspect ratio of the disk, the radial migration timescale in the retrograde case may be appreciably shorter than in the prograde case. We also provide the smoothing length required in 2D simulations in order to account for 3D effects.

Orbital evolution of gas-driven inspirals with extreme mass-ratios: retrograde eccentric orbits

“…Given their low q and high M, EMRIs in retrograde orbits cannot open a gap in the disk (McKernan et al 2014;Ivanov et al 2015;Sánchez-Salcedo et al 2018) and, in addition, their accretion radii R acc are generally much smaller than the vertical scaleheight H of the disk. For instance, consider a retrograde EMRI at a radial distance R p embedded in a disk with constant h. The relative velocity of the CO with respect to the gas is V 2 rel 4GM • /R p (being this expression more accurate for small values of e).…”

“…The limiting case i = 180 • (retrograde orbit) and e = 0 (circular orbit), was studied in Ivanov et al (2015) and Sánchez-Salcedo et al (2018). In this case, the perturber moves supersonically (Mach numbers of 40 − 100).…”

“…In this case, the perturber moves supersonically (Mach numbers of 40 − 100). As a result, the perturber catches its own wake repeatedly and, in fact, the pull imparted by the wake ahead of the perturber cannot be ignored unless the mass ratio q is small enough (Sánchez-Salcedo et al 2018).…”

Orbital Evolution of Eccentric Low-mass Companions Embedded in Gaseous Disks: Testing the Local Approximation

“…Even in razor thin disks, the range of parameters within which the local approximation is accurate has not been clearly established. One would expect that the local approximation overestimates the force because it ignores the curvature of the wake which is expected to reduce the magnitude of F 1 (e.g., Kim & Kim 2007;Sánchez-Salcedo et al 2018). However, a rough comparison with the simulations in Cresswell & Nelson (2006) indicates that the local approximation underestimates the torque by a factor of 2 (see fig.…”

Formation and Evolution of Compact Object Binaries in AGN Disks

“…In this study, we ignored several processes for simplicity. These include exchange of binary components at binary-single interaction, the formation and evolution of stellar binaries, radial migration of stars due to torque from the AGN disk, evolution of compact objects other than BHs, the Kozai-Lidov effect of the SMBH or a third stellar-mass object on binaries, dynamical relaxation processes, counter rotating BHs or stars in the AGN disk (Ivanov et al 2015;Sánchez-Salcedo et al 2018), stellar evolution, supernova feedback, binary mass transfer, and possible presence of massive perturbers like an SMBH companion and/or IMBHs. A few IMBHs, if present, may efficiently disrupt most BH binaries which may greatly reduce the merger rates (Deme et al 2019).…”