Nonlinear Dynamical Friction of a Circular-Orbit Perturber in a Gaseous Medium

Abstract

We use three-dimensional hydrodynamic simulations to investigate the nonlinear gravitational responses of gas to, and the resulting drag forces on, very massive perturbers moving in circular orbits. This work extends our previous studies that explored the cases of low-mass perturbers in circular orbits and massive perturbers on straight-line trajectories. The background medium is assumed to be non-rotating, adiabatic with index 5/3, and uniform with density ρ 0 and sound speed a 0 . We model the gravitating perturber using a Plummer sphere with mass M p and softening radius r s in a uniform circular motion at speed V p and orbital radius R p , and run various models with differing R ≡ r s /R p , M ≡ V p /a 0 , and B ≡ GM p /(a 2 0 R p ). A quasi-steady density wake of a supersonic model consists of a hydrostatic envelope surrounding the perturber, an upstream bow shock, and a trailing low-density region. The continuous change in the direction of the perturber motion reduces the detached shock distance compared to the linear-trajectory cases, while the orbit-averaged gravity of the perturber gathers the gas toward the center of the orbit, modifying the background preshock density to ρ 1 ≈ (1+0.46B 1.1 )ρ 0 depending weakly on M. For sufficiently massive perturbers, the presence of a hydrostatic envelope makes the drag force smaller than the prediction of the linear perturbation theory, resulting in1; the drag force for low-mass perturbers with η B < 0.1 agrees well with the linear prediction. The nonlinear drag force becomes independent of R as long as R < η B /2, which places an upper limit on the perturber size for accurate evaluation of the drag force in numerical simulations.

Intermediate-mass black holes from Population III remnants in the first galactic nuclei

“…Capturing the effects of nonlinear dynamical friction along an accelerated trajectory, in a non-uniform background medium, would require hydrodynamical simulations, including the self-gravity of the surrounding medium. This is outside the scope of this paper, but we note that existing studies of dynamical friction in a nonuniform medium or for perturbers on nonlinear trajectories (e.g Sánchez-Salcedo & Brandenburg 2001;Just & Peñarrubia 2005;Kim & Kim 2007;Kim 2010), do not report major differences from the Chandrasekhar formula. We therefore simply evaluate the formulae given above, by using the value of the density at the coordinates of each BH; this is the typical approach taken in similar numerical studies (e.g.…”

Templates of Binary-induced Spiral-shell Patterns around Mass-losing Post-main-sequence Stars

“…In the cases of moderate mass ratios, the density distribution and its shape could be interpolated between the numerical results of Model 3 and Model 4 to determine the degree to which the features are turbulent. Kim & Kim (2009) and Kim (2010Kim ( , 2011 described that the formation of turbulent flows takes place during the oscillation process of a buoyant expansion of vortices within a bow shock as a part of the gravitational density wake generated around the companion star. Although their assumption of a static background fluid velocity field differs from the radially expanding velocity field adopted in this paper, their explanation carries over for the origin of turbulent flows in Model 4 (also Model 2).…”

Gravitational drag on a point mass in hypersonic motion through a gaseous medium

“…Tanaka & Haiman (2009) combined the prescriptions of Ostriker (1999) and Escala et al (2004) into a formula that is used as a prescription of the gaseous drag on black holes in numerical simulations. In order to isolate the physical reason of the failure of Ostriker’s formula, Kim & Kim (2009) and Kim (2010) carried out axisymmetrical simulations of a massive body in rectilinear orbit with different values of the strength of the gravitational perturbation due to the body as measured by where r s is the softening radius of the Plummer perturber. They find that the functional form of the gravitational drag is not so peaked as the linear theory predicts and conclude that the discrepancy between the numerical and Ostriker results are most likely due to the non‐linear effect.…”

“…They find that the functional form of the gravitational drag is not so peaked as the linear theory predicts and conclude that the discrepancy between the numerical and Ostriker results are most likely due to the non‐linear effect. It is important to note that in the simulations of Escala et al (2004), Kim & Kim (2009) and Kim (2010), the perturber simply provides a smooth gravitational potential and does not hold any absorbing surface. Without any absorbing inner boundary condition, a hydrostatic envelope with front‐back symmetry is formed near the perturber.…”