Analytic solution to the dynamical friction acting on circularly moving perturbers
Vincent Desjacques, Adi Nusser, Robin Buehler
备注：
(v1) 6 pages, 4 figures, comments welcome (v2) extended version with revised discussion of the divergence, accepted for publication in ApJ. Code computing the circular DF available at https://github.com/nyalothep/dynfricGas
We present an analytic approach to the dynamical friction (DF) acting on a circularly moving point mass perturber in a gaseous medium. We demonstrate that, when the perturber is turned on at $t=0$, steady-state (infinite time perturbation) is achieved after exactly one sound-crossing time. At low Mach number $\mathcal{M}~\ll~1$, the circular-motion steady-state DF converges to the linear-motion, finite time perturbation expression. The analytic results describe both the radial and tangential forces on the perturbers caused by the backreaction of the wake propagating in the medium. The radial force is directed inward, toward the motion centre, and is dominant at large Mach numbers. For subsonic motion, this component is negligible. For moderate and low Mach numbers, the tangential force is stronger and opposes the motion of the perturber. The analytic solution to the circular-orbit DF suffers from a logarithmic divergence in the supersonic regime. This divergence appears at short distances from the perturber solely (unlike the linear motion result which is also divergent at large distances) and can be encoded in a maximum multipole. This is helpful to assess the resolution dependence of numerical simulations implementing DF at the level of Liénard-Wiechert potentials. We also show how our approach can be generalised to calculate the DF acting on a compact circular binary.
An extended gravitational object embedded in a parent system comprised of gas and collisionless particles may undergo both dynamical friction (DF) and mass loss by tidal forces. If the object is compact enough, it can increase its mass through accretion of material from the surrounding medium. We extend the classical linear analysis of DF on a constant-mass body in a gaseous medium to the case where its mass changes with time. We show that the structure of the wake may differ significantly from the constant-mass case. For instance, the front-back symmetry of density about subsonic constant-mas…
Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. This interaction is usually derived assuming that the perturber has a constant velocity. In realistic situations, motion is accelerated as for instance by dynamical friction itself. Here, we study the effect of acceleration on the dynamical friction force. We characterize the density enhancement associated with a constantly accelerating perturber with rectilinear motion in an infinite homogeneous gaseous medium and show that dynamical friction is not a local force and that…
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 on circular orbits. This work extends our previous studies that explored the cases of low-mass perturbers on 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 rho0 and sound speed a0. We model the gravitating perturber using a Plummer sphere with mass Mp and softening radius rs in a uniform circu…
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Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. We study the effects of the presence of a boundary on dynamical friction by studying analytically the interaction of perturber with uniform rectilinear motion in a uniform homogeneous medium with a reflecting planar boundary. Wake reflection at a medium's boundary may occur at the edges of truncated disks perturbed by planetary or stellar companions as well as in numerical simulations of planet-disk interaction with no-outflow boundary conditions. In this paper, we show th…
Using high-resolution, two-dimensional hydrodynamic simulations, we investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a very massive perturber M_p moving at velocity V_p through a uniform gaseous medium of adiabatic sound speed a_0. We model the perturber as a Plummer potential with softening radius r_s, and run various models with differing A=GM_p/(a_0^2 r_s) and M=V_p/a_0 by imposing cylindrical symmetry with respect to the line of perturber motion. For supersonic cases, a massive perturber quickly develops nonlinear flows that produce a detached bow s…
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We present and validate a novel semi-analytical approach to study the effect of dynamical friction on the orbits of massive perturbers in rotating stellar discs. We find that dynamical friction efficiently circularises the orbit of co-rotating perturbers, while it constantly increases the eccentricity of counter-rotating ones until their angular momenta reverse, then once again promoting circularisation. Such "drag toward circular corotation" could shape the distribution of orientations of kinematically decoupled cores in disc galaxies, naturally leading to the observed larger fraction of co-r…
The evolution of planets, stars and even galaxies is driven, to a large extent, by dynamical friction of gravitational origin. There is now a good understanding of the friction produced by extended media, either collisionless of fluid-like. However, the physics of accretion or protoplanetary disks, for instance, is described by slab-like geometries instead, compact in one spatial direction. Here, we find, for the first time, the gravitational wake due to a massive perturber moving through a slab-like medium, describing e.g. accretion disks with sharp transitions. We show that dynamical frictio…
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We examine the origin of dynamical friction using a non-perturbative, orbit-based approach. Unlike the standard perturbative approach, in which dynamical friction arises from the LBK torque due to pure resonances, this alternative, complementary view nicely illustrates how a massive perturber significantly changes the energies and angular momenta of field particles on near-resonant orbits, with friction arising from an imbalance between particles that gain energy and those that lose energy. We treat dynamical friction in a spherical host system as a restricted three-body problem. This treatmen…
Fifteen years after the discovery of dynamical friction by Chandrasekhar, Michel Henon attempts to solve the longstanding problem of the divergence of the friction suffered by the perturber and caused by the most distant cluster stars. His solution laid the foundation to the current understanding of dynamical friction as a non-local transitory force.
Dynamical friction is a fundamental and important phenomenon in astrophysics. The Chandrasekhar formula is a well-known analytical estimation of the effect. However, current astrophysicists have realized that the formula is not correct in some cases because of several approximations dared in the formulation and/or complex non-linearities in the real universe. For example, it has been indicated that the dynamical friction doesn't work in cored density profiles (constant density in the central region) despite that the Chandrasekhar formula predicts drag force even in the constant densities. In t…
Not all cores are equal: Phase-space origins of dynamical friction, stalling and buoyancy
Yale University（耶鲁大学）；Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）；Nanjing University（南京大学）；The Hebrew University（希伯来大学）；University of California, Santa Cruz（加州大学圣克鲁兹分校）
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