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 circular motion at speed Vp and orbital radius Rp, and run various models with differing R=rs/Rp, Mach=Vp/a0, and B=G*Mp/(a0^2*Rp). 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 makes the detached shock distance reduced 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 rho1=(1 + 0.46B)*rho0 depending weakly on Mach. For sufficiently massive perturbers, the presence of a hydrostatic envelope makes the drag force smaller than the prediction of the linear perturbation theory, resulting in F = 4*pi*rho1*(G*Mp/Vp)^2 * (0.7/etaB) for etaB = B/(Mach^2 -1) > 0.1; the drag force for low-mass perturbers with etaB < 0.1 agrees well with the linear prediction. The nonlinear drag force becomes independent of R as long as R < etaB/2, which places an upper limit on the perturber size for accurate evaluation of the drag force in numerical simulations.
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…
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 $R_{\rm soft}$ can be accounted for by a scattering approach if $R_{\rm soft}<0.3H$, where $H$ is defin…
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 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 f…
Dynamical friction is often modeled with reasonable accuracy by the widely used Chandrasekhar formula. However, in some circumstances, Chandrasekhar's local and uniform approximations can break down severely. An astrophysically important example is the "core stalling" phenomenon seen in N-body simulations of massive perturber inspiralling into the near-harmonic potential of a stellar system's constant-density core (and possibly also in direct observations of dwarf galaxies with globular clusters). In this paper we use the linearized collisionless Boltzmann equation to calculate the global resp…
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…
Dynamical friction is typically regarded a secular process, in which the subject ('perturber') evolves very slowly (secular approximation), and has been introduced to the host over a long time (adiabatic approximation). These assumptions imply that dynamical friction arises from the LBK torque with non-zero contribution only from pure resonance orbits. However, dynamical friction is only of astrophysical interest if its timescale is shorter than the age of the Universe. In this paper we therefore relax the adiabatic and secular approximations. We first derive a generalized LBK torque, which re…
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…
We compute the dynamical friction on a small perturber moving through an inviscid fluid, i.e., a superfluid. Crucially, we account for the tachyonic gravitational mass for sound waves, reminiscent of the Jeans instability of the fluid, which results in non-zero dynamical friction even for subsonic velocities. Moreover, we illustrate that the standard leading order effective theory in the derivative expansion is in general inadequate for analysing supersonic processes. We show this in two ways: (i) with a fluid treatment, where we solve the linearized hydrodynamical equations coupled to Newtoni…
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…
Dynamical friction is thought to be a principal mechanism responsible for orbital evolution of massive black holes (MBHs) in the aftermath of galactic mergers and an important channel for formation of gravitationally bound MBH binaries. We use 2D radiative hydrodynamic simulations to investigate the efficiency of dynamical friction in the presence of radiative feedback from an MBH moving through a uniform density gas. We find that ionizing radiation that emerges from the innermost parts of the MBH's accretion flow strongly affects the dynamical friction wake and renders dynamical friction inef…
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…
We consider the gravitational force exerted on a point-like perturber of mass $M$ travelling within a uniform gaseous, opaque medium at constant velocity $V$. The perturber irradiates the surrounding gas with luminosity $L$. The diffusion of the heat released is modelled with a uniform thermal diffusivity $χ$. Using linear perturbation theory, we show that the force exerted by the perturbed gas on the perturber differs from the force without radiation (or standard dynamical friction). Hot, underdense gas trails the mass, which gives rise to a new force component, the heating force, with direct…
Coalescence of intermediate-mass black holes (IMBHs) as a result of the migration toward galactic centers via dynamical friction may contribute to the formation of supermassive BHs. Here we reinvestigate the gaseous dynamical friction, which was claimed to be inefficient with radiative feedback from BHs in literature, by performing 3D radiation-hydrodynamics simulations that solve the flow structure in the vicinity of BHs. We consider a $10^4~M_\odot$ BH moving at the velocity $V_{\rm flow}$ through the homogeneous medium with metallicity $Z$ in the range of $0-0.1~Z_\odot$ and density $n_{\in…
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）
In this paper, we systematically explore the impact of a galactic bar on the inspiral time-scale of a massive object (MO) within a Milky Way-like galaxy. We integrate the orbit of MOs in a multi-component galaxy model via a semi-analytical approach that accounts for dynamical friction generalized to rotationally supported backgrounds. We compare the MO evolution in a galaxy featuring a Milky Way-like rotating bar to the evolution within an analogous axisymmetric galaxy without the bar. In agreement with previous studies, we find that the bar presence may significantly affect the inspiral, some…
Using time-dependent linear theory, we investigate the morphology of the gravitational wake induced by a binary, whose center of mass moves at velocity Vcm against a uniform background of gas. For simplicity, we assume that the binary's components are on circular orbits about their common center of mass. The consequences of dynamical friction is twofold. First, gas dynamical friction may drag the binary's center of mass and cause the binary to migrate. Second, drag forces also induce a braking torque, which causes the orbits of the binary components to shrink. We compute the drag forces acting…
The supersonic motion of gravitating objects through a gaseous medium constitutes a classical problem in theoretical astrophysics. Its application covers a broad range of objects and scales from planets up to galaxies. Especially the dynamical friction, caused by the forming wake behind the object, plays an important role for the dynamics of the system. To calculate the dynamical friction, standard formulae, based on linear theory are often used. It is our goal to check the general validity of these formulae and provide suitable expressions for the dynamical friction acting on the moving objec…
A large fraction of galactic nuclei is expected to host supermassive black hole binaries (BHB), likely formed during the early phase of galaxies assembly and merging. In this paper, we use a large set of state-of-art numerical models to investigate the interplay between a BHB and a massive star cluster (GCs) driven toward the galactic centre by dynamical friction. Varying the BHB mass and mass ratio and the GC orbit, we show that the reciprocal feedback exerted between GCs and the BHB shapes their global properties. We show that, at GC-to-BHB mass ratios above 0.1, the GC affects notably the B…
We attempt to fit the observed radial velocities (RVs) of ${\,{\sim}\,}30$ Local Group (LG) galaxies using a 3D dynamical model of it and its immediate environment within the context of the standard cosmological paradigm, $Λ$CDM. This extends and confirms the basic results of our previous axisymmetric investigation of the LG (MNRAS, 459, 2237). We find that there remains a tendency for observed RVs to exceed those predicted by our best-fitting model. The typical mismatch is slightly higher than in our 2D model, with a root mean square value of ${\,{\sim}\,}50$ km/s. Our main finding is that in…
Galaxies are self-gravitating structures composed by several components encompassing spherical, axial and triaxial symmetry. Although real systems feature heterogeneous components whose properties are intimately connected, semi-analytical approaches often exploit the linearity of the Poisson's equation to represent the potential and mass distribution of a multi-component galaxy as the sum of the individual components. In this work, we expand the semi-analytical framework developed in Bonetti et al. (2020) by including both a detailed implementation of the gravitational potential of exponential…
We propose a new mechanism for the growth of supermassive black hole (BH) seeds in the star-forming progenitors of local early-type galaxies (ETGs) at $z\gtrsim 1$. This envisages the migration and merging of stellar compact remnants (neutron stars and stellar-mass BHs) via gaseous dynamical friction toward the central high-density regions of such galaxies. We show that, under reasonable assumptions and initial conditions, the process can build up central BH masses of order $10^4-10^6\, M_\odot$ within some $10^7$ yr, so effectively providing heavy seeds before standard disk (Eddington-like) a…
Tidal interaction between a gaseous disk and a massive orbiting perturber is known to result in angular momentum exchange between them. Understanding astrophysical manifestations of this coupling such as gap opening by planets in protoplanetary disks or clearing of gas by binary supermassive black holes (SMBHs) embedded in accretion disks requires knowledge of the spatial distribution of the torque exerted on the disk by a perturber. Recent hydrodynamical simulations by Dong et al (2011) have shown evidence for the tidal torque density produced in a uniform disk to change sign at the radial se…
Most of giant molecular clouds (GMCs) in M 33 are connected with spiral-like gaseous arms (filaments) with the exception of the inner 2 kpc region where the link between the arms and GMCs disappears (see Tosaki et al. 2011). We check whether it may be caused by the dynamic friction retarding the clouds. Using semi-analytical model for this galaxy we calculate the dynamics of GMCs of different masses situated at different initial galactocentric distances in the disk plane. We demonstrate that the dynamical friction may really change the orbits of GMCs in the central 2 kpc-size region. However i…
We use the problem of dynamical friction within the periodic cube to illustrate the application of perturbation theory in stellar dynamics, testing its predictions against measurements from $N$-body simulation. Our development is based on the explicitly time-dependent Volterra integral equation for the cube's linear response, which avoids the subtleties encountered in analyses based on complex frequency. We obtain an expression for the self-consistent response of the cube to steady stirring by an external perturber. From this we show how to obtain the familiar Chandrasekhar dynamical friction …
An over-dense wake is created by a gravitating object moving through a gaseous medium, and this wake pulls back on the object and slows it down. This is conventional dynamical friction in a gaseous medium. We argue that if the object drives a sufficiently powerful outflow, the wake is destroyed and instead an extended under-dense region is created behind the object. In this case the overall gravitational force is applied in the direction of the object's motion, producing a negative dynamical friction (NDF). Black holes in dense gas drive powerful outflows and may experience the NDF, although e…
The orbital decay of a perturber within a larger system plays a key role in the dynamics of many astrophysical systems -- from nuclear star clusters or globular clusters in galaxies, to massive black holes in galactic nuclei, to dwarf galaxy satellites within the dark matter halos of more massive galaxies. For many decades, there have been various attempts to determine the underlying physics and time-scales of the drag mechanism, ranging from the local dynamical friction approach to descriptions based on the back-reaction of global modes induced in the background system. We present ultra-high-…
We study the formation of a supermassive black hole (SMBH) binary and the shrinking of the separation of the two holes to sub-pc scales starting from a realistic major merger between two gas-rich spiral galaxies with mass comparable to our Milky Way. The simulations, carried out with the Adaptive Mesh Refinement (AMR) code RAMSES, are capable of resolving separations as small as 0.1 pc. The collision of the two galaxies produces a gravo-turbulent rotating nuclear disk with mass (10^9 Msun) and size (60 pc) in excellent agreement with previous SPH simulations with particle splitting that used a…
Using N-body/SPH simulations we study the evolution of the separation of a pair of SMBHs embedded in a star forming circumnuclear disk (CND). This type of disk is expected to be formed in the central kilo parsec of the remnant of gas-rich galaxy mergers. Our simulations indicate that orbital decay of the SMBHs occurs more quickly when the mean density of the CND is higher, due to increased dynamical friction. However, in simulations where the CND is fragmented in high density gaseous clumps (clumpy CND), the orbits of the SMBHs are erratically perturbed by the gravitational interaction with th…
We explore a ballistic orbit model to infer the gravitational drag force on an accreting point mass M, such as a black hole, moving at a hypersonic velocity v_{0} through a gaseous environment of density ρ_{0}. The streamlines blend in the flow past the body and transfer momentum to it. The total drag force acting on the body, including the nonlinear contribution of those streamlines with small impact parameter that bend significantly and pass through a shock, can be calculated by imposing conservation of momentum. In this fully analytic approach, the ambiguity in the definition of the lower c…
From Inspiral to Expansion: The Wake-Driven Torque on Binary Black Holes in Gaseous Medium
Tsinghua University（清华大学）；The Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Department of Astronomy, School of Physics, Peking University（北京大学物理学院天文学系）；University of California Berkeley（加州大学伯克利分校）
We develop an analytical model for the accretion and gravitational drag on a point mass that moves hypersonically in the midplane of a gaseous disk with a Gaussian vertical density stratification. Such a model is of interest for studying the interaction between a planet and a protoplanetary disk, as well as the dynamical decay of massive black holes in galactic nuclei. The model considers that the flow is ballistic, and gives fully analytical expressions for both the accretion rate onto the point mass, and the gravitational drag it suffers. The expressions are further simplified by taking the …
Motivated by observational searches for massive black hole (MBH) pairs at kiloparsec separations we develop a semi-analytic model to describe their orbital evolution under the influence of stellar and gaseous dynamical friction (DF). The goal of this study is to determine how the properties of the merger remnant galaxy and the MBHs affect the likelihood and timescale for formation of a close MBH pair with separation of < 1 pc. We compute approximately 40,000 configurations that cover a wide range of host galaxy properties and investigate their impact on the orbital evolution of unequal mass MB…
