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 shock and a vortex ring, which is unlike in the linear cases where Mach cones are bounded by low-amplitude Mach waves. The flows behind the shock are initially non-steady, displaying quasi-periodic, overstable oscillations of the vortex ring and the shock. The vortex ring is eventually shed downstream and the flows evolve toward a quasi-steady state where the density wake near the perturber is in near hydrostatic equilibrium. We find that the detached shock distance $δ$ and the nonlinear drag force F depend solely on η=A/(M^2-1) such that δ/r_s=ηand F/F_{lin}=(η/2)^{-0.45} for η>2, where F_{lin} is the linear drag force of Ostriker (1999). The reduction of F compared with F_{lin} is caused by front-back symmetry in the nonlinear density wakes. In subsonic cases, the flows without involving a shock do not readily reach a steady state. Nevertheless, the subsonic density wake near a perturber is close to being hydrostatic, resulting in the drag force similar to the linear case. Our results suggest that dynamical friction of a very massive object as in a merger of black holes near a galaxy center will take considerably longer than the linear prediction.
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
When a gravitating point mass moves subsonically through a magnetized and isothermal medium, the dynamical structure of the flow is studied far from the mass using a perturbation analysis. Analytical solutions for the first-order density and the velocity perturbations are presented. Validity of our solutions is restricted to the cases where the Alfven velocity in the ambient medium is less than the accretor's velocity. The density field is less dense because of the magnetic effects according to the solutions and the dynamical friction force becomes lower as the strength of the magnetic field i…
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…
We have carried out a controlled comparison of the structural and kinematic properties of the circumgalactic medium (CGM) around Milky Way mass galaxies in the Illustris and IllustrisTNG simulations. Very striking differences are found. At z=0, gas column density and temperature profiles at large radii ($\sim 100$ kpc) correlate strongly with disk gas mass fraction in Illustris, but not in TNG. The neutral gas at large radii is preferentially aligned in the plane of the disk in TNG, whereas it is much more isotropic in Illustris. The vertical coherence scale of the rotationally supported gas i…
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…
The warm ($\log~T\approx5$) gas is an important gaseous component in the galaxy baryonic cycle. We built a 2-dimension disk-CGM model to study the warm gas distribution of the Milky Way (MW) using the absorption line surveys of Si IV and O VI. In this model, the disk component of both ions has the same density profile ($n(r, z)=n_0\exp(-|z|/z_0)\exp(-r/r_0)$) with a scale height of $z_0=2.6\pm0.4\rm~kpc$ and a scale length of $r_0=6.1\pm1.2\rm~kpc$. For this disk component, we calculate the warm gas mass of $\log(M/M_\odot)=(7.6\pm0.2)-\log\frac{Z}{Z_\odot}$. The similar disk density profiles …
Accretion at sustained or episodic super-Eddington (SE) rates has been proposed as a pathway to grow efficiently light seeds produced by Pop-III stars. We investigate if SE accretion can be sustained onto a black hole (BH) with $M_{\odot} \sim 10^3$~M$_{\odot}$ in the centre of a gas-rich proto-galaxy at $z=15$. We perform high-resolution smoothed-particle hydrodynamical simulations, including two different sub-grid models for SE accretion, one based on the slim disc paradigm, and one inspired by recent radiation-magnetohydrodynamical simulations by Jiang and collaborators. Radiative feedback …
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 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…
The circumgalactic medium (CGM), i.e. the gaseous haloes around galaxies, is both the reservoir of gas that fuels galaxy growth and the repository of gas expelled by galactic winds. Most cosmological, hydrodynamical simulations focus their computational effort on the galaxies themselves and treat the CGM more coarsely, which means small-scale structure cannot be resolved. We get around this issue by running zoom-in simulations of a Milky Way-mass galaxy with standard mass refinement and additional uniform spatial refinement within the virial radius. This results in a detailed view of its gaseo…
We present the analysis of the XMM-Newton data of the Circum-Galactic Medium of MASsive Spirals (CGM-MASS) sample of six extremely massive spiral galaxies in the local Universe. All the CGM-MASS galaxies have diffuse X-ray emission from hot gas detected above the background extending $\sim(30-100)\rm~kpc$ from the galactic center. This doubles the existing detection of such extended hot CGM around massive spiral galaxies. The radial soft X-ray intensity profile of hot gas can be fitted with a $β$-function with the slope typically in the range of $β=0.35-0.55$. This range, as well as those $β$ …
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…
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…
The abundant forms in which the major elements in the universe exist have been determined from numerous astronomical observations and meteoritic analyses. Iron (Fe) is an exception, in that only depletion of gaseous Fe has been detected in the interstellar medium, suggesting that Fe is condensed into a solid, possibly the astronomically invisible metal. To determine the primary form of Fe, we replicated the formation of Fe grains in gaseous ejecta of evolved stars by means of microgravity experiments. We found that the sticking probability for formation of Fe grains is extremely small; only se…
We study dynamical friction in interacting relativistic systems with arbitrary mean free paths and medium constituent masses. Our novel framework recovers the known limits of ideal gas and ideal fluid when the mean free path goes to infinity or zero, respectively, and allows for a smooth interpolation between these limits. We find that in an infinite system the drag force can be expressed as a sum of ideal-gas-like and ideal-fluid-like contributions leading to a finite friction even at subsonic velocities. This simple picture receives corrections in any finite system and the corrections become…
