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 $n_{\infty}$. We show that, if $n_{\infty} \lesssim 10^{6}~{\rm cm^{-3}}$ and $V_{\rm flow} \lesssim 60~{\rm km~s^{-1}}$, the BH is accelerated forward because of the gravitational pull from a dense shell ahead of an ionized bubble around the BH, regardless of the value of $Z$. If $n_{\infty} \gtrsim 10^{6}~{\rm cm^{-3}}$, however, our simulation shows the opposite result. The ionized bubble and associating shell temporarily appear, but immediately go downstream with significant ram pressure of the flow. They eventually converge into a massive downstream wake, which gravitationally drags the BH backward. The BH decelerates over the timescale of $\sim 0.01$~Myr, much shorter than the dynamical timescale in galactic disks. Our results suggest that IMBHs that encounter the dense clouds rapidly migrate toward galactic centers, where they possibly coalescence with others.
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…
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…
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…
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…
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…
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 …
The galactic gaseous halo is a gas reservoir for the interstellar medium in the galaxy disk, supplying materials for star formation. We developed a gaseous halo model connecting the galaxy disk and the gaseous halo by assuming the star formation rate on the disk is balanced by the radiative cooling rate of the gaseous halo, including stellar feedback. In addition to a single-temperature gaseous halo in collisional ionization equilibrium, we also consider the photoionization effect and a steady-state cooling model. Photoionization is important for modifying the ion distribution in low-mass gala…
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…
The extended hot X-ray emitting gaseous halo of the Milky Way has an optical depth $\sim1$ for the dominant emission lines of \ion{O}{7} and \ion{O}{8}, which are used to infer the halo properties. To improve on halo gas properties, we treat optical depth effects with a Monte-Carlo radiative transfer model, which leads to slightly steeper density profiles ($β\approx 0.5$) than if optical depths effects were ignored. For the preferred model where the halo is rotating on cylinders at $180$ km s$^{-1}$, independent fits to both lines lead to identical results, where the core radius is $2.5$ kpc a…
The putative ubiquity of massive black holes (MBH) at the center of galaxies, and the hierarchical progress of structure formation along the cosmic history, together necessarily imply the existence of a large population of cosmic MBH binaries. Such systems are understood to be the loudest sources of gravitational waves at mHz frequencies, the regime that will be probed by the next Laser Interferometer Space Antenna (LISA). It has been proposed that the rate at which MBHs pair and then bind to form binaries is critically dependent upon the feedback exerted by the MBHs on the surrounding gaseous…
We use a suite of hydrodynamical cosmological simulations from the Evolution and Assembly of GaLaxies and their Environments (EAGLE) project to investigate the formation of hot hydrostatic haloes and their dependence on feedback mechanisms. We find that the appearance of a strong bimodality in the probability density function (PDF) of the ratio of the radiative cooling and dynamical times for halo gas provides a clear signature of the formation of a hot corona. Haloes of total mass $10^{11.5}-10^{12}{\rm{M}}_{\odot}$ develop a hot corona independent of redshift, at least in the interval $z=0-4…
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…
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…
Existing ubiquitously in the Universe with the highest luminosity, the Lyman-$α$ emission line encodes abundant physical information about the gaseous medium it interacts with. Nevertheless, the resonant nature of Ly$α$ complicates the radiative transfer (RT) modeling of the line profile, making the extraction of physical properties of the surrounding gaseous medium notoriously difficult. In this paper, we revisit the problem of deciphering the Ly$α$ emission line with RT modeling. We reveal intrinsic parameter degeneracies in the widely-used shell model in the optically thick regime for both …
We study the orbital decay of a pair of massive black holes (BHs) with masses 5 * 10^5 and 10^7 M_sun, using hydrodynamical simulations of circumnuclear disks (CNDs) with the alternating presence of sub-grid physics such as radiative cooling, star formation, supernova feedback, BH accretion and feedback. In the absence of such processes, the orbit of the secondary BH decays over timescales of ~10 Myr to the center of the CND, where the primary BH resides. When strong dissipation operates in CNDs, fragmentation into massive objects the size of giant molecular clouds and with densities in the ra…
We present the study of a set of N-body+SPH simulations of a Milky Way-like system produced by the radiative cooling of hot gas embedded in a dark matter halo. The galaxy and its gaseous halo evolve for 10 Gyr in isolation, which allows us to study how internal processes affect the evolution of the system. We show how the morphology, the kinematics and the evolution of the galaxy are affected by the input supernova feedback energy E$_{\rm SN}$, and we compare its properties with those of the Milky Way. Different values of E$_{\rm SN}$ do not significantly affect the star formation history of t…
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）
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…
Theoretical and observational arguments suggest that there is a large amount of hot ($\sim 10^6$ K), diffuse gas residing in the Milky Way's halo, while its total mass and spatial distribution are still unclear. In this work, we present a general model for the gas density distribution in the Galactic halo, and investigate the gas evolution under radiative cooling with a series of 2D hydrodynamic simulations. We find that the mass inflow rate in the developed cooling flow increases with gas metallicity and the total gas mass in the halo. For a fixed halo gas mass, the spatial gas distribution a…
Galactic halo gas traces inflowing star formation fuel and feedback from a galaxy's disk and is therefore crucial to our understanding of galaxy evolution. In this review, we summarize the multi-wavelength observational properties and origin models of Galactic and low redshift spiral galaxy halo gas. Galactic halos contain multiphase gas flows that are dominated in mass by the ionized component and extend to large radii. The densest, coldest halo gas observed in neutral hydrogen (HI) is generally closest to the disk (< 20 kpc), and absorption line results indicate warm and warm-hot diffuse hal…
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 $β$ …
Dynamical friction (DF) against stars and gas is thought to be an important mechanism for orbital evolution of massive black holes (MBHs) in merger remnant galaxies. Recent theoretical investigations however show that DF does not always lead to MBH inspiral. For MBHs evolving in gas-rich backgrounds, the ionizing radiation that emerges from the innermost parts of their accretion flow can affect the surrounding gas in such a way to cause the MBHs to accelerate and gain orbital energy. This effect was dubbed "negative DF". We use a semi-analytic model to study the impact of negative DF on pairs …
The effects of Active Galactic Nuclei (AGNs) on their host-galaxies depend on the coupling between the injected energy and the interstellar medium (ISM). Here, we model and quantify the impact of long-range AGN ionizing radiation -- in addition to the often considered small-scale energy deposition -- on the physical state of the multi-phase ISM of the host-galaxy, and on its total Star Formation Rate (SFR). We formulate an AGN Spectral Energy Distribution matched with observations, which we use with the radiative transfer (RT) code Cloudy to compute AGN ionization in a simulated high-redshift …
