Black Hole Accretion Models Research Articles

κmonty: a Monte Carlo Compton scattering code including non-thermal electrons

ABSTRACT Low-luminosity active galactic nuclei are strong sources of X-ray emission produced by Compton scattering originating from the accretion flows surrounding their supermassive black holes. The shape and energy of the resulting spectrum depend on the shape of the underlying electron distribution function (DF). In this work, we present an extended version of the grmonty code, called κmonty. The grmonty code previously only included a thermal Maxwell–Jütner electron DF. We extend the grmonty code with non-thermal electron DFs, namely the κ and power-law DFs, implement Cartesian Kerr–Schild coordinates, accelerate the code with mpi, and couple the code to the non-uniform adaptive mesh refinement grid data from the general relativistic magnetohydrodynamics code bhac. For the Compton scattering process, we derive two sampling kernels for both DFs. Finally, we present a series of code tests to verify the accuracy of our schemes. The implementation of non-thermal DFs opens the possibility of studying the effect of non-thermal emission on previously developed black hole accretion models.

Millimeter observational signatures of flares in magnetically arrested black hole accretion models

ABSTRACT In general relativistic magnetohydrodynamic (GRMHD) simulations, accreted magnetic flux on the black hole horizon episodically decays, during which magnetic reconnection heats up the plasma near the horizon, potentially powering high-energy flares like those observed in M87* and Sgr A*. We study the mm observational counterparts of such flaring episodes in very high resolution GRMHD simulations. The change in 230 GHz flux during the expected high energy flares depends primarily on the efficiency of accelerating γ ≳ 100 (Te ≳ 1011 K) electrons. For models in which the electrons are heated to Te ∼ 1011 K during flares, the hot plasma produced by reconnection significantly enhances 230 GHz emission and increases the size of the 230 GHz image. By contrast, for models in which the electrons are heated to higher temperatures (which we argue are better motivated), the reconnection-heated plasma is too hot to produce significant 230 GHz synchrotron emission, and the 230 GHz flux decreases during high energy flares. We do not find a significant change in the mm polarization during flares as long as the emission is Faraday thin. We also present expectations for the ring-shaped image as observed by the Event Horizon Telescope during flares, as well as multiwavelength synchrotron spectra. Our results highlight several limitations of standard post-processing prescriptions for the electron temperature in GRMHD simulations. We also discuss the implications of our results for current and future observations of flares in Sgr A*, M87*, and related systems. Appendices contain detailed convergence studies with respect to resolution and plasma magnetization.

Using [Ne v]/[Ne iii] to Understand the Nature of Extreme-ionization Galaxies

Spectroscopic studies of extreme-ionization galaxies (EIGs) are critical to our understanding of exotic systems throughout cosmic time. These EIGs exhibit spectral features requiring >54.42 eV photons: the energy needed to ionize helium into He2+ fully and emit He ii recombination lines. Spectroscopic studies of EIGs can probe exotic stellar populations or accretion onto intermediate-mass black holes (∼102–105 M ⊙), which are the possibly key contributors to the reionization of the Universe. To facilitate the use of EIGs as probes of high-ionization systems, we focus on ratios constructed from several rest-frame UV/optical emission lines: [O iii] λ5008, Hβ, [Ne iii] λ3870, [O ii] λ λ3727, 3729, and [Ne v] λ3427. These lines probe the relative intensity at energies of 35.12, 13.62, 40.96, 13.62, and 97.12 eV, respectively, covering a wider range of ionization than traced by other common rest-frame UV/optical techniques. We use the ratios of these lines ([Ne v]/[Ne iii] ≡ Ne53, [O iii]/Hβ, and [Ne iii]/[O ii]), which are nearby in wavelength, mitigating the effects of dust attenuation and uncertainties in flux calibration. We make predictions from photoionization models constructed from Cloudy that use a broad range of stellar populations and black hole accretion models to explore the sensitivity of these line ratios to changes in the ionizing spectrum. We compare our models to observations from the Hubble Space Telescope and JWST of galaxies with strong high-ionization emission lines at z ∼ 0, z ∼ 2, and 5 < z < 8.5. We show that the Ne53 ratio can separate galaxies with ionization from “normal” stellar populations from those with active galactic nuclei and even “exotic” Population III models. We introduce new selection methods to identify galaxies with photoionization driven by Population III stars or intermediate-mass black hole accretion disks that could be identified in upcoming high-redshift spectroscopic surveys.

Black hole–galaxy scaling relations in FIRE: the importance of black hole location and mergers

ABSTRACT The concurrent growth of supermassive black holes (SMBHs) and their host galaxies remains to be fully explored, especially at high redshift. While often understood as a consequence of self-regulation via AGN feedback, it can also be explained by alternative SMBH accretion models. Here, we expand on previous work by studying the growth of SMBHs with the help of a large suite of cosmological zoom-in simulations (MassiveFIRE) that are part of the Feedback in Realistic Environments (FIRE) project. The growth of SMBHs is modelled in post-processing with different black hole accretion models, placements, and merger treatments, and validated by comparing to on-the-fly calculations. Scaling relations predicted by the gravitational torque-driven accretion (GTDA) model agree with observations at low redshift without the need for AGN feedback, in contrast to models in which the accretion rate depends strongly on SMBH mass. At high redshift, we find deviations from the local scaling relations in line with previous theoretical results. In particular, SMBHs are undermassive, presumably due to stellar feedback, but start to grow efficiently once their host galaxies reach M* ∼ 1010M⊙. We analyse and explain these findings in the context of a simple analytic model. Finally, we show that the predicted scaling relations depend sensitively on the SMBH location and the efficiency of SMBH merging, particularly in low-mass systems. These findings highlight the relevance of understanding the evolution of SMBH-galaxy scaling relations to predict the rate of gravitational wave signals from SMBH mergers across cosmic history.

Accretion of a Vlasov gas onto a black hole from a sphere of finite radius and the role of angular momentum

The accretion of a spherically symmetric, collisionless kinetic gas cloud on to a Schwarzschild black hole is analysed. Whereas previous studies have treated this problem by specifying boundary conditions at infinity, here the properties of the gas are given at a sphere of finite radius. The corresponding steady-state solutions are computed using four different models with an increasing level of sophistication, starting with the purely radial infall of Newtonian particles and culminating with a fully general relativistic calculation in which individual particles have angular momentum. The resulting mass accretion rates are analysed and compared with previous models, including the standard Bondi model for a hydrodynamic flow. We apply our models to the supermassive black holes Sgr A* and M87*, and we discuss how their low luminosity could be partially explained by a kinetic description involving angular momentum. Furthermore, we get results consistent with previous model-dependent bounds for the accretion rate imposed by rotation measures of the polarised light coming from Sgr A* and with estimations of the accretion rate of M87* from the Event Horizon Telescope collaboration. Our methods and results could serve as a first approximation for more realistic black hole accretion models in various astrophysical scenarios in which the accreted material is expected to be nearly collisionless.

Evolution of Black Hole and Galaxy Growth in a Semi-numerical Galaxy Formation Model

Abstract We present a simple semi-numerical model designed to explore black hole growth and galaxy evolution. This method builds on a previous model for black hole accretion that uses a semi-numerical galaxy formation model and universal Eddington ratio distribution to describe the full active galactic nucleus (AGN) population by independently connecting galaxy and AGN growth to the evolution of the host dark matter halos. We fit observed X-ray luminosity functions up to a redshift of z ∼ 4, as well as investigate the evolution of the Eddington ratio distributions. We find that the Eddington ratio distribution evolves with redshift such that the slope of the low-Eddington accretion rate distribution increases with cosmic time, consistent with the behavior predicted in hydrodynamical simulations for galaxies with different gas fractions. We also find that the evolution of our average Eddington ratio is correlated with observed star formation histories, supporting a picture in which black holes and galaxies evolve together in a global sense. We further confirm the impact of luminosity limits on observed galaxy and halo properties by applying selection criteria to our fiducial model and comparing to surveys across a wide range of redshifts.

The Sub-Eddington Boundary for the Quasar Mass–Luminosity Plane: A Theoretical Perspective

By exploring more than sixty thousand quasars from the Sloan Digital Sky Survey Data Release 5, Steinhardt &amp; Elvis discovered a sub-Eddington boundary and a redshift-dependent drop-off at higher black hole mass, possible clues to the growth history of massive black holes. Our contribution to this special issue of Universe amounts to an application of a model for black hole accretion and jet formation to these observations. For illustrative purposes, we include ~100,000 data points from the Sloan Digital Sky Survey Data Release 7 where the sub-Eddington boundary is also visible and propose a theoretical picture that explains these features. By appealing to thin disk theory and both the lower accretion efficiency and the time evolution of jetted quasars compared to non-jetted quasars in our “gap paradigm”, we explain two features of the sub-Eddington boundary. First, we show that a drop-off on the quasar mass-luminosity plane for larger black hole mass occurs at all redshifts. But the fraction of jetted quasars is directly related to the merger function in this paradigm, which means the jetted quasar fraction drops with decrease in redshift, which allows us to explain a second feature of the sub-Eddington boundary, namely a redshift dependence of the slope of the quasar mass–luminosity boundary at high black hole mass stemming from a change in radiative efficiency with time. We are able to reproduce the mass dependence of, as well as the oscillating behavior in, the slope of the sub-Eddington boundary as a function of time. The basic physical idea involves retrograde accretion occurring only for a subset of the more massive black holes, which implies that most spinning black holes in our model are prograde accretors. In short, this paper amounts to a qualitative overview of how a sub-Eddington boundary naturally emerges in the gap paradigm.

Spectra of black hole accretion models of ultraluminous X-ray sources

We present general relativistic radiation MHD simulations of super-Eddington accretion on a $10M_\odot$ black hole. We consider a range of mass accretion rates, black hole spins, and magnetic field configurations. We compute the spectra and images of the models as a function of viewing angle, and compare them with the observed properties of ultraluminous X-ray sources (ULXs). The models easily produce apparent luminosities in excess of $10^{40}~{\rm erg\,s^{-1}}$ for pole-on observers. However, the angle-integrated radiative luminosities rarely exceed $2.5\times10^{39}~{\rm erg\,s^{-1}}$ even for mass accretion rates of tens of Eddington. The systems are thus radiatively inefficient, though they are energetically efficient when the energy output in winds and jets is also counted. The simulated models reproduce the main empirical types of spectra --- disk-like, supersoft, soft, hard --- observed in ULXs. The magnetic field configuration, whether MAD ("magnetically arrested disk") or SANE ("standard and normal evolution"), has a strong effect on the results. In SANE models, the X-ray spectral hardness is almost independent of accretion rate, but decreases steeply with increasing inclination. MAD models with non-spinning black holes produce significantly softer spectra at higher values of $\dot{M}$, even at low inclinations. MAD models with rapidly spinning black holes are quite different from all other models. They are radiatively efficient (efficiency factor $\sim10-20\%$), super-efficient when the mechanical energy output is also included ($70\%$), and produce hard blazar-like spectra. In all models, the emission shows strong geometrical beaming, which disagrees with the more isotropic illumination favored by observations of ULX bubbles.

The disc-jet symbiosis emerges: modelling the emission of Sagittarius A* with electron thermodynamics

We calculate the radiative properties of Sagittarius A* -- spectral energy distribution, variability, and radio-infrared images -- using the first 3D, physically motivated black hole accretion models that directly evolve the electron thermodynamics in general relativistic MHD simulations. These models reproduce the coupled disc-jet structure for the emission favored by previous phenomenological analytic and numerical works. More specifically, we find that the low frequency radio emission is dominated by emission from a polar outflow while the emission above 100 GHz is dominated by the inner region of the accretion disc. The latter produces time variable near infrared (NIR) and X-ray emission, with frequent flaring events (including IR flares without corresponding X-ray flares and IR flares with weak X-ray flares). The photon ring is clearly visible at 230 GHz and 2 microns, which is encouraging for future horizon-scale observations. We also show that anisotropic electron thermal conduction along magnetic field lines has a negligible effect on the radiative properties of our model. We conclude by noting limitations of our current generation of first-principles models, particularly that the outflow is closer to adiabatic than isothermal and thus underpredicts the low frequency radio emission.

Chaotic cold accretion on to black holes in rotating atmospheres

Chaotic cold accretion (CCA) profoundly differs from classic black hole accretion models. Using 3D high-resolution simulations, we probe the impact of rotation on the hot and cold accretion flow in a typical massive galaxy. In the hot mode, with or without turbulence, the pressure-dominated flow forms a geometrically thick rotational barrier, suppressing the accretion rate to ~1/3 of the Bondi rate. When radiative cooling is dominant, the gas loses pressure support and quickly circularizes in a cold thin disk. In the more common state of a turbulent and heated atmosphere, CCA drives the dynamics if the gas velocity dispersion exceeds the rotational velocity, i.e., turbulent Taylor number < 1. Extended multiphase filaments condense out of the hot phase via thermal instability and rain toward the black hole, boosting the accretion rate up to 100 times the Bondi rate. Initially, turbulence broadens the angular momentum distribution of the hot gas, allowing the cold phase to condense with prograde or retrograde motion. Subsequent chaotic collisions between the cold filaments, clouds, and a clumpy variable torus promote the cancellation of angular momentum, leading to high accretion rates. The simulated sub-Eddington accretion rates cover the range inferred from AGN cavity observations. CCA predicts inner flat X-ray temperature and $r^{-1}$ density profiles, as recently discovered in M 87 and NGC 3115. The synthetic H{\alpha} images reproduce the main features of cold gas observations in massive ellipticals, as the line fluxes and the filaments versus disk morphology. Such dichotomy is key for the long-term AGN feedback cycle. As gas cools, filamentary CCA develops and boosts AGN heating; the cold mode is thus reduced and the rotating disk remains the sole cold structure. Its consumption leaves the atmosphere in hot mode with suppressed accretion and feedback, reloading the cycle.

A refined sub-grid model for black hole accretion and AGN feedback in large cosmological simulations

In large scale cosmological hydrodynamic simulations simplified sub-grid models for gas accretion onto black holes and AGN feedback are commonly used. Such models typically depend on various free parameters, which are not well constrained. We present a new advanced model containing a more detailed description of AGN feedback, where those parameters reflect the results of recent observations. The model takes the dependency of these parameters on the black hole properties into account and describes a continuous transition between the feedback processes acting in the so-called radio-mode and quasar-mode. In addition, we implement a more detailed description of the accretion of gas onto black holes by distinguishing between hot and cold gas accretion. Our new implementations prevent black holes from gaining too much mass, particularly at low redshifts so that our simulations are now very successful in reproducing the observed present-day black hole mass function. Our new model also suppresses star formation in massive galaxies slightly more efficiently than many state-of-the-art models. Therefore, the simulations that include our new implementations produce a more realistic population of quiescent and star-forming galaxies compared to recent observations, even if some discrepancies remain. In addition, the baryon conversion efficiencies in our simulation are - except for the high mass end - consistent with observations presented in literature over the mass range resolved by our simulations. Finally, we discuss the significant impact of the feedback model on the low-luminous end of the AGN luminosity function.

The accretion disc particle method for simulations of black hole feeding and feedback

Black holes grow by accreting matter from their surroundings. However, angular momentum provides an efficient natural barrier to accretion and so only the lowest angular momentum material will be available to feed the black holes. The standard subgrid model for black hole accretion in galaxy formation simulations – based on the Bondi–Hoyle method – does not account for the angular momentum of accreting material, and so it is not clear how representative the black hole accretion rate estimated in this way is likely to be. In this paper we introduce a new subgrid model for black hole accretion that naturally accounts for the angular momentum of accreting material. Both the black hole and its accretion disc are modelled as a composite accretion disc particle. Gas particles are captured by the accretion disc particle if and only if their orbits bring them within its accretion radius Racc, at which point their mass is added to the accretion disc and feeds the black hole on a viscous time-scale tvisc. The resulting black hole accretion rate powers the accretion luminosity ⁠, which drives black hole feedback. Using a series of controlled numerical experiments, we demonstrate that our new accretion disc particle method is more physically self-consistent than the Bondi–Hoyle method. We also discuss the physical implications of the accretion disc particle method for systems with a high degree of rotational support, and we argue that the MBH–σ relation in these systems should be offset from the relation for classical bulges and ellipticals, as appears to be observed.

Scalar field confinement as a model for accreting systems

We investigate the possibility of localizing scalar field configurations as a model for black hole accretion. We analyse and resolve difficulties encountered when localizing scalar fields in general relativity. We illustrate this ability with a simple spherically symmetric model which can be used to study features of accreting shells around a black hole. This is accomplished by prescribing a scalar field with a coordinate-dependent potential. Numerical solutions to the Einstein–Klein–Gordon equations are shown, where a scalar field is indeed confined within a region surrounding a black hole. The resulting spacetime can be described in terms of simple harmonic time dependence.

Towards a new standard model for black hole accretion

We briefly review recent developments in black hole accretion disk theory, emphasizing the vital role played by magnetohydrodynamic (MHD) stresses in transporting angular momentum. The apparent universality of accretion-related outflow phenomena is a strong indicator that large-scale MHD torques facilitate vertical transport of angular momentum. This leads to an enhanced overall rate of angular momentum transport and allows accretion of matter to proceed at an interesting rate. Furthermore, we argue that when vertical transport is important, the radial structure of the accretion disk is modified at small radii and this affects the disk emission spectrum. We present a simple model demonstrating how energetic, magnetically-driven outflows modify the emergent disk emission spectrum with respect to that predicted by standard accretion disk theory. A comparison of the predicted spectra against observations of quasar spectral energy distributions suggests that mass accretion rates inferred using the standard disk model may be severely underestimated.

Detection of Low‐Hard State Spectral and Timing Signatures from the Black Hole X‐Ray Transient XTE J1650−500 at Low X‐Ray Luminosities

Using the Chandra X-Ray Observatory and the Rossi X-Ray Timing Explorer, we have studied the black hole candidate (BHC) X-ray transient XTE J1650-500 near the end of its 2001-2002 outburst after its transition to the low-hard state at X-ray luminosities down to L = 1.5 × 1034 ergs s-1 (1-9 keV, assuming a source distance of 4 kpc). Our results include a characterization of the spectral and timing properties. At the lowest sampled luminosity, we used an 18 ks Chandra observation to measure the power spectrum at low frequencies. For the three epochs at which we obtained Chandra/RXTE observations, the 0.5-20 keV energy spectrum is consistent with a spectral model consisting of a power law with interstellar absorption. We detect evolution in the power-law photon index from Γ = 1.66 ± 0.05 to 1.93 ± 0.13 (90% confidence errors), indicating that the source softens at low luminosities. The power spectra are characterized by strong (20%-35% fractional rms) band-limited noise, which we model as a zero-centered Lorentzian. Including results from an RXTE study of XTE J1650-500 near the transition to the low-hard state by Kalemci and coworkers, the half-width of the zero-centered Lorentzian (roughly where the band-limited noise cuts off) drops from 4 Hz at L = 7 × 1036 ergs s-1 (1-9 keV, absorbed) to 0.067 ± 0.007 Hz at L = 9 × 1034 ergs s-1 to 0.0035 ± 0.0010 Hz at the lowest luminosity. While the spectral and timing parameters evolve with luminosity, it is notable that the general shapes of the energy and power spectra remain the same, indicating that the source stays in the low-hard state. This implies that the X-ray-emitting region of the system likely keeps the same overall structure, while the luminosity changes by a factor of 470. We discuss how these results may constrain theoretical black hole accretion models.

On the Nature of Angular Momentum Transport in Nonradiative Accretion Flows

The principles underlying a proposed class of black hole accretion models are examined. The flows are generally referred to as and are characterized by inward transport of angular momentum by thermal convection and outward viscous transport, vanishing mass accretion, and vanishing local energy dissipation. In this paper, we examine the viability of these ideas by explicitly calculating the leading-order angular momentum transport of axisymmetric modes in magnetized, differentially rotating, stratified flows. The modes are destabilized by the generalized magnetorotational instability, including the effects of angular velocity and entropy gradients. It is explicitly shown that modes that would be stable in the absence of a destabilizing entropy gradient transport angular momentum outward. There are no inward-transporting modes at all, unless the magnitude of the (imaginary) Brunt-Vaisala frequency is comparable to the epicyclic frequency, a condition requiring substantial levels of dissipation. When inward-transporting modes do exist, they appear at long wavelengths, unencumbered by magnetic tension. Moreover, very general thermodynamic principles prohibit the complete recovery of irreversible dissipative energy losses, a central feature of convection-dominated models. Dissipationless flow is incompatible with the increasing inward entropy gradient needed for the existence of inward-transporting modes. Indeed, under steady conditions, dissipation of the free energy of differential rotation inevitably requires outward angular momentum transport. Our results are in good agreement with global MHD simulations, which find significant levels of outward transport and energy dissipation, whether or not destabilizing entropy gradients are present.

On the internal structure of supermassive compact celestial bodies

The conceptual part of the physics of baryonic protomatter and the alternative approach to understanding the internal structure of highly compact stationary supermassive celestial bodies were previously suggested in [1–5]. There are a number of advantages to this approach, which differs in principle from the standard black hole accretion models and is in good agreement with the observational data from active galactic nuclei. In order to be more consistent and convinced in the correctness of previously drawn statements, in our research it has been advantageous to verify them by expansion of the basic ideas with the appropriate and consistent theoretical constructions backed up by detailed numerical studies of the models, which are physically more realistic, with the spherical-symmetric distribution of matter in many-phase stratified states. Multiple integrations in the aftermath prove the validity of the previous physical scenario and correctness of drawn statements that the process of inner distortion of the space-time continuum just serves as the eligible mechanism counteracting to collapse.

An introduction to the theory of internal structure of supermassive compact celestial bodies

Different in principle from the contemporary standard black hole accretion models, a new approach to the understanding of the internal structure of highly compact stationary supermassive celestial bodies has been worked out. The equations of equilibrium configurations of baryonic protomatter (ECBP) have been discussed. In a particular case of ideal degenerated neutron gas in absence of a process of inner distortion of the space and time, it has been shown that the theory suggested by Ter-Kazarian (1989c) leads to the same results as those obtained by Oppenheimer and Volkoff (1939) based on Einstein's theory. The numerical integration of equations of ECBP in the most simple case of equilibrium single-component configurations of degenerated ideal gas of neutrons in a presence of one-dimensional space-like inner distortion of space-time continuum is carried out. It has been shown that the stable stationary supermassive cores are formed in the central parts of the considered configurations. As the models of active galactic nuclei (AGNs) one has considered only the configurations that consisted of these cores surrounded by accretion disks. The fundamental difference from the standard black-hole accretion models is the fact that the central cores are in a stable equilibrium state with certain radial distributions of density and pressure and with a number of integral characteristics. The significant effect of metric singularity cut-off has been established, due to the action of which a singularity of metric ceased to be significant. The numerous integrations have also revealed the other fact of great importance, the presence within the outlined theory of a rigorous restriction on the upper limit of possible values of total masses of considered equilibrium configurations, which is to beM≤3.5×108M⊙. In the last section one has proceeded to the direct modelling of concrete AGNs (for 61 sources), the whole point of which comes to the solving of the inverse problem. The results of all calculations that have been carried out in the present work are summarized in Tables I–VII and represented by means of numerous figures. Finally, one should emphasize the important fact of the existence of BL Lac objects OJ 287, 3C 66A, and B2 1308+32, the observed time-scale for flux variations of which are inconsistent with contemporary black hole aceretion models. The case is quite different within the scope of the suggested theory. It seems that a decisive significance for these objects has the action of metric singularity cut-off effect. Due to this their observed sizes are less than the sizes of corresponding spheres of the event horizon. This may serve as a further indication that the suggested theory is preferable to the standard models.

Physics of the Central Engine

I discuss physical processes which may be important in the central engines of AGNs. Black hole accretion models have been elaborated during the past few years, and provide a plausible framework for jet and spectrum formation. However, the specific mechanisms responsible for producing the observed continuum radiation remain uncertain. I consider nonthermal models for the IR continuum, constraints on thermal plasma, and the production of relativistic electrons.

Direct evidence for gravitational domination of the motion of gas within one light-week of the central object in NGC 4151 and the determination of the mass of the probable black hole

view Abstract Citations (131) References (32) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Direct Evidence for Gravitational Domination of the Motion of Gas within One Light-Week of the Central Object in NGC 4151 and the Determination of the Mass of the Probable Black Hole Gaskell, C. Martin Abstract A practical method is demonstrated for determining the average direction of motion of broad-line region gas in quasars. Analysis of the variability of the blue and red wings of the C IV λ1549 and Mg II λ2798 lines and the UV continuum in the low-luminosity quasar in NGC 4151 reveals that the red sides of both lines lead to blue sides in their variations. Outflow of the high-velocity gas (v > 5000 km s^-1^) emitting the C IV and Mg II lines is excluded at the 99.5% confidence level. The dominant motion of the gas is most likely to be inward, although totally random or chaotic motions are excluded only at the 93% level. It is suggested that the gravitational domination of the motion of the broad-line region clouds at small radii is a consequence of their high densities (N_e_>10^11^ cm^-3^). The demonstration that the broad-line region has its motions dominated by gravity (versus domination by a wind or radiation pressure) puts black hole accretion models onto an observational footing and permits the first simple kinematic determination of the mass of the black hole in a galactic nucleus. The mass is 5 x 10^7^ M_sun_ if the gas is indeed inflowing. Publication: The Astrophysical Journal Pub Date: February 1988 DOI: 10.1086/165986 Bibcode: 1988ApJ...325..114G Keywords: Black Holes (Astronomy); Galactic Nuclei; Gas Dynamics; Quasars; Seyfert Galaxies; Carbon; Cross Correlation; Error Analysis; Magnesium; Monte Carlo Method; Ultraviolet Spectra; Astrophysics; BLACK HOLES; GALAXIES: INDIVIDUAL NGC NUMBER: NGC 4151; GALAXIES: INTERNAL MOTIONS; GALAXIES: NUCLEI; GALAXIES: SEYFERT; QUASARS full text sources ADS | data products SIMBAD (2) NED (2)