Convection-dominated Accretion Flows Research Articles

Quasi-stars as a Means of Rapid Black Hole Growth in the Early Universe

JWST observations demonstrate that supermassive black holes (SMBHs) exist by redshifts z ≳ 10, providing further evidence for “direct collapse” black hole (BH) formation, whereby massive (∼103–5 M ⊙) SMBH seeds are generated within a few million years as a byproduct of the rapid inflow of gas into the centers of protogalaxies. Here we analyze the intermediate “quasi-star” phase that accompanies some direct-collapse models, during which a natal BH accretes mass from and energetically sustains (through accretion) an overlying gaseous envelope. We argue that previous estimates of the maximum BH mass that can be reached during this stage, ∼1% of the total quasi-star mass, are unphysical, and arise from underestimating the efficiency with which energy can be transported outward from regions close to the BH. We construct new quasi-star models that consist of an inner, “saturated convection” region (which conforms to a convection-dominated accretion flow near the BH) matched to an outer, adiabatic envelope. These solutions exist up to a BH mass of ∼60% of the total quasi-star mass, at which point the adiabatic envelope contains only 2% of the mass (with the remaining ∼38% in the saturated-convection region), and this upper limit is reached within a time of 20–40 Myr. We conclude that quasi-stars remain a viable route for producing SMBHs at large redshifts, which is consistent with recent JWST observations.

Low-density, radiatively inefficient rotating-accretion flow on to a black hole

We study low-density axisymmetric accretion flows onto black holes (BHs) with two-dimensional hydrodynamical simulations, adopting the $\alpha$-viscosity prescription. When the gas angular momentum is low enough to form a rotationally supported disk within the Bondi radius ($R_{\rm B}$), we find a global steady accretion solution. The solution consists of a rotational equilibrium distribution at $r\sim R_{\rm B}$, where the density follows $\rho \propto (1+R_{\rm B}/r)^{3/2}$, surrounding a geometrically thick and optically thin accretion disk at the centrifugal radius, where thermal energy generated by viscosity is transported via strong convection. Physical properties of the inner solution agree with those expected in convection-dominated accretion flows (CDAF; $\rho \propto r^{-1/2}$). In the inner CDAF solution, the gas inflow rate decreases towards the center due to convection ($\dot{M}\propto r$), and the net accretion rate (including both inflows and outflows) is strongly suppressed by several orders of magnitude from the Bondi accretion rate $\dot{M}_{\rm B}$ The net accretion rate depends on the viscous strength, following $\dot{M}/\dot{M}_{\rm B}\propto (\alpha/0.01)^{0.6}$. This solution holds for low accretion rates of $\dot{M}_{\rm B}/\dot{M}_{\rm Edd}< 10^{-3}$ having minimal radiation cooling, where $\dot{M}_{\rm Edd}$ is the Eddington rate. In a hot plasma at the bottom ($r<10^{-3}~R_{\rm B}$), thermal conduction would dominate the convective energy flux. Since suppression of the accretion by convection ceases, the final BH feeding rate is found to be $\dot{M}/\dot{M}_{\rm B} \sim 10^{-3}-10^{-2}$. This rate is as low as $\dot{M}/\dot{M}_{\rm Edd} \sim 10^{-7}-10^{-6}$ inferred for SgrA$^*$ and the nuclear BHs in M31 and M87, and can explain the low luminosities in these sources, without invoking any feedback mechanism.

Structure of a hot accretion flow in the presence of outflow and convection with large ordered magnetic field

Hydrodynamics and magnetohydrodynamic simulations of hot accretion flow have indicated that there is an inward decreasing of mass accretion rate with decreasing radius. Consequently, we have a flatter density profile ($\rho \propto r^{-p}$ with $p\propto 1.5-s$ in the case of $\dot{M}\propto r^{s}$, $0 \leq s<1$) compared to the case of a constant accretion rate (($\rho \propto r^{-\frac{3}{2}}$). In order to describe this behavior two models have been proposed: inflow-outflow solution and convection-dominated accretion flows. We have studied the properties of a hot accretion flow in the presence of convection, large scale magnetic field and outflow. We consider an axisymmetric viscous flow in the steady state. We used the self-similar solutions to solve the 1.5 dimensional inflow-outflow equations. We have assumed that the convection as a free parameter in our model for simplicity. We have considered two components of magnetic field (toroidal and vertical) in this paper. We have shown that the strong convection makes the inflow accretes and rotates slower while it becomes hotter and thicker. We have found that the thickness of the disc deviates from non-convective solutions obviously. We have represented that two components of magnetic field have the opposite effects on the thickness of the disc and similar effects on the radial and angular velocities of the flow.

The influence of outflow and global magnetic field on the structure and spectrum of resistive CDAFs

We examine the effects of a global magnetic field and outflow on radiatively inefficient accretion flow (RIAF) in the presence of magnetic resistivity. We find self-similar solutions for the height integrated equations that govern the behavior of the flow. We use the mixing length mechanism for studying the convection parameter. We adopt the radius dependent mass accretion rate $\dot{M}=\dot{M}_{\mathrm{out}}{(\frac{r}{r_{\mathrm{out}}})^{s}}$ , with $s> 0$ , to investigate the influence of outflow on the structure of inflow where $s$ is a constant and is an indication of the effect of the wind. Also, we have studied the radiation spectrum and temperature of convection dominated accretion flows (CDAFs). The thermal bremsstrahlung emission as a radiation mechanism is taken into account for calculating the spectra emitted by the CDAFs. The energy that powers bremsstrahlung emission at large radii is provided by convective transport from small radii and viscous and resistivity dissipation. Our results indicate that the disc rotates slower and accretes faster, it becomes hotter and thicker for a stronger wind. By increasing all components of the magnetic field, the disc rotates faster and accretes more slowly, while it becomes hotter and thicker. We show that the outflow parameter and all components of the magnetic field have the same effects on the luminosity of the disc. We compare the dynamical structure of the disc in two different solutions (with and without resistivity parameter). We show that only the radial infall velocity and the surface density could be changed by the resistivity parameter obviously. Increasing the effect of the wind increases the disc’s temperature and the luminosity of the disc. The effect of the magnetic field is similar to the effect of the wind on the disc’s temperature and the luminosity of the disc, but the influence of the resistivity on the observational properties is not evident.

MEASURING MASS ACCRETION RATE ONTO THE SUPERMASSIVE BLACK HOLE IN M87 USING FARADAY ROTATION MEASURE WITH THE SUBMILLIMETER ARRAY

We present the first constraint on Faraday rotation measure (RM) at submillimeter wavelengths for the nucleus of M 87. By fitting the polarization position angles ($\chi$) observed with the SMA at four independent frequencies around $\sim$230 GHz and interpreting the change in $\chi$ as a result of \emph{external} Faraday rotation associated with accretion flow, we determine the rotation measure of the M 87 core to be between $-$7.5$\times$10$^{5}$ and 3.4$\times$10$^{5}$ rad/m$^{2}$. Assuming a density profile of the accretion flow that follows a power-law distribution and a magnetic field that is ordered, radial, and has equipartition strength, the limit on the rotation measure constrains the mass accretion rate $\dot{M}$ to be below 9.2$\times$10$^{-4}$ M$_{\odot}$~yr$^{-1}$ at a distance of 21 Schwarzchild radii from the central black hole. This value is at least two orders of magnitude smaller than the Bondi accretion rate, suggesting significant suppression of the accretion rate in the inner region of the accretion flow. Consequently, our result disfavors the classical \emph{advection dominated accretion flow} (ADAF) and prefers the \emph{adiabatic inflow-outflow solution} (ADIOS) or \emph{convection-dominated accretion flow} (CDAF) for the hot accretion flow in M 87.

Outflow from Hot Accretion Flows

AbstractNumerical simulations of hot accretion flows have shown that the mass accretion rate decreases with decreasing radius. Two models have been proposed to explain this result. In the adiabatic inflow-outflow solution (ADIOS), it is thought to be due to the loss of gas in outflows. In the convection-dominated accretion flow (CDAF) model, it is explained as because that the gas is locked in convective eddies. In this paper we use hydrodynamical (HD) and magnetohydrodynamical (MHD) simulations to investigate which one is physical. We calculate and compare various properties of inflow (gas with an inward velocity) and outflow (gas with an outward velocity). Systematic and significant differences are found. For example, for HD flows, the temperature of outflow is higher than inflow; while for MHD flows, the specific angular momentum of outflow is much higher than inflow. We have also analyzed the convective stability of MHD accretion flow and found that they are stable. These results suggest that systematic inward and outward motion must exist, i.e., the ADIOS model is favored. The different properties of inflow and outflow also suggest that the mechanisms of producing outflow in HD and MHD flows are buoyancy associated with the convection and the centrifugal force associated with the angular momentum transport mediated by the magnetic field, respectively. The latter mechanism is similar to the Blandford &amp; Payne mechanism but no large-scale open magnetic field is required here. Possible observational applications are briefly discussed.

Self-similar structure of magnetized advection-dominated accretion flows and convection-dominated accretion flows

(Abridged) We study the effects of a global magnetic field on viscously-rotating and vertically-integrated accretion disks around compact objects using a self-similar treatment. We extend Akizuki & Fukue's work (2006) by discussing a general magnetic field with three components ($r, \phi, z$) in advection-dominated accretion flows (ADAFs). We also investigate the effects of a global magnetic field on flows with convection. For these purposes, we first adopt a simple form of the kinematic viscosity $\nu=\alpha c_{s}^{2}/\Omega_{K}$ to study magnetized ADAFs. Then we consider a more realistic model of the kinematic viscosity $\nu=\alpha c_{s}H$, which makes the infall velocity increase but the sound speed and toroidal velocity decrease. We next use two methods to study magnetized flows with convection, i.e., we take the convective coefficient $\alpha_{c}$ as a free parameter to discuss the effects of convection for simplicity. We establish the $\alpha_{c}-\alpha$ relation for magnetized flows using the mixing-length theory and compare this relation with the non-magnetized case. If $\alpha_{c}$ is set as a free parameter, then $|v_{r}|$ and $c_{s}$ increase for a large toroidal magnetic field, while $|v_{r}|$ decreases but $|v_{\phi}|$ increases (or decreases) for a strong and dominated radial (or vertical) magnetic field with increasing $\alpha_{c}$. In addition, the magnetic field makes the $\alpha_{c}-\alpha$ relation be distinct from that of non-magnetized flows, and allows the $\rho\propto r^{-1}$ or $\rho\propto r^{-2}$ structure for magnetized non-accreting convection-dominated accretion flows with $\alpha+g\alpha_{c}< 0$ (where $g$ is the parameter to determine the condition of convective angular momentum transport).

Convection-Dominated Accretion Flows with Radiative Cooling

By numerically solving the set of basic equations describing blackhole accretion flows with low accretion rates, we show that althoughthe dynamical structure of these flows is essentially unaffected byradiative processes in comparison with the case in which the radiationis not considered, the radiative cooling can be more important than theadvective cooling in the flow's convection-dominated zone, and thisresult may have implications to distinguish observationallyconvection-dominated accretion flows from advection-dominated accretionflows.

Compton‐heated Outflow from Convection‐dominated Accretion Flows

Convection-dominated accretion flows (CDAFs) are expected to have a shallower density profile and a higher radiation efficiency compared to advection-dominated accretion flows (ADAFs). Both solutions have been developed to account for the observed properties of the low-luminosity, high-temperature X-ray sources believed to involve accretion onto massive black holes. Self-similar CDAFs also have steeper poloidal density gradients and temperatures close to the virial temperature. All these characteristics make CDAFs more capable of producing polar outflows driven by Compton heating as compared to other classical accretion disks. We investigate the conditions for producing such outflows in CDAFs and look for the mass accretion rate or, equally, the luminosity of CDAFs for which such outflows will exist. When the electron temperature saturates around 1011 K at the inner region, polar outflows are probable for 8 × 10-7 L/LE 4 × 10-5, where LE is the Eddington luminosity. Outflows are well collimated with small opening angles. The luminosity range for which outflow solutions exist is narrower for lower electron temperature flows and disappears completely for electron temperature 6 × 109 K. When the magnetic field is present, we find that outflows are possible if the magnetic field is less than from 10% to 1% of the equipartition field. We also find that outflows are more likely to be produced when the viscosity parameter α is small. The tendency for jetlike collimated outflows to result from these solutions is presumably astrophysically relevant given the high frequency of jets from active galactic nuclei.

XMM-Newtonobservations of the dwarf elliptical galaxy NGC 3226

We report on an XMM-Newton observation of the dwarf elliptical galaxy NGC 3226 performed in November 2000. The analysis of the 0.4-10 keV spectrum of its nucleus is consistent with a power law continuum (Γ ≈ 1.96) absorbed at low energies by neutral gas (with a hydrogen column density NH ≈ 3-8×10 21 cm −2 and a covering fraction greater than 85%) and by weakly ionized gas (NW ≈ 4-6 × 10 21 cm −2 with ξ ≈ 1-7 erg s −1 cm). However, the study indicates that a bremstrahlung model absorbed by neutral material is a better description reminiscent of the X-ray emission from advection-dominated accretion flows (ADAFs). The temperature of the best fit bremstrahlung model (T ≈ 10 8 K) and the absence of short and mid time-scale variability suggests that the X-ray emission originates from regions relatively far from the nucleus as in convection-dominated accretion flows (CDAFs) or in the so-called wind models. By comparing the 2-10 keV luminosity of the central object (LX = 2.58 × 10 40 erg s −1 after correction from Galactic and intrinsic absorption) with radio flux measurements, we find a mass in the range (1.7-50) × 10 7 Mfor the accreting black hole, a value comparable with an independent estimate from the dispersion of radial velocities. We argue that the dwarf elliptical galaxy NGC 3226 may harbor a sub-Eddington, super-massive black hole in a radiative inefficient state which is distinct from the near-Eddington, thermally dominated black holes presumably found in quasars and luminous Seyfert galaxies.

Global dynamics of radiatively inefficient accretion flows: advection versus convection

We obtain global solutions for radiatively inefficiently accretion flows around black holes. Whether and where convection develops in a flow are self-consistently determined by mixinglength theory. The solutions can be divided into three types according to the strength of normal viscosity. Type I solutions correspond to large viscosity parameter α 0.1 ‐ they are purely advection-dominated with no convection; they have been extensively studied in the literature. Type II solutions are for moderate α ∼ 0.01, and have a three-zone structure. The inner zone is advection-dominated, the middle zone is convection-dominated and ranges from a few tens to a few thousands of gravitational radii, and the outer zone is convectively stable and outwardly matches a Keplerian disc. The net energy flux throughout the flow is inward, as in type I solutions. Type III solutions, which are for small α 0.001, consist of two zones as Abramowicz et al. suggested previously: an inner advection-dominated zone and an outer convection-dominated zone, separated at a radius of a few tens of gravitational radii. This type of solution has an outward net energy flux. In both type II and type III solutions, the radial density profile is between the 1/2 law of the self-similar convection-dominated accretion flow model and the 3/2 law of the self-similar advection-dominated accretion flow model, and the efficiency of energy release is found to be extremely low. Our results are in good agreement with those of recent numerical simulations.

Three‐dimensional Magnetohydrodynamic Simulations of Radiatively Inefficient Accretion Flows

We present three-dimensional MHD simulations of rotating radiatively inefficient accretion flows onto black holes. We continuously inject magnetized matter into the computational domain near the outer boundary and run the calculations long enough for the resulting accretion flow to reach a quasi-steady state. We have studied two limiting cases for the geometry of the injected magnetic field: pure toroidal field and pure poloidal field. In the case of toroidal field injection, the accreting matter forms a nearly axisymmetric, geometrically thick, turbulent accretion disk. The disk resembles in many respects the convection-dominated accretion flows found in previous numerical and analytical investigations of viscous hydrodynamic flows. Models with poloidal field injection evolve through two distinct phases. In an initial transient phase, the flow forms a relatively flattened, quasi-Keplerian disk with a hot corona and a bipolar outflow. However, when the flow later achieves steady state, it changes in character completely. The magnetized accreting gas becomes two-phase, with most of the volume being dominated by a strong dipolar magnetic field from which a thermal low-density wind flows out. Accretion occurs mainly via narrow slowly rotating radial streams that "diffuse" through the magnetic field with the help of magnetic reconnection events.

On Angular Momentum Transport in Convection-dominated Accretion Flows

Convection-dominated accretion flow (CDAF) is a promising model to explain underluminous accreting black holes in X-ray binaries and galactic nuclei. I discuss the effects of angular momentum transport in viscous hydrodynamical and MHD CDAFs. In hydrodynamical CDAFs, convection transports angular momentum inward, and this, together with the outward convection transport of thermal energy, determine the radial structure of the flow. In MHD CDAFs, convection can transport angular momentum either inward or outward, depending on the properties of turbulence in rotating magnetized plasma, which are not fully understood yet. The direction of convection angular momentum transport can affect the law of rotation of MHD CDAFs.

The Magnetohydrodynamics of Convection‐dominated Accretion Flows

Radiatively inefficient accretion flows onto black holes are unstable due to both an outwardly decreasing entropy (`convection') and an outwardly decreasing rotation rate (the `magnetorotational instability'; MRI). Using a linear magnetohydrodynamic stability analysis, we show that long-wavelength modes are primarily destabilized by the entropy gradient and that such `convective' modes transport angular momentum inwards. Moreover, the stability criteria for the convective modes are the standard Hoiland criteria of hydrodynamics. By contrast, shorter wavelength modes are primarily destabilized by magnetic tension and differential rotation. These `MRI' modes transport angular momentum outwards. The convection-dominated accretion flow (CDAF) model, which has been proposed for radiatively inefficient accretion onto a black hole, posits that inward angular momentum transport and outward energy transport by long-wavelength convective fluctuations are crucial for determining the structure of the accretion flow. Our analysis suggests that the CDAF model is applicable to a magnetohydrodynamic accretion flow provided the magnetic field saturates at a sufficiently sub-equipartition value (plasma beta >> 1), so that long-wavelength convective fluctuations can fit inside the accretion disk. Numerical magnetohydrodynamic simulations are required to determine whether such a sub-equipartition field is in fact obtained.

Activity From Tidal Disruptions in Galactic Nuclei

The tidal disruption of a star by a supermassive black hole is expected to lead to a short bright flare followed by an extended period of low-level emission. Existing models of the late-time accretion of the stellar debris via a thin disk imply that the Galactic center source Sgr A* should be brighter than currently observed by several orders of magnitude. A similar problem exists for M31 and M32. This problem could be avoided if thin disk accretion transitions to low radiative efficiency accretion (e.g., advection-dominated or convection-dominated accretion flows) at low accretion rates (via evaporation of the thin disk). Alternatively, we show that the outer portions of a thin disk may become neutral and unable to sustain MHD turbulence on a timescale of less than the time between tidal disruption events; this may dramatically shorten the duration of the late accretion phase.

Evidence for Jet Domination of the Nuclear Radio Emission in Low-Luminosity Active Galactic Nuclei

We present simultaneous, subarcsecond (≤50 pc) resolution 5, 8.4, and 15 GHz Very Large Array observations of a well-defined sample of 16 low-luminosity active galactic nuclei. The radio emission in most of these nuclei does not show the rising spectrum (0.2 s 1.3, Lν νs) expected from thermal electrons in an advection-dominated accretion flow (ADAF) with or without weak to moderately strong outflows. Rather, the flat radio spectra are indicative of either synchrotron self-absorbed emission from jets, convection-dominated accretion flows (CDAFs) with L 10-5LEdd, or ADAFs with strong (p 0.6) outflows. The jet interpretation is favored by three factors: (1) the detection of parsec-scale radio extensions, morphologically reminiscent of jets, in the five nuclei with the highest peak radio flux density, (2) the domination of parsec-scale jet radio emission over unresolved core emission in the three best-studied nuclei, and (3) the lack of any clear correlation between radio spectral shape and black hole mass as would be expected from the dependence of the radio turnover frequency on black hole mass in ADAF and CDAF models. A jet domination of nuclear radio emission implies significantly lower accretion rates in ADAF-type models than earlier estimated from core radio luminosities.

Accretion Models of Gamma‐Ray Bursts

Many models of gamma-ray bursts (GRBs) involve accretion onto a compact object, usually a black hole, at a mass accretion rate on the order of a fraction of a solar mass per second. If the accretion disk is larger than a few tens or hundreds of Schwarzschild radii, the accretion will proceed via a convection-dominated accretion flow (CDAF) in which most of the matter escapes to infinity rather than falling onto the black hole. Models involving the mergers of black hole-white dwarf binaries and black hole-helium star binaries fall in this category. These models are unlikely to produce GRBs since very little mass reaches the black hole. If the accretion disk is smaller, then accretion will proceed via neutrino cooling in a neutrino-dominated accretion disk (NDAF) and most of the mass will reach the center. Models involving the mergers of double neutron star binaries and black hole-neutron star binaries fall in this category and are capable of producing bright GRBs. If the viscosity parameter α in the NDAF has a standard value of ~0.1, these mergers can explain short GRBs with durations under a second, but they are unlikely to produce long GRBs with durations of tens or hundred of seconds. If the accretion disk is fed by fallback of material after a supernova explosion, as in the collapsar model, then the timescale of the burst is determined by fallback, not accretion. Such a model can produce long GRBs. Fallback models again require that the accretion should proceed via an NDAF rather than a CDAF in order for a significant amount of mass to reach the black hole. This condition imposes an upper limit on the radius of injection of the gas.

The Association of Jet Production with Geometrically Thick Accretion Flows and Black Hole Rotation

A model is presented in which the strongest radio-emitting jet outflows are produced in black hole systems when the accretion is a geometrically thick (H/R ~ 1) inflow (e.g., an advection-dominated or a convection-dominated accretion flow) and if the black hole is rotating. For galactic black hole candidates, the model naturally accounts for the observed correlation of jet outflow with the black hole hard emission state and predicts an association of strong jets with rapid black hole rotation. When extended to the supermassive case, the model accounts for the highest radio galaxy and quasar jet powers and provides additional theoretical support for the spin paradigm, which asserts that radio-loud quasars are produced by Kerr holes and radio-quiet ones by Schwarzschild holes. In some cases, the angular momentum and energy outflow in the jet may be large enough to alter significantly the structure of the accretion flow from that predicted by current models.

Self‐similar Accretion Flows with Convection

We consider height-integrated equations of an advection-dominated accretion flow (ADAF), assuming that there is no mass outflow. We include convection through a mixing length formalism. We seek self-similar solutions in which the rotational velocity and sound speed scale as R^{-1/2}, where R is the radius, and consider two limiting prescriptions for the transport of angular momentum by convection. In one limit, the transport occurs down the angular velocity gradient, so convection moves angular momentum outward. In the other, the transport is down the specific angular momentum gradient, so convection moves angular momentum inward. We also consider general prescriptions which lie in between the two limits. When convection moves angular momentum outward, we recover the usual self-similar solution for ADAFs in which the mass density scales as rho ~ R^{-3/2}. When convection moves angular momentum inward, the result depends on the viscosity coefficient alpha. If alpha>alpha_{crit1} ~ 0.05, we once again find the standard ADAF solution. For alpha<alpha_{crit}, however, we find a non-accreting solution in which rho ~ R^{-1/2}. We refer to this as a solution or a convection-dominated accretion flow. Two-dimensional numerical simulations of ADAFs with values of alpha<0.03 have been reported by several authors. The simulated ADAFs exhibit convection. By virtue of their axisymmetry, convection in these simulations moves angular momentum inward, as we confirm by computing the Reynolds stress. The simulations give rho ~ R^{-1/2}, in good agreement with the convective envelope solution. The R^{-1/2} density profile is not a consequence of mass outflow.

Sagittarius A* Polarization: No Advection-dominated Accretion Flow, Low Accretion Rate, and Nonthermal Synchrotron Emission

The recent detection of polarized radiation from Sgr A* requires a nonthermal electron distribution for the emitting plasma. The Faraday rotation measure must be small, placing strong limits on the density and magnetic field strength. We show that these constraints rule out advection-dominated accretion flow models. We construct a simple two-component model that can reproduce both the radio-to-millimeter spectrum and the polarization. This model predicts that the polarization should rise to nearly 100% at shorter wavelengths. The first component, possibly a black hole-powered jet, is compact, low density, and self-absorbed near 1 mm with ordered magnetic field, relativistic Alfven speed, and a nonthermal electron distribution. The second component is poorly constrained, but may be a convection-dominated accretion flow with ~ 10-9 M☉ yr-1, in which feedback from accretion onto the black hole suppresses the accretion rate at large radii. The black hole shadow should be detectable with submillimeter VLBI.