Ken Ohsuga

Supercritical Accretion Flows around Black Holes: Two-dimensional, Radiation Pressure-dominated Disks with Photon Trapping

The quasi-steady structure of supercritical accretion flows around a black hole is studied based on two-dimensional radiation-hydrodynamic (2D-RHD) simulations. The supercritical flow is composed of two parts: the disk region and the outflow regions above and below the disk. Within the disk region the circular motion and the patchy density structure are observed, which is caused by Kelvin-Helmholtz instability and probably by convection. The mass accretion rate decreases inward, roughly in proportion to the radius, and the remaining part of the disk material leaves the disk to form the outflow because of the strong radiation pressure force. We confirm that photon trapping plays an important role within the disk. Thus, matter can fall onto the black hole at a rate exceeding the Eddington rate. The emission is highly anisotropic and moderately collimated so that the apparent luminosity can exceed the Eddington luminosity by a factor of a few in the face-on view. The mass accretion rate onto the black hole increases with the absorption opacity (metallicity) of the accreting matter. This implies that the black hole tends to grow faster in metal-rich regions, such as in starburst galaxies or star-forming regions.

GLOBAL STRUCTURE OF THREE DISTINCT ACCRETION FLOWS AND OUTFLOWS AROUND BLACK HOLES FROM TWO-DIMENSIONAL RADIATION-MAGNETOHYDRODYNAMIC SIMULATIONS

We present the detailed global structure of black hole accretion flows and outflows through newly performed two-dimensional radiation-magnetohydrodynamic simulations. By starting from a torus threaded with weak toroidal magnetic fields and by controlling the central density of the initial torus, ρ0, we can reproduce three distinct modes of accretion flow. In model A, which has the highest central density, an optically and geometrically thick supercritical accretion disk is created. The radiation force greatly exceeds the gravity above the disk surface, thereby driving a strong outflow (or jet). Because of mild beaming, the apparent (isotropic) photon luminosity is ~22L E (where L E is the Eddington luminosity) in the face-on view. Even higher apparent luminosity is feasible if we increase the flow density. In model B, which has moderate density, radiative cooling of the accretion flow is so efficient that a standard-type, cold, and geometrically thin disk is formed at radii greater than ~7 R S (where R S is the Schwarzschild radius), while the flow is radiatively inefficient otherwise. The magnetic-pressure-driven disk wind appears in this model. In model C, the density is too low for the flow to be radiatively efficient. The flow thus becomes radiatively inefficient accretion flow, which is geometrically thick and optically thin. The magnetic-pressure force, together with the gas-pressure force, drives outflows from the disk surface, and the flow releases its energy via jets rather than via radiation. Observational implications are briefly discussed.

Does the Slim-Disk Model Correctly Consider Photon-trapping Effects?

We investigate the photon-trapping effects in the supercritical black hole accretion flows by solving radiation transfer as well as the energy equations of radiation and gas. It is found that the slim-disk model generally overestimates the luminosity of the disk around the Eddington luminosity (LE) and is not accurate in describing the effective temperature profile since it neglects time delay between energy generation deeper inside the disk and energy release at the surface. The photon-trapping effects are especially appreciable even below L ~ LE, while they appear above ~3LE according to the slim disk. Through the photon-trapping effects, the luminosity is reduced and the effective temperature profile becomes flatter than r-3/4, as in the standard disk. In the case in which the viscous heating is effective only around the equatorial plane, the luminosity is kept around the Eddington luminosity even at a very large mass accretion rate, LE/c2. The effective temperature profile is almost flat, and the maximum temperature decreases in accordance with a rise in the mass accretion rate. Thus, the most luminous radius shifts to the outer region when /(LE/c2) 102. In the case in which the energy is dissipated equally at any height, the resultant luminosity is somewhat larger than in the former case, but the energy conversion still efficiently decreases with an increase of the mass accretion rate as well. The most luminous radius stays around the inner edge of the disk in the latter case. Hence, the effective temperature profile is sensitive to the vertical distribution of energy production rates, as is the spectral shape. Future observations of high L/LE objects will be able to test our model.

Global Radiation-Magnetohydrodynamic Simulations of Black-Hole Accretion Flow and Outflow: Unified Model of Three States

Black-hole accretion systems are known to possess several distinct modes (or spectral states), such as low/hard state and high/soft state. Since the dynamics of the corresponding flows is distinct, theoretical models were separately considered for each state. We here propose a unified model based on our new, global, two-dimensional radiation-magnetohydrodynamic simulations. By controlling a density normalization we could for the first time reproduce three distinct modes of accretion flow and outflow with one numerical code. When the density is large (model A), a geometrically thick, very luminous disk forms, in which photon trapping takes place. When the density is moderate (model B), the accreting gas can effectively be cooled by emitting radiation, thus generating a thin disk, i.e., a soft-state disk. When the density is too low for radiative cooling to be important (model C), a disk becomes hot, thick, and faint; i.e., a hard-state disk. The magnetic energy is amplified within the disk up to about twice, 30%, and 20% of the gas energy in models A, B, and C, respectively. Notably, the disk outflows with helical magnetic fields, which are driven either by radiation-pressure force or magnetic-pressure force, are ubiquitous in any accretion modes. Finally, our simulations are consistent with the phenomenological ˛-viscosity prescription; that is, the disk viscosity is proportional to the pressure.

RADIATION MAGNETOHYDRODYNAMICS SIMULATION OF PROTO-STELLAR COLLAPSE: TWO-COMPONENT MOLECULAR OUTFLOW

We perform a three-dimensional nested-grid radiation magnetohydrodynamics (RMHD) simulation with self-gravity to study the early phase of the low-mass star formation process from a rotating molecular cloud core to a first adiabatic core just before the second collapse begins. Radiation transfer is implemented with the flux-limited diffusion approximation, operator-splitting, and implicit time integrator. In the RMHD simulation, the outer region of the first core attains a higher entropy and its size is larger than that in the magnetohydrodynamics simulations with the barotropic approximation. Bipolar molecular outflow consisting of two components is driven by magnetic Lorentz force via different mechanisms, and shock heating by the outflow is observed. Using the RMHD simulation we can predict and interpret the observed properties of star-forming clouds, first cores, and outflows with millimeter/submillimeter radio interferometers, especially the Atacama Large Millimeter/submillimeter Array.

Why Is Supercritical Disk Accretion Feasible

Although the occurrence of steady supercritical disk accretion onto a black hole has been speculated about since the 1970s, it has not been accurately verified so far. For the first time, we previously demonstrated it through two-dimensional, long-term radiation-hydrodynamic simulations. To clarify why this accretion is possible, we quantitatively investigate the dynamics of a simulated supercritical accretion flow with a mass accretion rate of ~102LE/c2 (with LE and c being, respectively, the Eddington luminosity and the speed of light). We confirm two important mechanisms underlying supercritical disk accretion flow, as previously claimed, one of which is the radiation anisotropy arising from the anisotropic density distribution of very optically thick material. We qualitatively show that despite a very large radiation energy density, E0 102LE/4πr2c (with r being the distance from the black hole), the radiative flux F0 ~ cE0/τ could be small due to a large optical depth, typically τ ~ 103, in the disk. Another mechanism is photon trapping, quantified by vE0, where v is the flow velocity. With a large |v| and E0, this term significantly reduces the radiative flux and even makes it negative (inward) at r < 70rS, where rS is the Schwarzschild radius. Due to the combination of these effects, the radiative force in the direction along the disk plane is largely attenuated so that the gravitational force barely exceeds the sum of the radiative force and the centrifugal force. As a result, matter can slowly fall onto the central black hole mainly along the disk plane with velocity much less than the free-fall velocity, even though the disk luminosity exceeds the Eddington luminosity. Along the disk rotation axis, in contrast, the strong radiative force drives strong gas outflows.

Spectra from a Magnetic Reconnection-heated Corona in Active Galactic Nuclei

We investigate a corona coupled with an underlying disk through the magnetic field and radiation field and present emergent spectra. As a result of buoyancy, the magnetic flux loop emerges from the disk and reconnects with other loops in the corona, thereby releasing the magnetic energy to heat the coronal plasma. The energy is then radiated away through Compton scattering. By studying the energy balance in the corona, transition layer, and disk, we determine the fraction (f) of accretion energy dissipated in the corona for a given black hole mass and accretion rate, and then we determine the coronal and disk variables. This allows us to calculate emergent spectra through Monte Carlo simulations. The spectra are then determined as functions of black hole mass and accretion rate. We find two types of solutions corresponding to hard spectrum and soft spectrum. In the hard-spectrum solution, the accretion energy is dominantly dissipated in the corona, supporting a strong corona above a cool disk. The hard X-ray spectral indices are the same for different accretion rates, i.e., ? ~ 1.1 (F? ?-?). In the soft-spectrum solution, the accretion energy is mainly dissipated in the disk. The coronal temperature and density are quite low. Consequently, the spectra are dominated by the disk radiation peaked in UV and soft X-rays. For low-luminosity systems (L 0.2LEdd) there exists only the solution of hard spectra, while for high-luminosity systems (L 0.8LEdd) there exist solutions of both hard and soft spectra. For moderate-luminosity systems (0.2LEdd L 0.8LEdd), besides the hard spectra, moderately soft spectra composed of an inner soft-spectrum solution and an outer hard-spectrum solution may occur, the softness of which increases with increasing luminosity. The hard spectra are close to the observed spectra in Seyfert galaxies and radio-quiet QSOs. The composite spectra may account for the diversity of broadband spectra observed in narrow-line Seyfert 1 galaxies.

Feedback from Supercritical Disk Accretion Flows: Two-dimensional Radiation-Hydrodynamic Simulations of Stable and Unstable Disks with Radiatively Driven Outflows

The supercritical disk accretion flow with radiatively driven outflows is studied based on two-dimensional radiation-hydrodynamic simulations for a wide range of the mass input rate, input, which is the mass supplied from the outer region to the disk per unit time. The α-prescription is adopted for the viscosity. We employ α = 0.5, as well as α = 0.1, for input ≥ 3 × 102LE/c2 and only α = 0.5 for input ≤ 102LE/c2, where LE is the Eddington luminosity and c is the speed of light. The quasi-steady disk and radiatively driven outflows form in the case in which the mass input rate highly exceeds the critical rate, input > 3 × 102LE/c2. Then, the disk luminosity, as well as the kinetic energy output rate by the outflow, exceeds the Eddington luminosity. The moderately supercritical disk, input ~ 10-102LE/c2, exhibits limit-cycle oscillations. The disk luminosity goes up and down across the Eddington luminosity, and the radiatively driven outflows intermittently appear. The time-averaged mass, momentum, and kinetic energy output rates by the outflow, as well as the disk luminosity, increase with an increase of the mass input rate, ∝- for α = 0.5 and ∝- for α = 0.1. Our numerical simulations show that the radiatively driven outflow model for the correlation between black hole mass and bulge velocity dispersion proposed by Silk & Rees and King is successful if inputc2/LE ~ a few 10 (α = 0.5) or a few (α = 0.1).

Two-dimensional Radiation-Hydrodynamic Model for Limit-Cycle Oscillations of Luminous Accretion Disks

We investigate the time evolution of luminous accretion disks around black holes by conducting two-dimensional radiation-hydrodynamic simulations. We adopt the α prescription for the viscosity. The radial-azimuthal component of the viscous stress tensor is assumed to be proportional to the total pressure in the optically thick region and the gas pressure in the optically thin regime. The viscosity parameter, α, is taken to be 0.1. We find the limit-cycle variation in luminosity between high and low states. When we set the mass input rate from the outer disk boundary to be 100LE/c2, the luminosity suddenly rises from 0.3LE to 2LE, where LE is the Eddington luminosity. It decays after retaining the high value for about 40 s. Our numerical results can explain the variability amplitude and duration of the recurrent outbursts observed in microquasar GRS 1915+105. We show that multidimensional effects play an important role in the high-luminosity state. In this state, the outflow is driven by the strong radiation force, and some part of the radiation energy dissipated inside the disk is swallowed by the black hole due to the photon-trapping effects. This trapped luminosity is comparable to the disk luminosity. We also calculate two more cases: one with a much larger accretion rate than the critical value for the instability and the other with the viscous stress tensor being proportional to the gas pressure only, even when the radiation pressure is dominant. We find no quasi-periodic light variations in these cases. This confirms that the limit-cycle behavior found in the simulations is caused by the disk instability.

Clumpy Outflows from Supercritical Accretion Flow

Significant fraction of matter in supercritical (or super-Eddington) accretion flow is blown away by radiation force, thus forming outflows, however, the properties of such radiation-driven outflows have been poorly understood. We have performed global two-dimensional radiaion-magnetohydrodynamic simulations of supercritical accretion flow onto a black hole with 10 or 10^8 solar masses in a large simulation box of 514 r_S x 514 r_S (with r_S being the Schwarzschild radius). We confirm that uncollimated outflows with velocities of 10 percents of the speed of light emerge from the innermost part of the accretion flow over wide angles of 10 - 50 degree from the disk rotation axis. Importantly, the outflows exhibit clumpy structure above heights of ~ 250 r_S. The typical size of the clumps is ~ 10 r_S, which corresponds to one optical depth, and their shapes are slightly elongated along the outflow direction. Since clumps start to form in the layer above which (upward) radiation force overcomes (downward) gravity force, Rayleigh-Taylor instability seems to be of primary cause. In addition, a radiation hydrodynamic instability, which arises when radiation funnels through radiation-pressure supported atmosphere, may also help forming clumps of one optical depth. Magnetic photon bubble instability seems not to be essential, since similar clumpy outflow structure is obtained in non-magnetic radiation-hydrodynamic simulations. Since the spatial covering factor of the clumps is estimated to be ~ 0.3 and since they are marginally optically thick, they will explain at least some of rapid light variations of active galactic nuclei. We further discuss a possibility of producing broad-line clouds by the clumpy outflow.