Thick Accretion Flows Research Articles

THE GALACTIC CENTER WEATHER FORECAST

In accretion-based models for Sgr A* the X-ray, infrared, and millimeter emission arise in a hot, geometrically thick accretion flow close to the black hole. The spectrum and size of the source depend on the black hole mass accretion rate $\dot{M}$. Since Gillessen et al. have recently discovered a cloud moving toward Sgr A* that will arrive in summer 2013, $\dot{M}$ may increase from its present value $\dot{M}_0$. We therefore reconsider the "best-bet" accretion model of Moscibrodzka et al., which is based on a general relativistic MHD flow model and fully relativistic radiative transfer, for a range of $\dot{M}$. We find that for modest increases in $\dot{M}$ the characteristic ring of emission due to the photon orbit becomes brighter, more extended, and easier to detect by the planned Event Horizon Telescope submm VLBI experiment. If $\dot{M} \gtrsim 8 \dot{M}_0$ this "silhouette of the black hole will be hidden beneath the synchrotron photosphere at 230 GHz, and for $\dot{M} \gtrsim 16 \dot{M}_0$ the silhouette is hidden at 345 GHz. We also find that for $\dot{M} > 2 \dot{M}_0$ the near-horizon accretion flow becomes a persistent X-ray and mid-infrared source, and in the near-infrared Sgr A* will acquire a persistent component that is brighter than currently observed flares.

OBSERVATIONAL SIGNATURES OF TILTED BLACK HOLE ACCRETION DISKS FROM SIMULATIONS

Geometrically thick accretion flows may be present in black hole X-ray binaries observed in the low/hard state and in low-luminosity active galactic nuclei. Unlike in geometrically thin disks, the angular momentum axis in these sources is not expected to align with the black hole spin axis. We compute images from three-dimensional general relativistic magnetohydrodynamic simulations of misaligned (tilted) accretion flows using relativistic radiative transfer, and compare the estimated locations of the radiation edge with expectations from their aligned (untilted) counterparts. The radiation edge in the tilted simulations is independent of black hole spin for a tilt of 15 degrees, in stark contrast to the results for untilted simulations, which agree with the monotonic dependence on spin expected from thin accretion disk theory. Synthetic emission line profiles from the tilted simulations depend strongly on the observer's azimuth, and exhibit unique features such as broad "blue wings." Coupled with precession, the azimuthal variation could generate time fluctuations in observed emission lines, which would be a clear "signature" of a tilted accretion flow. Finally, we evaluate the possibility that the observed low- and high-frequency quasi-periodic oscillations (QPOs) from black hole binaries could be produced by misaligned accretion flows. Although low-frequency QPOs from precessing, tilted disks remains a viable option, we find little evidence for significant power in our light curves in the frequency range of high-frequency QPOs.

A Novel Jet Model: Magnetically Collimated, Radiation-Pressure Driven Jet

Abstract Relativistic jets from compact objects are ubiquitous phenomena in the Unvierse, but their driving mechanism has been an enigmatic issue for several decades. Two basic models have been extensively discussed: magnetohydrodynamic (MHD) jets and radiation-hydrodynamic (RHD) jets. Currently, the former is more widely accepted, since the magnetic field is expected to provide both acceleration and collimation mechanisms, whereas the radiation field cannot collimate the outflow. Here, we propose a new type of jets, radiation-magnetohydrodynamic (RMHD) jets, based on our global RMHD simulation of luminous accretion flows onto a black hole shining above the Eddington luminosity. The RMHD jet can be accelerated up to relativistic speed by the radiation-pressure force and collimated by the Lorentz force of a magnetic tower structure inflated by toroidal magnetic field lines accumulated around the black hole, though the radiation energy greatly dominates over the magnetic energy. This magnetic tower is collimated by a geometrically thick accretion flow supported by a radiation-pressure force. This type of jet may explain relativistic jets from Galactic microquasars, appearing at high luminosity.

An analytic relation for the thickness of accretion flows

We take the vertical distribution of the radial and azimuthal velocity into account in spherical coordinates, and find that the analytic relation c_{s0}/(v_K \Theta) = [(\gamma -1)/(2\gamma)]^{1/2} is valid for both geometrically thin and thick accretion flows, where c_{s0} is the sound speed on the equatorial plane, v_K is the Keplerian velocity, \Theta is the half-opening angle of the flow, and \gamma is the adiabatic index.

Faraday Rotation in Global Accretion Disk Simulations: Implications for Sgr A*

These Faraday rotation calculations of hot, thick accretion flows are motivated by the measured steady rotation measure (RM) of $\approx -6 \times 10^5$ rad m$^{-2}$ from Sgr A*. In our numerical simulations, the quasi-steady state structure of the accretion flow, and the RM it produces, depends on the initial magnetic field. In spite of this dependence, we can draw several robust conclusions about Faraday rotation produced by geometrically thick accretion disks: i) the time averaged RM does not depend that sensitively on the viewing angle, but the stability of the RM can. Equatorial viewing angles show significant variability in RM (including sign reversals), while polar viewing angles are relatively stable if there is a large scale magnetic field threading the disk at large radii. ii) Most of the RM is produced at small radii for polar viewing angles while all radii contribute significantly near the midplane of the disk. Our simulations confirm previous analytic arguments that the accretion rate onto Sgr A* must satisfy $\dot M_{\rm in} \ll \dot M_{\rm Bondi} \sim 10^{-5} \mpy$ in order to not over-produce the measured RM. We argue that the steady RM $\approx -6 \times 10^5$ rad m$^{-2}$ from Sgr A* has two plausible explanations: 1) it is produced at $\sim 100$ Schwarzschild radii, requires $\dot{M}_{\rm in} \approx 3 \times 10^{-8} M_\odot$ yr$^{-1}$, and we view the flow at an angle of $\sim 30^\circ$ relative to the rotation axis of the disk; in our simulations, the variation in RM across a finite-sized source is sufficient to depolarize the emission below $\approx$ 100 GHz, consistent with observations. 2) Alternatively, the RM may be produced in the relatively spherical inflowing plasma near the circularization radius at $\sim 10^3-10^4$ Schwarzschild radii.

A Note on the Slim Accretion Disk Model

We show that when the gravitational force is correctly calculated in dealing with the vertical hydrostatic equilibrium of black hole accretion disks, the relationship that is valid for geometrically thin disks, i.e., $c_s/\Omega_K H =$ constant, where $c_s$ is the sound speed, $\Omega_K$ is the Keplerian angular velocity, and $H$ is the half-thickness of the disk, does not hold for slim disks. More importantly, by adopting the correct vertical gravitational force in studies of thermal equilibrium solutions, we find that there exists a maximally possible accretion rate for each radius in the outer region of optically thick accretion flows, so that only the inner region of these flows can possibly take the form of slim disks, and strong outflows from the outer region are required to reduce the accretion rate in order for slim disks to be realized.

New Analytical Formulae for Optically Thin Accretion Flows

Abstract In a previous paper, we described new analytic formulae for optically thick supercritical accretion flows (Watarai 2006, hereafter paper 1). Here, we present analytic formulae for optically thin one-temperature accretion flows including the advection-dominated regime, using the “semi-iterative” method, described in paper 1. Our analytic formulae have two real solutions. The first solution corresponds to advection-dominated accretion flow (ADAF), and the second solution corresponds to radiation-dominated accretion flow, described by Shapiro, Lightman, and Eardley (the so-called SLE model). Both solutions are given by a cubic equation for the advection parameter, $f$, which is the ratio of the advection cooling rate, $Q_{\rm adv}$, to the viscous heating rate, $Q_{\rm vis}$, i.e., $f=Q_{\rm adv}/Q_{\rm vis}$. Most previous studies assumed that $f$ is constant ($f \sim 1$ for the ADAF). However, it is clear that $f$ should be a function of the physical parameters of the radiative-cooling dominated regime. We found that the ratio $f$ can be written as a function of the radius, mass-accretion rate, and viscous parameter, $\alpha$. Using this formula, we can estimate the transition radius from the inner optically thin ADAF to the outer optically thick standard disk, which can be measured using observations of the quiescent state in black hole X-ray binaries.

Three routes to jet collimation by the Balbus—Hawley magnetorotational instability

Three completely different lines of work have recently led to the conclusion that the magnetorotational instability (MRI) may create a hoop-stress that collimates jets. One argument is based upon consideration that magnetohydrodynamic turbulence, in general, and turbulence driven by the MRI, in particular, is more nearly viscoelastic than it is viscous. Another argument is based upon the dispersion relation for the MRI in the context of 1D simulations of core collapse. Yet a third argument rests in the results of direct numerical magnetohydrodynamic simulations of collapsars and thick accretion flows. I elaborate on my previous work regarding the first argument above and I briefly discuss how these three sets of results are all related. I also discuss the different roles played by the magnetic tension and the magnetic pressure within the context of this work. I point out that this leads to consideration of the normal stress difference between the hoop stress and the radial stress, in preference to a focus on just the hoop stress itself. Additionally, I argue that simulations of thick accretion flows and collapsars are not self-consistent if they include a phenomenological model for an MRI-induced viscous stress but disregard these other MRI-induced stress components. I comment briefly on the RHESSI observation of polarization in the gamma-ray burst GRB0212206. I argue that this polarization is consistent with a tangled field, and does not require a large-scale organized field. Finally I suggest that the role of magnetic fields in creating jets, as described here, should be understood not to work within the confines of magnetocentrifugal models of jets, but rather as an alternative to them.

Radio/X-Ray Luminosity Relation for X-Ray–Bright Galactic Nuclei: Implications for Weighing Supermassive Black Holes

Optically thin and geometrically thick accretion flows are known to be responsible for the observed radio/X-ray luminosity relation of X-ray–bright galactic nuclei. It has also been suggested that supermassive black hole masses can be estimated from measurements of the core radio luminosity and the X-ray luminosity by using the advection-dominated accretion flow (ADAF) model. In this study we increase the amount of data available by compiling the radio/X-ray fluxes and the mass in published literatures, and compare the observed ratio of the luminosities with predictions from various models of optically thin accretion flows. Semianalytically derived relations of the luminosities are presented in cases of the standard ADAF model and modified ADAF models, in which a truncation of inner parts of the flows and winds causing a reduction of the infalling matter are included. We show that the observed relation can indeed be used to estimate the supermassive black hole mass, provided that properties of such accretion flows are known. Having investigated sensitivities of the method on modifications of the "standard" ADAF model, we find that a general trend of model predictions from the "standard" ADAF, the truncated ADAF, and the "windy" ADAF are somewhat indistinguishable. We also find, however, that the extreme case of the windy model is inconsistent with currently available observational data unless microphysics parameters are to be substantially changed. High-resolution radio observations, however, are required to avoid the contamination of nondisk components such as a jet component, which otherwise results in an overestimation of SMBH mass.

Super-Eddington Black-Hole Models for SS 433

Abstract We examine highly super-Eddington black-hole models for SS 433, based on two-dimensional hydrodynamical calculations coupled with radiation transport. The super-Eddington accretion flow with a small viscosity parameter, $ \alpha = 10^{-3}$, results in a geometrically–and optically-thick disk with a large opening angle of $ \sim 60^{\circ}$ to the equatorial plane and a very rarefied, hot, and optically-thin high-velocity jets region around the disk. The thick accretion flow consists of two different zones: an inner advection-dominated zone and an outer convection-dominated zone. The high-velocity region around the disk is divided into two characteristic regions, a very rarefied funnel region along the rotational axis and a moderately rarefied high-velocity region outside of the disk. The temperatures of $ \sim 10^7 \,\mathrm{K}$ and the densities of $ \sim 10^{-7} \,\mathrm{g} \,\mathrm{cm}^{-3}$ in the upper disk vary sharply to $ \sim 10^8 \,\mathrm{K}$ and $ 10^{-8}\,\mathrm{g} \,\mathrm{cm}^{-3}$, respectively, across the disk boundary between the disk and the high-velocity region. The X-ray emission of iron lines would be generated only in a confined region between the funnel wall and the photospheric disk boundary, where flows are accelerated to relativistic velocities of $ \sim 0.2 \,c$ due to the dominant radiation-pressure force. The results are discussed regarding the collimation angle of the jets, the large mass-outflow rate observed in SS 433, and the ADAFs and the CDAFs models.

ASCA Observation of the Superluminal Jet Source GRO J1655–40 in the 1997 Outburst

Abstract We report on the results of an ASCA observation of the Galactic jet source GRO J1655–40 performed from 1997 February 25 to February 28 covering a full orbital period (2.62 d). The averaged 2–10 keV flux was about 1.1 Crab. An absorption line feature centered at 6.8 keV was detected both in the GIS and SIS spectra. We interpret this as a blend of two resonance-absorption $\mathrm{K}\alpha$ lines from H-like and He-like iron ions. We can consistently explain both the ASCA spectra and the simultaneous RXTE/PCA spectrum by a combination of K-absorption lines and K-absorption edges of iron ions. The fact that the absorption line is stably present over the whole orbital phase implies that the distribution of the highly ionized plasma is not affected by the companion star, which is consistent with its presence around the black hole. A curve of growth analysis shows that the plasma contains velocity dispersion along the line-of-sight larger than $300~\mathrm{km}~\mathrm{s}^{-1}$ attributed to bulk motions. It is probably a part of a geometrically thick accretion flow in turbulent motions with velocities of $500$-$1600~\mathrm{km}~\mathrm{s}^{-1}$ at an estimated radius of $\sim10^{10}~\mathrm{cm}$.

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.

Adiabatic Shocks in Accretion Flows

Accretion flows onto compact astronomical sources are likely to be supersonic, and shock waves may therefore be common in such flows. Plasma passing through a shock front will be compressed and heated according to the jump conditions across the shock discontinuity. Shocks in accretion flows may therefore have important consequences for the flow structure and emission characteristics. The equations governing adiabatic (nonradiative) shocks in relativistic plasmas are presented. Relativistically correct equations of state are used that include the effects of radiation pressure and energy density, and pair equilibria are calculated for the postshock flow. Postshock states are determined for accretion flows with typical accretion-driven astronomical sources, and possible dynamics of the postshock flow are suggested. In particular, we find that cool, optically thick accretion flows undergoing shocks may become radiation or pair dominated and that the postshock plasma will likely become optically thin before returning to steady state conditions.

Numerical Simulations of Standing Shocks in Accretion Flows around Black Holes: A Comparative Study

We compare the results of numerical simulations of thin and quasi-spherical (thick) accretion flows with existing analytical solutions. We use a Lagrangian code based on the smooth particle hydrodynamics (SPH) scheme and an Eulerian finite difference code based on the total variation diminishing (TVD) scheme. In one-dimensional thin flows, the results of the simulations, with or without shocks, agree very well with each other and with analytical solutions. In two-dimensional thick flows, the general features, namely the locations and strengths of centrifugal and turbulent pressure supported shocks, centrifugal barriers, and the funnel walls that are expected from analytical models, agree very well, though the details vary. Generally speaking, the locations of the shocks may be better obtained by SPH since the angular momentum is strictly preserved in SPH, but the shocks themselves are better resolved by TVD. The agreement of these code test results with analytical solutions provides us with confidence to apply these codes to more complex problems, which we will discuss elsewhere.