Accretion Disk Theory Research Articles

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.

CONSTRAINING THE SIZE OF THE DARK REGION AROUND THE M87 BLACK HOLE BY SPACE-VLBI OBSERVATIONS

In order to examine if the next-generation space very long baseline interferometer (VLBI), such as VSOP-2 (VLBI Space Observatory Programme-2), will make it possible to obtain direct images of the accretion flow around the M87 black hole, we calculate the expected observed images by relativistic ray-tracing simulations under considerations of possible observational errors. We consider various cases of electron temperature profiles, as well various values for the distance, mass, and spin of the M87 black hole. We find it feasible to detect an asymmetric intensity profile around the black hole caused by rapid disk rotation, as long as the electron temperature does not rise steeply toward the black hole, as was predicted by the accretion disk theory and three-dimensional magnetohydrodynamic simulations. Further, we can detect a deficit in the observed intensity around the black hole when the apparent size of the gravitational radius is larger than ≳1.5 μas. In the cases that the inner edge of the disk is located at the radius of the innermost stable circular orbit (ISCO), moreover, even the black hole spin will be measured. We also estimate the required signal-to-noise ratio for achieving the scientific goals mentioned above, finding that it should be at least 10 at 22 GHz. To conclude, direct mapping observations by the next-generation space VLBI will provide us a unique opportunity to provide the best evidence for the presence of a black hole and to test the accretion disk theory.

ANGULAR MOMENTUM TRANSPORT IN PROTOPLANETARY AND BLACK HOLE ACCRETION DISKS: THE ROLE OF PARASITIC MODES IN THE SATURATION OF MHD TURBULENCE

The magnetorotational instability (MRI) is considered a key process for driving efficient angular momentum transport in astrophysical disks. Understanding its non-linear saturation constitutes a fundamental problem in modern accretion disk theory. The large dynamical range in physical conditions in accretion disks makes it challenging to address this problem only with numerical simulations. We analyze the concept that (secondary) parasitic instabilities are responsible for the saturation of the MRI. Our approach enables us to explore dissipative regimes that are relevant to astrophysical and laboratory conditions that lie beyond the regime accessible to current numerical simulations. We calculate the spectrum and physical structure of parasitic modes that feed off the fastest, exact (primary) MRI mode when its amplitude is such that the fastest parasitic mode grows as fast as the MRI. We argue that this "saturation" amplitude provides an estimate of the magnetic field that can be generated by the MRI before the secondary instabilities suppress its growth significantly. Recent works suggest that the saturation amplitude of the MRI depends mainly on the magnetic Prandtl number. Our results suggest that, as long as viscous effects do not dominate the fluid dynamics, the saturation level of the MRI depends only on the Elsasser number $\Lambda_\eta$. We calculate the ratio between the stress and the magnetic energy density, $\alpha_{\rm sat}\beta_{\rm sat}$, associated with the primary MRI mode. We find that for $\Lambda_\eta >1$ Kelvin-Helmholtz modes are responsible for saturation and $\alpha_{\rm sat}\beta_{\rm sat} = 0.4$, while for $\Lambda_\eta < 1$ tearing modes prevail and $\alpha_{\rm sat}\beta_{\rm sat} \simeq 0.5 \, \Lambda_\eta$. Several features of MRI simulations in accretion disks surrounding young stars and compact objects can be interpreted in terms of our findings.

Comparisons and connections between mean field dynamo theory and accretion disc theory

AbstractThe origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi‐analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha‐viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha‐accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Accretion discs in blazars

The characteristic properties of blazars (rapid variability, strong polarization and high brightness) are widely attributed to a powerful relativistic jet oriented close to our line of sight. Despite the spectral energy distributions being strongly jet-dominated, a ‘big blue bump’ has been recently detected in the sources known as flat spectrum radio quasars (FSRQs). These new data provide a unique opportunity to observationally test coupled jet–disc accretion models in these extreme sources. In particular, as energy and angular momentum can be extracted by a jet magnetically coupled to the accretion disc, the thermal disc emission spectrum may be modified from that predicted by the standard model for disc accretion. We compare the theoretically predicted jet-modified accretion disc spectra against the new observations of the ‘big blue bump’ in FSRQs. We find mass accretion rates that are higher, typically by a factor of 2, than predicted by standard accretion disc theory. Furthermore, our results predict that the high-redshift blazars PKS 0836+710, PKS 2149−307, B2 0743+25 and PKS 0537−286 may be predominantly powered by a low- or moderate-spin (a≲ 0.6) black hole with high-mass accretion rates ⁠, while 3C 273 harbours a rapidly spinning black hole (a= 0.97) with ⁠. We also find that the black hole masses in these high-redshift sources must be ≳5 × 109 M⊙.

Monitoring campaign of 1RXS J171824.2–402934, the low-mass X-ray binary with the lowest mass accretion rate

An X-ray monitoring campaign with Chandra and Swift confirms that 1RXS J171824.2–402934 is accreting at the lowest rate among the known persistently accreting low-mass X-ray binaries. A thermonuclear X-ray burst was detected with the all-sky monitor on RXTE. This is only the second such burst seen in 1RXS J171824.2–402934 in more than 20 Ms of observations done over 19 years. The low burst recurrence rate is in line with the low accretion rate. The persistent nature and low accretion rate can be reconciled within accretion disk theory if the binary system is ultracompact. An unprecedentedly short orbital period of less than <i>≈<i/>7 min would be implied. An ultracompact nature, together with the properties of the type I X-ray burst, suggests, in turn, that helium-rich material is accreted. Optical follow-up of the Chandra error region does not reveal an unambiguous counterpart.

Magnetic fields in Planetary Nebulae: paradigms and related MHD frontiers

AbstractMany, if not all, post AGB stellar systems swiftly transition from a spherical to a powerful aspherical pre-planetary nebula (pPNE) outflow phase before waning into a PNe. The pPNe outflows require engine rotational energy and a mechanism to extract this energy into collimated outflows. Just radiation and rotation are insufficient but a symbiosis between rotation, differential rotation and large scale magnetic fields remains promising. Present observational evidence for magnetic fields in evolved stars is suggestive of dynamically important magnetic fields, but both theory and observation are rife with research opportunity. I discuss how magnetohydrodynamic outflows might arise in pPNe and PNe and distinguish different between approaches that address shaping vs. those that address both launch and shaping. Scenarios involving dynamos in single stars, binary driven dynamos, or accretion engines cannot be ruled out. One appealing paradigm involves accretion onto the primary post-AGB white dwarf core from a low mass companion whose decaying accretion supply rate owers first the pPNe and then the lower luminosity PNe. Determining observational signatures of different MHD engines is a work in progress. Accretion disk theory and large scale dynamos pose many of their own fundamental challenges, some of which I discuss in a broader context.

Foundations of high-energy astrophysics

Written by one of today's most highly respected astrophysicists, Foundations of High-Energy Astrophysics is an introduction to the mathematical and physical techniques used in the study of high-energy astrophysics. Here, Mario Vietri approaches the basics of high-energy astrophysics with an emphasis on underlying physical processes as opposed to a more mathematical approach. Alongside more traditional topics, Vietri presents new subjects increasingly considered crucial to understanding high-energy astrophysical sources, including the electrodynamics of cosmic sources, new developments in the theory of standard accretion disks, and the physics of coronae, thick disks, and accretion onto magnetized objects.The most thorough and engaging survey of high-energy astrophysics available today, Foundations of High-Energy Astrophysics introduces the main physical processes relevant to the field in a rigorous yet accessible way, while paying careful attention to observational issues. Vietri's book will quickly become a classic text for students and active researchers in astronomy and astrophysics. Those in adjoining fields will also find it a valuable addition to their personal libraries.

Identifying deficiencies of standard accretion disc theory: lessons from a mean-field approach

Turbulent viscosity is frequently used in accretion disk theory to replace the microphysical viscosity in order to accomodate the observational need for in- stabilities in disks that lead to enhanced transport. However, simply replacing the microphysical transport coefficient by a single turbulent transport coeffi- cient hides the fact that the procedure should formally arise as part of a closure in which the hydrodynamic or magnetohydrodynamic equations are averaged, and correlations of turbulent fluctuations are replaced by transport coefficients. Here we show how a mean field approach leads quite naturally two transport coefficients, not one, that govern mass and angular momentum transport. In particular, we highlight that the conventional approach suffers from a seemingly inconsistent neglect of turbulent diffusion in the surface density equation. We constrain these new transport coefficients for specific cases of inward, outward, and zero net mass transport. In addition, we find that one of the new transport terms can lead to oscillations in the mean surface density which then requires a constant or small inverse Rossby number for disks to maintain a monotonic power-law surface density.

Saturation of the magnetorotational instability at large Elsasser number

AbstractThe magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still but not negligible. The regime explored retains the condition that (viscous and ohmic) dissipative forces do not play a role in the leading order linear instability mechanism. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Hydrodynamical activity in thin accretion disks

An asymptotic treatment of thin accretion disks, introduced by Kluźniak and Kita [Kluźniak, W., Kita, D., 2000. Three-dimensional structure of an alpha accretion disk. Available from: <arXiv:astro-ph/0006266v1> (KK)] for a steady-state disk flow, is extended to a time-dependent problem. Transient growth of axisymmetric disturbances is analytically shown to occur on the global disk scale. The implications of this result on the theory of hydrodynamical thin accretion disks, as well as future prospects, are discussed.

Jet-enhanced accretion growth of supermassive black holes

We investigate the effect of a disc-driven jet on the accretion growth of cosmological supermassive black holes (SMBHs). The presence of a jet enhances the mass growth rate because for a given luminosity, the mass accretion rate, is higher (or equivalently, the radiative efficiency e_r is lower for a fixed mass accretion rate) than that predicted by standard accretion disc theory. As jets carry away very little of the accreting matter, a larger proportion of the rest mass can reach the black hole during episodes of jet activity. We show quantitatively that the conditions required to grow a rapidly spinning black hole to a mass ~ 10^9 solar masses by redshift z ~ 6, whilst satisfying the observational constraint e_r > 0.1, are considerably less restrictive for jet-enhanced disc accretion than for standard disc accretion, which requires implausibly high super-Eddington accretion rates. Furthermore, jet-enhanced accretion growth offers a viable explanation for the observed correlation between black hole mass and radio-loudness of quasars.

TOWARDS A NEW STANDARD THEORY FOR ASTROPHYSICAL DISK ACCRETION

We briefly review recent developments in black hole accretion disk theory, placing new emphasis on 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 vertical transport of angular momentum by large-scale MHD torques is important and may even dominate radial transport by small-scale MHD turbulence. 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 and this affects the disk emission spectrum. We present a simple model demonstrating that energetic, magnetically-driven outflows give rise to a disk spectrum that is dimmer and redder than a standard accretion disk accreting at the same rate. We briefly discuss the implications of this key result for accreting black holes in different astrophysical systems.

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.

Accretion discs with strong toroidal magnetic fields

Simulations and analytic arguments suggest that the turbulence driven by magnetorotational instability (MRI) in accretion discs can amplify the toroidal (azimuthal) component of the magnetic field to a point at which magnetic pressure exceeds the combined gas + radiation pressure in the disc. Arguing from the recent analysis by Pessah & Psaltis, and other MRI results in the literature, we conjecture that the limiting field strength for a thin disc is such that the Alfvén speed roughly equals the geometric mean of the Keplerian speed and the speed of sound in gas. We examine the properties of such magnetically dominated discs, and show that they resolve a number of outstanding problems in accretion disc theory. The discs would be thicker than standard (Shakura–Sunyaev) discs at the same radius and accretion rate, and would tend to have higher colour temperatures. If they transport angular momentum according to an α prescription, they would be stable against the thermal and viscous instabilities that are found in standard disc models. In discs fuelling active galactic nuclei, magnetic pressure support could also alleviate the restriction on accretion rate imposed by disc self-gravity.

A Stellar-Mass Black Hole in the Ultraluminous X-Ray Source M82 X-1?

We have analyzed the archival XMM-Newton data of the archetypal Ultra-Luminous X-ray Source (ULX) M82 X-1 with an LO5 ksec exposure when the source was in the steady state. Thanks to the high photon statistics from the large effective area and long exposure, we were able to discriminate different X-ray continuum spectral models. Neither the standard accretion disk model (where the radial dependency of the disk effective temperature is T(r) proportional to r(sup -3/4)) nor a power-law model gives a satisfactory fit. In fact, observed curvature of the M82 X-1 spectrum was just between those of the two models. When the exponent of the radial dependence (p in T(r) proportional to r(sup -P)) of the disk temperature is allowed to be free, we obtained p = 0.61 (sup +0.03)(sub -0.02). Such a reduction of p from the standard value 3/4 under extremely high mass accretion rates is predicted from the accretion disk theory as a consequence of the radial energy advection. Thus, the accretion disk in M82 X-1 is considered to be in the Slim disk state, where an optically thick Advection Dominant Accretion Flow (ADAF) is taking place. We have applied a theoretical slim disk spectral model to M82 X-1, and estimated the black hole mass approximately equal to 19 - 32 solar mass. We conclude that M82 X-1 is a stellar black hole which has been produced through evolution of an extremely massive star, shining at a several times the super-Eddington luminosity.

Testing Accretion Disk Theory in Black Hole X‐Ray Binaries

We present results from spectral modeling of three black hole X-ray binaries: LMC X-3, GRO J1655-40, and XTE J1550-564. Using a sample of disk dominated observations, we fit the data with a range of spectral models that includes a simple multitemperature blackbody (DISKBB), a relativistic accretion disk model based on color-corrected blackbodies (KERRBB), and a relativistic model based on non-LTE atmosphere models within an alpha prescription (BHSPEC). BHSPEC provides the best fit for a BeppoSAX observation of LMC X-3, which has the broadest energy coverage of our sample. It also provides the best fit for multiple epochs of Rossi X-ray Timing Explorer (RXTE) data in this source, except at the very highest luminosity (L/L_{Edd} >~ 0.7), where additional physics must be coming into play. BHSPEC is also the best-fit model for multi-epoch RXTE observations of GRO J1655-40 and XTE J1550-564, although the best-fit inclination of the inner disk differs from the binary inclination. All our fits prefer alpha=0.01 to alpha=0.1, in apparent disagreement with the large stresses inferred from the rapid rise times observed in outbursts of these two sources. In all three sources our fits imply moderate black hole spins (a/M ~ 0.1 - 0.8), but this is sensitive to the reliability of independent measurements of these system parameters and to the physical assumptions which underly our spectral models.

Color variations of gravitationally lensed quasars as a tool for accretion disk size estimation

AbstractSince the amplitude of microlensing variability depends on a source size the monitoring of gravitationally lensed quasars can produce the valuable information about the accretion disk size. Comparison of standard deviations in two wavebands yields useful constraints from quite moderate number of multicolor observations.Existing optical VRI monitoring data for the quadruple gravitationally lensed quasar Q2237+ 0305 allow to obtain the source size ratio in two bands, V and R or V and I, as a function of size in the V band. Agreement with the standard accretion disk theory which predicts the dependency of a source size on wavelength ∼ λ4/3 can be achieved only if the quasar size in V band is comparable with the Einstein radius (≃ 1017 cm).

On the limit-cycle instability in magnetized accretion discs

Observational evidence accumulated over the past decade indicates that accretion discs in X-ray binaries are viscously stable unless they accrete very close to the Eddington limit. This is at odds with the most basic standard accretion disc theory, but could be explained by either having the discs to be much cooler whereby they are not radiation pressure dominated, or by a more sophisticated viscosity law. Here we argue that the latter is taking place in practice, on the basis of a stability analysis that assumes that the magneto-rotational-instability (MRI) responsible for generating the turbulent stresses inside the discs is also the source for a magnetically dominated corona. We show that observations of stable discs in the high/soft states of black hole binaries, on the one hand, and of the strongly variable microquasar GRS 1915+105 on the other, can all be explained if the magnetic turbulent stresses inside the disc scale proportionally to the geometric mean of gas and total pressure with a constant of proportionality (viscosity parameter) having a value of a few times 10^{-2}. Implications for bright AGN are also briefly discussed

The Effect of Internal Dissipation and Surface Irradiation on the Structure of Disks and the Location of the Snow Line around Sun‐like Stars

In theory of accretion disks, angular momentum and mass transfer are associated with the generation of energy through viscous dissipation. In the construction of SED models of protostellar disks, the stellar irradiation is usually assumed to be the dominant heating source. Here we construct a new set of self-consistent analytical disk models by taking into account both sources of thermal energy and the thermal structure of the disk across the midplane. We deduce a set of general formulae for the relationship between the mass accretion rate and the surface density profile. We apply it to determine the structure of protostellar disks under a state of steady accretion and derive the radial distribution of surface density and midplane temperature. The incorporation of the viscous heating in our model reduces the disk flaring angle and leads to lower photospheric temperatures than previously thought. Around T Tauri stars, the snow line can evolve from outside 10 AU during FU Orionis outbursts, to 2 AU during the quasi-steady accretion phase, to 0.7 AU when the accretion rate falls to about 10-9 M☉ yr-1, and finally reexpand beyond 2.2 AU during the protostellar-to-debris disk transition. The nonmonotonous evolution of the snow line may lead to the observed isotopic composition of water on both Venus and Earth. We also infer the presence of a marginally opaque, isothermal region with a surface density distribution similar to that of the MSN model. With a 40% higher temperature than that in the region immediately within, this transition may lead to an upturn in the SEDs in the MIR (24-70 μm) wavelength range. The optically thin, outermost regions of the disk have a shallow surface density profile of the dust that is consistent with millimeter observations of spatially resolved disks.