Dynamo action by internal waves in accretion disks

In this paper, we study the propagation and stability of nonlinear sound waves in accretion disks. Using the shearing box approximation, we derive the form of these waves using a semi-analytic approach and go on to study their stability. The results are compared to those of numerical simulations performed using finite difference approaches such as employed by ZEUS as well as Godunov methods. When the wave frequency is between Omega and two Omega (where Omega is the disk orbital angular velocity), it can couple resonantly with a pair of linear inertial waves and thus undergo a parametric instability. Neglecting the disk vertical stratification, we derive an expression for the growth rate when the amplitude of the background wave is small. Good agreement is found with the results of numerical simulations performed both with finite difference and Godunov codes. During the nonlinear phase of the instability, the flow remains well organised if the amplitude of the background wave is small. However, strongly nonlinear waves break down into turbulence. In both cases, the background wave is damped and the disk eventually returns to a stationary state. Finally, we demonstrate that the instability also develops when density stratification is taken into account and so is robust. This destabilisation of freely propagating nonlinear sound waves may be important for understanding the complicated behaviour of density waves in disks that are unstable through the effects of self-gravity or magnetic fields and is likely to affect the propagation of waves that are tidally excited by objects such as a protoplanet or companion perturbing a protoplanetary disk. The nonlinear wave solutions described here as well as their stability properties were also found to be useful for testing and comparing the performance of different numerical codes.

The propagation properties of internal gravity waves in a rotating torus are considered. The oscillations are assumed to be axisymmetric and adiabatic. In the short-wavelength limit in the vertical direction, the gravity waves whose frequency is ω are confined in the region in which [ω – N(r)][ω – κ(r)] < 0 holds, where N and κ are the Brunt-Väisälä frequency for vertical displacement and the epicyclic frequency, respectively, and r is the radial coordinate. We find that the gravity waves are resonantly absorbed to heat the plasma at the radius where ω equals N(r). This radius is probably located in the innermost region of the torus, where most X-rays are emitted. Some implications of this result, with respect to quasi-periodic oscillations obserbed from low-mass X-ray binaries, are briefly discussed.

Magnetic fields are present in many different astrophysical objects, such as accretion discs, stars, and planets. They influence the evolution and dominate the interior dynamics of these objects, in particular their evolutionary stages. The presence of a weak (subthermal) magnetic field plays a crucial role to drive turbulence in accretion discs thus leading to the stresses needed for accretion and angular momentum transport. This instability is known as the Magneto Rotational Instability (MRI) and it has been studied intensively for the last two decades. Recent numerical results show the importance of understanding the dynamo process in accretion discs. Small-scale dynamo action could prevent the saturation of MRI modes whereas the generation of large-scale magnetic fields provides a suitable coherent field for the angular-momentum transport by MRI modes. Observations show a huge variety of stellar and planetary magnetic fields. Cosmic magnetic fields differ in their magnitude, topology and time dependence. Of particular interest is the understanding of cyclic field variations, as known from the Sun. They are often explained by an important Ω effect, i.e., by the stretching of field lines because of strong differential rotation. We computed the dynamo coefficients for an oscillatory dynamo model with the help of the so-called test-field method. We argue that this example is of α2Ω-type and here the Ω-effect alone is not responsible for its cyclic time variation. More general conditions which lead to dynamo waves in global direct numerical simulations are presented. Zonal flows driven by convection in planetary interiors may lead to secondary instabilities. We showed that a simple, modified version of the MRI (so-called MSMRI) can develop in the Earth's outer liquid core (Petitdemange, Dormy, Balbus, GRL,35, 2008). The force balance in the Earth's core and in classical astrophysical applications of the MRI (such as gaseous discs around stars) is different. The weak differential rotation in planetary interiors yields an instability by its constructive interaction with the much larger rotation rate of the planets. The resulting destabilizing mechanism is just strong enough to counteract the stabilizing resistive effects, and to produce growth on geophysically interesting time scales. MRI and dynamo action are both interesting in their own right, however, their interaction is crucial in order to understand the dynamics of accretion discs, stellar and planetary interiors.

Supermassive black holes (SMBHs) like M87* and Sgr A* have been observed with the Event Horizon Telescope (EHT), facilitating the investigation of null geodesics near a black hole. The null geodesic around black holes and relevant features such as photon ring, lensing ring and black hole shadow, have been modeled analytically. The emission and absorption of plasmas surrounding a black hole is highly related to the physical quantities such as mass density, momentum, internal energy, magnetic field, black hole spin and angular momentum. The images of accretion disks around black holes are affected by Doppler shift, gravitational redshift, and frequency-dependent emissivity and absorption coefficient, which can be assessed by numerical simulations. In this work, a numerical ray-tracing scheme and a covariant radiative transfer scheme are proposed to simulate the photon trajectories emitting from the accretion disks around Kerr black holes, hence to reconstruct their images. A set of magnetized, geometrically thick accretion disks are adopted to compute the emissivity and absorption coefficient, which are then used to reconstruct the images of the subject accretion disks. The effects of magnetization, black hole spin, angular momentum and geometry of the disks are studied. The effects of Doppler shift, gravitational lensing, and frequency-dependent emissivity and absorption coefficient are investigated by simulations.

MHD turbulence is generally believed to have two important functions in accretion disks: it transports angular momentum outward, and the energy in its shortest wavelength modes is dissipated into the heat that the disks radiate. In this paper we examine a pair of mechanisms that may play an important role in regulating the amplitude and spectrum of this turbulence: photon diffusion and viscosity. We demonstrate that in radiation pressure-dominated disks, photon damping of compressive MHD waves is so rapid that it likely dominates all other dissipation mechanisms.

Context. The Tayler-Spruit dynamo (TSD) is capable of generating a small-scale magnetic field in the differentially rotating, stably stratified layers of stars. Its activity was recently observed in numerical simulations. In parallel, the propagation of internal gravity waves in stars can be modified in the presence of a magnetic field. Aims. We want to estimate the interaction between a magnetic field generated by the TSD and internal gravity waves in the radiative cores of low-mass stars. This allows us to characterise the effect of this interplay on the observed standing mode spectrum and on the internal transport of angular momentum via progressive waves. Methods. We used the STAREVOL evolution code to compute the structure of low-mass rotating stars with various transport and mixing mechanisms along their evolution. We implemented the formalism to describe the TSD and estimate regions where the magnetic field generated by TSD is strong enough to change the identity of internal gravity waves to magneto-gravity waves. In addition, we evaluated the possible limitation of angular momentum transport via the combined action of rotation and magnetism. Results. Along the pre-main sequence and main sequence evolution of low-mass stars, the lowest frequencies of the excited gravity wave spectrum should be converted to magneto-gravity waves by the magnetic field generated by the TSD. On the red giant branch, we find that most of the excited spectrum of progressive internal gravity waves could be converted into magneto-gravity waves.

The mesoscale eddy and internal wave both are phenomena commonly observed in oceans. It is aimed to investigate how the presence of a mesoscale eddy in the ocean affects wave form deformation of the internal solitary wave propagation. An ocean eddy is produced by a quasi-geostrophic model in f-plane, and the one-dimensional nonlinear variable-coefficient extended Korteweg-de Vries (eKdV) equation is used to simulate an internal solitary wave passing through the mesoscale eddy field. The results suggest that the mode structures of the linear internal wave are modified due to the presence of the mesoscale eddy field. A cyclonic eddy and an anticyclonic eddy have different influences on the background environment of the internal solitary wave propagation. The existence of a mesoscale eddy field has almost no prominent impact on the propagation of a smallamplitude internal solitary wave only based on the first mode vertical structure, but the mesoscale eddy background field exerts a considerable influence on the solitary wave propagation if considering high-mode vertical structures. Furthermore, whether an internal solitary wave first passes through anticyclonic eddy or cyclonic eddy, the deformation of wave profiles is different. Many observations of solitary internal waves in the real oceans suggest the formation of the waves. Apart from topography effect, it is shown that the mesoscale eddy background field is also a considerable factor which influences the internal solitary wave propagation and deformation.

view Abstract Citations (49) References (30) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Local Magnetohydrodynamic Instabilities and the Wave-driven Dynamo in Accretion Disks Vishniac, Ethan T. ; Diamond, Patrick Abstract We consider the consequences of magnetic buoyancy and the magnetic shearing instability (MSI) on the strength and organization of the magnetic field in a thin accretion disk. We discuss a model in which the wave-driven dynamo growth rate is balanced by the dissipative effects of the MSI. As in earlier work, the net helicity is due to small advective motions driven by nonlinear interactions between internal waves. Assuming a simple model of the internal wave spectrum generated from the primary m = 1 internal waves, we find that the magnetic energy density saturates at about (H/r) exp 4/3 times the local pressure (where H is the disk thickness and r is its radius). On very small scales the shearing instability will produce an isotropic fluctuating field. For a stationary disk this is equivalent to a dimensionless 'viscosity' of about (H/r) exp 4/3. The vertical and radial diffusion coefficients will be comparable to each other. Magnetic buoyancy will be largely suppressed by the turbulence due to the MSI. We present a rough estimate of its effects and find that it removes magnetic flux from the disk at a rate comparable to that caused by turbulent diffusion. Publication: The Astrophysical Journal Pub Date: October 1992 DOI: 10.1086/171881 Bibcode: 1992ApJ...398..561V Keywords: Accretion Disks; Dynamo Theory; Magnetohydrodynamic Stability; Stellar Physics; Buoyancy; Computational Astrophysics; Interstellar Magnetic Fields; Magnetohydrodynamic Turbulence; Propagation Modes; Viscosity; Astrophysics; ACCRETION; ACCRETION DISKS; INSTABILITIES; MAGNETOHYDRODYNAMICS: MHD full text sources ADS |

The nonhydrostatic pressure effects on the generation and propagation of wind-forced internal waves are studied with a two-dimensional numerical ocean model. A one-way directed wind pulse over a stratified ocean initiates surface and internal waves in a closed basin. The studies are performed with horizontal grid sizes in the range from 1 km to 62.5 m. The experiments are performed with both a hydrostatic and a nonhydrostatic model, facilitating systematic studies of the sensitivity of the numerical model results to the grid size and to the nonhydrostatic pressure adjustments. The results show that the nonhydrostatic pressure effects are highly dependent on the grid size and grow with increased resolution. In the internal depression wave, the horizontal nonhydrostatic pressure gradients reach the same order of magnitude as the hydrostatic gradients in the high-resolution nonhydrostatic studies. In these studies, the nonhydrostatic pressure gradients approximately balance the corresponding hydrostatic pressure gradients in the internal depression wave, and the wave degenerates into a train of soliton waves. The time for the soliton form to develop agrees with the steepening timescale calculated from Korteweg-de Vries theory. In the high-resolution hydrostatic model, the internal depression wave takes the form of a single wave front. When the internal waves are generated in the boundary layers, the nonhydrostatic pressure gradients are much smaller than the hydrostatic gradients and the generation processes are not effected by the nonhydrostatic pressure with the present range of grid sizes.

We discuss the problem of the formation of a large-scale magnetic field in the accretion disks around black holes, taking into account the non-uniform vertical structure of the disk. The high electrical conductivity of the outer layers of the disk prevents the outward diffusion of the magnetic field. This implies a stationary state with a strong magnetic field in the inner parts of the accretion disk close to the black hole, and zero radial velocity at the surface of the disk. Structure of advective accretion disks is investigated, and conditions for formation of optically thin regions in central parts of the accretion disk are found. The problem of jet collimation by magneto-torsion oscillations is considered.

The authors investigate some aspects of accretion onto static black holes immersed in a uniform magnetic field. The Ernst metric is employed to find the 'Keplerian' angular momentum distribution and the efficiency of mass-to-energy conversion for a plasma and for test particles. Under almost all physically reasonable conditions for hydrodynamic accretion the effect of the magnetic field is small. However, for test particles the effect can be very important and the efficiency can approach unity.

During the collapse of a massive star greater than 35- 40 M ⊙ , stellar core is considered to promptly collapse to a black hole. and stellar material may fall onto the hole greater than several solar masses with extremely high accretion rates (> 1 M ⊙ s -1 ). If the star has a sufficiently high angular momentum before the collapse, an accretion disk is likely to form around the black hole. Jets are suggested to be launched from the inner region of the accretion disk near the hole through magnetic and/or neutrino processes. Gamma-Ray Bursts (GRBs) are expected to be driven by the jets. This scenario of GRBs is called the collapsar model. Recently, magnetohydrodynamic (MHD) simulations were performed of the collapse of rapidly rotating, magnetized 25 M ⊙ and 40 M ⊙ stars in light of the collapsar model of GRBs (see papers listed at the end of the paper). For assumed angular velocity distributions and the uniform magnetic fields, the collapsars are shown to eject jets driven through the magnetic pressure. The simulations are however performed up to 4 s, which are shorter than durations of long GRBs ∼ 10 s. In the present work. we have performed long-tern (∼ 10 s), two-dimensional, MHD simulations of the collapse of a rapidly totaling, magnetized 40 M ⊙ star.

Cataclysmic variables are very close binary stars in which the primary component is a white dwarf. The secondary star, usually a low-mass main-sequence star, is filling its Roche lobe and transferring material to the white dwarf. This material has too much angular momentum to fall directly on to the white dwarf and instead forms an accretion disc, which makes up the third major component of the cataclysmic variable. A magnetic field can be associated with each of the two stars and the disc. In the case of the white dwarf the field is frozen in. It can be strong enough to disrupt all or part of the accretion disc and force the accreting matter to fall in along field lines. The fields associated with the red dwarf and accretion disc appear to be dynamo generated. They cannot be measured directly but must be inferred from other properties of the systems. In cataclysmic variables, conservative mass transfer would lead to the secondary star shrinking within its Roche lobe until it expanded on a nuclear timescale. For almost all systems this exceeds the age of the Galaxy by several orders of magnitude. Nor can simple mass loss drive the observed mass transfer and an alternative angular momentum loss mechanism is required. At the shortest periods gravitational radiation suffices but at longer periods magnetic braking seems to be more likely. Any determination of the mass transfer rate can then constrain the field strength and structure and ultimately the nature of any magnetic dynamo. In the absence of viscosity, transferred material would accumulate in a ring around the white dwarf. Viscosity allows this ring to spread out into a disc so that matter accretes while angular momentum is returned to the orbit. Some form of radial magnetic field in the disc provides the most viable source of viscosity. It appears to be necessary to generate this field by dynamo action within the disc itself. Dwarf novae undergo periodic outbursts that are due to changes in accretion rate through the disc. This time dependent behaviour probes the strength of the radial and azimuthal field and hence any disc dynamo.

view Abstract Citations (47) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A General Relativistic Toroid around a Black Hole Nishida, Shogo ; Eriguchi, Yoshiharu Abstract We present a powerful new numerical method to obtain the equilibrium states of a toroid around a black hole. The integral representation of Einstein's equations used in this paper has several advantages, one of which is that it can easily take into account the asymptotic behavior of the metric. This computational scheme can be applied to configurations with any strength of gravity of toroids and any amount of rotation of black holes. By using this scheme, we have obtained many new equilibrium configurations of general relativistic thick toroids. Highly relativistic effects of toroids on black holes or on external spacetimes have been investigated. In particular, dragging of inertial frames and tidal forces due to toroids can be clearly seen by studying the angular momentum of a black hole when the mass of the toroid is varied. Some black holes are found to have an ergoregion even if their angular momentum is zero. We find that the shape of a black hole becomes spherical when its angular momentum vanishes, even if a massive toroid exists around it. From this result, we can define nonrotating or 'spherical' black holes as those which have zero angular momentum irrespective of their angular velocity. We can, therefore, extract energy from spherical black holes, because spherical black holes can have an ergoregion. Furthermore, our schemes and results will contribute to the study of the stability of relativistic self-gravitating thick toroids by allowing the investigation of circular orbits of free particles around black holes. Publication: The Astrophysical Journal Pub Date: May 1994 DOI: 10.1086/174153 Bibcode: 1994ApJ...427..429N Keywords: Accretion Disks; Applications Of Mathematics; Black Holes (Astronomy); Equilibrium Methods; Relativity; Toroids; Angular Momentum; Angular Velocity; Circular Orbits; Gravitation; Inertial Reference Systems; Planetary Temperature; Astrophysics; ACCRETION; ACCRETION DISKS; BLACK HOLE PHYSICS; RELATIVITY full text sources ADS |

<p indent="0mm">Black hole X-ray binary (BHXRB) forms an accretion disk by accreting material from a companion star, producing intense X-ray radiation. During an outburst of a BHXRB, the mass accretion rate to the black hole (BH) varies over several orders of magnitude, often reaching even higher values. Correspondingly, the accretion process transitions between different modes make it an ideal laboratory for studying black hole accretion. The BH accretion process is often accompanied by relativistic jets, which are associated with the magnetic field in the vicinity of the black hole. Studying accretion physics can help us understand the evolution and transportation of large-scale magnetic fields in accretion discs and the mechanisms that generate the jets. Therefore, the study of black hole accretion is one of the frontier research fields in astrophysics. In this paper, we briefly introduce the multi-wavelengths observational features of BHXRBs in the outbursts, and introduce the advances in the black hole accretion in recent years based on the data from HXMT from the spectral and timing perspectives. Regarding accretion flow, the accretion disk truncation model is a widely accepted theoretical framework for interpreting the state transitions of X-ray binaries. However, it is still unclear how disk and corona evolve in both geometry and dynamics. Recent studies using spectral fitting and timing analysis of MAXI J1820+070 suggest a reduction in the spatial extent of the corona. An unusual decrease in the reflection fraction suggests an outflowing corona, which accelerates as it approaches the black hole. It has been found that the black hole’s spin, measured from energy spectra, appears smaller at high luminosities. This phenomenon is successfully interpreted when considering the influence of disk winds on the energy spectra. This suggests that the evolution of the measured spin could be evidence of the disk wind. On the topic of magnetic fields and jets, it is believed that a magnetically arrested disk (MAD) can form in BHXRBs when the magnetic field in the accretion flow is sufficiently strong to counteract gravity, although definitive observational evidence is still lacking. In the decaying hard state of MAXI J1820+070, the radio and optical fluxes are delayed by about 8 and 17 days respectively, compared to the X-ray flux. This could be evidence for the formation of a MAD. The magnetic field, amplified by an expanding corona, forms a MAD around the peak of the radio emission. This review also introduces recent observational and theoretical advances in timing analysis. BHXRBs often exhibit quasi-periodic oscillations (QPOs) in X-ray flux. The Lense-Thirring precession of the jet or corona may be the origin of QPOs. A simulation code based on the Lense-Thirring precession model has been developed, and several properties of QPOs have been predicted, which have been confirmed using observational data from HXMT. Thanks to the broad energy range of HXMT, QPO signals above 200 keV have been observed in MAXI J1820+070. A soft lag increasing with energy has also been observed, suggesting that the QPOs may originate from jet precession.