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1.
The dynamics of small global perturbations in the form of a linear combination of a finite number of non‐axisymmetric eigenmodes is studied in the two‐dimensional approximation. The background flow is assumed to be an axisymmetric perfect fluid with adiabatic index γ = 5/3 rotating with a power law angular velocity distribution Γ ∝ r–q , 1.5 < q < 2.0, confined by free boundaries in the radial direction. The substantial transient growth of acoustic energy of optimized perturbations is discovered. An optimal energy growth G is calculated numerically for a variety of parameters. Its value depends essentially on the perturbation azimuthal wavenumber m and increases for higher values of m. The closer the rotation profile to the Keplerian law, the larger growth factors can be obtained but over a longer time. The highest acoustic energy increase found numerically is of order ∼102 over ∼6 typical Keplerian periods. Slow neutral eigenmodes with corotation radius beyond the outer boundary mostly contribute to the transient growth. The revealed linear temporal behaviour of perturbations may play an important role in angular momentum transfer in toroidal flows near compact relativistic objects (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
The instability of axisymmetric flows of ideal incompressible fluid with respect to infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. The problem has been solved for two types of rotation profiles of an unperturbed flow: with zero and nonzero pressure gradients at the flow boundaries. Both rigid and free boundary conditions have been considered. The stability of axisymmetric flows with free boundaries is of great importance in disk accretion problems. Our calculations have revealed a crucial role of the flow pattern near the boundaries in the instability of the entire main flow. When the pressure gradient at the boundaries is zero, there is such a limiting scale of perturbations in azimuthal coordinate that longer-wavelength perturbations grow, while growing shorter-wavelength perturbations do not exit. In addition, for a fixed radial flow extent, there exists a nonzero minimum amplitude of the deviation of the angular velocity from the Keplerian one at which the instability vanishes. For a nonzero pressure gradient at the boundaries, the flow is unstable with respect to perturbations of any scale and at any small deviation of the angular velocity from the Keplerian one. 相似文献
3.
Cool weakly ionized gaseous rotating disk form the basis for many models in astrophysics objects. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Traditionally, axisymmetric magnetohydrodynamic (MHD) and recently Hall‐MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against axisymmetric perturbations in incompressible rotating fluid in external poloidal and toroidal magnetic field is considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
We explore an accretion model for low luminosity AGN (LLAGN) that attributes the low radiative output to a low mass accretion
rate,
, rather than a low radiative efficiency. In this model, electrons are assumed to drain energy from the ions as a result of
collisionless plasma microinstabilities. Consequently, the accreting gas collapses to form a geometrically thin disk at small
radii and is able to cool before reaching the black hole. The accretion disk is not a standard disk, however, because the
radial disk structure is modified by a magnetic torque which drives a jet and which is primarily responsible for angular momentum
transport. We also include relativistic effects. We apply this model to the well known LLAGN M87 and calculate the combined
disk-jet steady-state broadband spectrum. A comparison between predicted and observed spectra indicates that M87 may be a
maximally spinning black hole accreting at a rate of ∼10−3
M
⊙ yr−1. This is about 6 orders of magnitude below the Eddington rate for the same radiative efficiency. Furthermore, the total jet
power inferred by our model is in remarkably good agreement with the value independently deduced from observations of the
M87 jet on kiloparsec scales. 相似文献
5.
The normal mode oscillations of thin accretion disks around black holes and other compact objects are analyzed and contrasted with those in stars. For black holes, the most robust modes are gravitationally trapped near the radius at which the radial epicyclic frequency is maximum. Their eigenfrequencies depend mainly on the mass and angular momentum of the black hole. The fundamental g-mode has recently been seen in numerical simulations of black hole accretion disks. For stars such as white dwarfs, the modes are trapped near the inner boundary (magnetospheric or stellar) of the accretion disk. Their eigenfrequencies are approximately multiples of the (Keplerian) angular velocity of the inner edge of the disk. The relevance of these modes to the high frequency quasi-periodic oscillations observed in the power spectra of accreting binaries will be discussed. In contrast to most stellar oscillations, most of these modes are unstable in the presence of viscosity (if the turbulent viscosity induced by the magnetorotational instability acts hydrodynamically). 相似文献
6.
We explore an accretion model for low luminosity AGN (LLAGN) that attributes the low radiative output to a low mass accretion
rate,
, rather than a low radiative efficiency. In this model, electrons are assumed to drain energy from the ions as a result of
collisionless plasma microinstabilities. Consequently, the accreting gas collapses to form a geometrically thin disk at small
radii and is able to cool before reaching the black hole. The accretion disk is not a standard disk, however, because the
radial disk structure is modified by a magnetic torque which drives a jet and which is primarily responsible for angular momentum
transport. We also include relativistic effects. We apply this model to the well known LLAGN M87 and calculate the combined
disk-jet steady-state broadband spectrum. A comparison between predicted and observed spectra indicates that M87 may be a
maximally spinning black hole accreting at a rate of ∼10−3
M
⊙ yr−1. This is about 6 orders of magnitude below the Eddington rate for the same radiative efficiency. Furthermore, the total jet
power inferred by our model is in remarkably good agreement with the value independently deduced from observations of the
M87 jet on kiloparsec scales.
* This paper has previously been published in Astrophysics and Space Science, vol. 310:3–4. 相似文献
7.
Raines SN Watson DM Pipher JL Forrest WJ Greenhouse MA Satyapal S Woodward CE Smith HA Fischer J Goetz JA Frank A 《The Astrophysical journal》2000,533(2):L115-L118
When some magnetic field lines connect a Kerr black hole with a disk rotating around it, energy and angular momentum are transferred between them. If the black hole rotates faster than the disk, ca&solm0;GMH>0.36 for a thin Keplerian disk, then energy and angular momentum are extracted from the black hole and transferred to the disk (MH is the mass and aMH is the angular momentum of the black hole). This way, the energy originating in the black hole may be radiated away by the disk. The total amount of energy that can be extracted from the black hole spun down from ca&solm0;GMH=0.998 to ca&solm0;GMH=0.36 by a thin Keplerian disk is approximately 0.15MHc2. This is larger than approximately 0.09MHc2, which can be extracted by the Blandford-Znajek mechanism. 相似文献
8.
We study the excitation of density and bending waves and the associated angular momentum transfer in gaseous discs with finite thickness by a rotating external potential. The disc is assumed to be isothermal in the vertical direction and has no self-gravity. The disc perturbations are decomposed into different modes, each characterized by the azimuthal index m and the vertical index n , which specifies the nodal number of the density perturbation along the disc normal direction. The n = 0 modes correspond to the two-dimensional density waves previously studied by Goldreich & Tremaine and others. In a three-dimensional disc, waves can be excited at both Lindblad resonances (LRs; for modes with n = 0, 1, 2, … ) and vertical resonances (VRs; for the n ≥ 1 modes only). The torque on the disc is positive for waves excited at outer Lindblad/vertical resonances and negative at inner Lindblad/vertical resonances. While the n = 0 modes are evanescent around corotation, the n ≥ 1 modes can propagate into the corotation region where they are damped and deposit their angular momenta. We have derived analytical expressions for the amplitudes of different wave modes excited at LRs and/or VRs and the resulting torques on the disc. It is found that for n ≥ 1 , angular momentum transfer through VRs is much more efficient than LRs. This implies that in some situations (e.g. a circumstellar disc perturbed by a planet in an inclined orbit), VRs may be an important channel of angular momentum transfer between the disc and the external potential. We have also derived new formulae for the angular momentum deposition at corotation and studied wave excitations at disc boundaries. 相似文献
9.
In this paper, forward modelling is used to investigate the relation between given temperature and density perturbations and
the resulting (synthesised) intensity perturbations, as would be observed by, e.g., TRACE and EIS (onboard Hinode). Complex and highly non-linear interactions between the components which make up the intensity (density, ionisation balance
and emissivity) mean that it is non-trivial to reverse this process, i.e., obtain the density and temperature perturbations associated with observed intensity oscillations. In particular, it is found
that the damping rate does not often ‘survive’ the forward modelling process, highlighting the need for a very careful interpretation
of observed (intensity) damping rates. With a few examples, it is demonstrated that in some cases even the period of the oscillations
can be altered and that it is possible for two different sets of input temperature and density to lead to very similar intensities
(the well-known ‘ill-posed’ inversion process). 相似文献
10.
In this paper we consider the equilibrium of a magnetofluid disc in Schwarzschild background with an external magnetic field,
having the azimuthal and the radial components of the flow velocity nonzero. The electrical conductivityσ of the fluid is taken to be finite and thus the solution for the electromagnetic field is required to satisfy the Ohm’s law
too with the four-current having onlyJ
ϕ andJ
t nonzero. The various physical parameters that have to correlate for possible equilibrium configurations are identified and
their respective magnitudes estimated. It is found that for a given angular momentum distribution the inner edge of the disc
can reach well within the usual6m limit only when the surface magnetic field of the central object is not too high when the matter density at the outer edge
of the disc and the accretion rate are taken with reasonable limits 相似文献
11.
We fit the spectra of Cyg X-1 using two component advective flows with Keplerian accretion disks on the equatorial plane surrounded
by sub-Keplerian disks when standing shocks are present. The soft photons generated by the bremsstrahlung and synchrotron
processes in the sub-Keplerian flow, as well as the multi-colour black body emission from the Keplerian disk are Comptonized
by the thermal and non-thermal electrons. By varying Keplerian and sub-Keplerian rates we are able to reproduce the observed
soft and hard states as far as X-ray region is concerned and ‘low γ-ray intensity’ and ‘high γ-ray intensity’ states as far as the soft γ-ray region is concerned. We also find two pivotal points where the spectra intersect as is observed in Cyg X-1.
相似文献
12.
13.
The accretion of hot slowly rotating gas onto a supermassive black hole is considered. The important case where the velocities
of turbulent pulsations at the Bondi radius r
B are low, compared to the speed of sound c
s, is studied. Turbulence is probably responsible for the appearance of random average rotation. Although the angular momentum
at r
B is low, it gives rise to the centrifugal barrier at a depth r
c = l
2
/GM
BH ≪ r
B, that hinders supersonic accretion. The numerical solution of the problem of hot gas accretion with finite angular momentum
is found taking into account electron thermal conductivity and bremsstrahlung energy losses of two temperature plasma for
density and temperature near Bondi radius similar to observed in M87 galaxy. The saturation of the Spitzer thermal conductivity
was also taken into account. The parameters of the saturated electron thermal conductivity were chosen similar to the parameters
used in the numerical simulations of interaction of the strong laser beam radiation with plasma targets. These parameters
are confirmed in the experiments. It is shown that joint action of electron thermal conductivity and free-free radiation leads
to the effective cooling of accreting plasma and formation of the subsonic settling of accreting gas above the zone of a centrifugal
barrier. A toroidal condensation and a hollow funnel that separates the torus from the black hole emerge near the barrier.
The barrier divides the flow into two regions: (1) the settling zone with slow subKeplerian rotation and (2) the zone with
rapid supersonic nearly Keplerian rotation. Existence of the centrifugal barrier leads to significant decrease of the accretion
rate Ṁ in comparison with the critical Bondi solution for γ = 5/3 for the same values of density and temperature of the hot gas near Bondi radius. Shear instabilities in the torus and
related friction cause the gas to spread slowly along spirals in the equatorial plane in two directions.As a result, outer
(r > r
c) and inner (r < r
c) disks are formed. The gas enters the immediate neighborhood of the black hole or the zone of the internal ADAF flow along
the accretion disk (r < r
c). Since the angular momentum is conserved, the outer disk removes outward an excess of angular momentum along with part of
the matter falling into the torus. It is possible, that such outer Keplerian disk was observed by Hubble Space Telescope around
the nucleus of the M87 galaxy in the optical emission lines. We discuss shortly the characteristic times during which the
accretion of the gas with developed turbulence should lead to the changes in the orientation of the torus, accretion disk
and, possibly, of the jet. 相似文献
14.
15.
Summary. Recent papers dealing with the most controversial aspects of AGNs are reviewed. They suggest interesting conclusions: all
Seyferts can be described by a single parameter, the X-ray column density; radio loud AGNs may host a rapidly spinning black
hole and radio quiet AGNs a slowly spinning black hole; high-ionization AGNs (Seyfert galaxies and QSOs) contain an optically
thick, geometrically thin accretion disk, while low-ionization AGNs (Liners) contain an optically thin, geometrically thick
accretion disk; a number of blazars have been classified as BLLs on the basis of insufficient data; most objects with weak
broad emission lines are in fact HPQs; many objects have been called Liners although they are not AGNs but rather the result
of stellar activity; type 2 QSOs exist, but are quite inconspicuous if radio quiet.
Received 16 November 1999 / Published online: 15 February 2000 相似文献
16.
J.L. Johnson 《Astronomische Nachrichten》2011,332(8):841-845
We calculate the amount of angular momentum that thermal photons carry out of a viscous black hole accretion disk, due to the strong Doppler shift imparted to them by the high orbital velocity of the radiating disk material. While thermal emission can not drive accretion on its own, we show that along with disk heating it does nonetheless result in a loss of specific angular momentum, thereby contributing to an otherwise viscosity‐driven accretion flow. In particular, we show that the fraction of the angular momentum that is lost to thermal emission at a radius r in a standard, multi‐color disk is ∼0.4rs/r, where rs is the Schwarzschild radius of the black hole. We briefly highlight the key similarties between this effect and the closely related Poynting‐Robertson effect (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
The stability of a self‐gravitating infinitesimally thin gaseous disk rotating around a central mass is studied. Our global linear analysis concerns marginal stability, i.e. it yields the critical temperature for the onset of instability for any given ratio of the disk mass to the central mass. Both axisymmetric and low‐m nonaxisymmetric excitations are analysed. When the fractional disk mass increases, the symmetry character of the instability changes from rings (m = 0) to one‐armed trailing spirals (m = 1). The distribution of the surface density along the spiral arms is not uniform, but describes a sequence of maxima that might be identified with forming planets. The number of the mass concentrations decreases with increasing fractional disk mass. We also obtain solutions in the form of global nonaxisymmetric vortices, which are, however, never excited. 相似文献
18.
We perform an extensive linear investigation of the nonaxisymmetric disk modes referred to in the literature as P, I, and J modes in self-gravitating polytropic toroids with power law angular velocity distributions. For selected models, we also
follow the development of instability from the linear regime through the quasi-linear regime to deep into the nonlinear regime.
We consider modes with azimuthal dependence e
imφ
, where m is an integer and φ is the azimuthal angle. We find that instability sets in through m=2 barlike I modes at T/|W|∼0.16–0.18 depending upon the chosen angular velocity law where T is the rotational kinetic energy and W is the gravitational energy of the toroid. Instability in the barlike I mode peaks in strength around T/|W|=0.22–0.23 after which it weakens, eventually stabilizing around T/|W|∼0.25–0.26. One-armed modes (m=1 modes) become unstable just after instability in the m=2I modes sets in; instability in m=1 modes sets in at T/|W|∼0.19. They dominate the barlike I modes in toroids with T/|W|≳0.25. However, almost immediately after the m=1 mode overtakes the barlike I mode, higher-m
J modes appear. J modes with m=2, 3, and 4 become unstable for T/|W|≳0.25–0.26, 0.23–0.25, and 0.25–0.26, respectively. m≥3J modes dominate the m=1 mode in toroids with T/|W|≳0.27. As T/|W| increases further, nonaxisymmetric instability sets in through higher and higher m modes. We find quantitative agreement between the early nonlinear behavior of the tested unstable toroids and our linear
results. Quasi-linear modeling suggests that a gravitational self-interaction torque which arises early in the nonlinear regime
saturates growth of the mode and leads to significant transport of mass and angular momentum. Neither I mode nor J mode instabilities produce prompt fission in toroids. 相似文献
19.
Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow
modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous
(on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing,
centrally symmetric ellipses (2: 1 orbits). Depending on the density distribution in the system and the degree of halo inhomogeneity,
the orbit precession can be both prograde and retrograde, in contrast to systems with 1: 1 elliptical orbits where the precession
is unequivocally retrograde. In the first paper, we show that in the case where at least some of the orbits have a prograde
precession and the stellar distribution function is a decreasing function of angular momentum, an instability that turns into
the well-known radial orbit instability in the limit of low angular momenta can develop in the system. We also explore the
question of whether the so-called spoke approximation, a simplified version of the slow mode approximation, is applicable
for investigating the instability of stellar systems with highly elongated orbits. Highly elongated orbits in clusters with
nonsingular gravitational potentials are known to be also slowly precessing 2: 1 ellipses. This explains the attempts to use
the spoke approximation in finding the spectrum of slow modes with frequencies of the order of the orbit precession rate.
We show that, in contrast to the previously accepted view, the dependence of the precession rate on angular momentum can differ
significantly from a linear one even in a narrow range of variation of the distribution function in angular momentum. Nevertheless,
using a proper precession curve in the spoke approximation allows us to partially “rehabilitate” the spoke approach, i.e.,
to correctly determine the instability growth rate, at least in the principal (O(α
T−1/2) order of the perturbation theory in dimensionless small parameter α
T, which characterizes the width of the distribution function in angular momentum near radial orbits. 相似文献
20.
In this paper we have presented a very general class of solutions for rotating fluid disks around massive objects (neglecting
the self gravitation of the disk) with density as a function of the radial coordinate only and pressure being nonzero. Having
considered a number of cases with different density and velocity distributions, we have analysed the stability of such disks
under both radial and axisymmetric perturbations. For a perfect gas disk with γ= 5/3 the disk is stable with frequency (MG/r3)1/2 for purely radial pulsation with expanding and contracting boundary. In the case of axisymmetric perturbation the critical
γc for neutral stability is found to be much less than 4/3 indicating that such disks are mostly stable under such perturbations.
On leave of absence from Government College, Jagdalpur 494005. 相似文献