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1.
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   

2.
The phenomenon of negative viscosity-alpha in convectively unstable Keplerian accretion discs is discussed. The convection is considered as a random flow with an axisymmetric mesoscale pattern. Its correlation tensor is computed with a time-averaging procedure using Kley's 2D hydrocode. There is a distinct anisotropy between the turbulence intensities in the radial and azimuthal directions, i.e. the radial velocity rms dominates the azimuthal one. As a consequence, an extra term in the expression for the turbulent transport of angular momentum appears which does not vanish for rigid rotation ('Λ-effect'). It is negative ('inwards transport') and even seems to dominate the positive contribution of the eddy viscosity representing outwards transport of angular momentum. For a turbulence model close to that of the mixing-length theory, the rotational influence on the anisotropy of the turbulence intensities,     , and the covariance  〈 u ' R u ' φ 〉  – representing the angular momentum transport – is computed and compared with the accretion disc simulations. Indeed, the negative angular momentum transport can be explained with the observed dominance of the radial turbulence intensity. If, on the other hand, in turbulence fields the azimuthal intensity would dominate or the turbulence is even isotropic, then we always find a positive transport of the angular momentum.  相似文献   

3.
The possibility that the magnetic shear-flow instability (also known as the 'Balbus–Hawley' instability) might give rise to turbulence in a thin accretion disc is investigated through numerical simulations. The study is linear and the fluid disc is supposed to be incompressible and differentially rotating with a simple velocity profile with Ω∝ R − q . The simplicity of the model is counterbalanced by the fact that the study is fully global in all three spatial directions with boundaries on each side; finite diffusivities are also allowed. The investigation is also carried out for several values of the azimuthal wavenumber of the perturbations in order to analyse whether non-axisymmetric modes might be preferred, which may produce, in a non-linear extension of the study, a self-sustained magnetic field.
  We find the final pattern steady, with similar kinetic and magnetic energies and the angular momentum always transported outwards. Despite the differential rotation, there are only small differences for the eigenvalues for various non-axisymmetric eigensolutions. Axisymmetric instabilities are by no means preferred; in fact for Prandtl numbers between 0.1 and 1, the azimuthal wavenumbers m =0,1,2(1016 g s-1). All three quantities appear to be equally readily excited. The equatorial symmetry is quadrupolar for the magnetic field and dipolar for the flow field system. The maximal magnetic field strength required to cause the instability is almost independent of the magnetic Prandtl number. With typical white dwarf values, a magnetic amplitude of 105 G is estimated.  相似文献   

4.
The non-axisymmetric features observed in the discs of dwarf novae in outburst are usually considered to be spiral shocks, which are the non-linear relatives of tidally excited waves. This interpretation suffers from a number of problems. For example, the natural site of wave excitation lies outside the Roche lobe, the disc must be especially hot, and most treatments of wave propagation do not take into account the vertical structure of the disc.
In this paper I construct a detailed semi-analytical model of the non-linear tidal distortion of a thin, three-dimensional accretion disc by a binary companion on a circular orbit. The analysis presented here allows for vertical motion and radiative energy transport, and introduces a simple model for the turbulent magnetic stress. The   m =2  inner vertical resonance has an important influence on the amplitude and phase of the tidal distortion. I show that the observed patterns find a natural explanation if the emission is associated with the tidally thickened sectors of the outer disc, which may be irradiated from the centre. According to this hypothesis, it may be possible to constrain the physical parameters of the disc through future observations.  相似文献   

5.
Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto‐rotational instability or, in the non‐magnetic case, by an explicit and artificial forcing term in the momentum equation. Unlike the magnetic case, where most of the dissipation occurs in the disc corona, in the forced hydrodynamic case most of the dissipation occurs near the midplane. In the hydrodynamic case evidence is presented for the stochastic excitation of epicycles. When the vertical and radial epicyclic frequencies are different (modeling the properties around rotating black holes), the beat frequency between these two frequencies appear to show up as a peak in the temporal power spectrum in some cases. Finally, the full turbulent resistivity tensor is determined and it is found that, if the turbulence is driven by a forcing term, the signs of its off‐diagonal components are such that this effect would not be capable of dynamo action by the shear–current effect. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

6.
We have undertaken an extensive study of X-ray data from the accreting millisecond pulsar XTE J1751 − 305 observed by RXTE and XMM–Newton during its 2002 outburst. In all aspects this source is similar to the prototypical millisecond pulsar SAX J1808.4 − 3658, except for the higher peak luminosity of 13 per cent of Eddington, and the optical depth of the hard X-ray source, which is larger by a factor ∼2. Its broad-band X-ray spectrum can be modelled by three components. We interpret the two soft components as thermal emission from a colder  ( kT ∼ 0.6 keV)  accretion disc and a hotter (∼1 keV) spot on the neutron star surface. We interpret the hard component as thermal Comptonization in plasma of temperature ∼40 keV and optical depth ∼1.5 in a slab geometry. The plasma is heated by the accretion shock as the material collimated by the magnetic field impacts on to the surface. The seed photons for Comptonization are provided by the hotspot, not by the disc. The Compton reflection is weak and the disc is probably truncated into an optically thin flow above the magnetospheric radius. Rotation of the emission region with the star creates an almost sinusoidal pulse profile with an rms amplitude of 3.3 per cent. The energy-dependent soft phase lags can be modelled by two pulsating components shifted in phase, which is naturally explained by a different character of emission of the optically thick spot and optically thin shock combined with the action of the Doppler boosting. The observed variability amplitude constrains the hotspot to lie within 3°–4° of the rotational pole. We estimate the inner radius of the optically thick accreting disc to be about 40 km. In that case, the absence of emission from the antipodal spot, which can be blocked by the accretion disc, gives the inclination of the system as ≳70°.  相似文献   

7.
Gravitational wave signal characteristics from a binary black hole system in which the companion moves through the accretion disc of the primary are studied. We chose the primary to be a super-massive  ( M = 108 M⊙)  Kerr black hole and the companion to be a massive black hole  ( M = 105 M⊙)  to clearly demonstrate the effects. We show that the drag exerted on the companion by the disc is sufficient to reduce the coalescence time of the binary. The drag is primarily due to the fact that the accretion disc on a black hole deviates from a Keplerian disc and becomes sub-Keplerian due to inner boundary condition on the black hole horizon. We consider two types of accretion rates on to the companion. The companion is deeply immersed inside the disc and it can accrete at the Bondi rate which depends on the instantaneous density of the disc. However, an accretion disc can also form around the smaller black hole and it can accrete at its Eddington rate. Thus, this case is also studied and the results are compared. We find that the effect of the disc will be significant in reducing the coalescence time and one needs to incorporate this while interpreting gravitational wave signals emitted from such a binary system.  相似文献   

8.
The radial–azimuthal instability of a hot two-temperature accretion disc with advection is examined in this paper. We find that the inclusion of very little advection has significant effects on two acoustic modes for a geometrically thin, cooling-dominated two-temperature disc, but has no effect on acoustic modes for a geometrically slim, cooling-dominated two-temperature disc. We also find that, when azimuthal perturbations are considered, the stability properties of the disc are different from those in the pure radial perturbation case. An increase of the azimuthal wavenumber will stabilize the acoustic modes but make the viscous and thermal modes more unstable for a geometrically thin, cooling-dominated two-temperature disc. It makes the thermal mode more unstable and the acoustic mode more stable, but only affects the instability of the viscous mode for short-wavelength perturbations for a geometrically slim, cooling-dominated two-temperature disc. For a geometrically slim, advection-dominated two-temperature disc, the increase of the azimuthal perturbation makes the I- and O-modes more stable and the thermal mode more unstable, but has no effect on the viscous mode.  相似文献   

9.
The irradiation of protoplanetary discs by central stars is the main heating mechanism for discs, resulting in their flared geometric structure. In a series of papers, we investigate the deep links between two-dimensional self-consistent disc structure and planetary migration in irradiated discs, focusing particularly on those around M stars. In this first paper, we analyse the thermal structure of discs that are irradiated by an M star by solving the radiative transfer equation by means of a Monte Carlo code. Our simulations of irradiated hydrostatic discs are realistic and self-consistent in that they include dust settling with multiple grain sizes  ( N = 15)  , the gravitational force of an embedded planet on the disc and the presence of a dead zone (a region with very low levels of turbulence) within it. We show that dust settling drives the temperature of the mid-plane from an   r −3/5  distribution (well mixed dust models) towards an   r −3/4  . The dead zone, meanwhile, leaves a dusty wall at its outer edge because dust settling in this region is enhanced compared to the active turbulent disc at larger disc radii. The disc heating produced by this irradiated wall provides a positive gradient region of the temperature in the dead zone in front of the wall. This is crucially important for slowing planetary migration because Lindblad torques are inversely proportional to the disc temperature. Furthermore, we show that low turbulence of the dead zone is self-consistently induced by dust settling, resulting in the Kelvin–Helmholtz instability (KHI). We show that the strength of turbulence arising from the KHI in the dead zone is  α= 10−5  .  相似文献   

10.
We excite an epicyclic motion, the amplitude of which depends on the vertical position, z , in a simulation of a turbulent accretion disc. An epicyclic motion of this kind may be caused by a warping of the disc. By studying how the epicyclic motion decays, we can obtain information about the interaction between the warp and the disc turbulence. A high-amplitude epicyclic motion decays first by exciting inertial waves through a parametric instability, but its subsequent exponential damping may be reproduced by a turbulent viscosity. We estimate the effective viscosity parameter, α v, pertaining to such a vertical shear. We also gain new information on the properties of the disc turbulence in general, and measure the usual viscosity parameter, α h, pertaining to a horizontal (Keplerian) shear. We find that, as is often assumed in theoretical studies, α v is approximately equal to α h and both are much less than unity, for the field strengths achieved in our local box calculations of turbulence. In view of the smallness (∼0.01) of α v and α h we conclude that for β p gas p mag∼10 the time-scale for diffusion or damping of a warp is much shorter than the usual viscous time-scale. Finally, we review the astrophysical implications.  相似文献   

11.
We present a perturbation theory for studying the instabilities of non-axisymmetric gaseous discs. We perturb the dynamical equations of self-gravitating fluids in the vicinity of a non-axisymmetric equilibrium, and expand the perturbed physical quantities in terms of a complete basis set and a small non-axisymmetry parameter ε. We then derive a linear eigenvalue problem in matrix form, and determine the pattern speed, growth rate and mode shapes of the first three unstable modes. In non-axisymmetric discs, the amplitude and the phase angle of travelling waves are functions of both the radius R and the azimuthal angle φ. This is due to the interaction of different wave components in the response spectrum. We demonstrate that wave interaction in unstable discs, with small initial asymmetries, can develop dense clumps during the phase of exponential growth. Local clumps, which occur on the major spiral arms, can constitute seeds of gas giant planets in accretion discs.  相似文献   

12.
We consider the effect of a supernova (SN) explosion in a very massive binary that is expected to form in a portion of Population III stars with the mass higher than  100 M⊙  . In a Population III binary system, a more massive star can result in the formation of a black hole (BH) and a surrounding accretion disc. Such BH accretion could be a significant source of the cosmic reionization in the early Universe. However, a less massive companion star evolves belatedly and eventually undergoes a SN explosion, so that the accretion disc around a BH might be blown off in a lifetime of companion star. In this paper, we explore the dynamical impact of a SN explosion on an accretion disc around a massive BH, and elucidate whether the BH accretion disc is totally demolished or not. For the purpose, we perform three-dimensional hydrodynamic simulations of a very massive binary system, where we assume a BH of  103 M⊙  that results from a direct collapse of a very massive star and a companion star of  100 M⊙  that undergoes a SN explosion. We calculate the remaining mass of a BH accretion disc as a function of time. As a result, it is found that a significant portion of gas disc can survive through three-dimensional geometrical effects even after the SN explosion of a companion star. Even if the SN explosion energy is higher by two orders of magnitude than the binding energy of gas disc, about a half of disc can be left over. The results imply that the Population III BH accretion disc can be a long-lived luminous source, and therefore could be an important ionizing source in the early Universe.  相似文献   

13.
In differentially rotating discs with no self-gravity, density waves cannot propagate around the corotation, where the wave pattern rotation speed equals the fluid rotation rate. Waves incident upon the corotation barrier may be super-reflected (commonly referred to as corotation amplifier), but the reflection can be strongly affected by wave absorptions at the corotation resonance/singularity. The sign of the absorption is related to the Rossby wave zone very near the corotation radius. We derive the explicit expressions for the complex reflection and transmission coefficients, taking into account wave absorption at the corotation resonance. We show that for generic discs, this absorption plays a much more important role than wave transmission across the corotation barrier. Depending on the sign of the gradient of the vortensity of the disc,  ζ=κ2/(2ΩΣ)  (where Ω is the rotation rate, κ is the epicyclic frequency and Σ is the surface density), the corotation resonance can either enhance or diminish the super-reflectivity, and this can be understood in terms of the location of the Rossby wave zone relative to the corotation radius. Our results provide the explicit conditions (in terms of disc thickness, rotation profile and vortensity gradient) for which super-reflection can be achieved. Global overstable disc modes may be possible for discs with super-reflection at the corotation barrier.  相似文献   

14.
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15.
A semi-analytic method is presented for solving for the radial and vertical structures of an accretion disc, with a magnetically channelled wind flowing from its surfaces. Both magnetic and turbulent viscous effects are taken into account, and the essential wind properties are related to the disc structure. The angular momentum removed by the wind plays a major part in driving the inflow through the disc, with photospheric temperatures being sufficient to generate the required wind mass flux. The magnetic field is generated by an αω-dynamo, but the method of solution should have application with other magnetic field sources. Self-consistent disc-wind solutions result, with rms turbulent Mach numbers which are in good agreement with those found in simulations of turbulence generated from magnetic shearing instabilities.  相似文献   

16.
We investigate the growth or decay rate of the fundamental mode of even symmetry in a viscous accretion disc. This mode occurs in eccentric discs and is known to be potentially overstable. We determine the vertical structure of the disc and its modes, treating radiative energy transport in the diffusion approximation. In the limit of very long radial wavelength, an analytical criterion for viscous overstability is obtained, which involves the effective shear and bulk viscosity, the adiabatic exponent, and the opacity law of the disc. This differs from the prediction of a two-dimensional model. On shorter wavelengths (a few times the disc thickness), the criterion for overstability is more difficult to satisfy because of the different vertical structure of the mode. In a low-viscosity disc a third regime of intermediate wavelengths appears, in which the overstability is suppressed as the horizontal velocity perturbations develop significant vertical shear. We suggest that this effect determines the damping rate of eccentricity in protoplanetary discs, for which the long-wavelength analysis is inapplicable and overstability is unlikely to occur on any scale. In thinner accretion discs and in decretion discs around Be stars overstability may occur only on the longest wavelengths, leading to the preferential excitation of global eccentric modes.  相似文献   

17.
A new theory of eccentric accretion discs is presented. Starting from the basic fluid-dynamical equations in three dimensions, I derive the fundamental set of one-dimensional equations that describe how the mass, angular momentum and eccentricity vector of a thin disc evolve as a result of internal stresses and external forcing. The analysis is asymptotically exact in the limit of a thin disc, and allows for slowly varying eccentricities of arbitrary magnitude. The theory is worked out in detail for a Maxwellian viscoelastic model of the turbulent stress in an accretion disc. This generalizes the conventional alpha viscosity model to account for the non-zero relaxation time of the turbulence, and is physically motivated by a consideration of the nature of magnetohydrodynamic turbulence. It is confirmed that circular discs are typically viscously unstable to eccentric perturbations, as found by Lyubarskij, Postnov & Prokhorov, if the conventional alpha viscosity model is adopted. However, the instability can usually be suppressed by introducing a sufficient relaxation time and/or bulk viscosity. It is then shown that an initially uniformly eccentric disc does not retain its eccentricity as had been suggested by previous analyses. The evolutionary equations should be useful in many applications, including understanding the origin of planetary eccentricities and testing theories of quasi-periodic oscillations in X-ray binaries.  相似文献   

18.
Using smoothed particle hydrodynamics, we numerically simulate steady-state accretion discs for cataclysmic variable dwarf novae systems that have a secondary-to-primary mass ratio  0.35 ≤ q ≤ 0.55  . After these accretion discs have come to quasi-equilibrium, we rotate each disc out of the orbital plane by  δ= (1, 2, 3, 4, 5 or 20)°  to induce negative superhumps. For accretion discs tilted  5°  , we generate light curves and associated Fourier transforms for an atlas on negative superhumps and retrograde precession. Our simulation results suggest that accretion discs need to be tilted more than 3° for negative superhumps to be statistically significant. We also show that if the disc is tilted enough such that the gas stream strikes a disc face, then a dense cooling ring is generated near the radius of impact.
In addition to the atlas, we study these artificially tilted accretion discs to find the source to negative superhumps. Our results suggest that the source is additional light from innermost disc annuli, and this additional light waxes and wanes with the amount of gas stream overflow received as the secondary orbits. The nodes, where the gas stream transitions from flowing over to under the disc rim (and vice versa), precess in the retrograde direction.  相似文献   

19.
In this paper we present a fully relativistic approach to modelling both the continuum emission and the reflected fluorescent iron line from a primary X-ray source near a Kerr black hole. The X-ray source is located above an accretion disc orbiting around the black hole. The source is assumed to be a static point source located on an arbitrary position above the disc, on or off the axis of rotation. We carry out Monte Carlo simulations in order to estimate the iron line spectrum as well as its equivalent width. Because of the gravitational lensing effect, an enhancement of the iron line is expected when the primary source is located close to the central black hole. We find that for a source located on the axis of rotation the enhancement is relatively modest. An observer at inclination 30° would measure an equivalent width of ∼300 eV in the extreme case of a maximally rotating black hole and a source located at height 1.5 gravitational radii from the centre. This corresponds to an equivalent width enhancement factor of about 2 compared with the classical value where no lensing effect comes into play. However, when allowing the source to be located off the axis of rotation, much stronger enhancement can be obtained. In the extreme case of a maximally rotating black hole and a source located just above the approaching side of the disc, an observer at inclination 30° could measure an equivalent width as high as ∼1.5 keV (i.e., ∼10 times the classical value). We also find that observers located at high inclination angles observe a stronger line than observers at low inclination angles.  相似文献   

20.
In addition to the scalar Shakura–Sunyaev α ss turbulent viscosity transport term used in simple analytic accretion disc modelling, a pseudo-scalar transport term also arises. The essence of this term can be captured even in simple models for which vertical averaging is interpreted as integration over a half-thickness and each hemisphere is separately studied. The additional term highlights a complementarity between mean field magnetic dynamo theory and accretion disc theory treated as a mean field theory. Such pseudo-scalar terms have been studied, and can lead to large-scale magnetic field and vorticity growth. Here it is shown that vorticity can grow even in the simplest azimuthal and half-height integrated disc model, for which mean quantities depend only on radius. The simplest vorticity growth solutions seem to have scales and vortex survival times consistent with those required for facilitating planet formation. In addition, it is shown that, when the magnetic back-reaction is included to lowest order, the pseudo-scalar driving the magnetic field growth and that driving the vorticity growth will behave differently with respect to shearing and non-shearing flows: the former pseudo‐scalar can more easily reverse sign in the two cases.  相似文献   

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