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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
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The instability of a supercritical Taylor‐Couette flow of a conducting fluid with resting outer cylinder under the influence of a uniform axial electric current is investigated for magnetic Prandtl number Pm = 1. In the linear theory the critical Reynolds number for axisymmetric perturbations is not influenced by the current‐induced axisymmetric magnetic field but all axisymmetric magnetic perturbations decay. The nonaxisymmetric perturbations with m = 1 are excited even without rotation for large enough Hartmann numbers (“Tayler instability”). For slow rotation their growth rates scale with the Alfvén frequency of the magnetic field but for fast rotation they scale with the rotation rate of the inner cylinder. In the nonlinear regime the ratio of the energy of the magnetic m = 1 modes and the toroidal background field is very low for the non‐rotating Tayler instability but it strongly grows if differential rotation is present. For super‐Alfv´enic rotation the energies in the m = 1 modes of flow and field do not depend on the molecular viscosity, they are almost in equipartition and contain only 1.5 % of the centrifugal energy of the inner cylinder. The geometry of the excited magnetic field pattern is strictly nonaxisymmetric for slow rotation but it is of the mixed‐mode type for fast rotation – contrary to the situation which has been observed at the surface of Ap stars. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law discs. Although the cut-out discs are remarkably stable to bisymmetric perturbations, they are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilizing influence. A physical mechanism for the generation of the one-armed instabilities is put forward. Incoming trailing waves are reflected as leading waves at the inner cut-out, thus completing the feedback for the swing-amplifier. Growing three-armed and four-armed modes occur only at very low temperatures. However, neutral m = 3 and m = 4 modes are possible at higher temperatures for some discs. The rotation curve index β has a marked effect on stability. For all azimuthal wavenumbers, any unstable modes persist to higher temperatures and grow more vigorously if the rotation curve is rising (β < 0) than if the rotation curve is falling (β > 0). If the central regions or outer parts of the disc are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law discs possess a number of unusual stability properties. There is no natural time-scale in the self-consistent disc. If a mode is admitted at some pattern speed and growth rate, then it must be present at all pattern speeds and growth rates. Our analysis — although falling short of a complete proof — suggests that such a two-dimensional continuum of non-axisymmetric modes does not occur and that the self-consistent power-law discs admit no global non-axisymmetric normal modes whatsoever. Without reflecting boundaries or cut-outs, there is no resonant cavity and no possibility of unstable growing modes. The self-consistent power-law discs certainly admit equi-angular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes. 相似文献
5.
The nonaxisymmetric Tayler instability of toroidal magnetic fields due to axial electric currents is studied for conducting incompressible fluids between two coaxial cylinders without endplates. The inner cylinder is considered as so thin that the limit of Rin → 0 can be computed. The magnetic Prandtl number is varied over many orders of magnitudes but the azimuthal mode number of the perturbations is fixed to m = 1. In the linear approximation the critical magnetic field amplitudes and the growth rates of the instability are determined for both resting and rotating cylinders. Without rotation the critical Hartmann numbers do not depend on the magnetic Prandtl number but this is not true for the corresponding growth rates. For given product of viscosity and magnetic diffusivity the growth rates for small and large magnetic Prandtl number are much smaller than those for Pm = 1. For gallium under the influence of a magnetic field at the outer cylinder of 1 kG the resulting growth time is 5 s. The minimum electric current through a container of 10 cm diameter to excite the instability is 3.20 kA. For a rotating container both the critical magnetic field and the related growth times are larger than for the resting column (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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The stability of a plane-stratified slab of perfectly conducting, rotating, compressible, inviscid plasma accelerated by a magnetic field is considered. Exact solutions for the growth rates of the unstable modes are determined for a -law gas when the undisturbed equilibrium is an isothermal atmosphere of semi-infinite extent with no frozen-in field. It is shown that the rotation has no effect on the region of unstable modes which has wavelengths long compared with the atmospheric scale height. On the other side, the growth rates in the presence of rotation are less than those in the absence of rotation for unstable modes. 相似文献
8.
Tidally forced viscous heating in a partially molten Io 总被引：1，自引：0，他引：1
We investigate tidal dissipative heating in two different models of Io. The partially molten asthenosphere model consists of a rigid inner core and a thin (less than 40 km thick) partially molten “decoupling” layer (asthenosphere) surrounded by an elastic lithosphere. In the partially molten interior model the interior beneath the lithosphere is partially molten throughout. The partially molten region in each model assumed to possess negligible shear strength and to be characterized by a Newtonian viscosity. Tidal deformation and dissipation in the core of the thin asthenosphere model are assumed negligible. Fluid in the viscous layers is forced to circulate by the tidal distortion of the outer shell, modeled here as a sinusoidal variation with time of the distortion amplitude. As a result, heat is generated in the fluid by viscous dissipation. There are two heating mechanisms in our models: “elastic” dissipation in the lithosphere ∞ 1/Q and viscous dissipation in the partially molten region. Numerical calculatons are carried out for a 90-km-thick lithosphere with Q = 100. This thickness maximizes dissipation in a decoupled lithosphere; other reasonable values of lithosphere thickness do not alter our conclusions. Under the constraint that total dissipation equals the observed radiated heat loss we derived the iscosity of the partially molten region in each model. We a posteriori evaluate the assumption that the lithosphere is decoupled from the interior by calculating the distortion of an elastic shell due to the viscous stresses on the lower surface of the outr shell. If the interior viscosity is such that the total dissipation is equal to the observed heat flux from Io, viscous stresses produce negligible distortion of a 90-km-thick shell. This validates the assumption of a decoupled shell. The derived viscosity for both models is characteristic of a partially molten rock. In the thin asthenosphere model the derived viscosity is so low that a very high degree of partial melt is necessary, about 40% crystal fraction in a 400-km-thick asthenosphere and about 0% in a 1-km-thick asthenosphere. In the partially molten interior model the derived viscosity corresponds to a magma with about 60% crystals. Consideration of convective efficiencies demonstrates the plausibility of a stable thermal steady state for both models. A significant portion (75% for Q = 100) of Io's tidal heating can be the result of viscous dissipation in a partially molten region that decouples the outer shell from the interior. The partially molten layer can be considered a “global magma ocean”. 相似文献
9.
A. I. Chugunov 《Monthly notices of the Royal Astronomical Society》2006,369(1):349-354
We study eigenmodes of acoustic oscillations of high multipolarity l ∼ 100–1000 and high frequency (∼100 kHz), localized in neutron star envelopes. We show that the oscillation problem is self-similar. Once the oscillation spectrum is calculated for a given equation of state (EOS) in the envelope and given stellar mass M and radius R , it can be rescaled to a star with any M and R (but the same EOS in the envelope). For l ≳ 300, the modes can be subdivided into the outer and inner ones. The outer modes are mainly localized in the outer envelope. The inner modes are mostly localized near the neutron drip point, being associated with the softening of the EOS after the neutron drip. We calculate oscillation spectra for the EOSs of cold-catalyzed and accreted matter and show that the spectra of the inner modes are essentially different. A detection and identification of high-frequency pressure modes would allow one to infer M and R and determine also the EOS in the envelope (accreted or ground state) providing a new, potentially powerful method to explore the main parameters and internal structure of neutron stars. 相似文献
10.
The eigen-vibrational frequencies of Xiong Da-run's nonlocal and local convection models of solar envelope are calculated and compared. The differences between the observational and theoretical vibrational frequencies are less than 1%. They can be divided into two isolated groups. For modes with l ≥ 60, all the differences between observed and theoretical eigen-vibrational frequencies are distributed in a narrow and inclined belt in the (Δv ≈ v)-diagram. This shows that the theoretical model of solar convective region can approximately reflect the intrinsic structure of the sun in the region of r = (0.70–0.95)R. The discrepancies between the theoretical and observational frequencies come from the outer layers. For modes with l < 60, the theoretical vibrational frequency is smaller than the observational one. This implies that the temperature of the upper part of the convectively unstable region is rather low. The frequency difference is more dispersed in the local convection model than in the nonlocal convection model. For the intermediate- and low-frequency ranges (v < 3000), the difference between the two models is small, while for the high-frequency range (v ≥ 3000) the frequency in the local model is higher than in the nonlocal model. This means that the temperature of the radiation region beneath the convective region is higher in the local convection model than in the nonlocal convection model. The nonlocal model is nearer to the observation than the local model. 相似文献
11.
New models for the interiors of Io, Ganymede, and Callisto are proposed. The model of Io consists of a thin, high-rigidity outer layer separated from a solid interior by a thin, molten or partially molten shell. The modulus of rigidity of the outer layer must be at least 100 times larger than that of the underlying partially molten shell. These layers have thicknesses of order 100 km or less. The near-surface partially molten layer was most likely produced early in Io's history as a consequence of accretional heating; enhanced tidal heating in the outer rigid layer has kept the underlying region partially molten to the present day. The model of Ganymede consists of an ice outer layer, a shell of undifferentiated, primordial ice-silicate mixture, and a rock core. Accretional heating is responsible for melting the ice in the outer layers of Ganymede's initially homogeneous ice-silicate interior. Most of the rock in this outer layer accumulates in a shell on top of Ganymede's early cold and rigid central region; the water in the outer layer quickly refreezes. Heating of the undifferentiated region by the decay of radioactive elements in the silicate fraction would gradually warm it and reduce its viscosity. The rock layer would become gravitationally unstable and sink through the undifferentiated materials to form a rock core. Callisto's heavily cratered surface strongly suggests that relatively little, if any, ice-rock differentiation has occured in its interior. 相似文献
12.
Yu. V. Vandakurov 《Solar physics》1975,45(2):501-520
This paper is a continuation of the author's work on stellar convection (Vandakurov, 1975a; hereafter referred to as Paper I). The approximate equations for convective perturbations in Paper I are somewhat corrected and generalized to include both nonlinear terms and possible variations in molecular weight. A crude estimate of the nonlinear terms is given by means of an expansion of the solution in powers of the perturbation amplitude. We assume that only the most rapidly growing unstable modes are of significance and that the initial kinetic energy of each independent mode is the same. An expansion in powers of the angular velocity is also performed. (This means that some upper stellar layers with small, but not very small, superadiabaticity are considered.) It is shown that an azimuth-averaged azimuthal force is created by the unstable perturbations. In particular, it is most likely that in the upper part of any stellar convection envelope the rigid rotation is nonequilibrious. A simple formula for the above azimuthal force is derived in the case of a latitudedependent angular velocity and a small viscosity of the medium. If the perturbed characteristic scaleheight is sufficiently small, the azimuthal force created by the most unstable modes is equivalent to a viscous force, but with a negative viscosity coefficient. In the approximation under consideration, the heat flux is spherically symmetric. 相似文献
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14.
H. Salo 《Earth, Moon, and Planets》1984,30(2):113-128
Steady-state solutions for the optical thickness of Saturn's rings are studied in terms of Hämeen-Anttila's (1983) theory of bimodal gravitating systems. The elastic properties of particles determine the behaviour of the rarefied mode (gaps), while the dense mode (ringlets) depends on the size and the internal density of the particles. In the outer parts of the rings the dense mode is unstable against the growth of gravitational perturbations. Inside the Roche distance this produces only very narrow ring-shaped configurations with helical orbits around them, and the system is not destroyed. The outer boundary of the rings corresponds to the distance beyond which the gravitational instability transforms the dense mode into strictly local condensations (moons). The inner boundary of the ring system is caused by the absence of dense mode near Saturn. The rarefied mode is stable in a larger region. 相似文献
15.
P. J. Luyten 《Astrophysics and Space Science》1988,141(1):27-43
The oscillations and stability of a homogeneous self-gravitating rotating cylinder in a toroidal magnetic field are investigated. It is assumed that the field is proportional to the distance to the axis of the cylinder. We show the existence of four infinite discreta spectra of magnetic (or rotational) modes. Rotation stabilizes the magneticm=1 instability. The magnetic field decreases the growth rate of rotational instability and reduces the interval of unstable wavenumbers. Ifm=1, instability always occurs with the exception of the equipartition state. Ifm>1, the instability can be suppressed by a sufficiently large magnetic field. Resistivity decreases the growth rate of magnetic instability, but increases the growth rate of rotational instability. For zero wavenumber perturbations secular instability occurs due to the action of resistivity before a neutral point is attained where a second secular instabiliity initiates due to the action of resistivity. 相似文献
16.
The problem of steady-state accretion to nonrotating black holes is examined. Advection is included and generalized formulas
for the radiation pressure in both the optically thick and thin cases are used. Special attention is devoted to models with
a high accretion rate. Global solutions for accretion disks are studied which describe a continuous transition between an
optically thick outer region and an optically thin inner region. It is shown that there is a maximum disk temperature for
the model with a viscosity parameter α = 0.5. For the model with α = 0.1, no optically thin regions are found to exist for
any accretion rate. 相似文献
17.
D. J. Saikia C. Konar V. K. Kulkarni 《Monthly notices of the Royal Astronomical Society》2006,366(4):1391-1398
We report the discovery of a double–double radio galaxy (DDRG), J0041+3224, with the Giant Metrewave Radio Telescope (GMRT) and subsequent high-frequency observations with the Very Large Array (VLA). The inner and outer doubles are aligned within ∼4° and are reasonably collinear with the parent optical galaxy. The outer double has a steeper radio spectrum compared to the inner one. Using an estimated redshift of 0.45, the projected linear sizes of the outer and inner doubles are 969 and 171 kpc, respectively. The time-scale of interruption of jet activity has been estimated to be ∼20 Myr, similar to other known DDRGs. We have compiled a sample of known DDRGs, and have re-examined the inverse correlation between the ratio of the luminosities of the outer to the inner double and the size of the inner double, l in . Unlike the other DDRGs with l in ≳ 50 kpc , the inner double of J0041+3224 is marginally more luminous than the outer one. The two DDRGs with l in ≲ few kpc have a more luminous inner double than the outer one, possibly due to a higher efficiency of conversion of beam energy as the jets propagate through the dense interstellar medium. We have examined the symmetry parameters and found that the inner doubles appear to be more asymmetric in both its armlength and its flux density ratios compared to the outer doubles, although they appear marginally more collinear with the core than the outer double. We discuss briefly the possible implications of these trends. 相似文献
18.
Classical trans-Neptunian objects (TNOs) are believed to represent the most dynamically pristine population in the trans-Neptunian
belt (TNB) offering unprecedented clues about the formation of our Solar System. The long term dynamical evolution of classical
TNOs was investigated using extensive simulations. We followed the evolution of more than 17000 particles with a wide range
of initial conditions taking into account the perturbations from the four giant planets for 4 Gyr. The evolution of objects
in the classical region is dependent on both their inclination and semimajor axes, with the inner (a<45 AU) and outer regions (a>45 AU) evolving differently. The reason is the influence of overlapping secular resonances with Uranus and Neptune (40–42 AU)
and the 5:3 (a∼
∼42.3 AU), 7:4 (a∼
∼43.7 AU), 9:5 (a∼
∼44.5 AU) and 11:6 (a∼
∼ 45.0 AU) mean motion resonances strongly sculpting the inner region, while in the outer region only the 2:1 mean motion
resonance (a∼
∼47.7 AU) causes important perturbations. In particular, we found: (a) A substantial erosion of low-i bodies (i<10°) in the inner region caused by the secular resonances, except those objects that remained protected inside mean motion
resonances which survived for billion of years; (b) An optimal stable region located at 45 AU<a<47 AU, q>40 AU and i>5° free of major perturbations; (c) Better defined boundaries for the classical region: 42–47.5 AU (q>38 AU) for cold classical TNOs and 40–47.5 AU (q>35 AU) for hot ones, with i=4.5° as the best threshold to distinguish between both populations; (d) The high inclination TNOs seen in the 40–42 AU region
reflect their initial conditions. Therefore they should be classified as hot classical TNOs. Lastly, we report a good match
between our results and observations, indicating that the former can provide explanations and predictions for the orbital
structure in the classical region. 相似文献
19.
A horizontal magnetic field if increasing in strength downwards can cause a horizontal layer of electrically conducting fluid to become unstable, a phenomenon known as ‘magnetic buoyancy’, and sometimes thought to have relevance to magnetic A stars, and to sunspot creation. Analyses that assume infinite thermal and electrical conductivities (and zero viscosity) predict that modes of zero horizontal wave-length, in the direction perpendidular to the field, are maximally unstable but are stabilised by even small Coriolis forces. It is shown here, however, that when proper allowance is made for the finite (though large) conductivities of the fluid the layer may experience a ‘conductive instability’ that grows on the ohmic time-scale and is maximally unstable to a mode of non-zero horizontal extent. 相似文献
20.
Peter G. Martin 《Astrophysics and Space Science》1970,7(1):119-138
A polytropic theory for investigating the structure of rapidly rotating close binary systems is developed on the basis of the works of Chandrasekhar (1933) and Monaghan and Roxburgh (1965). In this method each component is divided into an inner and outer region; it is shown that the inner region is the interior of the Emden sphere. Solutions for the interior and exterior potentials and densities are found, consistent to the seventh power of the ratio of the undistorted radius (a) to the separation (R); i.e.(a/R)7.The surface, surface gravity and potential are found. These results are used to discuss the critical configurations and contact equipotentials, and the existence of semi-detached and contact binary systems. The theory is compared to previous work, in particular the case of rotation alone and the Roche model. 相似文献