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1.
We show that the overall densityg() of asymptotic acoustic frequencies of a star obeys a Weyl lawg() D–1, whereD is the dimensionality of the oscillating stellar configuration. For realistic stars with a finite non-zero surface sound speed,D is equal to the actual dimensionality of the star,D=3. For formal models with a vanishing sound velocity at the surface, heuristic arguments lead to a dimensionality parameterD=4.5. The empirical frequencies of Eddington's standard model are found to be consistent with the latter distribution, with reasonable agreement already occurring in the low-frequency range > i 2× fundamental radial mode. We argue that real stars obey this 3.5-power law in some finite frequency interval i << f , f being a very high frequency critically depending on the surface sound velocity, while the full asymptotic law, withD=3, holds for > f .  相似文献   

2.
In this paper, a theoretical investigation is undertaken of the group travel-time for the Sun's pulses to travel from the source of the pulse to the solar surface. For mathematical simplicity, we consider a simple ionized model of the Sun that includes the thermal effect and rotation with uniform angular velocity. The expression for the group travel time gives two terms: the term arising from the linear theory which varies inversely to (2-)1/2 and the term introduced by the thermal effect which is inversely proportional to (2-)7/2. The thermal effect variation has been shown and an estimation of the temperature of the medium has been made. Furthermore, the velocity distribution and the amplitude of the magnetic field of the wave, arising from the damping of ionized particles, have been calculated.  相似文献   

3.
The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases 1 = 22 and 1 = 32. The motion is unstable for all the values of parameters q and A when 1 = 22 and the motion is unstable and stable depending upon the values of the parameters q and A when 1 = 32. Here q is the radiation parameter and A is the oblateness parameter.  相似文献   

4.
The problem of single Compton scattering is considered and the resulting spectrum, angular distribution and polarization of scattered photons in a general case are obtained. The inverse Compton scattering (ICS) for arbitrary energies of electronsE and photons 0 is investigated in detail. In the case of isotropically-distributed initial photons and relativistic electrons, a strong rise of the scattered spectrum near the upper edge takes place, starting from the values of the characteristic parameterb4E 010 (in units of mc2=1). The energy-loss rate of relativistic electrons due to ICS is calculated. It is shown that the relativistic electrons of the energiesE100 MeV, when scattering on the X-rays with 0~10KeV, transmit the dominant part of their energy to the photons which fall after scattering into the energy range of the electrons (100 MeV).The radiation spectrum of ICS, as well as the energy-losses of relativistic electrons distributed by power-lawE –, are calculated. The radiation spectrum reveals the power-law behaviour with the different indices in two limits: the dependence –(1)/2 at 01 gradually changes to –(+1) ln (0) law for 01.  相似文献   

5.
The recent discovery of localised intense magnetic fields in the solar photosphere is one of the major surprises of the past few years. Here we consider the theoretical nature of small amplitude motions in such an intense magnetic flux tube, within which the field strength may reach 2 kG. We give a systematic derivation of the governing expansion equations for a vertical, slender tube, taking into account the dependence upon height of the buoyancy, compressibility and magnetic forces. Several special cases (e.g., the isothermal atmosphere) are considered as well as a more realistic, non-isothermal, solar atmosphere. The expansion procedure is shown to give good results in the special case of a uniform basic-state (in which gravity is negligible) and for which a more exact treatment is possible.The form of both pressure and velocity perturbations within the tube is discussed. The nature of pressure perturbations depends upon a critical transition frequency, p , which in turn is dependent upon depth, field strength, pressure and density in the basic (unperturbed) state of the tube. At a given depth in the tube pressure oscillations are possible only for frequencies greater than p for frequencies below p exponentially decaying (evanescent) pressure modes occur. In a similar fashion the nature of motions within the flux tube depends upon a transition frequency, v . At a given depth within the tube vertically propagating waves are possible only for frequencies greater than v ; for frequencies below v exponentially decaying (evanscent) motions occur.The dependence of both v and p on depth is determined for each of the special cases, and for a realistic solar atmosphere. It is found that the use of an isothermal atmosphere, instead of a more realistic temperature profile, may well give misleading results.For the solar atmosphere it is found that v is zero at about 12 km above optical depth 5000= 1, thereafter rising to a maximum of 0.04 s–1 at some 600 km above 5000 = 1. Below 5000 = 1, in the convection zone, v has a maximum of 0.013 s–1. The transition frequency, p , for the pressure perturbations, is peaked at 0.1 s–1 just below 5000 = 1, falling to a minimum of 0.02 s–1 at about one scale-height deeper in the tube  相似文献   

6.
In our preceding paper {see [L. Sh. Grigorian and S. Gottlöber, Astrofizika (in press)]} we investigated a self-gravitating system consisting of a scalar field and a linear tensor field ik= ki with minimal coupling and with allowance for the action of vacuum polarization effects. In the present paper we investigate the case of a nonlinear tensor field ik. The action S () of the field ik is determined by the difference Rik — ik, where Rik is the space-time Ricci tensor and Rik is the analogous quantity constructed using the metric ik=gik+ik induced by ik ( is a free parameter). Here S () coincides with the previously known expression for the action of a linear field ik. Equations of motion are derived for ik in curved space-time. The energy-momentum metric tensor, determining the contribution of ik to the gravitational field equations, is calculated.Translated from Astrofizika, Vol. 39, No. 1, pp. 135–144, January-March, 1996.  相似文献   

7.
It is shown that bremsstrahlung from electrons with Lorentz factor 1 is suppressed for >p in a plasma with plasma frequency p compared with emission in vacuo. For p the ratio of the power emitted per unit frequency in the plasma to that in vacuo varies as 2.This suppression effect is analogous to the suppression of synchrotron radiation in a plasma (Razin-Tsytovich effect). It is argued that such suppression is a characteristic property of emission by relativistic particles in a plasma.  相似文献   

8.
The Hall effect on the unsteady hydromagnetic free-convection resulting from the combined effects of thermal and mass diffusion of an electrical-conducting liquid through a porous medium past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean skin friction, and mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Ekman numberE, and permeability parameterK * on the flow field are discussed with the help of graphs and tables.Nomenclature C p specific heat at constant pressure - C the species concentration inside the boundary layer - C w the species concentration at porous plate - C the species concentration of the fluid at infinite - C dimensionless species concentration - D chemical molecular diffusivity - E Ekman number - Ec Eckert number - g acceleration due to gravity - Gr Grashof number - Gm modified Grashof number - H 0 applied magnetic field - (J x, Jy, Jz) components of current density - M magnetic parameter - m Hall parameter - P Prandtl number - q m mean rate of heat transfer - Sc Schmidt number - t time - t dimensionless time - T temperature of fluid - T w temperature of the plate - T temperature of fluid at infinite - T dimensionless temperature - (u, v, w) components of the velocityq - w 0 suction velocity - (x, y, z) Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - * coefficient of thermal expansion with concentration - frequency - dimensionless frequency - k thermal conductivity - K * permeability parameter - dinematic viscosity - density of the fluid in the boundary layer - coefficient of viscosity - e magnetic permeability - angular velocity - electrical conductivity of the fluid - m mean skin friction - mn mean skin friction in the direction ofx - mv mean skin friction in the direction ofy  相似文献   

9.
We semi-quantitatively calculate the distribution of energy in frequency and angle emitted from a sheet of charges that are moving out relativistically along dipolar magnetic field lines originating near the magnetic polar caps of a rotating neutron star. The angular distribution is conical with the angle of maximum intensity varying with frequency as –1/4 for c 2 c /(R M 2), whereRM is the initial angular radius of the charge sheet at the surface of the star of radiusR. At higher frequencies the width of the angular cone remains constant. The radiation is linearly polarized with the polarization vector in the plane of the line of sight and the magnetic axis. A sheet of uniform charge density and finite thickness has a frequency spectrum that varies from –3/2 to –4 for c and c , respectively. These features are in good general agreement with the observed characteristics of the intensity, pulse shape, and frequency spectrum of the radio pulses from pulsars.Operated by Associated Universities, Inc., under contract with the National Science Foundation.  相似文献   

10.
Karlický  Marian 《Solar physics》2003,212(2):389-400
Using a 2-D MHD model, the magnetic field reconnection in the current sheet and corresponding plasma resonance lines (surfaces in 3-D), where the upper-hybrid frequency equals one of harmonics of the electron gyrofrequency, UH=(pe 2+Be 2)1/2=sBe (UH, pe, and Be are the upper hybrid, electron plasma, and cyclotron frequencies, respectively, and s is the integer harmonic number) are computed. Then at selected times and positions in the magnetic reconnection the spatial and time spectra of upper hybrid frequencies along the resonance lines are calculated. These spectra are discussed from the point of view of radio fine structures as narrowband dm-spikes, zebras, and lace bursts. It is shown that not only turbulent plasma outflows, suggested in the paper by Bárta and Karlický (2001), but also perturbed zones near the reconnection slow-mode shocks can be locations of the narrowband dm-spikes (and/or continua). Sources of the lace bursts (i.e. bursts with irregular lines) can be located in the reconnection space, too. On the other hand, the zebras (bursts with regular separations of zebra lines) need to be generated out of strongly perturbed reconnection areas.  相似文献   

11.
This paper is devoted to Force-Free Electromagnetic Oscillations in a constant magnetic field. A correction is made in the derivation of the basic equation. The paper confirms the predicted spectrum of frequencies, namely n = o (n + 1)1/2;n = 0, 1, 2, .... In addition it is suggested that hybrid frequency n = ( n 2 + H 2 )1/2 should be found in observational data.  相似文献   

12.
Two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid, past an infinite, vertical porous plate, is considered, when the flow, is subjected in the action of uniform transverse magnetic field. The magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids. Analytical expressions for the velocity field and temperature field are given, as well as for the skin friction and the rate of heat transfer for the case of the mean steady flow and for the unsteady one. The influence of the magnetic parameter,M, modified Grashof numberG c , Schmidt numberS c and frequency , on the flow field, is discussed with the help of graphs, when the plate is being cooled, by the free convection currents (G r ,E>0), or heated (G r ,E<0). A comparative study with hydrodynamic case (M=0) and the hydromagnetic one (M0) is also made whenever necessary.List of symbols B0 applied magnetic field - |B| amplitude of the skin friction - C concentration inside the boundary layer - C concentration in the free stream - C w concentration at the porous plate - C p specific heat at constant pressure - D diffusion coefficient - E Eckert number - g x acceleration due to gravity - G c modified Grashof number - G r Grashof number - M magnetic parameter - N u Nusselt number - P Prandtl number - |Q| amplitude of the rate of heat transfer - S c Schmidt number - T temperature of the fluid - T w temperature of the plate - T temperature of the fluid in the free stream - T r ,T i fluctuating parts of the temperature profile - u, v velocity components in thex, y directions - u dimensionless velocity in thex direction - u 0 mean steady velocity - u 1 unsteady part of the velocity - u r ,u i fluctuating parts of the velocity profile - U dimensionless free stream volocity - U 0 mean free stream velocity - v 0 suction velocity - x, y co-rodinate system Greek Symbols phase angle of the skin-friction - coefficient of volume expansion - * coefficient of expansion with concentration - phase angle of the rate of heat transfer - dimensionless co-ordinate normal to the plate - dimensionless temperature - 0 mean steady temperature - 1 unsteady part of temperature - k thermal conductivity - v kinematic viscocity - density of fluid in the boundary layer - density of fluid in the free stream - electrical conductivity of the fluid - skin friction - 0 mean skin friction - frequency - dimensionless frequency  相似文献   

13.
We obtain an approximate analytic solution of a set of nonlinear model -dynamo equations. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field, is incorporated into the model. To single out the effect of the Lorentz force on the -effect, the effect of the Lorentz force on the -effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo numberN. The amplitude is proportional toN–1, while the period is almost exactly the same as the dissipation time of the unstable mode [proportional toN; note the linear oscillation period is proportional toN/(N–1) which is quite different for the solar situation whereN1].  相似文献   

14.
Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density and an angular velocity . Self-similarity as a statement of the absence of scales implies that and can be written as=c 2/4Gr, =c/r, and demands that and be pure numbers.  相似文献   

15.
We investigate the stability of the triangular libration points when both the attracting bodies are radiating under the resonance conditions 1 = 22 and 32.  相似文献   

16.
We study near-Lagrange collinear configurations in the three-dimensional three-body problem, with arbitrary gravitating masses. A general method, previously developed for Coulombian systems, which provides a unique formalism for treating few-body systems close to the breakup threshold, has been employed to study the motion of three bodies both for bounded and unbounded configurations. The dependence of the triple-escape function on the small total energy E has been evaluated, as well as rovibronic configurations for bounded motion. An approximate characteristic constant is found for symmetrical systems, /, where and are the vertical libration mode and rotational mode angular frequencies, respectively, and is the threshold exponent. For equal-mass systems this constant acquires the value 1.05288.  相似文献   

17.
The two time variable method is used to investigate the stability of and the motion about the equilibrium point of an autonomous Hamiltonian system of two degrees of freedom when the HamiltonianH is indefinite and the relation between the frequencies 1 and 2 of the linearized system is 1 22. Also, the conditions for periodic orbits and the stability of these orbits are obtained.  相似文献   

18.
Nonlinear propagation of strong low-frequency waves, as emitted by pulsars or compact galactic nuclei at their rotation frequencies, in a magnetized plasma is investigated. It is shown that even rather small amplitude waves can drive electrons to ultrarelativistic energies. In the limit when the electrons are ultrarelativistic but the ions are immobile, two types of circularly polarized waves (i.e., ± modes) are excited. In the wave zone of the Crab pulsar, both the electric field ( 3 V m–1) and the wavelength (108 m) of the - mode are larger, by an order of magnitude, than those of the + wave mode. Both ± modes can become modulationally unstable due to their nonlinear interaction with density fluctuations induced by the electrostatic waves.  相似文献   

19.
The structure of strong shock waves in a thermally-radiating and electrically-conducting fluid is studied by method of asymptotic matching principle. It is assumed that upstream of the shock the gas is cold and does not radiate thermally while the Mach number (M) is very high so that after being shocked the gas now thermally radiates. The viscosity of the gas () depends on temperature (T) in the simple manner T where is a constant exponent. The problem is worthy of note in high-temperature phenomena in hypersonic flow.  相似文献   

20.
In this paper we have studied B-D theory and general scalar tensor theory of Gravitation for anisotropic cosmological model in the false vacuum state. The possibility of both exponential inflation and power function inflation are examined for constant or variable coupling parameter . Also asymptotic limit of the scalar field and are discussed.  相似文献   

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