共查询到20条相似文献，搜索用时 62 毫秒
1.
M. Goossens 《Astrophysics and Space Science》1976,44(2):397-404
A perturbation method has been applied for the determination of the frequencies of the linear and adiabatic oscillations of a gaseous polytropic configuration pervaded by a purely toroidal magnetic field. The influence of a toroidal magnetic field on the frequencies of the different types of spheroidal oscillation modes is discussed. 相似文献
2.
The effect of a weak magnetic field on the adiabatic radial and non-radial oscillations of a stellar configuration is studied by means of a perturbation method. Special attention is devoted to the perturbation of the oscillation frequencies resulting from the change of the boundary conditions caused by the magnetic field. This change is related to the fact that the introduction of a magnetic field removes the singularity at the surface of the equilibrium configuration. The perturbation method is applied to Ferraro's model and the influence of a magnetic field on the frequencies of the different types of oscillation modes is discussed. 相似文献
3.
M. Goossens 《Astrophysics and Space Science》1977,52(1):3-10
The frequencies of the linear and adiabatic oscillations of a gaseous polytrope with a poloidal magnetic field are determined with the aid of a perturbation method. The influence of the poloidal magnetic field on the different types of spheroidal oscillation modes is discussed. The poloidal magnetic field generally strengthens the stability of the oscillation modes and this effect is the largest in the case of the non-radialp-modes. 相似文献
4.
M. Goossens 《Astrophysics and Space Science》1976,39(1):9-18
The frequencies of the linear and adiabatic oscillations of Prendergast's model are determined with the aid of a perturbation method. The influence of the magnetic field on the frequencies of the different types of spheroidal oscillation modes is discussed. 相似文献
5.
A. R. Garlick 《Astrophysics and Space Science》1982,84(1):205-223
As a paradigm for various explosive processes in the interstellar medium we consider the problem of an adiabatic explosion into a uniform magnetic field which is frozen to the gas. A typical numerical run is described and reveals the following features. The outer shock becomes oblate with respect to the field lines whereas the inner hot gas prolate density and temperature contours. During the later stages the shock weakens and the explosion comes into equilibrium with the interstellar medium. The dominant feature at this stage is a concentration of accelerated material at each pole. We then try to interpret this analytically, considering the magnetic field as a small perturbation to a spherical explosion. This enables us to derive a formula for the eccentricity, which is proportional tot
6/5. However, the linear perturbation is singular at the centre and needs to be matched to a self-similar flow there, for which we give an approximation. This similarity solution is eventually important outside the region occupied by the material initially responsible for the explosion. We give some discussion of the various asymptotic regimes involved. 相似文献
6.
Unrestricted second-order tensor virial equations for linear oscillations of magnetic configurations
M. Goossens 《Astrophysics and Space Science》1979,60(2):401-421
This paper deals with the second-order tensor virial equations for the linear oscillations of a gaseous mass in the presence of a magnetic field. It is shown that the commonly used linearized versions of the tensor virial equations are restricted integral equations that incorporate the linearized equation of motion but not the boundary condition. These restricted equations only allow trial functions that fulfil the boundary condition and are of limited practical value.The unrestricted variational principle for the linear oscillations of a magnetic configuration is used to derive a more general formulation of the second-order tensor virial equations so that the linear trial function i =X
ij
x
j can be used to study the oscillations of a configuration with a magnetic field that extends in the exterior vacuum. The unrestricted virial equations have been applied to Ferraro's model and approximate results for the eigenfrequencies and eigenfunctions have been obtained for nine oscillation modes. 相似文献
7.
A good method of finding the magnetic field above an active region from the normal field at the photosphere in the linear force-free field model is the one by Chiu and Hilton [1]. In its previous applications, however, the eigenfunctions that appear in the problem were simply discarded for lack of a practical way of their determination. In this paper we examine the effect of the eigenfunctions on the field configuration in the solution. We propose a method of estimating the eigenfunctions from Hα photographs and hence to get a more realistic solution. 相似文献
8.
M. Goossens 《Astrophysics and Space Science》1972,16(3):386-404
A generalization of the perturbation method is applied to the problem of the radial and the non-radial oscillations of a gaseous star which is distorted by a magnetic field. An expression is derived for the perturbation of the oscillation frequencies due to the presence of a weak magnetic field when the equilibrium configuration is a spheroid. The particular application to the homogeneous model with a purely poloidal field inside, due to a current distribution proportional to the distance from the axis of symmetry, and a dipole type field outside is considered in detail. The main result is that the magnetic field has a large and almost stabilizing effect on unstableg-modes, particularly on higher order modes. With the considered magnetic field the surface layers appear to have a large weight. 相似文献
9.
The differential equations describing stellar oscillations are transformed into an algebraic eigenvalue problem. Frequencies of adiabatic oscillations are obtained as the eigenvalues of a banded real symmetric matrix. We employ the Cowling-approximation, i.e. neglect the Eulerian perturbation of the gravitational potential, and, in order to preserve selfadjointness, require that the Eulerian pressure perturbation vanishes at the outer boundary. For a solar model, comparison of first results with results obtained from a Henyey method shows that the matrix method is convenient, accurate, and fast. 相似文献
10.
A perturbation method is derived forr-modes in a slowly and uniformly rotating star. In contrast to previous studies, the perturbation of the gravitational potential is included in the perturbation method.On the assumption that the effects of the centrifugal force are taken into account in the equilibrium model up to the second order in the angular velocity, an eigenvalue problem of sixth-order in the radial coordinate is derived that allows one to determine the zeroth-order toroidal displacement field and the third-order term in the expansion of the eigenfrequency. Furthermore, another eigenvalue problem is derived that governs the first-order toroidal displacement field and the fourth-order term in the expansion of the eigenfrequency. This second eigenvalue problem is also of the sixth-order in the radial coordinate.It is shown that the third-order term in the expansion of the eigenfrequency is real, and that the fourth-order term is zero. 相似文献
11.
S. P. S. Anand 《Astrophysics and Space Science》1972,15(3):415-425
The theory for investigating the equilibrium and stability of a uniformly rotating gaseous system with a prevalent magnetic field is developed by using the virial tensor approach. Most of the discussion in this paper depends on the assumption that on the surface of the system, the magnetic field is zero. In Appendix A, however, we have considered the case in which the surface magnetic field is non-zero.We have obtained the nine modes of oscillations, grouped into the transverse shear, toroidal and pulsation modes. From this analysis have also found the conditions under which the sequence of a uniformly rotating axially symmetric configuration in the presence of a magnetic field should have a point of bifurcation, that is, a point where objects with genuine triplanar symmetry branch off. This condition is also generalized in the Appendix to include the effects of differential rotation and non-zero surface magnetic field.Applications to the cosmogonic fission problem, the study of the pulsation of rotating magnetic stars and some radio astrophysical problems are briefly discussed. 相似文献
12.
This paper concerns a model problem illustrating the techniques needed to analyze weakly nonlinear oscillator systems wherein two small divisors (resonances) may occur separately or simultaneously. The method of multiple scales in combination with singular perturbation methods is used to construct a uniformly valid asymptotic solution to the proposed model equation. It is shown that matching is necessary in order to establish a composite solution uniformly valid for the entire phase plane. The model equation does not encompass the class of problems where occurrence of two simultaneous small divisors leads to Kolmogorov-Arnol'd-Moser amplitude instability.This work was supported in part by the National Science Foundation under NSF Grant Number GP-32030. 相似文献
13.
Mário J. P. F. G. Monteiro 《Astrophysics and Space Science》2008,316(1-4):121-127
The Porto Oscillation Code (posc) has been developed in 1995 and improved over the years, with the main goal of calculating linear adiabatic oscillations for models of solar-type stars. It has also been used to estimate the frequencies and eigenfunctions of stars from the pre-main sequence up to the sub-giant phase, having a mass between 0.8 and 4 solar masses. The code solves the linearised perturbation equations of adiabatic pulsations for an equilibrium model using a second order numerical integration method. The possibility of using Richardson extrapolation is implemented. Several options for the surface boundary condition can be used. In this work we briefly review the key ingredients of the calculations, namely the equations, the numerical scheme and the output. 相似文献
14.
Oscillations of magnetic structures in the solar corona have often been interpreted in terms of magnetohydrodynamic waves.
We study the adiabatic magnetoacoustic modes of a prominence plasma slab with a uniform longitudinal magnetic field, surrounded
by a prominence – corona transition region (PCTR) and a coronal medium. Considering linear small-amplitude oscillations, we
deduce the dispersion relation for the magnetoacoustic slow and fast modes by assuming evanescentlike perturbations in the
coronal medium. In the system without PCTR, a classification of the oscillatory modes according to the polarisation of their
eigenfunctions is made to distinguish modes with fastlike or slowlike properties. Internal and external slow modes are governed
by the prominence and coronal properties, respectively, and fast modes are mostly dominated by prominence conditions for the
observed wavelengths. In addition, the inclusion of an isothermal PCTR does not substantially influence the mode frequencies,
but new solutions (PCTR slow modes) are present. 相似文献
15.
Klaus Jockers 《Solar physics》1968,3(4):603-610
The stability of the solar wind is studied in the case of spherical symmetry and constant temperature. It is shown that the stability problem must be formulated as a mixed initial and boundary-value problem in which are prescribed the perturbation values of velocity and density at an initial time and additionally the velocity perturbation at the base of the corona for all times. The solution is constructed by linear superposition of normal solutions, which contain the time only in an exponential factor. The stability problem becomes a singular eigenvalue problem for the amplitudes of the velocity and pressure perturbations, since additionally to the boundary condition at the base of the corona one must add the condition that the amplitudes behave regularly at the critical point. It is proved that only stable eigenvalues exist. 相似文献
16.
We compute the continuous part of the ideal-magnetohydrodynamic (ideal-MHD) frequency spectrum of a polar mountain produced by magnetic burial on an accreting neutron star. Applying the formalism developed by Hellsten & Spies, extended to include gravity, we solve the singular eigenvalue problem subject to line-tying boundary conditions. This spectrum divides into an Alfvén part and a cusp part. The eigenfunctions are chirped and anharmonic with an exponential envelope, and the eigenfrequencies cover the whole spectrum above a minimum ωlow . For equilibria with accreted mass 1.2 × 10−6 ≲ M a /M⊙ ≲ 1.7 × 10−4 and surface magnetic fields 1011 ≲ B * /G ≲ 1013 , ωlow is approximately independent of B * , and increases with M a . The results are consistent with the Alfvén spectrum excited in numerical simulations with the zeus-mp solver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than ∼100 Hz. The implications for gravitational-wave searches for low-mass X-ray binaries are considered briefly. 相似文献
17.
Tsutomu Tamao 《Planetary and Space Science》1978,26(12):1149-1159
Mechanism of flux modulations of energetic protons and electrons, associated with the long-period geomagnetic pulsations in the outer magnetosphere, is examined theoretically. In the first part, a linear perturbation theory of the guiding centre distribution function averaged over the bounce phase of an interacting particle is developed for the case of the three-dimensional magnetic oscillations with a sufficiently long period compared with the bounce time of the particle. Secondly we extend the formulation to include some effects of the perturbed drift orbit on the particle distribution such as the particle trapping in the wave field and the phase bunching process. The latter is important for the interaction with the coupling Alfvén mode of magnetic oscillations. Applying these results together with the basic characteristics of the coupling hydromagnetic oscillations in a non-uniform plasma, we discuss the possibilities for the observed particle flux modulations in two different cases, separately, i.e. flux oscillations due to the compressional magnetic perturbation and those from the nearly transverse magnetic variations. 相似文献
18.
19.
Jayanta Kar 《Astrophysics and Space Science》1987,133(1):29-44
The unrestricted second-order virial tensor formalism has been used to calculate the characteristic frequencies of linear adiabatic oscillations of a composite stellar model having an isothermal core and a polytropic envelope in presence of a weak poloidal magnetic field. The frequencies of the transverse shear mode and the nonradial pulsation mode for both a radiative and a convective envelope (corresponding to polytropic index 3 and 1.5, respectively) alongwith that of the toroidal mode for the radiative envelope get increased in presence of the magnetic field. However, the frequency of the toroidal mode for the convective envelope registers a decrease in presence of the field. The corrections to the various frequencies decrease with increasing values of the parameter characterizing the lowering of the core temperature in presence of the magnetic field. 相似文献
20.
S. Barcza 《Astrophysics and Space Science》1980,72(2):497-507
A new method is presented in a general form to solve the Schrödinger equation of helium-like ions. The wave function is expanded in terms of the eigenfunctions of a moving electron in the field of two Coulombic ions which are fixed in space. This makes the method similar to the Dirac perturbation theory (perturbation theory for time-dependent problems). In the present method an infinitely coupled system of infinitely many second-order ordinary differential equations must be solved instead of one second-order partial differential equation of three variables. The nature of the singular points and boundary conditions are discussed and some general relations are given which are useful for the numerical treatment. 相似文献