Unstable non-radial modes in radial pulsators: theory and an example

We study the possibility of the excitation of non-radial oscillations in classical pulsating stars. The stability of an RR Lyrae model is examined through non-adiabatic non-radial calculations. We also explore stability in the presence of non-linear coupling between radial and non-radial modes of nearly identical frequency.   In our model, a large number of unstable low-degree (ℓ = 1,2) modes have frequencies in the vicinity of unstable radial mode frequencies. The growth rates of such modes, however, are considerably smaller than those of the radial modes. We also recover an earlier result that at higher degrees (ℓ = 6–12) there are modes trapped in the envelope with growth rates similar to those of radial modes.   Subsequently, monomode radial pulsation of this model is considered. The destabilizing effect of the 1:1 resonance between the radial mode and nearby non-radial modes of low degrees is studied, with the assumption that the excited radial mode saturates the linear instability of all other modes. The instability depends on the radial mode amplitude, the frequency difference, the damping rate of the non-radial mode, and the strength of the non-linear coupling between the modes considered. At the pulsation amplitudes typical for RR Lyrae stars, the instability of the monomode radial pulsation and the concomitant resonant excitation of some non-radial oscillation modes is found to be very likely.     

Nonresonant three-mode coupling as a model for double-mode pulsators

If one is only interested in the behaviour of a few longlived modes, the simplest model for the evolution to steady nonlinear stellar pulsation is nonresonant interaction. As the coupled-mode equations are generically not dependent upon a particular stellar model, qualitative ideas about the eventual evolution of mode energies give scenarios that depend mainly upon nonlinear coupling constants and linear growth rates. Two linearly unstable modes are considered in the presence of a representative stable or slave mode. One scenario models a double-mode pulsator, without it being necessary that all coupling constants be negative, if only the model is well behaved enough in excluding unbounded solutions and in avoiding finite amplitudes for the slave modes. The influence of driving on slave modes is then such that all slave modes ultimately decay away. Other scenarios show evolution to classic pulsators. A discussion is given of the modelling of a classic Cepheid in a mode which is not the linearly most unstable one. Findings of the present paper show the need for additional theoretical and numerical modelling and a cautious discussion thereof.     

The effects of the tidal force on shear instabilities in the dust layer of the solar nebula

The linear analysis of the instability due to vertical shear in the dust layer of the solar nebula is performed. The following assumptions are adopted throughout this paper: (1) The self-gravity of the dust layer is neglected. (2) One fluid model is adopted, where the dust aggregates have the same velocity with the gas due to strong coupling by the drag force. (3) The gas is incompressible. The calculations with both the Coriolis and the tidal forces show that the tidal force has a stabilizing effect. The tidal force causes the radial shear in the disk. This radial shear changes the wave number of the mode which is at first unstable, and the mode is eventually stabilized. Thus the behavior of the mode is divided into two stages: (1) the first growth of the unstable mode which is similar to the results without the tidal force, and (2) the subsequent stabilization due to an increase of the wave number by the radial shear. If the midplane dust/gas density ratio is smaller than 2, the stabilization occurs before the unstable mode grows largely. On the other hand, the mode grows faster by one hundred orders of magnitude, if this ratio is larger than 20. Because the critical density of the gravitational instability is a few hundreds times as large as the gas density, the hydrodynamic instability investigated in this paper grows largely before the onset of the gravitational instability. It is expected that the hydrodynamic instability develops turbulence in the dust layer and the dust aggregates are stirred up to prevent from settling further. The formation of planetesimals through the gravitational instabilities is difficult to occur as long as the dust/gas surface density ratio is equal to that for the solar abundance. On the other hand, the shear instability is suppressed and the planetesimal formation through the gravitational instability may occur, if dust/gas surface density ratio is hundreds times as large as that for the solar abundance.     

Alfvén-Jeans and Magnetosonic Modes in Multispecies Self-Gravitating Dusty Plasmas

Perpendicularly propagating electromagnetic waves in magnetized, multispecies, self-gravitating dusty plasmas are investigated in terms of their wave dispersion properties as well as with respect to their susceptibility to gravitational collapse. In particular, waves on the ordinary as well as extraordinary mode branches are considered. Within the one-dimensional propagation model employed, all modes except the ordinary mode produce density perturbations that can be unstable to gravitational collapse. The wavelengths that are unstable are comparable to the well-known Jeans length for a neutral gas/dust, but there are interesting modifications due to the presence of a magnetic field and charged particles. Furthermore, the effects of the gravitational coupling of a multicomponent plasma to a neutral dust are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

The radial–azimuthal instability of a hot two-temperature accretion disc with advection

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.     

Quantum and thermal phenomena in the matter-gravity system

The matter-gravity system is examined in a path integral approach for the case of conformal matter coupled to a Friedman-Robertson-Walker space time. In particular the case of gravitational potentials of interest in cosmology for which the universe tunnels from a small radius is examined. It is observed that in the presence of such gravitational horizons the universe evolves in a complex time and it is shown how a classical time and temperature emerge. Correspondingly, one will have compensating quantum and thermal fluctuations for the matter and gravity system and it is noted that the unstable mode of gravity corresponding to the universe tunneling into existence will be compensated by an analogous mode for matter corresponding to its creation. This last point is examined in a simple De Sitter model with conformal matter and a relation is found between the cosmological constant, the number of matter fields and the self coupling of matter responsable for its instability.     

The plasma radiation of flare kernels

We survey the mathematics of non-linear Hamiltonian oscillations with emphasis being laid on the more recently discovered Kolmogorov instability. In the context of radial adiabatic oscillations of stars this formalism predicts a Kolmogorov instability even at low oscillation energies, provided that sufficiently high linear asymptotic modes have been excited. Numerical analysis confirms the occurrence of this instability. It is found to show up already among the lowest order modes, although high surface amplitudes are then required (¦δr¦/R ～ 0.5 for an unstable fundamental mode - first harmonic coupling). On the basis of numerical evidence we conjecture that in the Kolmogorov unstable regime the enhanced coupling due to internal resonance effects leads to an equipartition of energy over all interacting degrees of freedom. We also indicate that the power spectrum of such oscillations is expected to display two components: A very broad band of overlapping pseudo-linear frequency peaks spread out over the asymptotic range, and a strictly non-linear l/f-noise type component close to the frequency origin. It is finally argued that the Kolmogorov instability is likely to occur among non-linearly coupled non-radial stellar modes at a surface amplitude much lower than in the radial case. This lends support to the view that this instability might be operative among the solar oscillations.     

Current-driven Alfvén waves in dusty magnetospheric plasmas

It is shown that the sheared flow of electrons and ions in the presence of heavy stationary dust gives rise to unstable Alfvén waves. The coupling of newly studied low frequency electrostatic current-driven mode with the electromagnetic Alfvén and drift waves is investigated. The instability conditions and the growth rates of both inertial and kinetic Alfvén waves are estimated. The theoretical model is applied to the night side boundary regions of Jupiter’s magnetosphere which contain positive dust. The growth rates increase with increase in sheared flow speed. In the nonlinear regime, both inertial and kinetic Alfvén waves form dipolar vortices whose speed and amplitude depend upon the magnitude of the zero-order current.     

太阳5分钟振荡的激发机制

1 引言 太阳5分钟振荡是上世纪1个重要的发现[1],它使得人们可以通过观测太阳表面的振动来探测其内部的结构,日震学已取得了巨大的进展,然而我们至今仍不了解其脉动的激发机制,它依然是1个存在争议的问题.太阳位于造父变星脉动不稳定区之外,所以大多数人都相信,由于对流的阻尼,太阳是脉动稳定的,太阳和太阳型恒星的振荡都是由所谓的湍流随机激发机制所激发[2-8].     

ULF pulsation mode coupling in the ionosphere and magnetosphere

The effect of realistic ionospheric Hall conductances on axisymmetric toroidal mode hydromagnetic wave resonances is investigated. The toroidal modes couple to evanescent poloidal modes near the ionospheres such that the composite modes resonate at the constant frequencies of the corresponding single-field-shell resonances for zero Hall conductance. A model for these composite modes is developed which has narrow but finite latitudinal resonance widths such as to make the modes valid solutions of the hydromagnetic equations. The modes also suggest that “shell” solutions can realistically describe such properties of real pulsations as frequency, damping, phase variation along the field-line and node-antinode behaviour at the ionospheres. Estimates of ionospheric coupling strength are obtained and compared with magnetospheric coupling strength. It is found that magnetospheric coupling dominates ionospheric coupling for any single non-axisymmetric mode. However, ionospherically coupled axisymmetric modes should be necessary components of the Fourier sum of modes required to model any real pulsation of low to moderate apparent azimuthal wave number.Estimates of the range of magnetospheric coupling strength are obtained for pulsations under a variety of conditions.     

The Radial-Azimuthal Instability of Gas-Pressure-Dominated Accretion Disk with Advection

The radial-azimuthal instability of gas-pressure-dominated accretion disk with advection is examined in this paper. We find that the including of very little advection has significant effects on two acoustic modes, which are no longer complex conjugates of each other. They increase the instability of the O-mode and damp that of the I-mode. We also find that when the azimuthal perturbations are considered, the stability properties of disk are different from that in pure radial perturbation case. The increase of azimuthal wave number will stabilize the acoustic modes but make the viscous mode more unstable and does not change the thermal mode very much for optically thin disk. The I-mode is more stable. The O-mode, viscous mode and thermal mode tend to become more unstable with the increase of azimuthal perturbation wavenumber for optically thick disk. For a geometrically slim, advection-dominated disk, the increasing of azimuthal perturbations make thermal mode more unstable and acoustic mode more stable. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mode coupling due to twisting of magnetic field lines

A new approach to the theory of mode coupling in an inhomogeneous, birefringent medium is used to treat mode coupling in a magnetized plasma with a twisted magnetic field. The twist introduces a resonance, corresponding to the rate of twisting being equal to the rate of generalized Faraday rotation. When this resonance occurs it introduces a new regime of strong mode coupling. The implications of this regime are discussed in connection with the long-standing problem in solar radiophysics that mode coupling appears to be stronger than theory implies, but no obvious resolution of the problem is found.     

The Influence of Guiding Field on Low-frequency Electromagnetic Instabilities in Collisionless Current Sheets

This work investigates the effect of guiding field on low-frequency electromagnetic instabilities in collisionless current sheets using the dispersion relation obtained in the collisionless and compressible magnetohydrodynamic model. The results in the following three cases show that the guiding field can strongly affect the 3-dimensional propagating disturbed waves. (1) On the middle plane of the current sheet (z = 0), if there is no guiding field, then no instability is observed. But if there a guiding field, then instability can take place. (2) Near the middle plane of the current sheet (z = 0.2), the current sheet becomes unstable. With increasing the intensity of the guiding field, the instability grows obviously. The wave mode may be whistler or low-hybrid wave. (3) Near the edge of the current sheet (z = 0.8), the guiding field exhibits no evident effect and the unstable wave mode is a quasi-parallel whistler wave.     

Dynamical instability of laminar axisymmetric flows of ideal compressible fluid

The instability of axisymmetric flows of inviscid compressible fluid with respect to two-dimensional infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. The compressibility is taken into account for a homentropic flow with an adiabatic index varying over a wide range. The problem has been solved for two angular velocity profiles of an initial axisymmetric flow. In the first case, a power-law rotation profile with a finite enthalpy gradient at the flow edges has been specified. For this angular velocity profile, we show that the instability of sonic and surface gravity modes in a nearly Keplerian flow, when a radially variable vorticity exists in the main flow, can be explained by the combined action of the Landau mechanism and mode coupling. We also show that including a radially variable vorticity makes the limiting exponent in the rotation law at which the unstable surface gravity modes vanish dependent on the fluid compressibility. In the second case, a Keplerian rotation law with a quasi-sinusoidal deviation has been specified in such a way that the enthalpy gradient vanished at the flow edges. We have found than the sonic modes are then stabilized and the flow is unstable only with respect to the perturbations that also exist in an incompressible fluid.     

Study of nonlinear interaction of waves through plasma-maser in magnetosphere plasma

A theoretical study is made on the generation mechanism of electrostatic Bernstein mode wave in the presence of electromagnetic Kinetic Alfven wave turbulence in magnetized inhomogeneous plasma on the basis of plasma-maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Kinetic Alfven wave turbulence. Because of the universal existence of the Kinetic Alfven waves in large-scale plasmas, the result has potential importance in space and astrophysical radiation process. The growth rate of the test high-frequency Bernstein mode wave is obtained with the involvement of spatial density gradient parameter. A comparative study on the role of density gradient in the generation of Bernstein mode on the basis of plasma-maser effect is presented.     

Magnetic resistivity and Hall currents effects on the stability of a self-gravitating plasma of varying density in variable magnetic field

The effect of Hall currents have been studied on the instability of a stratified layer of a self-gravitating finitely conducting plasma of varying density. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. The stability analysis has been carried out for longitudinal mode of wave propagation. The solution has been obtained through integral equation approach. The dispersion relation has been derived and solved numerically. It is found that both the Hall currents and finite conductivity have a destabilizing influence on the growth rate of the unstable mode of disturbance.     

Radial and nonradial pulsation of a rotating partially degenerate standard model

The effect of slow uniform rotation on the radial and nonradial modes of partially degenerate standard models has been investigated. For the case of the radial mode, it is shown that the destabilizing effect of slow uniform rotation reduces with increased central condensation of the model. However, it is found that the models with a strongly degenerate interior, become more unstable dynamically as a result of slow uniform rotation. Further, it is noted that the frequency of the nonradial modes of oscillation (Kelvin mode) increases due to the presence of rotation. Thus the period of radial modes of oscillation of a slowly uniformly rotating partially degenerate standard model are much larger than the corresponding periods of nonradial (Kelvin) modes.     

The effect of the lower ionosphere on hydromagnetic modes in the plasmasphere

Dimensionless resonant frequencies of hydromagnetic modes have been calculated for a simple model plasmasphere including a lower ionosphere. Results for the Alfvén mode are broadly consistent with those obtained by Hughes and Southwood [1976]. It is further concluded that the lower ionosphere, despite its strong damping effect for part of the day, does not provide much dissipative coupling between adjacent magnetic field shells in the Alfvén mode. The fast mode is found to be only slightly damped for horizontal wavelengths of global extent.     

Cover Picture: Astron. Nachr. 3/2012

Surface map of the radial magnetic field component for a nonaxisymmetric unstable mode excited by the MRI including Hall effect (see T. Kondic et al., this issue, p. 202) (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Alfvén wave parallel electric field in non-uniform space plasmas

We suggest a two-step mechanism for the generation of the parallel electric field at the Alfvén wave. At the first step, the coupling with the compressional mode due to the magnetic field non-uniformity and finite plasma pressure provides the parallel magnetic field of Alfvén wave. At the second step, the compressional mode acquires the parallel electric field due to coupling with the electrostatic mode as required by the quasi-neutrality condition in kinetics. The parallel electric field acquired by the Alfvén mode is considerably larger than that due to the single-step coupling between the Alfvén and electrostatic modes in kinetics.