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1.
本文对充满垂直均匀磁场的等温大气内的磁声重力波做了严格的解析分析,并将其通解表述成广义超几何函数的形式。该解可用于对磁大气内振荡现象的进一步数值模拟研究。对解的分析澄清了若干磁声重力波的传播性质。  相似文献   

2.
An analysis of magneto-acoustic-gravity waves in the case of an isothermal atmosphere permeated by a uniform magnetic field is presented. The general solution is expressed in terms of generalized hypergeometric functions. It can be used in numerical simulation of oscillations in a magnetic atmosphere.

It is shown that the elliptically polarized magneto-acoustic-gravity waves consist of a pair of surface waves and a pair of body waves above the cut-off frequency. The body waves along the magnetic field are similar to acoustic waves in an atmosphere and their cut-off frequency is unaffected by magnetic field. The transverse oscillation decreases with height. For the usual boundary condition, the longitudinal oscillation decreases with height; however, in some cases, it may contain terms that increase with height. The solution is singular on a family of ellipses in the frequency - horizontal wave number plane. Near these ellipses, the wave components grow indefinitely.  相似文献   


3.
Seismology of the solar atmosphere   总被引：1，自引：0，他引：1  
We describe a new instrument for seismically probing the properties of the Sun's lower atmosphere, and present some first results from an observational campaign carried out at the geographic South Pole during the austral summer of 2002/2003. A preliminary analysis of the data (simultaneous, high-cadence observations of the velocity signals from the photosphere and low chromosphere) shows that the well-known suppression of acoustic power in regions of strong magnetic field, and enhancement of high-frequency power around active regions (acoustic halos), are both consistent with a spreading out of the magnetic field lines with increasing height in the atmosphere. The data have also revealed some unexpected wave behavior. First, evanescent-like waves are found at frequencies substantially above the acoustic cut-off frequency in regions of intermediate magnetic field. Second, upward- and downward-propagating waves are detected in areas of strong magnetic field such as sunspots and plage: even at frequencies below the acoustic cut-off frequency. Third, the wave behavior in regions of strong magnetic field can change over periods of a few hours from propagating to evanescent. While we have no concrete explanation for the first two results, the latter result opens up the question of whether sound waves are involved in short-term events such as flares or CME's.  相似文献   

4.
The frequency of the sixth mode observed in HR 1217 cannot currently be understood in the light of the asymptotic theory for high-frequency acoustic modes, valid for adiabatic pulsations in spherically symmetric stars. Deviations from spherical symmetry will change the frequency of the observed oscillations away from the frequencies predicted by the asymptotic theory. Among other things, the presence of a magnetic field in the star will introduce such deviations from spherical symmetry. In the present work we inspect the effect of the magnetic field on the oscillations of HR 1217. Although we model HR 1217 in a rather simplified manner, we believe, as argued in the text, that the essence of the conclusions would not be modified if a more sophisticated model were to be used instead. The results show that the frequency of the sixth mode observed in HR 1217 might be understood if the effect of the magnetic field on the frequencies of the oscillations is fully taken into account. Moreover, we interpret the sixth frequency as a mode of even degree, and explain the absence from the observations of an intermediate l =1 , m =0 mode as the result of large energy losses associated with the coupling of the latter with Alfvénic waves, in the strongly magnetized outer layers of the star. Finally, we show how, in the light of this explanation, the frequency of the sixth mode might be used in order to put constraints on the parameters characterizing the star.  相似文献   

5.
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6.
The pulsation of the solar surface is caused by acoustic waves traveling in the solar interior. Thorough analyses of observational data indicate that these f and p helioseismic oscillation modes are not bounced back completely at the surface but they partially penetrate into the atmosphere. Atmospheric effects and their possible observational application are investigated in one‐dimensional magnetohydrodynamic models. It is found that f and p mode frequencies are shifted of the order of μHz due to the presence of an atmospheric magnetic field. This shift varies with the direction of the wave propagation.Resonant coupling of global helioseismic modes to local Alfvén and slow waves reduce the life time of the global modes. The resulting line width of the frequency line is of the order of nHz, and it also varies with propagation angle. These features enable us to use helioseismic observations in magnetic diagnostics of the lower atmosphere. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

7.
P. S. Cally  M. Goossens 《Solar physics》2008,251(1-2):251-265
The efficacy of fast?–?slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfvén and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfvén wave may couple to the magnetoacoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical “scattering experiment,” placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvénic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfvén waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfvén fluxes are produced when the field is inclined 30°?–?40° from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60°?–?80°.  相似文献   

8.
p-mode oscillations in solar-like stars are excited by the outer convection zone in these stars and reflected close to the surface. The p modes are trapped inside an acoustic cavity, but the modes only stay trapped up to a given frequency [known as the acoustic cut-off frequency  (νac)  ] as modes with larger frequencies are generally not reflected at the surface. This means that modes with frequency larger than the acoustic cut-off frequency must be travelling waves. The high-frequency modes may provide information about the physics in the outer layers of the stars and the excitation source and are therefore highly interesting as it is the estimation of these two phenomena that cause some of the largest uncertainties when calculating stellar oscillations.
High-frequency modes have been detected in the Sun, in β Hydri and in α Cen A and α Cen B by smoothing the so-called echelle diagram and the large frequency separation as a function of frequency has been estimated. The large frequency separation has been compared with a simple model of the acoustic cavity which suggests that the reflectivity of the photosphere is larger at high frequency than predicted by standard models of the solar atmosphere and that the depth of the excitation source is larger than what has been estimated by other models and might depend on the order n and degree l of the modes.  相似文献   

9.
Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental     torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.  相似文献   

10.
We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l , the fundamental mode (without radial nodes) has a frequency of ∼300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies ≳20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (having approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.  相似文献   

11.
The influence of a constant coronal magnetic field on solar global oscillations is investigated for a simple planar equilibrium model. The model consists of an atmosphere with a constant horizontal magnetic field and a constant sound speed, on top of an adiabatic interior having a linear temperature profile. The focus is on the possible resonant coupling of global solar oscillation modes to local slow continuum modes of the atmosphere and the consequent damping of the global oscillations. In order to avoid Alfvén resonances, the analysis is restricted to propagation parallel to the coronal magnetic field. Parallel propagating oscillation modes in this equilibrium model have already been studied by Evans and Roberts (1990). However, they avoided the resonant coupling to slow continuum modes by a special choice of the temperature profile. The physical process of resonant absorption of the acoustic modes with frequency in the cusp continuum is mathematically completely described by the ideal MHD differential equations which for this particular equilibrium model reduce to the hypergeometric differential equation. The resonant layer is correctly dealt with in ideal MHD by a proper treatment of the logarithmical branch cut of the hypergeometric function. The result of the resonant coupling with cusp waves is twofold. The eigenfrequencies become complex and the real part of the frequency is shifted. The shift of the real part of the frequency is not negligible and within the limit of observational accuracy. This indicates that resonant interactions should definitely be taken into account when calculating the frequencies of the global solar oscillations.  相似文献   

12.
We study the effect of a large-scale surface magnetic field on the non-radial acoustic modes of roAp stars. Special attention is given to the use of a variational principle which is used for determining the shifts in the frequencies with relative ease, enabling us to avoid having to calculate the perturbed eigenfunctions. With knowledge of the frequency shifts we then estimate the eigenfunctions in a simpler, albeit approximate way. The results indicate frequency shifts of the order of few μHz, which depend on the order, degree and azimuthal order of the mode. The loss of energy through Alfvén waves is also estimated from the imaginary parts of the frequency shifts. The results indicate that the loss is particularly high near specific frequencies. This might indicate the presence of a selection effect, which could make some modes more likely to be excited than others. However, our results do not explain why the modes observed appear always to be aligned with the axis of the magnetic field. Finally, the estimated perturbed eigenfunctions contain strong components of spherical harmonics that differ from those of the original unperturbed modes.  相似文献   

13.
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14.
Solar active regions are distinguished by their strong magnetic fields. Modern local helioseismology seeks to probe them by observing waves which emerge at the solar surface having passed through their interiors. We address the question of how an acoustic wave from below is partially converted to magnetic waves as it passes through a vertical magnetic field layer where the sound and Alfvén speeds coincide (the equipartition level), and find that (i) there is no associated reflection at this depth, either acoustic or magnetic, only transmission and conversion to an ongoing magnetic wave; and (ii) conversion in active regions is likely to be strong, though not total, at frequencies typically used in local helioseismology, with lower frequencies less strongly converted. A simple analytical formula is presented for the acoustic-to-magnetic conversion coefficient.  相似文献   

15.
Rapidly oscillating Ap stars constitute a unique class of pulsators with which to study non-radial oscillations under some — even for stars — unusual physical conditions. These stars are chemically peculiar, they have strong magnetic fields and they often pulsate in several high-order acoustic modes simultaneously. We discuss here an excitation mechanism for short-period oscillation modes based on the classical κ mechanism. We particularly stress the conditions that must be fulfilled for successful driving. Specifically, we discuss the roles of the chemical peculiarity and strong magnetic field on the oscillation modes and what separates these pulsators from δ Scuti and Am-type stars.  相似文献   

16.
Observations carried out with the Magneto-Optical Filter at Two Heights (MOTH) experiment show upward-traveling wave packets in magnetic regions with frequencies below the acoustic cut-off. We demonstrate that the frequency dependence of the observed travel times, i.e. the dispersion relation, shows significant differences in magnetic and non-magnetic regions. More importantly, at and above the layer where the Alfvén speed equals the sound speed we do not see the dispersion relation of the slow acoustic mode with a lowered cut-off frequency. Our comparisons with theoretical dispersion relations suggest that this is not the slow acoustic wave type for the upward low-frequency wave. From this we speculate that partial mode conversion from the fast acoustic to the fast magnetic wave might take place.  相似文献   

17.
We study torsional Alfvén oscillations of magnetars, that is neutron stars with a strong magnetic field. We consider the poloidal and toroidal components of the magnetic field and a wide range of equilibrium stellar models. We use a new coordinate system  ( X , Y )  , where     and     and a 1 is the radial component of the magnetic field. In this coordinate system, the one+two-dimensional evolution equation describing the quasi-periodic oscillations (QPOs), see Sotani et al., is reduced to a one+one-dimensional equation where the perturbations propagate only along the y -axis. We solve the one+one-dimensional equation for different boundary conditions and the open magnetic field lines, that is magnetic field lines that reach the surface and there match up with the exterior dipole magnetic field as well as closed magnetic lines, i.e. magnetic lines that never reach the stellar surface. For the open field lines, we find two families of QPO frequencies: a family of 'lower' QPO frequencies which is located near the x -axis and a family of 'upper' frequencies located near the y -axis. According to Levin, the fundamental frequencies of these two families can be interpreted as the turning point of the continuous spectrum. We find that the upper frequencies are multiples of the lower ones by a constant equalling  2 n + 1  . For the closed lines, the corresponding factor is   n + 1  . By using these relations, we can explain both the lower and the higher observed frequencies in SGR 1806−20 and SGR 1900+14.  相似文献   

18.
We study properties of waves of frequencies above the photospheric acoustic cut-off of ≈5.3 mHz, around four active regions, through spatial maps of their power estimated using data from the Helioseismic and Magnetic Imager (HMI) and Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). The wavelength channels 1600 Å and 1700 Å from AIA are now known to capture clear oscillation signals due to helioseismic p-modes as well as waves propagating up through to the chromosphere. Here we study in detail, in comparison with HMI Doppler data, properties of the power maps, especially the so-called “acoustic halos” seen around active regions, as a function of wave frequencies, inclination, and strength of magnetic field (derived from the vector-field observations by HMI), and observation height. We infer possible signatures of (magneto)acoustic wave refraction from the observation-height-dependent changes, and hence due to changing magnetic strength and geometry, in the dependences of power maps on the photospheric magnetic quantities. We discuss the implications for theories of p-mode absorption and mode conversions by the magnetic field.  相似文献   

19.
The systematic patterns of separations between frequencies of modes of different degree and order are a characteristic of p-mode oscillations of stars. The frequency separations depend on the internal structure of the star and so measuring them in the observed oscillation spectra of variable stars gives valuable diagnostics of the interior of a star. Roxburgh & Vorontsov proposed using the ratio of the so-called small frequency separation to the large frequency separation as a diagnostic of the stellar interior, and demonstrated that this ratio was less sensitive than the individual frequency separations themselves to uncertain details of the near-surface structure. Here we derive kernels relating the frequency separation ratio to structure, and show why the ratio is relatively insensitive to the near-surface structure in terms of the very small amplitude of the kernels in the near-surface layers. We also investigate the behaviour of the separation ratio for stars of different masses and ages, and demonstrate the usefulness of the ratio in the so-called asteroseismic Hertzsprung–Russell diagram.  相似文献   

20.
Just as a rotating magnetized neutron star has material pulled away from its surface to populate a magnetosphere, a similar process can occur as a result of neutron-star pulsations rather than rotation. This is of interest in connection with the overall study of neutron star oscillation modes but with a particular focus on the situation for magnetars. Following a previous Newtonian analysis of the production of a force-free magnetosphere in this way Timokhin et al., we present here a corresponding general-relativistic analysis. We give a derivation of the general relativistic Maxwell equations for small-amplitude arbitrary oscillations of a non-rotating neutron star with a generic magnetic field and show that these can be solved analytically under the assumption of low current density in the magnetosphere. We apply our formalism to toroidal oscillations of a neutron star with a dipole magnetic field and find that the low current density approximation is valid for at least half of the oscillation modes, similarly to the Newtonian case. Using an improved formula for the determination of the last closed field line, we calculate the energy losses resulting from toroidal stellar oscillations for all of the modes for which the size of the polar cap is small. We find that general relativistic effects lead to shrinking of the size of the polar cap and an increase in the energy density of the outflowing plasma. These effects act in opposite directions but the net result is that the energy loss from the neutron star is significantly smaller than suggested by the Newtonian treatment.  相似文献   

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