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1.
We examine the non-radial modes of oscillation, belonging to spherical harmonics of ordersl=1 andl=3, of a gaseous polytrope with a toroidal magnetic field. We find that a toroidal magnetic field increases the growth rate of convective instability for deformations belonging to the spherical harmonicl=1 whereas it decreases the growth rate of convective instability for deformations belonging to the harmonicsl=2 andl=3. The frequencies of the ‘acoustic’ mode and the ‘Kelvin’ mode are decreased by the presence of the toroidal magnetic field.  相似文献   

2.
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   

3.
Third order virial equations have been used to investigate the oscillations and the stability of the sequence of differentially rotating, compressible Maclaurin spheroids in the presence of toroidal magnetic fields. It is shown that the neutral point occurring at eccentricitye=0.731 13, which is the analogue of the first point of bifurcation along the Dedekind sequence, remains unaffected by the presence of differential rotation or a toroidal magnetic field. The point of onset of dynamical instability corresponding to the third harmonic deformations does, however, depend upon the magnetic field. It is shifted to values higher thane=0.966 96, the value that obtains in the case of uniform rotation; and a sufficiently large magnetic field can suppress this point. Complete frequency spectra (‘Kelvin’ modes belonging to the harmonicsl=3 and compressible modes belonging tol=1) are obtained in two cases of interest: when the equilibrium state is one of equipartition, and when toroidal magnetic and velocity fields (vanishing at the surface) are present in a configuration rotating with a constant angular velocity.  相似文献   

4.
The fundamental frequencies of the non-radial mode of oscillation belonging to the second harmonic (l=2) of magnetically distorted polytropic gas spheres are evaluated in the second approximation by a variational method. The magnetic field is assumed to have both the toroidal and the poloidal components. We find that the frequencies of oscillation are increased due to the presence of the magnetic field and that these depend only slightly on the value of , the ratio of the specific heats. We have also determined the value of <1+1/n for the mode of oscillation which exhibits convective instability. This value is lower than the one which is obtained in the absence of a magnetic field.  相似文献   

5.
The radial and the non-radial (l=2) modes of oscillation of a gaseous polytrope with a toroidal magnetic field are examined using a variational principle. It is found that the frequencies of oscillation of the radial mode and the Kelvin mode (l=2) decrease due to the presence of the magnetic field. The shift in the frequency of the Kelvin mode may be split up into two parts, viz. the shift in frequency due to the magnetic field on the unperturbed sphere [(12)m, say] and the shift in frequency due to the distortion of the structure by the magnetic field [(12)s, say]. In the first order calculations using one parameter trial function, it is found that (12)m is indeed positive but is overweighed by a negative (12)s. In the second order calculations using a trial function with two variational parameters, we find that the general behaviour of (12)m and (12)s is unchanged but that (12)m becomes negative for polytropic indicesn1.5.In Appendix I we study the effect of a small rotation and toroidal magnetic field on the structure of a polytrope. It is found that the resulting configuration is a prolate spheroid, a sphere or an oblate spheroid according as respectively. Here denotes the magnetic energy andT the kinetic energy due to rotation andq is a constant which depends on the polytropic indexn. The values ofq are given in Table I.  相似文献   

6.
We investigate the equilibrium, oscillations, and stability of uniformly rotating masses with a toroidal magnetic field, proportional with the distance to te axis of rotation. The equilibrium is an oblate or prolate spheroid according as the rotational energy is greater or smaller than the magnetic energy. The sequence of equilibrium figures exhibits a maximum value for the angular velocity in the oblate case and a maximum for the angular momentum in the prolate case. The dispersion relation is derived using Bryan's modified spheroidal coordinates. One obtains 2(n–m)+4 solutions for the oscillation frequency ifm0 and 1/2n or 1/2(n+1) solutions for 2 according asn is even or odd ifm=0. The point where the Jacobi ellipsoids bifurcate from the MacLaurin sequence is unaffected by the magnetic field. However, the points of the onset of dynamical instability corresponding to the second and third harmonics and the point where a pear-shaped sequence bifurcate, depend upon the magnetic field. They are shifted to higher values for the eccentricity and can be suppressed by a sufficiently large magnetic field.  相似文献   

7.
In this paper an excitation of waves is considered during the time interval in which the undisturbed magnetic field changes its direction. If this interval is taken to be 2 years, which is shorter than the 11-year cycle, then the undisturbed components of the magnetic field may be linearly dependent on time and independent of the coordinates. The excitation of waves is due to the undisturbed stationaryV 0 flow with divV 0 = 0 and with (V 0 rot0) = constant.We use the local Cartesian coordinate system, which is immovable towards the solar centre, and consider the case when the toroidal component of the undisturbed magnetic field changes its sign simultaneously with one of the axial components. The third component does not change its direction.The efficiency of the enhancement of the magnetic field and velocity disturbances depends on the Alfvén wave frequency, A. When A = 0, the component of the disturbed velocity, which is directed along the constant component of the undisturbed magnetic field, increases. In this case the shear waves excite the carrier (high) frequency (KV 0), whereK is the wave vector. Due to the shear instability the amplitude of the velocity increases during 1 year before the moment of reversal of the global magnetic field polarity (RGMFP) for an arbitrary latitude. It reaches a maximum at RGMFP and decreases in the next year. When A > 0, then the amplitudes of the disturbed values reach maxima before the moment of RGMFP, and when A < 0, they reach maxima after it.We argue that the shear waves propagate from middle latitudes to the pole and equator. Using the results of the analytical solutions and leaning on the evidence of the observational data (Gigolashvili and Japaridze, 1992), we derive the result that the component of the undisturbed magnetic field, which is perpendicular to the solar surface, changes its sign simultaneously with the toroidal component.  相似文献   

8.
Nonradial oscillations of a partially degenerate standard model, approximating a class of low-mass stars, have been studied in the presence of a weak poloidal magnetic field. The magnetic field in the interior of the configuration is taken to be continuous across the equilibrium surface and is matched with an external dipole field. Using a variational formulation, corrections to the oscillation frequencies of the Kelvin mode have been found for different values of the central degeneracy. It has been noted that the effect of the magnetic field is to increase the frequency of nonradial (l=2) mode of pulsation.  相似文献   

9.
The nonlinear pseudo-radial mode of oscillation of a rotating magnetic star is studied. It is shown that for a general rotational field, the coupling between magnetic field and rotation tends to reduce the average rotational energy parameterT. This result in a lowering of the maximum pulsation amplitudeq max, which depends on strength of rotation and magnetic field. The configuration tends, therefore, to a new equilibrium state at lower value ofq max. The analytic solution of the pulsation equation for the case ofy=5/3 in the presence of rotation and magnetic field has also been derived in the Appendix.  相似文献   

10.
First-order perturbation theory results for the changes in pulsation frequencies of a Cowling model star containing a magnetic field with both poloidal and toroidal components are presented. A toroidal field large enough to stabilize the poloidal field may reverse the sign of the frequency change caused by a purely poloidal field for some modes, including the fundamental radial mode.  相似文献   

11.
The degree of association between geoeffective (SID producing) flares (hereafter called SID flares) and sunspot morphology is examined. It is found that: (1) the frequency of SID flares associated with sunspot groups is linear function of sunspot area and rate of change in area; (2) the SID flare intensity is dependent on the sunspot area and on the magnetic morphology (field geometry); (3) the probability of a sunspot group being magnetically complex (henceforth called complex ratio) is a linear function of spot area, the larger this area the more likely a group is in the βγ or δ magnetic class; (4) the complex ratio exhibits the greatest degree of association to SID flare frequency. We conclude from these results that a higher frequency of D-region ionizing flares (emitting a soft X-ray flux >2 × 10?3 erg cm?2 s?1) is likely to accompany the disk transit of large area, complex spot groups. This combination of morphological factors reflects a shearing of the associated force-free magnetic field, with accumulation of free magnetic energy to power SID flares. Mutual polarity intrusion would be one observational signature of the pre-flare energy storing process.  相似文献   

12.
Energy is stored when the force-free magnetic field in an active region departs from a potential field, the departure showing up as a shear in the field. As soon as the field untwists, energy will be released to produce flares. Based on this idea, we derived an analytical solution of the equation of force-free field under the assumption of a constant force-free factor, and found expressions for seven important quantities for quadrupolar sunspots: the magnetic energy of the twisted field, that of potential field, the extractable free energy ΔM, the magnetic flux, the total current, the force-free factor and the field decay factor, in terms of three observables: the field intensity, the twist angle and the distance between two spots of the same polarity. The expression for ΔM can be useful in solar prediction work. For the active region of August, 1972, we found ΔM up to 6 × 1032 erg, sufficient to supply the energy of the observed flare activity. Observations of this active region are in good general agreement with our theoretical expectations: in the entire twisting of the quadrupolar sunspot group, each spot assumes the form of a complete spiral in the clockwise direction for each of the four spots.  相似文献   

13.
《Planetary and Space Science》2007,55(14):2113-2120
The shear-driven electrostatic ion-cyclotron instability (EICI) is studied using the loss-cone distribution function by particle aspect analysis. The effect of the loss-cone distribution on the dispersion relation and growth rate of weak shear-driven EICI is studied. The whole plasma is considered to consist of resonant and non-resonant particles. The wave is assumed to propagate obliquely to the static magnetic field. It is found that the frequency of the EICI is Doppler shifted due to the transverse inhomogeneous flow in the direction of the magnetic field. It is also found that for anisotropic plasma the critical velocity shear needed to excite EICI depends upon the loss-cone distribution index (J). With the increasing values the loss-cone distribution indices (J), the critical value of normalized velocity shear needed to generate EICI in anisotropic plasma, decreases and is of the order of the weak shear. The loss-cone distribution acts as a source of free energy and generates the weak shear-driven EICI at longer perpendicular perturbations. It also lowers the transverse and parallel energy of the resonant ions. The study may explain the frequently observed EICI in the auroral acceleration region.  相似文献   

14.
In this paper, the presence of Faraday rotation in measurements of the orientation of a sunspot's transverse magnetic field is investigated. Using observations obtained with the Marshall Space Flight Center's (MSFC) vector magnetograph, the derived vector magnetic field of a simple, symmetric sunspot is used to calculate the degree of Faraday rotation in the azimuth of the transverse field as a function of wavelength from analytical expressions for the Stokes parameters. These results are then compared with the observed rotation of the field's azimuth which is derived from observations at different wavelengths within the Fei 5250 Å spectral line. From these comparisons, we find: the observed rotation of the azimuth is simulated to a reasonable degree by the theoretical formulations if the line-formation parameter η o is varied over the sunspot; these variations in η o are substantiated by the line-intensity data; for the MSFC system, Faraday rotation can be neglected for field strengths less than 1800 G and field inclinations greater than 45°; to minimize the effects of Faraday rotation in sunspot umbrae, MSFC magnetograph measurements must be made in the far wings of the Zeeman-sensitive spectral line.  相似文献   

15.
The rapidly oscillating Ap stars pulsate in high-overtone, low degreep-modes with their pulsation axes aligned with their oblique magnetic axes. They show non-linearity in their pulsation in three ways:
  1. The harmonics of the basic pulsation frequency are detectable.
  2. The pulsation phase seems to vary stochastically on a time scale of days to years depending on the star.
  3. The form of the nonradial surface distortion is not constant with time.
These three effects are illustrated with HR 3831, the best studied of the roAp stars. HR 3831 pulsates in distorted dipole mode which can be modelled as a linear sum of axisymmetricl = 0, 1, 2, and 3 spherical harmonics aligned with the magnetic axis. This gives rise to a 7-frequency multiplet split by exactly the rotation frequency. The form of the distortion shows small changes on a time-scale of years. HR 3831 shows a 5-frequency rotationally split first harmonic multiplet, a 3-frequency rotationally split second harmonic multiplet, and a single third harmonic frequency has probably been detected at an amplitude of 0.065 mmag. The first harmonic has changed its form significantly over the last 10 years. A technique for decomposing the fundamental frequency septuplet into its component spherical harmonics is used to fit the pulsation phase as a function of rotation phase. This allows a unique O-C to be defined for any length of light curve. The long term behaviour of the O-C diagram cannot be modelled adequately with a combination of periodic (Doppler shift) and quadratic (evolution) terms; there seems to be a significant stochastic component. The direction of the pulsation phase reversal at rotational phase 0.747 is indeterminate; sometimes it is a positive-going reversal, sometimes negative-going. At present it is not known whether this is a numerical artifact, or a physical effect in the star. If it is a physical effect, it means that small non-periodic differences in pulsation amplitude between the bipolar hemispheres have been detected.  相似文献   

16.
Frequencies of non-radial oscillation of polytropic models of stars, belonging to spherical harmonics of ordersl=1, 2 and 3, are evaluated, in a second approximation, by a variational method. Equilibrium configurations in the presence of toroidal magnetic fields are obtained numerically without any restriction on the field strength. The value of the ratio of the specific heats, , is assumed to be equal to 5/3 and only two polytropic indeces,n=1.5 and 3.0, are considered. It is found that a polytropic star stays stable for magnetic fields considerably stronger than expected from the results obtained by the weak field perturbation methods.  相似文献   

17.
The sunspot occurrence probability defined in Paper I is used to determine the Legendre-Fourier (LF) terms in the rate of emergence of toroidal magnetic flux,Q(, t), above the photosphere per unit latitude interval, per unit time. Assuming that the magnetic flux tubes whose emergence yields solar activity are produced by interference of global MHD waves in the Sun, we determine how the amplitudes and phases of the LF terms in the toroidal magnetic fieldB , representing the waves, will be related to those of the LF terms inQ(, t). The set of LF terms in Q that represents the set of waves whose interference produces most of the observed sunspot activity is {l = 1, 3, , 13;v =nv *,n = 1, 3, 5}, wherev * = 1/21.4 yr–1. However, among the shapes of sunspot cycles modeled using various sets of the computed LF terms the best agreement with the observed shape, for each cycle, is given by the set {l = 3 orl = 3, 5; andn = 1, 3 orn = 1, 3, 5}. The sets of terms: {l = 1, 3, 5, 7;n = 1}, {l = 1, 3, 5, 7;n = 3}, {l = 9, 11, 13, 15;n = 1} and {l = 9, 11, 13, 15;n = 3} seem to represent four modes of global MHD oscillation. Correlations between the amplitudes (and phases) of LF terms in different modes suggest possible existence of cascade of energy from constituent MHD waves of lowerl andn to those of higherl andn. The spectrum of the MHD waves trapped in the Sun may be maintained by the combined effect of this energy cascade and the loss of energy in the form of the emerging flux tubes. The primary energy input into the spectrum may be occurring in the mode {l = 1, 3, 5, 7;n = 1). As expected from the above phenomenological model, the size of a sunspot cycle and its excess over the previous cycle are well correlated (e.g., 90%) to the phase-changes of the two most dominant oscillation modes during the previous one or two cycles. These correlations may provide a physical basis to forecast the cycle sizes.  相似文献   

18.
We have used a 5.5 min time-sequence of spectra in the Fe i lines λ5576 (magnetically insensitive), λ6301.5 and λ6302.5 (magnetically sensitive) to study the association of concentrated magnetic regions and velocity in the quiet Sun. After the elimination of photospheric oscillations we found downflows of 100–300 m s ?1, displaced by about 2″ from the peaks of the magnetic field; this velocity is comparable to downflow velocity associated with the granulation and of the same order or smaller than the oscillation amplitude. Quasi-periodic time variations of the vertical component of the magnetic field up to ± 40% were also found with a period near 250 s, close to the values found for the velocity field. Finally we report a possible association of intensity maxima at the line center with peaks of the oscillation amplitude.  相似文献   

19.
Based on photospheric vector magnetograms obtained at Huairou Solar Observing Station (HSOS), non-potential characteristics of the magnetic field beneath the filament in active region NOAA 9077 are investigated. We focus on the structure and evolution of the magnetic field from 00:08 UT to 10:25 UT of 14 July before the Bastille event. Particular attention is paid to transverse field strength, shear degree and horizontal gradient of the line-of-sight magnetic field around the filament and filament channel. The following characteristics are found. (1) The magnetic non-potentiality has an obviously non-uniform distribution. The shear degree of the transverse field (Hagyard et al., 1984) is very large, up to 75° in some sites beneath the filament, such as the initial brightening site in TRACE 1600 Å images and the breaking site of the filament. The transverse field and the horizontal gradient of the line-of-sight field are very large in some parts corresponding to the hottest and continuously brightening portions. (2) The mean strength and mean shear angle of the transverse field and mean horizontal gradient of the line-of-sight field have obviously dropped in most parts beneath the filament for two hours before the filament eruption and onset of the X5.7/3B flare. After comparing simultaneous UV and EUV images, H filtergrams and Dopplergrams at solar atmosphere, we suggest that magnetic cancellation is likely to quickly transport the magnetic energy and complexity into the higher atmosphere in these two hours. This leads to magnetic instability in the filament and eventually causes the eruption of filament and onset of the flare.  相似文献   

20.
Macroscopic equations of motion are used to derive several forms of the generalized Ohm's law for partially ionized ternary gases in magnetic fields, and a conductivity σ is defined that is independent of the magnetic field. A flux theorem is derived using a velocityu H that can be defined to be the velocity of magnetic field lines;u H is only slightly different from the velocity of the electron component of the gas. It is shown that σ is the conductivity relevant to the decay of magnetic flux through any surface moving everywhere with velocityu H . The rate of increase of the thermal energy density of the gas arising through collisions between particles of different species can be resolved into Joule heating at the ratej 2/σ, wherej is the current density, and heating associated with ambipolar drift. The latter, contrary to what has been claimed by some authors, is not necessarily fully compensated by a decrease in the energy of the electromagnetic field. In many applications such compensation does occur, but it may not in interstellar clouds where large amounts of gravitational energy can be made available by collapse, and then both heating and an increase in electromagnetic field energy may occur.  相似文献   

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