The continuous spectrum of MHD waves in 2D solar loops and arcades. First results on poloidal mode coupling for poloidal magnetic fields

A first attempt is made to study the continuous spectrum of linear ideal MHD for 2D solar loops and to understand how 2D effects change the continuum eigenfrequencies and continuum eigenfunctions. The continuous spectrum is computed for 2D solar loops with purely poloidal magnetic fields and it is investigated how non-circularity of the cross-sections of the poloidal magnetic surfaces and variations of density along the poloidal magnetic field lines change the continuous spectrum and induce poloidal wave number coupling in the eigenfunctions. Approximate analytical results and numerical results are obtained for the eigenfrequencies and the eigenfunctions and the poloidal wave number coupling is clearly illustrated. It is found that the continuum frequencies are substantially increased, that the ranges of the continuum frequencies are considerably enlarged and that the derivatives of the continuum frequencies normal to the magnetic surfaces are substantially increased. The eigenfunctions are strongly influenced by poloidal wave number coupling. Implications of these findings for the heating mechanisms of resonant absorption and phase mixing are briefly considered.Research Assistant of the Belgian National Fund for Scientific Research.     

On the existence of the continuous spectrum of ideal MHD in a 2D magnetostatic equilibrium

The continuous spectrum of a 2D magnetostatic equilibrium with y-invariance is derived. It is shown that the continuous spectrum is given by an eigenvalue problem on each magnetic surface and is related to the different behaviour of the equilibrium quantities in different magnetic surfaces. The special case of a uniform poloidal magnetic field in a 1D equilibrium that is stratified with height, has been considered in detail and it is found that there is no continuous spectrum. It is shown that this result relies completely on the artificial property that the behaviour of the equilibrium quantities along a magnetic field line is independent of the field line considered. As a consequence the non-existence of a continuous spectrum in a 1D equilibrium with a uniform magnetic field cannot be used to argue that the continuous spectrum has no physical relevance.Research Assistant of the Belgian National Fund for Scientific Research.     

On the energy distribution in the continuous spectrum

Byurakan Astrophysical Observatory; TETRA Corporation, USA. Translated from Astrofizika, Vol. 33, No. 1, pp. 39–45, July–August, 1990.     

Nonresonant mode coupling in double-mode pulsators

The simplest model for the evolution to steady nonlinear stellar pulsation is nonresonant interaction involving two linearly unstable modes. One scenario models a double-mode pulsator, while another one shows evolution to classic pulsators. In all cases exact shock-like solutions have been obtained.     

On the hydrodynamic mechanism of the generation of the global poloidal flux on the Sun

The mechanism of the generation of the poloidal flux on the Sun caused by the differential rotation of the star is considered. Ranges have been found in which the poloidal flux is generated.     

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.     

On the existence of the relative equilibria of a rigid body in the J 2 problem

The motion of a point mass in the J ₂ problem has been generalized to that of a rigid body in a J ₂ gravity field for new high-precision applications in the celestial mechanics and astrodynamics. Unlike the original J ₂ problem, the gravitational orbit-rotation coupling of the rigid body is considered in the generalized problem. The existence and properties of both the classical and non-classical relative equilibria of the rigid body are investigated in more details in the present paper based on our previous results. We nondimensionalize the system by the characteristic time and length to make the study more general. Through the study, it is found that the classical relative equilibria can always exist in the real physical situation. Numerical results suggest that the non-classical relative equilibria only can exist in the case of a negative J ₂, i.e., the central body is elongated; they cannot exist in the case of a positive J ₂ when the central body is oblate. In the case of a negative J ₂, the effect of the orbit-rotation coupling of the rigid body on the existence of the non-classical relative equilibria can be positive or negative, which depends on the values of J ₂ and the angular velocity Ω _e . The bifurcation from the classical relative equilibria, at which the non-classical relative equilibria appear, has been shown with different parameters of the system. Our results here have given more details of the relative equilibria than our previous paper, in which the existence conditions of the relative equilibria are derived and primarily studied. Our results have also extended the previous results on the relative equilibria of a rigid body in a central gravity field by taking into account the oblateness of the central body.     

Determination of intrinsic mode and linear mode coupling in solar microwave bursts

An explicit equation of the propagational angle of microwave emission between the line-of-sight and the local magnetic field is newly derived based on the approximated formulae of nonthermal gyrosynchrotron emission (Dulk and Marsh in Astrophys. J. 259, 350, 1982). The existence of the solution of propagational angle is clearly shown under a series of typical parameters in solar microwave observations. It could be used to determine the intrinsic mode and linear mode coupling in solar microwave bursts by three steps. (1) The mode coupling may happen only when the angle approximately equals to 90 degrees, i.e., when the emission propagates through the quasi-transverse region (Cohen in Astrophys. J. 131, 664, 1960). (2) The inversion of polarization sense due to the weakly mode coupling takes place only when the transition frequency defined by Cohen (1960) is larger than the frequency of microwave emission, and an observable criterion of the weakly mode coupling in flaring loops was indicated by the same polarization sense in the two footpoints of a flaring loop (Melrose and Robinson in Proc. Astron. Soc. Aust. 11, 16, 1994). (3) Finally, the intrinsic mode of microwave emission is determined by the observed polarization and the calculated direction of local magnetic field according to the general plasma dispersion relation, together with the mode coupling process. However, a 180-degree ambiguity still exists in the direction of longitudinal magnetic field, to produce an uncertainty of the intrinsic mode. One example is selected to check the feasibility of the method in the 2001 September 25 event with a loop-like structure nearby the central meridian passage observed by Nobeyama Radio Heliograph and Polarimeters. The calculated angle in one footpoint (FP) varied around 90^° in two time intervals of the maximum phase, which gives a direct evidence of the emission propagating through a quasi-transverse region where the linear mode coupling took place, while, the angle in another FP was always smaller than 90^° where the mode coupling did not happen. Moreover, the right-circular sense at 17 GHz was always observed in both two FPs during the event, which supports that the transition frequency should be larger than 17 GHz in the first FP together with strong magnetic field of over 2000 Gauses in photosphere, where the weakly coupled case should happen. Moreover, there are two possibilities of the intrinsic mode in the two FPs due to the 180-degree ambiguity. (1) The emission of extraordinary (X) mode from the first FP turns to the ordinary (O) mode in the two time intervals of the maximum phase, while, the X-mode is always emitted from the second FP. (2) The inversion from O-mode to X-mode takes place in the first FP, while the O-mode keeps in the second FP. If the magnetic polarities in photosphere and corona are coincident in this event, the intrinsic mode belongs to the second case.     

On non-axisymmetric magnetic equilibria in stars

In previous work, stable approximately axisymmetric equilibrium configurations for magnetic stars were found by numerical simulation. Here, I investigate the conditions under which more complex, non-axisymmetric configurations can form. I present numerical simulations of the formation of stable equilibria from turbulent initial conditions and demonstrate the existence of non-axisymmetric equilibria consisting of twisted flux tubes lying horizontally below the surface of the star, meandering around the star in random patterns. Whether such a non-axisymmetric equilibrium or a simple axisymmetric equilibrium forms depends on the radial profile of the strength of the initial magnetic field. The results could explain observations of non-dipolar fields on stars such as the B0.2 main-sequence star τ Sco or the pulsar 1E 1207.4-5209. The secular evolution of these equilibria due to Ohmic and buoyancy processes is also examined.     

Deviations from the normal mode spectrum of asymptotic theory

The work of Hill (1985a) on the low-degree 5 min eigenfrequency spectrum of the Sun based on differential radius observations combined with Doppler shift and total irradiance observations has been extended to include the work of Harvey and Duvall (1984) and Libbrecht and Zirin (1986). The differences between eigenfrequencies obtained in this analysis are compared to the predictions of asymptotic theory, and the deviations between observation and theory are observed to be 4 times larger than expected based on estimated accuracy of eigenfrequency determinations. These deviations are tested for departures from predictions of asymptotic theory which are quasi-periodic as a function of radial ordern and degreel. It is observed that the superposition of the seven distributions of frequency differences vsn obtained forl=0, ..., 6 generates an overdetermined quasi-periodic function when n/l=0.420±0.018 and v/l=–0.35 Hz in the superposition process. The probability that this quasi-periodic parent function is obtained from seven independent random distributions is estimated to be 1.2×10^–7. Numerical experiments performed with theoretical eigenfrequency spectra demonstrate that the existence of a quasiperiodic behaviour in the superposed spectrum of frequency differences is physically plausible and that the parameters used in the superposition process are consistent with theory. One significant theoretical quasiperiodic behaviour is obtained for n/l=0.399. By comparing the properties of the observed quasi-periodic behaviour with those obtained in the numerical experiments, we infer that the location of the region which leads to the greatest departure from asymptotic theory predictions is 0.757±0.002 solar radii, which suggests that this region is connected with the transition zone between the radiative interior and the convection zone.     

A continuous spectrum of a white-light flare

White-light continuum was observed at the Norikura Solar Observatory in a 2B flare of 10 September 1974 in the spectral region between 3600 Å and 4000 Å. The duration of continuum emission was 8–12 min. The continuum shows a Balmer free-bound component, but the main contribution to the continuum between 3646 Å and 4000 Å is H^– emission. The white-light continuum, therefore, is thought to be of photospheric origin. The energy loss in the continuum is 10²⁷ erg s^–1.     

On the stability of strongly non-homogeneous self-gravitating equilibria

The stability analysis of several stronglynon-homogeneous, self-gravitating, one-dimensionalunstable equilibrium systems is carried out with the help of numerical techniques. The evolution of the perturbed unstable equilibria is studied by following the motion of the boundary curves of water bag configurations defining the systems.It is found that initial perturbations drive the unstable equilibrium states out of equilibrium at rates depending on the typical scale length of the perturbations : the instability rates increase with .     

Bounds on the stability of 3D magnetic equilibria in the solar corona

A necessary and a sufficient condition are derived for the ideal magnetohydrodynamic stability of any 3D magnetohydrostatic equilibrium using the energy method and incorporating photospheric line-tying. The theory is demonstrated by application to a simple class of theoretical 3D equilibria. The main thrust of the method is the formulation of the stability conditions as two sets of ordinary differential equations together with appropriate boundary conditions which may be numerically integrated along tied field lines one at a time. In the case of the shearless fields with non-negligible plasma pressure treated here the conditions for stability arenecessary and sufficient. The method employs as a trial function a destabilizing ballooning mode, of large wave number vector perpendicular to the equilibrium field lines. These modes may not be picked up in a solution of the full partial differential equations which arise from a direct treatment of the problem.     

The high-dispersion continuous ultraviolet solar spectrum and the Balmer-jump

Among the intensities, determined at about 200 wavelengths between 3000 and 4100 Å in the spectrum of the centre of the sun's disk (Houtgast, 1965), the 32 highest ones (windows) were plotted and compared with absolute intensities given by other authors.The intensities in between the Fraunhofer lines from 3600 to 4000 Å, as determined here for the first time with high dispersion, reveal a detailed picture of several absorption features, one of which can be attributed to a Balmer jump of 0.03, a value in accordance with that found for stars and in agreement with the strengths of the high Balmer lines.The much higher value of the Balmer jump for the sun, as quoted in literature, in reality refers to the total intensity jump between 4000 and 3600 Å, which is mainly due to the crowding of Fraunhofer lines.     

Observations of mode coupling in the solar corona and bipolar noise storms

We review high-spatial-resolution observations of the Sun which reflect on the role of mode coupling in the solar corona, and present a number of new observations. We show that typically polarization inversion is seen at 5 GHz in active region sources near the solar limb, but not at 1.5 GHz. Although this is apparently in contradiction to the simplest form of mode coupling theory, in fact it remains consistent with current models for the active region emission. Microwave bursts show no strong evidence for polarization inversion. We discuss bipolar noise storm continuum emission in some detail, utilizing recent VLA observations at 327 MHz. We show that bipolar sources are common at 327 MHz. Further, the trailing component of the bipole is frequently stronger than the leading component, in apparent conflict with the leading-spot hypothesis. The observations indicate that at 327 MHz mode coupling is apparently strong at all mode-coupling layers in the solar corona. The 327 MHz observations require a much weaker magnetic field strength in the solar corona to explain this result than did earlier lower-frequency observations: maximum fields are 0.2 G. This is a much weaker field than is consistent with current coronal models.On leave from the Indian Institute for Astrophysics, Bangalore, India.     

On the variability of emission spectrum of the Sy2 galaxy Mark 6

According to Ambartsumyan, one of the forms of galactic activity is the outflow of gaseous material in the form of jets or clouds from the region of the nucleus at velocities up to hundreds or thousands of km/s, which sometimes leads to the breakup of the nucleus and the ejection of large bursts of material from it. Quite a lot is known about the results of these ejections, especially for quasars and active galaxies. They have been detected and studied in detail with regard to changes in their outer appearance. However, the exact time of the ejections is not known, although statistically they occur frequently and irregularly. The detection of changes in the spectra of galaxies is of special interest, but these are much harder to detect over short times. Nevertheless, the probability of detecting the time of an ejection within a short time is nonzero. Additional new emission components of the hydrogen Hα, Hβ, and Hγ lines over a year in the spectrum of the Sy2 galaxy Mark 6 were first discovered by Khachikian and Weedman in 1969. This paper describes the origin and subsequent interesting fate of this new hydrogen formation (cloud).     

On the intensity ratio of emission lines of Nai D1 to D2 in prominences

Spectroscopic observations of the Nai D emission lines of prominences were made with the Domeless Solar Telescope in Hida Observatory. When active prominences are bright in the D₂ emission line, the intensity ratio of D₁ to D₂ is found to deviate significantly from the theoretical ratio of the optically-thin case. On the other hand, the intensity ratio is close to the theoretical ratio for the most part of quiescent prominences. Furthermore, the full widths at half maximum intensity of the D₂ emission line for active prominences become wider than those of the D₁ line, as the intensity of the D₂ line gets higher. These observed features clearly show that the emitting region of the Nai D lines is optically thick in some types of prominences. Non-LTE calculations were made by taking the ionization degree of hydrogen atoms and the thickness of the prominences and the electron temperature as free parameters. It is shown that the electron temperature of the emitting region of the Nai D lines should be as low as 4000 K for an explanation of the large optical thickness of the Nai D lines for active prominences. Brief discussions are included about the possible existence of low temperatures in active prominences.     

New approach of studying electromagnetic mode coupling in inhomogeneous magnetized plasma

In this paper we use a new approach to derive the system of first-order coupled equations governing the propagation of electromagnetic waves in an inhomogeneous magnetized plasma for normal incidence. In this new approach we employ a step model and use Maxwell's equations indirectly. The method we present here possesses simplicity in mathematical manipulation and gives a clearer physical picture of the mechanism of mode-coupling. The variablesE _i used in the coupled equations are directly related to experimental measurements. Our result is shown to be equivalent to that obtained by Budden and Clemmow (1957).