HALF-WIDTH OF A SOLAR DYNAMO WAVE IN PARKER'S MIGRATORY DYNAMO

A kinematic -dynamo model of magnetic field generation in a thin convection shell with nonuniform helicity for large dynamo numbers is considered in the framework of Parker's migratory dynamo. The asymptotic solution obtained of equations governing the magnetic field has the form of an anharmonic travelling dynamo wave. This wave propagates over most latitudes of the solar hemisphere from high latitudes to the equator, and the amplitude of the magnetic field first increases and then decreases with propagation. Over the subpolar latitudes, the dynamo wave reverses; there the dynamo wave propagates polewards and decays with latitude. The half-width of the maximum of the magnetic field localisation and the phase velocity of the dynamo wave are calculated. Butterfly diagrams are plotted and analysed and these show that even a simple model may reveal some properties of the solar magnetic fields.     

The flux ejection dynamo with small diffusivity

A number of examples are worked out to illustrate the consequences of reverse flux ejection from the surface of a convective layer of conducting fluid. Generally the reverse flux ejection has the opposite effect of magnetic buoyancy, tending to bury the fields rather than bringing them through the surface. Even a weak flux ejection effect prevents the excape of magnetic field through the surface. Reverse flux ejection at the surface of an -dynamo profoundly alters the character of the solutions of the dynamo equations. Altogether, flux ejection serves to obscure the interpretation of magnetic observations. The outstanding problem now is to determine under what circumstances there exists cyclonic convection with rotations in excess of ±1/2 in the rising columns of fluid. Negative turbulent diffusion is expected to be a close companion of the flux ejection effect.This work was supported by the National Aeronautics and Space Administration under grant NGL 14-001-001.     

Phase relation between the poloidal and toroidal solar-cycle general magnetic fields and location of the origin of the surface magnetic fields

The phase relation of the poloidal and toroidal components of the solar-cycle general magnetic fields, which propagate along isorotation surfaces as dynamo waves, is investigated to infer the structure of the differential rotation and the direction of the regeneration action of the dynamo processes responsible for the solar cycle. It is shown that, from the phase relation alone, (i) the sign of the radial gradient of the differential rotation (/r) can be determined in the case that the radial gradient dominates the differential rotation, and (ii) the direction of the regeneration action can be determined in the case that the latitudinal gradient (/) dominates the differential rotation. Examining the observed poloidal and toroidal fields, it is concluded that (i) the / should dominate the differential rotation, and (ii) the determined sign of the regeneration factor (positive [negative] in the northern [southern] hemisphere) describing the direction of the regeneration action requires that the surface magnetic fields should originate from the upper part of the convection zone according to the model of the solar cycle driven by the dynamo action of the global convection.     

The disk dynamo

The simplest dynamo in a thin disk is analysed. It the antisymmetric helicity function (z) (wherez is a coordinate perpendicular to the disk plane) is smooth and limited, then the conditions for generating a magnetic field and the symmetry of the resulting solutions depend only on the form of at the segment (0,h) — whereh is the half-thickness of the disk — and the value of the dimensionless dynamo numberD. When (z) does not change its sign at this segment andD>D _c (the critical dynamo number), the excitation of non-oscillating even (quadrupole) and oscillating odd (dipole) fields are possible. When (z) changes its sign at the segment indicated, non-oscillating odd magnetic fields can also be excited.The old exact solutions of the disk dynamo are studied and new ones are found. The results can be of importance when applied to the problem of the generation of a magnetic field in galactic and turbulent disks appearing around some X-ray sources.     

A mechanism of helicity variations on the Sun

Helicity of solar magnetic fields plays an important role in dynamo theories of the solar cycle. The helicity has been known to vary with the main 11-year period (Hale's cycle). Recent observations have revealed significant helicity variations on a shorter time scale, with a characteristic period of approximately 2 years. We suggest an explanation for the observed variations of the magnetic helicity, based on our model of the double magnetic cycle of solar activity. The quasi-biennial variations of the helicity are the consequence of the influence of erupted magnetic fields of the main cycle on the helicity in the regions of generation of the high-frequency component of magnetic field. This model suggests that the low-frequency component is generated at the base of the convective zone due to large-scale radial shear /r of angular velocity . The high-frequency component may be generated in the subsurface region due to latitudinal shear / or due to the radial shear in this region.     

On the generation of the large-scale and turbulent magnetic fields in solar-type stars

It is thought that the large-scale solar-cycle magnetic field is generated in a thin region at the interface of the radiative core (RC) and solar convection zone (SCZ). We show that the bulk of the SCZ virogoursly generates a small-scale turbulent magnetic field. Rotation, while not essential, increases the generation rate of this field.Thus, fully convective stars should have significant turbulent magnetic fields generated in their lower convection zones. In these stars the absence of a radiative core, i.e., the absence of a region of weak buoyancy, precludes the generation of a large-scale magnetic field, and as a consequence the angular momentum loss is reduced. This is, in our opinion, the explanation for the rapid rotation of the M-dwarfs in the Hyades cluster.Adopting the Utrecht's group terminology, we argue that the residual chromospheric emission should have three distinctive components: the basal emission, the emission due to the large-scale field, and the emission due to the turbulent field, with the last component being particularly strong for low mass stars.In the conventional dynamo equations, the dynamo frequencies and the propagation of the dynamo wave towards the equator are based on the highly questionable assumption of a constant . Furthermore, meridional motions, a necessary consequence of the interaction of rotation with convection, are ignored. In this context we discuss Stenflo's results about the global wave pattern decomposition of the solar magnetic field and conclude that it cannot be interpreted in the framework of the conventional dynamo equations.We discuss solar dynamo theories and argue that the surface layers could be essential for the generation of the poloidal field. If this is the case an -effect would not be needed at the RC-SCZ interface (where the toroidal field is generated). The two central problems facing solar dynamo theories may the transport of the surface poloidal field to the RC-SCZ interface and the uncertainty about the contributions to the global magnetic field by the small-scale magnetic features.Visitor, National Solar Observatory, National Optical Astronomy Observatories.The National Optical Astronomy Observatories are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.     

The dynamo dilemma

The recent determination that the angular velocity of the Sun declines downward through the convective zone raises serious questions about the nature of the solar dynamo. The principal qualitative features of the Sun are the azimuthal fields that migrate toward the equator in association with an oscillating poloidal field which reverses at about the time of maximum appearance of bipolar magnetic regions. If decreases downward, or is negligible, the horizontal gradient in produces a dynamo with some of these essential characteristics. There is reason to think that the dynamo is confined to the lower half of the convective zone where has the opposite sign from the usual ( > 0 in the northern hemisphere) producing equatorward migration but reversing the sign of the associated poloidal field. Meridional circulation may play an essential role in shaping the dynamo. At the present time it is essential to measure accurately and determine the nature of the meridional circulation.Solar Cycle Workshop Paper.     

Magnetic-cloud chamber effects behind flare-generated shock waves

A mechanism explaining the generation of the helium-enriched plasma-condensation colud (HAE-events) behind the front of shock waves associated with mass-ejecting flares is presented. The mechanism is based on the occurence of physical conditions, analogous to those in a Wilson cloud chamber in a magnetic field, behind the front of a flare-generated shock wave propagation out into interplanetary space. Consequently, if the solar atmosphere above the flare active region is saturated with ejected helium plasma, conditions are created for the forming of the helium-enriched plasma-condensation colud in the temperature-depressed region behind the shock wave front.     

The loss-cone driven instability for Langmuir waves in an unmagnetized plasma

Analytic and numerical results are presented for the growth rate of Langmuir waves due to a loss-cone distribution of energetic electrons. The effect of the magnetic field on the wave-particle interaction is ignored, and the resonance condition is described in terms of a resonance hyperboloid in momentum space. The collisional evolution of a distribution of magnetically trapped electrons is followed numerically to show how a gap distribution develops. The growth is most favorable for an intermediate sized loss cone ( 45 °) and a gap distribution in which the mean energy of the suprathermal electrons is much larger than the thermal energy of the background electrons. It is plausible that loss-cone gap distributions do develop in the solar corona, and that they should lead to second harmonic plasma emission weakly polarized in the x-mode.     

Variations of the Chromospheric Network with the Solar Cycle

We have digitized a small sample of Caii K spectroheliograms from the photographic archive of Arcetri Observatory for the period 1950–1970. For each digitized plate, active regions have been automatically identified and masked by applying an algorithm based on the geometrical connection between active pixels. Contrast histograms have been derived for the full disk and for quiet regions. Both of them show a neat Gaussian profile on the dark side and a significant tail on the bright side, due to the brightness enhancements associated with magnetic fields. A solar cycle dependence of the histogram asymmetry is clearly evident in quiet region data, thus confirming that the network component might provide a significant contribution to long-term variations of the total irradiance.     

Взаимооействие Излучения Рентгеновскооо Истооника с АтмосФерой Нормальной Звезды в Тесных Двойных Системах

, . : , . , . . ( ) . . . HZ Her=Her X1, . . , . , ., hv 15–30 . , . Sco X1 .     

Некоторые асимптотические решения в ограниченной задаче трех тел

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Some asymptotic solutions in the restricted problem of three bodies by L. G. Lukjanov.

Some particular solutions of the plane restricted problem of three bodies in the form of Liapunov's series are obtained. These solutions asymptotically approach the Lagrange solutions. Convergence is proved.

     

On the occurrence of critical levels in solar magnetohydrodynamics

It is shown that the singular behaviour exhibited by a solution of the magnetoatmospheric wave equation for motion in the presence of a horizontal magnetic field is a special case of the valve type critical level discussed by Acheson (1973), with the difference that the valve effect does not strictly occur; waves are captured as they approach the singular level from either side and are neither reflected or transmitted, but constrained to propagate along the field line. This effect is also likely to occur for purely vertical fields. The possible importance of such critical levels to solar physics is discussed.     

Возможный механизм радиоизлучения пульсаров

, , , , , . , , . - . — , , .     

Solar magnetic fields and convection

The flux-rope-fibre model of solar magnetic fields is developed further to cover post-spot evolution of the fields, faculae, and the influence of magnetic fields on some convective motions. (i) Unipolar magnetic regions of a strongly dominant polarity are explained, as are some fields outside the network, and some tiny reversed polarity fields. (ii) The migration of magnetic regions is explained: the following regions to the poles where most of the flux just vanishes and the preceding towards the equator. (iii) The model explains the rotation of the gross pattern of background fields with a period of 27 days. It explains the puzzling features of active longitudes and of magnetic longitudes extending across the equator. (iv) The magnetic model provides a framework for the various chromospheric fine structures, the rosettes, bushes, double chains, mottles and spicules. It provides qualitative models of these features and points the way to a very complicated quantitative model of the network. (v) Several new convective patterns are described and explained in terms of magnetic stresses. The first is the moat around sunspots, which replaces the supergranule motions there. The second is the long-lived (4–7 days) supergranule cell enclosed by strong fields. The third is a small-scale () convective motion, and the fourth is aligned or long granules, both caused by small-scale magnetic fields. (vi) Photospheric line faculae and photospheric continuum faculae are different phenomena. The former, like the chromospheric faculae, are caused by Alfvén-wave heating. The latter are caused by a new small-scale convective motion. (vii) A model of the 3-min oscillation is described.     

The solar wind cycle,the sunspot cycle,and the corona

Recent theories of the solar cycle and of coronal heating strongly suggest that solar cycle variations of different quantities (i.e. sunspots, coronal green line, etc.) ought not to be expected to be in phase with one another. In agreement with this notion we note that the shape of the corona typical of a maximum eclipse occurs 1.5yr before sunspot maximum, compared with 2 yr as might be expected from Leighton's standard model. Further, we argue that the phase of the solar wind cycle can be determined from geomagnetic observations. Using this phase, a solar cycle variation of 100 km s^–1 in the solar wind velocity and 1 in the magnetic field intensity becomes apparent. In general, the solar wind cycle lags the coronal-eclipse-form cycle by 3 yr, compared with the 2 yr that might be expected from model calculations.     

Topology of the magnetic field and geomagnetism

We define the topology of an (axisymmetric) magnetic field, a set of qualitative labels characterizing the connectivity of the lines of force. Under the special continuous deformations of theB-field defined by time evolution under the dynamo equation in the convective regime (where the frozen-in behavior dominates the diffusion), this topology is preserved. This theorem should have applications to the study of time-varying magnetic fields in that regime in the case that exact or even approximate solutions are difficult to obtain. A partial generalization to the general case of convection and diffusion is made. As an application, a critique of Hibberd's recent theory of a time-dependent axisymmetric geomagnetic dynamo whose dipole-like field undergoes successive reversals is given.     

A physical mechanism for the production of solar flares

The weakly ionized photospheric layer in the sunspot environment satisfies certain dynamo inequalities (Equations (11) and (13)) resulting in photospheric Hall current systems. The corresponding Joule dissipation is associated with the surrounding plage area. For critical values of the driving or convective winds (speeds 1 km/s), two stream instability results. The computed energy is of the order of that found in solar flares.     

Is there a weak mixed polarity background field? Theoretical arguments

A number of processes associated with the formation of active regions produce U-loops: fluxtubes having two ends at the photosphere but otherwise still embedded in the convection zone. The mass trapped on the field lines of such loops makes them behave in a qualitative different way from the omega-loops that form active regions. It is shown that U-loops will disperse though the convection zone and form a weak (down to a few gauss) field that covers a significant fraction of the solar surface. This field is tentatively identified with the inner-network fields observed at Kitt Peak and Big Bear. The process by which these fields escape through the surface is described; a remarkable property is that it can make active regions fields apparently disappear in situ. The mixed polarity moving magnetic features near sunspots are interpreted as a locally intense form of this disappearance by escape of U-loops.     

The solar dynamo and the convective rolls

The most sophisticated attempts to model the convection zone have yielded results in which the angular velocity increases outwards and the largest scales of convection take the form of banana cells aligned with the rotation axis. However, not only does the sign of the angular velocity gradient present problems for dynamo theory, but attempts to detect banana type cells have so far been unsuccessful. Although by no means conclusive, current tracer, spectropic, and radiative data all tend to support models of azimuthal rolls encircling the axis as the fundamental mode.It is shown here that convective upflows and downflows are preferentially generated along the rotation axis and thus initially the large-scale eddies may take the form of azimuthal rolls surrounding the poles. It is then shown that such a system may generate a progressive dynamo wave propagating from pole to equator. Since Parker has shown that an azimuthal magnetic toroid can generate a thermal shadow above it which suppresses its buoyancy, the corresponding temperature deficit so formed becomes the natural site for the downflow of the azimuthal rolls. Thus as the dynamo propagates towards the equator, so will the convective rolls. Finally the compatibility of the most recent helioseismology data with the azimuthal roll model is discussed.Solar Cycle Workshop Paper.