A Rossby-wave dynamo for the sun,I

There is increasing interest in the possible existence of large horizontally flowing eddies or Rossby waves in the sun's convection zone and photosphere. We present here and in Part II a mathematical model which shows that flows of this type, driven by an assumed latitudinal temperature gradient, can act as hydromagnetic dynamos to induce magnetic fields that periodically reverse.In this part, we discuss the assumptions for the model, review earlier linear analyses that demonstrate the ability of Rossby waves to induce solar-like magnetic fields, and finally derive the non-linear equations that govern the model. The analysis is simplified by confining the fluid and magnetic fields to a thin rotating annulus. The flow is taken to be nearly incompressible, heliostrophic and hydrostatic. Induced magnetic fields are allowed to react upon the inducing motions. Transports of momentum and magnetic flux by smaller scale convective motions, and the transport of heat by these motions and radiation, are parameterized by diffusion coefficients. The solar convection is also assumed to be responsible for the latitudinal temperature gradient.Part II will be published in Solar Phys. 9, No. 1.     

Evidence for the phi-dependent rotation-oscillation of the Sun (and for the driving mechanism of the asymmetric dynamo)

Longitude-dependent oscillations of the solar rotation are derived from the 27-day averages of the photospheric velocity data. Two pairs of prominent periods are obtained. Their harmonic means correspond to a semiannual variation and to the first harmonic of the latter. To explain the origin of the oscillation the corona and the interplanetary material are supposed to rotate parallel to the planetary plane with an inclination to the solar equator. The non-uniform shearing around the equator is assumed to result in oscillation with a period of half of a year.     

A dynamo scenario

In this paper, the term dynamo refers to the complex of physical mechanisms that cause solar magnetic activity in all its manifestations. Properties of that dynamo are inferred from observational indications to fit them into a scenario. Properties and models of the manifestations of strong magnetic field are briefly summarized, together with their formation during the emergence of -shaped loops from the toroidal flux system in the interface below the convection zone. The evolution of magnetic concentrations and the flux removal from the atmosphere, with indications for flux retraction, are considered. Then the weak (INF) fields are discussed, together with the role of upward floating LI- shaped loops in the removal of toroidal flux. Finally features of strong and weak fields are fitted into a scenario for a cyclic dynamo, in which the regeneration of the poloidal field of proper sign relies on the cancellation of magnetic flux in the surface transport interpreted as reconnection, followed by retraction of reconnected loops.Dedicated to Cornelis de JagerBased on an invited talk during Solar Cycle Workshop, March 28–30, 1996, Tucson.     

On a Babcock-Leighton dynamo model with a deep-seated generating layer for the toroidal magnetic field, II

In a previous paper (Paper I), we studied a dynamo model of the Babcock-Leighton type (i.e., the surface eruptions of toroidal magnetic field are the source for the poloidal field) that included a thin, deep seated, generating layer (GL) for the toroidal field, B. Meridional motions (of the order of 12 m s^–1 at the surface), rising at the equator and sinking at the poles were essential for the dynamo action. The induction equation was solved by approximating the latitudinal dependence of the fields by Legendre polynomials. No solutions were found with _p = _f where _p and _f are the fluxes for the preceding and following spot, respectively. The solutions presented in Paper I, had _p = –0.5 _f , were oscillatory in time, and large radial fields, B, were present at the surface.Here, we resume the study of Paper I with a different numerical approach allowing for a much higher resolution in , the polar angle. The time dependent partial differential equations for the toroidal and poloidal field are solved with the help of a second order, time and space centered, finite difference scheme. Oscillatory solutions with _p = _f are found for various values of the meridional motions and diffusivity coefficients. The surface values of B, while considerably smaller than those of Paper I, are still unacceptably large, specially at the poles. The reason can be traced to the eruption of toroidal field at high latitudes. It appears that in order to obtain small values for the radial field in the polar regions, high latitude sources ( smaller than /4, say), must reach their maximum below the surface. Weaker meridional motions near the poles than in the equatorial region are also suggested.     

A planetary dynamo model

Using the Lagrangian approach, the author considered the temporal evolution of an ensemble of interacting magnetohydrodynamic cyclones, obeying equations of the Langevin type, in a rotating medium. The problem is topical for fast-rotating convective objects: cores of planets and a number of stars, where the Rossby numbers are much less than unity and the geostrophic balance of forces is observed. In this work, results of simulation are given both for the two-dimensional case, when axes of cyclones can rotate only in the vertical plane, and for the three-dimensional case when the axes are rotating by two angles. It is shown that a change in the heat flux on the shell boundary impacts the frequency of reversals of the mean dipole magnetic field, which agrees with results of simulation in three-dimensional models of a planetary dynamo. Applications of the model for the giant planets are considered, and an explanation of certain episodes of the geomagnetic field in the past is offered.     

A magnetic dynamo in the moon?

The existence of fossil lunar magnetism has caused speculation that the Moon had, at one time, an internally produced dynamo magnetic field. Quantitative analysis of this idea, constrained by the largest iron lunar core compatible with observations, implies that the Moon would have had to rotate faster than its breakup angular velocity in order to support a dynamo magnetic field.A paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

A nonlinear model of the solar dynamo

The role of nonlinearity is explored in a mean-field dynamo model. Magnetic fields are amplified by the combined action of the and-effects, and as the field's intensity increases the Lorentz force becomes important. Torsional oscillations and meridional circulations are driven by the Lorentz force, and the oscillations are consistent with those measured on the surface of the Sun. The torsional oscillations feedback in the induction equation and saturate the magnetic field's growth by quenching differential rotation. This model can also help us understand the processes responsible for the range of periods seen in the activity cycles of other stars like the Sun.     

A joined model for solar dynamo and differential rotation

A model for the solar dynamo, consistent in global flow and numerical method employed with the differential rotation model, is developed. The magnetic turbulent diffusivity is expressed in terms of the entropy gradient, which is controlled by the model equations. The magnetic Prandtl number and latitudinal profile of the alpha-effect are specified by fitting the computed period of the activity cycle and the equatorial symmetry of magnetic fields to observations. Then, the instants of polar field reversals and time-latitude diagrams of the fields also come into agreement with observations. The poloidal field has a maximum amplitude of about 10 Gs in the polar regions. The toroidal field of several thousand Gauss concentrates near the base of the convection zone and is transported towards the equator by the meridional flow. The model predicts a value of about 10³⁷ erg for the total magnetic energy of large-scale fields in the solar convection zone.     

A dynamo scenario for polar and whole-surface starspot generation

Rapidly rotating young (T Tauri, pre-Main-Sequence, and Main-Sequence) stars as well as subgiants seem to show starspots not only at low and middle latitudes, as the Sun, but also at high latitudes and even around the poles. We consider a simple nonlinear Parker migratory dynamo model working in a thin shell in order to investigate how high latitude and polar spots may be produced for different values of the dynamo layer radius and thickness and for various rotation rates. Simple assumptions on the angular velocity gradient and helicity distribution are made according to symmetry properties and recent solar and stellar observations. A recently proposed asymptotic WKB-type approach is used to solve the dynamo problem and its drawbacks and advantages in the solar and stellar contexts are discussed. As a general result, we find that a sizable toroidal field can be produced over a much more extended latitude range than in the Sun, thus explaining in a natural way the occurrence of activity from the poles to the equator in such stars. Our approach complements that proposed by Schüssler et al. (1996) which is focused on the instability and emergence of the azimuthal flux tubes, as well as the analyses based on a dynamo working over an extended part of the stellar convective envelope (Moss, Tuominen, and Brandenburg, 1991; Moss et al., 1995).     

Towards a model for the solar dynamo

We study a mean field model of the solar dynamo, in which the non-linearity is the action of the azimuthal component of the Lorentz force of the dynamo-generated magnetic field on the angular velocity. The underlying zero-order angular velocity is consistent with recent determinations of the solar rotation law, and the form of the alpha effect is chosen so as to give a plausible butterfly diagram. For small Prandtl numbers we find regular, intermittent and apparently chaotic behaviour, depending on the size of the alpha coefficient. For certain parameters, the intermittency displays some of the characteristics believed to be associated with the Maunder minimum. We thus believe that we are capturing some features of the solar dynamo.     

A thin disc model of the galactic dynamo

An axisymmetric αω-dynamo model of the Galactic disc is investigated. The disc is thin and its width, 2h^*, varies slowly with distance, ωT^*, from the axis of symmetry. The strength of the α^*, varies linearly with axialdistance, z^*, while differential rotation, dΩ^*/dωT^*, remains constant. Otherwise α^* and dΩ^*/dωT^* are arbitrary functions of ωT^*. The results are applied to the special case of the oblate spheroid first investigated by STIX (1976) and later by WHITE (1977). In the limit of small aspect ratio the new results agree with those obtained by WHITE and confirm that the dynamo numbers computed by STIX are too small.     

A dynamo theory of solar flares

It is proposed that the solar flare phenomenon can be understood as a manifestation of the electrodynamic coupling process of the photosphere-chromosphere-corona system as a whole. The system is coupled by electric currents, flowing along (both upward and downward) and across the magnetic field lines, powered by the dynamo process driven by the neutral wind in the photosphere and the lower chromosphere. A self-consistent formulation of the proposed coupling system is given. It is shown in particular that the coupling system can generate and dissipate the power of 10²⁹ erg s^#X2212;1 and the total energy of 10³² erg during a typical life time (10³ s) of solar flares. The energy consumptions include Joule heat production, acceleration of current-carrying particles along field lines, magnetic energy storage and kinetic energy of plasma convection. The particle acceleration arises from the development of field-aligned potential drops of 10–150 kV due to the loss-cone constriction effect along the upward field-aligned currents, causing optical, X-ray and radio emissions. The total number of precipitating electrons during a flare is shown to be of order 10³⁷–10³⁸.     

A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields

More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric  α²– Ω  dynamo model is derived to explore the characteristics of the axisymmetric  ( m = 0)  and the first non-axisymmetric  ( m = 1)  modes and to provide a theoretical basis with which to explain the 'active longitude', 'flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the  α²–Ω  and the  α–Ω  models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.     

On the non-symmetric solar dynamo

The external field of the solar magnetohydrodynamic dynamo is expressed in terms of spherical harmonics and in powers of 1/r. The non-symmetric dynamo is stabilized by a -dependent rotational oscillation which interacts with the magnetic field, thus compensating for Ohmic loss. As a consequence, the axis of a dipole wave is found to move on a great circle, with revolution time equal to the magnetic cycle.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Magnetoconvection and the solar dynamo

We review current understanding of the interaction of magnetic fields with convective motions in stellar convection zones. Among the most exciting recent results is the discovery that magnetic fields need not primarily be confined to the stable layer below the convection zone; numerical simulations have shown that surprisingly, strong magnetic fields can be maintained in the interior of the convection zone.     

Observational arguments for a local dynamo

Regions of rigid rotation, or Pivot Points, can be seen in the deviations from the classical law of solar differential rotation. These Pivot Points set up a local dynamo that is reflected in the emergence of the magnetic flux of the Active Centers.     

"日中乌"辨析

从观测资料可认证史载“日中乌”是指太阳黑子,而“阳乌载日”则是日全食时的日冕。二者并非神话,而是写实文字。     

Ca II K line profile of the truly quiet Sun

While evaluating the chromospheric variability (solar cycle related or any other) using the Ca II K line (3933.684 Å) as an indicator, an essential prerequisite is the knowledge of the profile of a truly quiet Sun in the integrated light. Such a profile can serve as a bench mark over which enhancements can be measured, particularly when modelling variability. This paper describes how such a K-line profile has been derived for the quiet Sun using disc-integrated light.