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.     

Early martian dynamo generation due to giant impacts

During late-stage planet formation, giant impacts produce localized mantle melt regions within which impactor iron droplets settle to the bottom near a permeability horizon. After accumulation, iron heated by the impact migrates downward to the core through colder, mostly solid mantle. The degree of thermal equilibration and partitioning of viscous heating between impactor iron and silicates depends on the mechanism of iron transport to the core. Simple estimates suggest that, following a giant impact, the temperature difference between iron delivered to the core and the mantle outside the impact heated region can be ∼10³ K. Hot impactor iron mergers with the core where it may be efficiently mixed or remain stratified due to thermal buoyancy. In either case, collisional energy carried to the core by impactor iron helps establish conditions favorable for early core cooling and dynamo generation. In this study, we consider the end-member scenario in which impactor iron forms a layer at the top of the core. Energy transfer from the impactor iron layer to the mantle is sufficient to power a dynamo for up to ∼30 Myr even in the limit of a very viscous mantle and heat flux limited by conduction. Using two-dimensional finite element calculations of mantle convection, we show that large-scale mantle flow driven by the buoyancy of the impact thermal anomaly focuses plumes in the impact region and increases both dynamo strength and duration. Melting within the mantle thermal boundary layer likely leads to formation of a single superplume in the location of the impact anomaly driven upwelling. We suggest that formation of magnetized southern highland crust may be related to spreading and differentiation of an impact melt region during the impact-induced dynamo episode.     

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 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 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.     

A Rossby-wave dynamo for the Sun,II

To make the analysis more tractable, we simplify the equations of Part I to apply to two superposed layers of fluid, with horizontal variations in the motion and magnetic field represented by a small number of Fourier harmonics. The resulting set of eighteen ordinary nonlinear differential equations in time for the Fourier amplitudes is integrated numerically. We analyze in detail the dynamo action from a typical Rossby wave motion and compare it with the solar cycle.The field reversal process is similar in some respects to that put forth by Babcock. Toroidal fields are dragged up by vertical motions in the Rossby waves to form large-scale vertical fields, whose polarities alternate with longitude roughly like bipolar magnetic regions. Vertical fields of preferentially one polarity are carried toward the pole by the meridional motion in the wave to form an axisymmetric poloidal field. This poloidal field is then stretched out by the differential rotation into a new toroidal field of the opposite sign from the original. The poloidal field changes sign when the toroidal and bipolar region like fields are maximum, and vice versa.For the case studied, the reversal period is too short ( 2 years) and the poloidal fields too large ( 40 G) for the sun. Improvements for the model are discussed.Part I has been published in Solar Phys. 8, 316.     

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.     

The complementarity of Doppler imaging and photometric starspot modelling

Certain essential formal similarities between the modelling of photometric maculation effects and spectrometric Doppler imaging are pointed out. This parallelism opens the way to a methodological approach to Doppler imaging on quite parallel lines to the authors' studies of stars that exhibit photometric maculation waves. The information content of either form of data set is thence compared.     

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.     

Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model

In the Sun and Sun-like stars,it is believed that cycles of the large-scale magnetic field are produced due to the existence of differential rotation and helici...     

The longitudinal distribution of sunspots and the RS CVn starspot model

The longitudinal distribution of the sunspots has been investigated by using the observations made at the University Observatory of Istanbul in 1979. In order to take into account the activity as a whole, we obtained a new weighting system which depends on the area of spots and used it in our calculations. Differential rotation appeared to effect the considered distribution. It was determined that this longitudinal distribution of spots is not uniform but forms two maxima for two different longitudes. The obtained result verifies one of the main assumptions had been proposed in the starspot model in which accounts for the distortion wave appeared in the light curves of RS CVn-type binaries.     

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.     

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.     

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.     

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.     

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.     

Meridional circulation and dynamo waves

The effect of meridional circulation on spherical shell dynamos is considered in the Parker approximation. We demonstrate that the type of the exited solution crucially depend on the intensity of the meridional circulation. If the circulation is equatorward or if it is polarward however do not exceed some critical value, an oscillating solution in form of an equatorward traveling wave is excited. If the polarward meridional circulation becomes too intensive the solution becomes steady growing. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A hit-and-run giant impact scenario

The formation of the Moon from the debris of a slow and grazing giant impact of a Mars-sized impactor on the proto-Earth (Cameron and Ward [1976]. Lunar Planet. Sci. Conf.; Canup and Asphaug [2001]. Nature 412, 708) is widely accepted today. We present an alternative scenario with a hit-and-run collision (Asphaug [2010]. Chem. Erde 70, 199) with a fractionally increased impact velocity and a steeper impact angle.     

Simultaneous light and velocity curve solution and probable starspot activities for the W UMa system U Pegasi

A statistical study is presented on the distribution of different kinds of massive star classes in the HR diagram using recent calculations of massive single star and massive close binary evolution. The influence of the mass transfer process during the critical Roche lobe overflow phase of a primary component on the relative frequency of the different classes is outlined. It is shown that without an exact knowledge of how mass transfer takes place, the meaning of an initial mass function determined by classical methods is unclear whereas a direct comparison of the observed and theoretically predicted blue/red star ratio is meaningless. The number of O- and WR-type stars with compact companions is expected to be very low (<5%). If mass transfer in binaries is largely conservative, the contribution of real single stars to the supernova II population is low (10–25%).