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.     

Numerical dynamo models of Uranus' and Neptune's magnetic fields

The non-axisymmetric, non-dipolar magnetic fields of Uranus and Neptune are markedly different from the axially-dipolar dominated fields of the other planets in our Solar System with active dynamos. Stanley and Bloxham [Stanley, S., Bloxham, J., 2004. Nature 428, 151-153] used numerical modeling to demonstrate that Uranus' and Neptune's unusual fields could be the result of a different convective region geometry in these planets. They found that a numerical dynamo operating in a thin shell surrounding a stably-stratified fluid interior produces magnetic field morphologies similar to those of Uranus and Neptune. This geometry for the convective region was initially proposed by Hubbard et al. [Hubbard, W.B., Podolak, M., Stevenson, D.J., 1995. In: Cruickshank, D. (Ed.), Neptune and Triton. Univ. of Arizona Press, Tucson, pp. 109-138] to explain both the magnetic field morphology as well as the low intrinsic heat flows from these planets. Here we examine the influence of varying the stable layer radius in numerical models and compare the results to thin shell models surrounding solid inner cores. We find that a limited range of stable-layer shell thicknesses exist in which Uranus/Neptune-like field morphologies result. This allows us to put constraints on the size of the convective layers in Uranus and Neptune.     

Hierarchial galactic dynamo and seed magnetic field problem

A new approach to the galactic seed magnetic field problem is briefly discussed. It is shown that, in early stages of galactic evolution, the hierarchial agglomeration and fragmentation processes can account for the generation of a dynamically important magnetic field. The amplification of this field follows an inverse cascade since a non-zero average value of the field amplified on a smaller scale serves as a seed field on the next (earlier) hierarchial scale. In such a scenario, a problem of how to get things started never occurs as any infinitesimally small battery generated seed field (Lazarian 1992a) can be efficiently amplified passing by through a sufficient number of amplification cascades.     

On the parametric resonance in a thin disk galactic dynamo

The absence of a parametric resonance by the generation of a large scale bisymmetric magnetic field in a thin galactic disk with periodically time dependent properties in the frames of the simplest thin disk galactic dynamo model is shown.     

Star formation and galactic dynamo model with helicity fluxes

We propose a possible scenario of large-scale magnetic field evolution for galaxies with star formation. An important point affecting the results of our calculations is a parametrization of dynamo-governing quantities. In comparison with previous works, we have reconsidered the views of how star formation affects the stationary magnetic field strength, viscosity, and other parameters important for galactic dynamos. The calculations have been performed by taking into account the magnetic helicity fluxes, which introduce an additional nonlinearity into the model and change the regime of galactic dynamo action. We have confirmed the previously suggested idea that for weak star formation its influence on the magnetic field strength is minor and the relationship between them clearly manifests itself only when the star formation rate reaches a certain threshold value. In this case, on the one hand, the threshold lowers-this effect manifests itself at a star formation surface density greater than that in the Milky Way by a factor of 5. On the other hand, intense star formation can cause both a monotonic decay of the large-scale magnetic field and its oscillations near some value.     

Invisible dynamo in mean-field models

The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.     

Stochasticity in galactic models

We study the effect of a spiral-like perturbation in the orbits of an axisymmetric galactic potential using surfaces of section. We find that the perturbation induces stochasticity and diffusion of orbits in phase space.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Mean-field approach to spherical dynamo models

The mean-field approach to dynamo theory has proved to be a useful tool in the investigation of cosmical magnetic fields. This paper gives a systematic discussion of this approach for spherical dynamo models as suggested by cosmical bodies. At first some fundamentals of dynamo theory are explained with particular attention to formulations in terms of toroidal and poloidal magnetic fields. Starting from the general ideas of mean-field magnetohydrodynamics the relevant mean-field equations for the models envisaged are derived and discussed. The considerations are not restricted to motions of turbulent nature, motions with more or less regular flow patterns are admitted too. A new representation of the crucial electromotive force caused by the fluctuating motions is given. For an important special case the dependence of this electromotive force on the motions is calculated. The mean-field concept is in particular elaborated under the assumption that the motions show certain symmetry and stationarity properties as to be expected at cosmical bodies. The respective results for the electromotive force caused by the fluctuating motions are discussed in detail. Within this frame the possibilities of dynamo mechanisms are systematically studied. In addition to the well-known α² and αω-mechanisms some others, termed β², βω, and δω-mechanisms, are envisaged, whose relevance for cosmical objects remains to be investigated. In a following paper numerical results are given for dynamo models with mechanisms as envisaged here.     

Investigations of spherical kinematic mean-field dynamo models

The paper supplements an earlier one on the mean-field approach to spherical kinematic dynamo models (Rädler 1980a) by results of numerical investigations. A number of dynamo models working on the basis of the α²-mechanism are considered. Cases of pure α²-mechanism are studied, which includes only the simplest form of α-effect and no other induction effect, as well as cases with several additional effects due to fluctuating or mean motions. By the pure α²-mechanism axisymmetric and non-axisymmetric fields, can be excited and maintained with nearly equal ease. Part of the additional induction effects, however, clearly favour axisymmetric fields, and others non-axisymmetric fields. The non-axisymmetric fields are waves which travel in azimuthal direction, eastward or westward, depending on the models. For special dynamo models the transition from α² to αω-mechanism and properties of the latter are investigated. The results support the presumption that the αω-mechanism is able to maintain only axisymmetric but never non-axisymmetric fields. Conditions for the occurrence of non-oscillatory or oscillatory fields are discussed, and again the influence of additional induction effects is studied. There are further presented a model with βω-mechanism maintaining an axisymmetric non-oscillatory field, and models with two kinds of δω-mechanisms allowing axisymmetric non-oscillatory and oscillatory fields. Some ideas concerning dynamo models for the Earth, the Sun and magnetic stars are discussed. It seems possible to construct dynamo models for the Earth, on the basis of the α²-mechanism which explain not only the presence of a magnetic field with a strong dipole part but also the inclination of the dipole axis against the axis of rotation, the occurrence of higher multipoles and the westward drift of the non-axisymmetric parts. Models with αω, βω or δω-mechanism, which have to be considered in the case of a strong differential rotation inside the core, provide an explanation at first only of the axisymmetric parts of the field, and the non-axisymmetric parts have then to be interpreted, for example, as MAC-waves. As far as dynamo models for the Sun are concerned, in addition to the possibility of an αω-mechanism also that of a βω or δω-mechanism is discussed, which, however, does not look not very promising. In the models developed so far, which work with the αω-mechanism, only a few of the induction effects of fluctuating motions have been included; it seems necessary to investigate also influences of other effects. The sectorial structure of the solar magnetic field can hardly be understood in terms of the traditional mean-field concept. The magnetic stars possess fields which strongly deviate from symmetry with respect to the axis of rotation. The occurrence of such fields seems understandable only if there is no noticeable differential rotation. They can be maintained by an α²-mechanism but hardly by αω, βω or δω-mechanisms.     

Three-integral models for axisymmetric galactic discs

We present new equilibrium component distribution functions that depend on three analytic integrals in a Stäckel potential, and that can be used to model stellar discs of galaxies. These components are generalizations of two-integral ones and can thus provide thin discs in the two-integral approximation. Their most important properties are the partly analytical expression for their moments, the disc-like features of their configuration space densities (exponential decline in the galactic plane and finite extent in the vertical direction) and the anisotropy of their velocity dispersions. We further show that a linear combination of such components can fit a van der Kruit disc.     

The current status of kinematic solar dynamo models

This review provides a historical overview of how research in kinematic solar dynamo modeling evolved during the last few decades and assesses the present state of research. The early pioneering papers assumed the dynamo to operate in the convection zone. It was suggested in the 1980s that the dynamo operates in a thin layer at the bottom of the convection zone. Some researchers in recent years are arguing that the poloidal field is produced near the surface—an idea that goes back to Babcock (1961) and Leighton (1969).     

Solar dynamo theory and the models of Babcock and Leighton

The dynamo theory of the solar cycle as developed by Parker and others, and the observational models of Babcock and Leighton have been examined, with the conclusion that the dynamo theory is not applicable to the Sun and that the models fail.An essential part of the theory is an adequate effective diffusion coefficient. Fields are continuously sheared and amplified and, in this theory, these may not be allowed to accumulate; all subsurface fields of an old cycle must be eliminated. Ohmic diffusion is negligible and turbulent diffusion is invoked. However, this requires that all solar fields are tangled to a small scale, which is contrary to observation; for Hale's polarity laws are strictly observed, and large-scale surface features are common at the end of an 11-yr cycle in the same general area where new fields are appearing.The erupted (sunspot) fields lie generally above the unerupted, toroidal fields so that, even if they are merged as required, the centroid of the new system would be above that of the old. The result is not a steady-state oscillator, as required, but the complete loss of the solar field.It is concluded that for these and other reasons a shallow, reversing field is unacceptable, and that a deeply penetrating field is required. Reference is made to an alternative theory of the solar cycle based on a deep magnetic field.     

Axisymmetric galactic models in spherical potentials

We study projected kinematic characteristics of a class of axisymmetric models for the luminous components of galaxies. Models of this class are known as extended Osipkov-Merritt models and have been studied first by Arnold (1990). The line-of-sight velocity dispersions are given and the profiles of the projected velocity distribution are described using their Gauss-Hermite moments.     

On the number of effective integrals in galactic models

Three different numerical techniques are tested to determine the number of integrals of motion in dynamical systems with three degrees of freedom.

1. The computation of the whole set of Lyapunov Characteristic Exponents (LCE).
2. The triple sections in the configurations space.
3. The Stine-Noid box-counting technique.

These methods are applied to a triple oscillator with coupling terms of the third order. Cases are found for which one effective integral besides the Hamiltonian subsists during a very long time. Such orbits display simultaneously chaotic and quasi-periodic motion, according to which coordinates are considered. As an application, the LCE procedure is applied to a triaxial elliptical galaxy model. Contrary to similar 2-dimensional systems, this 3-dimensional one presents noticeable zones in the phase space without any non-classical integral.     

Global solar dynamo models: Simulations and predictions

Flux-transport type solar dynamos have achieved considerable success in correctly simulating many solar cycle features, and are now being used for prediction of solar cycle timing and amplitude. We first define flux-transport dynamos and demonstrate how they work. The essential added ingredient in this class of models is meridional circulation, which governs the dynamo period and also plays a crucial role in determining the Sun’s memory about its past magnetic fields. We show that flux-transport dynamo models can explain many key features of solar cycles. Then we show that a predictive tool can be built from this class of dynamo that can be used to predict mean solar cycle features by assimilating magnetic field data from previous cycles.     

Analytical galactic models with mild stellar cusps

In the past two decades, it has been established by high-resolution observations of early-type galaxies that their nuclear surface brightness and corresponding stellar mass densities are characterized by cusps. In this paper, we present a new spherical analytical model family describing mild cuspy centres. We study isotropic and anisotropic models of Osipkov–Merritt type. It is shown that the associated distribution functions and intrinsic velocity dispersions can be represented analytically in a unified way in terms of hypergeometric series, allowing thus a straightforward comparison of these important global quantities for galaxies having underlying mass densities which may differ significantly in their degree of central cuspiness or radial falloff.     

New photometric models of galactic evolution applied to the HDF

We summarize our modelling of galaxy photometric evolution (the GRASIL code). By including the effects of dust grains and PAH molecules in a two-phase clumpy medium, where clumps are associated with star-forming regions, we reproduce the observed UV to radio SEDs of galaxies with star formation rates from zero to several hundred M _⊙ yr^-1.GRASIL is a powerful tool for investigating star formation, the initial mass function and the supernova rate in nearby starbursts and normal galaxies, as well as for predicting the evolution of luminosity functions of different types of galaxies at wavelengths covering six decades. It may be interfaced with any device to provide the star formation and metallicity histories of a galaxy. As an application, we have investigated the properties of early-type galaxies in the HDF, tracking the contribution of this population to the cosmic star formation history, which has a broad peak between z = 1.5 and 4.To explain the absence of objects at z ≳ 1.3, we suggest a sequence of dust-enshrouded merger-driven starbursts in the first few Gyr of galaxy lifetimes. We are at present working on a complementary sample of late-type objects selected in a similar way. This revised version was published online in July 2006 with corrections to the Cover Date.