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We present an optimized design of our recently realized disc dynamo. Like the original set-up, the optimized dynamo consists of a flatmulti-arm spiral coil and a co-axially placed disc which is connected to the former by sliding liquid metal contacts. In contrast to the original set-up, the disc and the coil in the optimized design have different sizes. This allows the disc to capture more of the high-density magnetic flux generated in the inner part of the coil and to avoid the reverse flux in the outer part of the coil. By optimizing the coil and dics radii, the critical magnetic Reynolds number can be reduced from -34.6 when the disc and the coil have equal inner and outer radii with the ratio ri/ro -0.36 to Rm-11.6. This lowest possible disc dynamo threshold is attained when the disc and the coil have relatively narrow widths. Using a slightly suboptimal but more practical set-up with the inner and outer radii of the disc and coil equal to (0.3,0.9) and (0.74,1), respectively, self-excitationis expected at Rm-14.6. [ABSTRACT FROM AUTHOR]

The magnetic fields take place in different astrophysical objects, such as stars, planets, galaxies, accretion discs etc. Their evolution is usually described by the dynamo model. The equations of the dynamo are quite difficult to be solved, so different approximations are often used. One of the most successful ones are connected with the no- model which has been developed for thin discs that can be a good model for galaxies and accretion discs. In this paper we study the magnetic field evolution in the case of Keplerian rotation law. The results have been obtained for the simplest case and for the model with helicity fluxes. This approach can be useful while researching the role of convective flows in the discs. It is shown that the magnetic field can have oscillations in this case. Also we show the evolution of the energy which can significantly change because of the convective flows. [ABSTRACT FROM AUTHOR]

In fluid dynamics, the scaling behaviour of flow length scales is commonly used to infer the governing force balance of a system. The key to a successful approach is to measure length scales that are simultaneously representative of the energy contained in the solution (energetically relevant) and also indicative of the established force balance (dynamically relevant). In the case of numerical simulations of rotating convection and magnetohydrodynamic dynamos in spherical shells, it has remained difficult to measure length scales that are both energetically and dynamically relevant, a situation that has led to conflicting interpretations, and sometimes misrepresentations of the underlying force balance. By analysing an extensive set of magnetic and non-magnetic models, we focus on two length scales that achieve both energetic and dynamical relevance. The first one is the peak of the poloidal kinetic energy spectrum, which we successfully compare to crossover points on spectral representations of the force balance. In most dynamo models, this result confirms that the dominant length scale of the system is controlled by a previously proposed quasi-geostrophic (QG-) MAC (Magneto-Archimedean-Coriolis) balance. In non-magnetic convection models, the analysis generally favours a QG-CIA (Coriolis-Inertia-Archimedean) balance. Viscosity, which is typically a minor contributor to the force balance, does not control the dominant length scale at high convective supercriticalities in the non-magnetic case, and in the dynamo case, once the generated magnetic energy largely exceeds the kinetic energy. In dynamo models, we introduce a second energetically relevant length scale associated with the loss of axial invariance in the flow. We again relate this length scale to another crossover point in scale-dependent force balance diagrams, which marks the transition between large-scale geostrophy (the equilibrium of Coriolis and pressure forces) and small-scale magnetostrophy, where the Lorentz force overtakes the Coriolis force. Scaling analysis of these two energetically and dynamically relevant length scales suggests that the Earth's dynamo is controlled by a QG-MAC balance at a dominant scale of about |$200 \, \mathrm{km}$|⁠ , while magnetostrophic effects are deferred to scales smaller than |$50 \, \mathrm{km}$|⁠. [ABSTRACT FROM AUTHOR]

This paper reviews the remarkable developments in numerical geodynamo simulations over the last few years. Simulations with Ekman numbers as low as are now within reach and more and more details of the observed field are recovered by computer models. However, some newer experimental and ab initio results suggest a rather large thermal conductivity for the liquid iron alloy in Earth's core. More heat would then simply be conducted down the core adiabat and would not be available for driving the dynamo process. The current status of this topic is reported and alternative driving scenarios are discussed. The paper then addresses the question whether dynamo simulations obey the magnetostrophic force balance that characterises the geodynamo and proceeds with discussing related problems like scaling laws and torsional oscillations. Finally, recent developments in geomagnetic data assimilation are reviewed, where geomagnetic data and dynamo simulations are coupled to form a tool for interpreting observations and predicting the future evolution of Earth's magnetic field. [ABSTRACT FROM AUTHOR]

It is widely accepted that astrophysical magnetic fields are generated by dynamo action. In many cases, these fields exhibit organisation on a scale larger than that of the underlying turbulent flow (e.g. the 11-year solar cycle). The mechanism for the generation of so-called large-scale fields remains an open problem. In cases where the magnetic Reynolds number (Rm) is small, dynamo-generated fields are coherent but at (the astrophysically relevant) high Rm, the fields are overwhelmed by small-scale fluctuating field. Recently Tobias and Cattaneo have shown that an imposed large-scale shear flow can suppress the small-scale fluctuations and allow the large-scale temporal behaviour to emerge. Shear is also believed to modify the electromotive force by introducing correlations between the flow and the field. However, in previous models at high Rm the shear is often artificially imposed or driven by an arbitrary body force. Here we consider a simple kinematic model of a convective dynamo in which shear is self-consistently driven by the presence of a horizontal temperature gradient (resulting in a thermal wind) and a rotation vector that is oblique to gravity. By considering a -dimensional system, we are able to reach high Rm so that the dynamo approaches the asymptotic regime where the growth rate becomes approximately independent of Rm. We find the flows studied here to be excellent small-scale dynamos, but with very little systematic behaviour evident at large Rm. We attribute this to being unable to self-consistently generate flows with both large (net) helicity and strong shear in this setup. [ABSTRACT FROM AUTHOR]

We consider the effect of a subadiabatic layer at the base of the convection zone on convection itself and the associated large-scale dynamos in spherical wedge geometry. We use a heat conduction prescription based on the Kramers opacity law which allows the depth of the convection zone to dynamically adapt to changes in the physical characteristics such as rotation rate and magnetic fields. We find that the convective heat transport is strongly concentrated towards the equatorial and polar regions in the cases without a substantial radiative layer below the convection zone. The presence of a stable layer below the convection zone significantly reduces the anisotropy of radial enthalpy transport. Furthermore, the dynamo solutions are sensitive to subtle changes in the convection zone structure. We find that the kinetic helicity changes sign in the deeper parts of the convection zone at high latitudes in all runs. This region expands progressively towards the equator in runs with a thicker stably stratified layer. [ABSTRACT FROM AUTHOR]

In this paper, we study the correlation functions for magnetic energy and magnetic helicity generated by a small-scale dynamo mechanism in a mirror-asymmetric and isotropic turbulent conductive fluid. Solving the Kazantsev system for small-scale generation by an iterative approach, we restore the correlation functions in spatial and spectral representations. Studying scales of localisation and their dependence on magnetic Reynolds number, we propose approximate functions, which can be applied for energy and helicity in a spectral space. We show the absence of 3/2-spectrum for Kazantsev assumptions at and helicity sign changing at. Using our results and estimating the relation between helicity and energy at different scales, we speculate about what can be considered as a small scale in a spectral space, and how this scale can be connected with mean-field processes. [ABSTRACT FROM AUTHOR]

Numerical models of planetary MHD dynamos have led to many advances in the last twenty years. However, the accessible parameter space of these models is somewhat limited due to computational constraints. A number of numerically based scaling laws have been proposed, but it has been difficult to reliably confirm them from the simulation data alone. Since these scaling laws have to be used to extend the numerical models into the planetary parameter regime, getting correct scalings is an important issue. Here some possible balances between the relevant terms in the dynamo equations are considered, and a number of different known and new scaling laws are proposed and justified from analytical point of view. Some of these laws are compatible with the widely known Christensen and Aubert (Geophys. J. Int. 2006, 166) scaling for the magnetic field strength. Plausible estimates of the typical values of the important quantities in the Earth's core and other Terrestrial planets are made, and the extent to which the various scaling laws are consistent with these estimates is discussed. [ABSTRACT FROM AUTHOR]

An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of this paper is to analyse the energetics of chiral magnetically driven turbulence and its effect on the generation and dynamics of the magnetic field using direct numerical simulations. We study these effects for different initial conditions, including a variation of the initial chiral chemical potential and the magnetic Prandtl number,. In particular, we determine the ratio of kinetic to magnetic energy, , in chiral magnetically driven turbulence. Within the parameter space explored in this study, reaches a value of approximately 0.064–0.074–independently of the initial chiral asymmetry and for. Our simulations suggest, that decreases as a power law when increasing by decreasing the viscosity. While the exact scaling depends on the details of the fitting criteria and the Reynolds number regime, an approximate result of is reported. Using the findings from our numerical simulations, we analyse the energetics of chiral magnetically driven turbulence in the early Universe. [ABSTRACT FROM AUTHOR]

The magnetic fields in the inner parts of some spiral galaxies are understood quite well. Their generation is connected with the dynamo mechanism that is based on the joint action of turbulent diffusion and the α-effect. Usually the galactic dynamo is described with the so-called no-z approximation which takes into account that the galaxy disc is quite thin, with the implication that some spatial derivatives may be replaced by algebraic expressions. Some galaxies have outer rings that are situated at some distance from the galactic centre. The magnetic field can be described there also using the no-z model. As the thickness of such objects is comparable with their width, it is necessary to take into account the z-dependence of the field. We have studied the magnetic field evolution using the no-z approximation and torus dynamo model for the torus with rectangular cross-section in the axisymmetric case. [ABSTRACT FROM AUTHOR]

The project DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies) conducted at Helmholtz–Zentrum Dresden–Rossendorf (HZDR) provides a new platform for a variety of liquid sodium experiments devoted to problems of geo- and astrophysical magnetohydrodynamics. The most ambitious experiment within this project is a precession-driven dynamo experiment that currently is under construction. It consists of a cylinder filled with liquid sodium that simultaneously rotates around two axes. The experiment is motivated by the idea of a precession-driven flow as a complementary energy source for the geodynamo or the ancient lunar dynamo. In the present study, we address numerical and experimental examinations in order to identify parameter regions where the onset of magnetic field excitation will be most probable. Both approaches show that in the strongly nonlinear regime the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves that arise from nonlinear self-interactions. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane, which, however, only occurs in a very limited range of the precession ratio. This axisymmetric mode turns out to be beneficial for dynamo action, and kinematic simulations of the magnetic field evolution induced by the time-averaged flow exhibit magnetic field excitation at critical magnetic Reynolds numbers around , which is well within the range of the planned liquid sodium experiment. [ABSTRACT FROM AUTHOR]

Magnetic fields of planets, stars and galaxies are generated by self-excitation in moving electrically conducting fluids. Once produced, magnetic fields can play an active role in cosmic structure formation by destabilising rotational flows that would be otherwise hydrodynamically stable. For a long time, both hydromagnetic dynamo action as well as magnetically triggered flow instabilities had been the subject of purely theoretical research. Meanwhile, however, the dynamo effect has been observed in large-scale liquid sodium experiments in Riga, Karlsruhe and Cadarache. In this paper, we summarise the results of liquid metal experiments devoted to the dynamo effect and various magnetic instabilities such as the helical and the azimuthal magnetorotational instability and the Tayler instability. We discuss in detail our plans for a precession-driven dynamo experiment and a large-scale Tayler–Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear. [ABSTRACT FROM AUTHOR]

Abstract Employing the standard solar interior model as input we construct a dynamically-consistent nonlinear dynamo model that takes into account the detailed description of the Λ - effect, turbulent pumping, magnetic helicity balance, and magnetic feedback on the differential rotation and meridional circulation. The background mean-field hydrodynamic model of the solar convection zone accounts the solar-like angular velocity profile and the double-cell meridional circulation. We investigate an impact of the nonlinear magnetic field generation effects on the long-term variability and properties of the magnetic cycle. The nonlinear dynamo solutions are studied in the wide interval of the α effect parameter from a slightly subcritical to supercritical values. It is found that the magnetic cycle period decreases with the increasing cycle's magnitude. The periodic long-term variations of the magnetic cycle are excited in case of the overcritical α effect. These variations result from the hemispheric magnetic helicity exchange. It depends on the magnetic diffusivity parameter and the magnetic helicity production rate. The large-scale magnetic activity modifies the distribution of the differential rotation and meridional circulation inside convection zone. It is found that the magnetic feedback on the global flow affects the properties of the long-term magnetic cycles. We confront our findings with solar and stellar magnetic activity observations. [ABSTRACT FROM AUTHOR]

The debate on the role of Euler potentials (EP), α∇β, in the dynamo theory is a long-standing one. It is known that the cross-product of gradients of two the potentials may represent magnetic fields lines. However, 2D and 3D dynamo hydromagnetic simulations suggest that their utility as analogues of magnetic field potential is restricted. This raises questions about their utility in the broader context of magneto-genesis and dynamo theories. We reexamine this and find that a reinterpretation of such potentials offers a new insight into the role EP may play in the general evolution of magnetic fields. [ABSTRACT FROM AUTHOR]

Various approaches to forecasting the solar cycle based on solar dynamo models are considered. The importance of separating predictions of catastrophic events such as the Maunder minimum, predictions of general trends in solar activity between Grand minima, and forecasts of the next cycle, based on current knowledge of previous cycles is noted. The role of fluctuations of dynamo drivers for the forecast is emphasized. The polar magnetic field in the current cycle is considered as a natural predictor of the amplitude of the following cycle. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the description of kinematic dynamo action in a sphere and its analytical treatment with the BULLARD-GELLMAN formalism. One goal of dynamo theory is to answer the question: Can magnetic fields of stellar objects be generated or sustained due to (fluid) motion in the interior? BULLARD and GELLMAN were among the first to study this question, leading the way for many subsequent studies, cf. Bullard (Philos Trans R Soc A 247(928):213-278, 1954). In their publication the differential equations resulting from a toroidal-poloidal decomposition of the velocity and magnetic field are stated without an in-depth discussion of the employed methods and computation steps. This study derives the necessary formalism in a compact and concise manner by using an operator-based approach. The focus lies on the mathematical steps and necessary properties of the considered formalism. Prior to that a derivation of the induction equation is presented based on rational continuum electrodynamics. As an example of the formalism the decay of two magnetic fields is analyzed. [ABSTRACT FROM AUTHOR]

To investigate the differential rotation of sunspot groups using the Greenwich data, we propose an approach based on a statistical analysis of the histograms of particular longitudinal velocities in different latitude intervals. The general statistical velocity distributions for all such intervals are shown to be described by two rather than one normal distribution, so that two fundamental rotation modes exist simultaneously: fast and slow. The differentiality of rotation for the modes is the same: the coefficient at sin2 in Faye’s law is 2.87-2.88 deg/day, while the equatorial rotation rates differ significantly, 0.27 deg/day. On the other hand, an analysis of the longitudinal velocities for the previously revealed two differing populations of sunspot groups has shown that small short-lived groups (SSGs) are associated with the fast rotation mode, while large long-lived groups (LLGs) are associated with both fast and slow modes. The results obtained not only suggest a real physical difference between the two populations of sunspots but also give new empirical data for the development of a dynamo theory, in particular, for the theory of a spatially distributed dynamo. [ABSTRACT FROM AUTHOR]

Dynamo theory suggests that there are two types of solar dynamo, namely the conventional mean-field dynamo, which produces large- and small-scale magnetic fields involved in the activity cycle, and also the small-scale dynamo, which produces a cycle independent smallscale magnetic field. The relative contribution of the two mechanisms to solar magnetism remains a matter of scientific debate, which includes the opinion that the contribution of the small-scale dynamo is negligible. Here, we consider several tracers of magnetic activity that separate cycle-dependent contributions to the background solar magnetic field from those that are independent of the cycle. We call background fields the magnetic fields outside active regions and give further development of this concept. The main message of our paper is that background fields include two relative separate populations. The background fields with a strength up to 100 Mx cm-2 are very poorly correlated with the sunspot numbers and vary little with the phase of the cycle. In contrast, stronger magnetic fields demonstrate pronounced cyclic behaviour.We discuss how this result can be included in the above-mentioned concepts of solar dynamo studies. [ABSTRACT FROM AUTHOR]

The initial magnetic field of previous magnetorotational instability (MRI) simulations has always included a significant system-scale component, even if stochastic. However, it is of conceptual and practical interest to assess whether the MRI can grow when the initial field is turbulent. The ubiquitous presence of turbulent or random flows in astrophysical plasmas generically leads to a small-scale dynamo (SSD), which would provide initial seed turbulent velocity and magnetic fields in the plasma that becomes an accretion disc. Can the MRI grow from these more realistic initial conditions? To address this, we supply a standard shearing box with isotropically forced SSD generated magnetic and velocity fields as initial conditions and remove the forcing. We find that if the initially supplied fields are too weak or too incoherent, they decay from the initial turbulent cascade faster than they can grow via the MRI. When the initially supplied fields are sufficient to allow MRI growth and sustenance, the saturated stresses, large-scale fields and power spectra match those of the standard zero net flux MRI simulation with an initial large-scale vertical field. [ABSTRACT FROM AUTHOR]

We conducted a paleomagnetic study of the matrix of Allende CV3 chondritic meteorite, isolating the matrix's primary remanent magnetization, measuring its magnetic fabric and estimating the ancient magnetic field intensity. A strong planar magnetic fabric was identified; the remanent magnetization of the matrix was aligned within this plane, suggesting a mechanism relating the magnetic fabric and remanence. The intensity of the matrix's remanent magnetization was found to be consistent and low (~6 μT). The primary magnetic mineral was found to be pyrrhotite. Given the thermal history of Allende, we conclude that the remanent magnetization was formed during or after an impact event. Recent mesoscale impact modeling, where chondrules and matrix are resolved, has shown that low-velocity collisions can generate significant matrix temperatures, as pore-space compaction attenuates shock energy and dramatically increases the amount of heating. Nonporous chondrules are unaffected, and act as heat-sinks, so matrix temperature excursions are brief. We extend this work to model Allende, and show that a 1 km/s planar impact generates bulk porosity, matrix porosity, and fabric in our target that match the observed values. Bimodal mixtures of a highly porous matrix and nominally zero-porosity chondrules make chondrites uniquely capable of recording transient or unstable fields. Targets that have uniform porosity, e.g., terrestrial impact craters, will not record transient or unstable fields. Rather than a core dynamo, it is therefore possible that the origin of the magnetic field in Allende was the impact itself, or a nebula field recorded during transient impact heating. [ABSTRACT FROM AUTHOR]

In this paper, we present the results of a preliminary analytical and numerical study of new derived system of single and double coupled self-exciting Faraday disk homopolar dynamos by Hide et al [3, 7]. Also, well-known systems including, Rikitake and Bullard systems have been reached by using Tikhonov theorem [6, 10] and eliminating method. [ABSTRACT FROM AUTHOR]

In dynamo theory the toroidal velocity theorem in its classical version (Elsasser, Phys. Rev. 1946, vol. 69, pp. 106-116, Bullard and Gellman, Phil. Trans. R. Soc. Lond. 1954, vol. A247, pp. 213-278) rules out dynamo action in a spherical conducting volume provided that the fluid is incompressible, the conductivity is uniform, and the velocity field is purely toroidal. We prove in this note that this result is robust in the sense that slight compressibility of the fluid, small non-radial variations and even large radial variations in conductivity, and the presence of a small non-toroidal velocity component do not invalidate the theorem. Moreover, by proper choice of the conductivity distribution modelling the conducting volume, small deviations from spherical symmetry of the conductor can also be taken into account. [ABSTRACT FROM AUTHOR]

Magnetic dynamo action caused by themagnetorotational instability is studied in the shearingbox approximation with no imposed net magnetic flux. Consistent with recent studies, the dynamo action is found to be sensitive to the aspect ratio of the box: it is much easier to obtain in tall boxes (stretched in the direction normal to the disc plane) than in long boxes (stretched in the radial direction). Our direct numerical simulations indicate that the dynamo is possible in both cases, given a large enough magnetic Reynolds number. To explain the relatively larger effort required to obtain the dynamo action in a long box, we propose that the turbulent eddies caused by the instability most efficiently fold and mix the magnetic field lines in the radial direction. As a result, in the long box the scale of the generated strong azimuthal (stream-wise directed) magnetic field is always comparable to the scale of the turbulent eddies. In contrast, in the tall box the azimuthal magnetic flux spreads in the vertical direction over a distance exceeding the scale of the turbulent eddies. As a result, different vertical sections of the tall box are permeated by large-scale non-zero azimuthal magnetic fluxes, facilitating the instability. In agreement with this picture, the cases when the dynamo is efficient are characterized by a strong intermittency of the local azimuthal magnetic fluxes. [ABSTRACT FROM AUTHOR]

Compositional convection is thought to be an important energy source for magnetic field generation within planetary interiors. The Prandtl number, Pr , characterizing compositional convection is significantly larger than unity, suggesting that the inertial force may not be important on the small scales of convection as long as the buoyancy force is not too strong. We develop asymptotic dynamo models for the case of small Rossby number and large Prandtl number in which inertia is absent on the convective scale. The relevant diffusivity parameter for this limit is the compositional Roberts number, q = D / η , which is the ratio of compositional and magnetic diffusivities. Dynamo models are developed for both order one q and the more geophysically relevant low q limit. For both cases the ratio of magnetic to kinetic energy densities, M , is asymptotically large and reflects the fact that Alfvén waves have been filtered from the dynamics. Along with previous investigations of asymptotic dynamo models for Pr = O ( 1 ) , our results show that the ratio M is not a useful indicator of dominant force balances in the momentum equation since many different asymptotic limits of M can be obtained without changing the leading order geostrophic balance. Furthermore, the present models show that inertia is not a requirement for driving low q , large-scale dynamos. [ABSTRACT FROM AUTHOR]

Modern models of nonlinear dynamo saturation in celestial bodies (specifically, on the Sun) are largely based on the consideration of the balance of magnetic helicity. This physical variable has also a topological meaning: it is associated with the linking coefficient of magnetic tubes. In addition to magnetic helicity, magnetohydrodynamics has a number of topological integrals of motion (the so-called higher helicity moments). We have compared these invariants with magnetic helicity properties and concluded that they can hardly serve as nonlinear constraints on dynamo action. [ABSTRACT FROM AUTHOR]

In dynamo power-based scaling laws, the powerinjected by buoyancy forces is measured by a so-called flux-based Rayleigh number, denoted as(see Christensen and Aubert, Geophys. J. Int. 2006, vol. 166, pp. 97–114). Whereas it is widely accepted that this parameter is measured (as opposite to controlled) in dynamos driven by differential heating, the literature is much less clear concerning its nature in the case of imposed heat flux. We clarify this issue by highlighting that in that case, theparameter becomes controlled only in the limit of large Nusselt numbers (). We then address the issue of the robustness of the original relation betweenandwith the geometry and the thermal boundary conditions. We show that in the cartesian geometry, as in the spherical geometry with a central mass distribution, this relation is purely linear, in both differential and fixed-flux heating. However, we show that in the geometry commonly studied by geophysicists (spherical with uniform mass distribution), its validity places an upper-bound on the strength of the driving which can be envisaged in a fixed Ekman number simulation. An increase of the Rayleigh number indeed yields deviations (in terms of absolute correction) from the linear relation betweenand. We conclude that in such configurations, the parameter range for whichis controlled is limited. [ABSTRACT FROM PUBLISHER]

We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local galactic dynamo solution, parametrized by the disc radius. Namely, the critical (zero growth) solution obtained by treating the dynamo equation as a perturbed diffusion equation is normalized using a non-linear solution that makes use of the ‘no-z’ approximation and the dynamical α-quenching non-linearity. This overall solution is found to be reasonably accurate when compared with detailed numerical solutions. It is thus potentially useful as a tool for predicting observational signatures of magnetic fields of galaxies. In particular, such solutions could be painted on to galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure data sets. Further, we explore the properties of our numerical solutions, and their dependence on certain parameter values. We illustrate and assess the degree to which numerical solutions based on various levels of approximation, common in the dynamo literature, agree with one another. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution ofWolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behaviour of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 yr ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 per cent correlation over all intervals of observation (about 270 yr). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependences are in good agreement with observations. [ABSTRACT FROM AUTHOR]

The paper by Popova et al. presents an oversimplified mathematical model of solar activity with a claim of predicting/postdicting it for several millennia ahead/backwards. The work contains several flaws devaluating the results: (1) the method is unreliable from the point of view of signal processing (it is impossible to make harmonic predictions for thousands of years based on only 35 years of data) and lacks quality control; (2) the result of post-diction apparently contradicts the observational data. (3) theoretical speculations make little sense. To summarize, a multi-harmonic mathematical model, hardly related to full solar dynamo theory, is presented, which is not applicable to realistic solar conditions because of the significant chaotic/stochastic intrinsic component and strong non-stationarity of solar activity. The obtained result is apparently inconsistent with the data in the past and thus cannot be trusted for the future predictions. [ABSTRACT FROM AUTHOR]

Recent data on superflares on Sun-like stars and radiocarbon data on solar activity in the past are both indicative of transient epochs of unusually high magnetic activity. We propose an explanation for the grand activity maxima in the framework of a solar dynamo model with fluctuating parameters. Solar-type dynamos are oscillatory because of the combination of the solar-type differential rotation with positive (in the Northern hemisphere) alpha-effect. An artificial reversal of the sign in the alpha-effect changes the dynamo to a steady regime with hundreds of times larger magnetic energy compared to the amplitude of the cyclic dynamo. Sufficiently large and durable fluctuations reversing the sign of the alpha-effect during the growth phase of a magnetic cycle can, therefore, cause a transient change to a steady dynamo with considerably increased magnetic energy. This qualitative scenario for grand activity maxima is supported by computations of the dynamo model with a fluctuating alpha-effect. The computed statistics of several thousand magnetic cycles gives examples of cycles with very high magnetic energy. Our preliminary estimations, however, suggest that the probability of solar superflares is extremely low. [ABSTRACT FROM AUTHOR]

Excitations of two oppositely directed waves of stellar activity generated by two dynamo-active layers located in a single stellar hemisphere are examined using simple dynamo models. The domains of model parameters corresponding to various types and directions of the activity waves are found. It is shown that oppositely directed waves of activity are generated if the dynamo numbers have the same order of magnitude, ~10−10, but opposite signs. How frequently this case can be observed among real stars remains open to question. The report of oppositely directed waves of stellar activity in the literature is especially valuable in this connection. [ABSTRACT FROM AUTHOR]

Convective instabilities of viscous conducting fluids play an important role in many physical phenomena in planets and stars. Astrophysical magnetic fields are usually explained in a framework of the dynamo theory, describing transformation of the kinetic energy of a flow into magnetic energy. Therefore, an analysis of purely convective states and their bifurcations, as a control parameter is changed, provides a detailed framework for the subsequent study of magnetic field generation by these states. In this paper, three-dimensional Rayleigh–Bénard convection in the absence of magnetic field is investigated numerically for various values of the Rayleigh number and a fixed Prandtl number (corresponding to its value for convection in the Earth’s outer core). On increasing the Rayleigh number, we identified periodic, quasiperiodic, chaotic and hyperchaotic attractors of the convective system and their bifurcations, thereby describing a route to spatiotemporal chaos in the convective system. The occurrence of on–off intermittency in the energy time series is discussed. [ABSTRACT FROM AUTHOR]

We investigate the frequency of all (X-ray flare events higher than class B1.0), B, C, M and X-class flares, respectively, derived from the National Geophysical Data Center (NGDC) list of solar flares between May 1983 and September 2014, which corresponds to the two complete solar cycles (SCs) 22 and 23 as well as the rise and maximum phases of SC 24. Analysis shows that the temporal behavior for these various class flares is quite different. The main findings of this study, confirmed by using the Hinode flare catalog where possible, are as follows. (1) The B-class flares are in complete antiphase with all, C, M and X-class flares. (2) While, there is a small decreasing trend in the peak values of the smoothed monthly C-class flare numbers from SC 22 to 24, the occurrence rate of M and X-class flares dropped by almost half and two-thirds, respectively, during SC 23 and remained almost the same during SC 24. This class-dependent temporal behavior provides support for dynamo models that involve the coexistence of a deep global and a superficial local dynamo. [ABSTRACT FROM AUTHOR]

In our earlier works (Ivanov and Miletsky, 2012, 2014), we demonstrated that (1) the evolution of average sunspot latitudes can be described by a universal latitude curve, the shape of which does not depend on the cycle amplitude and (2) at the cycle decline phase, these latitudes correlate well with the current level of solar activity. In this work, we demonstrate that these features of the latitude evolution of the cycle, as well as the empirical Waldmeier rule, can be described by a simple model of a convective α-ω dynamo in a thin spherical layer with the addition of some nonlinearities. [ABSTRACT FROM AUTHOR]

The ordered magnetic field observed via polarised synchrotron emission in nearby disc galaxies can be explained by a mean-field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical-flux initial conditions are potentially able to influence this dynamo via the occurrence of the magnetorotational instability (MRI). We aim to study the influence of various initial field configurations on the saturated state of the mean-field dynamo. This is motivated by the observation that different saturation behaviour was previously obtained for different supernova rates. We perform direct numerical simulations (DNS) of three-dimensional local boxes of the vertically stratified, turbulent interstellar medium, employing shearing-periodic boundary conditions horizontally. Unlike in our previous work, we also impose a vertical seed magnetic field. We run the simulations until the growth of the magnetic energy becomes negligible. We furthermore perform simulations of equivalent 1D dynamo models, with an algebraic quenching mechanism for the dynamo coefficients. We compare the saturation of the magnetic field in the DNS with the algebraic quenching of a mean-field dynamo. The final magnetic field strength found in the direct simulation is in excellent agreement with a quenched α) dynamo. For supernova rates representative of the Milky Way, field losses via a Galactic wind are likely responsible for saturation. We conclude that the relative strength of the turbulent and regular magnetic fields in spiral galaxies may depend on the galaxy's star formation rate. We propose that a mean field approach with algebraic quenching may serve as a simple sub-grid scale model for galaxy evolution simulations including a prescribed feedback from magnetic fields. (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

There has for many years been interest in finding necessary conditions for dynamo action. These are usually expressed in terms of bounds on integrated properties of the flow. The bounds can clearly be improved when the flow structure can be taken into account. Recent research presents techniques for finding optimised dynamos (that is with the lowest dynamo threshold) subject to constraints, (e.g. with fixed mean squarevorticity). It is natural to ask if such an optimum solution can exist when the mean squarevelocityis fixed. The aim of this note is to show that this is not the case and in fact that a steady or periodic dynamo can exist in a bounded conductor with an arbitrarily small value of the kinetic energy. [ABSTRACT FROM PUBLISHER]

Using different proxies of solar activity, we have studied the following features of the solar cycle: i) The linear correlation between the amplitude of cycle and its decay rate, ii) the linear correlation between the amplitude of cycle $n$ and the decay rate of cycle $(n - 1)$, and iii) the anti-correlation between the amplitude of cycle $n$ and the period of cycle $(n - 1)$. Features ii) and iii) are very useful because they provide precursors for future cycles. We have reproduced these features using a flux-transport dynamo model with stochastic fluctuations in the Babcock-Leighton $\alpha$ effect and in the meridional circulation. Only when we introduce fluctuations in meridional circulation, are we able to reproduce different observed features of the solar cycle. We discuss the possible reasons for these correlations. [ABSTRACT FROM AUTHOR]

Based on an analysis of the observational data for solar cycles 12-23 (Royal Greenwich Observatory-USAF/NOAA Sunspot Data), we have studied various parameters of the 'Maunder butterflies.' Based on the observational data for cycles 16-23, we have found that BT/ Land S depend linearly on each other, where B is the mean magnetic field of the cycle, T is the cycle duration, S is the cycle strength, and L is the mean sunspot latitude in the cycle (the arithmetic mean of the absolute values of the mean latitudes in the north and south). The connection of the observed quantities with the α- ω-dynamo theory is discussed. [ABSTRACT FROM AUTHOR]

We propose a self-consistent dynamo mechanism for the generation of large-scale magnetic fields in natural objects. Recent computational studies have described the formation of large-scale vortices in rotating turbulent convection. Here we demonstrate that for magnetic Reynolds numbers below the threshold for small-scale dynamo action, such turbulent flows can sustain large-scale magnetic fields, i.e., fields with a significant component on the scale of the system. [ABSTRACT FROM AUTHOR]

Context. The (Zeeman-)Doppler imaging studies of solar-type stars very often reveal large high-latitude spots. This also includes F stars that possess relatively shallow convection zones, indicating that the dynamo operating in these stars differs from the solar dynamo. Aims. We aim to determine whether mean-field dynamo models of late-F type dwarf stars can reproduce the surface features recovered in Doppler maps. In particular, we wish to test whether the models can reproduce the high-latitude spots observed on some F dwarfs. Methods. The photometric inversions and the surface temperature maps of AF Lep were obtained using the Occamian-approach inversion technique. Low signal-to-noise spectroscopic data were improved by applying the least-squares deconvolution method. The locations of strong magnetic flux in the stellar tachocline as well as the surface fields obtained from mean-field dynamo solutions were compared with the observed surface temperature maps. Results. The photometric record of AF Lep reveals both long- and short-term variability. However, the current data set is too short for cycle-length estimates. From the photometry, we have determined the rotation period of the star to be 0.9660 ± 0.0023 days. The surface temperature maps show a dominant, but evolving, high-latitude (around +65°) spot. Detailed study of the photometry reveals that sometimes the spot coverage varies only marginally over a long time, and at other times it varies rapidly. Of a suite of dynamo models, the model with a radiative interior rotating as fast as the convection zone at the equator delivered the highest compatibility with the obtained Doppler images [ABSTRACT FROM AUTHOR]

Context. The large-scalemagnetic field of solar-type stars reconstructed from their spectropolarimetric observations provide important insight into their underlying dynamo processes. Aims. We aim to investigate the temporal variability of the large-scale surface magnetic field and chromospheric activity of a young solar analogue, the G0 dwarf HN Peg. Methods. The large-scale surface magnetic field topology is reconstructed using Zeeman Doppler imaging at six observational epochs covering seven years. We also investigated the chromospheric activity variations by measuring the flux in the line cores of the three chromospheric activity indicators: Ca II H&K, Ha, and the Ca II IRT lines. Results. The magnetic topology of HN Peg shows a complex and variable geometry. While the radial field exhibits a stable positive polarity magnetic region at the poles at each observational epoch, the azimuthal field is strongly variable in strength, where a strong band of positive polarity magnetic field is present at equatorial latitudes. This field disappears during the middle of our timespan, reappearing again during the last two epochs of observations. The mean magnetic field derived from the magnetic maps also follow a similar trend to the toroidal field, with the field strength at a minimum in epoch 2009.54. Summing the line of sight magnetic field over the visible surface at each observation, HN Peg exhibits a weak longitudinal magnetic field (B1) ranging from -14 G to 13 G, with no significant long-term trend, although there is significant rotational variability within each epoch. Those chromospheric activity indicators exhibit more long-term variations over the time span of observations, where the minimal is observed in Epoch 2008.71. [ABSTRACT FROM AUTHOR]

We present an investigation of dynamo in a simultaneous dependence on the non-uniform stratification, electrical conductivity of the inner core and the Prandtl number. Computations are performed using the MAG dynamo code. In all the investigated cases, the generated magnetic fields are dipolar. Our results show that the dynamos, especially magnetic field structures, are independent in our investigated cases on the electrical conductivity of the inner core. This is in agreement with results obtained in previous analyses. The influence of non-uniform stratification is for our parameters weak, which is understandable because most of the shell is unstably stratified, and the stably stratified region is only a thin layer near the CMB. The teleconvection is not observed in our study. However, the influence of the Prandtl number is strong. The generated magnetic fields do not become weak in the polar regions because the magnetic field inside the tangent cylinder is always regenerated due to the weak magnetic diffusion. [ABSTRACT FROM AUTHOR]

Jupiter’s dynamo is modelled using the anelastic convection-driven dynamo equations. The reference state model is taken from French et al. [2012]. Astrophys. J. Suppl. 202, 5, (11pp), which used density functional theory to compute the equation of state and the electrical conductivity in Jupiter’s interior. Jupiter’s magnetic field is approximately dipolar, but self-consistent dipolar dynamo models are rather rare when the large variation in density and the effective internal heating are taken into account. Jupiter-like dipolar magnetic fields were found here at small Prandtl number, Pr = 0.1 . Strong differential rotation in the dynamo region tends to destroy a dominant dipolar component, but when the convection is sufficiently supercritical it generates a strong magnetic field, and the differential rotation in the electrically conducting region is suppressed by the Lorentz force. This allows a magnetic field to develop which is dominated by a steady dipolar component. This suggests that the strong zonal winds seen at Jupiter’s surface cannot penetrate significantly into the dynamo region, which starts approximately 7000 km below the surface. [ABSTRACT FROM AUTHOR]

We propose two new analytical expressions to fit the Mauersberger-Lowes geomagnetic field spectrum at the core-mantle boundary. These can be used to estimate the radius of the outer liquid core where the geodynamo operates, or more generally the radius of the planetary dynamo regions. We show that two sub-families of the geomagnetic field are independent of spherical harmonics degree n at the core-mantle boundary and exhibit flat spectra. The first is the non-zonal field, i.e., for spherical harmonics order m different from zero. The second is the quadrupole family, i.e., n+m even. The flatness of their spectra is motivated by the nearly axisymmetric time-average paleomagnetic field (for the non-zonal field) and the dominance of rotational effects in core dynamics (for the quadrupole family). We test our two expressions with two approaches using the reference case of the Earth. First we estimate at the seismic core radius the agreement between the actual spectrum and the theoretical one. Second we estimate the magnetic core radius, where the spectrum flattens. We show that both sub-families offer a better agreement with the actual spectrum compared with previously proposed analytical expressions, and predict a magnetic core radius within less than 10 km of the Earth's seismic core radius. These new expressions supersede previous ones to infer the core radius from geomagnetic field information because the low degree terms are not ignored. Our formalism is then applied to infer the radius of the dynamo regions on Jupiter, Saturn, Uranus and Neptune. The axisymmetric nature of the magnetic field of Saturn prevents the use of the non-zonal expression. For the three other planets both expressions converge and offer independent constraints on the internal structure of these planets. These non-zonal and quadrupole family expressions may be implemented to extrapolate the geomagnetic field spectrum beyond observable degrees, or to further regularize magnetic field models constructed from modern or historical observations. [ABSTRACT FROM AUTHOR]