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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]

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]

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]

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]

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]

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]

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]

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]

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 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]

Direct measurements of the vector turbulent emf in a driven two-vortex flow of liquid sodium were performed in the Madison Dynamo Experiment [K. Rahbarnia et al., Astrophys. J. 759, 80 (2012)]. The measured turbulent emf is anti-parallel with the mean current and is almost entirely described by an enhanced resistivity, which increases the threshold for a kinematic dynamo. We have demonstrated that this enhanced resistivity can be mitigated by eliminating the largest-scale eddies through the introduction of baffles. By tailoring the flow to reduce large-scale components and control the helical pitch, we have reduced the power required to drive the impellers, doubled the magnetic flux generated by differential rotation, and increased the decay time of externally applied magnetic fields. Despite these improvements, the flows remain sub-critical to the dynamo instability due to the reemergence of turbulent fluctuations at high flow speeds. [ABSTRACT FROM AUTHOR]

The generation of a magnetic field by dynamo action in a Taylor-vortex flow is investigated numerically.We first discuss how the Taylor vortices generate a spatially subharmonic dynamo, for which the axial wavelength of the magnetic field is twice the one of the flow pattern. Then, we investigate the influence of the Reynolds number and the turbulent fluctuations on the structure and the onset of the Taylor-Couette dynamo. Finally, based on the subharmonic nature of this dynamo, we propose new configurations which could be relevant for laboratory experiments. [ABSTRACT FROM AUTHOR]

The axisymmetric kinematic dynamo problem is reconsidered, and a number of open questions are answered. Apart from axisymmetry and smoothness of data and solution we deal with this problem under quite general conditions; i.e., we assume a compressible fluid of variable (in space and time) conductivity moving in an arbitrary (axisymmetric) domain. We prove unconditional, pointwise, and exponential decay of the magnetic field and electric current to zero. The decay rate of the external (meridional) magnetic field can become very small (compared to free decay) for special flow fields and large magnetic Reynolds numbers, as we demonstrate with an example. On the other hand, we show for fluids with weak variation of mass density and conductivity that the meridional and azimuthal decay rates do not drop significantly below those of free decay. [ABSTRACT FROM AUTHOR]

Context. Based on the rapidly increasing all-sky data of Faraday rotation measures and polarised synchrotron radiation, the Milky Way's magnetic field can now be modelled with an unprecedented level of detail and complexity. Aims. We aim to complement this phenomenological approach with a physically motivated, quantitative dynamo model - a model that moreover allows for the evolution of the system as a whole, instead of just solving the induction equation for a fixed static disc. Methods. Building on the framework of mean-field magnetohydrodynamics and extending it to the realm of a hybrid evolution, we performed three-dimensional global simulations of the Galactic disc. To eliminate free parameters, closure coefficients embodying the mean-field dynamo were calibrated against resolved local simulations of supernova-driven interstellar turbulence. Results. The emerging dynamo solutions comprise a mixture of the dominant axisymmetric S0 mode with even parity, and a subdominant A0 mode with odd parity. Notably, this superposition of modes creates a strong localised vertical field on one side of the Galactic disc. Moreover, we found significant radial pitch angles that decay with radius, which can be explained by flaring of the disc. In accordance with previous work, magnetic instabilities appear to be restricted to the calmer outer Galactic disc. Their main effect is to create strong fields at large radii such that the radial scale length of the magnetic field increases from 4 kpc (for a mean-field dynamo alone) to about 10 kpc in the hybrid models - the latter being in much better agreement with observations. Conclusions. There remain aspects (e.g., spiral arms, X-shaped halo fields, fluctuating fields) that are not captured by the current model and that will require further development towards a fully dynamical evolution. Nevertheless, we demonstrate that a hybrid modelling of the Galactic dynamo is feasible and can serve as a foundation for future efforts. [ABSTRACT FROM AUTHOR]

The article focuses on the dynamo process in the Earth and its importance in the longevity of the magnetic field and core and mantle in the planet. It says that the dynamo region in the solid silicate mantle can support the global system of plate tectonics resulting to the sustainability of the dynamo process in the Earth. It mentions that the supercritical state of geodynamo is responsible for the polarity reversals of the solar dynamo.

We have investigated the behavior of dynamo waves within the framework of a nonlinear αω-dynamo by taking into account the thickness of the convective zone, turbulent diffusivity, and meridional circulation. We show that there exists a regime in the model where short and longer patterns are simultaneously observed in the butterfly diagrams for the magnetic field. This regime is similar to the mixed cycle of the Sun, when fast quasi-biennial oscillations are observed against the background of the 22-year cycle. [ABSTRACT FROM AUTHOR]

The parameters of a special type of α-effect known in dynamo theory as the Babcock-Leighton mechanism are estimated using the data of sunspot catalogs. The estimates support the presence of the Babcock-Leighton α-effect on the Sun. Fluctuations of the α-effect are also estimated. The fluctuation amplitude appreciably exceeds themean value, and the characteristic time for the fluctuations is comparable to the period of the solar rotation. Fluctuations with the parameters found are included in a numericalmodel for the solar dynamo. Computations show irregular changes in the amplitudes of the magnetic cycles on time scales of centuries and millennia. The calculated statistical characteristics of the grand solar minima and maxima agree with the data on solar activity over the Holocene. [ABSTRACT FROM AUTHOR]

We consider an unforced, incompressible, turbulent magnetofluid constrained by concentric inner and outer spherical surfaces. We define a model system in which normal components of the velocity, magnetic field, vorticity, and electric current are zero on the boundaries. This choice allows us to find a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity and current. The model dynamical system represents magnetohydrodynamic (MHD) turbulence in a spherical domain and is analyzed by the methods similar to those applied to homogeneous MHD turbulence. We find a statistical theory of ideal (i.e. no dissipation) MHD turbulence analogous to that found in the homogeneous case, including the prediction of coherent structure in the form of a large-scale quasistationary magnetic field. This MHD dynamo depends on broken ergodicity, an effect that is enhanced when total magnetic helicity is increased relative to total energy. When dissipation is added and large scales are only weakly damped, quasiequilibrium may occur for long periods of time, so that the ideal theory is still pertinent on a global scale. Over longer periods of time, the selective decay of energy over magnetic helicity further enhances the effects of broken ergodicity. Thus, broken ergodicity is an essential mechanism and relative magnetic helicity is a critical parameter in this model MHD dynamo theory. [ABSTRACT FROM AUTHOR]

Recent discoveries of water-rich, sub-Neptunian- to Neptunian-massed exoplanets with short-period orbits present a new parameter space for the study of exoplanetary dynamos. We explore the geometry of the dynamo source region within this parameter space using 1D interior structure models. We model planets with four chemically distinct layers that consist of (1) an iron core, (2) a silicate layer, (3) an H2O layer, and (4) an H/He envelope. By varying the total planetary mass in the range of 1-19 M⊕, the mass fraction of the H/He envelope between 0.1% and 5.1%, and the equilibrium temperature between 100 K and 1000 K, a survey of the parameter space for potential dynamo source region geometries is conducted. We find that due to the nature of the phase diagram of water at pressure and temperature conditions of planetary interiors, two different dynamo source region geometries are obtainable. Specifically, we find that smaller planets, and planets with thicker H/He envelopes, are likely to be in the regime of a thick-shelled dynamo. Massive planets, and planets with thin H/He envelopes, are likely to be in the regime of a thin-shelled dynamo. Also, small variations of these parameters can produce large interior structure differences. This implies the potential to constrain these parameters based on observations of a planet's magnetic field signature. [ABSTRACT FROM AUTHOR]

Chaotic behavior and detailed parameter analysis of stretch-twist-fold (STF) flow are investigated. STF flow is associated with fluid particle motion which naturally arises in the dynamo theory. It proposes a mechanism, by which a celestial bodies, such as earth and sun, can maintain and amplify the magnetic field continuously. Parameter analysis is performed using linearization theory for different choices of parameters. The existence of Heteroclinic trajectory of Sil'nikov type is proved using an undetermined coefficient method. It connects two non trivial equilibrium points. As a consequence, the Sil'nikov criterion guarantees that STF flow has Smale horseshoes chaos. [ABSTRACT FROM AUTHOR]

We construct a series of kinematic axisymmetric mean-field dynamo models operating in the αΩ, α²Ω and α² regimes, all using the full α-tensor extracted from a global magnetohydrodynamical simulation of solar convection producing large-scale magnetic fields undergoing solar-like cyclic polarity reversals. We also include an internal differential rotation profile produced in a purely hydrodynamical parent simulation of solar convection, and a simple meridional flow profile described by a single cell per meridional quadrant. An α²Ω mean-field model, presumably closest to the mode of dynamo action characterizing the MHD simulation, produces a spatiotemporal evolution of magnetic fields that share some striking similarities with the zonally-averaged toroidal component extracted from the simulation. Comparison with α² and αΩ mean-field models operating in the same parameter regimes indicates that much of the complexity observed in the spatiotemporal evolution of the large-scale magnetic field in the simulation can be traced to the turbulent electromotive force. Oscillating α²solutions are readily produced, and show some similarities with the observed solar cycle, including a deep-seated toroidal component concentrated at low latitudes and migrating equatorward in the course of the solar cycle. Various numerical experiments performed using the mean-field models reveal that turbulent pumping plays an important role in setting the global characteristics of the magnetic cycles. [ABSTRACT FROM AUTHOR]

Abstract: Mars Global Surveyor measurements revealed that the Martian crust is strongly magnetized in the southern hemisphere while the northern hemisphere is virtually void of magnetization. Two possible reasons have been suggested for this dichotomy: a once more or less homogeneously magnetization may have been destroyed in the northern hemisphere by, for example, resurfacing or impacts. The alternative theory we further explore here assumes that the dynamo itself produced a hemispherical field (Stanley et al., 2008; Amit et al., 2011). We use numerical dynamo simulations to study under which conditions a spatial variation of the heat flux through the core–mantle boundary (CMB) may yield a strongly hemispherical surface field. We assume that the early Martian dynamo was exclusively driven by secular cooling and we mostly concentrate on a cosine CMB heat flux pattern with a minimum at the north pole, possibly caused by the impacts responsible for the northern lowlands. This pattern consistently triggers a convective mode which is dominated by equatorially anti-symmetric and axisymmetric (EAA, Landeau and Aubert, 2011) thermal winds. Convective up- and down-wellings and thus radial magnetic field production then tend to concentrate in the southern hemisphere which is still cooled efficiently while the northern hemisphere remains hot. The dynamo changes from an for a homogeneous CMB heat flux to an -type in the hemispherical configuration. These dynamos reverse on time scales of about 10kyrs. This too fast to allow for the more or less unidirectional magnetization of thick crustal layer required to explain the strong magnetization in the southern hemisphere. [Copyright &y& Elsevier]

Aims. We use observations of solar activity to constrain parameters relating to the α effect in stochastic nonlinear dynamo models. Methods. This is achieved through performing a comprehensive statistical comparison by computing probability distribution functions (PDFs) of solar activity from observations and from our simulation of α - Ω mean field dynamo model. The observational data that are used are the time history of solar activity inferred for C14 data in the past 11 000 years on a long time scale and direct observations of the sun spot numbers obtained in recent years 1795-1995 on a short time scale. Monte Carlo simulations are performed on these data to obtain probability distribution functions (PDFs) of the solar activity on both long and short time scales. These PDFs are then compared with predicted PDFs from numerical simulation of our α - Ω dynamo model, where α is assumed to have both mean α0 and fluctuating α' parts. Results. By varying the correlation time τα of fluctuating α', the ratio of the amplitude of the fluctuating to mean alpha αR = √α'2≺/α20 (where angular brackets ≺ ≻ denote ensemble average), and the ratio of poloidal to toroidal magnetic fields, we show that the results from our stochastic dynamo model can match the PDFs of solar activity when τα ϵ [22, 44] years with αR ϵ [0.21, 0.24]. [ABSTRACT FROM AUTHOR]

The induction equation of magnetohydrodynamics (MHD) is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent developments concerning the numerical implementation of this scheme and its applications to various forward and inverse problems in dynamo theory and applied MHD. [ABSTRACT FROM PUBLISHER]

Context. Observations of rapidly rotating M dwarfs show a broad variety of large-scale magnetic fields encompassing dipoledominated and multipolar geometries. In dynamo models, the relative importance of inertia in the force balance, which is quantified by the local Rossby number, is known to have a strong impact on the magnetic field geometry. Aims. We aim to assess the relevance of the local Rossby number in controlling the large-scale magnetic field geometry of M dwarfs. Methods. We have explored the similarities between anelastic dynamo models in spherical shells and observations of activeM-dwarfs, focusing on field geometries derived from spectropolarimetric studies. To do so, we constructed observation-based quantities aimed to reflect the diagnostic parameters employed in numerical models. Results. The transition between dipole-dominated and multipolar large-scale fields in early to mid M dwarfs is tentatively attributed to a Rossby number threshold. We interpret late M dwarfs magnetism to result from a dynamo bistability occurring at low Rossby number. By analogy with numerical models, we expect different amplitudes of differential rotation on the two dynamo branches. [ABSTRACT FROM AUTHOR]

In stars and planets, magnetic fields are believed to originate from the motion of electrically conducting fluids in their interior, through a process known as the dynamo mechanism. In this Letter, an optimization procedure is used to simultaneously address two fundamental questions of dynamo theory: "Which velocity field leads to the most magnetic energy growth?" and "How large does the velocity need to be relative to magnetic diffusion?" In general, this requires optimization over the full space of continuous solenoidal velocity fields possible within the geometry. Here the case of a periodic box is considered. Measuring the strength of the flow with the root-mean-square amplitude, an optimal velocity field is shown to exist, but without limitation on the strain rate, optimization is prone to divergence. Measuring the flow in terms of its associated dissipation leads to the identification of a single optimal at the critical magnetic Reynolds number necessary for a dynamo. This magnetic Reynolds number is found to be only 15% higher than that necessary for transient growth of the magnetic field. [ABSTRACT FROM AUTHOR]

We have constructed a dynamo model for the magnetic field in spiral galaxies that takes into account the differences in star formation rates in different galaxies. The difficulty in constructing the model is that the star formation rate does not enter directly into the equations of magnetohydrodynamics, which include only the root-mean-square velocity of the interstellar gas, its density, and the half-thickness of the ionized gas disk. We propose a parametrization of these quantities that relates them to the star formation rate and investigate our model in terms of the so-called no- z approximation, which neglects the details of the magnetic field structure in a direction perpendicular to the galactic disk. The influence of the star formation rate on the galactic dynamo is a threshold one. This influence is small at moderate star formation rates and significant only at very high star formation rates. If the starburst intensity reaches some critical level (exceeding that in the Milky Way by an order of magnitude), then the large-scale magnetic field is destroyed and it is restored only after completion of the starburst. We provide a list of galaxies that exhibit a fairly high star formation rate and that can be interesting to study their magnetic fields. [ABSTRACT FROM AUTHOR]

Understanding the in situ amplification of large-scale magnetic fields in turbulent astrophysical rotators has been a core subject of dynamo theory. When turbulent velocities are helical, large-scale dynamos that substantially amplify fields on scales that exceed the turbulent forcing scale arise, but the minimum sufficient fractional kinetic helicity fh,c has not been previously well quantified. Using direct numerical simulations for a simple helical dynamo, we show that fh,c decreases as the ratio of forcing to large-scale wave numbers kF/kmin increases. From the condition that a large-scale helical dynamo must overcome the back reaction from any nonhelical field on the large scales, we develop a theory that can explain the simulations. For kF/kmin ⪰ 8 we find fh,c ≲ 3%, implying that very small helicity fractions strongly influence magnetic spectra for even moderate-scale separation. [ABSTRACT FROM AUTHOR]

ABSTRACT We develop and subsequently explore the solution space of a simple flux transport dynamo model that incorporates a time-dependent large-scale meridional circulation. Based on recent observations, we prescribed an analytical form for the amplitude of this circulation and study its impact in the evolution of the magnetic field. We find that cyclic variations in the amplitude and frequency of the meridional flow affect the strength of the solar cycle. Variations in the amplitude of the fluctuations influence the shape of the solar cycle but are only relevant to the cycle's strength variations when they occur at a frequency different from or out of phase of the solar cycle's. [ABSTRACT FROM AUTHOR]

Numerical simulations of the kinematic induction equation are performed on a model configuration of the Cadarache von-K´arm´an-sodium dynamo experiment. The effect of a localized axisymmetric distribution of relative permeability μr that represents soft iron material within the conducting fluid flow is investigated. The critical magnetic Reynolds number Rmc for dynamo action of the first non-axisymmetric mode roughly scales like Rmc μr − Rmc 1 / μ−1/2 r , i.e. the threshold decreases as μr increases. This scaling law suggests a skin effect mechanism in the soft iron discs. More important with regard to the Cadarache dynamo experiment, we observe a purely toroidal axisymmetric mode localized in the high-permeability discs which becomes dominant for large μr. In this limit, the toroidal mode is close to the onset of dynamo action with a (negative) growth rate that is rather independent of the magnetic Reynolds number. We qualitatively explain this effect by paramagnetic pumping at the fluid/disc interface and propose a simplified model that quantitatively reproduces numerical results. The crucial role of the high-permeability discs in the mode selection in the Cadarache dynamo experiment cannot be inferred from computations using idealized pseudovacuum boundary conditions (H ×n = 0). [ABSTRACT FROM AUTHOR]

ABSTRACT The transfer of magnetic chirality in solar active regions is related to the emerging magnetic flux ropes generated in the subatmosphere. This analysis has been presented based on the calculation of the injection of magnetic helicity at the solar surface. As the long-term evolution of the accumulated magnetic helicity is followed, it is found that the transfer of reversal magnetic helicity of active regions is a complex process, and is not monotonic with the same sign. It is found that the dominant contribution of helicity occurs mainly in the fast-developing stage of active regions. By considering the hemispheric trends of magnetic helicity, it is proposed that the reversal helicity in solar active regions has two possible causes: local generation in the convection zone, and trans-equatorial processes in the subatmosphere. In addition to the mirror-symmetrical reverse of twisted magnetic field in the convection zone, the possibility of a trans-equatorial process is discussed in this paper. [ABSTRACT FROM AUTHOR]

Massive stars are crucial building blocks of galaxies and the universe, as production sites of heavy elements and as stirring agents and energy providers through stellar winds and supernovae. The field of magnetic massive stars has seen tremendous progress in recent years. Different perspectives-ranging from direct field measurements over dynamo theory and stellar evolution to colliding winds and the stellar environment-fruitfully combine into a most interesting and still evolving overall picture, which we attempt to review here. Zeeman signatures leave no doubt that at least some O- and early B-type stars have a surface magnetic field. Indirect evidence, especially non-thermal radio emission from colliding winds, suggests many more. The emerging picture for massive stars shows similarities with results from intermediate mass stars, for which much more data are available. Observations are often compatible with a dipole or low order multi-pole field of about 1 kG (O-stars) or 300 G to 30 kG (Ap/Bp stars). Weak and unordered fields have been detected in the O-star ζ Ori A and in Vega, the first normal A-type star with a magnetic field. Theory offers essentially two explanations for the origin of the observed surface fields: fossil fields, particularly for strong and ordered fields, or different dynamo mechanisms, preferentially for less ordered fields. Numerical simulations yield the first concrete stable (fossil) field configuration, but give contradictory results as to whether dynamo action in the radiative envelope of massive main sequence stars is possible. Internal magnetic fields, which may not even show up at the stellar surface, affect stellar evolution as they lead to a more uniform rotation, with more slowly rotating cores and faster surface rotation. Surface metallicities may become enhanced, thus affecting the mass-loss rates. [ABSTRACT FROM AUTHOR]

We discuss the effect of stochastic resonance on a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a nontrivial amplification of stochastic resonance induced by turbulent fluctuations, i.e. the amplitude of the external periodic perturbation needed for stochastic resonance to occur is much smaller than the one estimated by the equilibrium probability distribution of the unperturbed system. We argue that similar amplifications can be observed in many physical systems where turbulent fluctuations are needed to maintain large scale equilibria. [ABSTRACT FROM AUTHOR]

ABSTRACT Observations of magnetism in very low mass stars recently made important progress, revealing characteristics that are now to be understood in the framework of dynamo theory. In parallel, there is growing evidence that dynamo processes in these stars share many similarities with planetary dynamos. We investigate the extent to which the weak-field versus strong-field bistability predicted for the geodynamo can apply to recent observations of two groups of very low mass fully-convective stars sharing similar stellar parameters but generating radically different types of magnetic fields. Our analysis is based on previously published spectropolarimetric and spectroscopic data. We argue that these can be interpreted in the framework of weak- and strong-field dynamos. [ABSTRACT FROM AUTHOR]

The steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an electrically conducting incompressible viscous fluid toward a shrinking sheet is investigated. The sheet is shrunk in its own plane with a velocity proportional to the distance from the stagnation-point and a uniform magnetic field is applied normal to the sheet. Velocity component parallel to the sheet is found to increase with an increase in the magnetic field parameter M. A region of reverse flow occurs near the surface of the shrinking sheet. It is shown that as M increases, the tendency of this flow reversal decreases. It is also observed that the nonalignment of the stagnation-point flow and the shrinking sheet considerably complicates the flow structure. The effect of the magnetic parameter M on the streamlines is shown for both aligned and nonaligned cases. The temperature distribution in the boundary layer is found when the surface is held at constant temperature. The analysis reveals that the temperature at a point increases with increasing M in a certain neighborhood of the surface but beyond this, the temperature decreases with increasing M. For fixed M, the surface heat flux decreases with increase in the shrinking rate. [ABSTRACT FROM AUTHOR]

Abstract: In this work we use a low order dynamo model and study under which conditions can it reproduce solar grand minima. We begin by building the phase space of a proxy for the toroidal component of the solar magnetic field and we develop a model, derived from mean field dynamo theory, that gives the time evolution of the toroidal field. This model is characterized by a non-linear oscillator whose coefficients retain most of the physics behind dynamo theory. In the derivation of the model we also include stochastic oscillations in the effect. We found evidences that stochastic fluctuations in effect can trigger grand minima episodes in this model under some considerations. We also explore other ways of creating grand minima by looking into the physical mechanisms that compose the coefficients of the oscillator. The balance between meridional circulation and magnetic diffusivity as well as the field intensification by buoyancy driven instabilities, might have a crucial role in inducing grand minima. [ABSTRACT FROM AUTHOR]

Abstract: Campanelli et al. (2009) have recently shown that electromagnetic fluctuations in Lorentz violation theories Colladay and Kostelecky (1998) along differential rotation may induce galactic dynamo amplification of magnetic fields from primordial seeds. In this Letter, instead of using the Maxwell–Chern–Simmons–Lagrangian used in their paper, one adopts the Lagrangean of the type , where represent the torsion modes, without dynamical curvature. This so-called Minkowski–Cartan spacetime torsion modes, allows us to handle QED vacuum in any Ricci scalar electrodynamics Lagrangean. It is shown that axial-torsion modes electrodynamics allows us to obtain a slow decay of magnetic fields. Thus primordial seed fields are amplified from differential rotation and protogalaxy turbulence as galactic dynamo action. This is mainly due to the fact that the collapse of the protogalaxy induces a strong suppression of the magnetic field decay. Magnetic field anisotropies are also considered. To resume, photon-torsion axial coupling in the quantum electrodynamics (QED) framework in Riemann flat contortioned spacetime may induce galactic dynamos. Fourier space transformation are used to compute electrodynamic equations. [ABSTRACT FROM AUTHOR]