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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]

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]

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]

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]

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 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]

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]

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]

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]

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]

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]

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]

Ionospheric disturbance dynamo is one of the main processes that causes perturbations in the upper atmosphere during a magnetic storm. We present a new method, based on the least square fitting, for estimation of the magnetic signatures associated with ionospheric disturbance currents. Using a wavelet semblance analysis, the durations of disturbance dynamo electric fields have been investigated at three longitudinal sectors. For that we have analyzed the disturbance dynamo (Ddyn) for 19 magnetic storms. It has been found that during CME generated storms magnetic signature of Ddyn may be observed—depending on strength of the storm as well as on the duration of interplanetary magnetic field (IMF) Bz southward—in one, two or all three longitudes. The Oscillatory behavior of IMF Bz during the high‐speed solar wind streams (HSSWs) generates Ddyn globally and the corresponding effects are observed at all low latitude magnetic observatories. In this regard, the Joule heating estimation shows that CME and HSSWs generated storms have very different patterns. The Ddyn duration is found to be maximum for the storms occurring during equinox season. Moreover, the HSSWs events are more likely to cause—because of the oscillatory IMF Bz—long lasting Ddyn as compared to CME generated counterpart. This study presents a detailed analysis of disturbance dynamo as affected by longitudinal and seasonal variations. In this regard the difference in magnetic signatures, of CME and HSSWs originated storms, have been highlighted. Plain Language Summary: Space weather activities significantly perturb the quiet time ionosphere through various coupling mechanisms. Ionospheric disturbance dynamo is one of the main processes that causes perturbations in the upper atmosphere during a magnetic storm. We present a new method for estimation of the magnetic signatures associated with ionospheric disturbance currents. The durations of disturbance dynamo electric fields have been investigated at three longitudinal sectors for 19 magnetic storms. It has been found that during CME generated storms magnetic signature of Ddyn may be observed in one, two or all three longitudes. The Oscillatory behavior of IMF Bz during the high speed solar wind streams (HSSWs) generates Ddyn globally and the corresponding effects are observed at all low latitude magnetic observatories. In this regard, the Joule heating estimation shows that CME and HSSWs generated storms have very different patterns. The Ddyn duration is found to be maximum for the storms occurring during equinox season. Moreover, the HSSWs events are more likely to cause long lasting Ddyn as compared to CME generated counterpart. This study presents a detailed analysis of disturbance dynamo of CME and HSSWs originated storms. Key Points: A least‐square fitting method has been used to evaluate the magnetic signatures disturbance dynamo electric fieldsDifferences in the magnetic signatures of CME and high‐speed solar wind streams generated magnetic storms are identifiedWe have analyzed disturbance dynamo in three different longitudinal sectors, as affected by seasonal and longitudinal variations [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]

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]

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]

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]

The Juno gravity measurements indicate that zonal flows within Jupiter make an important contribution to the planet's gravity field. Atmospheric zonal flows extending ∼3,000 km deep can produce gravity harmonics that are consistent with the Juno inferred values. Deeper down, zonal flow in the dynamo region (i.e., below ∼0.90 RJ, where RJ is Jupiter's radius) may make a sizable contribution to the gravity harmonics. In this paper, we estimate the gravity harmonics (J2–J10) produced by zonal flows in Jupiter's dynamo region. Using Ferraro's law of isorotation, we construct physically motivated profiles for dynamo region zonal flow. We use the vorticity equation to determine the density perturbations associated with the flows and then calculate the gravity harmonics. We find that dynamo zonal flows with root mean square (RMS) velocities of 10 cm s−1 would produce J3 values on the same order of magnitude as the Juno inferred value and J2 and J4 values on the same order as ∼3,000 km deep atmospheric zonal flow, but would not contribute much to higher‐order gravity harmonics. Zonal flows above Jupiter's dynamo region would be responsible for producing dynamical gravity harmonics above J4. Slower dynamo zonal flow with a RMS velocity of 1 cm s−1 would have a relatively small contribution to all of the gravity harmonics. Plain Language Summary: Within Jupiter, large‐scale fluid motions perturb the planet's gravity field. Flows in the atmosphere extending ∼3,000 km deep can explain most of the structure of the observed gravity field that arises from the dynamics. Beneath the atmospheric flows, 0.1–20 cm s−1 flow is expected in the dynamo region, where the magnetic field is generated. The gravity contribution from this deeper flow has not yet been investigated. In this paper, we construct physically motivated models of dynamo zonal flow and estimate their gravity contributions. We find that ~10 cm s-1 dynamo flow would make an important contribution to Jupiter's gravity field. Our calculation shows that atmospheric flows do not have to fully explain the dynamical portion of Jupiter's gravity field. Some of the contribution can come from dynamo flows. Therefore, when explaining the structure of Jupiter's gravity field, contributions from flows in both the dynamo region and the deep atmosphere should be taken into account. Key Points: We estimate the zonal gravity harmonics produced by zonal flow in Jupiter's dynamo regionZonal flow in the dynamo region with a RMS velocity of 10 cm s-1 would produce large J2, J3, and J4 valuesZonal flows above the dynamo region are responsible for producing dynamical gravity harmonics above J4 [ABSTRACT FROM AUTHOR]

Context. Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid of constant density, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation. Aims. The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular, with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Methods. Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. Results. The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings. [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]

Asymptotic methods are used to study a one-dimensional kinematic-Parker dynamo wave model in the limit when the strength of the-sources, as measured by the dynamo number, is large. The model includes the influence of meridional circulation with a characteristic poleward velocity (strictly a magnetic Reynolds number), and builds on the earlier work of Popova and Sokoloff (Meridional circulation and dynamo waves.Astron. Nachr. 2008,329, 766–768). On increasing, the equatorward phase velocity of the Parker dynamo wave is decreased and, when a particular value of(say) is reached, non-oscillatory solutions ensue. Though a complete analytic solution is not possible for, the nature of the transition from travelling waves to non-oscillatory solution, as the value ofvaries across, is readily understood within the asymptotic framework. It is remarkable that such a simple one-dimensional model can illustrate the possibility of either travelling waves or non-oscillatory solutions dependent on the magnitude of the meridional circulation, a feature, which has long been known from the numerical study of the full partial differential equations governing axisymmetric-dynamos (e.g. Roberts, P.H., Kinematic dynamo models.Phil. Trans. R. Soc. Lond. A1972,272, 663–698). [ABSTRACT FROM PUBLISHER]

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.

A solar-type dynamo model in a spherical shell is developed with allowance for random dependence of the poloidal field generation mechanism on time and latitude. The model shows repeatable epochs of a strongly decreased amplitude of magnetic cycles similar to the Maunder minimum of solar activity. Random dependence of dynamo parameters on latitude breaks the equatorial symmetry of generated fields. The model shows the correlation of the occurrence of grand minima with deviations in the dynamo field from dipolar parity. An increased north-south asymmetry of magnetic activity can, therefore, be an indicator of transitions to grand minima. Qualitative interpretation of this correlation is suggested. Statistics of grand minima in the model are close to the Poisson random process, indicating that the onset of a grand minimum is statistically independent of preceding minima. [ABSTRACT FROM AUTHOR]

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]

We investigate the saturation level of hydromagnetic turbulence driven by the magnetorotational instability in the case of vanishing net flux. Motivated by a recent paper of Bodo et al., we here focus on the case of a non-isothermal equation of state with constant thermal diffusivity. The central aim of the paper is to complement the previous result with closure parameters for mean-field dynamo models, and to test the hypothesis that the dynamo is affected by the mode of heat transport. We perform computer simulations of local shearing-box models of stratified accretion disks with approximate treatment of radiative heat transport, which is modeled via thermal conduction. We study the effect of varying the (constant) thermal diffusivity, and apply different vertical boundary conditions (BCs). In the case of impenetrable vertical boundaries, we confirm the transition from mainly conductive to mainly convective vertical heat transport below a critical thermal diffusivity. This transition is however much less dramatic when more natural outflow BCs are applied. Similarly, the enhancement of magnetic activity in this case is less pronounced. Nevertheless, heating via turbulent dissipation determines the thermodynamic structure of accretion disks and clearly affects the properties of the related dynamo. This effect, however, may have been overestimated in previous work, and a careful study of the role played by boundaries will be required. [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]

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]

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]

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]

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]

Understanding the origin of pallasites, stony-iron meteorites made mainly of olivine crystals and FeNi metal, has been a vexing problem since their discovery. Here, we show that pallasite olivines host minute magnetic inclusions that have favorable magnetic recording properties. Our paleointensity measurements indicate strong paleomagnetic fields, suggesting dynamo action in the pallasite parent body. We use these data and thermal modeling to suggest that some pallasites formed when liquid FeNi from the core of an impactor was injected as dikes into the shallow mantle of a -200-kilometer-radius protoplanet. The protoplanet remained intact for at least several tens of millions of years after the olivine-metal mixing event. [ABSTRACT FROM AUTHOR]

The relation of the hydrodynamic helicity and alpha-effect predicted by the mean-field dynamo theory is considered using the three-dimensional dynamo model in the rapidly rotating flat layer heated from below. Despite the theoretical limitations associated with the requirement of uniformity and isotropism of random fields, the alpha-effect is actually proportional to helicity in the geostrophic flows under consideration. Interpretation of this nice agreement is proposed. [ABSTRACT FROM AUTHOR]

Abstract: When the core dynamo of Mars initiated and when and why it ceased is not well understood. Attempt is made in this study to constrain the active period of the core dynamo, assuming that it was powered by vigorous thermal convection in the liquid iron core. Two distinct periods of the planet are investigated: the latest stage of accretion when the growing Mars embryo likely experienced high-velocity embryo–embryo collisions, and during the late bombardment at ∼4Ga that created 20 giant basins on Mars. The impact heating of Mars embryo by a large embryo, 1000 or 1500km diameter, results in thermal stratification of the core where temperature increases with radius. The thermally stratified core requires 50–120Myr to cool and regain vigorous convection, powering a strong core dynamo. The almost non-magnetic extended area of the primordial crust in the southern hemisphere supports this likely scenario. The impact heating of Mars by the seven largest of the 20 impacts is studied in detail. The collective battering the core dynamo by the impacts probably kills the dynamo. A strong core dynamo existed for ∼350Myr, until Ares and the following Amazonis impacts introduced substantial perturbations to the core temperature and constrained the core convection to the upper ∼200km for ∼28Myr, during which no strong core dynamo was generated in this part of the core. However, it is possible that the strong dynamo that existed deep in the core prior to Ares impact retained its strength while the condition gradually changed from supercritical to subcritical until Acidalia impact which likely killed the dynamo. [Copyright &y& Elsevier]

The eigenvalue problem for Parker's dynamo model is considered. We study how the intensity of convection in the liquid core of the Earth affects the generation of the geomagnetic field with different directions of latitudinal field propagation. The scenarios of transition of the geomagnetic field from frequent to rare reversals are suggested. [ABSTRACT FROM AUTHOR]

We build a hydrodynamic model for computing and understanding the Sun's large-scale high-latitude flows. including Coriolis forces, turbulent diffusion of momentum, and gyroscopic pumping. Side boundaries of the spherical "polar cap," our computational domain, are located at latitudes ≥ 60°. Implementing observed low-latitude flows as side boundary conditions, we solve the flow equations for a Cartesian analog of the polar cap. The key parameter that determines whether there are nodes in the high-latitude meridional flow is ε = 2Ωnπ H²/v, where Ω is the interior rotation rate, n is the radial wave-number of the meridional flow, H is the depth of the convection zone, and v is the turbulent viscosity. The smaller the ε (larger turbulent viscosity), the fewer the number of nodes in high latitudes. For all latitudes within the polar cap, we find three nodes for v = 1012 cm² s-1, two for 1013, and one or none for 1015 or higher. For v near 1014 our model exhibits "node merging": as the meridional flow speed is increased, two nodes cancel each other, leaving no nodes. On the other hand, for fixed flow speed at the boundary, as v is increased the poleward-most node migrates to the pole and disappears, ultimately for high enough v leaving no nodes. These results suggest that primary poleward surface meridional flow can extend from 60° to the pole either by node merging or by node migration and disappearance. [ABSTRACT FROM AUTHOR]

We use a truncated dynamo model and observations of the sunspot number to infer cycle-to-cycle variations of several dynamo parameters. A correlation study between model parameters and solar cycle observables (period, amplitude, and rising time) is done, and our results are compared with the results of other authors. Using the strongest correlations found, we determined a series of relationships that can be used for prediction purposes. This technique indicates that solar cycle 24 will have a sunspot maximum of approximately 84 around June of 2013. In the context of the used model, most of the variability found in the solar cycle can be attributed to changes in the strength of the meridional circulation. The results also point to a common origin for the source of variation of the meridional flow and differential rotation and/or the α-effect. [ABSTRACT FROM AUTHOR]