Geodynamo Research Articles

Research on magnetic fields of galaxies using RZ-model

The generation of magnetic fields of galaxies is usually described by the dynamo mechanism. This process is characterized by the Steenbeck – Krause – Rädler equation, which is the result of averaging the magnetohydrodynamics equations by distances which are associated with the size of turbulent cells in the interstellar medium. This equation is quite difficult to solve both from an analytical and numerical point of view. For galaxies, the no-z approximation is widely used. It describes the magnetic fields in thin discs. For such objects, where it is important to study the vertical structure of the field, it is not very applicable, so it is quite useful to adopt the RZ-model, which takes into account the dependence of the distance from the equatorial plane. During our research we have obtained the critical values of the dynamo number for galaxies with large half-thickness. We have also described typical z-structure for the magnetic field. Moreover, we have demonstrated that it is possible to generate dipolar magnetic fields.

Does Machine Learning reconstruct missing sunspots and forecast a new solar minimum?

The retrodiction and prediction of solar activity are two closely-related problems in dynamo theory. We applied Machine Learning (ML) algorithms and analyses to the World Data Center’s newly constructed annual sunspot time series (1700–2019; Version 2.0). This provides a unique model that gives insights into the various patterns of the Sun’s magnetic dynamo that drives solar activity maxima and minima. We found that the variability in the ~ 11 -year Sunspot Cycle is closely connected with 120-year oscillatory magnetic activity variations. We also identified a previously under-reported 5.5 year periodicity in the sunspot record. This 5.5-year pattern is co-modulated by the 120-year oscillation and appears to influence the shape and energy/power content of individual 11-year cycles. Our ML algorithm was trained to recognize such underlying patterns and provides a convincing hindcast of the full sunspot record from 1700 to 2019. It also suggests the possibility of missing sunspots during Sunspot Cycles −1, 0, and 1 (ca. 1730s-1760s). In addition, our ML model forecasts a new phase of extended solar minima that began prior to Sunspot Cycle 24 (ca. 2008–2019) and will persist until Sunspot Cycle 27 (ca. 2050 or so). Our ML Bayesian model forecasts a peak annual sunspot number (SSN) of 95 with a probable range of 80–115 for Cycle 25 between 2023 and 2025.

Gradual onset of the Maunder Minimum revealed by high-precision carbon-14 analyses

The Sun exhibits centennial-scale activity variations and sometimes encounters grand solar minimum when solar activity becomes extremely weak and sunspots disappear for several decades. Such an extreme weakening of solar activity could cause severe climate, causing massive reductions in crop yields in some regions. During the past decade, the Sun’s activity has tended to decline, raising concerns that the Sun might be heading for the next grand minimum. However, we still have an underdeveloped understanding of solar dynamo mechanisms and hence precise prediction of near-future solar activity is not attained. Here we show that the 11-year solar cycles were significantly lengthened before the onset of the Maunder Minimum (1645–1715 CE) based on unprecedentedly high-precision data of carbon-14 content in tree rings. It implies that flow speed in the convection zone is an essential parameter to determine long-term solar activity variations. We find that a 16 year-long cycle had occurred three solar cycles before the onset of prolonged sunspot disappearance, suggesting a longer-than-expected preparatory period for the grand minimum. As the Sun has shown a tendency of cycle lengthening since Solar Cycle 23 (1996–2008 CE), the behavior of Solar Cycle 25 can be critically important to the later solar activity.

On the representation of dense plasma focus as a circuit element

The dense plasma focus is a plasma discharge powered by a capacitor bank. Standard diagnostics include the measurement of the time derivative of the current through and the voltage across its connections with the capacitor bank. Interpretation of this diagnostic data often involves some assumptions regarding the representation of the dense plasma focus as a time varying inductance. One of the characteristic features of the current derivative waveform is a relatively sharp dip and an associated sharp voltage spike. This has often been interpreted as a result of a rapid rise in the time varying inductance of the plasma. Sometimes, an anomalous plasma impedance is invoked. This Letter discusses instances where such interpretation creates conceptual difficulties. A first principles approach to the representation of the dense plasma focus as a circuit element reveals some fundamental problems with the traditional representation of plasma focus as a time varying inductance. The anomalous impedance is shown to be necessary to account for the difference in the motional impedance implied by a time-varying inductance in the circuit element representation and a first principles description based on Poynting's theorem. Dynamo effects that convert post-stagnation local motion of plasma into three-dimensional magnetic fields are shown to contribute to the effective inductance of the plasma focus and resolve the observed conceptual difficulties.

Constraining the Decline of the Lunar Dynamo Field at ≈3.1 Ga Through Paleomagnetic Analyses of Apollo 12 Mare Basalts

AbstractRecent paleomagnetic studies of lunar rocks have suggested that the magnetic field of the Moon reached peak intensities on the order of ≈77 μT between 3.85 billion and 3.56 billion years ago (Ga) and subsequently declined to surface intensities of ≈4 μT by 3.19 Ga. However, this decline in the intensity of the lunar field has only been shown in a small number of samples, presenting challenges for constraint of its timing and thus the dynamo generation mechanisms that could be responsible. We present microscopic and magnetic analyses of Apollo samples 12008, 12009, and 12015, three fine‐grained mare vitrophyre basalts with high magnetic fidelity, indicating that these samples were not magnetized in conditions consistent with a planetary magnetic field exceeding 4–7 μT during their formation. We further report updated radiometric ages for samples 12008 and 12009 and the first‐ever radiometric age for sample 12015, dating this lunar field intensity constraint to ≈3.1 Ga. These data are consistent with results of previous work on the initial decline of the Moon's magnetic field and confirm that the mechanism of lunar dynamo generation changed dramatically between 3.6 and 3.1 Ga.

Giant white-light flares on fully convective stars occur at high latitudes

White-light flares are magnetically driven localized brightenings on the surfaces of stars. Their temporal, spectral, and statistical properties present a treasury of physical information about stellar magnetic fields. The spatial distributions of magnetic spots and associated flaring regions help constrain dynamo theories. Moreover, flares are thought to crucially affect the habitability of exoplanets that orbit these stars. Measuring the location of flares on stars other than the Sun is challenging due to the lack of spatial resolution. Here we present four fully convective stars observed with the Transiting Exoplanet Survey Satellite (TESS) that displayed large, long-duration flares in white-light which were modulated in brightness by the stars' fast rotation. This allowed us to determine the loci of these flares directly from the light curves. All four flares occurred at latitudes between 55 deg and 81 deg, far higher than typical solar flare latitudes. Our findings are evidence that strong magnetic fields tend to emerge close to the stellar rotational poles for fully convective stars, and suggest that the impact of flares on the habitability of exoplanets around small stars could be weaker than previously thought.

Progress in Solar Cycle Predictions: Sunspot Cycles 24–25 in Perspective

The dynamic activity of the Sun -- sustained by a magnetohydrodynamic dynamo mechanism working in its interior -- modulates the electromagnetic, particulate and radiative environment in space. While solar activity variations on short timescale create space weather, slow long-term modulation forms the basis of space climate. Space weather impacts diverse space-reliant technologies while space climate influences planetary atmospheres and climate. Having prior knowledge of the Sun's activity is important in these contexts. However, forecasting solar-stellar magnetic activity has remained an outstanding challenge. In this review, predictions for sunspot cycle 24 and the upcoming cycle 25 are summarized, and critically assessed. The analysis demonstrates that while predictions based on diverse techniques disagree across solar cycles 24--25, physics-based predictions for solar cycle 25 have converged and indicates a weak sunspot cycle 25. It is argued that this convergence in physics-based predictions is indicative of progress in the fundamental understanding of solar cycle predictability. Based on this understanding, resolutions to several outstanding questions related to solar cycle predictions are discussed.

Long-term evolution of a merger-remnant neutron star in general relativistic magnetohydrodynamics: Effect of magnetic winding

Long-term ideal and resistive magnetohydrodynamics (MHD) simulations in full general relativity are performed for a massive neutron star formed as a remnant of binary neutron star mergers. Neutrino radiation transport effects are taken into account as in our previous papers. The simulation is performed in axial symmetry and without considering dynamo effects as a first step. In the ideal MHD, the differential rotation of the remnant neutron star amplifies the magnetic-field strength by the winding in the presence of a seed poloidal field until the electromagnetic energy reaches $\sim 10\%$ of the rotational kinetic energy, $E_{\rm kin}$, of the neutron star. The timescale until the maximum electromagnetic energy is reached depends on the initial magnetic-field strength and it is $\sim 1$ s for the case that the initial maximum magnetic-field strength is $\sim 10^{15}$ G. After a significant amplification of the magnetic-field strength by the winding, the magnetic braking enforces the initially differentially rotating state approximately to a rigidly rotating state. In the presence of the resistivity, the amplification is continued only for the resistive timescale, and if the maximum electromagnetic energy reached is smaller than $\sim 3\%$ of $E_{\rm kin}$, the initial differential rotation state is approximately preserved. In the present context, the post-merger mass ejection is induced primarily by the neutrino irradiation/heating and the magnetic winding effect plays only a minor role for the mass ejection.

The Turbulent Dynamo.

The generation of magnetic field in an electrically conducting fluid generally involves the complicated nonlinear interaction of flow turbulence, rotation and field. This dynamo process is of great importance in geophysics, planetary science and astrophysics, since magnetic fields are known to play a key role in the dynamics of these systems. This paper gives an introduction to dynamo theory for the fluid dynamicist. It proceeds by laying the groundwork, introducing the equations and techniques that are at the heart of dynamo theory, before presenting some simple dynamo solutions. The problems currently exercising dynamo theorists are then introduced, along with the attempts to make progress. The paper concludes with the argument that progress in dynamo theory will be made in the future by utilising and advancing some of the current breakthroughs in neutral fluid turbulence such as those in transition, self-sustaining processes, turbulence/mean-flow interaction, statistical and data-driven methods and maintenance and loss of balance.

Unified theories metrics and primordial magnetic fields in Riemann–Cartan spacetime

Several spacetime metrics in teleparallel geometry of Einstein like unified field theory (UFT) are presented. Cosmic magnetic fields are obtained in terms of the early universe torsion and other stages of the universe. For example, in one of the metrics, integration of the 2-form torsion 0-component is written in terms of magnetic flux, from Faraday’s induced equation. These ideas were obtained from a recent paper we published [Class. Quantum Grav. (2015)] on non-stationary teleparallel metrics, where at coherent length of [Formula: see text] a magnetic field of [Formula: see text] is obtained. At early universe, a torsion of [Formula: see text] leads us to a magnetic field of the order of [Formula: see text] which is weaker than the Bierman battery effect magnetic field of the order of [Formula: see text]. Hence this new metric indicates that unifield theory metrics a la Schrödinger may be used to obtain primordial magnetic fields. Other tests of this metric led to the nowadays magnetic field of [Formula: see text] from the torsion at present universe (at the laboratory using dual maser obtained by Kostelecky et al. [Phys. Rev. Lett.]) of [Formula: see text]. Cartan torsion has been frequently associated to topological defects in crystals or in pseudo-magnetic torsional fields. In this paper, we discuss how from teleparallel gravity one may obtain a theory of electromagnetism from metrics in spacetime. Topological defects given by Letelier [Class. Quantum Grav. 12 (1995) 1133] and Tod [Class. Quantum Grav. 11(5) (1994)] metrics can also be associated with pseudo-magnetic fields. Electromagnetism is geometrized via a bimetric theory of gravity where one metric is responsible for Ampere’s law and the other by the Faraday induction equation which gives rise to dynamo equation.

Axisymmetric dynamo action produced by differential rotation, with anisotropic electrical conductivity and anisotropic magnetic permeability

The effect on dynamo action of an anisotropic electrical conductivity conjugated to an anisotropic magnetic permeability is considered. Not only is the dynamo fully axisymmetric, but it requires only a simple differential rotation, which twice challenges the well-established dynamo theory. Stability analysis is conducted entirely analytically, leading to an explicit expression of the dynamo threshold. The results show a competition between the anisotropy of electrical conductivity and that of magnetic permeability, the dynamo effect becoming impossible if the two anisotropies are identical. For isotropic electrical conductivity, Cowling's neutral point argument does imply the absence of an azimuthal component of current density, but does not prevent the dynamo effect as long as the magnetic permeability is anisotropic.

Characteristic periods of the paleosecular variation of the Earth's magnetic field during the Holocene from global paleoreconstructions

The knowledge of the secular variation of the geomagnetic field at different time scales is important to determine the mechanisms that maintain the geomagnetic field and can help to establish constraints in dynamo theories. We have focused our study on the secular variation at millennial and centennial time scale searching for characteristic periods during the last 10 kyr. The frequency study was performed using four recent updated global paleomagnetic field reconstructions (SHA.DIF.14k, CALS10k.2, BIGMUDI4k and SHAWQ2k) by applying three techniques commonly used in signal analysis: the Fourier transform, the Empirical Mode Decomposition, and the wavelet analysis.Short-term variability of the geomagnetic field energy shows recurrent periods of around 2000, 1000–1400, and 600–800 and 250–400 years. The characteristic time around 600–800 years is well determined in all paleomagnetic reconstructions and it is mostly related to the axial dipole and axial octupole terms, but also observable in the equatorial dipole. In addition to this period, longer characteristic times of around 1000–1400 years are found particularly in the equatorial dipole and quadrupole terms in SHA.DIF.14k, CALS10k.2 and BIGMUDI4k while the 2000 year period is only well determined in the total geomagnetic field energy of SHA.DIF.14k and CALS10k.2. The most detailed paleoreconstructions for younger times also detect shortest characteristic times of around 250–400 years.The long-term variation of the geomagnetic energy is only observable in the axial dipole. A characteristic period of around 7000 years in both SHA.DIF.14k and CALS10k.2 has been found. This long period is related to two decays in the dipole field and a period of increasing intensity. The oldest decay took place between 7000 BCE and 4500 BCE and the present decay that started around 100 BCE. We have modeled the 4500 BCE up to present variation as a combination of a continuous decay, representing the diffusion term of the geomagnetic field, and one pulse that reinforces the strength of the field. Results show a characteristic diffusion time of around 11,000–15,000 years, which is compatible with the diffusion times of the dipole field used in geodynamo theories.

Low dimensional models of dynamo action in rotating magnetoconvection

Abstract Two low-dimensional models for nonlinear dynamo action in Rayleigh-Benard convection in presence of rigid body rotation about vertical axis are constructed for metallic fluids with finite magnetic Prandtl number ( P m ) and small (or zero) thermal Prandtl number ( P r ). Dynamo effect is seen for P m ≥ 0.75 with P r = 0.025 and Taylor number, 0 T a ≤ 1000 . The value of reduced Rayleigh number at the dynamo onset ( r d ) varies with P m , P r and T a . The value of r d decreases with increase in P m and T a separately, if the other two parameters are kept fixed to some small values. However r d increases slightly if P r is increased, the value being minimum for P r = 0 . When 0.75 ≤ P m 4 , dynamo onset appears as intermittent chaotic burst. The intermittent burst changes to continuous chaos with rise in P m . The probability mass of the height of peak in average magnetic energy follows power law when P m is small. For 4 ≤ P m 6 and 600 ≤ T a 1000 dynamo effect starts at the onset of convection as finite oscillation. This effect continues in a small window of r and then disappears. The dynamo action again appears as quasi-periodic wave or chaotic wave for further increase in r .

No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

Biermann battery as a source of astrophysical magnetic fields

Abstract A large number of galaxies have large-scale magnetic fields which are usually measured by the Faraday rotation of radio waves. Their origin is usually connected with the dynamo mechanism which is based on differential rotation of the interstellar medium and alpha-effect characterizing the helicity of the small-scale motions. However, it is necessary to have initial magnetic field which cannot be generated by the dynamo. One of the possible mechanisms is connected with the Biermann battery which acts because of different masses of protons and electrons passing from the central object. They produce circular currents which induce the vertical magnetic field. As for this field we can obtain the integral equation which can be solved by simulated annealing method which is widely used in different branches of mathematics

Universal dynamo paradigm for solar activity, Higgs fields and disasters

There is still a problem of a correct and accurate description of the dynamo and its uses in various fields of physics. To solve this problem, a special and universal representation of dynamo is proposed. The magnetic induction equation of dynamo is presented in the form of a Lienard relaxation oscillator with cubic nonlinear restoring force corresponding to the Mexican hat or champagne bottle potential which is used to determine the Higgs fields which are considered here in its general sense. Universal dynamo paradigm in field theory which can be used to describe disasters is proposed. Using solar activity as an example, it is shown how a dynamo induces a magnetic analogue of the Higgs fields with a broken symmetry of the magnetic field. Various dynamo modes are considered and different dynamo numbers are estimated. The dynamo effect can be used in field theory as an alternative to spontaneous symmetry breaking. Opportunities for the promotion of the new dynamo paradigm are discussed.

Kepler-411 Differential Rotation from Three Transiting Planets

Abstract The differential rotation of the Sun is a crucial ingredient of the dynamo theory responsible for the generation of its magnetic field. Currently, the rotation profile of a star that hosts one or more transiting planet can be estimated. By detecting the same spot in a later transit, it is possible to infer the stellar rotation period at that latitude. In this work, we apply for the first time transit spot mapping to determine the differential rotation of Kepler-411, a K2V-type star with an average rotation period of 10.52 days, a radius of 0.79 R ⊙, and a mass of 0.83 M ⊙. Kepler-411 hosts at least four planets, the inner planet is a super-Earth with a radius of 1.88 R ⊕ and an orbital period of 3.0051 days, whereas the two larger transiting planets are mini Neptunes with radii of 3.27 and 3.31 R ⊕, and periods of 7.834435 and 58.0204 days, respectively. Their orbits are such that they transit the star at latitudes of −11°, −21°, and −49°. Analysis of the transit light curves of the three planets resulted in the detection of a total of 198 spots. For each transit latitude, the rotation period of the star was estimated and the differential rotation pattern estimated independently. Then a solar-like differential rotation profile was fit to the three rotation periods at the distinct latitudes, and the result agreed extremely well with the previous ones, resulting in a differential shear of 0.0500 ± 0.0006 rd day−1 or a relative differential rotation of 8.4% ± 0.1%.

Возникновение контрастных структур для галактического магнитного поля: теоретические оценки и моделирование на видеокартах

Magnetic field generation in galaxies turns out to be a significant problem both for cosmic magnetohydrodynamics and mathematical physics. It is based on dynamo mechanism characterising the transition between the energy of medium turbulent motions and the magnetic field energy. The evolution of the field is described with the help of mean field dynamo equations. For galaxies the solutions are commonly found using so-called “no-z” approximation, while the half-thickness of the galactic disc is considered negligible. In nonlinear case mentioned equations admit contrast structure formation, predicted by the singular perturbation theory, describing equations with small parameter at the elder derivative. From astronomical point of view some authors tend to connect such solutions with the spiral structure of the galaxies and the formation of magnetic field reversals (when in different parts of galaxy there are regions with opposite directions of magnetic, divided by a thin transition layer). From numerical point of view finding the solution of two-dimensional system of equations requires large computational resources, for this reason using GPU and parallel calculations turns out to be reasonable. One of the implementation methods is calculating using OpenCL, which allows one to increase the process efficiency several times. OpenCL is a perspective crossplatform standard for development of applications, particularly involving GPU, the efficiency of which is rapidly increasing as the drivers evolve. The present work presents basic theoretical assessments of magnetic field behaviour, which are further confirmed and clarified during the computations. It is shown that the formation of the transition layers is described by fundamentally different mechanisms in radial and azimuthal directions. While radial reversals of the field turn out to be rather stable, all of the azimuthal structures are rapidly blurred due to the nature of the interstellar medium motions. That also indicates the practical impossibility of non-axisymmetric distributions of the field.

No-z model: results and perspectives for accretion discs

Accretion discs surround different compact astrophysical objects such as black holes, neutron stars and white dwarfs. Also they are situated in systems of variable stars and near the galaxy center. Magnetic fields play an important role in evolution and hydrodynamics of the accretion discs: for example, they can describe such processes as the transition of the angular momentum. There are different approaches to explain the magnetic fields, but most interesting of them are connected with dynamo generation. As for disc, it is quite useful to take no-$z$ approximation which has been developed for galactic discs to solve the dynamo equations. It takes into account that the disc is quite thin, and we can solve the equations only for two plane components of the field. Here we describe the time dependence of the magnetic field for different distances from the center of the disc. Also we compare the results with another approaches which take into account more complicated field structure.

Small-scale Dynamo in Stably Stratified Turbulence

Abstract We present numerical investigations into three principal properties of a small-scale dynamo in stably stratified turbulence: the onset criterion, the growth rate, and the nature of the magnetic field anisotropy in the kinematic regime. The results suggest that all three dynamo properties are controlled by the scale separation between the Ozmidov scale and the viscous or resistive scale. In addition to the critical magnetic Reynolds number, this allows for the definition of critical buoyancy and magnetic buoyancy Reynolds numbers for stratified small-scale dynamo onset in the high and low magnetic Prandtl number regimes, respectively. The presence of a small-scale dynamo in stellar radiative zones could affect dynamics through the resulting Maxwell stresses or its influence on large-scale dynamo mechanisms in regions of differential rotation. Taking the solar radiative zone as a representative example and applying the onset criterion, we find that the stratification is strong enough to make the small-scale dynamo marginally active in the stably stratified turbulence of the solar tachocline.