Geodynamo Research Articles

Eigenvalue Problem for a Reduced Dynamo Model in Thick Astrophysical Discs

Magnetic fields of different astrophysical objects are generated by the dynamo mechanism. Dynamo is based on the alpha-effect and differential rotation, which are described using a system of parabolic equations. Their solution is an important problem in magnetohydrodynamics and mathematical physics. They can be solved assuming exponential growth of the solution, which leads to an eigenvalue problem for a differential operator connected with spatial coordinates. Here, we describe a system of equations connected with the generation of magnetic field in discs, which are associated with galaxies and binary systems. For an ideal case of an infinitely thin disc, the eigenvalue problem can be precisely solved. If we take into account the finite thickness of the disc, the problem becomes more difficult. The solution can be found using asymptotical methods based on perturbations of the eigenvalues. Here, we present two different models which describe field evolution for different cases. For the first, we find eigenvalues taking into account linear and quadratic terms for the perturbations in the eigenvalue problem. For the second, we find eigenvalues using only linear terms; this is quite sufficient. Results were verified through numerical modeling, and basic computational tests show proper correspondence between different methods.

Galactic Dynamos

Spiral galaxies, including the Milky Way, have large-scale magnetic fields with significant energy densities. The dominant theory attributes these magnetic fields to a large-scale dynamo. We review the current status of dynamo theory and discuss various numerical simulations designed either to explain particular aspects of the problem or to reproduce galactic magnetic fields globally. Our main conclusions can be summarized as follows: ▪Idealized direct numerical simulations produce mean magnetic fields, whose saturation energy density tends to decline with increasing magnetic Reynolds number. This is still an unsolved problem.▪Large-scale galactic magnetic fields of microgauss strengths can probably be explained only if helical magnetic fields of small or moderate length scales can be rapidly ejected or destroyed.▪Small-scale dynamos are important throughout a galaxy's life and probably provide strong seed fields at early stages.▪The circumgalactic medium (CGM) may play an important role in driving dynamo action at small and large length scales. These interactions between the galactic disk and the CGM may provide important insights into our understanding of galactic dynamos. We expect future research in galactic dynamos to focus on the cosmological history of galaxies and the interaction with the CGM as means of replacing the idealized boundary conditions used in earlier work.

Magnetic Activity–Rotation–Age–Mass Relations in Late-pre-main-sequence Stars

We study the four-dimensional relationships between magnetic activity, rotation, mass, and age for solar-type stars in the age range 5–25 Myr. This is the late-pre-main-sequence (l-PMS) evolutionary phase when rapid changes in a star's interior may lead to changes in the magnetic dynamo mechanisms. We carefully derive rotational periods and spot sizes for 471 members of several l-PMS open clusters using photometric light curves from the Zwicky Transient Facility. Magnetic activity was measured in our previous Chandra-based study, and additional rotational data were obtained from other work. Several results emerge. Mass-dependent evolution of rotation through the l-PMS phase agrees with astrophysical models of stellar angular momentum changes, although the data suggest a subpopulation of stars with slower initial rotations than commonly assumed. There is a hint of the onset of unsaturated tachoclinal dependency of X-ray activity on rotation, as reported by Argiroffi et al., but this result is not confidently confirmed. Both X-ray luminosity and starspot area decrease approximately as t −1 for solar-mass stars, suggesting that spot magnetic fields are roughly constant and l-PMS stars follow the universal solar-scaling law between the X-ray luminosity and surface magnetic flux. Assuming convective dynamos are dominant, theoretical magnetic fluxes fail to reveal the universal law for l-PMS stars that enter late Henyey tracks. Altogether we emerge with a few lines of evidence suggesting that the transition from the turbulent to solar-type dynamo occurs at the later stages of l-PMS evolution as stars approach the zero-age main sequence.

Long-term forcing of the Sun’s coronal field, open flux, and cosmic ray modulation potential during grand minima, maxima, and regular activity phases by the solar dynamo mechanism

ABSTRACT Magnetic fields generated in the Sun’s interior by the dynamo mechanism drive solar activity over a range of time-scales. Direct sunspot observations exist for a few centuries; reconstructed variations based on cosmogenic isotopes in the solar open flux and cosmic ray flux exist over thousands of years. While such reconstructions indicate the presence of extreme solar activity fluctuations in the past, causal links between millennia scale dynamo activity, consequent coronal field, solar wind, open flux and cosmic ray flux variations remain elusive; a lack of coronal field observations compounds this issue. By utilizing a stochastically forced solar dynamo model and potential field source surface extrapolation, we perform long-term simulations to illuminate how dynamo generated magnetic fields govern the structure of the solar corona and the state of the heliosphere – as indicated by variations in the open flux and cosmic ray modulation potential. We establish differences in the nature of the large-scale structuring of the solar corona during grand maximum, minimum, and regular solar activity phases and simulate how the open flux and cosmic ray modulation potential vary across these different phases of activity. We demonstrate that the power spectrum of simulated and observationally reconstructed solar open flux time series are consistent with each other. Our study provides the theoretical foundation for interpreting long-term solar cycle variations inferred from cosmogenic isotope based reconstructions and establishes causality between solar internal variations to the forcing of the state of the heliosphere.

Fluctuation-induced dynamo effect in a magnetic confinement plasma

Fluctuation-induced dynamo effect in a magnetic confinement plasma

Vortex Dynamo in Rotating Media

The review highlights the main achievements in the theory of the vortex dynamo in rotating media. Various models of a vortex dynamo in rotating media are discussed: a homogeneous viscous fluid, a temperature-stratified fluid, a moist atmosphere, and a stratified nanofluid. The main analytical and numerical results for these models obtained by the method of multiscale asymptotic expansions are presented. The main attention is paid to models with a non-spiral external force. For a rotating moist atmosphere, characteristic estimates of the spatial and temporal scales of the generated vortex structures are obtained. New effects of the vortex dynamo in a rotating stratified nanofluid, which arise due to thermophoresis and Brownian motion of nanoparticles, are shown. The results of the analysis of the nonlinear equations of the vortex dynamo in the stationary regime are presented in the form of spiral kinks, periodic nonlinear waves, and solitons.

Supernova Dynamo Effect in Neutrino Spectra and Perspective of Observations by Large Volume Telescopes

Supernova Dynamo Effect in Neutrino Spectra and Perspective of Observations by Large Volume Telescopes

Progenitor Constraint with Circumstellar Material for the Magnetar-hosting Supernova Remnant RCW 103

Stellar winds blown out from massive stars (≳10 M ⊙) contain precious information on the progenitor itself, and in this context the most important elements are carbon (C), nitrogen (N), and oxygen (O), which are produced by the CNO cycle in the H-burning layer. Although their X-ray fluorescence lines are expected to be detected in swept-up shock-heated circumstellar materials in supernova remnants, those of C and N have been particularly difficult to detect so far. Here, we present high-resolution spectroscopy of the young magnetar-hosting supernova remnant RCW 103 with the Reflection Grating Spectrometer on board XMM-Newton and report on the detection of the N vii Lyα (0.50 keV) line for the first time. By comparing the obtained abundance ratio of N to O (N/O = 3.8 ± 0.1) with various stellar evolution models, we show that the progenitor of RCW 103 is likely to have a low mass (10–12 M ⊙) and medium rotation velocity (≲100 km s−1). The results also rule out the possibility of dynamo effects in massive (≥35 M ⊙) stars as a mechanism for forming the associated magnetar 1E 161348−5055. Our method is useful for estimating various progenitor parameters for future missions with microcalorimeters such as XRISM and Athena.

Causality in heliophysics: Magnetic fields as a bridge between the Sun’s interior and the Earth’s space environment

Our host star, the Sun, is a middle-aged main sequence G type star whose activity varies. These variations are primarily governed by solar magnetic fields which are produced in the Sun’s interior via a magnetohydrodynamic dynamo mechanism. Solar activity manifests across different timescales, spanning transient phenomena such as flares, energetic particle events and coronal mass ejections to short to long-term modulation of solar irradiance, plasma winds, open flux and cosmic ray flux in the heliosphere. Collectively, these phenomena define space weather and space climate, which impact the state of the near-Earth space environment, the Earth’s magnetosphere, atmosphere and our space-reliant technologies. Understanding physical processes that are at the heart of solar variability and which causally connect the Sun–Earth system is therefore of immense importance to humanity. Such understanding leads to predictions of the impact of solar activity on our planet and provides a window to explore the plasma universe and other star–planet systems, including assessing the habitability of (exo)planets. In this review, based on our research on the solar–terrestrial system and extant scientific literature, we illuminate processes related to the genesis of solar magnetic fields in the Sun’s interior, their emergence and evolution, their manifestation as solar eruptive events, and their eventual impact on the geospace environment mediated via solar winds and storms. We focus on few phenomena that establish causal connections and demonstrate how our current understanding can lead to development of predictive capabilities encompassing the domain of heliophysics.

Novel Approach to Forecasting Photospheric Emergence of Active Regions

One key aspect of understanding the solar dynamo mechanism and the evolution of solar magnetism is to properly describe the emergence of solar active regions. In this Letter, we describe the Lagrangian photospheric flows dynamics during a simulated flux emergence that produces an active region formed by pores. We analyze the lower photospheric flow organization prior, during and following the rise of an active region, uncovering the repelling and attracting photospheric structures that act as sources and sinks for magnetic element transport. Our results show that around 10 hr before the simulated emergence, considerable global changes are taking place on mesogranular scales indicated by an increase of the number of regions acting as a source to the multiple and scattered emergences of small-scale magnetic flux. At the location of active region’s appearance, the converging flows become weaker and there is an arising of a diverging region 8 hr before the emergence time. Our study also indicates that the strong concentration of magnetic field affects the flow dynamics beyond the area of the actual simulated pores, leading to complex and strongly diverging flows in the neighboring regions. Our findings suggest that the Lagrangian analysis is a powerful tool to describe the changes in the photospheric flows due to magnetic flux emergence.

Исключение интегрального члена в уравнениях одной эредитарной системы, связанной с задачей гидромагнитного динамо

В работе изучается двумерная система интегро-дифференциальных уравнений, которая является простейшей эредитарной моделью двумодового гидромагнитного динамо. Учет пространственной и временной нелокальности взаимодействий в динамо-системах сейчас активно исследуется. В маломодовых приближениях уравнений динамо можно рассматривать только временную нелокальность, т.е. эредитарность (память). Память в исследуемой системе реализована в виде обратной связи, распределенной по всем прошлым состояниям системы. Обратная связь представлена с помощью интегрального члена типа свертки от квадратичной комбинации фазовых переменных с ядром достаточно общего вида. Этот член моделирует подавление турбулентного генератора поля (α-эффекта) квадратичной формой от фазовых переменных. В реальных динамо-системах такое подавление обеспечивается силой Лоренца. Основной результат работы – доказательство возможности исключения интегрального члена для одного класса ядер. Такие ядра являются решениями однородного линейного дифференциального уравнения с постоянными коэффициентами. Доказано, что исследуемую интегро-дифференциальную систему можно заменить дифференциальной системой большей размерности с подходящими начальными условиями на дополнительные фазовые переменные. Если ядро является решением уравнения n-го порядка, то размерность системы может достигать 3n−2 и зависит от начальных условий, которым удовлетворяет ядро. В работе используются классические методы теории дифференциальных уравнений. Приводятся примеры динамических систем, возникающих при некоторых ядрах в результате исключения интегрального члена. Результаты работы можно использовать для верификации вычислительных алгоритмов и программных кодов, разработанных для решения интегро-дифференциальных уравнений.We study a two-dimensional system of integro-differential equations, which is the simplest hereditary model of a two-mode hydromagnetic dynamo. Accounting for the spatial and temporal nonlocality of interactions in dynamo systems is currently being actively studied. In the low-mode approximations of the dynamo equations, one can consider only temporal nonlocality, i.e. heredity (memory). Memory in the system under study is implemented in the form of feedback distributed over all past states of the system. The feedback is represented by a convolution-type integral term of a quadratic combination of phase variables with a fairly general kernel. This term models the quenching of the turbulent field generator (α-effect) by a quadratic form in phase variables. In real dynamo systems, such quenchingn is provided by the Lorentz force. The main result of the work is a proof of the possibility of eliminating the integral term for one class of kernels. Such kernels are solutions of a homogeneous linear differential equation with constant coefficients. It is proved that the studed integro-differential system can be replaced by a higher-dimensional differential system with suitable initial conditions for additional phase variables. If the kernel is a solution to an n-order equation, then the dimension of the system can reach 3n−2 and depends on the initial conditions that the kernel satisfies. The work uses classical methods of the theory of differential equations. Examples are given of dynamical systems that arise for some kernels as a result of the elimination of the integral term. The results of the work can be used to verify computational algorithms and program codes developed for solving integro-differential equations.

Overview of the Spectral Coherence between Planetary Resonances and Solar and Climate Oscillations

The complex dynamics of solar activity appear to be characterized by a number of oscillations ranging from monthly to multimillennial timescales, the most well-known of which being the 11-year Schwabe sunspot cycle. Solar oscillations are important because they also characterize the oscillations observed in Earth’s climate and can thus be used to explain and forecast climate changes. Thus, it is important to investigate the physical origin of solar oscillations. There appear to be two possibilities: either the oscillations in solar activity are exclusively controlled by internal solar dynamo mechanisms, or the solar dynamo is partially synchronized to planetary frequencies by planetary forcings. The latter concept has recently gained support from a growing amount of evidence. In this work, we provide an overview of the many empirical facts that would support a planetary hypothesis of the variability of solar activity and emphasize their importance for climate research. We show that the frequencies produced by the complex interactions of all of the planets are coherent with the major solar activity and climate cycles, from monthly to multimillennial timescales, including the well-known Schwabe 11-year solar cycle. We provide some persuasive theoretical and empirical support for the planetary hypothesis of solar and climate variability.

Topologically protected quantum dynamo effect in a driven spin-boson model

We describe a quantum dynamo effect in a driven system coupled to a harmonic oscillator describing a cavity mode or to a collection of modes forming an Ohmic bosonic bath. When the system Hamiltonian changes in time, this induces a dynamical field in the bosonic modes having resonant frequencies with the driving velocity. This field opposes the change of the external driving field in a way reminiscent of Faraday's law of induction, justifying the term 'quantum dynamo effect'. For the specific situation of a periodically driven spin-$\frac{1}{2}$ on the Bloch sphere, we show that the work done by rolling the spin from north to south pole can efficiently be converted into a coherent displacement of the resonant bosonic modes, the effect thus corresponds to a work-to-work conversion and allows to interpret this transmitted energy into the bath as work. We study this effect, its performance and limitations in detail for a driven spin-$\frac{1}{2}$ in the presence of a radial magnetic field addressing a relation with topological systems through the formation of an effective charge in the core of the sphere. We show that the dynamo effect is directly related to the dynamically measured topology of this spin-$\frac{1}{2}$ and thus in the adiabatic limit provides a topologically protected method to convert driving work into a coherent field in the reservoir. The quantum dynamo model is realizable in mesoscopic and atomic systems.

Magnetic fields with random initial conditions in discs with Kepler rotation curve

AbstractMagnetic fields of various astrophysical objects are described using the dynamo mechanism. Corresponding equations in the three-dimensional case are quite difficult to be solved. So, the two-dimensional models can be useful for such problems. For galactic and accretion discs, it is convenient to use the no-zzapproximation. The initial conditions for the magnetic field have a special interest. It seems that the seed field is generated by the Biermann mechanism, and after that they are transformed by the small-scale dynamo which gives a random structure of the field. Previously it has been shown that random initial conditions can lead to generation of large-scale magnetic field structures which correspond to the galaxies at the moment. In this work, we have studied generation of the magnetic field for the case of Kepler rotation curve, which is mostly suitable to the accretion discs. Here, we have studied the field generation in the thin disc for rapidly changing angular velocity in the case of simple model assumptions.

Magnetic Dynamo Caused by Axions in Neutron Stars.

The coupling between axions and photons modifies Maxwell's equations, introducing a dynamo term in the magnetic induction equation. In neutron stars, for critical values of the axion decay constant and axion mass, the magnetic dynamo mechanism increases the total magnetic energy of the star. We show that this generates substantial internal heating due to enhanced dissipation of crustal electric currents. These mechanisms would lead magnetized neutron stars to increase their magnetic energy and thermal luminosity by several orders of magnitude, in contrast to observations of thermally emitting neutron stars. To prevent the activation of the dynamo, bounds on the allowed axion parameter space can be derived.

Prediction for the amplitude and second maximum of Solar Cycle 25 and a comparison of the predictions based on strength of polar magnetic field and low-latitude sunspot area

ABSTRACTThe maximum of a solar cycle contains two or more peaks, known as Gnevyshev peaks. Studies of this property of solar cycles may help in better understanding the solar dynamo mechanism. We analysed the 13-month smoothed monthly mean Version-2 international sunspot number (SN) during the period 1874–2017 and found that there exists a good correlation between the amplitude (value of the main and highest peak) and the value of the second maximum (value of the second highest peak) during the maximum of a solar cycle. Using this relationship and the earlier predicted value 86 ± 18 (92 ± 11) of the amplitude of Solar Cycle 25, here we predict a value 73 ± 15 (79 ± 15) for the second maximum of Solar Cycle 25. The ratio of the predicted second maximum to the amplitude is found to be 0.85, almost the same as that of Solar Cycle 24. The least-square cosine fits to the values of the peaks that occurred first and second during the maxima of Solar Cycles 12–24 suggest that in Solar Cycle 25 the second maximum would occur before the main maximum, the same as in Solar Cycle 24. However, these fits suggest ≈106 and ≈119 for the second maximum and the amplitude of Solar Cycle 25, respectively. Earlier, we analysed the combined Greenwich and Debrecen sunspot-group data during 1874–2017 and predicted the amplitude of Solar Cycle 25 from the activity just after the maximum of Solar Cycle 24 in the equatorial latitudes of the Sun’s Southern hemisphere. Here, from the hindsight of the results we found the earlier prediction is reasonably reliable. We analysed the polar-fields data measured in Wilcox Observatory during Solar Cycles 20–24 and obtained a value 125 ± 7 for the amplitude of Solar Cycle 25. This is slightly larger – whereas the value ≈86 (≈92) predicted from the activity in the equatorial latitudes is slightly smaller – than the observed amplitude of Solar Cycle 24. This difference is discussed briefly.

Comment on “Tidally Synchronized Solar Dynamo: A Rebuttal” by Nataf (Solar Phys. 297, 107, 2022)

Nataf (Solar Phys.297, 107, 2022) has recently asserted that the hypothesis that the solar dynamo may be synchronized by planetary tidal forces is unsupported by any evidence. He reached this conclusion by adopting a simplistic tidal model (which was discussed in his Appendix A) that relies solely on the effect of Mercury, Venus, Earth, and Jupiter whose orbits were assumed to be circular. His model was unable to produce tides with periods compatible with those of the Schwabe 11-year solar cycle. I demonstrate here that the modeling in Nataf (2022) is erroneous and that a correct modeling and interpretation of the planetary tidal function, which accounts for all planets and their true orbits, fits well with the spectral requirements of the Schwabe 11-year solar cycle. This result has been already shown and discussed in a substantial body of scholarly research on the subject, which Nataf apparently ignored. A recent and extended review of the empirical and theoretical evidences supporting the planetary synchronized solar dynamo theory was offered by Scafetta and Bianchini (Front. Astron. Space Sci.9, 937930, 2022).

Impact of tides on non-coplanar orbits of progenitors of high-mass X-ray binaries

Context. An important stage in the evolution of massive binaries is the formation of a compact object in the system. It is believed that in some cases a momentum kick is imparted to the newly born object, changing the orbital parameters of the binary, such as eccentricity and orbital period, and even acquiring an asynchronous orbit between its components. In this situation, tides play a central role in the evolution of these binaries. Aims. In this work we aim to study how the orbital parameters of a massive binary change after the formation of a compact object when the stellar spin of the non-degenerate companion is not aligned with the orbital angular momentum. Methods. We used MESA, which we modified to be able to evolve binaries with different values of the inclination between the orbital planes before and just after the formation of the compact object. These modifications to the equations solved by the MESA code are extended to the case of non-solid body rotation. Results. We find that the impact of having different initial inclinations is mostly present in the evolution towards an equilibrium state that is independent of the inclination. If the binary separation is small enough such that the interaction happens when the star is burning hydrogen in its core, this state is reached before the beginning of a mass-transfer phase, while for a wider binary not all conditions characterizing the equilibrium are met. We also explore the effect of having different initial rotation rates in the stars and how the Spruit-Tayler dynamo mechanism affects the angular momentum transport for a non-coplanar binary. Conclusions. These findings show that including the inclination in the equations of tidal evolution to a binary after a kick is imparted onto a newly born compact object changes the evolution of some parameters, such as the eccentricity and the spin period of the star, depending on how large this inclination is. Moreover, these results can be used to match the properties of observed X-ray binaries to estimate the strength of the momentum kick.

Turbulent Magnetic Diffusivity β Effect in a Magnetically Forced System

We have studied the large-scale dynamo forced with helical magnetic energy. Compared to the kinetic forcing process, the magnetic process is not clearly observed nor intuitive. However, it may represent the actual B field amplification in the stellar corona, accretion disk, plasma lab, or other magnetically dominated systems where the strong kinetic effect does not exist. The interaction between the magnetic field and the plasma is essentially nonlinear. However, when the plasma system is driven by helical energy, whether kinetic or magnetic, the nonlinear process can be linearized with pseudotensors a, β and the large-scale magnetic field . Conventionally, the α effect is thought to be the main dynamo effect converting kinetic energy into magnetic energy and transferring it to the large-scale regime. In contrast, β effect has been thought to diffuse magnetic energy. However, these conclusions are not based on the exact definition of α and β. In this paper, instead of the analytic definition of α and β, we derive a semi-analytic equation and apply it to the simulation data. The half analytic and numerical result shows that the averaged α effect is not so important in amplifying the field. Rather, it is the negative β effect combined with the Laplacian (∇2 → −k 2) that plays a key role in the dynamo process. Further, the negative magnetic diffusivity accounts for the attenuation of the plasma kinetic energy in large scales. We discuss this process using the theoretical method and the intuitive field structure model.

Performance of AICC Statistic as Time Series Modeling and Forecasting of Sunspots

Dynamics of the Sun is quite complex. Sunspot number is an important index to understand the solar dynamo mechanism that governs the solar magnetic cycle. This paper is an attempt to forecast Sunspots number by finding an appropriate time series model. For the purpose, Sunspots datasets from 1749 to 2010 were used. Also, 23 minimum to minimum (m-m) and 24 maximum to minimum (M-m) Sunspots cycles were investigated. The results show that Autoregressive Moving average (ARMA) time series models fit the Sunspots number well. They have corrected predictions of the future trend of the Sunspots number within the sample period of study. The results obtained showed that the probability of the AIC corrected model was found better fitted. The problem of over parameterization exited in the model used, but under parameterization was found to minimal.