Dynamo Modes Research Articles

Correction to: Why the observed spin evolution of older-than-solar-like stars might not require a dynamo mode change

Correction to: Why the observed spin evolution of older-than-solar-like stars might not require a dynamo mode change

Variabilities in the polar field and solar cycle due to irregular properties of bipolar magnetic regions

ABSTRACT Decay and dispersal of the tilted bipolar magnetic regions (BMRs) on the solar surface are observed to produce the large-scale poloidal field, which acts as the seed for the toroidal field and, thus, the next sunspot cycle. However, various properties of BMR, namely, the tilt, time delay between successive emergences, location, and flux, all have irregular variations. Previous studies show that these variations can lead to changes in the polar field. In this study, we first demonstrate that our 3D kinematic dynamo model, STABLE, reproduces the robust feature of the surface flux transport (SFT) model, namely the variation of the generated dipole moment with the latitude of the BMR position. Using STABLE in both SFT and dynamo modes, we perform simulations by varying the individual properties of BMR and keeping their distributions the same in all the cycles as inspired by the observations. We find that randomness due to the distribution in either the time delay or the BMR latitude produces negligible variation in the polar field and the solar cycle. However, randomness due to BMR flux distribution produces substantial effects, while the scatter in the tilt around Joy’s law produces the largest variation. Our comparative analyses suggest that the scatter of BMR tilt around Joy’s law is the major cause of variation in the solar cycle. Furthermore, our simulations show that the magnetic field-dependent time delay of BMR emergence produces more realistic features of the magnetic cycle, consistent with observation.

Spatio-temporal non-localities in a solar-like mean-field dynamo

ABSTRACT The scale separation approximation, which is in the base of the solar mean-field dynamo models, can be hardly justified both by observations and theoretical applications to astrophysical dynamos. The general expression for the mean turbulent electromotive force can be written in integral form with convolution of the turbulent effects and mean magnetic field variations over scales of the turbulent flows and global scales of the mean-field dynamo. Following results of direct numerical simulations (DNS), which had been reported earlier, we take the Lorentzian form of the integral convolution kernels as an experimental fact. It allows us to approximate the governing equation for the mean electromotive force by the reaction–diffusion type equation. Solution of the eigenvalue problem reveals a few curious properties of the dynamo model with the non-local mean electromotive force. We find a decrease of the critical dynamo instability threshold, and an increase the dynamo periods of the unstable modes, as reported in earlier studies. Simultaneously, the non-local model shows substantially lower growth rate of the unstable dynamo modes in proximity of the critical threshold than the model which employs the scale separation approximation. We verify these findings using the non-linear solar dynamo model. For the supercritical regime, when the α-effect magnitude is about twice of the instability threshold, the model shows the Parker’s dynamo wave solutions with the wave propagating from the mid-latitude at the bottom of the convection zone towards the solar equator at the surface.

Why the observed spin evolution of older-than-solar-like stars might not require a dynamo mode change

ABSTRACT The spin evolution of main-sequence stars has long been of interest for basic stellar evolution, stellar ageing, stellar activity, and consequent influence on companion planets. Observations of older-than-solar late-type main-sequence stars have been interpreted to imply that a change from a dipole-dominated magnetic field to one with more prominent higher multipoles might be necessary to account for the data. The spin-down models that lead to this inference are essentially tuned to the Sun. Here, we take a different approach that considers individual stars as fixed points rather than just the Sun. We use a time-dependent theoretical model to solve for the spin evolution of low-mass main-sequence stars that includes a Parker-type wind and a time-evolving magnetic field coupled to the spin. Because the wind is exponentially sensitive to the stellar mass over radius and the coronal base temperature, the use of each observed star as a separate fixed point is more appropriate and, in turn, produces a set of solution curves that produces a solution envelope rather than a simple line. This envelope of solution curves, unlike a single line fit, is consistent with the data and does not unambiguously require a modal transition in the magnetic field to explain it.

Inferring Quadrupolar Dynamo Mode from Sunspot Statistics

Observations of long-term north-south asymmetry in solar activity demand the equator-symmetric (quadrupolar) mode be present in the solar magnetic field in line with the dominant antisymmetric (dipolar) mode. This paper proposes treating the sunspot area as a proxy for subsurface toroidal magnetic flux to infer the quadrupolar mode of the solar dynamo from sunspot data. Toroidal pseudo-fluxes (PF) in the northern and southern hemispheres are defined as a signed sunspot area with plus or minus sign prescribed to them in accord with the Hale's sunspot polarity rules. Statistical correlation analysis and wavelet analysis of so-defined PFs reveal quadrupolar oscillations with a period of about 16 yr and amplitude of about 0.17 relative to the amplitude of the dominant 22-yr dipolar mode.

Gravitoturbulent dynamo in global simulations of gaseous disks

Context. The turbulence driven by gravitational instabilities (GIs) can amplify magnetic fields in massive gaseous disks. This GI dynamo may appear in young circumstellar disks, whose weak ionization challenges other amplification routes, as well as in active galactic nuclei. Although regarded as a large-scale dynamo, only local simulations have so far described its kinematic regime. Aims. We study the GI dynamo in global magnetohydrodynamic (MHD) models of accretion disks, focusing on its kinematic phase. Methods. We perform resistive MHD simulations with the PLUTO code for different radiative cooling times and electrical resistivities. A weak magnetic field seeds the dynamo, and we adopt mean-field and heuristic models to capture its essence. Results. We recover the same induction process leading to magnetic field amplification as previously identified in local simulations. The dynamo is, however, global in nature, connecting distant annuli of the disk via a large-scale dynamo mode of a fixed growth rate. This large-scale amplification can be described by a mean-field model that does not rely on conventional α-Ω effects. When varying the disk parameters we find an optimal resistivity that facilitates magnetic amplification, whose magnetic Reynolds number, ℛm ≲ 10, is substantially smaller than in local simulations. Unlike local simulations, we find an optimal cooling rate and the existence of global oscillating dynamo modes. The nonlinear saturation of the dynamo puts the disk in a strongly magnetized turbulent state on the margins of the effective range of GI. In our simulations, the accretion power eventually exceeds the threshold required by local thermal balance against cooling, leaving the long-term nonlinear outcome of the GI dynamo uncertain.

Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model

In the Sun and Sun-like stars, it is believed that cycles of the large-scale magnetic field are produced due to the existence of differential rotation and helicity in the plasma flows in their convection zones (CZs). Hence, it is expected that for each star, there is a critical dynamo number for the operation of a large-scale dynamo. As a star slows down, it is expected that the large-scale dynamo ceases to operate above a critical rotation period. In our study, we explore the possibility of the operation of the dynamo in the subcritical region using the Babcock–Leighton type kinematic dynamo model. In some parameter regimes, we find that the dynamo shows hysteresis behavior, i.e., two dynamo solutions are possible depending on the initial parameters—decaying solution if starting with weak field and strong oscillatory solution (subcritical dynamo) when starting with a strong field. However, under large fluctuations in the dynamo parameter, the subcritical dynamo mode is unstable in some parameter regimes. Therefore, our study supports the possible existence of subcritical dynamo in some stars which was previously demonstrated in a mean-field dynamo model with distributed α and MHD turbulent dynamo simulations.

Dynamo Model for North–South Asymmetry of Solar Activity

Abstract Observations reveal a relatively small but statistically significant north–south (NS) asymmetry in sunspot activity varying on a timescale of several solar cycles. This paper proposes a dynamo model for the phenomenon of long-term NS asymmetry. The model separates dynamo equations for magnetic fields of dipolar and quadrupolar equatorial parity. The NS asymmetry results from the superposition of dipolar and quadrupolar fields. Model computations confirm the formerly proposed excitation of the quadrupolar dynamo mode by a dominant dipolar mode mediated by the equator-symmetric fluctuations in the α-effect as a mechanism for the long-term NS asymmetry. An analytically solvable example of oscillations excited by short-term random forcing is given to justify the numerical result of NS asymmetry coherent on a timescale of several (about six in the present model) solar cycles resulting from random variations in the α-effect on a timescale of one solar rotation. The model computations show the phase-locking phenomenon of dipolar and quadrupolar fields oscillating predominantly in phase (northern type asymmetry) or in antiphase (southern type asymmetry) with relatively short irregular transitions between these two states. Large asymmetry in the simulated Grand minima is found and explained by weak magnetic quenching of the α-effect during the minima. The possibility of polar field asymmetry in activity minima as a precursor of sunspot asymmetry in the following activity cycles is discussed based on the dynamo model and observations.

Large-scale Dynamo in a Primordial Accretion Flow: An Interpretation from Hydrodynamic Simulation

Abstract Without an existing large-scale coherent magnetic field in the early universe, Population III stars would likely rotate at or near breakup speed. In this work, focusing on the accretion phase of Population III stars, we investigate the possibility of generating a coherent magnetic field through large-scale dynamo processes, as well as the corresponding field saturation level. Using results from hydrodynamic simulations performed with a cylindrical grid, we demonstrate that primordial accretion disks are turbulent with a Shakura–Sunyaev disk parameter α ss ≳ 10−3 and evidence for helical turbulence with a dynamo number ∣D αΩ∣ ≫ 10. The presence of helical turbulence at these levels allows large-scale dynamo modes to grow, and the saturation level is determined by the amount of net helicity remaining in the dynamo active regions (i.e., the quenching problem). We demonstrate that if the accretion could successfully alleviate the quenching problem, the magnetic field can reach approximate equipartition with B/B eq ∼ 3.

Dynamical Coupling of a Mean-field Dynamo and Its Wind: Feedback Loop over a Stellar Activity Cycle

Abstract We focus on the connection between the internal dynamo magnetic field and the stellar wind. If the star has a cyclic dynamo, the modulations of the magnetic field can affect the wind, which, in turn, can back-react on the boundary conditions of the star, creating a feedback loop. We have developed a 2.5D numerical setup to model this essential coupling. We have implemented an alpha–omega mean-field dynamo in the PLUTO code and then coupled it to a spherical polytropic wind model via an interface composed of four grid layers with dedicated boundary conditions. We present here a dynamo model close to a young Sun with cyclic magnetic activity. First, we show how this model allows one to track the influence of the dynamo activity on the corona by displaying the correlation between the activity cycle, the coronal structure, and the time evolution of integrated quantities. Then we add the feedback of the wind on the dynamo and discuss the changes observed in the dynamo symmetry and wind variations. We explain these changes in terms of dynamo modes; in this parameter regime, the feedback loop leads to a coupling between the dynamo families via a preferred growth of the quadrupolar mode. We also study our interface in terms of magnetic helicity and show that it leads to a small injection in the dynamo. This model confirms the importance of coupling physically internal and external stellar layers, as it has a direct impact on both the dynamo and the wind.

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.

ДОВГОТРИВАЛІ ВАРІАЦІЇ МАГНІТНОЇ АКТИВНОСТІ СОНЦЯ

The main law of the evolution of the Earth’s climate is the cyclical nature of global changes in the latter. One of the possible explanations for the cyclical nature of global climate changes is provided by the astrophysical model of fluctuations in the insolation of the Earth’s surface by solar radiation. Modern climate change is mainly associated with variations in the magnetic activity of the Sun, one of the main proxies of which are sunspots. The decrease in the number of sunspots coincides with the epochs of cooling on the Earth, while during the maximum number of sunspots warming is observed. The paper reviews cosmogenic reconstructions of long-term variations in the Sun’s magnetic activity (large minima and large maxima) during the Holocene (last 12,000 years). The accidental appearance of large minima and maxima can to some extent be reproduced by modern models of a turbulent dynamo with a stochastic drive. An important key to studying the impact of solar activity variations on the Earth’s climate is the Maunder minimum (late 17th century), during which extremely little sunspots were observed. Applying the method of analysis of rare events to these observations led researchers to conclude that the appearance of sunspots at the Maunder minimum was characterized by a weak amplitude of 22 years. The concept of continuity of magnetic cycles at this time is also confirmed by measurements of cosmogenic radionuclides in natural terrestrial archives. Therefore, today it is believed that during the Maunder minimum, the cyclic magnetic activity of the Sun did not stop, although the amplitude of the cycles was quite low. In the αΩ-dynamo model, this may be due to the fact that the magnitude of the magnetic induction of the toroidal field excited by radial differential rotation in the solar convection zone at this time did not reach the threshold value required for lifting magnetic power tubes on the solar surface (nonlinear dynamo mode). Possible physical mechanisms describing the suppression of the dynamo process at intervals when no sunspots were observed are analyzed. A scenario for explaining the north-south asymmetry of magnetic activity during the Maunder minimum is proposed. A key role in the proposed scenario is played by the special nature of the internal rotation of the Sun, revealed as a result of helioseismological experiments. The modern grand maximum of solar activity, which began in the 1940s, has ceased after solar cycle 23, and activity of the Sun seems to be returning to its normal moderate level.

Identifying solar-like magnetic cycles with Zeeman-Doppler-Imaging

ABSTRACT We are reaching the point where spectropolarimetric surveys have run for long enough to reveal solar-like magnetic activity cycles. In this paper, we investigate what would be the best strategy to identify solar-like magnetic cycles and ask which large-scale magnetic field parameters best follow a solar-type magnetic cycle and are observable with the Zeeman-Doppler-Imaging (ZDI) technique. We approach these questions using the 3D non-potential flux transport simulations of Yeates & Mackay (2012) modelling the solar vector magnetic field over 15 yr (centred on solar cycle 23). The flux emergence profile was extracted from solar synoptic maps and used as input for a photospheric flux transport model in combination with a non-potential coronal evolution model. We synthesize spectropolarimetric data from the simulated maps and reconstruct them using ZDI. The ZDI observed solar cycle is set into the context of other cool star observations and we present observable trends of the magnetic field topology with time, sunspot number, and S-index. We find that the axisymmetric energy fraction is the best parameter of the ZDI detectable large-scale field to trace solar-like cycles. Neither the surface averaged large-scale field or the total magnetic energy is appropriate. ZDI seems also to be able to recover the increase of the toroidal energy with S-index. We see further that ZDI might unveil hints of the dynamo modes that are operating and of the global properties of the small-scale flux emergence like active latitudes.

Reconstruction of the Solar Activity in 1000–1700 Based on Auroral Data with Allowance for the Contribution of the Main Magnetic Field of the Earth

A new reconstruction of the number of sunspots (SN) in 1000–1700, along with possible errors, has been obtained based on an analysis of auroral observations at middle and low latitudes and data on the Earth’s magnetic field at that time. The intensity and configuration of the main magnetic field of the Earth affect the penetration of the Earth’s magnetosphere and atmosphere by aurora-induced, charged, solar-wind particles. Our reconstruction differs from other authors in that we have taken into account this effect on the frequency of auroras. The time variation of the reconstructed SN shows the previously known minima of Oort, Wolf, Sporer, and Maunder. The SN values for 1100–1150 (medieval maximum) are comparable to those observed in the second half of the XX century during the current period of high solar activity. It is shown that SN decreases by approximately two times during the Maunder minimum in comparison with the previous period, but it can reach SN ≈ 40 in some years. Bifurcation and degeneration of the 11-year cycle occurs at the beginning of the Maunder minimum. It can be associated with the difference in solar dynamo modes.

Shapes of stellar activity cycles

Context.Magnetic activity cycles are an important phenomenon both in the Sun and other stars. The shape of the solar cycle is commonly characterised by a fast rise and a slower decline, but not much attention has been paid to the shape of cycles in other stars.Aims.Our aim is to study whether the asymmetric shape of the solar cycle is common in other stars as well, and compare the cycle asymmetry to other stellar parameters. We also study the differences in the shape of the solar cycle, depending on the activity indicator that is used. The observations are also compared to simulated activity cycles.Methods.We used the chromospheric Ca IIH&K data from the Mount Wilson Observatory HK Project. In this data set, we identified 47 individual cycles from 18 stars. We used the statistical skewness of a cycle as a measure of its asymmetry, and compared this to other stellar parameters. A similar analysis has been performed for magnetic cycles extracted from direct numerical magnetohydrodynamic simulations of solar-type convection zones.Results.The shape of the solar cycle (fast rise and slower decline) is common in other stars as well, although the Sun seems to have particularly asymmetric cycles. Cycle-to-cycle variations are large, but the average shape of a cycle is still fairly well represented by a sinusoid, although this does not take its asymmetry into account. We find only slight correlations between the cycle asymmetry and other stellar parameters. There are large differences in the shape of the solar cycle, depending on the activity indicator that is used. The simulated cycles differ in the symmetry of global simulations that cover the full longitudinal range and are therefore capable of exciting non-axisymmetric large-scale dynamo modes, and wedge simulations that cover a partial extent in longitude, where only axisymmetric large-scale modes are possible. The former preferentially produce positive and the latter negative skewness.

A Transition of Dynamo Modes in M Dwarfs: Narrowing Down the Spectral Range Where the Transition Occurs*

Abstract Houdebine et al. combined Ca ii data with projected rotational velocities (v sin i) to construct rotation-activity correlations (RAC) in K-M dwarfs. The RAC slopes were used to argue that a transition between dynamo modes occurs at a spectral type between M2 and M3. H17 suggested that the dynamo transition corresponds to a transition to complete convection (TTCC). An independent study of GAIA data led Jao et al. to suggest that the TTCC sets in “near M3.0V,” close to the H17 result. However, the changes in a star that cause TTCC signatures in GAIA data might not lead to changes in Ca ii emission at an identical spectral type: the latter are also affected by magnetic effects, which depend on certain properties of convection in the core. Here, we use Ca ii emission fluxes in a sample of ∼600 M dwarfs, and attempt to narrow down the transition from one dynamo mode to another: rather than relying on RAC slopes, we quantify how the Ca ii emission flux varies with spectral type to identify “steps” where the flux decreases significantly across a narrow range of spectral types. We suggest that the dynamo mode transition may be narrowed down to between M2.1 and M2.3. This is close to, but earlier than, the TTCC location identified by Jao et al. We suggest that the transition in dynamo mode may be related to the existence of a small convective core, which occurs for a finite time interval in certain low-mass stars.

Solar dynamo modes of oscillations and the long- term prediction of solar activity

We verify that the values and dates of occurrence of sunspot maxima during Schwabe sunspot cycles ##19 to 24 as predicted by Derek Justin Schove in 1955 coincide with the actually observed ones with a high degree of accuracy. A question arises from this result: why is such a deterministic behavior apparent in a system, like the solar dynamo, that is in principle stochastic. We find that solar activity related data may be well represented by the addition of a constant level and eight modes of oscillation. The repetitive behavior and the relationships that appears to exist between these modes, opens the possibility for a long-term prediction of solar activity. In that line, we forecast the Gleissberg cycle for the forthcoming two centuries and data on sunspot maxima for the next century. Thus, we predict the values and dates of occurrence of sunspot maxima ##25 to 35 and find that the new Episode of solar activity that started during polar cycle #24, as a follow-up of the 20th century Grand Maximum, is of the Regular type and, as the ongoing Hallstatt oscillation will pass through zero from negative to positive around the year 2036, it will last for the remainder of the present millennium. We also find that modes of oscillations are mutually related through a forced non-linear oscillator with a persistent asymmetry. A brief discussion of the origin of this behavior on the excitation of solar dynamo motions by solar-planetary forces is presented.

Stellar Dynamos in the Transition Regime: Multiple Dynamo Modes and Antisolar Differential Rotation

Abstract Global and semi-global convective dynamo simulations of solar-like stars are known to show a transition from an antisolar (fast poles, slow equator) to solar-like (fast equator, slow poles) differential rotation (DR) for increasing rotation rate. The dynamo solutions in the latter regime can exhibit regular cyclic modes, whereas in the former one, only stationary or temporally irregular solutions have been obtained so far. In this paper we present a semi-global dynamo simulation in the transition region, exhibiting two coexisting dynamo modes, a cyclic and a stationary one, both being dynamically significant. We seek to understand how such a dynamo is driven by analyzing the large-scale flow properties (DR and meridional circulation) together with the turbulent transport coefficients obtained with the test-field method. Neither an αΩ dynamo wave nor an advection-dominated dynamo are able to explain the cycle period and the propagation direction of the mean magnetic field. Furthermore, we find that the α effect is comparable or even larger than the Ω effect in generating the toroidal magnetic field, and therefore, the dynamo seems to be of α 2Ω or α 2 type. We further find that the effective large-scale flows are significantly altered by turbulent pumping.

A Model of a Tidally Synchronized Solar Dynamo

We discuss a solar dynamo model of Tayler-Spruit type whose Omega-effect is conventionally produced by a solar-like differential rotation but whose alpha-effect is assumed to be periodically modulated by planetary tidal forcing. This resonance-like effect has its rationale in the tendency of the current-driven Tayler instability to undergo intrinsic helicity oscillations which, in turn, can be synchronized by periodic tidal perturbations. Specifically, we focus on the 11.07 years alignment periodicity of the tidally dominant planets Venus, Earth, and Jupiter, whose persistent synchronization with the solar dynamo is briefly touched upon. The typically emerging dynamo modes are dipolar fields, oscillating with a 22.14 years period or pulsating with a 11.07 years period, but also quadrupolar fields with corresponding periodicities. In the absence of any constant part of alpha, we prove the subcritical nature of this Tayler-Spruit type dynamo. The resulting amplitude of the alpha oscillation that is required for dynamo action turns out to lie in the order of 1 m/s, which seems not implausible for the sun. When starting with a more classical, non-periodic part of alpha, even less of the oscillatory alpha part is needed to synchronize the entire dynamo. Typically, the dipole solutions show butterfly diagrams, although their shapes are not convincing yet. Phase coherent transitions between dipoles and quadrupoles, which are reminiscent of the observed behaviour during the Maunder minimum, can be easily triggered by long-term variations of dynamo parameters, but may also occur spontaneously even for fixed parameters. Further interesting features of the model are the typical second intensity peak and the intermittent appearance of reversed helicities in both hemispheres.

Modes of magnetic field generation in models of a αΩ-dynamo with a power type α-generator

In the dynamic model αΩ-dimensions are simulated reversions of the magnetic field with a varying intensity of the α-generator. The change of the α-generator intensity as a result of synchronization of higher modes of the velocity field and the magnetic field is regulated by a function Z(t) with a power kernel. Dynamo modes are obtained for two types of radial component in the scalar parameterization of the α-effect. The results were analyzed depending on the change in the exponent of the kernel of the function Z(t) and the type of the power kernel, also a comparative analysis with the results of the study [9], where the exponential kernel of the function Z(t) was used.