Dynamo Model Research Articles

A Time‐Resolved Paleomagnetic Record of Main Group Pallasites: Evidence for a Large‐Cored, Thin‐Mantled Parent Body

AbstractSeveral paleomagnetic studies have been conducted on five Main Group pallasites: Brenham, Marjalahti, Springwater, Imilac, and Esquel. These pallasites have distinct cooling histories, meaning that their paleomagnetic records may have been acquired at different times during the thermal evolution of their parent body. Here, we compile new and existing data to present the most complete time‐resolved paleomagnetic record for a planetesimal, which includes a period of quiescence prior to core solidification as well as dynamo activity generated by compositional convection during core solidification. We present new paleomagnetic data for the Springwater pallasite, which constrains the timing of core solidification. Our results suggest that in order to generate the observed strong paleointensities (∼65–95 μT), the pallasites must have been relatively close to the dynamo source. Our thermal and dynamo models predict that the Main Group pallasites originate from a planetesimal with a large core (>200 km) and a thin mantle (<70 km).

Dynamical study of Lyapunov exponents for Hide’s coupled dynamo model

Abstract In this paper, we introduced the Lyapunov exponents (LEs) as a significant tool that is used to study the numerical solution behavior of the dynamical systems. Moreover, Hide’s coupled dynamo model presents a valuable dynamical study. We simulate the convergence of the LEs of the model in three cases by means of periodic flow, regular flow, and chaos flow. In addition, we compared these cases in logic connections and proved them in a mathematical way.

Effects of observational data shortage on accuracy of global solar activity forecast

ABSTRACT Building a reliable forecast of solar activity is a long-standing problem that requires an accurate description of past and current global dynamics. Relatively recently, synoptic observations of magnetic fields and subsurface flows have become available. In this paper, we present an investigation of the effects of short observational data series on the accuracy of solar cycle prediction. This analysis is performed using the annual sunspot number time-series applied to the Parker–Kleeorin–Ruzmaikin dynamo model and employing the Ensemble Kalman Filter (EnKF) data assimilation method. The testing of cycle prediction accuracy is performed for the last six cycles (for Solar Cycles 19–24) by sequentially shortening the observational data series to predict a target cycle and evaluate the resulting prediction accuracy according to specified criteria. According to the analysis, reliable activity predictions can be made using relatively short time-series of the sunspot number. The accuracy of the solar activity has a weak dependence on the length of available observations. It is demonstrated that at least three cycles of observations are needed to obtain robust forecasts.

Recent advances in the 3D kinematic Babcock–Leighton solar dynamo modeling

In this review, we explain recent progress made in the Babcock-Leighton dynamo models for the Sun, which have been most successful to explain various properties of the solar cycle. In general, these models are 2D axisymmetric and the mean-field dynamo equations are solved in the meriodional plane of the Sun. Various physical processes (e.g., magnetic buoyancy and Babcock-Leighton mechanism) involved in these models are inherently 3D process and could not be modeled properly in a 2D framework. After pointing out limitations of 2D models (e.g., Mean-field Babcock-Leighton dynamo models and Surface Flux Transport models), we describe recently developed next-generation 3D dynamo models that implement more sophisticated flux emergence algorithm of buoyant flux tube rise through the convection zone and capture Babcock-Leighton process more realistically than previous 2D models. The detailed results from these 3D dynamo models including surface flux transport counterpart are presented. We explain the cycle irregularities that are reproduced in 3D dynamo models by introducing scattering around the tilt angle only. Some results by assimilating observed photospheric convective velocity fields into the 3D models are also discussed, pointing out the wide opportunity that these 3D models hold to deliver.

Stable stratification promotes multiple zonal jets in a turbulent jovian dynamo model

The ongoing NASA's Juno mission puts new constraints on the internal dynamics of Jupiter. Data gathered by its onboard magnetometer reveal a dipole-dominated surface magnetic field accompanied by strong localised magnetic flux patches. The gravity measurements indicate that the fierce surface zonal jets extend several thousands of kilometers below the cloud level before rapidly decaying below 0.94 − 0.96RJ, RJ being the mean Jovian radius at the one bar level. Jupiter's internal structure can be grossly decomposed in two parts: (i) an outer layer filled with a mixture of molecular hydrogen and helium where the zonal flows are thought to be driven; (ii) an inner region where hydrogen becomes metallic and dynamo action is expected to sustain the magnetic field. Several internal models however suggest a more intricate structure with a thin intermediate region in which helium would segregate from hydrogen, forming a compositionally-stratified layer. Here, we develop the first global Jovian dynamo which incorporates an intermediate stably-stratified layer between 0.82RJ and 0.86RJ. Using much lower diffusivities than previous models enables us to more clearly separate the dynamics of the metallic core and the molecular envelope. Analysing the energy balance reveals that magnetic energy is almost one order of magnitude larger than kinetic energy in the metallic region, while most of the kinetic energy is pumped into zonal motions in the molecular envelope. Those result from the different underlying force hierarchy with a triple balance between Lorentz, Archimedean and ageostrophic Coriolis forces in the metallic core and inertia, buoyancy and ageostrophic Coriolis forces controlling the external layers. The simulation presented here is the first to demonstrate that multiple zonal jets and dipole-dominated dynamo action can be consolidated in a global simulation. The inclusion of a stable layer is a necessary ingredient that allows zonal jets to develop in the outer envelope without contributing to the dynamo action in the deeper metallic region. Stable stratification however also smooths out the small-scale features of the magnetic field by skin effect, yielding a too-dipolar surface field as compared to the observations. These constraints suggest that possible stable layers in Jupiter should be located much closer to the surface (0.9 − 0.95RJ).

Supercriticality of the Dynamo Limits the Memory of the Polar Field to One Cycle

Abstract The polar magnetic field precursor is considered to be the most robust and physics-based method for the prediction of the next solar cycle strength. However, to make a reliable prediction of a cycle, is the polar field at the solar minimum of the previous cycle enough or do we need the polar field of many previous cycles? To answer this question, we performed several simulations using Babcock–Leighton-type flux-transport dynamo models with a stochastically forced source for the poloidal field (α term). We show that when the dynamo is operating near the critical dynamo transition or only weakly supercritical, the polar field of cycle n determines the amplitude of the next several cycles (at least three). However, when the dynamo is substantially supercritical, this correlation of the polar field is reduced to one cycle. This change in the memory of the polar field from multiple to one cycle with the increase of the supercriticality of the dynamo is independent of the importance of various turbulent transport processes in the model. Our this conclusion contradicts the existing idea. We further show that when the dynamo operates near the critical transition, it produces frequent extended episodes of weaker activity, resembling the solar grand minima. The occurrence of grand minima is accompanied by the multicycle correlation of the polar field. The frequency of grand minima decreases with the increase of supercriticality of the dynamo.

Variations of helioseismic parameters due to magnetic field generated by a flux transport model

The change of sound speed has been found at the base of the convection during the solar cycles, which can be used to constrain the solar internal magnetic field. We aim to check whether the magnetic field generated by the solar dynamo can lead to the cyclic variation of the sound speed detected through helioseismology. The basic configuration of magnetic field in the solar interior was obtained by using a Babcock-Leighton (BL) type flux transport dynamo. We reconstructed one-dimensional solar models by assimilating magnetic field generated by an established dynamo and examined their influences on the structural variables. The results show that magnetic field generated by the dynamo is able to cause noticeable change of the sound speed profile at the base of the convective zone during a solar cycle. Detailed features of this theoretical prediction are also similar to those of the helioseismic results in solar cycle 23 by adjusting the free parameters of the dynamo model.

Solar large-scale magnetic field and cycle patterns in solar dynamo

ABSTRACT We compare spectra of the zonal harmonics of the large-scale magnetic field of the Sun using observation results and solar dynamo models. The main solar activity cycle as recorded in these tracers is a much more complicated phenomenon than the eigen solution of solar dynamo equations with the growth saturated by a back reaction of the dynamo-driven magnetic field on solar hydrodynamics. The nominal 11(22)-yr cycle as recorded in each mode has a specific phase shift varying from cycle to cycle; the actual length of the cycle varies from one cycle to another and from tracer to tracer. Both the observation and the dynamo model show an exceptional role of the axisymmetric ℓ5 mode. Its origin seems to be readily connected with the formation and evolution of sunspots on the solar surface. The results of observations and dynamo models show a good agreement for the low ℓ1 and ℓ3 modes. The results for these modes do not differ significantly for the axisymmetric and non-axisymmetric models. Our findings support the idea that the sources of the solar dynamo arise as a result of both the distributed dynamo processes in the bulk of the convection zone and the surface magnetic activity.

A Knee Point in the Rotation–Activity Scaling of Late-type Stars with a Connection to Dynamo Transitions

Abstract The magnetic activity of late-type stars is correlated with their rotation rates. Up to a certain limit, stars with smaller Rossby numbers, defined as the rotation period divided by the convective turnover time, have higher activity. A more detailed look at this rotation–activity relation reveals that, rather than being a simple power-law relation, the activity scaling has a shallower slope for the low-Rossby stars than for the high-Rossby ones. We find that, for the chromospheric Ca II H&K activity, this scaling relation is well modeled by a broken two-piece power law. Furthermore, the knee point of the relation coincides with the axisymmetry to nonaxisymmetry transition seen in both the spot activity and surface magnetic field configuration of active stars. We interpret this knee point as a dynamo transition between dominating axi- and nonaxisymmetric dynamo regimes with a different dependence on rotation and discuss this hypothesis in the light of current numerical dynamo models.

Forward Modeling Helioseismic Signatures of One- and Two-cell Meridional Circulation

Abstract Using a 3D global solver of the linearized Euler equations, we model acoustic oscillations over background velocity flow fields of single-cell meridional circulation with deep and shallow return flows as well as double-cell meridional circulation with strong and weak reversals. The velocities are generated using a mean-field hydrodynamic and dynamo model—moving through the regimes with minimal parameter changes, counterrotation near the base of the tachocline is induced by sign inversion of the nondiffusive action of turbulent Reynolds stresses (Λ-effect) due to the radial inhomogeneity of the Coriolis number. By mimicking the stochastic excitation of resonant modes in the convective interior, we simulate realization noise present in solar observations. Using deep-focusing to analyze differences in travel-time signatures between the four regimes, as well as comparing to solar observations, we show that current helioseismology techniques may offer important insights about the location and strength of the return flow; however, it may not currently be possible to definitively distinguish between profiles of single-cell or double-cell meridional circulation.

Chaotic transients and hysteresis in an α 2 dynamo model

The presence of chaotic transients in a nonlinear dynamo is investigated through numerical simulations of the 3D magnetohydrodynamic equations. By using the kinetic helicity of the flow as a control parameter, a hysteretic blowout bifurcation is conjectured to be responsible for the transition to dynamo, leading to a sudden increase in the magnetic energy of the attractor. This high-energy hydromagnetic attractor is suddenly destroyed in a boundary crisis when the helicity is decreased. Both the blowout bifurcation and the boundary crisis generate long chaotic transients that are due, respectively, to a chaotic saddle and a relative chaotic attractor.

First palaeointensity data from the cryogenian and their potential implications for inner core nucleation age

SUMMARY The timing of inner core nucleation is a hugely significant event in Earth's evolution and has been the subject of intense debate. Some of the most recent theoretical estimates for the age of nucleation fall throughout the Neoproterozoic era; much younger than previously thought. A young inner core requires faster recent core cooling rates and a likely hotter early core; knowledge of its age would be invaluable in understanding Earth's thermal history and total energy budget. Predictions generated by numerical dynamo models need to be tested against such data, but records are currently much too sparse to constrain the event to a precise period of time. Here, we present results from 720 Ma dolerite dykes (and one sill) from the Franklin Large Igneous Province, which fall within a crucial 300 Myr gap in palaeointensity records. This study uses three independent techniques on whole rocks from 11 sites spread across High Arctic Canada and Greenland to produce virtual dipole moments ranging from 5 to 20 ZAm2 (mean 11 ZAm2); almost one order of magnitude lower than the present-day field. These weak-field results agree with recent ultralow palaeointensity data obtained from Ediacaran rocks formed ∼150 Myr later and may support that the dynamo was on the brink of collapse in the Neoproterozoic prior to a young inner core formation date.

Radial Velocity Monitoring of the Young Star Hubble 4: Disentangling Star-spot Lifetimes from Orbital Motion*

Abstract We studied the weak-lined T Tauri star Hubble 4, a known long-period binary, and its star-spot phenomena. We used optical radial velocity (RV) data taken over a span of 14 yr (2004–2010, 2017–2019) at the McDonald Observatory 2.7 m Harlan J. Smith Telescope and single epoch imaging from the Hubble Space Telescope (HST)/Wide Field Camera 3 instrument. The observed and apparent RV variations show contributions, respectively, from the binary motion as well as from a large spot group on one of the stars, presumed to be the primary. Fitting and removing the orbital signal from the RVs, we found the lower bound on the lifetime of a previously identified large spot group on the surface of the star to be at least 5.1 yr. An ∼5 yr lower limit is a long, but not unprecedented, duration for a single spot group. The later epoch data indicate significant spot evolution has occurred, placing an upper bound on the spot group lifetime at 12 yr. We find that pre-main-sequence evolutionary models for the age of Taurus (∼2 Myr), combined with component mass estimates from the literature, permit us to reproduce the HST relative photometry and the binary-induced contribution to the apparent RV variations. The long-lived star spot we find on Hubble 4 has significant implications for dynamo models in young stars, as it adds evidence for long lifetimes of magnetic field topologies. There are also significant implications for young star exoplanet searches, as long-lived coherent RV signals may be spot induced and not the result of planetary motion.

The Polar Precursor Method for Solar Cycle Prediction: Comparison of Predictors and Their Temporal Range

Abstract The polar precursor method is widely considered to be the most robust physically motivated method to predict the amplitude of an upcoming solar cycle. It uses indicators of the magnetic field concentrated near the poles around the sunspot minimum. Here, we present an extensive analysis of the performance of various such predictors, based on both observational data (Wilcox Solar Observatory (WSO) magnetograms, Mount Wilson Observatory polar faculae counts, and Pulkovo A(t) index) and outputs (polar cap magnetic flux and global dipole moment) of various existing flux transport dynamo models. We calculate Pearson correlation coefficients (r) of the predictors with the next cycle amplitude as a function of time measured from several solar cycle landmarks: setting r = 0.8 as a lower limit for acceptable predictions, we find that observations and models alike indicate that the earliest time when the polar predictor can be safely used is 4 yr after the polar field reversal. This is typically 2–3 yr before the solar minimum and about 7 yr before the predicted maximum, considerably extending the usual temporal scope of the polar precursor method. Reevaluating the predictors another 3 yr later, at the time of the solar minimum, further increases the correlation level to r ≳ 0.9. As an illustration of the result, we determine the predicted amplitude of Cycle 25 based on the value of the WSO polar field at the now official minimum date of 2019 December as 126 ± 3. A forecast based on the value in early 2017, 4 yr after the polar reversal would have only differed from this final prediction by 3.1 ± 14.7%.

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.

Dynamical Systems and Topology of Magnetic Fields in Conducting Medium

We discuss application of contemporary methods of the theory of dynamical systems with regular and chaotic hyperbolic dynamics to investigation of topological structure of magnetic fields in conducting media. For substantial classes of magnetic fields, we consider well-known physical models allowing us to reduce investigation of such fields to study of vector fields and Morse–Smale diffeomorphisms as well as diffeomorphisms with nontrivial basic sets satisfying the A axiom introduced by Smale. For the point–charge magnetic field model, we consider the problem of the separator playing an important role in the reconnection processes and investigate relations between its singularities. We consider the class of magnetic fields in the solar corona and solve the problem of topological equivalency of fields in this class. We develop a topological modification of the Zeldovich funicular model of the nondissipative cinematic dynamo, constructing a hyperbolic diffeomorphism with chaotic dynamics that is conservative in the neighborhood of its transitive invariant set.

Solar dynamo cycle variations with a rotational period

ABSTRACT Using non-linear mean-field dynamo models, we calculate magnetic cycle parameters, such as the dynamo cycle period, the amplitude of the total magnetic energy and the Poynting flux luminosity from the surface, for solar analogues with rotation periods in the range of 1–30 d. We perform simulations for both kinematic and non-kinematic dynamo models. The kinematic dynamo models, which take into account the non-linear α-effect and the loss of the magnetic flux due to magnetic buoyancy, show a decrease of the magnetic cycle with the decrease of the stellar rotation period. Stars with a rotational period of fewer than 10 d show non-stationary long-term variations of magnetic activity. The non-kinematic dynamo models take into account the magnetic field feedback on the large-scale flow and heat transport inside the convection zone. They show the non-monotonic variation of the dynamo period with the rotation rate. The models for rotational periods fewer than 10 d show non-stationary evolution with a slight increase in the primary dynamo period with the increase of the rotation rate. The non-kinematic models show the growth of the dynamo-generated magnetic flux with the increase of the rotation rate. There is a dynamo saturation for a star rotating with a period of 2 d or less. The saturation of the magnetic activity parameters is accompanied by a depression of the differential rotation.

A secular variation candidate model for IGRF-13 based on Swarm data and ensemble inverse geodynamo modelling

This paper describes the design of a candidate secular variation model for the 13th generation of the International Geomagnetic Reference Field. This candidate is based upon the integration of an ensemble of 100 numerical models of the geodynamo between epochs 2019.0 and 2025.0. The only difference between each ensemble member lies in the initial condition that is used for the numerical integration, all other control parameters being fixed. An initial condition is defined as follows: an estimate of the magnetic field and its rate-of-change at the core surface for 2019.0 is obtained from a year (2018.5–2019.5) of vector Swarm data. This estimate (common to all ensemble members) is subject to prior constraints: the statistical properties of the numerical dynamo model for the main geomagnetic field and its secular variation, and prescribed covariances for the other sources. One next considers 100 three-dimensional core states (in terms of flow, buoyancy and magnetic fields) extracted at different discrete times from a dynamo simulation that is not constrained by observations, with the time distance between each state exceeding the dynamo decorrelation time. Each state is adjusted (in three dimensions) in order to take the estimate of the geomagnetic field and its rate-of-change for 2019.0 into account. This methodology provides 100 different initial conditions for subsequent numerical integration of the dynamo model up to epoch 2025.0. Focussing on the 2020.0–2025.0 time window, we use the median average rate-of-change of each Gauss coefficient of the ensemble and its statistics to define the geomagnetic secular variation over that time frame and its uncertainties.

Non-monotonic growth and motion of the South Atlantic Anomaly

The South Atlantic Anomaly (SAA) is a region at Earth’s surface where the intensity of the magnetic field is particularly low. Accurate characterization of the SAA is important for both fundamental understanding of core dynamics and the geodynamo as well as societal issues such as the erosion of instruments at surface observatories and onboard spacecrafts. Here, we propose new measures to better characterize the SAA area and center, accounting for surface intensity changes outside the SAA region and shape anisotropy. Applying our characterization to a geomagnetic field model covering the historical era, we find that the SAA area and center are more time dependent, including episodes of steady area, eastward drift and rapid southward drift. We interpret these special events in terms of the secular variation of relevant large-scale geomagnetic flux patches on the core–mantle boundary. Our characterization may be used as a constraint on Earth-like numerical dynamo models.

The magnetic helicity density patterns from non-axisymmetric solar dynamo

We study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density patterns around the bipolar regions depend on the configuration of the ambient large-scale magnetic field, and in general they show a quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time–latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regions shows two bands of sign for the density distributions in each hemisphere. Similar helicity density patterns are provided by the helicity density flux from the emerging bipolar regions subjected to surface differential rotation.