Dynamo Simulations Research Articles

Probing the Morphology of Polarized Emission Induced by Fluctuation Dynamo Using Minkowski Functionals

The morphology and the characteristic scale of polarized structures provide crucial insights into the mechanisms that drive turbulence and maintain magnetic fields in magneto-ionic plasma. We aim to establish the efficacy of Minkowski functionals as quantitative statistical probes of filamentary morphology of polarized synchrotron emission resulting from fluctuation dynamo action. Using synthetic observations generated from magnetohydrodynamic simulations of fluctuation dynamos with varying driving scales (ℓ f) of turbulence in isothermal, incompressible, and subsonic media, we study the relation between different morphological measures and their connection to fractional polarization (p f). We find that Faraday depolarization at low frequencies gives rise to small-scale polarized structures that have higher filamentarity as compared to the intrinsic structures that are comparable to ℓ f. Above ∼3 GHz, the number of connected polarized structures per unit area (N CC,peak) is related to the mean p f (〈p f〉) of the emitting region as 〈pf〉∝NCC,peak−1/4 , provided the scale of the detectable emitting region is larger than ℓ f. This implies that N CC,peak represents the number of turbulent cells projected on the plane of the sky and can be directly used to infer ℓ f via the relation ℓf∝NCC,peak−1/2 . An estimate of ℓ f thus directly allows for pinning down the turbulence-driving mechanism in astrophysical systems. While the simulated conditions are mostly prevalent in the intracluster medium of galaxy clusters, the qualitative morphological features are also applicable in the context of interstellar medium in galaxies.

Weather at the core: Defining and categorizing geomagnetic excursions and reversals

Summary Paleomagnetic records provide us with information about the extreme geomagnetic events known as excursions and reversals, but the sparsity of available data limits detailed knowledge of the process and timing. To date there are no agreed on criteria for categorizing such events in terms of severity or longevity. In an analogy to categorizing storms in weather systems, we invoke the magnitude of the global (modified) paleosecular variation index $P_{i_D}$ to define the severity of the magnetic field state, ranging in level from 0 to 3, and defined by instantaneous values of $P_{i_D}$ with level 0 being normal ($P_{i_D}<0.5$) to extreme ($P_{i_D}\ge 15$). We denote the time of entry to an excursional (or reversal) event by when $P_{i_D}$ first exceeds 0.5, and evaluate its duration by the time at which $P_{i_D}$ first returns below its median value, termed the end of event threshold. We categorize each excursional event according to the peak level of $P_{i_D}$ during the entire event, with a range from Category-1 (Cat-1) to Cat-3. We explore an extended numerical dynamo simulation containing more than 1200 events and find that Cat-1 events are the most frequent (72%), but only rarely lead to actual field reversals where the axial dipole, $g_1^0$, has reversed sign at the end of the event. Cat-2 account for about 20% of events, with 34% of those leading to actual reversals, while Cat-3 events arise about 8% of the time but are more likely to produce reversals (43%). Higher category events take as much as 10 times longer than Cat-1 events. Two paleomagnetic field models separately cover the Laschamp excursion and Matuyama-Brunhes (M-B) reversal which are Cat-2 events with respective durations of 3.6 and 27.4 ky. It seems likely that Cat-2 may be an underestimate for M-B due to limitations in the paleomagnetic records. Our overall results suggest no distinction between excursions and reversals other than a reversal having the ending polarity state opposite to that at the start.

Solar internetwork magnetic fields: Statistical comparison between observations and MHD simulations

Context. Although the magnetic fields in the quiet Sun account for the majority of the magnetic energy in the solar photosphere, inferring their exact spatial distribution, origin, and evolution poses an important challenge because the signals lie at the limit of today’s instrumental precision. This severely hinders and biases our interpretations, which are mostly made through nonlinear model-fitting approaches. Aims. Our goal is to directly compare simulated and observed polarization signals in the Fe I 6301 Å and 6302 Å spectral lines in the very quiet Sun, the so-called solar internetwork (IN). This way, we aim to constrain the mechanism responsible for the generation of the quiet Sun magnetism while avoiding the biases that plague other diagnostic methods. Methods. We used three different three-dimensional radiative magneto-hydrodynamic simulations representing different scenarios of magnetic field generation in the internetwork: small-scale dynamo, decay of active regions, and horizontal flux emergence. We synthesized Stokes profiles at different viewing angles and degraded them according to the instrumental specifications of the spectro-polarimeter (SP) on board the Hinode satellite. Finally, we statistically compared the simulated spectra to the Hinode/SOT/SP observations at the appropriate viewing angles. Results. Of the three simulations, the small-scale dynamo best reproduced the statistical properties of the observed polarization signals. This is especially prominent for the disk center viewing geometry, where the agreement is excellent. Moving toward more inclined lines of sight, the agreement worsens slightly. Conclusions The agreement between the small-scale dynamo simulation and observations at the disk center suggests that small-scale dynamo action plays an important role in the generation of quiet Sun magnetism. However, the magnetic field around 50 km above the continuum layer in this simulation does not reproduce observations as well as at the very base of the photosphere.

Nonparametric Bayesian reconstruction of Galactic magnetic fields using information field theory

Context. Ultrahigh-energy cosmic rays (UHECRs) are charged particles with energies surpassing 1018 eV. Their sources remain elusive because they are obscured by deflections caused by the Galactic magnetic field (GMF). This challenge is further complicated by our limited understanding of the 3D structure of the GMF because current GMF observations primarily consist of quantities that are integrated along the line of sight (LOS). Nevertheless, data from upcoming stellar polarization surveys along with Gaia stellar parallax data are expected to yield local GMF measurements. Aims. This study is the second entry in our exploration of a Bayesian inference approach to the local GMF that uses synthetic local GMF observations that emulate forthcoming local GMF measurements, and attempts to use them to reconstruct its 3D structure. The ultimate aim is to trace back observed UHECRs and thereby update our knowledge about their possible origin. Methods. In this proof-of-concept work, we assumed as ground truth a magnetic field produced by a dynamo simulation of the Galactic ISM. We employed methods of Bayesian statistical inference in order to sample the posterior distribution of the GMF within part of the Galaxy. By assuming a known rigidity and arrival direction of an UHECR, we traced its trajectory back through various GMF configurations drawn from the posterior distribution. Our objective was to rigorously evaluate the performance of our algorithm in scenarios that closely mirror the setting of expected future applications. In pursuit of this, we conditioned the posterior to synthetically integrated LOS measurements of the GMF, in addition to synthetic local plane of sky-component measurements. Results. Our results demonstrate that for all locations of the observed arrival direction on the plane of sky, our algorithm is able to substantially update our knowledge on the original arrival direction of UHECRs with a rigidity of E/Z = 5 × 1019 eV, even without any LOS information. When the integrated data are included in the inference, the regions of the celestial sphere in which the maximum error occurs are greatly reduced. The maximum error is diminished by a factor of about 3 even in these regions in the specific setting we studied. Additionally, we are able to identify the regions in which the largest error is expected to occur.

Regionally-triggered geomagnetic reversals

Systematic studies of numerical dynamo simulations reveal that the transition from dipole-dominated non-reversing fields to models that exhibit reversals occurs when inertial effects become strong enough. However, the inertial force is expected to play a secondary role in the force balance in Earth’s outer core. Here we show that reversals in numerical dynamo models with heterogeneous outer boundary heat flux inferred from lower mantle seismic anomalies appear when the amplitude of heat flux heterogeneity is increased. The reversals are triggered at regions of large heat flux in which strong small-scale inertial forces are produced, while elsewhere inertial forces are substantially smaller. When the amplitude of heat flux heterogeneity is further increased so that in some regions sub-adiabatic conditions are reached, regional skin effects suppress small-scale magnetic fields and the tendency to reverse decreases. Our results reconcile the need for inertia for reversals with the theoretical expectation that the inertial force remains secondary in the force balance. Moreover, our results highlight a non-trivial non-monotonic behavior of the geodynamo in response to changes in the amplitude of the core-mantle boundary heat flux heterogeneity.

Iterative removal of sources to model the turbulent electromotive force

ABSTRACT We describe a novel method to compute the components of dynamo tensors from direct magnetohydrodynamic (MHD) simulations. Our method relies upon an extension and generalization of the standard Högbom CLEAN algorithm widely used in radio astronomy to systematically remove the impact of the strongest beams on to the corresponding image. This generalization, called the Iterative Removal of Sources (IROS) method, has been adopted here to model the turbulent electromotive force (EMF) in terms of the mean magnetic fields and currents. Analogous to the CLEAN algorithm, IROS treats the time series of the mean magnetic field and current as beams that convolve with the dynamo coefficients which are treated as (clean) images to produce the EMF time series (the dirty image). We apply this method to MHD simulations of galactic dynamos, to which we have previously employed other methods of computing dynamo coefficients such as the test-field method, the regression method, as well as local and non-local versions of the singular value decomposition (SVD) method. We show that our new method reliably recovers the dynamo coefficients from the MHD simulations. It also allows priors on the dynamo coefficients to be incorporated easily during the inversion, unlike in earlier methods. Moreover, using synthetic data, we demonstrate that it may serve as a viable post-processing tool in determining the dynamo coefficients, even when the power of additive noise to the EMF is twice as much the actual EMF.

How well does surface magnetism represent deep Sun-like star dynamo action?

Context. For Sun-like stars, the generation of toroidal magnetic field from poloidal magnetic field is an essential piece of the dynamo mechanism powering their magnetism. Previous authors have estimated the net toroidal flux generated in each hemisphere of the Sun by exploiting its conservative nature. This only requires observations of the photospheric magnetic field and surface differential rotation. Aims. We explore this approach using a 3D magnetohydrodynamic dynamo simulation of a cool star, for which the magnetic field and its generation are precisely known throughout the entire star. Methods. Changes to the net toroidal flux in each hemisphere were evaluated using a closed line integral bounding the cross-sectional area of each hemisphere, following the application of Stokes theorem to the induction equation; the individual line segments correspond to the stellar surface, base, equator, and rotation axis. We evaluated the influence of the large-scale flows, the fluctuating flows, and magnetic diffusion on each of the line segments, along with their depth-dependence. Results. In the simulation, changes to the net toroidal flux via the surface line segment typically dominate the total line integral surrounding each hemisphere, with smaller contributions from the equator and rotation axis. The surface line integral is governed primarily by the large-scale flows, and the diffusive current; the latter acting like a flux emergence term due to the use of an impenetrable upper boundary in the simulation. The bulk of the toroidal flux is generated deep inside the convection zone, with the surface observables capturing this due to the conservative nature of the net flux. Conclusions. Surface magnetism and rotation can be used to produce an estimate of the net toroidal flux generated in each hemisphere, allowing us to constrain the reservoir of magnetic flux for the next magnetic cycle. However, this methodology cannot identify the physical origin or the location of the toroidal flux generation. In addition, not all dynamo mechanisms depend on the net toroidal field produced in each hemisphere, meaning this method may not be able to characterise every magnetic cycle.

Exploring Spatial and Temporal Patterns in the Debrecen Solar Faculae Database: Part I

Photospheric faculae are markers of the solar magnetic field, appearing as bright regions along the edges of granules on the Sun’s surface. Using data from the Debrecen Solar Faculae Database, we investigated the spatiotemporal distribution of photospheric faculae between 2010 May 1 and 2014 December 31 and found the following. (i) At lower latitudes, there is an enhanced abundance of faculae appearing as stripes at given Carrington longitudes, which are interpreted as indicative of the presence of active longitudes. (ii) At higher latitudes, we identified so-called crisscross patterns of facular appearance. These patterns are likely the result of faculae in regions situated along the boundaries of supergranules. Last but not least, (iii) various periods of oscillatory phenomena were identified in this facular data set, including a longer periodic range consistent with the quasi-biennial oscillations and shorter ones with periods of 4–12 days. Our findings are supported by the visualization of a simple heuristic thought experiment and more complex dynamo simulations, strengthening the proposed interpretation of the three observed solar phenomena reported.

Rapid Changes in Strength and Direction of Earth's Magnetic Field Over the Past 100,000 Years

AbstractPrevious studies of rapid geomagnetic changes have highlighted the most extreme changes in direction and field strength found in paleomagnetic field models over the past 100 ky. Here we study distributions of rates of change in both time and space. Field models based on direct observations provide the most accurate values for rates of change, but their short duration precludes a complete description of field behavior. Broader representation is provided by time‐varying paleofield models, here including GGF100k, GGFSS70, LSMOD.2, CALS10k.2, HFM.OL1.A1, pfm9k.2, and SHAWQ‐iron age although variability across models and lack of temporal and spatial resolution of fine scale variations make direct comparisons difficult. For the paleofield we define rapid changes as exceeding the peak overall value of 0.4° yr−1 for directional changes and 150 nT yr−1 for intensities as established by the gufm1 model spanning 1590–1990 CE. We find that rapid directional changes are associated with low field strength and can spread across all latitudes during such episodes. Distributions of directional rates of change exhibit high skewness for models that include excursions. Rates of change in field intensity exceeding 150 nT yr−1 arise in brief intervals during the Holocene particularly associated with the strong field Levantine Iron Age Anomaly. Around the Laschamp excursion there are also rare localized occurrences of rapid intensity change. Limitations in current models make it difficult to define absolute rates for past changes, but we see that rapid changes are essential field characteristics not observed in the modern field that should nevertheless be regarded as an essential for Earth‐like dynamo simulations.

Magnetochronology of solar-type star dynamos

In this study, we analyse the magnetic field properties of a set of 15 global magnetohydrodynamic (MHD) simulations of solar-type star dynamos conducted using the ASH code. Our objective is to enhance our understanding of these properties by comparing theoretical results to current observations, and to finally provide fresh insights into the field. We analysed the rotational and magnetic properties as a function of various stellar parameters (mass, age, and rotation rate) in a ‘Sun in time’ approach in our extended set of 3D MHD simulations. To facilitate direct comparisons with stellar magnetism observations using various Zeeman-effect techniques, we decomposed the numerical data into vectorial spherical harmonics. A comparison of the trends we find in our simulations set reveals a promising overall agreement with the observational context of stellar magnetism, enabling us to suggest a plausible scenario for the magneto-rotational evolution of solar-type stars. In particular, we find that the magnetic field may reach a minimum amplitude at a transition value of the Rossby number near unity. This may have important consequences on the long-term evolution of solar-type stars, by impacting the relation between stellar age, rotation, and magnetism. This supports the need for future observational campaigns, especially for stars in the high Rossby number regime.

From convective stellar dynamo simulations to Zeeman-Doppler images

Context. Zeeman-Doppler imaging (ZDI) is used to reconstruct the surface magnetic field of late-type stars from high-resolution spectropolarimetric observations. The results are usually described in terms of characteristics of the field topology, such as poloidality versus toroidality and axisymmetry versus non-axisymmetry, in addition to the field strength. Aims. In this study, we want to test how well these characteristics are preserved when applying the ZDI method to simulated data. We are particularly interested in how accurately the field topology is preserved and to what extent stellar parameters, such as projected rotation velocity and rotation axis inclination, influence the reconstruction. Methods. For these tests, we used published magnetic field vector data from direct numerical magnetohydrodynamic simulations taken near the surface of the simulation domain. These simulations have variable rotation rates and therefore represent different levels of activity of an otherwise Sun-like setup with a convective envelope of solar thickness. Our ZDI reconstruction is based on spherical harmonics expansion. By comparing the original values to those of the reconstructed images, we study the ability to reconstruct the surface magnetic field in terms of various characteristics of the field. Results. In general, the ZDI method works as expected. The main large-scale features are reasonably well recovered, but the strength of the recovered magnetic field is just a fraction of the original input. The quality of the reconstruction shows clear correlations with the data quality. Furthermore, there are some spurious dependencies between stellar parameters and the characteristics of the field. Conclusions. Our study uncovers some limits of ZDI. Firstly, the recovered field strength will generally be lower than the ‘real’ value, as smaller structures with opposite polarities will be blurred in the inversion. This is also seen in the relative distribution of magnetic energy in terms of the angular degree ℓ. Secondly, the axisymmetry is overestimated. The poloidality versus toroidality is better recovered. The reconstruction works better for a stronger field and faster rotation velocity. Still, the ZDI method works surprisingly well even for a weaker field and slow rotation provided the data have a high signal-to-noise ratio and good rotation phase coverage.

On the role of numerical diffusivity in MHD simulations of global accretion disc dynamos

Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin and requires that the plasma ${\beta \sim 1}$ . Until now, most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at $\beta \gg 1$ . This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of $\beta \gg 1$ . We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as ${\mathcal {R}}_{m}^{2/3}$ . We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around six orders of magnitude less than the physical value found in dwarf nova discs of ${\mathcal {R}}_{m} \sim 10^{10}$ . We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the time being, a step too far.

Co-estimation of core and lithospheric magnetic fields by a maximum entropy method

SUMMARY Satellite observations of the geomagnetic field contain signals generated in Earth’s interior by electrical currents in the core and by magnetized rocks in the lithosphere. At short wavelengths the lithospheric signal dominates, obscuring the signal from the core. Here we present details of a method to co-estimate separate models for the core and lithospheric fields, which are allowed to overlap in spherical harmonic degree, that makes use of prior information to aid the separation. Using a maximum entropy method we estimate probabilistic models for the time-dependent core field and the static lithospheric field that satisfy constraints provided by satellite observations while being consistent with prior knowledge of the spatial covariance and expected magnitude of each field at its source surface. For the core field, we find that between spherical harmonic degree 13 and 22 power adds coherently to the established structures, and present a synthetic test that illustrates the aspects of the small scale core field that can reliably be retrieved. For the large scale lithospheric field we also find encouraging results, with the strongest signatures below spherical harmonic degree 13 occurring at locations of known prominent lithospheric field anomalies in the northern part of Eastern Europe, Australia and eastern North America. Although the amplitudes of the small scale core field and large scale lithospheric field are likely underestimated we find no evidence that obvious artefacts are introduced. Compared with conventional maps of the core–mantle boundary field our results suggest more localized normal flux concentrations close to the tangent cylinder, and that low latitude flux concentrations occur in pairs with opposite polarities. Future improvements in the recovery of the small scale core field and large scale lithospheric field will depend on whether more detailed prior information can be reliably extracted from core dynamo and lithospheric magnetization simulations.

Tayler–Spruit dynamo simulations for the modeling of radiative stellar layers

Context. Maxwell stresses exerted by dynamo-generated magnetic fields have been proposed as an efficient mechanism to transport angular momentum in radiative stellar layers. Numerical simulations are still needed to understand its trigger conditions and the saturation mechanisms. Aims. The present study follows up on a recent paper where we reported on the first simulations of Tayler-Spruit dynamos. Here we extend the parameter space explored to assess in particular the influence of stratification on the dynamo solutions. We also present numerical verification of theoretical assumptions made previously that were instrumental in deriving the classical prescription for angular momentum transport implemented in stellar evolution codes. Methods. A simplified radiative layer is modeled numerically by considering the dynamics of a stably stratified, differentially rotating, magnetized fluid in a spherical shell. Results. Our simulations display a diversity of magnetic field topologies and amplitudes depending on the flow parameters, including hemispherical solutions. The Tayler-Spruit dynamos reported here are found to satisfy magnetostrophic equilibrium and achieve efficient turbulent transport of angular momentum, following Spruit’s heuristic prediction.

Role of magnetic pressure forces in fluctuation dynamo saturation

ABSTRACT Using magnetohydrodynamic simulations of fluctuation dynamos in turbulent flows with rms Mach numbers $\mathcal {M}_{\rm rms}= 0.2, 1.1$, and 3, we show that magnetic pressure forces play a crucial role in dynamo saturation in supersonic flows. First, as expected when pressure forces oppose compression, an increase in anticorrelation between density and magnetic field strengths obtains even in subsonic flows with the anticorrelation arising from the intense but rarer magnetic structures. In supersonic flows, due to stronger compressive motions density and magnetic field strength continue to maintain a positive correlation. However, the degree of positive correlation decreases as the dynamo saturates. Secondly, we find that the unit vectors of ∇ρ and ∇B2 are preferentially antiparallel to each other in subsonic flows. This is indicative of magnetic pressure opposing compression. This antiparallel alignment persists in transonic and supersonic flows at dynamo saturation. However, compressive motions also lead to the emergence of a parallel alignment in these flows. Finally, we consider the work done against the components of the Lorentz force and the different sources of magnetic energy growth and dissipation. We show that while in subsonic flows, suppression of field line stretching is dominant in saturating the dynamo, the picture is different in supersonic flows. Both field line stretching and compression initially amplifies the field. However, growing magnetic pressure opposes further compression of magnetic flux which tends to reduce the compressive motions. Simultaneously, field line stretching also reduces. But, suppression of compressive amplification dominates the saturation of the dynamo.

Simulations of dynamo action in slowly rotating M dwarfs: Dependence on dimensionless parameters

Aims. The aim of this study is to explore the magnetic and flow properties of fully convective M dwarfs as a function of rotation period Prot and magnetic Reynolds ReM and Prandlt numbers PrM. Methods. We performed three-dimensional simulations of fully convective stars using a star-in-a-box set-up. This set-up allows global dynamo simulations in a sphere embedded in a Cartesian cube. The equations of non-ideal magnetohydrodynamics were solved with the PENCIL CODE. We used the stellar parameters of an M5 dwarf with 0.21 M⊙ at three rotation rates corresponding to rotation periods (Prot) of 43, 61, and 90 days, and varied the magnetic Prandtl number in the range from 0.1 to 10. Results. We found systematic differences in the behaviour of the large-scale magnetic field as functions of rotation and PrM. For the simulations with Prot = 43 days and PrM ≤ 2, we found cyclic large-scale magnetic fields. For PrM > 2, the cycles vanish and the field shows irregular reversals. In the simulations with Prot = 61 days for PrM ≤ 2, the cycles are less clear and the reversal are less periodic. In the higher PrM cases, the axisymmetric mean field shows irregular variations. For the slowest rotation case with Prot = 90 days, the field has an important dipolar component for PrM ≤ 5. For the highest PrM the large-scale magnetic field is predominantly irregular at mid-latitudes, with quasi-stationary fields near the poles. For the simulations with cycles, the cycle period length slightly increases with increasing ReM.

Exploring the reliability of polar field rise rate as a precursor for an early prediction of solar cycle

ABSTRACT The prediction of the strength of an upcoming solar cycle has been a long-standing challenge in the field of solar physics. The inherent stochastic nature of the underlying solar dynamo makes the strength of the solar cycle vary in a wide range. Till now, the polar precursor methods and the dynamo simulations that use the strength of the polar field at the cycle minimum to predict the strength of the following cycle have gained reasonable consensus by providing convergence in the predictions for Solar Cycles 24 and 25. Recently, it has been shown that just by using the observed correlation of the polar field rise rate with the peak of the polar field at the cycle minimum and the amplitude of the following cycle, a reliable prediction can be made much earlier than the cycle minimum. In this work, we perform surface flux transport (SFT) simulations to explore the robustness of this correlation against the stochastic fluctuations of bipolar magnetic region (BMR) tilt properties including anti-Joy and anti-Hale type anomalous BMRs, and against the variation of meridional flow speed. We find that the observed correlation is a robust feature of the solar cycles and thus it can be utilized for a reliable prediction of the solar cycle much earlier than the cycle minimum – the usual landmark of the solar cycle prediction.

Effects of the centrifugal force in stellar dynamo simulations

Context.The centrifugal force is often omitted from simulations of stellar convection either for numerical reasons or because it is assumed to be weak compared to the gravitational force. However, the centrifugal force might be an important factor in rapidly rotating stars, such as solar analogs, due to its Ω2scaling, where Ω is the rotation rate of the star.Aims.We study the effects of the centrifugal force in a set of 21 semi-global stellar dynamo simulations with varying rotation rates. Included in the set are three control runs aimed at distinguishing the effects of the centrifugal force from the nonlinear evolution of the solutions.Methods.We solved the 3D magnetohydrodynamic equations with the PENCILCODEin a solar-like convective zone in a spherical wedge setup with a 2πazimuthal extent. The rotation rate and the amplitude of the centrifugal force were varied. We decomposed the magnetic field into spherical harmonics and studied the migration of azimuthal dynamo waves (ADWs), the energy of different large-scale magnetic modes, and differential rotation.Results.In the regime with the lowest rotation rates, Ω = 5 − 10 Ω⊙, where Ω⊙is the rotation rate of the Sun, we see no marked changes in either the differential rotation or the magnetic field properties. For intermediate rotation, Ω = 20 − 25 Ω⊙, we identify an increase in the differential rotation as a function of centrifugal force. The axisymmetric magnetic energy tends to decrease with centrifugal force, while the non-axisymmetric one increases. The ADWs are also affected, especially in the propagation direction. In the most rapidly rotating set with Ω = 30 Ω⊙, these changes are more pronounced, and in one case the propagation direction of the ADW changes from prograde to retrograde. The control runs suggest that the results are a consequence of the centrifugal force and not due to the details of the initial conditions or the history of the run.Conclusions.We find that the differential rotation and properties of the ADWs only change as a function of the centrifugal force when rotation is rapid enough.

Wave-like motions and torques in Earth's core as inferred from geomagnetic data: A synthetic study

Here, we present a synthetic validation for the inversion of transient fluid motions at the surface of Earth's core. It is based on a numerical simulation of the geodynamo in which the main time-scales (based on rotation, magnetic field and velocity) are sufficiently separated to give rise to a variety of hydro-magnetic waves. We focus the study on wave-like motions with periods commensurate to the Alfvén time, which is based on the strength of the magnetic field in the core interior. Synthetic magnetic data are generated over 90 Alfvén times, representative of the era covered by observatory and satellite measurements. These synthetic data are inverted to estimate a magnetic field model. Thereafter, we apply the pygeodyn data assimilation tool to recover core surface flows. We investigate the quality of their reconstruction as a function of their time scale. The success of the reconstruction depends on the data accuracy and coverage and on the magnitude of the flow. We also retrieve axi-symmetric torsional Alfvén waves, despite their relatively weak magnitude.We use the synthetic data to investigate the exchanges of angular momentum between core and mantle that induce length-of-day (LOD) changes. These exchanges result from the electromagnetic torque between the fluid core and the mantle and the gravitational torque between the inner core and the mantle. The inverted flows convincingly predict LOD variations in the dynamo calculation. We find that core surface zonal motions match well with the geostrophic (axially invariant) motions at the origin of the LOD changes, on all considered time-scales. We also investigate the different contributions to the electro-magnetic torque. In the dynamo simulation, only a small part can be attributed to the leakage torque caused by electrical currents flowing from the core to the mantle. The relative contribution from the poloidal field induced in the mantle, which amounts to about 1/3 of the total torque, is significantly larger than estimated in previous studies, based on geomagnetic observations. The remaining torque, which is associated with the toroidal induced field, mostly stems from the solid body rotation interacting with the radial magnetic field up to spherical harmonic degree 30.

The role of magnetic waves in tangent cylinder convection

The secular variation of the geomagnetic field suggests that there are anticyclonic polar vortices in the Earth's core. Under the influence of a magnetic field, the polar azimuthal flow is thought to be produced by one or more coherent upwellings within the tangent cylinder, offset from the rotation axis. In this study, convection within the tangent cylinder in rapidly rotating dynamos is investigated through the analysis of forced magnetic waves. The first part of the study investigates the evolution of an isolated buoyancy disturbance in an unstably stratified rotating fluid subjected to an axial magnetic field. It is shown that the axial flow intensity of the slow Magnetic-Archimedean-Coriolis (MAC) waves becomes comparable to that of the fast MAC waves when |ωM/ωC|∼0.1, where ωM and ωC are the Alfvén wave and inertial wave frequencies respectively. In spherical shell dynamo simulations, the isolated upwellings within the tangent cylinder are shown to originate from the localized excitation of slow MAC waves in the dipole-dominated regime. Axial flow measurements in turn reveal the approximate parity between the slow and fast wave intensities in this regime, which corresponds to the existence of strong polar vortices in the Earth's core. To obtain the observed peak azimuthal motions of 0.6–0.9∘yr−1, the Rayleigh number in the low-inertia geodynamo must be ∼103 times the Rayleigh number for the onset of nonmagnetic convection. However, if the forcing is so strong as to cause polarity reversals, the field within the tangent cylinder decays away, and the convection takes the form of an ensemble of plumes supported entirely by the fast waves of frequency ω∼ωC. The resulting weak polar circulation is comparable to that obtained in nonmagnetic convection.