Field Dynamo Research Articles

Modeling reversals of galactic magnetic fields at large distances from centers of milky-way-like galaxies using computations on GPUs

Nowadays it is strongly believed that in a large number of spiral galaxies there are regular magnetic fields. Their existence is proved by measurements of the Faraday rotation of polarization plane of electromagnetic waves which are received on modern radio telescopes. The theoretical description of magnetic fields generation is connected with the mean field dynamo mechanism. It is based on joint action of the ?-effect and differential rotation. At the first stage of evolution, magnetic fields enlarge exponentially with the growth rate described by the largest eigenvalue of the corresponding differential operator. If the field becomes comparable with the equipartition value, the nonlinear terms become more important, and they are connected with saturation of the field growth. The non-linear system of equations has several stationary points, and some of them are stable. According to the contrast structures theory for a quite small turbulent viscosity and some initial conditions, in different regions there will be magnetic fields of opposite directions, and they will be divided by narrow transition layers. Such features, for example, characterize the magnetic field of the Milky Way. Most of the existing works describe reversals for quite moderate distances from the galaxy center. However, it was shown previously that the magnetic field can principally be generated also in outer parts of galaxies, which are situated at distances of more than 10 kpc from the rotation axis. It is interesting to describe the appearance of reversals in such parts of galaxies. In this work we have studied the dynamo action in outer parts of the Milky-Way-like galaxies. It is shown that it is possible to generate opposite magnetic fields there. We have used random initial conditions to obtain spatial reversals. Because of a large volume of computations, they were carried out by using graphics processing units (GPUs).

Quasi-geostrophic convection-driven dynamos in a thick spherical shell

SUMMARYWe present dynamos computed using a hybrid QG-3D numerical scheme in a thick spherical shell geometry. Our model is based on a quasi-geostrophic convection code extended with a 3-D treatment of heat transport and magnetic induction. We find a collection of self-sustained, multipolar, weak field dynamos with magnetic energy one or two orders of magnitude lower than the kinetic energy. The poloidal magnetic energy is weak and, by construction, there is a lack of equatorially antisymmetric components in the Buoyancy and Lorentz forces. This leads to configurations where the velocity field is only weakly impacted by the magnetic field, similar to dynamos found in 3-D simulations where zonal flows and the Ω-effect dominate. The time-dependence of these dynamos is characterized by quasi-periodic oscillations that we attribute to dynamo waves. The QG-3D dynamos found so far are not Earth-like. The inability of our setup to produce strong, dipole-dominated, magnetic fields likely points to a missing ingredient in our QG flows, and a related lack of helicity and α-effect. The models presented here may be more relevant for studying stellar dynamos where zonal flows are known to dominate. This study was carried out at modest control parameters, however moving to lower Ekman numbers, when smaller values of both the magnetic and hydrodynamic Prandtl numbers can be of interest, our approach will be able to gain in efficiency by using relatively coarse grids for the 3-D magnetic and temperature fields and a finer grid for the QG velocity field.

Impact of a mean field dynamo on neutron star mergers leading to magnetar remnants

Impact of a mean field dynamo on neutron star mergers leading to magnetar remnants

Unified treatment of mean-field dynamo and angular-momentum transport in magnetorotational instability-driven turbulence.

Magnetorotational instability-driven (MRI-driven) turbulence and dynamo phenomena are analyzed using direct statistical simulations. Our approach begins by developing a unified mean-field model that combines the traditionally decoupled problems of the large-scale dynamo and angular momentum transport in accretion disks. The model consists of a hierarchical set of equations, capturing up to the second-order correlators, while a statistical closure approximation is employed to model the three-point correlators. We highlight the web of interactions that connect different components of stress tensors-Maxwell, Reynolds, and Faraday-through shear, rotation, correlators associated with mean fields, and nonlinear terms. We determine the dominant interactions crucial for the development and sustenance of MRI turbulence. Our general mean-field model for the MRI-driven system allows for a self-consistent construction of the electromotive force, inclusive of inhomogeneities and anisotropies. Within the realm of large-scale magnetic field dynamo, we identify two key mechanisms-the rotation-shear-current effect and the rotation-shear-vorticity effect-that are responsible for generating the radial and vertical magnetic fields, respectively. We provide the explicit (nonperturbative) form of the transport coefficients associated with each of these dynamo effects. Notably, both of these mechanisms rely on the intrinsic presence of large-scale vorticity dynamo within MRI turbulence.

Astrophysical chiral dynamos and strain-torsioned Weyl materials

Our goal in this paper is two-fold: First we show that in the absence of four-fermion interactions, from Einstein–Cartan–Maxwell (ECM) anisotropy cosmology, one may derive instabilities in chiral dynamo equations from magnetic perturbations. They are obtained from a model, where the spinning-fluid does not couple directly to the Einstein–Maxwell model. Instead spin fluid enter into the evolution equation of density perturbations. Chiral dynamo equation is obtained from magnetic perturbations in the particular case where the perturbations in the chiral magnetized plasma can be neglected in second order of perturbations. The vanishing of the Nieh–Yan (NY) topological density in this Bianchi type-I model is also investigated. In the second example, use of the magnetic and torsion perturbations are given by the technique of encoding the magnetic perturbations in the metric constrained by teleparallelism. We consider non-uniform chiral chemical potential in the chiral flipping equation in order to obtain the magnetic field dynamo amplification. Dynamo effects are obtained from current perturbations expressed in terms of chiral chemical potential when number density of left-handed chiral particles is approximately zero. The damping found in magnetic field by the end of inflation, may help to explain why so weak galactic dynamo seeds are found at present universe. Furthermore, damping depends upon the strain–torsion relation of the Weyl topological materials. Though in general, torsion does not couple to electromagnetic fields, it influences the magnetic field through strain–torsion pseudo-magnetic potential.

General Relativistic Magnetohydrodynamics Mean-Field Dynamos

Large-scale, ordered magnetic fields in several astrophysical sources are supposed to be originated, and maintained against dissipation, by the combined amplifying action of rotation and small-scale turbulence. For instance, in the solar interior, the so-called α−Ω mean-field dynamo is known to be responsible for the observed 22-years magnetic cycle. Similar mechanisms could operate in more extreme environments, like proto neutron stars and accretion disks around black holes, for which the physical modelling needs to be translated from the regime of magnetohydrodynamics (MHD) and Newtonian gravity to that of a plasma in a general relativistic curved spacetime (GRMHD). Here we review the theory behind the mean field dynamo in GRMHD, the strategies for the implementation of the relevant equations in numerical conservative schemes, and we show the most important applications to the mentioned astrophysical compact objects obtained by our group in Florence. We also present novel results, such as three-dimensional GRMHD simulations of accretion disks with dynamo and the application of our dynamo model to a super massive neutron star, remnant of a binary neutron star merger as obtained from full numerical relativity simulations.

Gravitational wave signature of proto-neutron star convection: I. MHD numerical simulations

ABSTRACT Gravitational waves provide a unique and powerful opportunity to constrain the dynamics in the interior of proto-neutron stars during core collapse supernovae. Convective motions play an important role in generating neutron stars magnetic fields, which could explain magnetar formation in the presence of fast rotation. We compute the gravitational wave emission from proto-neutron star convection and its associated dynamo, by post-processing three-dimensional MHD simulations of a model restricted to the convective zone in the anelastic approximation. We consider two different proto-neutron star structures representative of early times (with a convective layer) and late times (when the star is almost entirely convective). In the slow rotation regime, the gravitational wave emission follows a broad spectrum peaking at about three times the turnover frequency. In this regime, the inclusion of magnetic fields slightly decreases the amplitude without changing the spectrum significantly compared to a non-magnetized simulation. Fast rotation changes both the amplitude and spectrum dramatically. The amplitude is increased by a factor of up to a few thousands. The spectrum is characterized by several peaks associated with inertial modes, whose frequency scales with the rotation frequency. Using simple physical arguments, we derive scalings that reproduce quantitatively several aspects of these numerical results. We also observe an excess of low-frequency gravitational waves, which appears at the transition to a strong field dynamo characterized by a strong axisymmetric toroidal magnetic field. This signature of dynamo action could be used to constrain the dynamo efficiency in a proto-neutron star with future gravitational wave detections.

Mean field dynamo action in shearing flows – II. Fluctuating kinetic helicity with zero mean

ABSTRACT Here we explore the role of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in the presence of a background linear shear flow. Key techniques involved here are same as in our earlier work, where we have used the renovating flow based model with shearing waves. Both the velocity and the helicity fields are treated as stochastic variables with finite correlation times, τ and τh, respectively. Growing solutions are obtained when τh > τ, even when this time-scale separation, characterized by m = τh/τ, remains below the threshold for causing the turbulent diffusion to turn negative. In regimes when turbulent diffusion remains positive, and τ is of the order of eddy turnover time T, the axisymmetric modes display non-monotonic behaviour with shear rate S: both, the growth rate γ and the wavenumber k* corresponding to the fastest growing mode, first increase, reach a maximum and then decrease with |S|, with k* being always smaller than eddy-wavenumber, thus boosting growth of magnetic fields at large length-scales. The cycle period Pcyc of growing dynamo wave is inversely proportional to |S| at small shear, exactly similar to the fixed kinetic helicity case of our earlier work. This dependence becomes shallower at larger shear. Interestingly enough, various curves corresponding to different choices of m collapse on top of each other in a plot of mPcyc with |S|.

The Occurrence Feature of Plasma Bubbles in the Equatorial to Midlatitude Ionosphere During Geomagnetic Storms Using Long‐Term GNSS‐TEC Data

AbstractWe performed a superposed epoch analysis of solar wind, interplanetary magnetic field, geomagnetic index, and the rate of total electron content (TEC) index (ROTI) derived from global navigation satellite system‐TEC data during 652 geomagnetic storm events (minimum SYM‐H < −40 nT), to clarify the occurrence features and causes of storm‐time plasma bubbles in the equatorial to mid‐latitude ionosphere. In this analysis, we defined the time of the SYM‐H minimum as the zero epoch. As a result, the ROTI enhancement started at the duskside magnetic equator and expanded to higher latitudes during the main phase. Approximately 1 h after the onset of the recovery phase, the ROTI values at the magnetic equator in the dusk‐to‐midnight sectors decreased while those in the dawn sector increased. This situation persisted for at least 12 h. The ratio of the ROTI during the main phase to that during the quiet period in the dusk sector is the largest in May–July. The ratio of the ROTI during the recovery phase decreased during dusk with increasing solar activity. Considering the requirement of the Rayleigh‐Taylor instability, the difference in the magnetic local time of the ROTI signature, between the main and recovery phases, can be explained by a local time distribution of storm‐time electric fields associated with a prompt penetration electric field and disturbance dynamo. This implies that the occurrence feature of the plasma bubble is different from that during quiet times when the input of solar wind energy to the magnetosphere and ionosphere increases significantly.

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

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

Mean field dynamo action in shear flows. I: fixed kinetic helicity

ABSTRACT We study mean field dynamo action in a background linear shear flow by employing pulsed renewing flows with fixed kinetic helicity and non-zero correlation time (τ). We use plane shearing waves in terms of time-dependent exact solutions to the Navier–Stokes equation as derived by Singh & Sridhar (2017). This allows us to self-consistently include the anisotropic effects of shear on the stochastic flow. We determine the average response tensor governing the evolution of mean magnetic field, and study the properties of its eigenvalues that yield the growth rate (γ) and the cycle period (Pcyc) of the mean magnetic field. Both, γ and the wavenumber corresponding to the fastest growing axisymmetric mode vary non-monotonically with shear rate S when τ is comparable to the eddy turnover time T, in which case, we also find quenching of dynamo when shear becomes too strong. When $\tau /T\sim {\cal O}(1)$, the cycle period (Pcyc) of growing dynamo wave scales with shear as Pcyc ∝ |S|−1 at small shear, and it becomes nearly independent of shear as shear becomes too strong. This asymptotic behaviour at weak and strong shear has implications for magnetic activity cycles of stars in recent observations. Our study thus essentially generalizes the standard αΩ (or α2Ω) dynamo as also the α effect is affected by shear and the modelled random flow has a finite memory.

Large-scale poloidal magnetic field dynamo leads to powerful jets in GRMHD simulations of black hole accretion with toroidal field

ABSTRACT Accreting black holes (BHs) launch relativistic collimated jets, across many decades in luminosity and mass, suggesting the jet launching mechanism is universal, robust, and scale-free. Theoretical models and general relativistic magnetohydrodynamic (GRMHD) simulations indicate that the key jet-making ingredient is large-scale poloidal magnetic flux. However, its origin is uncertain, and it is unknown if it can be generated in situ or dragged inward from the ambient medium. Here, we use the GPU-accelerated GRMHD code h-amr to study global 3D BH accretion at unusually high resolutions more typical of local shearing box simulations. We demonstrate that turbulence in a radially extended accretion disc can generate large-scale poloidal magnetic flux in situ, even when starting from a purely toroidal magnetic field. The flux accumulates around the BH till it becomes dynamically important, leads to a magnetically arrested disc (MAD), and launches relativistic jets that are more powerful than the accretion flow. The jet power exceeds that of previous GRMHD toroidal field simulations by a factor of 10 000. The jets do not show significant kink or pinch instabilities, accelerate to γ ∼ 10 over three decades in distance, and follow a collimation profile similar to the observed M87 jet.

Generation of strong magnetic fields in a nascent neutron star accounting for the chiral magnetic effect

We propose the mean field dynamo model for the generation of strongest magnetic fields, $B\sim 10^{15}\,{\rm G}$, in a neutron star (NS) accounting for the chiral magnetic effect (CME) driven by the shock in a supernova (SN) progenitor of that NS. The temperature jump at a narrow shock front, where an initial magnetic field existing in inflowing matter rises sharply, is the source of the CME that prevails significantly the erasure of the CME due to the spin-flip through Coulomb collisions in plasma. The growth of the magnetic field just behind the shock given by the instability term $\nabla\times (\alpha {\bf B})$ in induction equation, stops after a successful SN explosion that throws out the mantle of a protoneutron star. As a result, such an explosion interrupts the transfer of strongly magnetized plasma from the shock onto NS surface and leads to the saturation of the magnetic field. Assuming the rigid protostar rotation, we employ the mean field dynamo, which is similar to the $\alpha^2$-dynamo known in the standard magnetohydrodynamics (MHD). The novelty of our model is that $\alpha^2$-dynamo is based on concepts of particle physics, applied in MHD, rather than by a mirror asymmetry of convective vortices in the rotating convection.

Magnetar formation through a convective dynamo in protoneutron stars.

The release of spin-down energy by a magnetar is a promising scenario to power several classes of extreme explosive transients. However, it lacks a firm basis because magnetar formation still represents a theoretical challenge. Using the first three-dimensional simulations of a convective dynamo based on a protoneutron star interior model, we demonstrate that the required dipolar magnetic field can be consistently generated for sufficiently fast rotation rates. The dynamo instability saturates in the magnetostrophic regime with the magnetic energy exceeding the kinetic energy by a factor of up to 10. Our results are compatible with the observational constraints on galactic magnetar field strength and provide strong theoretical support for millisecond protomagnetar models of gamma-ray burst and superluminous supernova central engines.

Gravitoturbulent dynamos in astrophysical discs

The origin of large-scale and coherent magnetic fields in astrophysical discs is an important and long standing problem. Researchers commonly appeal to a turbulent dynamo, sustained by the magneto-rotational instability (MRI), to supply the large-scale field. But research over the last decade in particular has demonstrated that various non-ideal MHD effects can impede or extinguish the MRI, especially in protoplanetary disks. In this paper we propose a new scenario, by which the magnetic field is generated and sustained via the gravitational instability (GI). We use 3D stratified shearing box simulations to characterise the dynamo and find that it works at low magnetic Reynolds number (from unity to ~100) for a wide range of cooling times and boundary conditions. The process is kinematic, with a relatively fast growth rate ($< 0.1 \Omega$), and it shares some properties of mean field dynamos. The magnetic field is generated via the combination of differential rotation and spiral density waves, the latter providing compressible horizontal motions and large-scale vertical rolls. At greater magnetic Reynolds numbers the build up of large-scale field is diminished and instead small-scale structures emerge from the breakdown of twisted flux ropes. We propose that GI may be key to the dynamo engine not only in young protoplanetary discs but also in some AGN and galaxies.

Solar radius and luminosity variations induced by the internal dynamo magnetic fields

Although the occurrence of solar irradiance variations induced by magnetic surface features (e.g., sunspots, faculae, magnetic network) is generally accepted, the existence of intrinsic luminosity changes due to the internal magnetic fields is still controversial. This additional contribution is expected to be accompanied by radius variations, and to be potentially significant for the climate of the Earth. We aim to constrain theoretically the radius and luminosity variations of the Sun that are due to the effect of the variable magnetic fields in its interior associated with the dynamo cycle. We have extended a one-dimensional stellar evolution code to include several effects of the magnetic fields on the interior structure. We investigate different magnetic configurations, based on both observational constraints and on the output of state-of-the-art mean field dynamo models. We explore both step-like and simply periodic time dependences of the magnetic field peak strength. We find that the luminosity and radius variations are in anti-phase and in phase, respectively, with the magnetic field strength. For peak magnetic field strengths of the order of tens of kilogauss, luminosity variations ranging between 10^{-6} and 10^{-3} (in modulus) and radius variations between 10^{-6} and 10^{-5} are obtained. Modest but significant radius variations (up to 10^{-5} in relative terms) are obtained for magnetic fields of realistic strength and geometry, providing a potentially observable signature of the intrinsic variations. Establishing their existence in addition to the accepted surface effects would have very important implications for the understanding of solar-induced long-term trends on climate.

Minimal perturbation flows that trigger mean field dynamos in shear flows

Using a variational optimization method we find the smallest flow perturbations that can trigger kinematic dynamo action in Kolmogorov flow. In comparison to previous work, a second-order mean field dynamo model is used to track down the optimal dynamos in the high magnetic Reynolds number limit ($Rm$). The magnitude of minimal perturbation flows decays inversely proportional to the magnetic Reynolds number. We reveal the asymptotic high-$Rm$ structure of the optimal flow perturbation and the magnetic eigenmode. We identify the optimal dynamo as of $\unicode[STIX]{x1D6FC}{-}\unicode[STIX]{x1D6FA}$ type, with magnetic fluctuations that localize on a critical layer.

Variational Estimation of the Large-scale Time-dependent Meridional Circulation in the Sun: Proofs of Concept with a Solar Mean Field Dynamo Model

Abstract We present in this work the development of a solar data assimilation method based on an axisymmetric mean field dynamo model and magnetic surface data. Our midterm goal is to predict quasi-cyclic solar activity. Here we focus on the ability of our algorithm to constrain the deep meridional circulation of the Sun based on solar magnetic observations. To that end, we develop a variational data assimilation technique. Within a given assimilation window, the assimilation procedure minimizes the differences between the data and the forecast from the model by finding an optimal meridional circulation in the convection zone and an optimal initial magnetic field via a quasi-Newton algorithm. We demonstrate the capability of the technique to estimate the meridional flow through a closed-loop experiment involving 40 years of synthetic, solar-like data. By assimilating the synthetic magnetic proxies, we are able to reconstruct a (stochastic) time-varying meridional circulation that is also slightly equatorially asymmetric. We show that the method is robust in estimating a flow whose level of fluctuation can reach 30% about the average, and that the horizon of predictive capability of the method is of the order of one cycle length.

Magnetic field dynamos and magnetically triggered flow instabilities

The project A2 of the LIMTECH Alliance aimed at a better understanding of those magnetohydrodynamic instabilities that are relevant for the generation and the action of cosmic magnetic fields. These comprise the hydromagnetic dynamo effect and various magnetically triggered flow instabilities, such as the magnetorotational instability and the Tayler instability. The project was intended to support the experimental capabilities to become available in the framework of the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN). An associated starting grant was focused on the dimensioning of a liquid metal experiment on the newly found magnetic destabilization of rotating flows with positive shear. In this survey paper, the main results of these two projects are summarized.

Magnetic spiral arms in galaxy haloes

We seek the conditions for a {\it steady} mean field galactic dynamo. The parameter set is reduced to those appearing in the $\alpha^2$ and $\alpha/\omega$ dynamo, namely velocity amplitudes, and the ratio of sub-scale helicity to diffusivity. The parameters can be allowed to vary on conical spirals. We analyze the mean field dynamo equations in terms of scale invariant logarithmic spiral modes and special exact solutions. Compatible scale invariant gravitational spiral arms are introduced and illustrated in an appendix, but the detailed dynamical interaction with the magnetic field is left for another work. As a result of planar magnetic spirals `lifting' into the halo, multiple sign changes in average rotation measures forming a regular pattern on each side of the galactic minor axis, are predicted. Such changes have recently been detected in the CHANG-ES survey.