Small-scale Dynamo Research Articles

From Primordial Seed Magnetic Fields to the Galactic Dynamo

The origin and maintenance of coherent magnetic fields in the Universe is reviewed with an emphasis on the possible challenges that arise in their theoretical understanding. We begin with the interesting possibility that magnetic fields originated at some level from the early universe. This could be during inflation, the electroweak, or the quark-hadron phase transitions. These mechanisms can give rise to fields which could be strong, but often with much smaller coherence scales than galactic scales. Their subsequent turbulent decay decreases their strength but increases their coherence. We then turn to astrophysical batteries which can generate seed magnetic fields. Here the coherence scale can be large, but the field strength is generally very small. These seed fields need to be further amplified and maintained by a dynamo to explain observed magnetic fields in galaxies. Basic ideas behind both small and large-scale turbulent dynamos are outlined. The small-scale dynamo may help to understand the first magnetization of young galaxies, while the large-scale dynamo is important for the generation of fields with scales larger than the stirring scale, as observed in nearby disk galaxies. The current theoretical challenges that turbulent dynamos encounter and their possible resolution are discussed.

Dynamical evolution of magnetic fields in the intracluster medium

We investigate the evolution of magnetic fields in galaxy clusters starting from constant primordial fields using highly resolved ($\approx \rm 4 ~kpc$) cosmological MHD simulations. The magnetic fields in our sample exhibit amplification via a small-scale dynamo and compression during structure formation. In particular, we study how the spectral properties of magnetic fields are affected by mergers, and we relate the measured magnetic energy spectra to the dynamical evolution of the intracluster medium. The magnetic energy grows by a factor of $\sim$ 40-50 in a time-span of $\sim 9$ Gyr and equipartition between kinetic and magnetic energy occurs on a range of scales ($< 160 \rm ~kpc$ at all epochs) depending on the turbulence state of the system. We also find that, in general, the outer scale of the magnetic field and the MHD scale are not simply correlated in time. The effect of major mergers is to shift the peak magnetic spectra to it smaller scales, whereas the magnetic amplification only starts after $\lesssim$ 1 Gyr. In contrast, continuous minor mergers promote the steady growth of the magnetic field. We discuss the implications of these findings in the interpretation of future radio observations of galaxy clusters.

Turbulent Dynamo in a Weakly Ionized Medium

Abstract The small-scale turbulent dynamo is an important process contributing to the cosmic magnetization. In partially ionized astrophysical plasmas, the dynamo growth of magnetic energy strongly depends on the coupling state between ions and neutrals and the ion-neutral collisional damping effect. A new damping stage of turbulent dynamo in a weakly ionized medium was theoretically predicted by Xu &amp; Lazarian. By carrying out a 3D two-fluid dynamo simulation, we have for the first time numerically confirmed the physical conditions and the linear-in-time growth of the magnetic field strength of the damping stage of a dynamo. The dynamo-amplified magnetic field has a characteristic length as the damping scale, which increases with time and can reach the injection scale of turbulence after around eight turnover times of the largest eddy, given sufficiently low ionization fraction and a weak initial magnetic field. Due to the weak coupling between ions and neutrals, most turbulent energy carried by neutrals cannot be converted to magnetic energy, resulting in a relatively weak magnetic field at the end of the dynamo. This result has important implications for the growth of magnetic fields in the partially ionized interstellar medium and shock acceleration of Galactic cosmic rays.

The small-scale dynamo in a spectral representation

ABSTRACTIn this paper, we study the correlation functions for magnetic energy and magnetic helicity generated by a small-scale dynamo mechanism in a mirror-asymmetric and isotropic turbulent conductive fluid. Solving the Kazantsev system for small-scale generation by an iterative approach, we restore the correlation functions in spatial and spectral representations. Studying scales of localisation and their dependence on magnetic Reynolds number, we propose approximate functions, which can be applied for energy and helicity in a spectral space. We show the absence of 3/2-spectrum for Kazantsev assumptions at and helicity sign changing at . Using our results and estimating the relation between helicity and energy at different scales, we speculate about what can be considered as a small scale in a spectral space, and how this scale can be connected with mean-field processes.

A priori study of the subgrid energy transfers for small-scale dynamo in kinematic and saturation regimes

The statistical properties of the subgrid energy transfers of homogeneous small-scale dynamo are investigated during the kinematic, nonlinear, and statistically saturated stages. We carry out an a priori analysis of data obtained from an ensemble of direct numerical simulations on 5123 grid points and at unity magnetic Prandtl number. In order to provide guidance for subgrid-scale (SGS) modelling of different types of energy transfer that occur in magnetohydrodynamic dynamos, we consider the SGS stress tensors originating from inertial dynamics, Lorentz force, and the magnetic induction separately. We find that all SGS energy transfers display some degree of intermittency as quantified by the scale-dependence of their respective probability density functions. Concerning the inertial dynamics, a depletion of intermittency occurs in the presence of a saturated dynamo.

Towards Exascale Simulations of the ICM Dynamo with WENO-Wombat

In galaxy clusters, modern radio interferometers observe non-thermal radio sources with unprecedented spatial and spectral resolution. For the first time, the new data allows to infer the structure of the intra-cluster magnetic fields on small scales via Faraday tomography. This leap forward demands new numerical models for the amplification of magnetic fields in cosmic structure formation—the cosmological magnetic dynamo. Here we present a novel numerical approach to astrophyiscal MHD simulations aimed to resolve this small-scale dynamo in future cosmological simulations. As a first step, we implement a fifth order WENO scheme in the new code WOMBAT. We show that this scheme doubles the effective resolution of the simulation and is thus less expensive than common second order schemes. WOMBAT uses a novel approach to parallelization and load balancing developed in collaboration with performance engineers at Cray Inc. This will allow us scale simulation to the exaflop regime and achieve kpc resolution in future cosmological simulations of galaxy clusters. Here we demonstrate the excellent scaling properties of the code and argue that resolved simulations of the cosmological small scale dynamo within the whole virial radius are possible in the next years.

Convection-driven kinematic dynamos with a self-consistent shear flow

ABSTRACTIt is widely accepted that astrophysical magnetic fields are generated by dynamo action. In many cases, these fields exhibit organisation on a scale larger than that of the underlying turbulent flow (e.g. the 11-year solar cycle). The mechanism for the generation of so-called large-scale fields remains an open problem. In cases where the magnetic Reynolds number (Rm) is small, dynamo-generated fields are coherent but at (the astrophysically relevant) high Rm, the fields are overwhelmed by small-scale fluctuating field. Recently Tobias and Cattaneo have shown that an imposed large-scale shear flow can suppress the small-scale fluctuations and allow the large-scale temporal behaviour to emerge. Shear is also believed to modify the electromotive force by introducing correlations between the flow and the field. However, in previous models at high Rm the shear is often artificially imposed or driven by an arbitrary body force. Here we consider a simple kinematic model of a convective dynamo in which shear is self-consistently driven by the presence of a horizontal temperature gradient (resulting in a thermal wind) and a rotation vector that is oblique to gravity. By considering a -dimensional system, we are able to reach high Rm so that the dynamo approaches the asymptotic regime where the growth rate becomes approximately independent of Rm. We find the flows studied here to be excellent small-scale dynamos, but with very little systematic behaviour evident at large Rm. We attribute this to being unable to self-consistently generate flows with both large (net) helicity and strong shear in this setup.

Magnetic fields in the intergalactic medium and in the cosmic web

AbstractIn these proceedings we discuss advances in the theory and observation of magnetic fields in the intergalactic medium and in the cosmic web. We make the point that, despite perhaps unsurmountable obstacles in simulating a small-scale dynamo, currently most cosmological magnetohydrodynamical simulations paint a similar picture of magnetic field amplification in the cosmos. However, observations of magnetic fields in the intergalactic medium turn out to be very difficult. As a case in point, we present recent work on Faraday rotation measurement in the direction of a giant galaxy with the Low Frequency Array (LOFAR). These observations demonstrate the currently unique capability of LOFAR to measure Faraday rotation at the high accuracy and angular resolution required to investigate the magnetisation of large-scale structure filaments of the cosmic web.

Каталог активных областей 24-го цикла

При помощи данных инструмента HMI, установленного на борту орбитальной обсерватории SDO, рассчитан магнитный поток от АО, находящихся на видимой солнечной поверхности в период с 2010 по 2017 гг. Области распределены по категориям по принципу соответствия теории глобального динамо среднего поля: А - правильные биполярные области; U - одиночные пятна; В - биполярные области с отклонениями от одной из основных закономерностей теории динамо (либо закона полярностей Хейла, либо закона Джоя, либо с лидирующим пятном, меньшим, чем основное последующее пятно). Группа В разбита, в свою очередь, на соответствующие подмножества. Всего изучено 1684 АО с потоком не менее 1020 Мх. Составлен каталог, содержащий для каждой АО вычисленный нами магнитный поток, установленную категорию и другие данные. Каталог может быть использован для изучения изменений магнитного потока от АО выделенных категорий с солнечным циклом. На его основе могут быть проведены исследования соотношения между глобальным динамо среднего поля и мелкомасштабным турбулентным динамо для выяснения источников генерации магнитного поля Солнца.

Breaking Taylor–Proudman Balance by Magnetic Fields in Stellar Convection Zones

Abstract We carry out high-resolution calculations for the stellar convection zone. The main purpose of this Letter is to investigate the effect of a small-scale dynamo on the differential rotation. The solar differential rotation deviates from the Taylor–Proudman state in which the angular velocity does not change along the rotational axis. To break the Taylor–Proudman state deep in the convection zone, it is thought that a latitudinal entropy gradient is required. In this Letter, we find that the small-scale dynamo has three roles in the deviation of the stellar differential rotation from the Taylor–Proudman state. 1) The shear of the angular velocity is suppressed. This leads to a situation where the latitudinal entropy gradient efficiently breaks the Taylor–Proudman state. 2) The perturbation of the entropy increases with the suppression of the turbulent velocity between upflows and downflows. 3) The convection velocity is reduced. This increases the effect of the rotation on the convection. The second and third factors increase the latitudinal entropy gradient and break the Taylor–Proudman state. We find that an efficient small-scale dynamo has a significant impact on the stellar differential rotation.

Varying the forcing scale in low Prandtl number dynamos

Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale-separation between the size of the simulation domain and the integral scale of the turbulence, i.e., the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed.

Small-scale Dynamo Simulations: Magnetic Field Amplification in Exploding Granules and the Role of Deep and Shallow Recirculation

Abstract We analyze recent high-resolution photospheric small-scale dynamo simulations that were computed with the MURaM radiative MHD code. We focus our analysis on newly forming downflow lanes in exploding granules, as they show how weakly magnetized regions in the photosphere (the center of granules) evolve into strongly magnetized regions (downflow lanes). We find that newly formed downflow lanes initially exhibit mostly a laminar converging flow that amplifies the vertical magnetic field embedded in the granule from a few 10 G to field strengths exceeding 800 G. This results in extended magnetic sheets that have a length comparable to granular scales. Field amplification by turbulent shear first happens a few 100 km beneath the visible layers of the photosphere. Shallow recirculation transports the resulting turbulent field into the photosphere within minutes, after which the newly formed downflow lane shows a mix of strong magnetic sheets and turbulent field components. We stress in particular the role of shallow and deep recirculation for the organization and strength of magnetic field in the photosphere and discuss the photospheric and sub-photospheric energy conversion associated with the small-scale dynamo process. While the energy conversion through the Lorentz force depends only weakly on the saturation field strength (and therefore deep or shallow recirculation), it is strongly dependent on the magnetic Prandtl number. We discuss the potential of these findings for further constraining small-scale dynamo models through high-resolution observations.

Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. II. Simulations

Abstract Using direct numerical simulations (DNS), we study laminar and turbulent dynamos in chiral magnetohydrodynamics with an extended set of equations that accounts for an additional contribution to the electric current due to the chiral magnetic effect (CME). This quantum phenomenon originates from an asymmetry between left- and right-handed relativistic fermions in the presence of a magnetic field and gives rise to a chiral dynamo. We show that the magnetic field evolution proceeds in three stages: (1) a small-scale chiral dynamo instability, (2) production of chiral magnetically driven turbulence and excitation of a large-scale dynamo instability due to a new chiral effect (α μ effect), and (3) saturation of magnetic helicity and magnetic field growth controlled by a conservation law for the total chirality. The α μ effect becomes dominant at large fluid and magnetic Reynolds numbers and is not related to kinetic helicity. The growth rate of the large-scale magnetic field and its characteristic scale measured in the numerical simulations agree well with theoretical predictions based on mean-field theory. The previously discussed two-stage chiral magnetic scenario did not include stage (2), during which the characteristic scale of magnetic field variations can increase by many orders of magnitude. Based on the findings from numerical simulations, the relevance of the CME and the chiral effects revealed in the relativistic plasma of the early universe and of proto-neutron stars are discussed.

Consequences of high effective Prandtl number on solar differential rotation and convective velocity

Observations suggest that the large-scale convective velocities obtained by solar convection simulations might be over-estimated (convective conundrum). One plausible solution to this could be the small-scale dynamo which cannot be fully resolved by global simulations. The small-scale Lorentz force suppresses the convective motions and also the turbulent mixing of entropy between upflows and downflows, leading to a large effective Prandtl number (Pr). We explore this idea in three-dimensional global rotating convection simulations at different thermal conductivity (κ), i.e., at different Pr. In agreement with previous non-rotating simulations, the convective velocity is reduced with the increase of Pr as long as the thermal conductive flux is negligible. A subadiabatic layer is formed near the base of the convection zone due to continuous deposition of low entropy plumes in low-κ simulations. The most interesting result of our low-κ simulations is that the convective motions are accompanied by a change in the convection structure that is increasingly influenced by small-scale plumes. These plumes tend to transport angular momentum radially inward and thus establish an anti-solar differential rotation, in striking contrast to the solar rotation profile. If such low diffusive plumes, driven by the radiative-surface cooling, are present in the Sun, then our results cast doubt on the idea that a high effective Pr may be a viable solution to the solar convective conundrum. Our study also emphasizes that any resolution of the conundrum that relies on the downward plumes must take into account the angular momentum transport and heat transport.

Far-infrared–radio correlation and magnetic field strength in star-forming early-type galaxies

A tight far-infrared - radio correlation similar to that in star-forming late-type galaxies is also indicated in star-forming blue early-type galaxies, in which the nuclear optical-line emissions are primarily due to star-forming activities without a significant contribution from active galactic nuclei. The average value of far-infrared to 1.4 GHz radio flux-ratio commonly represented as the $'q'$ parameter is estimated to be $2.35\pm0.05$ with a scatter of 0.16 dex. The average star formation rate estimated using 1.4 GHz radio continuum is $\sim6$ M$_{\odot}$ yr$^{-1}$ in good agreement with those estimated using far-infrared and H$\alpha$ luminosities. The radio emission is detected mainly from central region which could be associated with the star-forming activities, most likely triggered by recent tidal interactions. The average thermal contribution to total radio flux is estimated to be $\sim12$ per cent. The average value of the magnetic field strengths in the star-forming early-type galaxies is estimated to be 12$^{+11}_{-4}$ $\mu$G. These magnetic fields are very likely generated via fast amplification in small-scale turbulent dynamos acting in the star-bursting regions.

Angular momentum transfer in primordial discs and the rotation of the first stars

We investigate the rotation velocity of the first stars by modelling the angular momentum transfer in the primordial accretion disc.Assessing the impact of magnetic braking, we consider the transition in angular momentum transport mode at the Alfv$\acute{\rm e}$n radius, from the dynamically dominated free-fall accretion to the magnetically dominated solid-body one.The accreting protostar at the centre of the primordial star-forming cloud rotates with close to breakup speed in the case without magnetic fields.Considering a physically-motivated model for small-scale turbulent dynamo amplification, we find that stellar rotation speed quickly declines if a large fraction of the initial turbulent energy is converted to magnetic energy ($\gtrsim 0.14$). Alternatively, if the dynamo process were inefficient, for amplification due to flux-freezing, stars would become slow rotators if the pre-galactic magnetic field strength is above a critical value, $\simeq 10^{-8.2}$G, evaluated at a scale of $n_{\rm H} = 1 {\rm cm}^{-3}$, which is significantly higher than plausible cosmological seed values ($\sim 10^{-15}$G). Because of the rapid decline of the stellar rotational speed over a narrow range in model parameters, the first stars encounter a bimodal fate: rapid rotation at almost the breakup level, or the near absence of any rotation.

Small-Scale Magnetic Helicity and Nonlinear Stabilization of the Dynamo

According to present-day ideas, nonlinear saturation of the astrophysical dynamo and, in particular, the solar dynamo, are based on the consideration of the magnetic helicity balance, to which the helicities of the large-scale magnetic field and small-scale field related to it contributed. We show that, in a mirrorasymmetric medium, the small-scale magnetic field generated by the small-scale dynamo also has a nonzero magnetic helicity, which also should be taken into account in the magnetic helicity balance.

Enhancement of Small-scale Turbulent Dynamo by Large-scale Shear

Abstract Small-scale dynamos (SSDs) are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology, and structure formation. Using high-resolution direct numerical simulations, we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports SSD action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate γ of the SSD and the turbulent rms velocity with shear rate S that are independent of the magnetic Prandtl number: and . For large fluid and magnetic Reynolds numbers, γ, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the SSD exhibits the scaling, , arising solely from the induction equation for a given velocity field.

Resolved magnetic dynamo action in the simulated intracluster medium

Faraday rotation and synchrotron emission from extragalactic radio sources give evidence for the presence of magnetic fields extending over ~Mpc scales. However, the origin of these fields remains elusive. With new high-resolution grid simulations we studied the growth of magnetic fields in a massive galaxy cluster that in several aspects is similar to the Coma cluster. We investigated models in which magnetic fields originate from primordial seed fields with comoving strengths of 0.1 nG at redshift z=30. The simulations show evidence of significant magnetic field amplification. At the best spatial resolution (3.95 kpc), we are able to resolve the scale where magnetic tension balances the bending of magnetic lines by turbulence. This allows us to observe the final growth stage of the small-scale dynamo. To our knowledge this is the first time that this is seen in cosmological simulations of the intracluster medium. Our mock observations of Faraday Rotation provide a good match to observations of the Coma cluster. However, the distribution of magnetic fields shows strong departures from a simple Maxwellian distribution, suggesting that the three-dimensional structure of magnetic fields in real clusters may be significantly different than what is usually assumed when inferring magnetic field values from rotation measure observations.

A small-scale dynamo in feedback-dominated galaxies – III. Cosmological simulations

Magnetic fields are widely observed in the Universe in virtually all astrophysical objects, from individual stars to entire galaxies, even in the intergalactic medium, but their specific generation has long been debated. Due to the development of more realistic models of galaxy formation, viable scenarios are emerging to explain cosmic magnetism, thanks to both deeper observations and more efficient and accurate computer simulations. We present here a new cosmological high-resolution zoom-in magnetohydrodynamic (MHD) simulation, using the adaptive mesh refinement (AMR) technique, of a dwarf galaxy with an initially weak and uniform magnetic seed field that is amplified by a small-scale dynamo driven by supernova-induced turbulence. As first structures form from the gravitational collapse of small density fluctuations, the frozen-in magnetic field separates from the cosmic expansion and grows through compression. In a second step, star formation sets in and establishes a strong galactic fountain, self-regulated by supernova explosions. Inside the galaxy, the interstellar medium becomes highly turbulent, dominated by strong supersonic shocks, as demonstrated by the spectral analysis of the gas kinetic energy. In this turbulent environment, the magnetic field is quickly amplified via a small-scale dynamo process and is finally carried out into the circumgalactic medium by a galactic wind. This realistic cosmological simulation explains how initially weak magnetic seed fields can be amplified quickly in early, feedback-dominated galaxies, and predicts, as a consequence of the small scale dynamo process, that high-redshift magnetic fields are likely to be dominated by their small scale components.