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We consider astrophysically relevant nonlinear MHD dynamo at large Reynolds
numbers (Re). We argue that it is universal in a sense that magnetic energy
grows at a rate which is a constant fraction C_E of the total turbulent
dissipation rate. On the basis of locality bounds we claim that this
"efficiency of small-scale dynamo", C_E, is a true consta...
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Citations
... We consider that the solenoidal turbulence with super-Alfvénic injection velocity shows a power spectrum with a well-established inertial range. In such a situation, a fixed fraction (η B ≈ 0.05) of the turbulent energy flux is consumed through amplification of the magnetic field (e.g., Cho et al. 2009;Beresnyak 2012;Xu & Lazarian 2016). MHD simulations of galaxy clusters succeed in resolving the small-scale turbulent dynamo in the central region (e.g., ZuHone et al. 2011;Vazza et al. 2018;Domínguez-Fernández et al. 2019;Steinwandel et al. 2022), but this effect is quenched in the cluster periphery due to the limited resolution. ...
... The tracer approach is also important for that issue. Following the energy gain and loss of CRes with a tracer method in a simulated galaxy cluster, Beduzzi et al. (2023) demonstrated that ≈22%-57% of the megahalo region (0.4R 500 < r < R 500 ) is filled with radio-emitting CRes. Although the details of the simulation setup and the definition of the volume filling factor are different from our study, their result suggests that the cluster-scale diffuse emission is produced through multiple episodes of turbulent reacceleration. ...
... However, it is also possible that the "initial spectrum" is affected by the turbulent reacceleration working before the time of the snapshot. Recent simulation by Beduzzi et al. (2023) observed that the radioemitting CRes in the ICM experience multiple episodes of reacceleration. In such a case, the peak of the seed CRe spectrum should appear at a larger momentum p 10 10 min 2 3 ...
Recent radio observations with the Low Frequency Array (LOFAR) discovered diffuse emission extending beyond the scale of classical radio halos. The presence of such megahalos indicates that the amplification of the magnetic field and acceleration of relativistic particles are working in the cluster outskirts, presumably due to the combination of shocks and turbulence that dissipate energy in these regions. Cosmological magnetohydrodynamical (MHD) simulations of galaxy clusters suggest that solenoidal turbulence has a significant energy budget in the outskirts of galaxy clusters. In this paper, we explore the possibility that this turbulence contributes to the emission observed in megahalos through second-order Fermi acceleration of relativistic particles and magnetic field amplification by the dynamo. We focus on the case of A2255 and find that this scenario can explain the basic properties of the diffuse emission component that is observed under assumptions that are used in previous literature. More specifically, we conduct a numerical follow-up, solving the Fokker–Planck equation by using a snapshot of an MHD simulation and deducing the synchrotron brightness integrated along the lines of sight. We find that a volume-filling emission, ranging between 30% and almost 100% of the projected area, depending on our assumptions on the particle diffusion and transport, can be detected at LOFAR sensitivities. Assuming a magnetic field B ∼ 0.2 μ G, as derived from a dynamo model applied to the emitting region, we find that the observed brightness can be matched when ∼1% of the solenoidal turbulent energy flux is channeled into particle acceleration.
... However, observations of the Faraday rotation measure in the ICM reveal a typical reversal scale of the magnetic field of a few kiloparsecs (e.g., Bonafede et al. 2010 for the Coma cluster). This could indicate that the small-scale dynamo is in the nonlinear evolutionary stage, where magnetic energy shifts to larger spatial scales (Schekochihin et al. 2002;Beresnyak 2012;Schleicher et al. 2013). Whether or not this scenario can explain the existence of µG magnetic fields in galaxy clusters depends on the properties of ICM turbulence across cosmic times. ...
Context. The intracluster medium (ICM) is the low-density diffuse gas that fills the space between galaxies within galaxy clusters. It is primarily composed of magnetized plasma, which reaches virial temperatures of up to 10 ⁸ K, probably due to mergers of subhalos. Under these conditions, the plasma is weakly collisional and therefore has an anisotropic pressure tensor with respect to the local direction of the magnetic field. This triggers very fast, Larmor-scale, pressure-anisotropy-driven kinetic instabilities that alter magnetic field amplification.
Aims. We aim to study magnetic field amplification through a turbulent, small-scale dynamo, including the effects of the kinetic instabilities, during the evolution of a typical massive galaxy cluster. A specific aim of this work is to establish a redshift limit from which a dynamo has to start to amplify the magnetic field up to equipartition with the turbulent velocity field at redshift z = 0.
Methods. We implemented one-dimensional radial profiles for various plasma quantities for merger trees generated with the modified GALFORM algorithm. We assumed that turbulence is driven by successive mergers of dark matter halos and constructed effective models for the Reynolds number Re eff dependence on the magnetic field in three different magnetization regimes (unmagnetized, magnetized “kinetic”, and magnetized “fluid”), including the effects of kinetic instabilities. The magnetic field growth rate is calculated for the different Re eff models.
Results. The model results in a higher magnetic field growth rate at higher redshift. For all scenarios considered in this study, to reach equipartition at z = 0, it is sufficient for the amplification of the magnetic field to start at redshift z start ≈ 1.5 and above. The time to reach equipartition can be significantly shorter in cases with systematically smaller turbulent forcing scales and for the highest Re eff models.
Conclusions. The origin of magnetic fields in the weakly collisional ICM can be explained by the small-scale turbulent dynamo, provided that the dynamo process starts beyond a given redshift. Merger trees are useful tools for studying the evolution of magnetic fields in weakly collisional plasmas, and could also be used to constrain the different stages of the dynamo that could potentially be observed by future radio telescopes.
... While the kinematic phase is very short (Kazantsev 1968;Kulsrud & Anderson 1992;Rogachevskii & Kleeorin 1997;Schober et al. 2012b), at z 4 the dynamo could still be in the nonlinear stage. In this phase (Beresnyak 2012), saturation is reached at the smallest length scales of the turbulent inertial range and there is an inverse cascade of magnetic energy to larger scales. Semi-analytical models by Schober et al. (2013) predict that the dynamo saturates on time scales of 4−270 Myr, depending on the driving mechanism of turbulence. ...
Context. The infrared-radio correlation (IRRC) of star-forming galaxies can be used to estimate their star formation rate (SFR) based on the radio continuum luminosity at MHz–GHz frequencies. For its practical application in future deep radio surveys, it is crucial to know whether the IRRC persists at high redshift z .
Aims. Previous works have reported that the 1.4 GHz IRRC correlation of star-forming galaxies is nearly z -invariant up to z ≈ 4, but depends strongly on the stellar mass M ⋆ . This should be taken into account for SFR calibrations based on radio luminosity.
Methods. To understand the physical cause behind the M ⋆ dependence of the IRRC and its properties at higher z , we constructed a phenomenological model for galactic radio emission. Our model is based on a dynamo-generated magnetic field and a steady-state cosmic ray population. It includes a number of free parameters that determine the galaxy properties. To reduce the overall number of model parameters, we also employed observed scaling relations.
Results. We find that the resulting spread of the infrared-to-radio luminosity ratio, q ( z , M ⋆ ), with respect to M ⋆ is mostly determined by the scaling of the galactic radius with M ⋆ , while the absolute value of the q ( z , M ⋆ ) curves decreases with more efficient conversion of supernova energy to magnetic fields and cosmic rays. Additionally, decreasing the slope of the cosmic ray injection spectrum, α CR , results in higher radio luminosity, decreasing the absolute values of the q ( z , M ⋆ ) curves. Within the uncertainty range of our model, the observed dependence of the IRRC on M ⋆ and z can be reproduced when the efficiency of supernova-driven turbulence is 5%, 10% of the kinetic energy is converted into magnetic energy, and α CR ≈ 3.0.
Conclusions. For galaxies with intermediate to high ( M ⋆ ≈ 10 9.5 − 10 ¹¹ M ⊙ ) stellar masses, our model results in an IRRC that is nearly independent of z . For galaxies with lower masses ( M ⋆ ≈ 10 8.5 M ⊙ ), we find that the IR-to-radio flux ratio increases with increasing redshift. This matches the observational data in that mass bin which, however, only extends to z ≈ 1.5. The increase in the IR-to-radio flux ratio for low-mass galaxies at z ≳ 1.5 that is predicted by our model could be tested with future deep radio observations.
... One of aspects of MHD turbulence responsible for such difficulty is the MHD dynamo, which amplifies the magnetic fields by converting kinetic energy into magnetic energy, starting at the smallest scales [1,[5][6][7]. In some cases, the MHD dynamo can produce amplification several orders of magnitude greater than that of the original fields [1,4]. ...
... In some cases, the MHD dynamo can produce amplification several orders of magnitude greater than that of the original fields [1,4]. To resolve this magnetic field amplification, one must run simulations at the smallest of scales, where the MHD dynamo is most efficient [5]. This scale is set by the Reynolds number, Re, of the flow. ...
The modeling of multi-scale and multi-physics complex systems typically involves the
use of scientific software that can optimally leverage extreme scale computing. Despite major developments
in recent years, these simulations continue to be computationally intensive and time consuming.
Here we explore the use of AI to accelerate the modeling of complex systems
at a fraction of the computational cost of classical methods, and
present the first application of physics informed neural operators to model 2D
incompressible magnetohydrodynamics simulations. Our AI models incorporate tensor Fourier neural
operators as their backbone, which we implemented with the TensorLY package. Our results
indicate that physics informed neural operators can accurately capture the physics of magnetohydrodynamics
simulations that describe laminar flows with Reynolds numbers $Re\leq250$. We also explore the
applicability of our AI surrogates for turbulent flows, and discuss a variety of methodologies that may be
incorporated in future work to create AI models that provide a computationally efficient and high fidelity
description of magnetohydrodynamics simulations for a broad range of Reynolds numbers. The scientific software
developed in this project is released with this manuscript.
... It is believed that when the self-generated seed magnetic field passes through plasma turbulence, the random motion of the fluid will stretch, fold, compress, and amplify the magnetic field, i.e. the turbulence generator effect. However, the evolution of the magnetic field and the maintenance mechanism of the amplified magnetic field are not entirely understood [5][6][7][8][9][10][11][12]. ...
Local magnetic field enhancement in supernova remnants (SNRs) is a natural laboratory for studying the amplification effect of turbulent magnetic fields. In recent years, high-power laser devices have gradually matured as a tool for astronomical research that perfects observations and theoretical models. In this study, a model of the amplification effect of the turbulent magnetic field in SNRs by an intense laser is simulated using the radiation magnetohydrodynamic simulation program. We investigate and compare the evolutionary processes of unstable turbulence under different initial disturbance modes, directions, and intensities of external magnetic fields and obtain the magnetic energy spectrum and magnetic field magnification. The results demonstrate that the fluid motion associated with Rayleigh-Taylor instability (RTI) will stretch the environmental magnetic field significantly, with an intensity amplified by two orders of magnitude. The environmental magnetic field perpendicular to the laser injection direction is decisive during magnetic field amplification which is necessary to clarify the physical mechanism of magnetic field amplification in SNRs. Furthermore, it will deepen the understanding of the interstellar magnetic field’s evolution. The results also establish a reference for laser-driven magnetized plasma experiments in a robust magnetic environment.
... τ inj ∼ τ η ). Hence, τ inj ∼ L inj /v inj ∼ τ η ∼ l 2 η /η, which yields the expected k η ∼ Pm 1/2 Re 1/2 k inj (Schekochihin, Cowley & Yousef 2008 ; in numerous prior works (Kulsrud & Anderson 1992 ;Schekochihin et al. 2002a ;Beresnyak et al. 2009 ;Cho et al. 2009 ;Beresnyak 2012 ). Hu et al. ( 2022 ) applied this model to analyse the dynamo growth rate in shock-driven turbulence. ...
Small-scale fluctuating magnetic fields of order nG are observed in supernova shocks and galaxy clusters, where its amplification is likely caused by the Biermann battery mechanism. However, these fields cannot be amplified further without the turbulent dynamo, which generates magnetic energy through the stretch-twist-fold (STF) mechanism. Thus, we present here novel three-dimensional magnetohydrodynamic (MHD) simulations of a laser-driven shock propagating into a stratified, multiphase medium, to investigate the post-shock turbulent magnetic field amplification via the turbulent dynamo. The configuration used here is currently being tested in the shock tunnel at the National Ignition Facility (NIF). In order to probe the statistical properties of the post-shock turbulent region, we use 384×512×384 tracers to track its evolution through the Lagrangian framework, thus providing a high-fidelity analysis of the shocked medium. Our simulations indicate that the growth of the magnetic field, which accompanies the near-Saffman kinetic energy decay (Ekin∝t−1.15) without turbulence driving, exhibits slightly different characteristics as compared to periodic box simulations. Seemingly no distinct phases exist in its evolution, because the shock passage and time to observe the magnetic field amplification during the turbulence decay are very short (∼0.3 of a turbulent turnover time). Yet, the growth rate is still consistent with those expected for compressive (curl-free) turbulence driving in subsonic, compressible turbulence. Phenomenological understanding of the dynamics of the magnetic and velocity fields are also elucidated via Lagrangian frequency spectra, which are consistent with the expected inertial range scalings in the Eulerian-Lagrangian bridge.
... Several magnetohydrodynamical simulations have found that galactic magnetic fields are amplified by gas turbulence at very short timescales (i.e., ∼100 Myr) (e.g., Brandenburg & Subramanian 2005;Beresnyak 2012;Schober et al. 2012;Bovino et al. 2013;Schleicher & Beck 2013). The primary driver of gas turbulence in the ISM of galaxies is supernova explosion (Bacchini et al. 2020), the rate of which is in turn directly coupled to the SFR in the galaxy. ...
We have estimated the magnetic field strengths of a sample of seven galaxies using their nonthermal synchrotron radio emission at meter wavelengths, and assuming energy equipartition between magnetic fields and cosmic-ray particles. We tested for deviation of magnetic fields from energy equipartition with cosmic-ray particles, and found that deviations of ∼25% are typical for the sample galaxies. Spatially resolved star formation rates (SFRs) were estimated for the seven galaxies along with five galaxies studied previously. For the combined sample of 12 galaxies, the equipartition magnetic fields ( B eq ) are correlated with the SFR surface densities (Σ SFR ) at sub-kiloparsec scales with B eq ∝ Σ SFR 0.31 ± 0.06 , consistent with model predictions. We estimated gas densities ( ρ gas ) for a subsample of seven galaxies using archival observations of the CO rotational transitions and the atomic hydrogen (H i ) 21 cm line and studied the spatially resolved correlation between the magnetic fields and ρ gas . Magnetic fields and gas densities are found to be correlated at sub-kiloparsec scale as B eq ∝ ρ gas 0.40 ± 0.09 . This is broadly consistent with models, which typically predict B ∝ ρ gas 0.5 .
... One of aspects of MHD turbulence responsible for such difficulty is the MHD dynamo, which amplifies the magnetic fields by converting kinetic energy into magnetic energy, starting at the smallest scales [1,[5][6][7]. In some cases, the MHD dynamo can produce amplification several orders of magnitude greater than that of the original fields [1,4]. ...
... In some cases, the MHD dynamo can produce amplification several orders of magnitude greater than that of the original fields [1,4]. To resolve this magnetic field amplification, one must run simulations at the smallest of scales, where the MHD dynamo is most efficient [5]. This scale is set by the Reynolds number, Re, of the flow. ...
We present the first application of physics informed neural operators, which use tensor Fourier neural operators as their backbone, to model 2D incompressible magnetohydrodynamics simulations. Our results indicate that physics informed AI can accurately model the physics of magnetohydrodynamics simulations that describe laminar flows with Reynolds numbers $Re\leq250$. We also quantify the applicability of our AI surrogates for turbulent flows, and explore how magnetohydrodynamics simulations and AI surrogates store magnetic and kinetic energy across wavenumbers. Based on these studies, we propose a variety of approaches to create AI surrogates that provide a computationally efficient and high fidelity description of magnetohydrodynamics simulations for a broad range of Reynolds numbers. Neural operators and scientific software to produce simulation data to train, validate and test our physics informed neural operators are released with this manuscript.
... The rest is dissipated via fast stochastic reconnection (Lazarian & Vishniac 1999;Eyink et al. 2011), including natural mechanisms of viscous heating and turbulent diffusion (Kolmogorov 1941;Kulsrud & Anderson 1992). Similar scalings, with corresponding linear growth 1 , up until the suggested ∼ inj Pm 1/2 Re 1/2 = inj Rm 1/2 at saturation 2 have also been observed in numerous prior works (Kulsrud & Anderson 1992;Schekochihin et al. 2002a;Cho et al. 2009;Beresnyak et al. 2009;Beresnyak 2012). 1 Alternatively, consider simply that /ℓ ∼ /ℓ 2 , which gives ℓ ∼ (ℓ / ) 1/2 ∼ ( ) 1/2 . The selective decay mechanism suppresses high -modes, which triggers a magnetic back-reaction when 2 ∼ 2 . ...
Small-scale fluctuating magnetic fields of order $n$G to $\mu$G are observed in supernova shocks and galaxy clusters, where amplifications of the field are likely caused by the Biermann battery mechanism. However, these fields cannot be amplified further without the turbulent dynamo, which generates magnetic energy through the stretch-twist-fold (STF) mechanism. Thus, we present here novel three-dimensional magnetohydrodynamic (MHD) simulations of a laser-driven shock propagating into a stratified, multiphase medium, to investigate the post-shock turbulent magnetic field amplification via the turbulent dynamo. The configuration used here is currently being tested in the shock tunnel at the National Ignition Facility (NIF). In order to probe the statistical properties of the post-shock turbulent region, we use $384 \times 512 \times 384$ tracer trajectories to track its evolution through the Lagrangian framework, thus providing a high-fidelity analysis of the shocked medium. Our simulations indicate that the growth of the magnetic field, which accompanies the near-Saffman power-law kinetic energy decay ($E_{\textrm{kin}} \propto t^{-1.15})$ in the absence of turbulence driving, exhibits slightly different characteristics as compared to periodic box simulations. Seemingly no distinct phases exist in its evolution, because the shock passage and time to observe the magnetic field amplification during the turbulence decay are very short, with only $\sim0.3$ of a turbulent turnover time. Yet, the growth rates are still consistent with those expected for compressive (curl-free) turbulence driving in subsonic, compressible turbulence. Phenomenological understanding of the dynamics of the magnetic and velocity fields are also elucidated via Lagrangian frequency spectra, which are consistent with the expected inertial range scalings via the Eulerian-Lagrangian bridge.
... ∼100 Myr) (e.g. Brandenburg & Subramanian 2005;Beresnyak 2012;Schober et al. 2012;Schleicher & Beck 2013;Bovino et al. 2013). The primary driver of gas-turbulence in the ISM of galaxies is supernova explosion (Bacchini et al. 2020), the rate of which is in turn directly coupled to the SFR in the galaxy. ...
We have estimated the magnetic field strengths of a sample of seven galaxies using their non-thermal synchrotron radio emission at metre wavelengths, and assuming energy equipartition between magnetic fields and cosmic ray particles. Spatially resolved star formation rates (SFR) were estimated for the seven galaxies along with five galaxies studied previously. For the combined sample of twelve galaxies, the equipartition magnetic fields (B$_\textrm{eq}$) are correlated with the SFR surface densities ($\Sigma_\textrm{SFR}$) at sub-kpc scales with B$_\textrm{eq}$ $\propto$ $\Sigma_\textrm{SFR}^ {0.31\pm0.06}$, consistent with model predictions. We estimated gas densities ($\rho_\textrm{gas}$) for a sub-sample of seven galaxies using archival observations of the carbon monoxide (CO) rotational transitions and the atomic hydrogen (HI) 21 cm line and studied the spatially-resolved correlation between the magnetic fields and $\rho_\textrm{gas}$. Magnetic fields and gas densities are found to be correlated at sub-kpc scale as B$_\textrm{eq}$ $\propto$ $\rho_\textrm{gas}^{0.40\pm0.09}$. This is broadly consistent with models, which typically predict B $\propto$ $\rho_\textrm{gas}^{0.5}$.
