arXiv subjects

Axel Brandenburg

Publications and source records attributed to Axel Brandenburg.

At least 37 records · Page 2Linked to original sources

arXiv2025

Kinematic dynamos and resolution limits for Smoothed Particle Magnetohydrodynamics

Understanding the origin and evolution of magnetic fields on cosmological scales opens up a window into the physics of the early Universe. Numerical simulations of such fields require a careful treatment to faithfully solve the equations of magnetohydrodynamics (MHD) without introducing numerical artefacts. In this paper, we study the growth of the magnetic fields in controlled kinematic dynamo setups using both smoothed particle hydrodynamics implementations in the SWIFT code. We assess the quality of the reconstructed solution in the Roberts flow case against the reference implementation in the Pencil code and find generally a good agreement. Similarly, we reproduce the known features of the more complex ABC flow. Using a simple induction-diffusion balance model to analyse the results, we construct an "overwinding" trigger metric to locally detect regions where the magnetic diffusion cannot counteract the expected induction because of limitations in the method's ability to resolve magnetic field gradients. This metric is then used to identify the necessary resolution and resistivity levels to counteract the overwinding problem. We finally apply this metric to adiabatic cosmological simulations and discuss the resolution requirements needed to resolve the growth of the primordial fields without artefacts.

astro-ph.CO↗

arXiv2025

Theory of the kinetic helicity effect on turbulent diffusion of magnetic and scalar fields

Kinetic helicity is a fundamental characteristics of astrophysical turbulent flows. It is not only responsible for the generation of large-scale magnetic fields in the Sun, stars, and spiral galaxies, but it also affects turbulent diffusion resulting in the dissipation of large-scale magnetic fields. Using the path integral approach for random helical velocity fields with a finite correlation time and large Reynolds numbers, we show that turbulent magnetic diffusion is reduced by the kinetic helicity, while the turbulent diffusivity of a passive scalar is enhanced by the helicity. The latter can explain the results of recent numerical simulations for forced helical turbulence. One of the crucial reasons for the difference between the kinetic helicity effect on magnetic and scalar fields is related to the helicity dependence of the correlation time of a turbulent velocity field.

physics.flu-dyn↗

arXiv2025

Magnetic helicity fluxes in dynamos from rotating inhomogeneous turbulence

We analyze direct numerical simulations of large-scale dynamos in inhomogeneous nonhelically driven rotating turbulence with and without shear. The forcing is modulated so that the turbulent intensity peaks in the middle of the computational domain and drops to nearly zero at the two ends above and below the midplane. A large-scale dynamo is driven by an $α$ effect of opposite signs in the two hemispheres. In the presence of shear, the hemispheric magnetic helicity flux from small-scale fields becomes important and can even overcompensate for the magnetic helicity transferred by the $α$ effect between large and small scales. This effect has not previously been observed in nonshearing simulations. Our numerical simulations show that the hemispheric magnetic helicity fluxes are nearly independent of the magnetic Reynolds number, but those between large and small scales, and the consequent dynamo effect, are still found to decrease with increasing Reynolds number -- just like in nonshearing dynamos. However, in contrast to nonshearing dynamos, where the generated mean magnetic field declines with increasing magnetic Reynolds number, it is now found to remain independent of it. This suggests that catastrophic dynamo quenching is alleviated by the shear-induced hemispheric small-scale magnetic helicity fluxes that can even overcompensate the fluxes between large and small scales and thereby cause resistive contributions.

physics.plasm-ph↗

arXiv2025

Helicity effect on turbulent passive and active scalar diffusivities

Turbulent flows are known to produce enhanced effective magnetic and passive scalar diffusivities, which can fairly accurately be determined with numerical methods. It is now known that, if the flow is also helical, the effective magnetic diffusivity is reduced relative to the nonhelical value. Neither the usual second-order correlation approximation nor the various $τ$ approaches have been able to capture this. Here we show that the helicity effect on the turbulent passive scalar diffusivity works in the opposite sense and leads to an enhancement. We have also demonstrated that the correlation time of the turbulent velocity field increases with the kinetic helicity. This is a key point in the theoretical interpretation of the obtained numerical results. Simulations in which helicity is being produced self-consistently by stratified rotating turbulence resulted in a turbulent passive scalar diffusivity that was found to be decreasing with increasing rotation rate.

physics.flu-dyn↗

arXiv2025

Magnetically assisted vorticity production in decaying acoustic turbulence

We study vorticity production in isothermal, subsonic, acoustic (nonvortical), and decaying turbulence due to the presence of magnetic fields. Using three-dimensional numerical simulations, we find that the resulting kinetic energy cascade follows the ordinary Kolmogorov phenomenology involving a constant spectral energy flux. The nondimensional prefactor for acoustic turbulence is larger than the standard Kolmogorov constant due to the inefficient dissipation of kinetic energy. We also find that the Lorentz force can drive vortical motions even when the initial field is uniform, by converting a fraction of the acoustic energy into vortical energy. This conversion is shown to be quadratic in the magnetic field strength and linear in the acoustic flow speed. By contrast, the direct production of vortical motions by a non-force-free magnetic field is linear in the field strength. Our results suggest that magnetic fields play a crucial role in vorticity production in cosmological flows, particularly in scenarios where significant acoustic turbulence is prevalent. We also discuss the implications of our findings for the early Universe, where magnetic fields may convert acoustic turbulence generated during cosmological phase transitions into vortical turbulence.

physics.flu-dyn↗

arXiv2025

Lattice simulations of axion-U(1) inflation: gravitational waves, magnetic fields, and scalar statistics

We numerically study axion-U(1) inflation, focusing on the regime where the coupling between axions and gauge fields results in significant backreaction from the amplified gauge fields during inflation. These amplified gauge fields not only generate high-frequency gravitational waves (GWs), but also enhance spatial inhomogeneities in the axion field. GWs serve as key probe for constraining the coupling strength between the axion and gauge fields. We find that, when backreaction is important during inflation, the constraints on the coupling strength due to GW overproduction are relaxed compared to previous studies, in which backreaction matters only after inflation. Moreover, our results suggest that the probability density function (PDF) of axion fluctuations tends toward a Gaussian distribution even in cases where gauge field backreaction is important only after inflation. This aligns with previous studies where the same effect was observed for cases with strong backreaction during inflation. This finding can be crucial for future studies of primordial black hole (PBH) formation, which can further constrain the coupling strength. We also calculate the spectrum of the produced magnetic fields in this model and find that their strength is compatible with the observed lower limits.

astro-ph.CO↗

arXiv2025

Spectra of magnetic fields from electroweak symmetry breaking

We characterize magnetic fields produced during electroweak symmetry breaking by non-dynamical numerical simulations based on the Kibble mechanism. The generated magnetic fields were thought to have an energy spectrum $\propto k^3$ for small wavenumbers $k$, but here we show that it is actually a spectrum $\propto k^4$ along with characteristic fluctuations in the magnetic helicity. Using scaling results from MHD simulations for the evolution and assuming that the initial magnetic field is coherent on the electroweak Hubble scale, we estimate the magnetic field strength to be $\sim 10^{-13}\, \rmG$ on kpc scales at the present epoch for non-helical fields. For maximally helical fields we obtain $\sim 10^{-10}\, \rmG$ on Mpc scales. We also give scalings of these estimates for partially helical fields.

astro-ph.CO↗

arXiv2025

Inverse cascade from helical and nonhelical decaying columnar magnetic fields

Powerful lasers may in future produce magnetic fields that would allow us to study turbulent magnetohydrodynamic inverse cascade behavior. This has so far only been seen in numerical simulations. In the laboratory, however, the produced fields may be highly anisotropic. Here, we present corresponding simulations to show that, during the turbulent decay, such a magnetic field undergoes spontaneous isotropization. As a consequence, we find the decay dynamics to be similar to that in isotropic turbulence. We also find that an initially pointwise nonhelical magnetic field is unstable and develops magnetic helicity fluctuations that can be quantified by the Hosking integral. It is a conserved quantity that characterizes magnetic helicity fluctuations and governs the turbulent decay when the mean magnetic helicity vanishes. As in earlier work, the ratio of the magnetic decay time to the Alfvén time is found to be around $50$ in the helical and nonhelical cases. At intermediate times, the ratio can even reach a hundred. This ratio determines the endpoints of cosmological magnetic field evolution.

physics.plasm-ph↗

arXiv2025

Reality of inverse cascading in neutron star crusts

The braking torque that dictates the timing properties of magnetars is closely tied to the large-scale dipolar magnetic field on their surface. The formation of this field has been a topic of ongoing debate. One proposed mechanism, based on macroscopic principles, involves an inverse cascade within the neutron star's crust. However, this phenomenon has not been observed in realistic simulations. In this study, we provide compelling evidence supporting the feasibility of the inverse cascading process in the presence of an initial helical magnetic field within realistic neutron star crusts and discuss its contribution to the amplification of the large-scale magnetic field. Our findings, derived from a systematic investigation that considers various coordinate systems, peak wavenumber positions, crustal thicknesses, magnetic boundary conditions, and magnetic Lundquist numbers, reveal that the specific geometry of the crustal domain-with its extreme aspect ratio-requires an initial peak wavenumber from small-scale structures for the inverse cascade to occur. However, this same aspect ratio confines the cascade to structures on the scale of the crust, making the formation of a large-scale dipolar surface field unlikely. Despite these limitations, the inverse cascade remains a significant factor in the magnetic field evolution within the crust and may help explain highly magnetized objects with weak surface dipolar fields, such as low-field magnetars and central compact objects.

astro-ph.HE↗

arXiv2025

Turbulent magnetic decay controlled by two conserved quantities

The decay of a turbulent magnetic field is slower with helicity than without. Furthermore, the magnetic correlation length grows faster for a helical than a nonhelical field. Both helical and nonhelical decay laws involve conserved quantities: the mean magnetic helicity density and the Hosking integral. Using direct numerical simulations in a triply periodic domain, we show quantitatively that in the fractionally helical case the mean magnetic energy density and correlation length are approximately given by the maximum of the values for the purely helical and purely nonhelical cases. The time of switch-over from one to the other decay law can be obtained on dimensional grounds and is approximately given by $I_\mathrm{H}^{1/2}I_\mathrm{M}^{-3/2}$, where $I_\mathrm{H}$ is the Hosking integral and $I_\mathrm{M}$ is the mean magnetic helicity density. An earlier approach based on the decay time is found to agree with our new result and suggests that the Hosking integral exceeds naive estimates by the square of the same resistivity-dependent factor by which also the turbulent decay time exceeds the Alfvén time. In the presence of an applied magnetic field, the mean magnetic helicity density is known to be not conserved, and we show that then also the Hosking integral is not conserved.

physics.plasm-ph↗

arXiv2024

Intergalactic medium rotation measure of primordial magnetic fields

The Faraday rotation effect, quantified by the Rotation Measure (RM), is a powerful probe of the large-scale magnetization of the Universe - tracing magnetic fields not only on galaxy and galaxy cluster scales but also in the intergalactic Medium (IGM; referred to as $\mathrm{RM}_{\text{IGM}}$). The redshift dependence of the latter has extensively been explored with observations. It has also been shown that this relation can help to distinguish between different large-scale magnetization scenarios. We study the evolution of this $\mathrm{RM}_{\text{IGM}}$ for different primordial magnetogenesis scenarios to search for the imprints of primordial magnetic fields (PMFs; magnetic fields originating in the early Universe) on the redshift-dependence of $\mathrm{RM}_{\text{IGM}}$. We use cosmological magnetohydrodynamic (MHD) simulations for evolving PMFs during large-scale structure formation, coupled to the light cone analysis to produce a realistic statistical sample of mock $\mathrm{RM}_{\text{IGM}}$ images. We study the predicted behavior for the cosmic evolution of $\mathrm{RM}_{\text{IGM}}$ for different correlation lengths of PMFs, and provide fitting functions for their dependence on redshifts. We compare these mock RM trends with the recent analysis of the the LOw-Frequency ARray (LOFAR) RM Grid and find that large-scale-correlated PMFs should have (comoving) strengths $\lesssim 0.75$ nanoGauss, if originated during inflation with the scale invariant spectrum and (comoving) correlation length $\sim 19$ cMpc/h or $ \lesssim 30$ nanoGauss if they originated during phase-transition epochs with the comoving correlation length $\sim 1$ cMpc/h. Our findings agree with previous observations and confirm the results of semi-analytical studies, showing that upper limits on the PMF strength decrease as their coherence scales increase.

astro-ph.CO↗

arXiv2024

Magnetogenesis from axion-SU(2) inflation

We describe a novel proposal for inflationary magnetogenesis by identifying the non-Abelian sector of Spectator Chromo Natural Inflation (SCNI) with the $\rm{SU(2)}_{\rm L}$ sector of the Standard Model. This mechanism relies on the recently discovered attractor of SCNI in the strong backreaction regime, where the gauge fields do not decay on super-horizon scales and their backreaction leads to a stable new trajectory for the rolling axion field. The large super-horizon gauge fields are partly transformed after the electroweak phase transition into electromagnetic fields. The strength and correlation length of the resulting helical magnetic fields depend on the inflationary Hubble scale and the details of the SCNI sector. For suitable parameter choices we show that the strength of the resulting magnetic fields having correlation lengths around $1\, {\rm {Mpc}}$ are consistent with the required intergalactic magnetic fields for explaining the spectra of high energy $γ$ rays from distant blazars.

astro-ph.CO↗

arXiv2024

Efficiency of dynamos from an autonomous generation of chiral asymmetry

At high energies, the dynamics of a plasma with charged fermions can be described in terms of chiral magnetohydrodynamics. Using direct numerical simulations, we demonstrate that chiral magnetic waves (CMWs) can produce a chiral asymmetry $μ_5 = μ_\mathrm{L} - μ_\mathrm{R}$ from a spatially fluctuating (inhomogeneous) chemical potential $μ= μ_\mathrm{L} + μ_\mathrm{R}$, where $μ_\mathrm{L}$ and $μ_\mathrm{R}$ are the chemical potentials of left- and right-handed electrically charged fermions, respectively. If the frequency of the CMW is less than or comparable to the characteristic growth rate of the chiral dynamo instability, the magnetic field can be amplified on small spatial scales. The growth rate of this small-scale chiral dynamo instability is determined by the spatial maximum value of $μ_5$ fluctuations. Therefore, the magnetic field amplification occurs during periods when $μ_5$ reaches temporal maxima during the CMW. If the small-scale chiral dynamo instability leads to a magnetic field strength that exceeds a critical value, which depends on the resistivity and the initial value of $μ$, magnetically dominated turbulence is produced. Turbulence gives rise to a large-scale dynamo instability, which we find to be caused by the magnetic alpha effect. Our results have consequences for the dynamics of certain high-energy plasmas, such as the early Universe.

physics.plasm-ph↗

arXiv2024

Backreaction of axion-SU(2) dynamics during inflation

We consider the effects of backreaction on axion-SU(2) dynamics during inflation. We use the linear evolution equations for the gauge field modes and compute their backreaction on the background quantities numerically using the Hartree approximation. We show that the spectator chromo-natural inflation attractor is unstable when back-reaction becomes important. Working within the constraints of the linear mode equations, we find a new dynamical attractor solution for the axion field and the vacuum expectation value of the gauge field, where the latter has an opposite sign with respect to the chromo-natural inflation solution. Our findings are of particular interest to the phenomenology of axion-SU(2) inflation, as they demonstrate the instability of the usual trajectory due to large backreaction effects. The viable parameter space of the model becomes significantly altered, provided future non-Abelian lattice simulations confirm the existence of the new dynamical attractor. In addition, the backreaction effects lead to characteristic oscillatory features in the primordial gravitational wave background that are potentially detectable with upcoming gravitational wave detectors.

astro-ph.CO↗

arXiv2024

Relic Gravitational Waves from the Chiral Plasma Instability in the Standard Cosmological Model

In the primordial plasma, at temperatures above the scale of electroweak symmetry breaking, the presence of chiral asymmetries is expected to induce the development of helical hypermagnetic fields through the phenomenon of chiral plasma instability. It results in magnetohydrodynamic turbulence due to the high conductivity and low viscosity and sources gravitational waves that survive in the universe today as a stochastic polarized gravitational wave background. In this article, we show that this scenario only relies on Standard Model physics, and therefore the observable signatures, namely the relic magnetic field and gravitational background, are linked to a single parameter controlling the initial chiral asymmetry. We estimate the magnetic field and gravitational wave spectra, and validate these estimates with 3D numerical simulations.

astro-ph.CO↗

arXiv2024

Chiral anomaly and dynamos from inhomogeneous chemical potential fluctuations

In the standard model of particle physics, the chiral anomaly can occur in relativistic plasmas and plays a role in the early Universe, protoneutron stars, heavy-ion collisions, and quantum materials. It gives rise to a magnetic instability if the number densities of left- and right-handed electrically charged fermions are unequal. Using direct numerical simulations, we show this can result just from spatial fluctuations of the chemical potential, causing a chiral dynamo instability, magnetically driven turbulence, and ultimately a large-scale magnetic field through the magnetic alpha effect.

physics.plasm-ph↗

arXiv2023

Turbulent processes and mean-field dynamo

Mean-field dynamo theory has important applications in solar physics and galactic magnetism. We discuss some of the many turbulence effects relevant to the generation of large-scale magnetic fields in the solar convection zone. The mean-field description is then used to illustrate the physics of the $α$ effect, turbulent pumping, turbulent magnetic diffusivity, and other effects on a modern solar dynamo model. We also discuss how turbulence transport coefficients are derived from local simulations of convection and then used in mean-field models.

astro-ph.SR↗

arXiv2023

Magnetohydrodynamics predicts heavy-tailed distributions of axion-photon conversion

The interconversion of axionlike particles (ALPs) and photons in magnetised astrophysical environments provides a promising route to search for ALPs. The strongest limits to date on light ALPs use galaxy clusters as ALP-photon converters. However, such studies traditionally rely on simple models of the cluster magnetic fields, with the state-of-the-art being Gaussian random fields (GRFs). We present the first systematic study of ALP-photon conversion in more realistic, turbulent fields from dedicated magnetohydrodynamic (MHD) simulations, which we compare with GRF models. For GRFs, we analytically derive the distribution of conversion ratios at fixed energy and find that it follows an exponential law. We find that the MHD models agree with the exponential law for typical, small-amplitude mixings but exhibit distinctly heavy tails for rare and large mixings. We explain how non-Gaussian features, e.g.~coherent structures and local spikes in the MHD magnetic field, are responsible for the heavy tail. Our results suggest that limits placed on ALPs using GRFs are robust.

hep-ph↗