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Axel Brandenburg

Publications and source records attributed to Axel Brandenburg.

At least 55 records · Page 3Linked to original sources
arXiv2023

Shallow relic gravitational wave spectrum with acoustic peak

We study the gravitational wave (GW) spectrum produced by acoustic waves in the early universe, such as would be produced by a first order phase transition, focusing on the low-frequency side of the peak. We confirm with numerical simulations the Sound Shell model prediction of a steep rise with wave number $k$ of $k^9$ to a peak whose magnitude grows at a rate $(H/k_\text{p})H$, where $H$ is the Hubble rate and $k_\text{p}$ the peak wave number, set by the peak wave number of the fluid velocity power spectrum. We also show that hitherto neglected terms give a shallower part with amplitude $(H/k_\text{p})^2$ in the range $H \lesssim k \lesssim k_\text{p}$, which in the limit of small $H/k$ rises as $k$. This linear rise has been seen in other modelling and also in direct numerical simulations. The relative amplitude between the linearly rising part and the peak therefore depends on the peak wave number of the velocity spectrum and the lifetime of the source, which in an expanding background is bounded above by the Hubble time $H^{-1}$. For slow phase transitions, which have the lowest peak wave number and the loudest signals, the acoustic GW peak appears as a localized enhancement of the spectrum, with a rise to the peak less steep than $k^9$. The shape of the peak, absent in vortical turbulence, may help to lift degeneracies in phase transition parameter estimation at future GW observatories.

gr-qc↗
arXiv2023

Inverse cascading for initial MHD turbulence spectra between Saffman and Batchelor

In decaying magnetohydrodynamic (MHD) turbulence with a strong magnetic field, the spectral magnetic energy density is known to increase with time at small wavenumbers $k$, provided the spectrum at low $k$ is sufficiently steep. This process is called inverse cascading and occurs for an initial Batchelor spectrum, where the magnetic energy per linear wavenumber interval increases like $k^4$. For an initial Saffman spectrum that is proportional to $k^2$, however, inverse cascading has not been found in the past. We study here the case of an intermediate $k^3$ spectrum, which may be relevant for magnetogenesis in the early Universe during the electroweak epoch. This case is not well understood in view of the standard Taylor expansion of the magnetic energy spectrum for small $k$. Using high resolution MHD simulations, we show that also in this case there is inverse cascading with a strength just as expected from the conservation of the Hosking integral, which governs the decay of an initial Batchelor spectrum. Even for shallower $k^α$ spectra with spectral index $α>3/2$, our simulations suggest a spectral increase at small $k$ with time $t$ proportional to $t^{4α/9-2/3}$. The critical spectral index of $α=3/2$ is related to the slope of the spectral envelope in the Hosking phenomenology. Our simulations with $2048^3$ mesh points now suggest inverse cascading even for an initial Saffman spectrum.

physics.plasm-ph↗
arXiv2023

Galactic Dynamos

Spiral galaxies, including the Milky Way, have large-scale magnetic fields with significant energy densities. The dominant theory attributes these magnetic fields to a large-scale dynamo. We review the current status of dynamo theory and discuss various numerical simulations designed to explain either particular aspects of the problem or to reproduce galactic magnetic fields globally. Our main conclusions can be summarized as follows. Idealized direct numerical simulations produce mean magnetic fields, whose saturation energy density tends to decline with increasing magnetic Reynolds number. This is still an unsolved problem. Large-scale galactic magnetic fields of microgauss strengths can probably only be explained if helical magnetic fields of small or moderate length scales can rapidly be ejected or destroyed. Small-scale dynamos are important throughout a galaxy's life, and probably provide strong seed fields at early stages. The circumgalactic medium (CGM) may play an important role in driving dynamo action at small and large length scales. These interactions between the galactic disk and the CGM may provide important insights into our understanding of galactic dynamos. We expect future research in galactic dynamos to focus on the cosmological history of galaxies and the interaction with the CGM as means of replacing the idealized boundary conditions used in earlier work.

astro-ph.GA↗
arXiv2023

Electromagnetic conversion into kinetic and thermal energies

Conversion of electromagnetic energy into magnetohydrodynamic energy occurs when the electric conductivity changes from negligible to finite values. This process is relevant during the epoch of reheating of the early Universe at the end of inflation and before the emergence of the radiation-dominated era. We find that conversion into kinetic and thermal energies is primarily the result of electric energy dissipation and that the magnetic energy plays only a secondary role in this process. This means that, since electric energy dominates over magnetic energy during inflation and reheating, significant amounts of electric energy can be converted into magnetohydrodynamic energy when conductivity emerges early enough, before the relevant length scales become stable.

physics.plasm-ph↗
arXiv2023

Chiral magnetohydrodynamics with zero total chirality

We study the evolution of magnetic fields coupled with chiral fermion asymmetry in the framework of chiral magnetohydrodynamics with zero initial total chirality. The initial magnetic field has a turbulent spectrum peaking at a certain characteristic scale and is fully helical with positive helicity. The initial chiral chemical potential is spatially uniform and negative. We consider two opposite cases where the ratio of the length scale of the chiral plasma instability (CPI) to the characteristic scale of the turbulence is smaller and larger than unity. These initial conditions might be realized in cosmological models such as certain types of axion inflation. The magnetic field and chiral chemical potential evolve with inverse cascading in such a way that the magnetic helicity and chirality cancel each other at all times. The CPI time scale is found to determine mainly the time when the magnetic helicity spectrum attains negative values at high wave numbers. The turnover time of the energy-carrying eddies, on the other hand, determines the time when the peak of the spectrum starts to shift to smaller wave numbers via an inverse cascade. The onset of helicity decay is determined by the time when the chiral magnetic effect becomes efficient at the peak of the initial magnetic energy spectrum. When spin flipping is important, the chiral chemical potential vanishes and the magnetic helicity becomes constant, which leads to a faster increase of the correlation length, as expected from magnetic helicity conservation. This also happens when the initial total chirality is imbalanced. Our findings have important implications for baryogenesis after axion inflation.

hep-ph↗
arXiv2023

Confronting the neutron star population with inverse cascades

The origin and evolution of magnetic fields of neutron stars from birth has long been a source of debate. Here, motivated by recent simulations of the Hall cascade with magnetic helicity, we invoke a model where the large-scale magnetic field of neutron stars grows as a product of small-scale turbulence through an inverse cascade. We apply this model to a simulated population of neutron stars at birth and show how this model can account for the evolution of such objects across the $P\dot{P}$ diagram, explaining both pulsar and magnetar observations. Under the assumption that small-scale turbulence is responsible for large-scale magnetic fields, we place a lower limit on the spherical harmonic degree of the energy-carrying magnetic eddies of $\approx 40$. Our results favor the presence of a highly resistive pasta layer at the base of the neutron star crust. We further discuss the implications of this paradigm on direct observables, such as the nominal age and braking index of pulsars.

astro-ph.HE↗
arXiv2023

Modified propagation of gravitational waves from the early radiation era

We study the propagation of cosmological gravitational wave (GW) backgrounds from the early radiation era until the present day in modified theories of gravity. Comparing to general relativity (GR), we study the effects that modified gravity parameters, such as the GW friction $α_{\rm M}$ and the tensor speed excess $α_{\rm T}$, have on the present-day GW spectrum. We use both the WKB estimate, which provides an analytical description but fails at superhorizon scales, and numerical simulations that allow us to go beyond the WKB approximation. We show that a constant $α_{\rm T}$ makes relatively insignificant changes to the GR solution, especially taking into account the constraints on its value from GW observations by the LIGO--Virgo collaboration, while $α_{\rm M}$ can introduce modifications to the spectral slopes of the GW energy spectrum in the low-frequency regime depending on the considered time evolution of $α_{\rm M}$. The latter effect is additional to the damping or growth occurring equally at all scales that can be predicted by the WKB approximation. In light of the recent observations by pulsar timing array (PTA) collaborations, and the potential observations by future detectors such as SKA, LISA, DECIGO, BBO, or ET, we show that, in most of the cases, constraints cannot be placed on the effects of $α_{\rm M}$ and the initial GW energy density $\mathcal{E}_{\rm GW}^*$ separately, but only on the combined effects of the two, unless the signal is observed at different frequency ranges. In particular, we provide some constraints on the combined effects from the reported PTA observations.

gr-qc↗
arXiv2023

Turbulence with Magnetic Helicity that is Absent on Average

Magnetic helicity plays a tremendously important role when it is different from zero on average. Most notably, it leads to the phenomenon of an inverse cascade. Here, we consider decaying magnetohydrodynamic (MHD) turbulence as well as some less common examples of magnetic evolution under the Hall effect and ambipolar diffusion, as well as cases in which the magnetic field evolution is constrained by the presence of an asymmetry in the number density of chiral fermions, whose spin is systematically either aligned or anti-aligned with its momentum. In all those cases, there is a new conserved quantity: the Hosking integral. We present quantitative scaling results for the magnetic integral scale as well as the magnetic energy density and its spectrum. We also compare with cases were a magnetic version of the Saffman integral is initially finite. Rotation in MHD turbulence tends to suppress nonlinearity and thereby also inverse cascading. Finally, the role of the Hosking and magnetic Saffman integrals in shell models of turbulence is examined.

physics.plasm-ph↗
arXiv2023

Decay law of magnetic turbulence with helicity balanced by chiral fermions

In plasmas composed of massless electrically charged fermions, chirality can be interchanged with magnetic helicity while preserving the total chirality through the quantum chiral anomaly. The decay of turbulent energy in plasmas such as those in the early Universe and compact stars is usually controlled by certain conservation laws. In the case of zero total chirality, when the magnetic helicity density balances with the appropriately scaled chiral chemical potential to zero, the total chirality no longer determines the decay. We propose that in such a case, an adaptation to the Hosking integral, which is conserved in nonhelical magnetically dominated turbulence, controls the decay in turbulence with helicity balanced by chiral fermions. We show, using a high resolution numerical simulation, that this is indeed the case. The magnetic energy density decays and the correlation length increases with time just like in nonhelical turbulence with vanishing chiral chemical potential. But here, the magnetic helicity density is nearly maximum and shows a scaling with time $t$ proportional to $t^{-2/3}$. This is unrelated to the $t^{-2/3}$ decay of magnetic {\it energy} in fully helical magnetic turbulence. The modulus of the chiral chemical potential decays in the same fashion. This is much slower than the exponential decay previously expected in theories of asymmetric baryon production from the hypermagnetic helicity decay after axion inflation.

physics.plasm-ph↗
arXiv2023

Cross-helicity effect on $α$-type dynamo in non-equilibrium turbulence

Turbulence is typically not in equilibrium, i.e. mean quantities such as the mean energy and helicity are typically time-dependent. The effect of non-stationarity on the turbulent hydromagnetic dynamo process is studied here with the use of the two-scale direct-interaction approximation (TSDIA), which allows to explicitly relate the mean turbulent Reynolds and Maxwell stresses and the mean electromotive force (EMF) to the spectral characteristics of turbulence, such as e.g. the mean energy, as well as kinetic and cross-helicity. It is demonstrated, that the non-equilibrium effects can enhance the dynamo process when the magnetohydrodynamic (MHD) turbulence is both helical and cross-helical. This effect is based on the turbulent infinitesimal-impulse cross-response functions, which do not affect turbulent flows in equilibrium. The evolution and sources of the cross-helicity in MHD turbulence is also discussed.

physics.flu-dyn↗
arXiv2023

Inflationary and phase-transitional primordial magnetic fields in galaxy clusters

Primordial magnetic fields (PMFs) are possible candidates for explaining the observed magnetic fields in galaxy clusters. Two competing scenarios of primordial magnetogenesis have been discussed in the literature: inflationary and phase-transitional. We study the amplification of both large- and small-scale correlated magnetic fields, corresponding to inflation- and phase transition-generated PMFs, in a massive galaxy cluster. We employ high-resolution magnetohydrodynamic cosmological zoom-in simulations to resolve the turbulent motions in the intracluster medium. We find that the turbulent amplification is more efficient for the large-scale inflationary models, while the phase transition-generated seed fields show moderate growth. The differences between the models are imprinted on the spectral characteristics of the field (such as the amplitude and the shape of the magnetic power spectrum) and therefore on the final correlation length. We find a one order of magnitude difference between the final strengths of the inflation- and phase transition-generated magnetic fields, and a factor of 1.5 difference between their final coherence scales. Thus, the final configuration of the magnetic field retains information about the PMF generation scenarios. Our findings have implications for future extragalactic Faraday rotation surveys with the possibility of distinguishing between different magnetogenesis scenarios.

astro-ph.CO↗
arXiv2022

Quadratic growth during the COVID-19 pandemic: merging hotspots and reinfections

The existence of an exponential growth phase during early stages of a pandemic is often taken for granted. However, for the 2019 novel coronavirus epidemic, the early exponential phase lasted only for about six days, while the quadratic growth prevailed for forty days until it spread to other countries and continued, again quadratically, but with a larger coefficient. Here we show that this rapid phase is followed by a subsequent slow-down where the coefficient is reduced to almost the original value at the outbreak. This can be explained by the merging of previously disconnected sites that occurred after the disease jumped (nonlocally) to a relatively small number of separated sites. Subsequent variations in the slope with continued growth can qualitatively be explained as a result of reinfections and changes in their rate. We demonstrate that the observed behavior can be described by a standard epidemiological model with spatial extent and reinfections included. Time-dependent changes in the spatial diffusion coefficient can also model corresponding variations in the slope.

q-bio.PE↗
arXiv2022

Hosking integral in nonhelical Hall cascade

The Hosking integral, which characterizes magnetic helicity fluctuations in subvolumes, is known to govern the decay of magnetically dominated turbulence. Here we show that, when the evolution of the magnetic field is controlled by the motion of electrons only, as in neutron star crusts, the decay of the magnetic field is still controlled by the Hosking integral, but now it has effectively different dimensions than in ordinary magnetohydrodynamic (MHD) turbulence. This causes the correlation length to increase with time $t$ like $t^{4/13}$ instead of $t^{4/9}$ in MHD. The magnetic energy density decreases like $t^{-10/13}$, which is slower than in MHD, where it decays like $t^{-10/9}$. These new analytic results agree with earlier numerical simulations for the nonhelical Hall cascade.

physics.plasm-ph↗
arXiv2022

Low frequency tail of gravitational wave spectra from hydromagnetic turbulence

Hydrodynamic and magnetohydrodynamic turbulence in the early Universe can drive gravitational waves (GWs) and imprint their spectrum onto that of GWs, which might still be observable today. We study the production of the GW background from freely decaying magnetohydrodynamic turbulence from helical and nonhelical initial magnetic fields. To understand the produced GW spectra, we develop a simple model on the basis of the evolution of the magnetic stress tensor. We find that the GW spectra obtained in this model reproduce those obtained in numerical simulations if we consider the detailed time evolution of the low-frequency tail of the stress spectrum from numerical simulations. We also show that the shapes of the produced GW frequency spectra are different for helical and nonhelical cases for the same initial magnetic energy spectra. Such differences can help distinguish helical and nonhelical initial magnetic fields from a polarized background of GWs -- especially when the expected circular polarization cannot be detected directly.

astro-ph.CO↗
arXiv2022

Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos

The magnetic fields in galaxy clusters and probably also in the interstellar medium are believed to be generated by a small-scale dynamo. Theoretically, during its kinematic stage, it is characterized by a Kazantsev spectrum, which peaks at the resistive scale. It is only slightly shallower than the Saffman spectrum that is expected for random and causally connected magnetic fields. Causally disconnected fields have the even steeper Batchelor spectrum. Here we show that all three spectra are present in the small-scale dynamo. During the kinematic stage, the Batchelor spectrum occurs on scales larger than the energy-carrying scale of the turbulence, and the Kazantsev spectrum on smaller scales within the inertial range of the turbulence -- even for a magnetic Prandtl number of unity. In the saturated state, the dynamo develops a Saffman spectrum on large scales, suggestive of the build-up of long-range correlations. At large magnetic Prandtl numbers, elongated structures are seen in synthetic synchrotron emission maps showing the parity-even E polarization. We also observe a significant excess in the E polarization over the parity-odd B polarization at subresistive scales, and a deficiency at larger scales. This finding is at odds with the observed excess in the Galactic microwave foreground emission, which is believed to be associated with larger scales. The E and B polarizations may be highly non-Gaussian and skewed in the kinematic regime of the dynamo. For dust emission, however, the polarized emission is always nearly Gaussian, and the excess in the E polarization is much weaker.

astro-ph.GA↗
arXiv2022

A Comparative Analysis of Machine-learning Models for Solar Flare Forecasting: Identifying High-performing Active Region Flare Indicators

Solar flares create adverse space weather impacting space and Earth-based technologies. However, the difficulty of forecasting flares, and by extension severe space weather, is accentuated by the lack of any unique flare trigger or a single physical pathway. Studies indicate that multiple physical properties contribute to active region flare potential, compounding the challenge. Recent developments in machine learning (ML) have enabled analysis of higher-dimensional data leading to increasingly better flare forecasting techniques. However, consensus on high-performing flare predictors remains elusive. In the most comprehensive study to date, we conduct a comparative analysis of four popular ML techniques (k-nearest neighbor, logistic regression, random forest classifier, and support vector machine) by training these on magnetic parameters obtained from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) for the entirety of solar cycle 24. We demonstrate that the logistic regression and support vector machine algorithms perform extremely well in forecasting active region flaring potential. The logistic regression algorithm returns the highest true skill score of $0.967 \pm 0.018$, possibly the highest classification performance achieved with any strictly parametric study. From a comparative assessment, we establish that the magnetic properties like total current helicity, total vertical current density, total unsigned flux, R_VALUE, and total absolute twist are the top-performing flare indicators. We also introduce and analyze two new performance metrics, namely, severe and clear space weather indicators. Our analysis constrains the most successful ML algorithms and identifies physical parameters that contribute most to active region flare productivity.

astro-ph.SR↗
arXiv2022

Scaling of the Hosking integral in decaying magnetically-dominated turbulence

The Saffman helicity invariant of Hosking and Schekochihin (2021, PRX 11, 041005), which we here call the Hosking integral, has emerged as an important quantity that may govern the decay properties of magnetically dominated nonhelical turbulence. Using a range of different computational methods, we confirm that this quantity is indeed gauge-invariant and nearly perfectly conserved in the limit of large Lundquist numbers. For direct numerical simulations with ordinary viscosity and magnetic diffusivity operators, we find that the solution develops in a nearly self-similar fashion. In a diagram quantifying the instantaneous decay coefficients of magnetic energy and integral scale, we find that the solution evolves along a line that is indeed suggestive of the governing role of the Hosking integral. The solution settles near a line in this diagram that is expected for a self-similar evolution of the magnetic energy spectrum. The solution will settle in a slightly different position when the magnetic diffusivity decreases with time, which would be compatible with the decay being governed by the reconnection time scale rather than the Alfvén time.

physics.plasm-ph↗
arXiv2022

Collision fluctuations of lucky droplets with superdroplets

It was previously shown that the superdroplet algorithm for modeling the collision-coalescence process can faithfully represent mean droplet growth in turbulent clouds. But an open question is how accurately the superdroplet algorithm accounts for fluctuations in the collisional aggregation process. Such fluctuations are particularly important in dilute suspensions. Even in the absence of turbulence, Poisson fluctuations of collision times in dilute suspensions may result in substantial variations in the growth process, resulting in a broad distribution of growth times to reach a certain droplet size. We quantify the accuracy of the superdroplet algorithm in describing the fluctuating growth history of a larger droplet that settles under the effect of gravity in a quiescent fluid and collides with a dilute suspension of smaller droplets that were initially randomly distributed in space ('lucky droplet model'). We assess the effect of fluctuations upon the growth history of the lucky droplet and compute the distribution of cumulative collision times. The latter is shown to be sensitive enough to detect the subtle increase of fluctuations associated with collisions between multiple lucky droplets. The superdroplet algorithm incorporates fluctuations in two distinct ways: through the random spatial distribution of superdroplets and through the Monte Carlo collision algorithm involved. Using specifically designed numerical experiments, we show that both on their own give an accurate representation of fluctuations. We conclude that the superdroplet algorithm can faithfully represent fluctuations in the coagulation of droplets driven by gravity.

physics.ao-ph↗