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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 $\gamma$ rays from distant blazars.

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 extreme aspect ratio limits the inverse cascade to magnetic field structures on scales comparable to the neutron star's crust, making the formation of a large-scale dipolar surface field unlikely. Despite this limitation, the inverse cascade can significantly impact the magnetic field evolution in the interior of the crust, potentially explaining the observed characteristics of highly magnetized objects with weak surface dipolar fields, such as low-field magnetars or central compact objects.

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.

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 $\mu_5 = \mu_\mathrm{L} - \mu_\mathrm{R}$ from a spatially fluctuating (inhomogeneous) chemical potential $\mu = \mu_\mathrm{L} + \mu_\mathrm{R}$, where $\mu_\mathrm{L}$ and $\mu_\mathrm{R}$ 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 $\mu_5$ fluctuations. Therefore, the magnetic field amplification occurs during periods when $\mu_5$ 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 $\mu$, 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.

Magnetic fields generated in the early Universe undergo turbulent decay during the radiation-dominated era. The decay is governed by a decay exponent and a decay time. It has been argued that the latter is prolonged by magnetic reconnection, which depends on the microphysical resistivity and viscosity. Turbulence, on the other hand, is not usually expected to be sensitive to microphysical dissipation, which affects only very small scales. We want to test and quantify the reconnection hypothesis in decaying hydromagnetic turbulence. We performed high-resolution numerical simulations with zero net magnetic helicity using the Pencil Code with up to $2048^3$ mesh points and relate the decay time to the Alfvén time for different resistivities and viscosities. The decay time is found to be longer than the Alfvén time by a factor that increases with increasing Lundquist number to the 1/4 power. The decay exponent is as expected from the conservation of the Hosking integral, but a timescale dependence on resistivity is unusual for developed turbulence and not found for hydrodynamic turbulence. In two dimensions, the Lundquist number dependence is shown to be leveling off above values of $\approx25,000$, independently of the value of the viscosity. Our numerical results suggest that resistivity effects have been overestimated in earlier work. Instead of reconnection, it may be the magnetic helicity density in smaller patches that is responsible for the resistively slow decay. The leveling off at large Lundquist number cannot currently be confirmed in three dimensions.

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.

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.

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.

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.

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.

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.

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.

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 $\alpha$ 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.

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.

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 $\alpha_{\rm M}$ and the tensor speed excess $\alpha_{\rm T}$, 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 $\alpha_{\rm T}$ 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 $\alpha_{\rm M}$ can introduce modifications to the spectral slopes of the GW energy spectrum in the low-frequency regime depending on the considered time evolution of $\alpha_{\rm M}$. 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 $\alpha_{\rm M}$ 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.

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.

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.

Small-scale dynamos play important roles in modern astrophysics, especially on Galactic and extragalactic scales. Owing to dynamo action, purely hydrodynamic Kolmogorov turbulence hardly exists and is often replaced by hydromagnetic turbulence. Understanding the size of dissipative magnetic structures is important in estimating the time scale of Galactic scintillation and other observational and theoretical aspects of interstellar and intergalactic small-scale dynamos. Here we show that, during the kinematic phase of the small-scale dynamo, the cutoff wavenumber of the magnetic energy spectra scales as expected for large magnetic Prandtl numbers, but continues in the same way also for moderately small values - contrary to what is expected. For a critical magnetic Prandtl number of about 0.3, the dissipative and resistive cutoffs are found to occur at the same wavenumber. In the nonlinearly saturated regime, the critical magnetic Prandtl number becomes unity. The cutoff scale now has a shallower scaling with magnetic Prandtl number below a value of about three, and a steeper one otherwise compared to the kinematic regime.

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.

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.

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.

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.

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.

In many astrophysical environments, self-gravity can generate kinetic energy, which, in principle, is available for driving dynamo action. Using direct numerical simulations, we show that in unstirred self-gravitating subsonic turbulence with helicity and a magnetic Prandtl number of unity, there is a critical magnetic Reynolds number of about 25 above which the work done against the Lorentz force exceeds the Ohmic dissipation. The collapse itself drives predominantly irrotational motions that cannot be responsible for dynamo action. We find that, with a weak magnetic field, one-third of the work done by the gravitational force goes into compressional heating and the remaining two-thirds go first into kinetic energy of the turbulence before a fraction of it is converted further into magnetic and finally thermal energies. Close to the collapse, however, these fractions change toward 1/4 and 3/4 for compressional heating and kinetic energy, respectively. When the magnetic field is strong, the compressional heating fraction is unchanged. Out of the remaining kinetic energy, one quarter goes directly into magnetic energy via work against the Lorentz force. The fraction of vortical motions diminishes in favor of compressive motions that are almost exclusively driven by the Jeans instability. For an initially uniform magnetic field, field amplification at scales larger than those of the initial turbulence are driven by tangling.

We revisit the big bang nucleosynthesis (BBN) limits on primordial magnetic fields and/or turbulent motions accounting for the decaying nature of turbulent sources between the time of generation and BBN. This leads to larger estimates for the gravitational wave (GW) signal than previously expected. We address the detection prospects through space-based interferometers (for GWs generated around the electroweak energy scale) as well as pulsar timing arrays and astrometric missions (for GWs generated around the quantum chromodynamics energy scale).

We study the leading-order nonlinear gravitational waves (GWs) produced by an electromagnetic (EM) stress in reheating magnetogenesis scenarios. Both nonhelical and helical magnetic fields are considered. By numerically solving the linear and leading-order nonlinear GW equations, we find that the GW energy from the latter is usually larger. We compare their differences in terms of the GW spectrum and parameterize the GW energy difference due to the nonlinear term, $\Delta\mathcal{E}_{\rm GW}$, in terms of EM energy $\mathcal{E}_{\rm EM}$ as $\Delta\mathcal{E}_{\rm GW}=(\tilde p\mathcal{E}_{\rm EM}/k_*)^3$, where $k_*$ is the characteristic wave number, $\tilde p=0.84$ and $0.88$ are found in the nonhelical and helical cases, respectively, with reheating around the QCD energy scale, while $\tilde p=0.45$ is found at the electroweak energy scale. We also compare the polarization spectrum of the linear and nonlinear cases and find that adding the nonlinear term usually yields a decrease in the polarization that is proportional to the EM energy density. We parameterize the fractional polarization suppression as $|\Delta \mathcal{P}_{\rm GW}/\mathcal{P}_{\rm GW}|=\tilde r \mathcal{E}_{\rm EM}/k_*$ and find $\tilde r = 1.2 \times 10^{-1}$, $7.2 \times 10^{-4}$, and $3.2 \times 10^{-2}$ for the helical cases with reheating temperatures $T_{\rm r} = 300 {\rm TeV}$, $8 {\rm GeV}$, and $120 {\rm MeV}$, respectively. Prospects of observation by pulsar timing arrays, space-based interferometers, and other novel detection proposals are also discussed.

Chirality, or handedness, enters astrophysics in three distinct ways. Magnetic field and vortex lines tend to be helical and have a systematic twist in the northern and southern hemispheres of a star or a galaxy. Helicity is here driven by external factors. Chirality can also enter at the microphysical level and can then be traced back to the parity-breaking weak force. Finally, chirality can arise spontaneously, but this requires not only the presence of an instability, but also the action of nonlinearity. Examples can be found both in magnetohydrodynamics and in astrobiology, where homochirality among biomolecules probably got established at the origin of life. In this review, all three types of chirality production will be explored and compared.

Primordial magnetic fields could explain the large-scale magnetic fields present in the Universe. Inflation and phase transitions in the early Universe could give rise to such fields with unique characteristics. We investigate the magneto-hydrodynamic evolution of these magnetogenesis scenarios with cosmological simulations. We evolve inflation-generated magnetic fields either as (i) uniform (homogeneous) or as (ii) scale-invariant stochastic fields, and phase transition-generated ones either as (iii) helical or as (iv) non-helical fields from the radiation-dominated epoch. We find that the final distribution of magnetic fields in the simulated cosmic web shows a dependence on the initial strength and the topology of the seed field. Thus, the observed field configuration retains information on the initial conditions at the moment of the field generation. If detected, primordial magnetic field observations would open a new window for indirect probes of the early universe. The differences between the competing models are revealed on the scale of galaxy clusters, bridges, as well as filaments and voids. The distinctive spectral evolution of different seed fields produces imprints on the correlation length today. We discuss how the differences between rotation measures from highly ionized regions can potentially be probed with forthcoming surveys.

We study the dynamics of magnetic fields in chiral magnetohydrodynamics, which takes into account the effects of an additional electric current related to the chiral magnetic effect in high energy plasmas. We perform direct numerical simulations, considering weak seed magnetic fields and inhomogeneities of the chiral chemical potential mu_5 with a zero mean. We demonstrate that a small-scale chiral dynamo can occur in such plasmas if fluctuations of mu_5 are correlated on length scales that are much larger than the scale on which the dynamo growth rate reaches its maximum. Magnetic fluctuations grow by many orders of magnitude due to the small-scale chiral dynamo instability. Once the nonlinear backreaction of the generated magnetic field on fluctuations of mu_5 sets in, the ratio of these scales decreases and the dynamo saturates. When magnetic fluctuations grow sufficiently to drive turbulence via the Lorentz force before reaching maximum field strength, an additional mean-field dynamo phase is identified. The mean magnetic field grows on a scale that is larger than the integral scale of turbulence after the amplification of the fluctuating component saturates. The growth rate of the mean magnetic field is caused by a magnetic alpha effect that is proportional to the current helicity. With the onset of turbulence, the power spectrum of mu_5 develops a universal k^(-1) scaling independently of its initial shape, while the magnetic energy spectrum approaches a k^(-3) scaling.

In relativistic magnetized plasmas, asymmetry in the number densities of left- and right-handed fermions, i.e., a non-zero chiral chemical potential mu_5, leads to an electric current along the magnetic field. This causes a chiral dynamo instability for a uniform mu_5, but our simulations reveal a dynamo even for fluctuating mu_5 with zero mean. It produces magnetically-dominated turbulence and generates mean magnetic fields via the magnetic alpha effect. Eventually, a universal scale-invariant k^(-1) spectrum of mu_5 and a k^(-3) magnetic spectrum are formed independently of the initial condition.

Using numerical simulations of helical inflationary magnetogenesis in a low reheating temperature scenario, we show that the magnetic energy spectrum is strongly peaked at a particular wavenumber that depends on the reheating temperature. Gravitational waves (GWs) are produced at frequencies between 3 nHz and 50 mHz for reheating temperatures between 150 MeV and 3x10^5 GeV, respectively. At and below the peak frequency, the stress spectrum is always found to be that of white noise. This implies a linear increase of GW energy per logarithmic wavenumber interval, instead of a cubic one, as previously thought. Both in the helical and nonhelical cases, the GW spectrum is followed by a sharp drop for frequencies above the respective peak frequency. In this magnetogenesis scenario, the presence of a helical term extends the peak of the GW spectrum and therefore also the position of the aforementioned drop toward larger frequencies compared to the case without helicity. This might make a difference in it being detectable with space interferometers. The efficiency of GW production is found to be almost the same as in the nonhelical case, and independent of the reheating temperature, provided the electromagnetic energy at the end of reheating is fixed to be a certain fraction of the radiation energy density. Also, contrary to the case without helicity, the electric energy is now less than the magnetic energy during reheating. The fractional circular polarization is found to be nearly hundred per cent in a certain range below the peak frequency range.

We use direct numerical simulations of decaying primordial hydromagnetic turbulence with helicity to compute the resulting gravitational wave (GW) production and its degree of circular polarization. We find a clear dependence of the polarization of the resulting GWs on the fractional helicity of the turbulent source and we show that driven magnetic fields produce GWs more efficiently than magnetic fields that are initially present, leading to larger spectral amplitudes. The helicity does not have a huge impact on the maximum spectral amplitude in any of the two types of turbulence considered. However, the GW spectrum at wave numbers away from the peak becomes smaller for larger values of the magnetic fractional helicity. The degree of circular polarization approaches zero at frequencies below the peak, and reaches its maximum at the peak. At higher frequencies, it stays finite if the magnetic field is initially present, and it approaches zero if it is driven. We predict that the spectral peak of the GW signal can be detected by LISA if the turbulent energy density is at least $\sim 3\%$ of the radiation energy density, and the characteristic scale is a hundredth of the horizon at the electroweak scale. We show that the resulting GW polarization is unlikely to be detectable by the anisotropies induced by our proper motion in the dipole response function of LISA. Such signals can, however, be detectable by cross-correlating data from the LISA-Taiji network for turbulent energy densities of $\sim 5\%$, and fractional helicity of 0.5 to 1. Second-generation space-based GW detectors, such as BBO and DECIGO, would allow for the detection of a larger range of the GW spectrum and smaller amplitudes of the magnetic field.

We present three-dimensional direct numerical simulations of the production of magnetic fields and gravitational waves (GWs) in the early Universe during a low energy scale matter-dominated post-inflationary reheating era, and during the early subsequent radiative era, which is strongly turbulent. The parameters of the model are determined such that it avoids a number of known physical problems and produces magnetic energy densities between 0.2% and 2% of the critical energy density at the end of reheating. During the subsequent development of a turbulent magnetohydrodynamic cascade, magnetic fields and GWs develop a spectrum that extends to higher frequencies in the millihertz (nanohertz) range for models with reheating temperatures of around 100 GeV (150 MeV) at the beginning of the radiation-dominated era. However, even though the turbulent cascade is fully developed, the GW spectrum shows a sharp drop for frequencies above the peak value. This suggests that the turbulence is less efficient in driving GWs than previously thought. The peaks of the resulting GW spectra may well be in the range accessible to space interferometers, pulsar timing arrays, and other facilities.

In this study we present a compressible test-field method (CTFM) for computing $\alpha$ effect and turbulent magnetic diffusivity tensors, as well as those relevant for mean ponderomotive force and mass source, applied to the full MHD equations. We describe the theoretical background of the method, and compare it to the quasi-kinematic test-field method, and to the previously studied variant working in simplified MHD (SMHD). We present several test cases using velocity and magnetic fields of the Roberts geometry, and also compare with the imposed-field method. We show that, for moderate imposed field strengths, the nonlinear CTFM (nCTFM) gives results in agreement with the imposed-field method. Comparison of different flavors of the nCTFM in the shear dynamo case also agree up to equipartition field strengths. Some deviations between the CTFM and SMHD variants exist. As a relevant physical application, we study non-helically forced shear flows, which exhibit large-scale dynamo action, and present a re-analysis of low Reynolds number, moderate shear systems, where we previously neglected the pressure gradient in the momentum equation, and found no coherent shear-current effect. Another key difference is that in the earlier study we used magnetic forcing to mimic small-scale dynamo action, while here it is self-consistently driven by purely kinetic forcing. The kinematic CTFM with general validity forms the core of our analysis. We still find no coherent shear-current effect, but do recover strong large-scale dynamo action that, according to our analysis, is driven through the incoherent effects.

Clustering of inertial particles is important for many types of astrophysical and geophysical turbulence, but it has been studied predominately for incompressible flows. Here we study compressible flows and compare clustering in both compressively (irrotationally) and vortically (solenoidally) forced turbulence. Vortically and compressively forced flows are driven stochastically either by solenoidal waves or by circular expansion waves, respectively. For compressively forced flows, the power spectrum of the density of inertial particles is a useful tool for displaying particle clustering relative to the fluid density enhancement. Power spectra are shown to be particularly sensitive for studying large-scale particle clustering, while conventional tools such as radial distribution functions are more suitable for studying small-scale clustering. Our primary finding is that particle clustering through shock interaction is particularly prominent in turbulence driven by spherical expansion waves. It manifests itself through a double-peaked distribution of spectral power as a function of Stokes number. The two peaks are associated with two distinct clustering mechanisms; shock interaction for smaller Stokes numbers and the centrifugal sling effect for larger values. The clustering of inertial particles is associated with the formation of caustics. Such caustics can only be captured in the Lagrangian description, which allows us to assess the relative importance of caustics in vortically and compressively forced turbulence. We show that the statistical noise resulting from the limited number of particles in the Lagrangian description can be removed from the particle power spectra, allowing us a more detailed comparison of the residual spectra. We focus on the Epstein drag law relevant for rarefied gases, but show that our findings apply also to the usual Stokes drag.

We consider a generic dispersive massive gravity theory and numerically study its resulting modified energy and strain spectra of tensor gravitational waves (GWs) sourced by (i) fully developed turbulence during the electroweak phase transition (EWPT) and (ii) forced hydromagnetic turbulence during the QCD phase transition (QCDPT). The GW spectra are then computed in both spatial and temporal Fourier domains. We find, from the spatial spectra, that the slope modifications are weakly dependent on the eddy size at QCDPT, and, from the temporal spectra, that the modifications are pronounced in the $1$--$10{\rm nHz}$ range -- the sensitivity range of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) -- for a graviton mass $m_{\rm g}$ in the range $2\times10^{-23}{\rm eV}\lesssim m_{\rm g}c^2\lesssim7\times10^{-22}{\rm eV}$.

We study the gravitational wave (GW) signal sourced by primordial turbulence that is assumed to be present at cosmological phase transitions like the electroweak and quantum chromodynamics phase transitions. We consider various models of primordial turbulence, such as those with and without helicity, purely hydrodynamical turbulence induced by fluid motions, and magnetohydrodynamic turbulence whose energy can be dominated either by kinetic or magnetic energy, depending on the nature of the turbulence. We also study circularly polarized GWs generated by parity violating sources such as helical turbulence. Our ultimate goal is to determine the efficiency of GW production through different classes of turbulence. We find that the GW energy and strain tend to be large for acoustic or irrotational turbulence, even though its tensor mode amplitude is relatively small at most wave numbers. Only at very small wave numbers is the spectral tensor mode significant, which might explain the efficient GW production in that case.

We perform numerical simulations of gravitational waves (GWs) induced by hydrodynamic and hydromagnetic turbulent sources that might have been present at cosmological quantum chromodynamic (QCD) phase transitions. For turbulent energies of about 4% of the radiation energy density, the typical scale of such motions may have been a sizable fraction of the Hubble scale at that time. The resulting GWs are found to have an energy fraction of about $10^{-9}$ of the critical energy density in the nHz range today and may already have been observed by the NANOGrav collaboration. This is further made possible by our findings of shallower spectra proportional to the square root of the frequency for nonhelical hydromagnetic turbulence. This implies more power at low frequencies than for the steeper spectra previously anticipated. The behavior toward higher frequencies depends strongly on the nature of the turbulence. For vortical hydrodynamic and hydromagnetic turbulence, there is a sharp drop of spectral GW energy by up to five orders of magnitude in the presence of helicity, and somewhat less in the absence of helicity. For acoustic hydrodynamic turbulence, the sharp drop is replaced by a power law decay, albeit with a rather steep slope. Our study supports earlier findings of a quadratic scaling of the GW energy with the magnetic energy of the turbulence and inverse quadratic scaling with the peak frequency, which leads to larger GW energies under QCD conditions.

Relic gravitational waves (GWs) can be produced by primordial magnetic fields. However, not much is known about the resulting GW amplitudes and their dependence on the details of the generation mechanism. Here we treat magnetic field generation through the chiral magnetic effect (CME) as a generic mechanism and explore its dependence on the speed of generation (the product of magnetic diffusivity and characteristic wavenumber) and the speed characterizing the maximum magnetic field strength expected from the CME. When the latter exceeds the former (regime I), the regime applicable to the early universe, we obtain an inverse cascade with moderate GW energy that scales with the third power of the magnetic energy. When the generation speed exceeds the CME limit (regime II), the GW energy continues to increase without a corresponding increase of magnetic energy. In the early kinematic phase, the GW energy spectrum (per linear wavenumber interval) has opposite slopes in both regimes and is characterized by an inertial range spectrum in regime I and a white noise spectrum in regime II. The occurrence of these two slopes is shown to be a generic consequence of a nearly monochromatic exponential growth of the magnetic field. The resulting GW energy is found to be proportional to the fifth power of the limiting CME speed and the first power of the generation speed.

We perform direct numerical simulations to compute the net circular polarization of gravitational waves from helical (chiral) turbulent sources in the early Universe for a variety of initial conditions, including driven (stationary) and decaying turbulence. We investigate the resulting gravitational wave signal assuming different turbulent geneses such as magnetically or kinetically driven cases. Under realistic physical conditions in the early Universe we compute numerically the wave number-dependent polarization degree of the gravitational waves. We find that the spectral polarization degree strongly depends on the initial conditions. The peak of the spectral polarization degree occurs at twice the typical wavenumber of the source, as expected, and for fully helical decaying turbulence, it reaches its maximum of nearly 100\% \it only at the peak. We determine the temporal evolution of the turbulent sources as well as the resulting gravitational waves, showing that the dominant contribution to their spectral energy density happens shortly after the activation of the source. Only through an artificially prolonged decay of the turbulence can further increase of the gravitational wave amplitude be achieved. We estimate the detection prospects for the net polarization, arguing that its detection contains \it clean information (including the generation mechanisms, time, and strength) about the sources of possible parity violations in the early Universe.

Radiation transport plays important roles in stellar atmospheres, but the effects of turbulence are being obscured by other effects such as stratification. Using radiative hydrodynamic simulations of forced turbulence, we determine the decay rates of sinusoidal large-scale temperature perturbations of different wavenumbers in the optically thick and thin regimes. Increasing the wavenumber increases the rate of decay in both regimes, but this effect is much weaker than for the usual turbulent diffusion of passive scalars, where the increase is quadratic for small wavenumbers. The turbulent decay is well described by an enhanced Newtonian cooling process in the optically thin limit, which is found to show a weak increase proportional to the square root of the wavenumber. In the optically thick limit, the increase in turbulent decay is somewhat steeper for wavenumbers below the energy-carrying wavenumber of the turbulence, but levels off toward larger wavenumbers. In the presence of turbulence, the typical cooling time is comparable to the turbulent turnover time. We observe that the temperature takes a long time to reach equilibrium in both the optically thin and thick cases, but in the former, the temperature retains smaller scale structures for longer.

The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time $t$: $\propto t^{-2/5}$ instead of $\propto t^{-2/3}$ in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber $k$ is compatible with earlier findings for the forced Hall cascade, i.e., proportional to $k^{-7/3}$, but in the decaying cases, the subinertial range spectrum steepens to a novel $k^5$ slope instead of the $k^4$ slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the root-mean square (rms) magnetic field. For neutron star conditions with an rms magnetic field of a few times $10^{14}\,$G, the large-scale magnetic field might only be $10^{11}\,$G, while still producing magnetic dissipation of $10^{33}\,$erg$\,$s$^{-1}$ for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries.

The possibility of explaining shear flow dynamos by a magnetic shear-current (MSC) effect is examined via numerical simulations. Our primary diagnostics is the determination of the turbulent magnetic diffusivity tensor $\boldsymbol{\eta}$. In our setup, a negative sign of its component $\eta_{yx}$ is necessary for coherent dynamo action by the SC effect. To be able to measure turbulent transport coefficients from systems with magnetic background turbulence, we present an extension of the test-field method (TFM), applicable to our setup where the pressure gradient is dropped from the momentum equation: the nonlinear TFM (NLTFM). Our momentum equation is related to Burgers' equation and the resulting flows are referred to as magnetized burgulence. We use both stochastic kinetic and magnetic forcings to mimic cases without and with simultaneous small-scale dynamo action (SSD). When we force only kinetically, negative $\eta_{yx}$ are obtained with exponential growth in both the radial and azimuthal mean magnetic field components. Using isotropic magnetic forcing, the field growth is no longer exponential, while NLTFM yields positive $\eta_{yx}$. By employing an alternative forcing from which wavevectors having small components are removed, the exponential growth is recovered, but the NLTFM results do not change significantly. Analyzing the dynamo excitation conditions for the coherent SC and incoherent $\alpha$ and SC effects shows that the incoherent effects are the main drivers of the dynamo in the majority of cases. We find no evidence for MSC-effect-driven dynamos in our simulations.

Stellar winds are an integral part of the underlying dynamo, the motor of stellar activity. The wind controls the star's angular momentum loss, which depends on the magnetic field geometry which varies significantly in time and latitude. Here we study basic properties of a self-consistent model that includes simple representations of both the global stellar dynamo in a spherical shell and the exterior in which the wind accelerates and becomes supersonic. We numerically solve an axisymmetric mean-field model for the induction, momentum, and continuity equations using an isothermal equation of state. The model allows for the simultaneous generation of a mean magnetic field and the development of a Parker wind. The resulting flow is transonic at the critical point, which we arrange to be between the inner and outer radii of the model. The boundary conditions are assumed to be such that the magnetic field is antisymmetric about the equator, i.e., dipolar. At the solar rotation rate, the dynamo is oscillatory and of $\alpha^2$ type. In most of the domain, the magnetic field corresponds to that of a split monopole. The magnetic energy flux is largest between the stellar surface and the critical point. The angular momentum flux is highly variable in time and can reach negative values, especially at midlatitudes. At rapid rotation of up to 50 times the solar value, most of the magnetic field is lost along the axis within the inner tangential cylinder of the model. The model reveals unexpected features that are not generally anticipated from models that are designed to reproduce the solar wind: highly variable angular momentum fluxes even from just an $\alpha^2$ dynamo in the star. A major caveat of our isothermal models with a magnetic field produced by a dynamo is the difficulty to reach small enough plasma betas without the dynamo itself becoming unrealistically strong inside the star.

A handedness in the arrival directions of high-energy photons from outside our Galaxy can be related to the helicity of an intergalactic magnetic field. Previous estimates by arXiv:1310.4826 and arXiv:1412.3171 showed a hint of a signal present in the photons observed by the Fermi Large Area Telescope (LAT). An update on the measurement of handedness in Fermi-LAT data is presented using more than 10 years of observations. Simulations are performed to study the uncertainty of the measurements, taking into account the structure of the exposure caused by the energy-dependent instrument response and its observing profile, as well as the background from the interstellar medium. The simulations are required to accurately estimate the uncertainty and to show that previously the uncertainty was significantly underestimated. The apparent signal in the earlier analysis of \em Fermi-LAT data is rendered non-significant.

Motivated by a scenario of magnetogenesis in which a homogeneous magnetic field is generated during inflation, we study the magnetohydrodynamic evolution of the primordial plasma motions for two kinds of initial conditions -- (i) a spatially homogeneous field with an unlimited correlation length, and (ii) a zero flux scale-invariant statistically homogeneous magnetic field. In both cases, we apply, for a short initial time interval, monochromatic forcing at a certain wave number so that the correlation length is finite, but much smaller than the typical length scale of turbulence. In particular, we investigate the decay of nonhelical and helical hydromagnetic turbulence. We show that, in the presence of a homogeneous magnetic field, the decay of helical and nonhelical small-scale fields can occur rapidly. This is a special property of a system with a perfectly homogeneous magnetic field, which is sometimes considered as a local approximation to a slowly varying background field. It can never change and acts as an imposed magnetic field. This is in a sharp contrast to the case of a statistically homogeneous magnetic field, where we recover familiar decay properties: a much slower decay of magnetic energy and a faster growth of the correlation length, especially in the case with magnetic felicity. The result suggests that a homogeneous magnetic field, if generated during inflation, should persist under the influence of small-scale fields and could be the origin of the large-scale magnetic field in the Universe.

We discuss selected aspects regarding the magnetic field evolution of solar-type stars. Most of the stars with activity cycles are in the range where the normalized chromospheric Calcium emission increases linearly with the inverse Rossby number. For Rossby numbers below about a quarter of the solar value, the activity saturates and no cycles have been found. For Rossby numbers above the solar value, again no activity cycles have been found, but now the activity goes up again for a major fraction of the stars. Rapidly rotating stars show nonaxisymmetric large-scale magnetic fields, but there is disagreement between models and observations regarding the actual value of the Rossby number where this happens. We also discuss the prospects of detecting the sign of magnetic helicity using various linear polarization techniques both at the stellar surface using the parity-odd contribution to linear polarization and above the surface using Faraday rotation.

The large-scale magnetic field of the Milky Way is thought to be created by an alpha-Omega dynamo, which implies that it should have opposite handedness North and South of the Galactic midplane. Here we attempt to detect a variation in handedness using polarization data from the Wilkinson Microwave Anisotropy Probe. Previous analyzes of the parity-even and parity-odd parts of linear polarization of the global dust and synchrotron emission have focused on quadratic correlations in spectral space of, and between, these two components. Here, by contrast, we analyze the parity-odd polarization itself and show that it has, on average, opposite signs in Northern and Southern Galactic hemispheres. Comparison with a Galactic mean-field dynamo model shows broad qualitative agreement and reveals that the sign of the observed hemispheric dependence of the azimuthally averaged parity-odd polarization is not determined by the sign of alpha, but by the sense of differential rotation.

We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the center of the galaxy and are not a signature of magnetic helicity.

The alpha effect is believed to play a key role in the generation of the solar magnetic field. A fundamental test for its significance in the solar dynamo is to look for magnetic helicity of opposite signs in the two hemispheres, and at small and large scales. However, measuring magnetic helicity is compromised by the inability to fully infer the magnetic field vector from observations of solar spectra, caused by what is known as the "pi ambiguity" of spectropolarimetric observations. We decompose linear polarisation into parity-even and parity-odd E and B polarisations, which are not affected by the "pi ambiguity". Furthermore, we study whether the correlations of spatial Fourier spectra of B and parity-even quantities such as E or temperature T are a robust proxy for magnetic helicity of solar magnetic fields. We analyse polarisation measurements of active regions observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics observatory. Theory predicts the magnetic helicity of active regions to have, statistically, opposite signs in the two hemispheres. We then compute the parity-odd E B and T B correlations, and test for systematic preference of their sign based on the hemisphere of the active regions. We find that: (i) E B and T B correlations are a reliable proxy for magnetic helicity, when computed from linear polarisation measurements away from spectral line cores, and (ii) E polarisation reverses its sign close to the line core. Our analysis reveals Faraday rotation to not have a significant influence on the computed parity-odd correlations. The EB decomposition of linear polarisation appears to be a good proxy for magnetic helicity independent of the "pi ambiguity". This allows us to routinely infer magnetic helicity directly from polarisation measurements.

For velocity and magnetic fields, the turbulent pressure and, more generally, the squared fields such as the components of the turbulent stress tensor, play important roles in astrophysics. For both one and three dimensions, we derive the equations relating the energy spectra of the fields to the spectra of their squares. We solve the resulting integrals numerically and show that for turbulent energy spectra of Kolmogorov type, the spectral slope of the stress spectrum is also of Kolmogorov type. For shallower turbulence spectra, the slope of the stress spectrum quickly approaches that of white noise, regardless of how blue the spectrum of the field is. For fully helical fields, the stress spectrum is elevated by about a factor of two in the subinertial range, while that in the inertial range remains unchanged. We discuss possible implications for understanding the spectrum of primordial gravitational waves from causally generated magnetic fields during cosmological phase transitions in the early universe. We also discuss potential diagnostic applications to the interstellar medium, where polarization and scintillation measurements characterize the square of the magnetic field.

In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (2012, Phys. Rev. Lett. 109, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behavior is different from that of an alpha^2 dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time-dependent. The growing mean field can be modeled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (2015, J. Fluid Mech. 783, 23), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15% supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos.

We study a turbulent helical dynamo in a periodic domain by solving the ideal magnetohydrodynamic (MHD) equations with the FLASH code using the divergence-cleaning eight-wave method and compare our results with direct numerical simulations (DNS) using the Pencil Code. At low resolution, FLASH reproduces the DNS results qualitatively by developing the large-scale magnetic field expected from DNS, but at higher resolution, no large-scale magnetic field is obtained. In all those cases in which a large-scale magnetic field is generated, the ideal MHD results yield too little power at small scales. As a consequence, the small-scale current helicity is too small compared with that of the DNS. The resulting net current helicity has then always the wrong sign, and its statistical average also does not approach zero at late times, as expected from the DNS. Our results have implications for astrophysical dynamo simulations of stellar and galactic magnetism using ideal MHD codes.

If the alpha effect plays a role in the generation of the Sun's magnetic field, the field should show evidence of magnetic helicity of opposite signs at large and small length scales. Measuring this faces two challenges: (i) in weak-field regions, horizontal field measurements are unreliable because of the pi ambiguity, and (ii) one needs a truly global approach to computing helicity spectra in the case where one expects a sign reversal across the equator at all wavenumbers. Here we develop such a method using spin-2 spherical harmonics to decompose the linear polarization in terms of the parity-even and parity-odd E and B polarizations, respectively. Using simple one- and two-dimensional models, we show that the product of the spectral decompositions of E and B, taken at spherical harmonic degrees that are shifted by one, can act as a proxy of the global magnetic helicity with a sign that represents that in the northern hemisphere. We then apply this method to the analysis of solar synoptic vector magnetograms, from which we extract a pseudo-polarization corresponding to a "pi-ambiguated" magnetic field, i.e., a magnetic field vector that has no arrow. We find a negative sign of the global EB helicity proxy at spherical harmonic degrees of around 6. This could indicate a positive magnetic helicity at large length scales, but the spectrum fails to capture clear evidence of the well-known negative magnetic helicity at smaller scales. This method might also be applicable to stellar and Galactic polarization data.

Large-scale magnetic fields in stars and galaxies are thought to arise by mean-field dynamo action due to the combined influence of both helical turbulence and shear. Those systems are also highly conducting and the turbulence therein leads to a fluctuation (or small-scale) dynamo which more rapidly amplifies magnetic field fluctuations on the eddy scales and smaller. Will this then interfere with and suppress the mean (or large-scale) field growth? Using direct numerical simulations of helical turbulence (with and without shear), we identify a novel quasi-kinematic large-scale dynamo which operates as the small-scale dynamo saturates. Thus both dynamos operate efficiently, one after the other, and lead to the generation of significant large-scale fields.

We show that at large magnetic Prandtl numbers, the Lorentz force does work on the flow at small scales and drives fluid motions, whose energy is dissipated viscously. This situation is opposite to that in a normal dynamo, where the flow does work against the Lorentz force. We compute the spectral conversion rates between kinetic and magnetic energies for several magnetic Prandtl numbers and show that normal (forward) dynamo action occurs on large scales over a progressively narrower range of wavenumbers as the magnetic Prandtl number is increased. At higher wavenumbers, reversed dynamo action occurs, i.e., magnetic energy is converted back into kinetic energy at small scales. We demonstrate this in both direct numerical simulations forced by volume stirring and in large eddy simulations of solar convectively driven small-scale dynamos. Low density plasmas such as stellar coronae tend to have large magnetic Prandtl numbers, i.e., the viscosity is large compared with the magnetic diffusivity. The regime in which viscous dissipation dominates over resistive dissipation for large magnetic Prandtl numbers was also previously found in large eddy simulations of the solar corona, i.e., our findings are a more fundamental property of MHD that is not just restricted to dynamos. Viscous energy dissipation is a consequence of positive Lorentz force work, which may partly correspond to particle acceleration in close-to-collisionless plasmas. This is, however, not modeled in the MHD approximation employed. By contrast, resistive energy dissipation on current sheets is expected to be unimportant in stellar coronae.

We study the effects of ambipolar diffusion (AD) on hydromagnetic turbulence. In most of the cases, we use the single fluid approximation where the drift velocity between charged and neutral particles is proportional to the Lorentz force. In two cases we also compare with the corresponding two-fluid model, where ionization and recombination are included in the continuity and momentum equations for the neutral and charged species. We consider the regime of large magnetic Prandtl number, relevant to the interstellar medium. The magnetic field properties are found to be well represented by the single fluid approximation. We quantify the effects of AD on total and spectral kinetic and magnetic energies, the Ohmic and AD dissipation rates, the statistics of the magnetic field, the current density, and the linear polarization as measured by the rotationally invariant E and B mode polarizations. We show that the kurtosis of the magnetic field decreases with increasing AD. The E mode polarization changes its skewness from positive values for small AD to negative ones for large AD. Even when AD is weak, changes in AD have a marked effect on the skewness and kurtosis of E, and only a weak effect on those of B. These results open the possibility of employing E and B mode polarizations as diagnostic tools for characterizing turbulent properties of the interstellar medium.

We perform direct numerical simulations of magnetohydrodynamic turbulence in the early universe and numerically compute the resulting stochastic background of gravitational waves and relic magnetic fields. These simulations do not make the simplifying assumptions of earlier analytic work. If the turbulence is assumed to have an energy-carrying scale that is about a hundredth of the Hubble radius at the time of generation, as expected in a first-order phase transition, the peak of gravitational wave power will be in the mHz frequency range for a signal produced at the electroweak scale. The efficiency of gravitational wave (GW) production varies significantly with how the turbulence is driven. Detectability of turbulence at the electroweak scale by the planned Laser Interferometer Space Antenna (LISA) requires anywhere from 0.1% to 10% of the thermal plasma energy density to be in plasma motions or magnetic fields, depending on the model of the driving process. Our results predict a new universal form below the spectral peak frequency that is shallower than previously thought. This implies larger values of the GW energy spectra in the low-frequency range. This extends the range where turbulence is detectable with LISA to lower frequencies, corresponding to higher energy scales than the assumed energy-carrying scale.

We compute magnetic helicity and energy spectra from about 2485 patches of about 100 megameters (Mm) side length on the solar surface using data from Hinode during 2006--2017. An extensive database is assembled where we list magnetic energy and helicity, large- and small-scale magnetic helicity, mean current helicity density, fractional magnetic helicity, and correlation length along with the Hinode map identification number (MapID), as well as Carrington latitude and longitude for each MapID. While there are departures from the hemispheric sign rule for magnetic and current helicities, the weak trend reported here is in agreement with the previous results. This is argued to be a physical effect associated with the dominance of individual active regions that contribute more strongly in the better resolved Hinode maps. In comparison with earlier work, the typical correlation length is found to be 6-8 Mm, while the length scale relating magnetic and current helicity to each other is found to be around 1.4 Mm.

Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudo-vacuum condition on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha^2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, most of the magnetic helicity losses occur at large scales. Whether this changes at even larger magnetic Reynolds numbers, as required for alleviating the catastrophic dynamo quenching problem, remains still unclear.

Explicit radiation hydrodynamic simulations of the atmospheres of massive stars and of convection in accretion discs around white dwarfs suffer from prohibitively short time steps due to radiation. This constraint is related to the cooling time rather than the radiative pressure, which also becomes important in hot stars and discs. We show that the radiative time step constraint is governed by the minimum of the sum of the optically thick and thin contributions rather than the smaller one of the two. In simulations with the Pencil Code, their weighting fractions are found empirically. In three-dimensional convective accretion disc simulations, the Deardorff term is found to be the main contributor to the enthalpy flux rather than the superadiabatic gradient. We conclude with a discussion of how the radiative time step problem could be mitigated in certain types of investigations.

We study the evolution of kinetic and magnetic energy spectra in magnetohydrodynamic flows in the presence of strong cross helicity. For forced turbulence, we find weak inverse transfer of kinetic energy toward the smallest wavenumber. This is plausibly explained by the finiteness of scale separation between the injection wavenumber and the smallest wavenumber of the domain, which here is a factor of 15. In the decaying case, there is a slight increase at the smallest wavenumber, which is probably explained by the dominance of kinetic energy over magnetic energy at the smallest wavenumbers. Within a range of wavenumbers covering almost an order of magnitude the decay is purely exponential, which is argued to be a consequence of a suppression of nonlinearity due to the presence of strong cross helicity.

(abridged) Context: Turbulent diffusion of large-scale flows and magnetic fields play major roles in many astrophysical systems. Aims: Our goal is to compute turbulent viscosity and magnetic diffusivity, relevant for diffusing large-scale flows and magnetic fields, respectively, and their ratio, the turbulent magnetic Prandtl number, ${\rm Pm}_{\rm t}$, for isotropically forced homogeneous turbulence. Methods: We use simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity is computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity is computed using the test-field method. The scale dependence of the coefficients is studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results: We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (${\rm Re}$) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. The results for the turbulent transport coefficients appear to converge at sufficiently high values of ${\rm Re}$ and the scale separation ratio. However, a weak decreasing trend is found even at the largest values of ${\rm Re}$. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large ${\rm Re}$ whereas for small ${\rm Re}$, we find values between 0.5 and 0.6. Conclusions: The turbulent magnetic diffusivity is in general consistently higher than the turbulent viscosity. The actual value of ${\rm Pm}_{\rm t}$ found from the simulations ($\approx0.9\ldots0.95$) at large ${\rm Re}$ and scale separation ratio is higher than any of the analytic predictions.

Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the $f$-mode, which emerges from the density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localized bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the $f$-mode is significantly larger at high horizontal wavenumbers $k$, but the fanning is weaker for the localized subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the $f$-mode in the $k\omega$ diagram increases proportionally in such a way that the normalized $f$-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localized magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the $f$-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of $f$-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots.

The chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in the Maxwell equations leads to a modified set of MHD equations. We discuss how the CME is implemented in the PENCIL CODE. The CME plays a key role in the evolution of magnetic fields since it results in a dynamo effect associated with an additional term in the induction equation. This term is formally similar to the $\alpha$ effect in classical mean-field MHD. However, the chiral dynamo can operate without turbulence and is associated with small spatial scales that can be, in the case of the early Universe, orders of magnitude below the Hubble radius. A chiral $\alpha_\mu$ effect has also been identified in mean-field theory. It occurs in the presence of turbulence but is not related to kinetic helicity. Depending on the plasma parameters, chiral dynamo instabilities can amplify magnetic fields over many orders of magnitude. These instabilities can affect the propagation of MHD waves, which is demonstrated by our DNS. We also study the coupling between the evolution of the chiral chemical potential and the ordinary chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. An important consequence of this coupling is the emergence of chiral magnetic waves (CMWs). We confirm numerically that linear CMWs and MHD waves are not interacting. Our simulations suggest that the chemical potential has only a minor effect on the non-linear evolution of the chiral dynamo.

Gradient- and curl-type or E- and B-type polarizations have been routinely analyzed to study the physics contributing to the cosmic microwave background polarization and galactic foregrounds. They characterize the parity-even and parity-odd properties of the underlying physical mechanisms, for example hydromagnetic turbulence in the case of dust polarization. Here we study spectral correlation functions characterizing the parity-even and parity-odd parts of linear polarization for homogeneous and inhomogeneous turbulence to show that only the inhomogeneous helical case can give rise to a parity-odd polarization signal. We also study nonhelical turbulence and suggest that a strong nonvanishing (here negative) skewness of the E polarization is responsible for an enhanced ratio of the EE to the BB (quadratic) correlation in both helical and nonhelical cases. This could explain the enhanced EE/BB ratio observed recently for dust polarization. We close with a preliminary assessment of using linear polarization of the Sun to characterize its helical turbulence without being subjected to the pi ambiguity that magnetic inversion techniques have to address.

The full-sky Planck polarization data at 850um revealed unexpected properties of the E and B mode power spectra of dust emission in the interstellar medium (ISM). The positive cross-correlation between the total dust intensity, T, with the B modes has raised new questions about the physical mechanisms that affect dust polarization, such as the Galactic magnetic-field structure. This is key both to better understanding ISM dynamics and to accurately describing Galactic foregrounds to the polarization of the Cosmic Microwave Background (CMB). In this theoretical paper we investigate the possibility that the observed cross-correlations in the dust polarization power spectra, and specifically between T and B, can be related to a parity-odd quantity in the ISM such as the magnetic helicity. We produce synthetic dust polarization data, derived from 3D analytical toy models of density structures and helical magnetic fields, to compare with the E and B modes of observations. Focusing on the observed T-B correlation, we propose a new line of interpretation of the Planck observations based on a large-scale helical component of the Galactic magnetic field in the solar neighborhood. Our analysis shows that: I) the sign of magnetic helicity does not affect E and B modes for isotropic magnetic-field configurations; II) helical magnetic fields threading interstellar filaments cannot reproduce the Planck results; III) a weak helical left-handed magnetic field structure in the solar neighborhood may explain the T-B correlation seen in the Planck data. This work suggests a new perspective for the interpretation of the dust polarization power spectra, which strongly supports the imprint of a large-scale structure of the Galactic magnetic field in the solar neighborhood.

We test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent convection simulations with respect to Mach number, thermal and magnetic boundary conditions, and the centrifugal force. We find that varying the luminosity, which also controls the Mach number, has only a minor effect on the large-scale dynamics. A similar conclusion can also be drawn from the comparison of two formulations of the lower magnetic boundary condition with either vanishing electric field or current density. The centrifugal force has an effect on the solutions, but only if its magnitude with respect to acceleration due to gravity is by two orders of magnitude greater than in the Sun. Finally, we find that the parameterisation of the photospheric physics, either by an explicit cooling term or enhanced radiative diffusion, is more important than the thermal boundary condition. In particular, runs with cooling tend to lead to more anisotropic convection and stronger deviations from the Taylor-Proudman state. In summary, the fully compressible approach taken here with the Pencil Code is found to be valid, while still allowing the disparate timescales to be taken into account.