In this paper, we propose a novel minimal physical model to elucidate the long-term stochastic variability of blazars. The model is built on the realistic background of magnetized plasma jets dissipating energy through a turbulent cascade process that transfers energy to small-scale structures with highly anisotropic radiation. The model demonstrates the ability to spontaneously generate variability features consistent with observations of blazars under uniformly random fluctuations in the underlying physical parameters. This indicates that the model possesses self-similarity across multiple time scales, providing a natural explanation for the universal power spectral density (PSD) structure observed in different types of blazars. Moreover, the model exhibits that when the cascade process produces a relatively flat blob energy distribution, the spectral index of the model-simulated PSD in the high-frequency regime will be steeper than that predicted by the Damped Random Walk (DRW) model, which is in agreement with recent observations of active galactic nucleus (AGN) variability, providing a plausible theoretical explanation. The model is also able to reproduce the observed fractional variability amplitude (FVA) characteristics of blazars, and suggests that the specific particle acceleration and radiative cooling processes within the blob may not be the key factor shaping the long-term stochastic variability. This minimal model provides a new physical perspective for understanding the long-term stochastic variability of blazars.
Secondary γ-rays from intergalactic cascades may contribute to observable spectra of blazars, also modifying observable angular and temporal distributions. In this paper we briefly review basic features of intergalactic electromagnetic cascade physics, suggest a new approximation for γ-ray mean free path, consider angular patterns of magnetically broadened cascade emission, and present an example of a fit to the observable blazar spectrum.
We present a very brief overview of some recent gamma-ray observations of selected blazars to reveal an indication for a considerable or even dominant contribution of secondary gamma-rays from electromagnetic cascades to the observable spectra in the 1-500 GeV energy range.
It is well known that the effect of gamma-ray absorption on extragalactic background light (EBL) is weakly expressed in the spectra of some blazars. It is shown that a secondary component generated by electromagnetic cascades might considerably decrease the statistical significance of this anomaly. Observational results indicate the existence of the cascade component in the spectra of extragalactic gamma-ray sources, thus supporting the proposed model.
Recent blazar detections by HESS, MAGIC, and VERITAS suggest that very-high-energy (VHE, E > 100 GeV) gamma-rays may be produced in most, if not all, types of blazars, including those that possess intense circumnuclear radiation fields. In this paper, we investigate the interaction of nuclear VHE gamma-rays with the circumnuclear radiation fields through gamma-gamma absorption and pair production, and the subsequent Compton-supported pair cascades. We have developed a Monte-Carlo code to follow the spatial development of the cascade in full 3-dimensional geometry, and calculate the radiative o…
The author is developing a numerical code with thousands of emission zones to simulate the time-dependent multi-waveband emission from blazars. The code is based on a model in which turbulent plasma flowing at a relativistic speed down a jet crosses a standing conical collimation shock that accelerates electrons to maximum energies in the 5-100 GeV range. This paper reports early results produced by the model. The simulated light curves and time profiles of the degree and position angle of polarization have a number of features in common with the observational data of blazars. Maps of the pola…
Attenuation of the TeV gamma-ray flux from distant blazars through pair production with extragalactic background light leads to the development of electromagnetic cascades and subsequent, lower energy, GeV secondary gamma-ray emission. Due to the deflection of VHE cascade electrons by extragalactic magnetic fields (EGMF), the spectral shape of this arriving cascade gamma-ray emission is dependent on the strength of the EGMF. Thus, the spectral shape of the GeV-TeV emission from blazars has the potential to probe the EGMF strength along the line of sight to the object. We investigate constraint…
Time-variable polarization is an extremely valuable observational tool to probe the dynamical physical conditions of blazar jets. Since 2008, we have been monitoring the flux and linear polarization of a sample of gamma-ray bright blazars at optical frequencies. Some of the observations were performed on nightly or intra-night time-scales in four optical bands, providing information on the frequency and time dependence of the polarization. The observed behavior is similar to that found in simulations of turbulent plasma in a relativistic jet that contains a standing shock and/or a helical back…
Context. Most of the studies on extragalactic γ-ray propagation performed up to now only accounted for primary gamma-ray absorption and adiabatic losses ("absorption-only model"). However, there is growing evidence that this model is oversimplified and must be modified in some way. In particular, it was found that the intensity extrapolated from the optically-thin energy range of some blazar spectra is insufficient to explain the optically-thick part of these spectra. This effect was interpreted as an indication for γ-axion-like particle (ALP) oscillation. On the other hand, there are many hin…
As very high energy (VHE) photons propagate through the extragalactic background light (EBL), they interact with the soft photons and initiate electromagnetic cascades of lower energy photons and electrons. The collective intensity of a cosmological population emitting at VHEs will be attenuated at the highest energies through interactions with the EBL and enhanced at lower energies by the resulting cascade. We calculate the cascade radiation created by VHE photons produced by blazars and investigate the effects of cascades on the collective intensity of blazars and the resulting effects on th…
We investigate the spectral properties of the brightest gamma-ray flares of blazars detected by the Fermi Large Area Telescope. We search for the presence of spectral breaks and measure the spectral curvature on typical time scales of a few days. We identify significant spectral breaks in fewer than half of the analyzed flares, but their parameters do not show any discernible regularities, and in particular there is no indication for gamma-ray absorption at any fixed source-frame photon energy. More interestingly, we find that the studied blazars are characterized by significant spectral varia…
Recently, particle in cell (PIC) simulations have shown that relativistic turbulence in collisionless plasmas can result in an equilibrium particle distribution function where turbulent heating is balanced by radiative cooling of electrons. Strongly magnetized plasmas are characterized by higher energy peaks and broader particle distributions. In relativistically moving astrophysical jets, it is believed that the flow is launched Poynting flux dominated and that the resulting magnetic instabilities may create a turbulent environment inside the jet, i.e., the regime of relativistic turbulence. …
Context. Very high-energy (VHE) $γ$-ray measurements of distant TeV blazars can be nicely explained by TeV spectra induced by ultra high-energy cosmic rays. Aims. We develop a model for a plausible origin of hard spectra in distant TeV blazars. Methods. In the model, the TeV emission in distant TeV blazars is dominated by two mixed components. The first is the internal component with the photon energy around 1 TeV produced by inverse Compton scattering of the relativistic electrons on the synchrotron photons (SSC) with a correction for extragalactic background light absorbtion and the other is…
Low ($\lesssim 1\%$) levels of circular polarization (CP) detected at radio frequencies in the relativistic jets of some blazars can provide insight into the underlying nature of the jet plasma. CP can be produced through linear birefringence, in which initially linearly polarized emission produced in one region of the jet is altered by Faraday rotation as it propagates through other regions of the jet with varying magnetic field orientation. Marscher has begun a study of jets with such magnetic geometries using the Turbulent Extreme Multi-Zone (TEMZ) model, in which turbulent plasma crossing …
Recent data from the \emph{Fermi} Large Area Telescope have revealed about a dozen distant hard-spectrum blazars that have very-high-energy (VHE; $\gtrsim 100$ GeV) photons associated with them, but most of them have not yet been detected by imaging atmospheric Cherenkov telescopes. Most of these high-energy gamma-ray spectra, like those of other extreme high-frequency peaked BL Lac objects, can be well explained either by gamma rays emitted at the source or by cascades induced by ultra-high-energy cosmic rays, as we show specifically for KUV 00311$-$1938. We consider the prospects for detecti…
Extreme TeV blazars (ETBs) are active galactic nuclei with jets presumably pointing towards the observer having their intrinsic spectral energy distributions (SEDs) peaked at an energy in excess of 1 TeV. These sources typically reveal relatively weak and slow variability as well as an extremely high frequency of the low-energy SED peak compared to other classes of blazars. It proved to be exceedingly hard to incorporate all these peculiar properties of ETBs into the framework of a reasonable $γ$-ray emission model. ETB physics have recently attracted great attention in the astrophysical commu…
Blazars may accelerate protons and/or nuclei as well as electrons. The hadronic component of accelerated particles in blazars may constitute the bulk of their high-energy budget; nevertheless, this component is elusive due to a high value of the energy threshold of proton interaction with photon fields inside the source. However, broad line regions (BLRs) of some flat spectrum radio quasars (FSRQs) may contain a sufficient amount of matter to render primary protons "visible" in $γ$ rays via hadronuclear interactions. In the present paper we study the persistent $γ$-ray emission of the FSRQ PKS…
We estimate the contribution to the extragalactic gamma-ray background (EGRB) from both intrinsic and cascade emissions produced by blazars using a simple semi- analysis method for two models of the blazar gamma-ray luminosity function (GLF). For the cascade emission, we consider two possible contributions: one is due to that the flux of the cascade emission is lower than the Fermi LAT sensitivity (case I), which is independent on the extragalactic magnetic field (EGMF), another is due to the fact that the flux of the cascade emission is larger than the Fermi LAT sensitivity but the emission a…
Most of the recent research on extragalactic $γ$-ray propagation focused on the study of the $γγ\rightarrow e^{+}e^{-}$ absorption process ("absorption-only model"). Starting from a possible anomaly at very high energies (VHE, E >100 GeV), we briefly review several existing deviations from this model. The exotic interpretation of the VHE anomaly is not supported by the recent works. On the other hand, the process of intergalactic electromagnetic cascade development naturally explains these effects. We discuss phenomenology of intergalactic cascades and the main spectral signatures of the elect…
A non-zero intergalactic magnetic field (IGMF) would potentially produce detectable effects on cascade emission from blazars. Depending on the strength of the IGMF, the cascade emission may be time delayed or angularly broadened compared to the blazar's primary, unscattered emission. Ground-based imaging atmospheric-Cherenkov telescopes, such as VERITAS, have the precise angular resolution needed to search for magnetically-broadened emission. We present the latest VERITAS results on the search for extended gamma-ray emission, based on observations of a number of strongly-detected TeV blazars a…
As very-high--energy photons propagate through the extragalactic background light (EBL), they interact with the soft photons and initiate electromagnetic cascades of lower energy photons and electrons. The collective intensity of a cosmological population emitting at very-high energies (VHE) will be attenuated at the highest energies through interactions with the EBL and enhanced at lower energies by the resulting cascade. We calculate the cascade radiation created by VHE photons produced by blazars and investigate the effects of cascades on the collective intensity of blazars and the resultin…
Blazars are among the most powerful accelerators and are expected to produce a bright TeV $γ$-ray flux. However, TeV $γ$-rays are attenuated by interactions with intergalactic radiation before reaching Earth. These interactions produce cascades that transfer TeV power into the GeV band, powering both extended halos around bright sources and a large contribution to the isotropic $γ$-ray background (IGRB). Using conservative blazar models and recent IGRB measurements, we rule out scenarios where blazars effectively transfer their multi-TeV power into GeV $γ$-rays. Three possible solutions includ…
Recent progress in very high energy (VHE, E >100 GeV) $γ$-ray observations, together with advances in the extragalactic background light (EBL) modelling, allows to search for new phenomena such as $γ$-axion-like particle ($γ\rightarrow$ ALP) oscillation and to explore the extragalactic magnetic field (EGMF) strength and structure. These studies are usually performed by searching for some deviation from the so-called absorption-only model, that accounts for only primary photon absorption on the EBL and adiabatic losses. In fact, there exist several indications that the absorption-only model is …
TeV emission from blazars can be used to probe the intergalactic magnetic fields and measure their intensity, coherence length, and helicity. Intergalactic magnetic fields deflect the electron-positron pairs produced by very-high-energy gamma-rays from blazars, resulting in broadened beams of cascade gamma-rays developing along the projected direction of the blazar jet. We present an analysis that uses for the first time the jet orientation of 12 high-synchrotron-peaked (HSP) BL~Lac-type blazars from VLBA radio observations to search for signatures of pair haloes in the Fermi-LAT data. Our sea…
The observation in the GeV band of distant blazars has been recently used to put constraints on the Extragalactic Background Light (EBL) and Extragalactic Magnetic Fields (EGMF). To support such claims one has to assume that the leptonic component of the electromagnetic cascade initiated by blazar gamma-rays is deflected away by strong enough EGMF, suppressing the signal in the Fermi window. Apart from magnetic fields, the development of such a cascade might be affected by plasma instabilities due to interactions with the ionized component of the Intergalactic Medium (IGM). In this paper we mo…
The author presents a model for variability of the flux and polarization of blazars in which turbulent plasma flowing at a relativistic speed down a jet crosses a standing conical shock. The shock compresses the plasma and accelerates electrons to energies up to gamma(max) > 1E4 times their rest-mass energy, with the value of gamma(max) determined by the direction of the magnetic field relative to the shock front. The turbulence is approximated in a computer code as many cells, each with a uniform magnetic field whose direction is selected randomly. The density of high-energy electrons in the …
This work revisits the electrostatic instability for blazar-induced pair beams propagating through IGM with the methods of linear analysis and PIC simulations. We study the impact of the realistic distribution function of pairs resulting from interaction of high-energy gamma-rays with the extragalactic background light. We present analytical and numerical calculations of the linear growth rate of the instability for arbitrary orientation of wave vectors. Our results explicitly demonstrate that the finite angular spread of the beam dramatically affects the growth rate of the waves, leading to f…
We discuss the production of ultra-high-energy cosmic ray (UHECR) nuclei and neutrinos from blazars. We compute the nuclear cascade in the jet for both BL Lac objects and flat-spectrum radio quasars (FSRQs), and in the ambient radiation zones for FSRQs as well. By modeling representative spectral energy distributions along the blazar sequence, two distinct regimes are identified, which we call "nuclear survival" -- typically found in low-luminosity BL Lacs, and "nuclear cascade" -- typically found in high-luminosity FSRQs. We quantify how the neutrino and cosmic-ray (CR) emission efficiencies …
We present a search for magnetically broadened gamma-ray emission around active galactic nuclei (AGN), using VERITAS observations of seven hard-spectrum blazars. A cascade process occurs when multi-TeV gamma rays from AGN interact with extragalactic background light (EBL) photons to produce electron-positron pairs, which then interact with cosmic microwave background (CMB) photons via inverse-Compton scattering to produce gamma rays. Due to the deflection of the electron-positron pairs, a non-zero intergalactic magnetic field (IGMF) would potentially produce detectable effects on the angular d…
We briefly review contemporary extragalactic γ-ray propagation models. It is shown that the Extragalactic Magnetic Field (EGMF) strength and structure are poorly known. Strict lower limits on the EGMF strength in voids are of order 10^{-17}--10^{-20} G, thus allowing a substantial contribution of a secondary component generated by electromagnetic cascades to the observable spectrum. We show that this "electromagnetic cascade model" is supported by data from imaging Cherenkov telescopes and the Fermi LAT detector.
Recent claims that the strength B_IGMF of the intergalactic magnetic field (IGMF) is >~ 1e-15 G are based on upper limits to the expected cascade flux in the GeV band produced by blazar TeV photons absorbed by the extragalactic background light. This limit depends on an assumption that the mean blazar TeV flux remains constant on timescales >~2 (B_ IGMF/1e-18 G)^2 / (E/{10 GeV})^2 yr for an IGMF coherence length ~ 1 Mpc, where E is the measured photon energy. Restricting TeV activity of 1ES 0229+200 to ~3 -- 4 years during which the source has been observed leads to a more robust lower limit o…
The typical blazar S5 0716$+$714 is very interesting due to its rapid and large amplitude variability and high duty cycle of micro-variability in optical band. We analyze the observations in I, R and V bands obtained with the $1.0m$ telescope at Weihai observatory of Shandong University from 2011 to 2018. The model of synchrotron radiation from turbulent cells in a jet has been proposed as a mechanism for explaining micro-variability seen in blazar light curves. Parameters such as the sizes of turbulent cells, the enhanced particle densities, and the location of the turbulent cells in the jet …
Recent detections of very-high-energy (VHE, E > 100 GeV) gamma-ray blazars which do not belong to the high frequency peaked BL Lac (HBL) class, suggest that gamma-gamma absorption and pair cascading might occur in those objects. In the presence of even weak magnetic fields, these Compton-supported pair cascades will be deflected and contribute to the Fermi gamma-ray flux of radio galaxies. We demonstrate that, in this scenario, the magnetic field can not be determined from a fit of the cascade emission to the gamma-ray spectrum alone, and the degeneracy can only be lifted if the synchrotron em…
The peculiar high-energy emission spectrum of the so-called extreme BL Lacs (EHBL) challenges the standard emission models of blazars. Among the possible solutions, the so-called hadronic cascade scenario assumes that the observed high-energy radiation is produced in the intergalactic space through photo-hadronic reactions by ultra-high energy cosmic rays (UHECR) with energies up to $10^{19-20}$ eV beamed by the blazar jet. Under the assumption -- implicit in this model -- that the intrinsic high-energy synchrotron-self Compton emission of the blazar does not substantially contribute to the ob…
We statistically examine the gamma-ray burst (GRB) photon indices obtained by the Fermi-GBM and Fermi-LAT observations and compare the LAT GRB photon indices to the GBM GRB photon indices. We apply the jitter radiation to explain the GRB spectral diversities in the high-energy bands. In our model, the jitter radiative spectral index is determined by the spectral index of the turbulence. We classify GRBs into three classes depending on the shape of the GRB high-energy spectrum when we compare the GBM and LAT detections: the GRB spectrum is concave (GRBs turn out to be softer and are labeled as …
The intergalactic magnetic field (IGMF) in cosmic voids can be indirectly probed through its effect on electromagnetic cascades initiated by a source of TeV gamma rays, such as blazars, a subclass of active galactic nuclei. Blazars that are sufficiently luminous at TeV energies, "extreme TeV blazars", can produce detectable levels of secondary radiation from inverse Compton scattering of the electrons in the cascade, provided that the IGMF is not too large. We reveiw recent work in the literature which utilizes this idea to derive constraints on the IGMF for three TeV-detected blazars-1ES 0229…
Ultrahigh energy protons and nuclei from extragalactic cosmic ray sources initiate intergalactic electromagnetic cascades, resulting in observable fluxes of $γ$-rays in the GeV-TeV energy domain. The total spectrum of such cascade $γ$-rays of hadronic nature is significantly harder than the one usually expected from blazars. The spectra of some sources known as "extreme TeV blazars" could be well-described by this "intergalactic hadronic cascade model" (IHCM). We calculate the shape of the observable point-like spectrum, as well as the observable angular distibution of $γ$-rays, for the first …
Stochastic acceleration of nonthermal electrons is investigated in the context of hard photon spectra of blazars. It is well known that this acceleration mechanism can produce a hard electron spectrum of $m \equiv \partial \ln n_{\rm e}(γ)/\partial \ln γ= 2$ with the high-energy cutoff, called an ultrarelativistic Maxwellian-like distribution, where $n_{\rm e}(γ)$ is an electron energy spectrum. We revisit the formation of this characteristic spectrum, considering a particular situation where the electrons are accelerated through gyroresonant interaction with magnetohydrodynamic wave turbulenc…
The growing number of extragalactic high-energy (HE, E > 100 MeV) and very-high-energy (VHE, E > 100 GeV) gamma-ray sources that do not belong to the blazar class suggests that VHE gamma-ray production may be a common property of most radio-loud Active Galactic Nuclei (AGN). In a previous paper, we have investigated the signatures of Compton-supported pair cascades initiated by VHE gamma-ray absorption in monochromatic radiation fields, dominated by Ly-alpha line emission from the Broad Line Region. In this paper, we investigate the interaction of nuclear VHE gamma-rays with the thermal infrar…
We present a procedure to generally constrain the environments of neutrino-producing sites in photomeson production models of jetted Active Galactic Nuclei (AGN) where any origin of the dominant target photon field can be accommodated. For this purpose we reconstruct the minimum target photon spectrum required to produce the (observed) neutrino spectrum, and derive the distributions of all corresponding secondary particles. These initiate electromagnetic cascades with an efficiency that is linked to the neutrino production rate. The derived photon spectra represent the minimum radiation emergi…
There is a large variety in the models explaining blazar flares. Here, we study the flare profile induced by a moving and expanding blob with special emphasize on the gamma-gamma pair production. We first develop a simple semi-analytical model to study the evolution of the particle distribution in the expanding blob and show the influence of the pair production. In a second step, we produce a realistic simulation using the OneHaLe code based upon parameters of PKS 1510-089. The semi-analytical model shows that the pair production significantly influences the flare evolution, while the opening …
Blazars show variability on timescales ranging from minutes to years, the former being comparable to and in some cases even shorter than the light-crossing time of the central black hole. The observed gamma-ray lightcurves can be described by a power-law power density spectrum (PDS), with a similar index for both BL Lacs and flat-spectrum radio quasars. We show that this variability can be produced by turbulence in relativistic jets launched by magnetically arrested accretion flows (MADs). We perform radiative transport calculations on the turbulent, highly-magnetized jet launching region of a…
High energy photons from blazars interact within tens of kpc with the extragalactic photon background, initiating electromagnetic pair cascades. The charged component of such cascades is deflected by extragalactic magnetic fields (EGMF), leading to halos even around initially point-like sources. We calculate the intensity profile of the resulting secondary high-energy photons for different assumptions on the initial source spectrum and the strength of the EGMF, employing also fields found earlier in a constrained simulation of structure formation including MHD processes. We find that the obser…
Motivated by the observation of a $>290$ TeV muon neutrino by IceCube, coincident with a $\sim$6 month-long $γ$-ray flare of the blazar TXS 0506+056, and an archival search which revealed $13 \pm 5$ further, lower-energy neutrinos in the direction of the source in 2014-2015, we discuss the likely contribution of blazars to the diffuse high-energy neutrino intensity, the implications for neutrino emission from TXS 0506+056 based on multi-wavelength observations of the source, and a multi-zone model that allows for sufficient neutrino emission so as to reconcile the multi-wavelength cascade cons…
The discovery of very-high-energy (VHE, E > 100 GeV) gamma-ray emission from intermediate- and low-frequency peaked blazars suggests that gamma-gamma absorption and pair cascading might occur in those objects. In previous papers, we investigated the Compton emission from VHE gamma-ray induced pair cascades, deflected by moderate magnetic fields, in a largely model-independent way, and demonstrated that this emission can explain the Fermi fluxes and spectra of the radio galaxies Cen A and NGC 1275. In this paper, we describe a generalization of our Monte-Carlo cascade code to include the angle-…
A single measurement of linear polarization of a nonthermal source provides direct information about the mean direction and level of ordering of the magnetic field. Monitoring of the polarization in blazars, combined with millimeter-wave VLBI imaging in both total and polarized intensity, has the potential to determine the geometry of the magnetic field. This is a key probe of the physical processes in the relativistic jet, such as ordered field components, turbulence, magnetic reconnections, magnetic collimation and acceleration of the jet flow, particle acceleration, and radiative processes …
Detection of the IceCube-170922A neutrino coincident with the flaring blazar TXS 0506+056, the first and only 3-sigma high-energy neutrino source association to date, offers a potential breakthrough in our understanding of high-energy cosmic particles and blazar physics. We present a comprehensive analysis of TXS 0506+056 during its flaring state, using newly collected Swift, NuSTAR, and X-shooter data with Fermi observations and numerical models to constrain the blazar's particle acceleration processes and multimessenger (electromagnetic and high-energy neutrino) emissions. Accounting properl…
At TeV energies and above gamma rays can induce electromagnetic cascades, whose charged component is sensitive to intervening intergalactic magnetic fields (IGMFs). When interpreting gamma-ray measurements in the energy range between a few GeV and hundreds of TeV, one has to carefully account for effects due to IGMFs, which depend on their strength and power spectrum. Therefore, gamma-ray-induced electromagnetic cascades can be used as probes of cosmic magnetism, since their arrival distribution as well as spectral and temporal properties can provide unique information about IGMFs, whose origi…
The intergalactic magnetic field (IGMF) in cosmic voids can be indirectly probed through its effect on electromagnetic cascades initiated by a source of TeV gamma-rays, such as active galactic nuclei (AGN). AGN that are sufficiently luminous at TeV energies, "extreme TeV blazars" can produce detectable levels of secondary radiation from inverse Compton (IC) scattering of the electrons in the cascade, provided that the IGMF is not too large. We review recent work in the literature which utilizes this idea to derive constraints on the IGMF for three TeV-detected blazars-1ES 0229+200, 1ES 1218+30…
Very-high-energy (VHE, E \gtrsim 100 GeV) gamma rays emitted by extragalactic sources, such as blazars, initiate electromagnetic cascades in the intergalactic medium. The cascade photons arrive at the earth with angular and temporal distributions correlated with the extragalactic magnetic field (EGMF). We have developed a new semi-analytical model of the cascade properties which is more accurate than previous analytic approaches and faster than full Monte Carlo simulations. Within its range of applicability, our model can quickly generate cascade spectra for a variety of source emission models…
The presence of asymmetry between fermions of opposite handedness in plasmas of relativistic particles can lead to exponential growth of a helical magnetic field via a small-scale chiral dynamo instability known as the chiral magnetic effect. Here, we show, using dimensional arguments and numerical simulations, that this process produces through the Lorentz force chiral magnetically driven turbulence. A k^{-2} magnetic energy spectrum emerges via inverse transfer over a certain range of wavenumbers k. The total chirality (magnetic helicity plus normalized chiral chemical potential) is conserve…
