Using direct numerical simulations (DNS), we study laminar and turbulent dynamos in chiral magnetohydrodynamics with an extended set of equations that accounts for an additional contribution to the electric current due to the chiral magnetic effect (CME). This quantum phenomenon originates from an asymmetry between left-and right-handed relativistic fermions in the presence of a magnetic field and gives rise to a chiral dynamo. We show that the magnetic field evolution proceeds in three stages: (1) a small-scale chiral dynamo instability, (2) production of chiral magnetically driven turbulence and excitation of a large-scale dynamo instability due to a new chiral effect (alpha(mu) effect), and (3) saturation of magnetic helicity and magnetic field growth controlled by a conservation law for the total chirality. The alpha(mu) effect becomes dominant at large fluid and magnetic Reynolds numbers and is not related to kinetic helicity. The growth rate of the large-scale magnetic field and its characteristic scale measured in the numerical simulations agree well with theoretical predictions based on mean-field theory. The previously discussed two-stage chiral magnetic scenario did not include stage (2), during which the characteristic scale of magnetic field variations can increase by many orders of magnitude. Based on the findings from numerical simulations, the relevance of the CME and the chiral effects revealed in the relativistic plasma of the early universe and of protoneutron stars are discussed.

The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right-and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (chiral magnetic effect). We present a self-consistent treatment of the chiral MHD equations, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfven wave for incompressible flows, increases the frequencies of the Alfven wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark-gluon plasma.

Using numerical simulations of forced turbulence, we show that for magnetic Reynolds numbers larger than unity, that is, beyond the regime of quasilinear theory, the turbulent magnetic diffusivity attains an additional negative contribution that is quadratic in the kinetic helicity. In particular, for large magnetic Reynolds numbers, the turbulent magnetic diffusivity without helicity is about twice the value with helicity. Such a contribution was not previously anticipated, but, as we discuss, it turns out to be important when accurate estimates of the turbulent magnetic diffusivity are needed.

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 conserved in this system. Therefore, as the helical magnetic field grows, most of the total chirality gets transferred into magnetic helicity until the chiral magnetic effect terminates. Quantitative results for height, slope, and extent of the spectrum are obtained. Consequences of this effect for cosmic magnetic fields are discussed.

A key for understanding the evolution of galaxies and in particular their star formation history will be future ultradeep radio surveys. While star formation rates (SFRs) are regularly estimated with phenomenological formulas based on the local FIR-radio correlation, we present here a physically motivated model to relate star formation with radio fluxes. Such a relation holds only in frequency ranges where the flux is dominated by synchrotron emission, as this radiation originates from cosmic rays produced in supernova remnants, therefore reflecting recent star formation. At low frequencies, synchrotron emission can be absorbed by the free-free mechanism. This suppression becomes stronger with increasing number density of the gas, more precisely of the free electrons. We estimate the critical observing frequency below which radio emission is not tracing the SFR, and use the three well-studied local galaxies M51, M82, and Arp 220 as test cases for our model. If the observed galaxy is at high redshift, this critical frequency moves along with other spectral features to lower values in the observing frame. In the absence of systematic evolutionary effects, one would therefore expect that the method can be applied at lower observing frequencies for high-redshift observations. However, in case of a strong increase of the typical gas column densities towards high redshift, the increasing free-free absorption may erase the star formation signatures at low frequencies. At high radio frequencies both, free-free emission and the thermal bump, can dominate the spectrum, also limiting the applicability of this method.

Theoretical scenarios, including the turbulent small-scale dynamo, predict that strong magnetic fields already exist in young galaxies. Based on the assumption of energy equipartition between magnetic fields and turbulence, we determine the galactic synchrotron flux as a function of redshift z. Galaxies in the early universe are different from local galaxies, in particular, the former have more intense star formation. To cover a large range of conditions, we consider two different systems: one model galaxy comparable to the Milky Way and one typical high-z starburst galaxy. We include a model of the steady-state cosmic ray spectrum and find that synchrotron emission can be detected up to cosmological redshifts with current and future radio telescopes. The turbulent dynamo theory is in agreement with the origin of the observed correlation between the far-infrared (FIR) luminosity L-FIR and the radio luminosity L-radio. Our model reproduces this correlation well at z = 0. We extrapolate the FIR-radio correlation to higher redshifts and predict a time evolution with a significant deviation from its present-day appearance already at z approximate to 2 for a gas density that increases strongly with z. In particular, we predict a decrease of the radio luminosity with redshift which is caused by the increase of cosmic ray energy losses at high z. The result is an increase of the ratio between L-FIR and L-radio. Simultaneously, we predict that the slope of the FIR-radio correlation becomes shallower with redshift. This behavior of the correlation could be observed in the near future with ultra-deep radio surveys.

The origin of strong magnetic fields in the Universe can be explained by amplifying weak seed fields via turbulent motions on small spatial scales and subsequently transporting the magnetic energy to larger scales. This process is known as the turbulent dynamo and depends on the properties of turbulence, i.e., on the hydrodynamical Reynolds number and the compressibility of the gas, and on the magnetic diffusivity. While we know the growth rate of the magnetic energy in the linear regime, the saturation level, i.e., the ratio of magnetic energy to turbulent kinetic energy that can be reached, is not known from analytical calculations. In this paper we present a scale-dependent saturation model based on an effective turbulent resistivity which is determined by the turnover time scale of turbulent eddies and the magnetic energy density. The magnetic resistivity increases compared to the Spitzer value and the effective scale on which the magnetic energy spectrum is at its maximum moves to larger spatial scales. This process ends when the peak reaches a characteristic wave number k(star) which is determined by the critical magnetic Reynolds number. The saturation level of the dynamo also depends on the type of turbulence and differs for the limits of large and small magnetic Prandtl numbers Pm. With our model we find saturation levels between 43.8% and 1.3% for Pm >> 1 and between 2.43% and 0.135% for Pm << 1, where the higher values refer to incompressible turbulence and the lower ones to highly compressible turbulence.