The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak 'seed' magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has kinetic helicity. Large scale dynamos produce small scale helical fields as a waste product that quench the large scale dynamo and hence the alpha effect. With this in mind, the microscopic theory of the alpha effect is revisited in full detail and recent results for the loss of helical magnetic fields are reviewed.Comment: 285 pages, 72 figures, accepted by Phys. Re

The universe is magnetized on all scales probed so far. On the largest scales, galaxies and galaxy clusters host magnetic fields at the micro Gauss level coherent on scales up to ten kpc. Recent observational evidence suggests that even the intergalactic medium in voids could host a weak  ∼  10(-16) Gauss magnetic field, coherent on Mpc scales. An intriguing possibility is that these observed magnetic fields are a relic from the early universe, albeit one which has been subsequently amplified and maintained by a dynamo in collapsed objects. We review here the origin, evolution and signatures of primordial magnetic fields. After a brief summary of magnetohydrodynamics in the expanding universe, we turn to magnetic field generation during inflation and phase transitions. We trace the linear and nonlinear evolution of the generated primordial fields through the radiation era, including viscous effects. Sensitive observational signatures of primordial magnetic fields on the cosmic microwave background, including current constraints from Planck, are discussed. After recombination, primordial magnetic fields could strongly influence structure formation, especially on dwarf galaxy scales. The resulting signatures on reionization, the redshifted 21 cm line, weak lensing and the Lyman-α forest are outlined. Constraints from radio and γ-ray astronomy are summarized. Astrophysical batteries and the role of dynamos in reshaping the primordial field are briefly considered. The review ends with some final thoughts on primordial magnetic fields.

The evolution and viscous damping of cosmic magnetic fields in the early universe, is analysed. Using the fact that the fluid, electromagnetic, and shear viscous energy-momentum tensors are all conformally invariant, the evolution is transformed from the expanding universe setting into that in flat spacetime. Particular attention is paid to the evolution of nonlinear Alfvén modes. For a small enough magnetic field, which satisfies our observational constraints, these wave modes either oscillate negligibly or, when they do oscillate, become overdamped. Hence they do not suffer Silk damping on galactic and subgalactic scales. The smallest scale which survives damping depends on the field strength and is of order a dimensionless Alfvén velocity times the usual baryon-photon Silk damping scale. After recombination, nonlinear effects can convert the Alfvén mode into compressional, gravitationally unstable waves and seed cosmic structures if the cosmic magnetic field is sufficiently strong.

We discuss, using simple analytical models and MHD simulations, the origin and parameters of turbulence and magnetic fields in galaxy clusters. Three physically distinct regimes can be identified in the evolution of cluster turbulence and magnetic fields. Firstly, the fluctuation dynamo will produce microgauss-strong, random magnetic fields during cluster formation and major mergers. Turbulent velocity of about 300 km/s can be maintained at scales 100-200 kpc. The magnetic field is intermittent, has a smaller scale of 20-30 kpc and average strength of 2 microgauss. Secondly, when major mergers end, turbulent speed and magnetic field undergo a power-law decay, decreasing in strength but increasing in scale by a factor of about two. Thirdly, smaller-mass subclusters and cluster galaxies produce turbulent wakes, with turbulent speeds and magnetic field strengths similar to those quoted above. The velocity scales are about 200 kpc and 10 kpc respectively, and the magnetic field scale is about 6 times smaller. Although these wakes may fill only a small fraction of the cluster volume, their area covering factor can be close to unity. So one can potentially reconcile observations that indicate the coexistence of turbulence with ordered filamentary gas structures, as in the Perseus cluster. Random Faraday rotation measure is estimated to be typically 100-200 rad/m^2, in agreement with observations. We predict detectable synchrotron polarization from cluster radio halos at wavelengths 3-6 cm, if observed at sufficiently high resolution (abridged).Comment: 20 pages, 9 figures, Replaced to match version accepted by MNRA

We explore the ways in which primordial magnetic fields influence the thermal and ionization history of the post‐recombination Universe. After recombination, the Universe becomes mostly neutral, resulting also in a sharp drop in the radiative viscosity. Primordial magnetic fields can then dissipate their energy into the intergalactic medium via ambipolar diffusion and, for small enough scales, by generating decaying magnetohydrodynamics turbulence. These processes can significantly modify the thermal and ionization history of the post‐recombination Universe. We show that the dissipation effects of magnetic fields, which redshifts to a present value B0= 3 × 10−9 G smoothed on the magnetic Jeans scale and below, can give rise to Thomson scattering optical depths τ≳ 0.1, although not in the range of redshifts needed to explain the recent Wilkinson Microwave Anisotropy Probe (WMAP) polarization observations. We also study the possibility that primordial fields could induce the formation of subgalactic structures for z≳ 15. We show that early structure formation induced by nanoGauss magnetic fields is potentially capable of producing the early reionization implied by the WMAP data. Future cosmic microwave background observations will be very useful to probe the modified ionization histories produced by primordial magnetic field evolution and constrain their strength.

We investigate the interplay of cosmic ray (CR) propagation and advection in galaxy clusters. Propagation in form of CR diffusion and streaming tends to drive the CR radial profiles towards being flat, with equal CR number density everywhere. Advection of CR by the turbulent gas motions tends to produce centrally enhanced profiles. We assume that the CR streaming velocity is of the order of the sound velocity. This is motivated by plasma physical arguments. The CR streaming is then usually larger than typical advection velocities and becomes comparable or lower than this only for periods with trans-and super-sonic cluster turbulence. As a consequence a bimodality of the CR spatial distribution results. Strongly turbulent, merging clusters should have a more centrally concentrated CR energy density profile with respect to relaxed ones with very subsonic turbulence. This translates into a bimodality of the expected diffuse radio and gamma-ray emission of clusters, since more centrally concentrated CR will find higher target densities for hadronic CR proton interactions, higher plasma wave energy densities for CR electron and proton re-acceleration, and stronger magnetic fields. Thus, the observed bimodality of cluster radio halos appears to be a natural consequence of the interplay of CR transport processes, independent of the model of radio halo formation, be it hadronic interactions of CR protons or re-acceleration of low-energy CR electrons. Energy dependence of the CR propagation should lead to spectral steepening of dying radio halos. Furthermore, we show that the interplay of CR diffusion with advection implies first order CR re-acceleration in the pressure-stratified atmospheres of galaxy clusters. Finally, we argue that CR streaming could be important in turbulent cool cores of galaxy clusters since it heats preferentially the central gas with highest cooling rate.

We review current ideas on the origin of galactic and extragalactic magnetic fields. We begin by summarizing observations of magnetic fields at cosmological redshifts and on cosmological scales. These observations translate into constraints on the strength and scale magnetic fields must have during the early stages of galaxy formation in order to seed the galactic dynamo. We examine mechanisms for the generation of magnetic fields that operate prior during inflation and during subsequent phase transitions such as electroweak symmetry breaking and the quark-hadron phase transition. The implications of strong primordial magnetic fields for the reionization epoch as well as the first generation of stars is discussed in detail. The exotic, earlyUniverse mechanisms are contrasted with astrophysical processes that generate fields after recombination. For example, a Biermann-type battery can operate in a proto-

Helical turbulence may provide the key to the generation of large-scale magnetic fields. Turbulence also generically leads to rapidly growing small-scale magnetic fields. These two processes are usually studied separately. We give here a unified treatment of both processes, in the case of random fields, incorporating also a simple model nonlinear drift. We uncover an interesting plausible saturated state of the small-scale dynamo and a novel analogy between quantum mechanical (QM) tunneling and the generation of large-scale fields. A field generated by the small-scale dynamo, can "tunnel" to produce large-scale correlations, which in steady state, correspond to a force-free "mean" field. 47.65. + a, 95.30.Qd Large-scale magnetic fields in astronomical objects are thought to be generated by dynamo action involving helical turbulence and rotational shear [1,2]. Here large-scale refers to scales much larger than the outer scale, say L, of the turbulence. However, turbulent motions, with a large enough magnetic Reynolds number (MRN), can also excite a small-scale dynamo, which exponentiates fields correlated on the tubulent eddy scale, at a rate much faster than the mean field growth rate [1,3]. These two dynamo problems, viz. the small-scale dynamo (SSD) and large-scale dynamo (LSD), are usually treated separately. However, this separation is often artificial; there is no abrupt transition from the field correlated on scales smaller than L and that correlated on larger scales. We show here that the equations for the magnetic correlations, which involve both the longitudinal and helical parts, are already sufficiently general to incorporate both small-and largescale dynamos in the case of random fields. They provide us with a paradigm to study the dynamics in a unified fashion, which could be particularly useful to study a possible inverse cascade of magnetic fields, to scales larger than L.Consider the induction equation for the magnetic field,where B is the magnetic field, v is the velocity of the fluid, and h is the Ohmic resistivity. Take v v T 1 v D , the sum of an externally prescribed stochastic field v T , and a drift component v D , which models the nonlinear back reaction of the growing Lorentz force. We assume v T to be an isotropic, homogeneous, Gaussian random velocity field with zero mean. For simplicity, we also assume v T to have a delta function correlation in time (Markovian approximation). Its two point correlation is specified as ͗y i T ͑x, t͒y j T ͑ y, s͒͘ T ij ͑r͒d͑t 2 s͒ with (cf.[4])Here ͗ ͘ denotes ensemble averaging, r jx 2 yj, and r i x i 2 y i . T L ͑r͒ and T N ͑r͒ are the longitudinal and transverse correlation functions for the velocity field while C͑r͒ represents the helical part of the velocity correlations. If = ? v T 0, T N ͑1͞2r͒d͑r 2 T L ͒͞dr.(Note v T is also not correlated with the magnetic field.) To model the drift velocity in a tractable manner, but one which nevertheless gives some feel for possible nonlinear effects, we proceed as follows. As the magnetic field grows, th...