Nonperturbative quasilinear approach to the shear dynamo problem

We study large-scale dynamo action due to turbulence in the presence of a linear shear flow. Our treatment is quasilinear and equivalent to the standard `first order smoothing approximation'. However it is non perturbative in the shear strength. We first derive an integro-differential equation for the evolution of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. We show that, for non helical turbulence, the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves; this is valid for any Galilean-invariant velocity field, independent of its dynamics. Hence, to all orders in the shear parameter, there is no shear-current type effect for non helical turbulence in a linear shear flow, in quasilinear theory in the limit of zero resistivity. We then develop a systematic approximation of the integro-differential equation for the case when the mean magnetic field varies slowly compared to the turbulence correlation time. For non-helical turbulence, the resulting partial differential equations can again be solved by making a shearing coordinate transformation in Fourier space. The resulting solutions are in the form of shearing waves, labeled by the wavenumber in the sheared coordinates. These shearing waves can grow at early and intermediate times but are expected to decay in the long time limit.Comment: 31 pages: typos corrected & references adde

Fluctuation dynamos and their Faraday rotation signatures

Turbulence is ubiquitous in many astrophysical systems like galaxies, galaxy clusters and possibly even the IGM filaments. We study fluctuation dynamo action in turbulent systems focusing on one observational signature; the Faraday rotation measure (RM) from background radio sources seen through the magnetic field generated by such a dynamo. We simulate the fluctuation dynamo (FD) in periodic boxes up to resolutions of 512^3, with varying fluid and magnetic Reynolds numbers, and measure the resulting random RMs. We show that, even though the magnetic field generated is intermittent, it still allows for contributions to the RM to be significant. When the dynamo saturates, it is of order 40%-50% of the value expected in a model where fields of strength B_rms uniformly fill cells of the largest turbulent eddy but are randomly oriented from one cell to another. This level of RM dispersion obtains across different values of magnetic Reynolds number and Prandtl number explored. We also use the random RMs to probe the structure of the generated fields to distinguish the contribution from intense and diffuse field regions. We find that the strong field regions (say with B > 2B_rms) contribute only of order 15%-20% to the RM. Thus rare structures do not dominate the RM; rather the general 'sea' of volume filling fluctuating fields are the dominant contributors. We also show that the magnetic integral scale, L_{int}, which is directly related to the RM dispersion, increases in all the runs, as Lorentz forces become important to saturate the dynamo. It appears that due to the ordering effect of the Lorentz forces, L_{int} of the saturated field tends to a modest fraction, 1/2-1/3 of the integral scale of the velocity field, for all our runs. These results are then applied to discuss the RM signatures of FD generated fields in young galaxies, galaxy clusters and intergalactic filaments.Comment: 14 pages, 12 figures, version accepted to MNRA

Primordial Magnetic Fields in the Post-recombination Era and Early Reionization

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 (IGM) via ambipolar diffusion and, for small enough scales, by generating decaying MHD 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 $B_{0}=3\times 10^{-9}$ Gauss smoothed on the magnetic Jeans scale and below, can give rise to Thomson scattering optical depths \tau \ga 0.1, although not in the range of redshifts needed to explain the recent WMAP polarization observations. We also study the possibility that primordial fields could induce the formation of subgalactic structures for z \ga 15. We show that early structure formation induced by nano-Gauss magnetic fields is potentially capable of producing the early re-ionization implied by the WMAP data. Future CMB observations will be very useful to probe the modified ionization histories produced by primordial magnetic field evolution and constrain their strength.Comment: 19 pages, 7 figures, Minor changes to match version accepted in MNRA

Cosmic Microwave Background Polarization Signals from Tangled Magnetic Fields

Tangled, primordial cosmic magnetic fields create small rotational velocity perturbations on the last scattering surface (LSS) of the cosmic microwave background radiation (CMBR). For fields which redshift to a present value of $B_0 = 3\times 10^{-9}$ Gauss, these vector modes are shown to generate polarization anisotropies of order $0.1\mu K - 4 \mu K$ on small angular scales ($500 < l < 2000$), assuming delta function or a power law spectra with $n=-1$. About 200 times larger signals result for $n=2$ spectra. Unlike inflation generated, scalar modes, these signals are dominated by the odd parity, B-type polarization, which could help in their detection.Comment: 4 pages, Revtex, matches version to be published in Phys. Rev. Let