Fluctuation dynamos and their Faraday rotation signatures

Turbulence is ubiquitous in many astrophysical systems like galaxies, galaxy clusters and possibly even the filaments in the intergalactic medium. We study fluctuation dynamo action in turbulent systems focusing on one observational signature, the random Faraday rotation measure (RM) from radio emission of background sources seen through the intermittent magnetic field generated by such a dynamo. We simulate the fluctuation dynamo 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, the rms value of RM is of the order of 40-50 per cent 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 is obtained 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 the order of 15-20 per cent 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 Faraday rotation signatures of fluctuation dynamo generated fields in young galaxies, galaxy clusters and intergalactic filaments.