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.