Fluctuation dynamos and their Faraday rotation signatures

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We study fluctuation dynamo (FD) action in turbulent systems like galaxy-clusters focusing on the Faraday rotation signature. This is defined as RM = K ∫_Ln_eB ⋅ dl where n_e is the thermal electron density, B is the magnetic field, the integration is along the line of sight from the source to the observer, and K = 0.81 rad m⁻² cm⁻³ μG⁻¹ pc⁻¹. We directly compute, using the simulation data, ∫ B ⋅ dl, and hence the Faraday rotation measure (RM) over 3N² lines of sight, along each x, y and z-directions. We normalise the RM by the rms value expected in a simple model, where a field of strength B_rms fills each turbulent cell but is randomly oriented from one turbulent cell to another. This normalised RM is expected to have a nearly zero mean but a non-zero dispersion, σ_RM. We show in Fig. 1a and 1b, that a suite of simulations, on saturation, obtain the value of σ_RM = 0.4−0.5, and this is independent of P_M, R_M and the resolution of the run. This is a fairly large value for an intermittent random field; as it is of order 40%–50%, of that expected in a model where B_rms strength fields volume fill each turbulent cell, but are randomly oriented from one cell to another. We also find that the regions with a field strength larger than 2B_rms contribute only 15–20% to the total RM (see Fig. 1a). This shows that it is the general ‘sea’ of volume filling fluctuating fields that contribute dominantly to the RM produced, rather than the the high field regions.