Turbulent magnetic energy spectrum and the cancellation function of solar photospheric magnetic fields

A simple analytical relation of form = 2 - 1 between the magnetic energy spectral exponent of the turbulent magnetic field in the solar photosphere and its magnetic flux cancellation exponent , valid under certain restrictive assumptions, is tested and extended outside its range of validity in a series of Monte Carlo simulations. In these numerical tests artificial magnetograms are constructed in 1D and 2D by superposing a discrete set of Fourier modes of the magnetic field distribution with amplitudes following a power law spectrum and measuring the cancellation function on these simulated magnetograms. Our results confirm the validity of the analytical relation and extend it to the domain < -1 where 0 as -. The observationally derived upper limit of 0.38 on implies < -0.24 in the granular size range, apparently at odds with a small scale dynamo driven in the inertial range. ((c) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)