Turbulent magnetic energy spectrum and the cancellation function of solar photospheric magnetic fields
Abstract
A simple analytical relation of form α=2κ-1 between the magnetic energy spectral exponent α of the turbulent magnetic field in the solar photosphere and its magnetic flux cancellation exponent κ, 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 α<-1 where κ-> 0 as α-> -∞. The observationally derived upper limit of 0.38 on κ implies α<-0.24 in the granular size range, apparently at odds with a small scale dynamo driven in the inertial range.
- Publication:
-
Astronomische Nachrichten
- Pub Date:
- November 2013
- DOI:
- 10.1002/asna.201211968
- arXiv:
- arXiv:1404.1772
- Bibcode:
- 2013AN....334..952M
- Keywords:
-
- magnetohydrodynamics (MHD);
- Sun: atmosphere;
- Sun: magnetic fields;
- turbulence;
- Astrophysics - Solar and Stellar Astrophysics
- E-Print:
- 4 pages, 4 figures