http://arxiv.org/abs/1906.03877
If the alpha effect plays a role in the generation of the Sun’s magnetic field, the field should show evidence of magnetic helicity of opposite signs at large and small length scales. Measuring this faces two challenges: (i) in weak-field regions, horizontal field measurements are unreliable because of the pi ambiguity, and (ii) one needs a truly global approach to computing helicity spectra in the case where one expects a sign reversal across the equator at all wavenumbers. Here we develop such a method using spin-2 spherical harmonics to decompose the linear polarization in terms of the parity-even and parity-odd E and B polarizations, respectively. Using simple one- and two-dimensional models, we show that the product of the spectral decompositions of E and B, taken at spherical harmonic degrees that are shifted by one, is a good proxy of the magnetic helicity. We then apply this method to the analysis of solar synoptic vector magnetograms, from which we extract a pseudo-polarization corresponding to a “pi-ambiguated” magnetic field, i.e., a magnetic field vector that has no arrow. We find opposite signs of the global helicity proxy for spherical harmonic degrees larger or smaller than around 10, which corresponds to an effective wavenumber of around 0.014 Mm^{-1}. We argue that our global two-scale helicity proxy constitutes a new powerful measure that is worth applying routinely and over many more synoptic vector magnetograms. It might also be applicable to stellar and Galactic polarization data.
A. Brandenburg
Tue, 11 Jun 19
10/60
Comments: 8 pages, 6 figures, 3 tables, submitted to ApJ
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