Two-scale analysis of solar magnetic helicity

We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancelation with conventional methods. We verify this approach using first a synthetic one-dimensional magnetic field and then two-dimensional slices from a three-dimensional alpha effect-type dynamo-generated magnetic field with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistics, data from three consecutive Carrington rotations (2161--2163) are combined into a single map. We find that the spectral magnetic helicity representative of the northern hemisphere is negative at all wavenumbers and peaks at ~ 0.06 Mm^{-1} (scales around 100 Mm). There is no evidence of bihelical magnetic fields that are found in three-dimensional turbulence simulations of helicity-driven alpha effect-type dynamos.