MAGNETIC HELICITY AND ENERGY SPECTRA OF A SOLAR ACTIVE REGION
We compute for the first time the magnetic helicity and energy spectra of the solar active region NOAA 11158 during 2011 February 11-15 at 20° southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field. The sign of the magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ≈ 0.4 Mm{sup –1}, corresponding to a scale of 2π/k ≈ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k {sup –11/3} power law at large wavenumbers, which implies a k {sup –5/3} spectrum for the modulus of the current helicity. A k {sup –5/3} spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm{sup –1}, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artifacts at small scales.