Magnetic Helicity and Energy Spectra of a Solar Active Region

We compute magnetic helicity and energy spectra of the solar active region NOAA 11158 during 11–15 February 2011 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 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 relative magnetic helicity is around 8% and strongest at intermediate wavenumbers of k ≈ 0.4Mm, corresponding to a scale of 2π/k ≈ 16Mm. The same sign and a somewhat smaller value is also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The current helicity spectrum is estimated from the magnetic helicity spectrum and its modulus shows a k spectrum at large wavenumbers. A similar power law is also obtained for the magnetic energy spectrum. The comparison of energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3Mm, corresponding to scales above 2Mm. This gives some justification to our assumption of isotropy and places limits resulting from instrumental artefacts at small scales. Subject headings: Sun: activity—Sun: magnetic topology—Sun: photosphere—Sun: dynamo