Parameters of the turbulent magnetic field in the solar photosphere: Power spectrum of the line-of-sight field

Abstract

Ground-based (Big Bear Solar Observatory) and extra-atmospheric (SOHO/MDI) measurements of the photospheric line-of-sight magnetic field of one active and two quiet regions are used to calculate power spectra of the field, taking into account the characteristic function for the diffraction limit of the telescope resolution. At high frequencies, the physically meaningful linear interval in the spectrum extends to a wave number of k=4.6 Mm−1 (spatial scale l=1.4 Mm) for the quiet regions and k=3.35 Mm−1 (l=1.9 Mm) for the active region. A high-frequency spectral break at k≥3 Mm−1 is associated with the characteristic telescope function; the position of the break and the spectral slope beyond the break do not reflect the turbulent state of the field. As the field recording improves, the break shifts toward higher frequencies. The spectral indices in the physically meaningful linear interval are substantially different for the active and quiet regions: in the active region (NOAA 8375), the spectrum behaves as E(k)≈k−1.7 (very close to the Kolmogorov index, −5/3) in the interval 0.78≤k≤3.35 Mm−1, while in the quiet regions E(k)≈k−1.3 for 0.77≤k≤4.57 Mm−1. This difference can be explained by the additional effect of a small-scale turbulent dynamo in the unperturbed photosphere. In this case, this mechanism can generate at least 6% of the magnetic energy of the photospheric line-of-sight field in quiet regions.