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We study structure and dynamics of the turbulent photospheric magnetic fieldin the active region NOAA 11158 by characterizing the spatial and temporalscaling properties of the line-of-sight (LOS) component. Using high-resolutionhigh-cadence LOS magnetograms from SDO/HMI, we measured power-law exponents$\alpha$ and $\beta$ describing wavenumber- ($k$) and frequency-domain ($f$)Fourier power spectra, respectively, and investigated their evolution duringthe passage of the active region through the field of view of HMI. Flaringactive region NOAA 11158 produces an average one-dimensional spatial powerspectral density that follows approximately a $k^{-2}$ power law -- a spectrumthat suggests parallel MHD fluctuations in an anisotropic turbulent medium. Inaddition, we found that values of $\alpha$ capture systematic changes in theconfiguration of LOS photospheric magnetic field during flaring activity in thecorona. Position-dependent values of the temporal scaling exponent $\beta$showed that, on average, the core of the active region scales with $\beta >$ 3surrounded by a diffusive region with an approximately $f^{-2}$-type spectrum.Our results indicate that only about 1 - 3 \% of the studied LOS photosphericmagnetic flux displays $\beta\approx\alpha$, implying that Taylor's hypothesisof frozen-in-flow turbulence is typically invalid for this scalar in presenceof turbulent photospheric flows. In consequence, both spatial and temporalvariations of the plasma and magnetic field must be included in a completedescription of the turbulent evolution of active regions.

Spatio-temporal scaling of turbulent photospheric line-of-sight magnetic field in active region NOAA 11158