Results of a statistical analysis of solar granulation are presented. A data set of 36 images of a quiet Sun area on the solar disk center was used. The data were obtained with the 1.6 m clear aperture New Solar Telescope (NST) at Big Bear Solar Obse
rvatory (BBSO) and with a broad-band filter centered at the TiO (705.7 nm) spectral line. The very high spatial resolution of the data (diffraction limit of 77 km and pixel scale of 0.$$0375) augmented by the very high image contrast (15.5$pm$0.6%) allowed us to detect for the first time a distinct subpopulation of mini-granular structures. These structures are dominant on spatial scales below 600 km. Their size is distributed as a power law with an index of -1.8 (which is close to the Kolmogorovs -5/3 law) and no predominant scale. The regular granules display a Gaussian (normal) size distribution with a mean diameter of 1050 km. Mini-granular structures contribute significantly to the total granular area. They are predominantly confined to the wide dark lanes between regular granules and often form chains and clusters, but different from magnetic bright points. A multi-fractality test reveals that the structures smaller than 600 km represent a multi-fractal, whereas on larger scales the granulation pattern shows no multi-fractality and can be considered as a Gaussian random field. The origin, properties and role of the newly discovered population of mini-granular structures in the solar magneto-convection are yet to be explored.
We present results of a study of intermittency and multifractality of magnetic structures in solar active regions (ARs). Line-of-sight magnetograms for 214 ARs of different flare productivity observed at the center of the solar disk from January 1997
until December 2006 are utilized. Data from the Michelson Doppler Imager (MDI) instrument on-board the {it Solar and Heliospheric Observatory} (SOHO) operating in the high resolution mode, the Big Bear Solar Observatory digital magnetograph and {it Hinode} SOT/SP instrument were used. Intermittency spectra were derived via high-order structure functions and flatness functions. The flatness function exponent is a measure of the degree of intermittency. We found that the flatness function exponent at scales below approximately 10 Mm is correlated to the flare productivity (the correlation coefficient is - 0.63). {it Hinode} data show that the intermittency regime is extended toward the small scales (below 2 Mm) as compared to the MDI data. The spectra of multifractality, derived from the structure functions and flatness functions, are found to be more broad for ARs of highest flare productivity as compared to that of low flare productivity. The magnetic structure of high-flaring ARs consists of a voluminous set of monofractals, and this set is much richer than that for low-flaring ARs. The results indicate relevance of the multifractal organization of the photospheric magnetic fields to the flaring activity. Strong intermittency observed in complex and high-flaring ARs is a hint that we observe a photospheric imprint of enhanced sub-photospheric dynamics.
Line-of-sight magnetograms for 217 active regions (ARs) of different flare rate observed at the solar disk center from January 1997 until December 2006 are utilized to study the turbulence regime and its relationship to the flare productivity. Data f
rom {it SOHO}/MDI instrument recorded in the high resolution mode and data from the BBSO magnetograph were used. The turbulence regime was probed via magnetic energy spectra and magnetic dissipation spectra. We found steeper energy spectra for ARs of higher flare productivity. We also report that both the power index, $alpha$, of the energy spectrum, $E(k) sim k^{-alpha}$, and the total spectral energy $W=int E(k)dk$ are comparably correlated with the flare index, $A$, of an active region. The correlations are found to be stronger than that found between the flare index and total unsigned flux. The flare index for an AR can be estimated based on measurements of $alpha$ and $W$ as $A=10^b (alpha W)^c$, with $b=-7.92 pm 0.58$ and $c=1.85 pm 0.13$. We found that the regime of the fully-developed turbulence occurs in decaying ARs and in emerging ARs (at the very early stage of emergence). Well-developed ARs display under-developed turbulence with strong magnetic dissipation at all scales.
