Magnetic Energy Spectra in Active Regions

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 from {\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.Comment: 14 pages, 4 figure

25 Years of Self-Organized Criticality: Numerical Detection Methods

The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines - the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.Comment: Space Science Review series on SO

Photospheric Signatures of Granular-scale Flux Emergence and Cancellation at the Penumbral Boundary

We studied flux emergence events of sub-granular scale in a solar active region. New Solar Telescope (NST) of Big Bear Solar Observatory made it possible to clearly observe the photospheric signature of flux emergence with very high spatial (0".11 at 7057{\AA}) and temporal (15 s) resolution. From TiO observations with the pixel scale of 0".0375, we found several elongated granule-like features (GLFs) stretching from the penumbral filaments of a sunspot at a relatively high speed of over 4 km s-1. After a slender arched darkening appeared at a tip of a penumbral filament, a bright point (BP) developed and quickly moved away from the filament forming and stretching a GLF. The size of a GLF was approximately 0.5" wide and 3" long. The moving BP encountered nearby structures after several minutes of stretching, and a well-defined elongated shape of a GLF faded away. Magnetograms from SDO/HMI and NST/IRIM revealed that those GLFs are photospheric indicators of small-scale flux emergence, and their disappearance is related to magnetic cancellation. From two well-observed events, we describe detailed development of the sub-structures of GLFs, and different cancellation processes that each of the two GLFs underwent.Comment: Accepted for publication in The Astrophysical Journa

Intermittency in the photosphere and corona above an active region

Recent studies undoubtedly demonstrate that the magnetic field in the photosphere and corona is an intermittent structure, which offers new views on the underlying physics. In particular, such problems as the existence in the corona of localized areas with extremely strong resistivity (required to explain magnetic reconnection of all scales) and the interchange between small and large scales (required in study of the photosphere/corona coupling), to name a few, can be easily captured by the concept of intermittency. This study is focused on simultaneous time variations of intermittency properties derived in the photosphere, chromosphere and corona. We analyzed data for NOAA AR 10930 acquired between Dec 08, 2006 12:00 UT and Dec 13, 2006 18:45 UT. Photospheric intermittency was inferred from Hinode magnetic field measurements, while intermittency in the transition region and corona was derived from Nobeyama 9 GHz radio polarization measurements, high cadence Hinode/XRT/Be-thin data as well as GOES 1-8\AA flux. Photospheric dynamics and its possible relationship with the intermittency variations were also analyzed by calculating the kinetic vorticity. For this case study we found the following chain of events. Intermittency of the photospheric magnetic field peaked after the specific kinetic vorticity of plasma flows in the AR reached its maximum level (4 hour time delay). In turn, gradual increase of coronal intermittency occurred after the peak of the photospheric intermittency. The time delay between the peak of photospheric intermittency and the occurrence of the first strong (X3.4) flare was approximately 1.3 days. Our analysis seems to suggest that the enhancement of intermittency/complexity first occurs in the photosphere and is later transported toward the corona

Parameters of the Magnetic Flux inside Coronal Holes

Parameters of magnetic flux distribution inside low-latitude coronal holes (CHs) were analyzed. A statistical study of 44 CHs based on Solar and Heliospheric Observatory (SOHO)/MDI full disk magnetograms and SOHO/EIT 284\AA images showed that the density of the net magnetic flux, $B_{{\rm net}}$, does not correlate with the associated solar wind speeds, $V_x$. Both the area and net flux of CHs correlate with the solar wind speed and the corresponding spatial Pearson correlation coefficients are 0.75 and 0.71, respectively. A possible explanation for the low correlation between $B_{{\rm net}}$ and $V_x$ is proposed. The observed non-correlation might be rooted in the structural complexity of the magnetic field. As a measure of complexity of the magnetic field, the filling factor, $f(r)$, was calculated as a function of spatial scales. In CHs, $f(r)$ was found to be nearly constant at scales above 2 Mm, which indicates a monofractal structural organization and smooth temporal evolution. The magnitude of the filling factor is 0.04 from the Hinode SOT/SP data and 0.07 from the MDI/HR data. The Hinode data show that at scales smaller than 2 Mm, the filling factor decreases rapidly, which means a mutlifractal structure and highly intermittent, burst-like energy release regime. The absence of necessary complexity in CH magnetic fields at scales above 2 Mm seems to be the most plausible reason why the net magnetic flux density does not seem to be related to the solar wind speed: the energy release dynamics, needed for solar wind acceleration, appears to occur at small scales below 1 Mm.Comment: 6 figures, approximately 23 pages. Accepted in Solar Physic