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Sequences of line-of-sight (LOS) magnetograms recorded by the Michelson-Doppler Imager are used to quantitatively characterize photospheric magnetic structure and evolution in three active regions that rotated across the Suns disk during the Whole Heliosphere Interval (WHI), in an attempt to relate the photospheric magnetic properties of these active regions to flares and coronal mass ejections (CMEs). Several approaches are used in our analysis, on scales ranging from whole active regions, to magnetic features, to supergranular scales, and, finally, to individual pixels. We calculated several parameterizations of magnetic structure and evolution that have previously been associated with flare and CME activity, including total unsigned magnetic flux, magnetic flux near polarity inversion lines, amount of cancelled flux, the proxy Poynting flux, and helicity flux. To catalog flare events, we used flare lists derived from both GOES and RHESSI observations. By most such measures, AR 10988 should have been the most flare- and CME-productive active region, and AR 10989 the least. Observations, however, were not consistent with this expectation: ARs 10988 and 10989 produced similar numbers of flares, and AR 10989 also produced a few CMEs. These results highlight present limitations of statistics-based flare and CME forecasting tools that rely upon line-of-sight photospheric magnetic data alone.
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With multiple vantage points around the Sun, STEREO and SDO imaging observations provide a unique opportunity to view the solar surface continuously. We use He II 304 A data from these observatories to isolate and track ten active regions and study their long-term evolution. We find that active regions typically follow a standard pattern of emergence over several days followed by a slower decay that is proportional in time to the peak intensity in the region. Since STEREO does not make direct observations of the magnetic field, we employ a flux-luminosity relationship to infer the total unsigned magnetic flux evolution. To investigate this magnetic flux decay over several rotations we use a surface flux transport model, the Advective Flux Transport (AFT) model, that simulates convective flows using a time-varying velocity field and find that the model provides realistic predictions when information about the active regions magnetic field strength and distribution at peak flux is available. Finally, we illustrate how 304 AA images can be used as a proxy for magnetic flux measurements when magnetic field data is not accessible.
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.
Solar active regions contain electric currents. Information on the distribution of currents is important for understanding the processes of energy release on the surface of the Sun and in the overlying layers. The paper presents an analysis of the probability density function (PDF) of the absolute value of the photospheric vertical electric current density ($|j_z|$) in 48 active regions before and after flares in 2010--2017. Calculation of $|j_z|$ is performed by applying the differential form of Amperes circuital law to photospheric vector magnetograms obtained from observations of the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). It has been established that for the studied active regions PDF($|j_z|$) is described by the Gauss function in the low-$|j_z|$ region ($|j_z| < 10110 pm 1321$ statampere/cm$^2$) and the decaying power-law function in the region of higher $|j_z|$ values. Also, for some active regions PDF($|j_z|$) can be described by the special kappa-function. The distributions of the parameters of the approximating functions are obtained using the least squares method. The average absolute value of the power-law function index is $3.69 pm 0.51$, and $3.99 pm 0.51$ of the kappa-function. No systematic changes in parameters during the flares are detected. An explicit connection between the parameters and the flare X-ray class, as well as with the Hale magnetic class of the active regions, is not found. Arguments are presented in favor of the suggestion that the Gaussian distribution in the low-value region of PDF($|j_z|$) represents noise in the data, while the power-law tail reflects the nature of electric currents in the solar active regions.
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.
The observations of magnetic field variations as a signature of flaring activity is one of the main goal in solar physics. Some efforts in the past give apparently no unambiguous observations of changes. We observed that the scaling laws of the current helicity inside a given flaring active region change clearly and abruptly in correspondence with the eruption of big flares at the top of that active region. Comparison with numerical simulations of MHD equations, indicates that the change of scaling behavior in the current helicity, seems to be associated to a topological reorganization of the footpoint of the magnetic field loop, namely to dissipation of small scales structures in turbulence. It is evident that the possibility of forecasting in real time high energy flares, even if partially, has a wide practical interest to prevent the effects of big flares on Earth and its environment.
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