Changyi Tan

The Statistical Relationship between the Photospheric Magnetic Parameters and the Flare Productivity of Active Regions

Using line-of-sight Michelson Doppler Imager (MDI) magnetograms of 89 active regions and Solar Geophysical Data (SGD) flare reports, we explored, for the first time, the magnitude scaling correlations between three parameters of magnetic fields and the flare productivity of solar active regions. These parameters are (1) the mean value of spatial magnetic gradients at strong-gradient magnetic neutral lines, ()NL; (2) the length of strong-gradient magnetic neutral lines, LGNL; and (3) the total magnetic energy, (Bz) dA, dissipated in a layer of 1 m during 1 s over the active regions area. The MDI magnetograms of active regions used for our analysis are close to the solar central meridian (within ±10°). The flare productivity of active regions was quantified by the soft X-ray flare index for different time windows from the time interval of the entire disk passage down to +1 day from the time of the analyzed magnetogram. Our results explicitly indicate positive correlations between the parameters and the overall flare productivity of active regions, and imminent flare production as well. The correlations confirm the dependence of flare productivity on the degree of nonpotentiality of active regions.

FREE MAGNETIC ENERGY AND FLARE PRODUCTIVITY OF ACTIVE REGIONS

In this study, the photospheric vector magnetograms, obtained with the Spectro-Polarimeter of the Solar Optical Telescope on board Hinode, are used as the boundary conditions to extrapolate the three-dimensional nonlinear force-free (NLFF) coronal magnetic fields. The observed non-force-free photospheric magnetic fields are preprocessed toward the nearly force-free chromospheric magnetic fields. The performance of the preprocessing procedure is evaluated by comparing with chromospheric magnetic fields obtained by the Vector SpectroMagnetograph instrument located on the Synoptic Optical Long-term Investigations of the Sun Tower. Then, the weighted optimization method is applied to the preprocessed boundary data to extrapolate the NLFF fields with which we are able to estimate the free magnetic energy stored in the active regions. The magnitude scaling correlation between the free magnetic energy and the soft X-ray flare index (FI) of active regions is then studied. The latter quantifies the impending flare production of active regions over the subsequent 1, 2, and 3 day time windows. Based on 75 samples, we find a positive correlation between the free energy and the FI. We also study the temporal variation of free magnetic energy for three active regions, of which two are flare-active and one is flare-quiet during the observation over a period of several days. While the magnitude of free magnetic energy unambiguously differentiates between the flare-active and the flare-quiet regions, the temporal variation of free magnetic energy does not exhibit a clear and consistent pre-flare pattern. This may indicate that the trigger mechanism of flares is as important as the energy storage in active regions.

EVOLUTION OF OPTICAL PENUMBRAL AND SHEAR FLOWS ASSOCIATED WITH THE X3.4 FLARE OF 2006 DECEMBER 13

The rapid and irreversible decay of penumbrae related to X-class flares has been found in a number of studies. Since the optical penumbral flows are closely associated with the morphology of sunspot penumbra, we use state-of-the-art Hinode data to track penumbral flows in flaring active regions as well as shear flows close to the flaring neutral line. This paper concentrates on AR 10930 around the time of an X3.4 flare on 2006 December 13. We utilize the seeing-free solar optical telescope G-band data as a tracer to obtain the horizontal component of the penumbral and shear flows by local correlation tracking, and Stokes-V data to register positive and negative magnetic elements along the magnetic neutral line. We find that: (1) an obvious penumbral decay appears in this active region intimately associated with the X3.4 flare; (2) the mean magnitude of the horizontal speeds of the penumbral flows within the penumbral decay areas temporally and spatially varies from 0.6 to 1.1 km s?1; (3) the penumbral flow decreases before the flare eruption in two of the four penumbral decay areas; (4) the mean shear flows along the magnetic neutral line of this ?-sunspot started to decrease before the flare and continue to decrease for another hour after the flare. The magnitude of this flow apparently dropped from 0.6 to 0.3 km s?1. We propose that the decays of the penumbra and the penumbral flow are related to the magnetic rearrangement involved in the coronal mass ejection/flare events.

A Statistical Study of Rapid Sunspot Structure Change Associated with Flares

We reported recently some rapid changes of sunspot structure in white-light (WL) associated with major flares. We extend the study to smaller events and present here results of a statistical study of this phenomenon. In total, we investigate 403 events from 1998 May 9 to 2004 July 17, including 40 X-class, 174 M-class, and 189 C-class flares. By monitoring the structure of the flaring active regions using the WL observations from the Transition Region and Coronal Explorer (TRACE), we find that segments in the outer sunspot structure decayed rapidly right after many flares; and that, on the other hand, the central part of sunspots near the flare-associated magnetic neutral line became darkened. These rapid and permanent changes are evidenced in the time profiles of WL mean intensity and are not likely resulted from the flare emissions. Our study further shows that the outer sunspot structure decay as well as the central structure darkening are more likely to be detected in larger solar flares. For X-class flares, over 40% events show distinct sunspot structure change. For M- and C-class flares, this percentage drops to 17% and 10%, respectively. The results of this statistical study support our previously proposed reconnection picture, i.e., the flare-related magnetic fields evolve from a highly inclined to a more vertical configuration.

Statistical Correlations between Parameters of Photospheric Magnetic Fields and Coronal Soft X-Ray Brightness

Using observations of more than 160 active regions, we investigate the relationship between the coronal X-ray brightness, LB, and five parameters derived from the photospheric magnetic fields. The coronal X-ray brightness and the magnetic measures were obtained from co-aligned SFD composite images from the Yohkoh SXT and full-disk magnetograms from the SOHO MDI, respectively. The magnetic parameters are (1) the length of strong-gradient magnetic neutral lines, GNL, (2) the magnetic energy dissipation, , (3) the unsigned line-of-sight magnetic flux, Φ, (4) the horizontal velocities, Vh, of random footpoint motions in the photosphere, and (5) a proxy for the Poynting flux, E = (1/4π) 2, which characterizes the energy flux from the photosphere into the corona due to random footpoint motions. All measures except Vh were analyzed in both the extensive (total) and intensive (average over an area) forms. In addition, we used the area-averaged strong gradient (>50 G) of the magnetic field, ∇Bz, as an intensive form of GNL. We found that the Pearson correlation coefficient between the total X-ray brightness and the total magnetic measures decreases as 0.97, 0.88, 0.86, and 0.47 for Φ, E, , and GNL, respectively. The correlation coefficient between the averaged X-ray brightness and the averaged magnetic measures varied as 0.67, 0.71, 0.57, and 0.49 for , , , and , respectively. We also found that the velocities of the footpoint motions have no dependencies with Φ and LB. We concluded that the observed high correlation between LB and E is mainly due to the magnetic field. The energy of the Poynting flux is in the range 106.7-107.6 ergs cm-2 s-1 for the majority of active regions, which is sufficient to heat the corona due to footpoint random motions of magnetic flux tubes.