Courtesy of NASA

   A solar flare is a sudden, rapid, and intense brightening usually in a magnetically complicated solar active region (AR). Solar flares produce high energy particles, radiation, and erupting magnetic structure that are related to geomagnetic storms. Their strong electromagnetic radiations from radio waves to Gamma-rays have direct effect on cell phones and the Global Positioning System and heat up the terrestrial atmosphere within minutes so that satellites drop into lower orbits (Schwenn 2006). Enormous economic and commercial losses can be caused by these effects (Baker 2004).

   Therefore, there have been significant efforts to develop flare forecasting systems as part of the space weather service. It is generally thought that flare-productive ARs exhibit complex and non-potential magnetic structures related to the stored magnetic energy to power flares. For this reason, we have studied the relationship between the solar flare and magnetic helicity. Magnetic helicity is a measure of twists, kinks, and inter-linkages of magnetic field lines (Berger & Field 1984) and it is a useful parameter to indicate topology and non-potentiality of a magnetic field system.

   Our daily forecasts of the flare index and the probability of flare occurrence are based on the statistical study of helicity injection in 378 ARs (Park et al. 2009). In detail, we first calculate the average helicity injection rate for a target AR during 24-hour period after the AR appears or rotates to a position within 0.6 of the solar radius from the apparent disk center. Based on the historical correlation data between helicity injection rate and soft X-ray flux in ARs, we then predict the flare index and the flare-productive probability for the time windows of the next 1^st and 2^nd days following the 24-hour period of the helicity measurement.

   The daily soft X-ray flare index (F_idx) was first introduced by Antalova (1996), and was later applied by Abramenko (2005):

F_idx  =  ( 100×S^(X) + 10×S^(M) + 1×S^(C) + 0.1×S^(B) ) / τ ,

where τ is the time interval (measured in days), and S^(j) is the sum of GOES flare significands in the ith GOES class over τ.

References

Abramenko, V.I.   2005, ApJ, 629, 1141

Antalova, A.   1996, Contrib. Astron. Obs. Skalnate Pleso, 26, 98

Berger, M. A. &  Field, G. B.   1984, J. Fluid Mech., 147, 133

Baker, D. N.   2004, Lecture Notes in Physics, 656, 3

Park, S.-H., Lee, J., Choe, G. S., Chae, J., Jeong, H., Yang, G., Jing, J., & Wang, H. 2008, ApJ, 686, 1397

Park, S.-H., Chae, J., & Wang, H. 2009, ApJ, in revision

Schwenn, R.   2006, Living Rev. Sol. Phys., 3, 2