Survey of Magnetic Helicity Injection in Regions Producing X-Class Flares

Virtually all X-class flares produce a coronal mass ejection (CME), and each CME carries magnetic helicity into the heliosphere. Using magnetograms from the Michelson Doppler Imager on the Solar and Heliospheric Observatory, we surveyed magnetic helicity injection into 48 X-flare-producing active regions recorded by the MDI between 1996 July and 2005 July. Magnetic helicity flux was calculated according to the method of Chae for the 48 X-flaring regions and for 345 non-X-flaring regions. Our survey revealed that a necessary condition for the occurrence of an X-flare is that the peak helicity flux has a magnitude >6 × 10³⁶ Mx² s^-1. X-flaring regions also consistently had a higher net helicity change during the ~6 day measurement intervals than nonflaring regions. We find that the weak hemispherical preference of helicity injection, positive in the south and negative in the north, is caused by the solar differential rotation, but it tends to be obscured by the intrinsic helicity injection, which is more disorganized and tends to be of opposite sign. An empirical fit to the data shows that the injected helicity over the range 10³⁹-10 ⁴³ Mx² s^-1 is proportional to magnetic flux squared. Similarly, over a range of 0.3-3000 days, the time required to generate the helicity in a CME is inversely proportional to the magnetic flux squared. Most of the X-flare regions generated the helicity needed for a CME in a few days to a few hours.