Magnetic Helicity of Solar Active Regions as Revealed by Vector Magnetograms and Coronal X-Ray Images

We have used photospheric vector magnetograms of 15 different solar active regions to calculate the current helicity parameter, α_av, and the linear force-free field (LFFF) parameter, α_best, that fits best the observed transverse field. The data were obtained with the Solar Magnetic Field Telescope at the Huairou Solar Observing Station, the National Astronomical Observatories of China, the Solar Flare Telescope of the National Astronomical Observatory of Japan, and the Haleakala Stokes Polarimeter at the Mees Solar Observatory, University of Hawaii, from 1997 to 2000. The agreement in sign of α_av between three vector magnetographs is better than 90%. For α_best, the agreement is 80%-90%. The line-of-sight magnetograms observed with the Michelson-Doppler Imager (MDI) on SOHO and coronal X-ray images observed with the Soft X-ray Telescope (SXT) on Yohkoh have been used to determine the constant α_c of the LFFF in the corona. The value of α_c corresponds to the extrapolated coronal field whose field lines best match, by visual inspection, the structure of coronal loops in X-ray images. It is found that the sign agreement between photospheric α_av or α_best and coronal α_c is lower (60%-85%). We consider the differences in measurements, observing conditions, data reduction methods, and limitation in LFFF extrapolation, and discuss their contributions to the dispersions in the hemispheric sign rule of helicity.