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

Abstract

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, ℒGNL, (2) the magnetic energy dissipation, ε, (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) | V h,||BZ |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 ℒGNL. 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, ε, and ℒGNL, 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 (Φ), (E), (ε), and (∇BZ), 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. © 2007. The American Astronomical Society. All rights reserved.