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, L sub(B), 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, pound sterling sub(CNL), (2) the magnetic energy dissipation, epsilon , (3) the unsigned line-of-sight magnetic flux, Phi , (4) the horizontal velocities, V sub(h), of random footpoint motions in the photosphere, and (5) a proxy for the Poynting flux, E = (1/4 capital pi ) degree 'V sub(h) degree ' degree ' [unk] degree ' super(2), which characterizes the energy flux from the photosphere into the corona due to random footpoint motions. All measures except V sub(h) 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, gradient B sub(x), as an intensive form of pound sterling sub(CNL). 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 Phi , E, epsilon , and pound sterling sub(CNL), 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 ( [unk]), (E), [unk], and ( gradient B sub(x)), respectively. We also found that the velocities of the footpoint motions have no dependencies with Phi and L sub(B). We concluded that the observed high correlation between L sub(B) and E is mainly due to the magnetic field. The energy of the Poynting flux is in the range 10 super(6.7)-10 super(7.6) ergs cm super(-2) s super(-1) for the majority of active regions, which is sufficient to heat the corona due to footpoint random motions of magnetic flux tubes.