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_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, ℒ_GNL, (2) the magnetic energy dissipation, ε, (3) the unsigned line-of-sight magnetic flux, Φ, (4) the horizontal velocities, V_h, of random footpoint motions in the photosphere, and (5) a proxy for the Poynting flux, E = (1/4π) | V _h,||B_Z |², which characterizes the energy flux from the photosphere into the corona due to random footpoint motions. All measures except V_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, ∇B_Z, as an intensive form of ℒ_GNL. 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 ℒ_GNL, 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 (∇B_Z), respectively. We also found that the velocities of the footpoint motions have no dependencies with Φ and L_B. We concluded that the observed high correlation between L_B and E is mainly due to the magnetic field. The energy of the Poynting flux is in the range 10^6.7-10^7.6 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.