Coronal heating and photospheric turbulence parameters: Observational aspects

In this study, the soft X-ray luminosity of the solar corona, measured by the Yohkoh spacecraft for 104 well-developed and decaying active regions, is compared to the magnetic field parameters determined from SOHO MDI high-resolution magnetograms. We calculate and compare (1) two area-independent characteristics of the magnetic field: the index (alpha) of the magnetic power spectrum, E(k) similar to k(-alpha) and the magnetic energy dissipation rate ((epsilon) over bar/eta), which is a proxy for the energy of random footpoint motions induced by turbulent convection in the photosphere and below; and (2) four area- independent parameters of the soft X-ray emission: the area- normalized flux in Yohkoh A1.1 and AlMgMn channels, and the emission measure and temperature of the coronal plasma. Here we report that the area- normalized soft X-ray flux correlates with both the power index alpha(Pearson correlation coefficient p = A1.1 and 0.73/AlMgMn) and the magnetic energy dissipation rate (epsilon) over bar/eta (p = 0.68 0.70/AlMgMn). Also, both magnetic parameters are well- correlated with the logarithm of the emission measure and the logarithm of temperature [p = 0.59/alpha and 0.63/ ((epsilon) over bar/eta)]. Our results present strong observational support to those coronal heating models that rely on random footpoint motions as an energy source to heat the corona above active regions.