NORMAL INCIDENCE X-RAY TELESCOPE POWER SPECTRA OF X-RAY-EMISSION FROM SOLAR ACTIVE REGIONS .2. THEORY

In a previous paper, we used the very high resolution images of coronal active regions obtained by the Normal Incidence X-Ray Telescope to study the size distribution of X-ray-emitting structures. A Fourier analysis of these images showed a broad-band, isotropic, power-law spectrum for the spatial distribution of soft X-ray intensities. The presence of a broad-band spectrum indicates that magnetic structures of all sizes are present, at least down to the resolution limit of the instrument, which is about 3/4''. In the present paper, we present a model that relates the basic features of coronal magnetic fluctuations to the subphotospheric hydrodynamic turbulence that generates them. The main result of this paper is that from this model we obtain a theoretical power spectrum for the X-ray intensity, which falls off with increasing wavenumber as k-3, fitting remarkably well the observed spectra that we obtained from a sample of topologically different active regions. We speculate that the nonlinear interactions of these externally driven fluctuations will contribute to establish a magnetohydrodynamic turbulent regime in the corona. We suggest that the bulk of the energy delivered to the corona from footpoint motions directly cascades down to very microscopic length scales, where it efficiently dissipates and heats the plasma. However, since the wavenumber range associated with the cascade and dissipation regions are still beyond present-day spatial resolution limits, the presence of a turbulent regime cannot be observationally confirmed.