Three-dimensional structure of microwave sources from solar rotation stereoscopy versus magnetic extrapolations

We use rotation stereoscopy to estimate the height of a steady-state solar feature relative to the photosphere, based on its apparent motion in the image plane recorded over several days of observation. The stereoscopy algorithm is adapted to work with either one- or two-dimensional data (i.e., from images or from observations that record the projected position of the source along an arbitrary axis). The accuracy of the algorithm is tested on simulated data, and then the algorithm is used to estimate the coronal radio source heights associated with the active region NOAA 10956, based on multifrequency imaging data over seven days from the Siberian Solar Radio Telescope near 5.7GHz, the Nobeyama Radio Heliograph at 17GHz, as well as one-dimensional scans at multiple frequencies spanning the 5.98-15.95GHz frequency range from the RATAN-600 instrument. The gyroresonance emission mechanism, which is sensitive to the coronal magnetic field strength, is applied to convert the estimated radio source heights at various frequencies, h(f), to information about magnetic field versus height B(h), and the results are compared to a magnetic field extrapolation derived from photospheric magnetic field observations obtained by Hinode and Michelson Doppler Imager. We found that the gyroresonant emission comes from heights exceeding the location of the third gyrolayer irrespective of the magnetic extrapolation method; implications of this finding for coronal magnetography and coronal plasma physics are discussed.