Measurements of three-dimensional coronal magnetic fields from coordinated extreme-ultraviolet and radio observations of a solar active region sunspot

We observed NOAA Active Region 8108 around 1940 UT on 1997 November 18 with the Very Large Array and with three instruments aboard the NASA/ESA Solar and Heliospheric Observatory satellite, including the Coronal Diagnostic Spectrometer, the EUV Imaging Telescope, and the Michelson Doppler Imager. We used the right-hand and left-hand circularly polarized components of the radio observing frequencies, along with the coordinated EUV observations, to derive the three-dimensional coronal magnetic field above the regions sunspot and its immediate surroundings. This was done by placing the largest possible harmonic (which corresponds to the smallest possible magnetic field strength) for each component of each radio frequency into appropriate atmospheric temperature intervals such that the calculated radio brightness temperatures at each spatial location match the corresponding observed values. The temperature dependence of the derived coronal magnetic field, B(x, y, T), is insensitive to uncertainties on the observed parameters and yields field strengths in excess of 580 G at 2 x 10(6) K and in excess of 1500 G at 1 x 10(6) K. The height dependence of the derived coronal magnetic field, B(x, y, T), varies significantly with our choice of magnetic scale height L-B. Based on L-B = 3.8 x 10(9) cm derived from the relative displacements of the observed radio centroids, we find magnetic field strengths in excess of 1500 G at heights of 15,000 km and as great as 1000 G at 25,000 km. By observing a given target region on several successive days, we would obtain observations at a variety of projection angles, thus enabling a better determination of L-B and, ultimately, B(x, y, h). We compare coronal magnetic fields derived from our method with those derived from a potential extrapolation and find that the magnitudes of the potential field strengths are factors of 2 or more smaller than those derived from our method. This indicates that the sunspot field is not potential and that currents must be present in the corona. Alfven speeds between 25,000 and 57,000 km s(-1) are derived for the 1 x 10(6) K plasma at the centroids of the radio observing frequencies. Filling factors between 0.003 and 0.1 are derived for the 1 x 10(6) K plasma at the centroids of the radio observing frequencies.