In this paper we present for the first time a new approach to determine the solar magnetic fields of active regions based on measurements of the spectrum and polarization of the bremsstrahlung radio emission. In a number of previous studies this emission was analyzed either for the optically transparent coronal emission (spectral index n=2) or for chromospheric structures. In the latter case the optical thickness is large and a weak polarization is due to the gradient of temperature, then the spectral index should be found from observations or taken a priori.
The new approach provides both chromospheric and coronal field values, if spectral intensity and polarization measurements are available. More than that the parameter <tT>, representing mostly the emission measure of the corona, can be found from the same observations. This was found to be in good agreement with our previous tomography study (Bogod & Grebinskij ).
As far as magnetic fields concerned the most important conclusion is the high value of the magnetic field in the corona above active regions. We found (in one example) the maximum values of 50-150G in plage areas (chromosphere-corona), while we derived 80-300G on optical magnetograms for the same active region. This implies a ratio of 0.6-0.7 for radio to optical magnetic fields. It is of interest that similarly high ratios (up to 0.8) have been found for the magnetic fields above sunspots (see Shibasaki et al. ; Akhmedov et al. ), though the latter analysis was based on a different method, namely the usage of thermal cyclotron emission on the third harmonic of the electron gyrofrequency. This result is interpreted in terms of the very low height of the corona above sunspots.
From a methodical point of view, another important conclusion is the dominance of the coronal versus chromospheric contribution to the observed polarized component of solar emission below GHz. The reason for the low contribution of the chromosphere to the polarized component is not model dependent and has a clear physical significance. The reason for the low degree of polarization of the chromospheric plasma is the low temperature gradients. So, both x-mode and o-mode are generated in layers with the same electronic kinetic temperature and produce the emission at brightness temperatures close to with the result of . The details of this effect certainly should be found from spectral-polarization observations with high spatial resolution. It is of practical interest that observations at cm made with V-maps Nobeyama radioheliograph include already significant parts of the chromospheric magnetic field. Additional information on the magnetic fields both in the corona and chromosphere can be gained from regular and high spatial resolution data, especially at 34 GHz with Nobeyama and 90 GHz with Metsähovi.
Our results show, that the measurements of brightness and circular polarization spectra of solar bremsstrahlung at microwaves give an efficient method to measure magnetic fields in the chromosphere and corona above active regions. However, to proceed significantly into this direction we still need large improvements both in imaging techniques (with high angular and spectral-polarization resolution) and interpretation (taking into account of spatial fine-structure effects).
This research has been partially supported by the Russian Foundation for Basic Research (RFBR) Projects 99-02-16403a and 99-02-16171a, INTAS - RFBR grants 95-316 and 97-1088.
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