Using the full magnetoionic theory in the microwave region along a ray-path through the solar chromosphere and corona we have obtained a convenient expression, and from it a simple diagram which permits the direct computation of the brightness temperature and circular polarization from a thermal source, for any combination of the physical parameters which enter in their computation.
IntroductionThe study of solar active regions at cm and mm wavelengths has provided considerable insight into the electron densities, temperatures and magnetic fields in these areas. High resolution microwave observations by Kundu et al. (1974) have shown that active regions consist of one or more extremely hot cores, only a few arc seconds in diameter, surrounded by an extended halo, which is not as hot. The high brightness temperatures and often high degrees of circular polarization observed in the cores are due to gyroresonance effects. The brightness temperature and polarizations of the halos on the other hand, where the magnetic fields are weaker, are due to free-free absorption produced by enhanced electron densities (5-10 times normal) over the entire active region.A complete understanding of the physics of active regions before, during, and after flare events (Alissandrakis and Kundu, 1975;Lang, 1974) is of utmost importance and this will necessitate the detailed study of the changes which occur not only in the hot cores but also in the large halos which surround them. The method developed in this paper can be applied in the study of the halos from high resolution maps of active regions as well as in the analysis of other thermal regions such as plage areas without sunspots, decaying active regions, and the cooler regions which surround solar filaments (Straka et al., 1975). Fitting a physical model to the observed values of left (Tz) and right (Tr) circularly polarized brightness temperatures is a rather complicated problem, primarily because of the several variable parameters involved. One possible simplification is to use a constant effective magnetic field for the emission region under consideration. This approach is suggested by the fact that the thermal emission in the microwave domain originates in a rather narrow layer in the upper chromosphere. Figure 1 shows the contribution to the brightness temperature (ATb/zlh) in the emission layer at 3.8cm for different models of the solar atmosphere.