Abstract

From maps of the brightness temperatures Tb of a thermal radio source, at frequency vo, one obtains angular areas enclosed by contours, w(T (vo)); this function is such that Tb> Tb' within the area w(Tb'). The spectrum of the total flux density, Sp, observed at many frequencies V, may be fitted to an analytic function of a frequency variable x = f(v). It is shown that, using an inverse Laplace transform, one obtains Te (E) as a function of V = E/ Te312, where Te is the electron temperature, E is the emission measure, and (E) is such that E> E' within the angular area Assuming a value for Te, one may deduce (Tb(Vo)) from the spectrum observations. Adjustment of Te can be made so as to obtain a best fit to a)(Tb(vo)) deduced from observations with high angular resolution. If significant structural detail has not been resolved, the results obtained for Te will tend to be too small. Information concerning the extent to which structural detail is resolved can be deduced if an independent estimate of Te is available. For the Orion nebula, line observations at optical and radio wavelengths indicate that Te = 9000+ 1000 K. It is shown that the radio continuum data is consistent with this result, but that full resolution of structural detail has not been achieved in some of the published work on brightness contours. For the compact H+ region DR2I the best fit is obtained with Te = 8ooo K, in agreement with the work of Harris, but the available data does not exclude a higher value of Te, say Te = 9000 K. Various sources of error in the processes of observation and analysis are discussed.