Determining the shape of spectra in extended radio sources

We present an innovative technique for determining the shape of the synchrotron spectra in extended radio sources. This method involves a three-frequency "color-color" diagram that emphasizes differences in the shapes of various theoretical models. The advantages of this technique over standard multifrequency mapping are that (1) it is easy to collect the necessary data (only three frequencies required), (2) it highlights the curvature changes in the spectrum, and (3) it puts data from all regions of the source onto one plane; and if a global spectrum exists, (4) it allows for effectively continuous sampling in frequency, (5) it provides sampling over a much larger range of electron energies, and (6) both the shape of the spectrum and the injection index, if it exists, can be determined by three-frequency data. Once the shape of the spectrum is understood, it is possible to pursue questions concerning synchrotron and Compton losses, adiabatic expansion, and particle acceleration. We have applied this technique to the multifrequency data of Cygnus A collected by Carilli et al. (1991). We find a single spectral shape which appears to fit all positions in the source, from the high emissivity hot spots to the diffuse lobes. This shape is different than the standard models; in particular we see no evidence that the spectrum is a power law in any frequency range. This study therefore calls into question the nature of the injected electron energy distribution and the validity of all current spectral analyses.