6.4. An Alternative: The Universal Spectrum
The basic premises of spectral ageing analyses of the type discussed above have been called into question recently by Rudnick and Katz-Stone (1996), Rudnick, Katz-Stone, and Anderson (1994), Katz-Stone and Rudnick (1994), and Katz-Stone, Rudnick, and Anderson (1993). They re-analyze the spectral data for Cygnus A and reach some disconcerting conclusions. First, they question the existence of a power-law in any region of the spectrum. And second, they find that all spectra in the source, hotspots and lobes alike, can be explained by simply shifting (in the log plane) a single continuous function. They argue for a `universal spectrum', with `no evidence for evolution of the electron energy distribution', other than this simple scaling in frequency and/or intensity.
They reach these conclusions through the use of a radio `color-color' diagram. The radio color-color diagram entails plotting for each position in the source the observed spectral index between two frequencies against that between two other frequencies. They point out that such two-color diagrams have a few advantages over multi-frequency spectral model fitting, including: emphasizing more clearly curvature in spectra and `displaying information from all positions in a source in a way that enables one to see the real connections between the various spectra'. Most importantly, their approach is strictly empirical, and hence may reveal trends in the data which are missed in an analysis fundamentally tied to a physical model.
The color-color diagram for Cygnus A reveals a well-defined locus of points. This locus can be described empirically by a single spectral shape (the `universal spectrum') through simple scalings in frequency and/or intensity. As further proof Rudnick et al. have taken spectra from three different regions of Cygnus A (hotspots and lobes included) and scaled each accordingly to fit this universal spectrum.
Katz-Stone et al. (1994) have shown that given a spectral index image, an image of total intensity, and the empirically derived universal spectrum, one can derive images based on products of pairs of three basic physical parameters: the magnetic field strength, the relativistic particle density, and the `characteristic energy' for the particle distributions. They apply this `color-correction' technique to Cygnus A and find that the eastern lobe shows a bright `channel which straddles the counterjet.' They suggest that this channel is dominated by a density enhancement, rather than by magnetic or energy effects.
The fundamental appeal of the two-color analysis is its independence from physical assumptions. The ultimate goal of relating the results to fundamental source physics remains under investation (Rudnick and Katz-Stone 1996). One particular question that must be addressed is: how to avoid the inevitable effects of synchrotron losses on the emitted spectra? Also, the fact remains that in terms of a proper 2 fitting with well defined errors, spectral ageing theory cannot be precluded by the data (Carilli et al. 1991a).
Overall, the numerous spectral studies of Cygnus A have emphasized the fundamental difficulty in quantitative analysis of radio continuum spectra, namely, the extremely broad range in frequency required to constrain the various models. Further insight into the validity of spectral ageing theory, or a universal spectrum, requires either arc-second resolution imaging at very low frequency ( 100 MHz), or extremely sensitive observations at high frequency, both of which are at the limit of current instrumentation.