12.4.5. Empirical Relations
The establishment of relations between the various observed radio source properties is clearly important to the understanding of the origin and evolution of extra-galactic sources. Some of the better-determined relations are summarized below. Some of these are well understood in terms of current theory, while others are not.
Spectral index-angular size. All of the sources with flat or inverted spectra ( - 0.5) have components with small angular dimensions ( << 1"). This is well understood as the effect of self-absorption.
Spectral-index variability. All of the sources which show flux density variations have flat ( - 0.5) or CPX spectra in the spectral region where the intensity varies. This is a reflection of the fact that only the opaque or partially opaque sources vary. Sources which have a single sharp low-frequency cut-off generally do not vary as much, at least over the time scales for which accurate observations are available.
Radio-optical variability. Sources which show large radio flux density variations also frequently show large variations at optical wavelengths as well, but there is no simple one-to-one relationship.
Variability-wavelength. The largest and most rapid variations generally occur at the shorter wavelengths.
Spectral-index-luminosity. Among the extended transparent radio galaxies there is a tendency for the most luminous sources to have the steepest spectra (Heeschen, 1960), particularly for sources with Class S spectra. This relationship does not seem to hold, however, for the quasars which all have a very high radio luminosity.
Luminosity-structure. Sources with relatively simple brightness distributions are of relatively low luminosity.
Luminosity-brightness. Sources with a high surface brightness have a high radio luminosity. Two sequences are apparent, as shown in Figure 13.9. The apparent continuity of the quasars and radio galaxies in this Heeschen diagram, if the quasar redshifts are assumed cosmological, is often taken as evidence of the cosmological origin of the redshifts. However, if the redshifts are local, then the quasars fall in the same high brightness-low luminosity part of the diagram as the cores of E galaxies such as M87, NGC 1052, and the Seyfert galaxy nuclei, so that the argument can go either way.
Polarization-wavelength. For the transparent sources (Class S spectra) the observed polarization is greatest at shorter wavelengths. In the opaque sources the reverse is true.
Circular polarization is found only in some compact sources.
The greatest linear polarization is found in the sources with low surface brightness, or in low surface brightness regions of resolved sources.
Sources found in clusters tend to have smaller dimensions.
The strong radio galaxies nearly all show intense emission lines.
The two most rapidly varying sources, BL Lac and OJ287, appear to be quasars, but their optical spectra do not show the emission lines common to other quasars.