The Spectra of Opaque Radio Sources

Abstract

Radio spectra are shown for thirty radio sources that show evidence of synchrotron self-absorption. As a result of inverse Compton cooling and adiabatic expansion, all opaque components have a maximum brightness temperature in the range 10 u-10 12 ° K. The magnetic field deduced from the surface brightness and cutofi frequency in these sources is generally about lO-4 * 1 gauss. The variable components appear to have somewhat stronger magnetic fields. The form of the spectra of radio sources depends on two parameters : the energy distribution of the relativistic electrons and their optical depth. The accurate determination of radio spectra thus provides a means of investigating the distribution of relativistic electrons both in energy and in space. New measurements at 2.7 GHz (Kellermann, Pauliny-Toth, and Tyler 1968), 5 GHz (Pauliny-Toth and Kellermann 1968a) and unpublished measurements at 0.4, 0.75, 1.4, 10.6, 15.3, and 31.6 GHz combined with published data now allow a detailed description of radio spectra for some sources over a range of more than 1000 to 1 in frequency. Figures 1, 2, and 3 show examples chosen to illustrate the various types of spectra that we have observed. The sources shown in Figure 1 have small opacities over the entire observed frequency range, and their spectra depend only on the distribution in energy of the relativistic electrons; those in Figures 2 and 3 contain one or more opaque components. The data refer mostly to the epoch 1967 .°. Of the sources with small opacities, some (e.g., 3C 2) are found to retain the "classical" power-law spectrum with a constant spectral index 1 over the entire range of observed frequencies. Others (e.g., 3C 161, 3C 410) have spectra that can be described by two indices, one index at high frequencies and a numerically smaller one at low frequencies. In these sources the curvature of the spectrum is not continuous but is generally confined to a narrow range of frequencies near 1 GHz. This particular frequency may not be significant, however, as it is near the geometric mean of the observed frequency range and it would be difficult to distinguish spectral curvature below a few hundred megahertz or above a few gigahertz from the effect of small errors in the flux densities. The change in the spectral index in these sources is probably mostly due to the modification of the initial electron energy distribution by synchrotron or inverse Comp-ton losses. In some sources partial self-absorption may also contribute to the flattening of the spectrum at low frequencies. It is significant that there are no extended sources (greater than 1 arc second) that have a well-defined power-law spectrum over any frequency range with an index greater than-0.5 (7 < 2.0). Flatter spectra and hence lower values of 7 are observed in very compact components of some radio sources such as 3C 120 (Pauliny-Toth and Kellermann 19686) or 3C 273 (Dent 1968). However, most of the apparently flat spectra found in radio sources cannot be described by a power law but show considerable structure. This suggests that these spectra are the result of the superposition of several components , each of which has a different low-frequency cutoff, rather than a single com-* Operated by Associated Universities, Inc., under contract with the National Science Foundation. 1 The spectral index, a, is defined as follows: flux density oc (frequency)®; it is related to the index, 7, of the electron energy distribution, N(E)dE Er y dE, by 7 = 1-2a. L71