The turnover in the radio spectrum is a defining characteristic of the GPS and CSS sources. It contains information on the source size, its physical properties, and its environment.
2.1. Spectral Shape and Implications for Lifetimes
The shapes of the radio spectra are one of the chief identifying characteristics of the GPS and CSS sources (see Fig. 1 and Fanti et al. 1985, 1989; Schilizzi et al. 1990; Steppe, Salter, & Saikia 1990; O'Dea et al. 1990b; Kameno et al. 1995; Steppe et al. 1995; Stanghellini et al. 1996, 1998b; de Vries et al. 1997a). These sources have simple peaked spectra with steep spectral indices at high frequencies. O'Dea et al. (1990b, 1991) noted that the spectra of GPS sources can be quite narrow with values for the full width to half the peak flux density of around 1-1.5 decades of frequency. The GPS source with the most inverted spectrum is 0108+388 (Baum et al. 1990), which has a value of 2 and approaches the canonical value of 2.5 for a simple homogeneous synchrotron source. However, the fact that none of the GPS or CSS sources have spectra as inverted as 2.5 suggests that there is inhomogeneity in the radio structure (this is of course confirmed by the radio imaging [section 3], which shows cores, jets, hot spots, and lobes in these objects).
Figure 1. Radio spectra of GPS and CSS radio sources (S. Jeyakumar 1997, private communication; see also Steppe et al. 1995). Vertical axis is flux density in Jy, and horizontal axis is frequency in GHz.
The distribution of spectral index above the peak is shown in Figure 2. This plot combines the data for the Fanti et al. (1990b) sample of CSSs and the Stanghellini et al. (1998b) sample of GPSs (shaded). The lower limit at about -0.5 is imposed by the selection criteria. (3) There is a broad distribution from -0.5 to -1 with a few sources around -1.1 to -1.3. (4) The GPS and CSS sources have similar distributions. There is a slight suggestion that the GPS sources have flatter spectra than the CSSs, but this may be mainly a result of the fact that the spectral indices are measured closer to the spectral peak in the GPSs than in the CSSs. de Vries et al. (1997a) have determined an "average" radio spectrum for a sample of 72 GPS radio sources. The average spectral indices below and above the spectral peak are 0.56 and -0.77, respectively. The average value of -0.77 is also typical for the large-scale powerful sources (see, e.g., Kellermann 1966b), suggesting that relativistic electron acceleration and energy loss mechanisms preserve the same average spectral index over most of the lifetime of the source.
Figure 2. Histogram of spectral index above the spectral peak. The sources are the Fanti et al. CSS sample and the Stanghellini et al. GPS sample (shaded).
If the turnover is due to synchrotron self-absorption, then from equation (2) the generally narrow spectrum implies that there is a limited range of spatial scales that contribute to the bulk of the radio luminosity; i.e., there is a cutoff in both the largest and smallest scales (see also Phinney 1985). This is consistent with the lack of large-scale structure in these sources.
The spectra tend to be fairly straight (constant spectral index) at high frequencies with few sources showing either steepening from radiation losses, or flattening due to a compact component (though there are examples of both phenomena). This has consequences for the inferred "spectral age" of the radiating electrons. Two possible explanations for the lack of an observed break are that the spectral break is either (1) still at higher frequencies (100 GHz) or (2) hidden below the spectral peak. As pointed out by Kardashev (1962), continuous resupply will limit the change in spectral index at the break frequency to 0.5 instead of an exponential drop. Thus, if the jets supply sufficient energy to the extended radio structure that Kardashev's condition is met, it is possible that the break is below the spectral peak for the sources with a high-frequency spectral index steeper than -1. For sources with flatter spectra the implied initial spectrum -0.5 may be too flat to be consistent with the extended optically thin emission, and these sources may have their break at high frequency. Because of both continuing resupply and adiabatic losses, which will have opposite effects on the spectrum, the interpretation of the spectral age is uncertain. The electron lifetime is given by
where B is the magnetic field in G, BR 4(1 + z)2 × 10-6 G is the equivalent magnetic field of the microwave background, and b is the break frequency in Hz (van der Laan & Perola 1969). For a high value of break frequency b = 100 GHz, for a GPS source (B = 10-3 G) and a CSS source (B = 10-4 G), the electron lifetimes are t 2 × 103 yr and t 7 × 104 yr, respectively. However, for a low value of the break frequency b = 100 MHz, the ages are t 7 × 104 yr and t 2 × 106 yr, respectively. Given the uncertainties, the range of spectral indices is consistent with a range of electron lifetimes among these sources, with some sources having possibly quite short electron lifetimes. The correspondence between electron lifetime and source age is not yet clear - though these results could be consistent with a range of ages for the GPS and CSS sources, with some of them, especially the GPS sources with flatter spectra, being quite young ( 104 yr). Katz-Stone & Rudnick (1997) have presented a "spectral tomography" analysis of two CSS sources, 3C 67 and 3C 190. They find complex spectral structure in these two sources and suggest that the sources could be young if the initial injection spectrum is as steep as -0.8. It is clear that images of spectral index are necessary to fully address the questions of electron age and source lifetime.
3 Note that there is some small inconsistency, since the updated values of spectral index used here are not the same as those originally used to define these samples. Back.
4 Curiously, the spectra can be as steep as those of the high-redshift ultrasteep-spectrum sources (see, e.g., Röttgering et al. 1994).