15.4.3. Spectral-Index Distributions
Two-point spectral indices (1, 2) have been measured between 1 1.4 GHz and 2 5 GHz for a number of flux-limited source samples. The integral number N(| S, ) d of sources per steradian with spectral indices to + d and flux densities S at frequency is shown for S 0.8 Jy at = 5 GHz in Figure 15.7(a). This (unnormalized) spectral-index distribution consists of a narrow steep-spectrum component with <> 0.7 and a broader flat-spectrum component centered on <>0.0. As the sample selection frequency is lowered, the number of steep-spectrum sources increases rapidly and the median spectral indices <> of both components increase. The increase in <> of each spectral component is proportional to the square of its width (Kellermann 1964), so the median spectral index of the flat-spectrum component changes more rapidly with frequency. These effects can be seen by comparing Figure 15.7(a) with the spectral-index distribution of sources stronger than S = 2 Jy at = 1.4 GHz [Figure 15.7(b)]. The fraction of flat-spectrum sources may also change with the sample flux-density limit S at a given frequency . Figure 15.7(c) gives the spectral-index distribution of fainter (S 0.035 Jy) sources selected at = 4.8 GHz.
Figure 15.7. (a) Spectral-index distribution of 320 sources stranger than S = 0.8 Jy at = 5 GHz (Witzel et al. 1979). (b) Spectral-index distribution of 202 sources stronger than S = 2 Jy at = 1.4 GHz as compiled by Condon (1984b). (c) Spectral-index distribution of 479 sources stronger than S = 0.035 Jy at = 4.8 GHz (Owen et al. 1983). Abscissas: spectral index between 1.4 and 5 GHz. Ordinates: number of sources per steradian per unit .