15.4.5. Redshift and Luminosity Distributions of Strong Sources
Spectroscopic redshifts exist for nearly all 3CR sources stronger than 10 Jy at 178 MHz (Laing et al. 1983, Spinrad et al. 1985) and for most of the stronger flat-spectrum sources found in high-frequency radio surveys (Kühr et al. 1981, Véron-Cetty and Véron 1983, Wall and Peacock 1985). Photometric redshifts of the remaining strong sources identified with galaxies can be estimated from Hubble relations such as log(z) (m - 22.5) / 6 valid for first-ranked cluster galaxies and 3CR and 4C radio galaxies (van der Laan and Windhorst 1982, Windhorst 1986); empty-field sources can be treated as galaxies just fainter than the plate limit. Redshift distributions of quasar candidates may be approximated by the redshift distributions of known quasars or by a broad Hubble relation (Wall and Peacock 1985). Let N(z | S, ) d[log(z)] be the integral number of sources per steradian with redshifts log(z) to log(z) + d[log(z)] and stronger than S at frequency . Such an (unnormalized) redshift distribution of 202 extragalactic sources stronger than S = 2 Jy at = 1.4 GHz is shown in Figure 15.9.
Figure 15.9. Redshift distribution of 202 sources stronger than S = 2 Jy at = 1.4 GHz. Spectroscopic redshifts are indicated by heavy shading, estimated redshifts by hatching. Abscissa: log redshift. Ordinate: number of sources per steradian per decade of redshift.
Since most of the sources in a flux-limited sample are within a factor of two of the flux-density limit, the integral luminosity distribution N(L| S, ) d[log(L)], or number of sources per steradian with luminosities log(L) to log(L) + d[log(L)] that are stronger than flux density S at frequency , can be used almost interchangeably with the integral redshift distribution. However, both of these distributions bin the (S, z)-data and hence do not make the most efficient possible use of the strong-source data (Peacock 1985).