Annu. Rev. Astron. Astrophys. 1988. 26: 561-630
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7.4. Evolution Inferred From Quasar Counts

Two aspects of the quasar distribution functions N(m) and N(z) give the strongest geometrical evidence for evolution.

7.4.1. SLOPE OF THE COUNT-BRIGHTNESS RELATION   The first evidence for evolution using optically selected quasars was the pronounced non-Euclidean slope to log N(m) for quasars in the magnitude interval 18.1 < B < 21.4 (Sandage & Luyten 1969). The three N(m), B mag data points of (0.4, 18.1), (5, 19.4), and (100, 21.4) set out by these authors give d log N(m) / dm = 0.75. This is much steeper than 0.6 for nonexpanding Euclidean space. The redshift K correction to the observed magnitude is close to zero, appropriate for a mean quasar spectrum of nu-1 (Sandage 1966). The observed slope is steeper than the N(m), relation appropriate to expanding spaces, where d log N(m)/dm ~ 0.4 is predicted from Figure 2.

Modern quasar counts, summarized by (among others) Mitchell et al. (1984) at the bright end and by Koo et al (1986, their Figure 7), Koo & Kron (1988b), and Boyle et al. (1987, their F1igure 1) at the faint end, confirm these early numbers.

From the count data alone one cannot decide if the evolution is due to luminosity brightening with look-back time or to increased number of objects (density evolution). Entrance to the large literature on this problem can be achieved from Schmidt & Green (1983) and from the review by Boyle et al. (1987). The 1987 consensus opinion is that the steep quasar count-magnitude distribution is due mainly to luminosity evolution.

7.4.2. DECREASE OF dN(z)/dz AT HIGH z   The possibility of a redshift cutoff high z(geq 3) was identified early in the analysis of radio quasars listed in the 3C Cambridge catalog. Observational selection effects in this radio-selected sample were assessed (Sandage 1972c), and none were found that could artificially produce the apparent cutoff, whose cause could be the first light from galaxies at high look-back times, i.e. from galaxy creation itself.

In the ensuing years, the reality of the quasar cutoff has been widely debated, usually by analyzing optically selected samples that have multiple selection effects not present in the radio samples. A number of deep surveys were begun early in quest of a cutoff. A review by Smith (1978) of the first phases of this activity sets the stage for Osmer's (1982) convincing study using optically selected quasars, where he concludes that "the apparent space density must decrease significantly at 3.7 < z < 4.7."

In an independent deep survey using CCD detection with the Hale 200-inch reflector, Schmidt et al. (1986) concur. Their conclusion is that "quasars with an absolute magnitude of MB ~ - 25 suffer a redshift cutoff near or below a redshift of 3." A contrary discussion is given by Koo & Kron (1988b), who find no evidence for a redshift cutoff.

Any such large variation (if real) of any property of any type of object at large redshift is, of course, evidence for secular evolution of mean parameter values with look-back time. Convincing proof would be evidence for an evolving rather than a steady-state universe. If indeed evolution does occur, it is a most powerful, albeit elementary, verification of the most important prediction of the standard model - that the present Universe is of finite age. However, if secular evolution cannot be found where it should occur, the standard model fails. Although there are strong arguments in favor of evolution [Butcher-Oemler, Dressler-Gunn, quasar N(m) slope, perhaps a redshift cutoff for quasars], the data in 1987 are not yet quite overwhelming.

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