Annu. Rev. Astron. Astrophys. 1984. 22: 471-506
Copyright © 1984 by . All rights reserved

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Even if AGNs are precursors on the route toward black hole formation (cf. Figure 1) rather than structures associated with black holes that have already formed, it seems hard to escape the conclusion that massive black holes must exist in profusion as remnants of past activity; they would be inconspicuous unless infall onto them recommenced and generated a renewed phase of accretion-powered output or catalyzed the extraction of latent spin energy.

Estimates of the masses and numbers of "dead" AGNs are bedeviled by uncertainty about how long individual active objects live and the evolutionary properties (i.e. the z-dependence) of the AGN population. As regards the latter, see, for instance, (81, 114, 127) for recent reviews of optical data, and (95, 126) for radio studies. It has long been known that the evolution is strong, amounting to a factor of up to 1000 in comoving density for the strongest sources; the evolution is differential, being less steep for lower-luminosity objects of all kinds. It is now feasible to refine these statements, though it is still premature to be extremely precise about the redshift dependence of the multivariate function f (Lrad, Lopt, LX). And we are still a long way from having much astrophysical understanding of why the luminosity function evolves in this way. Anyway, at the epoch z = 2, the population of strong sources declined on a time scale tEv appeq 2 × 109 h100 yr; this is of course an upper limit to the "half-life" of a particular source, since there may be many generations of objects within the period tEv.

Soltan (120) has given an argument that bypasses the uncertainty in AGN lifetimes but nevertheless yields useful constraints on the masses involved in such phenomena and the kinds of galaxies in which they can reside. The overall energy budget for AGNs is dominated by QSOs (most of which are "radio quiet"); they contribute an integrated background luminosity amounting to

Equation 35 (35)

This estimate involves an uncertain bolometric correction; the main measured contribution to nu L(nu) is typically at ~ 1015 Hz (i.e. in the ultraviolet). Although some individual quasars could emit more power in (for instance) the far-ultraviolet, hard X-rays, or gamma rays, we know enough about the isotropic background in these bands to be sure that such emission cannot permit a huge bolometric correction for the typical quasar. The main contribution to (35.) comes from quasars with 19 < B < 21 (corresponding to bolometric luminosities of 1045 - 1046 h100-2 erg s-1 if they are typically at z appeq 2); the counts flatten off at fainter magnitudes, so (35.) is unlikely to be a severe underestimate. The energy output from radio galaxies and other manifestations of active nuclei is much smaller than that from optically selected quasars; we are therefore probably justified in using (35.) in the discussion that follows.

The individual remnant masses can be estimated as

Equation 36 (36)

where epsilon is the overall efficiency with which rest mass is converted into electromagnetic radiation over a typical quasar's active lifetime tQ (defined as the time for which the magnitude is M < - 24). If quasars were associated with all "bright" galaxies (M < - 21.3), whose space density is known, the mean hole mass would be ~ 2 × 106 h100-3 epsilon-1 Msun. If only a small fraction of galaxies had ever harbored active nuclei, the masses (and lifetimes) of each would be correspondingly increased.

The above discussion is important if one wishes to relate nuclear activity to galactic morphology. However, it is also relevant as a discriminant between different models (99). If individual quasars are as long lived as is compatible with the cosmological evolution of the quasar population [i.e. tQ = tEv in (36.)], their remnant masses must be as large as ~ 109 h100-3(epsilon / 0.1) Msun (the present space density of remnants being only about that of radio sources with P178 > 1023 h100-2 W Hz-1 sr-1). But the luminosity of a "typical" quasar (M appeq - 25.5 for h100 = ½) corresponds to the Eddington limit for a mass of "only" ~ 108 Msun; so if quasars resemble radiation-supported tori, then they must have lifetimes such that (tQ / tEv) << 1, and individual quasars must be "switched off" by something internal to the particular system, rather than being influenced by any change in the overall cosmic environment (which could occur only on time scales ~ tEv) (38, 77).

Because of space limitations, I do not speculate here about how different forms of AGNs might be interrelated. Another contentious issue is the role of beaming (25, 28, 32, 113), which has been advocated to explain compact radio sources (and perhaps also extreme optical outbursts in OVVs). There is no reason to invoke it, however, for the typical radio-quiet quasar, and any case it cannot affect the estimation of (35.). Suffice it to say, as emphasized by Phinney (99), that tentative "demographic" studies of imply the following:

  1. If strong radio sources involve ion-supported tori around holes of mass gtapprox 109 Msun, they could be the "reactivated" remnants of long-lived quasars (with tQ = tEv).

  2. If quasars radiate at the Eddington limit, then their lifetimes would be ~ 4 × 107 h(epsilon/0.1) yr (cf. Equation 4). Even if their efficiency epsilon is high, they must be short lived compared with tEv. The space density of remnants cannot exceed 10-3 h1002(epsilon/0.1)-1 Mpc-3 unless their luminosities are highly "super-Eddington."

  3. If Seyfert galaxies are quasar remnants, they cannot be modeled by radiation-supported tori.

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