Wavelength A

Figure 5.19. Two Hp profiles representing extreme values of FWHM/aUne. PG 1700+518 (dotted line; FWHM/ajine = 0.71) has an Hp profile that is narrower at the peak and broader at the base than a Gaussian of comparable width. Conversely, Akn 120 (solid line; FWHM/ajine = 3.45) has much stronger shoulders and is relatively more rectangular.

limit will depend on the spectral resolution and signal-to-noise ratio of the observations used in the analysis. Tight constraints are drawn from very-high-resolution observations of the least-luminous AGNs, with the most-recent limit based on Keck spectra of the dwarf Seyfert 1 galaxy NGC 4395 (Laor et al. 2006). This argument and other evidence are leading to complete abandonment of the notional discrete-cloud model in favor of some kind of a continuous flow.

5.9.2 Physical conditions in the BLR As noted above, multiple reverberation measurements of the Hp response in NGC 5548 reveal that the "BLR size" varies with continuum luminosity - when the nucleus is in a brighter state, the BLR is "bigger." The uncomfortable question that naturally arises is the following: how does the BLR know precisely where to be? What fine tunes the size of the BLR? Of course, the answer to this question is obvious from the BLR stratification results (Table 5.2): the BLR gas is distributed over a very wide range of distances, between at least ~ 2 and ~ 30 lt-days from the central source, in the case of NGC 5548. The

Figure 5.20. Contours of constant equivalent width for a grid of photoionization-equilibrium models, as a function of input ionizing flux ($(H) = Qion/(4nr2)) and particle density n(H) for strong emission lines in AGN spectra. Dotted contours are separated by 0.2 dex and solid coutours by 1 dex. The solid star is a reference point to "standard BLR parameters," i.e. the best single-zone model. The triangle shows the location of the peak equivalent width for each line. Adapted from Korista et al. (1997).

Figure 5.20. Contours of constant equivalent width for a grid of photoionization-equilibrium models, as a function of input ionizing flux ($(H) = Qion/(4nr2)) and particle density n(H) for strong emission lines in AGN spectra. Dotted contours are separated by 0.2 dex and solid coutours by 1 dex. The solid star is a reference point to "standard BLR parameters," i.e. the best single-zone model. The triangle shows the location of the peak equivalent width for each line. Adapted from Korista et al. (1997).

very-well-defined emission-line responses that we measure indicate that the responsiv-ity is well localized; the responsivity is clearly a very sensitive function of the physical conditions in the BLR. The dominant response we observe comes from where the physical conditions are optimal for a particular emission line. This is at least qualitatively consistent with the expectations of the "locally optimally emitting cloud (LOC)" model of Baldwin et al. (1995). In Figure 5.20, we show emissivity contours for various strong emission lines as a function of the ionizing photon flux $(H) and proton density n(H) predicted by an LOC model.

It is perhaps worth mentioning that, in contrast to the other broad lines, the optical Fe ii blends just longward and shortward of Hp do not have a strongly localized reverberation signature, even though they do clearly vary (e.g. Vestergaard & Peterson 2005). This may be because the optimal responsivity for these blends is not sharply localized in U-nH space.

5.9.3 The mass of the BLR We used Equation (5.15) to estimate the mass of gas in the NLR. We neatly side-stepped this particular issue in our earlier preceding discussion of the BLR. We could in principle have carried out a nearly identical calculation for the BLR and found that the total amount of gas required to account for the Balmer-line emission is about > M0 for moderate-luminosity AGNs. There is a hidden assumption in such calculations that the gas is emitting at high efficiency. The reverberation results clearly indicate that there is a lot of gas in the BLR that is radiating quite inefficiently at any given time. When this is taken into account, Baldwin et al. (2003) estimate that the total amount of gas in the BLR is closer to (104-105)M0, indicating that the BLR gas flow is fairly massive.

5.9.4 The kinematics of the BLR

Members of a small subset of AGNs have the double-peaked profiles that are characteristic of disks in Keplerian rotation. The best examples (e.g. Storchi-Bergmann et al. 2003) are in the Balmer lines of lower-luminosity objects in cases where the line widths are very large. Double-peaked profiles sometimes become apparent in difference profiles (i.e. the spectrum formed by subtracting a low-flux state spectrum from a high-flux state spectrum), and in other cases we see consistent and similar weak signatures in the form of strong shoulders or secondary peaks in Balmer lines. It seems plausible that double-peak disk components are indeed present in virtually all AGNs, though they are sometimes masked by low inclination or by the presence of another emission-line component, namely a disk wind.

Disk winds have been invoked in order to describe a number of observed AGN features. Elvis (2000) presents a fairly comprehensive phenomenological disk-wind model that unifies several AGN emission- and absorption-line characteristics in a physically well-motivated way. A theoretical driver for disk winds is that hydromagnetically accelerated winds can serve to remove angular momentum that is carried in by infalling matter. Observational evidence supporting disk winds includes the following.

• Strong blueward asymmetries are present in the higher-ionization lines in NLS1s (e.g. Leighly 2000). This would occur if there were a strong outflow component with the far (receding) side partially obscured from our view (presumably by the torus).

• Peaks of high ionization lines tend to be blueshifted relative to systemic, and the maximum observed blueshift increases with source luminosity (e.g. Espey 1997, and references therein).

• In radio-loud quasars, the widths of the bases of the CIV lines are larger in edge-on sources than in face-on sources, implying that the wind has a strong radial (as opposed to polar) component to it (Vestergaard et al. 2000). Also, Rokaki et al. (2003) have shown that line width is anticorrelated with several beaming indicators, again arguing that the velocities are largest in the disk plane.

A natural explanation for at least some of the diversity in line profiles is that both components are present in Type 1 AGN spectra, in varying relative strength: the disk wind, however, is weak in low-accretion-rate objects and stronger in high-accretion-rate objects. This is hardly a radical suggestion. As noted earlier, at least two physical components are required to account for the strength of the low-ionization lines (which are strong in the dense rotating-disk component, which might in fact be thought of as an extension of the accretion-disk structure itself) versus the high-ionization lines (which are presumably strong in the wind component). This is consistent with double-peaked profiles being primarily a Balmer-line phenomenon and strong blueward-asymmetric (and sometimes self-absorbed) components appearing primarily in UV resonance lines.

Consider the following simple argument. Equation (5.5) tells us that the source luminosity depends on accretion rate as L x M. We also have a relationship between luminosity and BLR radius, R x L1/2 (Equation (5.31)). Now, using the virial equation (Equation (5.32)), we can write the dependence of the line width as

. fGM\1/2 ( M \1/2 ( M \1/2 (M\1/4 , , x (gm) x \lm2j x (mm^j x y • (5.35)

This suggests that at a fixed black-hole mass, the line width reflects the Eddington rate m (as defined in Equation (5.6)). Objects with high Eddington rates are those with narrower lines, such as NLS1 galaxies, which are also the objects with the strongest evidence for massive outflows. Certainly, in Galactic binary systems, high accretion rates and high outflow rates are closely coupled, and it stands to reason that this holds for larger-mass systems as well.

5.9.5 Dust and the BLR Sanders et al. (1989) showed that spectral energy distributions of AGNs have a local minimum at a wavelength ~ 1 |im (see Figure 5.5). They argued that the IR emission longward of 1 |im is attributable to dust, as had others previously (e.g. Rieke 1976), at the sublimation temperature of ~ 1500 K. This corresponds to a minimum distance from the AGN, the sublimation radius, at which dust can exist. For graphite grains, this is approximately

where Luv is the UV luminosity of the AGN and T is the grain sublimation temperature (Barvainis 1987). Clavel et al. (1989) first showed that IR-continuum variations followed those in the UV/optical with a time lag that is consistent with the IR emission arising at the sublimation radius. The IR-continuum emission we see is reprocessed UV/optical emission from the inner regions. This effect, sometimes referred to as "dust reverberation," has now been observed in several AGNs. Suganuma et al. (2006) show that in each case where measurements are available the emission-line lags are always slightly smaller than or comparable to the IR-continuum lags. This indicates that the outer boundary of the BLR is defined by the sublimation radius, as suggested by Laor (2003).

5.10. Unification issues and the NLR

5.10.1 The geometry of the obscuring torus The notion of an obscuring torus surrounding the central source and BLR has been the key feature of AGN unification models for nearly two decades. The left panel of Figure 5.21 illustrates the torus more or less as it was envisaged by Antonucci & Miller (1985). The opening angle of the torus is a free parameter that can be selected to match the observed space densities of Seyfert 1 and Seyfert 2 galaxies, as noted earlier.

There are significant problems with the "doughnut" view of the torus (Elitzur & Shlosman 2006), notably in terms of stability and size; with regard to the latter point, Elitzur (2006) notes that a conventional torus model such as that in the left panel of Figure 5.21 is predicted to have a size of hundreds of parsecs for a galaxy like NGC 1068, although mid-IR observations show that the core is no larger than a few parsecs. By introducing a large number of smaller clouds, the size of the torus can be made much smaller because of the larger radiating surface area, and the clumpy medium better reproduces

Figure 5.21. The illustration on the left shows the standard "doughnut" torus as originally envisaged by Antonucci & Miller (1985). The diagram on the right illustrates a more plausible arrangement of dusty obscuration in the vicinity of the AGN. Adapted from Elitzur et al. (2004).

the IR spectra of AGNs. Moreover, the clumpy medium has a natural origin in the disk wind.

5.10.2 Type 2 quasars

Among lower-luminosity AGNs, Seyfert 2 galaxies significantly outnumber Seyfert 1 galaxies, by a ratio of perhaps 3:1. However, there is a decreasing number of Type 2 AGNs at higher luminosity, i.e. "Type 2 quasars." Indeed, Type 2 quasars are rare and were not known in any reasonable numbers until the advent of the SDSS, which turned up a few hundred candidates (Zakamska et al. 2003). One possible explanation for this is that the inner edge of the obscuring torus is larger for more-luminous objects because the sublimation radius (Equation (5.36)) increases with luminosity. If the height of the torus remains the same or increases only slowly with luminosity (cf. Simpson 2005), the effective opening angle increases with luminosity, thus decreasing the numbers of obscured (Type 2) objects. This is sometimes referred to as the "receding-torus" model (Lawrence 1991).

5.10.3 The NLRs in Type 1 and Type 2 AGNs

A naive expectation of AGN unification is that the narrow-line spectra of Type 1 and Type 2 AGNs should be the same. If not stated directly, this is implicit, for example, in AGN sample selection based on the luminosity of particular narrow emission lines, such as [O iii] A5007, where the underlying assumption is that the narrow lines are emitted isotropically. Careful comparison of the narrow-line components of Seyfert 1 galaxies with the narrow-line spectra of Seyfert 2 galaxies reveals that they are not identical (e.g. Schmitt 1998). For example, Seyfert 1 galaxies have relatively stronger high-ionization lines, which is probably because the most highly ionized NLR gas is at least partially within the throat of the obscuring torus and not visible in the directions from which the source would be viewed as a Seyfert 2. Also, it is observed that the size of the NLR scales differently with luminosity for the two types, with r <x L0'44 for Type 1 objects and r <x L0'29 for Type 2 objects. Bennert et al. (2006) suggest that this difference can be explained by invoking the differences in how the NLR projects onto the sky in a receding-torus model as a function of inclination.

5.11. Cosmological implications

Ever since their discovery, quasars have been recognized as potentially important cosmological probes.

Figure 5.22. The comoving space density of QSOs with absolute magnitude Mi450 < -26.7 mag. The lower-redshift result (full line) is from the 2DF survey (Croom et al. 2004). The dashed line is from Fan et al. (2001) and the dotted line is from Schmidt et al. (1995). The single point at high redshift is based on the ~ 19 quasars at z > 5.7 that were discovered in the SDSS. Adapted from Fan (2006), with permission of Elsevier.

Figure 5.22. The comoving space density of QSOs with absolute magnitude Mi450 < -26.7 mag. The lower-redshift result (full line) is from the 2DF survey (Croom et al. 2004). The dashed line is from Fan et al. (2001) and the dotted line is from Schmidt et al. (1995). The single point at high redshift is based on the ~ 19 quasars at z > 5.7 that were discovered in the SDSS. Adapted from Fan (2006), with permission of Elsevier.

(i) Because of their high luminosities, quasars can be seen at great distances. By determining the evolution of the luminosity function over cosmic time, we can trace the development of supermassive black holes and galaxies over the history of the Universe.

(ii) By using quasars simply as distant beacons, we can observe the cosmic evolution of the intergalactic medium through study of absorption lines that arise along our line of sight to quasars.

(iii) The appearance of the first quasars marks the appearance of discrete structures in the Universe and places strong constraints on models of galaxy formation (see Chapter 3 of this volume). Similarly, the presence of emission lines from elements more massive than helium places very stringent contraints on star formation in the early Universe (see Chapter 6 of this volume).

Determining the luminosity function over the history of the Universe obviously requires surveying large areas of the sky as deeply as possible using techniques that are designed to identify quasars efficiently, missing as few as possible while avoiding as many "false positives" as possible. It is also necessary to understand in detail the biases in selection methods so that survey selection functions can be used to correct statistically for biases. As discussed in Chapter 2 of this volume, emission-line surveys are an especially effective means of identifying quasars. Rather than repeat any of that discussion, we will concentrate on the results.

5.11.1 The space density of AGNs Figure 5.22 shows the comoving1 space density of the brightest quasars as a function of redshift. As soon as quasars were found in large numbers, it became apparent, even through such simple tests as V/Vmax (Schmidt 1968) that quasars were much more common in the past than they are now. By the early 1980s, Osmer (1982) was able to conclude, however, that the density of quasars drops off dramatically by z « 3.5. The

1 A "comoving volume" is one that expands with the Universe, in contrast to a "proper volume," which is fixed in an absolute sense.

"quasar era" corresponds to the redshift range 2 < z < 3, when the comoving density of bright quasars was at a maximum.

Modern surveys, such as the Two-Degree Field (2DF) (Croom et al. 2004) and the SDSS (York et al. 2000), have been very successful at identifying large numbers of quasars out to very large redshifts. The space density of quasars remains very hard to constrain, however, above z « 6. At such large redshifts, Lya, the shortest-wavelength strong emission line in AGN spectra, is shifted into the near infrared, and shortward of this quasar spectra are heavily absorbed by the "Lya forest," i.e. absorption by neutral intergalactic hydrogen at lower redshift. In other words, at z « 6, quasars are extremely faint throughout the entire optical (observed frame) spectrum.

It is quite profound that quasars at z > 5 are found at all: this means that supermassive black holes must have been in place by the time the Universe was only a few hundred million years old. Furthermore, the spectra of these very-high-redshift quasars do not seem to be much different from those of relatively nearby AGNs; in particular, emission lines due to metals such as carbon, nitrogen, and iron are all present, which means that the material in the quasar BLRs must have been processed through at least one generation of massive stars within a few hundred million years of the Big Bang.

5.11.2 The luminosity function It is customary to parameterize the quasar luminosity function as a double power law,

$(M, z) = 100.4(a+!)(M-M*) + 100.4(p+1)(M-M*) ' (5.38)

where M* and L* refer to a redshift-dependent fiducial luminosity,1 and $(L*) and $(M*) represent the comoving density (normalized with respect to z = 0) of AGNs at the fiducial luminosity. Figure 5.23 shows the quasar luminosity function for several redshift ranges between z « 0.5 (when the Universe was about 80% its current age) and z « 2 (when the Universe was about 20% its current age) from the 2DF survey. For the lowest-redshift bin in Figure 5.23 (i.e. 0.40 < z < 0.68), a « -3.3 and 3 « -1.1 in Equations (5.37) and (5.38).

A major goal of quasar surveys is to understand how the luminosity function evolves with time. There are two simple descriptions of quasar evolution since z « 2.

• Pure (density evolution describes a situation in which the number of AGNs per unit comoving volume decreases at a similar rate for all luminosities; in other words, the density of quasars decreases as individual quasars "turn off" or enter radiatively inefficient states such as the black hole at the center of the Milky Way (which is, in fact, probably a dead AGN). In this case, the luminosity function as shown in Figure 5.23 evolves by translating directly downward with time. There are many problems with this particular scenario, among the most important being that pure density evolution greatly overpredicts the number of very luminous quasars that should be found locally.

• Pure luminosity evolution supposes that all quasars simply become less luminous with time; in other words, the luminosity function shown in Figure 5.23 evolves by

1 The transformation between the two equations above is shown explicitly by Peterson (1997).

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