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black holes (Figure 5.5), so, even though we cannot model the spectrum in detail at this time, the balance of evidence still supports their existence.

5.5.4 The broad-line region Broad (FWHM > 1000 km s—1) emission lines are almost uniquely an AGN phenomenon; such broad emission lines are seen nowhere else in nature other than in the spectra of supernova remnants. As shown below, the BLR is spatially unresolved - even in the nearest AGNs, the projected size of the BLR is of order tens of microarcseconds.

To some low order of approximation, the relative strengths of the various emission lines in AGN spectra are very similar to those emitted by a wide variety of astrophysical plasmas, such as planetary nebulae, HII regions, and supernova remnants, for the simple reason that photoionization equilibrium of all these gases occurs at the same temperature, T « 104 K.

Photoionization equilibrium is attained when the rate of photoionization is balanced by the rate of recombination. To determine the conditions under which photoionization equilibrium is achieved requires detailed calculation of models that produce predictions of the relative strengths of various emission lines and these are then compared with the observed relative strengths of these lines. Simple photoionization-equilibrium models are characterized by (1) the shape of the ionizing continuum, (2) the elemental abundances of the gas, (3) the particle density of the gas, and (4) an ionization parameter

4nr2nHC

where the rate at which the central source produces ionizing photons is given by

where Lv is the specific luminosity of the ionizing source and the integral is over ionizing photon energies. Thus the ionization parameter U essentially reflects the ratio of the rate at which photoionization occurs, which is proportional to Qion(H), to the recombination rate, which is proportional to the particle density nH.

It is conventional to describe photoionization-equilibrium models in terms of the value of U at the face of a cloud exposed to the incident radiation from the central source. Over a rather broad range in values of U, photoionization equilibrium occurs at electron temperatures in the range 10 000-20 000 K, thus accounting for the similarities of their spectra. The differences in the spectra of the astrophysical plasmas in this temperature range are attributable primarily to the shape of the ionizing spectrum and gas density, and in some cases to the gas dynamics and elemental abundances.

Early photoionization-equilibrium models of the BLR were single-zone models, i.e. the emission was modeled in the context of multiple clouds with identical physical properties and ionization structure. An example of such a model is shown in Figure 5.6. Single-zone models suggest nH « 3 x 109 cm-3, on the basis of the presence of broad C Ill] A1909 and the absence of broad [O Ill] AA4959, 5007. Acceptable matches to the C Ill] A1909/C IV A1549 and Lya A1215/C iv A1549 flux ratios are obtained for U « 0^01.

The strong forbidden lines seen in the spectra of low-density plasmas (e.g. [N II] AA6548, 6584 and [O III] AA4363, 4959, 5007) are absent from BLR spectra. Thus, the physical diagnostics that can be used in lower-density gases (see Chapter 1 of this volume) cannot be used to determine the particle density or temperature of the BLR gas. The absence of forbidden lines, however, can be used to place a lower limit on the particle density in the gas. In the first generation of AGN photoionization-equilibrium models, the presence of

Figure 5.6. Results of a single-cloud photoionization equilibrium calculation, for an assumed particle density of 3 x 109 cm-3. The predicted strengths of the broad components of O VIA1034, Lya A1215, OIV A1402, Ha A6563, CII] A2326, C Ill] A1909, and Mg IIA2798 are shown relative to CIV A1549, as a function of the ionization parameter U. The top line shows the total power emitted by the entire BLR (line and diffuse continuum), relative to CIV A1549. The total power radiated in CIV A1549 in units of 1042 erg s-1 is shown for the Seyfert galaxy NGC4151 under the assumption that all the ionizing flux from the central source is absorbed by the BLR. From Ferland & Mushotzky (1982).

Figure 5.6. Results of a single-cloud photoionization equilibrium calculation, for an assumed particle density of 3 x 109 cm-3. The predicted strengths of the broad components of O VIA1034, Lya A1215, OIV A1402, Ha A6563, CII] A2326, C Ill] A1909, and Mg IIA2798 are shown relative to CIV A1549, as a function of the ionization parameter U. The top line shows the total power emitted by the entire BLR (line and diffuse continuum), relative to CIV A1549. The total power radiated in CIV A1549 in units of 1042 erg s-1 is shown for the Seyfert galaxy NGC4151 under the assumption that all the ionizing flux from the central source is absorbed by the BLR. From Ferland & Mushotzky (1982).

the semi-forbidden line C iii] A1909 in AGN broad-line spectra suggested an upper limit on the particle density of about 3 x 109 cm-3. However, with the advent of reverberation mapping (see below), it became clear that the other strong UV lines arise in a different part of the BLR than where the C Ill] A1909 line arises, so that a particle density of 3 x 109 cm-3 is in fact a lower limit on the particle density for the C iV-emitting part of the BLR.

Photoionization modeling is a powerful tool of long standing (Davidson & Netzer 1979) for trying to understand the physical nature of the line-emitting regions in AGNs. While progress was made in determining some of the physical parameters that characterize the BLR (e.g. relatively high nebular densities and electron temperatures), it became clear early that single-zone models could not simultaneously reproduce the relative strengths of both the low- and the high-ionization lines (Collin-Souffrin et al. 1986). Furthermore, an energy-budget problem was identified: the total amount of line emission observed exceeds the amount of continuum radiation available to power the lines (Netzer 1985; Collin-Souffrin 1986).

Wavelength, A (A)

Figure 5.7. Composite spectra from the Sloan Digital Sky Survey, binned by luminosity. Note the similarity of the spectra, with the exception of the "Baldwin effect" in CIV A1549; i.e., relative to the continuum and the other lines, CIV is stronger in lower-luminosity objects. Courtesy of D. Vanden Berk, based on an original from Vanden Berk et al. (2004).

Wavelength, A (A)

Figure 5.7. Composite spectra from the Sloan Digital Sky Survey, binned by luminosity. Note the similarity of the spectra, with the exception of the "Baldwin effect" in CIV A1549; i.e., relative to the continuum and the other lines, CIV is stronger in lower-luminosity objects. Courtesy of D. Vanden Berk, based on an original from Vanden Berk et al. (2004).

Temperatures of around 104 K correspond to thermal line widths of order 10kms_1, so the BLR gas moves supersonically. If the lines are Doppler-broadened, either the gas is moving in a deep gravitational potential or it is accelerated to high velocities, perhaps hydromagnetically or by radiation pressure. How the BLR gas is moving, whether in gravitational infall, in radiation-pressure-driven or hydromagnetically accelerated outflow, or in orbital motion, remains unknown, though the evidence (described below) points to gravitationally bound motions.

Perhaps surprisingly, emission-line profiles alone only weakly constrain the BLR kinematics. Numerous profoundly different kinematic models yield similar "logarithmic" profiles in which the flux at some displacement AA from line center is proportional to — ln AA, for AA not too close to line center. This represents a rather idealized case since in many instances, especially among lower-luminosity AGNs, the line profiles have some structure, variously described as "bumps," "shelves," or "asymmetric wings." Emission-line profiles can change, in some cases drastically, on timescales comparable to the BLR dynamical timescale Tdyn « ñBLR/FWHM, which is typically a few years for Seyfert galaxies of moderate luminosity.

Figure 5.7 shows several composite spectra of AGNs for various luminosity ranges. Their similarity suggests that not only the temperature of the line-emitting gas, but also the particle density and ionization parameter, are quite similar for AGNs of different luminosities. The only strong luminosity-dependence of AGN emission-line spectra is the equivalent width (i.e. the ratio of line flux to underlying continuum flux) in the CIV A1549 emission line; relative to the continuum, CIV is weaker in more-luminous objects, a well-known anticorrelation known as the "Baldwin effect" (Baldwin 1977). The physical origin of the Baldwin effect is not known.

There are additional correlations among spectroscopic properties, some of which have been identified through principal-component analysis (PCA), such as that undertaken by Boroson & Green (1992). Given a set of input values (e.g. ratios of line fluxes, equivalent widths of lines, Doppler widths of lines), which are treated as vectors, PCA identifies the parameters that cause the greatest variation within a population. These are expressed as eigenvectors (also known as principal components), with a coefficient for each of the input vectors. We are thus able to identify correlated parameters, bearing in mind always that correlation does not necessarily imply causality - but it does give us a useful place to start. For Type 1 AGNs, Eigenvector 1 shows a strong anticorrelation between the strength of the optical Fe II blends on either side of the Hp emission line and the flux in [O III] A5007, while Eigenvector 2 shows a correlation between luminosity and the strength of He IIAA4686 emission. Boroson (2002) argues that Eigenvector 1 is driven by the Eddington ratio (Equation (5.6)) and that Eigenvector 2 is driven by the accretion rate dM/dt.

5.5.5 The narrow-line region Narrow (FWHM < 1000 km s—1, typically) emission lines arise in a region that is spatially extended and is in fact at least partially resolvable in nearby AGNs. As in the BLR, the velocities are supersonic, indicating large-scale bulk motions of gas. The particle densities in the NLR are much lower than those in the BLR, so many forbidden lines over a wide range of ionization potential are present, and the emissivity per unit volume is much lower than that in the BLR, so the total amount of mass is large.

In many respects, understanding the NLR is much simpler than understanding the BLR.

(i) Since the NLR is spatially resolved, the kinematics are less ambiguous than in the BLR.

(ii) Forbidden-line emission allows use of temperature and density diagnostics, so the physical conditions are relatively better understood.

(iii) Forbidden lines are not self-absorbed, so the radiative-transfer problem is simpler than in the BLR.

Offsetting these tremendous advantages relative to the BLR is that dust, which extinguishes and reddens optical and ultraviolet radiation, is present in the NLR.

Relative line strengths for a typical NLR spectrum are shown in Table 5.1. The first column indicates the emission line and the second column gives the relative (unred-dened) flux, normalized with respect to an Hp value of unity, as is the usual convention. The third column gives the relevant ionization potential. For collisionally excited lines, the ionization potential is that necessary to achieve this particular ionization state. For recombination lines (e.g. all the hydrogen lines), the relevant ionization potential is that of the next-highest state of ionization, since it is recombination from these higher states that produces the observed emission lines. The fourth column gives the critical density for each particular line, as we describe below.

Table 5.1 reveals the presence of many of the lines seen also in other nebulae at temperatures of > 104 K, such as Galactic HII regions and planetary nebulae. However, AGN narrow-line spectra are distinguished by the presence of very-high-ionization lines, such as [Ne v], [Ar III], [Fe VII], and [Fe x]; the iron lines in particular are often referred to as "coronal lines" since they were first detected in the Solar corona, where the temperature is of order 106 K. The presence of these lines is due to the "hardness" of the AGN ionizing continuum, i.e. the relatively large fraction of very energetic ionizing photons compared with the Wien tail of a thermal spectrum of the type that powers Galactic nebulae.

The presence of forbidden and semi-forbidden lines is attributable to the low particle densities in the NLR. Consider for a moment a simple two-level atom with a ground state 1 and an excited state 2 at some higher energy AE. As discussed in Chapter 1 of this volume, in low-density gases in which the collision rate is low, each transition into the excited state 2 will ultimately lead to a radiative transition to the ground state, producing

Table 5.1. Strong narrow lines in Seyfert spectra

Relative Ionization Critical density

Table 5.1. Strong narrow lines in Seyfert spectra

Relative Ionization Critical density

Lya A1216

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