Annu. Rev. Astron. Astrophys. 1999. 37: 487-531
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2.2. Origin of the Broad Emission Lines

Quasar emission-line research is an example of the inverse problem in astrophysics. We know the answer - the observed spectrum of a quasar, and we are trying to understand the question - the conditions that created it. Any model of the line-forming regions will have uncertainties related to uniqueness, but these can be minimized by considering the astrophysical context and by limiting the models to essential properties. The essential properties of the BEL region (BELR) are as follows:

  1. The BELR is photoionized. The main evidence for photoionization is that the emission-line spectra change in response to changes in the continuum, with lag times corresponding to characteristic radii of the BELR (Peterson 1993). The shape of the ionizing continuum is a fundamental parameter and is in itself an area of active research (e.g. Zheng et al. 1997, Korista et al. 1997a, Brunner et al. 1997, Laor 1998). Below we present calculations using simple power laws between 1 µm and 100 keV, and we describe results that do not depend strongly on the continuum shape.
  2. The BELR spans a range of distances from the central object. The line variability or reverberation studies just mentioned find different lag times for different ions. Highly ionized species tend to tie closer to the continuum source. Overall, the radial distances scale with luminosity, such that R approx 0.1 (L / 1046 ergs s-1)1/2 pc is a typical value (Peterson 1993).
  3. The BELR has a wide range of densities and ionization states. The range in ionization follows simply from the lines detected, from OI lambda1303 to at least NeVIII lambda774 (Hamann et al. 1998). The range in density comes mainly from the estimated radii and photoionization theory (e.g. Ferland et al. 1992). Clouds (1) with densities from 108 to >1012 cm-3 may be present. [We use the term "cloud" loosely, referring to some localized part of the BELR but not favoring any particular model or geometry (see Arav et al. 1998, Mathews & Capriotti 1985)]. Any given object could have a broad mixture of BELR properties (Baldwin et al. 1995, 1996).
  4. The BELR probably has large column densities. Large column densities, typically NH gtapprox 1023 cm-2, were originally used in BELR simulations to produce a wide range of ionizations in single clouds (Kwan & Krolick 1981, Ferland & Persson 1989). These large column densities might not apply globally because we now know that different lines form in different regions. In our calculations below, we truncate the clouds at the hydrogen recombination front, with the result that different clouds/calculations can have different total column densities. However, the truncation depths are in all cases large enough to include the full emission regions of the relevant lines.
  5. Thermal velocities within clouds are believed to dominate the local line broadening and radiative transfer. The observed line widths are thus caused entirely by bulk motions of the gas. This issue is important because (a) continuum photoexcitation (pumping) can overwhelm other excitation processes if the local line broadening (e.g. microturbulence) is large, and (b) the line optical depths and thus photon escape probabilities (see below) vary inversely with the amount of line broadening. The interplay between these factors makes it hard to predict the behavior of a given line without explicit calculations. Shields et al. (1995) plot some line-strength behaviors for the particular case of low-column-density clouds. One argument against significant microturbulence involves the Lyalpha / Hbeta intensity ratio. Simple recombination theory predicts a ratio of ~ 34 (Osterbrock 1989), although the observed value is far smaller, closer to 10 (Baldwin 1977a). This discrepancy is worsened by microturbulence (Ferland 1999). The solution probably requires severely trapped Lyalpha photons resulting from large optical depths at thermal line widths (see also Netzer et al. 1995).

1 We use the term "cloud" loosely, referring to some localized part of the BELR but not favoring any particular model or geometry (see Arav et al. 1998, Mathews & Capriotti 1985). Back.

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