The Ultraviolet and Optical Continuum Emission in Active Galactic Nuclei: The Status of Accretion Disks

To understand the nature of the BBB we first need to determine its SED and thus determine its strength compared to the AGN's SED. Although this task seems relatively simple, there are a lot of observational problems. One of the most important problems is that a substantial part of the BBB in any particular source is in the unobservable part of the electromagnetic spectrum (13.6 eV–0.1 keV), where it is hidden by Galactic absorption. Therefore, the characteristics of this region need to be inferred from theoretical considerations. In the optical/UV wavelength region, where AGNs can be observed, the spectra have the characteristic strong broad emission lines whose wings make assignment of "line‐free continuum" regions very difficult. Further, the Balmer continuum and the many blended Fe ii emission lines produce a relatively smooth feature in the AGN spectrum that also has to be accounted for in the continuum fitting process (Wills, Netzer, & Wills 1985). Thus, in this section we discuss the shape of the BBB by considering the optical/UV region and the far‐UV/soft X‐ray regions separately. We also discuss in detail the observational caveats in each spectral region. We will often discuss composite spectra that have been generated by co‐adding several hundred optical/UV spectra in the AGN rest frame. These composites serve as a high signal‐to‐noise ratio reference to the "observed" AGN shape, because although individual AGN spectra differ in detail, they all have similar characteristic features. It is important to remember, however, that a composite spectrum really has no physical meaning, and models must be fitted to spectra of individual sources.

3.1.1. The Optical to UV Region

3.1.2. The Far‐UV to Soft X‐Ray Region

Historically, because a substantial part of this wavelength region is unobservable, there have been two approaches to inferring the BBB shape. In the first approach, the BBB continuum was associated with thermal emission from an accretion disk (Shields 1978; Malkan 1983; Kolykhalov & Sunyaev 1984). In the second approach, the shape of the BBB was obtained by comparing photoionization model predictions with observed emission‐line strengths (Mathews & Ferland 1987). Both these approaches indicated that the BBB is energetically very important, peaking in the extreme UV and usually dominating the quasar luminosity (MacAlpine 1981; Czerny & Elvis 1987; Mathews & Ferland 1987; Sun & Malkan 1989; Shields 1989; Laor 1990; Bechtold et al. 1994; Walter et al. 1994).

The two recent HST and Roentgen Satellite (ROSAT) investigations by Zheng et al. (1997) and Laor et al. (1997), respectively, allow us to investigate observationally the "observed" shape of the BBB in the 13.6 eV–1 keV region of the continuum. The UV composite spectrum of Zheng et al. was compiled using HST Faint Object Spectrograph (FOS) observations. This sample contained quasars with mean redshifts ∼1, which allowed determination of the UV composite spectrum in the rest wavelength range ∼300–3000 Å (see Fig. 2). The individual spectra in the composite have been corrected for Galactic reddening and intergalactic absorption. The UV composite spectrum of AGNs does not appear to rise to shorter wavelengths but seems to roll over shortward of 1000 Å. Laor et al. (1997) produced a composite soft X‐ray spectrum of a complete sample of low redshift quasars using ROSAT Position Sensitive Proportional Counter (PSPC) observations. The soft X‐ray data seem to be just an extension of the UV composite spectrum (see Fig. 3). If taken at face value, the UV and X‐ray composite spectra indicate that the BBB may not be as energetically dominant as thought previously. Further, the peak of the "observed" BBB does not seem to be in the extreme‐UV (100–800 Å) but rather in the far‐UV region (900–1100 Å).

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3.1.3. Observational Caveats

There are a number of observational issues that can affect the observed shape of the BBB. These issues should especially be kept in mind when considering the shape of the BBB, as determined by the UV and X‐ray composite spectra, because they affect each individual object in a different manner and thus possibly create an unphysical effect in the composite spectrum. Below we discuss the various issues in detail.

• Host galaxy contamination.—The optical/UV region of an AGN spectrum is also where stars put out most of their radiation. Thus careful galaxy subtraction is necessary if we are to determine the shape of the BBB accurately. In low‐redshift AGNs, such corrections are often made by subtracting with galaxy bulge template spectra. However, this may be inadequate because the correction does not effectively correct for a starburst population. HST imaging observations of Seyfert galaxies show that nuclear star formation is often occurring well within 05–10 of the nucleus. Depending on the dominance of these star‐forming regions, they can contribute substantially toward the optical/UV light that is seen in most ground‐based apertures. A comparison of contemporaneous HST and ground‐based spectroscopy of NGC 7469 clearly shows this problem (see Figs. 4 and 5). In this particular object, ∼70% of the starlight falls within 01 of the nucleus! For ground‐based observations, this problem is exacerbated owing to effects of seeing. Although nuclear starbursts are likely to be present in the host galaxies of high‐luminosity AGNs (QSOs), more than 80% of the radiation is from the QSO. Therefore for these objects we do not expect substantial contamination in the optical/UV region from the host galaxy.
• Intrinsic reddening.—Intrinsic reddening in the AGN plays an important role when determining the optical/UV continuum. It is generally assumed that the intrinsic reddening in AGNs is small [E(B−V) = 0.05–0.1 mag], independent of the reddening law. Although this small amount of reddening does not affect the optical fluxes dramatically, it has a dramatic effect at UV wavelengths. This reddening correction becomes extremely crucial for high‐z AGNs since the reddening correction is applied to the far‐UV rest wavelengths. Thus applying a reddening correction, even a very small one, can effectively change the shape of the observed BBB spectrum.In most analyses the continuum is corrected for Galactic reddening, and there may sometimes be an attempt to correct for intervening intergalactic absorption. An attempt to correct for intrinsic reddening via line ratios is also often made, but depending on the line ratios, one can get significantly differing amounts for the correction. In addition, the reddening might be different for the line‐ and continuum‐emitting regions. A systematic analysis of the reddening indicators and effects of dust in multiwavelength spectra needs to be undertaken, especially now that we have mounting evidence for dust in the nuclei of AGNs (Malkan, Gorjian, & Tam 1998).The UV composite spectrum generated by Zheng et al. (1997) has a spectral break at 1000 Å. Could this prominent continuum feature be due to inaccurate corrections for intrinsic reddening in each individual AGN? Laor & Draine (1993) have shown that dust opacity peaks at ∼700–800 Å and drops sharply at shorter wavelengths. If the far‐UV spectral slope change in the Zheng et al. spectrum was due to dust, then below 700 Å the composite spectrum should have "recovered" by 400 Å. Such a change in continuum slope is not seen, which indicates perhaps that the effects of intrinsic dust reddening are not important. However, it must be noted that the far‐UV spectral region of the composite has few objects contributing to the spectrum. These objects are at high redshifts, and their continua have been statistically corrected for intervening intergalactic absorption (for clouds with N_H<10¹⁶ cm⁻²), and additional corrections if the objects were known to have intervening absorption systems.In an individual spectrum, reddening will not cause a spectral break at 1000 Å but will just change the slope of the spectrum dramatically at these short wavelengths. In fact, because of the composite nature of the spectrum, it may be possible that the spectral break is prominent owing to incorrect reddening corrections in each of the individual spectra that extend over limited regions of the entire wavelength range of the composite. Notwithstanding the above observational caveats, the incidence of the spectral break at 1000 Å, so close to the Lyman limit, is tantalizingly suggestive of an intrinsic emission mechanism as the cause.
• Extreme‐UV energy distribution.—As mentioned earlier, to understand the primary emission mechanism in AGNs, it is crucial to know the shape of the BBB in the extreme‐UV (EUV). We have to determine if the UV composite truly represents the EUV SED in AGNs. At wavelengths less than 800 Å, only a few objects are contributing toward the UV composite of Zheng et al. (1997). There are very few observations of AGNs in this region that can be used for a quantitative analysis of the EUV energy distribution. For both Seyfert galaxies and QSOs, there are individual objects in which the BBB SED is not similar to that derived from the UV and X‐ray composite spectra (e.g., HS 1700+6416, HS 1103+6416, and HE 2347−4342 from Reimers et al. 1998; PG 1211+14; Zheng et al. 1999). Figure 6 shows the far‐UV and EUV SED in luminous AGNs. The variety of the EUV SEDs indicate that describing the BBB with simple models will not be possible and that the task is much more complex, and the SED at these short wavelengths needs to be quantified better.
• Soft X‐ray issues.—The soft X‐ray excess component in AGNs is important for the evaluation of accretion disk models because it is often interpreted as the high‐energy tail of the BBB and it helps determine the total energy emitted in the BBB. There are a number of spectral components that contribute to the X‐ray excess region (0.1 to ∼1 keV), including the underlying X‐ray power law and the "warm absorber" (absorption in the 0.5–1.5 keV range dominated by O vii and O viii K‐shell absorption edges in material with N_H ∼ 10²² cm⁻²). All these spectral components complicate the theoretical interpretation of this region. A detailed analysis of ASCA data by George et al. (1998) challenges the presence of the soft X‐ray excess in some objects, and recent BeppoSAX data fail to show a soft X‐ray excess in many sources in which such an excess was claimed to exist before (Matt 1998). The presence of a warm absorber in Seyfert galaxies and the lack of warm absorbers in high‐luminosity AGNs has lead to some extent to more observational uncertainty.To add to the modeling difficulties, simultaneous data obtained with ASCA and ROSAT showed different slopes in the 0.2–1 keV bands. The soft X‐ray slopes observed by Laor et al. (1997) need to be verified because there have been observational issues concerning the accuracy of the ROSAT PSPC calibration matrix, especially at low flux levels (which is obviously the case for X‐ray observations of AGNs). However, the H i columns determined by Laor et al. agree remarkably well with the accurate 21 cm H i columns, which suggests that the ROSAT PSPC calibration matrix may be quiet reliable.It is difficult to compare the ROSAT and ASCA observatories. ASCA cannot observe the soft X‐rays (≲0.6 keV) and has a broad wave band (0.4–10 keV) and high energy resolution, while the ROSAT PSPC observed soft energies (0.1 keV) but did not have a broad wave band or high energy resolution. The presence of numerous spectral components and their relative contributions at various energy bands further complicates comparisons between the two observatories. Thus, interpretation of the soft X‐ray excess depends on our understanding of the broader X‐ray wave band.
• Sample consistency.—The UV X‐ray composite shown in Figure 3 is based on two different samples. The far‐UV composite is based mainly on quasars with z>1, while the soft X‐ray composite is based exclusively on quasars with z<0.4. Thus, if the quasar SED evolves with z, it may be misleading to combine the SED of high‐ and low‐z samples. One clearly needs to measure the far‐UV and soft X‐ray continuum for the same population of quasars in order to establish the shape of the BBB.

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The accretion disks of AGNs are thought to include thermally radiating regions with temperatures in the range 30,000–300,000 K. A fundamental signature of thermal gas is that the emitted spectrum should show spectral features that are associated with large changes in opacity of the gas. At the expected temperatures and densities of an accretion disk, neutral hydrogen ionizes, and there is a large change in the opacity of the gas. The ionization of hydrogen should give rise to spectral features at the Lyman limit (912 Å). The SED in the Lyman limit region can therefore be used as an important diagnostic of accretion disk characteristics. The exact nature of the Lyman edge feature, which will be discussed in § 4.2, depends on the viewing angle of the disk, the conditions in the disk atmosphere (e.g., vertical structure of the disk, atomic level populations), the conditions in the accretion system (e.g., the accretion rate, black hole mass), and general relativistic effects.

Since the strength and shape of the Lyman limit feature are diagnostics of the properties of the gas, observational studies have concentrated on quantifying the nature of the spectral feature at the Lyman limit. The Lyman edge region for AGNs has now been investigated at high (Antonucci, Kinney, & Ford 1989), intermediate (Koratkar, Kinney, & Bohlin 1992), and low (Kriss et al. 1996; Kriss et al. 1997; Zheng et al. 1995) redshifts. Figure 7 shows the variety of continuum distributions seen in the Lyman limit region. Of the 73 AGNs investigated in these studies, only eight candidate objects were found that might have an intrinsic Lyman edge that may be associated with an accretion disk. In these candidate "partial" Lyman edge objects, there is no sharp discontinuity in the continuum at the Lyman limit but usually just a change in continuum slope on either side of 912 Å (see Fig. 7). In objects in which a sharp Lyman absorption edge is present, nearly 25% of objects investigated, the feature can clearly be associated with intervening absorbing material such as broad emission line clouds in the AGN or gas in the AGN host galaxy. Two (Sun, Malkan, & Chang 1993 and Tytler & Davis 1993) seemingly contradictory results concerning the statistics of Lyman edges in HST data have been reported. A uniform detailed analysis needs to be conducted. Analyses so far conclude that intrinsic Lyman edge features that can be associated with accretion disk features are rare in AGNs, and more importantly there has been no reported case of a Lyman edge feature in emission.

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On a statistical basis, one could use the UV composite spectrum (Zheng et al. 1997) to determine the nature of the Lyman edge. In this spectrum the edge is seen only as a 10% effect (see Fig. 8). This may be indicating that many AGNs have a very weak Lyman edge feature. But given the fact that intrinsic Lyman forest lines and reddening can have a dramatic effect on the correction for the SED in this region, the 10% effect cannot be used effectively to quantify the nature of the spectral feature at the Lyman limit.

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To investigate the Lyman edge in AGNs, the observational studies have been over a limited wavelength region in both low‐redshift and high‐redshift objects. Since the accretion disk is in the black hole environment, the Lyman edge is expected to be broadened by disk rotation and by general relativistic effects (owing to the extreme depth of the local potential). Testing the theoretical models would ideally involve high signal‐to‐noise ratio observations over a wavelength range ∼450 to ∼1200 Å in the AGN rest frame. This is observationally extremely difficult because complete access to this region at low redshifts is limited by Galactic hydrogen opacity, and at high redshifts by the intervening intergalactic medium! The detection of z>2 QSOs in the Hamburg quasar survey, which are not only bright but also have a clear line of sight, are ideal to investigate the Lyman limit region. Five of these objects have HST/FOS spectroscopy in the ∼300 to ∼1000 Å wavelength range. There does not seem to be any evidence of a Lyman edge feature in these objects after the spectra have been dereddened, corrected for the individual Lyman limit systems and cumulative H i continuum absorption of Lyα clouds with low column densities. Once again, if we use the Zheng et al. UV composite, the Lyman edge feature is quite narrow (∼5%) and is thus not likely to be from a disk. With the Far‐Ultraviolet Spectroscopic Explorer (FUSE) coming on‐line, we will have opportunity to investigate the ∼450 to ∼1200 Å region in the AGN rest frame for a larger sample of objects.

In simple geometrically thin, optically thick accretion disk models, the atmospheric opacities may be dominated by electron‐scattering opacity. Also, as we discuss in § 4 below, Compton scattering is often used to alleviate the Lyman edge problem. In a quasi‐flattened geometry, the scattering of photons (both Thompson and Compton) leads to polarization of the photons. Thus polarization of the optical/UV continuum in AGNs can also be used as a diagnostic of accretion disk characteristics.

As we noted above at the end of § 2, observations do not confirm the simple electron‐scattering–dominated accretion disk predictions for polarization. Observed polarizations are low and are parallel to the inferred disk axis (Stockman et al. 1979, 1984; Antonucci 1988). These observations also found that there was no wavelength dependence of the polarization. Recent optical spectropolarimetry of intermediate and high redshift quasars by Berriman et al. (1990) and Antonucci et al. (1996) confirm the earlier results; i.e., unobscured AGNs show low optical polarization with no statistically significant wavelength dependence.

In the unified scheme for AGNs, the accretion disk will not be viewed over the full range of inclination angles because of the obscuring torus. Assuming that the accretion disk axis and the torus axis are aligned, then depending on the opening angle of the torus, the expected polarization range is no longer 0%–11.7% (see § 2) but is reduced. Figure 9 compares the observed polarization of PG QSOs to the predictions for an optically thick, pure electron‐scattering slab. In this comparison the viewing angle ranges between 0° and 60°. The comparison shows that the theoretical predictions are inconsistent with the data, i.e., calculations predict more objects with higher polarization than are observed. But, if there is a range in the opening angle of the torus around 30°, then the expected polarization would be in the range 0%–0.5%, which could become consistent with the data. The slightly higher polarization seen in some sources could then be due to larger torus opening angles. Note that in this argument, we have assumed that the disk and torus are aligned, which may not be the case. The important point is that although it may be possible to explain to some extent the low magnitude of polarization that is observed in AGNs, the polarization angle is observed to be parallel to the inferred disk axis. This polarization angle dependence is perpendicular to that expected from a pure electron‐scattering slab! Until recently, the disk axis has been inferred only in radio‐loud AGNs by determining the radio jet axis. We now have the ability to resolve the central radio source in radio‐quiet AGNs, and it will certainly be interesting to check the alignment of the polarization angle in these objects.

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HST/FOS spectropolarimetry allowed us to probe the ∼700 Å to ∼1300 Å region of 10 intermediate‐redshift quasars (Koratkar et al. 1995; Impey et al. 1995; Koratkar et al. 1998). Using ground‐based spectropolarimetry, Antonucci et al. (1996) have observed three high‐redshift AGNs shortward of the Lyman limit and 20 intermediate‐redshift AGNs in the ∼1100 Å to ∼3000 Å region. Although the current data cannot be used to make any statistically significant conclusions, there are certain trends seen in this small sample. The data show that polarization is not only low in the optical region but also continues to remain low (≲1.5%) even in the UV (up to ∼1000 Å). Further, there is no statistical wavelength dependence to the polarization for wavelengths greater than 1000 Å. Investigations shortward of the Lyman limit region found that some radio‐quiet AGNs are polarized in this region, and the polarization has some wavelength dependence (see Fig. 10). Approximately 30% of the objects investigated in the Lyman limit region show a rise in polarization shortward of the Lyman edge; i.e., these objects show higher polarizations shortward of the Lyman edge and no polarization longward of the Lyman edge. In one case, PG 1630+377, the polarization is ∼20%! The other 70% of the sample showed no significant polarization (see Fig. 11). The 95% confidence level upper limits on linear polarization shortward of the Lyman limit for these objects is ≲4%. It must be noted here that most of the objects that showed polarization shortward of the Lyman limit also showed a candidate partial Lyman edge feature, while except for one object, all the objects that had no detected Lyman edge feature showed no polarization.

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The Fe Kα emission line, interpreted as arising from fluorescence in the X‐ray–illuminated disk, is extremely broad and redshifted, which provides dramatic support for an accretion disk in a relativistic potential well (Tanaka et al. 1995). It is perhaps the best evidence for accretion disks in the innermost regions of the central engines of AGNs. It certainly provides the only direct evidence for cold gas with a large column density very close to the central engine. It is therefore important to investigate the nature of the Lyman edge feature in objects that have such convincing evidence of an accretion disk. Unfortunately, there are no observations spanning a reasonable wavelength region (see § 3.2) around the Lyman limit for an AGN that also shows a broad Fe Kα line. The best data come from the Hopkins Ultraviolet Telescope (HUT) on low‐redshift Seyfert galaxies (Kriss et al. 1997), and ASCA observations of these Seyfert galaxies. There are only six Seyfert galaxies that have both Lyman edge and Fe Kα line observations. Except for perhaps one object (NGC 3516), none of the remaining five objects shows a clear intrinsic Lyman edge feature in total flux. Confusion with Galactic absorption in high‐n Lyman series lines and the Lyman continuum preclude using the HUT data to search for the smeared edge features expected from a relativistic disk.

Observations of the Fe Kα emission line and the Lyman limit region can be used to constrain the theoretical accretion disk models. The Fe Kα line profiles and line peaks are dependent on the inclination angle of the accretion disk. Although the black hole mass and geometry influence the line profile shape, in general the models predict that the line profiles are broader and the line peaks are bluer for edge‐on disks than for face‐on disks (see Fig. 12). Therefore, if the line profile is accurately determined, it places strict constraints on the disk inclination angle. Next, if one assumes that the Lyman edge is also from the same disk structure (which need not be the case), then the predicted Lyman edge can be compared with observations (see Figs. 12 and 13). The current Fe Kα emission‐line profiles exclude edge‐on disks whose Lyman edges are easier to hide owing to large relativistic smearing. The disk inclination angles derived from the Fe Kα emission‐line profiles indicate that in a "bare" disk (i.e., no Comptonization), the Lyman edge should be detectable. The current data therefore once again suggest that Comptonization is important.

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The Lyman edge problem indicates that to understand the emission mechanism in AGNs, multiwavelength data are essential to constrain the models. With FUSE coming on‐line, in addition to high‐energy resolution X‐ray telescopes such as the X‐ray Multi‐Mirror Observatory (XMM), there will soon be an opportunity to investigate the Fe Kα emission line and the Lyman edge simultaneously.

The extraordinary luminosities of AGNs are observed to vary. Variability studies provide crucial data concerning the timescales of variation, the nature of spectral variation, and the delays between the various spectral regions. Variability data are also essential for understanding the nature of accretion disks in AGNs because variability timescales allow us to probe the nuclear regions (<10¹⁴–10¹⁸ cm). If characteristic timescales are found, these would allow us to investigate the physical mechanisms that drive the fluctuations. By comparing multi–wave‐band light curves, the nature of propagation of a signal can be investigated.

3.5.1. Variability Timescales

3.5.2. Spectral Variations in the Optical/UV/X‐Rays

The nature of the spectral variations allows us to characterize the emission mechanism and the factors that cause changes in the emission mechanism. Spectral variations are such that the optical/UV continuum hardens as the nucleus brightens (see Fig. 14). The shortest wavelengths vary the fastest (Clavel et al. 1992; Edelson et al. 1996; Peterson 1993; Nandra et al. 1998). In the X‐rays, the power‐law component often varies with no spectral variation (Ulrich et al. 1996; Nandra et al. 1998), but sometimes the spectrum does change, becoming softer as the object brightens (e.g., 3C 390.3, Leighly et al. 1997; NGC 5548, Magdziarz et al. 1998). Increased Compton cooling of the X‐ray–emitting plasma, possibly because of a change in the disk geometry producing more UV photons (see Magdziarz et al. 1998; see § 5 below), may be an explanation for this. We discuss the implications of spectral variations further in § 4 below.

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3.5.3. Correlations between the Optical/UV and X‐Rays

One of the main characteristics of optically thick accretion disks is that different portions of the optical/UV spectrum arise predominately from spatially separated locations in the flow that have different overall size scales. Variability in the continuum might therefore have wavelength‐dependent timescales and amplitudes, and one might also expect time lags owing to finite signal propagation speeds between different regions of the flow. For quite some time now, it has been known that variations in the optical/UV continuum of Seyfert galaxies and QSOs are highly correlated and imply signal propagations on faster timescales than the viscous or even sound‐crossing times in the flow (Alloin et al. 1985; Cutri et al. 1985; Courvoisier & Clavel 1991). One possible explanation for this is that optical/UV variations are driven by reprocessing of UV or X‐ray radiation from the inner parts of the disk (Krolik et al. 1991; Collin‐Souffrin 1991). This is confirmed by simultaneous, multiwavelength monitoring campaigns of the Seyfert galaxies NGC 4151 and NGC 5548, which show correlated variability between optical/UV and X‐ray energies (Edelson et al. 1996; Clavel et al. 1992).

NGC 7469 has been intensively monitored for the longest duration so far, and this campaign allowed time lags between the different continuum wave bands to be measured for the first time. In this source, optical/UV continuum variability is highly correlated and shows a monotonically increasing time lag τ with wavelength λ, which can be fitted with τ∝λ^4/3, the prediction for a T_eff∝r^-3/4 accretion disk (Wanders et al. 1997; Collier et al. 1998). The time delays ranged from ≃0.2 to 2 days, and their statistical significance is difficult to determine. A conservative analysis by Peterson et al. (1998) finds them to be marginally significant (>2.2 σ). Peterson et al. (1998) also showed that if the results for NGC 7469 are real and if we scale all the other AGNs with previous observations, the data from previous campaigns did not have the temporal resolution to detect lags if they were present.

More interestingly, variability in the X‐rays and optical/UV is not correlated on such short timescales (Nandra et al. 1998). However, one can interpret the data in terms of an anticorrelation between the X‐rays and UV, with the X‐rays leading the UV by 4 days. Alternatively, the UV correlates with the X‐rays, with the UV leading by 4 days. Neither of these statements provides a satisfactory representation of the light curves, which appear to show the UV leading the X‐rays near the peak fluxes, while they both achieve approximate simultaneity near the minimum flux levels (see Fig. 15). The X‐rays also show short timescale variability (50% in 1 day), which is not observed in the UV. While this last fact is consistent with the optical/UV radiation arising on larger scales from reprocessing of X‐rays from the inner disk, the lack of short timescale correlations presents a severe problem for this simple picture. Models in which the UV drive the X‐rays by providing the seed photons for Compton scattering are also too simple to explain the observations. As Nandra et al. (1998) point out, the observations require a more complex interaction between the UV‐ and X‐ray–emitting regions. One possibility that they propose is that in bright states the source of UV seed photons lies 4 lt‐days out from the X‐ray source and drives the X‐ray variability. This source of seed photons is lost in faint states, where closer sources of seed photons become important. It is not yet clear how to reconcile the UV/X‐ray variations with a flow geometry.

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Another indication from the NGC 7469 campaign that things are not so simple is the fact that, while the broad emission lines do tend to show correlated, lagged variability with the observed UV continuum, in this particular campaign they also showed long‐term trends that were not present in the continuum, which suggests that either the observed UV photons are not in fact a good representation of the variability in the (unobservable) ionizing photon spectrum or that the broad line region is evolving over this period.

As we noted in the Introduction, direct imaging of the central accretion flow will be impossible for the foreseeable future because of the small size scales involved. Reverberation mapping in the X‐rays may provide one way of probing the accretion flow with the next generation of high‐throughput X‐ray satellites such as XMM and Constellation‐X. In addition, Nature has provided us with a cosmic telescope that can optically perform this feat, at least in one source. The line of sight to quasar Q2237+0305 passes right through the central core of a foreground, face‐on spiral galaxy. This galaxy lenses the quasar into four images that make up the "Einstein Cross" (Huchra et al. 1985). Because of the large surface density of stars in the galaxy's central region, microlensing is observed in the images (Irwin et al. 1989; Pettersen 1990; Corrigan et al. 1991; Racine 1991; Nadeau et al. 1991; Racine 1992; Østensen et al. 1996). The size of microlensing variations implies that the quasar emission region must be smaller than the scale of variations in the caustic network formed by the foreground stars. This scale is typically given by the Einstein radius ∼10¹⁷ M^1/2 cm, where M is the mass of the lensing star in solar masses. If a rapid microlensing event is resolved in time, even more stringent constraints can be placed on the source size. The most rapid observed event in image "A" (Irwin et al. 1989) constrains the size of the optical emission region to be ≲2 × 10¹⁵ cm (Wambsganss, Schneider, & Paczyński 1990). This is far below any length scale that can be probed by other techniques.

The small size of the optical emission region places strong constraints on accretion disk models. Rauch & Blandford (1991) found that to explain both the observed luminosity and the microlensing size scale, an emissivity in excess of the blackbody limit was required. In other words, a thermal accretion disk is too large (by about a factor 3) to fit within the microlensing size constraint. Somewhat different modeling by Jaroszyński, Wambsganss, & Paczyński (1992) found that accretion disks were consistent with the microlensing constraint. Part of the difference between these two papers was that Jaroszyński et al. considered accretion disks around Kerr holes, whereas Rauch & Blandford considered only Schwarzschild holes. This allowed the former authors to consider more compact disks, as well as producing a greater concentration of luminosity in a hot spot produced by beaming of radiation toward the observer by the orbiting emitting plasma.

However, an even more important difference between the two papers is how the SED problem was handled. As we have pointed out here in this review, luminous accretion disks produce SEDs that are too blue compared to observations. To get around this, Rauch & Blandford modified the radial emissivity of the disk to be flatter than equation (1) above, i.e., allowing more of the accretion power to be dissipated at larger radii. This is one way of explaining the red observed SEDs of AGNs but of course leads to larger optically emitting regions than the standard disk. Jaroszyński et al., on the other hand, kept the standard radial emissivity and assumed instead that there was another source of red light in the source that arises from farther out and is not microlensed. Both approaches are ad hoc, although there are other reasons for believing that the radial emissivity profile that Rauch & Blandford assume is correct: optical/UV variability suggests that it arises from reprocessing of radiation from the inner disk. Czerny, Jaroszyński, & Czerny (1994) have explored the problem of irradiated disks and again find accretion disks to be consistent with the microlensing data. However, they found it necessary to consider accretion luminosities half that of Eddington, so a slim disk (see § 5.2 below) really needs to be considered. The microlensing problem is clearly intimately tied to the SED problem, and continued monitoring is crucial to tighten the observational constraints.

While the microlensing observations have often been presented as a challenge for accretion disk models, it is perhaps worthwhile pointing out that they do in fact prove that the optical emission in at least this quasar originates very close to the central black hole. This is at least in qualitative agreement with the idea that the central accretion flow is responsible for the BBB.

Broad emission lines are characteristic of the spectra of AGNs. If these lines arise in a disk, one expects them to exhibit the double‐peaked profile structure that is commonly seen in the optical/UV emission lines from accretion disks in cataclysmic variables (see, e.g., Marsh & Horne 1988). Yet, only a fraction of radio‐loud AGNs, and a handful of radio‐quiet AGNs, show such lines (Eracleous & Halpern 1994; Storchi‐Bergmann et al. 1997). This has been raised as a problem for accretion disk models of AGNs (Kinney 1994). However, it is also worth noting that Livio & Xu (1997) have shown that the double‐peaked lines cannot be produced by two line‐emitting jets, thus leaving the accretion disk as the only viable site for the production of such lines.

In accretion disk models the optical/UV continuum is generated from disks whose extent is 10–1000R_g. If the optical/UV continuum is generated by an accretion disk, it is tempting also to hypothesize that the broad emission line spectrum is due to the disk. Collin‐Souffrin (1987) showed that if a disk is illuminated by an external X‐ray source, then the disk could contribute toward the emission‐line spectrum, but the emission lines were from the outer parts of the disk at ∼1000R_g, and broad emission lines were not observed from the inner parts of the disk (Dumont & Collin‐Souffrin 1990a, 1990b). Models by Chen, Halpern, & Filippenko (1989) and Chen & Halpern (1989) also effectively illuminate the outer parts of the disk to produce the low‐ionization lines (Mg ii and Balmer lines). In all the models, although the emission lines may be related to the disk phenomenon, the lines are formed at relatively large distances from the massive black hole, and we are interested in the inner parts of the accretion disk that predominantly contribute to the optical/UV continuum. Therefore in this paper we do not discuss broad emission line profiles further. Ultimately, the ionizing continuum that is generated by the inner disk drives the emission lines, and in a realistic model both the lines as well as the continuum will have to be explained. For a review on emission‐line profiles from disks, we refer the reader to Eracleous (1998).

Before leaving this subject entirely, it is perhaps worthwhile pointing out that the Fe Kα line observed by ASCA in many Seyfert galaxies does occasionally have a double‐peaked shape (see, e.g., Tanaka et al. 1995). We have discussed the Fe Kα line in § 3.4 since this line is expected to arise within 100R_g.

Since the SED predicted by luminous accretion disks is generally bluer than the optical spectra observed in AGNs, traditionally theoretical fits to the data included an additional infrared power‐law component that changed the optical slope that the accretion disk model had to fit. But, with mounting evidence that thermal dust emission produces the infrared, this ad hoc procedure is not valid, and such disk models do not provide a satisfactory fit to the observations. Driven by the challenges posed by observations to the standard model, much more sophisticated modeling of accretion disks has occurred in recent years.

Before turning to these more sophisticated models, it is important to be clear as to what the elementary blackbody disk models can and cannot do. Naively, one would expect these simple models to predict that the SED should be F_ν∝ν^1/3. However, the simplest thin disk models around supermassive (M≥10⁶ M_⊙) black holes often do not produce ν^1/3 spectra throughout the optical/UV. In order for the disk not to produce so much radiation pressure that it becomes geometrically thick, the accretion rate is limited to about 0.2–0.3 times the Eddington rate (see, e.g., Laor & Netzer 1989, but see § 5.2 below). Simple blackbody disk models around supermassive black holes have maximum temperatures less than 3–8 × 10⁵ K, depending on the black hole spin, and their SED in the optical/UV can be significantly redder than the ν^1/3 prediction (see Fig. 16), particularly when viewed face‐on.

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A fit to the Francis et al. (1991) composite spectrum is shown in Figure 17. There is no problem fitting the data with a simple blackbody disk model, provided the disk is cool. The Schwarzschild fit shown in this figure has L/L_Edd ≃0.1(M/10⁹ M_⊙), whereas the Kerr fit has L/L_Edd ≃3 × 10^-3(M/10⁹). Such cool disk spectra turn over in the optical/UV, which is why they can have such red slopes. This curvature in the disk spectrum immediately provides an explanation for why the optical/UV continuum might get harder when brighter: varying the maximum temperature, e.g., by varying the accretion rate, will change the overall slope of the spectrum (Collin‐Souffrin 1991; Molendi, Maraschi, & Stella 1992). However, such cool disks are probably not sufficiently luminous, at least if they are around low‐mass black holes, and they certainly do not produce much in the way of ionizing photons! One possibility may be that the optically thick portion of the disk does not extend all the way to the innermost stable orbit, which allows it to have a smaller maximum temperature as the flow transitions into some other, hotter phase (see, e.g., § 5.5 below).

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The more difficult continuum SED problem with thin disk models is not how to explain a red optical/UV spectrum but rather how to explain the origin of the higher energy EUV/X‐ray emission. In Figure 17 we see how the theoretical continuum SED falls off sharply in the EUV. This problem is highlighted when one tries to understand the AGN emission‐line spectrum. For example, since the BBB drives the emission lines seen in the spectra of AGNs, Korista, Ferland, & Baldwin (1997) compared the predicted and observed emission‐line strengths using the "observed" UV X‐ray composite BBB SED (see § 3.1) in photoionization models. The "observed" BBB SED does not reproduce the observed line strengths. MacAlpine et al. (1985) first showed that the He ii line equivalent widths were indicative of substantial intrinsic UV excess seen by the broad‐line clouds. To explain the discrepancies between the "observed" BBB and the theoretical predictions, we either have to assume that the observations are invalid or that the BLR clouds see a very different continuum than that observed by us. This exercise clearly indicates that geometry of the gas near the AGN central engine and/or the presence of another emission component that generates a significant amount of the ionizing radiation must also be considered.

If the accretion disk itself is to be hot enough to produce sufficient ionizing continuum, then the optical SED predicted by simple blackbody models will indeed be too blue to explain the observations. The accretion disk is not likely to emit locally as a blackbody, however. As noted in § 2, for example, electron scattering can significantly flatten the spectrum in frequency (i.e., make it redder) if it dominates the opacity at the photosphere and produces a modified blackbody spectrum. Whether or not this happens depends on the very uncertain vertical structure of the disk. Laor & Netzer (1989) were the first to make a serious attempt at improving the simple models by calculating the vertical structure and radiative transfer in an approximate fashion, including bound‐free as well as free‐free and electron‐scattering opacities. They found that the photosphere temperature is everywhere close to the effective temperature for most of their AGN disk models, which indicates that a blackbody spectrum is a better local approximation than a modified blackbody. However, this conclusion is uncertain, as it depends crucially on the density at the photosphere that in their models was equal to the midplane density. This may have artificially enhanced the role of absorption opacity to scattering opacity at the photosphere. Ross, Fabian, & Mineshige (1992) improved on the Laor & Netzer models by again assuming a constant density with height but including a better treatment of Comptonization in both the radiative transfer and thermal balance. They found that the overall spectrum did deviate significantly from the blackbody assumption, at least for their chosen viscosity. More detailed treatments of the vertical structure in such models, but that neglect bound‐free and bound‐bound opacities, have been performed by Shimura & Takahara (1993, 1995) and Dörrer et al. (1996).

One way of redistributing the energy in the BBB and changing the optical/UV continuum slope is to assume that the optical/UV arises from reprocessing of radiation from the inner disk. A flat disk irradiated by a central source still produces an r^-3/4 temperature profile, so flaring or warping is required to change the spectral shape (see § 5.4). Until recently, the reprocessing assumption was valid because the variability campaigns indicated that the optical/UV and X‐ray variations were correlated with nearly no lag. However, the NGC 7469 campaign raises a number of issues that make this simple picture of reprocessing even more complicated (see § 3.5.3).

To explain the dearth of Lyman edges in AGNs, the new accretion disk models have considered a number of theoretical approaches and improvements. The new models now include complex stellar atmosphere effects, and modern state‐of‐the‐art stellar atmosphere codes. Preliminary steps have been taken toward investigating two‐phase accretion disk models and including relativistic transfer functions in the codes.

The original calculations of accretion disks by Kolykhalov & Sunyaev (1984) relied on existing stellar atmosphere libraries and thus predicted large Lyman edge features. These libraries completely neglected non‐LTE effects. These can be very important in the Lyman limit region because the large hydrogen photoionization opacity generally means that the Lyman continuum originates high in the atmosphere, where densities are low and radiative transition rates can dominate collisional transition rates. Even more important, the atmospheres that exist in those libraries generally have high densities compared to what is possible in high‐luminosity accretion disks. This limited the range of parameter space that Kolykhalov & Sunyaev could explore to low‐α parameter (α<10^-2), high photospheric density models. Because the neutral fraction of hydrogen becomes larger at high densities, this resulted in very large Lyman edge absorption opacity, thereby producing very large absorption edges in these disk models.

Low densities in the disk photosphere will reduce the ratio of Lyman continuum absorption opacity to scattering opacity and thereby decrease the flux difference at an absorption edge or even drive it into emission (Czerny & Pojmański 1990). Ab initio radiative transfer calculations confirm this behavior (Coleman & Shields 1993; Shields & Coleman 1994; Hubeny & Hubeny 1997; Sincell & Krolik 1998), which shows that as the maximum effective temperature and/or the ratio of luminosity to Eddington luminosity increase, Lyman absorption edges become weaker, then disappear, become moderate emission edges, and finally become weak emission edges as the hydrogen becomes fully ionized and recombination rates are low. Non‐LTE effects produce similar results (Sun & Malkan 1989; Shields & Coleman 1994; Störzer, Hauschildt, & Allard 1994; Hubeny & Hubeny 1997; Collin & Dumont 1997; Czerny & Dumont 1998). Ironically, non‐LTE effects can also enhance the He ii Lyman continuum (Hubeny & Hubeny 1997), which would have important implications for photoionization of the broad‐line region clouds in AGNs. To get rid of the Lyman edge completely in a given atmosphere at a given radius in the disk using these effects would require fine tuning, but it is clear that the overall edge produced from an integration of diverse atmospheres at different disk radii, some with absorption edges and some with emission edges, might generically produce a small net effect (see Fig. 18). Note, however, that the requirement that the disk be hot enough to drive the edge into emission in the innermost radii requires high accretion rates compared to Eddington, which drives the optical/UV SED closer to the classic F_ν∝ν^1/3 limit (Sincell & Krolik 1998). The relatively cool disks discussed in the previous subsection to explain the SED would probably have observable Lyman absorption edges (see Fig. 22). There is as yet no accretion disk model that solves both problems (the Lyman edge and the optical/UV continuum slope) simultaneously.

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To explain the X‐ray spectra observed in AGNs, a number of models invoke thermal Comptonization of optical/UV photons by an energetically powerful, magnetized corona above the disk (see, e.g., Haardt & Maraschi 1991). Strong support for such models has been provided by the observation of Compton reflection features in hard X‐rays (Nandra & Pounds 1994), which require that cold matter (presumably the disk) cover approximately half of the sky as seen from the X‐ray source. Until recently, most accretion disk model calculations explored the parameter space for a "bare" accretion disk and neglected the effects of external heating of the disk atmosphere. Sincell & Krolik (1997) have taken the first steps in calculating the spectrum from an X‐ray–illuminated accretion disk. In their simple two‐phase model, all the accretion power is assumed to be dissipated in a corona above the disk. X‐rays from the corona irradiate the accretion disk and the UV continuum is produced by reradiation of absorbed energy. There is no internal disk heating. Their calculations showed large Lyman edge features in emission, which are not present in the observations. Figure 19 shows the emission edges produced for three observer viewing angles by the Sincell & Krolik (1997) models. The sharpest edges occur for face‐on disks, but substantial edges are still produced for edge‐on disks. Physically, these large emission edges arise because taking accretion power out of the disk and putting it in the corona robs the disk of pressure support, producing larger photospheric densities and therefore larger hydrogen recombination rates. Although the simple two‐phase model disagrees with the observations in the Lyman limit region, the parameter space for this model has not been thoroughly examined, and many sophisticated radiative transfer effects, particularly non‐LTE effects on the level populations of the irradiated hydrogen gas, have not been included.

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The accretion disk is embedded in the deep potential well of the supermassive black hole. It is then natural that many authors have considered the effects of relativistic Doppler shifts and gravitational redshifts to explain the dearth of Lyman edge features in AGNs (Sun & Malkan 1989; Laor & Netzer 1989; Lee, Kriss, & Davidsen 1992; Laor 1992; Shields & Coleman 1994; Wehrse 1997). The amount of Lyman edge smearing is inclination angle–dependent, with the largest effect seen when the object is viewed edge‐on. In the unified schemes for AGNs, the objects for which we have observational data (Seyfert 1 galaxies and QSOs) are most likely to be viewed face‐on, where the effect of smearing is predicted to be the smallest. The smearing also depends on the black hole spin. Kerr holes are more effective than Schwarzschild holes because the innermost stable orbit can be much closer to the horizon. However, to test effectively the accretion disk models that include all these effects is nearly impossible. Ideally, the observations need to be of an AGN with a "reasonably clean" line of sight and over a large wavelength region, and, as discussed in § 3.2, such observations are rare!

One of the many ways to account for the few observed Lyman edge features in AGNs is to invoke a Compton scattering atmosphere (Czerny & Zbyszewska 1991; Lee et al. 1992). In these models, the spectral shape in the Lyman limit region is a function of the electron temperature of the Comptonizing corona, the optical depth to Compton scattering, and the inclination angle of the accretion disk. The Lyman edge is smeared out because Lyman limit photons are scattered across the Lyman edge, which makes the Lyman limit feature more difficult to detect. The models predict a definite break in the shape of the continuum at the Lyman limit (Lee et al. 1992). This is qualitatively similar to observations of the few candidate "partial" Lyman edge objects. As discussed in the next section, Compton scattering may impart polarization to the radiation higher than observed, but if the corona is magnetized, Faraday rotation can alleviate this problem.

Metal line opacity is likely to be important in the Lyman limit region, and no models exist as yet that properly take this into account. Hubeny & Hubeny (1998) have included this in a preliminary way by including the line opacity and emissivity in radiative transfer calculations through atmospheres whose structure was calculated by neglecting these lines. While not fully self‐consistent, the results suggest rather strongly that the Lyman edge will be swamped by metal line features (see Fig. 20). Figure 18 shows the corresponding total spectra after integrating over all disk radii and folding through the relativistic transfer function (Agol, Hubeny, & Blaes 1998b). Even in the pure hydrogen/helium models, the Lyman edge is greatly reduced. A change in slope is still evident in the μ = 0.5 case, although it occurs shortward of 912 Å. A bump is present redward of 912 Å in the near face‐on case. This is produced because the Lyman edge is in emission in the (more redshifted) inner parts of the disk and in absorption in the (less redshifted) outer parts of the disk (see Fig. 20). When metal lines are included, the change in slope near this bump is reduced but is still detectable conceivably. In addition, the dramatic reduction in flux shortward of 850 Å caused by the line‐blanketing in this model could be detected. However, this is the face‐on case in which relativistic smearing is most reduced. Self‐consistent calculations need to be performed to make firmer predictions, but this work is encouraging.

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At long wavelengths the spectra shown in Figure 18 obey F_λ∝λ^-7/3, in agreement with the standard F_ν∝ν^1/3 accretion disk prediction. However, flux is lost by the line‐blanketing effects of metals, which causes the SED to drop at short wavelengths. In a self‐consistent calculation, this absorbed radiation will have to be reemitted somewhere in the SED, and it is therefore conceivable that the overall SED continuum shape will change, likely becoming redder and therefore in better agreement with observations. Once again, this needs to be checked by computing self‐consistent line‐blanketed, non‐LTE models in a broad range of parameter space.

An important fact about all the new "bare" accretion disk calculations is that the strength of the Lyman edge feature is not as strong as thought in the earlier models, but getting rid of the Lyman edge is difficult. Self‐consistent calculations of Lyman edge features in disk‐corona or multiphase accretion flow models are badly needed.

The Chandrasekhar (1960) calculation of polarization emerging from pure electron‐scattering atmospheres is unlikely to apply to real accretion disk atmospheres, which have nonzero absorption opacity. Laor, Netzer, & Piran (1990) made the first attempt at calculating the effects of absorption opacity on the disk polarization of AGNs. They did this by simply multiplying the Chandrasekhar polarization by the ratio of Thomson opacity to total opacity,

which they took to be independent of depth at each radius in the disk. Because q<1 at all frequencies ν by definition, this gives the physically reasonable result that absorption opacity always reduces polarization. The total disk polarization was therefore reduced in their calculations, which therefore produced better agreement with observations. Once again we note, however, that their models may have had high photospheric densities and therefore might have exaggerated the importance of absorption opacity compared to scattering opacity. In general they predicted that the polarization should rise with decreasing wavelength up to around the Lyman edge, then drop because of the increase in bound‐free opacity, and then rise again. Laor et al. (1990) also included the effects of the relativistic transfer function on polarization and found that at very short wavelengths the plane of polarization rotates away from being parallel to the disk plane.

The effects of absorption opacity on polarization can actually be more subtle than assumed by Laor et al. (1990). Polarization emerging from an atmosphere depends on both the presence of scattering opacity and the degree of anisotropy of the radiation field (limb‐darkening or limb‐brightening). While absorption opacity reduces the importance of scattering, it can also enhance the anisotropy, depending on the thermal source function gradient. This can sometimes lead to an increase in polarization over and above that expected for a pure electron‐scattering atmosphere (Harrington 1969; Loskutov & Sobolev 1979; Bochkarev, Karitskaya, & Sakhibullin 1985). The effect is illustrated in Figure 21, which shows polarization as a function of q for thermal source functions that vary linearly with total optical depth τ in the atmosphere:

where the constant β determines the steepness of the thermal source function gradient. As shown in the figure, inclusion of absorption opacity (q dropping below unity) can produce an increase in polarization if the thermal source function gradient is steep. In addition, flat thermal source function gradients can produce strong negative polarizations, in which the polarization is perpendicular to the disk plane (the "Nagirner effect"). The Nagirner effect might be one way of reconciling the fact that the polarization observed in AGNs is parallel to the radio axes and perpendicular to the Chandrasekhar (1960) prediction. However, it may be difficult for it to produce an optical polarization which is wavelength independent, as observed.

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Blaes & Agol (1996) attempted to use these atmosphere effects to explain the steep rises in polarization observed blueward of the Lyman edges in some quasars, discussed above in § 3.3. A good qualitative fit was obtained to the data for PG 1222+228 (Impey et al. 1995) by invoking a relatively cool disk whose overall SED turns over in the Lyman edge region (see Fig. 22). As discussed in § 4.1, this may be a way of explaining the red SEDs observed in quasars. However, a quantitative fit was not achieved, and the predicted polarization rise is not as steep as observed. Moreover, they were unable to explain the very steep rise observed in PG 1630+377 (Koratkar et al. 1995). In addition, they neglected the relativistic transfer function, which tends to smear and reduce the polarization rise (Agol 1997; Shields, Wobus, & Husfeld 1998), although this may not be a problem if the optically thick portion of the disk does not extend all the way down to the innermost stable orbit.

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Shields et al. (1998) have produced a model that produces excellent quantitative agreement with the observations of steep polarization rises near the Lyman edge but is based on ad hoc assumptions. They assume that at every radius the disk produces a spectrum with a sharp Lyman edge in absorption, together with a large Lyman polarization edge in emission. In particular, the polarization is assumed to be zero redward of the edge and an arbitrarily high multiple of the Chandrasekhar (1960) pure electron‐scattering polarization blueward of the edge. These spectra are then passed through the relativistic transfer function and can be made to fit the observations quantitatively with few free parameters (see Fig. 23). This is a considerable achievement, but it relies on having a large intrinsic polarization jump at the Lyman limit from the disk. Shields et al. suggest that this might be produced by Lyman continuum photons emitted and scattered by an optically thin, ionized region of the accretion disk, but this remains to be demonstrated. The relativistic transfer function is crucial to their fits, and they require the disk to be viewed nearly edge‐on (all their successful fits had inclination angles greater than 75°). The Blaes & Agol (1996) models also required rather large inclination angles (53°–66°).

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One of the more successful theoretical solutions to the Lyman edge problem in total flux has been Comptonization of the intrinsic disk spectrum by a corona. Comptonization will of course imprint its own polarization signature on the emerging spectrum. Hsu & Blaes (1998) have presented radiative transfer calculations of Compton scattering of polarized radiation in two‐phase accretion disk models with plane‐parallel geometry. For featureless spectra, Compton scattering generally produces less polarization than Thomson scattering with the same optical depth. Nevertheless, when Compton scattering is sufficient to smear out a Lyman edge, it generally produces significant polarization in the overall spectrum. Interestingly, Compton scattering can produce very large polarizations parallel to the disk axis blueward of an input Lyman edge, and at the same time the edge is smeared out in total flux. However, the rise in polarization magnitude is not steep enough to explain the rises observed in several QSOs (see § 3.3).

Lee & Blandford (1997) suggested that resonance line scattering by an externally illuminated slab may explain the high polarization seen shortward of the Lyman edge in PG 1630+377. To test this model further, we need high‐resolution spectropolarimetry in the rest wavelength range 500–1000 Å.

It may in fact be that optical/UV radiation emerging from the accretion disks of AGNs exhibits very little polarization. Magnetic fields are widely believed to play an important role in accretion disks, and they can significantly reduce the polarization emerging from the disk photosphere through Faraday rotation (Gnedin & Silant'ev 1978; Blandford 1990; Matt, Fabian, & Ross 1993; Begelman 1994). The Faraday rotation angle at wavelength λ is ≃0.1τ_T(λ/5000 Å)²(B_∥/1 G), where τ_T is the Thomson depth near the scattering photosphere and B_∥ is the component of field strength along the line of sight. The equipartition field strength in the inner regions of an α disk is ∼10⁴ G α^-1/2(M/10⁸ M_⊙)^-1/2. Hence unless the filling factor of magnetized regions on the disk photosphere is very small, the optical (and UV perhaps) radiation from the disk should be completely depolarized. Detailed polarized radiative transfer calculations through disks with pure electron‐scattering atmospheres confirm this (Agol & Blaes 1996). Complications arise when absorption opacity is included, but generally the effect of magnetic fields is still to reduce the overall polarization. The only exception is when the Nagirner effect is present, where modest magnetic fields can actually increase polarization (Agol, Blaes, & Ionescu‐Zanetti 1998a).

If Faraday rotation or some other process wipes out optical continuum polarization from the accretion disk photosphere, then one must still find an explanation for the small polarization that is actually observed. One possibility is dust and electron scattering in a stratified wind on scales much larger than the central accretion flow. This mechanism is capable of explaining both the large perpendicular polarizations in Seyfert 2 galaxies and the small parallel polarizations in Seyfert 1 galaxies in a manner consistent with unification schemes (Kartje 1995). Thomson scattering in a fast wind near the accretion disk is also capable of producing polarizations parallel to the disk axis (Beloborodov 1998) because relativistic aberration makes the radiation field limb‐brightened in the rest frame of the scattering electrons.

The current spectropolarimetric observations place strong constraints on the models. The low polarization observed in AGNs indicates that if electron‐scattering–dominated disk atmospheres are considered, then magnetic field effects must be included in the calculations.

At both low and high accretion rates, it is possible for internal pressure to become just as important as gravity and rotation. The vertical thickness can then become comparable to the radius, which will result in a thick disk. Such disks can resemble tori and/or quasi‐spherical accretion flows. At high accretion rates, the outward radiation flux saturates near the Eddington limit (Begelman & Meier 1982), and radiation pressure becomes very important and might support a thick disk geometry. Most of the models of radiation pressure–supported thick disks assume that away from the innermost regions, the flow is in hydrostatic equilibrium on an orbital timescale. This necessarily requires that the flow have a low viscosity parameter α, which is simply the ratio of the orbital time to the infall time for geometrically thick flows. Exceedingly low viscosities are also required in order that the flow be optically thick (see, e.g., Rees 1984). Models of radiation‐supported thick disks or tori have been constructed by Paczyński & Wiita (1980), Jaroszyński, Abramowicz & Paczyński (1980), and Abramowicz, Calvani, & Nobili (1980). The geometry of such models is determined by their surface distribution of specific angular momentum, which is not known a priori and is presumably determined by the "viscous" angular momentum transport. In addition to the viscosity constraints, such models in their simplest (nonaccreting!) forms may be subject to global hydrodynamical instabilities (Papaloizou & Pringle 1984), which produce strong spiral waves in the flow (Hawley 1991). Accretion through the disk may, however, reduce the effects of these instabilities (Blaes 1987; Gat & Livio 1992; Dwarkadus & Balbus 1996).

There have been very few predictions of the observed properties of radiation‐supported thick disks. Madau (1988) has modeled the emerging SED, which has a strong dependence on viewing angle. This is because most of the luminosity originates in the central funnel region, which is shadowed by the outer torus‐shaped disk for large viewing angles. Observers who can view the funnel see a spectrum that extends up to the soft X‐rays, whereas observers who view the disk more edge‐on see a much cooler spectrum. High inclination angles may be required to make the models compatible with observed UV/soft X‐ray flux ratios in Seyfert 1 galaxies (Walter & Fink 1993). This may be incompatible with the unified model and low inclination angles inferred from Fe Kα lines, but it should be pointed out that thin disk models have not succeeded in explaining the soft X‐ray excess in a self‐consistent fashion either. In addition, the optical/UV SED for thick disks suffers the same problem as in thin disks in being bluer than observed. On the other hand, scattering in the funnel provides a way of producing polarization parallel to the radio axis (Coleman & Shields 1990; Kartje & Königl 1991). In addition, because heat diffuses in all directions, not just vertically, all elements of the photosphere are thermally coupled together, and optical and UV radiation might therefore be expected to exhibit correlated variability with no lags (see the discussion by Szuskiewicz, Malkan & Abramowicz 1996), as observed.

The usual α‐viscosity prescription, in which the viscous stress is proportional to the total (gas plus radiation) pressure, leads to disks that are thermally and viscously unstable in cases in which the accretion rate is high enough that the inner regions of the disk are supported by radiation pressure (see, e.g., Shakura & Sunyaev 1976). Whether such instabilities are real is not at all clear because of the strong dependence on the ad hoc viscosity prescription (see, e.g., Piran 1978). However, if they are real, it may be that the disk jumps to a higher accretion rate, optically thick, geometrically "slim" (not thin) disk, in which the flow is stabilized by advection of heat into the black hole (Abramowicz et al. 1988). Even ignoring such instabilities, thin disk models are inconsistent at accretion rates above 20%–30% of the Eddington rate, where the flow probably adopts a slim disk geometry and advection must be included. Slim disks are essentially the same as the geometrically thick disks discussed above, except that the radial and vertical structure can be modeled separately. In particular, one can still use vertically integrated equations to describe the radial variation of flow variables. At high, super‐Eddington accretion rates, this approximation must eventually break down, and the full two‐dimensional thick disk equations must be solved (see, e.g., Papaloizou & Szuszkiewicz 1994).

Slim disk models are probably more appropriate for bright AGNs than standard thin disks, but once again, very little work has been done on their predicted SED. Szuszkiewicz et al. (1996) have calculated emergent spectra of slim disks by assuming that each annulus emits as a modified blackbody. Such models therefore make no predictions of discrete features such as the Lyman edge. Within this approximation, slim disk spectra are identical to thin disk spectra at low accretion rates, but at high (super‐Eddington) accretion rates, the SED of a slim disk becomes redder in the extreme UV than that of a thin disk model with the same mass and accretion rate. The differences in the optical/UV SED predictions between the thin and slim disk models remain small, and slim disks still do not provide a satisfactory fit to the observations if the infrared bump is indeed due to thermal dust emission. Szuszkiewicz et al. (1996) propose that the optical/UV continuum may arise from reprocessing of radiation from the inner disk, which as noted above is one way out of this difficulty (see § 4). Slim disks do have an advantage over thin disks in that they can produce thermal soft X‐rays without being inconsistent, because Eddington or super‐Eddington accretion rates are required. Even here though the modified blackbody approximation produces a steeply falling soft X‐ray excess, which does not seem to explain the comparatively flat spectra of QSOs. Better atmosphere modeling may provide better agreement. Slim disks might be able to explain the steep soft X‐ray excesses observed in narrow line Seyfert 1 galaxies (Szuszkiewicz 1997).

Provided the accretion rate is not too high, it is possible for the surface density of the disk to be so low that Coulomb interactions alone are not sufficient to maintain thermal coupling between ions and electrons on the infall timescale. Assuming nothing else couples these particles together, then the thermal energy of the ions will not be radiated away and instead may simply be advected into the central black hole. If the gravitational energy released is channeled primarily into the ions, rather than into the electrons, then the ions can become very hot and produce a gas pressure–supported disk with a very low radiative efficiency (Ichimaru 1977; Rees et al. 1982). Such advection‐dominated accretion flows (ADAFs) have received considerable attention in recent years, thanks to the seminal work of Abramowicz et al. (1995) and Narayan & Yi (1995), who showed them to be thermally and viscously stable. The connection between the thin disk, slim disk, and two‐temperature ADAF solutions as a function of black hole mass, accretion rate, radius, and viscosity parameter has been discussed by Chen et al. (1995).

It is not clear yet whether the two requirements for an ADAF (low thermal coupling between the ions and electrons and predominately ion heating rather than electron heating) can truly be satisfied in a realistic flow. Begelman & Chiueh (1988) have identified unstable plasma modes that could significantly heat electrons in regions of the flow in which a high level of small‐scale magnetohydrodynamic turbulence is present. Such modes may destroy the two‐temperature structure of an ADAF, especially in AGNs, if collisionless shocks exist in the flow with sufficiently high filling factor (Narayan & Yi 1995). In addition, the magnetohydrodynamic turbulence that drives accretion primarily heats the electrons unless the magnetic field is significantly below equipartition strength (Quataert 1998; Gruzinov 1998; Quataert & Gruzinov 1998).

Two‐temperature ADAFs are by definition very inefficient and are therefore most applicable to low‐luminosity AGNs. The most successful application of the theory is perhaps to explaining the broadband emission from the Galactic center (Narayan, Yi, & Mahadevan 1995). ADAFs may also serve as useful models of X‐ray–emitting coronae in brighter AGNs.

Accretion disks may not be flat in shape. If the angular momentum of the flow is misaligned with the spin axis, then the disk will be warped in such a way as to allow the inner parts to lie in the equatorial plane of the hole (Bardeen & Petterson 1975). It may be that the radiation‐induced warping instability (Pringle 1997) could extend to the inner regions of accretion disks or that other warping modes exist there (see, e.g., Marković & Lamb 1998). Such warping would immediately produce less overall polarization in the direct emitted spectrum, owing to the breaking of plane‐parallel geometry (cf. the surface irregularities discussed by Coleman & Shields 1990). However, it would also open the possibility of scattering of optical/UV radiation by different parts of the disk, thereby producing different polarization signatures. In addition, if a warped disk intercepts and reprocesses radiation from the inner regions, the effective temperature distribution could flatten from the canonical T_eff∝r^-3/4 to r^-1/2, which would produce a long‐wavelength SED of F_ν∝ν^-1, much redder than the canonical ν^1/3 distribution, and perhaps more in line with observations. The theoretical problem of the spectral and polarization properties of the radiation emerging from a warped disk in an AGN remains to be explored.

The problems with accretion disk models have led some authors to propose optically thin emission as a possible explanation for the BBB. The simplest model is simply free‐free emission in an optically thin plasma (see, e.g., Barvainis 1993), possibly powered by reprocessing of X‐rays or by direct mechanical heating. Reprocessing of X‐rays into BBB photons by cool, optically thin clouds has been considered by many authors (Ferland & Rees 1988; Ferland, Korista, & Peterson 1990; Celotti, Fabian, & Rees 1992; Collin‐Souffrin et al. 1996; Kuncic, Celotti, & Rees 1997). Optically thin emission is of course also accompanied by substantial line and edge features, but just as in disks (see, e.g., Kriss 1994), Comptonization and relativistic smearing might help to reduce them in the observed SED.

The inner regions of accretion disks themselves may be very inhomogeneous and exist in a multiphase flow consisting of clouds in a hot, magnetized intercloud medium. Krolik (1998) has proposed that such an equilibrium would be both thermally and viscously stable, in contrast to the standard radiation pressure–supported thin disk with the usual α‐viscosity. Gammie (1998) has found that magnetized, radiation pressure supported disks are likely to suffer from a dynamical photon bubble instability, which might in fact lead to just such a multiphase equilibrium.

As we noted in § 4.1, the real problem facing accretion disk models may be in explaining the origin of the ionizing continuum. In addition to the usual disk and hot, Comptonizing corona, Magdziarz et al. (1998) have invoked a third phase to explain the EUV and soft X‐rays in NGC 5548: a warm (∼0.3 keV), optically thick Comptonizing medium (see Fig. 24). This component is reminiscent of models of the soft X‐ray excess that invoke thermal Comptonization in the inner regions of the accretion disk itself (Czerny & Elvis 1987; Maraschi & Molendi 1990; Ross et al. 1992; Shimura & Takahara 1993, 1995; Dörrer et al. 1996). Note that Zheng et al.'s (1997) interpretation of the EUV/soft X‐ray component in the HST composite was also based on Comptonization but in a hotter, more optically thin medium. The geometry of the three components is very unclear, however. A thermal Comptonization origin would be one way of getting rid of the Lyman edge in this Seyfert galaxy. In addition, it provides another interpretation of the fact that the optical/UV component becomes harder when brighter—here the disk component could be constant, while the soft excess component becomes brighter. Much more work needs to be done on theoretical models of such multiphase flows.

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We thank E. Agol, R. Antonucci, A. Frey, C.‐M. Hsu, I. Hubeny, A. Kinney, J. Krolik, J. Pringle, and G. Shields for useful discussions. We also thank E. Agol, I. Hubeny, A. Laor, K. Nandra, D. Reimers, M. Sincell, W. Welsh, and W. Zheng for supplying data and figures. E. Agol, S. Collin, A. Laor, M. Livio, G. Shields, and P. Stockman supplied comments that greatly improved the paper. This work was supported by NSF grant AST 95‐29230, NASA grant NAG5‐7075, and HST GO grants GO‐6109 and GO‐6705 provided by the Space Telescope Science Institute, which is operated by the Association of Universities for research in Astronomy Inc., under NASA contract NAS 5‐26555.