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In this section we summarize the observational and theoretical facts of accretion disks in AGNs and suggest a few directions for future work. Once again, we emphasize that we have concentrated on radio-quiet AGNs.

The optical/UV continuum slopes are redder than predicted by most luminous thin disk models whose spectra extend to the extreme ultraviolet. Bare accretion disks that produce substantial numbers of ionizing photons generally have optical/UV SEDs that are too blue.

The UV and X-ray composite spectra indicate that the BBB may not be as energetically dominant as thought previously. However, in both Seyfert galaxies and QSOs, there are individual objects that show a large range in BBB properties. Intrinsic reddening, geometry, etc. may also play an important role in modifying the BBB SED. Therefore, it is possible that the intrinsic BBB SED is very different from the observed BBB SED. There has not yet been a systematic study of a "complete" sample of AGNs over a wide wavelength range to determine the range of BBB properties.

Intrinsic Lyman edges that can be associated with accretion disks are rare in AGNs. More importantly, Lyman edges have never been seen in emission. Although the new accretion disk calculations demonstrate that the strength of the Lyman edge feature is not nearly as strong as thought in the earlier models, getting rid of the Lyman edge is difficult.

Both Seyfert galaxies and QSOs show very low optical polarization. QSOs also show low UV polarization (up to 1000 Å), and there seems to be no wavelength dependence in the polarization signature. The low polarization indicates that a simple geometrically thin, optically thick accretion disk with pure electron-scattering opacity is ruled out, unless magnetic fields are invoked to reduce the polarization through Faraday rotation. A handful of QSOs have shown a wavelength-dependent polarization shortward of the Lyman edge, but as yet there is no satisfactory theoretical model that explains these observations.

The spectropolarimetric observations provide information along a different sight line to the nucleus and hence provide clues to the geometry of this region. Obtaining high signal-to-noise ratio data is time-consuming, but when such data are obtained, they place strong constraints on the disk geometry, atmosphere, emission mechanism, and magnetic fields. Hence these observations are essential to understanding the accretion disks of AGNs.

Fe Kalpha emission lines with a range of properties have been observed in Seyfert galaxies, but no such observations exist for QSOs. Although the Fe Kalpha line indicates the presence of an accretion disk, a full multiwavelength theoretical interpretation has been undertaken for only one object.

X-rays are an important contributor to the bolometric luminosity of low-luminosity AGNs (Seyfert galaxies), and there are strong indications that at least some of the optical/UV arises from reprocessing of the X-rays, which in turn feed back through Compton scattering to produce the X-rays themselves. Variability campaigns such as the recent one on NGC 7469 indicate that this reprocessing is more complex than anticipated. Nevertheless, it is clear that X-rays play an energetically important role, and they will clearly modify the properties of the optical/UV emitting plasma. Sophisticated, self-consistent calculations of the atmosphere structure and optical/UV/X-ray radiative transfer through illuminated accretion disks need to be performed. Also, high time resolution variability monitoring campaigns that span a large wavelength region are once more essential to our understanding of the emission mechanism in AGNs.

Variability data also show that the optical/UV continuum slope is bluer when the object is brighter. Variations in the accretion rate of a cool bare disk can explain this, but they may also indicate a variation in the luminosity from a separate, EUV/soft X-ray-emitting phase of the flow.

The Einstein Cross provides a unique probe of the central emitting regions of this particular QSO. Monitoring of this source has already placed severe constraints on the size scale of the optical emitting regions, which may be problematic for accretion disk models. Multicolor photometric monitoring of this source should be continued in the optical and in fact in other wave bands to strengthen these constraints. Such observations complement variability campaigns in other sources in probing the geometry and size of the inner accretion flow.

Sophisticated atmosphere modeling is now being applied to the accretion disks of AGNs to improve on the naive blackbody assumption. However, once one leaves the blackbody prescription, then the vertical density and temperature structure must be specified. Unfortunately, this is likely to remain very uncertain for some time to come, until the viscous transport of angular momentum is better understood. Ultimately, radiative transfer calculations coupled with the results of magnetohydrodynamic simulations may be necessary to put the theory on somewhat firmer (i.e., based on first principles) ground. Even assuming the vertical structure can be calculated, atmosphere calculations need to be improved to include non-LTE effects, Compton scattering, and opacity from metals - particularly metal lines, in a self-consistent way. No models exist as yet which do this.

The assumptions of the standard thin accretion disk are inconsistent at high luminosities, and the sophisticated atmosphere models need to be applied to slim disks.

The dynamics and thermodynamics of magnetized, radiation-supported accretion flows need to be better understood. Is an accretion disk a good description of such flows, or are they broken up into a complex, multiphase medium?

The possibility of reprocessing of photons from the inner disk or corona by an outer warped, flared, or ruffled disk needs to be explored.

A better understanding of jet formation in AGNs can also contribute to an understanding of disks. The Galactic black hole sources (e.g., GRS 1915+105; Mirabel et al. 1998) are nearby objects that will be extremely useful to study in detail.

To really test accretion disk models requires high signal-to-noise ratio observational data that cover all the energetically important (X-ray, far-UV, and the UV/optical) wave bands. Only then can the Fe Kalpha emission line, the BBB region, and the Lyman limit region all be investigated simultaneously. Further, variability constraints indicate the need for simultaneous or near-simultaneous observations from the optical to hard X-ray bands. Monitoring campaigns to understand the nature of the correlations between the spectral wave bands are also essential.

Another important observational criterion must be the choice of targets. Given the various parameters that can influence the theoretical calculations, the sample needs to be carefully selected. The objects must have a reasonably clean line of sight so that observational difficulties can be minimized and high signal-to-noise ratio data can be effectively and efficiently obtained. Although AGNs are known to be similar across many orders in luminosity, there are/may be differences that could indicate subtle variations in the nature of the central power house, dependent on luminosity. Therefore, observations must include objects that span the the luminosity range of AGNs. Then accretion disk structure can be discussed as a function of luminosity. Currently, many observational facts are used to try and constrain accretion disk theory without regard to the fact that these constraints arise from AGNs with different luminosities.

The present generation of telescopes (HST, RXTE, ASCA) and the telescopes that will be flying in the next few years (FUSE, XMM) provide us with an opportunity to obtain high spectral resolution observations of the BBB in a complete sample of AGNs.

Theoretical models of the accretion flow are still primitive and ultimately must deal with at least four components: the dynamics and thermodynamics of a turbulent, magnetized flow; radiative transfer through that flow; Comptonization in both a hot corona and perhaps an intermediate phase to explain the EUV/soft X-ray ionizing continuum; and probably also high-energy emission from a jet or other outflow. There are observational indications that multiphase models and geometry are important, and these need to be explicitly considered in future theoretical models.

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.

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