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\begin{document}

\title{THE ULTRAVIOLET AND OPTICAL CONTINUUM EMISSION IN ACTIVE
GALACTIC NUCLEI:  THE STATUS OF ACCRETION DISKS}

\author{Anuradha Koratkar\\
\\
Space Telescope Science Institute\\
\\
3700 San Martin Drive\\
\\
Baltimore, MD 21218\\
\and
Omer Blaes\\
\\
Physics Department\\
\\
University of California\\
\\
Santa Barbara, CA 93106}
\pub{{\em January 1999 issue of} PASP {\em as an invited review}}
%\tobe{January 1999}{PASP}
\recacc{28 September 1998}{2 October 1998}
\url{1296}
\maketitle
\abstract{
A fundamental component of models of Active Galactic Nuclei (AGN) is an
accretion disk around a supermassive black hole.  However, the nature
of this accretion disk is not well understood and current models do not
provide a satisfactory explanation of the optical/UV continuum observed
in AGN. In this paper we review the substantial theoretical and
observational progress made in the field.  We also try to point out
future research directions which would be fruitful in trying to obtain
a complete, self-consistent model of the continuum emitting regions.}
\base

\section{INTRODUCTION}

Active Galactic Nuclei (AGN) are galaxies whose nuclei are highly
luminous, with spectra showing broad emission lines covering a wide
range of ionization.  AGN activity spans a broad range of luminosity,
from the brightest quasi-stellar objects (QSOs) to the more common but
less luminous Seyfert galaxies.  Two significant facts about AGN make
them very interesting to study.  The first is their ability to generate
extraordinary luminosities (up to 10$^{47}$ ergs~s$^{-1}$) in tiny
volumes ($\aplt2 \times 10^{14}$~cm, e.g., Edelson \ea
1996).  The second is the similarity in their spectral features over 
7~orders of magnitude in luminosity, across most of the electromagnetic
spectrum.  No other phenomena have these unusual properties.  The
similarity in spectral properties over many orders of luminosity
indicates that the central engine in AGN must have the ability to scale
with luminosity.  It is widely believed that accretion of gas into a
central supermassive black hole lies at the heart of the phenomenon
(e.g., Rees 1984).  The accretion flow is thought to be the source of
the X-ray, ultraviolet (UV) and optical continuum emission, which
ionizes circumnuclear gas in both the Broad Line Region and Narrow Line
Region, and may also be the launch site for winds and jets.  Well
outside the Broad Line Region lies a dusty torus (or perhaps a warped
disk) which obscures some lines of sight to the nucleus and accounts
for some of the observed diversity in the AGN phenomenon (Antonucci
1993).  Readers interested in a broad overview and introduction to the
field of AGN can find several good textbooks, including Peterson (1997)
and Krolik (1999).

The standard picture of the central engine of AGN now has limited
observational support. On the smallest scales from {\it Hubble Space
Telescope\/} ({\it HST\/}) imaging and spectroscopic observations, there is
evidence for the existence of massive compact objects at the centers of
galaxies (Kormendy \ea 1996a, 1996b, and 1997; van der Marel \ea 1997;
Ford \ea 1994; Harms \ea 1994; Macchetto \ea 1997; Bower \ea 1997; van
der Marel \& van den Bosch 1998; Richstone 1998; Magorrian \ea 1998).
Very broad Fe~K$\alpha$ lines observed by the {\it Advanced Satellite
for Cosmology and Astrophysics\/} ({\it ASCA\/}) indicates the presence of
gas moving in a relativistic potential well (Tanaka \ea 1995; Mushotzky
\ea 1995; Nandra \ea 1997a).  On parsec scales, {\it HST\/} imaging
observations (Walter \ea 1996; Ford 1998) and water mega-maser
observations of a handful of nearby AGN show a disk structure, possibly
the thick molecular torus (Nakai, Inoue \& Miyoshi 1993; Greenhill \ea
1995; Braatz, Wilson \& Henkel 1997).

Despite the fact that much of the large scale structure has now been
observationally verified, we still do not understand the central engine
itself.  The main difficulty in achieving this goal is that the central
accretion flow, which is responsible for the observed optical, UV, and
X-ray spectrum, is too small ($\sim10R_G=5\times10^{-5}$~pc for a
10$^8$ solar mass black hole, where $R_G=GM/c^2$ is the gravitational
radius of the black hole) to resolve at the distances of even the
nearest AGN.  (There is one interesting exception: the Einstein Cross,
which we discuss in section~3.6 below.) Therefore, we are forced to
rely on theoretical models, their predictions and comparison with
observations in order to make progress.

The theoretical accretion models are distinguished by the assumed flow
geometry, the state of the plasma within the flow, and the mechanism
whereby gravitational energy is converted into observed radiative and
kinetic power.  The simplest flow geometry is spherical, but such flows
are generally very inefficient radiators unless there is some internal
source of dissipation, e.g., shocks (M\'esz\'aros \& Ostriker 1983).
Observations on larger scales than the central accretion flow suggest
that spherical symmetry is probably broken, and that a well-defined
axis is present in the central engine.  These include the evidence for
large scale gaseous disks as discussed above,  as well the presence of
jets in both radio loud and radio quiet AGN (Livio 1997; Blundell \&
Beasley 1998).  The axis is generally believed to be associated with
the angular momentum of the accretion flow and the hole itself.  The
specific angular momentum of gas in the central regions of galaxies
generally greatly exceeds that of a particle in a circular orbit near
the black hole ($\sim R_G c$).  To have less than this critical value
of angular momentum, material one parsec away from a $10^8$~M$_\odot$
black hole would have to have non-radial velocity components less than
$\simeq 1$~km~s$^{-1}$.  Centrifugal forces on material of fixed
specific angular momentum vary with radius $r$ as $r^{-3}$, while
gravity varies as $r^{-2}$.  Therefore, unless angular momentum is
transported outwards on a dynamical time scale as material flows inward
from large scales down to the black hole, the flow must become
rotationally supported, and form an {\it accretion disk\/}.  As first
pointed out by Salpeter (1964) and Zeldovich \& Novikov (1964),
accretion disks can provide a high efficiency of matter-to-energy
conversion in a very small volume.  The outward transport of angular
momentum occurs slowly through poorly understood dissipative processes
(``viscosity''), thereby converting a significant fraction of
gravitational energy into heat, magnetic fields, and/or outflowing
kinetic energy.  It is this largely {\it theoretical\/} reasoning that
has made disks so ubiquitous as models of the central parts of the
accretion flow in AGN.

The most common assumption about the state of the plasma within the
disk is that it is optically thick and thermal.  This immediately
implies that a substantial fraction of the bolometric power should be
in the form of UV photons: a blackbody emitting at a significant
fraction of the Eddington luminosity on size scales associated with
supermassive black holes has a temperature in the UV range.  In fact, a
lot of power in AGN is emitted in the optical/UV region of the spectrum
(the Big Blue Bump), but the full spectral energy distribution (SED) is
rather more complicated than that.  As shown in figure~1, the overall
broadband AGN continuum is relatively flat in $\nu F_{\nu}$ and extends
over nearly seven orders of magnitude in frequency, implying that
approximately the same amount of energy is emitted  per decade of
frequency. For radio quiet AGN, this broad band spectrum can be divided
into three major components: the infrared bump, the big blue bump and
the X-ray region.
\begin{figure*}%1
\figurenum{1}
\centerline{\epsfysize=3in\epsfbox{p1296f1.eps}}
\caption{Schematic representation of the broadband continuum spectral
energy distribution seen in the different types of AGN.  The radio
quiet spectrum can be divided into three major components: the infrared
bump, which is thought to arise from reprocessing of the UV emission by
dust in a range of temperatures and at a range of distances; the Big
Blue Bump, which is directly related to the main energy production
mechanism and may be due to an accretion disk; and the X-ray region,
which can be interpreted as the high energy continuation of the Big
Blue Bump together with a Comptonized power-law with fluorescence and
reflection from ``cold'' material.}
\end{figure*}

The Big Blue Bump (BBB) continuum component in AGN extends from the
near-infrared at 1$\mu$m to past 1000~\AA\ in the UV and in some cases
apparently all the way to the soft X-ray region of the spectrum.  More
than half the bolometric luminosity of an unobscured AGN is typically
emitted within this spectral range, and thus its origin is directly
related to the main energy production mechanism.  The BBB is thought to
arise from an accretion disk, and is the spectral region that we will
mostly be discussing in this paper.  We discuss the observed properties
of the BBB extensively in section~3.

The broad infrared bump extends from $\sim100\mu$m to $\sim1\mu$m.
Quasars show a deep minimum at 1$\mu$m and have a sharp cutoff in the
submillimeter. In Seyferts, the 1$\mu$m minimum is rarely detected
because of galaxy starlight contamination (Neugebauer \ea 1987; Sanders
\ea 1989).  Prior to longer wavelength observations, it was thought
that the near infrared emission in radio quiet AGN could be due to
synchrotron emission, which could extend as a power-law to higher
photon energies underneath the BBB.  Today, however, the infrared bump
is generally thought to arise from reprocessing of the BBB emission by
dust with temperature in the range of 10-1800~K, and at a range of
distances from the central UV source (Barvainis 1987, 1990; Sanders,
Scoville, \& Soifer 1988; Phinney 1989).  The spectral trough at 1$\mu$m 
is then naturally interpreted as being due to the finite
sublimation temperature ($\sim 1800$~K) of dust.  Additional evidence
for the dust interpretation is the fact that the infrared hump shows no
rapid variability (e.g., Hunt \ea 1994), and that the long wavelength
turnover in the submillimeter is very steep (e.g., Hughes \ea 1993).
Observations of a handful of radio quiet AGN in the far infrared using
the {\it Infrared Space Observatory\/} show strong evidence for thermal
emission (Haas \ea 1998). In the radio loud AGN, the infrared emission
is a mixture of thermal and non-thermal radiation, but in most cases
one of the two components is dominant (Haas \ea 1998).

In the soft X-ray region, many objects show a ``soft X-ray excess"
which is emission that exceeds the extrapolation from the observed hard
X-ray power-law continuum (Turner \& Pounds 1989; Masnou \ea 1992).
This excess is subject to a number of observational difficulties, and
is probably the least well understood component of the AGN SED.  It may
be that it is the high energy continuation of the BBB, but this
interpretation is not straightforward.  We discuss the details in
section~3.1 below.  The characteristics of the soft X-ray excess in
both Seyfert galaxies and quasars are not well quantified.  Radio quiet
QSOs have a mean energy spectral index ($F_\nu\propto \nu^{\alpha_X}$)
of $\alpha_X=-1.72\pm0.09$ in the soft X-ray band (Laor \ea  1997),
while Seyfert~1 galaxies have $\alpha_X \sim -1.37$ (Turner et~al.\ 1993;
Walter \& Fink 1993).

In the hard X-ray band, the AGN spectrum consists of a power-law with
energy spectral index $\sim-0.9$.  This power-law is almost universally
believed to be due to Compton upscattering of optical/UV photons by hot
or nonthermal electrons somewhere in the central engine, possibly a
hot, magnetized corona above the disk.  Superposed on this power-law
are an Fe K$\alpha$ emission line at 6.4~keV and a Compton reflection
hump above 10~keV, at least in the case of some Seyfert galaxies
(Pounds \ea 1989; Nandra \& Pounds 1994).  These two features are
thought to be due to fluorescence and reflection from ``cold''
material, possibly the accretion disk itself in the case of Seyfert~1s.  
This is supported by the fact that the Fe K$\alpha$ emission line
is observed to be very broad (Tanaka \ea  1995).  Both the reflection
hump and the hard X-ray power-law extend up to high energies before
cutting off at around several hundred keV (Gondek \ea 1996).  The hard
X-ray properties of high luminosity AGN (QSOs) are not as well
understood, partly because they are relatively faint in the hard X-rays
given their optical/UV luminosity compared to Seyferts.  The Fe
K$\alpha$ line and reflection hump are relatively weak or non-existent
(Iwasawa \& Taniguchi 1993; Nandra \ea  1995; Nandra et~al.\  1997b).

It is the purpose of this paper to review the current status of the
observational and theoretical research effort to understand the central
accretion flow and its relation to the BBB.  We focus almost
exclusively on radio quiet AGN, whose emission is dominated by the
accretion flow.  Radio loud objects can also have substantial
contributions to their observed emission from jets and outflows, and we
refer the reader to the excellent review of Urry \& Padovani (1995) for
a discussion of their properties.  While we will mention the important
clues being provided by other regions of the electromagnetic spectrum,
particularly X-rays, we concentrate here on the optical/UV BBB.  We
begin section~2 of the paper by discussing the early, simple accretion
disk models which were first applied to the AGN problem.  These models
have proved to be very inadequate, and we discuss the main
observational problems in section~3.  We then turn to more recent
efforts to improve these models and how they fare against the
observations in section~4.  We discuss alternatives to the standard
accretion disk paradigm in section~5.  Finally, we summarize our main
conclusions in section~6, pointing out the main research directions,
both theoretical and observational, which we feel will lead to further
progress in our understanding of the primary power source of AGN.

\section{EARLY ACCRETION DISK MODELS}

Even if one assumes that angular momentum plays an important role in
the dynamics of the central accretion flow, the flow geometry is still
very uncertain.  The simplest assumption that one can make is that the
radial dynamics of the flow is dominated by gravitation and rotation,
with radiation pressure, gas pressure, and magnetic forces being
negligible by comparison.  The plasma in the disk then orbits the black
hole on nearly circular test particle (``Keplerian'') orbits, and the
flow takes the form of a geometrically {\it thin disk\/}.  The vertical
extent of this disk is determined by balancing the small (by
assumption!) internal pressure of the disk with the small vertical
component of gravity from the central black hole.  At large radii,
self-gravity can also become important.  The thin disk assumption
necessarily breaks down at high accretion luminosities approaching the
Eddington limit where radiation pressure becomes important.  In
addition it may not be a good assumption at very low accretion rates.
We will discuss these complications further in section~5 below.

The fundamental uncertainty which plagues all theoretical models of
accretion disks is the mechanism of outward angular momentum transfer,
which is responsible for the slow inward spiral of material which
converts gravitational potential energy into radiation and/or an
outflow.  There are two particularly promising mechanisms for angular
momentum transfer in disks, both of which involve magnetic fields.  The
first is a magnetohydrodynamic (MHD) outflow, where magnetic fields
supply torques to the disk and carry away angular momentum in the
outflow (Blandford \& Payne 1982).  The second is internal MHD
turbulence, as seen in simulations of the nonlinear development of the
Balbus-Hawley instability (Balbus \& Hawley 1991; Stone \ea 1996;
Balbus \& Hawley 1998).  Very few models of the radiation produced in
the accretion flow are based on these ideas, however, and generally
angular momentum transport is treated through a parameterized viscous
stress.  The most popular prescription is the $\alpha$-viscosity of
Shakura \& Sunyaev (1973), in which the radial/azimuthal component of
the viscous stress is taken to be a parameter $\alpha$ times the total
(gas plus radiation) pressure.  We will have very little to say here
about the detailed mechanisms whereby gravitational energy is converted
to radiative and kinetic power in AGN.  Nevertheless, until this is
understood, models and interpretation of observations will be severely
handicapped.

The basic theoretical models of stationary, geometrically thin disks
around black holes were developed by Shakura \& Sunyaev (1973) and
Novikov \& Thorne (1973) (see also Page \& Thorne 1974; Eardley \&
Lightman 1975; Riffert \& Herold 1995; and Abramowicz, Lanza, \&
Percival 1997 for important corrections and refinements to these
fundamental papers). From the point of view of predicting the observed
spectrum, such models are the most well-constrained of all the possible
accretion flows considered to date.  They make several key assumptions
about the flow.  In particular, the disk is stationary and
axisymmetric, and extends down to the innermost stable circular orbit,
where zero stress is assumed to be exerted on the disk.  Inside this
point material falls quickly into the hole and emits very little
radiation.  Angular momentum transport within the disk occurs by local
``viscous'' stresses which convert gravitational energy entirely into
heat.  Because the disk is thin, this heat is assumed to flow
vertically out of the disk, thereby being emitted at the same radius as
it was generated.  Under these assumptions, the radiative flux emerging
from each face of the disk at radius~$r$ is given by 
\begin{equation}
F(r)={3GM\dot{M}\over8\pi r^3}{\cal I}(r), 
\end{equation} 
where $M$ is the mass of the black hole, $\dot M$ is the mass accretion
rate, and ${\cal I}(r)$ is a correction factor which depends on the
mass and angular momentum of the hole, and which approaches unity at
large radii.  The local disk flux therefore depends only on the
properties of the black hole and the accretion rate.  At large radii,
$F(r)\propto r^{-3}$, implying that the effective temperature of the
disk surface varies as $T_{eff}\propto r^{-3/4}$.

The geometry of the thin disk allows one to calculate the overall
emergent spectrum from this {\it total\/} flux by dividing the disk into
concentric annuli, calculating the spectrum emitted by each annulus,
and then summing them all together.  The very simplest assumption is
that each annulus radiates like a blackbody.  The $r^{-3/4}$ effective
temperature distribution at large radii then gives a long wavelength
SED of $F_\nu\propto\nu^{1/3}$.  As we discuss in section 3.1 below,
this is much bluer than is typically observed in the optical/UV spectra
of AGN.

Blackbody emission is unlikely to be a good approximation to the
spectrum at each radius, even if the disk were optically thick, which
it may not be!  Careful modeling of the vertical structure and
radiative transfer through each annulus is necessary to calculate the
overall emitted spectrum.  In contrast to the radial structure, the
vertical structure of the disk is highly dependent on the assumed
mechanism of angular momentum transfer, including {\it its\/} vertical
dependence.  Vertical energy transport can proceed by bulk motions of
plasma and magnetic fields as well as by radiation through a supposedly
stationary medium.  Magnetic and turbulent stresses may well contribute
to the vertical pressure support.  The disk can be effectively
optically thin in the vertical direction, particularly in the innermost
regions if the viscosity is high.  Even in models where the disk is
optically thick and vertical energy transport occurs through radiation,
stellar atmosphere modeling is necessary.  In addition to atomic
opacity sources, including lines broadened by turbulence, electron
scattering (both Thomson and Compton) is crucial in determining both
the radiative transfer and the vertical disk structure.  High
temperatures and low densities mean that many atomic level populations
are strongly coupled to the radiation field, and non-LTE effects are
important.  Illumination of the disk photosphere by external sources of
X-ray radiation with significant power is also important, particularly
in Seyferts.  Relativistic effects must be included.  Gravitational
light bending will change the flux distribution above through
absorption and reprocessing (as will flaring or warping of the outer
disk).  Corrections must be made for the relativistic ``transfer
function'' (Cunningham 1975; Speith, Riffert, \& Ruder 1995; Agol
1997), i.e., the spectrum observed at infinity is altered by Doppler
shifts, aberration, gravitational redshifts, and light bending.
Radiation from disks around rapidly rotating Kerr holes can also be
focussed back onto the disk, modifying the emerging spectrum
(Cunningham 1976).  Given the enormous complexities and uncertainties,
it is essential that models pay close attention to, and be guided by,
observations.

A crude, first order modification to the blackbody assumption is to
take into account the fact that Thomson scattering opacity may dominate
absorption opacity in the innermost regions of the accretion flow.  The
spectrum at each annulus may then be crudely modeled as a modified
blackbody.  This flattens the SED and produces more high energy photons
(Shakura \& Sunyaev 1973).  This is an important effect in accretion
disks around stellar mass black holes, but whether or not it occurs in
AGN disks depends on the detailed vertical structure of the disk (see
section~4).

Shields (1978) proposed that the optical continuum in AGN could be due
to thermal emission from an accretion disk. He fit the SED of 3C~273 by
a nonthermal power-law which extended from the infrared to the X-rays
with an additional thermal component in the optical/UV. Thus, the BBB
was for the first time associated with thermal accretion disk
radiation. The nonthermal continuum prescription continued to be used
in later models (Malkan 1983; Sun \& Malkan 1989; Laor \& Netzer 1989;
Laor 1990) to account for the flat optical continua observed in AGN
spectra (see section~3.1).

Multi-wavelength observations of other AGN were first compared to
accretion disk models by Malkan (1983). In his comparisons, there were
three components: a non-thermal infrared to X-ray power-law spectrum, a
thermal accretion disk spectrum and a recombination spectrum. The
accretion disk models in this early work were just face-on disks where
the emergent flux was described by blackbodies. The models did account
for relativistic effects in the disk structure as well as the effects
of the relativistic transfer function.  The results of this work showed
that accretion was at super-Eddington rates in bright QSOs, where the
assumptions of these accretion disk models break down. This work also
discussed many observational tests for accretion disks. Sun \& Malkan
(1989) extended this work to include disk inclination angle effects and
fit many more sources.  However, the fits relied crucially on the
assumption of an underlying infrared power-law, and the emergent flux
was still approximated by blackbodies.

The earliest attempt at calculating the detailed overall spectrum of
optically thick, geometrically thin accretion disks using stellar
atmosphere models appropriate for AGN was by Kolykhalov \& Sunyaev
(1984).  They used the $\alpha$-viscosity prescription to calculate the
vertical structure of each annulus.  They then took existing stellar
atmosphere models from the libraries existing at that time (e.g.,
Kurucz 1979) with appropriate surface gravities and effective
temperatures, and then summed them together to generate overall
spectra.  The most interesting result of their calculations was the
existence of very large absorption edges at the hydrogen Lyman 
limit---edges which existed even when the smearing effects of the 
relativistic transfer function were included.  As we discuss in 
section~3.2 below, such edges are not observed, and they noted this 
discrepancy at the time.  This problem motivated much of the later 
theoretical and observational work on the Lyman edge region of AGN 
spectra.  But as we discuss in section~4, these early calculations 
suffered from severe limitations.

Because electron scattering opacity is important in the disk atmosphere
at the expected temperatures and densities, the radiation emerging from
the disk can be substantially polarized.  Most of the early work
assumed that the polarization would be similar to that emerging from an
optically thick, pure electron scattering atmosphere.  In this case the
polarization is perpendicular to the disk axis and has a strong aspect
angle dependence, varying from 0\% for a face-on disk (because of
symmetry) to $11.7$\% for an edge-on disk (Chandrasekhar 1960; Rees
1975; Lightman \& Shapiro 1975).  Pioneering work in the 1980s showed
that optical polarization in AGN is generally much lower ($\aplt
1$\%) than predicted by these simple models.  Often no
polarization is detected, and the polarizations are {\it parallel\/} to
the nuclear axes, when the latter can be inferred from a radio jet
position angle (Stockman, Angel \& Miley 1979; Antonucci 1988).

\section{OBSERVATIONS}

\subsection{The Big Blue Bump}

To understand the nature of the BBB we first need to determine its SED
and thus determine its strength compared to the AGN 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 AGN 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 which 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 which
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
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 {\it a composite
spectrum really has no physical meaning\/}, and models must be fit to
spectra of individual sources.

\subsection*{3.1.1. The Optical to UV region}

The median optical to UV continuum slope in radio quiet QSOs is
$\alpha\simeq-0.32$ ($F_{\nu} \propto \nu^{\alpha}$ (Francis \ea
1991).  The slope was determined in the 1300--5500~\AA\ region after
the Balmer continuum and the Fe~II line emission were accounted for in
the continuum fitting process. Using {\it International Ultraviolet
Explorer\/} ({\it IUE\/}) data, O'Brien, Gondhalekar \& Wilson (1988) found
that the rest frame UV slope (1200--1900~\AA) is slightly steeper
than the optical and that higher luminosity objects have flatter slopes
than lower luminosity objects.  The rest frame UV slope (1050--2200~\AA) 
from {\it HST\/} data is $-$0.99 (Zheng \ea 1997). It must be
noted here that there is substantial scatter in the slopes of the
individual objects, yet the optical/UV continuum is redder than
the long wavelength prediction of stationary accretion disk models.

\subsection*{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 \ea 1994; Walter \ea
1994).

The two recent {\it HST\/} and {\it Roentgen Satellite\/} ({\it ROSAT\/})
investigations by Zheng \ea  (1997) and Laor \ea (1997) respectively
allow us to observationally investigate the ``observed'' shape of the
BBB in the 13.6~eV--1~keV region of the continuum.  The UV composite
spectrum of Zheng \ea was compiled using {\it HST Faint Object
Spectrograph\/} ({\it FOS\/}) observations.  This sample contained quasars
with mean redshifts $\sim1$, which allowed determination of the UV
composite spectrum in the rest wavelength range $\sim300$~\AA--3000~\AA\ 
(see Figure~2). The individual spectra in the composite have
been corrected for Galactic reddening and intergalactic absorption.
The UV composite spectrum of AGN does not appear to rise to shorter
wavelengths, but seems to roll over shortward of 1000~\AA.  Laor \ea
(1997) produced a composite soft X-ray spectrum of a complete sample of
low redshift quasars using {\it ROSAT Position Sensitive Proportional
Counter\/} ({\it PSPC\/}) observations.  The soft X-ray data seem to be
just an extension of the UV composite spectrum (see Figure~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~\AA--800~\AA), but rather in the far UV region 
(900~\AA--1100~\AA).
\begin{figure*}[tp]%2
\figurenum{2}
\centerline{\psfig{figure=p1296f2.eps,width=5in,angle=-90}}
\caption{The UV composite spectrum compiled using {\it HST/FOS\/}
observations. The individual spectra in the
composite have been corrected for Galactic reddening and intergalactic
absorption.  Note that the composite spectrum does not appear to rise
to shorter wavelengths, but seems to roll over shortward of 1000~\AA.
The 1050--2200~\AA\ region can be fit by a power-law continuum
$F_{\nu} \propto \nu^{-0.99}$. Shortward of 1000~\AA, the spectrum in
$F_{\nu}$ is close to $\nu^{-2}$ and seems to allow a smooth  extension
into the soft X-rays. (Courtesy W.~Zheng.)}
\end{figure*}
\begin{figure*}[tp]%3
\figurenum{3}
\centerline{\psfig{figure=p1296f3.ps,height=3in}}
\caption{Composite ``observed'' optical--soft X-ray spectrum for
AGN.  The composite UV spectra for radio loud (RL) and radio quiet (RQ)
objects are plotted as a thin solid line. The thick solid lines
represent the optical and soft X-ray composite spectra. The dotted line
is the spectral shape predicted by Mathews and Ferland (1987), while
the dashed line shows a simple power-law model ({\it not\/} an accretion
disk) with a thermal cutoff corresponding to $T=5.4\times10^5$~K.  The
data suggest that the far-UV power-law extends into the soft X-ray
regime.  The 0.2--2.0~keV spectral slope is much flatter than
predicted by the simplest thin accretion disk models, which have
exponential cutoffs in this waveband.  (Courtesy A.~Laor.)}
\end{figure*}

\subsection*{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.

\begin{itemize}

\item{{\it 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 accurately determine the shape of the BBB. In low redshift
AGN 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.
{\it HST\/} imaging observations of Seyfert galaxies show that nuclear
star formation is often occurring well within 0.5--1.0$^{\prime\prime}$
of the nucleus. Depending on the dominance of these star forming
regions, they can contribute substantially towards the optical/UV light
that is seen in most ground-based apertures. A comparison of
contemporaneous {\it HST\/} and ground-based spectroscopy of NGC~7469
clearly shows this problem (see Figures~4 and~5). In this particular
object, $\sim70$\% of the starlight falls within 0.1$^{\prime\prime}$
of the nucleus! For ground based observations, this problem is
exacerbated due to effects of seeing. Although nuclear starbursts are
likely to be present in the host galaxies of high luminosity AGN
(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.}
\begin{figure}[tp]%4
\figurenum{4}
\centerline{\psfig{figure=p1296f4.eps,width=3in}}
\caption{The {\it HST Wide Field Planetary Camera 2\/} image of the nuclear
region of NGC~7469.
The 3$^{\prime\prime}$ diameter starburst ring is clearly visible. The
nucleus of the galaxy is saturated in this image. Note that in a ground
based slit spectrum, depending on the slit (usually 1$^{\prime\prime}$
in width) orientation, the ring contaminates the spectrum. Further,
such rings would also have contaminated the UV spectra obtained by {\it
IUE\/} whose aperture was $10^{\prime\prime}\times20^{\prime\prime}$. The
square represents the 0.86$^{\prime\prime}$ square FOS aperture.
(Courtesy W.~Welsh.)}
\end{figure}
\begin{figure}[tp]%5
\figurenum{5}
\centerline{\psfig{figure=p1296f5.ps,width=3in,angle=-90}}
\caption{A comparison of the contemporaneous {\it HST/FOS\/} (lower
curve) and ground-based spectroscopy of NGC 7469. The {\it HST/FOS\/}
spectrum is through a 0.86\arcsec\/ square aperture while the
ground-based spectroscopy is mostly through a 10\arcsec $\times$
16.8\arcsec\ slit (similar in size to the {\it IUE\/} large aperture
data). The estimated host galaxy contamination is $\sim18$\% at
5400~\AA\ which we see in the figure is highly underestimated.  The
gross difference between the {\it HST/FOS\/} and ground-based fluxes is
due to the host galaxy and starburst ring contribution in the
ground-based spectrum. This figure highlights the value of high spatial
resolution spectroscopy. (courtesy Welsh.)} 
\end{figure}

\item{{\it 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 AGN 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 $z$ AGN 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 multi-wavelength spectra needs to be
undertaken, especially now that we have mounting evidence for dust in
the nuclei of AGN (Malkan \ea 1998).

The UV composite spectrum generated by Zheng \ea (1997) has a spectral
break at 1000~\AA. 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
$\sim700$--800~\AA\ and drops sharply at shorter wavelengths. If the far
UV spectral slope change in the Zheng \ea spectrum was due to dust,
then below 700~\AA\ the composite spectrum should have ``recovered'' by
400\AA. Such a change in continuum slope is not seen, indicating
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$_H <$ 10$^{16}$
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~\AA, but will just change the slope of the spectrum dramatically 
at this short wavelengths. In fact, because of the composite 
nature of the spectrum, it may be possible that the spectral break is
prominent due to incorrect reddening corrections in each of the
individual spectra which 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~\AA, so close to the Lyman limit, is tantalizingly suggestive of
an intrinsic emission mechanism as the cause. }

\item{{\it Extreme UV energy distribution:}
As mentioned earlier, to understand the primary emission mechanism in
AGN, 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 AGN.  At wavelengths $<800$~\AA\ only a few objects are
contributing towards the UV composite of Zheng \ea (1997).  There are
very few observations of AGN in this region which 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.,  HS1700+6416, HS1103+6416 and HE 2347$-$4342 from Reimers \ea
1998; PG~1211+14, Zheng \ea in prep.) Figure~6 shows the Far-UV and EUV
SED in luminous AGN. The variety of the EUV SEDs indicate that
describing the BBB with simple models will not be possible and that the
task is much more complex, and the SED at these short wavelengths needs
to be quantified better.}
\begin{figure}[tp]%6
\figurenum{6}
\centerline{\psfig{figure=p1296f6.ps,width=3in}}
\caption{The spectral energy distributions for four high redshift QSOs
detected in the Hamburg quasar survey. The spectra are shown in the
rest frame of the quasar. The UV continua derived for the
dereddened spectra have been corrected for HI continuum absorption of
the Lyman Limit systems. An additional correction for the cumulative HI
continuum absorption of Ly$\alpha$ clouds with log N(HI) $\leq16$
cm$^{-2}$ is indicated by the dotted lines. We see that each of these
AGN show dramatically different EUV distributions. (Courtesy D.~Reimers)}
\end{figure}

\item{{\it Soft X-ray issues:}
The soft X-ray excess component in AGN 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--$\sim1$~keV), including the
underlying X-ray power-law and the ``warm absorber'' (absorption in the
0.5--1.5~keV dominated by O~VII and O~VIII K~shell absorption edges
in material with N$_H\sim10^{22}$ cm$^{-2}$).  All these spectral
components complicate the theoretical interpretation of this region. A
detailed analysis of {\it ASCA\/} data by George \ea (1998) challenges
the presence of the soft X-ray excess in some objects, and recent {\it
BeppoSAX\/} data fail to show a soft X-ray excess in many sources where
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 AGN has lead to some extent to more observational
uncertainty.

To add to the modeling difficulties, simultaneous data obtained with
{\it ASCA\/} and {\it ROSAT\/} showed different slopes in the 0.2--1~keV
bands.  The soft X-ray slopes observed by Laor \ea (1997) need to be
verified, because there have been observational issues concerning the
accuracy of the {\it ROSAT PSPC\/} calibration matrix, especially at low
flux levels (which is obviously the case for X-ray observations of
AGN).  However, the H~I columns determined by Laor \ea agree remarkably
well with the accurate 21cm H~I columns, suggesting that the {\it ROSAT
PSPC\/} calibration matrix may be quiet reliable.

It is difficult to compare the {\it ROSAT\/} and {\it ASCA\/}
observatories.  {\it ASCA\/} cannot observe the soft X-rays ($\aplt
0.6$~keV), has a broad waveband (0.4--10~keV) and high
energy resolution, while the {\it ROSAT PSPC\/} observed soft
energies (0.1~keV) but did not have a broad waveband 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
waveband.}

\item 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.

\end{itemize}

\subsection{Lyman Edges}

AGN accretion disks are thought to include thermally radiating regions
with temperatures in the range 30,000~K--300,000~K. A fundamental
signature of thermal gas is that the emitted spectrum should show
spectral features which 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~\AA).  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 section~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 AGN has now been investigated at high
(Antonucci \ea 1989), intermediate (Koratkar \ea 1992), and low (Kriss
\ea 1996; Kriss \ea 1997; Zheng \ea 1995) redshifts. Figure~7 shows the
variety of continuum distributions seen in the Lyman limit region.  Of
the 73~AGN investigated in these studies, only 8 candidate objects were
found which might have an intrinsic Lyman edge which maybe associated
with an accretion disk.  In these candidate ``partial'' Lyman edge
objects, there is {\it no sharp discontinuity\/} in the continuum at the
Lyman limit, but usually just a change in continuum slope on either
side of 912~\AA\ (see Figure~7).  In objects where 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 \ea 1993 and Tytler \ea 1993) seemingly contradictory
results concerning the statistics of Lyman edges in {\it 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 {\it rare\/} in AGN, and more
importantly there has been {\it no\/} reported case of a Lyman edge
feature {\it in emission\/}.
\begin{figure}[tp]%7
\figurenum{7}
\centerline{\psfig{figure=p1296f7.eps,width=3in}}
\caption{The spectral energy distribution in the Lyman limit region.
The spectrum of PG~1630+377 (top panel) is an example with a possible
intrinsic Lyman edge. The Lyman limit in this object shows no sharp
discontinuity like that seen in PG~0117+213 (bottom panel), but a
change in slope on either side of the Lyman limit. The spectrum of
0743--673 (middle panel) is an example where we see no Lyman edge. The
spectrum of PG~0117+213 (bottom panel) shows sharp Lyman edges at
$\sim850$~\AA\ and $\sim750$~\AA\ due to intervening absorbing
material. The location of the intrinsic Lyman limit is indicated by 
the arrows in each panel.}
\end{figure}

On a statistical basis, one could use the UV composite spectrum (Zheng
\ea 1997) to determine the nature of the Lyman edge.  In this spectrum
the edge is seen only as a 10\% effect (see Figure~8).  This may be
indicating that many AGN 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.
\begin{figure}[tp]%8
\figurenum{8}
\centerline{\psfig{figure=p1296f8.eps,width=3in,angle=-90}}
\caption{The spectral energy distribution in the Lyman limit region for
the UV composite generated from {\it HST/FOS\/} data. The dotted line
represents the continuum fit using the entire {\it HST\/} composite. The
$\chi^2$ for each bin relative to the continuum fit are shown in the
bottom panel. The $\sim10$\% trough seen shortward of the Lyman limit
may be indicating that many AGN have a very weak Lyman edge feature.
But given the observational caveats discussed in section~3.1, the
presence of this feature cannot be used effectively to quantify the
nature of the spectral feature at the Lyman limit. (Courtesy W.~Zheng.)}
\end{figure}

To investigate the Lyman edge in AGN, 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 observations over a wavelength
range $\sim450$~\AA\ to $\sim1200$~\AA\ 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 {\it
HST/FOS\/} spectroscopy in the $\sim300$~\AA--$\sim1000$~\AA\
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 HI
continuum absorption of Ly$\alpha$ clouds with low column densities.
Once again, if we use the Zheng et~al.\ UV composite, the Lyman edge
feature is quite narrow ($\sim5$\%), and is thus not likely to be from
a disk.  With the {\it Far-Ultraviolet Spectroscopic Explorer\/} ({\it
FUSE\/}) coming on-line, we will have opportunity to investigate the
$\sim450$~\AA\ to $\sim1200$~\AA\ region in the AGN rest-frame for a
larger sample of objects.

\subsection{Polarization}

In simple geometrically thin, optically thick accretion disk models,
the atmospheric opacities may be dominated by electron scattering
opacity.  Also, as we discuss in section~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 AGN can also be used as a diagnostic of accretion disk
characteristics.

As we noted above at the end of section~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 \ea 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 \ea (1990) and Antonucci \ea (1996)
confirm the earlier results; i.e.,  {\it unobscured AGN show low optical
polarization with no statistically significant wavelength dependence\/}.

In the unified scheme for AGN, 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 section 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--60\deg.  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\deg, 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 {\it magnitude\/} of
polarization that is observed in AGN, the polarization angle is
observed to be {\it 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 AGN by determining the radio jet axis. We
now have the ability to resolve the central radio source in radio quiet
AGN, and it will certainly be interesting to check the alignment of the
polarization angle in these objects.
\begin{figure}[tp]%9
\figurenum{9} 
\centerline{\epsfxsize=3in\epsfbox{p1296f9.ps}}
\caption{Observed optical polarization of PG QSOs compared to
predictions (short dashed line) for optically thick, pure
electron-scattering slabs with viewing angles in the range of 0--60\deg 
inclination angles.  The comparison shows that the theoretical
predictions are inconsistent with the data, i.e., calculations predict
more objects with higher polarization than are observed.  The
polarization data are based on the figure by Berriman \ea  1990.
The long dashed line represents the the polarization distribution given
the observational errors.  The dotted line represents the distribution
for interstellar polarization only. (courtesy E.~Agol)} 
\end{figure}

{\it HST/FOS\/} spectropolarimetry allowed us to probe the $\sim700$~\AA\
to $\sim1300$~\AA\ region of 10 intermediate redshift quasars (Koratkar
\ea 1995; Impey \ea 1995; Koratkar \ea 1998).  Using ground-based
spectropolarimetry, Antonucci \ea (1996) have observed 3 high redshift
AGN shortward of the Lyman limit and 20 intermediate redshift AGN in
the $\sim1100$~\AA\ to $\sim3000$~\AA\ 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 continues to
remain low ($\aplt1.5$\%) even in the UV (up to
$\sim1000$~\AA).  Further there is no statistical wavelength dependence
to the polarization for wavelengths $>1000$~\AA.  Investigations
shortward of the Lyman limit region found that some radio quiet AGN are
polarized in this region, and the polarization has some wavelength
dependence (see Figure~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 {\it shortward of the Lyman edge and no polarization
longward of the Lyman edge\/}.  In one case, PG~1630+377, the
polarization is $\sim20$\%!  The other 70\% of the sample showed no
significant polarization (see Figure~11).  The 95\% confidence level
upper limits on linear polarization shortward of the Lyman limit for
these objects is $\aplt4$\%.  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.
\begin{figure}[tp]%10
\figurenum{10}
\centerline{\epsfxsize=3.0in\epsfbox{p1296f10.eps}}
\caption{{\it HST/FOS\/} spectropolarimetry of PG~1630+377 in the Lyman
limit region. The normalized Stokes parameters $Q/I$ and $U/I$ are
shown in the top two panels. The bottom panel shows the total flux
($F_{\lambda}$) in units of 10$^{-15}$ erg s$^{-1}$cm$^{-2}$
\AA$^{-1}$. Such a high degree of polarization is rare in radio quiet
AGN. Approximately 30\% of the objects investigated in the Lyman limit
region show a rise in polarization shortward of the Lyman edge.}
\end{figure}
\begin{figure}[tp]%11
\figurenum{11}
\centerline{\epsfxsize=3in\epsfbox{p1296f11.eps}}
\caption{{\it HST/FOS\/} spectropolarimetry of PG~0743$-$673 in the Lyman
limit region. The normalized Stokes parameters Q/I and U/I are shown in
the top two panels. The bottom panel shows the total flux
(F$_{\lambda}$) in units of 10$^{-15}$ erg s$^{-1}$cm$^{-2}$
\AA$^{-1}$. Approximately 70\% of the sample observed in the Lyman
limit showed no significant polarization.} 
\end{figure}

\subsection{ Fe K$\alpha$ Emission Line and the Lyman Edge}

The Fe~K$\alpha$ emission line, interpreted as arising from
fluorescence in the X-ray illuminated disk, is extremely broad and
redshifted, providing dramatic support for an accretion disk in a
relativistic potential well (Tanaka \ea 1995).  It is perhaps the best
evidence for accretion disks in the innermost regions of AGN central
engines. 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 section~3.2) around the Lyman limit for an AGN
which also shows a broad Fe~K$\alpha$ line.  The best data come from
the {\it Hopkins Ultraviolet Telescope\/} ({\it HUT\/}) on low redshift
Seyferts (Kriss \ea 1997), and {\it ASCA\/} observations of these
Seyferts.  There are only six Seyferts that have both Lyman edge and 
Fe~K$\alpha$ line observations.  Except for maybe one object (NGC~3516),
none of the remaining five objects show 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 {\it HUT\/}
data to search for the smeared edge features expected from a
relativistic disk.

Observations of the Fe~K$\alpha$ emission line and the Lyman limit
region can be used to constrain the theoretical accretion disk models.
The Fe~K$\alpha$ 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 Figure~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 Figures~12 and~13).  The current Fe~K$\alpha$
emission line profiles exclude edge-on disks whose Lyman edges are
easier to hide due to large relativistic smearing.  The disk
inclination angles derived from the Fe~K$\alpha$ 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.

The Lyman edge problem indicates that to understand the emission
mechanism in AGN, multi-wavelength data are essential to constrain the
models.  With {\it FUSE\/} coming on-line, in addition to high energy
resolution X-ray telescopes such as the {\it X-ray Multi-Mirror
Observatory\/} ({\it XMM\/}), there will soon be an opportunity to
investigate the Fe~K$\alpha$ emission line and the Lyman edge
simultaneously.
\begin{figure}[tp]%12
\figurenum{12}
\centerline{\epsfxsize=3in\epsfbox{p1296f12.ps}}
\caption{Fe~K$\alpha$ line profiles for accretion disks around a
Schwarzschild black hole at different inclination angles $i$
($\mu\equiv\cos i$).  The line is assumed to be emitted locally as
nearly a delta function in energy at 6.4~keV, and a line emissivity
profile $f(r)$ which falls off as $1/r$ with radius $r$ has been
assumed, extending from the innermost stable orbit to 14.8~$R_G$.
Lines are broader for edge-on disks than for face-on disks.  This
figure should be compared with figures~13 and~19, which show
predictions for Lyman edges at similar inclination angles.}
\end{figure}
\begin{figure}[tp]%13
\figurenum{13} 
\centerline{\epsfxsize=3in\epsfbox{p1296f13.ps}}
\caption{The predicted spectral energy distribution in the Lyman limit
region for accretion disks around a Schwarzschild black hole at
different inclination angles $i$ ($\mu\equiv\cos i$).  Spectral
features are much more visible for face-on disks ($cos i = 0.98$) than
for edge on disks.  Here the accretion disk is considered to be made of
pure Hydrogen and Helium.  Non-LTE effects and relativistics transfer
function have been fully incorporated.  External illumination of the
disk by X-rays has been neglected, which may increase the prominence of
the Lyman edges (cf.\ figure~19).} 
\end{figure}

\subsection{Variability}

The extraordinary luminosities of AGN are observed to vary.
Variability studies provide crucial data concerning the time scales 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 AGN because variability
time scales allow us to probe the nuclear regions ($< 10^{14}$ to
$10^{18}$~cm). If characteristic time scales are found, these would
allow us to investigate the physical mechanisms that drive the
fluctuations. By comparing multi-waveband light curves, the nature of
propagation of a signal can be investigated.


\subsection*{3.5.1. Variability Time Scales}

Variability time scales range from hours to years depending on the
luminosity of the AGN and the observed wavelength range. The most
commonly observed X-ray variations in Seyfert galaxies are $\sim$few
hours (Green, MacHardy \& Lehto 1993; Nandra \ea 1997c).  The shortest
time scale variation in the optical/UV observed so far is $\sim2$ days
for NGC~4151 (Crenshaw \ea 1996). Although ultra-rapid variations are
seen in the X-rays, there is as yet no detection of ultra-rapid
variability (i.e., variations on time scales of hours) in the optical
and UV (Welsh \ea 1998).  On the average, the optical/UV continuum in
Seyfert galaxies and lower luminosity quasars varies over times scales
of weeks to months (Kaspi \ea 1996; Givon \ea 1998).  The monitoring
campaigns so far have found no convincing evidence for any
characteristic time scales or periodicities (see e.g., Netzer \&
Peterson 1997; Ulrich, Maraschi \& Urry, 1996; Mushotzky, Done \&
Pounds 1993 for excellent reviews).

\subsection*{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 Figure~14). The shortest
wavelengths vary the fastest (Clavel \ea 1992; Edelson \ea 1996;
Peterson 1993; Nandra \ea 1998;).  In the X-rays, the power-law
component often varies with no spectral variation (Ulrich \ea 1996;
Nandra \ea  1998), but sometimes the spectrum does change, becoming
softer as the object brightens (e.g., 3C~390.3, Leighly \ea 1997; 
NGC~5548, Magdziarz \ea 1998).  Increased Compton cooling of the X-ray
emitting plasma, possibly because of a change in the disk geometry
producing more UV photons (cf.\ Magdziarz \ea 1998, see section~5
below) may be an explanation for this.  We discuss the implications of
spectral variations further in section~4 below.
\begin{figure*}[tp]%14
\figurenum{14}
\centerline{\psfig{figure=p1296f14.ps,width=6in,angle=-90}}
\caption{{\it HST/FOS\/} observations of NGC~3516. The observations were 
obtained over a period of a year and show a factor $\sim5$ variation 
at 1360~\AA, and a factor of $\sim2$ variation at 2200~\AA. This type 
of variation, where the shortest wavelengths vary more than the longer
wavelengths, is typical of AGN. Thus the optical/UV continuum hardens
as the nucleus brightens.}
\end{figure*}
 
\subsection*{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 which have different
overall size scales.  Variability in the continuum might therefore have
wavelength dependent time scales and amplitudes, and one might also
expect time lags due 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 Seyferts and QSOs
are highly correlated and imply signal propagations on faster time
scales than the viscous or even sound-crossing times in the flow
(Alloin \ea 1985; Cutri \ea 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 \ea 1991, Collin-Souffrin 1991).  This is confirmed
by simultaneous, multiwavelength monitoring campaigns of the Seyferts
NGC~4151 and NGC~5548, which show correlated variability between
optical/UV and X-ray energies (Edelson \ea 1996; Clavel \ea
1992).

NGC~7469 has been intensively monitored for the longest duration so
far, and this campaign allowed time lags between the different
continuum wavebands to be measured for the first time.  In this source,
optical/UV continuum variability is highly correlated and shows a
monotonically increasing time lag $\tau$ with wavelength $\lambda$
which can be fit with $\tau\propto\lambda^{4/3}$, the prediction for a
$T_{eff}\propto r^{-3/4}$ accretion disk (Wanders \ea 1997; Collier \ea
1998).  The time delays ranged from $\simeq0.2$ to 2~days, and their
statistical significance is difficult to determine.  A conservative
analysis by Peterson \ea  (1998) finds them to be marginally
significant ($>2.2\sigma$).  Peterson \ea  (1998) also showed that if
the results for NGC~7469 are real, and we scale all the other AGN 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 {\it
not\/} correlated on such short time scales (Nandra \ea 1998).  However,
one can interpret the data in terms of an {\it anticorrelation\/} between
the X-rays and UV, with the X-rays leading the UV by four days.
Alternatively, the UV correlates with the X-rays, with the UV leading
by four 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 Figure~15).  The X-rays
also show short time scale variability (50~percent in one 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 time scale 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
\ea (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 four light 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.
\begin{figure*}[tp]%15
\figurenum{15}
\centerline{\epsfxsize=4in\epsfbox{p1296f15.eps}}
\caption{The X-ray and UV variability for NGC~7469.
The UV variations are leading the X-rays near the peak fluxes, while 
they both achieve approximate simultaneity near the minimum flux levels.  
The X-rays also show short time scale variability (50~percent in one day) 
which is not observed in the UV. These observations indicate that there 
is complex interaction between the UV and X-ray emitting regions, and 
it is not clear how to reconcile the UV/X-ray variations with a flow 
geometry. (Courtesy K.~Nandra)}
\end{figure*}

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 which were {\it
not\/} present in the continuum, suggesting 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.

\subsection{Microlensing}

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 {\it XMM\/} and
{\it 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 which make up the ``Einstein Cross''
(Huchra \ea 1985).  Because of the large surface density of stars in
the galaxy's central region, microlensing is observed in the images
(Irwin \ea 1989; Pettersen 1990; Corrigan \ea 1991; Racine 1991; Nadeau
\ea 1991; Racine 1992; {\O}stensen \ea  1996).  The size of
microlensing variations imply 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 $\sim10^{17}M^{1/2}$~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 \ea 1989)
constrains the size of the optical emission region to be
$\lta2\times10^{15}$~cm (Wambsganss, Schneider \& Paczy\'nski 1990).
This is far below any length scale which 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 Jaroszy\'nski, Wambsganss, \& Paczy\'nski (1992) found that
accretion disks were consistent with the microlensing constraint.  Part
of the difference between these two papers was that Jaroszy\'nski et
al. considered accretion disks around Kerr holes, whereas Rauch \&
Blandford only considered 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 towards 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 which are too blue
compared to observations.  To get round 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 AGN, but of course leads to larger optically emitting regions than
the standard disk.  Jaroszy\'nski \ea, on the other hand, kept the
standard radial emissivity, and assumed instead that there was another
source of red light in the source which arises from further out and is
not microlensed.  Both approaches are {\it 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, Jaroszy\'nski \& 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
section~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.

\subsection{Double-Peaked Line Profiles}

Broad emission lines are characteristic of AGN spectra. 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 (e.g., Marsh \& Horne 1988).
Yet, only a fraction of radio loud AGN, and a handful of radio quiet
AGN show such lines (Eracleous \& Halpern 1994; Storchi-Bergmann \ea
1997).  This has been raised as a problem for accretion disk models of
AGN (Kinney 1994). However, it is also worth noting that Livio \& Xu
(1997) have shown that the double-peaked line cannot be produced by
two line emitting jets, thus leaving the accretion disk as the only
viable site for the production of such a line.

In accretion disk models the optical/UV continuum is generated from
disks whose extent is 10$R_g$--1000$R_g$.  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 towards the
emission line spectrum, but the emission lines were from the outer
parts of the disk at $\sim1000R_g$ and broad emission lines were not
observed from the inner parts of the disk (Dumont \& Collin-Souffrin
1990a, 1990b). Models by Chen \ea (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
which predominantly contributes 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~K$\alpha$ line observed by {\it ASCA\/} in many
Seyferts does occasionally have a double-peaked shape (e.g., Tanaka \ea
1995). We have discussed the Fe~K$\alpha$ line in section~3.4
since this line is expected to arise within 100$R_g$.

\section{MORE RECENT ACCRETION DISK MODELS}

\subsection{The Big Blue Bump}

Since the SED predicted by luminous accretion disks is generally bluer
than the optical spectra observed in AGN, traditionally theoretical
fits to the data included an additional infrared power-law component
which changed the optical slope that the accretion disk model had to
fit.  But, with mounting evidence that thermal dust emission produces
the infrared, this {\it 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 $F_\nu\propto\nu^{1/3}$.  However, the simplest thin disk
models around supermassive ($M\ge10^6$~M$_\odot$) black holes often
{\it do not\/} produce $\nu^{1/3}$ 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 (e.g., Laor \& Netzer 1989, but see
section~5.2 below).  Simple blackbody disk models around supermassive
black holes have maximum temperatures less than 3--$8\times10^5$~K,
depending on the black hole spin, and their SED in the optical/UV can
be significantly redder than the $\nu^{1/3}$ prediction (see Figure~16), 
particularly when viewed face-on.
\begin{figure}[tp]%16
\figurenum{16}
\centerline{\epsfxsize=3in\epsfbox{p1296f16.ps}}
\caption{The optical/UV slopes predicted by simple blackbody accretion
disk models around Schwarzschild black holes, as a function of
luminosity.  The relativistic transfer function has been included here,
with the upper (solid) and lower (dotted) of each pair of curves
corresponding to inclination angles of 66$^\circ$ and 26$^\circ$,
respectively.  (The former are close to what one obtains when
neglecting the transfer function.) The slopes are calculated between
1450 and 5050~\AA.  These predicted slopes are significantly redder
than the $\nu^{1/3}$ long wavelength limit.  The mean continuum slope
determined by Francis et~al.\ (1991) can be generated by a range of disk
parameters.  (For blackbody disks, the shape of the spectrum depends
only on $L/L_{Edd}/M$, and all the curves for a given inclination angle
lie on top of each other when plotted against this parameter.)}
\end{figure}

A fit to the Francis \ea (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 {\it cool\/}.  The Schwarzschild fit shown in
this figure has $L/L_{Edd}\simeq0.1(M/10^9~{\rm M}_\odot)$, whereas the
Kerr fit has $L/L_{Edd}\simeq3\times10^{-3}(M/10^9~{\rm M}_\odot)$.
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, allowing it to have a smaller
maximum temperature as the flow transitions into some other, hotter
phase (see e.g., section~5.5 below).
\begin{figure}[tp]%17
\figurenum{17}
\centerline{\epsfxsize=3in\epsfbox{p1296f17.ps}}
\caption{Best fit blackbody accretion disk spectra to the line-free
continuum windows of the composite quasar spectrum of Francis \ea
(1991).  The solid curve shows the composite spectrum, the short dashed
curve a disk model around a Schwarzschild hole, and the long dashed
curve a disk model around a Kerr hole with $a=0.98M$.  The relativistic
transfer function has not been included in these fits.  Note that the
data in the composite spectrum shortward of the Ly$\alpha$/NV line is
contaminated by intervening absorption in the intergalactic medium.}
\end{figure}

The more difficult continuum SED problem with thin disk models is not
how to explain a red optical/UV spectrum, but 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
AGN spectra, Korista, Ferland, \& Baldwin (1997) compared the predicted
and observed emission line strengths using the ``observed'' UV X-ray
composite BBB SED (see section~3.1) in photoionization models.  The
``observed'' BBB SED does not reproduce the observed line strengths.
MacAlpine \ea (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 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 section~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, indicating that a blackbody spectrum is a
better local approximation than a modified blackbody.  This conclusion
is however uncertain, as it depends crucially on the density at the
photosphere which 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 which
{\it neglect\/} bound-free and bound-bound opacities, have been performed
by Shimura \& Takahara (1993, 1995) and D\"orrer 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
section~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 section~3.5.3).

\subsection{The Lyman Edge}

To explain the dearth of Lyman edges in AGN, 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 towards 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 which 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 which Kolykhalov \&
Sunyaev could explore to low $\alpha$ parameter ($\alpha<10^{-2}$),
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 \& Pojma\'nski 1990).  {\it Ab~initio\/} radiative
transfer calculations confirm this behavior (Coleman 1993; Shields \&
Coleman 1994; Hubeny \& Hubeny 1997; Sincell \& Krolik 1998), showing
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;
St\"orzer, Hauschildt, \& Allard 1994; Hubeny \& Hubeny 1997; Collin \&
Dumont 1997; Czerny \& Dumont 1998).  Ironically, non-LTE effects can
also {\it enhance\/} the He~II Lyman continuum (Hubeny \& Hubeny 1997),
which would have important implications for photoionization of the
broad-line region clouds in AGN.  To completely get rid of the Lyman
edge 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 Figure~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 $F_\nu\propto\nu^{1/3}$ limit (Sincell \& Krolik 1998).  The
relatively cool disks discussed in the previous subsection to explain
the SED would probably have observable Lyman absorption edges (cf.\
Figure~22).  There is as yet no accretion disk model which solves both
problems (the Lyman edge and the optical/UV continuum slope)
simultaneously.
\begin{figure}[tp]%18
\figurenum{18}
\centerline{\epsfxsize=3in\epsfbox{p1296f18.eps}}
\caption{Predicted SED of the accretion disk model of figure~20, after
folding through the relativistic transfer function for three different
observer inclination angles $i$ (mu~$\equiv\cos i$).  Dashed curves show
the non-LTE hydrogen/helium spectra, while solid curves show the
spectra as modified by LTE metal line emission and absorption, but
neglecting metals in the atmosphere structure calculation.  The Lyman
edge is virtually undetectable except for the near face-on model
(mu~= 0.98) which for clarity is blown up on a linear scale in the
inset.  Here the Lyman limit is shown by a vertical dashed line. In
this model, a change in continuum slope in the Lyman limit region is
still evident for a substantial parameter space. (Courtesy E.~Agol)}
\end{figure}

To explain the X-ray spectra observed in AGN, a number of models invoke
thermal Comptonization of optical/UV photons by an energetically
powerful, magnetized corona above the disk (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, {\it 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 re-radiation 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.
\begin{figure}[tp]%19
\figurenum{19}
\centerline{\epsfxsize=3in\epsfbox{p1296f19.ps}}
\caption{Predicted spectra for X-ray irradiated accretion disk with
accretion luminosity equal to 3~percent of Eddington, around a
non-rotating black hole of mass $2.7\times10^8$~M$_\odot$.  Each of the
three sets of points corresponds to a different observer inclination
angle $i$, where $\mu\equiv\cos i$. The top set of points is more
face-on while the bottom set is more edge-on. The large Lyman edges
predicted by these models are not observed.  (Courtesy M.~Sincell.)}
\end{figure}

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 AGN (Sun \&
Malkan 1989; Laor \& Netzer 1989; Lee \ea 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 AGN, the objects
for which we have observational data (Seyfert 1s 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
effectively test the accretion disk models which 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 section~3.2. such observations
are rare!

One of the many ways to account for the few observed Lyman edge
features in AGN is to invoke a Compton scattering atmosphere (Czerny \&
Zbyszewska 1991; Lee \ea 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, making
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
\ea  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 which 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 {\it
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 Figure~20).  Figure~18 shows the corresponding total
spectra after integrating over all disk radii and folding through the
relativistic transfer function (Agol, Hubeny, \& Blaes 1998).  Even in
the pure hydrogen/helium models, the Lyman edge is greatly reduced.  A
change in slope is still evident in the $\mu=0.5$ case, although it
occurs shortward of 912~\AA.  A bump is present redward of 912~\AA\ 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 (cf.\ Figure~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~\AA\ caused by the
line-blanketing in this model could be detected.  However, this is the
face-on case where relativistic smearing is most reduced.
Self-consistent calculations need to be performed to make firmer
predictions, but this work is encouraging.

At long wavelengths the spectra shown in figure~18 obey
$F_\lambda\propto\lambda^{-7/3}$, in agreement with the standard
$F_\nu\propto\nu^{1/3}$ 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 re-emitted 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.
\begin{figure}[tp]%20
\figurenum{20}
\centerline{\epsfxsize=3in\epsfbox{p1296f20.ps}}
\caption{Predicted flux emerging locally from various annuli at
different radii in an accretion disk model around a Kerr hole of mass
$2\times10^9$~M$_\odot$ and spin $a/M=0.998$.  The accretion rate
through the disk is 1~M$_\odot$/yr.  Only the wavelength range near the
Lyman limit is shown.  Solid curves show the full spectra, including a
metal line source function in LTE, but with a fixed atmosphere
structure calculated by neglecting metals.  The solid curves are
therefore not self-consistent, but indicate that metal lines are likely
to be important.   Dashed curves show the self-consistent non-LTE
continuum spectra computed by neglecting metals.  (data
courtesy I.~Hubeny)} 
\end{figure}

An important fact about all the new ``bare'' accretion disk
calculations is that {\it 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.

\subsection{Polarization}

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 AGN disk polarization.  They did this by simply
multiplying the Chandrasekhar polarization by the ratio of Thomson
opacity to total opacity,
\begin{equation}
q(\nu)={\kappa_{es}\over\kappa_{es}+\kappa_{ab}(\nu)},
\end{equation}
which they took to be independent of depth at each radius in the disk.
Because $q<1$ at all frequencies $\nu$ 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 {\it 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, then rise again.  Laor
\ea (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 \ea (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 {\it
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 which vary linearly with total optical
depth $\tau$ in the atmosphere:  
\begin{equation}
S(\tau)=S(0)(1+\beta\tau), 
\end{equation} 
where the constant $\beta$ 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, {\it flat\/} thermal source function gradients can produce
strong {\it 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 AGN 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.
\begin{figure}[tp]%21
\figurenum{21}
\centerline{\epsfxsize=3in\epsfbox{p1296f21.ps}}
\caption{Polarization as a function of the ratio of scattering opacity
to total opacity $q$ for various values of the thermal source function
gradient $\beta$. From bottom to top, the solid curves represent
$\beta=0$, 0.5, 1, 2, 5, and $\infty$.  The dashed line is the
approximation used by Laor \ea  (1990).  The observer inclination
angle is $63^\circ$ for all curves.  All curves approach the
Chandrasekhar (1960) value for this inclination angle as
$q\rightarrow1$, the pure electron scattering limit.  Positive values
of polarization correspond to the plane of polarization being parallel
to the disk plane, while negative values correspond to the plane of
polarization being parallel to the disk symmetry axis. (Figure modified
from Agol, Blaes, \& Ionescu-Zanetti 1998.) } 
\end{figure}

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 section~3.3.  A good
qualitative fit was obtained to the data for PG~1222+228 (Impey \ea
1995), by invoking a relatively cool disk whose overall SED turns over
in the Lyman edge region (see Figure~22).  As discussed in section~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
\ea 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.
\begin{figure*}[tp]%22
\figurenum{22}
\centerline{\epsfxsize=4in\epsfbox{p1296f22.ps}}
\caption{Flux and polarization vs.\ observed wavelength ($z=2.047$) of
PG~1222+228.  The solid curve is a fit for a single atmosphere with
effective temperature of 20,000~K and surface gravity of 130~cm~s$^{-2}$.
The dashed curve shows a fit with the same model, but including Faraday
rotation effects.  Finally, a fit for a standard thin accretion disk
model is shown as a short dashed line.  From Blaes \& Agol (1996).}
\end{figure*}

Shields, Wobus \& Husfeld (1998) have produced a model which produces
excellent quantitative agreement with the observations of steep
polarization rises near the Lyman edge, but is based on {\it 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
quantitatively fit the observations with few free parameters (see
Figure~23).  This is a considerable achievement, but relies on having a
large intrinsic polarization jump at the Lyman limit from the disk.
Shields \ea 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\deg).  The Blaes \& Agol (1996)
models also required rather large inclination angles
(53$^\circ$--66$^\circ$).
\begin{figure*}[tp]%23
\figurenum{23}
\centerline{\epsfxsize=5in\epsfbox{p1296f23.ps}}
\caption{Flux (top), degree of polarization (middle) and polarization
position angle (bottom) model fits to the observed data of PG~1630+377,
from Shields \ea (1998).  The position angle of the accretion disk
axis is unknown so the overall offset in angle in the bottom figure is
not significant.  The inclination angle of the disk is assumed to be
84\deg (nearly edge-on).  Different black hole spin parameters $a$, in
units of $M$ are shown.  The accretion disk models assume a
polarization locally emitted by the disk of zero redward of the edge
and 4.4, 4.4, and 5.7 times the Chandrasekhar (1960) value blueward of
the edge for $a/M=0$, 0.5, and 0.9 respectively.  (Courtesy G.~Shields.)} 
\end{figure*}

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 {\it 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 section~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~\AA.

It may in fact be that optical/UV radiation emerging from AGN accretion
disks 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 $\lambda$ is
$\simeq0.1\tau_T(\lambda/5000~{\rm \AA})^2(B_\parallel/1{\rm G})$, where
$\tau_T$ is the Thomson depth near the scattering photosphere and
$B_\parallel$ is the component of field strength along the line of
sight.  The equipartition field strength in the inner regions of an
$\alpha$ disk is $\sim10^4$~G~$\alpha^{-1/2}(M/10^8~{\rm
M}_\odot)^{-1/2}$.  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 {\it increase\/}
polarization (Agol, Blaes, \& Ionescu-Zanetti 1998).

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~2s and the small parallel polarizations in
Seyfert~1s 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 AGN indicates that if
electron scattering dominated disk atmospheres are considered, then
magnetic field effects must be included in the calculations.

\section{ALTERNATIVES TO STANDARD ACCRETION DISKS}

The geometrically thin disk models we have been discussing so far have
been explored most extensively.  However, there are good reasons to
believe that accretion flows in AGN may not always (if ever!) adopt
such a simple geometry.  In this section we discuss the alternatives,
and point out, where we can, the main observational and theoretical
difficulties.  However, it should be borne in mind that much more
theoretical work needs to be done to enable these models to be compared
with observations.  In many cases the models have not yet received the
theoretical attention necessary to enable them to address some of the
main observational issues discussed in this review.

\subsection{Thick Disks}

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, resulting
in a {\it 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 time scale.  This
necessarily requires that the flow have a low viscosity parameter
$\alpha$, 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 (e.g., Rees
1984).  Models of radiation-supported thick disks or tori have been
constructed by Paczy\'nski \& Wiita (1980), Jaroszy\'nski, Abramowicz
\&  Paczy\'nski (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 {\it 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 which 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~1s (Walter \& Fink 1993).  This may be incompatible with the
unified model and low inclination angles inferred from Fe K$\alpha$
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 \& K\"onigl 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 (cf. discussion by Szuskiewicz, Malkan \&
Abramowicz 1996), as observed.

\subsection{Slim Disks}

The usual alpha-viscosity prescription, in which the viscous stress is
proportional to the total (gas plus radiation) pressure, leads to disks
which are thermally and viscously unstable in cases where the accretion
rate is high enough that the inner regions of the disk are supported by
radiation pressure (e.g., Shakura \& Sunyaev 1976).  Whether such
instabilities are real is not at all clear because of the strong
dependence on the {\it ad~hoc\/} viscosity prescription (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 \ea 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 (e.g., Papaloizou \& Szuszkiewicz 1994).

Slim disk models are probably more appropriate for bright AGN than
standard thin disks, but once again, very little work has been done on
their predicted SED.  Szuszkiewicz \ea (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 like 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 \ea (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 section~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 1s (Szuszkiewicz 1997).

\subsection{Advection Dominated Accretion Flows}

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 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 \ea 1982).  Such advection
dominated accretion flows (ADAFs) have received considerable attention
in recent years, thanks to the seminal work of Abramowicz \ea (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 which could significantly heat electrons in regions of the
flow where a high level of small scale magnetohydrodynamic turbulence
is present.  Such modes may destroy the two-temperature structure of an
ADAF, especially in AGN, if collisionless shocks exist in the flow with
sufficiently high filling factor (Narayan \& Yi 1995).  In addition,
the magnetohydrodynamic turbulence which 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 AGN.  The most successful
application of the theory is perhaps to explaining the broad band
emission from the Galactic Center (Narayan, Yi, \& Mahadevan 1995).
ADAFs may also serve as useful models of X-ray emitting coronae in
brighter AGN.

\subsection{Warped Disks}

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 (e.g., Markovi\'c \& Lamb 1998).  Such warping would immediately
produce less overall polarization in the direct emitted spectrum, due
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 $T_{eff}\propto r^{-3/4}$
to $r^{-1/2}$, which would produce a long wavelength SED of
$F_\nu\propto\nu^{-1}$, much redder than the canonical $\nu^{1/3}$
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.

\subsection{Optically Thin Emission and Multiphase Flows}

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 (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 \ea 1996; Kuncic,
Celotti, \& Rees 1997).  Optically thin emission is of course also
accompanied by substantial line and edge features, but just as in
disks (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 alpha viscosity.  Gammie (1998) has found that magnetized,
radiation pressure supported disks are likely to suffer from a {\it
dynamical\/} photon bubble instability which might in fact lead to just
such a multiphase equilibrium.

As we noted in section~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 ($\sim0.3$~keV), optically thick
Comptonizing medium (see Figure~24).  This component is reminiscent of
models of the soft X-ray excess which invoke thermal Comptonization in
the inner regions of the accretion disk itself\pagebreak\ (Czerny \& 
Elvis 1987; Maraschi \& Molendi 1990; Ross, Fabian, \& Mineshige 1992; 
Shimura \&
Takahara 1993, 1995; D\"orrer et~al.\ 1996).  Note that Zheng et~al.'s
(1997) interpretation of the EUV/soft X-ray component in the {\it 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.  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.
\begin{figure}[tp]%24
\figurenum{24}
\centerline{\epsfxsize=3in\epsfbox{p1296f24.eps}}
\caption{The broadband average spectrum of NGC~5548, from simultaneous
archival optical/{\it IUE\/}/{\it Ginga\/} data, as well as non-simultaneous
{\it ROSAT\/} and {\it GRO/OSSE\/} data.  The upper panel shows the data
and fitted model, while the lower panel shows a decomposition of the
spectrum into disk and thermal Comptonization continuum components.
The dot-short-dashed curve shows the disk, modeled using blackbodies.
The short-dashed curve is the soft excess component, modeled with
thermal Comptonization in an optically thick, warm medium.  This
component dominates the spectrum from the optical/UV to 1~keV.  The
long-dash and dotted curves show the hot thermal Comptonization and
reflection components, respectively.  The dot-long-dash curve shows the
disk component fitted to the optical/IUE data separately, and is
analogous to the cool disk fit to the composite spectrum shown in
figure~17. (From Magdziarz \ea 1998.)} 
\end{figure}

\section{SUMMARY AND DIRECTIONS FOR THE FUTURE}


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

\begin{itemize}

\item 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 which produce substantial numbers of ionizing photons
generally have optical/UV SEDs which are too blue.

\item {The UV and X-ray composite spectra indicate that the BBB may not
be as energetically dominant as thought previously. However, in both
Seyferts 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
AGN over a wide wavelength range to determine the range of BBB
properties.}

\item Intrinsic Lyman edges that can be associated with accretion disks
are rare in AGN. 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.

\item {Both Seyferts and QSOs show very low optical polarization. QSOs
also show low UV polarization (up to 1000~\AA) 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 which 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 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 AGN
accretion disks.}
 
\item {Fe~K$\alpha$ emission lines with a range of properties have been
observed in Seyferts, but no such observations exist for QSOs. Although
the Fe~K$\alpha$ line indicates the presence of an accretion disk, a
full multiwavelength theoretical interpretation has only been
undertaken for one object.}

\item X-rays are an important contributor to the bolometric luminosity
of low-luminosity AGN (Seyferts), and there are strong indications that
at least some of the optical/UV arises from reprocessing of the X-rays,
which in turn feedback 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 which span a large
wavelength region are once more essential to our understanding of the
emission mechanism in AGN.

\item 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 it may also indicate a variation
in the luminosity from a separate, EUV/soft X-ray emitting phase of the
flow.

\item{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 {\it
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 wavebands to strengthen
these constraints.  Such observations complement variability campaigns
in other sources in probing the geometry and size of the inner
accretion flow.}

\item {Sophisticated atmosphere modeling is now being applied to AGN
accretion disks 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.}

\item 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.

\item 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?

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

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

\end{itemize}


To really test accretion disk models requires high signal-to-noise
observational data which covers all the energetically important (X-ray,
far-UV and the UV/optical) wavebands.  Only then can the Fe~K$\alpha$
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 spectra wavebands 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
data can be effectively and efficiently obtained. Although AGNs are
known to be similar across many orders in luminosity, there are/may be
differences which could indicate subtle variations in the nature of the
central power house, dependent on luminosity.  Therefore, observations 
must include objects that span the AGN luminosity range. 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 
AGN with different luminosities.

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

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.

\acknow
 
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 which greatly improved the paper.  This work
was supported by NSF grant AST~95-29230, NASA grant NAG5-7075, and {\it
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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