Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://hea-www.harvard.edu/QEDT/Papers/color-color.ps Äàòà èçìåíåíèÿ: Tue Apr 4 18:24:33 1995 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:48:22 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: extreme ultraviolet

TESTING MODELS FOR THE QUASAR BIG BLUE
BUMP VIA COLOR­COLOR DIAGRAMS.
Aneta Siemiginowska, Olga Kuhn, Martin Elvis, Fabrizio Fiore \Lambda
Jonathan McDowell and Belinda J. Wilkes
Harvard­Smithsonian Center for Astrophysics
60 Garden St, Cambridge MA 02138
\Lambda Present address: Osservatorio Astronomico di Roma
via dell'Osservatorio 5, Monteporzio­Catone (RM), I00040 Italy
April 3, 1995

Abstract
We discuss several models of quasar big blue bump emission in color­color and
color­luminosity diagrams. We define several broad passbands: IR (0:8 \Gamma 1:6¯m), VIS
(4000 \Gamma 8000 š A), UV (1000 \Gamma 2000 š A), UV1(1400 \Gamma 2000 š A) and UV2 (1000 \Gamma 1400 š A),
SX(0.2­0.4 keV). The colors have been chosen to investigate characteristics of the
big blue bump: (1) IR/VIS color represents the importance of the IR component
and shows the contribution around ¸ 1¯m; (2) UV/VIS color shows the slope of
the big blue bump: in a region where it dominates a higher value means the bump
gets steeper; (3) the combination of IR/VIS/UV colors shows the relative strength
of the big blue bump and the IR component; (4) UV1/UV2 color is important as an
indicator of a flattening of the spectrum in this region and the presence of the far­UV
turn­over. (5) UV/SX tests the relationship between the big blue bump and the soft
X­ray component. All colors are needed to investigate the range of model parameters.
We describe the colors for several models: accretion disk models in
Schwarzschild and Kerr geometries, single temperature optically thin emission, com­
bination of the main emission model and non­thermal power law or dust, irradiation
of the disk surface. We test models against the sample of 47 low redshift quasars
from Elvis et al. (1994, Paper I). We find: (1) modified blackbody emission from an
accretion disk in a Kerr geometry can successfully reproduce both the luminosities and
colors of the quasars except for the soft X­ray emission; (2) no additional components
(hot dust or power law) are needed to fit the optical­UV colors when the irradiation
of the surface of the disk is included in the model; (3) even modest (10%) irradiation
of the surface of the disk modifies significantly the optical colors; (4) the simplest,
single temperature, free­free models need either an additional component or a range
of temperatures to explain the observations.
Tables of predicted colors for each model family are provided on the AAS
CD­ROM.
1

1 INTRODUCTION
Quasars emit efficiently over a very broad energy range with a significant
fraction (Elvis et al. 1994 (Paper I)) of power in the infrared to soft­X­ray band.
The most prominent feature in quasar spectral energy distributions is an excess of
power, called the big blue bump which extends from ¸1¯m into the unobserved far
ultraviolet band. Shields (1978) suggested that this feature, observed in 3C273 may
be due to thermal emission from an accretion disk around a supermassive black hole.
This was the first attempt at identifying a signature of the primary quasar emission.
While the generally accepted source of quasar luminosity is the release of gravitational
energy in the vicinity of a supermassive black hole, the problem of how this energy
is converted into the radiation, and which parts of the spectrum show the primary
emission component is still open. The origin of the big blue bump emission and its
connection to the primary power engine is disputed ­ both disk and free­free emission
have evidence in their favor (see Czerny vs. Antonucci discussion, IAU Symposium
no 159, 1993).
In the past fifteen years a number of efforts have been made to fit the optical­
UV data of quasars and so constrain parameters in a variety of models (Malkan 1983,
Bechtold et al. 1987, Sun & Malkan 1989, Sanders et al. 1989, Laor 1990, Bechtold et
al. 1994, Kuhn et al. 1994). Much of this work focused on the individual objects rather
than on examining global properties of the models and data together. While fits to
the individual spectra are generally successful, the large number of parameters render
them ineffective in constraining or excluding any of the models. Several combinations
of model parameters usually yield equally good fits. Also the wide variety of observed
strengths and shapes of the big blue bump is not easily seen by examining one object
at a time.
The method presented in this paper allows examination of the full available
set of data and models simultaneously by means of color­color diagrams. These are
valuable in gaining insight to the global properties of data and models. By using fully
observed continua (Paper I) we are free to choose constant rest­frame colors, different
from the standard photometric, UBVRI, bands, that pick out various features of
the quasar continuum (e.g. the strength of the big blue bump, the slope of the UV
continuum or the connection between UV and the soft­X­rays). We have constructed
colors for sets of models to study how changes in either the model parameters or
assumptions (e.g. Kerr vs. Schwarzschild disks) affect the continuum shapes. We
make comparisons between the data and two competing models for the blue bump:
accretion disk emission and thermal bremsstrahlung. We also discuss the effects of
adding other components (a power­law or hot dust) and irradiation of the surface of
an accretion disk.
In the next section color­color diagrams are discussed. Section 3 describes the
dataset. Section 4 discusses models. In section 5 we compare the models and data.
2

Section 6 summarizes the conclusions that can be made from this study.
2. COLOR­COLOR DIAGRAMS
Color­color and color­luminosity diagrams have been widely used in studies of
populations of stars (Hertzsprung 1905, Russel 1912, 1914), low mass X­ray binary
systems (Van der Klis 1989), stellar clusters (Sandage 1957) and galaxies (Tinsley
1973). Applying this approach to quasars has the problem that their large range of
redshifts cause any set of observed colors to span a wide range of emitted wavelengths
within a given sample. This makes it hard to plot colors of models on the same
diagram as the data. Quasars have been analyzed in luminosity vs. spectral index
(Wandel & Petrosian 1988, Wandel 1991, Tripp, Bechtold & Green 1994), in color­
color (Sandage 1973) and in color­luminosity diagrams by Caditz (1993). Caditz
(1993) used the readily available U and B bands for samples of quasars (V'eron­Cetty
& V'eron 1989, Boyle et al. 1990) and built color­luminosity plots at two chosen
redshifts. He analyzed the colors in the observed frame, transferring models to the
correct frequencies. The method is useful, since a large number of objects is accessible
from existing catalogs, however, it requires redshift bins to be small, so that there
is no major change in the continuum slope within a redshift bin. Furthermore when
using standard filter bands the inherently uncertain contribution from any broad
emission lines in particular bands has to be taken into account, and some redshifts
with large line contributions are thus excluded. Finally, since the same part of the
intrinsic spectrum cannot be tracked with redshift, it is not possible to investigate
the evolution of the quasar population with this method.
Because we begin with completely sampled continua we are able to use the
same rest frame frequencies for all our analyses. The definition of model colors are
thus straightforward, as is the interpretation of colors defined at the source, moreover
emission lines can be avoided. The biggest effort was preparing the data since we
need to transfer all spectra to the correct rest frame frequencies, correct the data for
intergalactic reddening and for the contribution from a host galaxy (this is important
for low luminosity objects).
The observed big blue bump covers more than two decades in frequency, ¸
10 14:5 Hz ­ 10 17 Hz (1¯m ­ 0.5 keV), although there is no clear evidence that the
far­UV and soft X­ray emission are parts of the same component (Fiore et al. 1994,
1995). An adequate representation of the big blue bump thus requires the use of well
separated bands, which must also be broad (\Delta–=– o ¸ 1) to obtain good signal­to­
noise, especially in the UV.
In order to describe the shape of the blue bump component, we define a set
of octave wide bands: IR (0:8 \Gamma 1:6¯m), VIS(4000 \Gamma 8000 š A), UV (1000 \Gamma 2000 š A),
UV1(1400 \Gamma 2000 š A) and UV2 (1000 \Gamma 1400 š A), SX(0.2­0.4 keV). A color is a ratio of
luminosities in two bands.
3

Fig. 1 shows a typical IR­X­ray quasar spectral energy distribution in the rest
frame and shows where each color band lies with respect to the big blue bump. From
this it can be seen that each color studies particular features of the quasar continuum:
--IR/VIS color shows the contribution around ¸ 1¯m;
--UV/VIS color shows the slope of the big blue bump: in a region where it dominates
a higher value means the bump gets steeper.
-- the combination of IR/VIS/UV colors shows the relative strength of the big blue
bump and the IR component.
--UV1/UV2 color is important as an indicator of a flattening of the spectrum in this
region and the presence of a far­UV turn­over. Positive values of log (UV1/UV2)
indicate flattening in this band.
--UV/SX tests the relationship between the big blue bump and the soft X­ray
component.
We do not consider the NUV (2000 \Gamma 4000 š A) band discussed in Paper I. It
covers the near ultraviolet region of the spectrum dominated by the `small bump' of
blended Fe II and Balmer continuum emission (Wills, Netzer and Wills 1985).
3. THE DATA SET
We considered the sample of 47 quasars (the `UVSX' sample) described in
detail in Paper I. All objects in the sample have:
1) UV spectra (1200 ­ 3000 š A) from IUE;
2) soft X­ray spectra (0.1­4.0 keV) from the Einstein IPC;
3) spectrophotometry and/or photometry in the optical;
4) photometric data in the infrared;
5) radio data.
The quasars are at low redshift (0:025 Ÿ z ! 1, mostly around z¸ 0:1) and are
bright (m V !17). The bolometric luminosities (integrated from 10 9 Hz ­ 10 18 Hz) of
the sample objects range from about 10 45 erg s \Gamma1 to 10 47 erg s \Gamma1 . We have assumed
H 0 = 50 km/s/Mpc,
and\Omega 0 = 1.
The requirement that the `UV' quasars have more than 300 counts (a signal­
to­noise ratio better than ¸ 10) in the IPC (Wilkes and Elvis 1987) introduces a bias
towards objects with a large amount of X­ray emission relative to the optical and also
towards those that are relatively optically bright and nearby.
The collection and reduction of these data are discussed in detail in the `Atlas
of Quasar Energy Distributions' (Paper I). Briefly, the steps in the reduction of these
data were the following:
4

1) dereddening by the Galactic value;
2) blueshifting by (1+z) and binning data into line­free frequency bins;
3) subtracting emission lines;
4) subtracting a template host galaxy;
5) time averaging the data within the same frequency bin.
We list all quasars in Table 1. The table gives the common name of the
quasar and the name of the associated host galaxy where appropriate, the redshift
and typical V magnitude. Each object is given a classification: radio­quiet (RQ)
or radio­loud (RL). Following the convention of V'eron­Cetty & V'eron (1989) and
Schmidt & Green (1983), radio­quiet objects with absolute visual magnitude fainter
than \Gamma23:0 calculated according to their prescription (but using our cosmological
parameters) are designated as Seyfert 1 (Sy1); 8 objects in the UVSX sample satisfy
this criterion.
7 objects (indicated by a star in Table 1.) from our sample show a soft­X­ray
``excess'' in the Einstein IPC observations (Masnou et al. 1991). We calculated the
soft X­ray (SX) luminosity for these quasars by including only the emission in the
soft­X­ray excess component. This component, which can dominate at 0.4 keV was
derived by subtracting the contribution from the hard energy power law, which is
known to be a separate component (Turner & Pounds 1990) We used the data and
spectral parameters given in Masnou et al. (1991).
3.1. Time­variability and averaging.
While most of the data were taken between 1978 and 1988, the full time span
is over 25 years, from 1964 ­ 1989. A potentially severe limitation on our dataset is
that the observations are typically not simultaneous, although the optical and ground
based IR data were generally obtained within about one month. This problem is worst
in the ultraviolet since the amount of variability increases with frequency throughout
the UVOIR region (Cutri et al 1985). The magnitude of typical variations is sufficient
to contribute to the scatter in the ultraviolet energy distributions.
For about one third of the objects we have observations at two epochs
(occasionally more) in a given waveband, so we can make a crude estimate of the
degree of variability. The optical and infrared variability is not a serious problem for
these `normal' quasars, but in the ultraviolet the variability is significant on timescales
of a few years, although typically it is less than a factor of two (Elvis et al., 1994;
Kinney et al., 1991).
To generate a single mean energy distribution for each quasar, we have taken an
average (in log šF (š)) of all the data in each frequency bin. This approach gives error
bars which account for variability in our non­simultaneous data. In the UV1/UV2
5

bands when the simultaneous data are available the error bars should be much smaller
than we use.
For the IUE data, because of the increased problem of variability and also
the widely different S/N among observations, we have been selective in the data we
chose to include in the average. Specifically, where simultaneous data from the long
(LWP/LWR) and short (SWP) wavelength cameras were available, we have included
them and excluded `orphan' LWP/LWR or SWP exposures.
3.2 Luminosities in individual bands.
To characterize the large scale distribution of the energy output of the quasars,
we calculate integral luminosites in the set of broad bands defined above (see section
2.). The IR, VIS and UV luminosities are the same as in Paper I. The UV1, UV2
luminosities are new to this paper. The integrals are calculated by running a simple
linear interpolation through the data points in log šL š space, i.e. connecting the
individual points with a power law. The errors indicated in the tables are estimated
by performing the integrals using the one sigma high and one sigma low flux values
instead of the nominal values. For upper limits we interpolate between detections on
either side. The lower of the interpolated value and the upper limit is used as the
nominal flux estimate, but the errors are estimated using zero as the lower error bar
and the upper limit as the upper error bar. The logarithms of the calculated integral
luminosities in units of erg s \Gamma1 are tabulated in Table 2.
The colors are determined by taking the logarithm of the ratio between the
luminosities within two bands. The estimated uncertainties are a quadrature sum of
the errors in the luminosities.
4.0 MODELS
We consider the main models that have been widely discussed in the literature:
1. An accretion disk.
We consider the standard ff­disk models in both Schwarzschild and Kerr geometries
(as in Laor & Netzer 1990, Sun & Malkan 1989). We include the modification due to
electron scattering and Comptonization of soft photons in the disk atmosphere again
for both Schwarzschild (Czerny & Elvis 1987, Maraschi & Molendi 1990) and Kerr
geometries. We also investigate irradiation of the disk by an external X­ray source
(as in Matt, Fabian & Ross, 1993).
2. Thermal bremsstrahlung (free­free) from a single temperature optically thin cloud
(as in Barvainis 1993).
3. The combination of the accretion disk and another component:
a) non­thermal power law (as in Czerny & Elvis 1987, Carleton et al. 1987 );
6

b) thermal emission from a hot dust (as in Sanders et al.1989; Loska, Szczerba &
Czerny 1993).
4. The combination of one temperature thermal bremsstrahlung and another compo­
nent:
a) non­thermal power law;
b) thermal emission from a hot dust (as in Barvainis 1993).
In the following section we give the details of the construction of each model.
4.1 Accretion Disk.
4.1.1. Local Blackbody Emission.
We assume that the disk radiates locally as a black body, so the total flux
depends only on the effective temperature distribution (Shakura & Sunyaev 1973).
Equations of the disk structure are taken from Novikov & Thorne (1973) and Page
& Thorne (1974) and include the general relativistic treatment of an accretion disk
around a black hole in Schwarzschild and Kerr geometries. General relativistic effects
on the propagation of light in the vicinity of the rotating black hole (Cunningham
1975) are calculated using the transfer function tabulated by Laor, Netzer & Piran
(1990). It takes into account the effect of limb­darkening due to electron scattering
in the atmosphere of the disk and the heating of the disk by returning photons
(Cunningham 1976).
The inner edge of the disk, R in , is assumed to be the radius of the last
marginally stable orbit (e.g. 6GM=c 2 for a Schwarzschild and 1.23GM=c 2 for a
maximal­Kerr black hole, where M is the mass of a black hole). The outer radius
R out of the disk is more difficult to define. The location of R out determines the
frequency at which the emitted flux changes its dependence on frequency, from š 2 , to
š 1=3 (Frank, King, Raine 1992; Bechtold et al. 1987). Although, for large distances
the blackbody temperature is low enough to place the characteristic frequency in
the IR band, which is usually dominated by other emission components, the chosen
value of R out does affect the computed IR/VIS color of the disk emission (Bechtold
et al. 1987). A possible constraint on the extent of the disk might be the radius at
which the self­gravity of the disk dominates over the central gravitational force (Laor
& Netzer 1989). However, St¨orzer (1993) has shown that the effective temperature
distribution of a self­gravitating disk is similar to the distribution in the standard disk
even if the vertical structures are different. We assumed the same outer radius 2500R S
(R S = 2GM=c 2 is the Schwarzschild radius), in all our models. For the highest central
black hole masses (10 9 M fi , 10 10 M fi ) this radius is located in the region dominated by
the disk gravity.
4.1.2. Electron Scattering
7

For sufficiently high accretion rates, the atmosphere of the disk is dominated
by the electron scattering opacity (Shakura & Sunyaev 1973). Such a spectrum is
flatter and much harder than that of local blackbody emission from the disk above
the critical frequency log š crit ¸ 15.0 (Novikov & Thorne 1973; Czerny & Elvis 1987;
Laor & Netzer 1989, Ross & Fabian 1993). The modification occurs in the ultraviolet
part of the spectrum and affects the UV colors. We calculate the spectrum using
the method described by Czerny & Elvis (1987) which includes modification to the
opacity and Comptonization of soft photons due to the presence of hot electrons in
the atmosphere of the disk (Svensson 1984, Czerny & Elvis 1987). The bound­free
opacities are included following the Maraschi & Molendi (1990) approximation.
4.2. Irradiation of the Accretion Disk
X­ray spectra of Seyfert galaxies show signatures of reflection off cold, Comp­
ton thick material (Mushotzky, Done & Pounds 1993). While there are other possi­
bilities (eg. Guilbert & Rees 1988; Nandra & George 1994), an accretion disk is a
natural source for this mirror.
We assumed that the irradiation gives an extra flux component to the viscously
generated local flux. The total local flux is described by (Czerny, Czerny & Grindlay
1987; Malkan 1991, Ko & Kallman 1991, Czerny, Jaroszynski & Czerny 1994):
F (R) = F 0 + f irr j —
Mc 2
4úR 2
; (1)
where F 0 is the flux generated in the disk; —
M is the accretion rate in g s \Gamma1 ; f irr
represents the importance of the irradiation in comparison with the total luminosity,
it describes the efficiency with which the available X­ray flux illuminates the disk
and includes the dependence on the changes in the disk shape, on the angular change
to the X­ray source seen by the particular part of the disk, on the scattering in the
corona above the disk etc.; j is the efficiency of converting the gravitational energy
into radiation (j is 0.06 for non­rotating and 0.32 for maximally rotating black holes).
This approach corresponds to the case in which irradiation is due to the central X­ray
radiation scattered in the corona. The form of equation (1) implies the existence of
a critical radius beyond which irradiation dominates the locally generated flux in the
disk (Ko & Kallman 1991). The critical distance can be calculated (we ignore here
the relativistic effects, which can cause an increase in the irradiation (Cunningham
1976)):
R crit = 3GM
2f irr jc 2
= 3
4
1
f irr j
R S (2)
In a simple picture the whole disk can be divided into two parts: an inner part
(R!R crit ) where the radial effective temperature distribution is dominated by local
8

energy generation (as for the standard disk, T eff (R) ¸ R \Gamma3=4 ); and an outer part
(R?R crit ) where irradiation changes the temperature distribution: T eff (R) ¸ R \Gamma1=2 .
The two parts emit spectra with different slopes: F in
š ¸ š 1=3 for the inner part,
F out
š ¸ š \Gamma1 for the outer part. There exists a critical frequency at which the
modification to the disk spectrum caused by the irradiation significantly changes
the slope of the spectrum compared with that of the original disk. We can calculate
this critical frequency from the definition of the blackbody spectrum emitted by each
part of the disk using the condition:
F š crit
(irr) = F š crit
(disk) (3)
and
F š crit = ú
Z R 2
R 1
B š (T eff (R))RdR (4)
where B š is the Planck function and the radial temperature distribution is given
above. The limits of the integral are given by the inner radius, the critical radius and
outer radius of the disk. Then a comparison between the two parts of the disk with
their different temperature distributions gives the critical frequency:
š crit = 1:23 \Theta 10 16 M \Gamma1=4
8 (L=LEdd ) 1=4 f 3=4
irr j 1=2 Hz (5)
M 8 = M=10 8 M fi , L=j —
Mc 2 is a luminosity and LEdd is the Eddington luminosity.
Equation (5) shows that irradiation affects the spectrum somewhat more in the case
of small central masses. The variability of the high energy radiation will be correlated
with the variability of the optical­UV part of the spectrum for small central mass (and
presumably low luminosity) objects, while for large mass (high luminosity) objects,
no correlation will be present. For example in the case of 10 10 M fi (for irradiation
factor f irr =0.1, j = 0:34 and L/LEdd =0.3) the critical frequency is log š crit =14.47
(¸ 1¯m) and only the spectrum at lower frequencies will be influenced by irradiation,
leaving the optical­UV part dominated by the emission from the disk, while for 10 7 M fi ,
log š crit =15.22 (¸ 1800 š A ) making the optical­UV spectrum influenced by irradiation.
4.3 Single temperature Thermal Bremsstrahlung
Barvainis (1993) has suggested that the big blue bump is due to optically
thin thermal emission. We consider the simplest such case of single temperature
thermal bremsstrahlung emission from an optically thin (Ü eff = (Ü š (Ü š +Ü es )) 1=2 ! 1),
spherical and isothermal cloud. We assume the radius R and density n e of the cloud
to be consistent with an optical depth smaller than 1. The luminosity generated by
such a cloud is described by (Rybicki & Lightman, 1979):
L š = 9:5 \Theta 10 \Gamma38 V n 2
e T \Gamma1=2 exp(\Gamma
hš
kT
)g ff erg s \Gamma1 Hz \Gamma1 (6)
9

g ff is the Gaunt factor which we approximate using the formula from Gronenschild &
Mewe (1978). The shape of the spectrum is constant, and the peak of the spectrum
is shifted to higher frequencies with increasing temperature. Such a cloud emits
in the optical­UV (T ?
¸ 10 4 K), and for sufficiently high temperatures (T ?
¸ 10 6 K), also
contributes to the soft­X­rays.
4.4 Additional Components
Modeling of the observed IR/optical/UV quasar spectra requires usually more
than the one emission component. The emission from an accretion disk is not enough
to account for the observed power in our IR band. Two main additional components
have been considered in the literature: a non­thermal power law and thermal emission
from hot dust heated by the primary continuum. We will consider the direction in
which the colors of the basic models can be modified by each of these two components
separately. In practice, mixtures of both components may be present.
4.4.1 Power Law
A non­thermal power­law extending from far­IR to the X­ray band was
considered by a number of authors (Elvis & Lawrence 1985, Elvis et al. 1986, Carleton
et al. 1987, Brissenden 1989, Grossan 1993). There is no compelling evidence for the
presence of such a component, however by assuming such an additional power law it
is possible to fit the data over a wide range of frequencies with a minimum of free
parameters (Fiore et al. 1995).
We define the power law normalization by the ratio: L
2000 š A
/ L 3¯m . We use
the spectral index (šL š ¸ š \Gammaff OIR ) ff OIR = 1.23 ( +
\Gamma 0.28 (1oe)) given by the averaged
ratio for our sample (Paper I). We discuss the consequences of changing the power
law spectral index and normalization on the calculated colors.
4.4.2a. Hot Dust: Optically Thick
There are observational indications that hot dust is located in the nuclear
region (e.g. Fairall 9 in Clavel et al.1992; NGC 3783 Glass 1992; GQ Comae in
Sitko et al. 1993). Assuming that the luminosity of the big blue bump provides the
flux irradiating the dust, we analyze the variations in colors due to emission from a
hot, optically thick torus of dust. Since the central continuum is the main source of
energy for the dust, its effective temperature at a certain radius depends only on its
distance from the continuum source (Barvainis 1990, Laor & Draine 1993). We adopt
the relation given by Laor & Draine (1993) for an optically thick, plane parallel dust
slab:
T eff (R) = T max ( R
R in
) \Gamma1=2 ; (7)
10

where T max is the maximum dust temperature at the inner radius, R in , of the dust.
The minimum radius of the hot dust is defined (for a given central luminosity) by
the sublimation temperature of the grains present, and depends on their size and the
chemical composition. This temperature ranges from ¸900K for silicon to ¸1750K
for mixtures of graphite grains. We calculated the spectra emitted by the hot dust
assuming evaporation temperatures ranging from 900K to 1750K to define the inner
radius of the dust. We assume that the dust is optically thick and we calculate the
blackbody emission from a flat disk viewed face­on. This gives a maximum dust
contribution at the near infrared frequencies. The outer radius of the dust is defined
by the lower temperature cut which we take to be 250K, to put the cut off well outside
the IR band. We examine the two component models in the color­color diagrams.
4.4.2b. Hot Dust: Optically Thin
The hot dust in the central parsec can also form an optically thin shell around
the central continuum source, causing absorption of the optical­UV continuum (Laor
& Draine 1993, Loska, Szczerba & Czerny 1993). The spectrum emitted by the disk
(or other source) is reprocessed by the shell of dust. The emergent spectrum depends
on the continuum input spectrum, the chemical composition of the dust, the size of
dust grains, the size of the dust region, the disk inclination angle. In general our
UV band will be affected slightly more than the VIS band. We do not calculate
this model since it requires a detailed treatment of the radiation transfer through the
dust, which we do not consider. In the figures 2, 3 we show the vector pointing in
the direction the colors would change due to the presence of the optically thin dust.
The vector shows the reddening given by Laor & Draine (1993) for a spherical shell
of dust (graphite+SiC) with E(B­V) =0.033.
5. COLOR­COLOR, COLOR­LUMINOSITY DIAGRAMS
We discuss the color­color and color­luminosity diagrams for each group of
models. The primarily diagram is that of VIS/UV1/UV2 because it is most sensitive
to the slope of the big blue bump.
5.1 Thermal Bremsstrahlung.
The spectrum of a hot, optically­thin plasma emitting free­free depends on
its temperature (Eq.6) and has a well defined shape. We show the change in the
VIS/UV1/UV2 colors due to variations in temperature as the dotted line in Figure 2,
which also shows the data points. (Error bars that also allow for variability (section
3.1) are plotted in Figure 7). We indicate radio­loud objects with solid triangles and
radio­quiet with empty squares. There is no difference in the scatter of the radio­loud
and radio­quiet objects in this diagram. The data points are distributed over a larger
region than the simple free­free emission can produce.
11

While optically thin plasmas with temperatures between 5\Theta10 4 --10 7 K produce
spectra within the observed range of UV1/UV2 colors, they do not simultaneously
give the VIS/UV1 colors required by the observations. The theoretical spectra
predict a continuum shape which is too flat for some objects and the VIS/UV1 is
too large (Fig.2). Adding a non­thermal power law component mainly increases
the VIS luminosity and gives a possible explanation for some of the data points.
But the objects with VIS/UV1 color smaller than that of pure free­free emission
(below log(VIS/UV1)¸ \Gamma0:15) are not reachable by this means. The dashed line in
Figure 2 shows the colors of the single temperature blackbody emission. Moderate
optical depths (0! Ü ! few) can populate the region between the BB and free­free
lines (Collin­Souffrin et al., 1995). Objects with larg