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TO APPEAR IN APJ SEPTEMBER 20, 2008
Preprint typeset using LATEX style emulateapj v. 10/09/06
AGN DUSTY TORI: II. OBSERVATIONAL IMPLICATIONS OF CLUMPINESS
MAIA NENKOVA1 , MATTHEW M. SIROCKY 2 , ROBERT NIKUTTA2, ŽELJKO IVEZI ´C3 AND MOSHE ELITZUR2
To appear in ApJ September 20, 2008
ABSTRACT
From extensive radiative transfer calculations we find that clumpy torus models withN0 ∼ 5–15 dusty clouds
along radial equatorial rays successfully explain AGN infrared observations. The dust has standard Galactic
composition, with individual cloud optical depth τV ∼ 30–100 at visual. The models naturally explain the
observed behavior of the 10µm silicate feature, in particular the lack of deep absorption features in AGN
of any type. The weak 10µm emission feature tentatively detected in type 2 QSO can be reproduced if in
these sources N0 drops to ∼2 or τV exceeds ∼100. The clouds angular distribution must have a soft-edge,
e.g., Gaussian profile, the radial distribution should decrease as 1/r or 1/r2. Compact tori can explain all
observations, in agreement with the recent interferometric evidence that the ratio of the torus outer to inner
radius is perhaps as small as ∼5–10. Clumpy torus models can produce nearly isotropic IR emission together
with highly anisotropic obscuration, as required by observations. In contrast with strict variants of unification
schemes where the viewing-angle uniquely determines the classification of an AGN into type 1 or 2, clumpiness
implies that it is only a probabilistic effect; a source can display type 1 properties even from directions close
to the equatorial plane. The fraction of obscured sources depends not only on the torus angular thickness but
also on the cloud number N0. The observed decrease of this fraction at increasing luminosity can be explained
with a decrease of either torus angular thickness or cloud number, but only the latter option explains also the
possible emergence of a 10µm emission feature in QSO2. X-ray obscuration, too, has a probabilistic nature.
Resulting from both dusty and dust-free clouds, X-ray attenuation might be dominated by the dust-free clouds,
giving rise to the observed type 1 QSO that are X-ray obscured. Observations indicate that the obscuring torus
and the broad line region form a seamless distribution of clouds, with the transition between the two regimes
caused by dust sublimation. Torus clouds may have been detected in the outflow component of H2O maser
emission from two AGN. Proper motion measurements of the outflow masers, especially in Circinus, are a
promising method for probing the morphology and kinematics of torus clouds.
Subject headings: dust, extinction — galaxies: active — galaxies: Seyfert — infrared: general — quasars:
general — radiative transfer
1. INTRODUCTION
Recent VLTI interferometric observations in the 8–13 µm
wavelength range by Tristram et al. (2007) confirm the pres-
ence of a geometrically thick, torus-like dust distribution in
the nucleus of Circinus, as required by unification schemes
of Seyfert galaxies. Several aspects of their data require that
this torus is irregular, or clumpy, in agreement with the earlier
prediction of Krolik & Begelman (1988).
We have recently developed the first formalism for handling
clumpy AGN tori and presented initial results (Nenkova et al.
2002; Elitzur et al. 2004; Elitzur 2006, 2007). The reported
clumpy models have since been employed in a number of
observational studies, including the first analysis of Spitzer
observations by the GOODS Legacy project (Treister et al.
2004). Our clumpy torus models were also employed
in the analysis of spatially-resolved, near-diffraction-limited
10 µm spectra of the NGC 1068 nucleus (Mason et al.
2006). The geometry and kinematics of both water maser
(Greenhill & Gwinn 1997; Gallimore et al. 2001) and narrow-
line emission (Crenshaw & Kraemer 2000) indicate that the
NGC 1068 torus and accretion disk are oriented nearly edge-
on. The Mason et al. clumpy model for IR emission is the
1 Seneca College, 1750 Finch Ave. East, Toronto, ON M2J 2X5, Canada;
maia.nenkova@senecac.on.ca
2 Department of Physics and Astronomy, University of Kentucky,
Lexington, KY 40506-0055; sirockmm@pa.uky.edu, robert@pa.uky.edu,
moshe@pa.uky.edu
3 Department of Astronomy, University of Washington, Seattle, WA
98105; ivezic@astro.washington.edu
first to correctly reproduce the observed near-IR flux with an
edge-on orientation. In contrast, smooth-density models re-
quire viewing angles 22◦–30◦ above the equatorial plane in
order to bring into view the warm face of the torus backside
(Granato et al. 1997; Gratadour et al. 2003; Fritz et al. 2006).
Clumpiness is also essential for understanding the puzzling
interferometry result that dust temperatures as different as &
800 K and ∼200–300 K are found at such close proximity
to each other (Schartmann et al. 2005). The mounting ob-
servational evidence in favor of clumpy, rather than smooth,
dust distribution in AGN tori has sparked additional modeling
efforts by Dullemond & van Bemmel (2005) and Hönig et al.
(2006).
This two-paper series expands the analysis of
Nenkova et al. (2002). In its first part (Nenkova et al.
2008, part I hereafter) we develop the full formalism for
continuum emission from clumpy media and construct the
source functions of dusty clouds—the building blocks of the
AGN torus. Here we assemble these clouds into complete
models of the torus, and study the model predictions and
their implications to IR observations. In comparing the
predictions of any torus model with observations one faces
a difficult problem—the overwhelming majority of these
observations do not properly isolate the torus IR emission.
Starburst emission is increasingly recognized as an important
component of the IR flux measured in many, perhaps most,
AGN (e.g., Netzer et al. 2007). In addition to this well known
contamination, even IR from the immediate vicinity of the
AGN may not always originate exclusively from the torus,

2 Nenkova et al
further complicating modeling efforts. A case in point is
the Mason et al. (2006) modeling of NGC1068. All flux
measurements with apertures < 0.5′′ are in good agreement
with the model results, but the flux collected with larger aper-
tures greatly exceeds the model predictions at wavelengths
longer than ∼4µm. This discrepancy can be attributed to IR
emission from nearby dust outside the torus. Mason et al
show that the torus contributes less than 30% of the 10 µm
flux collected with apertures ≥ 1′′ and that the bulk of the
large-aperture flux comes at these wavelengths from dust in
the ionization cones; while less bright than the torus dust,
it occupies a much larger volume (see also Poncelet et al.
2007). On the other hand, the torus dominates the emission
at short wavelengths; at 2 µm, more than 80% of the flux
measured with apertures ≥ 1′′ comes from the torus even
though its image size is less than 0.04′′ (Weigelt et al. 2004).
These difficulties highlight a problem that afflicts all IR
studies of AGN. The torus emission can be expected to dom-
inate the AGN observed flux at near IR because such emis-
sion requires hot dust that exists only close to the center. But
longer wavelengths originate from cooler dust, and the torus
contribution can be overwhelmed by the surrounding regions.
Unfortunately, there are not too many sources like NGC1068.
No other AGN has been observed as extensively and almost
no other observations have the angular resolution necessary
to identify the torus component, making it impossible to de-
termine in any given source which are the wavelengths dom-
inated by torus emission. There are no easy solutions to this
problem. One possible workaround is to forgo fitting of the
spectral energy distribution (SED) in individual sources and
examine instead the observations of many sources to iden-
tify characteristics that can be attributed to the torus signa-
ture. One example for the removal of the starburst compo-
nent is the Netzer et al. (2007) composite SED analysis of the
Spitzer observations of PG quasars. Netzer et al identify two
sub-groups of “weak FIR” and “strong FIR” QSOs and a third
group of far-IR (FIR) non-detections. Assuming a starburst
origin for the far-IR, they subtract a starburst template from
the mean SED of each group. The residual SEDs are remark-
ably similar for all three groups, and thus can be reasonably
attributed to the intrinsic AGN contribution, in spite of the
many uncertainties. However, while presumably intrinsic to
the AGN, it is not clear what fraction of this emission origi-
nates from the torus as opposed to the ionization cones. An
example of sample analysis that may have identified the torus
component is the Hao et al. (2007) compilation of Spitzer IR
observations. In spite of the large aperture of these measure-
ments, Seyfert 1 and 2 galaxies show a markedly different be-
havior for the 10µm feature, both in their mean IR SEDs and
in their distributions of feature strength. Furthermore, Ultra-
luminous IR Galaxies (ULIRG) that are not associated with
AGN show yet another, entirely different behavior, indicating
that the observed mean behavior of Seyfert galaxies is intrin-
sic to the AGN. Accepting the framework of the unification
scheme, the differences Hao et al find between the appear-
ances of Seyfert 1 and 2 can be reasonably attributed to the
torus contribution; the ionization cones dust is optically thin,
therefore its IR emission is isotropic and cannot generate the
observed differences between types 1 and 2.
Here we invoke both approaches in comparing our model
predictions with observations. We start by assembling dusty
clouds into complete models of the torus, as described in §2.
Our model predictions for torus emission and the implications
to IR observations are presented in §§3–5, while in §6 we dis-

i
σ
Rd Ro
to observer

Rd Ro
σ
i to observer
FIG. 1.— Model geometry: Dusty clouds, each with an optical depth τV
at visual, occupy a toroidal volume from inner radius Rd, determined by dust
sublimation (eq. 1), to outer radius Ro = YRd. The radial distribution is a
power law r−q, the total number of clouds along a radial equatorial ray is
N0. Various angular distributions, characterized by a width parameter σ,
were considered. The angular distribution has a sharp-edge on the left and a
smooth boundary (e.g., a Gaussian) on the right.
cuss aspects of clumpiness that are unrelated to the IR emis-
sion, such as the torus mass, unification statistics, etc. In §7
we conclude with a summary and discussion.
2. MODEL OF A CLUMPY TORUS
Consider an AGN with bolometric luminosity L surrounded
by a toroidal distribution of dusty clouds (Fig. 1). The
“naked” AGN flux at distance D is FAGN = L/4πD2 at any
direction, but because of absorption and re-emission by the
torus clouds the actual flux distribution is anisotropic, with
the level of anisotropy strongly dependent on wavelength.
The grain mix has standard interstellar properties (see paper
I, §3.1.1 for details), the optical depth of each cloud is τV at
visual.
2.1. Dust Sublimation
The distribution inner radius Rd is set by dust sublimation
at temperature Tsub. From §3.1.2 in part I,
Rd ≃ 0.4
(
L
1045 ergs−1
)1/2(1500K
Tsub
)2.6
pc. (1)
Barvainis (1987) derived an almost identical relation for Rd.
His eq. 5 has the same normalization and only a slight dif-
ference in the power of Tsub (2.8 instead of 2.6); this dif-
ference reflects the more detailed radiative transfer calcula-
tions we perform. Here the distance Rd is determined from
the temperature on the illuminated face of an optically thick
cloud of composite dust representing the grain mixture. The
sharp boundary we employ is an approximation. In reality,
the transition between the dusty and dust-free environments
is gradual because individual components of the mix subli-
mate at slightly different radii, with the largest grains surviv-
ing closest to the AGN (Schartmann et al. 2005). From near-
IR reverberation measurements, Minezaki et al. (2004) and
Suganuma et al. (2006) find that the inner radius of the dusty
region is indeed proportional to L1/2, but the time lags they
report are ∼2–3 times shorter than predicted by eq. 1. While
this equation gives the smallest radius at which the dust ab-
sorption coefficient reflects the full grain mixture, the largest
grains survive to closer radii, where they are presumably de-
tected by the reverberation measurements.
2.2. The Cloud Distribution
The torus extends radially out to Ro = YRd, with Y a free
parameter. The total number of clouds, on average, along any
radial equatorial ray is specified by the parameter N0. We
studied various forms for the variation of NT(β), the total
number of clouds along rays at angle β from the equator. Fig-
ure 1 shows on the left a sharp-edge uniform distribution with

AGN Dusty Tori: II. Observational Implications 3
λ (µm)1 10 100
P e
sc
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
N

= 2
N

= 15
τV

= 20
40
60
100
Viewing Angle, i (deg)
0 20 40 60 80
P e
sc
0.0
0.5
1.0
N0 = 1
15
2
5
10
200
500
FIG. 2.— Behavior of the probability for photon escape along a path con-
taining N clouds (eq. 4 part I). Upper panel: Wavelength variation of Pesc for
the indicated N when the single cloud optical depth is τV at visual. Lower
panel: The probability for an AGN photon to escape through the torus in
direction i from the pole when each cloud is optically thick; this is also the
probability for unobscured view of the AGN at viewing angle i. The to-
tal number of clouds varies according to NT(β) = N0 exp(−β2/σ2), where
β = 12 pi − i is angle from the equatorial plane, with σ = 45
◦ andN0 as marked.
NT(β) = N0 within the angular width |β| ≤ σ. In a Gaussian
distribution, NT(β) = N0 exp(−β2/σ2).
The emission from the clumpy torus is found by integra-
tion along paths through the cloud distribution (eq. 5, part I).
Some of the computation technicalities are described in the
Appendix. The calculation requires the single cloud source
function Sc,λ, derived in part I, and the number of clouds per
unit length, NC(r,β), as a function of β and radial distance
r. For this distribution we assume a separable function with
power law radial behavior r−q so that
NC(r,β) = C NT(β)Rd ×
(
Rd
r
)q
(2)
where C = (∫ Y1 dy/yq)−1 is a dimensionless constant (for
a given Y and σ), ensuring the normalization NT(β) =
∫
NC(r,β)dr.
The observed torus radiation is affected not only by the
emission from individual clouds but also by the probability
that emitted photons escape through the rest of the path. The
escape probability, Pesc, is given in eq. 4 part I. For an overall
number of clouds N along a path, Pesc ≃ exp(−N τλ) at wave-
lengths in which the optical depth of a single cloud obeys
τλ < 1, and Pesc ≃ exp(−N ) when τλ > 1. Many of the de-
tailed results presented below can be readily understood from
the dependence of Pesc on wavelength and on torus viewing
angle, shown in figure 2.
2.3. Scaling
Because of general scaling properties of radiatively heated
dust (Ivezic´ & Elitzur 1997), the only effect of the overall lu-
minosity is in setting up the bolometric flux FAGN and the dust
sublimation radius Rd (eq. 1). For a given torus model, the
distributions of dust temperature and of brightness are unique
functions of the scaled radial distance r/Rd: two sources with
the same cloud properties but different luminosities will have
the same distributions in terms of r/Rd, only the more lumi-
nous one will have its brightness spread over a larger area
because of its larger Rd (this point is explained further in the
Appendix). Denoting the torus flux by Fλ, the spectral shape
Fλ/FAGN is independent of L. The dependence of the torus
SED on the spectral shape of the AGN input radiation is lim-
ited to scattering wavelengths, disappearing altogether at λ &
2–3 µm. There is a similarly weak dependence on Tsub. The
output spectrum depends primarily on τV and the cloud distri-
bution. Although the luminosity does not affect the radiative
transfer, it is entirely possible for torus properties to be corre-
lated with L for some other reasons (e.g. σ, as in the receding
torus model).
2.4. The AGN Contribution
In most figures we show only the contribution of the torus
emission. However, since the medium is clumpy, there is al-
ways a finite probability for an unobscured view of the AGN,
irrespective of the viewing angle. Because of the probabilistic
nature of the problem it is only possible to display the emerg-
ing spectral shape with or without the AGN contribution and
the probability for each case (see bottom panel of figure 2).
3. MODEL SPECTRA
We proceed now with the model results. In all calculations
the AGN input radiation follows the “standard” spectrum de-
scribed in §3.1.1, part I.
3.1. Geometrical Shape
Figure 3 shows model results for sharp-edged and Gaussian
angular distributions. The sharp-edge geometry produces a
bimodal distribution of spectral shapes, with little dependence
on viewing angle other than the abrupt change that occurs be-
tween the torus opening and the obscured region. In contrast,
the Gaussian distribution produces a larger variety in model
spectral shapes, with a smooth, continuous dependence on i.
We investigated a larger family of angular distributions of the
form NT(β) = N0 exp(− |β/σ|m), with m a free parameter. In
this family, m = 2 is the Gaussian and as m increases, the
transition region around β = σ becomes steeper. Generally,
“softer” distributions with m . 10 show behavior similar to
the Gaussian while those with larger m produce results simi-
lar to the sharp-edge geometry.
The SED dichotomy produced by sharp boundaries con-
flicts with observations. Alonso-Herrero et al. (2003) studied
the 0.4–16 µm nuclear emission from a complete sample of 58
Seyfert galaxies, selected from the CfA sample. In a compar-
ison with theoretical models, Alonso-Herrero et al. point out
that a common prediction of all smooth-density models is a di-
chotomy of SED between type 1 and 2, similar to the one dis-
played in the upper panel of fig. 3, and that such a dichotomy

4 Nenkova et al
i

= 0ο
λ F
λ
/ F
A
G
N
10-4
10-3
10-2
10-1
100
i

= 0ο
λ (µm)
1 10 100
10-4
10-3
10-2
10-1
0
Gaussian Angular Distribution
Sharp Cone Boundaries
90ο
90ο
10
FIG. 3.— Model spectra for a torus of clouds, each with optical depth
τV = 60. Radial distribution with q = 1 out to Y = 30, with N0 = 5 clouds
along radial equatorial rays (see eq. 2). The angular distribution is sharp-
edged in the top panel, Gaussian in the bottom one (cf. fig. 1); both have a
width parameter σ = 45◦. Different curves show viewing angles that vary
in 10◦ steps from pole-on (i = 0◦) to edge-on (i = 90◦). Fluxes scaled with
FAGN = L/4piD2.
is not observed in their sample; the dichotomy is present even
in model geometries with soft edges because the exp(−τ ) at-
tenuation factor varies rapidly, resulting in a sharp transition
around τ ∼ 1 between dusty and dust-free viewing. As is
evident from the lower panel of fig. 3, this SED dichotomy
problem is solved by soft-edge clumpy tori. Therefore, in the
following we consider only Gaussian angular distributions.
3.2. Observations and Model Parameters
As discussed in the Introduction, torus IR observations are
hampered by uncertainties that are partially alleviated by con-
sidering composite spectra. Figure 4 shows compilations of
type 1 and type 2 data and some representative models, up-
dating a similar figure presented in Nenkova et al. (2002). The
type 1 data additionally include the recent Spitzer composite
spectra from Hao et al. (2007) and Netzer et al. (2007). The
close agreement between these two SEDs in their common
spectral region, λ = 5–38µm, indicates that they may have
captured the torus emission in outline, if not in details. The
upturn around 60µm in the Netzer et al spectrum likely re-
flects the transition to starburst dominance. To ensure the
smallest possible apertures in type 2 sources, the data for in-
dividual objects are mostly limited to ground based and HST
observations. The data in both panels of this figure display
the general characteristics that have to be reproduced by the
same models in pole-on and edge-on viewing. The updated
models plotted with the data differ from the original ones in
Nenkova et al. (2002) in three significant ways: (1) the optical
λ F
λ
(ar
b.
u
n
its
)
10-4
10-3
10-2
10-1
Type 1
λ (µm)
1 10 100
10-4
10-3
10-2
10-1
Type 2
q = 0
3
2
1
q = 0
3
2
1
avg. of 24 quasars, Hao et al (2007)
avg. of 47 quasars, Elvis et al (1994)
avg. of PG quasars L12 <1, Sanders et al (1989)
avg. of PG quasars L12 >1, Sanders et al (1989)
intrinsic QSO spectrum, Netzer et al (2007)
NGC 1068, ref. a)
NGC 1068, ref. b)
NGC 7674, ref. c)
Mkn 573, ref. c)
Circinus, ref. d)
FIG. 4.— Observations of type 1 and type 2 sources compared with clumpy
torus model spectra. The type 1 composite data are from Sanders et al.
(1989), Elvis et al. (1994), Hao et al. (2007) and Netzer et al. (2007). The
type 2 data are from the following sources: a) Mason et al. (2006); b) var-
ious observations with aperture ≤ 0.5′′ listed in Mason et al. (2006); c)
Alonso-Herrero et al. (2003); d) Prieto et al. (2004). In the model calcula-
tions, plotted with broken lines, each cloud has optical depth τV = 30. Other
parameters are σ = 30◦ , q = 0–3, as marked, Y = 30 and N0 = 5. The angular
distribution in this and all subsequent figures is Gaussian. The models in the
upper panel are for pole-on viewing (i = 0◦), in the bottom panel for edge-on
(i = 90◦).
properties of the silicate component of the dust are taken from
the tabulation for “cool” silicates in Ossenkopf et al. (1992)
instead of the Draine & Lee (1984) dust; (2) the clouds angu-
lar distribution is Gaussian rather than sharp-edged; and (3)
the torus radial thickness Y is 30 instead of 100. As is evident
from the figure, the model spectra are generally in reasonable
agreement with the data.
We produced a large number of models for various param-
eter sets4, and we now present model results and discuss their
observational implications. The models are characterized by
free parameters that describe individual clouds (τV ), control
the total number of clouds (N0) and specify the geometrical
properties of their angular and radial spatial distributions (σ,
q and Y ). Note that, except for N0, smooth-density models
also require all of these parameters to describe the dust dis-
tribution. In the following, the parameters are varied one at
a time, and from comparison with observations we attempt to
identify the likely range of each of them. The effect of the ra-
dial thickness parameter Y is described separately in the next
section (§4), devoted to a discussion of the torus size.
3.3. Single Cloud Optical Depth
4 Tabulations of all the models discussed here as well as many additional
cases are available at http://www.pa.uky.edu/clumpy/

AGN Dusty Tori: II. Observational Implications 5
λ F
λ
/F
A
G
N
10-3
10-2
10-1
100
λ (µm)
1 10 100
10-3
10-2
10-1
0
10
20
40
60
100
200
1 10 100100
i

= 0oq = 1
q = 1 i = 90
o
q = 2
q = 2
τV
100
FIG. 5.— Dependence of the torus SED on the single cloud optical depth
τV . Other parameters are σ = 45◦ ,N0 = 5 and Y = 30. Radial power law with
q = 1 in the left panels, q = 2 in the right ones. Pole-on viewing in the top
panels, edge-on at the bottom.
Figure 5 shows the effect of varying the optical depth of in-
dividual clouds from 10 to 200. The SED hardly varies when
τV increases beyond∼ 100, reflecting the similar behavior for
emission from a single cloud (see Fig. 11, Part I). The fig-
ure shows the torus emission for both pole-on and edge-on
viewing. Smooth-density models (e.g., Pier & Krolik 1992;
Granato & Danese 1994) consistently produce the 10 µm sili-
cate feature in emission and absorption, respectively, for polar
and equatorial viewing. As the figure shows, in a clumpy dis-
tribution the feature displays a more complex pattern, unlike
anything produced in smooth-density models. At i = 0◦, the
feature appears in emission as long as τV . 20. When the
optical depth increases further, the feature disappears and the
SED is essentially featureless across the 10µm region. How-
ever, the feature reappears in weak emission when τV & 100.
At i = 90◦, a weak, broad emission feature is evident when
τV = 10. When τV ≥ 20, the spectra display a clear absorp-
tion feature; although similar to that of smooth-density mod-
els, the feature is never deep, reflecting the shallow absorption
displayed by a single cloud (see §4.5 part I). A most peculiar
result is the reversal from absorption to an emission feature,
which emerges when τV increases beyond ∼ 100.
The complex behavior of the 10 µm feature arises from a
rather intricate interplay between the emission spectrum of a
single cloud and the collective effect of the entire cloud en-
semble. The different patterns can be understood in terms
of the competition between emission and absorption along a
given path, taking account of the flattening of the escape fac-
tor Pesc across the 10µm feature when τV is increasing (fig.
2). The behavior of the 10 µm feature is studied separately at
greater depth in §5.1 below.
3.4. Number of Clouds
Figure 6 shows model spectra of torus emission when N0,
the average of the total number of clouds along radial equato-
rial rays, varies from 2 to 15. The models produce broad IR
emission in the λ∼ 1–100 µm range. Values ofN0 larger than
15 produce a very narrow IR bump peaking beyond 60 µm.
Such SED’s have not been observed thus far, therefore N0 is
likely no larger than ∼10–15 at most.
As is evident from figure 6, when N0 increases, the emis-
sion in the near- to mid-IR region steepens considerably for
viewing close to equatorial. Composite IR SED of Seyfert
2 galaxies constructed by Silva et al. (2004) show only mild
λ F
λ
/F
A
G
N
10-3
10-2
10-1
100
10-3
10-2
10-1
0
N0 = 2q = 1
i = 0o
q = 2
100
10-3
10-2
10-1
0
λ (µm)
1 10 100
10-3
10-2
10-1
0
1 10 100
90o
10
N0 = 5
N0 = 10
N0 = 15
FIG. 6.— Dependence of the torus SED on the number of clouds along a
radial equatorial ray. Each cloud has τV = 60. Angular width σ = 45◦ , power
law radial distribution with q = 1 (left panels) and 2 (right), extending to Y
= 30. Different curves in each panel show viewing angles that vary from 0◦
(top curve) to 90◦ (bottom) in 10◦ steps.
λ F
λ
/F
A
G
N
10-3
10-2
10-1
100
λ (µm)
1 10 100
10-3
10-2
10-1
0
1 10 100
N0 = 2
i = 0o
100
90o
N0 = 10
N0 = 5
N0 = 15
10
FIG. 7.— Model spectra as in figure 6 for q = 2, only with the AGN
contribution added. For each set of parameters, the probability that the AGN
emission will actually be observed can be read from the plots of Pesc in the
lower panel of figure 2. The break in the SED at λ = 1 µm is an artefact of
our parametrization of the input spectrum (see §3.1.1, part I).
dependence on X-ray absorbing column density as long as
NH ≤ 1024 cm−2, with considerable steepening when NH is
in the range 1024–1025 cm−2. This behavior is similar to the
N0-dependence displayed in fig. 6, thus Compton thick X-ray
absorbing columns might be correlated with a larger N0. For
pole-on viewing, the 10 µm feature appears in weak emission
when N0 < 5. As N0 increases, the emission switches to ab-

6 Nenkova et al
λ F
λ
/F
A
G
N
10-3
10-2
10-1
100
λ (µm)
1 10 100
10-3
10-2
10-1
0
1 10 100
i = 0o
100
90o
σ = 45o
10
σ = 15o σ = 30o
σ = 60o
FIG. 8.— Dependence of the torus model spectra on the width parameter
σ of the Gaussian angular distribution. Each cloud has τV = 60. The cloud
radial distribution is a power law with N0 = 5 and q = 2 extending to Y = 30.
Viewing angles vary from 0◦ to 90◦ in 10◦ steps.
sorption that deepens with N0. Moving away from the axis,
the feature displays weak emission when N0 = 2 but appears
in absorption in all other cases.
In contrast with the smooth-density case, clumpy models
always display some emission at λ < 1µm that arises from
scattering of the AGN radiation toward the observer by clouds
on the torus far side. Some fraction of this radiation will al-
ways get through the torus near side. The probability for that
is controlled purely by the number of clouds since individ-
ual clouds are always optically thick at UV and optical wave-
lengths. Varying the number of clouds produces two compet-
ing effects, most clearly visible in figure 6 from the behavior
of the q = 1 models at i = 0◦. Increasing the number of clouds
from N0 = 2 to 5 raises the level of the radiation that gets
through because there are more scattering clouds. With fur-
ther increase in N0, obscuration by intervening clouds takes
over and the emerging intensity decreases. It is hard to as-
sess the observational significance of this aspect of the results.
Our models include a single type of clouds and no intercloud
medium. Such a medium with an optical depth τV of only a
few would attenuate all wavelengths shorter than ∼1 µm in
the model spectra without significantly affecting the infrared.
We plan a detailed study of these effects in future work.
Like most models presented here, fig. 6 shows only the
torus emission, corresponding to type 2 SED. Our model pre-
dictions for type 1 SED can always be obtained by adding the
AGN direct radiation. However, unlike the smooth-density
case, the probability for a clear view of the AGN depends not
only on the viewing angle but also on the number of clouds
(see §2.4). Figure 7 displays again the q = 2 models shown
in fig. 6, but this time the AGN contribution is added in. The
probability that this would be the SED actually detected in a
given source is given by the corresponding Pesc, shown in the
lower panel of figure 2. When visible, the AGN dominates
the emission at λ . 3µm. The transition from AGN to torus
domination of the SED is an important issue that requires de-
tailed observations of type 1 sources in the near- and mid-IR
regions.
3.5. The Torus Angular Width
The effect of the angular distribution width is shown in fig-
ure 8, which displays results for a few representative σ. The
spectral shapes of models with σ = 15◦ are in general agree-
ment with observed SED but the dependence on viewing an-
λ F
λ
/F
A
G
N
10-3
10-2
10-1
100
1 10 100
10-3
10-2
10-1
0
1 10 100
q = 0
i = 0o
100
90o
q = 2
q = 1
q = 3
10
λ F
λ
/F
A
G
N
10-3
10-2
10-1
100
λ (µm)
1 10 100
10-3
10-2
10-1
0
1 10 100
q = 0
i = 0o
100
90o
q = 2
q = 1
q = 3
10
Y = 10
Y = 30
FIG. 9.— Dependence of the torus model spectra on the power q of the
radial density distribution, which extends to Y = 10 in the top panels and Y =
30 in the bottom ones. N0 = 5 clouds with τV = 60 each. Angular width σ =
45◦. Viewing angles from 0◦ to 90◦ in 10◦ steps. The emission anisotropy
decreases when q increases.
gle displays a bi-modal distribution that conflicts with obser-
vations of Seyfert galaxies (§3.1). Values in the range 30◦–
50◦ produce similar spectral shapes, all in general agreement
with observations. The σ = 30◦ models provide the best match
to the behavior of the 10µm feature in the average spectra of
Seyfert 1 and 2 galaxies (see §5.1). Estimates of the torus
angular width based on statistics of Seyfert galaxies that take
proper account of clumpiness give σ ∼ 30◦ (see §6.3). At σ
= 60◦, the 10µm feature appears in pronounced absorption at
all viewing angles. Increasing the width parameter further all
the way to σ = 85◦ has little effect on the SED, except that the
dependence on viewing angle decreases, as is expected from
the approach to spherical symmetry.
3.6. Radial Profile and IR Emission Anisotropy
Figure 9 shows the SED when q, the index of the power-
law radial distribution, varies in the range 0–3 for two values
of the radial thickness Y . Since N0 is kept fixed, varying q
changes only the placement of clouds between the inner, hot-
ter parts and the outer, cooler regions, shifting the emission
between near- and far-IR. Steep radial distributions (q = 2, 3)
produce nearly identical spectral shapes for Y = 10 and 30 be-
cause the clouds are concentrated near the inner boundary in
these cases.
The variation of SED with viewing angle displayed
in fig. 9 is much smaller than in smooth-density models
(Pier & Krolik 1992, 1993; Efstathiou & Rowan-Robinson
1995; Granato & Danese 1994; Granato et al. 1997;

8 Nenkova et al
λ F
λ
/F
A
G
N
10-3
10-2
10-1
100
λ (µm)
1 10 100
10-3
10-2
10-1
0
Y = 5
Y = 10
Y = 30
Y = 100
Y = 200
1 10 100
q = 1
100
q = 1
q = 2
q = 2
10
i = 90o
i = 0o
FIG. 12.— Dependence of the SED of a clumpy torus on the radial thickness
Y = Ro/Rd, as marked. Radial distribution with q = 1 (left panels) and 2
(right). All models haveN0 = 5 clouds with τV = 60 each, and σ = 45◦. Pole-
on viewing in the top panels, edge-on at the bottom. Note that the curves in
the left-bottom panel have a similar shape at λ . 15 µm and would nearly
overlap if normalized to a common wavelength in that range instead of FAGN.
of the two populations are essentially identical within the ob-
servational errors, and note the conflict with the anisotropy
predicted by smooth-density torus models. The Lutz et al.
finding was confirmed by Horst et al. (2006), who used the
same approach with ground based, and thus better resolution,
observations at 12 µm. Buchanan et al. (2006) conducted
Spitzer observations of 87 Seyfert galaxies in the λ = 5–35
µm range and normalized the IR fluxes with the optically thin
radio emission. Although at 6 µm they find a larger variation
than Lutz et al., they also find that the emission from Seyfert
1 and 2 galaxies are within factor 2 of each other for all λ &
15 µm, and note the discrepancy with smooth-density mod-
els. Finally, the average spectra of Seyfert 1 and 2 galaxies
derived by Hao et al. (2007) from Spitzer observations have
nearly identical shapes, except for the 10µm silicate region.
The moderate level of anisotropy found in the observations
suggests that, if the torus radial thickness is & 20 then the
steeper radial profile q = 2 might be more appropriate than
q = 1. It may be noted that the clumpy torus models in
Mason et al. (2006), which utilized Y = 100, yielded the best
fits to the observations of NGC 1068 with q = 2.
4. TORUS SIZE
The fraction of the sky obscured by the torus determines the
relative numbers of type 1 and 2 sources, and the statistics of
Seyfert galaxies show that the height and radius of obscuring
dusty torus obey H/R ∼ 1 (see §6.3). Since obscuration does
not depend separately on either H or R, only on their ratio,
neither quantity is determined individually. An actual size
can only be determined from the torus emission.
4.1. SED Analysis
In the absence of high-resolution IR observations, early es-
timates of the torus size came from theoretical analysis of the
SED. For a given dust sublimation temperature, the torus in-
ner radius Rd is determined from the AGN luminosity (eq.
1). The dust temperature distribution, and with it all model
results, depends only on r/Rd. Therefore, the only size pa-
rameter that can be determined from SED modeling is the
radial thickness Y = Ro/Rd. Pier & Krolik (1992) performed
the first detailed calculations with a uniform density torus and
found Y ∼ 5–10. However, in subsequent work Pier & Krolik
(1993) speculated that this compact structure might be em-
bedded in a much larger, and more diffuse torus, extending
typically to∼ 30–100 pc. Granato & Danese (1994) extended
the smooth-density calculations to more elaborate toroidal ge-
ometries. They conclude that “The broadness of the IR con-
tinuum of Seyfert 1 nuclei requires an almost homogeneous
dust distribution extending at least to a few hundred pc (Ro/Rd
& 300 or Ro & 300L1/246 pc)” and that “broad (Ro ≃ 1000L1/246
pc) tori” would be “fully consistent with available broad-band
data and high-resolution IR spectra of Seyfert 1 and 2 nu-
clei”. Although subsequent modeling produced somewhat
smaller sizes (Granato et al. 1997; Fritz et al. 2006), the orig-
inal requirements of uniform density and large dimensions
directly reflect the large amounts of cool dust necessary for
producing the torus IR emission. This requirement arises be-
cause in smooth density distributions, the dust temperature
is uniquely related to distance from the AGN. While this
statement is strictly correct only for single-size dust grains,
even when dust size distribution in invoked in smooth dust
models, the observations still favor clumpy dust distribution
(Schartmann et al. 2005).
The one-to-one correspondence between distance and tem-
perature does not hold in clumpy media, where different dust
temperatures coexist at the same distance and where the same
temperature can be found at different distances (see part I,
§3.1.2 and §4.2). For example, in the model discussed in
Fig. 7 from part I, the dust temperature at Y = 10 ranges from
150 K to 600 K, while Schartmann et al. (2005) find using
smooth models with realistic dust size distribution that the
temperature range at Y = 10 is 250-300 K (i.e. a ratio of 1.2
vs. 4 for clumpy dust). In contrast with smooth density dis-
tributions, a clumpy torus contains cool dust on the dark sides
of clouds much closer to the heating source and thus can emit
IR efficiently from its inner regions.
Figure 12 shows our model results for the SED of clumpy
tori with various radial thicknesses for q = 1 and 2. In spite of
the factor 40 variation in torus thickness, the SED is quite
similar for all the q = 2 models. The reason is simple—
irrespective of the torus size, at least 80% of all clouds are
located within r ≤ 5Rd in this case. The models with q = 1
display discernible variations, but these variations are mostly
confined to λ & 15µm. The large differences apparent at
shorter wavelengths in the edge-on viewing do not reflect in-
trinsic variation of the SED, only the scaling with the bolo-
metric flux. If these curves were scaled instead to the same
value at, say, 2µm, they would all overlap up to λ ∼ 15µm,
similar to the pole-on viewing. These differences can be fur-
ther understood with the aid of figure 13, which shows the
fraction of the overall flux contained within circular apertures
of increasing size. This fraction, as well as the brightness
distribution, is a function of θ/θd (= r/Rd), where θ is angu-
lar displacement from the center and θd = Rd/D. The figure
shows that at wavelengths shorter than 5µm, almost all the
flux is originating from inside 3θd irrespective of the value of
Y . Therefore, such wavelengths cannot determine the torus
size. In the q = 2 case, even longer wavelengths cannot dis-
tinguish between the different sizes because 80% of the flux
always originates from the inner 10 θd. In the q = 1 case the
portions beyond 10θd contribute significantly to the flux of a
larger torus, but only at wavelengths longer than ∼12–15µm.
These results show that the model SED do display apprecia-
ble differences among tori of different sizes when q = 1 and
that determining the torus size in this case would require mea-

AGN Dusty Tori: II. Observational Implications 9
q = 1
i = 0o i = 90o
Y = 10
0.00
0.25
0.50
0.75
1.00
Y = 30
Fr
ac
tio
n

o
f E
n
cl
o
se
d
Fl
u
x
0.00
0.25
0.50
0.75
1.00
1 10 100
0.00
0.25
0.50
0.75
1.00
1 10 100
588
588
2.2
588
q = 2
i = 0o i = 90o
Y = 30
θ/θd
1 10 1001 10 100
588
588
2.2
588
Y = 30
Y = 10Y = 10
Y = 30
2.2
588
2.2
588
Y = 100Y = 100 Y = 100 Y = 100
Y = 10 Y = 10
Y = 30Y = 30
2.2
588
24
70
1010 10100
θ/θd
24
2.2 µm
4.8 µm
12 µm
24 µm
70 µm
588 µm
24
2.2
588
FIG. 13.— Fraction of the torus flux enclosed within a circle with angular radius θ centered on the AGN. Wavelengths, in µm, as labeled (some labels omitted
for clarity). θd is the angle equivalent of the torus inner radius Rd (eq. 1) at the observer’s location; for reference, θd= 0.′′02 for Rd = 1 pc at 10 Mpc. All models
have N0 = 5, τV = 60, σ = 45◦ and q = 1 or q = 2, as marked. In each case, pole-on viewing in the left panels, edge-on at right. Torus sizes, from top to bottom,
are Y = 10, 30 and 100.
surements of its flux at λ& 15 µm. Because of the large beam
sizes at such long wavelengths, current observations generally
cannot distinguish between the contributions of the torus and
its surroundings to the overall flux. For example, as noted
in the Introduction, in NGC 1068 the torus contributes less
than 30% to the 10 µm flux measured with apertures ≥ 1′′
(Mason et al. 2006). The q = 2 density profile, which might be
the more common radial distribution (§3.6), does not gener-
ate any discernible distinctions among spectral shapes. There-
fore, the radial size of a clumpy torus cannot be constrained
by SED measurements. Only high-resolution observations can
determine the torus size — the SED does not have the neces-
sary discriminative power.
4.2. Brightness Profiles
Because of the discrete nature of a clumpy medium, differ-
ent lines of sight will generally produce a different brightness
even when crossing similar regions. Our formalism provides
the statistical average along such rays; fluctuations around this
average can be large (see §2.1, part I).
Figure 14 shows model intensity profiles for pole-on view-
ing of a torus with Y = 30. The curves show only the torus
emission, starting at its inner edge θ = θd. The AGN emission,
which is not shown, would produce a narrow spike between
0 ≤ θ ≤ θAGN, where θAGN/θd ∼ (Tsub/Tb,AGN)2 and Tb,AGN is
the AGN brightness temperature (e.g., Ivezic´ & Elitzur 1997).
Therefore, θAGN/θd ≪ 1 under all circumstances. The set
of displayed wavelengths extends from the K-band, where
most of the current imaging observations are performed, to
588 µm, one of the wavelengths that will become available
for high-resolution imaging when ALMA is fully operational.
The torus intensity is highest on or close to its inner edge.
The brightness is highest around 12 µm, as is evident from
the figure bottom panel. For both radial density profiles used
in this figure, the brightness declines to half its peak value
within θ < 5θd at all displayed wavelengths. At 12µm and
shorter wavelengths, the brightness declines to 1% of peak
value within θ ≤ 10θd. Evidently, observations attempting to
probe the torus structure must combine high resolution with a
large dynamic range.
Near-IR wavelengths provide little information about the
torus structure and size. As is evident from the figure, at 2 µm
it would be difficult to distinguish between q = 1 and 2 radial
density distributions even with high-resolution observations.
The steep brightness decline at these wavelengths also makes
it practically impossible to determine the torus full size. Since
the brightness falls under 1% of its peak value at θ = 4θd for
either density profile, determining whether the torus ends at
that point or continues to larger radii would be a difficult task.
A Y = 10 torus is indistinguishable from the inner 10θd of a
torus as large as Y = 100, as is evident also from figure 13.
As the wavelength increases, the brightness fall-off becomes
less steep. VLTI interferometry has angular resolution of or-
der 0.′′01 at 12 µm, but it would still be difficult to distinguish
between the two displayed radial density profiles even in sys-
tems where θd is of a similar order of magnitude. The two
density profiles produce distinctly different brightness profiles
at 70µm, but there are no instruments with the required angu-
lar resolution at that wavelength. In the foreseeable future,
ALMA seems to be the only facility with a realistic chance
to determine through 588 µm observations the radial cloud
distribution and whether a torus does extend beyond Y = 30.
4.3. Observations
With the advent of high-resolution IR observations, di-
rect imaging is now available for some AGN tori, and up-

10 Nenkova et al
θ / θd
1 10
N
o
rm
al
iz
ed
In
te
n
sit
y
Pr
o
fil
es
10-4
10-3
10-2
10-1
100
q = 1
q = 2
588 µm
70
12 µm
2.2 µm
I ν

(Jy
/m
as
2 )
10-6
10-5
10-4
10-3
10-2
10-1
q = 1
q = 2
λ (µm)
1 10 100 1000
T b
(K
)
10
100
1000
q = 1
q = 2
FIG. 14.— Surface brightness for torus models with τV = 60, N0 = 5, σ
= 45◦, Y = 30 and q = 1 and 2, as indicated. The top panel shows the radial
variation of intensity with angular displacement from the center for pole-on
viewing and a set of wavelengths as marked. The AGN emission, which is not
shown, corresponds to a narrow spike at θ/θd ≪ 1 (see text). Each intensity
profile is normalized to its brightness level at θ = θd, shown in the bottom
panel together with the corresponding brightness temperature.
per limits have been set on the dimensions of the nuclear IR
source in others. Interferometric observations at 8–13 µm
with the VLTI have resolved by now the nuclear region in
three AGN: NGC 1068, Circinus and Cen A. The thermal
emission in all three cases is rather compact. In NGC 1068
Jaffe et al. (2004) find that the emission extends to R = 1.7 pc.
Poncelet et al. (2006) reanalyzed the same data with slightly
different assumptions and obtained a similar result, R = 2.7
pc. The AGN bolometric luminosity is ∼ 2×1045 erg s−1 in
this case (Mason et al. 2006), so that Rd is ∼0.6 pc and the
torus mid-IR emission is confined within ∼3–5 Rd. In Circi-
nus, Tristram et al. (2007) find that the torus emission extends
to R = 1 pc. The AGN bolometric luminosity is ∼ 8×1043
erg s−1 (Oliva et al. 1999), so Rd ≃ 0.1 pc and the outer radius
of the mid-IR emission is ∼10Rd. The nature of the mid-
IR emission from the Cen A nucleus is somewhat involved—
Meisenheimer et al. (2007) conclude that it contains an un-
resolved synchrotron core and thermal emission within a ra-
dius of ∼0.3 pc. Since the AGN bolometric luminosity is ∼
1×1043 erg s−1 (Whysong & Antonucci 2004), Rd is ∼0.04 pc
and the torus emission does not exceed ∼8Rd in this source.
One other case of resolved mid-IR emission involves NGC
7469, where Soifer et al. (2003) find a 12.5 µm compact nu-
clear structure contained within R < 13 pc. Unfortunately,
NGC 7469 is a clear case where the IR signature is dominated
by the starburst component even though the AGN dominates
the optical classification (Weedman et al. 2005), therefore the
resolved compact structure cannot be identified with the torus
(see also Davies et al. 2004).
Although there are no other reports of resolved torus emis-
sion at this time, upper limits on the torus size have been
reported in some additional sources. Prieto & Meisenheimer
(2004) studied a number of AGN in the 1–5 µm range. In
all cases the observations show unresolved nuclear emission
at these wavelengths, setting upper limits on the torus ra-
dius of . 5–10 pc, depending on the target distance. Even
more significant are the upper limits reported at mid IR.
Radomski et al. (2003) place an upper limit R < 17 pc at 10
µm and 18 µm on the nuclear component in NGC 4151, while
Soifer et al. (2003) place the tighter constraint R < 5 pc at
12.5 µm. Soifer et al. also find an upper limit R < 14 pc for
the 12.5 µm compact nuclear emission in NGC 1275.
4.4. How Big is the Torus?
All current observations are consistent with a torus radial
thickness Y = Ro/Rd that is no more than ∼ 20–30, and per-
haps even as small as ∼ 5–10. Although larger values cannot
be ruled out, nothing in the currently available IR data re-
quires their existence. Similarly, molecular line observations
do not give any evidence for large toroidal structures with
the height-to-radius ratio H/R ∼ 1 required from unification
statistics (see §6.3 below). In NGC 1068, Schinnerer et al.
(2000) find from CO velocity dispersions that at R≃ 70 pc the
height of the molecular cloud distribution is only H ∼ 9–10
pc, for H/R ∼ 0.15. Galliano et al. (2003) model H2 and CO
emission from the same source with a clumpy molecular disk
with radius 140 pc and scale height 20 pc, for the same H/R
∼ 0.15. Therefore, although resembling the putative torus,
the distribution of these clouds does not meet the unification
scheme requirement H/R∼ 1. Evidently, the detected molec-
ular clouds are located in a thinner disk-like structure outside
the torus. Recent 10µm imaging polarimetry of NGC 1068
by Packham et al. (2007) shed some light on the continuity
between the torus and the host galaxy’s nuclear environments.
As is evident from the above discussion, determining the
torus actual endpoint is rather difficult, if not impossible; in
fact, insisting on an endpoint for a steep 1/r2 distribution is
meaningless in practice (with the currently available observa-
tions). The torus is embedded in the central region of the host
galaxy, and the steep radial decline of its brightness implies
that its emission is unlikely to be cleanly separated from the
surroundings. The only observations holding realistic chance
for doing that are future high resolution sub-mm measure-
ments with ALMA. Even those would require detailed anal-
ysis that takes into account the emission from both the torus
and its surrounding.
It seems safe to conclude that there is no compelling evi-
dence at this time that torus clouds beyond Y ∼ 20–30 need
be considered, although such large sizes cannot be excluded.
From eq. 1, a conservative upper bound on the torus outer ra-

12 Nenkova et al
-1
0
1
S 1
0
-1
0
1
i = 0o i = 90o
σ=15oσ=15o
-2
0
2
EW
10

( µ
m
)
-2
0
2
i = 0o i = 90o
N0= 2
5
10
15
σ=15o
σ=30o
σ=15o
σ=30o
N0= 2
5
10
15
N0= 2
5
10
15
N0= 2
5
15
N0= 2
5
10
15
N0= 2
5
10
15
τV
10 100
-1
0
1
10 100
N0= 2
5
10
15
σ=45oN0= 2
5
10
15
σ=30o
10
σ=45o
σ=30oN0= 2
5
Col 2 vs Col 3
Col 2 vs Col 4
Col 2 vs Col 5
Col 2 vs Col 6
τV
10 100
-2
0
2
10 100
N0= 2
5
10
15
σ=45o
σ=45oN0= 2
5
10
15
N0= 2
5
10
15 10
15
FIG. 16.— Indicators of the 10 µm silicate feature (see eq. 3): variations of the feature strength (left) and equivalent width (right) with the optical depth τV of
individual clouds. Model parameters are q = 2, Y = 30. Other parameters as marked. The overall optical depth along radial equatorial rays extends all the way to
N0τV = 4,500 in these models, yet the 10µm absorption feature is never deep.
emission feature emerges in edge-on viewing at τV & 100.
This peculiarity arises because individual clouds become op-
tically thick across the entire feature. The radiation emerging
at this spectral range is then dominated by emission from the
bright faces of clouds on the torus far side escaping through
clear lines of sight. The effect becomes more pronounced as
N0 decreases.
The 10 µm feature peaks at 10.0 µm in the absorption co-
efficients from Ossenkopf et al. (1992), and radiative transfer
effects introduce occasional small shifts (no larger than 0.5
µm, mostly toward shorter wavelengths) around this value in
the emerging spectra. To quantify the feature’s strength and
width we introduce two indicators:
S10 = ln
Fλ
Fc,λ
, EW10 =
∫ 14µm
7µm
Fλ − Fc,λ
Fc,λ
dλ (3)
The feature strength S10 is evaluated at the extremum near
10.0 µm of the continuum-subtracted spectrum. Positive val-
ues of S10 indicate an emission feature, negative values an ab-
sorption feature. Delineating the feature from noise in the data
requires a certain minimum for the equivalent width EW10,
depending on the detection system. Our sign definitions are
matched for both indicators so that absorption produces a neg-
ative EW10, the opposite of the standard.
Figure 16 displays the variations of S10 and EW10 with the
single cloud optical depth τV for pole-on and edge-on viewing
and various model parameters that bracket the likely range in
AGN tori. If the feature width were the same in all models,
S10 and EW10 would be equivalent to each other5, but because
of variations in the feature shape (see figure 15), EW10 con-
5 If the feature is parametrized as aFc,λe−(δλ/∆)
2
, where δλ is wavelength
shift from the peak, then S10= ln(1 + a) while EW10 =
√
pi a∆.
tains independent information. Figure 16 shows that pole-on
viewing produces an emission feature only for a limited set
of parameters. Clouds heated indirectly do not produce the
emission feature when τV & 20 (sec. 3.2, part I). The radia-
tion from a directly illuminated cloud displays the feature in
emission only toward directions with a view of a sufficiently
large fraction of the cloud’s illuminated face (see fig. 12, part
I). An observer along the pole of a toroidal distribution will
detect an emission feature only from direct viewing of clouds
located within β < 45◦ from the equator. Such clouds will be
obscured by foreground clouds in most cases, except when the
torus width is small (σ = 15◦) or the overall optical depth of
the clumpy medium is small (small N0 and τV ). Therefore, at
i = 0◦, only a small region of parameter space produces mod-
els with a weak emission feature while most other parameters
produce either a featureless SED or a weak absorption feature.
It is also evident from figure 16 that edge-on viewing is insen-
sitive to the angular thickness σ. Irrespective of optical depth,
the absorption feature produced by a clumpy torus is never
deep. Figure 17 shows the variation of the two indicators with
viewing angle for one value of τV , a likely representative of
actual torus clouds.
Comparison with observations is hampered by the angular
resolution problem. In the Mason et al. (2006) observations
of NGC1068, the feature strength in the central 0.′′4, presum-
ably dominated by the AGN torus, is S10 = −0.4. Scanning
along the ionization cones in 0.′′4 steps shows large varia-
tions in S10 and a strong asymmetry in its spatial distribution.
Measurements with larger apertures contain significant con-
tribution from the ionization cones, and Spitzer observations
may be further contaminated by still larger dusty structures.
Nevertheless, when these observations produce clear differ-
ences between type 1 and type 2 sources, it seems reason-

AGN Dusty Tori: II. Observational Implications 13
N0 = 2
S 1
0
-1
0
1
N0 = 2
-1
0
1
N0 = 2
Viewing Angle, i (deg)
0 30 60 90
-1
0
1
σ = 45o
σ = 30o
σ = 15o
10 15
5
10 15
5
5
10 15
N0 = 2
EW
10
(µ
m
)
-2
0
2
N0 = 2
-2
0
2
N0 = 2
Viewing Angle, i (deg)
0 30 60 90
-2
0
2
σ = 45o
σ = 30o
σ = 15o
10
15
5
10
15
5
5
10
15
FIG. 17.— Variation of the 10 µm feature strength (left) and equivalent width (right) with viewing angle. Model parameters are τV = 60 q = 2, Y = 30. Other
parameters as marked.
able to attribute such global trends to differences in viewing
angles and to compare our model results with the observed
trends while considering the actual numerical values only as
guidance. The most detailed data come from the recent com-
pilation of Spitzer mid-IR spectra by Hao et al. (2007). Al-
though a loosely defined sample, it is the largest gathered thus
far, including 24 type 1 quasars, 45 Seyfert 1 and 47 Seyfert
2 galaxies. The QSOs display almost exclusively an emis-
sion feature with 0.45 ≥ S10 ≥ 0.05, but the Seyfert 1 galax-
ies are clustered around zero feature strength, occupying the
range 0.35 ≥ S10 ≥ −0.25. Almost all Seyfert 2 galaxies dis-
play the 10 µm feature in absorption, with the distribution
showing a strong peak at −0.1 ≥ S10 ≥ −0.4. In addition to
the Hao et al. results, an intriguing recent development comes
from the Spitzer observations of seven high-luminosity type 2
QSOs by Sturm et al. (2006). Although the individual spec-
tra appear featureless, the sample average spectrum shows
the 10µm feature in emission. More recently, Polletta et al.
(2008) did find the feature in absorption in a larger sam-
ple of mid-IR selected obscured QSOs, while Weedman et al.
(2006) found the 10µm feature either in absorption or absent
in a sample of X-ray and mid-IR selected obscured AGN.
A striking characteristic of all AGN spectra is the ab-
sence of any deep 10 µm absorption features. Given the
large optical depths implied by the X-ray data, smooth dust
models predict very deep absorption features. Shallow ab-
sorption features are a hallmark of clumpy dust distributions
irrespective of geometry (part I), and the mild absorption
strengths evident in our model results reflect this general prop-
erty. In contrast, ULIRGs display features that reach ex-
treme depths (Hao et al. 2007). This different behavior can
be attributed to deep embedding in a dust distribution that is
smooth, rather than clumpy (Levenson et al. 2007; see also
Spoon et al. 2007, Sirocky et al. 2008). In principle, cold
foreground screens intercepting the intrinsic IR emission of
ULIRGs could also account for the deep silicate absorption
in these sources. However, such an explanation would require
two distinct dust components: a very optically thick dust blan-
keting the primary radiation source and reprocessing its in-
trinsic radiation to emerge at the enormous IR luminosities
that identify ULIRGs, and an additional foreground screen
that absorbs the reprocessed IR radiation to produce the deep
silicate absorption. To remain cold, the foreground screen
cannot provide the main reprocessing of the huge intrinsic
luminosity, yet it must always be aligned along the line of
sight with the primary dust blanket. Furthermore, the aligned
screens have to be selectively associated with ULIRGs identi-
fied with LINER- and H II-like features because, unlike AGN,
these sources never show shallow absorption (see fig. 11 in
Sirocky et al. 2008). Such screens present a contrived solu-
tion for the 10µm absorption in ULIRGs. In contrast, a single
entity of smooth-density embedding dust that is both geomet-
rically and optically thick accounts naturally for the total IR
characteristics of deeply absorbed ULIRGs.
Our calculations show that clumpy tori with N0 = 2 never
produce an absorption feature and thus are ruled out for
Seyfert galaxies, though perhaps not for quasars (see §6.4 be-
low). The properties of the 10 µm feature found in Seyfert
galaxies are reproduced by our models for N0 ∼ 5–15, σ
∼15◦–45◦ and τV ∼30–100. When τV increases above ∼
100, these models produce at equatorial viewing a weak 10
µm emission feature with a small equivalent width, offering

14 Nenkova et al
log λFλ(1.6µm)/λFλ(3.5µm)
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5
lo
g
λF
λ(
3.
5µ
m
)/λ
F λ
(10
µm
)
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Sy 1.8-2 Sy 1-1.5
N0= 5 (white)
N0=10 (gray)
N0=15 (black)
i = 90o
i = 0o
.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
20
40
60
100
200
τV =
FIG. 18.— Data and model results for a color-color diagram. Dashed
lines outline the areas occupied by type 1 and type 2 sources in the
Alonso-Herrero et al. (2003) expanded CfA sample of Seyfert galaxies. Mod-
els have Y = 30, q = 2, σ = 45◦, and τV and N0 as coded, respectively, with
symbols and shades. The AGN flux is added to the torus emission (type 1
model spectrum) whenever the probability for direct view of the center ex-
ceeds 50%. Each model produces a track. Positions along the track corre-
spond to viewing angles, varying in steps of 10◦ from i = 0◦ on the right to i
= 90◦ on the left.
a potential explanation for the Sturm et al. finding in QSO2:
the small equivalent width would make it hard to discern the
feature in individual sources, bringing it out of the noise only
in composite spectra. Therefore, if this finding is verified it
could indicate that the optical depths of torus clouds perhaps
are larger in QSOs than in Seyfert galaxies. However, this
is not a unique interpretation. Another possible explanation
is that the cloud number N0 decreases as the luminosity in-
creases. This point is discussed further in §6.4 below.
5.1.1. Apparent Optical Depth
The overall optical depth at visual along a radial ray in the
torus equatorial plane is N0τV . With the standard dust prop-
erties employed here, the magnitude of the optical depth at
10µm is τ10 = 0.07N0τV . Another quantity frequently em-
ployed in data analysis of absorption features is the apparent
optical depth at maximum absorption, obtained from I = e−τapp
where I is the residual intensity. Therefore, from eq. 3,
τapp,10 = −S10. When the absorption is by a cold foreground
screen that does not emit itself at these wavelengths, τapp,10
is the actual 10µm optical depth of the screen. But when the
absorption arises from a temperature gradient in the emitting
dust, τapp,10 can differ substantially from the actual optical
depth, and the dependence of the two quantities on the dust
column may bear little resemblance to each other. This is es-
pecially true of the torus emission. As is evident from figures
16 and 17, the relation between τ10, the actual optical depth,
and τapp,10 is multi-valued. Furthermore, although τ10 exceeds
300 in these figures, τapp,10 is never larger than unity. The ap-
parent optical depth τapp,10 is a poor indicator of the actual
optical depth.
5.2. Color Analysis
Color-color plots, showing correlations between two col-
ors, are a useful way to separate objects with similar
types of spectra and reveal underlying physical similarities.
Alonso-Herrero et al. (2003) present data for nuclear fluxes
from visual to 16 µm for an expanded set of the CfA sam-
ple of Seyfert galaxies. Removing all known sources of bias
in the original CfA selection, they have constructed what is
arguably the most complete sample of AGN currently avail-
able. Torus observations at wavelengths up to 10 µm are
likely to be less contaminated by emission from the surround-
ings. From the Alonso-Herrero et al. (2003) data we find that
fluxes at 1.6 µm, 3.5 µm and 10 µm provide a useful set
of colors for comparison with our model results. Compared
with other combinations, the models separate better with this
choice of colors because the spectral slopes change the most
around the selected wavelengths. Figure 18 shows colors for
sets of torus models with σ = 45◦, Y = 30, q = 2 and vari-
ous combinations of τV and N0. The AGN flux is added to
the torus emission whenever the probability for direct view
of the nucleus exceeds 50%. In each case the colors depend
on the viewing angle, resulting in a track of model results.
Colors corresponding to type 1 viewing populate the upper
right end of the track, type 2 viewing the lower left. Model
parameters that explain the observations of the 10µm fea-
ture also give good qualitative agreement with the data from
Alonso-Herrero et al. (2003), which fall inside the two re-
gions delineated with dashed lines in the figure. While type
2 models are spread out along the track, type 1 are grouped
together more closely at the upper end since their spectra are
dominated by the AGN continuum and thus are similar despite
the broad range of parameters.
6. ADDITIONAL IMPLICATIONS OF CLUMPINESS
Comparison with IR observations shows that the likely
range for optical depths of individual torus clouds is τV ∼
30–100 and there are N0 ∼ 5–15 clouds, on average, along
radial equatorial rays. Assuming standard dust-to-gas ratio,
the column density of a single cloud is N(1)H ∼ 1022–1023 cm−2
and the torus equatorial column density is N(eq)torus = N0N(1)H ∼
1023–1024 cm−2. Taking account of the torus clumpiness has
immediate implications for a number of other issues not di-
rectly related to its IR emission.
6.1. The Torus Mass
As shown in §2.3 of part I, the total mass in torus clouds
can be written as Mtorus = mH N(1)H
∫
NC(r,β)dV ; note that Mtorus
does not involve the volume filling factor. With the cloud dis-
tribution from eq. 2 and taking for simplicity a sharp-edge
angular distribution, so that the integration is analytic, the
torus mass is Mtorus = 4πmH sinσN(eq)torusRd2Y Iq(Y ), where Iq =
1, Y/(2 lnY ) and 13Y for q = 2, 1 and 0, respectively. Taking
Rd from eq. 1, the mass ratio of the torus and the central black
hole is
Mtorus
M•
= 2×10−4 L
LEdd
sinσN(eq)torus ,23 Y Iq (4)
where LEdd is the Eddington luminosity and N(eq)torus,23 is the
equatorial column density in 1023 cm−2. Since the radial
thickness Y is likely . 20–30 (§4), the torus mass is always
negligible in comparison with M• when q = 2. If the radial
cloud distribution is flatter, eq. 4 may constrain the torus prop-
erties to keep its mass below that of the black-hole.
6.2. Total Number of Clouds
As shown in part I, the total number of clouds, ntot, is the
only torus property whose estimate involves the cloud size
Rc. Equivalently, Rc can be replaced by the volume filling
factor φ, since inserting eq. 2 into eq. 3 of part I yields Rc =

AGN Dusty Tori: II. Observational Implications 15
φRd/N0 at the torus inner edge. If φ is constant throughout the
torus then ntot ≃N 30/φ2 for the 1/r2 distribution, independent
of the torus radial thickness Y . For example, if the volume
filling factor is 10%, in order to encounter N0 = 5–10 clouds
along each radial equatorial ray, the torus must contain ntot ≃
104–105 clouds,
6.3. AGN Unification
The classification of AGN into types 1 and 2 is based on
the extent to which the nuclear region is visible. In its stan-
dard formulation, the unification approach posits the viewing
angle as the sole factor in determining the AGN type, and
this is indeed the case for any smooth-density torus whose
column density declines with angle β away from the equato-
rial plane. The AGN is obscured from directions that have
e−τV(β) ≫ 1 and visible from those with e−τV(β) ≪ 1. Be-
cause of the steep variation of e−τ with τ , the transition be-
tween these two regions is sharp, occurring around the direc-
tion where τV(β) = 1. Denote this angle σ then, so long as
τV(0)≫ 1 and τV( 12π)≪ 1, all AGN viewed at 0 ≤ i < 12π −σ
appear as type 1 sources, those at 12π −σ ≤ i ≤ 12π as type 2.
If f2 denotes the fraction of type 2 sources in the total popu-
lation then f2 = sinσ for all smooth-density tori, irrespective
of their specific angular profiles. This relation has been em-
ployed in all studies of source statistics performed to date.
From statistics of Seyfert galaxies Schmitt et al. (2001) find
that f2 ≃ 70%, hence their estimate σ ≃ 45◦. The issue is cur-
rently unsettled because Hao et al. (2005) have recently found
that f2 is only about 50% in Seyfert galaxies, or σ ≃ 30◦.
Within the clumpy torus paradigm, the difference between
types 1 and 2 is not truly an issue of orientation but of prob-
ability for direct view of the AGN. Since that probability
is always finite, type 1 sources can be detected from what
are typically considered type 2 orientations, even through the
torus equatorial plane: if N0 = 5, for example, the prob-
ability for that is e−5 = 1/148 on average. This might of-
fer an explanation for the few Seyfert galaxies reported by
Alonso-Herrero et al. (2003) to show type 1 optical line spec-
tra together with 0.4–16 µm SED that resemble type 2. Con-
versely, if a cloud happens to obscure the AGN from an ob-
server, that object would be classified as type 2 irrespective
of the viewing angle. In cases of such single cloud obscu-
ration, on occasion the cloud may move out of the line-of-
sight, creating a clear path to the nucleus and a transition to
type 1 spectrum. The time scale for such an event is deter-
mined by the cloud size and velocity. Neither quantity can be
found from the SED since optical depth is the only property
of a single cloud that can be determined from SED analysis.
However, at a distance rpc (in pc) from a black-hole with mass
107M•7 (in M⊙), the local Keplerian speed is 208(M•7/rpc)1/2
km s−1 and resistance to tidal sheer implies that the size of
a cloud with column density 1023NH,23 cm−2 is restricted to
. 1016NH,23r3pc/M•7 (e.g., Elitzur & Shlosman 2006). The ra-
tio of this cloud size and local Keplerian speed produces a
time scale of 17NH,23r3.5pc /M1.5•7 years, an order-of-magnitude
estimate for a cloud crossing time across the line of sight. Al-
though the likelihood of catching such crossing by chance is
small, transitions between type 1 and 2 line spectra have been
observed in a few sources (see Aretxaga et al. 1999, and ref-
erences therein), and Goodrich (1989, 1995) has argued that a
couple of these cases are consistent with the change in redden-
ing expected from cloud motion across the line of sight. It is
worthwhile conducting monitoring observations in an attempt
to detect additional such transitions. The most promising can-
didates would be obscured systems with relatively small X-
ray obscuring columns, which may minimize the number of
clouds along the line of sight, small torus sizes, i.e., lower
luminosities, and large black-hole masses.
Accounting for the torus clumpiness, the fraction of type 2
sources is f2 = 1 −
∫ pi/2
0 e
−NT(β) cosβdβ (eq. 9, paper I). The
sharp-edge clumpy torus has f2 = (1 − e−N0) sinσ, practically
indistinguishable from a smooth-density torus when N0 ex-
ceeds ∼ 3–4. However, the situation changes fundamentally
for soft-edge distributions because at every viewing angle,
the probability of obscuration increases with the number of
clouds. As is evident from figure 19, the Gaussian distribution
produces a strong dependence on N0 and significant differ-
ences from the sharp-edge case. Since the sharp-edge angular
distribution is ruled out by observations (§3.1), the fraction of
obscured sources depends not only on the torus angular width
but also on the average number of clouds along radial rays.
While the fraction f2 = 70% requires σ = 45◦ in the sharp-edge
case, in a Gaussian clumpy torus it implies σ = 33◦ whenN0 =
5 and σ = 27◦ when N0 = 10; in terms of the torus height and
radius, H/R (= tanσ) is reduced from ∼ 1 to ∼ 0.7. It is note-
worthy that the behavior of the 10µm feature in the σ = 30◦
models comes closest to matching the observed averages of
both type 1 and type 2 AGN, as is evident from figure 16.
6.4. A Receding Torus?
The fraction f2 of obscured AGN decreases when the bolo-
metric luminosity increases. This has been verified in a large
number of observations that estimate the luminosity depen-
dence of either f2 or f1 (the fraction of unobscured sources),
or differences between the luminosity functions of type 1 and
2 AGN (see Hao et al. 2005; Simpson 2005; Maiolino et al.
2007). As is evident from figure 19, the observed decrease of
f2 when L increases can be produced by either a decrease of σ
at constantN0 or a decrease ofN0 at constant σ. Both options
are equally plausible because the torus inner radius increases
as L1/2 (eq. 1). The decreasing-σ option would arise if the
torus height is independent of luminosity or increases more
slowly than L1/2, the decreasing-N0 option would arise if the
torus outer radius is independent of luminosity or increases
more slowly than L1/2.
The observed trend of f2 to decrease with L may arise from
either σ or N0 or both. Source statistics cannot distinguish
between the various possibilities, the only way to decide be-
tween them is to find L-dependence in other observable quan-
tities. The 10 µm silicate feature offers such an indicator
(§5.1). Among type 1 AGN, quasars consistently produce
an emission feature but Seyfert galaxies are featureless on
average, displaying either weak emission or absorption scat-
tered around zero feature strength. In type 2 AGN the feature
switches from clear absorption in Seyfert galaxies to appar-
ent emission in QSO2. That is, in both type 1 and type 2
AGN the feature moves toward emission with the increase
from Seyfert to quasar luminosities. As is evident from fig-
ure 16, the decreasing-N0 option naturally produces such a
universal trend: the feature appears in emission for both pole-
on and edge-on viewing when N0 decreases to ∼ 2 at a fixed
σ. In contrast, the decreasing-σ option produces the observed
trend toward stronger emission feature only in type 1 AGN,
not in type 2; varying σ has virtually no effect on the 10µm
feature in type 2 viewing. Explaining the switch toward ap-
parent emission feature in QSO2 would require that in this

16 Nenkova et al
N0
2 4 6 8 10 12 14 16 18 20
0
20
40
60
80
100
σ = 10°
20°
30°
40°
50°
σ (deg)
0 20 40 60 80
f 2

(%
)
0
20
40
60
80
100
N0 = 2
20 10 5
sharp-edge
3
(a) (b)
FIG. 19.— AGN statistics: The fraction f2 of obscured sources for a clumpy torus with Gaussian angular distribution as a function of (a) the torus width
parameter σ and (b) the cloud number N0. The fraction decreases when either σ decreases at a fixed N0 or N0 decreases at a fixed σ. The dashed line in panel
(a) is for a clumpy torus with sharp-edged angular profile and N0 & 3–4.This curve describes also the fraction f2 for every smooth-density torus, whatever its
angular distribution.
case higher luminosities not only reduce σ but are also ac-
companied by an increase in the optical depth of individual
clouds.
As is evident from this discussion, current observations, if
accepted at face value and assuming that the torus contribu-
tion dominates the 10 µm spectral range on average, can be
explained if an increasing luminosity causes a decrease in the
number of clouds N0. Whether or not this is also accompa-
nied by a decrease in the torus angular width cannot be ruled
in or out. Obscuration statistics and the 10µm feature do not
yet provide decisive information to uniquely constrain the be-
havior of the torus parameters with increasing luminosity.
The decreasing-σ scenario is known as the receding torus
model, first suggested by Lawrence (1991). It is intriguing
that Arshakian (2005) and Simpson (2005) derived indepen-
dently an almost identical relation tanσ ∝ L−0.27. However,
both studies, as well as every other analysis of obscuration
statistics thus far, were based on sharp-edge angular obscura-
tion. Removing this assumption affects profoundly the foun-
dation of the receding torus model because the dependence
on the number of clouds necessitates analysis with two free
parameters, therefore σ cannot be determined without N0.
6.5. X-rays and the AGN Torus
Dusty material absorbs continuum radiation both in the
UV/optical and X-rays, therefore the dusty torus also provides
X-ray obscuration. But dust-free gas attenuates just the X-ray
continuum, so clouds inside the dust sublimation radius will
provide additional obscuration only in this band.
Observations give overwhelming evidence for the orienta-
tion dependent X-ray absorption expected from AGN unifi-
cation. In general, the 2–10 keV X-ray continuum is heav-
ily obscured in type 2 sources and relatively unobscured in
type 1 AGN (see Maiolino & Risaliti 2007, and references
therein). The strong orientation-dependence of the absorp-
tion cannot be attributed to the host galaxy because the AGN
axis, as traced by the jet position angle, is randomly ori-
ented with respect to the galactic disk in Seyfert galaxies
(Kinney et al. 2000) and the nuclear dust disk in radio galax-
ies (Schmitt et al. 2002). Yet in spite of the overall correspon-
dence between the optical and X-ray obscuration, there is a
significant number of AGN for which the expected charac-
teristics are different in the two bands. Although substan-
tial X-ray absorption is common among type 2 AGN, there
are also unabsorbed X-ray sources that present only narrow
emission lines in their optical spectra. Such cases can be ex-
plained with the observational selection effect suggested by
Severgnini et al. (2003) and Silverman et al. (2005): in these
sources, the optical light of the host galaxy outshines the AGN
continuum and broad lines. This suggestion is supported by
the subsequent studies of Page et al. (2006) and Garcet et al.
(2007). The opposite case, obscuration only in X-rays, exists
too—there are type 1, broad line AGN with significant X-ray
absorption (Perola et al. 2004; Eckart et al. 2006; Garcet et al.
2007). Extreme cases include quasars whose optical spectrum
shows little or no dust extinction while their X-ray continuum
is heavily affected by Compton thick absorption (Braito et al.
2004; Gallagher et al. 2006). This cannot be attributed to ob-
servational selection effects.
Obscuration that affects the X-rays but not the optical arises
naturally from absorption by dust-free clouds. Conclusive ev-
idence for such absorption comes from the short time scales
for transit of X-ray absorbing clouds across the line of sight,
which establish the existence of obscuring clouds inside the
dust sublimation radius (Risaliti et al. 2002). Extreme cases
involve 4 hour variability (Elvis et al. 2004) and variations in
absorbing column of more than 1024 cm−2 within two days, in-
dicating Compton thick X-ray absorption from a single cloud
in the broad-lines region (Risaliti et al. 2007). These obser-
vations show that the torus extends inward beyond the dust
sublimation point to some inner radius Rx < Rd. Clouds
at Rx ≤ r ≤ Rd partake in X-ray absorption but do not con-
tribute appreciably to optical obscuration or IR emission be-
cause they are dust-free. Since every cloud that attenuates
the optical continuum contributes also to X-ray obscuration
but not the other way round, the X-ray absorbing column
always exceeds the UV/optical absorbing column, as ob-
served (Maccacaro et al. 1982; Gaskell et al. 2007). Further,
Maiolino et al. (2001) find that the X-ray absorbing column

AGN Dusty Tori: II. Observational Implications 17
exceeds the reddening column in each member of an AGN
sample by a factor ranging from ∼3 up to ∼100, implying
that the bulk of the X-ray absorption comes from the clouds
in the dust-free inner portion of the torus. This could explain
the Guainazzi et al. (2005) finding that at least 50% of Seyfert
2 galaxies are Compton thick.
In steep radial distributions such as 1/r2, which seems to
adequately describe the torus dusty portion, most clouds are
located close to the inner radius. If this radial profile contin-
ued inward into the dust-free zone, that region would domi-
nate the X-ray obscuration—as observed. Similar to the op-
tical regime, the observed fraction of X-ray absorbed AGN
varies inversely with intrinsic luminosity (Ueda et al. 2003;
Hasinger 2004; Akylas et al. 2006). This fraction is usually
derived from the statistics of sources that have at least one
X-ray obscuring cloud along the line of sight to the AGN,
therefore it follows the behavior plotted in figure 19 but with
N0 corresponding to the total number of (dusty and dust-free)
clouds. As the previous section shows, either the radial thick-
ness σ or the cloud number N0 could be responsible for a
decreasing f2. Maiolino et al. (2007) find that the f2 fractions
follow similar trends with L in the X-ray and optical regimes,
indicating that whichever intrinsic parameter is responsible
for these trends it might behave similarly in the dusty and
dust-free portions of the torus.
6.6. What is the Torus?
In the ubiquitous sketch by Urry & Padovani (1995), the
AGN central region, comprised of the black hole, its accre-
tion disk and the broad-line emitting clouds, is surrounded
by a large doughnut-like structure—the torus. This hydro-
static object is a separate entity, presumably populated by
molecular clouds accreted from the galaxy. Gravity controls
the orbital motions of the clouds, but the origin of vertical
motions capable of sustaining the “doughnut” as a hydro-
static structure whose height is comparable to its radius was
recognized as a problem since the first theoretical study by
Krolik & Begelman (1988).
Two different types of observations now show that the
torus may be a smooth continuation of the broad lines region
(BLR), not a separate entity. IR reverberation observations by
Suganuma et al. (2006) show that the dust innermost radius
scales with luminosity as L1/2 and is uncorrelated with the
black hole mass, demonstrating that the torus inner boundary
is controlled by dust sublimation (eq. 1), not by dynamical
processes. Moreover, in each AGN for which both data ex-
ist, the IR time lag is the upper bound on all time lags mea-
sured in the broad lines, a relation verified over a range of
106 in luminosity. This finding shows that the BLR extends
all the way to the inner boundary of the dusty torus, validat-
ing the Netzer & Laor (1993) proposal that the BLR size is
bounded by dust sublimation. The other evidence is the find-
ing by Risaliti et al. (2002) that the X-ray absorbing columns
in Seyfert 2 galaxies display time variations caused by cloud
transit across the line of sight. Most variations come from
clouds that are dust free because of their proximity (< 0.1
pc) to the AGN, but some involve dusty clouds at a few pc.
Other than the different time scales for variability, there is no
discernible difference between the dust-free and dusty X-ray
absorbing clouds, nor are there any gaps in the distribution.
These observations suggest that the X-ray absorption, broad
line emission and dust obscuration and reprocessing are pro-
duced by a single, continuous distribution of clouds. The dif-
ferent radiative signatures merely reflect the change in cloud
composition across the dust sublimation radius Rd. The inner
clouds are dust free. Their gas is directly exposed to the AGN
ionizing continuum, therefore it is atomic and ionized, pro-
ducing the broad emission lines. The outer clouds are dusty,
therefore their gas is shielded from the ionizing radiation, and
the atomic line emission is quenched. Instead, these clouds
are molecular and dusty, obscuring the optical/UV emission
from the inner regions and emitting IR. Thus the BLR occu-
pies r < Rd while the torus is simply the r > Rd region. Both
regions absorb X-rays, but because most of the clouds along
each radial ray reside in its BLR segment, that is where the
bulk of the X-ray obscuration is produced. Since the X-ray
obscuration region (XOR) coincides mostly with the BLR, it
seems appropriate to name this region instead BLR/XOR. By
the same token, since the unification torus is just the outer por-
tion of the cloud distribution and not an independent structure,
it is appropriate to rename it the TOR for Toroidal Obscura-
tion Region. The close proximity of BLR and TOR clouds
should result in cases of partial obscuration, possibly leading
to observational constraints on cloud sizes.
The merger of the ionized and the dusty clouds into a sin-
gle population offers a solution to the torus vertical structure
problem. Mounting evidence for cloud outflow (see, e.g.,
Elvis 2004) indicates that instead of a hydrostatic “doughnut”,
the TOR is just one region in the clumpy wind coming off the
black-hole accretion disk (see Elitzur & Shlosman 2006, and
references therein). The accretion disk appears to be fed by a
midplane influx of cold, clumpy material from the main body
of the galaxy. Approaching the center, conditions for devel-
oping hydromagnetically- or radiatively-driven winds above
this equatorial inflow become more favorable. The disk-
wind rotating geometry provides a natural channel for angu-
lar momentum outflow from the disk and is found on many
spatial scales, from protostars to AGN (Blandford & Payne
1982; Emmering et al. 1992; Ferreira 2007). The compo-
sition along each streamline reflects the origin of the out-
flow material at the disk surface. The disk outer regions are
dusty and molecular, as observed in water masers in some
edge-on cases (Greenhill 2005). At smaller radii the dust is
destroyed and the disk composition switches to atomic and
ionized, producing a double-peak signature in some emis-
sion line profiles (Eracleous 2004). The outflow from the
atomic and ionized inner region feeds the BLR and produces
many atomic line signatures, including evidence for the disk
wind geometry (Hall et al. 2003). Clouds uplifted from the
disk dusty and molecular outer region feed the TOR and
may have been detected in water maser observations of Circi-
nus (Greenhill et al. 2003) and NGC 3079 (Kondratko et al.
2005). Indeed, Elitzur & Shlosman (2006) derive the cloud
properties from constraints deduced from clumpy models for
the IR emission and find that they provide the right conditions
for H2O maser action. In both the inner and outer outflow re-
gions, as the clouds rise and move away from the disk they
expand and lose their column density, limiting the vertical
scope of X-ray absorption, broad line emission and dust ob-
scuration and emission. The result is a toroidal geometry for
both the BLR/XOR and the TOR. Because of the strong pho-
toionization heating of BLR clouds they may rise to relatively
lower heights than the TOR dusty clouds. Detailed compar-
isons of X-ray and optical obscuration in individual sources
and in large samples should help to constrain the parameters
N0, σ and τV separately for the TOR and the BLR/XOR. Such
comparisons must consider the large scatter of obscuration in
individual sources around the sample mean (see paper I, §4.2).

18 Nenkova et al
In the outflow scenario, the TOR disappears when the bolo-
metric luminosity decreases below ∼ 1042 erg s−1 because the
accretion onto the central black hole can no longer sustain the
required cloud outflow rate (Elitzur & Shlosman 2006; Elitzur
2007). With further luminosity decrease, suppression of cloud
outflow spreads radially inward and the BLR, too, disappears.
The recent review by Ho (2008) presents extensive observa-
tional evidence for the disappearance of the torus and the BLR
in low luminosity AGN.
The Circinus Seyfert 2 core provides the best glimpse of the
AGN dusty/molecular component. Water masers trace both
a Keplerian disk and a disk outflow (Greenhill et al. 2003).
Dust emission at 8–13µm shows a disk embedded in a slightly
cooler and larger, geometrically thick torus (Tristram et al.
2007). The dusty disk coincides with the maser disk in both
orientation and size. The outflow masers trace only parts
of the torus. The lack of full coverage can be attributed to
the selectivity of maser operation—strong emission requires
both pump action to invert the maser molecules in individual
clouds and coincidence along the line of sight in both position
and velocity of two maser clouds (Kartje et al. 1999). Proper
motion measurements and comparisons of the disk and out-
flow masers offer a most promising means to probe the struc-
ture and motion of TOR clouds.
7. SUMMARY AND DISCUSSION
We have developed a formalism for handling radiative
transfer in clumpy media and applied it to the IR emission
from the AGN dusty torus. In the calculations we execute
only the first two steps of the full iteration procedure out-
lined in §3.2, paper I, and the moderate total number of clouds
considered here validates this procedure. When that number
increases, the probability for unhindered view of the AGN
decreases, the role of indirectly heated clouds becomes more
prominent and eventually requires higher order iterations. Our
current calculations employ some additional simplifying ap-
proximations: The grain mixture is handled in the composite-
grain approximation, all dust is in clouds without an inter-
cloud medium and all clouds are identical. We have already
begun work on removing these assumptions and will report
the results in future publications.
In contrast with the smooth-density case, the clumpy prob-
lem is not well defined because clouds can have arbitrary
shapes, and any given set of parameters can have many
individual realizations. Our formalism invokes a statisti-
cal approach for calculating an average behavior, and it is
encouraging that other approaches produce similar results.
Dullemond & van Bemmel (2005) conduct “quasi-clumpy”
calculations in which the torus is modeled as a set of axisym-
metric rings, and compare the results with the smooth-density
case. In agreement with our conclusions they find that only
smooth-density models can produce very deep absorption fea-
ture while clumpy dust produces stronger near-IR, broader
SED and much more isotropic IR emission. Hönig et al.
(2006) employ 3D Monte carlo calculations that bypass some
of our approximations. They also treat different cloud realiza-
tions for the same global parameters, allowing them to show
the intrinsic scatter in SED due to the stochastic nature of the
problem. Their results are in agreement with ours, validat-
ing our approach and the approximations we employ. Since
the dust properties in their calculations are from Draine & Lee
(1984), the 10 µm feature reaches somewhat larger strengths
than in our calculations, which employ the Ossenkopf et al.
(1992) “cool" dust (but are similar to our original results
in Nenkova et al. 2002, which also employed Draine & Lee
dust). In spite of these differences, Hönig et al. (2006) too
find that the silicate absorption feature is never as deep as ex-
pected for a uniform dust distribution, and obtain qualitatively
similar behavior of the silicate emission feature and overall
SED shape.
The models presented here show that clumpy torus models
are consistent with current AGN observations if they contain
N0 ∼5–15 dusty clouds along radial equatorial rays, each with
an optical depth τV ∼30–100. The cloud angular distribution
should decline smoothly toward the axis, for example, a Gaus-
sian profile centered on the equatorial plane. Power-law radial
distributions r−1 – r−2 produce adequate results. Dust grains
with optical properties of the standard Galactic mixture pro-
vide satisfactory explanation to the IR observations. The be-
havior of the 10µm silicate feature, in particular the lack of
any deep absorption features, is reproduced naturally without
the need to invoke any special dust properties. Several sugges-
tions that the abundance or composition of AGN dust might
differ from its Galactic counterpart can be discarded because
of subsequent developments. Risaliti et al. (1999) note that,
assuming standard dust abundance, the large column densities
discovered in X-ray absorption imply torus masses in excess
of the dynamical mass, posing a problem for the system stabil-
ity. However, their mass estimates were based on the uniform
mass distribution and large torus sizes derived from smooth-
density models. The compact sizes and steep density distri-
butions of clumpy models eliminate the problem (see §6.1).
Maiolino et al. (2001) suggested that the widely different UV
and X-ray extinctions they found in individual sources could
imply low dust abundance, but the subsequent discovery of
rapid variations shows that X-ray obscuration by dust-free
clouds is the more likely explanation (see §6.5). They also
invoked the lack of prominent 10µm absorption features as an
indication that AGN dust is different from Galactic, but this is
a natural consequence of clumpy dust distributions (see §5.1).
Intrinsic extinction curves deduced from spectral analysis of
type 1 sources (see Czerny 2007 for a recent review and a
comprehensive discussion of uncertainties) generally indicate
a depletion of small grains, as could be expected: the obscu-
ration in type 1 sources is dominated by the dusty clouds clos-
est to the center and these clouds contain predominantly large
grains, which survive at the smallest distances from the AGN
(see §2.1). There is no compelling evidence for significant
differences between the properties of AGN and Galactic dust.
Other dust compositions are not ruled out, but nothing in the
current data requires major departures from the dust grains we
use.
The close proximity of dust temperatures as different as &
800 K and∼200–300 K found in interferometry around 12µm
cannot be explained by smooth-density models even when
they account for the individual temperatures of grains with
different sizes (Schartmann et al. 2005). Clumpiness resolves
this puzzling observation because the dust on the dark side
of an optically thick cloud is much cooler than on the bright
side. Thanks to the mixture of different dust temperatures at
the same radial distance, clumpy models naturally explain the
torus compact size. In spite of the high anisotropy of its ob-
scuration, the torus emission is observed to be nearly isotropic
at λ & 12 µm. Clumpy models resolve this puzzle too, since
the emission from a torus with radial thickness Y = 10 varies
little with viewing angle. The variation is especially small if
the radial distribution is 1/r2 or steeper, and such steep radial
profiles maintain a nearly isotropic emission even at larger

AGN Dusty Tori: II. Observational Implications 19
torus sizes.
In addition to IR observations, clumpiness significantly im-
pacts the analysis of other data, in particular obscuration
statistics. The fraction f2 of obscured sources is controlled
not only by the torus angular thickness σ, as in all analyses to
date, but also by the cloud number N0. With N0 = 5, a 70%
fraction of type 2 AGN implies σ ∼ 30◦ instead of the stan-
dard 45◦. Observations indicate that increasing the bolometric
luminosity from the Seyfert to the quasar regime induces (1)
a decrease of f2 and (2) a switch to emission feature at 10
µm for both type 1 and some type 2 AGN. Both trends can
be explained with a change in a single torus parameter—N0
decreases from ∼ 5 in Seyfert galaxies to ∼ 2 in QSO (see
figures 16 and 19). Decreasing σ, the scenario known as the
receding torus model, explains the first trend but has no ef-
fect on the second. The emergence of the 10 µm in emission
would require in this case the additional increase of individual
clouds optical depth to τV & 100 in QSO.
The decreasing-N0 scenario provides the simplest explana-
tion for the trends observed when L is increasing, but that
does not guarantee its validity. This demonstrates the diffi-
culties in deducing the model parameters from observations
that cannot yet resolve the torus basic ingredient—the indi-
vidual dusty clouds. The problem is compounded by the lack
of angular resolution that hinders clean separation of the torus
component from the flux measured at most IR wavelengths
and by the degeneracies of the radiative transfer solutions that
prevent decisive, one-to-one associations between model pa-
rameters and observable quantities. The only practical way
around these difficulties is to match trends identified in the
data with similar general properties of the models.
Our main conclusions can be summarized as follows:
• The torus angular distribution has to be soft edged
• Clumpy models can produce nearly isotropic IR emis-
sion together with extremely anisotropic obscuration
• Clumpy models can explain all current observations
with compact torus sizes; SED fitting is a poor con-
straint on the size
• Standard interstellar dust describes adequately AGN
observations; there does not seem to be a need for any
major modifications of grain properties
• Clumpy sources never produce a very deep silicate fea-
ture; apparent optical depth, obtained from I = e−τapp
where I is the residual intensity at maximum absorp-
tion, is a poor indicator of the actual optical depth
• The probability for direct line-of-sight to the AGN at
large viewing angles is small, but not zero
• The statistics of obscured sources depend on both the
torus angular thickness and the number of clouds along
radial rays
• The torus and the BLR are the dusty (outer) and dust-
free (inner) regions in a continuous cloud distribution;
a more appropriate designation for the torus is Toroidal
Obscuration Region (TOR)
• X-ray obscuration comes from both TOR and, predom-
inantly, BLR clouds
As long as IR observations are incapable of resolving indi-
vidual torus clouds, one must rely on the combined evidence
for clumpy structure instead of on a “smoking gun”. Individ-
ual TOR clouds seem to have been resolved in observations
of outflow water masers in Circinus and NGC 3079. Proper
motion measurements and comparison of these masers with
their disk counterparts provide the most promising method
for probing the TOR structure and kinematics. The Circinus
AGN, whose dust emission has been resolved in VLTI obser-
vations, is an especially attractive target for studying the dusty
and molecular content of TOR clouds.
ACKNOWLEDGMENTS
Part of this work was performed while M.E. spent a most
enjoyable sabbatical at LAOG, Grenoble. We thank Almu-
dena Alonso-Herrero, Nancy Levenson and Maria Polletta for
useful comments on the manuscript. Partial support by NSF
and NASA is gratefully acknowledged.
APPENDIX
TECHNICALITIES
The relevant coordinates in describing both the cloud distribution and the source function are the cloud’s radial distance r,
angle β from the equatorial plane and the angle α between its radius vector and the AGN–observer axis (see eq. 2, and part I
figure 2 and eq. 8). The torus emission requires an integration along a path inclined by the viewing angle i from the torus axis at
some displacement from the center (eq. 5, part I). To handle the geometry we introduce a cartesian coordinate system centered
on the AGN with z toward the observer and x–y in the plane of the sky, with the torus axis in the y–z plane at angle i from the
z axis. The integration path is specified by its fixed values of x and y, so that the angular displacement is (θx,θy) = (x/D,y/D)
and the angular impact parameter in brightness profiles is θ =
√
x2 + y2/D. The integration variable is z. At any point ~r = (x,y,z)
along the path, the cloud coordinates are found from
r2 = x2 + y2 + z2, tanβ = ysin i + zcos i√
x2 + (ycos i − zsin i)2
, cosα = z
r
. (A1)
The path integration in eq. 5, part I, produces the intensity generated by the cloud distribution. Since our source function
calculations involve only the first two steps of the full iteration procedure described in §3.2, part I, we must introduce a correction
to take proper account of flux conservation. With pAGN the fraction of the AGN luminosity that gets through the torus (eq. 8, part
I), we calculate ICλ (x,y; i), the brightness map of clumpy torus emission in the direction i, from
ICλ =
L(1 − pAGN)
4π
∫
d cos i
∫
dλ
∫
Hλdxdy
Hλ, where Hλ(x,y; i) =
∫
Pesc,λ(~r)Sc,λ(~r)NC(~r)dz (A2)
Here Sc,λ(~r) and NC(~r) are, respectively, the source function and column density of clouds at position ~r along the integration path,
and Pesc,λ(~r) is the probability for a photon of frequency λ to escape from that point through the rest of the path. The torus flux
at distance D and viewing angle i is calculated from FCλ (i) = (1/D2)
∫
ICλ (x,y; i)dxdy. With these expressions, the spectral shape is

20 Nenkova et al
determined from the first two iteration steps while ensuring that the torus emission properly obeys flux conservation (eq. 17, part
I).
The quantity Hλ is intrinsically a function of scaled variables, Hλ = Hλ(x/Rd,y/Rd; i), because the brightness at position (x,y)
depends only on the distribution of dust in temperature and optical depth along the path (Ivezic´ & Elitzur 1997). Therefore, from
eq. A2 the brightness has the form ICλ (θx,θy; i) = (L/4πRd2) f (θx/θd,θy/θd), where f is a dimensionless function of the scaled
angular displacements. Since the brightness scale L/4πRd2 is determined by the dust sublimation temperature Tsub (eq. 1) , the
only effect of the luminosity is to set the overall angular scale θd, effecting a self-similar stretch of the brightness map. Similarly,
the flux, FCλ , is a product of the bolometric flux FAGN and a luminosity-independent spectral shape.
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