# AGN torus detectability at sub-millimeter wavelengths:
What to expect from ALMA continuum data

Alice Pasetto  Omaira González-Martín  Donaji Esparza-Arredondo  Natalia
Osorio-Clavijo  Cesar Victoria-Ceballos  Instituto de Radioastronomía y
Astrofísica (IRyA-UNAM), 3-72 (Xangari), 8701, Morelia, Mexico  Mariela
Martínez-Paredes  Instituto de Radioastronomía y Astrofísica (IRyA-UNAM), 3-72
(Xangari), 8701, Morelia, Mexico  Korea Astronomy and Space Science Institute
776, Daedeokdae-ro, Yuseong-gu, Daejeon, Republic of Korea (34055)

(Received ??; Revised ??; Accepted ??)

###### Abstract

Dust close ($\sim$few pc) to the accretion disk in active galactic nuclei
(AGN) is key to understand many of their observational signatures and it is
key to trace how the AGN is fed or even evolve along its duty cycle. With
estimated sizes of less than 10 pc, as constrained by mid-infrared high
angular resolution data, only the superb spatial resolution achieved by ALMA
is able to actually image this dusty structure. However, the question
regarding the conditions in which the dust at sub-milimeter (sub-mm)
wavelengths where ALMA operates, arises. We study the detectability of the
emission associated with the AGN dusty structure at sub-mm wavelengths using
ALMA, in a theoretical and observational way. Theoretically, we use the Clumpy
models from Nenkova et al. together with the mid-infrared to X-ray and the
radio fundamental plane scaling relations. We find that it is more likely to
detect bigger and denser dusty tori at the highest ALMA frequency (666 GHz/450
$\mu$m). We also find that with 1h at 353 GHz/850 $\mu$m and 10h at 666
GHz/450 $\mu$m we can detect, with a high detection limit, a 1 mJy torus
(characteristic of bright AGN). This means, an object for which the unresolved
SED at 12 $\mu$m has a flux $\sim 1$ mJy. Observationally, we use four
prototypical AGN: NGC 1052 (low-luminosity AGN), NGC 1068 (Type-2), NGC 3516
(Type 1.5), and IZw1 (QSO), with radio, sub-millimeter, and mid-IR data
available. All the mid-infrared spectra are best fit with the smooth model
reported by Fritz et al. A power law and a single, or a composition of,
synchrotron component/s reproduce the cm radio wavelengths. We combined and
extrapolated both fits to compare the extrapolation of both torus and jet
contributors at sub-mm wavelengths with data at these wavelengths. Our
observational results are consistent with our theoretical results. The most
promising candidate to detect the torus is the QSO IZw1 (therefore, highly
accreting sources in general), although it cannot be resolved due to the
distance of this source. We suggest that to explore the detection of a torus
at sub-mm wavelengths, it is necessary to perform an SED analysis including
radio data, with particular attention to the angular resolution.

††journal: ApJ

##  1 Introduction

Although the unification scheme (e.g., Antonucci, 1993; Urry & Padovani, 1995)
of active galactic nuclei (AGN) may not be universal, the most accepted
description is that dust surrounding the central engine is key to explain some
observational differences between AGN classes. As a first approach, the point
of view of the observer with respect to this dusty structure is able to
explain the type-1/type-2 dichotomy (Pier & Krolik, 1993; Granato & Danese,
1994; Efstathiou & Rowan-Robinson, 1995).

The morphology and properties of this dusty structure are far from being
understood (e.g., see Netzer, 2015). The torus dust grains absorb ultraviolet
photons from the central engine and re-radiate them in the infrared (IR),
peaking at mid-IR wavelengths around 5-35 $\rm{\mu m}$ (e.g., Sanders et al.,
1989; Sargsyan et al., 2011; Shi et al., 2014). Thus, from the observational
point of view, many studies have been devoted to study the Spectral Energy
Distribution (SED) of the dusty region at near- and mid-IR wavelengths.
Several model fittings aimed to extract physical and geometrical properties
from unresolved SED, by using high angular resolution data (subarcseconds)
(e.g., Ramos Almeida et al., 2009, 2011; Alonso-Herrero et al., 2011;
Martínez-Paredes et al., 2015; Fuller et al., 2016; Lopez-Rodriguez et al.,
2016; Martínez-Paredes et al., 2017; González-Martín et al., 2017; García-
Burillo et al., 2017) and, in some cases, milliarcseconds interferometric
observations (e.g., Hönig et al., 2010a; Tristram & Schartmann, 2011). They
found that for Seyferts the dusty structure should be concentrated into the
inner $\rm{<}$5 pc, as derived from near- and mid-IR wavelengths (Radomski et
al., 2008; Ramos Almeida et al., 2009, 2011; Alonso-Herrero et al., 2011),
that extend for the highest AGN luminosities (Martínez-Paredes et al., 2017)
and it is even smaller than 1 pc for low-luminosity AGN (LLAGN, González-
Martín et al., 2017).

Ramos Almeida et al. (2014) found that a minimal set of data (J+K+M band
photometry + N-band spectroscopy) is necessary to constrain the geometrical
parameters of the dusty torus using clumpy models for Seyfert galaxies.
However, to have a reliable estimate of the torus size at mid-infrared, it is
necessary to add the FIR emission to the SED in order to probe the coolest
dust of the torus (García-Burillo et al., 2016; Fuller et al., 2016; Lopez-
Rodriguez et al., 2018). This implies the need of FIR sub-arcsec resolution
data. Infrared interferometry constitutes one of the most precise ways of
characterizing the dusty structure using observations by comparing them with
torus models (Hönig et al., 2006; Tristram & Schartmann, 2011). However, the
signal-to-noise ratio (S/N) required for, e.g., the Very Large Telescope
Interferometer (ESO-VLTI) observations strongly restricts the number of
observable sources.

This has changed with the new sub-millimeter (sub-mm) capabilities as Atacama
Large Millimeter Array (ALMA) or Large Millimeter Telescope (LMT). High
resolution sub-mm observations are important in probing the morphology, column
density and dynamics of obscuring matter in AGN. ALMA is able to achieve 0.02
arcsec resolution continuum images at $\rm{>400\mu m}$. Very recently, some
works attempted to detect and study the dusty torus, e.g., Izumi et al. (2018)
studied the dusty central region of the Circinus galaxy testing the muti-phase
dynamic torus model and Combes et al. (2018) explored the close environment
around 7 seyfert/LINER galaxy detecting a molecular torus. However, none of
them achieved to detect the inner dusty structure. Only García-Burillo et al.
(2016) claimed the detection of an elongated continuum structure of
$\rm{4\times 7\,pc^{2}}$ associated to the dusty torus (see also Gallimore et
al., 2016).

However, two main issues need to be faced when using sub-mm telescopes to
study the dust in AGN: (1) Sensitivity issue: the peak of the dusty emission
is below 30 $\rm{\mu m}$. The total flux expected above $\rm{400\mu m}$ must
be only a small fraction of what it is observed at mid-infrared wavelengths.
Thus, although ALMA has a very good sensitivity limit, a proper study on the
detectability of the dusty continuum at sub-mm wavelengths needs to be
addressed. Aalto et al. (2017) were not able to detect the dusty structure in
the radio-quiet NGC 1377 using a similar waveband compared to that used by
García-Burillo et al. (2017); and (2) Jet contribution: most of these AGN show
a strong synchrotron contribution coming from the radio jet. This contribution
is expected to be dominant at radio frequencies but a tail of this emission
can contribute at other wavelengths, with non-negligible contribution to the
sub-mm wavelengths. Izumi et al. (2017) studied the LLAGN NGC 1097 with less
than 10 pc resolution at $\rm{\sim 800\mu m}$. Indeed, they claimed that most
of the sub-mm continuum emission is dominated by the jet thanks to the study
of long-term variations at sub-mm wavelengths.

It is the aim of this paper to study the detectability of extended emission
associated to AGN dusty structure at sub-mm wavelengths using ALMA. For this
purpose we will consider the most used SED models for dusty AGN emission as
the Clumpy models (Nenkova et al., 2008a, b) together with known scaling
relations between the accretion disk luminosity and the torus continuum
(Gandhi et al., 2009; Netzer, 2015; Asmus et al., 2015), and the accretion
disk luminosity, jet contribution, and super massive black-hole (SMBH) mass
(Bonchi et al., 2013; Saikia et al., 2015) (see Section 2). In section 3, we
study the sensitivity and contributors to the sub-mm wavelengths of four
prototypical AGN, covering a wide range of AGN classes: NGC 1052 (LLAGN), NGC
1068 (Type-2 Seyfert), NGC 3516 (Type-1.5 Seyfert) and I Zw1 (QSO). Details on
the target selection are given in Section 3.1. Using these targets, we will
study the detectability of the sub-mm torus with available archival and/or
literature data, combining together mid-IR, radio and sub-mm continuum flux
densities (see Section 3). Our findings are discussed in Section 4 and a short
summary of results is given in Section 5. We use the standard cosmology with
$\rm{H_{0}=70km/s/Mpc}$ along the text.

Figure 1: Torus (top) and jet (bottom) flux contributions to the sub-mm
wavelengths compared to the X-ray luminosity. The torus contribution is
extrapolated from the Clumpy torus libraries, using the X-ray to mid-IR
relation. The jet contribution is computed assuming a single synchrotron
component and the radio fundamental plane (see text).

Figure 2: Distribution of the torus contributions at 450$\rm{\mu m}$ compared
to the 2-10 keV X-ray flux density depending on the inclination angle i (top-
left panel), equatorial number of clouds N0 (top-middle panel), torus outer
radius Y (top-right panel), half openning angle of the torus $\sigma$ (bottom-
left panel), slope of the radial distribution of clouds q (bottom-middle
panel), and the optical depth of the clouds $\tau_{\nu}$ (bottom-right panel).

Figure 3: Jet contributions at 666GHz/450$\rm{\mu m}$ depending on the X-ray
luminosity (top-left panel), BH mass (top-right panel), the synchrotron
spectral index (bottom-left panel), and the accretion rate(bottom-right
panel).

##  2 Torus detection with ALMA through theoretical predictions

We compute the expected contributions to the sub-mm range as the ratio between
the flux at sub-mm wavelengths and that at X-ray wavelengths. This allows us
to scale the sub-mm flux density to the accretion disk flux density. We use
the integrated luminosity in the 2-10 keV band (hereinafter
$\rm{L_{[2-10keV]}}$) for the X-ray luminosity and the monochromatic
luminosities at 100 GHz (3000 $\rm{\mu m}$, ALMA band 3), 353 GHz (850
$\rm{\mu m}$, ALMA band 7), and 666 GHz (450 $\rm{\mu m}$, ALMA band 9) for
the sub-mm wavelengths. Hereinafter we refer to the fluxes at these bands as
$\rm{F_{\nu=100GHz}^{\lambda=3000\mu m}}$, $\rm{F_{\nu=353GHz}^{\lambda=850\mu
m}}$, $\rm{F_{\nu=666GHz}^{\lambda=450\mu m}}$, respectively. We chose these
bands because they cover the full waveband covered by ALMA. These three bands
can achieve an spatial resolution of 0.2, 0.06, and 0.03${}^{\prime\prime}\;$,
respectively, considering the largest configuration (C43-7 available during
cycle 6). The 666 GHz continuum emission (band 9) was chosen by García-Burillo
et al. (2016) (see also Imanishi et al., 2016a) and Aalto et al. (2017) to
identify the torus contribution to the continuum at sub-mm wavelengths for NGC
1068 and NGC 1377, respectively (see Section 1). In the same manner, Izumi et
al. (2017) used 350 GHz (band 7) to try to recover the torus contribution to
the sub-mm wavelengths for NGC 1097. We also test band 3 (100 GHz) because it
provides slightly better sensitivity compared to the other bands.

Note that in this section we do not take into account the dilution, although
it might be important if spatial resolution is moderate (see Section 3, e.g.
for the case of NGC 1068). For instance, the MIR flux will change if the field
of view of the observations change (e.g Tristram et al., 2014; Prieto, 2010)

###  2.1 Torus contribution

In order to estimate the torus contribution to the sub-mm range we estimate
two ratios: (1) the 12 $\rm{\mu m}$ to 2-10 keV flux ratio ($\rm{F_{12\mu
m}/F_{[2-10keV]}}$) and (2) the sub-mm to the 12 $\rm{\mu m}$ flux ratio
($\rm{F_{\nu}^{\lambda}/F_{12\mu m}}$).

We use the well established mid-IR to X-ray scaling relation for AGN (Lutz et
al., 2004; Gandhi et al., 2009) to estimate the $\rm{F_{12\mu
m}/F_{[2-10keV]}}$ ratio. The most updated version of this relation is
presented by Asmus et al. (2015) using a sample of 152 nearby AGN, and can be
written as:

$\displaystyle log\left(\frac{L^{nuc}_{12\mu
m}}{10^{43}ergs^{-1}}\right)=(0.30\pm 0.03)+$ $\displaystyle(0.98\pm
0.03)log\left(\frac{L^{int}_{[2-10]KeV}}{10^{43}ergs^{-1}}\right)$ (1)

We then compute the expected $\rm{F_{\nu}^{\lambda}/F_{12\mu m}}$ using the
SEDs of clumpy torus model produced by Nenkova et al. (2008b). This clumpy
torus model depends on six parameters: the observer inclination angle towards
the torus $\rm{i}$, half angular width of the torus $\rm{\sigma}$, outer
radius of the torus scaled to the inner radius $\rm{Y=R_{out}/R_{in}}$111The
inner radius of the torus is set to the sublimation radius of the dust that
depends on the accretion disk bolometric luminosity, the number of clouds at
the equatorial plane of the torus $\rm{N_{0}}$, the steepness of the radial
distribution of clouds $\rm{q}$, and the opacity of the individual clouds
$\rm{\tau_{\nu}}$. Thus, our $\rm{F_{\nu}^{\lambda}/F_{12\mu m}}$ ratio
depends on these six parameters. Note that the SEDs of the clumpy torus model
cover up to 1000$\rm{\mu m}$. We linearly extrapolate the SEDs above
1000$\rm{\mu m}$ to estimate the expected flux at 3000$\rm{\mu m}$ (i.e. band
3 at 100 GHz).

The distribution of torus $\rm{F_{\nu}^{\lambda}/F_{[2-10keV]}}$ ratios are
shown in the top panel of Fig. 1. As expected, the highest torus contribution
is obtained in the 666 GHz (450 $\rm{\mu m}$), with a sub-mm flux density
$\rm{\sim 10^{-6}-10^{-3}}$ times the X-ray flux density.

We also show how the parameter space affects the torus contribution to the
sub-mm wavelengths in Fig. 2. Each panel shows the distribution of the
$\rm{F_{\nu=666GHz}^{\lambda=450\mu m}/F_{[2-10keV]}}$ ratio for the lowest
(light gray) and highest (dark gray) values for each parameter. The highest
values are obtained for higher number of clouds in the equatorial plane
($\rm{N_{0}}$), larger outer radius of the torus compared to the inner one
($\rm{Y}$), larger half angular width of the torus ($\rm{\sigma}$), flatter
radial distribution of clouds ($\rm{q}$), and larger values of the optical
depth of individual clouds ($\rm{\tau_{\nu}}$). No significant effect is
produced by edge-on or face-on torus (the inclination angle i). All together
means that, as expected, bigger and denser dusty tori are more likely to be
detected at sub-mm wavelengths. Finally we also considered how the fraction of
the sky obscured by dust, i.e. the covering factor, at the highest ALMA
frequency can be incisive in the torus detectability and the result is shown
in Fig. 4. Large covering factor values (fcov $>$ 0.6) are those for which the
torus contribution could be important in the sub-mm window. However, because
of the wide width of the distribution it is worth notice that large covering
factor is not a determinant condition.

Figure 4: Histogram of the covering factor distribution. Values larger than
fcov $>$ 0.6 could be important for the contribution of the torus in the sub-
mm band. However, due to its wide width, this parameter is not determinant.
Small values of the covering factor, fcov $<$ 0.4 are not determinant at all.

Finally, we investigate how these results could be influenced by the torus
model selected. Fig. 5 shows the distribution of the clumpy torus model by
Nenkova et al. (2008b), the smooth torus model by Fritz et al. (2006) and the
disk + wind model by Hönig & Kishimoto (2017) together with the jet
contribution at the highest ALMA frequency considered (666GHz/450$\mu$m, for
which the highest torus contribution is obtained). The contribution of the AGN
dusty torus depends on the distribution of the dust grains. For the case of a
polar dusty wind torus distribution, the model predicts a negligible
contribution of torus emission in the sub-mm band, while for dust grains
distributed in a smooth torus , the model predicts larger contribution. Even
if the most optimistic model, i.e. the smooth model, is used, the torus seems
to be difficult to be detected at sub-mm wavelengths (see Sect. 3). The
histogram is also telling us that an important contribution from the
synchrotron emission from the radio jet could contaminate the dust emission
over the most common used clumpy torus.

Moreover, we also considered additional contribution from the hot graphite
dust and the dusty NLR clouds as proposed in several works to describe the
main emission components in the near and mid-IR spectra, e.g (Mor et al.,
2009; Mor & Netzer, 2012). The former contributes mainly a $\sim$ 3 $\mu$m and
it decays very steeply while the last could contribute to the mid-IR spectrum.
Indeed, it contributes above 10 micron and could be as large as 40% of the
total emission at 24 $\mu$m. Assuming this percentage of contribution remains
the same at sub-mm wavelengths, a shift of the torus models distributions in
Fig. 5 by a factor of 0.2 towards the right. Thus the NLR contribution do not
have a large impact on the result presented above.

Figure 5: Distribution of the disk+wind (gray), clumpy (white) and smooth
(cyan) torus models together with the radio jet distribution (brown) at
666GHz/450$\mu$m.

###  2.2 Jet contribution

We extrapolate the contribution of the radio jet in the sub-mm range using the
so-called fundamental plane relation (Merloni et al., 2003), for which radio
luminosity (L${}_{\nu}^{\lambda}$) is correlated with both the (hard) X-ray
luminosity L[2-10keV] (from a corona closely linked to the accretion disk
emission) and the mass of the SMBH (MBH). This implies that a correlation
between jet and disk flux density is unavoidable. Bonchi et al. (2013)
measured a fundamental plane for the largest AGN-only sample for which radio,
X-ray and K-band luminosity information exists. Moreover, they added radio
upper limits and they considered a wide range of redshifts (up to z$\sim$ 5).
The fundamental plane relation obtained is the following:

$\displaystyle\log L_{R}=0.39\log(L_{[2-10keV]})+0.68\log(M_{BH})$
$\displaystyle+16.61,$ (2)

where LR is the 5-GHz nuclear luminosity in units of erg s-1, with 1.4 GHz
radio luminosities converted into 5 GHz luminosities assuming a radio spectral
index $\alpha$ = –0.7 (where Lν $\propto$ $\nu^{\alpha}$), L[2-10keV] is the
2-10 keV nuclear X-ray luminosity in units of erg s-1, and MBH is the SMBH
mass in units of M ⊙ (Merloni et al., 2003). It is from the equation 2 that we
extrapolate our expected sub-mm jet luminosity. Therefore, we derive our sub-
mm fundamental plane as:

$\displaystyle\log(L_{\nu}^{\lambda})=0.39\log(L_{[2-10keV]})+0.68\log(M_{BH})$
$\displaystyle+16.61-\alpha\log\left(\frac{5_{[GHz]}}{\nu}\right),$ (3)

where $\alpha$ represents the spectral index; i.e, the slope, for an optically
thin radio component emitting synchrotron radiation, and $\nu$ are the three
possible ALMA frequencies considered in this paper (i.e. 100 GHz, 353 GHz, and
666 GHz). Therefore, the ratio between F${}_{\nu}^{\lambda}$/F[2-10keV] still
depends on the X-ray luminosity L[2-10keV] as it follows:

$\displaystyle\log\left(\frac{F_{\nu}^{\lambda}}{F_{[2-10keV]}}\right)=C(\alpha,\nu)-0.61\log(L_{[2-10keV]})$
$\displaystyle+0.68\log(M_{BH})$ (4)

where the constant C($\rm{\alpha}$, $\rm{\nu}$) = $\rm{16.61-\alpha
log(5_{[GHz]}/\nu)}$.

For the purpose of our study we explore typical ranges for the parameters:
spectral indexes for local AGN (Condon et al., 2002; Sadler et al., 2014) of
$\alpha$=[–0.5,–0.7], X-ray luminosity of L[2-10keV]=[1042,1046] erg s-1, and
SMBH masses of MBH=[106, 109] M⊙. The distribution of the sub-mm jet
contribution peaks at around $\rm{\sim 10^{-6}}$, irrespective of the chosen
sub-mm frequency (see bottom panel histogram in Fig. 1). Note that this value
might be an overestimate of the jet contribution. Saikia et al. (2018),
investigated whether or not 1.4 GHz fluxes can trace nuclear activity (using
10149 AGN taken from the Faint Images of the Radio Sky at Twenty-centimeters,
FIRST, survey White et al., 1997). They concluded that the 1.4 GHz FIRST
fluxes do not trace the pure ”core” jet and instantaneous nuclear activity.
Bonchi et al. (2013), mostly used data from the FIRST survey (with angular
resolution of 5${}^{\prime\prime}\;$) and they considered sources in a wide
range of redshifts, meaning that several synchrotron components could
contribute within the radio beam. Therefore, the radio flux density could be
contaminated by radio extended emission, e.g., from the radio lobe, that can
overestimate the radio flux density. This can produce an up-shift in the
fundamental plane. In the practice, this means that pure core-jet component
would have a lower flux density and the histograms showed in Fig. 1 (bottom
panel) would move towards lower values. To isolate as much as possible the
central radio components, observations at high resolution (e.g., using the
JVLA in its A-configuration) and at high radio frequencies are needed.

We also show how the X-ray luminosity L[2-10keV], the SMBH mass MBH, the
synchrotron spectral index ($\alpha$), and the accretion rate
$\rm{L_{bol}/L_{Edd}}$ parameters affect the jet contribution considering the
highest frequency band (666GHz/450$\mu$m) in Fig. 3. The lowest jet
contribution in this band is obtained considering high X-ray luminosity, low
SMBH masses, and, therefore, high accretion rates. No significant effect is
produced by the narrow range of $\alpha$. It is worth to mention that a
spectral index of –0.5 or –0.7 are tracing similar class of objects. Merloni
et al. (2003) claimed that using a wide range of $\alpha$ (i.e., flat radio
source with $\alpha$ $>$ –0.4 and steep radio sources with $\alpha$ $<$ –0.4)
the fundamental plane shows a considerable scatter. In order to reduce this
scatter they suggest to restrict to a specific class of object, as we did
considering the narrow $\alpha$ range of [–0.5, –0.7]. Also note that we
exclude from this plot the lowest values of the total distribution because
they are obtained with $\rm{L_{bol}}$ above the Eddington limit. Nevertheless,
note that the radio jet contribution seems to be present for a wide range of
cases in the sub-mm band, effectively showing
$\rm{F_{\nu=666GHz}^{\lambda=450\mu m}/F_{[2-10keV]}\sim 10^{-8}-10^{-4}}$.

Component | $\rm{\nu/\lambda}$ |  log($\rm{F_{\nu}^{\lambda}/F_{(2-10keV)}}$) | Percentage |  $\rm{F_{\nu}^{\lambda}}$ [$\mu$Jy] |  |  $\rm{F_{ALMA,rms}}$ [$\mu$Jy]
---|---|---|---|---|---|---
|  |  | (%) | $\rm{F_{12\mu m}=150\,mJy}$ | $\rm{F_{12\mu m}=10\,Jy}$ |  |  1$\sigma$ 1hr |  1$\sigma$ 10hr
Torus |  100GHz/3000$\rm{\mu m}$ |  $-$9.33 [$-$10.68,$-$7.93] | 0.02 [0, 10.8] |  $<$0.1 |  $<$10 |  | 12 | 4
|  353GHz/850$\rm{\mu m}$ |  $-$6.18 [$-$7.46,$-$4.86] | 34.6 [0.1, 99.7] |  $<$80 | 4 [0, 6400] |  | 85 | 30
|  666GHz/450$\rm{\mu m}$ |  $-$4.6 [$-$5.84, $-$3.31] | 96.2 [5.5, 99.9] | 2 [0, 2200] | 100 [0.2, 160000] |  | 260 | 80
Jet |  100GHz/3000$\rm{\mu m}$ |  $-$5.57 [$-$7.01,$-$4.12] | 99.98 [89.2, 100.0] |  $<$100 | 20 [0, 8200] |  | 12 | 4
|  353GHz/850$\rm{\mu m}$ |  $-$5.89 [$-$7.34, $-$4.44] | 65.4 [0.3, 99.9] |  $<$60 | 7 [0, 4400] |  | 85 | 30
|  666GHz/450$\rm{\mu m}$ |  $-$6.06 [$-$7.51, $-$4.61] | 3.8 [0, 94.5] |  $<$40 | 5 [0, 3200] |  | 260 | 80
Table 1: Expected sub-mm versus X-ray flux ratio (Col. 3), percentage (Col.
4), and the flux density [$\mu$Jy] of an hypothetical source with 150mJy (Col.
5) and 10Jy (Col. 6) for the torus and jet contributions. These values are
computed at the three frequencies/wavelengths. The noise level (rms, 1$\sigma$
level [$\mu$Jy]) reached with 1 hr or 10 hr of ALMA integration time (IT) is
shown in Col. 7 and 8.

###  2.3 Detectability of the torus using ALMA

We discussed in previous sub-sections in which conditions the torus and jet
have a maximum or minimum contribution to the sub-mm wavelengths. Here we
study (1) the detectability of the torus compared to the jet contribution and
(2) the detectability of the torus considering the sensitivity limits of ALMA
at the studied frequencies.

We computed the mean, 10% and 90% percentiles of the torus and jet
distributions at 100 GHz, 353 GHz, and 666 GHz compared to the X-ray flux
($\rm{F_{\nu}/F_{(2-10keV)}}$). These numbers are reported in Col. 3 of Table
1 (10% and 90% recorded within brackets). We then computed the median
percentage of contribution for both torus and jet contribution. The minimum
(maximum) percentage is computed using the minimum (maximum) ratio for one of
the component and the maximum (minimum) ratio for the other. These percentages
are reported in Col. 4 of Table 1. The jet component fully dominates the 100
GHz/3000 $\rm{\mu m}$ band. The torus component could dominate over the jet
component in the 353 GHz/ 850$\rm{\mu m}$, although the median contribution is
$\rm{\sim}$35%. As expected, the best chances to detect the torus over the jet
contribution are obtained for the 666 GHz/450 $\rm{\mu m}$ frequency, with an
average $\rm{\sim}$96% of torus component. However, even using this frequency,
the contribution of torus can be as low as $\rm{\sim}$5%.

We then computed the expected flux density at sub-mm wavelengths for a typical
AGN of $\rm{F_{12\mu m}=150\,mJy}$ and $\rm{F_{12\mu m}=10\,Jy}$ (reported in
Cols. 5 and 6 in Table 1). For that purpose we used the X-ray to mid-IR
relation to convert mid-IR flux $\rm{F_{12\mu m}}$ to X-ray flux
$\rm{F_{(2-10keV)}}$. We then used the median, minimum and maximum for
$\rm{F_{\nu}/F_{(2-10keV)}}$ to estimate the expected flux at the three sub-mm
frequencies studied. The ALMA sensitivity limits, or the root mean square
(rms), according to the exposure time calculator, considering one hour (on-
source) observing time using the most sensitive ALMA configuration and the
full bandwidth (BW) receivers ($\sim$ 8 GHz BW) are $\sim$12, $\sim$85, and
$\sim$260 $\mu$Jy at 100 GHz/3000 $\rm{\mu m}$, 353 GHz/850 $\rm{\mu m}$, and
666 GHz/450 $\rm{\mu m}$, respectively. Comparing our results with these
limits, further constrains the plausible detectability of the torus. A torus
at 100 GHz/3000 $\mu$m is not detectable, even with observations of 10 hours
long. This integration time would gives an rms of 4$\mu$Jy, but it is still
not enough to detect, with a marginal detection limit (5$\sigma$), the flux
density of the brightest torus (10 $\mu$Jy at 100 GHz/3000 $\rm{\mu m}$).
Using the 350 GHz/850 $\rm{\mu m}$ band it is possible to have a good
detection (a 10 $\sigma$ detection) for a torus with flux density larger than
850 $\mu$Jy ($\sim$ 1 mJy), selecting a sample of bright AGN (with flux
density as bright as $\sim$ 10 Jy). Fainter tori are not detectable even with
larger integration time. A 10-hr, integration time observation at this
frequency band can reach an rms of 30 $\mu$Jy. However, this is still not
enough to detect a 4 $\mu$Jy torus or the tori of those AGN with hundred of
mJy flux density. Therefore, although a large fraction of torus could be
detected at the 353 GHz/850 $\rm{\mu m}$ (see col. 4 in Table 1), its median
values would never be detected for an AGN with 150 mJy at 12 $\rm{\mu m}$ and
for an AGN as bright as 10 Jy.

A larger flux density is expected for the torus contribution at the 666
GHz/450 $\rm{\mu m}$. At this frequency it is possible to have good detection
(a 10 $\sigma$ detection) for tori brighter than $\sim$2.6 mJy, therefore
selecting bright tori of bright AGN (with flux density as bright as $\sim$ 10
Jy). Using longer integration time, e.g. 10 hr, the rms can go down to $\sim$
80 $\mu$Jy, giving the chance to detect tori brighter than 800 $\mu$Jy.
However, in this scenario it is still difficult to detect the flux density of
the brightest torus for a 150 mJy AGN (it would be detected at $\sim$
3$\sigma$ detection limit). Overall, the result is that, even if on average
the torus dominates at this frequency (see col. 4 in Table 1), it will not be
detected considering the median of the distribution.

Knowing the ALMA rms estimate of 1 hr or 10 hr integration time, the median
value of the radio jet is, in principle, not detected in the sub-mm range.
However, bright radio jets for bright AGN (with flux density as bright as
$\sim$ 10 Jy) can contaminate the sub-mm continuum flux density at all the
three frequency/wavelength bands considered.

Thus, only the brightest, largest, thickest, and with the largest number of
clouds tori (see Section 2.1) will produce enough flux to be detected at
either the 353 GHz/850 $\rm{\mu m}$ and 666 GHz/450 $\rm{\mu m}$ sub-mm
frequencies. To give a general estimate of the ALMA detectability of the torus
and to summarize the above paragraph, we can say that 1 mJy torus
(characteristics of bright AGN, with flux density at 12 $\mu$m S $\sim$10 Jy)
can be detected with 10-$\sigma$ detection limit, observing: 1 hr at 353
GHz/850 $\rm{\mu m}$ and 10 hr at 666 GHz/450 $\rm{\mu m}$. However, the
observer has to be aware of the possible contamination (and in some cases with
very high percentage) by the radio jet at these sub-mm bands. In fact, Tab. 1
shows that the median value of the jet contributor, is not detected at any the
three ALMA frequencies and considering 1 hr or the longer 10 hr integration
time. However, bright radio jet for bright AGN might dominate at these
frequencies.

##  3 Torus detection with ALMA through observations

###  3.1 Cases of study

With no attempt to define a complete sample, we select four AGN to confront
our predictions on the detectability of the torus at sub-mm wavelengths with
actual data. As we showed in section 2, the detectability is sensitive to the
brightness at X-ray/mid-IR wavelengths, the accretion rate, and the BH mass.
It also depends on the torus parameters but we cannot know these parameters
ahead of the analysis.

We select targets with available radio data to trace the jet contribution,
mid-IR data to trace the torus contribution, and with continuum sub-mm
observations. Additionally, we selected our targets by probe different optical
classes. These targets are: the Low-Luminosity AGN (LLAGN) NGC 1052, the
Type-2 Seyfert NGC 1068, the Type-1.5 Seyfert NGC 3516, and the QSO IZw 1. Our
four AGN cover a wide range of X-ray luminosity with more than 2 orders of
magnitude, a factor of 10 in BH masses, and a wide range of 12 $\rm{\mu m}$
fluxes from 150 mJy to 35 Jy. General information about our selected targets
are shown in Table 2.

NGC 1052 is a nearby ($z=0.005$; we used the average distance independent on
redshift reported in NED222The NASA/IPAC Extragalactic Database (NED) is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration.)
elliptical galaxy which hosts a LLAGN in its center (with luminosity between
1GHz and 100 GHz: L$\rm{{}_{1-100GHz}=4.4\times 10^{40}}$ erg s-1 ; Wrobel,
1984). It shows a twin-jet system in the east-west direction at radio kpc and
pc scales, oriented close to the plane of the sky (Vermeulen et al., 2003;
Cooper et al., 2007) which is contained within the optical galaxy. Its optical
spectrum is characterized by strong forbidden lines from low-ionization
states. For this reason this source is considered a prototypical LINER (low-
ionization nuclear emission line region; Heckman, 1980) galaxy. The X-ray
images of NGC 1052 show a point-like X-ray source and its X-ray spectrum is
extremely flat, most likely explained by the advection dominated accretion
flow (ADAF) mechanism (Guainazzi et al., 2000a). To model the AGN X-ray
spectrum, large absorbing column densities have been discussed, supporting the
idea of a highly dense obscuring torus (e.g., Risaliti et al., 2002). Evidence
of an obscuring torus has also been suggested from VLBI observations in the
radio regime; a prominent emission gap has been detected between the twin-jet
system (e.g., Kadler et al., 2003). Although NGC 1052 has been part of large
samples to study the torus component in LLAGN (Mason et al., 2012; González-
Martín et al., 2015, 2017), its torus has never been modeled individually.

NGC 1068 ($z=0.002$; redshift-independence reported in NED) is the prototype
Seyfert 2 galaxy, where the central engine is supposed to be blocked by the
dusty torus. It has been studied at a large number of wavelengths: e.g., in
the radio band (at 5-GHz and 8.4 GHz) using Very Long Baseline Interferometry
(VLBI) technique (Muxlow et al., 1996; Gallimore et al., 2004); in mm band
(Krips et al., 2006); in near- and mid-IR bands (Marco & Alloin, 2000;
Galliano & Alloin, 2002; Jaffe et al., 2004; Galliano et al., 2005); and at
high energy X-rays (Guainazzi et al., 2000b). The relativistic jet is
prominent and it extends for several kpc in both directions. It changes the
direction about 0.2${}^{\prime\prime}\;$ from the nuclear region. This change
is presumed to be the result of an interaction with a molecular cloud
(Gallimore et al., 2004). Significant near- and mid-IR emission is associated
with the inner radio jet (Marco & Alloin, 2000; Jaffe et al., 2004; Galliano
et al., 2005) which is presumed to be the result of shock heating of the dust
in the ISM by the passage of the radio jet. Lopez-Rodriguez et al. (2018) used
SOFIA, infrared and sub-mm observations in order to characterize the emission
and distribution of the dust in NGC 1068. They fitted the nuclear SED of NGC
1068 using clumpy and smooth torus models, finding for clumpy torus: an
angular width $\rm{{\sigma=43^{+12}_{-15}}^{\circ}}$, a radial thickness
$\rm{Y=18^{+1}_{-1}}$, a number of equatorial clouds $\rm{N_{0}=4^{+2}_{-1}}$,
a radial distribution $\rm{q=0.08^{+0.19}_{-0.06}}$, an optical depth
$\rm{\tau_{V}=70^{+6}_{-14}}$, a viewing angle
$\rm{i={75^{+8}_{-4}}^{\circ}}$, an inner radius
$r_{in}=0.28^{+0.01}_{-0.01}pc$, and an outer radius
$r_{out}=5.1^{+0.4}_{-0.4}pc$ ; and for the smooth torus: an opening angle
$\rm{\theta_{A}=37^{+23}_{-8}}$, a radial thickness $\rm{Y=20^{+4}_{-4}}$, a
fixed radial distribution $\rm{q=1}$, an optical depth
$\rm{\tau_{V}=250^{+20}_{-10}}$, a viewing angle
$\rm{i={79^{+7}_{-10}}^{\circ}}$, an inner radius
$r_{in}=0.41^{+0.05}_{-0.02}pc$, and an outer radius
$r_{out}=8.5^{+7.9}_{-0.7}pc$. Moreover, Fritz et al. (2006) fitted the SED of
NGC 1068 using their smooth model and their parameters were: an opening angle
$\rm{\theta_{A}=160^{\circ}}$, a radial thickness $\rm{Y=20}$, a radial
density distribution $\rm{\beta=-1}$, a altitude density distribution
$\rm{\gamma=6}$, an optical depth $\rm{\tau_{V}=8}$ and a viewing angle
$\rm{i=70^{\circ}}$. They obtained a minimum radius $r_{min}=0.82pc$, and a
maximum radius $r_{max}=16.4pc$. Note that with both models, clumpy and
smooth, a similar torus size is obtained, given by the $Y$ parameter.

NGC 3516 is a bright type 1.5 Seyfert galaxy. It has a redshift of z = 0.012
(using redshift-independent measurement reported in NED). Its SMBH is
estimated to have a mass of MBH=1$\times$107M⊙ (Onken et al., 2003). NGC 3516
has been extensively observed and studied at UV and X-rays. This source has
strong UV absorption lines, specifically NV, CIV, and SiIV to have been
detected with the International Ultraviolet Explorer (IUE, Ulrich & Boisson,
1983). In several works it has been found that these lines vary on timescales
as short as weeks (Voit et al., 1987; Walter et al., 1990; Kolman et al.,
1993). Kraemer et al. (2002) found optical absorption features associated to
eight distinctive kinematic components. This complex outflowing features can
also be seen at X-rays (Netzer et al., 2002; Turner et al., 2005; Huerta et
al., 2014). Esparza-Arredondo et al. (in prep.) studies the mid-IR and X-ray
observations of NGC 3516 to explored the torus parameters. They fitted the SED
using the mid-IR (smooth torus model by Fritz et al., 2006) and X-ray (Borus
model, Baloković et al., 2018) models simultaneously and found that the torus
parameters for this sources are: viewing angle $\rm{i=10^{\circ}}$, torus
angular width $\rm{\sigma_{torus}}$ = 60∘, dust density radial profile
$\rm{\gamma}$=5.9, $\rm{\beta=10^{-2}}$, a radial extent $\rm{Y=11.9}$, and an
optical depth $\rm{\tau_{\nu}=3.5}$. No direct observations of its radio jet
have been performed so far.

I Zw1 is on of the prototypical Narrow Line Seyfert 1 (Osterbrock & Pogge,
1985) with narrow permitted lines, weak [O III] emission, strong [Fe II]
emission, a steep soft X-ray spectrum, and strong X-ray variability (Sargent &
Searle, 1968; Phillips, 1976; Oke & Lauer, 1979; Boller et al., 1996; Véron-
Cetty et al., 2004; Gallo et al., 2004). It is also classified as an infrared-
excess Palomar Green QSO and a possible candidate for an ongoing minor merger.
(Schmidt & Green, 1983). Its redshift is z = 0.059 (Ho & Kim, 2009), therefore
I Zw 1 is considered one of the closest QSOs. Martínez-Paredes et al. (2017)
studied the near- and mid-IR continuum emission of I Zw1, fitting the SED to
Clumpy models using BayesClumpy (Asensio Ramos & Ramos Almeida, 2009). The
parameters found were: a viewing angle $\rm{i=79\pm 3^{\circ}}$, a torus
angular width $\rm{\sigma_{torus}<17^{\circ}}$, a radial extent
$\rm{Y=67^{+15}_{-12}}$, a number of equatorial clouds $\rm{N_{0}<4}$, a
radial distribution $\rm{q=1.56^{0.04}_{0.03}}$, and an optical depth
$\rm{\tau_{\nu}=54\pm 4}$. No direct observations of its radio jet have been
performed so far.

Table 2: General information of our selected case of study. Obj name | Coordinates | Distance | $\rm{\log(M_{BH})}$ | $\mathrm{L_{(2-10)keV}}$ | $\rm{F_{12\mu m}}$ | Class. | Observations
---|---|---|---|---|---|---|---
| [J2000] | (Mpc) |  ($\rm{M_{\odot}}$) | (erg/s) | (mJy) |  | mid-IR | cm | sub-mm
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
NGC 1052 | 02:41:04.798 –08:15:20.75 | 20.6 | $\rm{8.1\pm 0.3^{(1)}}$ | $\mathrm{4.60\times 10^{41(a)}}$ | 150 | LINER |  IRS(LR)/_Spitzer_ | JVLA | ALMA
|  |  |  |  |  |  |  | Culgoora-3-3 |
|  |  |  |  |  |  |  | 11-m NRAO |
NGC 1068 | 02:42:40.711 –00:00:47.81 | 10.6 | $\rm{6.9\pm 0.1^{(2)}}$ | $\mathrm{1.0\times 10^{41(b)}}$ |  17$\rm{\times 10^{3}}$ | Seyfert 2 | T-ReCS/Gemini | JVLA | ALMA
NGC 3516 | 11:06:47.490 +72:34:06.88 | 51.5 | $\rm{7.0\pm 0.3^{(3)}}$ | $\mathrm{2.51\times 10^{43(c)}}$ | 300 | Seyfert 1.5 |  IRS(HR)/_Spitzer_ | JVLA | CARMA
I Zw 1 | 00:53:34.940 +12:41:36.20 | 240.7 | $\rm{7.13^{(4)}}$ | $\mathrm{7.1\times 10^{43(d)}}$ | 430 | QSO |  IRS(LR)/_Spitzer_ | JVLA | ALMA
|  |  |  |  |  |  |  |  | JCMT

###  3.2 The data

####  3.2.1 Mid-IR data

The sources NGC 1052, NGC 3516, and IZw1 are point-like sources at several
wavelengths (e.g Schmidt & Green, 1983; Burtscher et al., 2013; Capetti &
Balmaverde, 2005), and their mid-IR emission is mostly dominated by the AGN
itself (Esparza-Arredondo et al. in prep., González-Martín et al., 2017;
Martínez-Paredes et al., 2017). For this reason we used the high and low-
resolution _Spitzer_ /IRS spectral data from the
CASSIS333http://http://cassis.sirtf.com/atlas/  catalog (the Cornell AtlaS of
_Spitzer_ /IRS Sources, Lebouteiller et al., 2011). The resolution of
_Spitzer_ /IRS is R $\rm{\sim}$ 60-130. CASSIS provides flux-calibrated
nuclear spectra associated with each observation. The source NGC 1068, is
characterized by well-known mid-IR extended emission that dominates the
Spitzer spectrum (see Lopez-Rodriguez et al., 2018); therefore high angular
resolution data are mandatory to decontaminate the mid-IR emission from the
contribution of the host galaxy. For this reason, we used the N and Q bands
data from the Thermal-Region Camera Spectrograph (T-ReCS, Telesco et al. 1998,
De Buizer & Fisher, 2005) located in the 8.1 m Gemini-South Telescope. These
data better isolate ($\rm{\sim}$0.3-0.4 ${}^{\prime\prime}\;$ PSF) the torus
component from other dust contributors. T-ReCS data were processed using the
pipeline RedCan (González-Martín et al., 2013) and have also been previously
used by Ramos Almeida et al. (2014).

####  3.2.2 Radio cm and sub-mm data

For the purpose of our project, we collected radio continuum data observed
with the Karl. G. Jansky Very Large Array (JVLA) of the National
Radioastronomy Observatory (NRAO)444The NRAO is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc. in its A-configuration to be able to isolate the radio
emission of the the central engine as much as possible. We obtained the
A-configuration radio data from the JVLA data archive or literature. For the
sources I Zw 1 and NGC 3516, in order to obtain a better radio SED fit, we
also added data from literature obtained at different JVLA configuration.
These data points continue to well represent the central engine flux density.
As well for the source NGC 1052, two data points obtained with radio
instruments different from the JVLA, have been used to better constrain the
radio SED. Information about the JVLA project ID, the JVLA A-configuration
clean beam, its position angle (PA) and literature references, are reported in
Table 5 in Appendix A.

In the sub-mm window, we collected data from the ALMA archive. When ALMA data
were not available, sub-mm flux densities obtained using other sub-mm
instruments and already published, have been used. In particular, we used the
Combined Array for Research in Millimeter-wave Astronomy (CARMA) data
published by Behar et al. (2018) for the source NGC 3516 and the James Clerk
Maxwell Telescope (JCMT) data published by Hughes et al. (1993) for the source
I Zw1. Table 6, in Appendix A, summarizes the sub-mm information at our
disposal.

JVLA archival data have been calibrated using the data-reduction package CASA
(Common Astronomy Software Applications
555https://science.nrao.edu/facilities/vla/data-processing; version 5.1.2).
Standard procedure for flux density, using the standard calibrators 3C 286 and
3C 48, and phase calibration have been applied. Moreover, for the more recent
wide band projects (IDs: 16B-289 and 16B-343) also channel flagging procedures
and standard bandpass and delay calibration have been performed. From the
calibrated data, Stokes I images were made for all the targets at each band
running the CASA clean task. In order to isolate as much as possible the
central radio component, we performed the cleaning using robust 0 or uniform
weighting. Because the majority of the data sets come from the old JVLA
correlator (consisting on 2 intermediate frequencies, IFs, of 50 MHz bandwidth
each), the nterm parameter has been set equal to 1 (i.e., the change in the
spectral index within that small bandwidth is neglected). On the cleaned maps,
a Gaussian fit has been performed on the point like central radio component.
Because of the complex morphology of the source NGC 1068, an additional
process have been perform to the radio images at X and Ku bands (8.4 and 15.0
GHz). We convolved the uniform weighted maps to the L band resolution (1.4 GHz
with $\sim$ 1${}^{\prime\prime}\;$ angular resolution) in order to perform a
proper Gaussian fit to the elongated structure resulted from the cleaning. All
the compact radio components that are present in the central position of this
AGN are well resolved only when reaching sub-arcsec angular resolution
(therefore at Q band, 43 GHz, for our case). In order to match spatial
resolutions during the fitting procedure, we sum the flux densities of the
four 43 GHz radio components (NE, C, S1 and S2) that are clearly resolved and
studied by Gallimore et al. (1996) and (Cotton et al., 2008).

ALMA continuum flux densities have been collected analyzing the products
continuum Stokes I maps available for each projects at the ALMA archive web
page 666https://almascience.eso.org/alma-data/archive. On the continuum Stoke
I maps, a Gaussian fit on the central sub-mm component has been performed to
obtain the sub-mm flux density value. The flux densities for each targets at
each frequency are listed in Table 7 in Appendix A.

###  3.3 Fitting procedure and results

Table 3: Fitting results of the mid-IR spectra to the smooth torus model
described by Fritz et al. (2006).

Par. | Object
---|---
| NGC 1052 | NGC 1068 | NGC 3516 | I Zw1
$i$ | $61_{-2}^{+4}$ | $60\pm 9$ | $1.9_{-0.7}^{+1.1}$ | $<11$
$\sigma$ | $>20.0$ | $20\pm 8$ | $58.5_{-0.4}^{+0.3}$ | $>58$
$\gamma$ | 0.14* | 0.01* | $<6.0$ | $3.2\pm 0.4$
|  | 3.91 |  |
$\beta$ | $-0.03_{-0.07}^{+0.02}$ | -0.99 | $<0.01$ | $-0.95\pm 0.04$
$Y$ | $10.7\pm 0.3$ | $142\pm 19$ | $11.5\pm 0.1$ | $19^{-1}_{+2}$
$\tau$ | $4.0_{-0.4}^{+0.5}$ | $1.81\pm 0.2$ | $3.81_{-0.06}^{+0.07}$ | $1.37^{-0.12}_{+0.76}$
|  | $0.29\pm 0.1$ |  |
$R_{out}$ |  $\sim$0.4 |  $\sim$2.3 |  $\sim$2.9 |  $\sim$8.1
$\chi^{2}/DOF$ | 1217.72/993 | 70.98/262 | 9575.07/1471 | 721.05/992

NOTE– $i$ viewing angle toward the torus; $\sigma$ angular width of the torus;
$\beta$ inversely related to the amount of absorption; $\gamma$ exponent of
the logarithmic azimuthal density distribution; $Y$ ratio between the outer
and the inner radius of the torus; and $\tau$ silicate dust contribution. The
asterisks represent frozen parameters, which could not be constrained. First
and second rows in NGC1068 shows the two values reported for $\gamma$ and
$\tau$ parameters for the N- and Q-bands, respectively (see text).

Figure 6: Mid-IR spectral fit to the smooth dusty model described by Fritz et
al. (2006) for NGC 1052 (top-left), NGC 1068 (top-right), NGC 3516 (bottom-
left) and IZw 1 (bottom-right). For each object we show the best fit to the
data in the top panel and the ratio between model and data in the bottom
panel. The blue shaded area show the error on the measurement. The red long-
dashed line shows the dusty model best-fit and the black solid line show the
total fit, i.e. toroidal model $+$ emission lines (see text).

####  3.3.1 Mid-infrared spectral fit to dusty models

Our purpose is to extrapolate the mid-IR spectral fit to sub-mm wavelengths to
establish the detectability of the torus component at those wavelengths. For
that purpose we fit the mid-IR data to dusty models. Note that we are not
interested in well sample the near- to mid-IR SEDs therefore, we will not
focus on the finding of a very detailed derivation of the model parameters.
Instead, we will test our theoretical predictions from model extrapolations.

The dusty models can be grouped into four classes: smooth (Fritz et al., 2006;
Feltre et al., 2012), clumpy (Nenkova et al., 2008a, b; Hönig et al., 2010a;
Hönig & Kishimoto, 2010b), smooth + clumpy (Stalevski et al., 2012), and windy
(Hönig & Kishimoto, 2017; Siebenmorgen et al., 2015). Among them the most
extensively used to fit data at mid-IR wavelengths is the clumpy model by
Nenkova et al. (2008b) due to their large number of SEDs and probed ability to
explain the spectra of low luminous (González-Martín et al., 2017),
intermediate luminous (Ramos Almeida et al., 2009; Alonso-Herrero et al.,
2011), and high luminous (Nikutta et al., 2009; Martínez-Paredes et al., 2017)
AGN. However, smooth models have been proposed to explain some peculiar
anomalies of the spectra of high luminous AGN (Martínez-Paredes et al., 2017).
Furthermore, windy models are based on a more realistic configuration of dust
according to dynamical arguments (Elitzur, 2006; Elitzur & Ho, 2009, and
references therein). We have tested in this work all the models that have
public access to a SED library: 1. Smooth model by Fritz et al. (2006); 2.
Clumpy model by Nenkova et al. (2008b), 3. Clumpy model by Hönig & Kishimoto
(2010b), 4. Windy model by Siebenmorgen et al. (2015), and 5. Windy model by
Hönig & Kishimoto (2017). We are currently working on a paper that fully
examines the similarities and differences between these five models (González-
Martín et al. 2019A in prep.) and which model better describe current mid-IR
spectra of AGN (González-Martín et al. 2019B in prep.).

We converted these SED libraries to multi-parametric models within the
spectral fitting tool xspec. xspec is a command-driven, interactive, spectral-
fitting program within the HEASOFT777https://heasarc.gsfc.nasa.gov software.
xspec provides a wide range of tools to perform spectral fitting to data,
being able to process in parallel in order to speed them up. To use these
capabilities we need to convert our SEDs to xspec format in order to upload
our models within xspec as additive tables. The basic concept of a table model
is that the file contains an N-dimensional grid of model spectra with each
point on the grid having been calculated for particular values of the N
parameters in the model. xspec is able to interpolate on the grid. We have
created an additive table for each torus model. For further details on the
conversion into xspec format please refer to Esparza-Arredondo et al. (in
prep.).
We also converted the mid-IR _Spitzer_ spectrum into xspec format using
flx2xsp task within HEASOFT. This tool reads a text file containing one or
more spectra and errors and writes out a standard xspec pulse height amplitude
(PHA888Engineering unit describing the integrated charge per pixel from an
event recorded in a detector.) and response files. This allows us to use all
the observed data points within xspec to fit to the data.

We fitted the mid-IR data for the four sources to the five models described
above. In the cases of NGC 3516 and NGC 1052 we included some emission lines
reported in previous works. We used the _addline_ tool available in xspec to
identify and model each line with Gaussian profiles. All the models provide a
reasonable fit to the data. However, the smooth dusty model described by Fritz
et al. (2006) is the only one that does not need an additional component to
provide a good fit to the data. For the others, a stellar component999The
stellar library provided by Bruzual & Charlot (2003) is used to model the
stellar component. We have included this SED library as additive tables within
xspec, similarly to what we did with the torus models. is needed to account
for the short wavelengths (below 10$\rm{\mu m}$). Thus, we used the smooth
dusty model reported by Fritz et al. (2006) hereinafter since, providing an
equally good fit ($\rm{\Delta\chi^{2}/dof<0.1}$), is the simplest baseline
model that satisfactory describes the data. The main difference between the
resulting fit occurs at short wavelengths, so long wavelengths are quite
insensitive to the model used. Therefore we do not expect large discrepancies
on the expected contribution of dust at sub-mm wavelengths due to the
selection of models.
In the case of NGC 1068 we consider initial inclination angles valid for
type-2 Seyfert and toroidal sizes according to those found in the literature
(see García-Burillo et al. (2016) and Lopez-Rodriguez et al. (2018)) using
mid-IR high angular resolution data. However, we were not able to fit both N-
and Q-bands of NGC 1068 with the same values for the parameters of the torus
model. We try different fits; first we link the parameters in both bands,
without getting a good fit. We also tried adding the _constant_ multiplicative
model available in xspec to mimic a possible different resolution (or perhaps
flux slit losses) between the bands but they failed to reproduce both bands at
the same time. Essentially, the shapes of the N- and Q-band spectra cannot be
fitted with the same SED. Then we unlink some parameters individually between
both bands. We tested several combinations of unlinked parameters (e.g. $Y$
and $\tau$). The best result is obtained unlinking $\gamma$, $\beta$ and
$\tau$ parameters (i.e. the coefficients within the density function and the
optical depth). Note that although we use the model by Fritz et al. (2006) for
our fit, we obtain different values of the parameters, since they add to their
fit an IR template of a starburst galaxy to reproduce the colder component of
the emission of dust. NGC 1068 has a well reported complex dust distribution
(Lopez-Rodriguez et al., 2018, and references therein). Indeed, the _Spitzer_
spectrum shows a continuum flux more than 10 times brighter than the ground-
based T-ReCS spectra, indicating external dust contributors at radii larger
than a few hundred of parsecs. We interpret that this behavior of the N- and
Q-bands reflects a complex structure of the dust within the inner
$\rm{\sim}$100 pc that cannot be easily reproduced with a simple dusty model.

Figure 6 shows the best-fit for the targets using the smooth dusty model by
Fritz et al. (2006). The resulting parameters of the mid-IR fitting are
reported in Table LABEL:tab:MIRparam for completeness purposes and the errors
were calculated using the $\mathrm{error}$ tool101010This tool determines the
error ranges by sorting the Monte Carlo chain values and taking a central
percentage of the values corresponding to the confidence level as indicated by
delta fit statistic. in xspec with a 99% confidence. It is out of the scope of
this work to properly characterize the torus properties of our sample. For
that purpose, near-IR (Ramos Almeida et al., 2014) and/or X-ray (Esparza-
Arredondo et al. (prep)) data are needed. From our fitting we find that the
viewing angle for the type-1 AGN (i.e. IZw1 and NGC 3516) is consistent with a
direct view of the central engine while that of the type-2 AGN (i.e. NGC 1068)
is consistent with the interception of the dusty torus in the line of sight,
as previously found using well sampled near to mid-IR unresolved SEDs (e.g.,
Esparza-Arredondo et al. (prep), Lopez-Rodriguez et al., 2018; González-Martín
et al., 2017; Martinez-Paredes17.)

Table 4: Best Fit parameters for the radio spectrum fitting

Source | Model | $\alpha_{thin}$ | $\nu_{0}$ |  S${}_{\nu_{0}}$ | $\tiny{\chi^{2}/\textit{dof}}$
---|---|---|---|---|---
name |  |  | [GHz] | [mJy] |
NGC 1052 | SSA2 |  $-$0.7 | $\rm{0.06\pm 0.01}$ | $\rm{3760\pm 430}$ | 515
|  |  $-$0.7 | $\rm{10.70\pm 0.02}$ | $\rm{2612\pm 14}$ |
NGC 1068 | PL | $\rm{-1.07\pm 0.01}$ | $\dots$ | . . . | 33
NGC 3516 | SSA | $\rm{-0.97\pm 0.07}$ | $\rm{1.8\pm 0.2}$ | $\rm{6\pm 1}$ | 0.7
I Zw1 | PL | $\rm{-0.65\pm 0.04}$ | $\dots$ | . . . | 0.1

NOTE: Col. (1), source name; Col. (2), best fit where PL is a simple power-law
fit (fitting the synchrotron optically thin part of the spectrum only), SSA is
a single synchrotron self-absorption component, and SSA2 is the combination of
two synchrotron self-absorption components; Col. (3), spectral index value in
the optically thin part of the spectrum; Col. (4), frequency value where the
synchrotron emission changes from optically thick to optically thin and its
relative flux density value in Col. (5); Col. (6), the statistical value of
$\chi^{2}$/dof.

Figure 7: Radio spectrum fitting for the sources NGC 1052, NGC 1068, NGC 3516,
and I Zw1. Power-law model has been used for NGC 1068 and I Zw1, a single
synchrotron component model for NGC 3516, and two synchrotron components model
for NGC 1052. Blue square points are the cm wavelength data, green square
points are sub-mm ALMA data, and magenta crosses are sub-mm data from other
instruments. Black arrows mark those data points for which the angular
resolution is larger than 0.3${}^{\prime\prime}\;$, where extended
contributors might be present. The orange straight lines, where present,
represent the single synchrotron components while the red straight line and
the blue transparent band are the total fit of the radio data (i.e.,
considering the JVLA/cm data only) together with its error. The fundamental
plane prediction together with its uncertainty, of an order of magnitude, is
also shown in the plots as the dashed green line and a gray band,
respectively.

####  3.3.2 Radio spectral fit to the synchrotron emission

The total intensity radio spectra of the targets have been fitted using a
power law ($\rm{S^{PL}_{\nu}}$), representing the optically thin part of a
radio synchrotron spectrum, and a single or a composition of two synchrotron
emitting components ($\rm{S^{SSA}_{\nu}}$ and $\rm{{}^{SSA2}_{\nu}}$),
considering homogeneous, self-absorbed sources. Each synchrotron emitting
component is modeled with power-law electron energy distributions with
spectral index in the optically thick and thin parts of the spectrum
$\rm{\alpha_{thick}}$=2.5 and $\rm{\alpha_{thin}}$, respectively. The
equations used for the radio spectra fitting are the following:

  * •

a power law (optically thin synchrotron spectrum) with a slope
$\rm{\alpha_{thin}}$ (left to vary):

$S^{PL}_{\nu}\propto\nu^{\alpha_{thin}};$ (5)

  * •

a single synchrotron self-absorption component ($\rm{S^{SSA}_{\nu}}$):

$S^{ssa}_{\nu}\propto\nu^{2.5}\left(1-\exp\left(-\left(\frac{\nu}{\nu_{0}}\right)^{\alpha_{thin}-2.5}\right)\right),$
(6)

where $\rm{\nu_{0}}$ is the frequency where the emission changes from
optically thick, with a spectral index of 2.5, to optically thin with a
spectral index $\rm{\alpha_{thin}}$ (left to vary);

  * •

a combination of two synchrotron components ($\rm{S^{SSA2}_{\nu}}$) with fixed
$\rm{\alpha_{thin}=-0.7}$ in order to reduce the number of free parameters.

To fit the above functions to the data we used the python task curvefit on the
cm wavelength data (i.e., JLVA data and cm wavelength from literature) only.
For this radio fitting procedure we considered the errors of the data points
as absolute. This allows to provide the variance of the estimated fit
parameters as the square root of the diagonal of the covariance matrix. For
each source, we selected the best model according to the lowest statistical
reduced chi-squared test ($\rm{\chi^{2}}$/dof) value.

The resulting parameters of the radio fitting are reported in Tab. 4. Fig. 7
shows the results of the radio fitting of the targets using a single power law
for the sources I Zw1 and NGC 1068, one synchrotron component for the source
NGC 3516 and two synchrotron components for the source NGC 1052. Sub-mm data
points (ALMA and CARMA or JCMT) are also shown in the plots (as green squares
and magenta crosses respectively). We marked with a black arrow those ALMA
data for which the angular resolution is larger that 0.3${}^{\prime\prime}\;$
(which correspond to a spatial resolution of $\sim$340, $\sim$140, $\sim$800
pc for NGC 1052, NGC 1068 and NGC 3516 respectively and $\sim$4 kpc for I Zw
1). These data, together with sub-mm data obtained from other sub-mm
telescopes (i.e., magenta cross) could overestimate the flux density at that
frequency due to the large beam size. We will discuss this issue in section 4.
The radio spectra fitting works very well for the sources I Zw1 and NGC 3516,
while the fit shows large $\rm{\chi^{2}}$/dof values for the sources NGC 1068
and NGC 1052. The fit cannot represent the JVLA high frequency data point (at
43.4 GHz) for NGC 1068 without adding a second synchrotron component in the
sub-mm window (see the discussion section). NGC 1052 shows a complex behavior,
that cannot be accounted for with our fit, due to its variability at mid and
high radio frequencies (for $\rm{\nu>}$5 GHz); multi-frequencies instantaneous
radio observations could resolve this issue.

The fundamental plane prediction (green-dashed line and gray band) shown in
each plot, gives an idea of the order of magnitude of the flux density of the
radio jet. The fundamental plane, considering its uncertainties, follows the
trend of the radio emission described by the jet in all cases except for NGC
3516 where the fundamental plane is an order of magnitude above the radio
emission. Moreover, it does not account for the complexity of the radio
emission. For example, in the case of NGC 1052 it is clear that the AGN needs
two synchrotron components in order to represent the high radio frequency part
of the spectrum (for frequencies larger than $\sim$ 10 GHz or wavelength
smaller that $\sim$ 3$\times$104, see Tab. 4); instead, the fundamental plane
prediction goes below the high frequency JVLA data. For NGC 1068 and NGC 1052,
for which we have much more sub-mm values at our disposal, the sub-mm flux
densities increase towards larger wavelengths, opposite to what is expected if
this emission is associated to dust. Although the possible inaccuracies
described above, it is worth to notice that the fundamental plane seems to
include, in all the case of study, a non-negligible jet contribution to the
sub-mm band.

These fits probe that the sub-mm part of the spectra is still (partially)
contaminated by synchrotron emission (perhaps dominating for NGC 1052 and NGC
1068). However, a better analysis on this aspect is given in Section 4, where
the mid-IR fit and the radio fit are combined together, giving a broad view on
the contributors to the SED of these four AGN.

##  4 Discussion

Figure 8: SED fit for NGC 1052 to the mid-IR spectra (black spectrum) with the
torus model (long-dashed line) and to the cm wavelengths (blue points) with
synchrotron emission (dotted line). Green stars are sub-mm and far-infrared
data. Arrows indicate plausible upper limits when the spatial resolution is
worse than 0.3${}^{\prime\prime}\;$ (see text).

There is no doubt that the dust around AGN plays an important role in
obscuring the central engine and eventually fueling the accretion disk
(Netzer, 2015, and references therein). Therefore, the distribution and
composition of the dust in AGN and how they might evolve at different stages
of the AGN evolution is of great importance (Elitzur, 2006; Elitzur et al.,
2014; Elitzur & Netzer, 2016). This is why the torus properties in AGN have
been largely discussed in the literature, mainly through unresolved SED
fitting (e.g. Ramos Almeida et al., 2009, 2011; Alonso-Herrero et al., 2011;
González-Martín et al., 2015; Martínez-Paredes et al., 2015; Fuller et al.,
2016; González-Martín et al., 2017; Martínez-Paredes et al., 2017), and also
with mid-IR interferometric measurements (Tristram et al., 2009; Tristram &
Schartmann, 2011; Tristram et al., 2014), since its size ($\rm{<10pc}$) cannot
be resolved with arcsecond resolution images. The only facility able to
achieve sub-arcsecond angular resolution at sub-mm, and therefore to actually
image (at least some) of the AGN tori is ALMA. This sub-mm interferometer
provides a unique opportunity to directly measure the size of the torus.
However, this wavelength band could be contaminated by the contribution of
synchrotron emission by the jet and/or dust heated by star-formation (Alonso-
Herrero et al., 2014; Esquej et al., 2014; Esparza-Arredondo et al., 2018;
Martínez-Paredes et al., 2018). The latter might be decontaminated thanks to
the super spatial resolution of ALMA data. In this work we use two main
assumptions to compute the percentage of torus contribution at sub-mm
wavelengths: (1) the continuum of dust at mid-IR wavelengths follows a well
reported relation with the X-ray luminosity (Lutz et al., 2004; Gandhi et al.,
2009; Asmus et al., 2015) and (2) the 5 GHz luminosity is also linked to the
X-ray luminosity, known the BH mass of the system (known as the radio
fundamental plane Bonchi et al., 2013). We used the dusty torus models of
Nenkova et al. (2008b) for mid-IR wavelengths and a power-law distribution for
cm wavelengths to extrapolate these predictions to the sub-mm wavelengths. In
this way we showed that the chances to detect the torus are low. These chances
slightly increase when using the lowest ALMA wavelengths (or the highest ALMA
frequencies, see Fig. 1) and high accretion sources (mainly low BH mass and
high luminous sources, see Fig. 3). Among all of these assumptions the most
risky one is the radio fundamental plane. It actually traces radio-core
emission however, compact new radio jet component (therefore dominating at
higher radio frequency) could contribute to the radio band and, in particular,
substantially to the sub-mm band. Indeed, in the previous section we show that
the fundamental plane is a rough estimator of the sub-mm contribution of the
jet (see Fig. 7). However, it cannot describe a possible complex behavior in
the radio band, as clearly seen at least in NGC 1052 (and perhaps in NGC 1068,
see below). Furthermore, in the particular case of NGC 3516, the fundamental
plane over-predicts the jet contribution compared to the detailed analysis of
the SED.

Figure 9: SED fit for NGC 1068 to the mid-IR spectra (black spectrum) with the
torus model (long-dashed and dot-dashed lines show the fit to the N- and
Q-band respectively, see text) and to the cm wavelengths (blue points) with
synchrotron emission (dotted line). Cyan circles are the SOFIA data points.
Green stars are sub-mm and far-infrared data. Arrows indicate plausible upper
limits when the spatial resolution is worse than 0.3${}^{\prime\prime}\;$ (see
text). Note that residuals for the sub-mm data are computed using the Q-band
mid-IR fit to the torus together with the VLA fit to the jet.

In order to make a clear picture on the contributors to sub-mm wavelengths, we
show the full SED fitting when combining together the mid-IR and the radio
data for NGC 1052, NGC 1068, NGC 3516, and IZw 1 in Figs. 8, 9, 10, and 11,
respectively. We kept the same symbols and colors to describe the mid-IR and
radio data as those used during the separated fitting procedure. The ALMA data
with angular resolution larger than 0.3${}^{\prime\prime}\;$ are marked with a
black arrow. These data points, together with JCMT and CARMA data, could be
overestimating the flux density at that frequency/wavelength due to external
contributors, because of the relatively large beam size. Both fits have been
extrapolated in the sub-mm window and the sum of the two components are shown
as black straight lines.

For the LLAGN NGC 1052 the radio jet contribution expands towards the sub-mm
window while the torus contribution falls down very quickly at $\sim$100$\mu$m
(Fig. 8). This is consistent with our theoretical predictions which show that
the low accreting AGN (with high BH mass and low X-ray luminosity) tend to be
highly dominated by the jet at sub-mm wavelengths (see Section 2.2). It is
also in agreement with previous analysis of ALMA data for the LLAGN NGC 1097
(Izumi et al., 2017) and NGC 1377 (Aalto et al., 2017), where they report
strong contributions of a variable component associated to the jet.

Indeed, the jet of NGC 1052 dominates the vast majority of the emission in the
$\rm{5-10^{6}\mu m}$ range, with the overall peak of the emission at radio
frequencies. This is not the case for the rest of the three sources, where the
overall peak of the emission is below 50$\rm{\mu m}$. In any of these cases,
neither the torus or the jet can explain solely or as combined effect the sub-
mm emission with a ratio between data and model of $\rm{\sim}$3, 8 and even
100 for NGC 1068, NGC 3516, and I Zw1, respectively.

Figure 10: SED fit for NGC 3516 to the mid-IR spectra (black spectrum) with
the torus model (long-dashed line) and to the cm wavelengths (blue points)
with synchrotron emission (dotted line). Pink cross is sub-mm data.

Very complex is the situation for NGC 1068. We could not fit the N- and Q-band
mid-IR spectra to a single model. On the contrary, we needed to allow three
parameters ($\gamma$, $\beta$ and $\tau$ see Tab. LABEL:tab:MIRparam)
111111Although beta was set as free parameter, both bands gave the same
result. to behave differently while the rest of the parameters are set to the
same value. In this way we obtained two extrapolations of the torus component
to the sub-mm wavelengths. We highlight to the reader that the fit reported
here is far from realistic but is a clear indication of complex configuration
of dust which cannot be fitted to a simple torus model (see Section 3.3.1),
which is well documented in the literature (see Lopez-Rodriguez et al., 2016,
and references therein).

Note that the SOFIA data reported by Lopez-Rodriguez et al. (2018) at the
$\rm{20-50\mu m}$ range show the peak of the mid-IR emission in $\rm{30-40\mu
m}$ range, consistent with the Q-band rather than with the N-band spectral
fit. After SED fitting to mid-IR and ALMA data at $\rm{\sim 450\mu m}$ (i.e.
666 GHz), they reported a torus outer radius of $\rm{\sim 5}$ pc. This outer
radius is larger than the one reported here ($\rm{\sim 2pc}$, see Table
LABEL:tab:MIRparam). However, they argue that the use of SOFIA and ALMA data
yields to larger estimate on the outer radius of the torus. This was also
shown by García-Burillo et al. (2016), Gallimore et al. (2016), and Imanishi
et al. (2018). The question we would like to answer here is whether the sub-mm
ALMA data is actually tracing the dust in the torus. Indeed the mid-IR Q-band
spectral fit can easily account for the $\rm{\sim 450\mu m}$ density flux
(Fig. 9). Moreover, the mid-IR N-band fit could even predict the ALMA upper
limits at $\rm{\sim 3000\mu m}$. However, the entire SED at sub-mm wavelengths
(with flux densities increasing with wavelength) is tough to explain with any
complex scenario of dust. When considering NGC 1068 radio cm and sub-mm data
points altogether for the radio fitting, the result is a combination of two
synchrotron components with two different spectral indexes representing the
optically thin parts (see Fig. 12). The first synchrotron component peaks at
2.24 ($\pm$ 0.09) [GHz] with flux density 3088 ($\pm$ 301) [mJy] and has a
spectral index value of $\alpha_{th1}$ $\sim$ –2.0 $\pm$ 0.1 ; the second
component peaks at 60 ($\pm$ 2) [GHz] with a flux density of 50 ($\pm$ 2)
[mJy] and a spectral index value of $\alpha_{th2}$ $\sim$ –0.75 $\pm$ 0.03.
The $\chi^{2}/dof$ value of the fit is 0.8. The former value represents an
”aged” distribution of synchrotron electrons while the last is flatter. This
increases the jet contribution in the sub-mm window placing further the
possibility to detect the emission from the dusty torus at this wavelength
band.

Figure 11: SED fit for I Zw1 to the mid-IR spectra (black spectrum) with the
torus model (long-dashed line) and to the cm wavelengths (blue points) with
synchrotron emission (dotted line). Green star and pink crosses are sub-mm and
far-infrared data, respectively. Arrows indicate plausible upper limits when
the spatial resolution is worse than 0.3${}^{\prime\prime}\;$ (see text).
Figure 12: Radio cm and sub-mm fit for NGC 1068. Best fit and its error are
shown with red straight line and transparent blue band. Orange straight lines
are the two single synchrotron components, both with free spectral index
values. Blue data are cm data points, green data are ALMA data points. Dashed
green line and gray band are the fundamental plane prediction together with
its uncertainty.

Also puzzling is the case of NGC 3516. The sub-mm data point (CARMA data) does
not lie on its predicted value if it is the sum of the jet and the torus
contributors (large angular resolution). Thus, either the parameters of the
torus obtained from the mid-IR wavelengths are wrong or there is another
component contributing to the sub-mm wavelength. This extra component could be
(1) dust heated by star-formation (considering the lower-spatial resolution of
the sub-mm data point) or (2) a younger knot component of the jet as seen in
NGC 1052 or NGC 1068.

In the case of I Zw1 the sub-mm data points are well above the prediction,
most likely because of the large angular resolution. This object is clearly
extended at MIR on scales of few hundred pc (Martínez-Paredes et al., 2017),
but it is still not clear if the extended emission is related with the
possible presence of a circumnuclear ring ($\sim 1.7$ kpc of diameter)
detected by Schinnerer et al. (1998) using 12CO(2-1) and 13CO(1-0) molecular
lines. A fraction of this emission could be also be attributed to a silicate-
emitting dust component that extent until the inner part of the narrow line
region (Schweitzer et al., 2008). On the other hand, Hughes et al. (1993)
argued that a fraction of the emission at sub-mm wavelength could be
attributed to dust heated by an extended ($>1$ kpc) starburst region.
Therefore, the JCMT data (i.e. the magenta crosses) could be simply explained
by an additional dust contributor from star-formation, peaking around
$\rm{\sim 100-200\mu m}$. Uncertain is the ALMA data at 1000$\mu$m. Although
this point could be overestimating the flux density at this wavelength, it
lies where the contribution of the flux density changes from the torus to the
jet contributor. Dust heat by star-formation (as an extrapolation of the JCMT
data) could also explain the ALMA detected flux. However, even with all the
caveats in mind, this is the most promising case of torus being the dominant
contributor to sub-mm wavelength because at least a large fraction of emission
is expected to come from the dusty torus. This result is consistent with our
theoretical predictions because IZw 1 is the highest accreting source among
our sample (with relatively low BH mass and high X-ray luminosity, see Table
2). Finally, the estimated outer radius of the torus for this source is
$\rm{\sim 8}$ pc, which at the distance of I Zw1 (240.7 Mpc) implies that the
torus has an angular size on the sky of $\rm{\sim 0.007^{\prime\prime}\;}$.
The ALMA image in fact shows a point-like morphology with a beam size of
$\rm{\sim}$0.6${}^{\prime\prime}\;$ (Imanishi et al., 2016a). Thus, even if
the torus is dominating in this high accreting sources, it might be difficult
to resolve it with current interferometric observations.

As a final caveat, we would like to stress that our findings on the SED
fitting are biased toward the use of the library of SED models. Although we
tested up to the five most used dusty models (see Section 3.3.1), we decided
to use in all the cases the smooth torus model described by Fritz et al.
(2006). The rest of the models need an extra stellar component to account for
the short mid-IR wavelengths. Although, we do not expect large discrepancies
using any of the other models to extrapolate the torus to the sub-mm
wavelengths, all of them are (perhaps not very realistic) simplifications of
the configuration of dust in AGN. This is clearly shown in the case of NGC
1068 where a complex fit was needed to account for the spectral fit of both N-
and Q-bands together. Therefore, a much more complex scenario could yield to a
different contribution of the dusty torus at sub-mm wavelengths. Indeed, as
already mentioned in Sect. 2.1, we also considered the contributions from the
hot graphite dust and the dusty NLR clouds (Mor et al., 2009; Mor & Netzer,
2012). The contribution by the former is insignificant when extrapolated to
the sub-mm window and the contribution of the last, although it could be as
large as 40% of the total emission at 24 $\mu$m, is not enough to describe the
behavior in the sub-mm band.

The message to take away is that unfortunately there are very few chances to
detect the torus over the jet at sub-mm wavelengths. This has been claimed to
be the case for NGC 1068 (García-Burillo et al., 2016). They claimed the
detection of the dusty torus based on a fitting of the u-v visibilities within
a radius of 0.2${}^{\prime\prime}\;$. From this result the torus would be
within 0.1${}^{\prime\prime}\;$. However, looking at the resolution of their
continuum image, the source is only 2-3 beam resolved, therefore it is
marginally resolved. Moreover, although they do mention that 18% of the total
flux within that region could come from other mechanisms different from
thermal dust, from our theoretical calculation we do estimate that the
contribution from the synchrotron emission from the radio jet could be as high
as $\sim$94% at this high frequency. Indeed, from our SED analysis, this
observations might be contaminated by the jet components. The most promising
case among our targets is I Zw1. However, even in this case the chances to
spatially resolve it are low. We also explored the SED of the type Seyfert 2,
the Circinus galaxy. However, this is a complex source, as shown in the recent
work by Izumi et al. (2018), with a large ISM contamination in the mid-IR
Spitzer spectrum. Therefore, due to the large contamination of warm dust from
star formation, we could not extrapolate this contribution to the submm range.
Moreover, Elmouttie et al. (1998) revealed a very flat radio source at the
position of the nuclear region at frequency larger that 8 GHz. Therefore, also
in this case, it is plausible that there is still synchrotron emission
contamination in the sub-mm band, due to high frequency radio components from
the radio jet. We strongly suggest to perform SED analysis, including radio
data, with particular attention to the angular resolution used, before drawing
any conclusion on the detection of a torus at sub-mm wavelengths. Another
possibility already exploited by other authors (e.g. Izumi et al., 2017) is to
study the variability pattern of the sub-mm wavelengths because we do not
expect the torus to vary in a year-period basis while the jet would show such
variations.

##  5 Summary

This work aims to study the detectability of the torus in the sub-mm window.
Specifically, we wanted to analyze this aspect considering the ALMA
capabilities. Indeed, this sub-mm interferometer is the only facility able to
achieve sub-arcsec angular resolution and very good sensitivity (tens of
$\mu$Jy) to actually image the AGN tori. We hack this issue using two
approaches: the first is a theoretical approach and the second an
observational one.

For the former, we considered the most used SED models for dusty AGN emission
as the Clumpy models (Nenkova et al., 2008a, b) together with known scaling
relations between the accretion disk luminosity and the torus continuum
(Gandhi et al., 2009; Netzer, 2015; Asmus et al., 2015), and the accretion
disk luminosity, jet contribution and SMBH mass (Bonchi et al., 2013; Saikia
et al., 2015). We extrapolated the scaling relations to the sub-mm wavelengths
and we estimated in which conditions the torus could prevail on the radio jet.
The main result is that we are more likely to detect bigger and denser dusty
tori at the highest ALMA frequency (666 GHz/450 $\mu$m). A 1 mJy torus
(characteristics of bright AGN, with flux density S$\rm{\sim}$10 Jy) can be
detected with high detection limit, observing: 1h at 353 GHz/850 $\rm{\mu m}$
and 10h at 666 GHz/ 450$\rm{\mu m}$, being aware of the possible contamination
by the radio jet.

For the observational approach, we used four prototypical AGN: NGC 1052
(LLAGN), NGC 1068 (Type-2 Seyfert), NGC 3516 (Type-1.5 Seyfert) and I Zw1
(QSO). These targets have been selected to have available radio data (to trace
the jet contribution), mid-IR data (to trace the torus contribution), and
continuum sub-millimeter observations. After performing individual mid-IR
(using the smooth dusty model described by Fritz et al., 2006) and cm-radio
(using a power law and a single, or a composition of, synchrotron component/s)
fit to the spectra, we combined them together to compare the extrapolation of
both torus and jet contributors at sub-mm wavelengths with data at those
wavelengths. The radio jet of NGC 1052 dominates over the torus in the sub-mm
range. In all the other cases, neither the torus or the jet can explain the
sub-mm emission. This result is consistent with the theoretical predictions
for which: low accretion AGN are highly dominated by the jet, while high
accretion sources (like I Zw 1) might be good candidates to detect emission
from the torus at sub-mm wavelengths.

We therefore suggest to perform SED analysis including radio data in order to
isolate the torus contribution from jet or dust heat by the AGN.

## Acknowledgements

This paper is mainly funded by the DGAPA PAPIIT project IA103118. This paper
makes use of the following ALMA data:
2012.1.00034.S, 2013.1.01225.S, 2013.1.00055.S, 2013.1.01151.S,
2013.1.00221.S, 2015.1.00989.S, 2015.1.00591.S, 2016.1.00232.S. ALMA is a
partnership of ESO (representing its member states), NSF (USA) and NINS
(Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ.
Support for CARMA construction was derived from the states of California,
Illinois, and Maryland; the James S. McDonnell Foundation; the Gordon and
Betty Moore Foundation; the Kenneth T. and Eileen L. Norris Foundation; the
University of Chicago; the Associates of the California Institute of
Technology; and the National Science Foundation. Ongoing CARMA development and
operations are supported by the National Science Foundation under a
cooperative agreement, and by the CARMA partner universities.
The James Clerk Maxwell Telescope is operated by the East Asian Observatory on
behalf of The National Astronomical Observatory of Japan; Academia Sinica
Institute of Astronomy and Astrophysics; the Korea Astronomy and Space Science
Institute; the Operation, Maintenance and Upgrading Fund for Astronomical
Telescopes and Facility Instruments, budgeted from the Ministry of Finance
(MOF) of China and administrated by the Chinese Academy of Sciences (CAS), as
well as the National Key R&D Program of China (No. 2017YFA0402700). Additional
funding support is provided by the Science and Technology Facilities Council
of the United Kingdom and participating universities in the United Kingdom and
Canada.
This research has made use of the NASA/IPAC Extragalactic Database (NED),
which is operated by the Jet Propulsion Laboratory, California Institute of
Technology, under contract with the National Aeronautics and Space
Administration.
A.P. acknowledges support by UNAM-DGAPA and to Cátedra CONACyT. D.E.A. and
N.O.C. would like to acknowledge CONACYT scholarships No. 592884 and No.
897887, respectively. MM-P acknowledges support by UNAM-DGAPA and KASI PostDoc
fellowship.

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##  Appendix A Radio cm and sub-mm information

Here we report the radio cm and sub-mm information such as: the used radio cm
and sub-mm telescope band and frequency, the archival project ID, literature
references together with technical information (in Tab.s 5 and 6). Moreover,
the radio cm and sub-mm flux densities are reported in Tab. 7

Table 5: JVLA A-configuration and literature references information.

Source Name | Band |  $\nu$ [GHz] | Project ID |  Clean beam [${}^{\prime\prime}\;$] | PA [deg] | Reference
---|---|---|---|---|---|---
NGC 1052 | – | 0.08 | – | – | – |  Slee (1977)(1)
L | 1.4 | 16B-289 |  2.8$\times$1.0 | –47 | –
C | 4.4 | – | – | – |  Perley (1982)(2)
C | 6.2 | 16B-343 |  0.4$\times$0.3 | –30 | –
X | 8.4 | AW278 |  0.3$\times$0.2 | –24 | –
Ku | 14.9 | AF339 |  0.1$\times$0.09 | –30 | –
K | 22.1 | BC0066 |  0.09$\times$0.07 | 4 | –
– | 31.4 | – | – | – |  Geldzahler & Witzel (1981)(1)
NGC 1068 | L | 1.4 | AU079 |  1.5$\times$1.3 | –24 | –
X | 8.4 | AC467 |  0.2$\times$0.2 | 4 | –
Ku | 14.9 | AC467 |  0.1$\times$0.1 | –75 | –
Q | 43.0 | AC0565 | – | – |  Cotton et al. (2008)(2)
NGC 3516 | L | 1.4 | – | – | – |  Ulvestad & Wilson (1984)(2)
C | 4.8 | – | – | – |  Ulvestad & Wilson (1984)(2)
X | 8.4 | AF360 | – | – |  Mundell et al. (2009)(2)
Ku | 15.0 | AW0126 | – | – |  Ulvestad & Wilson (1989)(3)
I Zw 1 | L | 1.4 | AK406 |  1.3$\times$1.2 | 3 | –
C | 4.8 | AK406 |  0.4$\times$0.3 | –2 | –
X | 8.4 | AB0670 |  0.2$\times$0.2 | –9 | –
Ku | 15.0 | AA0048 | – | – |  Barvainis & Antonucci (1989)(4)

Note:
(1): two low angular resolution data points. These values are needed at the
time of fitting the radio SED: the 80 MHz data point (from radioheliograph
Culgoora-3) helps to search for the low/mid radio frequency synchrotron
component. The 31 GHz observation (from single dish NRAO 11-m telescope at
Kitt Peak) helps to find a good turn over point at high radio frequency. (2):
data obtained using JVLA at A configuration. (3): observation using JVLA at B
configuration, angular resolution at this frequency 0.4${}^{\prime\prime}\;$.
(4): this flux density has been obtained from VLA observation at C
configuration for which the angular resolution is 1.4${}^{\prime\prime}\;$. In
this work, the continuum flux densities at L band (6.22 + 0.35) and C band
(2.21 + 0.11) are also reported. These values are in agreement with higher
angular resolution L band (4.91 +- 0.12) and C band (2.41 +- 0.12) from the
project AK406. Therefore, we can assume that the Ku band flux density obtained
using C configuration well represent the core flux density at this frequency.

Table 6: Sub-mm information.

Source Name |  $\nu$ [GHz] | Project ID |  Clean beam [${}^{\prime\prime}\;$] | PA [deg] | Reference
---|---|---|---|---|---
NGC 1052 | 108 | 2015.1.00591.S |  0.7$\times$0.6 | –65 | –
113 | 2015.1.00989.S |  1.4$\times$1.3 | –20 | –
214 | 2013.1.01225.S |  0.3$\times$0.2 | 54 | –
230 | 2013.1.01225.S |  0.3$\times$0.2 | 54 | –
340 | 2013.1.01225.S |  0.20$\times$0.15 | 57 | –
350 | 2013.1.01225.S |  0.20$\times$0.15 | 57 | –
NGC 1068 | 93 | 2013.1.00055.S |  0.7$\times$0.5 | 74 | –
103 | 2013.1.01151.S |  4.6$\times$2.1 | 67 | –
223 | 2016.1.00232.S |  0.3$\times$0.3 | 80 | –
251 | 2013.1.00221.S |  0.5$\times$0.5 | 60 | –
350 | 2016.1.00232.S |  0.2$\times$0.2 | 77 | –
| 694 | 2013.1.00055.S |  0.07$\times$0.05 | 60 | García-Burillo et al. (2016)
NGC 3516 | 100 | – | – | – |  Behar et al. (2018)(1)
I Zw 1 | 252 | 2012.1.00034.S |  0.7$\times$0.6 | 60 | Imanishi et al. (2016b)
374 | – | – | – |  Hughes et al. (1993)(2)
666 | – | – | – |  Hughes et al. (1993)(2)

Note:
(1) Data using CARMA telescope at C-array configuration, providing an angular
resolution of $\sim$1${}^{\prime\prime}\;$. (2) Data using JCMT telescope,
providing an angular resolution at 374 GHz and at 666 GHz of
13.5${}^{\prime\prime}\;$ and 9${}^{\prime\prime}\;$ respectively.

Table 7: Radio and sub-mm flux densities of the targets.

Source Name | $\nu$ | S [mJy] | errS | Note
---|---|---|---|---
multirow144emNGC1052 | 0.08 | 4000 | 400 | (1)
| 1.4 | 663.3 | 2.0 |
| 4.8 | 1130.0 | 113.0 | (2)
| 6.2 | 1295.0 | 1.2 |
| 8.4 | 2910.0 | 30 |
| 14.9 | 1020.0 | 100.0 |
| 22.1 | 2460.0 | 20.0 |
| 31.4 | 1070.0 | 120.0 | (3)
| 108.0 | 750.0 | 7.4 |
| 113.7 | 773.0 | 3.0 |
| 214.1 | 495.1 | 3.4 |
| 229.4 | 456.6 | 4.0 |
| 340.8 | 299.3 | 1.3 |
| 352.8 | 283.1 | 1.1 |
NGC1068 | 1.4 | 1585.0 | 51.0 |
8.4 | 361.0 | 12.0 |
14.9 | 97.0 | 6.0 |
43.0 | 44.0 | 1.0 | (4)
93.1 | 46.0 | 2.0 |
103.0 | 54.0 | 2.0 |
223.6 | 26.0 | 4.0 |
252.0 | 28.0 | 2.0 |
351.0 | 19.2 | 1.0 |
| 694.0 | 13.8 | 1.0 | (∗)
NGC3516 | 1.4 | 5.0 | 1.0 | (5)
4.0 | 4.30 | 0.50 | (5)
8.0 | 2.50 | 0.20 | (6)
15.0 | 1.30 | 0.03 | (7)
100 | 1.84 | 0.29 | (8)
I Zw1 | 1.4 | 4.91 | 0.12 |
4.8 | 2.41 | 0.12 |
8.4 | 1.15 | 0.17 |
15.0 | 1.06 | 0.31 | (9)
252.0 | 1.20 | 0.06 | (10)
374 | 18.4 | 4.4 | (11)
666 | 225 | 75 | (11)

Note: (1) from Slee (1977); (2) from Perley (1982); (3) from Geldzahler &
Witzel (1981); (4) from Cotton et al. (2008); (5) from Ulvestad & Wilson
(1984); (6) from Mundell et al. (2009); (7) from Ulvestad & Wilson (1989);(8)
from Behar et al. (2018); (9) from Barvainis & Antonucci (1989); (10) from
Imanishi et al. (2016b); (11) from Hughes et al. (1993); (*) flux density from
García-Burillo et al. (2016): at the resolution 0.07${}^{{}^{\prime\prime}\;}$
$\times$ 0.05${}^{{}^{\prime\prime}\;}$ this value correspond to the flux
density of the claimed NGC 1068 core S1 component Gallimore et al. (2004)