# Determining the torus covering factors for a sample of type 1 AGN in the
local Universe

Savithri H. Ezhikode,1 Poshak Gandhi,2 Chris Done,3 Martin Ward,3 Gulab C.
Dewangan,4 Ranjeev Misra,4 Ninan Sajeeth Philip1
1 Department Of Physics, St. Thomas College, Kozhencherry, Kerala 689641,
India
2 School of Physics & Astronomy, University of Southampton, Highfield,
Southampton SO17 1BJ, UK
3 Centre for Extragalactic Astronomy, Department of Physics, Durham
University, South Road, Durham DH1 3LE, UK
4 Inter-University Centre for Astronomy & Astrophysics, Post Bag 4,
Ganeshkhind, Pune, India
Contact e-mail<EMAIL_ADDRESS>
###### Abstract

In the unified scheme of active galactic nuclei, a dusty torus absorbs and
then reprocesses a fraction of the intrinsic luminosity which is emitted at
longer wavelengths. Thus, subject to radiative transfer corrections, the
fraction of the sky covered by the torus as seen from the central source
(known as the covering factor $f_{c}$) can be estimated from the ratio of the
infrared to the bolometric luminosities of the source as $f_{c}$=$L_{\rm
torus}$/$L_{\rm Bol}$. However, the uncertainty in determining $L_{\rm Bol}$
has made the estimation of covering factors by this technique difficult,
especially for AGN in the local Universe where the peak of the observed SEDs
lies in the UV (ultraviolet). Here, we determine the covering factors of an
X-ray/optically selected sample of 51 type 1 AGN. The bolometric luminosities
of these sources are derived using a self-consistent, energy-conserving model
that estimates the contribution in the unobservable far-UV region, using
multi-frequency data obtained from SDSS, XMM-Newton, WISE, 2MASS and UKIDSS.
We derive a mean value of $f_{c}$ $\sim$ 0.30 with a dispersion of 0.17.
Sample correlations, combined with simulations, show that $f_{c}$ is more
strongly anti-correlated with $\lambda_{\rm Edd}$ than with $L_{\rm Bol}$.
This points to large-scale torus geometry changes associated with the
Eddington-dependent accretion flow, rather than a receding torus, with its
inner sublimation radius determined solely by heating from the central source.
Furthermore, we do not see any significant change in the distribution of
$f_{c}$ for sub-samples of radio-loud sources or Narrow Line Seyfert 1
galaxies (NLS1s), though these sub-samples are small.

###### keywords:

galaxies:active $-$ galaxies:Seyfert $-$ X-rays:galaxies $-$ ultraviolet:
galaxies $-$ infrared: galaxies

##  1 Introduction

Studying broadband spectral energy distributions (SEDs) of active galactic
nuclei (AGN) can shed light on the emission mechanisms operating in the
distinct physical components of the AGN. For example, the big blue bump (BBB)
(Richstone & Schmidt, 1980; Sanders et al., 1989; Elvis et al., 1994) in the
optical/UV band is associated with modified black body emission from the
accretion disc, whereas the Comptonised emission from the corona (Haardt &
Maraschi, 1993) produces an X-ray power law continuum above $\sim$ 2 keV. Even
though the spectral features of various classes of AGN are distinct, the so-
called unification scheme (for reviews see Antonucci, 1993; Urry & Padovani,
1995; Netzer, 2015) postulates that the different types of AGN are
intrinsically similar. The model suggests the presence of a dusty, molecular
torus shaped structure, surrounding the central source, which gives rise to
anisotropic emission in polar directions. The observed characteristics of AGN
are governed by the orientation of this obscuring torus with respect to our
line of sight.

This torus is optically-thick, with a size of 0.1$-$10 pc (Suganuma et al.,
2006; Kishimoto et al., 2007; Burtscher et al., 2013). The region has a gas
density in the range of 10${}^{4}-$107 cm-3 while the column density ranges
from $\sim 10^{22}$ to $\sim 10^{25}$ cm-2 (Netzer, 2013). In the most simple
orientation-based unification scheme, the broad-line region may or may not be
obscured by the torus material depending on the inclination angle of the
system with respect to our line of sight. In this picture, the classification
as a type 2 or a type 1 AGN is determined by the orientation alone. The
obscuration is parameterised by the opening angle of the torus which in turn
determines the covering factor $f_{c}$. Hence the covering factor is defined
as the fraction of the sky that the torus blocks/absorbs the emission from the
central source.

The torus is directly exposed to the emission from the central engine and the
photons illuminating this region are absorbed by the dust grains. The heated
dust then re-radiates these absorbed optical/UV photons in the infrared (IR)
band. Hence the IR continuum is attributed to the thermal emission from the
silicate and graphite grains with a broad temperature distribution extending
up to the sublimation temperatures of about 1500 K. Cooler dust on larger
scales emits at longer wavelengths and also shows a silicate feature around
$\sim$ 10 $\mu$m.

Dust grains can no longer survive if heated above their sublimation
temperature. As a result, the inner radius of the dust is determined by the
distance from the centre, at which the dust is sublimated by the primary
continuum. A more luminous AGN heats the dust more strongly and hence the
sublimation radius will be larger, with $R\propto L_{\rm Bol}^{1/2}$
(Barvainis, 1987). If the dust distribution has a fixed scale height (as
opposed to scaling with mass and/or mass accretion rate), then this means that
the covering factor of the dusty torus decreases as the luminosity of the
source increases. This anti-correlation between $f_{c}$ and the luminosity was
suggested by Lawrence (1991) and is called the receding torus model. This does
not depend on the detailed dust distribution. For example a clumpy torus
(Nenkova et al. 2008; Hönig & Kishimoto 2010) would exhibit much the same
behaviour as the covering factor is determined mostly by the total solid angle
covered by the dust. Similarly, if most of the mid-infrared (MIR) emission
arises from scales beyond the classical torus (Hönig et al., 2013; López-
Gonzaga et al., 2016; Asmus et al., 2016), then $f_{c}$ would be a measure of
the efficiency of this extended emission component and how it scales with AGN
power.

There are various methods for determining $f_{c}$. One is a statistical
approach, based on optical demographic studies of AGN which compared the
fraction of type 1 and 2 AGN, with $L_{[OIII]}$ used as a proxy for $L_{\rm
Bol}$. Alternatively, this can be done in X$-$rays, using the fraction of
X$-$ray unobscured to obscured AGN, with $L_{\rm X-ray}$ tracing $L_{\rm
Bol}$. Both types of studies generally find a decrease in the fraction of
obscured AGN with increasing luminosity, consistent with the receding torus
model (e.g. Simpson, 2005; Hao et al., 2005; Ueda et al., 2003; Steffen et
al., 2003; La Franca et al., 2005; Treister & Urry, 2006; Hasinger, 2008; Toba
et al., 2013; Mateos et al., 2016) but with a few exceptions (Dwelly & Page,
2006; Eckart et al., 2006) or additional correlations (Hasinger, 2008).
However, neither the X$-$rays nor the optical emission lines, used as proxies,
give a reliable estimate of the bolometric luminosity, $L_{\rm Bol}$
(Vasudevan & Fabian, 2007; Lusso et al., 2013; Jin et al., 2012a, b, hereafter
J12a, J12b), which is the key driving parameter in the receding torus model,
and there are also multiple selection effects (Lawrence & Elvis, 2010).

Alternatively, the SED can be fitted over as wide a bandpass as possible to
directly constrain $L_{\rm Bol}$ from observations, and then the ratio of the
IR luminosity to the bolometric luminosity $L_{\rm IR}/L_{\rm Bol}$ can be
used to derive $f_{c}$ based on dust (re)emission. Again these studies
generally show an anti-correlation with $L_{\rm Bol}$ (Gallagher et al., 2007;
Maiolino et al., 2007; Hatziminaoglou et al., 2008, 2009; Gandhi et al., 2009;
Roseboom et al., 2013; Lusso et al., 2013). Nonetheless, there are still
uncertainties. A major difficulty in the SED-based analysis is determining the
bolometric luminosity of the AGN. A substantial part of the AGN luminosity
emerges in the UV region and is unobservable due to the interstellar
absorption with our Galaxy. Furthermore, the IR luminosity can be self-
obscured, with radiation transfer effects through optically-thick dust
affecting the IR luminosity observed for type 2 (obscured) objects (Stalevski
et al., 2016; Treister et al., 2008; Pier & Krolik, 1992).

In this work, we use a sample of 51 unobscured AGN, so these should not be
affected by radiative transfer effects. They all have well sampled broadband
optical-UV-X$-$ray data to define the SED. Additionally, they have $L_{\rm
Bol}$ estimated by fits using a self-consistent energy-conserving model to
bridge across the unobservable far-UV (FUV) region (J12a, J12b). In this
paper, we extend these SEDs to include far-infrared (FIR) wavelengths to
estimate the covering factors of the AGN in our sample. We then investigate
the dependence of $f_{c}$ with different AGN properties.

This paper is organised as follows. In Section 2, we discuss the sample
selection and preparation of the multi-wavelength data. Section 3 gives a
detailed description of the modelling of the broadband SED of the sample.
Section 4 deals with the main results obtained in the work. Section 5 is
dedicated to the discussion of the results and the conclusions are given in
Section 6. The details regarding the local models used in this work, the
broadband SED plot for each source, notes on selected sources, and other
relevant information is given in the Appendix. Throughout this paper, we have
adopted a cosmology with Hubble constant of H0 = 70 km s-1 Mpc-1,
$\Omega_{\Lambda}$=0.73 and $\Omega_{M}$=0.27.

##  2 Sample Selection & Data Preparation

For our study, we choose the sample of 51 type 1 AGN analysed by J12a and
J12b. These are selected to have good SDSS spectra (DR7) with $z<0.4$ so that
H$\alpha$ and H$\beta$ lines (black hole mass estimator) are included in the
bandpass, and good quality XMM-Newton X-ray data are available, without
complex absorption features. Optical band continuum points were extracted from
the SDSS data by removing line emission, Balmer continuum, and host galaxy
contribution. The XMM-Newton satellite also has the Optical Monitor (OM) which
provides simultaneous optical-UV photometry. These photometric points were
extracted using 6″diameter apertures to minimise host galaxy contamination.
Therefore these sources all have well sampled SEDs, which can be modelled to
give a good estimate of their bolometric luminosity. The sample spans a broad
range of AGN types comprising 12 Narrow Line Seyfert 1 galaxies (NLS1s), 39
Broad Line Seyfert 1 galaxies (BLS1s), a broad absorption line (BAL) quasar
which is also radio-loud (PG 1004+130, No. 13) and two more radio-loud AGN RBS
0875 (No. 14) and PG 1512+370 (No. 45). Further information of these sources
is given in Table 1 of J12a.

Table 1: The bandwidth in $\mu$m (Col. 3), the effective wavelength $\lambda_{\rm eff}$ in $\mu$m (Col. 4), the zero-point flux density $F_{\nu 0}$ in Jy (Col. 5) to convert from magnitudes and the extinction correction factor (Col. 6) for WISE, 2MASS & UKIDSS bands. Survey | Band | Bandwidth | $\lambda_{\rm eff}$ | $F_{\nu 0}$ | $A_{\lambda}/A_{V}$
---|---|---|---|---|---
|  |  $\mu$m |  $\mu$m | Jy |
WISE |  W1 |  0.663$\pm$0.001 |  3.35$\pm$0.01 |  309.5$\pm$4.6 | 0.069
W2 |  1.042$\pm$0.001 |  4.60$\pm$0.02 |  171.8$\pm$2.5 | 0.053
W3 |  5.510$\pm$0.020 |  11.56$\pm$0.04 |  31.7$\pm$0.5 | 0.068
W4 |  4.100$\pm$0.040 |  22.09$\pm$0.12 |  8.4$\pm$0.3 | 0.052
2MASS | J |  0.162$\pm$0.001 |  1.235$\pm$0.006 |  1594.0$\pm$27.8 | 0.282
H |  0.251$\pm$0.002 |  1.662$\pm$0.009 |  1024.0$\pm$20.0 | 0.190
K |  0.262$\pm$0.002 |  2.159$\pm$0.011 |  666.7$\pm$12.6 | 0.114
UKIDSS | Y | 0.102 | 1.031 | 2026.0 | 0.380
J | 0.159 | 1.248 | 1530.0 | 0.282
H | 0.292 | 1.631 | 1019.0 | 0.190
K | 0.351 | 2.201 | 631.0 | 0.114
Figure 1: WISE colour-colour plot for our sample. The solid line describes the
AGN wedge (Mateos et al., 2012) and the colour-cut (Stern et al., 2012) is
plotted with the dashed line. Blue triangles denote objects with significant
host galaxy contribution ($L_{\rm host}>10\%$ of $L_{\rm Bol}$) in the model
fit.

###  2.1 IR Data

We extended the continuum of the SEDs discussed in J12b to include IR data
obtained from the Wide-field Infrared Survey Explorer (WISE; Wright et al.
2010), Two Micron All-Sky Survey (2MASS; Skrutskie et al. 2006) and UKIRT
Infrared Deep Sky Survey (UKIDSS) catalogues (Hewett et al., 2006). These span
a wavelength range from $\sim$ 1 $\mu$m to 20 $\mu$m, giving good coverage
from near-infrared (NIR) to mid-infrared wavelengths. For cases where both
2MASS and UKIDSS data were available for each source, we opted to use the
UKIDSS data for the NIR band due to its smaller aperture size. Our principal
results, and specifically the distribution of covering factors, do not depend
on the choice of 2MASS or UKIDSS data, a point which is expanded on in
Appendix E. We used 2MASS only for sources for which there are no UKIDSS
observations. One object in the sample (2XMM J100523.9+410746; No. 12) does
not have either UKIDSS or 2MASS data. In that case, we could use only the WISE
data for the IR analysis. The bandpasses with their zero magnitude flux and
aperture sizes are given in Table LABEL:tab_IRband, together with the
extinction corrections in each band, $A_{\lambda}$, extracted from Cardelli et
al. (1989) with $R_{V}$=3.1 (see Gandhi et al. (2011) and references therein
for WISE extinction corrections). The resulting NIR-MIR fluxes, corrected for
Galactic reddening, are listed in Table 2. We incorporate these into xspec
using the ftool flx2xsp.

We investigated the dominant IR emission mechanism based on WISE colour
selection thresholds of Mateos et al. (2012) and Stern et al. (2012). The MIR
colour-cut defined by Stern et al. (2012) identifies the AGN candidates with
W1-W2 $\geq$ 0.8. In addition, the AGN wedge of Mateos et al. (2012) is
designed to select objects with red MIR power-law SEDs in the first three
bands of WISE. Fig. 1 shows that most of the sources in our sample, except
2XMM J100523.9+410746 (No. 12), RX J1140.1+0307 (No. 20), RX J1233.9+0747 (No.
28), 1E 1346+26.7 (No. 36) & NGC 5683 (No. 42), are within the AGN wedge and
above the colour-cut. This confirms that the MIR is likely dominated by the
AGN rather than the host galaxy in most cases. The MIR fluxes for those which
lie below the colour wedge and the colour-cut are likely to be dominated by
the stellar population or star formation activity in the host galaxy,
especially in the case of W1 filter. For example, the MIR SED of NGC 5683 (No.
42) shows a significant contribution from the host galaxy.

##  3 The Broadband SED Model

Multiwavelength observations are a crucial ingredient in understanding the
physical processes occurring in AGN and to study the structure of their inner
regions. Some notable features in the broadband SED model of AGN are; the hard
X-ray power law, the soft X-ray excess below 2 keV, the big blue bump which
peaks in optical/UV region, and the infrared bump at $\sim$10 $\mu$m. The
optical/UV emission in AGN is thought to arise from a multi-temperature
accretion disc. The power-law component originates from the inverse Compton
scattering of accretion disc photons by a hot, optically-thin corona. The
infrared emission results from reprocessing of the absorbed optical/UV/X-ray
emission from the AGN.

###  3.1 Modelling the Optical/UV & X$-$rays

The SED can be phenomenologically fitted by a black body component for the
accretion disc and thermal Comptonisation from an optically-thin, high-
temperature corona to model the hard X-ray power law above 2 keV. At lower
wavelengths, the soft X-ray excess can be modelled with an optically-thick,
low-temperature thermal Comptonisation model. In J12b, they modelled the
Optical/UV & X$-$ray continua with the XSPEC model optxagnf 111A description
of optxagnf can be found in the XSPEC website
http://heasarc.nasa.gov/xanadu/xspec/models/optxagn.html (Done et al., 2012).
This model is fully self-consistent (energy conserving), and associates all
components with emission from the accretion disc itself and energy extracted
from it i.e. the soft X-ray component and the hard X-ray power-law. optxagnf
is parameterised by black hole mass (MBH), Eddington ratio ($L/L_{\rm Edd}$ or
$\lambda_{\rm Edd}$), black hole spin ($\sc a$), coronal radius ($R_{\rm
cor}$), outer radius of the accretion disc ($R_{\rm out}$), electron
temperature ($kT_{\rm e}$) and optical depth ($\tau$) of the corona producing
soft X-ray component, hard X-ray (2$-$10 keV) photon index ($\Gamma$),
fraction of the coronal energy emitted in the hard X-ray power law ($f_{\rm
pl}$) and redshift ($z$) i.e., ten parameters in total. In detail, this model
introduces $R_{\rm cor}$, the radius down to which the gravitational energy is
released as black body emission in the disc. Within this radius, the energy is
emitted as the soft X-ray excess and the high energy power law. In this model,
the mass accretion rate is constrained by the optical/UV luminosity. If the
black hole mass is known, then these parameters can be used to estimate the
total luminosity. J12b assumed an accretion efficiency of 0.057 for a
Schwarzschild black hole, and hence determined the total luminosity. The study
presented in J12b is a refinement to the SED fitting given in J12a. This now
includes a self-consistent colour temperature correction for the standard disc
emission.

We adopted the same procedures as described in J12b, and performed the
spectral analysis of the optical/UV and X-ray continua using optxagnf in XSPEC
version 12.8.2. We model the Galactic absorption and reddening using the
standard routines wabs and redden respectively, and any intrinsic
absorption/reddening using zwabs/zredden. The intrinsic column density was
left free to vary during the spectral fitting while the Galactic column
density for each source was frozen to the value obtained from LAB Survey
(Kalberla et al., 2005). We fixed the black hole mass to the best-fit value
obtained by J12b in their models, who fixed upper(lower) limits to the mass
from the broad(intermediate) velocity width of the H$\beta$ line
decomposition. We also follow the method described in J12a, J12b and fix the
outer radius of the accretion disc to be $\rm 10^{4}R_{g}$. This is probably
an upper limit to the size of the disc, as both the self-gravity radius and
the best-fit to the disc emission generally indicate a somewhat smaller disc
(Hao et al., 2010; Collinson et al., 2016). The redshift222Redshift for each
source is taken from https://ned.ipac.caltech.edu/ $z$ is fixed to the value
given in Table 2, this leaves 9 free parameters for the X-ray fitting portion
of the model.

###  3.2 Modelling the Infrared

Our extended wavelength IR coverage is modelled as a combination of dust re-
radiation and host galaxy emission. For the dust, we use the Seyfert 1
(unobscured) template of Silva et al. (2004), and for the host galaxy we use a
range of 13 templates spanning ellipticals, spirals, and star-forming
galaxies, from the SWIRE library (Polletta et al., 2007). We incorporate these
into xspec as local models, which we call agndust and hostpol. Further details
of agndust and hostpol templates are given in APPENDIX A. We use only the
Seyfert 1 dust template in our fits since all our objects are unobscured, but
we do investigate the entire range of host galaxy templates, and then adopt
the one which gives the best-fit to each object.

The optical/UV, X-ray and IR continua of each source in the sample were fitted
by the final model $constant$($hostpol+agndust+wabs\times redden\times
zwabs\times zredden\times$ optxagnf), where the constant only allows for small
cross-calibration differences in normalisation between the X-ray spectra
obtained from the three independent cameras EPIC-pn, MOS1 and MOS2, aboard the
XMM-Newton satellite. The broadband SED model for each source has 11 free
parameters (including the normalizations of agndust and hostpol), apart from
the multiplicative factor of the model constant. The fit-statistic and the
best-fit hostpol template for each source are given in Table
LABEL:tab_parameter. The plots showing the data and individual model
components for all the sources are given in the APPENDIX B. Mrk 0110 (No. 9)
shows a clear discrepancy in the SDSS data due to extreme variability, and
therefore has a very large $\chi^{2}$. Also, there are two super-Eddington
sources in our sample, KUG 1031+398 (No. 15) and PG 2233+134 (No. 50). These
sources are discussed individually in APPENDIX C. We note that the potential
discrepancies mentioned above do not influence any of our resulting inferences
on the $f_{c}$ distribution.

Table 2: Dereddened IR flux for the sample in each band of WISE, 2MASS, and UKIDSS. No. | Object | Redshift | IR flux (mJy)
---|---|---|---
|  |  | WISE | 2MASS | UKIDSS
|  |  |  W1 |  W2 |  W3 |  W4 | J | H | $K_{s}$ | Y | J | H | K
1 | UM 269 | 0.308 |  2.10$\pm$0.06 |  2.90$\pm$0.07 |  4.22$\pm$0.26 |  7.94$\pm$1.37 |  0.45$\pm$0.05 |  0.70$\pm$0.08 |  0.93$\pm$0.07 | - | - | - | -
2 | Mrk 1018 | 0.043 |  26.58$\pm$0.67 |  30.51$\pm$0.72 |  52.38$\pm$1.07 |  85.36$\pm$3.86 |  8.34$\pm$0.58 |  11.73$\pm$0.99 |  15.35$\pm$0.75 | - | - | - | -
3 | NVSS J030639 | 0.107 |  5.15$\pm$0.13 |  6.22$\pm$0.15 |  16.52$\pm$0.42 |  41.50$\pm$2.28 | - | - | - |  1.02$\pm$0.03 |  1.34$\pm$0.04 |  1.99$\pm$0.06 |  2.97$\pm$0.09
4 | 2XMM J074601.2+280732 | 0.145 |  1.35$\pm$0.04 |  1.53$\pm$0.04 |  2.43$\pm$0.18 |  3.84$\pm$1.19 |  0.52$\pm$0.06 |  0.66$\pm$0.09 |  0.79$\pm$0.08 | - | - | - | -
5 | 2XMM J080608.0+244421 | 0.358 |  1.12$\pm$0.03 |  1.56$\pm$0.04 |  3.58$\pm$0.22 |  8.00$\pm$1.28 | - | - | - |  0.25$\pm$0.01 |  0.30$\pm$0.01 |  0.40$\pm$0.01 |  0.56$\pm$0.02
6 | HS 0810+5157 | 0.377 |  1.89$\pm$0.05 |  3.18$\pm$0.08 |  7.99$\pm$0.25 |  21.07$\pm$1.51 |  0.63$\pm$0.06 |  0.87$\pm$0.09 |  1.29$\pm$0.09 | - | - | - | -
7 | RBS 0769 | 0.160 |  3.33$\pm$0.09 |  5.36$\pm$0.13 |  15.40$\pm$0.39 |  32.69$\pm$1.66 |  0.90$\pm$0.06 |  1.27$\pm$0.11 |  1.82$\pm$0.09 | - | - | - | -
8 | RBS 0770 | 0.033 |  37.65$\pm$0.97 |  45.26$\pm$1.07 |  105.76$\pm$2.17 |  211.87$\pm$8.67 |  10.03$\pm$0.46 |  13.40$\pm$0.73 |  20.01$\pm$0.75 | - | - | - | -
9 | Mrk 0110 | 0.035 |  21.67$\pm$0.56 |  29.57$\pm$0.70 |  65.58$\pm$1.39 |  109.36$\pm$4.88 |  4.57$\pm$0.23 |  5.65$\pm$0.32 |  8.58$\pm$0.33 | - | - | - | -
10 | PG 0947+396 | 0.206 |  7.93$\pm$0.20 |  12.71$\pm$0.3 |  26.91$\pm$0.57 |  55.27$\pm$2.77 |  1.99$\pm$0.08 |  2.75$\pm$0.11 |  5.34$\pm$0.17 | - | - | - | -
11 | 2XMM J100025.2+015852 | 0.373 |  0.30$\pm$0.01 |  0.54$\pm$0.02 |  1.47$\pm$0.14 |  4.46$\pm$1.05 | - | - | - |  0.11$\pm$0.01 |  0.11$\pm$0.01 |  0.16$\pm$0.01 |  0.21$\pm$0.01
12 | 2XMM J100523.9+410746 | 0.206 |  0.35$\pm$0.01 |  0.50$\pm$0.02 |  0.54$\pm$0.15 |  3.55$\pm$0.12 | - | - | - | - | - | - | -
13 | PG 1004+130 | 0.241 |  8.10$\pm$0.21 |  11.90$\pm$0.28 |  36.20$\pm$0.79 |  83.73$\pm$4.04 |  3.41$\pm$0.12 |  3.54$\pm$0.16 |  5.00$\pm$0.18 | - | - | - | -
14 | RBS 0875 | 0.178 |  6.72$\pm$0.17 |  8.86$\pm$0.21 |  14.84$\pm$0.41 |  29.33$\pm$1.9 |  1.70$\pm$0.10 |  2.21$\pm$0.15 |  3.58$\pm$0.15 | - | - | - | -
15 | KUG 1031+398 | 0.043 |  11.66$\pm$0.29 |  19.32$\pm$0.45 |  70.46$\pm$1.40 |  132.33$\pm$5.69 |  3.57$\pm$0.14 |  4.38$\pm$0.21 |  5.86$\pm$0.22 | - | - | - | -
16 | PG 1048+342 | 0.167 |  3.89$\pm$0.10 |  5.58$\pm$0.14 |  13.61$\pm$0.34 |  27.78$\pm$1.53 |  1.28$\pm$0.06 |  1.57$\pm$0.08 |  2.46$\pm$0.11 | - | - | - | -
17 | 1RXS J111007 | 0.262 |  2.07$\pm$0.05 |  3.08$\pm$0.07 |  8.62$\pm$0.27 |  22.14$\pm$1.33 |  0.33$\pm$0.05 |  0.71$\pm$0.07 |  1.16$\pm$0.09 | - | - | - | -
18 | PG 1115+407 | 0.155 |  9.00$\pm$0.23 |  11.54$\pm$0.27 |  24.18$\pm$0.53 |  49.53$\pm$2.36 |  2.21$\pm$0.12 |  3.14$\pm$0.18 |  5.36$\pm$0.20 | - | - | - | -
19 | 2XMM J112328.0+052823 | 0.101 |  2.64$\pm$0.07 |  3.65$\pm$0.09 |  9.43$\pm$0.28 |  16.42$\pm$1.30 | - | - | - |  0.49$\pm$0.02 |  0.64$\pm$0.02 |  0.96$\pm$0.03 |  1.55$\pm$0.05
20 | RX J1140.1+0307 | 0.081 |  1.35$\pm$0.04 |  1.32$\pm$0.04 |  4.28$\pm$0.19 |  12.06$\pm$1.35 | - | - | - |  0.35$\pm$0.01 |  0.45$\pm$0.01 |  0.65$\pm$0.02 | -
21 | PG 1202+281 | 0.165 |  7.41$\pm$0.19 |  10.57$\pm$0.25 |  29.02$\pm$0.65 |  87.03$\pm$3.74 |  2.03$\pm$0.08 |  2.53$\pm$0.10 |  4.82$\pm$0.15 | - | - | - | -
22 | 1AXG J121359+1404 | 0.154 |  1.06$\pm$0.03 |  1.34$\pm$0.04 |  2.89$\pm$0.17 |  7.57$\pm$1.08 | - | - | - |  0.36$\pm$0.01 |  0.47$\pm$0.01 |  0.61$\pm$0.02 |  0.79$\pm$0.02
23 | 2E 1216+0700 | 0.080 |  6.45$\pm$0.17 |  7.79$\pm$0.18 |  17.42$\pm$0.46 |  24.85$\pm$1.65 | - | - | - |  1.28$\pm$0.04 |  1.75$\pm$0.05 |  2.70$\pm$0.08 |  3.90$\pm$0.12
24 | 1RXS J122019 | 0.286 |  2.08$\pm$0.06 |  3.06$\pm$0.08 |  5.66$\pm$0.20 |  7.83$\pm$1.09 |  0.52$\pm$0.06 |  0.78$\pm$0.10 |  1.35$\pm$0.11 | - | - | - | -
25 | LBQS 1228+1116 | 0.236 |  3.08$\pm$0.08 |  4.68$\pm$0.12 |  11.17$\pm$0.28 |  30.99$\pm$1.86 | - | - | - |  0.96$\pm$0.03 |  0.99$\pm$0.03 |  1.29$\pm$0.04 |  1.56$\pm$0.05
26 | 2XMM J123126.4+105111 | 0.304 |  0.49$\pm$0.02 |  0.66$\pm$0.02 |  1.71$\pm$0.17 |  2.39$\pm$0.91 | - | - | - |  0.12$\pm$0.00 |  0.14$\pm$0.01 |  0.19$\pm$0.01 |  0.33$\pm$0.01
27 | Mrk 0771 | 0.064 |  13.34$\pm$0.35 |  18.42$\pm$0.43 |  57.38$\pm$1.17 |  159.39$\pm$6.68 |  4.63$\pm$0.26 |  6.15$\pm$0.37 |  9.46$\pm$0.39 | - | - | - | -
28 | RX J1233.9+0747 | 0.371 |  0.51$\pm$0.02 |  0.48$\pm$0.02 |  1.09$\pm$0.18 |  5.33$\pm$0.19 | - | - | - |  0.11$\pm$0.00 |  0.15$\pm$0.01 |  0.19$\pm$0.01 |  0.24$\pm$0.01
29 | RX J1236.0+2641 | 0.209 |  3.08$\pm$0.08 |  4.61$\pm$0.11 |  13.12$\pm$0.37 |  37.95$\pm$1.98 |  0.74$\pm$0.05 |  1.04$\pm$0.08 |  1.66$\pm$0.08 | - | - | - | -
30 | PG 1244+026 | 0.048 |  6.86$\pm$0.17 |  10.03$\pm$0.24 |  41.53$\pm$0.88 |  114.83$\pm$4.87 | - | - | - |  1.34$\pm$0.04 |  1.58$\pm$0.05 |  2.15$\pm$0.06 |  3.23$\pm$0.10
31 | 2XMM J125553.0+272405 | 0.316 |  1.13$\pm$0.03 |  1.36$\pm$0.04 |  2.39$\pm$0.17 |  6.37$\pm$0.93 | - | - | - |  0.28$\pm$0.01 |  0.35$\pm$0.01 |  0.51$\pm$0.02 |  0.78$\pm$0.02
32 | RBS 1201 | 0.091 |  3.20$\pm$0.08 |  3.59$\pm$0.09 |  8.29$\pm$0.25 |  19.65$\pm$1.43 | - | - | - |  1.03$\pm$0.03 |  1.27$\pm$0.04 |  1.74$\pm$0.05 |  1.92$\pm$0.06
33 | 2XMM J132101.4+340658 | 0.334 |  0.77$\pm$0.02 |  0.94$\pm$0.03 |  1.73$\pm$0.11 |  3.93$\pm$0.78 |  0.31$\pm$0.05 |  0.29$\pm$0.06 |  0.61$\pm$0.08 | - | - | - | -
34 | 1RXS J132447 | 0.306 |  1.65$\pm$0.05 |  2.23$\pm$0.06 |  4.21$\pm$0.18 |  11.40$\pm$1.06 | - | - | - |  0.82$\pm$0.03 |  0.84$\pm$0.03 |  0.96$\pm$0.03 |  1.19$\pm$0.04
35 | UM 602 | 0.237 |  3.74$\pm$0.10 |  5.19$\pm$0.13 |  8.34$\pm$0.23 |  18.25$\pm$1.31 | - | - | - |  0.52$\pm$0.02 |  0.57$\pm$0.02 |  0.80$\pm$0.02 |  1.47$\pm$0.04
36 | 1E 1346+26.7 | 0.059 |  4.34$\pm$0.13 |  4.87$\pm$0.13 |  18.74$\pm$0.42 |  34.30$\pm$1.86 | - | - | - |  1.09$\pm$0.03 |  1.40$\pm$0.04 |  2.12$\pm$0.06 |  2.66$\pm$0.08
37 | PG 1352+183 | 0.151 |  7.09$\pm$0.18 |  10.07$\pm$0.24 |  18.03$\pm$0.41 |  35.78$\pm$1.80 |  1.61$\pm$0.08 |  2.11$\pm$0.10 |  3.78$\pm$0.14 | - | - | - | -
38 | Mrk 0464 | 0.050 |  3.69$\pm$0.10 |  5.03$\pm$0.12 |  14.32$\pm$0.34 |  28.24$\pm$1.59 |  1.94$\pm$0.08 |  2.33$\pm$0.10 |  3.04$\pm$0.12 | - | - | - | -
39 | 1RXS J135724 | 0.106 |  0.78$\pm$0.02 |  1.00$\pm$0.03 |  3.51$\pm$0.12 |  15.31$\pm$1.16 |  0.28$\pm$0.05 |  0.53$\pm$0.08 |  0.59$\pm$0.09 | - | - | - | -
40 | PG 1415+451 | 0.114 |  10.39$\pm$0.27 |  13.31$\pm$0.31 |  29.32$\pm$0.62 |  64.93$\pm$2.93 |  3.80$\pm$0.12 |  5.59$\pm$0.19 |  8.69$\pm$0.27 | - | - | - | -
41 | PG 1427+480 | 0.221 |  3.64$\pm$0.09 |  5.57$\pm$0.13 |  14.18$\pm$0.33 |  46.39$\pm$2.24 |  1.33$\pm$0.07 |  1.68$\pm$0.10 |  2.76$\pm$0.12 | - | - | - | -
42 | NGC 5683 | 0.037 |  5.37$\pm$0.14 |  4.96$\pm$0.12 |  19.55$\pm$0.45 |  50.03$\pm$2.32 |  5.46$\pm$0.27 |  6.47$\pm$0.37 |  7.10$\pm$0.29 | - | - | - | -
43 | RBS 1423 | 0.208 |  3.80$\pm$0.10 |  5.74$\pm$0.14 |  12.26$\pm$0.31 |  25.90$\pm$1.56 | - | - | - |  0.50$\pm$0.02 |  0.70$\pm$0.02 |  0.99$\pm$0.03 |  1.94$\pm$0.06
44 | PG 1448+273 | 0.065 |  11.35$\pm$0.29 |  15.10$\pm$0.36 |  45.53$\pm$0.93 |  117.29$\pm$4.92 |  5.64$\pm$0.19 |  7.29$\pm$0.24 |  10.29$\pm$0.31 | - | - | - | -
45 | PG 1512+370 | 0.371 |  4.18$\pm$0.10 |  6.67$\pm$0.16 |  13.84$\pm$0.33 |  34.36$\pm$1.61 |  1.09$\pm$0.06 |  1.36$\pm$0.08 |  2.26$\pm$0.12 | - | - | - | -
46 | Q 1529+050 | 0.218 |  2.18$\pm$0.06 |  2.92$\pm$0.07 |  6.03$\pm$0.20 |  19.48$\pm$1.48 | - | - | - |  0.40$\pm$0.01 |  0.52$\pm$0.02 |  0.68$\pm$0.02 |  1.24$\pm$0.04
47 | 1E 1556+27.4 | 0.090 |  1.90$\pm$0.05 |  2.08$\pm$0.05 |  4.01$\pm$0.16 |  6.93$\pm$0.83 | - | - | - |  0.85$\pm$0.03 |  1.22$\pm$0.04 |  1.34$\pm$0.04 |  1.61$\pm$0.05
48 | Mrk 0493 | 0.031 |  19.93$\pm$0.51 |  24.46$\pm$0.58 |  72.03$\pm$1.43 |  162.81$\pm$6.67 |  6.00$\pm$0.29 |  8.21$\pm$0.45 |  10.65$\pm$0.44 | - | - | - | -
49 | IIZw 177 | 0.081 |  3.79$\pm$0.10 |  4.72$\pm$0.11 |  20.70$\pm$0.48 |  60.99$\pm$2.76 |  1.77$\pm$0.09 |  2.56$\pm$0.13 |  2.91$\pm$0.15 | - | - | - | -
50 | PG 2233+134 | 0.326 |  5.25$\pm$0.13 |  8.26$\pm$0.20 |  20.97$\pm$0.50 |  57.39$\pm$2.92 |  0.99$\pm$0.06 |  1.18$\pm$0.07 |  2.03$\pm$0.12 | - | - | - | -
51 | Mrk 0926 | 0.047 |  69.60$\pm$1.80 |  86.16$\pm$2.03 |  123.69$\pm$2.53 |  256.37$\pm$10.75 |  8.97$\pm$0.36 |  12.43$\pm$0.49 |  17.00$\pm$0.64 | - | - | - | -

##  4 Results

###  4.1 Broadband SEDs & Covering factors

Our best-fit model parameters for the SED fits are given in Table
LABEL:tab_parameter. We integrate the intrinsic optxagnf model (after
correcting for all absorption components) over the energy range of
10${}^{-6}-$100 keV ($\sim$10${}^{-5}-$1000 $\mu$m) to obtain $L_{\rm Bol}$,
and over 2$-$10 keV to get the hard X-ray luminosity $L_{\rm X-ray}$. Now, in
order to estimate the covering factor we can compare these to the IR
luminosity of the torus $L_{\rm torus}$, which we find by integrating the
agndust model component over $\sim$1$-$1000 $\mu$m. We also give the
luminosity of the host galaxy $L_{\rm host}$, obtained by integrating the host
galaxy template over $\sim$0.1$-$1000 $\mu$m, and give its type in Table
LABEL:tab_parameter. The distributions of these luminosities are shown in Fig.
2. The bolometric luminosities of most of the sources in our study are lower
than the values of J12b by a factor of $\sim$1.7. This is due to a change in
energy grid handling of optxagnf in an older version of XSPEC333See the XSPEC
patch 12.8.2j available at
https://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/issues/archive/issues.12.8.2q.html.
Though individual $L_{\rm Bol}$ values are affected, the overall sample trends
remain the same. The host galaxy is significantly detected in 38 sources. We
note that the host galaxy morphological types of 21 sources in our sample are
known from the literature and many of these (No. 8, 13, 15, 16, 20, 21, 23,
27, 30, 37, 38, 39, 42, 44, 48, 50) are different to those indicated by our
best-fit. We have refit these objects using the galaxy template fixed to the
literature values. Although there is a marginal increase in $\chi^{2}$ when
using the substituted templates, this has no significant impact on the
parameters derived for either the AGN or the torus.

The primary goal of this work is to determine the distribution of covering
factors $f_{c}$ of the unobscured AGN sample. This distribution of $f_{c}$
obtained from the ratio of the torus luminosity to the bolometric luminosity
is given in Fig. 3. The distribution, with an average value around 0.30, has a
scatter of $\sim$0.17. The source with the minimum covering factor is 1E
1556+27.4 (No. 47). The value of $f_{c}\sim$0.02 suggests that this source
could be a hot-dust-poor AGN (Hao et al., 2010) characterised by weak IR
emission. At the opposite extreme, 2E 1216+0700 (No. 23) has the maximum value
of $f_{c}$ ($\sim 0.88$).

###  4.2 Comparison with Previous Work

Many previous studies have discussed the obscured AGN fraction. Lawrence &
Elvis (2010) reviewed the studies that dealt with the fraction of obscured AGN
and concluded that the obscured fraction for the non-X-ray selected samples
has a mean value of about 0.58 with a dispersion of $\sim$ 0.05. They also
gave a rough estimate of 0.53 for the obscured fraction using the updated
Swift/BAT hard X-ray catalogue (Tueller et al., 2010), after applying the
correction for missing Compton thick objects (Risaliti et al., 1999). The
covering factors of a sample of 5281 WISE, UKIDSS and SDSS selected high
luminosity quasars ($L_{\rm Bol}>$1046 erg s-1) with redshift $<$ 1.5 was
determined by Roseboom et al. (2013). They found that the covering factors
(estimated by using the ratio of IR to UV/optical luminosity) obey a log-
normal distribution with a mean observed value of $\sim$ 0.39 and a dispersion
of $\sim$ 0.2. The study by Lusso et al. (2013) estimated the covering factor
for a sample of X-ray selected type 1 AGN with an even wider span of redshifts
(0.10 $\leq z\leq 3.75$). They determined the covering factor of the
optically-thin torus and this was observed to be in the range from $\sim 0.45$
to $\sim 0.75$. In comparison, the result from our sample is relatively low,
especially since our sample is comprised only of Seyfert type 1 objects, so
radiative transfer corrections, which reduce $f_{c}$ due to the torus being
optically-thick to its own radiation at high inclination, should not be
important (but see Stalevski et al. 2016). At high luminosities, two other
studies, Mor & Trakhtenbrot (2011) and Landt et al. (2011), concentrated on
the hot (NIR-emitting) dust component and found even lower hot dust covering
factors of $\sim$0.13 and $\sim$0.07, respectively.

In APPENDIX D, we investigate the effect of varying the template SEDs on the
$f_{c}$ measurements. In particular, we examined the impact of using two other
IR SEDs for type 1 AGN $-$(1) proposed by Mullaney et al. (2011) based upon
observations of local sources in which the AGN dominates the IR portion of the
SED over the host galaxy contribution; and (2) a theoretical clumpy torus SED
by Hönig & Kishimoto (2010). While the resultant mean $f_{c}$ value and the
distribution of values from these template fits do not dramatically differ
from those obtained previously when we used the SEDs from Silva et al. (2004),
we found that both these sets of templates required an additional hot dust
component in the NIR regime, suggesting that they are too restricted to
account for the broadband features in our observations. This finding is
interesting, but further investigation is beyond the scope of our present
paper. However, we note that similar hot dust components are required in other
quasar SED studies (e.g. Mor et al. (2009)).

###  4.3 $f_{c}$ in Sub-samples

From our main sample, we have constructed sub-samples of three radio-loud
objects and 12 NLS1 galaxies. The distributions of covering factor for these
sub-samples are shown in Fig. 3.

####  4.3.1 Radio-loud sources

A significant contribution from a jet may reduce the covering factor in radio-
loud sources. One of these objects in our sample, PG 1004+130 (No. 13), is a
BAL quasar with a very weak X-ray spectrum. J12b suggests that the origin of
X-rays in this source could be a sub-parsec-scale jet. However, the covering
factors of the three radio-loud objects (No. 13, No. 14 & No. 45) in our
sample are 0.33, 0.65 and 0.24, respectively, indicating that the covering
factors may not be affected by the radio-loudness/quietness of the sources,
although we cannot draw general conclusions from such a small sample of radio-
loud sources.

####  4.3.2 NLS1 galaxies

It is known that the NLS1s, in general, tend to have higher values of
Eddington ratio. Since there is an anti-correlation between $f_{c}$ and
$\lambda_{\rm Edd}$ we expect the 12 NLS1s in our sample to have low values
for $f_{c}$. The covering factors of NLS1s in our sample range from $\sim$0.06
to $\sim$0.38 with a mean value around 0.23 and a dispersion of about 0.1. The
Kolmogorov-Smirnov test (K-S test) with a probability of $\sim$75.5% reveals
that the distribution of $f_{c}$ in NLS1s does not differ significantly from
that of the overall sample. But we caution that no strong statement can be
made, based on such a small sub-sample of NLS1s. We need further
investigations to get better constraints on this result.

###  4.4 Correlations obtained

J12b carried out a systematic study of the correlation between the different
AGN parameters in this sample. We follow J12b, but also include the new torus
parameters, $L_{\rm torus}$ and covering fraction $f_{c}$ and compute the
correlations using the Spearman’s rank-order method (Press et al., 1992). The
rank coefficient $\rho_{s}$ and probability $d_{s}$ (also known as the
p-value) for the Spearman’s correlation between different parameters are
listed in Table 4. We recover most of the correlations, obtained by J12b,
between $L_{\rm Bol}$, $\lambda_{\rm Edd}$, $\Gamma$ and the hard X-ray
bolometric correction $\kappa_{2-10}$ defined as $L_{\rm Bol}$/$L_{\rm X-ray}$
(Vasudevan & Fabian, 2007). Additionally, we find a marginal correlation of
$f_{c}$ with $L_{\rm Bol}$ ($d_{s}$=0.05) and a stronger correlation between
$f_{c}$ and $\lambda_{\rm Edd}$ ($d_{s}$=0.002). But $f_{c}$ shows no
significant correlation with $L_{\rm X-ray}$ or $L_{\rm torus}$, as shown in
Fig. 4.

J12b suggest that the combination of $\lambda_{\rm Edd}$ and MBH drives the
correlations seen in the AGN parameters, with $\lambda_{\rm Edd}$ changing the
accretion flow geometry (resulting in the correlations in $\Gamma$, $R_{\rm
cor}$ and $f_{\rm pl}$ which drive the correlation with $\kappa_{2-10}$) while
MBH and $\lambda_{\rm Edd}$ together set the overall luminosity and the peak
temperature of the disc. As $f_{c}$ correlates with $\lambda_{\rm Edd}$ and
$L_{\rm Bol}\propto$ M${}_{\rm BH}\lambda_{\rm Edd}$ then it is clear that the
correlations of $f_{c}$ with $\lambda_{\rm Edd}$ and $L_{\rm Bol}$, shown in
Fig. 4, will also give rise to correlations of $f_{c}$ with the other AGN
parameters. However, the major statistical correlation with the new torus
parameters is that $f_{c}$ correlates with $\lambda_{\rm Edd}$ and $L_{\rm
Bol}$. This is in accord with the physical expectations that $\lambda_{\rm
Edd}$ and $L_{\rm Bol}$ are the two key parameters which determine the
properties of the accretion flow.

There is also a weak correlation between $L_{\rm host}$ and MBH. This is
expected from the black hole mass and bulge luminosity ($L_{\rm Bulge}$)
relation of Magorrian et al. (1998). Since the SED of a normal galaxy stellar
population peaks in the H-band, we calculated the corresponding luminosity for
our sample in terms of $L_{\rm host}$ and the relative H-band flux from
Polletta et al. (2007) SED templates. Here, we are not considering Mrk 0110
(No. 9) since $L_{\rm host}$ is not well constrained for this source. We find
that the sources in which our SED fits include a significant host galaxy
contribution approximately follow the Magorrian relationship, though there is
significant scatter ($\sim$0.5 dex) between MBH and $L_{\rm Bulge}$ (see Fig.
5). This shows that our host galaxy fitted components are largely reasonable.
Here, we note that among the 13 sources for which there is no significant host
galaxy contribution, most of them are fitted by starburst galaxy templates
(e.g. No. 50, No. 16). These starburst templates peak in the FIR and show a
minimum around NIR wavelengths. Since our SEDs do not cover the FIR
wavelengths and the starbursts tend to be extended we may be underestimating
their FIR emission, and also their bulge luminosities. In these few cases, we
cannot rule out that we are then over-estimating the torus contribution and
hence also their $f_{c}$ values. When excluding the 13 sources for which
$L_{\rm host}$ are not constrained, neither the scatter ($\sim 0.17$) nor the
mean value ($\sim 0.33$) for the remaining 38 sources are changed
significantly from the covering factors of the overall sample. This indicates
that the uncertainties in $L_{\rm host}$ do not strongly bias our overall
results.

Figure 2: The distribution of $L_{\rm Bol}$ (upper left), $L_{\rm X-ray}$
(2$-$10 keV) (upper right), $L_{\rm torus}$ (lower left) and $L_{\rm host}$
(lower right)

.

Figure 3: Histogram of covering factors for the sample of 51 type 1 AGN (thick black line) and the sub-samples of 12 NLS1s (dashed blue line) and 3 radio-loud sources (thin red line). Table 3: Broadband SED fitting results. hostpol model: best-fit hostpol template (∗starburst galaxies); $\chi^{2}_{red}$: reduced $\chi^{2}$ for the best-fit model; N${}_{\rm H}^{\rm Gal}\leavevmode\nobreak\ \&$ $N_{\rm H}^{\rm Int}$: Galactic and intrinsic column densities, respectively, in 1020cm-2; MBH: black hole mass in 107M⊙ (fixed to the best-fit values of J12b); $\lambda_{\rm Edd}$: Eddington ratio; Rcor: coronal radius in Rg; kTe: electron temperature for the soft Comptonisation component in keV; $\tau$: optical depth of the soft Comptonisation component; $\Gamma$: hard X-ray photon index; fpl: fraction of the power below Rcor emitted in the hard Comptonisation component; $L_{\rm X-ray}$: unabsorbed X-ray luminosity in the band of 2$-$10 keV; $L_{\rm host}$: host galaxy luminosity in the $\sim$0.1$-$1000 $\mu$m band; $L_{\rm torus}$: infrared ($\sim$1$-$1000 $\mu$m) luminosity of the torus emission; $L_{\rm Bol}$: bolometric luminosity in the range of 10${}^{-6}-$100 keV; $\kappa_{2-10}$: hard X$-$ray bolometric correction ($L_{\rm Bol}/L_{\rm X-ray}$); $f_{c}$: Covering factor, the ratio of $L_{\rm torus}$ and $L_{\rm Bol}$. All luminosities are expressed in 1044 erg s-1. No. | hostpol | $\chi_{red}^{2}$ | $N_{\rm H}^{\rm Gal}$ | $N_{\rm H}^{\rm Int}$ |  MBH | $\lambda_{\rm Edd}$ |  Rcor |  kTe | $\tau$ | $\Gamma$ |  fpl | $L_{\rm X-ray}$ | $L_{\rm host}$ | $L_{\rm torus}$ | $L_{\rm Bol}$ | $\kappa_{2-10}$ | $f_{c}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| model |  |  1020cm-2 |  1020cm-2 |  107 M⊙ |  |  Rg | keV |  |  |  |  1044 erg s-1 |  1044 erg s-1 |  1044 erg s-1 |  1044 erg s-1 |  |
1 | E5 | 1.34 | 1.79 | 3.43 | 41.00 | 0.11 | 97.0 | 0.11 | 28.1 | 1.85 | 0.49 | 3.0 |  $<$0.5 | 14.9 | 41.6 | 13.74 | 0.36
2 | S0 | 1.99 | 2.43 | 1.29 | 6.92 | 0.08 | 94.2 | 0.19 | 16.9 | 1.82 | 0.36 | 0.4 | 0.6 | 1.9 | 8.3 | 18.80 | 0.23
3 | S0 | 1.34 | 6.31 | 0.66 | 4.07 | 0.20 | 12.6 | 0.18 | 15.2 | 1.87 | 0.82 | 0.3 | 0.9 | 3.9 | 10.1 | 37.94 | 0.38
4 |  IRAS 22491-1808∗ | 1.23 | 3.49 | 2.69 | 60.00 | 0.01 | 84.3 | 0.34 | 14.3 | 1.67 | 0.45 | 0.5 |  $<$0.4 | 0.9 | 8.0 | 17.28 | 0.12
5 | S0 | 1.29 | 3.53 | 8.08 | 8.71 | 0.97 | 34.8 | 0.20 | 14.3 | 2.16 | 0.15 | 1.0 | 1.6 | 13.1 | 72.0 | 71.60 | 0.18
6 |  IRAS 22491-1808∗ | 1.39 | 4.24 | 0.00 | 31.40 | 0.29 | 21.0 | 0.42 | 11.0 | 1.85 | 0.45 | 2.4 | 17.1 | 28.8 | 73.8 | 30.90 | 0.40
7 |  IRAS 22491-1808∗ | 1.20 | 1.33 | 0.00 | 3.80 | 0.99 | 10.5 | 0.15 | 32.7 | 2.20 | 0.31 | 0.2 | 3.7 | 7.7 | 42.7 | 178.10 | 0.18
8 | S0 | 1.89 | 3.12 | 3.80 | 3.47 | 0.29 | 21.7 | 0.18 | 14.4 | 1.80 | 0.51 | 0.5 | 0.2 | 2.2 | 14.1 | 26.42 | 0.16
9 | Sa | 19.62 | 1.30 | 0.00 | 2.51 | 0.65 | 17.4 | 0.26 | 15.5 | 1.73 | 0.83 | 1.0 | $-$ | 1.4 | 22.5 | 22.70 | 0.06
10 | S0 | 1.70 | 1.74 | 1.01 | 21.90 | 0.38 | 39.5 | 0.49 | 9.6 | 1.76 | 0.28 | 2.7 |  $<$0.2 | 27.9 | 87.0 | 32.33 | 0.32
11 |  IRAS 20551-4250∗ | 1.00 | 1.72 | 0.00 | 8.32 | 0.38 | 23.1 | 0.45 | 12.3 | 1.54 | 0.84 | 1.0 | 8.1 | 4.1 | 22.8 | 23.05 | 0.18
12 | S0 | 1.17 | 1.20 | 0.00 | 6.61 | 0.05 | 19.3 | 0.10 | 54.1 | 1.94 | 0.88 | 0.2 | 0.7 | 1.1 | 3.5 | 17.81 | 0.30
13 |  IRAS 22491-1808∗ | 1.92 | 3.56 | 0.00 | 158.49 | 0.07 | 9.9 | 0.19 | 15.0 | 1.45 | 0.93 | 0.5 | 62.1 | 34.5 | 104.5 | 193.86 | 0.33
14 | S0 | 1.47 | 1.76 | 0.00 | 17.38 | 0.11 | 100.0 | 0.23 | 20.3 | 1.77 | 0.81 | 2.4 | 2.5 | 12.6 | 19.3 | 7.95 | 0.65
15 | Sd | 1.67 | 1.31 | 2.81 | 0.20 | 2.64 | 100.0 | 0.30 | 8.7 | 2.20 | 0.03 | 0.04 | 0.8 | 1.8 | 7.8 | 190.64 | 0.23
16 |  IRAS 22491-1808∗ | 1.50 | 1.70 | 2.21 | 19.95 | 0.18 | 28.9 | 0.30 | 13.0 | 1.74 | 0.34 | 1.2 |  $<$1.3 | 8.1 | 39.6 | 34.33 | 0.20
17 |  Arp 220∗ | 1.06 | 0.65 | 1.13 | 6.17 | 0.51 | 93.8 | 0.48 | 9.0 | 1.61 | 0.12 | 0.4 | 18.0 | 13.6 | 30.9 | 72.26 | 0.44
18 | E5 | 1.82 | 1.45 | 0.00 | 13.18 | 0.61 | 11.6 | 0.25 | 14.0 | 2.20 | 0.47 | 1.0 |  $<$0.1 | 13.4 | 91.9 | 94.83 | 0.15
19 | S0 | 1.00 | 3.70 | 0.00 | 5.10 | 0.04 | 69.1 | 0.16 | 20.6 | 1.94 | 0.21 | 0.1 | 0.3 | 2.0 | 2.5 | 36.39 | 0.78
20 | Sd | 1.24 | 1.91 | 0.00 | 0.63 | 0.19 | 18.0 | 0.20 | 22.5 | 2.20 | 0.57 | 0.1 | 0.5 | 0.5 | 1.6 | 30.18 | 0.30
21 |  M 82∗ | 3.82 | 1.77 | 0.00 | 9.60 | 0.46 | 23.7 | 0.21 | 18.6 | 1.77 | 0.78 | 3.0 |  $<$0.1 | 17.6 | 48.6 | 16.27 | 0.36
22 | S0 | 1.21 | 2.75 | 4.37 | 6.90 | 0.08 | 77.7 | 0.12 | 23.1 | 1.82 | 0.33 | 0.3 | 0.6 | 1.7 | 6.6 | 21.68 | 0.25
23 | S0 | 2.10 | 1.59 | 0.00 | 10.00 | 0.02 | 100.0 | 0.36 | 14.1 | 1.52 | 0.49 | 0.1 | 0.7 | 2.3 | 2.6 | 20.23 | 0.88
24 | S0 | 2.90 | 1.63 | 0.00 | 18.00 | 0.15 | 39.8 | 0.22 | 25.1 | 1.91 | 0.95 | 2.6 | 2.1 | 13.7 | 23.9 | 9.32 | 0.57
25 |  IRAS 22491-1808∗ | 2.00 | 2.34 | 0.01 | 26.92 | 0.33 | 16.2 | 0.34 | 13.0 | 1.79 | 0.52 | 2.3 |  $<$4.6 | 12.9 | 87.2 | 38.79 | 0.15
26 | S0 | 1.20 | 2.31 | 6.50 | 5.01 | 0.76 | 16.5 | 0.35 | 9.2 | 2.01 | 0.1 | 0.2 | 0.3 | 4.1 | 34.5 | 171.75 | 0.12
27 |  IRAS 22491-1808∗ | 1.68 | 2.75 | 1.59 | 7.24 | 0.16 | 28.3 | 0.11 | 20.1 | 2.20 | 0.29 | 0.3 | 4.5 | 3.9 | 15.8 | 47.15 | 0.24
28 | S0 | 1.64 | 1.45 | 5.55 | 9.12 | 0.67 | 75.3 | 0.37 | 10.6 | 1.69 | 0.22 | 1.4 | 0.6 | 4.9 | 50.0 | 36.17 | 0.10
29 |  Arp 220∗ | 1.23 | 1.18 | 1.31 | 7.41 | 0.46 | 12.9 | 0.15 | 15.0 | 2.18 | 0.45 | 0.5 | 21.2 | 11.9 | 35.6 | 73.93 | 0.34
30 |  IRAS 22491-1808∗ | 1.24 | 1.87 | 0.00 | 1.86 | 0.20 | 19.0 | 0.23 | 19.3 | 2.20 | 0.46 | 0.1 | 4.2 | 1.1 | 5.3 | 36.96 | 0.21
31 | Sb | 1.55 | 0.84 | 0.00 | 50.00 | 0.06 | 100.0 | 0.40 | 14.2 | 1.45 | 0.74 | 1.4 |  $<$0.7 | 8.1 | 19.9 | 14.59 | 0.41
32 | S0 | 1.64 | 0.90 | 0.00 | 4.17 | 0.11 | 100.0 | 0.34 | 13.3 | 1.85 | 0.49 | 0.4 | 0.6 | 1.5 | 5.7 | 13.23 | 0.26
33 | S0 | 2.05 | 1.07 | 0.00 | 8.32 | 0.33 | 13.6 | 0.20 | 20.2 | 2.19 | 0.79 | 0.6 | 0.8 | 6.9 | 23.3 | 39.45 | 0.29
34 | S0 | 1.48 | 1.83 | 1.96 | 51.00 | 0.06 | 54.7 | 0.23 | 16.4 | 1.87 | 0.40 | 1.4 | 5.3 | 10.9 | 28.6 | 20.36 | 0.38
35 | S0 | 2.67 | 1.76 | 0.00 | 4.64 | 0.90 | 77.5 | 0.31 | 18.4 | 1.90 | 0.97 | 6.2 | 1.4 | 13.6 | 41.0 | 6.67 | 0.33
36 | Sb | 1.43 | 1.18 | 2.48 | 1.00 | 0.20 | 25.6 | 0.44 | 7.9 | 2.19 | 0.34 | 1.0 | 0.4 | 1.0 | 2.8 | 36.25 | 0.35
37 | Sa | 1.84 | 1.82 | 0.98 | 17.00 | 0.18 | 93.1 | 0.16 | 20.1 | 2.12 | 0.39 | 1.4 | 0.3 | 9.8 | 37.2 | 26.10 | 0.26
38 | S0 | 1.56 | 1.42 | 0.65 | 6.17 | 0.01 | 100.0 | 0.23 | 14.1 | 1.72 | 0.90 | 0.2 | 0.2 | 0.6 | 1.1 | 7.31 | 0.55
39 |  Arp 220∗ | 1.01 | 1.36 | 1.45 | 2.19 | 0.08 | 91.9 | 0.22 | 17.5 | 2.08 | 0.35 | 0.1 | 4.2 | 0.6 | 2.2 | 25.06 | 0.27
40 | S0 | 2.15 | 0.77 | 0.00 | 7.59 | 0.20 | 15.5 | 0.35 | 11.7 | 1.93 | 0.45 | 0.4 | 2.5 | 8.4 | 19.2 | 45.35 | 0.44
41 |  IRAS 22491-1808∗ | 1.48 | 1.81 | 0.82 | 13.80 | 0.59 | 14.0 | 0.39 | 11.0 | 1.86 | 0.51 | 1.8 | 17.3 | 15.1 | 83.8 | 47.91 | 0.18
42 | Sc | 2.56 | 2.86 | 0.00 | 5.50 | 0.02 | 47.9 | 0.24 | 15.0 | 1.89 | 0.79 | 0.1 | 0.6 | 0.3 | 1.3 | 10.42 | 0.22
43 |  IRAS 22491-1808∗ | 1.54 | 2.69 | 0.23 | 12.00 | 0.36 | 100.0 | 0.29 | 13.3 | 1.87 | 0.46 | 3.2 |  $<$0.4 | 12.9 | 46.2 | 14.28 | 0.28
44 | E2 | 1.44 | 2.78 | 4.11 | 3.63 | 0.71 | 12.7 | 0.33 | 10.0 | 2.14 | 0.2 | 0.2 | 1.7 | 3.2 | 35.0 | 150.67 | 0.09
45 |  IRAS 20551-4250∗ | 2.54 | 1.46 | 2.26 | 60.26 | 0.42 | 49.7 | 0.20 | 16.9 | 1.93 | 0.37 | 9.3 |  $<$1.5 | 51.9 | 212.0 | 22.85 | 0.24
46 |  IRAS 22491-1808∗ | 1.59 | 4.02 | 11.36 | 36.00 | 0.06 | 100.0 | 0.11 | 31.5 | 1.93 | 0.40 | 1.4 |  $<$2.6 | 7.2 | 24.4 | 18.07 | 0.30
47 | E2 | 1.41 | 3.78 | 17.63 | 9.05 | 0.19 | 100.0 | 0.11 | 29.7 | 1.87 | 0.20 | 0.7 |  $<$0.1 | 0.6 | 23.2 | 33.66 | 0.02
48 | S0 | 1.42 | 2.11 | 0.00 | 2.95 | 0.09 | 35.1 | 0.37 | 11.6 | 1.91 | 0.24 | 0.1 | 0.2 | 1.2 | 3.7 | 38.05 | 0.32
49 |  M 82∗ | 1.51 | 4.90 | 0.00 | 5.30 | 0.07 | 100.0 | 0.19 | 24.4 | 2.20 | 0.50 | 0.2 | 3.7 | 1.4 | 4.7 | 25.65 | 0.30
50 |  IRAS 22491-1808∗ | 5.17 | 4.51 | 0.00 | 23.99 | 2.07 | 9.3 | 0.62 | 7.3 | 2.20 | 0.46 | 2.0 |  $<$20.5 | 49.4 | 430.3 | 216.60 | 0.11
51 | S0 | 2.25 | 2.91 | 0.87 | 3.98 | 0.19 | 100.0 | 0.13 | 39.6 | 1.78 | 0.96 | 1.5 | 0.4 | 5.9 | 9.8 | 6.51 | 0.60
Figure 4: The variation of $f_{c}$ with $\lambda_{\rm Edd}$ (upper left),
$L_{\rm Bol}$ (upper right), $L_{\rm X-ray}$ (lower left) and $L_{\rm torus}$
(lower right). Figure 5: Plot showing the relationship between the bulge
luminosity and the black hole mass. The circles are the data points and the
solid black line describes the Margorrian relationship (Magorrian et al.,
1998) for our data. The open circles with lower arrow denote the sources for
which we have considered the upper limits of $L_{\rm host}$. Figure 6:
Histogram of $f_{c}$ for the original sample (blue dashed line) and the
simulation (red solid line). Blue (dashed) and red (solid) vertical lines show
the mean values of the respective distributions of $f_{c}$. Figure 7:
Histogram of $\rho_{s}$ (upper panel) and $d_{s}$ (lower panel) of Spearman’s
correlation between $f_{c}$ and $L_{\rm Bol}$ for the simulation. The blue
dashed line denotes $\rho_{s}$ of the original data (upper panel), and
$\sim$36% of the realisations lie below this showing stronger anti-correlation
than the original sample. Figure 8: Histogram of $\rho_{s}$ (upper panel) and
$d_{s}$ (lower panel) of Spearman’s correlation between $f_{c}$ and
$\lambda_{\rm Edd}$ for 10000 realisations. Here, only $\sim$1% of the
realisations show stronger anti-correlation than the original data.

##  5 Discussion

The effect of the well-known receding torus model (Lawrence, 1991) predicts
that $f_{c}$ decreases with increasing $L_{\rm Bol}$. Whilst our data
marginally supports this prediction we find a stronger anti-correlation
between $f_{c}$ and $\lambda_{\rm Edd}$. So it is not clear which parameter
(or both) is the fundamental driver of the trends seen. This is made more
complex as $f_{c}=L_{\rm torus}/L_{\rm Bol}$, so there is an implicit bias
where $f_{c}$ will anti-correlate with $L_{\rm Bol}$.

In order to investigate this, we carried out a simulation to predict the
correlation between these parameters given our sample. We generated 10000
realisations of random data where pairs of $L_{\rm Bol}$ and $\lambda_{\rm
Edd}$ are drawn from the data using bootstrap sampling with replacement and
then assigned a redshift from the sample, $z$, again with replacement. A
sample of 51 $f_{c}$ values is produced from a uniform distribution within the
range of $0.0-0.9$, roughly corresponding to the observational range. This
allows us to calculate the IR flux which would result from assuming a random
distribution of covering fraction. We applied an effective IR detection
threshold to the simulations, similar to what is expected for the data. We use
the standard 12 $\mu$m limiting flux of 1 mJy for the WISE all-sky survey as
our threshold (Wright et al., 2010). If the simulated IR flux is more than 1
mJy and the corresponding IR luminosity is within the range of the original
data, the source is retained; otherwise, it is discarded and new values of
$L_{\rm Bol}$, $\lambda_{\rm Edd}$, $z$ and $f_{c}$ are drawn. We checked that
this gives rise to realisations with the same distribution of $L_{\rm torus}$
as found in the actual data. There is a difference at the level of 0.02
according to the K-S test, which is only marginally significant. Further tests
carried out with randomised log($f_{c}$), make the difference even less
significant. However, Fig. 6 shows that the distribution of $f_{c}$ in the
data is very different from the simulation, where an assumed initial random
distribution is modified by the IR selection.

In each realisation, we calculate the Spearman’s correlation between $L_{\rm
Bol}$ and $f_{c}$. The rank coefficient of the original data was $-0.27$, very
similar to the value of $\rho_{s}\sim-0.29$ seen in the simulation, and
$\sim$36% of the realisations show an anti-correlation stronger than that
found in the actual data (see Fig. 7). So, in our sample, there is no
significant anti-correlation between $L_{\rm Bol}$ and $f_{c}$.

We repeat this procedure for $\lambda_{\rm Edd}$ and $f_{c}$, but here the
results are very different. The rank coefficient of $\sim-0.43$ seen in the
data is very different to the rank coefficient of the simulation, with only
$\sim$1% of the realisations showing an anti-correlation stronger than that
based on the original data (see Fig. 8), so this is significant at close to
$3\sigma$.

Thus $f_{c}$ in our sample is not significantly correlated with $L_{\rm Bol}$,
but it is with $\lambda_{\rm Edd}$ at $\sim$99% significance. This indicates
that changes in the covering factor are driven more by changes in the
Eddington ratio, rather than by changes in the bolometric luminosity. This
adds to a growing body of evidence that there are large-scale changes in the
SED with $\lambda_{\rm Edd}$ (Vasudevan & Fabian, 2007, 2009; Lusso et al.,
2013, J12a, b). Therefore we find that the most basic of the unification
models in which it is proposed that the observed AGN properties only depend on
inclination are too simple, and there are changes in the shape of the SED
which depend on $\lambda_{\rm Edd}$, as well as MBH which sets the overall
luminosity scale. However, the anti-correlation of the dust covering fraction
with $\lambda_{\rm Edd}$ rather than $L_{\rm Bol}$ indicates a change in the
larger scale geometry of the AGN rather than just the expected response of the
dust to increasing illumination. Such a large-scale change may also be
required to produce the observed anti-correlation of the forbidden series of
the narrow emission lines with $\lambda_{\rm Edd}$, as Narrow Line Seyfert 1s
and other high $\lambda_{\rm Edd}$ AGN are known to have weak [OIII] (e.g.
Boroson & Meyers, 1992; Done & Jin, 2016). Furthermore, Leighly (2004)
speculate that this is due to the very inner regions of the accretion flow
being progressively shielded by a wind, with increasing $\lambda_{\rm Edd}$.
Thereby even if there is copious dust present, the irradiated fraction
decreases as the ionising radiation becomes more collimated, and hence the
reprocessed fraction drops. Fabian et al. (2008) have discussed the fact that
efficient coupling of dust to gas boosts the effect of radiation pressure
feedback. The result is that absorbed AGN are mostly found at low Eddington
ratios. Here, we are seeing a decrease of the (illuminated) dust fraction in
type 1 AGN. The effect could be related to that noted by Fabian et al. (2008)
in absorbed AGN, with the feedback in our sample occurring out of our direct
line of sight. Conversely, if the bulk of the MIR is emitted by dust located
in the polar directions, then this result relates to the relative efficiency
of illuminated dust emission in the line of sight.

Table 4: Spearman’s correlation between different parameters Parameter 1 | Parameter 2 | $\rho_{s}$ | $d_{s}$
---|---|---|---
$\lambda_{\rm Edd}$ | MBH | -0.17 | 0.24
$\lambda_{\rm Edd}$ | $L_{\rm Bol}$ | 0.61 | 1.64$\times 10^{-06}$
$\lambda_{\rm Edd}$ | $L_{\rm X-ray}$ | 0.28 | 0.04
$\lambda_{\rm Edd}$ | $L_{\rm torus}$ | 0.439 | 0.001
$\lambda_{\rm Edd}$ | $\kappa_{2-10}$ | 0.54 | 4.49$\times 10^{-05}$
$\lambda_{\rm Edd}$ | $R_{\rm cor}$ | -0.47 | 5.41$\times 10^{-05}$
$\lambda_{\rm Edd}$ | $f_{\rm pl}$ | -0.234 | 0.099
$\lambda_{\rm Edd}$ | $\Gamma$ | 0.26 | 0.06
$\lambda_{\rm Edd}$ | $f_{c}$ | -0.428 | 0.002
$L_{\rm Bol}$ | $L_{\rm X-ray}$ | 0.76 | 7.8$\times 10^{-11}$
$L_{\rm Bol}$ | $L_{\rm torus}$ | 0.87 | 1.15$\times 10^{-16}$
$L_{\rm Bol}$ | $\kappa_{2-10}$ | 0.34 | 0.02
$L_{\rm Bol}$ | $R_{\rm cor}$ | -0.368 | 0.008
$L_{\rm Bol}$ | $f_{\rm pl}$ | -0.08 | 0.56
$L_{\rm Bol}$ | $\Gamma$ | -0.08 | 0.57
$L_{\rm Bol}$ | $f_{c}$ | -0.27 | 0.05
MBH | $L_{\rm Bol}$ | 0.61 | 2.16$\times 10^{-06}$
MBH | $L_{\rm X-ray}$ | 0.69 | 1.71$\times 10^{-08}$
MBH | $L_{\rm torus}$ | 0.65 | 2.66$\times 10^{-07}$
MBH | $\kappa_{2-10}$ | -0.13 | 0.35
MBH | $R_{\rm cor}$ | 0.06 | 0.65
MBH | $f_{\rm pl}$ | 0.11 | 0.46
MBH | $\Gamma$ | -0.383 | 0.005
MBH | $f_{c}$ | 0.076 | 0.596
$L_{\rm X-ray}$ | $L_{\rm torus}$ | 0.79 | 8.66$\times 10^{-12}$
$L_{\rm X-ray}$ | $\kappa_{2-10}$ | -0.29 | 0.04
$L_{\rm X-ray}$ | $R_{\rm cor}$ | 0.05 | 0.71
$L_{\rm X-ray}$ | $f_{\rm pl}$ | 0.27 | 0.06
$L_{\rm X-ray}$ | $\Gamma$ | -0.34 | 0.01
$L_{\rm X-ray}$ | $f_{c}$ | 0.007 | 0.96
$L_{\rm torus}$ | $\kappa_{2-10}$ | 0.16 | 0.26
$L_{\rm torus}$ | $R_{\rm cor}$ | -0.234 | 0.098
$L_{\rm torus}$ | $f_{\rm pl}$ | 0.09 | 0.55
$L_{\rm torus}$ | $\Gamma$ | -0.14 | 0.33
$L_{\rm torus}$ | $f_{c}$ | 0.17 | 0.22
$\kappa_{2-10}$ | $R_{\rm cor}$ | -0.65 | 2.31$\times 10^{-07}$
$\kappa_{2-10}$ | $f_{\rm pl}$ | -0.52 | 7.89$\times 10^{-05}$
$\kappa_{2-10}$ | $\Gamma$ | 0.434 | 0.001
$\kappa_{2-10}$ | $f_{c}$ | -0.378 | 0.007
$R_{\rm cor}$ | $f_{\rm pl}$ | -0.07 | 0.61
$R_{\rm cor}$ | $\Gamma$ | -0.31 | 0.03
$R_{\rm cor}$ | $f_{c}$ | 0.32 | 0.02
$f_{\rm pl}$ | $\Gamma$ | -0.29 | 0.04
$f_{\rm pl}$ | $f_{c}$ | 0.3 | 0.03
$\Gamma$ | $f_{c}$ | -0.18 | 0.21

##  6 Conclusions

We present a detailed study of the dust covering factors for an
X-ray/optically selected sample of unobscured type 1 AGN in the local Universe
using the data available from XMM-Newton, SDSS, WISE, 2MASS, and UKIDSS. We
used the method of SED modelling analysis to determine the covering factor of
each source. Two important aspects of this work are that we have broadband
spectra to determine $L_{\rm Bol}$, and a self-consistent model to estimate
the contribution of the unobservable FUV region. We find a mean covering
factor of $f_{c}$ = 0.30, with 0.02 $<f_{c}<$ 0.88 and a dispersion of the
individual values of $\sigma_{f}$ = 0.17. The distribution shows a trend of
anti-correlation with $\lambda_{\rm Edd}$ and $L_{\rm Bol}$, but further
analysis based on simulations shows that only the trend with $\lambda_{\rm
Edd}$ is significant at $\sim$99%. This implies a large-scale change in the
geometry of the illuminated dust, rather than simply to a response from
increasing $L_{\rm Bol}$. Division into sub-samples of radio-loud AGN and
NLS1, do not reveal any significant differences in the distribution of
covering factors from the whole sample. This argues against the presence of a
strong additional driving parameter for $f_{c}$ in these sub-samples. However,
the number of objects is small, and further studies are needed.

Our study is based on 51 sources, for which we have comprehensive multi-
wavelength coverage. It would be valuable to extend this type of study to a
larger sample of AGN, with a wider range of redshifts to test the correlations
we find and the conclusions that we have drawn. It is relevant to select
sources with different combinations of black hole mass and accretion rate
since the behaviour of the accretion disc spectrum depends on these
parameters. Further extension of this study can be expected from AstroSat
(Singh et al., 2014) which can obtain simultaneous observations in X-ray and
UV bands.

## Acknowledgements

We thank the referee Konrad Tristram for his thorough review and useful
comments. We acknowledge the UGC-UKIERI Thematic Partnership 2015 (UGC
2014-15/02) for the support of the grant for this work. The first author is
grateful to the Department of Science and Technology (No.SR/S2/HEP-07/2012)
for the financial support. P.G. acknowledges the support of STFC (No.
ST/J003697/2). CD acknowledges support under STFC grant ST/L00075X/1.

This work is based on observations obtained with XMM-Newton, an ESA science
mission with instruments and contributions directly funded by ESA Member
States and NASA. This research has made use of the NASA/ IPAC Infrared Science
Archive, which is operated by the Jet Propulsion Laboratory, California
Institute of Technology, under contract with the National Aeronautics and
Space Administration. This publication makes use of data products from the
Wide-field Infrared Survey Explorer, which is a joint project of the
University of California, Los Angeles, and the Jet Propulsion
Laboratory/California Institute of Technology, funded by the National
Aeronautics and Space Administration. We have used the UKIDSS data from Data
Release 10. The UKIDSS project is defined in (Lawrence et al., 2007). UKIDSS
uses the UKIRT Wide Field Camera (WFCAM; Casali et al. (2007)). The
photometric system is described in Hewett et al. (2006), and the calibration
is described in Hodgkin et al. (2009). The pipeline processing and science
archive are described in Irwin et al (2009, in prep) and Hambly et al. (2008).
This publication makes use of data products from the Two Micron All Sky
Survey, which is a joint project of the University of Massachusetts and the
Infrared Processing and Analysis Center/California Institute of Technology,
funded by the National Aeronautics and Space Administration and the National
Science Foundation.

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan
Foundation, the Participating Institutions, the National Science Foundation,
the U.S. Department of Energy, the National Aeronautics and Space
Administration, the Japanese Monbukagakusho, the Max Planck Society, and the
Higher Education Funding Council for England. The SDSS Web Site is
http://www.sdss.org/.

The SDSS is managed by the Astrophysical Research Consortium for the
Participating Institutions. The Participating Institutions are the American
Museum of Natural History, Astrophysical Institute Potsdam, University of
Basel, University of Cambridge, Case Western Reserve University, University of
Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the
Japan Participation Group, Johns Hopkins University, the Joint Institute for
Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and
Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences
(LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for
Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico
State University, Ohio State University, University of Pittsburgh, University
of Portsmouth, Princeton University, the United States Naval Observatory, and
the University of Washington.

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.

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##  Appendix A IR SED templates

###  A.1 agndust templates

The model agndust makes use of the templates from Silva et al. (2004) who
derived the nuclear infrared spectral energy distributions for a sample of
obscured and unobscured Seyfert galaxies. They divided the observed IR SEDs
into intervals of intrinsic absorbing column density $N_{\rm H}$. In order to
exclude the objects with $N_{\rm H}>$ 1025 cm-2 these SEDs were already
normalised by the unabsorbed hard X$-$ray (2$-$10 keV band) flux. They
obtained four different SEDs averaged within bins of absorbing $N_{\rm H}$.
One among these nuclear IR SEDs corresponds to Seyfert 1 objects with $N_{\rm
H}\leavevmode\nobreak\ <\leavevmode\nobreak\ 10^{22}$ cm-2 and the other three
SEDs are for Seyfert 2 galaxies with $10^{22}<N_{\rm H}<10^{23}$ cm-2,
$10^{23}<N_{\rm H}<10^{24}$ cm-2 and $10^{24}<N_{\rm H}<10^{25}$ cm-2. The
agndust model can make use of the four SEDs for modelling the IR data. In view
of our sample selection, we make use of only the Seyfert 1 template by
excluding the part of the SED at shorter wavelengths, plotted in blue in
Fig. 9.

Figure 9: The rest-frame Silva SED templates (Silva et al., 2004) for Seyfert
1 and Seyfert 2 galaxies, normalised at 12 $\mu$m. Seyfert 2 (22-23), Seyfert
2 (23-24) and Seyfert 2 (24-25) denote SEDs with 10${}^{22}<N_{H}<$1023 cm-2,
10${}^{23}<N_{H}<$1024 cm-2 and 10${}^{24}<N_{H}<$1025 cm-2, respectively. We
isolate the infrared hump of the Seyfert 1 SED to concentrate on the dust
reprocessing component of the torus.

###  A.2 hostpol templates

Figure 10: The host galaxy SEDs from Polletta et al. 2007 (flux density normalised at 5500 Å) for spirals (S0$-$Sd), ellipticals (E2 & E5) and starburst galaxies. The starburst templates correspond to the SEDs of NGC 6090 (60), NGC 6240 (62), M 82 (82), Arp 220 (Ap), IRAS 22491-1808 (22), and IRAS 20551-4250 (20). Table 5: hostpol model components and corresponding SED templates of host galaxies used in our analysis (∗starburst galaxies). hostpol component | SED template
---|---
host01 | S0
host02 | Sa
host03 | Sb
host04 | Sc
host05 | Sd
host06 | E2
host07 | E5
host08 | NGC 6090∗
host09 | NGC 6240∗
host10 | M 82∗
host11 | Arp 220∗
host12 | IRAS 22491-1808∗
host13 | IRAS 20551-4250∗

The hostpol component uses the IR SED templates from SWIRE template library
(Polletta et al., 2007). The SWIRE template library has 25 IR SED templates
which cover the wavelength range between 1000Å and 1000$\mu$m. The library
consists of 3 ellipticals, 7 spirals, 6 starbursts, 7 AGN and 2 composite
(starburst+AGN) templates. The AGN templates comprise 3 type 1 and 4 type 2
AGN SEDs. The 13 SWIRE templates we used for modelling the host galaxy IR
emission using hostpol model (See Table 5) are plotted in Fig. 10.

##  Appendix B Broadband SED fits

The broadband SED fits for the complete sample are shown in Fig. 11.

Figure 11: The broadband SED fitting plots for the 51 sources. We fit the
absorbed SEDs to the observed data and the resultant best-fit models are shown
in dashed grey line. However, we are mainly concerned with the measurements of
$L_{\rm Bol}$, for which we illustrate the intrinsic model (solid red)
together with the deabsorption corrections applied to the data. The individual
model components optxagnf, agndust and hostpol are plotted in dashed blue,
solid green and solid yellow, respectively. Data from XMM-Newton EPIC, Optical
Monitor, SDSS, UKIDSS/2MASS, and WISE are respectively represented by black
dots, circles, diamonds, triangles, and squares. X-ray data have been rebinned
for plotting purpose.

##  Appendix C Notes on individual sources

###  C.1 Discrepancies in SDSS data

The SDSS data points in the SEDs of the objects Mrk 0110 (No. 9), PG 0947+396
(No. 10), PG 1202+281 (No. 21), LBQS 1228+1116 (No. 25), PG 1244+026 (No. 30),
RBS 1201 (No. 32), PG 1415+451 (No. 40), NGC 5683 (No. 42), PG 1512+370 (No.
45) and PG 2233+134 (No. 50) show some clear deviations from the broadband
continuum model. This may be attributed to the intrinsic variability of the
sources. Since the observations of SDSS and OM are not simultaneous, there may
be some discrepancy between the two data sets. The SED of Mrk 0110 shows large
offset in the SDSS data points. J12a discussed this source and mentioned that
it is an extreme example of this behaviour. In order to check the influence of
the discrepancy, we fit these sources with the same model without using the
SDSS data. We observed that $f_{c}$ remain unchanged in 8 sources, and in only
two cases (PG 0947+396 (No. 10) & PG 1202+281 (No. 21)), there is a drop by a
factor of $\sim$2.

###  C.2 Sources with multiple hostpol templates

In the case of Mrk 0110 (No. 9) and PG 1115+407 (No. 18), the normalisations
of all hostpol templates are nearly zero and are equally fitted by multiple
host galaxy templates. For Mrk 0110, all the hostpol templates provide the
same fit-statistic and even the same spectral parameters. However, Mrk 0110 is
identified as an Sa galaxy (Khorunzhev et al., 2012). Hence, in the main text,
we mentioned the SED of spiral galaxy type-a (host02) as the best-fit hostpol
model for this object. In the case of PG 1115+407, more than one hostpol
template gave the same $\chi^{2}$ and slightly different parameter values.
However, the morphological type of the source is unknown. In this case, we
have adopted S0 template as the best-fit component.

###  C.3 Super-Eddington sources

There are two sources in our sample, KUG 1031+398 (No. 15) and PG 2233+134
(No. 50), which have super-Eddington accretion rates. Among these KUG 1031+398
has the highest value of $\lambda_{\rm Edd}$ ($\sim$2.64) and lowest black
hole mass, whereas PG 2233+134 has the highest value of bolometric luminosity.
In these sources, we attempt to fit the data by fixing $\lambda_{\rm Edd}$ to
1 and letting MBH be a free parameter. For KUG 1031+398 this resulted in an
improvement in the fit ($\Delta\chi^{2}$ = -58.5) for a change in MBH from
1.7$\times$10${}^{6}M_{\odot}$ to 3.8$\times$10${}^{6}M_{\odot}$. Here, the
covering factor increased from 0.23 to 0.34. As discussed by Jin et al. (2016)
this may be a super-Eddington source and the black hole mass obtained from the
SED-fitting may not be correct. In such sources, the super-Eddington flow may
not be well fit by a model that conserves energy. In the case of PG 2233+134,
MBH remained unchanged while $\chi^{2}$(/dof) increased from 893.6(/173) to
2641.2(/173). In this case also, $f_{c}$ shows an increase from 0.11 to 0.22.
Although the inclination effects are not taken into account, it seems likely
that this AGN is indeed a super-Eddington source. It is perhaps surprising
that we are able to fit it as a super-Eddington source since such high
Eddington sources probably power strong winds. So energy conservation is not
appropriate due to loss of radiative power to the wind.

##  Appendix D Other Torus templates

Mullaney et al. (2011) (hereafter M11) have constructed a range of intrinsic
MIR to FIR (6-100 $\mu m$) SEDs of a sample of X-ray selected local AGN with
moderate luminosities. We have fitted our sample with M11 SED by extending it
down to about 0.6 $\mu m$ to match the range of our agndust (Silva et al.,
2004) template for Seyfert 1. The covering factors obtained with this template
have a very similar range, mean and scatter as that for agndust. Although the
SED fits and spectral parameters are comparable to that of agndust, for most
of the sources the fit resulted in comparatively poor $\chi^{2}$. This is
probably due to fact that the extended M11 SED is narrow and so fails to cover
the peak in emission around the NIR region.

We have also attempted fitting the data with Clumpy SED for type 1 AGN (Hönig
& Kishimoto, 2010) with inclination 30 degrees, by modifying the template to
match the wavelength range of agndust. But again we note that the template is
narrow compared to agndust SED, and peaks around 10$\mu$m. Also, the torus
luminosity for this component over 1$-$1000 $\mu$m is a factor of $\sim$1.3
lower than that for agndust SED. The fits provide poor statistic for $\sim$70%
of the sources in the sample and a lower range of covering factors $\sim
0.01-0.5$ with a mean around 0.18.

The data appear to require an extra hot dust component in the NIR, not covered
by the above templates. We tested this for UM 269 (No. 1) by adding a black
body component (XSPEC model bbody) with temperature $\sim$1000$-$1500 K. For
this source, a black body with $\sim$1000 K temperature in the NIR region, in
addition to the Clumpy SED provided a better $\chi^{2}$ and resulted in a
similar covering factor ($\sim$0.31) as we obtained when using agndust. Hence
the overall results are consistent with those obtained before.

The histograms of covering factors obtained for agndust, extended M11 and
Clumpy SEDs are shown in Fig. 12.

Figure 12: Histograms of covering factors for agndust SED (thick black line),
extended M11 SED (dashed red line) and Clumpy SED for type 1 AGN (thin green
line). The vertical lines represent the mean values of $f_{c}$ for different
distributions.

##  Appendix E Analysis with 2MASS data

As mentioned in Section 2.1 we opted to use NIR data from UKIDSS instead of
2MASS because of the smaller aperture size of the UKIDSS camera (2″diameter
for UKIDSS & 4″radius for 2MASS), which therefore reduces the contribution
from the host galaxy. Also, three sources in our sample lack 2MASS data and in
those cases we require UKIDSS data. However, for comparison, we have analysed
the entire sample by fitting the broadband SED with 2MASS data (if available)
for the NIR band. We find that the distribution of covering factors is similar
to that obtained when using the UKIDSS data. Both distributions of $f_{c}$
have the same mean and standard deviation. The histograms of $f_{c}$ are shown
in Figure 13. We have also checked the correlation of $f_{c}$ with $L_{\rm
Bol}$ and $\lambda_{\rm Edd}$ obtained for 2MASS data. The trend of $f_{c}$
between these parameters is essentially the same as we found when using the
UKIDSS data.

Figure 13: Distributions of covering factors obtained using 2MASS data (dashed
line) and UKIDSS data (solid line) for the NIR band.