# SMART: spectral energy distributions Markov chain analysis with radiative
transfer models

Charalambia Varnava and Andreas Efstathiou

School of Sciences, European University Cyprus, Diogenes street, Engomi, 1516
Nicosia, Cyprus
E-mail<EMAIL_ADDRESS>(CV)E-mail<EMAIL_ADDRESS>(AE)

(Accepted 2024 April 25; Received 2024 April 24; in original form 2023 October
27)

###### Abstract

In this paper we present the publicly available open-source spectral energy
distribution (SED) fitting code SMART (Spectral energy distributions Markov
chain Analysis with Radiative Transfer models). Implementing a Bayesian Markov
chain Monte Carlo (MCMC) method, SMART fits the ultraviolet to millimetre SEDs
of galaxies exclusively with radiative transfer models that currently
constitute four types of pre-computed libraries, which describe the starburst,
active galactic nucleus (AGN) torus, host galaxy and polar dust components. An
important novelty of SMART is that, although it fits SEDs exclusively with
radiative transfer models, it takes comparable time to popular energy balance
methods to run. Here we describe the key features of SMART and test it by
fitting the multi-wavelength SEDs of the 42 local ultraluminous infrared
galaxies (ULIRGs) that constitute the HERschel Ultraluminous Infrared Galaxy
Survey (HERUS) sample. The Spitzer spectroscopy data of the HERUS ULIRGs are
included in the fitting at a spectral resolution, which is matched to that of
the radiative transfer models. We also present other results that highlight
the performance and versatility of SMART. SMART promises to be a useful tool
for studying galaxy evolution in the JWST era. SMART is developed in PYTHON
and is available at https://github.com/ch-var/SMART.git.

###### keywords:

radiative transfer – galaxies: active – galaxies: interactions –quasars:
general – infrared: galaxies – submillimetre: galaxies.

††pubyear: 2024††pagerange: SMART: spectral energy distributions Markov chain
analysis with radiative transfer models–Appendix A: Plots and other SED
fitting results discussed in the paper††pubyear: 2024

##  1 Introduction

One of the most important and challenging areas of research in modern
Astrophysics concerns the study of the sequence of events that led to the
formation of galaxies and the supermassive black holes (SMBHs) that usually
reside at their centres. Understanding of the complex astrophysics that led to
the observed distribution of galaxies, both in terms of properties and
numbers, is usually sought within the framework of the standard $\Lambda$ cold
dark matter ($\Lambda$CDM) cosmological model (e.g. Lacey et al. 2016).

It is now clear that, in order to understand the numerous processes that
govern galaxy formation and evolution (star formation in secular processes and
in mergers, accretion onto SMBHs and feedback associated with them), we need
multi-wavelength or panchromatic observations of galaxies at all cosmic
epochs. This is mainly due to the presence of cosmic dust in the interstellar
medium (ISM) of galaxies, which significantly affects their ultraviolet (UV)
to millimetre spectra. The necessity of characterizing the panchromatic
emission of galaxies has led to a series of surveys at all wavelengths from
X-ray to radio, of ever improving sensitivity, resolution and sky coverage
(Lonsdale et al., 2003; Eales et al., 2010; Oliver et al., 2012; Shirley et
al., 2019, 2021). Most of these surveys can only be carried out from space,
which has largely become possible over the last two or three decades with
missions, such as IRAS, ISO, Spitzer, AKARI, Herschel, Planck, WISE, GALEX. At
the same time, significant progress has been made in the development of
models. Stellar population synthesis (SPS) models (Bruzual & Charlot, 1993,
2003; Maraston, 2005; Conroy et al., 2009; Eldridge et al., 2017; Byrne et
al., 2022) are an essential ingredient of models for the emission of galaxies.
Another essential ingredient is a model for interstellar dust. Such models
have been developed since the mid-80s (Draine & Lee, 1984; Siebenmorgen &
Krügel, 1992; Draine & Li, 2001; Li & Draine, 2001, 2002; Jones et al., 2017;
Hensley & Draine, 2023).

The spectra of galaxies are usually decomposed into a number of components. It
is widely acknowledged that radiative transfer models that include the effects
of cosmic dust in a realistic geometry are needed for proper interpretation of
the data and the self-consistent determination of a number of physical
quantities of interest, such as the stellar mass of a galaxy, its current star
formation rate (SFR) and active galactic nucleus (AGN) fraction. A number of
radiative transfer models for the emission of starbursts, spheroidal and disc
galaxies that take into account the effects of absorption, scattering and re-
emission by dust have been developed (Rowan-Robinson & Efstathiou, 1993;
Krügel & Siebenmorgen, 1994; Silva et al., 1998; Efstathiou et al., 2000;
Popescu et al., 2000, 2011, 2017; Siebenmorgen & Krügel, 2007; Groves et al.,
2008; Efstathiou & Siebenmorgen, 2009; Camps & Baes, 2020; Efstathiou et al.,
2021). Following the development of the unified model for AGN (Antonucci &
Miller, 1985; Antonucci, 1993), models for the emission of dusty tori of
increasing degree of sophistication have been developed since the early-90s
(Pier & Krolik, 1992; Rowan-Robinson et al., 1993; Efstathiou & Rowan-
Robinson, 1995; Fritz et al., 2006; Siebenmorgen et al., 2015; Stalevski et
al., 2016; Hönig & Kishimoto, 2017).

Model fitting techniques that can be used to aid the interpretation of multi-
wavelength observations of galaxies have also been developed (Efstathiou &
Rowan-Robinson, 2003; da Cunha et al., 2008; Noll et al., 2009; Chevallard &
Charlot, 2016; Eufrasio, 2017; Carnall et al., 2018; Boquien et al., 2019;
Johnson et al., 2021; Doore et al., 2023). However, the usual practice for the
starburst and host galaxy components is to use approximate methods, such as
energy balance. SED fitting results which incorporate radiative transfer
models for the starburst and host galaxy component have so far been limited
(Verma et al., 2002; Farrah et al., 2002, 2003; Vega et al., 2008; Herrero-
Illana et al., 2017; Kankare et al., 2021; Efstathiou et al., 2022). A
thorough review of spectral energy distribution (SED) fitting methods is given
in Pacifici et al. (2023).

Our aim is to develop an SED fitting tool, which will allow fitting of the
SEDs of local galaxies, for which rest frame mid-infared (MIR)
spectrophotometry from Spitzer and now JWST is available, but also for more
distant galaxies, where more limited photometry is available. MIR
spectrophotometry contains important features from dust, e.g. polycyclic
aromatic hydrocarbon molecule (PAH) features and silicate features that are
essential for constraining the energy source of galaxies (Efstathiou et al.,
2022). Code Investigating GALaxy Emission (CIGALE, Noll et al. 2009; Boquien
et al. 2019), being a grid-based method, only allows the specification of
discrete values for the model parameters. This limits its ability to model
spectrophotometry data, which are essential for decomposing the SEDs of
galaxies and inferring the contribution of star formation and AGN activity. In
our method we use the full range of the model parameters. This is particularly
important for key parameters like the AGN torus inclination. Although CIGALE
offers the option to add routines, we need a different concept to address our
scientific aims. Paspaliaris et al. (2021) fitted luminous infrared galaxies
(LIRGs) and ultraluminous infrared galaxies (ULIRGs) with CIGALE, but they did
not include the Spitzer MIR spectrophotometry. This is also the case for the
studies of Yang et al. (2020, 2022). We note that, of course, our method can
also be applied to a broad range of high redshift galaxies with limited
photometry, as we demonstrate in Section 4.5.

Considering all the above, we have developed a new method for fitting
radiative transfer models to data, using a Markov chain Monte Carlo (MCMC)
code: Spectral energy distributions Markov chain Analysis with Radiative
Transfer models (SMART). We currently test SMART with a large sample of
galaxies with excellent photometry and infrared (IR) spectrophotometry
obtained with the Infrared Spectrograph (IRS) onboard the Spitzer Space
Telescope. The novelty of SMART is that, although it utilizes exclusively
radiative transfer models, it takes comparable time to popular energy balance
methods.

In particular, we utilize four types of libraries of models as input to SMART
for fitting the SEDs: these are the starburst (Efstathiou et al., 2000;
Efstathiou & Siebenmorgen, 2009), AGN torus (Efstathiou & Rowan-Robinson,
1995; Fritz et al., 2006; Siebenmorgen et al., 2015; Stalevski et al., 2016),
spheroidal (Efstathiou et al., 2021) or disc (Efstathiou, in preparation) host
and polar dust (Efstathiou, 2006) models. These libraries are part of the
collection of radiative transfer models named CYprus models for Galaxies and
their NUclear Spectra (CYGNUS). We have also added a component of polar dust
in the fitting, which has been recognized as an important component in AGN
since the mid-90s (see also Efstathiou, Hough & Young 1995; Efstathiou 2006;
Mattila et al. 2018), and explore the use of other AGN torus models (e.g.
Fritz et al. 2006; Siebenmorgen et al. 2015; Stalevski et al. 2016). As an
MCMC sampler we utilize the publicly available emcee code, which is a pure-
PYTHON implementation of Goodman & Weare’s (2010) Affine Invariant MCMC
Ensemble sampler (Foreman-Mackey et al., 2013).

To test SMART, we fit the multi-wavelength SEDs for the HERschel Ultraluminous
Infrared Galaxy Survey (HERUS) sample (Farrah et al., 2013) at $z<0.27$,
assembled by Efstathiou et al. (2022). We are also testing SMART with other
hyperluminous obscured galaxies at $z>4$, such as the hyperluminous obscured
quasar at $z\sim 4.3$ discovered by Efstathiou et al. (2021) in the Herschel
Extragalactic Legacy Project (HELP, Shirley et al. 2021). We fit the data with
our method and the results of the fitting are then post-processed to derive
physical quantities, such as stellar mass, SFR, starburst timescale, AGN
fraction etc., which are essential for studying galaxy evolution. In a
companion paper Varnava & Efstathiou (in preparation) carry out a detailed
study with SMART of the recently discovered hyperluminous infrared galaxy
(HLIRG) COS-87529 at $z=6.853$ (Endsley et al., 2022). Efstathiou et al. (in
preparation) use SMART to put constraints on the starburst and AGN activity of
heavily obscured quasars at redshifts $z\sim 0.3-3$ discovered by Lonsdale et
al. (2015).

This paper is organized as follows: In Section 2 we describe our approach for
SED fitting, in Section 3 we test our method with the HERUS sample and in
Section 4 we provide case studies to display the versatility of our method. In
Section 5 we present our conclusions, as well as a few ideas for future
development. Throughout this work we assume $H_{0}=70$ km s-1 Mpc-1,
$\Omega=1$ and $\Omega_{\Lambda}=0.7$.

##  2 Our approach

SMART demonstrates the feasibility of fitting the panchromatic SEDs of a large
sample of galaxies exclusively with state-of-the-art radiative transfer models
and extracting the important physical parameters. Efstathiou et al. (2021) and
Efstathiou et al. (2022), as well as other previous studies by Herrero-Illana
et al. (2017), Mattila et al. (2018), Kankare et al. (2021), presented results
of SED fitting with radiative transfer models, using the IDL version of
Spectral energy distribution Analysis Through Markov Chains (SATMC, Johnson et
al. 2013) by employing the synthesis mode. SATMC by itself does not output
physical quantities, such as stellar mass, SFRs, AGN fraction, and therefore
additional post-processing routines were developed. More details of this
approach are described in Efstathiou (in preparation).

In our method we address the need of developing an SED fitting code, which is
specifically designed to fit efficiently galaxy SEDs, using exclusively
radiative transfer models. We use the MCMC code emcee as the core of the
method. The MCMC method, although computing intensive, gives the global best
fit. In addition, as the method produces the posterior parameter distribution,
realistic errors on the parameters can be estimated. This will motivate
further work in using similar techniques to fit the panchromatic SEDs of the
large samples of galaxies that have already been assembled by projects, such
as HELP.

We fit the UV to millimetre SEDs with radiative transfer models that currently
constitute four types of pre-computed libraries, which describe the starburst,
AGN, host galaxy and polar dust components. These four libraries are part of
CYGNUS. The starburst and AGN models are assumed to be independent of
redshift, whereas for the host galaxy a different library is selected
depending on the redshift. SMART allows us to explore the impact of four
different AGN models and therefore constrain the properties of the obscuring
torus (more details are given in Efstathiou et al. 2022, see also Section
2.1).

The main novel features of our approach, which make it state-of-the-art in the
field of SED fitting, are:

  1. 1.

SMART uses radiative transfer models that take properly into account the
effects of dust in a realistic geometry, whereas popular energy balance
methods, such as CIGALE (Noll et al., 2009; Boquien et al., 2019) and Multi-
wavelength Analysis of Galaxy Physical Properties (MAGPHYS, da Cunha et al.
2008), rely on various forms of attenuation laws. SMART can uniquely model a
galaxy explicitly as a spheroidal or disc galaxy, whereas it takes comparable
computing time to methods like CIGALE and MAGPHYS.

  2. 2.

The code is parallelized and it is considerably faster than other MCMC codes,
such as SATMC.

  3. 3.

We make use of four different AGN libraries, as in Efstathiou et al. (2022).

  4. 4.

As in Efstathiou et al. (2022), we can also optionally add a component of
polar dust in the fitting.

  5. 5.

SMART is designed to fit an SED in comparable time with a spheroidal or disc
host galaxy model.

  6. 6.

With SMART we can fit part of a galaxy and, if necessary, switch off any of
the four components (AGN torus, starburst, spheroidal/disc, polar dust).

SMART is an open-source and publicly available SED fitting code available at
https://github.com/ch-var/SMART.git. A user manual with plenty of examples is
also provided on the same website.

###  2.1 Description of the radiative transfer models

Our method relies on the availability of libraries of radiative transfer
models for the emission of starburst episodes, AGN tori and host galaxies. The
models are part of the collection of radiative transfer models named
CYGNUS111https://arc.euc.ac.cy/cygnus-project-arc. The parameters of the
models are listed in Table 1.

####  2.1.1 Starburst models

The starburst models currently included in CYGNUS were described in Efstathiou
et al. (2000) and Efstathiou & Siebenmorgen (2009). Models for massive star
formation and starbursts were also presented and discussed in Rowan-Robinson &
Crawford (1989); Rowan-Robinson & Efstathiou (1993); Efstathiou & Rowan-
Robinson (1994); Krügel & Siebenmorgen (1994); Silva et al. (1998); Takagi et
al. (2003); Dopita et al. (2005); Siebenmorgen & Krügel (2007). The starburst
model assumes the following parameters, which have the range given in
brackets: the age of the starburst ($t_{*}=5-35$ Myr), the giant molecular
clouds’ (GMCs’) initial optical depth ($\tau_{v}=50-250$) and the time
constant of the exponentially decaying SFR ($\tau_{*}=15-35$ Myr).

####  2.1.2 Spheroidal host models

The spheroidal host models are described in more detail in Efstathiou et al.
(2021). The models of Bruzual & Charlot (1993, 2003) are used in combination
with an assumed star formation history (SFH) to compute the spectrum of
starlight, which is illuminating the dust throughout the model galaxy. The
spectrum of starlight is assumed to be constant throughout the galaxy, but its
intensity varies throughout the galaxy according to a Sérsic profile with
$n=4$, which is equivalent to de Vaucouleurs’s law. Efstathiou & Rowan-
Robinson (2003) assumed an exponentially decaying SFH, whereas here we assume
a delayed exponential ($\dot{M}_{\ast}\propto t\times e^{-t/\tau^{s}}$), where
$\tau^{s}$ is the e-folding time of the exponential.

The spheroidal model assumes the following parameters, which have the range
given in brackets: the e-folding time of the assumed delayed exponential SFH
($\tau^{s}=0.125-8$ Gyr), the optical depth of the galaxy from its centre to
its surface ($\tau_{v}^{s}=0.1-15$) and a parameter that controls the
bolometric intensity of stellar emission relative to that of the bolometric
intensity of starlight in the solar neighborhood ($\psi^{s}=1-17$). In this
paper we use two libraries of spheroidal models, which were computed assuming
an age for the galaxy equal to the age of the Universe at a redshift of
$z=0.1$ and 4.3. We assumed that all the stars in the galaxy formed with a
Salpeter Initial Mass Function (IMF) out of gas with a metallicity of 40 per
cent of solar for the $z=0.1$ library and 6.5 per cent of solar for the
$z=4.3$ library.

####  2.1.3 Disc host models

The disc models library has been computed with a two-dimensional radiative
transfer code that combines the features of the code of Efstathiou & Rowan-
Robinson (1995) for modeling AGN tori, which does not include PAHs and small
grains, and the spheroidal code of Efstathiou et al. (2021), which does. In
the case of the disc models the distribution of stars, dust and molecular
clouds follows a double exponential (e.g. Silva et al. 1998) instead of the de
Vaucouleurs’s law assumed for the spheroidal models. The disc models have as
parameters the disc SFR e-folding time $\tau^{d}$, the starlight intensity
parameter $\psi^{d}$ and the equatorial optical depth in the V band
$\tau_{v}^{d}$. Additionally, the disc models have the inclination of the disc
as a parameter. The same dust model is used as in the case of the spheroidal
models. The library used in this paper assumes that all the stars in the
galaxy formed with a Salpeter IMF out of gas with a metallicity of 20 per cent
of solar. The disc models have been used in Kool et al. (2018) and Kankare et
al. (2021) to fit the SEDs of LIRGs. More details and applications of the disc
models are given in Efstathiou (in preparation).

####  2.1.4 AGN torus models

There are a number of AGN torus models available in the literature, which make
different assumptions about the obscurer geometry (Pier & Krolik, 1993; Rowan-
Robinson et al., 1993; Granato & Danese, 1994; Efstathiou & Rowan-Robinson,
1995; Nenkova et al., 2002, 2008; Dullemond & van Bemmel, 2005; Fritz et al.,
2006; Hönig et al., 2006; Schartmann et al., 2008; Heymann & Siebenmorgen,
2012; Stalevski et al., 2012, 2016; Efstathiou et al., 2013; Siebenmorgen et
al., 2015; Hönig & Kishimoto, 2017). In SMART we currently explore the impact
of four different AGN models, which are described in more detail in Efstathiou
et al. (2022):

  1. 1.

The CYGNUS AGN torus model. A number of results with this combination of
models using the MCMC code SATMC have previously been presented (Herrero-
Illana et al., 2017; Kool et al., 2018; Mattila et al., 2018; Pitchford et
al., 2019; Efstathiou et al., 2021; Kankare et al., 2021; Efstathiou et al.,
2022).

  2. 2.

The AGN torus model of Fritz et al. (2006).

  3. 3.

The two-phase AGN torus model SKIRTOR of Stalevski et al. (2016).

  4. 4.

The two-phase AGN torus model of Siebenmorgen et al. (2015).

It is generally acknowledged in the literature (e.g. Efstathiou et al. 2014;
Siebenmorgen et al. 2015; Efstathiou et al. 2022; García-Bernete et al. 2024)
that clumpy and two-phase torus models can not reproduce the deep silicate
absorption features observed in objects like IRAS 08572+3915, which we discuss
in Section 4.3 in detail. The parameter $p$ in the SKIRTOR model takes four
discrete values in the library (0, 0.5, 1 and 1.5). Assuming a value for
$p<1$, leads to AGN torus spectra with shallower silicate absorption features
and therefore worse fits with these models. We have therefore fixed $p$ to the
value of 1. The parameter $q$ in SKIRTOR concerns the azimuthal dependence of
the density distribution and it is unlikely to have much impact on the
silicate features. We have fixed this value at 1. The parameters of all of the
AGN torus models used in this paper are summarized in Table 1.

####  2.1.5 Polar dust model

The model assumes that polar dust is concentrated in discrete spherical
optically thick clouds, all of which are assumed to have constant temperature
for all dust grains (Efstathiou, 2006). The model assumes the same multi-grain
dust mixture as in the starburst radiative transfer model (Efstathiou &
Siebenmorgen, 2009), but the small grains and PAHs are assumed to be destroyed
by the strong radiation field of the AGN to which these clouds are directly
exposed. Unlike Efstathiou et al. (2022), in SMART the temperature of the
polar dust clouds $T_{p}$ is a free parameter in the fit and is assumed to
vary in the range 800K$-$1200K. We assume that all clouds have an optical
depth from the center to the surface in the V band of 100.

###  2.2 Procedure for running SMART

We have developed the PYTHON routine SMART that makes a sequence of runs for
different galaxies, which are selected from a list according to their flag.
For example, in the following list we run the galaxies with flag=1001:

    name               redshift        flag    AGN_type
    IRAS00188-0856      0.12840000     1001      2
    IRAS00397-1312      0.26170000     1001      2
    IRAS01003-2238      0.11780000     1001      2
    IRAS03158+4227      0.13440000     1001      2
    IRAS03521+0028      0.15190000     1001      2
    IRAS05189-2524     0.042560000     1001      2
    IRAS06035-7102     0.079470000     1001      2
    IRAS06206-6315     0.092440000     1001      2
    IRAS07598+6508      0.14830000     1001      1
    IRAS08311-2459      0.10040000     1001      2
    IRAS08572+3915     0.058350000     1001      2
    IRAS09022-3615     0.059640000     1001      2
    IRAS10378+1109      0.13620000     1001      2
    IRAS10565+2448     0.043000000     1001      2
    IRAS11095-0238      0.10660000     1001      2
    ...

The first column gives the name of the galaxy, which is also the name of the
file that contains the data. The second column gives the redshift of the
galaxy, the third column its selection flag and the fourth column indicates
whether the galaxy will be fitted with a type 1 or type 2 AGN torus model.

The fit for each galaxy takes $\sim$ 2$-$3 minutes on a machine with a few
CPUs. but, because the code is parallelized, can run much faster on a
supercomputer. SMART can optionally make a corner plot, in order to assess
whether there are any degeneracies in the model parameters. For this plot we
use the PYTHON package GETDIST (Lewis, 2015), which we incorporate into SMART.

Table 1: Parameters of the models currently used in SMART, symbols used, their
assumed ranges and summary of other information about the models. In the model
of Fritz et al. (2006) there are two additional parameters that define the
density distribution in the radial direction ($\beta$) and azimuthal direction
($\gamma$). In this paper we assume $\beta=0$ and $\gamma=4$. In the SKIRTOR
model there are two additional parameters that define the density distribution
in the radial direction ($p$) and azimuthal direction ($q$). In this paper we
assume $p=1$ and $q=1$. In addition, the SKIRTOR library fixes the fraction of
mass inside clumps to 97 per cent. There are four additional scaling
parameters for the starburst, spheroidal or disc, AGN and polar dust models,
$f_{SB}$, $f_{sph}$ or $f_{disc}$, $f_{AGN}$ and $f_{p}$, respectively.

Parameter | Symbol | Range | Comments
---|---|---|---
CYGNUS Starburst |  |  |
Initial optical depth of GMCs | $\tau_{v}$ | 50$-$250 |  Efstathiou et al. (2000), Efstathiou & Siebenmorgen (2009)
Starburst SFR e-folding time | $\tau_{*}$ | 10$-$35 Myr | Incorporates Bruzual & Charlot (1993, 2003)
Starburst age | $t_{*}$ | 5$-$35 Myr | Metallicity=solar, Salpeter IMF
|  |  | Standard galactic dust mixture with PAHs
CYGNUS Spheroidal Host |  |  |
Spheroidal SFR e-folding time | $\tau^{s}$ | 0.125$-$8 Gyr |  Efstathiou & Rowan-Robinson (2003), Efstathiou et al. (2021)
Starlight intensity | $\psi^{s}$ | 1$-$17 | Incorporates Bruzual & Charlot (1993, 2003)
Optical depth | $\tau_{v}^{s}$ | 0.1$-$15 | Range of metallicities, Salpeter IMF
|  |  | Standard galactic dust mixture with PAHs
CYGNUS Disc Host |  |  |
Disc SFR e-folding time | $\tau^{d}$ | 0.5$-$8 Gyr |  Efstathiou & Rowan-Robinson (2003), Efstathiou (in preparation)
Starlight intensity | $\psi^{d}$ | 1$-$9 | Incorporates Bruzual & Charlot (1993, 2003)
Optical depth | $\tau_{v}^{d}$ | 0.1$-$29 | Range of metallicities, Salpeter IMF
Inclination | $\theta_{d}$ | 0°$-$90° | Standard galactic dust mixture with PAHs
CYGNUS AGN torus |  |  |
Torus equatorial UV optical depth | $\tau_{uv}$ | 260$-$1490 | Smooth tapered discs
Torus ratio of outer to inner radius | $r_{2}/r_{1}$ | 20$-$100 |  Efstathiou & Rowan-Robinson (1995), Efstathiou et al. (2013)
Torus half-opening angle | $\theta_{o}$ | 30°$-$75° | Standard galactic dust mixture without PAHs
Torus inclination | $\theta_{i}$ | 0°$-$90° | The subranges $\theta_{o}$$-$90° and 0°$-$$\theta_{o}$ are assumed for
|  |  | AGN_type=2 and AGN_type=1, respectively.
Fritz et al. (2006) AGN torus |  |  |
Torus equatorial optical depth at 9.7$\mu m$ | $\tau_{9.7\mu m}$ | 1$-$10 | Smooth flared discs
Torus ratio of outer to inner radius | $r_{2}/r_{1}$ | 10$-$150 | Fritz et al. (2006)
Torus half-opening angle | $\theta_{o}$ | 20°$-$70° | Standard galactic dust mixture without PAHs
Torus inclination | $\theta_{i}$ | 0°$-$90° | The subranges $\theta_{o}$$-$90° and 0°$-$$\theta_{o}$ are assumed for
|  |  | AGN_type=2 and AGN_type=1, respectively.
SKIRTOR AGN torus |  |  |
Torus equatorial optical depth at 9.7$\mu m$ | $\tau_{9.7\mu m}$ | 3$-$11 | Two-phase flared discs
Torus ratio of outer to inner radius | $r_{2}/r_{1}$ | 10$-$30 |  Stalevski et al. (2012), Stalevski et al. (2016)
Torus half-opening angle | $\theta_{o}$ | 20°$-$70° | Standard galactic dust mixture without PAHs
Torus inclination | $\theta_{i}$ | 0°$-$90° | The subranges $\theta_{o}$$-$90° and 0°$-$$\theta_{o}$ are assumed for
|  |  | AGN_type=2 and AGN_type=1, respectively.
Siebenmorgen et al. (2015) AGN torus |  |  |
Cloud volume filling factor (per cent) | $V_{c}$ | 1.5$-$77 | Two-phase anisotropic spheres
Optical depth of the individual clouds | $A_{c}$ | 0$-$45 | Siebenmorgen et al. (2015)
Optical depth of the disc mid-plane | $A_{d}$ | 50$-$500 | Fluffy dust mixture without PAHs
Inclination | $\theta_{i}$ | 0°$-$90° | The subranges 45°$-$90° and 0°$-$45°are assumed for
|  |  | AGN_type=2 and AGN_type=1, respectively.
Polar dust |  |  |
Temperature | $T_{p}$ | 800K$-$1200K | Optically thick spherical clouds (Efstathiou, 2006)

A number of physical quantities are extracted with the routine post_SMART we
have developed. The names of the physical quantities are self-explanatory, but
we also list them and describe them briefly in Table 2.

Table 2: Derived physical quantities for the starburst, AGN torus and host combination (spheroidal/disc), as well as the symbol used. The luminosities are integrated over 1$-$1000 $\mu m$. Physical Quantity | Symbol
---|---
Observed AGN torus Luminosity | $L_{AGN}^{o}$
Corrected AGN torus Luminosity | $L_{AGN}^{c}$
Polar dust AGN Luminosity | $L_{p}$
Starburst Luminosity | $L_{SB}$
Spheroidal host Luminosity | $L_{sph}$
Disc host Luminosity | $L_{disc}$
Total observed Luminosity | $L_{tot}^{o}$
Total corrected Luminosity | $L_{tot}^{c}$
Starburst SFR (averaged over SB age) | $\dot{M}_{*}^{age}$
Spheroidal SFR | $\dot{M}_{sph}$
Disc SFR | $\dot{M}_{disc}$
Total SFR | $\dot{M}_{tot}$
Starburst Stellar Mass | $M^{*}_{SB}$
Spheroidal Stellar Mass | $M^{*}_{sph}$
Disc Stellar Mass | $M^{*}_{disc}$
Total Stellar Mass | $M^{*}_{tot}$
AGN fraction | $F_{AGN}$
Anisotropy correction factor | $A$

###  2.3 Description of the post-processing routines

The PYTHON routine post_SMART post-processes the output of the MCMC code. The
user has the option to post-process the data generated by SMART for a number
of galaxies, which are selected from a list according to their flag. The code
gives the option to plot the residuals, which give an indication of the
quality of the fit.

We have also developed the PYTHON routine reformatter_SMART that reformats the
output of SMART, in order to write the extracted physical quantities of the
selected sample of galaxies, as well as their errors, in the form of a LaTeX
table.

####  2.3.1 Calculation of luminosities and AGN fraction

SMART allows us to have the best fit spectrum for the total emission, as well
as each of the four components of emission: starburst, AGN torus, host galaxy
and polar dust. We calculate the total luminosity, as well as that of each
component separately, by integrating the spectra over the chosen wavelength
range. All luminosities given in Table 2 are 1$-$1000 $\mu m$ luminosities. We
can, of course, calculate the bolometric luminosities over the whole
wavelength range covered by the models. Having calculated the total luminosity
and that of the AGN torus, we can calculate the AGN fraction.

An important feature of the results from the SED fitting is that due to the
anisotropy of the emission from the AGN torus, which is usually optically
thick to its own radiation (Pier & Krolik, 1993; Efstathiou & Rowan-Robinson,
1995; Efstathiou et al., 2014), the AGN luminosity needs to be corrected by
the anisotropy correction factor $A(\theta_{i})$ defined in Efstathiou (2006):

$A(\theta_{i})={{\int_{0}^{\pi/2}~{}~{}S(\theta_{i}^{\prime})~{}~{}sin\theta_{i}^{\prime}~{}~{}d\theta_{i}^{\prime}}\over{S(\theta_{i})}},$
(1)

where $S(\theta_{i})$ is the bolometric emission over the relevant wavelength
range. $A(\theta_{i})$ is generally different for the IR and bolometric
luminosities and is significant for all the AGN torus models considered here.

####  2.3.2 Calculation of SFRs and stellar mass

With SMART we can calculate separately the SFR and stellar mass of the
starburst and the spheroidal or disc galaxy. All SFR and stellar mass
estimates are calculated self-consistently, as the radiative transfer models
used in the fits incorporate the SPS models of Bruzual & Charlot (1993, 2003).

Efstathiou et al. (2022) discussed two different estimates for the SFR of the
starburst: the SFR averaged over the age of the starburst,
$\dot{M}^{age}_{*}$, where the age is determined self-consistently from the
fit, and the SFR averaged over a flat timescale of 50 Myr, $\dot{M}^{50}_{*}$.
Efstathiou et al. (2022) derived a very good relationship for the HERUS sample
between the starburst luminosity and $\dot{M}^{age}_{*}$:

$\frac{{\dot{M}_{*}^{age}}}{M_{\odot}yr^{-1}}=(3.11\pm 0.05)\times
10^{-10}\frac{L_{SB}}{L_{\odot}}.$ (2)

In the case of the spheroidal or disc component we are interested in the SFR
at the time of observation. The SFR at all times of the history of the galaxy
can, of course, be obtained from the assumed SFH, which takes the form of a
delayed exponential.

####  2.3.3 Calculation of minimum reduced $\chi^{2}$

There is significant uncertainty in the models, which is primarily due to
uncertainties regarding the dust properties, the geometry, numerical errors
etc. The uncertainty in the observed photometry is primarily driven by the
calibration uncertainty of the instruments. We therefore define the $\chi^{2}$
statistic we use to compare the observed and the model SEDs as:

$\chi^{2}=\sum_{n}\left[\frac{\left(y_{n}-\mu_{n}\right)^{2}}{(\sigma_{\mu}\
\mu_{n})^{2}+(\sigma_{y}\ y_{n})^{2}}\right],$ (3)

where $y_{n}$ and $\mu_{n}$ are the observed data and the corresponding model
value respectively, $\sigma_{\mu}$ is the uncertainty of the model and
$\sigma_{y}$ is the uncertainty of the data.

Based on our analysis, in this paper we assumed that an uncertainty of 15 per
cent realistically represented our confidence in the model SEDs. We also
assumed 15 per cent of uncertainty in the observed photometry. The minimum
reduced $\chi^{2}$, $\chi^{2}_{min,\nu}$, can then be obtained by
${\chi^{2}_{min,\nu}=\frac{\chi^{2}_{min}}{\nu}},$ where the degrees of
freedom, $\nu=n-m$, equal the number of data points $n$ minus the number of
fitted parameters $m$.

##  3 Testing SMART with the HERUS sample

###  3.1 Sample details

The main sample of galaxies we will use for testing SMART is the HERUS sample
(Farrah et al., 2013). This sample consists of 40 ULIRGs included in the
Infrared Astronomical Satellite (IRAS) PSC-z survey (Saunders et al., 2000)
with 60$\mu m$ fluxes greater than 2 Jy. We also include three randomly
selected ULIRGs with lower 60$\mu m$ fluxes, IRAS 00397-1312 (1.8 Jy), IRAS
07598+6508 (1.7 Jy) and IRAS 13451+1232 (1.9 Jy). The quasar 3C 273 has been
excluded, as it is a Blazar, to give a sample of 42 galaxies. The sample,
strictly speaking, is not complete, but it includes nearly all known ULIRGs at
$z<0.27$ and so provides an almost unbiased benchmark of local ULIRGs. All 42
galaxies were observed with the IRS instrument (Houck et al., 2004) on board
Spitzer and by Herschel, as part of both the HERUS and SHINING surveys
(Fischer et al., 2010; Sturm et al., 2011; Hailey-Dunsheath et al., 2012;
González-Alfonso et al., 2013). HERUS studied some of the most luminous local
ULIRGs, including famous objects like Arp 220, Mrk 231 and Mrk 273. In Fig. 1
we show the plot of the SFR against the total stellar mass for the 42 galaxies
of the HERUS sample. In Fig. 2 we show the predicted contribution of starburst
and AGN in the HERUS galaxies.

The multi-wavelength photometry and how it was assembled is described in
Efstathiou et al. (2022), but we summarize the approach here as well. The far-
infrared (FIR) and submillimetre photometry refers to the whole galaxy, as the
aperture is always larger than the size of the galaxies. This is also the case
for the IRS spectroscopy, which has a slit width $>3.6$” that corresponds to a
scale $>5$kpc for a $z>0.1$ system in our sample. For the optical photometry
we use the total aperture derived either from Pan-STARRS, SDSS or from U et
al. (2012). The IRS data included in the fits have a wavelength grid that is
separated in steps of 0.05 in the log of the rest wavelength. We also add more
points around the 9.7$\mu m$ silicate feature and the PAH features to the
equally spaced wavelength grid. The total number of data points we fitted
varies from object to object. For example, in IRAS 03158+4227 we have a
minimum of 30 data points, whereas in Arp 220 we have a maximum number of 55
data points. There is only one ULIRG in our sample with clear signs of a type
1 AGN and we discuss this object in detail in Section 4.2.

Figure 1: Starburst or host SFR against total stellar mass for the HERUS
sample. Also plotted is the SFR$-$stellar mass ($\dot{M}_{*}-M_{*}$) ‘main-
sequence’ relation at $z=0.1$, calculated via equation (28) of Speagle et al.
(2014) with t=12.161 Gyr being the age of the Universe at $z=0.1$ for the
assumed cosmology. Figure 2: Left: Starburst and anisotropy-corrected AGN
luminosity against total corrected IR luminosity. The starburst usually
dominates the IR emission, except at $L_{tot}^{c}\gtrsim 3\times
10^{12}L_{\odot}$ when AGNs start to make a significant or dominant
contribution. Right: Observed and anisotropy-corrected AGN luminosity against
starburst luminosity. There is no clear evidence of a relation between
$L_{SB}$ and $L_{AGN}$.

###  3.2 Results for the HERUS sample

In this subsection we present the results of fitting the HERUS sample with
SMART. For most of the objects the fits are satisfactory and of similar
quality as in the fits with SATMC reported in Efstathiou et al. (2022). Tables
A1 and A2 give selected fitted parameters, along with their errors, of the
HERUS sample of 42 local ULIRGs, using the CYGNUS radiative transfer models
for starbursts, AGN tori, host galaxies and polar dust. In Figs A1, A2, A3,
A4, A5 and A6 we present the UV to millimetre SED fits of the HERUS sample.
The quality of the fits is demonstrated by a plot of the distribution of the
reduced $\chi^{2}$ shown in Fig. 3. We note that the distribution peaks at
$\sim$ 1.75 and, apart from the fit of Arp 220 which has
$\chi^{2}_{min,\nu}$=5.23, the fits for all other galaxies provide
$\chi^{2}_{min,\nu}<3.16$. The values of the reduced $\chi^{2}$ are, of
course, sensitive to the assumed values of $\sigma_{\mu}$ and $\sigma_{y}$ in
equation 3. Tables 3 and 4 give the extracted physical quantities, as well as
their errors. An example of a corner plot is shown in Fig. 4 for the SED fit
of IRAS 05189-2524, which we discuss in more detail in Section 4.1. For this
corner plot we omit some nuisance parameters (our scaling parameters) to make
the rest of them more visible.

Figure 3: Distribution of the reduced $\chi^{2}$ for the galaxies of the HERUS
sample, which shows that almost all the fits have $\chi^{2}_{min,\nu}\leq
3.5$. The exception is Arp 220. Figure 4: Corner plot of the ULIRG IRAS
05189-2524, which shows that most of the parameters of the models are
constrained very well with very little degeneracy Figure 5: Plot of
representative physical quantities for the 42 HERUS local ULIRGs extracted by
SMART against the same quantities extracted by Efstathiou et al. (2022) using
SATMC (blue). In two of the panels we also plot with red the corresponding
quantities extracted by CIGALE for seven of the HERUS ULIRGs by Paspaliaris et
al. (2021). Top left: Starburst luminosity. Top right: SFR. Bottom left:
Observed AGN torus luminosity. Bottom right: AGN fraction. Table 3: Selected
extracted physical quantities for the galaxies in the HERUS sample. For the
AGN and total luminosities the anisotropy-corrected luminosities are given.
All of the luminosities are 1-1000 $\mu m$ luminosities.

Name | $z$ | $L_{AGN}^{c}$ | $L_{SB}$ | $L_{sph}$ | $L_{p}$ | $L_{tot}^{c}$ | $\dot{M}^{age}_{*}$ | $\dot{M}_{sph}$
---|---|---|---|---|---|---|---|---
|  | $10^{12}L_{\odot}$ | $10^{11}L_{\odot}$ | $10^{10}L_{\odot}$ | $10^{10}L_{\odot}$ | $10^{12}L_{\odot}$ | $M_{\odot}yr^{-1}$ | $M_{\odot}yr^{-1}$
IRAS00188-0856 | 0.12840001 | $0.43^{0.11}_{-0.1}$ | $17.63^{0.88}_{-0.48}$ | $3.47^{8.95}_{-0.09}$ | - | $2.27^{0.14}_{-0.15}$ | $592.6^{7.1}_{-69.36}$ | $0.24^{2.71}_{-0.05}$
IRAS00397-1312 | 0.2617 | $19.42^{1.85}_{-1.52}$ | $69.97^{5.4}_{-2.61}$ | $5.39^{0.63}_{-0.31}$ | - | $26.25^{1.97}_{-1.1}$ | $1822.0^{107.8}_{-170.2}$ | $6.17^{0.63}_{-0.8}$
IRAS01003-2238 | 0.1178 | $7.07^{0.25}_{-0.39}$ | $5.56^{0.13}_{-0.5}$ | $2.3^{0.14}_{-0.37}$ | - | $7.6^{0.29}_{-0.34}$ | $134.8^{10.72}_{-8.25}$ | $2.94^{0.05}_{-0.44}$
IRAS03158+4227 | 0.1344 | $6.61^{1.48}_{-1.22}$ | $26.49^{3.6}_{-1.41}$ | $1.35^{1.71}_{-0.58}$ | - | $9.26^{1.38}_{-1.14}$ | $904.6^{37.53}_{-41.98}$ | $0.42^{2.44}_{-0.42}$
IRAS03521+0028 | 0.1519 | $1.98^{0.93}_{-0.82}$ | $19.51^{0.79}_{-2.43}$ | $1.84^{1.25}_{-0.5}$ | - | $3.91^{1.06}_{-0.83}$ | $667.3^{33.28}_{-95.5}$ | $0.0^{0.0}_{-0.0}$
IRAS05189-2524 | 0.04256 | $1.57^{0.08}_{-0.27}$ | $7.61^{0.47}_{-0.3}$ | $2.9^{0.17}_{-0.16}$ | $10.76^{1.47}_{-0.85}$ | $2.46^{0.08}_{-0.2}$ | $191.8^{9.85}_{-9.97}$ | $0.29^{0.03}_{-0.04}$
IRAS06035-7102 | 0.07947 | $0.4^{0.06}_{-0.06}$ | $12.74^{0.77}_{-0.54}$ | $9.7^{1.8}_{-5.87}$ | - | $1.82^{0.05}_{-0.19}$ | $342.8^{41.24}_{-32.88}$ | $2.14^{1.73}_{-2.14}$
IRAS06206-6315 | 0.09244 | $0.5^{0.08}_{-0.11}$ | $11.7^{0.52}_{-0.39}$ | $8.4^{0.82}_{-2.52}$ | - | $1.78^{0.06}_{-0.12}$ | $396.7^{42.52}_{-41.45}$ | $0.0^{0.01}_{-0.0}$
IRAS07598+6508 | 0.1483 | $1.11^{0.04}_{-0.07}$ | $21.32^{0.77}_{-1.32}$ | $0.29^{3.27}_{-0.28}$ | $84.17^{7.89}_{-19.47}$ | $4.02^{0.14}_{-0.16}$ | $546.5^{39.41}_{-36.79}$ | $0.0^{0.19}_{-0.0}$
IRAS08311-2459 | 0.1004 | $1.03^{0.46}_{-0.23}$ | $19.02^{1.48}_{-0.81}$ | $8.77^{0.75}_{-0.69}$ | - | $3.08^{0.38}_{-0.15}$ | $663.6^{70.47}_{-38.99}$ | $1.59^{4.81}_{-1.52}$
IRAS08572+3915 | 0.05835 | $12.85^{1.1}_{-1.36}$ | $5.46^{0.42}_{-1.07}$ | $1.67^{0.08}_{-0.09}$ | - | $13.34^{1.21}_{-1.4}$ | $154.0^{17.93}_{-48.26}$ | $1.52^{0.15}_{-0.13}$
IRAS09022-3615 | 0.05964 | $0.26^{0.13}_{-0.06}$ | $13.75^{0.75}_{-0.63}$ | $3.6^{0.51}_{-0.55}$ | - | $1.69^{0.08}_{-0.05}$ | $471.6^{12.54}_{-21.13}$ | $0.41^{0.08}_{-0.08}$
IRAS10378+1109 | 0.1362 | $2.35^{1.57}_{-0.74}$ | $12.68^{0.46}_{-0.54}$ | $3.59^{0.49}_{-0.26}$ | - | $3.68^{1.54}_{-0.81}$ | $435.9^{25.88}_{-43.45}$ | $1.01^{0.21}_{-0.18}$
IRAS10565+2448 | 0.043 | $0.32^{0.02}_{-0.02}$ | $8.64^{0.32}_{-0.27}$ | $2.07^{0.13}_{-0.08}$ | - | $1.21^{0.03}_{-0.04}$ | $395.6^{13.46}_{-13.02}$ | $0.0^{0.01}_{-0.0}$
IRAS11095-0238 | 0.1066 | $6.17^{3.61}_{-0.88}$ | $7.65^{0.84}_{-1.32}$ | $1.72^{1.65}_{-0.36}$ | - | $7.03^{3.35}_{-0.92}$ | $186.3^{27.94}_{-17.52}$ | $1.49^{0.71}_{-0.59}$
IRAS12071-0444 | 0.1284 | $2.22^{0.32}_{-0.1}$ | $13.46^{0.06}_{-0.7}$ | $8.4^{2.91}_{-3.0}$ | - | $3.65^{0.11}_{-0.12}$ | $362.8^{44.48}_{-36.01}$ | $2.89^{3.74}_{-0.89}$
IRAS13120-5453 | 0.03076 | $0.15^{0.03}_{-0.01}$ | $14.83^{0.77}_{-0.91}$ | $2.85^{1.38}_{-0.66}$ | - | $1.67^{0.06}_{-0.05}$ | $658.9^{40.2}_{-47.42}$ | $0.86^{1.11}_{-0.64}$
IRAS13451+1232 | 0.1217 | $3.73^{1.26}_{-0.19}$ | $5.5^{0.5}_{-1.06}$ | $23.45^{0.54}_{-0.42}$ | $4.23^{2.99}_{-1.24}$ | $4.59^{1.12}_{-0.24}$ | $131.7^{18.56}_{-22.22}$ | $11.79^{1.02}_{-3.94}$
IRAS14348-1447 | 0.0827 | $0.45^{0.25}_{-0.12}$ | $18.49^{1.0}_{-0.46}$ | $4.74^{1.5}_{-0.21}$ | - | $2.35^{0.28}_{-0.09}$ | $512.6^{49.4}_{-29.2}$ | $1.67^{1.33}_{-1.6}$
IRAS14378-3651 | 0.0676 | $0.46^{0.08}_{-0.12}$ | $10.18^{0.5}_{-0.2}$ | $2.1^{1.88}_{-0.6}$ | - | $1.47^{0.21}_{-0.12}$ | $287.7^{36.94}_{-21.34}$ | $0.02^{0.63}_{-0.01}$
IRAS15250+3609 | 0.05516 | $2.54^{0.55}_{-0.25}$ | $5.98^{0.56}_{-0.4}$ | $2.15^{0.33}_{-0.11}$ | - | $3.18^{0.41}_{-0.28}$ | $144.8^{9.01}_{-9.26}$ | $2.48^{0.19}_{-0.1}$
IRAS15462-0450 | 0.09979 | $0.6^{0.16}_{-0.2}$ | $11.49^{0.69}_{-1.5}$ | $2.36^{0.31}_{-0.25}$ | - | $1.72^{0.22}_{-0.18}$ | $268.0^{10.33}_{-16.77}$ | $0.73^{1.17}_{-0.71}$
IRAS16090-0139 | 0.13358 | $0.72^{0.18}_{-0.16}$ | $27.05^{0.86}_{-0.8}$ | $3.98^{2.82}_{-0.81}$ | - | $3.48^{0.12}_{-0.13}$ | $780.6^{76.4}_{-42.66}$ | $2.56^{2.89}_{-2.56}$
IRAS17208-0014 | 0.0428 | $0.11^{0.0}_{-0.02}$ | $21.66^{0.97}_{-0.78}$ | $1.57^{0.1}_{-0.02}$ | - | $2.29^{0.08}_{-0.08}$ | $809.4^{68.56}_{-30.52}$ | $0.19^{0.59}_{-0.08}$
IRAS19254-7245 | 0.061709 | $1.73^{0.63}_{-0.32}$ | $5.06^{0.39}_{-0.66}$ | $19.09^{5.14}_{-2.12}$ | - | $2.45^{0.52}_{-0.31}$ | $119.7^{6.24}_{-14.92}$ | $1.08^{0.45}_{-0.3}$
IRAS19297-0406 | 0.08573 | $0.31^{0.13}_{-0.08}$ | $23.3^{0.37}_{-1.78}$ | $4.1^{0.11}_{-0.08}$ | - | $2.66^{0.04}_{-0.06}$ | $660.0^{113.1}_{-21.46}$ | $0.0^{0.42}_{-0.0}$
IRAS20087-0308 | 0.10567 | $0.33^{0.04}_{-0.04}$ | $23.99^{0.74}_{-1.1}$ | $3.65^{0.78}_{-0.46}$ | - | $2.77^{0.05}_{-0.08}$ | $1108.0^{33.86}_{-59.3}$ | $0.0^{0.27}_{-0.0}$
IRAS20100-4156 | 0.12958 | $1.3^{0.18}_{-0.17}$ | $32.62^{1.63}_{-1.06}$ | $6.27^{5.04}_{-0.9}$ | - | $4.65^{0.26}_{-0.25}$ | $763.1^{43.59}_{-50.99}$ | $4.56^{3.76}_{-0.94}$
IRAS20414-1651 | 0.087084 | $0.22^{0.12}_{-0.04}$ | $12.35^{1.23}_{-0.23}$ | $1.31^{0.04}_{-0.07}$ | - | $1.56^{0.01}_{-0.09}$ | $495.1^{72.17}_{-4.58}$ | $0.18^{0.34}_{-0.07}$
IRAS20551-4250 | 0.042996 | $0.84^{0.18}_{-0.11}$ | $6.65^{0.63}_{-0.43}$ | $4.85^{0.73}_{-0.41}$ | - | $1.56^{0.18}_{-0.13}$ | $163.6^{20.84}_{-11.2}$ | $4.64^{0.38}_{-0.4}$
IRAS22491-1808 | 0.0778 | $1.13^{1.15}_{-0.17}$ | $8.39^{0.72}_{-1.2}$ | $7.9^{0.3}_{-4.03}$ | - | $2.07^{1.13}_{-0.2}$ | $209.5^{21.62}_{-46.27}$ | $6.27^{0.29}_{-2.25}$
IRAS23128-5919 | 0.0446 | $0.3^{0.04}_{-0.04}$ | $6.95^{0.39}_{-0.43}$ | $5.48^{1.56}_{-0.66}$ | - | $1.06^{0.03}_{-0.06}$ | $187.5^{8.98}_{-17.01}$ | $5.61^{0.74}_{-0.88}$
IRAS23230-6926 | 0.10659 | $1.33^{0.27}_{-0.15}$ | $12.28^{0.56}_{-0.81}$ | $9.41^{0.57}_{-1.79}$ | - | $2.62^{0.27}_{-0.13}$ | $303.4^{10.07}_{-14.64}$ | $5.74^{0.56}_{-0.96}$
IRAS23253-5415 | 0.13 | $1.16^{0.2}_{-0.07}$ | $19.08^{0.67}_{-0.95}$ | $6.83^{0.74}_{-0.83}$ | - | $3.18^{0.09}_{-0.11}$ | $674.3^{52.35}_{-80.31}$ | $0.82^{3.14}_{-0.79}$
IRAS23365+3604 | 0.0645 | $2.63^{0.37}_{-0.54}$ | $9.84^{1.34}_{-1.28}$ | $5.64^{1.21}_{-2.14}$ | - | $3.61^{0.54}_{-0.47}$ | $285.7^{101.3}_{-21.5}$ | $1.22^{1.32}_{-0.73}$
Mrk1014 | 0.16311 | $0.51^{0.02}_{-0.04}$ | $25.87^{0.99}_{-1.4}$ | $0.01^{6.39}_{-0.01}$ | - | $3.12^{0.09}_{-0.13}$ | $787.1^{49.55}_{-62.5}$ | $0.0^{4.95}_{-0.0}$
UGC5101 | 0.039367 | $0.22^{0.04}_{-0.02}$ | $6.85^{0.31}_{-0.24}$ | $11.25^{0.36}_{-0.45}$ | - | $1.02^{0.03}_{-0.03}$ | $168.6^{9.03}_{-8.99}$ | $1.43^{0.08}_{-0.14}$
Mrk231 | 0.04217 | $3.4^{0.38}_{-0.62}$ | $18.75^{1.6}_{-0.65}$ | $10.23^{3.05}_{-1.23}$ | - | $5.35^{0.44}_{-0.37}$ | $515.5^{33.35}_{-37.06}$ | $10.58^{2.95}_{-3.16}$
Mrk273 | 0.03778 | $0.26^{0.13}_{-0.04}$ | $10.54^{0.43}_{-0.44}$ | $3.52^{0.29}_{-0.25}$ | - | $1.38^{0.1}_{-0.08}$ | $356.0^{17.54}_{-14.23}$ | $0.46^{0.1}_{-0.1}$
Mrk463 | 0.050355 | $1.05^{0.05}_{-0.3}$ | $1.7^{0.24}_{-0.23}$ | $3.78^{0.83}_{-0.55}$ | - | $1.26^{0.02}_{-0.32}$ | $40.28^{5.74}_{-5.5}$ | $0.05^{1.01}_{-0.04}$
Arp220 | 0.018 | $2.6^{0.34}_{-0.29}$ | $5.71^{0.3}_{-0.22}$ | $1.93^{0.04}_{-0.04}$ | - | $3.2^{0.38}_{-0.26}$ | $216.8^{4.27}_{-12.76}$ | $0.03^{0.01}_{-0.0}$
NGC6240 | 0.0244 | $0.59^{0.13}_{-0.19}$ | $4.33^{0.3}_{-0.29}$ | $4.89^{0.78}_{-1.06}$ | - | $1.08^{0.15}_{-0.17}$ | $162.5^{19.42}_{-22.86}$ | $1.48^{0.44}_{-0.65}$

Table 4: Other extracted physical quantities for the galaxies in the HERUS
sample

Name | $\dot{M}_{tot}$ | ${M}^{*}_{sph}$ | ${M}^{*}_{SB}$ | ${M}^{*}_{tot}$ | $F_{AGN}$ | $A$
---|---|---|---|---|---|---
| $M_{\odot}yr^{-1}$ | $10^{10}M_{\odot}$ | $10^{9}M_{\odot}$ | $10^{10}M_{\odot}$ |  |
IRAS00188-0856 | $592.8^{7.29}_{-65.63}$ | $14.44^{2.94}_{-0.13}$ | $17.25^{0.03}_{-3.02}$ | $16.16^{2.64}_{-0.2}$ | $0.19^{0.03}_{-0.04}$ | $2.48^{0.37}_{-0.26}$
IRAS00397-1312 | $1827.0^{109.7}_{-169.2}$ | $9.7^{2.66}_{-1.79}$ | $13.19^{1.34}_{-1.91}$ | $11.03^{2.79}_{-1.72}$ | $0.73^{0.03}_{-0.02}$ | $8.26^{0.24}_{-0.3}$
IRAS01003-2238 | $137.6^{10.41}_{-8.06}$ | $2.21^{0.06}_{-0.27}$ | $1.74^{1.11}_{-0.25}$ | $2.35^{0.09}_{-0.13}$ | $0.93^{0.0}_{-0.01}$ | $5.57^{0.1}_{-0.06}$
IRAS03158+4227 | $907.5^{34.95}_{-44.92}$ | $4.0^{3.42}_{-1.96}$ | $24.02^{2.03}_{-2.02}$ | $6.31^{3.59}_{-1.74}$ | $0.7^{0.05}_{-0.04}$ | $6.43^{0.8}_{-1.01}$
IRAS03521+0028 | $667.3^{33.28}_{-95.5}$ | $7.96^{3.06}_{-1.55}$ | $19.9^{1.03}_{-2.48}$ | $9.94^{3.17}_{-1.44}$ | $0.51^{0.08}_{-0.13}$ | $7.67^{0.87}_{-2.51}$
IRAS05189-2524 | $192.2^{9.78}_{-10.01}$ | $10.42^{0.55}_{-0.53}$ | $3.79^{0.76}_{-0.56}$ | $10.79^{0.64}_{-0.55}$ | $0.63^{0.02}_{-0.06}$ | $2.89^{0.08}_{-0.06}$
IRAS06035-7102 | $344.6^{39.43}_{-30.82}$ | $16.99^{4.01}_{-2.43}$ | $2.68^{7.38}_{-0.45}$ | $17.41^{4.51}_{-2.6}$ | $0.22^{0.03}_{-0.02}$ | $2.13^{0.34}_{-0.13}$
IRAS06206-6315 | $396.7^{42.52}_{-41.45}$ | $26.0^{2.22}_{-3.49}$ | $10.83^{2.07}_{-1.05}$ | $27.07^{1.88}_{-3.1}$ | $0.28^{0.04}_{-0.05}$ | $2.88^{0.45}_{-0.4}$
IRAS07598+6508 | $546.8^{39.19}_{-36.99}$ | $0.96^{8.73}_{-0.92}$ | $13.51^{1.63}_{-1.87}$ | $2.33^{8.79}_{-0.86}$ | $0.28^{0.02}_{-0.02}$ | $0.55^{0.02}_{-0.01}$
IRAS08311-2459 | $664.2^{74.29}_{-37.32}$ | $31.8^{4.63}_{-13.73}$ | $17.2^{1.5}_{-0.85}$ | $33.47^{4.69}_{-13.63}$ | $0.34^{0.09}_{-0.06}$ | $1.79^{0.54}_{-0.25}$
IRAS08572+3915 | $155.5^{18.02}_{-48.19}$ | $2.19^{0.19}_{-0.15}$ | $0.9^{0.14}_{-0.07}$ | $2.28^{0.22}_{-0.16}$ | $0.96^{0.01}_{-0.01}$ | $14.2^{1.38}_{-1.29}$
IRAS09022-3615 | $471.9^{12.67}_{-21.17}$ | $12.93^{2.89}_{-1.95}$ | $13.12^{0.8}_{-0.81}$ | $14.3^{2.8}_{-1.94}$ | $0.15^{0.06}_{-0.03}$ | $1.53^{0.34}_{-0.16}$
IRAS10378+1109 | $436.9^{25.77}_{-40.16}$ | $11.46^{0.71}_{-1.38}$ | $11.62^{0.61}_{-1.06}$ | $12.68^{0.66}_{-1.47}$ | $0.64^{0.11}_{-0.09}$ | $6.07^{1.94}_{-0.5}$
IRAS10565+2448 | $395.6^{13.45}_{-13.02}$ | $9.94^{0.7}_{-0.51}$ | $12.13^{0.39}_{-0.48}$ | $11.13^{0.67}_{-0.5}$ | $0.27^{0.01}_{-0.02}$ | $3.31^{0.09}_{-0.26}$
IRAS11095-0238 | $188.3^{26.93}_{-18.01}$ | $2.5^{1.28}_{-0.82}$ | $3.83^{1.23}_{-1.64}$ | $2.79^{1.38}_{-0.64}$ | $0.88^{0.06}_{-0.02}$ | $8.1^{3.3}_{-0.79}$
IRAS12071-0444 | $365.7^{44.46}_{-36.9}$ | $17.75^{0.7}_{-3.39}$ | $2.17^{1.0}_{-0.21}$ | $17.97^{0.68}_{-3.37}$ | $0.61^{0.07}_{-0.01}$ | $2.82^{0.39}_{-0.16}$
IRAS13120-5453 | $659.2^{40.75}_{-44.06}$ | $6.68^{2.93}_{-2.56}$ | $19.86^{1.14}_{-2.21}$ | $8.74^{2.9}_{-2.85}$ | $0.09^{0.02}_{-0.01}$ | $2.1^{0.19}_{-0.13}$
IRAS13451+1232 | $143.8^{20.13}_{-27.22}$ | $25.61^{11.43}_{-3.77}$ | $1.8^{0.1}_{-0.34}$ | $25.8^{11.38}_{-3.76}$ | $0.82^{0.05}_{-0.01}$ | $3.65^{0.71}_{-0.11}$
IRAS14348-1447 | $514.3^{50.25}_{-29.42}$ | $13.48^{8.48}_{-3.64}$ | $15.4^{1.18}_{-0.82}$ | $14.98^{8.51}_{-3.61}$ | $0.19^{0.07}_{-0.04}$ | $3.73^{1.3}_{-0.47}$
IRAS14378-3651 | $289.2^{35.42}_{-22.87}$ | $8.1^{0.77}_{-1.64}$ | $8.91^{1.01}_{-0.75}$ | $8.95^{0.76}_{-1.44}$ | $0.31^{0.02}_{-0.06}$ | $3.6^{0.23}_{-0.68}$
IRAS15250+3609 | $147.5^{9.02}_{-9.49}$ | $2.32^{0.1}_{-0.11}$ | $3.81^{0.45}_{-0.49}$ | $2.68^{0.11}_{-0.09}$ | $0.81^{0.03}_{-0.03}$ | $6.9^{0.65}_{-0.53}$
IRAS15462-0450 | $269.0^{10.0}_{-17.79}$ | $8.54^{1.96}_{-4.37}$ | $4.4^{1.09}_{-1.18}$ | $9.03^{2.08}_{-4.38}$ | $0.34^{0.06}_{-0.06}$ | $1.73^{0.46}_{-0.46}$
IRAS16090-0139 | $783.4^{77.66}_{-45.3}$ | $8.84^{8.21}_{-3.58}$ | $23.86^{2.13}_{-1.45}$ | $11.21^{8.18}_{-3.64}$ | $0.21^{0.04}_{-0.04}$ | $2.73^{0.5}_{-0.31}$
IRAS17208-0014 | $809.6^{69.15}_{-30.6}$ | $6.31^{0.03}_{-2.71}$ | $24.22^{2.55}_{-0.47}$ | $8.72^{0.01}_{-2.44}$ | $0.05^{0.0}_{-0.01}$ | $2.52^{0.27}_{-0.37}$
IRAS19254-7245 | $121.0^{6.34}_{-15.08}$ | $51.24^{12.16}_{-7.97}$ | $1.25^{0.14}_{-0.13}$ | $51.38^{12.17}_{-7.98}$ | $0.71^{0.07}_{-0.05}$ | $3.91^{0.55}_{-0.36}$
IRAS19297-0406 | $660.0^{113.5}_{-21.24}$ | $20.25^{1.96}_{-2.62}$ | $20.3^{2.95}_{-0.89}$ | $22.26^{2.04}_{-2.58}$ | $0.12^{0.05}_{-0.03}$ | $2.0^{0.56}_{-0.28}$
IRAS20087-0308 | $1108.0^{33.56}_{-58.6}$ | $15.61^{2.0}_{-2.17}$ | $33.77^{1.05}_{-1.85}$ | $18.99^{2.13}_{-2.11}$ | $0.12^{0.02}_{-0.02}$ | $3.51^{0.36}_{-0.34}$
IRAS20100-4156 | $768.0^{42.35}_{-50.45}$ | $10.47^{2.3}_{-1.39}$ | $12.98^{3.04}_{-4.55}$ | $11.95^{2.12}_{-1.66}$ | $0.28^{0.03}_{-0.02}$ | $3.16^{0.41}_{-0.24}$
IRAS20414-1651 | $495.6^{71.76}_{-4.92}$ | $5.25^{0.15}_{-1.7}$ | $15.02^{1.83}_{-0.06}$ | $6.74^{0.34}_{-1.69}$ | $0.15^{0.07}_{-0.03}$ | $4.46^{2.07}_{-0.7}$
IRAS20551-4250 | $168.1^{20.4}_{-10.63}$ | $4.31^{0.23}_{-0.16}$ | $2.07^{0.66}_{-0.49}$ | $4.55^{0.15}_{-0.14}$ | $0.55^{0.03}_{-0.06}$ | $3.84^{0.45}_{-0.38}$
IRAS22491-1808 | $215.7^{21.48}_{-46.05}$ | $4.98^{0.14}_{-0.99}$ | $2.59^{4.17}_{-0.83}$ | $5.21^{0.14}_{-0.51}$ | $0.56^{0.15}_{-0.06}$ | $5.01^{1.68}_{-0.42}$
IRAS23128-5919 | $192.8^{9.28}_{-17.54}$ | $4.84^{0.29}_{-0.21}$ | $2.54^{0.69}_{-0.84}$ | $5.16^{0.19}_{-0.18}$ | $0.29^{0.02}_{-0.04}$ | $2.14^{0.14}_{-0.16}$
IRAS23230-6926 | $308.5^{11.22}_{-14.01}$ | $6.9^{0.53}_{-0.45}$ | $3.72^{1.0}_{-0.76}$ | $7.28^{0.54}_{-0.44}$ | $0.51^{0.04}_{-0.04}$ | $4.08^{0.39}_{-0.4}$
IRAS23253-5415 | $674.9^{52.35}_{-79.95}$ | $27.38^{1.65}_{-8.61}$ | $19.42^{0.95}_{-2.51}$ | $29.73^{1.41}_{-9.01}$ | $0.37^{0.04}_{-0.02}$ | $4.22^{0.43}_{-0.29}$
IRAS23365+3604 | $288.3^{99.23}_{-22.81}$ | $11.77^{0.71}_{-2.34}$ | $6.68^{1.97}_{-1.61}$ | $12.27^{1.0}_{-2.18}$ | $0.72^{0.02}_{-0.06}$ | $7.42^{2.17}_{-1.36}$
Mrk1014 | $787.1^{49.55}_{-58.96}$ | $0.01^{14.36}_{-0.01}$ | $15.0^{1.76}_{-2.19}$ | $1.87^{13.85}_{-0.39}$ | $0.16^{0.0}_{-0.01}$ | $0.6^{0.01}_{-0.03}$
UGC5101 | $169.8^{9.08}_{-8.86}$ | $20.14^{1.26}_{-0.77}$ | $1.66^{0.14}_{-0.15}$ | $20.32^{1.24}_{-0.78}$ | $0.22^{0.03}_{-0.02}$ | $2.42^{0.24}_{-0.15}$
Mrk231 | $524.3^{35.12}_{-36.04}$ | $12.39^{3.3}_{-0.74}$ | $10.03^{1.92}_{-2.49}$ | $13.32^{3.4}_{-0.86}$ | $0.64^{0.02}_{-0.06}$ | $2.44^{0.2}_{-0.34}$
Mrk273 | $356.3^{17.61}_{-13.92}$ | $11.77^{0.66}_{-0.47}$ | $9.6^{0.75}_{-0.71}$ | $12.7^{0.65}_{-0.42}$ | $0.19^{0.08}_{-0.03}$ | $2.68^{0.73}_{-0.35}$
Mrk463 | $40.28^{6.02}_{-5.33}$ | $14.9^{0.82}_{-0.82}$ | $0.62^{0.31}_{-0.22}$ | $14.99^{0.78}_{-0.85}$ | $0.82^{0.03}_{-0.03}$ | $1.97^{0.05}_{-0.57}$
Arp220 | $216.8^{4.28}_{-12.76}$ | $8.71^{0.12}_{-0.27}$ | $5.66^{0.2}_{-0.3}$ | $9.24^{0.16}_{-0.24}$ | $0.82^{0.01}_{-0.03}$ | $8.53^{0.52}_{-0.28}$
NGC6240 | $163.6^{19.99}_{-21.91}$ | $10.08^{0.96}_{-1.11}$ | $4.84^{0.44}_{-1.06}$ | $10.52^{0.97}_{-1.12}$ | $0.54^{0.06}_{-0.1}$ | $5.73^{0.84}_{-0.78}$

There are two ULIRGS (IRAS 01003-2238 and Mrk 1014) for which the fit is
unsatisfactory, despite repeated runs of the code. As also noted by Efstathiou
et al. (2022), in these objects there is most probably a dual AGN, one viewed
with its torus edge-on and dominating in the MIR, and one viewed face-on,
which dominates in the optical/UV. We have not developed yet SMART to deal
with the case of dual AGN, so in Figs A1 and A5 we plot the fit with a single
AGN.

For three of the ULIRGs plotted in Figs A1, A2 and A3 we run the code with
polar dust enabled, as we see evidence that the addition of polar dust can
improve the fit. These are IRAS 05189-2524, IRAS 07598+6508 and IRAS
13451+1232. We discuss IRAS 05189-2524 and IRAS 07598+6508 in more detail in
Sections 4.1 and 4.2, respectively.

###  3.3 Comparison with results from other approaches

In Fig. 5 we compare key physical quantities derived by SMART with those
obtained with SATMC, using the same multi-component CYGNUS radiative transfer
models as in Efstathiou et al. (2022). Regarding the luminosity and the SFR of
the starburst, we see that there is very good agreement between the estimates
of SMART and SATMC, with only a few exceptions. Some of the exceptions may be
attributed to the statistical nature of the methods and this issue certainly
deserves further exploration to understand these differences better. The
corresponding comparison for the observed AGN torus luminosity shows that
there is generally good agreement between the estimates with SMART and SATMC.
For the AGN fraction, as expected, there is more discrepancy. We attribute the
more scatter in the AGN fraction to the fact that it incorporates the
anisotropy corrections, so it is much more sensitive to changes to best fit
parameters compared to other quantities, such as the luminosity of the
starburst, the SFR of the starburst and the observed AGN torus luminosity. We
conclude that for most of the galaxies the fits with SMART are satisfactory
and of similar quality as in the fits with SATMC reported in Efstathiou et al.
(2022). It is, however, important to note that, even using the same models,
significant differences can arise in key physical quantities due to the
statistical nature of the SED fitting methods.

Eleven of the sources in the sample of Paspaliaris et al. (2021) are ULIRGs
and seven of them are included in the HERUS sample. We compare the results of
Paspaliaris et al. (2021) obtained with CIGALE and using the SKIRTOR AGN torus
model with those obtained with our method in Fig. 5. We observe good agreement
in the SFR predicted by SMART and CIGALE. The only exception is IRAS
08572+3915 for which CIGALE predicts a much lower SFR. This is the galaxy we
discuss in detail in Section 4.3. The model of Paspaliaris et al. (2021) fails
to reproduce the deep silicate absorption feature of this ULIRG, which in our
model is attributed to the fact that the smooth AGN torus is viewed almost
edge-on. It is well understood that two-phase models like SKIRTOR can not
produce deep silicate absorption features like the one observed in IRAS
08572+3915 (see, for example, discussion in Efstathiou et al. 2022). The
results of Paspaliaris et al. (2021) do not take into account the anisotropy
correction and this is probably one of the main reasons the AGN fraction of
the seven ULIRGs in common with our sample are lower.

##  4 Discussion

In this section we discuss the versatility of SMART by providing a number of
case studies. As part of this demonstration, we present a set of SED fits
derived from SMART and highlighting the key advantages of the method. All of
the following SED fits are done with the CYGNUS multi-component radiative
transfer models. In Sections 4.3 and 4.5 we present a comparison of our
results for the galaxies IRAS 08572+3915 and HELP_J100156.75+022344.7,
respectively, with the other AGN models that we have available (the smooth
torus model of Fritz et al. 2006 and the two-phase models of Siebenmorgen et
al. 2015 and SKIRTOR).

###  4.1 Fit of a ULIRG associated with polar dust

IRAS 05189-2524 is generally believed to be a ‘warm’ ULIRG and to contain an
obscured AGN with its torus viewed almost edge-on. This galaxy was recognized
from the mid-90s as a ULIRG that has similar characteristics to the
prototypical Seyfert 2 galaxy NGC 1068. It was found in particular by Young et
al. (1996) to show broad lines in polarized flux. NGC 1068 was also the first
LIRG that was recognized to have polar dust (Braatz et al., 1993; Cameron et
al., 1993; Efstathiou, Hough & Young, 1995). Efstathiou et al. (2022) found
that a fit with polar dust provides a better fit to the SED of IRAS 05189-2524
compared to a fit without polar dust. Reynolds et al. (2022) found evidence
that IRAS 05189-2524 recently experienced a dust obscured tidal disruption
event (TDE) with an IR echo from polar dust. This phenomenon was first
proposed for the TDE in the LIRG Arp 299 by Mattila et al. (2018).

We find that a fit with SMART with an obscured AGN and polar dust provides a
good fit to the SED. The model for polar dust incorporated in SMART has the
temperature of polar dust as a free parameter, whereas Efstathiou et al.
(2022) considered only a single temperature for the polar dust. We find that
the polar dust in IRAS 05189-2524 has a temperature of
$1050.6^{28.7}_{-23.2}$K. In Tables A1, A2, 3 and 4 we list all of the
important fitted parameters and extracted physical properties for this ULIRG.
The SED fit plot is shown in Fig. A1.

###  4.2 Fit of a ULIRG with an unobscured quasar and also associated with
polar dust

The galaxy IRAS 07598+6508 is the only ULIRG in the HERUS sample (apart from
3C 273 which we do not fit, as it clearly has a strong contribution in the
submillimetre from radio emission), which shows clear signs of a type 1 AGN
with a strong optical continuum with a power-law shape. This ULIRG was
therefore fitted with a type 1 AGN by Efstathiou et al. (2022).

In Fig. 6 we fit IRAS 07598+6508 with all four combinations of models without
polar dust. We observe that in all cases there is evidence that the torus
model by itself can not reproduce the (near-infrared) NIR spectrum. We
attribute this to the presence of polar dust in this object, which is more
visible because of the assumed face-on inclination. We can also see this from
the reduced $\chi^{2}$ we provide in Table 5. The $\chi^{2}_{min,\nu}$ of the
CYGNUS fit without polar dust is much higher compared to the fit with polar
dust shown in Table A1. The important fitted parameters and extracted physical
properties for this ULIRG are listed in Tables A1, A2, 3 and 4. The SED fit
plot with polar dust is shown in Fig. A2.

Table 5: Reduced $\chi^{2}$ of fits for IRAS 07598+6508 with all combinations of models without using the polar dust component AGN model | $\chi^{2}_{min,\nu}$
---|---
CYGNUS | 0.71
Fritz et al. (2006) | 0.89
SKIRTOR | 0.66
Siebenmorgen et al. (2015) | 2.82
Figure 6: Comparison SED fit plots of IRAS 07598+6508 without using the polar
dust component. The AGN torus, starburst, spheroidal host and total emission
are plotted as shown in the legend. The top row shows fits with the CYGNUS
combination of models. The second row shows fits with the CYGNUS AGN model
replaced by the model of Fritz et al. (2006), the third row replaces the
CYGNUS AGN model with the SKIRTOR model, while the bottom row replaces the
CYGNUS AGN model with the model of Siebenmorgen et al. (2015). The left panel
shows the fit over 0.1$-$1000 $\mu m$ range, the middle panel the approximate
range of the NIRspec instrument on JWST and the right panel the corresponding
range of the MIRI instrument.

###  4.3 Fit of the deeply obscured ULIRG IRAS 08572+3915

Efstathiou et al. (2014) proposed that the ULIRG IRAS 08572+3915 is the most
luminous IR galaxy in the local ($z<0.2$) Universe. It is an example of an
interacting ULIRG, which exhibits one of the deepest silicate absorption
features observed in a galaxy. Efstathiou et al. (2014) proposed that the deep
silicate absorption feature is due to the fact that the AGN torus in this
object is observed almost edge-on. The huge luminosity of this object, which
approaches or exceeds $10^{13}L_{\odot}$, is due to the large anisotropy
correction.

To explore further the properties of this system, we fit the SED with all four
combinations of AGN radiative transfer models. Two of the combinations assume
a smooth torus geometry (Efstathiou & Rowan-Robinson, 1995; Fritz et al.,
2006) and two combinations assume a two-phase geometry (Siebenmorgen et al.,
2015; Stalevski et al., 2016).

Figure 7: Comparison SED fit plots of IRAS 08572+3915. The AGN torus,
starburst, spheroidal host and total emission are plotted as shown in the
legend. The top row shows fits with the CYGNUS combination of models. The
second row shows fits with the CYGNUS AGN model replaced by the model of Fritz
et al. (2006), the third row replaces the CYGNUS AGN model with the SKIRTOR
model, while the bottom row replaces the CYGNUS AGN model with the model of
Siebenmorgen et al. (2015). The left panel shows the fit over 0.1$-$1000 $\mu
m$ range, the middle panel the approximate range of the NIRspec instrument on
JWST and the right panel the corresponding range of the MIRI instrument.

It is interesting that the smooth models fit much better than the two-phase
models. The last two in particular do not fit the deep silicate absorption
feature of this galaxy and predict that the object is starburst-dominated.
According to the fits of the smooth models, which perform much better, this is
an AGN-dominated object. In Tables 6, A3 and A4 we list all of the important
fitted parameters and extracted physical properties of the four combinations
of models. The comparison SED fit plots are shown in Fig. 7. The CYGNUS
combination of models gives a $\chi^{2}_{min,\nu}$ equal to 1.67, which is
significantly lower than the $\chi^{2}_{min,\nu}$ given by the other three
combinations and shows that the CYGNUS AGN model fits much better than the
other models. The Fritz et al. (2006) AGN model gives
$\chi^{2}_{min,\nu}=4.1$, the SKIRTOR AGN model gives $\chi^{2}_{min,\nu}=8.2$
and the AGN model of Siebenmorgen et al. (2015) gives
$\chi^{2}_{min,\nu}=8.28$.

Table 6: Selected fitted parameters for IRAS 08572+3915

AGN model | $t_{*}\ (10^{7}yr)$ | $\tau_{*}\ (10^{7}yr)$ |  |  |  | $\theta_{i}\ (\degr)$
---|---|---|---|---|---|---
CYGNUS |  |  | $r_{2}/r_{1}$ | $\tau_{uv}$ | $\theta_{o}\ (\degr)$ |
| $0.64^{0.28}_{-0.1}$ | $1.79^{0.34}_{-0.25}$ | $58.5^{9.8}_{-8.38}$ | $612.99^{14.44}_{-21.13}$ | $72.66^{1.05}_{-0.89}$ | $79.04^{0.74}_{-0.65}$
Fritz et al. (2006) |  |  | $r_{2}/r_{1}$ | $\tau_{9.7\mu m}$ | $\theta_{o}\ (\degr)$ |
| $2.37^{0.6}_{-0.6}$ | $1.93^{0.17}_{-0.17}$ | $117.4^{18.11}_{-18.11}$ | $9.39^{0.03}_{-0.03}$ | $54.48^{0.61}_{-0.61}$ | $84.54^{0.01}_{-0.01}$
SKIRTOR |  |  | $r_{2}/r_{1}$ | $\tau_{9.7\mu m}$ | $\theta_{o}\ (\degr)$ |
| $0.51^{0.02}_{-0.01}$ | $1.89^{0.53}_{-0.22}$ | $23.96^{4.5}_{-4.72}$ | $5.67^{2.13}_{-0.7}$ | $47.31^{16.22}_{-11.34}$ | $60.72^{13.35}_{-13.6}$
Siebenmorgen et al. (2015) |  |  | $A_{c}$ | $V_{c}$ | $A_{d}$ |
| $0.51^{0.02}_{-0.01}$ | $2.05^{0.74}_{-0.25}$ | $8.36^{14.42}_{-6.23}$ | $57.98^{47.19}_{-21.28}$ | $211.06^{126.38}_{-58.5}$ | $86.88^{6.87}_{-2.63}$

###  4.4 Fit of a LIRG associated with a spiral galaxy

To explore the option of fitting with a disc as a host galaxy component, we
fitted the LIRG VV 340a, which belongs to a pair of spiral galaxies known as
Arp 302, with the northern galaxy, VV 340a, being viewed edge-on and the
southern galaxy, VV 340b, viewed face-on. This pair of galaxies was discussed
extensively by Armus et al. (2009). We fitted this object twice, using the two
different host galaxy models that we have available, the spheroidal and the
disc model.

Figure 8: Comparison SED fit plots of VV 340a, which is a LIRG associated with
a spiral galaxy. The AGN torus, starburst, host and total emission are plotted
as shown in the legend. The top row shows the fit with the spheroidal host
galaxy model, while the second row replaces the spheroidal host galaxy model
with the disc host galaxy model. The left panel shows the fit over 0.1$-$1000
$\mu m$ range, the middle panel the approximate range of the NIRspec
instrument on JWST and the right panel the corresponding range of the MIRI
instrument.

We observe that the disc model appears to fit better not just the photometry
but also the Spitzer spectroscopy. The difference in the $\chi^{2}_{min,\nu}$
of the two different fits is also significant, with the disc model providing
the minimum value of 2.84, while the spheroidal model provides a
$\chi^{2}_{min,\nu}$ of 5.65, a factor of two higher. The best fits with the
two different host geometries are listed in Tables 7, A5 and A6 and plotted in
Fig. 8. The predicted disc morphology is consistent with the nature of this
galaxy. It is very interesting that the fit of VV 340a predicts an almost
edge-on view and this agrees with the image of the galaxy. This example is an
indication that SMART may be a useful tool for galaxy morphological
classification, especially in cases where an image of the galaxy is not
available.

Jiang et al. (2024) presented XMM-Newton data of VV 340a and VV 340b from
which they find evidence of a heavily obscured Seyfert 2-like AGN in VV 340a.
This is in agreement with our fit, which predicts the presence of an obscured
AGN with an anisotropy-corrected AGN luminosity of $0.25^{0.06}_{-0.04}\times
10^{12}L_{\odot}$. Our model, however, predicts a much higher SFR compared
with the estimate of Jiang et al. (2024) of 1$-$2 $M_{\odot}$/yr for this
galaxy, which is based entirely on X-ray data.

Table 7: Selected fitted parameters for VV 340a

Host galaxy model | $t_{*}\ (10^{7}yr)$ | $\tau_{*}\ (10^{7}yr)$ | $r_{2}/r_{1}$ | $\tau_{uv}$ | $\theta_{o}\ (\degr)$ | $\theta_{i}\ (\degr)$
---|---|---|---|---|---|---
Spheroidal | $3.38^{0.02}_{-0.16}$ | $1.46^{0.26}_{-0.22}$ | $78.02^{4.58}_{-6.31}$ | $760.03^{342.98}_{-182.2}$ | $56.9^{3.32}_{-3.09}$ | $55.81^{3.95}_{-4.56}$
Disc | $1.09^{0.1}_{-0.07}$ | $2.02^{0.05}_{-0.09}$ | $89.72^{5.24}_{-5.15}$ | $863.0^{117.51}_{-51.98}$ | $66.53^{1.41}_{-1.56}$ | $74.07^{0.53}_{-0.66}$

###  4.5 Fit of a hyperluminous obscured quasar at $z\sim 4.3$

The HLIRG HELP_J100156.75+022344.7 at a photometric redshift of $z\sim 4.3$
was discovered in the Cosmological Evolution Survey (COSMOS) field, one of the
fields studied by HELP. This is one of only a few $z>4$ hyperluminous obscured
quasars discovered to date and, according to the CYGNUS model presented by
Efstathiou et al. (2021), it is AGN-dominated with an AGN fraction of 82 per
cent. Efstathiou et al. (2021) also fitted HELP_J100156.75+022344.7 with
CIGALE and arrived at a similar conclusion. HELP_J100156.75+022344.7 is
predicted to have an SFR of $1051^{109}_{-268}$ $M_{\odot}yr^{-1}$ according
to CYGNUS and $991^{223}_{-223}$ $M_{\odot}yr^{-1}$ according to CIGALE.

In this paper we fit HELP_J100156.75+022344.7 with the four different
combinations of models, in order to quantify the uncertainty in the AGN
fraction and SFR. As noted by Efstathiou et al. (2021), in the SUPRIME N921
filter we see an excess in the photometry that deviates significantly from the
fit. This could be due to an emission line or a problem in the data reduction.
As in the models we use in our method emission lines are not included, we
opted to omit this data point from the fit.

For all the fits we fixed $\tau_{*}=2\times 10^{7}yr$ and two other
parameters. For the fits with the CYGNUS and Fritz et al. (2006) AGN models we
additionally fixed $\theta_{o}=45\degr$ and $r_{2}/r_{1}=60$. For the fit with
the AGN model SKIRTOR we fixed $\theta_{o}=45\degr$ and $r_{2}/r_{1}=20$,
whereas for the fit with the Siebenmorgen et al. (2015) AGN model we fixed
$A_{c}=3$ and $V_{c}=40$. The best fits with all combinations of models are
listed in Tables 8, A7 and A8 and plotted in Fig. 9. The CYGNUS, Fritz et al.
(2006) and SKIRTOR models predict a similar solution for the AGN fraction and
SFR, although there are significant differences in the $\chi^{2}_{min,\nu}$,
with the CYGNUS model giving the minimum value of 6.09. The SKIRTOR model
gives $\chi^{2}_{min,\nu}=6.69$ and the Fritz et al. (2006) model gives
$\chi^{2}_{min,\nu}=8.67$. The model of Siebenmorgen et al. (2015) gives the
worst fit with $\chi^{2}_{min,\nu}=12.03$ and predicts a significantly lower
SFR compared with the other models.

Figure 9: Comparison SED fit plots of the hyperluminous galaxy HELP_J100156.75+022344.7 at a photometric redshift of $z\sim 4.3$. The AGN torus, starburst, spheroidal host and total emission are plotted as shown in the legend. The top row shows fits with the CYGNUS combination of models. The second row shows fits with the CYGNUS AGN model replaced by the model of Fritz et al. (2006), the third row replaces the CYGNUS AGN model with the SKIRTOR model, while the bottom row replaces the CYGNUS AGN model with the model of Siebenmorgen et al (2015). Table 8: Selected fitted parameters for HELP_J100156.75+022344.7 AGN model | $\tau_{v}$ | $t_{*}\ (10^{7}yr)$ |  | $\theta_{i}\ (\degr)$
---|---|---|---|---
CYGNUS |  |  | $\tau_{uv}$ |
| $125.81^{34.15}_{-17.31}$ | $2.02^{0.19}_{-0.71}$ | $367.97^{207.86}_{-50.55}$ | $55.18^{0.48}_{-1.8}$
Fritz et al. (2006) |  |  | $\tau_{9.7\mu m}$ |
| $107.94^{33.15}_{-30.26}$ | $1.6^{0.45}_{-0.44}$ | $2.2^{1.6}_{-0.64}$ | $79.08^{4.53}_{-4.11}$
SKIRTOR |  |  | $\tau_{9.7\mu m}$ |
| $114.31^{92.24}_{-41.79}$ | $1.82^{1.05}_{-0.79}$ | $6.01^{1.4}_{-2.12}$ | $64.79^{5.57}_{-12.75}$
Siebenmorgen et al. (2015) |  |  | $A_{d}$ |
| $133.18^{54.28}_{-45.45}$ | $1.53^{0.82}_{-0.76}$ | $136.07^{37.17}_{-58.89}$ | $60.1^{5.86}_{-6.16}$

##  5 Conclusions

  1. 1.

In this paper we present SMART, a new fast code of fitting SEDs exclusively
with radiative transfer models. The method employs the MCMC code emcee and
uses pre-computed libraries for starbursts, AGN tori and host galaxies, which
can be modelled either with a spheroidal or disc geometry. The code takes
comparable time to energy balance codes like CIGALE and MAGPHYS. The method is
flexible in that it can fit SEDs which include MIR spectrophotometry, but also
galaxies where more limited photometry is available.

  2. 2.

As SMART can fit an SED with four different AGN torus models, it allows us to
constrain the properties of the obscuring torus in AGN and quantify the
uncertainties in AGN fraction and SFR. We consider four different AGN torus
models: the smooth tapered discs of Efstathiou & Rowan-Robinson (1995), the
smooth flared discs of Fritz et al. (2006), the two-phase flared discs of
Stalevski et al. (2012, 2016) and the two phase model of Siebenmorgen et al.
(2015). The first three models assume a normal interstellar mixture, whereas
the model of Siebenmorgen et al. (2015) assumes fluffy grains, which are more
efficient at emitting at submillimetre wavelengths.

  3. 3.

We test the method with the HERUS sample of ULIRGs and compare our results
with those obtained with the SATMC code by Efstathiou et al. (2022) and by
Paspaliaris et al. (2021) using CIGALE. We find that the results obtained with
SMART agree very well with those obtained with SATMC, except for the AGN
fraction, which shows considerable scatter. We attribute this to the strong
dependence of this quantity on the inclination. The SFRs predicted by CIGALE
generally agree with those with SMART, but the AGN fraction is significantly
lower, partly because CIGALE does not apply any anisotropy corrections to the
AGN luminosity.

  4. 4.

SMART is developed in PYTHON and is available at https://github.com/ch-
var/SMART.git.

We also briefly discuss some ideas for future development of SMART:

  1. 1.

The main limitation of SMART is that it currently assumes constant metallicity
and a parametric SFH and in particular a delayed exponential for the host
galaxy and an exponential for the starburst. Future developments of the code
will allow treatment of non-parametric SFH and metallicity histories.

  2. 2.

Another limitation of SMART is that it does not model nebular lines. A future
development could be to add nebular emission in the libraries used by SMART.
To do this, we would need to increase the spectral resolution of the models,
which is currently 223 points, to cover the wavelength range from the UV to
the millimetre.

  3. 3.

SMART currently fits the UV to millimetre SEDs. Therefore, another limitation
is that it does not model X-ray emission. This could be an additional
extension of SMART. We could follow the same methodology adopted in other
codes, such as X-CIGALE (Yang et al., 2020).

We conclude that SMART promises to be very useful for understanding galaxies
and AGN at any redshift in the JWST era, as well as galaxy formation and
evolution more generally.

## Data Availability Statement

The data underlying this article are available in the article, in public
databases Cornell Atlas of Spitzer/Infrared Spectrograph Sources (CASSIS) or
are publicly available in the literature.

## Acknowledgements

We would like to thank the anonymous referee for useful comments and
suggestions. The authors acknowledge support from the projects CYGNUS
(contract number 4000126896) and CYGNUS+ (contract number 4000139319) funded
by the cyanEuropean Space Agency. CV acknowledges a Ph.D. scholarship from
European University Cyprus.

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## Appendix A: Plots and other SED fitting results discussed in the paper

In this Appendix we give the plots of all of the SED fits with the CYGNUS
models, as well as their residuals, for the HERUS sample. We also give two
tables with the best fit parameters for the fits with the CYGNUS models for
the HERUS sample. In addition, we provide tables with extracted physical
quantities of the fits of IRAS 08572+3915, VV 340a and
HELP_J100156.75+022344.7.

Figure A1. SED fit plots of the first 8 objects from the list of the HERUS
sample, using the CYGNUS models. The AGN torus, starburst, spheroidal host,
polar dust and total emission are plotted as shown in the legend.

Figure A2. SED fit plots of the second 8 objects from the list of the HERUS
sample, using the CYGNUS models. The AGN torus, starburst, spheroidal host,
polar dust and total emission are plotted as shown in the legend.

Figure A3. SED fit plots of the third 8 objects from the list of the HERUS
sample. The AGN torus, starburst, spheroidal host, polar dust and total
emission are plotted as shown in the legend.

Figure A4. SED fit plots of the fourth 8 objects from the list of the HERUS
sample. The AGN torus, starburst, spheroidal host and total emission are
plotted as shown in the legend.

Figure A5. SED fit plots of the fifth 8 objects from the list of the HERUS
sample. The AGN torus, starburst, spheroidal host and total emission are
plotted as shown in the legend.

Figure A6. SED fit plots of the last 2 objects from the list of the HERUS
sample. The AGN torus, starburst, spheroidal host and total emission are
plotted as shown in the legend.

Table A1. Reduced $\chi^{2}$ and selected fitted parameters for the galaxies
in the HERUS sample

Name | $z$ | $\chi^{2}_{min,\nu}$ | $\tau_{v}^{s}$ | $\psi^{s}$ | $\tau^{s}\ (10^{7}yr)$ | $\tau_{v}$
---|---|---|---|---|---|---
IRAS00188-0856 | 0.12840001 | 2.66 | $1.23^{11.34}_{-0.61}$ | $5.59^{0.88}_{-0.92}$ | $147.11^{60.13}_{-9.47}$ | $128.66^{9.16}_{-17.77}$
IRAS00397-1312 | 0.2617 | 2.78 | $0.44^{0.54}_{-0.24}$ | $8.92^{6.17}_{-2.37}$ | $326.65^{50.05}_{-65.95}$ | $105.47^{5.39}_{-3.12}$
IRAS01003-2238 | 0.1178 | 1.3 | $0.77^{0.17}_{-0.36}$ | $2.56^{0.4}_{-0.4}$ | $778.94^{6.75}_{-29.1}$ | $65.58^{4.93}_{-7.73}$
IRAS03158+4227 | 0.1344 | 1.64 | $0.44^{0.67}_{-0.2}$ | $3.07^{2.46}_{-1.15}$ | $178.15^{208.11}_{-127.35}$ | $186.57^{12.27}_{-14.86}$
IRAS03521+0028 | 0.1519 | 3.16 | $4.42^{4.06}_{-1.95}$ | $2.28^{0.9}_{-0.45}$ | $25.37^{3.22}_{-4.22}$ | $179.99^{14.26}_{-15.5}$
IRAS05189-2524 | 0.04256 | 0.89 | $0.91^{0.45}_{-0.23}$ | $6.18^{1.3}_{-1.44}$ | $166.31^{3.02}_{-5.19}$ | $176.84^{12.32}_{-17.3}$
IRAS06035-7102 | 0.07947 | 0.87 | $9.24^{1.4}_{-5.56}$ | $3.7^{0.86}_{-0.28}$ | $205.86^{42.66}_{-174.51}$ | $144.96^{17.3}_{-51.06}$
IRAS06206-6315 | 0.09244 | 1.38 | $12.13^{2.21}_{-5.39}$ | $3.22^{0.89}_{-0.54}$ | $78.51^{16.17}_{-30.69}$ | $213.4^{13.74}_{-9.43}$
IRAS07598+6508 | 0.1483 | 0.22 | $1.0^{1.7}_{-0.59}$ | $4.98^{5.59}_{-2.37}$ | $96.56^{170.51}_{-60.04}$ | $74.93^{13.3}_{-10.46}$
IRAS08311-2459 | 0.1004 | 0.74 | $1.18^{0.84}_{-0.49}$ | $5.07^{2.71}_{-1.28}$ | $165.17^{128.78}_{-60.21}$ | $69.34^{11.08}_{-10.11}$
IRAS08572+3915 | 0.05835 | 1.67 | $0.49^{0.36}_{-0.15}$ | $10.43^{3.39}_{-2.12}$ | $443.13^{36.46}_{-43.89}$ | $95.82^{8.98}_{-11.97}$
IRAS09022-3615 | 0.05964 | 0.94 | $0.67^{0.39}_{-0.28}$ | $3.34^{1.99}_{-0.96}$ | $164.3^{9.07}_{-7.83}$ | $95.28^{11.97}_{-9.54}$
IRAS10378+1109 | 0.1362 | 1.65 | $1.14^{1.57}_{-0.45}$ | $3.91^{1.86}_{-1.08}$ | $182.55^{33.44}_{-6.78}$ | $121.63^{5.69}_{-7.35}$
IRAS10565+2448 | 0.043 | 1.69 | $0.47^{0.41}_{-0.18}$ | $5.68^{1.36}_{-1.68}$ | $85.35^{16.82}_{-14.77}$ | $142.66^{3.79}_{-3.43}$
IRAS11095-0238 | 0.1066 | 1.22 | $1.34^{5.09}_{-0.82}$ | $3.54^{1.66}_{-1.67}$ | $390.54^{211.33}_{-160.73}$ | $140.62^{23.68}_{-12.75}$
IRAS12071-0444 | 0.1284 | 1.67 | $4.26^{1.58}_{-1.35}$ | $1.55^{0.25}_{-0.44}$ | $228.69^{95.08}_{-13.62}$ | $142.81^{15.37}_{-19.74}$
IRAS13120-5453 | 0.03076 | 2.08 | $2.48^{2.31}_{-1.49}$ | $4.46^{1.95}_{-1.22}$ | $184.21^{140.39}_{-89.49}$ | $197.84^{1.39}_{-5.12}$
IRAS13451+1232 | 0.1217 | 1.84 | $8.19^{1.21}_{-0.61}$ | $1.67^{0.08}_{-0.21}$ | $322.61^{35.84}_{-67.3}$ | $130.6^{4.76}_{-8.16}$
IRAS14348-1447 | 0.0827 | 2.24 | $0.73^{1.26}_{-0.31}$ | $3.77^{1.1}_{-1.0}$ | $209.25^{70.78}_{-90.79}$ | $199.34^{11.04}_{-2.2}$
IRAS14378-3651 | 0.0676 | 2.65 | $0.83^{6.02}_{-0.54}$ | $3.38^{2.09}_{-0.94}$ | $114.47^{82.42}_{-26.81}$ | $198.56^{26.58}_{-3.49}$
IRAS15250+3609 | 0.05516 | 2.31 | $0.5^{0.94}_{-0.3}$ | $2.1^{0.56}_{-0.34}$ | $650.13^{69.35}_{-44.14}$ | $153.97^{8.23}_{-7.16}$
IRAS15462-0450 | 0.09979 | 1.39 | $0.27^{0.43}_{-0.16}$ | $2.91^{1.1}_{-1.26}$ | $187.39^{161.35}_{-53.98}$ | $166.57^{16.86}_{-34.6}$
IRAS16090-0139 | 0.13358 | 1.01 | $1.7^{2.62}_{-1.39}$ | $4.42^{1.19}_{-1.49}$ | $305.63^{326.12}_{-265.3}$ | $136.43^{5.64}_{-5.3}$
IRAS17208-0014 | 0.0428 | 2.55 | $0.18^{0.02}_{-0.04}$ | $1.14^{0.22}_{-0.01}$ | $166.87^{66.33}_{-10.54}$ | $198.93^{6.62}_{-0.24}$
IRAS19254-7245 | 0.061709 | 1.6 | $8.24^{2.27}_{-1.21}$ | $4.23^{2.07}_{-1.2}$ | $154.04^{5.2}_{-11.84}$ | $95.37^{25.1}_{-21.62}$
IRAS19297-0406 | 0.08573 | 2.21 | $0.28^{0.41}_{-0.14}$ | $3.82^{1.7}_{-1.28}$ | $70.94^{68.06}_{-38.8}$ | $195.56^{2.9}_{-5.88}$
IRAS20087-0308 | 0.10567 | 1.5 | $2.54^{1.06}_{-1.19}$ | $1.9^{1.19}_{-0.54}$ | $67.56^{48.77}_{-29.36}$ | $196.41^{2.76}_{-3.16}$
IRAS20100-4156 | 0.12958 | 2.54 | $1.58^{3.11}_{-0.96}$ | $4.19^{1.38}_{-1.47}$ | $335.05^{104.17}_{-60.68}$ | $198.37^{5.41}_{-7.53}$
IRAS20414-1651 | 0.087084 | 2.96 | $0.14^{0.04}_{-0.02}$ | $9.49^{3.49}_{-0.72}$ | $165.1^{31.41}_{-9.71}$ | $194.78^{4.1}_{-8.12}$
IRAS20551-4250 | 0.042996 | 1.77 | $2.03^{0.6}_{-0.34}$ | $2.83^{1.25}_{-0.69}$ | $636.41^{49.67}_{-44.28}$ | $147.0^{11.2}_{-10.93}$
IRAS22491-1808 | 0.0778 | 2.01 | $4.23^{0.22}_{-3.36}$ | $1.89^{0.71}_{-0.23}$ | $734.86^{25.11}_{-157.92}$ | $223.09^{15.12}_{-17.16}$
IRAS23128-5919 | 0.0446 | 1.33 | $1.87^{1.86}_{-0.98}$ | $4.61^{0.48}_{-0.64}$ | $698.76^{65.73}_{-111.18}$ | $227.74^{13.42}_{-7.57}$
IRAS23230-6926 | 0.10659 | 1.98 | $7.75^{0.65}_{-1.19}$ | $4.4^{1.88}_{-1.11}$ | $478.09^{39.74}_{-69.79}$ | $218.79^{15.4}_{-15.51}$
IRAS23253-5415 | 0.13 | 2.13 | $0.18^{0.07}_{-0.04}$ | $1.52^{0.33}_{-0.26}$ | $149.77^{65.7}_{-51.19}$ | $242.16^{3.92}_{-10.16}$
IRAS23365+3604 | 0.0645 | 3.09 | $5.63^{0.94}_{-4.44}$ | $2.67^{0.07}_{-0.18}$ | $210.06^{54.53}_{-36.89}$ | $229.65^{8.56}_{-6.56}$
Mrk1014 | 0.16311 | 2.62 | $1.73^{2.48}_{-0.52}$ | $3.57^{4.03}_{-1.21}$ | $227.58^{168.96}_{-129.66}$ | $52.81^{4.86}_{-0.99}$
UGC5101 | 0.039367 | 2.93 | $13.93^{0.5}_{-0.54}$ | $1.37^{0.1}_{-0.12}$ | $196.75^{3.92}_{-5.63}$ | $196.66^{4.3}_{-5.78}$
Mrk231 | 0.04217 | 0.58 | $0.57^{0.5}_{-0.41}$ | $2.31^{1.14}_{-0.79}$ | $514.11^{185.21}_{-157.76}$ | $145.48^{36.66}_{-14.34}$
Mrk273 | 0.03778 | 1.63 | $0.95^{0.38}_{-0.26}$ | $5.02^{0.77}_{-1.21}$ | $175.69^{4.72}_{-8.87}$ | $135.74^{15.82}_{-5.76}$
Mrk463 | 0.050355 | 1.5 | $1.32^{0.36}_{-0.45}$ | $3.4^{4.09}_{-0.92}$ | $116.4^{67.27}_{-21.8}$ | $116.17^{16.08}_{-11.1}$
Arp220 | 0.018 | 5.23 | $0.12^{0.03}_{-0.02}$ | $1.83^{0.53}_{-0.39}$ | $124.13^{1.71}_{-0.22}$ | $246.08^{2.19}_{-1.06}$
NGC6240 | 0.0244 | 1.62 | $3.23^{0.8}_{-1.16}$ | $3.96^{0.6}_{-0.24}$ | $247.7^{19.01}_{-37.22}$ | $76.64^{6.67}_{-6.98}$

Table A2. Other fitted parameters for the galaxies in the HERUS sample

Name | $t_{*}\ (10^{7}yr)$ | $\tau_{*}\ (10^{7}yr)$ | $r_{2}/r_{1}$ | $\tau_{uv}$ | $\theta_{o}\ (\degr)$ | $\theta_{i}\ (\degr)$ | $T_{p}$
---|---|---|---|---|---|---|---
IRAS00188-0856 | $3.22^{0.08}_{-0.19}$ | $1.55^{0.1}_{-0.05}$ | $57.42^{30.87}_{-21.08}$ | $394.96^{77.68}_{-18.89}$ | $46.42^{2.66}_{-3.95}$ | $76.46^{4.46}_{-0.37}$ | -
IRAS00397-1312 | $0.77^{0.14}_{-0.16}$ | $2.01^{0.22}_{-0.23}$ | $89.46^{6.71}_{-5.84}$ | $329.52^{9.58}_{-9.24}$ | $73.81^{0.27}_{-0.09}$ | $83.12^{1.11}_{-0.87}$ | -
IRAS01003-2238 | $1.38^{0.25}_{-0.19}$ | $1.45^{0.28}_{-0.11}$ | $52.48^{5.82}_{-3.25}$ | $1310.68^{86.96}_{-24.24}$ | $61.37^{0.19}_{-0.09}$ | $69.32^{0.27}_{-0.2}$ | -
IRAS03158+4227 | $3.03^{0.25}_{-0.39}$ | $1.39^{0.15}_{-0.15}$ | $30.93^{5.92}_{-3.6}$ | $959.57^{33.8}_{-51.93}$ | $53.97^{4.84}_{-2.01}$ | $76.88^{0.62}_{-0.6}$ | -
IRAS03521+0028 | $3.4^{0.07}_{-0.05}$ | $1.55^{0.2}_{-0.2}$ | $45.37^{1.6}_{-3.74}$ | $1245.22^{81.44}_{-99.23}$ | $58.9^{3.52}_{-3.74}$ | $70.52^{1.82}_{-1.4}$ | -
IRAS05189-2524 | $2.15^{0.42}_{-0.28}$ | $2.09^{0.21}_{-0.37}$ | $38.24^{4.1}_{-4.16}$ | $911.92^{72.26}_{-33.33}$ | $52.28^{3.43}_{-1.28}$ | $63.61^{1.75}_{-0.6}$ | $1050.6^{28.7}_{-23.2}$
IRAS06035-7102 | $0.84^{1.99}_{-0.14}$ | $2.03^{0.12}_{-0.43}$ | $43.38^{9.55}_{-4.72}$ | $361.74^{106.82}_{-22.29}$ | $48.28^{1.82}_{-8.36}$ | $68.39^{2.01}_{-2.32}$ | -
IRAS06206-6315 | $3.09^{0.2}_{-0.19}$ | $1.38^{0.11}_{-0.11}$ | $48.27^{4.85}_{-5.79}$ | $695.61^{36.17}_{-84.44}$ | $45.32^{4.21}_{-3.83}$ | $70.29^{1.12}_{-1.09}$ | -
IRAS07598+6508 | $2.83^{0.2}_{-0.52}$ | $2.08^{0.47}_{-0.4}$ | $36.43^{16.48}_{-10.28}$ | $723.81^{145.32}_{-106.6}$ | $63.02^{2.3}_{-1.76}$ | $15.27^{2.16}_{-2.84}$ | $1094.2^{72.0}_{-98.8}$
IRAS08311-2459 | $2.84^{0.15}_{-0.12}$ | $1.22^{0.23}_{-0.11}$ | $30.23^{6.94}_{-3.93}$ | $650.82^{97.1}_{-82.22}$ | $48.54^{4.38}_{-3.8}$ | $60.15^{2.95}_{-1.86}$ | -
IRAS08572+3915 | $0.64^{0.28}_{-0.1}$ | $1.79^{0.34}_{-0.25}$ | $58.5^{9.8}_{-8.38}$ | $612.99^{14.44}_{-21.13}$ | $72.66^{1.05}_{-0.89}$ | $79.04^{0.74}_{-0.65}$ | -
IRAS09022-3615 | $3.08^{0.24}_{-0.2}$ | $1.41^{0.12}_{-0.25}$ | $40.44^{8.88}_{-7.7}$ | $308.95^{38.16}_{-30.87}$ | $37.15^{3.16}_{-8.14}$ | $63.27^{2.77}_{-3.59}$ | -
IRAS10378+1109 | $2.98^{0.3}_{-0.22}$ | $1.3^{0.35}_{-0.14}$ | $31.19^{7.18}_{-5.31}$ | $1427.8^{51.92}_{-135.04}$ | $51.29^{1.97}_{-2.56}$ | $72.63^{0.81}_{-2.14}$ | -
IRAS10565+2448 | $3.47^{0.02}_{-0.02}$ | $1.05^{0.05}_{-0.04}$ | $44.7^{5.66}_{-5.41}$ | $825.07^{38.72}_{-59.02}$ | $54.12^{2.16}_{-1.54}$ | $66.1^{0.6}_{-0.75}$ | -
IRAS11095-0238 | $2.46^{0.81}_{-1.25}$ | $1.92^{0.57}_{-0.38}$ | $59.5^{11.12}_{-16.98}$ | $904.31^{53.4}_{-37.8}$ | $60.14^{2.46}_{-3.65}$ | $76.33^{0.79}_{-0.89}$ | -
IRAS12071-0444 | $0.63^{0.31}_{-0.12}$ | $1.88^{0.02}_{-0.1}$ | $38.36^{0.69}_{-2.4}$ | $794.25^{24.03}_{-30.22}$ | $47.29^{0.2}_{-3.41}$ | $66.95^{0.48}_{-0.8}$ | -
IRAS13120-5453 | $3.38^{0.08}_{-0.06}$ | $1.05^{0.06}_{-0.02}$ | $51.96^{3.76}_{-5.55}$ | $554.66^{9.27}_{-41.27}$ | $43.12^{5.92}_{-1.56}$ | $67.39^{0.75}_{-2.69}$ | -
IRAS13451+1232 | $1.49^{0.03}_{-0.15}$ | $1.49^{0.15}_{-0.17}$ | $39.07^{5.08}_{-3.41}$ | $1456.38^{19.18}_{-42.13}$ | $51.33^{0.54}_{-2.2}$ | $64.28^{0.35}_{-1.55}$ | $938.9^{33.3}_{-13.2}$
IRAS14348-1447 | $3.39^{0.07}_{-0.16}$ | $2.16^{0.28}_{-0.23}$ | $25.75^{3.24}_{-2.71}$ | $802.79^{96.15}_{-140.11}$ | $51.38^{4.0}_{-3.78}$ | $70.64^{1.35}_{-1.71}$ | -
IRAS14378-3651 | $3.43^{0.04}_{-0.03}$ | $2.26^{0.23}_{-0.58}$ | $43.77^{14.34}_{-4.42}$ | $1035.7^{252.4}_{-114.91}$ | $47.17^{4.29}_{-3.19}$ | $68.96^{1.95}_{-0.61}$ | -
IRAS15250+3609 | $2.99^{0.36}_{-0.64}$ | $2.87^{0.32}_{-0.4}$ | $34.51^{2.53}_{-2.87}$ | $927.48^{26.0}_{-29.82}$ | $55.78^{1.06}_{-1.94}$ | $76.97^{0.82}_{-0.49}$ | -
IRAS15462-0450 | $1.87^{0.59}_{-0.55}$ | $2.25^{0.52}_{-0.32}$ | $38.77^{17.9}_{-6.05}$ | $532.12^{78.8}_{-55.67}$ | $55.53^{7.7}_{-1.2}$ | $60.96^{3.81}_{-1.62}$ | -
IRAS16090-0139 | $3.44^{0.04}_{-0.08}$ | $2.01^{0.25}_{-0.31}$ | $46.52^{4.75}_{-3.4}$ | $545.12^{49.17}_{-24.69}$ | $46.62^{6.14}_{-3.44}$ | $72.82^{1.55}_{-1.13}$ | -
IRAS17208-0014 | $3.44^{0.0}_{-0.04}$ | $1.32^{0.01}_{-0.03}$ | $46.3^{2.02}_{-1.23}$ | $633.32^{1.29}_{-16.95}$ | $48.08^{3.57}_{-2.53}$ | $65.94^{0.29}_{-0.44}$ | -
IRAS19254-7245 | $1.13^{0.13}_{-0.2}$ | $2.53^{0.42}_{-0.45}$ | $43.82^{7.91}_{-4.61}$ | $780.52^{42.86}_{-98.51}$ | $55.46^{2.31}_{-1.32}$ | $68.66^{0.75}_{-0.66}$ | -
IRAS19297-0406 | $3.44^{0.01}_{-0.06}$ | $2.0^{0.22}_{-0.5}$ | $78.41^{9.95}_{-23.53}$ | $824.04^{81.58}_{-40.58}$ | $41.04^{2.88}_{-4.01}$ | $64.06^{2.21}_{-1.97}$ | -
IRAS20087-0308 | $3.48^{0.01}_{-0.02}$ | $1.04^{0.04}_{-0.03}$ | $49.76^{7.82}_{-4.88}$ | $316.83^{15.92}_{-16.97}$ | $58.14^{1.66}_{-2.27}$ | $80.16^{1.72}_{-2.36}$ | -
IRAS20100-4156 | $2.0^{0.45}_{-0.9}$ | $2.54^{0.68}_{-0.72}$ | $45.69^{9.01}_{-5.02}$ | $613.02^{65.63}_{-35.23}$ | $47.39^{3.11}_{-2.75}$ | $73.59^{0.81}_{-0.97}$ | -
IRAS20414-1651 | $3.4^{0.04}_{-0.03}$ | $1.22^{0.01}_{-0.04}$ | $51.91^{4.43}_{-5.34}$ | $620.3^{90.57}_{-47.04}$ | $62.2^{0.76}_{-2.88}$ | $70.79^{0.63}_{-0.31}$ | -
IRAS20551-4250 | $1.26^{0.36}_{-0.22}$ | $1.7^{0.37}_{-0.49}$ | $42.29^{4.32}_{-4.7}$ | $732.36^{24.46}_{-17.98}$ | $48.65^{2.84}_{-2.31}$ | $74.11^{0.85}_{-1.19}$ | -
IRAS22491-1808 | $1.46^{1.79}_{-0.48}$ | $2.45^{0.22}_{-0.3}$ | $32.91^{4.86}_{-4.48}$ | $1237.53^{109.38}_{-59.62}$ | $49.02^{1.98}_{-1.38}$ | $71.39^{0.67}_{-1.71}$ | -
IRAS23128-5919 | $1.55^{0.41}_{-0.5}$ | $1.21^{0.1}_{-0.13}$ | $31.21^{3.91}_{-4.0}$ | $612.96^{34.8}_{-35.47}$ | $44.41^{2.01}_{-1.94}$ | $63.37^{0.46}_{-0.81}$ | -
IRAS23230-6926 | $1.32^{0.27}_{-0.32}$ | $1.58^{0.28}_{-0.19}$ | $45.45^{5.7}_{-4.53}$ | $813.11^{29.03}_{-36.16}$ | $48.57^{2.3}_{-2.03}$ | $74.03^{0.72}_{-0.7}$ | -
IRAS23253-5415 | $3.21^{0.17}_{-0.1}$ | $1.39^{0.45}_{-0.24}$ | $93.24^{2.3}_{-4.69}$ | $1378.25^{41.64}_{-26.05}$ | $49.08^{1.76}_{-1.71}$ | $68.78^{0.59}_{-0.98}$ | -
IRAS23365+3604 | $2.54^{0.1}_{-0.18}$ | $1.19^{0.22}_{-0.04}$ | $26.41^{0.51}_{-1.68}$ | $1442.99^{22.88}_{-19.41}$ | $51.7^{2.1}_{-3.48}$ | $74.55^{0.19}_{-0.36}$ | -
Mrk1014 | $2.13^{0.2}_{-0.14}$ | $1.18^{0.16}_{-0.13}$ | $61.14^{11.1}_{-9.45}$ | $286.33^{103.28}_{-19.2}$ | $59.76^{1.04}_{-0.85}$ | $18.06^{1.83}_{-1.22}$ | -
UGC5101 | $1.05^{0.09}_{-0.06}$ | $1.51^{0.2}_{-0.08}$ | $76.09^{4.28}_{-8.96}$ | $339.69^{22.83}_{-23.61}$ | $46.29^{1.8}_{-2.13}$ | $75.48^{0.22}_{-1.19}$ | -
Mrk231 | $2.1^{0.33}_{-0.36}$ | $1.52^{0.14}_{-0.12}$ | $40.1^{4.43}_{-6.97}$ | $636.02^{35.16}_{-22.87}$ | $54.24^{2.76}_{-3.08}$ | $63.79^{1.22}_{-1.03}$ | -
Mrk273 | $2.98^{0.12}_{-0.16}$ | $1.33^{0.12}_{-0.08}$ | $37.9^{4.06}_{-1.1}$ | $788.22^{106.94}_{-91.5}$ | $44.88^{1.48}_{-2.48}$ | $66.61^{0.84}_{-1.83}$ | -
Mrk463 | $1.67^{0.46}_{-0.38}$ | $2.18^{0.16}_{-0.21}$ | $46.87^{5.6}_{-18.56}$ | $517.08^{68.32}_{-100.63}$ | $63.17^{3.89}_{-1.71}$ | $63.26^{1.56}_{-3.02}$ | -
Arp220 | $2.95^{0.04}_{-0.02}$ | $1.11^{0.08}_{-0.07}$ | $59.58^{15.48}_{-7.3}$ | $1447.17^{16.31}_{-4.36}$ | $48.24^{0.27}_{-1.42}$ | $78.29^{0.3}_{-0.57}$ | -
NGC6240 | $3.23^{0.18}_{-0.19}$ | $1.25^{0.23}_{-0.16}$ | $44.07^{4.56}_{-7.74}$ | $1097.07^{95.22}_{-76.14}$ | $54.62^{3.61}_{-2.12}$ | $71.3^{0.66}_{-0.67}$ | -

Table A3. Selected extracted physical quantities for IRAS 08572+3915. For the
AGN and total luminosities the anisotropy-corrected luminosities are given.

AGN model | $L_{AGN}^{c}$ | $L_{SB}$ | $L_{sph}$ | $L_{tot}^{c}$ | $\dot{M}^{age}_{*}$ | $\dot{M}_{sph}$
---|---|---|---|---|---|---
| $10^{12}L_{\odot}$ | $10^{11}L_{\odot}$ | $10^{10}L_{\odot}$ | $10^{12}L_{\odot}$ | $M_{\odot}yr^{-1}$ | $M_{\odot}yr^{-1}$
CYGNUS | $12.85^{1.1}_{-1.36}$ | $5.46^{0.42}_{-1.07}$ | $1.67^{0.08}_{-0.09}$ | $13.34^{1.21}_{-1.4}$ | $154.0^{17.93}_{-48.26}$ | $1.52^{0.15}_{-0.13}$
Fritz et al. (2006) | $4.14^{0.0}_{-0.55}$ | $2.07^{3.35}_{-0.0}$ | $2.73^{0.0}_{-1.0}$ | $4.38^{0.0}_{-0.22}$ | $55.93^{75.42}_{-0.0}$ | $2.31^{0.0}_{-1.56}$
SKIRTOR | $0.0^{0.01}_{-0.0}$ | $14.35^{0.15}_{-0.21}$ | $1.59^{0.1}_{-0.03}$ | $1.45^{0.02}_{-0.02}$ | $428.1^{9.09}_{-8.14}$ | $1.46^{0.1}_{-0.07}$
Siebenmorgen et al. (2015) | $0.01^{0.01}_{-0.0}$ | $14.33^{0.31}_{-0.22}$ | $1.57^{0.05}_{-0.05}$ | $1.46^{0.03}_{-0.03}$ | $430.1^{6.11}_{-10.15}$ | $1.42^{0.1}_{-0.07}$

Table A4. Other extracted physical quantities for IRAS 08572+3915

AGN model | $\dot{M}_{tot}$ | ${M}^{*}_{sph}$ | ${M}^{*}_{SB}$ | ${M}^{*}_{tot}$ | $F_{AGN}$ | $A$
---|---|---|---|---|---|---
| $M_{\odot}yr^{-1}$ | $10^{10}M_{\odot}$ | $10^{9}M_{\odot}$ | $10^{10}M_{\odot}$ |  |
CYGNUS | $155.5^{18.02}_{-48.19}$ | $2.19^{0.19}_{-0.15}$ | $0.9^{0.14}_{-0.07}$ | $2.28^{0.22}_{-0.16}$ | $0.96^{0.01}_{-0.01}$ | $14.2^{1.38}_{-1.29}$
Fritz et al. (2006) | $58.24^{73.86}_{-0.0}$ | $2.1^{2.28}_{-0.0}$ | $1.63^{0.18}_{-0.0}$ | $2.27^{2.3}_{-0.0}$ | $0.95^{0.0}_{-0.08}$ | $3.53^{0.5}_{-0.0}$
SKIRTOR | $429.8^{8.91}_{-8.48}$ | $2.24^{0.18}_{-0.13}$ | $2.11^{0.03}_{-0.03}$ | $2.45^{0.18}_{-0.14}$ | $0.0^{0.0}_{-0.0}$ | $1.4^{1.14}_{-0.36}$
Siebenmorgen et al. (2015) | $431.5^{6.05}_{-10.09}$ | $2.18^{0.14}_{-0.13}$ | $2.1^{0.07}_{-0.04}$ | $2.4^{0.14}_{-0.14}$ | $0.0^{0.0}_{-0.0}$ | $3.64^{0.38}_{-0.66}$

Table A5. Selected extracted physical quantities for VV 340a. For the AGN and
total luminosities the anisotropy-corrected luminosities are given.

Host galaxy model | $L_{AGN}^{c}$ | $L_{SB}$ |  $L_{sph}$ or $L_{disc}$ | $L_{tot}^{c}$ | $\dot{M}^{age}_{*}$ | $\dot{M}_{sph}$
---|---|---|---|---|---|---
| $10^{12}L_{\odot}$ | $10^{11}L_{\odot}$ | $10^{10}L_{\odot}$ | $10^{12}L_{\odot}$ | $M_{\odot}yr^{-1}$ | $M_{\odot}yr^{-1}$
Spheroidal | $0.05^{0.01}_{-0.02}$ | $2.55^{0.33}_{-0.45}$ | $16.12^{1.71}_{-0.55}$ | $0.46^{0.05}_{-0.04}$ | $78.21^{36.21}_{-3.35}$ | $3.81^{1.09}_{-0.62}$
Disc | $0.25^{0.06}_{-0.04}$ | $1.48^{0.23}_{-0.33}$ | $30.98^{2.1}_{-0.67}$ | $0.72^{0.04}_{-0.03}$ | $35.41^{5.26}_{-8.42}$ | $11.56^{1.28}_{-0.29}$

Table A6. Other extracted physical quantities for VV 340a

Host galaxy model | $\dot{M}_{tot}$ |  ${M}^{*}_{sph}$ or ${M}^{*}_{disc}$ | ${M}^{*}_{SB}$ | ${M}^{*}_{tot}$ | $F_{AGN}$ | $A$
---|---|---|---|---|---|---
| $M_{\odot}yr^{-1}$ | $10^{10}M_{\odot}$ | $10^{9}M_{\odot}$ | $10^{10}M_{\odot}$ |  |
Spheroidal | $81.98^{36.33}_{-3.32}$ | $21.24^{3.99}_{-1.01}$ | $2.38^{0.82}_{-0.13}$ | $21.47^{4.04}_{-1.0}$ | $0.1^{0.02}_{-0.03}$ | $1.65^{0.36}_{-0.67}$
Disc | $47.79^{4.43}_{-0.29}$ | $21.34^{0.78}_{-0.49}$ | $0.36^{0.03}_{-0.07}$ | $21.38^{0.77}_{-0.48}$ | $0.35^{0.07}_{-0.04}$ | $8.3^{0.84}_{-0.8}$

Table A7. Selected extracted physical quantities for HELP_J100156.75+022344.7.
For the AGN and total luminosities the anisotropy-corrected luminosities are
given.

AGN model | $L_{AGN}^{c}$ | $L_{SB}$ | $L_{sph}$ | $L_{tot}^{c}$ | $\dot{M}^{age}_{*}$ | $\dot{M}_{sph}$
---|---|---|---|---|---|---
| $10^{12}L_{\odot}$ | $10^{11}L_{\odot}$ | $10^{10}L_{\odot}$ | $10^{12}L_{\odot}$ | $M_{\odot}yr^{-1}$ | $M_{\odot}yr^{-1}$
CYGNUS | $23.54^{0.24}_{-5.08}$ | $40.83^{4.8}_{-5.05}$ | $9.88^{35.02}_{-1.78}$ | $27.45^{0.28}_{-4.27}$ | $994.3^{86.46}_{-110.2}$ | $7.29^{27.14}_{-2.58}$
Fritz et al. (2006) | $14.62^{1.28}_{-1.54}$ | $55.31^{7.92}_{-7.06}$ | $9.7^{7.53}_{-1.59}$ | $20.27^{1.15}_{-1.06}$ | $1349.0^{160.7}_{-204.4}$ | $8.19^{4.92}_{-1.19}$
SKIRTOR | $15.29^{4.65}_{-1.91}$ | $50.07^{12.52}_{-6.45}$ | $10.62^{4.41}_{-2.96}$ | $20.45^{5.35}_{-2.02}$ | $1267.0^{285.3}_{-206.3}$ | $8.2^{3.17}_{-2.2}$
Siebenmorgen et al. (2015) | $26.58^{5.32}_{-1.89}$ | $2.27^{17.66}_{-2.22}$ | $9.71^{6.72}_{-1.57}$ | $28.83^{3.34}_{-3.78}$ | $54.48^{461.9}_{-53.2}$ | $8.35^{4.4}_{-1.89}$

Table A8. Other extracted physical quantities for HELP_J100156.75+022344.7

AGN model | $\dot{M}_{tot}$ | ${M}^{*}_{sph}$ | ${M}^{*}_{SB}$ | ${M}^{*}_{tot}$ | $F_{AGN}$ | $A$
---|---|---|---|---|---|---
| $M_{\odot}yr^{-1}$ | $10^{10}M_{\odot}$ | $10^{9}M_{\odot}$ | $10^{10}M_{\odot}$ |  |
CYGNUS | $999.0^{132.2}_{-108.1}$ | $4.13^{0.31}_{-0.36}$ | $17.57^{0.98}_{-5.36}$ | $5.74^{0.23}_{-0.17}$ | $0.85^{0.01}_{-0.05}$ | $1.22^{0.07}_{-0.04}$
Fritz et al. (2006) | $1357.0^{160.4}_{-196.8}$ | $3.41^{0.46}_{-0.39}$ | $18.32^{7.54}_{-5.16}$ | $5.33^{0.34}_{-0.54}$ | $0.72^{0.04}_{-0.03}$ | $1.55^{0.07}_{-0.04}$
SKIRTOR | $1273.0^{292.2}_{-203.0}$ | $3.71^{0.45}_{-0.27}$ | $19.97^{14.84}_{-8.46}$ | $5.66^{1.69}_{-0.89}$ | $0.74^{0.05}_{-0.04}$ | $1.45^{0.24}_{-0.12}$
Siebenmorgen et al. (2015) | $62.2^{464.2}_{-49.23}$ | $3.16^{0.32}_{-0.53}$ | $0.94^{9.71}_{-0.93}$ | $3.18^{1.06}_{-0.21}$ | $0.99^{0.0}_{-0.07}$ | $1.36^{0.08}_{-0.2}$