# Fundamental X-ray Corona Parameters of Swift/BAT AGN

Jason T. Hinkle1,2 and Richard Mushotzky2,3
1Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Dr., Honolulu,
HI 96822, USA
2Department of Astronomy, University of Maryland, College Park, MD 20742, USA
3Joint Space-Science Institute, University of Maryland, College Park, MD
20742, USA E-mail<EMAIL_ADDRESS>
###### Abstract

While X-ray emission from active galactic nuclei (AGN) is common, the detailed
physics behind this emission is not well understood. This is in part because
high quality broadband spectra are required to precisely derive fundamental
parameters of X-ray emission such as the photon index, folding energy, and
reflection coefficient. Here we present values of such parameters for 33 AGN
observed as part of the 105 month Swift/BAT campaign and with coordinated
archival XMM-Newton and NuSTAR observations. We look for correlations between
the various coronal parameters in addition to correlations between coronal
parameters and physical properties such as black hole mass and Eddington
ratio. Using our empirical model, we find good fits to almost all of our
objects. The folding energy was constrained for 30 of our 33 objects. When
comparing Seyfert 1 - 1.9 to Seyfert 2 galaxies, a K-S test indicates that
Seyfert 2 AGN have lower Eddington ratios and photon indices than Seyfert 1 -
1.9 objects with p-values of $5.6\times 10^{-5}$ and $7.5\times 10^{-3}$
respectively. We recover a known correlation between photon index and
reflection coefficient as well as the X-ray Baldwin effect. Finally, we find
that the inclusion of the high energy Swift BAT data significantly reduces the
uncertainties of spectral parameters as compared to fits without the BAT data.

###### keywords:

black hole physics – galaxies: active – galaxies: Seyfert – quasars: general –
X-rays: galaxies

††pagerange: Fundamental X-ray Corona Parameters of Swift/BAT AGN–Appendix:
Comments on the Spectral Fits

##  1 Introduction

Active galactic nuclei (AGN) are the luminous centers of galaxies where matter
is actively accreting onto the central supermassive black hole (SMBH) (e.g.,
Rees, 1984; Antonucci, 1993; Urry & Padovani, 1995). AGN are fundamentally
multi-wavelength objects, with strong emission in the radio (e.g., Urry &
Padovani, 1995; Best et al., 2005), infrared (e.g., Sanders et al., 1988;
Sanders & Mirabel, 1996; Stern et al., 2005), optical (e.g., Boroson & Green,
1992; Kaspi et al., 2000; Kewley et al., 2006), ultraviolet (e.g., Murray et
al., 1995; Haardt & Madau, 1996), X-ray (e.g., Reynolds, 1997; Fabian, 2012),
and gamma-ray (e.g., Hartman et al., 1999; Acero et al., 2015) wavebands.
While the strength of emission in each energy band varies depending on the
class of AGN, luminous X-ray emission is nearly ubiquitous across the entire
family of AGN (e.g., Elvis et al., 1978; Mushotzky et al., 1993).

X-ray emission from AGN is commonly explained by a comptonizing region near
the accretion disk surrounding the SMBH. Physical models for this region
include a hot corona around the accretion disk (e.g., Haardt & Maraschi,
1991), a hot inner flow of electrons (e.g., Zdziarski & Gierliński, 2004; Done
et al., 2007), and the base of a jet along the rotation axis of the black hole
(e.g., Matt et al., 1991; Martocchia & Matt, 1996; Henri & Petrucci, 1997;
Markoff et al., 2005). Given the diversity of AGN X-ray spectra, it may be
true that each of these processes are important in different objects.

The putative X-ray spectrum of an AGN is comprised of several main components.
The underlying continuum radiation is roughly approximated by a power law,
caused by inverse Compton (IC) scattering of lower energy UV photons from the
accretion disk by hot, energetic electrons in the so-called corona (e.g.,
Antonucci, 1993; Nandra & Pounds, 1994). At energies below $\sim$ 1 keV, there
is a soft excess, the origin of which is largely unclear (e.g., Gierliński &
Done, 2004; Sobolewska & Done, 2007; Done & Nayakshin, 2007; Boissay et al.,
2016). However, some recent observational (e.g., Jin et al., 2012; Petrucci et
al., 2018) and theoretical (e.g., Różańska et al., 2015; Ballantyne, 2020;
Petrucci et al., 2020) studies have suggested the existence of a warm (kT
$\sim 1$ keV), optically thick ($\tau\sim 10-20$) corona as the source of the
soft excess. Furthermore, some studies have argued that the soft excess may be
well-modeled by relativistically blurred ionized reflection (e.g., Crummy et
al., 2006; García et al., 2019; Xu et al., 2021). Between a few keV and up to
hundreds of keV there is a reflection hump created by X-rays being IC
scattered (or reflected) off the colder accretion disk or more distant
material (e.g., Pounds et al., 1990; George & Fabian, 1991; Haardt & Maraschi,
1993; Nandra & Pounds, 1994; Magdziarz & Zdziarski, 1995).

For most AGN, the strongest emission line seen in the X-ray is the fluorescent
Fe K$\alpha$ line (e.g, Fabian et al., 2000; Reynolds & Nowak, 2003), which is
often broad and exhibits relativistic effects due to its creation close to the
SBMH (e.g., Pounds et al., 1990; Laor, 1991; Nandra et al., 1997; Reynolds &
Begelman, 1997; Elvis, 2000). However, there is also a relatively narrower Fe
K$\alpha$ component (Shu et al., 2010), which presumably originates from more
distant material. In some cases, the line profile of broad Fe K$\alpha$
emission can be used to constrain the spin of the black hole (e.g., Reynolds &
Fabian, 2008; Bambi et al., 2017; Jones et al., 2020; Abarr & Krawczynski,
2021).

Despite how pervasive X-ray emission from AGN is, the number of plausible
physical scenarios suggest that the fundamental physics behind this X-ray
emission is not well understood. This includes information on the shape, size,
and location of the X-ray corona. Two of the most fundamental parameters that
can be used to constrain the above characteristics are the photon index of the
underlying power law and the cutoff (or folding) energy of the continuum. The
folding energy, which is generally between 50 and 300 keV, is thought to be
related to the temperature of the hot comptonizing electrons in the corona
(Fabian et al., 2015; Tortosa et al., 2018). Additionally there seems to be a
relationship between the folding energy and the photon index (Dadina, 2007;
Perola et al., 2002; Panessa et al., 2011; de Rosa et al., 2012; Molina et
al., 2013; Ricci et al., 2017).

The lack of strong constraints on the physics of the X-ray emitting region is
in part due to the lack of high signal to noise ratio (S/N) data on AGN in the
requisite energy ranges at E $\gtrsim$ 75 keV where the effects of a folding
energy are best defined. This requires the analysis of hard X-ray data in
order to constrain the folding energy. Several previous studies have made use
of the Nuclear Spectroscopic Telescope Array (NuSTAR; Harrison et al., 2013)
satellite to probe the hard X-ray band up to roughly 60 keV. Studies such as
Brenneman et al. (2014), Baloković et al. (2015), Fabian et al. (2015), Matt
et al. (2015), Marinucci et al. (2014b), Marinucci et al. (2014a), Marinucci
et al. (2016) and Tortosa et al. (2017), have provided constraints on coronal
properties using NuSTAR and other X-ray satellites such as Suzaku (Mitsuda et
al., 2007), XMM-Newton (Jansen et al., 2001), and Swift (Gehrels et al.,
2004). To reduce uncertainties on the fundamental X-ray corona parameters and
provide stronger constraints on correlations between them, it is important to
include higher energy data (i.e. above 75 keV). For this reason, we
incorporate data from the Swift Burst Alert Telescope (BAT; Barthelmy et al.,
2005), in addition to NuSTAR and XMM-Newton data in this paper.

As we will show, the addition of the BAT data results in smaller uncertainties
on the values of the reflection coefficient, folding energy and photon index
in the simplest model, pexrav, which adequately describes the data. While more
sophisticated models exist (e.g. borus (Baloković et al., 2018) and mytorus
(Murphy & Yaqoob, 2009)) the additional numbers of degrees of freedom often
result in poorly constrained parameters for many sources, severely limiting
the sample size. Since we find that pexrav provides an acceptable fit to the
high energy continuum data for virtually all of our sources with reasonable
parameters, we have decided to systematically use this relatively simple model
rather attempt to fit more sophisticated models to this sample.

The Swift satellite (Gehrels et al., 2004) was launched in November 2004. One
of its instruments, the Swift BAT (Barthelmy et al., 2005) surveys the entire
sky between 14 and 195 keV (Oh et al., 2018), with a primary intent of quickly
detecting gamma-ray bursts to initiate rapid follow-up. Because of the large
field-of-view (FOV) of the BAT detector, there is a wealth of hard X-ray data
on X-ray sources across the sky, including over a thousand AGN of various
types.

There are many X-ray telescopes that operate at less than 10 keV, an important
energy range for studying the soft excess and Fe K$\alpha$ line properties of
AGN. For our purposes, the XMM-Newton satellite provides the best combination
of sensitivity, bandpass, and spectral resolution. The XMM-Newton satellite,
launched in December 1999, has two X-ray instruments, a grating spectrometer
and the European Photon Imaging Camera (EPIC). The EPIC instrument has three
detectors, two MOS CCDs (Turner et al., 2001) and one PN CCD (Strüder et al.,
2001).

The NuSTAR satellite (Harrison et al., 2013) was launched in June 2012. It is
comprised of two Wolter 1 telescopes which focus photons onto two separate
focal plane modules (FPMs). Its unique multi-layer design gives NuSTAR a
nominal energy range from 3 to 79 keV, a bandpass that was largely
understudied in the past. NuSTAR is vital to our analysis in this paper
because it links the lower energy data of XMM-Newton to the high energy data
of the Swift BAT.

In this study we make use of archival data from the Swift BAT, NuSTAR, and
XMM-Newton telescopes. We use stacked spectra from the BAT, two spectra (one
per FPM) from NuSTAR, and whenever possible, three EPIC spectra from XMM-
Newton to provide high-fidelity, high S/N spectra of the AGN in our sample. To
understand the complex inner regions of AGN, it is vital to look for
relationships between fundamental spectral parameters and physical quantities
such as the Eddington ratio and SMBH mass.

In this paper, we present a study of the derived spectral parameters of 33 AGN
and expected correlations between them. This paper is organized as follows.
Section 2 will describe our sample of AGN. Section 3 will detail our analysis
methods and fitting procedures. Section 4 will display our results and Section
5 will provide discussion on these results. Section 6 will summarize the paper
and its main conclusions. Throughout the paper we assume a cosmology of
$H_{0}$ = 70.0 km s-1 Mpc-1, $\Omega_{M}=0.27$, and $\Omega_{\Lambda}=0.73$.

##  2 Sample

We selected our current sample of AGN from the 105-Month Swift-BAT All-sky
Hard X-Ray Survey111https://swift.gsfc.nasa.gov/results/bs105mon/ (Oh et al.,
2018). Compiled from almost nine years of observations, this survey has a
sensitivity of 8.40 x 10-12 erg s-1 cm-2 in the 14 – 195 keV band over 90% of
the sky with eight-channel spectra averaged over the 105 month duration of the
survey. However, AGN are known to be variable at all wavelengths (e.g., Huchra
et al., 1983; Ulrich et al., 1997; Peterson et al., 2004; Drake et al., 2009).
Therefore, in order to avoid issues caused by changing spectral shapes over
the duration of the BAT 105-month survey, we restrict our analysis to sources
with simultaneous XMM-Newton and NuSTAR observations. While the BAT data is
stacked over several years, the earlier analyses of de Rosa et al. (2008) and
Ricci et al. (2011) using stacked INTEGRAL data provide a pathway for a
similar analysis with more sensitive and higher S/N hard X-ray data from the
Swift BAT. From the larger set of 1099 objects classified in the BAT 105-month
survey as Seyferts, ‘Unknown AGN’, and ‘Beamed AGN’, we found 42 objects that
had simultaneous XMM-Newton and NuSTAR observations with good quality data.

Within this larger group of objects, we exclude several from our analysis,
mainly due to known high amplitude spectral variability that caused offsets
between the simultaneous XMM-Newton and NuSTAR data from the stacked BAT data.
For NGC 3783, the line-of-sight column density is known to have changed
significantly over time and therefore does not fit the assumptions of our
simple models (Mao et al., 2019). NGC 1566 is a known changing-look AGN
(Parker et al., 2019), and it is likely that our simple model cannot capture
the more complex physics occurring in this object. Mrk 335 has been shown to
have long-term spectral trends in its X-ray light curves (Grupe et al., 2012).
NGC 1365 is known to have variable line-of-sight absorption, with changes on
sub-day timescales (Rivers et al., 2015). The spectral shape of Mrk 1044 is
variable over the period of the BAT observations (Mallick et al., 2018).
Additionally, for Mrk 1044 we find that when fitting the 2013 XMM-Newton and
2018 XMM-Newton spectra, we find a significant change in photon index, from
$2.36\pm 0.04$ in 2013 to $3.27\pm 0.01$ in 2018, and thus does not fit our
assumptions. 1H 0323+342 is variable in both X-ray flux and hardness ratio
over time, suggesting a changing spectral shape (Mundo et al., 2020).
1H0419-577 is variable in both X-ray flux and spectral shape over time, in
addition to a strong soft excess (Fabian et al., 2005; Jiang et al., 2019).
Fairall 49 shows large spectral variability even on short timescales (Iwasawa
et al., 2016). Finally, NGC 5548 is variable on roughly day timescales with
significant changes in spectral parameters (e.g., Chiang et al., 2000).

Additionally, there were several BAT AGN with simultaneous XMM-Newton and
NuSTAR data that we excluded from our sample due to low S/N data. As NuSTAR
data links the low and high energy data, it fundamentally drives our ability
to neatly constrain parameters. Therefore we impose a cutoff of 4000 counts in
the NuSTAR band, below which we do not include an object in our sample. With
fewer than 4000 NuSTAR counts, the constraints on fundamental parameters
become poor, either with uncertainties several times larger than the rest of
the sample or with a large number of upper/lower limits. The AGN excluded due
to low NuSTAR counts were 3C 234.0, IC 588, IC 751, NGC 3718, AM 0224-283,
SDSS J103315.71+525217.8, ESO 244-IG 030, and ESO 317- G 041.

While we only include AGN with simultaneous XMM-Newton and NuSTAR
observations, there may be other objects in the BAT 105-Month Survey that have
reasonably constant spectral shapes, and therefore the analysis presented in
this paper could be applied to them even with XMM-Newton and NuSTAR
observations at different times. Thus by requiring simultaneous observations,
our selection criteria likely biases our sample towards well-studied and/or
bright AGN.

For each object we used the NASA/IPAC Extragalactic
Database222https://ned.ipac.caltech.edu/ (NED; Helou et al., 1991) to
determine the classification and redshift of each AGN. Throughout the paper,
we group our sources into Seyfert 1 - 1.9 objects and Seyfert 2 objects. We
also used the High Energy Astrophysics Science Archive Research Center
(HEASARC) nH calculator (HI4PI Collaboration et al., 2016) to compute the
Galactic column density along the line of sight. This allowed us to fit for
the column density of the AGN host galaxy separately from the column density
contribution of the Milky Way.

##  3 Methods

###  3.1 Data Acquisition and Reduction

The data for this paper were obtained from the various archives corresponding
to the different telescopes used. The XMM-Newton Science
Archive333http://nxsa.esac.esa.int/nxsa-web/#search has reduced spectra for
each of the point sources in the observed FOV. For our XMM-Newton MOS and PN
spectra, we used the spectra for the central AGN point source. We used the
corresponding background and ancillary files from the XMM-Newton Science
Archive in addition to the appropriate canned response functions.

We obtained NuSTAR data from the HEASARC Browse
server444https://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3browse.pl. For the
NuSTAR observations, we ran the nuproducts function on the cleaned event files
to create appropriate spectral, background, ancillary, and response files. The
source and background extraction regions varied slightly for each object but
in general the source regions had radii of $\sim 1$ arcminute and the
background region was an annulus with outer radius of 4 - 5 arcminutes with
the corresponding source region subtracted. The source regions were centered
on the AGN. Whenever possible, the background region was an annulus centered
on the AGN. Otherwise, the background region was a source-free circle of 4 - 5
arcminutes in radius.

For our Swift BAT spectra, we used the stacked spectra for the 105 month
duration of Swift observations from the 105-Month Swift-BAT All-sky Hard X-Ray
Survey. In addition, a response matrix appropriate for all the BAT spectra was
used. For reproducibility, we list the observation ID numbers for the AGN in
our sample in Table 1.

Table 1: XMM-Newton, NuSTAR, and Swift BAT observation identification numbers for the sources in our sample. Object | BAT ID | XMM-Newton ID | NuSTAR ID
---|---|---|---
Mrk1501 | 8 | 0795620101 | 60301014002
Mrk1148 | 36 | 0801890301 | 60160028002
Fairall9 | 73 | 0741330101 | 60001130003
Mrk359 | 77 | 0830551001 | 60402021006
NGC931 | 129 | 0760530201 | 60101002002
NGC1052 | 140 | 0790980101 | 60201056002
NGC1068 | 144 | 0740060401 | 60002033002
3C109 | 212 | 0795600101 | 60301011002
3C120 | 226 | 0693781601 | 60001042003
Ark120 | 266 | 0721600401 | 60001044004
ESO362-18 | 269 | 0790810101 | 60201046002
Mrk3 | 325 | 0741050101 | 60002049002
IRAS09149-6206 | 447 | 0830490101 | 60401020002
NGC3227 | 497 | 0782520201 | 60202002002
NGC3998 | 579 | 0790840101 | 60201050002
NGC4151 | 595 | 0679780301 | 60001111005
Mrk766 | 608 | 0763790401 | 60101022002
3C273 | 619 | 0414191101 | 10002020003
NGC4579 | 1409 | 0790840201 | 60201051002
NGC4593 | 631 | 0740920201 | 60001149002
NGC4785 | 1411 | 0743010101 | 60001143002
Mrk273 | 1430 | 0722610201 | 60002028002
Mrk841 | 753 | 0763790501 | 60101023002
Mrk1392 | 754 | 0795670101 | 60160605002
3C382 | 984 | 0790600101 | 60202015002
SwiftJ2127.4+5654 | 1111 | 0693781801 | 60001110005
IIZw171 | 1143 | 0795620201 | 60301015002
NGC7314 | 1157 | 0790650101 | 60201031002
Mrk915 | 1161 | 0744490401 | 60002060002
MR2251-178 | 1172 | 0763920601 | 60102025004
NGC7469 | 1182 | 0760350801 | 60101001014
Mrk926 | 1183 | 0790640101 | 60201029002
NGC7582 | 1188 | 0782720301 | 60201003002

###  3.2 Spectral Fitting

We fit our spectra using version 12.10.1f of XSPEC (Arnaud, 1996). We used two
methods to fit the AGN in our sample. The choice of which model to use
depended on which better fit the soft X-ray emission. The first approach,
which generally worked for Type 1 AGN is a continuum comprised of a blackbody
and an exponentially cut-off power law with reflection, photoelectric
absorption, and a nominal Fe K$\alpha$ line:
constant$\times$TBabs$\times$TBabs$\times$(pexrav+zbbody+zgauss). The second,
which generally worked for Type 2 AGN, is a continuum comprised of an
exponentially cut-off power law with reflection, photoelectric absorption with
a variable covering fraction, and a nominal Fe K$\alpha$ line:
constant$\times$TBabs$\times$TBpcf$\times$(pexrav+zgauss). Generally we fit
the spectra between 0.5 keV and the upper end of the BAT bandpass. For some
sources, we ignored below certain energies mainly to avoid the effects of a
strong soft X-ray component or significant line emission over the soft X-ray
bandpass. The Appendix details sources for which the fitted energy range
begins above 0.5 keV. Using the estimated pile-up fractions from the XMM-
Newton spectral reductions, we find no sources with a pile-up fraction above
2%, with the mean and median fractions below 1%. None of our sources are
bright enough for significant NuSTAR pile-up.

For each approach, the constant allowed for an offset between the different
telescopes and instruments used in our analysis. To constrain absorption, we
used TBabs assuming the abundances of Wilms et al. (2000). By using two
separate absorption components, with one frozen to the Galactic value, we can
constrain the column density in the AGN host galaxy. The pexrav component
(Magdziarz & Zdziarski, 1995) is an exponentially cut off power law reflected
off of neutral material. While this “simple” model may not perfectly
encapsulate the detailed physics behind this emission, it works well for the
varying S/N of our data and provides us with constraints on the fundamental
parameters we wish to measure. The zgauss component was used to fit the Fe
K$\alpha$ line.

As mentioned previously, the salient difference between the two approaches is
the parameter corresponding to the soft X-ray emission. The zbbody component
is a redshifted blackbody, which, while it may not be an accurate physical
description of the soft excess, fits the emission well in most cases (e.g.,
Jiang et al., 2018). The TBpcf parameter is a partial covering model, where
clouds of gas in our line of sight absorb some fraction of the light from the
AGN. Some Seyfert 1 - 1.9 objects were fit using the partial covering model
rather than the blackbody model based on the existence of line emission in the
soft X-ray suggesting an ionized absorber. As the goal of our paper is to
characterize these sources with simple phenomenological models, we prioritize
a uniform approach that works rather than finding the best fit for each object
with more complex models.

As opposed to pexmon, where the Fe K$\alpha$ line is included as part of the
model, we fit the Fe K$\alpha$ line as a separate Gaussian component. We
consider the partial covering model to be phenomenological in that it well
describes objects not only with partial covering but independent soft
components due to photoionized gas emission due to star formation and X-ray
binaries. It is only in the very highest S/N observations that X-ray CCD data
can constrain such physical components. Thus, for the sake of uniformity we
have not added the other possibilities.

To estimate uncertainties on our best-fit values, we used the XSPEC routine
steppar to find the 90% confidence interval ($\Delta\chi^{2}=2.706$). For
several of our objects we ran a Markov Chain Monte Carlo program in XSPEC for
comparison. We found that in some cases, the two approaches yielded similar
uncertainties, but for others the MCMC uncertainties were significantly
smaller than those obtained using steppar. Thus, to avoid underestimating our
uncertainties, we used steppar for the remainder of our analysis.

Figure 1: Left panel: Histogram of hard X-ray luminosity in the 14 -195 keV
band as measured by the Swift BAT. In each panel Seyfert 1 - 1.9 objects are
shown in blue and Seyfert 2 AGN are shown in red. Seyfert 2 AGN are less
luminous than the Seyfert 1 - 1.9 AGN. Middle panel: Histogram of host galaxy
redshift. The large majority of AGN are local with z < 0.1. Right panel:
Histogram of central supermassive black hole mass, which is relatively flat.

###  3.3 Physical Parameters of Sample

Whenever possible, we obtained black hole masses for the objects in our sample
from BASS (BAT AGN Spectroscopic Survey; Koss et al., 2017; Ricci et al.,
2017). Unfortunately BASS only included parameters for the Swift BAT 70-Month
Hard X-ray Survey555https://swift.gsfc.nasa.gov/results/bs70mon/, which does
not include some of the objects in this paper. When not in BASS, we found
black hole masses in the literature if possible. In this pursuit, we made use
of the AGN Black Hole Mass Database (Bentz & Katz, 2015), to search for well-
studied AGN with virial masses. For several of the AGN, there were no
published black hole masses. We next searched the literature for velocity
dispersion measurements and applied the M-$\sigma$ relation of Gültekin et al.
(2009). Finally, if none of these were possible, we applied the scaling
relation between bulge near-infrared (NIR) luminosity and SMBH mass of Marconi
& Hunt (2003). We assumed that the AGN contributes 33% of the total flux in
the 2MASS passbands (the median value in Burtscher et al., 2015).

For each of the sources in our sample, we compute the bolometric luminosity
from the 14 - 195 keV luminosity following Winter et al. (2012). The Eddington
ratios were calculated using these bolometric luminosities and the appropriate
black hole mass. Three of the objects in our sample, 3C 109, 3C 273 and
MR2251-178, were found to be super-Eddington. For the case of 3C 109 however,
we note that recent X-ray analysis has called the virial SMBH mass into
question (Chalise et al., 2020). Additionally, the black hole mass for
MR2251-178 comes from NIR scaling relations, so the super-Eddington ratio
found here is tenuous. Several of the AGN in our sample have Eddington ratios
below $1\times 10^{-3}$, where there is a predicted change in the nature of
accretion and where transitions between high and low states in galactic black
holes are often seen (e.g, Merloni et al., 2003; Done et al., 2007). We note
that these objects do not appear to have anomalous properties compared to the
entire sample.

Distributions of the key physical parameters of our sample are shown in Figure
1. These are the hard X-ray luminosity (in the 14 - 195 keV band), redshift,
and black hole mass. The luminosities of the AGN in our sample range over 5
orders of magnitude, with Seyfert 2 objects tending to have lower
luminosities, consistent with the properties of the entire BAT sample (Ricci
et al., 2017). The overwhelming majority of the AGN in our sample are nearby,
with a redshift of less than 0.1. Only two AGN in our sample are at higher
redshift: 3C 109 (z = 0.3056) and 3C 273 (z = 0.1583). The black hole masses
in our sample are roughly evenly distributed between $10^{6.3}$ and $10^{9.0}$
M$\odot$, with no significant difference between Seyfert 1 - 1.9 and Seyfert 2
AGN.

It is important to note that the available black hole masses in the literature
are often derived using different methods. While we include references and
calculated uncertainties for the black hole masses when possible, this likely
introduces noise into any of our attempts to look at correlations with black
hole mass. For instance, Guo et al. (2020) suggest that AGN variability can
introduce a $\sim 0.3$ dex scatter in single epoch SMBH masses. We mitigate
these issues as much as possible by calculating bolometric luminosity and
Eddington ratio using a consistent approach.

##  4 Results

###  4.1 Coronal Parameters

With our phenomenological model we are able to derive a number of fundamental
parameters for the X-ray emitting corona. These include the photon index,
folding energy, and reflection coefficient. Additionally, we obtain
constraints on line of sight column density, equivalent width of the Fe
K$\alpha$ line, and soft excess parameters. In this section we will summarize
our results, look for correlations between parameters, and note the
differences between the Seyfert 1 - 1.9 and Seyfert 2 classes of objects in
our sample. Table 2 lists the results of using Kendall $\tau$ test to search
for correlations between various parameters. Table 3 shows the results of a
K-S test (Massey, 1951) comparing the Seyfert 1 - 1.9 and Seyfert 2 classes of
AGN. Table 4 lists the properties of the AGN in our sample as well as physical
and fundamental parameters of the X-ray corona. Unless otherwise stated,
errors and limits in this paper are reported to the 90% confidence level.

Figure 2: Upper left panel: Histogram of photon index and corresponding
cumulative distribution function. In each panel Seyfert 1 - 1.9 objects are
shown in blue and Seyfert 2 AGN are shown in red. The value of P[null] from
the K-S test indicates that the distributions of photon index for the
different Seyfert classes are likely to be drawn from different distributions.
Upper right panel: Histogram of the logarithm of the folding energy and
corresponding cumulative distribution function for constrained values only.
Lower left panel: Histogram of the reflection coefficient and corresponding
cumulative distribution function. Lower right panel: Histogram of the
logarithm of the Eddington ratio and corresponding cumulative distribution
function. The Seyfert 2 AGN have significantly lower Eddington ratios than the
Seyfert 1 - 1.9 objects as indicated by the K-S test.

Figure 2 shows the distributions of photon index, folding energy, reflection
coefficient, and Eddington ratio separated into Seyfert 1 - 1.9 and Seyfert 2
classes. For each of these parameters we use the K-S test to compute the
probability of the null hypothesis that the samples are drawn from the same
distribution. There are two parameters for which the Seyfert 1 - 1.9 and
Seyfert 2 objects show significantly different distributions. These are the
photon index and the Eddington ratio. The Seyfert 2 galaxies tend to have
harder spectral slopes than the Seyfert 1 - 1.9 galaxies, consistent with the
entire BAT sample (Ricci et al., 2017). The Eddington ratios of Seyfert 2 AGN
is lower than for Seyfert 1 - 1.9 galaxies, consistent with previous results
(e.g., Marinucci et al., 2012). The Eddington ratio difference is also
supported by the recent discoveries of optical changing-look AGN, where as the
source brightens emission lines become broader, which has been suggested to be
a result of an increased accretion rate (e.g., Shappee et al., 2014; Denney et
al., 2014; Yang et al., 2018).

The median column density for our sample was $3.6\times 10^{20}$ cm-2,
including physically reasonable upper limits. For some of our objects, the
best-fit column density was extremely low, so we froze it to $1\times 10^{19}$
cm-2 (a physically plausible limit) when fitting for the other parameters. The
median column density for Seyfert 1 - 1.9 objects was $1.1\times 10^{20}$
cm-2. This is less than the median column density for Seyfert 2 galaxies,
which was $37.4\times 10^{22}$ cm-2. This is as expected, as the unified model
of AGN (e.g., Antonucci, 1993) suggests that our line of sight to the central
SMBH in Seyfert 2 galaxies is obscured by a dusty torus. The K-S test between
the two Seyfert classes yields a p-value of $5.5\times 10^{-3}$, supporting
this conclusion. Similarly, as expected, all of the objects for which the
measured column density was consistent with zero were Seyfert 1 - 1.9
galaxies. Only one of the AGN in our sample, NGC 1068, is Compton thick, with
a column density of $(7.40^{+0.54}_{-0.62})\times 10^{24}$ cm-2.

The median photon index for our sample was $1.72$. Figure 2 shows that the
distribution of photon indices is consistent with those expected from
Comptonization (Zdziarski, 1985). As seen in previous work (e.g., Ricci et
al., 2017), the median photon index is slightly harder for the Seyfert 2s in
our sample, $1.46$, as compared to $1.77$ for the Seyfert 1 - 1.9 AGN. This
can additionally be seen in Figure 2, where the K-S test indicates that the
photon indices for the different Seyfert classes may be drawn from different
distributions, with a p-value of $7.5\times 10^{-3}$.

For a large majority of our sample (30 out of 33 objects), we are able to
constrain the folding energy rather than simply obtaining a lower limit. The
median constrained folding energy for our sample was $112.6$ keV, somewhat
higher than the median lower limit of $53.0$ keV. The minimum and maximum
constrained folding energies were $28.4^{+7.7}_{-4.0}$ and
$700.2_{-122.7}^{+187.8}$ keV respectively, indicating the very wide range of
this parameter and its fractional uncertainties. Figure 3 shows the
distribution of folding energies, both for constrained values and lower
limits. As expected from observations of the cosmic X-ray background (Gilli et
al., 2007), they tend to cluster below approximately 300 keV. This is
consistent with what has been seen in previous studies (Ghisellini et al.,
1993; Stern et al., 1995; Fabian et al., 2015). Figure 2 indicates that there
is no clear separation in the distributions of Seyfert 1 - 1.9 and Seyfert 2
AGN with respect to folding energy. Interestingly, the lower limits on folding
energy are disproportionately found for Seyfert 2s. Two of the seven Seyfert 2
AGN in our sample have lower limits on folding energy, as compared to one of
twenty-seven for the Seyfert 1 - 1.9 objects. We suspect this is due to the
smaller effective bandpass over which Seyfert 2 AGN are fit due to the high
columns, thus allowing more uncertainty in the other derived parameters
(photon index and reflection coefficient).

Figure 3: Histogram of the logarithm of the folding energies. The purple bars
represent values of the folding energies that were constrained in the fit. The
green bars are lower limits for those objects for which the folding energy
could not be constrained. The lower limits on folding energy lie at slightly
lower values than the constrained energies. The majority of objects have
folding energies less than 300 keV and there are no objects with limits above
1022 keV (twice the electron rest mass).

The reflection coefficient from our fit represents the solid angle of material
that the X-rays in the reflection hump see, in units of pi. The median
reflection coefficient for our sample was $0.41$, including physically
reasonable upper limits. For some of our objects, the best-fit reflection
coefficient was extremely low, so we froze it to 0.001 when fitting for the
other parameters. While some of these objects still have a detected Fe
K$\alpha$ line, this is likely either due to a high Fe abundance or material
with a low Compton optical depth but a moderate column density. A K-S test of
the reflection coefficients gives a p-value of $0.48$ indicating that the
distributions of Seyfert 1 - 1.9 and Seyfert 2 reflection coefficients are
statistically consistent. This is surprising, as the column density
distributions are different and some models link these variables (e.g., Murphy
& Yaqoob, 2009). Similar to the folding energy, upper limits on reflection
coefficient are found more often for Seyfert 2 AGN (4/7) than Seyfert 1 - 1.9
(7/26) objects. The constrained reflection coefficients for the AGN in our
sample are qualitatively similar to previous results in the literature (e.g.,
Zdziarski et al., 1999; Vasylenko et al., 2015; Lubiński et al., 2016; Lanz et
al., 2019).

To study the relationship between physical size and luminosity, we calculate
the compactness parameter (Guilbert et al., 1983; Fabian et al., 2015) If
present, we use the gravitational radii presented in Fabian et al. (2015), and
otherwise followed their assumption that the radius of the X-ray emitting
region is ten gravitational radii. The median compactness parameter was 16,
with a minimum value of $8.0\times 10^{-3}$ and a maximum value of 767. We
compute the electron temperature using $kT_{e}=E_{fold}/2$ and the
corresponding $\Theta=kT_{e}/m_{e}c^{2}$ (Petrucci et al., 2001; Fabian et
al., 2015; Middei et al., 2019). While this scaling between folding energy and
electron temperature is dependent on optical depth (with the above appropriate
for optical depths less than one), the S/N of many of our objects is not high
enough to directly fit for electron temperature using a Comptonization model.
In Figure 4 we compare the compactness to $\Theta$. As expected, the majority
of sources lie along the $e^{-}-e^{-}$ coupling line (Ghisellini et al., 1993;
Fabian et al., 2015) and below the pair balance line for a slab geometry
(Stern et al., 1995; Fabian et al., 2015). This indicates the importance of
pair production in regulating the X-ray corona of AGN and the resulting
spectral shape (Fabian et al., 2015). Only two of the AGN in our sample lie
above the slab line, with one having a lower limit on the electron
temperature, potentially indicating poor constraints on the underlying
Comptonized spectrum.

Figure 4: Compactness as compared to electron temperature. The blue circles
represent Seyfert 1 through Seyfert 1.9 classifications and the red diamonds
are Seyfert 2 galaxies. The gray dashed line is the e-e coupling line from
Ghisellini et al. (1993) and the black dotted line is the expectation for a
slab geometry (Stern et al., 1995). The majority of our sample lies below the
slab line (Stern et al., 1995), with only one AGN with a constrained folding
energy lying above the slab line.

###  4.2 Soft Excess Parameters

While not the primary focus of our analysis, for most of our AGN it is
necessary to include a model component to fit for the soft excess. This
allowed us to properly constrain the higher energy portion of the spectrum
from which the information on photon index, folding energy, and reflection
coefficient are derived. Similarly, we include a redshifted Gaussian in our
model to fit the strong Fe K$\alpha$ line. We have recorded each of the best
fit soft excess and Fe K$\alpha$ line parameters and present them in Table 5.

As detailed in Section 3.2, we fit the soft X-ray emission of the AGN in our
sample with two different approaches. The first was a redshifted blackbody.
This approach was mainly used for Seyfert 1 - 1.9 AGN. For this parameter we
recorded the temperature and the luminosity of the blackbody component. The
median temperature is $0.14$ keV, which is consistent with previous work using
this model (e.g., Gierliński & Done, 2004). The median luminosity of the
blackbody is log[L(erg s-1)] = $43.4$. As expected, this is significantly less
than the higher energy emission caused by IC scattering of softer photons.

The other approach we used to model the soft X-ray contribution was a partial
covering model. The median covering fraction for our entire sample was $0.93$.
For the Seyfert 1 - 1.9 objects, the median was $0.89$, lower that then median
covering fraction for the Seyfert 2 AGN at $0.94$, again expected from the AGN
unification model (Antonucci, 1993). The covering fractions for the AGN in our
sample are largely consistent with or slightly higher than previous results
(e.g., Mor et al., 2009; Ramos Almeida et al., 2011; Lanz et al., 2019; Zhao
et al., 2020a). Furthermore, the lower covering fractions for Seyfert 1 - 1.9
objects as compared to Seyfert 2s is in agreement with earlier studies, both
in the IR (Mor et al., 2009; Ramos Almeida et al., 2011) and the X-ray
(Lubiński et al., 2016). However, a K-S test for the Seyfert 1 - 1.9 and
Seyfert 2 AGN shows that the two classes are consistent with being drawn from
the same distribution with a p-value of $0.43$, possible due to the low number
of Seyfert 1 - 1.9 objects fit with this model.

###  4.3 Correlations Between Parameters

There exist many theoretically expected correlations between the X-ray corona
parameters and the physical properties of the AGN (e.g., Zdziarski et al.,
1999; Ricci et al., 2017; Tortosa et al., 2018). Some of these correlations
are based on the predicted geometries of the X-ray corona and the location of
X-ray emission. In addition, there are expected correlations between X-ray
properties and the driving physical parameters of the AGN such as mass of the
central SMBH and the Eddington ratio. In this section, we search for such
correlations and compare to previous analyses.

Table 2: Kendall $\tau$ correlation test values for different combinations of parameters. Throughout the paper, we consider correlations with p-values less than 0.05 as significant. Considering the $\sim 10$ correlations we search for in our study, if we make our threshold for significance 0.005, only the X-ray Baldwin effect and the correlation between photon index and reflection coefficient are recovered. The parameters are $\Gamma$ (photon index), Efold (e-folding energy), R (reflection coefficient), MBH (SMBH mass), $\lambda_{edd}$ (Eddington ratio), EW (Fe K$\alpha$ equivalent width), Lbol (bolometric luminosity), $\ell$ (compactness parameter), and NH (hydrogen column density). Parameter 1 | Parameter 2 | $\tau$ | p-value
---|---|---|---
$\Gamma$ | Efold | 1.97E-01 | 1.11E-01
$\Gamma$ | R | 3.64E-01 | 2.61E-03
$\Gamma$ | MBH |  $-$6.82E-02 | 5.90E-01
$\Gamma$ | $\lambda_{edd}$ | 1.29E-01 | 3.02E-01
$\Gamma$ | EW |  $-$2.61E-01 | 3.30E-02
$\Gamma$ | Lbol | 8.15E-02 | 5.05E-01
Efold | R |  $-$1.67E-01 | 1.79E-01
Efold | MBH | 1.52E-01 | 2.23E-01
Efold | $\lambda_{edd}$ | 7.58E-02 | 5.49E-01
Efold | $\ell$ | 4.92E-02 | 7.01E-01
R | EW | 1.02E-01 | 4.15E-01
EW | NH | 3.42E-01 | 5.28E-03
EW | Lbol |  $-$3.81E-01 | 1.84E-03
Figure 5: Folding energy as compared to the photon index. The blue circles
represent Seyfert 1 through Seyfert 1.9 classifications and the red diamonds
are Seyfert 2 galaxies. The purple pentagons are binned values of the folding
energy and the shading corresponds to 1$\sigma$ scatter on this binned point.
Figure 6: Reflection coefficient as compared to the folding energy. The blue
circles represent Seyfert 1 through Seyfert 1.9 classifications and the red
diamonds are Seyfert 2 galaxies. The purple pentagons are binned values of the
folding energy and the shading corresponds to 1$\sigma$ scatter on this binned
point.

For each combination of parameters, we used the Kendall $\tau$ correlation
test to look for evidence of correlations between the parameters, with the
results shown in Table 2. We chose to use this correlation test over the
Spearman correlation test, due to the robustness of the Kendall $\tau$ test to
smaller samples and outliers. We first did this with all our AGN in the
sample. If the corresponding p-value was larger than 0.05, we determined that
a correlation did not exist. However, considering the $\sim 10$ correlations
we search for in this study, if we make our threshold for significance 0.005,
of all the correlations found at a p-value of 0.05, only the X-ray Baldwin
effect and the relationship between photon index and reflection coefficient
are recovered. If this was the case, we repeated the Kendall $\tau$
correlation test on the Seyfert 1 - 1.9 and Seyfert 2 objects individually. If
there was a correlation between any sets of parameters, we used a Theil-Sen
estimator to find the slope of the correlation and 10,000 bootstrap iterations
with replacement to obtain uncertainties on the slope. By finding the median
slope between all pairs of values and computing our uncertainties from a
bootstrap approach, we are robust to outliers and limits in our data.
Additionally, we binned each of our combinations of parameters in four equal-
sized horizontal bins by taking the median of the vertical parameter and
plus/minus one sigma error bars. In the case of iron equivalent width (see
Section 4.4) we excluded the outlier NGC 1068 from our binning procedure to
ensure even sampling. These stacked points are shown in purple in our figures
to guide the eye, with shading corresponding to the uncertainties on the
stacked values.

Figure 5 shows a weak correlation between the photon index and folding energy,
albeit with large scatter. We note that the existence of a correlation between
these parameters has been found in other studies, but there is some dispute in
the literature as to whether this is a real correlation (e.g., Ricci et al.,
2017; Tortosa et al., 2017; de Rosa et al., 2008; Kamraj et al., 2018).
Additionally, the behavior of these two variables even for single AGN is not
fully understood (e.g., Kang et al., 2021). Answering these questions will
require even larger samples with broadband X-ray data similar to our sample,
since this correlation requires accurate estimates of the folding energy.

In Figure 6, we show the relationship between the reflection coefficient and
the folding energy. The objects with the highest reflection coefficients tend
to also have lower folding energies. At the highest values of folding energy,
above $\sim 100$ keV, the reflection coefficients are neatly collapsed onto a
sequence with values $\lesssim 1$.

Figure 7: Left panel: Photon index as compared to the SMBH mass, with no
strong correlation. The blue circles represent Seyfert 1 through Seyfert 1.9
classifications and the red diamonds are Seyfert 2 galaxies. Right panel:
Photon index as compared to the Eddington ratio, again showing no correlation.
The purple pentagons are binned values of the photon index and the shading
corresponds to 1$\sigma$ scatter on this binned point. In both cases, the
correlations seen in the Seyfert 2 AGN are stronger than the the Seyfert 1 -
1.9 AGN, but still not significant.

It is expected that AGN coronal parameters should be correlated with driving
physical parameters such as the SMBH mass and Eddington ratio. Figure 7 shows
the derived photon indices versus the SMBH masses and Eddington ratios. We do
not find any correlations with photon index and either black hole mass or
Eddington ratio. In both cases, the Seyfert 2 AGN have a higher Kendall $\tau$
value, although neither yields a significant p-value.

Figure 8 shows the derived folding energies versus the SMBH masses and
Eddington ratios. When considering all the objects in our sample, there are no
strong correlations between the folding energy and these physical parameters.
However, if we only look at Seyfert 2 objects, there is a weak positive
correlation between folding energy and black hole mass and a moderate negative
correlation between folding energy and Eddington ratio, in agreement with
Ricci et al. (2018). Several of the objects with the highest values of folding
energy have near- or super-Eddington luminosities. Nonetheless, there is still
significant scatter in the folding energies even close to an Eddington ratio
of one. There appears to be a similar weak correlation in terms of black hole
mass, with the highest folding energies occurring in AGN with the highest
central SMBH masses.

Figure 8: Left panel: Folding energy as compared SMBH mass. Right panel:
Folding energy as compared to the Eddington ratio. In both panels, the blue
circles represent Seyfert 1 through Seyfert 1.9 classifications and the red
diamonds are Seyfert 2 galaxies. The purple pentagons are binned values of the
folding energy and the shading corresponds to 1$\sigma$ scatter on this binned
point. In both cases, the correlations seen in the Seyfert 2 AGN are stronger
than the the Seyfert 1 - 1.9 AGN, but still not significant.

Previous studies of AGN samples have found a power-law relationship between
reflection coefficient and the photon index, which has been interpreted as the
reflecting material being a source of soft photons that are IC scattered to
higher energies (e.g., Zdziarski et al., 1999; Beloborodov, 1999; Vasylenko et
al., 2015; Lubiński et al., 2016). We show this relationship in Figure 9 with
the power-law relationship of Zdziarski et al. (1999). We find a p-value of
$2.6\times 10^{-3}$ for this correlation. Our results qualitatively agree with
these previous studies, although the increase in reflection coefficients for
our sample begins at a slightly flatter photon index. All of the AGN for which
the reflection coefficients are higher than $\sim 2$ are sources with soft
spectra. This is consistent with recent studies (Ezhikode et al., 2020).

Figure 9: Reflection coefficient as compared to photon index. The blue circles represent Seyfert 1 through Seyfert 1.9 classifications and the red diamonds are Seyfert 2 galaxies. The black solid line and dashed lines are the best-fit power-law and corresponding uncertainties respectively from Zdziarski et al. (1999), which qualitatively agree with our results. The purple pentagons are binned values of the reflection coefficient and the shading corresponds to 1$\sigma$ scatter on this binned point. Table 3: Kolmogorov-Smirnov test results comparing the Seyfert 1 - 1.9 and Seyfert 2 AGN for the various parameters measured in our sample. Parameter | D | P[null]
---|---|---
$\Gamma$ | 6.65E-01 | 7.54E-03
Efold | 3.57E-01 | 3.81E-01
R | 3.30E-01 | 4.82E-01
NH | 6.76E-01 | 5.46E-03
fcvr | 5.50E-01 | 4.29E-01
MBH | 4.29E-01 | 1.90E-01
$\lambda_{edd}$ | 8.85E-01 | 5.62E-05
Lbol | 5.99E-01 | 2.13E-02
$\ell$ | 8.46E-01 | 1.65E-04
EKα | 2.75E-01 | 6.99E-01
$\sigma_{K\alpha}$ | 2.91E-01 | 6.26E-01
EW | 7.31E-01 | 2.35E-03

###  4.4 Iron K$\alpha$ Line Characteristics

The fluorescent Fe K$\alpha$ line is produced by the reprocessing of radiation
by material near the central SMBH (e.g., Matt et al., 1991; Sulentic et al.,
1998). The location of Fe K$\alpha$ line production very close to the SMBH is
supported by its broad profile and evidence of general relativistic effects
(e.g. Fabian et al., 2000; Reynolds & Nowak, 2003; Reynolds & Fabian, 2008).
For many of the AGN in our sample, it was possible to constrain the energy and
width of the Fe K$\alpha$ line. For Mrk 1448 and 3C 273, the objects that did
not have a clear Fe K$\alpha$ line and for which we could not constrain a line
width, we froze the energy at a rest-frame energy $6.403$ keV and width at
$0.1$ keV and fit for the normalization. It should be noted that if there is
an intrinsically broad line that is undetected in these objects, our limits
obtained with a narrow line will be underestimated (Reynolds & Fabian, 1997).
All of the objects for which we had to freeze a line energy were Seyfert 1 -
1.9 AGN.

The median energy of the Fe K$\alpha$ line was $6.41$ keV, slightly blue-
shifted from the rest energy of $6.403$ keV, but consistent with the
calibration of the XMM-Newton detectors. Using a K-S test, the Fe K$\alpha$
line energies are consistent between the two classes with a p-value of $0.70$.
The median line width in our sample was $0.11$ keV. Again, the line widths of
the Seyfert 1 - 1.9 and Seyfert 2 classes are consistent based on a K-S test.
Each class of AGN has objects whose line widths were consistent with zero,
suggesting either an extremely narrow or weak Fe K$\alpha$ line.

Figure 10: Left panel: EW as compared to the reflection coefficient. The blue
circles represent Seyfert 1 through Seyfert 1.9 classifications and the red
diamonds are Seyfert 2 galaxies. Right panel: EW as compared to the column
density. The black solid line is the Theil-Sen estimator fit to the Seyfert 2
AGN and the dashed lines are plus/minus one sigma from our bootstrap runs.

To compare the strength of the Fe K$\alpha$ lines in our AGN, we measured the
equivalent width (EW). This allowed us to place constraints on the presence of
this emission even for the AGN where the fit did not converge on an energy for
the Fe K$\alpha$ line. The median EW for our entire sample was $110.2$ eV. The
Seyfert 1 - 1.9 AGN had generally weaker Fe K$\alpha$ emission, with a median
EW of $92.1$ eV. The Seyfert 2 AGN had stronger emission, at $259.2$ eV. The
EW distributions for these classes are distinct as show by the p-value of
$2.4\times 10^{-3}$ from a K-S test. In Figure 10, we compare the EW to the
reflection coefficient and column density. There is no correlation between EW
and reflection coefficient, but there is a positive correlation between EW and
the column density. We also find that the Seyfert 2 AGN tend to occupy
different regions of parameter space than the Seyfert 1 - 1.9 objects. There
is one outlier in our sample in terms of EW, NGC 1068 with an equivalent width
of 2875 eV. NGC 1068 also has highest column density of any of the objects in
our sample, over an order of magnitude higher than the next highest AGN. As is
shown in Figure 10, many of the objects with high EWs also have large
obscuration along the line of sight.

In Figure 11 we compare the EW of the Fe K$\alpha$ line to the bolometric
luminosity, calculated from the Winter et al. (2012) scaling of the the Swift
BAT 14 - 195 keV luminosity. Similar to Iwasawa & Taniguchi (1993) and Nandra
et al. (1997), we find a significant anti-correlation between the Fe K$\alpha$
line EW and X-ray luminosity. This relationship, otherwise known as the X-ray
Baldwin Effect, is the strongest correlation we find between any two
parameters in our sample, with a Kendall $\tau=-0.38$ and a corresponding
p-value of $1.8\times 10^{-3}$.

Figure 11: EW of the Fe K$\alpha$ line as compared to the bolometric
luminosity. The blue circles represent Seyfert 1 through Seyfert 1.9
classifications and the red diamonds are Seyfert 2 galaxies. The black solid
line is the Theil-Sen estimator fit to the Seyfert 2 AGN and the dashed lines
are plus/minus one sigma from our bootstrap runs. The purple pentagons are
binned values of the bolometric luminosity and the shading corresponds to
1$\sigma$ scatter on this binned point. Not shown in this plot is the outlier
NGC 1068, with an extremely large EW of 2875 eV.

In Figure 12 we compare the EW to the photon index. We find a weak, anti-
correlation between the photon index and the Fe K$\alpha$ line EW, although
this correlation is not recovered at the more stringent p-value of 0.005.
Additionally, many of the AGN with large equivalent widths have large
uncertainties on the photon index. It is worth noting that the photon index
and bolometric luminosity are not themselves correlated.

Figure 12: Photon index as compared to EW of the Fe K$\alpha$ line. The blue
circles represent Seyfert 1 through Seyfert 1.9 classifications and the red
diamonds are Seyfert 2 galaxies. The black solid line is the Theil-Sen
estimator fit to the Seyfert 2 AGN and the dashed lines are plus/minus one
sigma from our bootstrap runs. The purple pentagons are binned values of the
photon index and the shading corresponds to 1$\sigma$ scatter on this binned
point. Here we exclude the outlier NGC 1068, with an extremely large EW of
2875 eV.

###  4.5 Coronal Parameter Contours

In addition to obtaining constraints for the various coronal parameters
individually and looking for correlations between them, we also investigated
the covariance between the fundamental parameters. The combinations of
parameters examined here are the folding energy/photon index, folding
energy/reflection coefficient, and photon index/reflection coefficient. We
show this for three of our AGN, to illustrate several different
classifications of object and contour shapes.

In Figure 13 we plot the contours for the Seyfert 2 NGC 3227. For this object,
the contours are well-behaved, appearing as ellipses with relatively smooth
levels. There is only slight covariance between the sets of parameters.
Additionally, the sizes of the error bars on this source are small, indicating
a robust and good fit for this high S/N observation.

Figure 13: Left panel: Contours for the combination of folding energy and
photon index for NGC 3227. In each panel the best fit location is marked by
the black plus, with one, two, and three sigma contours shown in red, blue,
and gold respectively. Middle panel: Contours for the combination of folding
energy and reflection coefficient for NGC 3227. Right panel: Contours for the
combination of photon index and reflection coefficient for NGC 3227.

Next, in Figure 14 we show the same plots but for the Seyfert 1 NGC 7314. Here
there is noticeably more covariance between parameters, especially when one of
them is the folding energy. Unlike NGC 3227, the error bars on folding energy
are quite uneven, with the best-fit value lying towards the lower end of the
confidence interval. Despite the misshapen contours, the folding energy is
still constrained.

Figure 14: Left panel: Contours for the combination of folding energy and
photon index for NGC 7314. In each panel the best fit location is marked by
the black plus, with one, two, and three sigma contours shown in red, blue,
and gold respectively. Middle panel: Contours for the combination of folding
energy and reflection coefficient for NGC 7314. Right panel: Contours for the
combination of photon index and reflection coefficient for NGC 7314.

Finally, in Figure 15 we show the same plots for the Seyfert 1.2 Mrk 1501. For
this AGN, we can only obtain a lower limit on the folding energy.
Additionally, there are some jagged or sharp edges in the contours indicating
lower quality constraints on the parameters.

Figure 15: Left panel: Contours for the combination of folding energy and
photon index for Mrk 1501. In each panel the best fit location is marked by
the black plus, with one, two, and three sigma contours shown in red, blue,
and gold respectively. Middle panel: Contours for the combination of folding
energy and reflection coefficient for Mrk 1501. Right panel: Contours for the
combination of photon index and reflection coefficient for Mrk 1501.

##  5 Discussion

###  5.1 Inclusion of Stacked BAT data

When comparing our results to previous results (e.g., Ricci et al., 2017;
Tortosa et al., 2018; Zhao et al., 2020b), many using data from different
instruments and with varying assumptions, we find that our results are
generally consistent. The photon indices we obtain are usually within 10
percent of the values obtained in these studies. The folding energies are
largely consistent, and oftentimes the limits we obtain are considerably
smaller than in previous studies. In addition, for several objects, previous
results could not measure a folding energy while our analysis yields at least
lower limits for all our AGN. The reflection coefficients in our sample are
also roughly consistent, and we find fewer upper limits than previous
analyses. We should note though that in addition to using data from different
instruments, previous studies often use slightly different models. Table 6
lists our choice of model for each object studied here. This may affect the
best fit parameters we obtain as compared to results in the literature.

We additionally find that 29 out of our 33 objects are well-fit (reduced
$\chi^{2}<1.3$) by our simple models. When increasing the cutoff to a more
relaxed reduced $\chi^{2}$ of 1.5, we find that only one object, NGC 1068,
which has strong emission lines, has a higher reduced $\chi^{2}$. Some of the
objects did use a restricted energy range to avoid contamination by strong
emission lines in the soft X-ray, but nonetheless, these low reduced chi-
squared values indicate good fits in the energy range which determines the
free parameters (folding energy, photon index, and reflection coefficient) we
have focused on in this work.

The inclusion of the BAT data is crucial in constraining many of the
fundamental parameters describing the X-ray emitting corona. To quantify this,
we repeated our procedure for five AGN in our sample, with the Swift BAT data
removed. We then compared the uncertainties from the fits with and without the
BAT data. To test this over a range of different AGN types, we selected the
Seyfert 1.5 Mrk 841, the Seyfert 1s NGC 7314 and NGC 4593, the Seyfert 2 Mrk
3, and the radio-loud Seyfert 1 3C 120 to re-fit. The main parameters of
interest were the photon index, folding energy, and reflection coefficient.

When fitting only the XMM-Newton and NuSTAR data, we found that the
uncertainties on the photon index increased the least, by roughly 10% as
compared to when including the BAT data. This is to be expected, as
significant information on the spectral slope is contained in the bandpasses
covered by XMM-Newton and NuSTAR. All of the new photon indices were
consistent with the values obtained in our original fits.

The reflection coefficient was the second most affected parameter, with an
increase in the uncertainties by roughly 20%. Again, we found that while the
new errors were significantly larger, the values of the reflection coefficient
without the BAT data were consistent with the values obtained from our full
broadband fits. The one object with an upper-limit on the reflection
coefficient (Mrk 3) still had an upper-limit without the BAT data, but the
value of the limit was increased by 16%.

As expected, the folding energy was most affected by the inclusion of the BAT
data. On average, for these five objects, the uncertainties on folding energy
increased by a factor of 1.4 for the lower error bar and 3.7 for the upper
error bar as compared to including the BAT data. In two cases (NGC 7314 and
Mrk 3), the best-fit folding energies were roughly 25% lower, albeit still
consistent within uncertainties. Similarly, for Mrk 841, the new folding
energy was 60% higher than before, but consistent within uncertainties.
However, while with the BAT data, the folding energy was constrained for Mrk
841, without the BAT data, only a lower-limit was obtained. In the cases of
Mrk 841, NGC 4593, and Mrk 3, the upper error bars on the folding energy in
particular were multiple times those found when including the BAT data.

When we consider the fact that our approach yields results in rough agreement
with previous results, and our reduced uncertainties, we have shown that the
procedure of combining stacked BAT data with XMM-Newton and NuSTAR
observations is valid. This is unsurprising as it is a natural extension of
the earlier studies using stacked INTEGRAL data (de Rosa et al., 2008; Ricci
et al., 2011), the Rossi X-ray Timing Explorer (Rivers et al., 2013), and
shorter BAT datasets (Kawamuro et al., 2016).

With our small error bars and improved constraints on parameters like the
folding energy, we are able to continue the search for expected correlations
in greater detail. With our sample of 33 AGN with small errors, correlations
should be apparent. Some of these measured before, such as the X-ray Baldwin
effect (see Fig. 11) and the relationship between photon index and reflection
coefficient (see Fig. 9) are indeed significant in our sample. However,
correlations between fundamental corona parameters such as folding energy and
photon index and the physical parameters of the system, like the black hole
mass and Eddington ratio, are lacking even with the better constraints on all
the free parameters. For example, a correlation between the folding energy and
photon index is expected in thermal comptonization models from the analytic
expression for the slope in optical depth – electron temperature space. Our
small error bars here make this lack of correlation more stark than in
previous studies. Combining our analysis with the lack of expected
correlations found in other recent observational studies (e.g., Ricci et al.,
2017; Tortosa et al., 2018) suggests that such correlations are indeed absent.
This suggests that this set of free parameters might not be simply related to
the physics of the sources as expected. It also prompts the question of what
these lack of correlations mean in the context of our current understanding of
the X-ray corona?

###  5.2 Comparison with Black Hole Binaries

We find that our results are generally consistent with studies on
Comptonization in stellar mass black holes. When comparing our results on
compactness and electron temperature, we find our AGN parameters are roughly
consistent with those of Galactic black hole binaries (BHBs) (c.f. Fabian et
al., 2015). We also find that the values of electron temperature are roughly
consistent with well-studied BHBs (Burke et al., 2017; Banerjee et al., 2020),
although we find several AGN with higher temperatures. The range of Eddington
ratios is similar between the BHBs and our AGN, although the distribution of
BHB Eddington ratios may peak at lower values (Burke et al., 2017; Banerjee et
al., 2020). Additionally the gaps in Eddington ratio seen for BHBs is not seen
for our AGN. The reflection coefficients for our AGN on the lower end are
consistent with well-studied BHBs (Burke et al., 2017), but we have several
objects with significantly higher reflection coefficients, particularly those
with the softest spectra (see Fig. 9). Finally, the EW of the Fe K$\alpha$
lines between the BHBs and AGN are similar (Burke et al., 2017).

###  5.3 Detailed Measurements of AGN parameters

In Figure 4, we compared the electron temperature and compactness of our
sources to theoretical expectations. We found that the majority of sources
were below the lines from electron-electron pair annihilation and a slab
geometry. However, our electron temperatures are calculated using the simple
assumptions of Petrucci et al. (2001) and Fabian (2012) that
$\Theta=E_{fold}/2m_{e}c^{2}$. Additionally, when calculating the compactness
parameter, we follow the assumption that the radius of the emitting region is
10 gravitational radii unless the source has had more detailed measurements
(Fabian et al., 2015). This clearly introduces significant scatter into our
compactness measurements.

In the future, it will be imperative to constrain the sizes of AGN coronae
directly through gravitational lensing (e.g., Jovanović et al., 2008) and
X-ray timing analysis (e.g, Mohan & Mangalam, 2014). This will not only be
extremely valuable to understanding the structure of the X-ray corona, but
also to placing the results of spectral studies such as ours in the
appropriate context.

In this study we have also compared our best-fit parameters to physical
parameters of the AGN such as black hole mass and Eddington ratio. As
discussed previously, there is significant scatter in these values based on
the fact that the masses are derived from several different methods. Recently
there have been improvements in creating a consistent sample of black hole
masses, particularly through reverberation mapping (e.g., Bentz & Katz, 2015;
Fausnaugh et al., 2017). It will be important to obtain additional
measurements of black hole masses in a uniform manner to allow for direct
comparisons between physical and modeled parameters.

##  6 Conclusion

In this work we have combined Swift BAT data of 33 AGN in the Swift BAT 105
month survey with simultaneous XMM-Newton and NuSTAR observations. We have
used the simple pexrav model to obtain constraints on fundamental spectral
shape parameters such as the photon index, folding energy, and reflection
coefficient. We have also recorded soft excess, partial covering, and Fe
K$\alpha$ line characteristics. We note that the use of an empirical model
ignores much of the detailed physics driving the observed emission.
Nonetheless, we have shown our fits to be acceptable, and the lack of specific
choices on the underlying physics allows us to compare a broad sample of AGN
uniformly. We find that the uncertainties on our best-fit parameters are
significantly smaller than those in previously studies. In the case of the
folding energies, the uncertainties are roughly half those obtained without
the inclusion of the higher energy Swift BAT data in addition to NuSTAR.

We have compared the properties of the Seyfert 1 - 1.9 and Seyfert 2 AGN in
our sample and find that the Eddington ratio and photon index are the
parameters for which their distributions are significantly different. We have
recovered well-known relationships such as the one between reflection
coefficient and photon index (Zdziarski et al., 1999) and the X-ray Baldwin
effect (Iwasawa & Taniguchi, 1993; Nandra et al., 1997).

Despite the small statistical uncertainties for most of the parameters for the
bulk of the sample, we do not find strong correlations between coronal
temperatures, compactness, black hole mass and Eddington ratios. While
somewhat puzzling, this is consistent with previous work which had smaller
samples and larger uncertainties. This indicates that the fundamental physics
behind these Comptonization parameters is not yet understood. We hope that
this work will stimulate physical models which can be compared to the data. We
note that there is a wide range in effective folding energies which should be
taken into account in modeling the contribution of AGN to the X-ray background
and in calculating the effects of Comptonization on the continuum.

We are in the process of fitting Comptonization models such as compPS
(Poutanen & Svensson, 1996) to the high S/N data and our preliminary findings
show that this model can fit most of the sources – however there is a strong
correlation between the optical depth and electron temperature for many of the
sources, making direct comparisons of the folding energy and electron
temperature difficult. Alternatively the probability contours for the free
parameters y (the Comptonization parameter) and T are well behaved allowing
direct comparison.

In the late stages of preparing this manuscript, the Swift BAT 157 Month
survey666https://swift.gsfc.nasa.gov/results/bs157mon/ was released. This
expanded coverage will both increase the S/N of known AGN in our sample and
add additional sources for which a similar analysis can be conducted.
Additionally, while this study focused on AGN with simultaneous XMM-Newton and
NuSTAR observations, for sources with low variability it may be possible to
combine different epochs to increase S/N and the number of AGN for which such
an analysis can be done. Such studies with increased sample sizes and data
quality will be imperative to understanding if the lack of observed
correlations is a result of observational constraints or a sign of missing
physics in our understanding of AGN coronae.

## Acknowledgements

We thank the referee for helpful comments and suggestions that have improved
the quality of this manuscript. We thank Benjamin Shappee and Michael Tucker
for comments on the manuscript.

This research has made use of data and/or software provided by the High Energy
Astrophysics Science Archive Research Center (HEASARC), which is a service of
the Astrophysics Science Division at NASA/GSFC and the High Energy
Astrophysics Division of the Smithsonian Astrophysical Observatory. This
research has made use of the NASA/IPAC Extragalactic Database (NED), which is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration. We
acknowledge the use of public data from the Swift data archive.

## Data availability

The data underlying this article are available in the article and in its
online supplementary material.

Table 4: Spectral fit parameters of the objects in our sample, ordered by increasing right ascension. The references for black hole mass are as follows: (1) is Afanasiev et al. (2019), (2) is Koss et al. (2017), (3) is Denney et al. (2006), (4) is Lu et al. (2019), (5) is Oliva et al. (1999), (6) uses the M-$\sigma$ relation (Gültekin et al., 2009), (7) is Grier et al. (2012), (8) is Bentz et al. (2010), (9) is Bentz et al. (2009), (10) uses the NIR scaling of Marconi & Hunt (2003), (11) is Winter et al. (2010), (12) is Peterson et al. (1998), (13) is Peterson et al. (2004), (14) is U et al. (2013), (15) is Davis et al. (2019), (16) is Bentz et al. (2006), (17) is Ho et al. (2009), (18) is Walsh et al. (2012), (19) is McLure et al. (2006), (20) is Collier et al. (1998), (21) is Netzer et al. (1990), (22) is Peterson et al. (2002), (23) is De Marco et al. (2013), (24) is Kollatschny et al. (2014), (25) is Kaspi et al. (2000), (26) is Santos-Lleó et al. (1997). Object | Type | Redshift | log(M${}_{\textrm{BH}}$) | log($\lambda_{e}$) | n${}_{\textrm{H}}$ | $\Gamma$ | E${}_{\textrm{fold}}$ | R | $\ell$ |  $\chi^{2}$/d.o.f. | Ref.
---|---|---|---|---|---|---|---|---|---|---|---
|  |  | (M⊙) |  | (1022 cm-2) |  | (keV) |  |  |  |
Mrk1501 | S1.2 | 0.08934 | $8.07_{-0.17}^{+0.12}$ | $-0.43$ | $<2.90E-03$ | $1.77\pm 0.02$ | $>240.5$ | $0.089_{-0.086}^{+0.131}$ | $9.5E+01\pm 3.0E+00$ | 1.01 | 7
Mrk1148 | S1.5 | 0.06400 | $8.69\pm 0.18$ | $-1.44$ | $<2.00E-03$ | $1.82\pm 0.01$ | $100.6_{-9.1}^{+11.4}$ | $0.404_{-0.065}^{+0.064}$ | $1.0E+01_{-3.5E-01}^{+5.3E-01}$ | 1.01 | 1
Fairall9 | S1.2 | 0.04702 | $8.30_{-0.08}^{+0.12}$ | $-1.09$ | $<3.00E-03$ | $1.99\pm 0.01$ | $271.4_{-120.0}^{+528.6}$ | $0.962_{-0.165}^{+0.207}$ | $1.1E+01_{-8.6E-02}^{+1.6E-01}$ | 1.15 | 13,26
Mrk359 | S1.5 | 0.01739 | $7.03\pm 0.72$ | $-1.42$ | $<3.45E-03$ | $1.99\pm 0.01$ | $98.3_{-17.1}^{+25.7}$ | $3.05\pm 0.20$ | $1.6E+01_{-1.3E+00}^{+6.8E+00}$ | 0.90 | 2
NGC931 | S1 | 0.01665 | $7.64\pm 0.40$ | $-1.34$ | $2.66E-01_{-5.00E-03}^{+5.70E-03}$ | $1.75\pm 0.01$ | $141.8_{-27.1}^{+42.9}$ | $0.570_{-0.109}^{+0.117}$ | $1.6E+01_{-9.8E-01}^{+2.5E+00}$ | 1.21 | 23
NGC1052 | S2 | 0.00504 | $8.96\pm 0.29$ | $-4.16$ | $1.40E+01\pm 3.80E-01$ | $1.63_{-0.03}^{+0.04}$ | $374.7_{-211.1}^{+1522.0}$ | $<0.034$ | $3.5E-02_{-1.7E-03}^{+3.3E-03}$ | 1.15 | 2
NGC1068 | S2 | 0.00379 | $6.75\pm 0.08$ | $-2.13$ | $7.40E+02_{-5.37E+01}^{+6.20E+01}$ | $1.21_{-0.07}^{+0.13}$ | $28.4_{-4.0}^{+7.7}$ | $<0.002$ | $3.9E+00_{-6.6E-02}^{+7.9E-02}$ | 1.84 | 15
3C109 | S1.8 | 0.30560 | $8.30\pm 0.40$ | $0.15$ | $4.69E-01_{-3.16E-02}^{+3.56E-02}$ | $1.62\pm 0.03$ | $112.4_{-58.2}^{+62.1}$ | $<0.021$ | $3.0E+02_{-1.8E+01}^{+4.5E+01}$ | 1.03 | 19
3C120 | S1 | 0.03301 | $7.75\pm 0.04$ | $-0.56$ | $7.60E-03\pm 1.02E-03$ | $1.77\pm 0.01$ | $158.0_{-6.9}^{+7.5}$ | $0.273_{-0.018}^{+0.017}$ | $7.9E+01_{-7.0E-01}^{+7.2E-01}$ | 1.04 | 7,12,13,24
Ark120 | S1 | 0.03271 | $8.07_{-0.06}^{+0.05}$ | $-1.03$ | $<1.72E-03$ | $2.01\pm 0.01$ | $506.2_{-200.0}^{+813.8}$ | $0.985_{-0.121}^{+0.132}$ | $6.3E+01_{-1.9E+00}^{+1.7E+00}$ | 1.18 | 12,13
ESO362-18 | S1 | 0.01244 | $6.25\pm 0.16$ | $-0.35$ | $<1.60E-03$ | $1.46\pm 0.01$ | $88.8_{-24.6}^{+39.2}$ | $0.407_{-0.156}^{+0.209}$ | $3.4E+01_{-6.6E-01}^{+8.3E-01}$ | 1.42 | 10
Mrk3 | S2 | 0.01351 | $8.95\pm 0.30$ | $-2.42$ | $5.71E+01_{-2.68E+00}^{+3.53E+00}$ | $1.29\pm 0.14$ | $105.2_{-26.3}^{+10.8}$ | $<0.227$ | $1.3E+00_{-6.3E-02}^{+1.3E-01}$ | 1.06 | 2
IRAS09149-6206 | S1 | 0.05730 | $8.48\pm 0.06$ | $-1.32$ | $1.16E+00_{-5.40E-02}^{+5.50E-02}$ | $1.91\pm 0.04$ | $39.3_{-6.0}^{+9.1}$ | $2.04_{-0.39}^{+0.45}$ | $4.9E+00_{-3.4E-01}^{+1.0E+00}$ | 1.43 | 10
NGC3227 | S2 | 0.00386 | $7.18_{-0.88}^{+0.19}$ | $-2.00$ | $3.51E-02_{-2.43E-03}^{+9.83E-02}$ | $1.41\pm 0.01$ | $60.0_{-4.4}^{+4.5}$ | $0.302_{-0.068}^{+0.080}$ | $4.6E+00_{-4.0E-01}^{+2.5E-01}$ | 1.19 | 2
NGC3998 | S1 | 0.00350 | $8.91_{-0.10}^{+0.11}$ | $-4.88$ | $9.61E-02_{-6.33E-02}^{+1.55E-01}$ | $1.81_{-0.04}^{+0.05}$ | $115.0_{-38.6}^{+128.2}$ | $<0.230$ | $8.0E-03_{-1.6E-04}^{+2.3E-04}$ | 0.98 | 18
NGC4151 | S1.5 | 0.00332 | $7.55\pm 0.05$ | $-1.72$ | $1.03E+01_{-2.70E-01}^{+2.80E-01}$ | $1.67\pm 0.02$ | $177.4_{-13.3}^{+16.8}$ | $0.494_{-0.043}^{+0.048}$ | $7.6E+00_{-7.8E-02}^{+9.4E-02}$ | 1.16 | 16
Mrk766 | S1 | 0.01293 | $6.82_{-0.06}^{+0.05}$ | $-1.19$ | $4.43E-02_{-1.07E-02}^{+9.50E-03}$ | $1.96\pm 0.02$ | $124.5_{-40.2}^{+99.5}$ | $0.455_{-0.195}^{+0.225}$ | $7.9E+01\pm 2.9E+00$ | 1.25 | 8,9
3C273 | S1 | 0.15834 | $8.84_{-0.08}^{+0.11}$ | $0.67$ | $<1.45E-03$ | $1.67\pm 0.01$ | $700.2_{-122.7}^{+187.8}$ | $<0.034$ | $7.7E+02_{-1.2E+01}^{+2.3E+01}$ | 1.28 | 13,25
NGC4579 | S2 | 0.00506 | $7.77\pm 0.11$ | $-3.60$ | $3.62E-02_{-2.02E-02}^{+2.28E-02}$ | $1.72\pm 0.04$ | $67.4_{-15.5}^{+27.5}$ | $<0.195$ | $1.5E-01_{-3.4E-03}^{+4.4E-03}$ | 1.06 | 6,17
NGC4593 | S1 | 0.00900 | $6.88_{-0.08}^{+0.10}$ | $-1.01$ | $1.93E-02_{-1.93E-02}^{+2.27E-02}$ | $1.67\pm 0.03$ | $223.3_{-64.8}^{+137.0}$ | $0.193_{-0.122}^{+0.135}$ | $3.8E+01_{-6.7E-01}^{+1.0E+00}$ | 1.03 | 3
NGC4785 | S2 | 0.01227 | $7.99\pm 0.09$ | $-2.65$ | $3.74E+01_{-5.25E+00}^{+4.85E+00}$ | $1.46_{-0.38}^{+0.49}$ | $>53.0$ | $0.299_{-0.297}^{+0.797}$ | $9.9E-01_{-1.9E-02}^{+2.4E-02}$ | 1.01 | 5,6
Mrk273 | S2 | 0.03778 | $9.02\pm 0.04$ | $-3.11$ | $4.18E+01_{-7.94E+00}^{+7.28E+00}$ | $1.64_{-0.57}^{+0.38}$ | $>36.8$ | $1.24_{-0.99}^{+1.82}$ | $3.0E-01_{-2.7E-03}^{+2.9E-03}$ | 0.94 | 14
Mrk841 | S1.5 | 0.03642 | $8.76\pm 0.27$ | $-1.99$ | $<1.30E-02$ | $1.83\pm 0.01$ | $139.1_{-49.4}^{+142.2}$ | $0.776_{-0.239}^{+0.282}$ | $3.3E+00_{-1.5E-01}^{+2.8E-01}$ | 1.07 | 1
Mrk1392 | S1.8 | 0.03614 | $6.88\pm 0.14$ | $-0.40$ | $<1.10E-02$ | $2.11_{-0.06}^{+0.07}$ | $85.4_{-42.5}^{+414.6}$ | $4.68_{-2.05}^{+3.52}$ | $2.7E+01_{-5.2E-01}^{+6.5E-01}$ | 1.02 | 10
3C382 | S1 | 0.05787 | $8.01_{-0.05}^{+0.09}$ | $-0.33$ | $<3.00E-03$ | $1.72\pm 0.01$ | $163.4_{-33.8}^{+53.7}$ | $0.204_{-0.095}^{+0.103}$ | $1.2E+02_{-1.3E+00}^{+2.7E+00}$ | 1.06 | 4
SwiftJ2127.4+5654 | NLS1 | 0.01470 | $6.34\pm 0.19$ | $-0.38$ | $5.92E-03_{-1.76E-03}^{+1.74E-03}$ | $1.85\pm 0.01$ | $39.0_{-0.7}^{+0.8}$ | $1.83_{-0.040}^{+0.039}$ | $3.6E+01_{-2.2E+00}^{+1.1E+01}$ | 1.30 | 10
IIZw171 | S1 | 0.07000 | $7.33\pm 0.17$ | $-0.27$ | $<1.10E-02$ | $1.74\pm 0.04$ | $60.3_{-15.3}^{+28.9}$ | $<0.494$ | $3.1E+01_{-5.2E-01}^{+6.3E-01}$ | 1.13 | 10
NGC7314 | S1 | 0.00476 | $7.24\pm 0.56$ | $-2.18$ | $7.64E-01_{-8.80E-03}^{+9.00E-03}$ | $1.94\pm 0.01$ | $218.5_{-62.4}^{+138.3}$ | $0.715_{-0.121}^{+0.130}$ | $3.1E+00_{-2.3E-01}^{+8.2E-01}$ | 1.05 | 2
Mrk915 | S1 | 0.02411 | $7.76\pm 0.37$ | $-1.41$ | $1.36E+00_{-3.40E-02}^{+3.30E-02}$ | $1.38_{-0.03}^{+0.02}$ | $57.9_{-7.4}^{+11.2}$ | $<0.041$ | $1.4E+01_{-7.8E-01}^{+1.8E+00}$ | 1.05 | 2
MR2251-178 | S1.5 | 0.06398 | $7.82\pm 0.15$ | $0.05$ | $1.42E-01_{-5.00E-02}^{+4.85E-02}$ | $1.57\pm 0.03$ | $58.0_{-7.5}^{+9.5}$ | $<0.011$ | $5.4E+01_{-1.3E+00}^{+1.8E+00}$ | 1.11 | 10
NGC7469 | S1 | 0.01632 | $6.96\pm 0.05$ | $-0.61$ | $<1.90E-03$ | $1.94\pm 0.01$ | $112.8_{-21.9}^{+32.8}$ | $2.04_{-0.24}^{+0.26}$ | $8.7E+01_{-9.4E-01}^{+1.0E+00}$ | 1.17 | 13,20
Mrk926 | S1.5 | 0.04686 | $8.36\pm 0.02$ | $-0.75$ | $<4.65E-03$ | $1.70\pm 0.01$ | $172.8_{-26.4}^{+36.2}$ | $<0.051$ | $4.6E+01_{-2.1E-01}^{+2.2E-01}$ | 1.01 | 11
NGC7582 | S1 | 0.00525 | $7.67_{-0.08}^{+0.09}$ | $-2.37$ | $2.55E+01_{-6.10E-01}^{+6.30E-01}$ | $1.36_{-0.06}^{+0.07}$ | $72.8_{-9.9}^{+13.9}$ | $0.518_{-0.135}^{+0.174}$ | $1.9E+00_{-3.2E-02}^{+4.4E-02}$ | 1.08 | 15
Table 5: Soft X-ray emission and Fe K$\alpha$ line parameters for the objects in our sample. Object | kT | log(LBB) | Covering Fraction | Fe K$\alpha$ Energy | $\sigma$ | Fe K$\alpha$ Normalization | Fe K$\alpha$ EW
---|---|---|---|---|---|---|---
| (keV) | (erg s-1) |  | (keV) | (keV) | (photons cm-2 s-1) | (eV)
Mrk1501 | $2.03E-01_{-8.80E-03}^{+8.30E-03}$ | $43.5\pm 0.1$ | — | $6.33_{-0.08}^{+0.19}$ | $1.7E-01_{-1.3E-01}^{+2.8E-01}$ | $1.0E-05_{-3.7E-06}^{+6.4E-06}$ | 50.7
Mrk1148 | $1.41E-01\pm 2.40E-03$ | $43.8\pm 0.1$ | — | $6.40$ | $1.0E-01$ | $9.1E-06\pm 4.1E-06$ | 40.4
Fairall9 | $1.60E-01_{-3.00E-03}^{+4.00E-03}$ | $43.5\pm 0.1$ | — | $6.39\pm 0.02$ | $1.9E-01_{-5.4E-02}^{+6.4E-02}$ | $3.8E-05_{-5.0E-06}^{+5.7E-06}$ | 145.1
Mrk359 | $1.64E-01_{-4.30E-03}^{+4.40E-03}$ | $42.0\pm 0.1$ | — | $6.42_{-0.11}^{+0.05}$ | $<1.0E-01$ | $4.3E-06\pm 1.2E-06$ | 65.1
NGC931 | $6.66E-02_{-1.15E-03}^{+1.18E-03}$ | $43.7\pm 0.1$ | — | $6.44\pm 0.2$ | $1.4E-01_{-2.9E-02}^{+3.6E-02}$ | $3.8E-05_{-4.7E-06}^{+4.1E-06}$ | 136.1
NGC1052 | — | — | $0.93\pm 0.01$ | $6.40\pm 0.2$ | $5.8E-02_{-3.7E-02}^{+2.8E-02}$ | $1.4E-05_{-1.9E-06}^{+2.0E-06}$ | 140.6
NGC1068 | — | — | $0.88_{-0.01}^{+0.04}$ | $6.57\pm 0.01$ | $2.8E-01\pm 1.3E-02$ | $9.3E-04_{-2.2E-04}^{+1.3E-04}$ | 2875
3C109 | — | — | $0.98\pm 0.02$ | $6.60_{-0.12}^{+0.11}$ | $4.1E-01_{-1.6E-01}^{+2.4E-01}$ | $1.3E-05_{-3.8E-06}^{+5.3E-06}$ | 111.5
3C120 | $2.50E-01_{-3.20E-03}^{+2.90E-03}$ | $43.4\pm 0.1$ | — | $6.44\pm 0.03$ | $1.7E-01_{-4.2E-02}^{+5.6E-02}$ | $4.1E-05_{-4.2E-06}^{+3.8E-06}$ | 77.8
Ark120 | $1.54E-01_{-2.80E-03}^{+2.60E-03}$ | $43.5\pm 0.1$ | — | $6.50\pm 0.03$ | $4.1E-01_{-6.8E-02}^{+8.7E-02}$ | $8.9E-05_{-9.3E-06}^{+1.1E-05}$ | 218.1
ESO362-18 | $1.13E-01_{-1.80E-03}^{+1.70E-03}$ | $41.7\pm 0.1$ | – | $6.39\pm 0.01$ | $7.2E-02\pm 1.3E-02$ | $2.4E-05_{-1.3E-06}^{+1.4E-06}$ | 255.6
Mrk3 | — | — | $0.94\pm 0.01$ | $6.44\pm 0.03$ | $<7.1E-02$ | $9.1E-05_{-1.4E-05}^{+2.0E-05}$ | 309.4
IRAS09149-6206 | $1.26E-01_{-2.80E-03}^{+2.90E-03}$ | $45.1\pm 0.1$ | — | $6.40$ | $1.1E-01_{-3.8E-02}^{+3.6E-02}$ | $1.5E-05\pm 2.6E-06$ | 74.7
NGC3227 | — | — | $0.98_{-0.02}^{+0.63}$ | $6.41_{-0.01}^{+0.02}$ | $1.3E-01_{-2.3E-02}^{+2.8E-02}$ | $5.9E-05_{-4.8E-06}^{+5.2E-06}$ | 164.5
NGC3998 | — | — | $0.49_{-0.51}^{+0.21}$ | $<6.42$ | $<1.7E-05$ | $1.9E-06_{-1.5E-06}^{+1.7E-06}$ | 27.3
NGC4151 | — | — | $0.93\pm 0.01$ | $6.35_{-0.01}^{+0.02}$ | $6.8E-02_{-2.8E-02}^{+1.8E-02}$ | $1.5E-04_{-1.1E-05}^{+1.0E-05}$ | 88.4
Mrk766 | $7.50E-02_{-1.70E-03}^{+1.60E-03}$ | $43.0\pm 0.1$ | — | $6.55_{-0.14}^{+0.15}$ | $3.2E-01_{-1.5E-01}^{+1.8E-01}$ | $1.4E-05_{-4.9E-06}^{+5.5E-06}$ | 97.0
3C273 | $1.46E-01_{-2.80E-03}^{+2.70E-03}$ | $44.7\pm 0.1$ | — | $6.40$ | $1.0E-01$ | $1.5E-05_{-4.0E-06}^{+4.1E-06}$ | 17.0
NGC4579 | $1.54E-01_{-1.00E-02}^{+1.30E-02}$ | $41.0_{-0.1}^{+0.2}$ | — | $6.56\pm 0.06$ | $3.3E-01_{-6.7E-02}^{+8.2E-02}$ | $1.6E-05_{-2.5E-06}^{+2.7E-06}$ | 259.2
NGC4593 | $8.27E-02_{-6.22E-03}^{+5.51E-03}$ | $42.4\pm 0.1$ | — | $6.43\pm 0.04$ | $1.0E-01_{-6.7E-02}^{+9.5E-02}$ | $3.6E-05_{-7.5E-06}^{+8.7E-06}$ | 148.8
NGC4785 | — | — | — | $6.35\pm 0.06$ | $1.4E-01_{-8.8E-02}^{+9.3E-02}$ | $9.5E-06_{-2.5E-06}^{+3.3E-06}$ | 316.1
Mrk273 | — | — | $0.95_{-0.02}^{+0.06}$ | $6.37_{-0.21}^{+0.14}$ | $<5.2E-01$ | $6.4E-06_{-3.8E-06}^{+7.8E-06}$ | 197.8
Mrk841 | $8.67E-02_{-2.15E-03}^{+2.13E-03}$ | $43.5\pm 0.1$ | — | $6.42_{-0.07}^{+0.06}$ | $1.5E-01_{-7.5E-02}^{+1.3E-01}$ | $1.3E-05_{-3.5E-06}^{+4.5E-06}$ | 87.9
Mrk1392 | $7.91E-02_{-1.41E-02}^{+1.29E-02}$ | $43.1_{-0.1}^{+0.4}$ | — | $6.39_{-0.11}^{+0.15}$ | $1.0E-01$ | $6.8E-06_{-3.6E-06}^{+3.4E-06}$ | 110.2
3C382 | $1.17E-01_{-5.30E-03}^{+5.20E-03}$ | $43.7\pm 0.1$ | — | $6.44\pm 0.04$ | $1.1E-01_{-5.7E-02}^{+1.0E-01}$ | $3.2E-05_{-6.6E-06}^{+8.7E-06}$ | 80.1
SwiftJ2127.4+5654 | $2.66E-01\pm 4.50E-03$ | $42.3\pm 0.1$ | — | $6.41_{-0.04}^{+0.06}$ | $2.3E-01_{-1.8E-01}^{+2.9E-01}$ | $2.0E-05_{-2.6E-06}^{+2.6E-06}$ | 58.3
IIZw171 | $2.21E-01_{-1.12E-02}^{+1.02E-02}$ | $43.3\pm 0.1$ | — | $6.36_{-0.05}^{+0.19}$ | $<8.9E-01$ | $5.5E-06_{-1.6E-06}^{+1.4E-05}$ | 55.9
NGC7314 | $6.44E-02_{-1.41E-03}^{+1.40E-03}$ | $43.4\pm 0.1$ | — | $6.53\pm 0.05$ | $5.1E-01_{-7.6E-02}^{+9.4E-02}$ | $7.3E-05_{-8.4E-06}^{+9.5E-06}$ | 230.9
Mrk915 | — | — | $0.85\pm 0.01$ | $6.41_{-0.01}^{+0.02}$ | $1.1E-01_{-2.7E-02}^{+2.8E-02}$ | $1.5E-05_{-1.6E-06}^{+1.5E-06}$ | 148.4
MR2251-178 | $1.84E-01_{-9.70E-03}^{+1.18E-02}$ | $44.1\pm 0.2$ | — | $6.40$ | $>1.7E-02$ | $1.9E-05_{-6.8E-06}^{+7.8E-04}$ | 29.0
NGC7469 | $1.00E-01\pm 1.70E-03$ | $42.8\pm 0.1$ | — | $6.43\pm 0.01$ | $6.8E-02_{-2.3E-02}^{+2.4E-02}$ | $3.3E-05_{-3.8E-06}^{+3.7E-06}$ | 100.8
Mrk926 | $1.89E-01_{-7.40E-03}^{+7.00E-03}$ | $43.6\pm 0.1$ | — | $6.43\pm 0.06$ | $3.3E-01_{-6.0E-02}^{+1.1E-01}$ | $5.5E-05_{-8.4E-06}^{+5.6E-06}$ | 95.8
NGC7582 | — | — | — | $6.40\pm 0.01$ | $5.7E-02_{-1.9E-02}^{+1.6E-02}$ | $3.4E-05_{-2.7E-06}^{+3.2E-06}$ | 167.4
Table 6: Model parameters used in the fits for our various objects. Each object fit includes an additional TBabs component frozen to the Galactic value. Object | TBabs | TBpcf | zbbody | zgauss | pexrav | other
---|---|---|---|---|---|---
Mrk1501 | ✓ |  | ✓ | ✓ | ✓ |
Mrk1148 | ✓ |  | ✓ | ✓ | ✓ |
Fairall9 | ✓ |  | ✓ | ✓ | ✓ |
Mrk359 | ✓ |  | ✓ | ✓ | ✓ |
NGC931 | ✓ |  | ✓ | ✓ | ✓ |
NGC1052 |  | ✓ |  | ✓ | ✓ |
NGC1068 |  | ✓ |  | ✓ | ✓ |
3C109 |  | ✓ |  | ✓ | ✓ |
3C120 | ✓ |  | ✓ | ✓ | ✓ |
Ark120 | ✓ |  | ✓ | ✓ | ✓ |
ESO362-18 | ✓ |  | ✓ | ✓ | ✓ |
Mrk3 |  | ✓ |  | ✓ | ✓ |
IRAS09149-6206 | ✓ |  | ✓ | ✓ | ✓ |
NGC3227 |  | ✓ |  | ✓ | ✓ |
NGC3998 |  | ✓ |  | ✓ | ✓ |
NGC4151 |  | ✓ |  | ✓ | ✓ |
Mrk766 | ✓ |  | ✓ | ✓ | ✓ |
3C273 | ✓ |  | ✓ | ✓ | ✓ |
NGC4579 | ✓ |  | ✓ | ✓ | ✓ |
NGC4593 | ✓ |  | ✓ | ✓ | ✓ |
NGC4785 |  | ✓ |  | ✓ | ✓ |
Mrk273 |  | ✓ |  | ✓ | ✓ | ✓
Mrk841 | ✓ |  | ✓ | ✓ | ✓ |
Mrk1392 | ✓ |  | ✓ | ✓ | ✓ |
3C382 | ✓ |  | ✓ | ✓ | ✓ |
SwiftJ2127.4+5654 | ✓ |  | ✓ | ✓ | ✓ |
IIZw171 | ✓ |  | ✓ | ✓ | ✓ |
NGC7314 | ✓ |  | ✓ | ✓ | ✓ |
Mrk915 |  | ✓ |  | ✓ | ✓ |
MR2251-178 |  | ✓ |  | ✓ | ✓ |
NGC7469 | ✓ |  | ✓ | ✓ | ✓ |
Mrk926 | ✓ |  | ✓ | ✓ | ✓ |
NGC7582 |  | ✓ |  | ✓ | ✓ |

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## Appendix: Comments on the Spectral Fits

Fairall 9: We ignore below 0.7 keV for this source due to strong emission near
0.5 keV. Additionally, there is no MOS2 spectrum for this source from XMM-
Newton.
Mrk 359: We ignore below 0.7 keV for this source due to discrepancies between
the PN and MOS spectra from XMM-Newton.
NGC 1068: We fit this spectrum above 3 keV to avoid the strong complex of
emission lines below this energy. Without this, the fit is completed dominated
by the high S/N in the lower energy channels. There is no available PN
spectrum for the XMM-Newton epoch we use.
3C 120: The XMM-Newton epoch we used had no PN observation.
Ark 120: We ignore below 0.7 keV for this source.
Mrk3: Due to a strong soft component, with poor quality data, we ignore below
1.0 keV for this source.
IRAS09149-6206: Because of strong emission lines, we fit above 1.0 keV for
this source.
NGC3227: We ignore below 0.7 keV for this object.
NGC4151: We fit only above 2.0 keV to avoid strong emission lines.
NGC4593: For the XMM-Newton observations, only a MOS1 spectrum was available.
NGC4785: Because of emission lines and weak constraints on the soft X-rays, we
ignore below 3.0 keV.
Mrk273: To account for strong soft emission, we add an extra zgauss component
with an energy of 0.84 keV and a width of 0.16 keV.
Mrk1392: We excluded the MOS spectra from XMM-Newton for this object as fits
including this data were unstable.
IIZw171: We ignored below 0.8 keV for this object.
MR2251-178: We ignored below 1.0 keV because of evidence for broad emission
features.
Mrk926: We ignored below 0.8 keV for this object due to strong absorption
features.
NGC7582: There is an extremely strong soft excess and line emission below 3.0
keV that we have ignored.