# Lower-Luminosity Obscured AGN Host Galaxies are Not Predominantly in Major-
Merging Systems at Cosmic Noon

Erini L. Lambrides Department of Physics and Astronomy, Johns Hopkins
University, Bloomberg Center, 3400 N. Charles St., Baltimore, MD 21218, USA
Marco Chiaberge  AURA for the European Space Agency (ESA), ESA Office, Space
Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
Department of Physics and Astronomy, Johns Hopkins University, Bloomberg
Center, 3400 N. Charles St., Baltimore, MD 21218, USA  Timothy Heckman
Department of Physics and Astronomy, Johns Hopkins University, Bloomberg
Center, 3400 N. Charles St., Baltimore, MD 21218, USA  Allison Kirkpatrick
Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045,
USA  Eileen T. Meyer  Department of Physics, University of Maryland, Baltimore
County, 1000 Hilltop Circle, Baltimore, MD 21250, USA  Andreea Petric  Space
Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
Kirsten Hall  Schmidt Science Fellow  Atomic and Molecular Physics Division,
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA,
02138, USA  Arianna Long  Department of Physics and Astronomy, University of
California, Irvine, CA 92697, USA  Duncan J. Watts Institute of Theoretical
Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo, Norway
Roberto Gilli  INAF – Osservatorio di Astrofisica e Scienza dello Spazio di
Bologna, Via P. Gobetti 93/3, 40129 Bologna, Italy  Raymond Simons  Space
Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
Kirill Tchernyshyov  Department of Astronomy, University of Washington,
Seattle, WA, USA  Vicente Rodriguez-Gomez  Instituto de Radioastronomía y
Astrofísica, Universidad Nacional Autónoma de México, Apdo. Postal 72-3, 58089
Morelia, Mexico  Fabio Vito  Scuola Normale Superiore, Piazza dei Cavalieri 7,
56126, Pisa, Italy  Alexander de la Vega  Department of Physics and Astronomy,
Johns Hopkins University, Bloomberg Center, 3400 N. Charles St., Baltimore, MD
21218, USA  Jeffrey R. Davis  Department of Physics and Astronomy, Johns
Hopkins University, Bloomberg Center, 3400 N. Charles St., Baltimore, MD
21218, USA  Dale D Kocevski  Department of Physics and Astronomy, Colby
College, 5800 Mayflower Hill, Waterville, ME 04961, USA  Colin Norman  Space
Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
Department of Physics and Astronomy, Johns Hopkins University, Bloomberg
Center, 3400 N. Charles St., Baltimore, MD 21218, USA

(Received *; Revised *; Accepted *)

###### Abstract

For over 60 years, the scientific community has studied actively growing
central super-massive black holes (active galactic nuclei – AGN) but
fundamental questions on their genesis remain unanswered. Numerical
simulations and theoretical arguments show that black hole growth occurs
during short-lived periods ($\sim$ 107 -108 yr) of powerful accretion. Major
mergers are commonly invoked as the most likely dissipative process to trigger
the rapid fueling of AGN. If the AGN-merger paradigm is true, we expect galaxy
mergers to coincide with black hole accretion during a heavily obscured AGN
phase (NH $>10^{23}$ cm-2). Starting from one of the largest samples of
obscured AGN at 0.5 $<$ $z$ $<$ 3.1, we select 40 non-starbursting lower-
luminosity obscured AGN. We then construct a one-to-one matched redshift- and
near-IR magnitude- matched non-starbursting inactive galaxy control sample.
Combining deep color Hubble Space Telescope imaging and a novel method of
human classification, we test the merger-AGN paradigm prediction that heavily
obscured AGN are strongly associated with galaxies undergoing a major merger.
On the total sample of 80 galaxies, we estimate each individual classifier’s
accuracy at identifying merging galaxies/post-merging systems and isolated
galaxies. We calculate the probability of each galaxy being in either a major
merger or isolated system, given the accuracy of the human classifiers and the
individual classifications of each galaxy. We do not find statistically
significant evidence that obscured AGN at cosmic noon are predominately found
in systems with evidence of significant merging/post-merging features.

AGN

††software: pandas, scipy, ipython, matplotlib, pymc

##  1 Introduction

Super-massive blackholes (SMBHs) are essentially in every massive galaxy, and
when they are actively accreting matter, known as active galactic nuclei
(AGN), they can potentially inject energy into the gas and expel it and/or
prevent it from cooling and collapsing into stars(e.g. Bower et al., 2006;
Croton et al., 2006; Heckman & Best, 2014). Matter must lose almost all
($\sim$99.9%) of its angular momentum in order to accrete onto the SMBH, thus,
studying dissipative processes such as mergers, tidal interactions, stellar
bars and disk instabilities is central to understanding the details of AGN
fueling. Despite distinct differences between dissipative processes, neither
observational nor theoretical studies converge on a dominant mechanism for
funneling matter onto the central SMBH (Jogee, 2006). Galaxy mergers with
comparable mass ratios ($\geq 1:4$ also defined as major mergers) are one of
the most popular mechanisms invoked, yet the observational consensus is mixed.
While some empirical and theoretical studies find a connection between mergers
and ultra-luminous infrared galaxies (Sanders & Mirabel, 1996; Veilleux et
al., 2009; Lacy et al., 2018), local AGN (Koss et al., 2010; Ellison et al.,
2013, 2019; Gao et al., 2020), high-luminosity AGN (Urrutia et al., 2008;
Treister et al., 2012; Glikman et al., 2015; Donley et al., 2018), and radio-
loud AGN (Chiaberge et al., 2015), others find no connection between mergers
and X-ray detected AGN (Gabor et al., 2009; Georgakakis et al., 2009), high-
luminosity AGN (Villforth et al., 2014, 2017; Marian et al., 2019), and low-to
intermediate luminosity AGN (L${}_{\textrm{Bol}}<10^{44}$ ergs/s) (Grogin et
al., 2005; Schawinski et al., 2011; Rosario et al., 2015).

It is possible that the AGN-merger connection has been systematically missed
in some studies due to poor sampling of obscured AGN. If the AGN-merger
paradigm is true, then we can expect a heavily obscured accretion AGN phase to
coincide with galaxy coalescence (Sanders & Mirabel, 1996; Cattaneo et al.,
2005; Hopkins et al., 2008). In other words, if a major-merger triggers most
AGN, then AGN behind large neutral hydrogen column densities
($N_{\mathrm{H}}>10^{23}$ cm-2) should exist in association with the most
spectacular phases of mergers.

Obscured sources are inherently difficult to detect in the X-rays, but through
the combination of large and deep X-ray surveys with other multi-wavelength
observations, a large obscured AGN sample can be constructed. X-ray
observations are thought to provide one of the most reliable methods of both
selecting AGN and estimating the amount of AGN obscuration (Brandt & Hasinger,
2005; Xue et al., 2011; Liu et al., 2017); however this is not always true, as
Comastri et al. (2011); Donley et al. (2012) show that even some of the
deepest X-ray surveys miss a substantial fraction ($\sim 40$%) of heavily
obscured objects.

One of the first studies of its kind, Kocevski et al. (2015) analyzed a sample
of obscured AGN defined using a selection based on X-ray data from the Chandra
X-ray Observatory, with deepest observations at 4Ms (Xue et al., 2011). Using
a single Hubble Space Telescope(HST) near-IR(NIR) band, they found evidence
that heavily obscured AGN are more likely to be in mergers than their a less
obscured AGN counterparts: point-sources included 21.5%${}^{+4.2\%}_{-3.3\%}$
heavily obscured AGN in mergers versus 7.8%${}^{+1.9\%}_{-1.3\%}$.

In 2017, the 7MS Chandra Deep-Field South Survey (7MCDFS), the deepest X-ray
survey ever conducted was released. Within this substantially deeper catalog
and the combination of IR, optical, and radio data-sets, Lambrides et al.
(2020) find that $30\%$ of the X-ray-detected AGN were mis-classified as low-
luminosity un-obscured AGN. Lambrides et al. (2020) argues that these objects
instead represent the faintest, and potentially the most obscured AGN in the
7MCDFS sample. It is imperative that we morphologically analyze these objects
whose addition may either lend or remove credence to the obscured AGN-merger
paradigm.

In this work we combine the Lambrides et al. (2020) obscured AGN sample with
publicly available HST imaging to determine the merger status of the host
galaxies of obscured AGN. The first paper in our series, Lambrides et al.
(2021) (L21) introduced a novel statistical method where the accuracy of human
classifiers are taken into account in a Bayesian probabilistic framework to
determine the merger fraction and individual probabilities of a galaxy being
in a merging system. In section 2 we describe the obscured AGN sample, the
control sample, the HST data, and the simulated data used in this work. In
section 3, we describe the survey framework and statistical models used to
derive a merger fraction of a population. In section 4, we present the results
of the merger fraction of the obscured AGN population. In section 5, we
discuss how our results compare to other studies and the implications our
results have on AGN triggering models. In section 6, we present the summary
and conclusion. We use an $h=0.7$, $\Omega_{m}=0.3$, $\Omega_{\Lambda}=0.7$
cosmology throughout this paper. We use the k-sample Anderson-Darling mid-rank
statistic to test the null hypothesis that two samples are drawn from the same
population, and report the test statistic (DADK) significance level at which
the null hypothesis for the provided samples can be rejected (Scholz &
Stephens, 1987).

##  2 Sample Selection and Datasets

###  2.1 Heavily Obscured AGN

Figure 1: Non-absorption Corrected X-ray Luminosity vs Rest-Frame AGN MIR
Luminosity: Obscured AGN candidates straddle or lie below the blue shaded
region. As adapted by Lansbury et al. (2015), the un-obscured region parameter
space (red) indicates the range in intrinsic X-ray, 6 µm AGN luminosity
relationships between Gandhi et al. (2009) and Fiore et al. (2009). The
heavily obscured region (blue) indicates the same relationships but where the
X-ray luminosity is absorbed by a column density of $N_{\mathrm{H}}>10^{24}$
cm-2 (Lansbury et al., 2015)

Directly observing X-ray bright obscured AGN with the Chandra X-ray
Observatory has been possible, especially at energies greater than $2$ keV
where X-ray photons are less attenuated by the obscuring material. Generally,
X-ray AGN are commonly selected in the literature as sources with intrinsic
X-ray luminosities greater than the maximum luminosity one would expect from
host-galaxy emission only (i.e $>10^{42}$ erg/s) and/or sources with enough
X-ray photons in multiple energy bands to robustly model the X-ray spectrum.
The latter condition is especially required to estimate the level of
attenuation of the X-ray photons. In addition to X-rays, obscured AGN can also
be identified in the mid-infrared (MIR) due to the dust reprocessing of the
obscured UV light that emits from the central engine or through polarized
scattered light (Houck et al., 2005; Stern et al., 2012; Mateos et al., 2013).
The combination of wide and deep X-ray surveys with MIR multi-wavelength
catalogues have greatly increased the samples of obscured AGN (e.g. Stern et
al., 2005; Donley et al., 2012).

We derive our sample from the Lambrides et al. (2020), hereinafter L20, lower
luminosity obscured X-ray AGN catalogue. Utilizing the excellent wavelength
coverage of the GOODS-South field, L20 analyzed the X-ray luminosities of AGN
from the Chandra 7Ms survey (7MsCDFS) in the context of the radio (VLA 1.4
GHz), optical grism spectroscopy (HST-WFC3), high resolution optical/NIR
imaging and photometry (HST-ACS, HST-WFC3IR), and NIR/MIR/FIR photometry
(Spitzer IRAC,Spitzer IRS PUI, Spitzer MIPS, Herschel PACS). Using the
absorption corrected 2-7 keV X-ray luminosities provided in the Luo et al.
(2017) 7Ms catalogue, L20 derived an additional absorption correction factor
to X-ray luminosities and thus to the NH of each object. This was done by
measuring the offset of the Luo et al. (2017) luminosities from the X-ray
luminosity required to be in agreement to within 2$\sigma$ of the (Stern,
2015) empirical AGN X-ray to IR luminosity relationship where the IR estimate
of AGN power is the rest frame IR luminosity between 3.6 µmto 5.8 µm. Using
the IR excess in combination with X-ray and radio properties, L20 increased
the number of identified obscured AGN in the 7MsCDFS catalog at 0.5 $<$ z $<$
3 by 30%, bringing the total number of 7MsCDFS obscured AGN with
N${}_{H}>10^{23}$ cm-2 to $\sim 100$.

The 7Ms survey covers an area of $\sim$290 arcmin2, and the L20 sample is
distributed throughout this field. The Cosmic Assembly Near-IR Deep Extra-
galactic Legacy Survey (CANDELS) (Guo et al., 2013) and 3D-HST (Skelton et
al., 2014) programs and resulting catalogues provide HST coverage for a
portion of this field ($\sim$ 176 arcmin2). To derive a suitable sample for
this work, we first select the portion of the L20 sample that is within HST
coverage using the mosaics provided by the
3D-HST111https://archive.stsci.edu/prepds/3d-hst/ (Koekemoer et al., 2011;
Grogin et al., 2011; Skelton et al., 2014).

Reliable X-ray-to-HST associations have been found for the CDFS catalogue in
Luo et al. (2017) using the likelihood ratio technique presented in Luo et al.
(2010) with the X-ray full-band derived coordinates. We use the X-ray
counterpart F125W derived coordinates. The counterpart association described
in Luo et al. (2010), which takes into account positional uncertainties of the
X-ray and F125W band and expected magnitude distribution of counterparts has a
false-match probability $<$ 4%. From the CANDELS+3DHST combined catalogue, the
F125W band has a 5$\sigma$ limiting AB magnitude of 28.3. We test whether
there is a statistical difference in the redshift, X-ray-luminosity and NH
distributions of the AGN with HST coverage compared to the total L20 sample,
and find that the null hypothesis cannot be rejected where the null hypothesis
is that the distributions are identical (pADK $>$ 0.25). The redshifts are
provided in the Luo et al. (2017) Chandra 7Ms X-ray catalogue: 46 are
spectroscopic and 4 are photometric. In summary, we find a total of 50
obscured AGN out of the L20 obscured AGN sample with well covered ACS F435W,
ACS F775W, and WFC3-IR F160W imaging data.

####  2.1.1 X-ray and MIR Properties

These 50 objects occupy a wide range of X-ray and MIR luminosities. The X-ray
and MIR luminosities were derived in L20. The rest-frame MIR luminosity is
used as an additional probe of AGN power and is defined between 3.2 µm to 5.7
µm. AGN torus emission dominates over MIR star-formation (SF) processes in
this wavelength range which is especially pertinent for lower-luminosity,
moderate-redshift AGN where other photometric MIR diagnostics may fail to
capture these objects (Laurent et al., 2000; Nenkova et al., 2008; Kirkpatrick
et al., 2012; Lambrides et al., 2019). In L20, the rest frame AGN MIR
luminosity, referred to as LTorus∗, is calculating the photmetric luminosity
of a single datapoint using the passband that most closely corresponds to the
rest-frame wavelength range of interest. For the range of redshift spanned by
our sample, the passbands used are the IRAC 8 µm, IRS PUI 16 µm and MIPS 24 µm
and for further detail on the MIR cross-matching and rest-frame luminosity
calculation we refer the reader to the aforementioned paper.

In Figure 1, we show the non-absorption corrected X-ray luminosities compared
to the AGN luminosity in the MIR (LTorus∗). The red-shaded region corresponds
to the un-obscured AGN region of the parameter space. This is defined by the
range in intrinsic X-ray, rest AGN MIR luminosity relationships between two
different X-ray to MIR relationships: Gandhi et al. (2009) and Fiore et al.
(2009). The Gandhi et al. (2009) relationship was derived from a local sample
of type 1 AGN ($0.03<$ z , $8\times 10^{41}$ erg/s $<$ L${}_{X}<4\times
10^{43}$ erg/s), and decomposition of the nuclear 6 µm luminosity was
performed to minimize host-galaxy contamination. The Fiore et al. (2009)
relationship was derived from a sample that spanned a larger redshift and
X-ray luminosity range as compared to Gandhi et al. (2009) ($0.7<$ z $<2.2$,
$3\times 10^{43}$ erg/s $<$ L${}_{X}<10^{45}$ erg/s), and did not include
host-galaxy decomposition of the 6 µm luminosity. Due to the inherent
uncertainties of these relationships, instead of choosing a single empirical
relationship, L20 chose a conservative approach and instead used both of these
relationships to determine a region of the parameter space that corresponded
to less obscured AGN. The heavily obscured region indicates the same empirical
relationships but the X-ray luminosity is scaled down to represent a column
density of $N_{\mathrm{H}}>10^{24}$ cm-2 (Lansbury et al., 2015).

The blue points in Figure 1 comprise the heavily obscured AGN sub-sample from
L20 with HST coverage and are not-significantly star-bursting as described in
the previous section. In the next section we discuss the motivation and the
removal of AGN host galaxies with starbursts.

Figure 2: Parent Sample and This Work: Comparison of properties of the L20
Obscured AGN Sample to the non-starbursting, HST covered sub-sample used in
this work.

####  2.1.2 Removing Starbursts

A multitude of theoretical and observational evidence has accumulated that
potentially connect galaxy mergers and interactions to extreme bursts of star-
formation or starbursts (SB) (Sanders & Mirabel, 1996; Hibbard & van Gorkom,
1996; Hopkins et al., 2006; Davies et al., 2015; Cortijo-Ferrero et al., 2017;
Pearson et al., 2019; Moreno et al., 2019). The purpose of this work is to
test the prediction that obscured AGN are more likely to be found in galaxies
that are undergoing a significant merger. If there is a direct causal
connection between mergers and star-formation and a star-formation rate (SFR)
matched control sample is not used, an apparent secondary correlation between
AGN and mergers can be induced. Thus, assessing the star-formation properties
of the obscured AGN sample and the matched control sample is paramount. It is
difficult to calculate robust star-formation rates of AGN host galaxies from
photometry alone, and a careful analysis of the star-formation properties of
the obscured AGN hosts is outside the scope of this paper due to the type of
data in hand. Therefore, we identify sources that are likely undergoing the
most extreme episodes of star-formation for a given stellar mass and redshift,
and isolate them from the main sample. Due to the small number of obscured AGN
with SB in their hosts, our main analysis will focus on the non-SB obscured
AGN sample. The scope of this work is to test the hypothesis that the majority
of obscured AGN are predominately triggered by significant galaxy mergers. In
section 5, we explore the merger properties of the SB-obscured AGN sample, and
the implications of a SB-AGN-merger connection versus a non-SB-AGN merger
connection.

From this sample of 50 obscured AGN with HST coverage, we then select objects
that are either likely to be on the star-formation main sequence, or
quiescent. Utilizing the extensive wavelength coverage of the GOODS-S field,
we calculate the position of the obscured AGN relative to the SF main-sequence
for each galaxy’s redshift and stellar mass. The stellar masses of the sample
are given in the 3D-HST survey catalogue (Skelton et al., 2014). As described
in Skelton et al. (2014), these authors used the FAST code (Kriek et al.,
2009) to estimate the stellar properties of the entirety of the GOODS-S field.
Due to the obscured nature of the AGN, the derived stellar masses are more
robust than the other stellar properties estimated in the catalogue.

As is stressed in Skelton et al. (2014), the star-formation rates are
uncertain when they are derived solely from optical- near-IR photometry. Since
our obscured sample is heavily obscured (NH $>$ 5$\times 10^{23}$ cm-2), the
stellar masses are well constrained as they predominately depend on the rest-
frame optical fluxes of the galaxies where there is negligible contamination
from the central engine. The redshift range of our sources and the multiple
HST band coverage allow for the rest-frame optical fluxes of our galaxies to
be well measured. To estimate the SFR in our galaxies, we use the detections
(or lack of) in the far-infrared (FIR). The FIR is a more un-biased indicator
of star-formation than the MIR in AGN host-galaxies because the contribution
from nuclear hot dust heated by the AGN contributes less than $<$ 20% at
$>100$ µm even for the most powerful AGN (Kirkpatrick et al., 2015; Dai et
al., 2018; Brown et al., 2019). In this work, we estimate the SFR as traced by
the 100 µm and 160 µm Herschel PACS band, utilizing the redshift information
of the source and the SFR calibration provided in Calzetti et al. (2010). The
coverage and detection of the AGN sample at such wavelengths is discussed in
L20. For objects with non-detections, we estimate the SFR using
SFR${}_{160\micron}M_{\odot}yr^{-1}$ = L${}_{160\micron}/7\times 10^{42}$ for
$L_{160\micron}$ $>$ 2$\times$1042 erg s-1 $\sim 5.2\times 10^{8}$ L⊙. For the
31 non-detections, we estimate the SFR upper-limit by calculating the
$L_{160\micron}$ upper-limit using the 3$\sigma$ average depth limit of 2.7
mJy as presented in Elbaz et al. (2011).

We then use the SFR relation for main-sequence galaxies presented in Schreiber
et al. (2015) to calculate the SFR of the main-sequence galaxies at each
object’s mass and redshift. Starbursts are defined as 0.6 dex above the main-
sequence population for a given stellar mass, SFR and redshift (Rodighiero et
al., 2011). Of the 50 obscured AGN, we remove from the sample the sources that
are 0.6 dex or more above their main-sequence counterpart. This leaves the
final non-SB obscured AGN sample with 40 objects.

Figure 3: F160W AB magnitude versus Redshift: The grey points are the entirety
of the 7Ms sample with HST coverage for z $>$ 0.5 in GOODS-South. The blue
points are the redshifts and F160W magnitudes of the non-SB obscured AGN
sample. The orange points are for the counterpart inactive-galaxy control
sample.

In Figure 2, we show a comparison of the redshift, L${}_{\textrm{Torus}^{*}}$,
and stellar mass distributions of the L20 parent sample compared with the
limited sample used in this work. We calculate the k-sample Anderson-Darling
mid-rank statistic between the redshift, L${}_{\textrm{Torus}^{*}}$, and
stellar mass distributions of the L20 sample of heavily obscured AGN to the
sub-sample used in this work and find the null hypothesis cannot be rejected,
and thus the sample used in this paper is representative of the obscured AGN
found in the larger 7Ms survey.

###  2.2 Control Sample

Since the goal of this work is to measure any significant excess of mergers in
the obscured AGN sample as compared to non-active galaxies, a control sample
must be carefully selected to closely match the properties of the AGN hosts.
We one-to-one match the non-SB obscured AGN to non-AGN galaxies (within
$\Delta_{m_{F160W}}\pm 0.5,\Delta_{z}\pm 0.5$) using the 3D-HST photometry
catalogue (Skelton et al., 2014) and spectroscopically secure redshifts from
Momcheva et al. (2016). If multiple galaxies satisfy the $\Delta_{m_{F160W}}$,
$\Delta_{z}$ criteria, we select the galaxy with the smallest difference. The
mean differences of $\Delta_{m_{F160W}}$ and $\Delta_{z}$ between the non-SB
obscured AGN sample and counterpart sample are -0.04 and -0.03, respectively.
We choose only one counterpart galaxy per non-SB AGN to ensure the total
sample is of reasonable size for visually classification. We use this non-AGN
galaxy sample, herein called the control sample, to assess the presence of an
obscured AGN-merger connection.

Matching the control galaxy sample to the star-formation properties of the AGN
host galaxies is a necessity. We remove starburst galaxies from the catalog as
described in the previous section. In Figure 3, we show the redshift and F160W
magnitude distribution of the non-SB obscured AGN sample (blue points),
control sample (orange points), and the entire z $>$ 0.5 GOODS-South field
with starbursts and galaxies with photometric redshifts included (grey
points). We find the distributions in redshift and magnitude are statistically
indistinguishable between the non-SB obscured AGN and control sample: the
null-hypothesis that the two samples are drawn from the same distribution in
both z and Ks magnitudes cannot be rejected (pADK $>$ 0.25). In Figure 3, we
include the total GOODS-S z $>0.5$ sample to visually compare the region of
the parameter space the non-SB obscured AGN and counterpart sample occupies to
the in-active galaxies not matched to the non-SB obscured AGN sample.

To summarize, we cross-match a non-starbursting, HST covered sub-sample of the
L20 obscured AGN catalogue to the CANDELS+3DHST combined HST GOOD-S catalogue
(Skelton et al., 2014; Momcheva et al., 2016). The HST-covered L20 subsample
consists of 40 non-SB obscured AGN with 34 spectroscopic redshifts and 6
photometric redshifts. The control sample consists of 40 non-active redshift,
magF160W matched counterpart galaxies all with spectroscopic redshifts. The
distributions of the non-SB obscured AGN sample and control sample distributed
in redshift and F160W magnitude space are statistically identical with 0.5 $<$
$z$ $<$ 3.1 and 18.2 $<$ magF160W[AB] $<$ 25.1.

(a) Obscured AGN: ID 642 from Luo et al. (2017)

(b) Counterpart Non-AGN Galaxy: ID 18169 via Skelton et al. (2014)

Figure 4: Example of Sample Imaging: Obscured AGN RGB Image at z = 0.7 (a)
with its z, F160W matched non-AGN galaxy counterpart (b)

###  2.3 HST Datasets

The number density of obscured AGN is inferred to peak between 1 $<$ $z$ $<$ 2
(e.g. Gilli et al., 2007; Aird et al., 2015). Beyond optical z$\sim$ 1
imaging, surveys begin to probe the rest-frame UV morphologies of galaxies.
This is useful for probing the most active regions of unobscured SF, but may
miss the gaseous and stellar features associated with merging systems (i.e
shells, disk asymmetry). An additional complication with morphologically
analyzing z $>$ 1 galaxies is the increasing incidence of foreground and
background galaxies near the region of the object of interest. Color images
are helpful in determining whether a close pair is a random superposition of
galaxies, or two galaxies at the same redshift. Thus, we need multiple
optical/UV imaging bands at similar depth in order to assess the merger status
of a $z$ $>$ 1 galaxy.

In this study, we use the 3D-HST reduced and combined GOOD-S mosaics (Skelton
et al., 2014). We make a 6” x 6” cutout centered on the X-ray coordinates for
the obscured AGN sample, and the 3D-HST coordinates for the control sample.
Each of the postage stamps were individually inspected to ensure no prominent
image artifacts were in the cutouts. All the postage stamps of the obscured
and control sample in this study are made publicly
available.222erinilambrides.com/morphology_of_obscured_agn.

###  2.4 Mock Galaxy Sample

An important aspect of merger classification studies is the major uncertainty
associated with the accuracy of human classifiers. By accuracy, we mean the
ability of each person to correctly identify mergers and to disentangle them
from random super-positions, asymmetries in galaxy structure not due to tidal
interactions, and relaxed morphologies. Even if the classifiers are experts
and proper statistical analysis is performed to remove outliers (e.g. using
trimmed means as in Chiaberge et al., 2015), a bias can still be present. L21
found that when using one of the most standard statistical implementations
used to calculate the merger fraction in the literature, the effective bias
due to humans is dependent on the intrinsic merger fraction of a given sample.
The implications of this result cast doubt in the sole usage of a control
sample as justifiable means to encapsulate human bias. L21 proposed a method
of quantifying and accounting for merger biases of individual human
classifiers and incorporated these biases into a full probabilistic model to
determine the merger fraction of a population, and the probability of each
individual galaxy being in a merger. In subsection 3.2, we summarize the
formalism and results of L21 on the definition and effect of the bias
introduced by human classifiers in addition to the statistical framework used
to infer the merger fraction of a sample.

In L21 we introduced a new method to calibrate the accuracy of human
classifiers. An estimate of the classifier’s accuracy was used as a prior in
determining the merger fraction of a galaxy sample. The accuracy priors were
determined using simulated images from the VELA cosmological simulations
(Ceverino et al., 2014; Snyder et al., 2015; Simons et al., 2019). As shown in
L21, 50 mock images in three different bands (two in the optical and one near-
IR) were produced with the appropriate amount of Poisson noise to simulate the
real data-sets used in this research. The mock galaxy sample has the same
redshift distribution as the non-SB obscured AGN sample used in this work.
With their origin hidden, these simulated observations were also classified by
each of the co-authors in this work, and for more details on the construction
of the mock images we refer the reader to L21.

##  3 Determining a Data Driven Merger Fraction

At z$>$1, it becomes more difficult to accurately assess the merger state of a
galaxy as faint merger signatures may be undetectable (Lotz et al., 2004).
Despite the great potential of automated methods such as deep-learning for
merger identification, there currently is no tool that is robust enough to
handle the diverse presentations of merging galaxies in the earlier Universe
(Pearson et al., 2019). Visual human classification is the most commonly
employed method used to identify moderate samples of merging galaxies at
$z>1.0$, but rarely if ever do the authors of these studies attempt to control
for human bias in morphological studies aside from the usage of a control
sample.

In L21, we used simulated and observed data-sets, to create and validate a
data-driven merger fraction probability model, where the merger fraction is
defined as the fraction of galaxies within a given sample undergoing a
significant merger. For the observed data-sets, we used real human
classifications on a sample of mock images with known truth values derived
from cosmological simulations. We found that the bias introduced from human
classification is dependent on the intrinsic merger fraction of the
population, and not accounting for this bias can drive the resulting merger
classification rates to be significantly different from the intrinsic truth.
The statistical framework posed in L21 accounts for the merger classification
biases of individual human classifiers, and these biases are then incorporated
into a full probabilistic model to determine the merger fraction of a
population and the probability of an individual galaxy being in a merger. In
this section, we describe how the human classifications of the non-SB obscured
AGN and in-active galaxy counterpart sample were collected and analyzed using
the L21 framework 333The full source code of the likelihood maximization can
be found here: https://github.com/elambrid/merger_or_not.

###  3.1 Object Classification Method

We developed a website where classifiers could assess the morphologies of the
non-SB obscured AGN sample, the control sample, and the mock galaxy sample
without knowing which sample an object came from. The Morphology of Obscured
AGN (or MOOAGN) classifying framework comprises the entirety of the sample: 40
obscured AGN, 40 matched inactive galaxies, and 50 mock galaxies. We also
provided a demo survey of 5 objects (not used in the MOOAGN sample) to give
the classifiers a reference framework of the classification options and data
quality. At the end of the demo survey we give some example justifications of
why one would classify an object as such, (see Appendix A for demo survey and
example classifications). Ultimately, for our analysis we use only two
morphological classes: merging and not merging. Due to the difficulty in
constraining merger stage and mass ratio given the data in hand, further
morphological sub-divisions would yield potentially less accurate results.
Nonetheless, when the human classifiers are presented with the images they are
given multiple morphological divisions to choose from. This is to not only aid
in the human classification process, but also to take the most conservative
approach of testing for a merger excess in non-SB obscured AGN host galaxies.
We assume that any system with obvious merging features observed at these
redshifts must be significantly merging systems. If we are incorrect with this
assumption, then the merger fraction would be lower for major-merging systems.
After the sample was classified, the divisions were folded back into the two
morphological classes of merging or not merging. The five classification
options given to the human classifiers are as follows:

  1. 1.

Merging: Major (approximately similar size) - On-going interaction. This is
prior to coalescence i.e two distinct interacting galaxies of similar size.
Features for this classification can include tidal tails with distinct galaxy
pairs, enhanced star formation and morphological distortion along the closest
axis of approach between two pairs.

  2. 2.

Merging: Minor (approximately $<$ 1:4 size ratio) Similar to the major merger
classification with exception of size. If a galaxy pair has evidence of
interaction, and one of the bodies is roughly less than a 1/4 the size of the
larger galaxy it is classified as a minor interaction.

  3. 3.

Disturbance: Major: This is intended to capture galaxies that have coalesced
within 100 Myrs. Features can include highly irregular gas/stellar
morphologies and tidal tails with only one distinct central bulge

  4. 4.

Disturbance: Minor - This is intended to capture galaxies that are slightly
irregular, yet are indistinguishable from internal processes that could cause
the irregularity i.e star-forming clumps, disk instabilities.

  5. 5.

No Evidence of Merger/Interaction.

Examples of galaxies fitting the above criteria are shown in Appendix A. We
then collate the classifications of our fourteen human classifiers of all 130
objects on the MOOAGN sample.

###  3.2 Calculating the Merger Fraction Likelihood

As previously mentioned, even among experts, it is difficult to accurately
characterize whether a galaxy is undergoing a merger or is isolated. Because
of this, it is inevitable that any given classifier will obtain a merger
fraction that is different from another classifier’s assessment. For example,
one may be more inclined to classify objects as mergers even if the objects
display minor disturbances unrelated to galaxy encounters. L21 assumes that
the bias of human classifiers can be quantified in terms of their accuracy in
correctly classifying an intrinsically merging galaxy as a merger (and an
intrinsically isolated system as isolated). Previous works have assumed that
the effect of this bias on independent galaxy samples is similar (i.e if the
same set of humans are classifying a science and a control sample the
assumption is that the bias due to human classification is equally present in
both samples). Thus due to this assumption, and to account for other un-
quantified biases such as those potentially introduced during the method of
selecting the science sample in the first place, most merger studies do not
report absolute merger fractions of a specific population but rather compare
the merger fraction of the science sample to a well-justified control sample.
The control sample in this context is any sample of sources that lacks the key
feature that defines the science population in question, but shares any
relevant properties that might be correlated with the morphology or the
presentation of the morphology of an object (i.e redshift, stellar-mass, SFR
etc). Though, as shown in L21, if the underlying merger fraction of the two
populations (i.e science and control) are significantly different, this human
bias will not be evenly applied. Therefore, the bias introduced by using human
classifiers will still be present in any statistical comparison between the
merger fractions of the science and control sample.

Summarizing the L21 characterization of this bias, if one is shown a merging
(or isolated) galaxy, they will classify the galaxy correctly with probability
$r_{M}$ (or $r_{I}$). Therefore, if somebody is shown $N_{M}$ intrinsic
mergers and $N_{I}$ intrinsic isolated galaxies, on average they will measure
$\hat{N}_{M}=r_{M}N_{M}+(1-r_{I})N_{I}$ mergers. The inclusion of the
$(1-r_{I})N_{I}$ term represents the amount of galaxies that were incorrectly
classified as isolated and are truly mergers.

Using the formalism of $r_{M}$ (or $r_{I}$) to characterize the bias of human
classifiers, L21 shows that the use of relative significance between comparing
the merger fractions of the science and the control sample does not remove
this issue. By re-writing the measured $\hat{N}_{M}$ and measured
$\hat{N}_{M,c}$ in terms of the measured merger fraction for each sample and
the intrinsic value of $N_{M}$ and $N_{M,c}$ in terms of the intrinsic merger
fraction $f_{M}$ of each sample and taking the difference:

$\displaystyle\langle\hat{f}_{M}\rangle$
$\displaystyle=r_{M}f_{M}+(1-r_{I})(1-f_{M})$ (1)
$\displaystyle\langle\hat{f}_{M,c}\rangle$
$\displaystyle=r_{M}f_{M,c}+(1-r_{I})(1-f_{M,c})$ (2)
$\displaystyle\langle\Delta\hat{f}_{M}\rangle$
$\displaystyle=\langle\hat{f}_{M}\rangle-\langle\hat{f}_{M,c}\rangle$ (3)
$\displaystyle\langle\Delta\hat{f}_{M}\rangle$ $\displaystyle=r_{M}\Delta
f_{M}-(1-r_{I})\Delta f_{M}$ $\displaystyle=\Delta f_{M}[r_{M}+r_{I}-1]$ (4)

they find the difference between the measured merger fractions of the two
samples is still dependent on the intrinsic merger fraction of each sample.

Using the merger fraction likelihood algorithm presented in L21, we are able
to infer the underlying merger fraction by using a novel technique to quantify
the bias of each individual classifier. We then optimally combine the
individual classifier uncertainties with the individual classifications of
each galaxy in the sample. In the merger fraction statistical model presented
in L21, classifier accuracy is a nuisance parameter that can be marginalized
over. Further details on the construction of the algorithm can be found in the
aforementioned work. We briefly summarize the algorithm here.

A respondent $i$ is shown a true merger, and they classify it as a merger with
probability $r_{M}$, or classify it as an isolated galaxy with probability
$1-r_{M}$. Conversely, if the respondent is shown a true isolated galaxy, they
will say it is a merger with probability $1-r_{I}$ or say it is isolated with
probability $r_{I}$. Thus respondent $i$ classifies $j$th galaxy $G_{j}$ with
classification $m$ as

$p(m_{i}\mid G_{j})=\begin{cases}r_{M}&m_{i}=G_{j}=\mathrm{merger}\\\
1-r_{M}&m_{i}\neq G_{j}=\mathrm{merger}\\\
r_{I}&m_{i}=G_{j}=\mathrm{isolated}\\\ 1-r_{I}&m_{i}\neq
G_{j}=\mathrm{isolated}\end{cases}$ (5)

Figure 5: Merger Probabilities of non-SB Obscured AGN and Inactive Galaxy
Control Sample: We use the method presented in section 3.2 to calculate the
probabilities of each individual galaxy in the non-SB obscured AGN and control
samples being in a merging system. The blue distribution is merger fraction
distribution of the non-SB obscured AGN sample, and the orange outlined, un-
filled distribution is the merger fraction of the control sample. The blue
line is centered at the mean of the obscured AGN distribution, with the blue
dashed lines representing the 85th percentile. There is no significant
difference in the merger fractions.

The likelihood of the classifications of a single galaxy by multiple
classifiers given a merger fraction and classifier accuracies can be written
as

$\begin{split}p(\\{m_{i}\\}\mid\\{r_{i}\\},f_{M})=f_{M}\prod_{i}p(m_{i}\mid
G_{j}={\mathrm{M}})\\\ +(1-f_{M})\prod_{i}p(m_{i}\mid
G_{j}={\mathrm{I}}).\end{split}$ (6)

where $f_{M}$ is the merger fraction of a given population and index $i$
corresponds to an individual classifier. In this expression, the true nature
of the galaxy in question is marginalized out. Expanding to multiple galaxies,
we get the likelihood for the classifications of a collection of galaxies:

$p(\\{m_{ij}\\}\mid\\{r_{i}\\},f_{M})=\prod_{j}p(\\{m_{ij}\\}\mid\\{r_{i}\\},f_{M}).$
(7)

Multiplying this likelihood by a prior on the merger fraction and, if the
classifier accuracies are not held fixed, by a prior on accuracies gives the
unnormalized posterior probability distribution function for this model. If we
wish to recover the probability that a particular galaxy is a merger, we can
use the expression:

$p(G=M\mid\\{m_{i}\\},\\{r_{i}\\},f_{M})=\frac{f_{M}\prod_{i}p(m_{i}\mid
G=M)}{p(\\{m_{i}\\}\mid\\{r_{i}\\},f_{M})}.$ (8)

The probability that this galaxy is isolated is the complement of this
expression. This expression is evaluated with an informative prior on the
accuracies $r_{M}$, $r_{I}$. The prior is determined from the classifications
of the mock galaxies, which have known merger states. We refer the reader to
L21 for further details on the derived $r_{M}$, $r_{I}$ classifications. The
same set of human classifiers were used in both L21 and this work, and the
mean prior of $r_{M}$ $r_{I}$ is 0.74 and 0.63 respectively.

The strength of this method is its internal consistency: given a set of
observed mergers, the likelihood is maximized when a value of $f_{M}$ shown to
all classifiers is most plausible, given a prior on classifier accuracies and
the individual classifications of each galaxy. For example, in studies that
determine the merger fraction of a population from a set of galaxies
classified by a set of human classifiers, the merger fractions from each
classifier are collated and the error treatment uses the standard binomial
statistics. In this scenario, it is possible for classifiers to identify a
similar number of mergers, but be in disagreement with each other on the
classification of individual objects. This lack of inter-classifier agreement
would not be encapsulated in the standard error treatment. In the method
utilized in this work, the determination of the most plausible $f_{M}$
requires determining the most plausible classification of each individual
galaxy.

The likelihood function of a given galaxy having a specific morphological
classification requires a robust statistical description of a human
classifiers accuracy in assessing both merging and isolated systems. In the
previous step, where we maximize the likelihood of a population’s merger
fraction, our algorithm also maximizes the likelihood of an individual
galaxy’s classification. This allows for deeper data exploration on galaxy
samples that are normally too small to do anything but population averages.

Figure 6: Merger Probabilities of non-SB Obscured AGN and Inactive Galaxy
Control Sample in Two Redshift Bins: The dark blue filled histogram is the
merger probability distribution of the non-SB obscured AGN sample and the un-
filled orange histogram is the matched in-active galaxy sample. The left most
plot represents objects in the lower 50% of the redshift distribution (0.5 $<$
z $<$1.1 (20 objects), and the right-most plot the merger probability
distributions for the objects in the upper 50% of the sample redshift
distribution (1.1 $<$ z $<$3.5).

##  4 The non-SB Obscured AGN Merger Fraction

We first present the merger fractions of the non-SB obscured AGN and control
sample without taking into account the accuracies of the human classifiers. We
take the mean number of galaxies classified as either a major merger, minor
merger, or majorly disturbed system from each of the fourteen classifiers. We
also report the binomial confidence interval at the 68% level, or $1\sigma$,
using the Jeffreys interval, a Bayesian application to the binomial
distribution (Brown et al., 2001). The merger fraction and corresponding
1$\sigma$ error of the non-SB obscured AGN sample is 0.59
${}^{+0.06}_{-0.10}$. For the control sample, the merger fraction and 1
$\sigma$ error is 0.53 ${}^{+0.06}_{-0.11}$. The merger excess of non-SB
obscured AGN over a matched inactive control sample is 1.1 ${}^{+0.3}_{-0.2}$.
Thus, using the standard binomial method, the control sample and obscured
sample are not statistically separable. Yet, as shown in L21, the only
instance in which the relative comparison of two merger fractions using the
standard binomial method is not biased due to human classification is when the
two samples being compared have the same intrinsic merger fraction. Since we
do not know a priori the intrinsic merger fractions of the non-SB obscured AGN
and control sample, we must use our newly derived method to estimate the
merger fraction.

Figure 7: Merger Probabilities of non-SB Obscured AGN and Matched Inactive
Galaxy Control Sample in Two Stellar Mass Bins: The dark blue filled histogram
is the merger probability distribution of the obscured AGN sample and the un-
filled orange histogram is the matched in-active galaxy sample. We split the
non-SB obscured AGN sample on the median log stellar mass: 9.32 $<$ log (M∗
[M⊙]) $<$10.7 (20 objects), 10.7 $<$ log (M∗[M⊙]) $<$11.32 (20 objects). The
left most plot represents the merger probability distributions of the lower
stellar mass bin (log(M${}_{*,\textrm{mean}}$) = 10 M⊙), and the right-most
plot the merger probability distributions for the higher stellar mass bin
(log(M${}_{*,\textrm{mean}}$) = 11 M⊙).

Thus, we use the merger fraction likelihood framework presented in L21 and
summarized in subsection 3.2 to simultaneously calculate the probability of
the merger fraction of each sub-sample, the probability distribution of each
classifiers accuracy in measuring merging and isolating systems, and the
probability of each individual galaxy being in a merger. In Figure 5, we
report the merger fraction probability distribution of the non-SB obscured AGN
and control sample being in an merging system. The y-axis probabilities are
normalized such that the area under the distribution curve is equal to one. We
find the non-SB obscured AGN sample has a merger fraction probability of
54%$\pm 8\%$, and the inactive galaxy control sample is found to have a
53%$\pm 9\%$ mean probability of being in a merger.

The main result of our work is as follows: The obscured AGN merger fraction is
statistically indistinguishable from the control sample merger fraction ( $<$1
$\sigma$).

In the following sub-sections, we explore whether an intrinsic difference
exists between the merger state of obscured and inactive galaxies as a
function of various galaxy properties. We test the extent of the dependence on
merger probability on different galaxy and AGN properties by simply splitting
the sub-sample along the 50th percentile (or on either side of the median) of
the property being explored. We do this to have enough objects in each bin to
keep the error on the sub-sample size small enough for meaningful comparison
and to minimize assumptions on bin width.

Figure 8: Merger Probabilities of non-SB Obscured AGN in two NH bins: The
light blue filled histogram is for non-SB obscured AGN sample with objects
with N${}_{H}<$ 7$\times 10^{23}$ cm-2, and the dark blue un-filled histogram
for non-SB obscured AGN with N${}_{H}>$ 7$\times 10^{23}$ cm-2

###  4.1 Redshift Dependence

We first compare whether there is a difference in the merger fractions as a
function of redshift. We split the non-SB obscured AGN sample along the
median, 0.5 $<$ z $<$1.1 (20 objects), 1.1 $<$ z $<$3.5 (20 objects), and
split the control sample along those same bin definitions (the redshift median
of the control sample is also 1.1, 20 objects in each bin respectively). In
Figure 6, we show the merger probabilities of the non-SB obscured AGN and
control sample for each redshift bin. For the lower redshift bin, we find fM =
0.42 $\pm$ 0.11 and fM = 0.44 $\pm$ 0.12 for the non-SB obscured AGN sample
and matched control sample respectively. For the higher redshift bin, we find
fM = 0.51 $\pm$ 0.11 and fM = 0.49 $\pm$ 0.12 for the non-SB obscured AGN
sample and matched control sample respectively. We do not find any statistical
difference between the non-SB obscured AGN sample and the control sample for
either the lower redshift or higher redshift bin ($<1\sigma$ difference).

###  4.2 Galaxy Stellar Mass Dependence

We next explore if there is any difference in the merger probabilities between
non-SB obscured AGN and the control sample that is dependent on stellar mass.
In Figure 7, we again split the non-SB obscured AGN sample on the median log
stellar mass: 9.32 $<$ log (M∗ [M⊙]) $<$10.7 (20 objects), 10.7 $<$ log
(M∗[M⊙]) $<$11.32 (20 objects). Using the same bin widths, we split the
control sample (20 objects). For the lower mass bin, we find fM = 0.39 $\pm$
0.19 and fM = 0.45 $\pm$ 0.22 for the non-SB obscured AGN sample and matched
control sample respectively. For the higher mass bin, we find fM = 0.55 $\pm$
0.15 and fM = 0.49 $\pm$ 0.28 for the non-SB obscured AGN sample and matched
control sample respectively. We find that again the difference between the
non-SB obscured AGN sample and the control sample is not statistically
significant ($<2\sigma$ difference).

Figure 9: Merger Probabilities of non-SB Obscured AGN in two
L${}_{\textrm{Torus}^{*}}$ bins: The light blue filled histogram is for non-SB
obscured AGN sample with objects with L${}_{\textrm{Torus}^{*}}<$ 2.6$\times
10^{43}$ erg s-1, and the dark blue un-filled histogram for non-SB obscured
AGN with L${}_{\textrm{Torus}^{*}}>$ 2.6$\times 10^{43}$ erg s-1

###  4.3 Dependence on Obscuration and AGN Power

We then test whether there is any differences in merger probabilities for
different levels of AGN obscuration and/or AGN power. In Figure 8, we split
the non-SB obscured AGN sample along the median of obscuration to produce two
bins of less obscured AGN (22 objects) versus more obscured AGN (25 objects).
For the lower and higher NH bin, we find fM = 0.48 $\pm$ 0.11 and fM = 0.47
$\pm$ 0.11 respectively. We do not find a significant difference amongst the
extremely obscured objects versus the moderately obscured objects, as the
merger fractions are consistent with each other better than 1$\sigma$. As an
additional test, we compare the lower and higher NH bins against each of their
respective matched control samples. For the lower NH bin, we find fM = 0.48
$\pm$ 0.11 and fM = 0.46 $\pm$ 0.10 for the non-SB obscured AGN sample and
matched control sample respectively. For the higher NH bin, we find fM = 0.47
$\pm$ 0.13 and fM = 0.43 $\pm$ 0.25 for the non-SB obscured AGN sample and
matched control sample respectively.

We also test if there is a difference amongst the more powerful AGN in our
sample versus less powerful AGN. As in L20, we use L${}_{\textrm{Torus}^{*}}$
a rest-frame 5$\micron$ luminosity indicator, to probe AGN power. In Figure 9,
we show the merger probabilities of the non-SB obscured AGN split along the
median value of L5µm: 5.5$\times 10^{42}$ $<$ L5µm (ergs/s) $<$2.7$\times
10^{43}$ (32 objects), 2.7$\times 10^{43}$ $<$ L5µm (ergs/s) $<$ 2.3$\times
10^{45}$ (34 objects). For the lower and higher L5µm bin, we find fM = 0.37
$\pm$ 0.25 and fM = 0.47 $\pm$ 0.31 respectively. For the 5$\micron$ rest-
frame luminosity values we probe in our sample, we do not find a significant
difference between the two bins of non-SB obscured AGN, as the merger
fractions are consistent with each other better than 2$\sigma$. We then
compare the lower and higher L5µm bins against each of their respective
matched control samples. For the lower L5µm bin, we find fM = 0.49 $\pm$ 0.12
and fM = 0.47 $\pm$ 0.10 for the non-SB obscured AGN sample and matched
control sample respectively. For the higher L5µm bin, we find fM = 0.51 $\pm$
0.12 and fM = 0.48 $\pm$ 0.16 for the non-SB obscured AGN sample and matched
control sample respectively.

##  5 Discussion

In terms of merger fraction, we do not find any significant difference between
our non-SB obscured AGN sample and a redshift, F160W, non-starbursting non-AGN
galaxy sample. This is in tension with both theoretical and observational
works that place heavily obscured AGN within a major-merger-driven
evolutionary paradigm. It has been speculated that the AGN-merger connection
may have been systematically missed due to poor sampling of obscured AGN
(Kocevski et al., 2015). Kocevski et al. (2015) were amongst the first to
attempt a careful investigation of such a relationship, by selecting one of
the largest samples of obscured AGN of its time using multiple deep-field
X-ray data-sets. However, differently from our work, they only used one HST
NIR band (F160W), employed a smaller number of human classifiers (2), and
their statistical analysis did not consider the biases we work to address
here. Additionally, the control sample in Kocevski et al. (2015) consisted of
un-obscured X-ray selected AGN. They were selected to match their obscured
sample in both redshift and X-ray luminosity only. Conversely, in this work
our control sample consists of inactive galaxies. This is important because
un-obscured AGN may have a significant un-resolved point-like component in
their images, thus making morphological classification of and estimation of
the stellar properties of host galaxies with bright point-sources extremely
difficult. Interestingly, as noted by these authors, when they remove the
sources with point source morphologies, the significance of the merger excess
in the heavily obscured AGN sample drops from $3.8\sigma$ to $2.5\sigma$.

Another significant difference is the star-formation properties were not
determined prior to control sample creation. As mentioned in Section 2.1, both
theoretically and observationally there is a strong association between
mergers and starbursting galaxies (Sanders & Mirabel, 1996; Veilleux et al.,
2009; Kartaltepe et al., 2012; Rodríguez Montero et al., 2019). Many AGN
studies focusing on the morphology of AGN host galaxies do not properly remove
starburst galaxies from their samples. It is in fact very difficult to
adequately take this into account. Since large samples of AGN with deep
optical/UV imaging at the redshift distribution probed in this work usually
lack the required high S/N IR spectra to accurately de-tangle the SF and AGN
contribution to the IR. If the AGN sample contains more (or less) star-
bursting galaxies than the control sample, a non-causal merger excess (or
deficit) can be found in the obscured sample.

Figure 10: Including obscured AGN with hosts undergoing a star-bursts reveals
the importance of including SF properties in the counterpart sample creation.

To check if the uneven inclusion of starburst galaxies would generate any
significant bias on our results, we re-run our analysis of non-SB obscured AGN
while including potential starburst galaxies in the obscured sample. In
Section 2.1.2, we identified 10 starbursts in the HST-covered sub-sample of
the L20 obscured AGN sample. We input these additional 10 obscured AGN to the
non-SB obscured AGN sample used in this study, while also including 10 (non-
starbursting) redshift, and F160W matched to the control galaxy sample. We do
to this to mimic the effect of studies that do not take into account the
presences of SB in their sample creation, and may have uneven amounts of SBs
between their science sample and control sample. As seen in Figure 10, with
the inclusion of only 10 star-bursting galaxies, the obscured AGN merger
fraction increases by 8%, and if the results were taken at face value this
would imply a 2$\sigma$ excess in the merger fraction of the obscured AGN
sample with respect to the control sample. However, this is only due to a bias
resulting from the inclusion of the starburst galaxies, and not to any
intrinsic physical association between obscured AGNs and mergers. In other
words, we are only seeing the possible connection between starbursts and
mergers, and no information on the role of mergers in triggering AGNs could be
derived by such an analysis. Though it remains to be seen whether the AGN that
are triggered by significant mergers are those with SBs in their host
galaxies. Due to the lack of sufficient data at hand, we do not compare the
merger fractions of obscured AGN with SBs as compared to control galaxies with
SBs.

Instead, as we have shown above, we find that heavily non-SB obscured AGN
(mean N${}_{H}=1e24$ erg s-1) are not associated in heavily merging systems
more than their inactive galaxy counterparts. One major implication of our
finding is that the cause of obscuration in most non-SB obscured AGN does not
seem to be linked to the funneling of large quantities of gas and dust due to
a significant merger as theorized by Hopkins et al. (2008) and others. AGN may
also appear to be obscured due to the orientation of either the torus or the
host galaxy itself. Star-forming, inactive galaxies usually are observed being
characterized by column densities on the order of $>10^{23}$ cm-2 when viewed
completely edge on. A notable example of this is the Milky Way. At redshifts
higher than this work (i.e z = 4), where galaxies can be extremely dust rich,
Circosta et al. (2019) measure Compton thick AGN-like obscuration (i.e NH
$>10^{24}$ cm-2) in non-AGN galaxies.

In summary, our results disfavor the major-merger driven non-SB obscured AGN
paradigm as the dominant process behind AGN triggering and the cause of the
obscuration. As shown in Lambrides et al. (2020), the population of obscured
AGN in this sample is representative of the lower to moderate luminosity
regime of obscured AGN. This regime makes up the predicted bulk of the
obscured AGN population as estimated by X-ray background models Gilli et al.
(2007). The similar merger rates for the obscured sources and the control
sample indicate that most obscured AGN are not correlated with major-mergers.
Our work does not rule out whether the merger-paradigm works for the highest
end of the AGN luminosity or SMBH mass distribution, but other works do (i.e
Villforth et al., 2017; Marian et al., 2019). As previously mentioned, the
region of the AGN luminosity parameter space our sample includes represent the
bulk of AGN activity at these redshifts.

It is also possible that minor mergers play a role in triggering AGN.
Theoretically, these minor mergers and fly-bys may be able to trigger a disk
instability which would ultimately cause the funneling of gas and dust towards
the center (Hopkins & Hernquist, 2006, 2009). At z $>$ 2, simulations find
small mergers (M1/M2 $<$ 1/4), are the most frequent (Rodriguez-Gomez et al.,
2015). In contrast, McAlpine et al. (2020), find that galaxy mergers in the
EAGLE simulations with mass ratios between 0.1 and 0.25 are not a
statistically relevant fueling mechanism for SMBHs. These minor fly-bys and/or
mergers are difficult to identify at these redshifts with the data in hand.
Future work will entail exploring the fraction of minor mergers in obscured
AGN systems, and quantifying the ability for human classifiers to separate
minor from major merging systems. Additionally, we plan to carefully analyze
the star-formation properties of AGN within and without star-bursting host
galaxies in the context of a galaxy’s morphology.

##  6 Summary and Conclusion

We test a key prediction of the AGN-Merger paradigm that connects nuclear
obscuration of AGN as a consequence of a significant galactic merger. Using a
sample of 40 non-starbursting low to moderate luminosity obscured AGN in the
GOODS-S field at $0.5<$z$<3.1$ derived from the deepest X-ray survey to date,
we construct a study to test if non-SB obscured AGN are found predominately in
major-merging systems. We construct a redshift, magnitude matched inactive
galaxy control sample comprised of 40 non-starbursting galaxies. Due to the
higher redshifts probed in the sample, we are probing AGN host galaxies that
are ill-suited for the most common automated merger identification schemes,
and thus we use a sample of 14 expert human classifiers to visually identify
the merger status of each galaxy. We estimate each individual classifier’s
accuracy at identifying merging galaxies/post-merging systems, and isolated
galaxies. We calculate the probability of each galaxy being in either a merger
or in an isolated system where merger is defined as a galaxy that can either
be in a major merger, minor merger, or majorly disturbed system. We do not
find any statistically significant evidence that non-SB obscured AGN are
predominately found in systems with evidence of significant merging/post-
merging features. We further split the sample into different bins of galaxy
properties and confirm that is not evidence for statistically significant
merger enhancement in non-SB obscured AGN galaxies.

We thank the anonymous referee for their thoughtful insight and important
contributions to this work. ELL is supported by STSCI’s Director’s
Discretionary Fund (DDRF) with account number D0101.90261. RG acknowledges
support from the agreement ASI-INAF n. 2017-14-H.O. This research has made use
of the NASA/IPAC Infrared Science Archive, which is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration. This publication makes use
of data products from the Wide-field Infrared Survey Explorer, which is a
joint project of the University of California, Los Angeles, and the Jet
Propulsion Laboratory/California Institute of Technology, funded by the
National Aeronautics and Space Administration. This publication makes use of
data products from the Two Micron All Sky Survey, which is a joint project of
the University of Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National Aeronautics
and Space Administration and the National Science Foundation. We acknowledge
the extensive use of the following Python packages: (McKinney, 2010; Virtanen
et al., 2020; Pérez & Granger, 2007; Hunter, 2007, respectively). This
research made use of astropy, a community-developed core Python package for
Astronomy (Astropy Collaboration et al., 2013).

##  Appendix A Demo Survey

In the following figure, we show the demo survey with answers given to the
human classifiers prior to classifying the full sample.

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