# The Relation between Morphological Asymmetry and Nuclear Activity in Low-
redshift Galaxies

Yulin Zhao Kavli Institute for Astronomy and Astrophysics, Peking University,
Beijing 100871, China  Department of Astronomy, School of Physics, Peking
University, Beijing 100871, China  Yang A. Li Kavli Institute for Astronomy
and Astrophysics, Peking University, Beijing 100871, China  Department of
Astronomy, School of Physics, Peking University, Beijing 100871, China  Jinyi
Shangguan Max-Planck-Institut für Extraterrestrische Physik (MPE),
Giessenbachstr., D-85748 Garching, Germany  Kavli Institute for Astronomy and
Astrophysics, Peking University, Beijing 100871, China  Ming-Yang Zhuang Kavli
Institute for Astronomy and Astrophysics, Peking University, Beijing 100871,
China  Department of Astronomy, School of Physics, Peking University, Beijing
100871, China  Luis C. Ho Kavli Institute for Astronomy and Astrophysics,
Peking University, Beijing 100871, China  Department of Astronomy, School of
Physics, Peking University, Beijing 100871, China

###### Abstract

The morphology of galaxies reflects their assembly history and ongoing
dynamical perturbations from the environment. Analyzing stacked $i$-band
images from the Pan-STARRS1 $3\pi$ Steradian Survey, we study the optical
morphological asymmetry of the host galaxies of a large, well-defined sample
of nearby active galactic nuclei (AGNs) to investigate the role of mergers and
interactions in triggering nuclear activity. The AGNs, comprising 245 type 1
and 4514 type 2 objects, are compared with 4537 star-forming galaxies matched
in redshift ($0.04<z<0.15$) and stellar mass ($M_{*}>10^{10}\,M_{\odot}$). We
develop a comprehensive masking strategy to isolate the emission of the target
from foreground stars and other contaminating nearby sources, all the while
retaining projected companions of comparable brightness that may be major
mergers. Among three variants of nonparametric indices, both the popular CAS
asymmetry parameter ($A_{\mathrm{CAS}}$) and the outer asymmetry parameter
($A_{\mathrm{outer}}$) yield robust measures of morphological distortion for
star-forming galaxies and type 2 AGNs, while only $A_{\mathrm{outer}}$ is
effective for type 1 AGNs. The shape asymmetry ($A_{\rm shape}$), by
comparison, is affected more adversely by background noise. Asymmetry indices
$\gtrsim 0.4$ effectively trace systems that are candidate ongoing mergers.
Contrary to theoretical expectations, galaxy interactions and mergers are not
the main drivers of nuclear activity, at least not in our sample of low-
redshift, relatively low-luminosity AGNs, whose host galaxies are actually
significantly less asymmetric than the control sample of star-forming
galaxies. Moreover, type 2 AGNs are morphologically indistinguishable from
their type 1 counterparts. The level of AGN activity does not correlate with
asymmetry, not even among the major merger candidates. As a by-product, we
find, consistent with previous studies, that the average asymmetry of star-
forming galaxies increases above the main sequence, although not all major
mergers exhibit enhanced star formation.

galaxies: evolution — galaxies: formation — galaxies: active — galaxies:
bulges — galaxies: photometry — quasars: general

##  1 Introduction

Supermassive black holes (BHs) in the centers of galaxies grow mainly through
the accretion of gas (Sołtan, 1982), which loses angular momentum most
effectively through gravitational torques imparted by dynamical interactions
and mergers with neighboring galaxies (e.g., Hernquist 1989; Barnes &
Hernquist 1992; Di Matteo et al. 2005; Springel et al. 2005). This basic
theoretical expectation has led to a long historical prejudice that galaxies
hosting active galactic nuclei (AGNs) should manifest signatures of dynamical
perturbation, most readily in the form of external, large-scale morphological
asymmetry, such as tidal tails, lopsidedness, and perhaps even direct evidence
of ongoing disturbance by a visible companion. Moreover, if AGNs are triggered
externally by dynamical perturbations, one would naively expect a correlation
between the level of nuclear activity and the degree of perturbation.

Previous investigations paint a confusing picture. While many studies argue
that both the incidence and intensity of nuclear activity are linked to galaxy
mergers and interactions (e.g., Ellison et al. 2011; Silverman et al. 2011;
Bessiere et al. 2012; Treister et al. 2012; Hong et al. 2015; Goulding et al.
2018; Kim et al. 2021), the evidence becomes much murkier for less luminous
AGNs (e.g., Grogin et al. 2005; Cisternas et al. 2011; Villforth et al. 2014,
2017). X-ray-selected AGNs of moderate luminosity are especially challenging
because the majority reside in relatively late-type galaxies, whose very disky
nature casts doubt on the viability of the merger scenario for triggering the
activity (Schawinski et al., 2011, 2012; Kocevski et al., 2012; Simmons et
al., 2012). The resolution to these seemingly conflicting results lies in the
realization that the triggering mechanism depends on the level of AGN activity
(Hopkins & Hernquist, 2009; Draper & Ballantyne, 2012). Whereas the most
powerful quasars require a prodigious accretion rate that can only be supplied
by an external event as a galaxy merger, run-of-the-mill Seyferts, not to
mention of the even lower luminosity, radiatively inefficient nearby nuclei,
can be sustained by internal secular processes (Ho, 2008, 2009).

A closely related topic concerns the physical connection between AGNs of
different types. While the orientation-based unified model (Antonucci, 1993;
Urry & Padovani, 1995) has enjoyed much success in explaining the relationship
between broad-line (type 1) and narrow-line (type 2) AGNs, there has been
mounting observational evidence that the two AGN types must possess true
intrinsic differences, which are in part or in whole mediated by evolution
(e.g., Sanders et al. 1988). An incomplete list includes differences in host
galaxy morphology, star formation rate (SFR), velocity field, and environment
(Maiolino et al., 1997; Kim et al., 2006; Lacy et al., 2007; Greene et al.,
2011; Villarroel & Korn, 2014; Chen et al., 2015; Villarroel et al., 2017;
Zhuang & Ho, 2020).

Several practical hurdles need to be overcome in designing an effective
experiment to test the aforementioned ideas. Many older studies were plagued
by small-number statistics, which, fortunately, can now be ameliorated using
modern large-area surveys. Constructing an appropriate control sample is also
critically important to achieving a meaningful statistical comparison for
hypothesis testing. This, too, is helped enormously with the availability of
survey data. Finally, one should endeavor to abandon subjective visual
inspection and simplistic qualitative assessment (Lambrides et al., 2021), and
strive toward securing more rigorous, objective metrics to quantify the
morphological properties of galaxies.

The primary goal of this paper is to re-evaluate the question of whether the
host galaxies of AGNs are preferentially more morphologically disturbed than a
control sample of inactive galaxies of otherwise similar general makeup. As a
corollary, we evaluate whether the level of AGN activity varies with the
degree of morphological disturbance. Comprising both type 1 and type 2
sources, our AGN sample can further test for potential differences between the
two types, as might arise if they evolve from one to the other.

We take advantage of nonparametric measurements of galaxy structure, with
emphasis on several parameters commonly used to quantify the degree of
morphological asymmetry (Conselice, 2003; Wen et al., 2014; Pawlik et al.,
2016), and apply them to high-quality ground-based images from Data Release 2
of the Pan-STARRS1 $3\pi$ Steradian Survey (Chambers et al., 2016; Flewelling
et al., 2020). The stacked images of PanSTARRS have reasonable sensitivity
($5\,\sigma$ depth of 23.3, 23.2, 23.1, 22.3, and 21.3 mag in the $g$, $r$,
$i$, $z$, and $y$ band) and resolution [median full-width at half-maximum
(FWHM) of the point-spread function (PSF) is 1$\farcs$31, 1$\farcs$19,
1$\farcs$11, 1$\farcs$07, and 1$\farcs$02, respectively]. The original targets
were selected from the Sloan Digital Sky Survey (SDSS; York et al. 2000)
value-added MPA-JHU catalog (Brinchmann et al., 2004) of star-forming galaxies
(SFGs) and type 2 AGNs (AGN2s), supplemented by type 1 AGNs (AGN1s), which are
not included in the MPA-JHU database, from the catalog of Liu et al. (2019).

We carefully match the SFG, AGN2, and AGN1 samples according to their stellar
mass and redshift (Section 2.1). After developing a comprehensive strategy to
generate an effective mask to isolate the targets of interest from
contaminating sources (Section 2.3), we employ the statmorph package
(Rodriguez-Gomez et al., 2018) to calculate three frequently used
nonparametric measures of source asymmetry (Section 3): the CAS asymmetry
($A_{\mathrm{CAS}}$; Abraham et al. 1994, 1996; Conselice et al. 2000;
Conselice 2003), the outer asymmetry ($A_{\mathrm{outer}}$; Wen et al. 2014),
and the shape asymmetry ($A_{\mathrm{shape}}$; Pawlik et al. 2016). We
statistically compare the asymmetries of the three galaxy samples, assess the
incidence of major mergers, and discuss the connection between asymmetry and
nuclear activity and star formation (Section 4). A summary is given in Section
5. This paper assumes a Chabrier (2003) stellar initial mass function and a
cosmology with $H_{0}=70$ km s-1 Mpc-1, $\Omega_{m}=0.3$, and
$\Omega_{\Lambda}=0.7$.

##  2 Sample and Data Analysis

###  2.1 Sample Selection

We restrict our sample to low redshift ($0.04<z<0.15$) in order to avoid any
significant effect from cosmological evolution. We require $z>0.04$ to ensure
that the 3″ fiber of SDSS covers at least $20\%$ of each galaxy, to mitigate
aperture effects on emission-line measurements (Kewley et al., 2005). After
extensive visual inspection and experimentation, we find that the moderate
spatial resolution of the Pan-STARRS images renders it difficult to identify
clear morphological features for typical galaxies at $z\gtrsim 0.2$. This is
consistent with the study of de Albernaz Ferreira & Ferrari (2018), who
conclude that morphological classification of galaxies becomes challenging for
$z\gtrsim 0.2$ in images with PSF ${\rm FWHM}\gtrsim 1\arcsec$. We therefore
limit our sample redshift to $z<0.15$.

The MPA-JHU DR7 catalog (Brinchmann et al., 2004) provides the emission-line
measurements of active and inactive alaxies with narrow emission lines.
Following Kewley et al. (2006), we adopt the emission-line intensity ratio
diagnostic diagrams of Baldwin et al. (1981) to classify objects as star-
forming galaxies (SFGs), Seyferts, low-ionization nuclear emission-line
regions (LINERs), and composite sources. To obtain a robust classification, we
require the signal-to-noise ratio (S/N) of at least 3 for H$\alpha$, H$\beta$,
[O III] $\lambda$5007, [N II] $\lambda$6584, and [S II] $\lambda\lambda$6717,
6731. No S/N constraint was placed on the [O I] $\lambda 6300$ line, as it is
typically very weak. For the purposes of this study, our sample of AGN2s only
considers objects classified as Seyferts, whose accretion luminosities most
closely resemble those of the comparison sample of AGN1s selected from Liu et
al. (2019). We omit LINERs and composite sources, which, apart from having
characteristically lower luminosities, lower Eddington ratios, and a
distinctly different accretion mode compared to the Seyferts (Ho, 2009), also
suffer most readily from confusion by non-nuclear sources of excitation in
large-aperture spectra such as those of SDSS (Ho, 2008).

As the majority of nearby, optically selected AGNs reside in relatively
massive galaxies (Ho et al., 1997a; Kauffmann et al., 2003), we choose a
stellar mass cut of $M_{*}>10^{10}\,M_{\odot}$. We take advantage of the
GALEX-SDSS-WISE Legacy Catalog 2 (GSWLC-2; Salim et al. 2018), which provides
total stellar masses and SFRs based on analysis of the spectral energy
distribution covering photometric measurements of the entire galaxy from the
ultraviolet to the mid-infrared bands. These measurements are applicable to
the SFG and AGN2 subsamples. For the AGN1 sources, whose unobscured active
nucleus pollutes the integrated magnitude and colors of the host galaxy, we
derive $M_{*}$ from the empirical relation between BH mass and total stellar
mass, as recently calibrated by Greene et al. (2020).111We use the relation
for all galaxy types, $\log\,M_{*}=(\log\,M_{\mathrm{BH}}-7.43)/1.61+10.477$.
Although uncertain (0.81 dex intrinsic scatter), this method provides
practical, unbiased estimates of the stellar mass of AGN1s for statistical
study. The BH masses, with uncertainty 0.3–0.5 dex, were derived by Liu et al.
(2019) using the H$\beta$ virial BH mass estimator (for all bulge types) of Ho
& Kim (2015) and the conversion between H$\alpha$ and H$\beta$ line width from
Greene & Ho (2005).

Since the fraction of galaxy mergers depends on the mass of the system
(Hopkins et al., 2010), we match the stellar mass of the three samples. We
further match the redshift distribution of the samples because the galaxy size
relative to the spatial resolution also affects asymmetry measurements (Thorp
et al., 2021). Given the large uncertainty of the individual stellar masses
for AGN1s, we first match the distribution of redshifts and stellar masses for
the SFGs and AGN2s, and then proceed to match the AGN1s to the distributions
of SFGs and AGN2s. The sample matching is done following the acceptance-
rejection method used in Zhuang & Ho (2020), in redshift bins of size 0.02 and
stellar mass bins of size of size 0.1 dex, which yield an adequate number of
objects per bin to perform a Kolmogorov-Smirnov (K-S) test, which is used
extensively in our later analysis (Section 4).

The MPA-JHU catalog (see, e.g., Kauffmann et al. 2003) includes some so-called
intermediate-type (type 1.9) AGNs, which exhibit very weak broad H$\alpha$ but
no broad H$\beta$ emission (Osterbrock, 1989; Ho et al., 1997b). We regroup 22
such objects as AGN1s. After removing targets without robust asymmetry
measurements (Section 3), our final sample, summarized in Table 1, consists of
4537 SFGs, 4514 AGN2s, and 245 AGN1s. The three subsamples are well-matched in
stellar mass and redshift according to the K-S test (Figure 1). The small
number of AGN1s relative to AGN2s in our final sample is a consequence of our
mass-matching requirement. In a flux-limited survey, selection effects will
bias AGN1s to fainter (lower mass) host galaxies than AGN2s because the total
flux of AGN1s includes a nonstellar contribution from the bright active
nucleus.

Galaxies of a given stellar mass can have different bulge-to-total ratio or
light concentration. Following standard practice (Bershady et al., 2000;
Conselice, 2003), we define the concentration parameter as
$C=5\log\,(R_{80}/R_{20})$, where $R_{80}$ is the radius that contains 80% of
the light within 1.5 times the Petrosian (1976) radius $R_{\mathrm{P}}$, and
$R_{20}$ is the radius that contains 20% of the light within
$1.5\,\mbox{$R_{\mathrm{P}}$}$. Figure 2a illustrates that SFGs have lower $C$
(mean and standard deviation $2.99\pm 0.42$) than AGN1s ($3.24\pm 0.49$) or
AGN2s ($3.21\pm 0.41$) according to the Student’s $t$-test ($p<10^{-3}$),
while both AGN types are statistically similar ($p=0.11$). This is
unsurprising, for AGNs are selected to contain accreting central BHs, most
(Kormendy & Ho, 2013), if not all (Greene et al., 2020), of which reside in
bulges. Low-redshift AGNs are preferentially hosted by earlier type galaxies
(Ho et al. 1997a; Kauffmann et al. 2003; Bruce et al. 2016; Kim et al. 2017,
2021) which tend to have more prominent bulges (Simien & de Vaucouleurs, 1986;
Gao et al., 2019) and hence higher concentration (Strateva et al., 2001).
Moreover, earlier type galaxies tend to have lower asymmetry (e.g., Conselice,
2003). To ensure a rigorous match between the active and inactive samples, it
is desirable to control for the concentration. In the subsequent analysis, we
study the statistics of the asymmetry parameters using the samples with and
without matching for $C$ (Figure 2). However, we find that our main
conclusions are not sensitive to this choice, and, therefore, to maximize the
sample sizes we only report the results for the samples without matching in
$C$.

Table 1: Sample and Measurements

Index | R. A. | Decl. | $z$ | log $M_{*}$ | log SFR | log $L_{\text{[O\textrm{\tiny III}]}}$ | Merger | $C$ | $A_{\rm CAS}$ | $A_{\rm outer}$ | $A_{\rm shape}$ | $R_{\rm P}$ | $R_{\rm max}$ | $R_{\rm half}$ | Type
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (°) | (°) |  | ($M_{\odot}$) | ($M_{\odot}$ yr-1) | ($\mathrm{erg\,s^{-1}}$) | Flag |  |  |  |  | (″) | (″) | (″) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15) | (16)
1 | 243.21553 | 0.37976 | 0.045 | 10.27 | 0.28 |  $\cdots$ | 0 | 2.99 | 0.05 $\pm$ 0.07 | 0.01 $\pm$ 0.12 | 0.22 | 29.49 | 64.28 | 17.81 | SFG
2 | 191.71165 |  $-$0.73805 | 0.048 | 10.15 | 0.01 |  $\cdots$ | 0 | 2.61 |  $-$0.01 $\pm$ 0.04 |  $-$0.02 $\pm$ 0.05 | 0.17 | 30.54 | 44.59 | 16.36 | SFG
3 | 240.29665 |  $-$0.82616 | 0.058 | 10.73 | 0.82 |  $\cdots$ | 0 | 3.76 | 0.02 $\pm$ 0.01 | 0.03 $\pm$ 0.03 | 0.24 | 36.30 | 63.79 | 17.52 | SFG
4 | 202.05917 |  $-$0.39532 | 0.055 | 10.53 | 0.07 |  $\cdots$ | 0 | 3.56 |  $-$0.01 $\pm$ 0.07 |  $-$0.04 $\pm$ 0.10 | 0.20 | 27.95 | 67.27 | 17.71 | SFG
5 | 202.91333 |  $-$0.33779 | 0.056 | 10.32 |  $-$0.02 |  $\cdots$ | 0 | 2.43 | 0.00 $\pm$ 0.01 |  $-$0.02 $\pm$ 0.02 | 0.18 | 20.68 | 32.56 | 10.95 | SFG
6 | 221.38405 |  $-$1.15580 | 0.041 | 10.39 |  $-$0.75 | 39.83 | 0 | 3.91 | 0.03 $\pm$ 0.02 |  $-$0.01 $\pm$ 0.03 | 0.19 | 31.51 | 73.17 | 16.69 | AGN2
7 | 231.17522 |  $-$0.81717 | 0.052 | 10.53 | 0.19 | 39.99 | 0 | 2.97 | 0.01 $\pm$ 0.02 | 0.01 $\pm$ 0.05 | 0.25 | 21.51 | 55.89 | 14.94 | AGN2
8 | 244.38397 |  $-$0.28378 | 0.057 | 10.17 | 0.40 | 41.18 | 0 | 2.99 | 0.01 $\pm$ 0.01 |  $-$0.01 $\pm$ 0.04 | 0.19 | 10.17 | 26.42 | 4.96 | AGN2
9 | 240.82886 | 0.02428 | 0.041 | 10.17 |  $-$0.07 | 39.83 | 0 | 3.39 | 0.01 $\pm$ 0.02 |  $-$0.00 $\pm$ 0.04 | 0.19 | 21.76 | 58.49 | 13.67 | AGN2
10 | 214.25699 | 0.47709 | 0.052 | 10.90 | 0.27 | 39.97 | 0 | 3.43 | 0.03 $\pm$ 0.02 | 0.01 $\pm$ 0.03 | 0.27 | 59.02 | 113.90 | 30.47 | AGN2
11 | 10.65359 |  $-$10.82274 | 0.042 | 10.34 |  $\cdots$ | 41.42 | 0 | 3.60 | 0.09 $\pm$ 0.01 | 0.05 $\pm$ 0.04 | 0.23 | 18.70 | 45.64 | 8.41 | AGN1
12 | 12.85738 |  $-$10.44575 | 0.055 | 10.23 |  $\cdots$ | 39.97 | 0 | 3.26 | 0.02 $\pm$ 0.06 |  $-$0.01 $\pm$ 0.11 | 0.36 | 50.53 | 82.09 | 22.85 | AGN1
13 | 14.69785 |  $-$1.09716 | 0.047 | 10.47 |  $\cdots$ | 41.02 | 0 | 3.86 |  $-$0.00 $\pm$ 0.06 | 0.00 $\pm$ 0.09 | 0.19 | 29.54 | 48.62 | 13.26 | AGN1
14 | 20.49926 |  $-$1.04010 | 0.054 | 10.70 |  $\cdots$ | 41.76 | 0 | 4.56 | 0.11 $\pm$ 0.02 | 0.08 $\pm$ 0.05 | 0.18 | 31.32 | 74.67 | 14.25 | AGN1
15 | 120.68083 | 31.06759 | 0.041 | 10.88 |  $\cdots$ | 40.82 | 0 | 3.81 | 0.04 $\pm$ 0.03 | 0.06 $\pm$ 0.07 | 0.18 | 22.97 | 44.31 | 9.54 | AGN1

Note. — Column (1): Index number. Column (2): Right ascension. Column (3):
Declination. Column (4): Redshift. Column (5): Stellar mass of the host
galaxy. Column (6): Star formation rate. Column (7): [O III] luminosity,
corrected for Galactic but not internal extinction. Column (8): Merger flag: 0
= no candidate major merger pair; 1 = at least one candidate major merger
pair. Column (9): Optical concentration. Column (10): CAS asymmetry. Column
(11): Outer asymmetry. Column (12): Shape asymmetry. Column (13): Petrosian
radius. Column (14): The semi-major axis of the minimal ellipse (with fixed
center, elongation and orientation) that contains all of the main segment of
the shape asymmetry segmentation map. Column (15): The semi-major axis of an
elliptical aperture that contains 50% of the light. Column (16): Subsample
type.

(The full machine-readable table can be found in the online version.)

Figure 1:  (a) The final sample of 4537 star-forming galaxies (SFGs; blue),
4514 type 2 AGNs (AGN2; red), and 245 type 1 AGNs (AGN1; green) matched in (b)
redshift and (c) stellar mass. For clarity, the sample distributions in the
dense regions are represented by contours, with levels of 20 and 40
percentile. Figure 2: Distribution of optical concentration ($C$) for the
star-forming galaxy sample (SFGs; blue), the type 2 AGN sample (AGN2; green),
and the type 1 AGN sample (AGN1; red), (a) before and (b) after matching their
distributions.

###  2.2 Data Selection and Choice of Filter

We download the images from the Pan-STARRS1 data
archive222https://ps1images.stsci.edu/cgi-bin/ps1cutouts, adopting the stacked
images combined from multiple exposures (Waters et al., 2020), as they provide
the best S/N. We select image cutouts with a size that varies according to the
dimension of each target galaxy, choosing 20 $R_{\mathrm{P}}$ to ensure that
there is ample source-free region to measure the background accurately. The
Petrosian radius $R_{\mathrm{P}}$, which is insensitive to the depth of the
image and the S/N of the source (Rodriguez-Gomez et al., 2018), is obtained
from the SDSS DR16 database333https://www.sdss.org/dr16/data_access/ instead
of from the Pan-STARRS catalog, which lacks $R_{\mathrm{P}}$ measurements for
$\sim 10\%$ of our targets. Comparison of the size measurements for the
objects in common between the two catalogs reveals that $R_{\mathrm{P}}$ from
the SDSS catalog is on average $\sim 30\%$ lower than that measured from Pan-
STARRS images. We fit a linear relation between the two sets of data and use
it to convert the SDSS-based values of $R_{\mathrm{P}}$ to the Pan-STARRS zero
point.

Our analysis is based on $i$-band images, whose red bandpass offers the best
compromise in terms of sensitivity to stellar mass, minimization of the
effects of dust absorption, and PSF quality, while at the same time avoiding
the significant loss of sensitivity of the noisier $z$ and $y$ bands. We
explored the possibility of increasing the surface brightness sensitivity by
stacking the images of all five Pan-STARRS bands, and various combinations
thereof, but we finally abandoned the idea after discovering that the stacked
images occasionally introduced artifacts due to the uneven background and
ghost features, which can introduce spurious results in our asymmetry
measurements. For our purposes, the stacked images offered no advantage
compared to the $i$-band images.

Figure 3: (a) Example image of a target galaxy. The white dashed circle indicates $2\,\mbox{$R_{\mathrm{P}}$}$. Red and blue dashed circles mark the areas contaminated by unsaturated and saturated stars. Their masks are described by mask 1 and mask 2, respectively. (b) Segmentation map comprising mask 3 outside $2\,\mbox{$R_{\mathrm{P}}$}$ and mask 4 inside $2\,\mbox{$R_{\mathrm{P}}$}$. (c) Example image after all of the contaminated pixels have been masked by our final mask. Solid and open red stars mark the target galaxy and its candidate major merger companion, respectively, where the latter has a flux at least $1/4$ of that of the primary target. Table 2: SExtractor Parameters for Generating Masks | Stars | Galaxies
---|---|---
Parameters | Unsaturated | Saturated | Outside $2\,\mbox{$R_{\mathrm{P}}$}$ | Inside $2\,\mbox{$R_{\mathrm{P}}$}$
| mask 1 | mask 2 | mask 3 | mask 4
DETECT_THRESH | $1\,\sigma$
DETECT_MINAREA | 5
DEBLEND_NTHRESH | 32
BACK_SIZE | 32 | 256 | 256 | 256
DEBLEND_MINCONT | 0.001 | 1 | 0.001 | 0.005

###  2.3 Generating Segmentation Map and Mask

As our galaxies are typically not very extended ($\sim 30-50$ pixels in
diameter), determining the image background is not a critical step for the
asymmetry measurements, especially since the background of Pan-STARRS images
is usually relatively flat. Nevertheless, we recalculate and subtract the
median flux of the background, after iteratively clipping the source-free
image beyond $3\,\sigma$, where $\sigma$ is the standard deviation of the
background pixel distribution, using an initial mask generated with the
function make_source_mask in the Python package Photutils (Bradley et al.,
2020). We do not attempt higher-order fitting of the background in order to
avoid oversubtraction of real signal from the extended outskirts of galaxies.

For the actual measurement of asymmetry, we need a more elaborate procedure to
generate a mask that not only carefully flags contaminating sources and image
artifacts but also retains, if present, probable physical companions and
extended features arising from ongoing mergers and tidal interactions (Toomre
& Toomre, 1972; Barnes, 1992; Struck & Smith, 2012; Duc & Renaud, 2013). For
the majority of the non-stellar sources in the field, we do not know whether
they are associated with the primary target because they usually lack
spectroscopic redshifts, and photometric redshifts are both incomplete and not
accurate enough. Here we assume that any extended source projected within 2
$R_{\mathrm{P}}$ of the primary target having at least 25% of its flux to be a
candidate companion galaxy belonging to a major merger, which is normally
defined by a mass ratio of 1:4 (Bournaud et al., 2005; Conselice, 2014). We
make the simplifying assumption that the flux ratio in the $i$ band adequately
approximates the stellar mass ratio.

We use SExtractor (Bertin & Arnouts, 1996)444We verified that Photutils is
equally effective. to generate an image segmentation map to detect and deblend
sources. This code can generate a segmentation map with different levels of
complexity depending on the properties of the source and the goal of the
detection. This flexibility is necessary to cope with the many faint, small
sources that are often projected close to and overlap with the brighter, more
extended target of interest. Contamination by foreground stars, whether
saturated or not, also poses a challenge. Following common practice (e.g.,
Gray et al. 2009; Galametz et al. 2013; Sazonova et al. 2021), we use the
“cold” mode to identify the pixels of bright, extended sources using a high
detection threshold and a large minimum connecting area with proper
deblending. Faint, small sources are not detected in this mode. Meanwhile, a
“hot” mode that uses a low detection threshold and a small minimum connecting
area provides complementary information, at the expense of sometimes breaking
bright sources (e.g., a highly structured spiral galaxy) into many pieces
(Barden et al., 2012). The final source catalog then comprises objects
detected in the cold mode plus sources found in the hot mode where no cold
source was detected. The mask can then be generated by combining all the
source segments in the final catalog. We develop a new method that can detect
all sources comprehensively and generate a mask based on the area influenced
by them. We combine segmentation maps generated by SExtractor using four
modes, each designed to identify and mask a specific kind of contaminant.

SExtractor considers a source detected if there are at least DETECT_MINAREA
connected pixels above the detection threshold DETECT_THRESH, which is in
units of the background noise ($\sigma$). A low detection threshold
($\texttt{DETECT\\_THRESH}=1$) is effective to find all faint sources as well
as to capture the outskirts of bright stars. A source is classified as a star
or a galaxy based on a neural network algorithm (Nonino et al., 1999), with
the likelihood of it being a star indicated by the parameter CLASS_STAR
approaching unity. In common for all source types, we set
$\texttt{DETECT\\_THRESH}=1$ and $\texttt{DETECT\\_MINAREA}=5$. Two parameters
are important for deblending sources in a crowded field: the deblending
threshold (DEBLEND_NTHRESH) controls the level of deblending, and, following
the suggestion of the SExtractor manual, we set it to 32 to achieve strong
deblending; DEBLEND_MINCONT, the flux contrast to deblend several overlapping
objects, is set differently for different types of sources (Table 2). We set
the background mesh size to $\texttt{BACK\\_SIZE}=256$ pixels when we want to
detect the outskirts of a galaxy, and to 32 pixels for point sources, both
within the range suggested by Bertin & Arnouts (1996).

All the sources should be masked except for the target galaxy and, if present,
its possible major merger companion, which is defined as a non-stellar source
within $2\,\mbox{$R_{\mathrm{P}}$}$ from the central target having an
isophotal flux that exceeds 25% of the flux of the main target. Figure 3 gives
an example image of a target galaxy, its segmentation map, and final mask. We
classify the detected sources into four categories, each of which is treated
with a separate type of mask:

  1. 1.

Unsaturated stars (mask 1). We first generate the segmentation map with
$\texttt{BACK\\_SIZE}=32$ and deblend with contrast
$\texttt{DEBLEND\\_MINCONT}=0.001$. This step provides the list of all
detectable sources in the image. We mask the point sources (unsaturated stars)
with $\texttt{CLASS\\_STAR}>0.75$. The extended sources, which may be split up
by the aggressive deblending, are treated in subsequent steps. To fully mask
the wings of the PSF, we model the one-dimensional azimuthally averaged
surface brightness profile of the Pan-STARRS $i$-band PSF with a Moffat (1969)
function and estimate the full extent of the region influenced by the star.

  2. 2.

Saturated stars (mask 2). Saturated stars are characterized by a central core
flattened by the saturation limit and highly extended wings from the PSF. We
choose $\texttt{DEBLEND\\_MINCONT}=1$ to preclude deblending, so as to
guarantee the integrity of the segment of the saturated star, and a large
background mesh size of $\texttt{BACK\\_SIZE}=256$ in order to enclose the
outskirts of the extended emission. Instead of generating the mask based on
the isophotal flux, which is underestimated for saturated stars, we use the
isophotal segmentation area (ISOAREA_IMAGE) to trace the region influenced by
the saturated stars, adopting an empirical scaling between this area and the
radius of the circular mask.

  3. 3.

Galaxies at $>2\,\mbox{$R_{\mathrm{P}}$}$ (mask 3). To mask completely the
galaxies outside $2\,\mbox{$R_{\mathrm{P}}$}$, we again adopt
$\texttt{BACK\\_SIZE}=256$ and deblend the segmentation map with
$\texttt{DEBLEND\\_MINCONT}=0.001$ so as to separate the target from
neighboring galaxies. We then grow the segmentation map outside
$2\,\mbox{$R_{\mathrm{P}}$}$ by convolving it with a Gaussian kernel with
standard deviation 3 times the PSF FWHM (Figure 3c).

  4. 4.

Galaxies at $<2\,\mbox{$R_{\mathrm{P}}$}$ (mask 4). Within
$2\,\mbox{$R_{\mathrm{P}}$}$, we need to mask all stars and faint galaxies,
but keep the target and its possible major merger companion, if present. The
faint galaxies can be well masked by an elliptical aperture with semi-major
and semi-minor axis equal to 3 times those measured by SExtractor. To prevent
over-blending of fine structures such as tidal tails and spiral arms, we adopt
$\texttt{DEBLEND\\_MINCONT}=0.005$, which has moderate deblending effect, and
maintain BACK_SIZE = 256.

Figure 4: Analysis of an example star-forming galaxy using statmorph. (a)
Example image after the contaminated pixels have been masked by our final
mask. The target galaxy segmentation map is indicated by white contour. (b)
Residual image by subtracting the rotated image from the original image,
$I-I_{\mathrm{180}}$, around the asymmetry center marked by the blue dot.
$A_{\mathrm{CAS}}$ is integrated inside a circular region with radius
$1.5\,\mbox{$R_{\mathrm{P}}$}$ (blue dash aperture). (c) Same background as
panel (b), overlaid by an ellipse with semi-major axis $a=R_{\rm half}$ (solid
red) and another with $a=R_{\rm max}$ (dashed red); $A_{\mathrm{outer}}$ is
integrated between the two ellipses. (d) Segmentation map for calculating
$A_{\mathrm{shape}}$ within the green circle with radius $R_{\rm max}$.

##  3 Asymmetry Measurements

We use the Python package statmorph (Rodriguez-Gomez et al., 2018), with some
modifications, to calculate the asymmetry parameters. The code requires a
background-subtracted image, a mask image to identify the sources to be
ignored, and the segmentation map, which gives the position of the target and
is used to compute source properties such as its ellipticity and position
angle. The segmentation map derives from mask 4, after smoothing it with a box
kernel with size equal to $2\,\mbox{$R_{\mathrm{P}}$}$ of the target galaxy to
regularize it (Sazonova et al., 2021). Three types of asymmetry parameters can
be calculated by statmorph, and we use all of them in our analysis.

The “CAS” asymmetry is calculated by subtracting the target image with a
180°-rotated image of itself (Schade et al., 1995; Abraham et al., 1996;
Conselice et al., 2000):

$A=\frac{{\Sigma}_{i,j}|{I}_{ij}-{I}_{ij}^{180}|}{{\Sigma}_{i,j}|{I}_{ij}|}-\frac{N_{\mathrm{src}}\,\mbox{$A_{\mathrm{bkg}}$}}{{\Sigma}_{i,j}|{I}_{ij}|},$
(1)

where ${I}_{ij}$ and ${I}_{ij}^{180}$ are the pixel flux value and the one
rotated by 180°, respectively, ${A}_{\mathrm{bgk}}$ is the pixel-wise averaged
asymmetry of the background around the source, and $N_{\mathrm{src}}$ is the
number of unmasked pixels of the image of the source. The CAS asymmetry is
calculated within $1.5\,\mbox{$R_{\mathrm{P}}$}$ (Figure 4b). The rotation
center is the position that minimizes the asymmetry value. Instead of
measuring ${A}_{\mathrm{bgk}}$ within a single “sky box” that statmorph
adopts, we calculate it by randomly sampling the background 100 times,
requiring that there be $<10\%$ masked pixels inside the sample box (see
Appendix A for more details). We adopt a sample box size comparable to the
size of the target.

The outer asymmetry (Wen et al., 2014), $A_{\mathrm{outer}}$, also can be
defined by Equation (1). Instead of summing the pixels over the entire region
within 1.5 $R_{\mathrm{P}}$, we only sum the pixels inside an elliptical
annulus in the outskirts of the galaxy. The inner and outer semi-major axes of
the elliptical annulus are $R_{\rm half}$ and $R_{\rm max}$ (the red solid and
dashed ellipses in Figure 4c), where $R_{\rm max}$ is the maximum radius of
the target’s emission, which is defined rigorously below for the shape
asymmetry, and $R_{\rm half}$ is the radius that contains half of the total
flux within $R_{\rm max}$. The ellipticity and position angle of the annulus
are determined by the input segmentation map of the target (Rodriguez-Gomez et
al., 2018). The rotation center and ${A}_{\mathrm{bgk}}$ are identical to
those used for the CAS asymmetry.

In order to improve the sensitivity to the low surface brightness features of
the galaxy, the shape asymmetry ($A_{\mathrm{shape}}$; Pawlik et al. 2016) is
calculated using the same mathematical form as Equation (1), but based on the
“binary segmentation map” (Figure 4d), where the values of pixels belonging to
the target galaxy are 1, and the values of background pixels are 0. The key to
calculating the shape asymmetry calculation is separating target pixels from
background pixels. First, the background noise is estimated within a circular
annulus between 2 and 4 times $R_{\mathrm{P}}$. Within the annulus, pixels
with flux value above $3\,\sigma$ are iteratively clipped, until the mode
value converges to
$\texttt{mode}=2.5\times\texttt{median}-1.5\times\texttt{mean}$ (Bertin &
Arnouts, 1996). Second, contiguous pixels above the mode by $1\,\sigma$ are
considered as the target galaxy pixels, and they are marked with value 1; the
rest are marked with value 0. Lastly, we smooth this map by a $3\times 3$
boxcar filter to obtain the final binary segmentation map. The rotation center
is the same as that determined for the CAS asymmetry; the background asymmetry
($A_{\mathrm{bgk}}$) is, by definition, 0. We calculate $A_{\mathrm{shape}}$
within a radius $R_{\rm max}$ (green circle in Figure 4d), the distance of the
furthest galaxy pixel from the center.

During the course of making the asymmetry measurements, we flag and remove
from further consideration targets that fall under any of the following
conditions: (1) the target center is masked; (2) more than 20% of the pixels
within any of the regions used to calculate the three asymmetry parameters are
masked; (3) more than 20% of the pixels inside the input target segment region
are masked; and (4) the asymmetry center is incorrectly determined and far
from the target. A total of 11%, 12%, and 10% of the sources were removed for
these reasons from the SFG, AGN2, and AGN1 samples, respectively. We verified
through the K-S test that the remaining samples are still well-matched in
redshift and stellar mass.

Figures 5–7 give examples of the asymmetry parameters measured for the three
galaxy samples. The morphology of the galaxies becomes increasingly asymmetric
as $A_{\mathrm{CAS}}$, $A_{\mathrm{outer}}$, and $A_{\mathrm{shape}}$ progress
from low to high values. The rightmost column of each figure, which showcases
galaxies with the highest asymmetry, are mostly major mergers. The AGN1 sample
shows clear pointlike nuclei in some targets, although they are typically not
overwhelming. This is qualitatively consistent with the overall consistent
distribution of concentration parameters for the two AGN types (Figure 2a). As
discussed in Appendix A, while the $A_{\mathrm{CAS}}$ parameter of AGN1s may
be affected by nuclear emission, $A_{\mathrm{outer}}$ should be robust.

Comparing the three asymmetry parameters (Figure 8), we find very strong
correlations between $A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$ for all three
samples (Spearman correlation coefficient $\rho>0.9$ and $p<0.001$). However,
the correlations between $A_{\mathrm{CAS}}$ and $A_{\mathrm{shape}}$ are quite
weak for SFGs and AGN2s ($\rho\approx 0.2$, $p<0.001$), and it is
insignificant for AGN1s ($\rho=0.07$, $p=0.15$)555Throughout the paper, we
consider a result to be statistically significant if the $p$-value is smaller
than 0.01. We prefer 0.01 to 0.05 as the threshold because our sample sizes
are relatively large.. The parameter $A_{\mathrm{shape}}$, on account of its
strong sensitivity to the noise of the background, is only useful to identify
highly asymmetric sources and appears to be very uncertain when
$\mbox{$A_{\mathrm{shape}}$}<0.5$, which characterizes most of our targets.
Therefore, in the rest of the paper we mainly focus on $A_{\mathrm{CAS}}$ and
$A_{\mathrm{outer}}$ for SFGs and AGN2s, and for AGN1s we only use
$A_{\mathrm{outer}}$ to avoid possible systematic bias on $A_{\mathrm{CAS}}$
due to the central nucleus (Appendix A).

Figure 5: Example star-forming galaxies, showing (top) $A_{\mathrm{CAS}}$,
(middle) $A_{\mathrm{outer}}$, and (bottom) $A_{\mathrm{shape}}$, with
asymmetry values increasing from left to right, as labeled on the upper-right
corner of each panel. Figure 6: Example type 2 AGNs, showing (top)
$A_{\mathrm{CAS}}$, (middle) $A_{\mathrm{outer}}$, and (bottom)
$A_{\mathrm{shape}}$, with asymmetry values increasing from left to right, as
labeled on the upper-right corner of each panel. Figure 7: Example type 1
AGNs, showing (top) $A_{\mathrm{CAS}}$, (middle) $A_{\mathrm{outer}}$, and
(bottom) $A_{\mathrm{shape}}$, with asymmetry values increasing from left to
right, as labeled on the upper-right corner of each panel. Figure 8:
$A_{\mathrm{CAS}}$ versus (a) $A_{\mathrm{outer}}$ and (b)
$A_{\mathrm{shape}}$ for star-forming galaxies (SFG; blue), type 2 AGNs (AGN2;
green), and type 1 AGNs (AGN1; red). Major merger candidates are highlighted
as squares.

##  4 Results and Discussion

###  4.1 Comparing the Asymmetries of Star-forming Galaxies and AGNs

Figure 9 compares the measured asymmetry parameters of the three galaxy
samples. Somewhat to our surprise, the AGNs, whether both types combined or
each type separately, actually show lower levels of asymmetry compared to
SFGs, in all three asymmetry parameters, both for the whole sample covering
all redshifts ($0.04<z<0.15$) and separately for the lower ($0.04<z<0.10$) and
higher ($0.10<z<0.15$) redshift intervals. According to the K-S test and
Student’s $t$-test (Table 3), the null hypothesis that the asymmetry
parameters of the AGN and SFG samples are drawn from the same parent
population can be rejected with a probability of $p<10^{-3}$. This can be seen
in the slight but systematically lower mean and median values of the asymmetry
in AGNs compared to SFGs (Table 4). AGNs also have somewhat narrower asymmetry
distributions, as reflected in the lower standard deviations. As mentioned in
Section 2.1 (see Figure 2), the minor differences in concentration between the
AGNs and SFGs may be a potential source of concern when comparing active and
inactive galaxies. We have verified, but for the sake of brevity do not show,
that none of our main results are changed using subsamples that are matched in
$C$.

Our conclusions differ from those of Maiolino et al. (1997), who found that
Seyfert 2 galaxies are more likely to be interacting with a companion than are
the field galaxies and Seyfert 1 galaxies. The results of Maiolino et al.
(1997) were based on visual inspection of a relatively small sample, which, in
addition to being subjective, only pick up galaxy pairs or pre-mergers. Our
objective non-parametric method is more sensitive to weak morphological
distortions, and we have applied it to a large, homogeneous sample of AGNs and
a carefully matched sample of control galaxies. As discussed in Section 4.2,
AGN2s do not exhibit a higher incidence of candidate major merger pairs than
SFGs or AGN1s. The results are not sensitive to redshift. The typical half-
light radii of our sources is $\sim 2.5$ times the PSF size, and we have
verified that no strong dependence on redshift can be discerned (Figure 9),
consistent with the tests performed by Thorp et al. (2021) to evaluate the
effect of resolution on asymmetry measurements.

Another key finding is that both AGN types have statistically similar degrees
of asymmetry. We base this conclusion only on the results derived from
$A_{\mathrm{outer}}$, which, as argued in Section 3 and Appendix A, provides
the most reliable measure of asymmetry for AGN1s. Focusing on the entire
($0.04<z<0.15$) sample, the null hypothesis that AGN1s and AGN2s derive from
the same parent population can be rejected with a probability of $p=0.145$
according to the K-S test and $p=0.545$ according to Student’s $t$-test (Table
3).

Table 3: Results of Kolmogorov-Smirnov Test and Student’s $t$-test

|  | AGN1+AGN2/SFG |  | AGN2/SFG |  | AGN1/AGN2
---|---|---|---|---|---|---
$z$ | Parameter | K-S | $t$ |  | K-S | $t$ |  | K-S | $t$
(1) | (2) | (3) | (4) |  | (5) | (6) |  | (7) | (8)
0.04–0.10 | $A_{\mathrm{CAS}}$ | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$ |  | 0.060 | 0.114
$A_{\mathrm{outer}}$ | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$ |  | 0.025 | 0.099
$A_{\mathrm{shape}}$ | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$
0.10–0.15 | $A_{\mathrm{CAS}}$ | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$ |  | 0.046 | 0.300
$A_{\mathrm{outer}}$ | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$ |  | 0.516 | 0.439
$A_{\mathrm{shape}}$ | $<10^{-3}$ | 0.002 |  | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | 0.018
0.04–0.15 | $A_{\mathrm{CAS}}$ | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$ |  | 0.022 | 0.632
$A_{\mathrm{outer}}$ | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$ |  | 0.145 | 0.545
$A_{\mathrm{shape}}$ | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$ |  | $<10^{-3}$ | $<10^{-3}$

Note. — The $p$-values of the Kolmogorov-Smirnov test and Student’s $t$-test
on $A_{\mathrm{CAS}}$, $A_{\mathrm{outer}}$, and $A_{\mathrm{shape}}$
measurements of the SFG, AGN2, and AGN1 samples. Our analysis mainly focuses
on the $A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$ measurements of SFGs and
AGN2s and the $A_{\mathrm{outer}}$ results of AGN1s because the other
parameters are not robust (see Section 3 and Appendix A). Column (1): Redshift
range. Column (2): The three asymmetry parameters. Columns (3)–(4):
Comparisons between the AGN1+AGN2 and SFG samples. Columns (5)–(6):
Comparisons between the AGN2 and SFG samples. Columns (7)–(8): Comparisons
between the AGN1 and AGN2 samples.

Table 4: Statistics of the Asymmetry Parameters

$z$ | Parameter | Number |  | Mean |  | $\sigma$ |  | Median
---|---|---|---|---|---|---|---|---
SFG | AGN2 | AGN1 |  | SFG | AGN2 | AGN1 |  | SFG | AGN2 | AGN1 |  | SFG | AGN2 | AGN1
(1) | (2) | (3) | (4) | (5) |  | (6) | (7) | (8) |  | (9) | (10) | (11) |  | (12) | (13) | (14)
0.04–0.10 | $A_{\mathrm{CAS}}$ | 2542 | 2536 | 136 |  | 0.07 | 0.04 | 0.03 |  | 0.09 | 0.09 | 0.08 |  | 0.05 | 0.03 | 0.03
$A_{\mathrm{outer}}$ |  | 0.07 | 0.04 | 0.02 |  | 0.13 | 0.12 | 0.15 |  | 0.05 | 0.02 | 0.01
$A_{\mathrm{shape}}$ |  | 0.25 | 0.24 | 0.27 |  | 0.16 | 0.15 | 0.20 |  | 0.24 | 0.23 | 0.25
0.10–0.15 | $A_{\mathrm{CAS}}$ | 1995 | 1978 | 109 |  | 0.06 | 0.04 | 0.05 |  | 0.11 | 0.09 | 0.14 |  | 0.04 | 0.02 | 0.03
$A_{\mathrm{outer}}$ |  | 0.06 | 0.04 | 0.04 |  | 0.14 | 0.13 | 0.16 |  | 0.04 | 0.02 | 0.02
$A_{\mathrm{shape}}$ |  | 0.28 | 0.26 | 0.29 |  | 0.18 | 0.16 | 0.16 |  | 0.26 | 0.25 | 0.27
0.04–0.15 | $A_{\mathrm{CAS}}$ | 4537 | 4514 | 245 |  | 0.06 | 0.04 | 0.04 |  | 0.10 | 0.09 | 0.11 |  | 0.05 | 0.02 | 0.03
$A_{\mathrm{outer}}$ |  | 0.07 | 0.04 | 0.03 |  | 0.13 | 0.12 | 0.15 |  | 0.05 | 0.02 | 0.02
$A_{\mathrm{shape}}$ |  | 0.26 | 0.25 | 0.28 |  | 0.17 | 0.15 | 0.19 |  | 0.25 | 0.24 | 0.26

Note. — We randomly perturb the measured asymmetry parameters based on their
uncertainties and calculate the averaged mean, standard deviation ($\sigma$),
and median of the samples. The uncertainties of these parameters based on
bootstrapping are always smaller than 0.01. Column (1): Redshift range. Column
(2): The three asymmetry parameters. Columns (3)–(5): The number of sources in
each sample. Columns (6)–(8): The mean asymmetries of each sample. Columns
(9)–(11): The standard deviation of the asymmetries of each sample. Columns
(12)–(14): The median asymmetries of each sample.

Figure 9: Kernel-density estimates of (a) $A_{\rm CAS}$, (b) $A_{\rm outer}$,
and (c) $A_{\rm shape}$ for star-forming galaxies (SFG; blue), type 2 AGNs
(AGN2; green), and type 1 AGNs (AGN1; red), with median values indicated by
the vertical dashed lines, for objects with (left) $0.04<z<0.10$, (middle)
$0.10<z<0.15$, and (right) $0.04<z<0.15$ (whole sample).

###  4.2 Major Merger Fraction

As discussed in Section 2.3, we assume that any extended source projected
within 2 $R_{\mathrm{P}}$ of the primary target having at least 25% of its
flux to be a possible companion galaxy. We refer to these systems as major
merger candidates, with the caveat that the “post-mergers” when the two
galaxies are fully coalesced into one system are not being considered by this
definition. Among our total sample of 9296 galaxies, 293 ($\sim 3\%$) are
identified as major merger candidates, which are split roughly evenly among
the galaxy subsamples (146/4537 SFGs, 3.2%; 138/4514 AGN2s, 3.1%, and 9/245
AGN1s, 3.7%). This overall statistic is consistent with the fraction of major
mergers ($\sim 1\%-6\%$) among low-redshift galaxies with stellar mass
comparable to that of our sample galaxies ($M_{*}\gtrsim 10^{10}\,M_{\odot}$;
e.g., Darg et al. 2010; Mantha et al. 2018; Thibert et al. 2021). Figure 10
illustrates that the fraction of major merger candidates quickly reaches
nearly 100% when $A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$ exceed $\sim
0.4$. Although the merger fraction also increase toward higher values of
$A_{\mathrm{shape}}$, this parameter is less sensitive to mergers. In
agreement with previous studies (Conselice et al., 2000; Wen et al., 2014), we
concur that non-parametric asymmetry parameters offer a highly effective tool
to identify galaxy mergers, although previous studies, again, usually include
post-mergers which are also effectively selected using the asymmetry. The
overall consistency with previous works supports our assumption that most of
the major merger candidates are indeed physically related instead of projected
companions.

Figure 10: Fraction of major merger candidates (number ratio between major
merger candidates and all objects) as a function of (a) $A_{\rm CAS}$, (b)
$A_{\rm outer}$, and $A_{\rm shape}$ for star-forming galaxies (SFG; blue),
type 2 AGNs (AGN2; green), and type 1 AGNs (AGN1; red).

###  4.3 Relation with Nuclear Activity

Most AGNs in our sample are relatively symmetric. Unless the asymmetric
features of interaction quickly vanish in the $\lesssim 1~{}\mathrm{Gyr}$ time
lag between the merger event and the activation of the AGN (Wild et al., 2010;
Hopkins, 2012; Blank & Duschl, 2016; Yesuf & Ho, 2020), our results suggests
that galaxy-galaxy interactions and mergers, particularly major mergers, are
not the primary mechanism responsible for triggering nuclear activity in these
systems. In contrast to the evolutionary scenario, we also see no evidence
that asymmetry depends on AGN type. AGN2s have similar levels of asymmetry as
AGN1s. Neither of these results is surprising, in light of the very modest
levels of AGN activity present in the local Universe. For example, our sample
of AGN2s has a median [O III] luminosity of $10^{40.6}\,\mathrm{erg\,s^{-1}}$,
whereas for AGN1s $L_{\text{[O\textrm{\tiny III}]}}$
$=10^{41.0}\,\mathrm{erg\,s^{-1}}$, which, for a bolometric correction of
$L_{\rm bol}\approx 600$ $L_{\text{[O\textrm{\tiny III}]}}$ (Kauffmann &
Heckman, 2009), corresponds to $L_{\rm bol}\approx 10^{43.4}$ and
$10^{43.8}\,\mathrm{erg\,s^{-1}}$, respectively. With a median $M_{*}\approx
10^{10.8}\,M_{\odot}$, $M_{\rm BH}\approx 10^{8}\,M_{\odot}$, and AGN2s only
reach an Eddington ratio $\sim 0.002$, and for AGN1s $\sim 0.005$666The
foregoing estimates are based on [O III] luminosities that have been corrected
for Galactic extinction but not internal extinction. Zhuang & Ho (2020) report
a median internal extinction of $A_{V}=1.1$ mag for both low-redshift AGN1s
and AGN2s selected from SDSS, not dissimilar from those studied here.
Correcting for this amount of extinction would boost the luminosities and
Eddington ratios by a factor of $\sim 3$, not enough to materially alter our
conclusions.. Albeit substantially more active than the nearest supermassive
BHs (Ho, 2008), the level of nuclear activity in our sample is still much
lower than that of the bulk of low-redshift broad-line AGNs (e.g., Greene & Ho
2007; Liu et al. 2019) and type 2 quasars (Kong & Ho, 2018). These relatively
low-luminosity AGNs can be sustained largely by internal sources of fueling
mediated by secular processes (Ho, 2009) without the aid of external gas
supply furnished through dynamical interactions. The merger fraction of AGNs
studied by Treister et al. (2012), which have bolometric luminosity $\sim
10^{43.5}\,\mathrm{erg\,s^{-1}}$, agrees well with our results. Major mergers
only matter for more powerful sources (e.g., Weigel et al. 2018; Kim et al.
2021). For instance, studies based on images taken with the Hubble Space
Telescope find a major merger fraction of $\sim 20\%$ for type 1 quasars (Kim
et al., 2017; Zhao et al., 2021) and $\sim 40\%$ for type 2 quasars (Zhao et
al., 2019).

Does the degree of asymmetry correlate with the level of BH accretion in our
sample? We investigate this issue by examining the distribution of asymmetry
as a function of $L_{\text{[O\textrm{\tiny III}]}}$ and $M_{*}$, focusing
solely on the $A_{\mathrm{outer}}$ parameter, for which we have the greatest
confidence across all three galaxy samples (Section 3; Appendix A). We
separately identify the major merger candidates (Section 4.2), whose asymmetry
parameter was measured for the galaxy pair while the $L_{\text{[O\textrm{\tiny
III}]}}$ and $M_{*}$ pertain to the single central galaxy. Figure 11 indicates
that $A_{\mathrm{outer}}$ is distributed roughly uniformly for both AGN1s and
AGN2s. On average, $A_{\mathrm{outer}}$ among AGN2s shows a very moderate
tendency to increase toward higher $M_{*}$, which likely reflects the
environmental dependence of stellar mass (Hopkins et al., 2010; Weigel et al.,
2018). We hesitate to draw firm conclusions about the AGN1s, given their
limited statistics. The targets identified as major merger candidates show no
preference to host more luminous AGNs. Although $A_{\mathrm{CAS}}$ is less
robust for AGN1s, we confirm that all of the conclusions in Figure 11 hold if
we replace $A_{\mathrm{outer}}$ with $A_{\mathrm{CAS}}$. Our results resonate
with those of Stemo et al. (2021), whose analysis of a large sample of dual
AGNs reveals that the AGN luminosity of mergers is not significantly different
from that of the overall AGN population, while standing in contrast to the
general expectation that BH accretion should be enhanced by galaxy
interactions (Ellison et al., 2011; Van Wassenhove et al., 2012; Satyapal et
al., 2014).

Figure 11: The distribution of $L_{\text{[O\textrm{\tiny III}]}}$ vs. $M_{*}$
for (a) type 2 AGNs and (b) type 1 AGNs, color-coded by the
$A_{\mathrm{outer}}$ asymmetry index. Small circles are major merger
candidates (Section 4.2), and large squares represent the median values of the
other objects in bins of $M_{*}$ and $L_{\text{[O\textrm{\tiny III}]}}$. We
require that there are $\geq 10$ objects per bin in (a) and $\geq 5$ objects
per bin in (b).

###  4.4 Relation with Star Formation

Although not the main focus of this study, we briefly mention, for
completeness, the relation between morphological asymmetry and star formation,
as it pertains to the distribution of SFGs on the galaxy main sequence (e.g.,
Daddi et al. 2007; Elbaz et al. 2007; Noeske et al. 2007). It is evident from
Figure 12 that the average level of asymmetry ($A_{\mathrm{outer}}$) increases
mildly but systematically above the main sequence, echoing the recent findings
of Yesuf et al. (2021). Consistent with previous work (e.g., Cibinel et al.,
2019), major merger candidates (Section 4.2) stand out the most, but it is
notable that a significant fraction of major merger candidates also lie on and
below the main sequence (Figure 12b). From their morphological classication of
over 200,000 galaxies using convolutional neutral networks, Pearson et al.
(2019) recently also reported that mergers do not show significantly different
SFRs compared to non-mergers, although they find that the fraction of mergers
is significantly higher among galaxies above the main sequence. Perhaps the
major merger candidates below the main sequence are dominated by projected
pairs and are really not interacting systems. We visually checked these
targets but could not see any obvious clues. Tidal features are clearly seen
in some of them, proving that they are true physical mergers. Another
possibility is that the low-SFR pairs signify dry mergers or mixed mergers,
which dominate the merger population at low redshifts (Lin et al., 2008),
wherein at least one of the member galaxies is cold gas-deficient.

Figure 12: (a) The distribution of SFR vs. $M_{*}$ for the SFG sample, color-
coded by the $A_{\mathrm{outer}}$ asymmetry index. Small circles are major
merger candidates (Section 4.2), and large squares represent the median values
of the other objects in bins of $M_{*}$ and SFR. We require that there are
$\geq 10$ objects per bin. The dashed line is the local SFG main sequence from
Elbaz et al. (2007), converted to the stellar initial mass function of
Chabrier (2003). (b) The relation between $A_{\mathrm{outer}}$ asymmetry and
the distance from the main sequence, $\log\,({\rm SFR}/{\rm SFR}_{\rm MS})$,
where SFRMS is the SFR along the main sequence.

##  5 Summary

The morphological asymmetry parameter offers an efficient, model-independent
measure to constrain the local environment of large samples of galaxies. This
work uses three asymmetry indicators ($A_{\mathrm{CAS}}$,
$A_{\mathrm{outer}}$, and $A_{\mathrm{shape}}$), conveniently built into the
Python package statmorph, to quantify the morphological asymmetry of the
$i$-band images of over 9000 nearby ($0.04<z<0.15$), massive
($M_{*}>10^{10}\,M_{\odot}$) galaxies drawn from the SDSS spectroscopic
database and the Pan-STARRS1 $3\pi$ Steradian Survey, to investigate the role
of mergers and interactions in triggering nuclear activity. The active
galaxies, comprising both type 1 and type 2 AGNs, are carefully matched to a
control sample of star-forming galaxies. We develop a comprehensive strategy
to effectively isolate the signal from the target galaxy and associated
neighbors sizable enough to be a candidate major merger, all the while masking
other contaminating galaxies and field stars. We perform a variety of
experiments to test the efficacy and limitations of the three asymmetry
indicators, as well as to obtain robust estimates of their uncertainties.

Our main results are as follows:

  * •

While all three indicators can trace visible morphological distortions over a
wide dynamic range in asymmetry for the chosen sample and image quality of the
Pan-STARRS survey, the parameters $A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$
perform best for galaxies without a prominent nucleus (star-forming galaxies
and type 2 AGNs), $A_{\mathrm{outer}}$ can be effective even in the presence
of a bright nucleus (type 1 AGNs), and $A_{\mathrm{shape}}$ should be avoided
for all galaxy types because of its sensitivity to background noise.

  * •

Roughly 3% of the galaxies at $z<0.15$ are likely major merger systems that
can be identified effectively as having $A_{\mathrm{CAS}}$ and
$A_{\mathrm{outer}}$ values $\gtrsim 0.4$.

  * •

Contrary to the expectations of the merger-driven scenario for AGN evolution,
the host galaxies of AGNs exhibit lower degrees of asymmetry than the control
sample of star-forming galaxies. Both type 1 and type 2 AGNs also have
comparable levels of asymmetry. We find no clear correlation between asymmetry
and AGN luminosity, not even for major merger candidates.

  * •

A large portion of the star-forming galaxies with the largest asymmetry lie
offset above the star-forming main sequence in the regime occupied by
starbursts, but not all major merger candidates are actively forming stars,
possibly because they are gas-poor.

Y. Z. thanks Ruancun Li for his helpful technical advice. This research was
supported by the National Science Foundation of China (11721303, 11991052) and
the National Key R&D Program of China (2016YFA0400702).

##  Appendix A Uncertainties of Asymmetry Parameters

We follow the method of Shi et al. (2009) to calculate the uncertainty of the
CAS asymmetry, and we generalize the method to calculate the uncertainty of
the other asymmetry estimators. We show that the typical uncertainty of
individual targets is consistent with the width of the negative part of the
measured sample distribution, indicating that noise from the background
dominates the uncertainties of the CAS and outer asymmetry. Although the shape
asymmetry is not affected by the background, we can adopt a similar method to
estimate its uncertainty using the measured sample distribution of
asymmetries.

Based on mock images generated from observed galaxies and the background
without source emission, Shi et al. (2009) perform tests to estimate the
background CAS asymmetry (see Equation 1) and conclude that the minimum value
of the background asymmetry used by Conselice et al. (2000) overestimates the
total asymmetry. Shi et al. measure the background asymmetry by randomly
sampling regions around the target galaxy, estimating it with the 15th
percentile of the sampled distribution, because the correction of the
background noise tends to underestimate the asymmetry of the source. They find
that the real $3\,\sigma$ uncertainty of the background asymmetry is $\sim 2$
times the RMS of the sampled background asymmetry. The latter is adopted as a
conservative estimate of the uncertainty of the CAS asymmetry.

Defined as
$\mbox{$A_{\mathrm{bkg}}$}=\Sigma|B_{0}-B_{180}|/N_{\mathrm{pixels}}$, the
background asymmetry originally estimated in statmorph is calculated simply
from the asymmetry of a background region that is free of any masked pixels.
We adopt this definition but measure $A_{\mathrm{bkg}}$ by randomly sampling
the image. We require the sampled region to be masked by no more than 10% and
only use the unmasked pixels to calculate $A_{\mathrm{bkg}}$. Following Shi et
al. (2009), we then adopt the 15 percentile of the sampled distribution as the
estimated background asymmetry. As shown in Figure A1, our values of the
background asymmetry, denoted by $A_{\mathrm{bkg,S09}}$, are slightly lower
than, but still fall within the $1\,\sigma$ scatter of, the values obtained
through statmorph ($A_{\mathrm{bkg,statmorph}}$). This is expected because
$A_{\mathrm{bkg,statmorph}}$ is on average close to the median (50 percentile)
of the randomly sampled $A_{\mathrm{bkg}}$. Thorp et al. (2021) recently also
use simulated galaxies to study how to properly correct the background
asymmetry. Calculating the background asymmetry from a region offset from the
source using statmorph, they find that the intrinsic asymmetry can be
recovered best by adopting the measured background asymmetry after scaling it
down by $\sim$15%.

We adopt 2 times the RMS of the randomly sampled $A_{\mathrm{bkg}}$ as the
estimated uncertainty of $A_{\mathrm{bkg}}$ of the source asymmetry. We
propagate the uncertainty of $A_{\mathrm{bkg}}$ according to Equation (1) and
obtain the ($3\,\sigma$) uncertainty of the source asymmetry. This method was
proposed by Shi et al. (2009) for the CAS asymmetry. We adopt the same
approach to estimate the uncertainty of the outer asymmetry and confirm its
robustness below. The typical uncertainties of $A_{\mathrm{CAS}}$ and
$A_{\mathrm{outer}}$ of the SFG sample are 0.03 and 0.06, respectively, with
an RMS of $\sim 0.03$. The uncertainty of $A_{\mathrm{outer}}$ is somewhat
larger because the total flux (the denominator in Equation 1) used for
$A_{\mathrm{outer}}$ is usually lower than that for $A_{\mathrm{CAS}}$.

Shi et al. (2009) studied images of galaxies observed with the Hubble Space
Telescope, which have very different characteristics compared to the ground-
based images from Pan-STARRS investigated here. In order to test the
uncertainty estimates of our galaxies derived using Shi et al.’s method, we
compare the sample distribution of $A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$
with the typical uncertainties for individual targets. First, consider the SFG
sample. The distributions of the asymmetry parameters display a long tail
toward higher value (Figure A2). Since the asymmetry parameters cannot be
lower than zero if they are noise-free, we can use the negative part of the
sample distribution to estimate the average uncertainty of $A_{\mathrm{CAS}}$
and $A_{\mathrm{outer}}$. We fit a Gaussian profile to the negative part of
$A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$ distributions, fixing the mean to
0. The $3\,\sigma$ value of the best-fit Gaussian (red curve in Figure A2) is
0.04 for $A_{\mathrm{CAS}}$ and 0.09 for $A_{\mathrm{outer}}$, which is
largely consistent with but slightly larger than the typical uncertainties of
individual targets reported above. This confirms that the uncertainty
introduced by the background primarily contributes to the error budget of our
$A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$ measurements of the SFGs. Previous
studies (e.g., Conselice et al., 2000; Thorp et al., 2021) found that the
asymmetry is dominated by the background noise if the source S/N is below 100.
With a typical S/N $\gtrsim 100$, our galaxies should have reliable asymmetry
measurements. The asymmetry center of the target is well constrained, and we
confirm that the uncertainty of the asymmetry is dominated by the noise of the
background and is inversely proportional to the source flux.

We confirmed that the method proposed by Shi et al. (2009) can be applied to
Pan-STARRS images of SFGs to estimate the uncertainties of $A_{\mathrm{CAS}}$
and $A_{\mathrm{outer}}$. Does the same conclusion hold for AGNs? The typical
uncertainties of $A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$ of both the AGN2
and AGN1 samples, based on Shi et al.’s method, are very close to those of the
SFGs. The uncertainties estimated from the AGN2 sample distributions (Figure
A3) are also very close to those of the SFG sample. This is not surprising
because AGN2s, lacking bright nuclei, are not dissimilar from SFGs from a
measurement point of view. However, the situation for AGN1s appears somewhat
more complicated (Figure A4). The sample distribution of $A_{\mathrm{CAS}}$
for AGN1s indicates an uncertainty that is more than twice as large as that
derived from Shi et al.’s method. This is likely due to the contamination by
the nuclear emission. The largely symmetric PSF will reduce the total
asymmetry, such that AGN1s would appear to have lower intrinsic
$A_{\mathrm{CAS}}$, whose distribution at $\mbox{$A_{\mathrm{CAS}}$}<0$ is
broader than those of SFGs and AGN2s. On the other hand, the uncertainties of
$A_{\mathrm{outer}}$ estimated from the sample distribution are still largely
consistent with those derived from Shi et al.’s method, because the asymmetry
is only calculated in the outer region of the host galaxy. We conclude that
our uncertainties estimated from Shi et al.’s method are robust for both
$A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$ when applied to AGN2s, and for
$A_{\mathrm{outer}}$ when applied to AGN1s. The $A_{\mathrm{CAS}}$ asymmetry
of AGN1s likely is affected significantly by the nuclear emission and
therefore should not be used.

Since the shape asymmetry does not require a correction for the background
asymmetry, we estimate its uncertainty from the measured sample distribution
of the asymmetry parameter. Fitting a Gaussian model to the measured
$A_{\mathrm{shape}}$ distribution on the left side of the peak, which is
centered at $\mbox{$A_{\mathrm{shape}}$}\approx 0.2$ (Figures A1c–A3c), the
$3\,\sigma$ width of SFGs, AGN2s, and AGN1s are 0.11, 0.10, and 0.21,
respectively. The shape asymmetry, being more sensitive to the lower S/N
features of the galaxy (Pawlik et al., 2016), is expected to show lightly
larger uncertainty than $A_{\mathrm{CAS}}$ and $A_{\mathrm{outer}}$. As
discussed in Section 3, we will not rely on $A_{\mathrm{shape}}$ for our main
analysis.

Figure A1: Comparison of the background asymmetry measured by the original
statmorph method with our method of random sampling, which follows Shi et al.
(2009). For clarity, only 150 randomly selected targets are plotted; the
results for the entire sample are statistically the same. The median and RMS
of the deviation between the two methods is given on the upper-left corner of
the bottom panel, which shows the residuals of the one-to-one relation (dashed
line) in the top panel. Figure A2: Distribution of the measured (a)
$A_{\mathrm{CAS}}$, (b) $A_{\mathrm{outer}}$, and (c) $A_{\mathrm{shape}}$ of
the SFG sample (black histogram). A Gaussian model (red curve) is fitted to
the part of each distribution to the left of the dashed vertical line. The
$3\,\sigma$ of the best-fit Gaussian model is displayed in the legend of each
panel. Figure A3: Distribution of the measured (a) $A_{\mathrm{CAS}}$, (b)
$A_{\mathrm{outer}}$, and (c) $A_{\mathrm{shape}}$ of the AGN2 sample (black
histogram). A Gaussian model (red curve) is fitted to the part of each
distribution to the left of the dashed vertical line. The $3\,\sigma$ of the
best-fit Gaussian model is displayed in the legend of each panel. Figure A4:
Distribution of the measured (a) $A_{\mathrm{CAS}}$, (b) $A_{\mathrm{outer}}$,
and (c) $A_{\mathrm{shape}}$ of the AGN1 sample (black histogram). A Gaussian
model (red curve) is fitted to the part of each distribution to the left of
the dashed vertical line. The $3\,\sigma$ of the best-fit Gaussian model is
displayed in the legend of each panel.

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