# The evolution of merger fraction of galaxies at $\it{z}$ $<$ 0.6 depending
on the star formation mode in the AKARI NEP–Wide field

Eunbin Kim1, Ho Seong Hwang1,2,3, Woong-Seob Jeong1, Seong Jin Kim3, Denis
Burgarella4, Tomotsugu Goto3, Tetsuya Hashimoto3,5, Young-Soo Jo1, Jong Chul
Lee1, Matthew Malkan12, Chris Pearson18,19,20, Hyunjin Shim6, Yoshiki
Toba7,8,9, Simon C.-C. Ho3, Daryl Joe Santos3, Hiroyuki Ikeda10,11, Helen K.
Kim12, Takamitsu Miyaji13,14, Hideo Matsuhara15,16, Nagisa Oi17, Toshinobu
Takagi21, Ting-Wen Wang3
1Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu,
Daejeon 34055, Korea
2Astronomy Program, Department of Physics and Astronomy, Seoul National
University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea
3SNU Astronomy Research Center, Seoul National University, 1 Gwanak-ro,
Gwanak-gu, Seoul 08826, Republic of Korea
4Institute of Astronomy, National Tsing Hua University No. 101, Section 2,
Kuang-Fu Road, Hsinchu 30013, Taiwan
5Aix Marseille Université, CNRS, Laboratoire d’Astrophysique de Marselle UMR
7326, 13388 Marseille, France
6Centre for Informatics and Computation in Astronomy (CICA), National Tsing
Hua University, 101, Section 2. Kuang-Fu Road,
Hsinchu, 30013, Taiwan
7Department of Earth Science Education, Kyungpook National University, 80
Daehakro, Bukgu, Daegu 41566, Korea
8Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-
ku, Kyoto 606-8502, Japan
9Academia Sinica Institute of Astronomy and Astrophysics, 11F of Astronomy-
Mathematics Building, AS/NTU, No.1, Section 4,
Roosevelt Road, Taipei 10617, Taiwan
10Research Center for Space and Cosmic Evolution, Ehime University, 2-5
Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan
11National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan
12National Institute of Technology, Wakayama College, Gobo, Wakayama 644-0023,
Japan
13Department of Physics and Astronomy, UCLA, 475 Portola Plaza, Los Angeles,
CA 90095-1547, USA
14Instituto de Astronomá sede. Ensenada, Universidad Nacional Autónoma de
México (UNAM), Km 107, Carret. Tij.-Ens.,
Ensenada, 22060, BC, México
15Leibniz Institut für Astrophysik Potsdam, An der Sternwarte 16, 14482
Potsdam, Germany
16Department of Space and Astronautical Science,The Graduate University for
Advanced Studies, SOKENDAI, 3-1-1, Yoshinodai,
Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan
17Institute of Space and Astronautical Science, Japan Aerospace Exploration
Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara,
Kanagawa, 252-5210, Japan
18Tokyo University of Science, 1-3, Kagurazaka Shinjuku-ku Tokyo 162-8601
Japan
19RAL Space, STFC Rutherford Appleton Laboratory, Didcot, Oxfordshire, OX11
0QX, UK
20Oxford Astrophysics, University of Oxford, Keble Rd, Oxford OX1 3RH, UK
21The Open University, Milton Keynes, MK7 6AA, UK
22Japan Space Forum, 3-2-1, Kandasurugadai, Chiyoda-ku, Tokyo 101-0062, Japan
Contact<EMAIL_ADDRESS>Address: SI-analytics, Yusungdaero
1689 gil 70, Yusung-gu, Daejeon, 34047, Korea

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We study the galaxy merger fraction and its dependence on star formation mode
in the 5.4 square degrees of the North Ecliptic Pole-Wide field. We select
6352 galaxies with AKARI $9\ \mu$m detections, and identify mergers among them
using the Gini coefficient and M20 derived from the Subaru/HSC optical images.
We obtain the total infrared luminosity and star formation rate of galaxies
using the spectral energy distribution templates based on one band, AKARI $9\
\mu$m. We classify galaxies into three different star formation modes (i.e.
starbursts, main sequence, and quiescent galaxies) and calculate the merger
fractions for each. We find that the merger fractions of galaxies increase
with redshift at $\it{z}$ $<$ 0.6. The merger fractions of starbursts are
higher than those of main sequence and quiescent galaxies in all redshift
bins. We also examine the merger fractions of far-infrared detected galaxies
which have at least one detection from $\it{Herschel}$/SPIRE. We find that
$\it{Herschel}$ detected galaxies have higher merger fraction compared to
non-$\it{Herschel}$ detected galaxies, and both $\it{Herschel}$ detected and
non-$\it{Herschel}$ detected galaxies show clearly different merger fractions
depending on the star formation modes.

###### keywords:

galaxies: evolution – galaxies: formation – galaxies: spiral – galaxies:
starburst – galaxies: star formation – infrared : galaxies

††pubyear: 2021††pagerange: The evolution of merger fraction of galaxies at
$\it{z}$ $<$ 0.6 depending on the star formation mode in the AKARI NEP–Wide
field–LABEL:lastpage

##  1 INTRODUCTION

Galaxy interactions and mergers are thought to play an important role in
galaxy evolution, impacting their morphologies, gas kinematics, and star
formation rates (Toomre & Toomre, 1972; Sanders et al., 1988; Barnes &
Hernquist, 1996; Conselice, 2006). Cold dark matter models predict that
galaxies have accreted their mass through hierarchical mergers (De Lucia et
al., 2006). Mergers are also suspected to trigger luminosity increases, from
active galactic nuclei (AGNs, Sanders & Mirabel 1996) and starbursts (Barnes &
Hernquist, 1996; Mihos & Hernquist, 1996; Cox et al., 2006). Enhanced star
formation can result from the tidal interactions of the galaxies that
compress/shock the gas, causing it to collapse and form stars (Barnes, 2004;
Kim, Wise & Abel, 2009; Saitoh et al., 2009). These merger-induced starbursts
are sometimes observed as luminous/ultra-luminous infrared galaxies (LIRGs/
ULIRGs), which have extreme far-infrared (FIR) luminosities of 1011 L⊙ and
1012 L⊙, respectively (Sanders & Mirabel, 1996). Several studies have shown
that the infrared luminosity of galaxies is statistically correlated with
mergers (Ellison et al., 2013; Larson et al., 2016). These can be seen as
morphological disturbances in LIRGs and ULIRGs (Elbaz & Cesarsky, 2003; Hwang
et al., 2007; Hwang & Park, 2009; Kartaltepe et al., 2010; Ellison et al.,
2013).

However, the merger contributions to starbursts in general is still unclear.
At high redshifts, average star formation rates are higher. LIRGs and ULIRGs
are often found on the “main sequence”, that is, obeying the correlation
between SFR and stellar mass of typical galaxies at a given redshift (Daddi et
al., 2007; Elbaz et al., 2007). Thus, we will define starbursts by comparison
with the star formation of other galaxies of a given stellar mass in the same
redshift bin. Previous studies have defined starbursts as galaxies
experiencing star formation three or four times above the median of the SFRs
of main sequence of star-forming galaxies (Elbaz et al., 2011; Rodighiero et
al., 2011; Schreiber et al., 2015). In a similar way, we divide galaxies into
three different star formation “modes” (i.e. starbursts, main sequence and
quiescent galaxies) in each redshift bin.

It is challenging to identify a large number of merger galaxies out to large
redshifts. There are two main methods to identify mergers – selecting close
pairs (Bundy et al., 2009; de Ravel et al., 2009; Man, Zirm & Toft, 2016;
Duncan et al., 2019) or using morphological disturbances (Conselice et al.,
2003; Lotz et al., 2008, 2011). For example, Kado-Fong et al. (2018) used the
Subaru/HSC images to select the merger galaxies at 0.05 $<z<$ 0.45 using
visually identified tidal features (e.g. shell or stream features) However,
for using close pairs, spectroscopic velocities for both pairs are needed.
Because spectroscopic observations are expensive, merger studies based on them
will suffer from incompleteness. Deep and high-resolution imaging (e.g. Hubble
Space Telescope) could avoid that incompleteness, but the merger fraction from
galaxy imaging may be ambiguous. Morphological disturbances presented the
late-stage of mergers can be determined by visual inspection or discriminate
quantitative outliers of morphological disturbances. Visual inspection is
subjective and time-consuming. High redshift galaxies can also be easily
misclassified because of wavelength-dependent morphology and surface
brightness effects (Bolin et al., 1991; Kuchinski et al., 2000; Windhorst et
al., 2002; Kampczyk et al., 2007).

In general, morphological types of galaxies are classified by the light
profiles of galaxies. The measured profile is the average intensity of a
galaxy as a function of radius, and can be mathematically fitted (e.g. Sérsic
profile, Sersic 1963). These parametrizations historically have been used to
classify galaxies into Ellipticals, Spirals and Irregular galaxies. There are
also non-parametric measures for galaxy classification, such as concentration,
asymmetry, clumpiness (CAS, Conselice, Bershady & Jangren 2000; Conselice et
al. 2003; Menanteau et al. 2006). In addition, there have been many studies of
morphological classification using the parameters of Gini coefficient and M20
(Lotz, Primack & Madau, 2004; Lotz et al., 2008). The Gini coefficient is a
measure whether the flux of a galaxy is concentrated or spread out (to be
formally defined in Section 3), and M20 is the the second-order moment of the
brightest 20 percent of a galaxy (Lotz, Primack & Madau, 2004; Lotz et al.,
2008). The Gini coefficient is originally used in economics to statistically
describe the distribution of wealth within a society. This coefficient was
applied to astronomical images to quantify the spread of galaxy light (Abraham
et al., 2003; Lotz et al., 2008), which is now widely used for morphological
analysis in astronomy. Between these two approaches (parametric vs. non-
parametric), non-parametric measurements may be less impacted by redshift.
Concentration, asymmetry, clumpiness are used for merger-finding, but
asymmetry measurement is less sensitive to the late-stage of mergers (Lotz et
al., 2008). The Gini coefficient and M20 are used for wide area surveys (Lotz,
Primack & Madau, 2004; Lotz et al., 2010a, b). These parameters are more
effective in classifying galaxies and identifying late-stage mergers than
concentration and asymmetry, and also more robust for galaxies with low
signal-to-noise ratios (Lotz, Primack & Madau, 2004; Lotz et al., 2008).
Therefore, we use the Gini coefficient and M20 for identifying mergers, for
quantitative comparison with other studies, and to secure a large sample from
our data.

Figure 1: LIR(MIR-FIR) versus LTIR from AKARI $9\ \mu$m (Top). LIR(MIR-FIR) is
fitted by CIGALE including at least one FIR band detection (Wang et al.,
2020). Diamonds and triangles represent AGNs classified with spectra and WISE
colour cut, respectively. (Middle) The ratio of the LTIR to LIR(MIR-FIR) as a
function of LTIR. (Bottom) The ratio of the LTIR to LIR(MIR-FIR) as a function
of redshift. Colour codes represent galaxies in different redshift ranges.

In this paper, we examine the evolution of merger fractions of galaxies with
redshifts up to $\it{z}$ = 0.6 in the AKARI North Ecliptic Pole (NEP)–Wide
field, and the variations in merger fractions of galaxies in three different
star-formation modes (i.e. starbursts, main sequence, and quiescent galaxies).
We also study how the FIR detection affects the merger fractions. In Section
2, we summarise our observational data and sample selection. Section 3
describes the morphological analysis to classify the galaxies using the Gini
and M20. We present the results and discussion in Sections 4 and 5,
respectively.

##  2 DATA

###  2.1 Optical images

We use deep optical images taken with the Hyper Supreme-Cam (HSC) on Subaru
8-m telescope in the AKARI NEP–Wide field covering 5.4 deg2 (Goto et al. 2017,
Oi et al. in accepted). The HSC has a 1.5 deg field of view (FoV) covered with
104 red-sensitive CCDs, and the pixel scale is 0.17 arcsec. It is the largest
FoV among the 8-m telescopes, and the size of FoV covered the AKARI NEP–Wide
field with only four pointings (see Figure 2 in Goto et al. 2017, Figure 1 in
Oi et al. in accepted). The observations of the NEP–Wide field were performed
in June 30th 2014 and August 7-10th in 2015. The 5$\sigma$ detection limits
are 28.6, 27.3, 26.7, 26.0, 25.6 AB mag, and the median seeings are 0.68,
1.26, 0.84, 0.76, 0.74 for $\it{g,r,i,z}$ and $\it{y}$-band, respectively. The
total number of identified sources in 5 bands is 3.5 million and more detailed
information on the data set is described in Oi et al. (accepted).

###  2.2 Multi-wavelength Data

We have used the multi-wavelength data set based on the catalogue of AKARI
mid-IR (MIR) galaxies newly identified by an optical survey by Subaru/HSC (Oi
et al., 2021). The infrared galaxies detected by AKARI’s NEP–Wide survey (Kim
et al., 2012) were cross-matched against deep HSC optical data, thereafter all
available supplementary data over the NEP–Wide field were merged together (Kim
et al., 2021).

Data merging of these two catalogues were carried out by positional matching
with the matching radii defined by 3-sigma positional offsets, which are more
rigorous than using PSF sizes (Kim et al., 2021). This band-merged catalogue
has 91,000 objects including $\sim$ 70,000 objects detected in N2, N3, N4
bands, $\sim$ 20,000 objects detected in S7, S9, L11, L18, L24 bands, and is
the reference catalogue for our sample selection in this study. Optical to
submillimeter (submm) photometry for AKARI sources are also added. Original
AKARI NEP-Wide field catalogue (Kim et al., 2012) includes CFHT/MegaCam ${\it
u^{*},g^{\prime},r^{\prime},i^{\prime},z^{\prime}}$ (Hwang et al., 2007),
Maidanak observatory/ SNUCAM B, R, I-band data (Jeon et al., 2010) and KPNO
/FLAMINGOS J and H band data (Jeon et al., 2014). Supplementally, the observed
data from CFHT/MegaPrime $\it{u}$-band (Huang et al., 2020), CFHT/MegaCam
${\it u^{*},g^{\prime},r^{\prime},i^{\prime},z^{\prime}}$ (Oi et al., 2014;
Goto et al., 2018), WIRCam Y, J and Ks band (Oi et al., 2014) are added to the
main catalogue. The main catalogue is also cross-matched with the $\it{WISE}$
catalogue (Jarrett et al., 2011), $\it{Spitzer}$/IRAC (Nayyeri et al., 2018)
and $\it{Herschel}$/PACS and SPIRE (Pearson et al., 2017, 2019). This band-
merged catalogue adopted spectroscopic redshifts for objects from several
observations, which include Keck/DEIMOS (Shogak et al., 2018; Kim et al.,
2018) and MMT/Hectospec and WIYN /Hydra (Shim et al., 2013). Subaru/FMOS (Oi
et al., 2017), GTC (Miyaji et al. in preparation) and the SPICY survey (Ohyama
et al., 2018) are also included. Photometric redshifts are determined (Ho et
al., 2021) using 26 bands from optical to NIR with the public code LePhare
(Arnouts et al., 1999; Ilbert et al., 2006), and the photo-z accuracy is
$\sigma$ = 0.053.

Figure 2: Distribution of radius for galaxies. Dotted line represents the
seeing size, 0.6 arcsec in the HSC $\it{i}$-band image. Blue and red
histograms represent the galaxies with photo-z and spec-z.  Figure 3: Total
infrared luminosity distribution as a function of redshift for 9-$\micron$
selected galaxies. Black circles and red crosses represent the galaxies with
spec-z and photo-z.

###  2.3 Physical Parameters of Galaxies

We derive the total infrared luminosity ($L_{\rm TIR}$, 8–1000 µm) using a set
of template spectral energy distributions (SEDs) of main sequence galaxies in
Elbaz et al. (2011) with each of AKARI bands, S7, S9, S11, L15, L18 and L24.
They defined a typical IR SED for main sequence galaxies using $\it{Herschel}$
data, this SED could extrapolate the total IR luminosity for galaxies that
only one measurement exists. Although $L_{\rm TIR}$ derived with FIR data
could be more accurate than that without FIR data, the latter case enables us
to secure a large number of samples (Calzetti et al., 2010; Galametz et al.,
2013).

To assure the validity of the $L_{\rm TIR}$ from one-band, we compare the
$L_{\rm TIR}$ with infrared luminosity ($L_{\rm IR}$ derived from MIR-FIR
bands, Wang et al. 2020). They calculated the $L_{\rm IR}$ using SED modeling
code CIGALE (Burgarella et al., 2005; Noll et al., 2009) with 36 bands ranging
from optical to submm bands, which is represented as a sum of dust and AGN
activities.

As seen in Figure 1, we compared the difference between $L_{\rm TIR}$ from
one-band and $L_{\rm IR}$ from MIR–FIR bands as a functions of $L_{\rm TIR}$
and redshift. $L_{\rm TIR}$ and $L_{\rm IR}$ up to around $L_{\rm TIR}$ = 1013
L⊙ show good agreement below $\it{z}$ $\sim$ 0.8, which may originate from the
effect of galaxy evolution on the SED over the cosmic time. The relation
between the total IR luminosity and one-band IR lunminosity could have
discrepancy as redshift inceases depending on which IR-band is used (e.g. 24
vs 8 µm, Elbaz et al. 2011). Since such a trend is commonly found in every
AKARI MIR band (7 – 24 µm), we used 9 $\micron$ band (S9) for sample selection
because of the largest number of sample. In the middle panel, the standard
deviation in $L_{\rm IR}$/$L_{\rm TIR}$ of galaxies except AGNs is 0.71. A
detailed sample selection is described in Section 2.4 and Table 1.

Since the $L_{\rm TIR}$ is usually used as good star formation indicator, we
calculate the $L_{\rm TIR}$ from the initial mass function (IMF). We adopt the
Salpeter (1955) initial mass function (IMF), which is also used for
calculating $L_{\rm IR}$ with CIGALE in Wang et al. (2020). The star formation
rates are calculated from the formula (12) in Kennicutt & Evans (2012) which
is

$\rm{log\dot{M_{*}}(M_{\odot}\rm{year^{-1}})={log}L_{x}-{log}C_{x}},$ (1)

where Lx units are [ergs s-1] and logCx = 43.41 adopting the calibration
factors from Hao et al. (2011); Murphy (2011). The stellar mass ($M_{*}$) is
derived from SED fitting with LePhare (Arnouts et al., 1999; Ilbert et al.,
2006) using 13 multi-wavelength data of CFHT/MegaCam $\it{u^{\prime}}$,
Subaru/HSC $\it{g,r,i,z,Y}$, CFHT/Wircam $\it{J,Ks}$, and AKARI N2, N3, N4,
S7, S9 bands. We convert $M_{*}$ from LePhare based on Chabrier (2003) IMF to
$M_{*}$ based on Salpeter (1955) IMF by dividing by a factor of 0.63 to fairly
compare with others (e.g. Schreiber et al. 2015; Pearson et al. 2018).

The star forming galaxies in the main sequence follow an empirical power-law
relation between the SFR and stellar mass. However, Smercina et al. (2018);
Draine et al. (2020) showed that quiescent galaxies have considerable scatter
on this relation when they compared different indicators such as LTIR,
H$\alpha$, neon lines, etc. Thus, considering to adopt separate conversion
factor for deriving the SFR for each different star formation mode might
improve the relation. However, because we have constrained galaxies with the
range of 9.0 $<$ log(M∗/M⊙) $<$11.5 including relatively massive quiescent
galaxies, we do not apply the separate conversion factor for quiescent
galaxies in this paper.

The star forming galaxies show tight correlations between LTIR and SFR (e.g.,
Kennicutt & Evans 2012; Hwang et al. 2010, 2012). However, this tight
correlation can break down for quiescent galaxies, especially for those with
low infrared luminosities (e.g., Smercina et al. 2018; Draine et al. 2020.
Thus, it is conceivable that this difference might affect our results.
However, the infrared luminosities of our sample galaxies (even for quiescent
galaxies) are generally high enough, the impact of this different correlation
is insignificant.

Table 1: Number of Galaxies with 5-sigma detection in different AKARI/IRC bands Band | S7 | S9 | S11 | L15 | L18 | L24
---|---|---|---|---|---|---
Total | 5007 | 9076 | 9099 | 8592 | 10133 | 2384
spec-z | 1022 | 1417 | 1388 | 1117 | 1186 | 532
photo-z | 5003 | 9072 | 9096 | 8589 | 10130 | 2382
Total (z$<$0.8) | 3702 | 7236 | 7377 | 4640 | 5068 | 1349
spec-z | 861 | 1239 | 1220 | 927 | 971 | 443
photo-z | 3659 | 7173 | 7317 | 4580 | 5010 | 1320
Total (z$<$0.6) | 3407 | 6425 | 6200 | 3392 | 3805 | 1150
spec-z | 820 | 1169 | 1137 | 849 | 893 | 413
photo-z | 3348 | 6331 | 6107 | 3307 | 3718 | 1108
Herschel detection | 739 | 1048 | 1051 | 805 | 853 | 467
Figure 4: Example of the morphological measurements for the galaxy performed
by statmorph. (a), (b), (c) are example images of mergers, Spiral, and
Elliptical galaxies, respectively. Black solid contours represent segmentation
maps and text labels represent the values of the Gini, M20 and CAS. F(G,M20)
and S(G,M20) show that bulge statistic and merger statistic. Detailed
parameter description is in Rodriguez-Gomez et al. (2019).  Figure 5: The
Gini–M20 diagram for galaxies at different redshift ranges. Red and black dots
represent galaxies in $\it{r}$ and $\it{i}$ band, respectively. Dashed lines
separate the regimes according to their morphological types; mergers in above
the dashed line, Ellipticals in right regime, and Spirals in below the dashed
line.

###  2.4 Sample Selection

Considering the total number of detected sources at each AKARI band in the
band-merged catalogue, we selected the S9 (9 $\micron$) band for our study
(see Table 1). The total number of galaxies in Table 1 presents the number of
galaxies with redshift information estimated from either spectroscopic or
photometric measurement. Although the total number of galaxies with L18 is the
largest in the whole redshift range, we select 9 $\micron$ detected galaxies
for our sample, because the number of galaxies is the largest at the redshift
below $\it{z}$ $=$ 0.6 where we finally analyse the data. Note that the total
number of 9 $\micron$ detected galaxies is 9,076 and it is reduced to be 7,236
and 6,425 at $\it{z}$ $<$ 0.8 and $\it{z}$ $<$ 0.6, respectively. To examine
the contribution from AGNs in our analysis, we overplot 190 AGNs in Figure 1,
which were identified by Baldwin-Phillips-Terlevich (BPT) emission-line ratio
diagrams (Shim et al., 2013). In addition, 30 IR-bright AGNs are found through
WISE W1 - W2 and W2 - W3 colour-colour diagrams with the criteria of Jarrett
et al. (2011) and Mateos et al. (2012). Figure 1 shows that AGNs are
significantly off the linear correlation of $L_{\rm TIR}$ and $L_{\rm IR}$.
This is because AGN-dominant galaxies have higher MIR luminosities compared to
star-forming galaxies (Spinoglio et al., 1995). Due to these templates are
based on star-forming galaxies, we remove these 219 AGNs (73 AGNs in $\it{z}$
$<$ 0.6) from the further analysis, and end up having 6,352 galaxies at
$\it{z}$ $<$ 0.6.

Figure 2 shows the normalised histogram of distributions of seeing corrected
half light radius ($R_{h}$) for galaxies in each redshift bin, from top to the
bottom. We separate the redshift into the range of 0.2 bin and find most of
galaxies in size are larger than the seeing 0.6 arcsec in the HSC
$\it{i}$-band in all redshift bins. Figure 3 shows the distribution of sample
galaxies on the redshift and the total infrared luminosity. Red and black
circles represent the sample with spectroscopic and photometric redshifts,
respectively. Upper and right panels show histograms of redshift and $L_{\rm
TIR}$, respectively.

##  3 Measurement of morphological parameters

The morphological parameters allow us to classify the galaxy types. In order
to quantify galaxy morphologies, we used the Gini coefficient and M20
classification method (Lotz, Primack & Madau, 2004).

The Gini coefficient is a statistical measure of distribution of income in a
population in economics, and recently has applied to astronomy as well
(Abraham et al., 2003; Lotz, Primack & Madau, 2004). The Gini can be computed
sorting the $\it{f_{i}}$ pixel value increasing order as

$\rm{G=\frac{1}{|\overline{f}|n(n-1)}\sum_{i=1}^{n}(2i-n-1)|f_{i}|}$ (2)

where $\it{\overline{f}}$ is the mean over the pixel values and $\it{n}$ is
the number of pixels. If all the flux of a galaxy is concentrated in one
pixel, G = 1, while a galaxy has a homogeneous surface brightness, G = 0
(Glasser, 1962).

The M20 is the second order moment of brightest regions of a galaxy. The
brightest 20 $\%$ of the light is normalised to the total second-order central
moment, Mtot (Lotz, Primack & Madau, 2004). These are defined as

$\rm{M_{tot}={\sum_{i}^{n}M_{i}}=\sum_{i}^{n}f_{i}[(x_{i}-x_{c})^{2}+(y_{i}-y_{c})^{2}]},$
(3)

$\rm{M_{20}=\rm{log}_{10}{\frac{\sum_{i}M_{i}}{M_{tot}},while\sum_{i}f_{i}<0.2f_{tot}}},$
(4)

where $\it{f_{i}}$ is the pixel flux value and $\it{x_{c},y_{c}}$ is the
galaxy centre. The centre is the point where $\it{M_{tot}}$ is minimised. The
M20 is anti-correlated with concentration; low M20 represents highly
concentrated galaxy.

We derive the non-parametric Gini and M20 using statmorph python code
(Rodriguez-Gomez et al., 2019) on galaxies in cutouts of $\it{r}$ and
$\it{i}$-band images. It constructs a segmentation map for Gini measurements
to be insensitive to dimming surface brightness for distant galaxies (Lotz,
Primack & Madau, 2004). The image of a galaxy is convolved with the Gaussian
kernel $\sigma$ = rpetro/5, where rpetro is the Petrosian radius. The mean
surface brightness within the rpetro is used to define threshold of flux, then
the pixel value above the threshold is assigned to the galaxy in the
segmentation map. Both the Gini and M20 are calculated on the segmentation
map. Figure 4 shows the examples of segmentation maps of three galaxies with
measured Gini and M20. It should be noted that the high-column density of dust
could impact the morphological classification of galaxies in the Gini-M20
space (Lotz et al., 2008). To briefly test this effect, we examine the
distributions of Gini and M20 for Herschel detected and non-detected galaxies.
Because the Herschel detection requires larger submm flux densities (i.e.
larger amount of dust than those with similar M∗/SFRs/Tdust; Hildebrand 1983,
this comparison can show the impact of dust on the morphological measurements.
The comparison does not show any systematic differences of Gini and M20
estimates between the two samples (not shown here), which is supported by the
Kolmogorov-Smirnov test with high significance levels (p $<$ 0.35). We
therefore do not think that the dust introduces a systematic bias in our
measurements of Gini and M20 parameter.

As Lotz et al. (2008) proposed criteria to separate galaxies into three galaxy
types on the Gini - M20 diagram using galaxies at 0.2 $<$ $\it{z}$ $<$ 1.2, we
adopt the classification criteria from the equation (4) of Lotz et al. (2008)
to divide galaxies into mergers, Spirals and Ellipticals on the Gini and
$M_{20}$ diagram: Mergers: G $>$ –0.14 M20 \+ 0.33, E/S0/Sa: G $<$ –0.14 M20
\+ 0.33, and G $>$ 0.14 M20 \+ 0.80, Sb/Sc/Irr: G $\leq$ –0.14 M20 \+ 0.33,
and G $\leq$ 0.14 M20 \+ 0.80.

Figure 5 shows the G–M20 distribution of our sample on $\it{r}$-,
$\it{i}$-band images for different redshift bins. We find that the
distribution of these two morphological parameters for galaxies on $\it{r}$-,
$\it{i}$-band images are not significantly different. We derive morphological
parameters for both $\it{r}$\- and $\it{i}$-band images to select the one that
gives similar rest-frame wavelengths for the comparison of galaxies at
different redshifts. Therefore, we adopt the parameters from $\it{r}$-band
images for the galaxies at $\it{z}$ $<$ 0.2, and from $\it{i}$-band images for
those at $\it{z}$ $>$ 0.2. To verify our morphological classification based on
the measurements of Gini and M20, we also conduct the visual inspection of the
optical images of all the galaxies in our sample. We find that only 1$\%$ of
the galaxies classified as mergers in our sample turn out to be spirals, and
1.7$\%$ of ellipticals and 0.2 $\%$ of spirals based only on the G-M20
classification are mergers. This contamination is small enough to have no
significant impact on our result. We therefore decided to keep the results
based on the automated classification based on the estimates of Gini and M20
to avoid any possible subjective misclassification based on visual
classification, especially for faint galaxies. Also, since the FWHM of a point
source in the i-band images is 0.84 arcsec corresponding to $\sim$ 3.8 kpc at
our median redshift (i.e. z $\sim$ 0.3), we could hardly find patchy features
of star formation in the galaxy images that could affect the Gini during
visual inspection of galaxies.

Figure 6: Merger fractions as a function of LTIR at different redshift. Filled
red circle, open green triangle, open blue rectangle represent galaxies at 0.0
$<\it{z}<$ 0.2, 0.2$<\it{z}<$ 0.4, 0.4$<\it{z}<$ 0.6, respectively. Figure 7:
Star formation rates for 9-$\micron$ selected galaxies as a function of
stellar mass at different redshift range. Solid line represents the average
SFR for main sequence galaxies (Schreiber et al., 2015) and upper and lower
dashed lines represent a factor of two above and below of this fit at each
redshift range. Dash-dotted line represents log(M∗) = 10.5. Blue solid line
shows the best fits for the main sequence galaxies in SDSS (Elbaz et al.,
2007). Red and black dots represent the galaxies with spec-z and photo-z,
respectively.

##  4 Results

It has been well known that the infrared luminosity of galaxies is closely
related to the merger activity of galaxies (Hwang et al., 2007; Ellison et
al., 2013; Larson et al., 2016). However, the situation can differ if we
consider a wide range of redshift. For example, Figure 6 shows the merger
fraction of galaxies in our sample as a function of infrared luminosity at
different redshift ranges. As expected, the merger fraction increases with
LTIR for a given redshift range. However, because the merger fraction could be
different depending on the redshift despite similar LTIR, we examine the
merger fraction focusing on star formation mode.

###  4.1 Merger fractions of galaxies at different star formation modes

The relation between star formation rate and stellar mass of galaxies is
tightly related to the star formation mode. To investigate the cosmic
evolution out to $\it{z}$ $\sim$ 1 over the star formation mode, we divide our
sample at each redshift bin (see Figure 7). We adopt the average SFR of main
sequence galaxies with stellar mass and redshift from the equation (9) of
Schreiber et al. (2015) to resolve star formation modes. They present an
analysis of statistical properties of star-forming galaxies using the
$\it{Herschel}$ and $\it{Hubble}$ $\it{H}$-band images in the redshift range
of $\it{z}$ $>$ 0.3. We extrapolate their relation to 0 $<$ $\it{z}$ $<$ 0.2
bin, but found that the extrapolated SFRs are higher than those of previous
studies (Brinchmann et al., 2004; Elbaz et al., 2007). Therefore, we used the
relation derived from the galaxies at low redshifts (i.e. SDSS galaxies z
$\approx$ 0.1, Elbaz et al. 2007) to adjust the extrapolated relation; we set
the average SFR of main sequence to be equal to that of SDSS at log(M∗/M⊙) =
10.0 in the redshift range with 0.0 $<\it{z}<$ 0.2, as shown in the left top
panel of Figure 7. We define the galaxies within 2 and 0.5 times the average
SFRs (dashed lines in Figure 7) as main sequence (MS) galaxies. Galaxies above
the upper dashed line are considered as starbursts (SB, SFR $>$
2$\times$SFRMS), and galaxies below the lower dashed line as quiescent
galaxies (QS, SFR $<$ 0.5$\times$SFRMS). Our samples are distributed in three
different star formation modes at 0.0 $<$ $\it{z}$ $<$ 0.2, however there are
fewer quiescent galaxies as redshift increases because of the MIR detection
limit. Note that quiescent galaxies becomes much fainter in the MIR ranges at
higher redshift. Therefore, we constrain the galaxies mass range of 9.0 $<$
log(M∗/M⊙) $<$ 11.5 as total sample to avoid extreme mass range of galaxies
and select the uniform sample over the star formation mode.

To better understand the overall star formation activity for galaxies by
minimising the mass effects, we plot the starburstiness (RSB) distribution in
Figure 8. Starburstiness represents the star formation activity which is a
measure of the excess in specific star formation rate of a galaxy compared to
that of a main sequence galaxy with the same stellar mass and is defined as
RSB = sSFR/sSFRMS (Elbaz et al., 2011). Figure 8 displays RSB of galaxies in
total mass range 9.0 $<$ log(M∗/M⊙) $<$11.5 (black solid histogram) and those
at 10.5 $<$ log(M∗/M⊙) $<$11.5 (blue dashed histogram). The galaxies with RSB
$<$ 0.5 and 2 $<$ RSB represent quiescent and starburst systems, respectively.
As expected, both samples show peaks around RSB =1. However, the bin of 0.6
$<$ $\it{z}$ $<$ 0.8 has fewer quiescent and main sequence galaxies than other
bins because of detection limit. Therefore we remove the sample in 0.6 $<$
$\it{z}$ $<$ 0.8 for further analysis. Because the quiescent galaxies could be
still affected by detection limits at all redshifts bins except 0.0 $<$
$\it{z}$ $<$ 0.2, it should be noted that the merger fractions of quiescent
galaxies mean upper limits.

Figure 9 shows the evolution of merger fractions for starbursts, main
sequence, and quiescent galaxies as a function of the redshift. We define the
merger fraction as the ratio of a number of merging galaxies to total number
of galaxies in each star formation mode within the redshift range. To minimise
the mass effects on the comparisons of merger fractions between the samples,
we examine the trend of galaxies with total (9.0 $<$ log(M∗/M⊙) $<$ 11.5) and
narrow (10.5 $<$ log(M∗/M⊙) $<$ 11.5) mass range in the left and right,
respectively. We find that merger fractions of all three different modes of
galaxies marginally increase with redshift in both panels of different mass
ranges. The merger fractions of galaxies in the total mass range at 0.0 $<$
$\it{z}$ $<$ 0.2 are higher compared to those of galaxies in the narrow mass
range. This is because there are more galaxy samples in the log(M∗/M⊙) $<$
10.5 as shown in Fig 7. We also find that the merger fractions of galaxies
differ for three star formation modes, and the merger fractions of starbursts
are higher than those of main sequence and quiescent galaxies in both panels.

We fit the merger fractions evolution with power-law (Patton et al., 2002;
Conselice, Yang & Bluck, 2009), which is given by
f${}_{m}=\alpha(1+z)^{m}+\rm{C}$. We use six points of merger fraction with
binsize 0.1 of redshift. For starbursts and main sequence galaxies, we obtain
the index $\it{m}$ = 0.90 $\pm$ 0.18 and 2.04 $\pm$ 0.13 in total mass range,
respectively, and $\it{m}$ = 1.81 $\pm$ 0.12 and 1.21 $\pm$ 0.08 in narrow
mass range, respectively. These are relatively similar or lower than those of
others (Conselice et al., 2003; Lotz et al., 2008; Qu et al., 2017).

To examine whether our results are robust against different main sequence
selections, we also use the evolutionary trend of main sequence locus in
Pearson et al. (2018). Following the single power-law they used, S = $\alpha$
[log(M∗) + 10.5] + $\beta$ (Pearson et al., 2018; Whitaker et al., 2012),
where $\alpha$ and $\beta$ is the slop and the normalisation, respectively, we
calculate the fit of SFR and $M_{*}$ of galaxies. We fix the $\alpha$ as 0.5
and interpolate the $\beta$ using the parameters from the table 2 in Pearson
et al. (2018), and identify starbursts, main sequence and quiescent galaxies.
We analyse merger fractions of galaxies and find that the increase trends of
merger fractions for galaxies in different star formation modes as the
redshift increase, when we use both the average SFRs of Schreiber et al.
(2015) and Pearson et al. (2018), are consistent.

Figure 8: Starburstiness RSB distribution of galaxies at each redshift range.
Black solid and blue dashed line represent the galaxies in the stellar mass
range of 9.0 $<$ log(M∗/M⊙) $<$ 11.5 and 10.5 $<$ log(M∗/M⊙) $<$ 11.5,
respectively. Dotted and dash-dotted line represent the borders between
starbursts and main sequence, main sequence and quiescent galaxies,
respectively. Figure 9: Evolution of the merger fractions for starburst, main
sequence, and quiescent galaxies. Filled red circle, open green triangle, open
blue rectangle represent starbursts, main sequence, and quiescent galaxies,
respectively. Left panel shows galaxies in the entire stellar mass range, and
right panel shows the galaxies in 10.5 $<$ log(M∗/M⊙) $<$11.5.

###  4.2 Merger fraction of galaxies with and without $\it{Herschel}$
detections

It is well known that FIR bright galaxies tend to be found as mergers at low
redshifts. However, this is not always true for high redshift galaxies;
isolated disk galaxies at high redshifts can have high infrared luminosities
without any merger events because of their large amount of gas (Drew et al.,
2020). This suggests that the infrared luminosity may not reflect genuine
physical conditions of galaxies when comparing galaxies at different
redshifts. Instead, it is important to distinguish galaxies based on more
physically motivated parameters including star formation mode, which is the
main driver of this study. To better justify this point, we further examine
the merger fraction of FIR detected galaxies depending on the redshift and
star formation modes with that of FIR non-detected galaxies. Here, the FIR
detection means that the galaxies are detected at least one band of
$\it{Herschel}$/SPIRE 250, 350 and 500 $\micron$ wavelengths. Because the
$\it{Herschel}$/PACS covers only the NEP-Deep field unlike the
$\it{Herschel}$/SPIRE (see Fig. 1 in Kim et al. 2021), we use the only the
$\it{Herschel}$/SPIRE data to reduce the selection effect for the comparison.

We separate our 9 $\micron$ detected samples into $\it{Herschel}$ non-detected
and detected ones, and show their starburstiness at different redshift bins in
Figure 10. Black dashed and blue solid lines represent $\it{Herschel}$
detected and non-$\it{Herschel}$ detected sample, respectively. We find that
$\it{Herschel}$ detected samples have higher RSB than those of
non-$\it{Herschel}$ detected sample in all redshift bins as we can expect.
Figure 11 shows the evolution of galaxy merger fraction for
non-$\it{Herschel}$ detected and $\it{Herschel}$ detected samples in upper and
bottom panels, respectively. Right and left panels show the total and narrow
mass range, respectively. In the total mass range, we find that the merger
fraction of starburst galaxies with $\it{Herschel}$ detections seemingly
increase as the redshift increases compared to those of non-$\it{Herschel}$
detected galaxies. Also, the merger fraction of those with $\it{Herschel}$
detections is higher than those of non-$\it{Herschel}$ detected galaxies,
because of $\it{Herschel}$ detected galaxies have higher FIR luminosities.

We fit the merger fractions evolution with power-law (Patton et al., 2002;
Conselice, Yang & Bluck, 2009), which is given by
f${}_{m}=\alpha(1+z)^{m}+\rm{C}$. For non-$\it{Herschel}$ detected galaxies,
we obtain the index $\it{m}$ = 0.18 $\pm$ 0.62 and 0.81 $\pm$ 0.19 in total
mass range and $\it{m}$ = 0.46 $\pm$ 2.29 and 1.44 $\pm$ 2.12 in narrow mass
range for starbursts and main sequence galaxies, respectively. For
$\it{Herschel}$ detected galaxies, we obtain the index $\it{m}$ = 2.22 $\pm$
0.72 and 1.09 $\pm$ 0.78 in total mass range and $\it{m}$ = 2.71 $\pm$ 2.46
and 1.78 $\pm$ 2.04 in narrow mass range for starbursts and main sequence
galaxies, respectively. The indices for merger fractions of starbursts in
$\it{Herschel}$ detected galaxies are significantly different compared to
those in non-$\it{Herschel}$ detected galaxies. The comparison of them are
such as $\it{m}$ = 0.18 $\pm$ 0.62 vs. $\it{m}$ = 2.22 $\pm$ 0.72 in total
mass range, and $\it{m}$ = 0.46 $\pm$ 2.29 vs. $\it{m}$ = 2.71 $\pm$ 2.46 in
narrow mass range. The differences of main sequence galaxies are relatively
weak compared to those of starbursts such as $\it{m}$ = 0.81 $\pm$ 0.19 vs.
$\it{m}$ = 1.09 $\pm$ 0.78 in total mass range, and $\it{m}$ = 1.44 $\pm$ 2.12
vs. $\it{m}$ = 1.78 $\pm$ 2.04 in narrow mass range.

We also examine that the $\it{Herschel}$ detected samples have large range of
SFRs at low redshift, and the SFRs of those galaxies become higher as the
redshift increases. Thus, the increase tendency of merger fractions for
$\it{Herschel}$ detected samples may includes the cosmic evolution. To better
compare the merger fractions between $\it{Herschel}$ detected and
non-$\it{Herschel}$ detected galaxies by minimising the mass effects, we
compare the results in narrow mass range in the right panels of Figure 11.
Although errors are large, we find that the fraction at the same star
formation mode is not different depending on the $\it{Herschel}$ detection
considering the errors. Of course, the merger fractions of different star
formation modes are still different for both samples. This comparison shows
the importance of star formation mode in determining the merger fraction
regardless of FIR luminosities.

Figure 10: Distribution of starburstiness for galaxies at each redshift range.
Black dashed line represents non-$\it{Herschel}$ detected galaxies and blue
solid line represents $\it{Herschel}$ detected galaxies.  Figure 11: Evolution
of the merger fraction of starburst, main sequence, and quiescent galaxies for
non-$\it{Herschel}$ detected galaxies (upper) and $\it{Herschel}$ detected
galaxies (bottom). The left and right panels show galaxies with total and
fixed mass range of 9.0 $<$ log(M∗/M⊙) $<$ 11.5 and 10.5 $<$ log(M∗/M⊙) $<$
11.5. Coloured symbols are same as Fig 9.

##  5 DISCUSSION

###  5.1 Merger fractions over the star formation modes and their evolution

The evolution of galaxy merger fraction over the cosmic time has been examined
through numerical simulations and observational analysis. Some simulations
assuming cold dark matter Universe predicted a decreasing merger fraction of
galaxies with cosmic time (Fakhouri & Ma, 2008; Rodriguez-Gomez et al., 2015),
while other simulations show that the increasing of merger fraction to $z$
$\sim$ 1.5 and then constant as redshift increases (Kaviraj et al., 2015; Qu
et al., 2017; Snyder et al., 2017). In observations, Conselice et al. (2008)
showed that the merger fraction of very massive galaxies with
log(M∗/M${}_{\odot})>$ 10 appears to increase up to $\it{z}$ $\sim$ 3, while
the merger fraction of less massive galaxies has a peak $\it{z}$ $\sim$ 1.5 –
2.5 and decreases to high redshift. Ventou et al. (2017) also showed that the
merger fractions for galaxies with log(M∗/M${}_{\odot})>$ 9.5 increase to
around $\it{z}$ $\sim$ 2 and slowly decrease after that. Even in relatively
low redshift range, some authors found an increasing merger fraction with
redshift (López-Sanjuan et al., 2009; Ventou et al., 2017), however constant
merger fraction at $\it{z}$ $<$ 0.6 is also suggested (Conselice, Yang &
Bluck, 2009; Jogee et al., 2009). Our results are in agreement with the
observations suggesting that the merger fraction of galaxies slightly
increases with redshift $\it{z}$ $<$ 0.6 (López-Sanjuan et al., 2009; Man,
Zirm & Toft, 2016; Ventou et al., 2017). However, the absolute values of
merger fractions could differ due to different methods of sample selections
depending on luminosity, mass or definition of a merger, which will be
discussed in Section 5.3.

As shown Figure 9, merger fractions of starburst, main sequence and quiescent
galaxies are dependent of star formation mode. Although some authors suggested
the dependency of merger fraction of galaxies on the distance from the main
sequence (Cibinel et al., 2019; Pearson et al., 2019), the effect of star
formation modes could not be evaluated quantitatively. For the fair
comparison, we try to investigate the evolution of merger fraction for
galaxies with similar star formation activities.

Merger galaxies selected by morphology are mainly late-stage and disturbed
systems (Pearson et al., 2019). Because our merger galaxy samples are also
selected by morphology, the higher merger fraction in this study than those in
other studies can suggest that the star formation enhancement is prominent at
the late stage of merging (Sanders & Mirabel, 1996; Haan et al., 2011; Cox et
al., 2006; Hwang et al., 2012) and earlier stage of merging only cause mild
increase of SFRs for close pairs (Lin et al., 2007).

Regarding the evolution of merger fraction, Conselice, Yang & Bluck (2009)
showed diverse results through the fitting with a power-law function. They
found that the power-law slope changes from 1.5 to 3.8 depending on sample
selection and different merger fraction at $\it{z}$ = 0. The slope tend to be
higher for more massive galaxies and lower for less massive galaxies
(Conselice et al., 2003). Qu et al. (2017) used an exponential power-law
function for the simulation predictions, they found that the power-law slope,
$\it{m}$, for close pairs with $\it{z}$ $<$ 4 changes from 2.8 to 3.7
depending on the mass limits. Otherwise, others who used morphological
disturbances for merger selections and the redshift range of galaxies with
$\it{z}$ $<$ 1.2 (Lotz et al., 2008) obtained the mild slope of $\it{m}$ =
1.26. Considering similar merger selection and redshift range, our results on
the power-law slope of $\it{m}$ = 0.18 – 2.71 are consistent with those from
Lotz et al. (2008). However, they showed that the slope of merger fraction
could be easily affected by morphological diagnostics and timescales to
determine merger fractions.

###  5.2 Mergers for $\it{Herschel}$ detected galaxies

Galaxy merging is expected to drive star formation episodes (Barnes &
Hernquist, 1996; Mihos & Hernquist, 1996), however, UV/optical light is dimmed
and sources appear redder due to absorption and scattering by dust. Since
considerable amounts of the energy from star formations and AGNs have been
absorbed by gas and dust and re-emitted in FIR wavelengths (Puget et al.,
1996; Dole et al., 2006), FIR data set would be good for the study of star
formation activity (Pei, Fall & Hauser, 1999; Chary & Elbaz, 2001). Some
results for LIRGs and ULIRGs showed that FIR-bright galaxies are ongoing
mergers and have disturbed morphology, which are the evidence for merger
activities (Sanders et al., 1988; Clements et al., 1996; Hopkins et al., 2006;
Hwang et al., 2010). While these studies were mainly focused on FIR-bright
galaxies, our samples selected from MIR detections have a wider range of LTIR.
As shown in Figure 9 and 11, the merger fractions are strongly dependent of
star formation modes, irrespective of $\it{Herschel}$ detection. We also find
that the increasing slope of merger fraction for starbusrts detected in
$\it{Herschel}$ is steeper than that of non-$\it{Herschel}$ detected
starbursts. The difference of the slope for main sequence galaxies is not
significant compared to those of starbursts. Note that quiescent galaxies
shows the steepest slope, however merger fractions at $\it{z}$ $>$ 0.2 are
upper limit due to the lack of sample. These results could support that
$\it{Herschel}$ detected galaxies with high FIR luminosity such as LIRGs/UIRGs
are more stochastically in the merging stage. Although it is difficult to
compare with other results in the effectiveness of FIR detection, this can be
interpreted that the merger fractions of galaxies are determined not only by
the IR luminosity, but also by the star formation mode of galaxies at fixed
redshift range.

###  5.3 Comparison to other studies

To study the merger fraction of galaxies, one has to define a galaxy sample
along with redshift/mass range and galaxy classification method (Lotz et al.,
2008; Conselice, Yang & Bluck, 2009; Bundy et al., 2009; Man, Zirm & Toft,
2016; Delahaye et al., 2017; Watson et al., 2019). Therefore, it is important
to understand the sample selection including the merger identification scheme
to make fair comparison with other studies. Although it is difficult to
directly compare our results with other studies because of these differences,
we describe the similarity and the difference between our study and other
studies in this section.

Methodologically, merger galaxies can be identified by using galaxy pairs or
morphological disturbances. As morphological cases, Lotz et al. (2008) used
Gini and M20 for selecting merger galaxies in 0.2 $<$ $\it{z}$ $<$ 1.2 and
volume limited sample with B-band luminosity limits assuming the luminosity
evolution. They found weak evolution of the merger fractions of galaxies in
this redshift range. Conselice, Yang & Bluck (2009) derived the increasing
merger fraction using asymmetry and clumpiness with galaxies from COSMOS and
EGS between 0.2 $<$ $\it{z}$ $<$ 1.2. Although there are differences between
our sample and theirs such as redshift range and existence of MIR data, our
result is consistent with the previous ones (Lotz et al., 2008; Conselice,
Yang & Bluck, 2009) that the merger fractions for galaxies mildly increase as
redshift increases with using morphological selection for merger galaxies.

In addition to morphological method, there are studies of merger fractions
using galaxy pairs. Bundy et al. (2009) and de Ravel et al. (2009) use mass-
selected pairs and projected separation (Rproj) for selecting merger galaxies,
respectively. Watson et al. (2019) showed that the merger fraction for paired
galaxies in clusters is higher than those in field environments (Bundy et al.,
2009; de Ravel et al., 2009). Cibinel et al. (2019) compared the results from
the morphological classification with those from the pair identification. They
found that most of the starbursts galaxies are morphologically disturbed, but
for galaxy pairs, the merger fractions were small in starburst galaxies. Thus,
this can suggest that the merger fractions of this study could be higher than
that in other studies based on galaxy pairs.

Relatively high merger fractions of our results also can be explained by
sample selection criteria. Lotz et al. (2008) used luminosity-size limits for
selecting of massive galaxies. Conselice, Yang & Bluck (2009); López-Sanjuan
et al. (2009) used galaxies with M${}_{*}>$ $10^{10}$ M⊙. These criteria
secure limited galaxies compared to our sample that have mass range of 9.0 $<$
log(M∗/M⊙) $<$11.5. However, the largest difference of the sample selection
between ours and others is the use of the MIR detection in our study, which
can significantly affect the star formation activity. Then, the number of
sample can be limited, this small total number of sample which is denominators
of merger fractions could affect that the merger fractions of galaxies become
high compared to others. The method also can affect results; because Gini-M20
are sensitive to the features of minor mergers (Lotz et al., 2011), our method
may select more merger candidates than other studies based on CAS or asymmetry
criteria. Pearson et al. (2019) reported elevated merger fraction for galaxies
at 0 $<\it{z}<$ 4 based on CANDELS data compared to other studies. Such a
result may be arisen because the pixel size of galaxies within the images
becomes smaller and galaxies become fainter as redshift increases, then the
suppressed galaxy features counted as merger galaxies. Therefore, the direct
comparison of absolute values of merger fractions between different studies is
difficult.

##  6 SUMMARY

We used the galaxy sample detected at the MIR band (9 µm) of AKARI in the
NEP–Wide field. In order to identify the merging galaxies, the morphological
analyses were carried out relying on the Gini and M20 coefficients derived
from deep Subaru/HSC ($\it{r}$-, $\it{i}$-band) images. Using the
spectroscopic and photometric redshifts, we derived total infrared luminosity
and SFR from AKARI 9 $\micron$ detections. We compare the merger fractions
between three different star formation modes at $\it{z}<$ 0.6: starburst, main
sequence and quiescent galaxies. Our main results are as follows:

  1. 1.

The merger fractions for starbursts, main sequence, and quiescent galaxies
slightly increase with redshift at $\it{z}<$ 0.6.

  2. 2.

The galaxy merger fractions differ depending on the star formation mode. The
starbursts show higher merger fractions than those of main sequence and
quiescent galaxies.

  3. 3.

The increasing slope of the merger fractions for $\it{Herschel}$ detected
starbursts slightly steeper compared to those of non-$\it{Herschel}$ detected
starbursts.

Our results are in line with the idea that the merger fraction increases with
redshift in local Universe (Lotz et al., 2008; Conselice, Yang & Bluck, 2009;
López-Sanjuan et al., 2009) and galaxies in the different star formation modes
such as starbursts, main sequence and quiescent galaxies show different merger
fractions (Cibinel et al., 2019; Pearson et al., 2019). Regardless of the FIR
detection, the increasing trends of the merger fraction over local universe
ensure the consistency in all the different star formation modes. These
results underscore the importance of the star formation mode in the study of
evolution of galaxy merger fraction. To better understand the merger fraction
evolution with different star formation activities, it is important to secure
a larger, unbiased sample of high-$\it{z}$ galaxies, which does not suffer
from observational selection effects on the star formation mode.

## Acknowledgements

W-SJ, EK and Y-SJ acknowledges support from the National Research Foundation
of Korea (NRF) grant funded by the Ministry of Science and ICT (MSIT) of Korea
(NRF-2018M1A3A3A02065645). HSH was supported by the New Faculty Startup Fund
from Seoul National University. HShim acknowledges the support from the
National Research Foundation of Korea grant No. 2018R1C1B6008498. TH is
supported by the Centre for Informatics and Computation in Astronomy (CICA) at
National Tsing Hua University (NTHU) through a grant from the Ministry of
Education of the Republic of China (Taiwan).

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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