# The Subtle Effects of Mergers on Star Formation in Nearby Galaxies

Yang A. Li Kavli Institute for Astronomy and Astrophysics, Peking University,
Beijing 100871, P. R. China  Department of Astronomy, School of Physics,
Peking University, Beijing 100871, P. R. China  Luis C. Ho Kavli Institute for
Astronomy and Astrophysics, Peking University, Beijing 100871, P. R. China
Department of Astronomy, School of Physics, Peking University, Beijing 100871,
P. R. China  Jinyi Shangguan Max-Planck-Institut für extraterrestrische
Physik, Gießenbachstr. 1, D-85748 Garching, Germany

###### Abstract

Interactions and mergers play an important role in regulating the physical
properties of galaxies, such as their morphology, gas content, and star
formation rate (SFR). Controversy exists as to the degree to which these
events, even gas-rich major mergers, enhance star formation activity. We study
merger pairs selected from a sample of massive ($M_{*}\geq
10^{10}\,M_{\odot}$), low-redshift ($z=0.01-0.11$) galaxies located in the
Stripe 82 region of the Sloan Digital Sky Survey, using stellar masses, SFRs,
and total dust masses derived from a new set of uniformly measured
panchromatic photometry and spectral energy distribution analysis. The dust
masses, when converted to equivalent total atomic and molecular hydrogen,
probe gas masses as low as $\sim 10^{8.5}\,M_{\odot}$. Our measurements
delineate a bimodal distribution on the $M_{\rm gas}-M_{*}$ plane: the gas-
rich, star-forming galaxies that trace the well-studied gas mass main
sequence, and passive galaxies that occupy a distinct, gas-poor regime. These
two populations, in turn, map into a bimodal distribution on the relation
between SFR and gas mass surface density. Among low-redshift galaxies, galaxy
mergers, including those that involve gas-rich and nearly equal-mass galaxies,
exert a minimal impact on their SFR, specific SFR, or star formation
efficiency. Starbursts are rare. The star formation efficiency of gas-rich,
minor mergers even appears suppressed. This study stresses the multiple,
complex factors that influence the evolution of the gas and its ability to
form stars in mergers.

galaxies: evolution — galaxies: interactions — galaxies: ISM — galaxies:
starburst

##  1 Introduction

Interactions and mergers play an essential role in galaxy evolution in a
hierarchical Universe (White & Frenk, 1991). Apart from secular evolution
through accreting gas from filaments (Dekel et al., 2009), galaxies can
increase significantly their stellar mass ($M_{*}$) and halo mass through
merging with other galaxies (Blumenthal et al., 1984; Faber et al., 2007;
Neistein & Dekel, 2008; Cattaneo et al., 2011; Rodriguez-Gomez et al., 2016),
as well as drastically alter their structure through morphological
transformation (Toomre & Toomre, 1972; Mihos & Hernquist, 1996; Lotz et al.,
2010; Hambleton et al., 2011). Observations support the picture that merger-
induced instabilities drive gas flows into the center of merger remnants
(Blumenthal & Barnes, 2018), dilute the gas-phase metallicity (Rupke et al.,
2010; Torrey et al., 2012; Bustamante et al., 2018), and enhance the star
formation rate (SFR) on either nuclear or global scales (Ellison et al., 2008;
Ellison et al., 2010; Robotham et al., 2014; Xu et al., 2021). Numerical
simulations of galaxy pairs, which provide an idealized framework to elucidate
the merger process and its influence on the galaxy members, confirm that
galaxy interactions and mergers enhance the SFR (Di Matteo et al., 2007; Cox
et al., 2008; Scudder et al., 2012; Perret et al., 2014; Moreno et al., 2015,
2021) and regulate the gas content (Mihos & Hernquist, 1996; Sinha & Holley-
Bockelmann, 2009; Sparre et al., 2022) in the nuclear region (Moreno et al.,
2021), as well as set the stage to facilitate the ignition of black hole
activity (Di Matteo et al., 2005; Hopkins et al., 2006; Capelo et al., 2015,
2017; Byrne-Mamahit et al., 2023). The growth of the central black hole and
bulge, in turn, can quench star formation (Springel et al., 2005; Hopkins et
al., 2009a).

Mergers are often invoked as the triggering mechanism of starbursts. Tidal
compression and shocks induced by mergers enhance gas density (Barnes, 2004;
Schweizer, 2009; Renaud et al., 2014) to the point that the star formation
efficiency can be high enough to qualify the galaxy as a starburst, such as
those witnessed in luminous and ultraluminous infrared galaxies (Sanders &
Mirabel, 1996; Shangguan et al., 2019). However, the nature of star formation
activity in merging galaxies is far from clear-cut. A wide range of star
formation activity exists. Some studies find strong SFR enhancement in closely
projected merger pairs (Scudder et al., 2012; Davies et al., 2015; Garduño et
al., 2021) or in pairs of large separation (Ellison et al., 2010; Patton et
al., 2016), while others conclude that SFR is enhanced only moderately (Xu et
al., 2010; Knapen & James, 2009; Knapen et al., 2015; Barrera-Ballesteros et
al., 2015), typically by a factor of $\sim 2$ (Lin et al., 2007; Ellison et
al., 2013; Pan et al., 2018; Silva et al., 2018) or less (Wong et al., 2011;
Pearson et al., 2019). Knapen et al. (2015) even suggest that a considerable
fraction of merging galaxies, quite contrary to naive expectations, exhibit a
reduced level of star formation compared to non-mergers. Mergers may fail to
lead to starbursts because the timescale for the close encounter or
coalescence needed to trigger star formation enhancement ($\sim 10-100\,\rm
Myr$; Di Matteo et al., 2008; Cortijo-Ferrero et al., 2017; Pearson et al.,
2019) is very short compared to the period between encounters (Moreno et al.,
2019). Even galaxy pairs with small separation ($<15\,\rm kpc$) may be in a
stage that is still too early to boost star formation (Silva et al., 2018).
Simulations by Segovia Otero et al. (2022) and Renaud et al. (2022) suggest
that starbursts only occur after the disk has had time to form, when the
rotational motion of the gas overtakes its velocity dispersion. Although
mergers induce strong perturbations, the level of star formation in the galaxy
may saturate due to feedback processes in a clumpy, turbulent medium (Perret
et al., 2014).

Many previous studies have attempted to identify the main factors that govern
the star formation variance in mergers, including the stellar mass ratio of
the two galaxies, their initial orbital parameters, projected separation,
total stellar mass, bulge-to-total mass ratio, and environment (Di Matteo et
al., 2007; Cox et al., 2008; Ellison et al., 2008; Scudder et al., 2012;
Torrey et al., 2012; Perret et al., 2014; Domingue et al., 2016; Pan et al.,
2018; Qiu & Sun, 2020; Xu et al., 2021). The stellar mass ratio of the merger
pair ($f_{M_{*}}=M_{*,1}/M_{*,2}$, with $M_{*,1}<M_{*,2}$) is regarded as an
essential parameter, one used to separate major from minor mergers,
traditionally by $f_{M_{*}}=0.25$ (Robotham et al., 2013; Davis et al., 2015;
Pan et al., 2018; Q. Yu et al., 2022). Designating the more massive member as
the primary galaxy and the less massive one as the secondary, Davies et al.
(2015) find that the SFR is enhanced in all primary galaxies, both in major
and minor mergers. By comparison, star formation is suppressed in the
secondary component of minor mergers, presumably because the gas is heated or
stripped in lower-mass galaxies. However, even in this instance the outcome
can be complicated. On the one hand, Di Matteo et al. (2007) show that in
merger pairs the less massive galaxy experiences a stronger tidal effect. On
the other hand, the high-resolution simulations of Du et al. (2019)
demonstrate that while a large fraction of the gas from the less massive
galaxy is stripped by ram pressure, the residual gas, under the combined
effects of ram pressure confinement and tidal compression at pericentric
passages, can sustain bursty central star formation. This may offer an
alternative explanation to the observations by Silva et al. (2018), that the
less massive member in a merger pair experiences greater star formation
enhancement, which the authors attribute to gas content: splitting their
sample into dust-rich (wet), mixed, and dust-poor (dry) mergers according to
the colors of the individual galaxy components, they find a higher fraction of
starbursts among the dusty, low-mass, star-forming galaxies than in the high-
mass members.

Indeed, gas content is considered another critical factor that influences the
outcome of star formation in mergers, at least from a theoretical point of
view (e.g., Bournaud et al. 2011; Blumenthal & Barnes 2018; but see Perret et
al. 2014). The observational situation, however, again is rather muddled.
While many studies point to a direct causal connection between gas content and
star formation enhancement in mergers (e.g., Casasola et al. 2004; Ellison et
al. 2018; Moreno et al. 2019, 2021), others disagree (e.g., Hibbard & van
Gorkom 1996; Ellison et al. 2015; Zuo et al. 2018; Q. Yu et al. 2022). For
example, while Pan et al. (2018) find that in galaxy pairs of comparable
stellar mass, large enhancements of SFR are associated only with galaxies that
have a significant molecular gas fraction, Scudder et al. (2015) report an
inverse correlation between SFR enhancement and gas fraction, an effect that
they attribute to the dominance of the strong underlying dependence of SFR on
initial gas fraction. These ambiguities can perhaps be ascribed to the
difficulty of measuring the gas content of mergers, considering the limited
samples that have gas observations (Ellison et al., 2015, 2018; Zuo et al.,
2018; Xu et al., 2021; Q. Yu et al., 2022) or the potential confusion due to
blending by a large telescope beam (Casasola et al., 2004).

Lastly, we note an often less appreciated complication. It is nontrivial to
design a proper control sample to which the mergers need to be compared in
order to draw statistically meaningful conclusions about whether and how star
formation has been affected by the merging process. A common practice is to
create a control sample for each interacting galaxy and then compare its
physical properties with the median properties of the control sample. However,
most mergers that have gas measurements are star-forming galaxies, whereas
their counterparts in the control sample include both star-forming and passive
galaxies, if the matching is based only on stellar mass, redshift, and/or
environment (Davies et al., 2015; Ellison et al., 2018; Qiu & Sun, 2020), and
additionally morphology (Knapen et al., 2015) or bulge-to-total mass ratio (He
et al., 2022). Alternatively, one can construct a pool of star-forming
galaxies to define the control sample (Ellison et al., 2013; Scudder et al.,
2015; Quai et al., 2021), but the simultaneous matching of multiple physical
parameters reduces the control sample to a very small number ($\leq 5$)
galaxies. The mutual dependence of many galaxy parameters further frustrates
any attempt to define a meaningful “control” sample.

In this paper, we investigate the effect of tidal interactions on the star
formation activity and gas content of galaxies, by comparing the SFR,
$M_{\mathrm{gas}}$, and specific SFR (${\rm sSFR}\equiv{\rm SFR}/M_{*}$) and
star formation efficiency (${\rm SFE}\equiv{\rm SFR}/M_{\rm gas}$) of mergers
with non-mergers, where both populations are drawn from a large sample of
nearby galaxies selected from the Stripe 82 region (Annis et al., 2014) of the
Sloan Digital Sky Survey (SDSS; York et al. 2000), whose panchromatic, far-
ultraviolet (FUV) to far-infrared (FIR) spectral energy distribution (SED) and
physical parameters have been analyzed uniformly in the companion work of Li
et al. (2023). Section 2 introduces the parent sample, the selection criteria
for the merger subsample, as well as the derivation of the physical parameters
studied in this work. We present the results in Section 3, discuss their
implications in Section 4, and briefly summarize our main conclusions in
Section 5. We adopt a $\Lambda$CDM cosmology with $H_{0}=70\,\rm
km\,s^{-1}\,Mpc^{-1}$ and $\Omega_{\Lambda}=0.7$. The stellar masses and SFRs
are based on the stellar initial mass function of Chabrier (2003).

##  2 Data

###  2.1 Sample Definition

We make use of the local galaxies in the SDSS Stripe 82 region that are
covered by the Herschel Stripe 82 Survey (HerS; Viero et al. 2014) with the
SPIRE instrument (Griffin et al., 2010) onboard Herschel (Pilbratt et al.,
2010). The parent sample comes from the catalog produced by Li et al. (2023),
which is defined by the redshift range of $z=0.01-0.11$ and a stellar mass cut
of $M_{*}\geq 10^{10}\,M_{\odot}$, using values from the GALEX-SDSS-WISE
Legacy Catalog 2 (GSWLC-2; Salim et al. 2018). The lower limit on redshift
excludes very nearby galaxies, which can have unreliable distances based on
redshift, the overall narrow redshift range ensures negligible cosmic
evolution in global galaxy properties, and the stellar mass cut yields a
sample with high completeness. The parent sample of 2781 galaxies consists of
2668 galaxies with no broad emission lines and 17 broad-line active galactic
nuclei, as well as 96 galaxies that do not satisfy the stellar mass cut but
are retained because they are companions to a primary galaxy that does.

Interacting galaxies are defined as close pairs with a projected separation of
$\Delta\,r<50$ kpc, a physical scale that best captures galaxy pairs during
periods of the encounter and before the final coalescence (Ellison et al.,
2010; Calderón-Castillo et al., 2019). Galaxies in those periods have distinct
properties compared to isolated galaxies (Moreno et al., 2019, 2021). We
impose a radial velocity difference of $\Delta v<600\,\mathrm{km\,s^{-1}}$ to
select gravitationally bounded pairs. Some galaxies in the parent sample have
a projected close companion that, despite lacking a spectroscopic redshift,
exhibits an obvious tidal feature between them that strongly suggests an
interaction. We require that the photometric redshift of the close companion,
within its uncertainty, be consistent with the spectroscopic redshift of the
primary galaxy. Galaxies that lack a spectroscopic redshift are assumed to
have a redshift identical to that of their merger companion.

Among the 2685 galaxies in our parent sample, more than 300 have at least one
physically associated companion. We omit systems with three or more objects or
multi-component systems that involve the brightest galaxy in a cluster center,
as our primary focus is to investigate the influence on star formation induced
by companions with different physical properties. Systems that involve the
participation of more than one companion or that are situated in the complex
environment of cluster centers make it ambiguous to disentangle the influence
of individual members. While the primary galaxy must be a member of our parent
sample and have $M_{*}\geq 10^{10}\,M_{\odot}$, the secondary galaxy is
allowed to be less massive than this stellar mass limit in order to better
explore the effect of minor mergers, although we do not consider galaxy pairs
with stellar mass ratios $f_{M_{*}}<0.01$ to minimize confusion with bright
galactic substructures. Stellar mass ratios are evaluated by taking into
account the $3\sigma$ uncertainty of $M_{*}$, which is $\sim 0.15$ dex (Li et
al., 2023). The following analysis involves 174 merging galaxies and a control
sample of 2244 isolated galaxies.

###  2.2 Photometry and Physical Parameters

Li et al. (2023) presented detailed panchromatic photometry of the sample
galaxies, covering 17 bands from the FUV (1539 Å) to the FIR (500 $\mu$m). We
developed a new method to measure matched-aperture photometry consistently for
all the bands, in order to obtain robust total flux measurements of relatively
bright, nearby galaxies that are partly or fully resolved. Special care was
devoted to removing contamination from foreground stars, and simultaneous two-
dimensional image decomposition was performed using GALFITM (Häußler et al.,
2013) to deblend properly interacting/merging galaxies. Two-dimensional
decomposition is performed simultaneously with images from the FUV to
$4.6\,\mu$m, by assuming that the structural parameters change continuously
across the wavelengths. This procedure is physically well motivated because
these bands are dominated by the stellar emission of the galaxy. The bands at
longer wavelengths (W3, W4, and Herschel bands), which are dominated by dust
emission, are more challenging to decompose with GALFITM because of their
limited spatial resolution. We collect the photometric measurements of
Herschel observations from the Herschel Extragalactic Legacy Project (HELP;
Shirley et al. 2021). Fortunately, HELP provides the decomposed emission of
most of our galaxy pairs using a Bayesian-based deblending method that relies
on prior information from higher-resolution images in either the optical or
near-infrared. HELP provides the global flux of a small fraction of our galaxy
pairs whose decomposition failed. For these targets in the Herschel bands and
all the galaxy pairs in W3 and W4, we consider the global flux as the flux
upper limit of each component in their SED fitting. Extensive mock experiments
helped to establish reliable uncertainties, both statistical and systematic,
and to estimate upper limits. We employed the code CIGALE (Boquien et al.,
2019) to fit the broadband SED to estimate the global SFR, $M_{*}$, and dust
mass ($M_{\mathrm{dust}}$), the latter based on the dust emission model of
Draine & Li (2007). CIGALE gives the Bayesian probability distribution for the
model parameters. We consider flux upper limits in calculating the likelihoods
of the SED models, and we use mock tests to correct the physical parameters
for systematic biases that may arise from photometry of low signal-to-noise
ratio (see details in Section 4.4 of Li et al. 2023). We exclude a minority of
galaxies that have reduced $\chi^{2}>10$ in the SED fits, which typically stem
from sources that are decomposed poorly by GALFITM in some near-infrared
bands.

Our ensuing analysis relies critically on having access to a uniform set of
reliable gas masses for the merger galaxies and the control sample of non-
merger galaxies. Whereas most galaxy studies measure neutral atomic hydrogen
through the H i 21 cm line and molecular hydrogen through the rotational
transitions of CO, here we adopt the more expedient, indirect method of
probing the cold interstellar medium from the total dust mass derived from the
infrared continuum emission. This alternative method offers several
advantages. While extensive blind extragalactic H i 21 cm surveys have been
conducted (e.g., Koribalski et al. 2004; Haynes et al. 2018) and catalogs of
source parameters thereof have been published (e.g., Springob et al. 2005; N.
Yu et al. 2022), the current samples are limited thus far to relatively nearby
($z\lesssim 0.1$), gas-rich galaxies. Large, unbiased samples of galaxies with
CO observations are rarer still (Boselli et al. 2014; Saintonge et al. 2017;
see review in Saintonge & Catinella 2022). On the other hand, relatively deep,
homogeneous, and unbiased blind surveys of the FIR continuum from dust
emission have been conducted using Herschel, among them HerS (Viero et al.,
2014), offering an opportunity to secure the total dust, and hence gas,
content of large samples of galaxies. Moreover, even when CO observations are
available, the conversion factor from CO to $\rm H_{2}$ remains a perennial
topic of debate (Bolatto et al., 2013). The dust-based method of deriving
total gas mass sidesteps this issue.

We convert the total dust mass to total gas mass using the empirical relation
between gas-phase metallicity and gas-to-dust mass ratio
($\delta_{\mathrm{GDR}}$; Leroy et al. 2011). From the calibration of Magdis
et al. (2012),

$\displaystyle\mathrm{log}\,\delta_{\mathrm{GDR}}=$ $\displaystyle(10.54\pm
1.0)-(0.99\pm 0.12)$ $\displaystyle\times[12+\mathrm{log(O/H)}],$ (1)

where $12+\mathrm{log(O/H)}$ is the oxygen abundance empirically defined by
Pettini & Pagel (2004), which can be estimated from the stellar mass-
metallicity relation of local galaxies (Kewley & Ellison, 2008),

$\displaystyle 12+\mathrm{log(O/H)}$
$\displaystyle=23.9049-5.62784\,\mathrm{log\,}M_{*}$
$\displaystyle+0.64514\,(\mathrm{log\,}M_{*})^{2}-0.02351\,(\mathrm{log\,}M_{*})^{3}.$
(2)

Following Shangguan et al. (2018), we add 0.23 dex to $\delta_{\mathrm{GDR}}$
to account for the empirical difference between dust-converted gas masses and
direct gas observations. The total uncertainty of the gas masses, $\sim 0.45$
dex, stems from the scatter of 0.15 dex in $\delta_{\rm GDR}$ propagated from
the scatter of the stellar mass-metallicity relation and the typical
uncertainty of 0.42 dex for $M_{d}$ (Li et al., 2023), which principally
relates to uncertainties of the dust temperature and absorption coefficient.
Dust radiation is very sensitive to temperature; even a tiny change in
temperature can induce a large variation in dust mass (Lv et al., 2018).

Figure 1: Two-dimensional distribution of the total gas and dust mass versus
stellar mass. In panels (a) and (b), the background contours delineate the
$M_{\mathrm{gas}}-M_{*}$ distribution of our sample; in panel (b) the colored
points are taken from xCOLD GASS (Saintonge et al., 2017). The black solid
line indicates the best fit for the gas mass main sequence, which has a
$1\sigma$ scatter of 0.38 dex (gray dotted lines). The threshold for gas-rich
objects is given by the black dashed line, which is set to $2\sigma$ below the
gas mass main sequence. Panel (c) shows the $M_{\mathrm{dust}}-M_{*}$
distribution for our sample in contours, while the red points represent HRS
galaxies with dust masses derived by Ciesla et al. (2014).

##  3 Results

###  3.1 Total Gas Mass as a Function of Stellar Mass

We derive total gas masses for the local galaxies in the Stripe 82 field based
on their cold dust masses estimated from SED fitting (Section 2.2). Our
panchromatic SED fitting includes upper limits in all bands, which allows us
to measure meaningful, unbiased dust masses down to very low levels,
significant uncertainties notwithstanding. This approach makes it possible to
probe the gas mass distribution of gas-poor galaxies, down to $M_{\rm
gas}\approx 10^{8.5}\,M_{\odot}$ (Figure 1a). The star-forming and passive
galaxies form two distinct peaks on the $M_{\rm gas}-M_{*}$ diagram, separated
by a clear gap between them. This distribution qualitatively resembles the
bimodal distribution of the star-forming main sequence on the ${\rm
SFR}-M_{*}$ diagram (e.g., Noeske et al. 2007; Peng et al. 2010). The upper
part of the $M_{\rm gas}-M_{*}$ diagram has been studied in the literature
mainly through molecular gas measurements and is often called the gas mass
main sequence (e.g., Saintonge et al. 2016; Bolatto et al. 2017; Lin et al.
2019; Baker et al. 2023).

Figure 2: Kennicutt-Schmidt relation on the (a and b) $\Sigma_{\rm
SFR}$–$\Sigma_{\rm gas}$ and (c) $\Sigma_{\rm SFR}$–$\Sigma_{\rm dust}$
diagram, where $\Sigma_{\rm dust}$ is the dust mass surface density. The
distribution for our sample is plotted as the background contours. The dashed
lines in the panels are (a) the K-S law from de los Reyes & Kennicutt (2019)
for spiral galaxies: $\mathrm{log\,}\mbox{$\Sigma_{\rm
SFR}$}=1.41\,\mathrm{log\,}\mbox{$\Sigma_{\rm gas}$}-3.88$, with a scatter of
0.28 dex; (b) the K-S law from de los Reyes & Kennicutt (2019) for the
combination of spiral and dwarf galaxies: $\mathrm{log\,}\mbox{$\Sigma_{\rm
SFR}$}=1.26\,\mathrm{log\,}\mbox{$\Sigma_{\rm gas}$}-3.82$, with a scatter of
0.37 dex; and (c) the relation from Kennicutt & de los Reyes (2021):
$\mathrm{log\,}\mbox{$\Sigma_{\rm
SFR}$}=1.29\,\mathrm{log\,}\mbox{$\Sigma_{\rm dust}$}-1.23$, with a scatter of
0.32 dex. All the values of $\Sigma_{\rm SFR}$ are converted to the Chabrier
(2003) initial mass function. Figure 3: Distribution of our sample on the
$\Sigma_{\rm SFR}$–$\Sigma_{\rm gas}$ diagram. The red line shows the linear
fit for the entire sample, weighted by the uncertainties. The black dashed
line is the fit by de los Reyes & Kennicutt (2019) for spiral and dwarf
galaxies, which has a $1\sigma$ scatter of 0.37 dex (gray dotted lines).

Following the criterion of Saintonge et al. (2016) and Li et al. (2023) to
select gas-rich, star-forming galaxies, we choose galaxies with gas fraction
$f_{\mathrm{gas}}\equiv M_{\mathrm{gas}}/M_{*}>0.05$ to define the gas mass
main sequence. Averaging the gas mass in stellar mass bins of width
$\Delta\log M_{*}=0.15$ dex, we use the Python function curve_fit
111https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html
from the package scipy (Virtanen et al., 2020) to fit the binned data with the
linear relation

$\displaystyle\mathrm{log}\,M_{\mathrm{gas}}=0.5127\,\log\,({\mbox{$M_{*}$}}/10^{10}\,M_{\odot})+9.611,$
(3)

which has a $1\sigma$ total scatter of 0.36 dex. The limited dynamic range of
stellar mass in our sample does not justify a higher-order fit. We do not
attempt to correct for sample completeness because the main goal of this study
is simply to construct a sample distribution that can serve as the control
sample with which to compare the merger sample. We classify the gas content of
the galaxies in our sample based on their distance to the gas mass main
sequence. We define gas-rich galaxies as those that lie above the dashed line
in Figure 1a, which is $2\sigma$ below the best-fit main sequence relation of
Equation 3. Gas-poor galaxies sit below the dashed line.

To our knowledge, the lower peak of the $M_{\rm gas}-M_{*}$ distribution has
never been reported before. Direct observations of gas content in galaxies
through blind surveys of the H i 21 cm or CO lines generally lack the
sensitivity to detect large numbers of gas-poor galaxies. For example, the
total cold gas (neutral atomic and molecular hydrogen) masses of the xCOLD
GASS survey (Saintonge et al., 2017), to date the largest unbiased sample of
$\sim 500$ nearby galaxies with dedicated, relatively deep H i and CO
observations, largely populate the upper peak of the $M_{\rm gas}-M_{*}$
diagram; most of the gas-poor galaxies are upper limits and fail to delineate
the lower peak (Figure 1b). Dust masses are available for larger samples of
galaxies, but such measurements are biased because they derive from studies
that usually collect only detections from different databases to construct the
SED (e.g., Dunne et al. 2011; Berta et al. 2016). Dust masses are not given
for galaxies without FIR detections. In contrast, Li et al. (2023) showed that
the dust mass can be reasonably estimated when FIR upper limits are included
in the broadband SED fit, even if the uncertainties are considerable. This
point is demonstrated in detail using mock SEDs in Section 4.4 of Li et al.
(2023). Targetted Herschel observations of local galaxies, such as the
Herschel Reference Survey (HRS) for about 300 galaxies at 15–25 Mpc (Boselli
et al., 2010), can provide deep enough detection of cold dust in passive
galaxies (Ciesla et al., 2014). As shown in Figure 1c, the dust mass
measurements of the HRS sources are well consistent with the sample
distribution in this work. The passive galaxies in HRS, although limited in
number, overlap with the lower locus of our passive galaxies, which supports
the robustness of the dust masses of our passive galaxies. As discussed in
Section 3.2, the new dust (gas) masses of the gas-poor galaxy population obey
a relation between the surface density of SFR and gas mass that closely
follows the extrapolation of the well-studied Kennicutt-Schmidt (K-S: Schmidt
1959; Kennicutt 1998) law for gas-rich, star-forming galaxies. This, too,
lends confidence that the dust (gas) masses of the gas-poor subsample do yield
physically meaningful constraints on the cold interstellar medium of this
seldom-probed region of parameter space.

Figure 4: Distribution of (a) SFR, (b) sSFR, (c) SFE, and (d) gas-to-stellar
mass ratio $f_{\rm gas}$. Mergers and non-mergers are denoted as filled and
open histograms, respectively.

###  3.2 The Kennicutt-Schmidt Relation for Star-forming and Passive Galaxies

The availability of relatively sensitive gas mass estimates and SFRs for a
large, homogeneously studied sample of nearby galaxies affords us the
opportunity to revisit the star formation relation as commonly expressed using
the K-S law. Previous works, mainly based on direct gas measurements, found
power-law relations between the surface density of SFR and the surface density
of the total or molecular gas mass (Kennicutt, 1997; Leroy et al., 2008;
Martig et al., 2013; de los Reyes & Kennicutt, 2019),

$\displaystyle\mbox{$\Sigma_{\rm SFR}$}=\alpha\,\mbox{$\Sigma_{\rm
gas}$}^{\beta},$ (4)

where $\beta$ is the power-law slope that typically varies from 0.8 to 2,
depending on the sample and measurements, and $\alpha$ is the normalization.
As in Kennicutt & de los Reyes (2021), we calculate the surface densities
$\Sigma_{\rm SFR}$ and $\Sigma_{\rm gas}$ by dividing SFR and
$M_{\mathrm{gas}}$, respectively, by $\pi a^{2}$, where $a$ is the semimajor
axis of the galaxy stellar disk, which we approximate using $a_{25}$, the
isophotal radius at 25 $\mathrm{mag\,arcsec^{-2}}$ in the $r$ band, as listed
in the SDSS Stripe 82 database.

As with the distribution of $M_{\rm gas}$ versus $M_{*}$ (Figure 1), the
$\mbox{$\Sigma_{\rm SFR}$}-\mbox{$\Sigma_{\rm gas}$}$ diagram also exhibits a
bimodal distribution (Figure 2). The first peak, centered roughly at
$\log\,(\mbox{$\Sigma_{\rm gas}$}/M_{\odot}\,\rm pc^{-2})\approx 0.8$ and
$\log\,(\mbox{$\Sigma_{\rm SFR}$}/M_{\odot}\,\rm
yr^{-1}\,kpc^{-2})\approx-2.7$, pertains to the group of gas-rich, star-
forming galaxies commonly studied in the context of the K-S relation. We draw
attention to the gas-poor, passive galaxies clustered around
$\log\,(\mbox{$\Sigma_{\rm gas}$}/M_{\odot}\,\rm pc^{-2})\approx-0.4$ and
$\log\,(\mbox{$\Sigma_{\rm SFR}$}/M_{\odot}\,\rm
yr^{-1}\,kpc^{-2})\approx-4.7$. The entire distribution of the Stripe 82
galaxies is approximately consistent with a single relation that closely
resembles the K-S law, although the gas-poor population may present a mild
break below $\log\,(\mbox{$\Sigma_{\rm gas}$}/M_{\odot}\,\rm pc^{-2})\approx
0$. We overplot the K-S relation derived by de los Reyes & Kennicutt (2019)
for local star-forming spiral galaxies (Figure 2a) and spiral plus dwarf
galaxies combined (Figure 2b), which have slopes of 1.41 and 1.26,
respectively. The relation between $\Sigma_{\rm SFR}$ and dust mass surface
density ($\Sigma_{\rm dust}$) for star-forming spiral galaxies from Kennicutt
& de los Reyes (2021) has a similar slope (1.29; Figure 2c). The shaded
regions indicate the $1\sigma$ scatter of the corresponding relations, whose
zero points have been adjusted to be consistent with the initial mass function
of Chabrier (2003) adopted in this work. All three relations intersect well
the upper peak of star-forming galaxies in our sample. Although detailed
comparisons are beyond the scope of the current paper, the overall qualitative
consistency of our sample distribution with the K-S relations from previous
works provides independent confirmation of the robustness of the parameters
derived by Li et al. (2023), who employed different methods to measure SFR,
gas mass, and galaxy size.

We note that the published K-S relations typically encompass minimum surface
densities of only $\log\,(\mbox{$\Sigma_{\rm SFR}$}/M_{\odot}\,\rm
yr^{-1}\,kpc^{-2})\approx-4$, $\log\,(\mbox{$\Sigma_{\rm gas}$}/M_{\odot}\,\rm
pc^{-2})\approx 0$, and $\log\,(\mbox{$\Sigma_{\rm dust}$}/M_{\odot}\,\rm
pc^{-2})\approx-2$. Our work extends the traditional K-S law to lower gas and
dust surface densities by more than 1 order of magnitude and lower SFR surface
densities by nearly 2 orders of magnitude. To our knowledge, previous
observations never systematically investigated this regime of gas-poor,
passive galaxies. Our measurements, obtained from SFRs and dust masses derived
from fitting the FUV-to-FIR SEDs based on a new set of panchromatic photometry
of galaxies in the Stripe 82 region, carry significant uncertainty for
individual sources but no overall systematic bias (Li et al., 2023). Might the
observed correlation between $\Sigma_{\rm SFR}$ and $\Sigma_{\rm gas}$
($\Sigma_{\rm dust}$) arise artificially from the fact that both SFR and
$M_{\mathrm{dust}}$ derive from SED fitting? We do not think so. To
investigate this possibility, we replaced the SFRs from fitting the full
(FUV–FIR) SED with less accurate SFRs based only on modeling the photometry of
the five ($ugriz$) SDSS bands. The basic results shown in Figure 2 survive.

We fit the entire sample with the orthogonal distance regression method in the
Python package scipy.odr. This method is preferred over the simple $\chi^{2}$
method because the latter is strongly biased by the small fraction of targets
on the lower right wing of the sample distribution. The best-fit relation
($\alpha=1.50$, $\beta=-4.29$) is slightly steeper than that from de los Reyes
& Kennicutt (2019), such that the extrapolation of the latter deviates from
our relation in the regime of passive galaxies at $\log\,(\mbox{$\Sigma_{\rm
gas}$}/M_{\odot}\,\rm pc^{-2})\lesssim 0$. We emphasize that our fitted
relation mainly serves to facilitate qualitative comparison with the canonical
K-S relation. We opt not to fit the relation separately for the star-forming
and passive galaxies because of their limited dynamic range and the
considerable uncertainty of the gas masses. For completeness, we note that a
similar deviation in the regime of passive galaxies appears in the
$\mbox{$\Sigma_{\rm SFR}$}-\mbox{$\Sigma_{\rm dust}$}$ relation (Figure 2c;
Kennicutt & de los Reyes 2021).

Figure 5: Distribution of gas mass and stellar mass for the entire sample
(background contours) and for the different categories of mergers: (a) wet
major mergers, (b) wet minor mergers, (c) dry major mergers, (d) dry minor
mergers, (e) mixed major mergers, and (f) mixed minor mergers. The primary
galaxy of each pair is highlighted as a filled red point if it is star-forming
and as an open red point if it is passive, which is defined by $\rm
log\,(sSFR/yr^{-1})<-11$. The black solid line indicates the best fit for the
gas mass main sequence, which has a $1\sigma$ scatter of 0.38 dex (gray dotted
lines). The threshold for gas-rich objects is given by the black dashed line,
which is set to $2\sigma$ below the gas mass main sequence. Figure 6:
Distribution of SFR and stellar mass for the entire sample (background
contours) and for the different categories of mergers: (a) wet major mergers,
(b) wet minor mergers, (c) dry major mergers, (d) dry minor mergers, (e) mixed
major mergers, and (f) mixed minor mergers. The primary galaxy of each pair is
highlighted as a filled red point if it is star-forming and as an open red
point if it is passive, which is defined by $\rm log\,(sSFR/yr^{-1})<-11$. The
black solid line indicates the best fit for the star-forming galaxy main
sequence, which has a $1\sigma$ scatter of 0.3 dex (gray dotted lines). The
black dashed line separates star-forming galaxies from passive galaxies.

###  3.3 Gas Mass and SFR of Merger Galaxies

Figure 4 compares the distributions of SFR, sSFR, SFE, and $f_{\mathrm{gas}}$
for the merger and non-merger groups. The two-sample Kolmogorov-Smirnov
test222https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstest.html
rejects the null hypothesis that SFR, sSFR, and $f_{\rm gas}$ are drawn from
the same parent distribution, with a probability of $p=0.005$, 0.003, and
$<0.001$, respectively. Among the population of less actively star-forming
galaxies, mergers have somewhat higher SFR and sSFR but lower $f_{\rm gas}$
than non-mergers. These then conspire to produce statistically
indistinguishable SFEs for the two populations ($p=0.679$).

To facilitate the following discussion, we define star-forming galaxies as
objects with $\mathrm{sSFR}>10^{-11}\,\mathrm{yr^{-1}}$, and the rest as
passive galaxies. We further classify the galaxies into gas-rich and gas-poor
varieties, according to their distance from the gas mass main sequence, as
given by Equation 3. Galaxies located more than $2\sigma$ below the gas mass
main sequence are deemed gas-poor, while the rest are gas-rich. Consistent
with common practice, we designate the merger of two gas-rich galaxies a “wet
merger,” that of two gas-poor galaxies a “dry merger,” and the combination of
a gas-rich and a gas-poor galaxy a “mixed merger.” We also separate mergers
into major and minor categories based on whether their stellar mass ratio
$f_{M_{*}}>0.25$. In this study, we only investigate the more massive, primary
component of the galaxy pair, such that it always meets the stellar mass cut
of $M_{*}\geq 10^{10}\,M_{\odot}$, in order that the non-merger members in our
parent sample can serve as control galaxies. If both components of the galaxy
pair have comparable stellar masses within their $3\sigma$ measurement
uncertainty of 0.15 dex (Section 2), we include both in the merger sample.

####  3.3.1 Mergers on the Gas Mass Main Sequence

We examine the nature of merging galaxies on the gas mass main sequence of the
entire sample, splitting the mergers by their gas content and stellar mass
ratio. Most (74%) of the wet major mergers are star-forming galaxies (Figure
5a). However, interestingly, the remaining 26%, though massive and gas-rich,
are passive. This phenomenon is not unique to the merger sample, for a nearly
identical fraction (19%) of the gas-rich non-mergers are also passive. Very
few sources—only six, or $23\%$—actually lie $1\sigma$ above the gas mass main
sequence, which indicates that wet major mergers before coalescence do not
contain more cold gas than non-mergers. This is consistent with the previous
finding that only late-stage mergers show enhanced cold interstellar medium
(Shangguan et al., 2019). Wet minor mergers behave similarly but not
identically (Figure 5b). A higher fraction of galaxies (33%, almost double the
fraction among gas-rich non-mergers) lie $1\sigma$ above the gas mass main
sequence. A comparable fraction (28%) of the wet minor merging galaxies are
passive, moderately higher than the fraction of passive galaxies in non-merger
galaxies. As expected, dry mergers are dominated almost exclusively by
passive, gas-poor galaxies, with a tendency for systematically higher stellar
masses in minor mergers (Figure 5d) compared to major mergers (Figure 5c).
Mixed major mergers consist of $\sim\,$60% gas-poor galaxies (Figure 5e),
similar to the fraction of gas-rich objects, while gas-poor systems account
for the majority (85%) of mixed minor mergers (Figure 5f). The implications of
these results are discussed in Section 4.2.

####  3.3.2 Mergers on the SFR$-M_{*}$ Diagram

We also compare the merger galaxies with the entire galaxy sample on the
SFR$-$$M_{*}$ diagram (Figure 6). Irrespective of stellar mass ratio, wet
mergers largely, but not exclusively, reside along the star formation main
sequence. However, a significant fraction ($\sim 25\%-30\%$) occupies the so-
called green valley, despite the ready supply of fuel available for star
formation. Gas-poor systems are passive, as expected, while among mixed pairs
a considerably larger fraction of objects form stars in major mergers than
minor mergers. Most unexpected, perhaps, is the rarity of “starbursts,”
defined here as galaxies that scatter at least $1\sigma$ (0.3 dex) above the
star-forming main sequence (Elbaz et al., 2007; Ellison et al., 2020; Wang et
al., 2022). Among wet mergers, be they major or minor, only 7 sources or 9% of
the total qualify as starbursts. This low fraction is almost the same as that
for the control sample of non-mergers (8%).

Figure 7: Distribution of merger pairs on the $\Sigma_{\rm SFR}$–$\Sigma_{\rm
gas}$ plane, with the full sample shown as background contours, for the
different categories of mergers: (a) wet major mergers, (b) wet minor mergers,
(c) dry major mergers, (d) dry minor mergers, (e) mixed major mergers, and (f)
mixed minor mergers. The typical uncertainties for each subsample of mergers
are shown in the bottom-right corner of each panel. The black dashed line
gives the K-S law for spiral and dwarf galaxies from de los Reyes & Kennicutt
(2019), which has a $1\sigma$ scatter of 0.37 dex (gray dotted lines). Figure
8: Distance to the K-S law ($\Delta\alpha$) of de los Reyes & Kennicutt (2019)
for each galaxy in the sample of mergers, including both major and minor
pairs, as a function of (a) the stellar mass ratio ($f_{M_{*}}$) and (b)
projected separation ($\Delta r$). The Spearman’s rank correlation coefficient
$\rho$ and $p$-value are shown in the upper-left corner of each panel. A
positive correlation has $\rho>0$, and a negative correlation has $\rho<0$.
The values of $p<0.05$ and $|\rho|\approx 0.2$ imply that there is a weak
correlation between the two parameters. The black line indicates the average
trend in each panel.

####  3.3.3 Mergers on the Kennicutt-Schmidt Relation

Finally, we investigate the behavior of mergers on the $\Sigma_{\rm
SFR}$$-$$\Sigma_{\rm gas}$ plane. To first order, the overarching impression
from Figure 7 is that mergers in the local Universe leave, at best, a rather
weak imprint on the efficiency of star formation of galaxies. Consistent with
a theme echoed throughout this study, we find little evidence that mergers
significantly boost the SFE, certainly not to the extent expected of starburst
galaxies (Daddi et al., 2010b; Genzel et al., 2010; Saintonge et al., 2011;
Kennicutt & de los Reyes, 2021). Similar conclusions are also reached by Díaz-
García & Knapen (2020) and Violino et al. (2018), who, using a different
approach from ours, found that the gas depletion time of interacting galaxies
is not statistically different from that of non-interacting galaxies. Our
conclusion applies to mergers with varying degrees of gas-richness and stellar
mass ratio. Only two galaxies in the wet major merger subsample genuinely lie
above the 0.37 dex ($1\sigma$) scatter of the K-S relation of de los Reyes &
Kennicutt (2019) for spiral and dwarf galaxies. On the contrary, some galaxies
in wet major mergers even lie well below the K-S relation. This effect is most
pronounced for the sample of wet minor mergers, whose entire sample exhibits a
pronounced, systematic offset toward lower SFE. The existence of gas-rich yet
passive galaxies is puzzling. Note that these results remain qualitatively
unchanged if we substitute other published K-S relations as reference instead.

What factors drive the residual offset from the K-S law? Figure 8 shows that
among mergers, $\Delta\alpha$ with respect to the K-S law of de los Reyes &
Kennicutt (2019) systematically increases with increasing stellar mass ratio
($f_{M_{*}}$; panel a) and closer pair separation ($\Delta r$; panel b). We
emphasize that, despite the formal significance of the statistical test, the
correlations are only moderate and the scatter significant. In galaxy pairs of
comparable stellar mass (high log$\,f_{M_{*}}$) the SFR can be enhanced during
the late stage (small $\Delta\,r$) of the merger, presumably on account of the
strong tidal and turbulent compression of the gas. The large scatter of
$\Delta\alpha$ is due to the large uncertainty in the gas mass, propagated
from the uncertainty of the dust mass and $\delta_{\rm GDR}$. Those weak
trends demonstrate that the increase of SFE is not always effectively
triggered by mergers.

##  4 Discussion

###  4.1 Extension of the Kennicutt-Schmidt Relation to Quiescent Galaxies

Our improved photometric measurements and SED analysis have greatly expanded
the dynamical range over which SFR and dust (gas) mass can be measured in low-
redshift galaxies. In addition to the detailed quantification of uncertainties
and other technical improvements, our treatment of the upper limits for the
Herschel FIR data turns out to be critical to derive unbiased SFRs and dust
masses for the passive galaxies (Li et al., 2023). Although the measurements
are quite uncertain for individual sources, their sample distribution is
robust and still highly informative. For example, our sample reaches ${\rm
SFR}\approx 10^{-2}\,M_{\odot}\,\mathrm{yr^{-1}}$, an order of magnitude lower
than the values routinely obtained from SED fits that only include FIR
detections (e.g., Rowlands et al. 2012, 2014). Eales et al. (2017) report sSFR
$\approx 10^{-12.5}\,\mathrm{yr^{-1}}$ for the early-type galaxies from HRS
(distance 15–25 Mpc), which, with $M_{*}\approx 10^{10.5}\,M_{\odot}$, closely
resemble the passive galaxies in our sample. It is not surprising, then, to
discover some low-level star formation in our passive galaxies. Many
observations show that massive early-type galaxies can retain a large amount
of atomic or molecular gas (e.g., Combes et al. 2007; Babyk et al. 2019), even
though they are on or transiting to the red sequence (Young et al., 2014).

This study mainly covers star-forming and passive galaxies, with very few
starburst systems, owing to the unbiased nature of our sample selection. Not
surprisingly, then, the $\mbox{$\Sigma_{\rm SFR}$}-\mbox{$\Sigma_{\rm gas}$}$
relation of the star-forming subsample (Figure 3) agrees well with published
results (e.g., Kennicutt 1998; Kennicutt & de los Reyes 2021): the slope of
$\beta=1.50$ lies comfortably within the $1-2\sigma$ range of previous studies
(Leroy et al., 2008; Daddi et al., 2010a; Martig et al., 2013; Liu et al.,
2015). When extending to passive galaxies, the best-fitting slope deviates
from the extrapolation of the canonical relation based on spiral and dwarf
galaxies. The power-law index for the K-S relation may differ between star-
forming and starburst galaxies, and it depends on whether the gas measurement
includes total gas or just molecular gas. For example, while Kennicutt & de
los Reyes (2021) found a break in the slope of the K-S relation that involves
total gas density; when molecular gas is used, the relation is roughly linear
for all but the very lowest surface density systems, which fall below a
threshold density (de los Reyes & Kennicutt, 2019). The presence of a
threshold gas density is also suggested by Bigiel et al. (2008), who found
that star formation becomes inefficient when the local resolved gas surface
density $\mbox{$\Sigma_{\rm gas}$}\lesssim 10\,M_{\odot}\,\rm pc^{-2}$. At low
gas surface density, the interstellar medium resides mainly in atomic instead
of molecular phase, which leads to a steeper K-S relation (Leroy et al., 2008;
Bigiel et al., 2014; de los Reyes & Kennicutt, 2019).

Within our sample, a possible break in the $\Sigma_{\rm SFR}$–$\Sigma_{\rm
gas}$ relation occurs in the transition region between star-forming and
passive galaxies (Figure 3). The star-forming galaxies are mostly located
above $\mbox{$\Sigma_{\rm gas}$}\approx{\rm few}\,M_{\odot}\,\rm pc^{-2}$,
which is intriguingly close to the threshold of $\mbox{$\Sigma_{\rm
gas}$}\approx 10\,M_{\odot}\,\rm pc^{-2}$ discussed by Bigiel et al. (2008).
By contrast, the passive galaxies populate the region of lower density, at
$\mbox{$\Sigma_{\rm gas}$}\approx 0.1-1\,M_{\odot}\,\rm pc^{-2}$. The
numerical simulations of Becerra & Escala (2014) suggest that the
$\mbox{$\Sigma_{\rm SFR}$}-\mbox{$\Sigma_{\rm gas}$}$ relation may extend as
far as $\mbox{$\Sigma_{\rm gas}$}\approx 10^{-3}\,M_{\odot}\,\rm pc^{-2}$,
with a steepening of the slope at $\mbox{$\Sigma_{\rm gas}$}\lesssim
1\,M_{\odot}\,\rm pc^{-2}$, in good qualitative agreement with our
observations.

Why do passive galaxies have a steeper $\Sigma_{\rm SFR}$–$\Sigma_{\rm gas}$
relation? On the one hand, the superlinear relation between SFR and total gas
surface density can be shaped by the combination of a nearly linear molecular
gas relation and the almost vertical trend between SFR and atomic gas surface
density (Bigiel et al., 2008; Leroy et al., 2013). Since the molecular gas
mass fraction in the interstellar medium drops significantly when
$\mbox{$\Sigma_{\rm gas}$}\lesssim 10\,M_{\odot}\,\rm pc^{-2}$ (Wong & Blitz,
2002; Saintonge & Catinella, 2022), massive early-type galaxies may be
dominated by H i gas (Young et al., 2014; Saintonge et al., 2016), which may
not be conducive to forming stars (McKee & Ostriker, 2007; Krumholz, 2014).
Verley et al. (2010) observed a steep $\Sigma_{\rm SFR}$–$\Sigma_{\rm gas}$
relation for the H i-dominated regions of M 33. On the other hand, the
stability of a gas disk in a star-forming galaxy may be quite different from
that of a passive galaxy (Martig et al., 2009), in view of the much higher
concentration (bulge-dominance) of passive galaxies compared to star-forming
galaxies (Figure 9). High concentration produces a steeper gravitational
potential well and hence stronger shear in the velocity field, which, in turn,
increases Toomre’s (1964) $Q$ parameter and prevents the cold gas from
collapsing to form stars (Krumholz et al., 2005; Somerville & Davé, 2015).
Gas-rich, early-type galaxies can have SFEs lower by a factor of more than 2
compared to late-type galaxies at fixed gas surface density (Martig et al.,
2013; Davis et al., 2014). Interestingly, the concentration parameter almost
exactly demarcates the two populations of star-forming and passive galaxies in
Figure 9.

As a caveat, we emphasize that the SFRs and gas masses of individual passive
galaxies carry considerable uncertainties. Although Li et al. (2023) show that
the sample distribution of the measured physical quantities is unbiased, the
large uncertainties of the SFR and gas mass estimates can affect the sample
distribution and bias the slope of the $\mbox{$\Sigma_{\rm
SFR}$}-\mbox{$\Sigma_{\rm gas}$}$ relation for the star-forming and passive
populations. This effect is unlikely to affect the scaling relation of the
entire sample, given the large dynamic range of the overall distribution.
However, it may bias the slopes if one fits the star-forming and passive
subsamples separately. Moreover, we estimated the gas mass using the dust mass
and the mass–metallicity relation derived from star-forming galaxies (Kewley &
Ellison, 2008; Magdis et al., 2012). While we use different stellar mass
measurements than the estimates used by Kewley & Ellison (2008), it is
essential to adopt the $\delta_{\rm GDR}-\rm Z$ and $M_{*}-\rm Z$ relations
self-consistently in terms of the metallicity calibration (Berta et al.,
2016). Different calibrations can lead to significant systematic discrepancies
for the $M_{*}-\rm Z$ relation in terms of both its shape and scale (Kewley &
Ellison, 2008). In this work, estimations from Equations 2.2 and 2.2 are both
based on the calibration of Pettini & Pagel (2004) at $M_{*}\approx
10^{11}\,M_{\odot}$. The mass–metallicity relation may differ in passive
galaxies. Wu (2020) argues, for instance, that the gas-phase metallicity of
early-type galaxies is $\sim 0.1$ dex lower than in later-type, star-forming
galaxies, possibly as a result of dilution by pristine gas from the
intergalactic medium. It is beyond the scope of the current work to
investigate this effect. We simply note that a lower metallicity in passive
galaxies would correspond to a higher gas-to-dust ratio and, thus, a higher
gas mass, which may lead to an even steeper $\mbox{$\Sigma_{\rm
SFR}$}-\mbox{$\Sigma_{\rm gas}$}$ relation.

Figure 9: K-S relation for our sample (contours), color-coded by the average
concentration index $C\equiv R_{90}/R_{50}$ in two-dimensional bins of
$\Sigma_{\rm SFR}$ and $\Sigma_{\rm gas}$, with $R_{90}$ and $R_{50}$ the
Petrosian (1976) radii enclosing 90% and 50% of the $r$-band light,
respectively. The black dashed line gives the relation for spiral and dwarf
galaxies from de los Reyes & Kennicutt (2019), which has a $1\sigma$ scatter
of 0.37 dex (gray dotted lines).

###  4.2 The Low Frequency of Starbursts in Mergers

Only nine (5%) of the 174 primary galaxies in the merger sample qualify as
starburst galaxies, by the commonly adopted criterion that they should lie at
least $1\sigma$ ($>0.3$ dex) above the star-forming main sequence (Elbaz et
al., 2007; Ellison et al., 2020; Wang et al., 2022). This starburst fraction
is similar to that in the parent sample, which is dominated vastly by non-
mergers. Visual inspection reveals that these nine starburst galaxies all have
late-type structures, most showing obvious signs of morphological disturbance.
Moreover, all have high gas fractions and have a gas-rich companion. Six of
the nine can be considered major mergers, characterized by a median stellar
mass ratio of $\sim 0.7$. Our results, therefore, are consistent with previous
observations and simulations, which conclude that starburst galaxies, if
triggered by galaxy mergers, are primarily associated with gas-rich major
mergers, instead of other types of merger pairs (Kartaltepe et al., 2012; Hung
et al., 2013; Patton et al., 2013; Pan et al., 2018). Strong tidal torques
imparted by the merger of galaxies of comparable mass effectively promote gas
inflow and subsequent vigorous star formation (Mihos & Hernquist, 1996; Cox et
al., 2006; Renaud et al., 2014; Sparre et al., 2022).

At first glance, the absence of an increased incidence of starbursts in
mergers seems to conflict with previous works. For instance, luminous and
ultraluminous infrared galaxies (LIRGs and ULIRGs) mostly consist of galaxies
in different merger stages (Sanders & Mirabel, 1996; Kaviraj, 2009; Espada et
al., 2018; He et al., 2022). So-called submillimeter galaxies, the higher
redshift counterparts of the more nearby ULIRGs, are strong starburst systems
with SFR up to $1000\,M_{\odot}\,\rm yr^{-1}$ (Tacconi et al., 2006) that are
often affiliated with major mergers of gas-rich disks (Engel et al. 2010;
Michałowski et al. 2010; but see Cheng et al. 2022). However, we find that the
reverse does not hold. Major mergers, even when gas-rich, are not necessarily
starbursts (Figure 5a). Numerical simulations demonstrate that while the tidal
torque of a major merger drives cold gas to the center, gas simultaneously
also gets ejected to the outskirts of the galaxy in the form of tidal tails
(Di Matteo et al., 2007). The outer regions of interacting systems may store a
significant fraction of the gas ejected from the inner regions of the galaxies
(Perez et al., 2011). The gas at large radii only partially flows back to the
center at late times. The gas inflow depends on the details of the galaxy
encounter, such as the orientation, pericentric distance, and the size of the
gas disk (Blumenthal & Barnes, 2018). In addition to the well-known gas
inflow, other mechanisms, such as the interaction-triggered gas migration (Pan
et al., 2019), increased gas turbulence (Pan et al., 2018; Violino et al.,
2018), or the formation of internal structure in the galaxy (Espada et al.,
2018) can regulate the level of star formation in the merging components. Pan
et al. (2019) investigate the radial distribution of SFR derived from
H$\alpha$ emission for merging galaxies and a control sample. They find the
radial profiles of sSFR, which can be enhanced or suppressed, have
considerable variance across the merger stages, while the global sSFR before
the coalescence phase is not significantly enhanced. The probability of
witnessing a merger undergoing a starburst episode depends on when we happen
to catch it during its evolution, as well as sample selection bias (Murphy et
al., 1996). Furthermore, (U)LIRGs are very rare in the local Universe (Soifer
& Neugebauer, 1991; Knapen & James, 2009). Most (U)LIRGs are discovered during
the merging of two disk galaxies (Colina et al., 2001; Carpineti et al.,
2015), which constitute only a small fraction of the entire merger sample.
Studying a large sample of the nearest galaxies, Knapen & Cisternas (2015)
find that starbursts only show a moderate preference for interacting galaxies,
and that the results strongly depend on sample selection.

Wet minor mergers present an even more extreme situation with their apparently
suppressed SFE (Figure 7b). At fixed $\Sigma_{\rm gas}$, wet minor mergers
have systematically lower $\Sigma_{\rm SFR}$ compared to non-mergers. A few
outliers with significantly suppressed SFE can also be found among the wet
major mergers. Figure 9 offers a possible explanation for this otherwise
somewhat perplexing behavior. Some of the most extreme outliers below the K-S
relation have relatively high concentration, reminiscent of dust-rich early-
type galaxies, which, having experienced a recent minor merger now forms stars
inefficiently because the gas is still streaming toward the center or the
interstellar medium is heated by shocks and turbulence (Davis et al., 2015).
The huge scatter of mergers on the K-S relation confirms the suggestion of
Díaz-García & Knapen (2020, their Figure 4) that gas mass enhancement barely
correlate with SFR enhancement of SFR. Other recent observations arrive at
similar conclusions regarding the mild effect of mergers on the global SFR of
galaxies (e.g., Puech et al., 2014; Silva et al., 2018). Mergers and non-
mergers occupy almost indistinguishable positions on the star-forming main
sequence at $z\approx 0-4$ (Xu et al., 2010; Wong et al., 2011; Lackner et
al., 2014; Knapen et al., 2015; Silva et al., 2018; Pan et al., 2019; Pearson
et al., 2019; Díaz-García & Knapen, 2020). Only $\sim 12\%$ of massive,
closely separated ($\Delta r=3-15$ kpc) major mergers at $0.3<z<2.5$ are
starbursts (Silva et al., 2018). This fraction is higher than ours. Besides
the difference in redshift, our work in Stripe 82 detects more passive galaxy
components in dry and mixed mergers, which represent 27% and 30% of all
mergers in our sample, respectively. If we take this into consideration, the
fraction of starburst galaxies in our merger sample becomes even lower.

This work mainly focuses on the primary galaxy component of each merger pair.
Star formation in the less massive member of the pair may be impacted more
dramatically by tidal compression or gas stripping (Di Matteo et al., 2007;
Silva et al., 2018; Du et al., 2019). The detailed study of the secondary
companion is beyond the scope of this work.

##  5 Summary

The recently completed catalog of Li et al. (2023) provides uniformly measured
panchromatic photometry and physical parameters of 2685 massive ($M_{*}\geq
10^{10}\,M_{\odot}$), low-redshift ($z=0.01-0.11$) galaxies selected from the
SDSS Stripe 82 region. In addition to stellar masses and SFRs, the new
analysis supplies total (atomic and molecular hydrogen) gas masses inferred
from total dust masses derived from careful analysis of the full broadband
(FUV–FIR) SED. The accurate measurements of Li et al. (2023), in combination
with their SED analysis that fully incorporates proper uncertainties and upper
limits, yield an exceptionally wide dynamic range in parameter space. Our
catalog reaches ${\rm SFRs}\approx 10^{-2}\,M_{\odot}\,\mathrm{yr^{-1}}$ and
$M_{\rm gas}\approx 10^{8.5}\,M_{\odot}$, which enables us to probe the
unbiased star formation activity and gas content of the full population of
massive galaxies, including previously poorly studied gas-poor, largely
quiescent members.

We take advantage of this resource to investigate the effect of galaxy
interactions and mergers on star formation. Selecting merging galaxies in a
relatively advanced stage of interaction (projected separation $\Delta\,r<50$
kpc), we study the influence of late-stage mergers on the gas and star
formation properties, comparing them to the dominant, control sample of non-
merger galaxies within the framework of the well-established galaxy scaling
relations between SFR and $M_{*}$ on the one hand, and between $\Sigma_{\rm
SFR}$ and $\Sigma_{\rm gas}$ on the other hand. We consider the effect of
stellar mass ratio by categorizing the mergers as major or minor, and the
impact of gas fraction by defining them as wet, mixed, or dry from their
position relative to the gas mass main sequence on the
$M_{\mathrm{gas}}$$-$$M_{*}$ diagram.

Our main results can be summarized as follows:

  1. 1.

The distribution of galaxies in the $M_{\mathrm{gas}}$$-$$M_{*}$ plane is
bimodal. Apart from the gas-rich, mostly star-forming galaxies that trace the
gas mass main sequence, we identify a clearly distinct, secondary population
of gas-poor, largely quiescent galaxies.

  2. 2.

The bimodality of galaxies in the $M_{\mathrm{gas}}$$-$$M_{*}$ plane maps to a
similar bimodality in the $\Sigma_{\rm SFR}$$-$$\Sigma_{\rm gas}$ plane. The
entire population can be described by $\mbox{$\Sigma_{\rm
SFR}$}\propto\mbox{$\Sigma_{\rm gas}$}^{1.50}$, not dissimilar from previous
studies of the Kennicutt-Schmidt relation, although our sample extends to
considerably more passive, gas-poor galaxies that exhibit a steeper power-law
relation compared to the conventionally studied star-forming, gas-rich
systems.

  3. 3.

Low-redshift galaxy mergers show very minimal differences in their star
formation properties (SFR, sSFR, SFE) compared to non-mergers, although the
SFE of the galaxies in mergers varies mildly with stellar mass ratio and pair
separation. Contrary to popular wisdom, we find no excess of starbursts in
gas-rich, major mergers. Gas-rich, minor mergers, if anything, form stars even
less efficiently than non-merging galaxies.

  4. 4.

Our study highlights the subtle, even counterintuitive, impact of galaxy
interactions and mergers on star formation activity in galaxies. Whether
mergers convert gas into stars effectively or not depends on many factors,
including the phase of the orbital evolution of the merging pair and the
location of the gas as it responds to the tidal field of the gravitational
interaction.

We thank the anonymous referee for helpful comments. This work was supported
by the National Science Foundation of China (11721303, 11991052, 12011540375,
12233001), the National Key R&D Program of China (2022YFF0503401), and the
China Manned Space Project (CMS-CSST-2021-A04, CMS-CSST-2021-A06). We thank
the following individuals for their discussions and contributions to various
aspects of this work: Ruancun Li, Chao Ma, Yingjie Peng, Longfei Zhai, Dingyi
Zhao, and Ming-Yang Zhuang.

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