# The ALMaQUEST Survey XIII: Understanding radial trends in star formation
quenching via the relative roles of gas availability and star formation
efficiency

Hsi-An Pan (潘璽安)  Department of Physics, Tamkang University, No.151, Yingzhuan
Road, Tamsui District, New Taipei City 251301, Taiwan  Lihwai Lin  Institute
of Astronomy and Astrophysics, Academia Sinica, Taipei 10617, Taiwan  Sara L.
Ellison  Department of Physics and Astronomy, University of Victoria, Finnerty
Road, Victoria, British Columbia V8P 1A1, Canada  Mallory D. Thorp  Department
of Physics and Astronomy, University of Victoria, Finnerty Road, Victoria,
British Columbia V8P 1A1, Canada  Argelander-Institut für Astronomie,
Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany  Sebastián F. Sánchez
Instituto de Astronomía, Universidad Nacional Autónoma de México, A. P.
70-264, C.P. 04510, México, D.F., Mexico  Asa F. L. Bluck  Department of
Physics, Florida International University, 11200 SW 8th Street, Miami, FL
33199, USA  Francesco Belfiore  INAF— Osservatorio Astrofisico di Arcetri,
Largo E. Fermi 5, I-50125, Florence, Italy  Joanna M. Piotrowska  Cahill
Center for Astrophysics, California Institute of Technology, 1216 East
California Boulevard, Pasadena, CA 91125, USA  Jillian M. Scudder  Department
of Physics & Astronomy, Oberlin College, Oberlin, OH, 44074, USA  William M.
Baker  Kavli Institute for Cosmology, University of Cambridge, Madingley Road,
Cambridge, CB3 0HA, UK  Cavendish Laboratory—Astrophysics Group, University of
Cambridge, 19 JJ Thomson Avenue, Cambridge, CB3 0HE, UK

###### Abstract

Star formation quenching is one of the key processes that shape the evolution
of galaxies. In this study, we investigate the changes in molecular gas and
star formation properties as galaxies transit from the star-forming main
sequence to the passive regime. Our analysis reveals that as galaxies move
away from the main sequence towards the green valley the radial profile of
specific star formation rate surface density ($\Sigma_{\mathrm{sSFR}}$) is
suppressed compared with main sequence galaxies out to a galactocentric radius
of 1.5$R_{\mathrm{e}}$($\sim$ 7 kpc for our sample). By combining radial
profiles of gas fraction ($f_{\mathrm{gas}}$) and star formation efficiency
(SFE), we can discern the underlying mechanism that determines
$\Sigma_{\mathrm{sSFR}}$ at different galactocentric radii. Analysis of
relative contributions of $f_{\mathrm{gas}}$ and SFE to
$\Sigma_{\mathrm{sSFR}}$ uncovers a diverse range of quenching modes. Star
formation in approximately half of our quenching galaxies is primarily driven
by a single mode (i.e. either $f_{\mathrm{gas}}$ or SFE), or a combination of
both. A collective analysis of all galaxies reveals that the reduction in star
formation within the central regions ($R$ $<$ 0.5 $R_{\mathrm{e}}$) is
primarily attributable to a decrease in SFE. Conversely, in the disk regions
($R$ $>$ 0.5 $R_{\mathrm{e}}$), both $f_{\mathrm{gas}}$ and SFE contribute to
the suppression of star formation. Our findings suggest that multiple
quenching mechanisms may be at play in our sample galaxies, and even within a
single galaxy. We also compare our observational outcomes with those from
galaxy simulations and discuss the implications of our data.

††journal:

##  1 Introduction

Galaxies are typically classified into two main populations on the global star
formation rate (SFR) versus stellar mass ($M_{\ast}$) diagram: the star-
forming main sequence and the passive population (Strateva et al., 2001;
Brinchmann et al., 2004; Elbaz et al., 2007; Noeske et al., 2007). The star-
forming main sequence consists of mostly disk galaxies with higher specific
star formation rate (sSFR = SFR/$M_{\ast}$, where $M_{\ast}$ is global stellar
mass of a galaxy), while the passive population is predominantly composed of
quiescent spheroidal galaxies with lower sSFR (Schawinski et al., 2014).
However, there is an intermediate population that is sparsely populated
between these two regimes, known as the green valley (Wyder et al., 2007;
Martin et al., 2007; Salim, 2014). Green valley galaxies represent a
transitional population that is likely undergoing a shift from the star-
forming phase to the quiescent phase. Therefore, studying the physical
properties of green valley galaxies is crucial for gaining insights into the
processes of star formation quenching and galaxy evolution.

On a spatially-resolved scale, previous works have shown that the differences
in global sSFR between star-forming, green valley, and quiescent galaxies is
driven by variations in the fraction of “retired” regions that have ceased to
form new stars, with red galaxies exhibiting the highest fraction of retired
spaxels, and vice versa (Hsieh et al., 2017; Pan et al., 2018a; Cano-Díaz et
al., 2019; Lin et al., 2022). Since star formation primarily occurs in
molecular gas clouds, the presence of retired regions is expected to be linked
to the changes in the properties of molecular gas. Specifically, the decline
in star formation activity can be attributed to a depletion of molecular gas
and/or a reduction in its efficiency in forming stars, which could result from
factors such as inefficient cooling or turbulent pressure support (McKee &
Ostriker, 2007). These scenarios correspond to the changes in two observable
parameters: the gas fraction ($f_{\mathrm{gas}}$), defined as the molecular
gas mass of a galaxy relative to its stellar mass
($M_{\mathrm{H_{2}}}$/$M_{\ast}$), and the star formation efficiency (SFE),
which quantifies the conversion of gas into stars as the number of stars
formed per unit time (SFR/$M_{\mathrm{H_{2}}}$). Previous global studies of
molecular gas have demonstrated that star formation quenching is associated
with changes in both global $f_{\mathrm{gas}}$ and SFE (e.g., Sargent et al.,
2014; Saintonge et al., 2016; Colombo et al., 2020; Piotrowska et al., 2020;
Wylezalek et al., 2022), but there is no definitive conclusion regarding the
relative importance of one factor over the other.

A crucial step towards understanding the process of star formation quenching
is the investigation of the spatially-resolved molecular gas properties of
galaxies. The ALMaQUEST survey (ALMA-MaNGA Quenching and Star-Formation
Survey; Lin et al. 2020) was specifically designed to study the resolved
molecular gas properties of various types of galaxies, including those above
(Ellison et al., 2020a) and below (Lin et al., 2022) the global star-forming
main sequence, as well as galaxy mergers (Thorp et al., 2022).

Our most recent studies have unveiled important insights into the molecular
gas properties of galaxies. Specifically, we have found that retired regions
within galaxies generally exhibit lower $f_{\mathrm{gas}}$ and/or SFE compared
to active star-forming regions (Ellison et al., 2021b; Lin et al., 2022).
Interestingly, we have also observed that even the star-forming regions within
green-valley galaxies, which are in a transitional state, show lower sSFR,
SFE, and $f_{\mathrm{gas}}$ compared to star-forming regions of the star-
forming main sequence (Lin et al. 2022, see also Brownson et al. 2020 for the
similar results, but from different observations). This suggests that the
overall reduction in sSFR in green-valley galaxies is a result of not only an
increased fraction of retired regions but also by a decrease in sSFR within
their active star-forming regions (Lin et al. 2022, see also Ellison et al.
2018 and Belfiore et al. 2018). The suppressed sSFR, $f_{\mathrm{gas}}$, and
SFE in green-valley galaxies naturally gives rise to a range of resolved
scaling relations that deviate from those observed in normal star-forming
galaxies (Ellison et al. 2021a; Baker et al. 2022; Lin et al. 2022; Baker et
al. 2023; Ellison et al. 2024; see also Garay-Solis et al. 2023 for a
discussion based on non-ALMaQUEST observations).

On the other hand, the chosen analytical approach also plays a pivotal role in
interpreting the data. For instance, our analysis of the ALMaQUEST merger
sample (cf. Section 2.1) reveals that when all spaxels are considered
together, one might conclude that approximately half of the interaction-
triggered star formation is driven by $f_{\mathrm{gas}}$, and the remaining
half by SFE (Thorp et al., 2022). However, when examined on a per-galaxy
basis, it becomes evident that some galaxies are entirely driven by
$f_{\mathrm{gas}}$, while others are exclusively powered by SFE. Therefore,
combining all data may lead to a loss of information.

While our previous ALMaQUEST studies that focus on star formation quenching
(Ellison et al., 2021b; Lin et al., 2022) have primarily considered the
integral behaviors of the entire sample, this work specifically focuses on the
continuous changes in star formation and molecular gas properties as a
function of a galaxy’s distance to the star-forming main sequence.
Furthermore, we investigate the relative roles of $f_{\mathrm{gas}}$ and SFE
within individual galaxies, an aspect that has not been extensively addressed
thus far. Specifically, we aim to answer questions regarding 1) _how the
radial profiles of star formation and molecular gas properties change as a
function of a galaxy’s distance to the star-forming main sequence_ , and 2)
_whether there is a preference for a specific quenching driver (
$f_{\mathrm{gas}}$ or SFE) at different galactocentric radii_. Finally, we
will compare our observational findings with those obtained from galaxy
simulations in the literature.

The paper is structured as follows: Section 2 provides a description of the
multiwavelength data employed in this study. The main findings are presented
in Section 3, including the radial profiles of star formation and molecular
gas properties in Section 3.1 and the relative importance of
$f_{\mathrm{gas}}$ and SFE in Section 3.2. We discuss the implications of our
results and compare our observational results with those from galaxy
simulations in Section 4. Section 5 provides a summary of the results obtained
in this work. Throughout this paper, we adopt the following cosmological
parameters: $H_{\mathrm{0}}$ = 70 km s-1 Mpc-1, $\Omega_{\mathrm{m}}$ = 0.3,
and $\Omega_{\mathrm{\Lambda}}$ = 0.7. A Salpeter initial mass function
(Salpeter, 1955) is assumed in this work.

##  2 Data and Observations

###  2.1 The ALMaQUEST Survey

The main ALMaQUEST survey (Lin et al., 2020)111http://arc.phys.uvic.ca/
almaquest/ aims to investigate the molecular gas properties of 46 galaxies
selected from the MaNGA (Mapping Nearby Galaxies at APO) integral-field unit
(IFU) spectroscopic survey (Bundy et al., 2015). The 46 galaxies consist of 34
non-starburst and 12 starburst galaxies. The survey focuses on galaxies
spanning a wide range of log(sSFR/yr-1) from $-$9.4 to $-$12.2, covering the
starburst to green valley regime below the global star-forming main sequence
on the SFR versus $M_{\ast}$ plane. The ALMaQUEST sample have been expanded to
include 20 galaxy mergers (Thorp et al., 2022; Ellison et al., 2024), which
are not included in this work.

The stellar mass of the ALMaQUEST main sample spans from log($M_{\ast}$/M⊙)
$=$ 10.2 to 11.6. While the majority of the galaxies are selected based on
their global $M_{\ast}$ and sSFR, an additional criterion is applied to select
12 starburst galaxies. These galaxies are required to exhibit an elevated
$\Sigma_{\mathrm{SFR}}$ relative to the control spaxels within
0.5$R_{\mathrm{e}}$ by at least 50% (see Ellison et al., 2020a, for details).
These control spaxels are characterized by their similarity in $\Sigma_{\ast}$
and location within a comparable galactic radius to the spaxel in question,
and belong to galaxies with similar global $M_{\ast}$. Since the selection of
starburst galaxies in Ellison et al. (2020a) was based on the _relative_
profile, rather than an _absolute_ value, these galaxies do not necessarily
exhibit higher sSFR, both locally and globally, compared to other galaxies in
the ALMaQUEST sample, although a majority of them indeed do. It is important
to note that other galaxy properties and environmental factors are not
considered in the sample selection for the ALMaQUEST survey.

###  2.2 Star Formation Tracers: MaNGA

The MaNGA data used in this study are obtained from the MaNGA DR15 Pipe3D
value-added products (Sánchez et al., 2018). These Pipe3D products provide
both global properties of galaxies integrated over the MaNGA bundle field-of-
view, as well as spaxel-based measurements of local stellar mass and emission-
line fluxes. The stellar mass is derived based on the best-fit stellar
population model that describes the stellar continuum of a given spectrum. The
best-fit stellar continuum is then subtracted from the spectrum to obtain the
emission-line measurements. To account for the effect of dust extinction, we
apply a correction to the emission line fluxes using the Balmer decrement
computed at each spaxel. The correction is based on a Milky Way extinction
curve with a standard reddening parameter $R_{V}$ of 3.1 (Cardelli et al.,
1989).

In this study, we adopt H$\alpha$ emission as a tracer of ongoing star
formation activity. The extinction-corrected H$\alpha$ luminosity is converted
to the SFR using the calibration provided by Kennicutt (1998). To calculate
the SFR and stellar mass surface densities ($\Sigma_{\mathrm{SFR}}$ and
$\Sigma_{\ast}$) for each spaxel, we utilize the spaxel-based stellar mass and
SFR measurements from Pipe3D, taking into account the physical area of the
spaxel and applying an inclination correction.

However, it is important to note that H$\alpha$ emission can arise from
sources other than young stars, such as AGN and old stellar populations
(Kewley et al., 2006; Yan & Blanton, 2012). To classify the spaxels based on
the powering sources, we follow the method outlined in our previous papers
(Bluck et al., 2020a; Lin et al., 2022). In summary, we first utilize the
Baldwin–Phillips–Terlevich (BPT) diagnostics, a commonly used tool for
distinguishing between different sources of H$\alpha$ emission. Specifically,
we apply the Kewley and Kauffmann star-forming cut based on the [O
III]$\lambda$5007/H$\beta$ versus [N II]$\lambda$6584/H$\alpha$ line ratios
(Kauffmann et al., 2003; Kewley et al., 2006) to classify spaxels into star
formation, composite, or AGN. Our BPT analysis is limited to spaxels with a
signal-to-noise ratio (S/N) greater than 2 for all required emission lines.
_Star-forming spaxels_ are defined as those satisfying both the BPT star-
forming criteria and an H$\alpha$ equivalent width (EW) greater than 6Å
(Sánchez, 2020; Sánchez et al., 2021). H$\alpha$ luminosity is used to
estimate the $\Sigma_{\mathrm{SFR}}$ for star-forming spaxels.

We also compute $\Sigma_{\mathrm{SFR}}$ for two categories of non-star-forming
spaxels. The _AGN-contaminated spaxels_ are those in the AGN and composite
regimes on the BPT diagram. The _retired spaxels_ where the star formation is
largely suppressed are identified as those having S/N $>$ 2 and EW $<$ 3 Å in
H$\alpha$ (Lin et al., 2022). We estimate $\Sigma_{\mathrm{SFR}}$ for spaxels
that are not dominated by active star formation (either AGN-contaminated or
retired spaxels) using the relationship between $\Sigma_{\mathrm{SFR}}$ and
4000 Å break (D4000) as employed in previous MaNGA and ALMaQUEST papers (e.g.,
Spindler et al., 2018; Wang et al., 2019; Bluck et al., 2020a; Thorp et al.,
2022). In Figure 1, we show the method used to estimate
$\Sigma_{\mathrm{SFR}}$ for these spaxels. We first construct the
$\Sigma_{\mathrm{sSFR}}$-D4000 relation for our sample using star-forming
spaxels from the 34 non-starburst star forming galaxies. The median
$\Sigma_{\mathrm{sSFR}}$ value in each D4000 bin is calculated and represented
by the green solid curve. For any spaxel that does not meet our star-forming
criteria based on the BPT and EW cuts, we assign a $\Sigma_{\mathrm{sSFR}}$
value based on its D4000 and the corresponding median curve. Then, we convert
the $\Sigma_{\mathrm{sSFR}}$ to $\Sigma_{\mathrm{SFR}}$ by multiplying it with
the $\Sigma_{\ast}$ value of these spaxels. The empirical
$\Sigma_{\mathrm{sSFR}}$-D4000 relation shown in Figure 1 is consistent with
that derived from the full MaNGA sample (Bluck et al., 2020a; Thorp et al.,
2022).

Spaxels with D4000 $>$ 1.45 are generally considered quenched, and thus the
sSFR-D4000 relation is no longer applicable (Wang et al., 2018; Bluck et al.,
2020a). Therefore, we only utilize the $\Sigma_{\mathrm{sSFR}}$-D4000
calibration for spaxels with D4000 $<$ 1.45. This means that the
$\Sigma_{\mathrm{sSFR}}$-D4000 calibration limits the analysis to the
suppressed (D4000 $<$ 1.45), but not fully quenched (D4000 $>$ 1.45) regions
(see the discussion in Wang et al. 2018 and Bluck et al. 2020a). Note that
since the $\Sigma_{\mathrm{SFR}}$ values of the AGN-contaminated and retired
spaxels are inferred based on their D4000 values, some accuracy is traded for
completeness. Thus, the $\Sigma_{\mathrm{SFR}}$ values of these spaxels should
be interpreted with caution.

Finally, it is important to utilize the full sample of spaxels in order to
probe quenching (Bluck et al., 2020a). Therefore, we define _fully-quenched
spaxels_ as those having S/N $<$ 2 in H$\alpha$ or D4000 $>$ 1.45. In the
examined dataset, star-forming spaxels with a D4000 value of 1.45 span a range
from $-$11.7 to $-$9.5 in log($\Sigma_{\mathrm{sSFR}}$/yr-1), with a median
value of -10.7. Therefore, the fully-quenched spaxels are artificially
assigned to a fixed value of log($\Sigma_{\mathrm{sSFR}}$/yr-1) $=$ $-$12
(i.e., just below $-$11.7 as an upper limit for $\Sigma_{\mathrm{sSFR}}$),
following Bluck et al. (2020a). Our spaxel classification that includes star-
forming, AGN-contaminated, retired, and fully-quenched spaxels ensures that
$\sim$ 98% of spaxels have a valid $\Sigma_{\mathrm{SFR}}$ value. This allows
for the construction of a continuous star formation profile as a function of
galactocentric radius for all the galaxies in this work. Nevertheless, we have
verified that our conclusions remain qualitatively consistent even when
excluding the fully-quenched spaxels, which were assigned
log($\Sigma_{\mathrm{sSFR}}$/yr-1) $=$ $-$12 manually.

###  2.3 Molecular Gas Observations: ALMA

The ALMA observations at 12CO ($J$ $=$ 1 $\rightarrow$ 0; 115.271 GHz) were
designed to match the point-spread function (2.5$\arcsec$) of the MaNGA
observations, allowing for a simultaneous study of spatially-resolved star
formation and molecular gas properties at the same physical scale (PI: L. Lin
– 2015.1.01225. S, 2017.1.01093.S, 2018.1.00558.S; PI: S. Ellison –
2018.1.00541.S). Detailed information regarding ALMA data reduction and
imaging can be found in the survey paper by Lin et al. (2020).

In this study, the molecular mass surface density ($\Sigma_{\mathrm{H2}}$) is
calculated from the 12CO ($J$ $=$ 1 $\rightarrow$ 0) luminosity using a
constant Milky Way conversion factor ($\alpha_{\mathrm{CO}}$) of 4.35 M⊙ (K km
s-1 pc2)-1 (Bolatto et al., 2013). The value of $\alpha_{\mathrm{CO}}$ is not
universal and can vary with factors such as metallicity, cosmic ray density,
and UV radiation field (see the review by Bolatto et al., 2013). The
assumption of a constant $\alpha_{\mathrm{CO}}$ has been examined in previous
ALMaQUEST papers (Ellison et al., 2021a; Lin et al., 2020; Ellison et al.,
2024). On average, the difference in the global molecular gas mass
($M_{\mathrm{H_{2}}}$) obtained using a metallicity-dependent
$\alpha_{\mathrm{CO}}$ compared to the original $M_{\mathrm{H_{2}}}$ is
approximately 0.1 dex. Given the small difference, a constant
$\alpha_{\mathrm{CO}}$ is adopted in this work to maintain consistency with
previous ALMaQUEST papers. However, it is worth noting that although the
radial profiles of $\alpha_{\mathrm{CO}}$ are generally flat within a given
galaxy at kpc scale, galaxies often exhibit a decrease in
$\alpha_{\mathrm{CO}}$ within the inner 1 kpc (Sandstrom et al., 2013), which
corresponds to (or is slightly smaller than) the spatial scale that our ALMA
and MaNGA observations can resolve.

To recover the CO non-detection spaxel for spaxel completeness, a 3$\sigma$
upper limit is assigned to spaxels with S/N $<$ 2 in CO integrated intensity
map. The 3$\sigma$ upper limits of flux are calculated with
$3\sigma\times{\sqrt{\delta v\Delta V}}$, where $\sigma$ is the rms noise from
the spectral line data cube, $\delta v$ $=$ 11 km s-1 is the velocity
resolution of the data cube, and $\Delta V$ is the assumed 40 km s-1 line
width for a bulk of molecular cloud observed at kpc resolution. Two methods
were employed for measuring the local line width: pixel-by-pixel Gaussian
fitting of the data cubes and the CASA task immoment (moment 2), which
represents intensity-weighted line width around the mean without making any
assumptions about the line profile. Both methods show a median line width of
$\sim$40 km s-1. However, it is important to note that these estimates
inherently rely on the spaxels that have a CO detection.

Figure 1: D4000 and $\Sigma_{\mathrm{sSFR}}$ relation for the star-forming
spaxels in the ALMaQUEST sample. The color scale indicate the density of
spaxel at each D4000 and $\Sigma_{\mathrm{sSFR}}$ bins. The median
$\Sigma_{\mathrm{sSFR}}$ value in each D4000 bin is as green solid curve. The
standard deviation of $\Sigma_{\mathrm{sSFR}}$ within each bin is shown as a
green dashed lines. Spaxels with D4000 $>$1.45 (marked by a vertical gray
line) are fully quenched and therefore the sSFR-D4000 relation is no longer
viable (Bluck et al., 2020a). Therefore, D4000-based $\Sigma_{\mathrm{sSFR}}$
is computed for AGN-contaminated and retired spaxels only when their D4000 is
lower than 1.45. The fully quenched spaxels (D4000 $>$ 1.45) are artificially
assigned to a fixed value of log($\Sigma_{\mathrm{sSFR}}$/yr-1) $=$ $-$12\.

###  2.4 Sample Classification

The primary goal of this study is to investigate the continuous variations in
gas and star formation properties as galaxies transit away from the star-
forming main sequence. To achieve this, we classify the 34 non-starburst
galaxies into three groups based on their deviation from the global star-
forming main sequence ($\Delta$MS). The 12 starburst galaxies (which are
included in our sample, but treated as a separate class, see below) are also
on or slightly above the main sequence, exhibiting enhanced SFR in the centers
by design.

Figure 2 illustrates the global SFR-$M_{\ast}$ relation of our sample. The
background contours and gray scale show the galaxies from the MaNGA (SDSS
DR15) sample. The solid and dashed black lines represent the global star-
forming main sequence and its typical scatter of $\pm$0.32 dex for the MaNGA
sample, as determined by Sánchez et al. (2019) as

$\log(\mathrm{SFR_{H\alpha}})=(-8.96\pm 0.23)+(0.87\pm 0.02)\log(M_{\star}),$
(1)

where the SFR is in units of M☉ yr-1 and $M_{\ast}$ is in units of M☉.

In the work presented here, we have categorized the sample into three distinct
classes based on their sSFR: those with relatively high global sSFR
(log(sSFR/yr-1) $>$ $-$10.5; blue squares in Figure 2), moderate sSFR ($-$11.0
$<$ log(sSFR/yr-1) $<$ $-$10.5; green circles), and low sSFR (log(sSFR/yr-1)
$<$ $-$11.0; rad diamonds), which we hereafter refer to as the SFh, SFm, and
SFl samples, respectively. Broadly speaking, SFh galaxies are the main-
sequence, normal star-forming galaxies, SFm galaxies are located at the lower
end or just below the main-sequence, and SFl galaxies reside below the main-
sequence. For the 34 non central starburst galaxies, there are a total of 12
galaxies classified as SFh, 11 galaxies classified as SFm, and 11 galaxies
classified as SFl. Although the sample classification is defined by the
absolute value of global sSFR in this work, it is correlated with the distance
to the star-forming main sequence ($\Delta$MS), which has been used in other
studies to distinguish star-forming and quenched galaxies (e.g., Ellison et
al., 2018). Our sSFR boundaries in absolute unit correspond to $\Delta$MS of
$-$0.2 $<$ $\Delta$MS $<$ $+$0.4 dex for SFh, $-$0.7 $<$ $\Delta$MS $<$ $-$0.2
dex for SFm, and $-$1.7 $<$ $\Delta$MS $<$ $-$0.7 dex for SFl, where the
$\Delta$MS is calculated as the log difference between the SFR and the star-
forming main sequence in Equation 1 for given $M_{\ast}$. Table 1 provides an
overview of the sample classification and the corresponding range of global
sSFR and $\Delta$MS.

The central starburst galaxies (cSB) are shown as yellow triangles in Figure
2. cSB are all lying above the line of star-forming main sequence, with
$\Delta$MS of 0.04 – 0.90 dex. In the subsequent analysis, we will focus on
characterizing the spatial distribution of various gas and star formation
properties using radial analysis. As such, the 12 cSBs that were specifically
selected to exhibit centrally peaked starbursts (Ellison et al., 2020a) are
treated as their own class. They are presented where applicable for the
purpose of comparison.

| log(sSFR)[yr-1] |  $\Delta$MS [dex] | # of galaxies
---|---|---|---
| star-forming main sequence
SFh |  $>$ $-$10.5 |  $-$0.2 to $+$0.4 | 12
| quenching galaxies
SFm |  $-$11.0 to $-$10.5 |  $-$0.7 to $-$0.2 | 11
SFl |  $<$ $-$11.0 |  $-$1.7 to $-$0.7 | 11
Table 1: Sample classification. The sample classification is defined by the
absolute value of global sSFR (second left column), it is correlated with the
distance to the star-forming main sequence ($\Delta$MS; second right column)
which has been used in other studies to distinguish star-forming and quenched
galaxies. The number of galaxies in each category is presented in the right
column. Figure 2: Distribution of our sample on the global stellar mass
($M_{\ast}$) versus star formation rate (SFR) plane. The yellow triangles
represent the central starburst galaxies (cSB) in the ALMaQUEST survey. The
blue squares, green circles and red diamonds correspond to the SFh (sSFR
(log(sSFR/yr-1) $>$ $-$10.5), SFm ($-$11.0 $<$ log(sSFR/yr-1) $<$ $-$10.5),
and SFl ((log(sSFR/yr-1) $<$ $-$11.0) galaxies in this work, respectively.
They are classified based on the absolute value of global sSFR. The solid
black line marks the star-forming main sequence (Equation 1) estimated by
Sánchez et al. (2019) for the MaNGA sample. The scatter of the main sequence
is $\sim$ 0.32 dex (dashed lines). The contours represent the $M_{\ast}$ and
SFR distribution of $\sim$ 5000 galaxies included in data release SDSS DR15
measured by Pipe3D.

##  3 Results

###  3.1 Radial Profiles of Star Formation and Molecular Gas Properties

####  3.1.1 Radial Profiles of $\Sigma_{\ast}$, $\Sigma_{\mathrm{H2}}$ and
$\Sigma_{\mathrm{SFR}}$

We begin by analyzing the galaxy radial profiles in the ALMaQUEST sample.
Figures 3(a)-(c) present the radial profiles of $\Sigma_{\mathrm{SFR}}$,
$\Sigma_{\ast}$, and $\Sigma_{\mathrm{H2}}$, respectively. The subsets, namely
SFh, SFm, SFl, and cSB, are denoted by blue, green, red, and yellow colors,
respectively. The radial profile is sampled with a 0.18 $R_{\mathrm{e}}$
($\sim$ 0.8 kpc) steps within 1.5 $R_{\mathrm{e}}$ ($\sim$ 7 kpc at redshift
0.03). The inclination angle, along with the galaxy’s position angle, is
considered to deproject the geometries of the galaxies. The radial quantities
are determined by calculating the median value222In this work, we choose
median instead of mean so that the result suffers less from some extreme
outliers. of the star formation and molecular gas properties within each
deprojected annulus. Radial profiles are constructed using all spaxels with
valid values, regardless of whether these values were measured, inferred, or
represented as upper limits (see Section 2.2 and 2.3). As mentioned earlier,
this is to probe the quenched and gas-deficient regions. For each individual
galaxy, we display the radial properties using thin lines. The median profiles
of each subset, which are obtained by taking the median values from the
individual profiles, are shown using shaded colored regions. The height of the
shaded regions represents the standard error of the mean at each radial bin.
Note again that the cSB subset should be considered as a distinct population
since the sample was selected based on their radial profiles of local sSFR by
design (cf. Section 2.1).

The radial profiles of $\Sigma_{\mathrm{SFR}}$ exhibit a ranking across the
explored radial range, with a consistent increase in magnitude from SFl to
SFm, SFh, and to cSB galaxies at almost all radii (Figure 3(a)). Notably, the
differences between SFh, SFm, and cSB populations are more pronounced in the
inner region ($<$ 0.5 $R_{\mathrm{e}}$) of galaxies compared to the outer
region ($>$ 1.0 $R_{\mathrm{e}}$), consistent with the finding in previous
work with larger sample size (e.g., Ellison et al., 2018; Wang et al., 2019;
Bluck et al., 2020a). Conversely, the $\Sigma_{\mathrm{SFR}}$ of SFl galaxies
is significantly lower than that of the other populations at all
galactocentric radii. Several SFh galaxies exhibit a $\Sigma_{\mathrm{SFR}}$
higher than that of cSB galaxies. However, note that when normalized by
$\Sigma_{\ast}$ (Figure 5(a)), these galaxies typically show a lower
$\Sigma_{\mathrm{sSFR}}$ compared to cSB galaxies.

Due to the trade-off between $\Sigma_{\mathrm{SFR}}$ accuracy and
completeness, as discussed in Section 2.2, it is important to interpret Figure
3(a) with caution. Figure 4 shows the radial profiles of the percentage of
different type of spaxels. All the available spaxels from each individual
galaxy class are combined to generate the plot. Results for cSB, SFh, SFm, and
SFl galaxies are presented in panel (a) to (d), respectively. As shown in the
figure, there is a significant decline in the fraction of star-forming spaxels
(purple curve) when transitioning from cSB to SFl galaxies. Within SFl
galaxies (panel (d)), fully-quenched regions (light pink) dominate,
constituting over 50% of the regions at all radii. In these regions, the
log($\Sigma_{\mathrm{sSFR}}$/yr-1) is manually set to $-$12, and therefore
their $\Sigma_{\mathrm{SFR}}$ values depend on the $\Sigma_{\ast}$ of the
spaxel. Given that SFl galaxies are predominantly characterized by fully-
quenched regions at all radii, their $\Sigma_{\mathrm{SFR}}$ is notably lower
compared to other populations, as shown in Figure 3(a). While the majority of
SFl galaxies exhibit low $\Sigma_{\mathrm{SFR}}$ across their disks, one
galaxy (7977-9101) displays high $\Sigma_{\mathrm{SFR}}$ in its central
region. This is attributed to a relatively low D4000 value ($\sim$ 1.2,
comparable to that of star-forming regions) in its center, which is identified
as a _composite_ region based on the BPT analysis. The center of this galaxy
is associated with an AGN (Lin et al., 2017). Typically, such composite AGNs
are commonly linked with young stellar populations and low D4000 values,
indicative of a recent cessation of star-forming activities (e.g., Wang & Wei,
2008). The timescale of quenching is beyond the scope of this paper, but we
aim to delve into this question in future studies, focusing not only on the
ALMaQUEST sample but also extending the analysis to include the entire MaNGA
sample.

The proportion of retired regions (with D4000-based $\Sigma_{\mathrm{SFR}}$),
albeit at a low level, also increases from cSB to SFl galaxies (pink curve),
though not as substantially as observed for fully-quenched regions. The
occurrence of AGN-contaminated regions (also with D4000-based
$\Sigma_{\mathrm{SFR}}$) exhibits no discernible trend with galaxy populations
and remains at a low level, below 20%, across all populations (magenta
curves). Hence, the contribution of retired regions and AGN-contaminated
regions to Figure 3(a) is comparatively lower in contrast to star-forming and
fully-quenched regions.

Taking all of these factors into account, we can deduce that the offsets of
SFl from more star-forming galaxies are likely to be real (e.g., Bluck et al.,
2020b), but we refrain from drawing strong conclusions regarding the exact
profile and magnitude of this offset. Also, some green-valley galaxies in the
ALMaQUEST sample have high inclination (see Figure 2 in Lin et al. 2022).
While the inclination and position angle of a galactic disk are taken into
account during the construction of the radial profile for individual galaxies,
accurately deriving azimuthally-averaged radial profiles of
$\Sigma_{\mathrm{SFR}}$ (as well as other physical properties) remains
challenging for highly-inclined galaxies (Ibarra-Medel et al., 2019; Barrera-
Ballesteros et al., 2022).

Turning to $\Sigma_{\ast}$ in Figure 3(b), our galaxies show a strong and
smooth dependence of $\Sigma_{\ast}$ on galactic radius. The median profiles
of $\Sigma_{\ast}$ exhibit significant overlap among the different populations
across all the radii explored. This is somewhat expected, as our four
populations share the similar range in global $M_{\ast}$ as shown in Figure 2
(García-Benito et al., 2017). Due to the uniform distribution of
$\Sigma_{\ast}$, any observed differences in star formation and gas properties
among the galaxy populations (if present) are more likely to be genuine rather
than a result of systematic dependence on stellar mass.

Figure 3(c) displays the radial distribution of $\Sigma_{\mathrm{H2}}$. For
our galaxies, while there are no dramatic differences observed in the median
profiles among the galaxy populations, there is significant individual
variation in $\Sigma_{\mathrm{H2}}$, ranging from one to two orders of
magnitude from galaxy to galaxy. This variation can be attributed, at least in
part, to the structured and non-smooth disk of the ALMaQUEST galaxies and the
clumpy nature of molecular gas (Leroy et al., 2013; Stuber et al., 2023). The
dark blue and blue curves in Figure 4 represent the fractions of spaxels with
CO detection and those without detection (upper limits), respectively. For
cSB, SFh, and SFm galaxies, the relative proportions of these two types of
spaxels exhibit a considerable degree of similarity across the radial range
explored. However, it is noteworthy that SFl galaxies display notably lower
$\Sigma_{\mathrm{H2}}$ values than the other galaxy populations for $R$ $<$
1.0$R_{\mathrm{e}}$. This reduction in $\Sigma_{\mathrm{H2}}$ is attributed to
the significant presence of CO non-detection in this region, as illustrated in
Figure 4 (panel (d)). This is particularly true for the outer regions. Beyond
1.0$R_{\mathrm{e}}$, the radial profile of $\Sigma_{\mathrm{H2}}$ flattens due
to the increased prevalence ($>$ 50%) of CO non-detection in this regime.
However, it is worth noting that in the inner region, specifically at $<$
0.5$R_{\mathrm{e}}$, the detection of CO emission remains relatively robust in
SFl galaxies, even in the presence of low $\Sigma_{\mathrm{SFR}}$.

To summarize, the largely overlapping radial profiles of
$\Sigma_{\mathrm{H2}}$ (shaded lines in Figure 3(c)) suggest that galaxies
with the lowest levels of star formation activity (SFl) do not consistently
display a significant deficit in molecular gas. However, since there is
considerable variation in the $\Sigma_{\mathrm{SFR}}$ profiles (Figure 3(a)),
this implies that there must be a radial variations in $f_{\mathrm{gas}}$ and
SFE, which will be further discussed in the next section.

Finally, while our primary focus is on the median profiles, it is important to
note the substantial variation from galaxy to galaxy within a given category.
This variation is particularly pronounced for $\Sigma_{\mathrm{SFR}}$ and
$\Sigma_{\mathrm{H2}}$, but less so for $\Sigma_{\ast}$. The diverse
morphologies of the galaxies in the ALMaQUEST sample contribute to these
diverse profiles due to varied distributions of the clumpy star-forming
regions and molecular clouds across their disks (Leroy et al., 2013; Pan et
al., 2022; Stuber et al., 2023). Our sample includes a broad spectrum of
Hubble types, ranging from T-types of -1.6 to 6.5 (S0 to Scd), and features
both barred and non-barred galaxies along with different spiral patterns333The
T-type values for the ALMaQUEST galaxies are taken from the MaNGA Deep
Learning Morphology Value Added Catalogue (MDLM-VAC-DR17 Domínguez Sánchez et
al., 2022). This catalog has been developed through an automated
classification system that employs supervised deep learning. The Hubble T-type
classification primarily takes into account the ellipticity and the prominence
of spiral arms, but it does not specifically account for the presence or
absence of a galactic bar. The identification of a galactic bar and the
further verification of spiral arms are based on the updated Galaxy Zoo
classification (Walmsley et al., 2022) and by our kinematic analysis in the
forthcoming study by Lopez-Coba et al. (in preparation). Additionally, several
galaxies display asymmetric disks, suggesting a history of past interactions
(Ellison et al., 2024). Our current sample size is too limited to
systematically explore the potential effects of morphology and environment on
the radial profiles. However, such analysis can be conducted in a
statistically significant manner using the full MaNGA sample. This will be
similar to what has been done with the CALIFA galaxies, albeit with a smaller
sample size (González Delgado et al., 2016; Sánchez et al., 2021). .

Figure 3: Panel (a) – (c): Radial profiles of $\Sigma_{\mathrm{SFR}}$,
$\Sigma_{\ast}$, and $\Sigma_{\mathrm{H2}}$, respectively. The thin lines show
the the radial properties of each individual galaxy, with color indicating the
population of the galaxies (yellow: central starburst galaxies cSB, blue:
main-sequence galaxies SFh, green: galaxies just below the main sequence SFm,
and red: galaxies well below the main sequence SFl). The colored thick lines
denote the median profiles of the properties for galaxies in the corresponding
category. The height of the shaded regions represents the standard error of
the mean at each radial bin.  Figure 4: Panel(a) – (d): Fraction of spaxels
classified as star-forming (in purple), AGN-contaminated (in magenta), retired
(in pink), and fully-quenched (in light pink) spaxels at various radial bins
for cSB, SFh, SFm, and SFl galaxies, respectively. The dark blue and blue
curves represent the fraction of spaxels with and without significant CO
detection. The horizontal line represents a spaxel percentage of 50%. Caution
should be taken when interpreting the radial profiles in Figure 3 and 5,
particularly when the fraction of spaxels with upper limits exceeds 50%.
Figure 5: Panel (a) – (c): Radial profiles of $\Sigma_{\mathrm{sSFR}}$,
$f_{\mathrm{gas}}$, and SFE, respectively. The thin lines show the the radial
properties of each individual galaxy, with color indicating the population of
the galaxies (yellow: central starburst galaxies cSB, blue: main-sequence
galaxies SFh, green: galaxies just below the main sequence SFm, and red:
galaxies well below the main sequence SFl). The colored thick lines denote the
median profiles of the properties for galaxies in the corresponding category.
The height of the shaded regions represents the standard error of the mean at
each radial bin.

####  3.1.2 Radial Profiles of $f_{\mathrm{gas}}$, SFE, and
$\Sigma_{\mathrm{sSFR}}$

In this section, we present the radial profiles of various physical properties
derived from $\Sigma_{\mathrm{SFR}}$, $\Sigma_{\mathrm{H2}}$, and
$\Sigma_{\ast}$. Specifically, we present the radial specific SFR
($\Sigma_{\mathrm{sSFR}}$) defined as $\Sigma_{\mathrm{SFR}}$/$\Sigma_{\ast}$.
We note that the symbol for _surface density_ , $\Sigma$, is not necessary in
the expression for the radial (local) specific SFR as the “per area” component
cancels out. However, in order to distinguish between the _global_ and _local_
sSFR in this paper, we retain the $\Sigma$ in the symbol. Additionally, we
examine the molecular gas fraction ($f_{\mathrm{gas}}$) defined as
$\Sigma_{\mathrm{H2}}$/$\Sigma_{\ast}$ and the star formation efficiency (SFE)
defined as $\Sigma_{\mathrm{SFR}}$/$\Sigma_{\mathrm{H2}}$. Figures 5(a)-(c)
illustrate the radial profiles of $\Sigma_{\mathrm{sSFR}}$,
$f_{\mathrm{gas}}$, and SFE, respectively. The color scheme and line styles
employed are the same as for those used in Figure 3. We will begin by
examining the results obtained from the non-cSB sample, followed by an
examination of the results from the cSB population.

As galaxies move from the star-forming main sequence to lower SFR regimes, the
radial profiles of $\Sigma_{\mathrm{sSFR}}$ exhibit a dependency with respect
to global sSFR, displaying a decreasing trend in magnitude from SFh to SFl
(Figure 5(a)). This dependence agrees with previous studies conducted on
global scale (e.g., Saintonge et al., 2017; Piotrowska et al., 2020).
Furthermore, the decline in local $\Sigma_{\mathrm{sSFR}}$ is observed
consistently from the galactic center to 1.5 $R_{\mathrm{e}}$, indicating that
star formation quenching is a phenomenon that occurs globally within galaxies
(see also Catalán-Torrecilla et al., 2017; Belfiore et al., 2018; Bluck et
al., 2020a, b).

The radial profiles of SFh and SFm galaxies show in Figure 5(a) exhibit
remarkable similarity to that presented in Bluck et al. (2020b), which were
derived using the complete MaNGA DR15 sample, and with the fully-quenched
regions considered. The comparison validates that the $\Sigma_{\mathrm{sSFR}}$
trends of the ALMaQUEST sample, despite its smaller size, is representative of
that from larger sample of galaxies. However, the profiles in Figure 5(a) are
only _qualitatively_ consistent with the findings of Belfiore et al. (2018)
and Ellison et al. (2018) using full MaNGA sample and González Delgado et al.
(2016) using different IFU dataset from the CALIFA survey. While these studies
did demonstrate a dependence of local $\Sigma_{\mathrm{sSFR}}$ on global sSFR,
the radial profiles of $\Sigma_{\mathrm{sSFR}}$ exhibit some discrepancies.
This discrepancy arises because Belfiore et al. (2018), Ellison et al. (2018),
and González Delgado et al. (2016) did not account for fully-quenched regions
in their analyses. For instance, in Ellison et al. (2018), the quiescent
population display an increase in $\Sigma_{\mathrm{sSFR}}$ with radius, as
evident in their Figure 8, whereas in this work and Bluck et al. (2020b), the
profile remains relatively constant. The underlying reason for this contrast
is that our work and Bluck et al. (2020b) take into consideration the presence
of fully-quenched regions, whereas Ellison et al. (2018) (and other studies)
primarily focused on the regions with H$\alpha$ (emission lines) detection. In
short, these studies demonstrate that the _observed_ radial
$\Sigma_{\mathrm{sSFR}}$ is sensitive to the choice of methodology, namely,
between completeness and accuracy.

From SFh to SFm galaxies, the observed decrease in $\Sigma_{\mathrm{sSFR}}$
with decreasing radius, as illustrated in Figure 5(a), also implies an inside-
out quenching scenario, in which star formation ceases in the inner region of
the galaxy more pronouncedly than the outer regions. The inside-out quenching
scenario is in agreement with previous studies that utilized photometric
colors, such as $NUV-r$ or UV-optical gradients, as indicators of star
formation profiles (Pan et al., 2016; Liu et al., 2016; Wang et al., 2017).
Additionally, studies employing IFU (MaNGA, CALFA, and SAMI) with
$\Sigma_{\mathrm{sSFR}}$ based on emission lines analysis have yielded
consistent results (González Delgado et al., 2016; Belfiore et al., 2018;
Medling et al., 2018; Sánchez et al., 2018; Ellison et al., 2018; Lin et al.,
2019a; Sánchez et al., 2021; Villanueva et al., 2023). Recently, analysis of
the stellar-age gradients in late-type galaxies further reinforces the notion
of an inside-out cessation of star-forming activity in massive galaxies (Breda
et al., 2020; Wang et al., 2022; Lah et al., 2023).

Nevertheless, it is worth mentioning that Bluck et al. (2020b) demonstrated
that satellite galaxies with lower $M_{\ast}$ (log($M_{\ast}$/M☉) $<$ 10,
i.e., lower than that of ALMaQUEST sample) undergoing quenching display rising
star formation profiles, indicating outside-in quenching, unlike high-mass
central and satellites galaxies which clearly quench inside-out. Lin et al.
(2019a) also show the relative fraction of outside-in and inside-out quenching
mode indeed strongly dependent on $M_{\ast}$, with high-$M_{\ast}$ galaxies
exhibiting a greater fraction of inside-out quenching compared to
low-$M_{\ast}$ ones. Therefore, while the ALMaQUEST sample lacks
low-$M_{\ast}$ systems, it is important to note that the radial profiles of
$\Sigma_{\mathrm{sSFR}}$ shown in Figure 5(a) cannot be extrapolated to
low-$M_{\ast}$ population.

It is challenging to precisely quantify the extent of the decrease in
$\Sigma_{\mathrm{sSFR}}$ from SFm to SFl due to inherent limitations in the
accuracy of $\Sigma_{\mathrm{sSFR}}$ measurements, particularly for the SFl
population. This limitation is also emphasized in the analysis conducted by
previous observational studies (e.g., Belfiore et al., 2018; Ellison et al.,
2018; Wang et al., 2018; Bluck et al., 2020b), despite their larger sample
size. Nevertheless, it is apparent that SFl galaxies are experiencing star
formation at a substantially lower rate across their entire disk, even after
accounting for the normalization by stellar mass (i.e.,
$\Sigma_{\mathrm{sSFR}}$), indicating a global quenching scenario.

The radial profile of $f_{\mathrm{gas}}$ consistently shifts vertically
downwards decreasing global sSFR at almost all radii. Computed using
$\Sigma_{\ast}$ and $\Sigma_{\mathrm{H2}}$, $f_{\mathrm{gas}}$ demonstrates
less sensitivity to completeness and accuracy issues compared to
$\Sigma_{\mathrm{SFR}}$-related quantities. SFh and SFm galaxies show a mild
increasing trend with radius within the $R$ $<$ 1.0$R_{\mathrm{e}}$ regime.
However, it is important to note again that caution should be exercised when
interpreting the radial profile of $f_{\mathrm{gas}}$ beyond
1.0$R_{\mathrm{e}}$ in all populations, owing to the decreased accuracy of the
medians due to the increase in spaxel without CO detection, as illustrated in
Figure 4. For SFl galaxies, we are not able to precisely quantifying their
$f_{\mathrm{gas}}$ profile due to a significant number of CO non-detections.
Nonetheless, it is evident that SFl galaxies consistently exhibit lower gas
content compared to the other populations across all radii considered. A
similar conclusion is reached by other analysis based on CO analyses, as well
as those using the dust-to-gas relation as a proxy for molecular gas mass
(Saintonge et al., 2017; Sánchez et al., 2018; Lin et al., 2019b; Colombo et
al., 2020; Brownson et al., 2020; Piotrowska et al., 2022; Lin et al., 2022).
Our finding is further corroborated by the most recent analysis of
$f_{\mathrm{gas}}$ radial profiles for green valley galaxies using EDGE-CALIFA
data by Villanueva et al. (2023) (see their Figure 12), but note that this
study utilizes a smaller sample size.

The radial distribution of SFE also exhibits a clear ranking with global sSFR
in Figure 5(c). The median log(SFE/yr-1) for SFh galaxies ranges from
approximately $-$9.5 to $-$9.0, showing a rather flat profile from the
galactic center to the outer regions. The derived constant SFE for SFh
galaxies agrees with that of nearby large normal star-forming galaxies
observed at kpc scales (Leroy et al., 2008; Bigiel et al., 2011; Muraoka et
al., 2019; Sun et al., 2023). While the disk SFE of SFm is lower than that of
SFh by only 0.2 dex, a central suppression of SFE is seen, as a result of a
decease (increase) in the amount of star-forming (fully-quenched) regions
(Figure 5). A recent study by Villanueva et al. (2023), utilizing EDGE-CALIFA
data, also observes a systematic increase of SFE with increasing radius in
green valley galaxies; in contrast, the SFE in main sequence galaxies remains
almost constant across their disks. Although the radial profile of SFE for SFl
galaxies cannot be determined precisely due to the uncertainty associated with
$\Sigma_{\mathrm{SFR}}$ measurements, it is evident that the SFE of molecular
gas in SFl galaxies is significantly suppressed by at least an order of
magnitude compared to normal star-forming galaxies (SFh). A similar conclusion
is also reached by other studies on both global and radial SFEs (Saintonge et
al., 2017; Sánchez et al., 2018; Lin et al., 2019b; Colombo et al., 2020;
Brownson et al., 2020; Piotrowska et al., 2022; Lin et al., 2022).

Mathematically, the decrease in $f_{\mathrm{gas}}$ and SFE can be attributed
to an increase in the denominator ($\Sigma_{\ast}$ and $\Sigma_{\mathrm{H2}}$,
respectively) or a reduction in the numerator ($\Sigma_{\mathrm{H2}}$ and
$\Sigma_{\mathrm{SFR}}$, respectively). Figure 3(b) provides evidence that,
statistically, radial $\Sigma_{\ast}$ remains relatively consistent across the
sample. Consequently, any variations in $f_{\mathrm{gas}}$ primarily arise
from changes in $\Sigma_{\mathrm{H2}}$ (as also shown in Figure 9 of our
previous paper in Lin et al. 2022). In terms of SFE, both
$\Sigma_{\mathrm{H2}}$ and $\Sigma_{\mathrm{SFR}}$ exhibit lower values for
SFl galaxies compared to SFm and SFh galaxies. Therefore, the observed
variations in SFE within our sample are a combined outcome of changes in both
$\Sigma_{\mathrm{H2}}$ and $\Sigma_{\mathrm{SFR}}$.

Moving to the cSB galaxies, it is evident that their median
$\Sigma_{\mathrm{sSFR}}$ magnitudes are higher than those of other populations
at all radial bins (Figure 5(a)). Specifically, compared to galaxies located
around the star-forming main sequence (i.e., SFh galaxies in our sample), cSB
galaxies exhibit an enhancement in $\Sigma_{\mathrm{sSFR}}$ of approximately
0.5 dex in the innermost region and a consistently smaller enhancement of
approximately 0.3 dex in the $R$ $>$ 0.75 $R_{\mathrm{e}}$ regime. We note
again that the significant central enhancement in $\Sigma_{\mathrm{sSFR}}$ is
a result of sample selection (see §2.4).

Figure 5(b) and (c) shows enhancement in both $f_{\mathrm{gas}}$ and SFE for
cSB galaxies, the largest enhancements are seen in the inner regions ($R$ $<$
0.5 $R_{\mathrm{e}}$), which corresponds to the region where
$\Sigma_{\mathrm{sSFR}}$ is most enhanced. This similarity suggests a
potential link between the enhanced $\Sigma_{\mathrm{sSFR}}$ and SFE and/or
$f_{\mathrm{gas}}$ in cSB galaxies. We refer readers to Ellison et al. (2020a)
for a more detailed analysis and the implications on the link between
$\Sigma_{\mathrm{sSFR}}$, SFE and $f_{\mathrm{gas}}$ in cSB.

Finally, it is important to note that star formation and molecular gas can
extend beyond the galactocentric radius examined in this study
(1.5$R_{\mathrm{e}}$), as highlighted in previous works (e.g., Watson et al.,
2016; Bacchini et al., 2020; Koda et al., 2022). IFU observations conducted by
MaNGA and CALIFA have indicated that $\Sigma_{\mathrm{sSFR}}$ beyond the
radius of $>$ 1.5$R_{\mathrm{e}}$ is typically lower than that within
1.5$R_{\mathrm{e}}$ (e.g., González Delgado et al., 2016; Belfiore et al.,
2018; Sánchez et al., 2021). Hence, our results are not expected to be
strongly influenced by star formation in the outskirts. Furthermore, the
comparison of radial profiles between different galaxy populations is valid in
this study due to the relatively narrow range of global $M_{\ast}$ within the
ALMaQUEST sample. Previous studies have shown that the radial profiles of star
formation and (molecular) gas properties, including their shapes and
magnitudes, depend on the $M_{\ast}$ of galaxies (García-Benito et al., 2017;
Belfiore et al., 2018; Sánchez et al., 2021; Barrera-Ballesteros et al.,
2022). Therefore, such comparisons between galaxy populations (sub-samples)
should be approached with caution when dealing with a wide range of mass
values.

###  3.2 Relative Importance of $f_{\mathrm{gas}}$ and SFE in Quenching

Many previous studies have assessed the relative role of $f_{\mathrm{gas}}$
and SFE for _boosting_ star formation. For example, on global scale, there
exists a correlation between global SFE and distance above the main sequence
(e.g., Sargent et al., 2014; Genzel et al., 2015; Saintonge et al., 2017;
Tacconi et al., 2018). Conversely, other studies have shown that increased
$f_{\mathrm{gas}}$ plays a pivotal role in regulating star formation (e.g.,
Scoville et al., 2016; Lee et al., 2017). Pan et al. (2018) also found a
correlation between the level of merger-triggered starburst and global
$f_{\mathrm{gas}}$. To avoid the potential dilution of key physical processes
that may occur when averaging properties across entire galaxies, in our
previous work, we quantify the relative role of $f_{\mathrm{gas}}$ and SFE for
the cSB sample in the ALMaQUEST survey on a spatially resolved manner (Ellison
et al., 2020a). Our findings suggest that an elevated SFE is the primary
driver of central starburst activity. We also investigate the mechanisms
responsible for merger-triggered star formation using the ALMaQUEST merger
sample (Thorp et al., 2022). The analysis indicates that both
$f_{\mathrm{gas}}$ and SFE can drive merger-triggered star formation. In this
work, our focus shifts to assessing the relative significance of
$f_{\mathrm{gas}}$ and SFE in the context of suppressing, rather than
boosting, star formation.

To gain a deeper understanding of the factors influencing the radial profiles
of $\Sigma_{\mathrm{sSFR}}$ in quenching galaxies, we compare the extent of
quenching with the changes in $f_{\mathrm{gas}}$ and SFE relative to the
normal star-forming galaxies (SFh) within our sample. More specifically, for
each individual galaxy classified as SFm or SFl, we first calculate the
deviation of their $\Sigma_{\mathrm{sSFR}}$ (i.e.,
$\Delta$$\Sigma_{\mathrm{sSFR}}$) from the median $\Sigma_{\mathrm{sSFR}}$ of
all SFh galaxies (represented by the thick blue curve in Figure 5(a)) at each
radial bin. Similarly, we compute the radial $\Delta$$f_{\mathrm{gas}}$ and
$\Delta$SFE using the same approach. Then the relative significance of SFE and
$f_{\mathrm{gas}}$ can be quantified by comparing $\Delta$$f_{\mathrm{gas}}$
and $\Delta$SFE, specifically the value of the expression
$\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE. This expression allows for a ranking
of the two drivers (e.g., Ellison et al., 2020a; Brownson et al., 2020; Moreno
et al., 2021; Thorp et al., 2022; Garay-Solis et al., 2023), revealing which
one exerts a more pronounced influence on quenching star formation at
different galactocentric radii. A positive value for this expression indicates
that the deviation of $\Sigma_{\mathrm{sSFR}}$ from that of the main-sequence
galaxies is _primarily, but not necessarily exclusively_ , driven by an
increase in SFE. Conversely, a negative value signifies a scenario _primarily_
influenced by $f_{\mathrm{gas}}$. Note that regardless of which quenching
driver plays the dominant role, we do not deny the significance of the other
one. The uncertainty of $\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE is determined
through error propagation from the uncertainties of the raw curves.

Figure 6 displays the radial profiles of
$\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE for SFm galaxies on the left and SFl
galaxies on the right. The galaxies are color-coded based on their global
sSFR, which is related to their distance from the main sequence. The darkness
of the curve color increases with global sSFR values. The yellow horizontal
shaded region represents the regime ($-$0.15 $<$
$\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE $<$ 0.15) where
$\Sigma_{\mathrm{sSFR}}$ is determined by the combined effect of both
$f_{\mathrm{gas}}$ and SFE. The limit of $\pm$0.15 is approximately twice the
typical uncertainty of the $\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE profiles.
The choice of this limit should be considered as a conservative choice to
avoid the risk of over-interpretation. While the majority of galaxies in both
the SFm and SFl categories tend to be skewed towards being primarily driven by
SFE, there exists a diverse configurations in terms of the dominant factors
influencing star formation.

Figure 7 provides four illustrative examples. In each sub-figure, the upper-
left panel displays gray curves, with increasing darkness representing
$\Delta$$f_{\mathrm{gas}}$, $\Delta$SFE, and $\Delta$$\Sigma_{\mathrm{sSFR}}$,
respectively. Meanwhile, the lower-left panel presents the radial
$\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE profile. The right panel exhibits the
SDSS $gri$ composite image of the galaxy, with the outermost ellipse
highlighting the radius of 1.5$R_{\mathrm{e}}$. The upper-left panel of Figure
7 exemplifies a case (8082-12704) where the radial
$\Delta$$\Sigma_{\mathrm{sSFR}}$ is primarily influenced by SFE across the
entire radial range. Conversely, other panels show galaxies that demonstrate
signs of multiple mechanisms influencing their star formation. Specifically,
in the case of galaxy 8083-9101 (upper-right), SFE dominates in the inner
regions, while $f_{\mathrm{gas}}$ takes over in the outer regions, with a
transition occurring at approximately 0.6 $R_{\mathrm{e}}$. The lower two
panels show galaxies (8086-9101 and 8952-12701) exhibiting a more complex
pattern. Star formation in the inner regions (within 0.3 $R_{\mathrm{e}}$) of
8086-9101 is primarily driven by $f_{\mathrm{gas}}$, while in the intermediate
radial range (0.3 – 1.0 $R_{\mathrm{e}}$), SFE takes the lead. In the
outermost regime, both $f_{\mathrm{gas}}$ and SFE seem to play a role in
shaping star formation. For galaxy 8952-12701, star formation in the inner and
outermost regions is primarily governed by SFE. However, in the intermediate
radial range (0.5 – 1.0 $R_{\mathrm{e}}$), both $f_{\mathrm{gas}}$ and SFE
work together to regulate star formation.

Figure 6 and 7 provides compelling evidence that star formation in quenching
galaxies is governed by a range of diverse modes, SFE-driven,
$f_{\mathrm{gas}}$-driven, and by the combination of the two; such complexity
is also observed in galaxies experiencing enhanced star formation (Ellison et
al., 2020b; Thorp et al., 2022). Given the small size of our sample in this
work, it is challenging to pinpoint the exact underlying origin of the
multiple-mode drivers, such as different underlying mechanisms being
responsible for star formation quenching in different galactocentric regimes.
Further studies with larger sample sizes and increased statistical
significance are necessary to provide more robust constraints on the
prevalence and the nature of such multi-mode driver. Moreover, employing
different $\Sigma_{\mathrm{SFR}}$ tracers that are insensitive to
contamination from AGNs and older stellar populations, or are unaffected by
dust attenuation, will contribute to confirming our findings based on the
H$\alpha$ and D4000 star formation measurements.

Figure 6: Radial profile of $\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE for SFm
(left) and SFl (right) galaxies. A positive value for this expression
indicates that the deviation of $\Sigma_{\mathrm{sSFR}}$ from that of the
main-sequence galaxies is primarily driven by an increase in SFE. A negative
value suggests a scenario primarily influenced by $f_{\mathrm{gas}}$. The
darkness of the curve color increases with global sSFR values. The yellow
shaded region represents the regime ($-$0.15 $<$
$\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE $<$ 0.15) where
$\Sigma_{\mathrm{sSFR}}$ is determined by the combined effect of both
$f_{\mathrm{gas}}$ and SFE.

Figure 7: Examples of radial $\Delta$ properties for four galaxies exhibit
diverse configurations of dominant drivers within their disks. In each galaxy,
the upper-left corner displays gray curves, with increasing darkness
representing $\Delta$$f_{\mathrm{gas}}$, $\Delta$SFE, and
$\Delta$$\Sigma_{\mathrm{sSFR}}$, respectively. The lower-left corner presents
the radial $\Delta$$f_{\mathrm{gas}}$$-\Delta$SFE profile. The red dashed
lines mark the regime ($-$0.15 $<$ $\Delta$$f_{\mathrm{gas}}$$-\Delta$SFE $<$
0.15) where $\Sigma_{\mathrm{sSFR}}$ is determined by the combined effect of
both $f_{\mathrm{gas}}$ and SFE. The right panel shows the SDSS $gri$
composite image of the galaxy, with the outermost ellipse indicating the
radius of 1.5$R_{\mathrm{e}}$. For galaxies exhibiting multiple dominant
drivers at different radii (upper-right, lower-left, and lower-right
galaxies), the inner ellipse(s) indicate the radii where the dominant driver
changes.

####  3.2.1 Relative Importance of $f_{\mathrm{gas}}$ and SFE in Individual
Galaxies

In this section, we aim to discuss the spatial characteristics of individual
galaxies. Using the radial profiles of $\Delta$$f_{\mathrm{gas}}$-$\Delta$SFE
in Figure 6, we undertake a visual classification of galaxies into two
distinct groups based on the number of dominant factors influencing star
formation within their galactic disks. These groups are characterized as
either “single mode” or “multiple driver”. For example, the galaxy shown in
the upper-left panel of Figure 7 would be classified as a “single mode”
system, driven primarily by SFE. In contrast, other galaxies in Figure 7 would
fall into the “multiple driver” category, each displaying a complex
combination of factors influencing their star formation.

Using this classification approach, we identify 10 galaxies (4 SFm and 6 SFl;
1 $f_{\mathrm{gas}}$-driven and 9 SFE-driven) categorized as being driven by a
single mode and 12 galaxies (7 SFm and 5 SFl) classified as being influenced
by multiple modes. There is no significant difference in the number of
galaxies between these two modes, and there is no apparent trend regarding the
dominant mode of quenching for SFm and SFl galaxies. By combining the previous
ALMaQUEST results on enhanced star formation (Ellison et al., 2020b; Thorp et
al., 2022), we conclude that _both quenching and star formation boosting is
both individualized (from galaxy-to-galaxy) and can be complex even with a
given galaxy_.

####  3.2.2 Relative Importance of $f_{\mathrm{gas}}$ and SFE at Different
Radial Range

In the previous section, we discussed the individual behavior of the 22
galaxies below the main sequence (SFm and SFh), in this section, we will
answer the question of whether there is a preference for a specific quenching
driver ($f_{\mathrm{gas}}$, SFE, or a combination of both) at different
galactocentric radii. Figure 8 illustrates the distribution of the different
drivers across 198 azimuthal bins in the 22 quenching galaxies. When the value
of $\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE is precisely zero or when the
associated uncertainty encompasses $\pm$0.15, the region is considered to be
equally influenced by both drivers. First, we will examine all the radial bins
as a whole. Moreover, since the central region ($R$ $<$ 0.5$R_{\mathrm{e}}$)
exhibits the most pronounced quenching as galaxies begin to deviate downwards
from the main sequence (Figure 5(a); see also Ellison et al. 2018, Belfiore et
al. 2018, and Bluck et al. 2020b), it merits distinct discussion and is
separated from the remainder of the disk for discussion purposes. The
definition of the central region as $R$ $<$ 0.5$R_{\mathrm{e}}$, typically
dominated by galactic bulges (Kalinova et al., 2021, 2022), is also consistent
with the analysis taken in previous ALMaQUEST papers (Ellison et al., 2020a;
Lin et al., 2022). Correspondingly, the disk region is defined as the area
beyond 0.5$R_{\mathrm{e}}$.

Considering all the radial bins collectively (as represented by the dark gray
bars in Figure 8), SFE emerges as the dominant factor, accounting for
approximately 51% in determining the $\Sigma_{\mathrm{sSFR}}$. Following
closely behind is a mode where $f_{\mathrm{gas}}$ and SFE contribute equally,
constituting approximately 40%, while cases primarily driven by
$f_{\mathrm{gas}}$ account for only 9%. In the central region (consisting 66
radial bins for $R$ $<$ 0.5 $R_{\mathrm{e}}$; gray bars in Figure 8), the
trend aligns with the overall dataset, with SFE driving 66% of radial regions,
the combination of $f_{\mathrm{gas}}$ and SFE playing a significant role in
29% of the regions, and $f_{\mathrm{gas}}$ being the primary driver in 5% of
cases. Our findings regarding the central region are consistent with the
results of an integrated analysis conducted by Colombo et al. (2020). Their
study, based on EDGE-CARMA and APEX observations for approximately 470
galactic centers, similarly suggests that as galaxies depart from the main
sequence, it is the changes in SFE that primarily push a galaxy (more
specifically, their quenching center) further into the passive regime. It is
important to note that the term “center” as used in Colombo et al. (2020)
corresponds to $\sim$ 1.0$R_{\mathrm{e}}$, defined by the APEX beam at 230
GHz. This is larger than the definition of “center” used in our work. This
distinction in spatial definitions should be taken into account when comparing
results across different studies. We have evaluated our results using an
alternative definition of the center as $R$ $<$ 1.0$R_{\mathrm{e}}$. While
this adjustment alters the fraction of individual categories in Figure 8, the
relative differences among the various categories remain consistent.

In the disk region (consisting of 132 radial bins for $R$ $>$
0.5$R_{\mathrm{e}}$; light gray bars), a different pattern emerges. Here,
$f_{\mathrm{gas}}$ and SFE are equally important in driving star formation in
47% of the radial bins, becoming the most prevalent mode in this radial
regime. At the same time, SFE takes the lead as the dominant factor in 43% of
these radial bins, with $f_{\mathrm{gas}}$ remaining the least common driver,
accounting for only 10% of the regions in the disk region. Several prior
studies, relying on integrated measurements of entire galaxies, have
demonstrated the significance of both decreasing $f_{\mathrm{gas}}$ and SFE in
determining the distance from the star-forming main sequence (e.g., Saintonge
et al., 2017; Piotrowska et al., 2020). While these studies cannot distinguish
between the central and disk regions of galaxies, their findings are
presumably heavily influenced by the events transpiring in the disk regions.
This is due to the extensive size of these regions, which therefore
contributes significantly to the overall average quantity. Consequently, our
findings that the combination of $f_{\mathrm{gas}}$ and SFE is the most
prevalent mode in the disk regions can offer an explanation for the findings
of previous integrated studies.

In our analysis, we find that star formation in the radial regions considered
is primarily governed either by SFE or by the combined influence of
$f_{\mathrm{gas}}$ and SFE. The implication is consistent to that reported in
previous spatially-resolved analysis (Lin et al., 2017, 2022; Brownson et al.,
2020), namely that, statistically, both $f_{\mathrm{gas}}$ and SFE contribute
to the sSFR suppression in central and disk regions, but the relative
importance between the $f_{\mathrm{gas}}$ and SFE in lowering the
$\Sigma_{\mathrm{sSFR}}$ vary from galaxy to galaxy. It is essential to note
that while $f_{\mathrm{gas}}$ may not emerge as the statistically dominant
driver of star formation in any of the regions we have examined, this result
does not negate the fact that $f_{\mathrm{gas}}$ is indeed reduced in
quenching galaxies. Instead, what becomes evident is that the magnitude of the
reduction in $f_{\mathrm{gas}}$ alone is not substantial enough to account for
the degree of the suppression observed in star formation.

Figure 8: Distribution of different drivers across 198 azimuthal bins in the
22 quenching galaxies. When the value of
$\Delta$$f_{\mathrm{gas}}$$-$$\Delta$SFE is exactly zero, or when the
associated uncertainty encompasses $\pm$0.15, the region is considered to be
equally influenced by both drivers. The dark-gray histograms represent the
distribution for all radial bins, while the gray and light-gray histograms
represent the distributions for the central ($R$ $<$ 0.5$R_{\mathrm{e}}$) and
disk ($R$ $>$ 0.5$R_{\mathrm{e}}$) regions, respectively.

##  4 Discussion

The analysis of the radial profiles in this study, as shown in Figure 5,
provides a direct visualization of the significance of both $f_{\mathrm{gas}}$
and SFE in shaping the star formation behavior in galaxies undergoing
quenching. The clear ranking of radial $f_{\mathrm{gas}}$ and SFE values in
relation to the distance from the global star-forming main sequence, observed
across all radial ranges up to 1.5$R_{\mathrm{e}}$, suggests a gradual
suppression of both $f_{\mathrm{gas}}$ and SFE as galaxies moving downwards
from the main sequence. This finding is consistent with our previous work
within the ALMaQUEST series (Lin et al., 2017, 2022), as well as other
spatially-resolved studies (e.g., Brownson et al., 2020; Sánchez et al., 2021;
Villanueva et al., 2023).

###  4.1 Quenching Mechanisms

The diverse configuration of dominant quenching drivers, observed both within
individual galaxies and across all 22 quenching galaxies, points to a complex
set of quenching mechanisms operating within our galaxy sample. Several
mechanisms have been proposed to operate in the central regions of galaxies.
For instance, feedback from star formation (e.g., Murray et al., 2005; Hopkins
et al., 2014) and AGNs (e.g., Sijacki et al., 2007; Hlavacek-Larrondo et al.,
2012; Schaye et al., 2015; Weinberger et al., 2018) can disrupt and disperse
star-forming clouds, reducing the $f_{\mathrm{gas}}$ (e.g., Ellison et al.,
2021c; García-Burillo et al., 2021) and consequently lowering
$\Sigma_{\mathrm{sSFR}}$. Conversely, gas in galaxies can also be supported
thermally by AGN heating or by the non-thermal pressure from the magnetic
field, cosmic rays and turbulence to counteract gravitational collapse
(Tabatabaei et al., 2018). These effects can lower the SFE while not
necessarily reducing $f_{\mathrm{gas}}$. Figure 4 shows that AGN-contaminated
spaxels exist in all populations, but there does not appear to be a clear
relationship between the fraction of AGN-contaminated spaxels and the galaxy’s
deviation from the main sequence within our sample. Nonetheless, there might
be a significant time-lag between the initiation of star formation quenching
and the emergence of observable AGN signatures (Schawinski et al., 2009).

Beyond the central regions of galaxies, in the context of the morphological
quenching scenario (Martig et al., 2009), the formation of a bulge acts to
stabilize the gaseous disk of the galaxy, preventing its collapse (i.e.,
reduction of SFE), without necessarily requiring a mechanism to remove the gas
within it (Colombo et al., 2018; Méndez-Abreu et al., 2019). On the other
hand, molecular gas within the galactic disk can be removed when the ram
pressure of the ISM exceeds the gravitational force provided by the galaxy’s
disk (Gunn & Gott, 1972). This removal leads to a reduction in
$\Sigma_{\mathrm{sSFR}}$ due to the loss of molecular gas content
($f_{\mathrm{gas}}$) (Boselli et al., 2014a, 2016; Simpson et al., 2018; Owers
et al., 2019; Brown et al., 2023).

The presence of a stellar bar in galaxies also introduces a complex interplay
in star formation quenching (Masters et al., 2010; Fraser-McKelvie et al.,
2020). The bar-induced torque drives gas inflows toward the galactic center,
enhancing the gas content and star formation in the central region (this
phenomenon in fact contrasts with the _quenching_ process we have observed for
both molecular gas and star formation here) while depleting the bar region of
the gas ($f_{\mathrm{gas}}$) necessary for star formation (Kuno et al., 2007;
Ellison et al., 2011; Zhou et al., 2015; Spinoso et al., 2017; Khoperskov et
al., 2018; Chown et al., 2019; George & Subramanian, 2021). Conversely, the
bar can also induce shocks and shear, which increase the turbulence of the gas
in the bar region; this, in turn, stabilizes the gas against gravitational
collapse, leading to the suppression of disk star formation by lowering the
SFE (Reynaud & Downes, 1998; Verley et al., 2007; Haywood et al., 2016). A
subset of the ALMaQUEST galaxies has been visually identified as barred
galaxies through the Galaxy Zoo project; there is also an increasing
possibility (based on Galaxy Zoo) of a galaxy being a barred one from SFh, to
SFm, and to SFl galaxies. In our forthcoming papers (Hogarth et al. submitted,
Lopez-Coba et al. in preparation), we will investigate the properties of these
bars in relation to molecular gas and star formation characteristics to gain a
deeper understanding of their role in star formation quenching.

Within the ALMaQUEST sample, a few galaxies exhibit asymmetric optical disks,
indicating past or ongoing interactions with other galaxies. Previous studies
have demonstrated that galaxy interactions have a significant impact on star
formation and cold gas properties (Pan et al., 2018; Thorp et al., 2022;
Garay-Solis et al., 2023). However, the question of whether the merging
process of galaxies can lead to the quenching of star formation remains a
topic of debate (e.g., Gabor et al., 2010; Weigel et al., 2017; Rodríguez
Montero et al., 2019; Davies et al., 2022; Ellison et al., 2022; Quai et al.,
2023). Nevertheless, a larger sample is certainly needed to distinguish
between internal processes, such as bulge growth and bar formation, and
external processes like galaxy interactions and mergers that regulate star
formation and gas properties in galaxies.

While identifying the precise quenching mechanisms and their specific
contributions to the observed $\Sigma_{\mathrm{sSFR}}$, $f_{\mathrm{gas}}$,
and SFE is beyond the scope of this paper, it is plausible that distinct
quenching mechanisms play a role in suppressing star formation across
different radial regimes. These mechanisms could exert varying impacts on
molecular gas content, resulting in the observed diversity in dominant
quenching drivers ($f_{\mathrm{gas}}$, SFE, or both) within our sample.
Furthermore, the underlying quenching mechanisms may operate over varying time
scales. There is a growing consensus that quenching is not necessarily a rapid
process (Ellison et al., 2022) but instead unfolds gradually over a period of
1 – 4 Gyrs (Hahn et al., 2017; Foltz et al., 2018; Wright et al., 2019;
Sánchez et al., 2019). The exact timescale of quenching depends on various
factors, including galaxy stellar mass ($M_{\ast}$), whether the galaxy is
central or a satellite, and the particular underlying quenching mechanisms at
play.

###  4.2 Comparison with Simulations

Several recent studies have explored $\Sigma_{\mathrm{sSFR}}$ in simulated
green-valley galaxies using galaxy simulations such as FIRE, Illustris,
IllustrisTNG, EAGLE, and SIMBA (e.g., Orr et al., 2017; Starkenburg et al.,
2019; Appleby et al., 2020; Nelson et al., 2021; Corcho-Caballero et al.,
2023a, b; McDonough et al., 2023). Overall, most of the simulated galaxies
below the main sequence exhibit lower $\Sigma_{\mathrm{sSFR}}$ at nearly every
radius compared to star-forming galaxies with similar $M_{\ast}$. The
agreement between our observed radial $\Sigma_{\mathrm{sSFR}}$ profiles and
the trend observed in simulations strengthens the evidence for the global
quenching phenomenon. However, we also note that some simulations find
centrally enhanced sSFR, rather than the suppressed sSFR found in other
simulations (and observations) (FIRE of Orr et al. 2017 and Illustris and
EAGLE of Starkenburg et al. 2019).

While inside-out quenching mode is observed commonly in observations for high-
mass galaxies (this work; Belfiore et al. 2018; Brownson et al. 2020, ; Bluck
et al. 2020b; Nelson et al. 2021; Sánchez et al. 2021; Villanueva et al.
2023), both inside-out and outside-in modes are predicted by simulations for
galaxies with similar mass to our sample. The outside-in mode is concluded to
be as a result of a strong truncation in the sSFR profiles at $>$
1$R_{\mathrm{e}}$ for some simulated green-valley galaxies (Illustris and
EAGLE of Starkenburg et al. 2019 and SIMBA of Appleby et al. 2020). The sharp
cut-off is present in all AGN feedback variants; therefore, this may be
originated from the adopted star formation (rather than AGN) prescriptions
(Appleby et al., 2020). Furthermore, it is important to note that there is no
detection limit for $\Sigma_{\mathrm{SFR}}$ in simulations, unlike in
observations. The approach of dealing with the observed fully-quenched regions
(i.e., assigning an extremely low but not zero $\Sigma_{\mathrm{SFR}}$) would
naturally result in simulated galaxies experiencing quenching to a greater
degree than our observational galaxies.

Our most-quenched green-valley galaxies (SFl) consistently demonstrate lower
cold gas content ($\Sigma_{\mathrm{H2}}$ and $f_{\mathrm{gas}}$) compared to
other population groups, consistent with findings from simulations (Appleby et
al., 2020). Nevertheless, simulations show a rapid decline in
$\Sigma_{\mathrm{H2}}$ and $f_{\mathrm{gas}}$ at radial regimes below
approximately $<$ 0.6$R_{\mathrm{e}}$ for both main-sequence and green-valley
galaxies, with the drop being more pronounced for green-valley galaxies.
However, our observed data do not exhibit this pronounced decrease in central
$\Sigma_{\mathrm{H2}}$ and $f_{\mathrm{gas}}$ (Figure 3(c) and 5(b)). This
could be due to the overestimate of the feedback/energy injection of the
simulated AGNs and their influence in the quenching (Corcho-Caballero et al.,
2023a, b). On the other hand, the discrepancy of the central molecular gas
between simulated and observed galaxies could potentially be attributed to the
assigned CO upper limits for the central quenched regions, which result in an
overestimation of $\Sigma_{\mathrm{H2}}$ and, consequently, $f_{\mathrm{gas}}$
in observations. Nevertheless, the accuracy of $\Sigma_{\mathrm{H2}}$ is
presumed to be high, as the majority of spaxels in the central regions, even
within the most-quenched population (Figure 4), are detectable in CO.
Simulations have demonstrated that the gas content, including H I, H2, and CO,
of simulated main-sequence and green-valley galaxies is sensitive to feedback
processes from both star formation and AGN (e.g., Lagos et al., 2015; Crain et
al., 2017; Diemer et al., 2019; Davé et al., 2020; Ma et al., 2022). Further
investigation is required to understand the discrepancy between observations
and simulations, but it is evident that cold gas content and its distribution
within a galaxy provide strong constraints on feedback processes and galaxy
evolution models.

##  5 Summary

We utilize galaxies obtained from the ALMaQUEST survey (Lin et al., 2020) to
investigate the variations in radial profiles of star formation and molecular
gas properties. Our aim is to understand how these variations relate to star
formation quenching. For this purpose, the 34 non-starburst galaxies in the
ALMaQUEST main sample are categorized into three groups, including the star-
forming main sequence (SFh), galaxies at the lower end of the main sequence
scatter (SFm), and galaxies residing significantly below the main sequence
(SFl). Additionally, we also explore whether there exists a preference for a
particular quenching driver, such as gas fraction ($f_{\mathrm{gas}}$) or star
formation efficiency (SFE), at different galactocentric radii. The 12
starburst galaxies in the ALMaQUEST survey were specifically selected to
exhibit centrally peaked starbursts (Ellison et al., 2020a). These starburst
galaxies are presented as a distinct category and are included in the relevant
sections and figures for the purpose of comparison.

Our findings are as follows:

  * •

The median radial profiles of local stellar mass ($\Sigma_{\ast}$) and
molecular gas mass ($\Sigma_{\mathrm{H2}}$) of each subset, derived by
computing the median values from individual profiles, show no significant
variation among the three populations. However, the radial profiles of local
SFR ($\Sigma_{\mathrm{SFR}}$) exhibit a trend across the examined radial
range, with a consistent increase in magnitude observed from the SFl galaxies
to the SFm, and finally to the SFh galaxies at almost all radii (Section 3.1.1
and Figure 3).

  * •

Subsequently, we investigate the radial profiles of various physical
properties derived from $\Sigma_{\mathrm{SFR}}$, $\Sigma_{\mathrm{H2}}$, and
$\Sigma_{\ast}$. Specifically, we analyze the radial distribution of the
specific SFR ($\Sigma_{\mathrm{sSFR}}$ $=$
$\Sigma_{\mathrm{SFR}}$/$\Sigma_{\ast}$), molecular gas fraction
($f_{\mathrm{gas}}$ $=$ $\Sigma_{\mathrm{H2}}$/$\Sigma_{\ast}$), and star
formation efficiency (SFE $=$ $\Sigma_{\mathrm{SFR}}$/$\Sigma_{\mathrm{H2}}$).
Our findings reveal a significant correlation in both magnitude and radial
profile between these properties and the transition of galaxies from the star-
forming main sequence to lower SFR regimes. The radial profiles of
$\Sigma_{\mathrm{sSFR}}$, $f_{\mathrm{gas}}$, and SFE consistently exhibit a
gradual decrease in magnitude from the SFh group to the SFl group across
almost all radii. These observed trends are not a result of any inherent
dependence of gas and star formation properties on global $M_{\ast}$ or local
$\Sigma_{\ast}$, as the selected galaxies have a relatively narrow range of
$M_{\ast}$ (10.2 – 11.6 M☉ in log scale) and rather uniform $\Sigma_{\ast}$
profiles. Our findings also support an inside-out quenching scenario for these
relatively massive galaxies. (Section 3.1.2 and Figure 5).

  * •

We quantify the relative importance of $f_{\mathrm{gas}}$ and SFE at different
galactic radii for the galaxies undergoing quenching (SFm and SFl). This is
done by comparing the radial profile of $f_{\mathrm{gas}}$ and SFE of
individual quenching galaxies with the median profiles derived for the main
sequence galaxies. We found star formation in quenching galaxies is governed
by a range of diverse modes, $f_{\mathrm{gas}}$-driven, SFE-driven, or
equally-driven (combination of $f_{\mathrm{gas}}$ and SFE). In roughly half of
our quenching galaxies, star formation is predominantly regulated by modes
that operate across the entire galaxy – whether it is $f_{\mathrm{gas}}$, SFE,
or a combination of both. In contrast, the other half exhibits notable
complexity, with different drivers influencing star formation at various
radial ranges within these galaxies (Section 3.2.1, Figure 6 and 7).

  * •

When analyzing all galaxies together, statistical analysis reveals that the
decline in star formation within the central regions ($R$ $>$ 0.5
$R_{\mathrm{e}}$) of galaxies is primarily attributed to a reduction in SFE.
Conversely, in the disk regions ($R$ $<$ 0.5 $R_{\mathrm{e}}$), both
$f_{\mathrm{gas}}$ and SFE contribute to the suppression of
$\Sigma_{\mathrm{sSFR}}$ (Section 3.2.2 and Figure 8).

  * •

The diverse configuration of dominant quenching drivers, observed both within
individual galaxies and across all 22 quenching galaxies, suggests that
distinct quenching mechanisms may be responsible for suppressing star
formation across different radial regimes. These mechanisms, likely operating
over varying timescales, could have varying effects on molecular gas content,
leading to the observed diversity in the dominant quenching drivers, including
$f_{\mathrm{gas}}$, SFE, or a combination of both, within our sample (Section
4.1).

  * •

We compare the radial profiles of $\Sigma_{\mathrm{sSFR}}$ and molecular gas
properties observed in our study with those derived from galaxy simulations.
While inside-out quenching is frequently observed in high-mass galaxies in our
sample and other observations, simulations predict both inside-out and
outside-in quenching modes for galaxies with similar masses to the ALMaQUEST
sample. Additionally, simulations indicate a decrease in
$\Sigma_{\mathrm{H2}}$ and $f_{\mathrm{gas}}$ at radial distances below
0.6$R_{\mathrm{e}}$ for both main-sequence and green-valley galaxies, a trend
not observed in the current observational data. These discrepancies is likely
attributed to factors on both the simulation and observation sides, including
the adopted AGN and star formation prescriptions, as well as the treatments of
observational limitations and biases (Section 4.2).

In summary, our results offer valuable insights into the evolution of radial
star formation and molecular gas distribution as galaxies moving downwards
from the star-forming main sequence. To validate our findings, a larger sample
size is essential, enabling a more comprehensive analysis and the
differentiation of various quenching mechanisms and their impact on star
formation and molecular gas properties. In a companion paper (Lin et al. 2024
ApJ in press), we further investigate the dense gas content traced by HCN and
HCO+ of selected ALMaQUEST galaxies to shed light on the origin of low level
of star formation activity in transitioning galaxies. On the other hand,
achieving a successful galaxy quenching model also requires a thorough
comparison between simulations and observations.

We would like to thank the anonymous referee for their careful review and
valuable comments which improved the presentation of this manuscript. This
work is supported by the National Science and Technology Council of Taiwan
under grant 110-2112-M-032-020-MY3. LL acknowledges support from NSTC
111-2112-M-001-044- and NSTC 112-2112-M-001-062-. S.F.S. thanks the PAPIIT-
DGAPA AG100622 and CONACYT grant CF1939578 projects. JMS acknowledges support
from the National Science Foundation under Grant No 2205551.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2015.1.01225.S,
ADS/JAO.ALMA#2017.1.01093.S,
ADS/JAO.ALMA#2018.1.00541.S,
and ADS/JAO.ALMA#2018.1.00558.S. ALMA is a partnership of ESO (representing
its member states), NSF (USA) and NINS (Japan), together with NRC (Canada),
MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO,
and NAOJ.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS-IV acknowledges support and resources from
the Center for High-Performance Computing at the University of Utah. The SDSS
website is www.sdss.org. SDSS-IV is managed by the Astrophysical Research
Consortium for the Participating Institutions of the SDSS Collaboration
including the Brazilian Participation Group, the Carnegie Institution for
Science, Carnegie Mellon University, the Chilean Participation Group, the
French Participation Group, Harvard-Smithsonian Center for Astrophysics,
Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli
Institute for the Physics and Mathematics of the Universe (IPMU)/University of
Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik
Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-
Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für
Extraterrestrische Physik (MPE), National Astronomical Observatory of China,
New Mexico State University, New York University, University of Notre Dame,
Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State
University, Shanghai Astronomical Observatory, United Kingdom Participation
Group, Universidad Nacional Autónoma de México, University of Arizona,
University of Colorado Boulder, University of Oxford, University of
Portsmouth, University of Utah, University of Virginia, University of
Washington, University of Wisconsin, Vanderbilt University, and Yale
University.

##  Appendix A Radial Profiles for Individual Galaxies

Figure 9 to Figure 14 displays the radial profiles of 46 galaxies in the
ALMaQUEST main sample. For each galaxy, from left to right, the radial
profiles of $\Sigma_{\mathrm{SFR}}$, $\Sigma_{\ast}$, $\Sigma_{\mathrm{H2}}$,
$\Sigma_{\mathrm{sSFR}}$, $f_{\mathrm{gas}}$, and SFE are presented. Each
individual galaxy’s radial profile is shown as opaque dark-colored bands, with
the color representing the galaxy category (yellow for cSB, blue for SFh,
green for SFm, and red for SFl). The transparent colored bands represent the
median profiles of these properties for galaxies in each category, with the
thickness of the bands indicating the standard error of the mean at each
radial bin. The median profiles presented here are identical to those shown in
Figures 3 and 5.

Figure 9: Radial profiles for 46 galaxies in the ALMaQUEST main sample are
presented, showing the profiles of $\Sigma_{\mathrm{SFR}}$, $\Sigma_{\ast}$,
$\Sigma_{\mathrm{H2}}$, $\Sigma_{\mathrm{sSFR}}$, $f_{\mathrm{gas}}$, and SFE
from left to right. The individual galaxy profiles are shown with opaque
bands, while the transparent bands indicate the median profiles of these
properties for galaxies in each category. The median profiles shown here
correspond to those in Figures 3 and 5. Each line color corresponds to the
galaxy category, with yellow representing cSB, blue denoting SFh, green for
SFm, and red for SFl.

Figure 10: Continue of Figure 9.

Figure 11: Continue of Figure 10.

Figure 12: Continue of Figure 11.

Figure 13: Continue of Figure 12.

Figure 14: Continue of Figure 13.

## References

  * Appleby et al. (2020) Appleby, S., Davé, R., Kraljic, K., et al. 2020, MNRAS, 494, 6053. doi:10.1093/mnras/staa1169
  * Bacchini et al. (2020) Bacchini, C., Fraternali, F., Pezzulli, G., et al. 2020, A&A, 644, A125. doi:10.1051/0004-6361/202038962
  * Baker et al. (2022) Baker, W. M., Maiolino, R., Bluck, A. F. L., et al. 2022, MNRAS, 510, 3622. doi:10.1093/mnras/stab3672
  * Baker et al. (2023) Baker, W. M., Maiolino, R., Belfiore, F., et al. 2023, MNRAS, 518, 4767. doi:10.1093/mnras/stac3413
  * Barrera-Ballesteros et al. (2022) Barrera-Ballesteros, J. K., Sánchez, S. F., Espinosa-Ponce, C., et al. 2022, arXiv:2206.07058. doi:10.48550/arXiv.2206.07058
  * Belfiore et al. (2018) Belfiore, F., Maiolino, R., Bundy, K., et al. 2018, MNRAS, 477, 3014. doi:10.1093/mnras/sty768
  * Bigiel et al. (2011) Bigiel, F., Leroy, A. K., Walter, F., et al. 2011, ApJ, 730, L13. doi:10.1088/2041-8205/730/2/L13
  * Bluck et al. (2020a) Bluck, A. F. L., Maiolino, R., Sánchez, S. F., et al. 2020a, MNRAS, 492, 96. doi:10.1093/mnras/stz3264 doi:10.1093/mnras/stz3264
  * Bluck et al. (2020b) Bluck, A. F. L., Maiolino, R., Piotrowska, J. M., et al. 2020b, MNRAS, 499, 230. doi:10.1093/mnras/staa2806
  * Bolatto et al. (2013) Bolatto, A. D., Wolfire, M., & Leroy, A. K. 2013, ARA&A, 51, 207. doi:10.1146/annurev-astro-082812-140944
  * Boselli et al. (2014a) Boselli, A., Cortese, L., Boquien, M., et al. 2014, A&A, 564, A67. doi:10.1051/0004-6361/201322313
  * Boselli et al. (2016) Boselli, A., Roehlly, Y., Fossati, M., et al. 2016, A&A, 596, A11. doi:10.1051/0004-6361/201629221
  * Breda et al. (2020) Breda, I., Papaderos, P., Gomes, J. M., et al. 2020, A&A, 635, A177. doi:10.1051/0004-6361/201937193
  * Brinchmann et al. (2004) Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004, MNRAS, 351, 1151. doi:10.1111/j.1365-2966.2004.07881.x
  * Brown et al. (2023) Brown, T., Roberts, I. D., Thorp, M., et al. 2023, arXiv:2308.10943. doi:10.48550/arXiv.2308.10943
  * Brownson et al. (2020) Brownson, S., Belfiore, F., Maiolino, R., et al. 2020, MNRAS, 498, L66. doi:10.1093/mnrasl/slaa128
  * Bundy et al. (2015) Bundy, K., Bershady, M. A., Law, D. R., et al. 2015, ApJ, 798, 7. doi:10.1088/0004-637X/798/1/7
  * Cano-Díaz et al. (2019) Cano-Díaz, M., Ávila-Reese, V., Sánchez, S. F., et al. 2019, MNRAS, 488, 3929. doi:10.1093/mnras/stz1894
  * Cardelli et al. (1989) Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245. doi:10.1086/167900
  * Catalán-Torrecilla et al. (2017) Catalán-Torrecilla, C., Gil de Paz, A., Castillo-Morales, A., et al. 2017, ApJ, 848, 87. doi:10.3847/1538-4357/aa8a6d
  * Chown et al. (2019) Chown, R., Li, C., Athanassoula, E., et al. 2019, MNRAS, 484, 5192. doi:10.1093/mnras/stz349
  * Colombo et al. (2018) Colombo, D., Kalinova, V., Utomo, D., et al. 2018, MNRAS, 475, 1791. doi:10.1093/mnras/stx3233
  * Colombo et al. (2020) Colombo, D., Sanchez, S. F., Bolatto, A. D., et al. 2020, A&A, 644, A97. doi:10.1051/0004-6361/202039005
  * Corcho-Caballero et al. (2023a) Corcho-Caballero, P., Ascasibar, Y., Sánchez, S. F., et al. 2023a, MNRAS, 520, 193. doi:10.1093/mnras/stad147
  * Corcho-Caballero et al. (2023b) Corcho-Caballero, P., Ascasibar, Y., Cortese, L., et al. 2023b, MNRAS, 524, 3692. doi:10.1093/mnras/stad2096
  * Crain et al. (2017) Crain, R. A., Bahé, Y. M., Lagos, C. del P., et al. 2017, MNRAS, 464, 4204. doi:10.1093/mnras/stw2586
  * Davé et al. (2020) Davé, R., Crain, R. A., Stevens, A. R. H., et al. 2020, MNRAS, 497, 146. doi:10.1093/mnras/staa1894
  * Davies et al. (2022) Davies, J. J., Pontzen, A., & Crain, R. A. 2022, MNRAS, 515, 1430. doi:10.1093/mnras/stac1742
  * Diemer et al. (2019) Diemer, B., Stevens, A. R. H., Lagos, C. del P., et al. 2019, MNRAS, 487, 1529. doi:10.1093/mnras/stz1323
  * Domínguez Sánchez et al. (2022) Domínguez Sánchez, H., Margalef, B., Bernardi, M., et al. 2022, MNRAS, 509, 4024. doi:10.1093/mnras/stab3089
  * Elbaz et al. (2007) Elbaz, D., Daddi, E., Le Borgne, D., et al. 2007, A&A, 468, 33. doi:10.1051/0004-6361:20077525
  * Ellison et al. (2011) Ellison, S. L., Nair, P., Patton, D. R., et al. 2011, MNRAS, 416, 2182. doi:10.1111/j.1365-2966.2011.19195.x
  * Ellison et al. (2018) Ellison, S. L., Sánchez, S. F., Ibarra-Medel, H., et al. 2018, MNRAS, 474, 2039. doi:10.1093/mnras/stx2882
  * Ellison et al. (2020a) Ellison, S. L., Thorp, M. D., Pan, H.-A., et al. 2020a, MNRAS, 492, 6027. doi:10.1093/mnras/staa001
  * Ellison et al. (2020b) Ellison, S. L., Thorp, M. D., Lin, L., et al. 2020b, MNRAS, 493, L39. doi:10.1093/mnrasl/slz179
  * Ellison et al. (2021a) Ellison, S. L., Lin, L., Thorp, M. D., et al. 2021a, MNRAS, 501, 4777. doi:10.1093/mnras/staa3822
  * Ellison et al. (2021b) Ellison, S. L., Lin, L., Thorp, M. D., et al. 2021b, MNRAS, 502, L6. doi:10.1093/mnrasl/slaa199
  * Ellison et al. (2021c) Ellison, S. L., Wong, T., Sánchez, S. F., et al. 2021c, MNRAS, 505, L46. doi:10.1093/mnrasl/slab047
  * Ellison et al. (2022) Ellison, S. L., Wilkinson, S., Woo, J., et al. 2022, MNRAS, 517, L92. doi:10.1093/mnrasl/slac109
  * Ellison et al. (2024) Ellison, S. L., Pan, H.-A., Bluck, A. F. L., et al. 2024, MNRAS, 527, 10201. doi:10.1093/mnras/stad3778
  * Foltz et al. (2018) Foltz, R., Wilson, G., Muzzin, A., et al. 2018, ApJ, 866, 136. doi:10.3847/1538-4357/aad80d
  * Fraser-McKelvie et al. (2020) Fraser-McKelvie, A., Merrifield, M., Aragón-Salamanca, A., et al. 2020, MNRAS, 499, 1116. doi:10.1093/mnras/staa2866
  * Gabor et al. (2010) Gabor, J. M., Davé, R., Finlator, K., et al. 2010, MNRAS, 407, 749. doi:10.1111/j.1365-2966.2010.16961.x
  * Garay-Solis et al. (2023) Garay-Solis, Y., Barrera-Ballesteros, J. K., Colombo, D., et al. 2023, ApJ, 952, 122. doi:10.3847/1538-4357/acd781
  * García-Benito et al. (2017) García-Benito, R., González Delgado, R. M., Pérez, E., et al. 2017, A&A, 608, A27. doi:10.1051/0004-6361/201731357
  * García-Burillo et al. (2021) García-Burillo, S., Alonso-Herrero, A., Ramos Almeida, C., et al. 2021, A&A, 652, A98. doi:10.1051/0004-6361/202141075
  * Genzel et al. (2015) Genzel, R., Tacconi, L. J., Lutz, D., et al. 2015, ApJ, 800, 20. doi:10.1088/0004-637X/800/1/20
  * George & Subramanian (2021) George, K. & Subramanian, S. 2021, A&A, 651, A107. doi:10.1051/0004-6361/202140697
  * González Delgado et al. (2016) González Delgado, R. M., Cid Fernandes, R., Pérez, E., et al. 2016, A&A, 590, A44. doi:10.1051/0004-6361/201628174
  * Gunn & Gott (1972) Gunn, J. E. & Gott, J. R. 1972, ApJ, 176, 1. doi:10.1086/151605
  * Hahn et al. (2017) Hahn, C., Tinker, J. L., & Wetzel, A. 2017, ApJ, 841, 6. doi:10.3847/1538-4357/aa6d6b
  * Haywood et al. (2016) Haywood, M., Lehnert, M. D., Di Matteo, P., et al. 2016, A&A, 589, A66. doi:10.1051/0004-6361/201527567
  * Hlavacek-Larrondo et al. (2012) Hlavacek-Larrondo, J., Fabian, A. C., Edge, A. C., et al. 2012, MNRAS, 421, 1360. doi:10.1111/j.1365-2966.2011.20405.x
  * Hopkins et al. (2014) Hopkins, P. F., Kereš, D., Oñorbe, J., et al. 2014, MNRAS, 445, 581. doi:10.1093/mnras/stu1738
  * Hsieh et al. (2017) Hsieh, B. C., Lin, L., Lin, J. H., et al. 2017, ApJ, 851, L24. doi:10.3847/2041-8213/aa9d80
  * Ibarra-Medel et al. (2019) Ibarra-Medel, H. J., Avila-Reese, V., Sánchez, S. F., et al. 2019, MNRAS, 483, 4525. doi:10.1093/mnras/sty3256
  * Kalinova et al. (2021) Kalinova, V., Colombo, D., Sánchez, S. F., et al. 2021, A&A, 648, A64. doi:10.1051/0004-6361/202039896
  * Kalinova et al. (2022) Kalinova, V., Colombo, D., Sánchez, S. F., et al. 2022, A&A, 665, A90. doi:10.1051/0004-6361/202243541
  * Kauffmann et al. (2003) Kauffmann, G., Heckman, T. M., Tremonti, C., et al. 2003, MNRAS, 346, 1055. doi:10.1111/j.1365-2966.2003.07154.x
  * Kennicutt (1998) Kennicutt, R. C. 1998, ARA&A, 36, 189. doi:10.1146/annurev.astro.36.1.189
  * Kewley et al. (2006) Kewley, L. J., Groves, B., Kauffmann, G., et al. 2006, MNRAS, 372, 961. doi:10.1111/j.1365-2966.2006.10859.x
  * Khoperskov et al. (2018) Khoperskov, S., Haywood, M., Di Matteo, P., et al. 2018, A&A, 609, A60. doi:10.1051/0004-6361/201731211
  * Koda et al. (2022) Koda, J., Watson, L., Combes, F., et al. 2022, ApJ, 941, 3. doi:10.3847/1538-4357/ac9dfc
  * Kuno et al. (2007) Kuno, N., Sato, N., Nakanishi, H., et al. 2007, PASJ, 59, 117. doi:10.1093/pasj/59.1.117
  * Lagos et al. (2015) Lagos, C. del P., Crain, R. A., Schaye, J., et al. 2015, MNRAS, 452, 3815. doi:10.1093/mnras/stv1488
  * Lah et al. (2023) Lah, P., Scott, N., Barone, T. M., et al. 2023, PASA, 40, e002. doi:10.1017/pasa.2022.58
  * Lee et al. (2017) Lee, N., Sheth, K., Scott, K. S., et al. 2017, MNRAS, 471, 2124. doi:10.1093/mnras/stx1753
  * Leroy et al. (2008) Leroy, A. K., Walter, F., Brinks, E., et al. 2008, AJ, 136, 2782. doi:10.1088/0004-6256/136/6/2782
  * Leroy et al. (2013) Leroy, A. K., Lee, C., Schruba, A., et al. 2013, ApJ, 769, L12. doi:10.1088/2041-8205/769/1/L12
  * Lin et al. (2017) Lin, L., Belfiore, F., Pan, H.-A., et al. 2017, ApJ, 851, 18. doi:10.3847/1538-4357/aa96ae
  * Lin et al. (2019a) Lin, L., Hsieh, B.-C., Pan, H.-A., et al. 2019a, ApJ, 872, 50. doi:10.3847/1538-4357/aafa84
  * Lin et al. (2019b) Lin, L., Pan, H.-A., Ellison, S. L., et al. 2019b, ApJ, 884, L33. doi:10.3847/2041-8213/ab4815
  * Lin et al. (2020) Lin, L., Ellison, S. L., Pan, H.-A., et al. 2020, ApJ, 903, 145. doi:10.3847/1538-4357/abba3a
  * Lin et al. (2022) Lin, L., Ellison, S. L., Pan, H.-A., et al. 2022, ApJ, 926, 175. doi:10.3847/1538-4357/ac4ccc
  * Lin et al. (2024) Lin, L., Pan, H.-A., Ellison, S. L., et al. 2024, arXiv:2401.05976. doi:10.48550/arXiv.2401.05976
  * Liu et al. (2016) Liu, F. S., Jiang, D., Guo, Y., et al. 2016, ApJ, 822, L25. doi:10.3847/2041-8205/822/2/L25
  * Ma et al. (2022) Ma, W., Liu, K., Guo, H., et al. 2022, ApJ, 941, 205. doi:10.3847/1538-4357/aca326
  * Martig et al. (2009) Martig, M., Bournaud, F., Teyssier, R., et al. 2009, ApJ, 707, 250. doi:10.1088/0004-637X/707/1/250
  * Martin et al. (2007) Martin, D. C., Wyder, T. K., Schiminovich, D., et al. 2007, ApJS, 173, 342. doi:10.1086/516639
  * Masters et al. (2010) Masters, K. L., Mosleh, M., Romer, A. K., et al. 2010, MNRAS, 405, 783. doi:10.1111/j.1365-2966.2010.16503.x
  * McDonough et al. (2023) McDonough, B., Curtis, O., & Brainerd, T. 2023, arXiv:2309.16800. doi:10.48550/arXiv.2309.16800
  * McKee & Ostriker (2007) McKee, C. F. & Ostriker, E. C. 2007, ARA&A, 45, 565. doi:10.1146/annurev.astro.45.051806.110602
  * Medling et al. (2018) Medling, A. M., Cortese, L., Croom, S. M., et al. 2018, MNRAS, 475, 5194. doi:10.1093/mnras/sty127
  * Méndez-Abreu et al. (2019) Méndez-Abreu, J., Sánchez, S. F., & de Lorenzo-Cáceres, A. 2019, MNRAS, 488, L80. doi:10.1093/mnrasl/slz103
  * Moreno et al. (2021) Moreno, J., Torrey, P., Ellison, S. L., et al. 2021, MNRAS, 503, 3113. doi:10.1093/mnras/staa2952
  * Muraoka et al. (2019) Muraoka, K., Sorai, K., Miyamoto, Y., et al. 2019, PASJ, 71, S15. doi:10.1093/pasj/psz015
  * Murray et al. (2005) Murray, N., Quataert, E., & Thompson, T. A. 2005, ApJ, 618, 569. doi:10.1086/426067
  * Nelson et al. (2021) Nelson, E. J., Tacchella, S., Diemer, B., et al. 2021, MNRAS, 508, 219. doi:10.1093/mnras/stab2131
  * Noeske et al. (2007) Noeske, K. G., Weiner, B. J., Faber, S. M., et al. 2007, ApJ, 660, L43. doi:10.1086/517926
  * Orr et al. (2017) Orr, M. E., Hayward, C. C., Nelson, E. J., et al. 2017, ApJ, 849, L2. doi:10.3847/2041-8213/aa8f93
  * Owers et al. (2019) Owers, M. S., Hudson, M. J., Oman, K. A., et al. 2019, ApJ, 873, 52. doi:10.3847/1538-4357/ab0201
  * Pan et al. (2016) Pan, Z., Zheng, X., Lin, W., et al. 2016, ApJ, 819, 91. doi:10.3847/0004-637X/819/2/91
  * Pan et al. (2018a) Pan, H.-A., Lin, L., Hsieh, B.-C., et al. 2018a, ApJ, 854, 159. doi:10.3847/1538-4357/aaa9bc
  * Pan et al. (2018) Pan, H.-A., Lin, L., Hsieh, B.-C., et al. 2018b, ApJ, 868, 132. doi:10.3847/1538-4357/aaeb92
  * Pan et al. (2022) Pan, H.-A., Schinnerer, E., Hughes, A., et al. 2022, ApJ, 927, 9. doi:10.3847/1538-4357/ac474f
  * Piotrowska et al. (2020) Piotrowska, J. M., Bluck, A. F. L., Maiolino, R., et al. 2020, MNRAS, 492, L6. doi:10.1093/mnrasl/slz172
  * Piotrowska et al. (2022) Piotrowska, J. M., Bluck, A. F. L., Maiolino, R., et al. 2022, MNRAS, 512, 1052. doi:10.1093/mnras/stab3673
  * Quai et al. (2023) Quai, S., Byrne-Mamahit, S., Ellison, S. L., et al. 2023, MNRAS, 519, 2119. doi:10.1093/mnras/stac3713
  * Reynaud & Downes (1998) Reynaud, D. & Downes, D. 1998, A&A, 337, 671
  * Rodríguez Montero et al. (2019) Rodríguez Montero, F., Davé, R., Wild, V., et al. 2019, MNRAS, 490, 2139. doi:10.1093/mnras/stz2580
  * Saintonge et al. (2016) Saintonge, A., Catinella, B., Cortese, L., et al. 2016, MNRAS, 462, 1749. doi:10.1093/mnras/stw1715
  * Saintonge et al. (2017) Saintonge, A., Catinella, B., Tacconi, L. J., et al. 2017, ApJS, 233, 22. doi:10.3847/1538-4365/aa97e0
  * Salim (2014) Salim, S. 2014, Serbian Astronomical Journal, 189, 1. doi:10.2298/SAJ1489001S
  * Salpeter (1955) Salpeter, E. E. 1955, ApJ, 121, 161. doi:10.1086/145971
  * Sánchez et al. (2018) Sánchez, S. F., Avila-Reese, V., Hernandez-Toledo, H., et al. 2018, Rev. Mexicana Astron. Astrofis., 54, 217
  * Sánchez et al. (2019) Sánchez, S. F., Avila-Reese, V., Rodríguez-Puebla, A., et al. 2019, MNRAS, 482, 1557. doi:10.1093/mnras/sty2730
  * Sánchez (2020) Sánchez, S. F. 2020, ARA&A, 58, 99. doi:10.1146/annurev-astro-012120-013326
  * Sánchez et al. (2021) Sánchez, S. F., Walcher, C. J., Lopez-Cobá, C., et al. 2021, Rev. Mexicana Astron. Astrofis., 57, 3. doi:10.22201/ia.01851101p.2021.57.01.01
  * Sandstrom et al. (2013) Sandstrom, K. M., Leroy, A. K., Walter, F., et al. 2013, ApJ, 777, 5. doi:10.1088/0004-637X/777/1/5
  * Sargent et al. (2014) Sargent, M. T., Daddi, E., Béthermin, M., et al. 2014, ApJ, 793, 19. doi:10.1088/0004-637X/793/1/19
  * Schawinski et al. (2009) Schawinski, K., Virani, S., Simmons, B., et al. 2009, ApJ, 692, L19. doi:10.1088/0004-637X/692/1/L19
  * Schawinski et al. (2014) Schawinski, K., Urry, C. M., Simmons, B. D., et al. 2014, MNRAS, 440, 889. doi:10.1093/mnras/stu327
  * Schaye et al. (2015) Schaye, J., Crain, R. A., Bower, R. G., et al. 2015, MNRAS, 446, 521. doi:10.1093/mnras/stu2058
  * Scoville et al. (2016) Scoville, N., Sheth, K., Aussel, H., et al. 2016, ApJ, 820, 83. doi:10.3847/0004-637X/820/2/83
  * Sijacki et al. (2007) Sijacki, D., Springel, V., Di Matteo, T., et al. 2007, MNRAS, 380, 877. doi:10.1111/j.1365-2966.2007.12153.x
  * Simpson et al. (2018) Simpson, C. M., Grand, R. J. J., Gómez, F. A., et al. 2018, MNRAS, 478, 548. doi:10.1093/mnras/sty774
  * Spindler et al. (2018) Spindler, A., Wake, D., Belfiore, F., et al. 2018, MNRAS, 476, 580. doi:10.1093/mnras/sty247
  * Spinoso et al. (2017) Spinoso, D., Bonoli, S., Dotti, M., et al. 2017, MNRAS, 465, 3729. doi:10.1093/mnras/stw2934
  * Starkenburg et al. (2019) Starkenburg, T. K., Tonnesen, S., & Kopenhafer, C. 2019, ApJ, 874, L17. doi:10.3847/2041-8213/ab0f34
  * Strateva et al. (2001) Strateva, I., Ivezić, Ž., Knapp, G. R., et al. 2001, AJ, 122, 1861. doi:10.1086/323301
  * Stuber et al. (2023) Stuber, S. K., Schinnerer, E., Williams, T. G., et al. 2023, arXiv:2305.17172. doi:10.48550/arXiv.2305.17172
  * Sun et al. (2023) Sun, J., Leroy, A. K., Ostriker, E. C., et al. 2023, ApJ, 945, L19. doi:10.3847/2041-8213/acbd9c
  * Tabatabaei et al. (2018) Tabatabaei, F. S., Minguez, P., Prieto, M. A., et al. 2018, Nature Astronomy, 2, 83. doi:10.1038/s41550-017-0298-7
  * Tacconi et al. (2018) Tacconi, L. J., Genzel, R., Saintonge, A., et al. 2018, ApJ, 853, 179. doi:10.3847/1538-4357/aaa4b4
  * Thorp et al. (2022) Thorp, M. D., Ellison, S. L., Pan, H.-A., et al. 2022, MNRAS, 516, 1462. doi:10.1093/mnras/stac2288
  * Verley et al. (2007) Verley, S., Combes, F., Verdes-Montenegro, L., et al. 2007, A&A, 474, 43. doi:10.1051/0004-6361:20077650
  * Villanueva et al. (2023) Villanueva, V., Bolatto, A. D., Vogel, S. N., et al. 2023, arXiv:2312.03995. doi:10.48550/arXiv.2312.03995
  * Walmsley et al. (2022) Walmsley, M., Lintott, C., Géron, T., et al. 2022, MNRAS, 509, 3966. doi:10.1093/mnras/stab2093
  * Wang & Wei (2008) Wang, J. & Wei, J. Y. 2008, ApJ, 679, 86. doi:10.1086/587048
  * Wang et al. (2017) Wang, W., Faber, S. M., Liu, F. S., et al. 2017, MNRAS, 469, 4063. doi:10.1093/mnras/stx1148
  * Wang et al. (2018) Wang, E., Li, C., Xiao, T., et al. 2018, ApJ, 856, 137. doi:10.3847/1538-4357/aab263
  * Wang et al. (2019) Wang, E., Lilly, S. J., Pezzulli, G., et al. 2019, ApJ, 877, 132. doi:10.3847/1538-4357/ab1c5b
  * Wang et al. (2022) Wang, D., Croom, S. M., Bryant, J. J., et al. 2022, MNRAS, 516, 3411. doi:10.1093/mnras/stac2428
  * Watson et al. (2016) Watson, L. C., Martini, P., Lisenfeld, U., et al. 2016, MNRAS, 455, 1807. doi:10.1093/mnras/stv2412
  * Weigel et al. (2017) Weigel, A. K., Schawinski, K., Caplar, N., et al. 2017, ApJ, 845, 145. doi:10.3847/1538-4357/aa8097
  * Weinberger et al. (2018) Weinberger, R., Springel, V., Pakmor, R., et al. 2018, MNRAS, 479, 4056. doi:10.1093/mnras/sty1733
  * Wright et al. (2019) Wright, R. J., Lagos, C. del P., Davies, L. J. M., et al. 2019, MNRAS, 487, 3740. doi:10.1093/mnras/stz1410
  * Wyder et al. (2007) Wyder, T. K., Martin, D. C., Schiminovich, D., et al. 2007, ApJS, 173, 293. doi:10.1086/521402
  * Wylezalek et al. (2022) Wylezalek, D., Cicone, C., Belfiore, F., et al. 2022, MNRAS, 510, 3119. doi:10.1093/mnras/stab3356
  * Yan & Blanton (2012) Yan, R. & Blanton, M. R. 2012, ApJ, 747, 61. doi:10.1088/0004-637X/747/1/61
  * Zhou et al. (2015) Zhou, Z.-M., Cao, C., & Wu, H. 2015, AJ, 149, 1. doi:10.1088/0004-6256/149/1/1