# The EDGE-CALIFA survey: Molecular Gas and Star Formation Activity Across the
Green Valley

Vicente Villanueva ALMA-ANID Postdoctoral Fellow  Department of Astronomy,
University of Maryland, College Park, MD 20742, USA  Departamento de
Astronomía, Universidad de Concepción, Barrio Universitario, Concepción, Chile
Alberto D. Bolatto Department of Astronomy, University of Maryland, College
Park, MD 20742, USA  Stuart N. Vogel Department of Astronomy, University of
Maryland, College Park, MD 20742, USA  Tony Wong Department of Astronomy,
University of Illinois, Urbana, IL 61801, USA  Adam K. Leroy Department of
Astronomy, The Ohio State University, Columbus, OH 43210, USA  Center for
Cosmology and Astroparticle Physics, 191 West Woodruff Avenue, Columbus, OH
43210, USA  Sebastian F. Sánchez Instituto de Astronomía, Universidad Nacional
Autónoma de México, A.P. 70-264, 04510 México, D.F., México  Rebecca C. Levy
NSF Astronomy and Astrophysics Postdoctoral Fellow  Steward Observatory,
University of Arizona, Tucson, AZ 85721, USA  Erik Rosolowsky Department of
Physics, University of Alberta, 4-181 CCIS, Edmonton, AB T6G 2E1, Canada
Dario Colombo Argelander-Institut für Astronomie, Universität Bonn, Auf dem
Hügel 71, 53121 Bonn, Germany  Veselina Kalinova Max Planck Institute for
Radioastronomy, Auf dem Hügel 69, D-53121, Bonn, Germany  Serena Cronin
Department of Astronomy, University of Maryland, College Park, MD 20742, USA
Peter Teuben Department of Astronomy, University of Maryland, College Park, MD
20742, USA  Mónica Rubio  Departamento de Astronomía, Universidad de Chile,
Casilla 36-D Santiago, Chile  Zein Bazzi  Argelander-Institut für Astronomie,
Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany Vicente Villanueva
<EMAIL_ADDRESS>
(December 2023. Accepted for publication in ApJ)

###### Abstract

We present a 12CO($J$=2-1) survey of 60 local galaxies using data from the
Atacama Large Millimeter/submillimeter Compact Array as part of the
Extragalactic Database for Galaxy Evolution: the ACA EDGE survey. These
galaxies all have integral field spectroscopy from the CALIFA survey (Sánchez
et al., 2012, 2016a). Compared to other local galaxy surveys, ACA EDGE is
designed to mitigate selection effects based on CO brightness and
morphological type. Of the 60 galaxies in ACA EDGE, 36 are on the star-
formation main sequence, 13 are on the red sequence, and 11 lie in the “green
valley” transition between these sequences. We test how star formation
quenching processes affect the star formation rate (SFR) per unit molecular
gas mass, SFE${}_{\rm mol}=$SFR/$M_{\rm mol}$, and related quantities in
galaxies with stellar masses $10\leq$log[$M_{\star}/$M⊙]$\leq 11.5$ covering
the full range of morphological types. We observe a systematic decrease of the
molecular-to-stellar mass fraction ($R^{\rm mol}_{\star}$) with decreasing
level of star formation activity, with green valley galaxies having also lower
SFEmol than galaxies on the main sequence. On average, we find that the
spatially resolved SFEmol within the bulge region of green valley galaxies is
lower than in the bulges of main sequence galaxies if we adopt a constant CO-
to-H2 conversion factor, $\alpha_{\rm CO}$. While efficiencies in main
sequence galaxies remain almost constant with galactocentric radius, in green
valley galaxies we note a systematic increase of SFEmol, $R^{\rm
mol}_{\star}$, and specific star formation rate, sSFR, with increasing radius.
As shown in previous studies, our results suggest that although gas depletion
(or removal) seems to be the most important driver of the star-formation
quenching in galaxies transiting through the green valley, a reduction in star
formation efficiency is also required during this stage.

galaxies: evolution – galaxies: ISM – submillimeter: galaxies – ISM: lines and
bands

††software:  Astropy (Astropy Collaboration et al., 2018), MatPlotLib (Hunter,
2007), NumPy (Harris et al., 2020), SciPy (Virtanen et al., 2020), seaborn
(Waskom, 2021), Scikit-learn (Pedregosa et al., 2011).

##  1 Introduction

Star formation activity plays a key role in driving the growth and evolution
of galaxies. The production of stars is quantified through the star formation
rate (SFR) which is in principle a function of the physical conditions in the
dense interstellar medium (ISM). In the last decades, several studies have
revealed a tight correlation for many galaxies between the integrated SFR and
the stellar mass ($M_{\star}$) in galaxies, the so-called star-formation main
sequence (SFMS; e.g., Brinchmann et al., 2004; Daddi et al., 2007; Whitaker et
al., 2012; Saintonge et al., 2016; Colombo et al., 2020). This implies a
useful galaxy classification in terms of their star-formation status: “blue
cloud” galaxies, which show a direct correlation between $M_{\star}$ and SFR
for active star-forming galaxies; “red cloud,” where galaxies exhibit low SFRs
and no $M_{\star}$-SFR correlation; and the “green valley” (or transition
galaxies; Salim et al. 2007). The bimodality of the SFMS suggests fundamental
questions regarding the physical processes behind the transition from the SFMS
through the green valley the red cloud, which is mostly linked to the
cessation of star formation activity.

The term “quenching” has been adopted to include the variety of mechanisms
behind the cessation of star formation activity in galaxies. In particular,
Peng et al. (2010) suggest two different routes to classify quenching
processes: “environmental quenching”, which is coupled to the local
environmental conditions that may drive the decrease (or cessation) of SFR;
and “mass quenching”, which refers to internal/intrinsic galaxy mechanisms
affecting star formation. While environmental processes mostly take place in
galaxies residing in high-density environments (e.g., galaxy clusters),
encompassing a broad variety of environmental mechanisms (e.g.,
strangulation/starvation, Larson et al. 1980; Balogh & Morris 2000; ram
pressure stripping, Gunn & Gott 1972, galaxy interactions, Moore et al. 1996;
Smith et al. 2010), intrinsic mechanisms are usually associated with the
activation and regulation of the physical processes driving star formation
activity. Intrinsic quenching mechanisms are also expected to act differently
depending on the structural components within galaxies, resulting in
variations in the SFR when comparing bulges, bars, or disks. These intrinsic
mechanisms have been broadly associated with fast quenching processes
($\lesssim 100$ Myr; e.g. Bluck et al. 2020a, b), or slow ageing ($\sim
0.5$–$1$ Gyr; e.g. Corcho-Caballero et al. 2023), which act in different ways
to alter the physical conditions of the gas and span from strangulation (i.e,
star formation continues until the reservoirs of cold gas are depleted; e.g.,
Kawata & Mulchaey 2008; Peng et al. 2015) gas removal, either due to active
galactic nuclei (AGN) suppression (e.g., Oppenheimer et al., 2010; Page et
al., 2012), or via stellar feedback (e.g., SNe winds; Oppenheimer et al.
2010).

Recent theoretical models have shown that some of these intrinsic mechanisms
rely on modifying the physical properties of the ISM, thereby changing the
efficiency by which the molecular gas is transformed into stars. Martig et al.
(2009) proposed “morphological quenching”, a process in which star formation
is suppressed by the formation of a stellar spheroid. According to Martig et
al. (2009), morphological quenching reflects the stabilization of the disk by
the dominant presence of a pressure-supported stellar spheroid, which replaces
the stellar disk. The stabilization of the gas is a consequence of two
effects: i) the steep potential well induced by the spheroid, and ii) the
increase of a stellar spheroid relative to the stellar disk suppresses the
growth of perturbations in the gaseous disk. This process provides a mechanism
through which early-type galaxies (ETGs) lose their ability to form stars even
in the presence of significant cold gas reservoirs (e.g., Martig et al. 2013).
Gravitational instability is key to increase the SFR. In a simple model,
stability is typically estimated by the Toomre $Q$ parameter,
$Q=\frac{\kappa\sigma}{\epsilon G\Sigma}$ (Toomre, 1964), where $\sigma$ is
the one-dimensional dispersion velocity of the gas, $\sigma_{\rm gas}$, and
$\Sigma$ is the surface density of an infinitelly thin disk; $\kappa$ is the
epicyclic frequency, which is linked to the steepness of the gravitational
potential, and is of order the angular velocity $\Omega$. Axisymmetric
instabilities, which create rings that break-up into clouds, can grow in the
disks if $Q<1$. Martig et al. (2009) suggested that morphological quenching is
the severe suppression of star-formation activity in a massive gaseous disk
when it is embedded in a dominant bulge that stabilizes the gas (i.e.,
resulting in $Q\gg 1$). When compared with the star-formation activity in
spirals, the difference in disk stability in ETGs arises from two main
effects: i) the high central concentration of the stellar mass in ETGs
increases $\kappa$, consequently increasing the tidal forces as well; and ii)
the spheroidal distribution of stars dilutes the self-gravity of the gas, and
therefore gravitational collapse cannot counteract the tidal forces,
preventing the assembly of star-forming clumps. Also through numerical
simulations, Gensior et al. (2020) show that spheroids drive turbulence and
increase $\sigma_{\rm gas}$, increase the virial parameter, and cause the
turbulent pressure to increase towards a galaxy center; all these are mostly
dependant on the bulge mass ($M_{\rm b}$). They also find that turbulence
increases for more compact and more massive bulges. Although morphological
quenching is a process able to reduce the star formation during a well-defined
time range of a galaxy lifetime (t$\approx 7-11$ Gyr; Martig et al. 2009), it
is still not clear to what degree the ageing in ETGs is driven by this
mechanism, the reduction of the molecular gas content, or a combination of
multiple processes.

By obtaining high-resolution CO data, the new generation of mm/submm
telescopes has allowed us to analyze in detail how the physical conditions of
the molecular gas vary between the different structural components within
galaxies in the local Universe. In addition, multiwavelength galaxy surveys
have revealed the interplay between the different components of the ISM and
their role behind star formation activity. In this work, we present the ALMA
large mm/submm Compact Array Extragalactic Database for Galaxy Evolution, the
ACA EDGE survey. We investigate the star-formation activity in 60 nearby
massive galaxies using Atacama Compact Array (ACA) observations of the CO(2-1)
emission line in combination with optical Integrated Field Unit (IFU) data
from the CALIFA survey (Sánchez et al., 2012).

This paper is organized as follows: Section 2 presents the main features of
the ACA EDGE survey, including the sample selection, data processing, and the
ancillary data. In Section 3 we explain the methods applied to analyze the
data and the equations used to derive the physical quantities. Finally, in
Section 4 we present our results and discussion, and in Section 5 we summarize
the main conclusions. Throughout this work, we assume a $\Lambda$CDM
cosmology, adopting the values $\Omega_{\Lambda}=0.7$, $\Omega_{\rm DM}=0.3$
and H∘=$69.7$ km s-1 Mpc-1.

##  2 OBSERVATIONS

Figure 1: SFR-$M_{\star}$ relation for the 60 galaxies in the ACA EDGE survey
(blue circles), sampling the whole range of $z=0$ galaxy behavior for
log$[M_{*}/$M${}_{\odot}]\approx 10-11.5$, including the star formation main
sequence and quenched systems below it. Gray filled and unfilled circles are
CARMA EDGE and APEX EDGE galaxies included in Bolatto et al. (2017) and
Colombo et al. (2020), respectively. The black-solid and dashed-green lines
correspond to the best-linear fit for star-formation main sequence (Cano-Díaz
et al. 2016) and green valley (Colombo et al. 2020) galaxies, respectively.
ACA EDGE galaxies constitute a sample of the local universe with good
statistical characteristics and are easy to volume-correct to characterize the
star formation activity in nearby massive galaxies.
---
Figure 2: SDSS $r$ (red channel), $i$ (green channel), and $z$-bands (blue
channel) composite images for the 60 galaxies encompassed by the ACA EDGE
survey. These local galaxies show a broad variety of morphologies
representative of the distribution of galaxies in the local universe. This
enables one of the main ACA EDGE goals, to analyze the star-formation
quenching mechanisms at different evolutionary stages.

###  2.1 The ACA EDGE sample

We used the ALMA large mm/submm Compact Array (ACA) to observe 60 galaxies
drawn from the third public data release of the Calar Alto Legacy Integral
Field Area survey Data Release 3 (Sánchez et al., 2016b), in the context of
the Extragalactic Database for Galaxy Evolution (EDGE) surveys. Previous CO
surveys focus mainly (or exclusively) on “main sequence” or star forming
galaxies selected either due to their SFR/$M_{\star}$, morphology, or IR
brightness (e.g., the HERA CO Line Extragalactic Survey, HERACLES, Leroy et
al. 2008, 2013; the Herschel Reference Survey, HRS, Boselli et al. 2010; the
James Clerk Maxwell Telescope Nearby Galaxies Legacy Survey, NGLS, Wilson et
al. 2012; the CO Legacy Database for GALEX Arecibo SDSS Survey, COLD GASS and
the extended COLD GASS, xCOLD GASS, Saintonge et al. 2011, 2017; The
Extragalactic Database for Galaxy Evolution-Calar Alto Legacy Integral Field
Area, the EDGE-CALIFA survey, Bolatto et al. 2017; Virgo Environment Traced in
CO survey, VERTICO, Brown et al. 2021; the Physics at High Angular resolution
in Nearby Galaxies-ALMA survey, PHANGS-ALMA, Leroy et al. 2021a). ACA EDGE was
designed to probe into the low SFR/$M_{\star}$ regime to study processes
associated with galaxy quenching. CALIFA observed over 800 galaxies with IFU
spectroscopy at Calar Alto selected from a combination of the Sloan Digital
Sky Survey (SDSS; York et al. 2000; Alam et al. 2015) and an extension of
galaxies that fulfilled the observational setup (see Sánchez et al. 2016b for
more details), reflecting the $z=0$ galaxy population with
log$[M_{\star}/$M⊙]$=9-11.5$ in a statistically meaningful manner (Walcher et
al., 2014). ACA EDGE targets a subsample of CALIFA galaxies with declination
appropriate to observe with ALMA ($\delta<30^{\circ}$) and stellar mass
$M_{\star}>10^{10}$ M⊙, so that CO can be readily detected and metallicity
effects are not too severe. We impose no selection on SFR in order to cover
the full range of star formation activities in this mass range and enable the
study of quenching. The ACA EDGE survey complements the main science goals of
the CARMA EDGE survey (Bolatto et al., 2017, galaxies also drawn from CALIFA;
see Fig. 1), which encompasses CO observations for 126 CALIFA galaxies at
$\sim{4.5}^{\prime\prime}$ resolution but with significant biases. Although
CARMA EDGE-selected galaxies cover a broader range of masses
(log$[M_{\star}/$M⊙] $=9.1–11.5$), it mostly focused on late-type, far-IR
detected galaxies that are rich in molecular gas (hence actively star-
forming), with morphological types mainly spanning from Sa to Scd. The ACA
EDGE survey was designed to complement it by increasing the coverage of early-
type galaxies, thus adding more red cloud galaxies to CARMA EDGE in order to
drive more statistically significant results. A total of 60 galaxies were
observed in CO(2–1) by the ALMA Cycle 7 project 2019.2.00029.S (P.I. A. D.
Bolatto). The galaxies are listed in Table 1; SDSS images are shown in Figure
2. Optical inclinations and east-of-north position angles (PA) are taken from
HyperLEDA111https://leda.univ-lyon1.fr/ and recomputed (when applicable) using
fits files from SDSS $z$-band photometry (see §3.1).

Name | R.A. | Decl. | $i$ | P.A. | Redshift | rms | $\theta_{\rm min}$ | $\theta_{\rm maj}$ | P.A.beam | Distance | $R_{\rm e}$ | $r_{25}$
---|---|---|---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) | (deg) | (deg) |  | (mK) | (″) | (″) | (deg) | (Mpc) | (″) | (″)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13)
CGCG429-012 | 22h36m49.8s | 14∘23$\arcmin$13$.\arcsec$1 | 60 | 4* | 0.01751 | 12 | 5.3 | 9.7 | -36.0 | 84 | 5.3 | 25.0
IC1079 | 14h56m36.1s | 09∘22$\arcmin$11$.\arcsec$1 | 50 | 81* | 0.02907 | 16 | 6.3 | 7.7 | -83.0 | 114 | 19.3 | 43.4
IC1528 | 00h05m05.3s | 07∘05$\arcmin$36$.\arcsec$3 | 70 | 72* | 0.01250 | 13 | 4.6 | 8.2 | -77.0 | 48 | 16.9 | 64.1
IC2341 | 08h23m41.4s | 21∘26$\arcmin$05$.\arcsec$5 | 60 | 2* | 0.01701 | 18 | 6.2 | 8.0 | -72.0 | 75 | 8.0 | 35.2
MCG-01-01-012 | 23h59m10.8s | 04∘11$\arcmin$30$.\arcsec$6 | 90 | 70* | 0.01883 | 13 | 4.4 | 8.1 | 89.0 | 78 | 11.2 | 47.5
MCG-01-10-015 | 03h38m39.1s | 05∘20$\arcmin$50$.\arcsec$4 | 73 | 75* | 0.01343 | 12 | 5.1 | 8.3 | -48.0 | 90 | 11.8 | 43.4
MCG-01-52-012 | 20h37m49.9s | 06∘05$\arcmin$26$.\arcsec$7 | 43 | 72* | 0.01270 | 14 | 5.0 | 8.4 | -45.0 | 100 | 4.5 | 35.2
MCG-02-02-030 | 00h30m07.3s | 11∘06$\arcmin$49$.\arcsec$1 | 70 | 170* | 0.01179 | 13 | 4.4 | 8.3 | -76.0 | 42 | 13.9 | 55.9
MCG-02-51-004 | 20h15m39.8s | 13∘37$\arcmin$19$.\arcsec$3 | 68 | 159* | 0.01876 | 12 | 5.2 | 8.1 | -43.0 | 90 | 15.8 | 45.4
NGC0001 | 00h07m15.8s | 27∘42$\arcmin$29$.\arcsec$7 | 34 | 110* | 0.01511 | 15 | 4.9 | 11.7 | -24.0 | 74 | 9.2 | 47.5
NGC0155 | 00h34m40.0s | 10∘45$\arcmin$59$.\arcsec$4 | 40 | 169* | 0.02053 | 13 | 5.1 | 7.9 | -47.0 | 65 | 13.5 | 44.4
NGC0169 | 00h36m51.7s | 23∘59$\arcmin$25$.\arcsec$3 | 72 | 87* | 0.01525 | 15 | 5.0 | 10.1 | -31.0 | 98 | 19.4 | 45.4
NGC0171 | 00h37m21.5s | 19∘56$\arcmin$03$.\arcsec$3 | 33 | 101* | 0.01277 | 14 | 4.9 | 8.0 | -47.0 | 57 | 15.8 | 61.3
NGC0180 | 00h37m57.7s | 08∘38$\arcmin$06$.\arcsec$7 | 45 | 163* | 0.01743 | 13 | 5.6 | 8.9 | -30.0 | 61 | 20.2 | 65.6
NGC0693 | 01h50m30.8s | 06∘08$\arcmin$42$.\arcsec$8 | 90 | 106* | 0.00498 | 17 | 5.1 | 8.9 | -43.0 | 17 | 11.6 | 62.7
NGC0731 | 01h54m56.2s | 09∘00$\arcmin$38$.\arcsec$9 | 20 | 155* | 0.01296 | 12 | 5.1 | 8.2 | -49.0 | 55 | 10.4 | 50.9
NGC0768 | 01h58m40.9s | 00∘31$\arcmin$45$.\arcsec$2 | 68 | 28* | 0.02308 | 13 | 5.3 | 8.3 | -46.0 | 80 | 15.6 | 46.5
NGC0955 | 02h30m33.1s | 01∘06$\arcmin$30$.\arcsec$3 | 90 | 19* | 0.00489 | 17 | 5.2 | 8.5 | -44.0 | 24 | 9.4 | 80.7
NGC1056 | 02h42m48.3s | 28∘34$\arcmin$26$.\arcsec$8 | 53 | 162* | 0.00528 | 15 | 4.8 | 10.9 | -27.0 | 30 | 7.9 | 55.9
NGC1542 | 04h17m14.1s | 04∘46$\arcmin$53$.\arcsec$9 | 90 | 127* | 0.01235 | 18 | 4.8 | 8.2 | -42.0 | 70 | 9.5 | 36.9
NGC2449 | 07h47m20.2s | 26∘55$\arcmin$49$.\arcsec$1 | 70 | 135* | 0.01652 | 15 | 6.0 | 7.6 | -76.0 | 43 | 12.8 | 43.4
NGC2540 | 08h12m46.4s | 26∘21$\arcmin$42$.\arcsec$6 | 55 | 123* | 0.02088 | 17 | 5.7 | 9.7 | -21.0 | 75 | 15.4 | 37.2
NGC2554 | 08h17m53.5s | 23∘28$\arcmin$19$.\arcsec$9 | 47 | 153* | 0.01365 | 18 | 5.9 | 8.3 | -61.0 | 60 | 17.5 | 61.3
NGC2595 | 08h27m41.9s | 21∘28$\arcmin$44$.\arcsec$7 | 35 | 30* | 0.01429 | 18 | 5.8 | 8.5 | -63.0 | 64 | 24.1 | 49.8
NGC2596 | 08h27m26.4s | 17∘17$\arcmin$02$.\arcsec$3 | 68 | 63* | 0.01964 | 17 | 5.3 | 8.5 | -32.0 | 82 | 11.7 | 41.4
NGC3300 | 10h36m38.4s | 14∘10$\arcmin$16$.\arcsec$1 | 57 | 173* | 0.01012 | 16 | 5.8 | 7.7 | -76.0 | 47 | 13.3 | 45.4
NGC6427 | 17h43m38.5s | 25∘29$\arcmin$38$.\arcsec$1 | 70 | 35* | 0.01088 | 15 | 4.9 | 10.3 | -29.0 | 45 | 8.9 | 46.5
NGC7025 | 21h07m47.3s | 16∘20$\arcmin$09$.\arcsec$1 | 54 | 44* | 0.01639 | 13 | 4.9 | 9.1 | -49.0 | 75 | 18.2 | 59.9
NGC7194 | 22h03m30.9s | 12∘38$\arcmin$12$.\arcsec$4 | 43 | 17* | 0.02713 | 13 | 5.6 | 9.5 | -30.0 | 123 | 11.9 | 39.5
NGC7311 | 22h34m06.7s | 05∘34$\arcmin$11$.\arcsec$6 | 62 | 11* | 0.01495 | 13 | 5.1 | 8.9 | -41.0 | 61 | 10.6 | 44.4
NGC7321 | 22h36m28.0s | 21∘37$\arcmin$18$.\arcsec$5 | 56 | 17* | 0.02372 | 14 | 4.9 | 9.7 | -30.0 | 104 | 12.0 | 42.4
NGC7364 | 22h44m24.3s | 00∘09$\arcmin$43$.\arcsec$5 | 54 | 66* | 0.01605 | 14 | 4.5 | 8.4 | 86.0 | 68 | 10.6 | 49.8
NGC7466 | 23h02m03.4s | 27∘03$\arcmin$10$.\arcsec$1 | 66 | 25* | 0.02483 | 13 | 5.2 | 11.6 | -19.0 | 92 | 12.6 | 46.5
NGC7489 | 23h07m32.6s | 22∘59$\arcmin$53$.\arcsec$6 | 63 | 165* | 0.02071 | 14 | 5.0 | 9.7 | -30.0 | 70 | 16.6 | 36.9
NGC7625 | 23h20m30.0s | 17∘13$\arcmin$35$.\arcsec$0 | 40 | 45* | 0.00557 | 15 | 5.3 | 7.9 | -53.0 | 24 | 9.8 | 44.4
NGC7716 | 23h36m31.4s | 00∘17$\arcmin$50$.\arcsec$2 | 44 | 34* | 0.00851 | 15 | 4.9 | 7.5 | -69.0 | 36 | 14.2 | 54.6
UGC00312 | 00h31m23.9s | 08∘28$\arcmin$00$.\arcsec$6 | 63 | 7* | 0.01424 | 15 | 5.4 | 7.9 | -57.0 | 57 | 13.3 | 44.4
UGC00335NED02 | 00h33m57.3s | 07∘16$\arcmin$05$.\arcsec$9 | 50 | 147* | 0.01812 | 13 | 5.4 | 9.0 | -31.0 | 78 | 16.6 | 44.4
UGC01123 | 01h34m07.9s | 01∘01$\arcmin$56$.\arcsec$2 | 75 | 70* | 0.01615 | 12 | 5.2 | 8.4 | -43.0 | 54 | 9.8 | 36.9
UGC01368 | 01h54m13.1s | 07∘53$\arcmin$01$.\arcsec$1 | 73 | 51* | 0.02653 | 12 | 5.5 | 7.0 | -70.0 | 108 | 10.9 | 40.5
UGC01938 | 02h28m22.1s | 23∘12$\arcmin$52$.\arcsec$7 | 78 | 155* | 0.02108 | 14 | 5.2 | 9.4 | -25.0 | 96 | 8.6 | 35.2
UGC02099 | 02h37m13.0s | 21∘34$\arcmin$04$.\arcsec$0 | 66 | 138* | 0.02737 | 14 | 5.4 | 10.4 | -31.0 | 118 | 13.7 | 35.2
UGC04240 | 08h08m06.1s | 14∘50$\arcmin$16$.\arcsec$3 | 76 | 178* | 0.02886 | 12 | 5.3 | 8.3 | 87.0 | 163 | 10.2 | 37.8
UGC04245 | 08h08m45.7s | 18∘11$\arcmin$39$.\arcsec$0 | 70 | 107* | 0.01733 | 17 | 5.0 | 9.0 | -32.0 | 75 | 14.5 | 42.4
UGC04455 | 08h31m32.8s | 01∘11$\arcmin$51$.\arcsec$8 | 47 | 13* | 0.03044 | 16 | 5.0 | 7.7 | -81.0 | 128 | 7.9 | 25.0
UGC05396 | 10h01m40.4s | 10∘45$\arcmin$23$.\arcsec$0 | 75 | 145* | 0.01798 | 13 | 5.7 | 7.7 | -87.0 | 76 | 13.9 | 44.4
UGC08322 | 13h15m00.9s | 12∘43$\arcmin$31$.\arcsec$0 | 73 | 36* | 0.02540 | 15 | 5.8 | 7.9 | -82.0 | 98 | 8.5 | 33.7
UGC08781 | 13h52m22.7s | 21∘32$\arcmin$22$.\arcsec$0 | 50 | 161* | 0.02513 | 15 | 6.3 | 7.9 | -61.0 | 115 | 12.0 | 47.5
UGC10972 | 17h46m21.8s | 26∘32$\arcmin$36$.\arcsec$9 | 78 | 55* | 0.01539 | 15 | 4.8 | 10.7 | -28.0 | 63 | 19.0 | 62.7
UGC11649 | 20h55m27.6s | 01∘13$\arcmin$30$.\arcsec$9 | 42 | 90* | 0.01252 | 14 | 5.3 | 8.4 | -42.0 | 60 | 14.5 | 43.4
UGC11680NED02 | 21h07m45.8s | 03∘52$\arcmin$40$.\arcsec$4 | 40 | 205* | 0.02615 | 12 | 4.7 | 8.3 | 89.0 | 111 | 9.9 | 20.8
UGC11717 | 21h18m35.4s | 19∘43$\arcmin$07$.\arcsec$0 | 60 | 39* | 0.02088 | 19 | 5.5 | 8.6 | -54.0 | 90 | 11.8 | 36.1
UGC11792 | 21h42m12.7s | 05∘36$\arcmin$55$.\arcsec$1 | 78 | 160* | 0.01586 | 18 | 5.1 | 8.2 | 87.0 | 68 | 17.4 | 40.5
UGC11958 | 22h14m46.8s | 13∘50$\arcmin$27$.\arcsec$2 | 50 | 143* | 0.02618 | 13 | 5.5 | 9.8 | -31.0 | 112 | 17.0 | 59.9
UGC11982 | 22h18m52.9s | 01∘03$\arcmin$31$.\arcsec$2 | 78 | 171* | 0.01554 | 14 | 4.5 | 8.3 | -87.0 | 69 | 12.3 | 36.9
UGC12224 | 22h52m38.3s | 06∘05$\arcmin$37$.\arcsec$2 | 45 | 46* | 0.01156 | 13 | 5.2 | 8.9 | -41.0 | 50 | 22.4 | 44.4
UGC12250 | 22h55m35.8s | 12∘47$\arcmin$24$.\arcsec$9 | 53 | 12* | 0.02405 | 12 | 5.4 | 9.4 | -36.0 | 92 | 12.8 | 49.8
UGC12274 | 22h58m19.5s | 26∘03$\arcmin$43$.\arcsec$3 | 73 | 142* | 0.02538 | 13 | 5.0 | 11.4 | -23.0 | 110 | 12.4 | 40.5
UGC12348 | 23h05m18.8s | 00∘11$\arcmin$22$.\arcsec$3 | 75 | 136* | 0.02510 | 13 | 5.1 | 7.1 | -74.0 | 108 | 12.4 | 38.6
VV488NED02 | 22h56m50.8s | 08∘58$\arcmin$03$.\arcsec$1 | 82 | 73* | 0.01632 | 16 | 4.1 | 8.8 | -86.0 | 70 | 13.3 | 62.7

Table 1: The ACA EDGE target sample. Notes: Column (1): galaxy name; (2) R.A.
(J2000) of the galaxy optical center; (3) Decl. (J2000) of the galaxy optical
center; (4) optical SDSS $r$-band inclination; (5) optical SDSS $r$-band
position angle, calculated east of north. If no (*) is given, we give the
receding side of the galaxy. (6) stellar redshift; (7) root mean square flux
in 10 km s-1 channels; (8) minor axis of the synthesized beam; (9) major axis
of the synthesized beam; (10) position angle of the synthesized beam; (11)
distance; (12) effective radius; (13) optical size of the major axis measured
at 25 mag arcsec-2 in the $B$ band. Columns (2) and (3) are drawn from the
NASA/IPAC Extragalactic Databse, NED. Column (4) is derived by finding the
best fit for the SDSS $z$-band contours at $r\sim r_{25}$ as described in
§3.1. Columns (5) and (6) are drawn from HyperLEDA, except when kinematic
information overruled. Column (11) is derived from column (6) assuming a
$\Lambda$CDM cosmology with $\Omega_{\Lambda}=0.7$, $\Omega_{\rm DM}=0.3$, and
H∘=$69.7$ km s-1 Mpc-1. Column (12) is taken from CALIFA. Column (13) is taken
from de Vaucouleurs et al. (1991).

###  2.2 The CO data

CO observations of our ACA-only project were taken between December 2019 and
September 2021, spending between 15 and 43 minutes on-source for each galaxy.
We set a spectral bandwidth of $\approx$ 1980 MHz and a raw spectral
resolution of $\sim$ 1.938 MHz $\approx$ 2.5 km s-1. The scheduling blocks
were designed to detect the CO(2-1) emission line down to a root mean square
(rms) spanning from $\sim$12 to 18 mK at 10 km s-1 channel width
(corresponding to mass surface density of $\sim 0.9$ to $1.2$ M⊙ pc-2), and
from $\sim$5″ to 7″ angular resolution (i.e., probing physical scales $\sim
1.5$ kpc at the distance of ACA EDGE galaxies), depending on the declination
of the source.

Each galaxy was observed in a Nyquist spaced mosaic (between 10 and 14
pointings) aligned with the major axis, covering the source out to $r_{25}$.
As mentioned in the previous section, we obtained 7m ACA observations for 60,
with an FoV$\sim$1.2′. Finally, we obtain 5$\sigma$ CO detections for 46 ACA
EDGE galaxies, giving a detection rate of $\sim 77$%.

Figure 3: CO(2-1) spectra for ACA datacubes convolved to 1.1′ and 30 km s-1
channel width for the 60 galaxies. The spectra are taken from the central
pixel located at the optical center (columns 2 and 3 in Table 1), and
velocities are centered on the stellar redshift. Figure 4: ACA EDGE data
products for each galaxy. Panels cover an area of 1.25′$\times$ 1.25′. The
first panel shows the SDSS $riz$ multicolor image with contours from our
integrated intensity masked map overlaid. Contours correspond to $2\sigma$ and
$5\sigma$ CO(2-1) emission line levels. From left to right, the following
panels show the CO(2-1) emission line intensity (moment 0, in units of Jy/beam
km s-1), velocity (moment 1, in units of km s-1), and signal-to-noise peak
maps, respectively. The red crosses are the optical centers (columns 2 and 3
of Table 1). The black ellipses in the left bottom corner are the beam size of
the CO(2-1) data. Panels for the remainder of the survey can be found in the
Appendix.

###  2.3 Data reduction and products

We used $uv$ data delivered by ALMA and calibrated by the observatory pipeline
(Hunter et al., 2023), then we imaged the CO$(J=2–1)$ emission from each
target using the PHANGS–ALMA Imaging Pipeline Version 2.1 Leroy et al.
(2021b). Both the calibration and imaging utilized the Common Astronomy
Software Applications (CASA; CASA Team et al. 2022). The data were calibrated
in CASA 5.6.1-8 for data taken in 2019 and 2020 and CASA 6.2.1-7 for data
taken in 2021. We ran the PHANGS–ALMA imaging pipeline in CASA version
5.6.1-8.

Briefly, the PHANGS–ALMA imaging pipeline is designed to produce accurate
images of extended spectral line emission. The pipeline combines all $uv$ data
for a given target on a common spectral grid, subtracts continuum emission,
and then carries out a multi-step deconvolution. This includes an initial
multi-scale clean (we used scales of $0$, 5, and 10$\arcsec$) with a
relatively high S/N$\approx 4$ threshold, followed by a single scale clean
that uses an automatically generated, more restrictive clean mask and cleans
down to S/N$\approx 1$ by default. We used a Briggs weighting parameter of
$=0.5$ (Briggs, 1995) to achieve a good compromise between synthesized beam
size and signal to noise. We used a channel width of 5.08 km s-1 and adopted
the local standard of rest (LSR) as our velocity reference frame, using the
radio definition of velocity. After the initial imaging, the pipeline
convolves the cube to have a round synthesized beam, converts the image to
units of Kelvin, and downsamples the pixel gridding to save space while still
Nyquist sampling the beam. See Leroy et al. (2021b) for more details. We did
not use the noise modeling or product creation portions of the PHANGS–ALMA
pipeline, but instead used software based on previous EDGE work.

All cubes were visually inspected for obvious problems or imaging errors. We
note that NGC 0768, NGC 6427, NGC 7321, and UGC 12250 have incomplete CO line
coverage since their emission peaks are located at the edge of the ACA
spectral window. Although these galaxies have $5\sigma$ CO detections (see
§4.1), the CO line emission flux should just be taken as lower-limits.

We calculate moment maps and radial profiles using a masked cube. The
construction of our mask follows a two-step procedure. We first create a mask
using the CO cube, following the procedure for a “dilated mask” detailed in
Bolatto et al. (2017). This procedure includes in the mask areas around
spectral peaks detected at $\gtrsim 3.5\sigma$ significance (for more details,
see Rosolowsky & Leroy 2006; Bolatto et al. 2017). We put together a second
mask using information that is independent of the CO cube. We then use three
different procedures to generate this mask, and choose the one that recovers
the most CO emission flux. These procedures are:

  * •

H$\alpha$ mask (33 galaxies): We construct a mask using the central H$\alpha$
velocity map from CALIFA, and including around it a velocity region
[-FWHM,+FWHM] following the FWHM prescription from Figure 2 in Villanueva et
al. (2021). H$\alpha$ spaxels with SNR$<5$ in intensity are excluded from the
mask. This approach assumes that the kinematics of the CO are similar to the
kinematics of the H$\alpha$ (e.g., Levy et al. 2018).

  * •

Rotation mask (25 galaxies): We construct a mask assuming a very simple
generic rotation curve that assumes the velocity is constant for $r>5\arcsec$
and increases linearly inside this radius. We adopt the maximum apparent
rotation velocity reported in HI by HyperLEDA (vmaxg calculated from the 21-cm
line, which we call $V_{\rm\mbox{H{\small I}},max}$ here; Bottinelli et al.,
1982, 1990), and adopt the systemic stellar velocity from CALIFA. We include
the same velocity region around this central velocity as for the previous
mask. This mask only extends to $r=r_{25}$. The direction of rotation is
decided based on the H$\alpha$ or CO velocity field (if available) or
ultimately if neither are detected based on comparing the flux recovered
between the two senses of rotation. This approach assumes that the galaxy is
predominantly rotating, and that the CO emission spans the same velocities as
the HI.

  * •

Flat mask (2 galaxies): We construct a mask centered at the stellar systemic
velocity, including all the channels inside the maximum apparent rotation
velocity reported by HyperLEDA and extending out to $r=0.5\,r_{25}$. This
approach does not assume any particular kinematics and is the most relaxed of
the three, although it will also include more noise.

Our final step is to combine (through a logical OR operation) the best mask
derived from this procedure with the dilated mask obtained from the CO, in
order to obtain the final mask.

Figure 5: Comparison of the integrated CO($J$=2-1) emission line flux between
ACA (this work) and APEX (Colombo et al., 2020) datasets for 51 ACA galaxies.
ACA fluxes are derived after convolving datacubes to match the APEX angular
resolution (26.3″). The red dots correspond to NGC 0768, NGC 7321, and UGC
12250, which have incomplete ACA spectral coverage (see Fig. 3). The green
arrows are UGC 08322 and UGC 12274, which are detected by ACA but not APEX
(see Table 2). The figure shows good agreement between ACA and APEX fluxes.
However, fluxes measured by APEX are on average $\sim$20% brighter than in
ACA, likely due to calibration differences. Note that a lack of a detection by
ACA in a 26″ beam does not imply the source is not detected by ACA: for
interferometric data convolution results in removing visibilities in long
baselines (and thus collecting area and sensitivity).

We generate moment 0 maps (integrated intensity of the spectrum along the
spectral axis) from the CO(2-1) spectral line cubes, in units of Jy/beam km
s-1, and after multiplying them by our mask (see Fig. 4). To obtain the
uncertainties of the moment 0 maps, we compute the rms in the signal-free part
of the spectrum in each spaxel, $\sigma_{\rm i}$, and use the equation

$u_{\rm i}=\sigma_{\rm i}\sqrt{N}\Delta v.$ (1)

Here, $N$ is the number of channels included by the mask and $\Delta v$ is the
channel width (in km s-1). We also compute the velocity (moment 1) and peak
signal-to-noise ratio (SNRpeak) maps.

The moment 1 maps (or CO velocity maps, in units of km s-1) are derived by
multiplying the CO datacubes by the mask and using

$M_{\rm 1,i}=\frac{\Sigma I_{\rm i,j}v_{\rm j}}{M_{\rm 0,i}},$ (2)

where $I_{\rm i,j}$ is the CO intensity in the $j$th spectral channel of the
$i$th spaxel, $v_{\rm j}$ is the velocity of the $j$th channel, and $M_{0}$ is
the moment 0 map. Finally, we blank the pixels outside the 2$\sigma$ contour
for $M_{0}$. We also computed maps of the peak SNR, SNRpeak,i, at each
position. We use the following equation:

${\rm SNR_{\rm peak}}=\frac{max(I_{\rm i,j})}{\sigma_{\rm i}},$ (3)

where $max(I_{\rm i,j})$ is the maximum value of the CO intensity within the
spectrum of the $i$th spaxel. Both velocity and SNRpeak maps are included in
Figure 4.

We compare the 12CO(2-1) integrated fluxes for ACA EDGE galaxies to those from
Colombo et al. (2020), who report 12CO(2-1) fluxes for 51 of our galaxies
using APEX observations at 26.3″ resolution and 30 km s-1 channel width (as
part of the APEX EDGE survey). The APEX EDGE survey arises from either the
necessity of exploring whether star-formation quenching is driven by the
reduction in molecular gas content, a change in the star formation efficiency
of the molecular gas, or both. To address this, Colombo et al. (2020) use the
12CO(1–0) maps from the EDGE survey included in Bolatto et al. (2017) in
combination with APEX 12CO(2-1) measurements. With these maps, they
investigate the center of more than 470 galaxies selected from the CALIFA
survey (Sánchez et al., 2012) at different quenching stages. To compare the
fluxes, we convolve our CO datacubes to match the APEX angular resolution and
we take the spectrum of the pixel located at the galaxy center, correcting by
the recommended APEX main beam antenna efficiency (for the PI230 receiver at
this frequency, $\eta_{\rm mb}=0.80$). Finally, we integrate the spectra over
a spectral window defined by visual inspection (typically $\sim$500 km s-1
wide). Uncertainties are computed by deriving the RMS from the signal-free
part of the spectrum and using Equation 1. For non-detections, we estimate
1$\sigma$ upper-limits by computing the RMS over the velocity window given by
$V_{\rm\mbox{H{\small I}},max}$ and using Equation 1. Discrepancies between
both measurements can in principle be attributed to inconsistencies in
calibration, flux that is resolved out or lost due to imperfect deconvolution
for ACA measurements, or pointing for APEX. Although there are some
discrepancies between the two datasets and a handful of cases with incomplete
ACA spectral coverage, Figure 5 shows that there is reasonable consistency
between the ACA and APEX integrated CO fluxes. On average, we find that the
median ACA-to-APEX flux ratio is 0.82.

###  2.4 The CALIFA survey and ancillary data

The Calar Alto Legacy Integral Field Area survey, CALIFA (Sánchez et al.,
2012), comprises a sample of over 800 galaxies at $z\approx 0$. The data were
acquired using the PMAS/PPAK IFU instrument (Roth et al., 2005) at the 3.5 m
telescope of the Calar Alto Observatory. PMAS/PPAK uses 331 fibers each with a
diameter of $2.7\arcsec$ in an hexagonal shape covering a FoV of a square
arcminute. Its average spectral resolution is $\lambda/\Delta\lambda\sim 850$
at ${\rm\sim 5000\AA}$ for a wavelength range that spans from $\lambda=3745$
to ${\rm 7300\AA}$. As mentioned in §2.1, CALIFA galaxies are angular size-
selected such that their isophotal diameters, $D_{25}$, match well with the
PMAS/PPAK FoV. They range from $45$″ to $80$″ in the SDSS $r$-band (Walcher et
al., 2014). The CALIFA survey uses a data reduction pipeline designed to
produce datacubes with more than $5000$ spectra with a sampling of
$1\arcsec\times 1\arcsec$. For more details, see Sánchez et al. (2016b). These
cubes are processed using PIPE3D (Sánchez et al., 2016c, d) to generate maps
of derived quantities.

The final data compilation also contains ancillary data, including information
from HyperLEDA, NASA/IPAC Extragalactic Databse
(NED222https://ned.ipac.caltech.edu/), among others.

##  3 Methods and products

###  3.1 Basic equations and assumptions

To compute the extinction-corrected SFRs, we estimate the extinction (based on
the Balmer decrement; see Bolatto et al., 2017) for each 1″ spaxel using the
equation:

$A_{\rm H{\alpha}}=5.86\log{\left(\frac{F_{\rm H{\alpha}}}{2.86F_{\rm
H{\beta}}}\right)},$ (4)

where $F_{\rm H\alpha}$ and $F_{\rm H\beta}$ are the fluxes of the respective
Balmer lines, and the coefficients assume a Cardelli et al. (1989) extinction
curve and an unextinguished flux ratio of 2.86 for case B recombination. Then,
the corresponding SFR (in M⊙ yr-1) is obtained using (Rosa-González et al.,
2002)

${\rm SFR}=1.6\times 7.9\times 10^{-42}F_{\rm H{\alpha}}10^{\frac{A_{\rm
H{\alpha}}}{2.5}},$ (5)

which includes a correction factor of 1.6 to move from a Salpeter IMF (as
adopted by PIPE3D) to the more commonly used Kroupa IMF (Speagle et al.,
2014). We do this to compare our results with those for other galaxy surveys.
We use this to compute the star formation rate surface density, $\Sigma_{\rm
SFR}$ in M⊙ yr-1 kpc-2, by dividing by the face-on area corresponding to a 1″
spaxel, given the angular diameter distance to the galaxy. In order to produce
smooth SFR maps, we process the H${\alpha}$ and H${\beta}$ fluxes applying the
following recipe:

  1. 1.

We select pixels with non-NaN values for ${F_{{\rm H\alpha}}}$.

  2. 2.

We adopt a minimum H$\alpha$-to-H${\beta}$ flux ratio, ${F_{{\rm
H\alpha}}}$/${F_{{\rm H\beta}}}$ , of $2.86$. Therefore, if ${F_{{\rm
H\alpha}}}$/${F_{{\rm H\beta}}}<2.86$, we impose ${F_{{\rm
H\alpha}}}$/${F_{{\rm H\beta}}}=2.86$ (so $A_{\rm H\alpha}=0$).

  3. 3.

If ${F_{{\rm H\beta}}}$ is a NaN value for a given pixel, then we take the
average value of $A_{\rm H\alpha}$ (for pixels with $A_{\rm H\alpha}>0.0$) of
the whole $A_{\rm H\alpha}$ map.

We obtain the stellar mass surface density, $\Sigma_{\star}$, from the stellar
maps derived by PIPE3D. We correct the maps from the spatial binning effect by
applying the dezonification correction provided by PIPE3D datacubes. This is
to weight the $\Sigma_{\star}$ maps by the relative contribution to flux in
the $V$-band for each spaxel to the flux intensity of the bin in which it is
aggregated (for more details, see Sánchez et al. 2016d). Finally, we mask the
$\Sigma_{\star}$ maps to avoid the flux contribution from field stars and we
include the 1.6 correction factor to move from a Salpeter to a Kroupa IMF.

The molecular gas surface density, $\Sigma_{\rm mol}$, is derived from the
integrated CO intensity, $I_{\rm CO(2-1)}$, by adopting a constant CO-to-H2
conversion factor that is based on observations of the Milky Way: $X_{\rm
CO}=2\times 10^{20}$ cm-2 (K km s-1)-1, or equivalently $\alpha_{\rm
CO,MW}=4.3$ M⊙ $(\rm K\,km\,s^{-1}\,pc^{2})^{-1}$ for the CO($J$=1-0) line
(Walter et al. 2008). We also test how our results depend on our adopted
prescription by using the CO-to-H2 conversion factor from Equation 31 in
Bolatto et al. (2013):

$\alpha_{\rm CO}(Z^{\prime},\Sigma_{\rm
total})=2.9\exp\left(\frac{+0.4}{Z^{\prime}\Sigma^{100}_{\rm
GMC}}\right)\left(\frac{\Sigma_{\rm total}}{100\,\rm
M_{\odot}\,pc^{2}}\right)^{-\gamma},$ (6)

in M⊙ $\rm(K\,kms^{-1}\,pc^{-2})^{-1}$. $\gamma\approx 0.5$ for $\Sigma_{\rm
total}>100$ M⊙ pc-2 and $\gamma=0$ otherwise. Additionally, the metallicity is
normalized to the solar one, ${Z}^{\prime}=\rm[O/H]/[O/H]_{\odot}$, where
$\rm[O/H]_{\odot}=4.9\times 10^{-4}$ (Baumgartner & Mushotzky, 2006),
$\Sigma^{100}_{\rm GMC}$ is the average surface density of molecular gas in
units of 100 M⊙ pc-2, and $\Sigma_{\rm total}$ is the combined gas plus
stellar surface density on kpc scales. We are also interested in the global
variations of $\alpha_{\rm CO}({Z}^{\prime},\Sigma_{\rm total})$.To do so, we
adopt $\Sigma^{100}_{\rm GMC}=1$ and derive $Z^{\prime}$ using the
metallicity-stellar mass relation (based on the O3N2 calibrator; Marino et al.
2013) for CALIFA galaxies from Sánchez et al. (2017). We use the following
expression to obtain $\Sigma_{\rm mol}$

$\Sigma_{\rm mol}=\frac{\alpha_{\rm CO}}{R_{21}}\cos(i)\,I_{\rm CO(2-1)},$ (7)

which adopts the average line luminosity ratio of $R_{21}=I_{\rm
CO(2-1)}/I_{\rm CO(1-0)}=0.65$ based on Leroy et al. (2013) and den Brok et
al. (2021), measured at kpc scales; $i$ is the inclination of the galaxy. This
equation takes into account the mass correction due to the cosmic abundance of
helium. Although $i$ is generally drawn from HyperLEDA, we use SDSS $z$-band
images to obtain a better constraint on the inclination (particularly for
galaxies with $i>60^{\circ}$). To do so, we fit an ellipse to the SDSS
$z$-band contour for a major axis $A_{\rm maj}\sim 1.2r_{25}$. We obtain the
ratio between the minor and major axes, $A_{\rm min}/A_{\rm maj}$, and compute
the inclination by taking $i=\arccos[A_{\rm min}/A_{\rm maj}]$ (see column 4
in Table 1). This assumes an infinitely thin disk and introduces errors for
$i>85^{\circ}$, but we discard highly inclined galaxies from our analysis
anyway since most derived quantities are highly uncertain.

To compute the global values of the molecular gas mass, $M_{\rm mol}$,
$M_{\star}$, and SFR ($Q_{i}$ quantities), we use the following equation:

$Q_{\rm i}=\int_{A}\Sigma_{\rm i}(r)dA,$ (8)

where $A$ is the area within a circle defined by the geometrical parameters
included in Table 1 (with radius $r_{25}$ and centered at the optical center);
$\Sigma_{\rm i}$ is the surface densities for the pixels within $A$ and i $=$
SFR, mol, or $\star$.

We integrate the surface densities for the molecular gas, stars (assuming that
they are distributed along a thin disk), and the SFR to obtain the stellar
mass, molecular gas mass, and the SFR within the bulge:

$M_{{\rm b},i}=2\pi\int^{R_{\rm b}}_{0}\Sigma_{i}(r)\,rdr,$ (9)

where $R_{\rm b}$ is the bulge radius for the stellar component (see §3.3 for
more details), and $i=$ mol, $\star$, or SFR. We then calculate the integrated
ratios as the ratio of the integrated masses and the SFR.

Finally, we compute the resolved SFEmol (in units of yr-1) for each pixel,

${\rm SFE_{\rm mol}}=\frac{\Sigma_{\rm SFR}}{\Sigma_{\rm mol}}.$ (10)

In a similar way, we calculate the resolved molecular-to-stellar mass
fraction, $rR^{\rm mol}_{\star}=\Sigma_{\rm mol}/\Sigma_{\star}$, and the
specific star formation rate, sSFR$=\Sigma_{\rm SFR}/\Sigma_{\star}$ (in units
of yr-1).

Figure 6: Stellar ($\Sigma_{\star}$; red solid line) and molecular gas
($\Sigma_{\rm mol}$; blue solid line) surface densities, in units of M⊙ pc-2,
as a function of galactocentric radius, in units of the stellar effective
radius ($R_{\rm e}$), for the 30 ACA EDGE galaxies with $5\sigma$ CO
detections and inclinations $i\leq 70^{\circ}$. The blue shaded area is the
$\pm 1\sigma$ uncertainty. The brown dotted line is the SFR surface density,
$\Sigma_{\rm SFR}$. The gray shaded area is the region within the bulge
radius, $R_{\rm bulge}$. Dashed black lines correspond to the best exponential
function fit for stellar and molecular gas radial profiles, from top to
bottom. The dashed green line corresponds to $r=r_{25}$. The code on the left
bottom corner corresponds to the Hubble type and the nuclear activity (columns
5 and 6 in Table 2, respectively). SFRs at $r<0.5R_{\rm e}$ have been removed
for LINER and AGN galaxies since H$\alpha$ in this region is susceptible to
LINER/AGN contamination (see §4.2.2). Galaxies are classified based on their
$\Delta$SFMS as defined in §4.1, i.e., in main sequence (blue panels), green
valley (green panels), and red cloud (red panels). When using stellar profiles
as a benchmark, we note a systematic flattening of the molecular gas profiles
with $\Delta$SFMS. See also Fig. 12.

###  3.2 Radial profiles

Name | log[$M_{\star}$] | log[SFR] | log[$M_{\rm mol}$] | Morph. Class | Nuclear |  $\Delta$SFR Class | Quenching Stage | $l_{\star}$ | $l_{\rm CO}$ | $R_{\rm b}$ | $M_{\rm b}$
---|---|---|---|---|---|---|---|---|---|---|---
| (M⊙) | (M⊙ yr-1) | (M⊙) |  |  |  |  | (kpc) | (kpc) | (kpc) | ($M_{\odot}/M_{\star}$)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
CGCG429-012 | 10.46 | -1.68 |  $<$6.77 | E0 | … | RS | fR | … | … | … | …
IC1079 | 11.2 | -1.23 | 8.86$\pm$0.17 | E | … | RS | nR | 9.12$\pm$0.98 | … | 10.99$\pm$1.07 | 0.14$\pm$0.19
IC1528 | 10.76 | 0.23 | 8.83$\pm$0.02 | SBb | … | MS | SF | 4.8$\pm$2.01 | 5.13$\pm$1.25 | 0.52$\pm$0.39 | 0.01$\pm$0.38
IC2341 | 10.86 | -0.8 |  $<$7.4 | S0- | … | RS | fR | … | … | … | …
MCG-01-01-012 | 11.19 | 0.21 | 7.58$\pm$0.02 | SAab | … | GV | MX | … | … | … | …
MCG-01-10-015 | 9.95 | -0.01 | 8.32$\pm$0.03 | Sd | … | MS | SF | … | … | … | …
MCG-01-52-012 | 10.37 | -0.79 |  $<$6.56 | S0- | … | GV | nR | … | … | … | …
MCG-02-02-030 | 10.81 | 0.03 | 8.52$\pm$0.02 | SBa | AGN | MS | QnR | 3.95$\pm$1.43 | 23.27$\pm$49.75 | 1.35$\pm$0.28 | 0.1$\pm$0.07
MCG-02-51-004 | 10.94 | 0.64 | 9.19$\pm$0.02 | Sd | … | MS | SF | 6.93$\pm$0.74 | 19.56$\pm$5.93 | 0.87$\pm$0.69 | 0.02$\pm$0.36
NGC0001 | 10.84 | 0.57 | 9.87$\pm$0.02 | SAb | SF | MS | SF | 2.01$\pm$0.28 | 2.6$\pm$0.47 | 2.25$\pm$0.33 | 0.39$\pm$0.15
NGC0155 | 11.08 | -1.51 |  $<$7.45 | S0 | … | RS | fR | … | … | … | …
NGC0169 | 11.24 | 0.73 | 9.54$\pm$0.01 | SAab | LINER | MS | MX | … | … | … | …
NGC0171 | 10.77 | -0.12 | 8.98$\pm$0.02 | SBab | … | GV | cQ | 6.94$\pm$4.06 | 4.94$\pm$1.06 | 1.27$\pm$0.44 | 0.15$\pm$0.05
NGC0180 | 11.08 | 0.21 | 9.62$\pm$0.02 | SBbc | … | MS | QnR | 8.50$\pm$3.90 | 10.16$\pm$2.15 | 1.74$\pm$0.60 | 0.12$\pm$0.05
NGC0693 | 9.84 | -0.65 | 6.86$\pm$0.02 | S0/a | … | MS | SF | … | … | … | …
NGC0731 | 10.94 | -1.55 |  $<$6.84 | E | … | RS | fR | … | … | … | …
NGC0768 | 10.86 | 0.27 | 9.25$\pm$0.02 | SBbc | … | MS | SF | 7.92$\pm$2.74 | 17.97$\pm$6.58 | 1.87$\pm$0.60 | 0.13$\pm$0.09
NGC0955 | 10.11 | -1.08 | 6.53$\pm$0.04 | Sab | … | GV | nR | … | … | … | …
NGC1056 | 10.28 | 0.16 | 8.6$\pm$0.01 | Sa | SF | MS | SF | 1.47$\pm$1.20 | 2.66$\pm$3.95 | 0.56$\pm$0.12 | 0.08$\pm$0.04
NGC1542 | 10.57 | -0.03 | 6.34$\pm$0.47 | Sab | SF | MS | MX | … | … | … | …
NGC2449 | 11.13 | -0.2 | 9.03$\pm$0.02 | Sab | LINER | GV | MX | 6.97$\pm$10.57 | 4.63$\pm$2.16 | 0.72$\pm$0.27 | 0.03$\pm$0.16
NGC2540 | 10.54 | 0.11 | 9.47$\pm$0.03 | SBcd | … | MS | SF | 4.23$\pm$0.42 | 8.09$\pm$1.54 | 0.74$\pm$0.56 | 0.02$\pm$0.37
NGC2554 | 11.11 | 0.68 | 9.4$\pm$0.02 | S0/a | AGN | MS | nR | 3.89$\pm$0.43 | 3.85$\pm$0.68 | 5.25$\pm$0.51 | 0.47$\pm$0.35
NGC2595 | 10.9 | 0.12 | 9.57$\pm$0.02 | SABc | … | MS | QnR | 2.96$\pm$0.19 | 7.07$\pm$1.45 | 2.17$\pm$0.75 | 0.24$\pm$0.03
NGC2596 | 10.76 | 0.26 | 9.13$\pm$0.02 | Sb | … | MS | SF | 4.84$\pm$0.80 | 12.95$\pm$6.32 | 3.07$\pm$0.46 | 0.16$\pm$0.07
NGC3300 | 10.76 | -1.75 |  $<$6.84 | SAB | … | RS | fR | … | … | … | …
NGC6427 | 10.63 | -1.85 | 7.39$\pm$0.17 | S0- | … | RS | fR | 1.51$\pm$0.57 | … | 0.97$\pm$0.19 | 0.14$\pm$0.05
NGC7025 | 11.17 | 0.23 |  $<$7.6 | Sa | LINER | MS | nR | … | … | … | …
NGC7194 | 11.25 | -1.14 |  $<$7.86 | E | LINER | RS | fR | … | … | … | …
NGC7311 | 11.12 | 0.36 | 9.1$\pm$0.02 | Sab | LINER | MS | cQ | 2.77$\pm$0.58 | … | 0.99$\pm$0.31 | 0.06$\pm$0.14
NGC7321 | 11.13 | 0.53 | 9.41$\pm$0.02 | SBb | LINER | MS | QnR | 4.86$\pm$1.02 | 6.8$\pm$1.15 | 0.72$\pm$0.61 | 0.02$\pm$0.41
NGC7364 | 11.18 | 0.66 | 9.58$\pm$0.02 | S0/a | … | MS | SF | 2.18$\pm$0.29 | 2.76$\pm$0.47 | 5.55$\pm$0.35 | 0.75$\pm$0.47
NGC7466 | 10.95 | 0.36 | 9.56$\pm$0.02 | Sb | AGN | MS | SF | 4.05$\pm$0.38 | 6.91$\pm$1.10 | 1.51$\pm$0.56 | 0.10$\pm$0.13
NGC7489 | 10.83 | 0.54 | 9.42$\pm$0.02 | Sd | SF | MS | SF | 5.27$\pm$0.64 | 9.78$\pm$2.21 | 1.68$\pm$0.57 | 0.07$\pm$0.11
NGC7625 | 10.32 | 0.21 | 9.33$\pm$0.02 | SAa | SF | MS | SF | 1.13$\pm$0.81 | 0.74$\pm$0.35 | 0.14$\pm$0.11 | 0.01$\pm$0.43
NGC7716 | 10.69 | -0.18 | 7.86$\pm$0.08 | SABb | … | GV | cQ | 1.69$\pm$0.90 | … | 0.69$\pm$0.25 | 0.20$\pm$0.10
UGC00312 | 10.13 | 0.24 | 8.42$\pm$0.06 | SBd | SF | MS | SF | 4.45$\pm$1.09 | 8.72$\pm$4.18 | 1.08$\pm$0.37 | 0.04$\pm$0.14
UGC00335NED02 | 10.66 | -1.26 |  $<$7.58 | E | LINER | RS | nR | … | … | … | …
UGC01123 | 10.73 | -0.87 |  $<$6.73 | Sab | … | RS | MX | … | … | … | …
UGC01368 | 11.21 | 0.53 | 8.93$\pm$0.03 | Sab | … | MS | SF | … | … | … | …
UGC01938 | 10.64 | 0.13 | 8.68$\pm$0.03 | Sbc | … | MS | SF | … | … | … | …
UGC02099 | 11.14 | -0.49 |  $<$7.58 | S0 | … | RS | MX | … | … | … | …
UGC04240 | 10.98 | 0.37 | 9.19$\pm$0.02 | S | … | MS | SF | … | … | … | …
UGC04245 | 10.54 | -0.14 | 9.02$\pm$0.02 | SBb | … | MS | cQ | 6.04$\pm$0.95 | 23.75$\pm$14.75 | 1.45$\pm$0.53 | 0.05$\pm$0.14
UGC04455 | 11.5 | 0.26 |  $<$7.51 | SBa | … | GV | cQ | … | … | … | …
UGC05396 | 10.81 | 0.23 | 8.36$\pm$0.05 | Scd | SF | MS | SF | … | … | … | …
UGC08322 | 11.15 | 0.06 | 8.67$\pm$0.05 | Sa | … | GV | MX | … | … | … | …
UGC08781 | 11.09 | 0.37 | 8.65$\pm$0.13 | SBb | LINER | MS | cQ | 7.29$\pm$1.59 | … | 7.10$\pm$0.67 | 0.23$\pm$0.12
UGC10972 | 10.75 | -0.19 | 8.26$\pm$0.058 | Scd | LINER | GV | cQ | … | … | … | …
UGC11649 | 10.57 | -0.47 | 7.76$\pm$0.19 | SBa | LINER | GV | MX | 6.12$\pm$3.30 | … | 4.45$\pm$0.42 | 0.08$\pm$0.05
UGC11680NED02 | 11.17 | 1.0 | 9.82$\pm$0.02 | E | AGN | MS | SF | 1.55$\pm$0.17 | 1.95$\pm$0.18 | 2.64$\pm$0.54 | 0.52$\pm$0.12
UGC11717 | 11.28 | 0.61 | 9.6$\pm$0.02 | Sc | LINER | MS | MX | 3.79$\pm$0.73 | 4.36$\pm$0.58 | 0.65$\pm$0.52 | 0.02$\pm$0.41
UGC11792 | 10.64 | 0.02 | 8.67$\pm$0.02 | Sc | SF | MS | SF | … | … | … | …
UGC11958 | 11.2 | -0.4 |  $<$7.22 | E | LINER | RS | nR | … | … | … | …
UGC11982 | 10.04 | -0.36 | 7.53$\pm$0.12 | SBcd | … | MS | SF | … | … | … | …
UGC12224 | 10.18 | -0.3 | 9.22$\pm$0.02 | Scd | SF | MS | SF | 5.94$\pm$1.91 | 18.32$\pm$10.46 | 0.67$\pm$0.54 | 0.02$\pm$0.36
UGC12250 | 11.06 | 0.08 | 8.65$\pm$0.1 | SBb | … | GV | cQ | 10.39$\pm$5.26 | … | 1.71$\pm$0.57 | 0.17$\pm$0.09
UGC12274 | 11.09 | -0.69 | 8.47$\pm$0.09 | S | LINER | RS | nR | … | … | … | …
UGC12348 | 11.0 | 0.81 | 9.05$\pm$0.02 | Sa | AGN | MS | MX | … | … | … | …
VV488NED02 | 10.9 | 0.36 | 8.43$\pm$0.03 | SBc | SF | MS | SF | … | … | … | …

Table 2: Main properties of the ACA EDGE galaxies. Column (1): galaxy name.
Column (2) and (3): logarithmic of the total stellar masses and SFRs from
CALIFA. Column (4): logarithmic of the total molecular gas mass as derived
explained in §3.1. Column (5): morphological classification drawn from NED.
Column (6): emission line diagnostics for the optical nucleus spectrum for
CALIFA galaxies by García-Lorenzo et al. (2015), who classify them into star-
forming (SF), active galactic nuclei (AGN), and LINER-type galaxies. These
groups are also complemented by the type-I and type-II AGN classification by
Lacerda et al. (2020). Column (7): Galaxy classification according to
$\Delta$SFR as explained in §4.1.1: main sequence (MS), green valley (GV), and
red cloud (RS). Column (8): Two-dimensional emission line classification from
Kalinova et al. (2021, 2022), who classify galaxies in star-forming (SF),
quiescent-nuclear-ring (QnR), centrally quiescent (cQ), mixed (MX), nearly
retired (nR), and fully retired (fR). Columns (9) and (10): exponential scale
lengths of the molecular gas and stars, respectively, as derived in §4.1.2.
Columns (11) and (12): radius and mass of bulges, as derived in §3.3.

We obtain stellar and molecular gas radial profiles for a subsample of 30
galaxies with inclinations $\leq 70^{\circ}$ and $5\sigma$ integrated CO
detections (see §4.1), which represent well the distributions of stellar
masses and morphologies of the full ACA EDGE sample (see Table 2). We also
select spaxels with $3\sigma$ CO detections. We derive these profiles by
measuring the average azimuthal CO, stellar, and SFR surface densities in
elliptical annuli in the CO(2-1) datacubes. Figure 6 shows the molecular gas
radial profiles (blue solid line) and their $\pm 1\sigma$ uncertainties (blue
shaded areas), which are corrected by inclination (i.e., multiplied by a
factor of cos$(i)$). Annuli are centered on the optical galaxy position and
aligned with the centered major-axis position angle (column 5 in Table 1). We
compute the average $I_{\rm CO(2-1)}$ for a given annulus by summing the
velocity-integrated CO line emission intensities from the total pixels within
an annulus $\sim$5″ wide (average of the minor beam axes), and then we use
Equation 7 (adopting the constant $\alpha_{\rm CO}$ prescription; see §3.1) to
obtain the molecular gas surface density, $\Sigma_{\rm mol}$.

We implement the same method (averaging over all pixels in an annulus) for the
SFR and stars. Stellar and SFR radial profiles are shown in Fig. 6 by the red
solid and brown dotted lines, respectively. We remove SFRs at $r<0.5R_{\rm e}$
for galaxies classified as LINER or AGN (bottom-left corner legend in Fig. 6)
since H$\alpha$ in this region is susceptible to LINER/AGN contamination (see
§4.2.2 for more details).

###  3.3 Bulge radii and masses

In order to test the star-formation quenching mechanisms within the bulge
region (see §4.2.2), we derive the radius of the bulge, $R_{\rm b}$, for the
30 ACA EDGE galaxies included in Figure 6. We characterize the bulge-dominated
region by identifying the galactocentric radius where there is a break with
respect to the stellar radial profiles. Similar to Villanueva et al. (2022),
we adopt $R_{\rm b}=1$ kpc for spiral galaxies where we do not identify a
clear break or they have a predominant bar (e.g., SB galaxies have stellar
radial profiles mostly dominated by bars and stellar disks rather than
bulges). Since previous studies have shown that bulges for spirals are
typically $\lesssim 1.5$ kpc (e.g., Regan et al. 2001; Méndez-Abreu et al.
2017; Villanueva et al. 2021), we use the stellar and SFR maps at CALIFA’s
native resolution of 2.7″ to obtain the best physical resolution available
($\sim 0.9$ kpc at the median distance of ACA EDGE galaxies). Bulge radius
distributions for main sequence and green valley galaxies are centered at
log[$R_{\rm b}/($kpc$)]\sim 0.15$ and $\sim-0.1$, which are slightly larger
than those found by Querejeta et al. (2021), who compute the radius for the
central regions (including small bulges and nuclei) of 74 galaxies nearby
galaxies selected from PHANGS. By implementing a photometric decomposition
using GALFIT (Peng et al., 2010), they obtain a mean value of log[$R_{\rm
center}/r_{25}]\sim-1.5$, which on average is lower than that of our main
sequence galaxies (log[$R_{\rm center}/r_{25}]\sim-1.0$). While ACA EDGE
attempts to reflect the broad range of galaxy morphologies in the local
universe, PHANGS emphasizes late-type spirals of somewhat lower mass
($9.25\leq$log$[M_{\star}/$M${}_{\odot}]\leq 11.25$), which could result in
shorter bulge radii. Finally, red cloud galaxies have the largest bulge radii,
with $R_{\rm b}$ distributions centered at at log[$R_{\rm B}/($kpc$)]\sim
0.35$. These results are consistent with observational evidence. For instance,
Mendel et al. (2013) present a catalog of bulge, disk, and total stellar mass
estimates for $\sim 660,000$ galaxies from SDSS DR7, based on $g$ and $r$-band
photometry published in Simard et al. (2011) and using GIM2D (Simard et al.,
2002). By fitting Sérsic profiles ($n_{\rm S}$; Sersic, 1968) to elliptical,
disk, and bulge$+$disk, they find a Sérsic index distribution centered at
larger values for the former ($n_{\rm S}\sim$5) when compared to the latter
two groups ($n_{\rm S}\sim$1). In addition, Méndez-Abreu et al. (2017)
implement a 2D photometric decomposition using GASP2D (Méndez-Abreu et al.,
2008, 2014) for 404 CALIFA galaxies using $g$, $r$, and $i$ SDSS images,
including 28 ACA EDGE galaxies in their analysis. We obtain a close 1:1
relation when comparing the two sets of bulge radii (OLS $R_{\rm
b,CALIFA}=[0.83\pm 0.10]\times R_{\rm b,ACAEDGE}$), which also show a strong
correlation between them (Pearson $r_{\rm p}=0.92$; $p$-value$<<0.01$).

Figure 7: Top left: SFR-$M_{\star}$ diagram integrated over CALIFA SFR and
stellar maps, color-coded by the total molecular gas mass, $M_{\rm mol}$. The
solid black line is the SFMS fit by Cano-Díaz et al. (2016). Blue, green, and
red dashed areas define main sequence, green valley, and red cloud galaxies,
respectively, as defined by the bands (see §4.1 for more details). Top right:
SFR-$M_{\rm mol}$ relation color-coded by stellar mass. The dashed black
lines, from top to bottom, correspond to molecular gas depletion times
$\tau_{\rm dep}=0.1$, $1.0$, and $10$ Gyr, respectively. Blue, green, and red
circles are the centroids of SFR and $M_{\rm mol}$ values for galaxies with
5$\sigma$ CO detections (filled circles) of the groups as defined by the bands
in the top left panel. The blue and green squares correspond to the centroid
of SFR and $M_{\rm mol}$ values for main sequence and green valley CARMA EDGE
detected galaxies. Bottom: Distributions for the molecular-to-stellar mass
fraction ($R^{\rm mol}_{\star}=M_{\rm mol}/M_{\star}$; left) and the molecular
gas depletion time ($\tau_{\rm mol}=M_{\rm mol}/$SFR; right) for the three
categories (excluding CO upper-limits), as defined in top left panel. Vertical
and horizontal lines correspond to the average values and the standard
deviations of the distributions, respectively. The plots suggest that while
the transition from main sequence to green valley galaxies is mostly driven by
gas removal/depletion, the movement from the latter to the red cloud may be
determined by a reduction in the star formation efficiency of the molecular
gas (SFE${}_{\rm mol}=\tau^{-1}_{\rm dep}$).

Using $R_{\rm b}$, we compute the bulge mass, $M_{\rm b}$, in terms of the
total stellar mass, after numerically integrating the stellar profiles using
Equation 9. Table 2 summarizes the properties of the 60 ACA EDGE galaxies,
together with the values of $R_{\rm b}$ and $M_{\rm b}$ (columns 10 and 11).
Columns (4), (8), and (9) list $M_{\rm mol}$, $l_{\rm\star}$, and $l_{\rm
mol}$, respectively; the latter two are calculated from radial profiles in
§4.1.2.

##  4 Results and Discussion

In the next subsections we present the main properties of the 60 galaxies
included in the ACA EDGE survey. To do so, we divide our results in global
(i.e., quantities derived from integrated measurements) and spatially resolved
(i.e., quantities derived from pixel measurements). Unless otherwise
mentioned, we estimate the molecular gas related quantities by adopting a
constant Milky Way CO-to-H2 conversion factor (see §3.1).

###  4.1 Global quantities and relations

####  4.1.1 SFR versus stellar and molecular gas masses

The top left panel of Figure 7 shows the SFR-$M_{\star}$ relation, color-coded
by $M_{\rm mol}$, using the global values (pixels at $r<r_{25}$) of SFR and
$M_{\star}$ (see §3.1). On average, we note that galaxies near the SFMS (black
line; Cano-Díaz et al. 2016) tend to have higher molecular gas masses,
although there is not a clear region on the SFR-$M_{\star}$ relation
associated with low values of $M_{\rm mol}$ (see color-coded symbols). In
order to characterize the behaviour of the molecular gas as a function of the
difference between the SFR and the SFMS, $\Delta$SFMS$=$ log[SFR]$-$SFMS, we
classify our galaxies in three different groups based on their $\Delta$SFMS,
as shown by shaded areas in top left panel of Figure 7:

  1. 1.

Main sequence (36 galaxies, 34 with $5\sigma$ CO detections; blue shaded
area), which are galaxies with $-0.5$ dex$<\Delta$SFMS.

  2. 2.

Green valley (11 galaxies, 9 with $5\sigma$ CO detections; green shaded area),
encompassing galaxies with $-1.0$ dex$<\Delta$SFMS $\leq-0.5$ dex.

  3. 3.

Red cloud (13 galaxies, 3 with $5\sigma$ CO detections; red shaded area),
which includes galaxies with $\Delta$SFMS $\leq-1.0$ dex.

We choose these boundaries based on the typical values of the main-
sequence/green valley distribution scatters reported in recent studies, which
span from $\sim 0.2$ to $0.7$ dex (e.g., Schawinski et al., 2014; Chang et
al., 2015; Bland-Hawthorn & Gerhard, 2016; Cano-Díaz et al., 2016; Sánchez et
al., 2018; Colombo et al., 2020). The bottom left panel of Figure 7 shows the
distribution of the molecular-to-stellar mass fraction, $R^{\rm
mol}_{\star}=M_{\rm mol}/M_{\star}$, of the three groups for galaxies with
$5\sigma$ CO detections. Main sequence galaxies have the highest molecular gas
masses (with an average log$[R^{\rm mol}_{\star}]\sim-1.6$ dex; blue dashed
line), while on average both green valley and red cloud galaxies have
fractions about an order of magnitude lower (green solid and red dashed
lines).

The top right panel of Fig. 7 shows the SFR-$M_{\rm mol}$ relation, color-
coded by $M_{\star}$. The three dashed black lines correspond to three
different molecular depletion times, $\tau_{\rm dep}=M_{\rm mol}/$SFR = 0.1,
1.0, and 10 Gyr, going from top to bottom, respectively. It is interesting to
note that although most ACA EDGE galaxies are well represented by the
$\tau_{\rm dep}=1$ Gyr line, there is not a characteristic molecular depletion
time for the whole sample. This is confirmed when we analyze the molecular gas
depletion time distributions of the three groups (bottom right panel of Fig.
7); red cloud galaxies have $\tau_{\rm dep}$ around 3 and 6 times longer than
main sequence and green valley galaxies, respectively. However, these results
have to be considered carefully due to the small number of CO-detected red
cloud galaxies.

Our results are consistent with Colombo et al. (2020), who analyze
12CO($J$=2-1) APEX data at 26.3″ resolution (i.e., the region within $R_{\rm
e}$) for 472 EDGE galaxies. They note a strong correlation between
$\Delta$SFMS and the star formation efficiency of the molecular gas,
SFE${}_{\rm mol}=\tau^{-1}_{\rm dep}$, suggesting a scenario where the
transition of galaxies from the main sequence to the green valley is primarily
driven by the molecular gas lost. In addition, they propose that changes in
the SFEmol of the remaining cold gas is what modulates a galaxy’s retirement
from the green valley to the red cloud. Analyzing a compilation of $\sim$8000
galaxies from MaNGA, Sánchez et al. (2018) also note that the SFE decreases as
galaxies move out of the main sequence to the red cloud and pass through the
green valley, which is confirmed by several studies (e.g., Sánchez 2020;
Brownson et al. 2020; Sánchez et al. 2021a; Lin et al. 2022).

####  4.1.2 Exponential scale lengths

If gas removal/depletion is one of the main processes modulating the
transition from main sequence to green valley galaxies, it should impact the
distribution of the molecular gas. To test this, we compute the exponential
scale lengths for the molecular gas, $l_{\rm mol}$, and the stars,
$l_{\star}$, for the ACA EDGE galaxies in Figure 6. Figure 8 shows the
comparison between $l_{\rm mol}$ and $l_{\star}$ for main sequence ACA EDGE
galaxies with $i<70^{\circ}$ and $5\sigma$ CO detections (see §3.2). Galaxies
are color-coded by their $\Delta$SFMS according to the classification
explained in Figure 7. Out of the 30 galaxies with molecular gas and stellar
radial profiles, we have selected 23 galaxies with decreasing $\Sigma_{\rm
mol}$ profiles (i.e., $\Sigma_{\rm mol}$($r<$1 kpc)$>\Sigma_{\rm mol}(r=r_{\rm
max})$, where $r_{\rm max}$ is the largest radius at which we have a $5\sigma$
CO detection). Since we also restrict the $\Sigma_{\star}(r)$ exponential fit
to the stellar disk, we do not consider annuli within prominent bulges (i.e.,
E and S0 galaxies; Regan et al. 2001) and bars (i.e., SB, Sab, and Sbc
galaxies). These fits for $\Sigma_{\rm mol}$ and $\Sigma_{\star}$ profiles are
shown by the black dashed lines in Figure 6. We observe a significant
correlation between $l_{\rm mol}$ and $l_{\star}$ for main sequence and green
valley galaxies (blue and green circles; Pearson $r_{\rm p}=0.6$; $p$-value
$<0.01$). When we compute an ordinary least-square (OLS; blue solid line in
Fig. 8) bisector fit for the model $y=\alpha x$ for main sequence galaxies
with at least $5\sigma$ $l_{\rm mol}$ measurements (symbols with enhanced
color in Fig. 8), we obtain $l_{\rm mol}=(1.24\pm 0.05)\times l_{\star}$. We
test how this relation varies with angular resolution by fitting the CO radial
profiles derived from CO moment 0 maps smoothed at 10″ beamsize. Although
molecular length scales are slightly larger than for stars $l_{\rm
mol}=(1.15\pm 0.05)\times l_{\star}$, the best linear relation is still above
unity.

Figure 8: Comparison between the stellar, $l_{\star}$, and molecular, $l_{\rm
mol}$, scale lengths, computed by fitting exponential profiles to the
respective surface densities as a function of galactocentric radius. Blue
circles and green triangles correspond to 23 ACA EDGE galaxies with
$\Sigma_{\rm mol}>1$ M⊙ pc-2 for all the annuli within 1 kpc. The blue solid
line is the best fit for the model $y=\alpha x$ for main sequence, omitting
galaxies with low-quality $l_{\rm mol}$ fits (symbols with pale colors). The
gray dotted and orange-dotted lines are the best fit relation for CARMA EDGE
(Villanueva et al., 2021) and VERTICO (Villanueva et al., 2022), respectively.
The shaded gray area correspond to the median physical resolution of ACA EDGE
galaxies. On average, the figure shows a $\sim$6:5 relation between the
molecular and stellar scale lengths.

While several studies have found a close 1:1 relation between the molecular
gas and stars in main sequence star-forming galaxy samples based on galaxies
selected from the field (e.g., Young et al. 1995; BIMA Regan et al. 2001;
HERACLES, Leroy et al. 2008; CARMA EDGE, Bolatto et al. 2017; Villanueva et
al. 2021), quenching mechanisms have the potential to affect the distribution
of the molecular gas, atomic gas, and stars in different ways. On the one
hand, environmental mechanisms (e.g., ram pressure stripping, galaxy
interactions, among others) have been shown to compact the spatial extent of
the molecular gas, particularly in high-density environments (e.g., galaxy
clusters; Boselli et al. 2014; Zabel et al. 2022). For instance, Villanueva et
al. (2022) find a $\sim$3:5 relation for the molecular and stellar scale
lengths in a subsample of 28 Virgo Cluster galaxies selected from VERTICO
(Brown et al., 2021). On the other hand, intrinsic mechanisms tend to operate
either by removing (e.g., via AGN activity), re-distributing (e.g., via
stellar feedback), or depleting (e.g., via starvation) the cold gas
reservoirs. Figure 6 shows a broad variety of radial profiles that could be
explained by a different combination of mechanisms depending on the galaxy
$\Delta$SFMS. The best relation between molecular gas and stellar scale
lengths for ACA EDGE main sequence galaxies (blue solid circles in Fig. 8) is
close to a 6:5 relation. Although this is still consistent with the almost
$\sim$1:1 relation from Villanueva et al. (2021), $l_{\rm mol}$ values for ACA
EDGE galaxies are slightly larger when compared to CARMA EDGE spirals. This
seems to be the result of the lower molecular gas content in the central
regions of the former rather than the latter (as shown by the $M_{\rm mol}$
centroids in upper-right panel of Figure 7). This in consequence produces
flatter $\Sigma_{\rm mol}$ profiles in ACA EDGE galaxies than those for CARMA
EDGE, which were mainly selected to be bright in far-IR (i.e. rich in
molecular gas; see §2.1 and Bolatto et al. 2017 for more details).

Figure 9: Left: SFR surface density, $\Sigma_{\rm SFR}$, versus stellar
surface density, $\Sigma_{\star}$, color-coded by the resolved star formation
efficiency of the molecular gas, SFE$=\Sigma_{\rm SFR}/\Sigma_{\rm mol}$, for
pixels with $5\sigma$ CO detections and selected from the 30 galaxies included
in Figure 6. Blue and green density contours are 90%, 60%, and 30% of the
points for main sequence and green valley galaxies. Right: The resolved
SFR-$M_{\rm mol}$ relation, color-coded by the resolved molecular-to-stellar
mass gas fraction, $rR^{\rm mol}_{\star}=\Sigma_{\rm mol}/\Sigma_{\star}$.
Conventions are as in left panel. The black dashed lines corresponds to the
OLS bisector fit for main sequence galaxies using the model $y=\alpha x+\beta$
for the resolved SFMS (left) and the resolved Kennicutt-Schmidt (right)
relations. While the left panel exhibits an increasing in $\Sigma_{\star}$ for
pixels transiting from the main sequence to the green valley, the right panel
shows that pixels from these two populations cover a similar parameter space
although with a mild decreasing in $\Sigma_{\rm SFR}$. This suggests that
changes in star formation activity during the transition are driven not only
by a lowering in the molecular gas, but also due to a decrease of the star
formation efficiency.

###  4.2 Spatially resolved relations

####  4.2.1 SFR versus stellar and molecular gas surface densities

The left panel of Figure 9 shows $\Sigma_{\rm SFR}$ versus $\Sigma_{\star}$
(the so-called resolved SFMS, rSFMS; e.g., Cano-Díaz et al. 2016; Lin et al.
2019; Sánchez et al. 2021c; Ellison et al. 2021a), both in units of M⊙ kpc-2
and color-coded by the resolved star formation efficiency of the molecular
gas, SFE${}_{\rm mol}=\Sigma_{\rm SFR}/\Sigma_{\rm mol}$. The figure includes
pixels from the 30 ACA EDGE galaxies with $5\sigma$ global CO detections and
$i<70^{\circ}$. Similarly to §4.1, we classify pixels according to the
$\Delta$SFMS of the host galaxy as main sequence (blue contours), green valley
(green contours), and red cloud (red contours). Although there is not a
remarkable difference in the $\Sigma_{\star}$ range covered by the main
sequence and green valley pixels, there is a mild decrease in $\Sigma_{\rm
SFR}$ from the former (log$[\Sigma_{\rm SFR}]\sim-2.7$ dex) to the latter
(log$[\Sigma_{\rm SFR}]\sim-3.0$ dex). However, red cloud pixels have the
lowest SFR of all groups. To compare our results with previous studies, we
compute an OLS bisector fit for main sequence pixels using the model $y=\alpha
x+\beta$; we obtain $\rm\log[\Sigma_{\rm SFR}]=(1.20\pm
0.07)\times\log[\Sigma_{\star}]-(12.18\pm 0.60)$ (dashed black line in left
panel of Fig. 9). Our rSFMS best-fit slope, $\alpha_{\rm rSFMS}$, is slightly
higher than those for CARMA EDGE ($\alpha_{\rm rSFMS}\approx 1.01$; Bolatto et
al. 2017), PHANGS ($\alpha_{\rm rSFMS}\approx 1.04$; Pessa et al. 2021), and
other galaxy sample (see Sánchez et al. 2023 and references therein). However,
our results are consistent with the values found in several studies based on
galaxy samples similar to ACA EDGE (e.g. Lin et al. 2019). For instance,
Ellison et al. (2021a) analyze the rSFMS properties of $\sim$15,000 spaxels in
a sample of 29 galaxies selected from the ALMA-MaNGA QUEnching and STar
formation (ALMaQUEST) survey (Lin et al., 2020). Covering the same range of
stellar masses, ALMaQUEST was designed to investigate the star-formation
activity in galaxies from the green valley to the starburst regime,
complementing surveys with a better representation of galaxy properties in the
local Universe (e.g., CARMA EDGE). Implementing an orthogonal distance
regression (ODR) fit for the rSFMS, Ellison et al. (2021a) find
$\rm\log[\Sigma_{\rm SFR}]=(1.37\pm 0.01)\times\log[\Sigma_{\star}]-(13.12\pm
0.10)$, thus resulting in a steeper rSFMS slope (clearly above unity) for high
stellar mass galaxies.

Similarly to the rSFMS, the widely-studied resolved Kennicutt-Schmidt relation
(rKS; e.g., Bigiel et al. 2008; Leroy et al. 2008; Schruba et al. 2011; Pessa
et al. 2021; Sánchez et al. 2021b; Jiménez-Donaire et al. 2023; Sun et al.
2023) presents a complementary way to investigate how the SFR depends on the
ISM. The right panel of Figure 9 contains the rKS relation for ACA EDGE
galaxies, color-coded by the resolved molecular-to-stellar mass fraction,
$rR^{\rm mol}_{\star}=\Sigma_{\rm mol}/\Sigma_{\star}$, and density contours
as in the left panel. It is interesting to note that the OLS bisector fit for
main sequence galaxies also yields a rKS best-fit slope value, $\alpha_{\rm
rKS}$, above unity ($\rm\log[\Sigma_{\rm SFR}]=(1.19\pm
0.07)\times\log[\Sigma_{\rm mol}]-(10.62\pm 0.98)$; dashed black line in right
panel of Fig. 9). Although our $\alpha_{\rm rKS}$ is higher when compared to
that for CARMA EDGE ($\alpha_{\rm rKS}\approx 1.01$; Bolatto et al. 2017),
PHANGS ($\alpha_{\rm rKS}\approx 1.03$; Pessa et al. 2021), and other galaxy
samples from the literature (see Sánchez et al. 2023 and references therein),
it is consistent with the ODR fit for ALMaQUEST galaxies ($\rm\log[\Sigma_{\rm
SFR}]=(1.23\pm 0.01)\times\log[\Sigma_{\rm mol}]-(10.49\pm 0.06)$; Ellison et
al. 2021a). We note however that these results are very sensitive to the
adopted $\alpha_{\rm CO}$ prescription. For instance, Sun et al. (2023) show
that different assumptions of the CO-to-H2 conversion factor can result in
$\alpha_{\rm rKS}=0.9-1.2$, which translates into uncertainties up to 25% in
the CO related quantities of PHANGS galaxies. We also observe a systematic
decrease in both $\Sigma_{\rm SFR}$ and $\Sigma_{\rm mol}$ from the main
sequence to the green valley galaxies. In combination with the results shown
in the left panel, this may suggest that although the transition from main
sequence to the green valley is primarily driven by gas removal, a decrease in
SFEmol also plays a role in modifying the ability of the molecular gas to form
stars (see the color-coded points in left panel of Fig. 10).

####  4.2.2 SFE and bulge properties

Figure 10: Top: The resolved SFEmol versus galactocentric radius for SF pixels
within $R_{\rm b}$, color-coded by their $\Delta$SFMS. Black crosses are
pixels drawn for PHANGS-ALMA spirals. Solid blue and green lines correspond to
90%, 60%, and 30% density contours of main sequence and green valley pixels,
respectively. Dashed lines are density contours for pixels when adopting a
variable $\alpha_{\rm CO}(Z^{\prime},\Sigma_{\rm total})$ prescription (see
Eq. 6). Middle: The resolved SFEmol versus the resolved specific star
formation rate, sSFR, for the same groups as in top panel. Bottom:
Distribution of the resolved molecular-to-stellar mass fraction, $rR^{\rm
mol}_{\star}$, for main sequence and green valley galaxies included in the
upper panel. The vertical and horizontal lines are the mean and the standard
deviation values of the distributions, respectively. We note that the
spatially resolved SFEmol, sSFR, and $rR^{\rm mol}_{\star}$ within the bulges
have a systematic decrease with $\Delta$SFMS, and these trends seem to not
depend on the adopted $\alpha_{\rm CO}$ prescription.

To understand which mechanisms may be driving the star-formation quenching in
ACA EDGE galaxies, we analyze the impact of bulges on the star formation
efficiency of the molecular gas. It is important to mention that SFR
estimators derived from H$\alpha$ have to be taken carefully since they are
susceptible to contamination due to AGN activity, jets, shocks and post-
Asymptotic Giant Branch stars (Lacerda et al., 2020). To perform our analysis
only on star-forming pixels, we have used estimates of the nuclear activity of
CALIFA galaxies from García-Lorenzo et al. (2015) (column 5 in Table 2), who
classify galaxies according to the emission-line diagnostic of the optical
nucleus in star-forming (SF), AGN, and LINER-type galaxies. Although recent
studies have proposed the term LIERs (or “low ionization emission regions”) to
redefine the term “LINER” since the latter is not only limited to nuclear
regions neither restricted to galaxy centers (e.g., Singh et al. 2013;
Belfiore et al. 2016), for simplicity we use hereafter the term LINER. We
complement the AGN classification using Lacerda et al. (2020), who group
CALIFA galaxies as Type-I (galaxies with a broad H$\alpha$ width, i.e.
FWHM$>1000$ km s-1) or Type-II (galaxies above the Kewley et al. 2001 line on
the BPT diagram and H$\alpha$ line width$>3\rm\AA$) AGNs. Although galaxies
may host an AGN and actively form stars, we classify galaxies as SF if no
nuclear activity is detected. We adopt this since we do not see significant
variations between the results for confirmed SF-only galaxies and SF+not-
detected nuclear activity galaxies.

The top panel of Figure 10 shows the resolved SFEmol as a function of
galactocentric radius (in units of $r_{25}$), color-coded by the $\Delta$SFMS
of the host galaxy, for SF-pixels within $R_{\rm b}$. The figure also includes
the SFEmol pixels within the centers (including bulge and nucleus) of PHANGS-
ALMA galaxies drawn from Querejeta et al. (2021) (black crosses), which
complement the ACA EDGE sample by providing data at smaller galactocentric
radii. On average, ACA EDGE green valley pixels have lower efficiencies
compared to those for PHANGS and ACA EDGE main sequence galaxies, with the two
latter covering a similar range of SFEmol. To test how these results depend on
the $\alpha_{\rm CO}$ prescription, we compute the SFEmol by adopting a
variable $\alpha_{\rm CO}(Z^{\prime},\Sigma_{\rm total})$ (see Equation 6), as
shown in the top panel of Figure 10 by dashed contours. On average,
$\alpha_{\rm CO}(Z^{\prime},\Sigma_{\rm total})$ values are lower than for the
fixed prescription at $r\lesssim 1.5R_{\rm e}$ ; consequently, SFEmol are
higher when derived from $\alpha_{\rm CO}(Z^{\prime},\Sigma_{\rm total})$. We
note that green valley galaxies have a slightly higher increase in the
efficiencies than main sequence galaxies ($\sim 0.3$ dex) with the variable
$\alpha_{\rm CO}$, although with the former still having lower SFEmol than the
latter. The middle panel of Figure 10 shows the SFEmol as a function of the
specific star-formation rate, sSFR$=\Sigma_{\rm SFR}/\Sigma_{\star}$, for ACA
EDGE pixels within the bulge region. We note a systematic increase of the
efficiencies with sSFR, going from low SFEmol values for green valley galaxies
(log[SFEmol]$\sim$-10.3 and log[sSFR]$\sim$-12), to high SFEmol values for
main sequence galaxies (log[SFEmol]$\sim$-9.3 and log[sSFR]$\sim$-10.5). Even
though efficiencies are higher when compared to those derived from the fixed
$\alpha_{\rm CO}$, these tendencies do not change when adopting the variable
$\alpha_{\rm CO}$ prescription (as shown by dashed contours in top and middle
panels of Figure 10). These results are in agreement with several studies
reporting lower star formation efficiencies in bulge dominated galaxies (e.g.,
Colombo et al. 2018; Ellison et al. 2021b; Sánchez et al. 2021a). For
instance, Catalán-Torrecilla et al. (2017) report a decrease in the SFRs with
sSFR within bulges of CALIFA galaxies at any $M_{\star}$. Eales et al. (2020)
also find a clear correlation between the star formation efficiency and sSFR
in galaxies without prominent bulges and with the same morphological type. In
addition, they note a strong connection between massive bulges and low SFE.

Are the differences in SFEmol between main sequence and green valley bulges
primarily driven by gas depletion/removal? To test this, we compute the
resolved molecular-to-stellar mass fraction, $rR^{\rm mol}_{\star}=\Sigma_{\rm
mol}/\Sigma_{\star}$, for pixels within the bulge region from these two
groups. The bottom panel of Figure 10 shows the distribution of $rR^{\rm
mol}_{\star}$ of pixels within bulges and adopting the fixed (hatched
histograms) and variable (solid histograms) $\alpha_{\rm CO}$ prescriptions.
On average, $rR^{\rm mol}_{\star}$ values of green valley pixels are $\sim 3$
times lower than those within main sequence bulges when adopting the fixed
$\alpha_{\rm CO}$. Although we note a displacement to the left of the mean
$rR^{\rm mol}_{\star}$ values of the pixel distributions when adopting the
variable $\alpha_{\rm CO}$, the tendencies do not change significantly
($rR^{\rm mol}_{\star}$ values for green valley galaxies are $\sim 5$ times
lower than for main sequence galaxies).

Figure 11: Distributions of the bulge density (in units of M⊙ pc-3), for the
23 main sequence and 5 green valley galaxies included in Figure 6. The
vertical and horizontal lines are the mean and the standard deviation values
of the distributions, respectively. Although we do not see a statistically
significant difference between green valley and main sequence bulge densities,
we note that the former have on average denser bulges than the latter.

Similarly to the morphological quenching proposed by Martig et al. (2009),
numerical simulations performed by Gensior et al. (2020) show that bulges
drive turbulence and increase the gas velocity dispersion, $\sigma_{\rm gas}$,
virial parameter, and turbulent pressure, $P_{\rm turb}$, towards the galaxy
centers. They note that the more compact and more massive (therefore, the more
dense) the bulges are, the higher the level of turbulence. The star-formation
activity is, therefore, “dynamically suppressed” in the innermost parts of
bulge-dominant galaxies due to an increase of the gas turbulence that prevents
the gravitational instabilities. Figure 11 shows the distribution of the bulge
density, $\rho_{\rm b}$, for main sequence and green valley galaxies. To
compute $\rho_{\rm b}$, we assume a spheroidal distribution of the bulge, i.e.
we use $\rho_{\rm b}=M_{\rm b}/(\frac{4}{3}\pi R^{3}_{\rm b})$. Although green
valley galaxies are poorly represented, Figure 11 shows that, on average,
green valley bulges tend to be more dense than those for main sequence
galaxies. These results suggest that, when compared to main sequence pixels,
the lower SFEmol values within green valley bulges are not just a consequence
of a poor molecular gas content. In addition, dynamical suppression may be
reducing the star-formation rate in these regions due to an increase in
$\Sigma_{\star}$ with $\Delta$SFMS (green valley bulges are $\sim 3$ times
denser than those of main sequence galaxies).

Which quenching mechanism is more important? In agreement with our results,
recent studies support the idea that both changes in the gas reservoir and
efficiency are responsible for reduced star formation in the disk of green
valley galaxies. For instance, analyzing CO(1-0) data from the NOrthern
Extended Millimeter Array (NOEMA) and ALMA for 7 nearby green valley galaxies,
Brownson et al. (2020) show that the efficiency of star formation at their
centers is on average three times lower than expected from the rKS (with some
galaxies even up to 10 times less efficient). However, when they compare the
resolved molecular gas main sequence (rMGMS, $\Sigma_{\star}$-$\Sigma_{\rm
mol}$) and the rKS relations, they note that neither changes in the efficiency
nor gas content dominate at $r\gtrsim 0.6R_{\rm e}$. They conclude that while
offsets from the rMGMS appear to dominate in the central regions, the full
extents of the corresponding offsets from the rKS are unconstrained and make
them unable to rank the two drivers in these regions. Similar results are
shown by Lin et al. (2022), who analyze the quenching mechanism in 22 green
valley and 12 main sequence galaxies selected from ALMaQUEST. They note that
the reduction of SFE and $R^{\rm mol}_{\star}$ in green valley galaxies
(relative to main sequence galaxies) is seen in both bulge and disk regions
(although with larger uncertainties). Their results thus suggest that,
statistically, quenching in green valley galaxies may persist from the inner
to the outer regions, and also that both gas depletion/removal and dynamical
suppression are equally important.

####  4.2.3 What drives star-formation quenching in ACA EDGE galaxies?

The six panels in Figure 12 show the resolved SFEmol (top panels), $rR^{\rm
mol}_{\star}$ (middle panels), and the specific star formation rate,
sSFR$=\Sigma_{\rm SFR}/\Sigma_{\star}$ (bottom panels), versus galactocentric
radius (in radial bins of $0.3R_{\rm e}$, $\sim 1.5$ kpc resolution at the
mean distance) for the 30 galaxies included in Figure 6 (i.e. the 30 ACA EDGE
galaxies with $i<70^{\circ}$ and $5\sigma$ CO detections). In order to better
understand the different mechanisms behind star-formation quenching in ACA
EDGE galaxies, we split the panels of Figure 12 into two groups. Panels A, C,
and E include SF galaxies (hereafter no nuclear activity galaxies, NNA; i.e.,
pixels from galaxies without LINER/AGN activity), split by their $\Delta$SFMS
(i.e., main sequence, green valley, and red cloud). Panels B, D, and F include
pixels from NNA, LINER, and AGN galaxies (shaded purple, orange, and yellow
regions, respectively), according to their nuclear activity (column 5 in Table
2).

Figure 12: The resolved star formation efficiency of the molecular gas,
SFE${}_{\rm mol}=\Sigma_{\rm SFR}/\Sigma_{\rm mol}$ (panels A and B), the
resolved molecular-to-stellar mass fraction, $rR^{\rm mol}_{\star}=\Sigma_{\rm
mol}/\Sigma_{\star}$ (panels C and D), and the specific star formation rate,
sSFR$=\Sigma_{\rm SFR}/\Sigma_{\star}$ (panels E and F), in radial bins of
0.3$R_{\rm e}$ ($\sim$1.5 kpc) versus galactocentric radius for pixels from
the 30 galaxies included in Figure 6. The figure is color-coded according to
the three main groups. Panels A, C, and E encompass pixels from 20 galaxies
classified as SF (or with No Nuclear Activity, NNA; see column 5 in Table 2),
split by their $\Delta$SFMS (i.e., main sequence, green valley, and red cloud)
of the host galaxy. Panels B, D, and F include pixels from 30 ACA EDGE
galaxies grouped according to the nuclear activity of the host galaxy. The
grey shaded areas correspond to the regions where our H$\alpha$-based SFR
estimator is susceptible to AGN/LINER contamination, so SFR and quantities
related are only taken as upper-limits. In all panels, the vertical extent of
the shaded areas is the $1\sigma$ scatter distribution for any group. Also,
the vertical black dashed lines are located at $r=R_{\rm e}$, which we use to
divide galaxy regions in central and disk pixels. While efficiencies in main
sequence galaxies remain almost constant with galactocentric radius, in green
valley galaxies we note a systematic increase of SFEmol, $rR^{\rm
mol}_{\star}$, and sSFR, with increasing radius. We also observe slightly
higher SFEmol in the regions near the centers ($0.5R_{\rm e}\lesssim r\lesssim
1.2R_{\rm e}$) of AGNs when compared to their outskirts.

On average, the SFEmol remains almost constant with radius for NNA main
sequence, green valley, and red cloud galaxies (panel A). These results are
consistent with Villanueva et al. (2021); while they do not observe
significant variations of SFEmol with radius in the CARMA EDGE sample, they
also note a systematic decrease in the efficiencies from late- to early-type
galaxies. In addition, panel A shows that green valley galaxies have a mild
increase in SFEmol with radius. While main sequences and green valley galaxies
have similar $rR^{\rm mol}_{\star}$ for $r\gtrsim 1.8R_{\rm e}$ (see panel C),
the latter have significantly lower $rR^{\rm mol}_{\star}$ than the former at
$r\lesssim 1.5R_{\rm e}$. molecular-to-stellar mass fractions for green valley
galaxies can reach values even $\sim$0.8 dex below than those for main
sequence at $r\lesssim 0.5R_{\rm e}$. Similarly, sSFRs show almost the same
radial trends as that of $rR^{\rm mol}_{\star}$ (see panel E). The sSFR values
in green valley galaxies are typically about an order of magnitude below those
of main sequence galaxies ($\sim$1.2 dex). These results suggest that what is
driving the star-formation quenching in green valley galaxies is related to
both a decrease of the SFR (e.g., via changes in the star-formation
efficiency) and gas removal and/or depletion.

Figure 13: SFEmol distributions for pixels from no nuclear activity galaxies
(NNA), split in main sequence (blue bars) and green valley (green bars)
galaxies (from left to right panels, respectively). The two groups are split
by two radial bins according to the breaks identified in Fig. 12, thus between
pixels within the central (hatched unfilled bars) and outer (solid bars)
regions. To compute the SFEmol, we adopt a fixed CO-to-H2 conversion factor
(top panels), and the variable $\alpha_{\rm CO}(Z^{\prime},\Sigma_{\rm
total})$ from Equation 6 (bottom panels). While the distributions of SFEmol
for main sequences pixels within the two radial bins are similar when adopting
the two $\alpha_{\rm CO}$ prescriptions, green valleys show a more clear
bimodal behaviour when using a constant $\alpha_{\rm CO}$.

Similar to panel A of Figure 12, panel B shows that NNA galaxies (mostly
dominated by the main sequence) have on average flat SFEmol profiles. Although
both LINER and AGN galaxies have remarkably high efficiencies in the central
regions ($r\lesssim 0.5R_{\rm e}$; grey shaded area in panels B and F), these
values have to be considered carefully due to LINER/AGN contamination (as
explained in §4.2.2). Consequently, SFEmol (and quantities related) must be
considered only as upper-limits for these two groups within this region. While
LINERs and SFs show a flat SFEmol profile for $r\gtrsim 0.5R_{\rm e}$, AGNs
seem to have significantly lower efficiencies in the range $0.75R_{\rm
e}\lesssim r\lesssim 2.0R_{\rm e}$ than LINER/NNA galaxies, which finally
flatten at larger galactocentric radii. When analyzing $rR^{\rm mol}_{\star}$
as a function of galactocentric radius (shown in panel D), we observe a
systematic inside-out increase of the molecular fractions for with radius for
each of the three groups. However, LINERs/AGNs have $rR^{\rm mol}_{\star}$
values slightly lower than NNA galaxies ($\sim 0.2-0.5$ dex below) for the
galactocentric radius range covered here. We also note that, on average, sSFR
has a similar behaviour as SFEmol, particularly for AGN galaxies which show a
slight decrease of the sSFR with radius (similar to the one seen for SFEmol).
This may be suggesting that AGN activity mitigates the star formation
activity, although not necessarily by impacting the H2 reservoirs (e.g., Bluck
et al. 2020a, b).

Our results are consistent with CALIFA-based studies reporting lower molecular
gas fractions in centers of AGN hosting galaxies when compared to their
outskirts (e.g., Sánchez et al. 2018; Lacerda et al. 2020; Ellison et al.
2021b). However, observational evidence has also shown that the gas content in
AGN hosts can be similar (or even higher) than galaxies without nuclear
activity, either by analyzing the atomic (e.g., Ho et al. 2008; Fabello et al.
2011; Ellison et al. 2019), or molecular (e.g., Maiolino et al. 1997;
Saintonge et al. 2017; Koss et al. 2021; Esposito et al. 2022) gas reservoirs.

Figure 14: SFEmol distributions for pixels from star-forming (i.e., galaxies
with No Nuclear Activity, NNA; purple bars), LINER (orange bars), and AGN
(yellow bars) galaxies (from left to right panels, respectively). Conventions
are as in Fig. 13. While NNA and LINER pixels have similar SFEmol
distributions for the two radial bins and when testing the two $\alpha_{\rm
CO}$ prescriptions, we note a mild bimodal behaviour for AGNs.

These results suggest that the cessation of the star-formation activity has
different modes depending on galaxy substructures, morphological type, and
nuclear activity. NNA main sequence and green valley galaxies have SFEmol
consistent with local star-forming spirals (e.g., Villanueva et al., 2021,
2022), which on average remain constant with radius. Nevertheless, green
valley galaxies show signs of an inside-out increase in their efficiencies. To
better understand these differences, we compute the SFE distributions for NNA
galaxies by splitting them in to central pixels (i.e., pixels at $r<R_{\rm
e}$) and outer pixels (i.e., pixels at $r>R_{\rm e}$). We also test how these
distributions change with the two $\alpha_{\rm CO}$ prescriptions included in
this work (as shown in Figure 13). The distribution of SFEmol for main
sequence galaxies is almost identical when we split their pixels in to two
radial bins at $r=R_{\rm e}$. If we adopt fixed $\alpha_{\rm CO}$ (top
panels), green valley and red cloud pixels show a clear bimodal behaviour. We
test how the SFE distributions change by using the variable $\alpha_{\rm
CO}(Z^{\prime},\Sigma_{\rm total})$ prescription (bottom panels).
Interestingly, we note that green valley galaxies show mild bimodal
distributions. We perform a Student’s $t$-test to verify if the distribution
of SFEmol values in green valley galaxies are drawn from the same parent
population. We obtain $\lvert t\rvert=0.89$ for green valley (degrees of
freedom = $222$) pixel distributions, which is below the critical $t$-value
$t_{\alpha=0.05}\approx 1.96$; we thus can reject the null hypothesis that the
two green valley groups are drawn from the same underlying distribution with
95% confidence. Although these results suggest that morphological quenching
may be acting after the gas removal stage in green valley galaxies (e.g.,
Colombo et al., 2020), the small difference between these two distributions
may be caused by the poor spatial resolution of our CO observations ($\sim$1.5
kpc) when compared to the physical scale required to resolve bulges in ACA
EDGE galaxies ($\lesssim 500$ pc). In addition, some studies (e.g., Cook et
al., 2019, 2020) have discarded a scenario where bulges play a key role in
controlling the star-formation activity, suggesting that this could be
reflecting physical processes more associated with galaxy disks. Finally, when
analyzing the individual SFEmol pixel distributions within $R_{\rm e}$ for the
three green valley galaxies included in left panels of Figure 13 and using the
morphological and bar classification included in Kalinova et al. (2021) for
CALIFA galaxies, we note that spiral galaxies without bars (i.e., NGC 7716)
seem to have higher efficiencies than those with a predominant bar on their
disks (i.e., UGC 12250 and NGC 0171). However, due to the limited galaxy
sample included in this analysis, it is essential that future ACA EDGE survey
studies increase the green valley coverage to derive more statistically
significant conclusions about how structural components (e.g., bars) could
enhance the effects of morphological quenching.

Similarly to Figure 13, Figure 14 includes the SFEmol distributions for two
radial bins, i.e. for pixels within $r<1.2R_{\rm e}$ (hatched histograms) and
at $r>1.2R_{\rm e}$ (solid histograms), in NNA (purple bars), LINER (orange
bars), and AGN (yellow bars) galaxies. We also test how the distributions
change with the two $\alpha_{\rm CO}$ prescriptions. To avoid SFR
contamination due to AGN/LINER, we reject pixels at $r<0.5R_{\rm e}$. While
NNA, LINER, and AGN pixels have similar distributions for the two radial bins
and using the fixed $\alpha_{\rm CO}$ (top panels of Fig. 14), we note signs
of a bimodal behaviour for AGNs if we adopt the variable $\alpha_{\rm
CO}(Z^{\prime},\Sigma_{\rm total})$ prescription (bottom left panel). We
perform a Student’s $t$-test to verify if the AGN distributions are drawn from
the same parent population; we obtain $\lvert t\rvert=1.89$ (degrees of
freedom = $140$), which is lower than the critical $t$-value
$t_{\alpha=0.05}\approx 1.97$. We thus can reject the null hypothesis that the
two AGN groups are drawn from the same underlying distribution. Although
SFEmol values for AGNs are consistent with observational evidence showing that
optical and radio selected AGNs tend to have similar/lower SFRs than typical
main sequence galaxies (e.g., Ellison et al. 2016; Sánchez et al. 2018;
Lacerda et al. 2020), which appears to be mainly due in SFR within galaxy
centers (e.g., Ellison et al. 2018; Sánchez et al. 2018; Kalinova et al.
2021), these results could be also supporting the idea of a slight enhancement
of the star formation in these regions. However, studies have shown that the
impact of AGN ionization can reach as far out as 10s of kpc (e.g., Veilleux et
al., 2003; Husemann et al., 2008; Nesvadba et al., 2011). Although unlikely,
we cannot rule out that the high SFEs we measure at the centers of ACA EDGE
AGNs are due to contamination by AGN emission, even though we have excluded
pixels with $r<0.5R_{\rm e}$.

Morphological quenching has been shown to be a good candidate to explain the
decrease of the SFEmol observed in green valley ACA EDGE galaxies, perhaps via
gas stabilization or dynamical suppression (e.g., Martig et al., 2009; Gensior
et al., 2020; Gensior & Kruijssen, 2021), increasing the turbulent velocity
dispersion of the gas (e.g., Vollmer & Davies 2013), due to a sequence of
short-lived AGN (e.g., Bluck et al. 2020a, b), or a combination of mechanisms
(e.g., Lin et al. 2019). However, the similarity of the SFE distributions
shown in the bottom panels of Figures 13 and 14 (particularly for green valley
galaxies) suggest that these processes have a minimal impact on the
efficiencies. These mechanisms seem to respond to non-long-standing processes
and may only complement the gas depletion and/or removal. In addition, recent
studies have shown that the presence of a classical bulge seems to not be the
only necessary condition for morphological quenching in nearby galaxies. For
example, Kalinova et al. (2022) find that some galaxies with large central
bulges may actually correspond to star-forming systems, and conversely some
galaxies with small spheroids may be quenched. They also note that higher
central surface densities ($\sim 10^{4}$ M⊙ pc-2), no bars, and early-type
morphologies (i.e., no tight and prominent spiral arms) seem to be either
connected or an additional condition for dynamical suppression in galaxies.

Further studies based on CO data within galaxy centers with both higher
resolution and sensitivity than those presented in this work (e.g., at
physical scales $\lesssim 500$ pc) could give us more information about the
dynamical state of the molecular gas within bulges of green valley and red
cloud galaxies. These are essential to disentangle the actual connection
between the SFEmol and the gravitational stability of the gas, or the effects
of AGN in the star-formation activity in detail.

##  5 Summary and conclusions

We present a systematic study of the star formation efficiency and its
dependence on other physical parameters in 60 galaxies from the ACA EDGE
survey. We analyze 12CO($J=2-1$) data cubes and optical IFU data from CALIFA.
Compared to other local galaxy surveys, ACA EDGE is designed to mitigate
selection effects based on CO brightness and morphological type. This results
in a less biased galaxy survey and an ideal sample to investigate the effects
of star-formation quenching on massive local galaxies. We conduct a detailed
analysis to characterize the main properties of the molecular gas by deriving
global (e.g., integrated masses and SFRs) and resolved quantities out to
typical galactocentric radii of $r\approx 3R_{\rm e}$. We use a constant Milky
Way CO-to-H2 conversion factor $\alpha_{\rm CO,MW}=4.3$ M⊙ $(\rm
K\,km\,s^{-1}\,pc^{2})^{-1}$ (Walter et al., 2008) and a Rayleigh-Jeans
brightness temperature line ratio of $R_{21}=I_{\rm CO(2-1)}/I_{\rm
CO(1-0)}\sim 0.65$. We also test the impact of the constant CO-to-H2
conversion factor adopted in our results by using the variable $\alpha_{\rm
CO}(Z^{\prime},\Sigma_{\rm total})$ from Bolatto et al. (2013). We conduct a
systematic analysis to explore molecular and stellar scale lengths, bulge
physical properties, molecular-to-stellar mass fractions, and the SFE of the
molecular gas in ACA EDGE galaxies to compare them with the current
literature. Our main conclusions are enumerated as follows:

  1. 1.

We compute the molecular depletion times, $\tau_{\rm dep}$, of ACA EDGE
galaxies. Although the majority of galaxies have $\tau_{\rm dep}\sim 1$ Gyr,
we find that molecular depletion times varies significantly with distance of
the SFR to the star formation main sequence line, $\Delta$SFMS. Classifying
galaxies as main sequence ($-0.5$ dex$\leq\Delta$SFMS$\leq 0.5$ dex), green
valley ($-1.0$ dex$<\Delta$SFMS$\leq-0.5$ dex), and red cloud
($\Delta$SFMS$\leq-1.0$ dex) galaxies, we note a systematic decrease in the
molecular-to-stellar mass fraction, $R^{\rm mol}_{\star}$, and an increase in
$\tau_{\rm dep}$ with $\Delta$SFMS (see Fig. 7).

  2. 2.

We determine the molecular and stellar exponential disk scale lengths, $l_{\rm
mol}$ and $l_{\star}$, respectively (see Fig. 8). We fit an exponential
function to 23 molecular gas surface density, $\Sigma_{\rm mol}$, and 30
stellar surface density, $\Sigma_{\star}$, radial profiles from the 30 ACA
EDGE galaxies with $5\sigma$ CO detections and inclinations $<70^{\circ}$. We
find a close 6:5 relation between $l_{\rm mol}$ and $l_{\star}$
($l_{\star}=[1.24\pm 0.05]\times l_{\rm mol}$), which is consistent with
previous results from the literature for main sequence spirals (e.g.,
HERACLES, CARMA EDGE).

  3. 3.

We derive the $\Sigma_{\rm SFR}$-$\Sigma_{\star}$ and $\Sigma_{\rm
SFR}$-$\Sigma_{\rm mol}$ relations, the resolved star formation main sequence
(rSFMS) and the resolved Kennicutt-Schmidt (rKS) relations, respectively (see
Fig. 9). We find slopes of $\alpha_{\rm rSFMS}=[1.20\pm 0.07]$ and
$\alpha_{\rm rKS}=[1.19\pm 0.07]$ for the rSFMS and rKS. Although the slopes
for ACA EDGE galaxies are larger than those of spiral star-forming main-
sequence galaxies selected from the field (e.g., CARMA EDGE, PHANGS), they are
consistent with those found in galaxy surveys that are more oriented to
increase the coverage of green valley and red cloud galaxies (e.g.,
ALMaQUEST). However, we remark that these slopes are very sensitive to the
fitting method and the $\alpha_{\rm CO}$ prescription adopted.

  4. 4.

We compute the resolved star-formation efficiency of the molecular gas,
SFEmol, within the bulge region of 23 main sequence and 5 green valley ACA
EDGE galaxies. We find that SFEmol values within green valley bulges tend to
be lower than for main sequence galaxies ($\sim 3$ times lower). The results
suggest that in addition to poor molecular gas content, dynamical suppression
may be reducing the star-formation rate in the bulge region of green valley
galaxies due to a decrease in SFEmol with $\Delta$SFMS (see Fig. 10).

  5. 5.

We compute radial profiles for SFEmol, the resolved molecular-to-stellar mass
fraction $rR^{\rm mol}_{\star}=\Sigma_{\rm mol}/\Sigma_{\star}$, and the
resolved specific star formation rate sSFR$=\Sigma_{\rm SFR}/\Sigma_{\star}$,
for pixels grouped according to their $\Delta$SFMS and nuclear activity (see
Fig. 12). We note a systematic decrease in SFEmol, $rR^{\rm mol}_{\star}$, and
sSFR with $\Delta$SFMS. We also observe a slight inside-out increase in the
efficiencies in green valley galaxies out to $r\approx R_{\rm e}$; from this
point on, SFEmol increases until it reaches similar values to the almost
constant values we observe for main sequence galaxies. Although the
efficiencies of green valley galaxy centers are more similar to those of their
outer disks when we use the variable $\alpha_{\rm CO}(Z^{\prime},\Sigma_{\rm
total})$ prescription, on average their SFEmol distributions show lower
efficiencies in their central regions when compared to both those for their
outskirts ($\sim 2$-3 times lower) and the typical values of main-sequence
galaxies ($\sim 2$ times lower; see Fig. 13).

Our results suggest that although gas depletion and/or removal seem to be the
most important mechanisms behind the cessation of stellar production, they do
not completely explain the star-formation quenching processes in ACA EDGE
galaxies. Complementary mechanisms (such as morphological quenching and/or AGN
feedback) are therefore required to change the physical properties of the
molecular gas, which could impact its ability to form stars in galaxies
transiting through the green valley. The inside-out nature of these processes
is reflected by the decreasing of the SFEmol in the central regions of green
valley galaxies, although this change is dependant on the $\alpha_{\rm CO}$
prescription adopted. Future projects should focus on increasing the early-
type galaxy coverage to improve the statistical significance of these results.
In addition, high resolution CO observations in the central parts of green
valley and red cloud galaxies are essential to better understand how these
mechanisms may impact the stability of the gas at physical scales comparable
to those of molecular clouds ($\lesssim 100$ pc).

V. V. acknowledges support from the scholarship ANID-FULBRIGHT BIO 2016 -
56160020, funding from NRAO Student Observing Support (SOS) - SOSPADA-015, and
funding from the ALMA-ANID Postdoctoral Fellowship under the award
ASTRO21-0062. A. D. B, S. V., and V. V., acknowledge partial support from NSF-
AST1615960. R.C.L. acknowledges support for this work provided by a National
Science Foundation (NSF) Astronomy and Astrophysics Postdoctoral Fellowship
under award AST-2102625. This work is also supported by NSF under the awards
AST-2307440 and AST-2307441.

###  .1 Multi-panel Images

Figures 15 to 22 in this appendix follow the same format as Figure 4, and show
the products for 53 galaxies included in the ACA EDGE survey.

Figure 15: Images for ACA EDGE galaxies. See caption in Figure 4. Figure 16:
Images for ACA EDGE galaxies. See caption in Figure 4. Figure 17: Images for
ACA EDGE galaxies. See caption in Figure 4. Figure 18: Images for ACA EDGE
galaxies. See caption in Figure 4. Figure 19: Images for ACA EDGE galaxies.
See caption in Figure 4. Figure 20: Images for ACA EDGE galaxies. See caption
in Figure 4. Figure 21: Images for ACA EDGE galaxies. See caption in Figure 4.
Figure 22: Images for ACA EDGE galaxies. See caption in Figure 4.

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