The EDGE-CALIFA Survey: Molecular Gas and Star Formation Activity across the Green Valley

We present a 12CO(J = 2−1) survey of 60 local galaxies using data from the Atacama 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. 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, SFEmol = SFR/M mol, and related quantities in galaxies with stellar masses 10 ≤ log[M ⋆/M ⊙] ≤ 11.5 covering the full range of morphological types. We observe a systematic decrease of the molecular-to-stellar mass fraction ( R⋆mol ) with a decreasing level of star formation activity, with green valley galaxies also having 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, α 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⋆mol , and specific SFR 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.


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 condi-tions 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 ⋆ ) in galaxies, the so-called starformation 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 ⋆ and SFR for active star-forming galaxies; "red cloud," where galaxies exhibit low SFRs and no M ⋆ -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 (≲ 100 Myr; e.g.Bluck et al. 2020a,b), or slow ageing (∼ 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 = κσ ϵGΣ (Toomre 1964), where σ is the one-dimensional dispersion velocity of the gas, σ gas , and Σ is the surface density of an infinitelly thin disk; κ is the epicyclic frequency, which is linked to the steepness of the gravitational potential, and is of order the angular velocity Ω. 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 ≫ 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 κ, 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 σ 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 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≈ 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 ana-lyze 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 ΛCDM cosmology, adopting the values Ω Λ = 0.7, Ω DM = 0.3 and H • =69.7 km s −1 Mpc −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 ⋆ , morphology, or IR brightness (e.g., the HERA CO Line Extragalactic Survey, HERACLES, Leroy et al. 2008Leroy et al. , 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. 2011Saintonge et al. , 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 ⋆ regime to study processes associated with galaxy quenching.CALIFA observed over 800 galaxies with IFU spectroscopy at  2017) and Colombo et al. (2020), respectively.The black-solid and dashed-green lines correspond to the best-linear fit for starformation 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 volumecorrect to characterize the star formation activity in nearby massive galaxies.
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 ⋆ /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 (δ < 30 • ) and stellar mass M ⋆ > 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 CAL-IFA; see Fig. 1), which encompasses CO observations for 126 CALIFA galaxies at ∼ 4.5 ′′ resolution but with significant biases.Although CARMA EDGE-selected galaxies cover a broader range of masses (log[M ⋆ /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 HyperLEDA1 and recomputed (when applicable) using fits files from SDSS z-band photometry (see §3.1).

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 ≈ 1980 MHz and a raw spectral resolution of ∼ 1.938 MHz ≈ 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 ∼12 to 18 mK at 10 km s −1 channel width (corresponding to mass surface density of ∼ 0.9 to 1.2 M ⊙ pc −2 ), and from ∼5 ′′ to 7 ′′ angular resolution (i.e., probing physical scales ∼ 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∼1.2 ′ .Finally, we obtain 5σ CO detections for 46 ACA EDGE galaxies, giving a detection rate of ∼ 77%.

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 5.6.1-8for 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 ′′ ) with a relatively high S/N≈ 4 threshold, followed by a single scale clean that uses an automatically generated, more restrictive clean mask and cleans down to S/N≈ 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 5σ 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 ≳ 3.5σ 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: • Hα mask (33 galaxies): We construct a mask using the central Hα velocity map from CAL-IFA, and including around it a velocity region [-FWHM,+FWHM] following the FWHM prescription from Figure 2 in Villanueva et al. (2021).Hα spaxels with SNR< 5 in intensity are excluded from the mask.This approach assumes that the  ) 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.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.
kinematics of the CO are similar to the kinematics of the Hα (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 ′′ 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 HI,max here; Bottinelli et al. 1982Bottinelli et al. , 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 Hα 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.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, σ i , and use the equation Here, N is the number of channels included by the mask and ∆v is the channel width (in km s −1 ).We also compute the velocity (moment 1) and peak signal-to-noise ratio (SNR peak ) 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  2).The figure shows good agreement between ACA and APEX fluxes.However, fluxes measured by APEX are on average ∼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).
where I i,j is the CO intensity in the jth spectral channel of the ith spaxel, v j is the velocity of the jth channel, and M 0 is the moment 0 map.Finally, we blank the pixels outside the 2σ contour for M 0 .We also computed maps of the peak SNR, SNR peak,i , at each position.We use the following equation: where max(I i,j ) is the maximum value of the CO intensity within the spectrum of the ith spaxel.Both velocity and SNR peak maps are included in Figure 4. We compare the 12 CO(2-1) integrated fluxes for ACA EDGE galaxies to those from Colombo et al. (2020), who report 12 CO(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 sur-vey).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 12 CO(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, η mb = 0.80).Finally, we integrate the spectra over a spectral window defined by visual inspection (typically ∼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 nondetections, we estimate 1σ upper-limits by computing the RMS over the velocity window given by V HI,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.

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 ≈ 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 ′′ in an hexagonal shape covering a FoV of a square arcminute.Its average spectral resolution is λ/∆λ ∼ 850 at ∼ 5000 Å for a wavelength range that spans from λ = 3745 to 7300 Å.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 ′′ × 1 ′′ .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 (NED2 ), among others.

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: where F Hα and F Hβ 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 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, Σ 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 Hα and Hβ fluxes applying the following recipe: 1. We select pixels with non-NaN values for F Hα .
3. If F Hβ is a NaN value for a given pixel, then we take the average value of A Hα (for pixels with A Hα > 0.0) of the whole A Hα map.
We obtain the stellar mass surface density, Σ ⋆ , 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 Σ ⋆ 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 Σ ⋆ 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, Σ mol , is derived from the integrated CO intensity, I CO(2−1) , by adopting a constant CO-to-H 2 conversion factor that is based on observations of the Milky Way: X CO = 2 × 10 20 cm −2 (K km s −1 ) −1 , or equivalently α CO,MW = 4.3 M ⊙ (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-H 2 conversion factor from Equation 31 in Bolatto et al. (2013): GMC is the average surface density of molecular gas in units of 100 M ⊙ pc −2 , and Σ total is the combined gas plus stellar surface density on kpc scales.We are also interested in the global variations of α CO (Z ′ , Σ total ).To do so, we adopt Σ 100 GMC = 1 and derive Z ′ 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 Σ mol  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 • ).To do so, we fit an ellipse to the SDSS z-band contour for a major axis A maj ∼ 1.2r 25 .We obtain the ratio between the minor and major axes, A min /A maj , and compute the inclination by taking i = arccos[A min /A maj ] (see column 4 in Table 1).This assumes an infinitely thin disk and introduces errors for i > 85 • , 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 mol , M ⋆ , and SFR (Q i quantities), we use the following equation: 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); Σ i is the surface densities for the pixels within A and i = SFR, mol, or ⋆.
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: where R b is the bulge radius for the stellar component (see §3.3 for more details), and i = mol, ⋆, or SFR.We then calculate the integrated ratios as the ratio of the integrated masses and the SFR.Finally, we compute the resolved SFE mol (in units of yr −1 ) for each pixel, In a similar way, we calculate the resolved molecular-tostellar mass fraction, rR mol ⋆ = Σ mol /Σ ⋆ , and the specific star formation rate, sSFR= Σ SFR /Σ ⋆ (in units of yr −1 ).

Radial profiles
We obtain stellar and molecular gas radial profiles for a subsample of 30 galaxies with inclinations ≤ 70 • and 5σ 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 3σ 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 ±1σ 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 CO(2−1) for a given annulus by summing the velocity-integrated CO line emission intensities from the total pixels within an annulus ∼5 ′′ wide (average of the minor beam axes), and then we use Equation 7(adopting the constant α CO prescription; see §3.1) to obtain the molecular gas surface density, Σ mol .2, respectively).SFRs at r < 0.5Re have been removed for LINER and AGN galaxies since Hα in this region is susceptible to LINER/AGN contamination (see §4.2.2).Galaxies are classified based on their ∆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 ∆SFMS.See also Fig. 12.   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 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 e for galaxies classified as LINER or AGN (bottom-left corner legend in Fig. 6) since Hα in this region is susceptible to LINER/AGN contamination (see §4.2.2 for more details).

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 b , for the 30 ACA EDGE galaxies included in Figure 6.We characterize the bulgedominated 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 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 ≲ 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 (∼ 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 b /(kpc)] ∼ 0.15 and ∼ −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 center /r 25 ] ∼ −1.5, which on average is lower than that of our main sequence galaxies (log[R center /r 25 ] ∼ −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 ≤log[M ⋆ /M ⊙ ] ≤ 11.25), which could result in shorter bulge radii.Finally, red cloud galaxies have the largest bulge radii, with R b distributions centered at at log[R B /(kpc)] ∼ 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 ∼ 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 S ; Sersic 1968) to elliptical, disk, and bulge+disk, they find a Sérsic index distribution centered at larger values for the former (n S ∼5) when compared to the latter two groups (n S ∼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 b,CALIFA = [0.83± 0.10] × R b,ACAEDGE ), which also show a strong correlation between them (Pearson r p = 0.92; p-value<< 0.01).
Using R b , we compute the bulge mass, M 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 b and M b (columns 10 and 11).Columns (4), (8), and (9) list M mol , l ⋆ , and l mol , respectively; the latter two are calculated from radial profiles in §4.1.2.

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-H 2 conversion factor (see §3.1).

SFR versus stellar and molecular gas masses
The top left panel of Figure 7 shows the SFR-M ⋆ relation, color-coded by M mol , using the global values (pixels at r < r 25 ) of SFR and M ⋆ (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 ⋆ relation associated with low values of M 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, ∆SFMS= log[SFR]−SFMS, we classify our galaxies in three different groups based on their ∆SFMS, as shown by shaded areas in top left panel of Figure 7: 1. Main sequence (36 galaxies, 34 with 5σ CO detections; blue shaded area), which are galaxies with −0.5 dex< ∆SFMS.
2. Green valley (11 galaxies, 9 with 5σ CO detections; green shaded area), encompassing galaxies with −1.0 dex< ∆SFMS ≤ −0.5 dex.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 mol = τ −1 dep ).
The bottom left panel of Figure 7 shows the distribution of the molecular-to-stellar mass fraction, R mol ⋆ = M mol /M ⋆ , of the three groups for galaxies with 5σ CO detections.Main sequence galaxies have the highest molecular gas masses (with an average log[R mol ⋆ ] ∼ −1.6 dex; blue dashed line), while on average both green val-ley 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 mol relation, color-coded by M ⋆ .The three dashed black lines correspond to three different molecular depletion times, τ dep = M 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 τ 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 τ 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 12 CO(J=2-1) APEX data at 26.3 ′′ resolution (i.e., the region within R e ) for 472 EDGE galaxies.They note a strong correlation between ∆SFMS and the star formation efficiency of the molecular gas, SFE mol = τ −1 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 SFE mol of the remaining cold gas is what modulates a galaxy's retirement from the green valley to the red cloud.Analyzing a compilation of ∼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).

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 mol , and the stars, l ⋆ , for the ACA EDGE galaxies in Figure 6. Figure 8 shows the comparison between l mol and l ⋆ for main sequence ACA EDGE galaxies with i < 70 • and 5σ CO detections (see §3.2).Galaxies are colorcoded by their ∆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 Σ mol profiles (i.e., Σ mol (r <1 kpc)> Σ mol (r = r max ), where r max is the largest radius at which we have a 5σ CO detection).Since we also restrict the Σ ⋆ (r) exponential fit to the stellar disk, Figure 8.Comparison between the stellar, l⋆, and molecular, l 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 Σ mol > 1 M⊙ pc −2 for all the annuli within 1 kpc.The blue solid line is the best fit for the model y = αx for main sequence, omitting galaxies with low-quality l 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 ∼6:5 relation between the molecular and stellar scale lengths.
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 Σ mol and Σ ⋆ profiles are shown by the black dashed lines in Figure 6.We observe a significant correlation between l mol and l ⋆ for main sequence and green valley galaxies (blue and green circles; Pearson r 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 = αx for main sequence galaxies with at least 5σ l mol measurements (symbols with enhanced color in Fig. 8), we obtain l mol = (1.24± 0.05) × l ⋆ .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 mol = (1.15 ± 0.05) × l ⋆ , the best linear relation is still above unity.
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 highdensity environments (e.g., galaxy clusters; Boselli et al. 2014;Zabel et al. 2022).For instance, Villanueva et al. (2022) find a ∼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 ∆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 ∼1:1 relation from Villanueva et al. (2021), l 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 mol centroids in upper-right panel of Figure 7).This in consequence produces flatter Σ 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).

SFR versus stellar and molecular gas surface densities
The left panel of Figure 9 shows Σ SFR versus Σ ⋆ (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 colorcoded by the resolved star formation efficiency of the molecular gas, SFE mol = Σ SFR /Σ mol .The figure includes pixels from the 30 ACA EDGE galaxies with 5σ global CO detections and i < 70 • .Similarly to §4.1, we classify pixels according to the ∆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 Σ ⋆ range covered by the main sequence and green valley pixels, there is a mild decrease in Σ SFR from the former (log[Σ SFR ] ∼ −2.7 dex) to the latter (log[Σ SFR ] ∼ −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 = αx + β; we obtain log[Σ SFR ] = (1.20 ± 0.07) × log[Σ ⋆ ] − (12.18 ± 0.60) (dashed black line in left panel of Fig. 9).Our rSFMS best-fit slope, α rSFMS , is slightly higher than those for CARMA EDGE (α rSFMS ≈ 1.01; Bolatto et al. 2017), PHANGS (α rSFMS ≈ 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 ∼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 log[Σ SFR ] = (1.37 ± 0.01) × log[Σ ⋆ ] − (13.12 ± 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 mol ⋆ = Σ mol /Σ ⋆ , 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, α rKS , above unity (log[Σ SFR ] = (1.19±0.07)×log[Σmol ]−(10.62±0.98);dashed black line in right panel of Fig. 9).Although our α rKS is higher when compared to that for CARMA EDGE (α rKS ≈ 1.01; Bolatto et al. 2017), PHANGS (α rKS ≈ 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 (log[Σ SFR ] = (1.23 ± 0.01) × log[Σ mol ] − (10.49± 0.06); Figure 9. Left: SFR surface density, ΣSFR, versus stellar surface density, Σ⋆, color-coded by the resolved star formation efficiency of the molecular gas, SFE= ΣSFR/Σ mol , for pixels with 5σ 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 mol relation, color-coded by the resolved molecular-to-stellar mass gas fraction, rR mol ⋆ = Σ mol /Σ⋆.Conventions are as in left panel.The black dashed lines corresponds to the OLS bisector fit for main sequence galaxies using the model y = αx + β for the resolved SFMS (left) and the resolved Kennicutt-Schmidt (right) relations.While the left panel exhibits an increasing in Σ⋆ 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 ΣSFR.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.Ellison et al. 2021a).We note however that these results are very sensitive to the adopted α CO prescription.For instance, Sun et al. (2023) show that different assumptions of the CO-to-H 2 conversion factor can result in α 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 Σ SFR and Σ 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 SFE mol 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).

SFE and bulge properties
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 Hα 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 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 αCO(Z ′ , Σ total ) prescription (see Eq. 6).Middle: The resolved SFE mol versus the resolved specific star formation rate, sSFR, for the same groups as in top panel.Bottom: Distribution of the resolved molecularto-stellar mass fraction, rR mol ⋆ , 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 SFE mol , sSFR, and rR mol ⋆ within the bulges have a systematic decrease with ∆SFMS, and these trends seem to not depend on the adopted αCO prescription.
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 Hα width, i.e.FWHM> 1000 km s −1 ) or Type-II (galaxies above the Kewley et al. 2001 line on the BPT diagram and Hα line width> 3 Å) 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 SFE mol as a function of galactocentric radius (in units of r 25 ), color-coded by the ∆SFMS of the host galaxy, for SFpixels within R b .The figure also includes the SFE mol 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 SFE mol .To test how these results depend on the α CO prescription, we compute the SFE mol by adopting a variable α CO (Z ′ , Σ total ) (see Equation 6), as shown in the top panel of Figure 10 by dashed contours.On average, α CO (Z ′ , Σ total ) values are lower than for the fixed prescription at r ≲ 1.5R e ; consequently, SFE mol are higher when derived from α CO (Z ′ , Σ total ).We note that green valley galaxies have a slightly higher increase in the efficiencies than main sequence galaxies (∼ 0.3 dex) with the variable α CO , although with the former still having lower SFE mol than the latter.The middle panel of Figure 10 shows the SFE mol as a function of the specific star-formation rate, sSFR= Σ SFR /Σ ⋆ , for ACA EDGE pixels within the bulge region.We note a systematic increase of the efficiencies with sSFR, going from low SFE mol values for green valley galaxies (log[SFE mol ]∼-10.3 and log[sSFR]∼-12), to high SFE mol values for main sequence galaxies (log[SFE mol ]∼-9.3 and log[sSFR]∼-10.5).Even though efficiencies are higher when compared to those derived from the fixed α CO , these tendencies do not change when adopting the variable α 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 CAL-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.
IFA galaxies at any M ⋆ .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 SFE mol 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 mol ⋆ = Σ mol /Σ ⋆ , for pixels within the bulge region from these two groups.The bottom panel of Figure 10 shows the distribution of rR mol ⋆ of pixels within bulges and adopting the fixed (hatched histograms) and variable (solid histograms) α CO prescriptions.On average, rR mol ⋆ values of green valley pixels are ∼ 3 times lower than those within main sequence bulges when adopting the fixed α CO .Although we note a displacement to the left of the mean rR mol ⋆ values of the pixel distributions when adopting the variable α CO , the tendencies do not change significantly (rR mol ⋆ values for green valley galaxies are ∼ 5 times lower than for main sequence galaxies).
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, σ gas , virial parameter, and turbulent pressure, P 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, ρ b , for main sequence and green valley galaxies.To compute ρ b , we assume a spheroidal distribution of the bulge, i.e. we use ρ b = M b /( 4 3 πR 3 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 SFE mol 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 Σ ⋆ with ∆SFMS (green valley bulges are ∼ 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, Σ ⋆ -Σ mol ) and the rKS relations, they note that neither changes in the efficiency nor gas content dominate at r ≳ 0.6R 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 mol ⋆ 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 SFE mol (top panels), rR mol ⋆ (middle panels), and the specific star formation rate, sSFR= Σ SFR /Σ ⋆ (bottom panels), versus galactocentric radius (in radial bins of 0.3R e , ∼ 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 • and 5σ 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 ∆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).
On average, the SFE mol 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 SFE mol 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 SFE mol with radius.While main sequences and green valley galaxies have similar rR mol ⋆ for r ≳ 1.8R e (see panel C), the latter have significantly lower rR mol ⋆ than the former at r ≲ 1.5R e .molecular-tostellar mass fractions for green valley galaxies can reach values even ∼0.8dex below than those for main sequence at r ≲ 0.5R e .Similarly, sSFRs show almost the same radial trends as that of rR mol ⋆ (see panel E).The sSFR values in green valley galaxies are typically about an order of magnitude below those of main sequence galaxies (∼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.
Similar to panel A of Figure 12, panel B shows that NNA galaxies (mostly dominated by the main sequence) have on average flat SFE mol profiles.Although both LINER and AGN galaxies have remarkably high efficiencies in the central regions (r ≲ 0.5R 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, SFE mol (and quantities related) must be considered only as upper-limits for these two groups within this region.While LIN-ERs and SFs show a flat SFE mol profile for r ≳ 0.5R e , AGNs seem to have significantly lower efficiencies in the range 0.75R e ≲ r ≲ 2.0R e than LINER/NNA galaxies, which finally flatten at larger galactocentric radii.When analyzing rR mol ⋆ 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, LIN-ERs/AGNs have rR mol ⋆ values slightly lower than NNA galaxies (∼ 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 SFE mol , particularly for AGN galaxies which show a slight decrease of the sSFR with radius (similar to the one seen for SFE mol ).This may be suggesting that AGN activity mitigates the star formation activity, although not necessarily by impacting the H 2 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.
These results suggest that the cessation of the starformation activity has different modes depending on galaxy substructures, morphological type, and nuclear activity.NNA main sequence and green valley galaxies have SFE mol consistent with local star-forming spirals (e.g., Villanueva et al. 2021Villanueva et al. , 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 e ) and outer pixels (i.e., pixels at r > R e ).We also test how these distributions change with the two α CO prescriptions included in this work (as shown in Figure 13).The distribution of SFE mol for main sequence galaxies is almost identical when we split their pixels in to two radial bins at r = R e .If we adopt fixed α 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 α CO (Z ′ , Σ 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 SFE mol values in green valley galaxies are drawn from the same parent population.We obtain |t| = 0.89 for green valley (degrees of freedom = 222) pixel distributions, which is below the critical t-value t α=0.05 ≈ 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), (panels E and F), in radial bins of 0.3Re (∼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 ∆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 Hα-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 1σ scatter distribution for any group.Also, the vertical black dashed lines are located at r = Re, 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 SFE mol , rR mol ⋆ , and sSFR, with increasing radius.We also observe slightly higher SFE in the regions near the centers (0.5Re ≲ r ≲ 1.2Re) of AGNs when compared to their outskirts.
the small difference between these two distributions may be caused by the poor spatial resolution of our CO observations (∼1.5 kpc) when compared to the physical scale required to resolve bulges in ACA EDGE galaxies (≲ 500 pc).In addition, some studies (e.g., Cook et al. 2019Cook et al. , 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 ana-lyzing the individual SFE mol pixel distributions within R 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 essen-Figure 13.SFE mol 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 SFE mol , we adopt a fixed CO-to-H2 conversion factor (top panels), and the variable αCO(Z ′ , Σ total ) from Equation 6(bottom panels).While the distributions of SFE mol for main sequences pixels within the two radial bins are similar when adopting the two αCO prescriptions, green valleys show a more clear bimodal behaviour when using a constant αCO.
tial 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 SFE mol distributions for two radial bins, i.e. for pixels within r < 1.2R e (hatched histograms) and at r > 1.2R 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 α CO prescriptions.To avoid SFR contamination due to AGN/LINER, we reject pixels at r < 0.5R e .While NNA, LINER, and AGN pixels have similar distributions for the two radial bins and using the fixed α CO (top panels of Fig. 14), we note signs of a bimodal behaviour for AGNs if we adopt the variable α CO (Z ′ , Σ 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 |t| = 1.89 (degrees of freedom = 140), which is lower than the critical t-value t α=0.05 ≈ 1.97.We thus can reject the null hypothesis that the two AGN groups are drawn from the same underlying distribution.Although SFE mol 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., Figure 14.SFE mol 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 SFE mol distributions for the two radial bins and when testing the two αCO prescriptions, we note a mild bimodal behaviour for AGNs.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 e .
Morphological quenching has been shown to be a good candidate to explain the decrease of the SFE mol 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 (∼ 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 ≲ 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 SFE mol and the gravitational stability of the gas, or the effects of AGN in the star-formation activity in detail.

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 12 CO(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 ≈ 3R e .We use a constant Milky Way CO-to-H 2 conversion factor α CO,MW = 4.3 M ⊙ (K km s −1 pc 2 ) −1 (Walter et al. 2008) and a Rayleigh-Jeans brightness temperature line ratio of R 21 = I CO(2−1) /I CO(1−0) ∼ 0.65.We also test the impact of the constant CO-to-H 2 conversion factor adopted in our results by using the variable α CO (Z ′ , Σ 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. We compute the molecular depletion times, τ dep , of ACA EDGE galaxies.Although the majority of galaxies have τ dep ∼ 1 Gyr, we find that molecular depletion times varies significantly with distance of the SFR to the star formation main sequence line, ∆SFMS.Classifying galaxies as main sequence (−0.5 dex≤ ∆SFMS≤ 0.5 dex), green valley (−1.0 dex< ∆SFMS≤ −0.5 dex), and red cloud (∆SFMS≤ −1.0 dex) galaxies, we note a systematic decrease in the molecular-to-stellar mass fraction, R mol ⋆ , and an increase in τ dep with ∆SFMS (see Fig. 7).
2. We determine the molecular and stellar exponential disk scale lengths, l mol and l ⋆ , respectively (see Fig. 8).We fit an exponential function to 23 molecular gas surface density, Σ mol , and 30 stellar surface density, Σ ⋆ , radial profiles from the 30 ACA EDGE galaxies with 5σ CO detections and inclinations < 70 • .We find a close 6:5 relation between l mol and l ⋆ (l ⋆ = [1.24± 0.05] × l mol ), which is consistent with previous results from the literature for main sequence spirals (e.g., HERACLES, CARMA EDGE).
3. We derive the Σ SFR -Σ ⋆ and Σ SFR -Σ mol relations, the resolved star formation main sequence (rSFMS) and the resolved Kennicutt-Schmidt (rKS) relations, respectively (see Fig. 9).We find slopes of α rSFMS = [1.20 ± 0.07] and α rKS = [1.19± 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 α CO prescription adopted.
4. We compute the resolved star-formation efficiency of the molecular gas, SFE mol , within the bulge region of 23 main sequence and 5 green valley ACA EDGE galaxies.We find that SFE mol values within green valley bulges tend to be lower than for main sequence galaxies (∼ 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 SFE mol with ∆SFMS (see Fig. 10).
5. We compute radial profiles for SFE mol , the resolved molecular-to-stellar mass fraction rR mol ⋆ = Σ mol /Σ ⋆ , and the resolved specific star formation rate sSFR= Σ SFR /Σ ⋆ , for pixels grouped according to their ∆SFMS and nuclear activity (see Fig. 12).We note a systematic decrease in SFE mol , rR mol ⋆ , and sSFR with ∆SFMS.We also observe a slight inside-out increase in the efficiencies in green valley galaxies out to r ≈ R e ; from this point on, SFE mol 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 α CO (Z ′ , Σ total ) prescription, on average their SFE mol distributions show lower efficiencies in their central regions when compared to both those for their outskirts (∼ 2-3 times lower) and the typical values of main-sequence galaxies (∼ 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 SFE mol in the central regions of green valley galaxies, although this change is dependant on the α 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 (≲ 100 pc).

Figure 1 .
Figure 1.SFR-M⋆ 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⊙] ≈ 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 starformation 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 volumecorrect to characterize the star formation activity in nearby massive galaxies.

Figure 2 .
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.

Figure 3 .
Figure3.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 Table1), and velocities are centered on the stellar redshift.

Figure 4 .
Figure4.ACA EDGE data products for each galaxy.Panels cover an area of 1.25 ′ × 1.25 ′ .The first panel shows the SDSS riz multicolor image with contours from our integrated intensity masked map overlaid.Contours correspond to 2σ and 5σ 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 Table1).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.

Figure 5 .
Figure5.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 Table2).The figure shows good agreement between ACA and APEX fluxes.However, fluxes measured by APEX are on average ∼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).

Figure 6 .
Figure6.Stellar (Σ⋆; red solid line) and molecular gas (Σ 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 (Re), for the 30 ACA EDGE galaxies with 5σ CO detections and inclinations i ≤ 70 • .The blue shaded area is the ±1σ uncertainty.The brown dotted line is the SFR surface density, ΣSFR.The gray shaded area is the region within the bulge radius, R 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 = r25.The code on the left bottom corner corresponds to the Hubble type and the nuclear activity (columns 5 and 6 in Table2, respectively).SFRs at r < 0.5Re have been removed for LINER and AGN galaxies since Hα in this region is susceptible to LINER/AGN contamination (see §4.2.2).Galaxies are classified based on their ∆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 ∆SFMS.See also Fig.12.

Figure 7 .
Figure 7. Top left: SFR-M⋆ diagram integrated over CALIFA SFR and stellar maps, color-coded by the total molecular gas mass, M 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 mol relation color-coded by stellar mass.The dashed black lines, from top to bottom, correspond to molecular gas depletion times τ dep = 0.1, 1.0, and 10 Gyr, respectively.Blue, green, and red circles are the centroids of SFR and M mol values for galaxies with 5σ 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 mol values for main sequence and green valley CARMA EDGE detected galaxies.Bottom: Distributions for the molecular-to-stellar mass fraction (R mol ⋆ = M mol /M⋆; left) and the molecular gas depletion time (τ mol = M 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 mol = τ −1 dep ).

Figure 10 .
Figure10.Top: The resolved SFE mol versus galactocentric radius for SF pixels within R b , color-coded by their ∆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 αCO(Z ′ , Σ total ) prescription (see Eq. 6).Middle: The resolved SFE mol versus the resolved specific star formation rate, sSFR, for the same groups as in top panel.Bottom: Distribution of the resolved molecularto-stellar mass fraction, rR mol ⋆ , 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 SFE mol , sSFR, and rR mol

Figure 12 .
Figure12.The resolved star formation efficiency of the molecular gas, SFE mol = ΣSFR/Σ mol (panels A and B), the resolved molecular-to-stellar mass fraction, rR mol ⋆ = Σ mol /Σ⋆ (panels C and D), and the specific star formation rate, sSFR= ΣSFR/Σ⋆ (panels E and F), in radial bins of 0.3Re (∼1.5 kpc) versus galactocentric radius for pixels from the 30 galaxies included in Figure6.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 Table2), split by their ∆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 Hα-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 1σ scatter distribution for any group.Also, the vertical black dashed lines are located at r = Re, 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 SFE mol , rR mol ⋆ , and sSFR, with increasing radius.We also observe slightly higher SFE in the regions near the centers (0.5Re ≲ r ≲ 1.2Re) of AGNs when compared to their outskirts.

Figures
Figures 15 to 22 in this appendix follow the same format as Figure4, and show the products for 53 galaxies included in the ACA EDGE survey.

Figure 15 .
Figure 15.Images for ACA EDGE galaxies.See caption in Figure 4.

Figure 16 .
Figure 16.Images for ACA EDGE galaxies.See caption in Figure 4.

Figure 17 .
Figure 17.Images for ACA EDGE galaxies.See caption in Figure 4.

Figure 18 .
Figure 18.Images for ACA EDGE galaxies.See caption in Figure 4.

Figure 19 .
Figure 19.Images for ACA EDGE galaxies.See caption in Figure 4.

Figure 20 .
Figure 20.Images for ACA EDGE galaxies.See caption in Figure 4.

Figure 21 .
Figure 21.Images for ACA EDGE galaxies.See caption in Figure 4.

Figure 22 .
Figure 22.Images for ACA EDGE galaxies.See caption in Figure 4.