The ALMaQUEST Survey. XIII. Understanding Radial Trends in Star Formation Quenching via the Relative Roles of Gas Availability and Star Formation Efficiency

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

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

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

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

However, it is important to note that Hα emission can arise from sources other than young stars, such as active galactic nuclei (AGN) and old stellar populations (Kewley et al. 2006; Yan & Blanton 2012). To classify the spaxels based on the powering sources, we follow the method outlined in our previous papers (Bluck et al. 2020a; Lin et al. 2022). In summary, we first utilize the Baldwin–Phillips–Terlevich (BPT) diagnostics, a commonly used tool for distinguishing between different sources of Hα emission. Specifically, we apply the Kewley and Kauffmann star-forming cut based on the [O iii]λ5007/Hβ versus [N ii]λ6584/Hα line ratios (Kauffmann et al. 2003; Kewley et al. 2006) to classify spaxels into star formation, composite, or AGN. Our BPT analysis is limited to spaxels with a signal-to-noise ratio (S/N) greater than 2 for all required emission lines. Star-forming spaxels are defined as those satisfying both the BPT star-forming criteria and an Hα equivalent width (EW) greater than 6 Å (Sánchez 2020; Sánchez et al. 2021). Hα luminosity is used to estimate the Σ_SFR for star-forming spaxels.

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

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

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

The Atacama Large Millimeter/submillimeter Array (ALMA) observations at ¹²CO (J = 1 → 0; 115.271 GHz) were designed to match the point-spread function (25) of the MaNGA observations, allowing for a simultaneous study of spatially resolved star formation and molecular gas properties at the same physical scale (PI: L. Lin—2015.1.01225.S, 2017.1.01093.S, 2018.1.00558.S; PI: S. Ellison—2018.1.00541.S). Detailed information regarding ALMA data reduction and imaging can be found in the survey paper by Lin et al. (2020).

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

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

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

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

$$\begin{eqnarray}&&\mathrm{log}({\mathrm{SFR}}_{{\rm{H}}\alpha })=(-8.96\pm 0.23)+(0.87\pm 0.02)\mathrm{log}({M}_{\star }),\end{eqnarray} \tag{ 1 }$$

where the SFR is in units of M_☉ yr⁻¹ and M_* is in units of M_☉.

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

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

3.1.1. Radial Profiles of Σ_*, ${{\boldsymbol{\Sigma }}}_{{{\bf{H}}}_{{\bf{2}}}}$ _, and Σ_SFR

We begin by analyzing the galaxy radial profiles in the ALMaQUEST sample. Figures 3(a)–(c) present the radial profiles of Σ_SFR, Σ_*, and ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$, respectively. The subsets, namely, SF_h , SF_m , SF_l , and cSB, are denoted by blue, green, red, and yellow colors, respectively. The radial profile is sampled with 0.18 R_e (∼0.8 kpc) steps within 1.5 R_e (∼7 kpc at redshift 0.03). The inclination angle, along with the galaxy's position angle, is considered to deproject the geometries of the galaxies. The radial quantities are determined by calculating the median value ¹³ of the star formation and molecular gas properties within each deprojected annulus. Radial profiles are constructed using all spaxels with valid values, regardless of whether these values were measured, inferred, or represented as upper limits (see Sections 2.2 and 2.3). As mentioned earlier, this is to probe the quenched and gas-deficient regions. For each galaxy, we display the radial properties using thin lines. The median profiles of each subset, which are obtained by taking the median values from the individual profiles, are shown using shaded colored regions. The height of the shaded regions represents the standard error of the mean at each radial bin. Note again that the cSB subset should be considered as a distinct population since the sample was selected based on their radial profiles of local sSFR by design (see Section 2.1).

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The radial profiles of Σ_SFR exhibit a ranking across the explored radial range, with a consistent increase in magnitude from SF_l to SF_m , SF_h , and to cSB galaxies at almost all radii (Figure 3(a)). Notably, the differences between the SF_h , SF_m , and cSB populations are more pronounced in the inner region (<0.5 R_e) of galaxies compared to the outer region (>1.0 R_e), consistent with the finding in previous work with a larger sample size (e.g., Ellison et al. 2018; Wang et al. 2019; Bluck et al. 2020a). Conversely, the Σ_SFR of the SF_l galaxies is significantly lower than that of the other populations at all galactocentric radii. Several SF_h galaxies exhibit a Σ_SFR higher than that of cSB galaxies. However, note that when normalized by Σ_*, these galaxies typically show a lower Σ_sSFR compared to cSB galaxies.

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

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

Taking all of these factors into account, we can deduce that the offsets of SF_l from more star-forming galaxies are likely to be real (e.g., Bluck et al. 2020b), but we refrain from drawing strong conclusions regarding the exact profile and magnitude of this offset. Also, some green valley galaxies in the ALMaQUEST sample have a high inclination (see Figure 2 in Lin et al. 2022). While the inclination and position angle of a galactic disk are taken into account during the construction of the radial profile for individual galaxies, accurately deriving azimuthally averaged radial profiles of Σ_SFR (as well as other physical properties) remains challenging for highly inclined galaxies (Ibarra-Medel et al. 2019; Barrera-Ballesteros et al. 2023).

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

Figure 3(c) displays the radial distribution of ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$. For our galaxies, while there are no dramatic differences observed in the median profiles among the galaxy populations, there is significant individual variation in ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$, ranging from 1–2 orders of magnitude from galaxy to galaxy. This variation can be attributed, at least in part, to the structured and non-smooth disk of the ALMaQUEST galaxies and the clumpy nature of molecular gas (Leroy et al. 2013; Stuber et al. 2023). The dark blue and blue curves in Figure 4 represent the fractions of spaxels with CO detection and those without detection (upper limits), respectively. For cSB, SF_h , and SF_m galaxies, the relative proportions of these two types of spaxels exhibit a considerable degree of similarity across the radial range explored. However, it is noteworthy that SF_l galaxies display notably lower ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ values than the other galaxy populations for R < 1.0 R_e. This reduction in ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ is attributed to the significant presence of CO non-detection in this region, as illustrated in Figure 4 (panel (d)). This is particularly true for the outer regions. Beyond 1.0 R_e, the radial profile of ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ flattens due to the increased prevalence (> 50%) of CO non-detection in this regime. However, it is worth noting that in the inner region, specifically at < 0.5 R_e, the detection of CO emission remains relatively robust in SF_l galaxies, even in the presence of low Σ_SFR.

To summarize, the largely overlapping radial profiles of ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ (shaded lines in Figure 3(c)) suggest that galaxies with the lowest levels of star formation activity (SF_l ) do not consistently display a significant deficit in molecular gas. However, since there is considerable variation in the Σ_SFR profiles (Figure 3(a)), this implies that there must be radial variations in f_gas and SFE, which will be further discussed in the next section.

Finally, while our primary focus is on the median profiles, it is important to note the substantial variation from galaxy to galaxy within a given category. This variation is particularly pronounced for Σ_SFR and ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$, but less so for Σ_*. The diverse morphologies of the galaxies in the ALMaQUEST sample contribute to these diverse profiles due to varied distributions of the clumpy star-forming regions and molecular clouds across their disks (Leroy et al. 2013; Pan et al. 2022; Stuber et al. 2023). Our sample includes a broad spectrum of Hubble types, ranging from T types of −1.6 to 6.5 (S0 to Scd), and features both barred and non-barred galaxies along with different spiral patterns. ¹⁴ Additionally, several galaxies display asymmetric disks, suggesting a history of past interactions (Ellison et al. 2024). Our current sample size is too limited to systematically explore the potential effects of morphology and environment on the radial profiles. However, such analysis can be conducted in a statistically significant manner using the full MaNGA sample. This will be similar to what has been done with the CALIFA galaxies, albeit with a smaller sample size (González Delgado et al. 2016; Sánchez et al. 2021).

3.1.2. Radial Profiles of f_gas, SFE, and Σ_sSFR

In this section, we present the radial profiles of various physical properties derived from Σ_SFR, ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$, and Σ_*. Specifically, we present the radial specific SFR (Σ_sSFR) defined as Σ_SFR/Σ_*. We note that the symbol for surface density, Σ, is not necessary in the expression for the radial (local) sSFR as the per area component cancels out. However, in order to distinguish between the global and local sSFR in this paper, we retain the Σ in the symbol. Additionally, we examine the molecular gas fraction (f_gas) defined as ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$/Σ_* and the SFE defined as Σ_SFR/${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$. Figures 5(a)–(c) illustrate the radial profiles of Σ_sSFR, f_gas, and SFE, respectively. The color scheme and line styles employed are the same as those used in Figure 3. We will begin by examining the results obtained from the non-cSB sample, followed by an examination of the results from the cSB population.

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

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

From the SF_h to SF_m galaxies, the observed decrease in Σ_sSFR with decreasing radius, as illustrated in Figure 5(a), also implies an inside-out quenching scenario, in which star formation ceases in the inner region of the galaxy more pronouncedly than the outer regions. The inside-out quenching scenario is in agreement with previous studies that utilized photometric colors, such as NUV − r or UV-optical gradients, as indicators of star formation profiles (Liu et al. 2016; Pan et al. 2016; Wang et al. 2017). Additionally, studies employing IFU (MaNGA, CALFA, and SAMI) with Σ_sSFR based on emission lines analysis have yielded consistent results (González Delgado et al. 2016; Belfiore et al. 2018; Ellison et al. 2018; Medling et al. 2018; Sánchez et al. 2018; Lin et al. 2019a; Sánchez et al. 2021; Villanueva et al. 2024). Recently, analysis of the stellar-age gradients in late-type galaxies further reinforces the notion of an inside-out cessation of star-forming activity in massive galaxies (Breda et al. 2020; Wang et al. 2022; Lah et al. 2023).

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

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

The radial profile of f_gas consistently shifts vertically downward decreasing global sSFR at almost all radii. Computed using Σ_* and Σ_H2, f_gas demonstrates less sensitivity to completeness and accuracy issues compared to Σ_SFR-related quantities. SF_h and SF_m galaxies show a mild increasing trend with radius within the R < 1.0 R_e regime. However, it is important to note again that caution should be exercised when interpreting the radial profile of f_gas beyond 1.0 R_e in all populations, owing to the decreased accuracy of the medians due to the increase in spaxel without CO detection, as illustrated in Figure 4. For SF_l galaxies, we are not able to precisely quantify their f_gas profile due to a significant number of CO non-detections. Nonetheless, it is evident that SF_l galaxies consistently exhibit lower gas content compared to the other populations across all radii considered. A similar conclusion is reached by other analyses based on CO analyses, as well as those using the dust-to-gas relation as a proxy for molecular gas mass (Saintonge et al. 2017; Sánchez et al. 2018; Lin et al. 2019b; Brownson et al. 2020; Colombo et al. 2020; Lin et al. 2022; Piotrowska et al. 2022). Our finding is further corroborated by the most recent analysis of f_gas radial profiles for green valley galaxies using EDGE-CALIFA data by Villanueva et al. 2024 (see their Figure A4), but note that this study utilizes a smaller sample size.

The radial distribution of SFE also exhibits a clear ranking with global sSFR in Figure 5(c). The median log(SFE yr⁻¹) for SF_h galaxies ranges from approximately −9.5 to −9.0, showing a rather flat profile from the galactic center to the outer regions. The derived constant SFE for SF_h galaxies agrees with that of nearby large normal star-forming galaxies observed at kiloparsec scales (Leroy et al. 2008; Bigiel et al. 2011; Muraoka et al. 2019; Sun et al. 2023). While the disk SFE of SF_m is lower than that of SF_h by only 0.2 dex, a central suppression of SFE is seen, as a result of a decrease (increase) in the amount of star-forming (fully quenched) regions (Figure 5). A recent study by Villanueva et al. (2024), utilizing EDGE-CALIFA data, also observed a systematic increase of SFE with increasing radius in green valley galaxies; in contrast, the SFE in main-sequence galaxies remains almost constant across their disks. Although the radial profile of SFE for SF_l galaxies cannot be determined precisely due to the uncertainty associated with Σ_SFR measurements, it is evident that the SFE of molecular gas in SF_l galaxies is significantly suppressed by at least an order of magnitude compared to normal star-forming galaxies (SF_h ). A similar conclusion is also reached by other studies on both global and radial SFEs (Saintonge et al. 2017; Sánchez et al. 2018; Lin et al. 2019b; Brownson et al. 2020; Colombo et al. 2020; Lin et al. 2022; Piotrowska et al. 2022).

Mathematically, the decrease in f_gas and SFE can be attributed to an increase in the denominator (Σ_* and ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$, respectively) or a reduction in the numerator (${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ and Σ_SFR, respectively). Figure 3(b) provides evidence that, statistically, radial Σ_* remains relatively consistent across the sample. Consequently, any variations in f_gas primarily arise from changes in ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ (as also shown in Figure A1 of our previous paper, Lin et al. 2022). In terms of SFE, both ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ and Σ_SFR exhibit lower values for SF_l galaxies compared to SF_m and SF_h galaxies. Therefore, the observed variations in SFE within our sample are a combined outcome of changes in both ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ and Σ_SFR.

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

Figures 5(b) and (c) show enhancement in both f_gas and SFE for cSB galaxies, the largest enhancements are seen in the inner regions (R < 0.5 R_e), which correspond to the region where Σ_sSFR is most enhanced. This similarity suggests a potential link between the enhanced Σ_sSFR and SFE and/or f_gas in cSB galaxies. We refer readers to Ellison et al. (2020a) for a more detailed analysis and the implications of the link between Σ_sSFR, SFE, and f_gas in cSB.

Finally, it is important to note that star formation and molecular gas can extend beyond the galactocentric radius examined in this study (1.5 R_e), as highlighted in previous works (e.g., Watson et al. 2016; Bacchini et al. 2020; Koda et al. 2022). IFU observations conducted by MaNGA and CALIFA have indicated that Σ_sSFR beyond the radius of > 1.5 R_e is typically lower than that within 1.5 R_e (e.g., González Delgado et al. 2016; Belfiore et al. 2018; Sánchez et al. 2021). Hence, our results are not expected to be strongly influenced by star formation in the outskirts. Furthermore, the comparison of radial profiles between different galaxy populations is valid in this study due to the relatively narrow range of global M_* within the ALMaQUEST sample. Previous studies have shown that the radial profiles of star formation and (molecular) gas properties, including their shapes and magnitudes, depend on the M_* of galaxies (García-Benito et al. 2017; Belfiore et al. 2018; Sánchez et al. 2021; Barrera-Ballesteros et al. 2023). Therefore, such comparisons between galaxy populations (subsamples) should be approached with caution when dealing with a wide range of mass values.

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

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

Figure 6 displays the radial profiles of Δf_gas−ΔSFE for SF_m galaxies on the left and SF_l galaxies on the right. The galaxies are color coded based on their global sSFR, which is related to their distance from the main sequence. The darkness of the curve color increases with global sSFR values. The yellow horizontal shaded region represents the regime (−0.15 < Δf_gas−ΔSFE < 0.15) where Σ_sSFR is determined by the combined effect of both f_gas and SFE. The limit of ±0.15 is approximately twice the typical uncertainty of the Δf_gas−ΔSFE profiles. The choice of this limit should be considered as a conservative choice to avoid the risk of over-interpretation. While the majority of galaxies in both the SF_m and SF_l categories tend to be skewed toward being primarily driven by SFE, there exist diverse configurations in terms of the dominant factors influencing star formation.

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

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

3.2.1. Relative Importance of f_gas and SFE in Individual Galaxies

3.2.2. Relative Importance of f_gas and SFE at Different Radial Ranges

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

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

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

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

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

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

The presence of a stellar bar in galaxies also introduces a complex interplay in star formation quenching (Masters et al. 2010; Fraser-McKelvie et al. 2020). The bar-induced torque drives gas inflows toward the galactic center, enhancing the gas content and star formation in the central region (this phenomenon in fact contrasts with the quenching process we have observed for both molecular gas and star formation here), while depleting the bar region of the gas (f_gas) necessary for star formation (Kuno et al. 2007; Ellison et al. 2011; Zhou et al. 2015; Spinoso et al. 2017; Khoperskov et al. 2018; Chown et al. 2019; George & Subramanian 2021). Conversely, the bar can also induce shocks and shear, which increase the turbulence of the gas in the bar region; this, in turn, stabilizes the gas against gravitational collapse, leading to the suppression of disk star formation by lowering the SFE (Reynaud & Downes 1998; Verley et al. 2007; Haywood et al. 2016). A subset of the ALMaQUEST galaxies has been visually identified as barred galaxies through the Galaxy Zoo project; there is also an increasing possibility (based on Galaxy Zoo) of a galaxy being a barred one from SF_h to SF_m , and to SF_l galaxies. In our forthcoming papers (Hogarth et al. 2024; C. Lopez-Coba et al. 2024, in preparation), we will investigate the properties of these bars in relation to molecular gas and star formation characteristics to gain a deeper understanding of their role in star formation quenching.

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

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

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

While inside-out quenching mode is observed commonly in observations for high-mass galaxies (this work; Belfiore et al. 2018; Brownson et al. 2020; Bluck et al. 2020b; Nelson et al. 2021; Sánchez et al. 2021; Villanueva et al. 2024), both inside-out and outside-in modes are predicted by simulations for galaxies with similar mass to our sample. The outside-in mode is concluded to be a result of a strong truncation in the sSFR profiles at > 1 R_e for some simulated green valley galaxies (Illustris and EAGLE of Starkenburg et al. 2019 and SIMBA of Appleby et al. 2020). The sharp cutoff is present in all AGN feedback variants; therefore, this may have originated from the adopted star formation (rather than AGN) prescriptions (Appleby et al. 2020). Furthermore, it is important to note that there is no detection limit for Σ_SFR in simulations, unlike in observations. The approach of dealing with the observed fully quenched regions (i.e., assigning an extremely low but not zero Σ_SFR) would naturally result in simulated galaxies experiencing quenching to a greater degree than our observational galaxies.

Our most-quenched green valley galaxies (SF_l ) consistently demonstrate lower cold gas content (Σ_H2 and f_gas) compared to other population groups, consistent with findings from simulations (Appleby et al. 2020). Nevertheless, simulations show a rapid decline in ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ and f_gas at radial regimes below approximately <0.6 R_e for both main-sequence and green valley galaxies, with the drop being more pronounced for green valley galaxies. However, our observed data do not exhibit this pronounced decrease in the central ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ and f_gas (Figures 3(c) and 5(b)). This could be due to the overestimate of the feedback/energy injection of the simulated AGNs and their influence in the quenching (Corcho-Caballero et al. 2023a, 2023b). On the other hand, the discrepancy of the central molecular gas between simulated and observed galaxies could potentially be attributed to the assigned CO upper limits for the central quenched regions, which result in an overestimation of ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$, and consequently, f_gas in observations. Nevertheless, the accuracy of ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ is presumed to be high, as the majority of spaxels in the central regions, even within the most-quenched population (Figure 4), are detectable in CO. Simulations have demonstrated that the gas content, including H i, H₂, and CO, of simulated main-sequence and green valley galaxies is sensitive to feedback processes from both star formation and AGN (e.g., Lagos et al. 2015; Crain et al. 2017; Diemer et al. 2019; Davé et al. 2020; Ma et al. 2022). Further investigation is required to understand the discrepancy between observations and simulations, but it is evident that cold gas content and its distribution within a galaxy provide strong constraints on feedback processes and galaxy evolution models.