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

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

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

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

The proportion of retired regions (with D4000-based $\Sigma_{\mathrm{SFR}}$), albeit at a low level, also increases from cSB to 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 $\Sigma_{\mathrm{SFR}}$) exhibits no discernible trend with galaxy populations and remains at a low level, below 20%, across all populations (magenta curves). Hence, the contribution of retired regions and AGN-contaminated regions to Figure 3(a) is comparatively lower in contrast to star-forming and fully-quenched regions.

Taking all of these factors into account, we can deduce that the offsets of 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 high inclination (see Figure 2 in Lin et al. 2022). While the inclination and position angle of a galactic disk are taken into account during the construction of the radial profile for individual galaxies, accurately deriving azimuthally-averaged radial profiles of $\Sigma_{\mathrm{SFR}}$ (as well as other physical properties) remains challenging for highly-inclined galaxies (Ibarra-Medel et al., 2019; Barrera-Ballesteros et al., 2022).

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

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

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

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

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

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

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

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

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

It is challenging to precisely quantify the extent of the decrease in $\Sigma_{\mathrm{sSFR}}$ from SF_m to SF_l due to inherent limitations in the accuracy of $\Sigma_{\mathrm{sSFR}}$ 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., $\Sigma_{\mathrm{sSFR}}$), indicating a global quenching scenario.

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

The radial distribution of SFE also exhibits a clear ranking with global sSFR in Figure 5(c). The median log(SFE/yr^-1) for 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 kpc 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 decease (increase) in the amount of star-forming (fully-quenched) regions (Figure 5). A recent study by Villanueva et al. (2023), utilizing EDGE-CALIFA data, also observes a systematic increase of SFE with increasing radius in green valley galaxies; in contrast, the SFE in main sequence galaxies remains almost constant across their disks. Although the radial profile of SFE for SF_l galaxies cannot be determined precisely due to the uncertainty associated with $\Sigma_{\mathrm{SFR}}$ measurements, it is evident that the SFE of molecular gas in 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; Colombo et al., 2020; Brownson et al., 2020; Piotrowska et al., 2022; Lin et al., 2022).

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

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

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

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

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

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

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

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

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

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