Connecting Compact Star-forming and Extended Star-forming Galaxies at Low Redshift: Implications for Galaxy Compaction and Quenching

Our galaxy sample is selected from the NASA Sloan Atlas (NSA),⁶ which is a galaxy catalog constructed by Blanton et al. (2011) listing physical parameters for more than 640,000 local galaxies based on data from GALEX, SDSS, and the Two Micron All Sky Survey. We select the galaxy sample to locate in the ALFALFA⁷ (Arecibo Legacy Fast ALFA Survey; Giovanelli et al. 2005; Haynes et al. 2011) footprint. Thus, the H i mass of galaxies can be obtained. The left panel of Figure 1 shows the ALFALFA galaxy sample (small red dots) overlapped on the NSA footprint, indicated by all the individual galaxies (small black dots). Here we only use the galaxies of the northern galactic cap from the 70% ALFALFA catalog, since the southern galactic cap of ALFALFA has little overlap with the NSA footprint. The blue solid lines show the boundaries of the ALFALFA footprint, and 258,938 NSA galaxies are within the boundaries.

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The right panel of Figure 1 presents the stellar mass and redshift relation for the NSA sample within the ALFALFA footprint. According to this relation, we select a volume-limited sample with a stellar mass greater than 10^9.5${M}_{\odot }$ and a redshift of 0.02 < z < 0.05 to avoid the Malmquist bias, denoted by blue lines. The upper limit of redshift is selected by considering the redshift range of ALFALFA (z < 0.06), and the lower limit of the stellar mass is selected to include more galaxies. In addition, we exclude the highly inclined galaxies with a minor-to-major axis ratio of less than 0.5 to reduce the influence of the inclination effect on the measurements of ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ (Fang et al. 2013). According to the above criteria, in total 17,609 galaxies are selected. Since ALFALFA is a blind H i survey, we note that only a small fraction (27.5%) of galaxies in the selected sample are detected in 21 cm emission by ALFALFA. We combine the selected sample with the MPA-JHU catalog⁸ (Brinchmann et al. 2004) to obtain the physical quantities of individual galaxies, excluding 9.5% of unmatched sources. These unmatched sources are the galaxies in NSA catalog but not in the MPA-JHU catalog, because the NSA catalog includes galaxies from a series of redshift surveys, such as SDSS DR8, the NASA Extragalactic Database, and the Six-degree Field Galaxy Redshift Survey. Thus, our final sample includes 15,933 galaxies.

The MPA-JHU catalog provides the measurements of the main physical parameters used in this work, including SFR, gas-phase metallicity, and the relevant emission-line fluxes. The SFRs are measured by an updated version of the method of Brinchmann et al. (2004) using the Kroupa initial mass function (Kroupa & Weidner 2003). The measurements of gas-phase metallicity are estimated using the Charlot & Longhetti (2001) model, taken from Tremonti et al. (2004). The stellar masses are drawn from the NSA catalog. The surface mass density within a circular aperture of radius 1 kpc, denoted as ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$, is calculated by directly integrating the light profiles from the innermost point out to 1 kpc, adopting the relation between M_*/L_i (stellar mass divided by i-band luminosity) and the rest-frame g − i color from Fang et al. (2013): log M_*/L_i = 1.15 + 0.79 × (g − i). In practice, we generate the cumulative flux profile at a series of radii and obtain the total flux within 1 kpc by the cubic spline interpolation for the two bands, based on the azimuthally averaged radial surface brightness profile (also known as ProfMean in the output of the SDSS pipeline). The i-band luminosity and g − i color are corrected to the rest frame (Blanton & Roweis 2007) considering the galactic extinction (Schlegel et al. 1998). Our sample is selected to have a redshift of less than 0.05, where the half-width at half-maximum of the SDSS point-spread function (07) is comparable to the aperture of 0.68 kpc. This indicates that the seeing should not heavily affect the reliability of measurements of ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ (see more details in Fang et al. 2013). Although the main result in this work is presented based on the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$, we have also adopted the stellar mass surface density within the effective radius to reproduce the main result and find that our result still holds (see Appendix A). This indicates that our result is not sensitive to the definition of the compactness of galaxies.

Since only the most H i-rich galaxies have been detected in 21 cm emission, we adopt an H i mass estimator for the galaxies unmatched with ALFALFA, using the formula of Catinella et al. (2010): ${\mathrm{log}}_{10}{M}_{\mathrm{HI}}/{M}_{* }=-0.332\times {\mu }_{* ,z}\,-0.240\times (\mathrm{NUV}-r)+2.856$, where M_HI is the H i mass of galaxies, μ_*,z is the stellar mass surface density computed using the half-light radius of SDSS z-band images, and NUV $-r$ is the color between near-UV and SDSS r band. This relation is calibrated using the GASS (the GALEX Arecibo SDSS Survey; Catinella et al. 2010) sample with a scatter of ∼0.3 dex and suggests that galaxies with higher μ_*,z and redder NUV $-r$ color appear to be more H i deficient (Brown et al. 2015). Li et al. (2012) have found that this relation generally works well but underestimates the H i mass for the most H i-rich galaxies with ${\mathrm{log}}_{10}{M}_{\mathrm{HI}}/{M}_{* }\gt 0.0$. However, this should not be a concern, since the most H i-rich galaxies have the observed H i mass from ALFALFA and our purpose is to make a comparison of compact SF and extended SF galaxies.

We quantify the galaxy environment by using two independently derived parameters: the host halo mass and the local overdensity of galaxies. The host halo masses are derived from the SDSS DR7 (Abazajian et al. 2009) group catalog of Yang et al. (2007), which is based on a halo-based group-finding algorithm developed in Yang et al. (2005). The local overdensity (δ) is defined as $\delta =\rho /\bar{\rho }$, where ρ is the local matter density and $\bar{\rho }$ is the mean matter density. The local overdensity used here is drawn from the 3D reconstructed local mass density of SDSS DR7 (Abazajian et al. 2009) with a smoothed scale of 3 Mpc using the approach of a nonlinear, non-Gaussian full Bayesian large-scale structure analysis (Jasche et al. 2010).

Galaxies are bimodally distributed in the SFR–${M}_{* }$ relation (e.g., Brinchmann et al. 2004; Peng et al. 2010; Woo et al. 2013; Bluck et al. 2016), which is widely used to separate SF and quenched populations. The left panel of Figure 2 shows the SFR–${M}_{* }$ relation. As expected, the bimodal distribution of sample galaxies is clearly seen. We adopt the division line from Woo et al. (2013), ${\mathrm{log}}_{10}\mathrm{SFR}=0.64{\mathrm{log}}_{10}{M}_{* }-7.22$ (indicated by the red solid line), to separate SF galaxies and QGs. Thus, 8442 galaxies are classified as SF galaxies, and 7491 galaxies are quenched ones. According to this definition, some so-called "green valley" galaxies are classified into SF type. We have checked our main result by shifting the demarcation line to avoid or largely reduce the mixing effect of green valley galaxies with SF ones and find that the main result still holds. The SF galaxies lie in a tight sequence on the SFR–${M}_{* }$ plane, which is usually known as the star formation main sequence (SFMS). For SF galaxies, we present the median SFR in a series of stellar mass bins, indicated by black circles. We perform a linear fit to the data points,⁹ shown in the black solid line. This black solid line thus represents the normal SFMS of the sample galaxies.

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The right panel of Figure 2 shows the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ relation for SF galaxies (blue dots with gray contours) and QGs (red contours). As shown, linear correlations are clearly seen for both SF and QGs. The QGs reside in a narrow sequence on the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ diagram, while SF galaxies appear to be more scatteredly distributed with respect to the quenched population. Furthermore, the QGs appear to have higher ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ than SF galaxies across the whole stellar mass range. This is in good agreement with the previous finding that the existence of a mature bulge or a dense stellar core is a prerequisite to quench a galaxy (Cheung et al. 2012; Fang et al. 2013; Bluck et al. 2014; Barro et al. 2017). However, there is a significant fraction of SF galaxies that reside in the same region as QGs on the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ diagram. These galaxies are likely in the transitional phase from normal SF galaxies to QGs according to the compaction and quenching scenario. Studying these galaxies would probably give instructions on galaxy compaction and star formation quenching. Thus, we separate SF galaxies into two subsamples: the compact SF galaxies (cSFGs) and extended SF galaxies (eSFGs). We emphasize that the definition of compact galaxies is not based on galaxy radius, but on the central surface stellar mass density throughout this paper. The demarcation line is indicated by the black solid line, which is parallel to but 0.2 dex lower than the best-fit relation of ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ for QGs (the red solid line). This demarcation is selected to be in line with the bottom envelop of the red contour enclosing 75% of the quenched population. Although this demarcation is manually determined, it excellently distinguishes the Sérsic index of cSFGs and eSFGs (see details in Appendix B), suggesting that the classification is reasonable. Overall, the sample galaxies consist of three subsamples: 3452 cSFGs, 4990 eSFGs, and 7491 QGs.

The SF galaxies and QGs are found to have different sizes at both low and high redshift (e.g., Toft et al. 2007; Williams et al. 2010; Newman et al. 2012; van der Wel et al. 2014; Shibuya et al. 2015), suggesting the coevolution of the size and star formation status of galaxies. The left panel of Figure 3 presents the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ diagram of SF galaxies with the color-coding of the Petrosian radius (R_r,90), defined as the radius containing 90% of the Petrosian luminosity based on the SDSS r-band image. Here we use R_r,90 rather than half-light radius because R_r,90 is better representative of the global size of galaxies. The black dashed curves indicate the contours of constant R_r,90 on the diagram. As expected, at fixed stellar mass, the R_r,90 is dramatically decreasing when galaxies are getting more compact, indicating that the cSFGs are much smaller in size than eSFGs at a given stellar mass. This result can be seen more clearly in the right panel of Figure 3, where the R_r,90 as a function of stellar mass for eSFGs (blue squares), cSFGs (green circles), and QGs (red triangles) are shown. The representative scatter of the R_r,90–${M}_{* }$ relation is denoted in the lower right corner for each population. As shown, eSFGs have systematically higher R_r,90 than cSFGs (for up to 0.3 dex), while the cSFGs show a similar global size to QGs almost in the whole stellar mass range.

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Assuming that eSFGs need to evolve to cSFGs before quenching, eSFGs are becoming more and more compact, mainly via two approaches: the in situ star formation in their central regions and/or the shrinkage of their sizes with the radial migration of stars. These two different approaches result in different evolution tracks of eSFGs on the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ diagram. For a given eSFG in the lower left corner of the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ diagram, we naturally assume that it evolves with both increasing stellar mass and increasing ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ as time goes on. If the eSFG assembles its stellar mass only via in situ star formation on its stellar disk, the global size should not be changed, and then it would evolve along the contours of constant R_r,90 (see the dashed curves in the left panel of Figure 3). If the eSFG were getting compact mainly via the size shrinkage (possibly along with in situ star formation or mergers), it would evolve along a track that is steeper than the contours of constant R_r,90. In the case the eSFG evolves along a track flatter than the contours of constant R_r,90, which means that its stellar mass and size are growing without prominent growing of ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$, which is in good agreement with the inside-out growth scenario (e.g., Pérez et al. 2013; Goddard et al. 2017; Wang et al. 2018a). Thus, although the cSFGs are defined by using ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$, the compaction process discussed in this work includes the above two approaches of compaction.

The SFR and gas-phase metallicity are two basic properties of SF galaxies. SFR reflects the present growth rate of the stellar mass of galaxies, while metallicity plays an important role in many fundamental physical processes that regulate galaxy evolution, including gas cooling, star formation, and dust formation. The tight SFMS established at both low and high redshift (e.g., Brinchmann et al. 2004; Daddi et al. 2007; Salim et al. 2007; Elbaz et al. 2011) suggests that the bulk of star formation in the universe occurs in a quasi-steady state (Noeske et al. 2007) and that the fraction of the lifetime for a given SF galaxy during which it lies significantly above the SFMS is small. Similarly, the strong correlation between stellar mass and gas-phase metallicity has been found for decades (e.g., Lequeux et al. 1979; Tremonti et al. 2004; Ellison et al. 2008). The drop of metallicity at the low stellar mass end is usually interpreted as evidence for the ubiquity of galactic winds and their feedback in removing metals from galaxy potential wells. Thus, investigating these two scaling relations for cSFGs and eSFGs would provide clues for the compaction process under the compaction and quenching scenario.

The left two panels of Figure 4 show the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ relation for SF galaxies color-coded by SFR and gas-phase metallicity, respectively. At fixed stellar mass, the SFR appears to show no or very weak dependence on ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$, suggesting that cSFGs and eSFGs appear to have similar SFRs at fixed stellar mass as a whole, given their different structural properties. In contrast, the gas-phase metallicity is sensitive to ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ at the low stellar mass end (${M}_{* }$ < 10^10.5${M}_{\odot }$), with higher ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ corresponding to higher gas-phase metallicity. This indicates that cSFGs are more metal-rich than eSFGs at the low stellar mass end. We note that there is a lack of valid measurements of metallicity at the high-mass end (see the bottom left panel of Figure 4), which is due to the fact that the computing of metallicities requires galaxies to have 5σ detection of the emission lines for Hα, Hβ, and [N ii] (Tremonti et al. 2004).

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These results can be more clearly seen in the right two panels of Figure 4, where the median SFR–${M}_{* }$ and $12+\mathrm{log}({\rm{O}}/{\rm{H}})$-${M}_{* }$ relations are presented for cSFGs (green circles) and eSFGs (blue squares). As shown, the SFRs of cSFGs appear to be at most slightly higher than those of eSFGs (with an average of 0.06 dex), while we note that this result is preserved over the whole stellar mass range especially at the high stellar mass end. This indicates that under the compaction and quenching scenario, galaxies sustain or even slightly enhance their star formation activities during the evolution from eSFGs to cSFGs. In contrast, for the $12+\mathrm{log}({\rm{O}}/{\rm{H}})$–${M}_{* }$ relation, the pronounced differences between the two populations are shown. The differences become less significant with increasing stellar mass. Specifically, cSFGs are more metal-rich at ${M}_{* }$ ∼ 10^9.6${M}_{\odot }$ than eSFGs for ∼0.19 dex, while the gas-phase metallicities of the two become comparable to each other at ${M}_{* }$ ∼ 10^10.5 ${M}_{\odot }$. This finding is consistent with the result of Ellison et al. (2008) that the gas-phase metallicity strongly depends on the galaxy half-light radius, in the sense that more compact galaxies are more metal-rich at fixed stellar mass. Furthermore, the metallicity difference can be as large as 0.2 dex, which is roughly equal to what we find here. The dominated mechanism of this finding is still under debate (Ellison et al. 2008; Yabe et al. 2012; Sánchez Almeida et al. 2014; Wang et al. 2017; Sánchez Almeida & Dalla Vecchia 2018), which is likely a combined effect of metal-poor gas accretion, metal-rich gas outflow, and the metal enrichment from current star formation activities. However, the metallicity difference between cSFGs and eSFGs vanishes at stellar masses greater than 10^10.5${M}_{\odot }$. This is likely due to the fact that the metallicities from the MPA-JHU catalog are measured based on the 3'' fiber spectra, which could not represent the global metallicity for large galaxies. Considering that SF galaxies with a large stellar disk usually have a significant metallicity gradient (e.g., Sánchez et al. 2014; Carton et al. 2018), we suspect that the cSFGs likely have higher global metallicity than eSFGs even at high stellar mass if the metallicities are measured within the apertures that cover the whole galaxies (Wang et al. 2017).

Although the median SFRs of the two populations are similar at fixed stellar mass, the distribution of SFR of the two can be different. Indeed, we have checked the distribution of SFR for cSFGs and eSFGs at a given stellar mass and find that the SFR of cSFGs is more broadly distributed at the high-SFR end with respect to that of eSFGs. This is also confirmed by the standard deviation of SFR for cSFGs and eSFGs, shown in Figure 7. We will discuss this in detail in Section 4.1.

The cold gas in galaxies is the fuel to sustain their star formation (e.g., Sancisi et al. 2008; Conselice et al. 2013; Wang et al. 2013, 2015). Galaxies are usually quenched by exhausting or heating their cold gas, removing their cold gas, or stabilizing the gas disk against gravitational instabilities to suppress star formation. Thus, investigating the cold gas properties in galaxies is one of the most important keys to uncovering the process of star formation quenching. For instance, by using H i spectral stacking of a sample of early-type galaxies in the ALFALFA footprint, Fabello et al. (2011) did not find evidence that galaxies with a prominent bulge component are less efficient in turning their cold gas reservoirs into stars, which appears to be inconsistent with the "morphological quenching" picture (Martig et al. 2009). In this subsection, we will examine the H i properties of cSFGs and eSFGs and the possible evolution of gas content during the compaction process under the compaction and quenching scenario.

Since just a small fraction of the sample galaxies are matched with ALFALFA galaxies, we could not obtain the H i properties for each of the sample galaxies. This means that direct comparison of the observed H i content for all the cSFGs and eSFGs is not valid. Alternatively, we introduce a parameter, the H i detection rate, defined as the fraction of galaxies that are detected by the ALFALFA survey for a given subsample. Thus, for a given subsample of fixed stellar mass, the higher H i detection rate usually corresponds to the higher averaged H i content, since ALFALFA is a blind H i survey. Due to the detection limit of ALFALFA, there is a lack of H i sources with the H i mass below 10^9.7${M}_{\odot }$ at a redshift of 0.05, indicating that the detection limit of H i gas is ∼10^9.7${M}_{\odot }$ by this redshift. Thus, in order to reduce the effect of the detection limit, galaxies only with H i mass greater than 10^9.7${M}_{\odot }$ are treated as H i detected sources. In this way, there are in total 19.1% of cSFGs and 35.8% of eSFGs treated as H I detected sources.

The top left panel of Figure 5 shows the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ diagram with the color-coding of the H i detection rate. At fixed ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$, the H i detection rate slightly increases with increasing stellar mass, which is consistent with the fact that more massive SF galaxies usually host more H i gas (Catinella et al. 2010; Wang et al. 2015). However, at fixed stellar mass, the H i detection rate shows a rapid decline with increasing ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$. This result can be clearly seen in the top right panel of Figure 5, where the H i detection rate as a function of stellar mass for cSFGs and eSFGs is presented. As shown, the eSFGs exhibit a higher H i detection rate with respect to cSFGs, suggesting that eSFGs are on average more gas-rich than cSFGs. The bottom left panel of Figure 5 presents the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ diagram color-coded with the H i mass. The H i masses for galaxies with undetected 21 cm emission in ALFALFA are estimated by adopting the relation (see Section 2.2) from Catinella et al. (2010). As shown, the H i mass is strongly anticorrelated with ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$, indicating that eSFGs tend to be more H i-rich than cSFGs. Indeed, as shown in the bottom right panel of Figure 5, the eSFGs have higher median H i mass than cSFGs for ∼0.3 dex, which confirms the result found in the top two panels of Figure 5.

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We conclude that eSFGs are more H i-rich than cSFGs, which is consistent with the compaction and quenching scenario assuming that galaxies evolve along the direction of cold gas consumption.

Galaxies residing in different environments have different prevalences of quenched populations (e.g., Peng et al. 2010; Woo et al. 2015; Wang et al. 2018c), indicating that environmental effects play an important role in quenching a galaxy. The fraction of QGs is found to be correlated with halo mass and anticorrelated with halo-centric radius (e.g., Weinmann et al. 2006; van den Bosch et al. 2008; Wetzel et al. 2012; Kauffmann et al. 2013; Wang et al. 2018a, 2018c), indicating that galaxies residing in the inner region of massive halos are more likely to be quenched with respect to galaxies in the outer region of similar halos or the inner region of less massive halos. Not only working on the star formation quenching, environmental effects are believed to effectively transform the morphology of galaxies from disk-like to spheroid-like. For instance, major mergers can efficiently transform the SF disk galaxies to quenched ellipticals. In addition, numerical simulations have shown that disk galaxies in a rich cluster would suffer from frequent encounters with member galaxies and the cluster's tidal field (also known as galaxy harassment), along with a complete morphological transformation from disks to spheroids (e.g., Moore et al. 1996, 1998; Fujita 1998). However, it is still unclear what the role of environment is in the compaction process. In this subsection, we will examine the environment of cSFGs and eSFGs and try to find out whether the environment plays a key role in the compaction process under the scenario of compaction and quenching.

The left two panels of Figure 6 show the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ relation for SF galaxies with the color-coding of the host halo mass and the local overdensity. As shown, the host halo mass of both cSFGs and eSFGs strongly depends on stellar mass, while the overdensity of the two populations shows no or very weak dependence on the stellar mass. Specifically, the halo mass of SF galaxies shows a dramatic drop at a stellar mass of ∼10^10.3${M}_{\odot }$. This is because satellite galaxies dominate the galaxy population at the low stellar mass end, while central galaxies dominate the population at the high stellar mass end (Yang et al. 2009). We note that most of central galaxies with log₁₀ M_*/M_⊙ < 10.2 do not have a valid value of halo mass. These galaxies are not included in generating the top right panel of Figure 6, leading to a boost of halo mass at the low stellar mass end. In contrast, the overdensity of SF galaxies is almost independent of stellar mass, which seems to be inconsistent with the dependence of halo mass on stellar mass. Actually, this discrepancy is due to the exclusion of central galaxies with invalid halo mass at the low stellar mass end when generating the stellar mass-halo mass relation. In the present work, we do not divide galaxies into centrals and satellites because centrals and satellites are found to exhibit similar quenching behaviors when both halo mass and stellar mass are controlled (Hirschmann et al. 2014; Knobel et al. 2015; Wang et al. 2018a, 2018c). More importantly, at fixed stellar mass, the halo mass and/or overdensity of SF galaxies exhibit no or very weak dependence on ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$, indicating that cSFGs and eSFGs reside in halos of similar mass with similar overdensities. This result can be more clearly seen in the right panels of Figure 6, where the median halo mass and overdensity as a function of stellar mass for cSFGs, eSFGs, and QGs are shown. We find that the QGs more likely reside in more massive halos (or regions with higher matter densities) with respect to cSFGs or eSFGs at the low stellar mass end (${M}_{* }$ < 10^10.5${M}_{\odot }$), suggesting an environmentally driven quenching mechanism especially for less massive galaxies. However, we find that the environments of cSFGs and eSFGs do not show significant differences, suggesting that environmental effects do not play a major role in the compaction process under the scenario of compaction and quenching at least for the low-redshift universe.

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In Section 3.2, we find that cSFGs appear to have a slightly higher SFR than eSFGs. However, the SFR distribution of cSFGs and eSFGs can be different. We present the standard deviation of the SFR as a function of stellar mass for cSFGs and eSFGs in the left panel of Figure 7. The scatter of SFMS shown here is ∼0.3 dex, which is broadly consistent with the previous findings of 0.2–0.3 dex (e.g., Noeske et al. 2007; Whitaker et al. 2012; Speagle et al. 2014). As one can see, the standard deviations of SFR for cSFGs are systematically higher than those of eSFGs almost over the whole stellar mass range, suggesting that cSFGs have wider SFR distribution than eSFGs at fixed stellar mass. Indeed, we check the distribution of the two populations on the SFR–${M}_{* }$ diagram and find that 288 (∼8.3%) cSFGs lie above the normal SFMS for 0.5 dex, while only 86 (∼1.7%) eSFGs lie above the normal SFMS for 0.5 dex, indicating that galaxies with the most intense star formation activities tend to be cSFGs, rather than eSFGs at a given stellar mass (see Figure 2). This result is confirmed by the normalized distribution of ΔSFR, defined as the deviation from the normal SFMS in logarithmic space, for eSFGs and cSFGs. This result is also in good agreement with the cosmological simulations of Tacchella et al. (2016b), who found that galaxies in the upper envelope of the SFMS tend to be compact at a redshift of >1. We have checked the morphologies of these cSFGs with ΔSFR > 0.5 dex by visual inspection and find that only a few of them (<10%) exhibit clear features of an ongoing major merger.

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In the right panel of Figure 7, we present the SFR–${M}_{* }$ relation for SF galaxies with the color-coding of H i depletion time. The H i depletion time¹⁰ is computed assuming that (1) galaxies sustain their current SFR and (2) the replenishment of cold gas is negligible (Tacchella et al. 2016b). We do not consider the contribution of helium and the molecular gas in the calculation. As shown, the H i depletion time for galaxies with the most intense star formation activities can be as low as 1 Gyr. These galaxies are dominated with cSFGs and have strong star formation activities, suggesting that they likely suffer from the ongoing compaction along with the rapid buildup of their stellar cores (or bulges) and the rapid cold gas consumption.

In addition, we examine the median gas depletion time for cSFGs and eSFGs with the above assumptions. We find that the H i depletion time only weakly depends on stellar mass, with the median H i depletion time of ∼4 Gyr for cSFGs and ∼8 Gyr for eSFGs. This suggests that cSFGs are statistically closer to the quenched population than eSFGs along the evolution track. However, in computing H i depletion time, we assume that SF galaxies sustain their current SFR, which is not true in the real universe. Indeed, by investigating the simulated SF galaxies of high redshift (z > 1), Tacchella et al. (2016b) proposed that SF galaxies go up and down across the normal SFMS before quenching their star formation. Observationally, we find a small but significant fraction of cSFGs that lies above the normal SFMS by 0.5 dex. This suggests that the fraction of the lifetime for a cSFG during which it lies significantly above the normal SFMS is small but significant, assuming that lying significantly above the normal SFMS is a period of a SF galaxy during its lifetime. If this is the case, the cSFGs consume a bulk of their cold gas and build their stellar cores in a short timescale when they lie significantly above the normal SFMS, and subsequently they are back to the normal SFMS or even lower. Thus, it is not necessary to take 4–8 Gyr to quench a galaxy, because a bulk of its cold gas can be consumed in a short timescale when it lies significantly above the normal SFMS.

Assuming that galaxies evolve from eSFGs, through cSFGs, to the quenched population, the relative number of eSFGs and cSFGs would give instructions on the timescale of compaction and quenching. The fraction of cSFGs takes the proportion of ∼21.6% of the whole sample and ∼40.9% of all the SF galaxies, indicating that cSFGs are a non-negligible galaxy population. This suggests that the star formation quenching is likely not dominated by rapid processes at the local universe. This is different from the case of high redshift, where major mergers and cold gas accretions are believed to much more frequently occur than in the local universe (e.g., Rodriguez-Gomez et al. 2015; Tacchella et al. 2016a, 2016b), suggesting a different compaction and quenching timescale with respect to the low-redshift universe.

The AGN activities have been brought in to explain the link between inner structural properties of galaxies and star formation quenching (e.g., Croton et al. 2006; Fabian 2012; Cicone et al. 2014; Henriques et al. 2015), acting to expel/deplete the preexisting cold gas supply and/or prevent gas cooling and further star formation by strong feedback from central massive black holes. Since the buildup of stellar cores of cSFGs is probably connected to the growth of central massive black holes, the prevalence of AGNs in cSFGs and eSFGs is likely to be different. Indeed, by examining the fraction of massive cSFGs that host an AGN at a redshift of ∼2, Kocevski et al. (2017) found that ∼40% of compact SF galaxies host an X-ray-detected AGN, which is 3.2 times higher than the incidence of AGNs in extended SF galaxies of similar masses and similar redshifts, based on the combination of Hubble WFC3 imaging and Chandra X-ray observations. In low-redshift universe, Wang et al. (2017) have identified a sample of galaxies with "outside-in" assembly mode from MaNGA (Mapping Nearby Galaxies at Apache Point Observatory; Bundy et al. 2015), which are selected to have a lower 4000 Å break in the inner region than in the outer region. They found that these galaxies are likely in the transitional phase from normal SF galaxies to QGs, given their smaller size, higher SFR, and higher gas-phase metallicity with respect to normal SF galaxies of similar stellar mass. The properties of these galaxies resemble the properties of cSFGs investigated in this work, although the two populations are defined in totally different ways. In addition, the galaxies with outside-in assembly mode are more likely to host an AGN than normal SF galaxies, although with a limited sample size (Wang et al. 2017; Liu et al. 2018), suggesting a higher prevalence of AGNs in cSFGs than in eSFGs.

Figure 8 shows the fraction of optical AGNs for cSFGs and eSFGs as a function of stellar mass. The optical AGNs are identified on the basis of the BPT diagram (Baldwin et al. 1981), adopting the division lines of Seyfert galaxies from Kewley et al. (2001) and Cid Fernandes et al. (2010). The relevant emission lines are drawn from the MPA-JHU catalog, restricting the signal-to-noise ratios to be greater than 3.0. The emission-line fluxes are corrected for intrinsic extinction based on the Balmer decrement assuming a dust attenuation curve of the form λ^−0.7 (Charlot & Fall 2000) and an intrinsic flux ratio Hα/Hβ = 2.86. As shown in Figure 8, the fraction of Seyfert galaxies is increasing with increasing stellar mass for both cSFGs and eSFGs. More importantly, the cSFGs are more likely to host an AGN than eSFGs almost over the whole stellar mass range, and the differences between the two populations are more pronounced for low-mass galaxies. Our result confirms the result that cSFGs are more likely to host an AGN than eSFGs. However, whether the higher prevalence of AGNs in cSFGs than in eSFGs is the by-product of the compaction process or the cause of star formation quenching is still under debate (e.g., Lilly & Carollo 2016; Kocevski et al. 2017; Wang et al. 2018b).

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As shown in Figure 2, we present a simple line on the ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$–${M}_{* }$ diagram, above which galaxies are defined as compact SF galaxies. However, the threshold of ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ to separate cSFGs and eSFGs is dependent on stellar mass. We then define a parameter, the deviation of ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ from the demarcation line of cSFGs and eSFGs in logarithmic space (Δ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$), to quantify the compactness of the galactic center. The Δ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ does not depend on stellar mass: cSFGs with Δ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ > 0 and eSFGs with Δ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ < 0. Similarly, we use the deviation of SFR from the normal SFMS, ΔSFR, to quantify the star formation status of galaxies, which is independent of stellar mass.

The left panel of Figure 9 presents the ΔSFR–Δ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ diagram for all the sample galaxies with the color-coding of the H i detection rate. Galaxies on the ΔSFR–Δ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ diagram are mainly distributed in two branches, denoted by the gray contours. Galaxies in the upper branch are SF galaxies, whereas galaxies in the lower branch are quenched ones. Almost all the QGs have high inner surface stellar mass densities, indicated by the lack of galaxies in the lower left corner of Figure 9. This agrees with the previous finding that a compact stellar core is the requisite for quenching a galaxy (e.g., Fang et al. 2013; Bluck et al. 2014; Barro et al. 2017). More importantly, from eSFGs to cSFGs, and from cSFGs to the quenched population, the H i detection rate is significantly decreasing, which is consistent with the compaction and quenching scenario that the gas reservoirs for sustaining star formation become less and less along the quenching track. Moreover, we have checked the ΔSFR–Δ${{\rm{\Sigma }}}_{1\mathrm{kpc}}$ diagram with color-coding of the H i mass and find that the result strengthens the above statement.

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In the right panel of Figure 9, we present the sketch for galaxy evolution on the ΔSFR–ΔΣ_1kpc diagram under the scenario of compaction and quenching, which roughly demonstrates what happened to galaxies during the processes of compaction and quenching. From eSFGs to cSFGs, galaxies appear to significantly consume or lose their cold gas but sustain or even slightly enhance their star formation activities along with metal enhancement (for less massive galaxies) and central stellar mass assembly (see Figures 4 and 11). From cSFGs to the quenched population, galaxies appear to exhaust almost all their cold gas and shut down their star formation along with the buildup of their dense stellar cores or bulges (see Figures 9 and 11).

Thus, we propose a simple picture under the scenario of compaction and quenching to string the results together, where eSFGs first contract via a series of possible physical processes. The dominated processes for compaction are likely to be different at different redshifts. In the high-redshift universe (z > 1), major mergers and the accretion of counterrotating tidal streams occur more frequently than in the local universe (e.g., Conselice 2006; Bertone & Conselice 2009; Zolotov et al. 2015; Tacchella et al. 2016b). These processes are usually associated with violent disk instabilities, subsequently leading to the collapse of gaseous and/or stellar disks and the enhancement of star formation. However, the physical processes of compaction in the local universe are much gentler and have a longer timescale than those in the high-redshift universe. Minor mergers, interactions with close companions, and/or the bar-driven gas inflow in secular evolution are thought to play a role in enhancing star formation and contributing to the buildup of stellar cores or bulges for low-redshift galaxies (e.g., Moore et al. 1998; Bournaud et al. 2007; Di Matteo et al. 2007; Wang et al. 2012; Lin et al. 2017). This intense star formation could only be sustained for 1 Gyr or less (see the right panel of Figure 7), but it is efficient to consume the cold gas and assemble the stellar mass by in situ star formation in the inner regions of galaxies along with the metal enhancement. The major role of compaction is to transform an extended SF galaxy with a sufficient H i reservoir to a compact SF but H i-deficient galaxy (see Figures 5 and 11). Then this galaxy can be quenched by either the feedback of its central massive black hole or stabilizing the gaseous disk against collapse from forming stars because of the existence of a dominant core (or bulge), although the morphological quenching picture appears to be inconsistent with the fact that quenching inevitably invokes the loss of cold gas (see Figure 9). Alternatively, this galaxy can be quenched by the environmental effects, such as tidal stripping or strangulation if it is a less massive galaxy of a big cluster. We note that the cSFGs and eSFGs appear to reside in a similar environment, suggesting that the compaction process is independent of environmental effects.

We also remind the readers that there is no necessity for invoking the evolution from eSFGs and cSFGs to explain our result. It is also possible that the eSFGs and cSFGs are formed differently, owing to different formation and gas accretion histories. By investigating 100 simulated galaxies of various morphologies with Milky-Way-like halo mass drawn from the Galaxies–Intergalactic Medium Interaction Calculation (GIMIC), Sales et al. (2012) found that the coherent alignment of the angular momentum of accreted gas over galaxy formation is the key to galaxy morphology: spheroids more likely form when the spin of newly accreted gas is misaligned with that of the extant galaxy, whereas disk galaxies form usually with the similar alignment of angular momentum for the accreted gas and the earlier accreted material. Furthermore, under this scenario, the accreted gas flows more easily into the galactic center for spheroids than disk galaxies, associated with the enhancement of central star formation activities (Davis et al. 2011; Chen et al. 2016; Jin et al. 2016) and the possible feeding of central massive black holes (see Figure 8). This naturally leads to the cSFGs being more H i deficient than eSFGs owing to the rapid cold gas consumption in cSFGs, and the structural dependence of metallicity can be caused by either the metal-poor gas accretion of eSFGs or the metal enhancement of rapid star formation activities in the center of cSFGs (Yabe et al. 2012; Wang et al. 2017; Sánchez Almeida & Dalla Vecchia 2018). However, it is also possible that eSFGs accrete cold gas and/or dwarf galaxies with misaligned angular momentum and subsequently turn into cSFGs.