Revealing the Impact of Critical Stellar Central Density on Galaxy Quenching through Cosmic Time

In a previous work, we investigated the structural and environmental dependence on quenching in the nearby universe. In this work, we extend our investigations to higher redshifts by combining galaxies from the Sloan Digital Sky Survey and The FourStar Galaxy Evolution surveys. In low density, we find a characteristic Σ1 kpc above which the quenching is initiated as indicated by their population-averaged color. Σ1kpccrit shows only a weak mass dependency at all redshifts, which suggests that the internal quenching process is more related to the physics that acts in the central region of galaxies. In high density, Σ1kpccrit for galaxies at z > 1 is almost indistinguishable from their low-density counterparts. At z < 1, Σ1kpccrit for low-mass galaxies becomes progressively strongly mass dependent, which is due to the increasingly stronger environmental effects at lower redshifts. Σ1kpccrit in low density shows strong redshift evolution with ∼1 dex decrement from z = 2.5–0. It is likely that at a given stellar mass, the host halo is on average more massive and gas-rich at higher redshifts; hence, a higher level of integrated energy from a more massive black hole (BH) is required to quench. As the halo evolves from the cold to hot accretion phase at lower redshifts, the gas is shock-heated and becomes more vulnerable to the feedback processes from active galactic nucleus as predicted by theory. Meanwhile, angular momentum quenching also becomes more effective at low redshifts, which complements a lower level of integrated energy from the BH to quench.


Introduction
One of the long-standing puzzles of galaxy evolution is to understand how and why the star-forming activity in galaxies is seized (quenched).The processes to quench the star formation can be broadly classified into two categories (Kauffmann & Heckman 2003;Baldry et al. 2006;Peng et al. 2010): internally driven processes, i.e., mass quenching, which operates in both central and satellite galaxies; and externally driven processes, i.e., environmental quenching, which only operates in satellite galaxies.Various mechanisms have been proposed to account for the underlying physics.For mass quenching, the candidate mechanisms include active galactic nucleus (AGN) feedback (Croton et al. 2006;Darvish et al. 2015Darvish et al. , 2016;;Lin et al. 2016;De Lucia et al. 2019), morphological quenching (Martig et al. 2009), gravitational quenching (Genzel et al. 2014), and angular momentum quenching (Peng & Renzini 2020;Renzini 2020).Mechanisms for environmental quenching consist of strangulation (Balogh et al. 1997), ram pressure stripping (Gunn & Gott 1972;Abadi et al. 1999), tidal interaction (Sobral et al. 2011), and halo quenching (Dekel & Birnboim 2006).Despite being equipped with various options, a definitive consensus on which processes contribute to what extent is still lacking.
Attempts to push our understanding of quenching forward have been extensively made in investigating the correlations between various physical parameters and the quiescence of galaxies.Studies of massive galaxies suggest that the surface mass density within the central radius of 1 kpc (Σ 1 kpc ) is strongly correlated with the quenched fraction of galaxies, and hence, can be treated as an effective probe for quenching.The usage of Σ 1 kpc was first reported in Cheung et al. (2012), who found that high Σ 1 kpc performs best in predicting quenching at z ∼ 0.7.Fang et al. (2013) found that for nearby Sloan Digital Sky Survey (SDSS) galaxies, the specific star formation rate (sSFR) varies systematically relative to Σ 1 kpc , suggesting a mass-dependent threshold of Σ 1 kpc for the onset of quenching, possibly due to a threshold in BH mass.van Dokkum et al. (2014), Tacchella et al. (2015), and Barro et al. (2017) extended the use of Σ 1 kpc as a predictor of quenching to galaxies at higher redshifts.Whitaker et al. (2017) studied the population-averaged sSFR as a function of Σ 1 kpc for galaxies at 0.5 < z < 2.5, and found a sharp decrease in the sSFR as Σ 1 kpc exceeds some threshold.They also found that the critical Σ 1 kpc has strong redshift evolution.Chen et al. (2020) proposed an analytic model to explain the quenching boundaries as a competition of halo binding energy with the integrated power of AGN feedback.Luo et al. (2020) found that the offset to the running median of Σ 1 kpc has the power to distinguish the bulge types in nearby galaxies.More recently, Xu & Peng (2021) used a sample of nearby SDSS galaxies to study the distribution of population-averaged (near-UV (NUV − r)) color on the M å -Σ 1 kpc plane, and its environmental dependence.They found that for central galaxies in low density, there exists a critical central density of 1 kpc crit S M 10 10 kpc 9 9.2 2 - -, above which the quenching initiates.
Intriguingly, this 1 kpc crit S is only weakly dependent on the stellar mass.
Surprisingly, Σ 1 kpc appears to be also correlated with the quiescence of satellite galaxies.Woo et al. (2017) showed that Σ 1 kpc in quenched satellites is ∼0.3 dex higher than that of star-forming satellites at fixed stellar mass.Kawinwanichakij et al. (2017) and Guo et al. (2021) reach similar conclusions for satellites at high redshifts.Xu & Peng (2021) find that the critical Σ 1 kpc at the transition from star-forming to passive populations is strongly mass dependent for low-mass satellites.Moreover, they found that the mass dependence in 1 kpc crit S for low-mass satellites is a function of environment: 1 kpc crit

S
is lower in dense environments at fixed stellar mass.
It is naturally logical to extend the work of Xu & Peng (2021) to higher redshifts, to gain further insight into the underlying physics of quenching from the redshift evolution of star-forming activity, structure and environment, which is the goal of this paper.In this work, we utilize the samples of galaxies from SDSS and The FourStar Galaxy Evolution (ZFOURGE) surveys to perform a joint analysis of the structural and environmental dependence on quenching at 0 < z < 2.5.Photometric redshift based on broadband photometry with large uncertainty is the main obstacle to studying the galaxy environment at high redshifts.The ZFOURGE survey utilizes five near-IR medium-band filters to better constrain the photometric redshift, which enables a more precise characterization of the environment at high redshifts.Throughout, we adopt the following cosmological parameters where appropriate: H 0 = 70 km s −1 Mpc −1 , Ω m = 0.3, and Ω λ = 0.7.

Nearby Galaxies
In this work, we use the same sample of the nearby galaxy as used in Xu & Peng (2021), which was constructed from the SDSS DR7 catalog (Abazajian et al. 2009).The redshift range is 0.02 < z < 0.085, which guarantees reliable spectroscopic redshift measurements.Each galaxy is weighted by 1/TSR × 1/V max , where TSR is the spatial target sampling rate, determined using the fraction of objects that have spectra in the parent photometric sample within the minimum SDSS fiber spacing of 55″ of a given object.The V max values are derived from the k-correction program version 4.2 (Blanton & Roweis 2007).The use of V max weighting allows us to correct the effect of incompleteness of the sample down to a stellar mass of about 10 9 M e .
Integrated photometries in five bands were used in this study: u, g, r, i, and z bands from SDSS.The photometries were corrected for Galactic extinction and k-weighted to z = 0 using version 4.2 of the k-correct code package described in Blanton & Roweis (2007).The spectroscopic redshifts, total stellar mass, fiber velocity dispersion, and median signal-to-noise ratios in the spectra were obtained from the MPA/JHU DR7 value-added catalog.The stellar masses were computed by fitting the integrated SDSS photometry with the stellar population models (similar to the method in Salim et al. 2007).The structural parameters such as the Sérsic index n, effective radius R e , and ellipticity e are obtained from Simard et al. (2011).The axis ratio is computed as b/a = 1 − e as defined.

Galaxies at High Redshift
We select galaxies at 0.5 < z < 2.5 from the ZFOURGE survey (Straatman et al. 2016).The survey is composed of three 11″ × 11″ fields with coverage in the regions of CDFS (Giacconi et al. 2002), COSMOS (Scoville et al. 2007), and the UKIRT Infrared Deep Sky Survey (Lawrence et al. 2007) that overlap with the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011;Koekemoer et al. 2011), which also provide Hubble Space Telescope (HST), high-angular resolution imaging for 0.6-1.6 μm (see, e.g., van der Wel et al. 2012).ZFOURGE utilizes five near-IR medium-bandwidth filters J 1 , J 2 , J 3 , H s, and H l to better constrain the photometric redshift.The medium-band near-IR imaging in J 1 , J 2 , and J 3 reaches depths of ∼26 AB mag and ∼25 AB mag in H s and H l .We utilize ZFOURGE's main catalogs, which are provided on the official ZFOURGE website. 3The main catalogs are complete for galaxies to K s ∼ 25.5-26.0AB mag (see Straatman et al. 2016), and include photometric redshifts and rest-frame colors calculated using EAZY (Brammer et al. 2008) from 0.3-8 μm photometry for each galaxy.The typical photometric redshift uncertainties are σ z /(1 + z) = 0.01-0.02 to the K s -band magnitude limit for galaxies between z = 0.5 and 2.0, with negligible dependence on galaxy color (Straatman et al. 2016).In addition, the morphological data crossmatched with HST/ WFC3/F160W CANDELS data from van der Wel et al. (2012) are also included.

Sample Selections
We select the nearby galaxies above the SDSS spectroscopic limit (r = 17.77) and with the stellar mass log (M å /M e ) > 9. We discard galaxies with a low axis ratio with b/a < 0.5 to minimize the measurement bias due to the internal dust extinction.A final sample of 89,469 nearby galaxies is produced for the subsequent analysis.
For galaxies at high redshifts, we first select all the welldetected galaxies ("USE" flag = 1) with the stellar mass log (M å /M e ) > 9; we then discard galaxies with an H-band magnitude fainter than 24.5 AB mag to guarantee an accurate structural measurement (van der Wel et al. 2012).To see if this additional magnitude cut of H < 24.5 AB mag has any impact on the original stellar mass completeness determined based on the limit of K s ∼ 25.5-26.0AB mag (Kawinwanichakij et al. 2017), we compute the fraction of galaxies that have both H < 24.5 and K s < 25.5 to the galaxies that have K s < 25.5 only to evaluate the impact of the cut H < 24.5 (see Table 1).The fraction is higher than 97% at all redshifts, which indicates that the additional cut on the H band will not affect the level of completeness of the sample.
Similarly, we discard galaxies from the ZFOURGE catalog with an axis ratio of b/a < 0.5 to ensure reliable measurement of the Sérsic index n and R e .In addition, we use the quality flag to further exclude galaxies with bad GALFIT fitting in the F160W band (flag >1).A final sample of 4577 galaxies at 0.5 < z < 2.5 makes the cut.

Central 1 kpc Mass Density
We follow the procedures in Xu & Peng (2021) to compute the central 1 kpc surface mass density of Σ 1 kpc , by directly integrating the Sérsic light profile and scaling the integrated luminosity within the inner 1 kpc.This method has been widely used in many previous studies (Bezanson et al. 2009;Kawinwanichakij et al. 2017;Whitaker et al. 2017) and is described as follows.The two-dimensional Sérsic light profile can be described in the form of where I 0 is the central intensity, n is the Sérsic index, r eff is the circularized effective radii, and b n is defined as For the disk galaxies with a Sérsic index of n < 2.5 (Kennedy et al. 2015), the total luminosity is obtained by integrating over the two-dimensional light profile (Equation ( 1)).We then convert the total luminosity to the total stellar mass, assuming that the mass follows the light and that there are no strong color gradients.Finally, we calculate the stellar mass surface density in the inner 1 kpc by numerically integrating the following equation: where M å is the total stellar mass of the galaxy from the MPA/ JHU DR7 value-added catalog for nearby galaxies, and from the ZFOURGE main catalogs for galaxies at high redshifts; L model is the total luminosity from the Sérsic modeling, whereas L phot is the measured total luminosity within the aperture.There is only a slight difference ∼of 0.1 dex between L model and L phot (Kawinwanichakij et al. 2017;Whitaker et al. 2017), and we do not include this correction and set L model /L phot = 1 in this study, to maintain consistency of the computation on Σ 1 kpc in nearby and distant galaxies.For galaxies that have prominent bulge components with n > 2.5, we assume that they follow spherical light profiles and perform an Abel transform to deproject the circularized, three-dimensional light profile The total luminosity in this case is derived by integrating over the above three-dimensional light profile, and the central surface mass density is given as For each galaxy, we perturb the stellar mass M å , Sérsic index n, and size R e within their quoted 1σ error 40 times and compute the corresponding Σ 1 kpc .The uncertainty of Σ 1 kpc is evaluated as the standard deviation of the 40 perturbed Σ 1 kpc .

Characterization of the Galaxy Environment
Most methods to define and compute the environment of galaxies fall into two categories: those that use flexible apertures whose size is determined by the method of the nearest neighbor, and those that use fixed apertures.The choice is largely dependent on the scale being probed: the local environment that is internal to a halo is found to be best measured with the nearest neighbor method, whereas the fixed apertures best quantify the large-scale environment external to a halo (Muldrew et al. 2012).In this study, we characterize the environment of galaxies in the local and distant universe by their local projected overdensity using the distance to the Nth nearest neighbor.The dimensionless overdensity of 1 + δ is defined by Peng et al. (2012) as

áSñ áSñ
Since there are no physical constraints on the number N yet, the choice of N typically varies from 3 to 10, which largely depends on the survey (Muldrew et al. 2012;Peng et al. 2012;Kawinwanichakij et al. 2017).For nearby galaxies from SDSS, we adopt N = 5 and the overdensity is computed from the volume of the cylinder that is centered on each galaxy with a length of ±1000 km s −1 .All of the five closest neighbor galaxies have M B,AB −19.3 −z, where −z is used to approximate the luminosity evolution of both passive and active galaxies.For galaxies at high redshifts, since the sample with available spectroscopic redshift is very limited, the photometric redshift with larger uncertainty is used to characterize the environment at high redshifts.We adopt an empirical approach to optimize N and the redshift interval δz (or the length of the cylinder that is centered on each galaxy), which are vital to determine the overdensity.We use N = 8 and δz = 0.08 in this study.The details of the procedures can be found in Appendix A.

Star-forming Indicator
We use (U − V ) color as the indicator of star formation in this study, as is widely used in the literature.The rest-frame flux in the U and V bands was computed by spectral energy distribution (SED) fitting and provided in the ZFOURGE "REST-FRAME" catalogs.For nearby SDSS galaxies, Blanton & Roweis (2007) provided sets of empirical formulas in their Table 2 to convert u, g, and r photometries to U and V magnitudes, which are given as U u u g V g g r 0.0682 0.0140 1.2638 0.3516 0.7585 0.6102 .7 We use Equation (7) to convert the SDSS photometries to the rest-frame (U − V ) color to be in line with the high-redshift galaxies.The provided color dispersion of σ[u − g] = 0.26 and σ[g − r] = 0.15 were used to estimate the uncertainty of the converted (U − V ) color.

Dust Extinction Correction
Massive dusty galaxies with intense star-forming activity at high redshifts typically show red color, which makes them indistinguishable from passive galaxies based only on (U − V ) color.In the literature, the UVJ diagram is widely used to effectively break this color degeneracy (Williams et al. 2010), and classify galaxies as star-forming galaxies (SFGs) and quiescent galaxies (QGs).However, a continuous measurement of the level of star formation, instead of a dichotomy of galaxies suits this study more.Therefore, we attempt to assume a Calzetti law to correct the rest-frame (U − V ) color for the effect of dust extinction.For galaxies at high redshifts, A V is computed from SED fitting and is provided in the main catalogs of ZFOURGE.The value of R V = A V /E(B − V ) depends on the interstellar environment along the line of sight.In galactic diffuse regions, R V typically has an average value of 3.1 (Draine 2003), whereas in dense molecular clouds, R V could be as large as ∼6 (Mathis 1990;Fitzpatrick 1999), and it could be as ∼2 in low-density regions (Fitzpatrick 1999).A detailed evaluation of R V for different types of galaxies in our sample is definitely beyond the scope of this paper.Instead, we adopt an empirical methodology to optimize the value of R V to be in line with the classification based on the UVJ diagram.Overall, the classification based on the corrected (U − V ) color best matches that on the UVJ diagram when R V ∼ 5.1 (see the details in Appendix B), and we adopt this value of R V to correct the (U − V ) color.For nearby SDSS galaxies, A V for each galaxy is obtained by crossmatching our SDSS sample with the Galaxy Evolution Explorer (GALEX)-SDSS-Wide-field Infrared Survey Explorer (WISE) LEGACY CATALOG (GSWLC; Salim et al. 2007).To maintain consistency with galaxies at high redshifts, we use the same value of R V ∼ 5.1 to correct the (U − V ) color.
Figure 1 shows a comparison of the distribution of the extinction-corrected (U − V ) color at 0 < z < 2.5.Only galaxies with M M log 9.8 ( )  >  are selected to maintain the level of completeness of the sample up to z ∼ 2.5.Overall, the color of galaxies becomes redder as the redshift decreases.The color bimodality can be clearly observed at almost all the redshifts except for the highest redshift bin at 2 < z < 2.5.For galaxies at z > 0.5, the position of the trough between the two peaks is (U − V ) cor ∼ 1.25, and does not show significant redshift evolution.The color at z ∼ 0 is ∼0.3-0.7 dex redder than those at z > 0.5, which is consistent with the previous result in which the rest-frame (U − V ) color was directly derived from SED fitting (Bell et al. 2012).To better visualize the color distribution in galaxies at high redshifts and compare it with that of the nearby galaxies, we narrow down the color range of the whole sample by shifting the color distribution of SDSS galaxies by ∼0.3 dex toward the left as shown in Figure 1 (black-dashed line), to align the color trough of SDSS galaxies with those of galaxies at high redshifts.This shifting will not affect the subsequent determination of the critical Σ 1 kpc , which only depends on the relative position of the trough within the distribution.
In addition, we test if this color criterion is sensitive to the level of completeness of the sample.We repeatedly adjusted the lower bound of the stellar mass of the sample, replotted the color distribution, and found that the location of the trough  to guarantee completeness up to z ∼ 2.5 (Kawinwanichakij et al. 2017).Color bimodality can be observed at almost all the redshift bins except for the highest one at 2.0 < z < 2.5.The gray-dashed line marks the color criterion that separates the star-forming and passive populations for galaxies at high redshifts, which is (U − V ) cor ∼1.25.This color criterion is insensitive to the redshift and the level of completeness of the sample.The black-dashed line marks the position of the color trough that separates two peaks for SDSS galaxies, which is at ∼1.55.To better visualize the comparison between nearby and distant galaxies, we narrow down the color range of the whole sample by shifting the color distribution of SDSS galaxies by 0.3 dex toward the left (thin dashed line), to align the color trough of SDSS galaxies with those of galaxies at high redshifts.This shifting will not affect the determination of 1 kpc crit

S
, since the color criterion used in computing 1 kpc crit S shifts by the same amount as that for the whole distribution.remained similar.Therefore, we use (U − V ) cor ∼1.25 as a color criterion for the subsequent analysis.

Structural and Environmental Impact on Quenching
In this section, we study the structural and environmental impacts on quenching for galaxies at 0 < z < 2.5 by investigating the color distribution on the M å -Σ 1 kpc plane.We assign galaxies into five redshift bins to study their redshift evolution.To reveal their environmental dependence, we divide the galaxies in each redshift bin into three environment bins based on their rank in local overdensity. 4For each SDSS galaxy, we perform a V max -weighting correction to correct for the incompleteness, inside a box of 0.3 × 0.2 dex 2 that centers on each data point.We further smooth the data using the locally weighted regression method LOESS (Cleveland & Devlin 1988) as implemented by Cappellari et al. (2013).LOESS is useful in unveiling the overall underlying trends by reducing the intrinsic and observational errors, in particular in bins where the number of galaxies is small.
Similar to the approaches in Xu & Peng (2021), we focus on the structural dependence on quenching by quantitatively sketching the trends in Σ 1 kpc at the transition from star-forming to passive populations, which is (U − V ) cor ∼1.25 in this study, as discussed in Section 2.7 (also see Figure 1).
Figure 2 shows the central 1 kpc density Σ 1 kpc as a function of stellar mass M å in three environment bins and five redshift bins, color coded by LOESS-smoothed, extinction-corrected color (U − V ) cor .In each bin, we select data at the transition that have 1.25 − 0.15 < (U − V ) cor < 1.25 + 0.15, and 1 kpc crit S is computed as the running median of their Σ 1 kpc as a function of stellar mass.We overplot the transitional Σ 1 kpc as the magenta-dashed lines in Figure 2 for reference.The (U − V ) cor for the SDSS galaxies in Figure 2 is 0.3 dex lower than their original value as mentioned in Section 2.7.We replot all galaxies with their original color in Figure 9 in Appendix C.
for SDSS galaxies remains unchanged under the shifting in color space, as expected.
Overall, there is strong redshift evolution in (U − V ) cor color.At fixed stellar mass, the color at high redshifts is typically bluer than their low redshift counterparts.The critical Σ 1 kpc for massive galaxies appears higher at high redshifts and exhibits strong redshift evolution.At high redshift (z > 1), there is no significant difference in 1 kpc crit

S
for massive galaxies in different environments, whereas the transitional line becomes environmentally dependent at low redshift (z < 1), in particular, for low-mass galaxies.
We highlight these trends in Figure 3   For nearby SDSS galaxies, we add Gaussian random noise to the observed stellar mass and Σ 1 kpc , with 1σ uncertainty that is equal to their quoted errors.We also perturb the (U − V ) color by adding noise to the SDSS (u − g) and (g − r) colors with the quoted 1σ error (Blanton & Roweis 2007), and then propagate the errors using Equation (7).For the ZFOURGE galaxies, we perturb their stellar mass, Σ 1 kpc, and photometric redshift by adding Gaussian random noise with their quoted 1σ errors; we then rebin the simulated data based on their perturbed redshift and recalculate the local overdensity in each realization to account for the uncertainty in the photometric redshift.The colored shades in Figure 3 represent the running median and 1σ dispersion in 1 kpc crit

S
. The structural and environmental dependence on quenching and their evolution is clearly depicted in Figure 3.At z > 1, no clear environmental dependence has been detected in 1 kpc crit

S
, and in all environments appears to be flat and exhibits only a weak mass dependency.The mass dependence of 1 kpc crit S in different environments becomes distinguishable at z < 1: 1 kpc crit S remains weakly mass dependent in low density, but rapidly increases with the stellar mass for low-mass galaxies in dense environments, which is apparently due to the environmental effects.In low density, the weakly mass dependent 1 kpc crit S exhibits significant redshift evolution, which decreases by ∼1 dex from log 10 at z ∼ 0, whereas in dense environment, 1 kpc crit S evolves from being weakly mass dependent at z > 1, to mildly mass dependent at 0.5 < z < 1, and eventually to strongly mass dependent at z ∼ 0.
We use another star-forming indicator-the sSFR to investigate the critical Σ 1 kpc on the plane of M å -Σ 1 kpc as shown in Figure 11 in Appendix C. All trends in 1 kpc crit S remain similar.Furthermore, to enable a complete assessment of the effects of the environment, we also plot Σ 1 kpc as a function of the rank of log(1 + δ) color coded by (U − V ) cor and the sSFR for reference in Appendix D.

Discussion and Summary
We use samples of nearby and distant galaxies from the SDSS and ZFOURGE surveys to explore the structural and environmental impacts on the galaxy quenching and their redshift evolution, by studying the distribution of population-averaged color on the M å -Σ 1 kpc plane.In low density, we find that the critical Σ 1 kpc , which separates the star-forming and passive populations, is only weakly mass dependent.The presence of the weakly mass dependent 1 kpc crit

S
was first reported for central galaxies in the local Universe (Xu & Peng 2021), and our result confirmed that the weakly mass dependent 1 kpc crit S appears ubiquitous at all redshifts, in particular, for massive galaxies.We

S
in low density exhibits strong redshift evolution with more than a 1 dex decrement from z = 2.5-0 (blue data points in Figure 4).Meanwhile, 1 kpc crit S in dense environments are almost indistinguishable from their lowdensity counterparts at high redshifts, but become progressively mass dependent at z < 1, in particular, for low-mass galaxies.As suggested in Xu & Peng (2021), the mass dependent 1 kpc crit S for nearby low-mass galaxies is due to the environmental effects.Our result confirms that the bending in 1 kpc crit

S
for low-mass galaxies emerges at z ∼ 1.This is not surprising, since it is well established that the environmental effects become predominant in quenching the low-mass galaxies at z < 1 (Kawinwanichakij et al. 2017).In addition, without an accurate characterization of the environment at high redshifts, we are not able to identify various mass dependencies of 1 kpc crit S across different environments.Therefore, the use of ZFOURGE catalogs was initially motivated by the accuracy in measuring the photometric redshift, rather than the sample size.We notice that the photometric redshift in the latest released catalogs from CANDELS has been optimized with an uncertainty of ∼0.02 × (1 + z), by using statistics to correct the probability density functions of photometric redshift for biases and errors (Kodra et al. 2023).Data from larger surveys with similar accuracy in photometric redshift, such as CANDELS, would certainly be valuable for our future related studies.
van Dokkum et al. (2015) reported a threshold in central velocity dispersion of 225 km s −1 , based on the analysis of a sample of compact star-forming galaxies (cSFGs) at 1.5 < z < 3.0 with a median size of R e = 1.8 kpc.This quenching threshold increases to 234 km s −1 after normalizing the velocity dispersion to R e = 1 kpc following Cappellari et al. (2006).This threshold in

(
) S (see the magenta-dashed line in Figure 4) using the correlation between the Σ 1 kpc and velocity dispersion (Fang et al. 2013), which roughly agrees with our mass-averaged measurement of Whitaker et al. (2017) use a sample of high-redshift galaxies from the 3D-HST survey (Skelton et al. 2014) to study the population-averaged sSFR as a function of Σ 1 kpc . 5At each redshift, they derived a similar critical Σ 1 kpc at the transition from star-forming to passive populations, which is defined by the population-averaged sSFR (e.g., they explored both constant and evolving criteria in the sSFR).They also find a strong evolution in 1 kpc crit

S
(see the green data points in Figure 4), which is well consistent with our result.The new finding in our study is that we explicitly investigate the stellar mass and environmental dependences of 1 kpc crit

S
, which would place additional constraints on the underlying mechanisms for mass and environmental quenching.
On the other hand, Barro et al. (2017) use a sample of galaxies at 0.5 < z < 3.0 from the CANDELS survey to study Σ 1 kpc as a function of stellar mass M å for SFGs and QGs, respectively.For massive QGs, they find a very tight M å -Σ 1 kpc scaling relation at all redshifts, and the typical scatter of the scaling relation is only 0.14 dex.A similar scaling relation is also identified for SFGs, with a slightly larger scatter of ∼0.25 dex.They find that the slope of both scaling relations barely changes with the redshift (∼0.9 for SFGs and ∼0.66 for QGs), and only detects a weak redshift evolution in the zero-point (∼(1 + z) α , where α = 0.7-0.8).More recently, Chen et al. (2020) proposed a similar weak evolution of the normalization of the scaling relations for both populations, which can be parameterized as h(z) −0.74 , where h(z) = H(z)/H(0).
The significance of the redshift evolution in 1 kpc crit S may rely on the definition of the transitional core density, which varies in different studies.In Barro et al. (2017) and Chen et al. (2020), is defined as a boundary computed from the scaling relation of QGs, below which few quenched galaxies can be found.At the same time, as argued in Barro et al. (2017), such a boundary is only a necessary but not sufficient condition for quenching since there are some cSFGs found above the boundary.This boundary is essential to characterize the structural properties of the passive population, and its slow evolution (see the black and red solid lines in Figure 4) likely reflects that a higher core density is a prerequisite to quenching and the core density is less affected by the minor mergers that contribute the majority of the growth in size in passive galaxies.Meanwhile, in Whitaker et al. (2017) and Xu & Peng (2021), and this work, 1 kpc crit

S
is computed based on the criterion of population-averaged color or the sSFR.Though served in a statistical sense, the transitional core density defined in this way implicitly encodes the information of the relative abundance of star-forming and passive populations in the sense that the abundance of QGs should be higher than that of SFGs above the boundary.Therefore, the strong evolution in 1 kpc crit

S
(see the blue diamonds in Figure 4) may be attributed to the strong evolution in the number density of star-forming and passive populations (see

S
as a function of redshift (blue diamonds).Green circles represent the critical Σ 1 kpc from Whitaker et al. (2017), assuming an evolving limit in log(sSFR).The gray-dashed line indicates the expected cosmological evolution in surface density normalized at z = 0.25, Σ 1 kpc ∝ (1 + z) 2 .The red solid line denotes the redshift dependence of the normalization of the quenching boundary from Chen et al. (2020), normalized at z = 2.25.The black solid line marks the redshift evolution in the zero-point of the scaling relation of QGs from Barro et al. (2017).The magenta-dashed line represents the assumed constant threshold in velocity dispersion above which galaxies quench at 1.5 < z < 3.0 from van Dokkum et al. (2015).Cyan stars indicate the redshift evolution of M 0 , which corresponds to the bending mass scale of the star-forming main sequence at each redshift.The data are from Delvecchio et al. (2021), and M 0 is converted to Σ 1 kpc using the scaling relations in Barro et al. (2017).
Figures 1 and 10), combined with that Σ 1 kpc in QGs is typically higher than that of SFGs, at fixed stellar mass.
The weakly stellar mass dependent 1 kpc crit S implies that mass quenching is more sensitive to the central core density than other global properties such as stellar mass.A natural candidate mechanism is AGN feedback, since the BH mass is closely related to the central velocity dispersion and the central mass density (Fang et al. 2013;Bluck et al. 2014Bluck et al. , 2020;;Chen et al. 2020).As discussed in Xu & Peng (2021), the weakly mass dependent 1 kpc crit

S
is qualitatively consistent with the AGN feedback model prescription in IllustrisTNG (Terrazas et al. 2020), though the M M 10 BH crit 8.2  ~implemented in TNG is systematically higher than their inferred value in the local universe.
However, it is still challenging to account for the strong evolution in the population-averaged color or sSFR at fixed stellar mass and Σ 1 kpc (see Figures 2 and 11), or equivalently the strong evolution in 1 kpc crit

S
at fixed stellar mass, if the core density or the central BH is the only quenching engine since the quenching timescale due to AGN feedback is expected to be much shorter than t Hubble .Other physical processes are likely needed to assist shaping the strong evolution in 1 kpc crit

S
. We propose the following three scenarios to interpret such strong evolution.First, in the scenario of AGN feedback quenching, the integrated power output of AGN is dictated by the BH mass, and the shutdown of star formation initiates as the integrated energy from the BH becomes larger than the gravitational binding energy of gas within the halo (Chen et al. 2020;Terrazas et al. 2020;Piotrowska et al. 2022;Bluck et al. 2023).At a given stellar mass, the halo is on average more massive at higher redshift (Behroozi et al. 2019;Girelli et al. 2020); therefore, star formation in a massive halo swarmed with more gas requires a higher level of integrated energy from the BH to quench.
Second, the quenching process is also affected by the thermodynamical status of the gas.As argued in Dekel & Birnboim (2006), at z < 2 in massive halos with M h > M shock , the gas is inevitably heated by the virial shock, and it ultimately becomes diluted and more vulnerable to the feedback processes, including AGN feedback.Hence, a lower level of integrated energy (or a less massive BH) may be required to quench the massive galaxies in a halo with M h > shock in the hot accretion regimes at z < 2. Meanwhile, the gas at z > 2 is preferentially accreted in the form of a cold stream instead of a shock-heated medium.In this case, a more massive halo is required to shockheat the gas into puffy medium, thus enabling the quenching due to AGN feedback to proceed in such cold accretion regimes.Therefore, the strong evolution in 1 kpc crit S is likely to be a manifestation of the evolution of the boundary between the cold and hot medium, which is discussed in Dekel & Birnboim (2006).
There is some observational evidence to support the increasing mass scale with redshift, above which the cold gas supply is significantly reduced.For instance, some studies have argued that the bending of the star-forming main sequence (SFMS) at the high mass end is likely due to the diminished cold gas supply by halo shock heating (Delvecchio et al. 2021;Daddi et al. 2022;Popesso et al. 2023).Delvecchio et al. (2021) use a parametric form to quantitatively describe the bending of the SFMS, and find that the characteristic bending mass M 0 has a strong redshift evolution.We use the best-fitted M å -Σ 1 kpc scaling relations for SFGs to convert M 0 to Σ 1 kpc and plot them in Figure 4 (cyan stars).Interestingly, the slope of the redshift evolution of M 0 matches that of 1 kpc crit

S
very well, which lends support to the halo-heating scenario.However, such consistency remains only at a qualitative level, since the halo-heating scenario predicts that the quenching should also strongly correlate with the halo or stellar mass, which contradicts the observed weakly mass dependent 1 kpc crit S .Moreover, galaxies that live in halos with M h < M shock are expected to be in a cold accretion phase even at low redshifts, and quenching occurs in these galaxies cannot be interpreted by halo heating solely.Therefore, it is likely that both AGN feedback and halo heating are acting in concert to contribute to the observed evolution in 1 kpc crit

S
. Third, other alternative quenching mechanisms may also become more effective at low redshifts, such as angular momentum quenching (Peng & Renzini 2020;Renzini 2020).As the disks grow with cosmic time, the average angular momentum of galaxies gradually increases.At low redshifts, the accreted gas spirals in with too high angular momentum to enable a fast radial gas inflow to feed the inner regions of galaxies.Instead, these infalling gases would settle onto an outer ring that is stable against fragmentation and radial migration.The star formation in the inner regions of galaxies would eventually be terminated due to the reduced gas supply or strangulation.As a consequence, a lower level of integrated energy from the BH is required as the quenching power.
Finally, we caution that the observed correlation between the quiescence and central mass density does not necessarily imply causality, and a higher Σ 1 kpc is likely to be the consequence of the quenching processes.At this stage, we are neither able to disentangle the aforementioned scenarios, nor to ascertain the causal direction, given the current data.Future cold gas surveys (both H I and H II) and detailed comparisons between the observations and the predictions from numerical simulations will be crucial to unveil the underlying physics of this structural evolution accompanying the quenching.multiple choices of N in Figure 6.The best choice of N and δz appears to depend on the redshift, and there is no single choice of N and δz that prevails at all redshifts.For instance, at 0.5 < z < 1.0, the quiescent fraction in the densest bin is most sensitive to the overdensity with large N (N = 10) and small δz (δz = 0.04 × (1 + z)), while small N (N = 4) and large δz (δz = 0.12 × (1 + z)) appear to be a better choice at 1.0 < z < 1.5.We then add up the quiescent fraction over all the three redshit bins for each N and δz, and rank their performance.We find that the overdensity based on N = 8 and δz = 0.08 stands out as having the highest total quiescent fraction.Therefore, we use N = 8 and δz = 0.08 to compute the local overdensity of the galaxies at 0.5 < z < 2.5 in this study.

Appendix B Correction of Dust Extinction
We evaluate the suitable R V used in the dust extinction law to correct the (U − V ) color for the effect of dust extinction in this appendix.We first utilize the UVJ diagram of the select SFGs and QGs at 0.5 < z < 2.5.We follow the same selection criteria used in Kawinwanichakij et al. (2017), in which the rest-frame color satisfies: We then test seven choices of R V = 2.1, 2.6, 3.1, 3.6, 4.1, 4.6, and 5.1.For each galaxy with a given value of A V , we compute seven corrected (U − V ) colors by assuming a Calzetti law and a choice of R V .We find that the corrected color shows clear bimodality at almost all redshifts, and the color critertion that separates the SFGs and QGs is always ∼1.2 regardless of the choice of R V .Therefore, for each R V , we use (U − ) cor ∼1.2 as the color criterion to classify SFGs and QGs.Each classification was compared with the one based on the UVJ diagram and our aim is to select the classification with a suitable R V that best mimics the UVJ classification.We define the false positive rates for SFGs and QGs, respectively, to quantify the similarity of two classification schemes: f FP for SFGs is defined as the ratio of number of SFGs UVJ with (U − V ) cor >1.2 to the number of SFGs UVJ , while f FP for QGs is defined as the ratio of number of QGs UVJ with (U − V ) cor <1.2 to the number of QGs UVJ .We plot f FP as a function of redshift in Figure 7 for SFGs and QGs, respectively.As shown in Figure 7, f FP for SFGs (QGs) generally decreases (increases) with the redshift.A higher R V tends to produce more(less) misclassified SFGs (QGs).f FP for SFGs only has a mild redshift evolution, as f FP for SFGs is low on average (the highest f FP is <0.1), and variation in f FP over different R V is also small (<0.05), while R V has a stronger impact on the evolution of f FP for QGs, in particular, at high redshifts.For instance, at 2.5 < z < 3.0, R V = 2.1 will result in f FP > 0.6, which is much higher than f FP ∼ 0.15 with R V = 5.1.We plot (U − V ) cor as a function of stellar mass in four redshift bins with three different R V in Figure 8.As shown, a QG is more likely to be misclassified as an SFG when using (U − V ) cor with a lower R V , in particular, at high redshift.Therefore, we adopt a relatively high value of R V = 5.1 in this study to correct the (U − V ) color for galaxies, since overall QGs is much less abundant than SFGs at high redshifts.In Figure 1, we shift the color distribution of SDSS galaxies toward the left by 0.3 dex, and use the shifted color to evaluate the critical Σ 1 kpc for the SDSS galaxies in Figure 2. We emphasize that such shifting has no impact on the determination of 1 kpc crit

S
, but narrows down the color range across all the redshifts, and enhances the color contrast between the starforming and quiescent populations at high redshift.To avoid any confusion on this shifting, we plot Σ 1 kpc as a function of stellar mass, color coded by their original color in Figure 9.We repeated the same procedures as in Section 3 to compute 1 kpc crit S , and found that they indeed remain the same as in Figure 2.

C.2. M å versus Σ 1 kpc , Color Coded by the sSFR
In this appendix, we explore the distribution of the sSFR on the plane of M å -Σ 1 kpc .For SDSS galaxies, we utilize the data from the X2 version of GSWLC6 (Salim et al. 2016(Salim et al. , 2018)), which is a value-added catalog for SDSS galaxies at 0.01 < z < 0.3 within the GALEX All-sky Imaging survey footprint (Martin et al. 2005).SFRs are derived from SED fitting consisting of two GALEX UV bands, five SDSS optical and near-IR bands, and one mid-IR band (22 μm if available, otherwise 12 μm) from WISE (Wright et al. 2010).For the ZFOURGE galaxies, SFRs are estimated by combining the total IR luminosity (L IR = L 8−1000 μm ) of galaxies and the luminosity emitted in the UV (L UV at a rest frame of 2800 Å).The extracted 24-160 μm photometries from Spitzer/IRAC and MIPS images (in all fields) and Herschel/PACS images (available for CDFS only) were used to fit a model spectral template to calculate the total IR luminosity.L UV + L IR provides an estimate of the total Figure 10.Distribution of specific SFR at five redshift bins.We shift the original distribution of the sSFR for SDSS galaxies (black solid line) to the right by 1 dex (thin dashed line), to ease the comparison of color distribution on the M å -Σ 1 kpc plane.The gray-dashed line marks the critical sSFR that roughly separates the starforming and quiescent populations at all redshifts, which is log sSFR Gyr environments exhibits similar strong redshift evolution as depicted in the left panel of Figure 3.This is likely due to a large portion of massive galaxies being mass quenched at high redshift, when the environmental effects have yet to come into play.Quenching in these galaxies might occur in advance of their infall into dense environments.∼0.7 dex lower than that in the sparse environment.Such inverse proportionality was first reported in Xu & Peng (2021) for nearby galaxies, and our study shows that it has already been in place at z ∼ 1 (see the second column in Figure 12).It could be qualitatively accounted for by two facts, as suggested in Xu & Peng (2021): (1) there are more quenched galaxies in dense environments at fixed stellar mass; (2) the color of galaxies is strongly correlated with their structure such as Σ 1 kpc .Intriguingly, the environmental effects, such as gas stripping, are not supposed to significantly alter the stellar structure of galaxies.An almost vertical 1 kpc crit S is anticipated if gas stripping is the dominant effect of environment.Therefore, a non-vertical but tilted 1 kpc crit

S
would cast valuable constraints on the underlying physical mechanisms of environmental quenching.After all, a strong correlation between the color and Σ 1 kpc at fixed stellar mass favors those scenarios in which the structure of galaxies could be altered by environmental effects, such as tidal interaction or a minor merger or scenarios that galaxies with compact structures are more susceptible to environmental effects.
We also plot Σ 1 kpc as a function of the rank of log(1 + δ), color coded by their sSFR in Figure 13

Figure 1 .
Figure 1.Distribution of extinction-corrected rest-frame (U − V ) color at five redshift bins.Galaxies are selected with stellar mass M M log 9.8 ( )  > by plotting 1 kpc crit S as a function of stellar mass in different environments at five redshift bins.The uncertainty of kpc 1 crit S is estimated by Monte Carlo simulations.In each environment and redshift bin, we create 40 realizations of simulated data by perturbing various parameters.

Figure 2 .
Figure 2. Central 1 kpc surface mass density Σ 1 kpc as a function of stellar mass at five redshift bins (different columns) and three environment bins (different rows), color coded by the dust-corrected rest-frame (U − V ) color.For the SDSS spectroscopic sample, the data at 0.02 < z < 0.085 has been V max weighted; for the ZFOURGE photometric sample at z > 0.5, the gray-shaded region marks the range of stellar mass that is incomplete.The data in each bin has been LOESS smoothed.The magenta-dashed lines denote the transitional Σ 1 kpc at (U − V ) cor ∼ 1.25.
use a different star-forming indicator (U − V ) cor to compute 1 kpc crit S in this study, comparing it with the (near-UV − r) color used in Xu & Peng (2021).Despite ∼0.3 dex offset in the computed 1 kpc crit S , the trend of weak mass dependency is not affected by the different choices of the star-forming indicator.1 kpc crit

Figure
Figure 3. 1 kpc crit S as a function of stellar mass at five redshift bins and three environment bins.The color-shaded region marks the 1σ error of the critical line which is computed by averaging over lines in 40 Monte Carlo-simulated realizations in each redshift and environment bin.

Figure 5 .
Figure 5. Quiescent fraction as a function of local overdensity at three redshift bins.Different rows denote different choices of δz in computing the overdensity.Eight choices of N were used in each panel to compute the overdensity, as indicated by their colors.

Figure 6 .
Figure 6.Quiescent fraction in the densest bin as a function of δz at three redshift bins.Eight choices of N were used to compute the quiescent fraction in the densest bin, as indicated by their colors.

Figure 7 .
Figure 7. False positive rate for SFGs (QGs) as a function of redshift in the left (right) panel.Seven R V were used in computing the false positive rate, as indicated by their colors.
Stellar Mass versus Core Density C.1.M å versus Σ 1 kpc , Color Coded by the Original (U − V ) cor

Figure 8 .
Figure 8. Extinction-corrected rest-frame (U − V ) color as a function of stellar mass at three redshift bins.Different rows denote different choices of R V .Blue (red) data points represent the SFGs (QGs) identified by the UVJ diagram.Green-dashed lines mark the color criteria that separate the star-forming and quenching in process populations.

Figure 9 .
Figure 9. Similar to Figure 2. SDSS galaxies in the first column are color coded by their original (U − V ) cor without shifting.The magenta-dashed lines denote the transitional Σ 1 kpc at (U − V ) cor ∼ 1.55, as marked by the black-dashed line in Figure 1.
Figure10.Distribution of specific SFR at five redshift bins.We shift the original distribution of the sSFR for SDSS galaxies (black solid line) to the right by 1 dex (thin dashed line), to ease the comparison of color distribution on the M å -Σ 1 kpc plane.The gray-dashed line marks the critical sSFR that roughly separates the starforming and quiescent populations at all redshifts, which is log sSFR Gyr 9.5 1 ( ) ~--

Figure 12 .
Figure 12.Central 1 kpc surface mass density Σ 1 kpc as a function of the rank of overdensity log(1 + δ) at five redshift bins (different columns) and six stellar mass bins (different rows), color coded by the extinction-corrected (U − V ) color. the data at 0.02 < z < 0.085 (SDSS galaxies) has been V max weighted.The data in each bin has been LOESS smoothed.The magenta-dashed lines denote the transitional Σ 1 kpc at (U − V ) cor ∼ 1.25.

Figure 13 .
Figure 13.Similar to Figure 12.Galaxies are color coded by their sSFR.The magenta-dashed lines denote the transitional Σ 1 kpc at log sSFR Gyr 9.5 1 ( ) ~-- for reference.magentadashed lines denote.The trends in 1 kpc critSremain similar to those in Figure12.

Table 1
Fraction of Galaxies That Satisfy Two Different Magnitude Cuts at Four