A phase-space view of cold-gas properties of Virgo-cluster galaxies: multiple quenching processes at work?

In the EVCC, the listed galaxies are categorized into two categories in terms of the membership to the Virgo cluster, “secure” and “possible” members, based on the redshift comparison with a cluster infall model (Kim et al., 2014). It is known that there are several substructures in the Virgo cluster (Figure 1 (a), Binggeli et al., 1985, 1987, 1993; Sandage et al., 1985): A (or M 87) cluster, B (or M 49) cluster, NGC 4636 group, M cloud (Ftaclas et al., 1984), W’ cloud (de Vaucouleurs, 1961), and W cloud (de Vaucouleurs, 1961). Additionally, the galaxies at declination less than $5^{\circ}$ are called the “southern extension”. According to the EVCC classification, galaxies in the W and M clouds are partially and largely categorized to possible members, respectively. The mean velocity of these W and M cloud galaxies is $\sim 2000$ km s^-1 ($\sim 1000$ km s^-1 for the main body of the Virgo cluster) and they are considered to be located at twice the distance of the Virgo cluster (Binggeli et al., 1993). The M and W clouds galaxies are also categorized as possible members in the classical Virgo Cluster Catalogue (VCC, Binggeli et al., 1985).

On the other hand, Yoon et al. (2012); Yoon & Putman (2017) found that Ly$\alpha$-absorbing warm-hot gas ($T=10^{4-6}$ K) is associated with the substructures in the Virgo cluster including both the M and W clouds, and suggested that the observed warm gas is part of large-scale gas flows into the Virgo cluster. Such warm-hot gas is preferentially found in the outskirts rather than the central region of galaxy clusters (Yoon et al., 2012; Yoon & Putman, 2017; Burchett et al., 2018), which is also predicted in the hydrodynamic simulations of the galaxy clusters (Emerick et al., 2015), although the mass contribution of the warm-hot gas is not so large compared to the X-ray emitting hot gas ($\sim 3$ %, Burchett et al., 2018). Thus, we use both the secure and possible members of the Virgo cluster in the following analysis. The effect of the inclusion of the possible members on our results is discussed in Section 5.1.

For the $M_{\rm star}$ and SFR data, the EVCC is crossmatched with the sample galaxies in the project of “z = 0 Multiwavelength Galaxy Synthesis” (z0MGS, Leroy et al., 2019), resulting in 721 galaxies. Leroy et al. (2019) measured $M_{\rm star}$ and SFR of $\sim 15,750$ galaxies located at $<50$ Mpc which are observed with the Galaxy Evolution Explorer (GALEX, Martin et al., 2005) and the Wide-field Infrared Survey Explorer (WISE, Wright et al., 2010). The z0MGS project derived empirical relationship between $M_{\rm star}$ and WISE photometry at 3.4 $\mu$m, and SFR and WISE (22 $\mu$m) and GALEX (far-ultraviolet or near ultraviolet) photometry using data obtained in the GALEX-SDSS-WISE Legacy Catalog (GSWLC, Salim et al., 2016). Leroy et al. (2019) prioritizes a “hybrid” SFR estimation for galaxies which are observed and detected both with GALEX and WISE, i.e., SFR estimation with ultraviolet and mid-infrared data to account for both the obscured and unobscured components. The GSWLC project combined GALEX and WISE photometry with SDSS observations and conducted population synthesis modeling using the CIGALE code (Boquien et al., 2019). Salim et al. (2016) assumed a Chabrier IMF to derive $M_{\rm star}$ and SFR (Chabrier, 2003).

For the CO data, we used the literature data of Boselli et al. (1995), Chung et al. (2009b), Atlas 3D (Young et al., 2011), the Analysis of the interstellar Medium in Isolated GAlaxies (AMIGA, Lisenfeld et al., 2011), Herschel Reference Survey (HRS, Boselli et al., 2014a), and CO Multi-line Imaging of Nearby Galaxies (COMING, Sorai et al., 2019) and found 186 galaxies (175 with $M_{\rm star}$ and SFR measurements) without double counting. $M_{\rm H_{2}}$ is calculated from CO line luminosity ($L_{\rm CO}^{\prime}$) with a CO-to-H₂ conversion factor for the Milky Way ($\alpha_{\rm CO}=3.21$ M_⊙ [K km s^-1 pc²]^-1, which corresponds to $X_{\rm CO}=2.0\times 10^{20}$ cm^-2 [K km s^-1]^-1) as

where a factor of 1.36 accounts for the Helium contribution to mass (e.g., Bolatto et al., 2013). Here we do not consider the metallicity dependence of $\alpha_{\rm CO}$ since our sample galaxies are massive galaxies whose $M_{\rm star}$ are larger than $\sim 10^{9}$ M_⊙, which is near the turnover mass for the mass-metallicity relation of local galaxies (Andrews & Martini, 2013) and roughly corresponds to the Solar metallicity ($12+\log({\rm O/H})=8.69$, Asplund et al., 2009). At metallicities larger than the Solar value, the variation in $\alpha_{\rm CO}$ is small (Figure 9 of Bolatto et al., 2013). Additionally, it is claimed that the mass-metallicity relation of galaxies does not strongly depend on the galaxy environments and the metallicity of cluster galaxies is found to be slightly higher than that of field galaxies ($\sim 0.05$ dex, e.g., Mouhcine et al., 2007; Cooper et al., 2008; Ellison et al., 2009).

For the H i data, we crossmatched the EVCC galaxies with literature data obtained in The Arecibo Legacy Fast ALFA survey (ALFALFA, Giovanelli et al., 2005), Atlas 3D (Serra et al., 2012), and VLA Imaging of Virgo Spirals in Atomic Gas (VIVA, Chung et al., 2009a), resulting in 570 galaxies (271 with $M_{\rm star}$ and SFR measurements) without double counting. $M_{\rm atom}$ is calculated based on the optically thin assumption as

where the factor of 1.36 again accounts for the Helium contribution to mass, $D$ is the distance to the galaxies in Mpc (16.5 Mpc) and $\Sigma_{i}S_{i}\Delta v$ is the summation over the total emission in each channel in Jy km s^-1 (e.g., Wild, 1952).

The sky distribution of the secure/possible member galaxies in the EVCC is shown in Figure 1 and the crossmatch summary is presented in Table 1. Table 2 summarizes the subsamples in this study. Figure 2 shows the color-magnitude relation of target galaxies in this study and the EVCC galaxies with data of the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7, Abazajian et al., 2009). We can see that our sample galaxies are biased to bright objects, or massive galaxies that are expected to be less affected by their environments than less massive galaxies (Peng et al., 2010). Our main target is limited to massive galaxies with $M_{\rm star}>10^{9}$ M_⊙ that is the lowest $M_{\rm star}$ value of field samples for a comparison (sed Section 3.1). The completeness of our sample with $M_{\rm star}>10^{9}$ M_⊙ is $\sim 65-90$ % at absolute $r$-band magnitudes of $\lesssim-16.7$ mag (see the histograms in Figure 2).

With the physical values estimated above, we calculate the following “key quantities” of galaxies: specific SFR (${\rm sSFR}={\rm SFR}/M_{\rm star}$), atomic-gas mass fraction ($\mu_{\rm HI}=M_{\rm HI}/M_{\rm star}$), molecular-gas mass fraction ($\mu_{\rm H_{2}}=M_{\rm H_{2}}/M_{\rm star}$), (total) gas mass fraction [$\mu_{\rm gas}=(M_{\rm HI}+M_{\rm H_{2}})/M_{\rm star}=M_{\rm gas}/M_{\rm star}$], molecular gas to atomic gas mass ratio ($R_{\rm H_{2}}=M_{\rm H_{2}}/M_{\rm HI}$), star-formation efficiency (SFE) from atomic gas (SFE${}_{\rm HI}={\rm SFR}/M_{\rm HI}$), SFE from molecular gas (SFE${}_{\rm H_{2}}={\rm SFR}/M_{\rm H_{2}}$), and SFE from total gas (SFE${}_{\rm gas}={\rm SFR}/M_{\rm gas}$).

In the following sections, we compare the key quantities of Virgo galaxies on the best effort basis, i.e., we use all the galaxies with measurements including both detections and upper limits, of the numerators and denominators of the key quantities (hereafter, “best-effort sample”), and thus the number of galaxies in each plot is different depending on the quantities. To assess the sample bias due to this treatment, we also compute these values for galaxies with all the measurements of $M_{\rm star}$, SFR, H i, and CO (“CO+H i-obs. sample”, 113 galaxies) or galaxies with detections (“CO+H i-det. sample”, 70 galaxies) (see Table 2).

Figure 3 shows the $M_{\rm star}$ distribution of our seven subsample galaxies with $M_{\rm star}>10^{9}$ M_⊙, such as (a) galaxies with H i and CO measurements (“CO+H i-obs. sample”), (b) galaxies with H i measurements, (c) galaxies with CO measurements, (d) galaxies with $M_{\rm star}$ and SFR measurements, (e) galaxies with H i and CO detections (“CO+H i-det. sample”), (f) galaxies with H i detections, and (g) galaxies with CO detections. The “best-effort sample” consists of (a) for $\mu_{\rm gas}$, SFE_gas, and $R_{\rm H_{2}}$, (b) for $\mu_{\rm HI}$ and SFE_HI, (c) for $\mu_{\rm H_{2}}$ and SFE${}_{\rm H_{2}}$, and (d) for SFR and sSFR.

The $\log{(M_{\rm star}[{\rm M}_{\odot}])}$ medians of the field and Virgo galaxies and the $p$-value of the KS test are also presented in each panel (see Section 3.1 for the field sample). The $M_{\rm star}$ medians of the field galaxies are larger than those of the Virgo galaxies and the KS test shows that the difference of the $M_{\rm star}$ distribution between the field and the Virgo galaxies is statistically significant. Additionally, the KS test among the different Virgo subsamples show that the $M_{\rm star}$ distribution is different for (a) versus (d), (a) versus (f), (c) versus (d), (c) versus (f). The $M_{\rm star}$ medians of these subsample suggest that the galaxies with CO measurements are more massive ($\sim 10^{10.0}$ M_⊙) than those only with $M_{\rm star}$ and SFR measurements and those with H i detections ($\sim 10^{9.7}$ M_⊙). Therefore, the “best-effort sample” in plots for SFR and sSFR is slightly biased to lower mass systems compared to the other subsamples.

We compare the Virgo galaxies and field galaxies in Figure 4. Note that the left peaks for the gas fractions consist of the galaxies with the upper limits. In Appendix A, we also show the comparison of the key quantities of the Virgo and field galaxies without the upper limits (Figure 12). To derive empirical relationships of key quantities as a function of stellar mass in the field galaxies, we make use of data of the extended GALEX Arecibo SDSS Survey (xGASS, Catinella et al., 2018) for H i-related relations, and the extended CO Legacy Database for GASS (xCOLD GASS, Saintonge et al., 2017) for H₂-related relations. We adopted the star-forming main sequence (SFMS) galaxies defined in Speagle et al. (2014). The difference between the Virgo and field galaxies [$\Delta({\rm Field})$] in Figure 4 is calculated as $\Delta({\rm Field})=\log_{10}{\rm(X_{\rm Virgo}(M_{\rm star})/X_{\rm Field}(M_{\rm star}))}$, where $X_{\rm Virgo}(M_{\rm star})$ and $X_{\rm Field}(M_{\rm star})$ are key quantities for the Virgo and field galaxies at stellar mass of $M_{\rm star}$, which are derived based on polynomial regression with an order of three except for SFR and sSFR. Speagle’s SFMS is adopted for $X_{\rm Field}(M_{\rm star})$ for SFR and sSFR.

We find that the Virgo galaxies have lower medians of SFR, sSFR, gas fractions, and higher medians of $R_{\rm H_{2}}$ and SFEs than the field galaxies in both cases that the sample includes those with CO or H i upper limits (“best-effort sample”, Figure 4) and that the sample is limited to those with CO or H i detections (Figure 12 in Appendix A). These differences are confirmed to be statistically significant according to the KS test. Even in case we limit the sample to galaxies with CO and H i measurements, i.e., the “CO+H i-obs. sample”, the conclusions do not change.

It has been claimed that both the $\mu_{\rm H_{2}}$ and SFE${}_{\rm H_{2}}$ values of galaxies are related to the offset from the SFMS of the field galaxies, $\Delta$(MS)$=\log_{10}{\rm(SFR/SFR_{MS})}$, where ${\rm SFR_{MS}}$ is SFR of the SFMS field galaxies for a fixed stellar mass and redshift (e.g., Saintonge et al., 2012; Genzel et al., 2015; Scoville et al., 2017; Ellison et al., 2020). These relations are independent of the local galaxy number density at least for field and group galaxies (Koyama et al., 2017). Figure 5 compares the relationships of $\Delta$(MS) with cold-gas mass fractions, $R_{\rm H_{2}}$, and SFEs for the Virgo and field galaxies. Although most Virgo galaxies follow the same relation as field galaxies, the Virgo galaxies tend to be distributed at the lower $\Delta$(MS) regime in these plots. Interestingly, some Virgo galaxies, especially below the main sequence ($\Delta$(MS)$\sim-1$), seem to have decreased $\mu_{\rm H_{2}}$ and elevated $R_{\rm H_{2}}$ and SFEs compared to field galaxies for fixed $\Delta$(MS). We compare the medians of gas fractions, $R_{\rm H_{2}}$, and SFEs of the field and the Virgo galaxies with CO or H i detection depending on the quantities on the SFMS ($-0.5<\Delta$(MS)$<0.5$) as well as those below the SFMS ($-1.5<\Delta$(MS)$<-0.5$). We find that the Virgo galaxies have lower gas fractions and higher $R_{\rm H2}$ and SFEs than the field galaxies below the SFMS. The KS test shows that the differences between the field and the Virgo galaxies are statistically significant for the subsamples below the SFMS. It should be also noted that H i-related values of the Virgo galaxies show a wider variation than the field galaxies at a fixed $\Delta$(MS).

In the following sections, we use the $\Delta({\rm Field})$ values, i.e., the values from which $M_{\rm star}$-dependences of field galaxies have been subtracted, in order to investigate the environmental effect without the $M_{\rm star}$ effect.

The galaxy properties as a function of clustocentric distance have been investigated in many previous studies showing that galaxies nearer to the cluster center tend to be more passive and H i-deficient (e.g. Giovanelli & Haynes, 1985; Solanes et al., 2001). To investigate the radial variation of the galaxy properties, we divided our Virgo galaxies into six radial bins where each bin spans $0.5R_{200}$ as $R_{\rm proj}/R_{200}<0.5$ ($R_{1}$), $0.5\leq R_{\rm proj}/R_{200}<1.0$ ($R_{2}$), $1.0\leq R_{\rm proj}/R_{200}<1.5$ ($R_{3}$), $1.5\leq R_{\rm proj}/R_{200}<2.0$ ($R_{4}$), $2.0\leq R_{\rm proj}/R_{200}<2.5$ ($R_{5}$), and $R_{\rm proj}/R_{200}\geq 2.5$ ($R_{6}$), where $R_{\rm proj}$ is the projected distance from a galaxy to M 87. The most outskirt galaxy in our “best-effort sample” locates at $\sim 3R_{200}$.

Figure 6 shows the medians, 1st and 3rd quartiles of the key quantities for galaxies in each category. There is a radial tendency in SFR and cold gas fractions in galaxies where these values are lower for galaxies nearer to the cluster center than their counterparts in the outskirts. The Spearman’s rank-order correlation coefficient and the $p$-value confirm that the clustocentric distance positively correlates to SFR, sSFR, and gas fractions with correlation coefficients of $0.3-0.5$, and negatively correlates to SFE_gas, SFE_HI, and $R_{\rm H_{2}}$ with correlation coefficients ranging from $-0.4$ to $-0.3$. SFE${}_{\rm H_{2}}$ does not show a clear dependence on the clustocentric distance.

Additionally, the radial trends of the gas fractions are not completely continuous but there seems to be a bend between $R_{3}$ and $R_{4}$. Note that the galaxies in the W-cloud galaxies are excluded in Figure 6 since the cold-gas and star-formation properties are different from the surrounding galaxies. The inclusion of the W-cloud galaxies causes a jump rather than a bend between $R_{3}$ and $R_{4}$ in sSFR and $\mu_{\rm H_{2}}$. Here, the W-cloud galaxies are defined on the PSD by eye, and the definition is presented in Section 3.4. The properties of the W-cloud galaxies are discussed more in Sections 3.4 and 5.2.3.

For a comparison with the field galaxies (zero corresponds to the values of field galaxies), we can see that gas fractions, $R_{\rm H_{2}}$, SFE_gas, and SFE${}_{\rm H_{2}}$ are already comparable to field galaxies at $>R_{5}$ whereas the medians of SFR and sSFR are slightly lower than those of the field galaxies. On the other hand, SFE_HI tends to be higher than the field galaxies even at $>R_{5}$.

Note that the same tendency is observed even when we consider only the sample with CO and H i measurements, i.e., the “CO+H i-obs. sample”. If we limit the sample to galaxies with CO and H i detection (“CO+H i-det. sample”), the radial trends seen in SFR, sSFR, and gas fractions disappear.

Galaxy number density is one of the important parameters to understand the dominant quenching mechanism in cluster galaxies. If the dominant quenching mechanism is related to the local number density rather than the cluster ICM or potential, galaxy-galaxy interactions are expected to be important.

We adopt two distances to see the dependences of the key quantities on the local galaxy density: the distances to the 5-th nearest galaxy (1) on the sky ($R_{\rm 5,sky}$) and (2) on the PSD ($R_{\rm 5,PSD}$) where the vertical and horizontal axes are respectively $R_{\rm proj}/R_{200}$ and $\Delta v_{\rm gal}/\sigma_{\rm Virgo}$ and both values are dimensionless quantities ($\Delta v_{\rm gal}$ is the velocity difference between a galaxy to M 87). We make use of these two values complementarily to evaluate the effect of galaxy-galaxy interactions including the galaxy harassment (multiple high-speed galaxy-galaxy encounters) since some galaxy pairs can have a smaller $R_{\rm 5,sky}$ by chance even though the actual distance between them along the line of sight would be much larger than the projected distance, which can dilute the true relations between $R_{\rm 5,sky}$ and the key quantities. On the other hand, the comparison with $R_{\rm 5,PSD}$ would miss the effect of the galaxy harassment.

First, we compare $R_{\rm 5,sky}$ or $R_{\rm 5,PSD}$ with the projected clustocenteric distance (plots are shown in Figure 13 of the Appendix B). Overall, there are moderate and weak positive correlations between $R_{\rm 5,sky}$ and $R_{\rm 5,PSD}$ with the clustocenteric distance, respectively. The obtained positive correlations suggest that the dependence of the key quantities on clustocentric distance seen in Figure 6 might just reflect the dependence on the local densities, and vice versa. The exclusion of the W-cloud galaxies increases $R_{\rm 5,sky}$ and $R_{\rm 5,PSD}$ at the $R_{3}$ bin, but does not drastically change the overall trend.

Next, we compare $R_{\rm 5,sky}$ or $R_{\rm 5,PSD}$ with the key quantities. Plots for $R_{\rm 5,sky}$ and $R_{\rm 5,PSD}$ are shown in Figure 7 and Figure 14 in Appendix B, respectively. We observe positive correlations between $R_{\rm 5,sky}$ with SFR, sSFR, and gas fractions with correlation coefficients of $\sim 0.3-0.4$, and negative correlations with SFE_HI with a correlation coefficient of $\sim-0.3$. In case of the $R_{\rm 5,PSD}$, we find positive correlations with SFR, sSFR, and $\mu_{\rm HI}$ with correlation coefficients of $\sim 0.2$. The exclusion of the W-cloud galaxies basically does not change the results for $R_{\rm 5,sky}$ and $R_{\rm 5,PSD}$. If we limit sample to those with both the CO and H i measurements (“CO+H i-obs. sample”), the results do not change but the correlation between $R_{\rm 5,PSD}$ with $\mu_{\rm HI}$ becomes insignificant. Next if we limit sample to those with both the CO and H i detections (“CO+H i-det. sample”), all the correlations for $R_{\rm 5,sky}$ become insignificant.

Therefore the radial tendency observed in SFR, sSFR, and gas fraction can be partially attributed to the radial dependence of the local galaxy density where the local environment of galaxies becomes denser at nearer to the cluster center.

In order to see the effect of ram pressure, we divide the galaxies into two groups in terms of accretion phase on the projected PSD of the cluster: (1) “virialized” (VIR) and “stripping” (RPS), (2) “recent infall” (RIF). The RPS and VIR galaxies are respectively expected to be currently affected and to have been affected by the ram pressure but it turned out that there is no RPS galaxy in our sample. Jaffé et al. (2015) shows that on the projected PSD, galaxies oscillates in position and velocity drawing a “wedge” and fall into a cluster core in their simulations (galaxy trajectories on the PSD shown in Figure 4 of Jaffé et al., 2015). However, it should be noted that not all galaxies in the VIR region have necessarily experienced the ram-pressure stripping. The position on the PSD provides a statistical probability that each galaxy is in a different accretion phase and is not univocally associated to the quenching mechanisms. The probability for Milky Way-type galaxies being stripped by ram pressure is estimated to be $\gtrsim 60$ % in the VIR region of a $z\sim 0.2$ cluster (Figure 6 of Jaffé et al., 2015). The W-cloud galaxies are treated separately from the other RIF galaxies. Figure 8 shows the galaxy distribution on the PSD, color-coded according to the SDSS $(u-r)$ color and the galaxy classification on the PSD.

The classification is basically done following the procedures presented in Jaffé et al. (2015) and Yoon et al. (2017). The VIR region is enclosed by the line connecting the points of $(R_{\rm proj}/R_{200}$, $|\Delta v_{\rm gal}|/\sigma_{\rm Virgo})=(1.2,0.0)$ and $(0.0,1.5)$. Although there is no RPS galaxy in our sample, the RPS region is determined with the balance between the ram pressure, $P_{\rm ram}=\rho_{\rm ICM}v_{\rm 3D,gal}^{2}$, and the galaxy’s anchoring force per area, $\Pi_{\rm gal}=2\pi G\Sigma_{\rm star}\Sigma_{\rm gas}$, where $\rho_{\rm ICM}$, $v_{\rm 3D,gal}$, $G$, $\Sigma_{\rm d,star}$, and $\Sigma_{\rm d,gas}$ are the ICM density distribution, 3D velocity of the galaxy ($v_{\rm 3D,gal}=\sqrt{3}v_{\rm obs,gal}$), gravitational constant, surface mass density of stellar and gas disks, respectively (Gunn & Gott, 1972). The ram pressure felt by a member galaxy is a function of the clustocentric velocity of the galaxy and the density distribution of the ICM. On the other hand, the galaxy’s anchoring force per area is a function of surface densities of stellar and gas components at a galactic radius where stripping is active. The adopted boundary line in this study represents a galaxy with a stellar mass of $10^{9}$ M_⊙ and a scale length of 0.9 kpc (the median value for EVCC galaxies with $M_{\rm star}\sim 10^{9}$ M_⊙). This RPS boundary is a measure to assess whether or not the entire gas of a $10^{9}$ M_⊙ galaxy is stripped by ram pressure, i.e., even the gas at the galaxy center where the anchoring force is the strongest is removed. Generally, cold gas in less massive galaxies tends to be more easily stripped by ram pressure (see Figure 8). The model parameters to calculate a boundary line for the RPS galaxies are summarized in Table 3.

The W-cloud galaxies are defined on the PSD by eye as mentioned in Section 3.2. We consider that galaxies in an ellipse on the PSD with a central coordinate and semi-major/semi-minor axes of $(R_{\rm proj}/R_{200},|\Delta v_{\rm gal}|/\sigma_{\rm Virgo})=(1.2,1.6)$ and 0.6/0.3, respectively, are the W-cloud galaxies.

Figure 9 shows the comparison of cumulative histogram of the key quantities for the VIR, RIF, and W-cloud galaxies (the distributions of the key quantities on the PSD are presented in Appendix C). The VIR and W-cloud galaxies tend to have lower medians of SFR, sSFR, and gas fractions than the RIF galaxies. Furthermore, the W-cloud galaxies have lower medians of sSFR, $\mu_{\rm H_{2}}$ than the VIR galaxies. The W-cloud galaxies have higher $\mu_{\rm gas}$ and $\mu_{\rm HI}$ medians than the RIF galaxies. Based on the KS test, the following differences are significant: (1) SFR, sSFR, and all the gas fractions between the VIR and RIF galaxies, (2) $\mu_{\rm HI}$ and SFE_HI between the VIR and W-cloud galaxies, and (3) sSFR, $\mu_{\rm H_{2}}$, and SFE${}_{\rm H_{2}}$ between the W-cloud and RIF galaxies.

If we limit the sample to galaxies with H i or CO measurements (“CO+H i-obs. sample”), all the the differences in (3) disappear . If we limit the sample to galaxies with H i or CO detections (“CO+H i-det. sample”), on the other hand, the differences of SFR and sSFR between the VIR and RIF galaxies are statistically significant.

When we do not distinguish the W-cloud galaxies from the RIF galaxies, the VIR galaxies tend to have lower SFR, sSFR, gas fractions, and higher $R_{\rm H_{2}}$ medians than the RIF galaxies, while no significant difference is seen in SFE${}_{\rm H_{2}}$. SFR, sSFR, gas fractions, and SFE_HI are statistically different between VIR and RIF galaxies, according to the KS test.

The product of $(|\Delta v_{\rm gal}|/\sigma_{\rm Virgo})\times(R_{\rm proj}/R_{200})$ is claimed to be a measure of the accretion epoch where the galaxies with the lower value were accreted earlier time (Noble et al., 2013). Figure 10 shows the relationship between $(|\Delta v_{\rm gal}|/\sigma_{\rm Virgo})\times(R_{\rm proj}/R_{200})$ with the key quantities of galaxies without those in the W cloud. There are positive correlations between the accretion epoch and SFR, sSFR, and gas fractions with the correlation coefficients of $\sim 0.3-0.4$, i.e., galaxies with smaller clustocentric distance and velocity tend to have lower star-formation activity and cold-gas contents. The inclusion of the W-cloud galaxies diminishes the significance of the correlation with $\mu_{\rm H_{2}}$ ($r$ and $p$-value of $0.12$ and $0.1$, respectively) while the negative correlations with SFE_gas and $R_{\rm H_{2}}$ become significant ($r$ and $p$-value of $-0.23$ and $0.02$ for SFE_gas , respectively) by decreasing $\mu_{\rm H_{2}}$, SFE_gas and $R_{\rm H_{2}}$ at the largest bin of $(|\Delta v_{\rm gal}|/\sigma_{\rm Virgo})\times(R_{\rm proj}/R_{200})$.

The results do not drastically change even if we limit the sample to galaxies with H i and CO measurements (“CO+H i-obs. sample”). On the other hand, if we limit the sample to galaxies with H i and CO detections (“CO+H i-det. sample”), all the correlations disappear.

In this section, we investigate the effect of the inclusion of the possible members on the obtained results by removing them from the analysis. As we mentioned in Section 2.1, we use data of both the secure and possible members in the EVCC. The possible members mainly consist of the W-cloud galaxies and the southern-extension galaxies. We find that the galaxies in the W cloud have lower SFR $\mu_{\rm H_{2}}$ compared to the surrounding galaxies (Section 3.4). On the other hand, the southern-extension galaxies (galaxies with higher $R_{\rm proj}/R_{200}$ and higher $\Delta v_{\rm gal}/\sigma_{\rm Virgo}$ values on the PSD) tend to have a bluer SDSS color as seen in Figure 8, suggesting a higher SFR and abundant cold gas.

For the dependences on the clustocentric distance, overall trends are basically the same as what we find with the sample including both the secure and possible members. More specifically, we find the bend of the key quantities at $R_{3}$. For the dependence on the local galaxy densities, the results for $R_{\rm 5,sky}$ do not significantly change, while all the correlations disappear for $R_{\rm 5,PSD}$. This difference can be attributed for the disappearance of the galaxies with high SFR, sSFR, and $\mu_{\rm HI}$ at the sparser region on the PSD, i.e., the southern-extension galaxies. For the dependence on the accretion phase, we find that the median values of SFR and all the gas fractions are lower in the VIR galaxies than the RIF galaxies. According to the KS test, the differences in SFR and all the gas fractions are confirmed to be statistically significant. The correlations between $(|\Delta_{\rm gal}|/\sigma_{\rm Virgo})\times(R_{\rm proj}/R_{200})$ with SFR, sSFR, and gas fractions are still statistically significant even though the correlation coefficients decreases to $0.2-0.3$. Therefore the exclusion of the possible member galaxies of the EVCC does not drastically change our results obtained in the Sections 3 and 4 except for the $R_{\rm 5,PSD}$ dependence of the key quantities. Hereafter, we discuss possible quenching mechanisms at work in the Virgo galaxies based on the obtained results with both the secure and possible members in the following sections.

Our results show that SFR, sSFR, and gas fractions of galaxies are different in samples chosen at $R_{\rm proj}<1.5R_{200}$ and those at $R_{\rm proj}>1.5R_{200}$ (Figure 6). Considering that there is the boundary between the VIR and RIF regions around $R_{\rm proj}\sim 1.5R_{200}$, our results suggest that ram-pressure and/or long-period quenching mechanisms such as the strangulation and the tidal interaction with the cluster potential play a role in affecting cold-gas and star-formation properties of the Virgo galaxies. Additionally, the correlations between the projected local densities of galaxies on the sky with SFR, sSFR, and gas fractions suggest that galaxy-galaxy interaction also plays some roles in decreasing the star-formation activity in these galaxies (Figure 7). The weaker dependence of these key values on the local density on the PSD suggests that the galaxy harassment is especially important for decreasing gas reservoirs and star-formation activities of these galaxies (Figure 14).

Furthermore, we find that our Virgo sample tends to have a lower gas fraction and a higher SFE than the field galaxies. The field galaxies are known to follow “universal relations” between $\Delta({\rm MS})$ and $\mu_{\rm H_{2}}$ and between $\Delta({\rm MS})$ and SFE${}_{\rm H_{2}}$, where galaxies with lower $\Delta({\rm MS})$ tend to have a lower $\mu_{\rm H_{2}}$ and SFE${}_{\rm H_{2}}$ (e.g., Saintonge et al., 2012). However, our Virgo sample with lower $\Delta({\rm MS})$ is found to have lower gas fractions and higher SFEs than the field galaxies. This is why our Virgo sample has higher SFEs than the field galaxies even though they are less actively forming stars. This may suggest that the gas reduction process in those galaxies with lower $\Delta({\rm MS})$ takes place over a shorter timescale than the gas-depletion timescale by star formation, i.e., $M_{\rm gas}/{\rm SFR}\sim 3$ Gyr. Considering that $\Delta({\rm MS})$ is equal to $\Delta({\rm Field})$ of SFR, the positive correlations between the $\Delta({\rm Field})$ value of SFR with the clustocentric distance, the distance to the 5-th nearest neighbour, and $(|\Delta v_{\rm gal}|/\sigma_{\rm Virgo})\times(R_{\rm proj}/R_{200})$ indicate that the galaxies with lower $\Delta({\rm MS})$ values are located at nearer to the cluster center, have smaller clustocentric velocity, and reside in denser regions.

We discuss the environmental effects on cold-gas and star-formation properties in the following sections by focusing on ram-pressure and tidal stripping (Section 5.2.1), galaxy harassment (Section 5.2.2), preprocessing in a group environment (Section 5.2.3), and strangulation (Section 5.2.4).