VERTICO II: How H i-identified Environmental Mechanisms Affect the Molecular Gas in Cluster Galaxies

We use two types of comparison samples. First, the extended Galaxy Evolution Explorer (GALEX) Arecibo SDSS Survey (xGASS; Catinella et al. 2018) and the extended CO Legacy Database for GALEX Arecibo SDSS Survey (xCOLD GASS; Saintonge et al. 2017) are used to compare global H i and H₂ masses in VERTICO to those of the general population of galaxies at fixed stellar mass, and estimate H i and H₂ deficiencies. After applying a small number of selection criteria (described below), these samples comprise several hundreds of galaxies, thus providing a good representation of the galaxy population throughout the relevant stellar mass range. Second, for a comparison of resolved properties of VERTICO galaxies with control galaxies, we use the HEterodyne Receiver Array CO-Line Extragalactic Survey (HERACLES, Leroy et al. 2009). This sample is described in detail in Section 2.1.2.

In Figure A1, all three control samples, as well as the VERTICO sample, are shown on the SFR–M_⋆ plane. Stellar masses and star-formation rates for x(COLD) GASS were taken from GALEX-SDSS-WISE Legacy Catalog (GSWLC, Salim et al. 2016), as these are consistent with those from the z = 0 Multiwavelength Galaxy Synthesis (z0MGS, Leroy et al. 2019), which are adopted for the VERTICO sample (see Section 3.2.1). Galaxies for which no 22 μm detection is available (used for deriving SFRs) have upper limits on their SFRs are indicated with down-pointing triangles. VERTICO galaxies occupy a similar region in this plane as star-forming (i.e., non-quiescent) x(COLD) GASS galaxies. HERACLES galaxies have enhanced SFRs at fixed stellar mass, which is likely due to selection effects (Section 2.1.2) This implies that HERACLES galaxies may not be typical field galaxies, and may have increased gas fractions, if they follow the Kennicutt-Schmidt relation (Schmidt 1959; Kennicutt 1998). We should keep this in mind when we compare results from the VERTICO sample to those from the HERACLES sample.

2.1.1. xGASS & xCOLD GASS

2.1.2. HERACLES: A Resolved Control Sample

For the majority of this work, H i deficiencies are adopted from Chung et al. (2009), who use the Hubble-type independent definition from Haynes & Giovanelli (1984):

$$\begin{eqnarray}&&{\mathrm{def}}_{\mathrm{HI},{R}_{\star }}=\left\langle \mathrm{log}\ {\bar{{\rm{\Sigma }}}}_{\mathrm{HI}}\right\rangle -\mathrm{log}\ {\bar{{\rm{\Sigma }}}}_{\mathrm{HI}},\end{eqnarray} \tag{ 1 }$$

where ${\bar{{\rm{\Sigma }}}}_{\mathrm{HI}}\equiv {S}_{\mathrm{HI}}/{D}_{\mathrm{opt}}^{2}$, where S_Hi is the H i flux in Jy km s ⁻¹ and D_opt is the diameter of the optical disk in arcminutes. ${\bar{{\rm{\Sigma }}}}_{\mathrm{HI}}$ is the mean H i surface density within the optical disk, and $\left\langle \mathrm{log}\ {\bar{{\rm{\Sigma }}}}_{\mathrm{HI}}\right\rangle$ = 0.37 for all Hubble types. Uncertainties on the H i deficiency reflect the difference with the Hubble-type dependent deficiency for the same object (in reality $\left\langle \mathrm{log}\ {\bar{{\rm{\Sigma }}}}_{\mathrm{HI}}\right\rangle$ varies somewhat with Hubble type, see Section 5.5 in Chung et al. (2009) for more details). A common distance of 16 Mpc was adopted to calculate these deficiencies in Chung et al. (2009), sufficiently similar to the distance of 16.5 Mpc adopted in this work for any differences in H i measurements to be negligible.

Since such a well-defined mass–size relationship does not exist for CO, the expected molecular gas mass in the equation for gas deficiency (Equation (3)) is derived from the median molecular gas mass of control galaxies at fixed stellar mass, rather than the optical size of the host galaxy (see Section 3.2). To ensure a fair comparison between deficiencies in both gas phases, we consider a second definition of H i deficiency, similar to that for H₂ deficiency:

$$\begin{eqnarray}&&{\mathrm{def}}_{{\rm{H}}\,{\rm\small{I}},{M}_{\star }}=\mathrm{log}\ {M}_{{\rm{H}}\,{\rm\small{I}},\exp }-\mathrm{log}\ {M}_{{\rm{H}}\,{\rm\small{I}},\mathrm{meas}},\end{eqnarray} \tag{ 2 }$$

where the expected H i mass, ${M}_{{\rm{H}}\,{\rm\small{I}},\exp }$, is the median H i mass at fixed stellar mass from a control sample from xGASS (see 2.1.1), and M_{H i,meas} is the measured H i mass.

Uncertainties in def ${}_{{\rm{H}}\,{\rm\small{I}},{M}_{\star }}$ are calculated by combining the uncertainty in the H i mass and that resulting from the uncertainty in the stellar mass. The 1σ spread in H i mass fractions in the control sample is ∼0.7 dex and varies somewhat with stellar mass. This spread is not taken into account in the uncertainty in ${\mathrm{def}}_{{\rm{H}}\,{\rm\small{I}},{M}_{\star }}$. The resulting H i deficiencies are listed in Table 1.

The mass–size relation for H₂ has not been defined as well as for H i (see e.g., B21). Additionally, the scatter in the relationship between stellar mass and molecular gas mass is smaller than that in the relationship between optical size and molecular gas mass (Boselli et al. 2014a). Therefore, we use the median H₂ mass of a control sample at fixed stellar mass to estimate the expected H₂ mass. Then the H₂ deficiency can be defined as follows:

$$\begin{eqnarray}&&{\mathrm{def}}_{{{\rm{H}}}_{2}}=\mathrm{log}\ {M}_{{{\rm{H}}}_{2},\exp }-\mathrm{log}\ {M}_{{{\rm{H}}}_{2},\mathrm{meas}},\end{eqnarray} \tag{ 3 }$$

where ${M}_{{{\rm{H}}}_{2},\exp }$ corresponds to the expected molecular gas mass of a galaxy and ${M}_{{{\rm{H}}}_{2},\mathrm{meas}}$ is its measured global molecular gas mass. The control sample we use to calculate ${M}_{{{\rm{H}}}_{2},\exp }$ is xCOLD GASS (see Section 2.1.1).

Global molecular gas mass estimates for the VERTICO sample are described in detail in Section 4.4 of B21, and are summarized here. Molecular gas masses are derived from CO luminosities as follows:

$$\begin{eqnarray}&&{M}_{\mathrm{mol}}=\displaystyle \frac{{\alpha }_{\mathrm{CO}}}{{R}_{21}}{L}_{\mathrm{CO}},\end{eqnarray} \tag{ 4 }$$

where α_CO=4.35 M _⊙ pc⁻² (K km s⁻¹)⁻¹, corresponding to the Galactic value of X_CO = 2 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹ recommended by Bolatto et al. (2013), and R₂₁ ≡ CO(2 − 1)/CO(1 − 0) = 0.8 as found by e.g., Leroy et al. (2009) and B21. The CO line luminosities are calculated following Solomon & Vanden Bout (2005):

$$\begin{eqnarray}&&{L}_{\mathrm{CO}}=3.25\times {10}^{7}\ {S}_{\mathrm{CO}}\ {\nu }_{\mathrm{obs}}^{-2}\ {D}_{L}^{2}\,\end{eqnarray} \tag{ 5 }$$

where S_CO is the integrated CO line flux in Jy km s⁻¹, ν_obs the observed frequency in GHz, and D_L the luminosity distance to the source in Mpc.

Note that the adopted α_CO includes a 36% contribution from helium. Therefore, the masses calculated here are total molecular gas masses.

Uncertainties in H₂ deficiency are calculated by combining the uncertainty in the H₂ mass and that resulting from the uncertainty in the stellar mass. The 1σ spread in molecular gas fractions in the control sample is ∼0.4 dex and varies somewhat with stellar mass (see Figure 1). This spread is not taken into account in the uncertainty in ${\mathrm{def}}_{{{\rm{H}}}_{2}}$. Molecular gas mass deficiencies are listed in Table 1.

Molecular gas fractions in the VERTICO sample are shown in Figure 1 as orange dots, overlaid on the sample from xCOLD GASS (see Section 2.1.1), whose median is shown as a solid black line, while the 1, 2, and 3σ spread is shown as shaded gray areas. The medians of the VERTICO sample, in stellar mass bins of 0.5 dex, are shown as orange squares. H₂ fractions of the HERACLES sample are shown as teal diamond markers. VERTICO galaxies with stellar masses log M_⋆/M_⊙ ≳ 9.75 are marginally but systematically H₂ deficient, with the median molecular gas fractions of the stellar mass bins lying 0.1–0.5 dex below the xCOLD GASS rolling median. VERTICO galaxies with stellar masses log M_⋆/M_⊙ ≲ 9.75 have H₂ fractions similar to, or marginally higher than, those of xCOLD GASS galaxies at fixed stellar mass. HERACLES galaxies are H₂-rich compared to xCOLD GASS at fixed stellar mass (see also Section 2.1.2).

There is a subsample of VERTICO galaxies that overlaps with a subsample of the Herschel Reference Survey (HRS, Boselli et al. 2010) for which high-quality CO data are available (Kuno et al. 2007). H₂ deficiencies for these galaxies were estimated by Boselli et al. (2014a) similarly to this work, but where ${M}_{{{\rm{H}}}_{2},\exp }$ in Equation (3) is defined as follows:

$$\begin{eqnarray}&&\mathrm{log}\ M({{\rm{H}}}_{2})=c\times \mathrm{log}(\mathrm{Variable})+d,\end{eqnarray} \tag{ 6 }$$

where the coefficients c and d are derived from linear fits to the relationship between $\mathrm{log}M({{\rm{H}}}_{2})$ and Variable, where the latter is chosen to be M_⋆. The sample used to derive this linear fit consists of all HRS galaxies with H i deficiencies ≤ 0.4, and upper limits are treated as measurements. An extensive description of the calibration of this H₂ deficiency parameter can be found in Section 4.1 in Boselli et al. (2014a).

A comparison between H₂ deficiencies from that work and those derived here is shown in Figure A2(b). H₂ deficiencies of the VERTICO sample calculated using Equation (3) are systematically lower than those of the HRS sample by ∼0.25 dex, and by ∼0.5 dex in case of the two galaxies with the largest H₂ deficiencies. There is a systematic offset in molecular gas masses in VERTICO and published molecular gas masses for the same objects in Boselli et al. (2014a), which is the result of differences in the calibration approach (see Section 4.3 in B21). This likely causes differences in the derived H₂ deficiencies. Moreover, the control samples used to calibrate the relation are significantly different. Boselli et al. (2014a) calibrate the relation against a subsample of the HRS consisting of 101 spiral galaxies for which CO data are available, and which have H i deficiencies ≤ 0.4 dex. This method could introduce a bias toward gas-rich galaxies, which would result in an overestimation of H₂ deficiencies for the Virgo systems. Since our def ${}_{{\rm{H}}\,{\rm\small{I}},{M}_{\star }}$ parameter agrees well with the def ${}_{{\rm{H}}\,{\rm\small{I}},{R}_{\star }}$ parameter from Chung et al. (2009, see also Figure A2a), and H₂ deficiency was derived similarly, we are confident that the H₂ deficiencies we derive are suitable for the purpose of this work.

3.2.1. Stellar Masses and Radii

H₂ radial profiles are calculated as described in Section 4.3 of B21. In summary, they reflect the azimuthally averaged integrated H₂ surface densities in elliptical annuli overlaid on the moment 0 maps at native resolution (these maps can be seen in Appendix A of B21). While some authors opt to correct for inclination in order to obtain a measure of the intrinsic surface density (assuming the gas is distributed in a flat disk), here we do not apply this correction, due to the disturbed nature of several of the sources. Similarly, it should be kept in mind that any extraplanar gas that may be present in these disturbed sources could be assigned to artificially large radii due to projection effects, especially in highly inclined galaxies. This would result in a flattened radial profile, and possibly an overestimation of the radius of the molecular gas "disk."

Pixels that do not contain any detected emission are included as zeros. This means that the surface density at each radius represents the average surface density in the entire corresponding annulus, rather than the average surface density of the molecular gas detected inside the annulus. Therefore, on the outskirts of the molecular gas disks, where CO is not detected in all pixels, this can result in low average molecular gas surface densities. This effect will be stronger in galaxies with very asymmetric molecular gas disks. We continue to add annuli until there are no more detected pixels in the outer annulus. Since we are working with clipped moment 0 maps, all non-zero pixels in the map are significant.

To allow for accurate interpolation in our calculation of the radial profiles, we use annuli with widths of one pixel (2 '', equivalent to ∼160 pc at the distance of Virgo) across the minor axis. This approach differs from that of B21, who use annuli with widths of one beam (7''–10''; B21, Table 2) across the minor axis. To allow for a fair comparison between galaxies, we then interpolate the resulting radii (R) to match certain fractions of the galaxy's stellar radius (at each Δ0.2R_⋆). This means that in some cases ΔR can be smaller than one beam, in which case the integrated H₂ surface densities in the corresponding annuli are not independent. Since we are interested in the relative shapes of the profiles, and their corresponding radii and average surface densities, this will not impact our analysis.

The eccentricities of the annuli, along with the inclinations and position angles of the galaxies, are listed in Table 1 of B21. For highly inclined (i ≳ 80^o ) galaxies we take slices along the major axis instead of annuli (extending infinitely in the direction of the minor axis). The emission in the corresponding slices on each side of the galactic center (at the same galactocentric radius) is then averaged to obtain the radial profile (see also B21).

Molecular gas radial profiles of all CO-detected VERTICO galaxies are shown in B21; Figure 9, and in Figure A3 along with their H i radial profiles (which were calculated in the same way, i.e., by placing annuli on the observed (inclination-uncorrected) H i surface-density maps), as well as the ratio between both profiles. For this figure, the 15'' resolution VERTICO moment 0 maps were used, to match the H i data.

In this paper, the radius of the H₂ disk is defined as its isodensity radius: the radius at which the observed surface density of the molecular gas disk drops below a certain threshold value (henceforth referred to as the "isodensity threshold"). In cases where the surface density is not described by a strictly declining function (for example when a galaxy has pronounced spiral arms and inter-arm regions with low molecular gas surface densities), it is possible that this threshold is reached at multiple radii. In such cases, the outermost radius is defined to be the isodensity radius.

Typically, the radius of the H₂ disk is defined at isodensity thresholds of ∼5 M_⊙pc⁻², where the molecular gas starts dominating the cold gas reservoir (e.g., Walter et al. 2008; Leroy et al. 2008). However, depending on which part of the disk we are interested in (e.g., the core or the very outskirts), it is sometimes useful to use lower or higher isodensity thresholds. Throughout this work, we specify which isodensity threshold is used to define the radius of the molecular gas disk for a particular investigation (e.g., in Figure 4).

Because the main goal of this work is to compare different galaxies, and because we are interested in the relative size of the molecular gas disk, H₂ radii are normalized by the radius of the stellar disk (see Section 3.2.1).

The median H₂ surface density is here defined as the median H₂ surface density of the moment 0 map within an elliptical aperture of which the semimajor axis is a certain observed fraction of R_⋆. For highly inclined galaxies and galaxies with very little flocculent CO emission, such a median surface density is not well defined. For this reason, we do not measure it for the following galaxies: NGC4192, NGC4216, NGC4222, NGC4299, NGC4302, NGC4330, NGC4388, NGC4396, NGC4402, NGC4533, NGC4607, NGC4698, and NGC4772. As a result, median H₂ surface densities are measured for 34/49 detected VERTICO galaxies. Median H₂ surface densities will be studied as a function of H i and H₂ deficiency (see Section 4.4 and Figure 5).

Yoon et al. (2017) study in detail the H i properties of the galaxies in VIVA, the sample on which the VERTICO sample is based. They are particularly interested in H i deficiency, radius, and morphology, since any gas stripping is most notably reflected in these parameters. Therefore, to study the effects of gas stripping as systematically as possible, they define a classification for the Virgo galaxies based on the combination these H i properties. In particular, each class spans a limited range of H i deficiency and relative H i extent. This classification is described in detail in Section 2.1 of Yoon et al. (2017). In summary, galaxies comprising each class are:

• 1.  
  Galaxies with a one-sided H i feature, no truncation of the disk and a relatively symmetric stellar disk. Their H i deficiency varies but is overall close to that in field galaxies.
• 2.  
  Galaxies with highly asymmetric H i disks, caused by tails and/or asymmetric truncation, deficient in H i (average deficiency (def ${}_{{\rm{H}}\,{\rm\small{I}},{R}_{\star }}$) of ∼0.8 dex).
• 3.  
  Galaxies with symmetric but severely truncated H i disks that are extremely H i deficient (average deficiency of ≳ 1.4 dex).
• 4.  
  Galaxies with symmetric H i disks that are only marginally truncated, but with lower H i surface density than the other classes, and an average deficiency of ∼0.8 dex (similar to class ii).
• 5.  
  Galaxies that do not fit in the above classes, including galaxies that resemble "normal" field spirals, extremely H i-rich galaxies with extended H i disks, galaxies that have asymmetric H i disks but no truncation, showing clear signs of tidal interaction.

To build upon this work by Yoon et al. (2017), and investigate if there is any correlation between their H i classification and molecular gas deficiency, these classes are highlighted in Figure 2. Note that the dwarf galaxy NGC4533 is the only galaxy in the VERTICO sample for which no H i class is given in Yoon et al. (2017), who exclude 5 dwarf galaxies from the classification scheme. The reason for this is that such dwarf galaxies might be more sensitive to their local environment rather than their orbital history, which was the main focus of the VIVA classification.

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Figure 2 shows the relationship between H i deficiency and H₂ deficiency. The relationship is shown for two different definitions of H i deficiency: def ${}_{{\rm{H}}\,{\rm\small{I}},{R}_{\star }}$ in the left-hand panel, and def ${}_{{\rm{H}}\,{\rm\small{I}},{M}_{\star }}$ in the right-hand panel (see Section 3.1 for their respective definitions). H i deficiencies from both definitions correlate well (the typical scatter is ∼0.2 dex, see Figure A2(a)). The classes in the legend refer to the H i classification described in Section 3.6. Six well-studied cases of galaxies undergoing RPS are highlighted with red numbers 1–6, and listed in the top-left corner of the left-hand panel in order of pre-to-post RP peak (Vollmer 2003, 2009; Vollmer et al. 2004, 2008, 2012; Boselli et al. 2006, 2016; Lee et al. 2017; Lee & Chung 2018).

There is a weak correlation between H i and H₂ deficiency. The Spearman correlation coefficient is 0.28 ± 0.05 in the left-hand panel (where def _{H i} ≡ def ${}_{{\rm{H}}\,{\rm\small{I}},{R}_{\star }}$), with a typical p value of 0.05, and 0.36 ± 0.04 in the right-hand panel (where def _{H i} ≡ def ${}_{{\rm{H}}\,{\rm\small{I}},{M}_{\star }}$), with a typical p value of 0.01. Uncertainties on the Spearman correlation coefficient were obtained using a Monte Carlo analysis, and represent the spread in the values of Spearman's correlation coefficient after calculating it 1 × 10⁵ times, perturbing each point by its error bar. The weak correlation between H i and H₂ deficiency suggests that the environmental effects removing H i from galaxies also affect the molecular gas, albeit to a lesser extent.

Most galaxies are located in the upper-right quadrant of Figure 2, meaning they are both H i and H₂ deficient. This suggests that, despite the lack of a stronger correlation between their deficiencies, both the atomic and molecular gas phases are affected by environmental processes.

In terms of H i classes, there is a significant scatter in H₂ deficiency within each class. There are, however, some differences between the classes. Except for a few outliers, class 0 galaxies (galaxies with "normal" H i reservoirs that resemble those of field galaxies) have normal to high H₂ fractions, in line with their morphologically normal, non-deficient H i reservoirs. Class i galaxies, which exhibit one-sided H i features but otherwise have H i and stellar disks similar to those of field galaxies, are H₂ normal. Classes ii and iii (galaxies with moderate to extreme asymmetries and significant H i deficiencies) have moderately deficient H₂ reservoirs. Galaxies that are H i deficient due to their lower H i surface densities (class iv galaxies) have relatively high H₂ deficiencies. The six known RPS galaxies are relatively H₂ rich compared to other VERTICO galaxies with similar H i deficiencies.

Median ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ radial profiles are shown in Figure 3, they are divided into three equal bins of def ${}_{{\rm{H}}\,{\rm\small{I}},\ {R}_{\star }}$, indicated by the color bar. In the color bar, the white dots show the distribution of H i deficiencies. The solid lines show the medians of the radial profiles in each bin; the shaded areas cover the 16th to 84th percentile regions. The teal dashed line represents the median H₂ radial profile of the 21 galaxies in the HERACLES field sample, whose 16th to 84th percentiles are indicated with dotted lines. The x-axis is normalized by the isodensity radius of the stellar disk (at Σ_⋆(R_⋆) = 1M_⊙ pc⁻²), the y-axis is not normalized.

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More strongly H i-deficient galaxies have steeper and more truncated H₂ radial profiles. This suggests that the environmental processes acting on the atomic gas cause outside-in removal of the molecular gas. The median H₂ radial profile of the HERACLES sample lies between those of the most H i-rich and moderately H i-deficient VERTICO galaxies.

Figure 4 shows the H₂ disk radii (${R}_{{{\rm{H}}}_{2}}$) as a function of H i deficiency (left panel) and H₂ deficiency (right panel), for a ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ threshold 1 M_⊙pc⁻². As can be seen in Figure 3, this threshold probes the low-density gas at the outskirts of the H₂ disk, which is the gas most likely to be affected by environmental mechanisms. ${R}_{{{\rm{H}}}_{2}}$ declines significantly with H i deficiency; the Spearman correlation coefficient is r_S = − 0.44 ± 0.07, with a typical p value of 1.7 × 10⁻³. Outliers of this correlation are NGC4561, NGC4654, NGC4419, and NGC4380 (annotated in the figure). NGC4561 only has a few "blobs" of detected molecular gas, which means that it does not have a well-defined H₂ radius. NGC4380 has a large, regular-looking molecular gas disk. NGC4654 also has a large molecular gas disk, with a one-sided RPS feature. Although NGC4419 is not among the "well-studied" RPS cases, the morphology of its molecular gas disk suggests that it is likely also undergoing RPS (see Appendix A in B21).

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There is a weaker anticorrelation between H₂ radius and H₂ deficiency, which is likely intrinsic. The Spearman correlation coefficient of this relation is r_S = − 0.29 ± 0.05, with a typical p value of 0.04. Outliers of this relation are NGC4772, NGC4698, NGC4450, and NGC4394. Like NGC4561, NGC4772 only has very little, patchy, detected molecular gas, which results in a large radius for its strong H₂ deficiency. In NGC4698, the molecular gas is distributed in a ring, resulting in a similar effect. NGC4450 has a one-sided molecular gas feature, which is responsible for its relatively large H₂ radius. The molecular gas in NGC4394 is also patchy, again resulting in a strong deficiency compared to its H₂ radius.

The anticorrelation between H i deficiency and ${R}_{{{\rm{H}}}_{2}}$ suggests that the environmental mechanism(s) removing H i from galaxies also cause outside-in stripping of their molecular gas. On average, galaxies in the HERACLES sample have marginally smaller H₂ deficiencies and marginally larger H₂ radii. However, there is no statistically significant difference between both samples.

Figure 5 shows the median surface density of the molecular gas disk as a function of H i deficiency (left-hand panel) and H₂ deficiency (right-hand panel), within a radius of R = 0.1 R_⋆ (typically corresponding to several hundred pc, roughly equivalent to the inner resolution element of the moment 0 map for most galaxies in the sample). This radius was chosen because, if any inward compression of the gas is taking place, the effect is likely subtle and primarily visible in the very center of the galaxy. While, by eye, there appears to be a weak correlation between H i deficiency and central H₂ surface density, it is not statistically significant (the Spearman correlation coefficient is r_s = 0.26 ± 0.05 with a typical p value of 0.12).

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There is no correlation between H₂ deficiency and central H₂ surface density (the Spearman correlation coefficient is r_S = − 0.18 ± 0.09, with a typical p value of 0.3). On average, galaxies in the HERACLES sample have marginally smaller H₂ deficiencies and marginally larger central H₂ surface densities. However, there is no statistically significant difference between both samples.

Figures 4 and 5 are shown for specific choices of the H₂ radius: in Figure 4, the radius of the H₂ disk is defined at ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}=1\ {M}_{\odot }\ {\mathrm{pc}}^{-2}$ and, in Figure 5, the median H₂ surface density is measured inside 0.1 R_⋆. To investigate how the relationships shown in these plots change with the choice of radius (i.e., the isodensity threshold at which the H₂ radius is defined, and the semimajor axis of the ellipse enclosing the area in which the median H₂ surface density is calculated), we remake both figures using a number of different radii, and measure their Spearman correlation coefficients. Figure 6 shows these Spearman correlation coefficients for the relationships between H i deficiency (left-hand panel) and ${R}_{{{\rm{H}}}_{2}}$ and ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ (purple and orange, respectively), and, similarly, the relationships between H₂ deficiency and ${R}_{{{\rm{H}}}_{2}}$ and ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ (right-hand panel). Relationships for which the p value associated with Spearman's correlation is greater than 0.05 (and are thus considered to not be statistically significant) are indicated with semitransparent markers.

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The relationship between H i deficiency and ${R}_{{{\rm{H}}}_{2}}$ is strongest for low isodensity thresholds, and disappears for higher thresholds. Thus, this correlation is only seen when the lower density material at the outskirts of the molecular gas disk is taken into account. The higher density material at smaller radii is not affected significantly. This implies either outside-in stripping, or the removal of molecular gas throughout the disk, resulting in the low-surface-density gas at the outskirts dropping below our detection threshold. However, the latter explanation would result in H₂ radial profiles with shapes similar to those of field galaxies, but scaled down, which is not observed for VERTICO galaxies (see Figure 3). The relationship between H₂ deficiency and ${R}_{{{\rm{H}}}_{2}}$ is present for all values of the isodensity threshold except the very highest, and is likely intrinsic.

The relationship between H i deficiency and ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ is not statistically significant, and any hint of increased H₂ surface densities is only present in the very centers of galaxies (R < 0.1R_⋆). The moderate negative correlation between H₂ deficiency and median H₂ surface density is independent of the choice of radius, although it is no longer statistically significant when the median H₂ surface density is calculated in the central regions only. This correlation is likely intrinsic.

Truncated molecular gas disks could be explained by several environmental mechanisms, such as RPS, tidal interactions, and galaxy-galaxy encounters. However, tidal interactions and galaxy-galaxy encounters are expected to result in significant kinematic in addition to morphological disturbances, which are not evident in the moment 1 maps of VERTICO galaxies (see Appendix A in B21). Thermal evaporation can remove gas from the disk, which could result in observed truncation as the surface density of the molecular gas at the outskirts of the disk drops below the sensitivity limit of our observations. The same is true for starvation. However, both of these processes should result in relatively uniform removal of gas, which should not significantly change the shape of the ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ radial profile. Additionally, the large amounts of hot ICM required for thermal evaporation would automatically result in RPS as satellite galaxies move through it.

The most likely explanation for the observed truncated molecular gas disks is RPS. In the earlier stages of RPS, the outer parts of the radial profile are likely dominated by the gas tail, resulting in a relatively flat and extended radial profile. It is possible that, as the stripping continues, the outer parts of the stripped tail become undetectable, resulting in a steeper and more truncated profile. Additionally, RPS could result in the inward compression of gas, which would contribute to the steepness of the ${{\rm{\Sigma }}}_{{{\rm{H}}}_{2}}$ radial profiles, as also reported by, e.g., Mok et al. (2017).

Several moment zero maps of VERTICO galaxies exhibit clear RPS signatures (for example NGC4654; B21, Figure 4.22). If RPS is responsible for the truncation of the molecular gas disks, the lack of a stronger correlation between H i and H₂ deficiency suggests that it is not very effective at removing molecular gas from galaxies, or at least not in the early stages, when significant amounts of H i are still present. This is also reflected in Figure 2, which shows that the Virgo spirals with the clearest RPS signatures (including post-RPS peak galaxies) have relatively large H₂ fractions compared to other VERTICO galaxies with similar stellar masses. It is possible that only a small amount of low-density gas is stripped (at this stage).

One of the VERTICO galaxies with clear RPS signatures, NGC4402, has recently been studied in detail by Cramer et al. (2020) using high-resolution (1'' × 2'', ∼80–160 pc at the distance of the Virgo cluster) CO(2 – 1) observations from ALMA. They estimate the strength of the ram pressure at the location of NGC4402 and find that only diffuse, low-surface-density H₂ (up to 2.5 − 10 M_⊙ pc⁻², depending on the exact ICM density at its location) can be stripped from this galaxy by RP. This limit is likely similar or lower for other galaxies in the VERTICO sample, as NGC4402 is probably close to the cluster center (∼0.4 Mpc in projection), and ram pressure decreases rapidly with cluster-centric radius (p ∝ r⁻², Gunn & Gott 1972). This is in line with our findings, which suggest that RPS is acting on the molecular gas in VERTICO galaxies, but unable to remove significant amounts of it.

Cramer et al. (2020) also report a region with increased CO surface brightness as a result of RPS in NGC4402, resulting in enhanced star formation (which aids the removal of diffuse gas through stellar feedback). In a similar study of the CO in Coma cluster galaxy NGC 4921, Cramer et al. (2021) also find evidence for compression of the dense ISM on the leading side of this galaxy, accompanied by enhanced star-formation activity. As discussed above, similar results were found by Mok et al. (2017). Such increased molecular gas densities could explain the relatively large molecular gas fractions in well-studied RPS galaxies in the VERTICO sample (Figure 2), by offsetting the amount of diffuse H₂ lost through stripping. We do not find evidence for increased H₂ surface densities in this work. However, here we exclusively work with radially averaged radial profiles. More detailed (case) studies of the H₂ distribution and SFRs in VERTICO galaxies are needed to investigate how common regions with increased H₂ surface densities and star formation as a result of RPS are, and to what extent (and on what timescales) they can compensate the mass loss from the stripping of low-surface-density molecular gas.

Galaxies that do not show any sign of environmental effects on their H i reservoirs (class 0 galaxies in Yoon et al. 2017) are H₂ rich compared to galaxies that do. The difference in H₂ reservoirs between H i-normal and H i-disturbed objects confirms that the effects of environment on atomic gas also act on molecular gas. Galaxies with relatively low H i surface densities (class iv galaxies) are relatively H₂ poor. This suggests that (external or internal) processes resulting in lower gas surface densities are more effective at reducing the molecular gas reservoir than outside-in stripping. Galaxies with very strongly asymmetric and/or truncated H i disks cover a range in H₂ deficiencies, suggesting that the mechanisms causing these features do not necessarily significantly reduce the global molecular gas mass, at least on timescales where the galaxies still contain detectable H i.

Simulations of RPS acting on the multi-phase ISM (with H₂ treated as a separate component) have indeed shown that RPS can strip H₂ from the outer parts of galaxies, especially when the orientation of the wind is face-on (Lee et al. 2020). However, not all simulations agree on how molecular gas is impacted by RPS. Tonnesen & Bryan (2009) have shown, for example, that the fate of dense gas depends heavily on the strength of the RP: at low RP, the amount of high-density gas is enhanced, while it is depressed at high RPs. Similarly, Tonnesen (2019) find that, in recent infallers, compression can lead to high-density gas that is impossible to be stripped at later stages. Thus, whether significant amounts of H₂ are stripped, and whether H₂ is enhanced in galactic centers, likely varies between clusters, and depends on the locations of galaxies in phase space.

While simulations have rarely mapped H₂, some simulations show mild SF enhancement in RPS galaxies, particularly at the pericenter of their orbits (Bekki 2014; Steinhauser et al. 2016; Ruggiero & Lima Neto 2017). However, not all of them agree on where in galaxies these enhancements are found. Tonnesen & Bryan (2012), Bekki (2014), and Boselli et al. (2021) find that SF in generally enhanced in the centers, while Roediger et al. (2014) find that SF is only enhanced via compression at the disk edges, right before gas is removed. All in all, there is little evidence for central enhancement of SF from simulations, and therefore, assuming that SF traces H₂, of central enhancement of H₂.