VERTICO II: effects of HI-identified environmental mechanisms on molecular gas

In this VERTICO early science paper we explore in detail how environmental mechanisms, identified in HI, affect the resolved properties of molecular gas reservoirs in cluster galaxies. The molecular gas is probed using ALMA ACA (+TP) observations of 12CO(2-1) in 51 spiral galaxies in the Virgo cluster (of which 49 are detected), all of which are included in the VIVA HI survey. The sample spans a stellar mass range of 9<log M*/Msol<11. We study molecular gas radial profiles, isodensity radii, and surface densities as a function of galaxy HI deficiency and morphology. There is a weak correlation between global HI and H2 deficiencies, and resolved properties of molecular gas correlate with HI deficiency: galaxies that have large HI deficiencies have relatively steep and truncated molecular gas radial profiles, which is due to the removal of low-surface density molecular gas on the outskirts. Therefore, while the environmental mechanisms observed in HI also affect molecular gas reservoirs, there is only a moderate reduction of the total amount of molecular gas.


INTRODUCTION
Hosting hundreds to thousands of galaxies bound by a dark matter halo, galaxy clusters form the largest virialised structures in the Universe. In these high-contribute to this premature quenching, such as ram pressure stripping (RPS, Gunn & Gott 1972, see also Cortese et al. 2021 andBoselli et al. 2021 for recent reviews), the lack of fresh gas available for accretion, e.g. from the circum-galactic medium, causing a galaxy to deplete its gas reservoir (also referred to as "starvation", Larson et al. 1980), galaxy-galaxy interactions (Moore et al. 1996), tidal interactions, and thermal evaporation and viscous stripping (Cowie & Songaila 1977;Nulsen 1982, see also Cortese et al. 2021 for extensive descriptions of each environmental mechanism). The relative importance of these mechanisms, and to which extent this varies between clusters, is not yet well-understood.
Typically distributed within an extended disc (D Hi ∼ 1 − 2 D 25 , e.g. Verheijen & Sancisi 2001) and relatively loosely bound, atomic gas (Hi) is susceptible to environmental processes. Cluster galaxies are often Hi-deficient (i.e. they contain less Hi than expected from their optical size), and have truncated and/or asymmetric Hi discs (e.g. Giovanelli & Haynes 1985;Cayatte et al. 1990;Solanes et al. 2001;Schröder et al. 2001;Waugh et al. 2002;Gavazzi et al. 2005;Rasmussen et al. 2006;Hughes & Cortese 2009;Chung et al. 2009;Odekon et al. 2016;Yoon et al. 2017;Loni et al. 2021). Since atomic gas provides the fuel for molecular clouds, which will eventually collapse into stars, this removal of Hi might lead to the quenching of star formation.
More recently, it has been shown that, despite its more tightly bound and centrally located nature (e.g. Davis et al. 2013), molecular gas can also be directly affected by environmental processes. For example, molecular gas discs in cluster galaxies have been found to be truncated and/or morphologically and kinematically disturbed, while molecular gas fractions have been found to be deficient compared to field galaxies at fixed stellar mass (e.g. Vollmer et al. 2008;Fumagalli et al. 2009;Boselli et al. 2014a;Lee et al. 2017;Lee & Chung 2018;Zabel et al. 2019;Cramer et al. 2021;Brown et al. 2021). Additionally, molecular gas fractions can also be enhanced in cluster galaxies, as a result of ram pressure, which can facilitate the conversion of atomic into molecular gas (e.g. Moretti et al. 2020).
It is not yet clear to what extent the processes acting on the atomic gas also affect the molecular gas and, if they do, on what relative timescales. It is possible that: a) atomic and molecular gas are removed and disturbed simultaneously by the same environmental processes (for example by galaxy-galaxy interactions), b) the majority of the atomic gas is removed before the molecular gas (for example by RPS), or c) atomic and molecular gas are affected by different environmental processes entirely (for example, molecular gas is depleted through starvation while atomic gas is being stripped). Which of these options is closest to reality has strong implications for the process of environmental quenching, and the timescales on which this takes place.
Whether the molecular gas reservoirs of Virgo galaxies are different from those of their counterparts in the field has been a matter of debate (Stark et al. 1986;Kenney & Young 1989;Boselli et al. 1995;Mok et al. 2016Mok et al. , 2017. Boselli et al. (2014a) studied the H 2 content of ∼75 spiral galaxies in the Virgo cluster using the Herschel Reference Survey (HRS, Boselli et al. 2010) and compared them to the remaining field galaxies in the HRS. They find that, on average, Hi-deficient Virgo cluster galaxies have less molecular gas than Hi-normal field galaxies. Moreover, they find a weak but statistically significant increase in H 2 deficiency as a function of Hi deficiency. This suggests that both gas phases are affected simultaneously in the Virgo cluster. Resolved observations of 17 of these HRS Virgo galaxies (Kuno et al. 2007) show a decrease in the extent of the molecular gas disc with increasing Hi deficiency, which implies outside-in stripping of the molecular gas. On the other hand, Loni et al. (2021) find significant scatter in H 2 /Hi mass ratios in galaxies in the Fornax cluster (including both upper and lower limits), suggesting that the relative effects of environmental mechanisms on both gas phases are not straightforward.
This work is one of the early science papers of the Atacama Large Millimeter/submillimeter Array (ALMA) large programme the "Virgo Environment Traced in CO" (VERTICO, Brown et al. 2021, hereafter referred to as B21). VERTICO comprises homogeneous CO(2-1) observations of 51 spiral galaxies in the Virgo cluster (of which 49 are detected), and is designed to systematically study the physical mechanisms that drive galaxy evolution in dense environments. Because the VERTICO sample is selected from the Very Large Array Imaging of Virgo in Atomic gas survey (VIVA, Chung et al. 2009, see §2), ancillary Hi imaging is available for all CO-detected galaxies in the sample. In this work, we study the resolved atomic and molecular gas in the 49 Virgo galaxies detected in CO with VERTICO.
The Virgo cluster is a young and dynamically active cluster, with several sub-structures and infalling groups (e.g. Gavazzi et al. 1999;Solanes et al. 2002;Boselli et al. 2014b;Lisker et al. 2018). As the closest galaxy cluster to us (at ∼16.5 Mpc, Mei et al. 2007), it has been studied extensively in a range of wavelengths (Binggeli et al. 1985;McLaughlin 1999;Fouqué et al. 2001;Davies et al. 2010;Ferrarese et al. 2012;Mihos et al. 2017;Boselli et al. 2011Boselli et al. , 2018, see also the references in B21). Fol-lowing B21, we adopt a common distance of 16.5 Mpc for all galaxies in the sample.
In this work, we study how molecular gas is affected by environment in galaxies in the Virgo cluster. We make use of the homogeneity and resolution of VERTICO to study resolved properties of the molecular gas, such as sizes and radial profiles, and compare them to those of control galaxies. We probe the extent to which a galaxy is affected by environment, and the mechanism by which it is affected (if it is possible to identify this), using Hi data from the VIVA survey (Chung et al. 2009;Yoon et al. 2017).
This paper is organised as follows. In §2 the sample, observations, and data reduction are described. The control samples used to compare our results to are introduced here. §3 contains the methods used, as well as a description of various definitions adopted throughout this work. Deficiency parameters are defined for both the atomic and molecular gas, and the calculation of radial profiles, H 2 radii, and median H 2 surface densities is also described here. In §4 we describe the results, and provide brief interpretations, while in §5 we provide a more thorough interpretation and discussion, including comparison to previous work. Finally, a short summary, as well as an itemised list of the findings from this work, are given in §6.

SAMPLE, OBSERVATIONS & DATA REDUCTION
The sample used in this work consists of the 49 COdetected VERTICO galaxies. The sample selection and data reduction of VERTICO are described in detail in B21, and are summarised below.
VERTICO targeted the CO(2-1) line in 51 late-type galaxies that were part of the VIVA survey (Chung et al. 2009) using the ALMA Atacama Compact Array (ACA). Of these, 15 galaxies that were already observed with the ACA were taken from the ALMA archive. Archival galaxies primarily come from the ALMA component of the Physics at High Angular resolution in Nearby Galaxies project (PHANGS-ALMA; Leroy et al. 2021a, various project IDs; see table 2 in that work). One galaxy, NGC4402, comes from Cramer et al. (2020, project ID 2016. The final sample includes galaxies undergoing a variety of environmental effects, as identified in their Hi imaging (Chung et al. 2009). Our sample spans a stellar mass range of 10 9 ≤ M /M ≤ 10 11 . B21 calculated inclination and position angles from fits to Sloan Digital Sky Survey (SDSS, York et al. 2000;Alam et al. 2015) r -band images (see table 1 in B21).
The 36 galaxies that were not yet on the ALMA archive were observed during Cycle 7 under program ID 2019.1.00763.L. Total Power (TP) observations were  added for 25 targets for which the CO was expected to  extend beyond the largest recoverable angular size of  29 . For the 36 Cycle-7 galaxies we used the calibrated uvdata as delivered by ALMA. The raw uv -data of the remaining 15 objects were recalibrated using the Common Astronomy Software Applications package (CASA, McMullin et al. 2007), using the appropriate version. For the imaging of both the ACA and the TP data the PHANGS-ALMA Imaging Pipeline Version 1.0 and the PHANGS-ALMA TP Pipeline were used, respectively (Herrera et al. 2020;Leroy et al. 2021b). Three modifications were implemented in the Imaging Pipeline to optimise for the VERTICO sample, which are described in detail in §3.1 of B21. A Briggs weighting scheme was adopted (Briggs 1995), with a robust parameter of 0.5. The total-power data were processed at their native velocity resolution of ∼ 3 km s −1 , and no other modifications were made to the TP Pipeline. For the PHANGS-VERTICO galaxies, calibrated TP cubes were kindly provided to us by Adam Leroy on behalf of the PHANGS-ALMA team in private communication. Finally, the total-power data were combined with the ACA data via feathering using the PHANGS-ALMA pipeline (Leroy et al. 2021b).
The median spatial resolution of the resulting data cubes is ∼ 8 (∼640 pc at the distance of Virgo), and the final velocity resolution is 10 km s −1 . The flux calibration uncertainty is typically 5 − 10% 1 . The typical rootmean-square (rms) sensitivity reached with the ACA, after an average integration time of 3.7 hours on source, is 10.6 mJy beam −1 per 10 km s −1 channel. All galaxies were detected in CO except IC3418 and VCC1581, for which we calculated 3σ upper limits. Although the presence of Hi emission in IC3418 was confirmed later by Kenney et al. (2014), its image is not available (unlike VCC1581) and it is not considered in this work beyond Figure 1.

Control samples
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 Hi and H 2 masses in VERTICO to those of the general population of galaxies at fixed stellar mass, and estimate Hi and H 2 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 VER-TICO 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 §2.1.2.
In Figure A.1 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 Multi-wavelength Galaxy Synthesis (z0MGS, Leroy et al. 2019), which are adopted for the VERTICO sample (see §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 ( §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.

xGASS & xCOLD GASS
As described in §2, the VERTICO sample consists exclusively of late-type galaxies. In the field, such galaxies are expected to lie on, or close to, the star formation main sequence (SFMS). Therefore, to ensure a fair comparison with VERTICO, we only consider galaxies from xGASS and xCOLD GASS within 2σ from the SFMS (Elbaz et al. 2007). Furthermore, galaxies with confused Hi emission (i.e. the Hi emission from multiple sources cannot be separated reliably), as identified by Catinella et al. (2018), are eliminated from the xGASS sample. After applying these selection criteria, the comparison sample from xGASS consists of 541 galaxies with detected Hi, and 33 with upper limits.
Molecular gas masses from xCOLD GASS were corrected for the difference in α CO (see §3.2; xCOLD GASS uses the metallicity-dependent α CO from Accurso et al. 2017). The final comparison sample consists of 303 galaxies, 44 of which are upper limits.
Upper limits are taken into account in the calculation of the median H 2 mass using survival analysis (a statistical method designed to take into account "censored" data: measurements for which only an upper or lower limit is available). We used the Kaplan-Meier estimator, implemented in the Python package Lifelines (Davidson-Pilon 2019), to estimate the true cumulative distribution of H 2 mass with upper limits taken into account. The median H 2 mass was estimated from the resulting distribution. The Kaplan-Meier estimator takes censored data into account assuming they follow a similar distribution to the measured data. Finally, we calculate the rolling median of the H 2 mass by dividing the sample into 10 stellar mass bins and using a shift of half a bin.

HERACLES: a resolved control sample
We compare the resolved properties of VERTICO galaxies to those from HERACLES. We first remove galaxies that are also in VERTICO from the HERACLES sample (NGC4254, NGC4321, NGC4536, NGC4569, and NGC4579), as well as interacting galaxies (NGC2146, NGC2798, NGC3034, NGC3077, and NGC5713), except for those with a significantly less massive or gas-poor companion, such as NGC5194 (M51). The remaining sample consists of 21 galaxies detected in CO. Resolved quantities are calculated from the HERACLES moment 0 maps at native resolution (the typical beam size is b maj ∼ 13 ), in the same way as those of VERTICO. These maps are calculated from the 10 km s −1 cubes, using the VERTICO data products pipeline (B21, §4.1). NGC4214, NGC2841, and NGC4725 are omitted from the H 2 surface density analysis due to their high inclination (see §3.5).
Global molecular gas mass fractions of the HERA-CLES sample are shown in Figure 1. Here we can see that HERACLES galaxies are relatively gas-rich. The HERACLES sample was based on The Hi Nearby Galaxy Survey (THINGS, Walter et al. 2008), which was in turn based on the Space Infrared Telescope Facility (SIRTF) Nearby Galaxies Survey (SINGS, Kennicutt et al. 2003). By design, this sample has a flat far-infrared (FIR) luminosity distribution (as measured at 60µm with the Infrared Astrononical Satellite, IRAS). This means that, compared to the actual FIR luminosity distribution of galaxies in the local universe, FIR-faint galaxies are significantly under-represented (see also figure 6 in Kennicutt et al. 2003). Therefore, it is likely that the SINGS, THINGS, and HERACLES samples are biased towards galaxies with high (atomic and molecular) gas masses (e.g. Saintonge et al. 2018). This should be kept in mind throughout the remainder of this work.

H i deficiency
For the majority of this work, Hi deficiencies are adopted from Chung et al. (2009), who use the Hubble type independent definition from : whereΣ HI ≡ S HI /D 2 opt , where S HI is the Hi flux in Jy km s −1 and D opt is the diameter of the optical disc in arcminutes.Σ HI is the mean Hi surface density within the optical disc, and logΣ HI = 0.37 for all Hubble types. Uncertainties on the Hi deficiency reflect the difference with the Hubble-type-dependent deficiency for the same object (in reality logΣ HI varies somewhat with Hubble type, see §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 Hi 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 §3.2). To ensure a fair comparison between deficiencies in both gas phases, we consider a second definition of Hi deficiency, similar to that for H 2 deficiency: where the expected Hi mass, M Hi, exp , is the median Hi mass at fixed stellar mass from a control sample from xGASS (see 2.1.1), and M Hi, meas is the measured Hi mass. Uncertainties in def Hi, M are calculated by combining the uncertainty in the Hi mass and that resulting from the uncertainty in the stellar mass. The 1σ spread in Hi 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 def Hi, M . The resulting Hi deficiencies are listed in Table 1.

H 2 deficiency
The mass-size relation for H 2 has not been defined as well as for Hi (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 H 2 mass of a control sample at fixed stellar mass to estimate the expected H 2 mass. Then the H 2 deficiency can be defined as follows: where M H2,exp corresponds to the expected molecular gas mass of a galaxy, and M H2,meas is its measured global molecular gas mass. The control sample we use to calculate M H2,exp is xCOLD GASS (see §2.1.1). Global molecular gas mass estimates for the VER-TICO sample are described in detail in §4.4 of B21, and are summarised here. Molecular gas masses are derived from CO luminosities as follows: where α CO = 4.35 M pc −2 (K km s −1 ) −1 , corresponding to the Galactic value of X CO = 2 × 10 20 cm −2 (K km s −1 ) −1 recommended by Bolatto et al. (2013), and R 21 ≡ 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): 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 H 2 deficiency are calculated by combining the uncertainty in the H 2 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 def H2 . 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 §2.1.1), whose median is shown as a solid black line, while the 1, 2, and 3 σ spread is shown as shaded grey areas. The medians of the VERTICO sample, in stellar mass bins of 0.5 dex, are shown as orange squares. H 2 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 H 2 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 . H2 fractions of VERTICO (orange dots) and HERACLES (teal diamonds) galaxies compared to 303 galaxies from xCOLD GASS, as a function of stellar mass. Downward triangles represent upper limits. The solid black line represents the rolling median of the xCOLD GASS sample, while the shaded grey areas indicate the 1, 2, and 3 σ spread (from dark to light, respectively). The connected orange squares with black edges are the median H2 fractions of VERTICO galaxies in four equal stellar mass bins in log space (excluding the two upper limits). VERTICO galaxies with log M 9.75 log M are moderately but systematically H2 deficient, while low-mass VERTICO galaxies have H2 fractions similar to or higher than xCOLD GASS galaxies at fixed M . HERACLES galaxies are relatively H2-rich. stellar masses log M /M 9.75 have H 2 fractions similar to, or marginally higher than, those of xCOLD GASS galaxies at fixed stellar mass. HERACLES galaxies are H 2 -rich compared to xCOLD GASS at fixed stellar mass (see also §2.1.2).
There is a sub-sample of VERTICO galaxies that overlaps with a sub-sample of the Herschel Reference Survey (HRS, Boselli et al. 2010) for which high-quality CO data are available (Kuno et al. 2007). H 2 deficiencies for these galaxies were estimated by Boselli et al. (2014a) similarly to this work, but where M H2,exp in Equation 3 is defined as follows: where the coefficients c and d are derived from linear fits to the relationship between logM (H 2 ) and V ariable, where the latter is chosen to be M . The sample used to derive this linear fit consists of all HRS galaxies with Hi deficiencies ≤0.4, and upper limits are treated as measurements. An extensive description of the calibration of this H 2 deficiency parameter can be found in §4.1 in Boselli et al. (2014a). A comparison between H 2 deficiencies from that work and those derived here is shown in Figure A.2b. H 2 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 H 2 deficiences. There is a systematic offset in molecular gas masses in VER-TICO 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 §4.3 in B21). This likely causes differences in the derived H 2 deficiencies. Moreover, the control samples used to calibrate the relation are significantly different. Boselli et al. (2014a) calibrate the relation against a sub-sample of the HRS consisting of 101 spiral galaxies for which CO data are available, and which have Hi deficiencies ≤ 0.4 dex. This method could introduce a bias towards gas-rich galaxies, which would result in an overestimation of H 2 deficiencies for the Virgo systems. Since our def Hi,M parameter agrees well with the def Hi,R parameter from Chung et al. (2009, see also Figure A.2a), and H 2 deficiency was derived similarly, we are confident that the H 2 deficiencies we derive are suitable for the purpose of this work.

Stellar masses & radii
Stellar masses for the VERTICO sample are adopted from the z = 0 Multi-wavelength Galaxy Synthesis (z0MGS, Leroy et al. 2019), who use the initial mass function (IMF) from Kroupa & Weidner (2003). The only exception is IC3418, which is not included in z0MGS. For this galaxy we adopt a stellar mass of M = 10 8.37 M , following Fumagalli et al. (2011, see also §2.2 in B21). Stellar radii are here defined as the isodensity radius with a threshold of Σ = 1 M pc −2 . These radii are measured by identifying the outermost annulus or slice of the stellar mass radial profile (measured as described in §3.3) that is still above this threshold, and adopting its radius. For consistency with the gas radius and surface density measurements (see §3.3) the stellar surface density maps are not corrected for inclination before radial profiles are derived. The uncertainty in the radius is a combination of the resolution of the stellar mass surface density maps (9 , corresponding to ∼720 pc at the distance of the Virgo cluster) and the uncertainty in the stellar mass surface density.
We produce stellar mass surface density maps from Wide-field Infrared Survey Explorer (WISE) band 1 photometry, following the procedure laid out in Leroy et al. (2019, and therefore using the same IMF as that used for the stellar masses, see above). All images are convolved from their native resolution to a 9 Gaussian beam, using the convolution kernels from Aniano et al. (2011). All Gaia DR2 stars within the image area are masked. Image backgrounds are estimated and subtracted with the Background2D function from Astropy. For each pixel we determine the local mass-to-light ratio (at 3.4 µm) using the WISE band 3 to WISE band 1 colour as an 'sSFR-like' proxy, and following the calibrations given in the Appendix of Leroy et al. (2019). The WISE band 1 images are then combined with the derived mass-to-light ratios to produce resolved stellar mass surface density maps in units of M pc −2 .

Radial profiles
H 2 radial profiles are calculated as described in §4.3 of B21. In summary, they reflect the azimuthally averaged integrated H 2 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 "disc".
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 discs, 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 discs. 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 ∆0.2R ). This means that in some cases ∆R can be smaller than one beam, in which case the integrated H 2 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 centre (at the same galactocentric radius) is then averaged to obtain the radial profile (see also B21).
Molecular gas radial profiles of all CO-detected VER-TICO galaxies are shown in B21; figure 9, and in Figure A.3 along with their Hi radial profiles (which were calculated in the same way, i.e. by placing annuli on the observed (inclination-uncorrected) Hi 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 Hi data.

H 2 radii
In this paper, the radius of the H 2 disc is defined as its isodensity radius: the radius at which the observed surface density of the molecular gas disc 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 H 2 disc 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 disc 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 disc 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 disc, H 2 radii are normalised by the radius of the stellar disc (see §3.2.1).

Median H 2 surface densities
The median H 2 surface density is here defined as the median H 2 surface density of the moment 0 map within an elliptical aperture of which the semi-major axis is a certain observed fraction of R . For highlyinclined 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 H 2 surface densities are measured for 34/49 detected VERTICO galaxies. Median H 2 surface densities will be studied as a function of Hi and H 2 deficiency (see §4.4 and Figure  5). Yoon et al. (2017) study in detail the Hi properties of the galaxies in VIVA, the sample on which the VER-TICO sample is based. They are particularly interested in Hi 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 Hi properties. In particular, each class spans a limited range of Hi deficiency and relative Hi extent. This classification is described in detail in §2.1 of Yoon et al. (2017). In summary, galaxies comprising each class are:

Classification of H i removal stages
Class i Galaxies with a one-sided Hi feature, no truncation of the disc and a relatively symmetric stellar disc. Their Hi deficiency varies but is overall close to that in field galaxies.
Class ii Galaxies with highly asymmetric Hi discs, caused by tails and/or asymmetric truncation, deficient in Hi (average deficiency (def Hi,R ) of ∼0.8 dex).
Class iii Galaxies with symmetric but severely truncated Hi discs that are extremely Hi deficient (average deficiency of 1.4 dex).
Class iv Galaxies with symmetric Hi discs that are only marginally truncated, but with lower Hi surface density than the other classes, and an average deficiency of ∼0.8 dex (similar to class ii).
Class 0 Galaxies that do not fit in the above classes, including galaxies that resemble "normal" field spirals, extremely Hi-rich galaxies with extended Hi discs, galaxies that have asymmetric Hi discs 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 Hi 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 Hi 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. Figure 2 shows the relationship between Hi deficiency and H 2 deficiency. The relationship is shown for two different definitions of Hi deficiency: def Hi, R in the lefthand panel, and def Hi, M in the right-hand panel (see §3.1 for their respective definitions). Hi deficiencies from both definitions correlate well (the typical scatter is ∼0.2 dex, see Figure A.2a). The classes in the legend refer to the Hi classification described in §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(Vollmer , 2009Vollmer et al. 2004Vollmer et al. , 2008Vollmer et al. , 2012Boselli et al. 2006Boselli et al. , 2016Lee et al. 2017;Lee & Chung 2018).

Do H i deficiencies predict H 2 deficiencies?
There is a weak correlation between Hi and H 2 deficiency. The Spearman correlation coefficient is 0.28 ± 0.05 in the left-hand panel (where def Hi ≡ def Hi, R ), with a typical p-value of 0.05, and 0.36 ± 0.04 in the right-hand panel (where def Hi ≡ def Hi, M ), 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 × 10 5 times, perturbing each point by its errorbar. The weak correlation between Hi and H 2 deficiency suggests that the environmental effects removing Hi 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 Hi and H 2 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 Hi classes, there is a significant scatter in H 2 deficiency within each class. There are, however, some differences between the classes. Except for a few outliers, class 0 galaxies (galaxies with "normal" Hi reservoirs which resemble those of field galaxies) have normal to high H 2 fractions, in line with their morphologically normal, non-deficient Hi reservoirs. Class i galaxies, which exhibit one-sided Hi features, but otherwise have Hi and stellar discs similar to those of field galaxies, are H 2 normal. Classes ii and iii (galaxies with moderate to extreme asymmetries and significant Hi deficiencies) have moderately deficient H 2 reservoirs. Galaxies that are Hi deficient due to their lower Hi surface densities (class iv galaxies) have relatively high H 2 deficiencies. The six known RPS galaxies are relatively H 2 -rich compared to other VERTICO galaxies with similar Hi deficiencies. , based on deficiency and morphology. VCC1581, which was not detected in CO, is represented by the light-blue triangle, indicating the lower limit on its molecular gas deficiency. The x-shaped marker in the right panel indicates IC3418, which is a lower limit both in Hi and H2 deficiency (it is not present in the left-hand panel because no limit on the Hi deficiency was provided by Chung et al. 2009). The numbered galaxies (green numbers are placed below the relevant markers) represent well-studied "smoking-gun" RPS galaxies, listed in the top-left corner in order of pre-to-post RP peak. There is a weak correlation between Hi and H2 deficiency: the Spearman correlation coefficient is 0.28 ± 0.05, with a typical p-value of 0.05, for the left-hand panel and 0.36 ± 0.04, with a typical p-value of 0.01, for the right-hand panel. Most galaxies lie in the upper-right quadrant, and are thus both Hi and H2 deficient. On average, galaxies that have Hi reservoirs similar to those of field galaxies (class 0 galaxies) are least H2 deficient, while galaxies that are Hi-deficient because of their lower Hi surface densities (class iv galaxies) are most H2 deficient. VERTICO galaxies undergoing RPS are relatively H2-rich compared to other VERTICO galaxies with similar Hi deficiencies.

H 2 radial profiles by H i deficiency
Median Σ H2 radial profiles are shown in Figure 3, they are divided into three equal bins of def Hi, R , indicated by the colour bar. In the colour bar, the white dots show the distribution of Hi deficiencies. The solid lines show the medians of the radial profiles in each bin; the shaded areas cover the 16 th -to-84 th percentile regions. The teal dashed line represents the median H 2 radial profile of the 21 galaxies in the HERACLES field sample, whose 16 th -to-84 th percentiles are indicated with dotted lines. The x-axis is normalised by the isodensity radius of the stellar disc (at Σ (R ) = 1 M pc −2 ), the y-axis is not normalised.
More strongly Hi-deficient galaxies have steeper and more truncated H 2 radial profiles. This suggests that the environmental processes acting on the atomic gas cause outside-in removal of the molecular gas. The median H 2 radial profile of the HERACLES sample lies between those of the most Hi-rich and moderately Hi deficient VERTICO galaxies. Figure 4 shows the H 2 disc radii (R H2 ) as a function of Hi deficiency (left panel) and H 2 deficiency (right panel), for a Σ H2 threshold 1 M pc −2 . As can be seen in Figure  3, this threshold probes the low-density gas at the outskirts of the H 2 disc, which is the gas most likely to be affected by environmental mechanisms. R H2 declines significantly with Hi 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 welldefined H 2 radius. NGC4380 has a large, regular looking molecular gas disc. NGC4654 also has a large molecular gas disc, with a one-sided RPS feature. Although NGC4419 is not among the "well-studied" RPS cases, the morphology of its molecular gas disc suggests that it is likely also undergoing RPS (see Appendix A in B21).

H 2 Radii
There is a weaker anti-correlation between H 2 radius and H 2 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 Hi deficiency Figure 3. Observed median H2 radial profiles of VERTICO galaxies shown in three bins of ∼15 galaxies, sorted by Hi deficiency. The shaded areas highlight the 16 th -to-84 th percentile regions. The teal dashed line represents the median profile of 21 HERACLES field galaxies. Its 16 th -to-84 th percentiles are indicated with dotted lines. The distribution of the Hi deficiencies in the sample is shown on the colour bar using white dots. More Hi deficient galaxies have steeper and more truncated H2 radial profiles. The median radial profile of HERACLES galaxies lies between those of the most Hi-rich and moderately Hi-deficient VERTICO galaxies.
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 H 2 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 H 2 radius. The molecular gas in NGC4394 is also patchy, again resulting in a strong deficiency compared to its H 2 radius. The anti-correlation between Hi deficiency and R H2 suggests that the environmental mechanism(s) removing Hi from galaxies also cause outside-in stripping of their molecular gas. On average, galaxies in the HER-ACLES sample have marginally smaller H 2 deficiencies and marginally larger H 2 radii. However, there is no statistically significant difference between both samples. Figure 5 shows the median surface density of the molecular gas disc as a function of Hi deficiency (left panel) and H 2 deficiency (right 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 centre of the galaxy. While, by eye, there appears to be a weak correlation between Hi deficiency and central H 2 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).

Central H 2 surface densities
There is no correlation between H 2 deficiency and central H 2 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 H 2 deficiencies and marginally larger central H 2 surface densities. However, there is no statistically significant difference between both samples.

Effects of definition of H 2 radius
Figures 4 and 5 are shown for specific choices of the H 2 radius: in Figure 4 the radius of the H 2 disc is defined at Σ H2 = 1 M pc −2 and in Figure 5 the median H 2 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 H 2 radius is defined, and the semi-major axis of the ellipse enclosing the area in which the median H 2 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 Hi deficiency (left-hand panel) and R H2 and Σ H2 (purple and orange, respectively), and, similarly, the relationships between H 2 deficiency and R H2 and Σ H2 (right-hand panel). Relationships for which the p-  Figure 4. Radius of the molecular gas disc (normalised by the radius of the stellar disc) as a function of Hi deficiency (left panel) and H2 deficiency (right panel). Markers are the same as in Figure 1, but with the numbers indicating RPS galaxies now located to the upper-right of the relevant markers. In the right-hand panel the median values (both in x and y) of the VERTICO and HERACLES samples are indicated with orange and teal stars, respectively. The H2 radius at an observed isodensity threshold of ΣH 2 = 1 M pc −2 is plotted. There is an anti-correlation between Hi deficiency and RH 2 (the Spearman correlation coefficient is rs = −0.44 ± 0.07 with a typical p-value of 1.7 × 10 −3 ). The relation between H2 deficiency and RH 2 at this isodensity threshold is weaker (the Spearman correlation coefficient is rs = −0.29 ± 0.05, with a typical p-value of 0.04).
Hi deficiencies are associated with truncated H2 discs, likely through outside-in stripping.  Figure 5. Similar to Figure 4, but showing median central H2 surface densities within an ellipse with an observed semi-major axis of 0.1R (e.g. the extreme centres of galaxies). While, by eye, there appears to be a weak correlation between Hi deficiency and ΣH 2 , it is not statistically significant (the Spearman correlation coefficient is rs = 0.26 ± 0.05, with a typical p-value of 0.12). There is no correlation between H2 deficiency and ΣH 2 (the Spearman correlation coefficient is rs = −0.18 ± 0.09, with a typical p-value of 0.3). VERTICO galaxies have central median H2 surface densities similar to those HERACLES galaxies at similar defH 2 .
10 −2 10 −1 10 0 10 1 10 2 Σ H 2 (M pc −2 ) threshold at which R is defined Semi-major axis of enclosed surface area / R def Hi vs. Σ H2 def H2 vs. Σ H2 Figure 6. Left panel: Spearman correlation coefficients as a function of the observed isodensity threshold at which RH 2 is defined for the relationship between Hi (purple) and H2 (orange) deficiency and RH 2 . Spearman test results with p-values greater than 0.05 (i.e. relationships with no significant correlation) are indicated with semi-transparent markers. There is an anti-correlation between RH 2 and both Hi and H2 deficiency. The anti-correlation between RH 2 and Hi deficiency only exists if the isodensity radius of the H2 disc is defined at low H2 surface densities, i.e. the very outskirts of the disc. This is consistent with an outside-in stripping scenario of H2 in Hi deficient galaxies. Right panel: Spearman correlation coefficients as a function of the observed semi-major axis of the ellipse in which the median H2 surface density is calculated, for the relationships between Hi (purple) and H2 (orange) deficiency and H2 surface density.
There is an anti-correlation between H2 deficiency and ΣH 2 , which is likely intrinsic. Although there is a hint of slightly increased central H2 surface densities, the relationship between Hi deficiency and ΣH 2 is not statistically significant.
value associated with Spearman's correlation is greater than 0.05 (and are thus considered to not be statistically significant) are indicated with semi-transparent markers.
The relationship between Hi deficiency and R H2 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 disc 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 disc, resulting in the low-surface density gas at the outskirts dropping below our detection threshold. However, the latter explanation would result in H 2 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 H 2 deficiency and R H2 is present for all values of the isodensity threshold except the very highest, and is likely intrinsic.
The relationship between Hi deficiency and Σ H2 is not statistically significant, and any hint of increased H 2 surface densities is only present in the very centres of galaxies (R < 0.1R ). The moderate negative correlation between H 2 deficiency and median H 2 surface density is independent of the choice of radius, although it is no longer statistically significant when the median H 2 surface density is calculated in the central regions only. This correlation is likely intrinsic.

DISCUSSION
Globally, while Hi deficiency only correlates weakly to moderately with H 2 deficiency, Hi deficient galaxies are often also H 2 deficient to varying degrees. This suggests that the environmental mechanisms acting on the Hi in Virgo cluster galaxies simultaneously affect their H 2 . However, the lack of a stronger correlation between both deficiencies, in combination with smaller H 2 deficiencies compared to Hi deficiencies, implies that relatively little molecular gas has been removed from VERTICO galaxies. It is possible that H 2 deficiencies become more significant only after most of the Hi is removed.
A closer look at the resolved properties of the molecular gas in these galaxies has revealed that absence of a strong correlation does not necessarily mean that the H 2 content of Hi deficient galaxies remains undisturbed by environmental process(es). Σ H2 radial profiles of galaxies with larger Hi deficiencies are more truncated and steeper than those of their more Hi rich counterparts, indicating outside-in removal of molecular gas. We explored this result in more detail by studying the radius and average surface density of the molecular gas disc as a function of both Hi and H 2 deficiency. This has confirmed the presence of an anti-correlation between Hi deficiency and the radius of the H 2 disc (Figure 4). This correlation is only significant when the low-density molecular gas at the outskirts of the disc is taken into account ( Figure 6). Furthermore, there is a hint of a slight increase in median central surface density (R 0.1R ) of the H 2 disc with increasing Hi deficiency, although this is not statistically significant. In this work we have opted not to correct for inclination (see §3). The application of inclination corrections does not significantly alter the trends in any of the Figures, and therefore the broad conclusions of the paper remain the same with or without these corrections.
Our results partly agree with the results from Mok et al. (2017), who report steeper H 2 radial profiles of Virgo galaxies compared to those of galaxies in the field. They also find enhanced central surface densities, for which we do not find solid evidence here. Mok et al. (2017) mainly attribute this enhancement to radially inward migration of Hi as a result of RPS, after which it is more easily converted to H 2 . They also report increased global molecular gas masses of Virgo galaxies compared to field and group samples, which while here we mostly find H 2 deficiencies compared to main sequence galaxies from xCOLD GASS. This difference is possibly the result of the use of a Hi-mass selected sample by Mok et al. (2017).
Our results also agree partly with those from Boselli et al. (2014a). While they indeed find an anti-correlation between H 2 radius and Hi deficiency, they also report a strong correlation between Hi and H 2 deficiency, whereas we find a weak correlation. The strong correlation between Hi and H 2 deficiency found by Boselli et al. (2014a) is based on a sub-sample of 17 galaxies with high-quality data from Kuno et al. (2007). When the entire Virgo sample is taken into account, this relationship is not as strong (see figure 5 in Boselli et al. 2014a). The range of Hi deficiencies considered in this work is closer to that of the entire sample of Boselli et al. (2014a), rather than the sub-sample from Kuno et al. (2007). This sub-sample exclusively contains galaxies with Hi deficiencies between ∼0 and 1, where the slope is steepest (Figure 2). Therefore, it is possible that the relationship found in this work is weaker because of the wider range of Hi deficiencies, similar to figure 5 of Boselli et al. (2014a). Uncertainties in X CO and R 21 ≡ CO(2-1)/CO(1-0) may contribute to differences with previous work, although Boselli et al. (2014a) report a stronger correlation between Hi and H 2 deficiency for a constant X CO .

What causes H i and H 2 deficiencies?
Truncated molecular gas discs 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 disc, which could result in observed truncation as the surface density of the molecular gas at the outskirts of the disc drops below the sensitivity limit of our observations. The same is true for starvation. However, both these processes should result in relatively uniform removal of gas, which should not significantly change the shape of the Σ H2 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 discs 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 Σ H2 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 discs, the lack of a stronger correlation between Hi and H 2 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 Hi 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 H 2 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 H 2 (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 prob-ably close to the cluster centre (∼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 H 2 lost through stripping. We do not find evidence for increased H 2 surface densities in this work. However, here we exclusively work with radially averaged radial profiles. More detailed (case) studies of the H 2 distribution and SFRs in VERTICO galaxies are needed to investigate how common regions with increased H 2 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 Hi reservoirs (class 0 galaxies in Yoon et al. 2017) are H 2 -rich compared to galaxies that do. The difference in H 2 reservoirs between Hi-normal and Hi-disturbed objects confirms that the effects of environment on atomic gas also act on molecular gas. Galaxies with relatively low Hi surface densities (class iv galaxies) are relatively H 2 -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 Hi discs cover a range in H 2 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 Hi.
Simulations of RPS acting on the multi-phase ISM (with H 2 treated as a separate component) have indeed shown that RPS can strip H 2 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 in 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 H 2 are stripped, and whether H 2 is enhanced in galactic centres, likely varies between clusters, and depends on the locations of galaxies in phase-space.
While simulations have rarely mapped H 2 , some simulations show mild SF enhancement in RPS galaxies, particularly at the pericentre 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 centres, 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 H 2 , of central enhancement of H 2 .

SUMMARY
In this work we have investigated how environmental mechanisms acting on atomic gas affect the molecular gas in spiral galaxies in the Virgo cluster. Observations of 49 spiral galaxies in the Virgo cluster from the ALMA large program VERTICO: "the Virgo Environment Traced in CO" were used to study the resolved properties of the molecular gas. Their Hi deficiencies, as well as deficiency/morphology classifications, were adopted from the VLA Imaging of Virgo in Atomic gas survey (VIVA, Chung et al. 2009;Yoon et al. 2017). In particular, we studied how the H 2 radial profile, radius, and surface density change as a function of Hi deficiency, H 2 deficiency, and between different Hi deficiency/morphology classes. Our main findings are as follows: • Many VERTICO galaxies that are Hi deficient are also somewhat H 2 deficient, albeit to a lesser extent. There is a weak correlation between Hi deficiency and H 2 deficiency, although it exhibits significant scatter. This suggests that, although environmental effects simultaneously affect H 2 and Hi in VERTICO galaxies, Hi deficiency does not always predict H 2 deficiency (i.e. when significant amounts of Hi are removed from galaxies, they often still contain significant amounts of H 2 ).
• Galaxies with larger Hi deficiencies have steeper and less extended molecular gas radial profiles.
This means that the mechanism removing atomic gas from galaxies causes truncation of the molecular gas disc.
• We find an anti-correlation between Hi deficiency and H 2 radius, which confirms that the environmental mechanisms removing atomic gas from galaxies remove or redistribute molecular gas from the outside-in. This correlation is only significant when radius is measured at the outskirts of the H 2 disc, which implies that only the low-density gas at large radii is affected.
• The most likely explanation for the observed steepened shapes of the Σ H2 radial profiles of Hi deficient VERTICO galaxies is RPS, as other environmental processes are expected to result in the more uniform removal of H 2 .
• Galaxies that show clear signs of ongoing ram pressure stripping are H 2 -normal to H 2 -rich. This implies that RPS is not effective at reducing global molecular gas fractions on the timescales in which such features are still clearly visible.
• Galaxies with low Hi surface densities rather than asymmetries or truncation (class iv galaxies) are relatively H 2 -poor. This suggests that additional external or internal mechanisms which reduce the gas density are more effective at reducing H 2 fractions than external processes causing outside-in stripping (i.e. RPS).
In summary, the atomic and molecular gas in VER-TICO galaxies are affected by environment simultaneously. While Hi deficiency is not a very accurate predictor of global H 2 deficiency, Hi deficient VERTICO galaxies show clear signs of outside-in removal of molecular gas.

ACKNOWLEDGEMENTS
This work was carried out as part of the VERTICO collaboration.
The authors thank Cecilia Bacchini for pointing out errors in Table 1, which have been corrected in this version of the paper.
CDW acknowledges support from the Natural Sciences and Engineering Research Council of Canada and the Canada Research Chairs program.
BL acknowledges support from the National Science Foundation of China (12073002, 11721303).
ARHS is a grateful recipient of the Jim Buckee Fellowship at ICRAR. IDR acknowledges support from the ERC Starting Grant Cluster Web 804208.
AC acknowledges the support from the National Research Foundation grant No. 2018R1D1A1B07048314.
KS and LCP acknowledge support from the Natural Sciences and Engineering Research Council of Canada.
ST acknowledges support from the Simons Foundation.
LC acknowledges support from the Australian Research Council Discovery Project and Future Fellowship funding schemes (DP210100337, FT180100066). Parts of this research were conducted by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013.
Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013.
This work made use of HERACLES, 'The HERA CO-Line Extragalactic Survey' (Leroy et al. 2009).
This paper makes use of the following ALMA data:   Elbaz et al. (2007) in black (the thick, dotted line is an extrapolation of the solid line covering the stellar mass range in which the relationship was derived), and that from xCOLD GASS in purple (Saintonge et al. 2016). Stellar masses and star formation rates for the x(COLD) GASS samples were adopted from GSWLC for consistency with VERTICO, for which they are adopted from z0MGS. Objects for which no 22 µm detection is available are indicated with down-pointing triangles. Following the style of Saintonge et al. (2016), errorbars are omitted to improve readability. For the control sample used in this work, xGASS and xCOLD GASS galaxies within 2σ of the SFMS from Elbaz et al. (2007) are used, as indicated by the black dashed lines. While VERTICO and x(COLD) GASS are primarily scattered below the SFMS, HERACLES galaxies are distributed around higher SFRs. This is likely a result of selection. • H 2 • Hi -Hi/H 2 Figure A.3. H2 (blue) and Hi (green) radial profiles of all 49 CO-detected galaxies in VERTICO. The profile of the Hi-to-H2 ratio is shown in red. The borders of the subplots are colour-coded by the VIVA classification of the galaxy (see §3.6), indicated at the top of the Figure (no class is available for NGC4533, see §3.6). Some galaxies (NGC4694, NGC4606, and NGC4293) only have marginal Hi detections. Therefore, no reliable radial profiles could be made for them. NGC4533 was not detected in Hi. Highly-inclined galaxies (inc ≥ 80 o ) are indicated with a star in front of their name.