# VERTICO: The Virgo Environment Traced in CO Survey

Toby Brown, Christine D. Wilson, Nikki Zabel, Timothy A. Davis, Alessandro

Boselli, Aeree Chung, Sara L. Ellison, Claudia D. P. Lagos, Adam R. H.

Stevens, Luca Cortese, et al.

► To cite this version:

Toby Brown, Christine D. Wilson, Nikki Zabel, Timothy A. Davis, Alessandro Boselli, et al. VER- TICO: The Virgo Environment Traced in CO Survey. The Astrophysical Journal Supplement Series, 2021, 257, 24 pp. 10.3847/1538-4365/ac28f5. hal-03585956

HAL Id: hal-03585956

https://hal.science/hal-03585956v1

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# VERTICO: The Virgo Environment Traced in CO Survey

Toby Brown¹,² ID, Christine D. Wilson² ID, Nikki Zabel³, Timothy A. Davis⁴ ID, Alessandro Boselli⁵ ID, Aeree Chung⁶ ID, Sara L. Ellison⁷ ID, Claudia D. P. Lagos⁸,⁹, Adam R. H. Stevens⁸, Luca Cortese⁸,⁹ ID, Yannick M. Bahé¹⁰, Dhruv Bisaria¹¹, Alberto D. Bolatto¹²,¹³ ID, Claire R. Cashmore¹⁴, Barbara Catinella⁸,⁹ ID, Ryan Chown² ID, Benedikt Diemer¹² ID, Pascal J. Elahi¹⁵ ID, Maan H. Hani², María J. Jiménez-Donaire¹⁶,¹⁷ ID, Bumhyun Lee¹⁸ ID, Katya Leidig¹², Angus Mok¹⁹ ID, Karen Pardos Olsen²⁰ ID, Laura C. Parker², Ian D. Roberts¹⁰ ID, Rory Smith²¹,²² ID, Kristine Spekkens²³ ID, Mallory Thorp⁷ ID, Stephanie Tonnesen²⁴ ID, Evan Vienneau², Vicente Villanueva¹² ID, Stuart N. Vogel¹², James Wadsley², Charlotte Welker²⁵, and Hyein Yoon⁹,²⁶ ID

¹Herzberg Astronomy and Astrophysics Research Centre, National Research Council of Canada, 5071 West Saanich Rd., Victoria, BC V9E 2E7, Canada
tobiashenrybrown@gmail.com

²Department of Physics & Astronomy, McMaster University, 1280 Main Street W, Hamilton, ON L8S 4M1, Canada

³Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, NL-9700 AV Groningen, the Netherlands

⁴School of Physics & Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, UK

⁵Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France

⁶Department of Astronomy, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea

⁷Department of Physics & Astronomy, University of Victoria, Finnerty Road, Victoria, BC V8P 1A1, Canada

⁸International Centre for Radio Astronomy Research, The University of Western Australia, 35 Stirling Hwy, 6009 Crawley, WA, Australia

⁹ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia

¹⁰Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands

¹¹Department of Physics, Engineering Physics and Astronomy, Queen's University, Kingston, ON K7L 3N6, Canada

¹²Department of Astronomy, University of Maryland, College Park, MD 20742, USA

¹³Visiting Scholar at Flatiron Institute, Center for Computational Astrophysics, NY 10010, USA

¹⁴E. A. Milne Centre for Astrophysics, The University of Hull, Cottingham Road, Kingston upon Hull, HU6 7RX, UK

¹⁵Pawsey Supercomputing Centre, Commonwealth Scientific and Industrial Research Organisation, Australia

¹⁶Observatorio Astronómico Nacional (IGN), C/Alfonso XII, 3, E-28014 Madrid, Spain

¹⁷Centro de Desarrollos Tecnológicos, Observatorio de Yebes (IGN), E-19141 Yebes, Guadalajara, Spain

¹⁸Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People's Republic of China

¹⁹Department of Physics & Astronomy, The University of Toledo, Toledo, OH 43606, USA

²⁰Department of Astronomy and Steward Observatory, University of Arizona, Tucson, AZ 85721, USA

²¹Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea

²²University of Science and Technology (UST), Daejeon 34113, Republic of Korea

²³Royal Military College of Canada, P.O. Box 17000, Station Forces, Kingston, ON, K7K 7B4, Canada

²⁴CCA, Flatiron Institute, 162 5th Ave., New York, NY 10010, USA

²⁵Department of Physics and Astronomy, Krieger School of Art and Science, The Johns Hopkins University, Baltimore, MD, USA

²⁶Sydney Institute for Astronomy, School of Physics, University of Sydney, NSW 2006, Australia

Received 2021 June 15; revised 2021 September 7; accepted 2021 September 10; published 2021 November 10

## Abstract

We present the Virgo Environment Traced in CO (VERTICO) survey, a new effort to map ¹²CO (2–1), ¹³CO (2–1), and C¹⁸O (2–1) in 51 Virgo Cluster galaxies with the Atacama Compact Array, part of the Atacama Large Millimeter/submillimeter Array. The primary motivation of VERTICO is to understand the physical mechanisms that perturb molecular gas disks, and therefore star formation and galaxy evolution, in dense environments. This first paper contains an overview of VERTICO’s design and sample selection, ¹²CO (2–1) observations, and data reduction procedures. We characterize global ¹²CO (2–1) fluxes and molecular gas masses for the 49 detected VERTICO galaxies, provide upper limits for the two nondetections, and produce resolved ¹²CO (2–1) data products (median resolution = 8'' ≈ 640 pc). Azimuthally averaged ¹²CO (2–1) radial intensity profiles are presented along with derived molecular gas radii. We demonstrate the scientific power of VERTICO by comparing the molecular gas size–mass scaling relation for our galaxies with a control sample of field galaxies, highlighting the strong effect that radius definition has on this correlation. We discuss the drivers of the form and scatter in the size–mass relation and highlight areas for future work. VERTICO is an ideal resource for studying the fate of molecular gas in cluster galaxies and the physics of environment-driven processes that perturb the star formation cycle. Upon public release, the survey will provide a homogeneous legacy data set for studying galaxy evolution in our closest cluster.

*Unified Astronomy Thesaurus concepts: Galaxies (573); Virgo Cluster (1772); Interstellar medium (847); Molecular gas (1073)*

*Supporting material:* figure sets, FITS files

## 1. Introduction

Beginning with the pioneering works of Gunn et al. (1972), Cowie & Songaila (1977), and Larson et al. (1980), the past 50 years have seen a steady stream of work demonstrating that galaxies’ cold gas and star formation properties are influenced by

the environment in which they reside (see reviews by Haynes et al. 1984; Boselli & Gavazzi 2006; Cortese et al. 2021, and references therein).

Much of this work has focused on local galaxy clusters as laboratories for studying the role environment plays in galaxy
evolution. Containing hundreds or even thousands of galaxies, clusters are characterized by high internal velocity dispersion ($v_{disp} \sim 10^2-10^3$ km s⁻¹) and a hot, diffuse intracluster medium (ICM, $T \sim 10^7-10^8$ K, $n \sim 10^{-4}$ cm⁻³; Kaiser 1986; White et al. 1997).

Cluster members are subject to a diverse range of environmental effects that drive the observed increase in quenched (or quenching) galaxies with respect to the field (Balogh et al. 1998, 1999; Gómez et al. 2003; Boselli & Gavazzi 2006). Dynamical interactions between two or more systems can cause tidal stripping of stars and gas (Moore et al. 1999; Iono et al. 2005) or compression of the interstellar medium (ISM; Nehlig et al. 2016; Kaneko et al. 2018). Harassment by frequent, high-velocity galaxy–galaxy encounters is capable of tidally heating the ISM, shutting off inflow and evaporating gas reservoirs (Moore et al. 1996, 1998; Fujita 1998). Viscous stripping or thermal evaporation of the cold gas content of galaxies surrounded by a hot ICM can also suppress star formation (Cowie & Songaila 1977; Livio et al. 1980; Nulsen 1982). Starvation occurs when there is a lack of gas cooling and/or a cutoff in the external gas supply, either to the halo or to the galaxy itself, meaning that reservoirs consumed in star formation are not replenished (Larson et al. 1980; Balogh et al. 2000; Bekki et al. 2002). For galaxies entering a cluster, the interaction between the ISM and ICM has been observed to be strong enough to rapidly remove gas from the disk via ram pressure stripping (Gunn et al. 1972; Hester 2006; Chung et al. 2009a; Fumagalli et al. 2014). More recently, evidence has also been presented for elevated gas densities caused by ram pressure, affecting the star formation efficiency (SFE) and the transition of atomic hydrogen gas to its molecular phase (Ebeling et al. 2014; Lee et al. 2017; Mok et al. 2017; Vulcani et al. 2018; Moretti et al. 2020a, 2020b).

The common outcome of such processes is that they leave different imprints on galaxies’ cold gas reservoirs. Thus, to understand the nature of these effects, we must establish their influence on the constituent phases of the ISM. Pursuit of this understanding has demonstrated the widespread and systematic depletion of atomic hydrogen (HⅠ) gas reservoirs—considered the gas supply for future star formation—in cluster galaxies with respect to the field (e.g., Davies & Lewis 1973; Chamaraux et al. 1980; Giovanelli & Haynes 1985; Gavazzi et al. 2008; Chung et al. 2009a; Hughes & Cortese 2009; Cortese et al. 2011; Jaffé et al. 2016; Brown et al. 2017; Healy et al. 2020).

Similarly, there have been many efforts to determine cluster galaxies’ molecular hydrogen gas (H₂) content, the fuel for ongoing star formation. The low temperatures found in giant molecular gas clouds and lack of a dipole moment emission mechanism make the H₂ molecule very difficult to observe directly. Instead, the bulk of molecular gas is usually traced via indirect means, the most common and reliable of which are the low-J rotational transitions of carbon monoxide (CO), although even this method is not without its uncertainties (see Bolatto et al. 2013, for a thorough review of this topic).

Because of the more stringent instrumental and observational requirements relative to longer-wavelength radio observations, the findings from studies of molecular gas have necessarily focused on smaller samples and lacked the consistency found in HⅠ studies. A number of prominent early works using unresolved detections found no differences between the molecular gas content of field and cluster galaxies, concluding that molecular gas disks that are bound deep within the gravitational potential well of the

system are largely immune to environmental effects (Kenney & Young 1986, 1989; Stark et al. 1986; Boselli et al. 1997). However, more recent efforts to survey global molecular gas reservoirs in a large number of Local Cluster galaxies tend to favor a scenario whereby the star-forming gas is depleted in dense environments, albeit to a lesser extent than the HⅠ (Boselli et al. 2002, 2014; Wilson et al. 2009; Corbelli et al. 2012; Mok et al. 2016; Chung et al. 2017; Koyama et al. 2017; Stevens et al. 2021).

Studies using resolved observations of molecular gas in a small number of systems generally support the picture of environmental mechanisms perturbing molecular gas reservoirs in clusters and demonstrate that environmental influences often manifest themselves on the subkiloparsec scale of bars, disks, streams, tails, and warps (e.g., Nehlig et al. 2016; Lee et al. 2017; Mok et al. 2017; Lee & Chung 2018; Moretti et al. 2018; Cramer et al. 2019, 2020; Jáchym et al. 2019; Zabel et al. 2019; Lizée et al. 2021). Interestingly, some of these studies find that environmental mechanisms have contrasting effects on the gas content or star formation properties of galaxies. For example, elevated star formation has been found at the ISM–ICM interface in cluster galaxies, implying that ram pressure stripping is able to increase either the amount of gas available for star formation or the SFE of the surviving gas (or a combination of both; e.g., Ebeling et al. 2014; Nehlig et al. 2016; Zabel et al. 2020; Lizée et al. 2021). On the other hand, Moretti et al. (2018) find that ram pressure stripping decreases the SFE of stripped molecular gas, and Mok et al. (2017) report enhanced molecular gas masses in cluster galaxies relative to the field (see also Moretti et al. 2020b), concluding that the environment is aiding the transition from atomic to molecular gas while lowering the SFE. Recent work attributes the triggering of active galactic nuclei (AGN) to central gas flows driven by ram pressure, suggesting a causal link between galaxy environment and energetic AGN feedback (Poggianti et al. 2017).

Despite continuous progression in our understanding, the dichotomy in approaches taken by molecular gas studies—large statistical surveys of global properties versus resolved mapping of gas reservoirs in a small number of galaxies—has left two significant questions unanswered:

1. What is the relationship between different environmental mechanisms and molecular gas density, morphology, kinematics, and chemistry?

2. When, where, and how do environmental mechanisms alter the rate and efficiency of star formation?

Answering these questions requires a merging of these two methodologies. In other words, we need resolved spectroscopic imaging of molecular gas disks across a large homogeneous sample of galaxies that are experiencing the full complement of environmental mechanisms. These observations must be combined with multiwavelength data covering the full galactic ecosystem and accompanied by state-of-the-art models and simulations.

With this goal in mind, we present the Virgo Environment Traced in CO (VERTICO) survey, a Large Program with the Atacama Large Millimeter/submillimeter Array (ALMA) designed to map molecular gas in 51 Virgo Cluster galaxies on subkiloparsec scales. The primary motivation of VERTICO is to understand the physical mechanisms that drive galaxy evolution in dense environments. We also aim to provide a homogeneous legacy data set for studying galaxy evolution in the nearest massive cluster to the Milky Way.
This first paper contains an overview of the VERTICO survey design and sample selection, observations and data reduction procedures, global molecular gas properties, and derived data products. We present early science results on the radial distribution of molecular gas in VERTICO galaxies and compare the molecular gas disk sizes and masses to a control sample of field galaxies. We also highlight areas for future work. The paper is structured as follows: Section 2 presents the sample; Section 3 describes the observations, including our data reduction method and integrated CO properties; Section 4 gives the methodology and examples of key data products; Section 5 is a brief comparative analysis of molecular gas disk sizes and masses between VERTICO and a sample of field galaxies; finally, Section 6 presents a summary of this paper and looks forward to the next steps.

Throughout this paper, we assume a common distance of 16.5 Mpc to all Virgo galaxies based on the Virgo Cluster distance found by Mei et al. (2007). Where relevant, all astrophysical quantities are derived using a Kroupa initial mass function (IMF; Kroupa 2001) or rescaled from literature values using

$$M_{*,K} = 1.06 M_{*,C} = 0.62 M_{*,S}, \quad (1)$$

where the subscripts K, C, and S denote the Kroupa, Chabrier (2003), and Salpeter (1955) IMFs, respectively (Elbaz et al. 2007; Salim et al. 2007; Zahid et al. 2012; Speagle et al. 2014).

## 2. The VERTICO Sample

VERTICO targets 51 Virgo Cluster galaxies included in the Very Large Array Imaging of Virgo in Atomic gas (VIVA) survey (Chung et al. 2009a). The full VIVA survey contains 53 galaxies; however, we exclude two very low mass systems (IC 3355 and VCC 2062) that were deemed unlikely to be detected. VIVA was selected by Chung et al. (2009a) to sample a range of star formation properties in the classification scheme published by Koopmann & Kenney (2004; normal, enhanced, anemic, truncated), which is in turn based on the spatial distribution of Hα and R-band emission. The resulting sample of primarily late-type galaxies spans a broad range in stellar mass ($10^{8.3} \le M_*/M_\odot \le 10^{11}$) and specific star formation rate (sSFR = SFR/M$_*$; $10^{-11.5} \le sSFR/\text{yr}^{-1} \le 10^{-9.5}$). VERTICO targets have existing resolved multiwavelength observations tracing their stellar component, star formation activity, and H I gas content. Galaxy H I gas reservoirs exhibit signatures of the full complement of environmental effects, including the gas tails and truncated disks typical of stripping, fading gas disks of starvation, and morphological asymmetries and kinematic misalignment from gravitational perturbations (Chung et al. 2009a; Yoon et al. 2017). Every galaxy has existing resolved multiwavelength observations tracing the stellar component and star formation activity (e.g., Martin et al. 2005; Wright et al. 2010; Alam et al. 2015; see Section 2.1 for further details). Furthermore, 15 galaxies already have archival Atacama Compact Array (ACA) observations of the $^{12}$CO (2–1) emission line, hereafter CO (2–1). The remaining 36 targets were observable in CO (2–1) within a feasible amount of time for an ALMA Large Program using the ACA. The full VERTICO sample is listed in Table 1. Optical inclinations and east-of-north position angles are calculated from fits to the Sloan Digital Sky Survey (SDSS; York 2000; Alam et al. 2015) r-band photometry described in Section 4.2.

<table><caption>**Table 1**
The VERTICO Target Sample</caption><thead><tr><th>Galaxy</th><th>R.A. (J2000)</th><th>Decl. (J2000)</th><th>v<sub>opt</sub><br>(km s<sup>-1</sup>)</th><th>i<br>(deg)</th><th>P.A.<br>(deg)</th></tr></thead><tbody><tr><td>IC 3392<sup>a</sup></td><td>12h28m43s27</td><td>14°59′57″48</td><td>1678</td><td>68</td><td>219</td></tr><tr><td>IC 3418<sup>a</sup></td><td>12h29m43s50</td><td>11°24′08″00</td><td>38</td><td>62</td><td>233</td></tr><tr><td>NGC 4064</td><td>12h04m11s26</td><td>18°26′39″12</td><td>1000</td><td>70</td><td>150</td></tr><tr><td>NGC 4189<sup>a</sup></td><td>12h13m47s47</td><td>13°25′34″68</td><td>1995</td><td>42</td><td>70</td></tr><tr><td>NGC 4192<sup>a</sup></td><td>12h13m48s58</td><td>14°53′57″12</td><td>-118</td><td>83</td><td>333</td></tr><tr><td>NGC 4216<sup>a</sup></td><td>12h15m54s19</td><td>13°08′54″96</td><td>30</td><td>90</td><td>20</td></tr><tr><td>NGC 4222</td><td>12h16m22s56</td><td>13°18′25″20</td><td>225</td><td>90</td><td>238</td></tr><tr><td>NGC 4254<sup>a,b</sup></td><td>12h18m49s68</td><td>14°25′05″52</td><td>2453</td><td>39</td><td>243</td></tr><tr><td>NGC 4293<sup>a,b</sup></td><td>12h21m13s47</td><td>18°23′03″12</td><td>717</td><td>67</td><td>239</td></tr><tr><td>NGC 4294</td><td>12h21m17s81</td><td>11°30′39″24</td><td>421</td><td>74</td><td>151</td></tr><tr><td>NGC 4298<sup>a,b</sup></td><td>12h21m33s12</td><td>14°36′19″80</td><td>1122</td><td>52</td><td>132</td></tr><tr><td>NGC 4299<sup>a</sup></td><td>12h21m40s71</td><td>11°30′06″12</td><td>209</td><td>14</td><td>128</td></tr><tr><td>NGC 4302<sup>a</sup></td><td>12h21m42s24</td><td>14°35′57″12</td><td>1111</td><td>90</td><td>356</td></tr><tr><td>NGC 4321<sup>a,b</sup></td><td>12h22m54s77</td><td>15°49′33″24</td><td>1579</td><td>32</td><td>280</td></tr><tr><td>NGC 4330</td><td>12h23m16s95</td><td>11°22′04″08</td><td>1567</td><td>90</td><td>238</td></tr><tr><td>NGC 4351<sup>a</sup></td><td>12h24m01s30</td><td>12°12′15″12</td><td>2388</td><td>48</td><td>251</td></tr><tr><td>NGC 4380<sup>a</sup></td><td>12h25m22s16</td><td>10°01′00″12</td><td>935</td><td>61</td><td>158</td></tr><tr><td>NGC 4383<sup>a</sup></td><td>12h25m25s47</td><td>16°28′11″64</td><td>1663</td><td>56</td><td>17</td></tr><tr><td>NGC 4388</td><td>12h25m46s61</td><td>12°39′46″44</td><td>2538</td><td>83</td><td>271</td></tr><tr><td>NGC 4394</td><td>12h25m55s66</td><td>18°12′52″20</td><td>772</td><td>32</td><td>312</td></tr><tr><td>NGC 4396<sup>a</sup></td><td>12h25m59s66</td><td>15°40′10″20</td><td>-115</td><td>83</td><td>304</td></tr><tr><td>NGC 4402<sup>b</sup></td><td>12h26m07s34</td><td>13°06′45″00</td><td>190</td><td>80</td><td>270</td></tr><tr><td>NGC 4405</td><td>12h26m07s11</td><td>16°10′51″60</td><td>1751</td><td>46</td><td>18</td></tr><tr><td>NGC 4419</td><td>12h26m56s35</td><td>15°02′51″36</td><td>-228</td><td>74</td><td>131</td></tr><tr><td>NGC 4424<sup>a,b</sup></td><td>12h27m11s69</td><td>09°25′14″16</td><td>447</td><td>61</td><td>274</td></tr><tr><td>NGC 4450<sup>a</sup></td><td>12h28m29s23</td><td>17°05′04″56</td><td>2048</td><td>51</td><td>170</td></tr><tr><td>NGC 4457<sup>a,b</sup></td><td>12h28m59s02</td><td>03°34′14″16</td><td>738</td><td>37</td><td>256</td></tr><tr><td>NGC 4501<sup>a</sup></td><td>12h31m59s33</td><td>14°25′10″92</td><td>2120</td><td>65</td><td>320</td></tr><tr><td>NGC 4522</td><td>12h33m39s72</td><td>09°10′26″76</td><td>2332</td><td>82</td><td>35</td></tr><tr><td>NGC 4532<sup>a</sup></td><td>12h34m19s35</td><td>06°28′05″52</td><td>2154</td><td>64</td><td>159</td></tr><tr><td>NGC 4533</td><td>12h34m22s03</td><td>02°19′33″24</td><td>1753</td><td>80</td><td>342</td></tr><tr><td>NGC 4535<sup>a,b</sup></td><td>12h34m20s26</td><td>08°11′53″52</td><td>1973</td><td>48</td><td>12</td></tr><tr><td>NGC 4536<sup>a,b</sup></td><td>12h34m27s12</td><td>02°11′16″08</td><td>1894</td><td>74</td><td>118</td></tr><tr><td>NGC 4548<sup>a,b</sup></td><td>12h35m26s64</td><td>14°29′43″80</td><td>498</td><td>37</td><td>318</td></tr><tr><td>NGC 4561<sup>a</sup></td><td>12h36m08s14</td><td>19°19′21″72</td><td>1441</td><td>28</td><td>60</td></tr><tr><td>NGC 4567</td><td>12h36m33s07</td><td>11°15′29″16</td><td>2213</td><td>49</td><td>251</td></tr><tr><td>NGC 4568<sup>a</sup></td><td>12h36m34s34</td><td>11°14′21″84</td><td>2260</td><td>70</td><td>211</td></tr><tr><td>NGC 4569<sup>a,b</sup></td><td>12h36m50s12</td><td>13°09′55″08</td><td>-220</td><td>69</td><td>203</td></tr><tr><td>NGC 4579<sup>a,b</sup></td><td>12h37m43s44</td><td>11°49′05″52</td><td>1627</td><td>40</td><td>273</td></tr><tr><td>NGC 4580<sup>a</sup></td><td>12h37m48s38</td><td>05°22′06″24</td><td>1227</td><td>46</td><td>337</td></tr><tr><td>NGC 4606</td><td>12h40m57s62</td><td>11°54′43″56</td><td>1653</td><td>69</td><td>38</td></tr><tr><td>NGC 4607</td><td>12h41m12s39</td><td>11°53′09″60</td><td>2284</td><td>90</td><td>2</td></tr><tr><td>NGC 4651<sup>a</sup></td><td>12h43m42s72</td><td>16°23′37″68</td><td>788</td><td>53</td><td>75</td></tr><tr><td>NGC 4654<sup>a,b</sup></td><td>12h43m56s76</td><td>13°07′32″52</td><td>1035</td><td>61</td><td>300</td></tr><tr><td>NGC 4689<sup>a,b</sup></td><td>12h47m45s68</td><td>13°45′42″12</td><td>1522</td><td>38</td><td>341</td></tr><tr><td>NGC 4694<sup>a,b</sup></td><td>12h48m15s08</td><td>10°59′00″60</td><td>1211</td><td>62</td><td>323</td></tr><tr><td>NGC 4698<sup>a</sup></td><td>12h48m22s99</td><td>08°29′15″00</td><td>1032</td><td>66</td><td>347</td></tr><tr><td>NGC 4713<sup>a</sup></td><td>12h49m57s65</td><td>05°18′39″60</td><td>631</td><td>45</td><td>89</td></tr><tr><td>NGC 4772</td><td>12h53m29s12</td><td>02°10′06″24</td><td>1042</td><td>60</td><td>325</td></tr><tr><td>NGC 4808<sup>a</sup></td><td>12h55m48s94</td><td>04°18′15″12</td><td>738</td><td>72</td><td>127</td></tr><tr><td>VCC 1581</td><td>12h34m45s05</td><td>06°18′03″24</td><td>2141</td><td>43</td><td>329</td></tr></tbody></table>

**Notes.** Columns are (1) galaxy name and unique identifier in this paper; (2) R.A. (J2000) of the galaxy optical center; (3) decl. (J2000) of the galaxy optical center; (4) optical heliocentric recession velocity; (5) optical r-band inclination; (6) optical r-band position angle of the kinematically redshifted half of the galaxy, calculated east of north. Columns (2)–(4) are drawn from the NASA/IPAC Extragalactic Database (https://ned.ipac.caltech.edu/). Columns (5) and (6) are calculated using fits to SDSS photometry described in Section 4.2. This table is published in its entirety in machine-readable format. a Data are from 7 m and Total Power arrays. Other observations are 7 m array only.

b Data are archival ALMA ACA (7 m + total power) $^{12}$CO (2–1) observations at comparable sensitivity to our Cycle 7 observations. The sources of these data are the PHANGS-ALMA program (Leroy et al. 2021b; 14 galaxies) and one regular PI program (Cramer et al. 2019; NGC 4402). See Section 3 and the Acknowledgments section for further details. (This table is available in its entirety in FITS format.)
## 2.1. The Virgo Cluster

The Virgo Cluster resides at a distance of 16.5 Mpc and contains thousands of member galaxies, making it the closest massive galaxy cluster to the Milky Way. The main body of the cluster centered on M87 has an estimated mass $M_{200} = 10^{14} - 10^{14.6} M_{\odot}$ and radius $r_{200} = 1.08-1.55$ Mpc (Böhringer et al. 1994; Nulsen & Bohringer 1995; Girardi et al. 1998; Gavazzi et al. 1999; McLaughlin 1999; Schindler et al. 1999; Mei et al. 2007; Urban et al. 2011; Kim et al. 2014; Boselli et al. 2018), where $M_{200}$ is the total mass within $r_{200}$, the radius at which the enclosed mean mass density is 200 times the critical cosmic mass density. A comprehensive list of mass, size, and distance estimates for Virgo is provided by Boselli et al. (2018, Table 1 in that work). The cluster is dynamically young, contains significant substructure, and is actively accreting members. This ensures that Virgo's membership includes both infalling and virialized systems on a wide range of orbits throughout the cluster (Tully & Shaya 1984; Gavazzi et al. 1999; Karachentsev et al. 2014; Sorce et al. 2016; Yoon et al. 2017; Morokuma-Matsui et al. 2021).

For these reasons, the Virgo region has been remarkably well surveyed at almost every wavelength: X-ray (ROSAT—Böhringer et al. 1994; ASCA—Shibata et al. 2001; XMM-Newton—Urban et al. 2011), ultraviolet (UV; the GALEX Ultra-violet Virgo Cluster Survey, GUViCS—Boselli et al. 2011), optical (SDSS—York 2000; the Next Generation Virgo Survey, NGVS—Ferrarese et al. 2012; the Virgo Environmental Survey Tracing Ionized Gas Emission, VESTIGE—Boselli et al. 2018), infrared (the Wide-field Infrared Survey Explorer, WISE—Wright et al. 2010; the Herschel Reference Survey, HRS—Boselli et al. 2010; the Herschel Virgo Cluster Survey, HeViCS—Davies et al. 2010), and 21 cm radio (VIVA; Chung et al. 2009a). These surveys map the hot ICM and the stellar mass, dust, SFR, and atomic and ionized gas properties of Virgo members in extraordinary detail. Almost all these data have VERTICO's angular resolution or better, while the 21 cm observations are coarser (~15"). This combination of richness, proximity, wavelength coverage, and data quality is not available for any other galaxy cluster.

At millimeter wavelengths, Boselli et al. (2014) provide a census of unresolved CO (1–0) observations and global molecular gas properties for approximately 150 Virgo members, showing that Virgo galaxies are, on average, deficient in molecular gas in comparison to similar field galaxies. Resolved studies of CO (2–1) and CO (3–2) have mapped the distribution of molecular gas at 1–2 kpc scale in ~30 late-type cluster members (Pappalardo et al. 2012; Mok et al. 2017), and there are also published subkiloparsec-resolution CO (2–1) observations for a handful of Virgo spirals (Lee et al. 2017; Cramer et al. 2020; Lizée et al. 2021). The key contribution of VERTICO to this field is homogeneous observations of molecular gas at subkiloparsec resolution for a large sample of cluster galaxies.

## 2.2. Sample Properties

The global stellar mass and SFR estimates used in this paper are drawn from the $z=0$ Multiwavelength Galaxy Database (z0MGS; Leroy et al. 2019). They were downloaded via the NASA/IPAC Infrared Science Archive.<fnref n="27" /> The SFRs are derived from GALEX NUV and WISE band 4 (22 µm) luminosities, while the stellar masses are based on a variable WISE band 1

(3.4 µm) mass-to-light ratio predicted using the specific SFR-like quantity, SFR-to-WISE band 1 luminosity. Global H I mass estimates are taken from the VIVA survey. The median uncertainties are 0.1 dex for stellar and H I mass and 0.2 dex for SFR. One galaxy, IC 3418, is not included in the z0MGS, so we adopt the literature values of $M_{\star} = 10^{8.37} M_{\odot}$ and SFR = 0.1 $M_{\odot}$ yr$^{-1}$ (Fumagalli et al. 2011; Jáchym et al. 2013). These properties are derived using spectral energy distribution fits to optical and UV observations and a far-UV luminosity-SFR relation modified for dwarf galaxies. Without formal uncertainties quoted in these works, we assign an uncertainty of 0.3 dex to the logarithmic values of stellar mass and SFR for IC 3418.

Figure 1 presents the scaling relations between and distributions of global stellar mass, sSFR, and H I properties of the VERTICO sample (blue points and histograms). We compare the VERTICO sample with the 1179 galaxies in the extended GALEX Arecibo SDSS Survey (xGASS; gray distributions) that have their “best” SFR measurement within that catalog and including H I nondetections as 3σ upper limits (Catinella et al. 2018).<fnref n="28" /> Following Catinella et al. (2018), the xGASS sample is weighted to correct for the flat stellar mass distribution and recover a volume-limited sample for $M_{\star} \ge 10^9 M_{\odot}$ and $z \le 0.05$. The bottom left panel shows the normalized distribution of stellar mass for both samples. Barring two galaxies (IC 3418, VCC 1581), VERTICO targets have $M_{\star} \ge 10^9 M_{\odot}$. Compared to the representative xGASS sample, VERTICO has an excess of galaxies above $M_{\star} \sim 10^{10} M_{\odot}$. The stellar mass-sSFR relation is provided in the top left, and the sSFR distribution is shown in the bottom center. VERTICO contains galaxies that are either star-forming (i.e., blue cloud) or transitioning from star-forming toward quiescence (i.e., green valley) with no systems that are already quenched (sSFR $\le 10^{-11.5}$ yr$^{-1}$). We note that this bias toward star-forming or transitioning galaxies is by selection, with the VIVA survey not including quenched or early-type galaxies. Atomic gas fractions ($M_{H\,I}/M_{\star}$) as a function of stellar mass and sSFR are shown in the left and center panels of the second row, respectively. VERTICO galaxies exhibit a broad range in H I gas fraction for their stellar and star formation properties, spanning ~3 dex in gas fraction at both fixed stellar mass and sSFR. The distribution of $M_{H\,I}$ in the bottom right panel shows that the VERTICO sample is marginally offset to lower H I gas masses compared to the representative xGASS sample. Yoon et al. (2017) demonstrate that the majority of the VIVA (and therefore the VERTICO) sample entered the cluster relatively recently (i.e., are not yet virialized). Combined with the targeting of late-type galaxies that were likely to be detected in H I, this naturally results in an absence of passive systems. Indeed, in the SFR-$M_{\star}$ parameter space, Mun et al. (2021) show that the Virgo Cluster has a well-populated quiescent sequence that is not sampled by VIVA. Given that we are missing the bulk of the passive, gas-poor population, our sample thus cannot be considered representative of Virgo's entire population. This is by construction with the sample selection designed to target galaxies that are being, will be, or recently have been actively quenched. Despite the star-forming nature of the sample, VERTICO probes a large range in H I gas fraction, covering the full gas-rich to gas-poor parameter space at both fixed stellar mass and sSFR.

<footnote n="27">²⁷ https://irsa.ipac.caltech.edu/data/WISE/z0MGS/overview.html</footnote>

<footnote n="28">²⁸ https://xgass.icrar.org/</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Global properties of the VERTICO sample (blue points and histograms) compared to the representative xGASS survey (gray distributions, 1179 galaxies; Catinella et al. 2018). Left to right from the top left: sSFR vs. stellar mass, H I gas fraction vs. stellar mass, H I gas fraction vs. sSFR, the normalized stellar mass, sSFR, and H I mass distributions. Panels in the same row share the same y-axis range.</figcaption></figure>

Figure 2 shows the ROSAT All Sky Survey mosaic of the Virgo Cluster (hard band: 0.4–2.4 keV) with the VERTICO CO (2–1) peak temperature maps overlaid. ROSAT images and exposure maps were obtained from NASA’s High Energy Astrophysics Science Archive Research Center.<fnref n="29" /> An exposure-corrected X-ray mosaic of the Virgo cluster area was produced with the *reproject_image_grid* function from the Chandra Interactive Analysis of Observations<fnref n="30" /> software package (CIAO; Fruscone et al. 2006). This mosaic was then adaptively smoothed to emphasize emission on different scales

with the CIAO function *csmooth* (Ebeling et al. 2006). The figure shows VERTICO CO (2–1) peak temperature maps at the locations of the target galaxies relative to the ROSAT image. VERTICO galaxies are distributed throughout the Virgo Cluster with a large range of cluster-centric radii (~(0.2–2) × *r*<sub>200</sub>). For illustration, the angular size of the VERTICO maps has been increased by a factor of 20. See Section 4 for a full description of the CO maps.

### 3. Observations

We observed 36 targets in CO (2–1), ¹³CO (2–1), C¹⁸O (2–1), and ALMA Band 6 continuum in ALMA Cycle 7. We set a spectral bandwidth of 1875 MHz to ensure that we cover

<footnote n="29">²⁹ https://heasarc.gsfc.nasa.gov/</footnote>

<footnote n="30">³⁰ https://cxc.cfa.harvard.edu/ciao/</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Background-subtracted, exposure-corrected ROSAT All Sky Survey mosaic of the Virgo Cluster (hard band: 0.4–2.4 keV). We overlay the VERTICO CO (2–1) peak temperature maps for the 49 detected galaxies, increased in angular size by a factor of 20 for illustration. CO (2–1) observations of three galaxies (NGC 4254, NGC 4321, NGC 4501) do not cover the full extent of the CO disk, and, as such, their peak temperature maps are rectangular in shape. The white dashed circle denotes the radius of the Virgo Cluster, $r_{200} = 3^{\circ}9$ (~1.08 Mpc; Urban et al. 2011).</figcaption></figure>
emission from the target itself and potential interactions. We average the basic Frequency Division Mode channel spacing by a factor of four to achieve a raw spectral resolution of 1.953 MHz ≈ 2.5 km s⁻¹. We bin by a further factor of four during the data processing to yield cubes with a final resolution of ~10 km s⁻¹. While all lines are observed with the same bandwidth and approximate channel width, tuning constraints on the spectral setup means that we do not require the line frequencies to be in the center of the spectral window. The target galaxies are combined with archival ACA CO (2–1) data (7 m and Total Power arrays) for 14 massive Virgo Cluster spirals from the ALMA component of the Physics at High Angular resolution in Nearby GalaxieS project (PHANGS-ALMA; Leroy et al. 2021b) and one from a regular program (2016.1.00912.S; Cramer et al. 2020) to make the final VERTICO sample of 51 galaxies.

Observations and theory suggest that gas transitions from predominantly atomic to molecular at ~10 $M_\odot$ pc⁻² at solar metallicity (Leroy et al. 2008; Krumholz et al. 2009). CO (3–2) James Clerk Maxwell Telescope (JCMT) 15" observations of 13 H I-selected Virgo galaxies demonstrate $H_2$ surface densities of ~6 $M_\odot$ pc⁻² at the outskirts of molecular disks (Mok et al. 2017). We choose a 5σ sensitivity limit of 8.5 $M_\odot$ pc⁻² per 10 km s⁻¹ channel, ensuring that we detect the diffuse gas that is below the atomic-to-molecular transition density and most susceptible to environmental influence. This mass surface density sensitivity corresponds to an rms of 10.6 mJy beam⁻¹ per 10 km s⁻¹ channel. The total integration time required to successfully reach this sensitivity across all 36 Cycle 7 targets was 186.5 hr. Each galaxy was observed with a mosaic (between 3 and 31 pointings, with an average of 13) with Nyquist spacing. We obtained Total Power observations for 25 out of 36 Cycle 7 targets where galaxy CO disks were expected to extend more than 29".

### 3.1. Data Reduction

For the galaxies in the VERTICO Cycle 7 sample, we used the calibrated uv data delivered by ALMA and imaged all the available $J=2-1$ CO lines (CO (2–1), $^{13}$CO (2–1), $C^{18}$O (2–1)). All galaxies were observed with ACA mosaics. The spatial extent of each mosaic was set to cover the CO (3–2) emission from the JCMT-Next Generation Virgo Legacy Survey (JCMT-NGLS; Wilson et al. 2009) if available, or the Herschel Spectral and Photometric Imaging Receiver (SPIRE) 250 µm flux maps published by Ciesla et al. (2012) and downloaded from the Herschel Database in Marseille.<fnref n="31" /> For the 14 VERTICO targets that are also part of PHANGS-ALMA (which have CO (2–1), $C^{18}$O (2–1), ACA 7 m, and Total Power data), as well as for the one archival target that was not part of PHANGS-ALMA (NGC 4402; CO (2–1) only, no Total Power data), we retrieved the raw ACA uv data from the ALMA archive and calibrated it using CASA version 5.6. Three of these galaxies (NGC 4254, NGC 4321, NGC 4535) remained in ALMA quality assurance (QA3) at the time of VERTICO imaging, and the calibrated uv data for these galaxies were kindly provided to us in private communication by Adam Leroy on behalf of the PHANGS-ALMA team. The $^{13}$CO (2–1) and $C^{18}$O (2–1) observations have been processed in the same manner as the CO (2–1) data. However, the presentation of

those data, along with an expanded analysis using spectral stacking, will be the focus of future work.

To image the VERTICO ACA data, we used the PHANGS-ALMA Imaging Pipeline Version 1.0 (Leroy et al. 2021a) with three modifications to adapt the pipeline for these ACA-only images (note that the PHANGS survey and pipeline papers, as well as delivered data products, use and describe Version 2.0 of this pipeline). First, we added a continuum subtraction step to the PHANGS-ALMA pipeline. For 26 galaxies where the delivered products from ALMA suggested that the continuum was detected, we applied continuum subtraction in uv space to perform a first-order fit to the line-free channels across all spectral windows. Second, we removed the steps in building the single-scale clean mask where the mask was expanded in velocity space. This change was necessary to keep the mask from expanding out to include strong sidelobes present in some of the VERTICO data. Third, in addition to the maximum resolution cubes produced by the pipeline (median resolution = 8"), we also produced data cubes with a 9" beam (CO (2–1) only, and excluding NGC 4321 where the maximum resolution is 10" and a 15" beam (all lines). As a guide, 1" ≈ 80 pc at the distance of Virgo. For simplicity, these lower-resolution cubes were produced using the CASA task `imsmooth` rather than applying a uv taper at the initial imaging stage.

For VERTICO imaging, we use Briggs weighting (robust=0.5; Briggs 1995) and set the target velocity resolution to be 10 km s⁻¹ with the local standard of rest as our velocity reference frame, using the radio definition of velocity. We defined the reference phase center to be the centroid pixel determined from a map of the two-dimensional primary beam response in a single velocity channel. This step was necessary, as the phase centers specified in the observing stage were not always at the precise center of the resulting image mosaic. Using the observed offset phase center could produce a mildly to strongly asymmetric shape and sidelobe response of the point-spread function. We first carried out a multiscale clean down to signal-to-noise ratio (S/N) = 4, followed by a single-scale clean down to S/N = 1 in masked regions. All cubes were visually inspected for obvious problems or imaging errors. ALMA Band 6 observations have a 5%-10% flux calibration.<fnref n="32" />

For the Total Power data for galaxies in the VERTICO Cycle 7 sample, we started with the raw data delivered by ALMA and used version 1.0 of the PHANGS-ALMA Total Power pipeline (Herrera et al. 2020; Leroy et al. 2021a). The only modification we made to the pipeline was to remove the initial velocity binning, so that the Total Power data were processed at their native velocity resolution of ~3 km s⁻¹. We typically imaged a range of 1000 km s⁻¹ around the mean velocity of the galaxy. We then fit and removed a first-order baseline using the highest and lowest 200 km s⁻¹ of the cube. For five galaxies (IC 3392, NGC 4380, NGC 4383, NGC 4580, NGC 4651), the baseline region was shifted to avoid an atmospheric ozone line. For two galaxies (NGC 4302, NGC 4698), the ozone line overlaps with the CO (2–1) line at some velocities, and so the Total Power fluxes for those galaxies are less reliable. All Total Power cubes were inspected to check for any problems in the data reduction. For the PHANGS-VERTICO galaxies, calibrated Total Power cubes were kindly provided to us by Adam Leroy on behalf of the PHANGS-ALMA team in private communication.

<footnote n="31">³¹ http://hedam.lam.fr</footnote>

<footnote n="32">³² See Chapter 10 in the ALMA Cycle 7 Technical Handbook https://almascience.nrao.edu/documents-and-tools/cycle7/alma-technical-handbook/.</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Channel maps for NGC 4380. The circular beam size illustrated in the bottom left panel is 7"/5, the channel width is 10.6 km s⁻¹, and the rms intensity in one channel is 3.5 mK. The systemic velocity of each channel is given in the lower right corner. The color scale is fixed between channels.</figcaption></figure>

For all galaxies and lines for which Total Power data were available, the Total Power data were combined with the ACA data via feathering using the PHANGS-ALMA pipeline. This technique is described in full in Section 6 of Leroy et al. (2021a). The final high-resolution data cubes were binned by a factor of two to produce ≥3 pixels across the beam. We also

produced data cubes binned by factors of four (for the native and 9" resolution images) and eight (for the 15" resolution images).

As an example, Figure 3 shows the integrated intensity channel maps for NGC 4380. Each channel is 10.6 km s⁻¹ wide, with the channel systemic velocity shown in the lower
<figure><img src="image_6.png" /><figcaption>**Figure 4.** An example of the CO (2–1) data products available for each galaxy in the VERTICO survey. The left panel shows the SDSS *gri* composite image for NGC 4380 with molecular gas surface brightness contours at the 10th, 50th, and 90th percentiles of the distribution. The field of view of the ACA observations is defined where the primary beam response drops to 50% and is illustrated by the gray line. The rounded synthesized beam is 7.5" in diameter and illustrated in the lower left corner. This beam corresponds to ~600 pc at the distance of Virgo (16.5 Mpc). The VERTICO CO (2–1) data products available for each galaxy include maps of integrated intensity (top center panel), the velocity field (top right), observed line width, $\sigma_v$ (bottom center), and peak temperature (bottom left). The x- and y-axes of each moment map show the angular offset from the optical center listed in Table 1. The complete figure set containing 49 panel plots for all VERTICO-detected galaxies is available online.</figcaption></figure>

(The complete figure set (49 images) is available.)

right corner of each panel. The maps span the velocity range over which we detect CO (2–1) emission. The color scale is fixed from channel to channel.

## 4. Derived Data Products

We calculate moment maps, position–velocity diagrams (PVDs), and radial profiles for each galaxy from a masked signal cube. The masking process follows a revised version of the signal identification scheme described in Sun et al. (2018). This method uses a spatially and spectrally varying noise estimate (i.e., we estimate the noise at each pixel in every channel) computed from the signal cubes before primary beam correction and is described in detail in Section 7.2 of Leroy et al. (2021a). The original code is publicly available,<fnref n="33" /> and the steps are as follows:

1. Generate a core mask for spaxels with $S/N \ge 3.5$ in at least three consecutive channels.

2. Generate a wing mask for spaxels with $S/N \ge 2$ in at least two consecutive channels.

3. Combine the core mask with the wing mask to define a signal mask that encapsulates all detected spaxels.

4. Prune spaxels from the signal mask if the projected area of connected neighbors on the sky is smaller than one beam.

5. Expand the signal mask along the spatial dimensions by a given number of pixels or a fraction of the beam size.

6. Expand the signal mask by two velocity channels.

7. Apply the final signal mask to produce a signal cube from which all moments are calculated.

We now describe the science-ready data products that are derived from these masked cubes.

### 4.1. Moment Maps

We compute the zeroth-, first-, second-, and eighth-order two-dimensional moment maps from the CO (2–1) spectral line cubes. In order, these are as follows:

1. Integrated intensity of the spectrum along the spectral axis in $K \text{ km s}^{-1}$.

2. Intensity weighted spectral coordinate in $\text{km s}^{-1}$, often referred to as the velocity field.

3. Observed line width ($\sigma_v$, i.e., not corrected for broadening) along the spectral axis in kilometers per second.

4. Peak brightness temperature value of the spectrum in kelvin.

Although not shown in this paper, we calculate statistical uncertainty maps for the pixel-by-pixel integrated intensity,

<footnote n="33">³³ https://github.com/astrojysun/Sun_Astro_Tools/tree/master/Sun_astro_tools</footnote>
<figure><img src="image_7.png" /><figcaption>Figure 5. PVDs along the major (top panel) and minor (bottom panel) axes of NGC 4380, extracted along the respective axes with a slit one beam in width. The bottom and top x-axes show the angular and physical offset from the galaxy center, respectively. The y-axis shows the relative offset from the systemic velocity listed in Table 1. The position angle used is 158°, and the average uncertainty in each axis is illustrated in the upper right corner. The channel width is 10 km s⁻¹.</figcaption></figure>

velocity field, and observed line width maps. The uncertainty on the integrated intensity is

$$u_I = \sqrt{N} \sigma_T \Delta v, \qquad (2)$$

where N is the number of channels included in the mask, σ_T is the rms uncertainty across the integrated intensity map, and Δv is the velocity channel width. We then compute the uncertainty on the velocity field,

$$u_{\text{vel}} = \frac{\Delta v_{\text{line}} u_I}{2\sqrt{3} I}, \qquad (3)$$

where I is the integrated intensity and Δv_line is the spectral line width over which u vel is calculated. The uncertainty on the observed line width is given by

$$u_{\sigma_v} = \frac{u_I (\Delta v_{\text{line}})^2}{I 8\sqrt{5} \sigma_v}, \qquad (4)$$

where σ_v is the observed line width map. The derivation for these equations is provided in C. D. Wilson et al. (2021, in preparation).

Figure 4 illustrates the high quality of the VERTICO CO (2–1) moment maps for NGC 4380. An archetypal unbarred spiral, we choose this galaxy to showcase VERTICO, as it appears to be relatively unperturbed by its environment and has a bright, extended CO (2–1) gas disk. The left panel shows the SDSS gri composite image with molecular gas surface brightness contours at the 10th, 50th, and 90th percentiles. The integrated intensity, velocity field, peak temperature, and observed CO (2–1) line width maps are provided clockwise from the top middle panel. We calculate NGC 4380’s r-band

inclination to be 61°. Equivalent panel plots of the CO data products for the 49 detected VERTICO galaxies are in the online version of Figure 4.

The synthesized 7".5 beam of the NGC 4380 data corresponds to approximately 600 pc at the distance of Virgo (16.5 Mpc). On this scale, the VERTICO observations reveal the imprint of stellar structure in the molecular gas distribution of NGC 4380 in glorious detail. The northern and northeastern outskirts of the gas disk have a ridge of emission that is not found on the opposing side of the galaxy. We can also see a strong CO feature straddling the nucleus from the southeast to the northwest. Examining the central region in the peak temperature map shows that there are two symmetrical peaks of CO emission such as those commonly found in the centers of barred galaxies (e.g., Kenney et al. 1992; Muraoka et al. 2016).

## 4.2. Position–Velocity Diagrams

We create major- and minor-axis PVDs from the CO (2–1) signal cubes. The major-axis position angles are provided in Table 1 and were derived by fitting Kron ellipses to the background-subtracted, masked SDSS r-band images using the PHOTUTILS PYTHON package (Bradley et al. 2020). All Kron ellipses pass visual inspection to ensure a robust fit before being used. The position–velocity slit width is set to one beamwidth for each galaxy.

Figure 5 shows both PVDs for NGC 4380. The two x-axes denote the positional offset about the optical center of the galaxy (provided in Table 1) in physical and angular units. The major-axis PVD is shown in the top panel and reveals the increase in high-velocity emission at negative offsets compared to positive offsets. This asymmetry is also apparent in the northern regions of the peak temperature map in Figure 4 and is discussed in Section 4.1. The asymmetry that shows higher brightness temperatures at positive relative velocity offsets in the minor-axis PVD (bottom panel) highlights the concentration of emission along the northeast edge of the gas disk. More work is needed to determine whether the source of this asymmetry is secular (e.g., spiral arms, gas streaming motions) or environment driven (e.g., starvation, gravitational, and/or ICM interaction). Channel maps for NGC 4380’s unmasked CO (2–1) cube are shown in Figure 3.

## 4.3. Global CO Fluxes

The global CO line luminosity, L CO, and integrated flux, S CO, are calculated from global spectra derived from masked data cubes. In an effort to include fainter emission at the edges of each disk in the global estimate, we adopt a 2D masking process to calculate these global properties (adapted from the 3D method used to produce the moment maps described in Section 4.1, which we refer to as the Sun et al. 2018 method). The 2D masking process for making the spectra is as follows:

1. Create a 2D mask where pixels are masked if the conditions for masking described in Section 4.1 are met at that x-y position in every channel.

2. Dilate this mask in the x-y plane by the rounded beam size listed in Table 2.

3. Replicate the dilated mask in every channel and apply to the primary-beam-corrected, continuum-subtracted CO data cubes.
<table><caption>**Table 2**
Global CO (2–1) Line Properties for the 51 VERTICO Galaxies Fits</caption><thead><tr><th>Galaxy<br>(1)</th><th>S/N<br>(2)</th><th>θ<sub>b</sub><br>(arcsec)<br>(3)</th><th>Rms<br>(mJy)<br>(4)</th><th>v<sub>lsr</sub><br>(km s<sup>-1</sup>)<br>(5)</th><th>Δv<sub>line</sub><br>(km s<sup>-1</sup>)<br>(6)</th><th>S<sub>CO</sub><br>(Jy km s<sup>-1</sup>)<br>(7)</th><th>log L<sub>CO</sub><br>(K km s<sup>-1</sup> pc<sup>2</sup>)<br>(8)</th><th>I&#773;<sub>CO</sub><br>(K km s<sup>-1</sup>)<br>(9)</th><th>log M<sub>mol</sub><br>(M<sub>☉</sub>)<br>(10)</th></tr></thead><tbody><tr><td>IC 3392</td><td>28.3</td><td>8.4</td><td>134</td><td>1690</td><td>206</td><td>259 ± 9</td><td>7.63 ± 0.02</td><td>1.87 ± 0.07</td><td>8.37 ± 0.02</td></tr><tr><td>IC 3418<sup>a</sup></td><td></td><td>8.1</td><td>101</td><td></td><td></td><td>&lt;30.29</td><td>&lt;6.70</td><td>&lt;11.44</td><td>&lt;7.44</td></tr><tr><td>NGC 4064</td><td>23.3</td><td>9.0</td><td>32</td><td>954</td><td>225</td><td>285 ± 12</td><td>7.67 ± 0.02</td><td>2.48 ± 0.11</td><td>8.41 ± 0.02</td></tr><tr><td>NGC 4189</td><td>38.9</td><td>7.5</td><td>202</td><td>2133</td><td>289</td><td>545 ± 14</td><td>7.95 ± 0.01</td><td>1.59 ± 0.04</td><td>8.69 ± 0.01</td></tr><tr><td>NGC 4192</td><td>74.4</td><td>9.2</td><td>358</td><td>-143</td><td>518</td><td>1997 ± 27</td><td>8.52 ± 0.01</td><td>2.78 ± 0.04</td><td>9.26 ± 0.01</td></tr><tr><td>NGC 4216</td><td>40.9</td><td>7.2</td><td>304</td><td>160</td><td>621</td><td>1009 ± 25</td><td>8.22 ± 0.01</td><td>1.37 ± 0.03</td><td>8.96 ± 0.01</td></tr><tr><td>NGC 4222</td><td>12.5</td><td>8.4</td><td>26</td><td>230</td><td>255</td><td>128 ± 10</td><td>7.33 ± 0.03</td><td>0.58 ± 0.05</td><td>8.06 ± 0.03</td></tr><tr><td>NGC 4254</td><td>185.0</td><td>8.6</td><td>331</td><td>2447</td><td>320</td><td>8369 ± 45</td><td>9.14 ± 0.00</td><td>4.64 ± 0.03</td><td>9.88 ± 0.00</td></tr><tr><td>NGC 4293</td><td>48.8</td><td>7.6</td><td>328</td><td>936</td><td>297</td><td>810 ± 17</td><td>8.13 ± 0.01</td><td>3.80 ± 0.08</td><td>8.86 ± 0.01</td></tr><tr><td>NGC 4294</td><td>6.4</td><td>8.2</td><td>29</td><td>376</td><td>173</td><td>62 ± 10</td><td>7.01 ± 0.07</td><td>0.37 ± 0.06</td><td>7.75 ± 0.07</td></tr><tr><td>NGC 4298</td><td>82.7</td><td>7.5</td><td>191</td><td>1140</td><td>278</td><td>1336 ± 16</td><td>8.35 ± 0.01</td><td>2.50 ± 0.03</td><td>9.08 ± 0.01</td></tr><tr><td>NGC 4299</td><td>5.2</td><td>8.3</td><td>117</td><td>239</td><td>112</td><td>42 ± 8</td><td>6.84 ± 0.08</td><td>0.19 ± 0.04</td><td>7.58 ± 0.08</td></tr><tr><td>NGC 4302</td><td>67.2</td><td>7.7</td><td>313</td><td>1158</td><td>410</td><td>1375 ± 20</td><td>8.36 ± 0.01</td><td>3.39 ± 0.05</td><td>9.09 ± 0.01</td></tr><tr><td>NGC 4321</td><td>187.9</td><td>10.2</td><td>433</td><td>1590</td><td>279</td><td>7635 ± 41</td><td>9.10 ± 0.00</td><td>3.45 ± 0.02</td><td>9.84 ± 0.00</td></tr><tr><td>NGC 4330</td><td>16.4</td><td>7.7</td><td>32</td><td>1566</td><td>298</td><td>241 ± 15</td><td>7.60 ± 0.03</td><td>1.19 ± 0.07</td><td>8.34 ± 0.03</td></tr><tr><td>NGC 4351</td><td>11.8</td><td>8.5</td><td>149</td><td>2324</td><td>124</td><td>79 ± 7</td><td>7.11 ± 0.04</td><td>0.37 ± 0.03</td><td>7.85 ± 0.04</td></tr><tr><td>NGC 4380</td><td>35.3</td><td>7.5</td><td>249</td><td>990</td><td>307</td><td>432 ± 12</td><td>7.86 ± 0.01</td><td>0.90 ± 0.03</td><td>8.59 ± 0.01</td></tr><tr><td>NGC 4383</td><td>22.9</td><td>8.1</td><td>184</td><td>1715</td><td>206</td><td>263 ± 11</td><td>7.64 ± 0.02</td><td>1.26 ± 0.05</td><td>8.37 ± 0.02</td></tr><tr><td>NGC 4388</td><td>49.3</td><td>8.1</td><td>25</td><td>2501</td><td>486</td><td>859 ± 17</td><td>8.15 ± 0.01</td><td>2.86 ± 0.06</td><td>8.89 ± 0.01</td></tr><tr><td>NGC 4394</td><td>12.0</td><td>8.7</td><td>24</td><td>929</td><td>215</td><td>105 ± 9</td><td>7.24 ± 0.04</td><td>0.44 ± 0.04</td><td>7.98 ± 0.04</td></tr><tr><td>NGC 4396</td><td>10.0</td><td>7.8</td><td>217</td><td>-119</td><td>193</td><td>124 ± 12</td><td>7.32 ± 0.04</td><td>0.61 ± 0.06</td><td>8.05 ± 0.04</td></tr><tr><td>NGC 4402</td><td>83.1</td><td>7.6</td><td>30</td><td>248</td><td>357</td><td>1402 ± 17</td><td>8.37 ± 0.01</td><td>5.00 ± 0.06</td><td>9.10 ± 0.01</td></tr><tr><td>NGC 4405</td><td>18.3</td><td>7.7</td><td>33</td><td>1752</td><td>175</td><td>206 ± 11</td><td>7.53 ± 0.02</td><td>1.99 ± 0.11</td><td>8.27 ± 0.02</td></tr><tr><td>NGC 4419</td><td>121.2</td><td>8.1</td><td>32</td><td>-172</td><td>447</td><td>1399 ± 12</td><td>8.37 ± 0.00</td><td>5.71 ± 0.05</td><td>9.10 ± 0.00</td></tr><tr><td>NGC 4424</td><td>34.1</td><td>7.9</td><td>101</td><td>448</td><td>158</td><td>228 ± 7</td><td>7.58 ± 0.01</td><td>1.63 ± 0.05</td><td>8.31 ± 0.01</td></tr><tr><td>NGC 4450</td><td>31.8</td><td>7.6</td><td>233</td><td>1960</td><td>340</td><td>523 ± 16</td><td>7.94 ± 0.01</td><td>1.14 ± 0.04</td><td>8.67 ± 0.01</td></tr><tr><td>NGC 4457</td><td>63.6</td><td>7.8</td><td>238</td><td>905</td><td>297</td><td>1154 ± 18</td><td>8.28 ± 0.01</td><td>4.16 ± 0.07</td><td>9.02 ± 0.01</td></tr><tr><td>NGC 4501</td><td>219.6</td><td>8.0</td><td>302</td><td>2277</td><td>589</td><td>5499 ± 25</td><td>8.96 ± 0.00</td><td>7.61 ± 0.03</td><td>9.69 ± 0.00</td></tr><tr><td>NGC 4522</td><td>20.8</td><td>8.5</td><td>32</td><td>2351</td><td>217</td><td>223 ± 11</td><td>7.57 ± 0.02</td><td>1.13 ± 0.05</td><td>8.30 ± 0.02</td></tr><tr><td>NGC 4532</td><td>18.3</td><td>7.1</td><td>151</td><td>2037</td><td>227</td><td>198 ± 11</td><td>7.52 ± 0.02</td><td>1.03 ± 0.06</td><td>8.25 ± 0.02</td></tr><tr><td>NGC 4533</td><td>1.7</td><td>7.8</td><td>35</td><td>1698</td><td>103</td><td>10 ± 6</td><td>6.20 ± 0.26</td><td>0.04 ± 0.03</td><td>6.94 ± 0.26</td></tr><tr><td>NGC 4535</td><td>85.4</td><td>8.2</td><td>680</td><td>1978</td><td>270</td><td>2862 ± 34</td><td>8.68 ± 0.01</td><td>2.27 ± 0.03</td><td>9.41 ± 0.01</td></tr><tr><td>NGC 4536</td><td>88.4</td><td>8.6</td><td>452</td><td>1817</td><td>389</td><td>2465 ± 28</td><td>8.61 ± 0.01</td><td>1.90 ± 0.02</td><td>9.35 ± 0.01</td></tr><tr><td>NGC 4548</td><td>58.7</td><td>7.6</td><td>354</td><td>509</td><td>336</td><td>1085 ± 18</td><td>8.26 ± 0.01</td><td>1.01 ± 0.02</td><td>8.99 ± 0.01</td></tr><tr><td>NGC 4561</td><td>2.3</td><td>7.9</td><td>253</td><td>1433</td><td>92</td><td>23 ± 10</td><td>6.58 ± 0.19</td><td>0.14 ± 0.06</td><td>7.31 ± 0.19</td></tr><tr><td>NGC 4567</td><td>91.7</td><td>7.5</td><td>21</td><td>2295</td><td>258</td><td>766 ± 8</td><td>8.10 ± 0.00</td><td>2.60 ± 0.03</td><td>8.84 ± 0.00</td></tr><tr><td>NGC 4568</td><td>232.6</td><td>8.6</td><td>168</td><td>2279</td><td>382</td><td>2865 ± 12</td><td>8.68 ± 0.00</td><td>9.58 ± 0.04</td><td>9.41 ± 0.00</td></tr><tr><td>NGC 4569</td><td>158.6</td><td>7.5</td><td>433</td><td>-222</td><td>492</td><td>4204 ± 27</td><td>8.85 ± 0.00</td><td>6.00 ± 0.04</td><td>9.58 ± 0.00</td></tr><tr><td>NGC 4579</td><td>109.1</td><td>8.0</td><td>441</td><td>1517</td><td>458</td><td>2277 ± 21</td><td>8.58 ± 0.00</td><td>1.98 ± 0.02</td><td>9.31 ± 0.00</td></tr><tr><td>NGC 4580</td><td>40.1</td><td>8.4</td><td>179</td><td>1041</td><td>215</td><td>396 ± 10</td><td>7.82 ± 0.01</td><td>2.13 ± 0.05</td><td>8.55 ± 0.01</td></tr><tr><td>NGC 4606</td><td>25.0</td><td>7.6</td><td>21</td><td>1653</td><td>165</td><td>154 ± 6</td><td>7.41 ± 0.02</td><td>0.84 ± 0.03</td><td>8.14 ± 0.02</td></tr><tr><td>NGC 4607</td><td>33.9</td><td>7.5</td><td>26</td><td>2283</td><td>299</td><td>420 ± 12</td><td>7.84 ± 0.01</td><td>2.11 ± 0.06</td><td>8.58 ± 0.01</td></tr><tr><td>NGC 4651</td><td>51.0</td><td>7.9</td><td>165</td><td>805</td><td>368</td><td>640 ± 13</td><td>8.03 ± 0.01</td><td>1.94 ± 0.04</td><td>8.76 ± 0.01</td></tr><tr><td>NGC 4654</td><td>90.3</td><td>7.5</td><td>468</td><td>1042</td><td>377</td><td>2348 ± 26</td><td>8.59 ± 0.00</td><td>2.54 ± 0.03</td><td>9.33 ± 0.00</td></tr><tr><td>NGC 4689</td><td>62.2</td><td>7.6</td><td>293</td><td>1645</td><td>239</td><td>1175 ± 19</td><td>8.29 ± 0.01</td><td>1.65 ± 0.03</td><td>9.02 ± 0.01</td></tr><tr><td>NGC 4694</td><td>20.8</td><td>7.1</td><td>105</td><td>1234</td><td>278</td><td>188 ± 9</td><td>7.49 ± 0.02</td><td>1.05 ± 0.05</td><td>8.23 ± 0.02</td></tr><tr><td>NGC 4698</td><td>4.6</td><td>8.1</td><td>253</td><td>1023</td><td>451</td><td>97 ± 21</td><td>7.21 ± 0.10</td><td>0.29 ± 0.06</td><td>7.94 ± 0.10</td></tr><tr><td>NGC 4713</td><td>23.2</td><td>8.4</td><td>184</td><td>652</td><td>204</td><td>265 ± 11</td><td>7.64 ± 0.02</td><td>0.80 ± 0.03</td><td>8.38 ± 0.02</td></tr><tr><td>NGC 4772</td><td>1.6</td><td>7.5</td><td>31</td><td>1055</td><td>410</td><td>28 ± 17</td><td>6.66 ± 0.27</td><td>0.19 ± 0.11</td><td>7.40 ± 0.27</td></tr><tr><td>NGC 4808</td><td>44.9</td><td>8.2</td><td>91</td><td>779</td><td>307</td><td>607 ± 14</td><td>8.00 ± 0.01</td><td>1.80 ± 0.04</td><td>8.74 ± 0.01</td></tr><tr><td>VCC 1581<sup>a</sup></td><td></td><td>8.7</td><td>25</td><td></td><td></td><td>&lt;7.55</td><td>&lt;6.11</td><td>&lt;3.25</td><td>&lt;6.84</td></tr></tbody></table>

Notes. Columns are (1) galaxy identifier; (2) signal-to-noise ratio of the integrated spectrum; (3) diameter of the circularized synthesized beam; (4) integrated spectrum rms in 10.6 km s⁻¹ channels; (5) local standard of rest recession velocity of the line center, calculated as the midpoint of Δv<sub>line</sub>; (6) velocity width of the line at zero intensity; (7) velocity-integrated flux; (8) CO line luminosity given by Equation (5); (9) mean velocity-integrated CO intensity; (10) logarithm of molecular gas mass given by Equation (7). This table is published in its entirety in machine-readable format. We do not include the typical Band 6 calibration uncertainty of 5%–10% (0.02–0.04 dex) in the flux measurement uncertainties. One may add this in quadrature to account for this.

a Values are 3σ upper limits calculated over an on-sky circle with radius = 30'' (projected radius ≈2.4 kpc) and a line width of 100 km s⁻¹. The positions and systemic velocities used are listed in Table 1.

(This table is available in its entirety in FITS format.)
<figure><img src="image_8.png" /><figcaption>Figure 6. Normalized distribution of CO (2–1)/CO (1–0) global line ratios for the 35 VERTICO galaxies (blue filled histogram) that have CO (1–0) data presented in Boselli et al. (2014, Table 11). The orange step histogram shows the 25 galaxies in xCOLD GASS with high-quality aperture-corrected IRAM 30 m CO (1–0) and APEX CO (2–1) data. The mean and standard deviation of each distribution are provided in the upper left corner.</figcaption></figure>

The full figure set for spectra derived from these masked cubes for every galaxy is shown after the main text of the article. The integrated CO line properties and velocity widths at zero intensity over which the line fluxes are measured are provided in Table 2. We provide measurement uncertainties on the global CO line luminosities and fluxes. True uncertainties should also include the 5%–10% ALMA Band 6 calibration accuracy and distance uncertainties, added in quadrature, that are not accounted for in the quoted values. For the latter, the determination of reliable distance for cluster galaxies is nontrivial. However, the standard deviation of VERTICO galaxy distances taken from the z0MGS database (Leroy et al. 2019) is 1.65 Mpc, which is consistent with the range of Virgo size estimates ($r_{200} \approx 1.05–1.55$ Mpc; Boselli et al. 2018). There are four marginal detections with S/N < 4 (NGC 4533, NGC 4698, NGC 4561, and NGC 4772) and two nondetections (IC 3418 and VCC 1581) for which we provide $3\sigma$ upper limits.

Following Solomon & Vanden Bout (2005), we calculate the CO line luminosity, $L_{CO}$, in K km s$^{-1}$ pc$^2$, expressed as the product of the velocity-integrated source brightness temperature and the source area

$$L_{CO} = 3.25 \times 10^7 S_{CO} \nu_{obs}^{-2} D_L^2, \quad (5)$$

where $S_{CO}$ is the velocity-integrated flux in Jy km s$^{-1}$, $\nu_{obs}$ is the observed frequency in GHz, and $D_L$ is the luminosity distance to the source in Mpc. For clarity, $L_{CO}$ is $L'_{CO}$ in Equation (3) of Solomon & Vanden Bout (2005).

Figures 6 and 7 compare the CO (1–0) and CO (2–1) line luminosity ratio ($R_{21}$) and integrated flux densities for the 35 VERTICO galaxies that have CO (1–0) data compiled and presented by Boselli et al. (2014; blue solid histogram) for the HRS. Establishing $R_{21}$ across the sample is important for

<figure><img src="image_9.png" /><figcaption>Figure 7. Correlation between observed CO (1–0) and CO (2–1) line flux for the 35 VERTICO galaxies that have high-quality CO (1–0) data presented in Boselli et al. (2014, Table 11). The dashed, solid, and dotted-dashed lines represent $R_{21} = 0.6, 0.8, \text{and } 1$, respectively. For VERTICO, the average $R_{21}$ is $0.77 \pm 0.05$, while the median uncertainty on the CO (2–1) line flux is 16 Jy km s$^{-1}$ and thus within the marker size on the x-axis scale.</figcaption></figure>

deriving molecular gas masses (e.g., Equation (7)) and interpreting our results in the context of other studies. For this comparison, Boselli et al. (2014) fluxes are converted from $T_R^*$ (observed antenna temperature corrected for atmospheric attenuation, radiative loss, and forward and rearward scattering and spillover efficiency) to $T_A^*$ (observed antenna temperature corrected for atmospheric attenuation, radiative loss, and rearward scattering and spillover efficiency) temperature scales via the expression

$$T_A^* = \eta_{fss} T_R^*, \quad (6)$$

where $\eta_{fss}$ is the forward scattering and spillover efficiency of the telescope (Kutner & Ulich 1981). Following Boselli et al. (2014), we adopt $\eta_{fss} = 0.68$ for the National Radio Astronomy Observatory Kitt Peak 12 m telescope.

Figure 6 shows the distribution of observed $R_{21} = CO (2–1)/CO (1–0)$ line luminosity ratios for the VERTICO-HRS sample (blue histogram). We also show the observed $R_{21}$ ratio for the 25 xCOLD GASS galaxies with APEX CO (2–1) and high-quality IRAM 30 m CO (1–0) detections as presented in Saintonge et al. (2017; WCO\_FLAG and FLAG\_APEX = 1 in their catalog). We measure $\bar{R}_{21} = 0.77 \pm 0.05$ in VERTICO galaxies with a standard deviation of $\sigma = 0.3$, in agreement with the value of $\bar{R}_{21} = 0.79 \pm 0.03$ reported by Saintonge et al. (2017) and measured from their published data release, $\bar{R}_{21} = 0.81 \pm 0.07$, where their assumed metallicity-dependent $\alpha_{CO} > 1$ M$_\odot$ pc$^{-2}$ (K km s$^{-1}$)$^{-1}$. The minor difference between the reported and measured xCOLD GASS $R_{21}$ values is due to the exclusion of galaxies based on the quality of the APEX data in the published value (Saintonge, private communication). Based on our measured value and its agreement with the literature, we adopt a constant value of $R_{21} = 0.8$ throughout this work. We note that this is comparable to but slightly higher than reported values in other works (Leroy et al. 2013;
den Brok et al. 2021; Yajima et al. 2021). Further characterization of $R_{21}$ and its variation across the VERTICO sample will be the subject of future work.

Figure 7 plots the relation between the CO (1–0) and CO (2–1) integrated flux densities for the 35 VERTICO-HRS galaxies. For illustration, $R_{21} = 1, 0.8$, and $0.5$ are denoted by the dotted-dashed, solid, and dashed lines, respectively. The outlier with the lowest $R_{21}$ (above the main correlation) is NGC 4567, which is in very close proximity to NGC 4568. The original CO (1–0) data for this galaxy are drawn from Five College Radio Astronomy Observatory observations (45" beam size) published by Chung et al. (2009b). Determining whether physical or observational effects (e.g., source confusion) are responsible for NGC 4567’s low $R_{21}$ value is beyond the scope of this paper.

## 4.4. Global Molecular Gas Masses

We convert CO luminosity to molecular gas mass, including the contribution from heavy elements, in units of solar mass using the relation

$$M_{\text{mol}} = \frac{\alpha_{\text{CO}}}{R_{21}} L_{\text{CO}}, \qquad (7)$$

where $\alpha_{CO} = 4.35 M_{\odot} \text{pc}^{-2} (\text{K km s}^{-1})^{-1}$, the molecular gas mass-to-CO (1–0) luminosity ratio calculated for the Milky Way disk by Bolatto et al. (2013), and $R_{21} = 0.8$. Our $\alpha_{CO}$ corresponds to a CO (1–0)-to-H$_2$ conversion factor of $X_{CO} = 2 \times 10^{20} \text{ cm}^{-2} (\text{K km s}^{-1})^{-1}$ that is consistent with other surveys of CO emission in nearby galaxies (e.g., HERACLES—Leroy et al. 2009; JCMT-NGLS—Wilson et al. 2009; xCOLD GASS—Saintonge et al. 2011, 2017; EDGE-CALIFA—Bolatto et al. 2017).

All molecular gas masses quoted in this paper include the 36% contribution of helium (Kennicutt & Evans 2012; Bolatto et al. 2013). The true value of $\alpha_{CO}$ can be up to a factor of 5 lower in regions of increased average gas volume density such as in mergers and galaxy centers as has been shown in observations (e.g., Leroy et al. 2011; Smith et al. 2012; Sandstrom et al. 2013) and demonstrated with modeling (e.g., Narayanan et al. 2011, 2012; Shetty et al. 2011; Olsen et al. 2016). We leave a more detailed modeling and application of $\alpha_{CO}$ to future work.

Figure 8 compares the stellar mass, sSFR, and molecular gas mass properties of VERTICO galaxies (blue) with the volume-limited xCOLD GASS sample (orange; Saintonge et al. 2011, 2017).$^{34}$ As with xGASS, we apply the recommended weights published by Saintonge et al. (2017) to the xCOLD GASS data to achieve a volume-limited sample for $M_{\star} \ge 10^9 M_{\odot}$. We adjust the published xCOLD GASS molecular gas estimates to our assumed $\alpha_{CO}$ in Equation (7). The top left panel compares the distribution of xCOLD GASS and VERTICO in the stellar mass–sSFR plane, again highlighting VERTICO’s selection of star-forming and quenching galaxies, rather than quiescent galaxies (see Figure 1). The left and right panels in the middle row show molecular gas fraction ($M_{\text{mol}}/M_{\star}$) as a function of stellar mass and sSFR, respectively. While there are a small number of VERTICO galaxies with low molecular gas fractions, the majority of the sample is either normal or rich in molecular gas at fixed stellar mass and sSFR.

The bottom panels show the volume-limited stellar mass, sSFR, and molecular gas mass distributions. Interestingly, there is a significant fraction of xCOLD GASS galaxies that are more star-forming than VERTICO; however, this does not translate into an excess in the molecular gas mass distribution. Although more investigation is needed, this may at least be partially explained by the increased fraction of massive VERTICO galaxies in comparison to the xCOLD GASS sample (bottom left panel).

## 4.5. CO Radial Profiles

We measure azimuthally averaged CO intensity radial profiles in elliptical annuli overlaid on the integrated intensity maps described in Section 4.1. Annuli are centered on the optical position and aligned with the major-axis position angle. Eccentricity is derived from the optical inclination of the galaxy provided in Table 1. To ensure the independence of each measurement, the annulus width along the minor axis is set to the synthesized beam size. The corresponding radii are defined as the mean galactocentric radius of pixels in each annulus. The average intensity is calculated as the summed emission divided by the total area. This means that nondetectors (i.e., masked pixels) within each annulus are included in this calculation as zero intensity. This approach is conservative, especially where galaxies have asymmetric or fragmented gas disks, and results in radial profiles that can be considered lower limits on the true average CO surface brightness, particularly in the outskirts. Future work will explore the impact of this method on the measured radial profiles and isodensity radii.

For highly inclined galaxies this method does not work well, as the axial ratio becomes too small, causing highly eccentric annuli with the major axes extending beyond the galactic disk. Therefore, for galaxies with inclination $\ge 80^{\circ}$, we use a slice that is one beam thick aligned with the major axis. The integrated intensity as a function of radius is then calculated by averaging the emission in each slice.

Uncertainties on all the intensity profiles are calculated as

$$u_{\text{rp}} = \sigma(I_{\text{CO,pix}}) \sqrt{N_{\text{beam}}}, \qquad (8)$$

where $\sigma(I_{\text{CO,pix}})$ is the standard deviation of integrated intensity in each pixel and $N_{\text{beam}}$ is the number of beams within each annulus.

Figure 9 shows the mean surface brightness radial profiles of 49 VERTICO galaxies (IC 3418 and VCC 1581 are nondetections). The profiles are denoted by gray points, and their uncertainties are shown by the gray shaded regions. Radial profiles in surface brightness units are not corrected for inclination.

Although quantitative analyses of the molecular gas distribution in VERTICO galaxies will be the subject of upcoming work, here we comment briefly on the large range of gas disk morphologies exhibited by the CO surface brightness profiles. A significant number of profiles do not decrease steadily as a function of radius, showing bumps in the CO distribution at larger radii (e.g., NGC 4189, NGC 4450, NGC 4535, NGC 4548, NGC 4579, NGC 4808) or, perhaps most interestingly, signs of truncation at the outer edge of the disk (e.g., NGC 4064, NGC 4299, NGC 4402, NGC 4457, NGC 4532, NGC 4535, NGC 4580, NGC 4607). This variation contrasts with the findings from studies of nearby field galaxies, where the CO radial profiles are typically exponential with a comparable scale length as the stellar disk (Regan et al. 2001;

<footnote>$^{34}$ http://www.star.ucl.ac.uk/xCOLDGASS/</footnote>
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Global properties of the VERTICO sample (blue points and histograms) compared to the weighted xCOLD GASS catalog published by Saintonge et al. (2017; orange distributions). We include the 528 xCOLD GASS galaxies that have their recommended ("best") SFR estimate. We adjust all molecular gas estimates to our constant conversion factor, and the 199 CO nondetections in xCOLD GASS are included as 3σ upper limits. Left to right starting at the top left: sSFR vs. stellar mass, molecular gas fraction vs. stellar mass, molecular gas fraction vs. sSFR, the normalized stellar mass, sSFR, and molecular gas mass distributions. The three histogram panels share the same y-axis range. The two galaxies that are undetected in CO are shown with open markers, and inverted triangles denote their upper limits.</figcaption></figure>

Helfer et al. 2003; Leroy et al. 2009, 2013; Schruba et al. 2011; Bigiel & Blitz 2012; Bolatto et al. 2017), but is qualitatively closer to the observed surface brightness profiles of early-type galaxies, which do often show such enhancements and truncation (e.g., Davis et al. 2013). Given the observed diversity in the VERTICO galaxies’ stellar morphologies and the efficacy of CO as a dynamical tracer, the variety of shapes seen in the inner regions of VERTICO radial profiles could be driven by stellar bars or other dynamical features such as bulges or arms. Chown et al. (2019) clearly show that barred spiral

galaxies exhibit a large range of molecular gas radial profile shapes, molecular gas concentrations, and star formation histories in their inner regions. Furthermore, those authors find that the level of central star formation enhancement is correlated with gas concentration in barred galaxies. Related works show similar diversity in central molecular gas concentration (e.g., Sheth et al. 2005), star formation properties (e.g., Lin et al. 2017, 2020), and H I surface density (e.g., Wang et al. 2014). It is clear that the combination of gas morphology with the high angular resolution and sensitivity of these observations results in
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Azimuthally averaged surface brightness profiles as a function of galactocentric radius in kpc (bottom x-axis) and arcseconds (top). Radial profiles are denoted by the gray points, while their uncertainties are illustrated by the shaded region. The five largest galaxies are shown in the last row with a different x-axis range. We show all the profiles in the last panel of the ninth row, highlighting the diversity of profile shapes. The surface brightness radial profiles are not corrected for inclination. Table 3 contains the 50% and 90% flux radii ($r_{50,\text{mol}}$ and $r_{90,\text{mol}}$, respectively) and inclination-corrected isodensity radii ($r_{5,\text{mol}}$) for each galaxy, where possible.</figcaption></figure>

profiles that frequently depart from smoothly decreasing decline. We also note that we do not see a central hole in the CO surface brightness distribution for many galaxies, as is commonly found in other surveys (e.g., Bigiel & Blitz 2012). In contrast, the observed CO surface brightness distribution of VERTICO galaxies is closer to the typical shapes of Hα emission in Virgo

Cluster galaxies found by Koopmann et al. (2001). In this work, the Hα disks—as a close tracer of star formation—exhibit a similar range concentration and morphology to the CO, including systems that show elevated emission in the circumnuclear regions and truncation of star formation in the outer optical disk. A large range in concentration is also reported by
<table><caption>**Table 3**
Molecular Gas Disk Radii Estimates Fits</caption><thead><tr><th>Galaxy</th><th>r<sub>50,mol</sub><br>(kpc)</th><th>r<sub>90,mol</sub><br>(kpc)</th><th>r<sub>5,mol</sub><br>(kpc)</th></tr></thead><tbody><tr><td>IC 3392</td><td>1.16</td><td>2.32</td><td>2.41</td></tr><tr><td>NGC 4064</td><td>1.06</td><td>2.18</td><td>2.08</td></tr><tr><td>NGC 4189</td><td>1.27</td><td>3.23</td><td>3.57</td></tr><tr><td>NGC 4192</td><td>5.10</td><td>9.70</td><td></td></tr><tr><td>NGC 4216</td><td>6.51</td><td>11.58</td><td></td></tr><tr><td>NGC 4222</td><td>1.55</td><td>4.01</td><td></td></tr><tr><td>NGC 4254</td><td>1.94</td><td>5.72</td><td>8.33</td></tr><tr><td>NGC 4293</td><td>0.79</td><td>1.86</td><td>2.60</td></tr><tr><td>NGC 4294</td><td>1.55</td><td>3.20</td><td></td></tr><tr><td>NGC 4298</td><td>1.45</td><td>3.94</td><td>4.69</td></tr><tr><td>NGC 4299</td><td>1.15</td><td>1.85</td><td></td></tr><tr><td>NGC 4302</td><td>2.86</td><td>6.74</td><td></td></tr><tr><td>NGC 4321</td><td>1.03</td><td>5.95</td><td>9.74</td></tr><tr><td>NGC 4330</td><td>1.65</td><td>3.76</td><td></td></tr><tr><td>NGC 4351</td><td>0.88</td><td>2.12</td><td>0.80</td></tr><tr><td>NGC 4380</td><td>1.63</td><td>4.77</td><td>1.95</td></tr><tr><td>NGC 4383</td><td>0.84</td><td>1.84</td><td>1.94</td></tr><tr><td>NGC 4388</td><td>1.46</td><td>3.30</td><td>0.42</td></tr><tr><td>NGC 4394</td><td>0.50</td><td>2.85</td><td>0.82</td></tr><tr><td>NGC 4396</td><td>1.30</td><td>3.18</td><td></td></tr><tr><td>NGC 4402</td><td>2.69</td><td>5.21</td><td>5.63</td></tr><tr><td>NGC 4405</td><td>0.69</td><td>1.35</td><td>1.74</td></tr><tr><td>NGC 4419</td><td>1.24</td><td>2.70</td><td>3.69</td></tr><tr><td>NGC 4424</td><td>0.92</td><td>1.94</td><td>1.97</td></tr><tr><td>NGC 4450</td><td>0.85</td><td>2.78</td><td>2.04</td></tr><tr><td>NGC 4457</td><td>0.65</td><td>1.84</td><td>2.87</td></tr><tr><td>NGC 4501</td><td>2.20</td><td>6.54</td><td>8.97</td></tr><tr><td>NGC 4522</td><td>1.08</td><td>2.46</td><td></td></tr><tr><td>NGC 4532</td><td>0.95</td><td>2.30</td><td>1.65</td></tr><tr><td>NGC 4533</td><td>1.90</td><td>4.58</td><td></td></tr><tr><td>NGC 4535</td><td>0.74</td><td>6.39</td><td>8.29</td></tr><tr><td>NGC 4536</td><td>1.33</td><td>3.62</td><td>4.31</td></tr><tr><td>NGC 4548</td><td>0.78</td><td>6.31</td><td>1.29</td></tr><tr><td>NGC 4561</td><td>1.91</td><td>2.87</td><td></td></tr><tr><td>NGC 4567</td><td>1.06</td><td>3.16</td><td>3.71</td></tr><tr><td>NGC 4568</td><td>1.47</td><td>3.84</td><td>5.31</td></tr><tr><td>NGC 4569</td><td>1.12</td><td>4.12</td><td>6.42</td></tr><tr><td>NGC 4579</td><td>0.85</td><td>5.15</td><td>6.75</td></tr><tr><td>NGC 4580</td><td>0.98</td><td>2.01</td><td>2.50</td></tr><tr><td>NGC 4606</td><td>0.87</td><td>2.13</td><td>1.53</td></tr><tr><td>NGC 4607</td><td>1.19</td><td>2.75</td><td></td></tr><tr><td>NGC 4651</td><td>1.30</td><td>2.67</td><td>2.96</td></tr><tr><td>NGC 4654</td><td>1.52</td><td>4.97</td><td>6.15</td></tr><tr><td>NGC 4689</td><td>1.47</td><td>4.10</td><td>4.76</td></tr><tr><td>NGC 4694</td><td>0.85</td><td>2.41</td><td>1.38</td></tr><tr><td>NGC 4698</td><td>4.91</td><td>5.94</td><td></td></tr><tr><td>NGC 4713</td><td>1.17</td><td>2.72</td><td>1.98</td></tr><tr><td>NGC 4772</td><td>2.84</td><td>3.45</td><td></td></tr><tr><td>NGC 4808</td><td>1.65</td><td>3.59</td><td>3.32</td></tr></tbody></table>

Note. Columns are (1) galaxy identifier; (2) radius containing 50% of the global CO (2–1) flux; (3) radius containing 90% of the global CO (2–1) flux; (4) inclination-corrected molecular gas isodensity radius at $\Sigma_{mol}(r) = 5 M_{\odot} \text{ pc}^{-2}$, at the distance of Virgo 1" = 80 pc. This table is published in its entirety in machine-readable format.

(This table is available in its entirety in FITS format.)

studies of UV disk morphology in nearby galaxies (e.g., Muñoz-Mateos et al. 2009). Improved characterization and modeling of the CO radial profiles are required to understand the observed trends and differences between VERTICO and field galaxy samples.

## 5. The Molecular Gas Size–Mass Relation

The richness and quality of the VERTICO data enable many research avenues. As an initial demonstration of the survey’s scientific power, we now focus on establishing the relationship between the size and mass of molecular gas disks in the VERTICO sample and consider the effect of environment on this relation. The size–mass relation has been explored in detail for stellar and H I distributions in both theory and observation (e.g., Wang et al. 2016; Stevens et al. 2019; Sánchez Almeida 2020; Trujillo et al. 2020, and references therein). Stevens et al. (2019) and Sánchez Almeida (2020) respectively demonstrate for H I and stellar content that the tight correlation between galaxy radius—defined at a fixed surface density— and global mass is mathematically inevitable, given the limited range of physically plausible surface density profile shapes these components can have (e.g., saturated exponentials for H I, Sérsic stellar profiles). Indeed, Stevens et al. (2019) find that only a drastic change in H I disk morphology is able to cause significant deviation from the H I size–mass relation. Hereafter, the term “size–mass relation” refers to the molecular gas size–mass relation unless explicitly stated otherwise.

We use galaxies from the Heterodyne Receiver Array CO Line Extragalactic Survey (HERACLES; Leroy et al. 2009) as a convenient nearby field control sample ($2 < D/Mpc < 25$), which spans a comparable range in galaxy stellar mass and sSFR ($10^{8.5} < M_{\star}/M_{\odot} < 10^{11}$ and $10^{-11.5} < \text{sSFR/yr}^{-1} < 10^{-9.2}$, respectively). As with VERTICO, the stellar mass and SFR estimates are drawn from the z0MGS database (Leroy et al. 2019). There are 48 HERACLES galaxies with public CO (2–1) data cubes that have an angular resolution of $13''$ in $5 \text{ km s}^{-1}$ wide channels.<fnref n="35" /> Excluding 18 nondetections and five galaxies that overlap with the VERTICO sample (NGC 4579, NGC 4569, NGC 4536, NGC 4321, NGC 4254) leaves 25 galaxies for this comparison. Starting from the public cubes at their native $13''$ angular resolution and $10 \text{ km s}^{-1}$ channel width, we apply the same methodology used for the VERTICO data and described in Sections 4.3 and 4.4 to derive the molecular gas masses. The VERTICO masses and radii used in this section are presented in Tables 2 and 3, respectively.

Figure 10 shows the combined VERTICO and HERACLES molecular gas size–mass relation for two measurements of galaxy size as measured from the radial profiles. The first, shown in the right panel, is the radius enclosing 90% of the CO flux, $r_{90,mol}$. From here on, we use the term “flux-percentage radius” to refer generally to radii calculated at a given percentage of flux. Since, in this work, we simply scale the CO emission by $\alpha_{CO}$ to get molecular gas surface density, this 90%-light radius is also the 90%-mass radius. The second is the isodensity radius, $r_{5,mol}$ shown in the bottom panel, defined at fixed molecular gas surface density, $\Sigma_{mol}(r) = 5 M_{\odot} \text{ pc}^{-2}$, and calculated from the inclination-corrected surface density radial profiles. The uncertainties shown are the observation beam size listed in Table 2, converted into physical units. For highly inclined galaxies ($i \ge 80^{\circ}$), we assume an inclination of $80^{\circ}$ when calculating the inclination correction and exclude these from the fits described below. Unlike the flux-percentage radii, estimates of isodensity radii are not possible for every galaxy, so only the 58 galaxies (35 VERTICO, 23 HERACLES) where surface density profiles reach $\Sigma_{mol}(r) = 5 M_{\odot} \text{ pc}^{-2}$ are shown

<footnote n="35">³⁵ https://www.iram-institute.org/EN/content-page-242-7-158-240-242-0.html</footnote>
<figure><img src="image_12.png" /><figcaption>Figure 10. The molecular gas size-mass relation for 90% flux radii ($r_{90,mol}$; top panel) and inclination-corrected isodensity radii ($r_{5,mol}$; bottom panel). The former enclose 90% of the molecular gas flux (and thus mass for a fixed $\sigma_{CO}$), while the latter are defined as the radius where $\Sigma_{mol}(r) = 5 M_{\odot} pc^{-2}$. Galaxies from the VERTICO and HERACLES surveys are denoted by blue and green points, respectively. The rms scatter ($\sigma_{sm}$), intrinsic scatter accounting for errors ($\sigma_{sm,int}$), and Spearman rank coefficient ($r_{sp}$) for the combined VERTICO-HERACLES relation are given in the upper left corner of each panel. The best-fitting relation for all galaxies is shown by the black solid line, with $\pm 1\sigma_{sm}$ denoted by the black dashed lines (see text for fit parameters). Galaxies with inclination $\ge 80^{\circ}$ are denoted by open markers and not included in the fits to the data.</figcaption></figure>

in the bottom panel. The severity of the inclination correction for the highly inclined galaxies ($\cos(80^{\circ}) = 0.17$) means that an $r_{5,mol}$ measurement is only available for two such systems.

Throughout this analysis, VERTICO and HERACLES galaxies are denoted by blue circles and green stars, respectively. We use the LTSFIT PYTHON package to fit each relation. The method, described in detail by Cappellari et al. (2013, Section 3.2), accounts for measurement uncertainties to determine the best-fit parameters and scatter. We turn off outlier detection for this work. Using this approach, we derive the best fit to the 90% flux-percentage radius size-mass relation

(black solid lines) as

$$ \log\left(\frac{r_{90, mol}}{\text{kpc}}\right) = 0.54 + 0.20\left[\log\left(\frac{M_{mol}}{M_{\odot}}\right) - 8.83\right]. \quad (9) $$

Similarly, we fit the following relationship to the isodensity size-mass relation:

$$ \log\left(\frac{r_{5, mol}}{\text{kpc}}\right) = 0.55 + 0.45\left[\log\left(\frac{M_{mol}}{M_{\odot}}\right) - 8.94\right]. \quad (10) $$

Uncertainties on the fit parameters are provided in Table 4. The rms scatter, $\sigma_{sm}$, intrinsic scatter accounting for errors, $\sigma_{sm,int}$, and Spearman rank coefficient, $r_{sp}$, are printed in the upper left corner of each panel. The former is denoted by the black dashed lines.

We find that the flux-percentage size-mass relation has significantly larger rms and intrinsic scatter ($\sigma_{sm} = 0.19$ dex and $\sigma_{sm,int} = 0.16 \pm 0.02$ dex) than the isodensity size-mass relation ($\sigma_{sm} = 0.13$ dex and $\sigma_{sm,int} = 0.05 \pm 0.01$ dex). This result agrees both qualitatively and quantitatively with studies of stellar and H I disks that find that isodensity radii reduce the scatter to $\lesssim 0.1$ dex in the respective size-mass relations compared with flux-percentage radii (Saintonge & Spekkens 2011; Cortese et al. 2012; Wang et al. 2016; Stevens et al. 2019; Sánchez Almeida 2020; Trujillo et al. 2020). The larger Spearman rank coefficient ($r_{sp} = 0.87$) highlights the stronger statistical connection between global molecular gas mass and isodensity radii rather than flux-percentage radii ($r_{sp} = 0.59$).

Figure 11 shows the comparison between these two size estimates for VERTICO and HERACLES galaxies. At fixed $r_{5,mol}$, both VERTICO and HERACLES galaxies exhibit large range in $r_{90,mol}$, and while most galaxies tend to have consistently larger $r_{5,mol}$ than $r_{90,mol}$, this is not the case for approximately 25% of the combined sample. The scatter in $r_{90,mol}$ at fixed $r_{5,mol}$ reflects the different degrees of concentration in CO disks across both samples.

Figure 11 shows the comparison between these two size estimates for VERTICO and HERACLES galaxies. At fixed $r_{5,mol}$, both VERTICO and HERACLES galaxies exhibit large range in $r_{90,mol}$, and while most galaxies tend to have consistently larger $r_{5,mol}$ than $r_{90,mol}$, this is not the case for approximately 25% of the combined sample. The scatter in $r_{90,mol}$ at fixed $r_{5,mol}$ reflects the different degrees of concentration in CO disks across both samples.

We check the consistency of the size-mass relations between the VERTICO and HERACLES samples and, although we do not plot the fits, provide the best-fit parameters in Table 4. Where only the HERACLES sample is fit, we include the galaxies that overlap with VERTICO with their radii and masses measured from the public HERACLES data. This comparison demonstrates that the flux-percentage size-mass relation varies considerably between the VERTICO and HERACLES samples. On the other hand, the slope and scatter of the isodensity size-mass relation are remarkably consistent for both VERTICO and HERACLES. Given that many of the VERTICO gas disks are clearly perturbed by environment, this suggests that the observed isodensity size-mass relation does not have an environmental dependence, a result that is consistent with the findings of the H I size-mass relation studies (Wang et al. 2016; Stevens et al. 2019). Indeed, this invariance implies that external mechanisms act to suppress or remove galaxy gas content, rather than simply rearranging the distribution of gas within the disk. If environmental processes were to alter how gas is distributed throughout the galaxy without depleting the total amount of gas within the disk, one would expect such effects to drive galaxies away from the size-mass relation (above or below) as gas mass is conserved and isodensity radius is altered. It is reasonable to expect this scenario to result in a correlation of the form and scatter of
<table><caption>**Table 4**
Molecular Gas Size–Mass Relation Best-fit Parameters for the VERTICO, HERACLES, and Combined Samples</caption><thead><tr><th>Sample</th><th>y</th><th>a</th><th>b</th><th>Pivot</th><th>σ<sub>sm</sub></th><th>σ<sub>sm,int</sub></th><th>N</th></tr></thead><tbody><tr><td>Combined</td><td></td><td>0.54 ± 0.02</td><td>0.20 ± 0.03</td><td>8.83</td><td>0.19</td><td>0.16 ± 0.02</td><td>62</td></tr><tr><td>VERTICO</td><td>log (r<sub>90,mol</sub> / kpc)</td><td>0.54 ± 0.02</td><td>0.15 ± 0.04</td><td>8.66</td><td>0.16</td><td>0.12 ± 0.03</td><td>38</td></tr><tr><td>HERACLES</td><td></td><td>0.60 ± 0.04</td><td>0.27 ± 0.05</td><td>9.18</td><td>0.19</td><td>0.16 ± 0.03</td><td>29</td></tr><tr><td>Combined</td><td></td><td>0.54 ± 0.02</td><td>0.45 ± 0.03</td><td>8.94</td><td>0.13</td><td>0.05 ± 0.01</td><td>56</td></tr><tr><td>VERTICO</td><td>log (r<sub>5,mol</sub> / kpc)</td><td>0.52 ± 0.02</td><td>0.46 ± 0.03</td><td>8.83</td><td>0.12</td><td>0.04 ± 0.02</td><td>33</td></tr><tr><td>HERACLES</td><td></td><td>0.63 ± 0.02</td><td>0.45 ± 0.04</td><td>9.20</td><td>0.13</td><td>0.05 ± 0.02</td><td>28</td></tr></tbody></table>

Note. Columns are (1) the sample used to fit the molecular gas size–mass relation; (2) the definition of radius used; (3–5) the best-fit parameters for $y = a + b$ ($x$ – pivot), where $x$ is log $M_{\star}/M_{\odot}$; (6) the scatter about the fit, $\sigma_{\text{sm}} = \sigma(\text{fit} - \text{radius})$; (7) intrinsic scatter around the linear relation accounting for uncertainties ($\sigma_{\text{sm,int}}$ is called $\epsilon_y$ in Equation (6) of Cappellari et al. 2013); and (8) the number of galaxies used in each fit.

<figure><img src="image_13.png" /><figcaption>**Figure 11.** Isodensity radii ($r_{5,mol}$) vs. the 90% flux radii ($r_{90,mol}$) for VERTICO (blue) and HERACLES (green) galaxies. The isodensity radii are determined at $\Sigma(r_{5,mol}) = 5 M_{\odot} \text{ pc}^{-2}$ and have been corrected for inclination. Galaxies in the lower right portion tend to have CO distributions that are less concentrated than those in the upper left.</figcaption></figure>

size–mass relation with environment, which we do not see in the comparison between VERTICO and HERACLES. This paints a picture whereby, for VERTICO at least, any perturbation of the molecular gas distribution is also coupled with a change in total mass of the gas disk. Although we caution that a much more detailed exploration is required, the consistency and tightness in the size–mass relation defined using isodensity radii highlight the interesting possibility of using molecular gas mass as a predictor of gas disk size.

We now investigate the definitions of flux-percentage radius and isodensity radius that produce the least scatter and strongest correlation in the two size–mass relations. To this end, we repeat the analysis above for flux-percentage radii enclosing 50%, 60%, 70%, 80%, and 90% of the light and isodensity radii in the range $\Sigma_{\text{mol}}(r) = 1-20 M_{\odot} \text{ pc}^{-2}$, in increments of $1 M_{\odot} \text{ pc}^{-2}$. The left and right columns in Figure 12 show the resulting rms scatter ($\sigma_{\text{sm}} = \sigma(\text{fit} - \text{radius})$; top row), intrinsic scatter ($\sigma_{\text{sm,int}}$; second row), Spearman rank

coefficient (third row), and slope (bottom row) of the VERTICO-HERACLES size–mass relation versus the flux percentage at which radii are defined and isodensity $\Sigma_{\text{mol}}(r)$, respectively. The colors of the points in the top panels denote the number of galaxies in the given size–mass relation.

The scatter in the flux-percentage radius size–mass relation decreases gradually as the percentage of flux enclosed by the radius increases. By contrast, the isodensity size–mass relation scatter increases with $\Sigma_{\text{mol}}(r)$ above $\Sigma_{\text{mol}}(r) \sim 10 M_{\odot} \text{ pc}^{-2}$. We find that the rms scatter is minimized at $\Sigma_{\text{mol}}(r) \sim 5 M_{\odot} \text{ pc}^{-2}$, while the intrinsic scatter is lowest above $\Sigma_{\text{mol}}(r) \sim 5 M_{\odot} \text{ pc}^{-2}$. Using isodensity radii results in a stronger correlation, as quantified by the Spearman rank coefficient, than flux-percentage radii regardless of the exact definition. However, the Spearman rank coefficient of the flux-percentage radius size–mass relation increases with the percentage of enclosed flux. We also see a slight decrease in the correlation strength for isodensities of $\Sigma_{\text{mol}}(r) \gtrsim 10 M_{\odot} \text{ pc}^{-2}$. The flux-percentage radius size–mass relation steadily steepens as the enclosed percentage of flux increases, and while the isodensity relation is always steeper, there is some variation in its slope as a function of $\Sigma_{\text{mol}}(r)$. The radius definitions where scatter and Spearman rank coefficient are minimized and maximized, respectively, motivate the choices of $r_{90,mol}$ and $\Sigma_{\text{mol}}(r) \sim 5 M_{\odot} \text{ pc}^{-2}$ used in Figures 10 and 11.

Following the logic outlined in Stevens et al. (2019) and Sánchez Almeida (2020), it is expected that the isodensity size–mass relation should be consistently tighter than the flux-percentage radius relation because, broadly speaking, the surface density profiles decrease with radius. This means that for any two gas disks with the same total mass, their radial surface density profiles must intersect at a particular radius. Choosing a $\Sigma_{\text{mol}}(r)$ that is close to the surface density at this crossing radius necessarily reduces the scatter.

The natural next step is to consider why the scatter in the molecular gas isodensity relation falls to the levels found in the stellar and H I size–mass relations (~0.1 dex; see Wang et al. 2016; Trujillo et al. 2020) at approximately $\Sigma_{\text{mol}}(r) \sim 5 M_{\odot} \text{ pc}^{-2}$; increasing both above and below this value. While a full exploration of this issue is beyond the scope of this work, we note that the H I size–mass relation is both tight and consistent across samples because of the physical threshold in central H I surface densities of galaxies, above which gas becomes molecular (Stevens et al. 2019). No equivalent restriction on central surface density applies to molecular gas (or stellar densities). Not only is the ceiling for central molecular surface densities much higher
<figure><img src="image_14.png" /><figcaption>**Figure 12.** Scatter (top row), intrinsic scatter accounting for uncertainties (second row), Spearman rank coefficient (third row), and slope (bottom row) of the molecular gas size–mass relation as a function of flux-percentage radius percentage (left; i.e., radii are defined as enclosing a particular percentage of CO flux) and isodensity radius definition (right; i.e., radii are defined at mean molecular gas surface density, $\Sigma_{\text{mol}}(r)$). As with Figure 10, we exclude galaxies with inclinations $\ge 80^{\circ}$ from the fits.</figcaption></figure>

than H I, but Figure 9 shows that variable and nonmonotonic surface brightness (and therefore surface density) profiles are common. Naively, one would expect that the higher the threshold surface density used to define the isodensity radius, the more susceptible to variation in the surface density profiles the relationship is, thus increasing the scatter.

Molecular gas density profiles tend to be less well described by monotonically decreasing functions of radius than H I or stellar profiles, particularly at high resolution and sensitivity (e.g., Figure 9), and exhibit a wide range in concentration (e.g., Figure 11). Despite this, the small scatter in the measured gas disk size at fixed total mass suggests that galaxies tend to move along the size–mass relation, rather than deviating from it. Of course, this poses the altogether more interesting question, what is driving the observed diversity in molecular gas radial profile shapes? Addressing this will be the subject of future work aimed

at establishing a physically motivated definition for the size of molecular gas disks. However, it is interesting that the optimal isodensity value of $\Sigma_{\text{mol}}(r) = 5 M_{\odot} \text{pc}^{-2}$ is consistent with the total gas surface densities of $\sim 10 M_{\odot} \text{pc}^{-2}$, where gas disks are theoretically predicted to transition from being H I to H$_2$ dominated with an atomic-to-molecular ratio of $\sim 0.5$ at solar metallicity (Krumholz et al. 2009).

This work assumes a constant CO conversion factor across the sample. While this is likely a reasonable approximation given the mild gradients in $\alpha_{\text{CO}}$ as a function of radius observed in most galaxy disks (Sandstrom et al. 2013), it is important to consider how the prevalence of lower $\alpha_{\text{CO}}$ values in the inner parts of galaxies, as well as other variations in the conversion factor (e.g., metallicity driven), could impact the form of our observed isodensity size–mass relation (Wolfire et al. 2010; Sandstrom et al. 2013; Heyer &
Dame 2015; Accurso et al. 2017). Since $\alpha_{CO}$ is accounted for in both axes, a global variation in the conversion factor— without a change in shape between the CO and molecular gas surface density profiles—would simply shift galaxies along the relation. However, radially varying $\alpha_{CO}$, as seen in some galaxies by Sandstrom et al. (2013), is more difficult to properly understand without further work. That said, an interesting quality of the isodensity size-mass relation is its insensitivity to the significant variations in the gas surface density profiles seen in the VERTICO sample. In other words, despite the large differences in CO distribution throughout the VERTICO sample, almost all galaxies fall on the combined sample size-mass relation. This suggests that changes in the conversion factor as a function of radius would have to dramatically alter the gas surface density profiles for the effect to be noticeable in the size-mass relation.

Lastly, it is notable that the optimal $\Sigma_{mol}(r)$ should be in such good agreement with the predicted transition density, given the distance, $\alpha_{CO}$, and flux calibration uncertainties on our observations, in addition to less well-quantified physical effects such as metallicity variations and environment.

## 6. Summary

The VERTICO survey has mapped CO (2–1) in 51 Virgo Cluster galaxies on subkiloparsec scales. The primary motivation of this project is to understand the physical mechanisms that drive galaxy evolution in dense environments and provide a diverse, homogeneous legacy data set for studying galaxy evolution in our closest galaxy cluster.

The 36 targets observed in ALMA Cycle 7 are combined with archival CO (2–1) data for 15 Virgo Cluster spirals to make the final VERTICO sample of 51 galaxies. Our final data cubes have a resolving beam of $\sim 7''-10''$, corresponding to $\sim 0.6-0.8$ kpc at the distance of Virgo, and $10 \text{ km s}^{-1}$ velocity resolution. We provide global CO line luminosities and convert these into total molecular gas masses. We calculate $R_{21} = 0.8$ for the 35 galaxies with existing CO (1–0) data, in general agreement with other surveys of nearby galaxies.

We present the integrated intensity, velocity field, observed line width, and peak temperature maps for each galaxy. VERTICO’s sensitivity and depth ensure that these maps reveal the imprint of stellar structure (e.g., spiral arms, bars, bulges) and environmental processes (e.g., warps, tails, depletion) in the gas morphology and kinematics in great detail. We measure integrated CO intensity radial profiles, which show a large range in gas disk morphologies across the VERTICO sample. A significant number of the profiles do not decrease steadily as a function of radius, showing bumps in the CO distribution at larger radii or signs of truncation at the outer edge of the disk.

We investigate the scaling relation between the size and mass of the molecular gas distribution in VERTICO galaxies. This is compared to the same relation for the HERACLES survey of field galaxies. We find that the isodensity size-mass relation has less scatter and a stronger correlation than the flux-percentage radius size-mass relation. In agreement with studies of H I disks, we suggest that the observed consistency of the isodensity size-mass relation between field and cluster galaxies suggests that environment is not a driving factor in this relationship. We interpret this as evidence that the environmental processes that perturb the distribution of molecular gas in galaxies also affect the global gas mass. In this way, galaxies

undergoing environmental transformation move along the size-mass relation rather than deviating from it. Finally, we investigate the effect that radius definition has on this correlation and determine the optimal molecular gas isodensity ($\Sigma_{mol}(r) \sim 5 \text{ M}_\odot \text{ pc}^{-2}$) and flux-percentage ($r_{90,\text{mol}}$) radius definitions that produce the least scatter and strongest correlation.

Our intent with this work is to provide an overview of the VERTICO survey and highlight its potential as a resource for revealing the role environment plays in galaxy evolution. To this end, VERTICO will be used to study the fate of molecular gas in cluster galaxies and the physics of environment-driven processes that perturb the star formation cycle. It is our hope that VERTICO advances our understanding and provides a valuable legacy resource that serves the community for years to come.

The majority of this work was conducted on the traditional territory of the Lekwungen peoples. We acknowledge and respect the Songhees, Esquimalt, and WSÁNEĆ Nations, whose historical relationships with the land continue to this day.

We thank the anonymous referee and the editors for a considered and constructive review that improved the manuscript.

This work was carried out as part of the VERTICO Collaboration.

The authors wish to thank the members of the PHANGS-ALMA Collaboration for their support and advice in reducing the VERTICO data. In particular, we thank Adam Leroy for graciously providing us with the PHANGS-ALMA ACA data and imaging pipeline in advance of publication.

T.B. acknowledges support from the National Research Council of Canada via the Plaskett Fellowship of the Dominion Astrophysical Observatory. C.D.W. acknowledges support from the Natural Sciences and Engineering Research Council of Canada and the Canada Research Chairs program. T.A.D. acknowledges support from STFC grant ST/S00033X/1. L.P., J.W., and K.S. acknowledges support from the Natural Science and Engineering Council of Canada. L.C. acknowledges support from the Australian Research Council’s Discovery Project and Future Fellowship funding schemes (DP210100337, FT180100066). A.R.H.S. acknowledges receipt of the Jim Buckee Fellowship at ICRAR-UWA. I.D.R. acknowledges support from the ERC Starting Grant Cluster Web 804208. K. P.O. is funded by NASA under award No. 80NSSC19K1651. V. V. acknowledges support from the scholarship CONICYT PFCHA/ CONICYT-FULBRIGHT BIO 2016-56160020 and funding from NRAO Student Observing Support (SOS)—SOSPA7-014. Support for this work was also provided by the National Research Foundation of Korea (NRF) grant No. 2018R1D1A1B07048314. B.L. acknowledges support from the National Science Foundation of China (12073002, 11721303). Y.M.B. gratefully acknowledges funding from the Netherlands Organization for Scientific Research (NWO) through Veni grant No. 639.041.751. C.W. acknowledges the support of the National Science Foundation award 1815251 (United States) held by Dr. Susan Kassin. 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 No. CE170100013. M.H.H. acknowledges support from the William and Caroline Herschel Postdoctoral Fellowship
fund. C.D.P.L. has received funding from ASTRO 3D through project No. CE170100013. P.J.E. works on Whadjuk country and pays respect to the elders past, present, and emerging of the Noongar people. C.R.C. acknowledges support from STFC grant ST/R000840/1.

This paper makes use of the following ALMA data:

ADS/JAO.ALMA #2019.1.00763.L,
ADS/JAO.ALMA #2017.1.00886.L,
ADS/JAO.ALMA #2016.1.00912.S,
ADS/JAO.ALMA #2015.1.00956.S.

ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

In addition to the ALMA Science Archive, research made use of data and/or software provided by the following archives:

1. NASA/IPAC Infrared Science Archive, which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology

2. NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

3. The High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC.

4. The HRS data were accessed through the Herschel Database in Marseille (HeDaM— http://hedam.lam.fr) operated by CeSAM and hosted by the Laboratoire d'Astrophysique de Marseille.

We acknowledge the use of the ARCADE (ALMA Reduction in the CANFAR Data Environment) science platform. ARCADE is an ALMA Cycle 7 development study with support from the National Radio Astronomy Observatory, the North American ALMA Science Center, and the National Research Center of Canada. Our work used the facilities of the Canadian Astronomy Data Center, operated by the National Research Council of Canada with the support of the Canadian Space Agency, and the Canadian Advanced Network for Astronomy Research, a consortium that serves data-intensive storage, access, and processing needs of university groups and centers engaged in astronomy research (Gaudet et al. 2010).

This research has made use of data from the Herschel Reference Survey (HRS) project. HRS is a Herschel Key Programme utilizing Guaranteed Time from the SPIRE instrument team, ESAC scientists, and a mission scientist.

Here we acknowledge the key software used in this work:

1. Astropy,<fnref n="36" /> a community-developed core PYTHON package for Astronomy and affiliated packages (SPECTRAL-CUBE, REPROJECT, PHOTUTILS; Astropy Collaboration et al. 2013; Price-Whelan et al. 2018; Bradley et al. 2020).

2. The CASA (Common Astronomy Software Applications) package,<fnref n="37" /> a suite of applications for the reduction and analysis of radio astronomical data with a PYTHON interface (McMullin et al. 2007).

3. PHANGS-ALMA Imaging Pipeline, a library of programs that use CASA, Astropy, and affiliated packages (ANALYSISUTILS, SPECTRAL-CUBE, REPROJECT) to process data from the calibrated visibilities to science-ready data cubes (Leroy et al. 2021a).

4. MATPLOTLIB,<fnref n="38" /> a plotting library for the PYTHON programming language and its numerical mathematics extension NUMPY (Hunter 2007; Virtanen et al. 2020).

5. PANDAS,<fnref n="39" /> an open source, BSD-licensed library providing high-performance, easy-to-use data structures and data analysis tools for the PYTHON programming language (McKinney 2010).

6. CARTA: The Cube Analysis and Rendering Tool for Astronomy,<fnref n="40" /> an image visualization and analysis tool for radio astronomy data (Comrie et al. 2020).

7. The Ancillary Data Button,<fnref n="41" /> a selection of PYTHON scripts for acquiring and standardizing imaging data from a wide range of telescopes (Clark et al. 2018).

8. RSMF<fnref n="42" /> (right-size my figures), a PYTHON library that provides a means to automatically adjust figure sizes and font sizes in MATPLOTLIB to fit those commonly used in scientific journals.

9. The Chandra Interactive Analysis of Observations<fnref n="43" /> application package developed by the Chandra X-ray Center for analyzing X-ray data (Fruscione et al. 2006).

## Appendix
### Emission-line Spectra

Examples of the global CO (2–1) spectra derived from the masked data cubes described in Section 4.3 are shown in Figure 13. The complete figure set of ¹²CO (2–1) spectra for all 51 VERTICO galaxies is available in the online journal.

<footnote n="36">³⁶ http://www.astropy.org</footnote>

<footnote n="37">³⁷ https://casa.nrao.edu/</footnote>

<footnote n="38">³⁸ https:// matplotlib.org/</footnote>

<footnote n="39">³⁹ https://pandas.pydata.org/</footnote>

<footnote n="40">⁴⁰ https://cartavis.org/</footnote>

<footnote n="41">⁴¹ https://github.com/Stargrazer82301/AncillaryDataButton</footnote>

<footnote n="42">⁴² https://github.com/johannesjmeyer/rsmf</footnote>

<footnote n="43">⁴³ https://cxc.cfa.harvard.edu/ciao/</footnote>
<figure><img src="image_15.png" /><figcaption>**Figure 13.** $^{12}$CO (2–1) spectra at 10.6 km s$^{-1}$ resolution. The velocity limits used to estimate the velocity width and flux density for each galaxy are shown by the dashed vertical lines. The galaxy name, integrated CO line luminosity (Equation (5)), integrated flux density, molecular gas mass (Equation (7)), and S/N of the spectrum are shown in the upper left corner of each panel. The complete figure set containing 51 $^{12}$CO (2–1) spectra for all VERTICO galaxies is available online.
(The complete figure set (51 images) is available.)</figcaption></figure>

ORCID iDs

Toby Brown https://orcid.org/0000-0003-1845-0934

Christine D. Wilson https://orcid.org/0000-0001-5817-0991

Timothy A. Davis https://orcid.org/0000-0003-4932-9379

Alessandro Boselli https://orcid.org/0000-0002-9795-6433

Aeree Chung https://orcid.org/0000-0003-1440-8552

Sara L. Ellison https://orcid.org/0000-0002-1768-1899

Luca Cortese https://orcid.org/0000-0002-7422-9823

Alberto D. Bolatto https://orcid.org/0000-0002-5480-5686

Barbara Catinella https://orcid.org/0000-0002-7625-562X

Ryan Chown https://orcid.org/0000-0001-8241-7704

Benedikt Diemer https://orcid.org/0000-0001-9568-7287

Pascal J. Elahi https://orcid.org/0000-0002-6154-7224

María J. Jiménez-Donaire https://orcid.org/0000-0002-9165-8080

Bumhyun Lee https://orcid.org/0000-0002-3810-1806

Angus Mok https://orcid.org/0000-0001-7413-7534
Karen Pardos Olsen https://orcid.org/0000-0003-1250-5287

Ian D. Roberts https://orcid.org/0000-0002-0692-0911

Rory Smith https://orcid.org/0000-0001-5303-6830

Kristine Spekkens https://orcid.org/0000-0002-0956-7949

Mallory Thorp https://orcid.org/0000-0003-0080-8547

Stephanie Tonnesen https://orcid.org/0000-0002-8710-9206

Vicente Villanueva https://orcid.org/0000-0002-5877-379X

Hyein Yoon https://orcid.org/0000-0003-4048-2203

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