2.1. Starvation—halting gas accretion

At least for galaxies with stellar masses greater than $\sim10^{9}$ M $_{\odot}$ , the typical timescale for cold gas depletion (i.e., the ratio of gas mass to star formation rate, $\tau_{\rm dep}\equiv M_{\rm gas}/{\rm SFR}$ ) is a few billion years for both molecular and atomic phases, assuming a constant SFR (Kennicutt Reference Kennicutt1983b; Boselli et al. Reference Boselli, Gavazzi, Donas and Scodeggio2001; Saintonge et al. Reference Saintonge2017). This is generally used to argue that, in order to keep forming stars at a constant rate, the cold reservoir of galaxies in star-forming discs needs to be continuously replenished. Support to this picture also comes from the fact that, at least for molecular hydrogen, depletion times appear to have been even shorter at higher redshift (Schinnerer et al. Reference Schinnerer2016; Scoville et al. Reference Scoville2016).

While how gas gets into galaxies is still unclear, cosmological simulations suggest that, in the last few billion years, cold accretion via filaments and/or smooth accretion from the intergalactic medium (IGM) have gradually become inefficient (Dekel et al. Reference Dekel2009; Anglés-Alcázar et al. Reference Anglés-Alcázar, Faucher-Giguère, Kereš, Hopkins, Quataert and Murray2017; Grand et al. Reference Grand2019), as cold streams no longer reach the galactic disc. Instead, either accretion of gas-rich companions (i.e., minor or major mergers) or wind recycling (e.g., direct cooling of the hot circumgalactic medium (CGM) via galactic fountain; Fraternali & Binney Reference Fraternali and Binney2008; Marinacci et al. Reference Marinacci, Binney, Fraternali, Nipoti, Ciotti and Londrillo2010) appear to be the most likely accretion channels to keep local star-forming galaxies active. Regardless of which physical mechanism(s) is(are) responsible for quenching star formation in the first place, further accretion of cold gas needs to be prevented in order to avoid that quenched galaxies restart their star formation. Indeed, while rare, rejuvenation cases are both observed in the local Universe (Cortese & Hughes Reference Cortese and Hughes2009; Thilker et al. Reference Thilker2010) and predicted by numerical simulations (Birnboim, Dekel, & Neistein Reference Birnboim, Dekel and Neistein2007; Nelson et al. Reference Nelson2018). Thus, in general, a galaxy that no longer has access to a source of gas will eventually run out of fuel and stop forming stars (Figure 1, top row).

In the literature, the lack of replenishment of cold gas in the ISM is generally referred to as starvation. This general idea was originally proposed by Larson, Tinsley, & Caldwell (Reference Larson, Tinsley and Caldwell1980) to explain the existence of passive disc galaxies outside clusters, where stripping of the ISM could not be effective. In this case, accretion was thought to take place via either minor mergers or infall of clouds of cold gas (i.e., primarily atomic hydrogen), and galaxies with no access to such a supply would simply run out of gas. With the advent of semi-analytic cosmological models, this picture has significantly evolved into the removal of the hot gas component (only) in the halo of the galaxy (i.e., the primary reservoir of gas directly available to the galaxy to support star formation; Cole et al. Reference Cole, Lacey, Baugh and Frenk2000). This also corresponds to the introduction of the term strangulation (Balogh & Morris Reference Balogh and Morris2000), and now both starvation and strangulation are interchangeably used to refer to the cessation of accretion from both IGM and CGM.

Regardless of how exactly gas infall is halted, it is obvious that this is the necessary condition to turn a star-forming galaxy into a quiescent system and keep it passive for the rest of its life. Thus, we assume that gas accretion is prevented and focus on the ISM. Here, the challenge is to determine whether gas already in the disc is simply consumed by star formation, or other physical processes directly affect its ability to feed star formation.

2.2. Stripping—removing cold gas from the disc

A more dramatic way to deprive a galaxy of its fuel for star formation is to directly remove the cold ISM already in its disc (Figure 1, second row). For satellite galaxies, the interaction with the environment of their host halo provides several channels to remove star-forming gas. Broadly, these can be divided into two general classes.

1. (1) Hydrodynamical mechanisms. These involve the direct interaction between the ISM and the intra-group, or intracluster medium (ICM), and include ram pressure stripping (i.e., the removal of the ISM due to the pressure exerted by the ICM while a satellite is moving through its host halo; Gunn & Gott Reference Gunn and Gott1972), viscous stripping (i.e., the removal of the outer layer of the ISM due to the viscosity momentum transfer with the ICM; Nulsen Reference Nulsen1982) and thermal evaporation (increase of temperature, and subsequent evaporation of the cold ISM at the interface with the hot ICM; Cowie & Songaila Reference Cowie and Songaila1977). While the vast majority of past work has focused on ram pressure, we have observational evidence (as well as theoretical predictions) that both viscous stripping and thermal evaporation can play a role (e.g., Bureau & Carignan Reference Bureau and Carignan2002; Roediger & Hensler Reference Roediger and Hensler2005; Boselli & Gavazzi Reference Boselli and Gavazzi2006; Randall et al. Reference Randall, Nulsen, Forman, Jones, Machacek, Murray and Maughan2008). Unfortunately, it is extremely challenging to separate these three physical processes observationally, and it is expected that all three—if present—affect simultaneously the cold ISM of galaxies. It is also important to remember that, technically, starvation (i.e., the cessation of gas infall) is a hydrodynamical mechanism. It is, in practice, a mild ram pressure that is able to affect the gas in the halo but not that in the disc. This is primarily why starvation and ram pressure have been considered in the literature as two separate mechanisms, despite the physical process being most likely the same.

2. (2) Gravitational mechanisms. The ISM can also be removed from the disc by the gravitational pull affecting satellites while orbiting in groups and clusters (Boselli & Gavazzi Reference Boselli and Gavazzi2006). The key element here is the variation (temporal and/or spatial) of the external gravitational potentials that baryons in the disc are subjected to (Binney & Tremaine Reference Binney and Tremaine1987). This could be caused by fly-bys of companion satellites and/or interaction with the central galaxy (generally divided between low- and high-speed interactions depending on how the relative speed of the two galaxies compares to their rotational velocity), or by the interaction with the whole gravitational potential of groups and clusters (often referred to as the galaxy–cluster interaction; e.g., Byrd & Valtonen Reference Byrd and Valtonen1990). The combined effect of multiple high-speed galaxy–galaxy interactions over long timescales (i.e., longer than a typical crossing time, a mechanism generally referred to as harassment) has also been invoked to explain the properties of satellite galaxies in clusters (Moore et al. Reference Moore, Katz, Lake, Dressler and Oemler1996; Smith, Davies, & Nelson Reference Smith, Davies and Nelson2010a).

As discussed later, discriminating between hydrodynamical and gravitational processes on the ISM is not always straightforward, as both can perturb the cold ISM in the disc of galaxies in a similar way. Arguments based on geometry of disturbed features, on the comparison between gas and stellar distribution/kinematics, timescale of the interaction and distribution of star-forming regions can definitely help in the process but, as we will see, there is circumstantial evidence that both processes may sometime act simultaneously in galaxies and that direct stripping of the ISM from the disc is a fundamental step in the pathways of satellite galaxies towards quiescence.

2.3. Cold gas removal/heating by internal feedback mechanisms

Another way to remove cold ISM from galaxies is via internal feedback related to the star formation process (e.g., supernova feedback, stellar winds) or to the presence of an active galactic nucleus (AGN) at the centre of galaxies. In both cases, cold gas could be ejected from the disc and/or heated up, becoming unavailable for star formation (Figure 1, third row).

From a theoretical point of view, internal feedback is arguably the most popular mechanism invoked to explain the existence of passive central galaxies and to reproduce key statistical properties such as the SFR–stellar mass relation and the stellar mass function of galaxies (e.g., Croton et al. Reference Croton2006; De Lucia et al. Reference De Lucia, Springel, White, Croton and Kauffmann2006; Hopkins et al. Reference Hopkins, Hernquist, Cox and Kereš2008). However, the fact that satellite galaxies appear to have lower cold gas content (e.g., Brown et al. Reference Brown2017), less star formation, and a higher passive fraction at fixed stellar mass with respect to centrals (e.g., van den Bosch et al. Reference van den Bosch, Aquino, Yang, Mo, Pasquali, McIntosh, Weinmann and Kang2008; Davies et al. Reference Davies2019) has led to the conclusion that feedback may not always be the primary mechanism driving satellites into quiescence. Interestingly, it is certainly possible that feedback could still play a role by increasing the efficiency of other gas removal processes (see e.g., Sections 4.1 and 8), as also suggested by cosmological models (Zoldan et al. Reference Zoldan, De Lucia, Xie, Fontanot and Hirschmann2017; De Lucia, Hirschmann, & Fontanot Reference De Lucia, Hirschmann and Fontanot2019; Stevens Reference Stevens2019a). While neglected in the past due to a lack of observations, this is a scenario that may turn out to be more common than originally thought, thanks to the improvement of ground- and space-based facilities making it easier to identify gas outflows (e.g., via narrow-band imaging or integral field spectroscopy).

2.4. Stability of the cold gas against fragmentation and star formation

The processes discussed so far are related to the very first step of the star-formation cycle in galaxies (i.e., the availability of cold gas), based on the notion that, in order to stop forming stars, a galaxy must somehow run out of its atomic and molecular gas reservoirs. A different pathway to quenching is to affect the next steps of the cycle, that is, either the Hi-to- $\mathrm{H}_{2}$ conversion or the collapse of $\mathrm{H}_{2}$ into stars. Although the formation of molecular gas might not be strictly required to form stars (it could just be a by-product of the gravitational collapse of atomic gas on its way to star formation; Glover & Clark Reference Glover and Clark2012), this phase traces remarkably well the physical conditions under which new stars are formed (Krumholz, Leroy, & McKee Reference Krumholz, Leroy and McKee2011). In this sense, star formation could be halted by preventing the atomic gas reservoir from condensing into molecules and/or collapsing to form stars (Figure 1, bottom row). More specifically, atomic hydrogen could be kept stable on a rotating disc below the typical column density threshold for $\mathrm{H}_{2}$ formation, thus halting star formation (e.g., Blitz & Rosolowsky Reference Blitz and Rosolowsky2006; Bigiel et al. Reference Bigiel, Leroy, Walter, Brinks, de Blok, Madore and Thornley2008; Leroy et al. Reference Leroy, Walter, Brinks, Bigiel, de Blok, Madore and Thornley2008). Additional factors regulating the rate of condensation of atoms into molecules could be the metallicity of the ISM and the intensity of the interstellar radiation field (e.g., Krumholz, McKee, & Tumlinson Reference Krumholz, McKee and Tumlinson2009; Gnedin & Kravtsov Reference Gnedin and Kravtsov2011). Typical examples of cases in which atomic hydrogen does not appear to be efficiently converted into molecular phase include the outer parts of star-forming discs (Bigiel et al. Reference Bigiel, Leroy, Walter, Blitz, Brinks, de Blok and Madore2010a), low surface brightness galaxies (Wyder et al. Reference Wyder2009), early-type galaxies with significant Hi reservoirs (e.g., Knapp, Turner, & Cunniffe Reference Knapp, Turner and Cunniffe1985; Serra et al. Reference Serra2012), and the even more extreme case of the so-called HI-excess systems (galaxies with unexpectedly large Hi reservoirs based on their SFR and morphological structure; Geréb et al. Reference Geréb, Catinella, Cortese, Bekki, Moran and Schiminovich2016, Reference Geréb, Janowiecki, Catinella, Cortese and Kilborn2018).

Alternatively, even if molecular clouds can be formed, these could remain stable against collapse due to adverse local conditions (e.g., high gas turbulence and/or high stellar velocity dispersion), significantly reducing the efficiency of star formation. Examples of this scenario are the inner parts of the Milky Way (Longmore et al. Reference Longmore2013) and of nearby, bulge-dominated systems (Martig et al. Reference Martig, Bournaud, Teyssier and Dekel2009), where turbulence is driven by gravitationally induced pressure from the bulge. In other words, the stability of the gas disc is enhanced by the presence of a dispersion-supported bulge component. However, as we will see, observations seem to exclude this path as an important one for satellite galaxies in groups and clusters. This is also because the reduction in star formation efficiency is generally not large enough to fully quench galaxies (e.g., Davis et al. Reference Davis2014).

Of course, as mentioned at the beginning of this section, in order to be efficient in fully quenching star formation, gas stripping, gas ejection, and stability must be accompanied by a halt in gas replenishment onto the star-forming disc.

In what follows, we discuss the observational evidence in support or against these quenching scenarios and show that, after nearly half a century of observational work, we are in a position to build a coherent picture of the physical processes affecting the gas reservoir and star formation quenching in satellite galaxies at $z\sim$ 0. As a necessary step to quantify environmental effects on cold gas content, we begin by reviewing the various definitions of gas deficiency and their implications.

3.1. Definitions based on optical diameter

Early studies of cluster galaxies started quantifying gas deficiency by comparing total Hi mass-to-luminosity ratios (distance-independent quantities) of cluster and field systems at fixed luminosity and/or morphology (Robinson & Koehler Reference Robinson and Koehler1965; Davies & Lewis Reference Davies and Lewis1973; Huchtmeier et al. Reference Huchtmeier, Tammann and Wendker1976). However, it soon became clear that a more robust approach was to control galaxies by their morphological type and optical diameter (Chamaraux, Balkowski, & Gerard Reference Chamaraux, Balkowski and Gerard1980). Indeed, the optical size versus Hi mass relation turned out to be the tightest scaling relation (among those investigated at that time) linking Hi mass to optical galaxy properties. While Chamaraux et al. (Reference Chamaraux, Balkowski and Gerard1980) were among the first to introduce the concept of Hi deficiency, the first statistical definition of the concept of Hi normalcy and Hi deficiency (and arguably the foundation of this entire field) was presented by Haynes & Giovanelli (Reference Haynes and Giovanelli1984, hereafter HG84), in a study of a sample of 324 isolated galaxies extracted from the Karachentseva (Reference Karachentseva1973) Catalog of Isolated galaxies and the Uppsala General Catalog (Nilson Reference Nilson1973) and observed with the Arecibo 305-m radio telescope. They showed that, at fixed morphological type, the optical property most strongly correlated with global Hi mass is the galaxy isophotal optical diameter. This relation for isolated galaxies defines ‘Hi normalcy’ and can be used to predict the total Hi mass within $\sim$ 0.2–0.3 dex. Thus, Hi deficiency is defined as:

(1) \begin{equation}DEF_{\rm HI}= \log\!(M_{\rm HI}^{\rm pred}[T,D_{\rm opt}]) - \log\!(M_{\rm HI}^{\rm obs}), \\\end{equation}

where $M_{\rm HI}^{\rm pred}[T,D_{\rm opt}]$ is the Hi mass expected for an isolated galaxy with the same morphological type (T) and optical diameter ( $D_{\rm opt}$ ) as the observed galaxy, that is,

(2) \begin{equation}\log(h^{2}M_{\rm HI}^{\rm pred}[T,D_{\rm opt}])= a_{T} + b_{T}\log(hD_{\rm opt})^2,\end{equation}

where $h=\textrm{H}_{0}$ /100, H $_0$ is the Hubble constant, and $a_{T}$ and $b_{T}$ are the best-fitting coefficients tabulated as a function of morphological type.

In the past few decades, several independent works have presented revised versions of this calibration, primarily motivated by improvements in data quality, number statistics, morphological spread, and/or definition of isolated galaxy (e.g., Solanes, Giovanelli, & Haynes Reference Solanes, Giovanelli and Haynes1996; Boselli & Gavazzi Reference Boselli and Gavazzi2009; Toribio et al. Reference Toribio, Solanes, Giovanelli, Haynes and Martin2011; Dénes, Kilborn, & Koribalski Reference Dénes, Kilborn and Koribalski2014; Jones et al. Reference Jones2018). Remarkably, the most recent re-calibration of the optical diameter-based Hi deficiency presented by Jones et al. (Reference Jones2018)—based on the Analysis of the interstellar Medium in Isolated GAlaxies (AMIGA; Verdes-Montenegro et al. Reference Verdes-Montenegro, Sulentic, Lisenfeld, Leon, Espada, Garcia, Sabater and Verley2005) project—has shown that the original coefficients presented by HG84 are still very much consistent with those based on modern datasets. An additional variant of the HG84 definition is to ignore the morphological dependence and assume that all galaxies have the same average Hi surface density (Chung et al. Reference Chung, van Gorkom, Kenney, Crowl and Vollmer2009). While qualitatively consistent with the original calibration, this implementation is less robust as the typical Hi surface density of galaxies is not constant (Bigiel & Blitz Reference Bigiel and Blitz2012), but admittedly it has the advantage of not relying on morphological classification and all potential biases associated with this.

The fact that the isophotal diameter turned out to be more strongly correlated with total Hi mass than other optical properties (such as luminosity) should not come as a surprise. Firstly, for a self-gravitating disc, it is easy to show that the gas mass of the disc is more tightly connected to the specific angular momentum than the luminosity of a system (or even its stellar mass, see also Sections 3.3 and 3.4). Indeed, at fixed total mass, the scatter in cold gas mass is primarily driven by the spread of spin parameterFootnote a (Mo, Mao, & White Reference Mo, Mao and White1998; Boissier & Prantzos Reference Boissier and Prantzos2000; Huang et al. Reference Huang, Haynes, Giovanelli and Brinchmann2012; Maddox et al. Reference Maddox, Hess, Obreschkow, Jarvis and Blyth2015; Obreschkow et al. Reference Obreschkow, Glazebrook, Kilborn and Lutz2016) and, observationally, sizes are more directly linked to spin than optical luminosities. Secondly, for disc galaxies, scaling relations involving isophotal radii are always tighter than those based on scale lengths and/or effective radii (e.g., Saintonge & Spekkens Reference Saintonge and Spekkens2011; Cortese et al. Reference Cortese2012b; Sánchez Almeida Reference Sánchez Almeida2020; see also Section 4.3), as they better trace the outer parts, and thus the full extent, of the disc component of galaxies.Footnote b

A key point to note is that, by defining Hi deficiency at fixed morphology and optical diameter, we implicitly make strong assumptions on the type of physical processes that this indicator is sensitive to. Namely, we indirectly imply that the mechanism(s) removing the Hi: (a) does not change the morphology of the galaxy and (b) does not affect the extent of the stellar disc. Or, at the very least, the implication is that any morphological and/or size transformations take place on timescales significantly longer than those needed to make the galaxy Hi-deficient. Thus, while ideal to trace most hydrodynamical mechanisms (including outflows and starvation), this definition may not always be suited to identify stripping events where gas and stars are affected simultaneously (e.g., tidal stripping) or to follow the long-term evolution if the stellar distribution or morphology do change with time.

3.2. Definitions based on colour and structural properties

Despite its popularity over the past few decades, the HG84 definition of Hi deficiency has turned out not to be the ideal approach for an application to large datasets and comparison with cosmological simulations. With the advent of the Sloan Digital Sky Survey (SDSS, York et al. Reference York2000) in the early 2000s, isophotal radii have gradually become ‘less popular’ than effective radii, and reliable estimates have been rarely available for large datasets overlapping with Hi observations. At the same time, accurate determination of morphological types (e.g., the ability to discriminate between Sa, Sb, and Sc) for large statistical samples became more challenging already at distances beyond those of the Coma cluster ( $\sim$ 100 Mpc, $z\sim$ 0.023), potentially boosting the uncertainty in the estimate of deficiency. Moreover, morphological types based on visual classification are also not a standard and/or consistent output of numerical simulations, which parameterise galaxy morphology using more quantitative indicators. These issues prompted the community to develop new Hi deficiency estimators (and related definitions of Hi normalcy) which, in many instances, have also been used as basis to predict Hi masses for large samples of galaxies without 21-cm observations available.

One of such modern versions of Hi deficiency is the so-called Hi gas fraction plane introduced by Catinella et al. (Reference Catinella2010). By taking advantage of data from the GALEX Arecibo SDSS Survey (GASS), they show that the best predictor of Hi-to-stellar mass ratio is a linear combination of the observed (i.e., not corrected for internal dust attenuation) near-ultraviolet minus r-band colour (NUV-r) and stellar mass surface density ( $\mu_{*} \equiv M_{*}$ /(2 $\pi$ R $_{50,z}^{2})$ , where $M_{*}$ is the total stellar mass and $R_{50,z}$ is the radius containing 50% of the galaxy light in the z-band), with a typical scatter of $\sim$ 0.3 dex (see also Catinella et al. Reference Catinella2013):

(3) \begin{equation}\log(M_{\rm HI}/M_{*})= a_1(NUV-r) + a_2\mu_{*} +a_3,\end{equation}

where $a_i$ are the coefficients of the best fit. The potential advantage of this definition is that it does not require a morphological classification and is based on quantities that are now readily available for hundreds of thousands of nearby galaxies.

Interestingly, so far this technique has primarily been used to identify Hi-excess systems (see Section 2.4) and only Cortese et al. (Reference Cortese, Catinella, Boissier, Boselli and Heinis2011) have tested it as a potential indicator for Hi deficiency. They show that, while the deviations from the gas fraction plane and the HG84 Hi deficiency are correlated, the scatter can be significant ( $\sim$ 0.4 dex), with important systematic offsets. While this is partially due to the sample used to calibrate the scaling relations (e.g., isolated galaxies vs field objects vs centrals), there is a fundamental physical reason why these two techniques do not always agree. The position of a galaxy in the gas fraction plane is primarily driven by its NUV-r colour (i.e., a proxy for its unobscured SFR, traced by the NUV emission, per unit stellar mass, traced by emission in r-band), with a secondary dependence on optical size (via $\mu_*$ ). Indeed, it has been shown by several works that Hi is much more directly correlated with the star formation traced by the ultraviolet than with the bulk of (mostly obscured) star formation in galaxies (e.g., Bigiel et al. Reference Bigiel, Leroy, Seibert, Walter, Blitz, Thilker and Madore2010b; Catinella et al. Reference Catinella2018). Thus, contrary to the HG84 definition, the underlying assumption in this case is that Hi is affected but star formation is not (at least within the timescale traced by the NUV-r colour, i.e., $\sim10^{8}\ yr$ ). This implies that this parametrisation is sensitive only to processes that either: (a) remove cold gas from galaxies on a significantly shorter timescale than that needed to affect the star formation, or (b) act only on the part of the atomic gas reservoir that is not directly fuelling star formation (e.g., the outer discs of galaxies).

3.3. Definitions based on broad-band luminosity or stellar mass

Another approach to quantify gas deficiency is via correlations between gas mass and broad-band optical/near-infrared luminosities (or even stellar masses; Chamaraux et al. Reference Chamaraux, Balkowski and Gerard1980). This technique has recently regained some popularity thanks to Dénes et al. (Reference Dénes, Kilborn and Koribalski2014), who estimated scaling relations between Hi mass and luminosities in B, r, K, H, and J bands for galaxies detected by the Hi Parkes All Sky Survey (HIPASS; Barnes et al. Reference Barnes2001). Within the HIPASS sample, these relations have a typical scatter of $\sim$ 0.3 dex, comparable to that of other Hi deficiency proxies, and are used by the authors to identify Hi-excess and Hi-deficient galaxies.

While this approach has the advantage of requiring only a single band luminosity, recent works have highlighted its significant limitations (see also Bottinelli & Gouguenheim Reference Bottinelli and Gouguenheim1974 and HG84 for early discussions on why this approach may not be ideal). We now know that the optical luminosity/stellar mass versus Hi mass relation is primarily driven by the fact that there are increasing numbers of star-forming (gas-rich) galaxies compared to passive (gas-poor) systems as we shift to considering lower stellar masses (Brown et al. Reference Brown, Catinella, Cortese, Kilborn, Haynes and Giovanelli2015). Indeed, at fixed colour or SFR, the correlation becomes significantly weaker, with galaxies following shallower, parallel relations on the Hi gas fraction–stellar mass plane, and star-forming systems being systematically more gas-rich. Thus, this relation is not a direct physically motivated correlation compared to the other correlations with star formation rates or galaxy sizes, and it has a scatter significantly larger (0.5 dex or higher; Catinella et al. Reference Catinella2018).

The unusually small scatter of the Dénes et al. (Reference Dénes, Kilborn and Koribalski2014) calibration is simply due to a selection effect—because of its limited sensitivity, HIPASS detects only the most gas-rich galaxies in the local Universe (see also Lutz et al. Reference Lutz2017). As we discuss later in this work, this is a common issue for samples detected by Hi-blind surveys, which are primarily biased towards gas-rich galaxies within their volumes (e.g., Huang et al. Reference Huang, Haynes, Giovanelli and Brinchmann2012). The fact that the Hi mass versus luminosity/stellar mass scaling relation for a blind Hi survey is not representative of the global galaxy population, but offsets towards gas-rich systems, implies that galaxies with normal Hi content (according, e.g., to the HG84 definition) may be labelled as Hi-deficient. Moreover, from a physical point of view, the use of a deficiency parameter based only on mass/luminosity significantly complicates the interpretation of any trends. As all galaxy properties correlate with stellar mass, it is unclear whether gas deficiency with respect to mass is tracing environmental effects or more simply the bimodality of star-forming properties of galaxies, which has been shown to be well established in all environments (e.g., Baldry et al. Reference Baldry, Balogh, Bower, Glazebrook, Nichol, Bamford and Budavari2006).

3.4. Definitions based on specific angular momentum

In recent years, independent works have put forward a new definition of gas deficiency based on the angular momentum properties of galaxies. This idea has been proposed by a few authors throughout the last few decades (e.g., Zasov & Rubtsova Reference Zasov and Rubtsova1989; Safonova Reference Safonova2011) and most recently expanded by Li et al. (Reference Li, Obreschkow, Lagos, Cortese, Welker and Džudžar2020). Their approach is based on the assumption that, for a flat exponential disc with circular rotation, the maximum allowed, stable value of gas fraction strongly depends on the mass and kinematics of the disc. One way to parametrise this is through the dimensionless global disc stability parameter q (Obreschkow et al. Reference Obreschkow, Glazebrook, Kilborn and Lutz2016):

(4) \begin{equation}q=\frac{j\sigma}{GM},\end{equation}

where j is the baryonic (gas plus stars) specific angular momentum (i.e., angular momentum per unit mass) of the disc, $\sigma$ is the gas velocity dispersion, M is the total baryonic mass, and G is the gravitational constant. The relation with neutral atomic (Hi plus helium) gas fraction, $f_{\rm atm}=M_{\rm atm}/M_{\rm baryons}$ , can then be generally approximated by a truncated power law of the form:

(5) \begin{equation}f_{\rm atm} = \min\!\left\{1, 2.5q^{1.12}\right\}.\end{equation}

While this is arguably a more physically motivated definition of Hi deficiency (but see also Romeo & Mogotsi Reference Romeo and Mogotsi2018 for some potential limitations of this approach), the basic assumptions are the same behind the original HG84 definition. Indeed, Li et al. (Reference Li, Obreschkow, Lagos, Cortese, Welker and Džudžar2020) show that (at least in the case of galaxies in the Virgo cluster) the two definitions provide remarkably consistent results.

Figure 2. Comparison between different estimates of Hi deficiency ( $DEF_{\rm HI} \equiv \log(M_{\rm HI,pred})-\log(M_{\rm HI})$ ) calibrated on the Shark semi-analytical model of galaxy formation. From left to right, the panels show the specific angular momentum/stability parameter (q)-based, the stellar mass ( $M_{*}$ )-based, and gas fraction plane-based ( $(NUV-r)+\mu_{*}$ ) definitions against the one calibrated on the Hi mass versus optical disc size relation. The solid line shows the 1-to-1 relation, the grey band shows the region of ‘Hi-normalcy’ defined by the typical scatter in the scaling relations (i.e., $-$ 0.3 $<DEF_{\rm HI}<$ 0.3), and the dotted-dashed lines show the threshold of $DEF_{\rm HI}$ =0.5 that we use in the rest of this paper to isolate bona-fide Hi-deficient galaxies. See Section 3.5 for details on how each parameter has been estimated.

From a practical point of view, the main short-coming of this technique is that, in addition to being calibrated on pure-disc galaxies only, it requires information on both the two-dimensional distribution and velocity field for at least one baryonic component of galaxies, as well as the total baryonic mass, which is much more difficult to obtain than optical diameter measurements. Regardless, this method implicitly assumes that the process affecting the gas does not change significantly the kinematic properties of the baryons in the galaxy (i.e., the specific angular momentum is not altered), which is not so different from the basic assumption of the optical size-based deficiency. In other words, as already hinted in Section 3.1, this definition can be viewed as a physical explanation for the success of the optical diameter-based approach.

3.5. A direct comparison of different gas deficiency definitions

One of the key reasons why the above limitations have rarely been discussed in the literature is that we are still lacking galaxy samples that simultaneously cover wide ranges of environments (to include both gas-rich and gas-deficient systems), are representative of the local galaxy population (to calibrate reliable scaling relations) and for which sizes, luminosities and angular momentum can be homogeneously estimated (see however HG84, Cortese et al. Reference Cortese, Catinella, Boissier, Boselli and Heinis2011; Teimoorinia, Ellison, & Patton Reference Teimoorinia, Ellison and Patton2017; Li et al. Reference Li, Obreschkow, Lagos, Cortese, Welker and Džudžar2020 for discussions on different gas deficiency definitions and gas predictors in general).

Thus, in order to clarify the points discussed here, we take advantage of the semi-analytic cosmological model of galaxy formation and evolution Shark (Lagos et al. Reference Lagos, Tobar, Robotham, Obreschkow, Mitchell, Power and Elahi2018). The point of this exercise is not to reproduce the observed scaling relationsFootnote c but to show that, even if we calibrate gas deficiency definitions using exactly the same sample and assumptions, major biases still remain.

We compare the optical size, total stellar mass ( $M_{*}$ ), specific angular momentum (via the q parameter), and (NUV-r)+ $\mu_{*}$ -based approaches for galaxies with stellar masses between $10^{9}$ and $10^{11}$ M $_{\odot}$ . The first three definitions are calibrated on central galaxies within 1.5 $\sigma$ from the Shark main sequence of star-forming galaxies, whereas the (NUV-r)+ $\mu_{*}$ plane is estimated for all central galaxies with an atomic gas fraction greater than 1%, following Catinella et al. (Reference Catinella2010). For the optical size, we use the radius including 50% of the stellar mass of the disc ( $R_{*}(50)$ ), whereas we estimate q from the total baryonic specific angular momentum and baryonic mass. For each galaxy in the model, we then calculate deficiency as the logarithmic difference between the Hi content predicted from each scaling relation and the one given ( $DEF_{\rm HI}\equiv \log(M_{\rm HI,pred})-\log(M_{\rm HI})$ ). Galaxies with $DEF_{\rm HI}>$ 2.5 are set to 2.5 to encapsulate the inability of observations to detect cold gas in extremely gas-poor objects.

The results are shown in Figure 2. As expected, the size and q-based estimates generally agree and are not too offset from the 1-to–1 line (left panel), whereas larger systematic offsets are seen for the stellar mass (middle) and (NUV-r)+ $\mu_{*}$ (right) approaches. In particular, a significant fraction of Hi-normal galaxies (i.e., $-$ 0.3 $<DEF_{HI}<$ 0.3, indicated by the grey band) according to the size-based calibration would be classified as Hi-deficient using the stellar mass-based calibration (i.e., $DEF_{HI}>$ 0.5 to the right of the vertical dotted-dashed line in the middle panel), or even Hi-rich or Hi-excess galaxies (e.g., $DEF_{HI}<-$ 0.5). Conversely, many Hi-deficient systems according to the size-based approach would appear Hi-normal for the gas fraction plane definition (see also Cortese et al. Reference Cortese, Catinella, Boissier, Boselli and Heinis2011). As mentioned above, this is just due to the different samples used to calibrate the two recipes (all central galaxies with gas fraction above a threshold versus star-forming centrals only). Thus, to first order, Hi-deficient galaxies would move along the plane. If we calibrate the plane on just star-forming galaxies, the dependence on star formation disappears almost entirely (simply by selection: i.e., all galaxies have similar SFRs) and the plane becomes equivalent to the gas mass–optical size relation.

In summary, some care must be taken when it comes to the Hi deficiency parameter, as its definition and implications for environmental studies may differ significantly from one work to another. As we reviewed in this section, different scaling relations between cold gas content and another galaxy property (or a combination of two or more) can be used to define Hi normalcy, and offsets from it. The interpretation of such an offset as an indicator of Hi deficiency depends critically on three elements: (1) the choice of scaling relation, which implies underlying assumptions on the physical process that removes the gas; (2) the reference sample used to calibrate the scaling relation itself, typically isolated or field galaxies with Hi measurements. Clearly, reference samples biased towards gas-rich systems (such as detections from Hi-blind surveys) may lead us to misclassify Hi-normal systems as Hi-deficient ones; (3) the choice of a threshold separating Hi-poor from Hi-normal systems (typically from 0.3 to 0.5 dex, which is $\sim$ 1–1.5 times the scatter of these relations, see also Figure 2).

Definitions of Hi deficiency based on the size of the stellar disc or on its global-specific angular momentum are most sensitive to stripping processes, which may affect both gas content and star formation, hence are of particular relevance for this review (however, optical sizes are more readily available for large samples of galaxies). Choosing instead NUV-r colour (a proxy for unobscured specific SFR, see Section 3.2) as a scaling parameter implicitly assumes that gas is removed but star formation is not affected. We discourage the use of definitions based on stellar mass or luminosity alone, which have very large scatter (strongly dependent on SFR) and are often inconsistent with the ‘classical’, size-based Hi deficiency, even when based on the same calibration sample (Figure 2, middle panel).

Much of the literature on the effects of environmental processes on the Hi content of galaxies makes use of the optical size-based Hi deficiency parameter, and this is what we adopt in the rest of this review (using a conservative threshold of 0.5 dex to safely identify Hi-deficient galaxies, unless otherwise noted). However, these types of binary classifications, although initially convenient, never capture the complexity of galaxies nor the continuum of properties that we observe, thus we hope that the advent of new large-area blind surveys will see the community abandon this historical terminology and refer instead to offsets with respect to scaling relations, making sure that the calibration samples are representative of the galaxy population.

4.1. The case for H i stripping

We start by focusing on clusters of galaxies, as these are the environments where most of the progress has been made in the last few decades. In reality, as it will become immediately clear, our knowledge of cold gas in these environments is heavily based on studies of one single cluster, Virgo, in particular when it comes to resolved analysis. At a distance of just $\sim$ 16–18 Mpc (Mei et al. Reference Mei2007; Planck Collaboration et al. 2016) from Earth, and sitting in the middle of the northern Spring sky, Virgo has been the primary target of most gas surveys focusing on understanding the role of environment on the gas cycle of galaxies. Given that Virgo may not be the average nearby cluster, at least in terms of accretion history and number of substructures (Sorce, Blaizot, & Dubois Reference Sorce, Blaizot and Dubois2019), this is something to keep in mind.

The reason for our limited knowledge of gas content in cluster galaxies is that Hi-blind surveys, which have provided the largest samples of global Hi measurements, only detect the most gas-rich galaxies in their volumes (i.e., the star-forming population), hampering our ability to study systems in the process of being affected by the environment. To demonstrate this point, we take advantage of xGASS (the extended GASS survey; Catinella et al. Reference Catinella2018), a stellar mass-selected, gas fraction-limited survey of $\sim 1\,200$ galaxies that is the current benchmark for a representative sample in terms of Hi properties of nearby galaxies. In Figure 3, we show which parts of the stellar mass-SFR plane are typically detected by Hi-blind surveys, in comparison with xGASS (left panel). As a reference for Hi-blind surveys, we consider the upcoming Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY; Koribalski et al. Reference Koribalski2020), which, for unresolved sources, will have a factor $\sim$ 2 better sensitivity than the current state of the art, the Arecibo Legacy Fast ALFA (ALFALFA; Giovanelli et al. Reference Giovanelli2005) survey. We assume a typical root mean square (rms) noise for WALLABY of $\sigma=1.6$ mJy and, for each distance shown in Figure 3, we plot galaxies that will be detected above a 5 $\sigma$ threshold assuming a typical velocity width of 200 $\rm km\,s^{-1}$ . Given that not even xGASS detects all passive galaxies, here we take a conservative approach by plotting the upper limits of Hi non-detections (triangles). It is clear that, while at the distance of Virgo, both the star-forming and quiescent populations are mapped, beyond $\sim$ 60–100 Mpc a WALLABY-like survey will not be able to detect a large number of galaxies below the star-forming main sequence.

Figure 3. The ability of Hi surveys to detect galaxies across the stellar mass versus SFR plane. The left-most panel shows the distribution of galaxies in the xGASS survey, which we use as input. Circles and triangles indicate Hi detections and non-detections, respectively. Galaxies are colour-coded according to their Hi mass (circles) or provided upper limit (triangles). The dashed line shows 2 $\sigma$ below the star-forming main sequence. The remaining panels show which galaxies would be detected (at 5 $\sigma$ level assuming a velocity width of 200 km s^–1) by a survey with 1.6 mJy rms noise (close to the expected sensitivity of the WALLABY survey) for distances varying between 30 and 120 Mpc. We conservatively assume xGASS non-detections at their upper limit. It is clear that, above $\sim$ 40–50 Mpc, most of the passive population starts to disappear and at distances higher than $\sim$ 100 Mpc only galaxies in the main sequence are detected.

From the early works by Davies & Lewis (Reference Davies and Lewis1973) and Huchtmeier, Tammann, & Wendker (Reference Huchtmeier, Tammann and Wendker1976), every investigation of clusters of galaxies has found that the late-type population has significantly less Hi content than galaxies in isolation at fixed morphology, size, and/or optical luminosity. Most of the early statistical works in this area were carried out with single-dish antennae like the Arecibo and Nançay radio telescopes (e.g., Sullivan & Johnson Reference Sullivan and Johnson1978; Chamaraux et al. Reference Chamaraux, Balkowski and Gerard1980; Giovanelli, Chincarini, & Haynes Reference Giovanelli, Chincarini and Haynes1981; Giovanelli & Haynes Reference Giovanelli and Haynes1985; Haynes & Giovanelli Reference Haynes and Giovanelli1986), which simply provided global Hi masses, but no information on the spatial distribution of the gas within the galaxy. Despite this limitation, 21-cm-deep surveys of several clusters in the local Universe (e.g., Virgo, Coma, Abell 262, Abell 1367, Cancer, Abell 2147/2151) have shown that Hi deficiency is a widespread phenomenon in clusters and that, while deficiency does not strongly correlate with any galaxy or cluster property (see Figure 4), there is a common trend for the degree of deficiency to increase with decreasing distance from the cluster centre.

Figure 4. The fraction of Hi-deficient spiral galaxies as a function of cluster velocity dispersion (a proxy for cluster mass) for the sample of nearby clusters of galaxies studied in Solanes et al. (Reference Solanes, Manrique, Garca-Gómez, González-Casado, Giovanelli and Haynes2001). Points are colour-coded by X-ray temperature, $T_X$ . It is clear that the fraction of Hi-deficient spirals in clusters does not strongly depend on $T_X$ or mass of the cluster.

Nevertheless, the Hi deficiency versus cluster-centric distance relation has a large scatter (Solanes et al. Reference Solanes, Manrique, Garca-Gómez, González-Casado, Giovanelli and Haynes2001; Boselli & Gavazzi Reference Boselli and Gavazzi2006), with Hi-deficient galaxies observed up to a few Mpc projected distance from the centre, and both the shape and scatter of the correlation appear to depend on the dynamical state of the cluster (e.g., with Coma having a better defined correlation than Virgo). This result, combined with the initial evidence that gas-poor late-type galaxies follow more radial orbits than gas-rich systems (Dressler Reference Dressler1986; Giraud Reference Giraud1986; Solanes et al. Reference Solanes, Manrique, Garca-Gómez, González-Casado, Giovanelli and Haynes2001), provided the foundation to the idea that, in clusters, atomic hydrogen is directly removed from the disc during the infall, with hydrodynamical effects such as ram pressure being the primary suspect. However, it is worth noting that the same trends could also be explained via galaxy–galaxy interactions (e.g., Valluri & Jog Reference Valluri and Jog1990, Reference Valluri and Jog1991). In other words, direct stripping of the cold ISM seemed needed to explain the significant lack of gas observed in cluster spirals, but the primary driver remained elusive to single-dish observations.

The advent of radio interferometric observations dramatically improved the situation. Since the first observations of Virgo cluster galaxies by Warmels (Reference Warmels1988) and Cayatte et al. (Reference Cayatte, van Gorkom, Balkowski and Kotanyi1990), it became clear that not only the total amount of gas, but also its radial distribution changes when galaxies plunge into clusters. Hi-deficient cluster galaxies have surface density profiles significantly less extended than their optical sizes, as most of the hydrogen is missing from the outer parts of the disc, whereas the inner regions show little (e.g., within a factor of $\sim$ 2) variations in gas surface density. The transition between inner (gas-normal) and outer (gas-deficient) parts of the Hi disc is much sharper than observed in field spirals and can drop from a healthy $\geq$ 5 M $_{\odot}$ pc^–2 to less than 1 M $_{\odot}$ pc^–2 within just a couple of kiloparsec. This unique feature—generally referred to as truncation of the gas disc—represents one of the clearest (if not the clearest) observational pieces of evidence supporting the idea that gas is directly stripped from the disc. Indeed, it is difficult to imagine a scenario in which a simple cessation of gas infall and/or outflows could produce such a remarkable feature (Boselli et al. Reference Boselli, Boissier, Cortese, Gil de Paz, Seibert, Madore, Buat and Martin2006), without also affecting the stellar disc, which instead generally shows no sign of strong environmental perturbations in cluster galaxies.

In Figure 5, we take advantage of data from the VLA Imaging of Virgo in Atomic gas (VIVA; Chung et al. Reference Chung, van Gorkom, Kenney, Crowl and Vollmer2009) survey to show the strong correlation between Hi deficiency and the extent of the Hi disc normalised by the optical diameter. Hi diameters are iso-density diameters measured at 1 M $_{\odot}$ pc^–2 level, while optical ones are measured at the 25th magnitude per square arcsecond from the Third Reference Catalogue of Bright Galaxies (RC3; de Vaucouleurs et al. Reference de Vaucouleurs, de Vaucouleurs, Corwin, Buta, Paturel and Fouque1991). This illustrates how high deficiencies are associated with smaller Hi discs, confirming that gas removal happens preferentially outside-in. Points are colour-coded by the average Hi surface density within the Hi size. It is clear that there is not a strong difference in surface densities between Hi-deficient and Hi-normal galaxies (see also Wang et al. Reference Wang, Koribalski, Serra, van der Hulst, Roychowdhury, Kamphuis and Chengalur2016), as surface density appears to regulate the scatter of the relation for all deficiency values.

Figure 5. The Hi-to-optical isophotal diameter as a function of Hi deficiency for galaxies in the Virgo cluster included in the VIVA survey (Chung et al. Reference Chung, van Gorkom, Kenney, Crowl and Vollmer2009). Points are colour-coded by average Hi surface density. Vertical and horizontal dotted lines are shown to guide the eye and highlight that $DEF_{HI}\sim$ 0.5 roughly corresponds to gas removal up to the optical isophotal radius.

The detailed information provided by the resolved Hi maps of Virgo galaxies made it possible to start modelling the interaction with the cluster environment, thus getting closer to isolating the physical mechanism(s) responsible for the observed Hi deficiency. Fundamental in this area have been the works carried out by Vollmer et al. (Reference Vollmer, Cayatte, Balkowski and Duschl2001, Reference Vollmer, Balkowski, Cayatte, van Driel and Huchtmeier2004b) and Vollmer (Reference Vollmer2003) on individual Virgo galaxies, showing that stripping via a hydrodynamical process such as ram pressure is necessary to reproduce the three-dimensional distribution of atomic hydrogen in these systems. A similar conclusion was reached by interferometric studies of other nearby clusters such as Coma and Abell 1367 (Bravo-Alfaro et al. Reference Bravo-Alfaro, Cayatte, van Gorkom and Balkowski2000, Reference Bravo-Alfaro, Cayatte, van Gorkom and Balkowski2001; Scott et al. Reference Scott2010). More recently, the discovery of one-headed Hi tails, in some cases pointing away from the X-ray centre of clusters, has provided even more direct proof for the importance of stripping in removing cold hydrogen from the star-forming disc (e.g., Oosterloo & van Gorkom Reference Oosterloo and van Gorkom2005; Chung et al. Reference Chung, van Gorkom, Kenney and Vollmer2007; Ramatsoku et al. Reference Ramatsoku2019; Deb et al. Reference Deb2020). Indeed, for the typical ICM density of $\sim$ 10^–3 cm^–3 inferred from X-ray observations, infalling velocities of $\sim$ 1000 km $s^{-1}$ are enough for ram pressure to strip at least part of the atomic hydrogen content from the star-forming disc of galaxies (Gunn & Gott Reference Gunn and Gott1972; Boselli & Gavazzi Reference Boselli and Gavazzi2006; Köppen et al. Reference Köppen, Jáchym, Taylor and Palouš2018).

While all the observational evidence collected so far indicates that active stripping due to the interaction between the galactic ISM and the ICM is likely the main reason for the lack of Hi in disc galaxies, this does not mean that ram pressure is sufficient to explain the transformation of satellite galaxies. We now know plenty of galaxies for which at least one of the alternative environmental mechanisms described in the Introduction needs to be invoked to explain their properties. These include gravitational interactions needed to reproduce the kinematic properties of the stripped gas (e.g., NGC4254, Duc & Bournaud Reference Duc and Bournaud2008; NGC4438, Vollmer et al. Reference Vollmer, Braine, Combes and Sofue2005; Kenney et al. Reference Kenney, Tal, Crowl, Feldmeier and Jacoby2008; CGCG97-073/79, Gavazzi et al. Reference Gavazzi, Boselli, Mayer, Iglesias-Paramo, Vlchez and Carrasco2001), and feedback from star formation (e.g., NGC4424, Boselli et al. Reference Boselli2018). Moreover, there are also individual cases where gravitational interactions may be the dominant mechanism responsible for Hi stripping (e.g., NGC 4532/DDO 137 in Virgo, Koopmann et al. Reference Koopmann2008; NGC1427A in Fornax, Lee-Waddell et al. Reference Lee-Waddell2018; the Abell cluster 1367, Scott et al. Reference Scott2010). This should not come as a surprise, as the pericentre of the orbit of a satellite in a cluster is precisely where ram pressure, cluster tides, and number of high-speed encounters are expected to reach their peak intensity (e.g., Smith et al. Reference Smith, Davies and Nelson2010a). Once again, this highlights the complexity of galaxy evolution in clusters and, while focusing on a single physical mechanism might still prove useful for individual objects (where a given process might indeed explain the main current features of a galaxy, see e.g. Section 8), it would be reductive to expect that it alone could account for the full galaxy transformation over long times.

4.2. What about molecular hydrogen?

According to our current view of star formation in galaxies, it is now accepted that molecular hydrogen ( $\mathrm{H}_{2}$ ) is more directly connected to star formation than Hi on local (i.e. kiloparsec or smaller) scales (Bigiel et al. Reference Bigiel, Leroy, Walter, Brinks, de Blok, Madore and Thornley2008; Leroy et al. Reference Leroy, Walter, Brinks, Bigiel, de Blok, Madore and Thornley2008), with Hi simply providing the reservoir out of which molecular clouds are formed. As such, the link between Hi stripping and quenching of star formation is not straightforward. Is molecular gas directly stripped as well? Or is this denser phase of the ISM not strongly perturbed by the environment and simply consumed by star formation?

Answering these questions has been challenging because of the lack of molecular gas measurements for large statistical samples of galaxies, spanning different environments. The first complication is that, being a symmetric molecule with low mass, $\mathrm{H}_{2}$ does not emit at the low temperatures typical of molecular clouds ( $T<50$ K), and thus requires an indirect indicator. The most widely used tracer of $\mathrm{H}_{2}$ is carbon monoxide (CO), the most abundant molecule after $\mathrm{H}_{2}$ , whose rotational lines are easily excited in cold molecular clouds (see e.g., Bolatto, Wolfire, & Leroy Reference Bolatto, Wolfire and Leroy2013 for an extensive review on this topic). The second complication is that, unlike for Hi, there are no large-area, blind surveys of CO emission in the local Universe, and targeted samples are small. At the time of writing, quantification of global $\mathrm{H}_{2}$ scaling relations is limited to a few hundred galaxies (e.g., Saintonge et al. Reference Saintonge and Spekkens2011, Reference Saintonge2017; Bothwell et al. Reference Bothwell2014; Cicone et al. Reference Cicone2017), a number that drops even more when it comes to resolved properties (Leroy et al. Reference Leroy2009). Luckily, the Atacama Large Millimeter/submillimeter Array (ALMA; Wootten & Thompson Reference Wootten and Thompson2009) is already having a tremendous impact on this field, especially for galaxies at higher redshift.

The lack of representative samples suitable to define $\mathrm{H}_{2}$ normalcy for galaxies has meant that any potential quantification of $\mathrm{H}_{2}$ deficiency is made more challenging, due to selection biases and large scatter in scaling relations (Boselli, Lequeux, & Gavazzi Reference Boselli, Lequeux and Gavazzi2002). Nevertheless, all initial investigations suggested that galaxies in rich clusters have on average the same molecular hydrogen content as systems in isolation (e.g., Kenney & Young Reference Kenney and Young1986, Reference Kenney and Young1988; Stark et al. Reference Stark, Knapp, Bally, Wilson, Penzias and Rowe1986; Casoli et al. Reference Casoli, Boisse, Combes and Dupraz1991, Reference Casoli1998; Boselli et al. Reference Boselli, Gavazzi, Lequeux, Buat, Casoli, Dickey and Donas1997). From a theoretical point of view, this is fully consistent with an outside-in stripping scenario, where only the more diffuse gas phase (i.e., Hi) in the outer parts of the star-forming disc can be significantly affected by environment. Indeed, it can be easily shown analytically that giant molecular clouds are too dense to be appreciably stripped by the ram pressure wind (e.g., Yamagami & Fujita Reference Yamagami and Fujita2011).

The fact that $\mathrm{H}_{2}$ is significantly less affected by the cluster environment than Hi is evident in Figure 6, where we show $\mathrm{H}_{2}$ -to-Hi mass ratios as a function of stellar mass for disc galaxies (S0 or later types) in the Virgo cluster, taken from Boselli, Cortese, & Boquien (Reference Boselli, Cortese and Boquien2014a). These are compared with results from xGASS-CO (grey region; Catinella et al. Reference Catinella2018), a representative sample with CO( $J=1\rightarrow 0$ ) measurements from xCOLD GASS (the extended CO Legacy Database for GASS survey; Saintonge et al. Reference Saintonge2017). While Hi-normal galaxies (blue symbols) are consistent with galaxies from xGASS-CO, Hi-deficient systems in Virgo (red symbols) are clearly $\mathrm{H}_{2}$ -dominated (see also Mok et al. Reference Mok2016; Loni et al. Reference Loni2021). So, is $\mathrm{H}_{2}$ affected at all, or are cluster galaxies simply not $\mathrm{H}_{2}$ deficient?

Figure 6. The molecular-to-atomic hydrogen mass ratio for disc galaxies (S0 or later types) in the Virgo cluster (Boselli et al. Reference Boselli, Cortese and Boquien2014a). Circles indicate detections in both Hi and $\text{H}_{2}$ , upward and downward triangles are upper limits in Hi and $\text{H}_{2}$ , respectively. Galaxies are colour-coded by Hi deficiency. The grey region in the background shows the typical parameter space covered by local galaxies as traced by the xGASS-CO sample. It is clear that Hi-deficient galaxies in Virgo have elevated molecular-to-atomic gas ratios, confirming that Hi is much more affected by the cluster environment than $\text{H}_{2}$ .

Thanks to improvements of millimeter facilities, recent years have seen growing observational evidence in support of $\mathrm{H}_{2}$ deficiency being a natural step in the path of satellite galaxies toward quenching. One of the first and best direct examples of $\mathrm{H}_{2}$ stripping is probably NGC4522 in the Virgo cluster (Vollmer et al. Reference Vollmer, Braine, Pappalardo and Hily-Blant2008, but see also Vollmer et al. Reference Vollmer, Braine, Combes and Sofue2005), which shows extraplanar CO emission up to a few kpc from the disc, consistent with displacement due to ram pressure. Fumagalli et al. (Reference Fumagalli, Krumholz, Prochaska, Gavazzi and Boselli2009) extended this work by providing the first statistical evidence for a population of $\mathrm{H}_{2}$ -deficient galaxies in the Virgo cluster. By combining resolved Hi and $\mathrm{H}_{2}$ observations for 47 galaxies across different environments, they showed that, while H i deficiency by itself is not a sufficient condition for molecular gas depletion, ${H}_{2}$ reduction is associated with the removal of H i inside the galaxy’s stellar disc. This is consistent with the idea that the cold ISM is removed from the disc outside-in and molecular hydrogen, being more centrally concentrated than Hi, is affected only when the stripping becomes efficient within the radius of the stellar disc. Intriguingly, they did not interpret $\mathrm{H}_{2}$ deficiency as evidence for direct stripping of CO, but more as evidence that—when Hi is stripped—the remaining atomic gas is at too low column densities to condense and form molecules.

A similar trend was more recently presented by Boselli et al. (Reference Boselli, Cortese, Boquien, Boissier, Catinella, Gavazzi, Lagos and Saintonge2014c), who took advantage of single-dish CO observations for the volume- and K-band-limited Herschel Reference Survey (HRS, Boselli et al. Reference Boselli2010) to quantify $\mathrm{H}_{2}$ normalcy (based on either stellar mass or size) in a sample of nearby, Hi-normal late-type galaxies. They then quantified the degree of $\mathrm{H}_{2}$ deficiency in Virgo galaxies and showed that the most Hi-deficient galaxies are also $\mathrm{H}_{2}$ -deficient. Importantly, galaxies are $\mathrm{H}_{2}$ -deficient only when they have already lost $\sim$ 80–90% of their original atomic hydrogen reservoir (i.e., $DEF_{\rm HI}>$ 1). Contrary to Fumagalli et al. (Reference Fumagalli, Krumholz, Prochaska, Gavazzi and Boselli2009), they interpreted this trend as mainly due to active stripping of CO by ram pressure.

The difference in the interpretation between these two works, despite their similar observational results, reflects the gradual paradigm shift that was beginning to take place in the community a decade ago, based on the growing evidence for individual objects showing direct signs of molecular hydrogen stripping, via the presence of extraplanar CO and/or CO tails (Figure 7; e.g., Corbelli et al. Reference Corbelli2012; Scott et al. Reference Scott, Usero, Brinks, Boselli, Cortese and Bravo-Alfaro2013; Sivanandam, Rieke, & Rieke Reference Sivanandam, Rieke and Rieke2014; Jáchym et al. Reference Jáchym, Combes, Cortese, Sun and Kenney2014, Reference Jáchym2017, Reference Jáchym2019; Lee et al. Reference Lee2017; Lee & Chung Reference Lee and Chung2018; Chung et al. Reference Chung, Yun, Verheijen and Chung2017; Moretti et al. Reference Moretti2018, Reference Moretti2020a). Similar evidence supporting widespread CO stripping has also been reported for galaxies in the Fornax cluster (Zabel et al. Reference Zabel2019). While it is possible that part of the CO observed in the stripped tails was formed in situ (e.g., Jáchym et al. Reference Jáchym, Combes, Cortese, Sun and Kenney2014), the fact that these extraplanar features/tails do not show a clear separation from the CO disc suggests that at least part of the CO is being directly stripped from the disc.

Figure 7. Spectacular examples of stripping of molecular gas, as traced by the CO(2-1) transition line (in red). Left: ESO 137-001, a disc galaxy infalling into the Norma Cluster. CO(2-1) emission along with H $\alpha$ emission in green and X-ray contours are overlaid on a Hubble Space Telescope image (adapted from Figure 3 in Jáchym et al. Reference Jáchym2019). Right: JW100 in Abell 2626, with CO(2-1) emission overlaid on a composite V- (blue) and I-band (green) image extracted from Multi-Unit Spectroscopic Explorer (MUSE) observations (adapted from Figure 8 in Moretti et al. Reference Moretti2020a). Images reproduced with permission from the authors. Copyright by AAS.

Furthermore, it is now clear that cold dust is removed during the interaction with the ICM (e.g., Cortese et al. Reference Cortese2010a,Reference Corteseb, Reference Cortese2012a, Reference Cortese2016; Pappalardo et al. Reference Pappalardo2012; Bianconi et al. Reference Bianconi, Smith, Haines, McGee, Finoguenov and Egami2020) and that global oxygen abundance in the ISM of cluster galaxies shows clear enhancements with respect to isolated systems, with radial profiles sometimes steepening (e.g., Skillman, Kennicutt, & Hodge Reference Skillman, Kennicutt and Hodge1989; Shields, Skillman, & Kennicutt Reference Shields, Skillman and Kennicutt Robert1991; Petropoulou et al. Reference Petropoulou, Vílchez and Iglesias-Páramo2012; Hughes et al. Reference Hughes, Cortese, Boselli, Gavazzi and Davies2013; Gupta et al. Reference Gupta, Yuan, Tran, Martizzi, Taylor and Kewley2016). This is consistent with expectations in the case where metal-poor cold hydrogen, mostly found in the outer parts of the star-forming disc, is stripped more preferentially than the metal-enriched ISM, which is typical of the inner parts of the stellar disc. In other words, we now have plenty of evidence that the low density, diffuse, atomic gas is not the only ISM component that is affected by the cluster environment.

How can this conclusion be reconciled with the theoretical expectation that ram pressure can hardly directly strip molecular clouds? A possible explanation is that not all CO emission from galaxies is bound within giant molecular clouds, but a significant fraction of it could trace a diffuse, thick, low-volume density disc, as such more susceptible to environmental effects. While the first evidence for a CO-thick disc associated with a star-forming galaxy dates back nearly three decades (NGC 891; Garcia-Burillo et al. Reference Garcia-Burillo, Guelin, Cernicharo and Dahlem1992), observational support for this has been growing in recent years. On one side, the detailed analysis of M51 performed as part of the Plateau de Bure+30m Arcsecond Whirlpool Survey (PAWS; Schinnerer et al. Reference Schinnerer2013) demonstrated that practically 50% of the CO emission originates from structures on spatial scales larger than $\sim$ 1 kpc, consistent with the presence of a diffuse disc of molecular hydrogen with a typical scale height of $\sim$ 200 pc (Pety et al. Reference Pety2013). On the other side, detailed studies of the velocity broadening of the CO line in star-forming discs have shown that the line widths are significantly wider than that expected from a cold, thin molecular disc (i.e., $\sim$ 10-12 km s^–1 instead of $\sim$ 5 km s^–1, Caldú-Primo et al. Reference Caldú-Primo, Schruba, Walter, Leroy, Sandstrom, de Blok, Ianjamasimanana and Mogotsi2013, Reference Caldú-Primo, Schruba, Walter, Leroy, Bolatto and Vogel2015), and more in line with those observed for the Hi component, again suggesting that a significant fraction of the CO emission could come from warmer and more diffuse gas (e.g., $n\sim$ 100–500 cm^–3 and $T\sim$ 50–100 K; see also Liszt, Pety, & Lucas Reference Liszt, Pety and Lucas2010) than generally thought. This seems consistent with Milky Way observations, where diffuse CO emission associated with gas at surface densities more typical of Hi gas (e.g., <10 M $_{\odot}$ pc^–2; Roman-Duval et al. Reference Roman-Duval, Heyer, Brunt, Clark, Klessen and Shetty2016) appears to account for $\sim$ 25% of the total mass of CO-emitting gas, but can even dominate the mass budget at large galactocentric distances (e.g., $>$ 8 kpc). If so, it would be easy to explain cases of extraplanar CO emission, CO tails, and/or truncated CO discs observed in cluster galaxies. Indeed, this scenario seems to be consistent with recent high-resolution ALMA observations of NGC 4402 in Virgo (Cramer et al. Reference Cramer, Kenney, Cortes and Cortes2020).

However, it is important to acknowledge that there are also cases where no evidence for a significant thick CO component has been found (e.g., M33; Koch et al. Reference Koch, Rosolowsky, Schruba, Leroy, Kepley, Braine, Dalcanton and Johnson2019), and that we are still missing an extensive investigation of the frequency and properties of CO diffuse, thick discs, primarily due to the lack of CO observations able to trace emission at all physical scales. Moreover, it remains unclear if the fraction of diffuse CO emission maps directly into diffuse $\mathrm{H}_{2}$ or not, which would clearly impact the overall physical scenario of direct molecular hydrogen stripping. Hopefully, the advent of facilities such as ALMA will soon fill this important gap in the field.

In summary, there is mounting evidence supporting the idea that CO-emitting gas can be directly removed from the disc, even by ram pressure, at least in environments similar to (or harsher than) those of the Virgo cluster. However, it seems clear that satellite galaxies can become $\mathrm{H}_{2}$ -deficient only if environmental processes are strong enough to be efficient within the optical radius of infalling galaxies. Otherwise, despite becoming Hi-deficient, satellite galaxies could remain $\mathrm{H}_{2}$ -normal for a long time after infall (i.e., at least a couple of billion years after their first pericentre passage). This fully supports a scenario of outside-in removal of the ISM, where each component is affected differently, primarily depending on its radial distribution across the disc. As discussed below, this is a key element for our current picture of galaxy quenching, and for reconciling apparent contradictions within the literature.

4.3. The connection between cold gas stripping and star formation quenching

The evidence for cold gas stripping in clusters presented above may naively suggest that there is a one-to-one correlation between gas deficiency and star formation quenching. As we discuss in this section, the situation is slightly more complicated.

Due to the initial lack of CO observations, most of the early focus of the community has been on the link between Hi deficiency and star formation quenching. From the early work by Kennicutt (Reference Kennicutt1983a), and since then gradually confirmed with better data and larger samples (Gavazzi et al. Reference Gavazzi, Boselli, Pedotti, Gallazzi and Carrasco2002, Reference Gavazzi, Boselli, Cortese, Arosio, Gallazzi, Pedotti and Carrasco2006, Reference Gavazzi, Fumagalli, Fossati, Galardo, Grossetti, Boselli, Giovanelli and Haynes2013), it is now clear that satellite galaxies with at least a factor of $\sim$ 2–3 less Hi than expected from their size and morphology (i.e., $DEF_{\rm HI}\sim$ 0.3–0.5) have lower global SFRs than isolated systems. However, recent works have highlighted the presence of a significant population of Hi-deficient galaxies that still lie on the blue/main sequence of star-forming galaxies (Cortese & Hughes Reference Cortese and Hughes2009; Boselli et al. Reference Boselli, Cortese, Boquien, Boissier, Catinella, Lagos and Saintonge2014b). This nicely confirms what is seen for the molecular hydrogen component of the ISM: that is, as long as the environment is only able to affect the ISM outside the optical radius, its immediate effect ( $<$ 1Gyr) on star formation is minor or negligible. Indeed, for an outside-in gas removal scenario, those levels of Hi deficiency correspond to Hi discs affected up to one optical radius (see Figure 5).

Figure 8. Star-forming-to-optical (r-band) disc size ratio as a function of Hi deficiency. The panels show different SFR indicators and/or size estimates. Namely, from top to bottom: FUV isophotal and effective radii (Virgo cluster, Cortese et al. Reference Cortese2012a), H $\alpha$ effective radii (Virgo and Coma supercluster, Fossati et al. Reference Fossati2013), and 24 $\mu$ m effective radii (Local Cluster Survey, Finn et al. Reference Finn2018).

However, the clear proof of a direct connection between cold gas stripping and quenching of the star formation comes again from resolved studies. Particularly powerful have been narrow-band H $\alpha$ imaging surveys of nearby clusters of galaxies, which showed that the typical truncation of the gas disc in Hi-deficient galaxies is mirrored by a similar truncation in the SFR surface density profile. This field was pioneered by Koopmann & Kenney (Reference Koopmann and Kenney2004a,Reference Koopmann and Kenneyb) and Koopmann, Haynes, & Catinella (Reference Koopmann, Haynes and Catinella2006), who surveyed a sample of 55 Virgo cluster galaxies, and showed that their star formation activity is primarily truncated in the outer parts, with the inner parts of the disc showing normal—or sometimes slightly enhanced—SFR surface densities. While, statistically, these results are consistent with active removal of the ISM, they stressed that the physical mechanisms at play might not be the same for all galaxies in their sample.

The existence of a strong correlation between Hi deficiency and extent of the SFR density profiles (normalised to the extent of the optical disc) has now been confirmed by several independent works looking at different clusters and using H $\alpha$ , ultraviolet emission or 24 $\mu$ m emission as SFR indicators (Rose et al. Reference Rose, Robertson, Miner and Levy2010; Cortese et al. Reference Cortese2012a; Fossati et al. Reference Fossati2013; Finn et al. Reference Finn2018). However, as shown in Figure 8, the strength of the correlation varies significantly depending on the star formation tracer used and, most importantly, on whether disc sizes are estimated using effective or isophotal radii. The latter generally provide tighter correlations, as a result of being more directly sensitive to variations in SFR surface density in the outer parts of the disc (see also Section 3.1).

It is important to remember that the extent of the star-forming disc alone provides limited information on the actual causes of quenching and cannot be blindly used to discriminate between active environmental stripping and simple cessation of infall of cold gas onto the disc. This is because a reduction of the extent of the star-forming disc can take place even without a change in the shape of the profile (i.e., by systematically reducing SFR across the entire disc, see e.g., Boselli et al. Reference Boselli, Boissier, Cortese, Gil de Paz, Seibert, Madore, Buat and Martin2006), whereas it is the change in shape and the clear presence of a ‘truncation radius’ that supports the stripping scenario. This is exemplified by the apparent contradiction in the interpretation of H $\alpha$ morphology of cluster galaxies between Koopmann & Kenney (Reference Koopmann and Kenney2004a,Reference Koopmann and Kenneyb), Moss, Whittle, & Pesce (Reference Moss, Whittle and Pesce1998) and Moss & Whittle (Reference Moss and Whittle2000) on the origin of quenching of the star formation. Both groups reported that, in clusters, star-forming discs are more compact than in the field, but while the latter interpreted this as due to funneling of gas into their centres, feeding star formation primarily in the inner regions, the former argued for a stripping scenario. It is the ability to characterise the radial variation of SFR surface densities across the disc that allowed this debate to be settled, in favour of the stripping scenario. This is something to keep in mind, as the advent of large integral field spectroscopy (IFS) surveys allows us to push these studies beyond the cluster environment (e.g., Schaefer et al. Reference Schaefer2017; see Section 5.3) and better isolate the physical mechanisms affecting the shape of SFR surface density profiles in satellites.

4.3.1. How quickly is star formation quenched following cold gas stripping?

The link between gas stripping and quenching has been further reinforced by the ability to time the star formation quenching in the regions of the disc where gas has been stripped. This approach was pioneered by Crowl & Kenney (Reference Crowl and Kenney2008), who combined Hi, H $\alpha$ , and ultraviolet imaging with resolved optical spectroscopy to determine how long ago star formation was quenched (i.e., the quenching time) just outside the Hi truncation radius for 10 Virgo cluster galaxies. Assuming nearly instantaneous quenching ( $\lesssim$ 50 Myr), they found that, for all galaxies with truncated star-forming discs, the ages of the stellar populations outside the truncation radius are consistent with quenching within the last 0.5 Gyr. Remarkably, these quenching times agree with the time since when the gas was stripped, as estimated independently by, e.g., Vollmer et al. (Reference Vollmer, Balkowski, Cayatte, van Driel and Huchtmeier2004) and Vollmer (Reference Vollmer2009) using N-body simulations that included the effect of ram pressure stripping. This suggests that quenching is indeed very fast, once the gas has been stripped, and that this happens primarily close to the pericentre of the orbit around the cluster, which coincides with the time of peak intensity of ram pressure.

These results have been corroborated by several independent works (e.g., Pappalardo et al. Reference Pappalardo, Lançon, Vollmer, Ocvirk, Boissier and Boselli2010; Boselli et al. Reference Boselli2016; Ciesla et al. Reference Ciesla2016; Fossati et al. Reference Fossati2018; Owers et al. Reference Owers2019), using different techniques, timescale definitions, and multiwavelength datasets, confirming that in galaxies infalling into a cluster star formation has been quenched relatively recently ( $\sim$ 0.5 Gyr ago) and on short timescales ( $\lesssim$ 100–200 Myr) after the cold ISM has been removed from the disc. These techniques generally require knowledge of the location of the Hi and/or SFR truncation radius (i.e., 2D resolved maps) and this is why it has so far been applied only to a relatively small number of galaxies.

Figure 9. The $g-i$ (top) and $NUV-i$ colour (bottom) versus stellar mass diagrams for the bulk of galaxies in the Crowl & Kenney (Reference Crowl and Kenney2008) sample. Points are colour-coded according to the time since quenching. Stellar masses and colours are taken from Boselli et al. (Reference Boselli2014d). Grey-scale and contours show the same relations for a volume-limited sample of nearby galaxies (0.02 $<z<$ 0.05) extracted from the SDSS, shown to guide the eye on the location of the blue cloud ( $g-i \lesssim 0.8$ , $NUV-i \lesssim 4$ ) and red sequence ( $g-i \gtrsim 1$ , $NUV-i \gtrsim 5.5$ ). The region between the two is usually referred to as ‘green valley’.

One important point to note is that most of these works assume that, while the outer parts of the discs are consistent with rapid quenching of star formation, the inner parts do not show significant signs of quenching and their stellar populations are not dissimilar from those of unperturbed galaxies. While the sharp truncation seen in both Hi and SFR profiles clearly shows that star formation outside and inside the truncation radius proceeds in a different way, it is still unclear if/how environment is able to affect the star formation cycle in the inner parts of galaxies. Is low-density gas stripped and star formation affected also in the inner parts of the disc? Or can environment compress the gas in the disc, thus increasing its star formation efficiency (e.g., Mok et al. Reference Mok, Wilson, Knapen, Sánchez-Gallego, Brinks and Rosolowsky2017)? This is something that only future resolved studies of statistical samples of cluster galaxies will be able to address.

Regardless, it should not be ignored that none of the galaxies analysed by Crowl & Kenney (Reference Crowl and Kenney2008) are fully quenched, as they lie either in the lower part of the main sequence or in the green valley (Cortese & Hughes Reference Cortese and Hughes2009). This is shown in Figure 9, where we plot the position of most of Crowl & Kenney (Reference Crowl and Kenney2008) sample on the $g-i$ (top) and $NUV-i$ (bottom) colour versus stellar mass diagrams. Galaxies are colour-coded by the time since star formation ceased in the stripped part of the disc. Even after $\sim$ 0.5 Gyr since quenching occurred beyond the truncation radius, these objects have total $NUV-i$ colours a couple of magnitudes bluer than red sequence objects, while their optical colours are in most cases already consistent with passive galaxies. This is most likely because, even at pericentre, environment is not strong enough to perturb the inner parts of the disc of these relatively massive galaxies ( $M_* >10^{9.5}$ M $_{\odot}$ ). Conversely, galaxies that quenched earlier appear to lie already on the optical red sequence. This is just a consequence of the fact that optical colours saturate, therefore galaxies with residual star formation (using ultraviolet indicators) might appear completely passive (Cortese Reference Cortese2012), and shows that optical colours should not be blindly used to time quenching.

While for high stellar mass galaxies full quenching may not occur by the first pericentre passage, it now seems established that, at low stellar masses ( $< 10^{9}\,\text{M}_{\odot}$ ), most satellites close to (or past) their first pericentre passage have been fully stripped of their Hi reservoir and completely quenched (Boselli et al. Reference Boselli, Boissier, Cortese and Gavazzi2008, Reference Boselli, Cortese, Boquien, Boissier, Catinella, Lagos and Saintonge2014b; Hester et al. Reference Hester2010). As we discuss in Sections 4.5 and 7, this is a fundamental difference in how massive and dwarf galaxies respond to cold gas stripping mechanisms.

4.3.2. When cold gas stripping triggers star formation

While in the long-term cold gas stripping always leads to local quenching, on short timescales, it is reasonable to wonder whether the high pressure exerted by the ICM on the ISM of satellite galaxies is able to compress the gas and trigger bursts of star formation. Indeed, several theoretical works predict that, under particular conditions (e.g., the right combination of galaxy mass, ISM properties, inclination, infalling velocity and density of the ICM, etc.), the mechanism responsible for the stripping can also briefly enhance (either locally or globally) the star formation (Bekki & Couch Reference Bekki and Couch2003; Bekki Reference Bekki2013; Kronberger et al. Reference Kronberger, Kapferer, Ferrari, Unterguggenberger and Schindler2008; Kapferer et al. Reference Kapferer, Sluka, Schindler, Ferrari and Ziegler2009; Roediger et al. Reference Roediger, Bruggen, Owers, Ebeling and Sun2014; Steyrleithner, Hensler, & Boselli Reference Steyrleithner, Hensler and Boselli2020). While cases of galaxies showing clear examples of bow shocks and asymmetries in their H $\alpha$ distributions (consistent with star formation triggered by ram pressure) have been known for decades (e.g., Gavazzi et al. Reference Gavazzi, Contursi, Carrasco, Boselli, Kennicutt, Scodeggio and Jaffe1995; Chanamé, Infante, & Reisenegger Reference Chanamé, Infante and Reisenegger2000) and recent studies have suggested that extreme environmental effects may dramatically increase the efficiency of Hi condensation into $\mathrm{H}_{2}$ (Moretti et al. Reference Moretti2020b), the importance of these effects on the enhancement of the global SFRs of galaxies is still unclear, and most likely less than a factor of $\sim$ 2 (Iglesias-Páramo et al. Reference Iglesias-Páramo, Boselli, Gavazzi and Zaccardo2004). This seems in line with recent IFS observations showing that, even in the most extreme cases of ram pressure stripping, the global SFR is enhanced on average by less than a factor of 2 (i.e., less than the typical scatter observed in the star-forming main sequence; e.g., Vulcani et al. Reference Vulcani2018; Roberts & Parker Reference Roberts and Parker2020). Of course, locally this enhancement could be larger, and the advent of large IFS surveys targeting clusters of galaxies should provide some definite quantification of environmentally-driven local bursts of star formation (e.g., Vulcani et al. Reference Vulcani2020).

Figure 10. Examples of galaxies where ionised gas and/or active star formation is observed in the stripped gas tail. Red and blue indicate ionised gas (primarily traced by the H $\alpha$ line) and star-forming regions (traced by ultraviolet or optical continuum emission), respectively. Images show galaxies in different clusters (starting from the top left in clockwise order): Abell 2667 (NASA, ESA, Jean-Paul KneibFootnote d, see also Cortese et al. Reference Cortese2007), Norma (NASA/ESA/STScI/M. Sun,Footnote e see also Jáchym et al. Reference Jáchym, Combes, Cortese, Sun and Kenney2014), Abell 957 and IIZw108 (ESO/GASP collaboration,Footnote f see also Poggianti et al. Reference Poggianti2017), Abell 2744Footnote g (see also Owers et al. Reference Owers, Couch and Nulsen2012), IC 3418 in Virgo (NASA/JPL-CaltechFootnote h see also Hester et al. Reference Hester2010), Coma (image reproduced with permission from Figure 4 in Yagi et al. Reference Yagi2010, copyright AAS), and NGC 4569 in Virgo (kindly provided by A. Boselli, see also Boselli et al. Reference Boselli2016).

An unexpected region where it is now clear that stripping can trigger star formation is in the wake of the gas tail removed from the disc, where turbulence can compress atomic hydrogen, allowing its condensation into molecules and the onset of star formation. The presence of CO emission associated with the tails supports this scenario (e.g., Jáchym et al. Reference Jáchym, Combes, Cortese, Sun and Kenney2014, Reference Jáchym2019). Galaxies with prominent tails of star-forming knots started to be discovered in the mid 2000s, with probably the first confirmed cases presented by Owen et al. (Reference Owen, Keel, Wang, Ledlow and Morrison2006) and Cortese et al. (Reference Cortese2007) in clusters at $z\sim0.2$ (although, as also noted below, evidence for extraplanar Hii regions co-located with stripped gas in cluster galaxies had been around for much longer, e.g., Kenney & Koopmann Reference Kenney and Koopmann1999).

Thanks to the improvement of optical and ultraviolet telescopes, the number of these objects (lately dubbed ‘jellyfish’ galaxies) has increased dramatically, and we now know of more than 100 cases of galaxies showing active star formation in their tails (see Figure 10; e.g., Sun, Donahue, & Voit Reference Sun, Donahue and Voit2007; Yoshida et al. Reference Yoshida2008; Smith et al. Reference Smith2010b; Hester et al. Reference Hester2010; Owers et al. Reference Owers, Couch and Nulsen2012; Fumagalli et al. Reference Fumagalli, Gavazzi, Scaramella and Franzetti2011; Ebeling, Stephenson, & Edge Reference Ebeling, Stephenson and Edge2014; McPartland et al. Reference McPartland, Ebeling, Roediger and Blumenthal2016; Poggianti et al. Reference Poggianti2019). The increased focus of the community on jellyfish galaxies has also been driven by the ‘GAs Stripping Phenomena in galaxies with MUSE’ (GASP, Poggianti et al. Reference Poggianti2017) survey, which is providing us with one of the most detailed views on the properties of ionised gas and star formation in this unique class of galaxies (e.g., Poggianti et al. Reference Poggianti2019; Bellhouse et al. Reference Bellhouse2019).

Interestingly, the increase in the number of satellite galaxies with star-forming tails, and ensuing popularity of the ‘jellyfish’ term, has led part of the community to label as such every system showing a hint of a tail of stripped material, regardless of whether this material is star-forming (as in the original definition) or not (e.g., Chung et al. Reference Chung, van Gorkom, Kenney, Crowl and Vollmer2009; Boselli et al. Reference Boselli2016, see also Figure 10). If one adopts this broader definition, then the first clear cases of jellyfish galaxies date back at least three decades, with the first detections of radio continuum tails in clusters (Gavazzi & Jaffe Reference Gavazzi and Jaffe1987; Gavazzi et al. Reference Gavazzi, Contursi, Carrasco, Boselli, Kennicutt, Scodeggio and Jaffe1995), and it is pretty safe to assume that every satellite galaxy in clusters will go through some kind of jellyfish phase during its evolution.Footnote i

However, it is still unclear what is the fraction of cases in which the stripped material ‘lights-up’ and forms stars in the wake of the tail. Indeed, the reason why some gas tails are able to light-up, while others do not is not completely understood. Numerical simulations point to a combination of infalling velocity, ISM density, and ICM density and temperature, with the confining pressure of the ICM surrounding the tail likely playing an important role (Tonnesen, Bryan, & Chen Reference Tonnesen, Bryan and Chen2011). However, there are still a lot of open questions regarding the complex and intertwined roles of turbulence, magnetic fields, and thermal conduction within the wakes (Tonnesen & Stone Reference Tonnesen and Stone2014; Vijayaraghavan & Sarazin Reference Vijayaraghavan and Sarazin2017). Multi-phase, high-resolution observations able to resolve individual giant molecular clouds, measure the properties of star-forming complexes in the tails, and trace magnetic fields (Müller et al. 2020) should help with making further progress in this area.

Lastly, it is important to note that, while triggered star formation in the stripped gas tail is expected to be mainly associated with ram pressure, this does not mean that ram pressure is the only mechanism helping to light up the tail. We now know of several examples where gravitational interactions may also play a role. Probably, the best, most generally overlooked example is represented by the Small Magellanic Cloud, whose UV tail is reminiscent of many jellyfish galaxies (see Figure 11), despite the fact that ram pressure is known to be not the only mechanism at play in this case (e.g., D’Onghia & Fox Reference D’Onghia and Fox2016).

Figure 11. A GALEX far- (blue) and near-ultraviolet (yellow) colour composite image of the Small Magellanic Cloud. The star-forming tail associated with the galaxy closely resembles that of some jellyfish galaxies in clusters. The holes in the inner parts are due to the lack of GALEX pointings for the galaxy centre. Similarly, the yellow colour of most of the main body is simply due to the lack of far-ultraviolet imaging. Credit: GALEX/NASA/JPL-Caltech.Footnote j

4.4 Star formation quenching timescales

As discussed in the previous section, all observational evidence presented so far supports a scenario in which, when cold gas is stripped from the disc, star formation in the stripped regions is fully quenched quickly (i.e., on timescales of a few hundreds of Myr or less). This is consistent with the predictions from theoretical modelling of ram pressure stripping, leading many to associate hydrodynamical effects with short full quenching timescales. However, as argued below, this assumption is plainly incorrect and, combined with the different definitions of quenching timescales presented in the literature, caused considerable confusion.

The estimate of the time needed by cluster satellites to leave the main sequence of star-forming systems does not require any information on their cold gas content, but primarily a quantification of their stellar ages and/or recent star formation history. Thus, studies focused on timing the quenching of star formation in satellites have been able to benefit, in the last two decades, from the large statistics provided by wide-area photometric and spectroscopic surveys such as the SDSS, inevitably detaching themselves from the approaches adopted in the detailed studies of the few clusters with cold gas information available. In these statistical studies, the goal is not to determine quenching timescales for individual galaxies (something generally challenging with just UV/optical broad-band integrated photometry anyway), but to statistically infer them by matching the predictions of cosmological models of structure formation with the average properties of satellite galaxies, such as their passive fraction, their specific SFR distribution, and/or their 3D position within the cluster (e.g., Balogh, Navarro, & Morris Reference Balogh, Navarro and Morris2000; Wetzel et al. Reference Wetzel, Tinker, Conroy and van den Bosch2013; Haines et al. Reference Haines2015; Oman & Hudson Reference Oman and Hudson2016; Rhee et al. Reference Rhee, Smith, Choi, Contini, Jung, Han and Yi2020; Oman et al. Reference Oman, Bahé, Healy, Hess, Hudson and Verheijen2020). The use of merger trees in a cosmological context is the key element that makes this technique orthogonal to the one applied to individual galaxies and described in previous sections.

In order to illustrate the different definitions of quenching timescales adopted in the literature, we refer to Figure 12, which schematically shows the evolution of the SFR with cosmic time for a galaxy, highlighting four key epochs in its evolution: that is, the time when it first becomes a satellite (i.e., crossing the virial radius of a host halo at $t_{1^{\rm st}\ {\rm infall}}$ ), the time when it is accreted into an even bigger halo, such as a cluster of galaxies (crossing the cluster virial radius at $t_{\rm cluster\ infall}$ ), the time when its SFR starts being quenched by the environment ( $t_q$ ) and when it becomes passive ( $t_{\rm passive}$ ). The present day is indicated as $ t_{\rm now}$ .

Figure 12. Cartoon illustrating various definitions of satellite quenching timescales found in the literature. The solid plus dashed line shows the expected star formation history for a galaxy with stellar mass $\sim 10^{9.5}\,\text{M}_{\odot}$ at $z\sim$ 1 that stays on the main sequence until $z=$ 0. Five key timescales are indicated: $t_{1^{\rm st}\ \text{infall}}$ is the time when the galaxy becomes a satellite; $t_{\text{cluster infall}}$ is the time of infall into its current host (assumed to be a cluster in this case); $t_{q}$ is the time when environment starts affecting the galaxy’s SFR; $t_{\text{passive}}$ is the time when the galaxy crosses the SFR or sSFR threshold adopted to separate active and passive systems. The red lines show how its SFR can be affected by the cluster environment, depending on whether $t_{q}$ corresponds to the time of first infall, to the time of cluster infall, or to some later time. Red and blue arrows show the relative different definitions of delay and quenching timescales, with the direction of the arrow giving an idea of how time is generally assumed to proceed in the timescale estimate.

Going back now to the quenching timescales estimated via matching to cosmological merger trees, in this case the clock starts when the galaxy becomes a satellite (either at first infall— $t_{q}=t_{1^{\rm st}\ {\rm infall}}$ —or when it crosses the virial radius of the current cluster host— $t_{q}=t_{\rm cluster\ infall}$ ) and increases with the amount of time spent in the cluster until the object becomes passive. More recently, Oman et al. (Reference Oman, Bahé, Healy, Hess, Hudson and Verheijen2020) introduced a variant in which the clock starts at the time when a satellite reaches its first pericentre passage through the cluster (not shown in the figure).

Conversely, for the technique based on individual galaxies, the timescale is generally measured from $z=0$ ( $t_{\rm now}$ ) to the time when star formation starts being affected by the environment and is expressed in terms of how long ago the galaxies started quenching. The additional complication here is that sometimes quenching is assumed to be instantaneous, and what is determined is how long ago star formation ceased, instead of a quenching timescale.

It is clear that, with such different assumptions, the two broad approaches can only agree under extremely rare circumstances, for example, if: a) quenching is not assumed to be instantaneous, and b) the time of infall corresponds to the time when environmental quenching starts, and c) the object crosses the threshold used to divide star-forming from quenched galaxies at the time of the observation (i.e., $t_{\rm passive}=t_{\rm now}$ ).

Interestingly, the first applications of this technique to SDSS observations of cluster satellites (e.g., Balogh et al. Reference Balogh, Navarro and Morris2000) assumed that quenching starts indeed at the time of first infall and motivated this choice by the fact that, in most semi-analytic models at that time, the primary mechanism for environmentally driven quenching was stripping of the hot halo gas reservoir, which started as soon as a galaxy became a satellite (see also § 8). Under these assumptions, despite significant differences in the technique used to estimate quenching timescales (e.g., definition of virial radius, threshold used to separate star-forming from passive galaxies, observations used to constrain the model), all studies reached the same general conclusion: it takes a few billion years (e.g., from $\sim$ 2 to $\sim$ 6 Gyr) for satellites to become passive since the time of their infall (e.g., von der Linden et al. 2010; Weinmann et al. Reference Weinmann and Kauffmann2010; De Lucia et al. Reference De Lucia, Weinmann, Poggianti, Aragón-Salamanca and Zaritsky2012; Wetzel et al. Reference Wetzel, Tinker, Conroy and van den Bosch2013; Hirschmann et al. Reference Hirschmann, De Lucia, Wilman, Weinmann, Iovino, Cucciati, Zibetti and Villalobos2014b; Oman & Hudson Reference Oman and Hudson2016).

Such long quenching timescales have always been assumed to be inconsistent with expectations from stripping mechanisms that directly affect the cold ISM in a star-forming disc. Instead, they are more in line with theoretical estimates based on starvation/strangulation, whereby quenching is caused by halting the infall of gas onto the disc.Footnote k Indeed, regardless of the uncertainties associated with the various techniques, these timescales are arguably much longer than what is observed in the clearest cases of ram pressure stripping. Thus, either the detailed studies of individual galaxies in Virgo provide us with a biased and non-representative view of the quenching pathway followed by satellite galaxies, or the basic assumption in the statistical estimates of quenching timescales (i.e., that quenching starts at time of infall and proceeds exponentially since then) is incorrect.

Starting from the work presented by Wetzel et al. (Reference Wetzel, Tinker, Conroy and van den Bosch2013), the refinement in the techniques used for the statistical estimate of quenching timescales suggests that the main quenching phase does not start at the time of infall but is significantly delayed (e.g., $\sim$ 2–6 Gyr; Haines et al. Reference Haines2015; Oman & Hudson Reference Oman and Hudson2016; Rhee et al. Reference Rhee, Smith, Choi, Contini, Jung, Han and Yi2020; Oman et al. Reference Oman, Bahé, Healy, Hess, Hudson and Verheijen2020), as the star formation in satellites is not immediately affected by the environment after infall (indicated in light blue in Figure 12). After this delay phase, quenching proceeds extremely fast, with satellites becoming passive in one billion year or less (the exact value being again heavily model-dependent). Such a delay phase does not imply that the environment is not affecting satellites, but that its effect on star formation is negligible. Indeed, Maier et al. (Reference Maier, Ziegler, Haines and Smith2019) find that star-forming cluster galaxies show a $\sim$ 0.1–0.2 dex enhancement in their oxygen abundance well before a decrease in their SFR. This supports a ‘slow-then-rapid’ quenching scenario, where the ISM content and/or metal enrichment is affected before the SFR starts decreasing (e.g., infall is stopped and metals are gradually less diluted; see also Section 5.3.2).

Regardless of whether star formation remains constant or drops mildly after infall, it seems now well established that the main quenching phase (i.e., when satellites leave the locus of the star-forming sequence) does not start at the time of infall, but closer to the first cluster pericentre passage. This is a key point that allows us to reconcile different estimates of quenching timescales and build a coherent picture of quenching in clusters of galaxies.

In the rest of this section, we show how tensions between long and short quenching timescales for Virgo cluster galaxies that are clearly affected by ram pressure stripping can be resolved. From the HRS sample, we select late-type (Sa or later types) galaxies with active star formation (as traced by the H $\alpha$ emission line; Boselli et al. Reference Boselli, Fossati, Gavazzi, Ciesla, Buat, Boissier and Hughes2015), with observations of both global Hi and molecular hydrogen content (as traced by the CO(1-0) transition line; Boselli et al. Reference Boselli, Cortese and Boquien2014a), and for which at least one of the two phases has been detected. We then focus on the Hi-deficient cluster members ( $DEF_{\rm HI}>$ 0.5; Cortese et al. Reference Cortese, Catinella, Boissier, Boselli and Heinis2011). By selection, this sample includes the bulk of Virgo galaxies for which quenching timescales have been directly estimated, all suggesting either instantaneous or fast (a few hundred Myr or less—e.g., Crowl & Kenney Reference Crowl and Kenney2008; Pappalardo et al. Reference Pappalardo, Lançon, Vollmer, Ocvirk, Boissier and Boselli2010; Boselli et al. Reference Boselli2016; Ciesla et al. Reference Ciesla2016; Fossati et al. Reference Fossati2018) quenching timescales.

In the top row of Figure 13, we compare the location of these galaxies (filled circles) with that of non Hi-deficient HRS late types (blue spiral symbols) on the total cold gas mass versus stellar mass (left panel) and SFR versus stellar mass (middle) diagrams. The total gas mass is the sum of atomic and molecular gas masses, including a 30% correction for helium. As in Figure 6, we also show the distribution of the xGASS-CO representative sample as a reference for nearby galaxies (grey shaded area). Unsurprisingly, Hi-deficient galaxies are also more passive (i.e., offset towards lower SFR at fixed stellar mass) than Hi-normal systems but, by selection, none of them have stopped forming stars completely. Only few have already crossed the threshold separating passive from active galaxies, here indicated by the red line as defined in Wetzel et al. (Reference Wetzel, Tinker, Conroy and van den Bosch2013).

Figure 13. Properties of Hi-deficient spiral galaxies in the Virgo cluster. In all plots, large symbols show HRS star-forming, spiral galaxies observed in both Hi and H₂ and for which at least one of the two phases has been detected, separated into Hi-deficient Virgo members ( $DEF_{\text{HI}}>$ 0.5; circles, colour-coded by specific SFR) and Hi-normal systems in the Virgo volume and in the field (dark and light blue spiral symbols, respectively). Top row. Stellar mass is plotted versus total cold gas mass (left), SFR (middle), and total gas depletion time (i.e., total gas mass-to-SFR; right); grey shaded regions show the corresponding distributions for the xGASS-CO sample (no morphological selection) as a reference. The red line in the middle panel indicates the threshold used by Wetzel et al. (Reference Wetzel, Tinker, Conroy and van den Bosch2013) to separate star-forming from passive galaxies. Bottom row. Position of Virgo galaxies on the projected phase-space diagram, which is split into five regions as proposed by Rhee et al. (Reference Rhee, Smith, Choi, Yi, Jaffé, Candlish and Sánchez-Jánssen2017); these roughly correspond to increasingly longer infall time (since crossing the virial radius) populations, from first infallers (cyan), to recent and intermediate ones (green, orange, and pink), to ancient infallers/virialised (red). For the latter four regions, we provide typical infall times for the ‘Recent Infallers’ population as defined in Rhee et al. (Reference Rhee, Smith, Choi, Yi, Jaffé, Candlish and Sánchez-Jánssen2017). Symbols are as in the top row.

The fact that some of these galaxies have short quenching timescales (e.g., $\lesssim$ 0.2–0.5 Gyr) is not at odds with them not being fully quenched. As already noted, estimates obtained for individual galaxies are either local timescales for complete quenching (i.e., where star formation has already stopped, e.g., Crowl & Kenney Reference Crowl and Kenney2008; Fossati et al. Reference Fossati2018) or times since star formation started to decrease, regardless of whether the galaxy is already fully quenched (e.g., Ciesla et al. Reference Ciesla2016; Boselli et al. Reference Boselli2016). Thus, it is clear that quick—even instantaneous—local (i.e., in the outer disc) quenching via stripping does not automatically imply rapid global quenching of the star formation. This is a key misconception that has led to confusion in the literature. The reason why these galaxies are still star-forming is simple: while they have already lost most of their cold gas reservoir in the outer parts of the disc, cold gas is still present in the inner parts, where star formation is still ongoing. Indeed, as shown in the top right panel of Figure 13, the cold gas global depletion times for these galaxies are not too dissimilar from those observed in main sequence star-forming galaxies, and at least a couple of billion years, without even considering gas recycling (see also Cortese & Hughes Reference Cortese and Hughes2009 and Boselli et al. Reference Boselli2014d). Thus, without any additional major stripping event, billions of years are needed for these galaxies to become fully passive, despite the fact that they were selected to be Hi-deficient.

The next step is to estimate how long ago these galaxies became satellites of the Virgo cluster. To do so, we take advantage of the approach developed by Rhee et al. (Reference Rhee, Smith, Choi, Yi, Jaffé, Candlish and Sánchez-Jánssen2017) and look at the position of our Hi-deficient sample on the Virgo phase-space diagramFootnote l, practically extending the analysis recently published by Yoon et al. (Reference Yoon, Chung, Smith and Jaffé2017). By using cosmological hydrodynamic N-body simulations of clusters of galaxies, Rhee et al. (Reference Rhee, Smith, Choi, Yi, Jaffé, Candlish and Sánchez-Jánssen2017) provide an easy statistical way to assign infall timescales to different galaxy populations according to their position on the projected phase-space diagram. This is divided into five different regions, based on the typical fractions and relative infall times of different satellite populations (namely, first infallers, recent infallers, intermediate infallers, and ancient infallers). First infallers have not yet crossed the virial radius for the most part, whereas the other classes are already cluster satellites with gradually increasing infall times.

In the bottom panel of Figure 13, we show the position of the Hi-deficient Virgo satellites in phase space, with the coloured boxes highlighting the regions defined by Rhee et al. (Reference Rhee, Smith, Choi, Yi, Jaffé, Candlish and Sánchez-Jánssen2017). By selection, almost all our galaxies are at least recent infallers (i.e., they are already Virgo cluster members) and occupy the three regions (green, orange, and pink) typical of galaxies that are still completing their first orbit into the cluster (i.e., either just before or after first pericentre passage), in agreement with the detailed dynamical modelling of Virgo galaxies by Vollmer (Reference Vollmer2009). There is a dearth of galaxies in the ‘fully-virialised’ zone at the centre of the cluster (red region). This is simply by selection, as we do not include passive (and thus most likely virialised) galaxies in these plots. It is interesting to note that, when moving from the green to the pink region, the specific SFRs of Hi-deficient galaxies tend to decrease from levels typical of the star-forming main sequence (cyan circles) to lower values (violet and purple circles), supporting the idea that less active galaxies have spent longer times in the cluster. According to Rhee et al. (Reference Rhee, Smith, Choi, Yi, Jaffé, Candlish and Sánchez-Jánssen2017), galaxies in these regions have an 80% likelihood to have crossed the cluster virial radius at the very least $\sim$ 1–1.5 Gyr ago (i.e., the average value for ‘recent infallers’ varies between $\sim$ 1.6 and 2.3 Gyr, see bottom panel of Figure 13), consistently with the typical expectation that it takes $\sim$ 1 Gyr for a satellite to get from the virial radius to first pericentre (e.g., Lotz et al. Reference Lotz, Remus, Dolag, Biviano and Burkert2019). Intriguingly, the picture emerging from this exercise is qualitatively consistent with recent work by Oman et al. (Reference Oman, Bahé, Healy, Hess, Hudson and Verheijen2020), who combined numerical simulations, SDSS optical data, and ALFALFA Hi observations to revisit the connection between Hi stripping and full star formation quenching.

In summary, we have shown that the bulk of the Virgo Hi-deficient late-type galaxies with residual gas reservoir and star formation in their disc are consistent with stripping of cold (atomic) hydrogen by the cluster environment, they have been cluster satellites for at least 1 Gyr and have enough cold gas to keep forming stars (at the current rate) for at least another couple of billion years. Thus, if we had started the clock at the time of infall into the cluster, we would infer quenching timescales that are significantly longer than what one might expect from a simple ram pressure stripping scenario. In other words, while still a useful quantity, the global quenching timescale provides us with limited information on the physical process(es) responsible for halting star formation in satellite galaxies.

4.5. Drawing a coherent picture of the quenching of cluster satellites at z ∼ 0

Having reconciled the apparent tension between different estimates of quenching timescales, showing that observations of fast ‘local’ stripping are not in contradiction with claims of full quenching timescales of a few Gyr since infall, we can now combine all the evidence summarised above into a coherent picture of the typical pathway to quenching followed by cluster satellite galaxies. For simplicity, here we focus on the simple case of a galaxy becoming satellite for the first time when entering the cluster. We discuss how pre-processing might alter this picture in Section 6, after reviewing the role of cold gas stripping in the quenching of group satellites in Section 5.

First infall. After entering the cluster halo, it takes some time for the star-forming disc to feel the effect of the environment, and star formation does not drop immediately after crossing the virial radius. It is still unclear if gas accretion onto the disc remains active for some time after infall or if it stops immediately.

Approaching pericentre. The first major quenching phase starts only when active stripping of the cold ISM becomes efficient at least in the outer parts of the disc, which generally coincides with a few hundred Myr before pericentre passage. Stripping happens predominantly outside-in, perturbing first the outer parts of the disc that are less bound to the galaxy. While the primary mechanism at play seems to be hydrodynamical, in some cases gravitational interactions and/or internal mechanisms, such as feedback from supernovae or AGN, could increase the stripping efficiency (see e.g., Section 4.1). How far stripping gets inside the optical disc during the first pericentre passage likely depends on the properties of both satellite (e.g., its mass, orbit, ISM properties, etc) and cluster (e.g., ICM density, dynamical state, etc), though we are still missing a detailed characterisation of the physical parameters that determine the gas truncation radius. Moreover, parts of the ISM might be affected by the environment even inside the truncation radius, but testing this requires observations of the inner parts of the cold gas disc of satellite galaxies at kpc or sub-kpc spatial resolution.

Mass-dependent quenching. At least for a Virgo-like cluster, it appears that, to first order, low-mass galaxies ( $M_{*}<10^{9}\,\text{M}_{\odot}$ ) can be fully stripped at first pericentre (e.g., Boselli et al. Reference Boselli, Boissier, Cortese and Gavazzi2008), but massive systems ( $M_{*}>$ 10¹⁰ M $_{\odot}$ ) are not, as a significant fraction of their gas reservoir survives in the inner parts of the disc and keeps feeding star formation. This implies that, for massive galaxies, full quenching takes place significantly after the first pericentre passage and that ram pressure stripping alone is likely not enough to explain the properties of passive satellites. This also appears to be consistent with the presence of small molecular gas reservoirs in the inner parts of early-type galaxies in clusters (e.g., Young et al. Reference Young2011; Davis et al. Reference Davis2013). Admittedly, what happens to a galaxy’s remaining gas after pericentric passage is one of the most important missing pieces to the quenching puzzle. While environmental effects may still be playing a role, it is possible that the remaining gas is to a large extent exhausted internally via star formation or expelled/heated by feedback.

We note that a scenario in which low-mass satellites are quenched faster than higher mass ones may appear in contradiction with some claims of longer quenching timescales for low-mass systems (e.g., Wetzel et al. Reference Wetzel, Tinker, Conroy and van den Bosch2013, see also Section 5.4). However, this is again a matter of quenching timescale definitions. First, if the clock starts at time of first infall, it is natural that low-mass galaxies will take longer to be quenched as, on average, they spend longer in smaller groups before infalling into a cluster (De Lucia et al. Reference De Lucia, Weinmann, Poggianti, Aragón-Salamanca and Zaritsky2012). Second, the use of a simple threshold in specific SFR to separate passive and active galaxies may introduce systematic effects in the estimate of quenching timescales (e.g., Pasquali et al. Reference Pasquali, Smith, Gallazzi, De Lucia, Zibetti, Hirschmann and Yi2019; Rhee et al. Reference Rhee, Smith, Choi, Contini, Jung, Han and Yi2020). Indeed, even on the star-forming main sequence, high-mass galaxies have lower specific SFRs than low-mass ones. As such, once star formation stops, their specific SFR will reach any fixed threshold sooner than lower mass systems, even if the rate of quenching is the same. Indeed, when individual star formation histories are examined, both observations and simulations seem to agree that low-mass galaxies are quenched more rapidly (e.g., Pasquali et al. Reference Pasquali, Smith, Gallazzi, De Lucia, Zibetti, Hirschmann and Yi2019; Lotz et al. Reference Lotz, Remus, Dolag, Biviano and Burkert2019; Smith et al. Reference Smith, Pacifici, Pasquali and Calderón-Castillo2019).

Is stripping of cold ISM from the disc sufficient to halt star formation? The availability of cold gas in the inner part of massive discs that continues to feed star formation implies that, at high masses, direct stripping of the cold ISM from the disc of satellite galaxies is a necessary but not always sufficient condition to halt star formation. At face value, this means that neither the stripping of the cold ISM (e.g., ram pressure) nor the cessation of infall (e.g., starvation) alone is sufficient to explain the quenching of massive galaxies in clusters, but that both are required: environmental effects strip part of the cold gas and are responsible for stopping the infall of gas, but gas consumption via star formation likely affects the inner parts of the disc, where environment is less effective. In addition, it is possible that feedback may further contribute to emptying the inner cold gas reservoir of galaxies (see also Section 8). This highlights, once more, how inadequate it would be to invoke one single mechanism as the sole responsible for star formation quenching.

Figure 14. Examples of Hi stripping in galaxy groups. In all panels, Hi emission (in orange, blue, or white contours) is superposed on optical colour images. The images show the Vela group (a; from Figure 1 in English et al. Reference English, Koribalski, Bland-Hawthorn, Freeman and McCain2010), the galaxy group IC1459 (b; from Figure 6 in Serra et al. Reference Serra2015), the FGC1287 triplet (c; from Figure 1 in Scott et al. Reference Scott, Cortese, Brinks, Bravo-Alfaro, Auld and Minchin2012), the M81/M82 group (d; from Figure 6 in de Blok et al. Reference de Blok2018), and the Leo ring (e; from Figure 1 in Michel-Dansac et al. Reference Michel-Dansac2010). All images are reproduced with permission. Copyright by AAS or the authors.

5.1. Hi stripping in groups

Intriguingly, the first evidence for stripping of cold atomic hydrogen in groups emerged before that for clusters of galaxies. Since the first interferometric observations of the Magellanic Clouds (Kerr, Hindman, & Robinson Reference Kerr, Hindman and Robinson1954; Hindman, Kerr, & McGee Reference Hindman, Kerr and McGee1963), and of pairs and group galaxies in our nearest neighborhoods (Roberts Reference Roberts1968; Rots Reference Rots1975), it was clear that environment can directly remove Hi and create striking trails and streams. As showcased in Figure 14, we currently have a plethora of examples of Hi stripping in groups, with most of the evidence pointing towards gravitational interactions as primarily responsible for creating these features (e.g., Yun, Ho, & Lo Reference Yun, Ho and Lo1994; Hibbard et al. Reference Hibbard, van Gorkom, Rupen and Schiminovich2001; Williams, Yun, & Verdes-Montenegro Reference Williams, Yun and Verdes-Montenegro2002; Koribalski, Gordon, & Jones Reference Koribalski, Gordon and Jones2003; Kantharia et al. Reference Kantharia, Ananthakrishnan, Nityananda and Hota2005; English et al. Reference English, Koribalski, Bland-Hawthorn, Freeman and McCain2010; Michel-Dansac et al. Reference Michel-Dansac2010; Serra et al. Reference Serra2013, Reference Serra2015; Leisman et al. Reference Leisman, Haynes, Giovanelli, Józsa, Adams and Hess2016; Hess et al. Reference Hess, Cluver, Yahya, Leisman, Serra, Lucero, Passmoor and Carignan2017; de Blok et al. Reference de Blok2018; Lee-Waddell et al. Reference Lee-Waddell2019). This is due to the fact that, in most cases, stellar tidal features and/or peculiar optical morphologies are also clearly visible in these systems, suggesting a prominent role of tidal forces in affecting both their gas and stellar distributions.

However, one fundamental difference between the evidence for direct stripping in group versus cluster environment is that the vast majority of the galaxies in groups for which Hi streams and tails have been detected are still actively star-forming and not Hi-deficient (regardless of the exact definition of deficiency). This is primarily a selection effect, because interferometric observations of groups very rarely probe the Hi-poor regime, and thus preferentially pick gas-rich (or gas-normal) systems, whose outer gas discs are easily perturbed by the gravitational pull from other group members. Moreover, given the mild level of stripping, in some cases it is unclear how much of the displaced gas is no longer bound to the galaxy and will not ‘rain down’ onto the disc (or accrete onto another satellite), as we know of at least a few examples where this seems to be the case (e.g., Hibbard & Mihos Reference Hibbard and Mihos1995; Struck & Smith Reference Struck and Smith2003; Koribalski & Dickey Reference Koribalski and Dickey2004). Thus, these might not be examples of a direct link between stripping and quenching in groups. Access to the critical gas-poor regime is still primarily limited to single-dish telescopes, at the cost of losing spatial information. Even so, in the past few decades, a consistent picture is starting to emerge from Hi studies.

Since the late 20th century, there have been claims of the presence of Hi-deficient galaxies in loose or compact groups (e.g., Gerin & Casoli Reference Gerin and Casoli1994; Huchtmeier Reference Huchtmeier1997; Verdes-Montenegro et al. Reference Verdes-Montenegro, Yun, Williams, Huchtmeier, Del Olmo and Perea2001), but the installation of the multibeam receiver on the 64-m Parkes telescope and the HIPASS Hi-blind survey made large statistical studies more feasible, allowing us to quantify the Hi content of galaxies in different types of groups (e.g., Hickson Reference Hickson1982 compact groups, loose groups, X-ray selected groups, etc.; Stevens et al. Reference Stevens, Webster, Barnes, Pisano and Drinkwater2004; Omar & Dwarakanath Reference Omar and Dwarakanath2005; Sengupta & Balasubramanyam Reference Sengupta and Balasubramanyam2006; Kilborn et al. Reference Kilborn, Forbes, Barnes, Koribalski, Brough and Kern2009). The vast majority of these works found evidence for Hi-deficient galaxies in groups (but see e.g., Stevens et al. Reference Stevens, Webster, Barnes, Pisano and Drinkwater2004 for an opposite view), suggesting that, even in halos smaller than those of clusters, environmental processes are able to remove a significant fraction of the cold ISM from star-forming discs. Although different definitions of Hi deficiency (see Section 3) make quantitative comparisons difficult, all major statistical studies (Verdes-Montenegro et al. Reference Verdes-Montenegro, Yun, Williams, Huchtmeier, Del Olmo and Perea2001; Sengupta & Balasubramanyam Reference Sengupta and Balasubramanyam2006; Kilborn et al. Reference Kilborn, Forbes, Barnes, Koribalski, Brough and Kern2009) agree that Hi-deficient galaxies are preferentially found in X-ray bright groups and that, while Hi-poor galaxies are more common in the inner parts of groups, there is no strong correlation between gas content and distance from the centre of the group. This is not entirely surprising, given that such a correlation is weak even in clusters, as well as strongly affected by projections effects.

Interestingly, while both Verdes-Montenegro et al. (Reference Verdes-Montenegro, Yun, Williams, Huchtmeier, Del Olmo and Perea2001) and Kilborn et al. (Reference Kilborn, Forbes, Barnes, Koribalski, Brough and Kern2009) support gravitational interactions as the primary driver for Hi deficiency in groups, Sengupta, Balasubramanyam, & Dwarakanath (Reference Sengupta, Balasubramanyam and Dwarakanath2007) show that the Hi morphology of gas-deficient galaxies is similar to that observed in clusters and propose a scenario in which hydrodynamical mechanisms such as ram pressure may play an important role in removing cold gas from the disc. Similarly, Rasmussen, Ponman, & Mulchaey (Reference Rasmussen, Ponman and Mulchaey2006), Rasmussen et al. (Reference Rasmussen, Ponman, Verdes-Montenegro, Yun and Borthakur2008, Reference Rasmussen2012) claim that ram pressure is needed to explain the Hi properties of group galaxies, although it may not always be the dominant stripping mechanism.

At the same time, a similar picture emerged from studies of the Local Group, which showed a dramatic transition between gas-rich and gas-poor satellites across the virial radius of the Milky Way (Grebel, Gallagher, & Harbeck Reference Grebel, Gallagher John and Harbeck2003; Grcevich & Putman Reference Grcevich and Putman2009; Spekkens et al. Reference Spekkens, Urbancic, Mason, Willman and Aguirre2014; Westmeier et al. Reference Westmeier, Staveley-Smith, Calabretta, Jurek, Koribalski, Meyer, Popping and Wong2015; Putman et al. Reference Putman, Zheng, Price-Whelan, Grcevich, Johnson, Tollerud and Peek2021), with very little or no Hi found in satellites inside the virial radius. This was shown to be consistent with the expectation for ram pressure stripping by the Milky Way halo, although it is possible that gravitational interactions, supernova winds, and heating by the cosmic ultraviolet background could contribute by increasing the stripping efficiency (e.g., Mayer et al. Reference Mayer, Kazantzidis, Mastropietro and Wadsley2007; Kazantzidis et al. Reference Kazantzidis, Mayer, Callegari, Dotti and Moustakas2017).

More recently, the advent of deep targeted Hi surveys such as xGASS and the REsolved Spectroscopy Of a Local VolumE (RESOLVE) atomic gas survey (Stark et al. Reference Stark2016), along with the second-generation Hi-blind ALFALFA survey, have made it possible to extend studies of atomic hydrogen in groups to significantly larger samples and take advantage of the overlap with wide-area optical surveys such as SDSS. Perhaps the first evidence supporting the idea that Hi deficiency may be widespread in groups across a wide range of halo masses came from GASS (Catinella et al. Reference Catinella2013), a representative sample of $\sim$ 800 galaxies with stellar masses greater than $10^{10}\,\text{M}_{\odot}$ , limited an Hi-to-stellar mass fraction of $\sim$ 1.5%, which was later extended to smaller stellar masses (xGASS). Catinella et al. (Reference Catinella2013) showed that satellites in groups have significantly lower gas content than central galaxies of the same stellar mass and/or stellar mass surface density. Similar results were found by Stark et al. (Reference Stark2016) using RESOLVE, a targeted Hi survey designed to be baryonic (i.e., stellar plus atomic hydrogen) mass limited, as opposed to stellar mass selected as GASS/xGASS. Intriguingly, as shown in Figure 15 (left), the agreement between RESOLVE and xGASS is also quantitative, as both surveys provide a consistent view of the decrease of gas fraction at fixed halo mass from low- to high-mass groups. Unfortunately, most of the satellite population in large groups is still not detected even in these deep surveys, making it difficult to gain insights into the physical drivers of the observed trends.

Figure 15. The Hi-to-stellar mass ratio versus stellar mass relation for satellite galaxies as a function of mass of their host group halo. Results from targeted single-dish Hi surveys are shown in the left and middle panel, with circles and pentagons indicating xGASS (Catinella et al. Reference Catinella2018) and RESOLVE (Stark et al. Reference Stark2016), respectively. Colours correspond to different halo masses (as noted on the top-right corner of each panel), with arrows indicating bins dominated by upper limits. Only bins with at least 10 galaxies are shown. While the left panel shows medians values, the middle panel shows linear averages in each bin. The right panel shows the same plot obtained by Brown et al. (Reference Brown2017) via stacking of ALFALFA galaxies. By construction, this technique only provides linear averages and cannot be blindly compared with median scaling relations.

Similarly, works based on galaxies detected by ALFALFA (Hess & Wilcots Reference Hess and Wilcots2013; Yoon & Rosenberg Reference Yoon and Rosenberg2015; Odekon et al. Reference Odekon2016) found that the fraction of Hi-detected systems gradually decreases towards the centre of groups, with the effect being stronger in more massive halos. However, as also pointed out by Yoon & Rosenberg (Reference Yoon and Rosenberg2015), environmental studies based on Hi detections alone have limited informative power apart from simply confirming the presence of a morphology–density relation, thus providing little evidence for the presence of stripping and any links with star formation quenching.

The real breakthrough in this field came from spectral stacking, a technique used to constrain the statistical properties of a population of galaxies that lack individual detections in a survey. When applied to an Hi-blind survey, spectral stacking is a powerful tool to reach sensitivities well below the nominal one, provided that independent redshift measurements are available for large numbers of galaxies in the survey’s sky footprint. Briefly, this requires to extract individual Hi spectra at the known positions of the galaxies (regardless of whether these are formally detected or not), align in redshift and co-add (or stack)—the spectrum thus obtained gives an estimate of the total and average Hi content of the sample that was co-added. By binning galaxies according to a given property (e.g., stellar mass, colour, morphology, etc.) and stacking the corresponding Hi spectra in each bin, it is possible to study gas scaling relations (e.g., Fabello et al. Reference Fabello, Catinella, Giovanelli, Kauffmann, Haynes, Heckman and Schiminovich2011, Reference Fabello, Kauffmann, Catinella, Li, Giovanelli and Haynes2012; Geréb, Morganti, & Oosterloo Reference Geréb, Morganti and Oosterloo2014; Brown et al. Reference Brown, Catinella, Cortese, Kilborn, Haynes and Giovanelli2015, Reference Brown2017; Healy et al. Reference Healy, Blyth, Elson, van Driel, Butcher, Schneider, Lehnert and Minchin2019; Guo et al. Reference Guo, Jones, Haynes and Fu2020; Hu et al. Reference Hu, Catinella, Cortese, Staveley-Smith and Lagos2020).

Naturally, the gain in sensitivity afforded by spectral stacking comes at a cost, in terms of two important drawbacks. First, we only know the average Hi content of the population that was co-added, and nothing about its dispersion (although the scatter of a relation can be explored by binning according to multiple properties simultaneously, if the sample is large enough). Second, stacking is an intrinsically linear operation, thus only provides linear averages. This is in contrast to scaling relations based on targeted observations, which are typically presented in terms of medians or logarithmic averages (reflecting the fact that almost all galaxy properties follow a log-normal distribution). This is illustrated in Figure 15, where we show both medians and linear averages for xGASS and RESOLVE: the two averaging techniques do not provide the same answer, hence one cannot blindly compare results from targeted observations (left panel) with stacking (right panel), or even values for single galaxies with averages derived from stacking. This means that the power of spectral stacking for scaling relations lies in the determination of relative offsets between various samples or subsets, and that care must be taken when comparing scaling relations (and their detailed shape) from stacking with ones based on targeted observations and/or predictions from theoretical models.

Despite its limitations, stacking has provided us with the strongest observational evidence supporting cold gas stripping in groups. Fabello et al. (Reference Fabello, Kauffmann, Catinella, Li, Giovanelli and Haynes2012) first applied this technique to a sample of $\sim 5\,000$ galaxies with stellar mass $M_*>10^{10}$ M $_{\odot}$ and redshift $0.025<z<0.05$ , extracted from the overlap between ALFALFA and SDSS surveys. They found that, for galaxies with $M_*<10^{10.5}$ M $_{\odot}$ , the Hi-to-stellar mass ratio decreases with increasing local environmental density faster than the specific SFR, suggesting that galaxies first lose their cold gas and then have their star formation reduced. They interpreted this result as evidence for outside-in gas stripping/star formation quenching, favouring a scenario in which hydrodynamical mechanisms like those observed in clusters of galaxies play a role even in groups with halo masses down to $\sim 10^{13}\,\text{M}_{\odot}$ .

This work was further extended by Brown et al. (Reference Brown2017), who stacked the ALFALFA Hi spectra of $\sim 10\,600 $ satellite galaxies extracted from the SDSS-based group catalogue of Yang, Mo, & van den Bosch (Reference Yang, Mo and van den Bosch2009) to quantify the variation of Hi content as a function of halo mass and galaxy-projected density. They confirmed that at fixed stellar mass, or stellar mass surface density, or specific SFR, the Hi-to-stellar mass ratio of satellites monotonically decreases when moving from low to high halo masses and/or projected galaxy densities (Figure 15, right panel). Incidentally, the fact that similar trends are present at fixed specific SFR or stellar surface density (a proxy for morphology) implies that the results shown in Figure 15 are not simply a consequence of the well-known morphology/star formation rate–density relation (i.e., the fact that, at fixed stellar mass, groups have a higher fraction of gas-poorer, early-type galaxies than the field).

Very interestingly, the large number statistics allowed Brown et al. (Reference Brown2017) to go one step further and look for variations in Hi content as a function of environment and more than one galaxy property at the same time. First, they showed that Hi content decreases from small to larger halos even when controlling for both mass and SFR, which confirms that their findings are genuinely tracing environmentally-driven gas removal. They interpreted this trend as evidence that Hi is removed without any strong effects on star formation over timescales of $<$ 1 Gyr. They also showed that the decrease in Hi content depends more strongly on halo mass than local density, suggesting that the physical mechanism at work is more closely related to the size of the halo, rather than the galaxy distribution within it—again favouring active outside-in stripping, most likely by ram pressure, initiating the quenching phase of satellite galaxies.

It is important to note that, while qualitatively the results of the ALFALFA stacking agree with linear averages from xGASS and RESOLVE, there are still systematic differences, as clearly seen by comparing the middle and right panels of Figure 15. While the origin of such differences is still unclear, this highlights how more work in this area is much needed.

In summary, we have now plenty of evidence that cold Hi stripping is ubiquitous also in the group environment, although the degree of Hi deficiency is on average significantly lower than in clusters. However, the physical mechanism responsible for the removal of the gas remains unclear. Historically, gravitational interactions were the preferred option, as the dramatic effect of galaxy–galaxy encounters on the Hi distribution is very easy to spot in groups. In recent years, though, the popularity of hydrodynamical mechanisms as a cause for Hi stripping in groups has been increasing. But should we really expect ram pressure to be efficient in the group environment?

5.2. Is ram pressure efficient in the group environment?

Unlike in galaxy clusters, the observational evidence in support of ram pressure playing a significant role in groups is, arguably, circumstantial. The higher frequency of optically disturbed systems (highlighting the importance of gravitational interactions), combined with the lack of large samples of highly Hi-deficient galaxies, prompted the question of whether the interaction with the intra-group medium is strong enough to strip any gas from the satellites, in particular in groups without an IGM component detected in X-rays.

As mentioned above, perhaps the best case of ram pressure-driven gas deficiency in groups is our Local Group, where the lack of Hi detections in any of the dwarf satellites within the virial radius of the Milky Way is fully consistent with the predictions from a simple ram pressure stripping model (e.g., Gatto et al. Reference Gatto, Fraternali, Read, Marinacci, Lux and Walch2013; Spekkens et al. Reference Spekkens, Urbancic, Mason, Willman and Aguirre2014; Caproni et al. Reference Caproni, Amaral Lanfranchi, Campos Baio, Kowal and Falceta-Gonçalves2017). This indicates that, for dwarf galaxies, ram pressure can be efficient even for IGM densities of $\sim$ 1–2 $\times$ 10^–4 cm^–3, as expected for the corona of the Milky Way. This also seems to be consistent with the presence of Hi tails seen in isolated Local Group dwarf galaxies (e.g., McConnachie et al. Reference McConnachie, Venn, Irwin, Young and Geehan2007). Outside the Local Group, similar or even lower IGM densities have been shown to be sufficient to explain the Hi asymmetries and/or kinematic disturbances observed in group galaxies (e.g., Bureau & Carignan Reference Bureau and Carignan2002; Bernard et al. Reference Bernard2010; Westmeier, Braun, & Koribalski Reference Westmeier, Braun and Koribalski2011; Elagali et al. Reference Elagali2019), but admittedly it is not clear if ram pressure is powerful enough to reproduce the observed trends between Hi gas fractions and group halo mass.

The lack of an X-ray emitting IGM in many groups with clear signs of gas stripping has been commonly used to argue against ram pressure stripping (e.g., Scott et al. Reference Scott, Cortese, Brinks, Bravo-Alfaro, Auld and Minchin2012), on the basis that they are thought to lack a dense medium that could provide enough ram pressure to remove cold ISM from star-forming discs. However, this is definitely not the case. Indeed, individual groups with halo mass smaller than $\sim 10^{13}\,\text{M}_{\odot}$ are still partially out of reach of current X-ray missions (e.g., Mulchaey Reference Mulchaey2000; Finoguenov et al. Reference Finoguenov2009; Miniati et al. Reference Miniati, Finoguenov, Silverman, Carollo, Cibinel, Lilly and Schawinski2016) and can also host dense IGM at lower temperatures (e.g., 10^5-6 K) than larger groups and clusters. Interestingly, indirect proof of the presence of a significant IGM component in X-ray faint groups comes from the work of Freeland & Wilcots (Reference Freeland and Wilcots2011), who looked for bent-double radio sources in groups and estimated the density of the IGM, under the assumption that the radio jets are bent by ram pressure (see also the X-ray stacking results of Anderson, Bregman, & Dai Reference Anderson, Bregman and Dai2013; Anderson et al. Reference Anderson, Gaspari, White, Wang and Dai2015). They probed projected group distances between $\sim$ 20 kpc and 2 Mpc and targeted groups with velocity dispersions between 250 and 570 km s^–1, finding clear evidence for a significant IGM even at large group-centric distances, with volume densities between 3 $\times 10^{-3}$ and 2 $\times 10^{-4}$ cm^–3—that is, a factor of $\sim$ 1–10 lower than the typical density observed in the centre of clusters such as Virgo and Coma (e.g. Boselli & Gavazzi Reference Boselli and Gavazzi2006). While maybe not enough to fully strip a Milky Way-size galaxy in a group, these densities should be sufficient to remove the outer parts of the Hi disc, as well as a significant fraction of the gas reservoir of dwarf galaxies. To show this, we rewrite the standard Gunn & Gott (Reference Gunn and Gott1972) formalism for ram pressure ( $\rho v^{2} \geq 2\pi G \Sigma_{g} \Sigma_{s}$ , where $\rho$ is the volume density of the IGM, v is the orbital velocity of the galaxy, G is the gravitational constant, and $\Sigma_{g}$ , $\Sigma_{s}$ are the surface densities of gas and stars) by rescaling it to the conditions typical of the outer disc of a galaxy in a group:

(6) \begin{equation}\small\frac{\rho [\rm cm^{-3}]}{5\times10^{-4}} \left(\frac{v[\rm km\ s^{-1}]}{250}\right)^{2}\geq 0.88 \frac{\Sigma_{g}[\rm M_{\odot}\ pc^{-2}]}{5} \frac{\Sigma_{s}[\rm M_{\odot}\ pc^{-2}]}{5}.\end{equation}

It is clear that, for surface densities typically observed at a galaxy’s optical radius (e.g., Leroy et al. Reference Leroy, Walter, Brinks, Bigiel, de Blok, Madore and Thornley2008; Sánchez Almeida Reference Sánchez Almeida2020), ram pressure can be strong enough, even for IGM densities a factor of a few smaller and orbital velocities five times slower than for galaxies passing through the centre of massive clusters (see also the modelling presented by Hester Reference Hester2006 and Köppen et al. Reference Köppen, Jáchym, Taylor and Palouš2018).

In summary, Hi stripping by hydrodynamical processes such as ram pressure can be a viable scenario to explain the Hi properties of group galaxies and should not be dismissed simply based on a lack of an X-ray emitting IGM. However, even more than in clusters of galaxies, multiple physical mechanisms are likely playing a significant role in removing cold gas from the disc, and it is plausible that the primary mechanism responsible varies depending on the properties of the individual group and its satellites. Nevertheless, as discussed so far, it is clear that direct stripping of the cold ISM from the disc is widespread even in groups. So, the next step is to determine whether stripping is physically linked, or even driving, the quenching of star formation in group satellite galaxies.

5.3. Does cold gas stripping cause star formation quenching in groups?

The limited amount of Hi observations available for groups, combined with the lower efficiency of stripping, makes it more challenging to obtain direct observational proof of a tight connection between cold gas stripping and quenching. As will soon become clear in this section, this issue is made even worse by the lack of adequate molecular hydrogen information and resolved studies of star formation activity for large statistical samples of group galaxies. Thus, in addition to considering $\mathrm{H}_{2}$ and SFR properties of satellites in groups (as we did for galaxy clusters in Section 4), we are forced to resort to more indirect tracers, such as gas and stellar metallicities, in order to tease out the impact of environmental effects on the star formation cycle of galaxies in groups, and establish a connection between Hi gas stripping and quenching.

5.3.1. Molecular hydrogen in groups

Molecular hydrogen investigations for representative samples of satellite galaxies in groups are almost non-existent. So far, CO observations have primarily focused on pre-selected samples of Hickson/compact groups. In these environments, molecular hydrogen appears significantly less affected (if at all) than atomic hydrogen, cases of $\mathrm{H}_{2}$ deficiency are rare, and star formation efficiency appears to be the same as observed in isolated systems (e.g. Lisenfeld et al. Reference Lisenfeld, Appleton, Cluver, Guillard, Alatalo and Ogle2014, Reference Lisenfeld, Alatalo, Zucker, Appleton, Gallagher, Guillard and Johnson2017; Martinez-Badenes et al. Reference Martinez-Badenes, Lisenfeld, Espada, Verdes-Montenegro, García-Burillo, Leon, Sulentic and Yun2012). In some cases, galaxies whose star formation has already been significantly reduced show significant $\mathrm{H}_{2}$ reservoirs but low star formation efficiencies, perhaps suggesting that $\mathrm{H}_{2}$ suppression (either by stripping or starvation) may not always be needed to quench star formation (Alatalo et al. Reference Alatalo2015), but higher turbulence and/or gas heating may reduce the efficiency with which gas is turned into stars. However, it is still unclear if these findings are applicable to the average satellite galaxy in a group. Thus, it is still impossible to directly connect Hi to $\mathrm{H}_{2}$ in groups in a statistical sense and to use observations of cold gas in groups as direct evidence for star formation quenching.

Figure 16. SFR surface density radial profiles for satellite galaxies in different environments. SFR surface density is expressed in terms of deviation from the resolved star-forming main sequence ( $\Delta\Sigma_{\text{SFR}}$ ), with $\Delta\Sigma_{\text{SFR}}=0$ indicating regions that are forming stars as expected for their stellar mass surface density. Median $\Delta\Sigma_{\text{SFR}}$ radial profiles for low-mass (9 $<\log(M_{*}/{\rm M}_{\odot})<$ 10, left panel) and high-mass (10 $<\log(M_{*}/{\rm M}_{\odot})<$ 11.5, right panel) galaxies are split into ranges of local galaxy over-density evaluated at the 5th nearest neighbour ( $\delta_{5}$ ). The width of each coloured region indicates the 1 $\sigma$ uncertainty on the population average. While low-mass satellites show gradual ‘outside-in’ quenching, high-mass satellites are more consistent with either flat radial profiles or even ‘inside-out’ quenching. Adapted from Bluck et al. (Reference Bluck2020) and kindly provided by A. Bluck.

5.3.3. Gas-phase metallicities

It is now well established that, even when still forming stars at rates typical of what is observed in the star-forming main sequence, satellite galaxies in groups show gas-phase metallicities significantly higher ( $\sim$ 0.1–0.2 dex) than central galaxies of the same stellar mass. This increase in metallicity of the ISM has been reported by studies based on both fibre spectroscopy (e.g., Pasquali, Gallazzi, & van den Bosch Reference Pasquali, Gallazzi and van den Bosch2012; Peng & Maiolino Reference Peng and Maiolino2014; Wu et al. Reference Wu, Zahid, Hwang and Geller2017) and IFS data (e.g., Lian et al. Reference Lian, Thomas, Li, Zheng, Maraston, Bizyaev, Lane and Yan2019; Schaefer et al. Reference Schaefer2019b) and appears to become more and more prominent with decreasing galaxy stellar mass (see Figure 17). While these observational findings are overall in agreement with results from clusters of galaxies and generally interpreted as evidence for the cessation of infall of pristine gas and stripping of cold ISM from the outer disc (see Sections 4.2 and 4.4), for satellites in groups multiple scenarios have been proposed. Most importantly, it is still debated whether such an increase in metallicity is directly linked to stripping. Pasquali et al. (Reference Pasquali, Gallazzi and van den Bosch2012) put forward a scenario in which, at the same time, (a) the halting of gas infall prevents the galaxy from accreting pristine gas; (b) ram pressure removes the gas in the outer disc and prevents radial inflow of low-metallicity gas into the disc, and (c) metal-enriched outflows are prevented due to the external pressure of the IGM. A similar conclusion was reached by Wu et al. (Reference Wu, Zahid, Hwang and Geller2017), who linked the increase in metallicity to the lack of cold gas in satellites in high-density environments.

Figure 17. Gas-phase oxygen abundance distribution for star-forming centrals (solid lines) and star-forming satellites (dashed lines) for different stellar mass bins (coloured lines), based on SDSS. At the same stellar mass, the average metallicity of satellites is higher than that of centrals, especially at low stellar masses. Image reproduced with permission from Figure 2 in Peng & Maiolino (Reference Peng and Maiolino2014). Copyright by the authors.

Conversely, Peng & Maiolino (Reference Peng and Maiolino2014) argued that the increase in gas-phase metallicity has little to do with stripping or halting of gas inflow, but that it is primarily a consequence of the fact that satellites in groups accrete preferentially metal-enriched gas. They used the gas regulator model presented by Lilly et al. (Reference Lilly, Carollo, Pipino, Renzini and Peng2013) to show that a metallicity enhancement at fixed mass and SFR can simply be obtained by assuming that, in denser environments, the IGM is more metal enriched and, therefore, its infall into satellites would boost the metal content in their ISM. One of the key elements of their argument is indeed the presence of a clear metallicity offset between centrals and satellites having the same SFR. A similar conclusion was recently reached by Schaefer et al. (Reference Schaefer2019b), who looked at the resolved mass gas-phase metallicity of satellite and central galaxies extracted from the MaNGA survey.

The recent analysis presented by Lian et al. (Reference Lian, Thomas, Li, Zheng, Maraston, Bizyaev, Lane and Yan2019), and based again on MaNGA data, may provide an avenue to gradually discriminate between the different scenarios presented above. They found that, at least at low stellar masses (9 $<\log(M_{*}/{\rm M}_{\odot})<$ 9.7), the enhancement in gas-phase metallicity is associated with a gradual flattening of metallicity gradients with increasing environmental density. This is accompanied by a weak steepening of the SFR density profiles. Using a chemical evolution model, they showed that the observed changes in SFR and gas-phase metallicity profiles are more consistent with outside-in quenching and halting of gas infall primarily in the outer parts of the star-forming disc, rather than accretion of pre-enriched material. However, they stressed that larger number statistics is needed to fully reject the metal-enriched gas accretion scenario.

As argued by Schaefer et al. (Reference Schaefer2019b), the Lian et al. (Reference Lian, Thomas, Li, Zheng, Maraston, Bizyaev, Lane and Yan2019) sample extends to lower SFRs than the one used in other works, suggesting that they are much more sensitive to environmental effects than analyses focused on satellites that are pre-selected to lie on the star-forming main sequence. In other words, there may be multiple channels affecting the enrichment of satellite galaxies and our ability to trace them may heavily depend on sample selection criteria.

Intriguingly, a similar debate has recently emerged also from the analysis of cosmological simulations. For example, Bahé et al. (Reference Bahé, Schaye, Crain, McCarthy, Bower, Theuns, McGee and Trayford2017) take advantage of the Evolution and Assembly of GaLaxies and their Environments (EAGLE; Schaye et al. Reference Schaye2015) simulation to show that gas-phase metallicity enhancements are directly linked to environmental quenching, and due to the removal of metal-poor gas from the outskirts of the star-forming disc and suppression of gas inflows. Conversely, Gupta et al. (Reference Gupta2018) show that Illustris-TNG (Pillepich et al. Reference Pillepich2018) satellite galaxies in groups accrete more pre-enriched gas than galaxies in isolation and suggest that this can easily account for the observed difference in gas-phase metallicity between satellites and centrals. However, as extensively discussed in Bahé et al. (Reference Bahé, Schaye, Crain, McCarthy, Bower, Theuns, McGee and Trayford2017), even in the case of theoretical simulations, the selection criteria used to match simulated and observed data can significantly influence the results.

In summary, while further analysis is needed to determine the origin of the gas-phase metallicity enhancement observed in satellite galaxies, all evidence suggests that stripping of Hi can directly affect the outer parts of the star-forming disc, whereas for most of the optical disc changes in star formation activity and ISM enrichment appear more consistent with just a reduction of the gas infall rate onto the disc. This is particularly true for galaxies with stellar masses $M_{*}\geq$ 10¹⁰ M $_{\odot}$ .

5.4. Star formation quenching timescales in the group environment

It should be now clear to the reader that, even in groups, the picture emerging on the potential connection between stripping and quenching is not dramatically different from what we have seen for clusters. Thus, the key points on quenching timescales highlighted in Section 4.4 are applicable also to the group environment. However, here it is worth going into greater detail on issues that are directly relevant to group satellites.

Even in groups, it is natural to expect that, for low-mass galaxies ( $\lesssim 10^{8}\,\text{M}_{\odot}$ ), ram pressure is strong enough to remove all the cold gas reservoir soon after the crossing of the virial radius or at first pericentre passage. Thus, for these objects, quenching timescales (measured from the time of infall until the time of quenching) should be relatively short (i.e., $\sim$ 1 Gyr).

This is indeed the consistent picture emerging from all estimates of quenching timescales for galaxies in the Local Group (e.g., Fillingham et al. Reference Fillingham, Cooper, Wheeler, Garrison-Kimmel, Boylan-Kolchin and Bullock2015, Reference Fillingham2019; Wetzel, Tollerud, & Weisz Reference Wetzel, Tollerud and Weisz2015). Excitingly, with the advent of the Gaia mission (Gaia Collaboration et al. Reference Gaia2016), it has even become possible to reconstruct the orbits of satellites around the Milky Way and determine quenching timescales with unprecedented accuracy. By doing so, Fillingham et al. (Reference Fillingham2019) find quenching timescales (measured from the time when the galaxy crossed the virial radius of the Milky Way halo) $<$ 2 Gyr for all Milky Way satellites with stellar masses lower than $M_{*}\sim 10^{8}\,\text{M}_{\odot}$ . Moreover, as expected, the exact timescale strongly depends on the detailed orbital parameters of each satellite, with orbits with unusually large pericentre passages corresponding to significantly longer (i.e., several Gyr) quenching timescales. Interestingly, Wetzel et al. (Reference Wetzel, Tollerud and Weisz2015) report a trend of increasing quenching timescale with increasing stellar mass, consistent with the idea that the efficiency of the quenching mechanism decreases with increasing mass, as in the case of ram pressure stripping.

It would be natural to assume that, at fixed group mass, the trend of increasing quenching timescale with increasing mass can be extrapolated to higher stellar masses. However, the picture appears a bit more complicated. If we combine all most popular estimates of quenching timescales in satellites (see e.g., Wheeler et al. Reference Wheeler, Phillips, Cooper, Boylan-Kolchin and Bullock2014; Fillingham et al. Reference Fillingham, Cooper, Wheeler, Garrison-Kimmel, Boylan-Kolchin and Bullock2015, Reference Fillingham, Cooper, Pace, Boylan-Kolchin, Bullock, Garrison-Kimmel and Wheeler2016; Wetzel et al. Reference Wetzel, Tollerud and Weisz2015) an unexpected trend emerges, where quenching timescales increase with stellar mass of up to $\sim$ 6–8 Gyr for stellar masses of ${\sim}10^{9}\,\text{M}_{\odot}$ and start decreasing for higher stellar masses. The favoured interpretation of this trend is that $M_* \sim 10^{9}\,\text{M}_{\odot}$ represents the transition mass above which stripping of the cold ISM becomes inefficient and starvation becomes dominant. Thus, the decrease in quenching timescale at higher masses is supposedly just a consequence of shorter total gas depletion times in more massive galaxies (e.g., depletion time scaling with $M_{*}^{-0.3}$ ; Davé, Oppenheimer, & Finlator Reference Davé, Oppenheimer and Finlator2011).

While future investigations are needed to settle this issue, we recommend caution in interpreting such trends at face value. Not only are different group masses combined but, as discussed in Section 4.4, there are many caveats in the use of quenching timescales to isolate physical processes driving quenching, and mass trends could be a simple by-product of the threshold used to separate passive and active galaxies. Moreover, longer timescales may not mean less efficient quenching, but different orbital parameters/accretion histories. Quenching likely does not start at the time of crossing the virial radius, and there is evidence suggesting that it is this time delay between infall and onset of quenching that drives the mass dependency of quenching timescales in both groups and clusters (e.g., Wetzel et al. Reference Wetzel, Tinker, Conroy and van den Bosch2013; Rafieferantsoa, Davé, & Naab Reference Rafieferantsoa, Davé and Naab2019). Indeed, as already mentioned, when quenching timescale estimates do not depend on assumptions on delay time, mass dependencies either disappear or revert back to less massive systems being quenched faster (e.g., Smethurst et al. Reference Smethurst, Lintott, Bamford, Hart, Kruk, Masters, Nichol and Simmons2017; Pasquali et al. Reference Pasquali, Smith, Gallazzi, De Lucia, Zibetti, Hirschmann and Yi2019). This conclusion appears in line with the recent findings by Oman et al. (Reference Oman, Bahé, Healy, Hess, Hudson and Verheijen2020), who provide an extensive discussion on the biases and limitations of the various techniques used so far to infer quenching timescales and on how these could artificially introduce mass dependencies.

From a quantitative point of view, a more detailed analysis is required to determine whether a decrease in quenching timescale of a factor of $\sim$ 4 from stellar masses of 10⁹ to 10¹¹ M $_{\odot}$ (e.g., from 8 to 2 Gyr; Fillingham et al. Reference Fillingham, Cooper, Wheeler, Garrison-Kimmel, Boylan-Kolchin and Bullock2015) can be explained with just a variation in depletion time. At the time of writing, any mass dependence in the total gas depletion time observed in nearby galaxies rarely surpass a factor of $\sim$ 2, with a large scatter (see also Figure 13). Indeed, previous works have reported total gas depletion times even increasing with decreasing specific SFR (Boselli et al. Reference Boselli2014d), and molecular gas depletion times monotonically increasing with increasing mass and decreasing specific SFR (Saintonge et al. Reference Saintonge2017), that is, opposite to what is expected if cold gas depletion times drive quenching timescales.

Regardless of the exact mass dependence of quenching timescales for stellar masses larger than $\sim$ 10⁹ M $_{\odot}$ , it is clear that in groups, as in clusters, a few billion years (i.e., multiple pericentre passages) are needed to fully quench intermediate- and high-mass satellites. Most importantly, even in groups, it seems clear that both stripping of the cold ISM (for dwarf galaxies and the outer parts of discs in more massive systems) and slower quenching, at least partially associated with the halting of gas accretion onto the star-forming disc, are playing a role in driving satellites out of the star-forming main sequence.

6.1. Pre-processing

Given the focus of this review on the quenching of star-forming satellites, here we are interested in the potential role of pre-processing in starting (but not completing) the quenching phase of satellites before their infall into the current cluster (or large group; for simplicity, we refer only to clusters in the rest of this section). Indeed, while important for understanding the variation of the passive satellite fraction with environment and mass (e.g., De Lucia et al. Reference De Lucia, Weinmann, Poggianti, Aragón-Salamanca and Zaritsky2012; Wetzel et al. Reference Wetzel, Tinker, Conroy and van den Bosch2013; Haines et al. Reference Haines2015), pre-processed satellites infalling into the cluster already fully quenched are irrelevant for what was discussed in Section 4, and their quenching history (as well as the role of pre-processing) is fully encapsulated in Section 5, where we have seen how groups can quench star formation in their satellites.

Figure 18. Cumulative percentage of cluster satellites at $z=$ 0 that have spent more than a certain amount of time in a host before infall, as predicted by the Yonsei Zoom-in Cluster hydrodynamic simulation. The thick dark line shows the percentage of all members in the 15 clusters studied, while thinner lines (colour-coded by cluster mass) show individual clusters. Image reproduced with permission from Figure 2 in Han et al. (Reference Han, Smith, Choi, Cortese, Catinella, Contini and Yi2018). Copyright by AAS.

From a theoretical point of view, there is general agreement that roughly $\sim$ 30–40% of the satellite population found in cluster-size halos (e.g., 10¹⁴ M $_{\odot}$ ) fell into the cluster as a satellite of a halo of mass $\sim$ 10¹³ M $_{\odot}$ (e.g., McGee et al. Reference McGee, Balogh, Bower, Font and McCarthy2009; De Lucia et al. Reference De Lucia, Weinmann, Poggianti, Aragón-Salamanca and Zaritsky2012; Han et al. Reference Han, Smith, Choi, Cortese, Catinella, Contini and Yi2018). However, this fraction strongly depends on stellar mass, with more massive galaxies having an increased likelihood of infalling into clusters as centrals than lower mass systems (De Lucia et al. Reference De Lucia, Weinmann, Poggianti, Aragón-Salamanca and Zaritsky2012; Wetzel et al. Reference Wetzel, Tinker, Conroy and van den Bosch2013). Most importantly, the time spent as a satellite before infalling into the cluster can vary dramatically (e.g., from just $\sim$ 0.1 to 8 Gyr or more) but is generally $\sim$ 2–3 Gyr or less (e.g., see Figure 18). This is of the same order of magnitude, or even shorter, than the typical delay time before the onset of the major quenching phase in satellites ( $\sim$ 2–6 Gyr). In this time frame, pre-processing could definitely impact on the ability of satellites to accrete new gas and could also contribute to the removal of cold gas from the very outer discs. But it seems unlikely that, for the bulk of star-forming galaxies infalling into today’s clusters (which are the focus of this review), pre-processing plays a key role in their path towards quenching. This is simply because they are still in the star-forming main sequence when they reach the cluster environment and, by definition, their star formation activity has not yet been significantly affected by the environment experienced before infall.

Indeed, from an observational point of view, apart from peculiar cases of groups infalling into clusters (e.g., Cortese et al. Reference Cortese2006; Džudžar et al. Reference Džudžar, Kilborn, Murugeshan, Meurer, Sweet and Putman2019), the few observational pieces of evidence suggesting an effect of pre-processing on the gas reservoir of infalling star-forming satellites indicate just very small variations in Hi content ( $\sim$ 0.1–0.2 dex, e.g., Yoon & Rosenberg Reference Yoon and Rosenberg2015; Odekon et al. Reference Odekon2016). These are generally within the typical variation in the Hi content of galaxies on the star-forming main sequence (Janowiecki et al. Reference Janowiecki, Catinella, Cortese, Saintonge and Wang2020) and, indeed, the bulk of the population of infalling satellites in clusters has SFR and Hi content within $\sim$ 0.2 dex of those observed in isolated systems (e.g., Cortese & Hughes Reference Cortese and Hughes2009; Boselli et al. Reference Boselli2014d).

Admittedly, the limitation of current Hi and $\mathrm{H}_{2}$ surveys makes it impossible to further investigate the role of pre-processing in any detail and quantify its effect on cold gas content and SFR simultaneously as a function of group and satellite mass. However, it is clear that, when star-forming satellites infall into cluster-size halos ( $\sim$ 10¹⁴ M $_{\odot}$ or higher), the key paths driving the quenching of the star formation are those summarised in Section 4.5 (i.e., outside-in stripping and quenching), with group pre-processing potentially only making them more efficient.

6.2. Large-scale structure filaments

Even more circumstantial is the observational evidence for a connection between cold gas content, star formation quenching, and position of galaxies within filaments. Only a handful of studies have investigated the correlation between Hi mass and distance from the spine of large-scale structure filaments, and samples are still relatively small and generally biased towards gas-rich systems. While there seems to be common agreement that gas richness may vary with distance from the filaments (Kleiner et al. Reference Kleiner, Pimbblet, Jones, Koribalski and Serra2017; Crone Odekon et al. Reference Crone Odekon, Hallenbeck, Haynes, Koopmann, Phi and Wolfe2018; Blue Bird et al. Reference Blue Bird2020), additional work is needed to properly quantify these differences and their dependence on galaxy properties. For example, while Crone Odekon et al. (Reference Crone Odekon, Hallenbeck, Haynes, Koopmann, Phi and Wolfe2018) find an increase of Hi content with increasing distance from the spine of the large-scale structure, Kleiner et al. (Reference Kleiner, Pimbblet, Jones, Koribalski and Serra2017) report the opposite trend for galaxies with stellar masses greater than 10¹¹ M $_{\odot}$ . Perhaps more importantly for the focus of this review, both theoretical and observational studies seem to imply that the overall effect of filaments on gas content and star formation (at fixed group environment) should be relatively small ( $<0.3$ dex) and well within the scatter in properties observed for the star-forming galaxy population (indeed, the large-scale environment could well be one of the contributing causes of this scatter).

However, much like in the case of pre-processing, understanding the role played by filaments is most likely critical in regulating the inflow rate of gas into star-forming discs. We still know very little about how cold gas gets into the disc and whether, for fixed satellite and group properties, large-scale structure plays an important role in regulating when and how accretion occurs and stops. Looking ahead, it will be first necessary to carefully control for the effect of the group environment, in order to isolate filament-driven effects.

8.1. Do we need cold gas stripping?

In the last two decades, one of the most popular tools for studying the gas content of galaxy populations in a cosmological context has been semi-analytical models (SAMs). Most modern SAMs take the merger trees of dark matter only cosmological N-body simulations to follow the growth of structure through gravitational instability and then include a semi-analytical treatment of the various physical processes affecting the evolution of baryons (e.g., gas cooling, star formation, feedback, etc) to derive the properties of galaxies hosted within their dark matter halos. Because of the limited computational cost, they are extremely efficient at exploring large parameter space and investigating wide simulated volumes (e.g., Baugh Reference Baugh2006; Somerville & Davé Reference Somerville and Davé2015).

The vast majority of early SAMs implemented gas loss in satellite galaxies by removing only the hot gas content of galaxies instantly after they become satellites (Baugh, Cole, & Frenk Reference Baugh, Cole and Frenk1996; Springel et al. Reference Springel, White, Tormen and Kauffmann2001; Lagos, Cora, & Padilla Reference Lagos, Cora and Padilla2008). However, it soon became clear that the combination of instantaneous stripping with very efficient supernova feedback produced galaxies that tended to use up (or eject) their remaining cold disc gas too rapidly, resulting in fractions of red galaxies in groups and clusters that were too high compared to observations (Weinmann et al. Reference Weinmann, van den Bosch, Yang and Mo2006; Baldry et al. Reference Baldry, Balogh, Bower, Glazebrook, Nichol, Bamford and Budavari2006; Kimm et al. Reference Kimm2009). This also explains why early efforts to include ram pressure stripping of the cold ISM in SAMs (e.g., Okamoto & Nagashima Reference Okamoto and Nagashima2003; Lanzoni et al. Reference Lanzoni, Guiderdoni, Mamon, Devriendt and Hatton2005) reported no significant improvements in the ability of models to match the star formation properties of satellites (i.e., galaxies were quenched before ram pressure stripping of cold gas could play a role).

As a result, McCarthy et al. (Reference McCarthy, Frenk, Font, Lacey, Bower, Mitchell, Balogh and Theuns2008) provided new recipes derived from hydrodynamical simulations describing gradual hot gas stripping that, combined with an improved treatment of how the gas is re-heated by feedback, improved the match with observations (e.g., Font et al. Reference Font2008; Lagos et al. Reference Lagos, Davis, Lacey, Zwaan, Baugh, Gonzalez-Perez and Padilla2014; De Lucia et al. Reference De Lucia, Hirschmann and Fontanot2019). However, these changes were still insufficient to match the observed passive fractions (e.g., see Guo et al. Reference Guo2011; Hirschmann et al. Reference Hirschmann, De Lucia, Wilman, Weinmann, Iovino, Cucciati, Zibetti and Villalobos2014b; Henriques et al. Reference Henriques, White, Thomas, Angulo, Guo, Lemson, Springel and Overzier2015). Intriguingly, more recent work focused on the relative effect of hot gas stripping on the atomic-to-molecular hydrogen ratio has also highlighted that hot stripping alone would produce satellite galaxies with lower H $_2$ -to-Hi ratios than star-forming centrals of the same stellar mass (e.g., Xie et al. Reference Xie, De Lucia, Wilman, Fossati, Erwin, Gutiérrez and Kulkarni2018, Reference Xie, De Lucia, Hirschmann and Fontanot2020), contrary to what is observed in clusters.

These issues, combined with the increasing number of observational constraints on Hi and $\mathrm{H}_{2}$ properties of satellite galaxies, have prompted several groups to include recipes for cold gas stripping in their SAMs (e.g., Tecce et al. Reference Tecce, Cora, Tissera, Abadi and Lagos2010; Stevens & Brown Reference Stevens and Brown2017; Cora et al. Reference Cora2018; Xie et al. Reference Xie, De Lucia, Hirschmann and Fontanot2020). To do so, the general approach is to calculate the cold gas stripping radius analytically by balancing the galaxy’s restoring forces against the drag expected from ram pressure. Commonly, the hot halo gas shields the cold disc until it has been stripped, although the exact implementation varies somewhat between studies, as do the timescales for the gas to be removed, generally related to the time resolution of the simulation.

Although these studies concur that hot gas stripping is still the primary factor dictating the strength of quenching in most galaxies,Footnote m some works are starting to suggest that the inclusion of recipes for cold stripping is necessary for improving the match to observed quenching fractions (at least in clusters, e.g., Xie et al. Reference Xie, De Lucia, Hirschmann and Fontanot2020), supporting the idea that cold gas stripping is important for the evolution of satellite galaxies. More generally accepted is the fact that gas stripping appears indispensable to better reproduce the Hi content of satellites, the variation of Hi deficiency with cluster-centric distance, and the increase of H $_2$ /Hi fractions in clusters (e.g., Cora et al. Reference Cora2018; Stevens et al. Reference Stevens and Lagos2018; Xie et al. Reference Xie, De Lucia, Hirschmann and Fontanot2020). Nevertheless, the match between observations and SAMs when it comes to multi-phase gas properties of satellite galaxies is not yet perfect (e.g., it is still challenging to match the Hi and $\mathrm{H}_{2}$ content of satellites simultaneously, across all ranges of halo masses; Xie et al. Reference Xie, De Lucia, Hirschmann and Fontanot2020), implying that more work is needed to understand the interplay between stripping and quenching in these models.

In parallel to SAMs, in the last decade, large-scale hydrodynamical cosmological simulations have become a commonly used tool to study the evolving gas content of galaxy populations, with a clear explosion in the number of simulations readily available for a comparison with observations (e.g., EAGLE, Schaye et al. Reference Schaye2015; Illustris, Vogelsberger et al. Reference Vogelsberger2014; Illustris-TNG, Pillepich et al. Reference Pillepich2018; Horizon-AGN, Dubois et al. Reference Dubois2014; Magneticum, Hirschmann et al. Reference Hirschmann, Dolag, Saro, Bachmann, Borgani and Burkert2014a). As opposed to SAMs, cosmological hydrodynamical simulations follow gravitational and hydrodynamical processes in a self-consistent manner, so that cold gas stripping is inherently built-in to these simulations. Nevertheless, their typical resolution is still insufficient to trace the formation of the cold gas phase of the ISM, hence they have to rely on subgrid prescriptions to separate the atomic and molecular cold gas phases.

Contrary to SAMs, in cosmological hydrodynamical simulations, we cannot simply switch on and off cold stripping in order to answer the question ‘is cold stripping required to better match observations?’ What we can determine is whether cold gas stripping commonly happens in the path of a satellite towards quenching. Not surprisingly, the answer to this question appears to be a resounding ‘yes’ for both cosmological (e.g., Bahé et al. Reference Bahé, McCarthy, Balogh and Font2013; Bahé & McCarthy Reference Bahé and McCarthy2015; Cen Reference Cen2014; Marasco et al. Reference Marasco, Crain, Schaye, Bahé, van der Hulst, Theuns and Bower2016; Jung et al. Reference Jung, Choi, Wong, Kimm, Chung and Yi2018; Arthur et al. Reference Arthur2019; Stevens Reference Stevens2019a, Reference Stevens2020; Yun et al. Reference Yun2019; Rafieferantsoa et al. Reference Rafieferantsoa, Davé and Naab2019) and controlled hydrodynamical simulations (e.g., Quilis, Moore, & Bower Reference Quilis, Moore and Bower2000; Abadi, Moore, & Bower Reference Abadi, Moore and Bower1999, Roediger & Hensler Reference Roediger and Hensler2005; Roediger & Brüggen Reference Roediger and Brüggen2007; Bekki Reference Bekki2009, Reference Bekki2014; Tonnesen & Bryan Reference Tonnesen and Bryan2009). However, while hydrodynamical simulations include stripping by default, admittedly they have not always been able to fully reproduce the properties of satellites, yet.

Tremendous progress has been made in matching the global gas scaling relations of galaxies (i.e., the properties of centrals; e.g., see Davé et al. Reference Davé, Crain, Stevens, Narayanan, Saintonge, Catinella and Cortese2020), but in many instances satellite galaxies appear over-stripped and/or over-quenched (e.g., Brown et al. Reference Brown2017; Davé, Rafieferantsoa, & Thompson Reference Davé, Rafieferantsoa and Thompson2017; Stevens Reference Stevens2019a; Xie et al. Reference Xie, De Lucia, Hirschmann and Fontanot2020; Donnari et al. Reference Donnari, Pillepich, Nelson, Marinacci, Vogelsberger and Hernquist2020). The mismatch between simulations and observations varies as a function of both host and satellite mass, and the exact dependency changes if we consider quenching fractions instead of gas fractions, as well as varying from model to model. The reasons for such a mismatch are still unclear and can be multiple. Most certainly, too efficient feedback that would eject a large fraction of the ISM out of the disc (e.g., Stevens et al. Reference Stevens2019a) and/or insufficient resolution (i.e., 1 kpc or lower), which makes it impossible to conduct a proper partition between the different cold gas phases in order to trace the denser (and more difficult to strip) gas within the multi-phase ISM of their discs (e.g., Hu et al. Reference Hu, Naab, Walch, Glover and Clark2016), are among some of the most likely issues.

Thus, as in the case of SAMs, we are finding general support for the idea that cold gas stripping is part of a satellite’s pathway towards quenching, though more work is clearly needed to improve the ability of cosmological hydrodynamical simulations to match the observed properties of satellites.

8.2. Do simulations provide insight on mechanisms behind cold gas stripping?

Keeping in mind the limitations described above, it is nevertheless tempting to see if current simulations can provide insights on the nature of the mechanism(s) responsible for cold gas stripping.

In the case of SAMs, even if hydrodynamical mechanisms cannot be directly implemented, processes like stripping due to ram pressure appear to be preferred to tidal stripping by a host’s potential well. Indeed, SAMs typically calculate a tidal stripping radius and a ram pressure stripping radius for their satellite halos as they orbit through their hosts. These radii mark the boundary beyond which each stripping mechanism is effective, and most works (including those based on hydrodynamical simulations) agree that the ram pressure radius is typically smaller than the tidal stripping radius (McCarthy et al. Reference McCarthy, Frenk, Font, Lacey, Bower, Mitchell, Balogh and Theuns2008; Font et al. Reference Font2008; Bahé & McCarthy Reference Bahé and McCarthy2015; Cora et al. Reference Cora2018). This implies that, by the time a galaxy reaches the region within its host halo at which tidal stripping becomes efficient, ram pressure has typically already removed most of the gas.

Naively, we might expect that hydrodynamical cosmological simulations should provide the best opportunity to clearly isolate the physical processes responsible for cold gas stripping, given that detailed information about all of a galaxy’s mass components, and their time evolution is, in principle, available. However, the ability to self-consistently trace multiple and interconnected physical processes makes it even more challenging to pin-point what observers would call the ‘dominant mechanism’ at play. For example, the implementation of internal mechanisms such as star formation consumption and various forms of feedback may contribute to the stripping efficiency of different environmental mechanisms, meanwhile external factors such as the background UV field, tidal interactions, or hydrodynamical processes may all influence each other’s abilities to remove cold gas in complex and non-linear ways.

The complexity of this problem was clearly showcased by Marasco et al. (Reference Marasco, Crain, Schaye, Bahé, van der Hulst, Theuns and Bower2016), who tried to identify the responsible for cold gas stripping in groups and cluster galaxies (see also Xie et al. Reference Xie, De Lucia, Hirschmann and Fontanot2020 for a similar approach from the SAMs point of view). While they emphasise that, at $z\sim$ 0, ram pressure is the most common physical process stripping Hi from satellites, they also highlighted the importance of satellite–satellite encounters in stripping Hi from the disc (especially at large cluster-centric distances and higher redshift) and showed that there is rarely a single cold gas stripping mechanism acting individually in a cosmological context. Instead, the most frequent source of Hi gas mass loss is a combination of simultaneous ram pressure and satellite–satellite encounters (see Figure 19), with the balance between the two processes changing as a function of redshift (i.e., satellite–satellite interactions more important at earlier epochs; see also Hwang et al. Reference Hwang, Park, Banerjee and Hwang2018). Interestingly, this suggests that ram pressure is efficient also in groups of halo masses of $\sim 10^{13}\,\text{M}_{\odot}$ , consistently with what found in other cosmological (e.g., Bahé et al. Reference Bahé, McCarthy, Balogh and Font2013; Bahé & McCarthy Reference Bahé and McCarthy2015) and non-cosmological simulations (e.g., Bekki Reference Bekki2009, Reference Bekki2014). Overall, this is in line with the key message of this review: that is, environmental mechanisms that influence cold gas content are typically most efficient at the highest densities, for example, near the pericentre passage. Therefore, they tend to peak in strength at the same time and rarely occur in isolation.

Figure 19. The halo mass ( $M_{200}$ ) versus group-centric distance ( $d/r_{200})$ distribution of Hi-poor satellites in the EAGLE simulation, evaluated at the time of Hi loss (i.e., $ z=z_{\text{stripping}})$ . Lines show the parameter space occupied by satellites affected by different environmental processes: that is, tidal stripping by the host halo (blue solid), ram pressure stripping by the IGM (red thick dashed), satellite–satellite interactions (yellow dot-dashed), or none of the above (thin dashed), with contours enclosing 30%, 60%, and 90% of the satellites. Only systems with stellar mass (at $z=0$ ) larger than $10^9$ $\text{M}_{\odot}$ are considered. Image reproduced with permission from Figure 13 in Marasco et al. (Reference Marasco, Crain, Schaye, Bahé, van der Hulst, Theuns and Bower2016). Copyright by the authors.

A potential (and complementary) way forward to break this complexity is provided by controlled hydrodynamical simulations. Their controlled nature means that the effect of just one individual mechanism can be isolated. For example, in ram pressure stripping-only simulations (e.g., Roediger & Hensler Reference Roediger and Hensler2005; Roediger & Brüggen Reference Roediger and Brüggen2007; Tonnesen & Bryan Reference Tonnesen and Bryan2009; Steinhauser, Schindler, & Springel Reference Steinhauser, Schindler and Springel2016), it has been possible to clearly identify long, one-sided gas tails as observed in cluster satellites, providing some of the strongest theoretical support for the key role played by ram pressure in removing cold gas from star-forming satellite galaxies. By systematically adjusting input parameters, it has also been possible to quantify how the effects of ram pressure depend on disc inclination and orbits (Vollmer et al. Reference Vollmer, Cayatte, Balkowski and Duschl2001; Roediger & Brüggen Reference Roediger and Brüggen2007), presence of a bulge (Steinhauser et al. Reference Steinhauser, Haider, Kapferer and Schindler2012), or cluster dynamical state (Vijayaraghavan & Ricker Reference Vijayaraghavan and Ricker2013; Roediger et al. Reference Roediger, Lovisari, Dupke, Ghizzardi, Brüggen, Kraft and Machacek2012). This approach has been crucial for the development of accurate analytical recipes of gas stripping mechanisms, which can then be implemented in SAMs (Font et al. Reference Font2008), or used to identify when a mechanism plays a dominant role in hydrodynamical cosmological simulations (Marasco et al. Reference Marasco, Crain, Schaye, Bahé, van der Hulst, Theuns and Bower2016).

By limiting the simulation volume and duration, controlled simulations can also reach higher resolution or consider complex physics that would be otherwise computationally prohibitive. As such, they have been able to model and highlight the potential importance of viscous, turbulent stripping (Roediger & Hensler Reference Roediger and Hensler2005; Roediger & Brüggen Reference Roediger and Brüggen2007), a multiphase treatment of the ISM (Tonnesen et al. Reference Tonnesen, Bryan and Chen2011), the interplay between thermal evaporation and magnetic fields (Tonnesen & Stone Reference Tonnesen and Stone2014; Vijayaraghavan & Sarazin Reference Vijayaraghavan and Sarazin2017), and the importance of mixing (Tonnesen & Bryan Reference Tonnesen and Bryan2021) for the overall cold gas stripping process. This clearly confirms that, even when only stripping by hydrodynamical processes is considered, a complex set of poorly understood processes interact, including turbulence and magnetic fields, meaning that such modelling is highly challenging. Of course, as with every approach, even controlled simulations are limited by how well they are able to properly include and interconnect all the key physical processes at play.

In summary, theoretical models are overall providing a view consistent with that emerging from observations, where multiple physical processes generally act simultaneously on the cold gas reservoir in the ISM. While hydrodynamical stripping mechanisms appear to be the most efficient in Virgo-like and more massive clusters (at least at $z\sim$ 0), in smaller structures the picture is much more complex and additional work is required to characterise the net effect of the various physical processes affecting the ISM in satellite galaxies.

8.3. Are satellites fully stripped after first pericentre passage?

While the general scenario emerging from both SAMs and hydrodynamical simulations is that cold gas stripping is widespread in satellites and is needed to reproduce the observed properties of group and cluster galaxies, this does not necessarily imply that satellites are fully stripped (and then quenched) after first pericentre passage. Indeed, as for observations, models cast doubts that stripping completely halts star formation after one pericentre passage, even in Virgo-like clusters.

High-resolution controlled simulations suggest that $\sim$ Milky Way mass spirals would typically lose a substantial amount of their cold gas in a cluster but would become completely stripped only in extreme cases, with the amount of stripping being a sensitive function of galaxy orbit (e.g., Roediger & Hensler Reference Roediger and Hensler2005; Roediger & Brüggen Reference Roediger and Brüggen2007). Similarly, Steinhauser et al. (Reference Steinhauser, Schindler and Springel2016) find that discs galaxies with $V_{\rm circ}$ $\sim$ 110–170 km s^–1 are only fully stripped for very plunging orbits ( $R_{\rm peri} \sim$ 100 kpc), while star formation is only weakly affected for the rest of the orbits. Moving to cosmological simulations, Brüggen & De Lucia (Reference Brüggen and De Lucia2008) applied the results found by Roediger & Brüggen (Reference Roediger and Brüggen2007) to the Millenium simulation and showed that only a minority of disc galaxies with $V_{\rm circ}$ >200 km s^–1 are expected to be fully stripped in clusters ( $\sim$ 11–32% dependent on cluster mass), but that more than half ( $\sim$ 54–64%) would be heavily stripped. This is also consistent with the results by Cen (Reference Cen2014), who finds that in hydrodynamical simulations most of the cold gas within the inner parts of satellite galaxies (at least above $M_{*}\sim3\times10^{9}$ M $_{\odot}$ ) is unaffected by environmental effects.

Nevertheless, some cosmological simulations do seem to provide a different picture. For example, Jung et al. (Reference Jung, Choi, Wong, Kimm, Chung and Yi2018) find that almost half of their galaxies lose their cold gas before reaching the cluster pericentre, although many are already gas poor prior to cluster infall due to pre-processing. Using the Magneticum simulation, Lotz et al. (Reference Lotz, Remus, Dolag, Biviano and Burkert2019) report the removal of all the gas in more than 90% of cluster satellites after a single pericentre passage, with only some of their most massive galaxies (i.e., stellar masses a few times 10¹¹ M $_{\odot}$ ) able to remain star forming for more than 1 Gyr after infall. It is not yet clear what is the origin of these differences in cold gas stripping efficiency. Simulation resolution may play a role, limiting the ability to resolve both the denser phases of the ISM and the hydrodynamical stripping processes themselves. Moreover, differences in the treatment of subgrid physics such as feedback are also likely important, affecting both the density of ICM that galaxies pass through and the ease with which the cold disc gas can be removed.

Thus, while there is not a complete agreement between different theoretical models, we can conclude that the fact that full stripping is not widespread even in clusters does appear as a possible (if not likely) scenario. Thus, it is natural to ask how—in models—the remaining cold gas stops feeding star formation. Curiously, to our knowledge, there are few simulation papers specifically focused on this issue in the context of satellite galaxies in clusters, but we can use results obtained on quenching in a broader context to provide some insights on this issue.

It has been shown that enhanced star formation, either as a result of tidal shocking near pericentre or due to compression of one side of the gas disc by ram pressure (Bekki Reference Bekki2014; Steinhauser et al. Reference Steinhauser, Schindler and Springel2016; Lotz et al. Reference Lotz, Remus, Dolag, Biviano and Burkert2019; Troncoso-Iribarren et al. Reference Troncoso-Iribarren, Padilla, Santander, Lagos, García-Lambas, Rodríguez and Contreras2020; Lee et al. Reference Lee, Kimm, Katz, Rosdahl, Devriendt and Slyz2020), can potentially aid cold gas consumption. However, as discussed in Section 4.3.2, observationally such bursts appear to be relatively minor and thus unlikely to consume a significant fraction of the gas reservoir left in the disc. Feedback could also play a key role. SAMs already crucially rely on reheating and ejection of gas via supernova feedback with an efficiency that depends on redshift in order to reproduce stellar mass functions at high redshift (Hirschmann et al. Reference Hirschmann, De Lucia, Wilman, Weinmann, Iovino, Cucciati, Zibetti and Villalobos2014b; Cora et al. Reference Cora2018). Stellar feedback may also heat cold disc gas into more easily stripped and/or less star-forming phases or push the gas from inside the truncation radius to radii where it can be stripped, although so far this has only been modelled in the context of Local Group dwarf galaxies (Kazantzidis et al. Reference Kazantzidis, Mayer, Callegari, Dotti and Moustakas2017, but also see Emerick et al. Reference Emerick, Mac Low, Grcevich and Gatto2016), whose shallow potential wells may enhance the amount of material lost in this manner. In more massive galaxies, AGNs triggered in ram pressure stripped galaxies may also provide a source of feedback to the remaining cold disc gas (Ricarte et al. Reference Ricarte, Tremmel, Natarajan and Quinn2020). Finally, it should not be excluded that a more continuous loss of cold gas from the disc may also occur after pericentre passage via viscous and turbulent stripping at the ICM/disc boundary, as modelled for cluster satellites (Roediger & Brüggen Reference Roediger and Brüggen2007).

In conclusion, while numerical simulations generally agree that cold gas stripping is a normal path for satellite galaxies towards quenching, there are still many open questions also from the theory side. Specifically, the relative importance of various physical processes in driving gas stripping, as well as when and how the cold gas reservoirs of satellites stop forming stars are still highly debated questions, which are also model-dependent. In the case of hydrodynamical simulations, significant improvement will hopefully come from a more realistic multi-phase treatment of the ISM, including the role of magnetic fields, which should provide interesting clues on these open questions. At the same time, in the case of SAMs, the development of new analytical prescriptions, such as a more multi-phase treatment of the ISM (Tonnesen & Bryan Reference Tonnesen and Bryan2009), differing treatment of sub- and super-sonic discs (Roediger & Hensler Reference Roediger and Hensler2005), and inclusion of continuous gas mass loss mechanisms (Roediger & Brüggen Reference Roediger and Brüggen2007) could potentially reduce some of the tensions currently present between observations and simulations.

Figure 20. Illustration summarising the picture emerging from this review. When galaxies become satellites, their access to CGM gas (pink) is removed, and cold gas stripping appears widespread. However, there is no single physical mechanism driving the loss of gas and, consequently, quenching. Instead, multiple mechanisms can be at play, sometimes even simultaneously.

What is definitely already clear is that understanding the individual significance of the physical processes driving stripping in simulations remains at least as challenging as it is for observations. This is an area in which controlled simulations may yet provide the missing key for improving cosmological runs and our understanding of what can be learnt from them. On one side, they can help developing better prescriptions for SAMs and investigate issues of numerical convergence. On the other side, their higher spatial and mass resolutions, combined with their versatility, make controlled simulations able to include (and switch between) various complex baryonic physics that might be numerically unfeasible (or have unexpected consequences) in cosmological simulations, but could be critical for understanding environmental effects.