WALLABY Pilot Survey: the diversity of ram pressure stripping of the galactic HI gas in the Hydra Cluster

Galaxies evolve in their morphologies, kinematics and stellar population, a process which is accelerated when they are in clusters (Boselli & Gavazzi, 2006). Neutral atomic hydrogen (${\rm H}{\textsc{i}}$) is a major part of the interstellar medium (ISM) in a galaxy (e.g., Catinella et al., 2018; Wang et al., 2020a), and is a crucial component in the kinematic and thermal cooling of baryons (Putman et al., 2012). It is also an important step in the baryonic mass flow, and therefore an important key for understanding galaxy evolution. Clusters provide an environment where gravitational and hydrodynamic effects efficiently remove the ${\rm H}{\textsc{i}}$ in their constituent galaxies (e.g., Boselli & Gavazzi, 2006; Stevens et al., 2019), with ram pressure stripping identified as one of the most important mechanisms at low redshift.

Based on the analytical model of Gunn & Gott (1972), the strength of ram pressure stripping can be quantified by comparing the ram pressure from the intra-cluster medium (ICM) against the localized gravitational anchoring force of the galactic disk. We can thus expect that there is a diversity of the way that galaxies experience ram pressure stripping, as infalling galaxies have different distributions of mass and gas, and travel along different orbits and with different disk inclinations against the ICM wind. Hydrodynamical simulations of cluster systems confirm these complexities (Tonnesen, 2019; Lotz et al., 2019; Bekki, 2014; Jáchym et al., 2009; Roediger & Brüggen, 2007, 2006; Vollmer et al., 2001; Abadi et al., 1999) and further elaborate on the influence of other factors such as the multi-phase nature of gas (Stevens et al., 2020; Lee et al., 2020; Tonnesen & Bryan, 2010, 2009), magnetic fields (Ramos-Mart´ınez et al., 2018; Tonnesen & Stone, 2014), and sub-structures in clusters (Ruggiero et al., 2019; Tonnesen & Bryan, 2008). Probing the observational dependence of ram pressure stripping on galaxy properties requires statistically mapping the ${\rm H}{\textsc{i}}$ in cluster galaxies with high resolution. Ram pressure stripping is also studied with other tracers like the ionized gas (Jaffé et al., 2018) and the radio continuum (Chen et al., 2020), but this paper focuses on the ram pressure stripping of ${\rm H}{\textsc{i}}$ which is the reservoir for star formation.

Galaxies displaying ${\rm H}{\textsc{i}}$ tails that resemble expected ram pressure stripping morphologies have been identified in nearby clusters (e.g. Kenney et al., 2004; Chung et al., 2007, 2009; Koribalski, 2020). The shape, length and column density of those ${\rm H}{\textsc{i}}$ tails provide information regarding the progress of gas removal, orbits of infall, time since infall, and local ICM structures, particularly when they are combined with multi-wavelength information like the star formation rate (Jaffé et al., 2016; Vollmer et al., 2012), gas in other phases (Lee et al., 2017; Abramson et al., 2011; Moretti et al., 2020), dust (Crowl et al., 2005), radio polarization (Vollmer et al., 2013), and numerical simulations (Vollmer et al., 2001; Tonnesen & Bryan, 2010). Statistically, ram pressure stripping provides a good explanation for the observed distributions of star formation rates (SFR) and ${\rm H}{\textsc{i}}$-richness in clusters, including trends as a function of the cluster-centric projected distance (Gavazzi et al., 2006; Woo et al., 2013; Hess et al., 2015), cluster-centric radial velocity offset (Jaffé et al., 2015; Mahajan et al., 2011), and galactic stellar mass (Zhang et al., 2013). However, detailed studies of resolved systems have been mostly limited to a few systems, whilst statistical studies have mostly been based on spatially unresolved ${\rm H}{\textsc{i}}$ data.

Contiguously mapping the ${\rm H}{\textsc{i}}$ in clusters is essential to bridge the gap between signatures of ram pressure stripping in individual galaxies and the role that ram pressure stripping plays in cosmological galaxy evolution. The need for a cosmological context is because the majority of the galaxies infalling for the first time into massive clusters may have been pre-processed as satellites (Fujita, 2004; Cybulski et al., 2014; Bahé et al., 2019), or undergone “mass quenching” as centrals (Kauffmann et al., 2003) in less massive groups. It has been found that the timescale for quenching the SFR anti-correlates with the stellar mass of satellite galaxies, not because the more massive galaxies are more vulnerable to the current environment, but because they were fully or partly pre-processed or mass quenched for a longer time in their previous environments (De Lucia et al., 2012; Wetzel et al., 2013; Oman & Hudson, 2016; Rhee et al., 2020). It has also been found that 20-50% of low-mass satellite galaxies may have already or partly been quenched in star formation, with gas depleted to some extent, in another dark matter halo before being accreted into the current cluster (Wetzel et al., 2013; Hess & Wilcots, 2013; Haines et al., 2015; Jung et al., 2018). The galactic properties shaped by the past evolution strongly affect the strength and importance of environmental processing in the current cluster (Jung et al., 2018). A complete census of cluster galaxies is needed in order to properly account for the diversity of initial conditions at infall.

However, it has been hard to achieve both high completeness and high resolution in ${\rm H}{\textsc{i}}$ observations for clusters, mostly because covering a large area with interferometric 21 cm observations has been unfeasible. Extensive statistical studies based on more complete samples of galaxies detected in the nearby clusters Virgo, Coma, Abell 1367 and others have been conducted using ${\rm H}{\textsc{i}}$ data from blind single dish ${\rm H}{\textsc{i}}$ surveys, particularly ALFALFA (Haynes et al., 2018) and HIPASS (Meyer et al., 2004). They provide the bench mark for integral properties of ${\rm H}{\textsc{i}}$ in massive clusters, including the major scaling relations (Cortese et al., 2008, 2011; Dénes et al., 2014; Odekon et al., 2016) and mass functions (Gavazzi et al., 2006; Jones et al., 2016). Interferometric ${\rm H}{\textsc{i}}$ images of selected galaxies from these ${\rm H}{\textsc{i}}$ samples were also obtained to gain details about ongoing physical processes (Warmels, 1988; Gavazzi, 1989; Cayatte et al., 1990; Scott et al., 2010, 2018). Among them, the VIVA targeted survey of 50 late-type galaxies in the Virgo cluster (Chung et al., 2009) has been one of the largest resolved datasets. Further away, BUDHIES mapped two clusters (Jaffé et al., 2015) at relatively high redshifts ($z\sim 0.2$) out to $3r_{200}$ (where $r_{200}$ is the radius within which the averaged density is 200 times the critical density of the universe) with interferometry, with poorer resolution and mass sensitivity. Wang et al. (2020b) thus used the predicted ${\rm H}{\textsc{i}}$ radial distributions, in order to better exploit the low-resolution, wide-field ${\rm H}{\textsc{i}}$ data. Based on a relatively complete overlap between the ROSAT X-ray survey and the ALFALFA ${\rm H}{\textsc{i}}$ survey, for 26 massive clusters and around 200 galaxies, they showed that ram pressure stripping of the ${\rm H}{\textsc{i}}$ outer disks is prevalent out to 1.5 $r_{200}$ in Coma-like clusters, pointing out the potentially important role of weak ram pressure stripping on galaxy evolution in clusters.

Taking advantage of the high survey efficiency of ASKAP, the pilot survey of Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY ¹¹1https://wallaby-survey.org/, Koribalski et al. 2020) has been targeting nearby clusters and groups. In this study, we use its second internal data release of the Hydra cluster ²²2https://research.csiro.au/casda/.

As we will show in this paper, WALLABY is biased against galaxies with ${\rm H}{\textsc{i}}$ masses less than a few times $10^{8}~M_{\odot}$ at the distance of Hydra. Galaxies with stellar masses below around $10^{9}~M_{\odot}$ may therefore not appear in the WALLABY catalogue if they are highly ${\rm H}{\textsc{i}}$ deficient (Sec.3.2), which are the most commonly used samples for ram pressure stripping studies (e.g., Boselli et al. 2014). But the data fully cover the Hydra cluster out to 2 $r_{200}$ (Sec.3.1), and provide resolved ${\rm H}{\textsc{i}}$ distributions in a few galaxies, which we use as the test sample for predicting the ${\rm H}{\textsc{i}}$ distribution in the unresolved galaxies (Sec.2.3.2). Based on this, we attempt to quantify the instantaneous speed of ${\rm H}{\textsc{i}}$ depletion due to ram pressure stripping in the detected galaxies by quantifying the level of ram pressure, anchoring force, and mass of strippable ${\rm H}{\textsc{i}}$. The analysis thus provides statistics about the acceleration and speed of cluster processing through ram pressure stripping at a relatively early stage of ${\rm H}{\textsc{i}}$ depletion (i.e. before the ${\rm H}{\textsc{i}}$ deficiency level becomes high, as the sample is strongly biased toward ${\rm H}{\textsc{i}}$ rich galaxies). Although we do not know the initial conditions of galactic ${\rm H}{\textsc{i}}$ masses or distributions upon infall (passing 2$r_{200}$), the WALLABY coverage provides us with a snapshot of cluster processing, giving insight into the role of ram pressure stripping in removing ${\rm H}{\textsc{i}}$ from galaxies infalling into massive clusters. Observationally this is the first major study of a cluster beyond the local Virgo, Coma and A1676 clusters. The most extensively studied of these, Virgo, is not representative of clusters with similar masses as it is dynamically unrelaxed (Boselli et al., 2014). Furthermore, Virgo has an ICM which is more centrally concentrated compared to a dynamically mature cluster (Roediger & Brüggen, 2007).

Hydrodynamic (Oman et al., 2021; Ayromlou et al., 2020; Stevens et al., 2020; Lotz et al., 2019; Bahé et al., 2019; Jung et al., 2018; Bahé & McCarthy, 2015; Bahé et al., 2013) and semi-analytical (Xie et al., 2020; De Lucia et al., 2019; Stevens et al., 2019; Stevens & Brown, 2017; Luo et al., 2016) models have made progress in recent years narrowing the differences between predicted and observed distribution of ${\rm H}{\textsc{i}}$ density within galaxies and scaling relations of ${\rm H}{\textsc{i}}$ mass in galaxies. However, because galaxies are complex systems, many different mechanisms produce a similar trend (Stevens & Brown, 2017). So far as we know, after the early works of Vollmer et al. (2001); Boselli et al. (2014) and others for the Virgo cluster galaxies, there has been very few observational studies that directly provide the full distribution of the ram pressure$/$restoring forces and the mass of strippable ${\rm H}{\textsc{i}}$ for all the detected galaxies in the cluster. This is needed to separate the amount of gas loss due to ram pressure stripping from that due to feedback or star formation. Furthermore, resolved ${\rm H}{\textsc{i}}$ images are preferable to simple catalogues of HI detections. As we show in the paper (Sec.2.3.2), the radial distribution of ${\rm H}{\textsc{i}}$ in cluster galaxies differs from that of galaxies in the field, though they do obey the same size-mass relation (Wang et al., 2016; Stevens et al., 2019). As a result we apply a correction factor to the fraction of instantaneous strippable ${\rm H}{\textsc{i}}$ mass predicted with the typical radial profile of ${\rm H}{\textsc{i}}$ of field galaxies. Obviously one individual cluster is not enough to provide strong constraints to cosmological simulations, but the analysis presented in this paper can be extended with future WALLABY observations covering multiple clusters.

The outline of this paper is as follows. We present the data in Sec.2, discuss the phase-space distribution of ${\rm H}{\textsc{i}}$-detected galaxies and ram pressure stripping affected galaxies in Sec.3, the distribution of ${\rm H}{\textsc{i}}$ richness and ram pressure stripping strength in Sec.4, the timescales for ram pressure stripping to remove the currently affected ${\rm H}{\textsc{i}}$ and the existing ${\rm H}{\textsc{i}}$ reservoir in Sec.5. We assume a $\Lambda$CDM cosmology, with $\Omega_{m}=0.3$, $\Omega_{\lambda}=0.7$ and $h=0.7$. We assume the Chabrier (2003) initial mass function when estimating the stellar mass.

The main goal of this section is to obtain an overview of the distribution pattern of the ${\rm H}{\textsc{i}}$-detected galaxies and r1-RPS candidates in the Hydra cluster, and quantify the frequency of r1-RPS candidates among ${\rm H}{\textsc{i}}$-detected galaxies. The projected phase-space diagram is a good tool for statistically separating virialised cluster members, infalling galaxies and background/foreground galaxies (Oman & Hudson, 2016). Previous studies found good correspondence between the projected phase-space diagram positions and ${\rm H}{\textsc{i}}$-richness of galaxies (Yoon et al., 2017; Jaffé et al., 2015; Solanes et al., 2001). An investigation of the projected phase space diagram of optically detected galaxies in Hydra was presented by Lima-Dias et al. (2021).

The top panel of Fig. 3 displays the distribution of WALLABY-detected galaxies in the projected phase-space diagram, in comparison to that of optically identified Hydra members galaxies from Kourkchi & Tully (2017). It shows that the ${\rm H}{\textsc{i}}$-detected galaxies tend to avoid the inner part ($d_{proj}<0.5r_{200}$) of the virialized region in the projected phase-space diagram, in contrast to the optical members of the cluster. It suggests that the recent infallers are more likely ${\rm H}{\textsc{i}}$-rich, and is consistent with previous findings (Jaffé et al., 2015).

In the bottom panel of Fig. 3, we compare the projected phase-space distributions of r1-RPS and r1-non-RPS candidates. The r1-RPS candidates tend to be within 1.25$r_{200}$ and have higher $\Delta v_{rad}$ than the other galaxies in the cluster, which is expected from the way that ram pressure strength is estimated (Gunn & Gott, 1972), but the amount of ${\rm H}{\textsc{i}}$ and the anchoring force also play a role in the exact distribution of the galaxies in the projected phase-space diagram. Out to a $d_{proj}\sim 1.25r_{200}$, 70% (44%) of the ${\rm H}{\textsc{i}}$-detected galaxies in Hydra are r1-RPS (RPS) candidates.

In this section, we present an overview of the ${\rm H}{\textsc{i}}$ richness of the detected galaxies, and assess the extent of changes the current level of ram pressure stripping will make to those ${\rm H}{\textsc{i}}$ masses ($M_{{\rm HI}}$).

Fig. 5-a presents the relation between $M_{\rm HI}$ and $M_{*}$ for different sub-samples. We can see that the $M_{\rm HI}$ at a given $M_{*}$ is systematically lower than the mean relation of the galaxy population detected in the blind ${\rm H}{\textsc{i}}$ survey ALFALFA (Huang et al., 2012), but systematically higher than the median relation of the targeted survey of $M_{*}$-selected galaxies in xGASS (Catinella et al., 2018). The discrepancy between ALFALFA and WALLABY galaxies, which is more conspicuous at the high stellar mass end, is not majorly caused by the environment, but due to a volume effect. Although both surveys are relatively shallow, approximately flux-limited and have similar sensitivity, the WALLABY observations used here are limited to within $\sim$50 Mpc, whereas ALFALFA detections are within $\sim$200 Mpc (Haynes et al., 2011). At larger distances (where more massive systems are more likely found), the bias toward the most gas-rich systems becomes more important, hence affects ALFALFA more strongly than this WALLABY volume. As the ALFALFA relation fully covers the $M_{*}$ range of our sample, and roughly traces the upper envelope of $M_{\rm HI}$ distributions at a given $M_{*}$ (also see Maddox et al. 2015), we will use it as a reference line to calculate the relative $M_{\rm HI}$ of galaxies at the present and after stripping the currently strippable ${\rm H}{\textsc{i}}$ (the post-RPS status). The discrepancy of $M_{\rm HI}$ from the xGASS relation indicates that the sample misses the gas-poor, strongly depleted galaxies, due to the insufficient observational depth. Similarly, the $M_{\rm HI}$ distribution at a given $M_{*}$ does not differ significantly from that of relatively isolated galaxies targeted by the AMIGA project (Verdes-Montenegro et al., 2005) either (not shown in Fig. 5). So this study focuses on the onset and early stage of gas depletion in ${\rm H}{\textsc{i}}$-rich galaxies.

The r1-RPS candidates have similar distributions of $M_{\rm HI}$ at a given $M_{*}$ compared to the r1-non-RPS candidates, partly due to the relatively narrow range of $M_{\rm HI}$ detectable in WALLABY. There is a hint that the r1-RPS candidates lie on a slightly steeper $M_{{\rm HI}}$-$M_{*}$ relation than the r1-non-RPS candidates, as indicated by the best-fit linear relations in Fig. 5-b. The different slopes are mainly driven by the different $M_{{\rm HI}}$ distributions at low $M_{*}$. This supports the relatively greater effect of ram pressure stripping on low-mass galaxies.

To understand the influence of the observed ram pressure stripping on $M_{{\rm HI}}$, we investigate the distribution of $f_{RPS,pred}$ in Fig. 6-a. For 70% of the r1-RPS candidates, $f_{RPS,pred}$ broadly falls below 0.9. We note that the 1-$\sigma$ scatter of the median relation of $M_{\rm HI}$ versus $M_{*}$ from xGASS is $\sim$0.38 dex (Catinella et al., 2018), so the threshold $f_{RPS,pred}=$0.9 corresponds to a change in $M_{\rm HI}$ (i.e., $1-f_{RPS,pred}$) by around 2.5-$\sigma$ with respect to the median relation of $M_{\rm HI}$ versus $M_{*}$, after stripping the currently strippable ${\rm H}{\textsc{i}}$. If we decrease the $f_{RPS,pred}$ threshold to 0.8 (0.6), corresponding to a change in $M_{\rm HI}$ by 2 (1-)$\sigma$ with respect to the median relation of $M_{\rm HI}$ versus $M_{*}$, then 68% (58%) of the r1-RPS candidates still have $f_{RPS,pred}$ below the that. The large fraction of galaxies with low values of $f_{RPS,pred}$ implies that the present ram pressure stripping may not strongly deplete ${\rm H}{\textsc{i}}$ in many of the affected galaxies (partly a result of sample bias toward the ${\rm H}{\textsc{i}}$-rich galaxies).

The parameter $f_{RPS,pred}$ (and $f_{RPS}$) relates to the amount of strippable ${\rm H}{\textsc{i}}$, consisting of a spectrum of unresolved clouds with kinematics between those which are right to be accelerated by ram pressure and those which are right to disappear into the ICM. We investigate the post-RPS status quantified as $M_{{\rm HI}}(1-f_{RPS})$ and $M_{{\rm HI}}(1-f_{RPS,pred})$ for the RPS and r1-RPS candidates. For display purposes, we set the minimum post-RPS $M_{{\rm HI}}$ to be $10^{5.5}~M_{\odot}$.

We compare the post-RPS $M_{\rm HI}$ at a given $M_{*}$ with the detection limit of WALLABY in Fig. 5-c and d. We estimate the WALLABY detection limit for ${\rm H}{\textsc{i}}$ flux,

where the line width $v_{rot}$ ($km~s^{-1}$) is the rotational velocity predicted from the baryonic Tully-Fisher relation (McGaugh et al., 2000) assuming an edge-on view. The baryonic mass is the sum of $M_{*}$ and 1.4 (to account for helium) times $M_{{\rm HI}}$ predicted from the mean relation of $M_{{\rm HI}}$ versus $M_{*}$ taken from xGASS and extrapolated to the full $M_{*}$ range. The factor $F_{thresh}=3.5$ is the threshold for flux detection in units of the cube rms $\sigma_{cube}=2mJy~beam^{-1}$. The factor $F_{smooth}$ is set to $1/7.75$, accounting for the maximum extent of smoothing in the channel maps (2 FWHM of Gaussian beams across), and in the velocity direction (15 channels) during the source finding. Our estimate for $f_{lim}$ and $M_{HI,lim}$ is only a rough approximation, for multiple smoothing kernels were used in the source finding by SoFiA, and SoFiA further exploits a reliability parameter to exclude unreliable threshold-based detections by comparing pixel distribution properties between the detected sources and pure noise (Serra et al., 2015, 2012). These steps are missing in our rough derivation of the detection limit, and may be partly responsible for missing detections at high-$M_{*}$ ($>10^{9}~M_{\odot}$) between the derived detection limit and the xGASS relation in Fig. 5. Despite these complexities, the derived detection limit is close to the observed lower limit of detected fluxes at least for the low-$M_{*}$ galaxies (Fig. 5-a), and is enough for the following analysis.

In Fig. 5-c and d, we examine whether the post-RPS status of the r1-RPS (RPS) candidates will be observable by WALLABY in order to check the efficiency of ram pressure stripping. It also helps assess whether it is feasible to study the early (relatively weak) stage of ram pressure stripping based on the relatively shallow data of WALLABY. In other words, if all the post-RPS ${\rm H}{\textsc{i}}$ masses were below the WALLABY detection threshold, then ram pressure stripping would be highly efficient in the Hydra cluster in depleting the total ${\rm H}{\textsc{i}}$, and WALLABY would not be very useful to study even the early stage of ram pressure stripping. Based on the analysis of $f_{RPS}$ (Fig. 5-c), 3 out of the 10 resolved RPS candidates will be undetected (below the WALLABY detection threshold) after the present stripping. Based on analysis of $f_{RPS,pred}$ (Fig. 5-d), 39% (23%) of the r1-RPS candidates with $M_{*}$ below (above) $10^{9}~M_{\odot}$ will be undetected after the present stripping, but more than half of the r1-RPS candidates will only drop slightly in $M_{{\rm HI}}$ after the present removal, indicating the instantaneous ram pressure stripping to be weak in these galaxies.

In Fig. 5-d, we also compare these post-RPS $M_{{\rm HI}}$ at a given $M_{*}$ with the ALFALFA mean relation. From Fig. 5-d, we can see that $M_{\rm HI}$ changes significantly (by $>1$dex) for a few of the r1-RPS candidates, but by a relatively small extent (a few 0.1 dex) for the remaining many r1-RPS candidates. We calculate $M_{{\rm HI}}/M_{\rm HI,ALFALFA}$, the difference of $M_{\rm HI}$ from that indicated by the ALFALFA mean relation at the given $M_{*}$. Because many post-RPS $M_{\rm HI}$ drop below the displayed range in Fig. 5-d, we show the distributions of $M_{{\rm HI}}/M_{\rm HI,ALFALFA}$ for the r1-RPS galaxies at the present and in the post-RPS status in Fig. 6-b. By doing so, the fraction of r1-RPS galaxies undergoing big or small changes in $M_{\rm HI}$ after the present stripping can be better seen. We can see that, after stripping the currently strippable ${\rm H}{\textsc{i}}$, most ($\sim$2/3) of the r1-RPS candidates will remain relatively gas rich with $\log M_{{\rm HI}}/M_{\rm HI,ALFALFA}>-1$, and only $\sim$1/3 of them will be severely depleted in ${\rm H}{\textsc{i}}$. We investigated the positions of the $1/3$ most stripped galaxies in the projected phase-space diagram (not displayed in this paper). Not surprisingly, they tend to locate in the region with $\Delta v_{rad}/\sigma_{C}>1$ and $d_{proj}/r_{200}<0.5$, i.e. the region with the highest level of $P_{ram}$.

The distribution of the post-RPS ${\rm H}{\textsc{i}}$ richness (with respect to the WALLABY detection limit and with respect to the ALFALFA relation) helps explain the similarity of $M_{\rm HI}$ at a given $M_{*}$ between the r1-RPS and r1-non-RPS candidates. After a characteristic timescale for removing the currently strippable ${\rm H}{\textsc{i}}$ (the fraction indicated by $f_{RPS,pred}$), the strongly stripped galaxies will drop below the detection limit of WALLABY, the weakly stripped galaxies will only have a slightly decreased $M_{\rm HI}$, and some currently r1-non-RPS candidates will become r1-RPS candidates and recharge the population of ${\rm H}{\textsc{i}}$-rich r1-RPS population. In other words, the relatively narrow dynamical range of $M_{\rm HI}$ detectable by WALLABY, the cosmological context of galaxy infall, and the weak nature of a large fraction of the ram pressure stripping events may have worked together to produce a $M_{\rm HI}$-$M_{*}$ relation for the r1-RPS population that is very close to that of the r1-non-RPS population.

To summarize, comparing the post-RPS $M_{\rm HI}$ to the WALLABY detection limit and to the ALFALFA $M_{\rm HI}$-$M_{*}$ relation both suggest that, the current strength of ram pressure stripping can significantly deplete some galaxies (strong ram pressure stripping, $f_{RPS}>0.9$), but only weakly reduce $M_{\rm HI}$ (weak ram pressure stripping, $f_{RPS}<0.9$) for a large fraction of the affected galaxies.

At a first glance, a single temporal snapshot may not look particularly meaningful as the ram pressure will change (usually becoming strong) as galaxies move through the cluster; also, it may look obvious that $f_{RPS}$ should be low in many of these galaxies as they are not highly ${\rm H}{\textsc{i}}$ deficient. However, these results provide a first, comprehensive view of the weak ram-pressure regime in a nearby massive cluster, at a uniform detection limit. Although the instantaneous $f_{RPS,pred}$ is low in many cases, the compound effect is significant as galaxies travel through a large distance (and over a long time, $\sim$2 Gyr if traveling radially with a velocity of $\sigma_{C}$) from where ram pressure starts to strip ${\rm H}{\textsc{i}}$ ($\sim 1.25~r_{200}$), before reaching the core region ($<0.25r_{200}$, see Sec.5.2, Fig. 13) where ${\rm H}{\textsc{i}}$ is stripped throughout the disks. Such a cumulative effect has been hinted at in past hydrodynamic simulations, as the gas tails appear early (e.g. Tonnesen 2019), and are as prevalent in cluster galaxies as for the Hydra cluster (e.g. Yun et al. 2019) near the virial radius. Steinhauser et al. (2016) showed in their hydrodynamic simulations that at least for the low-mass galaxy model ($M_{*}=8.25\times 10^{9}~M_{\odot}$), the curve of growth of the stripped gas mass as a function of time is quite shallow (in contrast to an abrupt increase) during the ram pressure stripping history. Although the stripping of the outlying ${\rm H}{\textsc{i}}$ may not immediately affect the star-forming gas concentrated in the inner disk, it represents a shrinking of the gas reservoir for future star formation, and preludes the final gas depletion and star formation quenching. In order to break the degeneracy of HI depleting effects from ram pressure stripping, other environmental effects, and galactic internal mechanisms, it is necessary to consider the cumulative ram pressure stripping effect. In the future, many similar cluster observations will be provided by WALLABY, and combining them with cosmological simulations in a way like that of Rhee et al. (2020); Oman & Hudson (2016); Oman et al. (2021) will eventually quantify the cumulative effects of weak ram pressure stripping.

The ${\rm H}{\textsc{i}}$ images of resolved galaxies provide us with the opportunity to investigate how ram pressure stripping will deplete the ${\rm H}{\textsc{i}}$ in these galaxies. We note that these resolved galaxies typically (in 90%) have $M_{\rm HI}>10^{9.1}~M_{\odot}$ and $M_{*}>10^{8.4}~M_{\odot}$, so they represent a relatively restricted sample.

We investigate the capability of galaxies to restore their existing ${\rm H}{\textsc{i}}$ disks against ram pressure during the infall. We do a simplified experiment of putting each ${\rm H}{\textsc{i}}$ disk in our resolved sample at different projected distances $d$, and estimate the expected ${\rm H}{\textsc{i}}$ stripping fractions ($f_{RPS}(d)$). In the remaining part of this section, all estimates as a function of $d$ is denoted with “(d)”, and the real galactic properties of the present are denoted with the subscript “now” to avoid confusion. For each galaxy, we estimate the expected radial velocity offset at $d$ assuming the same infall acceleration profile as indicated by the projection averaged curve of $v_{esc}$ as a function of $d_{proj}$ (Fig. 3),

We then estimate the ram pressure $P_{ram}(d)$ at $v_{rad}(d)$ using the ICM density at $d$. We compare $P_{ram}(d)$ with the anchoring force profile of the galaxy, and calculate $f_{RPS}(d)$.

We plot the curve of $f_{RPS}(d)$ as a function of $d$ for both resolved RPS and non-RPS candidates in Fig. 8. Each curve describes the effective ram pressure strength as a function of $d$, measured by the anchoring force of the current disk. We define $d_{x}$ to be the projected cluster centric distance where $f_{RPS}(d)=x$ in the curve of a galaxy. So that $d_{0.1}$ indicates the maximum $d$ where the present ${\rm H}{\textsc{i}}$ disk can start to be stripped. From Fig. 8-b, there is quite a wide distribution of $d_{0.1}$ for the currently non-RPS candidates, ranging from 0.5 to 1.7 $r_{200}$, with a median value of 1.1$r_{200}$. It is consistent with the wide $d_{proj}$ range found for the r1-RPS candidates.

In the following, we will discuss questions related to the beginning and process of ram pressure stripping based on these curves.

With the WALLABY observations, we for the first time map the ${\rm H}{\textsc{i}}$ in the Hydra cluster out to 2.5$r_{200}$ (and full coverage out to 2$r_{200}$), detecting 105 members or infalling galaxies and resolving 27 of them. We quantify the extent of ${\rm H}{\textsc{i}}$ ram pressure stripping based on the ${\rm H}{\textsc{i}}$ images for the resolved galaxies, and also based on predicted ${\rm H}{\textsc{i}}$ radial distributions for all the galaxies. We emphasize that the analysis is limited to the ${\rm H}{\textsc{i}}$ rich galaxies which are at a relatively early stage of being processed by the cluster environment. Our main results are summarized below.

1. 1.

   A large fraction of ${\rm H}{\textsc{i}}$-rich galaxies in and near the Hydra cluster are affected by ram pressure stripping. Within a projected distance of $1.25r_{200}$, over two thirds of ${\rm H}{\textsc{i}}$-detected galaxies are likely affected by ram pressure stripping (the r1-RPS population).

2. 2.

   A large fraction of the ram pressure affected galaxies are likely being weakly stripped at the current time. With the present level of ram pressure, $M_{{\rm HI}}$ in around one third of the r1-RPS candidates may significantly drop (by $>1$ dex), but for the remaining two thirds, $M_{{\rm HI}}$ only slightly changes (by a few 0.1 dex). The cumulative effects of weak ram pressure stripping processes need to be further investigated.

3. 3.

   At least for the resolved galaxies ($M_{\rm HI}>10^{9.1}~M_{\odot}$ and $M_{*}>10^{8.4}~M_{\odot}$) once onset, ram pressure stripping is likely a slow process ($\gtrsim$ 600 Myr) for depleting the existing reservoir of ${\rm H}{\textsc{i}}$ in the galaxies. This is because for the ${\rm H}{\textsc{i}}$-rich galaxies with extended ${\rm H}{\textsc{i}}$ disks, ram pressure stripping can start at a relatively large cluster-centric distance ($d_{proj}\sim 1.25r_{200}$, see Reynolds et al. 2021 for a detailed analysis for one such galaxy), where the ram pressure changes slowly with cluster-centric distance. The different $d_{proj}$ for ram pressure stripping to onset, and the different speeds at which $f_{RPS}$ rises as a function of $d_{proj}$ may partly explain the scatter of quenching speed found for the SFR of cluster galaxies in the literature (Wetzel et al., 2013; Haines et al., 2015; Boselli et al., 2016).

4. 4.

   For most of the resolved RPS candidates, stripping the strippable ${\rm H}{\textsc{i}}$ is likely a relatively quick process, on time scales of $\lesssim$200 Myr, consistent with theoretical predictions. This short timescale is supported by the short distance between the current $d_{proj}$ and the predicted larger $d_{proj}$ where part (10%) of the current ${\rm H}{\textsc{i}}$ disk could already be stripped. It is also supported by the rough estimates of $\tau_{RPS}$ based on the cluster and galaxy properties, and simple kinematical and thermal models.

We look forward to expanding our analysis with larger samples from future WALLABY observations, supported by hydrodynamic and semi-analytical simulations.