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

Jing Wang (王菁) Kavli Institute for Astronomy and Astrophysics, Peking
University, Beijing 100871, China  Lister Staveley-Smith  International Centre
for Radio Astronomy Research, University of Western Australia, 35 Stirling
Highway, Crawley, WA 6009, Australia  ARC Centre of Excellence for All-Sky
Astrophysics in 3 Dimensions (ASTRO 3D), Australia  Tobias Westmeier
International Centre for Radio Astronomy Research, University of Western
Australia, 35 Stirling Highway, Crawley, WA 6009, Australia  ARC Centre of
Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
Barbara Catinella  International Centre for Radio Astronomy Research,
University of Western Australia, 35 Stirling Highway, Crawley, WA 6009,
Australia  ARC Centre of Excellence for All-Sky Astrophysics in 3 Dimensions
(ASTRO 3D), Australia  Li Shao (邵立) National Astronomical Observatories,
Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China
T.N. Reynolds  International Centre for Radio Astronomy Research, University
of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia  ARC
Centre of Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D),
Australia  Bi-Qing For  International Centre for Radio Astronomy Research,
University of Western Australia, 35 Stirling Highway, Crawley, WA 6009,
Australia  ARC Centre of Excellence for All-Sky Astrophysics in 3 Dimensions
(ASTRO 3D), Australia  Bumhyun Lee  Kavli Institute for Astronomy and
Astrophysics, Peking University, Beijing 100871, China  Ze-zhong Liang (梁泽众)
Department of Astronomy, School of Physics, Peking University, Beijing 100871,
People’s Republic of China  Shun Wang (王舜)  Kavli Institute for Astronomy and
Astrophysics, Peking University, Beijing 100871, China  Department of
Astronomy, School of Physics, Peking University, Beijing 100871, People’s
Republic of China  A. Elagali  Telethon Kids Institute, Perth Children’s
Hospital, Perth, Australia  H. Dénes  ASTRON - The Netherlands Institute for
Radio Astronomy, 7991 PD Dwingeloo, The Netherlands  D. Kleiner  INAF -
Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047 Selargius
(CA), Italy  Bärbel S. Koribalski  Australia Telescope National Facility,
CSIRO Astronomy and Space Science, P.O. Box 76, NSW 1710, Epping, Australia
Western Sydney University, Locked Bag 1797, Penrith, NSW 2751, Australia  K.
Lee-Waddell  International Centre for Radio Astronomy Research, University of
Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia  CSIRO
Astronomy and Space Science (CASS), PO Box 1130, Bentley, WA 6102, Australia
S-H. Oh  Department of Physics and Astronomy, Sejong University, 209
Neungdong-ro, Gwangjin-gu, Seoul, Republic of Korea  J. Rhee  International
Centre for Radio Astronomy Research, University of Western Australia, 35
Stirling Highway, Crawley, WA 6009, Australia  ARC Centre of Excellence for
All-Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  P. Serra  INAF -
Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047 Selargius
(CA), Italy  K. Spekkens  Royal Military College of Canada, PO Box 17000,
Station Forces, Kingston, Ontario, Canada K7K7B4  O. I. Wong  CSIRO Astronomy
and Space Science (CASS), PO Box 1130, Bentley, WA 6102, Australia
International Centre for Radio Astronomy Research, University of Western
Australia, 35 Stirling Highway, Crawley, WA 6009, Australia  ARC Centre of
Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  K.
Bekki  International Centre for Radio Astronomy Research, University of
Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia  ARC
Centre of Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D),
Australia  F. Bigiel  Argelander-Institut für Astronomie, Universität Bonn,
Auf dem Hügel 71, 53121 Bonn, Germany  H.M. Courtois  Univ Lyon, Univ Claude
Bernard Lyon 1, IUF, IP2I Lyon, F-69622, Villeurbanne, France  Kelley M. Hess
ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA,
Dwingeloo, The Netherlands  Kapteyn Astronomical Institute, University of
Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands  B.W. Holwerda
University of Louisville, Department of Physics and Astronomy, 102 Natural
Science Building, 40292 KY Louisville, USA  Kristen B.W. McQuinn  Rutgers
University, Department of Physics and Astronomy, 136 Frelinghuysen Road,
Piscataway, NJ 08854, USA  M. Pandey-Pommier  University Claude Bernard Lyon
1, 43 Boulevard du 11 Novembre 1918, 69100 Villeurbanne, France  J.M. van der
Hulst  Kapteyn Astronomical Institute, University of Groningen  L. Verdes-
Montenegro  Instituto de Astrofísica de Andalucía (CSIC)

###### Abstract

This study uses ${\rm H}{\textsc{i}}$ image data from the WALLABY pilot survey
with the ASKAP telescope, covering the Hydra cluster out to 2.5$r_{200}$. We
present the projected phase-space distribution of ${\rm
H}{\textsc{i}}$-detected galaxies in Hydra, and identify that nearly two
thirds of the galaxies within $1.25r_{200}$ may be in the early stages of ram
pressure stripping. More than half of these may be only weakly stripped, with
the ratio of strippable ${\rm H}{\textsc{i}}$ (i.e., where the galactic
restoring force is lower than the ram pressure in the disk) mass fraction
(over total ${\rm H}{\textsc{i}}$ mass) distributed uniformly below 90%.
Consequently, the ${\rm H}{\textsc{i}}$ mass is expected to decrease by only a
few 0.1 dex after the currently strippable portion of ${\rm H}{\textsc{i}}$ in
these systems has been stripped. A more detailed look at the subset of
galaxies that are spatially resolved by WALLABY observations shows that, while
it typically takes less than 200 Myr for ram pressure stripping to remove the
currently strippable portion of ${\rm H}{\textsc{i}}$, it may take more than
600 Myr to significantly change the total ${\rm H}{\textsc{i}}$ mass. Our
results provide new clues to understanding the different rates of ${\rm
H}{\textsc{i}}$ depletion and star formation quenching in cluster galaxies.

Galaxy evolution, interstellar medium

3

##  1 Introduction

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-Martínez 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.

##  2 Data and methodology

###  2.1 Data

The Hydra cluster has a distance of 47.5$\pm 3$ Mpc, a center at
$\alpha=159.0865^{\circ}$ and $\delta=-27.5629^{\circ}$, and a heliocentric
velocity of 3686 km s-1 (Kourkchi & Tully, 2017). Analysis based on X-ray data
suggested a characteristic radius $r_{200}\sim$1.35 Mpc, and the mass within
this radius, $M_{200}\sim 3.02\times 10^{14}~{}M_{\odot}$ (Reiprich &
Böhringer, 2002). Its velocity dispersion $\sigma_{C}=620~{}km~{}s^{-1}$ is
derived from $M_{200}$ using the equation of Evrard et al. (2008). The Hydra
cluster is a dynamically highly mature system, with a smooth X-ray halo, and
little substructure (Fitchett & Merritt, 1988; Lima-Dias et al., 2021). There
is a hint of two or three substructures in velocity near the cluster center
(within $0.4r_{200}$, Fitchett & Merritt 1988), but on the whole Hydra is
dynamically much more settled than the Virgo cluster. The Hydra cluster is
connected to the Antlia cluster via a filament, and the latter was mapped in
${\rm H}{\textsc{i}}$ by the Karoo Array Telescope (KAT-7) with a mosaic of
4.4 deg2 (Hess et al., 2015).

WALLABY mapped a 60 deg2 area around its center, reaching out to 4$r_{200}$
and fully covering the region within 2$r_{200}$. The WALLABY observation
reached a targeted sensitivity of $\sigma_{cube}=2.0\pm 0.5$ mJy/beam, with a
circular beam full-width half-maximum of $b_{maj}\sim$30 arcsec ($\sim$7 kpc
at the distance of Hydra) and a velocity spectral resolution of 4 km s-1. The
raw data was reduced with ASKAPsoft (Whiting, 2020), and ${\rm H}{\textsc{i}}$
sources were extracted using SoFiA 2 333https://github.com/SoFiA-Admin/SoFiA-2
with a multi-kernel smooth$+$clip algorithm (Serra et al. 2015, Westmeier et
al. submitted) at a significance level of 3.5-$\sigma$. Details about the
observation, data reduction and source finding are discussed in earlier
WALLABY publications (Koribalski et al., 2020; For et al., 2019; Kleiner et
al., 2019; Lee-Waddell et al., 2019; Elagali et al., 2019). More details of
the data used in this paper will be further elaborated in Westmeier et al. (in
prep). In this analysis we focus on the detections (N$=$105) with projected
distances within 2.5 $r_{200}$ and radial velocity differences within the
upper limit of the escape velocity from the cluster center. We highlight an
${\rm H}{\textsc{i}}$ overview of this phase-space region around the Hydra
center in Fig. 1.

We use the optical $g$ and $r$-band images from the second data release of
PanSTARRS (Waters et al., 2020) to derive optical properties. We use the
photometric pipeline described in Wang et al. (2017, 2018), which includes
standard procedures of background removal, masking, segmentation, and flux
measurements. We use Kron magnitudes, and the radial profiles of the surface
brightness. We correct for the Galactic extinction using the IRSA Dust
Extinction Service. We use the formula of Zibetti et al. (2009) to calculate
the $r$-band stellar mass to light ratio based on the $g-r$ color (assuming
the Chabrier (2003) initial mass function), and estimate the stellar mass
$M_{*}$ based on the $r$-band luminosity.

We exclude 9 systems which are likely to be strongly tidally interacting, have
highly irregular optical and ${\rm H}{\textsc{i}}$ morphologies, or have ${\rm
H}{\textsc{i}}$ bridges connecting two or multiply major galactic systems. We
also exclude 7 galaxies which do not have good optical images from PanSTARRS,
leaving 89 galaxies in our main sample.

Although we attempted to exclude major merger candidates, we cannot exclude
the influence from gravitational effects, including the harassment from
surrounding galaxies (Moore et al., 1996) and the tidal force from the main
cluster (Byrd & Valtonen, 1990). Simulations suggests that, in addition to
directly stripping the gas (Merritt, 1983; Łokas, 2020) and inducing gas
inflows (Byrd & Valtonen, 1990; Blumenthal & Barnes, 2018; Moreno et al.,
2019; Patton et al., 2020), gravitational effects may assist ram pressure
stripping by enhancing local ICM density (McPartland et al., 2016; Roediger et
al., 2011; Bekki et al., 2010; Markevitch & Vikhlinin, 2007) and relative
velocities (Ruggiero et al., 2019), and moving ${\rm H}{\textsc{i}}$ to
regions of lower anchoring force (Kapferer et al., 2008). There can be other
hydrodynamic effects from the environment like viscous stripping (Nulsen,
1982), but in this study we focus on the effect of ram pressuring stripping.

Figure 1:  WALLABY detected galaxies in the Hydra cluster. The frame is
$5.5r_{200}$ in width and $4.5r_{200}$ in height, where $r_{200}$ is the
cluster centric radius where the enclosed averaged density is 200 times the
cosmological critical density. The ${\rm H}{\textsc{i}}$ column density images
are shown in different slices of velocity offset from the cluster center
($\Delta v_{rad}$) around the X-ray halo of Hydra (grey scale, based on the
ICM model described in Sec.2.2). The column density images are enlarged by a
factor of 5 for clarity. A similar image has been shown for the Virgo Cluster
by (Chung et al., 2009) using targeted HI observations.

###  2.2 The ram pressure level

We largely follow the procedure of W20 to estimate the ram pressure and the
anchoring force. We use the equation from Ettori (2015) to convert the cluster
dynamic mass to ICM mass, and then convert the double-beta model of the X-ray
surface brightness radial profile (from Eckert et al. 2011) to the ICM number
density ($n_{{\rm ICM}}$) profile as a function of the cluster-centric radius
$r$:

$\begin{split}n_{{\rm ICM}}(r)/cm^{-3}=&0.003(1+(r/0.101~{}Mpc)^{2})^{-1}+\\\
&0.004(1+(r/0.027~{}Mpc)^{2})^{-1}.\end{split}$ (1)

The ram pressure is estimated as $P_{ram}=\rho(d_{proj})~{}\Delta v_{rad}^{2}$
(Gunn & Gott, 1972), where $\rho(d_{proj})=1.4m_{p}n_{{\rm ICM}}(d_{proj})$,
$m_{p}$ is the mass of proton and 1.4 accounts for mass contribution from the
helium, $d_{proj}$ is the projected distance from the cluster center, and
$\Delta v_{rad}$ is the velocity difference from the cluster center. Because
the observed $\Delta v_{rad}$ and $n_{{\rm ICM}}(d_{proj})$ are lower and
upper limits of the real relative velocity and the ICM density, their under-
and over-estimating effects to some extent cancel out in the estimate of
$P_{ram}$, mitigating the uncertainties from projection effects.

There may be additional uncertainties related to the assumptions of the
isothermal and smooth nature of the ICM distribution, and the extrapolation of
the ICM profile. These effects should be of lower importance than projection
effects, as Hydra is a dynamically relaxed cluster.

###  2.3  Quantifying the strippable ${\rm H}{\textsc{i}}$

The anchoring force (or restoring force) is estimated with a modified equation
of the Gunn & Gott (1972) model, as

$F_{anchor}=2\pi G(\Sigma_{*}+\Sigma_{{\rm HI}})\Sigma_{{\rm HI}},$ (2)

where $G$ is the gravitational constant, and $\Sigma_{*}$ and $\Sigma_{{\rm
HI}}$ are localized stellar and ${\rm H}{\textsc{i}}$ surface densities
(projection corrected) within the galaxy. Below we describe two parallel
methods of calculating $F_{anchor}$ and thereafter quantifying the ram
pressure stripping strength by comparing $F_{anchor}$ with $P_{ram}$. The
first method makes use of ${\rm H}{\textsc{i}}$ images and is most accurate
for the resolved galaxies. The second method makes use of predicted ${\rm
H}{\textsc{i}}$ radial distributions and works for the whole main sample. We
will use results (e.g. identification of ram pressure stripping candidates,
estimate of the strippable ${\rm H}{\textsc{i}}$ mass) from the first method
to check the reliability of results from the second method.

####  2.3.1 Quantifying the strippable ${\rm H}{\textsc{i}}$ with HI moment-0
images

We only consider the pixels of ${\rm H}{\textsc{i}}$ intensity images with a
column density $>10^{20}~{}cm^{-2}$, corresponding to a threshold of
2-$\sigma_{cube}$ with a velocity width of 20 $km~{}s^{-1}$. The ${\rm
H}{\textsc{i}}$ disks with an area larger than 6.2 times the beam area are
considered resolved, and others the unresolved disks. The threshold of 6.2
beam areas is equivalent to requiring a circle with the same area to have a
radius $>1.5b_{maj}$, as the beam area is estimated as 1.134 $b_{maj}^{2}$. We
use each of the pixels to estimate $\Sigma_{{\rm HI}}$ in a resolved ${\rm
H}{\textsc{i}}$ disk, and only use the pixel with the peak value in an
unresolved ${\rm H}{\textsc{i}}$ disk in order to have a conservative, high-
limit estimate of $F_{anchor}$. We extrapolate the stellar mass density
exponential profiles to match the radial extension of the ${\rm
H}{\textsc{i}}$ disks. We correct both ${\rm H}{\textsc{i}}$ and stellar
surface densities for projection effects by multiplying them by the optical
axis ratio, assuming infinitely thin disks. We caution that, the inner
$\Sigma_{\rm HI}$ can be both over-estimated and under-estimated when the
galaxies are marginally resolved. A general approach needs to be devised in
the future to correct for these beam smearing effects. By using the stellar
mass density profiles instead of two dimensional distributions, we may average
out outlying structures like faint spiral arms and cause a local under or
over-estimate of the anchoring forces, but it is the most reliable way to
derive $\Sigma_{*}$ in the low signal-to-noise ratio outer disks.

We compare the ram pressure with the anchoring force to estimate the fraction
of ${\rm H}{\textsc{i}}$ flux under stripping within a disk. For a resolved
${\rm H}{\textsc{i}}$ disk, we firstly produce an initial binary map for ram
pressure stripped pixels with lower anchoring force than the ram pressure. We
then undertake an “erode” and “dilate” process to remove unreliable pixels at
the edge of disks and to ensure that the ram pressure stripped region covers
at least one independent beam, which is 5 pixels across. This is done with two
iterations of each operation using the python package scipy.ndimage. Such a
treatment results in an identification bias against ram pressure stripped
pixels along the minor axis of disks, but ensures a relatively conservative
identification. We use this binary map to compute the fraction of ${\rm
H}{\textsc{i}}$ flux being stripped, $f_{RPS}$. We consider those galaxies
with $f_{RPS}>0.1$ as undergoing ram pressure stripping (referred to as RPS
candidates). We refer to the resolved galaxies which have $f_{RPS}<0.1$ as the
non-RPS candidates. By doing so, we attempt to catch the galaxies at an early
stage of continuous stripping, and do not include the galaxies which were
already severely stripped in the past, left with a heavily truncated disk of
${\rm H}{\textsc{i}}$ incapable of being stripped any more, and are extreme
${\rm H}{\textsc{i}}$ deficient at the present. We show later in Sec.2, that
the sample is strongly biased toward ${\rm H}{\textsc{i}}$ rich galaxies, and
more suitable to study the former type of galaxies than the latter.

Because we only consider the peak pixel, $f_{RPS}$ is either 1 or 0 for an
unresolved ${\rm H}{\textsc{i}}$ disk. We note that, $f_{RPS}$ for these
unresolved RPS candidates are only used for marking them as RPS candidates,
but not further analyzed.

The fraction of strippable ${\rm H}{\textsc{i}}$ ($f_{RPS}$) is of course an
underestimate as some ${\rm H}{\textsc{i}}$ will have already left the galaxy
and no longer visible. Indeed, with $f_{RPS}$ we do not attempt to quantify
the exact amount of stripped ${\rm H}{\textsc{i}}$ under the current or past
ram pressure, but instead use it as an indicator for the instantaneous ${\rm
H}{\textsc{i}}$ loss rate due to ram pressure stripping (or an indicator for
the stripping strength). Two assumptions have been made when $f_{RPS}$ is
interpreted in this way: the length of time for ram pressure to accelerate and
remove a strippable ${\rm H}{\textsc{i}}$ cloud cannot be ignored, and the
length of time for ram pressure to deplete the whole ${\rm H}{\textsc{i}}$
disk is relatively long compared to the removal of a strippable cloud. We show
in Sec.5 that both assumptions are reasonable for at least the resolved
galaxies.

In total, there are 27 resolved ${\rm H}{\textsc{i}}$ disks, among which 10
are identified to be potentially under ram pressure stripping. As can be seen
in Fig. 2-c, the majority of the RPS candidates have $f_{RPS}>0.25$, so the
sample and related results do not change much if we raise the criterion for
identifying RPS candidates to $f_{RPS}>0.2$. From the ${\rm H}{\textsc{i}}$
and ram pressure stripping atlas of these 10 resolved RPS candidates (Fig. 14
in the appendix), many of them display lopsidedness with respect to the
optical disks, indicative of ram pressure stripped tails. We do not clearly
observe tails in most of the galaxies, possibly because of the limited
resolution ($\sim$7 kpc) and depth ($10^{20}~{}cm^{-2}$) of the data. On the
other hand, the difficulty of identifying morphological features in weak RPS
galaxies has been previously pointed out in hydrodynamic simulations (Jung et
al., 2018). We find that those tentative tails (or lopsidedness) do not always
point away from the center of Hydra, which may result from the combined
projection effect of the viewing angle and the disk orientation with respect
to the orbits. The randomness in orientation of ram pressure stripped tails
was also noticed in the literature, both in observations (e.g. Kenney et al.
2014), and in hydro-dynamic simulations (Yun et al., 2019). Additionally there
are 13 unresolved RPS candidates.

There are also several sources of uncertainties in the estimate of
$F_{anchor}$, including the neglect of stellar bulges, dark matter halos and
circumgalactic medium, and most importantly the assumption of face-on infall
orientations. Uncertainties due to the neglect of the different galactic
components are mitigated by the fact that the ${\rm H}{\textsc{i}}$-rich
galaxies tend to have small bulges, and the high mass of Hydra tend to
truncate dark matter halos and remove the circumgalactic medium from galaxies
(Bahé et al., 2013; Bahé & McCarthy, 2015). Uncertainties due to the
assumption of face-on infall are mitigated by previous hydrodynamic simulation
results that orientations do not significantly affect ${\rm H}{\textsc{i}}$
mass loss due to ram pressure stripping unless the galaxies infall nearly
edge-on (inclination$>60^{\circ}$, Roediger & Brüggen 2006). Nevertheless,
given all these potential uncertainties, we caution that all results from the
ram pressure stripping analysis in this paper should be understood in a
statistical sense.

####  2.3.2 Quantifying the strippable ${\rm H}{\textsc{i}}$ with predicted HI
radial distributions

Since, as mentioned in the last section, when the HI disks are spatially
unresolved we can only identify the strongly stripped galaxies, we also use
the method of Wang et al. (2020b) based on the ${\rm H}{\textsc{i}}$ size-mass
relation to identify RPS candidates in the main sample. We use the ${\rm
H}{\textsc{i}}$ size-mass relation to estimate the radius $R_{{\rm HI}}$ where
the ${\rm H}{\textsc{i}}$ surface density $\Sigma_{{\rm HI}}\sim
1~{}M_{\odot}~{}pc^{-2}$ (Wang et al., 2016). We confirm in Fig. 2-a that at
least for the resolved galaxies, the size-mass relation still holds in the
Hydra cluster, consistent with the theoretical predictions of Stevens et al.
(2019). We then compare the ram pressure with the anchoring force at $R_{{\rm
HI}}$ for each galaxy, and identify the ram pressure stripping candidates (the
r1-RPS candidates hereafter). We identify 40 r1-RPS candidates from the whole
main sample. We check the reliability of r1-RPS identification in the bottom
panel of Fig. 3, by over plotting the r1-(non-)RPS and (non-)RPS candidates.
The r1-RPS identification is highly consistent with that based on ${\rm
H}{\textsc{i}}$ images when the disks are resolved. Particularly, all the RPS
(resolved and unresolved) candidates are successfully identified as r1-RPS
candidates, and only one non-RPS candidates is mistakenly identified as a
r1-RPS candidate. This galaxy (NGC 3336, WALLABY J104016-274630) has a strong
bar and spiral arms, which might have concentrated the ${\rm H}{\textsc{i}}$
into a bright ring in the inner disk, and caused the deviation of the real
$R_{\rm HI}$ from the predicted one.

Because different galaxies have similar profiles of $\Sigma_{{\rm HI}}$ as a
function of $r/R_{{\rm HI}}$ in the outer region (Wang et al., 2016), we use
the median profile of 168 late-type galaxies from Wang et al. (2016) to
estimate the ${\rm H}{\textsc{i}}$ stripping fraction $f_{RPS,pred}$ for the
r1-RPS candidates. For each galaxy, we have used the size-mass relation to
estimate $R_{\rm HI}$ from $M_{\rm HI}$. We combine $R_{\rm HI}$ with the
median profile of $\Sigma_{\rm HI}$ as a function of $r/R_{\rm HI}$ to predict
the profile of $\Sigma_{\rm HI}$ as a function of radius. We estimate the
radial profile of $F_{anchor}$ with the radial profiles of $\Sigma_{\rm HI}$
and $\Sigma_{*}$ based on Equ.2. We compare the $F_{anchor}$ profile with
$P_{ram}$ to determine the radial range where $F_{anchor}<P_{ram}$. We then
accumulate the $\Sigma_{\rm HI}$ profile within that radial range to estimate
the mass of strippable ${\rm H}{\textsc{i}}$, and calculate $f_{RPS,pred}$.
These steps are also summarized in Fig. 4. A similar technique was used in
Wang et al. (2020a) to successfully predict the ${\rm H}{\textsc{i}}$ mass
within and beyond the optical radius of individual galaxies. Comparing the
directly calculated $f_{RPS,pred}$ with $f_{RPS}$ for the resolved RPS
candidates suggests a correction factor of 1.4 be multiplied to $f_{RPS,pred}$
in order to match $f_{RPS}$. We show in Fig. 2-c that $f_{RPS,pred}$ is a good
predictor of $f_{RPS}$ for the resolved-RPS candidates, after such a
correction. Thus $f_{RPS,pred}$ hereafter has all been corrected in this way.
A maximum value of unity is set for $f_{RPS,pred}$ after the correction.

The correcting factor is likely because the median profile misses the ${\rm
H}{\textsc{i}}$ tails (lopsidedness) in the outer disks caused by ram pressure
stripping, and also misses the suppressed ${\rm H}{\textsc{i}}$ inner disks
possibly as a result pre-processing (Hess & Wilcots, 2013; Bahé & McCarthy,
2015). Hints for these two features can be seen by comparing the ${\rm
H}{\textsc{i}}$ radial profiles of the resolved galaxies to the median profile
of late-type galaxies (Wang et al., 2016, 2020a) (Fig. 2-b). The deviation of
shape in ${\rm H}{\textsc{i}}$ radial profiles cannot be fully explained as a
result of beam smearing, as we find that the under-estimation of $f_{RPS}$
with $f_{RPS,pred}$ does not increase with decreasing ${\rm H}{\textsc{i}}$
disk sizes. We caution that applying this correcting factor manually sets a
minimum value of 0.15 dex for $f_{RPS,pred}$, although it does not
significantly affect our major conclusion, that for many of the r1-RPS
candidates, the stripping efficiency is low. Note that such a treatment does
not affect our identification of r1-RPS candidates, which were performed
beforehand based on the size-mass relation of ${\rm H}{\textsc{i}}$.

In the rest of the paper, we analyze the RPS and r1-RPS candidates separately.
We use the r1-RPS sample for statistical trends, counts and distributions in
Sec. 3 and 4, though we also display corresponding results of the RPS sample
for a reference. We further use the resolved sample for a detailed analysis of
the ram pressure stripping history in Sec.5, through comparing the galactic
radial profiles of anchoring forces with the ram pressure levels at different
$d_{proj}$.

Tab. 1 lists the ram pressure stripping properties of galaxies derived above.

Figure 2: Radial measurements of ${\rm H}{\textsc{i}}$ for the 27 well-
resolved galaxies. Panel a: the size-mass relation of ${\rm H}{\textsc{i}}$.
The sizes $R_{\rm HI}$ have been corrected for the effect of beam smearing as
$R_{\rm HI}=\sqrt{R_{\rm HI,obs}^{2}-b_{maj}^{2}}$, where $R_{\rm HI,obs}$ is
directly derived from the ${\rm H}{\textsc{i}}$ images as the semi-major axis
of the ellipse with a de-projected surface density of
1$~{}M_{\odot}~{}pc^{-2}$. The mean relation and scatter from Wang et al.
(2016) is plotted as the grey line and shaded region. Panel b: the radial
profiles of ${\rm H}{\textsc{i}}$ surface density $\Sigma_{\rm HI}$. The
projection correction has been applied assuming an infinitely thin disk and an
axis ratio determined from the optical light. The radii are normalized by
$R_{\rm HI}$. The median profile of 168 late-type galaxies (Wang et al., 2016,
2020a) is plotted as a grey, thick curve. The green dashed line marks
$\Sigma_{\rm HI}=0.8~{}M_{\odot}$ corresponding to the detection limit of the
WALLABY data. Panel c: predicted versus observed fraction of strippable ${\rm
H}{\textsc{i}}$ mass over the total ${\rm H}{\textsc{i}}$ mass ($f_{RPS}$) for
the resolved RPS candidates. The predicted fraction $f_{RPS,pred}$ has been
corrected by multiplying by a factor of 1.4 (see text), in order to match the
observed $f_{RPS}$ on the one-to-one line. The 1-$\sigma$ rms of the
difference between the two quantities are 0.19 dex, which drops to 0.14 dex if
we exclude the one outlier which has $f_{RPS}$ close to the threshold of 0.1
for identifying RPS candidates. In all panels, RPS (non-RPS) candidates are in
red (blue).

Figure 3:  The projected phase-space diagram of the Hydra cluster. The dashed
straight line marks the border of the virialized region, and the dashed
(dotted) curve shows the averaged (upper limits of) projected escape
velocities as a function of the projected cluster centric distance $d_{proj}$,
which are expected for an NFW dark matter profile with a concentration of 4
(Navarro et al., 1997). Top: optical members of the Hydra cluster from
Kourkchi & Tully (2017) in orange pluses, and all the ${\rm H}{\textsc{i}}$
detections of WALLABY in black circles. Bottom: Only galaxies from the main
sample are displayed. The resolved RPS (non-RPS) candidates are marked by red
(blue) crosses respectively, and the unresolved RPS candidates in red “tri-
down” symbols. The filled circles are colored red (blue) if they are in the
r1-RPS (r1-non-RPS) type.  Figure 4:  Procedure to estimate the fraction of
strippable ${\rm H}{\textsc{i}}$ mass over the total ${\rm H}{\textsc{i}}$
mass ($f_{RPS,pred}$). We use the ${\rm H}{\textsc{i}}$ size-mass relation
${\rm H}{\textsc{i}}$ ($R_{\rm HI}$ versus $M_{\rm HI}$), and the median
profile of ${\rm H}{\textsc{i}}$ surface density ($\Sigma_{\rm HI}$) as a
function of $r/R_{\rm HI}$ from Wang et al. (2016). See text in Sec.2.3.2 for
details.

##  3 Distribution of galaxies in the projected phase space diagram

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.

##  4  HI richness and the influence from ram pressure stripping

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,

$f_{lim}/(Jy~{}km~{}s^{-1})=F_{thresh}F_{smooth}\sigma_{cube}2v_{rot}$ (3)

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.

Figure 5:  The relation between the ${\rm H}{\textsc{i}}$ mass ($M_{\rm HI}$)
and the stellar mass ($M_{*}$) of the main sample. Panel a: different types of
galaxies are plotted in the same symbols as in the bottom panel of Fig. 3. We
mark the mean relations from xGASS (grey dashed line) and ALFALFA (pink dashed
line), and the detection limit of WALLABY (green dotted line, see text). Panel
b: the best-fit linear relations for the r1-RPS (red) and r1-non-PRS (blue)
populations. The shaded regions mark the 1-$\sigma$ uncertainty of fitting.
Panel c: brown stars plot the predicted position (post-RPS status) of galaxies
after subtracting the strippable ${\rm H}{\textsc{i}}$, i.e. $M_{\rm
HI}(1-f_{RPS})$ versus $M_{*}$. Dotted lines link the observed and post-RPS
positions of each galaxy. Panel d: similar to panel c, but with the post-RPS
${\rm H}{\textsc{i}}$ mass estimated with $f_{RPS,pred}$ instead of $f_{RPS}$.
As indicated by the dotted lines, many post-RPS positions are at $M_{\rm HI}$
lower than the displayed range.  Figure 6:  Distributions of the ram pressure
stripping strengths for the r1-RPS candidates. Panel a plots the predicted
mass fraction of strippable ${\rm H}{\textsc{i}}$ ($f_{RPS,pred}$). Panel b
plots the difference of $M_{\rm HI}$ at a given $M_{*}$ with respect to the
ALFALFA mean relation of $M_{\rm HI}$ versus $M_{*}$ ($\log M_{\rm HI}/M_{\rm
HI,ALFALFA}$). The distributions of $\log M_{\rm HI}/M_{\rm HI,ALFALFA}$ at
the present and in the post-RPS status after removing the strippable ${\rm
H}{\textsc{i}}$ (i.e. $M_{\rm HI}(1-f_{RPS,pred})/M_{\rm HI,ALFALFA}$) are
plotted in red and blue respectively.

##  5 Ram pressure stripping of the resolved galaxies

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),

$\Delta v_{rad}(d)=(\Delta
v_{rad,now}^{2}+(v_{esc}^{2}(d)-v_{esc,now}^{2}))^{0.5}.$ (4)

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.

###  5.1  Time needed to strip the currently strippable HI in the RPS
candidates

For each of the resolved RPS candidates, at a projected distance of $d_{0.1}$,
which by definition is higher than $d_{now}$, the ram pressure is already high
enough to strip some of the currently strippable ${\rm H}{\textsc{i}}$, but
the strippable ${\rm H}{\textsc{i}}$ at $d_{0.1}$ can still be partly observed
at the present because the strippable ${\rm H}{\textsc{i}}$ clouds do not
immediately disappear into the ICM. The parameter $d_{0.1}-d_{now}$ is an
indicator ($\sim$ upper limit) of the timescale ($\tau_{RPS}$) needed for ram
pressrue to remove the strippable ${\rm H}{\textsc{i}}$.

From Fig. 8-a, $d_{0.1}-d_{now}<0.2r_{200}$ for all the resolved RPS
candidates, and also $<0.1r_{200}$ except for two galaxies (239 and 244 in
Fig. 14, with WALLABY ID J104059-270456 and J104142-284653 respectively). A
distance of $0.1r_{200}$ takes $\sim$200 Myr for a galaxy with velocity
$\sigma_{C}$ to travel through, suggesting that ram pressure stripping is a
relatively fast mechanism (with a timescale of $\sim$ hundreds Myr) when
removing the strippable gas.

Figure 7:  Figure 8:  The relation between expected fraction of strippable
${\rm H}{\textsc{i}}$ ($f_{RPS}(d)$) at different projected cluster centric
distances ($d/r_{200}$) for the resolved galaxies. The steep (shallow) curves,
which take less than (at least) 0.2$r_{200}$ for $f_{RPS}(d)$ to increase from
0.1 to 0.75, are in orange (green). The horizontal dashed lines mark the
positions for $f_{RPS}(d)$ equaling 0.1 and 0.75. Panel a: for the RPS
candidates; their observed $d_{proj}$ and $f_{RPS}$ are marked as dots. Panel
b: for the non-RPS candidates; $d_{proj}$ are larger than the displayed
maximum $d$ of each curve.

We roughly estimate $\tau_{RPS}$ for the resolved RPS candidates by
considering two scenarios. In the first scenario, the RPS is strong and the
stripped ${\rm H}{\textsc{i}}$ cloud quickly reaches the escape velocity. The
escape timescale is estimated as $\tau_{esc}=\sqrt{2}v_{rot}\Sigma_{{\rm
HI},p50}/P_{ram}$ (Vollmer et al., 2001), where $\Sigma_{{\rm HI},p50}$ is the
median $\Sigma_{{\rm HI}}$ of the currently strippable ${\rm H}{\textsc{i}}$.
In the second scenario, the ram pressure stripping is weak so that the
stripped cloud is evaporated in the ICM after leaving the ${\rm
H}{\textsc{i}}$ disk before being accelerated enough to escape. The timescale
is the sum of the time needed for the cloud to rise a distance $h$ above the
disk, and the time needed for the cloud to be evaporated. The former timescale
is estimated as $\tau_{rise}=(2h\Sigma_{{\rm HI},p50}/P_{ram})^{0.5}$ (Vollmer
et al., 2001), where we assume $h=5~{}kpc$. According to Cowie & McKee (1977),
the evaporating timescale is estimated as

$\begin{split}\tau_{evap}&=\frac{9.07\times 10^{7}(N_{{\rm
HI},p50}/10^{20}~{}cm^{-2})}{2.73(n_{{\rm
ICM}}/cm^{-3})(T/K)^{0.5}\sigma_{0}^{3/8}}yr\\\
\sigma_{0}&=\frac{(T/1.54\times 10^{7}~{}K)^{2}}{(n_{{\rm
ICM}}/cm^{-3})(R_{c}/pc)}\end{split}$ (5)

where $n_{{\rm ICM}}$ is the ICM density, $N_{{\rm HI},p50}$ is the column
density corresponding to $\Sigma_{{\rm HI},p50}$, the Hydra ICM temperature
$T=3.76\times 10^{7}~{}K$ (Eckert et al., 2011), and as in Vollmer et al.
(2001) we assume a cloud radius $R_{c}=10~{}pc$. Then $\tau_{RPS}$ is
estimated as the lesser of $\tau_{rise}+\tau_{evap}$ and $\tau_{esc}$. In
presence of magnetic fields, the real $\tau_{evap}$ can be a few times longer,
but ignoring this effect does not significantly affect our results because
$\tau_{rise}\gg\tau_{evap}$ in all cases. We also ignored the gravitational
force from the galaxy when estimating $\tau_{esc}$ and $\tau_{rise}$, but this
uncertainty is mitigated by the fact that most of the ram pressure stripped
pixels in the ${\rm H}{\textsc{i}}$ image have $P_{ram}>2F_{anchor}$ (Fig14).
Nevertheless, these timescales should only be viewed as an order-of-magnitude
estimate, due to uncertainties from the disk inclination and other factors.
From Fig. 10, most of the ram pressure stripped gas is lost through
evaporation in the RPS candidates, and the values of $\tau_{RPS}$ are
consistent with our interpretation of the $f_{RPS}(d)$ curves of the resolved
RPS candidates. The values are also consistent with theoretical predications
in the literature (e.g., Abadi et al., 1999; Roediger & Brüggen, 2006;
Tonnesen, 2019). They support the view that ram pressure stripping is a
relatively quick process when removing the strippable gas, even for cases
where the ram pressure is low and thus $f_{RPS}$ is low.

Figure 9:  Figure 10:  The estimated timescales for ram pressure stripped
clouds to escape ($\tau_{esc}$) and to be evaporated
($\tau_{rise}+\tau_{evap}$). The resolved (unresolved) RPS candidates are
plotted in red crosses (down-tri shapes). The dashed line marks the position
of $\tau_{esc}=\tau{rise}+\tau{evap}$.

###  5.2 Time needed to strip the existing ${\rm H}{\textsc{i}}$ reservoir

Another noticeable feature from Fig 8 is that the curves of $f_{RPS,exp}$ have
distinct slopes. We use $d_{0.1}-d_{0.75}<(>)0.3r_{200}$ as the criteria of
selecting the steep (shallow) $d_{proj,ex}$ curves. The parameter
$d_{0.1}-d_{0.75}$ can be viewed as an indicator of the length of time needed
to remove the majority of the existing ${\rm H}{\textsc{i}}$ reservoir in a
galaxy with ram pressure. Although the existing ${\rm H}{\textsc{i}}$ mass is
different from the initial ${\rm H}{\textsc{i}}$ mass upon infall,
investigating the time needed to significantly deplete it is still meaningful,
as most of the galaxies in our sample are still relatively ${\rm
H}{\textsc{i}}$-rich. Removing $75\%$ of the ${\rm H}{\textsc{i}}$ is
equivalent to decreasing $M_{\rm HI}$ by 0.6 dex. A distance of $0.3r_{200}$
takes $\sim$600 Myr for a galaxy with velocity $\sigma_{C}$ to travel through.
If we change the indicator $d_{0.1}-d_{0.75}$ to $d_{0.1}-d_{0.9}$, the
related distance (traveling time) will increase, and more of the resolved
galaxies will be classified with shallow curves, but the conclusions are
similar.

Galaxies with shallow $f_{RPS}(d)$ curves tend to be stripped for a relatively
long period of time ($\geq 600$ Myr, if we assume galaxies radially travel
with an average speed of $\sigma_{C}$). Fig 8 suggests that, the resolved
galaxies on shallow curves tend to have larger $d$ than those on steep curves,
with a K-S test probability of 0.01 for the distributions of $d_{proj}$ to be
similar among the two sub-samples. Due to the relatively small sample size, we
do not find statistically significant differences in other properties between
the galaxies with shallow and steep $f_{RPS}(d)$ curves. Fig 8-b suggests
that, most ($\sim$70%) of the currently non-RPS candidates will start the ram
pressure stripping process with shallow $f_{RPS}(d)$ curves.

The shallow $f_{RPS}(d)$ profiles, particularly for the non-RPS candidates in
the future, are likely due to the shallow ICM density profile beyond the core
region of the cluster, and the extended nature of ${\rm H}{\textsc{i}}$ disks.
Fig. 13 demonstrates these two effects. In Fig. 13-a, $\log P_{ram}$ rises by
three orders of magnitude when $d_{proj}<0.5r_{200}$, and only rises by two
orders of magnitude when $2.5r_{200}>d_{proj}>0.5r_{200}$. In Fig. 13-b, the
radial range of $F_{anchor}$ profiles (${\rm H}{\textsc{i}}$ disks) extends
far beyond the optical disk ($r_{90,r}$) in many galaxies, and the profiles
rise relatively smoothly (roughly exponentially) toward the galaxy centers. In
these resolved galaxies, $F_{anchor}>10^{-13}~{}Pa~{}s^{-1}$ throughout most
of the radial ranges. A ram pressure of $10^{-13}~{}Pa~{}s^{-1}$ already
starts at $d_{proj}\sim 1.25r_{200}$ in the infall region (far beyond the
triangle of virialized region) of the projected phase-space diagram (Fig.
13-a), consistent with where RPS and r1-RPS candidates start to be detected.
On the other hand, $P_{ram}$ needs to rise above $10^{-12}~{}Pa~{}s^{-1}$ (the
typical $F_{anchor}$ at $r_{90,r}$) in order to effectively strip the ${\rm
H}{\textsc{i}}$ within the optical disks. This requires the infalling galaxies
to reach $d_{proj}<0.5r_{200}$. It needs to further rise above
$10^{-11}~{}Pa~{}s^{-1}$ in order to completely strip the ${\rm
H}{\textsc{i}}$ from the majority of those resolved galaxies, which requires
the infalling galaxies to reach $d_{proj}<0.25r_{200}$. Indeed very few
galaxies (in total 4) are detected by WALLABY in the triangular region (the
“stripping zone” defined in Jaffé et al. 2015) of the projected phase-space
diagram where $P_{ram}>10^{-11}~{}Pa~{}s^{-1}$. The key point to make here is
that, galaxies travel for a large $d_{proj}$ (hence time) between the onset
and end of ram pressure stripping, emphasising the importance of the effect of
weak but cumulative ram pressure stripping forces.

Figure 11:  Figure 12:

Figure 13:  The ram pressure level of the Hydra cluster and the anchoring
force profiles of all the resolved galaxies. Panel a: The distribution of ram
pressure ($P_{ram}$) in the projected phase-space diagram. The projected
phase-space diagram is the same as in Fig. 3. The resolved RPS and non-RPS
candidates are in red and blue crosses respectively. Panel b: The azimuthally
averaged anchoring force ($F_{anchor}$) radial profile of galaxies. The
resolved RPS and non-RPS candidates are in red and blue respectively. The
radii of each profile are normalized by the 90%-light radius of the galaxy in
the $r$-band ($r_{90,r}$). The largest radius for each galaxy is determined by
the size of the ${\rm H}{\textsc{i}}$ disk. The space of $F_{anchor}$ is color
coded with the same scales as $P_{ram}$ in panel a.

Thus, we have observed diversities in ram pressure stripping not only for the
instantaneous strength ($f_{RPS}$), but also for the averaged speed
($d_{proj,ex,0.1}-d_{proj,ex,0.75}$). For the non-RPS candidates, there is
further a diversity in $d_{proj}$ for ram pressure stripping to onset. Modern
hydrodynamic simulations under a cosmological context predicted that most
galaxies lose the majority of ${\rm H}{\textsc{i}}$ through ram pressure
stripping in one passage of infall into massive clusters, but there is a large
scatter in the speed of ${\rm H}{\textsc{i}}$ depletion (Jung et al., 2018;
Oman et al., 2021; Lotz et al., 2019), not only because of scatter in the
infall orbits, but also because of scatter in the initial conditions. Our
results are qualitatively consistent with the latter. The early, strong and
rapid ram pressure stripping associated with large $d_{0.1}$, high $f_{RPS}$,
and low $d_{0.1}-d_{0.75}$ is more likely to link with a fast depletion, while
late, weak and slow ram pressure stripping associated with small
$d_{proj,ex,0.1},$low $f_{RPS}$ and high $d_{proj,ex,0.1}-d_{proj,ex,0.75}$ is
more likely to link with a slow depletion. A closer comparison in
distributions of $f_{RPS}$ and $d_{proj,ex,0.1}-d_{proj,ex,0.75}$ between the
observed and simulated datasets may help advance our understanding of the role
of ram pressure stripping in galaxy evolution, particularly when more clusters
are observed in the future.

The diversity in ram pressure stripping strength$/$speed may further link to
the diversity in star forming histories of cluster galaxies. There has been a
debate in the observational literature regarding the time needed to quench the
SFR of galaxies infalling into clusters. Analysis of star forming histories
has suggested a slow mode (2-4 Gyr, Wetzel et al. 2013; Paccagnella et al.
2016, a fast mode ($<1$ Gyr, Muzzin et al. 2014; Boselli et al. 2016), and a
combination of the two modes (Haines et al., 2015; Maier et al., 2019). In
those studies, slow quenching was typically attributed to the effect of
starvation where galaxies lose their hot gas halos due to ram pressure
stripping, stop gas accretion, and gradually quench when the remaining cold
gas is consumed (Larson et al., 1980). Fast quenching was typically linked to
strong ram pressure stripping that effectively removes ${\rm H}{\textsc{i}}$
throughout the disks (Jaffé et al., 2015). Our results suggest that ram
pressure starts to remove ${\rm H}{\textsc{i}}$ long before it affects the
whole ${\rm H}{\textsc{i}}$ disk. Although there can be considerable delay
between the significant removal of ${\rm H}{\textsc{i}}$ and the final
quenching of star formation (Cortese & Hughes, 2009; Boselli et al., 2014;
Oman et al., 2021), the scatter in the timescale for ram pressure stripping to
deplete most of the ${\rm H}{\textsc{i}}$ in a disk may contribute to the
scatter in the quenching timescale. The effect of weak ram pressure stripping
of ${\rm H}{\textsc{i}}$ on star formation is close to the traditionally
defined starvation caused by the removal of the hot gas halo (Larson et al.,
1980), because it gradually shrinks the extended ${\rm H}{\textsc{i}}$ disks,
which serve as the reservoir instead of the direct material for star
formation. The extended ${\rm H}{\textsc{i}}$ gradually flows radially inward
(Schmidt et al., 2016) to fuel the inner disks, and the inner ${\rm
H}{\textsc{i}}$ is converted to the molecular gas and then stars (Bigiel et
al., 2008; Wang et al., 2020a). But stripping of the ${\rm H}{\textsc{i}}$
should be more efficient than starvation in quenching, as ${\rm
H}{\textsc{i}}$ is a closer step to star formation than the hot gas halo. The
weak ram pressure stripping of ${\rm H}{\textsc{i}}$ thus adds an intermediate
step between the gentle starvation that starts at a large cluster-centric
radii ($\sim 3r_{200}$, Bahé & McCarthy 2015), and the violent strong ram
pressure stripping prevalent near the cores of clusters ($<0.3r_{200}$, Jaffé
et al. 2015), possibly leading to a stronger environmental effect and less
room for galactic internal mechanisms (like stellar feedbacks) in interpreting
the distribution of $M_{\rm HI}$ and SFR in cluster galaxies.

###  5.3 Caveats

Because the estimates of ram pressure stripping strength suffer from
uncertainties of projection, orbits and other effects, the analysis above
should be interpreted in a statistical sense, instead of a case-by-case
manner. When interpreting our results, we ignore many physical processes
including the cooling of ionized gas, the falling back of the stripped ${\rm
H}{\textsc{i}}$, the depletion due to star formation and feedback, the
redistribution of ${\rm H}{\textsc{i}}$ within the disk, the change in orbital
directions, external gravitational effects. Also, the analysis is not about
removing all the ${\rm H}{\textsc{i}}$ from the initial conditions upon
infall, but about removing what’s left at the current epoch. Thus the analysis
should be viewed as qualitative, with order-of-magnitude estimates.

Quantifying the star forming history (as in Boselli et al. 2016), using
dynamic simulations combined with ${\rm H}{\textsc{i}}$-richness and star
forming history to constrain the infall orbits (Vollmer et al. 2001), and$/$or
directly comparing the snapshots of ram pressure stripping presented in this
paper with cosmological hydrodynamic simulations in the future may assist in
gaining further insight into the gas depletion and star formation quenching
processes in clusters.

##  6 Summary

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.

We thank R. White, J. Fu, J.-Y. Tang, Z.-L. Zhang, L. Cortese, K. Oman, A.
Stevens, A. Bosma for useful discussions. JW acknowledges support from the
National Science Foundation of China (12073002, 11721303). Parts of this
research were supported by High-performance Computing Platform of Peking
University. Parts of this research were conducted by the Australian Research
Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO
3D), through project number CE170100013. This project has received funding
from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement no. 679627; project
name FORNAX). FB acknowledges funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No.726384/Empire). LVM acknowledges financial support from
the grants AYA2015-65973-C3-1-R and RTI2018-096228- B-C31 (MINECO/FEDER, UE),
as well as from the State Agency for Research of the Spanish MCIU through the
”Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de
Andalucía (SEV-2017-0709). SHO acknowledges support from the National Research
Foundation of Korea (NRF) grant funded by the Korea government (Ministry of
Science and ICT: MSIT) (No. NRF-2020R1A2C1008706). The Australian SKA
Pathfinder is part of the Australia Telescope National Facility which is
managed by CSIRO. Operation of ASKAP is funded by the Australian Government
with support from the National Collaborative Research Infrastructure Strategy.
ASKAP uses the resources of the Pawsey Supercomputing Centre. Establishment of
ASKAP, the Murchison Radio-astronomy Observatory and the Pawsey Supercomputing
Centre are initiatives of the Australian Government, with support from the
Government of Western Australia and the Science and Industry Endowment Fund.
We acknowledge the Wajarri Yamatji people as the traditional owners of the
Observatory sites. The Pan-STARRS1 Surveys (PS1) and the PS1 public science
archive have been made possible through contributions by the Institute for
Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-
Planck Society and its participating institutes, the Max Planck Institute for
Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial
Physics, Garching, The Johns Hopkins University, Durham University, the
University of Edinburgh, the Queen’s University Belfast, the Harvard-
Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global
Telescope Network Incorporated, the National Central University of Taiwan, the
Space Telescope Science Institute, the National Aeronautics and Space
Administration under Grant No. NNX08AR22G issued through the Planetary Science
Division of the NASA Science Mission Directorate, the National Science
Foundation Grant No. AST-1238877, the University of Maryland, Eötvös Loránd
University (ELTE), the Los Alamos National Laboratory, and the Gordon and
Betty Moore Foundation.

## References

  * Abadi et al. (1999) Abadi, M. G., Moore, B., & Bower, R. G. 1999, MNRAS, 308, 947. doi:10.1046/j.1365-8711.1999.02715.x
  * Abramson et al. (2011) Abramson, A., Kenney, J. D. P., Crowl, H. H., et al. 2011, AJ, 141, 164. doi:10.1088/0004-6256/141/5/164
  * Ayromlou et al. (2020) Ayromlou, M., Kauffmann, G., Yates, R. M., et al. 2020, arXiv:2011.05336
  * Bahé et al. (2013) Bahé, Y. M., McCarthy, I. G., Balogh, M. L., et al. 2013, MNRAS, 430, 3017. doi:10.1093/mnras/stt109
  * Bahé & McCarthy (2015) Bahé, Y. M. & McCarthy, I. G. 2015, MNRAS, 447, 969. doi:10.1093/mnras/stu2293
  * Bahé et al. (2019) Bahé, Y. M., Schaye, J., Barnes, D. J., et al. 2019, MNRAS, 485, 2287. doi:10.1093/mnras/stz361
  * Bekki (2014) Bekki, K. 2014, MNRAS, 438, 444. doi:10.1093/mnras/stt2216
  * Bekki et al. (2010) Bekki, K., Owers, M. S., & Couch, W. J. 2010, ApJ, 718, L27. doi:10.1088/2041-8205/718/1/L27
  * Bigiel et al. (2008) Bigiel, F., Leroy, A., Walter, F., et al. 2008, AJ, 136, 2846. doi:10.1088/0004-6256/136/6/2846
  * Blumenthal & Barnes (2018) Blumenthal, K. A. & Barnes, J. E. 2018, MNRAS, 479, 3952. doi:10.1093/mnras/sty1605
  * Boselli et al. (2020) Boselli, A., Fossati, M., Longobardi, A., et al. 2020, A&A, 634, L1. doi:10.1051/0004-6361/201937310
  * Boselli et al. (2014) Boselli, A., Voyer, E., Boissier, S., et al. 2014, A&A, 570, A69. doi:10.1051/0004-6361/201424419
  * Boselli et al. (2016) Boselli, A., Roehlly, Y., Fossati, M., et al. 2016, A&A, 596, A11. doi:10.1051/0004-6361/201629221
  * Boselli & Gavazzi (2006) Boselli, A. & Gavazzi, G. 2006, PASP, 118, 517. doi:10.1086/500691
  * Byrd & Valtonen (1990) Byrd, G. & Valtonen, M. 1990, ApJ, 350, 89. doi:10.1086/168362
  * Catinella et al. (2018) Catinella, B., Saintonge, A., Janowiecki, S., et al. 2018, MNRAS, 476, 875. doi:10.1093/mnras/sty089
  * Cayatte et al. (1990) Cayatte, V., van Gorkom, J. H., Balkowski, C., et al. 1990, AJ, 100, 604. doi:10.1086/115545
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763. doi:10.1086/376392
  * Chen et al. (2020) Chen, H., Sun, M., Yagi, M., et al. 2020, MNRAS, 496, 4654. doi:10.1093/mnras/staa1868
  * Chung et al. (2009) Chung, A., van Gorkom, J. H., Kenney, J. D. P., et al. 2009, AJ, 138, 1741. doi:10.1088/0004-6256/138/6/1741
  * Chung et al. (2007) Chung, A., van Gorkom, J. H., Kenney, J. D. P., et al. 2007, ApJ, 659, L115. doi:10.1086/518034
  * Cortese et al. (2008) Cortese, L., Minchin, R. F., Auld, R. R., et al. 2008, MNRAS, 383, 1519. doi:10.1111/j.1365-2966.2007.12664.x
  * Cortese & Hughes (2009) Cortese, L. & Hughes, T. M. 2009, MNRAS, 400, 1225. doi:10.1111/j.1365-2966.2009.15548.x
  * Cortese et al. (2011) Cortese, L., Catinella, B., Boissier, S., et al. 2011, MNRAS, 415, 1797. doi:10.1111/j.1365-2966.2011.18822.x
  * Cowie & McKee (1977) Cowie, L. L. & McKee, C. F. 1977, ApJ, 211, 135. doi:10.1086/154911
  * Crowl et al. (2005) Crowl, H. H., Kenney, J. D. P., van Gorkom, J. H., et al. 2005, AJ, 130, 65. doi:10.1086/430526
  * Cybulski et al. (2014) Cybulski, R., Yun, M. S., Fazio, G. G., et al. 2014, MNRAS, 439, 3564. doi:10.1093/mnras/stu200
  * De Lucia et al. (2019) De Lucia, G., Hirschmann, M., & Fontanot, F. 2019, MNRAS, 482, 5041. doi:10.1093/mnras/sty3059
  * De Lucia et al. (2012) De Lucia, G., Weinmann, S., Poggianti, B. M., et al. 2012, MNRAS, 423, 1277. doi:10.1111/j.1365-2966.2012.20983.x
  * Dénes et al. (2014) Dénes, H., Kilborn, V. A., & Koribalski, B. S. 2014, MNRAS, 444, 667. doi:10.1093/mnras/stu1337
  * Eckert et al. (2011) Eckert, D., Molendi, S., & Paltani, S. 2011, A&A, 526, A79. doi:10.1051/0004-6361/201015856
  * Elagali et al. (2019) Elagali, A., Staveley-Smith, L., Rhee, J., et al. 2019, MNRAS, 487, 2797. doi:10.1093/mnras/stz1448
  * Ettori (2015) Ettori, S. 2015, MNRAS, 446, 2629. doi:10.1093/mnras/stu2292
  * Evrard et al. (2008) Evrard, A. E., Bialek, J., Busha, M., et al. 2008, ApJ, 672, 122. doi:10.1086/521616
  * Fitchett & Merritt (1988) Fitchett, M. & Merritt, D. 1988, ApJ, 335, 18. doi:10.1086/166902
  * For et al. (2019) For, B.-Q., Staveley-Smith, L., Westmeier, T., et al. 2019, MNRAS, 489, 5723. doi:10.1093/mnras/stz2501
  * Fujita (2004) Fujita, Y. 2004, PASJ, 56, 29. doi:10.1093/pasj/56.1.29
  * Gallagher (1978) Gallagher, J. S. 1978, ApJ, 223, 386. doi:10.1086/156273
  * Gavazzi et al. (2006) Gavazzi, G., O’Neil, K., Boselli, A., et al. 2006, A&A, 449, 929. doi:10.1051/0004-6361:20053844
  * Gavazzi (1989) Gavazzi, G. 1989, ApJ, 346, 59. doi:10.1086/167985
  * Gunn & Gott (1972) Gunn, J. E. & Gott, J. R. 1972, ApJ, 176, 1. doi:10.1086/151605
  * Hess & Wilcots (2013) Hess, K. M. & Wilcots, E. M. 2013, AJ, 146, 124. doi:10.1088/0004-6256/146/5/124
  * Hess et al. (2015) Hess, K. M., Jarrett, T. H., Carignan, C., et al. 2015, MNRAS, 452, 1617. doi:10.1093/mnras/stv1372
  * Huang et al. (2012) Huang, S., Haynes, M. P., Giovanelli, R., et al. 2012, ApJ, 756, 113. doi:10.1088/0004-637X/756/2/113
  * Haines et al. (2013) Haines, C. P., Pereira, M. J., Smith, G. P., et al. 2013, ApJ, 775, 126. doi:10.1088/0004-637X/775/2/126
  * Haines et al. (2015) Haines, C. P., Pereira, M. J., Smith, G. P., et al. 2015, ApJ, 806, 101. doi:10.1088/0004-637X/806/1/101
  * Haynes et al. (2018) Haynes, M. P., Giovanelli, R., Kent, B. R., et al. 2018, ApJ, 861, 49. doi:10.3847/1538-4357/aac956
  * Haynes et al. (2011) Haynes, M. P., Giovanelli, R., Martin, A. M., et al. 2011, AJ, 142, 170. doi:10.1088/0004-6256/142/5/170
  * Jáchym et al. (2009) Jáchym, P., Köppen, J., Palouš, J., et al. 2009, A&A, 500, 693. doi:10.1051/0004-6361/200811469
  * Jaffé et al. (2015) Jaffé, Y. L., Smith, R., Candlish, G. N., et al. 2015, MNRAS, 448, 1715. doi:10.1093/mnras/stv100
  * Jaffé et al. (2016) Jaffé, Y. L., Verheijen, M. A. W., Haines, C. P., et al. 2016, MNRAS, 461, 1202. doi:10.1093/mnras/stw984
  * Jaffé et al. (2018) Jaffé, Y. L., Poggianti, B. M., Moretti, A., et al. 2018, MNRAS, 476, 4753. doi:10.1093/mnras/sty500
  * Jones et al. (2016) Jones, M. G., Papastergis, E., Haynes, M. P., et al. 2016, MNRAS, 457, 4393. doi:10.1093/mnras/stw263
  * Jung et al. (2018) Jung, S. L., Choi, H., Wong, O. I., et al. 2018, ApJ, 865, 156. doi:10.3847/1538-4357/aadda2
  * Kapferer et al. (2008) Kapferer, W., Kronberger, T., Ferrari, C., et al. 2008, MNRAS, 389, 1405. doi:10.1111/j.1365-2966.2008.13665.x
  * Kauffmann et al. (2003) Kauffmann, G., Heckman, T. M., White, S. D. M., et al. 2003, MNRAS, 341, 54. doi:10.1046/j.1365-8711.2003.06292.x
  * Kenney et al. (2004) Kenney, J. D. P., van Gorkom, J. H., & Vollmer, B. 2004, AJ, 127, 3361. doi:10.1086/420805
  * Kenney et al. (2014) Kenney, J. D. P., Geha, M., Jáchym, P., et al. 2014, ApJ, 780, 119. doi:10.1088/0004-637X/780/2/119
  * Kleiner et al. (2019) Kleiner, D., Koribalski, B. S., Serra, P., et al. 2019, MNRAS, 488, 5352. doi:10.1093/mnras/stz2063
  * Koopmann & Kenney (2004) Koopmann, R. A. & Kenney, J. D. P. 2004, ApJ, 613, 851. doi:10.1086/423190
  * Koribalski et al. (2020) Koribalski, B. S., Staveley-Smith, L., Westmeier, T., et al. 2020a, Ap&SS, 365, 118. doi:10.1007/s10509-020-03831-4
  * Koribalski (2020) Koribalski, B. S. 2020b, arXiv:2002.07312, IAU Symposium No. 355 ”The Realm of the Low-Surface-Brightness Universe” proceedings, 2020, eds. D. Valls-Gabaud, I. Trujillo & S. Okamoto
  * Kourkchi & Tully (2017) Kourkchi, E. & Tully, R. B. 2017, ApJ, 843, 16. doi:10.3847/1538-4357/aa76db
  * Larson et al. (1980) Larson, R. B., Tinsley, B. M., & Caldwell, C. N. 1980, ApJ, 237, 692. doi:10.1086/157917
  * Lee et al. (2020) Lee, J., Kimm, T., Katz, H., et al. 2020, ApJ, 905, 31. doi:10.3847/1538-4357/abc3b8
  * Lee et al. (2017) Lee, B., Chung, A., Tonnesen, S., et al. 2017, MNRAS, 466, 1382. doi:10.1093/mnras/stw3162
  * Lee-Waddell et al. (2019) Lee-Waddell, K., Koribalski, B. S., Westmeier, T., et al. 2019, MNRAS, 487, 5248. doi:10.1093/mnras/stz017
  * Lima-Dias et al. (2021) Lima-Dias, C., Monachesi, A., Torres-Flores, S., et al. 2021, MNRAS, 500, 1323. doi:10.1093/mnras/staa3326
  * Łokas (2020) Łokas, E. L. 2020, A&A, 638, A133. doi:10.1051/0004-6361/202037643
  * Lotz et al. (2019) Lotz, M., Remus, R.-S., Dolag, K., et al. 2019, MNRAS, 488, 5370. doi:10.1093/mnras/stz2070
  * Luo et al. (2016) Luo, Y., Kang, X., Kauffmann, G., et al. 2016, MNRAS, 458, 366. doi:10.1093/mnras/stw268
  * Maddox et al. (2015) Maddox, N., Hess, K. M., Obreschkow, D., et al. 2015, MNRAS, 447, 1610. doi:10.1093/mnras/stu2532
  * Mahajan et al. (2011) Mahajan, S., Mamon, G. A., & Raychaudhury, S. 2011, MNRAS, 416, 2882. doi:10.1111/j.1365-2966.2011.19236.x
  * Maier et al. (2019) Maier, C., Ziegler, B. L., Haines, C. P., et al. 2019, A&A, 621, A131. doi:10.1051/0004-6361/201834290
  * Markevitch & Vikhlinin (2007) Markevitch, M. & Vikhlinin, A. 2007, Phys. Rep., 443, 1. doi:10.1016/j.physrep.2007.01.001
  * Merritt (1983) Merritt, D. 1983, ApJ, 264, 24. doi:10.1086/160571
  * Meyer et al. (2004) Meyer, M. J., Zwaan, M. A., Webster, R. L., et al. 2004, MNRAS, 350, 1195. doi:10.1111/j.1365-2966.2004.07710.x
  * McGaugh et al. (2000) McGaugh, S. S., Schombert, J. M., Bothun, G. D., et al. 2000, ApJ, 533, L99. doi:10.1086/312628
  * McMahon et al. (1992) McMahon, P. M., van Gorkom, J. H., Richter, O.-G., et al. 1992, AJ, 103, 399. doi:10.1086/116068
  * McMahon et al. (1990) McMahon, P. M., Richter, O.-G., van Gorkom, J. H., et al. 1990, NASA Conference Publication, 3084, 217
  * McPartland et al. (2016) McPartland, C., Ebeling, H., Roediger, E., et al. 2016, MNRAS, 455, 2994. doi:10.1093/mnras/stv2508
  * Moore et al. (1996) Moore, B., Katz, N., Lake, G., et al. 1996, Nature, 379, 613. doi:10.1038/379613a0
  * Moore et al. (1998) Moore, B., Lake, G., & Katz, N. 1998, ApJ, 495, 139. doi:10.1086/305264
  * Moreno et al. (2019) Moreno, J., Torrey, P., Ellison, S. L., et al. 2019, MNRAS, 485, 1320. doi:10.1093/mnras/stz417
  * Moretti et al. (2020) Moretti, A., Paladino, R., Poggianti, B. M., et al. 2020, ApJ, 897, L30. doi:10.3847/2041-8213/ab9f3b
  * Muzzin et al. (2014) Muzzin, A., van der Burg, R. F. J., McGee, S. L., et al. 2014, ApJ, 796, 65. doi:10.1088/0004-637X/796/1/65
  * Navarro et al. (1997) Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ, 490, 493. doi:10.1086/304888
  * Nulsen (1982) Nulsen, P. E. J. 1982, MNRAS, 198, 1007. doi:10.1093/mnras/198.4.1007
  * Odekon et al. (2016) Odekon, M. C., Koopmann, R. A., Haynes, M. P., et al. 2016, ApJ, 824, 110. doi:10.3847/0004-637X/824/2/110
  * Oman et al. (2021) Oman, K. A., Bahé, Y. M., Healy, J., et al. 2021, MNRAS, 501, 5073. doi:10.1093/mnras/staa3845
  * Oman & Hudson (2016) Oman, K. A. & Hudson, M. J. 2016, MNRAS, 463, 3083. doi:10.1093/mnras/stw2195
  * Paccagnella et al. (2016) Paccagnella, A., Vulcani, B., Poggianti, B. M., et al. 2016, ApJ, 816, L25. doi:10.3847/2041-8205/816/2/L25
  * Patton et al. (2020) Patton, D. R., Wilson, K. D., Metrow, C. J., et al. 2020, MNRAS, 494, 4969. doi:10.1093/mnras/staa913
  * Putman et al. (2012) Putman, M. E., Peek, J. E. G., & Joung, M. R. 2012, ARA&A, 50, 491. doi:10.1146/annurev-astro-081811-125612
  * Ramos-Martínez et al. (2018) Ramos-Martínez, M., Gómez, G. C., & Pérez-Villegas, Á. 2018, MNRAS, 476, 3781. doi:10.1093/mnras/sty393
  * Rasmussen et al. (2012) Rasmussen, J., Mulchaey, J. S., Bai, L., et al. 2012, ApJ, 757, 122. doi:10.1088/0004-637X/757/2/122
  * Reiprich & Böhringer (2002) Reiprich, T. H. & Böhringer, H. 2002, ApJ, 567, 716. doi:10.1086/338753
  * Rhee et al. (2020) Rhee, J., Smith, R., Choi, H., et al. 2020, ApJS, 247, 45. doi:10.3847/1538-4365/ab7377
  * Roediger et al. (2011) Roediger, E., Brüggen, M., Simionescu, A., et al. 2011, MNRAS, 413, 2057. doi:10.1111/j.1365-2966.2011.18279.x
  * Roediger & Brüggen (2007) Roediger, E. & Brüggen, M. 2007, MNRAS, 380, 1399. doi:10.1111/j.1365-2966.2007.12241.x
  * Roediger & Brüggen (2006) Roediger, E. & Brüggen, M. 2006, MNRAS, 369, 567. doi:10.1111/j.1365-2966.2006.10335.x
  * Ruggiero et al. (2019) Ruggiero, R., Machado, R. E. G., Roman-Oliveira, F. V., et al. 2019, MNRAS, 484, 906. doi:10.1093/mnras/sty3422
  * Scott et al. (2018) Scott, T. C., Brinks, E., Cortese, L., et al. 2018, MNRAS, 475, 4648. doi:10.1093/mnras/sty063
  * Scott et al. (2010) Scott, T. C., Bravo-Alfaro, H., Brinks, E., et al. 2010, MNRAS, 403, 1175. doi:10.1111/j.1365-2966.2009.16204.x
  * Serra et al. (2015) Serra, P., Westmeier, T., Giese, N., et al. 2015, MNRAS, 448, 1922. doi:10.1093/mnras/stv079
  * Serra et al. (2012) Serra, P., Jurek, R., & Flöer, L. 2012, PASA, 29, 296. doi:10.1071/AS11065
  * Schmidt et al. (2016) Schmidt, T. M., Bigiel, F., Klessen, R. S., et al. 2016, MNRAS, 457, 2642. doi:10.1093/mnras/stw011
  * Solanes et al. (2001) Solanes, J. M., Manrique, A., García-Gómez, C., et al. 2001, ApJ, 548, 97. doi:10.1086/318672
  * Steinhauser et al. (2016) Steinhauser, D., Schindler, S., & Springel, V. 2016, A&A, 591, A51. doi:10.1051/0004-6361/201527705
  * Stevens & Brown (2017) Stevens, A. R. H. & Brown, T. 2017, MNRAS, 471, 447. doi:10.1093/mnras/stx1596
  * Stevens et al. (2019) Stevens, A. R. H., Diemer, B., Lagos, C. del P., et al. 2019, MNRAS, 490, 96. doi:10.1093/mnras/stz2513
  * Stevens et al. (2019) Stevens, A. R. H., Diemer, B., Lagos, C. del P., et al. 2019, MNRAS, 483, 5334. doi:10.1093/mnras/sty3451
  * Stevens et al. (2020) Stevens, A. R. H., Lagos, C. del P., Cortese, L., et al. 2020, MNRAS. doi:10.1093/mnras/staa3662
  * Tonnesen & Bryan (2008) Tonnesen, S. & Bryan, G. L. 2008, ApJ, 684, L9. doi:10.1086/592066
  * Tonnesen & Bryan (2009) Tonnesen, S. & Bryan, G. L. 2009, ApJ, 694, 789. doi:10.1088/0004-637X/694/2/789
  * Tonnesen & Bryan (2010) Tonnesen, S. & Bryan, G. L. 2010, ApJ, 709, 1203. doi:10.1088/0004-637X/709/2/1203
  * Tonnesen & Stone (2014) Tonnesen, S. & Stone, J. 2014, ApJ, 795, 148. doi:10.1088/0004-637X/795/2/148
  * Tonnesen (2019) Tonnesen, S. 2019, ApJ, 874, 161. doi:10.3847/1538-4357/ab0960
  * Verdes-Montenegro et al. (2005) Verdes-Montenegro, L., Sulentic, J., Lisenfeld, U., et al. 2005, A&A, 436, 443. doi:10.1051/0004-6361:20042280
  * Vollmer et al. (2001) Vollmer, B., Cayatte, V., Balkowski, C., et al. 2001, ApJ, 561, 708. doi:10.1086/323368
  * Vollmer et al. (2012) Vollmer, B., Wong, O. I., Braine, J., et al. 2012, A&A, 543, A33. doi:10.1051/0004-6361/201118690
  * Vollmer et al. (2013) Vollmer, B., Soida, M., Beck, R., et al. 2013, A&A, 553, A116. doi:10.1051/0004-6361/201321163
  * Wang et al. (2020a) Wang, J., Catinella, B., Saintonge, A., et al. 2020a, ApJ, 890, 63. doi:10.3847/1538-4357/ab68dd
  * Wang et al. (2020b) Wang, J., Xu, W., Lee, B., et al. 2020b, ApJ, 903, 103. doi:10.3847/1538-4357/abb9aa
  * Wang et al. (2018) Wang, J., Zheng, Z., D’Souza, R., et al. 2018, MNRAS, 479, 4292. doi:10.1093/mnras/sty1687
  * Wang et al. (2017) Wang, J., Koribalski, B. S., Jarrett, T. H., et al. 2017, MNRAS, 472, 3029. doi:10.1093/mnras/stx2073
  * Wang et al. (2016) Wang, J., Koribalski, B. S., Serra, P., et al. 2016, MNRAS, 460, 2143. doi:10.1093/mnras/stw1099
  * Warmels (1988) Warmels, R. H. 1988, A&AS, 72, 427
  * Waters et al. (2020) Waters, C. Z., Magnier, E. A., Price, P. A., et al. 2020, ApJS, 251, 4. doi:10.3847/1538-4365/abb82b
  * Wetzel et al. (2013) Wetzel, A. R., Tinker, J. L., Conroy, C., et al. 2013, MNRAS, 432, 336. doi:10.1093/mnras/stt469
  * Whiting (2020) Whiting, M. T. 2020, Astronomical Data Analysis Software and Systems XXVII, 522, 469
  * Woo et al. (2013) Woo, J., Dekel, A., Faber, S. M., et al. 2013, MNRAS, 428, 3306. doi:10.1093/mnras/sts274
  * Xie et al. (2020) Xie, L., De Lucia, G., Hirschmann, M., et al. 2020, MNRAS, 498, 4327. doi:10.1093/mnras/staa2370
  * Yoon et al. (2017) Yoon, H., Chung, A., Smith, R., et al. 2017, ApJ, 838, 81. doi:10.3847/1538-4357/aa6579
  * Yun et al. (2019) Yun, K., Pillepich, A., Zinger, E., et al. 2019, MNRAS, 483, 1042. doi:10.1093/mnras/sty3156
  * Zhang et al. (2013) Zhang, W., Li, C., Kauffmann, G., et al. 2013, MNRAS, 429, 2191. doi:10.1093/mnras/sts490
  * Zibetti et al. (2009) Zibetti, S., Charlot, S., & Rix, H.-W. 2009, MNRAS, 400, 1181. doi:10.1111/j.1365-2966.2009.15528.x
  * Zwaan et al. (2005) Zwaan, M. A., Meyer, M. J., Staveley-Smith, L., et al. 2005, MNRAS, 359, L30. doi:10.1111/j.1745-3933.2005.00029.x

##  Appendix A Atlas and table, and additional information on individual
resolved RPS candidates

We show an atlas of the ${\rm H}{\textsc{i}}$ contours on the resolved RPS
candidates (Fig. 14). We also list the galactic properties used in this study
in Tab. 1.

The strongest, resolved RPS candidate, NGC 3312, (189 in Fig. 14, WALLABY ID:
J103702-273359) was previously identified by its peculiar ${\rm
H}{\textsc{i}}$ and blue light distributions (McMahon et al. 1990; Gallagher
1978, but see McMahon et al. 1992). Its neighbor, NGC 3314A also shows ${\rm
H}{\textsc{i}}$ tails (McMahon et al., 1990), but overlaps with another bright
galaxy NGC 3314B, so has been excluded from our analysis. A detailed analysis
is under way for this system (Hess et al. in prep.).

One RPS candidate, ESO 501-G065 (212 in Fig. 14, WALLABY ID: J103833-274357)
shows a hint of a tidal tail in the optical with a corresponding ${\rm
H}{\textsc{i}}$ tail. It may be a case similar to the Magellanic system where
gravitational effects (tidal interactions or harassment) firstly perturb the
galaxy and then ram pressure is able to overide the anchoring force in the low
density gas produced by the gravitational perturbation. We do not exclude this
galaxy as it does not appear to experience a major merger. We leave a
statistical study of the combined effects of ram pressure and tidal
interactions in clusters to the future.

Detailed analysis of ram pressure stripping in ESO 501-G075 (239 in Fig. 14,
WALLABY ID: J103655-265412) can be found in Reynolds et al. (2021).

Figure 14:  Atlas of resolved RPS candidates. The galaxies are ordered by decreasing fraction of strippable ${\rm H}{\textsc{i}}$, $f_{RPS}$. Each galaxy has a pair of panels: the ${\rm H}{\textsc{i}}$ contours overlaid on the PanSTARRS optical image, and the RPS map. In the contour map, the cyan contours mark ${\rm H}{\textsc{i}}$ column density levels of 1, 2 and 5 times 10${}^{20}~{}cm^{-2}$. In the RPS map, the yellow and green colors mark the RPS pixels which have $P_{ram}>F_{anchor}$, and the yellow pixels are those with $P_{ram}>2F_{anchor}$. The blue color marks the ram pressure unaffected pixels. The white circle in the bottom-left corner of each RPS map shows the FWHM of the synthesis beam.  ID | WALLABY ID | $d_{proj}/r_{200}$ | $\Delta v_{rad}/\sigma_{C}$ | $\log M_{*}/M_{\odot}$ | $\log M_{\rm HI}/M_{\odot}$ | flagr1-RPS | flagRPS | $f_{RPS,pred}$ | $f_{RPS}$
---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
83 | J102107-281054 | 2.16 | 0.44 | 8.5 | 9.1 | 0 | 0 | - | -
97 | J102411-285533 | 1.91 | 0.25 | 8.9 | 8.9 | 0 | 0 | - | -
102 | J102430-290904 | 1.94 | 0.03 | 8.4 | 8.6 | 0 | 0 | - | -
103 | J102439-244547 | 2.38 | -0.36 | 8.3 | 9.0 | 0 | 0 | - | -
104 | J102439-274841 | 1.66 | -0.21 | 6.7 | 8.8 | 0 | 0 | - | -
116 | J102621-291150 | 1.74 | -0.05 | 8.2 | 8.9 | 0 | 0 | - | -
117 | J102629-285851 | 1.66 | -0.03 | 7.8 | 8.6 | 0 | 0 | - | -
118 | J102636-245116 | 2.16 | 0.39 | 8.6 | 8.7 | 0 | 0 | - | -
125 | J102818-255446 | 1.52 | 0.12 | 6.8 | 8.3 | 0 | 0 | - | -
127 | J102911-302031 | 2.02 | 0.67 | 10.1 | 9.3 | 0 | 0 | - | -
129 | J102934-261937 | 1.23 | 0.32 | 8.7 | 8.7 | 0 | 0 | - | -
130 | J103002-284116 | 1.16 | 0.17 | 8.6 | 8.6 | 0 | 0 | - | -
131 | J103004-253630 | 1.49 | -0.53 | 7.4 | 8.5 | 0 | 0 | - | -
134 | J103114-295837 | 1.69 | 0.72 | 8.5 | 8.6 | 0 | 0 | - | -
135 | J103124-295706 | 1.66 | 0.58 | 9.1 | 9.5 | 0 | 0 | - | -
137 | J103139-273049 | 0.69 | -0.25 | 7.9 | 8.7 | 0 | 0 | - | -
141 | J103241-273137 | 0.55 | 0.14 | 9.2 | 8.5 | 0 | 0 | - | -
142 | J103244-283639 | 0.86 | -0.17 | 10.5 | 9.3 | 0 | 0 | - | -
143 | J103248-273119 | 0.53 | -0.19 | 9.1 | 9.0 | 0 | 0 | - | -
144 | J103250-301601 | 1.77 | -0.41 | 10.2 | 9.3 | 0 | 0 | - | -
146 | J103258-274013 | 0.52 | -0.94 | 8.6 | 9.0 | 1 | 0 | 0.59 | -
147 | J103259-273237 | 0.51 | 1.63 | 8.7 | 8.5 | 1 | 1 | 0.79 | -
149 | J103335-272717 | 0.43 | -0.55 | 10.8 | 9.3 | 0 | 0 | - | -
151 | J103353-274945 | 0.43 | -1.54 | 8.8 | 9.0 | 1 | 1 | 1.00 | -
155 | J103420-264728 | 0.56 | 0.93 | 8.4 | 8.5 | 1 | 0 | 0.54 | -
156 | J103420-265408 | 0.50 | -0.00 | 7.9 | 8.8 | 0 | 0 | - | -
157 | J103436-273900 | 0.30 | -1.13 | 9.9 | 9.3 | 1 | 1 | 0.77 | 0.87
160 | J103455-273816 | 0.25 | -1.12 | 7.5 | 8.5 | 1 | 1 | 1.00 | -
161 | J103459-280440 | 0.42 | -2.13 | 9.7 | 8.5 | 1 | 0 | 0.67 | -
162 | J103502-293019 | 1.25 | 0.02 | 9.1 | 8.8 | 0 | 0 | - | -
163 | J103507-275923 | 0.36 | -2.05 | 8.7 | 8.8 | 1 | 1 | 1.00 | -
165 | J103521-272324 | 0.20 | -0.94 | 7.9 | 8.6 | 1 | 1 | 1.00 | -
166 | J103521-274137 | 0.21 | -1.33 | 8.3 | 9.0 | 1 | 1 | 1.00 | -
168 | J103523-281855 | 0.52 | -0.69 | 9.9 | 9.5 | 1 | 1 | 0.44 | 0.61
172 | J103546-273840 | 0.15 | 1.60 | 8.1 | 8.8 | 1 | 1 | 1.00 | -
174 | J103602-261141 | 0.82 | -0.72 | 8.1 | 8.5 | 1 | 0 | 0.27 | -
176 | J103603-245430 | 1.62 | 0.33 | 7.1 | 8.9 | 0 | 0 | - | -
178 | J103621-252235 | 1.32 | 0.44 | 9.3 | 8.9 | 0 | 0 | - | -
179 | J103627-255957 | 0.94 | -0.78 | 7.1 | 8.2 | 1 | 0 | 0.30 | -
180 | J103644-251543 | 1.39 | -0.11 | 8.8 | 8.8 | 0 | 0 | - | -
181 | J103645-281010 | 0.40 | -0.38 | 8.4 | 9.0 | 1 | 0 | 0.34 | -
182 | J103646-293253 | 1.25 | -0.26 | 8.7 | 9.0 | 0 | 0 | - | -
183 | J103650-260923 | 0.84 | -0.12 | 8.9 | 9.1 | 0 | 0 | - | -
186 | J103653-270311 | 0.29 | -0.29 | 9.0 | 9.1 | 1 | 1 | 0.34 | 0.43
187 | J103655-265412 | 0.38 | -0.77 | 8.0 | 9.2 | 1 | 1 | 0.81 | 0.93
189 | J103702-273359 | 0.05 | -1.39 | 10.9 | 9.4 | 1 | 1 | 1.00 | 0.96
190 | J103704-252038 | 1.34 | -0.03 | 9.1 | 8.9 | 0 | 0 | - | -
Table 1:  Galaxy properties. To be continued.  ID | WALLABY ID | $d_{proj}/r_{200}$ | $\Delta v_{rad}/\sigma_{C}$ | $\log M_{*}/M_{\odot}$ | $\log M_{\rm HI}/M_{\odot}$ | flagr1-RPS | flagRPS | $f_{RPS,pred}$ | $f_{RPS}$
---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
192 | J103719-281408 | 0.45 | -0.41 | 8.3 | 8.5 | 1 | 0 | 0.30 | -
194 | J103722-273235 | 0.09 | -1.54 | 8.0 | 8.6 | 1 | 1 | 1.00 | -
195 | J103725-251916 | 1.36 | -0.04 | 10.5 | 10.1 | 0 | 0 | - | -
200 | J103738-281216 | 0.44 | 1.54 | 8.1 | 8.5 | 1 | 1 | 1.00 | -
203 | J103804-284333 | 0.77 | 1.13 | 8.4 | 8.8 | 1 | 0 | 0.55 | -
204 | J103805-250537 | 1.51 | 0.35 | 9.0 | 8.8 | 0 | 0 | - | -
205 | J103809-260453 | 0.91 | -0.21 | 8.7 | 8.4 | 0 | 0 | - | -
207 | J103812-275607 | 0.33 | -1.38 | 7.6 | 8.3 | 1 | 1 | 1.00 | -
208 | J103818-285307 | 0.87 | 1.01 | 9.2 | 9.5 | 1 | 1 | 0.41 | 0.26
210 | J103821-254126 | 1.15 | -0.47 | 8.0 | 8.7 | 0 | 0 | - | -
211 | J103828-283056 | 0.66 | 0.98 | 8.1 | 8.8 | 1 | 0 | 0.55 | -
212 | J103833-274357 | 0.29 | 1.06 | 9.3 | 9.2 | 1 | 1 | 0.93 | 0.56
213 | J103840-283405 | 0.70 | -0.42 | 9.8 | 8.9 | 0 | 0 | - | -
214 | J103841-253530 | 1.22 | 0.18 | 7.6 | 8.9 | 0 | 0 | - | -
215 | J103842-281535 | 0.53 | -0.51 | 8.1 | 8.6 | 1 | 1 | 0.30 | -
220 | J103902-291255 | 1.09 | -0.84 | 8.3 | 8.9 | 1 | 0 | 0.24 | -
222 | J103914-271511 | 0.38 | 1.26 | 8.0 | 8.4 | 1 | 1 | 1.00 | -
223 | J103915-301757 | 1.75 | 0.07 | 10.4 | 9.8 | 0 | 0 | - | -
225 | J103922-293505 | 1.32 | 0.23 | 9.3 | 9.3 | 0 | 0 | - | -
226 | J103924-275442 | 0.44 | -0.80 | 9.0 | 8.9 | 1 | 0 | 0.51 | -
228 | J103927-271653 | 0.40 | -0.58 | 8.3 | 8.6 | 1 | 0 | 0.51 | -
229 | J103939-280552 | 0.54 | -0.53 | 8.1 | 8.8 | 1 | 0 | 0.37 | -
231 | J103958-301130 | 1.71 | -0.70 | 10.1 | 9.1 | 0 | 0 | - | -
232 | J104000-292445 | 1.25 | 0.06 | 8.3 | 9.2 | 0 | 0 | - | -
233 | J104004-301606 | 1.75 | -0.53 | 9.5 | 9.4 | 0 | 0 | - | -
234 | J104016-274630 | 0.51 | 0.38 | 10.1 | 9.8 | 1 | 0 | 0.25 | -
235 | J104026-274853 | 0.54 | 0.96 | 7.7 | 8.7 | 1 | 1 | 0.71 | -
236 | J104048-244003 | 1.85 | -0.11 | 8.3 | 9.0 | 0 | 0 | - | -
238 | J104058-274546 | 0.60 | 0.40 | 8.1 | 8.8 | 1 | 0 | 0.22 | -
239 | J104059-270456 | 0.64 | 1.57 | 10.1 | 9.5 | 1 | 1 | 0.56 | 0.44
240 | J104100-284430 | 0.95 | 0.03 | 9.1 | 8.9 | 0 | 0 | - | -
242 | J104139-254049 | 1.32 | 0.19 | 7.8 | 8.7 | 0 | 0 | - | -
243 | J104139-274639 | 0.69 | 0.98 | 8.0 | 8.7 | 1 | 0 | 0.55 | -
244 | J104142-284653 | 1.03 | 1.10 | 10.0 | 10.0 | 1 | 1 | 0.41 | 0.67
246 | J104221-291748 | 1.34 | 1.09 | 8.1 | 9.0 | 1 | 0 | 0.27 | -
251 | J104309-300301 | 1.79 | -0.85 | 9.1 | 9.6 | 0 | 0 | - | -
252 | J104311-261500 | 1.19 | 1.26 | 9.9 | 9.5 | 1 | 1 | 0.28 | 0.10
253 | J104326-251857 | 1.65 | 0.05 | 8.8 | 8.7 | 0 | 0 | - | -
256 | J104359-293304 | 1.59 | -0.61 | 8.5 | 8.4 | 0 | 0 | - | -
266 | J104629-253308 | 1.82 | -0.21 | 7.9 | 8.8 | 0 | 0 | - | -
269 | J104824-250944 | 2.17 | 0.03 | 10.7 | 9.7 | 0 | 0 | - | -
270 | J104905-292232 | 2.03 | 0.85 | 8.5 | 9.3 | 0 | 0 | - | -
272 | J105227-291155 | 2.37 | -0.46 | 7.6 | 8.7 | 0 | 0 | - | -
Table 1:  Galaxy properties. Column (1): id. Column (2): WALLABY identifier.
Column (3): the cluster centric projected distance. Column (4): the velocity
distance from cluster center. Column (5): stellar mass. Column (6): ${\rm
H}{\textsc{i}}$ mass. Column (7): flag for identification of r1-RPS candidates
(the major sample studied in Sec. 3 and 4), 1 for True and 0 for False. Column
(8): flag for identification of RPS candidates (both resolved and un-
resolved), 1 for True and 0 for False. The identification of unresolved RPS
candidates is incomplete. Column (9): the fraction of ${\rm H}{\textsc{i}}$
mass under ram pressure stripping derived from predicted ${\rm H}{\textsc{i}}$
radial profiles. Column (10): the fraction ${\rm H}{\textsc{i}}$ mass under
ram pressure stripping derived from ${\rm H}{\textsc{i}}$ moment-0 maps for
the resolved RPS candidates.