# Warped Disk Galaxies. I. Linking U-type Warps in Groups/Clusters to
Jellyfish Galaxies

Woong-Bae G. Zee∗ Department of Astronomy, Yonsei University, Seoul, 03722,
Republic of Korea  Center for Galaxy Evolution Research, Yonsei University,
Seoul, 03722, Republic of Korea  Suk-Jin Yoon∗ Department of Astronomy, Yonsei
University, Seoul, 03722, Republic of Korea  Center for Galaxy Evolution
Research, Yonsei University, Seoul, 03722, Republic of Korea  Jun-Sung Moon
Department of Astronomy, Yonsei University, Seoul, 03722, Republic of Korea
Center for Galaxy Evolution Research, Yonsei University, Seoul, 03722,
Republic of Korea  Sung-Ho An Department of Astronomy, Yonsei University,
Seoul, 03722, Republic of Korea  Center for Galaxy Evolution Research, Yonsei
University, Seoul, 03722, Republic of Korea  Sanjaya Paudel Department of
Astronomy, Yonsei University, Seoul, 03722, Republic of Korea  Center for
Galaxy Evolution Research, Yonsei University, Seoul, 03722, Republic of Korea
Kiyun Yun  Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117
Heidelberg, Germany

###### Abstract

Warped disk galaxies are classified into two morphologies: S- and U-types.
Conventional theories routinely attribute both types to galactic tidal
interaction and/or gas accretion, but reproducing of U-types in simulations is
extremely challenging. Here we investigate whether both types are governed by
the same mechanisms using the most extensive sample of $\sim$8000 nearby (0.02
$<$ z $<$ 0.06) massive ($M_{*}/M_{\odot}$ $>$ $10^{9}$) edge-on disks from
SDSS. We find that U-types show on average bluer optical colors and higher
specific star formation rate (sSFR) than S-types, with more strongly warped
U-types having higher sSFR. We also find that while the S-type warp properties
correlate with the tidal force by the nearest neighbor regardless of the
environment, there is no such correlation for U-types in groups/clusters,
suggesting a non-tidal environmental could be at play for U-types, such as ram
pressure stripping (RPS). Indeed, U-types are more common in groups/clusters
than in fields and they have stellar mass, gas fraction, sSFR enhancement and
phase-space distribution closely analogous to RPS-induced jellyfish galaxies
in clusters. We furthermore show that the stellar disks of most RPS galaxies
in the IllustirsTNG simulation are warped in U-shape and bent in opposite
direction of stripped gas tails, satisfying theoretical expectations for
stellar warps embeded in jellyfishes. We therefore suggest that despite the
majority of U-types that live in fields being still less explained, RPS can be
an alternative origin for those in groups/clusters.

Galaxy evolution (594), Galaxy interactions (600), Galaxy structure (622),
Star formation (1569)

††journal: ApJ**footnotetext: These authors contributed equally to this work.

##  1 Introduction

Observations over the past few decades showed that the warped disk structure
is common in the local universe. More than half of nearby edge-on disk
galaxies observed in optical and radio passbands exhibit warps at the
outskirts of disks (e.g., Sánchez-Saavedra et al. 1990; Bosma 1991;
Reshetnikov & Combes 1998; Reshetnikov et al. 2002; Castro-Rodríguez et al.
2002; García-Ruiz et al. 2002; Sánchez-Saavedra et al. 2003; Ann & Park 2006;
Reshetnikov et al. 2016; see also Chen et al. 2019; Cheng et al. 2020;
Chrobáková & López-Corredoira 2021 for the Milky Way’s warp). Optical stellar
warps are, in general, weaker than HI gaseous warps; however, the incidence of
optical warps is as prevalent as HI warps (e.g., Briggs 1990; Castro-Rodríguez
et al. 2002; García-Ruiz et al. 2002; Guijarro et al. 2010; Curran et al.
2008). The morphology of warped disks is classified into two types, S-
(integral-shaped) and U-type (bow-shaped) (Reshetnikov & Combes 1998; Ann &
Park 2006).

Galactic warps are often taken as results of galaxy–galaxy interactions. For
instance, simulations by Laporte et al. (2018) and Antoja et al. (2018)
reproduced the grand-design S-shaped warp of the Milky Way using the orbiting
Sagittarius dwarf and Magellanic Clouds. Kim et al. (2014) and Gómez et al.
(2017) suggested that the fly-by encounter is another warp formation
mechanism. Semczuk et al. (2020) used IllustrisTNG simulation to investigate
the origin of warped galaxies. The authors focused only on S-type warps and
showed that $\sim$30% of S-types are constructed by tidal interactions with
$\sim$15% being minor mergers and $\sim$15% fly-by encounters.
Observationally, some studies suggested that interacting galaxies are more
frequently warped than non-interacting galaxies (Reshetnikov & Combes 1998;
Schwarzkopf & Dettmar 2001; Ann & Park 2006). There is, however, only a weak
correlation (Kollatschny & Dietrich 1990; Reshetnikov & Combes 1998;
Schwarzkopf & Dettmar 2001) or even anti-correlation (García-Ruiz et al. 2002)
between the frequency of warps and the local environment, at variance with the
conventional tidal scenario. Moreover, several isolated galaxies in the field
exhibit warped disks (Briggs 1990; Verdes-Montenegro et al. 1997; Ann 2007;
López-Corredoira et al. 2008b). Thus, other alternative warp formation
mechanisms have been suggested, including cold gas flow (Ostriker & Binney
1989; Jiang & Binney 1999; Roškar et al. 2010; Rahmani et al. 2018),
interaction with the intergalactic accretion onto disks (López-Corredoira et
al. 2002; Sánchez-Salcedo 2006), ram-pressure by galaxies’ movement with
respect to the inter-galactic medium (Haan & Braun 2014), misalignment between
stellar disks and prolate/oblate dark matter halos (Sparke & Casertano 1988;
Kuijken 1991; Nelson & Tremaine 1995; Ideta et al. 2000; Jeon et al. 2009;
Dubinski & Chakrabarty 2009; Sellwood & Debattista 2021), and interaction with
the intergalactic magnetic field (Battaner et al. 1990; Battaner & Jiménez-
Vicente 1998). However, which mechanism dominates the warp formation remains
debated.

When it comes to U-type warps, many observations witnessed conspicuously
warped U-types (Reshetnikov et al. 2002; Sánchez-Saavedra et al. 2003; Ann &
Park 2006), but their physical origin is still a puzzle. Most of conventional
studies simply assumed that S- and U-types are results of the same warp
formation mechanism, such as the tidal interaction. However, simulations of
tidal interactions preferentially create S-types with no or few U-types (e.g.,
Weinberg 1995; Vesperini & Weinberg 2000; Weinberg & Blitz 2006; Mapelli et
al. 2008; Gómez et al. 2013; Kim et al. 2014; Gómez et al. 2017; Laporte et
al. 2018; Gómez et al. 2013; Antoja et al. 2018). On the other hand, López-
Corredoira et al. (2008a) elaborated that intergalactic gas accretion can
produce both types, in that S- and U-types are respectively made via angular
and linear momentum transmission during gas accretion. When intergalactic gas
is accreted from the nearly vertical direction to the galactic disk, galaxies
are bent into the U-shaped morphology. Alternatively, the simulation by Kipper
et al. (2020) showed that the warped disk’s morphology depends on infalling
galaxies’ relative direction to the dark matter particles. When a galaxy moves
through dark matter halo, tidal friction induced by the over-density region
behind the drifting galaxy produce U-shaped disks.

Our main questions in this study are: ($a$) whether S- and U-type warps are
crafted by the same mechanism? and ($b$) how can we explain the existence of
U-type warps? To address them, we construct the most extensive catalog of
nearby edge-on warped disk galaxies from Sloan Digital Sky Survey (SDSS) Data
Release 7 (DR7). We for the first time distinguish the intrinsic
characteristics of S- and U-type warped galaxies and report the discovery of
their discrepancy. We propose a new possibility that U-type warps in
groups/clusters could be related to ram-pressure stripping (RPS). The paper is
organised as follows. In Section 2, we introduce our data and explain how we
measure the warp structure using our newly developed, automated scheme. In
Section 3, we show the discrepancy in several intrinsic properties between S-
and U-types, including the optical color, specific star formation rate (sSFR)
and environmental effects. In Section 4, we compare the morphologies,
kinematics within groups/clusters, sSFR, stellar masses and gas fraction of S-
and U-types with those of RPS galaxies and discuss the possible jellyfish
origin of U-type warped disks. In Section 5 we summarise our results.

##  2 Data and Methodology

###  2.1 Observational Data

We select sample galaxies from the SDSS DR7 Legacy Survey (Abazajian et al.
2009). The SDSS Legacy Survey is a large optical imaging survey that provides
a map covering more than a quarter of the celestial sphere. The DR7 is the
final data release of the SDSS Legacy Survey. We chose $\sim$ 20,000 galaxy
targets ($0.02<z<0.06$) from the Main Galaxy Sample and retrieve their images
and spectra. We then select highly inclined edge-on disk galaxies by utilizing
the morphological classification data from the Galaxy Zoo 2 (GZ2) project. The
morphological classification was done by Willett et al. (2013) and we make use
of the class “spiral galaxy other,” which consists of highly inclined edge-on
spiral galaxies whose spiral arms cannot be distinguished. When selecting
edge-on galaxies we have the following criteria: ($a$) they are flagged as
spirals, which requires 80 % of the volunteer votes for the spiral category
after the de-biasing procedure, and ($b$) they are classified as edge-on
spirals for which more than a half of the volunteers voted for the spiral
category. Many of the sample galaxies are too small and/or too faint to
identify the presence of the warped structure. We only use galaxies large and
massive enough to analyze their warped disk structures. We select $\sim$11,000
edge-on disk galaxies with $g$-band isophotal major axis $A_{\rm
iso}>22^{\prime\prime}$ and stellar mass $M_{*}/M_{\odot}$ $>$ $10^{9}$.
Through visual inspection, we further remove $\sim$3000 galaxies that are not
suitable to measure their warped structures due to their intricate dust lanes,
spiral arms, and overlapped stars/galaxies at the edge of the galaxies.

The stellar masses are taken from the Mendel et al. (2014) catalog that
provides photometric data of one million galaxies in the SDSS. In the catalog,
the stellar masses for bulges, disks, and total are based on the updated bulge
+ disk decomposition data from Simard et al. (2011). In Simard et al. (2011),
they used a successful bulge + disk fitting code, GIM2D. The size measurements
from GIM2D are converted into the stellar masses for the decomposed bulge and
disk components separately using all $ugriz$ wavebands. However, Mendel et al.
(2014) cautioned that in the case of highly inclined edge-on galaxies, the
total stellar mass and the sum of decomposed bulge + disk stellar mass can
differ. We select only the reliable galaxies that are within the five times of
standard deviation from the correlation between the total stellar masses and
the sum of bulge + disk masses.

The optical colors and sSFR in this study are taken from the MPA/JHU catalog
(Brinchmann et al. 2004) that provides spectroscopic data of galaxies in the
SDSS. The MPA/JHU catalog lists optical colors as well as sSFR estimated from
emission lines such as H$\alpha$, H$\beta$, [OII], [NII], and [SII]. To
examine the sSFR enhancement across a galaxy, we use the aperture corrected
sSFR data. Galaxies that show emission lines of AGNs are also removed. The AGN
candidates are selected using the distribution on the BPT diagram (Baldwin et
al. 1981; Kauffmann et al. 2003). We exclude ‘AGN’ and ‘composite’ galaxies.
We note that this procedure can not classify $\sim$700 galaxies with feeble
emission lines because they are not shown on the BPT diagram. They are
essentially normal quiescent galaxies with no AGN activity and included in our
sample. Our sample contains $\sim$8000 non-AGN, edge-on galaxies.

###  2.2 Measurements of the Warped Stellar Disks

We retrieve the corrected frames of our sample galaxies from the SDSS Data
Archive Server. The corrected frame is an imaging frame from the SDSS imaging
pipeline that has been bias-subtracted, flat-flagged, and pixel-defect
corrected. We crop the field images based on the galaxy positions on the
frame. The resultant images used in our analysis are $500\times 500$ pixel
($3.3^{\prime}\times 3.3^{\prime}$) FIT images centered on the sample
galaxies. In this study, we use the $g$-band images. The signal-to-noise,
sensitivity for foreground stars, and dust extinction depend on wavebands, but
we do not find any dependence of measured warp properties on wavebands such as
$u$-, $r$-, $i$-, and $z$-band.

In order to extract the overall shape of disks, we blur the images of the
target galaxies using the SMOOTH function. This procedure returns a copy of
array smoothed with 5-pixel width. Thus, after the smoothing procedure, the
scale of our galaxy images becomes five times smaller ($100\times 100$ pixel).
The center of our target galaxy is defined as the location of the brightest
point in the smoothed image. The sky is not subtracted in the SDSS imaging
pipeline and we thus subtract the background sky values from the original
images. The background sky is measured as the median pixel value outside of
the region of interest.

To quantify the warp structure, we newly invent an automated warp measurement
scheme. Figure 1 illustrates the procedure of the warp angle measurement
through our automated scheme for the case of S-type (upper row) and U-type
warps (lower row). Specifically, we first align the major axes of galaxies
horizontally based on the position angle (PA) from SDSS DR7 database, which is
defined as the angle with respect to the north celestial pole following the
direction of the right ascension. We then derive the vertical brightness
distribution using a Gaussian function of the vertical distance from the major
central axis at each x-coordinate from the left to the right side. In this
procedure, we only use pixels whose value is brighter than five times the
standard deviation of the background sky value. We join all peak points of the
vertical brightness distribution at each x-coordinate as a single curved line,
which are defined as the ‘spine’ of target galaxy. To derive the central major
axis, we apply the orthogonal linear regression to the central spine points
within the half of disk size.

The estimated major axis is usually misaligned with the horizontal line due to
an inaccurate PA from the SDSS pipeline data, and even after the first
rotation of our target images, the PA is not zero. This misalignment impedes
the measurement of the exact value of warping amplitudes. Thus, we determine
the major axis and warped disk structure again by repeating the rearrangement
procedure until the calculated PA meets the tolerance (PA $<0.01^{\circ}$).
Finally, the warping amplitude, $\alpha$, is calculated as the degree of
misalignment between the central major axis and tips at the outermost bent
structures. The warping amplitudes are measured on both sides of the galactic
disk. To avoid spurious warp detection, we only consider a disk whose vertical
deviation at the outermost point is more significant ($>3\sigma$) than the
fluctuation of wobbling along the central major axis. Between the warping
amplitudes of the two sides, we take the larger one as the major warping
amplitude, $\alpha$. We then divide the morphology of disks into S-type,
U-type, and unwarped based on the degree and direction in which each endpoint
of the disk is bent (Reshetnikov & Combes 1998; Reshetnikov et al. 2002;
Sánchez-Saavedra et al. 2003; Ann & Park 2006).

###  2.3 Warped Disk Galaxy Sample

In this work, we present a new statistical analysis of optical warps of disk
galaxies with a much larger body of data than has been used in previous
studies (Reshetnikov & Combes 1998; Reshetnikov et al. 2002; Sánchez-Saavedra
et al. 2003; Ann & Park 2006; Reshetnikov et al. 2016). Using our automated
warp measurement scheme, after all pre-procedures, we identify 3662 warped
disk galaxies out of $\sim$8000 highly inclined edge-on galaxies in the local
universe ($0.02<z<0.06$). Among them, we have 2206 S-types and 1456 U-types.
Table 1 gives the basic properties of our S- and U-type warped galaxies,
including the number of galaxies, number fraction, median warp angle, and
median stellar mass. The properties are in agreement with the aforementioned
studies. In particular, warps are very common with the fraction of $\sim$50 %
of edge-on disk galaxies, and S-types are about 1.5 times more frequent and
exhibit slightly stronger warping amplitudes than U-types. Figure 2 shows some
randomly selected example images of S- and U-type warps among our final
catalog.

###  2.4 Control Sample

The upper panels of Figure 3 show the distributions of redshift and stellar
mass of unwarped and warped galaxies. Compared to the unwarped galaxies, the
warped galaxies exhibit slightly higher redshift and lower stellar mass. The
larger redshift for warped galaxies is likely due to the selection bias of
warp detection. Because of their closer distance and thus larger apparent
size, there is higher chance that target galaxies are overlapped with other
stars and/or galaxies. The different distribution of stellar mass between
warped and unwarped galaxies can be explained by the mass dependence on
external mechanisms. Simulations of galaxy–galaxy interactions showed that the
extent of the morphological changes depends on the mass ratio of interacting
galaxies, in the sense that less massive galaxies are more susceptible to
external forces (e.g., Cox et al. 2008; Gómez et al. 2017).

To avoid the effect of different redshift and stellar mass between warped and
unwpared galaxies, we carefully construct a control sample of unwarped edge-on
galaxies. We randomly select an unwarped galaxy for each warped galaxy within
the bin range of $\pm$ 0.005 in redshift and $\pm$ 0.1 dex in stellar mass. In
the lower panels of Figure 3, the control sample exhibits redshift and stellar
mass distributions nearly identical to those of warped galaxies.

##  3 Physical Properties of Warped Disk Galaxies

To address which mechanism governs the formation of the different warp
morphologies, we begin with comparison of some key properties of S- and U-type
warped galaxies with respect to those of the unwarped control sample,
including optical colors, sSFR, and environment.

###  3.1 The Optical Color and Star Formation Rate

In Figure 4, the upper panels show the distribution of SDSS optical $g-r$
colors of warped and unwarped galaxies as functions of stellar mass.
Interestingly, we discover an unexpected discrepancy between S- and U-type
warps in optical $g-r$ colors. While S-type warped galaxies show $g-r$ similar
to unwarped control sample, U-types are buler by $\sim$0.05 dex. In the lower
panels, we also find that U-type warps exhibit $\sim$0.25 dex higher sSFR than
unwarped control galaxies. The blue-ward color offset and the increase of sSFR
are greater for less massive galaxies ($M_{*}/M_{\odot}<10^{10}$).

In Figure 5, we compare the residuals of sSFR as a function of the warping
amplitude. We define the residual of sSFR, $\Delta$Log(sSFR), as the
difference in sSFR between the warp sample and the mean sSFR of its
corresponding stellar mass- and redshift-matched control sample in bins of
stellar mass. Pearson correlation coefficient (cc) is shown in each panel of
Figure 5. There is a distinct correlation between $\Delta$Log(sSFR) and
warping amplitudes only for U-type warps with cc = 0.185. Strongly warped
($\alpha>10^{\circ}$) U-type galaxies have $\sim 0.3$ dex higher sSFR than
weakly warped ($\alpha<5^{\circ}$) U-type ones. The enhancement of sSFR for
strongly warped U-type galaxies supports that the galaxies are associated with
more efficient star formation activity than S-types and unwarped galaxies.
This discrepancy between S- and U-type warps implies that the two morphologies
are probably governed by distinct mechanisms.

###  3.2 The Environment

Conventional simulations of galaxy-galaxy interactions suggested that S-type
warps are common products of tidal interactions (Kim et al. 2014; Gómez et al.
2017; Laporte et al. 2018; Antoja et al. 2018). However, whether formation of
U-type warps is governed by the same mechanism is unclear. To explore the
environmental effects on galactic warps, we examine the incidence and
amplitudes of S- and U-type warps as functions of environmental parameters
from the local to galaxy groups/clusters scale.

####  3.2.1 The Local Environmental Effect

We investigate the effect of the local environment on warp formation by
examining whether the frequency and amplitude of warps depend on environmental
parameters. We define two different local environmental parameters: ($a$)
local density of the surrounding area, $\Sigma_{\textrm{N}}$, ($b$) tidal
influence of the nearest neighboring galaxy, $F_{\textrm{tidal}}$. To estimate
the local density, we adopt the projected surface density used by Baldry et
al. (2006), such that

$\Sigma_{\textrm{N}}=\cfrac{N}{\pi{d_{\textrm{N}}}^{2}}\hskip 2.84526pt,$ (1)

where $d_{\textrm{N}}$ is the comoving distance to the Nth nearest galaxy. The
projected surface density Log($\Sigma_{\textrm{45}}$) is used for our study,
which is defined as the average value of Log($\Sigma_{\textrm{N}}$) for N = 4
and 5 as proposed by Baldry et al. (2006). We also use $F_{\rm tidal}$ defined
as

$F_{\textrm{tidal}}=\text{Log}(M_{*}/M_{\odot})-3\,\text{Log}(r_{\textrm{nearest}})\hskip
2.84526pt,$ (2)

where $M_{*}$ is the stellar mass of the closest neighboring galaxy and
$r_{\textrm{nearest}}$ is the distance to the neighboring galaxy in kpc. We
define the nearest neighbor as a galaxy that is of the closest projected
distance within a radial velocity difference of 1000 km s-1 and with mass
between 0.1 and 10 of the target galaxy.

Figures 6 and 7 show respectively the frequency and amplitude of warped
structures as functions of both local environmental parameters,
Log($\Sigma_{\textrm{45}}$) and $F_{\textrm{tidal}}$. In their upper panels,
there is no detectable environmental effect on the warp fraction and
amplitude. Intriguingly, the lower panels of Figures 6 and 7 show that S-type
warps depend on the tidal force by the nearest neighbor galaxies,
$F_{\textrm{tidal}}$. As the tidal influence increases, the incidence and the
warping amplitude of S-warps increases with cc = 0.189. When we consider the
strongly warped galaxies ($\alpha>3^{\circ}$), the correlation becomes
slightly more significant with cc = 0.203. Contrary to S-type warps, the
frequency and amplitudes of U-types depend on neither environmental
parameters. This implies that the tidal interaction plays a role in formation
of S- and U-type warps differently. This result is consistent with previous
theoretical studies, which usually reproduced S-types with few or no U-types
by tidal interactions (Weinberg 1995; Vesperini & Weinberg 2000; Weinberg &
Blitz 2006; Mapelli et al. 2008; Gómez et al. 2013; Kim et al. 2014; Gómez et
al. 2017; Laporte et al. 2018; Gómez et al. 2013; Antoja et al. 2018).

####  3.2.2 The Group/Cluster Effect

We examine the effect of the group/cluster environment on galactic warps. We
select the member galaxies of groups and clusters using the SDSS DR8
group/cluster member galaxy catalog by Tempel et al. (2012). The group/cluster
effects such as RPS and harassment are considered to happen usually in massive
clusters ($M_{\textrm{halo}}/M_{\odot}$ $>$ $10^{14}$). However, some recent
observations reported that RPS galaxies exist even in low-mass galaxy groups
(e.g., Westmeier et al. 2011; Rasmussen et al. 2012; Vulcani et al. 2018a;
Elagali et al. 2019). Tecce et al. (2011) determined the RPS effect in groups
and clusters with the halo mass range of $10^{12.5}$ $<$
$M_{\textrm{halo}}/M_{\odot}$ $<$ $10^{15.35}$. They concluded that the
strength of RPS becomes more prominent as the halo mass increases, but
galaxies in low-mass groups also experience mass loss by RPS. Poggianti et al.
(2016) reported 344 jellyfish candidates in 71 galaxy clusters and 75
candidates in lower mass groups ($10^{11}$ $<$ $M_{\textrm{halo}}/M_{\odot}$
$<$ $10^{14}$). Although the exact physical origin of jellyfishes in group
environments should be securely investigated, the authors introduced
convincing cases of jellyfish galaxies in group and lower mass halos. They
stated that “jellyfish galaxies could be present even in groups and lower mass
halos.” Roberts et al. (2021a) also identified 60 jellyfish galaxies in
$\sim$500 galaxy groups with halo mass of $10^{12.5}$ $<$
$M_{\textrm{halo}}/M_{\odot}$ $<$ $10^{14}$ and compared them with LOFAR Two-
metre Sky Survey (LoTSS) jellyfish galaxies.

Adopting the recent results, we use two different definition of group/cluster
environments: ($a$) a loose criterion including galaxy groups of low halo mass
($M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{12}$), ($b$) a conventional tight
criterion only including massive galaxy clusters
($M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{14}$). When we adopt the looser
criterion, 13.2% of S-types and 17.5% of U-types belong to groups. When using
the conventional criterion, 2.2% of S-types and 4.1% of U-types are classified
as cluster member galaxies. Figure 8 shows best example images of U-type
warped galaxies in massive clusters. While only a small fraction of warped
galaxies are involved in groups/clusters, U-type warps are slightly more
common in these environments. However, since the tidal and group/cluster
environmental effects occur simultaneously, we find no explicit dependency of
warp fractions and warping amplitudes on host halo masses.

To distinguish the effect of tidal interactions and group/cluster
environments, we examine the tidal effects for non-group/cluster and
group/cluster galaxies separately. In Figure 9, the upper panels show the
warping amplitudes of S- and U-type warps in non-group/cluster environments as
a function of $F_{\textrm{tidal}}$. The tidal force is exerted by the nearest
neighbor and thus isolated warped galaxies are not shown in this figure. The
middle and lower panels show warped galaxies in groups and clusters. We
exclude the central galaxy in each group/cluster to examine the the
group/cluster effect on infalling galaxies only. S-type warps in non-
group/cluster and group/cluster environments show similar positive
correlations with cc = 0.220. This implies that tidal interactions is
important in formation of S-types even in groups/clusters. By contrast,
U-types in groups/clusters show no correlation between warping amplitudes and
$F_{\textrm{tidal}}$ with relatively low cc = 0.037 and 0.027. This can be
explained by the fact that the imprints of tidal interactions on formation of
U-types in groups/clusters are vanished by non-tidal effects such as RPS.
Thus, it is necessary to investigate how non-tidal mechanisms are at work in
construction of U-types in groups/clusters.

##  4 Are U-type warps in groups/clusters jellyfishes?

RPS in groups/clusters often produces galaxies with disturbed HI gas disks and
tentacle-like structures, which are so-called “jellyfish galaxies” (e.g.,
Smith et al. 2010; Ebeling et al. 2014; Fumagalli et al. 2014; Poggianti et
al. 2016; Poggianti et al. 2017; Ramos-Martínez et al. 2018; Jaffé et al.
2018; Yun et al. 2019). Some simulations suggested that jellyfish galaxies can
exhibit U-shaped stellar disks during RPS, specifically at the very early
stage. For example, Smith et al. (2012) simulated that drag force on the gas
disk during RPS can be transmitted to the dark matter halo, and stellar disk
can be changed into a U-shape appearance briefly ($<$ 200 Myr). It is
noteworthy that, according to this simulation, U-shaped stellar disks in
jellyfishes are bent into the opposite direction of their stripped gas trails.
This theoretical expectation is consistent with the recent simulation of Lee
et al. (2022), in which a U-shaped stellar warp opposite to stripped gas tails
is present at the beginning of RPS ($t_{\textrm{form}}\sim$ 185 Myr).

Motivated by the previous work and our results on U-type warps in
groups/clusters not showing the tidal effect in local environments, we
investigate whether U-type warps in groups/clusters are related to jellyfish
galaxies. In this section, we discuss the possible link between U-type warps
in groups/clusters and jellyfish galaxies, considering their similarities in
optical morphology, kinematics in groups/clusters, sSFR, and HI fraction.

###  4.1 Warped Jellyfish Galaxies

We first look into the appearance of the warped stellar component of RPS
jellyfish galaxies in the literature. Although previous observational studies
on jellyfish galaxies did not delve into galaxies’ warped disk structures, we
find some interesting examples that show detectable U-shaped stellar disks
through our visual inspection on their optical images. Our examples include
MACSJ0451-JFG1, MACSJ0712-JFG1, MACSJ1752-JFG1 in HST F606W and F814W from
Ebeling et al. (2014), A1758N-JFG1 in HST F606W and F814W from Kalita &
Ebeling (2019), and JO113 in $g$-, $r$-, and $i$-bands from Gullieuszik et al.
(2020). We find other examples from Roberts & Parker (2020); at least five
U-shaped stellar warps among eight edge-on galaxies with no S-shaped ones.
Grishin et al. (2021) investigated the effect of RPS on low-mass galaxies in
the Coma and Abell 2147 clusters. We find through our visual inspection that
at least four out of five edge-on galaxies (GMP 3176, GMP 2639, GMP 4348, and
J160231.45+155749.9) are bent into U-shape morphologies. However, since these
observations did not include radio wavelengths, it is limited to directly
compare the directions of stellar warps and stripped gas tails.

Thanks to other recent multi-wavelength observations, we find further
promising examples consistent with the theoretical expectation by Smith et al.
(2012). Moretti et al. (2021) identified 13 jellyfish galaxies from Abell 2744
and Abell 370 clusters. They provided RGB images from HST of jellyfish
galaxies with overlapped [OII] emission from MUSE observation. We find two
edge-on galaxies, A370-06 and A370-08. Galaxy A370-06 shows a U-shaped stellar
disk bent in the opposite direction of gas tails. Roberts et al. (2021a)
provided $\sim$60 jellyfish galaxies’ $g$-band optical images with overlapped
LOFAR 144MHz maps. Through our visual inspection, we find one S-shaped stellar
disk (KUG0930+342) and two U-shaped disks (LEDA2158637 and LEDA2157975) among
20 edge-on galaxies from their sample. Specifically, LEDA2157975 exhibits a
U-shaped stellar disk clearly bent in the opposite direction of stripped gas
components.

We further investigate morphologies of stellar disks of jellyfish galaxies in
the Illustris TNG100 simulation (Pillepich et al. 2018; Nelson et al. 2019).
Yun et al. (2019) identified 800 candidates of jellyfish galaxies with host
halo mass of $10^{13}$ $<$ $M_{\textrm{halo}}/M_{\odot}$ $<$ $10^{14.6}$
through visual inspection. Figure 10 illustrates best example images of
stellar and gas components of the jellyfishes. We find 50 jellyfish galaxies
that show detectable U-shaped stellar disks and only one example of the
S-shape disk. The direction of warped stellar disks and gas tails are marked
as orange and cyan arrows, respectively. Most U-shaped jellyfish galaxies show
detectable U-type stellar warps bent in the opposite direction of their
stripped gas tails. This is consistent with the numerical expectation of Smith
et al. (2012) and Lee et al. (2022).

We note that there is one case of the S-shaped stellar warp (ID76093) among
Illustris TNG100 jellyfish candidates. The galaxy has the S-shaped gas
component; thus it seems that not only RPS but other gravitational mechanisms
influence both its stellar and gaseous disks. Still, it is necessary to trace
how the morphologies of warped disks evolve and prove whether the RPS govern
their appearances. We will investigate the time-dependent evolution of S- and
U-type warps using simulations in forthcoming papers.

###  4.2 The Phase-Space Distribution of Group/Cluster Galaxies

The spatial distribution and kinematics of galaxies in clusters allow us to
trace the evolutionary phases of the infalling process. This well-established
method is based on the ‘phase-space diagram’ (e.g., Mahajan et al. 2011; Oman
et al. 2013; Jaffé et al. 2015; Rhee et al. 2017; Smith et al. 2019; Pasquali
et al. 2019). The position where each galaxy is located on the diagram
indicates its evolutionary phase from beginning of infall to a cluster to
being entirely virialised. Figure 11 shows galaxies with host halo mass of
$M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{12}$ on the phase-space diagram
along with the caustic regions (Mamon et al. 2004; Mahajan et al. 2011;
Pasquali et al. 2019). Figure 12 shows the same but for galaxies with more
massive halo mass of $M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{14}$. We follow
the definition of Pasquali et al. (2019) [see their equations (3) and (4) from
p = 1 to 5]. The definition is valid for galaxies which are close to cluster
center ($R/R_{\textrm{vir}}<1.0$) and we use the subsample which are located
in the same range. Region 1 is for virialised galaxies, whereas galaxies in
Regions 5 and 6 begin to infall. As illustrated in Figure 11 and Figure 12,
while S-type warps are more concentrated in Region 1, the distribution of
U-types is more extended to outer regions on the phase-space diagram. For the
looser criterion of halo mass, 22.4% of S-types and 15.2% of U-types are
located in Region 1, respectively. The difference becomes greater when we only
use warped galaxies in more massive clusters; 35.1% of S-type and 15.5% of
U-type warps are populated in Region 1.

Many studies showed that jellyfish galaxies tend to spread to the higher value
of relative velocity on the phase-space diagram (e.g., Jaffé et al. 2018; Yun
et al. 2019). Intriguingly, S- and U-type warps among our sample show clearly
different distribution of relative velocity. Histograms in Figure 11 and
Figure 12 show that while S-type warps exhibit a similar distribution to
unwarped control galaxies, U-type warps are more widely in relative velocity.
Among others, Yun et al. (2019) classified $\sim$800 jellyfish galaxies from
Illustris TNG100 simulation and showed that the relative velocity distribution
of jellyfish galaxies are more extended than the undisturbed control sample.
In the bottom panels of Figure 11, our U-type warps show an extended
distribution in relative velocity similar to $\sim$ 150 jellyfish candidates
observed by Poggianti et al. (2016). In the bottom panels of Figure 12, when
we compare U-type warps and jellyfish candidates in more massive clusters,
they still show similar distribution of relative velocity. Also, we showed in
Section 3.2 that, while the S-type warps show systematic correlations with the
tidal interactions irrespective of cluster environments, U-types in clusters
are not related with the local environments. These results imply that most
U-type warps in galaxy clusters are still not virialised within clusters’
potential and seem to be affected by RPS like jellyfish galaxies.

###  4.3 Stellar Mass, Star Formation Rate, and Gas Mass Fraction

Jellyfish galaxies often exhibit increased star formation activity (Gavazzi &
Jaffe 1985; Porter et al. 2008; Mahajan et al. 2012; Bekki 2014; Poggianti et
al. 2016; Roberts et al. 2021c). The SF is enhanced at the infalling front of
jellyfishes in clusters where gas compression occurs (Kapferer et al. 2009;
Vulcani et al. 2018b; Ramatsoku et al. 2019; Roberts et al. 2021d). For
instance, Vulcani et al. (2018b) identified 42 RPS galaxies and found that
both disks and tails have systematically higher SFR than the control sample.
Roberts & Parker (2020) investigated RPS galaxies in the Coma cluster to find
that RPS galaxies exhibit a higher SFR relative to ‘normal’ star-forming
galaxies and isolated galaxies in fields. They suggested that RPS can trigger
star formation prior to quenching. Roberts et al. (2021b) identified four
jellyfish galaxies from the Perseus cluster and showed that all four
jellyfishes exhibit star formation enhancement along the opposite direction of
their stripped tails. Durret et al. (2021) found 79 jellyfish candidates from
the MACS0717 cluster and confirmed that jellyfishes tend to have higher sSFR
and bluer colors. They stated that “jellyfish galaxy candidates appear to have
somewhat larger SFRs than non-jellyfish star-forming galaxies.” Roberts et al.
(2022) identified 48 RPS galaxies in low-mass groups
($M_{\textrm{halo}}/M_{\odot}$ $<$ $10^{14}$) and massive clusters
($M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{14}$) by visual inspection using
the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) imaging and
showed that RPS galaxies commonly have enhanced SFRs.

However, some studies claimed the lack of observational evidence of the SFR
enhancement during RPS. For example, Mun et al. (2021) and Henriksen & Dusek
(2021) respectively investigated 48 RPS galaxies in the Virgo cluster and 180
galaxies of the merging cluster Abell 3266, and found no strong evidence of
RPS-induced global SF enhancement. Henriksen & Dusek (2021) suggested that
RPS-induced SF enhancement is only locally modest, and the overall effect of
SF quenching increases as the strength of RPS increases. However, the net
effect of SF enhancement strongly depends on gas fraction and galaxies’
evolutionary phase during RPS. Without morphological classification, these
studies do not represent the characteristics of U-shaped disk galaxies in
clusters. George et al. (2019) introduced a case of jellyfish galaxy JO201 in
which star formation is reduced during RPS. This galaxy shows a H2 cavity with
recently suppressed star formation by its AGN feedback in the last few
$10^{8}$ yr. However, we exclude AGN-hosting galaxies in our sample in this
study.

Now, we examine sSFR and star formation efficiency (SFE) of warped and
unwarped galaxies at given stellar and gas mass. Recent observations suggested
that on average RPS galaxies exhibit lower stellar mass and higher gas
fractions. For example, Gavazzi et al. (2018) suggested that galaxies with
lower stellar mass and higher gas fractions are more affected by RPS. Grishin
et al. (2021) found that $\sim$60% of RPS galaxies show higher gas fractions.
Even though infalling galaxies should lose their gas components during RPS,
most stripped galaxies still exhibit higher gas fractions. This result is
consistent with theoretical expectations of RPS galaxies. Smith et al. (2012)
demonstrated using their simulation that galaxies with higher gas mass
fractions exhibit clearer signs of U-shaped stellar disk structures. Yun et
al. (2019) found that jellyfishes are about three times more common at lower
stellar mass ($M_{*}/M_{\odot}<10^{10}$) than at higher mass
($M_{*}/M_{\odot}>10^{10}$). Following these recent findings, in the upper
panels of Figure 13 and Figure 14, we compare sSFRs and HI gas mass fractions
($f_{\textrm{HI}}=M_{\textrm{HI}}/M_{*}$) of galaxies in clusters, using
different halo mass criteria ($M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{12}$
and $M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{14}$). Our sample is matched
with the galaxies in the ALFALFA survey (Haynes et al. 2018) and S- and U-type
warps have HI detection rates of $\sim$2.4% and $\sim$3.6%, respectively.
Despite the small sample, U-type warps in clusters are, on average, of
slightly smaller stellar mass and higher $f_{\textrm{HI}}$, which are
susceptible to RPS.

The lower left panels of Figure 13 and Figure 14 show that, at the same
$f_{\textrm{HI}}$, U-type warps exhibit higher sSFR than S-types and unwarped
galaxies. This is more significant for galaxies in more massive host halos
($M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{14}$). The result indicates that
U-type warps in clusters have high SFE similar to jellyfish galaxies (Wang et
al. 2018; Ramatsoku et al. 2019; Safarzadeh & Loeb 2019; Ramatsoku et al.
2020). Using the EAGLE simulation, Troncoso Iribarren et al. (2016) found
clear evidence of asymmetric SFE enhancement of RPS galaxies at the windward
side. Safarzadeh & Loeb (2019) simulated that pressure by intracluster medium
can increase SFE under the assumption that galactic magnetic field halts
evaporation of gas clouds during RPS. Observationally, Ramatsoku et al. (2019)
and Ramatsoku et al. (2020) introduced the case of JO206 galaxy among the GAs
Stripping Phenomena in galaxies with MUSE (GASP) sample which show higher SFE
than field galaxies with similar stellar and gas mass. Specifically, RPS
jellyfish galaxies exhibit 5–10 times higher SFE at disk than stripping tails
due to compression of molecular gas by RPS. Even at the high redshift
universe, the enhancement of SFE of RPS galaxies is reported. Wang et al.
(2018) identified 14 member galaxies from a distant X-ray cluster CLJ1001 (z
$\sim$ 2) and found a clear trend of their SFE as a function of cluster
centric distance. Galaxies at the cluster center exhibit less molecular gas
than field galaxies, but, intriguingly, higher SFR. They suggested that
cluster environment effects such as RPS can delay quenching with increasing
SFE.

However, it is needed to consider that, in observations, one can detect not
the initial but present $f_{\textrm{HI}}$. Many simulations suggested that RPS
can remove the gas component efficiently, and RPS galaxies can change
systematically from gas-rich to gas-poor over time. For example, Yoon et al.
(2017) showed that RPS galaxies have a wide range of gas fractions. Using a
phase-space diagram and HI morphologies, they defined the evolutionary phase
of infalling galaxies and showed that the HI deficiency depends on the time
since the first infall. Specifically, only recently infalled galaxies exhibit
strongly disturbed HI morphologies and higher gas fractions. Similarly, Mun et
al. (2021) showed that the HI deficiency of RPS galaxies in the Virgo cluster
strongly depends on the evolutionary phase of infall.

Molnar et al. (2021) investigated RPS galaxies in the Coma cluster and showed
using a simple model that the distribution of $\Delta f_{\textrm{HI}}$ and
$\Delta$sSFR can trace the evolutionary phase of RPS. The residual of
$f_{\textrm{HI}}$, $\Delta f_{\textrm{HI}}$, is defined by the difference in
$f_{\textrm{HI}}$ between the warp sample and the mean $f_{\textrm{HI}}$ of
its corresponding control sample. According to their model, gas-rich galaxies
temporarily experience a short timescale ($\leq$ 300Myr) gas removal and
starburst, resulting in the still regular HI gas fraction and enhanced SFR at
the beginning of RPS. As galaxies evolve, the deficiency of HI increases and
SFR is suppressed. Along this evolution during RPS, galaxies move from the
first through second to third quadrant on the $\Delta
f_{\textrm{HI}}$–$\Delta$sSFR parameter space.

The lower right panels of Figure 13 and Figure 14 show the distribution of S-,
U-type warps and unwarped galaxies in clusters. In this $\Delta
f_{\textrm{HI}}$–$\Delta$sSFR plane, the symbol size represents the warping
amplitude. Most U-types are distributed in the first and second quadrants,
with only a few in the fourth quadrant. The absence of galaxies in the fourth
quadrant is similar to the RPS galaxies explored by Molnar et al. (2021). We
also find that more strongly warped U-types prefer the first quadrant. On
average, the mean value of warping amplitude of U-type warps in the first
quadrant is $\sim$5.5∘ greater than that of U-types in the third quadrant
regardless of the halo mass criteria of groups/clusters. This is consistent
with our aforementioned result on the correlation between sSFR enhancement and
warping amplitudes for U-type warps.

To be more quantitative, we estimate the orthogonal offsets of S- and U-type
warps from the unwarped galaxies. We fit the relation for unwarped galaxies in
clusters with host halo mass of $M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{12}$
[$\Delta\textrm{Log(sSFR)}=0.97\,\Delta\textrm{Log}(f_{\textrm{HI}})-0.01$]
and in clusters with host halo mass of $M_{\textrm{halo}}/M_{\odot}$ $\geq$
$10^{14}$
[$\Delta\textrm{Log(sSFR)}=0.94\,\Delta\textrm{Log}(f_{\textrm{HI}})$]. The
resulting distributions of offsets are illustrated in Figure 15. On average,
U-type warped galaxies show $\sim$ 0.2 dex higer offset than unwarped and
S-type ones. This result is consistent with theoretical expectation of Molnar
et al. (2021).

##  5 Summary and Discussion

Our main questions in this study are: ($a$) are S- and U-type warps created by
the same mechanism? and ($b$) how can we explain U-type warps? To address the
questions, we complete the most extensive catalog of $\sim$3000 nearby (0.02
$<$ z $<$ 0.06) massive ($M_{*}/M_{\odot}$ $>$ $10^{9}$) warped disk galaxies
through our new automatic warp measurement scheme. Then, we compare key
properties, including optical colors, sSFR, several environmental parameters,
warping amplitudes, and kinematics within groups/clusters, stellar mass and
gas fraction, between S- and U-type warped galaxies for the first time.

Our findings are summarised as follows.

  1. 1.

U-type warps exhibit bluer optical color and higher sSFR than S-types and
unwarped galaxies at a given stellar mass. The $\Delta$Log(sSFR) correlates
positively with warping amplitudes. The results indicates that U-type warp
formation mechanism entails higher sSFR.

  2. 2.

While warp properties of S-type warps are correlated with the tidal force by
the nearest neighbors irrespective of galaxy cluster membership, U-types in
clusters show no local environmental dependence. This implies that the
conventional gravitational interactions create S-type warps only and other
non-tidal alternative mechanisms are required to explain the existence of
U-type warps at least in clusters.

  3. 3.

A thorough visual inspection of jellyfish galaxies in literature leads us to
find some intriguing examples of RPS-driven U-shaped warped galaxies bent into
the opposite direction of stripped gas tails, which is consistent with
previously published theoretical expectations of RPS-driven stellar warps.

  4. 4.

There are considerable similarities between U-type warps in galaxy clusters
and RPS-induced jellyfish galaxies in terms of the morphology, location on the
phase-space diagram, sSFR and $f_{\textrm{{HI}}}$. The results suggest that
U-types in groups/clusters could be connected to jellyfish galaxies at the
very early stage of RPS, explaining the existence of U-types which are hard-
to-make in conventional galaxy–galaxy interaction simulations.

The discovery of similarities between U-type warps in groups/clusters and
jellyfish galaxies is encouraging in the context of unveiling the origin of
warped disk galaxies. Given that only 17.5$\%$ (4.1$\%$) of U-type warps
belong to groups/clusters with $M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{12}$
(more massive clusters with $M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{14}$),
the RPS origin of the group/cluster U-type warps remains to be approved by
follow-up observations such as integral field units and HI survey of the gas
component in these galaxies. Also, it is still limited to explain the other
majority of U-type warps which live in fields. Different pathways to form
U-shaped disk galaxies including galaxy-galaxy interactions, large-scale gas
infall, and interactions with misaligned dark matter halos remain to be fully
explored.

We propose that RPS galaxies can be observed as U-type warps with higher sSFR
and stronger warping amplitudes at the beginning of infall. Following our
scenario, it is natural to expect that U-type warps should be more common in
more massive clusters due to their stronger effect of RPS. However, the
incidence and strength of U-type warps in groups/clusters do not depend on
their host halo mass. The absence of a strong correlation between U-type warps
and groups/clusters’ halo mass can be explained by the short time-scale of
RPS-driven U-shaped stellar disks. Theoretical studies expected that U-shaped
stellar disks could be constructed very briefly ($\leq$ 200Myr) at the early
stage of RPS (Smith et al. 2012 and Lee et al. 2022). This time-scale is too
short to be observed as stable U-shaped stellar disks. In contrast, RPS occurs
slowly with a longer time-scale ($\sim$3 Gyr) in galaxy groups with less
massive halos. Thus, despite its lower efficiency of RPS, there is more chance
to detect stable stripped stellar disks in less massive groups than in more
massive clusters. It is necessary to investigate the time-dependence evolution
of RPS-driven stellar warps in detail by further cosmological simulations.

Our results are essential for galactic warp studies because U-shaped RPS
galaxies can lead to overestimation of the incidence of tidal-origin U-type
warps. Thus, warped galaxies in fields and clusters should be investigated
separately to assess the effect of the tidal interactions without the
contamination of cluster environment effects. Also, it is important for RPS
studies that suggest to look for warps as an additional sign of stripping.

The measurement of warp morphologies and warping amplitudes are affected by
the complex spiral arm, dust lanes, and the orientation angle from the
observer’s viewpoint. We thus need more massive data to study the effect of
the substructures on warp measurements. We initiated Poppin’
Galaxy111https://www.zooniverse.org/projects/wim0705/poppin-galaxy project
through the Zooniverse in 2018 to gather massive warped galaxies classified by
over 10,000 volunteers. In forthcoming papers, we are to investigate the
origin and properties of the warp phenomenon exploiting our extensive
observational data in comparison to high-resolution cosmological simulations
of galaxies.

S.-J.Y. acknowledges support by the Mid-career Researcher Program (No.
2019R1A2C3006242) through the National Research Foundation of Korea. Funding
for the Sloan Digital Sky Survey (SDSS) and SDSS-II has been provided by the
Alfred P. Sloan Foundation, the Participating Institutions, the National
Science Foundation, the U.S. Department of Energy, the National Aeronautics
and Space Administration, the Japanese Monbukagakusho, the Max Planck Society,
and the Higher Education Funding Council for England. The SDSS Web site is
http://www.sdss.org/. The SDSS is managed by the Astrophysical Research
Consortium (ARC) for the Participating Institutions. The Participating
Institutions are the American Museum of Natural History, Astrophysical
Institute Potsdam, University of Basel, University of Cambridge, Case Western
Reserve University, The University of Chicago, Drexel University, Fermilab,
the Institute for Advanced Study, the Japan Participation Group, The Johns
Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli
Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group,
the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the
Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for
Astrophysics (MPA), New Mexico State University, Ohio State University,
University of Pittsburgh, University of Portsmouth, Princeton University, the
United States Naval Observatory, and the University of Washington.

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Table 1: Basic statistics of warped disk galaxies in our sample. Morphology | Incidence | Number Fraction | Median Warp Angle | Median Log($M_{*}/M_{\odot}$)
---|---|---|---|---
S-type | 2206 | 27.6% | $5.45^{\circ}\pm 0.07^{\circ}$ | 10.39 $\pm$ 0.42
U-type | 1456 | 18.2% | $4.37^{\circ}\pm 0.08^{\circ}$ | 10.36 $\pm$ 0.43
Figure 1: The procedure of the warp angle measurement through our automated
scheme for the case of S-type (upper row) and U-type warps (lower row). (Left
column) The Gaussian fitted vertical distribution of pixel values from the
left side of the disk (blue) via the center peak (black) to the right side
(red) with respect to the major axis. (Right column) The warped structure of
the ‘spine’ is illustrated by blue (left side) and red (right side) solid
lines, respectively, on the contour image of each galaxy. The length of the
error bars is the standard error of the location of the spine at each
$\Delta$x bin. Figure 2: Randomly selected sample of multi-band SDSS images of
S- (upper eight panels) and U-type warped (lower eight panels) galaxies among
our final catalog. Figure 3: (Upper) Distributions of the redshift (left
column) and stellar mass (right) for unwarped galaxies (black histogram) and
warped galaxies (violet). For each normalised histogram, the integral under
the histogram is equal to one. Each p-value by the KS test is given on each
panel. (Lower) The same as the upper panels, but black histograms are for the
control sample. Figure 4: (Upper, left two panels) The $g-r$ colors versus
stellar mass for S-types (orange dots on the left panel) and U-types (cyan
dots on the right). The $g-r$ color is reddening- and k-corrected. Red, blue
solid and black dashed lines connect the median values of the
Log($M_{*}/M_{\odot}$) bins for S-type, U-type warps and unwarped control
galaxies, respectively. Black, red and blue dashed regions are standard
deviation scatter. The length of the error bars is the standard error, which
is estimated as the standard deviation divided by the square root of the
sample size at each mass bin. (Upper, rightmost panel) Each normalised
histogram shows the color distribution of S-types (red solid histogram) and
U-types (blue solid), the unwarped control sample (black dashed). (Lower) The
same as the upper panels, but for the Log(sSFR). Figure 5: (Left two panels)
The difference in sSFR between the warp sample and the mean sSFR of its
corresponding control sample, $\Delta$Log(sSFR), as a function of warping
amplitude, $\alpha$, for S-types (orange dots on the left panel) and U-type
(cyan dots on the left panel). Red and blue lines connect the median
$\Delta$Log(sSFR) values of the warp amplitude bins for S-types and U-types,
respectively. Red and blue dashed regions are standard deviation scatter. The
length of the error bars is the standard error, which is estimated as the
standard deviation divided by the square root of the sample size at each
$\alpha$ bin. For comparison, $\Delta$Log(sSFR) = 0.0 is marked by horizontal
grey dashed line. (Rightmost panel) Each normalised histogram shows the
$\Delta$Log(sSFR) distribution of S-types (red solid histogram) and U-types
(blue solid).

Figure 6: (Upper panels) Warped galaxy fraction of S-types (red line on the
left) and U-types (blue line on the right) as a function of local density,
Log($\Sigma_{45}$). The length of the error bars is the poission error in each
Log($\Sigma_{45}$) bin. (Lower panels) The same as the upper panels, but
warped galaxy fraction as a function of tidal force, $F_{\rm tidal}$, by the
closest neighbor galaxies.

Figure 7: (Upper panels) Distribution on the Log($\Sigma_{45}$) vs. warp
amplitude plane for S-types (orange dots on the left panel) and U-types (cyan
dots on the right). Red and blue lines connect the median $\alpha$ values of
the Log($\Sigma_{45}$) bins for S-types and U-types, respectively. Dashed and
solid lines follow the median distribution of all and strongly warped
($\alpha>3^{\circ}$) galaxies, respectively. Red and blue dashed regions are
standard deviation scatter. The length of the error bars is the standard
error, which is estimated as the standard deviation divided by the square root
of the sample size at each Log($\Sigma_{45}$) bin. We estimated the
correlation coefficient (cc) for all warpred and strongly warped galaxies.
(Lower panels) The same as the upper panels, but for the $F_{\rm tidal}$ vs.
warp amplitude plane.

Figure 8: Best sample of multi-band SDSS images of U-type warped galaxies in
massive clusters with their name.

Figure 9: The same as the lower panels of Figure 8, but for non-group/cluster
members (upper panels), group/cluster members with host halo masses of
$M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{12}$ (middle), and group/cluster
members with host halo masses of $M_{\textrm{halo}}/M_{\odot}$ $\geq$
$10^{14}$ (lower).

Figure 10: Example images of warped stellar disks (1st and 3rd columns) and
their gas components (2nd and 4th columns) for RPS-induced jellyfish galaxies
from IllustrisTNG simulation. The galaxies are classified as jellyfishes by
visual inspection by Yun et al. (2019) and their ID’s are given at the lower
left corner of the 1st- and 3rd-column panels. The directions of warped
stellar disks and those of corresponding gas tails are denoted as orange and
cyan arrows, respectively.

Figure 11: (Top left panel) Distribution of S-type warped (orange dots) and
unwarped (grey dots) galaxies in groups/clusters on the $R/R_{\rm
vir}$–$v_{\rm rel}/\sigma$ phase-space diagram. Black loci are the demarcation
lines given by Pasquali et al. (2019) and the regions ($R/R_{vir}<1.0$) are
labelled as Region 1 through 6. (Top right panel) The normalised $v_{\rm
rel}/\sigma$ distributions are illustrated for S-types (red solid histogram)
and unwarped (black dashed), along with the p-value from the KS test. (Middle)
The same as the top panel, but for U-type warped galaxies (cyan dots on the
left and blue solid histogram on the right). (Bottom) The same as the top
panel, but for U-type warped galaxies (cyan dots on the left and blue solid
histogram on the right) and jellyfish candidates (Poggianti et al. (2016) and
Jaffé et al. (2018); purple stars on the left and purple histogram on the
right).

Figure 12: The same as Figure 11, but for galaxies in groups/clusters with
massive host halo masses $M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{14}$.
Figure 13: Distribution on the stellar mass-$f_{\textrm{HI}}$ (Upper, left
panel), the stellar mass-sSFR (Upper, right panel), the $f_{\textrm{HI}}$-sSFR
(Lower, left panel) and the $\Delta f_{\textrm{HI}}$-$\Delta$sSFR plane
(Lower, right panel) for HI detected S-types (orange dots), U-types (cyan
dots) and unwarped (grey dots) galaxies in groups/clusters with halo masses of
$M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{12}$. Symbol sizes represent the
warping amplitudes as illustrated in the upper left panel. Black dashed lines
represent the linear fitted distribution of unwarped control galaxies. Figure
14: The same as Figure 13, but for galaxies in clusters with massive host halo
masses of $M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{14}$. Figure 15:
Distributions of the orthogonal $\Delta f_{\textrm{HI}}$-$\Delta$sSFR offsets
of S-type (red), U-type warped (blue), and unwarped galaxies (black dashed) in
groups/clusters with halo mass of $M_{\textrm{halo}}/M_{\odot}$ $\geq$
$10^{12}$ (left) and $M_{\textrm{halo}}/M_{\odot}$ $\geq$ $10^{14}$ (right).