11institutetext: Dipartimento di Fisica dell’Università degli Studi di Trieste
- Sezione di Astronomia, via Tiepolo 11, I-34143 Trieste, Italy 11email:
<EMAIL_ADDRESS>22institutetext: INAF - Osservatorio Astronomico di
Trieste, via Tiepolo 11, I-34143 Trieste, Italy 33institutetext: Fundación
Galileo Galilei - INAF (Telescopio Nazionale Galileo), Rambla José Ana
Fernández Perez 7, E-38712 Breña Baja (La Palma), Canary Islands, Spain
44institutetext: Instituto de Astrofísica de Canarias, C/Vía Láctea s/n,
E-38205 La Laguna (Tenerife), Canary Islands, Spain 55institutetext:
Departamento de Astrofísica, Univ. de La Laguna, Av. del Astrofísico Francisco
Sánchez s/n, E-38205 La Laguna (Tenerife), Spain 66institutetext: INAF -
Osservatorio Astronomico di Brera, via E. Bianchi 46, I-23807 Merate, Italy

# Accretion processes in the galaxy cluster Hydra A/Abell 780 ††thanks: Full
Table 1 is only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/

M. Girardi 1122 W. Boschin 33224455 M. Nonino 22 C. Innocentin 11 S. De Grandi
66

(Received / Accepted )

###### Abstract

Context. Clusters of galaxies evolve and accrete mass, mostly from small
galaxy systems.

Aims. Our aim is to study the velocity field of the galaxy cluster Abell 780,
which is known for the powerful radio source Hydra A at its center and where a
spectacular X-ray tail associated with the galaxy LEDA 87445 has been
discovered.

Methods. Our analysis is based on the new spectroscopic data for hundreds of
galaxies obtained with the Italian Telescopio Nazionale Galileo and the Very
Large Telescope. We have constructed a redshift catalog of 623 galaxies and
selected a sample of 126 cluster members. We analyze the internal structure of
the cluster using a number of techniques.

Results. We estimate the mean redshift $z=0.0545$, the line-of-sight velocity
dispersion $\sigma_{\rm V}\sim 800$ km s-1, and the dynamical mass
$M_{200}\sim 5.4$ $\times 10^{14}\;M_{\odot}$. The global properties of Abell
780 are typical of relaxed clusters. On a smaller scale, we can detect the
presence of a galaxy group associated with LEDA 87445 in projected phase
space. The mean velocity and position of the center of the group agree well
with the velocity and position of LEDA 87445. We estimate the following
parameters of the collision. The group is characterized by a higher velocity
relative to the main system. It is infalling at a rest frame velocity of
$V_{\rm rf}\sim+870$ km s-1and lies at a projected distance $D\sim 1.1$ Mpc to
the south, slightly southeast of the cluster center. The mass ratio between
the group and the cluster is $\sim$1:5. We also find evidence of an asymmetry
in the velocity distribution of galaxies in the inner cluster region, which
might be related to a small low-velocity group detected as a substructure at
$V_{\rm{rf}}\sim-750$ km s-1.

Conclusions. We conclude that A780, although dynamically relaxed at first
sight, contains small substructures that may have some impact on the
energetics of the core region.

###### Key Words.:

Galaxies: clusters: individual: Abell 780, Hydra A – Galaxies: clusters:
general – Galaxies: kinematics and dynamics

##  1 Introduction

It is well known that galaxy clusters are not simple relaxed systems, but that
they evolve and increase in mass through a hierarchical merging process from
poor groups to rich clusters. Large mergers involving two galaxy systems of
comparable mass are the most energetic events in the Universe since the Big
Bang. However, as numerical simulations show, accretion of smaller systems at
the galaxy or group scale is the main channel of cluster growth (e.g., Berrier
et al. 2009; McGee et al. 2009; Benavides et al. 2020). Observational evidence
for cluster accretion in the past comes from the presence of cluster
substructures detected in the distributions of member galaxies, gas, and mass
as determined by optical, X-ray, and gravitational lensing data (Feretti et
al. 2002 and Molnar 2015 for reviews). Detecting and studying the accretion of
small galaxy systems is more difficult than that of mergers of the same size.
Indeed, this requires the use of several hundred redshifts per cluster and/or
the isophotes of X-ray brightness residuals (e.g., Adami et al. 2005 in Coma
cluster; Girardi et al. 2015 for the CLASH-VLT survey; Lisker et al. 2018 in
Virgo cluster).

The detection of accreted small groups, and in particular their member
galaxies, is a fundamental step in understanding the effects of the cluster
environment on galaxies. Indeed, one of the key issues is to understand the
dicothomy of galaxy types between the cluster and the field environment, both
in terms of the mechanism that stalls star formation in galaxies (e.g., Peng
et al. 2015) and whether this is related to the environment of the cluster
(e.g., Treu et al. 2003) or with the earlier preprocessing in groups (e.g.,
Vijayaraghavan & Ricker 2013).

Observations of X-ray bright head-tail downstreams are generally interpreted
as direct evidence for the ongoing process of cluster accretion, in which the
gaseous component of the infalling galaxies (or galaxy groups) is stripped by
the intracluster medium (ICM). The observation of these features is quite
rare, probably due to the high quality of the X-ray data required. As a
concrete example, one can cite M86 in Virgo (Forman et al. 1979), NGC 1404 in
Fornax (Jones et al. 1997), A2142 (Eckert et al. 2014), Hydra A (De Grandi et
al. 2016), and Abell 85 (Ichinohe et al. 2015). In practice, these X-ray
bright tail streams could serve as reliable signposts for infalling galaxies
or groups into the cluster environment.

De Grandi et al. (2016) report the discovery of a structure with a spectacular
bright X-ray tail in the outskirts of the Abell~780 cluster (hereafter A780)
using deep wide-field observations with _XMM-Newton_ and _Suzaku_. They
suggest that this feature is related to an accreting galaxy group that is
clustered around the bright galaxy LEDA 87445, $\sim 17^{\prime}$ ($1.1$ Mpc)
south of the cluster center, with a wake of stripped gas extending behind the
group over a projected scale of 760 kpc. The temperature of the gas along the
wake is constant at $kT_{\rm X}\sim 1.3$ keV, which is about a factor of two
below the temperature of the surrounding ICM.

A780 is a modest cluster, characterized by low richness (Abell richness class
$R=0$, Abell et al. 1989), X-ray luminosity ($L_{\rm{X,bol}}\sim 2\times
10^{44}$ erg s-1, Zhang et al. 2011), and temperature ($kT_{\rm X}\sim 3-3.5$
keV, Sato et al. 2012, De Grandi et al. 2016). These X-ray values are typical
for small clusters as shown by the relation $L_{\rm X}-T_{\rm X}$ (see Fig. 13
of Osmond & Ponman 2004).

The A780 cluster shows typical properties of a dynamically relaxed galaxy
system. _Chandra_ and _XMM-Newton_ observations indicate the presence of a
cool core (McNamara et al. 2000; see also Fig. 2 of Simionescu et al. 2008).
_XMM-Newton_ observations show that the X-ray morphology of A780 is smooth
within 1 Mpc (see, e.g., Fig. 1 of De Grandi et al. 2016). As for the galaxy
component, no difference in the luminosity function of galaxies was detected
in different regions within 500 kpc (Durret et al. 2009).

Instead, A780 shows many small-scale substructures related to the AGN-ICM
interaction in the center of the cluster. In fact, A780 is better known for
the powerful radio source, Hydra A (3C 218), emanating from its central,
brightest galaxy (Matthews et al. 1964). The radio source has a complex
morphology that extends nearly $\sim$ 8$\mathrm{{}^{\prime}}\;$($500$ kpc) in
the north-south direction, slightly NNE-SSW (Lane et al. 2004), while active
jets have been detected in the central $\sim 50$ kpc region (Taylor et al.
1990). _Chandra_ X-ray observations have revealed a multicavity system, a
large-scale shock, an X-ray bright filament near the cluster center, and a
spiral like structure in the ICM (McNamara et al. 2000, Nulsen et al. 2005;
Wise et al. 2007; Laganá et al. 2010). According to general consensus, the
giant radio lobes, triggered by AGN jets interact with the surrounding ICM and
regulate the cooling flow in Hydra A.

There are few spectroscopic data in the literature for galaxies in the field
of A780. Durret et al. (2009) analyzed the region of 5 deg radius ($\sim$ 19
Mpc) around the center of the cluster using galaxies with available redshift
in the NASA/IPAC Extragalactic Database (NED). No obvious large-scale
structure was found within 5 Mpc of the cluster, and the cluster is likely
detected as a bound structure of 14 galaxies. To date, the only homogeneous,
one-source redshift catalog is that of Smith et al. (2004), who list data for
41 galaxies and one star as part of their wide-field imaging/spectroscopic
study of 93 clusters (NOAO Fundamental Plane Survey). We have previously
analyzed these data and extracted a subset of 33 fiducial member galaxies (De
Grandi et al. 2016, see Appendix A). In that work we have presented the first
evidence of a substructure in the galaxy distribution around LEDA 87445, but
more data are needed to determine the kinematic and dynamical properties of
the group and the parameters of the collision.

In this context, we have carried out an intensive observational campaign to
obtain new spectroscopic data with both the Italian Telescopio Nazionale
Galileo (TNG) and the Very Large Telescope (VLT). This paper is devoted to the
presentation of our results on the velocity field of A780. The paper is
organized as follows. We describe the optical observations and present our
spectroscopic data catalog in Sects. 2 and 3. We select the members of the
cluster, estimate the global properties, and analyze the substructure in
Sects. 4 and 5\. Section 6 is devoted to the interpretation and discussion of
our results. In Sect. 7, we give a brief summary and derive our conclusions.
In this work we use $H_{0}=70$ km s-1 Mpc-1 in a flat cosmology with
$\Omega_{0}=0.3$ and $\Omega_{\Lambda}=0.7$. In the assumed cosmology,
1$\mathrm{{}^{\prime}}\;$corresponds to $\sim 63.5$ kpc at the cluster
redshift. Recall that the velocities we derive for the galaxies are line-of-
sight velocities determined from the redshift, $V=cz$. Unless otherwise
stated, we report errors with a confidence level (c.l.) of 68%.

##  2 New spectroscopic data

Multi-object spectroscopic observations of A780 were performed at the TNG in
February 2016 (program AOT32-TAC25, PI: M. Girardi). We used the instrument
DOLoRes in MOS mode with the LR-B
Grism111http://www.tng.iac.es/instruments/lrs. In total, we observed five MOS
masks for a total of 194 slits. The total exposure time was 3600 s for each of
the five masks.

Spectral reduction and redshift estimation were performed using standard
IRAF222IRAF is distributed by the National Optical Astronomy Observatories,
which are operated by the Association of Universities for Research in
Astronomy, Inc., under a cooperative agreement with the National Science
Foundation. tasks and the cross-correlation technique (Tonry & Davis 1979).
The line-of-sight velocity errors are a result of the cross-correlation
technique. In 43 cases, the redshift was estimated by measuring the wavelength
position of emission lines in the spectra. Our spectroscopic catalog contains
165 galaxies. For five galaxies there are double redshift determinations
measured in different masks.

We have checked the consistency of redshift measurements in different masks
using the following procedure (see, e.g., Barrena et al. 2007; hereafter FIT-
ZZ procedure). For the five galaxies with double redshift determination, we
fitted the first measurement against the second by using a straight line and
accounting for errors in both coordinates (Press et al. 1992). The fitted line
agrees with the one-to-one relation, but the value of the
$\chi^{2}$-probability indicates that the errors are too small to explain the
observed scatter. Only when the nominal errors of the redshifts are multiplied
by a factor of two can the observed scatter be justified. We have corrected
the error estimates accordingly. For the galaxies with two redshift
measurements, we combined the two redshift determinations using weighted
averages and errors. Our final spectroscopic TNG catalog lists 160 galaxies
brighter than $r$=21 mag, most brighter than $r$=20 mag. The median value of
the $cz$ errors is 98 km s-1.

Multi-object spectroscopic observations of Hydra A were performed at the VLT
in January, February, and March 2017 (Program 098.A-0807(A), P.I.: M.
Girardi). We used the instrument VIMOS in MOS mode with the LR-blue grism. In
total, we observed three MOS mask pointings for a total of 1407 slitlets. The
total exposure time was six hours, distributed over three pointings. Spectral
reduction and calculation of radial velocities were performed using IRAF as
described above. We succeeded in obtaining a reliable determination of the
redshift for 478 galaxies. The success rate of $30\%$ was mainly due to the
poor weather conditions. We obtained duplicate determinations for 20 galaxies
measured in different masks, and we followed the FIT-ZZ procedure described
above to verify the consistency of measurements. This analysis shows that the
errors are underestimated by a factor 2.5 and we corrected them accordingly.
For the galaxies with two redshift measurements, we combined the duplicate
determinations as above. Our final spectroscopic VLT catalog lists 458
galaxies down to $r\sim$24 mag, about three magnitudes fainter than the data
from TNG. The median value of the $cz$ errors is 140 km s-1.

##  3 Spectroscopic catalog

In creating a unique catalog, we also took into account the redshift data
provided by Smith et al. (2004, hereafter S04 catalog, 41 galaxies), which
have already been analyzed in our previous study (De Grandi et al. 2016). We
verified the consistency of the S04 data with our new TNG data by applying the
FIT-ZZ procedure to the 13 objects listed in both catalogs. This analysis
shows that the S04 errors are underestimated by a factor of two and we
corrected them accordingly. For the galaxies listed in both catalogs, we
combined the duplicate redshift determinations as above. We obtained the
combined catalog TNG+S04 and compared it with the VLT catalog. We verified
their consistency by applying the FIT-ZZ procedure to 23 common objects and
combined the data to obtain a unique catalog. The final spectroscopic catalog
consists of 623 galaxies, mostly from VLT observations, covering mainly the
cluster core and the region around LEDA 87445.

We have also used public photometric data from the CFHT archive obtained with
the Megaprime/Megacam camera at the Canada-France-Hawaii Telescope. From the
CADC Megapipe archive (Gwyn 2009) we retrieved the catalogs for the images in
Megacam $g$ and $r$ bands and corrected the magnitudes for Galactic
extinction. The total area covered by the images is 1.05$\times$1.16 deg2. The
estimated limiting magnitudes (at the $5\sigma$ c.l.) are $g$ = 25.5 mag and
$r$ = 24.5 mag.

Table 1, available at CDS, lists the velocity catalog for the member galaxies,
as defined in Sect. 4: identification number of each galaxy, ID (Col. 1);
right ascension and declination, $\alpha$ and $\delta$ (J2000, Col. 2); $r$
magnitude (Col. 3); heliocentric radial velocities, $V=cz$ (Col. 4), with
errors, $\Delta V$ (Col. 5); source of spectroscopic data (V: VLT, T: TNG, L:
S04).

Figure 1 shows the cluster region sampled by our redshift catalog, with the
_XMM-Newton_ X-ray contours superimposed. Our new spectroscopic observations
are mainly focused on the south-southeastern part of A780, allowing us to
analyze the cluster galaxies from the cluster center out to LEDA 87445.

Table 1: Radial velocities of 126 member galaxies of A780

$\begin{array}[]{r c c r r c}\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\mathrm{ID}&\alpha,\delta\,(\mathrm{J}2000)&r&V&\Delta
V&\mathrm{Source}\\\ &&&\mathrm{\,(\,km}&\mathrm{s^{-1}\,)}&\\\
\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr 1&9\ 16\ 58.13,-12\ 05\
28.6&16.50&16338&50&\mathrm{L}\\\ 2&9\ 16\ 58.23,-12\ 14\
06.4&16.55&16200&58&\mathrm{L}\\\ 3&9\ 17\ 16.46,-12\ 19\
07.4&16.73&16988&72&\mathrm{L}\\\ 4&9\ 17\ 21.29,-12\ 18\
02.0&16.92&16583&56&\mathrm{L}\\\ 5&9\ 17\ 24.58,-12\ 23\
21.7&17.35&14401&130&\mathrm{L}\\\ 6&9\ 17\ 27.02,-12\ 29\
59.5&20.63&16534&210&\mathrm{V}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\end{array}$

333Full table is available at CDS.

Figure 1: CFHT/Megacam $r$-band image (north top and east left) of the galaxy
cluster A780 with the contour levels of the _XMM-Newton_ X-ray image
superimposed (photons in the energy range 0.7–1.2 keV, De Grandi et al. 2016).
Cluster members, as defined in Sect. 4, are highlighted by red circles (see
Table 1). The labels denote the galaxies discussed in the text, ID. 47 (the
BCG where the Hydra A radio source is located) and ID. 97 (LEDA 87445).

The cluster galaxy population is dominated by the brightest cluster galaxy
(BCG) ID 47, which is located in the center of the X-ray emission. The BCG was
described as a cD galaxy with an unresolved binary nucleus (Dewhirst 1959;
Matthews et al. 1964). The secondary nucleus was found to be blueshifted with
respect to the primary nucleus. Indeed, a diffraction-limited $K_{\rm s}$-band
image taken with the MCAO system of Gemini South (Neichel et al. 2014) shows
that there is a close companion galaxy to the southeast of the BCG (see also
our Fig. 2). In our catalog, the companion galaxy is identified as ID 50 and
is blueshifted of $\sim 900$ km s${}^{-1}\;$with respect to the BCG. Both
galaxies lie within the velocity distribution of member galaxies and are
separated by a value slightly larger than the velocity dispersion (see below,
Sect. 4). This confirms that ID 50 is an independent cluster galaxy projected
onto the cluster center, very close to the BCG. Another prominent galaxy is
LEDA 87445 (ID. 97), the galaxy associated with the bright X-ray tail (De
Grandi et al. 2016).

Figure 2: NIR diffraction-limited image of the BCG and ID 50 taken with the
MCAO system of the Gemini South telescope (adapted from Fig. 5 of Neichel et
al. 2014). The insets show the wavelength-calibrated TNG spectra of BCG and
its close projected companion.

##  4 Member selection and global properties

To select cluster members among the 623 galaxies in our spectroscopic catalog,
we used the two-step method known as the “Peak+Gap” (P+G), which was
previously applied by Girardi et al. (2015). The first step is the application
of the 1D adaptive-kernel DEDICA method (Pisani 1993 and Pisani 1996; see also
Girardi et al. 1996). This method detects A780 as a peak at $z\sim 0.0543$
populated by 131 galaxies. All but one the non-members are background
galaxies.

Figure 3: Distribution of galaxy redshifts within $z=0.2$. The histogram
refers to all galaxies with the spectroscopic redshift in the region of A780.
The histogram with the thick, red line refers to the 131 galaxies assigned to
the A780 peak by the 1D DEDICA reconstruction method (faint line). The inset
figure shows the 126 member galaxies with the redshifts of the BCG and LEDA
87445 indicated.

In a second step, we combine the spatial and velocity information by applying
the “shifting gapper” procedure (Fadda et al. 1996; Girardi et al. 1996). Of
the galaxies that lie within an annulus around from the center of cluster,
this procedure rejects those that are too far away in velocity from the main
body of galaxies, i.e. farther away than a fixed velocity gap. The position of
the annulus is shifted at increasing distances from the center of the cluster.
The procedure is repeated until the number of cluster members converges to a
stable value. Following Fadda et al. (1996), we use a gap of $1000$ km
s${}^{-1}\;$in the cluster rest-frame, and a annulus size of 0.6 Mpc or larger
at least to include 15 galaxies. In fixing the cluster center, we consider the
position in R.A. and Dec. of the BCG
[R.A.=$09^{\mathrm{h}}18^{\mathrm{m}}05\,\hbox
to0.0pt{\hbox{$\mathrm{{}^{s}}$}\hss}{\hbox{$.$}}\,66$,
Dec.=$+12\mathrm{{}^{\circ}}05\mathrm{{}^{\prime}}43\,\hbox
to0.0pt{\hbox{$\mathrm{{}^{\prime}\hskip-1.00006pt{}^{\prime}}$}\hss}{\hbox{$.$}}\,7$
(J2000.0)]. This procedure confirms 126 fiducial cluster members in the range
$14401\leq{\rm V}\leq 18745$ km s-1, i.e. $0.048036\leq{\rm z}\leq 0.062527$
(see Fig. 3).

Although A780 is a modest cluster, it is well isolated in projected phase
space, as shown in Fig. 4. Just to highlight the region of cluster members, we
also plot the escape velocity curves obtained with the mass estimate
calculated below and assuming an NFW mass density profile following the recipe
of den Hartog & Katgert (1996).

Figure 4: Rest-frame velocity $V_{\rm rf}=(V-<V>)/(1+z)$ versus projected
cluster-centric distance $R$ for galaxies with redshifts in the range $\pm
8000$ km s${}^{-1}\;$(black dots). Circles indicate the 126 members of the
cluster. The large and small red squares refer to the BCG and LEDA 87445,
respectively. The green curves contain the region where $|V_{\rm rf}|$ is
smaller than the escape velocity (see text).

The analysis of the velocity distribution of the 126 cluster members was
performed using the biweight estimators for location and scale (ROSTAT
software, Beers et al. 1990). Our measurement of the mean redshift of the
cluster is $\left<z\right>=0.0545\pm 0.0002$ (i.e., $\left<V\right>=16313\pm
71$ km s-1). We estimate the velocity dispersion, $\sigma_{\rm V}$, by
applying the cosmological correction and the standard correction for velocity
errors (Danese et al. 1980). We obtain $\sigma_{\rm V}=795_{-53}^{+44}$ km
s-1, where the errors are estimated by a bootstrap technique.

Using the fitted relation between the mass444We refer to $R_{\Delta}$ as the
radius of a sphere within which the mean mass density is $\Delta$ times the
critical density at the redshift of the galaxy system. $M_{\Delta}$ is the
mass contained in $R_{\Delta}$. $M_{200}$ and the velocity dispersion in
simulated clusters (Eq. 1 of Munari et al. (2013) we derive $M_{200}=5.4\pm
1.5$ $\times 10^{14}\;M_{\odot}\;$for the mass contained in $R_{200}=1.65\pm
0.10$ Mpc. The uncertainties of 6% and 28% for $R_{200}$ and $M_{200}$ are
calculated using the error propagation for $\sigma_{\rm V}$
($R_{200}\propto\sigma_{\rm V}$ and $M_{200}\propto\sigma_{\rm V}^{3}$) and an
additional uncertainty of $10\%$ for the mass due to the scatter around the
relation of Munari et al. (2013). Properties of the cluster are shown in Tab.
2.

Table 2: Global properties of A780

$\begin{array}[]{c c c c c c}\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr N_{\rm
gal}&{}^{\mathrm{a}}\alpha({\rm J}2000),\,\delta({\rm
J}2000)&\mathrm{<V>}&\sigma_{\rm V}&R_{200}&M_{200}\\\
&\mathrm{h:m:s,\mathrm{{}^{\circ}}:\mathrm{{}^{\prime}}:\mathrm{{}^{\prime}}\hskip-1.00006pt\mathrm{{}^{\prime}}\;}&\mathrm{km\
s^{-1}}&\mathrm{km\ s^{-1}}&{\rm Mpc}&10^{14}M_{\odot}\\\ \hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr 126&09\ 18\ 05.66,-12\ 05\ 43.8&16313\pm
71&795_{-53}^{+44}&1.65\pm 0.10&5.4\pm 1.5\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\end{array}$

  * a

As a center, we list the position of the BCG.

Figure 5 shows the distribution of the member galaxies in the ($g$$-$$r$ vs.
$r$) color-magnitude diagram, compared to all galaxies with redshift
measurements. The color-magnitude relation, indicating the location of the
early-type galaxies, can be seen out to faint magnitudes of $r\sim$21 mag.
Following Boschin et al. (2012) we use a $2\sigma$ rejection procedure to fit
$g$$-$$r$=1.34$-$0.03$\times$ $r$.

Figure 5: $g$$-$$r$ vs. $r$ diagram (aperture color vs. Kron-like magnitude).
All galaxies with available spectroscopy and member galaxies are indicated by
red crosses and blue squares, respectively. The large, blue square and
triangle indicate the BCG and LEDA 87445, respectively. The black line shows
the color-magnitude relation obtained for the member galaxies.

##  5 Substructure analysis

We analyzed the presence of substructures using the velocity distribution of
galaxies, their projected positions on the sky, and the combination of these
two pieces of information (1D, 2D, and 3D tests, respectively).

Using a number of indicators such as kurtosis, skewness, tail index, and
asymmetry index (Bird & Beers 1993), the analysis of the velocity distribution
shows no evidence of possible deviations from Gaussian distribution. Moreover,
the BCG is a good indicator of the mean redshift of the cluster as there is no
evidence for a peculiar velocity according to the Indicator test of Gebhardt &
Beers (1991).

We analyzed the spatial distribution of the 126 spectroscopic member galaxies
using the 2D adaptive-kernel method of Pisani et al. (1996, hereafter
2D-DEDICA, see also Girardi et al. 1996). Our results are shown in Fig. 6 and
Tab. 3. For each clump of galaxies detected with a c.l. higher than 99%, Table
3 contains the number of member galaxies, the position of the 2D density peak,
and its relative density $\rho$ with respect to the densest peak. Figure 6
shows a peak in the cluster core (Core) and other peaks in the south and
southeast (S, SSE, and SE). The BCG and LEDA 87445 belong to Core and SSE
galaxy groups, respectively. To verify that our results are independent of the
positioning of the spectroscopic masks, we performed the same analysis for the
497 non-member galaxies and found that non-members cluster in a different way.

Table 3: 2D DEDICA substructure $\begin{array}[]{l r c c c}\hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\mathrm{Group}&N_{\rm gal}&\alpha({\rm J}2000),\,\delta({\rm
J}2000)&\rho&\mathrm{<V>}\\\
&&\mathrm{h:m:s,\mathrm{{}^{\circ}}:\mathrm{{}^{\prime}}:\mathrm{{}^{\prime}}\hskip-1.00006pt\mathrm{{}^{\prime}}\;}&&\mathrm{km\
s^{-1}}\\\ \hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\mathrm{Core\leavevmode\nobreak\ (BCG)}&53&09\ 18\ 04.8,-12\ 05\
20&1.00&15990\pm 198\\\ \mathrm{S}&20&09\ 18\ 12.3,-12\ 15\ 17&0.46&16279\pm
189\\\ \mathrm{SSE\leavevmode\nobreak\ (LEDA)}&22&09\ 18\ 22.3,-12\ 20\
05&0.51&16766\pm 183\\\ \mathrm{SE}&9&09\ 18\ 38.6,-12\ 12\ 05&0.27&16663\pm
232\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\end{array}$

Figure 6: Spatial distribution of the 126 spectroscopic-determined cluster
members on the sky and the relative isodensity contour map obtained with the
2D DEDICA method (black dots and blue contours). The two black crosses
indicate the position of the BCG and LEDA 87445. The plot is centered on the
cluster center and circle contains the cluster within a radius of 0.5 Mpc
$\sim$ $1/3\times R_{200}$. Labels refer to the 2D DEDICA peaks in the galaxy
distribution shown in Tab. 3.

For each group, Table 3 lists the mean velocity of the member galaxies. The
mean velocity of the galaxies in the SSE group is $3\sigma$ higher than that
of the galaxies in the Core group ($\Delta V_{\rm rf}\sim 850$ km
s${}^{-1}\;$at the cluster rest frame). The velocity difference is of the same
order as that between the two brightest galaxies, the BCG and LEDA 87445.
However, the BCG velocity is significantly higher than the mean velocity of
the Core group, with a c.l. in the range 95-99% according to the Indicator
test. The velocity of LEDA 87445 is higher than that of the SSE group, with a
c.l. in the range 90-95%. These discrepancies could be the consequence of a
truly complex structure or contamination by projected galaxies. To address the
latter issue, we present below analyses based on both positions and
velocities.

As for the full 3D analysis, we looked for a correlation between velocity and
position information. The presence of a velocity gradient is quantified by a
multiple linear regression fit to the observed velocities with respect to the
galaxy positions in the plane of the sky (see also den Hartog & Katgert 1996).
The position angle on the celestial sphere is $PA=120_{-14}^{+20}$ degrees
(measured counterclockwise from the north), which means that high-velocity
galaxies are located in the southeastern region of the cluster (see Fig. 7).
To assess the significance of this velocity gradient, we performed 1000 Monte
Carlo simulations of clusters by randomly shuffling the velocities of the
galaxies. For each simulation, we determine the coefficient of multiple
determination ($RC^{2}$, NAG Fortran Workstation Handbook 1986). The
significance of the velocity gradient is the fraction of cases in which the
$RC^{2}$ of the simulated data is smaller than the observed $RC^{2}$. In A780,
the velocity gradient is significant at the $98.5\%$ confidence level.

We have used the classical $\Delta$-test of Dressler & Shectman (1988, DS
test). For each $i$-th galaxy, the deviation of the local mean velocity from
the global velocity is defined as $|\delta_{i}|$ with $\delta_{i}^{2}=[(N_{\rm
nn}+1)/\sigma^{2}_{\rm V}]\times[(\left<V\right>_{\rm
loc}-\left<V\right>)^{2}+(\sigma_{\rm V,loc}-\sigma_{\rm V})^{2}]$, where the
local mean velocity $\left<V\right>_{\rm loc}$ and velocity dispersion
$\sigma_{\rm V,loc}$ are calculated using the $i$-th galaxy and its
$N_{\rm{nn}}=10$ neighbors. For a cluster, the cumulative deviation is given
by the value of $\Delta$, which is the sum of the $|\delta_{i}|$ values of the
individual $N$ galaxies. We have also used the modified version that considers
only the indicator of local mean velocity, that is $\delta_{i,{\rm
V}}=[(N_{\rm nn}+1)^{1/2}/\sigma_{\rm V}]\times(\left<V\right>_{\rm
loc}-\left<V\right>)$ and $\Delta$ is the sum of the $|\delta_{i,{\rm V}}|$
values of the individual $N$ galaxies (DSV test, Girardi et al. 2010). As in
the calculation of the velocity gradient, the significance of the $\Delta$,
i.e. the presence of substructure, is based on 1000 Monte Carlo simulated
clusters. In A780, the significance of the substructure is larger than the
99.9% c.l. according to both DS and DSV tests. In Fig. 7 we show the Dressler
& Schectman bubble-plot resulting from the indicator of the DSV test,
$|\delta_{i,{\rm V}}|$. This plot shows very clearly how the galaxy LEDA 87445
is surrounded by galaxies that have higher velocities than the galaxies in the
core of the cluster.

Figure 7: Dressler & Schectman bubble plot for the DSV test. Spatial
distribution of the 126 cluster members, each indicated by a symbol: the
larger the symbol, the greater the deviation $|\delta_{i,{\rm V}}|$ of the
local mean velocity from the global mean velocity. The blue thin and red thick
circles indicate where the local mean velocity is smaller or larger than the
global mean velocity. The diagram is centered on the center of the cluster and
the large and small crosses indicate the BCG and LEDA 87445. The arrow
indicates the direction of the velocity gradient, which points towards the
region with high velocities.

As a first attempt to detect substructure members, we resorted to the
technique developed by Biviano et al. (2002). We compared the distribution of
$\delta_{i,{\rm V}}$-values of the real galaxies with the distribution of
$\delta_{i,{\rm V}}$-values of the galaxies of all 1000 Monte Carlo simulated
clusters (Fig. 8). According to the Kolmogorov-Smirnov test, the two
distributions differ at the $95\%$ confidence level. The distribution of the
values of the real galaxies shows a tail at low $\delta_{i,{\rm V}}$ values
and a tail at high $\delta_{i,{\rm V}}$ values. When considering galaxies with
$|\delta_{i,{\rm V}}|>2$, the 15 galaxies in the low tail are projected onto
the core region of the cluster and the 14 galaxies in the high tail are
projected onto the LEDA 87445 region.

Figure 8: Distribution of $\delta_{i,{\rm V}}$ values of the deviation of the
local mean velocity from the global velocity (according to the DSV test, see
text). The solid line histogram indicates the observed galaxies. The dashed
line histogram indicates the galaxies of the simulated clusters, normalized to
the number of observed galaxies. The red vertical lines mark the
$|\delta_{i,{\rm V}}|>2$ regions where we expect to find substructure members.

In order to better determine the members of the substructures, in particular
the group around LEDA 87445, we also analyzed our data using three methods. In
a first step, we analyzed the sample of 35 galaxies within 0.5 Mpc of LEDA
87445 using the Kaye’s Mixture Model (KMM). This method, as implemented by
Ashman et al. (1994), is useful for finding a possible group partitioning of
the velocity distribution. The KMM algorithm fits a user-specified number of
Gaussian distributions to a data set and evaluates the improvement of this fit
over a single Gaussian according to the likelihood ratio test statistic. The
algorithm also makes an assignment of galaxies into groups. When the KMM
method is applied to the sample of 35 galaxies, we find that a bimodal
distribution is better than a unimodal one at the $\sim 95\%$ confidence
level. We obtain a low-velocity group (LVG05) of 15 galaxies with
$\left<V\right>=15745$ km s-1and a high-velocity group (HVG05) of 20 galaxies
with $\left<V\right>=17273$ km s${}^{-1}\;$(see Fig. 9). The high velocity
group contains LEDA 87445.

Figure 9: Velocity distribution of all 35 galaxies within 0.5 Mpc of LEDA
87445. The blue curves show the two Gaussian curves resulting from the 1D KMM
analysis for the two detected groups LVG05 and HV05.

We also used the 3D DEDICA method (Pisani 1996; Bardelli et al. 1998). Table 4
lists the properties of the galaxy peaks that are detected with a probability
higher than the $>99\%$ c.l. and have a relative density $\rho\geq 0.3$: the
number of member galaxies, the positions of the peaks in velocity and spatial
coordinates, the relative densities. Figure 10 shows the positions of the
galaxies assigned to the detected groups. The group with the lowest velocity
(3DLVG) is projected onto the core of the cluster. The highest velocity group
(3DHVG) is the one projected onto the south-southeast region and contains LEDA
87445. Of the three intermediate velocity groups, 3DMVG2 is projected onto the
core of the cluster and contains the BCG. Since it is known that the
multidimensional application of the DEDICA algorithm may lead to spurious
substructure (Bardelli et al. 1998), we also applied the alternative version
of Balestra et al. (2016) based on the rule of thumb for the kernel size given
by Silverman (1986). The goal is to detect the major substructures at the cost
of losing some real minor substructures. The alternative procedure is
successful in recovering a main system (96 galaxies) and the 3DSHVG group (30
galaxies). The 3DSHVG group contains LEDA 87445 and is populated by the same
galaxies as the 3DHVG group, with the exception of two galaxies. This suggests
that the detection of a galaxy group related to LEDA 87445 is quite robust.

Table 4: 3D DEDICA substructure $\begin{array}[]{l r r c c }\hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\mathrm{Group}&N_{\rm gal}&V_{\rm peak}&\alpha({\rm
J}2000),\,\delta({\rm J}2000)&\rho\\\ &&{\rm
km\,s^{-1}}&\mathrm{h:m:s,\mathrm{{}^{\circ}}:\mathrm{{}^{\prime}}:\mathrm{{}^{\prime}}\hskip-1.00006pt\mathrm{{}^{\prime}}\;}&\\\
\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\mathrm{3DMVG2(BCG)}&34&15812&09\ 18\ 04.6,-12\ 05\ 12&1.00\\\
\mathrm{3DHVG(LEDA)}&32&16932&09\ 18\ 25.3,-12\ 21\ 06&0.30\\\
\mathrm{3DMVG1}&20&15761&09\ 18\ 08.4,-12\ 14\ 41&0.54\\\
\mathrm{3DLVG}&20&15521&09\ 18\ 04.3,-12\ 06\ 55&0.86\\\
\mathrm{3DMVG3}&11&16406&09\ 18\ 01.7,-12\ 15\ 44&0.33\\\ \vskip 3.0pt plus
1.0pt minus 1.0pt\cr\hline\cr\end{array}$

Figure 10: Spatial distribution of the 126 cluster members on the sky, with
the groups discovered with the 3D DEDICA method indicated by different
symbols. From low to high velocities: 3DLVG (blue circles), 3DMVG1 (cyan
rotated squares), 3DMVG2-BCG (cyan circles), 3DMVG3 (green square), and 3DHVG-
LEDA (red circles). Crosses indicate the BCG and LEDA 87445.  Figure 11:
Dendrogram obtained by the Htree algorithm. The x-axis is the binding energy,
here in arbitrary units with the lowest negative energy levels on the left.
The labels indicate prominent galaxies and structures.

As a final approach, we applied the method described by Serna & Gerbal (1996),
which is referred to in the literature as the Serna-Gerbal or H-tree method
(e.g., Durret et al. 2009,Girardi et al. 2011,Guennou et al. 2014). The H-tree
method uses hierarchical cluster analysis to determine the relationship
between galaxies based on their relative binding energy. The ignorance of the
mass associated with each galaxy is overcome by assuming the typical mass-to-
light of galaxy clusters for each galaxy halo. Figure 11 shows the resulting
dendrogram for the case $M/L_{r}$=200 $M_{\odot}/L_{\odot}\;$(e.g., Popesso et
al. 2005), where the total energy appears along the horizontal axis. At the
$\sim 30$ energy level (in normalized units), the cluster splits into two
groups, HTG1 and HTG2. The BCG and its close companion are located in the
potential hole of the HTG1 group, which is populated by 24 galaxies. LEDA
87445 is located in the potential hole of group HTG2, which is populated by
five galaxies. HTG1 and HTG2 probably correspond to the cores of the main
cluster and the LEDA 87445 group, respectively. Similar results are found in
the cases with $M/L_{r}$=150 and 250 $M_{\odot}/L_{\odot}$. Table 5 summarizes
the kinematic properties of the LEDA group obtained by different methods.

Table 5: Kinematic properties of the group related to LEDA 87445

$\begin{array}[]{l r c l l l }\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\mathrm{Group}^{\mathrm{a}}&N_{\rm gal}&{}^{\mathrm{b}}\alpha({\rm
J}2000),\,\delta({\rm J}2000)&\mathrm{<V>}&\sigma_{\rm V}&\mathrm{Method\ of\
detection}\\\
&&\mathrm{h:m:s,\mathrm{{}^{\circ}}:\mathrm{{}^{\prime}}:\mathrm{{}^{\prime}}\hskip-1.00006pt\mathrm{{}^{\prime}}\;}&\mathrm{km\
s^{-1}}&\mathrm{km\ s^{-1}}&\\\ \hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\mathrm{HVG05}&20&09\ 18\ 24.53,-12\ 20\ 52.2&17273\pm
97&419_{-52}^{+46}&\mathrm{1D-KMM\,within\,0.5\,Mpc}\\\ \mathrm{3DHVG}&32&09\
18\ 25.18,-12\ 23\ 25.9&17140\pm 92&509_{-56}^{+56}&\mathrm{3D-DEDICA}\\\
\mathrm{3DSHVG}&30&09\ 18\ 25.22,-12\ 22\ 58.2&17193\pm
89&478_{-52}^{+54}&\mathrm{3D-DEDICA-Silvermann}\\\ \mathrm{HTG2}&5&09\ 18\
29.15,-12\ 21\ 52.1&17285\pm 293&499_{-41}^{+322}&\mathrm{Htree}\\\ \vskip
3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\end{array}$

  * a

For comparison, the center and velocity of LEDA 87445 are 09 18 27.44-12 22
24.0 and $17236\pm 46$ km s-1, respectively.

  * b

As centers, we list the biweight mean values of galaxy right ascensions and
declinations.

##  6 Discussion

###  6.1 Cluster global properties

First, we discuss our results on global properties of A780. Our estimates for
the cluster mean redshift, $\left<z\right>=0.0545\pm 0.0002$, and velocity
dispersion, $\sigma_{\rm V}=795_{-53}^{+44}$ km s-1, agree within $1\sigma$
with our previous estimates in De Grandi et al. (2016). With four times as
many cluster members, the uncertainties are smaller by a factor of two. Using
our estimate of $\sigma_{\rm V}$ and the estimate of the global X-ray
temperature in the literature ($kT_{\rm X}\sim 3-3.5$ keV), we can calculate
the ratio of the energy per unit mass of galaxies and ICM, $\beta_{\rm
spec}=0.97_{-0.21}^{+0.26}$, where $\beta_{\rm spec}=\sigma_{\rm
V}^{2}/(kT_{\rm X}/\mu m_{\rm p})$ with $\mu=0.58$ the average molecular
weight and $m_{\rm p}$ the proton mass. Since $\beta_{\rm spec}=1$ is expected
when assuming density-energy equipartition between galaxies and ICM, our
result means that A780 is probably not far from the dynamical equilibrium.
This indication of large-scale relaxation is consistent with evidence reported
in the literature, such as the presence of a cool core and the smoothness of
the X-ray morphology of A780 within 1 Mpc (see Sect. 1).

The velocity of the BCG is very close to the mean velocity of the galaxy
cluster and we have found that there is no peculiarity in terms of the
velocity distribution of the cluster galaxies. For the BCG, we calculate
$|V_{\rm rf}/\sigma_{\rm V}|=0.08$, which places A780 in the low tail of the
$|V_{\rm rf}/\sigma_{\rm V}|$ distribution, as obtained by Lauer et al. (2014)
for 178 clusters. The BCG spectrum shows a few emission lines (see Fig. 2) and
the BCG color is bluer than that of the red sequence (see Fig. 5), which is
consistent with what is expected for BCGs in cool core clusters, especially
for BCGs with radio emission, as known in the literature (e.g., Crawford et
al. 1995). Thus, the BCG also exhibits the typical features of BCGs in relaxed
systems.

Our estimate of the dynamical mass, $M_{200}=5.4\pm 1.5$ $\times
10^{14}\;M_{\odot}$, is in agreement with the mass obtained from the
gravitational lensing, $M_{200,\rm{GL}}=3.7_{-1.4}^{+2.0}$ $\times
10^{14}\;M_{\odot}\;$(Okabe et al. 2016). Taking into account the large
uncertainties, there is also a $2\sigma$ agreement with the mass estimate from
X-ray data, $M_{200,\rm{X}}=2.84_{-0.27}^{+0.30}$ $\times
10^{14}\;M_{\odot}\;$(Zhu et al. 2021). However, our nominal value of the
dynamical mass is a factor of two higher than the value of the mass from
X-rays, and we prefer to discuss it a little more. Mass estimates of galaxy
clusters are subject to various systematic uncertainties and biases, depending
on the approach taken (see Pratt et al. 2019 for a review). This can justify
strong differences when comparing mass estimates for a single cluster. Indeed,
when samples of many clusters with high quality data are examined, generally
better agreement is found (Ettori et al. 2019).

Although our study is not dedicated to the study of the galaxy population, our
data show that the red sequence is visible at least down to $r\sim$ 21 mag,
about five magnitudes below the value of $M^{*}$ in the luminosity function
(see Fig. 5). This is consistent with previous studies that have looked at the
spectroscopically determined luminosity function in clusters down to similarly
deep magnitudes. These studies show that the red sequence in local clusters is
already established down to galaxies with faint magnitudes, albeit with
different levels of definition (Rines & Geller 2008; Aguerri et al. 2020 and
refs. therein). We refer the reader to the review by Boselli & Gavazzi (2014)
for a full discussion of the origin of the faint-end of the red sequence in
high-density environments.

###  6.2 Cluster substructure

Our study is designed to provide new insights into the small-scale structure
of A780, especially in the LEDA 87445 region. We present solid evidence for
the existence of a group of galaxies around LEDA 87445. The first evidence
comes from our 2D analysis (see Fig. 6). It is useful to compare our present
results with those based on photometric likely members in our previous study,
which uniformly cover the entire cluster field (see Fig. A.3 in De Grandi et
al. 2016). Both the old and new maps of the galaxy distribution show the
presence of a substructure related to LEDA 87445. This suggests that
photometric likely members can be a good alternative to study the internal
structure of the cluster, at least if the bright galaxies located in the red
sequence are considered (e.g., Lubin et al. 2000). The final evidence comes
from the the DS and DSV tests, which find a very significant correlation
between galaxy positions and velocities, confirming the presence of high-
velocity galaxies around LEDA 87445 (see Fig. 7).

Our spectroscopic catalog is extensive enough to make an attempt to identify
the members of the LEDA 87445 group and to obtain a first estimate of its
kinematic properties (see Tab. 5). For each method, we find good agreement
between the mean velocity of the group and the velocity of LEDA 87445, and
between the center of the group and the position of LEDA 87445. LEDA 87445 is
characterized by a higher velocity with respect to the cluster mean velocity,
with a velocity difference of $V_{\rm rf}\sim$ +870 km s-1. Depending on the
detection method, the velocity difference between the group and the cluster
ranges from $V_{\rm rf}=$+785km s${}^{-1}\;$to +920 km s-1. LEDA 87445 lies
$\sim$ 1.1 Mpc south of the cluster center. Our estimates of the group center
are around LEDA 87445, at distances in the range of 40-100 kpc. We thus find
no evidence of a systematic shift between the galaxies of the group and LEDA
87445 itself, which can be considered a good tracer of the group.

In De Grandi et al. (2016), we propose that the LEDA 87445 group is infalling
and moving in a circular orbit with a velocity of $510_{-340}^{+430}$ km
s${}^{-1}\;$relative to the main cluster, as seen from X-ray features. This
velocity estimate is subject to large uncertainties and no difference can be
detected with the $V_{\rm rf}$ estimated here. In De Grandi et al. (2016), we
also propose that the tail of the LEDA 87445 group is due to ram pressure.
According to new hydrodynamical simulations, Sheardown et al. (2019) claim
that the X-ray features are more consistent with the scenario of a slingshot
tail rather than a tail caused by ram pressure. In this scenario, the group
has already passed the cluster center with a large impact parameter and is now
near the apocenter, where it re-enters the cluster (see their Fig. 1).
However, Sheardown et al. (2019) do not give an estimate of the velocity of
the LEDA 87445 group.

Table 5 also reports the estimates for the velocity dispersion of group
galaxies. We emphasize that the estimate of the dispersion is less robust than
the estimate of the mean. In particular, possible contamination by non-member
galaxies is likely to lead an overestimation of the true value of the velocity
dispersion. The nominal values of the velocity dispersion range from
$\sigma_{\rm V}\sim$420 to $\sim$500 km s-1, that is $kT_{\rm X}\sim 1.1$-1.5
keV assuming $\beta_{\rm spec}=1$. This temperature estimate is in agreement
with X-ray data for the gas along the wake ($kT_{\rm X}\sim 1.3$, De Grandi et
al. 2016). Our estimate of the group mass, based on the value of $\sigma_{\rm
V}$ and the relation of Munari et al. (2013), is $M_{200}=0.8$-1.3 $\times
10^{14}\;M_{\odot}$, while the mass estimated by De Grandi et al. (2016) using
the $M_{500}$-$kT_{\rm X}$ relation of Sun et al. (2009) was found to be
$M_{\rm 500,X}=0.2$-0.5 $\times 10^{14}\;M_{\odot}$, i.e. $M_{\rm
200,X}=0.3$-0.7 $\times 10^{14}\;M_{\odot}$. In the case of the LEDA 87445
group, the main source of the uncertainty in the dynamical mass is probably
related to the selection of the group galaxies. On the other hand, the gas
content might suffer more from the interaction with the main system due to its
collisional nature, and therefore the X-ray mass is also quite uncertain.
Taking our nominal values of the mass for the LEDA 87445 group and the parent
cluster, we can estimate that their mass ratio is $\sim 1:5$.

We also obtain new information about the cluster core. The galaxy distribution
in the cluster core is characterized by some strong peculiarities. The phase-
space diagram of the cluster galaxies shows that the BCG velocity is close to
the cluster mean velocity (set to zero in Fig. 4), but in the inner regions,
within $\sim 0.5$ Mpc, galaxies with velocities larger than that of the BCG
are very few. This asymmetry is real with a probability of $99.1\%$, as
determined by applying a 2D Kolmogorov-Smirnov test to compare the
distributions of galaxies with positive and negative velocities within 0.5
Mpc. The mean velocity of the 44 galaxies within 0.5 Mpc is
$\left<V_{\rm{rf}}\right>=-259\pm 107$ km s-1, which differs from the expected
zero value at $99.3\%$, in agreement with the above test. Note for comparison
that the distribution of galaxies in the phase space outside 0.5 Mpc does not
show significant asymmetry between positive and negative velocities, despite
the presence of the LEDA 87445 group. Moreover, according to the DSV test, the
cluster core is characterized by galaxies with peculiar low velocity (see Fig.
7) and the BCG has a higher peculiar velocity with respect to the galaxy peak
detected by our 2D DEDICA analysis in the core. Another indication of a
peculiarity of the mass distribution in the cluster core comes from the
analysis of the weak lensing data, which are better described at the innermost
radius by a two-component model (Okabe et al. 2016).

A possible interpretation of the above features in the cluster core is that
there is a low-velocity group, still far from being virialized within the
cluster, which is projected onto the cluster core. Indeed, using the 3D DEDICA
method, we can detect a group of low-velocity galaxies in the core (3DLVG)
whose peak velocity is lower than the mean velocity of the cluster,
$V_{\rm{rf}}\sim-750$ km s-1, and the galaxy content is $\sim 10\%$ of the
whole system (see Tab. 4 and Fig. 10).

To check the above “group hypothesis”, we made a simple Monte Carlo simulation
to reproduce a combined system of cluster plus a group with the same center.
For a given mass $M_{200}$, we use the NFW model with the appropriate
concentration parameter (Navarro et al. 1997; Dolag et al. 2004) to simulate
the 2D galaxy distribution of galaxies out 2$R_{200}$ (e.g., Biviano & Girardi
2003; Rines et al. 2013). The velocities are distributed according to a
Gaussian. To mimic the cluster we use the mass and velocity dispersion of the
whole A780 ($M_{200}=5.4$ $\times 10^{14}\;M_{\odot}$, $\sigma_{\rm V}=795$ km
s-1) and distribute the particles in such a way to have 10000 particles within
$R_{200}=1.65$ Mpc, with zero mean velocity. The group is ten times less
massive ($M_{200}=0.54$ $\times 10^{14}\;M_{\odot}$, $\sigma_{\rm V}=369$ km
s-1), with 1000 particles within $R_{200}=0.767$ Mpc, and mean velocity equal
to $-750$ km s-1. Out of this combined system we randomly extract 1000 times
44 particles within $R=0.5$ Mpc from the center to obtain 1000 values of mean
velocity, $MV_{\rm{rf,sim}}$. The value of $\left<MV_{\rm{rf,sim}}\right>$ is
$-119$ km s-1, which differs at $\sim 90\%$ from the observed value
$\left<V_{\rm{rf}}\right>=-259\pm 107$ km s-1. In summary, the presence of a
group projected onto the cluster center can strongly reduce the significance
of the observed asymmetry in the velocity distribution. We stress that our
model is very simple. For instance, we assume that the particle number-density
rescale with the mass of the system, while the very luminous BCG in A780 may
indicate a different rescaling. Very luminous BCGs might be formed at the
expenses of the merger/cannibalization of surrounding galaxies with a
subsequent change of the luminosity function (e.g., see Zarattini et al.
2015). This would make the effect of the group more important.

Using N-body simulations, Vijayaraghavan et al. (2015) show that the core of a
group survives for many Gyr after a head-on merger with a cluster. On the
other hand, the presence of a group–cluster interaction would raise a new
issue since cool cores in clusters can be resilient for off-axis mergers but
not for head-on ones (Valdarnini & Sarazin 2021 and refs. therein). Therefore
we suggest that the low-velocity group, if confirmed, might be on its first
infall onto the cluster.

Finally, we discuss our results in terms of the central engine of the Hydra A
AGN. The shock detected in the _Chandra_ X-ray images, which is modeled as an
ellipse with a size of $\sim 400$ kpc, shows a displacement of the center with
respect to the AGN, and this displacement was caused by bulk flows or sloshing
in the ICM according to Simionescu et al. (2009). According to the authors,
these gas motions should be associated with velocities of the order of 600 km
s-1and could be related to a small merger. We detect a galaxy group related to
LEDA 87445 group with a comparably high relative velocity and the simulation
of Sheardown et al. (2019) explains the sloshing of the ICM at the cluster
center, in particular when the merging group is at its apocenter (see also the
third column of Fig. 7 in Sheardown et al. 2018).

##  7 Summary and conclusions

Our previous study (Appendix A of De Grandi et al. 2016) was based on the
largest available homogeneous sample of spectroscopic data at the time, with
41 galaxies (Smith et al. 2004), from which we selected 33 member galaxies. To
surpass our earlier study, we have acquired new spectroscopic data at TNG and
VLT, giving us a redshift catalog of 623 galaxies. Our new spectroscopic data
are mainly focused on the south-southeast region of the cluster, i.e. the
region of the bright X-ray tail. We have paid special attention to combining
data from different sources in order to obtain a homogeneous redshift catalog.
Our membership selection procedure leads to a catalog of 126 member galaxies,
which extends the data sample analyzed in our previous study by a factor four.
In the following, we list our main results.

  1. 1.

We derive the mean redshift of the cluster $\left<z\right>=0.0545\pm 0.0002$
and the line-of-sight velocity dispersion $\sigma_{\rm V}=795_{-53}^{+44}$ km
s-1. We estimate the dynamical mass $M_{200}=5.4\pm 1.5$ $\times
10^{14}\;M_{\odot}\;$within $R_{200}=1.65\pm 0.10$ Mpc. We find no evidence
for a deviation in the density-energy equipartition between galaxies and ICM
or for a peculiarity of the BCG, consistent with the cluster being relaxed on
a large scale.

  2. 2.

Using four different techniques, we detect the presence of a group related to
LEDA 87445 and list the fiducial members. For each technique, we calculate the
velocity and center of the group. The difference between these estimates and
the velocity and position of LEDA 87445 is less than 90 km s${}^{-1}\;$and 0.1
Mpc, respectively. Therefore, LEDA 87445 is an excellent tracer of the galaxy
group. Our estimate of the velocity dispersion of the group is $\sim$ 420 –
500 km s-1, leading to a group mass $M_{200}=0.8$–1.3 $\times
10^{14}\;M_{\odot}$.

  3. 3.

The parameters of the collision can be summarized with a relative line-of-
sight velocity of $V_{\rm rf}\sim+870$ km s-1, a projected distance $D=1.1$
Mpc, and a mass ratio of 1:5 between the group and the cluster.

  4. 4.

We present evidence of an asymmetry in the velocity distribution of galaxies
in the inner cluster region. This asymmetry might be related to the presence
of a small low-velocity group, as suggested by the detection of a substructure
projected onto the cluster center at $V_{\rm rf}=-750$ km s-1.

We conclude that A780, although dynamically relaxed at first sight, contains
minor substructures. As for the LEDA 87445 group, optical and X-ray data
result in a consistent scenario and previous studies have addressed its impact
on the energetics of the core region. To better understand the observed
velocity asymmetry in the cluster core, we stress the need for additional
redshifts of galaxies in that region.

###### Acknowledgements.

We thank the referee for her/his useful and constructive comments. M.G.
acknowledges the support from the grant MIUR PRIN 2017 WSCC32 “Zooming into
dark matter and proto-galaxies with massive lensing clusters”. This
publication is based on observations made on the island of La Palma with the
Italian Telescopio Nazionale Galileo (TNG), which is operated by the Fundación
Galileo Galilei – INAF (Istituto Nazionale di Astrofisica) and is located in
the Spanish Observatorio of the Roque de Los Muchachos of the Instituto de
Astrofísica de Canarias. This publication is based on observations collected
at the European Southern Observatory under ESO programme 098.A-0807(A). This
publication uses public data from the CFHT Science Archive, which contains
data provided by the Canada-France-Hawaii Telescope.

## References

  * Abell et al. (1989) Abell, G. O., Corwin, Harold G., J., & Olowin, R. P. 1989, ApJS, 70, 1
  * Adami et al. (2005) Adami, C., Biviano, A., Durret, F., & Mazure, A. 2005, A&A, 443, 17
  * Aguerri et al. (2020) Aguerri, J. A. L., Girardi, M., Agulli, I., et al. 2020, MNRAS, 494, 1681
  * Ashman et al. (1994) Ashman, K. M., Bird, C. M., & Zepf, S. E. 1994, AJ, 108, 2348
  * Balestra et al. (2016) Balestra, I., Mercurio, A., Sartoris, B., et al. 2016, ApJS, 224, 33
  * Bardelli et al. (1998) Bardelli, S., Pisani, A., Ramella, M., Zucca, E., & Zamorani, G. 1998, MNRAS, 300, 589
  * Barrena et al. (2007) Barrena, R., Boschin, W., Girardi, M., & Spolaor, M. 2007, A&A, 469, 861
  * Beers et al. (1990) Beers, T. C., Flynn, K., & Gebhardt, K. 1990, AJ, 100, 32
  * Benavides et al. (2020) Benavides, J. A., Sales, L. V., & Abadi, M. G. 2020, MNRAS, 498, 3852
  * Berrier et al. (2009) Berrier, J. C., Stewart, K. R., Bullock, J. S., et al. 2009, ApJ, 690, 1292
  * Bird & Beers (1993) Bird, C. M. & Beers, T. C. 1993, AJ, 105, 1596
  * Biviano & Girardi (2003) Biviano, A. & Girardi, M. 2003, ApJ, 585, 205
  * Biviano et al. (2002) Biviano, A., Katgert, P., Thomas, T., & Adami, C. 2002, A&A, 387, 8
  * Boschin et al. (2012) Boschin, W., Girardi, M., Barrena, R., & Nonino, M. 2012, A&A, 540, A43
  * Boselli & Gavazzi (2014) Boselli, A. & Gavazzi, G. 2014, A&A Rev., 22, 74
  * Crawford et al. (1995) Crawford, C. S., Edge, A. C., Fabian, A. C., et al. 1995, MNRAS, 274, 75
  * Danese et al. (1980) Danese, L., de Zotti, G., & di Tullio, G. 1980, A&A, 82, 322
  * De Grandi et al. (2016) De Grandi, S., Eckert, D., Molendi, S., et al. 2016, A&A, 592, A154
  * den Hartog & Katgert (1996) den Hartog, R. & Katgert, P. 1996, MNRAS, 279, 349
  * Dewhirst (1959) Dewhirst, D. W. 1959, in URSI Symp. 1: Paris Symposium on Radio Astronomy, ed. R. N. Bracewell, Vol. 9, 507
  * Dolag et al. (2004) Dolag, K., Bartelmann, M., Perrotta, F., et al. 2004, A&A, 416, 853
  * Dressler & Shectman (1988) Dressler, A. & Shectman, S. A. 1988, AJ, 95, 985
  * Durret et al. (2009) Durret, F., Slezak, E., & Adami, C. 2009, A&A, 506, 637
  * Eckert et al. (2014) Eckert, D., Molendi, S., Owers, M., et al. 2014, A&A, 570, A119
  * Ettori et al. (2019) Ettori, S., Ghirardini, V., Eckert, D., et al. 2019, A&A, 621, A39
  * Fadda et al. (1996) Fadda, D., Girardi, M., Giuricin, G., Mardirossian, F., & Mezzetti, M. 1996, ApJ, 473, 670
  * Feretti et al. (2002) Feretti, L., Gioia, I. M., & Giovannini, G. 2002, Merging Processes in Galaxy Clusters, Vol. 272
  * Forman et al. (1979) Forman, W., Jones, C., Schwarz, J., & Giacconi, R. 1979, in Bulletin of the American Astronomical Society, Vol. 11, 634
  * Gebhardt & Beers (1991) Gebhardt, K. & Beers, T. C. 1991, ApJ, 383, 72
  * Girardi et al. (2011) Girardi, M., Bardelli, S., Barrena, R., et al. 2011, A&A, 536, A89
  * Girardi et al. (2010) Girardi, M., Boschin, W., & Barrena, R. 2010, A&A, 517, A65
  * Girardi et al. (1996) Girardi, M., Fadda, D., Giuricin, G., et al. 1996, ApJ, 457, 61
  * Girardi et al. (2015) Girardi, M., Mercurio, A., Balestra, I., et al. 2015, A&A, 579, A4
  * Guennou et al. (2014) Guennou, L., Adami, C., Durret, F., et al. 2014, A&A, 561, A112
  * Gwyn (2009) Gwyn, S. D. J. 2009, in Astronomical Society of the Pacific Conference Series, Vol. 411, Astronomical Data Analysis Software and Systems XVIII, ed. D. A. Bohlender, D. Durand, & P. Dowler, 123
  * Ichinohe et al. (2015) Ichinohe, Y., Werner, N., Simionescu, A., et al. 2015, MNRAS, 448, 2971
  * Jones et al. (1997) Jones, C., Stern, C., Forman, W., et al. 1997, ApJ, 482, 143
  * Laganá et al. (2010) Laganá, T. F., Andrade-Santos, F., & Lima Neto, G. B. 2010, A&A, 511, A15
  * Lane et al. (2004) Lane, W. M., Clarke, T. E., Taylor, G. B., Perley, R. A., & Kassim, N. E. 2004, AJ, 127, 48
  * Lauer et al. (2014) Lauer, T. R., Postman, M., Strauss, M. A., Graves, G. J., & Chisari, N. E. 2014, ApJ, 797, 82
  * Lisker et al. (2018) Lisker, T., Vijayaraghavan, R., Janz, J., et al. 2018, ApJ, 865, 40
  * Lubin et al. (2000) Lubin, L. M., Brunner, R., Metzger, M. R., Postman, M., & Oke, J. B. 2000, ApJ, 531, L5
  * Matthews et al. (1964) Matthews, T. A., Morgan, W. W., & Schmidt, M. 1964, ApJ, 140, 35
  * McGee et al. (2009) McGee, S. L., Balogh, M. L., Bower, R. G., Font, A. S., & McCarthy, I. G. 2009, MNRAS, 400, 937
  * McNamara et al. (2000) McNamara, B. R., Wise, M., Nulsen, P. E. J., et al. 2000, ApJ, 534, L135
  * Molnar (2015) Molnar, S. 2015, Frontiers in Astronomy and Space Sciences, 2, 7
  * Munari et al. (2013) Munari, E., Biviano, A., Borgani, S., Murante, G., & Fabjan, D. 2013, MNRAS, 430, 2638
  * NAG Fortran Workstation Handbook (1986) NAG Fortran Workstation Handbook. 1986, NAG Fortran Workstation Handbook (Downers Grove, IL: Numerical Algorithms Group)
  * Navarro et al. (1997) Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ, 490, 493
  * Neichel et al. (2014) Neichel, B., Rigaut, F., Vidal, F., et al. 2014, MNRAS, 440, 1002
  * Nulsen et al. (2005) Nulsen, P. E. J., McNamara, B. R., Wise, M. W., & David, L. P. 2005, ApJ, 628, 629
  * Okabe et al. (2016) Okabe, N., Umetsu, K., Tamura, T., et al. 2016, MNRAS, 456, 4475
  * Osmond & Ponman (2004) Osmond, J. P. F. & Ponman, T. J. 2004, MNRAS, 350, 1511
  * Peng et al. (2015) Peng, Y., Maiolino, R., & Cochrane, R. 2015, Nature, 521, 192
  * Pisani (1993) Pisani, A. 1993, MNRAS, 265, 706
  * Pisani (1996) Pisani, A. 1996, MNRAS, 278, 697
  * Popesso et al. (2005) Popesso, P., Biviano, A., Böhringer, H., Romaniello, M., & Voges, W. 2005, A&A, 433, 431
  * Pratt et al. (2019) Pratt, G. W., Arnaud, M., Biviano, A., et al. 2019, Space Sci. Rev., 215, 25
  * Press et al. (1992) Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992, Numerical recipes in FORTRAN. The art of scientific computing (Cambridge University Press, Cambridge)
  * Rines & Geller (2008) Rines, K. & Geller, M. J. 2008, AJ, 135, 1837
  * Rines et al. (2013) Rines, K., Geller, M. J., Diaferio, A., & Kurtz, M. J. 2013, ApJ, 767, 15
  * Sato et al. (2012) Sato, T., Sasaki, T., Matsushita, K., et al. 2012, PASJ, 64, 95
  * Serna & Gerbal (1996) Serna, A. & Gerbal, D. 1996, A&A, 309, 65
  * Sheardown et al. (2019) Sheardown, A., Fish, T. M., Roediger, E., et al. 2019, ApJ, 874, 112
  * Sheardown et al. (2018) Sheardown, A., Roediger, E., Su, Y., et al. 2018, ApJ, 865, 118
  * Silverman (1986) Silverman, B. W. 1986, Density estimation for statistics and data analysis
  * Simionescu et al. (2009) Simionescu, A., Roediger, E., Nulsen, P. E. J., et al. 2009, A&A, 495, 721
  * Simionescu et al. (2008) Simionescu, A., Werner, N., Finoguenov, A., Böhringer, H., & Brüggen, M. 2008, A&A, 482, 97
  * Smith et al. (2004) Smith, R. J., Hudson, M. J., Nelan, J. E., et al. 2004, AJ, 128, 1558
  * Sun et al. (2009) Sun, M., Voit, G. M., Donahue, M., et al. 2009, ApJ, 693, 1142
  * Taylor et al. (1990) Taylor, G. B., Perley, R. A., Inoue, M., et al. 1990, ApJ, 360, 41
  * Tonry & Davis (1979) Tonry, J. & Davis, M. 1979, AJ, 84, 1511
  * Treu et al. (2003) Treu, T., Ellis, R. S., Kneib, J.-P., et al. 2003, ApJ, 591, 53
  * Valdarnini & Sarazin (2021) Valdarnini, R. & Sarazin, C. L. 2021, MNRAS, 504, 5409
  * Vijayaraghavan et al. (2015) Vijayaraghavan, R., Gallagher, J. S., & Ricker, P. M. 2015, MNRAS, 447, 3623
  * Vijayaraghavan & Ricker (2013) Vijayaraghavan, R. & Ricker, P. M. 2013, MNRAS, 435, 2713
  * Wise et al. (2007) Wise, M. W., McNamara, B. R., Nulsen, P. E. J., Houck, J. C., & David, L. P. 2007, ApJ, 659, 1153
  * Zarattini et al. (2015) Zarattini, S., Aguerri, J. A. L., Sánchez-Janssen, R., et al. 2015, A&A, 581, A16
  * Zhang et al. (2011) Zhang, Y. Y., Andernach, H., Caretta, C. A., et al. 2011, A&A, 526, A105
  * Zhu et al. (2021) Zhu, Z., Xu, H., Hu, D., et al. 2021, ApJ, 908, 17