# Merger histories of brightest group galaxies from MUSE stellar kinematics

S. I. Loubser1,2, P. Lagos3,1, A. Babul4, E. O’Sullivan5, S. L. Jung6, V.
Olivares7,8, and K. Kolokythas1
1Centre for Space Research, North-West University, Potchefstroom 2520, South
Africa
2National Institute for Theoretical and Computational Sciences (NITheCS),
Potchefstroom 2520, South Africa
3Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP,
Rua das Estrelas, 4150-762 Porto, Portugal
4Department of Physics and Astronomy, University of Victoria, Victoria, BC,
V8W 2Y2, Canada
5Center for Astrophysics | Harvard $\&$ Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
6Research School of Astronomy $\&$ Astrophysics, Australian National
University, Canberra, ACT 2611, Australia
7LERMA, Observatoire de Paris, PSL Research Univ., CNRS, Sorbonne Univ., 75014
Paris, France
8Department of Physics and Astronomy, University of Kentucky, 505 Rose Street,
Lexington, KY 40506, USA<EMAIL_ADDRESS>(SIL)

(Accepted 2022 June 24. Received 2022 June 24; in original form 2022 March 11)

###### Abstract

Using Multi-Unit Spectroscopic Explorer (MUSE) spectroscopy, we analyse the
stellar kinematics of 18 brightest group early-type (BGEs) galaxies, selected
from the Complete Local-Volume Groups Sample (CLoGS). We analyse the kinematic
maps for distinct features, and measure specific stellar angular momentum
within one effective radius ($\lambda_{e}$). We classify the BGEs as fast
(10/18) or slow (8/18) rotators, suggesting at least two different evolution
paths. We quantify the anti-correlation between higher-order kinematic moment
$h_{3}$ and V/$\sigma$ (using the $\xi_{3}$ parameter), and the kinematic
misalignment angle between the photometric and kinematic position angles
(using the $\Psi$ parameter), and note clear differences between these
parameter distributions of the fast and slow rotating BGEs. We find that all
10 of our fast rotators are aligned between the morphological and kinematical
axis, consistent with an oblate galaxy shape, whereas the slow rotators are
spread over all three classes: oblate (1/8), triaxial (4/8), and prolate
(3/8). We place the results into context using known radio properties, X-ray
properties, and observations of molecular gas. We find consistent merger
histories inferred from observations for the fast-rotating BGEs, indicating
that they experienced gas-rich mergers or interactions, and these are very
likely the origin of the cold gas. Observational evidence for the slow
rotators are consistent with gas-poor mergers. For the slow rotators with cold
gas, all evidence point to cold gas cooling from the intragroup medium.

###### keywords:

galaxies: groups: general, galaxies: elliptical and lenticular, cD, galaxies:
kinematics and dynamics, galaxies: stellar content

††pubyear: 2022††pagerange: Merger histories of brightest group galaxies from
MUSE stellar kinematics–B

##  1 Introduction

Studying the build-up of stellar mass of galaxies is a pivotal part of our
understanding of their evolutionary paths. This can be done through
cosmological simulations (e.g., Springel et al. 2005; De Lucia & Blaizot 2007;
Naab et al. 2014; Schaye et al. 2015; Oppenheimer et al. 2021), or through
studies of stellar dynamics in present-day galaxies to infer their individual
assembly history (e.g., Bender et al. 1994; Emsellem et al. 2011; Cappellari
2016; van de Sande et al. 2017; Falcón-Barroso et al. 2017). Detailed
dynamical studies, in particular when combined with simulations, provide
insight into the three-dimensional intrinsic shape of galaxies, which can not
be determined through photometric studies alone. Disturbances in the stellar
kinematics are also long-lived compared to merger signatures visible from
imaging (Cox et al., 2006; Glazebrook, 2013; Nevin et al., 2021). Integral
Field Spectroscopy (IFS) allows us to study the internal structure of galaxies
in detail, as this presents the two-dimensional view of the stellar kinematics
necessary to understand the assembly history and substructure of individual
galaxies that may distinguish different formation and evolution scenarios
(e.g. Emsellem et al. 2007, 2011; Sánchez et al. 2012; Loubser & Soechting
2013; Fogarty et al. 2015; Mentz et al. 2016; Brough et al. 2017; Tsatsi et
al. 2017; Krajnović et al. 2018; Graham et al. 2018; Li et al. 2018b; Pinna et
al. 2019, and many more).

In particular, we focus on the central, brightest members of galaxy groups,
how they evolve, and the corresponding signatures in the galaxy or group
properties (Le Brun et al., 2014; Liang et al., 2016; O’Sullivan et al., 2017;
Oppenheimer et al., 2021; Jung et al., 2022). With up to half of galaxies
residing in groups in the local Universe (Eke et al., 2004; Robotham et al.,
2011), we also need to understand the influence of the group environment on
galaxy evolution. Because of their location at the bottom of their host halo’s
gravitational potential well, we expect brightest group galaxies to experience
multiple mergers and tidal encounters with other group member galaxies over
their evolution. The merger driven size growth (for both central group and
cluster galaxies) is supported by the observed rate of mergers from galaxy
pair counts and identified interacting galaxies (e.g. Fakhouri et al. 2010;
Groenewald et al. 2017; Banks et al. 2021), as well as the signatures of
recent accretion events in the halos of galaxies observed through deep imaging
(e.g. Mihos et al. 2005; Mancillas et al. 2019; Nevin et al. 2021; Yoon et al.
2022). Simulations suggest that these interactions are responsible for the
stellar mass assembly of the brightest group galaxies, and may also induce
kinematic transformations (Pillepich et al. 2018; Tacchella et al. 2019;
Jackson et al. 2020; Jung et al. 2022, also see review by Oppenheimer et al.
2021). In this paper, we study brightest group galaxies classified as early-
type galaxies (Brightest Group Ellipticals, BGEs) from the Complete Local-
Volume Groups Sample (CLoGS) sample (as described in detail below)111See
O’Sullivan et al. (2017) for the detailed selection criteria of the CLoGS
sample. Of particular interest for this paper is that the groups were selected
to have an early-type galaxy as the central dominant galaxy, but were not
required to be X-ray bright..

Early-type galaxies can be separated into two kinematic classes, slow and fast
rotating galaxies, each class exhibiting very different dynamical properties
suggesting that there are at least two evolution paths that give rise to this
bimodality. A number of cosmological zoom-in simulations were developed to
understand the mechanisms that result in the formation of slow and fast
rotators, e.g. Bois et al. (2011); Khochfar et al. (2011); Naab et al. (2014);
Penoyre et al. (2017); Lagos et al. (2018); Choi et al. (2018); Schulze et al.
(2018); Pillepich et al. (2019); Frigo et al. (2019); Walo-Martín et al.
(2020); Pulsoni et al. (2020); Lagos et al. (2022b). Slow rotators,
particularly the most massive galaxies, appear to be the evolutionary endpoint
for galaxies that have ceased star formation and experienced at least one
major dry merger (or multiple minor dry mergers, e.g. Taranu et al. 2013),
while fast rotators represent an earlier stage of evolution. However, some
studies find more complex formation mechanisms for massive early-type galaxies
than the two unique formation histories suggested above (e.g. Jesseit et al.
2009, Bois et al. 2010, Naab et al. 2014, Jung et al. 2022).

The different evolutionary histories resulting in slow and fast rotators are
seemingly characterized by different numbers of mergers experienced, the
merger mass ratio, timing, gas fractions, and the configuration of merger
orbits (Naab et al., 2014; Penoyre et al., 2017). However, the details still
do not agree, with the added complication that it also depends on the cooling
and thermal stability of the gas surrounding the galaxies, as well as star
formation and AGN feedback models adopted by the simulations (Naab & Ostriker,
2017). In addition to the details of the formation of slow and fast rotators,
some other questions about the kinematic properties also remain, e.g. is the
distribution of rotation bimodal (slow vs fast rotators) with different
formation histories, or a continuous transition from one class into another
(see discussion in van de Sande et al. 2021a)?

Another outstanding question is whether the same processes are responsible for
the morphological (i.e. quenching of star formation) and kinematic
transformation in galaxies. One common conclusion among simulations is that
even if a slow rotator remnant is formed after a merger, continuous accretion
and star formation can rebuild the galaxy disk and turn the galaxy into a fast
rotator (Naab et al., 2014; Penoyre et al., 2017; Walo-Martín et al., 2020;
Lagos et al., 2022b). This suggests that quenching either prior or during the
kinematic transformation is required to more effectively decrease $\lambda$
and produce a slow rotator (Lagos et al., 2022b). Lagos et al. (2022b) find,
in the EAGLE simulations, that in most slow rotators quenching precedes
kinematic transformation by $\sim$2 Gyrs. Although they find several trends
between different types of mergers and slow rotator kinematic properties, they
could not identify a single galaxy property that can unambiguously indicate a
given assembly history.

Furthermore intrinsic properties, that can not be measured directly, inferred
from observed properties e.g. galaxy shape inversion from kinematic
misalignment measurements, are often not unique (Weijmans et al., 2014; Li et
al., 2018a; Bassett & Foster, 2019). However, when combined with higher-order
kinematics, as well as properties of the galaxies (and in our case also the
properties of the group halo’s) as observed in other wavelengths (e.g. X-ray
or radio observations), we have a more complete view of galaxies’ evolutionary
paths. This is particularly important for the central galaxies in galaxy
groups as there is no clear dominant transformation mechanism that galaxies
are subjected to, but rather multiple secular and external mechanisms
(Lovisari et al., 2021; Kleiner et al., 2021). Hence, we focus on a sample of
BGEs selected from a survey of galaxy groups well-studied through multi-
wavelength observations.

The Complete Local-Volume Groups Sample (CLoGS, O’Sullivan et al. 2017) is an
optically-selected sample of 53 nearby groups for which X-ray (Chandra & XMM-
Newton, O’Sullivan et al. 2017), radio (GMRT $\&$ VLA, Kolokythas et al. 2018,
2019) and mm (IRAM-30m $\&$ APEX, O’Sullivan et al. 2015; O’Sullivan et al.
2018) data have been collected. Stellar kinematics from archival long-slit
spectra from the Hobby-Ebberly Telescope for a sub-sample of 23 CLoGS BGEs
were presented in Loubser et al. (2018), and archival GALEX and WISE
photometry for all 53 BGEs in Kolokythas et al. (2022). This rich multi-
wavelength dataset places us in a unique position to study various properties
of BGEs that serve as signatures of their evolution and merger histories, and
interpret the influence of the environment.

This paper is part of a series analysing 18 Multi-Unit Spectroscopic Explorer
(MUSE; Bacon et al., 2010) cubes of CLoGS BGEs. Olivares et al. (2022) present
a detailed analysis of the ionised gas kinematics, Lagos et al. (2022a)
present an analysis of gas ionisation mechanisms and chemical abundances, and
here we present detailed stellar kinematics. Dynamical modelling, and stellar
population analyses will be presented in future papers. Section 2 contains a
summary of the data and data reduction, and the details of the spatial binning
and the stellar template fitting to derive the kinematics. Section 3.1
contains the kinematic maps, and analysis of the distinct kinematical
features. In Section 3.2, we measure the effective kinematic parameters, and
classify the BGEs as fast or slow rotators. Section 3.3 presents the higher-
order kinematics (including the $\xi_{3}$ parameter). Section 4 presents the
kinematic position angle and the misalignment with the photometric position
angle ($\Psi$), as well as the misalignment between the stellar and gas
kinematics. Section 5 contains a discussion on the merger histories inferred
from our stellar kinematic results, and combines our results with the multi-
wavelength data, before we conclude in Section 6.

##  2 Data and analysis

###  2.1 MUSE observations and data reduction

The observations and data reduction are fully described in Lagos et al.
(2022a) and Olivares et al. (2022), and we only summarise the most relevant
information here. Our sample consists of 18 BGEs from the CLoGS sample
(O’Sullivan et al., 2017), presented in Table 1. We have three objects, NGC
410, NGC 777 and NGC 1060, in common with the MASSIVE sample (Ma et al., 2014)
and we compare some of our derived properties in Appendix A. The observations
were made using the MUSE IFS, on the Very Large Telescope (VLT). The
observations were made over a 1${}^{\prime}\times$1′ Field of View (FoV)
sampled by 24 spectrographs with a spectral coverage between $\sim$4800 and
9300 Å, a spectral resolution of $\sim$2.6 Å and spatial sampling of 0.2′′ per
spaxel, leading to a total of $\sim$100,000 spectra per exposure. For each
galaxy at least three exposures, with a few arcsecond dither pattern, were
taken. The data were reduced using the MUSE pipeline (v2.6.2), and the data
cubes were corrected for Galactic extinction using the reddening function
given by Cardelli et al. (1989).

###  2.2 Photometric parameters

We define the effective radius ($R_{e}$) similar to comparable studies e.g.
Cappellari et al. (2011a) (ATLAS3D) and Ma et al. (2014) (MASSIVE), based on
the half-light radii from the 2MASS (Skrutskie et al., 2006) extended source
catalogue XSC (Jarrett et al. 2000, specifically the parameters j_r_eff,
h_r_eff, and k_r_eff). This radius is derived from the 2MASS surface
brightness profile in each of the three bands from the semi-major axis of the
ellipse that encloses half of the total light. For $R_{e}$, we use the median
value in the three bands222Ma et al. (2014) showed that $R_{e}$ calculated
this way correlates well with $R_{e}$ derived from optical (SDSS DR8),
although there is a systematic offset such that at $\sim$1 kpc, the optical
$R_{e}$ is a factor of $\sim$1.2 larger than the 2MASS $R_{e}$ (their equation
4). We use the 2MASS $R_{e}$ to be able to compare to ATLAS3D (Cappellari et
al., 2011a) and M3G (Krajnović et al., 2018). Where we compare our derived
values to MASSIVE in table 4, we use the 2MASS (and not SDSS) $R_{e}$ from Ma
et al. (2014).:

$R_{e}=\rm median(\text{j\textunderscore r\textunderscore eff,h\textunderscore
r\textunderscore eff,k\textunderscore r\textunderscore
eff})\sqrt{\text{sup\textunderscore ba}}$ (1)

where sup_ba is the minor-to-major axis ratio measured from the 2MASS 3-band
co-added image at the 3$\sigma$ isophote. With the exception of NGC 5846
(0.8$R_{e}$), all our maps cover at least 1.5$R_{e}$.

Figure 1: MUSE white-light images (showing log(flux) in arbitrary units). The
PAphot is anticlockwise (East of North). North is up, East is to the left. We
indicate PAphot with white lines (in NGC 978 we use the solid line for the
2MASS PAphot, and the dashed line for our PAphot). We use grey lines for the
fitted PAkin (see Section 4). We indicate $R_{e}$ with a black ellipse (dashed
line). We indicate close companions or objects in the line-of-sight with a
black solid line or ellipse.

Figure 2: continued

MUSE white-light images (showing log(flux) in arbitrary units). The PAphot is
anticlockwise (East of North). North is up, East is to the left. We indicate
PAphot with white lines. We use grey lines for the fitted PAkin (see Section
4). We indicate $R_{e}$ with a black ellipse (dashed line). We indicate close
companions or objects in the line-of-sight with a black solid line or ellipse
(for NGC 5846 where these areas fall within the region where the effective
parameters were measured, these areas were masked during the measurements).

We also use the total $K$-band luminosity (MK) obtained from the 2MASS XSC,
and we perform Galactic extinction and other corrections as described in
detail in Loubser et al. (2018) (their Section 3.2). We take the ellipticity
($\epsilon$) as 1 – sup_ba, and we also obtain the photometric position angle
PAphot from the 2MASS XSC as measured from the “total" isophote from the
3-band co-added image. We have a $\pm$0.1 fiducial uncertainty on the
ellipticity and $\pm$3 degree fiducial uncertainty on the PAphot. All the
photometric parameters are also presented in Table 1. PAphot from the 2MASS
XSC agrees with our MUSE white-light images (obtained by adding the MUSE cube
along the wavelength axis) as shown in Figure 1, except for NGC 978 where
2MASS gives 115$\degr$ (white solid line), but we find PAphot $\sim$75$\degr$
(white dashed line). This is presumably because the source was blended with
the close companion in the 2MASS measurements, therefore we use the latter
(75$\degr$).

Table 1: General parameters of our sample. Here Col. (1) gives the galaxy name, Cols. (2) and (3) the coordinates, and Col. (4) the redshift from NED. Col. (5) and (6) give $R_{e}$ (see Section 2), to convert from (5) to (6) we assume $H_{0}$ = 67.8 km/sec/Mpc, $\Omega_{\rm matter}$ = 0.308, $\Omega_{\rm vacuum}$ = 0.692 (these parameters have a negligible effect on the physical scales of the galaxies due to their close proximity). Col (7) give the spatial coverage of our data, in terms of $R_{e}$, along the photometric semi-major axis. Col (8) gives the total, Galactic extinction corrected MK as calculated in Loubser et al. (2018) (see their Section 3.2 for details). Col (9) gives the ellipticity ($\epsilon$), and Col (10) is PAphot as measured from the 2MASS “total" isophote (East of North). Name | RA | DEC | $z$ | 2MASS $R_{e}$ | 2MASS $R_{e}$ | Coverage | MK |  $\epsilon\pm$0.10 | PA${}_{\rm phot}\pm$3.0
---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) |  | (arcsec) | (kpc) | ($\times$ $R_{e}$) | (mag) |  | (deg)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
ESO 507-G025 | 12h51m31.8s | -26d27m07s | 0.0108 | 13.34 | 3.33 | 2.5 | –24.71$\pm$0.03 | 0.24 | 90.0
NGC 193 | 00h39m18.6s | +03d19m52s | 0.0147 | 11.84 | 3.39 | 2.0 | –24.65$\pm$0.03 | 0.28 | 70.0
NGC 410 | 01h10m58.9s | +33d09m07s | 0.0177 | 16.77 | 5.87 | 1.7 | –25.76$\pm$0.02 | 0.26 | 40.0
NGC 584 | 01h31m20.7s | -06d52m05s | 0.0060 | 19.55 | 2.09 | 1.7 | –24.22$\pm$0.03 | 0.34 | 62.5
NGC 677 | 01h49m14.0s | +13d03m19s | 0.0170 | 9.34 | 3.15 | 1.8 | –24.87$\pm$0.03 | 0.10 | 35.0
NGC 777 | 02h00m14.9s | +31d25m46s | 0.0167 | 14.57 | 4.87 | 1.7 | –25.61$\pm$0.02 | 0.10 | 145.0
NGC 924 | 02h26m46.8s | +20d29m51s | 0.0149 | 8.00 | 2.37 | 3.5 | –24.37$\pm$0.03 | 0.44 | 55.0
NGC 940 | 02h29m27.5s | +31d38m27s | 0.0171 | 7.61 | 2.61 | 2.8 | –24.83$\pm$0.03 | 0.30 | 15.0
NGC 978 | 02h34m47.6s | +32d50m37s | 0.0158 | 9.70 | 3.08 | 2.4 | –24.53$\pm$0.03 | 0.26 | 75
NGC 1060 | 02h43m15.0s | +32d25m30s | 0.0173 | 16.76 | 5.85 | 1.5 | –25.97$\pm$0.02 | 0.14 | 70.0
NGC 1453 | 03h46m27.2s | -03d58m08s | 0.0130 | 16.01 | 4.23 | 1.5 | –25.48$\pm$0.02 | 0.14 | 25.0
NGC 1587 | 04h30m39.9s | +00d39m42s | 0.0123 | 12.89 | 3.30 | 2.1 | –25.00$\pm$0.03 | 0.16 | 60.0
NGC 4008 | 11h58m17.0s | +28d11m33s | 0.0121 | 12.32 | 3.40 | 2.9 | –24.56$\pm$0.03 | 0.42 | 165.0
NGC 4169 | 12h12m18.8s | +29d10m46s | 0.0126 | 7.99 | 2.29 | 2.9 | –24.41$\pm$0.03 | 0.44 | 150.0
NGC 4261 | 12h19m23.2s | +05d49m31s | 0.0074 | 22.36 | 4.05 | 1.5 | –25.47$\pm$0.03 | 0.16 | 172.5
NGC 5846 | 15h06m29.3s | +01d36m20s | 0.0057 | 32.02 | 4.32 | 0.8 | –25.11$\pm$0.02 | 0.08 | 27.5
NGC 6658 | 18h33m55.6s | +22d53m18s | 0.0142 | 7.01 | 2.04 | 4.7 | –24.25$\pm$0.03 | 0.76 | 5.0
NGC 7619 | 23h20m14.5s | +08d12m22s | 0.0125 | 14.84 | 3.55 | 1.8 | –25.28$\pm$0.02 | 0.18 | 40.0

###  2.3 Voronoi binning

We use the Galaxy IFU Spectroscopy Tool (GIST) (Bittner et al., 2019), which
uses the well-known pPXF (Cappellari & Emsellem, 2004; Cappellari, 2017) and
GandALF (Sarzi et al., 2006) routines, to bin the spectra and extract stellar
kinematics. We logarithmically rebin the spectra (along the wavelength axis)
to have constant bins in velocity.

The higher-order moments, in particular, depend on a high signal-to-noise
ratio (S/N), and the data cubes were tessellated using the Voronoi-binning
method (Cappellari & Copin, 2003) to achieve adequate S/N (minimum
S/N$\sim$80) per spatial bin as measured from the continuum between 6000 and
6200 Å.

###  2.4 Kinematics extraction

We use pPXF (through GIST) to derive the line-of-sight velocity distribution
(LOSVD) described by the velocity $V$, velocity dispersion $\sigma$, and the
higher-order Gauss-Hermite moments $h_{3}$ and $h_{4}$ (Gerhard, 1993; van der
Marel & Franx, 1993). We use the E-MILES model library (Vazdekis et al.,
2015), covering the wavelength range used here at a spectral resolution of
$\sim$ 2.51 Å (Falcón-Barroso et al., 2011). An example of a spectrum
extracted from a central bin in ESO 507-G025 is shown in Figure 3. We also
masked potential emission lines or possible sky-line residuals during the fit,
as illustrated by the grey bands in Figure 3. Our stellar kinematic maps and
measurements agree with those from Olivares et al. (2022) who used the Indo-US
library (Valdes et al., 2004). We limit the fit to a wavelength range of 4800
to 6800 Å, to avoid any potentially strong telluric and sky residuals. We also
test the effect of wavelength range on the measured kinematics, and found that
at S/N = 80, there are negligible differences between using 4800 to 6800 Å and
slightly shorter wavelength ranges. We correct for the wavelength-dependent
line-spread-function of the MUSE observations by adopting the prescription
from Bacon et al. (2017).

Figure 3: Example of an extracted central spectrum (4800 to 6800 Å) for ESO
507-G025. The observed spectrum is indicated in black (in arbitrary flux
units), and the best-fitting stellar template in red (with the residual of the
two shown in green). Grey bands indicate potential emission-lines or possible
sky-line residuals masked during the fit.

In our stellar template fitting, we include an additive polynomial of the 4th
order to account for any potential deviations in the continuum shape between
the stellar template and observed galaxy spectra, or flux calibration
differences (Bittner et al., 2019). We initially use the default value for the
penalisation in pPXF (Cappellari & Emsellem, 2004), and then use 100 Monte-
Carlo simulations to compute errors on the kinematic parameters without the
penalisation term. The standard deviation of the measured kinematic parameters
is used as errors (see full description of the GIST kinematic prosedure in
Bittner et al. 2019).

##  3 Stellar kinematics results

We show maps of $V$ for each of the galaxies in Figure 5i. We show the rest of
the maps ($\sigma$, $h_{3}$, $h_{4}$, and $\lambda$) for ESO 507-G025 in
Appendix B as an example, and the maps for the other 17 BGEs are included as
supplementary information. The isophotes are based on flux from the MUSE cube
and displayed in steps of 0.5 magnitude. We discuss distinct features from the
$V$ and $\sigma$ maps in Section 3.1. We discuss the global extracted
properties and classifications in Section 3.2, and the higher order kinematics
($h_{3}$ and $h_{4}$) in Section 3.3. We measure the projected angular
momentum of each galaxy using the dimensionless parameter $\lambda$ (Emsellem
et al., 2007). The $\lambda$ parameter is used to quantify the dynamical
importance of rotation relative to random motion in a galaxy, as discussed in
detail in Section 3.2.

(a)  (b)  (c)

(d)  (e)  (f)

(g)  (h)  (i)

Figure 4: Maps of the stellar velocity field ($V$). The orientation of the
maps is the same as in Figure 1. All spatial scales are in arseconds. The
isophotes are based on flux from the MUSE cube and displayed in steps of 0.5
magnitude.

(a)  (b)

(c)

(d)  (e)

(f)

(g)  (h)

(i)

Figure 5: continued

Maps of the stellar velocity field ($V$). The orientation of the maps is the
same as in Figure 1. All spatial scales are in arseconds. The isophotes are
based on flux from the MUSE cube and displayed in steps of 0.5 magnitude.

###  3.1 Distinct features from the $V$ and $\sigma$ kinematic maps

We visually classify each galaxy according to its stellar velocity field
(Figure 5i). Various kinematic features are evident upon visual inspection of
the $V$ and $\sigma$ kinematic maps:

  1. 1.

Rotation

Despite being massive early-type galaxies, all our BGEs show some level of
rotation, as the MUSE data quality is such that even very little net rotation
can be detected (e.g. NGC 193, NGC 5846). At least half of the BGEs show
regular rotation with peak velocity in excess of 100 km s-1. A very small
number of massive galaxies show such rotation (see e.g. 2 out of 41 brightest
cluster galaxies, hereafter BCGs, in Loubser et al. 2008), but it is far more
prevalent in galaxies at lower masses (Brough et al., 2017).

We make a visual distinction between “regular rotator" (regular stellar
velocity field) or “non-regular rotator" (complex stellar velocity field). An
illustration of the visual classification of regular and non-regular rotators
can be seen in Figure 4 of Cappellari (2016)333We perform a qualitative
classification from the map following the illustration in Figure 4 of
Cappellari 2016. We do a quantitative classification in Section 3.2.. We find
the majority (10/18) of our BGEs to be regular rotators (RR): NGC 584, NGC
924, NGC 940, NGC 978, NGC 1453, NGC 1587, NGC 4008, NGC 4169, NGC 6658, and
NGC 7619. This is somewhat in contrast to e.g. Krajnović et al. (2018) who
find regular rotation only in their satellite galaxies and not their BCGs in
their M3G study (MUSE Most Massive Galaxies; PI: Emsellem), although their
central galaxies are more massive than the ones studied here (see Figure 8).
Non-regular rotation (NRR) is the most common characteristic of the Krajnović
et al. (2018) M3G BCGs, whereas we find it for only 8/18 BGEs: ESO 507-G025,
NGC 193, NGC 410, NGC 677, NGC 777, NGC 1060, NGC 5846, as well as NGC 4261
(which shows non-regular rotation around the major axis, as reported and
discussed by Davies & Birkinshaw 1986).

The regular or non-regular appearance of the velocity field of early-type
galaxies directly relates to the presence (or absence) of an embedded disc,
and also to the measured angular momentum (Krajnović et al., 2011; Emsellem et
al., 2011; Krajnović et al., 2020). Regular and non-regular rotation has also
been used to classify fast rotators (regular kinematics) and slow rotators
(non-regular kinematics), e.g. in Emsellem et al. (2011). We show that all our
regular rotators are fast rotators and all the non-regular rotators are slow
rotators in Section 3.2.

  2. 2.

Kinematically distinct cores (KDC):

The existence of a KDC is indicated by an abrupt change in the kinematic
position angle over a small radial range (e.g. Loubser et al. 2008). KDCs are
fairly rare in massive elliptical galaxies, Krajnović et al. (2018) find two
amongst their 14 massive galaxies (BCGs) in the M3G sample. Ene et al. (2018,
2020) also find two amongst 90 massive galaxies in their MASSIVE sample. We
find no KDCs in this sample of BGEs.

  3. 3.

Radial velocity dispersion ($\sigma$) profiles:

The most massive elliptical galaxies, BCGs, often exhibit velocity dispersion
profiles that rise from the centre of the galaxy to the outer parts (Loubser
et al., 2008; Loubser et al., 2018, 2020). This is less common amongst BGEs,
see e.g. Figure 3 in Loubser et al. (2018) which show only one (NGC 2768) out
of 23 BGEs from the CLoGS sample studied using long-slit spectra, compared to
the majority of the BCGs studied in the same analysis. NGC 2768 is not
included in our MUSE subsample of CLoGS BGEs. In fact, in this study, none of
the BGEs show rising velocity dispersion profiles (also see simulations in
Jung et al. 2022).

Table 2: Derived properties of our sample. RR or NRR refer to regular or non-regular rotation as visually classified in Section 3.1. The kinematic position angle, PAkin, is measured East of North to the maximum velocity. All other stellar kinematic parameters ($\Psi$, (V/$\sigma)_{e}$, $\lambda_{e}$, $\langle h_{4}\rangle_{e}$, and $\xi_{3}$), as well as the slow (SR) or fast (FR) rotator classification, are derived as described in the text. *For NGC 5846, we use values within 0.8$R_{e}$. Name | Rotation | PAkin | $\Psi$ | (V/$\sigma)_{e}$ | $\lambda_{e}$ | SR/FR | $\langle h_{4}\rangle_{e}$ | $\xi_{3}$
---|---|---|---|---|---|---|---|---
| RR/NRR | (deg) | (deg) |  |  |  |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
ESO 507-G025 | NRR | 289.0 $\pm$ 11.8 | 19.0 $\pm$ 12.2 | 0.080 | 0.085 | Slow | 0.037 | –0.84
NGC 193 | NRR | 167.3 $\pm$ 58.2 | 82.7 $\pm$ 58.3 | 0.035 | 0.030 | Slow | 0.035 | –0.35
NGC 410 | NRR | 189.1 $\pm$ 20.0 | 30.9 $\pm$ 20.2 | 0.054 | 0.046 | Slow | 0.065 | –1.03
NGC 584 | RR | 61.8 $\pm$ 0.9 | 0.7 $\pm$ 3.1 | 0.338 | 0.377 | Fast | 0.024 | –4.19
NGC 677 | NRR | 140.0 $\pm$ 5.5 | 75.0 $\pm$ 6.3 | 0.092 | 0.090 | Slow | 0.059 | –0.83
NGC 777 | NRR | 329.1 $\pm$ 20.9 | 4.1 $\pm$ 21.1 | 0.038 | 0.038 | Slow | 0.078 | –0.16
NGC 924 | RR | 52.7 $\pm$ 1.8 | 2.3 $\pm$ 3.5 | 0.374 | 0.497 | Fast | 0.056 | –11.95
NGC 940 | RR | 16.4 $\pm$ 0.9 | 1.4 $\pm$ 3.1 | 0.663 | 0.643 | Fast | 0.074 | –7.91
NGC 978 | RR | 70.9 $\pm$ 2.7 | 4.1 $\pm$ 4.0 | 0.213 | 0.255 | Fast | 0.052 | –4.74
NGC 1060 | NRR | 343.6 $\pm$ 23.6 | 86.4 $\pm$ 23.8 | 0.049 | 0.038 | Slow | 0.065 | –0.77
NGC 1453 | RR | 32.7 $\pm$ 3.6 | 7.7 $\pm$ 4.7 | 0.165 | 0.182 | Fast | 0.034 | –2.40
NGC 1587 | RR | 232.7 $\pm$ 3.6 | 7.3 $\pm$ 4.7 | 0.187 | 0.225 | Fast | 0.041 | –2.97
NGC 4008 | RR | 167.3 $\pm$ 2.7 | 2.3 $\pm$ 4.0 | 0.213 | 0.249 | Fast | 0.036 | –2.16
NGC 4169 | RR | 329.1 $\pm$ 2.7 | 0.9 $\pm$ 4.0 | 0.503 | 0.539 | Fast | 0.061 | –9.04
NGC 4261 | NRR | 60.0 $\pm$ 6.4 | 67.5 $\pm$ 7.1 | 0.044 | 0.046 | Slow | 0.028 | –0.19
NGC 5846 | NRR | 256.4 $\pm$ 34.5 | 48.9 $\pm$ 34.6 | *0.039 | *0.032 | Slow | *0.046 | –0.63
NGC 6658 | RR | 188.2 $\pm$ 0.9 | 3.2 $\pm$ 3.1 | 0.263 | 0.332 | Fast | 0.042 | –2.41
NGC 7619 | RR | 205.5 $\pm$ 3.6 | 14.5 $\pm$ 4.7 | 0.161 | 0.142 | Fast | 0.029 | –2.55

###  3.2 Effective kinematic parameters and fast vs slow rotator
classification

For early-type galaxies, visual morphology alone is not sufficient to infer
whether a galaxy formed via gas-rich or gas-poor mergers. A more robust method
is the fast/slow rotator classification, separating the two different classes
of early-type galaxies (Emsellem et al., 2007; Cappellari, 2016; Graham et
al., 2018).

Before we make any measurements of the effective kinematic parameters, we
correct for systemic velocity by subtracting the median of the velocity ($V$)
measurements over all spatial bins from every individual bin.

####  3.2.1 The ratio of ordered versus random motions ($V/\sigma$)

The ratio of ordered versus random motions ($V/\sigma$) within one effective
radius ($R_{e}$) is determined as in Cappellari et al. (2007):

$\left(\frac{V}{\sigma}\right)^{2}_{e}=\frac{\Sigma F_{i}V_{i}^{2}}{\Sigma
F_{i}\sigma_{i}^{2}}$ (2)

where $F_{i}$ is the flux in each bin. We sum only bins within an ellipse of
semi-major axis corresponding to one effective radius. These measurements are
presented in Table 2. Our measurements for the galaxies that we have in common
with the MASSIVE sample agree very well with theirs (see Appendix A for the
comparison). We use $V/\sigma$ further in Section 3.3, where we interpret
anti-correlations between $V/\sigma$ and $h_{3}$.

####  3.2.2 Classification according to the spin parameter ($\lambda_{e}$)

Following Emsellem et al. (2007), the $\lambda_{e}$ parameter is measured as

$\lambda_{e}=\frac{\Sigma F_{i}R_{i}|V_{i}|}{\Sigma
F_{i}R_{i}\sqrt{V_{i}^{2}+\sigma_{i}^{2}}}$ (3)

with the galactocentric radius $R_{i}$, the flux $F_{i}$, the radial velocity
$V_{i}$, and the velocity dispersion $\sigma_{i}$ for each individual spatial
bin within $R_{e}$ . We determine $\lambda_{e}$ using an ellipse444We use the
intrinsic radius (semi-major axis) instead of the projected (circular) radius
here, as the intrinsic radius follows the light profile of the galaxy more
accurately. van de Sande et al. (2017) quantify the possible effects by
measuring $\lambda_{e}$ using both methods. For round objects
($\epsilon<0.4$), the effect is especially small ($<0.01$). Our galaxies are
nearby and we can also assume $\lambda_{e}$ to be unaffected by seeing (see
Graham et al. 2018). of semi-major axis corresponding to one effective radius.

We classify our galaxies into fast or slow rotators, as this division connects
with two dominant channels of galaxy formation (as reviewed in Cappellari
2016). Following Emsellem et al. (2007) and Emsellem et al. (2011), we use the
spin parameter approximation $\lambda_{e}$ to separate fast-rotating galaxies
from slow-rotating galaxies by classifying galaxies above
$\lambda_{e}=0.31\sqrt{\epsilon}$ as fast rotators and below as slow rotators
(see Table 2).555We use $\lambda_{e}$ to quantitatively classify the BGEs into
fast and slow rotators, and since our fast/slow rotation classification
exactly agrees with our qualitative regular/non-regular rotator classification
from the velocity maps, any uncertainty on $R_{e}$ (propagated to
$\lambda_{e}$) does not affect our main conclusions. We plot $\lambda_{e}$ vs
$\epsilon$ in Figure 6 (the BGEs are indicated by blue and red symbols, for
fast and slow rotators). Here, we also indicate the 41 most massive galaxies
from the MASSIVE sample (Veale et al., 2017a) with grey circles. We indicate
the Emsellem et al. (2011) classification with a black dotted line, the Lauer
(2012) classification ($\lambda_{e}=0.2$) with a black dashed line, and the
Cappellari (2016) classification with a black solid line
($\lambda_{e}<0.08+\epsilon/4$ where $\epsilon<0.4$). We use the Emsellem et
al. (2011) classification here (but we get the same result if we use the
Cappellari (2016) classification), and the results correspond exactly to the
regular/non-regular rotation classification in that all regular rotating BGEs
are fast rotators, and all non-regular rotating BGEs are slow rotators. The
$\lambda_{e}$ parameter is also related to $(V/\sigma)_{e}$ (see equation B1
in Emsellem et al. 2011).

Figure 6 also show that all the BGEs classified as non-regular rotators are
all at $\epsilon<0.3$. This is in agreement with ATLAS3D, SAMI and CALIFA
kinematic results (Krajnović et al., 2011; Fogarty et al., 2015; Cappellari,
2016), and indicates that non-regular rotators are quite close to spherical
and only weakly triaxial (Cappellari, 2016).

Figure 6: We plot $\lambda_{e}$ vs $\epsilon$ for the BGEs (blue and red
symbols, for fast and slow rotators). Here, we also indicate the 41 most
massive galaxies from the MASSIVE sample (Veale et al., 2017a) with grey
circles. We indicate the Emsellem et al. (2011) fast vs slow rotator
classification with a black dotted line, the Lauer (2012) classification with
a black dashed line, and the Cappellari (2016) classification with a black
solid line. The green line is the prediction for an edge-on isotropic rotator
from Binney (2005) (Equation 14 in Cappellari 2016), and the magenta line is
the edge-on relation from Cappellari et al. (2007) (Equation 11 in Cappellari
2016).

####  3.2.3 Fast vs slow rotators as a function of luminosity and mass

For early-type galaxies, the ratio f(SR)/f(FR) between the fraction of slow
and fast-rotating galaxies seem to be a function (albeit not a simple one) of
environment, as well as a function of luminosity and stellar mass. Slow
rotators live predominantly in high density environments, such as massive
groups or clusters (Cappellari et al., 2011b). The ratio of fast and slow
rotators is nearly constant outside clusters, whereas it becomes a strong
function of the galaxy number density inside clusters (D’Eugenio et al., 2013;
Houghton et al., 2013; Scott et al., 2014; Fogarty et al., 2014). This
suggests that the formation of slow rotators must be linked to the clusters
themselves (Cappellari, 2016).

The fraction of slow rotators also strongly correlate with luminosity and mass
(Emsellem et al., 2011; van de Sande et al., 2017; Veale et al., 2017a; Greene
et al., 2017; Graham et al., 2018). These correlations are best studied with
samples which cover a wide range in mass, morphology and environment (Brough
et al., 2017; Wang et al., 2020; van de Sande et al., 2021b), nonetheless we
illustrate the distribution of the fast and slow-rotating BGEs as a function
of luminosity and mass below.

We plot $\lambda_{e}$ vs MK in Figure 7 separating the fast (blue) and slow
rotators (red). We can see that the six least luminous BGEs are fast rotators,
and the three most luminous BGEs are slow rotators (NGC 410, NGC 777, and NGC
1060), and an overlap between the two classes over a broad range of
luminosities in between. This trend, that towards higher stellar mass the
fraction of fast rotating galaxies decreases, agrees with previous studies.
Veale et al. (2017a) studied the fraction of slow rotators in bins of
luminosity for MASSIVE and ATLAS3D galaxies, and show that the fraction
increases dramatically from 10 per cent at M${}_{K}\sim-22$ mag to 90 per cent
at M${}_{K}\sim-26$ mag. A similar trend is shown for the ATLAS3D sample in
Emsellem et al. (2011).

The parameter $\lambda_{e}$ is a projected quantity, and we adopt a similar
approach to Brough et al. (2017) to estimate the effects of inclination for
our early-type galaxies. If we use $\lambda_{e}/\sqrt{\epsilon}$ (as
$\epsilon$ is also estimated as a global parameter) as an approximate
correction on $\lambda_{e}$ and investigate $\lambda_{e}/\sqrt{\epsilon}$ vs
MK instead, it does not affect our conclusion that the least luminous BGEs are
more likely to have a high spin parameter, and the most luminous BGEs more
likely to have a lower spin parameter.

Figure 7: The distribution of $\lambda_{e}$ with MK, separating the fast
(blue) and slow rotators (red). Figure 8: The mass (M∗) – size ($R_{e}$)
diagram. We indicate the fast (blue) and slow (red) rotating BGEs. We also
show the BCGs from the M3G sample (Krajnović et al., 2018). We also indicate
the characteristic mass at 2 $\times 10^{11}$ M☉ (above which passive slow
rotators dominate).

The distribution of galaxies in the size-mass plane is a well-studied scaling
relation (van der Wel et al., 2014; van de Sande et al., 2017; Krajnović et
al., 2018; Walo-Martín et al., 2020). We illustrate our fast and slow rotating
BGEs on the mass (M∗) – size ($R_{e}$) diagram in Figure 8. We estimate the
stellar mass of the BGEs using the widely-used conversion between $K$-band
luminosity and stellar mass for early-type galaxies from the ATLAS3D sample
(Cappellari, 2013):

$\log_{10}(\rm M_{*})=10.58-0.44(\rm M_{K}+23)$ (4)

We indicate the fast (blue) and slow (red) rotating BGEs. We also show the
BCGs from the M3G sample (Krajnović et al., 2018). We also indicate the
characteristic mass at 2 $\times 10^{11}$ M☉ (above which passive slow
rotators with cores dominate, see Krajnović et al. 2020), and find that all of
our slow rotators are above this limit.

###  3.3 Higher-order kinematics

Observational (e.g. van de Sande et al. 2017) as well as cosmological
hydrodynamical zoom-in studies (e.g. Naab et al. 2014) have shown that the
evolutionary history of galaxies cannot be accurately constrained from the
spin parameter alone, and should be complimented with the higher-order
kinematic measurements preferably from integral field spectroscopy. The
higher-order stellar kinematic moments $h_{3}$ and $h_{4}$, defined as the
deviations from a Gaussian line-of-sight velocity distribution (LOSVD), are
parameterized with Gauss-Hermite polynomials (van der Marel & Franx 1993;
Gerhard 1993).

####  3.3.1 Gauss-Hermite fourth moment ($h_{4}$)

We derive the luminosity-weighted $\langle h_{4}\rangle_{e}$ values within the
effective radius, and list them in Table 2. We also compare our measurements
to MASSIVE in Table 4 for our three galaxies in common, and find that our
values are slightly higher. But similar to Veale et al. (2017a) and Loubser et
al. (2020), we find positive $\langle h_{4}\rangle_{e}$ values for all our
galaxies. These positive values can either have a physical origin, e.g. a
superposition of components with different LOSVDs (see Gerhard 1993; Bender et
al. 1994; Baes et al. 2005), or can be the result of an observational bias or
template mismatch, e.g. in galaxies with a young stellar population component
(see discussion in section 3.2.7 of van de Sande et al. 2017, and section 3.2
in Loubser et al. 2020). Given the current unknown nature of the positive
$h_{4}$ values, we do not interpret them further.

####  3.3.2 Gauss-Hermite third moment ($h_{3}$)

Correlations between the $h_{3}$ and the line-of-sight velocity ($V$) in
spatially-resolved measurements allow us to probe the eccentricity of the
stellar orbits (Bender et al., 1994; Bureau & Athanassoula, 2005).

Figure 9: Spatially-resolved $V/\sigma$ and $h_{3}$ measurements from each of
the fast rotators in our sample (coded by colour). Top: Red – NGC 584, Black –
NGC 924, Blue – NGC 940, Green – NGC 978, Yellow – NGC 1453. Bottom: Red – NGC
1587, Black – NGC 4008, Blue – NGC 4169, Green – NGC 6658, Yellow – NGC 7619.

Figure 9 show how the spatially-resolved $V/\sigma$ and $h_{3}$ measurements
are anti-correlated within each of the fast rotators in our sample (coded by
colour), as expected for galaxies with embedded disk-like components (Naab &
Burkert, 2001; Jesseit et al., 2007; Hoffman et al., 2009, 2010; Naab et al.,
2014; Schulze et al., 2018). For each galaxy, the straight line shows our best
fit to the relation between $V/\sigma$ and $h_{3}$ (for a flux-weighted
parametrisation of the slope, see $\xi_{3}$ below). Such an anti-correlation
(with a slope of approximately –0.1) is expected from projection effects
(Bender et al., 1994). Similar to other studies (e.g. Krajnović et al. 2008,
2011; Veale et al. 2017a; van de Sande et al. 2017), we also find weaker anti-
correlations between the $V/\sigma$ and $h_{3}$ measurements for our slow
rotators, but steeper than for the fast rotators.

####  3.3.3 Kinematic asymmetry parameter ($\xi_{3}$)

Figure 10: Distribution of the kinematic asymmetry parameter ($\xi_{3}$) for
our fast (blue) and slow (red) rotators.

We quantify the differences between the $h_{3}$ and $V/\sigma$ anti-
correlations of the fast and slow rotators shown in Table 2. Following Frigo
et al. (2019), we use:

$\xi_{3}=\frac{\Sigma_{i}F_{i}h_{3,i}(V_{i}/\sigma_{i})}{\Sigma_{i}F_{i}h_{3,i}^{2}}$
(5)

where $i$ in this case is each spatial bin (summed out to $R_{e}$). This
global parameter measures the slope of the $h_{3}-V/\sigma$ anti-correlation,
and when $h_{3}$ and $V/\sigma$ are fully anti-correlated, the correlation is
given by $h_{3}=(1/\xi_{3})V/\sigma$ (Krajnović et al., 2020).

Frigo et al. (2019) present examples of various $h_{3}$ and $V/\sigma$
distributions with and without correlations, and their corresponding $\xi_{3}$
parameters. Fast-rotating galaxies have $\xi_{3}<-3$, while slow rotators have
$\xi_{3}$ close to 0. From Figure 10, we can see a clear difference between
the $\xi_{3}$ distributions of our fast and slow-rotating BGEs, but large
variations between individual fast-rotating galaxies. The lack of overlap
between the two distributions indicates a clear difference of the orientations
in the $h_{3}-V/\sigma$ plane.

##  4 Stellar kinematics position angle and misalignment

In this section, we discuss the misalignment angle ($\Psi$) between the
stellar kinematics PA (PAkin) and the photometric PA (PAphot), and use it as
an indicator of galaxy shape for the BGEs. We also investigate the
misalignment ($\Psi_{\rm gas}$) between the stellar kinematics (PAkin) and the
gas kinematics (PAgas).

###  4.1 Kinematic position angle (PAkin) and misalignment angle ($\Psi$) with
the photometric position angle (PAphot)

We use the fit_kinematic_pa666http://www-
astro.physics.ox.ac.uk/$\sim$mxc/software/ routine as described in Appendix C
of Krajnović et al. (2006) to measure the global kinematic position angle,
PAkin, from the stellar velocity map of each BGE. The routine uses the
observed velocity map to generate a model map for each possible PAkin value,
then determines the angle that minimizes the $\chi^{2}$ between the observed
map and the model map, finding the value of PAkin. PAkin is measured East of
North (anti-clockwise) to the maximum velocity. We masked close companions or
objects in the line-of-sight as indicated in Figure 1, and we use 100 steps to
calculate the model. In galaxies where we do not detect large net-streaming
motions (the non-regular/slow rotators), the uncertainty on PAkin is large.

From the photometric position angle PAphot and the kinematic position angle
PAkin, we find the kinematic misalignment angle ($\Psi$) following Franx et
al. (1991):

$\sin\Psi=|\sin(\rm PA_{\rm phot}-\rm PA_{\rm kin})|$ (6)

While the range of PAphot is 0$\degr$ to 180$\degr$ and the range of PAkin is
0$\degr$ to 360$\degr$, the misalignment angle by construction, is restricted
to be between 0$\degr$ and 90$\degr$. Thus, the misalignment of the two
position angles is measured regardless of the sense of the galaxy rotation.
Our measurements are listed in Table 2. For the uncertainty on $\Psi$, we add
the uncertainties on PAphot and PAkin in quadrature.

Figure 11: Top: Kinematic misalignment angle ($\Psi$) vs ellipticity
($\epsilon$) for the regular rotating (RR, also corresponding to fast rotator)
and non-regular rotating (NRR, also corresponding to slow rotator) BGEs.
Bottom: Kinematic misalignment angle ($\Psi$) vs $\lambda_{e}$ for the fast
(blue) and slow rotating (red) BGEs.

###  4.2 $\Psi$ as an indicator of galaxy shape

Analytical galaxy potentials suggest a correspondence between galaxy intrinsic
shape and the intrinsic misalignment angle between kinematic and morphological
axes (Franx et al. 1991, and subsequent studies).

We present the distribution of $\Psi$ as a function of the galaxy projected
ellipticity ($\epsilon$) in Figure 11 (top). Following Krajnović et al.
(2018), we draw two horizontal lines at 15$\degr$ and 75$\degr$ to separate
oblate, triaxial and prolate geometries. The figure shows that all BGEs
classified as regular rotators (RR, or fast rotators, shown in blue) fall in
the oblate category. They are spread over a range of $\epsilon$, and have very
well defined PAkin (and therefore $\Psi$). The BGEs classified as non-regular
rotators (NRR, slow rotators, shown in red) are all at $\epsilon<0.3$ (also
see Section 3.2), have large uncertainties on PAkin, and seem to be spread
over all three classes: oblate (1/8), triaxial (4/8), and prolate (3/8). The
bottom panel in Figure 11 clearly illustrates the difference in the
misalignment angle vs $\lambda_{e}$ distributions for the fast and slow
rotating BGEs.

Although the recovered intrinsic shape distributions from such methods are not
unique (Franx et al., 1991), results showing that all the fast rotators have
kinematic axes aligned with photometric axes suggest that they are nearly
axisymmetric (Cappellari et al., 2007; Emsellem et al., 2007; Krajnović et
al., 2011; Fogarty et al., 2015; Li et al., 2018b). In this case, the apparent
angular momentum coincides with the intrinsic angular momentum, $\Psi$ = 0
(Franx et al., 1991). We find here that all 10 of our fast rotators are
aligned ($\Psi<15\degr$). Ene et al. (2018) found that 91 per cent of their
fast rotators in the MASSIVE sample are aligned. Studies of lower mass early-
type galaxies find similar trends e.g. 83 per cent of the fast rotators are
aligned in the SAMI survey (Fogarty et al., 2015), and 96 per cent of the fast
rotators are aligned in ATLAS3D (Krajnović et al., 2011).

For slow rotators, the two axes can be misaligned (Weijmans et al., 2014;
Foster et al., 2017; Li et al., 2018b), showing the triaxial nature of
galaxies (Franx et al., 1991). Triaxial galaxies can exhibit any value of
$\Psi$, while prolate galaxies with significant rotation would have $\Psi$
closer to 90 degrees (Schechter & Gunn, 1979; Davies & Birkinshaw, 1988).
Galaxies with significant misalignment (typically galaxies more massive than
1011 M☉, Krajnović et al. 2018) have “prolate-like" rotation ($\Psi>75\degr$,
also called “minor axis" rotation), that is rotation around the major axis.

Krajnović et al. (2018) find that a third (5/14) of their M3G BCG galaxies
show prolate-like rotation ($\Psi>75\degr$), whereas studies of the MASSIVE
galaxy sample find $<20$ per cent prolate-like (Ene et al., 2020). Tsatsi et
al. (2017) find that 27 per cent of CALIFA galaxies and 23 per cent of ATLAS3D
galaxies ($M_{*}>10^{11.3}$ M☉) show prolate-like rotation. Here 3 out of the
18 BGEs (NGC 193, NGC 677, and NGC 1060) show $\Psi>75\degr$ (“minor axis" or
“prolate-like" rotation). Our sample is small in number, and the comparison is
complicated by the fact that misaligned galaxies have large uncertainties on
$\Psi$, but the fraction of prolate-like galaxies broadly agrees with that
from other samples of massive early-type galaxies.

Even though recent works have interpreted the existence of these massive
galaxies with 90-degrees misalignment as circumstantial evidence for prolate
galaxies (e.g. in M3G Krajnović et al. 2018), not all intrinsically prolate
galaxies are misaligned. For example, the Illustris simulations found
intrinsically prolate galaxies to range from showing no rotation to being
kinematically aligned (Li et al., 2018a; Bassett & Foster, 2019). However,
galaxies with prolate-like rotation cannot be oblate spheroids.

###  4.3 Misalignment between gas and stars ($\Psi_{\rm gas}$)

The misalignment of cold gas and ionised gas with the stellar rotation in
galaxies can suggest clues to the origin of accreted gas. We therefore use the
gas kinematic position angle (PAgas) from Olivares et al. (2022), and the
stellar PAkin measured here, to derive the misalignment between gas and stars
($\Psi_{\rm gas}$). Both the PAgas and PAkin were measured from North (anti-
clockwise) to maximum velocity, and the difference between the two angles is
defined as $\Psi_{\rm gas}$ measured between 0$\degr$ (fully aligned) to
180$\degr$ (fully counter-aligned).

Similar to previous studies (Lagos et al., 2015; Davis & Bureau, 2016; Bryant
et al., 2019; Xu et al., 2022), we assume that galaxies with a misalignment
angle of less than 30$\degr$ are aligned, galaxies with $30\degr<\Psi_{\rm
gas}<150\degr$ are misaligned, and galaxies with $150\degr<\Psi_{\rm
gas}<180\degr$ could be considered to be counter-rotating. However, this cut-
off is rather arbitrary, and in addition, the measurement errors (specifically
PAkin for slow rotators) can be large, and the PAs are projected values,
together resulting in an uncertainty on the $\Psi_{\rm gas}$ misalignment. For
a large sample of SAMI galaxies, Bryant et al. (2019) note that inspection of
galaxies with PA offsets between 30 – 40$\degr$ reveal that some are genuinely
misaligned while for others, the errors on the fits mean that they can also be
in agreement with a PA offset below 30$\degr$. They suggest to also consider a
PA offset cut-off of 40$\degr$ to account for the possible contamination. We
present this $\Psi_{\rm gas}$ classification in Table 3, and we indicate the
two BGEs with $\Psi_{\rm gas}$ between 30 – 40$\degr$. The exact value of this
cut-off (30$\degr$ or 40$\degr$) do not impact the main conclusions of this
paper. Our gas/stellar misalignment classifications agree with those of
Olivares et al. (2022) within the errors, given that PAkin were independently
measured, and from stellar velocity maps constructed using different minimum
S/N level spatial bins.

##  5 Discussion: Merger histories from stellar kinematics and multi-
wavelength data

We discuss the merger histories that can be inferred from the results
presented in Sections 3 and 4 in Section 5.1 by comparing to results from
simulations. In Section 5.2, we discuss whether this is consistent with the
formation histories derived from all the multi-wavelength observations
available.

###  5.1 Merger histories from stellar kinematics

####  5.1.1 Anti-correlations between $h_{3}$ and $V/\sigma$

Naab et al. (2014) divide the 44 central galaxies from their hydrodynamical
simulations into six different classes. Class A and B are fast rotators
($\lambda_{e}\sim 0.3-0.6$) that experienced gas-rich mergers, and have a
strong anti-correlation between $V/\sigma$ and $h_{3}$. Class C, E, and F are
slow rotators ($\lambda_{e}\sim 0.05-0.2$) that had late gas-rich mergers or
gas-poor minor and/or major mergers, and show a steep relation between $h_{3}$
and $V/\sigma$. Class D consists of galaxies with a late gas-poor merger
(intermediate $\lambda_{e}\sim 0.1-0.3$), roughly half of which would be
classified as fast rotators. These galaxies do not show a strong anti-
correlation between $h_{3}$ and $V/\sigma$, or any other signs of embedded
disk components (see also Naab & Burkert 2001; Jesseit et al. 2007, and
discussion in van de Sande et al. 2017). van de Sande et al. (2017) do not
find evidence for a significant population of fast-rotating galaxies without a
strong anti-correlation between $h_{3}$ and $V/\sigma$ in the SAMI survey.
Here, we find that all of the $h_{3}$ versus V/$\sigma$ anti-correlation
slopes of our fast rotating BGEs are around $\sim$ –0.1 as expected, with the
steepest being NGC 940 (–0.15) and NGC 7619 (–0.16). NGC 940 has
$\lambda_{e}\sim 0.6$, therefore NGC 7619 (with a fairly low $\lambda_{e}\sim
0.14$) is the only BGE that can potentially be similar to the Class D galaxies
in Naab et al. (2014).

These anti-correlations between $h_{3}$ and $V/\sigma$ ($\xi_{3}<-3$) are
typically found in remnants of gas-rich mergers (Bendo & Barnes, 2000;
González-García et al., 2006; Jesseit et al., 2007; Naab et al., 2007; Hoffman
et al., 2009; Röttgers et al., 2014) or in simulations without strong AGN
feedback (e.g. Dubois et al. 2016; Frigo et al. 2019). However, it should be
kept in mind that the predictions of simulations regarding AGN feedback
strongly depend on the particular models adopted by the simulations (Naab &
Ostriker, 2017), as well as other limiting factors e.g. the resolution of the
simulations.

####  5.1.2 Galaxy shapes

We find that all 10 of our fast rotators are consistent with an oblate shape.
Three slow-rotating galaxies show “prolate-like" rotation, although the
uncertainties on the kinematic position angle are large for the slow rotators.
Four of the other slow rotators can be classified as triaxial, and one as
oblate.

Simulations suggest galaxy shape depends on merger history, specifically the
configuration of the most recent merger (Jesseit et al., 2009; Taranu et al.,
2013; Moody et al., 2014; Bassett & Foster, 2019; Lagos et al., 2022b). In
particular, slow rotators are star-bursting disks at high redshift (Dekel et
al., 2009; Kereš et al., 2009), but the late evolution is dominated by dry
mergers (De Lucia & Blaizot, 2007; Kaviraj et al., 2015). This implies the
creation of triaxial or prolate-like systems (Krajnović et al., 2018). Ebrová
& Łokas (2017) identified a few examples of other possible formation channels,
but basically, all massive prolate (slow) rotators were created in major
mergers during the last 6 Gyr in the Illustris simulation. Other cosmological
simulations also agree that many massive galaxies are prolate-like, slow-
rotating and formed by major mergers with radial orbits (Li et al., 2018a;
Schulze et al., 2018). This is broadly consistent with observations that
kinematic misalignment between photometry and kinematics only happens in slow
rotators, and that slow rotators are prevalent above a characteristic stellar
mass of 2 $\times 10^{11}$ M☉ (Krajnović et al., 2011; Emsellem et al., 2011;
Cappellari et al., 2013; Li et al., 2018b). In particular, a late ($z<1$) dry
major merger seems to be essential to lower the angular momentum and create
the prolate-like rotation. Irrespective of earlier mergers, the last major
merger is the main trigger for the prolate shape (Li et al., 2018a; Lagos et
al., 2018; Schulze et al., 2018; Pillepich et al., 2019; Frigo et al., 2019;
Pulsoni et al., 2020).

####  5.1.3 Misalignment between gas and stars

We indicate whether the stars and ionised gas kinematics are aligned (3/15),
misaligned (8/15) or counter-rotating (4/15) in Table 3. In general, galaxies
can increase their gas supply through either internal or external processes.
For BGEs, internal processes can include stellar mass loss in which case one
can expect the resulting gas to have the same dynamics as the stars. External
accretion of gas can come from accretion of cold gas (e.g. Serra et al. 2014),
hot gas from the outer X-ray halo that cools down (Lagos et al., 2015), or
accretion from gas-rich mergers or interactions. In the case of external
accretion, the cold gas and the ionised gas may have angular momentum that is
misaligned with the stellar kinematics.

A complicating factor is the time-scale for the gas and stars to (re)align.
Raouf et al. (2021) investigate the stellar and gas kinematics of SAMI central
group galaxies to evaluate the role of group dynamical states. Their results
suggest that the gas accreted following a merger would settle (i.e. the gas
relaxation) in a way that its rotation axis is aligned with that of the
stellar component (co-rotating or counter-rotating) on a time-scale equal or
shorter than the time since the last major merger, otherwise the gas rotation
axis would deviate from that of the stars. However, this lifetime of
misalignment is also dependent on physical properties of the galaxies (e.g.
morphology and gas fraction), as shown in the analysis of Horizon-AGN
simulated galaxies by Khim et al. (2021).

###  5.2 Merger histories from multi-wavelength data

It is widely accepted that fast and slow rotators follow the gas-rich, gas-
poor merger evolutionary path. The question is whether this is supported by,
or contradictory to, the evolutionary paths inferred from the well-studied
radio, X-ray and cold gas properties of these BGEs. We show the main, very
diverse, properties from previous studies of the 18 BGEs in Table 3, and
briefly discuss how they relate to merger histories below.

#### Radio properties

In summary, 10/18 galaxies show point-like emission, 3/18 diffuse (extended
and amorphous) emission, 2/18 with large-scale and 2/18 with small-scale jet
radio morphologies from their 610 and 235 MHz observations (Kolokythas et al.,
2019). The four radio jet sources in the sample are all slow rotators. NGC 193
and NGC 4261 are two of the most radio-luminous AGNs in the CLoGS BGE sample
(Kolokythas et al., 2018, 2019).

#### X-ray properties

In our sample, 10/18 galaxies show group, 2/18 galaxy-like, and 3/18 point-
like morphology for the hot gas component from 0.3–2.0 keV XMM-Newton and
Chandra X-ray observations (O’Sullivan et al., 2017). The X-ray properties of
the slow rotators are fairly consistent. Ten of our 18 galaxies have group-
scale X-ray halos, of which seven are slow rotators. This is not unexpected if
both properties are more likely to be found in higher mass systems. The only
slow rotator that does not have a large X-ray halo is ESO 507-G025777If we use
the approximate correction on $\lambda_{e}$ for the effects of inclination
($\lambda_{e}/\sqrt{\epsilon}$, see Section 3.2.3), then ESO 507-G025 is
classified as a fast rotator..

Studying the thermodynamical properties of the X-ray atmospheres, Olivares et
al. (2022) find that the filamentary structures and compact disks (the
morphology of the ionised gas) are found in systems with small central entropy
values, short $t_{\rm cool}/t_{\rm ff}$ and $t_{\rm cool}/t_{\rm eddy}$ ratios
(NGC 193, NGC 410, NGC 677, NGC 777, NGC 978, NGC 1060, NGC 1587, NGC 4008,
NGC 4261, NGC 5846, NGC 7619). They suggest that these ionised gas features,
and the associated cold gas, are possibly formed from hot halo gas
condensations via thermal instabilities.

In Table 3, we also indicate the core-type classification of the groups as
cool-core/non-cool-core (CC/NCC) based on their temperature profiles
(O’Sullivan et al., 2017). The classification is not available for ESO
507-G025, but all the slow rotators except NGC 777 are hosted by CC groups. In
particular, all the slow rotators with cold gas are in CC groups (except ESO
507-G025 which has no hot gas component).

#### Cold gas detections

The majority (7) of the 10 fast rotators contain cold gas, whereas half (4/8)
of the slow rotators also contain cold gas (O’Sullivan et al., 2015;
O’Sullivan et al., 2018). The presence of cold gas in both kinematic classes
suggest different origins for the cold gas i.e. deposited during gas-rich
mergers or tidal interactions (fast rotators), or cooling from the intra-group
medium (IGrM, slow rotators). It should be noted that some BGEs that lack cold
gas detections do have ionised gas (H$\alpha$) detections (Olivares et al.,
2022; Lagos et al., 2022a), albeit less bright than the H$\alpha$ in the BGEs
with detected cold gas, and deeper observations might reveal some cold gas in
these BGEs.

#### Morphology

Some studies report evolutionary differences between S0s and Es in groups
(Wilman et al., 2009; Bekki & Couch, 2011; Deeley et al., 2021). We use the
morphological t-type parameter from the HyperLEDA catalog (see Makarov et al.
2014), and we indicate the apparent E or S0 morphology for our BGEs in Table
3.

If we consider this morphological classification of the fast and slow-rotating
BGEs, most of the BGEs classified as S0 are fast rotators, but two are slow
rotators (NGC 1060 and ESO 507-G025, although the latter can also be
classified as a fast rotator when inclination effects are taken into account).
In general, most S0s are fast rotators (e.g. ATLAS3D, Emsellem et al. 2011),
but slow rotating S0s can be formed through a disruptive merger event
(Querejeta et al., 2015; Deeley et al., 2021). However, the separation between
E and S0 morphologies can be problematic and ill-defined due to, e.g. non-
homogeneity in the classification process from different data collected in
databases, and effects of inclination. Indeed three of the seven S0 galaxies
are classified as E/S0. Therefore when connecting our BGEs to different
formation scenarios, we use the kinematic classification (fast vs slow
rotators), rather than the morphological classification (E vs S0).

#### Star forming rings

Previous studies suggest that H$\alpha$ rings are formed from an infall of
fresh gas (Mapelli et al., 2015). The ROMULUS simulation analysis of
specifically brightest group galaxies by Jung et al. (2022) highlights a case
study where a star formation ring can be seen 1.5 – 2 Gyr after a gas-rich
merger. We observe star formation rings in 4/18 BGEs (see Lagos et al. 2022a,
and Olivares et al. 2022) as also indicated in Table 3 (three are fast
rotators, and ESO 507-G025 is a slow rotator that can also be classified as a
fast rotator when inclination is taken into account). Point-like morphology in
X-ray for the hot gas component is found in three of our BGEs with H$\alpha$
rings (NGC 924, NGC 940, and NGC 4169), whereas ESO 507-G025 has no hot gas
component, potentially indicating that the cold gas is more likely to be the
result of gas-rich mergers or tidal interactions instead of cooling from a hot
IGrM.

#### FUV star formation rate

Six (of 47 with FUV available) of all the CLoGS BGEs are found to be bluer
than [FUV - Ks] = 8.8, and were therefore classified as star forming by
Kolokythas et al. (2022). Of the overlap with this study, two of these star-
forming BGEs are fast rotators (NGC 924 and NGC 940) and one is a slow rotator
(ESO 507-G025) that can also be classified as a fast rotator when inclination
is taken into account. The rest of our fast and slow rotators are not star
forming according to their classification (although NGC 4169 and 6658 are
unknown as their FUV photometry is unavailable).

The fact that the three star forming BGEs (NGC 924, NGC 940, and ESO 507-G025)
occupy X-ray faint systems suggest that the cold gas is unlikely to have
cooled from the hot IGrM, but was acquired through gas-rich mergers or tidal
interactions instead.

Considering all of the above, we discuss the classes of fast and slow rotating
BGEs separately below, indicating any inconsistencies between different
observations.

Table 3: Main BGE or host group properties from previous multi-wavelength studies (O’Sullivan et al., 2015; O’Sullivan et al., 2017, 2018; Kolokythas et al., 2018, 2019). Non-detections are indicated with a dash. The Richness (R) parameter refers to the richness of the group (see O’Sullivan et al. 2017), and M∗ is described in Section 3.2.3. We indicate the core-type classification of the groups as cool-core/non-cool-core (CC/NCC) based on their temperature profiles (O’Sullivan et al., 2017), and entries in brackets indicate the groups where only a projected temperature profile with <3 bins is available. The SFRFUV is from Kolokythas et al. (2022). The four BGEs with star forming (H$\alpha$) rings is from Olivares et al. (2022) and Lagos et al. (2022a), and their names are indicated in bold text. The column entitled “F or D” indicates whether the ionised gas has a filamentary (F) or disc (D) morphology (Olivares et al., 2022). We also indicate gas and stellar kinematic alignment (Aligned, Misaligned, or Counter-rotating) as described in Section 4.3. Name | E/S0 | R | M∗ | X-ray | Core | Radio | Cold gas | SFRFUV | F | gas vs stars
---|---|---|---|---|---|---|---|---|---|---
|  |  |  $\times 10^{11}$ M☉ | Hot gas |  |  |  | (M☉ yr-1) | or D | kinematics
Fast rotators
NGC 584 | E | 4 | 1.31 | none | – | point | HI | 0.018 | F | Misaligned (30.5$\degr$)
NGC 924 | S0 | 3 | 1.52 | – | – | point | CO+HI | 0.152 | D | Aligned
NGC 940 | S0 | 3 | 2.43 | point | – | point | CO+HI | 0.195 | D | Aligned
NGC 978 | E/S0 | 7 | 1.79 | galaxy | (NCC) | point | – | 0.045 | D | Aligned
NGC 1453 | E | 4 | 4.64 | GROUP | NCC | point | HI | 0.058 | D | Misaligned
NGC 1587 | E | 4 | 2.88 | GROUP | NCC | diffuse | CO+HI | 0.038 | F | Misaligned
NGC 4008 | E | 4 | 1.85 | galaxy | (NCC) | point | – | 0.020 | F | Counter-rotating
NGC 4169 | S0 | 4 | 1.59 | point | – | point | CO+HI | – | D | Counter-rotating
NGC 6658 | S0 | 4 | 1.35 | point | – | – | – | – | – | –
NGC 7619 | E | 8 | 3.83 | GROUP | CC | point | HI | 0.058 | F | Misaligned (37.5$\degr$)
Slow rotators
ESO 507-G025 | E/S0 | 4 | 2.15 | – | – | diffuse | CO+HI | 0.221 | D | Misaligned
NGC 193 | E | 7 | 2.02 | GROUP | CC | jet/large | – | 0.047 | F | Counter-rotating
NGC 410 | E | 6 | 6.23 | GROUP | CC | point | – | 0.117 | F | Counter-rotating
NGC 677 | E | 7 | 2.53 | GROUP | CC | diffuse | HI | 0.068 | F | –
NGC 777 | E | 5 | 5.35 | GROUP | NCC | point | – | 0.134 | F | –
NGC 1060 | E/S0 | 8 | 7.71 | GROUP | CC | jet/small | – | 0.097 | F | Misaligned
NGC 4261 | E | 7 | 4.64 | GROUP | CC | jet/large | CO | 0.092 | D | Misaligned
NGC 5846 | E | 5 | 3.22 | GROUP | CC | jet/small | CO | 0.057 | F | Misaligned

####  5.2.1 Fast rotators

NGC 584: This target belongs to an X-ray faint group, indicating that the cold
gas is unlikely to be the product of cooling from a hot IGrM, but acquired
through gas-rich mergers or tidal interactions instead. This is consistent
with our stellar kinematics, in that the BGE is classified as a fast rotator,
and the misalignment between the stellar and gas kinematics suggests external
accretion of gas.

NGC 924: The BGE is detected in HI and CO, with a high cold gas mass, and the
HI line profile is suggestive of a disk. Point-like morphology in both radio
and X-ray (hot gas) potentially indicates that the cold gas is more likely to
be the result of gas-rich mergers or tidal interactions instead of cooling
from a hot IGrM. This is consistent with our fast rotator classification. The
star forming ring for this galaxy also indicates a merger event. This is also
consistent with the star formation detected in FUV. The stellar and ionised
gas kinematics alignment suggest a merger in an earlier epoch.

NGC 940: The BGE is one of the most cold gas (H2 as well as CO) rich BGEs in
CLoGS. It is also HI-rich and highly FIR-luminous for an early-type galaxy.
The HI and H2 line profiles in NGC 940 are suggestive of a disk, and it has a
large fraction of dense gas in the disk (O’Sullivan et al., 2018). Again, the
point-like morphology in both radio and X-ray (hot gas) potentially indicate
that the cold gas is more likely to be the result of gas-rich mergers or tidal
interactions instead of cooling from a hot IGrM. This is also in agreement
with our fast rotator classification. The star forming ring for this galaxy
also indicates a merger event. This is also consistent with the star formation
detected in FUV. The BGE is classified as an intermediate disk according to
its WISE colours (Jarrett et al., 2019; Kolokythas et al., 2022). Similar to
NGC 924, the stellar and gas kinematics alignment suggest a merger in an
earlier epoch.

NGC 978: No cold gas was detected for this BGE, and it is hosted by a NCC
group. It is a fast-rotating BGE, and the aligned stellar and gas kinematics
suggest a merger in an earlier epoch.

NGC 1453: Even though this target is hosted by an X-ray bright group, the NCC
status of the group makes is unlikely that the cold gas originated from IGrM
cooling. This is consistent with the stellar kinematics (fast rotation, and
misalignment) which point towards a recent gas-rich merger origin.

NGC 1587: Similar to NGC 1453, this is hosted by an X-ray bright but NCC
group, making it unlikely that the cold gas originated from IGrM cooling.
Again this is consistent with the stellar kinematics (fast rotation, and
misalignment) which point towards a recent gas-rich merger origin.

NGC 4008: No cold gas was detected in this BGE. Stellar kinematics suggest a
gas-rich merger (fast rotation), with the merger possibly occurring in earlier
epoch (stellar and gas kinematically aligned).

NGC 4169: The point-like morphology in both radio and X-ray (hot gas)
indicates that the cold gas is more likely to be the result of gas-rich
mergers or tidal interactions instead of cooling from a hot IGrM. This is also
consistent with our fast rotator classification. The H$\alpha$ ring for this
galaxy also indicates a merger event. O’Sullivan et al. (2015); O’Sullivan et
al. (2018) finds NGC 4169 to be one of only two (out of 53) BGEs consistent
with the far-infrared version of the star formation main sequence. The stellar
and gas kinematics alignment suggest a merger in an earlier epoch.

NGC 6658: No cold gas was detected for this BGE. It is a fast rotating BGE,
suggesting a gas-rich merger.

NGC 7619: This target is also hosted by an X-ray bright group, and the only CC
group among the fast rotators with core-type classification available, making
it plausible that the cold gas could originate from IGrM cooling. However, the
stellar kinematics (fast rotation, and misalignment) point towards a recent
gas-rich merger. Cold gas from the IGrM, and from interaction with companions
do not necessarily have to be mutually exclusive.

Given the complexity of the processes that take place in the centres of
groups, we find very consistent merger histories inferred from different
observational evidence for the fast-rotating BGEs. The possible exception is
the three fast-rotating BGEs with star formation rings, where the rings may
indicate a recent/ongoing transformation, yet the stellar and ionised gas
kinematics are aligned. However, Bryant et al. (2019) argue that not all
externally accreted gas must necessarily accrete with an angular momentum axis
misaligned to the stars, and equally, not all misaligned gas is necessary
recently accreted because gas can form stable misaligned orbits.

For NGC 7619, hosted by a group where the thermodynamic properties are
conducive to cooling from the IGrM, cold gas contribution from external
sources (such as galaxy satellite interactions or gas-rich mergers) can not be
discarded (see also discussion in Olivares et al. 2022). Overall, the
observation evidence seem consistent that the fast-rotating BGEs experienced
gas-rich mergers, and these are very likely the origin of the cold gas as
well.

####  5.2.2 Slow rotators

ESO 507-G025: ESO 507-G025 has a relatively rich gas disk, and is the only
slow rotator with a star forming ring (Lagos et al., 2022a; Olivares et al.,
2022). ESO 507-G025 is detected in CO and is the HI-richest BGE in the CLoGS
sample, with a double-peaked line profile indicative of a rotating disk. ESO
507-G025 is also a relatively FIR-luminous galaxy, and actively star forming
from FUV photometry (see discussion in Kolokythas et al. 2022). It is hosted
by an X-ray faint group, indicating that the cold gas is unlikely to be the
product of cooling from a hot IGrM. It is likely that this BGE is incorrectly
classified as a slow rotator, e.g. a disky/oblate galaxy that is close to
face-on that appears to be a slow rotator simply because most of the
rotational motions are in the plane of the sky, and that it gained some star
formation after a gas-rich merger (as also suggested by the star forming
ring). If we use the approximate correction on $\lambda_{e}$ for the effects
of inclination ($\lambda_{e}/\sqrt{\epsilon}$, see Section 3.2.3), then this
BGE is indeed classified as a fast rotator, consistent with all the other
observed properties.

NGC 193: No cold gas was detected. It is hosted by an X-ray bright group, and
has strong radio jets (that are misaligned with the rotation axis of the
stars). Its slow rotator classification indicates a gas-poor merger, while the
aligned stellar and gas kinematics possibly indicates an earlier merger.

NGC 410: No cold gas was detected, even though it is hosted by an X-ray bright
(and CC) group, and IGrM cooling could have been possible. Its slow rotator
classification indicates a gas-poor merger, while the aligned stellar and gas
kinematics indicates an earlier merger.

NGC 677: The X-ray brightness and thermodynamic properties indicate that the
cold gas likely cooled from the IGrM. This is consistent with the slow rotator
classification indicating a gas-poor merger.

NGC 777: No cold gas was detected, even though it is hosted by an X-ray bright
group, it is a NCC group. The slow rotator classification suggests a gas-poor
merger, consistent with the absence of gas.

NGC 1060: It is hosted by an X-ray bright group, and has radio jets (that are
misaligned with the rotation axis of the stars), and no cold gas was detected.
Misalignment of the stellar and ionised gas kinematics suggests a recent
merger.

NGC 4261: It is hosted by an X-ray bright (and CC) group, with very strong
radio jets (that are misaligned with the rotation axis of the stars). IGrM
cooling is likely responsible for the cold gas (also see O’Sullivan et al.
2011). This BGE has a recent ALMA detection of a sub-kiloparsec scale CO disk
(Boizelle et al., 2021). At the edge of the Virgo cluster, the BGE also has
dust lanes along the major axis (Moellenhoff & Bender, 1987; Mahabal et al.,
1996), a disk of cool gas surrounding the nucleus (Jaffe et al., 1993), and
disturbed outer isophotes (Bílek et al., 2020; Ebrová et al., 2021). The slow
rotator classification, as well as the misalignment between the stars and the
gas, indicates a possible late, gas-poor merger.

NGC 5846: It is hosted an X-ray bright and CC group, with radio jets (that are
misaligned with the rotation axis of the stars). This BGE shows convincing
evidence that the molecular gas has cooled from the IGrM (Schellenberger et
al., 2020). The system hosts H$\alpha$ filaments resembling those in strong
cool-core galaxy clusters, with the molecular gas located within these
nebulae, with no sign of rotation or streaming motions (see discussion in
Kolokythas et al. 2022). This is consistent with its slow rotator
classification. There is some evidence that NGC 5846 experienced a recent
interaction with its companion, NGC 5846A, or other close companions in the
galaxy group (Mahdavi et al., 2005), as well as an increasing fraction of ex-
situ stars beyond 1$R_{e}$ (Davison et al., 2021). The stellar kinematics
(slow rotation and misalignment of stellar and ionised gas kinematics) suggest
that this was a dissipation-less and recent interaction.

In summary, ESO 507-G025 is most likely intrinsically a fast rotator,
classified as a slow rotator due to the effects of inclination. For the other
slow rotators with cold gas, all observational evidence point to cold gas
cooling from the IGrM.

##  6 Summary and Conclusions

We study 18 MUSE cubes of CLoGS brightest group ellipticals (BGEs) by
analysing the voronoi-binned kinematic maps ($V,\sigma,h_{3},h_{4},\lambda$).
We measure $\lambda_{e}$, a proxy for galaxy specific stellar angular momentum
within one effective radius, and use it to classify the BGEs as fast or slow
rotators. We quantify the anti-correlation between higher-order kinematic
moment $h_{3}$ with V/$\sigma$ (using the $\xi_{3}$ parameter), and the
kinematic misalignment angle between the photometric and kinematic position
angles (using the $\Psi$ parameter). We discuss predictions from simulations
to discern the intrinsic shapes of the galaxies and their possible merger
histories. Finally, we place the results into context by combining it with
known multi-wavelength properties of the BGEs and host groups. We summarise
our findings below:

  1. 1.

Through visual inspection, we classify the majority (10/18) of our BGEs as
regular rotators (RR), and 8/18 BGEs as non-regular rotators (NRR), in Table
2. Using the spin parameter ($\lambda_{e}$), we also classify our BGEs as fast
or slow rotators, and we find a one-to-one correspondence between the
quantitative classification of slow/fast rotator and the qualitative
classification of the kinematic morphology (non-regular/regular rotator). The
standard interpretation of this bimodality is that the slow rotator galaxies
experience a number of gas-poor mergers that effectively decrease their
angular momentum, while for fast rotators gas accretion and gas-rich mergers
tend to preserve the angular momentum, e.g. Naab et al. (2014).

  2. 2.

All our slow rotators are above the characteristic stellar mass of 2 $\times
10^{11}$ M☉, and our results agree with the known result from large samples
that the fraction of fast-rotating galaxies decreases towards higher stellar
mass. Indeed predictions from cosmological simulations show that slow rotators
are produced in merger(s), a process that occurs at all stellar masses, but it
is most efficient in transforming galaxies into slow rotators if the merger is
dry, which is more likely at higher masses (Naab et al., 2014; Rodriguez-Gomez
et al., 2016; Penoyre et al., 2017; Schulze et al., 2018; Lagos et al., 2018;
van de Sande et al., 2019; Walo-Martín et al., 2020).

  3. 3.

We quantify the Gauss-Hermite third moment ($h_{3}$) versus V/$\sigma$ anti-
correlation with the $\xi_{3}$ parameter. From Figure 10, we can see a clear
difference between the $\xi_{3}$ distributions of the fast and slow-rotating
BGEs, but large variations between individual fast-rotating galaxies. These
anti-correlations between $h_{3}$ and $V/\sigma$ (where $\xi_{3}<-3$ for fast
rotators) are typically found in remnants of gas-rich mergers (Naab et al.,
2014).

  4. 4.

We find that all 10 of our fast rotators are aligned between the morphological
and kinematical axis ($\Psi<15\degr$), consistent with an oblate shape. Three
galaxies, NGC 193, NGC 677, and NGC 1060 show $\Psi>75\degr$ (“minor axis" or
“prolate-like" rotation) although the uncertainties on the kinematic position
angle are large for the slow rotators. Four of the other slow rotators can be
classified as triaxial, and one as oblate.

  5. 5.

Using ionised gas kinematic position angles from Olivares et al. (2022), we
also derive the misalignment between the gas and stellar kinematics. We find
that 3/15 BGEs are aligned ($\Psi_{\rm gas}<30\degr$), 8/15 are misaligned
($30\degr<\Psi_{\rm gas}<150\degr$), and 4/15 can be considered to be aligned
but counter-rotating ($150\degr<\Psi_{\rm gas}<180\degr$). This misalignment
does not correspond to classifications of slow and fast rotators, but is
rather an indication of the time-scale since gas accretion.

  6. 6.

Seven (out of eight) of our slow rotators are among the 10/18 galaxies that
have group-scale X-ray halos. Both properties are more likely to be found in
higher mass systems. We find that the four radio jet sources in the sample are
all slow rotators.

  7. 7.

The majority (7) of the 10 fast rotators contain cold gas, whereas half (4/8)
of the slow rotators also contain cold gas (O’Sullivan et al., 2018). The
presence of cold gas in both classes suggest different origins for the cold
gas i.e. deposited during gas-rich mergers or tidal interactions (fast
rotators), or cooling from the IGrM (slow rotators).

The different observational evidence seem consistent that the fast-rotating
BGEs experienced gas-rich mergers or interactions, and these are very likely
the origin of the cold gas rather than cooling from the IGrM (with the
exception of NGC 7619, where it can be both). For the slow rotators with cold
gas, all observational evidence point to cold gas cooling from the IGrM.

Even though we find fairly consistent merger histories inferred from different
observational evidence for the BGEs, we caution that some properties (e.g.
morphology, misalignment between gas and stars, or even fast/slow rotation)
can not be considered in isolation to infer an evolutionary path, particularly
for complex cases such as brightest group galaxies.

## Acknowledgements

We thank the reviewer, Eric Emsellem, for his thorough and constructive
comments, and suggestions that improved the paper.

This work is based on the research supported in part by the National Research
Foundation of South Africa (NRF Grant Number: 120850). PL is supported in the
form of work contract (DL 57/2016/CP1364/CT0010) funded by national funds
through Fundação para a Ciência e Tecnologia (FCT). AB acknowledges support
from NSERC (Canada) through the Discovery Grant program. E.O’S. acknowledges
support from NASA through XMM-Newton award 80NSSC19K1056.

This research made use of Astropy,888http://www.astropy.org a community-
developed core Python package for Astronomy (Astropy Collaboration et al.,
2013, 2018), GIST999https://abittner.gitlab.io/thegistpipeline (Bittner et
al., 2019), the Voronoi-binning method (Cappellari & Copin, 2003), the
Penalized Pixel-Fitting (pPXF) method (Cappellari & Emsellem, 2004;
Cappellari, 2017) and fit_kinematic_pa101010All available at https://www-
astro.physics.ox.ac.uk/$\sim$mxc/software/ (Krajnović et al., 2006). Based, in
part, on observations obtained using MUSE (program ID 097.A-0366(A)).

Additionally, SLJ acknowledges the Ngunnawal and Ngambri people as the
traditional owners and ongoing custodians of the land on which the Research
School of Astronomy $\&$ Astrophysics is sited at Mt Stromlo. Similarly, AB
acknowledges the leḱwenen peoples on whose traditional territory the
University of Victoria stands, and the Songhees, Equimalt and W̱SÁNEĆ peoples
whose historical relationships with the land continue to this day.

Any opinion, finding and conclusion or recommendation expressed in this
material is that of the author(s) and the NRF does not accept any liability in
this regard.

## Data availability

The data underlying this article will be shared on reasonable request to the
corresponding author. The MUSE data underlying this article are available in
the ESO science archive facility111111http://archive.eso.org/cms.html (program
ID 097.A-0366(A)).

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##  Appendix A Comparison to MASSIVE

We have NGC 410, NGC 777 and NGC 1060 in common with the MASSIVE sample of Ma
et al. (2014), and we compare our measurements in Table 4. We note that the
spin parameter $\lambda_{e}$ measurements were made in circular apertures in
MASSIVE (Veale et al., 2017b), whereas our measurements are in elliptical
apertures. The misalignment angle (Mitchell data) $\Psi_{\rm Mitchell}$ is
main-body misalignment, whereas the misalignment angle (GMOS data) $\Psi_{\rm
GMOS}$ is just central misalignment (see Ene et al. 2020). For two galaxies
(NGC 410 and NGC 777), the central kinematic axis is well aligned with the
photometric axis, but the main-body kinematic axis is not. In general, we find
very good agreement with the previous measurements.

Table 4: Comparison with galaxies in common with the MASSIVE sample (Ma et al., 2014). $R_{e}$ (in arcsec, from 2MASS) are from Ma et al. (2014), and MK is the extinction-corrected total absolute $K$-band magnitude, also from Ma et al. (2014). PAphot is the photometric position angle in degrees East of North from Veale et al. (2017a). Slow/fast rotator classifications is from Veale et al. (2017b). The average $\langle h_{4}\rangle$ within $R_{e}$ is from Veale et al. (2018). The spin parameter $\lambda_{e}$ (unfolded) within $R_{e}$, PAkin,Mitchell and $\Psi_{\rm Mitchell}$ are from Ene et al. (2018). PAkin,GMOS and $\Psi_{\rm GMOS}$ are from Ene et al. (2020). |  | NGC 410 | NGC 777 | NGC 1060
---|---|---|---|---
|  | (MASSIVE) | (This study) | (MASSIVE) | (This study) | (MASSIVE) | (This study)
$R_{e}$ | (arcsec) | 16.8 | 16.77 | 14.6 | 14.57 | 16.8 | 16.76
MK | (mag) | –25.90 | –25.76 $\pm$ 0.02 | –25.94 | –25.61 $\pm$ 0.02 | –26.00 | –25.97 $\pm$ 0.02
PAphot | (deg) | 34.9 | 40.0 $\pm$ 3.0 | 148.4 | 145.0 $\pm$ 3.0 | 74.0 | 70.0 $\pm$ 3.0
$\langle h_{4}\rangle$ |  | 0.041 | 0.065 | 0.051 | 0.078 | 0.055 | 0.065
$\lambda_{e}$ (unfolded) |  | 0.048 | 0.046 | 0.060 | 0.064 | 0.048 | 0.039
Rotation |  | Slow rotator | Slow rotator | Slow rotator | Slow rotator | Slow rotator | Slow rotator
PAkin,Mitchell | (deg) | $161\pm 19$ | $\downarrow$ | $8.0\pm 10.0$ | $\downarrow$ | $342.0\pm 13.5$ | $\downarrow$
PAkin,GMOS | (deg) | $211\pm 9$ | 189.1 $\pm$ 20.0 | $311\pm 22$ | 329.1 $\pm$ 20.9 | $351\pm 10$ | 343.6 $\pm$ 23.6
$\Psi_{\rm Mitchell}$ | (deg) | 53.9 | $\downarrow$ | 39.6 | $\downarrow$ | 88.0 | $\downarrow$
$\Psi_{\rm GMOS}$ | (deg) | $4.8\pm 9.3$ | 30.9 $\pm$ 20.2 | $18.1\pm 21.5$ | 4.1 $\pm$ 21.1 | $83.8\pm 10.0$ | 86.4 $\pm$ 23.8

##  Appendix B Kinematics maps

We show the kinematic maps ($\sigma,h_{3},h_{4},\lambda$) for ESO 507-G025 as
an example in Figure 12. The kinematics maps for the other 17 BGEs are
included as supplementary information.

Figure 12: ESO 507-G025 maps of kinematic measurements (velocity dispersion
$\sigma$, Gauss-Hermite third moment $h_{3}$, Gauss-Hermite third moment
$h_{4}$, and angular momentum $\lambda$). The spatial scale is in arcseconds.