# Complex Velocity Structure of Nebular Gas in Active Galaxies Centred in
Cooling X-ray Atmospheres

Marie-Joëlle Gingras  Department of Physics and Astronomy, University of
Waterloo, Waterloo, ON N2L 3G1, Canada  Waterloo Centre for Astrophysics,
Waterloo, ON N2L 3G1, Canada  Alison L. Coil  Department of Astronomy and
Astrophysics, University of California, San Diego, La Jolla, CA 92093, USA
B.R. McNamara  Department of Physics and Astronomy, University of Waterloo,
Waterloo, ON N2L 3G1, Canada  Waterloo Centre for Astrophysics, Waterloo, ON
N2L 3G1, Canada  Serena Perrotta  Department of Astronomy and Astrophysics,
University of California, San Diego, La Jolla, CA 92093, USA  Fabrizio
Brighenti  Dipartimento di Fisica e Astronomia, Universitá di Bologna, Via
Gobetti 93/2, 40122, Bologna, Italy  H.R. Russell  School of Physics &
Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, UK
S. Peng Oh  Department of Physics, University of California, Santa Barbara,
Santa Barbara, CA 93106, USA

###### Abstract

[OII] emission maps obtained with the Keck Cosmic Web Imager (KCWI) are
presented for four galaxies lying at the centers of cooling X-ray cluster
atmospheres. Nebular emission reaching altitudes of tens of kpc is found in
systems covering a broad range of atmospheric cooling rates, cluster masses,
and dynamical states. The central galaxy in Abell 262 hosts high angular
momentum gas in a kpc-scale disk. The nebular gas in RXJ0820.9+0752 is offset
and redshifted with respect to the central galaxy by $10-20$ kpc and
$150\rm~{}km~{}s^{-1}$, respectively. The nebular gas in PKS 0745-191 and
Abell 1835, both experiencing strong radio-mechanical feedback, is being
churned to higher velocity dispersion by the buoyantly rising bubbles and
jets. Churning gas flows, likely outflows behind the rising radio bubbles, are
likely driven by buoyancy and ram pressure due to the galaxies’ motion with
respect to the gas. The churned gas is enveloped by larger scale, lower
velocity dispersion quiescent nebular emission. The mean radial speeds of the
churned gas, quiescent gas, and the central galaxy each differ by up to $\sim
150~{}\rm km~{}s^{-1}$, although speeds upward of $800~{}\rm km~{}s^{-1}$ are
found. Nebular gas is dynamically complex due to feedback, motion of the
central galaxy, and perhaps relative motion of the hot atmosphere from which
it presumably condensed. These motions will affect thermally unstable cooling
models, the dispersal of jet energy, and the angular momentum of gas accreting
onto the galaxy and its nuclear black hole.

Nebular Emission, X-ray Clusters, RXJ0820.9+0752, PKS 0745-191, Abell 1835,
Abell 262

††software: Astropy (Astropy Collaboration et al., 2013, 2018, 2022), Python
(Van Rossum & Drake, 2009), Numpy (van der Walt et al., 2011; Harris et al.,
2020), Matplotlib (Hunter, 2007), Scipy (Virtanen et al., 2020),

##  1 Introduction

Clusters of galaxies host the largest and most luminous elliptical galaxies at
their centres. These galaxies are often referred to as Brightest Cluster
Galaxies (BCGs) or central dominant galaxies. They also lie at the bases of
hot, X-ray atmospheres with luminosities of 10${}^{43}-10^{45}$ erg s-1 and
temperatures between 107 to 108 K. Gas densities surrounding central galaxies
are often upwards of $10^{-2}$ cm-3. At these densities atmospheres are
expected to cool and condense into molecular clouds and form stars (Fabian,
1994; Cavagnolo et al., 2008; Rafferty et al., 2008). Star formation is
observed in central galaxies, as in the systems studied here; however, the
star formation rates are more than an order of magnitude lower than those
expected by unimpeded cooling (Fabian, 1994; Peterson & Fabian, 2006). This
discrepancy between cooling models and the products of cooling suggests that
one or more heating mechanisms are suppressing cooling.

Energetic feedback from active galactic nuclei (AGN) is a likely heating
mechanism due to the prevalence of radio jets with sufficient power to
compensate for radiative cooling losses (McNamara & Nulsen, 2007, 2012). AGN-
driven jets and radio lobes also displace $10^{7}$ to $10^{10}$ M⊙ of hot gas
surrounding them carving X-ray cavities or bubbles that rise buoyantly through
the atmosphere (Bîrzan et al., 2004; Rafferty et al., 2006; Pope et al.,
2010). Several processes including, enthalpy released by rising bubbles
(McNamara & Nulsen, 2007), turbulence (Scannapieco & Brüggen, 2008; Gaspari et
al., 2012), shocks (Heinz et al., 1998; David et al., 2001), sound waves
(Fabian et al., 2003; Ruszkowski et al., 2004a, b; Voit & Donahue, 2005;
Nulsen & McNamara, 2013) and cosmic rays (Ruszkowski et al., 2008; Guo & Oh,
2008; Mathews & Brighenti, 2008), contribute to the propagation and
thermalization of energy from AGN feedback throughout hot atmospheres (Donahue
& Voit, 2022).

A spectrum of gas phases is observed surrounding central galaxies including,
cold molecular gas with temperatures of a few tens of Kelvins (Edge, 2001;
Salomé & Combes, 2003), warm molecular gas with temperatures less than 400 K
(Johnstone et al., 2007), warm ionized nebular gas with $\sim 10^{4}$ K
temperatures, coronal gas at $10^{6}$ K (Canning et al., 2011), and hot
$10^{7}-10^{8}$ K X-ray emitting gas. The discovery of bright nebular line
emission surrounding galaxies and often extending tens of kpc into the bright
X-ray atmospheres was the earliest evidence of atmospheric cooling (Heckman,
1981; Hu et al., 1985; Heckman et al., 1989; Crawford et al., 1999; Hatch et
al., 2007; McDonald et al., 2010; Fabian & Nulsen, 1977). The brightest
systems are associated with $10^{9}-10^{11}~{}\rm M_{\odot}$ of molecular gas,
often associated with star formation at rates of tens of solar masses per year
(Rafferty et al., 2008; Fogarty et al., 2019; Russell et al., 2019; Olivares
et al., 2019).

Observations of gas cooling through all phases place strong constraints on
thermally unstable cooling models. Bright nebular emission and star formation
in central cluster galaxies and giant ellipticals are generally associated
with systems with atmospheric cooling times lying below 1 Gyr. Other cooling
indicators include central entropy lying below 30 keV cm2 (Cavagnolo et al.,
2008; Rafferty et al., 2008) and ratios of cooling time to free-fall time
(t${}_{\textrm{cool}}$/t${}_{\textrm{ff}}$) below $\sim 35$. These thresholds
are believed to be closely related to the onset of thermal instabilities
(Nulsen, 1986; Pizzolato & Soker, 2005; McCourt et al., 2012; Sharma et al.,
2012; Gaspari et al., 2012; Voit et al., 2015; McNamara et al., 2016; Hogan et
al., 2017; Pulido et al., 2018; Donahue & Voit, 2022).

Thermally unstable cooling from hot atmospheres fuels star formation and could
provide a continual fuel source to maintain the feedback cycle.

In addition to heating the atmosphere, buoyantly rising radio bubbles and jets
may enhance thermally unstable cooling by lifting cooling parcels of gas to
higher altitudes (Revaz et al., 2008; McNamara et al., 2016; Donahue & Voit,
2022). In this scenario, as X-ray cavities rise through the hot atmosphere,
they entrain low entropy gas from the center of the galaxy to higher
altitudes, mixing the gas and transporting high metallicity material outside
the cluster core (Churazov et al., 2001; Simionescu et al., 2009; Pope et al.,
2010; Kirkpatrick et al., 2011; Gitti et al., 2011). Uplift may accelerate
thermally unstable cooling by increasing the infall time of the gas, lowering
t${}_{\textrm{cool}}$/t${}_{\textrm{ff}}$ below the threshold required for
thermal instabilities to occur.

Observations of nebular emission are central to understanding: the conditions
under which thermally unstable cooling proceeds, the forms of ionization and
heating, and the relationships between cooling inflows and AGN-driven outflows
that regulate the growth of galaxies. While nebular emission is sensitive to a
negligible fraction of the cooling mass, its high surface brightness probes
the full extent of the unstable cooling region as well as the gas dynamics
with respect to the central galaxy and its radio jets and lobes. To
investigate the behaviour of the warm nebular gas in and around the central
galaxies and its connection to both multiphase gas and AGN feedback, we
undertook new observations of four cooling cluster cores with the Keck Cosmic
Web Imager (Morrissey et al., 2018, KCWI). The integral field spectroscopy
(IFS) capabilities of KCWI provide high sensitivity and spectral and spatial
resolution over a large field of view (FOV). From our observations, we obtain
detailed maps of the morphology and the kinematics of various emission lines,
such as [OII]3726,9 Å, [OIII]4959 Å, [OIII]5007 Å, Hβ, Hγ, [NeIII]3869 Å, and
of the central galaxy’s stellar population. Combined with previous studies and
archival observations from the Atacama Large Millimeter/submillimeter Array
(ALMA), Very Large Array (VLA) and Chandra X-ray Observatory, we study the
dynamics of different phases of the ICM and their interactions with the
central galaxy, radio jets and X-ray cavities.

In this paper we analyze IFS observations of the central regions of Abell
1835, PKS 0745-191, Abell 262 and RXJ0820.9+0752, focusing on the morphology
and the kinematics of the [OII]3726,9 Å emission line doublet. The [OII]3726,9
Å emission doublet is the brightest emission line in the KCWI data for these
targets. Its high contrast against the declining U-band stellar continuum
below the 4000 Å break adds sensitivity to the imagery. The high sensitivity
images presented here trace the nebular emission to larger radii than earlier
studies. Its relatively high spectral and spatial resolutions permit detailed
studies of nebular gas velocities with respect to stellar velocities in the
central galaxy. Our targets are part of a pilot program on Keck chosen for
their range of properties and their complex structures.

In Section 2 we provide a comprehensive account of our observations, data
reduction techniques, and fitting methodology. We also discuss the
complementary archival observations that are used throughout the paper and
describe the analysis of the complementary data. In Section 3 we present flux
and kinematic maps for each of our targets (Abell 1835: Section 3.1, PKS
0745-191: Section 3.2, Abell 262: Section 3.3, RXJ0820.9+0752: Section 3.4).
In Section 4, we discuss the implications of our results and compare them to
AGN feedback models. Finally, in Section 5, we summarize the key takeaways.
Throughout this paper we use a flat $\Lambda$CDM cosmology with H${}_{0}=70$
km s-1 Mpc-1 and $\Omega_{\textrm{m}}=0.3$.

##  2 Observations and data reduction

Table 1: Targets properties

Target | R.A. | Dec. | z | R2500 | M2500 | t${}_{\textrm{cool}}$ | L${}_{\text{x}}$ | r(L${}_{\text{x}}$) | L${}_{\text{\textrm{H}}_{\alpha}}$ | L${}_{\text{radio}}$ | M${}_{\text{mol}}$ | M∗ | SFR${}_{\text{IR}}$ | Cooling rate | # of X-ray cavities | $E_{cav}$ | $P_{cav}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) |  | (kpc) | ($10^{13}M_{\odot}$) | (Gyr) | (erg s-1) | (kpc) | (erg s-1) | (erg s-1) | (M⊙) | (M⊙) | (M⊙ yr-1) | (M⊙ yr-1) |  | ($10^{57}$erg) | ($10^{43}$erg s-1)
Abell 1835 | 14:01:02.1 | +02:52:43 | 0.2514 | 711 | $61.0_{-2.5}^{+2.5}$ | $0.39_{-0.03}^{+0.04}$ | $1.6\times 10^{44}$ | 20 | $1.7\times 10^{42}$ |  | $5\times 10^{10}$ | $6\times 10^{11}$ | $125\pm 25$ | 1175 | 2 | $156^{+62}_{-43}$ | $165^{+102}_{-55}$
PKS 0745-191 | 07:47:31.3 |  $-$19:17:40 | 0.1024 | 614 | $36.5_{-2.8}^{+2.9}$ | $0.35_{-0.02}^{+0.02}$ | $4\times 10^{43}$ | 14 | $1.75\times 10^{42}$ |  | $(4.6\pm 0.3)\times 10^{9}$ | $5\times 10^{11}$ | 17.2 | $776\pm 18$ | 2 | $69^{+29}_{-21}$ | $51_{-16}^{+25}$
Abell 262 | 01:52:46.5 | +36:09:07 | 0.0160 | 286 | $3.40_{-0.10}^{+0.10}$ | $0.37^{+0.02}_{-0.02}$ | $1.69\times 10^{41}$ | 3.5 | $3.16\times 10^{39}$ |  | $3.4\times 10^{8}$ | $3.3\times 10^{11}$ | 0.54 | $\sim 3$ | 2 | $2.5^{+1.0}_{-0.7}$ | $1.6^{+1.2}_{-0.6}$
RXJ0820.9+0752 | 08:21:02.3 | +07:51:47 | 0.1103 | 357 | $6.9_{-1.3}^{+1.4}$ | $0.42^{+0.04}_{-0.04}$ | $6.5\times 10^{42}$ | 15 | $4.00\times 10^{41}$ |  | $3.9\times 10^{10}$ | $1.4\times 10^{11}$ | 37 | $34\pm 10$ | 1 | $1.1^{+0.6}_{-0.4}$ | $1.1^{+0.9}_{-0.5}$

Note. — Columns: (1) Galaxy name. (2) Right ascension (RA). (3) Declination
(Dec). (4) Redshift obtained from stellar absorption lines. Heliocentric
correction has been applied. (5) $R_{2500}$, radius where the mean density is
2500 times the critical density ($\rho_{c}$). (6) $M_{2500}$, where
M${}_{2500}=4\pi\bar{\rho}\textrm{R}_{2500}^{3}/3$ and
$\bar{\rho}=2500\rho_{c}$. (7) Cooling time within $0.02R_{2500}$. (8) X-ray
luminosity within the radius listed in column 9. (9) Radius chosen for the
X-ray luminosity listed in the previous column such that it covers a similar
extent as the detected [OII] emission. (10) Hα luminosity. (11) Radio
luminosity between 10MHz and 5GHz. (12) Molecular gas mass. (13) Stellar mass.
(14) Star formation rate from infrared luminosity. (15) Cooling rate obtained
from X-ray (Chandra) observations. (16) Number of known X-ray cavities. (17)
Total energy required to inflate known X-ray cavities. (18) Total AGN power
required to inflate the cavities.

References: (5)-(9), (17)-(18): (Hogan et al., 2017; Pulido et al., 2018).
(10): (Crawford et al., 1999, Abell 1835, Abell 262), (Hamer et al., 2016, PKS
0745, RXJ0820.9). (11): (Pulido et al., 2018). (12): (McNamara et al., 2014,
Abell 1835), (Russell et al., 2016, PKS 0745), (Olivares et al., 2019, Abell
262), (Edge, 2001, RXJ0820.9). (13): (Olivares et al., 2019, Abell 1835,
RXJ0820.9), (Donahue et al., 2011, PKS 0745), (Main et al., 2017, Abell 262).
(14) (Egami et al., 2006, Abell 1835), (O’Dea et al., 2008, PKS 0745, Abell
262, RXJ0820.9). (15) (McDonald et al., 2018, Abell 1835, PKS 0745, Abell
262), (Vantyghem et al., 2018, RXJ0820.9). (16): (McNamara et al., 2006, Abell
1835), (Sanders et al., 2014; Russell et al., 2019, PKS 0745), (Clarke et al.,
2009, Abell 262), (Vantyghem et al., 2019, RXJ0820.9).

###  2.1 Observations

Our four cluster targets were observed with KCWI (Morrissey et al., 2018),
which is installed on the Keck II telescope. For all targets we used the blue
low-dispersion (BL) grating with the medium slicer, which results in a FOV of
$16.5~{}\arcsec\times 20.4~{}\arcsec$ for each pointing. It has a spaxel scale
of $0.29~{}\arcsec\times 0.69~{}\arcsec$, and a spectral resolution of $\rm
R=1800$. We used a detector binning of $2\times 2$ for all targets. Table 2
lists additional observational parameters for each target. The exposure time
for each pointing is between 15-20 minutes. The number of pointings and the
total area covered for each object were chosen based on published observations
of nebular gas extent and morphology, when available, to focus on regions of
interest. Abell 262 did not have a published nebular gas map, so we used the
cold molecular gas distribution instead. Previous observations of similar
clusters have shown that nebular gas and molecular gas distributions often
spatially overlap, with nebular emission being more extended than molecular
gas (Olivares et al., 2019; Russell et al., 2019).

Table 2: KCWI Observations

Target | Date | Central wavelength | Blue filter | # of pointings | Total observing time | Seeing | Total FOV | Total extent
---|---|---|---|---|---|---|---|---
| (DD/MM/YYYY) | (Å) |  |  | (hrs) | (″) | ($\arcsec\times\arcsec$) | ($\textrm{kpc}\times\textrm{kpc}$)
Abell 1835 | 19/03/2021 | 5300 | None | 6 | 2 | 0.8 | $35\times 33$ | $141\times 134$
PKS 0745-191 | 12/02/2021 | 4650 | KBlue | 11 | 3.67 | 1.2 | $26\times 31$ | $52\times 61$
Abell 262 | 14/01/2022 | 4300 | None | 10 | 2.5 | 0.9 | $30\times 32$ | $10\times 11$
RXJ0820.9+0752 | 14/01/2022 | 4650 | None | 9 | 2.25 | 0.9 | $21\times 24$ | $44\times 50$

Note. — Columns: (1) Target name. (2) Date of KCWI observation. (3) Central
wavelength. (4) Blue filter used. (5) Number of pointings. (6) Total observing
time. (7) Seeing. (8) Total FOV obtained from the different pointings in
arcseconds. (9) Same as previous column in units of kpc.

###  2.2 Data reduction

We reduced the data using the KCWI Data Extraction and Reduction Pipeline
(KDERP) in IDL. This pipeline applies various corrections, including bias
subtraction, gain corrections and cosmic-ray rejections, and executes sky
subtraction. We manually masked any source emission from our images to create
blank sky images which we subtracted from our observations. In cases where the
source covered the entire pointing such that obtaining a blank sky image was
not possible, we used the sky image of a nearby pointing. The pipeline also
corrects for differential refraction. To resample our data on a
$0.29\arcsec\times 0.29\arcsec$ spaxel grid and create a mosaic for each
target, we used the IFSR_KCWIRESAMPLE and IFSR_MOSAIC routines from the IFSRED
library (Rupke, 2014a). Table 2 lists the resulting dimensions of each mosaic.
As Abell 262 is at a much lower redshift than the other targets, a smaller
central region is observed ($\sim$100 kpc2), whereas for the other targets we
observed areas at least 25 times larger. On the other hand, the low redshift
of Abell 262 provides exquisite spatial resolution with spaxel sizes of less
than $0.1~{}\rm kpc\times 0.1~{}kpc$.

###  2.3 Stellar continuum and emission line fitting

From the reduced mosaics, we used the IFSFIT IDL library (Rupke, 2014b) to fit
the spectrum in each spaxel. This library uses the Penalized Pixel-Fitting
method (PPXF) (Cappellari & Emsellem, 2004) and MPFIT (Markwardt, 2009) to fit
the stellar continuum and the emission lines, respectively. The fitting
procedure followed five steps:

  1. 1.

Creating a spatially-integrated spectrum:
To obtain a high quality spectrum of the stellar component of the BCG, we
first summed the spectra in the spaxels with strong stellar continuum
emission.

  2. 2.

Spatially-integrated Stellar Population Synthesis (SPS) model:
Using IFSFIT on the spatially-integrated spectrum, we obtain a SPS best fit
model for the stellar continuum at the very center of the galaxy. First the
emission lines are masked from the spectrum, which is then fitted using the
PPXF method of Cappellari & Emsellem (2004). The fit is a linear combination
of SPS models from González Delgado et al. (2005) and Legendre polynomials.
The SPS models are allowed to vary in age, but their metallicity is fixed to
that of the Sun. The SPS models are then summed over all stellar templates to
obtain the stellar continuum model fit. A linear combination of Legendre
polynomials are used to account for issues in data reduction such as scattered
light, atmospheric effects, and/or residual features in the stellar continuum.
We used Legendre polynomials of order 15.

From this fit, we obtain the stellar velocity in the centermost region of the
galaxy, which is then used as the systemic velocity of the system.

  3. 3.

Fitting each spaxel:
For each spaxel, the emission lines are masked and the starlight spectrum is
fitted, using the same method as in the previous step. MPFIT (Markwardt, 2009)
is then used to fit the emission lines in the continuum-substracted spectrum.
Before fitting, the model line profiles are convolved with the spectral
resolution. Each emission line is fit with 1 or 2 Gaussian profiles, as
needed. All emission lines are fit simultaneously with the same number of
velocity components. The gaussian components of the different emission lines
are all tied in redshift and linewidth to those of the [OIII]5007 emission
line. Since the [OII]3726,9 Å doublet is not spectrally resolved, the flux
ratio of [OII]3729/3726 is fixed to 1.2, assuming an electron density of 400
cm-3 (Pradhan et al., 2006).

  4. 4.

Determining the number of emission line velocity components:
For each target, IFSFIT is run twice, allowing one or two Gaussian components
for the emission lines. If the addition of a second Gaussian component does
not improve the fit, a one component fit is returned. The two velocity
component fits were used when: a) the flux for each component is positive and
has a $\text{S/N}\geq 2$, b) both components have velocity dispersions of
$\sigma<500$ km s-1, c) the flux ratio of the components is less than 10, and
d) the addition of a second component significantly improves the fit. This
last criterion is evaluated using the Bayesian Information Criterion (BIC):

$\text{BIC}=\chi^{2}+k\text{ln}(n)$ (1)

where $k$ is the number of parameters ($k=3$ for 1 component and $k=6$ for 2
components) and $n$ is the number of data points. A second component is used
when the BIC of the two components fit is smaller than the BIC of the one
component fit. Finally, we assume that spaxels requiring two Gaussian
components should be spatially clustered together and not distributed randomly
across the mosaic. Two component fits are used when neighbouring spaxels also
use two component fits. Of the four galaxies observed, Abell 1835 and PKS 0745
have regions where the fits require a second component. Abell 262 and RXJ0820
can be modelled using only one kinematic component.

###  2.4 Archival observations

Complimentary archival observations are used to compare the properties of the
ionized gas in the intracluster medium (ICM) with other gas phases, as well as
to study the interactions between AGN feedback and gas dynamics. Table 1 lists
various properties of our targets obtained from multi-wavelength observations.

Table 3: ALMA observations Target | Date of observation | Observing time | CO line | $\nu_{\textrm{obs}}$ | Beam size | Reference
---|---|---|---|---|---|---
|  | (min) |  | (GHz) | $\arcsec\times\arcsec$ |
Abell 1835 | 2012-03-28 | 59.5 | J$=3-2$ | 276.190 | $0.60\times 0.48$ | McNamara et al. (2014)
PKS 0745-191 | 2014-08-19 | 56.4 | J$=3-2$ | 313.562 | $0.27\times 0.19$ | Russell et al. (2016)
Abell 262 | 2016-06-27 | 11.1 | J$=2-1$ | 226.863 | $0.95\times 0.61$ | Olivares et al. (2019)
RXJ0820.9+0752 | 2016-10-01 | 22.7 | J$=3-2$ | 311.248 | $0.21\times 0.165$ | Vantyghem et al. (2017)

Cold molecular gas maps showing CO emission were obtained from Atacama Large
Millimeter/submillimeter Array (ALMA) archival observations for all four
targets. Table 3 gives the details of the ALMA observations. Maps of the CO
fluxes were measured by integrating over the targeted CO emission lines. The
resulting CO contours are consistent with results from previous papers
(McNamara et al., 2014; Russell et al., 2016; Vantyghem et al., 2017; Russell
et al., 2019; Olivares et al., 2019; Vantyghem et al., 2019).

Detected X-ray bubbles are also shown in the maps presented here. As discussed
in Section 1, X-ray cavities are believed to play an important role in
determining ICM dynamics. Combining previous cavity detections (McNamara et
al., 2006; Rafferty et al., 2006; Sanders et al., 2014; Vantyghem et al.,
2019) with nebular gas flux and kinematics maps, we can study how cavities
impact nebular gas dynamics as well as investigate whether different AGN
feedback models are consistent with observations.

##  3 Results

Using KCWI integral field spectroscopy, we study the morphology and kinematics
of the warm ionized gas in four cooling cluster cores. While various emission
lines are detected, including [OII], [NeIII], and [OIII], the [OII]3726,9 Å
doublet is the most prominent line in our data and is therefore the focus of
this paper. The analysis of other emission lines will be the focus of a future
paper. For all flux and kinematics maps of the [OII]3726,9 Å doublet, a
$\textrm{S/N}\geq 5$ flux threshold per spaxel is applied.

Table 4: [OII]3726+[OII]3729 integrated luminosity

Target | L[OII] | $\textnormal{M}_{\textnormal{ion}}$ | Area [OII] | Area CO
---|---|---|---|---
| erg s-1 | M⊙ | kpc2 | kpc2
Abell 1835 | $4.0\times 10^{42}$ | $1.1\times 10^{8}$ | 1467 | 84
PKS 0745-191 | $4.6\times 10^{41}$ | $1.3\times 10^{7}$ | 547 | 3.2
Abell 262 | $1.4\times 10^{40}$ | $4.2\times 10^{5}$ | 24 | 1
RXJ0820.9+0752 | $1.8\times 10^{41}$ | $5.2\times 10^{6}$ | 266 | 27

Note. — Columns: (1) Target name. (2) Total [OII] luminosity observed with
$\text{S/N}\geq 5$. (3) Ionized gas mass inferred from total [OII] luminosity.
(4) Total area with [OII] emission where $\text{S/N}\geq 5$ for the [OII]
flux. (5) Total area with detected CO emission, using a flux cut of 10% of the
peak CO flux.

###  3.1 Abell 1835

Abell 1835 is an archetype cool core cluster whose central galaxy is
experiencing powerful, radio-mechanical (radio-mode) feedback. Its powerful
mechanical AGN feedback, which is greater than $1.5\times 10^{45}$ erg s-1, is
capable of offsetting the system’s impressive 1175 M⊙/yr of cooling (McDonald
et al., 2018) (see Table 1). Despite the formidable jet power released over
the past several tens of Myr, the current radio source is relatively faint and
amorphous, with a flux density of 2.3 mJy at 4.76 GHz (O’Dea et al., 2010).
O’Dea et al. (2010) detected a 1.5 arcsecond jet in the core of the central
galaxy. Starting from the nucleus, the jet initially points to the west and
then gradually bends in the NW direction.

####  3.1.1 Abell 1835: Morphology

Figure 1: Left panel: Stellar continuum flux map for Abell 1835. The continuum
flux colorbar ranges between $2.5-80\times 10^{-16}$ erg s-1cm-2. Middle and
right panels: Continuum subtracted flux maps of [OII]3726,9$\lambda\lambda$
for Abell 1835, where $\text{S/N}\geq 5$. The magenta line shows stellar
continuum flux contours for 5, 10, 20%, 40%, and 80% of the maximum stellar
continuum flux. The red contours indicate the flux of CO(3-2) emission, where
the contours represent 10%, 20%, 40%, and 80% of the maximum CO(3-2) flux
(McNamara et al., 2014). The black dotted ellipses show the position of the
X-ray cavities (McNamara et al., 2006; Olivares et al., 2019).

The left panel of Fig. 1 shows the observed KCWI stellar continuum integrated
over the rest-frame wavelength range $3435-5035$ Å. The nucleus of the central
galaxy, located at the origin in Fig. 1, corresponds to the brightest spaxel
in the stellar continuum flux map.

The central galaxy is flanked in projection by several fainter galaxies. Eight
neighboring galaxies are observed within our full KCWI field of view.

Apart from one galaxy, the projected galaxies’ stellar velocities relative to
the central galaxy differ by thousands of km s-1. These high relative
velocities are inconsistent with interactions with the central galaxy. Only
one projected galaxy has similar velocity as the central galaxy, although
their projected separation of more than 60 kpc makes interactions between the
two galaxies very unlikely. Therefore, we do not expect the projected galaxies
to be interacting with the central galaxy or the surrounding gas. Above a flux
of $2.5\times 10^{-16}$ erg s-1cm-2, the stellar continuum is detected up to a
radius of $\sim 20$ kpc from the nucleus of the central galaxy. Half of the
total stellar continuum flux is contained within a radius of $\sim 9$ kpc
($2.2\arcsec$) from the center.

The middle and right panels of Fig. 1 show the detected [OII] flux in and
around the central galaxy. Half of the [OII] flux is emitted within a radius
of 7.3 kpc (1.8″) from the nucleus of the central galaxy. The [OII] detected
($\text{S/N}\geq 5$) spans more than 45 kpc in RA and 50 kpc on Dec. The total
[OII] luminosity is $4\times 10^{42}$ erg s-1; this is the most [OII] luminous
object in our sample (see Table 4).

From the [OII] luminosity, we can estimate the mass of ionized gas
($\textnormal{M}_{\textnormal{ion}}$) using:

$\textnormal{M}_{\textnormal{ion}}=\frac{\mu\textrm{m}_{\textrm{H}}\textrm{L}_{\textrm{[OII]}}}{\gamma_{\textrm{[OII]}}\textrm{n}_{\textrm{e}}}$
(2)

where $\mu$ is the mean mass per hydrogen atom which we set to $\mu=1.4$,
$\textrm{m}_{\textrm{H}}$ is the mass of the hydrogen atom, n${}_{\textrm{e}}$
is the electron density and $\gamma_{\textrm{[OII]}}$ is the effective line
emissivity (Osterbrock & Ferland, 2006). Assuming electron temperature of
$\sim 10000$ K and electron density of $\sim 400$ cm-3, we obtain an effective
line emissivity for the [OII] doublet of $\sim 1\times 10^{-25}$ cm3 erg s-1
(Luridiana et al., 2013). From the total [OII] luminosity, we estimate more
than $10^{8}$ M⊙ of nebular gas in the inner region of Abell 1835 (see Table
4).

Fig. 1 shows that the peak of the stellar continuum, [OII] flux, and CO(3-2)
flux all coincide. The stellar continuum and the [OII] emission overlap
spatially. Approximately 90% of the stellar continuum flux coincides with 96%
of the [OII] flux. Little nebular gas is detected outside of the region with
detectable starlight.

Most of the observed molecular gas in Abell 1835 is concentrated around the
nucleus, with the remaining molecular gas extending in roughly three filaments
(McNamara et al., 2014), a prominent northern filament, and smaller eastern
and western filaments. The N and W filaments appear to be trailing the NW
X-ray cavity, while the E filament seems to trail the SE cavity. The
distribution of nebular gas generally follows the distribution of cold
molecular gas but the nebular gas is far more extended, with a detected area
17 times greater than that of the detected cold gas (see Table 4). The [OII]
morphology observed in the core of Abell 1835 provides compelling evidence for
the impact of X-ray cavities on gas dynamics. The right panel of Fig. 1 shows
that the nebular gas is extended along the direction of the two X-ray
cavities. The detected [OII] emission spans 53 kpc along the axis of the
bubbles, compared to 32 kpc in the perpendicular direction.

####  3.1.2 Abell 1835: Kinematics

Figure 2: Line-of-sight (LOS) kinematics of the [OII]3726,9$\lambda\lambda$
emission line doublet in Abell 1835. Upper left panel: Median velocity
($v_{50}$). Upper right panel: Velocity dispersion ($\sigma$). Lower left
panel: Maximum redshifted velocity ($v_{02}$), defined as the velocity which
includes 2% of the cumulative velocity distribution. Lower right panel:
Maximum blueshifted velocity ($v_{98}$), defined as the velocity which
includes 98% of the cumulative velocity distribution. In the upper right
panel, the dotted ellipses show the position of the X-ray cavities.  Figure 3:
Median velocity maps (top) and velocity dispersion maps (bottom) for the first
(left) and second (right) gaussian components of the two kinematic component
fits for Abell 1835. The dotted ellipses in the upper panels show the position
of the X-ray cavities. Only spaxels where emission lines can be fitted by two
kinematic components, each with $\text{S/N}\geq 3$, are shown.

Fig. 2 presents the LOS kinematics of the [OII] emission at each spaxel in
Abell 1835. The panels shown are the median velocity (upper left), the
velocity dispersion (upper right), the maximum redshifted velocity, $v_{02}$,
(lower left), and the maximum blueshifted velocity, $v_{98}$, (lower right).
Positive velocities are redshifted with respect to the systemic redshift, and
negative velocities are blueshifted. The maximum redshifted (blueshifted)
velocities are obtained by determining the velocity at 2% (98%) of the
cumulative velocity distribution; these values probe the most extreme
velocities of the ionized gas.

The high spectral resolution of our data allows us to measure both nebular
emission lines and absorption lines from the starlight of the central galaxy.
The systemic redshift of the stars surrounding the nucleus is used to
determine the zero point of the velocity plots, as discussed in Section 2.3.
As detailed in Table 1, the systemic redshift of this system is $z=0.2514$. It
is the most distant cluster in the sample.

Fig. 2 reveals the complex gas dynamics surrounding the central galaxy. The
median velocites of the nebular gas range between $-30$ and $+286$ km s-1,
with respect to the systemic velocity. It is worth noting that overall, the
nebular gas is redshifted with respect to the systemic velocity, which is
defined as the central stellar velocity. On average, the nebular gas is almost
redshifted by an additional 150 km s-1. For average velocities, we use flux-
weighted mean velocities which are calculated as follows:

$\bar{\textrm{v}}=\frac{\sum_{\textrm{i}}\textrm{v}_{\textrm{i}}\times\textrm{f}^{\textrm{[OII]}}_{\textrm{i}}}{\sum_{\textrm{i}}\textrm{f}_{\textrm{i}}}$
(3)

where v is velocity (e.g. v50, $\sigma$, v02 or v98), and
$\textrm{f}^{\textrm{[OII]}}_{\textrm{i}}$ is the [OII] flux within the ith
spaxel of any given region. We use the flux-weighted mean velocity to obtain
an average velocity within a spatial region as if analyzing a single spaxel.

The gas with highest v50 and $\sigma$ lies 8 kpc east of the nucleus.
Analogously, on the other side of the nucleus, there is a low v50 region. This
could potentially indicate a bipolar outflow of gas caused by AGN activity in
the central galaxy. The system has two detected X-ray cavities, one on each
side of the center along the SE-NW axis. The NW cavity partially overlaps with
an extended low velocity filament while the SE cavity is projected onto
substantially redshifted nebular gas with large $\sigma$.

A sizable low $\sigma$ region is seen along the eastern and northern edges of
the [OII] emission. This region which contributes 20% of the total [OII] flux
and spans a length of 75 kpc, has a velocity dispersion of less than 100 km
s-1. This gas is not being significantly disturbed. Finding undisturbed gas
far from the nucleus implies that the main mechanism disrupting gas dynamics
emanates from within the galaxy.

Regions of interest in the kinematic maps are discussed in Appendix B.1.
Properties of the regions, including flux-weighted mean velocities, are listed
in Table 5.

Abell 1835 is one of the two targets where two distinct kinematic components
were detected. Fig. 3 shows the v50 and $\sigma$ separately for the first and
second kinematic components of the regions requiring at least two components
in the emission line fits. For Fig. 3, the spaxels included in the velocity
maps were chosen according to the method outlined in the fifth step of Section
2.3. To maximize the area where two kinematic components can be studied, we
only require that each component of the resulting fit has a $\text{S/N}\geq
3$.

The second component is defined such that its velocity dispersion is always
greater than that of the first component.

Showing the kinematics of the two components separately clearly results in a
different physical picture for each component. The top row of Fig. 3 shows
that substantial variations in gas velocities are mostly reflected in the
second component of the fits. The main features of the v50 map for the first
component are a slight increase in velocities $\sim 8$ kpc east of the nucleus
and lower velocities NW of the nucleus. The v50 map of the second component
(upper right panel) is very similar to the v50 map of the total [OII] emission
line. As seen in Fig. 3, the median velocity of the (broader) second component
varies the most between the different regions. The gradients in total median
velocities, both the one along the E-W axis and the one along the axis of the
cavities, are also observed in the v50 map for the second component of the
emission line fits.

The bottom row of Fig. 3 shows the velocity dispersion of the nebular gas
associated with each kinematic component. By definition, the second component
has larger $\sigma$. The velocity dispersion map of the first component (left
panel) shows a slight increase in $\sigma$ in the highest v50 region, with
$\sigma\sim 100$ km s-1, compared to the surrounding gas. We discussed above
the NE region with low $\sigma$ on the outskirts of the detected [OII]
emission. This low $\sigma$ region is due to the relatively quiescent gas in
the first component, as a second component is not used when fitting this
region.

The bottom right panel, showing the velocity dispersion of the second
component, varies more substantially. The region slightly east of the nucleus
is particularly disturbed, with large v50, $\sigma$ and v02 values (see Fig.
2). Another region with large velocity dispersion is located roughly 5 kpc
east and 8 kpc north of the center. However, due to the low flux of the second
component in this region, it is not seen as one of the prominent features on
the total kinematics maps. Actually, when applying the method described in
Section 2.3 to choose the optimal number of components, a one component fit is
preferred for this region. Deeper observations are needed to thoroughly
investigate the potentially complex gas dynamics obscured by the more
quiescent gas.

The use of two kinematic component fits is required for this galaxy’s
structure with the most complex dynamics being fit by the second component.
The second component is much more disturbed that the first, as shown by the
second component’s large $\sigma$ and wide v50 range. The kinematics in Fig. 3
are consistent with the galaxy having a quiescent gas component and a churned
component which are modelled by the first and second kinematic components of
our fits, respectively. The ionized gas seen in the second component emits a
substantial fraction (45%) of the total [OII] flux observed. For spaxels which
require the use of the two components fit, 55% of the total [OII] emission
comes from the churned component.

###  3.2 PKS 0745-191

PKS 0745-191 is a strong cool core cluster known for its powerful radio
emission. First discovered as a radio source, this object has a radio
luminosity (between 10 MHz and 5000 GHz) of $3.87\times 10^{42}$ erg s-1
(Pulido et al., 2018), more than ten times higher than the other objects in
our sample (see Table 1). The radio emission is diffuse and amorphous, showing
no clear jets or radio lobes. Based on the lack of radio jets and other
structures in the radio emission, jets, which inflated the detected X-ray
cavities, may have been disrupted by the dense environment of the galaxy’s
core (Russell et al., 2016). Baum & O’Dea (1991) suggested that a merger may
have disrupted the jet by changing its orientation.

####  3.2.1 PKS 0745-191: Morphology

Figure 4: Left panel: Stellar continuum map for PKS 0745-191. The continuum
flux colorbar ranges between $(2.5-40)\times 10^{-16}$ erg s-1cm-2. Middle and
right panels: Continuum subtracted flux maps of [OII]3726,9$\lambda\lambda$,
where $\text{S/N}\geq 5$. The magenta lines show stellar continuum contours
for 20%, 40%, and 80% of the maximum stellar continuum flux. The red contours
map the flux of CO(3-2) emission, where the contours represent 10%, 20%, 40%,
and 80% of the maximum CO(3-2) (Russell et al., 2016). The black dotted
ellipses show the position of the two X-ray cavities (Sanders et al., 2014;
Russell et al., 2019).

The left panel of Fig. 4 shows the stellar flux at rest-frame wavelengths
between $3356-5017$ Å. Above a stellar flux per spaxel of $2.5\times 10^{-16}$
erg s-1 cm-2, the stellar continuum is detected in a roughly circular region
with a radius of 8.3 kpc around the brightest stellar spaxel. This target has
a total stellar luminosity of $1.78\times 10^{43}$ erg s-1, half of which is
emitted within an inner region of 4.1 kpc in radius.

This target has one projected galaxy within the FOV shown in Fig. 4, which is
located 8.5 kpc SW of the nucleus of the central galaxy. The projected galaxy
and the central galaxy may be interacting as they have similar stellar
velocities, with a difference of only 34 km s-1. The stellar flux map shown in
the left panel of Fig. 4 does not show any obvious sign of interactions
between the two galaxies. These dynamics will be discussed in depth in a
future paper focused on the stellar properties of our targets.

The middle and right panels of Fig. 4 show the continuum-subtracted [OII] flux
map. The total [OII] luminosity is $4.7\times 10^{41}$ erg s-1, corresponding
to $\sim 10^{7}$ M⊙ of nebular gas ($T_{e}\sim 10000$ K, $n_{e}\sim 400$ cm-3)
as shown in Table 4. Half of the [OII] flux is emitted within a radius of 3.8
kpc (1.96″) from the nucleus of the central galaxy. The [OII] emission spans
over 33 kpc in RA and 30 kpc in Dec, covering a total area of 542 kpc2 (see
Table 4). The [OII] morphology is related to the position of the X-ray
cavities. As previously observed in many galaxies (Russell et al., 2016;
Olivares et al., 2019), the [OII] emission extends from the nucleus towards
and around the edges of the two X-ray cavities. The X-ray cavities, which are
roughly aligned along the SE-NW axis, are not at the same distance from the
nucleus. The NW cavity is more than three times as far from the center of the
galaxy as the SE cavity. This asymmetry is reflected in the [OII]
distribution. Along the SE-NW axis, the detected [OII] emission extends
slightly past the inner edge of each cavity. Therefore, the different cavity
heights are reflected in the asymmetric nebular gas distribution along
cavities’ axis. This shows a clear relation between X-ray cavities and nebular
gas morphology.

Fig. 4 shows that the peaks in stellar, [OII] and CO(3-2) emission roughly
coincide spatially. The peak of CO(3-2) is 2.5 kpc east of our nucleus. This
corresponds to a small offset at the scale studied. The central panel of Fig.
4 highlights the significant differences in the extent of the [OII] emission
and the stellar continuum. The nebular emission is much more extended than the
stellar emission towards the NW. Only 37% of the area with [OII] emission also
has detectable stellar emission. However, since most of the [OII] flux is
emitted near the bright galaxy center, 82% of the [OII] emission comes from
regions with detected stellar emission. While we observe nebular emission to
be more than twice as extended as the stellar continuum, most of the nebular
gas coincides with starlight from the central galaxy.

The right panel of Fig. 4 shows contours of the CO(3-2) emission superimposed
on the [OII] flux map. Most of the cold gas is located within a radius of 5
kpc from the nucleus. The molecular gas is mostly contained in three filaments
(Russell et al., 2016). As we observed for the nebular gas, the cold gas
filaments are extended in the direction of the cavities, one filament trailing
the SE cavity and two filaments trailing the NW cavity.

The detected CO(3-2) emission spans a much smaller area than the nebular gas.
The detected [OII] emission covers a projected area 45 times larger than that
of the CO(3-2) emission (Table 4). The distribution of molecular gas coincides
with the brightest nebular regions, as shown by previous observations (Russell
et al., 2019; Olivares et al., 2019). Deeper observations of the CO emission
at the center of this galaxy may reveal a much large cold gas reservoir.

####  3.2.2 PKS 0745-191: Kinematics

Figure 5: Kinematics of the [OII]3726,9$\lambda\lambda$ emission line doublet
in PKS 0745-191. The velocity plots are as in Fig. 2. Figure 6: Similar to
Fig. 6, v50 (top) and $\sigma$ (bottom) maps for the first (left) and second
(right) kinematic components for PKS 0745-191. Only spaxels where
$\text{S/N}\geq 3$ for each component are included. The dotted ellipses in the
top panels show the position of the cavities.

Fig. 5 shows the LOS kinematics of the [OII] emitting gas with maps of the
median velocities (upper left panel), velocity dispersion (upper right), most-
redshifted velocities (lower left) and most-blueshifted velocities (lower
right).

From the continuum absorption lines in the core of the galaxy, we measure a
systemic redshift of 0.1024 (see Table 1). As is the case for other targets in
our sample, the nebular gas is redshifted with respect to the systemic
velocity. On average, the nebular gas is redshifted by $\sim 135$ km s-1. As
shown in the top left panel of Fig. 5, the total median velocities observed
are mostly redshifted, with v50 values between $-74$ km s-1 and 402 km s-1.

The gas with the most redshifted total median velocities, with v${}_{50}>225$
km s-1, lies in a 20 kpc filament roughly 8.5 kpc from the center of the
galaxy. The lowest v50 gas is observed in the westernmost part of the detected
emission.

Of the four central galaxies in our sample, PKS 0745-191 has the broadest
emission lines observed. As seen in the top right panel of Fig. 5, the nebular
gas in the core of PKS 0745-191 has $\sigma$ up to 400 km s-1, which is almost
twice that of our other targets.

Two lines of high $\sigma$ nebular gas are seen in the right upper panel of
Fig. 5, forming a yellow cross roughly centered on the nucleus. The two
regions with largest total velocity dispersion are located at the eastern end
of the high $\sigma$ cross. They are located roughly 5 kpc NE and SE of the
nucleus. The gas within these areas of the nebula is highly disturbed, having
a total velocity dispersion greater than any other object in our sample. The
lower left panel of Fig. 5 shows that some of the gas in the NE high $\sigma$
region is extremely redshifted. With v02 greater than 1250 km s-1, there may
be an extremely powerful outflow in this region.

This system has two known cavities within our FOV, roughly along the SE-NW
axis, which are shown as dotted ellipses in the top right panel of Fig. 5. The
SE high $\sigma$ region is located within the SE cavity, while the upper part
of the high v50 filament partially overlaps with the NW cavity.

While the core of PKS 0745-191 has a large reservoir of nebular gas with
$\sigma>200$ km s-1, the top right panel of Fig. 5 also shows low $\sigma$ gas
in the outermost regions. While these low $\sigma$ regions are quite extended,
with a total area of $\sim 200$ kpc2, they are also quite faint such that gas
with total $\sigma\leq 100$ km s-1 contributes to only 5.5% of the total [OII]
flux. Other regions of interest are discussed in Appendix B.2.

Fig. 6 shows v50 and $\sigma$ for each of the kinematic components. As we
observed in Abell 1835, Fig. 6 shows that the gas associated with the second
component is much more churned-up than the gas in the first component. The
v${50}$ and $\sigma$ maps for the total emission lines (Fig. 5) are different
than the ones for the first and second components. While v50 for the second
kinematic component (top right panel Fig. 6) does not look like the total v50
map (top left panel Fig. 5), it does share similarities with the total
$\sigma$ map (top right panel Fig. 5). This indicates that the broadening of
the [OII] emission line is predominantly caused by significant differences in
the v50 of the first and second components. This is clearly seen in the
integrated spectra shown in Fig. 25 in Appendix B.2.

The top right panel of Fig. 6 shows the second components’ v50. It highlights
the redshifted gas observed NE, NW and SE of the nucleus. In comparison, the
median velocities of the first kinematic component, seen in the upper left
panel, show little variation.

The bottom right panel of Fig. 6, which maps $\sigma$ for to the second
kinetic component, shows the distribution of the most disturbed gas in the
central galaxy. The gas with the largest $\sigma$ lies around the nucleus and
extends in the NE direction. This picture is consistent with a central
mechanism, such as the AGN, disturbing gas around the nucleus. Comparing the
v50 and $\sigma$ second component maps, some of the central high $\sigma$ gas
also has v${}_{50}>500$ km s-1. The dynamics of the churned gas are consistent
with an AGN driven outflow.

The complex dynamics in the core of PKS 0745-191 requires the use of two
components fits to properly model the [OII] emission lines. Fig. 6 highlights
the contrasting dynamics of the quiescent (first) component and the churned
(second) component. A significant fraction of the nebular gas is churned,
accounting for $\sim 39$ % of the total [OII] emission and $\sim 49$ % of the
[OII] flux in spaxels with two kinematic components.

###  3.3 Abell 262

The central galaxy in Abell 262 has the lowest redshift and the lowest mass in
our sample (see Table 1). Abell 262 is different than our other targets as it
hosts a molecular circumnuclear disk with a radius of 1.5 kpc (Salomé &
Combes, 2003; Russell et al., 2019) embedded in a more extended disk of
ionized gas (Hatch et al., 2007). Circumnuclear disks in the core of central
galaxies are rare, but not unheard of (Rose et al., 2019, HydraA).

The central galaxy in Abell 262 has well known AGN jets oriented to the east
and west, both with linear sizes of $\sim 11~{}\rm kpc$ by $\sim 4~{}kpc$
(Clarke et al., 2009). Extended radio lobes and jet inflated X-ray (Blanton et
al., 2004; Bîrzan et al., 2008; Clarke et al., 2009) are found between 8 and
29 kpc from the core of the central galaxy. Due to the low redshift of the
source, our FOV is too small to include the X-ray cavities, the closest of
which are 8-10 kpc east and west of the nucleus.

####  3.3.1 Abell 262: Morphology

Figure 7: Left panel: Smooth stellar continuum map for Abell 262. The
continuum flux colorbar ranges between $(15-75)\times 10^{-16}$ erg s-1cm-2.
Middle and right panels: Continuum-subtracted flux maps of
[OII]3726,9$\lambda\lambda$ for Abell 262. Magenta contours show the stellar
flux at 20%, 40%, and 80% of the maximum stellar flux. Red contours show the
flux of CO(2-1) emission, where the contours represent 20%, 40%, and 80% of
the maximum CO(2-1) (Davis et al., 2017).

Abell 262 has a substantially lower redshift than our other targets, such that
the KCWI FOV only covers the inner part of the central galaxy. The KCWI
spectra cover rest-frame wavelengths between $\rm 3445~{}\AA$ and $\rm
5118~{}\AA$. Fig. 7 shows the stellar flux map and the continuum-subtracted
[OII] flux map for Abell 262 in the left panel and middle and right panels,
respectively.

Above a stellar flux per spaxel of $1.5\times 10^{-15}$ erg s-1 cm-2, we
detect a total stellar luminosity of $3.6\times 10^{42}$ erg s-1 in a roughly
circular region with a radius of 2.5 kpc. Half of the total stellar flux is
emitted within a radius of 1.43 kpc around the nucleus. The central galaxy of
Abell 262 has a known dust lane. This dust lane is seen in the left panel of
Fig. 7, cutting vertically through the center of the galaxy. Absorption from
the central dust lane causes a decrease of the flux in the central region.
Therefore, contrary to the other targets in our sample, the brightest stellar
continuum spaxel does not provide an accurate position of the nucleus.
Instead, the location of the nucleus is defined by the spaxel with the largest
stellar velocity dispersion.

The middle and right panels of Fig. 7 show the continuum-subtracted [OII] flux
map. X-ray cavities have been detected in this system, however they are not
shown in Fig. 7 as they are beyond the FOV of our maps. The two closest X-ray
cavities are roughly 8-10 kpc from the nucleus along the E-W axis.

Within our FOV we measure a total [OII] luminosity of $1.4\times 10^{40}$ erg
s-1. For an electron temperature of $\sim 10000$ K and density of $\sim$ 400
cm-3, this corresponds to an ionized gas mass of $\sim 10^{5}$ M⊙ (see Table
1). Half of the [OII] emission comes from a central region with a radius of
1.32 kpc. The detected [OII] emission spans 5.45 kpc in RA and 8.58 kpc in
Dec. The [OII] emission is spatially highly asymmetric. Fig. 7 shows prominent
filaments extending to the SW and NW of the nucleus, with another small
filament to the SE. Contrary to Abell 1835 and PKS 0745-191, where the nebular
gas is most extended towards the cavities, the gas here is more extended along
the north-south axis, which is perpendicular to the axis of the cavities.

The middle panel of Fig. 7 shows that most (64%) of the area with detected
[OII] emission also has detected stellar emission. The stellar continuum and
the [OII] emission have different morphologies. The asymmetry of the nebular
gas is not present in the stellar continuum map. The upper half of the NW
filament and the bottom half of the SW filament are the main regions where
nebular gas is detected without a stellar counterpart. Since the regions with
the brightest stellar continuum and brightest [OII] emission overlap, only 20%
of the [OII] flux is emitted from regions without detectable starlight.

The right panel of Fig. 7 superimposes CO(2-1) contours, in red, onto the
[OII] flux map (Davis et al., 2017). Most of the detected molecular gas
($>70\%$) lies very close to the nucleus, in a roughly elliptical region with
major and minor axes of $\sim 2$ kpc and $\sim 1$ kpc, respectively. Previous
studies of the dynamics of the molecular gas in this system concluded that it
is consistent with a rotating circumnuclear disk (Russell et al., 2019;
Olivares et al., 2019).

The spatial distributions of molecular gas and nebular gas are consistent with
each other. CO(2-1) emission is detected where the nebular gas is the
brightest. As detailed in Table 4, [OII] emission is much more extended than
CO(2-1) emission, spanning a projected area 24 times larger. The morphologies
of the nebular gas and the cold gas in this system are consistent with models
where molecular gas cools out of its warmer surroundings.

####  3.3.2 Abell 262: Kinematics

Figure 8: Kinematics of the [OII]3726,9$\lambda\lambda$ emission line in Abell
262. The velocity plots are as in Fig. 2. Figure 9: Velocity dispersion of the
[OII] nebular gas as in the top right panel of Fig. 8. Contours of the flux
density at 1.4 GHz are overlaid as solid black lines on the $\sigma$ map
(Clarke et al., 2009). The dotted ellipses show the position of the X-ray
cavities (Blanton et al., 2004; Clarke et al., 2009).

Fig. 8 maps the LOS kinematics of the [OII] emission in the innermost region
of the central galaxy of Abell 262. The [OII] emission lines are fit using
only one kinematic component. While the spectral fits hint to the possibility
of a second kinematic component, especially for the more disturbed gas, we
cannot robustly detect it with our current data. Additional observations are
needed to further study the possibility of multiple kinematic components in
this nebula.

We observe a discrepancy between the systemic velocity and the central
velocity of the nebular gas. Within a radius of 1” around the nucleus, the
nebular gas has a mean [OII] flux-weighted v50 of $+105$ km s-1, with median
velocities in each spaxel ranging between $+10$ km s-1 and $+172$ km s-1.
However, the [OII] flux-weighted median velocity across our entire FOV is
closer to the systemic velocity, with a relative velocity of only $+39$ km
s-1.

The v50, v02 and v98 maps (Fig. 8) show a clear gradient in velocities along
the north-south axis. The nebular gas is redshifted in the north and
blueshifted in the south, indicating ordered motion in a nascent disk. This is
consistent with the molecular gas dynamics previously observed by Russell et
al. (2019). v50 values range from $-314$ km s-1 to $+422$ km s-1. In addition
to the main velocity gradient along the NS axis, the northern ionized gas
filament has an east-west gradient of $\sim 150$ km s-1.

The top right panel of Fig. 8 shows the LOS velocity dispersion of the ionized
gas. The majority of the gas is fairly quiescent, with more than 50% of the
[OII] flux being emitted from gas with $\sigma<100$ km s-1. There is a high
$\sigma$ region roughly centered on the nucleus and extending $\sim
25^{\circ}$ north of east. The gas is highly disturbed, with velocity
dispersion up to 200 km s-1. This region, where $\sigma\geq 140$ km s-1, has a
length of $\sim 2.5$ kpc and a width of $\sim 0.64$ kpc, emitting roughly one
fifth of the total [OII] flux. The velocity dispersion gradually decreases
away from the high $\sigma$ region. Most of the remaining gas is quiescent,
with few slightly more disturbed knots of gas with $\sigma$ between 80 km s-1
and 125 km s-1.

Fig. 9 shows VLA 1.4 GHz radio emission contours (Clarke et al., 2009)
superimposed on the [OII] LOS velocity dispersion map. The dotted ellipses
indicate the position of two detected X-ray cavities in the system. Fig. 9
shows that the central high $\sigma$ region roughly extends along the axis of
the radio jets. This is consistent with the high $\sigma$ gas being disturbed
by powerful AGN-driven jets. Fig. 9 shows that the maximum extent of the 1.4
GHz radio emission coincides with the position of the X-ray cavities. This is
also consistent with mechanical AGN feedback model where AGN-driven jets
inflate X-ray cavities which rise buoyantly in the surrounding atmosphere.

###  3.4 RXJ0820.9+0752

This system is known for the significant offset between its central galaxy and
its molecular and nebular gas reservoirs, which lie nearly 20 kpc north-west
of the galaxy’s core (Bayer-Kim et al., 2002; Salomé & Combes, 2004; Vantyghem
et al., 2017; Olivares et al., 2019). Vantyghem et al. (2019) detected a
possible X-ray cavity, which has yet to be confirmed from radio observations,
located 6.4 kpc to the west of the nucleus (see Fig. 10, middle and rights
panels). With an estimated power of $1.14\times 10^{43}$ erg s-1, its cavity
power is insufficient to produce the galaxy’s massive cold gas reservoir
solely through simulated cooling of uplifted gas (Vantyghem et al., 2019). The
$10^{10}$ M⋅ molecular gas reservoir (see Table 1) likely results from
sloshing caused by galaxy interactions. Based on the presence of a secondary
galaxy $\sim 8$ kpc away from the main galaxy and the significant offset of
the molecular and nebular gas reservoirs, galaxy interactions are believed to
play a crucial role in the dynamics of multiphase gas in the core of
RXJ0820.9+0752.

####  3.4.1 RXJ0820.9+0752: Morphology

Figure 10: Left panel: Smooth stellar continuum map for RXJ0820.9+0752. The
flux colorbar ranges between $(5-50)\times 10^{-16}$ erg s-1cm-2. Middle and
right panels: Continuum-subtracted flux maps of [OII]3726,9$\lambda\lambda$.
The magenta lines show stellar flux contours for 20%, 40%, and 80% of the peak
stellar flux. The red contours show the CO(3-2) flux, where the contours
represent 10%, 20%, 40%, and 80% of the maximum CO(3-2) flux (Vantyghem et
al., 2017). The black dash-dotted ellipse shows the position of the putative
X-ray cavity (Vantyghem et al., 2019).

The left panel of Fig. 10 shows the stellar continuum map between $3300-5100$
Å . This map only includes spaxels with observed continuum flux of at least
$6\times 10^{-16}$ erg s-1 cm-2. The continuum emission spans $\sim 14$ kpc in
RA and Dec, roughly in the shape of an ellipse with major and minor axes of 17
kpc and 11 kpc, respectively. The total stellar luminosity is $2.3\times
10^{43}$ erg s-1. Half of the continuum flux is emitted within a central
circular region with a radius of 3.6 kpc.

This system has a secondary galaxy projected $\sim$7.8 kpc to the south-east
of the central galaxy. It is seen in Fig. 10 as a secondary peak in the
stellar continuum map. The stellar flux of the central galaxy is $\sim$3 times
greater than for the secondary galaxy, with stellar luminosities within 5 kpc
of their respective peaks of $1.7\times 10^{43}$ erg s-1 and $6.0\times
10^{42}$ erg s-1. The two galaxies have a relative velocity of almost 100 km
s-1, with the secondary galaxy being more redshifted. The proximity of the
galaxies and their relative velocity indicate that they are likely
interacting.

The middle and right panels of Fig. 10 show the [OII] continuum-subtracted
flux maps. Stellar continuum contours are overlaid onto the [OII] map in
magenta for the middle panel, highlighting the spatial offset of the nebula.
Similarly, the CO(3-2) emission, seen as red contours in the rightmost panel
of Fig. 10, is significantly offset from the stellar peak.

The central galaxy has a total [OII] luminosity of $1.82\times 10^{41}$ erg
s-1, half of which is emitted within a radius of 7.3 kpc from the [OII] peak.
As listed in Table 4, an ionized gas mass of $\sim 5\times 10^{6}$ M⊙ can be
inferred from the total OII luminosity, assuming T${}_{\textrm{e}}=10000$ K
and n${}_{\textrm{e}}=400$ cm-3.

The [OII] flux map shows extended nebular gas spanning roughly 24 kpc in RA
and 15 kpc in Dec. The nebular gas distribution is asymmetrical about the peak
in [OII] emission, extending mostly to the NW of the peak. Contrary to the
other systems presented here, the nebular gas extends beyond the X-ray cavity.
The nebular gas is extended roughly along the major axis of the cavity.

The middle panel of Fig. 10 demonstrates the significant morphological
differences between the stellar continuum and the nebular emission. Less than
30% of the area with detected [OII] emission also has detected stellar
emission. Although most of the nebular gas is offset from the stellar
continuum, the [OII] flux peak is fairly close to the stellar peak, located
$\sim 3.3$ kpc NNW of the nucleus.

For the molecular gas, most of the CO(3-2) emission lies in a region spanning
$\sim 8.7$ kpc in RA and $\sim 6.3$ kpc in Dec. The molecular gas reservoir,
which is not centered on the nucleus, mostly consists of a single filament,
with two denser gas clumps. The brighter clump is located $\sim 3$ kpc NNW of
the nucleus, while the fainter clump is $\sim 3.5$ kpc east of the brighter
clump. The CO(3-2) emission is slightly east of the X-ray cavity, partially
overlapping with it.

As observed in our previous targets, the morphology of the CO(3-2) emission is
quite similar to that of the nebular gas, although spanning a much smaller
area. As detailed in Table 4, the projected area of the [OII] nebula is ten
times greater than for the CO(3-2) emission. This central galaxy, which is
known for its extensive molecular gas reservoir, has the smallest [OII]
detection area to CO detection area ratio of the four objects studied in this
paper.

####  3.4.2 RXJ0820.9+0752: Kinematics

Figure 11: Kinematics of the [OII]3726,9$\lambda\lambda$ line for
RXJ0820.9+0752. The velocity plots are as in Fig. 2.

Fig. 11 displays the LOS kinematic maps of the nebular gas in the central
galaxy of RXJ0820.9+0752, which has a redshift of $z=$0.1103 (see Table 1). As
shown in the top left panel of Fig. 11, the nebular gas is substantially
redshifted with respect to the systemic velocity. The [OII] median velocities
range between $-12$ km s-1 and $+286$ km s-1, with a flux weighted mean v50 of
$\sim 150$ km s-1.

The v50 map shows interesting dynamics for the gas with large v50 ($\geq+150$
km s-1). The two regions with largest v50, located $\sim 3.7$ kpc north and
$\sim 16.9$ kpc north-west of the nucleus, are connected by a slightly lower
velocity filament ($+146$ km s${}^{-1}\leq$ v${}_{50}\leq+174$ km s-1). The
gas with lowest v50 is located $\sim 14$ kpc west of the nucleus.

The top right panel of Fig. 11 shows that the gas is generally undisturbed.
Almost 80% of the nebular gas has $\sigma$ less than 100 km s-1. The most
disturbed gas lies in a small region located $\sim 1.6$ kpc south-west of the
nucleus. The few regions where $\sigma\geq 100$ km s-1 lie on the edge of the
detected [OII] nebula. Appendix B.3 describes more in depth the properties of
five regions of interest from the kinematic maps.

The bottom panels of Fig. 11, which show the most-redshifted and most-
blueshifted velocities, do not reveal extreme velocities in this nebula. These
velocity maps, as well as the $\sigma$ map, support a quiescent scenario for
the nebular gas, even though it is substantially offset from the center of the
main galaxy.

##  4 Discussion

###  4.1 Nebular Gas Structures: Peculiar Velocities With Respect to the
Central Galaxy

The v50 maps, shown in the top left panel of Figures 2, 5, 8, and 11, reveal
little blueshifted gas in three of our four targets. Surprisingly, most of the
nebular gas in Abell 1835, PKS 0745-191 and RXJ0820.9+0752 is redshifted by
$\sim+140$ km s-1 with respect to the central galaxy. Assuming that the
nebular gas is bound to the central galaxy, we would expect its mean velocity
to be close to that of the stars. We performed rigorous tests to ensure that
our measurements are free of systematic bias. This is discussed in Section 2.3
and in Appendix A. We are aware of no additional biases that would lead to an
overall velocity shift.

In three out of four targets, the nebular gas has a redshift of almost 150 km
s-1 with respect to the central galaxy. Although the nebular gas is
redshifted, and not blueshifted, with respect to the systemic velocity in our
three targets with significant velocity offsets, we must refrain from drawing
any definitive conclusion regarding the direction of the velocity offset due
to our small sample size. Nonetheless, our observations clearly show that the
velocity of the central galaxy and that of the nebular gas can differ on the
order of 100s of km s-1

The relative velocities indicate that the nebular gas and the central galaxies
are, to some degree, dynamically decoupled. The velocity offset reflects
overall motion of the nebular gas with respect to the central galaxy. While
initially surprising, velocity and positional offsets between nebular gas and
central galaxies in the sky plane have been observed in many systems such as
RXJ0820.9+0752, Abell 1991, Abell 3444 and Ophiuchus (Hamer et al., 2012).
Therefore, velocity offsets of this magnitude may be a common phenomenon, with
potentially significant consequences for feedback. We have yet to compare the
velocity of the stars in the BCG with the velocity of the cooling X-ray
atmosphere, which is believed to be tied to the dark matter halo. However,
central galaxies are expected to oscillate with respect to the barycenter by
$\sim 100~{}\rm km~{}s^{-1}$ (van den Bosch et al., 2005; De Propris et al.,
2021).

The nebular and molecular gas in RXJ0820.9+0752 (Vantyghem et al., 2017) are
spatially offset from the central galaxy indicating relative motion in the sky
plane. Its LOS velocity offset of $\sim 150~{}\rm km~{}s^{-1}$ indicates
redshifted motion similar to Abell 1835 and PKS 0745-191.

A displacement of one kpc can be achieved in approximately $\sim 10$ Myr
assuming a relative velocity of $100~{}\rm km~{}s^{-1}$. Therefore, the event
triggering gas displacements would have occurred between a few tens to 100 Myr
ago. Known phenomena include sloshing induced by in-falling galaxies and halos
(Markevitch & Vikhlinin, 2007; Zuhone & Roediger, 2016), AGN outbursts, and
larger-scale dynamical oscillations (van den Bosch et al., 2005).

The feedback timescale may be estimated by the time since the last major AGN
outburst in a system. X-ray cavity buoyancy ages lie between a few Myr to 120
Myr, which is consistent with our measurements. On the other hand, central
galaxies may oscillate in the cluster potential continually. This motion could
lead to several interesting effects. For example, cooling and star formation
may be offset from the center of the galaxy. Motion of the central galaxy with
nuclear black hole in tow would distribute the energy released by the AGN
throughout the atmosphere. This added heat circulation may help circumvent a
potential problem with anisotropic heating models (Heinz et al., 2006;
Vernaleo & Reynolds, 2006; Babul et al., 2013). The relative motion may
explain why radio bubbles are often misoriented with respect to the active
radio source (Fabian et al., 2006; Ubertosi et al., 2021). Ram pressure
against radio jets and lobes may disrupt and redistribute the radio plasma
into the amorphous radio emission seen in these and other systems. The
peculiar motion of the galaxy with respect to the gas may have significant
consequences for thermally unstable cooling and the observed gas kinematics.
Assuming that the quiescent nebular gas recently cooled from the hot
atmosphere and is raining (precipitating) down on the galaxy, fueling
molecular and atomic clouds, the gas and stars should have significant angular
momentum with respect to the central galaxy. Angular momentum and the change
in the apparent gravitational acceleration of cooling gas parcels could alter
substantially the assumed conditions required for thermally unstable cooling
(Pizzolato & Soker, 2005; McCourt et al., 2012; Gaspari et al., 2013; Voit et
al., 2015).

###  4.2 Systems with Simple Gas Kinematics

The simplest gas motions are found in Abell 262 and RXJ0820.9+0752. Much of
the nebular gas and all of the molecular gas in Abell 262 is in rotation about
the nucleus of the central galaxy along an E-W axis. Radio jets, oriented
$\sim 25^{\circ}$ north of east, roughly align with the angular momentum axis
of the disk. The velocity dispersion of the nebular gas sharply rises along
the jets, as seen in Fig. 9, indicating that the jets are interacting with and
disturbing the nebula. A more complete analysis of the gas and stellar
velocity fields in Abell 262 will be presented in a future paper.

The nebular gas in RXJ0820.9+0752 is offset from the central galaxy in the sky
plane and in velocity along the LOS. The gas is largely quiescent. Only a few
regions are churning with $\sigma>100$ km s-1, and they are located on the
edges of the [OII] nebula. The higher $\sigma$ edge regions may reflect
interactions with the secondary galaxy, with the star formation occurring
there, or with the atmosphere itself due to their relative motion. A secondary
galaxy lies at a projected distance of only $\sim 7.8$ kpc from the central
galaxy, with relative one dimensional speeds of $\sim 100$ km s-1. These
properties are consistent with the model proposed by Vantyghem et al. (2018)
which suggests that sloshing motions caused by the secondary galaxy may have
lifted gas from the core of the galaxy to altitudes where thermal
instabilities may occur.

###  4.3 Powerful Feedback Systems with Complex Velocity Fields

The two systems examined here, Abell 1835 and PKS 0745-191, were chosen since
their central galaxies host some of the most powerful radio AGN as well as
having some of the largest star formation rates known in a central galaxy.
Their nebular gas structures are similar. The total $\sigma$ maps reveal
larger values in the inner regions indicating disturbed gas. The nebular gas
at larger radii is more quiescent apart from regions near X-ray cavities or
jets. The inner gas is apparently churned-up by the radio AGN. These
disturbances are likely not the result of larger scale processes such as
sloshing or mergers.

Abell 1835 and PKS 0745-191 require two kinematic component fits. The second
component is sensitive to high $\sigma$ and extreme velocities. Regions with
two distinct kinematic components roughly coincide with the inner regions
where churned-up gas is found. Total v50 and $\sigma$ maps can be deceiving
when multiple kinematic components are present. Large total $\sigma$ values
may indicate broad emission lines from disturbed gas or two narrow kinematic
components with different median velocities. In two component fits, v02 and
v98 maps, as well as individual component maps, enable us to disentangle
kinematic components, map the distribution of disturbed gas, and to identify
potential inflows and outflows.

The v50 of quiescent and churned gas along the same LOS can differ by hundreds
of km s-1. However, the churned and quiescent gas in the brightest spaxels,
which contain the majority of the nebular gas, have similar median velocities,
with differences of less than 100 km s-1. Therefore, the flux-weighted median
velocities for the churned and quiescent nebular gas are similar. For Abell
1835, $\bar{\textrm{v}}_{50}$ is $+121$ km s-1 and $+175$ km s-1 for the
quiescent and the churned gas, respectively. For PKS 0745-191,
$\bar{\textrm{v}}_{50}$ is $+126$ km s-1 and $+161$ km s-1 for the quiescent
and the churned gas, respectively.

Figure 12: Median velocity map of the quiescent nebular gas in the core of
Abell 1835. For spaxels where two kinematic components were observed, the
median velocity of the first kinematic component is shown. Otherwise, the
median velocity from the one component fit is shown. The black contour roughly
encompasses the region where two kinematic components can be detected. The
dotted magenta circles show the position of the X-ray cavities.

Figures 3 and 6 show the spaxels where two kinematic components can be
disentangled along the LOS. Low velocity dispersion gas is associated with the
first kinematic component while gas associated with the second component is
significantly more disturbed and represents the churned part of the nebular
gas.

Generally, for spaxels where only one kinematic component is observed, the
nebular gas is quiescent and has properties similar to the first kinematic
component as seen in Fig. 12. Fig. 12 shows the median velocities of the
quiescent nebular gas in the central galaxy of Abell 1835. The black contour
roughly separates between the inner region, where two kinematic components are
observed, and the outer region, where only one kinematic component is
observed. We see a smooth transition in the v50 map between the inner region,
showing v50 for the first kinematic component of the two components fit, and
the outer region, showing the v50 of the one component fit.

Our observations are consistent with a model where extended quiescent nebular
gas surrounds embedded, churned-up gas which lies closer to the central AGN. A
schematic representation of this configuration is shown in Fig. 13. Our model
includes quiescent nebular gas (shown in blue) which extends to the outer
parts of the nebula and appears to have recently cooled from the X-ray
atmosphere; perhaps sharing similar kinematics to the hot atmosphere. The
inner gas is churned-up, associated with more extreme gas dynamics likely due
largely but perhaps not exclusively, to interactions with the radio jets and
lobes. As the outer gas moves into the inner regions, it can be disturbed and
lifted back out by the outward motion of the radio jets and bubbles. This
scenario is consistent with the dynamics of the different components of the
nebular gas observed in Abell 1835 and PKS 0745-191. Similar velocity
structures are observed in the Perseus cluster nebula, where churned-up gas is
present in the inner 10 kpc near the radio bubbles while quiescent, low
velocity dispersion gas extends out to 50 kpc (Vigneron et al., 2024).

This model will be clarified by X-Ray Imaging and Spectroscopy Mission (XRISM)
high resolution spectroscopy which will reveal the velocity dispersion and
radial speed of the hot atmosphere to precision similar to the Keck data.

###  4.4 Velocity Structures Near the Radio Lobes and X-ray Bubbles

Figure 13: Schematic representation of the relationships between the dynamical
states of the central galaxy (central spheroid) and its radio source (black
lines), the large-scale quiescent nebular emission (blue), and the churned
inner nebular gas (red) in the vicinity of Abell 1835’s central radio source.
PKS 0745-191 is likely similar but with the radio jets/lobes seen nearly pole-
on. Figure 14: Median velocity of the second kinematic component of the [OII]
emitting gas as a function of its projected distance along the cavities’ axis
for Abell 1835. The bottom left figure shows the v50 map for the second
component as in the top right panel of Fig. 3. The darker region shows the
spaxels included in the v50 vs distance plot and the black line shows the
projection axis. The black star shows the position of the nucleus and the grey
dashed line projects the position of the nucleus onto the cavities’ axis.
Figure 15: Median velocity of the second kinematic component of the [OII]
emitting gas as a function of its projected distance along the axis shown in
the top right figure. Symbol coding is the same as in Fig. 14.  Figure 16:
Median velocity of the second kinematic component of the [OII] emitting gas as
a function of its projected distance along the axis shown in the embedded
figure. The embedded figure shows the v50 map for the second component of PKS
0745-191 as in the top right panel of Fig. 6. Symbol coding is the same as in
Fig. 14. Figure 17: Median velocity of the second kinematic component of the
[OII] emitting gas as a function of its projected distance along the axis
shown in the embedded figure. The v50 map and other elements of the figure are
the same as in Fig. 16.

High resolution X-ray observations using the Chandra X-ray Observatory have
played a pivotal role in our understanding of AGN mechanical feedback. Large
radio jet energies can be measured to high accuracy by estimating the work
required to overpower the atmospheric pressure and inflate massive X-ray
cavities (Bîrzan et al., 2004; McNamara & Nulsen, 2007). Here we take a
different approach, using the kinematics of the nebular emission to estimate
the power required for such dynamics to occur.

To do so, we focus on the second kinematic component of the emission line fits
for Abell 1835 and PKS 0745-191 since it corresponds to the most disrupted
part of the nebula. Using the second component v50 maps (see the top right
panel of Figures 3 and 6), we searched for ordered motion and looked for signs
of interactions between the [OII] gas and the AGN feedback process. We
identified possible inflows and outflows by searching for velocity gradients
in the churned nebular gas v50 maps. Once an axis is defined along some
velocity gradient, we extract the v50 values along the projected axis and
analyze the evolution of nebular gas velocities along the chosen axis.

Different scenarios ought to be considered when testing possible gas inflows
and outflows. First, as nebular gas is observed in projection, clouds may lie
on the near side or the far side of the central galaxy. Whether the gas
associated with the observed velocity gradient, or filament, is an inflow or
an outflow depends on whether the filament is in front or behind the core of
the central galaxy. Similarly, the choice of rest-frame for the nebular gas,
usually either the gas located at the nucleus or at the other end of the
filament, impacts the inferred model. Therefore, we will generally consider
four possible scenarios, with either 1) the velocity centered on the nucleus,
or centered on the end of the filament and 2) the filament either in front of
the central galaxy or behind it. Discarding unphysical models, we can identify
possible inflows and outflows of nebular gas in our systems.

Fig. 14 shows the median velocity of the churned nebular gas in the central
galaxy of Abell 1835 projected along the X-ray cavities’ axis, shown by the
black solid line. The v50 map of the churned component is embedded in the
bottom left of Fig. 14. The median velocities are plotted as a function of
their distance along the projected axis. The zero distance is defined as the
projected position of the nucleus onto the cavities’ axis, which is where the
grey dashed line and the solid black line intersect.

Fig. 14 shows an overall gradient in the velocity of the churned nebular gas
along the cavities’ axis. From the SE to the NW cavity, the gas velocity
decreases from $+350$ km s-1 to $-30$ km s-1, with a central velocity of
roughly $+165$ km s-1. Centering the rest-frame velocity on the nebular gas
velocity at the nucleus, the filament extending towards the SE cavity is
redshifted, while the one extending towards the NW cavity is blueshifted.

For the negative distances in Fig. 14 which correspond to gas SE of the
nucleus, the projected median velocities increase linearly towards the SE
cavity. This suggests a constant acceleration where we can calculate the
average acceleration using:

$a=\frac{v^{2}-v_{0}^{2}}{2\Delta x},$ (4)

where $a$ is the acceleration, $v$ is the final velocity, $v_{0}$ is the
initial velocity and $\Delta x$ is the distance covered by the nebular gas. We
calculate a mean acceleration of $1.28\times 10^{-14}$ km s-2 along the SE
filament, for a velocity change ($\Delta$v) of 118 km s-1 and a length of 17.6
kpc. If the SE filament is in front of the central galaxy, the gas, which is
redshifted, must be moving towards the center of the galaxy and decelerating
as it moves closer to the nucleus. This scenario can be discarded as it is
unphysical and cannot be achieved through gravitational infall onto the
central galaxy, jet activity or as a result of galaxy motion without extreme
fine-tuning. On the other hand, if the SE filament is behind the central
galaxy, the gas accelerates away from the central galaxy in an outflow. This
is consistent with jet-driven outflows.

Fig. 14 shows another filament, NW of the nucleus, where gas velocities
decrease away from the nucleus. With the same rest-frame velocity as before,
the NW filament is blueshifted and accelerating away from the nucleus.
Contrary to the SE filament, the curve in the velocity function indicates that
gas acceleration is not constant, with slight changes in acceleration at both
ends of the filament. With a $\Delta$v of 213 km s-1 along a 19.2 kpc
filament, we calculate a mean acceleration of $3.82\times 10^{-14}$ km s-2. If
the NW filament is in front of the central galaxy, the gas is blueshifted,
accelerating away from the nucleus, which is consistent with a jet-driven
outflow. The NW filament cannot be behind the central galaxy as this would
correspond to a decelerating inflow of gas, which is unphysical.

The velocity gradient observed along the cavities’ axis in the central galaxy
of Abell 1835 is consistent with a bipolar jet outflow. Both the NW and SE
filaments are observed trailing known X-ray cavities, which supports the
theory of bipolar jet driven outflows, including the entrainment and
subsequent cooling of central gas by X-ray cavities. As expected for bipolar
outflows, one cavity, NW, is on the near side of the central galaxy while the
other one, SE, is on the far side. The dynamics of the churned disturbed gas
along the axis connecting the SE and NW cavity is consistent with bipolar jet-
driven outflows of gas and entrainment.

In order to test for possible errors which may cause erroneous detections of
velocity gradients in our kinematic maps, we applied our analysis method to
the axis perpendicular to the cavities’ axis as we do not expect coherent
motion there unless caused by a separate process. As expected, the v50 of the
churned nebular gas show no correlation with the distance along the axis
orthogonal to the X-ray cavities.

Fig. 15 is similar to Fig. 14 and shows the median velocities of the churned
gas as a function of its projected distance from a different axis of interest,
which is identified in the embedded figure.

Fig. 15 shows a velocity gradient running from $\sim 13$ kpc east to $\sim 13$
kpc west of the nucleus. The east-west v50 decrease from $+380$ km s-1 to
$+15$ km s-1. The scatter in the trend increases dramatically at 7 kpc to the
east and to a lesser degree at a similar distance to the west. The eastern
increase in scatter roughly occurs at the peak v50 region, identified as
Region B in Appendix B.1. This region corresponds approximately to the
location of known molecular clouds (McNamara et al., 2014). The amplitude of
the velocity scatter exceeds $600~{}\rm km~{}s^{-1}$ far from the nucleus,
indicating a strong interaction or high impact event.

For the motion observed in Fig. 15, we considered three possible rest-frame
scenarios for the nebular gas, with it being at rest at the
easternmost/westernmost point or at the nucleus. Scenarios with the rest-frame
centered on either end of the filament are unlikely as the nebular gas would
need to continuously accelerate past the nucleus which cannot be achieved from
gravitational infall, AGN-driven outflows or central galaxy motion alone and
without fine-tuning. Therefore, we focus on the scenario where the nebular gas
at the center of the galaxy is at rest such that the eastern gas is redshifted
and the western gas is blueshifted.

The median velocities of the gas west of the nucleus, which has positive
projected distances in Fig. 15, decrease away from the nucleus. The velocity
curve shows a non-constant acceleration, with the acceleration decreasing with
projected distance from the nucleus. The nebular gas is blueshifted with an
average acceleration of $3.41\times 10^{-14}$ km s-2 for a velocity change of
177 km s-1 along a 14.9 kpc filament. The western filament is in front of the
central galaxy. In this scenario, the nebular gas accelerates away from the
central galaxy, which is consistent with an AGN-driven outflow. The western
filament being behind the central galaxy would result in a decelerating gas
inflow which is unphysical.

For the negative projected distances of Fig. 15, east of the nucleus and up to
$\sim 6$ kpc away, v50 increase with distance from the nucleus. The velocity
curve shows roughly constant acceleration. The churned gas within 6 kpc east
of the nucleus is redshifted with an average acceleration of $2.06\times
10^{-14}$ km s-2 for a velocity change of 86 km s-1 along the inner 5.8 kpc of
the eastern filament. Analogously to the western filament, the eastern
filament must be located behind the central galaxy, resulting in an
accelerated outflow consistent with jet-driven motion.

Using the churned nebular gas velocity at the projected nucleus as the rest-
frame of our system, the velocity gradients observed in Figures 14 and Figures
15 are consistent with four jet-driven outflows. The SE and NW filaments
appear to be trailing the SE and NW cavities which is consistent with the
uplift model. The filaments roughly coincide with the 1.5 ″radio jet observed
by O’Dea et al. (2010). This jet, discovered using VLA 5 GHz observations,
initially points towards the west and then curves to point in the NW
direction. This roughly corresponds to the two velocity gradient axes seen in
the churned nebular gas v50 map.

Nebular gas inflows and outflows are also seen in the second kinematic
component velocity maps of PKS 0745-191. The second component v50 map, shown
in the top right panel of Fig. 6, appears to have two velocity gradients.
Figures 16 and 17 show the median velocities of the churned nebular gas
projected onto the NE-SW and SE-NW axes, respectively, as a function of their
projected distance from the projected center. The embedded figures show the
v50 map of the second component, as in the top right panel of Fig. 6. The
symbols and lines overlaid on the velocity maps are analogous to the ones in
Figures 14 and 15.

Fig. 16 shows a smooth gradient along a NE-SW axis, about $\pm 2-3~{}\rm kpc$
on either side of the nucleus with an amplitude of about $200~{}\rm
km~{}s^{-1}$. At the projected center, v50 is $\sim+135$ km s-1. This
corresponds to a mean accelerations of $1.7\times 10^{-14}$ km s-2 and
$5.7\times 10^{-14}$ km s-2 in the innermost kpc along the NE and the SW
filaments, respectively. Beyond a radius of $-3~{}\rm kpc$ the gas accelerates
dramatically to $+850$ km s-1 along the NE filament.

Similarly to the gas motion along the two axes in Abell 1835, the rest-frame
velocity is taken to be the velocity of the nebular gas at the projected
centroid since using the NE or SW end of the overall filament results in an
unphysical model. The NE filament cannot be located in front of the central
galaxy as this would result in a decelerating gas inflow, which is unphysical.
Instead, it is located behind the central galaxy, corresponding to an
accelerated outflow. Similarly, the motion of the SW filament corresponds to
an accelerated gas outflow, located in front of the central galaxy.

The motion of the churned-up nebular gas along the NE-SW axis seen in Fig. 16
is consistent with two accelerated outflows with the NE filament located
behind the central galaxy and the SW filament in front. Although the gas
kinematics observed along the NE-SW axis are similar to those seen in AGN-
driven outflows, there is a lack of evidence of AGN activity such as jets
and/or cavities along this axis. The relationship between these velocity
structures and the central AGN, if any, is unclear.

Fig. 17 shows the median velocity of the nebular gas as a function of their
projected distance along the SE-NW axis. This axis somewhat aligns with the
position of the SE and NW X-ray cavities. Fig. 17 shows two velocity
gradients, with a V shape, whose vertex lies $\sim 2.4$ kpc NW of the nucleus.
The gas velocity at the vertex is close to 0 km s-1.

Median velocities of the churned nebular gas along the SE cut increase
smoothly away from the vertex from $-20$ km s-1 to $+200~{}\rm km~{}s^{-1}$ at
$-3$ kpc, resulting in a mean acceleration of $1.2\times 10^{-13}$ km s-2. At
larger negative distances the scatter in v50 dramatically increases, with
values between $+625$ km s-1 and $-100$ km s-1. The explanation for this large
increase in scatter is unknown. Projection effects may be responsible for this
large scatter in v50.

North-west of the vertex, projected churned-up gas velocities increase from
$-20$ km s-1 up to $+300$ km s-1 at $+7$ kpc NW of the nucleus with a mean
acceleration of $3.7\times 10^{-13}$ km s-2. Beyond $\sim 7$ kpc NW of the
projected centroid, the scatter in median velocities significantly increases,
with v50 between $+250$ km s-1 and $+625$ km s-1. Similar sudden increases in
velocity scatter have been observed in gas outflows, usually associated with
high impact events, such as colliding with denser gas clouds, or other
significant interactions.

To determine the positions of the churned-up gas filaments, the rest-frame is
taken to be the velocity of the gas at the vertex, as other choices of rest-
frame are either unphysical or require unlikely fine-tuning. If either the SE
or the NW filament are located in front of the central galaxy, the resulting
decelerating gas inflow would be unphysical. Therefore, both the SE and the NW
filaments must be located behind the central galaxy, which corresponds to
accelerated gas outflows. With the SE and NW filaments roughly trailing the SE
and NW X-ray cavities, the kinematics of the churned-up nebular gas along the
SE-NW axis are consistent with AGN-driven outflows and subsequent gas uplift.
According to this model, both the SE and the NW cavities are located behind
the central galaxy.

The position of the X-ray cavities is unconventional, and so is the shape of
the velocity function (Fig. 17). Bipolar jet-driven outflows generally have
one cavity in front of the central galaxy and one behind, contrary to our
observations for PKS 0745-191 which indicate that both cavities are behind the
central galaxy.

As the SE cavity is much closer to the nucleus than the NW cavity, this could
be explain by different epochs of cavities, where the jet strongly precesses
between outbursts. Multiple epochs of cavities in varying directions have been
observed in other systems, supporting the theory that jets can change
orientation (Perseus (Dunn et al., 2006), Abell 2390 (Augusto et al., 2006),
RBS797 (Gitti et al., 2006), RX J1532.9+3021 (Hlavacek-Larrondo et al.,
2013)). However, while multiple outbursts and jet precession could explain the
position of the cavities, we do not observe any indication of counter-jets
associated with these outbursts, making this theory unlikely.

Figure 18: Diagram of the motion of the X-ray cavities and their surroundings
in a system with significant motion of the central galaxy along our LOS. The
top panel shows the system at the time when the AGN-driven jets inflate the
X-ray cavities. The model assumes that the cavities are inflated along the
plane of the sky. The top panel shows the position of the X-ray cavities at a
time $\Delta$t after the cavities were inflated. The cavities are shown as
dotted circles. The blue arrows show the galaxy’s peculiar velocity and the
resulting wind velocity. The purple arrows show the buoyancy velocity of the
cavities, which always points away from the central galaxy. In the lower
panel, the black arrows show the resulting velocity on each cavity. The gas
trailing the X-ray cavities is shown in red.

Peculiar motion of the central galaxy is another possible explanation for the
shape of the velocity function and the unconventional position of the
cavities. We suggest that the V-shaped velocity gradient seen in Fig. 17 is
caused by the peculiar motion of the central galaxy combined with AGN-driven
jets and subsequent X-ray cavities inflated roughly in the plane of the sky.
Fig. 18 shows a diagram of the motion of the X-ray cavities and their
associated gas in a system with significant peculiar motion of the central
galaxy. The top panel describes the dynamics in the core of PKS 0745-191
initially at time $t=0$ after the jet inflates the cavities. The lower panel
shows the cavity trajectories governed by buoyancy and ram pressure vectors at
a later time $\Delta$t. The red dots represent cool [OII] gas which we assume
has been advected outwards creating the observed velocity gradients. As seen
in the lower panel of Fig. 18, both cavities are located behind the central
galaxy, which is consistent with our observations. This model can explain how
two cavities, which were inflated at the same time and by the same bipolar
jet, can both lie behind the central galaxy. In the plane of the sky, Fig. 18
shows that the SE cavity ends up closer to the nucleus than the NW cavity,
which is consistent with observations (Sanders et al., 2014).

###  4.5 Molecular Gas Masses

The targets presented here have been observed with ALMA for CO(1-0), CO(2-1),
or CO(3-2), or a combination thereof. Throughout the result section, we have
highlighted similarities in the distributions of nebular gas and molecular
gas. Although detected CO emission is significantly less extended that
detected [OII] emission, for regions where both CO and [OII] emission are
detected, the ratio of CO flux to [OII] flux is roughly constant. Therefore,
since detection of CO emission is more challenging than [OII] detection, we
tried using [OII] as a proxy for CO, allowing for an hypothetical extended
study of the molecular gas.

To do so, we determine the ratio of the [OII] luminosity to
M${}_{\textrm{mol}}$ within the region where the CO integrated flux is at
least 10% of its peak value. This region corresponds to the areas enclosed by
the CO contours in the right panel of Figures 1, 4, 7, and 10. Then, using
this ratio and the total [OII] luminosity within the FOV, we scale the
observed molecular gas mass to estimate the total M${}_{\textrm{mol}}$ that
could be spanning the same spatial region as the extended nebula. Table 4
enumerates the values used in our calculations. Under the assumption that the
ratio of [OII] luminosity to molecular gas mass within an object is constant,
we infer possible molecular gas masses of $1.3\times 10^{11}$ M⊙, $3.0\times
10^{10}$ M⊙, $1.3\times 10^{9}$ M⊙ and $1.1\times 10^{11}$ M⊙ for Abell 1835,
PKS 0745-191, Abell 262 and RXJ0820.9+0752, respectively. Therefore, if the
L[OII] to Mmol ratio is roughly constant, our central galaxies may harbour
cold gas reservoirs three to six times greater than is currently observed.

###  4.6 Molecular Gas Kinematics

In comparing the kinematics of the nebular and molecular gas, it is worth
noting that gas velocities depend on the choice of systemic velocity. Both the
molecular and the nebular gas must be using the same systemic velocity. For
our four targets, previous papers studying their molecular gas dynamics used
emission lines, either from CO or from ionized gas, to determine the system’s
systemic velocity. We defined our systemic velocities based on stellar
velocities in the core of the central galaxies. Our systemic redshifts are all
lower than the ones used for the molecular gas dynamics (McNamara et al.,
2014; Russell et al., 2016; Olivares et al., 2019; Vantyghem et al., 2018),
with velocity differences of 192 km s-1, 111 km s-1, 64 km s-1 and 156 km s-1
for Abell 1835, PKS 0745-191, Abell 262 and RXJ0820.9+0752, respectively. The
molecular and nebular gas velocities discussed in this section have been
shifted to a common systemic velocity.

For Abell 1835, McNamara et al. (2014) reported a possible bipolar flow of
$10^{10}~{}M_{\sun}$ of molecular gas to the north-west and east of the
nucleus. Similar outflows to the ones depicted in Figures 14 and 15 are
observed in CO(1-0) (see Figure 5 in McNamara et al. (2014)). General velocity
trends observed in the molecular gas maps are also seen in the nebular gas
maps. The eastern high velocity gas clump and the NW lower velocity clump
shown here were observed in the molecular gas by McNamara et al. (2014).
However, the increase in velocity in the eastern gas clump is more pronounced
for the CO(1-0) map than for the [OII] map. Overall, similarities between the
kinematics of molecular and nebular gas seem to indicate that the dynamics of
the molecular gas generally consistent with what is observed for the nebular
gas. This supports the theory that the molecular gas has cooled out of the
surrounding gas.

Here we look into the power required to displace the molecular gas. Table 4
shows that the mass of molecular gas is 2-3 orders of magnitude larger than
the mass of ionized gas. Therefore, when calculating the energy or the power
of a system, we use the molecular mass. As the velocities of the nebular gas
are similar to those of the molecular gas, we use the nebular gas’
acceleration in our calculations. Taking the acceleration values calculated in
Section 4.6 for the four potential gas outflows observed in the core of Abell
1835 and using a displaced mass of 1010 M⊙, forces of $7.6\times 10^{34}$ erg
cm-1, $2.6\times 10^{34}$ erg cm-1, $6.8\times 10^{34}$ erg cm-1 and
$7.6\times 10^{34}$ erg cm-1 are required for the motion observed along the
NW, SE, W and E filaments, respectively. This corresponds to kinetic energies
of $2.3\times 10^{57}$ erg, $6.9\times 10^{56}$ erg, $1.6\times 10^{57}$ erg
and $3.6\times 10^{56}$ erg, for the NW, SE, W and E filaments, respectively.
We take the kinetic energy to be the product of the displacement force and the
displacement, where the former is taken to be half of the length of the
nebular gas filament detected. Using X-ray mass profiles from Hogan et al.
(2017) and Pulido et al. (2018), the gravitational potential energy of the
molecular gas in each filament is estimated to be roughly 1059 erg. The
gravitational potential energy is generally two orders of magnitude greater
than the kinetic energy associated with gas dynamics such that the total
energy of each of the four tentative outflows is taken to be $10^{59}$ erg.

Flow time is estimated using the velocity and acceleration values previously
calculated from nebular gas dynamics. The age of the gas filament is:

$t=\frac{v-v_{0}}{a}$ (5)

where $v$ is the final velocity, $v_{0}$ is the initial velocity and $a$ is
the acceleration. Since the nebular gas velocity at the nucleus is taken as
the rest-frame, the initial velocity is zero, by definition, and the final
velocity is the change in velocity from the edge of the filament to its
beginning. The age of the filaments are 177 Myr, 291 Myr, 165 Myr and 131 Myr
for the NW, SE, W and E filaments, respectively. Dividing the total energy of
each filament by its age, we obtain the minimum power required for these
potential outflows. The NW, SE, W and E filaments require powers of 2$\times
10^{43}$ erg s-1, $10^{43}$ erg s-1, 2 $\times 10^{43}$ erg s-1 and 3 $\times
10^{43}$ erg s-1, respectively. Many assumptions were made in these
calculations but overall, for outflows containing $\sim 10^{10}$ M⊙ of cold
and warm gas (McNamara et al., 2014), powers of $\sim 10^{43}$ erg s-1 are
required to drive the gas motions observed. This is consistent with powers
observed in other systems with AGN-driven outflows (Pulido et al., 2018;
Tamhane et al., 2022).

Copious amounts of molecular gas lie in the inner regions of PKS 0745-191,
which has been observed through CO(1-0) and CO(3-2) emission. Almost $5\times
10^{9}$ M⊙ of molecular gas is distributed in three filaments, N, SE and SW
(Russell et al., 2016). The [OII] emission is much more extended than the CO
emission, resulting in only a small area where nebular and molecular gas
velocities can be compared. For the regions where this is possible, we do not
observe a clear relation between velocities of the molecular and nebular gas.

For RXJ0820.9+0752 and Abell 262, the median velocities of the nebular gas
show similar trends as for the molecular gas (Vantyghem et al., 2018; Olivares
et al., 2019).

For RXJ0820.9+0752, the molecular gas systemic velocity from Vantyghem et al.
(2018) is obtained from spatially-integrated CO emission lines. For regions
with both molecular and nebular gas, the velocity maps of the CO(1-0) and
CO(3-2) are similar to the velocity maps we observe. Vantyghem et al. (2018)
detected two kinematic components, in both CO(1-0) and CO(3-2), while we
detected only one kinematic component in our observations. However, deeper
observations of the warm ionized gas may reveal a second kinematic component,
allowing for the comparison of molecular and nebular gas velocities for each
kinematic component.

The similar median velocities of the molecular and nebular gas in Abell 262
support the idea that the circumnuclear disk around the central AGN contains
multiphase gas, with both molecular and nebular gas coexisting. The nebular
gas in the circumstellar disk is more disturbed than the molecular gas, with
$\sigma_{\textrm{[OII]}}$ up to 193 km s-1, while the molecular gas velocity
dispersion plateaus around 130 km s-1.

##  5 Summary

We investigate the dynamics of the warm nebular gas in and around the central
galaxies of four clusters, Abell 1835, PKS 0745-191, Abell 262 and
RXJ0820.9+0752, using KCWI observations. We explore both the morphology and
the dynamics of these four galaxies, focusing on the [OII] nebular emission.
We combine our observations with previous multiwavelength studies, including
radio and X-ray observations, delving into the dynamics of the multiphase gas
in clusters cores.

  * •

We detect significant line of sight velocity differences, roughly $+150$ km
s-1, between the nebular gas and the stars in the core of the central galaxy
in three of our four targets: Abell 1835, PKS 0745-191 and RXJ0820.9+0752.
Comparing the morphology and the kinematics of the central galaxy and its
nebular gas, we conclude that the central galaxy has a peculiar velocity with
respect to its surroundings. Peculiar motion of central cluster galaxies in
the plane of the sky have been inferred to explain spatial offsets between
central galaxies and their associated nebular gas as is found here in
RXJ0820.9+0752. The LOS velocity offsets measured here are consistent with
inferred velocities in the sky plane required to explain spatial offsets and
asymmetries in galaxy morphologies.

  * •

Two distinct velocity components are found in the nebular gas surrounding the
Abell 1835 and PKS 0745-191 central galaxies. Higher velocity dispersion
churned gas is found towards and behind X-ray cavities surrounded by lower
velocity dispersion, quiescent gas extending to higher altitudes. Median
velocities of the quiescent and churned nebulae differ by $\sim 45$ km s-1.
Energy input from the AGN is likely churning up the gas.

  * •

Molecular and nebular gas in central galaxies are spatially correlated such
that the brightest CO and [OII] emission are coincident. However, the detected
[OII] gas is much more extended by tens of kpc. Three to six times the
molecular gas mass of the bright, centrally located molecular clouds may lie
in a diffuse state. The velocity structures of the molecular and nebular gas
are broadly similar but do not match in detail.

  * •

High velocity dispersion nebular gas (Fig. 9) is observed along the radio jets
in the Abell 262 central galaxy, indicating a strong interaction between the
jets and surrounding gas. The jets are emerging along the angular momentum
axis of a disturbed, possibly nascent circumnuclear disk.

The data presented herein were obtained at the W. M. Keck Observatory, which
is operated as a scientific partnership among the California Institute of
Technology, the University of California, and the National Aeronautics and
Space Administration. The observatory was made possible by the financial
support of the W. M. Keck Foundation. We wish to recognize and acknowledge the
very significant cultural role and reverence that the summit of Maunakea has
always had within the indigenous Hawaiian community. We are most fortunate to
have the opportunity to conduct observations from this mountain. We thank
Prathamesh Tamhane and Adrian Vantyghem for generously providing us with CO
detection maps. B.R.M acknowledges support from the Natural Sciences and
Engineering Council of Canada and the Canadian Space Agency Space Science
Enhancement Program. A. L. C. acknowledges support from the Ingrid and Joseph
W. Hibben endowed chair at UC San Diego.

##  Appendix A Appendix A

Figure 19: Fit of the spatially-integrated stellar continuum at the core of
the central galaxy of Abell 1835. The top panel shows the spectrum, in black,
and the stellar continuum fit, in red, from which the systemic velocity of the
system was obtained. The bottom panel shows the same spectrum and, in blue,
the stellar fit shifted to the flux-weighted median v50. The fitting method
used is described in Section 2.3. Figure 20: Fit of the spatially-integrated
stellar continuum in the core of the central galaxy of PKS 0745-191. As in
Fig. 19, the top panel shows the stellar fit at the systemic velocity and the
bottom panel shows the same fit shifted to the flux-weighted median v50.
Figure 21: Fit of the spatially-integrated stellar continuum in the core of
the central galaxy of RXJ0820.9+0752. As in Fig. 19, the top panel shows the
stellar fit at the systemic velocity and the bottom panel shows the same fit
shifted to the flux-weighted median v50.

The measurement of systemic velocities followed the procedure outlined in
Section 2.3. In our approach, we employ stellar absorption lines and stellar
population models to derive the stellar velocity of the systems, operating
under the assumption that these stars are gravitationally bound to the central
galaxy, with the central stellar velocity reflecting the velocity of the
central galaxy. Spaxels surrounding the peak of the stellar emission are
spatially-integrated, yielding a high-quality central spectrum. Then, masking
the emission lines, the stellar continuum is fitted using a combination of
stellar templates. The mean stellar velocity in the core of the galaxy is
obtained from this fit and used as the systemic velocity.

The top panel of Fig. 19, 20 and 21 show the central stellar fits obtained for
Abell 1835, PKS 0745-191 and RXJ0820.9+0752, respectively. For Abell 1835 and
PKS 0745-191, the stellar continuum shows strong Balmer absorption lines which
are caused by a strong intermediate age stellar population. This raised
concern that this population, if kinematically distinct from the older stellar
population, may bias our systemic velocity and not properly represent the
velocity of the central galaxy. To verify that the older stellar population,
which is expected to be strongly bounded to the core of the central galaxy, is
correctly fitted by our stellar model, we looked at the goodness of the fit
for the Ca H & K lines, which originate primarily from old stars. The figures
embedded in the upper panel of Fig. 19, 20 and 21 show that the Ca H & K lines
are correctly fitted by the model, showing that the intermediate stellar
population is not biasing our systemic velocities.

Fig. 19, 20 and 21 show velocity differences of $\sim 150$ km s-1 between the
central nebular gas and the systemic velocities in three out of our four
target systems, as discussed in Section 4.1. The lower panels of Fig. 19, 20
and 21 show the stellar continuum models shifted to the central nebular gas
velocity. In all instances, the shifted stellar models do not fit the observed
spectrum as well as the non-shifted one, thus confirming the reality of the
peculiar nebular velocities.

##  Appendix B Additional comments on kinematics

###  B.1 Abell 1835

Figure 22: Kinematics of the [OII]3726,9$\lambda\lambda$ emission line doublet
in Abell A1835 as in Fig. 2 with regions of interest listed in Table 5
identified by solid ellipses. Table 5: Abell 1835 regions

Region |  v50 | $\sigma$ |  v02 |  v98 |  Fraction L[OII] | Dist | $\theta$ | Area
---|---|---|---|---|---|---|---|---
|  (km s-1) |  (km s-1) |  (km s-1) |  (km s-1) | (%) | (kpc) |  (⋅) |  (kpc2)
A | 165 | 136 | 482 | -102 | 21.08 | 0.0 | 0 | 52
B | 227 | 164 | 633 | -61 | 12.61 | 8.3 | 0 | 83
C | 224 | 150 | 536 | -83 | 2.82 | 13.2 | 297 | 122
D | 51 | 111 | 312 | -236 | 15.73 | 13.5 | 52 | 201
E | 87 | 125 | 352 | -175 | 5.51 | 10.7 | 264 | 88
F | 211 | 100 | 416 | 5 | 0.42 | 25.1 | 45 | 39

Note. —

(1) Region identified in Fig. 22.

(2) [OII] flux weighted mean of the median velocity within the region.

(3) [OII] flux weighted mean of the velocity dispersion within the region.

(4) [OII] flux weighted mean of the v02 within the region.

(5) [OII] flux weighted mean of the v98 within the region.

(6) Fraction of the total [OII] luminosity observed from the spaxels included
in the region.

(7) Distance between the central point of the region and the nucleus.

(8) Average angle between the center of the galaxy and the region. The angle
is 0∘ when pointing east and increases clockwise.

(9) Area of the region.

Figure 23: Fit of the [OII] emission line from the spatially-integrated
spectrum of each of the six regions identified in Fig. 22 and Table 5. The
black histogram shows the observed spectrum, the red and blue dashed lines
show the first and second Gaussian kinematic components of the fit,
respectively. The black solid line shows the resulting total fit of the
emission line. The turquoise dotted line identifies the systemic velocity used
for this target.

Fig. 22 shows the same panels as in Fig. 2 using different color scale bars to
emphasize differences. Six regions, A-F, are identified on the velocity maps
as regions of interest. Various properties of these regions are listed in
Table 5, including position, size, flux-weighted mean velocities (see equation
3), and relative contribution to [OII] luminosity.

To get a clear picture of the kinematics in each region, Fig. 23 shows the
[OII] line doublet and the best-fit model for each of the regions identified
in Fig. 22. It is worth noting that since [OII]3726,9 is a doublet, each
component is comprised of two Gaussians, one for each doublet line. The higher
signal-to-noise in the spatially-integrated spectra can reveal a second
kinematic component within a region which is not always robustly detected in
the individual spaxels.

Region A is a circle with a radius of 1” centered on the nucleus. The ionized
gas at the very center of the galaxy does not share the same velocity as its
projected stellar population. The central gas is overall redshifted by 165 km
s-1 with respect to the systemic velocity.

The nebular gas in region B has the largest v50, $\sigma$ and v02 values
observed in this system. Region B is located just north of the edge of the SE
cavity, although it is not located along the axis of the cavities. The high
velocity dispersion, $\geq 150$ km s-1 indicates that the gas is disturbed.
Fig. 23 shows the two component fit for region B. The second component (shown
in blue) is significantly more redshifted ($>+130$ km s-1) and broader
($\sigma\sim 95$ km s-1) than the first component (shown in red).

Region E is located on the opposite side of the nucleus, roughly at the same
distance from the center as region B. While the gas in region B is redshifted
with respect to the gas in the nucleus, the gas in region E is blueshifted.
The spectral fits of regions A, B and E in Fig. 23 show that both kinematic
components are redshifted from region A to region B, and conversely are
blueshifted from region A to region E. The second, broader kinematic component
has the most significant velocity differences, of order of hundreds of km s-1.
The dynamics of the nebular gas in regions A, B and E seem to indicate motion
of the nebular gas along the E-W axis passing through the center.

Regions C and D are another interesting pair of regions which spatially
overlap with the SE and NW X-ray cavities, respectively. Both regions are
roughly 13 kpc from the nucleus. The nebular gas in region C is redshifted
with respect to the central nebular gas, while the nebular gas in region D is
blueshifted. The spectral fits of the [OII] doublet for regions A, C and D
(see Fig. 23) show significant shifts in velocities, especially for the second
component with v50 differences of more than 150 km s-1. Additionally, there is
substantial broadening of the second component in region C compared to region
A, and slight broadening of the second component in region D compared to
region A. The spatial overlap with X-ray cavities and the substantial velocity
shifts and line broadenings are consistent with the cavities playing an
important role in the nebular gas dynamics of regions C and D.

The nebular gas in region F has higher v50 and slightly higher $\sigma$ than
the surrounding gas. While this region overlaps partially with one of the
projected galaxies, it is not expected to significantly affect the gas
dynamics in this region, as the velocity difference of almost 1000 km s-1
between the projected galaxy and the nebular gas argues against any
interaction between them. Region F also overlaps with the northern edge of the
NW cavity. However, as the edges of X-ray cavities are particularly
challenging to precisely define, we cannot confidently ascertain a relation
between the NW cavity and this region.

###  B.2 PKS 0745-191

Figure 24: Kinematics of the [OII]3726,9$\lambda\lambda$ emission line doublet
in PKS 0745-191 as in Fig. 5 with regions of interest mentioned in Table 6
identified by solid ellipses. Table 6: PKS 0745-191 regions

Region |  v50 | $\sigma$ |  v02 |  v98 |  Fraction L[OII] | Dist | $\theta$ | Area
---|---|---|---|---|---|---|---|---
|  (km s-1) |  (km s-1) |  (km s-1) |  (km s-1) | (%) | (kpc) |  (⋅) |  (kpc2)
A | 130 | 267 | 889 | -597 | 22.81 | 1.1 | 0 | 11
B | 166 | 309 | 1145 | -350 | 1.78 | 4.3 | 148 | 6
C | 189 | 304 | 814 | -439 | 0.63 | 5.6 | 315 | 9
D | 246 | 222 | 718 | -187 | 9.69 | 8.7 | 23 | 39
E | 304 | 99 | 509 | 99 | 0.32 | 9.9 | 257 | 16
F | 81 | 146 | 429 | -260 | 9.56 | 9.7 | 69 | 53

Note. —

(1) Region identified in Fig. 24.

(2) [OII] flux weighted mean of the median velocity within the region.

(3) [OII] flux weighted mean of the velocity dispersion within the region.

(4) [OII] flux weighted mean of the v02 within the region.

(5) [OII] flux weighted mean of the v98 within the region.

(6) Fraction of the total [OII] luminosity observed from the spaxels included
in the region.

(7) Distance between the central point of the region and the nucleus.

(8) Average angle between the center of the galaxy and the region.

(9) Area of the region.

Figure 25: Spectra for the summed regions identified in Fig. 24 and Table 6.
The turquoise dotted line identifies the systemic velocity used for this
target.

Fig. 24 defines six regions of interest in the LOS kinematics map, shown as
black solid ellipses. Otherwise, Fig. 24 is identical to Fig. 5. Following the
same method as in Section 3.1.2, Table 6 lists some properties of the
highlighted regions and Fig. 25 shows the best-fit model of the spatially-
integrated spectrum around the [OII] doublet for each region.

Region A is the central region with high velocity dispersion gas and large v02
and v98 values. This region includes the center of the galaxy, defined using
the stellar flux. The center of Region A is offset $\sim 1$ kpc east of the
nucleus. The nebular gas in this central region is redshifted by +130 km s-1.
Fig. 25 shows that the gas associated with the second component of the fit is
very disturbed, with a velocity dispersion $\sim 420$ km s-1. Even the narrow
component of the fit for Region A is quite broad, with $\sigma=162$ km s-1.
The most-redshifted gas velocities of almost $+900$ km s-1 and the most-
blueshifted velocities of almost $-600$ km s-1 result from the extreme
velocities attained by the very disturbed central gas.

Region B has the nebular gas with the largest total velocity dispersion and
the most-redshifted velocities observed in this galaxy. Fig. 25 shows that the
large $\sigma$ and v02 values are caused by the broad and redshifted second
kinematic component. The nebular gas modelled by the second kinematic
component, which emits 40% of the total flux in Region B, has v50 and $\sigma$
values greater than 450 km s-1. These dynamics are consistent with a very
powerful outflow.

The gas in Region C has $\sigma$ values similar to the gas in Region B.
However, the most-redshifted gas in Region C is not as redshifted as in Region
B, with flux-weighted mean v02 of $+814$ km s-1 and $+1145$ km s-1,
respectively. Fig. 25 shows similarities in the integrated spectra of regions
B and C. The gas associated with the first component have similar kinematics.
In both regions, the second kinematic component is significantly redshifted,
with v${}_{50}\sim+518$ km s-1 for Region C. The main difference in the gas
kinematics of Regions B and C is the velocity dispersion of the second
component. The gas associated with the second component in Region C is
disturbed, with $\sigma=183$ km s-1, albeit significantly less than the high
velocity gas in Region B where the velocity dispersion is more that 2.5 times
larger. The large gas velocities of the second kinematic component in Region C
are consistent with an inflow or outflow of gas. The significant difference in
the velocity dispersion of the high velocity gas in Regions B and C hint to
different mechanisms responsible for the gas dynamics in each region, with a
more gentle process occurring in Region C. Region C lies within the SE cavity,
which may be disturbing surrounding gas and causing the several hundred km s-1
gas motions.

Regions D and E encompass the large v50 filament as seen in the top left panel
of Fig. 24. The $\sigma$, v02 and v98 maps in Fig. 24 show clear differences
between the upper and lower regions of the $\sim+280$ km s-1 filament. Region
D corresponds to the northern, more disturbed, part of the filament while
Region E represents the southern, more quiescent part.

Region D encompasses the northernmost section of the redshifted filament. The
gas in Region D is quite disturbed, with $\sigma>200$ km s-1. Most of the gas
in Region D is modelled by the second component of the fit as shown in Fig.
25. The majority of the nebular gas in Region D is redshifted by $\sim+300$ km
s-1 and significantly disturbed. Part of Region D lies within and on the edge
of the NW cavity. The large v50 filament lies south of the NW cavity. It does
not align with the nucleus-cavity axis where we would expect gas entrained by
X-ray cavities to lie.

Region E contains the southern, more quiescent, part of the high v50 filament.
Fig. 25 shows that Region E is the only region whose spatially-integrated
spectrum is fitted using a single kinematic component. In Region D, the first
kinematic component (red) is quite faint. It becomes too faint to be detected
in Region E. Region E has the most redshifted total median velocities,
although the gas associated with the second kinematic component in Regions B
and C is more redshifted. Interestingly, the gas in Region E has large v50 but
low $\sigma$, such that while the nebular gas is moving at a speed of $\sim
300$ km s-1, it is not being significantly disturbed.

Region F is the region NW of the nucleus which has low v50 (see Fig. 24, upper
left panel) and low $\sigma$ compared to surrounding gas (see Fig. 24, upper
right panel). Region F partially overlaps with the NW cavity. Although the
edges of the cavities are quite uncertain, the edge of the NW cavity roughly
coincides with the place where the low v50 filament separates into two
filaments. The gas in Region F has low velocity dispersion compared to the gas
in Regions A, B, C and D. However, as seen in Fig. 25, the broadcomponent of
the [OII] emission line fit in Region F has $\sigma>200$ km s-1. A significant
fraction of the nebular gas in Region F is disturbed, albeit not as much as
some of the other regions studied. The NW cavity may be playing an important
role in the kinematics of Region F, although we cannot confidently establish a
link between the two structures.

###  B.3 RXJ0820.9+0752

Figure 26: Kinematics of the [OII]3726,9$\lambda\lambda$ emission line doublet
in RXJ0820 as in Fig. 11 with regions of interest mentioned in Table 7
identified by solid black ellipses. Table 7: RXJ0820.9+0752 regions

Region |  v50 | $\sigma$ |  v02 |  v98 |  Fraction L[OII] | Dist | $\theta$ | Area
---|---|---|---|---|---|---|---|---
|  (km s-1) |  (km s-1) |  (km s-1) |  (km s-1) | (%) | (kpc) |  (⋅) |  (kpc2)
A | 139 | 122 | 391 | -114 | 9.65 | 0.6 | 0 | 28
B | 210 | 74 | 362 | 57 | 24.47 | 3.7 | 81 | 50
C | 170 | 112 | 400 | -61 | 7.81 | 16.9 | 38 | 28
D | 160 | 79 | 324 | -4 | 22.30 | 10.8 | 38 | 41
E | 47 | 104 | 262 | -168 | 12.28 | 14.1 | 7 | 45

Note. —

(1) Region identified in Fig. 26.

(2) [OII] flux weighted mean of the median velocity within the region.

(3) [OII] flux weighted mean of the velocity dispersion within the region.

(4) [OII] flux weighted mean of the v02 within the region.

(5) [OII] flux weighted mean of the v98 within the region.

(6) Fraction of the total [OII] luminosity observed from the spaxels included
in the region.

(7) Distance between the central point of the region and the nucleus.

(8) Average angle between the center of the galaxy and the region. The angle
is 0∘ pointing east and increases clockwise.

(9) Area of the region.

Fig. 26 depicts the same kinematic maps as in Fig. 11, using a different
colormap to highlight differences in velocity. The ellipses identify five
regions of interest whose properties are detailed in Table 7.

Region A is one of two regions where the stellar continuum is detected. This
region encompasses the nebular gas closest to the nucleus. With a [OII] flux-
weighted mean v50 of $+139$ km s-1, region A reiterates the significant
differences in kinematics between the nebular gas and the stellar continuum.
This region has the largest velocity dispersion. The few spaxels with
$\sigma>150$ km s-1 are only $\sim 1.9$ kpc SW of the nucleus.

Region B is the second region where stellar continuum is observed. Region B
has the gas with the largest median velocities. Although the gas in region B
has, on average, velocities greater than $+200$ km s-1, the gas is quiescent
with the lowest mean velocity dispersion ($\sigma=74$ km s-1) of the five
regions examined. Therefore, there is either a process displacing almost 25%
of the observed nebular gas at $\sim 200$ km s-1 while barely disrupting it,
and/or the stellar population in the core of the system, from which we measure
the systemic velocity, is moving at $\sim 200$ km s-1 with respect to the
nebular gas in region B.

Region C is another region with large median velocities, located roughly 15
kpc away from region B. Contrary to region B, the gas in region C is somewhat
disturbed, with $\sigma=112$ km s-1. Region B and C, the two highest v50
regions, appear to be connected through a $\sim 160$ km s-1 filament, which is
identified in Fig. 26 as region D. The velocity dispersion in region D is
below 80 km s-1, indicating that the nebular gas in region D is fairly
quiescent. This “filament” contains $\sim 22\%$ of the observed nebular gas.

Region E contains the nebular gas with the smallest velocities with respect to
the systemic velocity. The gas is slightly disturbed, with $\sigma\sim 104$ km
s-1. The $\sim 100$ km s-1 change in velocities between the gas in Region E
and the surrounding gas may explain the increase in velocity dispersion.

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