# A Massive, Clumpy Molecular Gas Distribution and Displaced AGN in Zw 3146

A. N. Vantyghem1 B. R. McNamara2,3,4 C. P. O’Dea1 S. A. Baum1 F. Combes5,6 A.
C. Edge7 A. C. Fabian8 M. McDonald9 P. E. J. Nulsen9,10 H. R. Russell8 P.
Salomé5 1 University of Manitoba, Department of Physics and Astronomy,
Winnipeg, MB R3T 2N2, Canada<EMAIL_ADDRESS>
2 Department of Physics and Astronomy, University of Waterloo, Waterloo, ON
N2L 3G1, Canada
3 Waterloo Centre for Astrophysics, Waterloo, ON N2L 3G1, Canada
4 Perimeter Institute for Theoretical Physics, Waterloo, Canada
5 LERMA, Observatoire de Paris, PSL University, CNRS, Sorbonne University
Paris, France
6 Collège de France, 11 place Marcelin Berthelot, 75005 Paris
7 Department of Physics, Durham University, Durham DH1 3LE
8 Institute of Astronomy, Madingley Road, Cambridge CB3 0HA
9 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA
02138, USA
10 ICRAR, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009,
Australia

(February 2, 2021)

###### Abstract

We present a recent ALMA observation of the CO(1-0) line emission in the
central galaxy of the Zw 3146 galaxy cluster ($z=0.2906$). We also present
updated X-ray cavity measurements from archival Chandra observations. The
$5\times 10^{10}\,M_{\odot}$ supply of molecular gas, which is confined to the
central 4 kpc, is marginally resolved into three extensions that are
reminiscent of the filaments observed in similar systems. No velocity
structure that would be indicative of ordered motion is observed. The three
molecular extensions all trail X-ray cavities, and are potentially formed from
the condensation of intracluster gas lifted in the wakes of the rising
bubbles. Many cycles of feedback would be require to account for the entire
molecular gas reservoir. The molecular gas and continuum source are mutually
offset by 2.6 kpc, with no detected line emission coincident with the
continuum source. It is the molecular gas, not the continuum source, that lies
at the gravitational center of the brightest cluster galaxy. As the brightest
cluster galaxy contains possible tidal features, the displaced continuum
source may correspond to the nucleus of a merging galaxy. We also discuss the
possibility that a gravitational wave recoil following a black hole merger may
account for the displacement.

###### Subject headings:

galaxies: active — galaxies: clusters: individual (ZwCl 3146) — galaxies: ISM
— galaxies: kinematics and dynamics

##  1\. Introduction

Galaxy clusters are permeated by a hot ($10^{7}-10^{8}\rm\;K$), diffuse
intracluster medium (ICM) that shines brightly in X-rays. In cool core galaxy
clusters the central density is sharply peaked at the position of the
brightest cluster galaxy (BCG). The correspondingly high X-ray luminosity in
the cluster core should result in the ICM condensing into clouds of cold,
molecular gas and forming stars at rates of hundreds to thousands of solar
masses per year (Fabian 1994; Peterson & Fabian 2006). Indeed, the BCGs in
cool core clusters are the largest and most luminous elliptical galaxies in
the Universe. They are burgeoning with star formation proceeding at rates of
$\sim 1-500\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$ (e.g.
McNamara 2004; O’Dea et al. 2008; McDonald et al. 2011; Donahue et al. 2015;
Tremblay et al. 2015; McDonald et al. 2018), host luminous emission-line
nebulae (e.g. Lynds 1970; Heckman 1981; Cowie et al. 1983; Hu et al. 1985;
Crawford et al. 1999), and harbour molecular gas reservoirs more massive than
even gas-rich spiral galaxies, sometimes exceeding
$10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ (Edge 2001; Edge et al. 2002; Edge &
Frayer 2003; Salomé & Combes 2003). These signatures of gas condensation are
prevalent in systems whose central cooling times fall below a sharp threshold
of $1\rm\;Gyr$ (Cavagnolo et al. 2008; Rafferty et al. 2008; Pulido et al.
2018). Nevertheless, they account for less than 10% of what would be expected
from an unimpeded cooling flow.

Active galactic nuclei (AGN) feedback regulates the rate of ICM cooling (for
reviews, see McNamara & Nulsen 2007, 2012; Fabian 2012). The “radio-mode” of
AGN feedback is nearly ubiquitous in giant ellipticals and galaxy clusters
with short central cooling times (Burns 1990; Dunn & Fabian 2006; Best et al.
2007; Bîrzan et al. 2012). Radio jets launched by the central AGN inflate
bubbles, drive shock fronts, and generate sound waves in the hot atmosphere
(e.g. McNamara et al. 2000; Churazov et al. 2000, 2001; Blanton et al. 2001;
Fabian et al. 2006). The sizes and surrounding pressures of radio bubbles,
which manifest as cavities in the X-ray surface brightness, are used in a
direct estimate of the AGN power output. In a large sample of objects, the AGN
power output closely matches the radiative losses from the surrounding ICM
(Bîrzan et al. 2004; Dunn & Fabian 2006; Rafferty et al. 2006; Nulsen et al.
2009). This, along with the preponderance of systems with central cooling
times $<1\rm\;Gyr$, implies that AGN heating and radiative cooling are coupled
in a long-lived feedback loop.

In order to establish and maintain such a feedback loop, radiative losses in
the ICM must be tied to accretion onto the central supermassive black hole
(SMBH). Molecular gas is the most likely intermediary. Overdensities in the
ICM, generated by turbulence or AGN feedback, rapidly condense into a
multiphase atmosphere that is dominated by molecular gas (e.g. Sharma et al.
2012; McCourt et al. 2012; Gaspari et al. 2013, 2017; Li & Bryan 2014; Voit
2018). Ram pressure and collisions between cold clouds are both effective
mechanisms for driving cold clouds toward the galactic center (Pizzolato &
Soker 2005, 2010). This results in “chaotic cold accretion” (Gaspari et al.
2013), where the stochastic production of cold clouds feeds black hole growth
and regulates the feedback loop between ICM cooling and AGN heating.

Though molecular gas is the fuel for AGN feedback, its distribution is also
shaped by the AGN. Radio jets drive fast outflows of ionized, neutral, and
molecular gas on $\rm\;pc$ to $\rm\;kpc$ scales (e.g. Morganti et al. 2005,
2013; Nesvadba et al. 2006; Alatalo et al. 2011; Dasyra & Combes 2011; Sturm
et al. 2011; Tadhunter et al. 2014; Morganti et al. 2015). A gentler coupling
between AGN feedback and molecular gas is observed in BCGs (Olivares et al.
2019; Russell et al. 2019). The rotationally-supported disks that would be
expected from the long-lived accumulation of molecular clouds in the galactic
center are rare (Hamer et al. 2014; Russell et al. 2019). Instead, billions of
solar masses of cold gas are situated in kpc-scale filaments that trail X-ray
cavities (e.g. Salomé et al. 2006, 2008; Lim et al. 2008, 2012; McDonald et
al. 2012a; McNamara et al. 2014; Russell et al. 2014, 2016, 2017a, 2017b;
Vantyghem et al. 2016, 2018, 2019). The detection of redshifted absorption
lines indicates that some of this gas rains back onto the central galaxy in a
circulation flow (David et al. 2014; Tremblay et al. 2016, 2018; Rose et al.
2019b, a, 2020).

Motivated by these observations, McNamara et al. (2016) proposed the
“stimulated feedback” paradigm (see also Revaz et al. 2008). As radio bubbles
rise buoyantly, they uplift low-entropy ICM from the cluster core to an
altitude where it becomes thermally unstable. The cold clouds decouple from
the radio bubbles and fall back onto the central galaxy as in chaotic cold
accretion. In this way, AGN feedback stimulates the production of its own
fuel.

Mapping the spatial distribution of cold gas in BCGs in all but the closest
and most gas-rich systems has only become possible with the arrival of the
Atacama Large Millimeter Array (ALMA). Here we present a new ALMA observation
targeting the CO(1-0) emission line in the BCG of Zw 3146, which is one of the
most extreme cool core clusters and brightest CO emitters known. If left
unimpeded, its soft ($0.1-2.4\rm\;keV$) X-ray luminosity of $2\times
10^{45}\hbox{$\rm\;erg\rm\;s^{-1}\,$}$ (Ebeling et al. 1998; Böhringer et al.
2000) would lead to a mass deposition rate of $1250\hbox{$\hbox{$\rm\thinspace
M_{\odot}$}\rm\;yr^{-1}\,$}$ (Edge et al. 1994). Indeed, the BCG in Zw 3146 is
exceptionally active, showing a blue continuum and luminous nebular emission
lines (Allen et al. 1992; Hicks & Mushotzky 2005), an infrared luminosity of
$4\times 10^{11}\hbox{$\rm\thinspace L_{\odot}$}$ (Egami et al. 2006b), an
$8\times 10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ reservoir of cold molecular
gas (Edge 2001; Edge & Frayer 2003), and strong molecular H2 emission lines
from $\sim 10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ of warm H2 (Egami et al.
2006a). The infrared luminosity implies a star formation rate of $\sim
70\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$ (Egami et al.
2006b; Edge et al. 2010; Hicks et al. 2010; Hoffer et al. 2012).

Spectroscopic measurements indicate that the true mass deposition rate is much
lower than implied by the X-ray luminosity (e.g. Egami et al. 2006b). Any
continuous radiative cooling flow from the bulk temperature at $4\rm\;keV$ to
$0.01\rm\;keV$ is less than $50\hbox{$\hbox{$\rm\thinspace
M_{\odot}$}\rm\;yr^{-1}\,$}$ (Liu et al. in preparation, see also Liu et al.
2019). The rate of gas cooling to $0.7\rm\;keV$ is
$130\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$, with less than
$78\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$ cooling to lower
temperatures. AGN feedback is likely responsible for the heavily suppressed
cooling rate. The X-ray atmosphere hosts several cavities that replenish
energetic losses at a rate of $\sim 6\times
10^{45}\hbox{$\rm\;erg\rm\;s^{-1}\,$}$ (Rafferty et al. 2006). The combination
of a massive reservoir of molecular gas and powerful AGN feedback make Zw 3146
a prime candidate to contain molecular filaments trailing X-ray cavities, as
observed in other BCGs.

Throughout this work we assume a standard $\Lambda$-CDM cosmology with
$H_{0}=70\hbox{$\hbox{$\rm\;km\rm\;s^{-1}\,$}\rm\;Mpc^{-1}\,$}$, $\Omega_{{\rm
m},0}=0.3$, and $\Omega_{\Lambda,0}=0.7$. At the redshift of Zw 3146
($z=0.29007$), the angular scale is $1^{\prime\prime}=4.35\rm\;kpc$ and the
luminosity distance is $1500\rm\;Mpc$.

##  2\. Observations and Data Reduction

The BCG of the ZwCl 3146 galaxy cluster (2MASX J10233960+0411116 – R.A.:
10:23:39.6340, decl.: +4:11:10.660) was observed with ALMA in Band 3 (Cycle 4,
ID 2018.1.01056.S, PI Vantyghem), centered on the CO(1-0) line at
$89.316\rm\;GHz$. The observations were conducted in three blocks from 15-19
August 2019, with a total on-source integration time of 106 minutes. Each
observing block was split into $\sim 6$ minute on-source integrations
interspersed with observations of the phase calibrator. The 69.2 arcsec
primary beam was centered on the BCG nucleus in a single pointing common to
each observing block. 41-44 antennas were used in these observations, with
baselines ranging from $41$ to $3637\rm\;m$. This corresponds to a maximum
recoverable scale of $10^{\prime\prime}$. A single spectral window in the
frequency division correlator mode was used to study the CO spectral line with
1.875 GHz bandwidth and 488 kHz ($1.6\hbox{$\rm\;km\rm\;s^{-1}\,$}$) frequency
resolution, though the data were later smoothed to a coarser velocity grid. An
additional three basebands with the time division correlator mode, each with a
2 GHz bandwidth and frequency resolution of $15.625\rm\;MHz$, were employed in
order to measure the continuum source.

The observations were calibrated in casa version 5.4.0 (McMullin et al. 2007)
using the pipeline reduction scripts. Continuum-subtracted data cubes were
created using uvcontsub and clean. Additional phase self-calibration was
attempted, but the continuum source was too faint to provide an improvement in
signal-to-noise. Images of the line emission were reconstructed using Briggs
weighting with a robust parameter of 0.5. The final CO(1-0) data cube had a
synthesized beam of $0.30\times 0.26$ arcsec (P.A. $-79.5^{\circ}$) and was
binned to a velocity resolution of $20\hbox{$\rm\;km\rm\;s^{-1}\,$}$. The RMS
noise in line-free channels was $2.4\rm\;mJy~{}{\rm beam}^{-1}$.

###  2.1. Systemic Velocity

The gas velocities presented in this work are measured in the molecular gas
rest frame. This was determined by extracting a spectrum from a
$3^{\prime\prime}\times 3^{\prime\prime}$ region that encompasses all of the
observed line emission, as shown in Fig. 1. A single-gaussian fitted to the
spectrum yields a molecular gas redshift of $0.29007\pm 0.00003$. This is
consistent with the CO(1-0) velocity centroids measured in previous work (e.g.
Edge 2001).

Previous works on Zw 3146 generally adopted a redshift of $0.29060\pm
0.00010$, which was determined from the emission-line nebula (Allen et al.
1992). The molecular gas rest frame is blueshifted by $158\pm
30\hbox{$\rm\;km\rm\;s^{-1}\,$}$ from this nebular redshift. The discrepancy
may originate from differences in the distribution of gas traced by each
observation. The molecular gas is confined to the central few kpc of the BCG,
while nebular emission is present on larger scales.

Table 1Parameters of Molecular Features

Region |  $\chi^{2}/$dof | Velocity Center | FWHM | Integrated Flux† | Gas Mass†
---|---|---|---|---|---
|  | ($\rm\;km\rm\;s^{-1}\,$) | ($\rm\;km\rm\;s^{-1}\,$) | ($\rm\;Jy\rm\;km\rm\;s^{-1}\,$) | ($10^{8}\hbox{$\rm\thinspace M_{\odot}$}$)
All Emission | 221.2/197 | $0.0\pm 10$ | $353\pm 24$ | $2.78\pm 0.17$ | $504\pm 30$
Central Clump | 226.3/197 | $-59.6\pm 8.2$ | $265\pm 19$ | $0.201\pm 0.013$ | $36.4\pm 2.3$
Clump 1 | 224.0/197 | $17.2\pm 6.1$ | $177\pm 14$ | $0.289\pm 0.02$ | $52.7\pm 3.7$
Clump 2 | 221.6/197 | $28\pm 12$ | $288\pm 28$ | $0.429\pm 0.036$ | $78.3\pm 6.7$
Clump 3 | 218.6/197 | $-69\pm 17$ | $415\pm 41$ | $0.46\pm 0.04$ | $83.7\pm 7.1$

Notes: All spectra have been corrected for the response of the primary beam
and instrumental broadening.

##  3\. Results

Figure 1.— CO(1-0) spectrum extracted from a $13\times 13\rm\;kpc$
($3^{\prime\prime}\times 3^{\prime\prime}$) box that contains all of the
observed emission.

###  3.1. Molecular Gas Mass

The integrated flux ($S_{\rm CO}\Delta v$) of the CO(1-0) line can be
converted to molecular gas mass through (Solomon et al. 1987; Solomon & Vanden
Bout 2005; Bolatto et al. 2013)

$M_{\rm mol}=1.05\times 10^{4}\frac{X_{\rm CO}}{X_{\rm
CO,gal}}\left(\frac{S_{\rm CO}\Delta
v~{}D_{L}^{2}}{1+z}\right)\hbox{$\rm\thinspace M_{\odot}$},$ (1)

where $z$ is the redshift of the source, $D_{L}$ is the luminosity distance in
Mpc, and $S_{\rm CO}\Delta v$ is in $\rm\;Jy\rm\;km\rm\;s^{-1}\,$. The CO-
to-H2 conversion factor, $X_{\rm CO}$, has been studied extensively in the
local Universe. Its nominal value is the mean empirically-derived Galactic
value, $X_{\rm CO,gal}=2\times
10^{20}\hbox{$\rm\;cm^{-2}\,$}(\rm\;K\hbox{$\rm\;km\rm\;s^{-1}\,$})^{-1}$
(Bolatto et al. 2013).

Lacking an independent calibration of $X_{\rm CO}$ in BCGs, we follow standard
practice by adopting the Galactic value throughout this work. The only
estimate of $X_{\rm CO}$ in a BCG was obtained recently through the detection
of 13CO(3-2) emission in RXJ0821.0+0752 (Vantyghem et al. 2017). As 13CO is an
optically thin emission line, it provided a direct measurement of the 13CO
column density. In combination with a measurement of CO(1-0) and CO(3-2) line
intensities and a number of assumptions, $X_{\rm CO}$ was estimated to be half
of the Galactic value. This is reassuringly close to the Galactic value given
the significant morphological differences between BCGs and the Milky Way disk.
Until a direct calibration in BCGs is available, we continue to follow the
standard practice of adopting the Galactic $X_{\rm CO}$.

The primary reasons for the CO-to-H2 conversion factor to vary between
galaxies are the gas metal abundance and excitation conditions. In metal-poor
dwarf galaxies $X_{\rm CO}$ is elevated by more than an order of magnitude
because CO traces a smaller fraction of the overall H2 distribution (Bolatto
et al. 2013). The molecular gas in BCGs likely forms by condensation of the
hot atmosphere, which has typical metallicities of $\sim
0.6-0.8\hbox{$\thinspace\mathrm{Z}_{\odot}$}$ (e.g. De Grandi & Molendi 2001;
De Grandi et al. 2004). The metal abundance of molecular clouds in BCGs is
therefore expected to be similar to that of the Milky Way.

$X_{\rm CO}$ is driven downward by factors of $\sim 5$ in starbursts (e.g.
Ultra-Luminous Infrared Galaxies; ULIRGs), where the hot, dense molecular gas
has an elevated luminosity per unit mass. BCGs also have high star formation
rates, approaching $1000\hbox{$\hbox{$\rm\thinspace
M_{\odot}$}\rm\;yr^{-1}\,$}$ in the most extreme cases (e.g. the Phoenix
Cluster; McDonald et al. 2012b). However, the molecular gas in BCGs is often
distributed over much larger spatial scales than in ULIRGs, where the gas is
confined to the central kpc. Despite their elevated SFRs, BCGs still lie on
the Kennicutt-Schmidt relation (Kennicutt 1998; Kennicutt & Evans 2012)
alongside normal galaxies (see e.g. McNamara et al. 2014; Russell et al. 2014;
Vantyghem et al. 2018).

The SFR in Zw 3146, $70\hbox{$\hbox{$\rm\thinspace
M_{\odot}$}\rm\;yr^{-1}\,$}$ (Egami et al. 2006b), is comparable to other BCGs
for which the Galactic $X_{\rm CO}$ has been adopted. However, Zw 3146 is also
the most luminous and distant H2 emitter observed, with a line luminosity of
$L[{\rm H}_{2}\ 0-0\ S(3)]=6.1\times 10^{42}\hbox{$\rm\;erg\rm\;s^{-1}\,$}$
(Egami et al. 2006b). A cosmic-ray dominated region or excitation through
shocks driven by the AGN may be required to explain such strong rotational H2
lines (Ferland et al. 2009; Bayet et al. 2010; Guillard et al. 2012). This
could impact the value of $X_{\rm CO}$. Strong H2 line emission is observed in
many cool core clusters (Donahue et al. 2011) and radio galaxies (Ogle et al.
2010).

A spatially-integrated CO(1-0) spectrum was extracted from a $13\times
13\rm\;kpc$ ($3^{\prime\prime}\times 3^{\prime\prime}$) box containing all of
the detected line emission. The spectrum, shown in Fig. 1, is best-fit by a
single Gaussian with total flux $2.78\pm
0.17\hbox{$\rm\;Jy\rm\;km\rm\;s^{-1}\,$}$. This corresponds to $5.05\pm
0.50\times 10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ of molecular gas. A list
of all fitted parameters is provided in Table 1. No other CO(1-0) line
emission was detected throughout the $70^{\prime\prime}$ primary beam of these
observations.

Previous single-dish and interferometric radio observations of Zw 3146 with
the IRAM-30m telescope and Owens Valley Radio Telescope (OVRO) yielded CO(1-0)
integrated fluxes of $5.2\pm 1.2\hbox{$\rm\;Jy\rm\;km\rm\;s^{-1}\,$}$ and
$5.7\pm 0.9\hbox{$\rm\;Jy\rm\;km\rm\;s^{-1}\,$}$, respectively (Edge 2001;
Edge & Frayer 2003). Our ALMA observation recovers 50% of this flux; a similar
fraction to other BCGs (e.g. David et al. 2014; Russell et al. 2014; McNamara
et al. 2014; Vantyghem et al. 2018). The line emission in the OVRO
observations, which recovers all of the single-dish flux, is unresolved by the
$6.7^{\prime\prime}\times 4.7^{\prime\prime}$ beam. This suggests that our
ALMA observations are missing large-scale flux, predominantly on scales of
$\sim 5^{\prime\prime}$ ($22\rm\;kpc$).

Figure 2.— A multiwavelength view of the Zw 3146 cluster. The top-left panel
shows the lightly-smoothed Chandra X-ray $0.5-7\rm\;keV$ image. The box
indicates the field-of-view for all three images on the right. From top to
bottom these are the HST WFPC2 F606W image, Ly-$\alpha$, and far-UV (Tremblay
et al. 2015). The most prominent substructures in the HST F606W image have
been identified. Note that the F606W filter includes a contribution from
H$\beta$ and [Oiii] line emission. The rectangle in each of the panels on the
right indicate the field-of-view of the ALMA CO(1-0) image, shown on the
bottom-left. The solid black ellipse is the synthesized beam. The blue
contours and $+$ indicate the CO(1-0) emission and its centroid, respectively.
The red contours correspond to $4\sigma$ steps in the $\rm\;mm$ continuum,
beginning at $3\sigma$ and with $\sigma=7.45\hbox{$\rm\;\mu
Jy\rm\;beam^{-1}\,$}$.

###  3.2. Molecular Gas Distribution and Kinematics

Figure 3.— Maps of velocity centroid and line FWHM determined by the pixel-by-
pixel fitting scheme discussed in Section 3.2. These images have the same
field-of-view as the CO(1-0) flux map in Fig. 2. The solid black ellipse is
the synthesized beam.

Maps of integrated flux, velocity, and FWHM of the CO(1-0) line were created
by fitting the spectra extracted from individual pixels within the data cube.
Each spectrum was averaged over a box the size of the synthesized beam. We
allowed for the possibility of multiple coincident velocity structures by
fitting each spectrum with up to two Gaussian components. The significance of
each velocity component was tested using a Monte Carlo analysis employing
10000 iterations, with a detection requiring $5\sigma$ significance. The
presence of one component was required before attempting to fit a second. We
found that a single Gaussian component was sufficient to accurately model the
spectrum for each pixel. Instrumental broadening has been incorporated into
the model.

The integrated flux map is presented in the lower left panel of Fig. 2, and
the velocity centroid and full-width at half maximum (FWHM) maps are presented
in Fig. 3. The molecular gas distribution is compact, with all of the detected
gas confined to a $1^{\prime\prime}$ ($4.35\rm\;kpc$) radius. It is marginally
resolved into three extensions to the NE, SE, and W. These extensions do not
exhibit any clear velocity gradients. The emission is at its most blueshifted
($-150\hbox{$\rm\;km\rm\;s^{-1}\,$}$) at the central peak and in the farthest
extent of the SE extension. The NE and W extensions have more moderate
velocities ($0$ to $50\hbox{$\rm\;km\rm\;s^{-1}\,$}$), but the velocity
transition to the central value occurs over the span of about a beam, so it is
likely the result of the resolution element smearing two distinct velocities
together. The linewidths, which range from $100$ to
$400\hbox{$\rm\;km\rm\;s^{-1}\,$}$ FWHM, are broader than those seen along
filaments in other systems ($<100\hbox{$\rm\;km\rm\;s^{-1}\,$}$) (e.g. Russell
et al. 2016; Vantyghem et al. 2016, 2018), consistent with a superposition of
gas structures at a range of velocities.

Chandra X-ray, HST WFPC2 F606W, Ly-$\alpha$ (HST ACS/SBC F140LP), and FUV (HST
ACS/SBC F165LP) images (O’Dea et al. 2010; Tremblay et al. 2015) are shown
alongside the CO(1-0) total flux map in Fig. 2. The box in the X-ray image
corresponds to the fields-of-view for the HST images, while the ALMA field-of-
view is shown in the HST images. The central galaxy contains bright knots of
nebular emission and FUV flux from recent star formation, one of which is
coincident with the molecular gas. A brighter Ly-$\alpha$ and FUV peak is
located $3.25\rm\;kpc$ ESE of the molecular gas peak. No molecular gas is
present at this position; the CO emission truncates where the Ly-$\alpha$ and
FUV fluxes begin to increase. Dust attenuation may account for this anti-
correlation between the molecular gas and FUV emission. Features that may be
indicative of a merger remnant are seen in the HST F606W image. The most
prominent clumps and filament are identified in Fig. 2. However, this filter
also includes H$\beta$ and [Oiii] line emission, which may account for some of
the observed features.

The molecular gas is offset by $10\rm\;kpc$ to the south of the peak in X-ray
emission, which itself does not coincide with structure at any other
wavelength. The bright X-ray emission in the cluster core arcs around the
position of the CO(1-0) peak. In addition, the X-ray atmosphere contains a
series of depressions that likely correspond to cavities inflated by the
central AGN (see Section 3.5).

Figure 4.— Maps of the integrated CO(1-0) flux after subtracting a point
source centered on the peak of the gas distribution. The contours correspond
to the original distribution of integrated flux, as shown in Fig. 3.

The molecular extensions can be better visualized by subtracting the
contribution from an unresolved point source coincident with the CO(1-0) peak.
This is shown in Fig. 4. First we created an image of the beam centered on the
pixel with the largest integrated flux. This image was further convolved with
a beam-shaped tophat kernel, as the pixel-based spectral fitting used to
create the maps extracts the emission from a region of this shape. The image
was then scaled to match the flux of the brightest pixel and subtracted from
the integrated flux map. The unresolved emission subtracted from the
integrated flux map amounted to 22% of the total flux.

Figure 5.— CO(1-0) spectral to the three clumps identified in Fig. 4.

The resulting map shows that the gas morphology is separated into the three
extensions, although none of them are resolved. They have been identified in
Fig. 4. The corresponding spectra are shown in Fig. 5, and their spectral fits
are listed in Table 1.

Figure 6.— Radio spectral energy distribution, with the ALMA continuum source
measurement shown in blue. The best-fitting power law, indicated by the dashed
line, has a slope of $-0.685\pm 0.063$.

###  3.3. Millimetre Continuum

An image of the continuum at $96.193\rm\;GHz$ ($3.1166\rm\;mm$) was created by
imaging the line-free channels in a square region measuring
$40^{\prime\prime}$ on each side. A single, unresolved source was identified
(R.A.: 10:23:39.5948, decl.: +4:11:11.032), which had a total integrated flux
density of $133\pm 13\rm\;\mu Jy$. The contours for this source are shown in
red Fig. 2. These contours begin at $3\sigma$, where
$\sigma=7.45\hbox{$\rm\;\mu Jy\rm\;beam^{-1}\,$}$, and increase in $4\sigma$
steps. A two-dimensional gaussian fit to the continuum flux yielded an
accuracy for the centroid of $0.006$ arcseconds. We searched for, but did not
detect, evidence for absorption against the continuum source using the native
velocity resolution of the observations.

In Fig. 6 we plot the ALMA continuum alongside flux measurements at lower
frequencies, which were obtained from either the VLA or BIMA (Egami et al.
2006b; Coble et al. 2007; Giacintucci et al. 2014). Error bars are included,
but are smaller than the markers for all measurements except those provided in
this work. The spectral energy distribution (SED) is best fit by a power law
with spectral index111Following the convention $S_{\nu}\propto\nu^{-\alpha}$
$\alpha=0.685\pm 0.063$, which is a typical value for an AGN (e.g. Hogan et
al. 2015).

Figure 7.— DECaLS r-band image of Zw 3146 in the same field-of-view as the HST
F606W image in Fig. 2. Contours of the ALMA CO(1-0) emission and continuum
source are shown in blue and red, respectively. Te black contours correspond
to the DECaLS r-band flux. The black rectangle indicates the ALMA CO(1-0)
field-of-view as shown in Fig. 2.

###  3.4. The Molecular Gas-AGN Offset

As is evident in Fig. 2, the molecular gas and continuum source are mutually
offset. The two peaks are $2.6\rm\;kpc$ ($0.6^{\prime\prime}$) apart, and only
a minimal overlap is present in the fainter reaches of the two distributions.
This offset cannot originate from a phase calibration issue, as the continuum
and line measurements are obtained from the same observation.

Independent observations of the radio continuum at lower resolution confirm
the position of the $\rm\;mm$ continuum source identified here. In a VLA 4.9
GHz observation the continuum centroid is $0.3^{\prime\prime}$ SSW of the ALMA
continuum source (O’Dea et al. 2010). Though the coarse resolution
($1.4^{\prime\prime}\times 0.9^{\prime\prime}$) prevents the CO(1-0) centroid
and continuum source from being definitively distinguished, the VLA centroid
is closer to the ALMA continuum position. Note that the VLA coordinates were
reported in the B1950 equinox, so have been converted to J2000. Giacintucci et
al. (2014) also report a continuum centroid corresponding to VLA 4.9 and 8.5
GH observations in the C configuration. The position is consistent with the
location of the ALMA continuum source, although no uncertainties are provided
and the beam sizes are larger. Nevertheless, these independent radio
observations indicate that the ALMA continuum position reported here is likely
accurate.

The stellar continuum is difficult to disentangle from nebular emission in the
HST images. In order to determine the position of the galactic center, we
obtained a Dark Energy Camera Legacy Survey (DECaLS) $r$-band image using the
legacy skyviewer222https://www.legacysurvey.org/viewer, which is shown in Fig.
7. This image is uncontaminated by nebular line emission and stellar features
from a merger remnant, providing a smooth tracer of the stellar continuum.
Contours of molecular line emission and continuum source are overlaid in blue
and red, respectively, in Fig 7, along with black contours tracing the stellar
emission. It is the molecular gas that is coincident with the galactic center,
not the continuum emission from the AGN.

All taken together, these results imply that the molecular gas resides at the
galactic center while the continuum source is offset by $2.6\rm\;kpc$. The
molecular gas is coincident with both the stellar centroid and bright knots of
nebular emission and star formation, while the continuum position is
consistent with independent measurements at lower frequencies. This
correspondence spanning multiple types of observations indicates that the
astrometry of the ALMA observation is reliable. We explore possible physical
interpretations for this offset in Section 4.1.

###  3.5. X-ray Cavities

In order to investigate any possible connection between the molecular gas and
X-ray cavities, we present a new search for cavities in Zw 3146 using the
Chandra data reduced by Hogan et al. (2017) and Pulido et al. (2018). The
$0.5-7\rm\;keV$ X-ray surface brightness image is shown in Fig. 2. In
addition, we have processed this image using the gaussian gradient magnitude
algorithm (GGM; Sanders et al. 2016a, b) with a radially-dependent filtering
kernel. This algorithm enhances edges in surface brightness. The resulting
image is shown in Fig. 8, sharing a field-of-view with the X-ray image in Fig.
2. The X-ray atmosphere contains a series of surface brightness depressions
and edges corresponding to X-ray cavities and cold fronts, respectively
(Forman et al. 2002; Rafferty et al. 2006).

Figure 8.— X-ray image processed using the GGM algorithm to enhance surface
brightness edges, shown with the same field-of-view as the X-ray image in Fig.
2. Six candidate X-ray cavities have been identified. The location of the
cluster center is indicated by the black ”Y”. The blue $+$ indicates the
molecular gas centroid.

We manually identified six candidate X-ray cavities using a combination of the
GGM filtered image and original X-ray image. The sizes were determined
qualitatively by estimating the size of the surface brightness depressions,
using the edges identified in the GGM image as a guide. The cavities are shown
and labelled in Fig. 8. Two cavities were previously reported by Rafferty et
al. (2006), though their work used a shallower X-ray image. Judging from the
radial distances and sizes of these cavities, one corresponds directly to
Cavity ”A”. The other cavity reported by Rafferty et al. is identified as two
in our work – ”B” and ”C”. Cavity ”D” is located close to the cluster center
and may correspond to motions unrelated to AGN activity, but we tabulate its
derived properties nonetheless. Cavities ”E” and ”F” are located outside of a
cold front and are less well-defined than their counterparts.

A list of all cavity parameters can be found in Table 2. A qualitative figure
of merit (FOM), which describes a cavity’s contrast with its surroundings, was
provided for each cavity (Rafferty et al. 2006). High contrast cavities (${\rm
FOM}=1$) are surrounded by bright rims, medium contrast (${\rm FOM}=2$) are
partially surrounded by bright rims, and low contrast (${\rm FOM}=3$) have no
or faint rims. All necessary thermodynamic quantities were obtained by
interpolating the deprojected radial profiles from Pulido et al. (2018). Note
that the proximity of cavity D to the cluster center has a strong systematic
effect on the cavity age, and therefore its power. The cluster centroid was
determined from an aperture with a $20^{\prime\prime}$ ($87\rm\;kpc$) radius.
It is offset from the X-ray peak by $6\rm\;kpc$.

The enthalpy required to inflate a cavity filled with relativistic gas is
given by $E_{\rm cav}=4pV$, where $p$ is the cavity pressure and $V$ is its
volume. The cavity was assumed to be in pressure balance with the surrounding
gas. The confining pressure was interpolated from the deprojected pressure
profile to a radius equal to the distance to the cavity center ($R$).

The cavity volume was estimated as the geometric mean of the volumes of oblate
and prolate geometries, with semiaxes $a$ and $b$ matching those of the fitted
ellipse, so that $V=\frac{4}{3}\pi(ab)^{3/2}$. This is equivalent to assuming
that the length of the semiaxis along the line-of-sight is $r=\sqrt{ab}$. The
uncertainty for each cavity volume was determined in two ways. First, a $15\%$
uncertainty was assumed in both $a$ and $b$ and propagated. Second, we used
the prolate and oblate geometries as measures of the minimum and maximum
volumes, respectively. The volume uncertainty was then taken to be the
difference between maximum (minimum) volume and cavity volume, in absolute
value. This evaluates to a fractional uncertainty of $\sqrt{a/b}-1$ for an
oblate geometry and $1-\sqrt{b/a}$ for prolate, which are respectively the
positive and negative errors. This is the dominant uncertainty when $a/b\geq
1.74$ when compared to a $15\%$ uncertainty in both $a$ and $b$.

The cavity age was estimated using both the sound crossing time and buoyant
rise time (Bîrzan et al. 2004). The sound crossing time, which assumes the
cavity rises at the speed of sound ($c_{s}$), is simply a function of ICM
temperature, and is given by

$t_{c_{s}}=R/c_{s}=R\sqrt{\mu m_{H}/\gamma kT},$ (2)

where $\gamma=5/3$ is the ratio of specific heats for an ideal gas, and
$\mu=0.6$ is the mean particle weight for the ICM. The buoyant rise time is
the time taken for the cavity to rise to its current projected distance at its
terminal velocity ($v_{t}$),

$t_{\rm buoy}=R/v_{t}\simeq R\sqrt{SC/2gV}.$ (3)

Here $C=0.75$ is the drag coefficient (Churazov et al. 2001) and $S$ is the
bubble cross-section, which is assumed to be its projected area. The
acceleration under gravity at radius $R$ was determined using the cluster mass
profile from Pulido et al. (2018). The two timescales agree to within $20\%$
for all cavities. The buoyancy time was used to determine the mean cavity
power, $P_{\rm cav}=E_{\rm cav}/t_{\rm buoy}$.

These quantities were then used to place mass constraints on the AGN
outbursts. The first, $M_{\rm acc}=E_{\rm cav}/\epsilon c^{2}$, is the mass
that must be accreted onto the black hole to fuel the outburst at an
efficiency of $\epsilon$, which we assume to be $0.1$. The total accreted gas
mass of $4.6\times 10^{7}\hbox{$\rm\thinspace M_{\odot}$}$ can easily be
supplied by the observed $5\times 10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ of
molecular gas. The corresponding accretion rate, $\dot{M}_{\rm acc}=P_{\rm
cav}/\epsilon c^{2}$, ranges from $\sim 0.1-0.3\hbox{$\hbox{$\rm\thinspace
M_{\odot}$}\rm\;yr^{-1}\,$}$ for each cavity. The other interesting mass is
that of hot gas displaced by the cavities, as this mass dictates the maximum
mass that can be lifted by the cavities. The mass of displaced gas is given by
$M_{\rm disp}=n\mu m_{H}V$, where $n=n_{e}+n_{H}$ is the density of the
surrounding gas. Each of the three larger cavities can lift a few
$10^{10}\hbox{$\rm\thinspace M_{\odot}$}$, so the observed molecular gas
supply could have been lifted by the cavities.

Table 2Cavity Measurements

Cavity | FOMa | Major | Minor | $R$ | $4pV$ | $t_{cs}$ | $t_{\rm buoy}$ | $P_{\rm cav}$ | $M_{\rm acc}$ | $\dot{M}_{\rm acc}$ | $M_{\rm disp}$
---|---|---|---|---|---|---|---|---|---|---|---
|  | $\rm\;kpc$ | $\rm\;kpc$ | $\rm\;kpc$ | $10^{58}\rm\;erg$ | $\rm\;Myr$ | $\rm\;Myr$ | $10^{44}\hbox{$\rm\;erg\rm\;s^{-1}\,$}$ | $10^{6}\hbox{$\rm\thinspace M_{\odot}$}$ | $\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$ | $10^{10}\hbox{$\rm\thinspace M_{\odot}$}$
A | 1 | $21.1$ | $15.3$ | $41.7$ | $161^{+58}_{-56}$ | $38^{+3.2}_{-2.5}$ | $41.2\pm 2.8$ | $12.4^{+4.6}_{-4.4}$ | $9.02^{+3.3}_{-3.1}$ | $0.219^{+0.081}_{-0.077}$ | $2.69\pm 0.85$
B | 2 | $22.2$ | $16.3$ | $38.5$ | $214^{+77}_{-74}$ | $34^{+2.8}_{-2.2}$ | $36.3\pm 2.4$ | $18.7^{+6.9}_{-6.6}$ | $12^{+4.3}_{-4.2}$ | $0.33\pm 0.12$ | $3.35\pm 1.1$
C | 2 | $30$ | $15.2$ | $70$ | $204^{+86}_{-68}$ | $57.5^{+3.2}_{-2.6}$ | $71.2^{+4.4}_{-4.3}$ | $9.08^{+3.9}_{-3.1}$ | $11.4^{+4.8}_{-3.8}$ | $0.16^{+0.068}_{-0.054}$ | $2.76^{+1.1}_{-0.88}$
D | 1 | $9.01$ | $6.72$ | $7.65$ | $30.6\pm 11$ | $8.81^{+0.7}_{-0.59}$ | $6.68^{+0.62}_{-0.6}$ | $14.5^{+5.5}_{-5.3}$ | $1.71^{+0.63}_{-0.61}$ | $0.257^{+0.097}_{-0.094}$ | $0.815\pm 0.26$
E | 3 | $20.6$ | $11.7$ | $47.5$ | $86.6^{+31}_{-29}$ | $45.2^{+2.9}_{-2.3}$ | $52.1\pm 3.3$ | $5.27^{+1.9}_{-1.8}$ | $4.85^{+1.7}_{-1.6}$ | $0.0931^{+0.034}_{-0.032}$ | $1.58^{+0.52}_{-0.5}$
F | 3 | $22.3$ | $14.2$ | $70$ | $118^{+40}_{-39}$ | $57.5^{+3.2}_{-2.6}$ | $77.9^{+4.8}_{-4.7}$ | $4.8\pm 1.6$ | $6.61\pm 2.2$ | $0.0847\pm 0.029$ | $1.6\pm 0.51$

Notes: a The cavity figure of merit, which is a qualitative measure of the
contrast between a cavity and its surroundings: (1) high contrast, bright rim
surrounds cavity; (2) medium contrast, bright rim partially surrounds cavity;
and (3) low contrast, no rim, or faint rim surrounds cavity.

##  4\. Discussion

###  4.1. Origin of the Molecular Gas-AGN Offset

As discussed in Section 3.4, the molecular gas and continuum source are
mutually offset. The molecular gas resides at the galactic center, while the
continuum source is located $2.6\rm\;kpc$ to the NW. In this Section we
discuss potential causes for this offset. The first two attribute the
continuum emission to a source other than the SMBH of the BCG, namely emission
from a single lobe of a radio jet or the nucleus of a secondary galaxy. The
latter two – gravitational wave recoil and acceleration by an asymmetric radio
jet – are mechanisms that would naturally kick or accelerate the black hole
from the galactic center.

Offsets between SMBHs and their galactic centers have been observed in other
systems (see Bartlett et al. 2020, for an extensive list). Most common are the
$\sim 10-100\rm\;pc$ displacements, which are consistent with an oscillating
SMBH following a gravitational wave recoil (e.g. Lena et al. 2014). M87 is an
example of such a system, as its SMBH is offset from the photo-center by
$6.8\rm\;pc$ (Batcheldor et al. 2010). More exceptional displacements are also
observed. The radio-loud quasar 3C 186, for example, harbors an $11\rm\;kpc$
displacement with a corresponding velocity of
$-2170\hbox{$\rm\;km\rm\;s^{-1}\,$}$ (Chiaberge et al. 2017).

####  4.1.1 Emission from a lobe

Instead of originating from the supermassive black hole’s accretion disk, the
detected continuum emission could instead originate from the lobe of a radio
jet. This would naturally explain the offset, although it requires that the
emission from both the core and a second lobe are undetected. Given the RMS in
the continuum image of $7.5\hbox{$\rm\;\mu Jy\rm\;beam^{-1}\,$}$, any source
brighter than $22.5\rm\;\mu Jy$ would be detected in our observations.

The continuum emission, with a spectral index of $0.7$, is consistent with
originating from an AGN. Spectral indices steeper than $0.5$ are generally
associated with non-cores, which include lobes, mini-halos, and relics (Hogan
et al. 2015). If the continuum emission arises from a radio lobe, then it is
poorly associated with the X-ray cavities. The continuum emission that would
correspond to the putative lobe is located NW of the galactic center, while
the most prominent cavities are either to the SE or SW. Cavity D is coincident
with the continuum emission, although its overlap with the galactic center
makes it difficult to interpret the direction in which the jet would have been
launched.

####  4.1.2 The SMBH of a secondary galaxy

The spatially offset continuum emission could also originate from the SMBH in
a secondary galaxy that is projected near the BCG core. This SMBH could either
be in an independent background galaxy or the center of a galaxy merging with
the BCG.

The probability that the continuum source is a chance alignment with an
unrelated background radio source is low, based on our estimates of the source
density of radio continuum sources at 100 GHz. Lacking a $100\rm\;GHz$ survey
sensitive enough to detect the source density down to $0.13\rm\;mJy$, we have
instead used a $31\rm\;GHz$ survey of known extragalactic sources (Mason et
al. 2009). A source density of $16.7\deg^{-2}$ is appropriate for sources with
flux densities $\geq 1\rm\;mJy$ at $31\rm\;GHz$, which translates to a flux of
$0.6\rm\;mJy$ at $100\rm\;GHz$, assuming a spectral index of 0.4 (Marriage et
al. 2011). We then randomly populated 1000 fields each with a source density
of $16.7\deg^{-2}$. This exercise results in a probability of $1.2\times
10^{-6}$ that two sources are separated by $<0.6^{\prime\prime}$. While our
assumed density is based on a flux limit of $1\rm\;mJy$, which is higher than
the Zw 3146 continuum source flux ($0.133\rm\;mJy$), the actual source density
would need to be several orders of magnitude larger to exceed a probability of
close but random coincidence of even a few percent.

The likelihood that the continuum source originates from the core of a merger
remnant is much higher. Clumps and trails possibly corresponding to stellar
emission from a merger remnant are detected in the HST F606W image (Fig. 2).
H$\beta$ and [Oiii] line emission may also contribute to these features.
Unlike in systems with dual nuclei, we do not detect excess optical emission
at the position of the continuum source. A similar conclusion was drawn in Zw
8193, where the unresolved radio emission is offset from the center of the BCG
by 3 arcsec and may be associated with a merging galaxy (O’Dea et al. 2010).

####  4.1.3 Gravitational wave recoil

As two galaxies merge, their black holes migrate toward the center of the
gravitational potential through dynamical friction (Begelman et al. 1980). The
resulting binary system tightens through interactions with nearby stars or
gravitational drag from gas until the SMBHs eventually coalesce (Merritt &
Milosavljević 2005; Mayer et al. 2007). During the final stage of coalescence,
the anisotropic emission of gravitational waves imparts a recoil velocity to
the coalesced object (González et al. 2007; Campanelli et al. 2007). This
“kick” can in rare circumstances be as large as
$4000\hbox{$\rm\;km\rm\;s^{-1}\,$}$, so can result in large displacements
between the resulting SMBH and the galactic center.

When a SMBH experiences a large recoil ($v_{\rm kick}\sim 40-90\%$ of the
escape velocity) in an elliptical galaxy potential, its subsequent motion is
characterized by three phases (Gualandris & Merritt 2008). First, the large-
scale perturbations – those exceeding the core radius ($r_{c}\sim 1\rm\;kpc$)
– are damped within $\sim 10^{7}\rm\;yr$. Then, when the amplitude becomes
comparable to the galaxy’s core radius, the oscillations of the SMBH persist
for $\sim 1\rm\;Gyr$. Finally, the SMBH reaches thermal equilibrium with the
stars, at which point the oscillations are negligibly small.

The large ($2.6\rm\;kpc$) displacement observed in Zw 3146 implies that any
SMBH coalescence would have occurred recently – within the last
$10^{7}\rm\;yr$. In a merger between two galaxies with $\sim
10^{9}\hbox{$\rm\thinspace M_{\odot}$}$ SMBHs, coalescence occurs within
$1-2\rm\;Gyr$ (Khan et al. 2012). Stellar disturbances from a merger will
persist for about $2\rm\;Gyr$ (Lotz et al. 2008), but may be shorter lived in
a rich cluster. The features observed in the HST F606W image (Fig. 2) may
correspond to tidal features induced by a merger. Thus, it is plausible that
the SMBHs have recently coalesced and that gravitational wave recoil accounts
for the displacement of the continuum source.

####  4.1.4 Acceleration by an asymmetric radio jet

If the radio jets are intrinsically asymmetric in their power output, then the
SMBH will experience a net thrust that will displace it from its equilibrium
position (Shklovsky 1982). When the black hole is accreting near the Eddington
limit, the resulting thrust can cause it to oscillate within the host galaxy
(Wang et al. 1992; Tsygan 2007; Kornreich & Lovelace 2008; Lena et al. 2014).
Clusters are generally not expected to contain asymmetric jets, as even in the
most powerful systems the SMBH resides at the center of the BCG and, on parsec
scales, the jets are two-sided (Liuzzo et al. 2010). However, while most
cavities in Zw 3146 are balanced by another on the opposite side of the BCG,
the innermost cavity (cavity D) has no discernible counterpart. Since this
cavity is positioned opposite the displacement direction, it can conceivably
account for the displacement, provided it was inflated by an asymmetric jet.

The momentum flux for a one-sided relativistic jet is $P_{\rm jet}/c$. This is
the reaction force applied to the black hole from which the jet originates.
The resulting acceleration for a SMBH of mass $M_{\bullet}$ is

$a_{\bullet}=\frac{P_{\rm jet}}{M_{\bullet}c}\approx 1.7\times
10^{-8}\left(\frac{P_{\rm
jet}}{10^{45}\hbox{$\rm\;erg\rm\;s^{-1}\,$}}\right)\left(\frac{M_{\bullet}}{10^{9}\hbox{$\rm\thinspace
M_{\odot}$}}\right)^{-1}\hbox{$\rm\;cm\rm\;s^{-2}\,$}.$ (4)

The black hole mass in the Zw 3146 BCG, estimated using the 2MASS K-band
magnitude, is $M_{\bullet}=1.6\times 10^{9}\hbox{$\rm\thinspace M_{\odot}$}$
(Main et al. 2017). The black hole acceleration for cavity D, using $P_{\rm
cav}$ as an estimate for jet power (see Table 2), evaluates to $1.5\times
10^{-8}\hbox{$\rm\;cm\rm\;s^{-2}\,$}$.

A displaced black hole will experience a restoring acceleration from the
gravitational pull of the BCG. Assuming the BCG is represented by a singular
isothermal sphere with velocity dispersion
$\sigma_{\ast}=300\hbox{$\rm\;km\rm\;s^{-1}\,$}$, the gravitational
acceleration ($2\sigma^{2}/R$) at a displacement of $R=1\rm\;kpc$ is
$5.8\times 10^{-7}\hbox{$\rm\;cm\rm\;s^{-2}\,$}$. This is 40 times larger than
the acceleration that would be imparted by cavity D assuming that it has no
counter-jet. An asymmetric jet can therefore not account for the $2.6\rm\;kpc$
displacement of the continuum source.

Figure 9.— Comparison between total integrated flux maps for Zw3146 CO(1-0)
with PKS0745-191 CO(1-0) and CO(3-2).

###  4.2. Comparison to other BCGs

The majority of BCGs contain molecular gas distributions that do not resemble
those in gas-rich spiral galaxies. Instead of rotationally-supported disks or
rings, the cold gas in BCGs is generally filamentary (e.g. Olivares et al.
2019; Russell et al. 2019). In a sample of 12 BCGs, only two have $\leq 10\%$
of their total molecular gas located in filaments (Russell et al. 2019). The
filaments in the remaining systems account for $30-100\%$ of their molecular
gas supplies. These filaments can extend anywhere from several to several tens
of kpc from the galactic center, often in the direction of X-ray cavities
(e.g. McNamara et al. 2014; Russell et al. 2016; Vantyghem et al. 2016). Their
velocity gradients are often smooth, but are shallower than would be expected
from free-fall.

The three extensions in Zw 3146 CO(1-0) likely correspond to molecular
filaments that are about $4\rm\;kpc$ in length. The outer portions of the
filaments, identified by the boxes in Fig. 4, account for $40\%$ of the total
flux. Radial filaments extending into the galactic center would contain an
even larger fraction of the flux. Nevertheless, we are unable to rule out the
presence of a molecular disk. The velocity structure, however, is inconsistent
with the smooth gradient expected for a disk, so if a disk is present it must
be unresolved. Similarly we do not observe the double-horned profile in the
CO(1-0) spectrum that is typical of disks.

The system that compares most closely to the Zw 3146 CO(1-0) morphology is
PKS0745-191, also at CO(1-0) (Russell et al. 2016). Both exhibit a bright peak
near the center of the gas distribution as well as three poorly-resolved
radial extensions. However, the CO(3-2) observation of PKS0745-191 clearly
resolves the three molecular filaments with no significant nuclear structure.
The central peak at CO(1-0) results from the coarser resolution blending
together the radial filaments. A comparison of Zw 3146 CO(1-0) with both
PKS0745-191 CO observations is shown in Fig. 9.

Subtracting the central, unresolved emission from the PKS0745-191 CO(1-0) data
(see Section 3.2 for the same analysis on Zw 3146), $52\%$ of the total flux
can be attributed to an unresolved clump at the peak emission position. This
is larger than the $22\%$ measured for Zw 3146 CO(1-0), while in PKS0745-191
CO(3-2) $<5\%$ of the emission is located at the vertex of its three
filaments. Without additional higher resolution observations of Zw 3146 we
cannot conclusively determine its true molecular gas morphology. However, the
similarities with PKS0745-191 suggest that it could share the morphology of
three radial filaments with little central emission, observed with
intermediate resolution.

###  4.3. Origin of the Molecular Gas

The massive ($5\times 10^{10}\hbox{$\rm\thinspace M_{\odot}$}$) reservoir of
cold gas residing in the central 4 kpc of the Zw 3146 BCG places stringent
requirements on its origin. Several tens of gas-rich spiral galaxies would
need to be stripped to account for this gas supply. In cluster cores these are
rare, as most central galaxies are red, gas-poor ellipticals (Best et al.
2007). Sustained stellar mass loss will contribute to the molecular gas
supply, but cannot account for the entire reservoir (Sparks et al. 1989; Voit
& Donahue 2011). Instead, like most BCGs, the primary mechanism for forming
the molecular gas is the condensation of the hot atmosphere.

Although the hot atmosphere contains ample fuel to produce the molecular gas
reservoir, the region covered by molecular emission is dominated by molecular
gas. Only $2.5\pm 0.2\times 10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ of hot
gas is present within the central $10\rm\;kpc$, while the $5\times
10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ of cold gas is located in the central
$4\rm\;kpc$. Zw 3146 is not unique in this regard. In other systems observed
by ALMA, the molecular gas mass is approximately equal to the hot gas mass
when considering only the region that contains molecular emission (Russell et
al. 2019). Forming all of the molecular gas in this region would result in a
significant inflow as the central hot atmosphere is depleted. Alternatively,
the cold gas could be formed on larger scales in filaments that are too faint
to be detected. The Ly-$\alpha$ emission, which could be coincident with this
fainter molecular line emission, extends well beyond the inner 4 kpc in which
the molecular gas is confined. Gas condensing out of the central $20\rm\;kpc$
would have $2\times 10^{11}\hbox{$\rm\thinspace M_{\odot}$}$ of hot gas to
draw from.

In the stimulated feedback paradigm, molecular gas condenses from intracluster
gas that has been entrained and uplifted by a radio bubble (McNamara et al.
2016). Zw 3146 harbours multiple X-ray cavities that have likely arisen from
$2-3$ cycles of AGN activity. All three molecular extensions are projected
behind an X-ray cavity. The SE and W extensions trail the two most prominent
cavities – A and B, respectively. The NE extension trails the most distant and
poorly-defined cavity (F).

By Archimedes’ principle, the maximum mass of gas that can be uplifted in the
wake of a rising bubble is given by the mass it has displaced. This demand is
alleviated by a factor of a few because the hot atmosphere is initially
buoyantly neutral, making the gas easier to lift (Su et al. 2017). The
cavities that are associated with a molecular extension have each displaced
several $10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ of hot gas (see Table 2).
This is several times larger than the mass of the molecular gas in the
extensions (Table 1). Combined, the cavities displace a total of $1.3\times
10^{11}\hbox{$\rm\thinspace M_{\odot}$}$ of hot gas. Thus these cavities could
have initiated the formation of the entire $5\times
10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ reservoir of cold gas.

Spectroscopic estimates of the mass deposition rate made using Chandra suggest
that the hot atmosphere is condensing at a rate of
$300\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$ (Egami et al.
2006b). However, a recent spectral analysis conducted using archival data from
the XMM-Newton Reflection Grating Spectrometer, following the prescription of
Liu et al. (2019), measured $<50\hbox{$\hbox{$\rm\thinspace
M_{\odot}$}\rm\;yr^{-1}\,$}$ of continuous radiative cooling from the bulk
temperature ($4\rm\;keV$) down to $0.01\rm\;keV$ (Liu et al. in preparation).
This includes $130\pm 60\hbox{$\hbox{$\rm\thinspace
M_{\odot}$}\rm\;yr^{-1}\,$}$ of gas cooling to $0.7\rm\;keV$, with
$<78\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$ cooling below
that. This is closely matched to the star formation rate of $70\pm
14\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$. It would take
$1\rm\;Gyr$ to produce the observed reservoir with condensation proceeding at
$50\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$. Condensation at
this rate over the age of a single cavity would contribute a few
$10^{9}\hbox{$\rm\thinspace M_{\odot}$}$ of cold gas. The age of the AGN two
most energetic AGN outbursts, determined by the buoyancy time of their
respective cavities, are $\sim 4\times 10^{7}\rm\;yr$ and $\sim 7\times
10^{7}\rm\;yr$. This translates to the formation of $2-3.5\times
10^{9}\hbox{$\rm\thinspace M_{\odot}$}$ of molecular gas, $4-7\%$ of the total
supply.

Stimulated feedback can therefore contribute significantly to the reservoir of
molecular gas, but many cycles of AGN feedback would be required to account
for the entire reservoir. Each cycle of AGN feedback can stimulate the
formation of a few $10^{9}\hbox{$\rm\thinspace M_{\odot}$}$ of molecular gas.
This process must be sustained for 1 Gyr or longer in order to accumulate the
cold gas mass that is observed. The consumption of cold gas in star formation
complicates this picture, however, as the star formation rate is comparable to
the mass deposition rate.

##  5\. Conclusions

Our ALMA CO(1-0) observations of the Zw 3146 BCG have revealed a massive
($5\times 10^{10}\hbox{$\rm\thinspace M_{\odot}$}$) reservoir of molecular gas
located within $4\rm\;kpc$ of the galactic center. The gas distribution is
marginally resolved into three filaments. We have also identified six cavities
in the Chandra X-ray image. Each molecular filament trails one of the X-ray
cavities.

The cavities have displaced a mass of intracluster gas several times larger
than the molecular gas mass, suggesting that stimulated cooling – where low
entropy gas from the cluster core is uplifted by rising radio bubbles until it
becomes thermally unstable and condenses – may be responsible for the
formation of the molecular gas. However, stimulated cooling would have
difficulty accounting for the entire reservoir, as the cavity ages are more
than ten times shorter than the 1 Gyr it would take to form $5\times
10^{10}\hbox{$\rm\thinspace M_{\odot}$}$ of cold gas at the observed
condensation rate. The total gas supply is likely accumulated over many cycles
of AGN feedback, with each cycle shaping its distribution.

While the molecular gas is centered within the BCG, the continuum source
originating from the AGN is not. The continuum source is located $2.6\rm\;kpc$
away from the peak of the CO(1-0) emission, placing it at the outer extent of
the molecular filaments. The displacement between the continuum source and the
galactic center was likely caused by a merger. Possible tidal features within
the BCG may be indicative of a merger remnant. The continuum source may
correspond to the nucleus of this secondary galaxy. Alternatively, a
gravitational wave recoil following a recent ($<10^{7}\rm\;yr$) black hole
merger may account for this displacement. Alternative mechanisms – such as a
chance alignment with a background galaxy, the continuum corresponding to the
lobe of a jet, or an asymmetric jet accelerating the SMBH of the BCG – are
unlikely.

We thank the anonymous referee for their helpful comments that improved this
paper. ANV thanks Yjan Gordon and Cameron Lawlor-Forsyth for their support.
ANV, BRM, CPO, and SAB are supported by the Natural Sciences and Engineering
Research Council of Canada. This paper makes use of the ALMA data ADS/JAO.ALMA
2018.1.01056.S. ALMA is a partnership of the ESO (representing its member
states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA
(Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of
Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. This
research made use of Astropy, a community-developed core Python package for
Astronomy. This research made use of APLpy, an open-source plotting package
for Python hosted at http://aplpy.github.com.

## References

  * Alatalo et al. (2011) Alatalo, K., Blitz, L., Young, L. M., et al. 2011, ApJ, 735, 88
  * Allen et al. (1992) Allen, S. W., Edge, A. C., Fabian, A. C., et al. 1992, MNRAS, 259, 67
  * Bartlett et al. (2020) Bartlett, D. J., Desmond, H., Devriendt, J., Ferreira, P. G., & Slyz, A. 2020, arXiv e-prints, arXiv:2007.01353
  * Batcheldor et al. (2010) Batcheldor, D., Robinson, A., Axon, D. J., Perlman, E. S., & Merritt, D. 2010, ApJ, 717, L6
  * Bayet et al. (2010) Bayet, E., Hartquist, T. W., Viti, S., Williams, D. A., & Bell, T. A. 2010, A&A, 521, A16
  * Begelman et al. (1980) Begelman, M. C., Blandford, R. D., & Rees, M. J. 1980, Nature, 287, 307
  * Best et al. (2007) Best, P. N., von der Linden, A., Kauffmann, G., Heckman, T. M., & Kaiser, C. R. 2007, MNRAS, 379, 894
  * Bîrzan et al. (2004) Bîrzan, L., Rafferty, D. A., McNamara, B. R., Wise, M. W., & Nulsen, P. E. J. 2004, ApJ, 607, 800
  * Bîrzan et al. (2012) Bîrzan, L., Rafferty, D. A., Nulsen, P. E. J., et al. 2012, MNRAS, 427, 3468
  * Blanton et al. (2001) Blanton, E. L., Sarazin, C. L., McNamara, B. R., & Wise, M. W. 2001, ApJ, 558, L15
  * Böhringer et al. (2000) Böhringer, H., Voges, W., Huchra, J. P., et al. 2000, ApJS, 129, 435
  * Bolatto et al. (2013) Bolatto, A. D., Wolfire, M., & Leroy, A. K. 2013, ARA&A, 51, 207
  * Burns (1990) Burns, J. O. 1990, AJ, 99, 14
  * Campanelli et al. (2007) Campanelli, M., Lousto, C. O., Zlochower, Y., & Merritt, D. 2007, Phys. Rev. Lett., 98, 231102
  * Cavagnolo et al. (2008) Cavagnolo, K. W., Donahue, M., Voit, G. M., & Sun, M. 2008, ApJ, 683, L107
  * Chiaberge et al. (2017) Chiaberge, M., Ely, J. C., Meyer, E. T., et al. 2017, A&A, 600, A57
  * Churazov et al. (2001) Churazov, E., Brüggen, M., Kaiser, C. R., Böhringer, H., & Forman, W. 2001, ApJ, 554, 261
  * Churazov et al. (2000) Churazov, E., Forman, W., Jones, C., & Böhringer, H. 2000, A&A, 356, 788
  * Coble et al. (2007) Coble, K., Bonamente, M., Carlstrom, J. E., et al. 2007, AJ, 134, 897
  * Cowie et al. (1983) Cowie, L. L., Hu, E. M., Jenkins, E. B., & York, D. G. 1983, ApJ, 272, 29
  * Crawford et al. (1999) Crawford, C. S., Allen, S. W., Ebeling, H., Edge, A. C., & Fabian, A. C. 1999, MNRAS, 306, 857
  * Dasyra & Combes (2011) Dasyra, K. M., & Combes, F. 2011, A&A, 533, L10
  * David et al. (2014) David, L. P., Lim, J., Forman, W., et al. 2014, ApJ, 792, 94
  * De Grandi et al. (2004) De Grandi, S., Ettori, S., Longhetti, M., & Molendi, S. 2004, A&A, 419, 7
  * De Grandi & Molendi (2001) De Grandi, S., & Molendi, S. 2001, ApJ, 551, 153
  * Donahue et al. (2011) Donahue, M., de Messières, G. E., O’Connell, R. W., et al. 2011, ApJ, 732, 40
  * Donahue et al. (2015) Donahue, M., Connor, T., Fogarty, K., et al. 2015, ApJ, 805, 177
  * Dunn & Fabian (2006) Dunn, R. J. H., & Fabian, A. C. 2006, MNRAS, 373, 959
  * Ebeling et al. (1998) Ebeling, H., Edge, A. C., Bohringer, H., et al. 1998, MNRAS, 301, 881
  * Edge (2001) Edge, A. C. 2001, MNRAS, 328, 762
  * Edge et al. (1994) Edge, A. C., Fabian, A. C., Allen, S. W., et al. 1994, MNRAS, 270, L1
  * Edge & Frayer (2003) Edge, A. C., & Frayer, D. T. 2003, ApJ, 594, L13
  * Edge et al. (2002) Edge, A. C., Wilman, R. J., Johnstone, R. M., et al. 2002, MNRAS, 337, 49
  * Edge et al. (2010) Edge, A. C., Oonk, J. B. R., Mittal, R., et al. 2010, A&A, 518, L47
  * Egami et al. (2006a) Egami, E., Rieke, G. H., Fadda, D., & Hines, D. C. 2006a, ApJ, 652, L21
  * Egami et al. (2006b) Egami, E., Misselt, K. A., Rieke, G. H., et al. 2006b, ApJ, 647, 922
  * Fabian (1994) Fabian, A. C. 1994, ARA&A, 32, 277
  * Fabian (2012) —. 2012, ARA&A, 50, 455
  * Fabian et al. (2006) Fabian, A. C., Sanders, J. S., Taylor, G. B., et al. 2006, MNRAS, 366, 417
  * Ferland et al. (2009) Ferland, G. J., Fabian, A. C., Hatch, N. A., et al. 2009, MNRAS, 392, 1475
  * Forman et al. (2002) Forman, W., Jones, C., Markevitch, M., Vikhlinin, A., & Churazov, E. 2002, arXiv e-prints, astro
  * Gaspari et al. (2013) Gaspari, M., Ruszkowski, M., & Oh, S. P. 2013, MNRAS, 432, 3401
  * Gaspari et al. (2017) Gaspari, M., Temi, P., & Brighenti, F. 2017, MNRAS, 466, 677
  * Giacintucci et al. (2014) Giacintucci, S., Markevitch, M., Venturi, T., et al. 2014, ApJ, 781, 9
  * González et al. (2007) González, J. A., Sperhake, U., Brügmann, B., Hannam, M., & Husa, S. 2007, Phys. Rev. Lett., 98, 091101
  * Gualandris & Merritt (2008) Gualandris, A., & Merritt, D. 2008, ApJ, 678, 780
  * Guillard et al. (2012) Guillard, P., Ogle, P. M., Emonts, B. H. C., et al. 2012, ApJ, 747, 95
  * Hamer et al. (2014) Hamer, S. L., Edge, A. C., Swinbank, A. M., et al. 2014, MNRAS, 437, 862
  * Heckman (1981) Heckman, T. M. 1981, ApJ, 250, L59
  * Hicks & Mushotzky (2005) Hicks, A. K., & Mushotzky, R. 2005, ApJ, 635, L9
  * Hicks et al. (2010) Hicks, A. K., Mushotzky, R., & Donahue, M. 2010, ApJ, 719, 1844
  * Hoffer et al. (2012) Hoffer, A. S., Donahue, M., Hicks, A., & Barthelemy, R. S. 2012, ApJS, 199, 23
  * Hogan et al. (2017) Hogan, M. T., McNamara, B. R., Pulido, F., et al. 2017, ApJ, 837, 51
  * Hogan et al. (2015) Hogan, M. T., Edge, A. C., Hlavacek-Larrondo, J., et al. 2015, MNRAS, 453, 1201
  * Hu et al. (1985) Hu, E. M., Cowie, L. L., & Wang, Z. 1985, ApJS, 59, 447
  * Kennicutt & Evans (2012) Kennicutt, R. C., & Evans, N. J. 2012, ARA&A, 50, 531
  * Kennicutt (1998) Kennicutt, Jr., R. C. 1998, ARA&A, 36, 189
  * Khan et al. (2012) Khan, F. M., Preto, M., Berczik, P., et al. 2012, ApJ, 749, 147
  * Kornreich & Lovelace (2008) Kornreich, D. A., & Lovelace, R. V. E. 2008, ApJ, 681, 104
  * Lena et al. (2014) Lena, D., Robinson, A., Marconi, A., et al. 2014, ApJ, 795, 146
  * Li & Bryan (2014) Li, Y., & Bryan, G. L. 2014, ApJ, 789, 54
  * Lim et al. (2008) Lim, J., Ao, Y., & Dinh-V-Trung. 2008, ApJ, 672, 252
  * Lim et al. (2012) Lim, J., Ohyama, Y., Chi-Hung, Y., Dinh-V-Trung, & Shiang-Yu, W. 2012, ApJ, 744, 112
  * Liu et al. (2019) Liu, H., Pinto, C., Fabian, A. C., Russell, H. R., & Sanders, J. S. 2019, MNRAS, 485, 1757
  * Liuzzo et al. (2010) Liuzzo, E., Giovannini, G., Giroletti, M., & Taylor, G. B. 2010, A&A, 516, A1
  * Lotz et al. (2008) Lotz, J. M., Jonsson, P., Cox, T. J., & Primack, J. R. 2008, MNRAS, 391, 1137
  * Lynds (1970) Lynds, R. 1970, ApJ, 159, doi:10.1086/180500
  * Main et al. (2017) Main, R. A., McNamara, B. R., Nulsen, P. E. J., Russell, H. R., & Vantyghem, A. N. 2017, MNRAS, 464, 4360
  * Marriage et al. (2011) Marriage, T. A., Baptiste Juin, J., Lin, Y.-T., et al. 2011, ApJ, 731, 100
  * Mason et al. (2009) Mason, B. S., Weintraub, L., Sievers, J., et al. 2009, ApJ, 704, 1433
  * Mayer et al. (2007) Mayer, L., Kazantzidis, S., Madau, P., et al. 2007, Science, 316, 1874
  * McCourt et al. (2012) McCourt, M., Sharma, P., Quataert, E., & Parrish, I. J. 2012, MNRAS, 419, 3319
  * McDonald et al. (2018) McDonald, M., Gaspari, M., McNamara, B. R., & Tremblay, G. R. 2018, ApJ, 858, 45
  * McDonald et al. (2012a) McDonald, M., Veilleux, S., & Rupke, D. S. N. 2012a, ApJ, 746, 153
  * McDonald et al. (2011) McDonald, M., Veilleux, S., Rupke, D. S. N., Mushotzky, R., & Reynolds, C. 2011, ApJ, 734, 95
  * McDonald et al. (2012b) McDonald, M., Bayliss, M., Benson, B. A., et al. 2012b, Nature, 488, 349
  * McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell, 127
  * McNamara (2004) McNamara, B. R. 2004, in The Riddle of Cooling Flows in Galaxies and Clusters of galaxies, ed. T. Reiprich, J. Kempner, & N. Soker
  * McNamara & Nulsen (2007) McNamara, B. R., & Nulsen, P. E. J. 2007, ARA&A, 45, 117
  * McNamara & Nulsen (2012) —. 2012, New Journal of Physics, 14, 055023
  * McNamara et al. (2016) McNamara, B. R., Russell, H. R., Nulsen, P. E. J., et al. 2016, ApJ, 830, 79
  * McNamara et al. (2000) McNamara, B. R., Wise, M., Nulsen, P. E. J., et al. 2000, ApJ, 534, L135
  * McNamara et al. (2014) McNamara, B. R., Russell, H. R., Nulsen, P. E. J., et al. 2014, ApJ, 785, 44
  * Merritt & Milosavljević (2005) Merritt, D., & Milosavljević, M. 2005, Living Reviews in Relativity, 8, 8
  * Morganti et al. (2013) Morganti, R., Fogasy, J., Paragi, Z., Oosterloo, T., & Orienti, M. 2013, Science, 341, 1082
  * Morganti et al. (2015) Morganti, R., Oosterloo, T., Oonk, J. B. R., Frieswijk, W., & Tadhunter, C. 2015, A&A, 580, A1
  * Morganti et al. (2005) Morganti, R., Tadhunter, C. N., & Oosterloo, T. A. 2005, A&A, 444, L9
  * Nesvadba et al. (2006) Nesvadba, N. P. H., Lehnert, M. D., Eisenhauer, F., et al. 2006, ApJ, 650, 693
  * Nulsen et al. (2009) Nulsen, P., Jones, C., Forman, W., et al. 2009, in American Institute of Physics Conference Series, Vol. 1201, The Monster’s Fiery Breath: Feedback in Galaxies, Groups, and Clusters, ed. S. Heinz & E. Wilcots, 198–201
  * O’Dea et al. (2008) O’Dea, C. P., Baum, S. A., Privon, G., et al. 2008, ApJ, 681, 1035
  * O’Dea et al. (2010) O’Dea, K. P., Quillen, A. C., O’Dea, C. P., et al. 2010, ApJ, 719, 1619
  * Ogle et al. (2010) Ogle, P., Boulanger, F., Guillard, P., et al. 2010, ApJ, 724, 1193
  * Olivares et al. (2019) Olivares, V., Salome, P., Combes, F., et al. 2019, A&A, 631, A22
  * Peterson & Fabian (2006) Peterson, J. R., & Fabian, A. C. 2006, Phys. Rep., 427, 1
  * Pizzolato & Soker (2005) Pizzolato, F., & Soker, N. 2005, ApJ, 632, 821
  * Pizzolato & Soker (2010) —. 2010, MNRAS, 408, 961
  * Pulido et al. (2018) Pulido, F. A., McNamara, B. R., Edge, A. C., et al. 2018, ApJ, 853, 177
  * Rafferty et al. (2008) Rafferty, D. A., McNamara, B. R., & Nulsen, P. E. J. 2008, ApJ, 687, 899
  * Rafferty et al. (2006) Rafferty, D. A., McNamara, B. R., Nulsen, P. E. J., & Wise, M. W. 2006, ApJ, 652, 216
  * Revaz et al. (2008) Revaz, Y., Combes, F., & Salomé, P. 2008, A&A, 477, L33
  * Rose et al. (2019a) Rose, T., Edge, A. C., Combes, F., et al. 2019a, MNRAS, 489, 349
  * Rose et al. (2019b) —. 2019b, MNRAS, 485, 229
  * Rose et al. (2020) —. 2020, MNRAS, 496, 364
  * Russell et al. (2014) Russell, H. R., McNamara, B. R., Edge, A. C., et al. 2014, ApJ, 784, 78
  * Russell et al. (2016) Russell, H. R., McNamara, B. R., Fabian, A. C., et al. 2016, MNRAS, 458, 3134
  * Russell et al. (2017a) Russell, H. R., McDonald, M., McNamara, B. R., et al. 2017a, ApJ, 836, 130
  * Russell et al. (2017b) Russell, H. R., McNamara, B. R., Fabian, A. C., et al. 2017b, MNRAS, 472, 4024
  * Russell et al. (2019) —. 2019, MNRAS, 490, 3025
  * Salomé & Combes (2003) Salomé, P., & Combes, F. 2003, A&A, 412, 657
  * Salomé et al. (2008) Salomé, P., Combes, F., Revaz, Y., et al. 2008, A&A, 484, 317
  * Salomé et al. (2006) Salomé, P., Combes, F., Edge, A. C., et al. 2006, A&A, 454, 437
  * Sanders et al. (2016a) Sanders, J. S., Fabian, A. C., Russell, H. R., Walker, S. A., & Blundell, K. M. 2016a, MNRAS, 460, 1898
  * Sanders et al. (2016b) Sanders, J. S., Fabian, A. C., Taylor, G. B., et al. 2016b, MNRAS, 457, 82
  * Sharma et al. (2012) Sharma, P., McCourt, M., Quataert, E., & Parrish, I. J. 2012, MNRAS, 420, 3174
  * Shklovsky (1982) Shklovsky, I. S. 1982, in IAU Symposium, Vol. 97, Extragalactic Radio Sources, ed. D. S. Heeschen & C. M. Wade, 475–481
  * Solomon et al. (1987) Solomon, P. M., Rivolo, A. R., Barrett, J., & Yahil, A. 1987, ApJ, 319, 730
  * Solomon & Vanden Bout (2005) Solomon, P. M., & Vanden Bout, P. A. 2005, ARA&A, 43, 677
  * Sparks et al. (1989) Sparks, W. B., Macchetto, F., & Golombek, D. 1989, ApJ, 345, 153
  * Sturm et al. (2011) Sturm, E., González-Alfonso, E., Veilleux, S., et al. 2011, ApJ, 733, L16
  * Su et al. (2017) Su, Y., Nulsen, P. E. J., Kraft, R. P., et al. 2017, ApJ, 847, 94
  * Tadhunter et al. (2014) Tadhunter, C., Morganti, R., Rose, M., Oonk, J. B. R., & Oosterloo, T. 2014, Nature, 511, 440
  * Tremblay et al. (2015) Tremblay, G. R., O’Dea, C. P., Baum, S. A., et al. 2015, MNRAS, 451, 3768
  * Tremblay et al. (2016) Tremblay, G. R., Oonk, J. B. R., Combes, F., et al. 2016, Nature, 534, 218
  * Tremblay et al. (2018) Tremblay, G. R., Combes, F., Oonk, J. B. R., et al. 2018, ApJ, 865, 13
  * Tsygan (2007) Tsygan, A. I. 2007, Astronomy Reports, 51, 97
  * Vantyghem et al. (2016) Vantyghem, A. N., McNamara, B. R., Russell, H. R., et al. 2016, ApJ, 832, 148
  * Vantyghem et al. (2017) Vantyghem, A. N., McNamara, B. R., Edge, A. C., et al. 2017, ApJ, 848, 101
  * Vantyghem et al. (2018) Vantyghem, A. N., McNamara, B. R., Russell, H. R., et al. 2018, ArXiv e-prints, arXiv:1807.04331
  * Vantyghem et al. (2019) —. 2019, ApJ, 870, 57
  * Voit (2018) Voit, G. M. 2018, ApJ, 868, 102
  * Voit & Donahue (2011) Voit, G. M., & Donahue, M. 2011, ApJ, 738, L24
  * Wang et al. (1992) Wang, J. C. L., Sulkanen, M. E., & Lovelace, R. V. E. 1992, ApJ, 390, 46