# WALLABY Pilot Survey: HI in the host galaxy of a Fast Radio Burst

M. Glowacki International Centre for Radio Astronomy Research (ICRAR), Curtin
University, Bentley, WA 6102, Australia  K. Lee-Waddell International Centre
for Radio Astronomy Research (ICRAR), The University of Western Australia, 35
Stirling Hwy, Crawley, WA 6009, Australia  CSIRO Space and Astronomy, PO Box
1130, Bentley, WA 6102, Australia  International Centre for Radio Astronomy
Research (ICRAR), Curtin University, Bentley, WA 6102, Australia  A. T. Deller
Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn, VIC, 3122, Australia  N. Deg  Department of Physics,
Engineering Physics, and Astronomy, Queen’s University, Kingston, ON, K7L 3N6,
Canada  A. C. Gordon  Center for Interdisciplinary Exploration and Research in
Astrophysics and Department of Physics and Astronomy, Northwestern University,
2145 Sheridan Road, Evanston, IL 60208-3112, USA  J. A. Grundy  International
Centre for Radio Astronomy Research (ICRAR), Curtin University, Bentley, WA
6102, Australia  CSIRO Space and Astronomy, PO Box 1130, Bentley, WA 6102,
Australia  L. Marnoch  School of Mathematical and Physical Sciences, Macquarie
University, NSW 2109, Australia  Astronomy, Astrophysics and Astrophotonics
Research Centre, Macquarie University, Sydney, NSW 2109, Australia  CSIRO,
Space and Astronomy, PO Box 76, Epping NSW 1710 Australia  ARC Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  A.
X. Shen  CSIRO Space and Astronomy, PO Box 1130, Bentley, WA 6102, Australia
S. D. Ryder  School of Mathematical and Physical Sciences, Macquarie
University, NSW 2109, Australia  Astronomy, Astrophysics and Astrophotonics
Research Centre, Macquarie University, Sydney, NSW 2109, Australia  R. M.
Shannon  Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn, VIC, 3122, Australia  O. I. Wong  CSIRO Space and
Astronomy, PO Box 1130, Bentley, WA 6102, Australia  International Centre for
Radio Astronomy Research (ICRAR), The University of Western Australia, 35
Stirling Hwy, Crawley, WA 6009, Australia  ARC Centre of Excellence for All
Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  H. Dénes ASTRON,
Netherlands Institute for Radio Astronomy, Oude Hoogeveensedĳk 4, 7991 PD
Dwingeloo, The Netherlands  B. S. Koribalski CSIRO Astronomy and Space
Science, Australia Telescope National Facility, P.O. Box 76, NSW 1710,
Australia  School of Science, Western Sydney University, Locked Bag 1797,
Penrith, NSW 2751, Australia  C. Murugeshan  CSIRO Space and Astronomy, PO Box
1130, Bentley, WA 6102, Australia  ARC Centre of Excellence for All Sky
Astrophysics in 3 Dimensions (ASTRO 3D), Australia  J. Rhee  International
Centre for Radio Astronomy Research (ICRAR), The University of Western
Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia  ARC Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  T.
Westmeier  International Centre for Radio Astronomy Research (ICRAR), The
University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D),
Australia  S. Bhandari  ASTRON, Netherlands Institute for Radio Astronomy,
Oude Hoogeveensedĳk 4, 7991 PD Dwingeloo, The Netherlands  Joint institute for
VLBI ERIC, Oude Hoogeveensedĳk 4, 7991 PD Dwingeloo, The Netherlands  Anton
Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904,
1098 XH, Amsterdam, The Netherlands  CSIRO, Space and Astronomy, PO Box 76,
Epping NSW 1710 Australia  A. Bosma  Aix Marseille Univ, CNRS, CNES, LAM,
Marseille, France  B. W. Holwerda  University of Louisville, Department of
Physics and Astronomy, Natural Science Building 102, 40292 KY Louisville, USA
J. X. Prochaska  Department of Astronomy and Astrophysics, University of
California, Santa Cruz, CA 95064, USA  Kavli Institute for the Physics and
Mathematics of the Universe, 5-1-5 Kashiwanoha, Kashiwa 277-8583, Japan
Simons Pivot Fellow

###### Abstract

We report on the commensal ASKAP detection of a fast radio burst (FRB), FRB
20211127I, and the detection of neutral hydrogen (Hi) emission in the FRB host
galaxy, WALLABY J131913–185018 (hereafter W13–18). This collaboration between
the CRAFT and WALLABY survey teams marks the fifth, and most distant, FRB host
galaxy detected in Hi, not including the Milky Way. We find that W13–18 has a
Hi mass of MHI = 6.5 $\times$ 109 M⊙, a Hi-to-stellar mass ratio of 2.17, and
coincides with a continuum radio source of flux density at 1.4 GHz of 1.3 mJy.
The Hi global spectrum of W13–18 appears to be asymmetric, albeit the Hi
observation has a low S/N, and the galaxy itself appears modestly undisturbed.
These properties are compared to the early literature of Hi emission detected
in other FRB hosts to date, where either the Hi global spectra were strongly
asymmetric, or there were clearly disrupted Hi intensity map distributions.
W13–18 lacks sufficient S/N to determine whether it is significantly less
asymmetric in its Hi distribution than previous examples of FRB host galaxies.
However, there are no strong signs of a major interaction in the optical image
of the host galaxy that would stimulate a burst of star formation and hence
the production of putative FRB progenitors related to massive stars and their
compact remnants.

HI line emission — Fast radio bursts — Radio transient sources — Galaxy
mergers

##  1 Introduction

To date, we do not know the origin of fast radio bursts (FRBs; Lorimer et al.,
2007), the highly energetic radio pulses occurring on timescales of
milliseconds and found to originate at extragalactic distances. While several
theories exist (see review by Cordes & Chatterjee, 2019), this is an ongoing
area of debate. To best address this issue, we need to better identify and
dissect the host galaxies of FRBs, through localisation of their radio signal.
One of the main aims of the Commensal Real-time ASKAP Fast Transients survey
(CRAFT; Macquart et al., 2010; Bannister et al., 2017) is to localise FRBs at
sub-arcsecond scales with the Australian Square Kilometre Array Pathfinder
telescope (ASKAP; Deboer et al., 2009). Dedicated follow-up observations (e.g.
in optical wavelengths) of these localised FRB positions give us important
information to categorise the host galaxies and better understand the possible
mechanisms behind FRBs (Bhandari et al., 2022).

The stellar information alone does not inform us on the _gas_ content and
distribution, from which stars form and can lead to FRB progenitors. One way
to map the gas distribution is through the neutral hydrogen (Hi) 21-cm
transition with radio telescopes. The Hi spatial distribution and kinematics
can constrain the recent history of a galaxy. Since Hi gas often extends
beyond the stellar distribution, we can also better see the indicators of
recent galaxy interactions, such as tidal tails and extensions (Holwerda et
al., 2011; Reynolds et al., 2019). Such features may be difficult to detect in
optical studies, but can be prominent in Hi intensity maps and velocity
fields. Another possible indicator of galaxy interactions can be seen in
asymmetries of the Hi global spectrum (e.g. Deg et al., 2020).

Table 1: Summary of other Hi emission detections for FRB host galaxies. Each host galaxy was concluded to have had a recent (or ongoing) galaxy merger or interaction event. FRB Name | Host Galaxy | Redshift |  Notes on Hi content and host galaxy
---|---|---|---
FRB 20171020A | ESO 601–G036 | 0.008672 | Lee-Waddell et al. (submitted). The host galaxy has a faint stellar
|  |  |  companion and tidal tail visible in the Hi intensity map and a lopsided Hi
|  |  | global spectrum. Both features are attributed to a galaxy interaction event.
FRB 20180916B | SDSS J0158+6542 | 0.03399 |  Kaur et al. (2022) presented disturbed Hi distribution from intensity and
|  |  | velocity maps, and concluded this galaxy is merging.
FRB 20181030A | NGC 3252 | 0.0038 |  Michałowski (2021) found Hi global spectrum from Masters et al. (2014) to
|  |  | be strongly asymmetric relative to general galaxy population and GRBs.
FRB 20200120E | M81 | 0.00014 | M81 is the dominant galaxy of the M81/M82/NGC 3077 group. The data
|  |  |  in Chynoweth et al. (2008) shows a complex structure of the overall Hi
|  |  | distribution in this group, and the global spectrum of M81 by itself is
|  |  | strongly asymmetric relative to general galaxy population and GRB hosts.
FRB 20200428 | Milky Way | – |  Asymmetric Hi distribution covered in review by Kalberla & Kerp (2009).
|  |  | Interacting with the Large Magellanic Cloud and Small Magellanic Cloud.

Thus far, many identified FRB host galaxies show evidence of star formation
and would hence be expected to contain Hi. However Hi emission has only been
detected in four FRB host galaxies, outside of the Milky Way, due to the
current limited number ($<30$) of localised FRBs and the large distances to
their hosts limiting the ability to directly detect Hi emission (the median
redshift of localised FRB hosts used in James et al., 2022 is
$z~{}=~{}0.237$). In Table 1, we summarise these galaxies with Hi emission
detections. With the issues arising from low number statistics in mind, one
early trend that has emerged is that all of these host galaxies were claimed
to have strongly asymmetric 21-cm spectra or highly disturbed Hi
distributions. Michałowski (2021) highlights that the two published FRB host
galaxies at the time that were known to have Hi emission – not including the
Galactic magnetar in the Milky Way – had highly asymmetric Hi global spectra,
to a far greater degree than what is typically seen for the general galaxy
population or hosts of long-duration gamma-ray bursts (GRBs). While the Hi
global spectrum analysed by Michałowski (2021) for one FRB host is of the M81
group, fig. 2 of Chynoweth et al. (2008) showcases the strongly asymmetric
spectrum for M81 in isolation. We also note that the Masters et al. (2014)
spectrum of NGC 3252 analysed by Michałowski (2021) includes a baseline
ripple. Our Milky Way is currently interacting with other systems e.g. the
Large and Small Magellanic Clouds. Recently, Kaur et al. (2022) reported a
Giant Metrewave Radio Telescope (GMRT) detection of Hi in the host galaxy of
the repeating FRB 20180916B. They found that the Hi distribution was highly
disturbed, the source had two tidal tails, and there was a clear Hi deficit
between the centre of the galaxy and FRB location. Additionally, Lee-Waddell
et al., (submitted), using data from the Australia Telescope Compact Array,
showed that the identified host galaxy of FRB 20171020A (Mahony et al., 2018)
has an asymmetric Hi global spectrum and a clear Hi tail. Hsu et al. (2023)
recently presented asymmetric profiles of molecular gas (CO) in the host
galaxy of FRB 20180924B, and proposed FRBs could commonly appear in
kinematically disturbed environments.

In all of these studies, the cause of the Hi global spectrum asymmetry or
disturbed Hi distribution has been attributed to ongoing or recent galaxy
interaction events. The tidal activity enhances star formation in the host,
which supports “fast FRB channels” (Michałowski, 2021), i.e. a massive star
collapsing in a supernova explosion into a magnetar with a short delay time
acting as the FRB progenitor (as theorised for the FRB studied in Kaur et al.,
2022). However, the current sample size is small and the statistics must be
significantly improved to better understand the FRB progenitor environment. Is
it possible that a massive star as the FRB progenitor could be created without
the need for a galaxy interaction, e.g. simply within a spiral galaxy arm?
Will this trend persist for _all_ FRB host galaxies observed in Hi or is the
story more complicated?

In this paper, we report on the Hi content of one of these FRB hosts, FRB
20211127I, as derived from commensal ASKAP observations of the Widefield ASKAP
L-band Legacy All-sky Blind surveY (WALLABY; Koribalski et al., 2020) Pilot
Survey Phase 2. During these observations, FRB 20211127I was detected by the
CRAFT survey and subsequently localised to a nearby galaxy. In Section 2, we
describe the WALLABY observations and source finding process. Section 3.1
presents the analysis of the Hi properties. We compare with the existing
literature of Hi in FRB host galaxies in Section 3.2 and summarise our
conclusions in Section 4.

##  2 Data

###  2.1 ASKAP observations

The original WALLABY observations of regions in the vicinity of the NGC 5044
galaxy group were taken in late November 2021 and spanned a frequency range of
1151.5 - 1439.5 MHz. These observations had been affected by technical issues
in the calibration data and could not be used for spectral line imaging.
However, as part of the commensal observing strategy of CRAFT, an FRB was
successfully detected with a signal-to-noise ratio S/N of 38 on 27 November
2021 UT 00:00:10, and localised to J2000 13:19:14.08, –18:50:16.7, with an
estimated uncertainty of $0.2"$ in RA and $0.8"$ in Dec. The localisation made
use of the astrometric pipeline initially described in Bannister et al. (2019)
and extended in Day et al. (2020); see also Scott et al. (2023). The S/N of
the FRB in the post-processed image was 73, meaning that the positional
uncertainty is dominated by the accuracy with which systematic offsets can be
estimated and removed using background radio sources detected in an image of
the field made using the 3.1s of voltage data (Deller et al., in prep). This
source was found to be coincident with the galaxy WISEA J131913.96–185016.2
(also known as 6dFGS gJ131914.0-185017, WALLABY J131913–185018, and here after
W13–18), with a redshift $z=0.0469$ (Jones et al., 2009) that is consistent
with the dispersion measure DM = 227 pc cm-3 via the Macquart Relation
(Macquart et al., 2020). Additional optical follow-up of the FRB site and its
host galaxy using $g$ and $I$ band imaging was performed with the FORS2
instrument mounted on Unit Telescope 1 (UT1) of the European Southern
Observatory’s Very Large Telescope (VLT). These data were reduced using
standard pipelines to produce the images shown in Fig 1; further analysis will
be forthcoming in Deller et al. (in prep).

After the calibration issues on ASKAP were rectified, the same regions, which
included W13–18, were re-observed in early December 2021, under scheduling
block (SB) IDs 34167 and 34278, as part of Pilot Phase 2 WALLABY observations.
These data were edited, calibrated, and imaged using the automated ASKAPsoft
processing pipeline (version 1.6.2; Whiting, 2020) and standard WALLABY
processing parameters. Observations and data reduction were as described for
the Phase 1 Pilot Survey (Westmeier et al., 2022). In short, the observations
included 15,552 spectral channels across the frequency range of 1151.5–1439.5
MHz, with only the upper 144 MHz retained due to radio frequency interference
(RFI) below 1300 MHz. Continuum emission was subtracted from the visibility
data through a sky model derived from the calibrated and deconvolved continuum
image, and imaging performed with a robust weighting of 0.5. Further continuum
subtraction was then performed in the image domain. The multi-scale CLEAN
algorithm was used for deconvolution. The one difference for Phase 2 data
processing is using holography constrained beams for the primary beam
correction, rather than circular Gaussian beams, for more accurate image
fluxes.

Each night of observations comprised one 36-beam footprint that was processed
individually. Resulting data products are publicly available on CSIRO ASKAP
Science Data Archive (CASDA; Huynh et al., 2020) under the associated SBIDs.
The image products for corresponding footprints (i.e. footprints A and B with
a common tile name) were mosaicked together to produce the final full
sensitivity images and cubes. The combined WALLABY spectral line cube – imaged
using ASKAP baselines up to 2 km – has a 30 arcsec synthesized beam, $\sim$4
km s-1 spectral resolution, and an RMS of $\sim$1.6 mJy beam-1 per channel in
the region around W13–18. We note this is the idealised RMS value for central
beams in ASKAP’s FOV. The combined continuum map – imaged using all ASKAP
baselines – has a 9 arcsec resolution and RMS of 20-30 $\mu$Jy beam-1.

Source finding was carried out using the Source Finding Application 2 (SoFiA
2; Serra et al., 2015; Westmeier et al., 2021) through a custom pipeline
developed by the Australian SKA Regional Centre (AusSRC), with a minimum S/N
threshold of 3. Westmeier et al. (2022) provides a detailed description of the
process used for WALLABY. W13–18 was identified, from the pipelined source
finding, with a central position offset by 0.32$"$ and 2.8$"$ from the optical
position of WISEA J131913.96–185016.2 (Jarrett et al., 2000) in right
ascension and declination respectively, consistent with the expected WALLABY
centroid errors.

##  3 Results and Discussion

###  3.1 HI and stellar properties

Table 2: Measured properties of W13–18 in order of Hi flux, Hi mass, W50 (with error measured from generating synthetic spectra by perturbing each channel by the noise; see Section 3.2), stellar mass, radio continuum flux, total global SFR from the radio continuum (total and after subtracting unresolved core emission), SFR from WISE mid-infrared photometry, the SFR of the last 30 Myr measured from the Prospector SED model, the SFR from GALEX NUV photometry, 1D asymmetry measurements (lopsidedness and residual of the integrated spectrum), and the 2D asymmetry measure. Quantity | Value
---|---
$S_{\rm HI}$ |  0.63 $\pm$0.1 Jy km s-1
$M_{\rm HI}$ |  6.5 $\pm$ 1.3 $\times$ 109 M⊙
$W50$ |  150 $\pm$ 19 km s-1
$M_{*}$ |  3.0 $\pm$0.1 $\times$ 109 M⊙
$S_{\rm 1.37}$ | 1.3 mJy
SFRradio |  2.91$\begin{subarray}{c}+1.70\\\ -1.07\end{subarray}$ $\begin{subarray}{c}+0.05\\\ -0.05\end{subarray}$ $M_{\odot}$ yr-1
SFR${}_{\rm radio~{}no~{}core}$ |  1.77$\begin{subarray}{c}+1.04\\\ -0.66\end{subarray}$ $\begin{subarray}{c}+0.07\\\ -0.07\end{subarray}$ $M_{\odot}$ yr-1
SFRWISE |  2.57 $\pm$ 0.28 $M_{\odot}$ yr-1
SFRSED |  0.45$\begin{subarray}{c}+0.59\\\ -0.36\end{subarray}$ M⊙ yr-1
SFRUV |  1.22 $\pm$ 0.05 $M_{\odot}$ yr-1
$A_{\rm flux}$ |  1.12 $\pm$ 0.13
$A_{\rm spec}$ |  0.296 $\pm$ 0.091
$A_{2D}$ | 0.23

In Fig. 1 we present the intensity map for W13–18, displayed as contours
overlaid on the VLT image of the FRB host galaxy. The false colour image used
the VLT/FORS2 $g$-band for blue, VLT/FORS2 $I$-band for red, and an average of
the two optical band images for green, which were combined through astropy’s
“make_lupton_rgb” function. The FRB localisation at 68% confidence is overlaid
as a red ellipse. Fig. 2 shows the Hi global spectrum of the host galaxy, from
the raw spectral cube, including a version at lower spectral resolution by
resampling the spectrum by a factor of 5. We also investigated a SoFiA-masked
spectrum that was Hanning-smoothed by a factor of 5. The velocity resolution
of the raw spectrum of the host galaxy is 4.28 km s-1. In Fig. 3 we display
the intensity map contours overlaid on the velocity map (left panel), and the
radio continuum map (right panel). We do not detect any other Hi sources along
the line of sight to the galaxy in the SoFiA search, nor within the vicinity
of the FRB signal. The Hi mass sensitivity of the WALLABY observation
following equation 157 of Meyer et al. (2017), assuming a S/N of 5, velocity
width of 200 km s-1, RMS of 1.6 mJy per channel per beam, and an unresolved Hi
galaxy, is MHIlim = 2.4 $\times$ 109 M⊙. The Hi mass sensitivity is lower near
the edges of the footprints.

Figure 1: Hi intensity (moment 0) contour map of W13–18, from the SoFiA source
finding output with contour levels shown at 0.6, 1.2, 2.4, 4.8 $\times$ 1020
atoms cm-2, overlaid on a VLT g-band and I-band image (the RMS of the WALLABY
observation corresponds to 0.2 $\times$ 1020 atoms cm-2). The narrow red
ellipse marks the localised position of FRB 20211127I (Deller et al. in prep).
The ASKAP synthesized beam (with spatial resolution = 30$"$) is indicated by
the white ellipse in the lower left. Figure 2: Hi global spectrum for W13–18
in the heliocentric reference frame. The raw Hi spectrum is given in black,
and a resampled spectrum by a factor of 5 in blue. The optical spectroscopic
redshift is indicated in red. Figure 3: Left panel: Hi velocity (moment 1) map
that has been masked using the lowest contour level (0.6 $\times$ 1020 atoms
cm-2) of the moment 0 map. Right panel: Hi moment 0 contours (same levels as
Fig. 1) overlaid on the radio continuum. The 9 arcsec continuum beam, which is
at higher resolution than the spectral line cube due to the inclusion of all
ASKAP baselines during imaging, is indicated by the smaller yellow ellipse in
the bottom left of the panel B. Both panels show the FRB localised position.

We summarise the following properties calculated from the Hi data and
ancillary data in Table 2. Using the optical redshift of $z~{}=~{}0.04695$
(Jones et al., 2009, corresponding distance of 215 Mpc assuming Planck
cosmology and $H_{\rm 0}$ = 67.7 km s-1 Mpc-1 (Planck Collaboration et al.,
2016)), we find MHI = 6.5 $\pm$1.3 $\times$ 109 M⊙, where we include an
assumed 5% calibration error for WALLABY in addition to the measured noise
($\pm$1.0 $\times$ 109 M⊙). Using $griz$ photometry and spectroscopy from the
Southern Astrophysical Research (SOAR) Telescope (PI Gordon, program
SOAR2022B-007), $YJKs$ photometry from VISTA (McMahon et al., 2013), and W1-W4
photometry from WISE (Wright et al., 2010), Gordon et al. (2023) determines
the SED-derived stellar mass of W13–18 is 3.0 $\times$ 109 M⊙ (log($M_{*}$/M⊙)
= 9.48 $\begin{subarray}{c}+0.02\\\ -0.01\end{subarray}$ $M_{\odot}$). This
value was calculated using the Bayesian stellar population synthesis code
Prospector (Johnson et al., 2021). Further details on the data collection,
reduction, assumed priors, and additional stellar population parameters for
this galaxy are reported in Gordon et al. (2023). Our Hi-to-stellar mass ratio
is hence $f_{\rm HI}$ = $M_{\rm HI}$/$M_{*}$ $\sim$ 2.17 (log ratio of 0.34),
higher than the 1.3 ratio found for the FRB host studied by Kaur et al.
(2022).

We attempt to estimate the total dynamical mass, $M_{\rm dyn}$, of W13–18,
using equation 2 of Lee-Waddell et al. (2016). However, due to the low spatial
resolution and S/N, we are unable to obtain a reliable estimate. In order to
obtain an improved mass estimate, we attempted to kinematically model this
galaxy using both 3DBarolo (3D-Based Analysis of Rotating Objects From Line
Observations; Di Teodoro & Fraternali 2015) and a modified version of WKAPP
(WALLABY Kinematic Analysis Proto-Pipeline; Deg et al., 2022). Unfortunately
the low spatial resolution and $S/N$ precludes such sophisticated modelling.
As shown in Deg et al. (2022), kinematic modelling of WALLABY detections even
with full $3D$ codes requires ell_maj $\geq 2$ beams and $\log(S/N)\geq 1.25$,
and this detection satisfies neither requirement.

A radio continuum source with a flux density of 1.3 mJy is associated with the
stellar disk at $\sim 5\sigma$ significance. The flux-weighted centre of the
continuum source, determined through ProFound (Hale et al., 2019), is
13:19:14.06, -18:50:16.0. The angular separation between this source and the
FRB localisation is within the image resolution of the synthesised beam
(9$"$). Using the ASKAP spectral width at the 50% flux level of the masked
spectrum ($W50$) of 150 km s-1, we estimate the rotation curve amplitude
($V_{\rm max}$) to be $\sim$100 km s-1 after correcting for relativistic
effects and expected turbulence broadening following Meyer et al. (2008) and
also correcting for inclination (19.8 ∘ from 2MASS) following Meurer et al.
(2006). We find this $V_{\rm max}$ to be consistent with the stellar mass
estimate for the host galaxy (Wong et al., 2016).

We follow the method described in Grundy et al. (2023) applied to WALLABY
galaxies to estimate the total global star formation rate (SFR) from the radio
continuum. Using the relationship from Molnár et al. (2021) calibrated against
the FIR-radio correlation:

${\rm log_{10}(\frac{SFR_{\rm 1.4}}{M_{\odot}\,yr^{-1}})=(0.823\pm
0.009)log_{10}(}\frac{L_{\rm 1.4}}{{\rm W\,Hz^{-1}}})+17.5\pm 0.2,$ (1)

we find the SFR to be 2.91$\begin{subarray}{c}+1.70\\\ -1.07\end{subarray}$
$\begin{subarray}{c}+0.05\\\ -0.05\end{subarray}$ $M_{\odot}$ yr-1. While the
WALLABY continuum value is not quite at 1.4 GHz (1.3675 GHz), in the Eridanus
pre-pilot WALLABY field the flux values for isolated-unresolved sources are
consistent with NVSS at 1.4 GHz within the scatter, so we use WALLABY fluxes
without correction. As the origin of the central continuum emission could be
due to star formation or a radio-quiet AGN, we also estimate the total SFR
beyond the host galaxy core (after subtracting the unresolved core emission)
to be 1.77$\begin{subarray}{c}+1.04\\\ -0.66\end{subarray}$
$\begin{subarray}{c}+0.07\\\ -0.07\end{subarray}$ $M_{\odot}$ yr-1. We present
both estimates as it is currently unclear whether the FRB relates to a star-
forming region within the core or the inner spiral arm of this host galaxy.
The first and second set of uncertainties are the systematic and measured
uncertainties for each SFR estimate.

The WISE colours of $W1-W2$ = 0.10 $\pm$ 0.29 mag and $W2-W3$ = 3.47 $\pm$
0.28 mag suggest that W13–18 is unlikely to host a highly efficient accreting
AGN as it fits among the normal star-forming spiral region of the WISE colour-
colour diagram. As in Grundy et al. (2023), we calculate the integrated WISE
W3PAH (polycyclic aromatic hydrocarbon) SFR, following the relationship given
in Cluver et al. (2014):

${\rm log_{10}(\frac{SFR_{\rm
W3PAH}}{M_{\odot}\,yr^{-1}})=1.13log_{10}(}v_{\rm W3}*\frac{L_{\rm
W3PAH}}{L_{\odot}})-10.24,$ (2)

calibrated against H$\alpha$ observations. The WISE W3PAH is calculated by
subtracting 15.8% of the total WISE W1 flux from the WISE W3 flux (both
measured by ProFound) to account for the contribution of the evolved stellar
population to the W3 flux, as in Jarrett et al. (2011); Cluver et al. (2017)
and references therein. We find the WISE SFRW3PAH = 2.57 $\pm$ 0.28
$M_{\odot}$ yr-1, which agrees well with the radio continuum SFR.

The GALEX near-UV (NUV) magnitude is 17.7345 mag. Converting to a NUV
luminosity, we then use equation 6 of Schiminovich et al. (2007),

${\rm
SFR_{NUV}({M_{\odot}\,yr^{-1}})=10^{-28.165}}L_{\nu}{\rm(ergs^{-1}Hz^{-1})},$
(3)

and find a SFRNUV of 1.22 $\pm$ 0.05 $M_{\odot}$ yr-1.

The radio continuum SFR and $M_{\rm HI}$ estimates implies that the star
formation efficiency log(SFEHI) = -10.2$\begin{subarray}{c}+0.36\\\
-0.70\end{subarray}$ yr-1, where SFEHI is simply SFR/$M_{\rm HI}$. This SFEHI
is consistent with the scatter of SFEHI in the sample of Hi-selected star-
forming disk galaxies studied by Wong et al. (2016), who argued that the
constant global SFEHI observed for star forming disk galaxies across 5 orders
of stellar mass magnitude can be described by self-regulation in a constant
marginally-stable disk.

From the Prospector SED model, the present-day SFR for W13–18 is
0.45$\begin{subarray}{c}+0.59\\\ -0.36\end{subarray}$ M⊙ yr-1 (Gordon et al.,
2023). This value describes the SFR of the last 30 Myr, which is sensitive to
the youngest stars in the galaxy. Gordon et al. (2023) finds that a starburst
event may have occurred $\sim$100 Myr ago in W13–18. The optically-derived
specific SFR (sSFR) is $\sim$1.5$\times$ 10-10 yr-1 (log value of –9.82).
Considering both table 1 and fig. 6 of Catinella et al. (2018)’s analysis of
xGASS (the extended GALEX Arecibo SDSS Survey), as done in fig. 2 of Kaur et
al. (2022), W13–18 is gas-rich for galaxies in the mass bin of log$M_{*}$ =
9.44. The xGASS weighted average of logarithm gas fraction is
–0.459$\pm$0.067, which is lower than the value we find for W13–18 of 0.34 (at
the top of the scatter for xGASS). W13–18 also lies above the log($M_{\rm
HI}$/$M_{*}$)-log(sSFR/yr-1) relation as the log(sSFR) bin of –9.72 has a
corresponding log mass ratio of –0.063$\pm$0.041. The galaxy studied in Kaur
et al. (2022) was further above the envelope of the xGASS distribution
compared to where W13–18 would lie, at a similar sSFR (Fig 4). The gas
richness of both galaxies may indicate that both FRB hosts recently acquired a
large amount of Hi. Relative to xGASS, W13–18 lies on the star forming main
sequence when considering the optical SFR for the last 30 Myr, or slightly
above it when using the total WISE SFR (without subtracting core emission).

Figure 4: The Hi-to-stellar mass ratio, plotted against sSFR, for xGASS
galaxies given by the grey points with median in blue diamonds (Catinella et
al., 2018), the FRB host studied by Kaur et al. (2022) (SDSS J0158+6542; red
star), and W13–18 (green cross). Both W13–18 and SDSS J0158+6542 have higher
Hi-to-stellar mass ratio, albeit SDSS J0158+6542 is notably higher than
galaxies with comparable sSFR measures to itself.

###  3.2 Investigating the early trend of strong asymmetry and disturbed HI

As discussed in Section 1, other FRB host galaxies found to contain Hi gas
have shown an early trend: strongly asymmetric Hi global spectra and/or
disturbed intensity maps indicating these host galaxies are undergoing, or
have recently undergone, merger/interaction events. It has been hypothesised
that certain merger activity could result in a burst of star formation that in
turn could create an FRB progenitor. In these scenarios, the FRB progenitor
would be a massive star (Kaur et al., 2022) originating from a fast FRB
channel model (Michałowski, 2021).

For the host galaxy of FRB 20211127I, we are limited by S/N and spatial
resolution to confidently state whether this remains the case. The Hi
intensity map for W13–18 (Fig. 1) is fairly featureless and far less disturbed
than the Hi map of SDSS J0158+6542 presented in Kaur et al. (2022), albeit the
available spatial resolution is low. The only unusual detail is a _possible_
feature to the south west traced by the lower contour of 0.6 $\times$ 1020
atoms cm-2, with three possibilities. One is that this Hi feature is
associated with a nearby dwarf galaxy; however, there is no associated source
in the optical data, and only nearby faint radio continuum emission.

The second possibility is the feature is part of a tidal tail connected to the
main emission but the spatial resolution is not sufficient to confirm this
notion. Furthermore, this feature is on the opposite side of the galaxy from
the FRB localisation and would likely not contribute to any enhanced star
formation at the FRB source. The third and most likely possibility is that
this feature is noise, especially considering its level of significance.

The only indication of any galaxy interaction is a very faint stellar
overdensity extending to north-west of the galaxy in the VLT optical image,
which appears to correspond with the extension in the Hi intensity map. The
overall position angle and inclination of the Hi in W13–18 does not appear to
be aligned with the stellar spiral structure; however, higher spatial
resolution Hi observations at greater sensitivity are required for more
detailed analysis.

The Hi global spectrum has a higher amount of flux on the left hand
(approaching) side. In order to best compare the level of its asymmetry with
FRB hosts studied in Michałowski (2021), we adopt the same asymmetry
measurement definitions used in that study and the values from Reynolds et al.
(2020) , for both the masked and unmasked resampled spectra (bottom panel of
Fig. 2). The ratio of the integrated flux in the left and right halves of the
spectrum is (see also e.g. Richter & Sancisi, 1994; Haynes et al., 1998;
Espada et al., 2011):

$A_{\rm flux}=|F_{l}/F_{h}|~{},$ (4)

where

$F_{l}=\int_{v_{l}}^{v_{\rm{sys}}}F(v)dv~{},$ (5)

and

$F_{h}=\int_{v_{\rm{sys}}}^{v_{r}}F(v)dv~{},$ (6)

where $\nu_{\rm sys}$ is the systemic velocity defined as the mid-point of the
spectrum at the 20% flux level (i.e. $W_{\rm 20}$ line width), and $\nu_{l}$
and $\nu_{r}$ are the left- and right-hand optical velocities where the flux
density drops to 20% of the peak flux density. We also adopt equation 8 of
Reynolds et al. (2020), the residual of the integrated spectrum that was found
to have the most significant trend with local galaxy density. Simultaneously,
Deg et al. (2020) found the residual of the integrated spectrum to be the best
indicator for visually classified asymmetries, as employed in Glowacki et al.
(2022). The integrated spectrum residual is defined as:

$A_{\rm spec}=\frac{\sum_{i=1}|S(i)-S_{\rm flip}(i)|}{\sum_{i=1}|S(i)|}~{},$
(7)

where $S(i)$ and $S_{\rm flip}(i)$ are the fluxes in channel $i$ of the
original and flipped spectrum, with the flip axis being the flux-weighted mean
systemic velocity. We estimate the error in $A_{\rm flux}$ and $A_{\rm spec}$
in the same way as in Michałowski (2021): we construct a Gaussian distribution
using the standard deviation of line-free channels as the width, and perturbed
each channel in the spectrum 1000 times by a value drawn from this Gaussian
distribution. The standard deviation of the asymmetry measures of these
synthetic spectra was taken as the uncertainty.

Figure 5: Comparison of $A_{\rm flux}$ (left panel) and $A_{\rm spec}$ (right
panel) for W13–18 with the two FRBs presented in Michałowski (2021) (red and
yellow respectively). We include the two GRB hosts (green) and the asymmetry
values for the the LVHIS and HALOGAS Hi surveys from Reynolds et al. (2020)
(black) as in fig. 3 of Michałowski (2021).

Michałowski (2021) found $A_{\rm flux}$ values of 1.314 $\pm$ 0.072 and 1.505
$\pm$ 0.002, and $A_{\rm spec}$ values of 0.5719 $\pm$ 0.0351 and 0.5108 $\pm$
0.0005 (see table 1 of their study), significantly greater than the values
found in Reynolds et al. (2020) for the Local Volume Hi Survey (LVHIS;
Koribalski et al., 2018) and the Hydrogen Accretion in Local Galaxies Survey
(HALOGAS; Heald et al., 2011) (values of $A_{\rm flux}$ = 1.110 $\pm$ 0.070
and 1.070 $\pm$ 0.050; and $A_{\rm spec}$ = 0.2160 $\pm$ 0.1060, 0.1450 $\pm$
0.059 respectively). The unmasked, resampled spectrum of W13–18 has asymmetry
values of $A_{\rm flux}$ = 1.12 $\pm$ 0.13, and $A_{\rm spec}$ = 0.296 $\pm$
0.091, in agreement with those for the masked resampled spectrum ($A_{\rm
flux}$ = 1.14 $\pm$ 0.13, $A_{\rm spec}$ = 0.272 $\pm$ 0.097). Figure 5
compares these values using the unmasked resampled spectrum for W13–18.

In $A_{\rm flux}$ the W13–18 value differs from the FRB hosts examined by
Michałowski (2021) by 1.31–2.96$\sigma$, and in $A_{\rm spec}$
2.36–2.86$\sigma$, not quite sufficient to conclusively state W13-18 does not
show the same level of asymmetry as previous hosts. W13-18 is within
0.36$\sigma$ and 1.39$\sigma$ of the mean of the LVHIS and HALOGAS asymmetry
values ($A_{\rm flux}$ and $A_{\rm spec}$ respectively). The two FRBs examined
by Michałowski (2021), meanwhile, diverge from those Hi surveys by
2.03–8.69$\sigma$ and 2.78–6.22$\sigma$, again in $A_{\rm flux}$ and $A_{\rm
spec}$ respectively.

In addition to the Hi global spectrum asymmetries, it is possible to calculate
the 2D asymmetry, $A_{2D}$, using the technique of Conselice et al. (2000) and
Conselice (2003), which has been applied in previous studies (e.g. Holwerda et
al. (2011)) to determine the galaxy merger fraction. The 2D equation is the
same as Eqn. 7 for $A_{\rm{spec}}$, except the flipping is done in two
dimensions and the rotation point is the center of the galaxy. Using a center
point of $(22.3,17.1)$ pixels on the moment 0 map yields a value of
$A_{2D}=0.23$, which is significantly lower than $A_{\rm{spec}}$, but not
surprising given the low resolution of the observations (see fig. 12 of Giese
et al., 2016).

It is important to consider the effects of noise on both $A_{\rm{spec}}$ and
$A_{2D}$. These are channel-by-channel and pixel-by-pixel measurements so
noise fluctuations will increase the asymmetry measurement. Noise can also
contribute to the lopsidedness measured but since it is an integrated
quantity, the effect of noise is decreased (see fig. 3 and section 3.2 of Deg
et al. (2020), where a Monte Carlo simulation was performed to explore the
effects of S/N on measured asymmetry statistics). Thus, the ‘true’ level of
asymmetry that can be attributed to the galaxy itself rather than from the
noise is lower than our values of $A_{\rm spec}$ = 0.296 and $A_{2D}=0.23$.

The mean velocity field for W13–18 (left panel of Fig. 3) does not appear to
be symmetric, which could be attributed to a warp in the outer disk of W13–18.
The outer edges of the velocity field does not have a smooth gradient,
particularly on the higher velocity end. The beam size is larger than those
high-velocity features and taking into account our limited S/N, we are hence
unable to draw any firm conclusions from the velocity field alone.

Wong et al. (2016) argued that self-regulated or secular star formation within
disk galaxies across 5 orders of magnitude in stellar mass can be governed by
a constant marginally stable disk model. For a galaxy with $V_{\rm max}$ of
$\sim$100 km s-1, this model predicts a SFR of 1.3 $M_{\odot}$ yr-1. This is a
factor of $\sim$2 lower than the MIR and radio continuum SFR (albeit in
agreement within 1$\sigma$ of SFRradio following subtraction of the unresolved
core emission), in agreement with the NUV SFR, and higher than the optical SFR
in the past 30 years by almost a factor of 3. The nearest WALLABY source to
W13–18 is 16.5 Mpc away (down to a $M_{\rm HI}$ sensitivity of 2.4 $\times$
109 M⊙), suggesting that this host galaxy is relatively isolated in Hi.

What does it mean for the FRB progenitor? For the previous FRB host galaxies
detected in Hi, the characteristics of their Hi spectra and intensity maps
were attributed to merger/interaction events. However, noting the limitations
of the WALLABY data, our Hi data products for W13–18 do not allow us to decide
for or against the hypothesis of a galaxy interaction or merger occurring,
which would lead to a recent increase in star formation and the creation of an
FRB progenitor (in the form of a massive star). We note that Hi asymmetry does
not always correspond to a galaxy merger or interaction; internal processes
such as AGN or starburst feedback can also be a potential cause (Sancisi et
al., 2008; Fraternali, 2017). Minor mergers are also not always evident in Hi
spectra or intensity maps.

We stress that the inability to currently determine a high or low Hi asymmetry
does not necessarily argue against a fast FRB channel model for this FRB
progenitor. For instance, the FRB localisation is _not inconsistent_ with a
spiral arm, which is generally a region of higher active star formation that
could possibly be the source of a fast FRB channel progenitor. Furthermore,
the high Hi-to-stellar mass ratio observed for the host galaxy, the slight
stellar overdensity to the north-west, and the warped velocity field could
suggest a minor merger event that could trigger a fast FRB channel for the
progenitor. This scenario supports the hypothesis in Michałowski (2021) where
the delay between the birth of the progenitor (e.g. a massive star) and the
FRB emission is 10–100 Myr, rather than billions of years. However, if such a
galaxy interaction event had occurred, it is not strongly reflected in the
other Hi properties of W13–18, especially compared to FRB host galaxies
presented in Michałowski (2021), Kaur et al. (2022) or Lee-Waddell et al.
(submitted). Ultimately, a larger sample of localised FRBs with corresponding
host galaxy Hi information will be required in order to definitively ascertain
the extent to which FRBs are associated with merger-driven star formation.

##  4 Conclusions

We present the commensal detection of Hi alongside the localisation for FRB
20211127I to W13–18 through a collaboration between the CRAFT and WALLABY
surveys. W13–18 has an Hi mass of 6.5 $\pm$1.3 $\times$ 109 M⊙. Despite the
high Hi-to-stellar mass ratio of 2.17, and a possible warp in the Hi velocity
field, we see no strong disturbances in the Hi intensity map, with the only
notable feature possibly attributed to noise. The Hi intensity map would
benefit from an improved S/N and spatial resolution, but we nonetheless report
the 1D and 2D asymmetry values, which are 1.31–2.96$\sigma$ lower than the
FRBs studied in Michałowski (2021) in $A_{\rm flux}$, and 2.36–2.86$\sigma$
lower in $A_{\rm spec}$. Higher S/N and spatial resolution Hi observations are
required to better investigate this FRB host galaxy.

It is important to remember that W13–18 is only the fifth (and most distant)
case of Hi emission associated with an external galaxy hosting an FRB. We are
still working with low number statistics and are currently treating each
detection individually. With a larger sample size, it could be possible that
we find convincing examples of non-asymmetric Hi or find that disturbed Hi
profiles and intensity maps are the norm for FRB hosts. As localisations of
FRB emission by CRAFT rapidly increase (to $\sim$ 1 per two days) and as Hi
emission surveys such as WALLABY progress, the sample of Hi galaxies that host
FRBs should also increase to the point required for a meaningful statistical
study (from extragalactic Hi surveys with ASKAP, we predict $\sim$5 new Hi
detections a year as commensally discovered CRAFT FRB host galaxies, not
including follow-up studies with other telescopes). Such Hi properties for
future FRBs can also be used to probe the recent history of the host galaxy,
where the star formation history is not available at the time of the FRB
detection and localisation.

##  5 Acknowledgements

We thank the referee for useful feedback that has improved this paper. We
thank Barbara Catinella, Ronald Ekers, Pascal Elahi, Karl Glazebrook, Kelley
Hess, Clancy James, Dane Kleiner, Ángel R. López-Sánchez, Elizabeth Mahony,
Gerhardt Meurer, Tom Oosterloo, Javi Román, Lister Staveley-Smith and Lourdes
Verdes-Montenegro for useful discussions and feedback on the paper. MG is
supported by the Australian Government through the Australian Research
Council’s Discovery Projects funding scheme (DP210102103). LM acknowledges the
receipt of an MQ-RES scholarship from Macquarie University. RMS acknowledges
support from the Australian Research Council Future Fellowship FT190100155. SB
is supported by a Dutch Research Council (NWO) Veni Fellowship
(VI.Veni.212.058). AB acknowledges support from the Centre National d’Etudes
Spatiales (CNES), France. JXP as a member of the Fast and Fortunate for FRB
Follow-up team acknowledges support from NSF grants AST-1911140 and
AST-1910471.

This scientific work uses data obtained from Inyarrimanha Ilgari Bundara, the
CSIRO Murchison Radio-astronomy Observatory. We acknowledge the Wajarri Yamaji
People as the Traditional Owners and native title holders of the Observatory
site. CSIRO’s ASKAP radio telescope is part of the Australia Telescope
National Facility (https://ror.org/05qajvd42). Operation of ASKAP is funded by
the Australian Government with support from the National Collaborative
Research Infrastructure Strategy. ASKAP uses the resources of the Pawsey
Supercomputing Research Centre. Establishment of ASKAP, Inyarrimanha Ilgari
Bundara, the CSIRO Murchison Radio-astronomy Observatory and the Pawsey
Supercomputing Research Centre are initiatives of the Australian Government,
with support from the Government of Western Australia and the Science and
Industry Endowment Fund. We also thank the MRO site staff. This research has
made use of the NASA/IPAC Extragalactic Database (NED) which is operated by
the Jet Propulsion Laboratory, California Institute of Technology, under
contract with the National Aeronautics and Space Administration. Parts of this
research were supported by the Australian Research Council Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through
project number CE170100013. This research is based on observations collected
at the European Southern Observatory under ESO programme 0105.A-0687(C) (PI:
J.-P. Macquart). We acknowledge support from the Australian SKA Regional
Centre (AusSRC).

The stellar mass and associated SFR measures are based on observations
obtained at the Southern Astrophysical Research (SOAR) telescope, which is a
joint project of the Ministério da Ciência, Tecnologia e Inovações do Brasil
(MCTI/LNA), the US National Science Foundation’s NOIRLab, the University of
North Carolina at Chapel Hill (UNC), and Michigan State University (MSU).

## References

  * Bannister et al. (2017) Bannister, K. W., Shannon, R. M., Macquart, J. P., et al. 2017, ApJ, 841, L12, doi: 10.3847/2041-8213/aa71ff
  * Bannister et al. (2019) Bannister, K. W., Deller, A. T., Phillips, C., et al. 2019, Science, 365, 565, doi: 10.1126/science.aaw5903
  * Bhandari et al. (2022) Bhandari, S., Heintz, K. E., Aggarwal, K., et al. 2022, AJ, 163, 69, doi: 10.3847/1538-3881/ac3aec
  * Catinella et al. (2018) Catinella, B., Saintonge, A., Janowiecki, S., et al. 2018, MNRAS, 476, 875, doi: 10.1093/mnras/sty089
  * Chynoweth et al. (2008) Chynoweth, K. M., Langston, G. I., Yun, M. S., et al. 2008, AJ, 135, 1983, doi: 10.1088/0004-6256/135/6/1983
  * Cluver et al. (2017) Cluver, M. E., Jarrett, T. H., Dale, D. A., et al. 2017, ApJ, 850, 68, doi: 10.3847/1538-4357/aa92c7
  * Cluver et al. (2014) Cluver, M. E., Jarrett, T. H., Hopkins, A. M., et al. 2014, ApJ, 782, 90, doi: 10.1088/0004-637X/782/2/90
  * Conselice (2003) Conselice, C. J. 2003, ApJS, 147, 1, doi: 10.1086/375001
  * Conselice et al. (2000) Conselice, C. J., Bershady, M. A., & Jangren, A. 2000, ApJ, 529, 886, doi: 10.1086/308300
  * Cordes & Chatterjee (2019) Cordes, J. M., & Chatterjee, S. 2019, ARA&A, 57, 417, doi: 10.1146/annurev-astro-091918-104501
  * Day et al. (2020) Day, C. K., Deller, A. T., Shannon, R. M., et al. 2020, MNRAS, 497, 3335, doi: 10.1093/mnras/staa2138
  * Deboer et al. (2009) Deboer, B. D. R., Gough, R. G., Bunton, J. D., et al. 2009, Proc. IEEE, 97, 1507, doi: 10.1109/JPROC.2009.2016516
  * Deg et al. (2020) Deg, N., Blyth, S. L., Hank, N., Kruger, S., & Carignan, C. 2020, MNRAS, 495, 1984, doi: 10.1093/mnras/staa1368
  * Deg et al. (2022) Deg, N., Spekkens, K., Westmeier, T., et al. 2022, PASA, 39, e059, doi: 10.1017/pasa.2022.43
  * Di Teodoro & Fraternali (2015) Di Teodoro, E. M., & Fraternali, F. 2015, MNRAS, 451, 3021, doi: 10.1093/mnras/stv1213
  * Espada et al. (2011) Espada, D., Verdes-Montenegro, L., Huchtmeier, W. K., et al. 2011, A&A, 532, A117, doi: 10.1051/0004-6361/201016117
  * Fraternali (2017) Fraternali, F. 2017, in Astrophysics and Space Science Library, Vol. 430, Gas Accretion onto Galaxies, ed. A. Fox & R. Davé, 323, doi: 10.1007/978-3-319-52512-9_14
  * Giese et al. (2016) Giese, N., van der Hulst, T., Serra, P., & Oosterloo, T. 2016, MNRAS, 461, 1656, doi: 10.1093/mnras/stw1426
  * Glowacki et al. (2022) Glowacki, M., Deg, N., Blyth, S. L., et al. 2022, arXiv e-prints, arXiv:2209.09269.  https://arxiv.org/abs/2209.09269
  * Gordon et al. (2023) Gordon, A. C., Fong, W.-f., Kilpatrick, C. D., et al. 2023, arXiv e-prints, arXiv:2302.05465.  https://arxiv.org/abs/2302.05465
  * Grundy et al. (2023) Grundy, J. A., Wong, O. I., Lee-Waddell, K., et al. 2023, PASA, 40, e012, doi: 10.1017/pasa.2023.11
  * Hale et al. (2019) Hale, C. L., Robotham, A. S. G., Davies, L. J. M., et al. 2019, MNRAS, 487, 3971, doi: 10.1093/mnras/stz1462
  * Haynes et al. (1998) Haynes, M. P., Hogg, D. E., Maddalena, R. J., Roberts, M. S., & van Zee, L. 1998, AJ, 115, 62, doi: 10.1086/300166
  * Heald et al. (2011) Heald, G., Józsa, G., Serra, P., et al. 2011, A&A, 526, A118, doi: 10.1051/0004-6361/201015938
  * Holwerda et al. (2011) Holwerda, B. W., Pirzkal, N., Cox, T. J., et al. 2011, MNRAS, 416, 2426, doi: 10.1111/j.1365-2966.2011.18940.x
  * Hsu et al. (2023) Hsu, T.-Y., Hashimoto, T., Hatsukade, B., et al. 2023, MNRAS, 519, 2030, doi: 10.1093/mnras/stac3655
  * Huynh et al. (2020) Huynh, M., Dempsey, J., Whiting, M. T., & Ophel, M. 2020, in Astronomical Society of the Pacific Conference Series, Vol. 522, Astronomical Data Analysis Software and Systems XXVII, ed. P. Ballester, J. Ibsen, M. Solar, & K. Shortridge, 263
  * James et al. (2022) James, C. W., Ghosh, E. M., Prochaska, J. X., et al. 2022, MNRAS, 516, 4862, doi: 10.1093/mnras/stac2524
  * Jarrett et al. (2000) Jarrett, T. H., Chester, T., Cutri, R., et al. 2000, AJ, 119, 2498, doi: 10.1086/301330
  * Jarrett et al. (2011) Jarrett, T. H., Cohen, M., Masci, F., et al. 2011, ApJ, 735, 112, doi: 10.1088/0004-637X/735/2/112
  * Johnson et al. (2021) Johnson, B. D., Leja, J., Conroy, C., & Speagle, J. S. 2021, ApJS, 254, 22, doi: 10.3847/1538-4365/abef67
  * Jones et al. (2009) Jones, D. H., Read, M. A., Saunders, W., et al. 2009, MNRAS, 399, 683, doi: 10.1111/j.1365-2966.2009.15338.x
  * Kalberla & Kerp (2009) Kalberla, P. M. W., & Kerp, J. 2009, ARA&A, 47, 27, doi: 10.1146/annurev-astro-082708-101823
  * Kaur et al. (2022) Kaur, B., Kanekar, N., & Prochaska, J. X. 2022, ApJ, 925, L20, doi: 10.3847/2041-8213/ac4ca8
  * Koribalski et al. (2018) Koribalski, B. S., Wang, J., Kamphuis, P., et al. 2018, MNRAS, 478, 1611, doi: 10.1093/mnras/sty479
  * Koribalski et al. (2020) Koribalski, B. S., Staveley-Smith, L., Westmeier, T., et al. 2020, Ap&SS, 365, 118, doi: 10.1007/s10509-020-03831-4
  * Lee-Waddell et al. (2016) Lee-Waddell, K., Spekkens, K., Chandra, P., et al. 2016, MNRAS, 460, 2945, doi: 10.1093/mnras/stw1162
  * Lorimer et al. (2007) Lorimer, D. R., Bailes, M., McLaughlin, M. A., Narkevic, D. J., & Crawford, F. 2007, Science, 318, 777, doi: 10.1126/science.1147532
  * Macquart et al. (2010) Macquart, J.-P., Bailes, M., Bhat, N. D. R., et al. 2010, PASA, 27, 272, doi: 10.1071/AS09082
  * Macquart et al. (2020) Macquart, J. P., Prochaska, J. X., McQuinn, M., et al. 2020, Nature, 581, 391, doi: 10.1038/s41586-020-2300-2
  * Mahony et al. (2018) Mahony, E. K., Ekers, R. D., Macquart, J.-P., et al. 2018, ApJ, 867, L10, doi: 10.3847/2041-8213/aae7cb
  * Masters et al. (2014) Masters, K. L., Crook, A., Hong, T., et al. 2014, MNRAS, 443, 1044, doi: 10.1093/mnras/stu1225
  * McMahon et al. (2013) McMahon, R. G., Banerji, M., Gonzalez, E., et al. 2013, The Messenger, 154, 35
  * Meurer et al. (2006) Meurer, G. R., Hanish, D. J., Ferguson, H. C., et al. 2006, ApJS, 165, 307, doi: 10.1086/504685
  * Meyer et al. (2017) Meyer, M., Robotham, A., Obreschkow, D., et al. 2017, PASA, 34, 52, doi: 10.1017/pasa.2017.31
  * Meyer et al. (2008) Meyer, M. J., Zwaan, M. A., Webster, R. L., Schneider, S., & Staveley-Smith, L. 2008, MNRAS, 391, 1712, doi: 10.1111/j.1365-2966.2008.13424.x
  * Michałowski (2021) Michałowski, M. J. 2021, ApJ, 920, L21, doi: 10.3847/2041-8213/ac2b35
  * Molnár et al. (2021) Molnár, D. C., Sargent, M. T., Leslie, S., et al. 2021, MNRAS, 504, 118, doi: 10.1093/mnras/stab746
  * Planck Collaboration et al. (2016) Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A13, doi: 10.1051/0004-6361/201525830
  * Reynolds et al. (2020) Reynolds, T. N., Westmeier, T., Staveley-Smith, L., Chauhan, G., & Lagos, C. D. P. 2020, MNRAS, 493, 5089, doi: 10.1093/mnras/staa597
  * Reynolds et al. (2019) Reynolds, T. N., Westmeier, T., Staveley-Smith, L., et al. 2019, MNRAS, 482, 3591, doi: 10.1093/mnras/sty2930
  * Richter & Sancisi (1994) Richter, O. G., & Sancisi, R. 1994, A&A, 290, L9
  * Sancisi et al. (2008) Sancisi, R., Fraternali, F., Oosterloo, T., & van der Hulst, T. 2008, A&A Rev., 15, 189, doi: 10.1007/s00159-008-0010-0
  * Schiminovich et al. (2007) Schiminovich, D., Wyder, T. K., Martin, D. C., et al. 2007, ApJS, 173, 315, doi: 10.1086/524659
  * Scott et al. (2023) Scott, D. R., Cho, H., Day, C. K., et al. 2023, arXiv e-prints, arXiv:2301.13484, doi: 10.48550/arXiv.2301.13484
  * Serra et al. (2015) Serra, P., Westmeier, T., Giese, N., et al. 2015, MNRAS, 448, 1922, doi: 10.1093/mnras/stv079
  * Westmeier et al. (2021) Westmeier, T., Kitaeff, S., Pallot, D., et al. 2021, MNRAS, 506, 3962, doi: 10.1093/mnras/stab1881
  * Westmeier et al. (2022) Westmeier, T., Deg, N., Spekkens, K., et al. 2022, PASA, 39, e058, doi: 10.1017/pasa.2022.50
  * Whiting (2020) Whiting, M. T. 2020, in Astronomical Society of the Pacific Conference Series, Vol. 522, Astronomical Data Analysis Software and Systems XXVII, ed. P. Ballester, J. Ibsen, M. Solar, & K. Shortridge, 469
  * Wong et al. (2016) Wong, O. I., Meurer, G. R., Zheng, Z., et al. 2016, MNRAS, 460, 1106, doi: 10.1093/mnras/stw993
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868, doi: 10.1088/0004-6256/140/6/1868


[a, b]Ludwig M. Böss

# Galaxy Cluster simulations with a spectral Cosmic Ray model - "Wrong Way"
Radio Relics

Ulrich P. Steinwandel  Klaus Dolag

###### Abstract

Non-thermal emission from relativistic electrons gives insight into the
strength and morphology of intra-cluster magnetic fields, as well as providing
powerful tracers of structure formation shocks. Emission caused by Cosmic Ray
(CR) protons on the other hand still challenges current observations and is
therefore testing models of proton acceleration at intra-cluster shocks.
Large-scale simulations including the effects of CRs have been difficult to
achieve and have been mainly reduced to simulating an overall energy budget,
or tracing CR populations in post-processing of simulation output and has
often been done for either protons or electrons. We use an efficient on-the-
fly Fokker-Planck solver to evolve distributions of CR protons and electrons
within every resolution element of our simulation. The solver accounts for CR
acceleration at intra-cluster shocks, based on results of recent PIC
simulations, re-acceleration due to shocks and MHD turbulence, adiabatic
changes and radiative losses of electrons. We apply this model to zoom
simulations of galaxy clusters, recently used to show the evolution of the
small-scale turbulent dynamo on cluster scales. For these simulations we use a
spectral resolution of 48 bins over 6 orders of magnitude in momentum for
electrons and 12 bins over 6 orders of magnitude in momentum for protons. We
present preliminary results about a possible formation mechanism for Wrong Way
Radio Relics in our simulation.

##  1 Introduction

One of the most prominent indications for the presence of Cosmic Ray (CR)
electrons in galaxy clusters (GCs) are the so-called "Radio Relics". These are
concave, arc-like structures of up-to several Mpc in size which are found in
the periphery of galaxy clusters. They are typically associated with ongoing
mergers between massive galaxy clusters [see e.g. 8, 9, for reviews] and are
observed as synchrotron emission in the radio bands where they can show strong
polarisation, synchrotron spectral indices typically in the range
$\alpha_{0}\sim[-0.6,-0.8]$ and a steepening of these spectra towards the
cluster center and with that indicating an aging CR electron population [see
48, for a recent review]. The common ground in the literature to date is that
these relics originate from electrons accelerated at shocks via diffusive
shock acceleration (DSA) [e.g. 19, for a review]. However their high surface
brightness seems to be incompatible with current models of CR electron
acceleration [see e.g. 6, and references therin], indicating that we lack
understanding in the exact process of efficient CR electron acceleration in
high-$\beta$ plasmas, with $\beta\equiv\frac{P_{\mathrm{th}}}{P_{B}}\sim
20-100$ typical for the intra-cluster medium (ICM). Recent observations show a
class of radio relics that show puzzling features, such as convex morphologies
[e.g. 7, 32, 31], deformations across the shock surface [e.g. 47], filamentary
structures [e.g. 29, 30, 31, 11] and strong variations of spectral index
across the relic [e.g. the southern relic in 13]. Simulations can provide
insights into some of these features such as complex relic morphology [e.g.
34, and references therein], surface brightness variations [e.g. 16, 44] and
evolution of the spectral index of the relic [e.g. 39, 18, 43] also including
multi-shock scenarios [e.g. 23]. However simulations face the problem that the
gap between the mass of an individual electron and the mass of a resolution
element typically spans 60-70 orders of magnitude. Therefore radio emission in
simulations are typically studied by applying models for synchrotron emission
in post-processing [e.g. 14, 21, 22, 40, 18, 10], or applying a Fokker-Planck
solver to tracer particles to evolve populations of electrons in time [e.g.
17, 42, 41]. We present preliminary results of a sibling-simulation to the one
presented in [37] including the CR model introduced in [5], which traces the
time evolution of populations of CR electrons and protons within every
resolution element of the simulation.

##  2 Methods

The simulation used in this work was carried out with the Tree-SPMHD code
OpenGadget3. OpenGadget3 is a derivative of Gadget2 [35] with improvements to
the hydro and gravity solvers as well as additional physics modules. The hydro
solver is updated as described in [2] and we employ the magnetohydrodynamics
(MHD) implementation by [15] with updates to include non-ideal MHD in the form
of constant (physical) diffusion and dissipation, as presented in [4]. The
magnetic dissipation heats the gas with the magnetic field that is lost due to
magnetic reconnection. (An)isotropic conduction is modelled via a
(bi-)conjugate gradient solver [28, 1, 36]. We adopt a Wendland C4 kernel with
200 neighbors and bias correction as suggested by [12].
We employ the on-the-fly spectral CR model Crescendo introduced in [5] to
model the time evolution of CR protons and electrons in every resolution
element of our simulation. The time evolution of distributions of CRs in the
absence of CR transport, diffusion in momentum space and catastrophic losses
can be described by

$\displaystyle\frac{Df(p,\mathbf{x},t)}{Dt}$
$\displaystyle=\left(\frac{1}{3}\nabla\cdot\mathbf{u}\right)p\frac{\partial
f(p,\mathbf{x},t)}{\partial p}$ (1)
$\displaystyle+\frac{1}{p^{2}}\frac{\partial}{\partial
p}\left(p^{2}\sum_{l}b_{l}f(p,\mathbf{x},t)\right)$ (2)
$\displaystyle+j(\mathbf{x},p,t),$ (3)

where we used the convective derivative $\frac{Df}{Dt}=\frac{\partial
f}{\partial t}+\mathbf{u}\cdot\nabla f$ due to the Lagrangian nature of our
code. The right side of Eq. 1 describes changes due to adiabatic compression
or expansion of the surrounding gas, Eq. 2 describes energy losses and Eq. 3
is the source term. We represent $f(p,\mathbf{x},t)$ as piece-wise powerlaws
in momentum space with 2 bins/dex for protons and 8 bins/dex for electrons in
the dimensionless momentum range
$\hat{p}\equiv\frac{p_{i}}{m_{i}c}\in[0.1,10^{5}]$, where $p_{i}$ and $m_{i}$
refer to the momentum and mass for protons and electrons, respectively. The
distribution function is updated at every timestep following the two-moment
approach following [26] by computing CR number and energy changes per bin. We
model energy losses of electrons due to synchrotron emission and inverse
Compton scattering off CMB photons. As a source term (Eq. 3) we employ the DSA
parametrisation by [25] for the dependency on sonic Mach number
($\eta(\mathcal{M}_{s})$) and the model by [27] for the dependency on shock
obliquity ($\eta(\theta_{B})$) and divert a fraction

$\eta_{\mathrm{tot}}=\eta(\mathcal{M}_{s})\times\eta(\theta_{B})$ (4)

of the entropy change over the shock into the CR component. To detect the
shock properties on-the-fly in the simulation we use the shock finder
introduced by [3] with improvements to compute the shock obliquity as the
angle between the pressure gradient within the kernel (which we treat as the
shock normal $\hat{\mathbf{n}}$) and the magnetic field vector upstream of the
shock $\mathbf{B}_{u}$. The slope of the injected CR spectrum follows linear
DSA theory and we use a fixed electron to proton injection ratio of
$K_{e/p}=0.01$. The CR component exerts feedback on the thermal gas by solving
the pressure integral

$P_{\mathrm{CR},c}=\frac{1}{3}\>a^{4}\>\int\limits_{p_{\mathrm{min}}}^{p_{\mathrm{cut}}}dp\>4\pi
cp^{3}f(p)$ (5)

between the minimum momentum $p_{\mathrm{min}}$ represented by the CR
population and the cutoff of the distribution function $p_{\mathrm{cut}}$. We
start the CR injection at $z=4$ to avoid too strong time-constraints due to
very efficient high-momentum energy losses of CR electrons.
We employ a zoomed-in initial condition of a massive galaxy cluster with a
virial mass of $M_{\mathrm{vir}}\approx 1.3\times 10^{15}~{}M_{\odot}$ from
the sample presented in [4]. The cluster is up-sampled to 250x base
resolution, which corresponds to a mass resolution of $M_{\mathrm{DM}}\approx
4.7\times 10^{6}M_{\odot}$ and $M_{\mathrm{gas}}\approx 8.7\times
10^{5}M_{\odot}$ for dark matter and gas particles, respectively. This leads
to a maximum resolution of $h_{\mathrm{sml,min}}\approx 1$ kpc. The parent
simulation used a WMAP7 cosmology with $\Omega_{0}=0.24$,
$\Omega_{\Lambda}=0.76$, $\Omega_{\mathrm{baryon}}=0.04$, $h=0.72$ and
$\sigma_{8}=0.8$, which we also adopt for the present simulation. We start the
simulation at redshift $z=310$ and seed a constant magnetic field in
x-direction with $B_{0}=$10-14 G [see 36, for a study of the impact of the
choice of $B_{0}$]. The initial conditions of this cluster at this resolution
have been used to study the interaction between internal- and accretion shocks
in [46, 45] and its magnetic field has been studied in [37].

##  3 "Wrong Way" Relics

###  3.1 Merger Geometry

Figure 1: We show the time evolution of the merger geometry from left to
right. Arrows indicate the path of the subhalos labeled with $M_{1}-M_{3}$.
$S_{1}$ and $S_{2}$ indicate the resulting merger shocks. Contours show
synchrotron surface brightness.

The "Wrong Way" relic in our simulation originates from a triple-merger at
$z\sim 0.4-0.2$. We show the schematic of the merger geometry in Fig. 1. A
high-velocity merger with a $\sim 1:10$ mass ratio between impactor ($M_{2}$)
and target ($M_{1}$) with a large impact parameter of $b\approx 500$ kpc
drives two shock waves. These shocks follow the canonical picture [e.g. fig.
14 in 48] of the lighter merging partner ($M_{2}$) driving a strong bow-shock
($S_{1}$ in our schematic), while the heavier merging partner ($M_{1}$) drives
a weaker counter shock ($S_{2}$) in the in-fall direction of the lighter
partner. This counter shock is subsequently impacted by a third merger partner
($M_{3}$), which ultimately passes through the shock surface and falls into
the larger merger partner ($M_{1}$) in a low-impact parameter merger. This
impact deforms the weaker counter shock ($S_{2}$) first from a concave shape
at $z=0.32$ to a flat shape at $z=0.29$ and subsequently to a convex shape
pointing towards the cluster center at $z=0.27$.

###  3.2 Time Evolution

Figure 2: From left to right we show Xray surface brightness, integrated
energy density contained in CR electrons with energies above 1 GeV,
synchrotron surface brightness at 1.4 GHz and slope of the synchrotron
spectrum between 144 MHz and 1.4 GHz. From top to bottom the first three
panels show the time evolution of the relic and the lowest panel shows the
relic rotated by $90^{\circ}$.

Fig. 2 from top to bottom shows the time evolution of the counter shock
$S_{2}$ and its phasing through morphologies matching various "Wrong Way"
relics in the $xz$-plane of the simulation. The bottom row shows the same
relic as the row above in the $yz$-plane. From left to right we show the Xray
surface brightness, CR electron energy contained in the part of the
potentially synchrotron bright population with $E>1$ GeV, the synchrotron
surface brightness at 1.4 GHz and the slope of the synchrotron spectrum by
fitting a powerlaw to the surface brightness at 144 MHz (not shown) and 1.4
GHz. Initially, in the top row of Fig. 2, we see the acceleration of CR
electrons at the counter shock of the main merger event. We can readily
identify the part of the shock surface that accelerates CRs in the center of
the images, as it is the most synchrotron bright part and shows a relatively
flat synchrotron specrtum. The steeper parts of the spectrum in the upper
right corner of the images indicates that these electrons have been
accelerated at ealier times of the shock propagation and have been freely
cooling since. The counter shock is initially not very synchrotron bright,
akin to the counter-shock in Abell 3667 [e.g. 47]. The collision between
outwards traveling counter shock and the bow-shock of the infalling group
($M_{3}$) increases the sonic Mach number and with that the acceleration
efficiency of the shock, which significantly increases the synchrotron surface
brightness at the contact surface of the shocks. The infalling sub-structure
deforms the outwards traveling shock towards a relic pointing "the wrong way",
similar to the source D1 observed by [32]. In the case of our relic the flat
spectrum part is further extended, which we attribute to the projection of the
relic. Here the surface of the collision between outwards and inwards
traveling shock is pointed roughly $45^{\circ}$ out of the image plane, while
D1 seems to be viewed almost perfectly edge-on. The collision between shock
waves is also visible in our Xray image (left panel, second row in Fig. 2),
which matches the detection of a shock in Xray by [33]. As the in-falling halo
passes through the outwards traveling shock its own bow-shock collides with
the older shock, causing the relic to deform further into a v-shaped
morphology, such as in the counter shock to the sausage relic [e.g. 38, 13],
or the relic in Abell 2256 [31]. The relic in our simulation shows strong
spectral slope variations at $z=0.27$, as can be seen in the right panels of
the bottom two rows in Fig. 2. For the lower panels we rotate the image, as
this projection more closely resembles the observations of [13]. This
variation stems from sonic Mach number variations across the surface of the
shock. The majority of the shock surface is super-sonic, but sub-critical
($1\leq\mathcal{M}_{s}<2$), leading to a cooling dominated part of the relic
surface and an injection dominated part. The injection dominated part shows a
flatter spectrum, indicating that that in our scenario the variations of
spectral index can be understood as a superposition of cooling, adiabatic
compression and (re-)acceleration.

##  4 Discussion

The shock collision scenario proposed here produces a "Wrong Way" radio relic
with convex morphology and a steep synchrotron spectrum as seen in recent
observations [e.g. 13, 7, 32, 31]. The relic also lies within $r_{500}$ which
is unlikely in the classical picture of radio relics [e.g. 40], indicating
that the collision of shocks boosts the (re-)acceleration of CR electrons,
making the resulting relics more easy to detect [as suggested in 24]. The
steep spectrum of some of these relics can be explained in a scenario similar
to the one here, where electrons accelerated at an outwards traveling shock
have already undergone cooling and a collision with an infalling substructure
adiabatically compresses the population and some regions experience efficient
re-acceleration by the re-energized shock [see e.g. 24, for a theoretical
approach]. The strong variations of synchrotron spectral index is still under
debate [see discussion in 13]. In the context of our model it can be
understood as a part of the outwards traveling shock being cooling dominated,
while the part that collides with an inwards traveling shock is injection
dominated. There are detections of additional infalling substructures along
currently ongoing merger axis [e.g. 20] indicating that the geometric setup is
possible, albeit rare.

##  5 Conclusion and Outlook

We showed preliminary results of a high-resolution simulation of a massive
galaxy cluster with an on-the-fly Fokker-Planck solver to study the
acceleration, advection and aging of CR electrons in a cosmological context.
We used this simulation to study a rare form of radio relics that show convex,
instead of the typical concave morphologies. We find that a multi-merger
scenario where the counter-shock of an ongoing merger is deformed by an
infalling sub-structure can reproduce the morphologies of some of the current
known "Wrong Way" relics. We will present a more complete study of our
proposed formation process of "Wrong Way" Relics in an upcoming publication
(Böss et. al. (in prep)).

## Acknowledgments

LMB and KD are acknowledging support by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) under Germanys Excellence Strategy –
EXC-2094 – 390783311 and support for the COMPLEX project from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation program grant agreement ERC-2019-AdG 860744. UPS is supported by
the Simons Foundation through a Flatiron Research Fellowship at the Center for
Computational Astrophysics of the Flatiron Institute. The Flatiron Institute
is supported by the Simons Foundation.

## References

  * Arth et al. [2014] Arth A., Dolag K., Beck A. M., Petkova M., Lesch H., 2014, arXiv e-prints, p. arXiv:1412.6533
  * Beck et al. [2016a] Beck A. M., et al., 2016a, MNRAS, 455, 2110
  * Beck et al. [2016b] Beck A. M., Dolag K., Donnert J. M. F., 2016b, MNRAS, 458, 2080
  * Bonafede et al. [2011] Bonafede A., Dolag K., Stasyszyn F., Murante G., Borgani S., 2011, MNRAS, 418, 2234
  * Böss et al. [2023] Böss L. M., Steinwandel U. P., Dolag K., Lesch H., 2023, MNRAS, 519, 548
  * Botteon et al. [2020] Botteon A., Brunetti G., Ryu D., Roh S., 2020, A&A, 634, A64
  * Botteon et al. [2021] Botteon A., et al., 2021, ApJl, 914, L29
  * Brüggen et al. [2012] Brüggen M., Bykov A., Ryu D., Röttgering H., 2012, SSR, 166, 187
  * Brunetti & Jones [2014] Brunetti G., Jones T. W., 2014, International Journal of Modern Physics D, 23, 1430007
  * Brunetti & Vazza [2020] Brunetti G., Vazza F., 2020, PRL, 124, 051101
  * Chibueze et al. [2023] Chibueze J. O., et al., 2023, PASJ, 75, S97
  * Dehnen & Aly [2012] Dehnen W., Aly H., 2012, MNRAS, 425, 1068
  * Di Gennaro et al. [2018] Di Gennaro G., et al., 2018, ApJ, 865, 24
  * Dolag & Enßlin [2000] Dolag K., Enßlin T. A., 2000, A&A, 362, 151
  * Dolag & Stasyszyn [2009] Dolag K., Stasyszyn F., 2009, MNRAS, 398, 1678
  * Domínguez-Fernández et al. [2021] Domínguez-Fernández P., Brüggen M., Vazza F., Banda-Barragan W. E., Rajpurohit K., Mignone A., Mukherjee D., Vaidya B., 2021, MNRAS, 500, 795
  * Donnert [2014] Donnert J. M. F., 2014, MNRAS, 438, 1971
  * Donnert et al. [2016] Donnert J. M. F., Stroe A., Brunetti G., Hoang D., Roettgering H., 2016, MNRAS, 462, 2014
  * Drury [1983] Drury L. O., 1983, Reports on Progress in Physics, 46, 973
  * Hoang et al. [2019] Hoang D. N., et al., 2019, A&A, 622, A20
  * Hoeft & Brüggen [2007] Hoeft M., Brüggen M., 2007, MNRAS, 375, 77
  * Hoeft et al. [2008] Hoeft M., Brüggen M., Yepes G., Gottlöber S., Schwope A., 2008, MNRAS, 391, 1511
  * Inchingolo et al. [2022] Inchingolo G., Wittor D., Rajpurohit K., Vazza F., 2022, MNRAS, 509, 1160
  * Kang [2021] Kang H., 2021, arXiv e-prints, p. arXiv:2108.01876
  * Kang & Ryu [2013] Kang H., Ryu D., 2013, ApJ, 764, 95
  * Miniati [2001] Miniati F., 2001, Computer Physics Communications, 141, 17
  * Pais et al. [2018] Pais M., Pfrommer C., Ehlert K., Pakmor R., 2018, MNRAS, 478, 5278
  * Petkova & Springel [2009] Petkova M., Springel V., 2009, MNRAS, 396, 1383
  * Rajpurohit et al. [2020a] Rajpurohit K., et al., 2020a, A&A, 636, A30
  * Rajpurohit et al. [2020b] Rajpurohit K., et al., 2020b, A&A, 642, L13
  * Rajpurohit et al. [2023] Rajpurohit K., et al., 2023, A&A, 669, A1
  * Riseley et al. [2022] Riseley C. J., et al., 2022, MNRAS, 515, 1871
  * Sanders et al. [2022] Sanders J. S., et al., 2022, A&A, 661, A36
  * Skillman et al. [2013] Skillman S. W., Xu H., Hallman E. J., O’Shea B. W., Burns J. O., Li H., Collins D. C., Norman M. L., 2013, ApJ, 765, 21
  * Springel [2005] Springel V., 2005, MNRAS, 364, 1105
  * Steinwandel et al. [2022] Steinwandel U. P., Böss L. M., Dolag K., Lesch H., 2022, ApJ, 933, 131
  * Steinwandel et al. [2023] Steinwandel U. P., Dolag K., Böss L., Marin-Gilabert T., 2023, arXiv e-prints, p. arXiv:2306.04692
  * Stroe et al. [2013] Stroe A., van Weeren R. J., Intema H. T., Röttgering H. J. A., Brüggen M., Hoeft M., 2013, A&A, 555, A110
  * Stroe et al. [2016] Stroe A., et al., 2016, MNRAS, 455, 2402
  * Vazza et al. [2012] Vazza F., Brüggen M., Gheller C., Brunetti G., 2012, MNRAS, 421, 3375
  * Winner et al. [2019] Winner G., Pfrommer C., Girichidis P., Pakmor R., 2019, MNRAS, 488, 2235
  * Wittor et al. [2017] Wittor D., Vazza F., Brüggen M., 2017, MNRAS, 464, 4448
  * Wittor et al. [2019] Wittor D., Hoeft M., Vazza F., Brüggen M., Domínguez-Fernández P., 2019, MNRAS, 490, 3987
  * Wittor et al. [2023] Wittor D., Brüggen M., Grete P., Rajpurohit K., 2023, MNRAS, 523, 701
  * Zhang et al. [2020a] Zhang C., Churazov E., Dolag K., Forman W. R., Zhuravleva I., 2020a, MNRAS, 494, 4539
  * Zhang et al. [2020b] Zhang C., Churazov E., Dolag K., Forman W. R., Zhuravleva I., 2020b, MNRAS, 498, L130
  * de Gasperin et al. [2022] de Gasperin F., et al., 2022, A&A, 659, A146
  * van Weeren et al. [2019] van Weeren R. J., de Gasperin F., Akamatsu H., Brüggen M., Feretti L., Kang H., Stroe A., Zandanel F., 2019, Space Science Reviews, 215