11institutetext: Netherlands Institute for Radio Astronomy (ASTRON), Oude
Hoogeveensedijk 4, 7991 PD Dwingeloo, the Netherlands 22institutetext: Dept.
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Africa 33institutetext: Kapteyn Astronomical Institute, University of
Groningen, PO Box 800, 9700 AV Groningen, The Netherlands 44institutetext:
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Selargius, CA, Italy 55institutetext: Adjunct Astronomer, Green Bank
Observatory, 155 Observatory Road, Green Bank, WV 24944, USA 66institutetext:
Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France 77institutetext:
Department of Physics and Astronomy, University of Manitoba, Winnipeg,
Manitoba, Canada, R3T 2N2, Canada 88institutetext: INAF – Padova Astronomical
Observatory, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
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University of Western Australia, 35 Stirling Highway, Crawley, WA 6009,
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700, Las Condes, Santiago, Chile 1212institutetext: Department of Physics and
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KY, 40292, USA 1313institutetext: Ruhr University Bochum, Faculty of Physics
and Astronomy, Astronomical Institute (AIRUB), Universitätsstrasse 150, 44801
Bochum, Germany 1414institutetext: Max-Planck-Institut für Radioastronomie,
Auf dem Hügel 69, 53121, Bonn, Germany 1515institutetext: Department of
Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH
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Town, South Africa 1818institutetext: Southern African Larger Telescope
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Physics, Durham University, South Road, Durham DH1 3LE, UK 2020institutetext:
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South Road, Durham DH1 3LE, UK 2121institutetext: Max Planck Institute for
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M13 9PL, UK 4949institutetext: School of Mathematical and Physical Sciences,
Macquarie University, Balaclava Road, North Ryde, Sydney, NSW 2109, Australia

# MHONGOOSE — A MeerKAT Nearby Galaxy H i Survey

W.J.G. de Blok 112233 J. Healy 11 F.M. Maccagni 1144 D.J. Pisano 2255 A. Bosma
66 J. English 77 T. Jarrett 22 A. Marasco 88 G.R. Meurer 99 S. Veronese 1133
F. Bigiel 1010 L. Chemin 1111 F. Fraternali 33 B.W. Holwerda 1212 P. Kamphuis
1313 H.R. Klöckner 1414 D. Kleiner 1144 A.K. Leroy 15151616 M. Mogotsi
17171818 K.A. Oman 19192020 E. Schinnerer 2121 L. Verdes-Montenegro 2222 T.
Westmeier 99 O.I. Wong 232399 N. Zabel 22 P. Amram 66 C. Carignan 242422 F.
Combes 2525 E. Brinks 2626 R.J. Dettmar 1313 B.K. Gibson 2727 G.I.G. Jozsa
14142828 B.S. Koribalski 29293030 S.S. McGaugh 3131 T.A. Oosterloo 1133 K.
Spekkens 32323333 A.C. Schröder 3434 E.A.K. Adams 1133 E. Athanassoula 66 M.A.
Bershady 3535171722 R.J. Beswick 3636 S. Blyth 22 E.C. Elson 3737 B.S. Frank
2217173838 G. Heald 2323 P.A. Henning 39394040 S. Kurapati 22 S.I. Loubser
4141 D. Lucero 4242 M. Meyer 99 B. Namumba 43432222 S.-H. Oh 4444 A. Sardone
1515 K. Sheth 4545 M.W.L. Smith 4646 A. Sorgho 2222 F. Walter 2121 T. Williams
4747 P.A. Woudt 22 A. Zijlstra 48484949

(Received –, 2023; accepted –, 2023)

The MHONGOOSE (MeerKAT H i Observations of Nearby Galactic Objects: Observing
Southern Emitters) survey maps the distribution and kinematics of the neutral
atomic hydrogen (H i) gas in and around 30 nearby star-forming spiral and
dwarf galaxies to extremely low H i column densities. The H i column density
sensitivity (3$\sigma$ over 16 km s-1) ranges from $\sim 5\cdot 10^{17}$ cm-2
at $90^{\prime\prime}$ resolution to $\sim 4\cdot 10^{19}$ cm-2 at the highest
resolution of $7^{\prime\prime}$. The H i mass sensitivity ($3\sigma$ over 50
km s-1) is $\sim 5.5\cdot 10^{5}$ $M_{\odot}$ at a distance of 10 Mpc (the
median distance of the sample galaxies). The velocity resolution of the data
is 1.4 km s-1. One of the main science goals of the survey is the detection of
cold, accreting gas in the outskirts of the sample galaxies. The sample was
selected to cover a range in H i masses, from $10^{7}$ $M_{\odot}$ to almost
$10^{11}$ $M_{\odot}$, to optimally sample possible accretion scenarios and
environments. The distance to the sample galaxies ranges from 3 to 23 Mpc. In
this paper, we present the sample selection, survey design, and observation
and reduction procedures. We compare the integrated H i fluxes based on the
MeerKAT data with those derived from single-dish measurement and find good
agreement, indicating that our MeerKAT observations are recovering all flux.
We present H i moment maps of the entire sample based on the first ten percent
of the survey data, and find that a comparison of the zeroth- and second-
moment values shows a clear separation between the physical properties of the
H i in areas with star formation and areas without, related to the formation
of a cold neutral medium. Finally, we give an overview of the H i-detected
companion and satellite galaxies in the 30 fields, five of which have not
previously been catalogued. We find a clear relation between the number of
companion galaxies and the mass of the main target galaxy.

###### Key Words.:

galaxies: ISM –- galaxies: spiral – galaxies: dwarf – galaxies: kinematics and
dynamics – radio lines: galaxies

##  1 Introduction

The evolution of the baryonic matter in the Universe can to a large degree be
described as the gradual transformation of primordial atomic hydrogen into
galaxies over cosmic time. This transformation involves physical processes on
many scales, from the size of galaxy clusters to those of individual gas
clouds within a galaxy. These processes, such as gas infall, collapse of
clouds, formation of stars, feedback due to stellar winds and supernovae, form
part of the “baryon cycle”. Although many of them act on sub-galactic scales,
they nevertheless affect the evolution of galaxies as whole.

The only place where a comprehensive detailed survey of these processes can be
made is the nearby Universe: locally we can study, in detail, all aspects of
the baryon cycle. Resolved observations of the cold gas, and, specifically of
neutral hydrogen (H i) can contribute to determining how galaxies acquire
their gas, how star formation is sustained, and ultimately how the dark and
visible matter interact to determine and regulate the evolution of galaxies.

We concentrate here on the first issue of the origin of gas in galaxies. This
question first arose from the observation that in the inner regions of nearby
spiral galaxies, time scales for consumption of gas by star formation are much
shorter than a Hubble time, even though the star formation rate (SFR) has been
approximately constant over most of the lifetime of the galaxies (e.g.,
Kennicutt 1998; Bigiel et al. 2011; Leroy et al. 2013; Fraternali & Tomassetti
2012). If galaxies are to continue forming stars at their current rate beyond
the current epoch, there must be a gas supply external to galaxies. A similar
argument can also be made looking at high-redshift galaxies (e.g., Saintonge
et al. 2013; Tacconi et al. 2018). These form stars at a rate much higher than
observed in the local Universe. This would imply a strong decrease in the gas
content of galaxies between then and now, yet we observe an almost constant
density, again implying there is an external supply of gas (see, e.g., Walter
et al. 2020). In other words, we observe that the gas depletion time for high-
redshift galaxies is $\sim 1$ Gyr or less (Saintonge et al. 2013; Tacconi et
al. 2018) and yet most galaxies are not quenched and keep forming stars for a
much longer time until today.

Galactic disks can, in principle, be replenished by accreting gas-rich
companion galaxies, but the slope of the H i mass function is not steep enough
for small companions to supply larger galaxies with a substantial amount of
gas for a sufficiently long time (Sancisi et al. 2008). In addition,
observations suggest that gas-rich mergers can provide at most 20% of the gas
required to maintain the SFR in nearby late-type galaxies (Di Teodoro &
Fraternali 2014). This implies that spirals have to accrete directly from the
intergalactic medium (IGM).

The presence of cold gas in the halos of our Milky Way and other galaxies has
been known for several decades (see, e.g., Wakker & Woerden 1997; Oosterloo et
al. 2007; Sancisi et al. 2008; Heald et al. 2011 and the reviews by Putman et
al. 2012 and Tumlinson et al. 2017). H i in some halos may be part of a star
formation-driven “galactic fountain” (Shapiro & Field 1976). This galactic
fountain has been proposed to lead to an “indirect” cold gas accretion
mechanism, where the gas that is expelled from the disk, drags additional halo
gas along as it returns to the disk (Marasco et al. 2012; Fraternali 2017;
Marasco et al. 2019).

This is suggested, for example, for the galaxy NGC 2403 by the observation
that most of its extra-planar H i has a similar projected radial distribution
as the star formation in the disk and that it has disk-like kinematics:
rotating but lagging behind the main disk (see, e.g., Fraternali et al. 2001).
Similar conclusions were reached for nearby galaxy NGC 253 (Lucero et al.
2015). Note, though, that in NGC 2403, we also observe H i in the halo that
likely has an external origin (Veronese et al. 2023), and indeed some of the H
i complexes found outside of the main H i disks of galaxies are counter-
rotating with respect to the disk, confirming that they cannot have originated
from it. Numerical simulations (e.g., Kereš et al. 2005; Ramesh et al. 2023)
predict that filaments of cooler gas from the IGM can penetrate the hot halos
surrounding galaxies and deposit gas onto the disk. This process is called
“cold accretion”. These filaments are a prediction of high-resolution
cosmological hydrodynamical simulations of structure formation (e.g., Davé et
al. 1999; Crain et al. 2016; Ramesh et al. 2023). These suggest that most of
the baryons at low redshift are in a warm-hot ($T\sim 10^{5}-10^{7}$ K)
intergalactic medium and most of the gas in the cosmic web is therefore
ionised and difficult to observe directly. To detect the smaller fraction of
cooler ($T<10^{4}$ K) baryons in the cosmic web, an H i column density
sensitivity of $\sim 10^{17-18}$ cm-2 is required (Popping et al. 2009).

It is in the context of this cold accretion that the study of H i halos of
galaxies is relevant: it could provide direct observations of the accretion of
gas onto galaxies as well as a strong observational test for models of galaxy
evolution.

An extensive study of the H i halos of nearby spiral galaxies was made by the
Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) project on the Westerbork
Synthesis Radio Telescope (WSRT; Heald et al. 2011). For it, 22 disk galaxies
were mapped down to an H i column density limit of $\sim 10^{19}$ cm-2, i.e.,
an order of magnitude lower than the surface densities typically found in
star-forming H i disks. The results of HALOGAS indicate that some galaxies
have more extended low column density emission, while others do not: extended
H i distributions have been detected in about 12 of the 22 galaxies observed.
It is possible that some of this gas is related to star formation and galactic
fountain processes (Marasco et al. 2019), but external accretion cannot be
excluded. The average cold neutral hydrogen gas accretion rate for the HALOGAS
galaxies is between 0.05 and 0.09 $M_{\odot}$ yr-1 (Kamphuis et al. 2022),
with the exact value depending on the treatment of H i that is detected by the
Green Bank Telescope (GBT) but not by the WSRT. This accretion rate is
generally lower than the SFR (cf. Table 4 in Kamphuis et al. 2022). If in the
HALOGAS sample, the H i accretion rate balances the star formation rate,
direct accretion must occur at much lower neutral gas column densities than
detected by HALOGAS and on spatial scales not resolved by the GBT.

Very deep single-dish H i observations show the presence of H i at these very
low-column densities. Braun & Thilker (2004), for example, observed low-column
density features around and between M31 and M33 and, using the WSRT as a
single dish, reached a $3\sigma$ limit over 16 km s-1 of $1.1\cdot 10^{17}$
cm-2, but with an angular resolution of $\sim 49^{\prime}$. Further deep
observations with the GBT of the HALOGAS (Heald et al. 2011) and The H i
Nearby Galaxy Survey (THINGS; Walter et al. 2008) galaxies are described in
Pisano (2014), de Blok et al. (2014) and Pingel et al. (2018). These reach a
$3\sigma$ over 16 km s-1 sensitivity of $\sim 6\cdot 10^{17}$ cm-2 at an
angular resolution of about $9^{\prime}$ or $\sim$ 14 kpc and $\sim 24$ kpc at
the median distances of, respectively, the THINGS and HALOGAS galaxies.
However, sheer column density sensitivity is not enough, as these relatively
coarse spatial resolutions already suggest. Wolfe et al. (2013, 2016) show
that the diffuse $\sim 10^{17}$ cm-2 low column density gas between M31 and
M33 observed by Braun & Thilker (2004) is resolved in several kpc-sized clouds
with peak column densities of a few times $10^{18}$ cm-2 when observed at
higher spatial resolutions.

To properly detect and characterise accretion features both a kpc-scale (or
better) spatial resolution and a column density sensitivity of $\sim 10^{18}$
cm-2 (or better) are thus needed. Surveys such as THINGS (Walter et al. 2008)
and HALOGAS (Heald et al. 2011), have concentrated on either obtaining a high
spatial resolution or a high column density sensitivity. Optimising both
simultaneously is rarely an option; this has so far limited our knowledge of
how any low column density gas is connected with the cosmic web and where
accretion occurs.

##  2 The MHONGOOSE survey

The MeerKAT radio telescope (Jonas 2018; Camilo 2018; Mauch et al. 2020) is
making it possible to take this large step forward. MeerKAT consists of 64
dishes each with an effective diameter of 13.5m, located in the Karoo semi-
desert in South Africa. The array has a compact and dense core (the shortest
baseline being 29m), with 70% of the collecting area located close to the
centre of the array, and with longest core baselines of 1 km. The rest of the
array is distributed at larger distances, to a maximum baseline of 7.7 km.
This combination of a dense core and long baselines means the telescope has
the ability to produce high-resolution imaging, while retaining a good column
density sensitivity. A third factor contributing to the high sensitivity is
the low system temperature of the receivers. At 1.4 GHz, the effective system
temperature is $T_{\rm sys}/\eta\simeq 20.5$K (where $\eta$ is the antenna
efficiency).

The array design of MeerKAT is such that the noise level for observations
producing beam sizes between $\sim 6^{\prime\prime}$ and $\sim
90^{\prime\prime}$ is approximately flat (see Fig. 1). MeerKAT is therefore
not optimised for one particular resolution, but allows high-quality imaging
over a large range in resolutions using weighting or tapering.

Thanks to the combination of exquisite column density sensitivity, high
spatial resolution (down to $\sim 7^{\prime\prime}$ for H i) and a large field
of view with a primary beam full width at half-maximum (FWHM) diameter of 1∘,
we can study nearby galaxies in H i at the required quality to characterise
any low-column density H i that may be accreting onto a galaxy.

MHONGOOSE (MeerKAT H i Observations of Nearby Galactic Objects: Observing
Southern Emitters) is a MeerKAT Large Survey Project designed to produce
ultra-deep H i observations of 30 nearby gas-rich spiral and dwarf galaxies in
order to detect and characterise any low-column density, potentially
infalling, atomic gas, and to probe its link to star formation (see also de
Blok et al. 2016, 2020). These deep observations can provide information on
gas flows into and out of the galaxy disks, accretion from the IGM, the
fuelling of star formation, the connection with the cosmic web and even the
possible existence of low-mass cold dark matter (CDM) halos. The relation
between dark and baryonic matter and the distribution of dark matter within
galaxies can also be comprehensively studied due to the high resolution
combined with high sensitivity. The large field of view of MeerKAT means a
significant fraction of the virial volumes of the target galaxies can be
observed.

For the MHONGOOSE survey, each sample galaxy is observed for 55 hours in order
to reach a $3\sigma$ over 16 km s-1 sensitivity limit of $5\cdot 10^{17}$ cm-2
to detect the low-column density component discussed above. Such column
densities are close to three orders of magnitude below those typically found
in the star-forming disks of galaxies and equal those of the accreting cool
neutral gas as predicted by many numerical simulations (Kereš et al. 2005;
Popping et al. 2009; Ramesh et al. 2023)

Figure 1: Noise level as a function of resolution for the HALOGAS, THINGS and
MHONGOOSE surveys. The blue curve shows that the MHONGOOSE survey has a flat
noise distribution, meaning equally sensitive imaging can be obtained over a
large range of resolutions between $\sim 6^{\prime\prime}$ and $\sim
90^{\prime\prime}$. The dashed brown curve shows the HALOGAS survey, with an
optimal sensitivity around $\sim 20^{\prime\prime}$. The dashed red curve
represents the THINGS survey. This is a combination of three separate VLA
array configurations (also shown at the top of the plot calculated using the
correct relative observing times). THINGS has optimal sensitivity around $\sim
15^{\prime\prime}$ and $\sim 50^{\prime\prime}$. All noise values are
calculated over a 5 km s-1 channel.

###  2.1 Comparison with other surveys

Figure 2 compares the MHONGOOSE column density sensitivities with those from
previous H i surveys using both interferometers and single-dish telescopes.
Interferometric targeted surveys shown here are THINGS (Walter et al. 2008),
HALOGAS (Heald et al. 2011), the Westerbork H i Survey Project (WHISP; van der
Hulst et al. 2001), the Local Irregulars That Trace Luminosity Extremes, The
HI Nearby Galaxy Survey (LITTLE THINGS; Hunter et al. 2012) and the Local
Volume H i Survey (LVHIS; Koribalski et al. 2018). Also shown is the
untargeted Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY;
Koribalski et al. 2020). For the single-dish observations we show the column
density sensitivities for the H i Parkes All Sky Survey (HIPASS; Barnes et al.
2001; Meyer et al. 2004), the Arecibo Legacy Fast ALFA (ALFALFA; Haynes et al.
2018), the Arecibo Galaxy Environment Survey (AGES; Auld et al. 2006), deep
observations of M31 (Wolfe et al. 2016) and NGC 2903 (Irwin et al. 2009), as
well as a number of deep GBT and Parkes observations of nearby galaxies
(Sorgho et al. 2018, Sardone et al. 2021, Pingel et al. 2018, D.J. Pisano,
priv. comm.). We also show a number of representative deep H i observations
taken with the Five-hundred-meter Aperture Spherical Telescope (FAST) from Xu
et al. (2022) and Liu et al. (2023).

To ensure a proper comparison we have taken the noise per channel and the
channel widths from the source papers or the corresponding publicly available
data and homogenized these quantities to a common channel width of 16 km s-1,
assuming square-root scaling of noise with channel-width. A 16 km s-1 channel
width corresponds approximately to the FWHM of an H i line with a velocity
dispersion of 7 km s-1, which is comparable to the lowest values seen in
previous H i observations of nearby galaxies (Ianjamasimanana et al. 2017).

In Fig. 2 we show the sensitivities of these H i surveys and compare these
with the observed sensitivity of MHONGOOSE. It is clear that at all
resolutions the MHONGOOSE data are significantly more sensitive than previous
interferometric observations. Note that the sensitivity does not change simply
as the inverse of the beam size squared (which would be a straight line with a
slope of $-2$) as one might expect. This is due to the different weightings
and taperings used to produce the data at the various resolutions. We will
return to this in Sec. 5.6.

For comparison, we also show estimated sensitivities for H i surveys on SKA-
MID. These are simply calculated by scaling up the MeerKAT collecting area to
the SKA-MID “baseline design” collecting area (i.e., the equivalent of 64
MeerKAT dishes with 13.5m diameter and 133 SKA dishes with 15m diameter) and
should therefore only be regarded as indicative, as they do not take into
account potentially different baseline distributions, dish designs, or system
temperatures.

Figure 2: Sensitivity versus resolution in H i surveys. Colored symbols show
the $3\sigma$ column density sensitivity over 16 km s-1 for various
interferometric and single-dish surveys, as indicated by the labels and legend
and listed in the text. The thick blue line shows the observed MHONGOOSE
sensitivities. MHONGOOSE reaches single-dish sensitivities but at a 10–50
times better angular resolution. To give an indication of the physical scales:
at 10.3 Mpc (the median distance of the MHONGOOSE sample), $10^{\prime\prime}$
corresponds to 0.5 kpc. Galaxies that are part of a sample with a fixed
angular resolution (THINGS $30^{\prime\prime}$, GBT, and PKS) were given
small, random horizontal offsets for clarity. References are given in the
text.

A striking aspect of the comparison is that between $\sim 30^{\prime\prime}$
and $\sim 100^{\prime\prime}$, MHONGOOSE is probing unexplored territory, with
observations that have the column density sensitivity of deep single-dish H i
observations of the Local Universe, but at an angular resolution that is more
than an order of magnitude better. With these observations it will therefore
be possible to investigate the low-column density H i, from the outskirts of
the star-forming disks out into the far reaches of the dark matter halo.

##  3 Sample Selection

One of the main goals of MHONGOOSE is to trace accretion and star formation
processes over a large range in galaxy properties. It is thus important to
ensure that within the limited observing time available a representative range
of H i masses, stellar masses, star formation rates and rotation velocities
(and hence, halo masses) is sampled. Furthermore, to isolate accretion
features from tidal and interaction features as much as possible, strongly
interacting galaxies and dense environments are to be avoided.

Primary critera for the sample selection are that the galaxies should have
been detected in H i and located in the southern hemisphere. This makes the
HIPASS catalogue (Meyer et al. 2004) a natural starting point. To ensure the
availability of a significant set of multi-wavelength data, we limited our
selection to HIPASS galaxies that are part of the Survey of Ionization in
Neutral Gas Galaxies (SINGG; Meurer et al. 2006) and the Survey of Ultraviolet
emission in Nearby Galaxies (SUNGG; Wong et al. 2016). These surveys collected
H$\alpha$, optical, infrared and ultraviolet data for a large number of
HIPASS-detected nearby galaxies.

The SINGG/SUNGG criteria were as follows:

  1. (i)

HIPASS peak flux density $>50$ mJy ($3.8\sigma$ in HIPASS),

  2. (ii)

galactic latitude $|b|>30^{\circ}$,

  3. (iii)

projected distance from the center of the Large (Small) Magellanic Cloud
$>10^{\circ}$ ($>5^{\circ}$),

  4. (iv)

Galactic standard of rest velocity $>200$ km s-1.

This SINGG/SUNGG proto-sample was divided in bins of 0.2 dex in $\log(M_{{\rm
H{\hskip 0.56917pt\tt I}}})$ and in each bin the closest 30 to 40 galaxies
were selected. This gave a flat number distribution in the range
$8.5<\log(M_{{\rm H{\hskip 0.56917pt\tt I}}}/M_{\rm\odot})<10.5$, with an
additional, small number of galaxies around $\log(M_{{\rm H{\hskip
0.56917pt\tt I}}}/M_{\rm\odot})\sim 7.0$ and $\log(M_{{\rm H{\hskip
0.56917pt\tt I}}}/M_{\rm\odot})\sim 11$. Most of these selected galaxies have
a radial velocity $<2000$ km s-1 with a median velocity of 1300 km s-1. These
criteria resulted in the final SINGG sample of 468 galaxies as published in
Meurer et al. (2006). The key characteristic of this selection is that it was
done uniformly in $\log(M_{{\rm H{\hskip 0.56917pt\tt I}}})$ in order to
guarantee the broadest possible range in H i masses.

For MHONGOOSE we further narrowed down the SINGG sample by requiring that for
a given galaxy, a complete set of H$\alpha$, $R$-band and GALEX ultra-violet
data was available. This reduced the number of galaxies to 151. To retain
sufficient spatial resolution, we furthermore removed all galaxies with a
distance $D>30$ Mpc (heliocentric velocity $v_{\rm hel}>2100$ km s-1). In
addition, we only selected galaxies with a southern declination, and we
excluded the survey area of the MeerKAT Fornax Survey (Serra et al. 2023). We
additionally checked that the potential sample galaxies were not located in
the densest environments (i.e., inner parts of galaxy clusters or major galaxy
groups). Galaxies that were located in the outer parts of (smaller) groups
were retained (as were, obviously, isolated galaxies). This enables
quantifying the effects of environment on accretion processes in medium- to
low-density environments, without the target galaxies themselves being majorly
affected by the environment. Studies of isolated galaxies have shown that the
gas captured from companion galaxies and galactic fountain processes (due to
SF and Active Galactic Nuclei [AGN]) are minimised there (Jones et al. 2017;
Espada et al. 2011b, a; Leon et al. 2008; Sabater et al. 2012; Lisenfeld et
al. 2007). These criteria resulted in a sample of 88 galaxies.

As the goal of MHONGOOSE is to characterise the low-column density H i over a
large range in H i masses, we aimed for a flat number distribution in
$\log(M_{{\rm H{\hskip 0.56917pt\tt I}}})$ over the available mass range
$6.0<\log(M_{\rm{\rm H{\hskip 0.56917pt\tt I}}}/M_{\rm\odot})<10.5$, analogous
to SINGG. To compensate for the smaller number of galaxies, we used six bins
each with a width of 0.5 dex, except for the lowest-mass bin which we defined
as $\log(M_{{\rm H{\hskip 0.56917pt\tt I}}}/M_{\odot})<8.0$.

The final sample size of 30 galaxies was set by the assigned observing time
and the desired column density sentivity. This total number implies a total of
five galaxies per mass bin. To optimise the selection for the science
objectives of the survey, we required that galaxies be in one of three well-
defined inclination categories as follows: i) (close to) face-on, ii) (close
to) edge-on and iii) inclination (close to) 60 degrees. Face-on allows the
best characterization of the morphology of the interstellar medium (ISM), as
well as determination of vertical motions. Edge-on allows an unambiguous
characterization of the vertical structure of the ISM and possibly the dark
matter distribution out of the disk plane. The intermediate inclination range
allows (following a limited amount of modeling) determination of both, and can
be used to tie results from edge-on and face-on classes together. It is also
an optimal inclination for rotation curve measurements and mass-modeling of
the galaxy.

Selection of the final 30 galaxies was done in two steps. In the first step,
optical SINGG and Digital Sky Survey images were examined and galaxies that
were affected by bright foreground stars were rejected. In addition, we
rejected cases where the galaxy was too big to comfortably fit in the
$1^{\circ}$ FWHM MeerKAT primary beam. This to avoid reduced sensitivity to H
i in the outer parts of the galaxies (due to the primary beam attenuation) and
to ensure mosaicking was not needed. Generally we insisted that the optical
diameter was smaller than $15^{\prime}$ (though few galaxies actually reached
that size). In SINGG, the optical diameter is determined from optical surface
brightness profiles and corresponds to twice the radius beyond which no
detectable R-band, H$\alpha$, or UV emission is found. Meurer et al. (2013)
show that this radius appears to correspond to the edge of the stellar disk.

We also did not include galaxies that were clearly strongly interacting.
Finally, we checked that no extremely bright radio continuum sources were
present within or close to the galaxy positions. All of this resulted in the
rejection of 11 galaxies.

We then stepped through each of the mass bins and used the SINGG imaging to
select in each bin the most optimal edge-on, face-on, and intermediate-
inclination galaxies. Factors that went into this were how close the galaxies
were to the preferred inclinations (as judged from the apparent major to minor
axis ratios estimated from the SINGG $R$-band images), their angular sizes,
and their distances (where the nearest galaxies were preferred). A secondary
condition was to ensure that a range in star formation rates (as judged from
the SINGG H$\alpha$ SFR measurements) was covered for each bin.

This resulted in the final sample of 30 galaxies. These are listed in Table 1
along with some fundamental properties. Note that some properties listed here
are different from those given in the earlier sample table in de Blok et al.
(2020). That table lists the sample with the galaxy parameters originally used
for the sample selection as based on parameters and distances from
SINGG/SUNGG. In the current paper, we have adopted more recent distance
estimates for the galaxies (including Tip of the Red Giant Branch [TRGB]
measurements). These revised distances resulted in small changes in distance-
dependent properties (such as the H i mass), sometimes resulting in a galaxy
moving to a different H i mass bin. These changes have no significant impact
on the final science goals. The sample still covers the desired large range in
H i mass as well as a representative range in (gas-rich) galaxy properties.
The current Table lists the galaxies in order of H i mass assuming the revised
distances. For the median distance of the galaxies in the MHONGOOSE sample
(10.3 Mpc), $10^{\prime\prime}$ corresponds to 0.5 kpc. H i-related parameters
listed in the Table are based on the observations presented in this paper. The
inclination values are based on the optical axis ratios and should be regarded
as indicative only.

In Table 1 we also give the stellar masses and star formation rates based on
WISE infrared measurements. The stellar masses were derived using the new GAMA
Stellar Masses calibration and (light and colors) method of Jarrett et al.
(2023). The star formation rates are a combination mid-IR and UV SFR based on
the method described in Cluver et al. (in prep.). Figure 3 shows the
distribution of the MHONGOOSE galaxies along the SFR-$M_{\star}$ main sequence
(defined by the upper ridges in the diagrams). As the sample was selected to
be representative of gas-rich, star-forming galaxies, it therefore covers the
main sequence well. The only galaxy not on it is NGC 1371 (J0335–24) which has
a low SFR for its stellar mass.

Figure 3: Top panel: Star formation rate of the MHONGOOSE galaxies plotted
against their stellar mass. The SFR is derived using the method described in
Cluver et al. (in prep.) based on mid-IR and UV SFRs. The stellar masses are
derived from WISE W3 and W4 luminosities as described in Jarrett et al.
(2023). Background grayscale and gray contours show the distribution of
galaxies in the local Universe based on mid-IR and UV data (Jarrett & Cluver,
in prep.). The MHONGOOSE sample was selected to be representative of the
SFR-$M_{\star}$ main sequence (the upper ridge of the distributions) and
almost all galaxies are indeed on this sequence. Only NGC 1371 (J0335–24) has
a low SFR for its mass. Galaxies with uncertain SFR values are not plotted
(see Tab. 1). UGCA320 (J1303–17b) has a low signal-to-noise in the WISE
observations as indicated by the diamond symbol. The purple dashed curve shows
the average trend derived in Cluver et al. (in prep.). Bottom panel: Specific
SFR of the MHONGOOSE galaxies plotted against stellar mass. Symbols and curves
as in top panel. In addition, the blue curve shows a fit to the data presented
in Leroy et al. (2019). The diagonal gray dashed lines indicate corresponding
SFR values in $M_{\odot}$ yr-1.

The MHONGOOSE sample galaxies span a range of galaxy environments, although,
as described above, the selection was intentionally biased against those
galaxies residing in the densest environments. Using the group catalog from
Kourkchi & Tully (2017), we quantify the group environment for all 30
galaxies. Of our sample galaxies, 13 are “isolated”; that is, not in a group
with another galaxy although they are still in larger associations. The
remaining 17 galaxies reside in groups with anywhere from 2–31 members. Their
dynamical group masses range from those of dwarf galaxy associations
($\lesssim 10^{12}$ $M_{\odot}$) or single, massive galaxies up to – for a few
galaxies – those of small groups ($\sim 10^{13}$ $M_{\odot}$).

The identification and masses of all groups and associations as listed in the
Kourkchi & Tully (2017) catalog are given in Table 2. A number of galaxies are
found to be part of the same groups or associations as indicated in Table 2.

In addition, we use the stellar masses and distances given in Table 1 to
calculate the halo mass $M_{200}$ using the stellar mass-halo mass relation
given in Moster et al. (2013). Using standard cosmology ($H_{0}=69$ km s-1
Mpc-1, $\Omega_{\Lambda}=0.27$) we also derive the virial radius $R_{200}$ for
the target galaxies. We also list the ratio of a $1.5^{\circ}$ field of view
(cf. Sect. 5.7) in kpc at the distance of the galaxy, and the virial diameter
$D_{200}=2R_{200}$. Note that we have made no attempt to homogenize the
Kourkchi & Tully (2017) and Moster et al. (2013) numbers, so some differences
may exist in halo or group masses due to different methods, assumptions or
input data.

Table 1: Basic properties of galaxies in the MHONGOOSE sample

HIPASS | Name |  $\alpha$ (J2000.0) |  $\delta$ (J2000.0) | $D$ | $V_{\rm cen}$ | $\log(M_{\rm HI})$ | $i$ | $W_{20}$ | $\log(M_{\rm\star})$ |  log(SFR)gg$g$Values in parentheses are uncertain due to faintness of the mid-IR emission and should be regarded as indicative only.
---|---|---|---|---|---|---|---|---|---|---
|  | $(^{h}\ {}^{m}\ {}^{s})$ | $(^{\circ}\ {}^{\prime}\ {}^{\prime\prime})$ | (Mpc) |  (km s-1) |  [$M_{\odot}$ ] | $({}^{\circ})$ |  (km s-1) |  [$M_{\odot}$ ] |  [$M_{\odot}$ yr-1]
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
J0049–20 | UGCA015 | 00 49 49.20 | –21 00 54.0 | 3.4 | 293.8 | 6.99 | 66 | 32 | 6.50 |  (-2.52)
J0008–34 | ESO349-G031 | 00 08 13.36 | –34 34 42.0 |  3.3bb$b$Tully et al. (2013) | 219.6 | 7.11 | 35 | 39 | 6.13 |  (-2.52)
J1321–31 | KK98-195 | 13 21 08.20 | –31 31 45.0 |  5.2dd$d$Pritzl et al. (2003) | 570.8 | 7.60 | 63 | 38 | 4.71 |  (-2.29)
J0310–39 | ESO300-G016 | 03 10 10.48 | –40 00 10.5 |  8.0cc$c$Tully et al. (2016) | 707.6 | 7.80 | 36 | 42 | 7.22 |  (-2.52)
J0031–22 | ESO473-G024 | 00 31 22.51 | –22 45 57.5 |  7.2cc$c$Tully et al. (2016) | 538.1 | 7.95 | 57 | 50 | 6.84 | -2.22
J1337–28 | ESO444-G084 | 13 37 19.99 | –28 02 42.0 |  4.6ee$e$Karachentsev et al. (2002) | 586.7 | 8.02 | 40 | 74 | 6.69 |  (-2.52)
J0320–52 | NGC1311 | 03 20 06.96 | –52 11 07.9 | 5.6 | 569.5 | 8.05 | 74 | 101 | 8.23 | -1.62
J0454–53 | NGC1705 | 04 54 13.50 | –53 21 39.8 | 5.7 | 631.6 | 8.07 | 42 | 155 | 8.37 | -1.61
J0429–27 | NGC1592 | 04 29 40.13 | –27 24 30.7 | 10.3 | 943.2 | 8.10 | 60 | 80 | 8.49 | -1.57
J0135–41 | NGC0625 | 01 35 04.63 | –41 26 10.3 | 4.0 | 393.4 | 8.12 | 71 | 95 | 8.61 | -1.28
J1106–14 | KKS2000-23 | 11 06 12.00 | –14 24 25.7 |  13.9cc$c$Tully et al. (2016) | 1035.9 | 8.74 | 70 | 92 | 7.51 |  ( -1.82)
J1253–12 | UGCA307 | 12 53 57.29 | –12 06 21.0 | 11.0 | 821.7 | 8.88 | 60 | 89 | 8.05 | -1.56
J0309–41 | ESO300-G014 | 03 09 37.87 | –41 01 49.7 | 10.9 | 953.6 | 8.89 | 59 | 140 | 8.90 | -0.99
J0331–51 | IC1954 | 03 31 31.39 | –51 54 17.4 |  12.8ff$f$Anand et al. (2021) | 1057.1 | 8.90 | 62 | 231 | 9.63 | -0.35
J0351–38 | ESO302-G014 | 03 51 40.90 | –38 27 08.0 | 16.8 | 869.6 | 8.90 | 28 | 82 | 8.19 |  (-2.52)
J2009–61 | IC4951 | 20 09 31.77 | –61 51 01.7 | 11.6 | 811.4 | 8.93 | 80 | 131 | 8.60 | -1.45
J2357–32 | NGC7793 | 23 57 49.83 | –32 35 27.7 |  3.6ff$f$Anand et al. (2021) | 225.7 | 8.96 | 47 | 189 | 9.34 | -0.71
J1303–17b | UGCA320 | 13 03 16.74 | –17 25 22.9 | 6.0 | 739.9 | 8.97 | 83 | 125 | 7.91 | -1.02
J1318–21 | NGC5068 | 13 18 54.81 | –21 02 20.8 |  5.2ff$f$Anand et al. (2021) | 668.9 | 9.01 | 28 | 107 | 9.36 | -0.54
J0546–52 | NGC2101 | 05 46 24.17 | –52 05 18.7 | 16.4 | 1186.8 | 9.22 | 47 | 117 | 9.00 | -0.73
J1254–10a | NGC4781 | 12 54 27.00 | –10 30 30.0 |  11.3ff$f$Anand et al. (2021) | 1255.9 | 9.22 | 65 | 250 | 9.52 | -0.28
J0516–37 | ESO362-G011 | 05 16 38.80 | –37 06 09.1 | 15.6 | 1337.0 | 9.57 | 81 | 289 | 9.68 | -0.22
J0459–26 | NGC1744 | 04 59 57.80 | –26 01 20.0 | 9.3 | 739.9 | 9.54 | 57 | 207 | 9.18 | -0.78
J1103–23aa$a$pair with NGC 3513. | NGC3511 | 11 03 23.77 | –23 05 12.4 |  13.9ff$f$Anand et al. (2021) | 1099.1 | 9.54 | 70 | 307 | 9.94 | -0.03
J2257–41 | NGC7424 | 22 57 18.37 | –41 04 14.1 | 7.9 | 936.6 | 9.60 | 32 | 170 | 9.56 | -0.46
J1153–28 | UGCA250 | 11 53 24.06 | –28 33 11.4 | 20.2 | 1696.1 | 9.84 | 82 | 285 | 9.76 | -0.34
J0335–24 | NGC1371 | 03 35 01.34 | –24 55 59.6 | 22.7 | 1456.4 | 9.97 | 46 | 398 | 10.63 | -0.62
J0052–31 | NGC0289 | 00 52 42.36 | –31 12 21.0 | 21.5 | 1620.1 | 10.35 | 45 | 292 | 10.43 | 0.16
J0419–54 | NGC1566 | 04 20 00.42 | –54 56 16.1 |  17.7ff$f$Anand et al. (2021) | 1496.0 | 10.08 | 37 | 219 | 10.68 | 0.61
J0445–59 | NGC1672 | 04 45 42.50 | –59 14 49.9 |  19.4ff$f$Anand et al. (2021) | 1327.0 | 10.29 | 34 | 298 | 10.69 | 0.75

111 Columns: (1) HIPASS identification. (2) Common name. (3) Right ascension
(J2000.0). (4) Declination (J2000.0). (5) Distance. Distances taken from Leroy
et al. (2019), unless noted in the notes below. (6) Central velocity (this
work). (7) Logarithmic H i mass (this work). (8) Indicative inclination (NED).
(9) $W_{20}$ H i velocity width (this work). (10) WISE-derived logarithmic
stellar mass (11). WISE-derived logarithmic SFR.
_Distance references:_ , , , , .

Table 2: Group membership and halo properties of the galaxies in the MHONGOOSE
sample

HIPASS | Name | PGC | PGC1 | PGC1+ | $N$ | $\log(M_{K})$ | $\log(M_{d})$ | $\log(M_{200})$ | $R_{200}$ | $f_{D200}$
---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  [$M_{\odot}$ ] |  [$M_{\odot}$ ] |  [$M_{\odot}$ ] | (kpc) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
J0049–20 | UGCA015 | 2902 | 2789 |  2789AAfootnotemark: $A$ | 4 | 12.78 | 12.71 | 9.93 | 67 | 0.67
J0008–34 | ESO349-G031 | 621 | 621 |  2789AAfootnotemark: $A$ | 1 | 10.02 | – | 9.77 | 59 | 0.73
J1321–31 | KK98-195 | 166163 | 48082 |  46957aa$a$Part of same group and association. | 13 | 12.25 | 12.59 | 9.20 | 38 | 1.79
J0310–39 | ESO300-G016 | 11842 | 12209 | 12209 | 3 | 12.53 | 12.43 | 10.24 | 85 | 1.23
J0031–22 | ESO473-G024 | 1920 | 2789 |  2789AAfootnotemark: $A$ | 4 | 12.78 | 12.71 | 10.07 | 74 | 1.28
J1337–28 | ESO444-G084 | 48111 | 48082 |  46957aa$a$Part of same group and association. | 13 | 12.25 | 12.59 | 10.07 | 74 | 0.81
J0320–52 | NGC1311 | 12460 | 12460 | 12460 | 1 | 10.61 | – | 10.66 | 116 | 0.63
J0454–53 | NGC1705 | 16282 | 16282 | 16282 | 1 | 10.72 | – | 10.70 | 121 | 0.62
J0429–27 | NGC1592 | 15292 | 15292 | 15292 | 1 | 10.65 | – | 10.78 | 128 | 1.05
J0135–41 | NGC0625 | 5896 | 5896 |  2789AAfootnotemark: $A$ | 1 | 10.91 | – | 10.83 | 133 | 0.39
J1106–14 | KKS2000-23 | 3097702 | 3097702 | 3097702 | 1 | 10.54 | – | 10.26 | 86 | 2.12
J1253–12 | UGCA307 | 43851 | 43851 |  41220CCfootnotemark: $C$ | 1 | 10.73 | – | 10.53 | 106 | 1.36
J0309–41 | ESO300-G014 | 11812 | 12209 | 12209 | 3 | 12.53 | 12.43 | 11.01 | 153 | 0.93
J0331–51 | IC1954 | 13090 | 13090 | 14391 | 2 | 11.52 | 10.70 | 11.29 | 190 | 0.88
J0351–38 | ESO302-G014 | 13985 | 13985 | 12209 | 1 | 10.59 | – | 10.61 | 113 | 1.95
J2009–61 | IC4951 | 64181 | 64181 | 62836 | 1 | 10.92 | – | 10.82 | 132 | 1.15
J2357–32 | NGC7793 | 73049 | 73049 | 2789 | 1 | 11.23 | – | 11.15 | 170 | 0.28
J1303–17b | UGCA320 | 45084 | 45084 |  46400BBfootnotemark: $B$ | 2 | 10.99 | 9.00 | 10.65 | 116 | 0.68
J1318–21 | NGC5068 | 46400 | 46400 |  46400BBfootnotemark: $B$ | 1 | 11.43 | – | 11.17 | 173 | 0.39
J0546–52 | NGC2101 | 17793 | 17822 | 17822 | 2 | 11.18 | 10.67 | 11.00 | 152 | 1.41
J1254–10a | NGC4781 | 43902 | 42407 |  41220CCfootnotemark: $C$ | 17 | 13.37 | 13.96 | 11.24 | 183 | 0.81
J0516–37 | ESO362-G011 | 17027 | 17027 |  13418DDfootnotemark: $D$ | 2 | 11.59 | 7.83 | 11.31 | 193 | 1.06
J0459–26 | NGC1744 | 16517 | 16517 | 16517 | 1 | 10.97 | – | 11.07 | 160 | 0.76
J1103–23 | NGC3511 | 33385 | 33385 | 33385 | 2 | 11.86 | 10.73 | 11.46 | 216 | 0.84
J2257–41 | NGC7424 | 70096 | 70096 | 70096 | 1 | 11.35 | – | 11.19 | 175 | 0.59
J1153–28 | UGCA250 | 37271 | 37061 | 37061 | 25 | 13.32 | 13.17 | 11.36 | 200 | 1.32
J0335–24 | NGC1371 | 13255 | 13419 |  13418DDfootnotemark: $D$ | 29 | 13.33 | 13.25 | 12.16 | 370 | 0.80
J0052–31 | NGC0289 | 3089 | 3089 | 3089 | 11 | 12.57 | 12.84 | 11.86 | 293 | 0.96
J0419–54 | NGC1566 | 14897 | 14765 |  13418DDfootnotemark: $D$ | 31 | 13.45 | 13.54 | 12.26 | 399 | 0.58
J0445–59 | NGC1672 | 15941 | 15941 | 15941 | 5 | 12.31 | 12.44 | 12.28 | 406 | 0.63

222 Columns: (1) HIPASS identification. (2) Common name. (3) PGC number of
galaxy. (4) PGC number of dominant galaxy in group. (5) PGC number of dominant
galaxy in association. (6) Number of galaxies in group. (7) Logarithmic total
mass of group based on luminosity. (8) Logarithmic total mass of group based
on velocity dispersion (only for $>1$ group members). Columns (3) to (8) from
Kourkchi & Tully (2017). (9) Logarithmic total halo mass $M_{200}$ derived
from stellar mass given in Table 1 and the stellar mass-halo mass relation in
Moster et al. (2013). (10) $R_{200}$ (virial) radius based on column (9) and
standard cosmology. (11) Ratio of the diameter of a $1.5^{\circ}$ field of
view in kpc at the distance of the galaxy and the $D_{200}$ diameter, where
$D_{200}=2R_{200}$. $A,B,C,D$$A,B,C,D$footnotetext: Part of same association
as indicated by footnote label.

##  4 Observations

The MeerKAT MHONGOOSE observations started in October 2020. For ease of
scheduling, the 55h of observing time per galaxy are divided into 10
observations of 5.5h. These consist of five “rising” observations and five
“setting” ones, each of which is referred to as a “single track” in this
paper. The complete 55h observation is referred to as the “full-depth” data.

The rising observations generally start sometime in the first 1.5 hours after
the source has become visible to MeerKAT, and end when the source is close to
transit. The setting observations start close to transit and generally end in
the last 1.5 hours before it crosses MeerKAT’s observing horizon. There is
some overlap between rising and setting tracks close to transit. The amount of
overlap depends on the declination of the galaxy but is never more than 1.5
hours.

A typical 5.5h observation consists of 10 mins of observing time on one of the
primary calibrators J1939–6342 or J0408–6545. This is then followed by five
cycles of _(i)_ two mins on a secondary or phase calibrator and _(ii)_ a
subsequent $\sim 55$ mins on the target galaxy. The duration of the latter
varies slightly from galaxy to galaxy to take into account the different
slewing times while staying within the 5.5h overall duration.

If J1939–6342 was used as the primary calibrator, two additional three-minute
observations of a polarisation calibrator were inserted between different
cycles. If J0408–6545 was used, a polarization calibrator was observed for
three minutes at the end of every phase calibrator-target cycle. This
increased number of polarization calibrator observations reflects the less
well-characterised polarisation properties of J0408–6545. However, since we
are only concerned with the Stokes $I$ data, we will not discuss the
polarization aspects here.

A small number of observations deviated from our standard observing template.
For J0008–34, J0031–22 and J2257–41 no suitable polarization calibrator was
available during the rising observations, so these were extended to 6.5h. The
corresponding setting observations were reduced to 4.5h.

We used the c856M4k_n107M SKARAB correlator mode, allowing for a 32k narrow
band (primarily used for H i studies) and a 4k wide band (primarily used for
continuum and polarization studies) to be used simultaneously. The narrow band
has 32768 channels of 3.265 kHz (0.7 km s-1 at the H i rest-frequency) each,
giving a total bandwidth of 107 MHz. The 4k-mode gives 4096 channels of
208.984 kHz ($\sim 43$ km s-1 at the H i rest-frequency), covering the total
bandwidth of MeerKAT of 856 MHz. For the MHONGOOSE observations, the central
topocentric frequency of the 32k narrow-band was always set to 1390 MHz. For
the 4k-mode this value was 1284 MHz. Both modes observed four polarizations,
though for the narrowband mode (H i) we only used the HH and VV polarisations.
The correlator data were integrated over 8s in the correlator before being
output.

To ensure high-quality data, observations were only started if there were 58
or more active antennas present in the array. As the science critically
depends on the detection of diffuse low-column density gas, additional checks
were made prior to observing to ensure that a sufficient number of short
baselines was present in the array, with the strictest checks for the shortest
baselines. An overview of the required fraction of the number of total
baselines as a function of baseline length is given in Table 3.

A small number of early observations were done partly during daytime, but it
was quickly found that solar radio frequency interference (RFI) had a severe
impact on the shortest baselines. Observations that were too severely affected
were re-done, while for less-affected ones, baselines shorter than 1.5
k$\lambda$ (or 315m for rest-frame 21-cm emission) were flagged. To avoid
solar RFI affecting the short baselines, all other observations were done at
night time.

Table 3: Baseline requirements

Baseline range | number | required
---|---|---
| in range | fraction
(1) | (2) | (3)
$<$ 50m | 5 | 80%
50–100m | 29 | 66%
100–200m | 118 | 66%
200–400m | 314 | 66%
400–1000m | 568 | 66%
1000–3000m | 563 | 66%
3000–6000m | 405 | 50%
$>$ 6000m | 14 | 0%
333Total number of antennas must be 58 or more. (1) Range in baseline length.
(2) Maximum number of baselines in this range. (3) Fraction of baselines in
this range that needs to be present before observation can commence.

##  5 Data Reduction

After an observation was completed and deposited in the SARAO MeerKAT archive,
we extracted the data covering the channel range 16384 to 26383 (10,000
channels) from the 32k narrowband data set retaining only the HH and VV
polarisations. This covers the topocentric frequency range 1390.0–1422.7 MHz.
These data were binned by two channels leading to a 5000-channel measurement
set with a channel width of 6.53 kHz (1.4 km s-1). The data were then
processed using the CARACal data reduction pipeline444CARACal and its related
software packages can be found in the repository collection at
https://github.com/caracal-pipeline/ (Józsa et al. 2020). As the observations
cover multiple years, and MHONGOOSE observations took place simultaneously
with CARACal development, several (pre-)releases of CARACal were used. Where
necessary data were re-reduced to ensure consistent outcomes.

CARACal is a python-based, containerised pipeline that uses a “best-of”
approach to link together reduction and analysis tasks and applications from
various radio astronomy packages to optimally reduce the data, passing it
seamlessly between the various reduction stages using Stimela (Makhathini
2018). These stages consist of:

  1. (i)

flagging the calibrators;

  2. (ii)

deriving and applying the cross-calibration to the target;

  3. (iii)

flagging the target;

  4. (iv)

imaging the continuum for several cycles of self-calibration;

  5. (v)

transferring the self-calibration solutions to the original measurement set;

  6. (vi)

using the self-calibration sky model to subtract the continuum from the
original measurement set;

  7. (vii)

creating and deconvolving the spectral line H i data cubes.

We will describe these steps in some more details below. Much of the reduction
procedure was developed in collaboration with the MeerKAT Fornax Survey (Serra
et al. 2023). The description given here should therefore be regarded as
complementary to that given in Serra et al. (2023). Unless stated otherwise,
all software tasks mentioned below in Sec. 5.1–5.7 were executed as part of
the CARACal pipeline environment. All reduction was done on the dedicated
MeerGas cluster at ASTRON consisting of four computing nodes with 128 cores
and 1 Tb of memory each.

###  5.1 Cross calibration

The calibrator observations were split off in a separate measurement set and
flagged for shadowing and RFI where necessary. For the latter aoflagger (as
included in CARACal) searched and flagged in Stokes Q. The frequency range
$1419.8$–$1421.3$ MHz ($+125$ to $-190$ km s-1) was also flagged to avoid
contamination from Galactic emission.

For each observation the primary calibrator was used to derive the delay, gain
and bandpass calibration using baselines longer than 150m. To improve the
signal-to-noise, the bandpass was smoothed using a 9-channel box-car filter.
Any gaps in the bandpass (e.g., due to the flagging of the Galactic emission)
were interpolated. A second cycle of flagging and calibrating then refined
these solutions, which were subsequently applied to the secondary calibrator.
The latter was used to track the gain and phase variations over time. These
time-dependent solutions were also derived twice with an intermediate flagging
step. The final solutions were then applied to the target observations.

###  5.2 Self calibration and continuum subtraction

The cross-calibrated target scans were checked for shadowing (where the line-
of-sight to the source is partially or fully blocked by another antenna) and
RFI and, when found, flagged. The clean RFI environment at MeerKAT, and the
targets being located in the protected frequency band, meant that on average
only 1-2 percent of the data were flagged.

For the self-calibration procedure the target measurement set was binned in
frequency to a channel width of 1 MHz. The frequency range covering Galactic
emission was flagged, as well as the frequency range of the target galaxy. The
latter was done to prevent bright H i features (present for some galaxies)
from entering the self-calibration procedure.

Three cycles of imaging and self-calibration were then performed using three
spectral solution intervals of $\sim 10$ MHz each. During each cycle, the data
were deconvolved and imaged (using wsclean; Offringa et al. 2014 ) to
progressively deeper limits from 5 times the noise for the first imaging run,
to 3.5 times the noise for final imaging. We imaged an area of $3\times 3$
degrees, using a robust weighting value of $-0.5$, a taper of
$10^{\prime\prime}$ and a pixel size of $4^{\prime\prime}$. The SoFiA source
finder (Serra et al. 2015) (as implemented in CARACal) was used to
automatically create a mask of the sky based on the output cleaned image. Care
was taken that a sufficiently large window for the noise measurement was
chosen such that bright, extended continuum emission from some of the target
galaxies did not affect the measured noise levels and therefore the self-
calibration procedure. Using this mask, a new image and sky model were
created. This sky model was used for the self-calibration, after which a new
cycle of image, mask and sky-model calibration was started, followed by
further self-calibration. All cycles were phase-calibration only. In this way
the three cleaning and self-calibration cycles to progressively larger depths
lead to the final solutions.

The self-calibration solutions were interpolated in frequency and transferred
to the cross-calibrated target measurement set. The most recent self-
calibration sky-model clean components were also transferred to the target
measurement set at this stage, and subsequently subtracted using the
Crystalball software in CARACal. This step is time-consuming and accounts for
one-third to one-half of the total processing time.

A second follow-up continuum subtraction using the CASA task mstransform
within CARACal was used to subtract any residual continuum by fitting a first
or second-order polynomial to the line-free visibilities. A catalog of known H
i sources was used to define the line-free channels. This second procedure on
rare occasions produces bright artefacts related to the fitting of completely
flagged channels, and a simple sigma-clipping strategy was used as part of the
pipeline to remove these artefacts.

###  5.3 Quality control imaging

For each observation, two data cubes were created to check for any remaining
RFI or reduction artefacts and for general quality control. One cube has high
angular resolution using a robustness parameter of 0.5 and covering the 1000
km s-1 velocity range straddling the target galaxy with a channel spacing of
1.4 km s-1. A second, lower resolution cube also used a robustness parameter
of 0.5, but with a taper of $25^{\prime\prime}$ applied. Here we imaged the
entire frequency range above 1390 MHz but at a velocity resolution of 7 km s-1
(5-channel binning).

###  5.4 $u=0$ flagging

After combining the separate observations of our first completed galaxies and
the subsequent creation of the first full-depth cubes, we encountered
unexpected coherent horizontal stripes in the data cubes. Investigation showed
that these were caused by RFI which in visibility space is located at $u=0$
over a small range of $\varv$-values centred symmetrically around $\varv=0$
(see Fig. 4). Most likely this is due to the low or zero fringe rate near
$u=0$ which allows low-level RFI to accumulate coherently. Away from $u=0$
this RFI is added incoherently due to the rapid change in amplitude and phase
of the visibilities. These stripes are an issue as they are at the level of
the faint H i emission that we are trying to detect and we thus need to remove
them from the data.

The $u=0$ artefacts have been seen before in observations taken with different
arrays (e.g., Hess et al. 2015; Lucero et al. 2015; Heald et al. 2016).
Generally, the solution has been to simply flag a small range around $u=0$ for
the relevant range in $\varv$. Applying these strategies to the MHONGOOSE data
would, however, result in flagging close to $\sim 10\%$ of the data, due to
the large number of short baselines in the MeerKAT array and the resulting
high filling factor of the inner $u\varv$ plane. Such a solution is clearly
not ideal, and we therefore developed a more sophisticated flagging strategy
(Maccagni et al. 2022) as described below.

We first split the observation into the separate target scans of $\sim 55$
minutes each, and then perform the following procedure on a scan-by-scan
basis. Since in each scan the $u\varv$-coverage is different, we calculate the
amplitude image of a Fast Fourier Transform (FFT) of the sum of 100 line-free
channels in a custom-made data cube of each scan. We adopt a pixel size of
$20^{\prime\prime}$ and an image size of $8000^{\prime\prime}$. This leads to
a pixel size of $25.8\lambda$ in the FFT image. The $u=0$ artefacts are then
visible as a vertical stripe ($u=0$ for a range in $\varv$) in the amplitude
image. We found that using an empty data cube created using a robust value of
1.5 combined with a $60^{\prime\prime}$ tapering as the basis for the FFT
image gave the best results.

Figure 4: Overview of the $u=0$ flagging procedure. The top row shows a
100-channel binned empty map with horizontal stripes of one target scan of a
NGC 1566 observation on the left, and on the right the corresponding FFT
amplitude image which shows a prominent vertical RFI feature at $u=0$. The
middle row shows the same plots, but after removal of the $u=0$ stripe using
our flagging procedure. The bottom row shows two zeroth-moment H i maps of NGC
1566, both created using a simple $2\sigma$ intensity cut. The bottom-left
panel shows the map with the $u=0$ RFI still included. The bottom-right panel
shows the same map but with the $u=0$ RFI removed.

We determine the median absolute deviation (MAD) of the distribution of
amplitudes $a_{i}$ in the $u\varv$-plane, where MAD $=$
median$(|a_{i,(u,\varv)}-{\rm median}(a_{i,(u,\varv)})|)$. We then define a
cutoff threshold (median$(a_{i,(u,\varv)})+M\times{\rm MAD}$) where
$M=100,150,200,300,500$. For each $M$, we find the pixels in the amplitude
image where the value is larger than the cut-off and we flag the corresponding
visibilities in the measurement set of that scan.

The empty cube is then re-imaged and the noise measured. We adopt the value of
$M$ that gives the lowest noise and identify the corresponding flagged pixels
in the amplitude image. Flags are extended by 1 pixel in $u$ and 2 in $\varv$
and the corresponding visibilities are flagged, but this time throughout the
entire spectral range of the measurement set of that scan. Doing this for all
scans in an observation results in removal of the $u=0$ artefacts at the cost
of flagging typically only a few tenths of a percent of the visibilities. This
$u=0$ flagging solution has been implemented in CARACal. We refer to Maccagni
et al. (2022) for further information on the flagging fraction and its sky
distribution.

###  5.5 Time flagging

The initial flagging steps removed most of the RFI in the data. However, we
found that in some cases the “wings” (i.e., ramp-up and ramp-down) of time-
variable strong RFI were not removed entirely. The most effective way to
remove these was by using a separate time-flagging step. This was done with
the CASA flagdata task (again within CARACal) where we average in bins of 100
channels, and use the tfcrop algorithm to fit the data in the time dimension
and remove outliers that deviate more than 5 times the standard deviation from
the fit. After merging with the initial pipeline flags, these flags are then
extended such that if more than half of the visibilities at a certain
observing time are flagged, all data at that time are flagged. Similarly for
the frequency channels: if more than half of the data in a frequency channel
are flagged, then all data at that frequency are flagged. These final flagging
steps complete the reduction of a single-track observation and the individual
measurement sets are now ready to be combined and for the full-depth data
cubes to be created.

###  5.6 Standard resolutions

MeerKAT is capable of producing high-quality images over a large range in
angular resolution (Fig. 1), resulting in mapping of compact, high-column
density sources, as well as extended, low-column density features (Fig. 2). It
is difficult to capture this wealth of structure in a single data cube at a
single resolution. For MHONGOOSE, we have therefore defined six standard
resolutions for our data products, which cover the angular resolution range of
MeerKAT as indicated in Fig. 2.

These different resolutions are achieved by changing the robust weighting
parameter used in creating the data cubes, and, for the two lowest
resolutions, some additional tapering. We find that these six standard
combinations give a comprehensive overview of the H i morphology and
kinematics of the sample galaxies.

Table 5 and Fig. 5 show the average noise per channel and beam size as derived
from the full-depth standard cubes of ten galaxies available at the time of
writing. We also list the column density sensitivities where we give the
values for $1\sigma$ over a single channel, as well as the $3\sigma$ over 16
km s-1 values used in Fig. 2. Finally, we also list the $3\sigma$ H i mass
detection limit for an unresolved source, assuming a distance of 10 Mpc (the
median distance of the galaxies in the sample) and a velocity width of 50 km
s-1.

The highest resolution of $\sim 8^{\prime\prime}$ is achieved using a
robustness parameter of zero. Decreasing the robustness parameter even further
to negative values resulted in too small a decrease of the beam size to
justify the loss of sensitivity. This loss is due to the relatively small
number of longest baselines (cf. Table 3). Emphasising these through weighting
does therefore not result in an improvement in image quality at these
resolutions. For the purpose of MHONGOOSE H i imaging, a robustness parameter
of zero therefore yields the highest usable resolution.

On the opposite end of the resolution range, tapering beyond $\sim
90^{\prime\prime}$ does not yield additional gains due to the absence of
sufficiently short baselines (cf. Table 3). This can be seen by the upturn in
the noise curve at large resolutions in Fig. 1 and the top panel in Fig. 5.

Figure 5: Sensitivities of the full-depth data cubes. The top panel shows the
average noise per 1.4 km s-1 channel for the six standard resolutions, as
averaged over full-depth observations of ten galaxies (cf. Fig. 1). Error bars
show the rms difference in noise levels between the ten galaxies, but are
generally comparable to or smaller than the symbol size. The bottom panel
shows the $3\sigma$, 16 km s-1 column density sensitivities. These are the
same points as shown in Fig. 2.  Table 4: Standard resolutions

label | robust | taper | pixel | $b_{\rm maj}$ | $b_{\rm min}$ | $b_{\rm PA}$ | noise | $\log N_{{\rm H{\hskip 0.56917pt\tt I}}}^{1\sigma,1{\rm ch}}$ | $\log N_{{\rm H{\hskip 0.56917pt\tt I}}}^{3\sigma,16{\rm km/s}}$ | $\log{M_{{\rm H{\hskip 0.56917pt\tt I}}}}$
---|---|---|---|---|---|---|---|---|---|---
| value |  (′′) |  (′′) |  (′′) |  (′′) | $(^{\circ})$ |  (mJy beam-1) |  (cm${}^{-2})$ |  (cm-2) | $(M_{\odot})$
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
r10_t90 | 1.0 | 90 | 30 | 94.2 | 91.2 | 47 |  0.318 $\pm$ 0.011 | 16.76 | 17.77 | 6.05
r05_t60 | 0.5 | 60 | 20 | 65.3 | 64.0 | 92 |  0.250 $\pm$ 0.009 | 16.97 | 17.98 | 5.95
r15_t00 | 1.5 | 0 | 7 | 34.4 | 25.4 | 135 |  0.154 $\pm$ 0.004 | 17.44 | 18.44 | 5.74
r10_t00 | 1.0 | 0 | 5 | 26.4 | 18.2 | 136 |  0.150 $\pm$ 0.004 | 17.69 | 18.69 | 5.73
r05_t00 | 0.5 | 0 | 3 | 14.1 | 9.7 | 137 |  0.171 $\pm$ 0.005 | 18.29 | 19.29 | 5.78
r00_t00 | 0.0 | 0 | 2 | 8.2 | 7.1 | 142 |  0.219 $\pm$ 0.007 | 18.77 | 19.77 | 5.89

555(1) Label used to refer to this resolution. (2) Robustness weighting value.
(3) Taper used. ”0” mean no taper. (4) Pixel size of the data cubes and moment
maps. (5) Average major axis beam size. (6) Average minor axis beam size. (7)
Average position angle of major axis of beam. (8) Noise per channel. (9)
$1\sigma$, 1-channel column density sensitivity. (10) $3\sigma$, 16 km s-1
column density sensitivity. (11) H i mass sensitivity for a $3\sigma$, 50 km
s-1 unresolved source at 10 Mpc.

###  5.7 Creating the full-depth cubes

For the full-depth observations, we combine the ten individual 5.5h
observations and create data cubes measuring $1.5^{\circ}\times 1.5^{\circ}$
with a velocity range from $-500$ km s-1 to $+500$ km s-1 with respect to the
central velocity of the target galaxy. We choose to image an area larger than
the usual primary beam of $\sim 1^{\circ}$ due to the high sensitivity of the
observations which enable H i detections at a large distance from the pointing
center.

The ten input observations were first all corrected from a topocentric
spectral coordinate grid to a common heliocentric spectral grid. We adopt the
radio velocity definition where all channels have a constant frequency spacing
and velocity is defined as $\varv_{\rm radio}=c(\nu_{0}-\nu)/\nu_{0}$, where
$\nu_{0}$ is the rest-frequency and $\nu$ the observed frequency. The ten
measurement sets were then all simultaneously input into wsclean (Offringa et
al. 2014) to create and deconvolve the final data cubes. So-called “clean
masks” were used to indicate areas with emission where deconvolution was
necessary. These masks were created automatically using a sequence of cubes at
each of the standard resolutions listed in Table 5.

Starting at the lowest resolution r10_t90, we created an initial deconvolved
cube (cube_0) using the auto-masking option in wsclean, where the mask
(mask_0) was defined to include values of $5\sigma$ and higher. We then used
SoFiA-2 (Westmeier et al. 2021) outside of CARACal to create a new mask
(mask_1) based on the deconvolved cube_0.

Here, and for all subsequent SoFiA-2 runs, we used spatial kernels of 0 and 3
pixels, and velocity kernels of 0, 3, 7 and 15 channels. Using the smooth-and-
clip (S+C) method (Serra et al. 2012), we used a threshold of 4$\sigma$ to
define the mask with spectral noise scaling enabled. To define sources, valid
pixels were linked across a maximum spatial and spectral distance of,
respectively, 3 pixels or 3 channels. For the detected sources we then imposed
a spatial minimum size equal to the current beam size rounded up to the
nearest integer number of pixels. For the spectral minimum size, we used 10
channels (14 km s-1). Sources with negative flux density values were not
retained. These SoFiA-2 input parameters were extensively investigated to
ensure that they optimally captured the emission present in the cubes.

The resulting mask_1 was used to create and deconvolve a new cube_1. A new run
of SoFiA-2 on this cube resulted in a mask_2, which was in turn used to create
cube_2, which is the final deconvolved r10_t90 cube. Within the masks,
emission was deconvolved down to $0.5\sigma$. The gain value for the major
iterations in wsclean was set to 0.95 to ensure at least one cycle of
inversion of the clean model to visibility space.

For subsequent, higher spatial resolutions, the final mask of the previous,
lower resolution run was used as the initial mask. That is, for the r05_t60
cubes, the final mask_2 of the r10_t90 run was regridded and used as the
initial mask_0 of the r05_t60 runs.

The procedure is then as above where a cube_1 is produced and SoFiA-2 is run
on that cube to build a mask_1. This is then used to create and deconvolve the
final cube_2.

This is then repeated in sequence for each of the resolutions, where the final
mask of a given resolution is used as the initial mask of the next higher
resolution. This process is a fully automated part of our reduction pipeline.
It delivers high-quality deconvolved cubes almost entirely unsupervised.

As expected, the noise in the data cubes keeps decreasing as the square root
of the integration time as each of the ten observations is added in turn. This
is illustrated in Fig. 6 where we show the noise per channel measured in
natural-weighted data cubes of ESO 300-G014 (J0309–41), created by combining
an increasing number of tracks. We used natural weighting, instead of one of
the standard resolutions, to circumvent uncertainties due to changes in the
noise because of weighting and tapering and to enable an unambiguous
comparison with the expected theoretical noise. The latter is calculated based
on the number of visibilities and the properties of the MeerKAT antennas
(13.5m dishes and $T_{\rm sys}/\eta=20.5$ K) and is also shown in Fig. 6. The
theoretical values have (by definition) a slope of $-0.5$. The measured values
have a slope of $-0.504$. The very small offset between the lines is
equivalent to an offset in $T_{\rm sys}/\eta$ of $\sim 0.4$ K, in the sense
that MeerKAT performs slightly better than our assumptions (though such a
small offset is likely to be within the variations between different
observations).

Figure 6: Natural-weighted noise values measured over a 1.4 km s-1 channel as
a function of integration time for the observations of ESO 300-G014
(J0309–41). The black, filled points indicate the measured noise level. The
blue line shows the expected theoretical noise levels with a slope of $-0.5$.
A linear fit to the observed noise levels gives a slope of $-0.504$. The red
star indicates the target sensitivity from de Blok et al. (2016).

The measured noise level thus meets the requirements presented in the
MHONGOOSE white paper (de Blok et al. 2016), where a noise level of 0.074 mJy
beam-1 per 5 km s-1 channel after 48 hours of on-source is specified. Scaling
this to the channel width and observing time that were eventually used, we see
an almost exact match, as indicated in Fig. 6, showing that the full-depth
MHONGOOSE data are of the required sensitivity to deliver the envisaged survey
science.

###  5.8 Creating full-depth moment maps

We also create zeroth-, first- and second-moment maps showing the integrated H
i distribution, the intensity-weighted mean velocity and the velocity width,
repectively.

The second-moment map is commonly referred to as a velocity dispersion map.
However, strictly speaking, second-moment values only represent a physically
meaningful velocity dispersion in cases where the H i emission line profile is
well approximated by a single Gaussian666Note that here we adopt the informal
definition that the second moment is equal to the dispersion. Mathematically,
the second moment is defined as the variance.. In all other cases (non-
Gaussian profiles or multiple separate components) they simply quantify the
spread of H i velocities along each line of sight.

We used SoFiA-2 to find the signal in the cubes and create the masks. The
signal-to-noise ratio S/N in the cubes is high, and we found that we only
needed a limited number of spatial kernels to isolate the signal. In fact,
using spatial kernels larger than $\sim 1$–$2$ beam sizes had the effect of
introducing additional noise into the moment maps at the edges of the disks
and these larger kernels were therefore avoided. We used cubes that were not
corrected for the primary beam. This correction was applied to the zeroth-
moment maps afterwards.

The SoFiA parameters we eventually used were spatial kernels of 0 and 4 pixels
and velocity kernels of 0, 9 and 25 channels using a source-finding S+C
threshold of $4\sigma$. Sources were linked over a maximum of 5 pixels
spatially and 8 channels spectrally. Minimum sizes of 4 spatial pixels and 15
channels were imposed.

We then used the reliability parameter, as implemented in SoFiA, to further
separate signal from the noise. We did find, however, that this parameter was
less critical as almost all sources were well separated from the noise and an
integrated S/N cut was usually sufficient to identify the significant sources.
In our case, we mostly used a reliability value of 0.8 and an integrated S/N
value of 5.0.

The masks as defined here are stricter than the masks used during
deconvolution. This is due to the different purpose that they serve. The
deconvolution masks were created to include all emission at many scales, even
if this leads to including some noise in the masks. For the moment maps,
instead, it is important that as little noise as possible is included in the
masks to avoid affecting the moment values.

###  5.9 Examples of full-depth moment maps

A full scientific analysis of the full-depth data will be presented in
forthcoming papers. For this reason, and as data are still being collected, we
restrict ourselves here to presenting a short overview of the full-depth data
for two of the galaxies that were completed early in the survey. We refer to
Healy et al. (2023) and Maccagni et al. (in prep.) for an in-depth discussion.
The main purpose of this overview is to give an indication of the high quality
of the data.

Figure 7 shows multi-resolution maps of the H i distribution in NGC 1566
(J0419–54) and NGC 5068 (J1318–21). Here we show for five of the six standard
resolutions the contour at the column density level that corresponds to S/N =
3 in the zeroth-moment map at that resolution.

During the initial reduction procedure, the velocity channels were not
Hanning-smoothed and binned in velocity every two input channels (cf. Sect.
5). The channels in the current data cubes are therefore independent, meaning
that the noise is expected to behave as $\sqrt{N}$ when summing $N$ channels.

We therefore can construct a noise map with pixel values defined as
$\sigma_{\rm chan}\,\delta v\,\sqrt{N}$, where $\sigma_{\rm chan}$ is the
average noise value measured in empty channel maps, $\delta v$ is the velocity
width of a channel (in this case 1.4 km s-1) and $N$ is the number of
independent channels contributing to each pixel in the zeroth moment map.

Taking the ratio of the zeroth-moment map and this noise map then gives a S/N
map. We derive the median column density value of all pixels with $2.75<{\rm
S/N}<3.25$ and adopt this as the column density corresponding to S/N = 3 (also
known as the “pseudo-3$\sigma$” column density; see Verheijen & Sancisi 2001;
Kregel et al. 2004)

We plot contours of multiples of this value, thus clearly capturing in a
single figure the detailed, compact high-column density distribution at the
highest resolutions, and then transitioning into the diffuse, extended
distribution of the low-column density H i at the lowest resolutions. Note the
extended and irregular distribution of H i in the outer parts of NGC 1566, as
well as the clumpy outer H i in NGC 5068. At column densities of $\sim
10^{20}$ cm-2 (corresponding with the edge of the main star-forming disks)
very little of this irregular outer H i would be detected and both galaxies
would give the impression of regular, symmetric disks; cf. the observations of
NGC 1566 in Elagali et al. (2019) which concentrated on the high-column
density disk. As we will show below, the outer H i components contain only a
small fraction of the total H i mass of the galaxies, but they dramatically
change the apparent morphology. As mentioned, more extensive analyses of these
and other sample galaxies will be presented in future papers, but Fig. 7
already shows the power of these deep observations.

Figure 7: Multi-resolution zeroth-moment maps of NGC 1566 (left panel) and NGC
5068 (right panel) based on the full-depth data. For each resolution, contours
of $2^{n}$ times the S/N = 3 value are shown (as listed in the legend). The
resolutions shown are r05_t00 (red), r10_t00 (green), r15_t00 (blue), r05_t60
(purple), r10_t90 (olive). For each resolution two contours are shown, i.e.,
$n=0,1$, except for the highest resolution r05_t00 (red contour), where
$n=0,1,2,...$ The r05_t00 moment map is shown in the background as a false
colour image, with the column density levels indicated by the colour bar on
the right. The beam sizes (colored according to the respective resolution) are
shown in the bottom-right corner.

Figure 8: Example single-track moment maps using the r05_t00 resolution for
two MHONGOOSE galaxies. Top row: NGC 1566 (J0419–54); bottom row: NGC 5068
(J1318–21). From left to right: _(i):_ Combined _grz_ -colour image from
DECaLS. _(ii):_ primary-beam corrected zeroth-moment or integrated H i
intensity map. Contours as indicated in the Figure. The lowest contour
represents S/N = 3, with subsequent contour levels increasing by a factor of
two. _(iii):_ First-moment map or intensity-weighted velocity field. Red
colours indicate the receding side, blue colours the approaching side. The
central velocity (listed in Tab. 1) is indicated by the thick contour. Other
contours are spaced by 10 or 20 km s-1, as indicated in the Figure. _(iv):_
Second-moment map: the colours show the range from 0 (light-blue) to 30 (red)
km s-1. The lowest contour shows the 12 km s-1 level, and subsequent contours
are spaced by 12 km s-1. The 24 km s-1 contour is shown in black. For both the
first- and second-moment maps, pixels corresponding to values below the S/N =
3 column density in the zeroth-moment map were blanked. See Appendix A for a
more extensive description.

###  5.10 Single-track moment maps

At the time of writing observations are still ongoing, and full-depth
observations are not yet available for the entire sample. However, every
galaxy in the sample has by now been observed for at least one 5.5h track. The
results presented in the remainder of this paper are based on the single track
data, unless otherwise stated. To give an overview of the sample and pursue
initial sample-wide science, we created single-track moment maps at two of the
standard resolutions r05_t00 and r15_t00 (beam size of $\sim
12^{\prime\prime}$ and $\sim 30^{\prime\prime}$, respectively) in an identical
manner as for the full-depth data. We have limited this to two resolutions as
the differences between the standard resolutions are not as pronounced here
due to the ten times shorter integration time. Average beam sizes for these
single-track observations are identical to those listed in Table 5, while
column density and mass limits are a factor $\sqrt{10}$ less (cf. Fig. 6).
These moment maps give a comprehensive overview of the entire MHONGOOSE sample
as observed by MeerKAT.

In Fig. 8 we show the r05_t00 single-track moment maps for NGC 1566 (J0419–54)
and NGC 5068 (J1318–21) which were also discussed in Sect. 5.9. In the Figure,
we show the Dark Energy Camera Legacy Survey
(DECaLS)777http://www.legacysurvey.org (Dey et al. 2019) optical image, the
zeroth-moment (integrated H i intensity) map, the first-moment (intensity-
weighted mean velocity field)888The colour map used for the velocity field is
based on the perception-based colour maps available as part of the
CosmosCanvas project: https://ascl.net/code/v/3580 and finally, the second-
moment map. For both the first- and second-moment maps, pixels corresponding
to values below the S/N = 3 column density in the zeroth-moment map were
blanked. A comparison between Figs. 7 and 8 for these galaxies clearly show
the improvement in sensitivity that we can expect from the full survey.

Moment maps for the r05_t00 resolution of the complete sample are given in
Appendix A and we refer to this Appendix for a more extensive description.

##  6 Global H i Profiles

The global H i profile or integrated H i spectrum of a galaxy shows the
spatially-integrated H i flux density as a function of velocity or frequency.
It is often used in scaling relation studies, such as the Tully-Fisher
relation (Tully & Fisher 1977) and also in studies involving the total H i
masses of galaxies. Global H i profiles are often measured using single-dish
telescopes. These measure the total power, and therefore the total H i mass.
Global H i profiles measured with synthesis radio telescope arrays are less
straight-forward to interpret. Depending on the baseline distribution of the
array and the extent of the source, these may suffer from the so-called
“missing spacing” problem, which is caused by a lack of short baselines which
prevents measurements of flux on larger angular scales. For galaxies that have
an angular size similar or larger than the scales probed by the shortest
baselines of the array this can lead to a severe underestimate of the total H
i mass. In these cases, a comparison with the single-dish H i global profile
is often used to determine whether any H i has been missed in the synthesis
observations. For MeerKAT, with a shortest baseline of 29m, the largest scale
at which signal can be detected is $\sim 20^{\prime}$.

Comparisons between the single-dish H i profiles and those derived from
synthesis observations have been used to constrain the existence of low-column
density H i in galaxies (e.g., Pingel et al. 2018; Kamphuis et al. 2022). The
underlying assumption is that any flux not detected in the synthesis
observations must be extended and/or of low column density.

MeerKAT has been specifically designed to have a compact core with many short
baselines, and one may expect that any missing-spacing issue will be less
severe. The MHONGOOSE data, both the single-track and full-depth observations,
offer a chance to systematically compare the measured masses with single-dish
masses for a significant number of our sample galaxies. Below we first compare
the single-track and full-depth profiles to gauge whether the increased
observing time led to the detection of additional H i. This is then followed
by a comparison with the single-dish measurements.

###  6.1 Comparing the single-track and full-depth profiles

A first step is to compare the H i global profiles of the single-track data
and full-depth data which differ by a factor of ten in observing time. This
obviously means an increase in signal-to-noise for the full-depth data, but an
interesting question is whether this can be used to deduce the existence of
low-column density H i.

Figure 9: Single-track (blue) and full-depth (orange) global H i profiles for
ten of the MHONGOOSE galaxies as identified in the top left of each panel. The
green arrows indicate the central velocities. We show only the velocity ranges
where signal was present in the mask.

We compare the global profiles and total H i masses for ten of the MHONGOOSE
galaxies for which the full-depth global profiles were determined. The global
profiles are derived by measuring the flux in each channel, applying the masks
that were used to create the moment maps. The fluxes are corrected for primary
beam attenuation. The global profiles are compared in Fig. 9 with the
corresponding flux densities (as listed in Table 9). The full-depth H i masses
are on average $\sim 2\%$ higher than the single-track H i masses. Such
differences may sound insignificant, but they make a big difference when it
comes to deducing the existence of a low-column density component.

If we assume that for each galaxy, the “extra” detected H i is due to a
previously undetected low-column density H i component that is spread evenly
over the H i disk, then we can use the additional mass and the area of the
disk to calculate the column density. This results in column density
components of a few times $10^{17}$ cm-2 to a few times $10^{18}$ cm-2, as
listed in Table 9. This is consistent with the increase in column density
detection limits going from single-track to full-depth observations. These
numbers highlight that to deduce the presence or absence of low column density
gas based purely on global profiles, an accuracy of a few percent or better is
needed. Such an accuracy is much higher than the typical absolute flux
calibration uncertainty of H i observations. This is compounded when comparing
with results from different telescopes.

Table 5: H i mass comparison between full-depth and single-track MeerKAT
observations

Galaxy | $S_{f}$ | $S_{s}$ | $S_{f}/S_{s}$ | $\log{M_{{\rm H{\hskip 0.56917pt\tt I}},f}/M_{\odot}}$ | $\log{M_{{\rm H{\hskip 0.56917pt\tt I}},s}/M_{\odot}}$ | $\log{\Delta N_{{\rm H{\hskip 0.56917pt\tt I}}}/{\rm cm}^{-2}}$
---|---|---|---|---|---|---
|  (Jy km s-1) |  (Jy km s-1) |  |  |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7)
J1321–31 | 6.45 | 6.23 | 1.036 | 7.615 | 7.599 | 17.65
J1337–28 | 21.18 | 21.11 | 1.004 | 8.024 | 8.023 | 17.21
J1106–14 | 12.28 | 12.10 | 1.014 | 8.748 | 8.742 | 18.35
J1253–12 | 26.73 | 26.29 | 1.017 | 8.883 | 8.875 | 17.98
J0309–41 | 27.61 | 27.52 | 1.003 | 8.889 | 8.887 | 17.65
J1303–17b | 114.23 | 110.47 | 1.034 | 8.987 | 8.972 | 18.60
J1318–21 | 167.21 | 161.56 | 1.035 | 9.028 | 9.013 | 18.29
J1254–10a | 57.08 | 54.61 | 1.045 | 9.236 | 9.216 | 18.79
J1153–28 | 71.96 | 71.22 | 1.010 | 9.841 | 9.836 | 18.56
J0419–54 | 164.90 | 163.98 | 1.006 | 10.086 | 10.084 | 18.03
999(1) Galaxy name. (2) Flux density $S_{f}$ from full-depth data. (3) Flux
density $S_{s}$ from single-track data. (4) Ratio of full-depth and single-
track flux $S_{f}/S_{s}$. (5) H i mass from full-depth data. (6) H i mass from
single-track data. (7) Column density of the additional H i in the full-depth
data calculated as ratio of additional H i and H i disk area as derived from
the zeroth-moment maps.

###  6.2 Comparison with single dish profiles

We have shown that the longer integration times of the full-depth data allow
us to detect a small amount of additional H i. However, this internal
comparison does not address the “missing spacing” issue. Is MeerKAT able to
give us an accurate measurement of the total H i mass of our galaxies?

As the MHONGOOSE sample is ultimately selected from HIPASS, single-dish Parkes
observations are available with a beam size of $15^{\prime}$ and flux
measurements for all but one of the sample galaxies are given in the HIPASS
Bright Galaxy Catalog ( BGC; Koribalski et al. 2004). The one galaxy that is
not in the BGC (J0429–27) falls below that catalogue’s flux limit. Instead we
use the flux density value as listed in the Meyer et al. (2004) HIPASS
Catalogue. In addition, 15 of our galaxies have been observed with the GBT
with a beam size of $9^{\prime}$ (Sorgho et al. 2018; Sardone et al. 2021).

We can therefore test whether the MHONGOOSE observations manage to recover the
total flux. As the differences between the flux densities derived from the
single-track and full-depth data are only small (as discussed above), we use
the single-track flux densities here, as this maximises the number of galaxies
where a comparison can be made.

The single-track flux densities are listed in Tab. 6, with the velocity widths
given in Tab. 1. These are based on the r15_t00 data using masks as described
in Sect. 5.10 and 6.1. The 20% velocity width $W_{20}$ is defined as the
difference between the velocities where the profile reaches 20% of its peak
value. The central velocity is defined to be halfway between these velocities.

We additionally list the HIPASS and GBT flux densities in Tab. 6 for those
galaxies where at least one single-dish measurement is available. We have re-
measured the GBT flux densities from the original profiles, as the values
listed in Sardone et al. (2021) represent cumulative flux densities integrated
over the entire respective areas mapped by the GBT, rather than direct
integration of the global profiles as discussed here. The H i profiles
themselves are shown and compared in Fig. 10. Where necessary we have shifted
the literature spectra to the same radio velocity scale as the MeerKAT
profiles. Any “peaks” detected in the single-dish data outside the velocity
range of the target galaxies (e.g., the HIPASS profile of J0008–34 at $v\sim
270$ km s-1 in Fig. 10) are due to noise.

Figure 10: Comparison of the MeerKAT and single dish profiles. MeerKAT r15_t00
profiles are shown in black, GBT profiles (Sardone et al. 2021) in cyan, and
HIPASS profiles (Koribalski et al. 2004) in red. The green arrows indicate the
central velocties as derived from the MeerKAT data.

In Fig. 11 we compare the MHONGOOSE, HIPASS and GBT flux densities. The HIPASS
values are systematically lower than the MeerKAT and GBT values. One
explanation could be that some of the H i has been subtracted during data
processing by the running bandpass correction method (Barnes et al. 2001). The
flux densities of H i-bright galaxies are also known to be affected by the
gridding used in the HIPASS pipeline (Barnes et al. 2001; Koribalski et al.
2004).

The agreement with the re-measured GBT flux densities is good. The ratio of
the GBT and MeerKAT flux densities is $1.058\pm 0.080$, so the GBT on average
detects $\sim 6\%$ more flux, but this is within the scatter of $\sim 8\%$. A
least-squares fit to the linear values, as shown in Fig.11, has a slope of
0.964, but this slope is mainly determined by NGC 7424 (J2257–41), the galaxy
with the largest flux density, where we find that the GBT actually detects
less H i than MeerKAT. Leaving that point out we end up with a slope of 0.997,
again indicating good agreement between the MeerKAT and GBT fluxes. This is
especially so when one considers the uncertainty in the MeerKAT flux
calibration of $\sim 10\%$ (Serra et al. 2023) and a most likely similar
uncertainty in the GBT flux calibration. The good agreement is consistent with
the fact that most sample galaxies are significantly less extended than the
$\sim 20^{\prime}$ maximum angular scale that the MeerKAT shortest baseline of
29m is sensitive to.

Figure 11: Comparison of the single-track MeerKAT flux densities with single-
dish flux densities. Stars (orange) indicate HIPASS values, filled circles
(blue) GBT values. The full black line indicates a unity slope. The left panel
compares the flux densities on a logarithmic scale, the right panel shows the
same data points on a linear scale. The dashed blue line is a fit to the GBT
points. The fit to the logarithmic GBT values has a slope of 0.968, the linear
values give a fit with a slope of 0.954. The dotted orange line is a fit to
the HIPASS data. Here the logarithmic slope is 0.964, the linear fit gives a
slope of 0.860. Table 6: MeerKAT and single-dish H i mass comparison

Galaxy |  $S$ (MKT) |  $S$ (HIPASS) |  $S$ (GBT)
---|---|---|---
|  (Jy km s-1) |  (Jy km s-1) |  (Jy km s-1)
(1) | (2) | (3) | (4)
J0008–34 | 5.3 | 5.8 | -
J0031–22 | 7.3 | 7.2 | -
J0049–20 | 3.6 | 3.9 | 3.6
J0052–31 | 206.3 | 159.1 | -
J0135–41 | 34.7 | 30.9 | -
J0309–41 | 27.5 | 26.1 | 29.4
J0310–39 | 4.2 | 4.4 | 4.5
J0320–52 | 15.3 | 14.6 | -
J0331–51 | 20.7 | 19.4 | -
J0335–24 | 76.6 | 68.8 | 70.2
J0351–38 | 12.0 | 11.2 | 13.47
J0419–54 | 164.0 | 140.0 | -
J0429–27 | 5.0 | 5.9 | 5.8
J0445–59 | 220.7 | 198.8 | -
J0454–53 | 15.3 | 15.4 | -
J0459–26 | 170.4 | 144.3 | 171.7
J0516–37 | 64.9 | 59.6 | -
J0546–52 | 26.3 | 24.3 | -
J1103–23 | 76.6 | 80.4 | 75.0
J1106–14 | 12.1 | 11.2 | 14.2
J1153–28 | 71.2 | 68.1 | 80.3
J1253–12 | 26.3 | 27.2 | 28.3
J1254–10a | 54.6 | 59.4 | -
J1303–17b | 110.5 | 92.6 | 117.5
J1318–21 | 161.6 | 128.6 | 159.0
J1321–31 | 6.2 | 5.9 | 7.0
J1337–28 | 21.1 | 21.1 | -
J2009–61 | 26.6 | 23.9 | -
J2257–41 | 271.9 | 227.0 | 257.8
J2357–32 | 295.5 | 278.5 | -
101010(1) Galaxy identification. (2) Single-track MHONGOOSE flux density. (3)
HIPASS flux density from Koribalski et al. (2004), except for J0429–27 where
the flux density is from Meyer et al. (2004). (4) GBT flux density rederived
from Sardone et al. (2021).

##  7 Comparing the moment maps

###  7.1 Pixel-pixel density histograms of individual galaxies

The moment maps presented in Fig. A.18 give an overview of the morphology and
kinematics of the H i in the MHONGOOSE galaxies. In terms of column density
sensitivity these single-track observations approach the sensitivity of the
HALOGAS survey to within a factor of two (cf. Fig. 2, shifting the MHONGOOSE
line up by 0.5 dex).

An efficient method to further summarise this information is pixel-by-pixel
scatter plots of the various moment values: for each location (pixel) the
value of one moment is plotted against that of a different moment at that same
location. A number of previous studies have used these plots to study
properties of galaxies. For example, de Blok et al. (2018) used the
distribution of the zeroth- and second-moment values of the H i distribution
in the M81 triplet to find that each of the three triplet galaxies occupied
unique positions in that particular parameter space, and addressed the
question of whether the M81 triplet could be the equivalent of a
Lyman-$\alpha$ absorber (cf. their Fig. 20). Maccagni et al. (2021) presented
optical line emission data of Fornax A and used the distribution of zeroth-
and first-moment values to distinguish between rotating and outflowing gas.
Sun et al. (2018, 2020) studied the zeroth and second moments of the CO
distribution in the Physics at High Angular resolution in Nearby GalaxieS
(PHANGS) galaxies.

The single-track MHONGOOSE observations give us the opportunity to do a
similar analysis for 30 galaxies in H i, with all of them observed and reduced
in an identical, homogeneous manner. Here we explore the relation between
column density and velocity width (zeroth and second moment).

We use the r15_t00 data of all of our galaxies and plot the zeroth- and
second-moment map pixels of each of our galaxies against each other. The $\sim
30^{\prime\prime}$ resolution data gives a good column density sensitivity
while not greatly sacrificing angular resolution (cf. Fig. 5). We realise that
the individual pixels are not independent of each other. However, here we only
consider the relative distributions at a single resolution. Taking the size of
the beam into account would only change the absolute scaling.

Rather than using scatter plots where subtle differences are often difficult
to make out, we derive a two-dimensional density histogram covering the column
density-velocity width parameter space with a $75\times 75$ grid.

The zeroth-moment values are corrected for inclination and converted to
surface densities by multiplying them by $\cos i$, where we assume the
inclinations given in Table 1. We found that this simple correction was
sufficient for our purposes, with conclusions insensitive to the exact
inclinations values.

Figure 12: Two-dimensional density histograms showing the distribution of
inclination-corrected column densities and second moment values for the
MHONGOOSE galaxies. Each histogram consists of $75\times 75$ hexagonal bins,
and only bins containing more than 4 pixels are shown. The colour bar on the
right in each panel indicates the number of pixels per bin. The background
contours indicate the total distribution of the entire sample as shown in Fig.
13. Galaxies are divided in three bins in rotation velocity. Within each bin,
galaxies are ordered by increasing inclination, with the most face-on galaxies
in the top-left, and the most edge-on in the bottom-right. The two light-gray
bars between the panels in each bin indicate inclinations of 50∘ $(b/a=0.67)$
and 70∘ $(b/a=0.33)$, respectively.

The panels in Fig. 12 show, for each galaxy, the number of pixels having
values corresponding to any given combination of column density (horizontal
axis) and velocity spread (vertical axis). This is shown as a two-dimensional
density-histogram with each bin having the value given by the colour scale for
that panel. Bins are only shown if there are a minimum of four moment pixels
falling in them. The contours show a similar density histogram but in this
case derived from all the single-track moment maps of all galaxies combined.
The juxtaposition of the two distributions allows for a quick comparison of
the distribution for a particular galaxy with that of the entire sample. This
total distribution is further discussed in Sect. 7.2.

To highlight any differences between galaxies of different masses, we divide
the galaxies in three equal-number bins in rotation velocity, as shown in Fig.
12. The rotation velocities are calculated from the $W_{20}$ and $i$ values
given in Tab. 1. Within each rotation velocity bin we show the galaxies in
order of increasing inclination.

We see a large spread in the typical second-moment values for each galaxy.
Compare for example the high values found in J1318-21 with the low ones in
J0351-38. While our galaxies have a range in distance, this is not the cause
of the spread in these typical values (which would be due to the beam
measuring a larger number of kpc for more distant galaxies, and thus
potentially capturing a larger range in velocities). The main determining
factor seems to be the SFR. We discuss this further below.

In the highest-rotation velocity bin we can make out a number of interesting
trends. The lowest inclination galaxies in general cover most of the parameter
space as traced by the entire sample. The only exception is J2257–41 which has
low second-moment values. Moving to the high-inclination galaxies we see that
they exclusively cover the upper part of the diagram. This is not a beam-
smearing effect, but is rather caused by the longer line-of-sight through the
disk, resulting in increased linewidths. We refer to Appendix B for a more in-
depth discussion of the impact of beam smearing and inclination.

The face-on massive galaxies show significantly increased second-moment values
at the highest column densities. While some of this will be due to beam
smearing in combination with a steeply rising inner rotation curve, part of it
will be intrinsic to the galaxies. Most of these high values occur in the
central parts of the galaxies and are likely related to the intense star
formation in these portions of the galaxy. They mark the presence of winds or
outflows powered by star formation or an AGN. The most massive galaxies in the
sample, NGC 1566 (J0419–54), NGC 1672 (J0445–59), NGC 1371 (J0335–24) and NGC
289 (J0052–31), are known Seyfert galaxies.

The lowest-rotation velocity galaxies do not show these extreme second-moment
values, but rather cling to the bottom of the distribution for the lower
inclinations, though we do see larger second-moment values towards the more
edge-on galaxies.

The situation for the intermediate rotation velocity galaxies is complex. We
do not see a clear trend of the distribution changing with inclination. An
extreme example is NGC 5068 (J1318–21) which shows the highest second-moment
values in this bin, yet is the most face-on galaxy. The complex situation in
this galaxy is described in more detail in Healy et al. (2023). Another
complex distribution can be seen for NGC 1705 (J0454–53). This is a
starbursting dwarf galaxy, and the parallel track of high second-moment values
are indications of the gas outflows in this galaxy (cf. Meurer et al. 1998). A
few more of these intermediate-rotation velocity galaxies show multiple
velocity width values at a given surface density. In many cases the high
second-moment values are linked to locations where there are multiple
components along the line of sight due to, e.g., spiral arms, the presence of
extra-planar gas, or long lines of sight through the disk.

An in-depth analysis of these density histograms, with the addition of
information on the distribution of molecular gas, such as presented in Sun et
al. (2018, 2020), will give much information on the conditions for star
formation in nearby galaxies and the link with the properties of the atomic
and molecular gas. Such a quantitative analysis is, however, beyond the scope
of this paper.

###  7.2 Total pixel-by-pixel density histogram

We now consider the surface density-velocity width density histogram of the
entire sample. Here we again use the same $75\times 75$ grid to sample the
displayed parameter range, but only display bins containing more than eight
sample values. This integrated histogram is shown in Fig. 13 and contains
several interesting features. Some of these are known from the literature, but
others have not been explicitly noted before.

Figure 13: Two-dimensional density histograms showing the distribution of
zeroth and second moment values for the entire MHONGOOSE sample. The histogram
consists of $75\times 75$ hexagonal bins, and only bins containing more than 8
pixels are shown. The colour bar indicates the number of pixels with the H i
column density and velocity widths indicated by the horizontal and vertical
axes, respectively.

Figure 14: Illustration of the change in zeroth- and second-moment values due
to masking. The top panel shows a number of Gaussians, here plotted as a
function of velocity as given by the vertical axis, while the horizontal axis
indicates the peak value of the Gaussian in terms of S/N. From right to left
the peak values are 1000, 100, 50, 10 and 5 times the S/N. The dashed vertical
black line indicates the 4 times S/N level where masking occurs. Each profile
has a velocity dispersion of 10 km s-1 as indicated by the horizontal dashed
green lines, and, for each Gaussian separately, the dotted vertical green
lines. The thick red lines indicate the measured second-moment values for each
Gaussian, assuming they are masked at 4 times the S/N. The bottom panel shows
the change in zeroth and second moment values. Here we have lined up the
positions of the peaks in the top panel with those of the points in the bottom
panel by assuming that a column density of $10^{21}$ cm-2 corresponds to a S/N
of 1000. This is consistent with the data presented in Fig. 13 that are shown
here as contours. The curve extending to the left (open circles) takes into
account that the total flux of the Gaussian decreases due to masking, the
right-hand curve (closed circles) ignores this. For other assumed velocity
dispersions, the shape of the curve does not change but will shift up (larger
dispersions) or down (lower dispersions).

At the highest column densities we see a steep drop-off in the density
distribution, despite this being the part of the diagram with the highest
signal-to-noise. This drop-off occurs at surface density values of
$\log(N_{{\rm H{\hskip 0.56917pt\tt I}}}/{\rm cm}^{-2})\sim 21.1$, or $\sim
10$ $M_{\odot}\,{\rm pc}^{-2}$, and thus implies an upper limit to the H i
column density (at this resolution). This value agrees well with the upper
limit of $\approx 9$ $M_{\odot}\,{\rm pc}^{-2}$ found by Bigiel et al. (2008)
for the THINGS sample at similar resolutions (also see Leroy et al. 2008; for
a more detailed observational view, see Schruba et al. 2017). A comparison
with molecular gas column density values shows that this upper limit
corresponds with a transition from an atomic to a molecular ISM (cf. Krumholz
et al. 2009; McKee & Krumholz 2010; Sternberg et al. 2014)

Turning to the second-moment values, we see that at surface densities
$\log(N_{{\rm H{\hskip 0.56917pt\tt I}}}/{\rm cm}^{-2})>19.5$ there is a well-
defined lower limit to the second-moment values. This limit occurs at $\sim
8.5$ km s-1. Given the 1.4 km s-1 velocity resolution of the data
(corresponding to the lower limit of the plotted second-moment range) and the
high signal-to-noise of the profiles in this part of the diagram, this cannot
be a velocity resolution artefact but must indicate an absence of H i profiles
with second-moment values less than $\sim 8.5$ km s-1. To first order, the ISM
is considered to consist of a cool neutral medium (CNM) with a temperature of
a few tens of K and a warm neutral medium (WNM) with temperatures around $\sim
8000$K . The CNM line profiles have a line width of $\sim 1$ km s-1 while WNM
line width are $\sim 8$ km s-1 (in the absence of any other processes that can
broaden line-widths) (Braun 1997; Wong & Blitz 2002; Wolfire et al. 2003). The
lower limit found in our data does not indicate an absence of CNM, but merely
shows that the H i emission, and therefore the line width, is dominated by the
WNM, where the latter has a lower limit to its observed velocity dispersion as
shown in Fig. 13.

As is evident from Fig. 12, many of the galaxies show distinct local density
concentrations in the histograms. We also see this in the total density
histogram, suggesting this is a general feature of our sample. Figure 13 shows
a local maximum in the combined distribution centered on $\log(N_{{\rm
H{\hskip 0.56917pt\tt I}}}/{\rm cm}^{-2})\sim 20.6$ and another (less
concentrated) one around $\log(N_{{\rm H{\hskip 0.56917pt\tt I}}}/{\rm
cm}^{-2})\sim 19.5$. Comparison with the integrated H i maps as well as SINGG
H$\alpha$ and GALEX UV images shows that the profiles corresponding to the
high-column density concentration are generally found in the star-forming
disks of the galaxies. The profiles contributing to the low-column density
concentration are generally found in the outer disk or in inner disk regions
with little to no detected star formation as seen in the H$\alpha$ and FUV
images. The high-density clump in Fig. 13 also shows a “tail” at high velocity
dispersion, which is not visible in the low density clump, possibly induced by
feedback from star formation.

Perhaps the most interesting is the clear division between these two
concentrations around $\log(N_{{\rm H{\hskip 0.56917pt\tt I}}}/{\rm
cm}^{-2})\sim 20.3$ ($N_{{\rm H{\hskip 0.56917pt\tt I}}}\sim 2\cdot
10^{20}{\rm cm}^{-2}$). If H i complexes gradually collapse either under their
own gravity or triggered by an external event, we would expect the observed H
i column density to continuously increase, and therefore expect to see a
continuous H i column density distribution in Fig. 13. If we assume that
collapsing H i complexes move from left to right in the Figure (i.e., from
low- to high-column density), then the presence of the division points to a
short timescale for this column density increase.

A possible explanation for the presence of this division is related to the
formation of the CNM. This was put in a physical context in Kanekar et al.
(2011). Based on measurements of the spin temperature in a large number of
Galactic H i clouds they identify a rapid change in spin temperature at $\sim
2\cdot 10^{20}$ cm-2. They associate this with a threshold H i surface density
for formation of the CNM. Above this $\sim 2\cdot 10^{20}$ cm-2 threshold, the
H i can sufficiently self-shield against UV photons to enable formation of a
cool component. Below this threshold the UV photons can heat and ionise the
gas, preventing the formation of a CNM. Note that this threshold also
corresponds to that used to define a Damped Lyman-$\alpha$ system.

Following the interpretation by Kanekar et al. (2011), these data show that
the existence of a CNM, which is more closely associated with star formation,
leaves an imprint on the moment maps, including a rapid transition to higher
column densities once this component starts forming. Figure 13 thus shows, in
a single plot, the various transitions occurring towards star formation. At
the lowest column densities, between $\sim 10^{19}$ and $\sim 10^{20}$ cm-2,
the gas is dominated by the WNM, and there is little or no star formation
(Bigiel et al. 2010; Serra et al. 2012; Maccagni et al. 2017). At $\sim 2\cdot
10^{20}$ cm-2 the gas is sufficiently dense that a significant CNM can rapidly
develop. The approximate column density limits of the high-column density
concentration correspond closely to the values given in Bigiel et al. (2010)
($\sim 3-10$ $M_{\odot}\,{\rm pc}^{-2}$ or $\log(N_{\rm H{\hskip 0.56917pt\tt
I}}/{\rm cm}^{-2})\sim 20.5-21.1$) where star formation is efficient

We expect that the CNM will still be embedded in a WNM (at the resolution of
our observations), where the WNM is the source of the observed second-moment
values. We therefore do not see the lower CNM velocity dispersions reflected
in the plot, but studies of the individual profiles should provide clear
evidence for its presence. The gas turns completely molecular at the column
density cut-off discussed above.

It will be interesting to repeat this analysis once all full-depth data are
available. The increase in S/N will allow exploration at different angular
resolutions, but also, perhaps more crucially, at identical physical
resolutions.

###  7.3 Masking and moments

One of the distinct features in Figs. 12 and 13 is the tail of decreasing
second-moment values towards low surface densities. Naively, one might presume
that this could be a consequence of the low-column density gas being mostly in
the outer disk where there is less energy available to heat and stir up the
gas, leading to a low velocity dispersion. The true cause is more prosaic,
however, as we show here that it is caused by the masking procedure used to
create the moment maps.

The SoFiA-2 moment map creation steps described above are a sophisticated
combination of source finding and masking at different spatial and velocity
scales. The essentials of this can, fortunately, already be captured by
considering an idealised Gaussian H i profile with constant velocity
dispersion and variable normalisation or peak value (corresponding to
different column densities).

We consider a data cube with a noise per channel $\sigma_{\rm ch}$ in which we
embed Gaussian line profiles with a fixed velocity dispersion and a peak value
expressed as some multiple of $\sigma_{\rm ch}$. Analogous to our SoFiA moment
map construction, we assume that we mask the data at the $4\sigma_{\rm ch}$
level. For a Gaussian with a peak close to the noise level most of the profile
will be masked, while a high S/N profile will be much less affected.

We consider the second moment of the remaining $>4\sigma_{\rm ch}$ profile
_after masking_ as a function of the signal-to-noise of the profile. Without
masking (and for noise-free data), this would equal the velocity dispersion of
the Gaussian. With masking, it decreases as the peak value decreases.

A second effect is that the area underneath the masked Gaussian (the zeroth-
moment value or integrated flux) also decreases after masking due to removal
of the high- and low-velocity wings of the profile. This also causes a
relatively larger decrease in column density as the peak flux density
declines.

In Fig. 14, we plot the curve showing the calculated changes in the measured
zeroth- and second-moment values for a single fixed-velocity dispersion
Gaussian as a function of its peak value and superimpose this on the surface
density-velocity width density histogram. The absolute vertical position of
the curve is determined by the input velocity dispersion of the Gaussian. The
horizontal position of the curve is fixed by identifying the typical S/N for a
given column density. In Fig. 14 we show the resulting changes for a Gaussian
masked at $4\sigma_{\rm ch}$ with a velocity dispersion of 10 km s-1, and a
S/N of 1000 for a column density of $10^{21}$ cm-2. This is approximately
correct for the data shown here, as deduced from the S/N maps discussed in
Sect. 5.8 and 5.10. We show two models in Fig. 14, one where we ignore the
decrease in flux due to masking, and one where we do take this into account.
The latter extends to lower column densities.

For the assumptions made here, the shape of this relation is fixed. Changing
the input velocity dispersion merely shifts it up and down, while increasing
the S/N of the underlying data would shift it horizontally. The tail towards
lower column densities is therefore an unavoidable byproduct of the masking
procedure. Longer integrations (i.e., a decreasing noise) would push the tail
to lower column densities. A similar analysis using full-depth cubes would
result in the tail starting at column densities that are $\sqrt{10}$, or 0.5
dex lower in column density.

Note how well the down-turn in the tail is described by the simple single
Gaussian model. We can deduce for the masking procedure described here, that
at S/N values between $\sim 50$ and $\sim 10$, the second moment values start
to underestimate the velocity dispersion. At a ${\rm S/N}\sim 5$, the second
moment underestimates the velocity dispersion by a factor of $\sim 2.5$.
Column densities, though not as affected, can nevertheless be underestimated
by factors of $\sim 1.6$ at these lower S/N values. Multiple components along
the line of sight will not significantly influence the lower bounds of the
distribution as, at a given column density, these will be found at higher
second-moment values. Nevertheless, fitting multiple Gaussians to the velocity
profiles could further elucidate (or better: circumvent) the effects of
masking in the presence of multiple profiles.

In short, in our specific case of masking at $4\sigma$, moment values below a
S/N $\sim 20$ should be used with care, as these will introduce significant
biases with respect to the true column density or velocity dispersion.
Different masking levels and methods produce different S/N level limits, but
the general conclusion remains and will always be relevant when masking is
used. As noted, deeper data cannot totally remove this this issue, but will
shift these effects towards lower column densities.

##  8 Other galaxies in the MHONGOOSE fields

The sensitivity and large field of view of MeerKAT result in the detection of
additional companion and field galaxies. Here we give a first inventory of the
galaxies detected in the 1.5∘ by 1.5∘ single-track fields in a velocity range
of $-500$ to $+500$ km s-1 with respect to the central velocity of the target
galaxies. Detections are based on the single-track zeroth-moment maps. A list
of these additional galaxies is given in Table 7. For the fields where
additional galaxies are present, Fig. 15 shows the positions of these
galaxies. We expect an even larger number of galaxies to be detected in the
full-depth data once available. While the search volume is defined with
respect to our target galaxies, this does not imply that every one of these
additional galaxies is also physically associated with those target galaxies.
Most of them will be, but it is possible that (especially at the edges of the
volume probed) we are picking up some foreground or background galaxies

The Table reports a variety of integrated H i properties, as well as the
identification of the optical counterparts. These identifications were made by
consulting the SIMBAD and NED data bases. We find that half of the additional
H i detections can be definitively associated with an optical counterpart
through a match both in position (generally to within one or two beams) and in
velocity (generally to within a few tens of km s-1). Most of the other half
can be reliably associated with an optical counterpart through a position
match only, because no previously measured velocity is noted in either the NED
or SIMBAD databases, and our redshifts are the first ones measured for these
objects. Finally, we find four galaxies (indicated with the MKT prefix in
Table 7) that have no previous identification, but where an optical
counterpart is clearly visible in DECaLS images.

Three additional galaxies visible in the moment maps are partially outside of
the volume of the data cubes used here. These are LEDA 583148 in the J0309–41
field, ESO 486–21 in the J0459–26 field, and MKT J125225.4-124304.1 in the
J1253–12 field. For these three galaxies we list the position and approximate
radial velocity in Table 7. We refrain from presenting their H i line widths
and fluxes because the large uncertainty due to the incomplete coverage by the
data used here. The last of these three galaxies is a fifth, previously
uncatalogued galaxy. All of the additional galaxies listed here can thus be
associated with an optical counterpart; we have not found any “dark” galaxies.

We note that one of our lowest H i mass galaxies, UGCA 15 (J0049–20), is
itself a companion to the larger galaxy NGC 247. This is the only case where a
“companion” galaxy is more massive than the target galaxy and we do not
include NGC 247 in the following analysis.

Figure 16 shows the integrated H i maps overlaid on optical DECaLS images
along with the global H i profiles (corrected for the primary beam) of the
additional galaxies.

Figure 15: Overview of the zeroth-moment maps of the fields where additional
galaxies are present. The HIPASS name of the target galaxy (center) is
identified in the top-right corner of the zeroth-moment maps. The additional
galaxies are indicated by blue circles and their properties are listed in
Table 7. A small number of galaxies are not indicated as they partially fall
outside of the field of view shown here. The large dotted circles indicate a
diameter of 1 degree, equivalent to the FWHM of the MeerKAT primary beam. The
maps have been corrected for primary beam attenuation.  Figure 16: Grayscale
cutouts from DECaLS DR10 $g$-band centred on the additional H i detections.
Contours indicate H i column densities at S/N = 3, 5, 10 (from orange to red).
Spectra have been binned by a factor two with a resulting channel width of 2.8
km s-1. These spectra were used to derive the parameters listed in Table 7.
All spectra are based on r15_t00 data, except for J0546-52 LEDA 454649 which
is based on r05_t00 data.

The number of additional galaxies detected varies significantly from field to
field. Some target galaxies have no additional galaxy in the field, while
others boast five or six companions. We can get a first indication of the
variety of the environments around the target galaxies by plotting the number
of additional galaxies per field as a function of the H i mass and the stellar
mass of the target galaxy as shown in Fig. 17. It is striking that we see only
one additional galaxy until just below $M_{{\rm H{\hskip 0.56917pt\tt I}}}\sim
10^{9}$ $M_{\odot}$. Above that mass the number of additional galaxies
suddenly increases. A similar steep increase can be seen at a stellar mass
$M_{\star}\sim 10^{8}$ $M_{\odot}$.

We can compare this with a similar observational result found by Zhu & Putman
(2023). In a census of gaseous satellites around spiral galaxies, they
identify companion galaxies around local spiral galaxies identified in the
ALFALFA survey, and find that the number starts to increase at a halo mass of
$\log(M_{\rm halo}/M_{\odot})\sim 11.5$. Using their Table 1 for a first-order
conversion of their halo masses to H i masses, we find that this sudden
increase occurs at an H i mass just below $10^{9}$ $M_{\odot}$, strikingly
close to where we find an increase in our sample.

Applying a more restrictive definition of a companion galaxy, analogous to
that used in Zhu & Putman (2023), does not substantially change our results.
For example, imposing a cut of $\pm 300$ km s-1 with respect to the systemic
velocity, and a cut in projected separation to the companion of $200$ kpc (the
approximate value of the virial radius $R_{200}$ for the upper mass range of
the sample) does not change the observed sudden increase.

It is interesting to note that that many of these gas-rich companion galaxies
are found projected within the virial radius, contrary to what we see in the
Local Group (Spekkens et al. 2014), but consistent with recent SAGA results
(Mao et al. 2021) with many star forming galaxies projected within the virial
radii.

A more complete census of the companion galaxy population will be possible
when the full-depth data for the full sample are available and we can probe
the companion population to the fullest extent possible for our survey. As
with the galaxies presented here, these satellites and companions will be
resolved spatially and spectrally, meaning that in-depth studies of the dark
matter content and baryon fractions can be made down to an H i mass limit of
$\sim 10^{6}$ $M_{\odot}$ (cf. Table 5), a regime previously only accessible
in the Local Group. A first discovery of such a low-mass galaxy in the
MHONGOOSE observations is presented in Maccagni et al. (subm.).

Figure 17: Number of additional galaxies in a 1.5∘ $\times$ 1.5∘ area around
the target galaxies, within a velocity range of $-500$ to $+500$ km s-1 with
respect to the central velocity of the target galaxy. This number is plotted
against the H i mass of the target galaxy in the left panel and against the
stellar mass in the right panel. Note the sudden increase at $M_{{\rm H{\hskip
0.56917pt\tt I}}}\sim 10^{9}$ $M_{\odot}$ (left) and $M_{\star}\sim 10^{8}$
$M_{\odot}$ (right). Table 7: Additional galaxies in the field

Field | Galaxy |  $\alpha$ (J2000.0) |  $\delta$ (J2000.0) | $V_{\rm central}$ | $W_{20}$ | $W_{50}$ | $S_{{\rm H{\hskip 0.56917pt\tt I}}}$
---|---|---|---|---|---|---|---
|  |  |  |  (km s-1) |  (km s-1) |  (km s-1) |  (Jy km s-1)
J1321-31 | LEDA 46885 | 13 24 35.7 | -30 58 18.3 | 484.0 | 25.7 | 18.4 | 0.075
J1253-12 | NGC 4802 | 12 55 49.7 | -12 03 25.3 | 923.8 | 143.4 | 94.7 | 0.531
J1253-12 | LCRS B125209.0-112324 | 12 54 45.9 | -11 39 39.6 | 857.7 | 38.6 | 22.1 | 0.892
J0331-51 | ESO 200-G045 | 03 35 00.8 | -51 27 15.0 | 1023.4 | 52.4 | 38.6 | 1.001
J0331-51 | MKT J033131.9-520400 | 03 31 31.9 | -52 04 00.0 | 1014.1 | 28.5 | 11.9 | 0.225
J0331-51 | LEDA 457253 | 03 30 11.3 | -51 21 14.4 | 1102.3 | 56.0 | 37.7 | 0.212
J0309-41 | LEDA 88064 | 03 10 59.2 | -41 39 40.7 | 1343.0 | 107.5 | 66.2 | 1.227
J0309-41 | LEDA 200114 | 03 09 48.0 | -41 39 25.5 | 1330.3 | 59.7 | 38.6 | 1.225
J1303-17b | LEDA 886203 | 13 05 03.9 | -17 15 24.1 | 723.9 | 44.1 | 27.8 | 0.872
J1303-17b | UGCA 319 | 13 02 14.5 | -17 14 17.8 | 724.3 | 34.0 | 22.1 | 3.300
J0546-52 | MKT J054753.5-515635 | 05 47 53.5 | -51 56 35.9 | 1171.6 | 29.4 | 13.8 | 0.130
J0546-52 | NGC 2104 | 05 47 04.4 | -51 33 02.4 | 1162.6 | 167.2 | 146.1 | 5.868
J0546-52 | ESO 204-G034 | 05 44 41.5 | -51 57 48.7 | 1227.4 | 104.8 | 93.7 | 3.294
J0546-52 | ESO 159-G025 | 05 43 07.2 | -52 42 13.9 | 1097.5 | 94.7 | 76.3 | 1.156
J0546-52 | ESO 204-IG028 | 05 41 45.9 | -51 44 35.8 | 1277.0 | 63.4 | 49.6 | 0.350
J0546-52 | LEDA 454649 | 05 47 30.7 | -51 35 45.7 | 1181.9 | 64.3 | 56.1 | 0.171
J1254-10a | UGCA 308 | 12 55 31.1 | -10 23 39.8 | 1317.4 | 74.4 | 55.1 | 5.590
J1254-10a | 2MASX J12551835-1103580 | 12 55 18.2 | -11 04 02.3 | 1104.8 | 108.4 | 68.0 | 0.430
J1254-10a | NGC 4790 | 12 54 51.5 | -10 14 43.4 | 1353.6 | 216.9 | 182.0 | 14.917
J0459-26 | MKT J045920.2-252959 | 04 59 20.2 | -25 29 59.8 | 692.1 | 40.4 | 31.2 | 0.087
J1103-23 | NGC 3513 | 11 03 46.1 | -23 14 31.4 | 1190.9 | 98.3 | 80.0 | 20.664
J0516-37 | ESO 362-G016 | 05 19 18.8 | -37 06 32.1 | 1334.6 | 91.0 | 75.4 | 3.029
J0516-37 | LEDA 630916 | 05 16 44.7 | -36 55 28.9 | 1329.4 | 24.8 | 13.8 | 0.184
J0516-37 | WISEA J051522.96-370331.3 | 05 15 23.1 | -37 03 31.1 | 1360.8 | 38.6 | 31.2 | 0.074
J0335-24 | NGC 1385 | 03 37 28.8 | -24 30 12.7 | 1492.4 | 214.1 | 186.5 | 6.488
J0335-24 | ESO 482-G013 | 03 36 53.8 | -24 54 46.2 | 1830.1 | 127.7 | 79.9 | 2.121
J0335-24 | ESO 482-G011 | 03 36 17.3 | -25 36 18.6 | 1578.5 | 148.9 | 130.5 | 0.379
J1153-28 | ESO 440-G030 | 11 55 25.7 | -28 44 10.1 | 1804.1 | 110.3 | 91.9 | 0.763
J1153-28 | LEDA 737259 | 11 54 14.8 | -28 48 20.2 | 1763.8 | 38.6 | 24.8 | 0.609
J1153-28 | LEDA 746393 | 11 53 10.5 | -28 03 28.6 | 1833.1 | 79.0 | 74.4 | 0.113
J1153-28 | ESO 440-G023 | 11 52 33.3 | -29 07 20.2 | 1865.8 | 110.3 | 85.5 | 0.351
J1153-28 | 6dFGS gJ115153.3-281047 | 11 51 53.3 | -28 10 44.4 | 1424.1 | 52.4 | 21.1 | 0.063
J1153-28 | ESO 440-G014 | 11 50 03.4 | -28 40 17.9 | 1855.8 | 54.2 | 28.5 | 0.113
J2257-41 | MKT J225656.8-411815 | 22 56 56.8 | -41 18 15.9 | 1292.8 | 40.4 | 20.2 | 0.148
J0419-54 | NGC 1581 | 04 24 44.4 | -54 56 31.2 | 1632.8 | 216.9 | 190.2 | 0.387
J0419-54 | LEDA 414611 | 04 22 00.9 | -54 54 41.5 | 1437.4 | 43.2 | 22.1 | 0.131
J0419-54 | LSBG F157-052 | 04 20 26.8 | -54 44 25.1 | 1340.2 | 71.7 | 52.4 | 0.192
J0445-59 | NGC 1688 | 04 48 23.4 | -59 47 50.4 | 1225.5 | 160.8 | 143.4 | 4.775
J0445-59 | ESO 119-G003 | 04 48 07.4 | -59 24 54.6 | 1211.4 | 77.2 | 63.4 | 2.155
J0445-59 | ESO 118-G042 | 04 45 27.6 | -59 04 21.4 | 1207.9 | 71.7 | 34.9 | 0.922
J0445-59 | ESO 118-G034 | 04 40 16.6 | -58 44 37.4 | 1153.1 | 85.5 | 51.4 | 0.171
J0052-31 | ESO 411-G031 | 00 55 42.5 | -30 32 23.7 | 1558.7 | 68.9 | 63.4 | 1.524
J0052-31 | 2dFGRS TGS369Z051 | 00 53 30.1 | -30 50 29.0 | 1555.6 | 51.5 | 30.3 | 0.665
J0052-31 | ESO 411-G026 | 00 52 45.2 | -31 43 08.4 | 1590.7 | 113.0 | 98.3 | 3.037
J0052-31 | 2dFGRS TGS370Z277 | 00 52 25.7 | -30 54 25.7 | 1436.0 | 35.8 | 13.8 | 0.078
J0052-31 | LEDA 715942 | 00 51 52.0 | -30 32 46.0 | 1528.4 | 72.6 | 35.8 | 0.542
Galaxies with uncertain parameters |  |  |  |  |  |
J0309–41 | LEDA 583148 | 03 08 38.0 | -40 43 29.5 |  (1412.1) | – | – | –
J0459–26 | ESO 486-21 | 05 03 16.2 | -25 25 18.8 |  (845.8) | – | – | –
J1253–12 | MKT J125225.4-124304.1 | 12 52 25.4 | -12 43 04.1 |  (401.7) | – | – | –

111111Galaxies in a bold font match their optical counterparts both in