PASA 2024

# GASKAP-HI Pilot Survey Science I: ASKAP Zoom Observations of Hi Emission in
the Small Magellanic Cloud

N. M. Pingel1 J. Dempsey1,2 N. M. McClure-Griffiths1 J. M. Dickey3 K. E.
Jameson4 H. Arce5 G. Anglada6 J. Bland-Hawthorn7 S. L. Breen8 F. Buckland-
Willis9 S. E. Clark10,11 J. R. Dawson12,13 H. Dénes14 B.-Q. For15,16 Tyler J.
Foster17 J. F. Gómez6 H. Imai18,19 G. Joncas20 C.-G. Kim21 M.-Y. Lee22 C.
Lynn1 D. Leahy23 Y. K. Ma1,24 A. Marchal25 D. McConnell13 M.-A. Miville-
Deschênes9 V. A. Moss13,26 C. E. Murray27 D. Nidever28 J. Peek27,29 S.
Stanimirović30 L. Staveley-Smith15,16 E. M. di Teodoro27 T. Tepper-
Garcia16,26,31 C. D. Tremblay4 L. Uscanga32 J. Th. van Loon33 E. Vázquez-
Semadeni34 J. R. Allison13,35 C. S. Anderson36 Lewis Ball8,13 M. Bell37 D.
C.-J. Bock13 J. Bunton13 F. R. Cooray13 T. Cornwell13 B. S. Koribalski13,38 N.
Gupta13,39 D. B. Hayman13 L. Harvey-Smith38,40 K. Lee-Waddell4,15 A. Ng13 C.
J. Phillips13 M. Voronkov13 T. Westmeier15 M. T. Whiting13 1Research School of
Astronomy and Astrophysics, The Australian National University, Canberra, ACT
2611, Australia  2CSIRO Information Management and Technology, GPO Box 1700,
Canberra, ACT 2601, Australia  3School of Natural Sciences, University of
Tasmania, Hobart, TAS 7001, Australia  4CSIRO Space and Astronomy, PO Box
1130, Bentley, WA 6102, Australia  5Department of Astronomy, Yale University,
New Haven, CT 06520, USA  6 Instituto de Astrofísica de Andalucía, CSIC,
Glorieta de la Astronomía s/n, 18008 Granada, Spain  7Department of Physics,
University of Sydney, Sydney, NSW 2006, Australia  8SKA Observatory, Jodrell
Bank, Lower Withington, Macclesfield, Cheshire SK11 9FT, UK  9AIM, CEA, CNRS,
Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité,
F-91191 Gif-sur-Yvette, France  10Department of Physics, Stanford University,
382 Via Pueblo Mall, Stanford, CA 94305, USA  11Kavli Institute for Particle
Astrophysics & Cosmology, P.O. Box 2450, Stanford University, Stanford, CA
94305, USA  12Department of Physics and Astronomy and MQ Research Centre in
Astronomy, Astrophysics, and Astrophotonics, Macquarie University, NSW 2109,
Australia  13Australia Telescope National Facility, CSIRO Space and Astronomy,
PO Box 76, Epping NSW 1710, Australia  14ASTRON - The Netherlands Institute
for Radio Astronomy, 7991 PD Dwingeloo, The Netherlands  15International
Centre for Radio Astronomy Research (ICRAR), The University of Western
Australia, 35 Stirling Hwy, Crawley, WA, 6009, Australia  16ARC Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D)  17Department
of Physics & Astronomy, Brandon University, 270-18 Street, Brandon, Manitoba,
Canada  18Center for General Education, Comprehensive Institute of Education,
1-21-30 Korimoto, Kagoshima 890-0065, Japan  19Amanogawa Galaxy Astronomy
Research Center, Graduate School of Science and Engineering, 1-21-30 Korimoto,
Kagoshima 890-0065, Japan  20Université Laval, Pavillon Alexandre-Vachon 1045,
Avenue de la Medecine, Canada  21Department of Astrophysical Sciences,
Princeton University, Princeton, NJ 08544, USA  22Korea Astronomy and Space
Science Institute, 776, Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of
Korea  23Department of Physics and Astronomy, University of Calgary, Calgary,
AB T2N 1N4, Canada  24Max-Planck-Institut für Radioastronomie, Auf dem Hügel
69, D-53121 Bonn, Germany  25Canadian Institute for Theoretical Astrophysics,
University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada
26Sydney Institute for Astronomy, School of Physics, The University of Sydney,
NSW 2006, Australia  27Department of Physics & Astronomy, Johns Hopkins
University, 3400 N. Charles Street, Baltimore, MD 21218  28Department of
Physics, Montana State University, P.O. Box 173840, Bozeman, MT 59717-3840,
USA  29Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA  30Department of Astronomy, University of Wisconsin-Madison, 475
North Charter Street, Madison, WI 53706-15821, USA  31Centre for Integrated
Sustainability Analysis, School of Physics, The University of Sydney, NSW
2006, Australia  32University of Guanajuato, A.P. 144, 36000, Guanajuato,
Gto., Mexico  33Lennard-Jones Laboratories, Keele University, ST5 5BG, UK
34Instituto de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de
México, Apdo. Postal 3-72, Morelia, Michoacán, 58089, México.  35Sub-Dept. of
Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson
Building, Keble Rd., Oxford, OX1 3RH, United Kingdom  36Jansky Fellow of the
National Radio Astronomy Observatory, P. O. Box 0, Socorro, NM 87801, USA
37University of Technology Sydney, 15 Broadway, Ultimo, NSW 2007, Australia
38Western Sydney University, Locked Bag 1797, Penrith, NSW 2751, Australia
39Inter-University Centre for Astronomy and Astrophysics, Post Bag 4,
Ganeshkhind, Pune 411 007, India  40Faculty of Science, UNSW Sydney, NSW 2052
Australia

###### Abstract

We present the most sensitive and detailed view of the neutral hydrogen (Hi)
emission associated with the Small Magellanic Cloud (SMC), through the
combination of data from the Australian Square Kilometre Array Pathfinder
(ASKAP) and Parkes (Murriyang), as part of the Galactic Australian Square
Kilometre Array Pathfinder (GASKAP) pilot survey. These GASKAP-HI pilot
observations, for the first time, reveal Hi in the SMC on similar physical
scales as other important tracers of the interstellar medium, such as
molecular gas and dust. The resultant image cube possesses an rms noise level
of 1.1 K (1.6 mJy/beam) per 0.98 km s-1 spectral channel with an angular
resolution of 30′′ ($\sim$10 pc). We discuss the calibration scheme and the
custom imaging pipeline that utilizes a joint deconvolution approach,
efficiently distributed across a computing cluster, to accurately recover the
emission extending across the entire $\sim$25 deg2 field-of-view. We provide
an overview of the data products and characterize several aspects including
the noise properties as a function of angular resolution and the represented
spatial scales by deriving the global transfer function over the full spectral
range. A preliminary spatial power spectrum analysis on individual spectral
channels reveals that the power-law nature of the density distribution extends
down to scales of 10 pc. We highlight the scientific potential of these data
by comparing the properties of an outflowing high velocity cloud with previous
ASKAP+Parkes Hi test observations.

###### doi:

10.1017/pas.2024.xxx

###### keywords:

Small Magellanic Cloud – Hi line emission – Dwarf irregular Galaxies –
Interstellar medium

##  1 INTRODUCTION

The evolution of the interstellar medium (ISM), which is driven by processes
such as gas infall, star formation and subsequent stellar feedback, is
fundamentally linked to the formation and overall evolution of galaxies.
Stellar feedback in the form of outflows from sites of massive star formation
greatly influences the overall anatomy of the ISM by means of the enrichment
of heavy elements (Nomoto et al., 2013), mixing (Kreckel et al., 2020), and
transfer of kinetic energy (Fierlinger et al., 2016). In terms of gas infall —
which ultimately fuels star formation — the accretion of diffuse gas onto the
disks of galaxies is the leading explanation for how galaxies have continued
to form stars while retaining a nearly constant atomic neutral hydrogen (Hi)
content since $z\sim$2 (Noterdaeme et al., 2012; Madau & Dickinson, 2014).
Hydrogen is characterized into several phases in models of the ISM (e.g.,
Wolfire et al. 1995, 2003; Vázquez-Semadeni 2012), assuming solar metallicty:
molecular (H2; $T$ $\leq$ 50 K), cold neutral medium (CNM; $T$ $\sim$ 100 K),
lukewarm neutral medium (LNM; 100 K$\leq T\leq$ 6000 K), warm neutral medium
(WNM; $T\geq$ 6000 K), and ionized ($T\geq$ 8000 K). While hydrogen in all its
phases dominates the composition of the ISM (Wolfire et al., 1995, 2003;
Kalberla & Haud, 2018), the densest and coolest regions that host and fuel
site of star formation contain mostly molecular gas, including the CO-dark
phase consisting of H2 that lies outside carbon monoxide (CO) emitting regions
(T$\sim$10 K; $n\sim$1000 cm-3; Gnedin et al. 2009).

There is an abundance of theoretical work that describes the astrophysics
behind the life cycle of the multi-phase ISM (e.g., McKee & Ostriker 1977;
Wolfire et al. 2003; Audit & Hennebelle 2005; Vázquez-Semadeni 2012); however,
there are few observational studies that thoroughly explore the interconnected
roles of dense molecular gas, dust, and the cold and warm neutral phases as
traced by Hi at equivalent spectral ($<$ 1 km s-1) and physical pc scales.
This paper introduces the first images from the Hi pilot observations of the
Galactic Australian Square Kilometre Array Pathfinder (GASKAP; Dickey et al.
2013) Survey, which aims to explore the relationship between Hi and other
fundamental phases of the ISM within the Milky Way and nearby Magellanic
System.

The proximity of the Large and Small Magellanic Clouds (LMC and SMC), two
nearby dwarf galaxies at the respective distances of 50 kpc and 60 kpc
(Hilditch et al., 2005; Pietrzyński et al., 2013), makes them a unique
laboratory for the detailed study of the impact from powerful outflows on the
makeup of the surrounding ISM and thus the overall regulation of star
formation. The GASKAP Hi spectral line cubes possess the sensitivity, angular
resolution, and spectral resolution to study the ISM at scales approaching the
molecular gas observed with ALMA ($\sim$0.5′′ to 3′′; 0.15 pc to 0.90 pc at
the distance of the SMC) and comparable to dust as revealed by space-based
telescopes in the far-IR such as the Spitzer Space Telescope and the Herschel
Space Observatory ($\sim$20′′ to 40′′; 6 pc to 12 pc at the distance of the
SMC). McClure-Griffiths et al. (2018) and Dempsey et al. (2020) identified
cool Hi outflows around the SMC in emission and absorption, respectively.
Furthermore, Di Teodoro et al. (2019b) detected for the first time 12CO gas
entrained within one of these Hi outflows at anomalous SMC velocities. The
presence of molecular gas within outflowing Hi at velocities exceeding the
escape velocity suggests that the SMC could eject its entire cool gas
reservoir that fuels star formation within $\sim$1–3 Gyr, while also enriching
the surrounding circum-galactic medium and ultimately feeding this gas to the
Milky Way. On the other hand, the reservoir of cold gas could be replenished
by gas infall, which has been suggested for regions of the LMC from the
Magellanic Bridge based on anomalous kinematic features in Hi (Indu &
Subramaniam, 2015). The pilot GASKAP observations presented here are ideal for
the detailed study of both inflowing and outflowing Hi and high velocity
clouds (HVCs) around the SMC and the beginnings of the Stream and Bridge,
which will ultimately inform important constraints on the future evolution of
the Magellanic System and Milky Way.

Turbulence is another key process that drives the evolution of the ISM
(Elmegreen & Scalo, 2004; Mac Low & Klessen, 2004) on a variety of length
scales. For example, the accretion of circumgalactic material (Klessen &
Hennebelle, 2010), galactic-scale gravitational instabilities, and
magnetorotational instabilities likely inject turbulent energy on large scales
($>$ kpc; Krumholz & Burkhart 2016; Ibáñez-Mejía et al. 2017), while stellar
feedback from outflows and supernova explosions inject energy on smaller
scales ($\sim$ 10 pc; Padoan et al. 2016; Grisdale et al. 2017). Similar to
studies of star formation, there are a multitude of theoretical works that
characterize turbulence over a range of length scales and density regimes
(Kowal & Lazarian, 2007; Padoan et al., 2012; Agertz et al., 2015); however,
few observational studies have attempted to probe turbulent properties in the
context of a multi-phase ISM over similar physical scales (Stanimirović et
al., 1999; Padoan et al., 2006; Burkhart et al., 2010; Pingel et al., 2013).
Specific to the SMC, Szotkowski et al. (2019) used early pilot ASKAP
observations to investigate spatial variations of the Hi power spectrum and
found the spectral slopes to be relatively uniform. Kalberla & Haud (2019)
investigated the turbulent properties of Hi separated into the CNM, LNM, and
WNM to reveal that each phase has distinct turbulent properties. Eden et al.
(2021) analyzed the two-dimensional spatial power-spectrum of maps of the
dense gas mass fraction derived independently from a combination of H2 column
density estimated from dust continuum and the ratio of CO intensities to show
$\sim$10 pc is the characteristic scale for the largest variations in the
clump and star formation efficiencies in CO-traced clouds formed by supersonic
turbulence. Pingel et al. (2018) explicitly compared the turbulent properties
of several multi-wavelength tracers in the Perseus molecular cloud including
dust, Hi, and CO. Each tracer showed characteristics of a distinct turbulent
environment, such as self-gravitating, supersonic medium in the dust and
mostly transonic medium in the Hi. Each of these studies were able to draw
conclusions on how turbulence influences the structure and dynamics of
different ISM phases. However, a true multi-phase characterization of ISM
turbulence has been limited by differences in the angular and spectral
resolutions of observational data.

The GASKAP survey is designed as a high angular and spectral resolution ASKAP
survey of the Milky Way Galactic plane and the Magellanic System in Hi and
hydroxyl (OH) spectral lines at frequencies of $\lambda=21~{}{\rm cm}$ and
$18~{}{\rm cm}$. The Hi component of the GASKAP survey (hereafter referred to
as GASKAP-HI) will probe the properties of Hi in our own Galaxy and the nearby
Magellanic System at unprecedented spatial resolution ($\sim$10 pc at the
distance of the SMC), similar to the scale of individual dark and star forming
regions in Galactic molecular clouds (e.g., Perseus, Lee et al. 2012) and
spectral ($\sim$0.5 km s-1) resolutions. The OH component of GASKAP will serve
as an important probe of the molecular content of the ISM not associated with
CO emission (Allen et al., 2012; Allen et al., 2015; Busch et al., 2021). The
survey’s primary objective is to follow the cycle of gas evolution from
diffuse, warm Hi through cold Hi, to molecular gas as traced by OH, and
finally to star formation and evolution through OH masers (Dickey et al.,
2013).

Many previous surveys have looked at the Hi in the Galaxy and Magellanic
System. However, previous large-area single dish surveys of the Hi (McClure-
Griffiths et al., 2009; Kerp et al., 2011; Peek et al., 2018; Martin et al.,
2015; HI4PI Collaboration et al., 2016) have all lacked sufficient spatial
resolution to probe the structure and dynamics at small scales.
Interferometers, on the other hand, sacrifice surface brightness sensitivity
(Braun & Walterbos, 1985; Stanimirović, 2002) for high angular resolution in
order to reveal bright, small-scale structures with narrow velocity widths.
GASKAP-HI builds on the Canadian Galactic Plane Survey (Taylor et al., 2003),
Southern Galactic Plane Survey (SGPS; McClure-Griffiths et al. 2005), VLA
Galactic Plane Survey (VGPS; Stil et al. 2006), the HI/OH Recombination-line
Survey of the Inner Milky Way (THOR; Beuther et al. 2016), the Southern
Galactic Centre Survey (McClure-Griffiths et al., 2012), and surveys of the
Magellanic System (Kim et al., 1998; Staveley-Smith et al., 1997; Stanimirović
et al., 1999) by increasing the angular resolution to arcsecond scales (a
factor of two increase relative to SGPS and VGPS), increasing the spectral
resolution to 0.5 km s-1 (useful to probe kinetic temperatures of $\sim$6 K),
and expanding the instantaneous $uv$-coverage to characterize a virtually
continuous range of spatial frequencies. Combining these novel GASKAP-HI data
with data from the 64 m Parkes single dish telescope (Murriyang) will allow,
for the first time, a view of nearby Hi emission at similar physical scales as
dust and molecular gas in the Magellanic System and supplement the
aforementioned surveys of the Galactic Plane. Furthermore, coupling the
detailed view of the Hi emission structure with high spectral resolution Hi
absorption measurements will facilitate accurate measurements of the spin
temperature, placing lower limits on the kinetic temperatures of the WNM and
LNM. The high number densities in CNM thermalise the Hi line in this phase
such that absorption measurements will provide the true kinetic temperature.

Each antenna element of the Australian Square Kilometer Array Pathfinder
(ASKAP; Hotan et al. 2021) telescope is outfitted with a Phased Array Feed
(PAF) receiver and a matched set of digital equipment that forms 36
simultaneous primary beams on the sky, expanding the instantaneous field of
view (FoV) from $\sim$1 deg2 to $\sim$25 deg2. The unique wide-field imaging
capability of ASKAP presents several unique data processing challenges that
the GASKAP-HI survey must address before beginning full survey operation. For
example, it is paramount to remove the inherent instrumental point-spread
function (PSF) from a sky brightness distribution that extends over the
boundaries of multiple beams without degrading the recovered structure. It is
also crucial to combine ASKAP data with data from a single dish to fill in the
missing short-spacings filtered out by the fixed antenna distribution
(Stanimirović et al., 1999; Stanimirović, 2002).

ASKAP surveys, including GASKAP, were selected in 2009 based on scientific
merit during the construction phase of the telescope. The plans and
specifications of each survey have been progressively refined in the
intervening years to match the telescope capabilities and increased computing
power, as described in Hotan et al. (2021). In late 2019, ASKAP commenced
pilot observations for each survey, allocating 100 hours of observing time to
each survey team to test full survey operations. In this paper, we present the
first GASKAP-HI pilot observations of the SMC, obtained in December 2019. The
observations are one part of a multi-faceted pilot survey, covering an
extended region of the SMC, the starts of the Magellanic Stream and Bridge, as
well as two fields in the Milky Way Galactic Plane. These images are also the
first to be produced by our custom imaging pipeline built around WSClean, a
command-line application first introduced by Offringa et al. (2014) that is
specifically designed to perform efficient wide-field imaging. This software
allows us to perform joint deconvolution distributed over a computing cluster,
which ensures accurate reconstruction of the extended Hi emission intrinsic to
the Galaxy and Magellanic System while also managing the overall memory
footprint.

This paper is structured as follows: Section 2 describes the philosophy and
parameters of the GASKAP-HI pilot survey; Section 3 explains the calibration
procedure, provides a thorough description of our custom imaging pipeline,
including the combination with Parkes data to correct for the missing short-
spacings, and discusses our quality assessment methods; Section 4 outlines the
noise properties of our final image cubes and derives the global transfer
function to fully characterize the represented spatial frequencies; Section 5
highlights the advantages of the increased sensitivity and angular/spectral
resolution through global channel maps of the SMC and presents an analysis of
a known outflowing high velocity cloud; finally, in Section 6, we summarize
these results from the SMC and anticipate future results from our other pilot
fields and the eventual full GASKAP-HI survey.

##  2 ASKAP Observations and the GASKAP-HI Pilot Survey

GASKAP-HI makes optimum use of ASKAP’s wide field-of-view and bi-modal antenna
baseline distribution with peaks near 500 m and 3000 m to simultaneously image
the diffuse emission with high surface brightness sensitivity and high angular
resolution for point sources, such as Hi absorption against continuum sources.
GASKAP-HI will give a detailed view of gas evolution in galaxies by targeting
the three very different galaxies: the Milky Way, the LMC and SMC.

GASKAP is unique amongst the ASKAP surveys in its requirement for high
spectral resolution. The standard ASKAP spectral resolution is
$\Delta\nu=1~{}{\rm MHz}$ for the continuum surveys (EMU; Norris et al. 2011;
POSSUM Murphy et al. 2013; VAST; Anderson et al. 2021) and
$\Delta\nu=18.5~{}{\rm kHz}$, optimised for extragalactic Hi surveys like
WALLABY (Koribalski et al., 2020), DINGO (Meyer et al., 2017), and FLASH
(Allison et al., 2020). By contrast, GASKAP is designed to fully resolve the
spectral linewidths observed in cold Hi, OH masers, and OH absorption,
requiring frequency resolution of $\Delta\nu\lesssim 5~{}{\rm kHz}$. This is
achieved through a ‘zoom’ mode of the ASKAP poly-phase filterbank, through
which observations can be obtained with one of several different spectral
resolutions between $\Delta\nu=0.58~{}{\rm kHz}$ and the standard resolution
of $\Delta\nu=18.5~{}{\rm kHz}$. GASKAP-HI plans to use a spectral resolution
of $\Delta\nu=1.15~{}{\rm kHz}$, giving a velocity resolution of $\Delta
v\approx 0.3~{}{\rm km~{}s^{-1}}$ over a total bandwidth of $18~{}{\rm MHz}$
spanning 15552 fine channels. We inclusively select the fine channels 7887 to
9934 $\sim$400 km s-1 to $-100$ km s-1) in the topocentric reference frame,
which captures Hi emission from the Magellanic System and Milky Way, to reduce
the total amount of data that needs processing. The center frequency of each
measurement set is 1419.81 MHz in the topocentric reference frame.

Our observations of the SMC total 20.9 h of integration, split equally into
two separate sessions. Each session is known as a schedule block (SB) and
identified with IDs (SBIDs) 10941 and 10944, making it easier to identify
observations in the CSIRO ASKAP Science Data Archive
(CASDA111https://data.csiro.au/collections/domain/casdaObservation/search/).
The PAF footprint, known as closepack36, was centered on J2000 RA =
00h58m43.280s, Dec = $-$72d31m49.03s. This particular PAF footprint places 36
simultaneously formed beams in a 6$\times$6 hexagonal grid such that the beam
centers are separated by 0.9 deg to provide more uniform sensitivity
(McConnell, 2016; Hotan et al., 2021). Throughout the observation, every 10
minutes the PAF footprint cycles through three pointing centers provided in
Table 1. This process, known as interleaving, ensures uniform sensitivity
across the FoV. Due to beams formed offset from the pointing center, it is
necessary to track the parallactic angle on the sky throughout the
interleaving process. The ASKAP antennas achieve this through a unique third
axis of rotation on the reflector itself, in addition to a simple azimuth-
elevation mount. Table 1 summarizes the observational setup.

Table 1: Summary of GASKAP-HI pilot observations. $t_{\rm int}$ is the
integration time spend on each interleave position (20.9 h total integration),
$\nu_{0}$ is the central frequency of our measurement sets (see text) in a
topocentric frame, $BW$ is the total bandwidth, $B$ is the native spectral
resolution, and $\theta_{\rm PAF}$ is the PAF rotation, which refers to the
total rotation of the footprint on the sky, including the natural $-$45 deg
rotation to align with celestial coordinates. Note that the pointing centers
were cycled every 10 minutes throughout the listed UTC date and time ranges.

Interleave |  $t_{\rm int}$ [h] |  $\nu_{0}$ [MHz] |  $BW$ [MHz] |  $B$ [kHz] | J2000 | Galactic | UTC Date & Time Range (SB10941) | UTC Date & Time Range (SB10944) |  $\theta_{\rm PAF}$ [deg]
---|---|---|---|---|---|---|---|---|---
A | 6.97 | 1419.81 | 18.5 | 1.157 | RA = 00h58m43.3s, Dec = $-$72d31m49.0s |  $l$=302.18∘, $b$=$-$44.59∘ | 2019 Dec 22 06:12:04.8 to 16:07:37.1 | 2019 Dec 23 06:06:40.8 to 16:16:39.0 |  $-$48.0
B | 6.97 | 1419.81 | 18.5 | 1.157 | RA = 01h04m26.2s, Dec = $-$72d14m31.6s |  $l$=301.53∘, $b$=$-$44.85∘ | 2019 Dec 22 06:22:21.9 to 16:17:54.2 | 2019 Dec 23 06:16:57.9 to 16:31:44.7 |  $-$49.4
C | 6.97 | 1419.81 | 18.5 | 1.157 | RA = 01h04m58.2s, Dec = $-$72d45m36.6s |  $l$=301.53∘, $b$=$-$44.33∘ | 2019 Dec 22 06:32:39.0 to 16:28:01.3 | 2019 Dec 23 06:27:05.0 to 16:41:51.9 |  $-$49.5

##  3 Data Reduction

###  3.1 ASKAPsoft Pipeline

ASKAP observations are calibrated and imaged using a high-performance
processing pipeline (Whiting, 2020; Hotan et al., 2021) that runs on the
Galaxy supercomputer at the Pawsey Supercomputing Centre. This typically
includes all of the steps necessary to calibrate the data and produce images
and spectral cubes of the observation, using the ASKAPsoft package (Guzman et
al., 2019). For the GASKAP-HI processing, since the imaging is done in the
joint-imaging pipeline described below, the ASKAP pipeline was limited to
bandpass calibration, flagging, and self-calibration of the time-dependent
gains.

####  3.1.1 Bandpass and Flux Scale Calibration and Flagging

Prior to self-calibration, the ASKAP pipeline prepares the data through
calibration of the bandpass and flagging of unwanted signal. The bandpass and
overall flux scale is calibrated using the primary flux calibrator PKS
B1934$-$638\. The target and flux calibrator data are then flagged to remove
radio-frequency interference (RFI). This employs a dynamic flagging algorithm
operating in the time-domain for each channel, which flags discrepant time
ranges based on the Stokes V flux.

Data is then averaged to form 1 MHz-wide channels (that is, averaging 864
channels together), which will be used to create the continuum images used in
the self-calibration. Those channels that are identified to contain HI
emission are then flagged for this step, so that only continuum emission
contributes to the resulting images.

####  3.1.2 Self-calibration

The derived beamforming weights are generally updated once every day or two
and require 2.5 hours of telescope overhead for calibraiton (Hotan et al.,
2021). In lieu of spending time on traditional phase calibration methods —
such as regularly observing a reference source near the science target — the
amount of flux within the wide ASKAP FoV at any given time ensures adequate
flux to utilize an in-field self-calibration scheme to correct for time-
varying phase errors. The ASKAPsoft pipeline creates continuum images for each
beam from the calibrated, flagged, and averaged science visibilities to use as
initial models. No modeling of the spectral index is performed due to the
relative narrow bandwidth.

Due to the relatively weak continuum in this field, no baselines were excluded
in the continuum imaging. For future GASKAP-HI fields on the Galactic Plane or
LMC, baselines below 500 m will be excluded. An image of the field is produced
with the ASKAPsoft BasisfunctionMSF solver with Hogbom clean and a shallow sky
model of the field is made from that image. A total of 257 w-planes are used
in this image. This model is used to calibrate the complex gains over short
intervals ($\approx 30$ sec) across the entire observation. To preserve the
flux scale, we perform phase-only self-calibration by fixing the amplitude of
the calibration parameters to 1. The resulting calibration parameters are
applied to both the continuum and spectral visibility data sets, and a
subsequent continuum image is made using the calibrated data.

###  3.2 Observation Diagnostics

The size of the calibrated visibilities from a typical GASKAP-HI field,
consisting of roughly 20 hours of integration time, 2048 spectral channels,
and 108 total beams (36 beams$\times$3 interleaves) in closepack36
configuration, totals $\sim$ 7 TB. Before expending the large effort required
for spectral line imaging to create an 11 GB image cube, it is important to
understand the quality of an observation. This allows us to verify that the
observation is suitable for its intended science use. In particular, we need
to know whether

  * •

the sensitivity across the field is even, so that features can be compared
across the field;

  * •

there are enough data available from short baselines to provide good
sensitivity to large scale structure and low surface brightness features;

  * •

there are enough data available from long baselines to adequately sample fine
structure and to detect absorption;

  * •

the calibration bandpasses are reasonably free of structure.

We produce a diagnostics report to describe the quality of the
observation.222https://casda.csiro.au/validation/10941/AS108/validation_gaskap_10941/
and https://casda.csiro.au/validation/10944/AS108/validation_gaskap_10944/ It
summarises and visualises outputs produced by the ASKAPsoft (Guzman et al.,
2019) pipeline up to the production of calibrated measurement sets, along with
the continuum image and source catalogue of the field. The report provides a
snapshot of the overall quality and is generally sufficient to determine
whether to proceed with imaging or re-observe.

The first two sections of the report provide details of the observation and
the continuum image. In the observation we need to know where the field is and
how it was observed — duration, beam pattern (or PAF footprint), and the
correlator mode. The footprint is also used later to determine the layout of
beam based plots. Noting that the continuum data is well covered by the ASKAP
continuum validation report, the continuum image report is limited to basic
details.

To allow assessment of the calibration we visualise the median calibration
bandpasses both by beam and by antenna. In the plots we highlight up to 10
bandpasses that either have

  1. a)

a median more than one standard deviation from the median of all bandpasses,
or

  2. b)

an amplitude range that is more than one standard deviation from the median
amplitude range of all bandpasses.

The first rule highlights antenna sensitivity issues and the second calls out
structure in the calibration bandpasses. As the raw ASKAP visibilities are not
retained to manage disk space, recalibration is not possible, so any problems
reflected here would generally mean the dataset needs to be rejected and the
field re-observed.

In the diagnostics section, we largely focus on what data have been flagged by
the ASKAPSoft pipeline (see Section 3.1.1) within the measurement sets and the
effect this has on the suitability of the dataset for different science cases.
The flagging of the measurement sets is done in four dimensions: by baseline
(or combinations of antennas), by beam, by channel, and by time. Flagging is
generally used to remove bad data from the dataset, whether for an antenna
that is performing incorrectly, an antenna that is in the shadow of another
antenna with respect to the target source, or for radio frequency
interference. We provide plots of the flagging

  1. a)

by baseline, (see Figure 1), which shows if there is any bias in coverage by
angular scale,

  2. b)

by time to show if our u-v coverage is even, and

  3. c)

by percentage of each baseline flagged to highlight frequency based flagging.

For example, the histogram of the baseline coverage across all beams and all
channels for the entire observation for SBID 10944 in Figure 1 shows a
majority of the available baselines remain unflagged during this scheduling
block. Figure 1 also demonstrates that flagged baselines are evenly
distributed across the entire range of available baselines. This ensures there
are no unexpected gaps in the continuous $uv$-coverage, which would lead to
potential artifacts at particular spatial scales in the final images. The two
distinct peaks between 400 and 1200 m, and 2 km and 3 km are ideal for
synthesised beam sizes between 30′′ to 60′′ to detect Galactic and Magellanic
Hi in emission. The longest baseline of 6 km produces a beam size of
$\sim$10′′ that is necessary for absorption measurements. All diagnostic plots
are sourced from the flagging summary files for each measurement set. As is
done in the WALLABY diagnostics (For et al., 2019; Koribalski et al., 2020),
the linked diagnostic reports also provide plots of

  1. a)

the fraction flagged by beam,

  2. b)

the number of antennas flagged in each beam and from these,

  3. c)

the expected RMS per channel for each beam of the observation.

Figure 1: Baseline coverage for the ASKAP-36 array showing the proportion of
baselines flagged and unflagged in the observation. The flagging proportion is
measured across all beams and all channels. However, any time periods where
the data is entirely flagged are excluded. The blue profile shows all
available baselines, while the transparent orange profile denotes unflagged
baselines. A histogram of the flagged baselines (excluding the automatically
flagged autocorrelations) is outlined by the dotted line. The two vertical
dotted lines represent the definition for short ($l_{\text{baseline}}<500$ m)
and long baselines ($l_{\text{baseline}}>2000$ m)

To assist the assessment of quality of the observation we report five metrics
on a good, uncertain, and bad scale.

  1. 1.

The percentage of data flagged from short baselines ($l_{\text{baseline}}<500$
m). These are crucial for large scale emission and low surface brightness
sensitivity.

  2. 2.

The percentage of data flagged from long baselines ($l_{\text{baseline}}>2000$
m). These baselines are essential for tracing fine detail and for detecting
absorption.

  3. 3.

The percentage difference of the expected RMS across the field:

$\text{difference}=\frac{\rm RMS_{\text{exp,max}}-RMS_{\text{exp,min}}}{\rm
RMS_{\text{exp,min}}}$ (1)

which is used to show how even the sensitivity is across the field.

  4. 4.

The percentage of integrations with less than 5% of channels flagged. In
observations of local Hi we do not want the diffuse emission spectral lines
flagged out.

  5. 5.

The number of unflagged antennas with a phase RMS $\geq 40^{\circ}$. These are
antennas where the phase solutions are severely unstable over the course of
the observation, leading to poor positional accuracy.

These metrics are made available both in the report and on CASDA (Huynh et
al., 2020). The metrics and their threshold values are shown in Table 2. For
an observation to be acceptable for emission studies, both the short baseline
and the expected RMS variance tests must be in the uncertain or good ranges.
For an observation to be acceptable for absorption studies, both the long
baseline and the expected RMS variance tests must be in the uncertain or good
ranges.

Table 2: Observation Diagnostics Metrics Metric | Good | Uncertain | Bad | Units
---|---|---|---|---
Flagged Short Baselines | $<20$ | $20-40$ | $\geq 40$ | percent
Flagged Long Baselines | $<30$ | $30-45$ | $\geq 45$ | percent
Expected RMS Variance | $<10$ | $10-30$ | $\geq 30$ | percent
Unflagged Integrations | $>70$ | $70-50$ | $<50$ | percent
Bad Phase Antenna | $0$ | $1-2$ | $\geq 3$ | antenna

Based on these metrics, we find that the observations presented here are
suitable to use for emission line analysis. Whilst antennas (denoted by the
prefix ‘ak’) ak06 and ak32 are completely flagged out, the flagging is even
across baseline lengths, with flagging percentages of 16% on short baselines
and 25% on long baselines (denoted by the dashed lines in Figure 1). There is
increased flagging on integrations around the change of interleaves. In
scheduling block 10941, the last integrations for the observation in all
interleaves are heavily flagged. The calibration bandpasses exhibit structure
with small amplitudes, including dips at the 1 MHz beam forming intervals.
These dips are not an issue for GASKAP-HI due to our relatively narrow
bandpass.

###  3.3 Joint-Imaging Pipeline

The PAF receivers equipped on each ASKAP antenna extend the typical FoV for a
12 m diameter antenna from $\sim$1 deg2 to $\sim$25 deg2 by simultaneously
forming 36 distinct primary beams. Standard full-field ASKAP images are
produced by deconvolving the inherent PSF response from the sky-brightness
distribution of each separate beam independently and then linearly mosaicking
them together. This approach works for most other ASKAP surveys, as the
emission is small scale (e.g., distant galaxies with small angular size) and
generally is contained within a single beam. Such techniques work less well
for GASKAP-HI because the targeted diffuse Hi emission extends up to the
boundaries of the primary beam. To ensure we accurately recover the
distribution of structure down to baselines corresponding to the size of the
primary reflectors themselves (i.e., 12 m), fill in gaps between all the short
baselines, and deconvolve the images deeper, we must utilize a joint
deconvolution approach. Here, a large image is created from the ourier
inversion of the sampled visibilities from all beams (i.e., the ‘dirty image’)
before proceeding with deconvolution. Since the calibrated visibilities from
all of the beams must be managed simultaneously in a joint deconvolution
approach, the computation requirements — specifically the memory footprint —
are immense relative to other imaging techniques. As of publication, ASKAPsoft
1.3.0333https://www.atnf.csiro.au/computing/software/askapsoft/sdp/docs/current/general/releaseNotes.html,
the primary processing software utilized to image all other ASKAP data, is not
fully optimised to run a distributed joint deconvolution scheme.

Figure 2:  A flow chart summarizing the workflow of our custom pipeline used
to image a typical GASKAP-HI field. In brief, the phase centers for each of
the 108 measurement sets, which contain the gain-calibrated visibilities per
beam (36 beams$\times$3 interleaves), are set to single value using the
chgcentre utility available through the WSClean package. These altered
measurement sets can be binned and put through a $uv$-based continuum
subtraction scheme, respectively using the CASA tasks split and uvcontsub
within the scripts bin_All and uvcontsub_All, that is submitted in a
distributed manner for efficient processing. Single spectral channels are then
split out to ensure reasonable memory management. A series of batch jobs, each
utilizing 4 total CPU cores, are submitted with the 108 measurement sets per
spectral channel as input to the WSClean command-line imager to produce a
jointly deconvolved image. The final deconvolved images are then collated into
a single cube before combination with Parkes data to fill in the missing
short-spacings (see Section 3.3.3). The pipeline processes are represented as
rectangles, actual input/output of these processes are represented by
parallelograms, and the action of input is represented by the curved arrows.

We instead developed a custom imaging
pipeline444https://github.com/nipingel/GASKAP_Imaging that utilizes a
combination of Common Astronomy Software Application (CASA; McMullin et al.
2007) tasks to pre-process of the measurement sets,
WSClean555https://gitlab.com/aroffringa/wsclean to grid the multiple ASKAP
pointings onto a single grid for joint deconvolution using corresponding
primary beam models for each ASKAP primary beam, and miriad (Sault et al.,
1995) tasks to combine ASKAP and Parkes data to correct for short-spacings.
This imaging package enables efficient gridding of visibilities and stable
deconvolution, as demonstrated by the high-fidelity images produced of the
Galactic Centre with the MeerKAT telescope (Heywood et al., 2019). We input
the ASKAP primary beams measured from holography at 1.4 GHz (Hotan et al.,
2021) to ensure highly accurate gridding of the gain-calibrated visibilities
and scaling of the components subtracted from the dirty image during
deconvolution major and minor iterations, respectively. The pipeline takes
advantage of a high-performance computing (HPC) environment, while also
managing the memory footprint, by submitting simultaneous batch imaging jobs
of individual channels. A majority of the processing was performed with the
Avatar computing cluster located at the Australian National University
Research School of Astronomy and Astrophysics. The configuration of WSClean
imaging mode and resource allocation is performed by bash scripts specific to
both the Portable Batch System (PBS) and Simple Linux Utility for Resource
Management (SLURM) scheduling software.

Figure 2 summarizes the work flow of our joint-imaging pipeline to image a
single GASKAP-HI field. We download from CASDA 108 measurement set files that
contain the gain-calibrated visibilities for a field observed in the
closepack36 beam configuration. We then use the built-in WSClean tool
chgcentre to phase-rotate the visibilities to Pointing center 1 listed in
table 1, thus setting a common direction where all phases are zero and
effectively sets the center of the resultant image. To avoid smearing and
noncoplanar baseline effects (see Cornwell et al. 2005), such as the
distortion of sources sitting far away from the phase center, the phase
information in the measurement sets is updated during gridding based on the
individual beam phase centers provided to WSClean via a configuration file.

####  3.3.1 Binning and uv-based Continuum Subtraction

Figure 3:  The mean amplitude of XX and YY correlations averaged over 10000 s
as a function of binned channel for a central ASKAP beam taken from the
baseline between ak04 and07. The Hi emission-free channel range used to fit
and subtract a first order polynomial model of the continuum is denoted by the
shaded regions.

For the purpose of increasing the signal-to-noise ratio (SNR), we first bin
each measurement set by four channels, achieving a spectral resolution of
4.628 kHz ($\sim$0.98 km s-1 at the rest frequency of Hi) for a single
channel.

It is also necessary to remove the contribution from continuum sources in the
field to ensure we infer the correct physical properties of the Hi gas and to
aid deconvolution. We select a range of Hi emission-free channels by plotting
a mean spectrum from the visibilities contained in several central beams and
baselines between core antennas, which is expected to contain the brightest
emission. An example spectrum is shown in Figure 3. The continuum is removed
from the $uv$ spectra for each individual beam by fitting and subtracting a
first order polynomial to both the real and imaginary visibility spectra over
the binned channel range from 0 to 140 (1418.63 MHz to 1419.28 MHz), 300 to
340 (1420.01 MHz to 1420.20 MHz), and 400 to 500 (1420.48 MHz to 1420.94 MHz),
as no emission from the SMC or foreground Milky Way is observed in these
channels.

####  3.3.2 Joint Deconvolution

Table 3: WSClean parameters. See https://wsclean.readthedocs.io/_/downloads/en/latest/pdf/ for comprehensive documentation on these parameters. Parameter | Value [units]
---|---
size | 5000x5000 [pixels]
scale | 7 [′′]
niter | 25,000
mgain | 0.7
multiscale-scales | 0, 8, 16, 32, 64, 128, 256
multiscale-scale-bias | 0.85
weight | Briggs
robust parameter | 0.9
threshold | 5 [mJy]
beamsize | 30 [′′]

Individual channels are split out from each of the 108 measurement set files
to best manage the large memory footprint required by joint deconvolution. The
imaging of each channel is submitted as a separate batch job that utilizes a
total of 4 cores to take advantage of the built-in parallelization of multiple
compute threads. Table 3 summarizes the typical configuration to process a
single channel with significant emission. We perform a multiscale CLEAN
deconvolution (Cornwell, 2008) with: a pixel size (i.e., scale parameter) of
7′′, multi-scale scales set to 0, 8, 16, 32, 64, 128, and 256 pixels (angular
range between 0′′ to 30′), the total number of iterations (niter) set to
25,000, and mgain set to 0.7, meaning that the peak flux must be reduced by
70% to trigger the next major iteration; typical runs go through two to three
major iterations.

We set the auto-threshold parameter to 3, which sets the global stopping
threshold as 3 times the measured background noise. This value is
automatically computed at the end of each major iteration by measuring the
median absolute deviation (MAD) of the noise. In general, these parameters
allow the deconvolution to run until the peak residual reaches the global
stopping threshold. We set this threshold to 5 mJy, which is $\sim$2.5 times
the expected noise level, to avoid cleaning too deeply into the noise. The
‘smallscalebias’ parameter is set at 0.85 to bias the multiscale deconvolution
towards the smaller scales and aid cleaning of the expected small-scale
features, and the gridded visibilities are weighted (without excluding any
baselines) with a Briggs weighting scheme with a robust parameter of 0.9 to
generate a PSF with higher sensitivity but still reasonable sidelobe levels.

The final deconvolved images are spatially smoothed such that the final
restoring beam is 30${}^{\prime\prime}\times$30′′ as a compromise between
sensitivity to extended structure and final angular resolution. This is
comparable to the synthesized beam size expected from our robust weighting
applied to the $uv$ coverage. The total time to image a typical channel ranged
between 4 to 8 hours, depending on the complexity of the emission present in
the channel and number of major iterations. We find that the processing is
generally memory limited, though processing of other pilot fields will
increase optimisation and determine clear limitations.

####  3.3.3 Filling in the Missing Short-Spacings

The size of the primary reflectors on each antenna is an inherent physical
limitation of how closely individual elements of an interferometer can be
placed, thus filtering out the low spatial frequencies corresponding to the
dish diameter (and below) and eliminating sensitivity to large angular scales.
These missing baselines are commonly referred to as the missing short-
spacings. Observations of the same area of the sky with a large single dish
telescope with sufficient overlap in the $uv$-plane can be used to fill in the
baseline samples below that of the minimum spacing between antennas
(Stanimirović, 2002) (i.e., the shortest baseline), including the total power
at $u$ = $v$ = 0. The total flux and structure of diffuse emission on scales
larger than that sampled by the shortest baseline is then recovered in the
final map.

Several established techniques are available to combine interferometric and
single dish observations either in the $uv$-plane after deconvolution (e.g.,
Stanimirović 2002; Cotton 2017), the image plane directly (Faridani et al.,
2018) or through approximating the single dish data as artificial visibilities
to be included in the image reconstruction process applied to interferometer
data (Koda et al., 2011; Koda et al., 2019). More recently, Rau et al. (2019)
have developed a generic joint reconstruction algorithm called SDINT that
combines aspects from several of the aforementioned approaches. Given the
extremely extended nature and complexity of our targeted emission, we utilize
the most commonly used combination method called feathering, where the
combined image is constructed by computing the weighted sum of the single dish
and interferometer data in the $uv$-plane.

We use the miriad task, IMMERGE, to feather a cube extracted from the Parkes
Galactic All-Sky Survey (GASS666https://www.astro.uni-bonn.de/hisurvey/gass/;
McClure-Griffiths et al. 2009) with our deconvolved ASKAP image. This cube was
centered on the SMC and re-gridded to be on the same spectral and spatial grid
before combination. IMMERGE combines the two data sets by Fourier transforming
both the deconvolved ASKAP-only and Parkes images. The Parkes data are then
scaled by the ratio of the solid angle of the two beams,

$\alpha=\frac{\Omega_{\rm ASKAP}}{\Omega_{\rm Parkes}},$ (2)

where we find $\alpha$ to equal 9.77$\times$10-4, assuming the Parkes beam is
a Gaussian with a full-width at half maximum (FWHM) of 16′ at 1.4 GHz
(Kalberla et al., 2010). This factor accounts for the difference in flux
density of the two data sets based solely on the differences in resolution.
The ASKAP $uv$ data are then scaled by the factor

$\beta=1-\mathscr{F}[B_{\rm Parkes}],$ (3)

where the second term represents the 2D Fourier transform ($\mathscr{F}$) of
the Parkes beam, $B_{\rm Parkes}$. The two scaled $uv$ data sets are then
summed and Fourier transformed back to the image plane. The scaling depicted
in Equation 3 ensures the effects of the poorly sampled low spatial
frequencies in the ASKAP data are smoothly removed before the well-sampled low
spatial frequencies provided by the Parkes data are added. The effective beam
of the resultant image is the same as the original ASKAP restoring beam. The
above scaling assumes the two data sets are perfectly flux calibrated;
however, technical issues introduced by stray radiation and spillover make
single dish data notoriously difficult to correctly flux calibrate.

We take an interactive approach to determine the ideal flux calibration
factor, henceforth referred to as the single dish factor (SDF), by setting the
factor keyword in IMMERGE to be 0.5, 1.0, and 2.0 and then divide out this
same factor in the resulting cube to conserve flux. This wide range of
possible SDF values is useful to investigate the extremes of overestimating
and underestimating the correction. We then compute the spatial power spectrum
(SPS) of several spectral channels. The SPS is defined as

$P\left(k\right)=\mathscr{F}\left(k_{\rm RA},k_{\rm
Dec}\right)\times\mathscr{F}^{*}\left(k_{\rm RA},k_{\rm Dec}\right),$ (4)

where $k$ is the magnitude ($k=\sqrt{k_{\rm RA}^{2}+k_{\rm Dec}^{2}}$) of the
wavenumber ($k_{\rm RA/Dec}=\theta_{\rm RA/Dec}^{-1}$, where $\theta_{\rm
RA,Dec}$ is the angle on the sky along RA and Dec in rad),
$\mathscr{F}\left(k_{\rm RA},k_{\rm Dec}\right)$ is the 2D Fourier transform
of the image under study, and the ∗ symbol represents the complex conjugate.
This is a two-point correlation function that measures how power (i.e.,
structure) is distributed across spatial scales. In practice, the distribution
of power is measured by computing the 2D Fourier transforms of the integrated
intensity images and measuring the median power in progressively larger
annuli.

Figure 4: The SPS profiles of the spectral channel centered on 151.3 km s-1
made from an ASKAP-only cube (solid blue), Parkes (solid orange), and several
ASKAP+Parkes cubes where the sdfactor parameter (referred to as SDF in the
text) in miriad’s IMMERGE, which applies a scale factor to the single dish
data before the combination in order to correct for potential flux offsets, is
varied. The orange and blue dotted vertical lines denote the maximum
recoverable scale of ASKAP based on the smallest baseline distance of 22 m and
restoring beam size, respectively. Note that the profile for the SDF=1.0
values lies exactly on top of the ASKAP-only profile towards the smaller
angular scales.

Figure 4 shows the SPS profiles of the spectral channel centered on 151.3 km
s-1 in the Local Standard of Rest Kinematic (LSRK; Gordon 1976) reference
frame produced from combinations that vary the SDF, as well as profiles from
the deconvolved ASKAP-only cube and re-gridded Parkes image. Clearly, there is
a dearth of power at large scales in the ASKAP-only image, while there is a
large decrease in power detected in the Parkes image at scales below the
larger single dish beam. All combinations recover the power at large scales
since the feather procedure is designed to scale the flux density on those
scales to that of the single dish. Interestingly, the variation in SDF has the
most notable effect on the power at small scales. When the SDF is
underestimated and less than one, the power increases at small scales because
the scaling to conserve flux after the combination introduces a multiplicative
factor that increases the flux of the already existing small-scale structure
in the ASKAP-only image. When SDF is overestimated, the power decreases at
small scales because the low resolution single dish data effectively washes
out the observed small-scale structure.

We find that an SDF of 1.0 produces virtually an exact agreement with the
ASKAP-only profile that extends from the maximum recoverable scale of
$\sim$33′ down to the size of the 30′′ restoring beam. Figure 5 shows the
negative bowls in the ASKAP-only data, which are caused by the filtering of
spatial frequencies corresponding to structures on the largest scales, are
completely filled when applying a SDF of 1.0 during the combination. A SDF of
1.0 is reassuring and ensures we do not risk misrepresenting the observed
structure by over or under-weighting the power at a given scale. Most
importantly, the interesting structures at small scales are not washed-out.
SDF values of 0.9 and 1.1 produce noticeable offsets in the SPS profiles,
strengthening our conclusion. While we do not show an uncertainty envelope on
the SPS profiles for the sake of clarity, Section 4.3 demonstrates that the
typical uncertainties on individual power values are on the order of 5%.

Figure 5:  A comparison between the ASKAP-only (left) and resultant combined
ASKAP+Parkes image (right) for a single spectral channel centered on 151.3 km
s-1 in the LSRK reference frame. The optimal SDF factor of 1.0 was applied
during the combination.

###  3.4 Quality Assessment

The spectral line cubes produced from GASKAP-HI observations also need to be
validated, both to determine their suitability for science use and also to
compare different processing techniques. We aim to validate the representation
of the diffuse Hi of the Galactic plane and the Magellanic System in the
following ways:

  * •

that large scale emission is present in velocity ranges where it is expected
and not present where not expected, based on previous surveys;

  * •

that the noise level in the emission-free velocity range is close to
theoretical, but not below, and is even across the cube; and

  * •

that spectra taken at the locations of selected targets, such as against
bright sources, do not show any periodic features.

We validate the spectral line data at the ASKAP-only stage rather than after
they have been combined with Parkes data. This allows us to compare the ASKAP-
only data with data from GASS; McClure-Griffiths et al. 2009) in our tests for
expected presence and absence of emission. It also provides a more rigorous
test of noise levels in the ASKAP data.

To check for the presence or absence of emission, we define two $\Delta
v\approx 40~{}{\rm km~{}s^{-1}}$ regions where Hi line emission is either
present or not present in the GASS cube. We extract a slab from the ASKAP cube
covering each velocity region and use BANE (part of the Aegean suite; Hancock
et al. 2018), to produce a large-scale emission line image of each slab. The
large-scale emission line images exclude Hi point sources and smooth small-
scale fluctuations based on the synthesised beam size. We assess the maximum
flux density level of these images against the thresholds in Table 4.

We assess the spectral line noise by taking the standard deviation of each
pixel of the off-line slab (as described above) along the spectral axis. We
then compare the median value of this noise map to a fiducial value, the
theoretical noise, with the thresholds listed in Table 4. The theoretical
noise, at the beam centre and for natural weighting, is calculated as

$\sigma_{F}=\frac{\rm SEFD}{\epsilon_{\rm c}\sqrt{n_{\rm pol}n_{\rm
ant}(n_{\rm ant}-1)\Delta_{\rm f}t_{\rm 0}}}$ (5)

where SEFD is the System Equivalent Flux Density, $\epsilon_{\rm c}$ is the
correlator efficiency, npol is the number of polarisations, nant is the number
of antennas, $\Delta_{\rm f}$ is the channel width and t0 is the duration of
the observation. ASKAP has a SEFD = 1800 Jy, n${}_{\rm pol}=2$, and n${}_{\rm
ant}=$ 36 (Hotan et al., 2021). We assume that $\epsilon_{\rm c}$ is included
in the SEFD as the SEFD is measured through observations, but it should be
$\sim 1$ regardless (see Table 5). A typical GASKAP-HI observation of
t${}_{\rm 0}=20$ hours with $\Delta_{\rm f}=5$ kHz channels gives
$\sigma_{F}=1.89$ mJy/beam.

Figure 6: Map of the spectral line noise for the ASKAP-only SMC cube from scheduling blocks 10941 and 10944. There is high noise at the edges of the cube and a notable cross-hatch low level noise pattern in the main area of the cube. However, it shows a generally low and consistent noise level across the main area of the cube, with a median noise level of 2.34 mJy beam-1, 1.24 times theoretical. Table 4: Spectral Line Cube Diagnostics Metrics. These are the thresholds for the different quality tests on GASKAP-HI spectral line cubes to assess them with a rating of good, uncertain or bad. Metric | Good | Uncertain | Bad | Units
---|---|---|---|---
On-line emission | $\geq 20$ | $20-12$ | $<12$ | ${\rm Jy~{}beam^{-1}~{}km~{}s^{-1}}$
Off-line emission | $<5$ | $5-12$ | $\geq 12$ | ${\rm Jy~{}beam^{-1}~{}km~{}s^{-1}}$
Spectral Noise compared to theoretical noise | $<\sqrt{2}$ | $\sqrt{2}-2\sqrt{2}$ | $\geq 2\sqrt{2}$ | –
Spectra with periodic features | 0 | $1-4$ | $\geq 5$ | –

Lastly, we validate spectra extracted both from the locations of the 15
brightest sources (as identified in the continuum catalogue) and the centre of
each beam. At each position we extract a single pixel spectrum and plot these
spectra for visual inspection. We assess the spectra using a partial
autocorrelation function (PACF) to identify any periodic features in each
spectrum, requiring a 3-sigma result to classify a feature as periodic. We
rate the dataset based on the number of spectra with periodic features as
shown in Table 4.

We can use these metrics on the ASKAP-only image cube for the SMC field to
assess its quality. Emission is present (21 Jy beam-1 km s-1) where expected
in the range $119\leq$v${}_{\rm LSRK}\leq 165$ km s-1 and absent (0.4 Jy
beam-1 km s-1) where not expected in the range $30\leq$v${}_{\rm LSRK}\leq 73$
km s-1. Figure 6 shows a map of the spectral noise across the entire field.
The spectral noise is $2.34$ mJy per 5 kHz, or $1.24$ times theoretical, well
within the good range. The slightly loss in sensitivty can be attributed to
the Briggs weighting applied to the visibilities (see Section 4.2.) The noise
is generally smooth across the primary area of the field, however a grid
pattern is apparent in the noise at low levels. This structure is likely a
numerical artifact introduced by the Fourier Transform inversion of the
visibilities when gridded to a finite grid to return to the image domain
during major cleaning iterations. The effect of this structure is
characterized in Section 4.3. The highest noise is at the edges of the field
outside the FWHM of the formed primary beams, as expected. Finally, there are
no periodic features in the test spectra. With all metrics in the good range
we find that the SMC cube is suitable for science use.

##  4 Data Products

###  4.1 Image Cubes

The final product of our custom imaging pipeline, after masking the cube at
the 10% level of the combined primary beam response, is a
3901$\times$3471$\times$222 pixel image cube containing jointly deconvolved
ASKAP data feathered with regridded Parkes data that covers a LSRK velocity
range of 40.0 km s-1 to 253.9 km s-1 at a resolution of 0.98 km s-1. This cube
is publicly accessible through a unique Digital Object Identifier
(DOI)777https://doi.org/10.25919/www0-4p48. We measure the rms noise using the
source finding software, SoFiA 2; Serra et al. 2015; Westmeier et al. 2021,
which fits a Gaussian to the negative half of the histogram of pixel values.
This method is more robust against the presence of strong, extended emission
or artifacts than measuring the standard deviation of emission-free channels.
The width of this Gaussian is 1.1 K at the restoring beam size of
30${}^{\prime\prime}\times$30′′, corresponding to a 5$\sigma$ Hi column
density detection limit of 4.4$\times$1019 cm-2 over a 20 km s-1 linewidth.
This cube is the most sensitive and highest resolution image
(30${}^{\prime\prime}\times 30^{\prime\prime}$) of the SMC in Hi ever
achieved.

###  4.2 Noise as a Function of Angular Resolution

Two key science targets of GASKAP-HI are diffuse Hi emission distributed on
angular sizes larger than the synthesised beam and cold gas as revealed
through sensitive Hi absorption towards background continuum sources. It is
critical to ensure the brightness temperature rms noise, $\sigma_{\rm T}$, is
minimized and behaves as predicted at the angular resolutions relevant for key
GASKAP-HI science. Johnston et al. (2007) give the survey speed ($SS$) of
ASKAP in terms of $\sigma_{\rm T}$ as

$SS=FBn_{\rm pol}\left(\frac{\epsilon_{\rm c}\sigma_{\rm T}}{T_{\rm
sys}}\right)^{2}\left(\frac{f}{\epsilon_{\rm s}}\right)^{2},$ (6)

where $B$ is the spectral resolution, $F$ is the FoV, $n_{\rm pol}$ is the
number of polarizations (2), $\epsilon_{\rm c}$ is the correlator efficiency,
$T_{\rm sys}$ is the system temperature in emission-free regions, and the
filling factor of the array

$f=\frac{A\eta N\Omega\epsilon_{\rm s}}{\lambda},$ (7)

which describes the covering factor of the array in the aperture plane. Here,
$A$ is the area of a single antenna, $\eta$ is the aperture efficiency for a
single antenna, $N$ is the total number of antennas, and the solid angle of
the synthesized beam $\Omega$ = 1.13($\theta_{\rm s})^{2}$ in steradians (sr),
where the size of the synthesized beam is characterized by the FWHM along the
major and minor axis: $\theta_{\rm s}=\sqrt{\theta_{\rm maj}\cdot\theta_{\rm
min}}$

Finally, $\epsilon_{\rm s}$ is what is known as the synthesized aperture
efficiency, constrained to be $\leq$ 1 and relates to the weighting of the
gridded visibilities in the $uv$-plane before inversion to the image plane.
For example, applying a Briggs weighting scheme reduces $\epsilon_{\rm s}$,
since some baselines in the $uv$-plane become higher weighted than others.
Keeping all other parameters in Equations 6 and 7 fixed, we anticipate the rms
brightness temperature to scale as $\sigma_{\rm T}$ $\propto
f^{-1}\propto\theta_{\rm s}^{-2}$, where $\epsilon_{\rm s}$ encodes the
removal of baselines from the spatial smoothing. The telescope specifications
are summarized in Table 5.

Table 5: Noise Scaling Parameters Parameter | Symbol | Value [units]
---|---|---
Field-of-view | $F$ | 25 [deg2]
Dish Area | $A$ | 113 [m2]
Spectral Resolution | $B$ | 5 [kHz]
Number of polarisations | $n_{\rm p}$ | 2
Correlator efficiency | $\epsilon_{\rm c}$ |  $\sim$1
Number of antennas | $N$ | 36
Aperture efficiency | $\eta$ | 0.7
(Emission-free) system temperature | $T_{\rm sys}$ | 55 [K]
rms noise | $\sigma_{\rm T}$ | 1.1 [K]
Dwell Times | $t_{\rm int}$ | 12.5, 20.9 50, 200 [h]

Figure 7 compares the measured noise as a function of angular resolution with
the predictions from Dickey et al. (2013) (orange lines and crosses) at
varying angular resolutions. The predicted noise profiles are determined by
solving Equation 6 for $\sigma_{\rm T}$ for various dwell times ($t_{\rm
int}$) by setting $SS$=$F$/$t_{\rm int}$. We measure the noise in our cube by
imaging a sub-region of 4 beams $\times$ 3 interleaves of 20 contiguous
emission-free channels with natural weighting. We then apply a Gaussian taper
to the baselines in the $uv$-plane before the inversion to the image plane to
alter the final spatial resolution. The final beam size is a fit to the main
lobe of the resulting PSF after tapering. We create 30 sub-cubes each with a
different taper size that ranges from 12,000$\lambda$ to 400$\lambda$ equally
spaced in log-space. The final noise is again taken to be the width of a
Gaussian fit to the negative half of the histogram of pixel value as
determined by SoFiA.

The measured noise is in excellent agreement with the theoretical predictions
scaled to match the current telescope specifications (dotted black line). The
profiles begin to deviate from the predicted $-$2 power-law at larger
resolutions due to the dependence of $\epsilon_{\rm s}$ at larger $uv$
tapering. The agreement between the expected and measured scaling of the noise
is confirmation that the data products of GASKAP-HI are indeed pioneering in
terms of the trade-off between rms brightness temperature with angular
resolution for the study of nearby Hi.

Figure 7: The measured noise (blue points) within a sub-region of our GASKAP-
HI cube after applying gradually larger tapers to the baselines in the
$uv$-plane compared with the predictions shown in Figure 4 and Table 3 from
Dickey et al. (2013) (orange lines and black crosses). The dotted black line
denotes the updated theoretical noise using the measured $T_{\rm sys}/\eta$
scaled to an integration time of 20.9 h.

###  4.3 Represented Spatial Frequencies

We further characterize the range of spatial frequencies represented in our
final images after multi-scale joint deconvolution by employing the SPS as a
data quality assessment tool. Specifically, we investigate whether a two-
dimensional Gaussian function with a FWHM of 30′′ ($\sim$ 8 pc at the distance
of the SMC) is a good approximation for the restoring beam across all
available scales in the final image.

Similar to Section 3.3.3, we calculate the two-dimensional angular power
spectrum for each spectral plane of our final image cube. Many studies that
apply the SPS to column density or intensity images of various observational
tracers in the Milky Way show the density distribution of the ISM as a
function of scale is well described with a single power law (e.g., Martin et
al. 2015; Miville-Deschênes et al. 2016; Pingel et al. 2018). We therefore fit
the angular power spectrum profile $P\left(k\right)$ in each velocity channel
with a model

$P\left(k\right)=B\left(k\right)Ak^{-\gamma}+QP_{\rm noise}\left(k\right),$
(8)

where $B\left(k\right)$ is the power spectrum of our ideal 30′′ restoring
Gaussian beam to account for instrumental systematics that affect the overall
shape of the SPS, $Ak^{-\gamma}$ is the ISM power-law term, and $Q$ is a
multiplicative factor to the noise floor. The noise template, $P_{\rm
noise}\left(k\right)$, is estimated by taking the mean SPS profile for 40
emission-free channels. After fitting for $A$, $\gamma$, and $Q$ in each
velocity channel, Equation 8 can be rearranged to solve for

$\widetilde{B}\left(k,v_{\rm LSRK}\right)=\frac{P\left(k,v_{\rm
LSRK}\right)-Q\left(v_{\rm LSRK}\right)P_{\rm
noise}\left(k\right)}{A\left(v_{\rm LSRK}\right)k^{-\gamma\left(v_{\rm
LSRK}\right)}},$ (9)

where $A$, $Q$, and $P\left(k\right)$ now depend on $v_{\rm LSRK}$, the
observed radial velocity in the LSRK reference frame;
$\widetilde{B}\left(k,v_{\rm LSRK}\right)$ is the global transfer function,
which similar to optical systems specifies how the true sky brightness
distribution is represented in our image cube. For example, the absence of
structure in the transfer function indicates our data is the true sky
brightness distribution convolved with our 30′′ Gaussian restoring with added
radiometer noise.

In order to fully characterize the uncertainty on our model parameters, we
follow similar fitting procedures from Koch et al. (2020), who used the PYMC3
package (Salvatier et al., 2015), to run a Markov Chain Monte Carlo (MCMC)
sampling to fit our final models. Due to the large range of angular scales
spanned by the Hi emission, we assign uniform priors for each of our model
parameters and sample the amplitude $A$ in $log_{10}$ space:

$log_{10}A\sim\mathcal{U}(-20,20)$ (10) $\gamma\sim\mathcal{U}(0,5)$ (11)
$Q\sim\mathcal{U}(0,10)$ (12)

We found that the fitting routine converges quickly with these choices of
priors and the final fits are not affected by reasonable changes to the range
of these priors. The MAD is used as an estimate of the uncertainty in each
point $P_{i}$ in the azimuthally-averaged profile

$\sigma_{P(k)}=\mathrm{median}\left(\left|P_{i}-\mathrm{median}\left(P_{\rm
annuli}(k)\right)\right|\right).$ (13)

We compute the absolute deviation from the median power for each pixel within
each annulus in the spatial frequency domain and take the final uncertainty to
be the median of these deviations. The MAD is more robust against bias from
small sample sizes at the smallest annuli and outlying values than the
standard deviation. Each value of $P(k)$ is treated as an independent sample
drawn from a normal distribution with width equal to the MAD values in each
azimuthal bin. These samples are first drawn in $log_{10}$ space then
converted to linear scaling to avoid negative values for the power spectrum.
Finally, we restrict our fits to a range of spatial frequencies between
$k<k_{\rm min}/3$ — where $k_{\rm min}$ is one half the inverse of the largest
map dimension — and $3k_{\rm max}$, where $k_{\rm max}$ corresponds to the
Gaussian standard deviation of our 30′′ ideal beam. Fitting this range of
spatial frequencies avoids the fluctuations from the large-scale power and
bias from small-scale statistics at the smallest annuli, while also removing
influence from correlated small-scale structure below the size of the
restoring beam.

Figure 8 shows the measured transfer function for our SMC image cube. The
absence of structure in the transfer function at small angular scales
indicates that the density distribution of Hi in the SMC is well described by
a single power law down to the resolution limit of 10 pc, consistent with the
conclusions from the power spectrum analysis of Stanimirović et al. (1999),
which probed Hi in a combined ATCA and Parkes image cube down to 30 pc. We
discuss the interpretation of the Hi turbulent properties in Section 5.2

While the small-scale structure is well represented by the ISM power-law,
there is some structure towards the largest angular scales ($\gtrsim$ 160′),
highlighted in a zoomed version in the bottom panel of Figure 8. There are
several possible explanations for this discrepancy including: the presence of
large scale deconvolution residuals, imperfect combination with the Parkes
data, and large-scale structure in the noise. In regards to the presence of
structure in the noise, the noise template SPS profile shown in the top panel
of Figure 4 does begin to slightly deviate from the flat profile expected for
purely random Gaussian distributed noise at these larger angular scales and
also roughly correlates with the size scales of the low-level numerical
artifacts from the Fourier transforms seen in Figure 6. Consequently, the
structure in the transfer function at the largest angular scales likely
manifests from a combination of sources of error, including bias from small-
number statistics in the azimuthal binning of the smallest annuli and the
known structure in the noise. It could also trace the azimuthally averaged
baseline distribution. However, the power of these artifacts in the noise is
many orders of magnitude below the power of the signal at these spatial
frequencies and ultimately can be accounted for by restricting the range of
scales (e.g., up to $\sim$150′) fit during a power spectrum analysis.

Figure 8: Global transfer function of the SMC image cube. The transfer
function is useful for determining whether the observed sky brightness
distribution is the true sky brightness distribution convolved with our 30′′
Gaussian restoring beam with added radiometer noise. The top panel shows the
entire range of angular scales, while the bottom panel shows the response
between 200′ to the vertical dashed line at 150′ in the top panel to highlight
scales with the most significant structure in the transfer function. The
pixelated regions denote mostly emission-free channels.

For example, the emission SPS profile from the same representative spectral
channel in the top panel of Figure 9 is exceptionally well-fit by our model.
Inspection of other channels with extended emission show similar convergence.
By restricting the range of angular scales and allowing a multiplicative
factor for the noise, we ensure the presence of artifacts is taken into
account in our SPS analysis. Martin et al. (2015) demonstrated through similar
SPS that the noise is effectively the combination of receiver and sky noise
(Boothroyd et al., 2011), $Q=1+T_{\rm 0,b}/T_{\rm sys}$, where $T_{\rm 0,b}$
is a characteristic brightness temperature. We slightly alter the form of this
relationship to $Q=1+2T_{\rm 0,b}/T_{\rm sys}$, where the factor of 2 accounts
for the differences in the definitions of the linear XX and YY polarizations
between Boothroyd et al. (2011) and the ASKAPsoft calibration pipeline, i.e.
(XX+YY) versus (XX+YY)/2. In the bottom panel of Figure 9, we plot the fitted
$Q$ values versus the mean brightness temperature in each spectral channel. A
fit of a simple linear function to channels with significant emission returns
$Q=1.014(\pm 0.003)+0.0182(\pm 0.0004)T_{\rm 0,b}$, which gives $T_{\rm sys}$
= 54.97$\pm$0.02 K. This agrees exceptionally well with the expected $T_{\rm
sys}$ at 1.4 GHz (Hotan et al., 2021).

Figure 9: Top: an example fit of our single component power-law to a spatial
power spectrum profile from a representative emission channel with the
uncertainty derived from the MAD metric denoted by the shaded region. The
noise template SPS is shown in orange. Bottom: $Q$, the multiplicative factor
applied to the template SPS noise profile, as a function of the mean $T_{\rm
b}$ of each spectral channel. A linear fit to channels with significant
emission returns the expected $T_{\rm sys}$ of ASKAP at 1.4 GHz.

##  5 Gas Morphology

###  5.1 General Properties

The peak Hi intensity image presented in Figure 10 demonstrates the full
extent of the emission captured within a single $\sim$25 deg2 ASKAP footprint.
While not a true representation of the projected Hi density distribution, as
we simply select the peak brightness temperature value along the spectral
profile at each spatial pixel, this spectacular image reveals that an
incredible wealth of small-scale structure permeates the overall smooth
diffuse Hi component of the SMC. The extensive exo-galactic population of Hi
features identified in McClure-Griffiths et al. (2018) are clearly visible
throughout the northern regions of this map. We further highlight the
projected density distribution by computing the column density image shown in
Figure 11, assuming the Hi is optically thin:

$N(x,y)_{\rm HI}=1.82\times 10^{18}\int T_{\rm b}\left(x,y,v\right)dv\;{\rm
cm^{-2}},$ (14)

where the brightness temperature, $T_{\rm b}\left(x,y\right)$, at each spatial
pixel is integrated over the spectral range 235.4 km s-1 to 60.5 km s-1. The
boundaries of the ASKAP primary beams are overlaid to demonstrate that the
size scales of emission range from a single synthesized beam element up to the
extent of multiple formed primary beams. Strikingly, there are still some
indications of complex filamentary structure in the column density image,
highlighting that our increased angular resolution resolves a wealth of new
cold narrow features even when integrating across the entire spectral range.

The single channel shown in the top two panels of Figure 12 highlights the
improvement in angular resolution in our pilot data over the previous
generation image made with ATCA and Parkes. It could be argued that
intermediate scale features appear better recovered in the previous generation
ATCA+Parkes image. This is a combined effect of including emission over a
slightly larger spectral range (1.65 km s-1), spatial smoothing to a lower
angular resolution, and the difference in the $uv$-weighting applied during
imaging. Staveley-Smith et al. (1997) applied a robustness parameter of 0.0,
giving slightly less weight to sparsely sampled (i.e., long) baselines,
bringing out structure on these intermediate scales.

The abundance of small-scale Hi features in the Bar of the SMC, extending from
the north to the south-west and outlined by the white rectangle, trace the
stellar feedback effects from the strong ongoing star formation in this region
as seen in H$\alpha$ (Winkler et al., 2015) and other star burst regions such
as the N66/NGC 346 complex (Heydari-Malayeri & Selier, 2010). The detail in
small-scale features in a single spectral channel from our new GASKAP-HI data
approaches those traced by the far-infrared 250$\mu$m dust image produced as
part of the HERschel Inventory of The Agents of Galaxy Evolution (HERITAGE)
project (Meixner et al., 2013). A comparison of the properties of the Hi from
a single spectral channel with dust emission is not straightforward given the
continuum nature of the re-radiated emission arising from the cool dust.
Nevertheless, assuming the gas and dust are well-mixed due to the correlation
between color excess and total hydrogen column density (Rachford et al.,
2009), future studies will utilize the improved angular resolution to provide
insights into spatial variation of the dust-to-gas ratio across the entirety
of the SMC.

Towards the so-called Wing of the SMC, which extends towards the LMC, the
superior spectral and spatial resolution of these data reveal a complex
network of discrete linear plumes (see the arrow in the middle panel of Figure
12) with projected lengths of $\sim$ 0.5 kpc. A similar plume stemming just
east of the northern portion of the Bar extends almost 1 kpc. The spectral
resolution of our new image cube ensures these plumes and other interesting
features, such as the supershell centered on RA = 00h50m, Dec=$-$73d10m, are
fully resolved over 5 to 20 channels. Section 5.3 demonstrates how our
improved insight into the kinematic properties of these discrete features
helps with constraining important physical properties of the SMC.

Figure 10: The peak intensity along each line-of-sight from our combined ASKAP
and Parkes image cube of the SMC. Figure 11: ASKAP+Parkes Hi column density
image of the SMC produced from Equation 14 integrated over the LSRK velocity
range 60.5 km s-1 to 235.4 km s-1. The solid white circles denote the
locations of the 36 formed beams from interleave A. In order to demonstrate
the positional offset of the PAF footprint for each interleave position, we
overlay dashed circles at the locations of beam 36 in interleave B (upper) and
C (lower). This interleaving scheme ensures even sensitivity, and thus a
consistent noise level across the entire instantaneous 25 deg2 FoV. The red
rectangle region contains the high velocity cloud discussed in Section 5.3.
Figure 12: A visual comparison between a single spectral channel centered on
151.3 km s-1 in the LSRK reference frame from the previous generation
ATCA+Parkes of the SMC in Hi (top; Stanimirović et al. 1999), the new GASKAP-
HI (ASKAP+Parkes) Hi image (middle), and the 250$\mu$m dust image from the
Herschel space observatory (bottom; Gordon et al. 2014). The white rectangle
outlines the Bar region of the SMC and the white arrow points to resolved Hi
plumes in the Wing region. The extent and detail of the small-scale Hi
features in this individual spectral channel of the GASKAP-HI image are
similar to those seen in the dust continuum emission.

The three-colour images of selected spectral channel maps in Figure 13, which
stack emission from adjacent channels, highlight the complexity and narrow
spectral properties of the newly revealed small-scale structure. At more
redshifted velocities relative to the systemic velocity of 148 km s-1 LSRK (Di
Teodoro et al., 2019a), the Hi morphology is relatively smooth at large scales
but gradually transitions to a filamentary form on arcminute scales as the
velocity decreases. The Hi distribution becomes increasingly intricate near
the systemic velocity, taking the form of plumes, filaments, knots, and
shells. The discrete filamentary features are analogous to the slender Hi
fibres shown by Clark et al. (2014) to be aligned with the interstellar
magnetic field of the Milky Way, while the small-scale knots and arcs trace
structure on 10 pc scales, similar to the typical size of star-forming
regions. The multi-color nature of these features demonstrates a sharp
velocity gradient over just several adjacent spectral channels with linewidths
comparable to CO(2$\rightarrow$1) emission observed in individual molecular
clouds in other nearby external galaxies as reported by the PHANGS-ALMA survey
(Leroy et al., 2021). In our own Galaxy, the atomic-to-molecular (Hi-to-H2)
phase transition in the dense regions of GMCs, arising from the combined
effect of dust attenuation of far-ultraviolet radiation and H2 self-shielding
(Bialy et al. 2015 and references therein), traces sites of star formation.
Glover & Clark (2012) argue that the transition from the WNM to CNM phase is
an important step towards star formation. Studying the gas transition from Hi
to H2-dominated regions that fuel star formation within the Bar and comparing
with observational studies of Milky Way GMCs (e.g., Lee et al. 2012; Burkhart
et al. 2015; Wang et al. 2020) will be an invaluable step towards a complete
theory of star formation.

Towards blueshifted velocities (e.g., 131 km s-1), a prominent population of
compact, spatially anomalous Hi features surround the SMC. Considering the
general head-tail morphology of associated molecular gas by Di Teodoro et al.
(2019b), a majority of these anomalous features likely originate from strong
star-formation-driven outflows (McClure-Griffiths et al., 2018), though the
uncertain geometry of the SMC conspires against a definitive measure of the
escaping gas. Nevertheless, these novel observations will inform the
comparison between kinematic and geometric properties of infall/outflow
models.

Figure 13: Selected channel maps of the combined ASKAP+Parkes Hi image cube.
Red, green and blue are assigned sequentially to adjacent velocity channels,
each displayed with an arcsin colormap scaling over a brightness temperature
range of $T_{\rm b}$ = 1 K and 70 K. The colorscale of all panels is the same.
The LSRK velocity range is listed in each panel.

###  5.2 Hi Turbulent Properties

The extension of a single component power-law down to physical scales three
times smaller than previously measured demonstrates processes such as star
formation, which injects energy on several hundred pc scales (Mac Low &
Klessen, 2004), do not produce any special feature or deviation in the large-
scale SPS of the SMC. Either stellar feedback is not the dominant source of
energy injection at these scales and large-scale driving is more dominant (at
least within the SMC; Szotkowski et al. 2019), or energy is being injected
over a wide range of scales without preference at any particular scale (e.g.,
Norman & Ferrara 1996). This is also congruous with the notion that the power-
law form of the power spectrum arises from the fractal geometry of the ISM;
that is, the ISM displays hierarchical structuring over the entire range of
spatial scales (Stanimirović et al., 1999; Elmegreen & Falgarone, 1996).
Interestingly, the average spectral index measured for all slopes over
velocity range of 90 km s-1 to 190 km s-1 is $\gamma$ = $-$2.85$\pm$0.07,
which is slightly shallower than $\gamma$ = $-$3.04$\pm$0.04 measured by
Stanimirović et al. (1999). Shallower slopes across the entire velocity range
indicate more power on smaller scales, possibly from more abundant cold Hi
that is resolved by our higher angular resolution GASKAP-HI observations. On
the other hand, the differences in the average slopes could also be driven
from a statistical bias (e.g., small number statistics for the large-scale
power). Following the application of the discussion from Falconer (1997) and
Stanimirović et al. (1999), we exploit the Fourier Transform relationship
between the autocorrelation function and power spectrum to connect $\gamma$ to
the fractal function with the relation

$-\gamma-2=4-2s,$ (15)

where $s$ is the box-counting dimension. This value quantifies the fractal
nature of a subset of three-dimensional Euclidean space, R3, and provides an
upper limit for the fractal dimension (also known as the Hausdorff dimension).
For example, a perfectly smooth square has a fractal dimension of 2, while an
object with a non-integer fractal dimension indicates self-similarity over a
range of scales and thus the presence of hierarchical structure. We determine
the $s$ of the combined ASKAP and Parkes images of Hi emission to be
1.58$\pm$0.04, in agreement with the fractal analysis in Stanimirović et al.
(1999). The fractal dimension observed in molecular clouds is 1.36$\pm$0.02
from scales ranging from 100 pc to 0.02 pc (Falgarone et al., 1991). This
statistically significant difference indicates separate mechanisms drive the
dynamics in the WNM and molecular clouds.

Analogously, a clustering analysis applied to the upper main-sequence stars in
the SMC shown by Sun et al. (2018) shows young stellar structures, much like
the gas, are also organized in a hierarchical fashion. The consistent
description for both the gas and stars indicates similar mechanisms, such as
turbulence and/or hierarchical gravitational fragmentation of the denser gas
that forms stars (Vázquez-Semadeni et al., 2019), influence the properties of
the Hi across spatial scales extending from kpc down to the scales of
individual molecular clouds on sub-parsec scales. We note, however, that a
comprehensive analysis of the fractal structure, especially at individual
spectral channels, should account for the effects of self-absorption and
difficulty in disentangling the relative contributions of the CNM and WNM to
the overall Hi emission.

###  5.3 Properties of an Anomalous Hi Feature

Figure 14:  Combined ASKAP+Parkes Hi masked integrated intensity images of an
HVC centered on RA = 01h08m45s, Dec = $-$71d20m55s produced by the source
finding algorithm in BBarolo. The projected physical extent of this region is
300 pc at a distance of 60 kpc. The image made from our improved pilot survey
is on the left and the image from the test observations (McClure-Griffiths et
al., 2018) is on the right. In both cases, the detected emission was
integrated over $90\leq$v${}_{\rm LSRK}\leq 118$ km s-1. The contour levels
increase in steps of 29.5 K km s-1 and range from 5 K km s-1 to 300 km s-1,
inclusive. The red circle with a radius corresponding to 13 pc denotes the
approximate size of a shell-like feature identified in position-velocity
space. The orange contours in the left panel show the CO integrated
intensities at 0.02 and 0.04 K km s-1 from Di Teodoro et al. (2019b). The size
of the restoring beam for the ASKAP data sets is denoted by the circle in the
lower left corner.

The test observations presented in McClure-Griffiths et al. (2018) revealed a
considerable population of spatially and kinematically anomalous Hi features
that extend upwards of 2 kpc from the main body of the SMC. The increase in
spectral resolution and overall sensitivity of our pilot survey observations
facilitate more robust constraints of the physical properties of these
Magellanic HVCs — such as their mass, kinematics, and morphology. These in
turn trace fundamental properties of the circumgalactic environment around the
SMC and Milky Way halo like the total amount of outflowing gas and halo
pressure by relating head-tail morphologies with ram pressure and/or
instabilities.

We illustrate the power of our new pilot data to trace anomalous HVCs in the
Magellanic System by focusing on an outflowing HVC centered on RA = 01h08m45s,
Dec = $-$71d20m55s that entrains several compact 12CO(2$\rightarrow$1) clouds
(Di Teodoro et al., 2019b). The left and right panels of Figure 14 compare the
integrated intensity images of this HVC from the pilot and test observations,
respectively. We utilize the SEARCH task in BBarolo, a software package for
fitting 3D tilted-ring models to emission-line cubes (Di Teodoro & Fraternali,
2015), in order to exclude noisy pixels from the integration of the signal. We
set the SNR threshold for genuine signal to any pixel with SNR $>$ 5 over the
span of two or more adjacent channels, applied within the LSRK velocity range
of 95 km s-1 to 119 km s-1. The remaining task parameters use default values.
The images from the pilot and test observations show similar large-scale
morphology. However, the small-scale structures in the pilot data displays
more pronounced density gradients in individual clumps. This is due to the
twofold increase in sensitivity, fourfold increase in spectral resolution
(facilitating more narrow-line features to be resolved), and more complete
sampling of higher spatial frequencies from the additional antennas at longer
baselines. For example, let us focus on the northeast condensation with a peak
at RA = 01h09m35s, Dec = $-$71d17m15s. The mean column densities are roughly
similar at 1.3$\times$1020 cm-2 and 8.2$\times$1019 cm-2 in the pilot and test
images, respectively, giving a volume density $n\sim$ 1.6 cm-3 and 1.0 cm-3
assuming spherical symmetry, an angular extent of 90′′, and a distance of 60
kpc.

The full potential for constraining the physical properties of these HVCs is
realized through the increased spectral resolution. For example, we break up a
$2.5^{\prime}\times 2.5^{\prime}$ region centered on the peak intensity of
this condensation to the northeast for the pilot and test data into a
4$\times$4 grid to independently sample the emission across 16 restoring beam
elements and compute the integrated spectrum for each sample. We then shift
each integrated spectrum to the same peak velocity and average the profile.
Fitting a single Gaussian function to these averaged profiles returns $v_{\rm
FWHM}$ of 6.9$\pm$0.5 km s-1 and 13$\pm$2 km s-1 for the pilot and test data,
respectively; the differences arising from the differences in spectral
resolution. These $v_{\rm FWHM}$ provides an upper limit for the kinetic
temperature of the gas, $T_{\rm max,k}$ = 21.866$\times v_{\rm FWHM}^{2}$ of
1000$\pm$200 K and 4000$\pm$1000 K. We can use the $T_{\rm max,k}$ and $n$ to
obtain an estimate of the pressure of this condensation through the
approximation of an ideal gas, $P/k=nT_{\rm max,k}$, where $P$ is the pressure
and $k$ is the Boltzmann constant. The resulting upper limit pressures for the
pilot and test data are respectively $P/k=1600\pm 300$ K cm-3 and $P/k=4000\pm
1000$ K cm-3. The respective decrease of nearly 60% and 70% between the upper
limit pressures and final uncertainties demonstrates that the superior
spectral and angular resolution of the pilot data is crucial for constraining
important physical properties. This also demonstrates how increased angular
and spectral resolutions work together to improve estimates of intrinsic line
widths.

Figure 15:  Combined ASKAP+Parkes Hi channel maps of an HVC centered on RA =
01h08m45s, Dec = $-$71d20m55s. The black contours denote emission from the
pilot cube, while the white contours trace emission from the lower spectral
resolution test cube. Both sets of contours range between 5 K and 30 K and
increase in increments of 6.25 K. The increased spectral resolution of the
pilot cube resolves several notable features including a Hi hole between 110.3
and 105.4 km s-1. The approximate projected size of the shell at these
velocities is denoted by a black circle, assuming uniform expansion and
spherical symmetry. The restoring beam of the pilot data is shown in the lower
left corner of each panel. Figure 16:  Combined ASKAP+Parkes Hi position-
velocity distribution for three slices along RA. The top panel represents a
slice 30′′ above the center of the circle in the left panel of Figure 14 that
intercepts the Hi shell at an angle of 50∘ from a horizontal slice through the
center located at RA = 01h08m38s, Dec = $-$71d23m00s. The middle panel
represents a slice directly through the center, and bottom panel shows a slice
30′′ below the center that intercepts the shell at a $-$50∘ angle below a
horizontal slice through the center. Assuming the geometry outlined for a
uniformly expanding shell with $v_{\rm exp}$ = 2.0 km s-1 (much smaller than
the typical thermal line widths expected for the WNM), we show the predicted
position-velocity structure as a red ellipse. The emission contours are at
levels of 3, 5 K, 10 K, and 20 K.

The CO integrated intensity contours from the observations of Di Teodoro et
al. (2019b) overlap well both spatially and spectrally (see their Figure 3)
with the southern edge of the most pronounced Hi density gradient in this
cloud centered on RA = 01h08m33s, Dec = $-$71d24m21s. The emission
distribution in individual spectral channels in Figure 15 reveal a shell-like
structure appearing first at a velocity of 110.3 km s-1 before completely
breaking up at 103.4 km s-1 along the northern edge of this density gradient.

The distribution of emission in position-velocity space of several RA cuts in
Figure 16 hints at a characteristic ellipse structure expected from an
expanding shell, indicating spherical symmetry in 3D space. We determine the
center of the apparent shell-like feature to be RA = 01h08m38s, Dec =
$-$71d23m00s and measure $v_{\rm min}$ = 106$\pm$1 km s-1 and $v_{\rm max}$ =
110$\pm$1 km s-1 and thus a systemic velocity $v_{\rm sys}$ = 108$\pm$1 km
s-1. Assuming a uniformly expanding shell, the projected sizes in position-
velocity space are respectively

$v_{\rm proj}=v_{\rm exp}\cos{\theta_{\rm cut}}+v_{\rm sys}$ (16)

and

$R_{\rm pos}=R_{\rm ang}\cos{\theta_{\rm cut}},$ (17)

where $\theta_{\rm cut}$ represents the angle at which a horizontal cut is
above and below another horizontal cut through the center of the feature in
position-position space and $R_{\rm ang}$ is the angular projected radius at
the center and is determined to be 13 pc at the distance of adopted distance
of 60 kpc. The line-of-sight (LOS) geometry is estimated using

$\phi=\cos^{-1}\left(\frac{v_{\rm LSRK}-v_{\rm sys}}{v_{\rm exp}}\right)$ (18)
$R_{\rm proj}=R_{\rm ang}\sin{\phi},$ (19)

where $v_{\rm LSRK}$ is again the observed radial velocity in the LSRK
reference frame. Using these $v_{\rm min}$ and $v_{\rm max}$ and measuring the
velocity of the emission at the location of a horizontal cut that intercepts
the shell at an angles of $\theta_{\rm cut}=50^{\circ}$ and $\theta_{\rm
cut}=-50^{\circ}$ above and below the center, we estimate the expansion
velocity $v_{\rm exp}$ to be 2$\pm$1 km s-1. Using Equations 16-19, we show
the projected size in the relevant channel maps and in position-velocity
space.

A $v_{\rm exp}$ of 2$\pm$1 km s-1 is roughly five times smaller than typical
thermal line widths for the WNM, making it difficult to discern likely origin
scenarios based on input energy estimates for possible progenitors. A search
for bright ($G$ $<$ 20), blue (color $-$0.5 $<$ BP$-$RP $<$ 0) stars with
parallaxes corresponding to distances larger than 55 kpc within the Gaia Early
Data Release 3 catalogue (Gaia Collaboration et al., 2016, 2021) shows dozens
of stars in the field. However, we cannot point to an isolated population as
the potential progenitor of this expanding shell without further filtering
based on radial velocity measurements, which are currently unavailable.
Moreover, the measured mass within the aperture encompassing the feature is
$\sim$2240 M⊙, implying a corresponding thermal energy of 8.9$\times$1047 erg.
This is much lower than the input from a single core-collapse supernova
explosion (Hartmann, 1999). The absence of an isolated stellar association,
small $v_{\rm exp}$ relative to the thermal linewidth of the WNM, and
correspondingly low thermal energy point to a purely turbulent origin. Daigle
et al. (2007) note the presence of structures at similar scales as this
feature in simulated Hi image cubes with pure turbulent motions. Regardless of
the true origin, this investigation demonstrates that our GASKAP-HI data
provide a novel view into the kinematic properties of the diverse population
of exo-galactic clouds surrounding the SMC.

Figure 17:  Combined ASKAP+Parkes Hi maps of the intensity-weighted velocity
field (left) and velocity dispersion (right) of an HVC centered on RA =
01h08m45s, Dec = $-$71d20m55s produced by the source finding algorithm in
BBarolo. The velocity field contours range inclusively between the levels of
92.5 km s-1 and 115 km s-1 in steps of 2.5 km s-1. The contours of velocity
dispersion begin at a level of 1 km s-1 and increase up to 4 km s-1 in steps
of 0.75 km s-1. The gradient in the velocity field across the entirety of the
cloud and complexity of the velocity dispersion contours — especially towards
the northwest spur — are qualitatively consistent with this HVC being a wind-
swept cloud from a Galactic wind emanating from the SMC. The arrow denotes the
direction towards the nearest prominent star formation region, NGC 371/395.
The size of the restoring beam is shown in the lower left corner of both
panels.

The presence of galactic-scale external winds can explain the global observed
morphological and kinematic properties of this cloud. Galactic winds shape the
structures of the ISM, altering the kinematic and morphological properties of
the gas. Hot winds interacting with cold clumps of dense gas can excite
molecular species (Pon et al., 2012; Girichidis et al., 2021), transfer mass,
momentum, and energy (Vijayan et al., 2020; Schneider et al., 2020), and strip
the outer surface layer, forming elongated, filamentary structures that trail
the main body of the cloud (e.g., Banda-Barragán et al. 2016; Gronke et al.
2021). Di Teodoro et al. (2019b) suggests a scenario in which this particular
complex is launched from NGC 371/395, the nearest prominent star formation
region located south-west. The intensity-weighted velocity field shown in the
left panel of Figure 17 shows a clear gradient across the entirety of the
cloud. Such velocity gradients in discrete clouds are often interpreted as
rotation. However, the closed isovelocity contours in the western side of the
cloud that overlap with the expanding bubble, absence of a clear major axis,
and disturbed structure in the velocity dispersion map instead indicate these
motions are more likely due to shear. The population of discrete cloudlets to
the northwest in the individual spectral channels and moment maps is also
consistent with the expectation of the formation of head-tail structures from
the stripping of outer gas layers seen in simulations of wind-cloud
interactions and observations (Phillips et al., 2009; Grønnow et al., 2017;
Grønnow et al., 2018; Banda-Barragán et al., 2019, 2021).

The integrated spectrum shown in Figure 18, measured over the field of view
shown in Figures 14 and 15, further demonstrates the advantage of the
increased spectral resolution in deriving physical properties of HVCs around
the SMC. The pilot flux profile shows the multi-component kinematic properties
of this cloud, which is only hinted at in the coarser spectrum. Inspection of
the individual channel maps for velocities 105 km s-1 to 97 km s-1 shows the
flux offset between the two profiles occurs because a significant amount of
emission happens to sit at the boundary of a coarser spectral channel in the
test data, thus artificially extending the velocity range of the emission
distribution. Again assuming a distance of 60 kpc (McClure-Griffiths et al.,
2018), we achieve a more reliable measure of the Hi mass to be 15,100$\pm 300$
M⊙, as opposed to an overestimated value of 19,600$\pm$100 M⊙. This
discrepancy is likely related to improvements made in the calibration and
processing pipeline between November 2017 and December 2019.

Figure 18: Combined ASKAP+Parkes Hi integrated spectrum of the HVC measured
over the area shown in Figures 14 and 15.

These data enable us to derive a diverse range of physical properties for this
single HVC. Future detailed cataloging and study of the HVC population around
the SMC will inform mass outflow/inflow models to help determine whether such
features are outflowing or accreting, aid in constraining the overall dynamics
of the SMC, and trace the pressure equilibrium between cold and warm Hi phases
through Gaussian decomposition algorithms, such as the Regularized
Optimization for Hyper-Spectral Analysis (ROHSA) package (Marchal et al.,
2019) or GaussPy+ (Lindner et al., 2015; Riener et al., 2019).

##  6 Summary

Utilizing a combination of ASKAP and Parkes GASS Hi data to obtain a cube
covering all angular scales, we presented the most sensitive and detailed Hi
images of the SMC ever achieved. These images were produced by our custom
imaging pipeline, which is designed to optimize a joint deconvolution approach
in a cluster environment in order to recover an accurate representation of the
extended sky brightness distribution. In addition to a full description of the
calibration procedures, imaging pipeline, and quality assessments, we
demonstrated that:

  * •

the spatial power spectrum is a powerful tool in determining the correct
scaling factor applied to the total power observations when combining
interferometric and single dish data. For example, an overestimated scaling
factor results in a _decrease_ in power at small scales because the
combination effectively washes out the small-scale structure present in an
interferometer-only image.

  * •

The final SMC image cube possesses a rms noise level of 1.1 K per 0.98 km s-1
spectral channel and an angular resolution of 30′′ (8 pc at the distance of
the SMC). The noise properties of the final data are generally consistent
across the FoV until the sensitivity begins to drop at the edge of the PAF
footprint. A low-level grid pattern is apparent, likely stemming from
numerical artifacts from the Fourier Transforms that invert the gridded
visibilities to the image domain during major iterations. The noise scales as
predicted by Dickey et al. (2013) with the resolution of the restoring beam,
indicating these GASKAP-HI data are a breakthrough in terms of the compromise
between rms brightness temperature and angular resolution.

  * •

Our power spectrum analysis shows the distribution of Hi emission in the SMC
is well described by a single component power-law, consistent with the
interpretation that the ISM is fractal in nature and that stellar feedback is
probably not highlighted at any particular scale. Stochastic processes, such
as turbulence, therefore influence the structure of the ISM from scales
ranging from kpc down to sub-parsecs.

  * •

A comparison of the basic properties of an outflowing Hi complex derived from
test data with $\sim$4$\times$ worse spectral resolution relative to these new
pilot observations demonstrates the power of our pilot data to constrain
important ISM properties. The increase in spectral resolution allows us to
resolve an expanding Hi hole. The low thermal energy and expansion velocity
suggests a purely turbulent origin for this feature.

These new Hi images of the SMC show spectacular details on scales from 5 kpc
extending down to 10 pc and reveal previously unresolved narrow line features.
A separate paper will present the abundance of absorption detections in this
same field. These pilot data facilitate the study of how Hi contributes to the
conditions necessary for star formation, probe the hierarchical turbulent
spectrum down to physical scales three times smaller than previously measured,
and truly characterize the multi-phase make up of the interstellar medium.
GASKAP-HI provides an unequivocal view of the nearby Hi associated with the
detailed structures observed in the dust and molecular gas. Additionally, the
lessons learned from imaging extremely extended emission for the GASKAP-HI
survey will inform the data processing of future ultra wide-field surveys to
be undertaken by the Square Kilometer Array that will face identical imaging
challenges. The increase in brightness temperature sensitivity, coupled with
the unparalleled angular and spectral resolution, ensures the GASKAP-HI survey
will provide touchstone data products for the study of Hi in the Milky Way and
Magellanic System for the next decade and beyond.

###### Acknowledgements.

We thank the anonymous expert reviewer whose comments helped to focus the
presentation and discussion of these data products. The Australian SKA
Pathfinder is part of the Australia Telescope National Facility which is
managed by CSIRO. Operation of ASKAP is funded by the Australian Government
with support from the National Collaborative Research Infrastructure Strategy.
ASKAP uses the resources of the Pawsey Supercomputing Centre. Establishment of
ASKAP, the Murchison Radio-astronomy Observatory and the Pawsey Supercomputing
Centre are initiatives of the Australian Government, with support from the
Government of Western Australia and the Science and Industry Endowment Fund.
We acknowledge the Wajarri Yamatji people as the traditional owners of the
Observatory site. Pipeline development was tested on the OzSTAR supercomputer
under the project code, oz145, which is available through Swinburne
University’s Centre of Astrophysics and Supercomputing. This research was
supported by the Australian Research Council (ARC) through grant DP190101571.
N.M.-G. acknowledges the support of the ARC through Future Fellowship
FT150100024. G. A. and J. F. G. acknowledge support from the State Agency for
Research (10.13039/501100011033) of the Spanish MCIU, through grants
AYA2017-84390-C2-1-R and PID2020-114461GB-I00 (co-funded by FEDER) and the
“Center of Excellence Severo Ochoa” award for the Instituto de Astrofísica de
Andalucía (SEV-2017-0709). C. E. M. is supported by an NSF Astronomy and
Astrophysics Postdoctoral Fellowship under award AST-1801471.

## References

  * darkbluergb0,0,0.597656
  * Agertz et al. (2015) Agertz O., Romeo A. B., Grisdale K., 2015, darkblueMNRAS, 449, 2156
  * Allen et al. (2012) Allen R. J., Ivette Rodríguez M., Black J. H., Booth R. S., 2012, darkblueAJ, 143, 97
  * Allen et al. (2015) Allen R. J., Hogg D. E., Engelke P. D., 2015, darkblueAJ, 149, 123
  * Allison et al. (2020) Allison J. R., et al., 2020, darkblueMNRAS, 494, 3627
  * Anderson et al. (2021) Anderson C. S., et al., 2021, darkbluePASA, 38, e020
  * Audit & Hennebelle (2005) Audit E., Hennebelle P., 2005, darkblueA&A, 433, 1
  * Banda-Barragán et al. (2016) Banda-Barragán W. E., Parkin E. R., Federrath C., Crocker R. M., Bicknell G. V., 2016, darkblueMNRAS, 455, 1309
  * Banda-Barragán et al. (2019) Banda-Barragán W. E., Zertuche F. J., Federrath C., García Del Valle J., Brüggen M., Wagner A. Y., 2019, darkblueMNRAS, 486, 4526
  * Banda-Barragán et al. (2021) Banda-Barragán W. E., Brüggen M., Heesen V., Scannapieco E., Cottle J., Federrath C., Wagner A. Y., 2021, darkblueMNRAS, 506, 5658
  * Beuther et al. (2016) Beuther H., et al., 2016, darkblueA&A, 595, A32
  * Bialy et al. (2015) Bialy S., Sternberg A., Lee M.-Y., Le Petit F., Roueff E., 2015, darkblueApJ, 809, 122
  * Boothroyd et al. (2011) Boothroyd A. I., Blagrave K., Lockman F. J., Martin P. G., Pinheiro Gonçalves D., Srikanth S., 2011, darkblueA&A, 536, A81
  * Braun & Walterbos (1985) Braun R., Walterbos R. A. M., 1985, A&A, 143, 307
  * Burkhart et al. (2010) Burkhart B., Stanimirović S., Lazarian A., Kowal G., 2010, darkblueApJ, 708, 1204
  * Burkhart et al. (2015) Burkhart B., Lee M.-Y., Murray C. E., Stanimirović S., 2015, darkblueApJ, 811, L28
  * Busch et al. (2021) Busch M. P., Engelke P. D., Allen R. J., Hogg D. E., 2021, darkblueApJ, 914, 72
  * Clark et al. (2014) Clark S. E., Peek J. E. G., Putman M. E., 2014, darkblueApJ, 789, 82
  * Cornwell (2008) Cornwell T. J., 2008, darkblueIEEE Journal of Selected Topics in Signal Processing, 2, 793
  * Cornwell et al. (2005) Cornwell T. J., Golap K., Bhatnagar S., 2005, in Shopbell P., Britton M., Ebert R., eds, Astronomical Society of the Pacific Conference Series Vol. 347, Astronomical Data Analysis Software and Systems XIV. p. 86
  * Cotton (2017) Cotton W. D., 2017, darkbluePASP, 129, 094501
  * Daigle et al. (2007) Daigle A., Joncas G., Parizeau M., 2007, darkblueApJ, 661, 285
  * Dempsey et al. (2020) Dempsey J., McClure-Griffiths N. M., Jameson K., Buckland-Willis F., 2020, darkblueMNRAS, 496, 913
  * Di Teodoro & Fraternali (2015) Di Teodoro E. M., Fraternali F., 2015, darkblueMNRAS, 451, 3021
  * Di Teodoro et al. (2019a) Di Teodoro E. M., et al., 2019a, darkblueMNRAS, 483, 392
  * Di Teodoro et al. (2019b) Di Teodoro E. M., et al., 2019b, darkblueApJ, 885, L32
  * Dickey et al. (2013) Dickey J. M., et al., 2013, darkbluePASA, 30, e003
  * Eden et al. (2021) Eden D. J., et al., 2021, darkblueMNRAS, 500, 191
  * Elmegreen & Falgarone (1996) Elmegreen B. G., Falgarone E., 1996, darkblueApJ, 471, 816
  * Elmegreen & Scalo (2004) Elmegreen B. G., Scalo J., 2004, darkblueARA&A, 42, 211
  * Falconer (1997) Falconer 1997, in Sons J. W. ., ed., EAS Publications Series Vol. 1, Fractal Geometry. p. 25
  * Falgarone et al. (1991) Falgarone E., Phillips T. G., Walker C. K., 1991, darkblueApJ, 378, 186
  * Faridani et al. (2018) Faridani S., Bigiel F., Flöer L., Kerp J., Stanimirović S., 2018, darkblueAstronomische Nachrichten, 339, 87
  * Fierlinger et al. (2016) Fierlinger K. M., Burkert A., Ntormousi E., Fierlinger P., Schartmann M., Ballone A., Krause M. G. H., Diehl R., 2016, darkblueMNRAS, 456, 710
  * For et al. (2019) For B. Q., et al., 2019, darkblueMNRAS, 489, 5723
  * Gaia Collaboration et al. (2016) Gaia Collaboration et al., 2016, darkblueA&A, 595, A1
  * Gaia Collaboration et al. (2021) Gaia Collaboration et al., 2021, darkblueA&A, 649, A1
  * Girichidis et al. (2021) Girichidis P., Naab T., Walch S., Berlok T., 2021, darkblueMNRAS, 505, 1083
  * Glover & Clark (2012) Glover S. C. O., Clark P. C., 2012, darkblueMNRAS, 426, 377
  * Gnedin et al. (2009) Gnedin N. Y., Tassis K., Kravtsov A. V., 2009, darkblueApJ, 697, 55
  * Gordon (1976) Gordon M. A., 1976, darkblueMethods of Experimental Physics, 12, 277
  * Gordon et al. (2014) Gordon K. D., et al., 2014, darkblueThe Astrophysical Journal, 797, 85
  * Grisdale et al. (2017) Grisdale K., Agertz O., Romeo A. B., Renaud F., Read J. I., 2017, darkblueMNRAS, 466, 1093
  * Gronke et al. (2021) Gronke M., Oh S. P., Ji S., Norman C., 2021, arXiv e-prints, p. arXiv:2107.13012
  * Grønnow et al. (2017) Grønnow A., Tepper-García T., Bland-Hawthorn J., McClure-Griffiths N. M., 2017, darkblueApJ, 845, 69
  * Grønnow et al. (2018) Grønnow A., Tepper-García T., Bland-Hawthorn J., 2018, darkblueApJ, 865, 64
  * Guzman et al. (2019) Guzman J., et al., 2019, Astrophysics Source Code Library, p. ascl:1912.003
  * HI4PI Collaboration et al. (2016) HI4PI Collaboration et al., 2016, darkblueA&A, 594, A116
  * Hancock et al. (2018) Hancock P. J., Trott C. M., Hurley-Walker N., 2018, darkbluePublications of the Astronomical Society of Australia, 35, e011
  * Hartmann (1999) Hartmann D. H., 1999, darkblueProceedings of the National Academy of Science, 96, 4752
  * Heydari-Malayeri & Selier (2010) Heydari-Malayeri M., Selier R., 2010, darkblueA&A, 517, A39
  * Heywood et al. (2019) Heywood I., et al., 2019, darkblueNature, 573, 235
  * Hilditch et al. (2005) Hilditch R. W., Howarth I. D., Harries T. J., 2005, darkblueMNRAS, 357, 304
  * Hotan et al. (2021) Hotan A. W., et al., 2021, darkbluePASA, 38, e009
  * Huynh et al. (2020) Huynh M., Dempsey J., Whiting M. T., Ophel M., 2020, Astronomical Data Analysis Software and Systems XXVII. ASP Conference Series, 522, 263
  * Ibáñez-Mejía et al. (2017) Ibáñez-Mejía J. C., Mac Low M.-M., Klessen R. S., Baczynski C., 2017, darkblueApJ, 850, 62
  * Indu & Subramaniam (2015) Indu G., Subramaniam A., 2015, darkblueA&A, 573, A136
  * Johnston et al. (2007) Johnston S., et al., 2007, darkbluePASA, 24, 174
  * Kalberla & Haud (2018) Kalberla P. M. W., Haud U., 2018, darkblueA&A, 619, A58
  * Kalberla & Haud (2019) Kalberla P. M. W., Haud U., 2019, darkblueA&A, 627, A112
  * Kalberla et al. (2010) Kalberla P. M. W., et al., 2010, Astronomy and Astrophysics, 521, A17
  * Kerp et al. (2011) Kerp J., Winkel B., Ben Bekhti N., Flöer L., Kalberla P. M. W., 2011, darkblueAstronomische Nachrichten, 332, 637
  * Kim et al. (1998) Kim S., Staveley-Smith L., Dopita M. A., Freeman K. C., Sault R. J., Kesteven M. J., McConnell D., 1998, darkblueApJ, 503, 674
  * Klessen & Hennebelle (2010) Klessen R. S., Hennebelle P., 2010, darkblueA&A, 520, A17
  * Koch et al. (2020) Koch E. W., Chiang I.-D., Utomo D., Chastenet J., Leroy A. K., Rosolowsky E. W., Sandstrom K. M., 2020, darkblueMNRAS, 492, 2663
  * Koda et al. (2011) Koda J., et al., 2011, darkblueApJS, 193, 19
  * Koda et al. (2019) Koda J., Teuben P., Sawada T., Plunkett A., Fomalont E., 2019, darkbluePASP, 131, 054505
  * Koribalski et al. (2020) Koribalski B. S., et al., 2020, darkblueAp&SS, 365, 118
  * Kowal & Lazarian (2007) Kowal G., Lazarian A., 2007, darkblueApJ, 666, L69
  * Kreckel et al. (2020) Kreckel K., et al., 2020, darkblueMNRAS, 499, 193
  * Krumholz & Burkhart (2016) Krumholz M. R., Burkhart B., 2016, darkblueMNRAS, 458, 1671
  * Lee et al. (2012) Lee M.-Y., et al., 2012, darkblueApJ, 748, 75
  * Leroy et al. (2021) Leroy A. K., et al., 2021, arXiv e-prints, p. arXiv:2104.07739
  * Lindner et al. (2015) Lindner R. R., et al., 2015, darkblueAJ, 149, 138
  * Mac Low & Klessen (2004) Mac Low M.-M., Klessen R. S., 2004, darkblueReviews of Modern Physics, 76, 125
  * Madau & Dickinson (2014) Madau P., Dickinson M., 2014, darkblueARA&A, 52, 415
  * Marchal et al. (2019) Marchal A., Miville-Deschênes M.-A., Orieux F., Gac N., Soussen C., Lesot M.-J., d’Allonnes A. R., Salomé Q., 2019, darkblueA&A, 626, A101
  * Martin et al. (2015) Martin P. G., Blagrave K. P. M., Lockman F. J., Pinheiro Gonçalves D., Boothroyd A. I., Joncas G., Miville-Deschênes M. A., Stephan G., 2015, darkblueApJ, 809, 153
  * McClure-Griffiths et al. (2005) McClure-Griffiths N. M., Dickey J. M., Gaensler B. M., Green A. J., Haverkorn M., Strasser S., 2005, darkblueApJS, 158, 178
  * McClure-Griffiths et al. (2009) McClure-Griffiths N. M., et al., 2009, darkblueApJS, 181, 398
  * McClure-Griffiths et al. (2012) McClure-Griffiths N. M., Dickey J. M., Gaensler B. M., Green A. J., Green J. A., Haverkorn M., 2012, darkblueApJS, 199, 12
  * McClure-Griffiths et al. (2018) McClure-Griffiths N. M., et al., 2018, darkblueNature Astronomy, 2, 901
  * McConnell (2016) McConnell D., 2016, Field structure at the focus of paraboloidal reflectors and comparison with ASKAP beams, http://www.atnf.csiro.au/projects/askap/ACES-memos
  * McKee & Ostriker (1977) McKee C. F., Ostriker J. P., 1977, darkblueApJ, 218, 148
  * McMullin et al. (2007) McMullin J. P., Waters B., Schiebel D., Young W., Golap K., 2007, in Shaw R. A., Hill F., Bell D. J., eds, Astronomical Society of the Pacific Conference Series Vol. 376, Astronomical Data Analysis Software and Systems XVI. p. 127
  * Meixner et al. (2013) Meixner M., et al., 2013, darkblueAJ, 146, 62
  * Meyer et al. (2017) Meyer M., Robotham A., Obreschkow D., Westmeier T., Duffy A. R., Staveley-Smith L., 2017, darkbluePASA, 34, 52
  * Miville-Deschênes et al. (2016) Miville-Deschênes M. A., Duc P. A., Marleau F., Cuillandre J. C., Didelon P., Gwyn S., Karabal E., 2016, darkblueA&A, 593, A4
  * Murphy et al. (2013) Murphy T., et al., 2013, darkbluePASA, 30, e006
  * Nomoto et al. (2013) Nomoto K., Kobayashi C., Tominaga N., 2013, darkblueARA&A, 51, 457
  * Norman & Ferrara (1996) Norman C. A., Ferrara A., 1996, darkblueApJ, 467, 280
  * Norris et al. (2011) Norris R. P., et al., 2011, darkbluePASA, 28, 215
  * Noterdaeme et al. (2012) Noterdaeme P., et al., 2012, darkblueA&A, 547, L1
  * Offringa et al. (2014) Offringa A. R., et al., 2014, darkblueMNRAS, 444, 606
  * Padoan et al. (2006) Padoan P., Juvela M., Kritsuk A., Norman M. L., 2006, darkblueApJ, 653, L125
  * Padoan et al. (2012) Padoan P., Haugbølle T., Nordlund Å., 2012, darkblueApJ, 759, L27
  * Padoan et al. (2016) Padoan P., Pan L., Haugbølle T., Nordlund Å., 2016, darkblueApJ, 822, 11
  * Peek et al. (2018) Peek J. E. G., et al., 2018, darkblueApJS, 234, 2
  * Phillips et al. (2009) Phillips J. P., Ramos-Larios G., Perez-Grana J. A., 2009, darkblueMNRAS, 397, 1215
  * Pietrzyński et al. (2013) Pietrzyński G., et al., 2013, darkblueNature, 495, 76
  * Pingel et al. (2013) Pingel N. M., et al., 2013, darkblueApJ, 779, 36
  * Pingel et al. (2018) Pingel N. M., Lee M.-Y., Burkhart B., Stanimirović S., 2018, darkblueApJ, 856, 136
  * Pon et al. (2012) Pon A., Johnstone D., Kaufman M. J., 2012, darkblueApJ, 748, 25
  * Rachford et al. (2009) Rachford B. L., et al., 2009, darkblueApJS, 180, 125
  * Rau et al. (2019) Rau U., Naik N., Braun T., 2019, darkblueAJ, 158, 3
  * Riener et al. (2019) Riener M., Kainulainen J., Henshaw J. D., Orkisz J. H., Murray C. E., Beuther H., 2019, darkblueA&A, 628, A78
  * Salvatier et al. (2015) Salvatier J., Wiecki T., Fonnesbeck C., 2015, arXiv e-prints, p. arXiv:1507.08050
  * Sault et al. (1995) Sault R. J., Teuben P. J., Wright M. C. H., 1995, in Shaw R. A., Payne H. E., Hayes J. J. E., eds, Astronomical Society of the Pacific Conference Series Vol. 77, Astronomical Data Analysis Software and Systems IV. p. 433 (arXiv:astro-ph/0612759)
  * Schneider et al. (2020) Schneider E. E., Ostriker E. C., Robertson B. E., Thompson T. A., 2020, darkblueApJ, 895, 43
  * Serra et al. (2015) Serra P., et al., 2015, darkblueMNRAS, 448, 1922
  * Stanimirović (2002) Stanimirović S., 2002, in Stanimirovic S., Altschuler D., Goldsmith P., Salter C., eds, Astronomical Society of the Pacific Conference Series Vol. 278, Single-Dish Radio Astronomy: Techniques and Applications. pp 375–396 (arXiv:astro-ph/0205329)
  * Stanimirović et al. (1999) Stanimirović S., Staveley-Smith L., Dickey J. M., Sault R. J., Snowden S. L., 1999, darkblueMNRAS, 302, 417
  * Staveley-Smith et al. (1997) Staveley-Smith L., Sault R. J., Hatzidimitriou D., Kesteven M. J., McConnell D., 1997, darkblueMNRAS, 289, 225
  * Stil et al. (2006) Stil J. M., et al., 2006, darkblueAJ, 132, 1158
  * Sun et al. (2018) Sun N.-C., et al., 2018, darkblueApJ, 858, 31
  * Szotkowski et al. (2019) Szotkowski S., et al., 2019, darkblueApJ, 887, 111
  * Taylor et al. (2003) Taylor A. R., et al., 2003, darkblueAJ, 125, 3145
  * Vázquez-Semadeni (2012) Vázquez-Semadeni E., 2012, in de Avillez M. A., ed., EAS Publications Series Vol. 56, EAS Publications Series. pp 39–49, darkbluedoi:10.1051/eas/1256005
  * Vázquez-Semadeni et al. (2019) Vázquez-Semadeni E., Palau A., Ballesteros-Paredes J., Gómez G. C., Zamora-Avilés M., 2019, darkblueMNRAS, 490, 3061
  * Vijayan et al. (2020) Vijayan A., Kim C.-G., Armillotta L., Ostriker E. C., Li M., 2020, darkblueApJ, 894, 12
  * Wang et al. (2020) Wang Y., et al., 2020, darkblueA&A, 634, A139
  * Westmeier et al. (2021) Westmeier T., et al., 2021, darkblueMNRAS, 506, 3962
  * Whiting (2020) Whiting M. T., 2020, in Ballester P., Ibsen J., Solar M., Shortridge K., eds, Astronomical Society of the Pacific Conference Series Vol. 522, Astronomical Data Analysis Software and Systems XXVII. p. 469
  * Winkler et al. (2015) Winkler P. F., Smith R. C., Points S. D., MCELS Team 2015, in Points S., Kunder A., eds, Astronomical Society of the Pacific Conference Series Vol. 491, Fifty Years of Wide Field Studies in the Southern Hemisphere: Resolved Stellar Populations of the Galactic Bulge and Magellanic Clouds. p. 343
  * Wolfire et al. (1995) Wolfire M. G., Hollenbach D., McKee C. F., Tielens A. G. G. M., Bakes E. L. O., 1995, darkblueApJ, 443, 152
  * Wolfire et al. (2003) Wolfire M. G., McKee C. F., Hollenbach D., Tielens A. G. G. M., 2003, darkblueApJ, 587, 278