11institutetext: Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69,
53121 Bonn, Germany 22institutetext: Wits Centre for Astrophysics, School of
Physics, University of the Witwatersrand, 1 Jan Smuts Avenue, Johannesburg,
2000, South Africa 33institutetext: Department of Physics, University of
Pretoria, Private Bag X20, Pretoria 0028, South Africa 44institutetext: SKA
Observatory, Jodrell Bank, Lower Withington, Macclesfield, SK11 9FT, United
Kingdom 55institutetext: Research School of Astronomy & Astrophysics,
Australian National University, Canberra, ACT 2611, Australia

# The Galactic latitude dependency of Faraday complexity in the S-PASS/ATCA RM
catalogue

S. Ranchod E-mail<EMAIL_ADDRESS>S. A Mao 11 R. Deane 2233 S.
S. Sridhar 44 A. Damas-Segovia 11 J. D. Livingston 11 Y. K. Ma 55

(Received December 18, 2023; accepted March 14, 2024)

The S-band Polarisation All Sky Survey (SPASS/ATCA) rotation measure (RM)
catalogue is the largest broadband RM catalogue to date, increasing the RM
density in the sparse southern sky. Through analysis of this catalogue, we
report a latitude dependency of the Faraday complexity of polarised sources in
this catalogue within 10∘ of the Galactic plane towards the inner Galaxy. In
this study, we aim to investigate this trend with follow-up observations using
the Australia Telescope Compact Array (ATCA). We observe 95 polarised sources
from the SPASS/ATCA RM catalogue at 1.1 – 3.1 GHz with ATCA’s 6 km
configuration. We present Stokes QU fitting results and a comparative analysis
with the SPASS/ATCA catalogue. We find an overall decrease in complexity in
these sources with the higher angular resolution observations, with a
complexity fraction of 42%, establishing that the majority of the complexity
in the SPASS/ATCA sample is due to the mixing-in of diffuse Galactic emission
at scales $\theta>2.8^{\prime}$. Furthermore, we find a correlation between
our observed small-scale complexity $\theta<2.8^{\prime}$ and the Galactic
spiral arms, which we interpret to be due to Galactic turbulence or small-
scale polarised emission. These results emphasise the importance of
considering the maximum angular scale to which the observations are sensitive
in the classification of Faraday complexity; the effect of which can be more
carefully investigated with SKA-precursor and pathfinder arrays (e.g. MeerKAT
and ASKAP).

###### Key Words.:

Polarization – Radio continuum: galaxies – Galaxy: general – Techniques:
polarimetric

##  1 Introduction

Magnetic fields have an essential dynamic role in galaxy evolution,
particularly in influencing the distribution of cold and ionised gas and the
formation of stars (for a review, see Beck, 2015). It is therefore important
to fully understand the structure and strength of magnetic fields in galaxies.
For example, there remain unanswered questions concerning the role of magneto-
ionic turbulence in galaxy evolution and the correlation length of turbulence
in the interstellar medium (ISM). A primary observational tool for probing
magnetic fields in galaxies is the Faraday rotation of linearly polarised
synchrotron emission from a background source as it passes through an
intervening magneto-ionic medium (e.g. Lamee et al., 2016; Ma et al., 2020;
Eyles et al., 2020). This background synchrotron radiation is typically from
active galactic nuclei (AGN) and is parameterised by the Faraday rotation
measure (RM) or, in the general case, characterised by the Faraday depth
$\phi$ (Burn, 1966),

$\phi(L)=0.812\int_{\boldsymbol{s}=0}^{L}n_{\mathrm{e}}\boldsymbol{B}\cdot\mathrm{d}\boldsymbol{s}\;\;\mathrm{rad\,m}^{-2},$
(1)

where $n_{\mathrm{e}}$ and $\boldsymbol{B}$ are, respectively, the electron
density and magnetic field of intervening media along the line of sight
$\boldsymbol{s}$, from the source to the observer $L$. A linearly polarised
synchrotron-emitting source is considered Faraday simple when the entire
source is subjected to a single $\phi$ only (i.e. a single Faraday thin
polarised component is detected). Meanwhile, Faraday complex sources are
composed of multiple polarisation components, each experiencing a different
amount of Faraday rotation due to the distribution of the magneto-ionic medium
between them (e.g. Farnsworth et al., 2011; Anderson et al., 2015). Such
changes can either occur in the medium within or surrounding those sources, or
in the Galactic foreground. In Faraday complex cases, the Faraday depth
parameter allows for the characterisation of emitting Faraday components or
magnetised sources through techniques such as RM synthesis (Brentjens & de
Bruyn, 2005) and Stokes QU fitting (Farnsworth et al., 2011; O’Sullivan et
al., 2012). Faraday complexity is an observational classification and can be
affected by various observational parameters, such as angular resolution,
frequency, and telescope sensitivity (e.g. Sun et al., 2015).

Extragalactic sources (EGSs) exhibit a variation in complex Stokes Q and U
spectra as a function of $\lambda^{2}$, which encode the physical magnetic
field properties of the emitting sources and intervening Faraday screens (e.g.
Farnsworth et al., 2011; O’Sullivan et al., 2012). With the advent of
broadband receivers and backends in centimetre-wavelength radio telescopes –
for example, the Australia Telescope Compact Array (ATCA), Karl G. Jansky Very
Large Array (VLA), Australian Square Kilometre Array Pathfinder (ASKAP), and
MeerKAT – we are, in principle, able to disentangle the various contributions
in the polarised emission of Faraday complex sources by fitting multi-
component physical models to broadband Q and U spectra. This reveals rich
properties of the magneto-ionic medium that were previously inaccessible with
narrow-band data (e.g. O’Sullivan et al., 2017; Pasetto et al., 2018; Ma et
al., 2019a). Methods such as QU fitting (Farnsworth et al., 2011; O’Sullivan
et al., 2012) and RM synthesis (Brentjens & de Bruyn, 2005) enable a good
characterisation of Faraday complexity in EGSs; however, the field is still
developing and there are open questions as to how the classification of
Faraday complexities can be integrated into a physical model (e.g. Alger et
al., 2021).

Previous studies have reported trends in Faraday complexity due to various
foreground screens. Livingston et al. (2021) found that a large percentage
(95%) of their sample of EGSs in the Galactic centre region are Faraday
complex, which is attributed to small-scale ($\sim 3$ pc) turbulence in the
Galactic foreground screen driven by stellar feedback. Anderson et al. (2015)
analysed the environment of 14 Faraday complex sources at an arcminute
resolution and identified several possible contributors to complexity,
including foreground magneto-ionic galaxy clusters and an association of
complexity with ionisation fronts near neutral hydrogen structures in the ISM.

As this paper subsequently demonstrates, it is crucial to consider
observations at various angular scales to fully interpret the physical scale
of the Faraday complexity. In principle, interferometric observations using
long baselines can filter out the smoothly varying large-scale polarised
emission (e.g. from the Galactic plane) to better disentangle the
contributions of small-scale Faraday components in Faraday complex sources.
Such components can be associated with small-scale magneto-ionic turbulence
using the RM structure function (SF; Haverkorn et al., 2008; Stil et al.,
2011). The SF can be used to reveal the outer scale of turbulent cells and how
this changes with angular scale, as was done for the Galactic plane (Haverkorn
et al., 2008; Livingston et al., 2021), the Milky Way at high Galactic
latitudes (e.g. Mao et al., 2010), and Magellanic Clouds (e.g. Mao et al.,
2012). This method can also improve our understanding of turbulence within
nearby galaxies and the EGSs themselves (Anderson et al., 2015, 2016;
O’Sullivan et al., 2017).

RM grids allow us to understand the variation of magnetic fields on various
scales and in different cosmic environments, for example, nearby galaxies
(e.g. Gaensler et al., 2005; Mao et al., 2008; Livingston et al., 2022),
galaxy clusters (e.g. Anderson et al., 2021) or the Milky Way (Brown et al.,
2007; Haverkorn et al., 2008; Hutschenreuter et al., 2022), dependent on the
density of polarised background sources. This can be constrained by more
sensitive, large-area polarised intensity surveys. Modern large area
polarisation surveys at lower frequencies ($\leq$ 1.1 GHz) include the LOFAR
Two-metre Sky Survey (LoTSS, O’Sullivan et al., 2023) and Spectral and
Polarisation in Cutouts of Extragalactic sources from the Rapid ASKAP
Continuum Survey (SPICE-RACS, Thomson et al., 2023), with 2461 and 5818
sources respectively. The Taylor et al. (2009) catalogue derived from NRAO VLA
Sky Survey is the largest RM catalogue to date, containing $\sim
40\leavevmode\nobreak\ 000$ sources at DEC $>-40^{\circ}$, observed with two
narrow bands (42 MHz) at $\sim 1.4$ GHz. However, due to the limitations of
narrow-band spectropoliametry, this catalogue contains inaccurate RMs due to
the n$\pi$ ambiguity (Ma et al., 2019a), and increased RM uncertainties from
off-axis instrumental polarisation (Ma et al., 2019b). The SPASS/ATCA RM
catalogue (Schnitzeler et al., 2019, hereafter S19) is currently the most
extensive large-area broadband catalogue at cm-wavelengths, with $\sim 4500$
sources at DEC $<0^{\circ}$, covering 1–3 GHz. This catalogue has contributed
to improving the Galactic Faraday sky reconstruction, by increasing the RM
density to 1 RM per 5 deg2 in the “southern hole” (Hutschenreuter et al.,
2022). This unique catalogue will continue to have legacy value into the SKA-
era, due to its polarised source density, sky coverage and, most importantly
its broad bandwidth. It is therefore important to fully understand any
systematic trends observed. However, the SPASS/ATCA catalogue has several
limitations, particularly its low angular resolution, short integration time
and the spectra-extraction methods used. Follow-up observations can help us
better characterise these limitations to optimise the synergy and scientific
output of this catalogue in the pre-SKA and SKA eras.

In this paper, we present a study of the polarisation properties of a subset
of 95 sources from the SPASS/ATCA catalogue with follow-up observations from
the ATCA. We investigate the dependence of Faraday complexity with Galactic
latitude and how this dependency changes with higher angular resolution data.
Furthermore, through the QU fitting and the analysis of Faraday spectra, we
aim to discern whether this dependence is caused by mixed-in diffuse Galactic
emission or small-scale turbulence in the Galactic Plane.

This paper is organised as follows; In Sect. 2, we detail the systematics we
uncovered in the SPASS/ATCA catalogue and describe our observations and data
calibration methods. Section 3 describes our methods of extracting and
analysing the spectro-polarimetric data. Section 4 presents the results from
RM synthesis, QU fitting and Faraday complexity classification. In Sect. 5, we
discuss the physical origin of Faraday complex sources, how observational
constraints affect the perception of complexity and resulting caveats
regarding the SPASS/ATCA catalogue. We summarise and conclude in Sect. 6.

##  2 Data

###  2.1 The SPASS/ATCA RM catalogue

The SPASS/ATCA RM catalogue (S19) contains $\sim 4500$ polarised sources at
Dec $\leq 0$ deg. The survey was observed using an unconventional snapshot
mode ($\sim 36$ s on source integration time) with the ATCA in the 16 cm
(1.1–3.1 GHz) band. S19 used the hybrid ATCA configuration H168 (excluding
antenna 6) with baselines between 61 – 192 m. This configuration was chosen to
maximise $uv$-coverage for equatorial sources, and corresponds to an angular
scale of 2.8’ $<\theta<$ 9.0’, and a reported angular resolution of
$1^{\prime}\times 2^{\prime}$. The spectra were extracted directly from the
visibilities without forming spectral image cubes to reduce processing time
and the required storage space. The Stokes Q and U spectra were then fit
iteratively for up to 5 Faraday-thin (simple) polarised components using the
FIRESTARTER (Schnitzeler & Lee, 2017) fitting algorithm. Here, sources are
considered Faraday simple if they are best fit by a single polarised component
and Faraday complex if they are best fit by multiple polarised components. The
details of this classification and fitting methods used are elaborated on in
Sect. 3.2.

The spatial distribution of Faraday simple and Faraday complex source density
is shown in Fig. 1. In this plot, we find an increase in the number of sources
with multiple fitted polarised components (Faraday complex) towards the
Galactic plane, as well as a decrease in the number of sources with only one
fitted polarised component (Faraday simple) towards the plane. This systematic
trend was not previously noted in the literature. A reduction in Faraday
simple source density and a corresponding increase in Faraday complex source
density is seen above and below the Galactic plane. It is more pronounced
towards the inner Galaxy in Q1 and Q4 ( $30^{\circ}>l>0^{\circ}$,
$360^{\circ}>l>270^{\circ}$). We also observe a deficit of Faraday simple
sources at $b\sim 0^{\circ},l\sim 280^{\circ}$, which is likely produced by
the Gum Nebula (e.g. Stil et al., 2011; Purcell et al., 2015). The gap in
Faraday complex sources that are very close to the Galactic plane
($|b|<1.5^{\circ}$), in the right panel of Fig. 1, is a selection effect from
S19.

Figure 1: Sky source density distribution for Faraday simple ($n=1$, left) and
Faraday complex ($n>1$, right) polarised sources from the SPASS/ATCA catalogue
in Galactic Mollweide projection. The colour bar indicates the number of
sources per bin. Figure 2: Mean number of fitted polarised components for
sources in the SPASS/ATCA RM catalogue, as a function of Galactic latitude.
The different colours indicate different latitude bins. The grey, shaded
regions indicate the latitude range of our observations.

We further demonstrate this trend of increased complexity in Fig. 2, with the
increase in the mean number of fitted polarised components (i.e. the Faraday
complexity) as a function of Galactic latitude. The distribution is binned in
latitude with bin widths of 1, 2 and 4 degrees, and a respective average of
47, 95 and 189 sources per bin. There is an apparent increase in complexity
for sources closer to the Galactic plane at $|b|<10^{\circ}$. For larger
latitude bins, this effect is more pronounced at positive Galactic latitudes.
Sources that are Faraday complex, with multiple polarised components within
the beam volume (i.e. along the line of sight, or within the beam resolution)
that are intrinsic to the source, should be uniformly distributed across the
sky without a dependency on Galactic coordinates. We propose that the
increased complexity towards $b=0^{\circ}$ must therefore be Galactic in
origin.

The short baselines and the large beam size in the S19 observations can be
sensitive to the large-scale, diffuse polarised synchrotron emission in the
Milky Way. This could be a likely scenario for added complexities in Stokes Q
and U spectra close to the Galactic plane, particularly with the visibility
spectra extraction method used in S19. Another possible scenario for an
increase in Faraday complexity could be a turbulent foreground Faraday screen
caused by small-scale structures and fluctuations in electron density and
magnetic fields in the Milky Way (e.g. Haverkorn et al., 2008; Livingston et
al., 2021). With higher-angular-resolution broadband observations, we aim to
discern between the various scenarios to constrain the origin and scale of the
complexity at low Galactic latitudes.

###  2.2 ATCA observations

We selected a sample of 105 extragalactic sources with high polarised
intensities from the S19 catalogue for follow-up observations with the ATCA.
We selected sources in close proximity to the Galactic plane, with
$1.5^{\circ}<|b|<10^{\circ}$ and $310^{\circ}<l<360^{\circ}$, a polarised
intensity lower limit of $P>$ 6 mJy and polarised fractions $p_{f}>0.01$. Of
the selected sources, we classify ten as extended, and 95 as unresolved by
inspecting the Stokes I images from the Rapid ASKAP Continuum survey (RACS;
McConnell et al., 2020; Hale et al., 2021)-low DR1, at an angular resolution
of 25”.

A total of 24 hours of observations were obtained over two 12-hour observing
runs. The observations were done in the ATCA 16 cm band (1.1 – 3.1 GHz) with
the 6 km configuration. 48 sources ($l>333^{\circ}$) were observed on 28
January 2022. Each source was observed for a total of 9.5 minutes over six
(95-second) scans every $\sim 2$ hours, to optimise $uv-$coverage and
parallactic angle coverage. The primary flux and bandpass calibrator PKS
B1934$-$638 was observed for 20 minutes at the end of the observing run. We
selected the closest secondary phase calibrators from the ATCA calibrator
database. The secondary calibrators are summarised in Table 1. The six phase
calibrators were observed intermittently throughout the observations,
bracketing the scans of the target sources. The remaining 54 sources
($l<333^{\circ}$) were observed on 5 February 2022. Each source was observed
for a total of 8.2 minutes over seven (70-second) scans. We observed PKS
B1934$-$638 for 10 minutes and the four phase calibrators multiple times
($\sim 60$ seconds each) throughout the observation, as in the first
observations. Three of the phase calibrators were also science targets (marked
in Table 1).

Table 1: Source names and positions of secondary phase calibrators. The calibrators also used as science targets are marked with an asterisk. Observation date | Source name | RA (J2000) | Dec (J2000)
---|---|---|---
28 Jan 2022 | PKS B1421$-$490 | 14:24:32 |  $-$49:13:49
| PKS B1511$-$47* | 15:14:40 |  $-$47:48:30
| PKS B1600$-$44 | 16:04:31 |  $-$44:41:31
| PKS B1613$-$586* | 16:17:17 |  $-$58:48:07
| PKS B1511$-$55 | 15:15:12 |  $-$55:59:33
| PKS B1352$-$63 | 13:55:46 |  $-$63:26:42
5 Feb 2022 | PKS B1600$-$44 | 16:04:31 |  $-$44:41:32
| PKS B1622$-$310 | 16:25:55 |  $-$31:08:08
| PKS B1759$-$39* | 18:02:43 |  $-$39:40:08
| PKS B1740$-$517 | 17:44:25 |  $-$51:44:44

With our chosen array configuration, we have baselines from 192 m – 6 km,
resulting in angular scales of about $5.5"<\theta<2.8^{\prime}$. With a lower
maximum angular-scale sensitivity than S19, and a higher angular resolution,
we aim to filter out any large-scale diffuse polarised emission from the
Galactic plane and minimise beam depolarisation effects. These observations
have a factor $\sim$14 longer integration time than S19, and we expect a
factor $\sim$4 lower thermal noise. These conditions allow us to distinguish
whether the S19 observations have been contaminated by diffuse polarised
synchrotron Galactic emission and to identify localised small-scale regions of
magnetic field structure, for example, turbulence, patchy polarised emission.

###  2.3 Calibration and imaging

Data calibration was carried out following the standard procedure for Compact
Array Broadband Backend (CABB) data with the Miriad software (Sault et al.,
1995). PKS B1934$-$638 was used for bandpass, polarisation leakage and flux
calibration. The calibrators listed in Table 1 were used for complex gain
calibration. We did systematic manual and automatic flagging on all
calibrators before and after calibration, using Miriad tasks blflag and
pgflag. We flagged 100 MHz at the band edges due to poor sensitivity.

We created shallow Stokes I Multi-Frequency Synthesis (MFS) images for all
target sources using Miriad’s invert, clean and restore. Masks were generated
at a 10$\sigma$ threshold, and phase and amplitude self-calibration was
performed with Miriad’s selfcal. We used masked deconvolution to produce full-
Stokes MFS images. The image sizes were 2000$\times$2000 pixels with a pixel
size of 0.7” and we used a Briggs (Briggs, 1995) robust weighting of 0.5. We
applied primary beam correction and smoothed to a common beam of
15”$\times$15”, to account for beam variation across the 2 GHz bandwidth. This
resolution corresponds to the major axis of the beam at the low-frequency end
of the band, and at this angular resolution, 46 sources are spatially
unresolved, and 49 have another spatial component within the 2’ range of the
S19 beam. An example image of source SPASS J160700$-$452802 is shown in Fig.
3. The Stokes V MFS images have a mean rms of $\sim 97\,\mu$Jy beam-1, in
comparison to the theoretical rms of $\sim 80\,\mu$Jy beam-1.

Figure 3: Example of Stokes I (top) and polarised intensity (bottom) MFS
images from our observations for source SPASS J160700$-$452802\. The dashed
circles show the major and minor axes of the synthesised beam for the
Schnitzeler et al. (2019) data. The restoring beam for the example images is
shown in the bottom left corner (15”$\times$15”)

We imaged spectral cubes in Stokes I, Q, and U with Miriad, aiming to maximise
the per-channel signal-to-noise ratio (S/N) with broader channel width but
also considering the corresponding increase in bandwidth depolarisation
effects. In selecting an optimal channel width, we assumed a reasonable
depolarisation limit of 95% (Gaensler et al., 2001). Considering our lowest
unflagged frequency channel at 1.3 GHz and the highest $|\mathrm{RM}|$ from
the S19 selected sample, the maximum channel width with negligible bandwidth
depolarisation is $\Delta\nu=17$ MHz. Therefore, we correspondingly formed
spectral cubes with frequency steps of 17 MHz. The per-channel image sizes
were 2000$\times$2000 pixels with a pixel size of 0.7” and we used a Briggs
robust weighting of 0.5. As with the MFS images, we applied primary beam
correction and smoothed to a common beam of 15”$\times$15”.

In addition to the 95 target sources, we observed ten known extended sources,
as identified from RACS cutouts, to test the scale to which the selected array
configuration can filter out diffuse, extended emission. The RACS images have
an angular resolution of 25” $\times$ 25”. We find that these sources show no
smoothly varying diffuse emission at scales $>3^{\prime}$ in total intensity
or polarisation, and that this emission has successfully been filtered out in
our observations. In some cases, there is small-scale patchy emission visible
in the Stokes I MFS images. This emission all originates from the lobes of
resolved radio galaxies and is not Galactic. We measure the peak flux density
within the area of the S19 synthesised beam, and find on average that only 5%
of the S19 total intensity flux density is detected.

##  3 Spectro-polarimetric analysis

###  3.1 Total intensity and polarised data extraction

We used two different methods of extracting the total intensity flux density
values. Firstly, we determined the broadband total intensity
$I_{\mathrm{MFS}}$ by fitting 2D Gaussians to the Stokes I MFS images using
Casa (McMullin et al., 2007) imfit. Similarly, we fitted 2D Gaussians to the
2100 MHz frequency slice of the Stokes I image cubes to determine the total
intensity at 2100 MHz $I_{2100}$, for a more direct comparison to S19.
Secondly, we extracted spectra directly from the Stokes I, Q, and U spectral
cubes from the position of the peak pixel in the Stokes I MFS images. We
determined the RMS of the spectra from a 30” $\times$ 30” box at an angular
distance of $\sim 8^{\prime}$ from the pointing centre. Polarised intensity
$PI$ spectra were computed as

$PI(\lambda^{2})=\sqrt{Q(\lambda^{2})^{2}+U(\lambda^{2})^{2}}.$ (2)

We disregard the correction for noise bias due to the high signal-to-noise
ratios of polarised intensity in our observations (S/N $>10\sigma$, across the
band). It should be noted that the $PI$ spectra are only used for visual
inspection during QU fitting, and we report our polarised intensity
measurements and methods in Sect. 4.1.1. An example of the Stokes I, Q, U and
polarised intensity spectra for source SPASS J134355$-$564917 are shown in Fig
4.

Figure 4: Example of the spectra for source SPASS J134355$-$564917\. From top
to bottom: Panel 1 shows the total intensity spectrum as a function of
frequency. Panel 2 shows the Stokes Q/I and U/I spectra as a function of
$\lambda^{2}$, with the fractional polarisation spectrum indicated by the
dashed line. The fitted models for Stokes Q/I and U/I are also shown. In
panels 1 and 2, the shaded regions indicate the uncertainties. Panel 3 shows
the polarisation angle as a function of $\lambda^{2}$. Panel 4 shows the dirty
(green dotted) and cleaned (green solid) Faraday spectrum with the Rotation
Measure Spread Function (RMSF) in cyan. The black vertical line shows the peak
Faraday depth.

###  3.2 QU fitting

We use QU fitting (Farnsworth et al., 2011; O’Sullivan et al., 2012) to
characterise the magneto-ionic environment of the emitting source as well as
any polarised components within the beam volume. This is done by fitting
physical models describing the local and intervening magneto-ionic
environments to the polarised emission from a source (i.e. Stokes Q, U as a
function of $\lambda^{2}$). Broadband observations offer a unique advantage
for this. In particular, we want to characterise the complexity of sources in
the sample based on the model with the best fit. Here, we assume all targets
to be synchrotron-emitting point sources, with the possibility of the presence
of additional synchrotron-emitting Faraday-thin components within the beam
volume. This may include cases where the magnetised plasma is intrinsic to the
point source, or the Faraday-rotating foreground screen(s) is Faraday thick
(see Sect. 3.3) or turbulent. Before fitting, the Stokes Q and U spectra are
divided by the Stokes I spectrum to remove all first-order spectral index
effects. Following Schnitzeler & Lee (2017) and S19, we fitted models
describing the sum of up to five Faraday thin components:

$\displaystyle
q(\lambda^{2})=\sum^{n}_{j=1}q_{j}\left(\frac{\lambda^{2}}{\lambda_{\mathrm{ref}}{{}^{2}}}\right)^{-\delta\alpha_{j}/2}\mathrm{cos}[2(PA_{j}+\phi_{j}\lambda^{2})]$
(3) $\displaystyle
u(\lambda^{2})=\sum^{n}_{j=1}u_{j}\left(\frac{\lambda^{2}}{\lambda_{\mathrm{ref}}{{}^{2}}}\right)^{-\delta\alpha_{j}/2}\mathrm{sin}[2(PA_{j}+\phi_{j}\lambda^{2})],$
(4)

where $u=U/I$ and $q=Q/I$, $PA$ is the intrinsic polarisation angle, $\phi$ is
the rotation measure, $\delta\alpha$ is the remaining spectral index of a
given polarised component, and $\lambda_{\mathrm{ref}}$ is the wavelength at
which the spectral index is determined. We fitted all sources with
$n=[1,2,3,4,5]$. The derivation of this model and any assumptions made are
detailed in Appendix A. With this simplified model, any intrinsic complexity
within the source or turbulence in intervening Faraday screens will be
modelled as separate polarised components. We use this schema in lieu of more
complex models for a direct comparison of complexity classification with S19.
Here, a linearly polarised synchrotron-emitting source is considered Faraday
simple when there is a single polarised component within the beam volume
($n=1$), and Faraday complex when there are multiple or composite polarised
media ($n>1$). We compute the Bayesian Information Criterion (BIC) to select
the best-fit model. For two respective models, a difference in BIC greater
than 10 represents “very strong” evidence in favour of the model with the
smaller $n$. Given this definition, we select the model with the lowest BIC as
the preferred model, except if the difference between the two lowest BIC
values is less than 10. In this case, the model with the smallest $n$ is
selected. An example of the fitted QU-model for source SPASS J134355$-$564917
is shown in Fig. 4.

###  3.3 RM synthesis

The complex polarised intensity can be expressed as a function of Faraday
depth $\phi$, defined in Eq. 1,

$PI(\lambda^{2})=Q(\lambda^{2})+iU(\lambda^{2})=\int^{\infty}_{-\infty}F(\phi)\exp(2i\phi\lambda^{2})\mathrm{d}\phi.$
(5)

We note that $F(\phi)$ is the Faraday spectrum (historically referred to as
the Faraday dispersion function), the complex polarised intensity at a given
Faraday depth (Burn, 1966; Brentjens & de Bruyn, 2005). Sources are considered
Faraday simple when all polarised emission is at a single value of $\phi$
(i.e. the Faraday spectrum is a delta function). Physically, this could
interpreted as a single polarised component, limited by the given
$\lambda^{2}$ sampling. Sources are considered Faraday complex when they emit
at multiple $\phi$ values. In this case, there are multiple peaks at different
$\phi$ in their Faraday spectrum (i.e. multiple polarised components). From
the S19 catalogue, we expect a large fraction of our sample to be Faraday
complex.

The observed Faraday spectrum $\tilde{F}(\phi)$ is the convolution of
$F(\phi)$ with the Fourier transform of a weighted sampling function in the
$\lambda^{2}$ domain, called the RM spread function (RMSF). We require a
deconvolution algorithm to approximate the true $F(\phi)$. The resolution of a
Faraday spectrum and the precision of $\phi$ measurements determined through
RM synthesis are characterised by three quantities, $|\phi_{\mathrm{max}}|$
the maximum observable Faraday depth, $\delta\phi$ the resolution in Faraday
space, and the maximum scale in Faraday space to which one is sensitive. These
quantities are linked to the scale and resolution of the QU-spectra (Brentjens
& de Bruyn, 2005; Dickey et al., 2019). We determine the theoretical
measurements of these quantities to be
$|\phi_{\mathrm{max}}|=1732\leavevmode\nobreak\
\mathrm{rad}\,\mathrm{m}^{-2}$, $\delta\phi=92\leavevmode\nobreak\
\mathrm{rad}\,\mathrm{m}^{-2}$ and max-scale$\,=317\leavevmode\nobreak\
\mathrm{rad}\,\mathrm{m}^{-2}$ for our observation setup. After flagging,
calibration and RMsynthesis, we find the median observed FWHM of the RMSF to
be $\delta\phi_{\mathrm{obs}}=80\leavevmode\nobreak\
\mathrm{rad}\,\mathrm{m}^{-2}$.

We used RM synthesis (Brentjens & de Bruyn, 2005) with RM clean (Heald, 2009)
to determine the $|F(\phi)|$, RMSF and the peak Faraday depth(s) of the
sources. RM synthesis was performed using RM-Tools (Version 1.1.1, Purcell et
al., 2020) from the Canadian Initiative for Radio Astronomy Data Analysis
(CIRADA) tools. We used a clean threshold of $3\sigma$ for RM clean, and elect
to divide the Stokes Q and U spectra by a polynomial fit to the Stokes I
spectrum. Throughout this work, peak Faraday depth $\phi$ and RM are used
interchangeably.

##  4 Results

Of the 105 sources, we excluded extended sources, due to the expected non-
detection of large-scale emission. Our final sample consisted of 95 sources.
The brightest source in the sample is SPASS J160017$-$464922, with
$I_{\mathrm{MFS}}=5.1\pm 0.1\leavevmode\nobreak\ \mathrm{Jy}$ and the mean
Stokes I flux density is $I_{\mathrm{MFS}}=0.62\pm 0.08\leavevmode\nobreak\
\mathrm{Jy}$. We present a catalogue of all measured polarisation parameters
as well as the results of QU fitting. The catalogue is per the RMTable2023
standards presented in Van Eck et al. (2023), and is available as part of the
consolidated RMTable catalogue (v1.2.0) 111Source catalogue also available at:
https://doi.org/10.17617/3.NRFFQB.. This includes the following quantities and
their associated errors, total intensity $I_{\mathrm{MFS}}$, polarised
intensity, $\phi_{\mathrm{peak}}$. The catalogue also includes $\phi_{j}$ as
specified in Equations 3 and 4. An abridged version of the catalogue is shown
in Appendix B.

###  4.1 Verification of SPASS/ATCA catalogue

To verify the methods used in S19 and to assess our measurements, we compare
our results to those from S19. In this section, we compare flux density
measurements and RMs.

####  4.1.1 Flux density measurements

We consider the fractional difference between the Stokes I flux density
measurements in our work and various catalogues in the literature. Fig. 5
shows a fractional comparison $\Delta I_{2100}$ between the total intensity
flux density from the S19 catalogues $I_{\mathrm{S19}}$ and the measured flux
density at 2100 MHz, where

$\Delta I_{2100}=\frac{I_{2100}-I_{\mathrm{S19}}}{I_{2100}}.$ (6)

We find these flux density measurements broadly consistent, with a mean
$\Delta I_{2100}=0.050\pm 0.018$ (i.e. 5% of $I_{2100}$). We do expect a non-
zero residual due to the difference in $uv$-coverage between observations. We
also compare the measured MFS total intensity flux densities with the RACS
catalogue (Hale et al., 2021), assuming a spectral index of $\alpha=-0.7$ to
interpolate the RACS flux densities from 887 MHz to 2100 MHz,
$I_{\mathrm{RACS,2100}}$. Similar to Eq. 6, we define the fractional
comparison as

$\Delta
I_{\mathrm{MFS}}=\frac{I_{\mathrm{MFS}}-I_{\mathrm{RACS,2100}}}{I_{\mathrm{MFS}}}.$
(7)

A histogram of $\Delta I_{\mathrm{MFS}}$ is shown in Fig. 6. We find the flux
density measurements to be consistent, with a mean $\Delta
I_{\mathrm{MFS}}=0.024\pm 0.018$ (i.e. 2% of $I_{\mathrm{MFS}}$). In doing a
fractional comparison of the measured flux densities of $I_{\mathrm{MFS}}$ and
$I_{\mathrm{2100}}$, we find an inconsistency, with an 11% mean fractional
residual. Further investigation into the effect of broadband imaging on flux
density measurements and how this compares to visibility spectra is beyond the
scope of this work, given our objectives.

Figure 5: Histogram of $\Delta I_{2100}$, defined in Eq. 6. A Gaussian fit is
plotted in red, with the resultant mean and standard deviation shown on the
plot. The bin width is 0.1 Figure 6: Histrogram of $\Delta I_{\mathrm{MFS}}$,
defined in Eq. 7. A Gaussian fit is plotted in red, with the resultant mean
and standard deviation shown on the plot. The bin width is 0.1

For the purpose of the catalogue, we determined the $PI$ of a source as the
sum of the peak amplitudes in the Faraday spectrum. We find a broad agreement
between the measured $PI$ and the reported values in S19, with a mean
fractional residual of $0.06\pm 0.03$. The spread of the fractional residuals
is significantly larger than for the Stokes I flux densities (Fig. 5), with
$\sigma=0.30$. Furthermore, 18 sources have fractional residuals beyond
$3\sigma$. The majority of the outliers have low polarised intensity at
$PI<20$ mJy. Here, we see a deviation from the consistency with S19, with
larger $PI$ measurements in S19. On account of different observational setups,
we expect these inconsistencies in polarised intensity due to the filtering of
and sensitivity to different physical scales of linearly polarised emission.

####  4.1.2 Rotation measures

The mean $\phi$ of the sample is -$4.50\pm 13\leavevmode\nobreak\
\mathrm{rad}\,\mathrm{m}^{-2}$, the mean $|\phi|$ is $99\pm
13\leavevmode\nobreak\ \mathrm{rad}\,\mathrm{m}^{-2}$ and the maximum $|\phi|$
is 437.73 $\mathrm{rad}\,\mathrm{m}^{-2}$. The spatial distribution of our
sources and their peak Faraday depths are plotted in Fig. 7. Fig. 8 shows a
comparison between our measurements and those from the S19 catalogue. We find
the majority of $\phi$ measurements consistent with the S19 measurements, with
six outliers beyond 5$\sigma$. We examine the Faraday spectra of the 5$\sigma$
outliers on a case-by-case basis and identify three causes of this
inconsistency. These causes are listed below and are indicated in Fig. 8.

  1. (i)

sources with low S/N peak Faraday depth (i.e. depolarised in our
observations). Here, sources have S/N $<12$, that is, 10% of the mean S/N of
the sample.

  2. (ii)

sources where our peak Faraday depth measurement corresponds to a secondary
peak in the S19 Faraday spectra.

  3. (iii)

sources which are Faraday thick in the S19 Faraday spectra, or are composed of
multiple unresolved peaks. In this case, our determined $\phi$ from RM
synthesis lies within the Faraday depth range of the S19 extended structure
but has an offset from the maxima.

Figure 7: Spatial distribution of observed sources plotted on the Wisconsin
H-Alpha Mapper (WHAM) Sky Survey (Haffner et al., 2003) H$\alpha$ map of the
Galactic plane (greyscale). The marker size is proportional to the amplitude
of the measured peak Faraday depth of the source, as indicated in the legend.
Red upward triangles are positive $\phi$ and blue downward triangles are
negative $\phi$. Figure 8: Comparison between the measured $\phi$ from this
work and those from S19. The uncertainties on our $\phi$ measurements are
typically of order $\sim 1$ rad m-2 and are not visible on the scale of this
plot. The shaded region indicates 5$\sigma$ of the residuals. The outliers
beyond this are plotted in accordance with the explanation in the main text.
Cases (i), (ii) and (iii) are plotted as red stars, circles and triangles,
respectively.

###  4.2 Galactic latitude dependence of Faraday complexity

In this section, we present the Faraday complexity classification of sources
using the QU fitting method outlined in Sect. 3.2. We find that 40 (42%)
sources are complex, which is less than half of the 90% complex sources found
for the same sample in S19. The number of sources for a given number of
Faraday components in comparison to S19 is shown in Fig. 9.

Figure 9: Histogram comparing the number of sources best fit by a given QU
fitting model, as described in Eqs. 3 and 4, for this work (grey) and S19
(white).

In Fig. 10, we plot the average number of Faraday components as a function of
Galactic latitude. It should be noted that our sample is unevenly split on
either side of the Galactic plane, with 52 sources above the plane and 43
sources below the plane. We find an overall decrease in the number of
components per latitude bin in this work compared to S19, with a mean
difference in number of components as $|\Delta n|=1.1\pm 0.1$. We find the
slope of the increase of the average number of components towards the Galactic
plane to be lower below the plane in both samples, which is also observed for
the full S-PASS/ATCA catalogue, as shown in Fig. 2. In our measurements, we
also find that the average number of components is higher at positive
latitudes than at $b<0^{\circ}$. We note in Sect. 2.3 that 49 sources have a
secondary spatial component within the S19 beam. For these sources, the mean
$|\Delta n|=1.32\pm 0.1$, and for the unresolved sources, we find $|\Delta
n|=0.96\pm 0.1$. The increased $|\Delta n|$ for sources with multiple
components suggest that the exclusion of these spatial components from our
spectra does contribute to our observed reduction of complexity with respect
to S19. However, the $|\Delta n|\sim 1$ for unresolved sources indicates that
this is not the dominant effect for the reduced number of fitted components in
Fig. 10.

We return to the scenarios introduced in Sect. 2.1 for the cause of increased
Faraday complexity towards the Galactic plane, first considering the case for
small-scale turbulence. It is unlikely that small-scale turbulence has a
strong latitude-dependent effect on complexity at the angular resolution of
the S19 survey. Because we have an overall consistency of $\phi$ with the S19
catalogue, we do not spatially resolve turbulence within the Galactic plane
foreground. In the cases of multiple spatial components in the S19 beam, we
also find consistent $\phi$ with both the S19 catalogue and the brightest
component, with a median difference in $\phi$ of 7 rad m-2, well within
5$\sigma$ in Fig. 8. Basu et al. (2019) show through MHD simulations that
Faraday depth varies smoothly along the line of sight due to spatially
correlated structures in the magnetic field, and that the scale of magnetic
field variation is consistent with the driving scale of turbulence. If the
increase of complexity in S19 is purely due to Galactic plane turbulence, we
would observe the same number of Faraday components between this work and S19.

In the case for mixed-in Galactic diffuse emission, with the low angular
resolution S19 observations ($\sim 2^{\prime}$), approximately 64 times more
diffuse flux density would be detected than in our observational setup. This
would result in S19 detecting one additional Faraday component from diffuse
emission, as observed (Fig. 10). Because the average number of Faraday
components decreases by one in our observations, it is likely that the
filtered-out components correspond to large-scale regions of polarised
emission from the Galactic plane at scales $>2.8^{\prime}$, corresponding to
2.4 pc at a 3 kpc distance. This follows the assumption that the polarisation
angle of the extended Galactic foreground does not vary on large scales, and
that polarised intensity remains approximately constant. We can therefore
conclude that mixed-in polarised Galactic synchrotron emission is the dominant
cause for the increase of the number of Faraday components towards the
Galactic plane observed in S19, a trend that we no longer observe in
observations with a smaller maximum angular scale. Despite the overall
decrease in complexity, there remains complexity in 42% of the sources. We
suggest that these complexities are due to turbulence in the Galactic plane or
polarised emission at scales $<2.8^{\prime}$, and examine these sources on a
case-by-case basis in Sect. 5.

It should be noted that Fig. 10 shows an increase in complexity at $b\sim
5^{\circ}$. This is caused by a bias in observed sources, where we have an
overdensity of sources that are within 5 deg of longitude of the Galactic
centre at $b\sim 5^{\circ}$ (see Fig. 16). If we consider Fig. 10 excluding
sources with $l>355^{\circ}$, we no longer observe this trend.

Figure 10: The average number of fitted Faraday components of the observed
sources (green) and the same sources from S19 (red) as a function of Galactic
latitude. The errorbars are Poisson uncertainties. The central panel shows the
difference in the average number of components per bin between this work and
S19. The mean difference ($|\Delta n|=1.1\pm 0.1$) is plotted as the dashed
line. The bottom panel shows the number of sources in each 1-degree bin.

##  5 Discussion

In the following section, we outline the various physical mechanisms that
introduce Faraday complexity within a beam volume, and discuss how this can be
interpreted or perceived differently depending on the observational setup and
telescope limitations. In Sect. 5.2 we examine the origin of complexity in our
observed sample in detail.

###  5.1 The perception of complexity

Figure 11: Scatter plot of the polarised intensity and the MFS total intensity
flux densities. Faraday simple sources are plotted as blue crosses and Faraday
complex sources are plotted as orange triangles. The grey dashed lines
represent constant fractional polarisation, labelled as a percentage. The
histograms above (to the right of) the plot shows the distribution of the
total intensity (polarised intensity flux densities) for the Faraday simple
and complex sources, in blue and orange, respectively.

In Fig. 11 we plot the total intensity vs. polarised intensity, along with
histograms for the distributions for Faraday simple and complex sources. The
majority of sources have a fractional polarisation between 1% and 10%. We find
that Faraday complex sources have preferentially higher flux density values in
both polarised and total intensity. This shows that it is more likely for a
source to be classified as complex if it has a higher S/N polarised intensity
(based on the chosen method of classification). For fainter sources in
polarised intensity, possible secondary components may not be detected with
sufficient S/N, and these sources would preferentially be classified as
simple. This bimodality is more evident in total intensity and is consistent
with Anderson et al. (2015), who found through simulations that there is a
limit to the detection of complex sources with S/N. Although there are
significantly lower S/N levels in the S19 catalogue, we observe an overall
decrease in the number of complex sources due to the lower resolution and the
sensitivity to larger maximum angular scales in S19.

In Sect. 4.2, we find a significant difference in complexity fractions between
our observations and S19. The top row in Fig. 12 (panels A and B) shows a
depiction of the effect of multi-resolution observations on our perception of
Faraday complexity. Both depict a linearly polarised EGS with a smooth
polarised emitting foreground. Panel A describes a scenario where the
observational setup has a lower angular resolution and a larger maximum
angular scale (e.g. S19). In this case, the telescope is sensitive to the
linearly polarised emission from the observed background EGS, as well as the
foreground. The polarised emission of the background source undergoes Faraday
rotation when passing through the extended foreground. From the observer’s
point of view, there are two polarised components within the beam volume,
$n=2$ (Faraday complex), following the classification scheme in Sect. 3.2.
Panel B shows an identical system with a different observational setup. Here,
we have higher angular resolution, and the maximum angular scale of the
observation is smaller than the extended foreground polarised emission,
therefore, the majority of the foreground emission is filtered out (e.g. this
work). The emission from the EGS will undergo Faraday rotation from the
foreground, but only a single polarised component is detected within the beam
volume, $n=1$ (Faraday simple) within this observation setup.

Figure 12: Diagram illustrating the effect of multi-resolution observations on
the interpretation of Faraday complexity. The black circle indicates a
linearly polarised, synchrotron-emitting source, spatially unresolved in A, B
and C. The white ellipse indicates the angular resolution of the observations,
and the vertical arrows indicate the maximum angular scale of the
observations. The blue-shaded regions are the polarised emitting foreground,
with emission at smaller scales in panel C, and the yellow-shaded region is a
turbulent foreground screen. The dashed arrows show the paths of emission from
the various sources, and the number of observed Faraday components is
indicated in the top right corner.

For completeness, we illustrate two cases of foreground-induced complexity
detectable with our observational setup. Panel C is a similar case to panel B,
with a smooth, extended foreground component that has been filtered out.
However, here we consider small-scale (i.e. smaller than the beam), patchy
polarised emission in the foreground. The presence of such emission within the
beam volume will increase the number of Faraday components, that is, $n>1$.
Panel D illustrates an example of a turbulent foreground screen. Depending on
the scale of the turbulent cells (e.g. Livingston et al., 2021), various
regions of polarised emission from the background source may experience
different amounts of Faraday rotation, while passing through different
turbulent cells. This would result in multiple polarised components being
detected within the beam volume ($n>1$, Faraday complex). To ascertain this
and constrain the scale of turbulence, the extent of the background source
would have to be larger than the scale of turbulence. Observations of well-
modelled extended sources or a dense RM grid are required to investigate this
further.

Our results emphasise the importance of observing Faraday complexity at
different angular scales to disentangle various polarised components within
the beam volume. The removal of the smooth large-scale emission from the
foreground is crucial for an accurate interpretation of the linear
polarisation signal from background sources for Galactic magnetism studies.
The disregard of this can mislead our understanding of small-scale magnetic
structures through observation of background EGSs. In general, the effective
removal or filtering of Galactic contamination at all scales is important for
determining accurate polarisation information from EGSs. The effect of maximum
angular scale on Faraday complexity should be carefully considered depending
on the science goals. This effect can be further investigated with broadband
observations of the Galactic plane regions with more complex interferometer
arrays, such as the MPIfR-MeerKAT Galactic Plane Survey, (MMGPS; Padmanabh et
al., 2023). Within the footprint of this survey, it is expected that $\sim
2.5\times 10^{4}$ linearly polarised sources will be detected. Furthermore, a
larger sample will enable a more robust understanding of the effect of Faraday
complexity with angular scale. In comparison to cm-wavelengths, m-wavelength
observations of extragalactic sources are largely affected by depolarisation,
and are therefore not sensitive to Faraday complex sources. However, modern
m-wavelength surveys (LoTSS; O’Sullivan et al., 2023) can contribute to the
analysis of Faraday complexity by providing a confirmed Faraday simple sample
for a holistic investigation of this classification scheme.

###  5.2 The origin of complexity

In Sect. 4.2 we identified that the Faraday complexities in the observed
sample must originate from polarised emission at scales $<2.8^{\prime}$ (i.e.
the maximum angular scale of our observations), but it is difficult to
distinguish whether the additional polarised components are intrinsic to the
extragalactic source, or small-scale, patchy Galactic polarised emission (e.g.
Schnitzeler et al., 2009) or turbulence.

Figure 13: Spatial distribution of sources, as shown in Fig. 7. The Faraday
simple sources are indicated by blue crosses and the Faraday complex sources
are plotted as orange triangles.

Fig. 13 shows the spatial distribution of Faraday simple and complex sources.
From this figure, we show that the complex sources are not uniformly
distributed on the sky and it is, therefore, unlikely that the observed
complexity is solely intrinsic to the sources. We subsequently evaluate this
quantitatively in Sect. 5.2.3.

####  5.2.1 Faraday spectrum classification

With the limitations of our selected QU fitting models, we further investigate
the Faraday complex sources and the approximations made when fitting these
models. To better understand the origin of complexity for our observed
sources, we manually inspect and classify the Faraday spectra of the complex
sources, also considering the limitations in the Faraday depth domain and
Faraday resolution due to the observational parameters. We use four different
labels to classify the complex sources:

  1. (i)

‘Broad’: We fitted Gaussian functions to the dominant peak in the Faraday
spectrum and the RMSF. A source is considered broad if the FWHM of the Faraday
spectrum peak is 10% greater than that of the RMSF (see e.g. Ma et al.,
2019a). Additionally, more than one of the $\phi$ identified in QU fitting
should be within the Faraday spectrum peak. This scenario would describe an
external Faraday thick source, for instance, a Faraday rotating ‘slab’ of
thermal electrons and magnetic fields overlapping with the synchrotron-
emitting volume, leading to a differential Faraday rotation along the line of
sight. This scenario could also describe a secondary, low amplitude peak at a
$\phi<3\sigma$ of the dominant peak $\phi$, that cannot be fully resolved as a
separate peak within our Faraday depth resolution.

  2. (ii)

‘Unresolved’: The FWHM of the dominant peak is equal to, or up to 10% greater
than the FWHM of the RMSF, and there are multiple QU fitting identified $\phi$
values within the FWHM of the peak. This classification has the same physical
scenario as the broad classification, with the exception that the difference
in Faraday depth between multiple peaks or the Faraday thickness of the
intervening medium is unresolved in Faraday depth space with our frequency
sampling.

  3. (iii)

‘Big sec’: The secondary resolved peak, or any of the non-dominant Faraday
spectrum peaks, has an amplitude $\geq$50% of the amplitude of the dominant
peak. This scenario could describe a secondary Faraday rotating and emitting
source. From its high amplitude, we could assume this is likely not due to
Galactic polarised emission.

  4. (iv)

‘Small sec’: Any of the non-dominant peaks have an amplitude $<50$% of the
dominant peak.

In this scheme, spectra can be classified with any number of these labels
(e.g. broad and small sec) corresponding to properties of multiple peaks, and
an example of spectra for the various classifications is shown in Fig. 14. For
the broadened and unresolved sources, we cannot reliably derive the amplitude
of the multiple polarised components. In these cases, we consider an upper
limit as the amplitude of the Faraday spectrum at the Faraday depth of the
fitted RM. For sources classified as unresolved, we determine the difference
in Faraday depth between the two unresolved components
$|\mathrm{RM}_{1}-\mathrm{RM}_{2}|$, for RMs obtained from QU fitting. We find
15 unresolved sources, with a mean $|\mathrm{RM}_{1}-\mathrm{RM}_{2}|$ of
$34.35\,\mathrm{rad}\,\mathrm{m}^{-2}$. We provide a further discussion on
this classification in Sect. 5.2.3.

Figure 14: Examples of the Faraday spectrum classes ‘small sec’ (top),
‘unresolved’ (centre), and ‘broad’ (bottom) as described in Sect. 5.2.1. The
plots show the Faraday spectrum (green) and the fitted Gaussian (blue). The
same is shown for the RMSF and its Gaussian fit, in lower opacity. The red
vertical lines show the fitted $\phi$ from QU fitting and their uncertainties.
The 3$\sigma$ extent and the half-maximum amplitude of the fitted Gaussians
are indicated with dashed grey lines.

####  5.2.2 Multiple spatial components

In Sect. 2.3, we smoothed the MFS images and image cubes to a common
resolution of 15” $\times$ 15” to account for beam variation across the band.
To distinguish which sources have multiple spatial components within the beam,
we visually inspect the high-frequency end of the unsmoothed image cubes at
3014 MHz. These images have a typical resolution of 3.5” $\times$ 5.2”. We
manually identify sources with multiple components in total intensity within
the smoothed beam and find 23 (i.e. 24%) sources that have multiple spatial
components. We only consider the Stokes I images here, as we are unable to
reliably manually identify peaks in polarisation due to low S/N in the channel
maps. A breakdown of the complexity classification of these sources is given
in Table 2.

We do not detect multiple bright Faraday peaks (Big sec class) in any of these
sources and find that 8 (34%) of the multi-component sources have a faint
secondary Faraday peak (Small sec class). However, we cannot ascertain that
the multiple Faraday components correspond to the observed multiple spatial
components. Of the 23, 10 sources are Faraday simple. This is consistent with
O’Sullivan et al. (2017) and Ma et al. (2019a), who find that spatially
extended sources can be Faraday simple, at angular resolutions of 1” and 45”,
respectively. An explanation for this trend could be the Laing-Garrington
effect (Laing, 1988; Garrington et al., 1988), where we expect a large
asymmetry in polarised intensity between the two Faraday components due to
depolarisation. This may be an extreme case of the Laing-Garrington effect
where one spatial component is completely depolarised. A more likely
explanation is the effect of AGN lobe orientation, where both components
encounter similar Faraday screens along the line of sight (e.g. O’Sullivan et
al., 2017), and therefore have similar $\phi$. Given we have only 23 sources
with multiple spatial components, we do not have a large enough sample for a
deeper investigation into this trend. We would require higher resolution
observations across a broad frequency range to analyse these components
separately to better understand the individual systems.

We briefly discuss the case of Faraday complexity in sources with a single
spatial component (i.e. spatially unresolved). The complexity classification
for these sources is detailed in Table 2. We find that 38% of spatially
unresolved sources are Faraday complex. Although it has been shown in the
literature that Faraday complexities can be linked to source morphology at a
$\sim 10^{-2}$ arcsec scale (e.g. Ma et al., 2019a), we would require higher
resolution observations to explore this further and a statistically
significant sample size to investigate the prevalence of this. Because we find
a larger percentage of complex sources in spatially resolved sources (56%)
compared to spatially unresolved sources (38%), it is certainly possible that
the complexity is purely intrinsic to the EGSs. However, due to the Galactic
dependency of complexity in S19 (Sect. 2.1), it is important to investigate
whether the remaining complexity in the observed sample is Galactic in origin.
We do so in the following section.

Table 2: Number (percentage) of sources with each complexity classification and Faraday spectrum classification (Sect. 5.2.1) for the sources with multiple spatial components, as well as the number of sources with each complexity classification for sources with a single spatial component. It should be noted that Faraday complex sources may be classified into multiple categories. Source classification | Number
---|---
Multiple spatial components: | 23
Faraday simple | 10 (44%)
Faraday complex | 13 (56%)
Broad | 2
Unresolved | 6
Big sec | 0
Small sec | 8
Single spatial component: | 72
Faraday simple | 45 (62%)
Faraday complex | 27 (38%)

####  5.2.3 Galactic ISM and complexity in the spiral arms

We consider various interstellar media as possible tracers for turbulence or
small-scale fluctuations in the Galactic plane. In the presence of a turbulent
screen, we expect to observe depolarisation effects and detect multiple fitted
polarised components, given the QU fitting models we have used. Additionally,
Anderson et al. (2015) suggest that HI and H$\alpha$ regions act as a proxy
for identifying regions where complex Faraday screens are present. To
investigate this, we measure the HI column densities from the HI4PI survey
maps (McClure-Griffiths et al., 2009; HI4PI Collaboration et al., 2016), as
well as the H$\alpha$ flux densities from the WHAM H$\alpha$ map (Haffner et
al., 2003). We do not find a direct relationship between complexity and these
various gas density measurements. The typical angular resolution is 14.5’ for
the HI4PI maps in the southern sky and 1∘ for WHAM H$\alpha$, all
significantly larger than the scale at which we measure the complexity. It is
therefore difficult to reliably investigate this relation without higher
resolution observations.

Figure 15: Percentage of complex sources for each longitude bin of 4 deg
(black circles). The x error bars indicate the extent of the bin, and the y
errors are determined through bootstrapping. The dashed line shows the
percentage of complex sources for the full sample at 42%. The cyan-shaded
regions indicate longitudes which correspond to the Galactic spiral arms
listed in the text and the longitude range within 5 degrees of the Galactic
centre. The bottom panel is a histogram showing the number of sources in each
longitude bin. The green triangle shows the percentage of complex sources at
$355^{\circ}<l<360^{\circ}$ in Livingston et al. (2021). Figure 16: Spatial
distribution of sources, colourised by their Faraday complexity
classification, as described in Sect. 5.2.1. The cyan-shaded regions show
longitudes that correspond to the Galactic spiral arms listed in the text and
the longitude range within 5 degrees of the Galactic centre. The Faraday
simple sources are plotted as black dots. The size of the markers for Faraday
complex sources is scaled according to the number of QU-fitted components.

We have investigated the Galactic latitude dependence of Faraday complexity
and now consider an increase in complexity at particular Galactic longitudes
between $310^{\circ}<l<360^{\circ}$. Our observations include the Crux-
Centaurus ($l\sim 310^{\circ}$), Norma ($l\sim 328^{\circ}$), Inner Perseus
($l\sim 338^{\circ}$) and Inner Sagittarius ($l\sim 343^{\circ}$) spiral arm
tangents (e.g. Vallée, 2022) as well as the Galactic centre, where the spiral
arm tangents are estimated from the broad 12CO(1-0) tracer. In Fig. 15 we plot
the fraction of complex sources per longitude bin. It should be noted that the
longitude range for spiral arms on this figure is indicative, and we cannot
constrain the full extent of the individual spiral arms. We find that in
longitude bins including the spiral arms, we have a greater mean complexity
than over the whole sample. Considering a comparison of complexity fractions
with the literature, we also find this increased complexity within 5 degrees
of the Galactic centre, as consistent with Livingston et al. (2021) (95%
complexity). This increase could be due to the greater number of Faraday
components emitting at small scales in the spiral arms at Galactic latitudes
$1.5^{\circ}<|b|<10^{\circ}$. The observed sources in Livingston et al. (2021)
and O’Sullivan et al. (2017) are suitable for a direct comparison, as they
also use the 16 cm band in the ATCA with the 6 km baseline configuration,
ensuring similar spatial and frequency resolution. O’Sullivan et al. (2017)
select an extragalactic sample of sources away from the Galactic plane, but
with sources up to $|b|>20^{\circ}$. They find a 55% complexity fraction. This
is congruent with what we find, on average. Anderson et al. (2015) find a
complexity fraction of 12% for sources at $b\sim 55^{\circ}$, considering that
they have a lower resolution of $\sim 1^{\prime}$. This complexity fraction
for a non-Galactic region is consistent with the average complexity fraction
we find in the interarm regions (Fig. 15).

We determined the correlation between our binned sample and the positions of
the spiral arms using the Pearson Correlation Coefficient $\rho$. Here, each
spiral arm is simply modelled as a Gaussian, with the centroid and standard
deviation as the centre and width of the cyan bands in Fig. 15. We included an
additional component at the Galactic centre, with $x_{0}=0^{\circ}$ and
$\sigma=5^{\circ}$, and assume a complexity fraction of 100% at the centroid
of all spiral arms and the Galactic centre. We tested this by randomly
assigning a boolean complexity classification to 10 000 samples with the same
longitude distribution as our observed sources and a total complexity fraction
of 42%. We calculate $\rho$ for the random samples and the p-value, determined
as the probability of determining a correlation at least as strong as our
observed sample across the 10 000 random samples. We repeat this experiment
for longitude bin widths of $\Delta l=[3,4,5]$ degrees. The smallest possible
bin size with at least 1 source per bin is $\Delta l=3$ deg. The results are
displayed in Table 3. We find the strongest correlation at $\Delta l=5$ deg
with $\rho=0.65$, and that the correlation coefficients for all bins are
statistically significant with at least 97.9% confidence. This suggests a fair
correlation between increased complexity percentage and the longitudes of the
Galactic spiral arms. This result is consistent with the RM structure
functions in Haverkorn et al. (2008), who find a smaller driving scale of
turbulence ($\sim 1$ pc) in the spiral arm regions than in the interarm
regions ($\sim 100$ pc), and suggests that the increase of complexity is
attributed to turbulence at smaller scales in the spiral arms. However, a
larger observed sample and a more detailed Galactic plane model are required
to draw a more robust conclusion.

Table 3: Pearson Correlation coefficient $\rho$ for the correlation between the increased complexity classification and the positions of the Galactic spiral arms for different longitude bins. The associated p-value for 10 000 randomly assigned samples is also shown. $\Delta l$ bin | $\rho$ | p
---|---|---
3∘ | 0.57 | 0.010
4∘ | 0.63 | 0.011
5∘ | 0.65 | 0.021

To further investigate the origin of this complexity, we plot the distribution
of sources, colourised by their complexity classification in relation to the
spiral arms and Galactic centre (Fig. 16). Through visual inspection, we find
that sources classified as small sec and/or broad are concentrated around the
Galactic centre or the spiral arm regions, as expected in the presence of a
low flux density polarised emission. Here, it is possible that the broadening
is due to smaller amplitude secondary peaks caused by small-scale emission
within the Galactic plane that is unresolved at this Faraday depth resolution,
or a broadening effect from small-scale Faraday depth fluctuations caused by
turbulent cells. Both of these observed effects support the argument for a
smaller turbulent cell size in the spiral arm regions that in the interarm
regions. We discuss the cases for Faraday rotation and polarised emission
separately:

Pure rotation: In the interarm regions, we may be resolving out turbulence,
that is, a low number of turbulent cells per beam volume probed. This would
simply induce Faraday rotation, without increasing complexity. In the spiral
arm regions, with a smaller turbulent cell size, we have an increased number
of turbulent cells within the ISM volume probed by the beam. This would result
in Faraday dispersion, and cause a broadening in the Faraday spectrum (Sect.
5.2.1) and a complex classification.

Pure emission: We would expect smoother polarised emission in the interarm
regions, due to large-scale turbulence. This larger-scale emission is not
detected at the scales of our observations. In the spiral arm regions, we are
sensitive to the smaller scale, patchy emission, caused by the small-scale
turbulence.

As discussed above, both cases or a combination of the two could contribute to
the observed complexity in the spiral arm regions. However, we would require
higher resolution observations in both angular resolution and Faraday depth to
asses this fully.

In Fig. 16 we find that the majority of sources that are classified as
unresolved in Faraday depth are distributed on the northern half of the plane.
This is also what predominantly contributes to the increase of complexity at
northern latitudes, as shown in Fig. 10. This north-south Galactic asymmetry
is expected in polarised synchrotron emission (e.g. Vidal et al., 2015;
Robitaille et al., 2017). Although we find no relation between HI column
density and Faraday complexity at the positions of the individual sources, we
find that there is an increased average HI column density above the plane
($5.3\times 10^{21}\,\mathrm{cm}^{-2}$) than below the plane ($3.1\times
10^{21}\,\mathrm{cm}^{-2}$). Small-scale magneto-ionic structures (e.g.
filaments at scales of $\sim 10$ pc) with low amplitude
$n_{\mathrm{e}}\mathbf{B}$ within this extended HI region could be a possible
explanation for this increased complexity (e.g. Clark & Hensley, 2019; Ma et
al., 2023). With higher Faraday depth resolution observations and QU fitting
with more advanced models, we will be able to discern whether this is an
effect of unresolved Faraday dispersion by turbulence in the northern Galactic
plane Faraday screen or the effect of polarised structures in Galactic HI.

##  6 Conclusion

In this paper, we investigate the increase of Faraday complexity towards
$b=0^{\circ}$ in the S-PASS/ATCA RM catalogue (S19; Schnitzeler et al., 2019).
We obtain follow-up observations of 95 sources at higher angular resolution,
using the 6 km-baseline configuration of ATCA. We determine the peak Faraday
depth $\phi$ of the sources using RM synthesis and find these measurements to
be consistent with the S19 catalogue. By fitting Stokes Q and U spectra with
models describing the sum of multiple Faraday simple components, we classify
sources as Faraday simple or Faraday complex. With the higher resolution
observations, we find that 42% of the sources are complex ($n>1$), in
comparison to the 90% complexity in the same sample from S19. Furthermore, we
found that there is no longer a strong trend of increased Faraday complexity
towards the Galactic plane, limiting the scale of complexity to
$\theta<2.8^{\prime}$ (2.4 pc at a 3 kpc distance), the maximum angular scale
of our observations. From this, we constrain that the increase in complexity
in the S19 catalogue can be attributed to, on average, an additional polarised
components from mixed-in diffuse Galactic emission at scales
$\theta>2.8^{\prime}$.

To investigate the remaining complexity at smaller scales, we further classify
Faraday complex sources based on the characteristics in their Faraday spectra.
We find tentative evidence that there is an above-average complex source
percentage at longitudes corresponding to the Galactic spiral arms, suggesting
turbulence or small-scale patchy emission within these regions. In addition,
we observe a trend in an overdensity of sources with
$|\mathrm{RM}_{1}-\mathrm{RM}_{2}|$ smaller than the Faraday spectrum
resolution in the northern Galactic plane. This could be attributed to low
amplitude $n_{\mathrm{e}}\mathbf{B}$ fluctuations in the HI disk of the Milky
Way.

Overall, we find the total intensity and $\phi$ measurements in the S19
catalogue reliable and consistent with our observations, with the caveat that
particular care should be taken regarding the angular resolution and the
maximum angular scale when comparing polarised intensity measurements, QU
fitting results, and Faraday complexity between various observations at
$|b|<10^{\circ}$.

###### Acknowledgements.

We thank Rainer Beck for helpful discussions surrounding this work and
feedback on the manuscript, as well as Aritra Basu for QU fitting scripts. SR
acknowledges the support from the International Max Planck Research School
(IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and
Cologne. RPD acknowledges funding from the South African Research Chairs
Initiative of the Department of Science and Innovation and National Research
Foundation (Grant ID 77948). The Australia Telescope Compact Array is part of
the Australia Telescope National Facility (https://ror.org/05qajvd42) which is
funded by the Australian Government for operation as a National Facility
managed by CSIRO. We acknowledge the Gomeroi people as the Traditional Owners
of the Observatory site. The data used in this work will be shared upon
reasonable request to the authors.

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##  Appendix A QU fitting models

In this appendix, we detail the key assumptions made in the derivation of the
QU fitting model. As stated in Sect. 3.2, we consider a model describing the
sum of up to five Faraday thin components, where for a given component, the
polarised intensity is

$\displaystyle P(\lambda^{2})=P_{0}\exp\left(2i(\phi\lambda^{2}+PA)\right),$
(8)

where $P_{0}$ is the polarised intensity, $\phi$ is the Faraday depth, and
$PA$ is the polarisation angle. Because we are fitting the polarisation
fraction $p(\lambda^{2})$, we divide by by the total intensity spectrum,

$\displaystyle p(\lambda^{2})=\frac{P(\lambda^{2})}{I(\lambda^{2})},$ (9)

assuming $I(\nu)$ to be a power law as a function of frequency $\nu$:

$\displaystyle I(\nu)=I_{0}\left(\frac{\nu}{\nu_{0}}\right)^{-\alpha},$ (10)

where $I_{0}$ is the total intensity flux density at a reference frequency
$\nu_{0}$ and $\alpha$ is the spectral index. This can be written as,

$\displaystyle
I(\lambda^{2})=I_{0}\left(\frac{\lambda^{2}}{\lambda_{0}^{2}}\right)^{\alpha/2},$
(11)

resulting in

$\displaystyle
p(\lambda^{2})=p_{0}\left(\frac{\lambda^{2}}{\lambda_{0}^{2}}\right)^{-\alpha/2}\exp\left(2i(\phi\lambda^{2}+PA)\right).$
(12)

As specified in the text, dividing the Q and U spectra by the Stokes I
spectrum before fitting, will account for the dominant spectral index, (i.e.
the spectral index of the background source $\alpha_{0}$). This model serves
to fit any variation in spectral index as contributed from emitting components
within the beam volume, for which Equation 12 can be rewritten as

$\displaystyle
p(\lambda^{2})=p_{0}\left(\frac{\lambda^{2}}{\lambda_{0}^{2}}\right)^{-\delta\alpha/2}\exp\left(2i(\phi\lambda^{2}+PA)\right),$
(13)

where $\alpha=\alpha_{0}+\delta\alpha$.

##  Appendix B Source catalogue

Table 4: Catalogue of the 95 analysed sources. Column (1) is the source ID
from the S19 catalogue. Columns (2)–(5) have the positional information of
each source. Columns (6)–(7) contain the total intensity measurements and
columns (8)–(11) contain polarisation properties of each source. Sources
identified to have multiple spatial components within the 15”$\times$15” beam
(see Sect. 5.2.2) are marked with an asterisk.

S19 ID (1) RA (2) Dec (3) $l$ (4) $b$ (5) $I_{\mathrm{MFS}}$ (6) $I_{2100}$
(7) PI (8) $\phi_{\mathrm{peak}}$ (9) $n$ (10) $n$ (11) (J2000) (J2000) (deg)
(deg) (mJy) (mJy) (mJy) rad m-2 (this work) (S19) 1 NVSSJ161021-395858
16h10m17s $-39$d58m58.0s 339.162 $8.507$ 599$\pm$4 613$\pm$7 25.08$\pm$0.13
$-65.82\pm$0.16 2 2 2 NVSSJ161234-390625 16h12m36s $-39$d06m59.0s 340.093
$8.827$ 221$\pm$6 208$\pm$14 11.17$\pm$0.10 $-5.85\pm$0.35 1 1 3
NVSSJ161737-382827* 16h17m36s $-38$d28m32.0s 341.249 $8.606$ 172$\pm$6
163$\pm$9 1.19$\pm$0.10 $+20.40\pm$3.17 1 3 4 SPASSJ143426-623949 14h34m26s
$-62$d39m49.8s 314.448 $-2.118$ 431$\pm$5 403$\pm$6 28.63$\pm$0.12
$-30.62\pm$0.15 1 2 5 NVSSJ171148-333841 17h11m48s $-33$d38m42.0s 352.078
$3.407$ 200$\pm$2 225$\pm$9 0.93$\pm$0.11 $+110.09\pm$4.68 1 4 6
SPASSJ144346-631714* 14h43m46s $-63$d17m14.0s 315.168 $-3.116$ 568$\pm$15
495$\pm$26 13.05$\pm$0.22 $-119.86\pm$0.38 1 1 7 NVSSJ170918-352521* 17h09m18s
$-35$d25m24.0s 350.337 $2.77$ 1736$\pm$24 1687$\pm$30 66.55$\pm$0.60
$-296.36\pm$0.11 1 3 8 SPASSJ144453-552959* 14h44m53s $-55$d29m59.5s 318.578
$3.887$ 503$\pm$21 400$\pm$32 12.35$\pm$0.15 $-20.78\pm$0.35 2 3 9
NVSSJ175445-401157 17h54m43s $-40$d12m16.0s 351.229 $-7.344$ 326$\pm$38
209$\pm$43 6.85$\pm$0.12 $+96.26\pm$0.56 1 2 10 NVSSJ162732-353731* 16h27m31s
$-35$d37m37.0s 344.712 $9.172$ 544$\pm$10 479$\pm$9 9.98$\pm$0.17
$-6.04\pm$0.48 3 3 11 NVSSJ171257-280935* 17h12m55s $-28$d09m29.0s 356.689
$6.418$ 4275$\pm$94 3766$\pm$77 97.83$\pm$0.80 $+52.87\pm$0.09 3 3 12
SPASSJ153448-604059 15h34m48s $-60$d40m60.0s 321.652 $-3.894$ 228$\pm$11
170$\pm$14 11.43$\pm$0.19 $-162.65\pm$0.39 1 5 13 NVSSJ163736-330905 16h37m34s
$-33$d09m9.0s 347.982 $9.294$ 274$\pm$3 267$\pm$6 7.56$\pm$0.09
$-46.16\pm$0.50 1 2 14 NVSSJ171309-341830 17h13m09s $-34$d18m39.0s 351.703
$2.789$ 598$\pm$4 616$\pm$9 6.50$\pm$0.11 $-125.65\pm$0.71 1 3 15
NVSSJ171652-254925 17h16m50s $-25$d48m58.0s 359.123 $7.052$ 312$\pm$23
290$\pm$37 2.76$\pm$0.14 $-149.86\pm$1.39 1 2 16 NVSSJ171405-334539* 17h14m04s
$-33$d45m51.0s 352.258 $2.955$ 281$\pm$4 252$\pm$12 11.23$\pm$0.21
$-106.89\pm$0.55 2 5 17 SPASSJ155724-603116 15h57m24s $-60$d31m16.3s 323.943
$-5.476$ 288$\pm$21 251$\pm$19 7.82$\pm$0.11 $-51.38\pm$0.56 2 2 18
NVSSJ171609-280135 17h16m08s $-28$d01m37.0s 357.208 $5.915$ 203$\pm$23
361$\pm$95 5.29$\pm$0.15 $+110.46\pm$0.84 1 5 19 SPASSJ160009-581104 16h00m09s
$-58$d11m4.7s 325.737 $-3.931$ 760$\pm$21 685$\pm$21 31.45$\pm$0.24
$-90.51\pm$0.16 1 3 20 NVSSJ171736-334208 17h17m35s $-33$d42m17.0s 352.731
$2.394$ 786$\pm$15 869$\pm$17 34.55$\pm$0.18 $-248.25\pm$0.15 1 2 21
NVSSJ173725-394608* 17h37m24s $-39$d46m18.0s 349.892 $-4.275$ 404$\pm$7
369$\pm$13 9.48$\pm$0.11 $+305.37\pm$0.45 1 1 22 NVSSJ174840-365150 17h48m38s
$-36$d51m55.0s 353.531 $-4.639$ 751$\pm$39 770$\pm$123 15.33$\pm$0.15
$+201.40\pm$0.31 3 3 23 SPASSJ175715-414936 17h57m15s $-41$d49m36.0s 350.035
$-8.554$ 965$\pm$31 774$\pm$72 8.37$\pm$0.15 $+45.92\pm$0.69 1 4 24
SPASSJ160017-464922* 16h00m17s $-46$d49m22.5s 333.185 $4.655$ 5064$\pm$104
4616$\pm$98 429.88$\pm$1.70 $+41.12\pm$0.04 2 3 25 NVSSJ175622-312215
17h56m20s $-31$d22m26.0s 359.087 $-3.236$ 437$\pm$11 396$\pm$13 27.28$\pm$0.30
$+247.91\pm$0.21 1 3 26 NVSSJ175657-372326 17h56m57s $-37$d23m42.0s 353.907
$-6.338$ 162$\pm$7 141$\pm$13 7.83$\pm$0.15 $-57.96\pm$0.54 1 2 27
NVSSJ175659-345422* 17h56m58s $-34$d54m37.0s 356.079 $-5.113$ 615$\pm$17
565$\pm$14 13.31$\pm$0.21 $+149.15\pm$0.38 2 2 28 NVSSJ180347-384729 18h03m51s
$-38$d47m39.0s 353.336 $-8.206$ 317$\pm$9 267$\pm$21 35.96$\pm$0.13
$+86.67\pm$0.14 1 2 29 PKSB1425-692 14h29m46s $-69$d29m57.9s 311.399 $-8.261$
113$\pm$12 111$\pm$21 8.91$\pm$0.10 $+23.64\pm$0.54 1 2 30 PKSB1442-699*
14h47m06s $-70$d08m4.2s 312.521 $-9.447$ 496$\pm$12 433$\pm$11 22.10$\pm$0.16
$-39.34\pm$0.21 3 3 31 PKSB1517-682 15h22m16s $-68$d28m11.4s 316.089 $-9.542$
283$\pm$8 224$\pm$10 24.21$\pm$0.17 $+210.84\pm$0.16 1 1 32
SPASSJ160700-452802 16h07m00s $-45$d28m3.0s 334.962 $4.894$ 806$\pm$14
692$\pm$10 36.59$\pm$0.33 $-94.27\pm$0.14 3 3 33 SPASSJ161717-584807 16h17m17s
$-58$d48m7.0s 326.969 $-5.901$ 3777$\pm$54 4276$\pm$108 36.53$\pm$0.60
$+74.09\pm$0.23 2 2 34 NVSSJ165956-305205 16h59m55s $-30$d52m7.0s 352.801
$7.078$ 540$\pm$16 434$\pm$16 1.22$\pm$0.16 $+151.50\pm$3.85 2 3 35
SPASSJ134355-564917 13h43m56s $-56$d49m17.1s 310.101 $5.318$ 362$\pm$12
309$\pm$28 33.31$\pm$0.16 $+113.30\pm$0.15 1 3 36 SPASSJ135734-532128
13h57m34s $-53$d21m28.3s 312.813 $8.24$ 392$\pm$8 356$\pm$9 50.41$\pm$0.17
$-6.82\pm$0.08 3 3 37 SPASSJ163305-450926* 16h33m05s $-45$d09m26.9s 338.442
$1.887$ 514$\pm$23 392$\pm$30 25.52$\pm$0.31 $-209.79\pm$0.20 3 4 38
NVSSJ161809-391811 16h18m08s $-39$d18m14.0s 340.733 $7.946$ 570$\pm$14
517$\pm$16 15.56$\pm$0.23 $+128.50\pm$0.47 2 2 39 PKSB1508-649 15h12m34s
$-65$d06m47.8s 317.085 $-6.195$ 467$\pm$7 440$\pm$6 8.93$\pm$0.23
$-103.82\pm$0.50 1 3 40 SPASSJ144106-561659 14h41m06s $-56$d16m59.6s 317.768
$3.397$ 886$\pm$31 709$\pm$60 48.20$\pm$0.17 $-79.36\pm$0.12 1 2 41
SPASSJ144233-540746 14h42m33s $-54$d07m46.2s 318.85 $5.272$ 432$\pm$11
412$\pm$12 19.37$\pm$0.12 $+47.64\pm$0.21 2 2 42 NVSSJ172242-281953 17h22m42s
$-28$d19m57.0s 357.78 $4.554$ 870$\pm$12 794$\pm$12 26.90$\pm$0.42
$+97.56\pm$0.21 3 3 43 SPASSJ163158-593500 16h31m58s $-59$d35m0.2s 327.721
$-7.796$ 481$\pm$34 … 9.27$\pm$0.12 $+116.47\pm$0.44 2 3 44
SPASSJ145506-494805* 14h55m07s $-49$d48m5.8s 322.515 $8.309$ 612$\pm$14
550$\pm$20 15.27$\pm$0.10 $-9.93\pm$0.24 2 4 45 NVSSJ172337-272843 17h23m35s
$-27$d28m37.0s 358.603 $4.869$ 52$\pm$3 42$\pm$6 2.61$\pm$0.14 $-54.74\pm$1.69
2 2 46 SPASSJ151108-520350 15h11m08s $-52$d03m50.2s 323.626 $5.104$ 222$\pm$3
209$\pm$6 7.73$\pm$0.15 $-130.34\pm$0.41 2 2 47 SPASSJ151739-510634 15h17m39s
$-51$d06m34.4s 324.994 $5.389$ 139$\pm$6 151$\pm$17 5.29$\pm$0.15
$-82.71\pm$0.83 1 1 48 NVSSJ172836-271236 17h28m34s $-27$d12m41.0s 359.441
$4.097$ 437$\pm$6 373$\pm$12 5.11$\pm$0.30 $-60.90\pm$1.63 5 5 49
SPASSJ152154-531348 15h21m55s $-53$d13m49.0s 324.4 $3.251$ 280$\pm$12
222$\pm$26 6.45$\pm$0.11 $-20.22\pm$0.70 1 3 50 SPASSJ152426-483956 15h24m26s
$-48$d39m56.3s 327.252 $6.846$ 404$\pm$41 347$\pm$63 10.45$\pm$0.37
$-199.65\pm$1.21 2 3 51 SPASSJ152436-643159* 15h24m36s $-64$d31m59.6s 318.485
$-6.392$ 493$\pm$13 430$\pm$14 20.89$\pm$0.21 $+183.48\pm$0.21 1 2 52
SPASSJ153023-605032 15h30m23s $-60$d50m32.3s 321.12 $-3.714$ 147$\pm$4
126$\pm$8 10.60$\pm$0.14 $-144.69\pm$0.36 1 4 53 SPASSJ153419-535113 15h34m19s
$-53$d51m13.2s 325.575 $1.698$ 518$\pm$4 491$\pm$8 11.62$\pm$0.18
$-52.13\pm$0.31 1 4 54 PKSB1653-331 16h56m39s $-33$d11m37.0s 350.526 $6.196$
420$\pm$22 396$\pm$26 40.28$\pm$0.17 $-82.56\pm$0.12 2 3 55
SPASSJ140555-565946* 14h05m55s $-56$d59m46.3s 312.978 $4.416$ 713$\pm$16
598$\pm$24 28.98$\pm$0.23 $-74.08\pm$0.16 2 2 56 SPASSJ154607-465519 15h46m07s
$-46$d55m19.9s 331.247 $6.12$ 531$\pm$9 482$\pm$7 18.31$\pm$0.18
$+71.33\pm$0.22 1 2 57 SPASSJ155707-412646* 15h57m07s $-41$d26m46.0s 336.293
$9.095$ 418$\pm$10 361$\pm$15 33.13$\pm$0.12 $+9.76\pm$0.10 2 3 58
SPASSJ143353-533736 14h33m53s $-53$d37m36.2s 317.878 $6.246$ 221$\pm$8
189$\pm$12 2.83$\pm$0.15 $+77.68\pm$1.24 1 2 59 NVSSJ162743-395303 16h27m43s
$-39$d53m7.0s 341.615 $6.219$ 1305$\pm$24 1128$\pm$10 9.31$\pm$0.30
$-50.04\pm$0.74 3 3 60 SPASSJ145739-650240 14h57m39s $-65$d02m40.7s 315.745
$-5.362$ 259$\pm$8 215$\pm$11 12.18$\pm$0.12 $-42.07\pm$0.41 1 2 61
SPASSJ161255-573638 16h12m55s $-57$d36m38.9s 327.384 $-4.645$ 830$\pm$48
360$\pm$32 17.10$\pm$0.14 $-18.32\pm$0.24 1 4 62 SPASSJ161432-562236*
16h14m32s $-56$d22m36.6s 328.397 $-3.903$ 1529$\pm$28 1401$\pm$39
42.43$\pm$0.31 $-29.45\pm$0.10 3 3 63 SPASSJ154523-452432 15h45m23s
$-45$d24m32.9s 332.088 $7.388$ 170$\pm$14 143$\pm$15 11.67$\pm$0.13
$-64.49\pm$0.35 1 2 64 SPASSJ161451-434125 16h14m50s $-43$d41m25.0s 337.204
$5.238$ 512$\pm$16 474$\pm$35 4.63$\pm$0.11 $-0.04\pm$0.92 1 4 65
SPASSJ161551-633314 16h15m51s $-63$d33m14.4s 323.488 $-9.172$ 693$\pm$29
532$\pm$72 8.04$\pm$0.25 $+200.80\pm$0.61 2 4 66 SPASSJ162941-422659 16h29m41s
$-42$d26m59.0s 340.001 $4.187$ 205$\pm$4 181$\pm$5 … $+437.73\pm$5.35 1 4 67
SPASSJ161950-455109 16h19m50s $-45$d51m9.7s 336.325 $3.072$ 646$\pm$19
521$\pm$23 71.70$\pm$0.28 $-81.23\pm$0.08 2 4 68 SPASSJ162202-430822 16h22m02s
$-43$d08m22.0s 338.525 $4.716$ 984$\pm$26 802$\pm$54 24.97$\pm$0.27
$+80.83\pm$0.22 3 3 69 SPASSJ162346-564509 16h23m46s $-56$d45m9.8s 329.04
$-5.065$ 582$\pm$13 485$\pm$6 10.34$\pm$0.24 $+69.46\pm$0.64 2 2 70
SPASSJ161441-442447* 16h14m41s $-44$d24m47.5s 336.682 $4.736$ 1005$\pm$15
918$\pm$12 52.20$\pm$0.25 $+127.38\pm$0.08 2 4 71 SPASSJ162628-580020
16h26m28s $-58$d00m20.3s 328.389 $-6.197$ 330$\pm$16 252$\pm$43 11.16$\pm$0.15
$+49.93\pm$0.36 1 2 72 SPASSJ162650-421129 16h26m50s $-42$d11m29.0s 339.824
$4.746$ 714$\pm$100 … 15.24$\pm$0.28 $+6.32\pm$0.52 2 3 73 SPASSJ162701-604320
16h27m01s $-60$d43m20.1s 326.456 $-8.122$ … 78$\pm$15 3.89$\pm$0.12
$+98.83\pm$0.93 1 2 74 NVSSJ173620-283552 17h36m18s $-28$d36m2.0s 359.205
$1.907$ 183$\pm$4 156$\pm$7 14.76$\pm$0.21 $-348.57\pm$0.35 4 5 75
SPASSJ163056-580102* 16h30m56s $-58$d01m2.3s 328.789 $-6.635$ 292$\pm$8
246$\pm$7 5.70$\pm$0.08 $+89.20\pm$0.66 1 3 76 SPASSJ163958-603651 16h39m58s
$-60$d36m51.8s 327.612 $-9.227$ 638$\pm$56 207$\pm$22 10.94$\pm$0.15
$+97.14\pm$0.43 2 3

Table 4 Continued:

S19 ID (1) RA (2) Dec (3) $l$ (4) $b$ (5) $I_{\mathrm{MFS}}$ (6) $I_{2100}$
(7) PI (8) $\phi_{\mathrm{peak}}$ (9) $n$ (10) $n$ (11) (J2000) (J2000) (deg)
(deg) (mJy) (mJy) (mJy) rad m-2 (this work) (S19) 77 SPASSJ165908-532028*
16h59m08s $-53$d20m28.0s 334.961 $-6.644$ 538$\pm$12 465$\pm$11 38.41$\pm$0.17
$+118.12\pm$0.12 1 2 78 PKSB1637-319* 16h40m38s $-32$d04m37.0s 349.235 $9.51$
327$\pm$5 297$\pm$6 27.81$\pm$0.12 $-33.44\pm$0.14 1 1 79 SPASSJ151439-474835
15h14m40s $-47$d48m30.0s 326.338 $8.448$ 1082$\pm$11 1216$\pm$10
10.46$\pm$0.16 $-7.68\pm$0.30 1 1 80 SPASSJ171405-515258 17h14m05s
$-51$d52m58.0s 337.501 $-7.605$ 84$\pm$34 294$\pm$24 16.69$\pm$0.16
$-50.08\pm$0.27 1 3 81 SPASSJ171510-515708 17h15m09s $-51$d57m8.0s 337.541
$-7.781$ 440$\pm$18 270$\pm$33 11.11$\pm$0.19 $-50.43\pm$0.42 1 3 82
SPASSJ172135-514628 17h21m34s $-51$d46m28.0s 338.253 $-8.499$ 384$\pm$18
298$\pm$30 7.92$\pm$0.15 $+43.84\pm$0.54 1 3 83 SPASSJ172139-495033 17h21m38s
$-49$d50m33.0s 339.879 $-7.432$ 130$\pm$30 144$\pm$39 3.19$\pm$0.15
$-70.85\pm$1.47 1 3 84 SPASSJ172315-463135 17h23m14s $-46$d31m35.0s 342.798
$-5.8$ 516$\pm$40 266$\pm$36 38.81$\pm$0.16 $-91.50\pm$0.13 1 3 85
SPASSJ172456-444054 17h24m56s $-44$d40m54.0s 344.5 $-5.015$ 284$\pm$6
249$\pm$7 13.55$\pm$0.14 $+161.11\pm$0.32 1 1 86 SPASSJ173219-482740 17h32m19s
$-48$d27m40.0s 342.008 $-8.139$ 415$\pm$15 231$\pm$19 8.79$\pm$0.14
$-235.78\pm$0.52 2 4 87 SPASSJ173720-412636 17h37m19s $-41$d26m36.0s 348.465
$-5.154$ 317$\pm$31 377$\pm$83 10.66$\pm$0.13 $-108.20\pm$0.52 1 2 88
SPASSJ174304-405729 17h43m03s $-40$d57m29.0s 349.448 $-5.817$ 408$\pm$6
395$\pm$9 19.04$\pm$0.13 $-24.43\pm$0.23 1 3 89 SPASSJ175548-443006* 17h55m47s
$-44$d30m6.0s 347.534 $-9.615$ 407$\pm$11 363$\pm$11 7.88$\pm$0.18
$+49.90\pm$0.74 1 2 90 SPASSJ143012-545251 14h30m12s $-54$d52m51.9s 316.898
$5.29$ 373$\pm$21 259$\pm$32 5.04$\pm$0.13 $-176.49\pm$0.96 1 2 91
NVSSJ180242-394005 18h02m42s $-39$d40m8.0s 352.451 $-8.425$ 1270$\pm$4
1250$\pm$5 14.62$\pm$0.21 $+90.88\pm$0.18 1 1 92 PKSB1654-339* 16h57m07s
$-34$d00m0.0s 349.947 $5.623$ 112$\pm$3 117$\pm$8 7.78$\pm$0.14
$-142.62\pm$0.53 1 4 93 PKSB1657-261 17h00m57s $-26$d10m28.0s 356.716 $9.74$
1009$\pm$8 1059$\pm$12 25.13$\pm$0.21 $-27.97\pm$0.22 2 2 94 PKSB1657-340
17h00m15s $-34$d09m22.0s 350.227 $5.013$ 585$\pm$9 498$\pm$9 6.91$\pm$0.20
$-132.48\pm$0.68 4 4 95 SPASSJ170758-520057 17h07m58s $-52$d00m57.0s 336.838
$-6.916$ 96$\pm$3 … 8.01$\pm$0.14 $-106.38\pm$0.53 1 3