11institutetext: Astronomisches Institut der Ruhr-Universität Bochum (AIRUB),
Universitätsstrasse 150, 44801 Bochum, Germany 22institutetext: ASTRON, the
Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4,7991 PD
Dwingeloo, The Netherlands 33institutetext: Kapteyn Astronomical Institute,
University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
44institutetext: Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la
Astronomía s/n, 18008 Granada, Spain 55institutetext: CSIRO Astronomy and
Space Science, Australia Telescope National Facility, PO Box 76, Epping NSW
1710, Australia 66institutetext: Sydney Institute for Astronomy, School of
Physics, University of Sydney, Sydney, New South Wales 2006, Australia
77institutetext: Anton Pannekoek Institute, University of Amsterdam, Postbus
94249, 1090 GE Amsterdam, The Netherlands 88institutetext: University of Oslo
Center for Information Technology, P.O. Box 1059, 0316 Oslo, Norway
99institutetext: National Centre for Radio Astrophysics, Tata Institute of
Fundamental Research, Pune 411007, Maharashtra, India 1010institutetext:
Netherlands eScience Center, Science Park 140, 1098 XG, Amsterdam, The
Netherlands 1111institutetext: Dept. of Electrical Engineering, Chalmers
University of Technology, Gothenburg, Sweden 1212institutetext: Department of
Astronomy, University of Cape Town, Private Bag X3, Rondebosch 7701, South
Africa 1313institutetext: Cahill Center for Astronomy, California Institute of
Technology, Pasadena, CA, USA

# The Apertif science verification campaign

Characteristics of polarised radio sources

B. Adebahr 11 A. Berger 11 E. A. K. Adams 2233 K. M. Hess 442233 W. J. G. de
Blok 22121233 H. Dénes 22 V. A. Moss 556622 R. Schulz 22 J. M. van der Hulst
22 L. Connor 131322 S. Damstra 22 B. Hut 22 M. V. Ivashina 1111 G. M. Loose 22
Y. Maan 9922 A. Mika 22 H. Mulder 22 M. J. Norden 22 L. C. Oostrum 22771010 E.
Orrú 22 M. Ruiter 22 R. Smits 22 W. A. van Cappellen 22 J. van Leeuwen 2277 N.
J. Vermaas 22 D. Vohl 7722 J. Ziemke 2288

(-)

###### Abstract

Context. The characteristics of the polarised radio sky are a key ingredient
in constraining evolutionary models of magnetic fields in the Universe and
their role in feedback processes. The origin of the polarised emission and the
characteristics of the intergalactic medium on the line of sight can be
investigated using large samples of polarised sources. Ancillary infrared (IR)
and optical data can be used to study the nature of the emitting objects.

Aims. We analyse five early science datasets from the APERture Tile in Focus
(Apertif) phased array feed system to verify the polarisation capabilities of
Apertif in view of future larger data releases. We aim to characterise the
source population of the polarised sky in the L-Band using polarised source
information in combination with IR and optical data.

Methods. We use automatic routines to generate full field-of-view Q- and
U-cubes and perform Rotation Measure (RM)-Synthesis, source finding, and
cross-matching with published radio, optical, and IR data to generate
polarised source catalogues. All sources were inspected individually by eye
for verification of their IR and optical counterparts. Spectral energy
distribution (SED)-fitting routines were used to determine photometric
redshifts, star-formation rates, and galaxy masses. IR colour information was
used to classify sources as active galactic nuclei (AGN) or star-forming-
dominated and early- or late-type.

Results. We surveyed an area of 56 deg2 and detected 1357 polarised source
components in 1170 sources. The fraction of polarised sources is 10.57 % with
a median fractional polarisation of $4.70\pm 0.14$ %. We confirmed the
reliability of the Apertif measurements by comparing them with polarised
cross-identified NVSS sources. Average RMs of the individual fields lie within
the error of the best Milky Way foreground measurements. All of our polarised
sources were found to be dominated by AGN activity in the radio regime with
most of them being radio-loud (79 %) and of the Fanaroff-Riley (FR)II class
(87 %). The host galaxies of our polarised source sample are dominated by
intermediate disc and star-forming disc galaxies. The contribution of star
formation to the radio emission is on the order of a few percent for $\approx
10\,\%$ of the polarised sources while for $\approx 90\,\%$ it is completely
dominated by the AGN. We do not see any change in fractional polarisation for
different star-formation rates of the AGN host galaxies.

Conclusions. The Apertif system is suitable for large-area high-sensitivity
polarised sky surveys. The data products of the polarisation analysis pipeline
can be used to investigate the Milky Way magnetic field on projected scales of
several arcminutes as well as the origin of the polarised emission in AGN and
the properties of their host galaxies.

###### Key Words.:

Polarisation - Surveys - Methods: data analysis - Galaxies: active - Galaxies:
magnetic fields

##  1 Introduction

Surveys of the radio sky offer a unique opportunity to study the
characteristics and evolution of galaxies in the Universe. Radio emission is
capable of avoiding obscuration by dense gas, which is known to affect optical
and infrared (IR) studies. Radio continuum emission traces one of the key
ingredients needed for a full understanding of the physics of the Universe,
namely the magnetic field. At radio wavelengths in the centimetre regime and
beyond, continuum emission is dominated by gyrating relativistic electrons,
which exhibit synchrotron radiation. While the total radio synchrotron
emission traces the overall magnetic field, the polarised emission uncovers
the degree to which it is ordered.

It is known that the structure and strength of magnetic fields are important
for jet collimation in active galactic nuclei (AGN) and the collapse of
molecular clouds leading to star formation in galaxies (see Romero et al.
(2017) and Crutcher (2012) and references therein). These magnetic fields are
often expelled into the intergalactic space by AGN, producing powerful radio
jets and/or consecutive supernova explosions forming superbubbles generated by
star formation. Both processes are known to play a key role in the enrichment
of intergalactic space with particles and magnetic fields (Heckman & Best,
2014).

While AGN-dominated objects are more powerful, star-forming galaxies are more
numerous, meaning that which object class influences the enrichment of the
interstellar medium the most is a matter of debate, as is the degree to which
host galaxies can re-accrete the expelled material (Heckman & Best, 2014).
Therefore, understanding these processes on galactic and larger scales and
their influence over the lifetime of the Universe is key to a thorough
understanding of galaxy evolution.

Observing large fields in the radio regime allows investigation of this
context via a statistical approach. However, total power and polarised radio
sky surveys are biased towards the detection of different types of objects.
The radio sky at the milliJansky(mJy)-level in total intensity consists of
emission from AGN and star formation with increasing dominance of the latter
towards lower flux densities (Novak et al., 2018; Prandoni et al., 2018). On
the other hand, the polarised radio sky is mostly dominated by AGN emission
(Hales et al., 2014a; Stil et al., 2014). Large statistical samples of radio
sources in combination with information from their IR and optical emission not
only help us to understand the proportions of AGN and star-forming galaxies
(Mao et al., 2012; Hales et al., 2014a), but also provide insight into the
characteristics of their host galaxies.

Up to now, all unresolved or barely resolved polarised extragalactic objects
were identified as AGN. While the origin of the activity is known to be caused
by supermassive black holes (SMBH), the timing and intensity of their activity
are still unknown (Sabater et al., 2019; Shabala et al., 2020; Morganti et
al., 2021c). While some are found to be compact and their emission confined to
the host galaxies (O’Dea & Saikia, 2021), others exhibit megaparsec(Mpc)-scale
jets (Subrahmanyan et al., 1996). These jets often show brightness
enhancements towards their cores or lobes and are usually referred to as
Fanaroff-Riley-class (FR) I and II objects (Fanaroff & Riley, 1974),
respectively. While polarised emission from FRII-type AGN is primarily found
at the borders of their radio lobes, FRI-type AGN often show polarised
emission all over their extension. FRII objects are commonly found to be more
luminous and in less dense environments. The extent to which the parameters of
the surrounding medium —such as the morphology, gas composition, and gas
density of the host galaxy, as well as the magnetic field distribution and gas
density in the intragroup and intracluster medium surrounding the host galaxy—
are influencing the development into either an FRI or FRII source is not known
and a detailed understanding of their host galaxies and their evolution is
necessary (Gendre et al., 2013; Miraghaei & Best, 2017; Mingo et al., 2019;
Rodman et al., 2019; Vardoulaki et al., 2021).

Comparing data from radio wavelengths —where the direct synchrotron emission
from AGN activity is often dominating— with either IR or optical data —where
the prime emission mechanism is directly connected to the host galaxies— is an
important tracer of AGN activity and the influence of star formation on
feedback processes. Such studies led to the discovery of the famous radio–far-
infrared(FIR) correlation for star-forming galaxies (de Jong et al., 1985) or
the classification of AGN into radio-loud and radio-quiet (Kellermann et al.,
1989). While more luminous AGN are often also brighter in the IR, a subclass
is IR-faint (Norris et al., 2006). These IR-faint radio sources are known to
be high-z objects, which are mostly compact and/or often highly obscured
(Collier et al., 2014; Orenstein et al., 2019). The percentage of these
objects visible in faint radio surveys especially with respect to polarisation
is not known. Simulations and observations show that the amount of polarised
sources and their emission strength is by an order of magnitude smaller than
their total power counterparts (Bonaldi et al., 2019), meaning that large
areas have to be surveyed with high sensitivities in order to accomplish a
statistically relevant sample. Analysis in the past, mostly due to technical
limitations, could only reach such sensitivities for areas of several square
degrees with integration times of several tens or hundreds of hours. These
observations were mainly targeted at fields where ancillary data were
available to maximise the gain from the long observation times. Recent
improvements in receiver and computing technology now allow simultaneous
observations of large areas on the sky using phased array and phased-array
feed technologies (Verheijen et al., 2008; Hotan et al., 2021; van Cappellen
et al., 2021). This allows the execution of blind large-area surveys with
sensitivity previously only achievable by targeted observations.

APERture Tile in Focus (Apertif) is a new phased-array feed for the Westerbork
Synthesis Radio Telescope (WSRT), in place on 12 of the 14 dishes. Phased-
array feeds (PAFs) work by placing multiple elements in the focal plane of a
dish and correlating them to generate multiple beams. Apertif combines the
signal from 121 Vivaldi elements to provide 40 simultaneous beams on the sky
with a combined field of view of approximately 6.6 deg2. A full overview of
the Apertif system is provided by van Cappellen et al. (2021).

In this publication we use Apertif data of five observations taken during the
science verification campaign (SVC) to demonstrate the polarisation
capabilities of the system and verify the reliability of the measurements. We
describe the observations in Sect. 2 and the reduction of the data in Sect. 3.
The individual steps for the polarisation data analysis as well as an
assessment of the polarisation leakage are described in Sect. 4. Section 5
portrays the source statistics and compares the results with previous ones. In
Sect. 6 we analyse the characteristics of the polarised sources in view of the
host galaxy type and the AGN- and star-formation activity. We discuss our
results in Sect. 7 and summarise in Sect. 8.

In this publication we use the cosmological parameters $H_{0}=69.6$,
$\Omega_{M}=0.286$ and $\Omega_{vac}=0.714$ from Bennett et al. (2014).

##  2 Observations

The Apertif SVC was carried out between 18 March 2019 and 15 April 2019. Its
aim was to verify the scientific usage of the Apertif system. Two weeks within
this time period were dedicated to taking correlated imaging data including
full polarisation information and calibration. The goal of these observations
was scientific commissioning and finalisation of the survey strategy. During
the whole period, the science teams monitored the data as it was acquired and
provided immediate feedback on its quality.

Figure 1: Azimuthal north-pole equal-area projection showing the footprint of
the SVC fields. Blue and orange circles are objects from the 2MRS catalogue
(Huchra et al., 2012) and the Local Volume survey (Karachentsev et al., 2004),
respectively. The red dotted line represents a declination of +27∘, which is
the limit for the Apertif surveys. The five black boxes show the position and
size of the SVC survey fields. The blank region represents the Milky Way.

Five datasets between 8 and 11 April 2019 were recorded during this period,
which are representative of the final achievable data quality of the imaging
surveys. The data were publicly released through the Apertif Long Term Archive
(ALTA) 111https://alta.astron.nl. Figure 1 shows the location of the five SVC
fields.

The observations occurred at a central frequency of 1370 MHz with a bandwidth
of 300 MHz divided into 384 sub-bands with 64 channels each resulting in a
frequency resolution of 12.2 kHz. All four linear correlations (XX, YY, XY,
YX) were recorded. Due to the east to west alignment of the WSRT dishes, each
field was observed for 11.5 h on source to provide sufficient (u,v) coverage.
Each two observations were bracketed with four- to five-minute calibrator
scans centred in each of the 40 compound beams. Alternating scans were
performed on the unpolarised calibration source 3C196 and the polarised
calibration source 3C138. An exception to this strategy is the last
observation (field S1415+36), where only a single directly associated (e.g.
bracketing) calibrator scan was carried out. Therefore, a non-bracketing
calibrator scan was used from earlier in the observing run to provide full
polarimetric calibration. The observed fields and calibrator information are
listed in Table 1.

Table 1: Datasets of the SVC imaging survey fields

Target field | Flux calibrator | Polarisation calibrator
---|---|---
Field |  Name |  Task ID |  tobs (min) |  Name |  Obs IDs |  tobs (min) |  Name |  Task IDs |  tobs (min)
SVC1 |  S2248+33aa$a$Coordinates correspond to the telescope pointing positions. |  190409015 |  690 |  3C196 |  190408125-150 190409001-014aa$a$Coordinates correspond to the telescope pointing positions. |  5 |  3C138 |  190409016-055 |  4
SVC2 |  M1403+53 |  190409056 |  690 |  3C196 |  190410002-041 |  5 |  3C138 |  190409016-055 |  4
SVC3 |  M0155+33 |  190410001 |  690 |  3C196 |  190410002-041 |  5 |  3C138 |  190409016-055 |  4
SVC4 |  S2246+38 |  190411001 |  690 |  3C196 |  190410002-041 |  5 |  3C138 |  190411002-041 |  4
SVC5 |  S1415+36 |  190411042 |  690 |  3C196bb$b$$\sigma_{PI}$ and $\sigma_{TP}$ are the noise levels of the polarised intensity and total power images, respectively, which were derived by determining the lowest quartile of the pixel values of the corresponding rms maps from the PyBDSF source finding. |  190410002-041bb$b$$\sigma_{PI}$ and $\sigma_{TP}$ are the noise levels of the polarised intensity and total power images, respectively, which were derived by determining the lowest quartile of the pixel values of the corresponding rms maps from the PyBDSF source finding. |  5 |  3C138 |  190411002-041 |  4
222 aa$a$Coordinates correspond to the telescope pointing positions.Beams
31-39 failed (190409006-14 not on source) bb$b$$\sigma_{PI}$ and $\sigma_{TP}$
are the noise levels of the polarised intensity and total power images,
respectively, which were derived by determining the lowest quartile of the
pixel values of the corresponding rms maps from the PyBDSF source finding.Non-
bracketing flux calibrator used due to failure of observing session

##  3 Data reduction

During the SVC period, the imaging data were automatically run through the
Apertif imaging pipeline (Apercal) (Adebahr et al., 2022). In the following,
we want to describe the main calibration and imaging steps performed by
Apercal which are relevant for the generation of the continuum and
polarisation data products used in this publication. Apercal is publicly
available on github333https://github.com/apertif/apercal/releases. For the SVC
processing release version 2.4, ‘SVC-Reprocessing’ was used.

The data were acquired from ALTA. Early science data suffer from delay issues
due to an incomplete correction of the phase tracking for all beams. For
survey data, this correction is automatically applied before data are ingested
into ALTA. Specifically for the SVC data, an offline correction to the fringe-
stopping was applied immediately after retrieving the data. To mitigate the
influence of strong RFI and enhance the performance of automatic flagging
routines, only the frequency range between 1291.8 and 1441.8 MHz was used for
further processing resulting in an effective bandwidth of 150 MHz.

Flagging was executed in three steps: First, continuous problematic data
ranges were flagged. This included the first, central, and last channels of
each subband as well as flagging for shadowing of dishes. As a next step, the
data were carefully manually inspected for additional RFI or system issues.
For all fields, beams 16 and 18 were not processed as an inspection of their
phases revealed a problematic sub-band-based behaviour. For beam 01, RT9 was
also flagged for all observations as it showed variations and jumps in the
phases every 20 sub-bands. The first target field (S2248+33) also had several
additional flags applied. Beams 31-39 were not processed as the flux
calibrator observations were not successful. In addition, RTD was flagged for
beams 0-5; high temperatures in the electronics cabinet for this dish resulted
in some components shutting down for that time period, meaning corrupted data
were recorded. For the last target dataset (S1415+36), RTC was flagged due to
residual delay issues. Finally, we note that channels (of the full dataset)
10752–12287 (1380–1400 MHz) for the YY polarisation of RT5 are automatically
flagged by the system for the SVC data; this is a result of the correlator not
receiving the data.

The last flagging step was performed automatically using aoflagger (Offringa
et al., 2012) with a flagging strategy specifically tailored to the parameters
of the Apertif data (see Offringa et al. in prep. and Offringa et al. (2010)
for further details). The strategy uses a low-pass filter in combination with
the Sumthreshold and Scale Invariant Rank operations to detect spurious radio
frequency interference.

Residual delays, complex gains, bandpasses, and polarisation leakage solutions
were derived using the flux calibrator datasets. The polarisation angle and
time-dependent phase offsets between the feeds were derived using the
polarised calibrator dataset. For all steps, the Common Astronomical Software
Application (CASA) (McMullin et al., 2007) was used. All solutions were then
applied to the appropriate target datasets.

Further processing was performed using the Multichannel Image Reconstruction
Image Analysis and Display software (MIRIAD) (Sault et al., 1995). The data
were first converted to the MIRIAD format and then averaged in frequency by a
factor of 64, so that each individual channel encompasses the data of one sub-
band. Self-calibration was then performed for each individual target beam
dataset. This step consisted of three substeps. First, a frequency-dependent
model of the sky was generated using a combination of the catalogues of the
NRAO VLA Sky Survey (NVSS) (Condon et al., 1998), The Faint Images of the
Radio Sky at Twenty Centimeters (FIRST) Survey (Becker et al., 1995), and the
Westerbork Northern Sky Survey (WENSS) (Rengelink et al., 1997). This
parametric self-calibration step was followed by several iterations of phase
self-calibration, and, in cases with sufficient signal-to-noise ratio (S/N),
one iteration of amplitude self-calibration. For each self-calibration cycle,
the solution interval was decreased and the (u,v)-range of data to include was
increased. The specific details of the self-calibraton routines are described
in Adebahr et al. (2022).

The final self-calibrated data were used to produce a multi-frequency
synthesis Stokes I total power image. We cleaned the resulting image down to
the $1\sigma$ level within masks generated with a $5\sigma$ threshold, where
$\sigma$ is the calculated theoretical noise of the observation. In addition
to the total power image, we produced Stokes Q and U image cubes. For easier
handling, the Q- and U-data were imaged in chunks of 6.25 MHz bandwidth
resulting in 24 final images for each Stokes parameter over the total
bandwidth of 150 MHz. Cleaning of the individual images was performed using
the masks generated during the Stokes I imaging and cleaning down to the
$1\sigma$ level of the noise in the individual Stokes Q- and U-images. Stokes
V images were created using multi-frequency synthesis and cleaning down to the
$1\sigma$ level of the noise in the image using the same masks as before.

We created mosaics of all compound beams of the five different pointings in
Stokes I, Q, and U. For all mosaics, the central Beam (00) was excluded. This
beam delivers mostly redundant information and would therefore add correlated
noise to the data. For Stokes I, all successfully calibrated multi-frequency
images were used. Strong image artefacts or very high noise values of
individual images within a single Q or U cube can corrupt the entire
polarisation analysis. Therefore, we discarded all single image planes of
individual beams with noise values of $>300\,\upmu$Jy/beam. For further
polarisation analysis, all images of the same observation over the entire
frequency range need the same synthesised beam size. In order to mitigate the
effect of large final beams caused by individual images where data of long
baselines are missing, all images within a cube with
$\theta_{maj}>35^{\prime\prime}$ or $\theta_{min}>20.5^{\prime\prime}$ were
discarded, where $\theta_{maj}$ and $\theta_{min}$ are the FWHM of the major
and minor axis of the synthesised beam, respectively. To ensure constant
parameters for the polarisation analysis over the field of view of a single
pointing, the same frequency and spatial coverage has to be given for the
whole Stokes Q and U mosaic cubes. We therefore discarded images of entire
beams or all images at frequencies where two or more images were missing. This
ensures that no images containing only NaN values enter the polarisation
analysis.

Table 2: Accepted images for the SVC mosaicking routines.

Field | $N_{c}$ | $N_{p,f}$ | $N_{p,b}$
---|---|---|---
SVC1 | 28 | 22 | 28
SVC2 | 37 | 23 | 31
SVC3 | 37 | 23 | 37
SVC4 | 37 | 22 | 32
SVC5 | 37 | 22 | 36
444$N_{c}$ is the number of accepted continuum images and $N_{p,f}$ and
$N_{p,b}$ are the number of individual frequency and beam images accepted for
generating the Stokes Q- and U-image cube mosaics, respectively. The maximum
possible numbers would be $N_{c}=39$, $N_{p,f}=24$ and $N_{p,b}=39$

We then convolved all accepted Stokes-Q and -U images to the smallest common
synthesised beam and primary beam corrected them using Gaussian regression
models (Kutkin et al. in prep.). The images were then clipped at the 5% level
of the primary beam response and combined using an inverse square weighting of
the noise in the individual images.

##  4 Polarisation data analysis

In the following we present the strategy and software
routines555https://github.com/adebahr/aperpol to generate polarised source
catalogues from Apertif imaging data in a semi-automatic way. The SVC datasets
serve as a test-bed for the analysis of the polarisation data of the whole
Apertif survey.

###  4.1 Rotation measure synthesis

Stokes-Q and -U fluxes from astronomical sources exhibit a sinusoidal
dependence of the square of the observed wavelength. Depending on the value of
the rotation measure (RM) of the received signal, this can lead to
depolarisation within the observing band. To mitigate this effect, we
performed RM synthesis (Brentjens & de Bruyn, 2005) on the final Stokes Q- and
U-mosaic cubes to generate Faraday Q- and U-cubes. The resolution in Faraday
space $\delta\Phi$ is approximated by

$\delta\Phi\approx\frac{2\sqrt{3}}{\Delta\lambda^{2}},$ (1)

the maximum Faraday scale to which sensitivity has dropped to 50 % is

$\Phi_{ms}\approx\frac{\pi}{\lambda_{min}^{2}},$ (2)

and the maximum Faraday depth with more than 50 % sensitivity is

$||\Phi_{max}||\approx\frac{\sqrt{3}}{\delta\lambda^{2}},$ (3)

where $\delta\lambda^{2}$ is the channel width, $\Delta\lambda^{2}$ the width
of the $\lambda^{2}$ distribution, and $\lambda_{min}^{2}$ is the shortest
wavelength squared. We list the resulting parameters for our setup for all
five of our fields in Table 3.

Table 3: RM synthesis parameters for all five SVC fields.

Field | $\delta\Phi$ | $\Phi_{ms}$ | $\Phi_{max}$
---|---|---|---
| [rad/m$2$] | [rad/m$2$] | [rad/m$2$]
SVC1 | 378.33 | 72.34 | 3990.65
SVC2 | 353.60 | 71.72 | 3909.46
SVC3 | 353.60 | 71.72 | 3909.46
SVC4 | 378.33 | 72.34 | 3990.65
SVC5 | 378.33 | 72.34 | 3990.65
666$\delta\Phi$ is the resolution in Faraday space, $\Phi_{ms}$ the maximum
observable Faraday scale, and $\Phi_{max}$ the maximum observable Faraday
depth.

We sampled the Faraday axis in the range of -1024 rad/m${}^{2}\leq\Phi\leq$
1024 rad/m2 with a sampling interval of 8 rad/m2 resulting in Q- and U-Faraday
cubes of 257 planes each. The resulting rotation-measure transfer functions
(RMTFs) are shown in Fig. 2. The first sidelobes of the RMTF are located at
$\sim$500 rad/m2 and on a level of $\sim 20\%$. We want to note that the small
discrepancy in the two functions and the RM-synthesis parameters (Table 3) of
fields SVC1/4/5 and SVC2/3 originates from the slightly different frequency
coverage of the input images.

Figure 2: Rotation-measure transfer function for the SVC Faraday cubes for our
sampled Faraday range of -1024 rad/m${}^{2}\leq\Phi\leq$ 1024 rad/m2.

###  4.2 Faraday cube analysis

We determined polarised intensity (PI) and RM values from the resulting
Faraday cubes. First, the absolute of the complex polarisation vector Q+iU is
calculated, which results in a polarised intensity (PI) image cube. The
maximum of the PI along the Faraday axis represents the linear polarised flux
of the main polarised component along the axis. The position of this peak is
the RM value. For optimal determination of these values and to overcome the
limited sampling of the Faraday axis of 8 rad/m2, we search for the highest
value along the Faraday axis for all pixels in RA- and DEC directions in our
PI image cube. We then fit a one-dimensional parabola in Faraday space to this
value and the two neighbouring values. The resulting PI- and RM values are
saved to two-dimensional PI- and RM maps. We want to note that this analysis
technique is only sensitive to the brightest component in Faraday space.
Manual inspection of the Faraday cubes would be needed for analysis of
secondary or higher order components.

Figure 3: Polarised intensity image of the field M0155+33 (SVC3). The noise in
emission-free regions is 14 $\upmu$Jy/beam. The synthesised beam size is
$29.2^{\prime\prime}\times 16.1^{\prime\prime}$. Beams 16 and 18 are missing,
which appears as increased noise towards the southeast and southwest of the
central position. Several sources show artefacts around their positions, which
can be traced back to direction-dependent calibrations issues. The diffuse
polarised emission in the southeast originates from Galactic foreground
emission. Polarised intensity images for the other SVC fields are provided in
Appendix A. Table 4: Parameters of the SVC mosaics.

Field | Date of observation | RAaa$a$Coordinates correspond to the telescope pointing positions. | DECaa$a$Coordinates correspond to the telescope pointing positions. |  $\sigma_{PI}$bb$b$$\sigma_{PI}$ and $\sigma_{TP}$ are the noise levels of the polarised intensity and total power images, respectively, which were derived by determining the lowest quartile of the pixel values of the corresponding rms maps from the PyBDSF source finding. | FWHMPI |  $\sigma_{TP}$bb$b$$\sigma_{PI}$ and $\sigma_{TP}$ are the noise levels of the polarised intensity and total power images, respectively, which were derived by determining the lowest quartile of the pixel values of the corresponding rms maps from the PyBDSF source finding. | FWHMTP
---|---|---|---|---|---|---|---
| [dd-mm-yyyy] | [hh:mm:ss] | [dd:mm:ss] | [$\upmu$Jy/beam] | [”] | [$\upmu$Jy/beam] | [”]
SVC1 | 09-04-2019 | 22:48:39 | +33:56:40 | 14 | $32.1\times 18.0$ | 35 | $27.2\times 12.1$
SVC2 | 09-04-2019 | 14:03:24 | +53:24:05 | 13 | $19.3\times 14.6$ | 43 | $18.6\times 12.8$
SVC3 | 10-04-2019 | 01:55:19 | +33:56:40 | 14 | $29.2\times 16.1$ | 42 | $26.2\times 11.7$
SVC4 | 11-04-2019 | 22:46:24 | +38:48:32 | 16 | $24.8\times 14.8$ | 39 | $23.7\times 12.0$
SVC5 | 11-04-2019 | 14:15:53 | +36:22:36 | 16 | $31.2\times 17.7$ | 46 | $25.5\times 11.9$

777

###  4.3 Source finding

We performed source finding in the final PI maps using the Python Blob
Detector and Source Finder (PyBDSF) (Mohan & Rafferty, 2015). Our final PI
maps show artefacts around bright sources. These are caused by directional
calibration issues in combination with stacking of uncleaned sidelobes in the
individual Q- and U-images. To mitigate the influence of these artefacts on
our source-detection analysis, we used an rms box with an adaptive threshold
of $10.0\sigma$. The island threshold was set to $5.0\sigma$ and the pixel
threshold to $6.25\sigma$. The kernel filter parameter rms_box was set to
(60,20). To reduce false detections due to artefacts in the vicinity of strong
sources even further, we enabled the rms_box_bright parameter with values of
(20,8).

A source-detection mask and a source catalogue were generated for each field.
In order to calculate the fractional polarisation (FP) values of sources and
generate a total power (TP) catalogue for cross-matching in later stages of
the analysis, we performed another PyBDSF run on the Stokes I TP image. Here,
we used slightly different parameters because of the inherently different
distribution of sources and noise characteristics compared to the PI maps. An
adaptive rms box was enabled as well. We used thresholds of $4.0\sigma$ and
$5.0\sigma$ for islands and pixels, respectively. The parameter rms_box was
set to (100,10) and rms_box_bright to (20,2). In addition we forced the mean
map to be zero and fitted a rank-1 spline to the background.

We convolved the Stokes I total power image to the resolution of the PI-map
when calculating the FP maps. We then divided the PI map by the TP map. In
order to limit the PI, RM, and FP maps to regions of sufficient S/N, we used
the image masks generated by PyBDSF for the PI source finding to blank any
pixels outside of the masked regions for these images.

Our catalogues contain one entry for each detected component. Sources with
multiple components are associated by the same source ID. PI- and TP flux
densities as well as FP values are given individually for each component and
for the integrated fluxes of the sources. Calculating average RMs for sources,
especially in a resolved case, is difficult because of the strongly varying
values close to the borders of masks originating from lower S/Ns. Therefore,
we only include RM values for each individual component. These values were
determined using the RA- and DEC coordinates of the component in the PI
catalogue. For a description of the columns in the catalogue888The catalogue
data is available at https://vo.astron.nl/, see Appendix B.

###  4.4 Cross-matching

The RA- and DEC coordinates of each source in the PI catalogue were used for
cross-matching with our generated TP catalogues, the NVSS RM catalogue(Taylor
et al., 2009), the All Wide-field Infrared Survey Explorer (WISE) database
(Cutri et al., 2021), and the Sloan Digital Sky Survey (SDSS) DR16 database
(Ahumada et al., 2020). While full coverage of the SVC footprint is provided
by the NVSS and AllWISE databases, the SDSS coverage is 65.52 % (36.94 deg2
out of 56.38 deg2). To acquire the best possible results and keep false cross-
matching rates to a minimum, we proceeded in the following way.

An aliasing problem in the Apertif correlator is known to produce fake sources
at the central position of each compound beam. We made sure to exclude these
false detections from the catalogues by removing any detected TP- or PI source
within the radius of the FWHM of the synthesised beam in the central observed
pointing positions of each compound beam from our databases.

For each PI source, the closest TP source located within the major radius of
the synthesised beam of the PI image was associated as its counterpart. If a
TP source was found, the AllWISE
database999https://wise2.ipac.caltech.edu/docs/release/allwise/ was queried.
As polarised emission is often not coincident with the central position of an
object, especially for extended objects, we used the coordinates of the total
power cross-matched source. An AllWISE cross-match was identified if an entry
could be located within the major radius of the synthesised beam of the TP
image. The position, brightness, and S/N in all four WISE bands (3.4 $\upmu$m,
4.6 $\upmu$m, 12 $\upmu$m, 22 $\upmu$m) and their errors were acquired and
added to our database. Due to the better correlation of IR data to optical
data, we cross-matched our objects with the SDSS DR16
database101010https://www.sdss.org/dr16/ using the WISE coordinates. This
strategy has the advantage of producing much less false cross-matching results
than a direct cross-match using our radio continuum coordinates to SDSS. The
closest SDSS match was identified within the WISE resolution of 3.6”. If an
object was found, its brightness information in all five SDSS bands (u, g, r,
i, z) was added to our database including the redshift information, where
available.

For further analysis and verification of our results, we cross-matched all
polarised sources with the NVSS RM catalogue. Sources within the radius of the
synthesised beam of the PI image were checked. In case of a match, the PI-,
FP-, and RM NVSS values were added to our database.

###  4.5 Ancillary data

Ancillary data products generated during the analysis include images of all
four AllWISE bands and the SDSS g-band. Individual images for the entire
extent of each PI-image mosaic were downloaded and mosaicked using the astropy
affiliated Python wrapper MontagePy111111https://montage-
wrapper.readthedocs.io/en/v0.9.5/ for the Montage Astronomical Image Mosaic
Engine.

Mosaicking of the images was performed by first reprojecting them to the PI
image mosaic, adjusting and correcting the background of all images within a
pointing, and finally co-adding them to produce a single image spanning the
extent of each PI mosaic of one pointing. The final images are especially
useful for the manual inspection of sources and their cross-matches in later
stages of the analysis (see Sect. 4.6).

###  4.6 Catalogue generation

We generated different overlays (see Fig. 4) and saved them into a portable
document format (pdf) file to inspect each source in the PI catalogue
individually. The association of extended and complex sources with each other
as well as cross-matches with their TP-, AllWISE-, and SDSS counterparts are
checked for obvious errors. Interactive functions in the analysis pipeline
allow the removal of sources from the PI catalogue, the splitting of complex
sources into components, the combination of source components into a single
source, and manually searching for TP-, AllWISE-, and SDSS-counterparts at
given positions.

Sources with no TP counterpart or those showing obvious artefacts were
discarded. Individual components are combined into a single source, if they
are obviously originating from the same source. This is often the case for
resolved FR-class objects, where the core and hotspot or jet regions appear
disconnected. AllWISE- and SDSS counterparts were removed for incorrectly
identified counterparts. Often these sources are at the edge of the search
radius or the central position of diffuse and/or resolved sources could not
easily be calculated correctly due to their complexity. In the latter case,
the AllWISE and SDSS catalogues were manually checked for the central
positions of these sources which were identified by eye.

Figure 4: Example catalogue pdf document of the source APSVC 214.033+37.058
detected in field S1415+36 (SVC5). The source ID and the source code (S for
point-like, E for extended) are given in the caption. The images show the
following maps and contours: Top left: Polarised intensity and total power
continuum contours. Top centre: Total power continuum and polarised intensity
contours. Top right: Rotation measures and polarised intensity contours.
Centre left: Fractional polarisation and polarised intensity contours. Centre:
AllWISE 3.4 $\upmu$m and total power continuum contours. Centre right: AllWISE
4.6 $\upmu$m and total power continuum contours. Bottom left: SDSS and total
power continuum contours. Bottom centre: AllWISE 12 $\upmu$m and total power
continuum contours. Bottom right: AllWISE 22 $\upmu$m and total power
continuum contours. All PI contours start at the 6.25 $\sigma$-level of the
local noise and increase in powers of $\sqrt{2}$. TP contours start at the 7
$\sigma$-level of the local noise and increase in powers of two. Cyan crosses
in the top left and top central images show the central source positions of
the PI and TP sources, respectively. A red cross in the top central images
shows the position of a source identified in NVSS, if available. Green and
yellow crosses in the WISE and SDSS images mark the positions of the cross-
matched sources of these catalogues, respectively. Values measured from our
data and extracted ones from the cross-matched catalogues are always shown in
the top right corner of the relevant images.

###  4.7 Polarisation leakage

To verify the reliability of the identified source catalogue, we assess the
characteristics of the instrumental leakage of the Apertif system. Stokes V
represents the circular polarisation, which is a very rare phenomenon in
astronomical objects. Myserlis (2015) found a median degree of circular
polarisation in blazar sources of 0.4 %. A targeted survey of 150 polarised
AGN sources by Myserlis et al. (2018) revealed 10 circular polarised sources
with circular polarisation degrees of approximately 0.2 %. Bower et al. (2002)
detected circular polarisation degrees around 0.1 % for nearby low-luminosity
AGNs. Similar values were found by Rayner et al. (2000) and Homan et al.
(2001) for a sample of 12 and 11 AGN sources, respectively. We highlight the
fact that all of the above observations were targeted towards sources where a
significant fraction of circular polarisation was expected. Therefore, we can
assume that the large majority of sources with a Stokes V detection for our
Apertif data are dominated by instrumental leakage.

In order to set a limit where instrumental polarisation is dominant for our
sources, we measure the amount of fractional circular polarisation dependent
on the beam response. For this purpose, we performed a source detection using
PyBDSF on each individual Stokes I and V image. Since PyBDSF is only able to
detect positive values and Stokes V emission can exhibit both signs, we
performed the source finding twice, once on the original image and a second
time on the inverted one.

The two Stokes V source catalogues were combined for each beam and all
detected Stokes V sources were then cross-matched with the appropriate Stokes
I sources of the inspected beam. The response of the primary beam for these
sources was calculated by extracting the value at the position relative to the
pointing centre from the Gaussian regression beam models (Kutkin et al. in
prep.).

Figure 5: Primary beam responses of the detected sources in Stokes V vs. their
fractional circular polarisation. The different colours mark the fields in
which the sources were detected. The blue, green, and red dashed lines
represent the 1%, 2%, and 3% fractional polarisation levels, respectively.

Figure 5 shows the primary beam response of the detected circularly polarised
sources vs. their fractional circular polarisation. The fractional
polarisation stays constant at the level of about 1% up to a primary beam
response of 0.3. We do not see a specific bias towards a certain SVC field,
and so we conclude that there was a constant leakage during the whole SVC
campaign for our observations. Our individual beams overlap at an approximate
primary beam response of 0.5. Therefore, we use a lower limit of 1% for the
fractional polarisation of our polarised sources to include them in any
further steps in our analysis.

##  5 Results

We now want to verify the reliability of our source detection by first
comparing source densities and their median FP values with published works and
secondly comparing the RM- and FP values of individual sources with their
archival NVSS values. In addition, we analyse the usability of our RM
measurements for Milky Way foreground studies. For all further analyses, we
combined the data from all five survey fields to enhance our sample
statistics.

###  5.1 Source statistics

Our images cover an area of 56.38 deg2, in which we detected 12834 source
components in total emission and 1357 polarised source components. This
results in a fraction of 10.6 % of source components being polarised. Taylor
et al. (2007), Grant et al. (2010), Hales et al. (2014a), Rudnick & Owen
(2014), and Berger et al. (2021) found fractions of 10.6 %, 14.2 %, 5.9 %, 2.6
%, and 8.8 %, respectively, and so our values are consistent with the
previously reported ones.

The polarised source density for our imaged area corresponds to $\sim 21$ per
deg2 at an approximate noise level of 15$\upmu$Jy/beam (see Table 4). Several
other observations at the same frequency with similar noise levels found
consistent values. Hales et al. (2014b) observed between 16 and 23 polarised
sources per deg2 at a noise level of 25$\upmu$Jy/beam. Berger et al. (2021)
found 23 polarised sources per deg2 at noise levels of 7$\upmu$Jy/beam.
Rudnick & Owen (2014) predicted $35\pm 10$ polarised sources per deg2 based on
their deep observations of the GOODS-N field for a flux regime of
50$\upmu$Jy/beam.

Table 5: Source statistics for the SVC data.

Field | Area | NTP,c | NPI,c | PF | NPI | NPI,S | NPI,E | PF,S | PF,E | $\widetilde{FP}$ | $\widetilde{FP_{S}}$ | $\widetilde{FP_{E}}$
---|---|---|---|---|---|---|---|---|---|---|---|---
| [deg2] |  |  | [%] |  |  |  | [%] | [%] | [%] | [%] | [%]
SVC1 | 9.49 | 1961 | 199 | 10.15 | 178 | 126 | 52 | 70.80 | 29.20 | 4.79$\pm$0.34 | 4.56$\pm$0.38 | 5.59$\pm$0.67
SVC2 | 10.67 | 3126 | 296 | 9.47 | 254 | 161 | 93 | 60.38 | 36.62 | 4.28$\pm$0.30 | 3.59$\pm$0.35 | 5.33$\pm$0.54
SVC3 | 12.26 | 2322 | 299 | 12.88 | 254 | 166 | 88 | 65.34 | 34.66 | 5.18$\pm$0.29 | 4.70$\pm$0.39 | 5.70$\pm$0.41
SVC4 | 11.72 | 3030 | 299 | 9.87 | 254 | 150 | 104 | 59.06 | 40.94 | 4.92$\pm$0.29 | 4.85$\pm$0.38 | 4.97$\pm$0.46
SVC5 | 12.22 | 2395 | 264 | 11.02 | 230 | 175 | 55 | 76.06 | 23.94 | 4.51$\pm$0.33 | 3.91$\pm$0.36 | 6.77$\pm$0.70
All | 56.38 | 12834 | 1357 | 10.57 | 1170 | 778 | 392 | 66.50 | 33.50 | 4.70$\pm$0.14 | 4.33$\pm$0.17 | 5.47$\pm$0.24

121212Area is the imaged area of the entire mosaics down to the 5 % level,
NTP,c and NPI,c are the number of total power and polarised components,
respectively. PF is the percentage of polarised source components. NPI, NPI,S,
and NPI,E are the number of all polarised sources, unresolved polarised
sources, and resolved polarised sources, respectively. PF,S and PF,E are the
percentages of unresolved and resolved polarised sources. $\widetilde{FP}$,
$\widetilde{FP_{S}}$, and $\widetilde{FP_{E}}$ are the median fractional
polarisations of all polarised sources, unresolved polarised sources, and
resolved polarised sources, respectively.

Of the 1357 polarised source components, 1170 individual polarised sources
were identified. Of these, 778 were classified as unresolved and 392 as
resolved, which leads to fractions of 66.5 % and 33.5 %, respectively. The
median fractional polarisation of our complete sample is $4.70\pm 0.14$ %.
Studies of individual fields with areas covering several square degrees by
Hales et al. (2014a), Grant et al. (2010), Taylor et al. (2007), and Berger et
al. (2021) at the same wavelength report values of 6.2 %, 14.1 %, 10.6 %, and
5.4 %, respectively. Stil et al. (2014), using a stacking technique for
sources in the NVSS, found a lower value of $\leq 2.5$ %. O’Sullivan et al.
(2015) found a median fractional polarisation for an AGN sample using the NVSS
of 6.2 %. Subrahmanyan et al. (2010) found a linear increase in FP with lower
flux densities. Berger et al. (2021) showed that this trend is also visible in
the analyses by Grant et al. (2010), Hales et al. (2014a), and Taylor et al.
(2007) and originates from the sensitivity limited completeness of the survey.

We compared the percentage of polarised sources with their flux in TP
($S_{1.4GHz}$) for our SVC data, the NVSS total and polarised source
catalogues published in Condon et al. (1998) and Taylor et al. (2009),
respectively, and the catalogue of Hales et al. (2014a) by counting the number
of total power and polarised source components within a certain TP-flux bin
(see Fig. 6). For comparability, the same bins were chosen for all catalogues
and the Poisson error determined for each individual bin and catalogue. FP
uncertainties were then calculated using Gaussian error propagation.

Figure 6: Total power emission $S_{1.4GHz}$ plotted against the percentage of
sources showing polarised emission. The red, black, and blue dots show the
values from this work, a combination of the two NVSS catalogues published by
Condon et al. (1998) and Taylor et al. (2009), and the results from Hales et
al. (2014a).

All three catalogues show the same behaviour of a decreasing number of
polarised sources detected with TP flux. The noise in PI images for radio
observations is usually lower than for their accompanying TP images by a
factor of $\sqrt{2}$ because of the combination of the two independent Stokes
parameters Q and U. For a given source population with FP values of only a few
per cent, the PI counterparts of TP detections are often hidden below the
noise limits. This results in a large fraction of undetected polarised sources
especially towards lower TP fluxes, if we assume a constant FP over the whole
total power flux range.

The maximum fraction of polarised sources is $\approx 80\,\%$ for our data and
those of Hales et al. (2014a), while the NVSS data show a maximum of $\approx
60\,\%$. As expected, due to the lower sensitivity of the NVSS, the decrease
in percentage of polarised sources detected already starts at fluxes of
$S_{1.4GHz}\approx 0.8$ Jy and reaches nearly 0 % at $S_{1.4GHz}\approx
10^{-2}$ Jy. Comparing our data with those of Hales et al. (2014a) we notice a
decrease starting at $S_{1.4GHz}\approx 2\times 10^{-2}$ Jy, which reaches an
absolute minimum value of 0 % at $S_{1.4GHz}\leq 10^{-3}$ Jy. A combination of
effects can be responsible for these differences between the NVSS and the
SVC-/Hales et al. (2014a)-data, such as the different spatial and frequency
resolutions of the surveys, the use of the RM-synthesis technique, or physical
depolarisation effects. For a detailed discussion on this topic, we refer the
reader to Berger et al. in prep.

We notice a difference between our subsamples of resolved sources and
unresolved sources with median fractional polarisations of $5.47\pm 0.24$ %
and $4.33\pm 0.17$ %, respectively. This difference was previously found by
Grant et al. (2010), who also measured a higher median fractional polarisation
for resolved sources ($6.8\pm 0.7$ %) compared to compact ones ($4.4\pm 1.1$
%).

Table 6: Cross-match statistics for the SVC data.

Field | NNVSS | NWISE | NSDSS | NSDSS,z
---|---|---|---|---
SVC1 | 4 | 146 | 54 | 5
SVC2 | 4 | 207 | 121 | 26
SVC3 | 15 | 210 | 42 | 10
SVC4 | 16 | 207 | 1 | 0
SVC5 | 13 | 197 | 101 | 21
All | 52 | 967 | 319 | 62
131313NNVSS, NWISE, and NSDSS are the number of cross-matches found in the
NVSS-, AllWise-, and SDSS catalogues. NSDSS,z is the number of cross-matched
SDSS sources where a redshift is given.

We found 967 counterparts for our polarised sources in the AllWise catalogue
and 319 counterparts in the SDSS DR16 release, of which 62 have spectroscopic
redshift estimates. We note that 52 of our sources were previously known from
the NVSS RM catalogue. See Table 5 for an overview of the general statistics
of the SVC data, and see Table 6 for details of the cross-matches.

###  5.2 Comparison with NVSS

In the following, we compare our PI-, RM-, and FP values for the 52 sources
for which we were able to identify NVSS counterparts with literature values
from their data to further verify the reliability of our catalogues. Of these
sources, 35 are classified as resolved in the SVC, which is a fraction of
67.3%. This is higher than the average fraction of resolved sources of the
whole SVC data set by a factor of approximately two. This is not surprising
because the NVSS data are strongly biased towards bright sources, which have a
higher probability of being closer and therefore appear resolved. The median
ratio of PI between our detections and the NVSS counterparts is 1.18. If we
only look at the unresolved sources, this drops to a nearly matching ratio of
1.03 while it rises for extended sources to 1.20. We explain this difference
by the effect of beam depolarisation. Polarised sources in our survey can be
resolved and components separated, which, in the NVSS with its approximately
two times larger synthesised beam, become partly depolarised due to their
differing magnetic field directions within the same source and resolution
element.

For the FP, this behaviour is less pronounced with a ratio of 1.06, but we can
also trace a higher FP ratio between resolved and unresolved sources with
values of 1.08 and 1.02, respectively. For the PI and FP ratios, we checked
for any specific bias towards a certain SVC observation (see Fig. 7); none
could be found, and so we can again conclude that we see constant
characteristics of the Apertif instrument for all SVC observations.

Figure 7: Fractional polarisation of the SVC sources plotted against the
values of their NVSS counterparts from the NVSS RM catalogue (Taylor et al.,
2009). Data from the different fields is marked by colour. Filled circles are
unresolved sources while open circles represent resolved ones. The dashed
black line represents the 1:1 ratio of the FP values.

We determined the median RM values and their standard deviation for each
individual SVC field for all sources of a single field ($\widetilde{RM}$),
only the unresolved sources ($\widetilde{RM}_{S}$), and only the resolved
sources ($\widetilde{RM}_{E}$), as well as all sources with NVSS counterparts
($\widetilde{RM}_{NVSS}$). In addition, we cross-checked the central pointing
positions from Table 4 in the map of Oppermann et al. (2012), which represents
the RM caused by the Milky Way foreground magnetic field, and extracted the RM
value ($RM_{MW}$) at this position. The results are compiled in Table 7.

Table 7: Galactic coordinates and RMs for the SVC fields.

Field | $l$ | $b$ | $\widetilde{RM}$ | $\widetilde{RM}_{S}$ | $\widetilde{RM}_{E}$ | $\widetilde{RM}_{NVSS}$ | $RM_{MW}$
---|---|---|---|---|---|---|---
| [deg] | [deg] | [rad/m2] | [rad/m2] | [rad/m2] | [rad/m2] | [rad/m2]
SVC1 | 95.681 | -22.349 | $-126.19\pm 85.31$ | $-103.81\pm 87.77$ | $-155.42\pm 54.08$ | $-123.29\pm 93.68$ | $-131.07\pm 25.95$
SVC2 | 100.939 | 60.546 | $9.71\pm 33.68$ | $15.41\pm 35.36$ | $8.41\pm 30.19$ | $16.94\pm 11.79$ | $11.82\pm 4.81$
SVC3 | 137.785 | -27.078 | $-46.59\pm 38.21$ | $-41.46\pm 40.30$ | $-48.34\pm 33.11$ | $-55.40\pm 29.75$ | $-47.87\pm 14.88$
SVC4 | 97.789 | -17.882 | $-159.78\pm 104.27$ | $-156.20\pm 108.58$ | $-168.15\pm 96.96$ | $-127.87\pm 99.84$ | $-220.52\pm 22.77$
SVC5 | 65.517 | 69.869 | $0.28\pm 30.02$ | $0.55\pm 29.72$ | $-0.73\pm 30.88$ | $0.75\pm 25.12$ | $2.84\pm 3.54$

141414$l$ and $b$ are the Galactic longitude and latitude coordinates for each
SVC field calculated from the RA-/DEC-coordinates given in Table 4,
respectively. $\widetilde{RM}$, $\widetilde{RM}_{S}$, and $\widetilde{RM}_{E}$
are the median rotation measures and their standard derivation of all
polarised sources, unresolved polarised sources and resolved polarised sources
of a single SVC field, respectively. $\widetilde{RM}_{NVSS}$ is the median
rotation measure and its standard deviation of all sources where an NVSS
counterpart could be identified. $\widetilde{RM}_{MW}$ is the rotation measure
and its error extracted from the map of Oppermann et al. (2012) for the given
$l$\- and $b$-coordinates.

Except for field SVC4, we can see an agreement within a range of 10 rad/m2
between $\widetilde{RM}_{NVSS}$ and $RM_{MW}$, confirming the reliability of
our measurements compared with the reference values in the NVSS RM catalogue.
Figure 8 shows a direct comparison between the individual RM values for the
SVC detections and their NVSS counterparts. We see that sources for individual
fields are clustering around certain RM values. This is not surprising as the
RM of most of our sources mainly originates from the magnetic field in the
Milky Way foreground and is not intrinsic to the sources themselves, meaning
that regions of several square degrees show very similar values. Sources in
field SVC4 show a larger scatter compared to their NVSS RM values. We want to
mention two possible reasons for this. Firstly, the field is the closest one
in projection to the Milky Way disc out of the five SVC fields, where the
magnetic field of the Milky Way foreground becomes more turbulent and
therefore RM values on square-degree scales show greater variation. Secondly,
the NVSS observations were taken with two bands of 50 MHz in width with only a
single channel, meaning that the sensitivity of these observations might be
affected by bandwidth depolarisation. This effect would lead to smaller PI
values for sources with higher RMs.

###  5.3 Usability for RM gridding

Rotation-measure grids are one of the main tools for tracing the Milky Way
(Oppermann et al., 2012; Hutschenreuter & Enßlin, 2020) and intergalactic
magnetic fields (Gaensler et al., 2004). These fields are usually too weak for
a direct detection. Therefore, polarised background sources are used, where
the intervening magnetic field is adding its RM component to the one of the
background source. The precision of the RM grid is given by the source density
and (S/N) of the individual polarised source detections as well as their
uncertainties.

Comparing $\widetilde{RM}$ and $RM_{MW}$ we see an agreement of less than 5
rad/m2. This shows that most of the sources in our catalogue are suitable for
tracing the Milky Way magnetic field. Their sheer number, even though the
sources are generally fainter, can help to more precisely determine the RM of
the Milky Way foreground. The median RM values for unresolved and resolved
sources of individual fields differ by up to $\approx 12$ rad/m2 for fields
SVC2 to SVC4. For SVC1, this value differs by $\approx 52$ rad/m2. The RMs of
extended sources are often partly influenced by their intrinsic magnetic
fields. We want to note that for field SVC1, but also for fields SVC2 and
SVC3, $RM_{MW}$ lies in between $\widetilde{RM}_{S}$ and $\widetilde{RM}_{E}$.
For further discussion on this, we refer to Sect. 7.

Figure 8: Rotation measures of the SVC sources plotted against the values of
their NVSS counterparts from the NVSS RM catalogue (Taylor et al., 2009). Data
from the different fields are marked with different colours. The diamonds show
the RM value extracted from Oppermann et al. (2012) for the central pointing
positions (see Table 4) of the five SVC fields. The dashed black line
represents the 1:1 ratio of the RM values.

The five SVC fields cover absolute Galactic latitudes of $17.8<|b|<69.9$. We
observe higher absolute median RMs for sources closer to the Galactic plane as
well as higher standard deviations by a factor of up to three (see Fig. 9).
Regions closer to the Milky Way plane usually show higher absolute median RMs.
The stronger magnetic field and higher thermal particle density causes a
higher rotation of the electric field vector on the line of sight. In
addition, these fields are usually more turbulent and a higher variation of
the RMs of sources within these fields is expected.

Figure 9: Absolute Galactic latitude for the five SVC fields plotted vs. the
standard deviation of the RMs of the sources in the field. Black diamonds show
the values for compact and extended sources in an SVC field, small circles
show only compact sources, and large circles show only extended sources. Green
diamonds show only the values for the cross-matched NVSS sources and the red
diamonds the Milky Way foreground RM from Oppermann et al. (2012).

With our measurements of $RM_{MW}$ we can confirm the above expectations.
Therefore, we state that the variation within our fields is dominated by the
physical variations of the magnetic field of the Milky Way itself and is not
driven by uncertainties in our measurements.

##  6 Source characteristics

In the following, we aim to investigate the types of sources in our source
sample. The additional IR and optical information in our catalogues not only
allows us to distinguish our sources by their relative brightness or
morphology, but also by their host galaxy type, star-formation properties, and
absolute radio brightness. This allows us a statistical analysis of the types
of sources and the characteristics of the host galaxies, which dominate the
polarised sky down to $\upmu$Jy-levels.

###  6.1 AGN and star-forming galaxies

Polarised emission in galaxies can have two different origins, namely the
radio lobes generated by SMBHs situated in the centres of galaxies or the
superbubbles and/or outflows created by star formation. For the latter type,
polarised emission has only been detected in a handful of nearby galaxies
(Beck, 2015) while all polarised sources further away have so far been
classified as AGN. In the following, we aim to investigate our sample in view
of a possible contribution from star formation.

IR colours are known to be a good tracer of ongoing star formation (Rieke et
al., 2009) because of their good sensitivity to heated dust particles in star-
forming regions. One of the famous connections between star formation and FIR
luminosity is the several orders of magnitude in luminosity spanning FIR–radio
correlation (de Jong et al., 1985). While this close correlation was first
only shown to hold for nearby galaxies, later studies showed that it does not
evolve up to redshifts of $z\approx 4$ (Pannella et al., 2015). Vaddi et al.
(2016) found that the correlation can be extended towards the mid-infrared
(MIR) WISE bands for galaxies with redshifts up to $z\approx 0.03$. Rieke et
al. (2009) showed that 24 $\upmu$m-fluxes can be used to estimate star-
formation rates (SFRs) to within an order of magnitude for redshifts of up to
$z\approx 2$. Cluver et al. (2017) estimated that the WISE 12$\upmu$m- and
22$\upmu$m-bands are a good tracer of star formation over nearly five orders
of magnitude. We now want to investigate our sample for possible objects
dominated by star formation. Here we assume that the MIR–radio correlation
holds as well as the FIR–radio correlation for similar z ranges.

Figure 10: AllWISE 12$\upmu$m (left) and 22$\upmu$m (right) brightness vs. our
radio luminosity for all polarised sources with AllWISE counterparts. AllWISE
values are given in Vega magnitudes. The solid red line represents the
MIR–radio correlation from Vaddi et al. (2016) with the dotted lines showing
its uncertainties.

Figure 10 shows the MIR brightness in the AllWISE 12$\upmu$m and 22$\upmu$m
bands plotted against their total radio luminosity. Only one source
(APSVC_342.354+38.810 in SVC4) lies within the errors, which after closer
inspection shows a very faint MIR counterpart and a high FP of $\sim$26 %. For
a detection of polarised emission with a star-forming origin, we would expect
very low values of FP. We therefore conclude that our sample is dominated by
AGN-driven radio emission.

To investigate the MIR brightness contributed by star formation in the host
galaxies of our sample, we want to use criteria that are independent of the
radio measurements. Several authors have been able to successfully distinguish
between AGN- and star-formation-dominated sources using only the WISE MIR
colours (Jarrett et al., 2011; Stern et al., 2012; Mateos et al., 2012). All
of these latter authors used empirical criteria for the colour relations
between the WISE 3.4$\upmu$m-, 4.6$\upmu$m-, and 12$\upmu$m brightnesses.
While Stern et al. (2012) used a simple limit of $m_{3.4\mu m}$ \- $m_{4.6\mu
m}>0.8$, Jarrett et al. (2011) and Mateos et al. (2012) defined limits that
have a quadrangle- and wedge-shape, respectively. Mateos et al. (2012) showed
that the additional information of the WISE 22$\upmu$m-band does not improve
the quality of the selection criteria, mostly because of the usually lower S/N
in this band compared to the other three.

In order to distinguish between sources with high S/N (HS/N) and sources with
low S/N (LS/N), we set a S/N limit of $>5\sigma$ in all used WISE bands to
classify sources as HS/N. This criterion was also used by Mateos et al. (2012)
for their investigation. Of our 967 sources, 101 fall into the HS/N category
while 866 are identified as having LS/N. One, 142, and 865 sources are
categorised as LS/N because of the 5$\sigma$ limit in the WISE 3.4$\upmu$m,
4.6$\upmu$m, and 12$\upmu$m bands, respectively. Therefore, the high number of
LS/N sources is mostly caused by the lower sensitivity in the WISE 12$\upmu$m
band.

Figure 11: AllWISE 3.4$\upmu$m - 4.6$\upmu$m brightness vs. 4.6$\upmu$m -
12$\upmu$m brightness. All values are given in Vega magnitudes. Black and red
dots represent HS/N and LS/N sources, respectively. The green, cyan, and blue
dashed lines illustrate the AGN-selection criteria from Stern et al. (2012),
Jarrett et al. (2011), and Mateos et al. (2012), respectively. The grey dashed
lines divide the diagram into regions where AGN, spheroids, intermediate disc
galaxies, and star-forming galaxies are positioned following the criteria in
Jarrett et al. (2017).

Figure 11 shows the relation between $m_{3.4\mu m}$ \- $m_{4.6\mu m}$ and
$m_{4.6\mu m}$ \- $m_{12\mu m}$ for all polarised sources with IR
counterparts. The overall distribution of our sample looks very similar to
that of the sample in Mateos et al. (2012). The selection criteria from Stern
et al. (2012) (green line), Jarrett et al. (2011) (cyan quadrangle), and
Mateos et al. (2012) (blue wedge) show very similar results. Of the 101
sources with a HS/N, 49, 51, and 52 lie within the AGN-selection criteria
defined by Stern et al. (2012), Mateos et al. (2012), and Jarrett et al.
(2011), respectively, while only 115, 103, and 133 out of 866 sources are
situated inside the AGN regions for the LS/N sample, respectively. Most
sources not fulfilling these criteria are located in the range of $-0.5\leq
m_{3.4\mu m}-m_{4.6\mu m}\leq 0.5$. Using templates from Polletta et al.
(2008) for ultra-luminous infra-red galaxies (ULIRGs) and starburst sources
and a template from Dale & Helou (2002) for star-forming spiral galaxies,
Mateos et al. (2012) showed that this region is foremost dominated by
elliptical and star-forming galaxies. The large number of LSNR sources in this
area is mostly caused by the uncertainty in $m_{12\mu m}$, which only affects
the x-position of sources in Fig. 11. Therefore, this uncertainty cannot move
sources from the lower area of Fig. 11 up into the AGN area, meaning that a
misclassification of elliptical- and star-forming-dominated hosts is very
unlikely.

Jarrett et al. (2017, 2019) and Ching et al. (2017) used the same
colour–colour diagrams to separate hosts of radio galaxies according to their
morphological type. In the following, we use the criteria from Jarrett et al.
(2017) to distinguish between AGN, spheroids, intermediate discs, and star-
forming discs. A WISE colour of $m_{4.6\mu m}$ \- $m_{12\mu m}<2.0$ indicates
spheroids, $2.0\leq m_{4.6\mu m}$ \- $m_{12\mu m}<3.5$ indicates intermediate
disc galaxies, and $m_{4.6\mu m}$ \- $m_{12\mu m}\geq 3.5$ indicates star-
forming disc galaxies. Hosts with $m_{3.4\mu m}$ \- $m_{4.6\mu m}>0.8$ are
classified as AGN. The four different regions are shown in Fig. 11 as grey
dashed lines. We find 164 AGNs (17.0 %), 143 spheroids (14.8 %), 421
intermediate (43.5 %), and 239 star-forming disc galaxies (24.7 %). Comparing
our numbers to the results by O’Sullivan et al. (2015) —who used the NVSS
database and therefore mostly bright polarised sources to determine host
galaxy types from polarisation data— shows a significant difference. While our
sample is dominated by intermediate and star-forming disc galaxies, their
sample consists mainly of spheroidal galaxies. While sources in the faint sky
are more likely to be located at higher redshifts, Jarrett et al. (2017)
showed that for a redshift of $z=0.5,$ data points are moved towards the upper
left in Fig. 11 by values of $m_{3.4\mu m}$ \- $m_{4.6\mu m}=0.1$ and
$m_{4.6\mu m}$ \- $m_{12\mu m}=0.5$. Therefore, even a large contribution of
higher redshift objects cannot explain this discrepancy.

###  6.2 Redshift determination and distribution

In order to further investigate the characteristics of our polarised sources,
we need estimates of their distances. Only 62 out of our 1170 sources have
direct spectroscopic redshift data from the SDSS database. In order to enlarge
our sample, we fitted spectral energy distribution (SED) templates to the SDSS
and allWISE values from our cross-matches using the Galaxy redshifts and
physical parameters (GAZPAR151515https://gazpar.lam.fr/home) service. For this
purpose, the Photometric Analysis for Redshift Estimate package (Le
PHARE161616http://lephare.lam.fr) was used (Ilbert et al., 2006; Arnouts et
al., 1999) with the BC03-template (Bruzual & Charlot, 2003), which is known to
give a good representation of star-forming galaxies and AGN. The allWISE
12$\upmu$m and 22$\upmu$m data were not used because the BC03-templates do not
cover these wavelengths. We were able to determine photometric redshifts for
all our 319 sources where SDSS data were available. Of those, 257 did not have
spectroscopic redshifts beforehand.

Figure 12: Spectroscopic redshift from the SDSS database vs. photometric
redshifts from the SED-fitting. The dashed black line represents the 1:1 ratio
between the two values.

To verify the SED-fitting results, we compare the spectroscopic redshifts from
the SDSS sample with our fitted values (see Fig. 12). For most of our sources,
the two values deviate by no more than $\Delta z=0.1$, and so we conclude on
the robustness of the photometric redshift determination.

The redshift distribution of our sample is influenced by the completeness of
the underlying SDSS information and the observational biases of this survey.
To evaluate these parameters, we compare our data with the simulations of the
Tiered Radio Extragalactic Continuum Simulation (T-RECS) (Bonaldi et al.,
2019). We downloaded their AGN catalogue (agnswide.dat) which simulates the
distribution of AGN sources over an area of 400 square degrees down to a flux
limit of 100 nJy at 1.4 GHz. For comparability, we discarded all sources below
our average detection limit of 75 $\upmu$Jy in PI (see. Tbl. 4 and Sect. 4.3)
from their catalogue. The average source density per redshift bin $\Delta z$
was then calculated, where we used $\Delta z=0.1$ and areas of 400 deg2 for
the T-RECS dataset and 36.94 deg2 for the SDSS coverage of our data (see Sect.
4.4).

Figure 13: Redshift distribution vs. source density. Redshift bins are $\Delta
z=0.1$. The blue filled histogram shows the distribution of sources with
spectroscopic redshift information in the SVC-sample. The red histogram shows
the distribution of sources with photometric redshift estimates from our SED
fitting. These two histograms are stacked. The green line was derived from the
wide AGN-catalogue in Bonaldi et al. (2019).

The results are shown in Fig. 13. Even though we are dealing with low absolute
numbers of sources in our sample, the overall shape of the distribution for
redshifts up to $z=0.6$ fits the simulations. It is remarkable that we find
the exact source density predicted by the T-RECS simulations for redshifts up
to $z=0.1$. We see a continuous decrease in the absolute number density of
detected sources with respect to simulated ones with increasing redshift.
While this discrepancy is approximately a factor of 2.5 for redshifts of
$z=0.6$, it increases to a factor of six at redshifts of $z=1.2$. For higher
redshifts, we only detect a very small number of sources. This mostly results
from the fact that not all radio sources are equally bright in the optical,
meaning that our subsample with optical counterparts is most likely biased
towards radio sources with bright optical counterparts. In addition, we see a
lack of sources beyond redshifts of $z\geq 0.6$ even though the strong
decrease beyond $z\geq 0.8$ is still represented. There are far fewer sources
with determined redshift at this cosmic distance for the SDSS sample as well,
which is mostly due to sensitivity limitations (Orenstein et al., 2019).

###  6.3 Radio brightness and Fanaroff-Riley classification

AGN can generally be classified as radio-loud or radio-quiet, which also gives
an indication of their activity. Kellermann et al. (1989) defined the border
between radio-loud and radio-quiet AGN by the ratio of the flux density at 5
GHz $P_{5GHz}$ and the optical B-band $S_{B-band}$. Objects with ratios of
$P_{5GHz}/S_{B-band}\geq 10$ are radio-loud and sources below this level are
radio-quiet. While the former authors defined this criteria for Type 1 broad-
line AGN, Lal & Ho (2010) and Sikora et al. (2007) extended these criteria to
Type 2 narrow-line AGN, Seyfert galaxies, low-ionisation nuclear emission-line
regions (LINERs), FRI radio galaxies, and optically selected quasars. Often
radio-loud sources fall into the FRII category, while silent ones are more
common for FRI sources. Owen & Ledlow (1994) and Ledlow & Owen (1996) showed
for a sample of AGN observed at 1.4 GHz that the two FR phenotypes populate
different areas in a diagram of optical versus radio brightness.

In order to investigate the source distribution for our sample, we need to
calculate the absolute radio brightness $P_{1.4GHz}$ given in units of W Hz-1.
For this we use the standard equation

$P_{1.4GHz}=4\pi D_{L}^{2}S(1+z)^{-\alpha+1},$ (4)

where $D_{L}$ is the luminosity distance, $S$ is the total flux density at 1.4
GHz in Jy, $z$ is redshift, and $\alpha$ is the spectral index. For our
analysis, we limit our sample to sources where redshift information from SDSS
is available. In addition, we assume a canonical value of $\alpha=-0.7$ from
Condon et al. (2002) for the spectral index $\alpha$ with the definition
$S\propto\nu^{-\alpha}$, where $S$ is the radio flux in Jy, and $\nu$ the
observed frequency.

The SDSS does not observe directly in the optical B-band, and so we have to
calculate the B-magnitudes from the u- and g-band values. We used the
conversion equation given in Jester et al. (2005):

$B=g+0.17(u-g)+0.11.$ (5)

Figure 14: Absolute optical B-band magnitude $B_{mag}$ vs. absolute radio
brightness at 1.4 GHz $P_{1.4GHz}$. Red diamonds are sources with
spectroscopic redshift information from the SDSS. For the black squares,
photometric redshifts were determined (see Sect. 6.2). The border between
radio-loud and radio-quiet AGN defined by Kellermann et al. (1989) is plotted
as a dashed line. The relation described in Gendre & Wall (2008) to separate
FRI and FRII objects is shown as the dash-dotted line.

The final absolute optical brightness was then calculated using the distance
modulus. The results are shown in Fig. 14. Of our 319 sources, 253 (79%) and
66 (21%) are classified as radio-loud and radio-quiet, respectively, following
the criterion of Kellermann et al. (1989). Only 40 (13%) of our 319 sources
fulfil the criterion for an FRI-classification while 279 (87%) are classified
as FRII (Ledlow & Owen, 1996). We therefore conclude that our sample with
optical counterparts and redshift information is dominated by radio-loud AGN
mostly of the FRII type.

###  6.4 Influence of star formation

We show that, for a large part of our sample, the total radio flux is
dominated by the activity of the AGN, but star formation can also play an
important role. In order to estimate its contribution and its influence on the
polarisation degree of the sources, we used the SED fitting described in Sect.
6.2 to not only derive photometric redshifts, but also galaxy masses and SFRs
of the host galaxies, independent of the radio measurements. While galaxy
masses can be robustly derived by SED fitting, uncertainties for SFRs are
higher and sometimes show unrealistically low values. Elliptical galaxies with
the lowest known SFR are in the range of $10^{-4}$ M⊙yr-1 (Shapiro et al.,
2010). Therefore, we filtered out all objects with SFR values below $5\cdot
10^{-4}$ M⊙yr-1 and consider 198 out of 297 objects as valid.

Using the criteria described in Sect. 6.1, we classified 22, 116, 52, and 8
sources as spheroidal galaxies, intermediate disc galaxies, star-forming disc
galaxies, and AGN, respectively. To analyse the reliability of our SED fitting
in view of SFRs and galaxy masses, we show the distribution of the specific
star-formation rate (sSFR), that is the SFR per unit galaxy mass, in Fig. 15.

Figure 15: Histogram of the sSFRs estimated via SED fits to the host galaxies
of the polarised sources distinguished between spherical galaxies (Sph),
intermediate disc galaxies (ID), star-forming discs (SFD), and AGN using the
criteria in Sect. 6.1.

As expected, spheroidal galaxies populate the lower end of the distribution
mostly with sSFRs up to sSFRs $<10^{-11}$ (Sedgwick et al., 2021) while AGN
are mostly located at the high end with sSFRs $>10^{-9}$ (Husemann et al.,
2014). Most of the star-forming and intermediate disc galaxies are found in
the range of $10^{-12}<\textnormal{sSFR}<10^{-9}$ (Muñoz-Mateos et al., 2007).

To calculate the contribution of star formation to the absolute radio
brightness $P_{1.4GHz}$, we use the calibration defined by Yun et al. (2001)

$\textnormal{SFR}_{1.4GHz}=5.9\times 10^{-22}P_{1.4GHz},$ (6)

where SFR is the total SFR in units of $M_{\odot}yr^{-1}$. We then define the
radio excess parameter $\zeta$, which is the ratio between the SFR derived
from SED-fitting ($\textnormal{SFR}_{fit}$) and the one calculated from the
absolute radio brightness, as

$\zeta=\frac{\textnormal{SFR}_{fit}}{\textnormal{SFR}_{1.4GHz}}.$ (7)

Figure 16: Histogram of the radio excess parameter $\zeta$, which denotes the
ratios of the radio flux contribution of the star formation to the overall
radio luminosity for our successfully SED-fitted sample of host galaxies.

Figure 16 shows that the $\zeta$-values span a range between
$10^{-8}\leq\zeta\leq 1.3$. For most of our sources, $\zeta$-values are below
$10^{-2}$. We can identify a peak at $\zeta$-values around $10^{-4}$. We find
29 sources for which the contribution lies above 1 % and four sources with
$\zeta\geq 0.1$. We therefore conclude that star formation is not contributing
a significant part to the overall radio luminosity for approximately 90% of
our polarised sources. Surprisingly, we cannot identify a difference between
the relative distributions of spheroidal, intermediate disc, star-forming
disc, and AGN sources.

Figure 17: sSFR vs. the fractional polarisation of our host galaxies by galaxy
type (see Sect. 6.1). Data points are colour coded according to host galaxy
type as described in Fig. 15. The solid lines represent the median values over
logarithmically derived bins for each host galaxy type. The black line
represents the median values for the whole galaxy sample.

We now want to further investigate the extent to which the star formation in
the host galaxies of AGN amplifies or reduces the polarised emission detected
in our sources. For this purpose, we compared the sSFR of our host galaxies to
the measured FP values of the polarised radio emission (see Fig. 17). The
sSFRs span seven orders of magnitude between $10^{-7}$ and $10^{-14}$ yr-1. In
order to overcome this large scatter, we binned the data over FP values
between 0.1 and 0.25. This was performed on a logarithmic scale to mitigate a
bias towards the much larger number of sources at small FPs compared to large
ones. For each bin, the median was derived.

The medians for all our classified sources (black line in Fig. 17) do not show
any significant correlation or anti-correlation with sSFR or FP. Looking at
individual types of sources following our classification scheme, we can
clearly see a separation between the three groups of spheroidal galaxies,
intermediate disc/star-forming disc galaxies, and AGN according to their
sSFRs, as described earlier. Neither a correlation nor an anti-correlation can
be observed between sSFR and FP for the individual types. For a detailed
discussion, the reader is referred to Sect. 7.

###  6.5 Infrared faint radio sources

When comparing radio and IR fluxes, a specific class of objects show only very
faint IR compared to their radio emission. Such sources were first detected by
Norris et al. (2006) and are called IR-faint radio sources (IFRS). Later,
Norris et al. (2011) found them to be radio-loud AGN with redshifts $z>1$. As
our polarised source sample is most likely dominated by radio-loud AGN, and
IFRS investigated by Middelberg et al. (2011) showed strong polarised emission
(Middelberg et al., 2011), the contribution of IFRS to the faint polarised
radio sky could be relevant. This applies especially for the fitting procedure
described in Sect. 6.4. IFRS sources are highly obscured, high-redshift
galaxies. The SED of these sources most likely does not fulfill the typical
criteria for the used fitting templates. A significant contribution of such
sources to our sample could therefore corrupt the results.

Criteria for classifying sources as IFRS were generalised by Zinn et al.
(2011) in the following way: The flux ratio $S_{1.4GHz}/S_{3.6\mu m}$ exceeds
a factor of 500 and the $S_{3.6\mu m}$ is lower than $30\,\upmu$Jy, where
$S_{1.4GHz}$ and $S_{3.6\mu m}$ are the flux densities at 1.4 GHz and at
3.6$\upmu$m in Janskys (Jy), respectively. To convert AllWISE magnitudes to Jy
we used the relation given by Collier et al. (2014):

$S_{3.4\mu m}=306.682\times 10^{(-m_{3.4\mu m/2.5})}\textnormal{Jy}.$ (8)

Of the 967 sources in our sample, 922 fulfill the cutoff criterion and 126 are
then classified as IFRS by the flux density ratio. The number of resolved and
unresolved sources is nearly equal with 58 and 68, respectively. Zinn et al.
(2011) considered only unresolved radio sources without any signs of radio
lobe structure as IFRS candidates. Later studies revealed that IFRSs are often
high-z radio galaxies with double-lobed structures (Singh et al., 2017). In
the following, we therefore analyse the resolved and unresolved sample of IFRS
candidates independently.

Even though IFRSs are known to be very compact sources at high redshifts
(Orenstein et al., 2019), Middelberg et al. (2011) showed that even at these
distances, AGN sources with lobe structures of several kiloparsecs (kpc) can
easily appear as resolved because of the nearly constant relation between
apparent and linear size of 7 kpc/arcsec for redshift values of $z>0.5$. For
the average resolution of our observations, that is 20 arcsec, and assuming
that any source larger than one-fifth of the resolution would be classified as
resolved, we can estimate the maximum physical size of unresolved sources to
28 kpc. Using a combination of different radio surveys of two survey fields
with a combined area of 1.8 deg2 and resolutions of between 4 and 9.4 arcsec,
Singh et al. (2017) detected 14 unresolved IFRS sources and five resolved
ones, which corresponds to an IFRS source density of 10.6 per deg2. Middelberg
et al. (2011) found three out of 17 IFRS sources to be polarised, which would
correspond to a polarised IFRS source density of 1.86 per deg2. Our polarised
IFRS source density of 2.23 per deg2 is a close match to this latter estimate.

In addition to showing that IFRSs follow a similar redshift distribution to
high-redshift radio galaxies, Orenstein et al. (2019) measured the redshift of
131 IFRSs. The z-range was found to lie between $z=1.63$ and $z=4.39$. The
number of objects with measured spectroscopic redshifts determined by SDSS
drops significantly beyond a value of $z>0.8$ (Orenstein et al., 2019). As a
result, only one of our IFRS counterparts (APSVC_211.418+54.187) has a
spectroscopic redshift noted in the SDSS database with $z=0.46$. Closer
inspection of the source reveals a double-lobe-dominated AGN with a diameter
of 2 arcmin and a very faint IR counterpart in its centre, which corresponds
to a physical size of the source of 707 kpc. Singh et al. (2017) also reported
sizes for their IFRSs of up to 330 kpc, but at higher redshifts.

If IFRS sources were to follow the same distribution as our whole sample, for
which 62 SDSS redshifts are known, we would expect approximately seven sources
with noted SDSS redshifts. As the high-z region is not covered by SDSS, a
lower detection rate using the spectroscopic redshift data from SDSS for IFRS
would confirm the high-z nature of these sources. On the contrary, we find 25
sources with photometric redshifts fulfilling the IFRS criteria. A very
similar number of detections of approximately 28 sources is expected if the
IFRS source distribution follows the same distribution as our complete
photometric sample. We also compared the median redshift of both samples,
finding $z=0.57\pm 0.02$ for the whole sample and $z=0.60\pm 0.12$ for the
IFRS sample.

Three IFRS sources from Middelberg et al. (2011) show polarised emission with
FPs between 7% and 12%. For our IFRS sample, we report a median FP of $4.82\pm
0.34$% and do not see a significant difference between the polarised IFRS and
polarised non-IFRS median FP values ($4.77\pm 0.17$%). We see the same
difference between the values of unresolved and resolved IFRS sources as we
noted for the whole sample (see Sect. 5.1) of $4.04\pm 0.38$% and $5.41\pm
0.56$%, respectively.

Using the classification criteria above, a significant number of polarised
sources ($\sim 13\,\%$) in the faint polarised sky could fall into the IFRS
category. Surprisingly, their polarised source characteristics do not seem to
differ from the overall population of the faint polarised sky. This means that
their contribution does not influence the results of our statistical analysis.

##  7 Discussion

The low polarisation leakage for the Apertif system and similarity of PI-,
FP-, and RM values compared to reference sources using the NVSS database and
Milky Way foreground maps allows us to reliably analyse polarisation data.
Even though we excluded sources with FP values below the estimated leakage of
1 %, sources with overall low FP values are still more affected by leakage
than sources with higher values and can introduce a bias towards the faint end
of the polarised source population. In addition, the borders of our mosaics
are imaged up to the 5 % primary beam level where leakages can rise to several
percent (compare Fig. 5). As only $\sim 10\,\%$ of our overall imaged area lie
in the 1 % leakage area and sources are less likely to be detected there due
to the higher noise, we can exclude a major statistical contribution to our
analysis. This is also supported by the similarity of our median FP values and
source density compared to the publications by Hales et al. (2014a); Grant et
al. (2010); Taylor et al. (2007); Subrahmanyan et al. (2010). However, data of
individual sources at the mosaic borders should be handled with care.

RMs of polarised background sources are often used for analysis of magnetic
fields in nearby objects such as the Milky Way (Oppermann et al., 2012;
Hutschenreuter & Enßlin, 2020) or the Magellanic Clouds (Gaensler et al.,
2005; Mao et al., 2008). The resolution of such studies and therefore the
number and types of objects we are able to investigate using this RM gridding
technique are strictly coupled to the density of polarised background sources.
While the previous studies could only use a maximum of three polarised sources
per square degree due to their limited sensitivity, we detect a polarised
source density of 21 sources/deg2. This source density is very similar to
literature values found at the same frequency and with similar resolution.
However, the exact value is always dependent on the primary beam response
level up to which the data was imaged. To mitigate this effect, cumulative
source counts should be used. Preliminary results show that the Apertif
measurements (Berger et al. in prep.) are confirming the results shown in
Rudnick & Owen (2014). The usability of a polarised source for an RM grid is
also dependent on whether it is resolved or compact. Beck & Gaensler (2004)
assumed that only 50 % of the detected polarised sources can be used. From our
comparison of the standard deviations of the RM values of extended and compact
sources, we can assume that, at least for mildly resolved sources, the RM
value at their centres is a reliable probe of the intervening magnetic field
and is not significantly influenced by their internal RM. Of our sources, 67 %
show a compact morphology, and therefore the usable fraction of sources is
likely to be larger than the value given by Beck & Gaensler (2004).

Literature values for the fraction of polarised sources are scattered between
$\leq 2.5\,\%$ and 14.1 % (see Hales et al. (2014a); Grant et al. (2010);
Taylor et al. (2007); Stil et al. (2014); Subrahmanyan et al. (2010);
O’Sullivan et al. (2015)). Berger et al. (2021) showed that the FP of sources
is dependent on the completeness of the source sample as well as on its
redshift distribution. In addition to this, we show that the FP of a source is
dependent on whether it is compact or resolved with approximately 20 % more
polarised emission originating from resolved sources.

The independent combination of the two values in Stokes Q and U leads to a
factor of $\sqrt{2}$ lower theoretical noise in the resultant PI images
compared to the TP images. In addition, side-lobe confusion in TP images is
usually higher due to the larger number of sources, which enhances the noise
in those images. The use of individual channel images for generating PI
mosaics —where the primary beam response level is dependent on frequency— adds
additional noise at the borders and overlap regions of individual beams.
Therefore, the fraction of polarised sources is often influenced by these
factors, making a direct comparison between different instrumental setups
difficult. As the FP and the fraction of sources for which polarised emission
is detected are interconnected, the scatter seen in literature values is most
likely caused by differences in the sensitivity and/or resolution of the
individual surveys.

Differences in the FP values for compact and resolved polarised sources can
have an instrumental and/or intrinsic physical origin. Polarised emission from
sources with multiple components emitting at different polarisation angles
leads to beam depolarisation. For our sources, which are mostly jet-dominated
AGN, polarisation angles can change rapidly between the jets towards and
within the lobes (see Saikia & Salter (1988) and references therein for
resolved polarisation studies of FRI- and FRII-sources). O’Sullivan et al.
(2015) showed that sources with straight jets exhibit smaller FP values than
sources with bent jets. Grant et al. (2010) and Hogbom & Carlsson (1974)
argued for a high percentage of lobe-dominated sources within their extended
samples, which are known to exhibit higher degrees of polarisation.

Physical origins are more complex. Internal and external Faraday dispersion
can lead to a depolarisation of the signal by turbulent magnetic fields inside
the sources themselves, in the environment surrounding them (Farnes et al.,
2014), or on the line of sight to the observer (Burn, 1966; Sokoloff et al.,
1998). These fields can be comprised of varying media, from turbulent cosmic
magnetic fields over intracluster ones (Laing, 1988; Garrington et al., 1988)
to magnetic fields within star-formation regions in the host galaxies.

The role of these star-forming regions in the polarisation properties of
galaxies is not clear. While molecular clouds often host strong magnetic
fields in the mG-regime (Crutcher, 2012) and star-forming galaxies can
generate large-scale fields via star formation in combination with the
$\alpha\Omega$-dynamo (Beck, 2015), strong star formation, for example in
starburst galaxies like M 82, can lower the observed polarisation fraction due
to a more turbulent magnetic field morphology (Adebahr et al., 2017). An
interaction between AGN activity and molecular and neutral gas motions
followed by star formation has been shown by Morganti & Oosterloo (2018). The
early phases of the radio jet propagation within the inner few kpc of the host
galaxy environment are most important (Morganti et al., 2021a, b). However,
the influence of star formation on the polarised properties of the radio jets
is under debate. O’Sullivan et al. (2015) investigated the differences in
polarisation properties of radiative-mode AGN (high excitation radio galaxies
(HERGs) and quasi-stellar objects (QSOs), which are known to host a
radiatively efficient accretion disc and jet-mode AGN (low excitation radio
galaxies; LERGs), which are inefficiently accreting. Even though HERGs are
usually more powerful and larger objects, they showed lower median FPs than
the smaller and less powerful LERGs. O’Sullivan et al. (2015) also argue that
the differences in the polarisation properties of AGN are not intrinsic but
rather influenced by the magnetic field configuration of their local
environment.

For our sample, we are not able to find a correlation or an anti-correlation
of the FP with star-formation properties of the AGN host galaxies. This might
be the consequence of a combination of the large range of sSFR we cover
together with the rather small size of our sample. In addition, the derivation
of SFR and sSFR from SED fitting using only a maximum of six photometric data
points involves large uncertainties. Therefore, a larger source sample in
combination with a finer selection of host galaxy types would shed light on
this aspect.

We find a significant number of sources classified as IFRS using the criteria
by Zinn et al. (2011). The definition of an IFRS is not consistent in the
literature regarding the apparent size of these objects. While Orenstein et
al. (2019); Middelberg et al. (2011) and Norris et al. (2011) defined them as
being compact and mostly unresolved, Singh et al. (2017) also used the
classification for resolved sources. The criterion by Zinn et al. (2011) was
also used by the authors on a compact source sample. All definitions regarding
the compactness of IFRSs are based on the apparent radio morphology. Defining
a source as compact or extended is heavily dependent on the resolution of the
observations and therefore a uniform classification is difficult. Using the
criteria by Zinn et al. (2011) without an additional selection based on the
apparent source size, we confirm the IFRS polarised source density found by
Middelberg et al. (2011), but not the high FP values found by these authors.
This comparison has to be taken with care. The study by Middelberg et al.
(2011) only consists of three polarised sources and is therefore highly
susceptible to biases due to the small size of the sample. In addition, their
instrumental leakage properties are higher, leading to an additional selection
bias towards sources with higher FP values. We are also not able to find a
difference in the median FP for resolved or extended sources between our
complete sample and the IFRS one. This might suggest that IFRSs are not
different from typical polarised radio AGN regarding their polarisation
characteristics.

We want to note that our source sample is only representative of a typical
polarised radio AGN sample. Polarised source samples on the $\mu$Jy-level are
strongly biased towards AGN, while the total power samples in the radio regime
are mostly a mixture of star-formation-dominated galaxies and AGN. In
addition, even when only investigating the AGN sample, certain types of AGN
with different characteristics dominate polarised samples. O’Sullivan et al.
(2015) and Berger et al. (2021) showed that a marginal difference exists
between the FP of FRI and FRII sources, and also between radio-loud and radio-
quiet sources. Hammond et al. (2012) found a difference between the FP of SDSS
galaxies and radio-loud QSOs. The QSOs were found to have FP values reaching
as high as 30 %, while the FPs of SDSS galaxies reached only 15 %.

Comparing our classification distribution of the host galaxies with the one
from O’Sullivan et al. (2015), we see a large difference. While our sample
mainly consists of intermediate disc and star-forming disc galaxies, the
sample of O’Sullivan et al. (2015) is dominated by spheroidal ones. Making the
same comparison with the faint total power radio sky at longer wavelengths
shows a distribution very similar to ours (Mingo et al., 2022). The main
difference arises in the flux range that the different samples cover. While
O’Sullivan et al. (2015) used the NVSS, which probes the bright sky up to
several mJy, our sensitivities are higher by more than an order of magnitude.
Therefore, our source population is dominated by faint polarised sources in
the $\mu$Jy regime.

Several studies showed a discrepancy between the bright and faint polarised
sky in terms of the relation between FP and TP radio emission (see Berger et
al. (2021) and references therein). This relation has been found to be larger
for the bright sky. If the polarised source samples of the bright sky are
indeed dominated by spheroidal galaxies, which are known to more often host
the slightly stronger polarised FRI-type sources and exhibit less direct radio
emission from star formation, we would expect the median FP of the bright sky
to be lower than that from the spiral-galaxy- and QSO-dominated faint sky.
Whether the bright and faint polarised sky are intrinsically different or this
effect is a general selection bias remains unclear and further studies are
needed.

Selection bias in the present study could originate from the limiting
sensitivity of allWISE and SDSS. We base our analysis on the complementary
optical and IR data. Spheroidal galaxies are less likely to be detected than
brighter disc galaxies, meaning that counterparts for sources with late-type
hosts are easier to detect. The fraction of sources classified as early-type
by O’Sullivan et al. (2015) of more than 80 % is much larger than our fraction
of 14.8 %. The total number of polarised sources we find with IR counterparts
is 967 while the total number of polarised sources is 1170. If all remaining
polarised sources without an IR counterpart had an early-type host galaxy, the
fraction would only rise to 29.6 %, which is still very different from the
percentage found by O’Sullivan et al. (2015). We are therefore unable to
completely exclude a bias towards disc-type galaxies in our sample, but this
cannot explain the large differences we see.

##  8 Summary and outlook

The Apertif system on the WSRT telescope is one of the two radio
interferometers equipped with phased-array-feed technology allowing wide
observations of the polarised radio sky in the centimetre wavelength regime.
Using publicly available Science Verification Campaign data, we developed a
semi-automatic pipeline to analyse the polarisation data products. We
automatically mosaicked polarisation Stokes-Q and -U frequency cubes and
performed RM synthesis. We generated PI, RM and FP maps from the resulting
Faraday cubes. We used automatic source finding routines to generate polarised
source catalogues, which are used to identify IR and optical counterparts of
the polarised sources using the allWISE and SDSS databases.

We quantify the polarisation performance of the Apertif system by inspecting
the polarisation leakage. We find that up to a primary beam response of 30 %,
which is well within the overlap regions of individual beams for the mosaics,
a maximum of only 1 % of the FP originates from leakage. Therefore, all
sources with FPs of lower than 1 % were excluded from any further analysis.
Additional performance checks were conducted by comparing the PI, FP, and RM
values for sources with NVSS counterparts. We find only minimal differences
between the NVSS values and ours, which we attribute to the factor-two lower
resolution of the NVSS data.

We identify 1170 polarised sources within 56.38 deg2, which results in a
polarised source density of 21/deg2. This is comparable to literature values
at a similar wavelength and sensitivity. We estimated that at least two-thirds
of our sources can be used to perform RM gridding, which is more than in
previous studies of the Milky Way and Large Magellanic Cloud by a factor of at
least five. We show that our derived RMs originate from spatial variations in
the magnetic field of the Milky Way foreground and are not the result of
measurement uncertainties.

For all of the sources of our sample with an IR counterpart (82.6 % of the
total sample), we find that the total radio emission is dominated by the AGN
activity. We find a subsample consisting of the sources with distance
estimates (27.3 %) to be mostly radio-loud (79 %) and of FRII-type (87 %). In
contrast to the findings of an analysis of the bright sky using the NVSS, our
source sample with IR counterparts —surveying the faint sky— is dominated by
late-type galaxies instead of early-type ones. We are not able to explain this
difference by selection biases. An intrinsic difference in the type of host
galaxy for the bright and faint polarised sky might therefore be possible.

We notice an $\approx 20\,\%$ higher FP for resolved sources than for
unresolved sources. Reasons for this can be either beam depolarisation and/or
intrinsic to the sources themselves. We did not observe a correlation between
the FP and the star-formation density of the host galaxies.

Although we have now doubled the survey area of polarised radio surveys at 1.4
GHz in the $\mu$Jy regime, scientific analyses are still limited by the small
number of detected polarised sources. The Apertif Wide Extragalactic Survey
(AWES) will again extend this database to several tens of thousands of
polarised sources within an area of 2000 deg2 in the northern hemisphere.
Complementary data from the southern hemisphere will be available from the
Polarisation Sky Survey of the Universe’s Magnetism (POSSUM) survey conducted
by the Australian Square Kilometre Array Pathfinder (ASKAP). The combination
of Apertif and ASKAP data with surveys at different wavelengths such as the
LOFAR Two-metre Sky Survey (LoTSS), the LOFAR LBA Sky Survey (LoLSS), and the
VLA Sky Survey (VLASS) will enhance the capability of scientific analysis to
explore polarisation spectra and therefore the magnetic field morphology in
radio sources.

###### Acknowledgements.

This research made use of Montage. It is funded by the National Science
Foundation under Grant Number ACI-1440620, and was previously funded by the
National Aeronautics and Space Administration’s Earth Science Technology
Office, Computation Technologies Project, under Cooperative Agreement Number
NCC5-626 between NASA and the California Institute of Technology. The Montage
distribution includes an adaptation of the MOPEX algorithm developed at the
Spitzer Science Center. BA and AB acknowledge funding from the German Science
Foundation DFG, within the Collaborative Research Center SFB1491 ”Cosmic
Interacting Matters - From Source to Signal”. EAKA is supported by the WISE
research programme, which is financed by the Dutch Research Council (NWO). KMH
acknowledges funding from the State Agency for Research of the Spanish
Ministry of Science, Innovation and Universities through the ”Center of
Excellence Severo Ochoa” awarded to the Instituto de Astrofísica de Andalucía
(SEV-2017-0709); from grant RTI2018-096228-B-C31 (Ministry of Science,
Innovation and Universities / State Agency for Research / European Regional
Development Funds, European Union); and from the coordination of the
participation in SKA-SPAIN, funded by the Ministry of Science and innovation
(MICIN). JMvdH and KMH acknowledge funding from the European Research Council
under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC
Grant Agreement No. 291531 (‘HIStoryNU’). JvL acknowledges funding from the
European Research Council under the European Union’s Seventh Framework
Programme (FP/2007-2013)/ERC Grant Agreement n. 617199 (‘ALERT’), and from
Vici research programme ‘ARGO’ with project number 639.043.815, financed by
the Dutch Research Council (NWO). DV acknowledges support from the Netherlands
eScience Center (NLeSC) under grant ASDI.15.406. RS acknowledges funding from
the European Research Council under the European Union’s Seventh Framework
Programme (FP/2007-2013)/ERC Grant Agreement No. 617199. LCO acknowledges
funding from the European Research Council under the European Union’s Seventh
Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 617199.

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##  Appendix A SVC polarised intensity images

PI images of SVC-fields 1, 2, 4, and 5 are shown in the following while SVC
field 3 is shown in Fig. 3. The greyscale represents the PI in all images.
Compound beams missing in the data are given in the caption of each image
together with the final synthesised beam size.

Figure 18: Polarised intensity image of the field S2248+33 (SVC1). The noise
in emission-free regions is 14 $\upmu$Jy/beam. The synthesised beam size is
$32.1^{\prime\prime}\times 18.0^{\prime\prime}$. Beams 16, 18, and 31 to 39
are missing.

Figure 19: Polarised intensity image of the field M1403+53 (SVC2). The noise
in emission-free regions is 13 $\upmu$Jy/beam. The synthesised beam size is
$19.3^{\prime\prime}\times 14.6^{\prime\prime}$. Beams 6, 7, 13, 14, 16, 18
and 20 are missing.

Figure 20: Polarised intensity image of the field S2246+38 (SVC4). The noise
in emission-free regions is 16 $\upmu$Jy/beam. The synthesised beam size is
$24.8^{\prime\prime}\times 14.8^{\prime\prime}$. Beams 16, 18, 28, 29, 30, 35
and 36 are missing.

Figure 21: Polarised intensity image of the field S1415+36 (SVC5). The noise
in emission-free regions is 16 $\upmu$Jy/beam. The synthesised beam size is
$31.2^{\prime\prime}\times 17.7^{\prime\prime}$. Beams 16, 18 and 29 are
missing.

##  Appendix B Source catalogue

Our polarised source catalogues are released as ascii files and are available
via the ASTRON Virtual Observatotry171717https://vo.astron.nl/. In the
following, we describe the entries for each column. Each row in the catalogue
represents one source component, and so multiple entries with the same source
ID are multiple polarised components of one source. All NVSS information is
retrieved from Taylor et al. (2009), WISE data from Cutri et al. (2021), and
SDSS data from Ahumada et al. (2020). NaN values are inserted where no
information is available, which is usually the case for missing counterparts
in the AllWISE or SDSS databases.

ID: Source identifier concatenated from a prefix and the right ascension and
declination of the central position of the source in degrees.

RA: Right Ascension of the central position of the source in degrees.

RA_err: Uncertainty of the right Ascension of the central position of the
source in degrees.

DEC: Declination of the central position of the source in degrees.

DEC_err: Uncertainty of the declination of the central position of the source
in degrees.

PI: Integrated PI of the source in units of Jy.

PI_err: Uncertainty of the integrated PI of the source in units of Jy.

S_Code: S for unresolved sources, E for resolved sources

RA_Comp: Right ascension of the position of the source component in degrees.

RA_Comp_err: Uncertainty of the right ascension of the position of the source
component in degrees.

DEC_Comp: Declination of the position of the source component in degrees.

DEC_Comp_err: Uncertainty of the declination of the position of the source
component in degrees.

PI_Comp_peak: Peak polarised emission of the source component in units of Jy.

PI_Comp_peak_err: Uncertainty of the peak polarised emission of the source
component in units of Jy.

PI_rms: Standard deviation at the peak position of the source component in
units of Jy/beam.

RM_Comp: RM at the peak position of the source component in units of rad/m2.

RM_Comp_err: Uncertainty of the RM at the peak position of the source
component in units of rad/m2.

TP_ID: TP source identifier. For internal usage only. Was used for cross-
matching.

TP: Radio continuum flux of the cross-matched TP counterpart in units of Jy.

TP_err: Uncertainty of the radio continuum flux of the cross-matched TP
counterpart in units of Jy.

TP_RA: Right ascension of the central position of the TP counterpart in units
of degrees.

TP_RA_err: Uncertainty of the right ascension of the central position of the
TP counterpart in units of degrees.

TP_DEC: Declination of the central position of the TP counterpart in units of
degrees.

TP_DEC_err: Uncertainty of the declination of the central position of the TP
counterpart in units of degrees.

FP: FP of the source derived from the integrated PI and TP fluxes.

FP_err: Uncertainty of the FP of the source derived from the integrated PI and
TP fluxes.

NVSS_I: TP flux of a possible NVSS counterpart in units of Jy.

NVSS_I_err: Uncertainty of the TP flux of a possible NVSS counterpart in units
of Jy.

NVSS_PI: PI flux of a possible NVSS counterpart in units of Jy.

NVSS_PI_err: Uncertainty of the PI flux of a possible NVSS counterpart in
units of Jy.

NVSS_FP: FP of a possible NVSS counterpart.

NVSS_FP_err: Uncertainty of the FP of a possible NVSS counterpart.

NVSS_RM: RM of a possible NVSS counterpart in units of rad/m2.

NVSS_RM_err: Uncertainty of the RM of a possible NVSS counterpart in units of
rad/m2.

NVSS_RA: Right ascension of a possible NVSS counterpart in units of degrees.

NVSS_RA_err: Uncertainty of the right ascension of a possible NVSS counterpart
in units of degrees.

NVSS_DEC: Declination of a possible NVSS counterpart in units of degrees.

NVSS_DEC_err: Uncertainty of the declination of a possible NVSS counterpart in
units of degrees.

WISE_ID: AllWISE ID of a possible counterpart.

WISE_RA: Right ascension of a possible AllWISE counterpart in units of
degrees.

WISE_RA_err: Uncertainty of the right ascension of a possible AllWISE
counterpart in units of degrees.

WISE_DEC: Declination of a possible AllWISE counterpart in units of degrees.

WISE_DEC_err: Uncertainty of the declination of a possible AllWISE counterpart
in units of degrees.

WISE_Flux_3.4: Brightness of a possible AllWISE counterpart in units of mag at
3.4$\upmu$m.

WISE_Flux_3.4_err: Uncertainty of the brightness of a possible AllWISE
counterpart in units of mag at 3.4$\upmu$m.

WISE_Flux_3.4_snr: S/N of a possible AllWISE counterpart in units of mag at
3.4$\upmu$m.

WISE_Flux_4.6: Brightness of a possible AllWISE counterpart in units of mag at
4.6$\upmu$m.

WISE_Flux_4.6_err: Uncertainty of the brightness of a possible AllWISE
counterpart in units of mag at 4.6$\upmu$m.

WISE_Flux_4.6_snr: S/N of a possible AllWISE counterpart in units of mag at
4.6$\upmu$m.

WISE_Flux_12: Brightness of a possible AllWISE counterpart in units of mag at
12$\upmu$m.

WISE_Flux_12_err: Uncertainty of the brightness of a possible AllWISE
counterpart in units of mag at 12$\upmu$m.

WISE_Flux_12_snr: S/N of a possible AllWISE counterpart in units of mag at
12$\upmu$m.

WISE_Flux_22: Brightness of a possible AllWISE counterpart in units of mag at
22$\upmu$m.

WISE_Flux_22_err: Uncertainty of the brightness of a possible AllWISE
counterpart in units of mag at 22$\upmu$m.

WISE_Flux_22_snr: S/N of a possible AllWISE counterpart in units of mag at
22$\upmu$m.

SDSS_ID: SDSS DR16 ID of a possible counterpart.

SDSS_RA: Right ascension of a possible SDSS DR16 counterpart in units of
degrees.

SDSS_DEC: Declination of a possible SDSS DR16 counterpart in units of degrees.

SDSS_Flux_U: Brightness of a possible SDSS DR16 counterpart in units of mag in
the U filter.

SDSS_Flux_U_err: Uncertainty of the brightness of a possible SDSS DR16
counterpart in units of mag in the U filter.

SDSS_Flux_G: Brightness of a possible SDSS DR16 counterpart in units of mag in
the G filter.

SDSS_Flux_G_err: Uncertainty of the brightness of a possible SDSS DR16
counterpart in units of mag in the G filter.

SDSS_Flux_R: Brightness of a possible SDSS DR16 counterpart in units of mag in
the R filter.

SDSS_Flux_R_err: Uncertainty of the brightness of a possible SDSS DR16
counterpart in units of mag in the R filter.

SDSS_Flux_I: Brightness of a possible SDSS DR16 counterpart in units of mag in
the I filter.

SDSS_Flux_I_err: Uncertainty of the brightness of a possible SDSS DR16
counterpart in units of mag in the I filter.

SDSS_Flux_Z: Brightness of a possible SDSS DR16 counterpart in units of mag in
the Z filter.

SDSS_Flux_Z_err: Uncertainty of the brightness of a possible SDSS DR16
counterpart in units of mag in the Z filter.

SDSS_z: Photometric or if available sprectroscopic redshift of a possible SDSS
DR16 counterpart.

SDSS_z_err: Uncertainty of the photometric or if available sprectroscopic
redshift of a possible SDSS DR16 counterpart.