11institutetext: Kapteyn Astronomical Institute, University of Groningen, 9747
AD Groningen, The Netherlands
11email<EMAIL_ADDRESS>22institutetext: Jodrell Bank Centre for
Astrophysics/e-MERLIN, The University of Manchester, M13 9PL, United Kingdom
33institutetext: ASTRON, the Netherlands Institute for Radio Astronomy,
Postbus 2, 7990 AA Dwingeloo, The Netherlands 44institutetext: Leiden
Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
55institutetext: Centre for Astrophysics and Supercomputing, Swinburne
University of Technology, PO Box 218 Hawthorn, VIC 3122, Australia
66institutetext: Joint Institute for VLBI ERIC, Postbus 2, 7990 AA Dwingeloo,
The Netherlands

# Nowhere to Hide: Radio-faint AGN in the GOODS-N field ††thanks: a machine
readable catalogue accompanies this paper

I. Initial catalogue and radio properties

J. F. Radcliffe 112233 M. A. Garrett 2244 T. W. B. Muxlow 22 R. J. Beswick 22
P. D. Barthel 11 A. T. Deller 55 A. Keimpema 66 R. M. Campbell 66 N. Wrigley
22

(Received ¡date¿ / Accepted ¡date¿)

###### Abstract

Context. The occurrence of active galactic nuclei (AGN) is critical to our
understanding of galaxy evolution and formation. Radio observations provide a
crucial, dust-independent tool to study the role of AGN. However, conventional
radio surveys of deep fields ordinarily have arc-second scale resolutions
often insufficient to reliably separate radio emission in distant galaxies
originating from star-formation and AGN-related activity. Very long baseline
interferometry (VLBI) can offer a solution by identifying only the most
compact radio emitting regions in galaxies at cosmological distances where the
high brightness temperatures (in excess of $10^{5}$ K) can only be reliably
attributed to AGN activity.

Aims. We present the first in a series of papers exploring the faint compact
radio population using a new wide-field VLBI survey of the GOODS-N field. This
will expand upon previous surveys, permitting the characterisation of the
faint, compact radio source population in the GOODS-N field. The unparalleled
sensitivity of the European VLBI Network (EVN) will probe a luminosity range
rarely seen in deep wide-field VLBI observations, thus providing insights into
the role of AGN to radio luminosities of the order
$10^{22}\leavevmode\nobreak\ \mathrm{W\,Hz^{-1}}$ across cosmic time.

Methods. The newest VLBI techniques are used to completely cover an entire
7.′5 radius area to milliarcsecond resolutions, while bright radio sources
($S>0.1$ mJy) are targeted up to 25′ from the pointing centre. Multi-source
self-calibration, and a primary beam model for the EVN array are used to
correct for residual phase errors and primary beam attenuation respectively.

Results. This paper presents the largest catalogue of VLBI detected sources in
GOODS-N comprising of 31 compact radio sources across a redshift range of
0.11-3.44, almost three times more than previous VLBI surveys in this field.
We provide a machine-readable catalogue and introduce the radio properties of
the detected sources using complementary data from the e-MERLIN Galaxy
Evolution survey (eMERGE).

###### Key Words.:

catalogs - radio continuum: galaxies - galaxies: active, nuclei - techniques:
high angular resolution, interferometric

##  1 Introduction

Radio source counts above mJy flux densities are dominated by radio galaxies
and quasars powered by active galactic nuclei (AGN). Below mJy flux densities,
there is an observed upturn far in excess of those predicted by extrapolating
source counts of high luminosity radio galaxies and quasars. This upturn is
found to comprise an increasing fraction of active star forming galaxies and
faint ‘non-jetted’ or radio-quiet AGN plus a decreasing fraction of classical
radio-loud sources (see Prandoni et al., 2001; Huynh et al., 2015; Padovani,
2016, and references therein). The majority of extragalactic radio surveys are
carried out at arc-second resolutions (corresponding to galactic/$\sim$10’s
kpc physical scales at $z\geq 0.1$) where it can be difficult to distinguish
between the sub-kpc scale AGN activity and the kpc star-formation related
emission based purely on their radio morphologies. This is particularly
important if we are to characterise the properties of radio-quiet AGN whose
radio emission in local systems are confined within the host galaxy (see
Orienti et al., 2015, and references therein). As a result, these surveys rely
on multi-wavelength diagnostics, such as radio-excess, SED fitting, X-ray
emission etc., in order to identify any AGN activity (e.g. Bonzini et al.,
2013; Smolčić et al., 2017). These diagnostics are often incomplete with dust
masking the signatures of AGN activity. For example, X-rays often do not
detect Compton-thick AGN which are estimated to account for over a third of
the total AGN population (Mateos et al., 2017).

These hidden AGN can be found using high resolution, dust-independent radio
observations. Indeed, surveys using e-MERLIN, such as the e-MERlin Galaxy
Evolution (e-MERGE) survey (Muxlow et al. in prep., Muxlow et al. (2005)), and
Very Long Baseline Interferometry (VLBI) (e.g. Middelberg et al., 2011, 2013a;
Herrera Ruiz et al., 2017) have shown that deep, sub-arcsecond and sub-kpc
observations can effectively isolate AGN activity from compact star-forming
related emission in distant galaxies.

VLBI observations detect bright, compact objects with brightness temperatures
in excess of $10^{5}$ K. In nearby galaxies, these brightness temperatures can
be typically reached by either AGN, supernovae (SNe) and their remnants
(SNRs). However, in more distant galaxies ($z>0.1$), these brightness
temperatures can typically only be attained by AGN-related emission processes
(e.g. Kewley et al., 2000), thus making VLBI a unique and invaluable tool to
survey distant galaxies for AGN activity. However, until the last decade,
there have been many factors preventing VLBI from being used as a survey
instrument.

Conventional wide-field VLBI observations mapped a significant proportion of
the primary beam by using a single correlation pass at a ultra-fine temporal
and frequency resolution in order to limit time and bandwidth smearing towards
the edge of the primary beam (Garrett et al., 2001). As a result, the observer
would receive a single large and unwieldy (often $\sim$TB size) data set. With
the ever increasing number of VLBI-ready telescopes along with widening
bandwidths, the bit rates of modern VLBI arrays are rapidly increasing and
this method of correlation has become computationally infeasible. Software
correlators established the ‘multiple simultaneous phase centre observing’
approach to correlation (Deller et al., 2011; Morgan et al., 2011; Keimpema et
al., 2015) which substantially reduces the computational load. Here, the
observer defines a number of sub-fields (also referred to as phase centres)
which can be either sources of interest or can be arranged to cover the entire
primary beam. When correlated, these data are split and each sub-section is
correlated at the ultra high temporal and frequency resolution required to
restrain smearing. It is then copied and phase shifted to the various sub-
fields of interest and averaged to a small field-of-view (typically 30-60″).
The result is a small ($\sim$GB) dataset per sub-field which is easily
manageable and parallelisable when calibrating and imaging.

By combining multi-phase centre correlation with advanced calibration
techniques such as in-beam phase referencing (Garrett et al., 2001, 2005; Lenc
et al., 2008) and multi-source self-calibration (Middelberg et al., 2013a;
Radcliffe et al., 2016), wide-field VLBI surveys of milliarcsecond scale
extragalactic radio sources to $\mu$Jy flux densities have become increasing
feasible (e.g. Middelberg et al., 2011, 2013a; Chi et al., 2013; Morgan et
al., 2013; Cao et al., 2014; Deller & Middelberg, 2014; Rampadarath et al.,
2015; Herrera Ruiz et al., 2017).

We here present a new wide-field VLBI survey targeting the well studied Great
Observatories Origin Deep survey North (GOODS-N) field using the European VLBI
Network (EVN). The GOODS-N field covers 160 arcmin2 with complementary deep
multi-wavelength data including Chandra, Spitzer, Herschel, UBVRIJHK
photometry and spectroscopy.

Previous wide-field VLBI observations targeted the Hubble Deep Field (HDF) and
Flanking Fields (HFF) for which the GOODS-N field encompasses. Garrett et al.
(2001) used the EVN to target MERLIN sources within a 3.5′ radius from the EVN
pointing centre to r.m.s. sensitivities of 33 $\rm\mu Jy\,beam^{-1}$. This
resulted in the detection of 3 sources. These observations were substantially
expanded upon by Chi et al. (2013) who used Global VLBI to target the 92 VLA-
MERLIN sources of Muxlow et al. (2005) within a $10\arcmin\times 10\arcmin$
field to r.m.s. sensitivities of 7.3 $\rm\mu Jy\,beam^{-1}$. This resulted in
12 compact radio source detections (including the 3 detected by Garrett et al.
(2001)) thus beginning the characterisation of the faint compact radio
population in GOODS-N. However, these surveys were invariably limited because
computational limitations prevented imaging of the entire primary beam at that
time. Our survey aims to substantially expand upon this sample, encompassing
and surpassing the field-of-view and sensitivities of previous VLBI surveys in
GOODS-N by targeting sources within a $30\arcmin\times 30\arcmin$ area to
$1\sigma$ central sensitivity of $\sim 2\mbox{-}3\leavevmode\nobreak\ {\rm\mu
Jy\,beam^{-1}}$ with the completion of this survey.

In this paper, we present our initial catalogue of the 31 compact sources
detected in the first data release to a $1\sigma$ sensitivity of $\sim
9\leavevmode\nobreak\ {\rm\mu Jy\,beam^{-1}}$ (corresponding to $\sim$ 17.5hr
on source) along with derived radio properties of these objects using
complementary 1-2 GHz VLA data. In paper II, we compare our VLBI-selected
population to other AGN detection diagnostics used in other wavebands. A
future publication, paper III, will describe the final data release which will
include an additional 48 hours of observations which comprise of the first
wide-field VLBI observations using a combined eMERLIN-EVN array.

For this paper, we adopt a spatially-flat 6-parameter $\mathrm{\Lambda CDM}$
cosmology with $H_{0}=67.8\pm 0.9\leavevmode\nobreak\
\mathrm{km\,s^{-1}\,Mpc}$, $\Omega_{m}=0.308\pm 0.012$ and
$\Omega_{\Lambda}=0.692\pm 0.012$ (Planck Collaboration et al., 2016). We
assume $S_{\nu}\propto\nu^{\alpha}$ throughout, where $S_{\nu}$ is the radio
integrated flux density and $\alpha$ is the intrinsic source spectral index.

The paper is organised as follows. Section 2 outlines our observations, source
selection strategy, calibration and source detection methodology. Section 3
details the primary beam correction method used for the EVN. Section 4
describes the VLBI catalogue accompanying this paper while a formatted version
is presented in Tables 2 and 3. Section 5 presents our results and associated
discussion, including redshifts, astrometry, comparisons with other VLBI
surveys and the radio properties of the VLBI-selected population. We conclude
our findings in Section 6.

##  2 Observations & data reduction

###  2.1 EVN observations

The EVN observed the GOODS-N field at 1.6 GHz for 24 hours in total on the
5-6th June 2014 (EVN code EG078B). The pointing centre used was the Hubble
Deep Field-North (HDF-N), J2000 12:36:50.0 62:12:58.0. Ten telescopes,
including the 100m Effelsberg and the 76m Lovell (Jodrell Bank) telescopes,
were involved in the observation. In order to attain a uniform sensitivity
profile, the Effelsberg and Lovell telescopes were nodded between 5 different
pointing centres over the course of the observation while smaller telescopes
remained pointed at the HDF-N centre. The observing strategy and participating
telescopes are summarised in Table 1.

These data were recorded at a bit rate of 1024 Mbits/s (8 $\times$ 16MHz
bands) in both right and left hand circular polarizations. The fringe finders
used were 3C345 and DA193. The observations were made using the standard phase
referencing mode. Two phase calibrators were used; a strong, $\sim$0.4 Jy,
primary calibrator J1241+602 lying approximately $2^{\circ}$ from the target
centre, and a weaker, 17 mJy, secondary calibrator J1234+619 lying 23.5′ from
the target centre. The primary calibrator was observed for 1.5 min on source
every $\sim$$27$ minutes. To permit more accurate phase corrections, the
secondary calibrator was observed more frequently (1.5 min on source every
$\sim$$7.5$ min). In total, the on-source integration time on the GOODS-N
field was approximately 17.5 hr.

Table 1: EG078B observing strategy

Telescopes | Country | Diameter (Derived) / m
---|---|---
Ef | Germany | 100 (78)
Wb | Netherlands | 25
On | Sweden | 25
Nt | Italy | 32
Tr | Poland | 32
Sv | Russia | 32
Bd | Russia | 32
Zc | Russia | 32
Sh | China | 25 (22.5)
Jb1 | United Kingdom | 76 (67)

Target Fields | R.A. (J2000) | Dec. (J2000) | Telescopes
---|---|---|---
HDF-N | 12:36:50.0 | +62:12:58.0 | All
EFJB-P1 | 12:37:20.0 | +62:16:28.0 | Ef, Jb1
EFJB-P2 | 12:36:20.0 | +62:16:28.0 | Ef, Jb1
EFJB-P3 | 12:36:20.0 | +62:09:28.0 | Ef, Jb1
EFJB-P4 | 12:37:20.0 | +62:09:28.0 | Ef, Jb1
111Upper panel: Telescopes used in the EVN observations. Abbreviations, Ef:
Effelsberg, Wb: WSRT (single dish), On: Onsala, Nt: Noto, Tr: Torun, Sv:
Svetloe, Bd: Badary, Zc: Zelenchukskaya, Sh: Shanghai, Jb1: Jodrell Bank
(Lovell Telescope). The fitted HPBW of telescopes with primary beam estimates
are in brackets.
Lower panel: Pointing centres used for the duration of the observation. Ef and
Jb1 were nodded between all 5 pointing centres, whilst the rest of the array
were pointed at the HDF-N pointing centre.

####  2.1.1 Source selection & correlation

These data were correlated using the SFXC correlator (Keimpema et al., 2015)
at the Joint Institute for VLBI ERIC, Dwingeloo, the Netherlands. The
correlation implemented the multiple simultaneous phase centre observing
technique (see Deller et al., 2007, 2011; Keimpema et al., 2015) to target 699
sub-fields/phase centres. Two source selection strategies were implemented and
the criteria are as follows:

  1. (a)

A survey designed to completely cover the central 7.′5 radius area with VLBI
coverage whilst restraining bandwidth and time smearing to $<$10%. This is
designed to complement the 1.5 GHz eMERGE survey (Muxlow et al. in prep.) for
use in integrated imaging. This comprises of 582 phase centres split into
three main categories:

    1. i.

339 1.5 GHz eMERLIN-VLA sources complete to ~$11\,\mathrm{\mu Jy\,beam^{-1}}$
from the upcoming eMERGE survey (Muxlow et al. in prep.).

    2. ii.

151 SCUBA-2 850 $\rm\mu m$ sources (Smail priv. comm.).

    3. iii.

92 other positions, denoted ‘legacy’, which cover gaps in coverage across the
field.

  2. (b)

A targeted survey of 117 1.4 GHz VLA radio-bright sources outside the central
7.′5 radius area with integrated VLA flux densities, $S_{\mathrm{i,VLA}}$,
$>0.1\leavevmode\nobreak\ \mathrm{mJy}$ (Morrison et al., 2010). These are
split into:

    1. i.

91 sources with $0.1<S_{\mathrm{i,VLA}}<1$ mJy targeted to a radius of 12′
from the central pointing centre.

    2. ii.

26 sources with $S_{\mathrm{i,VLA}}>1$ mJy targeted to the edge of the
Morrison et al. (2010) VLA survey.We note that 4/26 of these sources are
within the 15′and were accidental double entries in the correlation catalogue.
These are kept in for clarity in-case these data are re-reduced in the future.

The source positions targeted are shown in Figure 1. With source positions
determined, correlation proceeded as follows. Short sub-integrations of data
were correlated at the required high spectral and temporal resolutions in
order to reduce time and bandwidth smearing. In this observation, each sub-
integration had a frequency resolution of 1.953 kHz and a time resolution of
13.056 ms in order to restrain time and bandwidth smearing to below 1% on the
longest baseline ($\sim 8400$ km) at 5′ from the pointing centre. At the end
of each sub-integration, the visibilities were phase shifted to every desired
source position to create a separate data set per position. Each data set was
averaged to a temporal resolution of 3s and a frequency spacing of ${\rm
0.5\,MHz}$ (corresponding to a 10% time and bandwidth smearing at 30″ from the
assigned source position) and then added to previous sub-integrations until
the entire data set was correlated. As a result, 699 separate, narrow field-
of-view (FoV) data sets were produced, one per source position. Attached to
one data set, containing source J123462+621331, were the scans of the phase
calibrators, J1241+602 and J1234+619, and the fringe finders, 3C345 and DA193
used for calibration. The phase referencing calibration and flagging tables
derived for this data set can then be easily copied to the other data sets.
Despite the total size being 3.79 TB, calibration of this data set is easily
parallelised and computationally less intensive than previous wide-field VLBI
projects (e.g. Chi et al., 2013). For further clarification, we will refer to
the target field as the GOODS-N field as a whole, while the sub-fields are the
small FoV phase centres within the GOODS-N field whose coordinates were
correlated upon.

Figure 1: Sources / sub-fields targeted by these observations. The central
7.′5 radius area complements the eMERGE survey and targets eMERLIN detected
sources (red circles), SCUBA sub-mm sources (yellow inverted triangles) and
legacy positions (green stars) which aim to fill in the gaps in coverage. The
outer annulus targets only the brightest sources detected by the VLA in
Morrison et al. (2010). Those with integrated flux densities
$0.1<S_{\mathrm{i,VLA}}<1$ mJy (blue heptagons) are targeted to a radius of
12′ and bright sources $S_{\mathrm{i,VLA}}>1$ mJy (black crosses) are targeted
to the edge of the Morrison et al. (2010) survey.  Figure 2: R.m.s.
sensitivity for our 1.6 GHz EVN observations after primary beam correction.
These data were optimally weighted for sensitivity (AIPS task IMAGR:
UVWTFN=‘NA’). The central r.m.s. is approximately ~9
$\mu\mathrm{Jy\,beam^{-1}}$. The red dashed circles correspond to the HPBW of
the Effelsberg telescope at 1.6 GHz ($\sim 7.\\!\arcmin 5$) at the pointing
centres specified in Table 1, and coloured markers correspond to the sub-
fields. Contours start at 15 $\rm\mu Jy\,beam^{-1}$ in increments of 5 $\rm\mu
Jy\,beam^{-1}$ in order to illustrate the rapid sensitivity losses outside the
primary beams of the large telescopes.

####  2.1.2 Data reduction

These data were reduced using the Astronomical image processing (AIPS)
software developed by NRAO222www.aips.nrao.edu (Greisen, 2003), and its Python
interface, Parseltongue (Kettenis et al., 2006).

Before describing the data reduction, we note that there was an error found in
the position of the secondary phase calibrator (J1234+619) when we tested
phase referencing from the primary calibrator (J1241+602) to the secondary
phase calibrator. This incorrect position originated from the Chi et al.
(2013) observations. The correct position was found to be J2000
12:34:11.7413(57) +61:58:32.478(07). Independent 5 GHz e-MERLIN observations
of J1234+619 using multiple phase calibrators verified that this new position
is correct (see Appendix A). The model of J1234+619 derived from initial phase
referencing tests were then used when fringe fitting in order to ensure the
correct position is used.

With this issue established and solved, these data were calibrated as follows.
Gains were calibrated using the system temperature, $T_{\mathrm{sys}}$,
measurements from each antenna and the data were edited to remove any Radio
Frequency Interference (RFI) using the AIPS tasks SPFLG and CLIP. Instrumental
phase offsets between the spectral windows333We use the term ‘spectral
windows’ to describe the sub-bands in frequency. They are synonymous with the
term IFs used in the AIPS data reduction package. were then removed by solving
for the phase and delays on a two minute integration of 3C345, using the task
FRING. This allowed the spectral windows to be combined when the data is
fringe fitted. We note that the dispersive delays were not corrected for,
however we are confident that this is a minimal contribution as the fully
calibrated data shows no phase deviations across the frequency band in excess
of 10-15 degrees on all baselines.

The group delays for the phase calibrators and fringe finders were calibrated
using FRING (using a model of J1234+619 created when investigating the
positional offsets), edited (using SNEDT) and smoothed (using SNSMO) to remove
noisy and spurious solutions. With the delays calibrated, the phase and rates
were then calibrated, edited and smoothed and applied to the data. We note
that fringe fitting was conducted on both phase calibrators. This is because
the Lovell Telescope (Jb) did not observe the primary phase calibrator due to
a restriction on the number source changes per hour. With fringe fitting
complete, the bandpass response was calibrated using AIPS task BPASS. 3C345
was used for bandpass calibration on all telescopes.

The primary phase calibrator (and furthest from the target), J1241+602,
underwent three rounds of phase only self calibration (with solution intervals
of five, one, and one minute(s) respectively) and one round of amplitude and
phase self-calibration with a five minute solution interval. These solutions
were applied to the closer, secondary phase calibrator, J1234+619. Three
rounds of phase only self-calibration (with solution intervals of five, four,
and two minutes respectively) were conducted on J1234+619 and these solutions
were then applied to the sub-field containing J123462+621331. Spectral windows
were not combined when self-calibration was performed on J1241+602, or during
the first round of self-calibration on J1234+619. This would effectively
correct any residual dispersive delay errors caused by a variable ionosphere
by approximating the true phase correction (smoothly variable with frequency)
with one that is a stepwise constant (one value per subband per solution
interval).

The calibration solutions and flagging tables derived and applied to
J123642+621331 were then applied to the other 698 sub-fields. All sub-fields
were then imaged using AIPS task IMAGR using both natural (UVWTFN=‘NA’) and
uniform weighting schemes and these images were searched for emission. A
detection threshold of $6\sigma$ was used to reduce the chance of false
positives (see Radcliffe et al., 2016, for more in depth discussion).

To reduce residual phase errors arising from atmospheric inhomogeneities
between the phase calibrator and target field, we utilised the Multi-source
Self-calibration (MSSC) technique developed by Middelberg et al. (2013b) and
Radcliffe et al. (2016). The nine brightest sources were used in MSSC. These
sources were detected when imaged with both uniform and natural weighting
schemes. If a source was detected in both images, it is highly suggestive that
the source can be detected on all baselines. As a conservative precaution, we
excluded sources outside the primary beam of the large telescopes (Effelsberg
and Lovell) because we would expect considerable phase and gain errors to be
induced by the attenuation of the primary beam. These errors would not be the
same for each sub-field and will simply add noise into the solutions for MSSC
when the individual sub-fields are combined. By performing this we ensure that
the dominant error is from differing atmospheric paths between the phase
calibrator and the target field. Three rounds of phase-only MSSC were
performed using a solution interval of 2 min and the corrections derived were
applied to all sub-fields. A primary beam correction scheme (outlined in
Section 3) was then applied to the central 7.′5 radius field and the sub-
fields were searched for emission. The following section describes the method
used to detect sources once MSSC and the primary beam correction was applied.

Figure 3: Composite image of 1.4 GHz WSRT radio-KPNO optical overlay of the
GOODS-N field, centred on the HDF-N (Garrett et al., 2000), surrounded by
postage stamp images of the 1.6 GHz 31 VLBI detected sources presented in this
paper. Those VLBI sources without adjoining red lines are located outside the
WSRT central figure. The VLBI contours are $\pm 1\sigma$ noise and then
linearly spaced between $1\sigma$ noise and the peak pixel brightness. This
image is an update on Figure 1 from Chi et al. (2013).

###  2.2 Source detection methodology

To determine accurate peak brightnesses and integrated flux densities, we
tested multiple source detection algorithms namely AIPS task SAD, BLOBCAT
(Hales et al., 2012) and PYBDSF (Mohan & Rafferty, 2015). It has been noted
that Gaussian fitting routines, namely SAD and PYBDSF, were found to routinely
over estimate integrated flux densities in the low signal-to-noise (S/N)
regime where noise fluctuations across the extent of a source can induce sub-
optimal fitting (see Middelberg et al., 2013a). In the low S/N regime (S/N
$\sim 6\mbox{-}10$), the measured integrated flux densities were on average
$\sim 16\%$ and $\sim 22\%$ higher than the BLOBCAT measured values when using
SAD and PYBDSF respectively. In the high S/N regime, the effects are less
pronounced with both SAD and PYBDSF reporting fluxes only 4-5% larger than
BLOBCAT.

We therefore used BLOBCAT to measure peak brightnesses and integrated flux
densities of our sources. Initially, BANE (Hancock et al., 2012) was used to
generate a r.m.s. map of each field which is in turn input to BLOBCAT. All
parameters were set to default apart from the surface brightness error which
was assumed to be $\sim$ 10% which is caused by amplitude calibration errors
(\--pasbe=0.1), the minimum S/N detection threshold (\--dSNR = 6) and, as our
point spread function (psf or synthesised beam) is vastly oversampled, the
peak brightness pixellation error was set to 1% (\--ppe=0.01; see Appendix A
of Hales et al. (2012) for more information). The surface brightness error
included an additional error factor which is proportional to the value of the
primary beam correction. Note that BLOBCAT does not provide any size
information therefore source sizes were measured using PYBDSM444As part of
these observations we have developed a generalised wrapper for source
detection in multi-phase centre VLBI observations that is publicly available.
It can generate catalogues using SAD, BLOBCAT and PYBDSF (see
https://github.com/jradcliffe5/General_VLBI_cataloger).

For the central 7.′5 radius field, each sub-field was imaged using natural
weighting only (to optimise sensitivity) and then the method outlined above
was used to search for detections. Detections were then imaged with uniform
weighting (whose r.m.s. is $\leavevmode\nobreak\ 1.6\times$ the naturally
weighted r.m.s.) in order to obtain the highest resolution image possible.

To optimise the number of detections, we used a different strategy to image
sub-fields outside the central 7.′5 radius field which are beyond the half-
power beam widths (HPBWs) of the large telescopes (Effelsberg and Lovell). Two
images were made for each sub-field. For the first image, the large telescopes
on all pointings apart from the closest pointing centre to the sub-field were
flagged. This was performed because while the large telescopes retain
significant sensitivity well beyond the HPBW of their primary beam, the
retention of the more distant pointing centres would induce significant
amplitude errors which would outweigh any sensitivity gains. This method
produced an additional 6 detections, the majority of which (4/6) are within a
12″ radius of the pointing centre. For the second image, all of the large
telescopes are flagged, so that sources up to the HPBW of the smaller 32m and
25m telescopes could be detected without being affected by amplitude errors
from the large telescopes still present in these data. This method produced
just one additional detection and none of the 6 sources detected with the
larger telescopes included were detected with this method. This is likely due
to the significant sensitivity reduction when the large telescopes are
removed. Additionally, we note that the primary beam models are poorly
constrained outside the HPBW, therefore these sub-fields do not have primary
beam correction applied.

Once detections were identified, each sub-field was re-imaged with both
uniform weighting ($\sim 5.3\times 4.5$ mas) and natural weighting ($\sim
16\times 16$ mas) schemes and re-catalogued resulting in a total of 31
detections (24 from the central field and 7 from the targeted survey beyond
the 7.′5 radius field). These detections are shown in Figure 3 which is an
update on Fig. 1 from Chi et al. (2013). We note that Radcliffe et al. (2016)
only stated an initial 20 sources, however this study invariably missed
detections because the majority of the annulus sub-fields were not included.
The derived peak brightnesses, flux densities and positions of our objects are
described in Table LABEL:Table:Source_catalog.

###  2.3 VLA observations

In addition to the EVN observations, archival L-band Karl. G. Jansky Very
Large Array (VLA) A-array data (P.I. F. Owen) were reduced to provide a zero-
spacing flux density for our VLBI sources and forms part of the eMERGE survey
data (Muxlow et al. in prep.). This section briefly describes the data
reduction process. The VLA observed the GOODS-N field between the 7th
August-11th September 2011 for a total of 38 hours, in the A-array
configuration. These data were flagged using the AOFlagger software (Offringa
et al., 2012) and calibrated using the VLA CASA calibration
pipeline555https://casa.nrao.edu (packaged with CASA version 4.3.1). These
data were transferred to AIPS and two sources (J123452+620236 and
J123538+621932) were peeled.

Due to the large fractional bandwidth ($\sim$68%) and large data size, postage
stamps centred on each VLBI detection were produced using the multi-term multi
frequency algorithm within CASA task tclean (Rau & Cornwell, 2011). These
images were primary beam corrected using the CASA routine widebandpbcor, which
also corrects for the induced spectral index caused by the varying primary
beam attenuation across the bandwidth. The resulting images have a r.m.s. of
$\sim 2\mbox{-}5\leavevmode\nobreak\ \mathrm{\mu Jy\,beam^{-1}}$ with a
restoring beam of $1.54\arcsec\times 1.34\arcsec$. Flux densities were
extracted using BLOBCAT (Hales et al., 2012) and we conservatively assign a
standard 10% surface brightness error originating from calibration.

##  3 EVN primary beam correction

For these observations, we used and developed one of first primary beam models
European VLBI Network (Keimpema et al. in prep.). We followed a similar
prescription to primary beam modelling as described in Strom (2004) and Cao et
al. (2014). Due to the lack of accurate primary beam models for many EVN
telescopes, the primary beam power response of each telescope can be
approximated by using a normalised, symmetric, 2D Gaussian of the form,

$P(\theta,\phi)\approx\exp\left(-{\frac{(\theta-\theta_{0})^{2}+(\phi-\phi_{0})^{2}}{2\sigma^{2}}}\right),$
(1)

where $P(\theta,\phi)$ is the relative primary beam power response. $\theta$
and $\phi$ are the respective azimuthal and polar angular distances from the
antennas’ pointing centres. The azimuthal and polar coordinates of the
telescope’s pointing centers are defined by $\theta_{0}$ and $\phi_{0}$
respectively. The standard deviation, $\sigma$, can be related to the FWHM of
the primary beam, $\theta_{1/2}$, through the expression,

$\sigma^{2}=\frac{\theta_{1/2}^{2}}{8\ln{2}},$ (2)

where the FWHM of the primary beam is defined as,

$\theta_{1/2}=K\frac{\lambda_{\mathrm{c}}}{D}.$ (3)

Here, $\lambda_{\mathrm{c}}$, is the observing wavelength, and $D$ is the
aperture diameter (Keimpema 2015, unpublished). A small correction factor,
$K=1.05$, was used to take into account any aperture blockages (Wrigley et
al., in prep.). For some telescopes (namely Effelsberg, Jodrell Bank and
Shenzhen in these observations) accurate beam models are available and
therefore replace $D/K$ in Eqn. 3 with the fitted HPBW of these telescopes. We
note that there are some uncertainties associated with the derived HPBW of
Jodrell Bank because this is derived from a modelled aperture distribution
rather than more accurate methods such as holographic scans (Wrigley, 2016).
The fitted aperture diameters are summarised in Table 1.

$P(\theta,\phi)^{-1/2}$, that is the inverse primary beam voltage response,
was calculated for each telescope at every time integration step, each
spectral window and each sub-field. These were recorded into an AIPS SN table
(one per sub-field) which were then be applied to the corresponding $uv$ data
set using AIPS task CLCAL. The application of this calibration table
multiplies the visibility amplitudes of each baseline by a correction factor
which is the inverse product of the primary beam voltage responses,
($P_{i}(\theta,\phi)^{-1/2}\times P_{j}(\theta,\phi)^{-1/2}$) of the two
telescopes $i,j$ that form the baseline. The application of this table also
adjusts the weights by the inverse of this correction factor. The simultaneous
adjustment of weights means this primary beam correction will also correctly
weight multiple pointings, thus permitting mosaicking using the EVN array.

We note that the use of a Gaussian model for our primary beam model implies
heavy tapering of EVN telescopes, however these telescopes were designed for
single dish observations so we would expect a large amount of tapering. In
addition, we tested multiple models (1D Gaussian, 2D Gaussian, Airy disk, and
a polynomial) when fitting to these beam models and found that differences
between the models are only significant towards the primary beam null and
these models are indistinguishable within the HPBW.

However, because of the lack of available primary beam models for many EVN
telescopes (most notably the Lovell telescope for this observation), there are
considerable uncertainties on the derived peak brightnesses and integrated
fluxes. Incorporating this model to include higher order corrections, such as
beam squint and more physically motivated models would be simple.
Nevertheless, if we are to significantly improve EVN primary beam correction,
beam measurements for all individual EVN stations are required, because
uncertainties towards the edge of the primary beam are dominated by the lack
of information on the primary beams’ HPBWs.

As a result of this, sub-fields which lie outside the central 7.′5 radius
area were not primary beam corrected because, the Effelsberg and Lovell
telescope corrections are beyond the FWHM of the Gaussian models derived, and
errors due to incorrect beam models will rapidly increase. Figure 2 shows the
r.m.s. sensitivity of our observations after primary beam correction using
natural weighting. The central r.m.s. is approximately 9 $\mathrm{\mu
Jy\,beam^{-1}}$.

We note that this primary beam correction is constantly under-development and
will be updated with the latest EVN beam models. The code is publicly
available and can be found at https://github.com/jradcliffe5/EVN_pbcor.

##  4 Catalogue description

Figure 4: Redshift distribution for our detected VLBI sources. There are 20
spectroscopic redshifts (dark grey) and 11 photometric redshifts (light grey)
for these objects. The over-density of sources at $z\sim 2$ are briefly
discussed in Section 5.1. Optimal bin widths were calculated using the
prescription in Knuth (2006).

In this section we describe the VLBI catalogue of 31 compact radio sources
which accompanies this paper (see Tables LABEL:Table:Source_catalog and
LABEL:Table:Derived_properties). The designated column numbers correspond to
the associated machine-readable version of the catalogue. The column
descriptors are as follows:

  1. Col. 1:

Source ID. Radio name adopted in this paper which is of the form
Jhhmmss+ddmmss based upon the J2000 Right Ascension (in hours) and Declination
(in degrees). Note that some source identifiers are slightly different to that
of Morrison et al. (2010) because of the improved astrometric accuracy.

  2. 2-4:

z. The redshifts for the 31 VLBI detected sources can be found in Column 2.
The 68% lower and upper confidence intervals are in Columns 3-4. A description
of how these redshifts were compiled can be found in Section 5.1.

  3. 5,6:

z type/ref. Column 5 describes how these redshifts were determined.
Spectroscopic redshifts are denoted with ‘S’ in the $z$ type column while
photometric redshifts are denoted with ‘P’. Column 6 contains the reference
for which the redshift was acquired

  4. 7:

R.A. (J2000) Right Ascension (J2000) in hours with the format hh:mm:ss.ssss.

  5. 8:

Dec. (J2000) Declination (J2000) in degrees with the format dd:mm:ss.sss.

  6. 9-10:

VLBI $P$. Peak brightness (Column 9) and associated error in
$\mu\mathrm{Jy\,beam^{-1}}$ (Column 10). This is determined using the flood-
filling algorithm BLOBCAT (Hales et al., 2012). Errors derive from source
fitting, calibration, and primary beam correction. Peak brightnesses of those
sources without primary beam correction are merely lower limits (denoted by
-99.0 in the error column in the machine-readable table).

  7. 11-12:

VLBI $I$. Integrated flux density (Column 11) and associated error in
$\mu\mathrm{Jy}$ (Column 12). This is determined when deriving the peak
brightness. Errors originate from source fitting, calibration, and primary
beam correction. Integrated flux densities of those sources without primary
beam correction are merely lower limits (denoted by -99.0 in the error column
in the machine-readable table).

  8. 13:

S/N. Signal-to-noise ratio.

  9. 14-16:

Beam. Major axes (Column 14), minor axes (Column 15) and position angle
(Column 16) of the CLEAN restoring beam in milliarcseconds. The two restoring
beams of $\sim 16\times 16$ mas and $\sim 5.3\times 4.5$ mas correspond to
natural weighting and uniform weighting schemes respectively. The VLBI peak
brightnesses and integrated flux densities presented in Columns 9-10 and 11-12
respectively have been derived using the beam sizes specified in these
columns.

  10. 17-18:

VLA $P$. Peak brightness (Column 17) and associated errors (Column 18) of the
1.5 GHz VLA observations described in Section 2.3. Errors are determined from
calibration ($\sim 10\%$) and source fitting.

  11. 19-20:

VLA $I$. Integrated flux density (Column 19) and associated errors (Column 20)
of the 1.5 GHz VLA observations. Errors originate from calibration ($\sim
10\%$) and source fitting.

  12. 21:

$\alpha$. Spectral index between the 5.5 GHz VLA observations of Guidetti et
al. (2017) and 1.5 GHz VLA observations presented in this paper.

  13. 22-23:

$L_{\mathrm{1.5GHz}}$. Monochromatic rest-frame radio luminosity in $\rm
W\,Hz^{-1}$ (Column 22) and its associated error (Column 23). Values were
derived using the 1.5 GHz VLA integrated flux densities and k-corrected using
the spectral index. Associated errors originate primarily from those sources
with photometric redshift errors. The median spectral index of $-0.56$ were
used to determine the radio luminosities of sources without spectral index
information.

  14. 24-26:

$T_{b}$. Brightness temperatures, in $\rm K$, calculated using Eqn. 5 (Column
24). Column 25 is a flag to denote lower limits (set as 1 in machine readable
version to denote lower limits) and Column 26 corresponds to whether the
brightness temperature was calculated using uniform or natural weighting. This
is denoted as U or N respectively in the machine-readable table and in Table
LABEL:Table:Derived_properties brightness temperatures derived using natural
weighting are italicised. See Section 5.4.3 for further details.

  15. 27-30:

Angular sizes. Columns 27 and 29 describe the major and minor axes of the
deconvolved projected angular size of the VLBI source in milliarcseconds.
Columns 28 and 30 contain flags to denote upper limits (hence unresolved
source sizes) for the major and minor axes respectively (set as 1 in machine
readable version to denote upper limits). Sizes were fitted using PYBDSF
(Mohan & Rafferty, 2015) and see Section 5.4.3 for further details.

  16. 31-34:

Linear size. Columns 31 and 33 describe the major and minor axes of the
deconvolved projected linear size of the VLBI source in parsecs and Columns 32
and 34 contain flags to denote upper limits for the major and minor axes
respectively (set as 1 in machine readable version to denote upper limits).

##  5 Results and discussion

###  5.1 Redshifts

The VLBI positions were matched to the many spectroscopic and photometric
catalogues to within a radius of one arc-second from the VLBI position. In
order to prevent mis-identifications potential matches were visually compared
to the HST optical/near-IR images of Skelton et al. (2014) to ensure the
correct redshift is assigned. Redshift information was found for all 31
objects. This comprises of 20 spectroscopic redshifts (Cowie et al., 2004;
Smail et al., 2004; Chapman et al., 2005; Barger et al., 2008; Murphy et al.,
2017, L. Cowie priv. comm.) and and 11 photometric redshifts (Skelton et al.,
2014; Yang et al., 2014; Cowie et al., 2017). The redshift distribution is
shown in Figure 4. The median redshift is 1.146 and ranges from 0.11 to 3.44.

The redshift distribution shows an abundance of sources around $\sim 2$ which
could be an imprint from the previously identified $z=1.99$ proto-cluster in
GOODS-N (Blain et al., 2004; Chapman et al., 2009). This proto-cluster has
approximate redshift bounds of $1.982<z<2.010$, and two VLBI sources
(J123618+625541 and J123621+621708) are associated this proto-cluster (Casey,
2016). It is expected that this structure is extended spatially beyond the
limited field-of-view of the GOODS-N survey as the deep spectra does not
extend much outside of the HST coverage. It has been suggested that
J123642+621331 ($z=2.018$) could also member of this proto-cluster (Murphy et
al., 2017), and it is also possible that J123721+621130 ($z=2.02$) could be
associated, however an accurate spectroscopic redshift would need to be
acquired. This raises possibility that, with deep VLBI surveys and improved
number densities of sources, over-densities of VLBI-detected AGN could act as
a tracer of proto-clusters for which there is evidence of enhanced AGN
activity in multiple wavebands including the radio (e.g. Wylezalek et al.,
2013; Krishnan et al., 2017).

###  5.2 Astrometry

In order to check the astrometry of these observations, we compared these VLBI
observations to the MERLIN-VLA observations from Muxlow et al. (2005),
hereafter M05), and the reprocessed wide-field images of the same data by
Wrigley (2016). The positions were not compared to the global VLBI
observations of Chi et al. (2013) due to the known positional uncertainty on
the phase calibrator used in those observations (see Appendix A), plus there
is a larger number of concordant sources between these EVN observations and
M05. Due to computational limitations at the time, M05 targeted 92 radio
sources within a $10\arcmin\times 10\arcmin$ square field with VLA-only flux
densities $>40\leavevmode\nobreak\ \mathrm{\mu Jy}$ in the HDF-N field to a
central r.m.s. of $3.3\mathrm{\mu Jy\,beam^{-1}}$.

These data were re-processed by (Wrigley, 2016) and a primary beam corrected
$18\arcmin\times 16\arcmin$ image was used for the subsequent analyses. We
used BLOBCAT (with a detection threshold of 6$\sigma$) to generate a catalogue
of 155 MERLIN-VLA detected sources (with a restoring beam of 0.2″). These were
then cross matched with the EVN positions to within 1 arcsecond. A total of
25/31 sources were matched to an MERLIN-VLA detected source with the remaining
unmatched sources beyond the sky area considered by Wrigley (2016). We
estimate a conservative 5 mas error for the astrometry of these new
observations, due to uncertainties on the position of the secondary phase
calibrator J1234+619, and a 10 mas error on the VLA-MERLIN data arising from
calibration and source fitting errors.

As Figure 5 shows, there is a small systematic offset of 5.5 mas in RA and 0.4
mas in Dec. Note that all sources apart from wide-angle tail FR-I source,
J123726+621129, are within 60 mas of the MERLIN-VLA positions. This source was
excluded from the derivation of the systematic astrometric offset and Figure
5. The systematic offsets can originate from core-jet blending of the radio
emission, standard errors associated with source fitting and calibration, and
also errors originating from repeated use of the AIPS task UVFIX when peeling
bright sources from the VLA-MERLIN data (e.g. see Morgan et al., 2011). The
astrometric scatter is expected to be dominated by blending in the MERLIN-VLA
data as substructure such as AGN jets will blend with AGN core emission thus
causing an offset in position of peak brightness. These errors should have
orientations which are randomly distributed, hence the median 5 mas astrometry
offset indicates that we are in fairly good agreement with the MERLIN-VLA
positions.

Figure 5: Relative astrometric precision between Muxlow et al. (2005) and
these observations. The blue dashed line is the mean RA and Dec shifts
corresponding to 5.5 and -0.4 milliarcseconds respectively. The black dot-
dashed line corresponds to $\Delta$RA=0 and $\Delta$Dec=0. The red cross
indicates the typical error per data point (which does not include core-jet
blending uncertainties).

###  5.3 Comparison to other VLBI surveys

As previously stated, the GOODS-N field has been targeted by two previous
wide-field VLBI surveys by Garrett et al. (2001) and Chi et al. (2013). It is
worth noting that surveys had restricted field-of-views which are encompassed
by the field-of-view of these new EVN observations, therefore we would expect
that we should be able to detect all previous identified sources. This survey
recovers 11/12 of the Chi et al. (2013) detections and all three of the
Garrett et al. (2001) detections. The missing source, J123642+621545,
illustrates significant radio variability and has an e-MERLIN integrated flux
density of only 60 $\mu$Jy during the period of these observations, whereas
Chi et al. (2013) detects an integrated flux density of 343 $\mu$Jy.

We compared our results with other wide-field VLBI surveys to ensure that our
observations and detection fractions are consistent. In order to calculate the
detection fraction, we used the VLA-A array observations provided by Morrison
et al. (2010) and cross-matched these with to our VLBI survey. For this
analysis, we only consider the central area where we have contiguous imaging
and where our primary beam model is most reliable. Within this region, our EVN
data were used to image the locations of the 314 VLA sources. Of these
sources, 94 were theoretically detectable assuming that they are unresolved on
VLBI angular scales with a flux density greater than our 6$\sigma$ VLBI
detection threshold (based upon the VLBI r.m.s. noise distribution, as shown
in Fig. 2). Of this sample 24 sources were detected with VLBI, thus giving a
detection threshold of $25.5$$\begin{subarray}{c}+5\\\ -4\end{subarray}$%
(24/94). Errors were determined using the Bayesian binomial estimator of
Cameron (2011). This is consistent with previous wide-field VLBI surveys. For
example, the Chandra Deep Field-South ($55\leavevmode\nobreak\ \mu$Jy beam-1
r.m.s., Middelberg et al., 2011) has a detection fraction of
$20\begin{subarray}{c}+5\\\ -4\end{subarray}\%$, the Lockman Hole/XMM
($24\leavevmode\nobreak\ \mu$Jy beam-1 r.m.s., Middelberg et al., 2013b)
detects $30\pm 3\%$ and the COSMOS survey ($10\leavevmode\nobreak\ \mu$Jy
beam-1 r.m.s., Herrera Ruiz et al., 2017) detects $20\pm 1\%$. The mJIVE
survey has a detection fraction of $20\pm 1\%$ to a an r.m.s. of $60\mu$Jy
beam-1 (Deller & Middelberg, 2014).

Note that there are some caveats because our VLBI sample is surface brightness
limited due to the resolution and flux sensitivity of our EVN observations.
For the fainter sources in our targeted sample (e.g. $S_{\rm VLBI}$
$\lesssim$100 $\mu$Jy), we can only detect those VLA sources with relatively
large VLBI-VLA flux density ratios. For example, as the median flux density
ratio is ~0.6 for this sample (see Section 5.4.1), most VLA sources with
integrated flux densities $\lesssim$ 100 $\mu$Jy will go undetected. This
motivates deeper VLBI observations in the future as the improved r.m.s. noise
levels will recover these sources.

###  5.4 Radio properties of the VLBI selected population

####  5.4.1 VLBI-VLA flux densities

We compared the 1.5 GHz VLA flux densities to our 1.6 GHz EVN observations in
order to investigate the origin of the radio emission. To do this we can use
the VLBI to VLA flux density ratio ($R$) to establish whether a source is
dominated by milliarcsecond-scale emission from AGN cores or arc-second scale
emission from AGN jets/lobes or star-formation related processes. Note that
for this comparison, we only use the VLBI sources which have been primary beam
corrected (24/31). As both the VLBI and VLA observations have complete 24hr
$uv$ coverage, we use the integrated flux density measurements to define the
VLA-VLBI flux density ratio ($R\equiv S_{\rm i,VLBI}/{S_{\rm i,VLA}}$).

We find that the 18/24 (66.7%) VLBI sources have over 50% of their radio
emission originating from a milli-arcsecond scale component. 2/24 (8%) has
$R>1$ which is most likely due to AGN variability because the observation
times of VLA (2011) and VLBI (2014) data vary by a few years. Excluding the
two known variable sources with $R>1$, we find that the median VLBI-VLA ratio
of our observations is 0.625. This is largely in agreement with the COSMOS
VLBI survey which find a median VLBI-VLA ratio of 0.6 (Herrera Ruiz et al.,
2017). We note that, at low flux densities, our VLBI observations are expected
to preferentially detect core-dominated systems, with the majority of VLA
arcsecond-scale emission confined to a high brightness temperature core which
is detectable by VLBI observations. This is consistent as only a small
fraction ($\sim 10\%$) of our VLBI-detected sources exhibit large-scale radio
jets or lobes, while the remaining sources are compact.

An evolution towards more core-dominated systems as we approach $\mathrm{\mu
Jy}$ flux densities has been hinted at in other VLBI surveys, most notably the
mJIVE-20 and COSMOS VLBI surveys (Deller & Middelberg, 2014; Herrera Ruiz et
al., 2017). There is some evidence that suggests that this evolution may be
true. It has been shown that a population of radio sources with core fraction
of $\sim$0.3 below a 1.4 GHz luminosity of $10^{25}\leavevmode\nobreak\
\mathrm{W\,Hz^{-1}}$ are required by empirical simulations in order to
accurately extrapolate the established populations from low-frequency ($<5$
GHz) surveys to the $>$ 10 GHz source populations (Whittam et al., 2017). This
could be equivalent to the postulated population of ‘FR0’ sources in the local
universe which have core dominated, compact radio emission extending to at
most just 3 kpc (Baldi et al., 2015). These wide-field VLBI surveys could be
beginning to detect the high-$z$ analogues to this population of radio
sources.

####  5.4.2 Luminosities

Figure 6: Radio power vs. redshift for our VLBI sources. 1$\sigma$
uncertainties on radio power and redshifts are plotted. The bold black curve
represents the theoretical radio power that these VLBI observations are
sensitive to (assuming all the VLA flux is contained in a milliarcsecond core)
corresponding to 54${\,\rm\mu Jy\,beam^{-1}}$ or $6\leavevmode\nobreak\
\times$ VLBI central r.m.s. The region above the blue shaded area represents
the AGN dominated regime defined using the selection criteria of Magliocchetti
et al. (2018). The histogram shows the distribution of the radio powers of
which peak between $10^{24}$ and $10^{25}$ ${\rm W\,Hz^{-1}}$.

The radio luminosity of an object can be used to determine the probability
that the radio emission of a source is dominated by AGN activity or star-
formation. The monochromatic 1.5 GHz radio power can be calculated using:

$L_{\mathrm{1.5GHz}}=\frac{4\pi d_{L}^{2}}{(1+z)^{1+\alpha}}S_{\mathrm{obs}},$
(4)

where $\alpha$ is the source spectral index, $z$ is the redshift, $d_{L}$ is
the luminosity distance and $S_{\mathrm{obs}}$ is the measured source flux
density (ideally, the zero spacing flux density). Integrated flux densities
for all 31 sources were derived using the VLA-A array data outlined in Section
2.3. Spectral indices for 24/31 sources were derived using the 5.5 GHz
integrated flux densities from the VLA 5.5 GHz survey of Guidetti et al.
(2017). For the seven remaining sources, we used the median spectral index of
$-0.56$ from the sources with 5.5 GHz detections, but we note in passing that
these redshift based k-corrections only contribute a small factor to the
resulting luminosities. As Figure 6 shows, we sample a large range of radio
powers from $\sim 10^{22}\mbox{-}10^{26}\leavevmode\nobreak\
\mathrm{W\,Hz^{-1}}$ which have a median luminosity of $2.7\times
10^{24}\leavevmode\nobreak\ \mathrm{W\,Hz^{-1}}$.

As expected, in the low redshift range ($0<z<1$), we detect lower luminosity
AGN of the order $10^{22}\mbox{-}10^{24}\leavevmode\nobreak\
\mathrm{W\,Hz^{-1}}$ which is typical of objects such as Seyfert galaxies.
Higher luminosity sources are not detected at low redshift due to the
combination of a low density of high power sources plus a smaller cosmic
volume surveyed due to the restricted field-of-view. At higher redshifts,
these observations preferentially detect higher luminosity objects of the
order $10^{24}\mbox{-}10^{26}\mathrm{W\,Hz^{-1}}$ which is a consequence of
the sensitivity (illustrated by the VLBI sensitivity limit plotted in Fig. 6).
This corresponds to radio-loud AGN systems such as FR-I, radio galaxies and
quasars (Owen & Ledlow, 1994; Smolčić et al., 2017). Only three of these
sources are lobe-dominated (J123644+621133, J123726+621128 and J123636+615659)
with extended morphologies in the lower resolution VLA data while the
remaining objects are core dominated, with any jets unresolved or of low
luminosity undetectable by the VLA.

We used the selection criteria of Magliocchetti et al. (2018) to illustrate
the radio populations that this survey is probing. Their criteria defines the
crossover point, $P_{\mathrm{cross}}$, as where AGN related emission is
dominant over star-formation related emission in a radio-selected population.
At $z\leq 1.8$, their selection is based upon the radio luminosity functions
of McAlpine et al. (2013). In this regime, $P_{\mathrm{cross}}$ approximately
scales with redshift as $10^{\log_{10}(P_{0,\mathrm{cross}})+z}$ where
$P_{0,\mathrm{cross}}=10^{21.7}\,\mathrm{W\,Hz^{-1}\,sr^{-1}}$ which is the
crossover point from the local universe. Above $z=1.8$, the radio luminosity
function for star forming galaxies drops off rapidly and $P_{\mathrm{cross}}$
is kept constant at $10^{23.5}\,\mathrm{W\,Hz^{-1}\,sr^{-1}}$. This selection
criteria was found to keep contaminants from star-forming galaxies to below
10% at $z>1.8$ (see Appendix of Magliocchetti et al., 2018).

As Figure 6 shows, these VLBI observations clearly probe the AGN dominated
regime with all radio luminosities at least $3\times P_{\mathrm{cross}}$. For
VLBI surveys to truly detect statistically significant samples of hybrid
systems with both AGN and star-formation related emission, and provide
valuable information regarding feedback, either ultra-wide surveys should be
used to probe the tail of star-forming galaxies within the AGN dominated
luminosity regime (e.g. Herrera Ruiz et al. (2016) investigated radio-quiet
AGN using the 2 square degree VLBA survey of COSMOS), or ultra-deep surveys
should to used to probe the star-formation dominated luminosity regime which
is potentially achievable using the EVN and SKA-VLBI. Nevertheless, we
undoubtedly have uncovered hybrid AGN-starburst systems, as we will show in
Paper II.

####  5.4.3 Brightness temperatures

Figure 7: Brightness temperature distribution with respect to redshift. The
black circles and red squares correspond to those sources detected with a
$\sim 5.3\times 4.5$ mas restoring beam and those detected with a $\sim
16\times 16$ mas beam respectively. Arrows correspond to the lower limits for
sources classified as unresolved (that is either $\theta_{\mathrm{maj}}$ or
$\theta_{\mathrm{min}}$ is less than the minimum resolvable size). The
histogram shows the distribution of brightness temperatures which is colour
coded with the markers. The majority of brightness temperatures are between
$10^{6}$ and $10^{8}$ K.

Brightness temperatures were calculated for the VLBI detected objects which
were primary beam corrected (24/31). For these measurements, we used PYBDSF
(Mohan & Rafferty, 2015) to fit an elliptical Gaussian model to each source.
We adopted a different selection criterion compared to our detection
methodology. In this criterion, referred to as the size measurement detection
threshold, sources would be excluded if their S/N ratio were less than ten.
This S/N cut-off was chosen because, when using randomly distributed model
sources injected onto a noise field from our VLBI data, PYBDSF does not detect
all of the injected sources when their $\mathrm{S/N}<10$. In addition, below
this threshold, the variance of fitted sizes is often larger than 20% of the
full-width half-maximum of the psf.

As we are concerned with only compact emission, we attempted to exclude
emission from radio jets or compact star formation by fitting to the uniformly
weighted images (with a restoring beam $\sim 5.3\times 4.5$ mas) if possible.
If the S/N of the uniformly weighted image was less than 10, then the
naturally weighted images (with restoring beam $\sim 16\times 16$ mas) would
be used to calculate the brightness temperatures. Sources with $S/N<10$ in
both weighting regimes would be excluded completely. Using this selection
criteria, 18 sources were selected, 9 using uniform weighting and 9 with
natural weighting.

For the calculation, we assume the brightness temperature distribution of a
source at redshift $z$ is can be modelled as an elliptical Gaussian radio
emission region with major axis $\theta_{\mathrm{maj}}$, minor axis,
$\theta_{\mathrm{min}}$, and position angle of the major axis $\phi$. Here in
our case, $\theta_{\mathrm{maj}}$, $\theta_{\mathrm{min}}$ and $\phi$ are the
deconvolved major and minor axes and their position angle of the deconvolved
elliptical Gaussian model. The brightness temperature, $T_{b}$ can then
approximated using,

$T_{b}=1.22\times
10^{12}(1+z)\left(\frac{S_{\mathrm{\nu}}}{1\mathrm{Jy}}\right)\left(\frac{\nu}{1\mathrm{GHz}}\right)^{-2}\left(\frac{\theta_{\mathrm{maj}}\theta_{\mathrm{min}}}{1\mathrm{mas}^{2}}\right)^{-1}\leavevmode\nobreak\
\mathrm{K},$ (5)

where $S_{\mathrm{\nu}}$ is the observed flux density and $\nu$ is the
observing frequency (Condon et al., 1982; Ulvestad et al., 2005). In addition,
we took into account the resolution limit for both $\theta_{\mathrm{maj}}$ and
$\theta_{\mathrm{min}}$ using the prescription described in Lobanov (2005).
The following expression for the minimum resolvable size,
$\theta_{\mathrm{lim},\psi}$, along each axes of the fitted Gaussian can be
calculated using the following equation,

$\theta_{\mathrm{lim},\psi}=2^{2-\beta/2}b_{\psi}\left[\frac{\ln(2)}{\pi}\ln{\left(\frac{\mathrm{S/N}}{\mathrm{S/N}-1}\right)}\right]^{1/2},$
(6)

where $b_{\psi}$ is the measured FWHM of the psf along the direction of the
axis for which the resolution limit is being calculated. S/N is the signal to
noise of the image and $\beta$ is a constant that takes into account the
weighting of the visibilities ($\beta=0$ for uniform weighting and $\beta=2$
for natural weighting). If $\theta_{\mathrm{maj}}$ or $\theta_{\mathrm{min}}$
were lower than the corresponding minimum resolvable size along each axes,
then $\theta_{\mathrm{lim},\psi}$ was used instead to calculate the source
frame brightness temperature. A source is classified as unresolved if either
axes was below the minimum resolution limit. In this case, the size of the
radio emitting region cannot be constrained and only lower limits to the
brightness temperature can be derived.

Figure 7 shows the brightness temperature distribution of our VLBI selected
sources. Lower limits are derived for those sources which are unresolved or
are unresolved in one axis. Sources detected with a 5.3$\times$4.5 mas
restoring beam have brightness temperatures of the order
$10^{7}\mbox{-}10^{9}$ K and, as expected, sources detected with only a
16$\times$16 mas restoring beam have lower brightness temperatures in the
range ($10^{5}\mbox{-}10^{6}$ K). In both weighting regimes, it is highly
unlikely that the radio emission is caused by star-formation related processes
as typical star-burst galaxies exhibit brightness temperatures of
$<10^{5}\mathrm{K}$ (Condon et al., 1991).

Note that the majority of the uniformly weighted sources (8/9) are unresolved,
hence emission in these objects come from a compact component. In the
naturally weighted sources, all of these are classified as resolved. This is
most likely caused by the improved surface brightness sensitivity as a result
of the increased weighting of the sensitive, but crucially shorter, central
European baselines (especially the Effelsberg to Lovell baseline). As the
uniformly weighted images have approximately 1.5 $\times$ the noise of the
naturally weighted images, sources detected in natural weighting will most
likely have a compact component with higher brightness temperatures, however
this component is currently below the size measurement detection threshold (10
$\sigma$) with uniform weighting. Indeed 6/9 sources do have a compact
component in the uniformly weighted images which is above the source detection
threshold of 6$\sigma$. The remaining three sources do not have a compact
component above $6\sigma$ indicating that some flux may be resolved between
the two weighting schemes.

##  6 Conclusions

We present a catalogue of 31 faint VLBI detected sources in GOODS-N to
~$9\leavevmode\nobreak\ \mu{\rm Jy\,beam^{-1}}$ 1$\sigma$ r.m.s. noise levels
and radio luminosities of the order $10^{22}\leavevmode\nobreak\ {\rm
W\,Hz^{-1}}$. This has substantially increased the number of VLBI detected
sources over previous GOODS-N surveys by Chi et al. (2013) and Garrett et al.
(2001), providing a valuable addition to the understanding of the AGN content
in this well studied field. We also present a primary beam correction scheme
developed for the European VLBI Network. This is publicly available and will
be constantly updated.

Additional ancillary information about the radio properties of these objects
were derived using VLA 1.5 and 5 GHz data. The detected objects have radio
luminosities of the order $10^{22}\mbox{-}10^{26}\leavevmode\nobreak\ {\rm
W\,Hz^{-1}}$ and brightness temperatures in the range
$10^{6}\mbox{-}10^{9}\leavevmode\nobreak\ {\rm K}$. The high fraction of
compact emission (as defined by the VLBI/VLA flux density ratio) may be
hinting at the existence of radio-loud but core-dominated systems at high
redshift which may be equivalent to the population of FR0 objects in the local
universe (Baldi et al., 2015, 2018).

With previous VLBI surveys effectively characterising the $>$50 $\rm\mu Jy$
radio sky, the scheduled 48 hours of remaining observations will enable us to
reach limiting r.m.s. sensitivities of $\sim 2\leavevmode\nobreak\ {\rm\mu
Jy\,beam^{-1}}$, thus providing the next step in analysing the faint radio-
selected AGN population in GOODS-N. The final data release will be able to
test whether the increasing fraction of star-forming galaxies at these low
flux densities are influenced by AGN activity as postulated in lower
resolution surveys. This will be presented in a future publication. In
addition, the last 24 hours of these observations will include the first ever
wide-field VLBI observations using an integrated EVN-eMERLIN array, providing
valuable surface brightness sensitivity improvements with the addition of
intermediate length baselines.

1]

Table 2: 1.6 GHz VLBI and 1.5 GHz VLA properties of the VLBI detected sources Source ID | $z$ |  $z$ typecc$c$S: spectroscopic redshift, P: photometric redshift./ref | R.A. (J2000) | Dec. (J2000) | VLBI $P$ | VLBI $I$ | S/N | Beam | VLA $P$ | VLA $I$
---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  | [$\rm\mu Jy\,beam^{-1}$] | [$\rm\mu Jy$] |  | [mas$\times$mas (deg)] | [$\rm\mu Jy\,beam^{-1}$] | [$\rm\mu Jy$]
(1) | (2-4) | (5,6) | (7) | (8) | (9,10) | (11,12) | (13) | (14-16) | (17,18) | (19,20)
J123555+620902aa$a$Sources detected using naturally weighted taper (UVWTFN=‘NA’ in AIPS task IMAGR) | 1.8750 | Sdd$d$Barger et al. (2008) | 12:35:55.1267 | +62:09:01.738 | 100.0$\pm$18.2 | 100.0$\pm$18.2 | 7.4 | 16.0$\times$15.2 (87.1) | 165$\pm$17 | 192$\pm$19
J123607+620951 | 0.6380 | Sdd$d$Barger et al. (2008) | 12:36:06.6120 | +62:09:51.159 | 118.0$\pm$22.8 | 118.0$\pm$21.2 | 6.1 | 5.3$\times$4.6 (3.0) | 169$\pm$17 | 205$\pm$21
J123608+621036aa$a$Sources detected using naturally weighted taper (UVWTFN=‘NA’ in AIPS task IMAGR) | 0.6790 | Sdd$d$Barger et al. (2008) | 12:36:08.1193 | +62:10:35.906 | 122.0$\pm$16.8 | 140.0$\pm$18.2 | 11.1 | 16.0$\times$15.4 (86.8) | 202$\pm$20 | 236$\pm$24
J123618+621541 | 1.9930 | See$e$Smail et al. (2004) | 12:36:17.5546 | +62:15:40.765 | 177.0$\pm$25.0 | 192.0$\pm$26.0 | 10.1 | 5.4$\times$4.6 (10.6) | 226$\pm$23 | 275$\pm$28
J123620+620844 | 1.0164 | Sdd$d$Barger et al. (2008) | 12:36:20.2620 | +62:08:44.268 | 185.0$\pm$25.8 | 185.0$\pm$24.0 | 10.3 | 5.3$\times$4.6 (3.3) | 141$\pm$14 | 156$\pm$16
J123621+621708aa$a$Sources detected using naturally weighted taper (UVWTFN=‘NA’ in AIPS task IMAGR) | 1.9920 | Sff$f$Chapman et al. (2005) | 12:36:21.2684 | +62:17:08.459 | 96.5$\pm$14.5 | 135.0$\pm$17.3 | 8.9 | 15.6$\times$15.3 (-8.2) | 138$\pm$14 | 190$\pm$19
J123623+620654aa$a$Sources detected using naturally weighted taper (UVWTFN=‘NA’ in AIPS task IMAGR) | $1.94\begin{subarray}{c}+0.12\\\ -0.12\end{subarray}$ | Pgg$g$Skelton et al. (2014) | 12:36:22.5086 | +62:06:53.844 | 114.0$\pm$19.0 | 144.0$\pm$21.4 | 8.2 | 16.1$\times$15.3 (86.3) | 222$\pm$22 | 249$\pm$25
J123624+621643 | 1.9180 | See$e$Smail et al. (2004) | 12:36:23.5437 | +62:16:42.746 | 222.0$\pm$28.2 | 383.0$\pm$42.0 | 12.8 | 5.4$\times$4.5 (10.6) | 384$\pm$39 | 411$\pm$41
J123641+621833 | 1.1456 | Sdd$d$Barger et al. (2008) | 12:36:40.5661 | +62:18:33.081 | 141.0$\pm$26.3 | 141.0$\pm$25.7 | 7.5 | 5.3$\times$4.5 (9.4) | 293$\pm$30 | 302$\pm$30
J123642+621331 | 2.0180 | Shh$h$Murphy et al. (2017) | 12:36:42.0899 | +62:13:31.428 | 97.4$\pm$18.0 | 233.0$\pm$27.9 | 6.5 | 5.4$\times$4.5 (12.6) | 432$\pm$44 | 477$\pm$48
J123644+621133 | 1.0128 | Sdd$d$Barger et al. (2008) | 12:36:44.3860 | +62:11:33.170 | 410.0$\pm$44.8 | 411.0$\pm$44.7 | 25.9 | 5.3$\times$4.5 (11.4) | 737$\pm$74 | 1710$\pm$171
J123646+621405 | 0.9610 | Sdd$d$Barger et al. (2008) | 12:36:46.3307 | +62:14:04.692 | 191.0$\pm$24.9 | 192.0$\pm$24.8 | 12.3 | 5.4$\times$4.5 (12.7) | 260$\pm$26 | 280$\pm$28
J123650+620738aa$a$Sources detected using naturally weighted taper (UVWTFN=‘NA’ in AIPS task IMAGR) | 1.6095 | Sdd$d$Barger et al. (2008) | 12:36:49.6399 | +62:07:37.844 | 77.3$\pm$17.3 | 98.7$\pm$19.9 | 6.5 | 15.4$\times$14.8 (80.9) | 267$\pm$27 | 301$\pm$30
J123653+621444aa$a$Sources detected using naturally weighted taper (UVWTFN=‘NA’ in AIPS task IMAGR) | 0.3208 | Sdd$d$Barger et al. (2008) | 12:36:52.8827 | +62:14:44.069 | 109.0$\pm$15.1 | 117.0$\pm$15.6 | 11.0 | 14.8$\times$14.7 (9.6) | 188$\pm$19 | 215$\pm$22
J123659+621833 | $2.17\begin{subarray}{c}+0.08\\\ -0.07\end{subarray}$ | Pgg$g$Skelton et al. (2014) | 12:36:59.3327 | +62:18:32.566 | 2530.0$\pm$328.9 | 4430.0$\pm$572.7 | 88.2 | 5.3$\times$4.5 (8.5) | 4250$\pm$427 | 4640$\pm$464
J123700+620910 | $2.58\begin{subarray}{c}+0.07\\\ -0.06\end{subarray}$ | Pgg$g$Skelton et al. (2014) | 12:37:00.2460 | +62:09:09.779 | 153.0$\pm$23.4 | 163.0$\pm$24.1 | 9.4 | 5.3$\times$4.5 (8.0) | 272$\pm$27 | 319$\pm$32
J123709+620838 | 0.9070 | Sll$l$Cowie et al. (2004) | 12:37:09.4300 | +62:08:37.587 | 125.0$\pm$21.4 | 127.0$\pm$21.5 | 7.3 | 5.3$\times$4.5 (6.4) | 155$\pm$16 | 163$\pm$16
J123714+621826 |  $3.44$mm$m$Unknown photometric error, conservatively set to $\pm 0.5$ in calculations of derived properties | Pii$i$Cowie et al. (2017) | 12:37:13.8694 | +62:18:26.301 | 501.0$\pm$56.8 | 629.0$\pm$69.4 | 25.6 | 5.3$\times$4.6 (6.9) | 575$\pm$58 | 637$\pm$64
J123715+620823 | 0.9335 | Sjj$j$Cowie priv. comm. | 12:37:14.9391 | +62:08:23.223 | 2680.0$\pm$272.9 | 2810.0$\pm$284.0 | 103.0 | 5.3$\times$4.6 (5.4) | 1940$\pm$195 | 2090$\pm$209
J123716+621512 | 0.5605 | Sdd$d$Barger et al. (2008) | 12:37:16.3730 | +62:15:12.343 | 125.0$\pm$20.3 | 125.0$\pm$19.7 | 7.9 | 5.4$\times$4.6 (9.9) | 165$\pm$17 | 178$\pm$18
J123717+621733 | 1.1460 | Sdd$d$Barger et al. (2008) | 12:37:16.6800 | +62:17:33.310 | 150.0$\pm$23.8 | 269.0$\pm$32.7 | 8.2 | 5.4$\times$4.6 (7.5) | 308$\pm$31 | 356$\pm$36
J123720+620741aa$a$Sources detected using naturally weighted taper (UVWTFN=‘NA’ in AIPS task IMAGR) | $0.91\begin{subarray}{c}+0.05\\\ -0.03\end{subarray}$ | Pkk$k$Yang et al. (2014) | 12:37:20.0139 | +62:07:41.410 | 94.8$\pm$14.6 | 112.0$\pm$15.8 | 8.8 | 15.9$\times$15.4 (67.2) | 122$\pm$13 | 132$\pm$13
J123721+621130 | $2.02\begin{subarray}{c}+0.06\\\ -0.06\end{subarray}$ | Pgg$g$Skelton et al. (2014) | 12:37:21.2517 | +62:11:29.961 | 328.0$\pm$38.3 | 364.0$\pm$41.6 | 20.2 | 5.3$\times$4.5 (8.8) | 338$\pm$34 | 385$\pm$39
J123726+621129aa$a$Sources detected using naturally weighted taper (UVWTFN=‘NA’ in AIPS task IMAGR) | 0.9430 | Sjj$j$Cowie priv. comm. | 12:37:25.9475 | +62:11:28.699 | 124.0$\pm$16.7 | 142.0$\pm$18.2 | 12.2 | 15.4$\times$15.1 (52.6) | 1190$\pm$120 | 5210$\pm$521
J123649+620439bb$b$Not primary beam corrected. | 0.1130 | Sdd$d$Barger et al. (2008) | 12:36:48.9965 | +62:04:38.850 |  $>$92.6 |  $>$102.0 | 10.5 | 12.5$\times$11.6 (1.2) | 608$\pm$61 | 834$\pm$83
J123701+622109bb$b$Not primary beam corrected. | 0.8001 | Sdd$d$Barger et al. (2008) | 12:37:01.1023 | +62:21:09.623 |  $>$111.0 |  $>$154.0 | 11.5 | 12.4$\times$11.0 (3.2) | 285$\pm$29 | 390$\pm$39
J123739+620505bb$b$Not primary beam corrected. | $2.99\begin{subarray}{c}+0.81\\\ -1.51\end{subarray}$ | Pkk$k$Yang et al. (2014) | 12:37:39.3204 | +62:05:05.489 |  $>$154.0 |  $>$194.0 | 11.6 | 12.1$\times$10.9 (5.6) | 223$\pm$23 | 258$\pm$26
J123751+621919bb$b$Not primary beam corrected. | $1.20\begin{subarray}{c}+0.11\\\ -0.05\end{subarray}$ | Pkk$k$Yang et al. (2014) | 12:37:51.2327 | +62:19:19.012 |  $>$111.0 |  $>$181.0 | 8.8 | 11.9$\times$10.5 (0.5) | 136$\pm$14 | 155$\pm$16
J123523+622248bb$b$Not primary beam corrected. | $1.42\begin{subarray}{c}+0.10\\\ -0.11\end{subarray}$ | Pkk$k$Yang et al. (2014) | 12:35:22.6144 | +62:22:48.028 |  $>$92.5 |  $>$144.0 | 7.3 | 12.1$\times$10.6 (7.0) | 1260$\pm$126 | 1690$\pm$169
J123510+622202bb$b$Not primary beam corrected. | $2.33\begin{subarray}{c}+0.52\\\ -0.24\end{subarray}$ | Pkk$k$Yang et al. (2014) | 12:35:10.2698 | +62:22:02.067 |  $>$88.9 |  $>$91.4 | 7.9 | 12.1$\times$10.6 (7.0) | 931$\pm$94 | 1280$\pm$128
J123656+615659bb$b$Not primary beam corrected. | $0.39\begin{subarray}{c}+0.05\\\ -0.04\end{subarray}$ | Pkk$k$Yang et al. (2014) | 12:36:55.8230 | +61:56:58.917 |  $>$518.0 |  $>$528.0 | 12.7 | 9.6$\times$9.0 (39.0) | 3590$\pm$361 | 26700$\pm$2670
666z: redshift, R.A.: Right Ascension (J2000), Dec.: Declination (J2000), VLBI
$P$: VLBI peak brightness ($\mathrm{\mu Jy\,beam^{-1}}$), VLBI $I$: VLBI
integrated flux density ($\mathrm{\mu Jy}$), N: noise ($\mathrm{\mu
Jy\,beam^{-1}}$), S/N: signal-to-noise, Beam: restoring beam in
milliarcseconds and beam angle in degrees (major axis $\times$ minor axis
(beam angle)), VLA $P$: VLA 1.5 GHz peak brightness, VLA $I$: VLA 1.5 GHz
integrated flux densities. Italiscised source IDs correspond to sources with
no-primary beam correction applied. The row of numbers below the column titles
correspond to the columns in the machine-readable table that accompanies this
paper.
Redshift references: , ,,,,,,,.

1]

Table 3: Derived VLA & VLBI radio properties of the 31 GOODS-N AGN. Source ID | $\alpha$ | $L_{\mathrm{{1.5GHz}}}$ | $T_{b}$ | Angular sizes | Linear sizes
---|---|---|---|---|---
|  | [$\rm W\,Hz^{-1}$] | [$\rm K$] | [mas] | [parsec]
(1) | (21) | (22,23) | (24-26) | (27-30) | (31-34)
J123555+620902 | - | $(2.7\pm 0.3)\times 10^{{24}}$ | - | - | -
J123607+620951 | $-1.02$ | $(3.1\pm 0.3)\times 10^{{23}}$ | - | - | -
J123608+621036 | $-0.46$ | $(3.3\pm 0.4)\times 10^{{23}}$ | $\mathit{1\times 10^{6}}$ | 11.1$\times$6.3 | 80.8$\times$45.8
J123618+621541 | $-0.62$ | $(4.5\pm 0.4)\times 10^{{24}}$ | $>3\times 10^{7}$ | 3.7$\times$$<$2.8 | 31.5$\times$$<$23.8
J123620+620844 | $-0.28$ | $(4.9\pm 0.6)\times 10^{{23}}$ | $>2\times 10^{7}$ |  $<$3.2$\times$$<$2.8 |  $<$26.3$\times$$<$22.9
J123621+621708 | $-0.78$ | $(3.3\pm 0.3)\times 10^{{24}}$ | - | - | -
J123623+620654 | $0.06$ | $(2.0\pm 0.7)\times 10^{{24}}$ | - | - | -
J123624+621643 | $-0.52$ | $(6.3\pm 0.7)\times 10^{{24}}$ | $2\times 10^{7}$ | 5.9$\times$4.0 | 50.8$\times$34.2
J123641+621833 | $-0.94$ | $(2.2\pm 0.2)\times 10^{{24}}$ | $\mathit{3\times 10^{6}}$ |  $<$12.3$\times$5.0 | 104.4$\times$42.6
J123642+621331 | $-1.05$ | $(1.4\pm 0.1)\times 10^{{25}}$ | $\mathit{3\times 10^{6}}$ | 12.1$\times$8.5 | 103.4$\times$73.2
J123644+621133 | $-0.56$ | $(3.1\pm 0.3)\times 10^{{24}}$ | $>1\times 10^{8}$ | 2.1$\times$$<$1.7 | 17.6$\times$$<$13.9
J123646+621405 | $-0.40$ | $(8.7\pm 1.0)\times 10^{{23}}$ | $>2\times 10^{7}$ |  $<$2.9$\times$$<$2.5 |  $<$23.9$\times$$<$20.1
J123650+620738 | $-0.56$ | $(3.1\pm 0.3)\times 10^{{24}}$ | - | - | -
J123653+621444 | $-0.11$ | $(5.3\pm 0.7)\times 10^{{22}}$ | $\mathit{2\times 10^{6}}$ | 9.2$\times$4.8 | 44.1$\times$23.0
J123659+621833 | $-1.19$ | $(2.0\pm 0.1)\times 10^{{26}}$ | $>1\times 10^{9}$ | 6.2$\times$$<$0.9 | 52.2$\times$$<$7.7
J123700+620910 | $-0.89$ | $(1.3\pm 0.1)\times 10^{{25}}$ | $\mathit{5\times 10^{6}}$ |  $<$9.5$\times$7.2 | 78.3$\times$59.1
J123709+620838 | $0.15$ | $(3.2\pm 0.5)\times 10^{{23}}$ | $\mathit{2\times 10^{6}}$ | 7.8$\times$6.1 | 63.0$\times$49.1
J123714+621826 | $-0.66$ | $(3.9\pm 1.2)\times 10^{{25}}$ | $>2\times 10^{8}$ | 3.8$\times$$<$1.7 | 28.5$\times$$<$12.9
J123715+620823 | $-0.04$ | $(4.8\pm 0.7)\times 10^{{24}}$ | $>3\times 10^{9}$ |  $<$1.0$\times$$<$0.8 |  $<$7.9$\times$$<$6.9
J123716+621512 | $-0.19$ | $(1.5\pm 0.2)\times 10^{{23}}$ | $\mathit{2\times 10^{6}}$ | 10.4$\times$6.5 | 69.1$\times$43.4
J123717+621733 | $-0.89$ | $(2.2\pm 0.2)\times 10^{{24}}$ | $\mathit{7\times 10^{6}}$ | 6.8$\times$5.1 | 57.6$\times$43.2
J123720+620741 | $-0.28$ | $(3.4\pm 0.6)\times 10^{{23}}$ | - | - | -
J123721+621130 | $0.01$ | $(3.5\pm 0.8)\times 10^{{24}}$ | $>9\times 10^{7}$ | 2.8$\times$$<$1.9 | 24.0$\times$$<$16.5
J123726+621129 | $-1.23$ | $(6.6\pm 0.4)\times 10^{{24}}$ | $\mathit{2\times 10^{6}}$ | 8.7$\times$6.9 | 71.0$\times$56.1
J123649+620439 | - | $(2.0\pm 0.4)\times 10^{{22}}$ | - | 8.3$\times$6.0 | 17.7$\times$12.7
J123701+622109 | - | $(7.0\pm 0.7)\times 10^{{23}}$ | - | 9.4$\times$7.3 | 72.8$\times$56.8
J123739+620505 | - | $(9.7\pm 8.9)\times 10^{{24}}$ | - | 8.6$\times$7.2 | 67.9$\times$56.7
J123751+621919 | - | $(8.2\pm 1.6)\times 10^{{23}}$ | - | - | -
J123523+622248 | - | $(1.1\pm 0.2)\times 10^{{25}}$ | - | - | -
J123510+622202 | - | $(2.4\pm 1.0)\times 10^{{25}}$ | - | - | -
J123656+615659 | - | $(1.7\pm 0.5)\times 10^{{24}}$ | - | 7.3$\times$$<$2.4 | 39.7$\times$$<$13.2
777$\alpha$: 1.5GHz-5.5 GHz spectral index, $L_{\mathrm{{1.5GHz}}}$:
monochromatic 1.5 GHz radio luminosity, $T_{b}$: brightness temperature
(italicised indicates that natural weighting was used to derive $T_{b}$),
Angular size: projected angular size using elliptical Gaussian fitting, Linear
size: projected linear size in parsecs. Italiscised source IDs correspond to
sources with no-primary beam correction applied. Row of numbers below the
column titles correspond to the columns in the machine-readable table that
accompanies this paper.

###### Acknowledgements.

We thank the anonymous referee for their comments which helped improve this
manuscript. The authors gratefully acknowledge Len Cowie and Amy Barger for
allowing us to use unpublished data and for their useful comments. We would
also like to thank P. Padovani and R. Windhorst for their useful discussions.
This research made use of Astropy, a community-developed core Python package
for Astronomy (Astropy Collaboration et al., 2013, 2018).
The research leading to these results has received funding from the European
Commission Seventh Framework Programme (FP/2007-2013) under grant agreement No
283393 (RadioNet3).
The European VLBI Network is a joint facility of European, Chinese, South
African, and other radio astronomy institutes funded by their national
research councils.
e-MERLIN is a National Facility operated by the University of Manchester at
Jodrell Bank Observatory on behalf of STFC.
The National Radio Astronomy Observatory is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc.

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##  Appendix A Astrometry of J1234+619

We acquired 12 hours of e-MERLIN time at 5 GHz in order to independently
confirm the position of J1234+619. In order to effectively characterise
changes in the delay path induced by tropospheric variations, we implemented a
multi-source phase referencing strategy using three VLBA calibrators
surrounding J1234+619. These sources have astrometric accuracies
$<2.6\leavevmode\nobreak\ {\rm mas}$. Whilst not as sophisticated as
astrometric techniques such as MultiView calibration (Rioja et al. 2017),
multi-source phase referencing has been used to obtain astrometric precisions
of $\sim 20{\rm\mu as}$ with the VLBA (Fomalont & Kopeikin 2002). We observed
three calibrators and then the target with a total cycle time, $t_{\rm cyc}$,
of $\sim 10\leavevmode\nobreak\ {\rm min}$ (summarised in Figure 8 and Table
4). The use of multiple phase calibrators in different relative positions
allows the spatial dependence of the phase to be resolved and a short cycle
time is desired in order to map the atmosphere-induced phase variations across
all sources more frequently.

In order to estimate the uncertainties in the astrometric measurements, we
consider the approach of Rioja et al. (2017). Errors arise from three main
sources: (1) Thermal noise which originates from the uncertainty in the
position measurement due to random noise. This is characterised as
$\sigma_{t}\sim\theta_{B}/2(\rm S/N)$ where $\theta_{B}$ is the restoring beam
and S/N is the signal-to-noise. The target field has a S/N of 182, hence the
thermal noise error is approximately 0.11 mas (2) Fractional flux recovery.
This is the difference between the peak brightness in the phase referenced
maps and the self-calibrated maps. (3) Accuracy. The observed phase reference
sources have astrometric errors $<2.6{\rm mas}$ with 2/3 having errors $<{\rm
0.5mas}$. Positional errors associated with effects such as the core-shift
effect, the use of phase delays over geodetic group delays (Porcas 2009) and
differential structure blending effects between the EVN VLBI observations at
1.6 GHz and these observations at 5 GHz is expected to be a few
milliarcseconds. In total, errors on these observations is expected to be
dominated by unknown effects such as core-jet blending. We therefore assign a
conservative estimate of $\leq$ 5 mas astrometric accuracy.

With the phase referencing from the three phase calibrators complete, these
solutions were transferred to J1234+619 and positions on the resultant image
were measured using AIPS task JMFIT. The results of these observations are
presented in Table 5. We find that the eMERLIN 5 GHz positions of J1234+619
are more consistent with those derived as part of these new EVN observations,
rather than than the position of Chi et al. (2013). However, due to the
unknown errors, such as core-jet blending and structure blending associated
with the differing resolutions, we will continue to use the positions derived
in these new VLBI observations, as they are more consistent with the 5 GHz
eMERLIN positions.

Figure 8: Sky distribution of sources observed with e-MERLIN at 5 GHz. Table 4
lists the source coordinates and associated astrometric errors. The dashed
arrows correspond to the source switching order of the observations.  Table 4:
Phase calibrators used in the 5GHz eMERLIN observations

IAU Name | R.A. (J2000) | Dec. (J2000) |  $\Delta$RA |  $\Delta$Dec
---|---|---|---|---
|  |  | [mas] | [mas]
J1229+6335 | 12:29:06.0260 | 63:35:00.980 | 1.80 | 2.58
J1241+6020 | 12:41:29.5906 | 60:20:41.322 | 0.27 | 0.29
J1219+6344 | 12:19:10.5831 | 63:44:10.718 | 0.34 | 0.48
999Phase calibrators and their associated astrometric uncertainties. Positions
acquired from VLBA calibrator list888http://www.vlba.nrao.edu/astro/calib/
(Fey et al. 2015). Abbreviations: RA: Right Ascension (J2000), Dec:
Declination (J2000), $\Delta$RA: error in RA (mas), $\Delta$Dec: error in Dec
(mas).

Table 5: Positions and relative offsets of J1234+619

| R.A. (J2000) | Dec. (J2000)
---|---|---
EVN | 12:34:11.7413(57) | +61:58:32.478(07)
C13 | 12:34:11.7430 | +61:58:32.480
eM5 | 12:34:11.7417(10) | +61:58:32.477(68)

| $\Delta\theta$ |  $\Delta$R.A. (J2000) |  $\Delta$Dec. (J2000)
---|---|---|---
| [mas] | [mas] | [mas]
C13-EVN | 11.74 | 11.58 | 1.93
C13-eM5 | 9.39 | 9.09 | 2.32
EVN-eM5 | 2.52 | 2.48 | 0.39
101010Top Panel: Positions of J1234+619 from Chi et al. (2013) (C13), this
paper (EVN), and eMERLIN 5GHz (eM5). Bottom Panel: Angular offsets between the
positions derived. Abbreviations: RA: Right Ascension (J2000), Dec:
Declination (J2000), $\Delta$RA: error in RA (mas), $\Delta$Dec: error in Dec
(mas), $\Delta\theta$: angular separation.