# Fundamental differences in the radio properties of red and blue quasars:
kiloparsec-scale structures revealed by e-MERLIN

D. J. Rosario1, D. M. Alexander1, J. Moldon2,3, L. Klindt1, A. P. Thomson3, L.
Morabito1, V. A. Fawcett1, C. M. Harrison4
1Centre for Extragalactic Astronomy, Department of Physics, Durham University,
South Road, DH1 3LE, Durham, UK
2Instituto de Astrofísica de Andalucía (IAA, CSIC), Glorieta de las
Astronomía, s/n, E-18008 Granada, Spain
3Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy,
University of Manchester, Manchester M13 9PL, UK
4School of Mathematics, Statistics and Physics, Newcastle University,
Newcastle Upon Tyne, NE1 7RU, United Kindgom

###### Abstract

Red quasi-stellar objects (QSOs) are a subset of the quasar population with
colours consistent with reddening due to intervening dust. Recent work has
demonstrated that red QSOs show special radio properties that fundamentally
distinguish them from normal blue QSOs, specifically a higher incidence of
low-power radio emission (1.4 GHz luminosities L1.4$\approx 10^{25}$ –
$10^{27}$ W Hz-1) that is physically compact when imaged by arcsecond-
resolution radio surveys such as FIRST. In this work, we present e-MERLIN
imaging of a set of intermediate-redshift ($1.0<z<1.55$), luminous (bolometric
luminosities L${}_{bol}\approx 10^{46}$ – $10^{47}$ erg s-1) red and normal
QSOs carefully selected to have radio properties that span the range over
which red QSOs show the most divergence from the general population. With an
angular resolution $\times 25$ better than FIRST, we resolve structures within
the host galaxies of these QSOs ($>2$ kpc). We report a statistically
significant difference in the incidence of extended kpc-scale emission in red
QSOs. From an analysis of the radio size distributions of the sample, we find
that the excess radio emission in red QSOs can be attributed to structures
that are confined to galaxy scales ($<10$ kpc), while we confirm previous
results that red and normal QSOs have similar incidences of radio jets and
lobes on circumgalactic or larger scales ($>10$ kpc). Our results indicate
that the primary mechanism that generates the enhanced radio emission in red
QSOs is not directly connected with the nuclear engine or accretion disc, but
is likely to arise from extended components such as AGN-driven jets or winds.

###### keywords:

quasars: individual – galaxies: jets – radio continuum: galaxies – methods:
observational – techniques: interferometric

##  1 Introduction

QSOs (Quasi-stellar objects) are the luminous tail of the population of active
galactic nuclei (AGNs) and account for a substantial part of the cosmic mass
growth in supermassive black holes (SMBHs). Their distinctive features, high
optical luminosities and clear spectroscopic signatures of broad emission
lines, are the manifestation of an unimpaired line-of-sight view towards the
central accretion engine and its immediate environment. Due to their bright
optical emission and relative ease of identification, QSOs are valuable
signposts of the locations at which the co-evolutionary connections between
galaxies and SMBHs are put into place. Therefore, a thorough understanding of
the processes by which QSOs regulate their own growth and influence their host
galaxies is valuable for our developing picture of the evolution of SMBH
scaling relations, and for the evolution of massive galaxies as a whole.

The majority of QSOs have blue ultraviolet-to-optical colours consistent with
direct thermal emission from an AGN accretion disc peaking in the extreme
ultraviolet (effective temperatures $\sim 10^{5}$ K). Large spectroscopic
surveys, such as the Sloan Digital Sky Survey (SDSS), have identified a subset
of QSOs which scatter to much redder colours (e.g. Richards et al. 2003). In
this work, we will use the abbreviation “rQSOs” to refer to red QSOs.

There are a number of possible reasons for the red colours of rQSOs, such as
intrinsically cooler accretion discs, host galaxy light, or doppler-boosted
synchrotron emission (e.g. Benn et al. 1998; Francis et al. 2001; Young, Elvis
& Risaliti 2008), but the vast majority of luminous rQSOs are reddened by
intervening dust (Richards et al. 2003; Glikman et al. 2004, 2012; Rose et al.
2013; Kim & Im 2018; Klindt et al. 2019).

As the colours of rQSOs are not as distinct as those of normal (blue) QSOs,
they can be difficult to separate photometrically from stars and compact
galaxies. In the early days of rQSO research, strong radio emission, a
hallmark of some classes of AGN, was widely used to select and study this sub-
population (Webster et al. 1995; Ivezić et al. 2002; White et al. 2003;
Glikman et al. 2004). Over time, growing evidence suggested that redder QSOs
were associated with a high fraction of radio sources (Richards et al. 2003;
White et al. 2007; Georgakakis et al. 2009; Tsai & Hwang 2017), though clear
conclusions were elusive due to the complex selection effects that were built
into the selection of rQSOs, including those related to radio emission itself
(e.g. Richards et al. 2002).

In order to make progress in this area, our team has recently undertaken a
careful and controlled study of the radio properties of rQSOs. In a pioneering
paper, Klindt et al. (2019) undertook a controlled study of QSOs selected from
the Sloan Digital Sky Survey (SDSS) and examined their incidence and
morphologies using data from the Faint Images of the Radio Sky at Twenty
centimetres survey (FIRST; Becker, White & Helfand 1995; Helfand, White &
Becker 2015). We found a much higher detection rate of radio sources among
rQSOs compared to equally luminous normal QSOs at the same redshifts. This
result is attributable to a substantial excess of compact radio sources among
rQSOs, with relatively low radio powers (L1.4$<10^{27}$ W Hz-1, where L1.4 is
the integrated rest-frame 1.4 GHz radio luminosity of a radio source). Taking
a similar strategy, Rosario et al. (2020) and Fawcett et al. (2020) confirmed
the results of Klindt et al. (2019) at regimes of fainter optical and radio
luminosities, different radio frequencies, and using higher resolution radio
images.

Our various studies clearly demonstrate that rQSOs have distinct radio
properties which cannot be easily explained by varying reddening over a parent
population of normal QSOs. The chief conclusion is that rQSOs sustain an
excess population of compact radio sources, with radio sizes smaller than the
FIRST survey beamsize (5 arcsecond; $\approx 40$ kpc at $z\sim 1$), and with
intermediate radio-loudness In this fashion, rQSOs are fundamentally different
from normal QSOs, and their properties suggest a deep connection between the
dust that reddens them and their radio emission mechanisms.

FIRST covers a large area of sky which enables an accurate statistical
assessment of the radio-detection statistics for SDSS QSOs. The angular
resolution of FIRST marks a large improvement over most earlier radio surveys,
but it offers only limited capabilities for the study of distant QSOs. In
particular, over the important redshift interval of $1<z<3$ which marks the
epochs at which most SMBH growth occurs, reliance on radio imaging with
resolutions of a few arcseconds restricts studies to scales $\gtrsim 10$ kpc,
larger than the stellar sizes of the massive galaxies that host QSOs (e.g.,
van der Wel et al. 2014). Since interstellar reddening requires modest columns
of gas and dust which are generally only available within galaxies, a clearer
understanding of the nature of the radio sources in rQSOs requires radio
observations with spatial resolutions of a few kpc or lower.

First steps towards a higher resolution study were undertaken by Fawcett et
al. (2020). Using images from the 1.4 GHz VLA/Stripe82 survey, we demonstrated
that rQSOs show a slight excess of radio sources with sizes that were close to
the resolution limit ($\approx 1.8$”; $\approx 15$ kpc at $z\sim 1$). This
cemented the notion that the key to understanding the rQSO phenomenon lay at
even smaller scales, well within the realm of the QSO hosts themselves.

Here we present e-MERLIN observations of rQSOs and cQSOs with the express aim
of understanding their morphologies and radio properties on scales of a few
kpc. Our study is designed to identify whether the peculiar morphological
properties of rQSOs extends down to galaxy scales much smaller than those
probed by FIRST. In Section 2, after a discussion of the sample and ancillary
data, we describe the new e-MERLIN observations, their reduction, and the
processing we have undertaken to characterise radio structure from the final
images. In Section 3, we lay out our key measurements and results, and discuss
their implications in Section 4 for the incidence, origin, and evolution of
kpc-scale radio structure in QSOs. We summarise our conclusions in Section 5.

Throughout this work, we assume a concordance cosmology (Planck Collaboration
et al. 2016) and implement it in our calculations using software built into
the AstroPy cosmology module.

##  2 Data and Methods

The QSOs in this study are selected from the SDSS QSO catalogue based on their
properties in the SDSS and FIRST surveys. We describe their selection and
general features below, followed by a detailed treatment of their e-MERLIN
observations and analysis.

###  2.1 SDSS colour-selected QSOs

####  2.1.1 Sample selection

We selected our targets for e-MERLIN imaging from the primary sample defined
in Klindt et al. (2019). Starting from the SDSS DR7 catalogue of QSOs
(Schneider et al. 2010), Klindt et al. (2019) applied a set of criteria to
minimise the complications of selection biases and allow a refined comparative
framework for their investigation into rQSOs. These involved: 1) the use of
the `UNIFORM_TARGET` flag, 2) the exclusion of pure radio-selected QSOs, 3) a
required detection in the WISE W1, W2, & W3 bands (3.5, 4.6 & 12 $\mu$m
respectively) to allow the characterisation of the accretion power the AGN,
and 4) the restriction to an upper redshift of $z=2.4$ to ensure that the
colour-selection of QSOs was not affected by the Lyman break. Following Klindt
et al. (2019), we will refer to this pre-selected subset of the DR7 QSO
catalogue as the ‘parent sample’.

At the accretion luminosities typical of high-redshift QSOs from the SDSS, the
rest-frame mid-infrared (MIR) is dominated by emission from nuclear dust
heated directly by the AGN. Since the MIR is negligibly affected by even
moderate levels of dust extinction, MIR luminosities serve as a good measure
of the nuclear power of these QSOs. From the WISE photometry available, by
construction, for the entire parent sample, we estimate the rest-frame 6
$\mu$m luminosity (L6μm) through a log-linear extrapolation of the WISE W2 and
W3 fluxes, following the method described in Klindt et al. (2019) and used by
other papers in this series.

Klindt et al. (2019) split QSOs from the parent sample into colour-selected
categories based on their observed-frame SDSS $g-i$ colour distributions as a
function of redshift. After grouping the parent sample into redshift-sorted
bins of 1000 QSOs, they identified rQSOs as those that lie in the upper 10th
percentile of the $g-i$ colour distribution in a bin. The rQSOs targeted with
eMERLIN are a subset of the rQSOs defined by Klindt et al. (2019).

For our control sample of ‘normal’ QSOs (henceforth, cQSOs), we identify the
50% of QSOs that lie about the median colour in the aforementioned redshift-
sorted bins. This approach differs from Klindt et al. (2019), who only use the
10% median to define their control sample. Our main motivation for
implementing an expanded colour definition of the control sample was to allow
more target choices after selection constraints on radio morphology and
redshift, luminosity matching requirements, and e-MERLIN observability
restrictions (see below). We are able to relax the colour-criteria for cQSOs
because Klindt et al. (2019) clearly demonstrated that the FIRST radio
properties of blue QSOs do not differ significantly across the full range of
colours shown by this population, implying that both 10% and 50% median cQSOs
have indistinguishable radio properties. This has been verified in more recent
work (Rosario et al. 2020; Fawcett et al. 2020), in which a 50% median control
sample, similar to the selection used in this paper, showed differences in
radio properties to rQSOs that are consistent with a 10% control.

A final selection requirement is that of radio compactness, since this is the
morphological class in which the largest differences were found between red
and normal QSOs. We identified compact radio sources through visual inspection
of images from the FIRST radio survey following the methodology laid out in
Klindt et al. (2019). In practice, such visual determination of morphology is
only accurate for sources with enough fidelity in the FIRST images. Based on
our experience with such visual inspection, we used a 1.4 GHz flux density cut
of 3 mJy and a peak S/N$>15$ as a rule of thumb. Sources with a flux offset
greater than a factor of 2 between FIRST and the 20 cm NRAO VLA Sky Survey
(NVSS) were also excluded; this criterion identifies systems in which large
extended radio lobes are resolved out by the FIRST imaging (Klindt et al.
2019).

Our final pool of candidate targets were chosen from both colour-selected
categories (rQSOs and cQSOs) in a small redshift interval ($1.0<z<1.55$),
display compact FIRST radio morphologies, and lie in a small interval in radio
luminosity ($25.5<\log L_{\rm 1.4}<26.5$ W Hz-1). The redshift interval was
chosen to minimise Malmquist biases. The radio luminosity interval spans the
low end of FIRST-detected radio QSOs at our redshifts of interest, a regime
where the various differences between red and normal QSOs are most pronounced.
As we discuss in Section 3.4, the relative radio-to-MIR luminosities of our
targets formally place them in the ‘radio-loud’ regime.

From this pool we refined our targets to a final set of 20 rQSOs and 20 cQSOs
that were matched in redshift and L6μm with a tolerance of 0.05 and 0.2 dex
respectively. The SDSS identifiers, redshifts, L6μm and other key properties
of the targeted QSOs are listed in Table 1. For brevity, in the rest of the
text and figures in this papers, we refer to the targets using a shortened
form of the SDSS identifier: SDSSJ082314.71+560948.9 is shortened to
0823+5609, and so on.

####  2.1.2 Sample properties

Figure 1:  Observed frame Galactic extinction-corrected $g-i$ colours of SDSS
DR7 QSOs in the redshift range $1.0<z<1.55$ used in this study. The small
coloured points are those of the parent sample after applying the colour
selections for rQSOs (red points) and cQSOs (cyan points). More details may be
found in Section 2.1.1. The targets for this e-MERLIN study as shown using
larger points following the same colour scheme as above except for the single
case of 0842+5804 (black square point), which was determined, after correction
for Galactic extinction, to have a $g-i$ colour lying outside our colour-
selection windows.

In Figure 1, we compare the $g-i$ colours against redshift of our e-MERLIN
targets to those of SDSS DR7 QSOs from the parent sample of Klindt et al.
(2019). Our targets are identified in the Figure using larger symbols, and the
plotting colour scheme of red/cyan for rQSOs/cQSOs that is used here will the
reproduced consistently throughout the rest of the paper. In the post-
observation analysis, we discovered that an incorrect level of Galactic
extinction was originally applied to one of our targets (0842+5804), which
initially selected it as an rQSO. With its updated Galactic extinction
correction, its $g-i$ colour now places it closer to the cQSOs in Figure 1.
Hence, we do not consider it as an rQSO for the rest of our analysis. We
discuss this object in more detail in Section 2.1.3.

All the rQSOs and 18 of the 20 cQSOs have estimates of black hole masses and
Eddington ratios from the value-added catalog of spectral properties of SDSS
QSOs from Rakshit, Stalin & Kotilainen (2020). We find a range in masses
($10^{8}$ – $10^{10}$ M⊙) and Eddington ratios ($0.02$ – $0.83$) in our
e-MERLIN targets, consistent with that of the parent sample at their
redshifts. Since the nature of the radio source emission is broadly related to
the Eddington ratios of AGN (Best & Heckman 2012), we note that our rQSOs and
cQSOs have similar median Eddington ratios of 0.12 and 0.15 respectively.
These high values confirm that rQSOs and cQSOs both harbour AGN powered by
emission from a radiatively-efficient accretion disc. Therefore, differences
in their nuclear engines are unlikely to be the root cause of any differences
in their radio properties.

The bright nuclei of our optically-luminous QSO targets prevents a
characterisation of their host galaxies. Assuming these are representative of
the hosts of typical $z\sim 1$ radio-loud QSOs, we expect them to be mostly
bulge-dominated massive galaxies (e.g., Kukula et al. 2001), with moderate-to-
strong levels of star-formation ($\sim 100$ M⊙ yr-1; e.g., Podigachoski et al.
2015). This is consistent with the extrapolation of trends found at low
redshifts, where radiatively-efficient “high-excitation” radio AGN are hosted
by galaxies with substantial bulges, and discs that feature on-going star-
formation (e.g., Smolčić 2009; Best & Heckman 2012). However, there is no
clear evidence that rQSOs have different host properties from cQSOs at $z\sim
1$ (Calistro Rivera et al. 2021), and the contaminating effects of host galaxy
light are not responsible for the red colours of rQSOs (Klindt et al. 2019,
and discussion below).

Figure 2 compares the composite rest-frame UV spectra of the 20 cQSOs and 19
rQSOs. These composites are derived by taking a mean of the stack of their
SDSS spectra, after correction for Galactic extinction by a Milky Way law of
Fitzpatrick (1999). Before stacking, the spectra were normalised to the flux
of the QSOs at a rest-frame wavelength of 1.7 $\mu$m, determined from a linear
interpolation of their WISE W1 and W2 fluxes. As the rest-frame near infra-red
luminosities of rQSOs are minimally affected by the small intrinsic dust
columns that redden these systems, with this choice of spectral normalisation,
we are able to demonstrate the combined effects of dust extinction as well as
reddening.

As mentioned above, the ensemble of rQSOs and cQSOs have approximately equal
MIR luminosities since they are matched in L6μm. Therefore, most of the
differences in the overall flux of their median rest-frame UV spectra is
attributable to the differences in intrinsic dust extinction and reddening
among the rQSOs. We demonstrate this using the dashed cyan line in Figure 2,
which arises from the application of a simple dust screen model to the cQSO
composite adopting an SMC-like extinction law (Pei 1992) set to A${}_{V}=0.2$
mag. Both the normalisation and much of the shape of the rQSO composite is
compatible with the effects of mild columns of intervening dust.

We note differences in some of the spectral features in these composites, such
the trough around the C III]$\lambda 1909$ line and the equivalent width of
the narrow [O II]$\lambda 3727$ line. We refrain from a discussion of these
differences in this work; a detailed statistical treatment of spectral
differences between red and blue QSOs is the topic of a future paper from our
team.

####  2.1.3 0842+5804: an outlier

Figure 2: Composite rest-frame UV spectra of rQSOs (red solid) and cQSOs (cyan
solid) derived from mean stacks of the SDSS spectra of our targets. The
spectra were corrected for Galactic extinction and normalised to the rest-
frame 1.7 $\mu$m fluxes of the corresponding QSOs before stacking. The cyan
dashed line is a version of the cQSO composite that has been reddened by an
SMC-like dust extinction law with A${}_{V}=0.2$ mag. The spectrum of 0842+5804
is separately shown in black, as it is in outlier in terms of colour and
spectral properties.

0842+5804 was initially selected as an rQSO, but subsequent reanalysis of its
Galactic foreground extinction placed its intrinsic colour closer to those of
the cQSOs. Its estimated Galactic visual extinction of $A_{V}=0.275$ is 0.23
mag higher than the median extinction suffered by our targets, and 0.08 mags
higher than the next most extinguished QSO. It lies in the vicinity of a high
Galactic latitude dust filament. It is possible that its estimate of
extinction, derived from the average of a 5 arcminute region surrounding the
QSO, could be incorrect.

The spectrum of 0842+5804 is plotted in Figure 2 with a black line to contrast
it with the mean composite spectra of the cQSOs and rQSOs. Its normalisation
is higher than both the composites because it has the bluest MIR-to-optical
colour of our entire sample. Despite this, it shows a UV spectral shape that
is a bit redder than the median cQSOs. It also shows the weakest Mg II$\lambda
2800$ equivalent width among our targets, as well as weaker than average Fe II
band emission. 0842+5804 is an outlier in both its reddening and its spectral
features.

In light of these complexities, we will exclude 0842+5804 from the statistical
comparison of rQSOs and cQSOs, which is the main theme of this work. The
exclusion of this one source does not greatly compromise the matched L6μm
distributions that were the basis for the initial sample selection. For
completeness, we will continue to include it in the Figures of this Section,
but we distinguish it using a black plotting colour. It serves as a useful
test of the methods we employ to identify extended structure from our eMERLIN
data.

###  2.2 Astrometrically accurate QSO positions

The high angular resolution and milliarcsecond astrometric accuracy of
e-MERLIN data surpasses the astrometric capabilities of the SDSS, which could
make a comparison of the optical and radio positions of the QSOs difficult. We
overcame this limitation by searching the GAIA DR2 catalogue (Gaia
Collaboration et al. 2018) for counterparts to our targets. Due to their
optical brightness and point-like nature, 39 QSOs have a GAIA measurement,
providing sub-milliarcsecond positional accuracies. In the various figures of
this paper where the optical positions of the targets are shown, for e.g.
Figure 3, we use these GAIA positions except for the cQSO 1511+3428, for which
only the SDSS position is available.

###  2.3 TGSS 150 MHz fluxes

The TIFR GMRT Sky Survey (TGSS) is a 150 MHz imaging survey of 90% of the sky
using the Giant Metrewave Radio Telescope (GMRT), reaching a median noise
level of 3.5 mJy. As part of TGSS Alternative Data Release (ADR; Intema et al.
2017), a catalogue of sources with a detection threshold of $7\sigma$ was
published. As our targets are compact in FIRST, we assume the TGSS source
photometry, obtained from images with a beamsize of $\approx 30$”, captures
all of their 150 MHz flux, though blending with nearby sources may be a source
of potential contamination.

39 of our e-MERLIN targets are covered by TGSS; one target, 0828+2731, lies at
the edge of a hole in the survey coverage. 8 are associated with single TGSS
detections within 5”, which we take to be their TGSS counterparts. We use
these TGSS fluxes, in addition to default limits for the non-detections, in
our analyses of radio spectral indices in Section 3.3.

Table 1: Key properties of the e-MERLIN targets SDSS identifier | RA (deg) | Dec (deg) | Redshift | L6μm | L1.4
---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6)
Red QSOs
SDSSJ082314.71+560948.9 | 125.811264 | 56.16362 | 1.4433 | 45.12 | 26.03
SDSSJ082837.75+273136.9 | 127.157333 | 27.52692 | 1.4846 | 45.39 | 25.86
SDSSJ094615.01+254842.0 | 146.562533 | 25.81170 | 1.1940 | 45.78 | 25.91
SDSSJ095114.35+525316.7 | 147.809845 | 52.88796 | 1.4270 | 45.89 | 26.35
SDSSJ100713.68+285348.4 | 151.806977 | 28.89678 | 1.0470 | 46.08 | 25.86
SDSSJ105705.15+311907.8 | 164.271484 | 31.31883 | 1.3282 | 45.74 | 26.33
SDSSJ112220.45+312440.9 | 170.585218 | 31.41139 | 1.4534 | 45.74 | 26.37
SDSSJ114046.80+441609.8 | 175.195022 | 44.26939 | 1.4086 | 45.34 | 26.18
SDSSJ115313.06+565126.3 | 178.304452 | 56.85729 | 1.2014 | 45.84 | 26.49
SDSSJ115924.05+215103.0 | 179.850216 | 21.85083 | 1.0461 | 45.37 | 25.75
SDSSJ120201.91+631759.4 | 180.508038 | 63.29984 | 1.4806 | 45.42 | 25.93
SDSSJ121101.81+222106.7 | 182.757562 | 22.35188 | 1.2994 | 45.99 | 25.79
SDSSJ125146.34+431729.7 | 192.943066 | 43.29158 | 1.4527 | 45.27 | 26.40
SDSSJ131556.37+201701.6 | 198.984945 | 20.28378 | 1.4296 | 45.80 | 25.94
SDSSJ132304.23+394855.0 | 200.767645 | 39.81529 | 1.2797 | 45.48 | 26.12
SDSSJ134236.96+432632.1 | 205.653994 | 43.44224 | 1.0426 | 45.54 | 26.31
SDSSJ141053.19+401618.5 | 212.721690 | 40.27183 | 1.0425 | 44.94 | 25.87
SDSSJ153133.53+452841.6 | 232.889728 | 45.47822 | 1.0221 | 45.46 | 25.69
SDSSJ153555.27+243428.6 | 233.980322 | 24.57461 | 1.0779 | 45.43 | 25.97
Control QSOs
SDSSJ074815.44+220059.4 | 117.064346 | 22.01652 | 1.0594 | 46.02 | 25.89
SDSSJ100318.93+272734.3 | 150.828904 | 27.45956 | 1.2893 | 45.85 | 25.95
SDSSJ101935.22+281738.9 | 154.896733 | 28.29416 | 1.0136 | 45.47 | 26.16
SDSSJ103850.89+415512.7 | 159.712031 | 41.92019 | 1.4678 | 45.99 | 25.97
SDSSJ104240.11+483403.4 | 160.667146 | 48.56762 | 1.0375 | 45.54 | 26.15
SDSSJ104620.18+342708.4 | 161.584121 | 34.45234 | 1.1964 | 45.75 | 26.59
SDSSJ105736.17+331545.9 | 164.400726 | 33.26276 | 1.4658 | 45.31 | 25.78
SDSSJ110352.48+584923.5 | 165.968689 | 58.82319 | 1.3300 | 45.63 | 25.95
SDSSJ120335.39+451049.5 | 180.897481 | 45.18043 | 1.0760 | 45.32 | 26.44
SDSSJ122221.37+372335.8 | 185.589086 | 37.39330 | 1.2647 | 45.31 | 26.11
SDSSJ130433.42+320635.5 | 196.139280 | 32.10989 | 1.3368 | 45.68 | 26.17
SDSSJ141027.58+221702.6 | 212.614950 | 22.28406 | 1.4181 | 45.47 | 26.59
SDSSJ142824.76+291606.7 | 217.103202 | 29.26856 | 1.0365 | 45.21 | 26.44
SDSSJ143249.54+292505.7 | 218.206450 | 29.41825 | 1.0403 | 45.38 | 26.10
SDSSJ151100.64+342842.4 | 227.752670a | 34.47845a | 1.4395 | 45.29 | 26.39
SDSSJ153044.08+231013.4 | 232.683666 | 23.17041 | 1.4068 | 46.09 | 25.88
SDSSJ155436.68+285942.5 | 238.652850 | 28.99514 | 1.1879 | 46.01 | 25.84
SDSSJ160245.92+453050.3 | 240.691330 | 45.51398 | 1.4074 | 45.58 | 25.93
SDSSJ163023.12+384700.7 | 247.596378 | 38.78352 | 1.5275 | 45.16 | 26.31
SDSSJ165724.82+204559.5 | 254.353437 | 20.76655 | 1.4679 | 45.48 | 26.20
Outlier
SDSSJ084255.56+580425.6 | 130.731537 | 58.07379 | 1.3384 | 45.72 | 26.29
1, 4: Identifier and redshift from SDSS DR7 QSO catalogue (Schneider et al.
2010).
2, 3: Coordinates from GAIA, except for a, for which coordinates come from
SDSS.
5: Rest-frame 6 $\mu$m luminosity from WISE photometry, in log erg s-1.
6: Rest-frame 1.4 GHz luminosity from FIRST photometry, in log W Hz-1.

###  2.4 1.4 GHz e-MERLIN imaging

####  2.4.1 Observations and reduction

Table 2: Details of the e-MERLIN observations SDSS identifier | Run ID | RMS | Peak | Extended?
---|---|---|---|---
(1) | (2) | (3) | (4) | (5)
Red QSOs
SDSSJ082314.71+560948.9 | `CY7220_L_004_20181218` | 0.07 | 10.55 | No
SDSSJ082837.75+273136.9 | `CY7220_L_002_20181214` | 0.06 | 1.19 | No
SDSSJ094615.01+254842.0 | `CY7220_L_002_20181214` | 0.08 | 1.06 | Yes
SDSSJ095114.35+525316.7 | `CY7220_L_004_20181218` | 0.08 | 10.71 | No
SDSSJ100713.68+285348.4 | `CY7220_L_002_20181214` | 0.08 | 4.23 | Yes
SDSSJ105705.15+311907.8 | `CY7220_L_001_20181214` | 0.06 | 13.38 | No
SDSSJ112220.45+312440.9 | `CY7220_L_001_20181214` | 0.06 | 9.16 | Yes
SDSSJ114046.80+441609.8 | `CY7220_L_004_20181218` | 0.09 | 5.63 | No
SDSSJ115313.06+565126.3 | `CY7220_L_004_20181218` | 0.09 | 6.01 | Yes
SDSSJ115924.05+215103.0 | `CY7220_L_001_20181214` | 0.08 | 9.31 | No
SDSSJ120201.91+631759.4 | `CY7220_L_006_20181220` | 0.10 | 2.26 | No
SDSSJ121101.81+222106.7 | `CY7220_L_001_20181214` | 0.06 | 4.82 | No
SDSSJ125146.34+431729.7 | `CY7220_L_006_20181220` | 0.09 | 34.58 | No
SDSSJ131556.37+201701.6 | `CY7220_L_003_20181216` | 0.10 | 3.82 | No
SDSSJ132304.23+394855.0 | `CY7220_L_006_20181220` | 0.06 | 10.84 | No
SDSSJ134236.96+432632.1 | `CY7220_L_006_20181220` | 0.06 | 20.14 | No
SDSSJ141053.19+401618.5 | `CY7220_L_006_20181220` | 0.06 | 6.03 | No
SDSSJ153133.53+452841.6 | `CY7220_L_005_20181220` | 0.07 | 6.26 | No
SDSSJ153555.27+243428.6 | `CY7220_L_005_20181220` | 0.14 | 4.78 | Yes
Control QSOs
SDSSJ074815.44+220059.4 | `CY7220_L_002_20181214` | 0.11 | 4.46 | No
SDSSJ100318.93+272734.3 | `CY7220_L_002_20181214` | 0.08 | 6.31 | No
SDSSJ101935.22+281738.9 | `CY7220_L_002_20181214` | 0.08 | 11.05 | No
SDSSJ103850.89+415512.7 | `CY7220_L_002_20181214` | 0.08 | 5.66 | No
SDSSJ104240.11+483403.4 | `CY7220_L_004_20181218` | 0.09 | 12.20 | No
SDSSJ104620.18+342708.4 | `CY7220_L_001_20181214` | 0.28 | 28.04 | No
SDSSJ105736.17+331545.9 | `CY7220_L_001_20181214` | 0.06 | 2.10 | No
SDSSJ110352.48+584923.5 | `CY7220_L_004_20181218` | 0.12 | 9.15 | No
SDSSJ120335.39+451049.5 | `CY7220_L_006_20181220` | 0.54 | 42.27 | No
SDSSJ122221.37+372335.8 | `CY7220_L_006_20181220` | 0.06 | 10.82 | No
SDSSJ130433.42+320635.5 | `CY7220_L_001_20181214` | 0.09 | 6.81 | No
SDSSJ141027.58+221702.6 | `CY7220_L_003_20181216` | 0.09 | 15.68 | Yes
SDSSJ142824.76+291606.7 | `CY7220_L_007_20190327` | 0.08 | 13.26 | No
SDSSJ143249.54+292505.7 | `CY7220_L_003_20181216` | 0.05 | 17.76 | No
SDSSJ151100.64+342842.4 | `CY7220_L_003_20181216` | 0.06 | 4.28 | Yes
SDSSJ153044.08+231013.4 | `CY7220_L_005_20181220` | 0.14 | 8.73 | No
SDSSJ155436.68+285942.5 | `CY7220_L_003_20181216` | 0.09 | 5.39 | No
SDSSJ160245.92+453050.3 | `CY7220_L_005_20181220` | 0.15 | 7.27 | No
SDSSJ163023.12+384700.7 | `CY7220_L_005_20181220` | 0.07 | 9.90 | No
SDSSJ165724.82+204559.5 | `CY7220_L_005_20181220` | 0.09 | 9.36 | No
Outlier
SDSSJ084255.56+580425.6 | `CY7220_L_004_20181218` | 0.10 | 6.64 | Yes
1: Identifier from SDSS DR7 QSO catalogue (Schneider et al. 2010).
2: e-MERLIN identifier for the observing run.
3: Root Mean Square (RMS) flux density of the final cleaned image ($3\sigma$
clipped; mJy beam-1).
4: Peak flux density of the final cleaned image (mJy beam-1).
5: As determined from both visual assessment and core/beam analysis of the
eMERLIN images.

Our 40 targets were observed with the e-MERLIN interferometer using its L-band
receivers ($1.23$–$1.74$ GHz). Six antennas were used for all the
observations; the large Lovell telescope was not used due to refurbishment
work at the time, but the sensitivity of the reduced array was adequate for
the science goals of this work. The 512 MHz bandwidth covered by the continuum
correlator was split into 8 spectral windows of 128 channels each. Shortest
integration intervals of $3$–$4$ seconds were used.

The observations were carried out over seven separate runs: six in December
2018 and an additional short run in March 2019 to reobserve a target with
better calibration. Each run consisted of a sequence of calibration scans
interspersed with science scans on targets. To maximise uv coverage, the
$\approx 1$ hour on-source time on each target was split into several sets of
typically three short scans (a few minutes each) separated by $1$–$2$ hours.
3C286 (1331+3030) was used as a flux reference for all runs.

OQ208 (1407+2827) was used as the primary bandpass calibrator and 3C84
(0319+4130) was used as a pointing calibrator for most of the runs. During
runs `CY7220_L_002_20181214` and `CY7220_L_004_20181218`, strong winds led to
the premature parking of one of the antennae in the array before it could
observe the nominal bandpass calibrator. Therefore, OQ208 was only used as a
pointing calibrator in `CY7220_L_004_20181218`, and 3C84 served as the primary
bandpass reference. Complex gain calibrators observed throughout the run were
boostrapped for bandpass corrections to recover the data from the associated
baselines from the troublesome antenna. In the case of
`CY7220_L_002_20181214`, 3C84 was used to calibrate the bandpass of the
antenna after it was brought back to operation.

The radio data were reduced using the newly developed e-MERLIN pipeline, which
employs a backbone of functions from the Common Astronomy Software
Applications (CASA) package to flexibly average, flag, calibrate, and image
data from the e-MERLIN correlator. For a few targets with faint phase
calibrators, and for the entire `CY7220_L_005_20181220` run taken under windy
conditions, we adapted the parameters from the pipeline (in particular the
averaging intervals for calibration solutions and associated minimum flagging
thresholds) to ensure that most of the data was unflagged and calibration
solutions were suitable.

Since the same bandpass and pointing calibrators were used in all seven runs,
we examined their calibrated flux densities to determine the relative flux
calibration of our observations. The largest variations were found for the
pointing calibrator which was often observed at a different part of a run
sequence than the flux and bandpass calibrators. We measured the maximal range
of the flux scale of the pointing calibrator to be $\approx 9$%, and we
conservatively adopt this as the relative flux calibration uncertainty of our
observations.

Using CASA, we post-processed the pipeline products for the science targets.
In some cases, a small amount of manual flagging was needed to deal with
residual RFI and phase errors. We also performed self-calibration on our
targets to reduce residual phase and amplitude noise and deal with cases where
a nearby bright source was affecting the images of the target.

Using WSCLEAN v2.6, we produced final images of our targets with a spatial
sampling of 0.03”/pixel and a size of 15.36” ($512\times 512$ pixels). The
image size was chosen to fully cover the 5” resolution element of the FIRST
survey with enough margin to pick up any structure that may have been barely
resolved in FIRST. The choice of pixel size ensured that the images sampled
across the minor axis of the highest resolution dataset with at least 3
pixels.

In Figure 3, we show the inner 2”$\times$2” region of the final e-MERLIN
images of the all the QSOs from our sample. With the long baselines of
e-MERLIN, the restoring beams of our images have a median major FWHM of
$0\aas@@fstack{\prime\prime}18$, which translates to projected scales of
$1.48$–$1.56$ kpc over the range of redshifts of our targets. Therefore, we
resolve radio structures within the confines of the host galaxies of these
QSOs, in contrast to the supergalactic scales ($>40$ kpc) that are probed by
the $5$” beam of their FIRST images.

Figure 3:  2”$\times$2” stamps from our e-MERLIN images centred on the GAIA-
based position of the targeted QSOs (magenta crosses). The top panels show the
rQSO targets, including the outlier case of 0842+5804 which was initially
selected as an rQSO (Section 2.1.3) The bottom panels show the cQSO targets.
In each panel, a small hatched grey ellipse shows the size and shape of the
restoring beam.

####  2.4.2 Gaussian image decomposition

Table 3: Results of Gaussian decomposition of the e-MERLIN images SDSS identifier | RA | Declination | Flux density | Major axis | Axis ratio | PA
---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7)
Single component fits
SDSSJ074815.44+220059.4 | 117.064356 | 22.01652 | 4.6 | 0.23 | 1.65 | 49.6
SDSSJ082314.71+560948.9 | 125.811277 | 56.16361 | 11.0 | 0.13 | 1.35 | 110.0
SDSSJ082837.75+273136.9 | 127.157346 | 27.52691 | 1.4 | 0.19 | 1.61 | 50.3
SDSSJ084255.56+580425.6 | 130.731569 | 58.07378 | 11.1 | 0.20 | 1.58 | 120.5
SDSSJ095114.35+525316.7 | 147.809856 | 52.88796 | 11.7 | 0.15 | 1.51 | 107.8
SDSSJ100318.93+272734.3 | 150.828926 | 27.45956 | 7.0 | 0.20 | 1.73 | 34.3
SDSSJ101935.22+281738.9 | 154.896744 | 28.29416 | 11.8 | 0.15 | 1.38 | 38.1
SDSSJ103850.89+415512.7 | 159.712043 | 41.92018 | 5.7 | 0.13 | 1.22 | 67.5
SDSSJ104240.11+483403.4 | 160.667154 | 48.56762 | 13.2 | 0.19 | 1.93 | 115.1
SDSSJ104620.18+342708.4 | 161.584125 | 34.45233 | 25.1 | 0.19 | 1.92 | 58.6
SDSSJ105705.15+311907.8 | 164.271490 | 31.31882 | 14.1 | 0.19 | 1.69 | 45.6
SDSSJ105736.17+331545.9 | 164.400738 | 33.26275 | 2.2 | 0.18 | 1.44 | 69.3
SDSSJ110352.48+584923.5 | 165.968715 | 58.82318 | 8.8 | 0.14 | 1.47 | 113.6
SDSSJ114046.80+441609.8 | 175.195025 | 44.26938 | 5.5 | 0.18 | 1.73 | 100.6
SDSSJ115924.05+215103.0 | 179.850226 | 21.85082 | 9.4 | 0.18 | 1.40 | 53.5
SDSSJ120201.91+631759.4 | 180.508065 | 63.29983 | 2.1 | 0.15 | 1.29 | 88.7
SDSSJ120335.39+451049.5 | 180.897500 | 45.18043 | 40.9 | 0.17 | 1.03 | 105.6
SDSSJ121101.81+222106.7 | 182.757572 | 22.35187 | 5.0 | 0.22 | 1.92 | 38.9
SDSSJ122221.37+372335.8 | 185.589098 | 37.39329 | 12.0 | 0.16 | 1.20 | 78.3
SDSSJ125146.34+431729.7 | 192.943078 | 43.29157 | 33.5 | 0.14 | 1.11 | 72.2
SDSSJ130433.42+320635.5 | 196.139294 | 32.10989 | 6.8 | 0.16 | 1.37 | 22.4
SDSSJ131556.37+201701.6 | 198.984948 | 20.28377 | 3.7 | 0.27 | 2.64 | 22.0
SDSSJ132304.23+394855.0 | 200.767657 | 39.81528 | 11.2 | 0.14 | 1.11 | 68.7
SDSSJ134236.96+432632.1 | 205.654007 | 43.44223 | 21.5 | 0.14 | 1.11 | 85.0
SDSSJ141053.19+401618.5 | 212.721700 | 40.27182 | 6.3 | 0.15 | 1.10 | 91.5
SDSSJ142824.76+291606.7 | 217.103210 | 29.26855 | 13.6 | 0.15 | 1.25 | 79.0
SDSSJ143249.54+292505.7 | 218.206458 | 29.41825 | 18.7 | 0.20 | 1.77 | 44.1
SDSSJ153044.08+231013.4 | 232.683674 | 23.17039 | 8.5 | 0.24 | 2.48 | 35.8
SDSSJ153133.53+452841.6 | 232.889736 | 45.47821 | 7.2 | 0.20 | 2.02 | 43.1
SDSSJ155436.68+285942.5 | 238.652863 | 28.99514 | 6.0 | 0.15 | 1.30 | 58.3
SDSSJ160245.92+453050.3 | 240.691333 | 45.51397 | 7.4 | 0.16 | 1.42 | 45.0
SDSSJ163023.12+384700.7 | 247.596391 | 38.78351 | 10.3 | 0.17 | 1.61 | 38.0
SDSSJ165724.82+204559.5 | 254.353443 | 20.76654 | 9.7 | 0.26 | 2.50 | 43.0
Multiple component fits
SDSSJ094615.01+254842.0 | 146.562520 | 25.81163 | 0.6 | 0.16 | 1.31 | 65.9
| 146.562515 | 25.81177 | 0.9 | 0.15 | 1.49 | 65.2
| 146.562468 | 25.81176 | 0.5 | 0.10 | 0.85 | -89.9
| 146.562552 | 25.81166 | 13.7 | 2.13 | 5.92 | -19.8
SDSSJ100713.68+285348.4 | 151.806988 | 28.89673 | 4.9 | 0.17 | 1.41 | 21.8
| 151.806990 | 28.89682 | 1.7 | 0.17 | 1.44 | 18.2
SDSSJ112220.45+312440.9 | 170.585230 | 31.41138 | 10.2 | 0.21 | 1.80 | 41.2
| 170.585219 | 31.41135 | 2.0 | 0.28 | 2.60 | 44.7
SDSSJ115313.06+565126.3 | 178.304467 | 56.85728 | 5.1 | 0.22 | 1.92 | 144.8
| 178.304431 | 56.85740 | 1.3 | 0.23 | 2.02 | 120.3
| 178.304464 | 56.85729 | 22.3 | 1.90 | 5.17 | -11.8
SDSSJ141027.58+221702.6 | 212.614961 | 22.28405 | 16.5 | 0.23 | 2.03 | 29.1
| 212.615037 | 22.28344 | 3.1 | 0.42 | 2.00 | -75.5
| 212.615104 | 22.28371 | 0.3 | 0.11 | 0.79 | -89.9
SDSSJ151100.64+342842.4 | 227.752709 | 34.47844 | 2.0 | 0.17 | 1.60 | 44.2
| 227.754067 | 34.47928 | 7.8 | 0.21 | 1.28 | 44.9
SDSSJ153555.27+243428.6 | 233.980320 | 24.57460 | 5.9 | 0.23 | 1.50 | 36.4
| 233.980388 | 24.57457 | 4.0 | 0.25 | 2.06 | 73.1
1: Identifier from SDSS DR7 QSO catalogue (Schneider et al. 2010).
2,3: Peak position of the component on the e-MERLIN image (degrees).
4: Observed e-MERLIN L-band flux density of the component (mJy).
5: Major axis FWHM of the component (arcsec).
6: Major-to-minor axis ratio of the component.
7: Position angle of the component, measured from North (∘).

In order to characterise the radio source structure in the e-MERLIN images, we
decomposed the images into a set of two-dimensional elliptical Gaussian
components. For this, we used the AstroPy modelling subpackage, with
minimisation through its implementation of a least-squares Simplex algorithm.
We set fitting bounds on the Gaussian components to ensure positive amplitudes
and sizes greater than 50% of the corresponding restoring beam111Fits to the
images with the CASA IMFIT task gave us very similar results. In this work, we
only report our AstroPy-based modelling, as this approach allowed for greater
flexibility in the choice of a robust minimisation algorithm..

In a first pass, we undertook a run of fits over the central 2” of each image
adopting only a single Gaussian model which was initialised to match the shape
of the restoring beam. After examining the fitting residuals visually, we
flagged the five cases in which a single Gaussian did not adequately represent
of the source structure. Two more objects showed emission beyond the central
2” which we also flagged. These seven images were then subjected to a second
round of fits using multiple ($>2$) Gaussian components.

In each of the multiple component fits, we first manually determined the
number of components to apply to the fit, and estimated initial amplitudes,
positions, and sizes for each component. After the fits, we examined the
residuals and added or removed components as needed to capture most of the
visual source structure. We required between 2 and 4 components to fit all the
sources with initial evidence for extended structure. Since the noise in the
e-MERLIN images have a large correlated component, we resorted to a visual
judgement of the fit quality rather than taking a more quantitative metric.
This lack of precision is not a major source of uncertainty for this work.

The results of the Gaussian decomposition of the e-MERLIN images are tabulated
in Table 3, and a visualisation of the final fits for all the targets is
available in the online material (Supplementary Figures 1 & 2). In Section
3.1, we provide a detailed description of the extended radio structure among
our targets.

####  2.4.3 Searching for additional extended sources

Figure 4: Left:  The ratio of the semi-major axis of the core component to
that of the restoring beam for sources that were visually determined to be
compact in the e-MERLIN images. Most of the core components have sizes
comparable to that of the beam, except for 0842+5804 (plotted in black). The
distribution of core extensions of rQSOs is marginally larger than those of
the cQSOs. Right:  The difference in position angle between the core
components and the restoring beam for sources that were visually determined to
be compact in the e-MERLIN images. Except for 0842+5804 (plotted in black) and
a few sources imaged with almost circular beams, the core components are
aligned with their beams. From these two figures, we conclude that the
majority of visually compact cores are unresolved in our e-MERLIN
observations.

To complement the visual analysis described above, we developed an approach to
search for additional extended source structure at the resolution limit of our
images. This was performed only on the 33 sources for which a single component
fit was determined to be an adequate representation of the images. We
distinguish between rQSOs and cQSOs in the analysis below, and also separately
include the outlier QSO 0842+5804 because it serves as a useful validation of
our technique.

We searched for evidence of extended structure through a comparison of the
parameters of the single-component Gaussian fits with those of the restoring
beam of the images. In the following description, we refer to this single
component as the ‘radio core’.

In the left panel of Figure 4, we plot the ratios of the semi-major axis of
the radio core component to that of the beam, splitting rQSOs and cQSOs into
different histograms. The distributions for most QSOs are centered about unity
indicating that these single component systems are unresolved in our e-MERLIN
imaging. 0842+5804, shown in black in Figure 4, is the only visually compact
object which has a significantly larger core size than the corresponding
restoring beam. While its radio core is fit well by a single Gaussian, the
size of this component is $\approx 30$% larger than the beam, showing that it
is definitely extended.

There is a mild suggestion that the ensemble of visually compact rQSOs are
marginally larger than their beams, by $1.1\pm 0.25$%, in contrast to the
ensemble of cQSOs which are consistent with unity at the same level of
uncertainty. However, the distributions of core/beam size ratios for the two
subsets are statistically indistinguishable with our current sample sizes.

We also compare the best-fit position angles (PAs) of the core components to
those of their respective restoring beams (right panel of Figure 4). Most of
the systems have core and beam PAs that agree within $\pm 10^{\circ}$. One
rQSO (1202+6317) and one cQSO (1203+4510) have almost circular beams, and
their core PAs are extremely uncertain, leading to large PA differences that
are not significant. The only object with a definite difference between the
core and beam PA is 0842+5804. Therefore, the relative core/beam size and PA
analyses yield consistent results, identifying 0842+5804 as a QSO with
extended emission that is not obvious from a visual assessment.

Figure 5: Spatial offsets between the GAIA positions of the optical QSOs and
the fitted centres of the radio core components for the targets that were
visually determined to be compact in the e-MERLIN images.

Taking advantage of the high astrometric accuracy of the e-MERLIN images and
the QSO positions from GAIA, we search for angular offsets between radio core
components and the optical positions of the unresolved or single-component
sources. As the optical position is centred on the true AGN nucleus, a
systematic measurable difference between the relative optical and radio
centroid could indicate that the radio core contains asymmetric emission below
the resolution of the e-MERLIN images, betraying the presence of radio
structure on sub-kpc scales.

We first verified that the optical positional offsets of the radio core
components distributed about a zero mean in both RA and Declination. This
ensures that any systematic astrometric error between the e-MERLIN and GAIA
reference frames are negligible, as expected. Translating the optical offsets
to an angular distance in milliarcseconds (mas), we compare, in Figure 5, the
distributions of the offsets for our sample, split into colour-selected
subsets.

We find that the single-component cQSOs and rQSOs show a similar range of
offsets between their optical and radio core positions. Most lie within 30
mas, the size of a single pixel in our images and $\approx 1/6$ of the typical
beamwidth of the images. This scatter is consistent with the errors of the
radio core centroids from our Gaussian component fits. There is a mild
difference in the shape of the offset distributions between cQSOs and rQSOs,
but we do not consider this to be significant based on a two-sided Kolmogorov-
Smirnov (K-S) test.

Two objects show offsets in the long tail of the distribution: 0842+5804 and
the cQSO 1003+2727. The evidence for extended structure in 0842+5804 has been
presented above, and this may explain its larger offset. 1003+2727, on the
other hand, has an image that is completely consistent with the restoring
beam, yet the respective panel in Figure 3 clearly shows a visible offset
between the centre of its apparently unresolved core and the optical position.
However, the gain calibration for this particular source was complicated by
heavy flagging of the calibrator scans by the pipeline, and the final
astrometric solution may be unreliable. In light of this, we do not place much
weight on the apparent offset, and henceforth treat 1003+2727 as a single
component core-dominated source. Possible higher frequency e-MERLIN
observations in the future may help to verify its nature.

##  3 Results

###  3.1 Visually extended radio sources

Five of our targets exhibit visually extended emission, both from an
examination of the central images (Figure 3) and based on their single-
component Gaussian fits: 0946+2548, 1007+2853, 1122+3124, 1153+5651, and
1535+2434. All five are rQSOs. In two cQSOs which have unresolved cores,
additional extended emission is seen on scales larger than the cutouts:
1511+3428 shows a bright radio hotspot 5” away from its core, and 1410+2217
has a faint lobe-like structure 2.2” from the core.

Figure 6: A montage of the visually extended sources from the e-MERLIN
observations. A bar corresponding to a scale of 2” is shown to the right of
each panel, which corresponds to the largest angular scale to which the
observations are sensitive. Red or cyan coloured borders indicate whether the
source is an rQSO or cQSO, respectively. Section 3.1 discusses these sources
in more detail. Figure 7: Images of the cQSO 1511+3428 from our e-MERLIN
observations (left panel), the VLA Sky Survey Quick Look (VLASS epoch1.1,
middle panel), and the NOAO Legacy Surveys in the z-band. The source is
strongly one-sided; a bright knot is seen to the north-east of the core, but
there is no detectable emission to the south-west. The z-band imaging does not
show any optical source at the location of the north-east knot, so we cannot
verify whether it corresponds to a galaxy in the vicinity of the QSO.

Here we summarise the properties of these 7 rQSOs and cQSOs with clearly
extended emission. High-contrast images covering their full extent are shown
in Figures 6 and 7, the multi-component fits are shown in Supplementary Figure
2 of the online material, and their parameters summarised in the lower part of
Table 3.

####  3.1.1 0946+2548

The presence of a nearby bright radio source affected the imaging of this
object, leading to a high level of noise. The final self-calibration was
performed on this nearby source, and then applied to the target.

The QSO radio source is composed of two bright resolved knots separated by
$0\aas@@fstack{\prime\prime}5$, along PA$=-17^{\circ}$ which we take to define
an axis for the system. The GAIA position of the QSO lies between the two main
knots, coinciding with another faint knot which has a marginal S/N (Figure 3).

The brighter north-western knot shows an extension perpendicular to the axis.
There is a hint of diffuse patchy emission oriented along the axis that
extends beyond the two knots, which may indicate partially-recovered extended
emission. We modelled the source using four components: two for the north-
western knot, one for the south-eastern knot, and a large elongated component
to capture the diffuse emission around the knots.

The elongated component dominates the total flux, but it may be influenced by
residual uv noise in the image. This may explain the $\approx\times 2.5$
greater flux that we measure in this source compared to its flux from the
FIRST survey (Section 3.2)

####  3.1.2 1007+2853

The source consists of two compact components separated by
$0\aas@@fstack{\prime\prime}34$ along PA$=0^{\circ}$, which we modelled using
two gaussian components. The QSO position lies between the two components,
suggesting that they are opposite lobes of a bipolar jet or outflow.

####  3.1.3 1122+3124

The source consists of a single dominant core component that shows a faint
elongation along PA$=205^{\circ}$. A single component fit leaves a definite
visible residual along the direction of the elongation. Therefore, two
components are required to fit the source adequately.

####  3.1.4 1153+5651

This source exhibits a complex morphology with a dominant central core and a
bipolar extension along PA$=171^{\circ}$. In addition to the bright unresolved
core, there is a mildly resolved knot $0\aas@@fstack{\prime\prime}42$ away,
from which a faint tendril of emission extends even further north. Towards the
south, faint emission appears to outline the edge of a poorly-defined lobe.

We model the source using three components, one each for the core, northern
knot and extended jet-like emission. The low S/N of the apparent lobe-like
southern feature prevents it from being modelled.

####  3.1.5 1535+2434

The pipeline-calibrated images of this source were strongly affected by two
bright sources a few arcminutes away. A first round of wide-field self-
calibration was used to model the target as well as these bright nearby
contaminants. After strong data averaging to smear out the effects of the
other sources, a final round of self-calibration was performed on the target
to obtain the final image.

The QSO radio source is composed of two bright knots separated by
$0\aas@@fstack{\prime\prime}27$ along PA$=115^{\circ}$. The GAIA position of
the QSO is close to the centre of the western knot, which is also extended
beyond the size of the beam.

####  3.1.6 1410+2217

This is one of two cQSOs with detectable extended emission. The source
structure is dominated by a bright unresolved core. South of the core,
$2\aas@@fstack{\prime\prime}25$ away along PA$=173^{\circ}$, a faint arc-like
feature marks the outer edge of a barely-defined lobe. We modelled the source
as a core component and two faint knots on the edge of this tentative lobe,
which we manually adjusted and tied during the fit.

####  3.1.7 1511+3428

The QSO was selected for visual compactness in its FIRST imaging, but our
e-MERLIN image clearly resolves it into two compact sources, of which the
fainter source corresponds to the optical location of the QSO (Figure 7). The
two knots are separated by $5\aas@@fstack{\prime\prime}06$ along
PA$=53^{\circ}$. The core is unresolved, but the north-eastern knot has a FWHM
that is 25% larger than the restoring beam, indicating a moderately resolved
structure.

The brighter north-eastern knot could be one hotspot of an asymmetric FRII-
like radio galaxy. Neither FIRST or VLASS images, or a natural-weighted large-
scale image of the e-MERLIN data, show any evidence of a south-eastern
counterpart to the north-eastern knot. Therefore, if this is a bipolar radio
galaxy, the two lobes would need to have a high contrast of greater than
$\approx 70$. The VLASS Quick Look image shown in Figure 7 suggests a hint of
emission between the core and knot, which lends credence to the radio galaxy
interpretation.

Moderately deep optical imaging of the region around the QSO from the NOAO
Legacy surveys does not show any optical counterpart at the location of the
north-eastern knot, which also supports its hotspot nature. On the other hand,
at the depth of the optical image ($z=23$ AB mag), the corresponding limit on
the equivalent rest-frame U-band luminosity of any galaxy at the redshift of
the QSO ($z=1.439$) yields a stellar mass of $\approx 7\times 10^{10}$ M⊙,
taking a solar-metallicity simple stellar population with an age $\approx 1.5$
Gyr, a reasonable model for a radio-loud galaxy host in the environment of the
QSO. The limit is only weakly dependent on the age or metallicity of the
assumed stellar population. Clearly, a rather massive galaxy in the vicinity
of the QSO could remain undetected with the available optical imaging, if it
was quiescent or dusty. Therefore, the absence of a visible optical
counterpart to the north-eastern knot should not be taken as strong evidence
that this object is a large asymmetric radio galaxy centred on the QSO.

###  3.2 FIRST vs. e-MERLIN radio fluxes

Figure 8: The ratio of the total measured e-MERLIN flux to the FIRST flux for
the radio QSOs from our study; rQSOs (red open histogram) and cQSOs (cyan
closed histogram) are plotted separately. The number in the upper left is the
probability that the flux ratios of the cQSOs and rQSOs are drawn from the
same parent distribution as determined by a K-S test. The downward triangles
mark the flux ratios for the five rQSOs (red points) and two cQSOs (cyan
points) that have extended radio emission in their e-MERLIN images. The cQSO
points have been slightly offset vertically in the Figure only to improve
their visibility.

The e-MERLIN interferometer has an L-band maximum angular scale of $\approx
2$”: our images are not sensitive to radio structures that are larger than
these scales. In contrast, the resolution of FIRST is at least 5” across.
Therefore, our radio QSOs could potentially have extended radio emission that
is invisible to e-MERLIN, yet remains unresolved with FIRST.

We can search for evidence of this by comparing the L-band radio fluxes from
FIRST to the fluxes we have measured from the e-MERLIN images through our
Gaussian component analysis (Section 2.4.2). A significant and systematic
excess of FIRST fluxes over e-MERLIN fluxes would suggest radio emission that
is resolved out by e-MERLIN.

In Figure 8, we plot the FIRST-to-e-MERLIN flux ratio distributions of the
rQSOs and cQSOs separately. The median ratio for rQSOs is 1.06, compared to
1.02 for cQSOs; the difference is not significant given the substantial
scatter of the observed flux ratios (standard deviations of $\approx 0.2$
dex). This is verified through a two-sided K-S test, which indicates that the
two distributions have a $80$% chance of being drawn from a common parent
sample.

The observed scatter of the flux ratios is larger than the estimated flux
scale uncertainty of our observations ($<10$%; Section 2.4.1). Therefore, we
attribute these flux differences primarily to radio source variability in
these compact QSOs over the $\approx 8$ years that separate the epochs of the
FIRST and e-MERLIN observations. Since the flux ratios of the rQSOs and cQSOs
do not differ significantly, we conclude that neither subsample shows any
conclusive evidence for the widespread presence of bright radio structure
extending beyond a few arcsec ($\gtrsim 15$ kpc at the redshifts of our QSOs).

Having said this, the seven sources with visual extended structure (downward
pointing triangular points in Figure 8) have flux ratios that are generally
shifted towards positive values, which may result from low-level extended
emission from radio lobes that has been resolved out. This emission is
unlikely to dominate the radio flux in these sources. The rQSO with a negative
ratio is 0946+2548, where the e-MERLIN flux estimate comes primarily from the
large low surface-brightness component which is poorly constrained, and
possibly overestimated. While we can trust the accuracy of the e-MERLIN flux
estimates for the core-dominated unresolved sources, the resolved sources
could have larger errors. As the FIRST fluxes will be reliable for all our
sources, we only use these in the following analyses of radio properties,
keeping in mind that variability sets a systematic scatter of a factor of 2 on
L1.4.

###  3.3 Radio spectral indices

Figure 9: 1.4 GHz flux densities from FIRST plotted against 150 MHz flux
densities from TGSS for the QSOs in our sample. The diagonal dotted lines mark
tracks of constant radio spectral index between the two frequencies, ranging
from an inverted spectrum ($\alpha=0.2$) in the lower right to a steep
spectrum ($\alpha=-1$) towards the middle left. QSOs that are extended in the
e-MERLIN images are shown with larger star-shaped points. The upper limits are
plotted at 24.5 mJy, the median detection limit of the TGSS survey.

Figure 9 plots the 1.4 GHz and 150 MHz flux densities of the 39 QSOs with
coverage in the TGSS ADR (Section 2.3). The dotted diagonal lines delineate
tracks of constant radio spectral index $\alpha$, where the flux density at a
radio frequency $\nu$ is given by S${}_{\nu}\propto\nu^{\alpha}$.

The spectral indices of the 8 TGSS-detected QSOs span values from -0.4 to
-0.8, fairly typical for AGN-powered radio sources. For the rest, we show
typical 7$\sigma$ ($=24.5$ mJy) upper limits on the 150 MHz flux densities.
These span a large range of possible spectral indices, and some of the QSOs
that are bright in FIRST are expected to have flat or inverted spectra,
characteristic of very compact core-dominated radio sources. Conversely, the
150 MHz fluxes of the TGSS-detected sources could arise from very extended
steep-spectrum lobes that do not appear in either FIRST or NVSS images. Future
LOFAR public survey data will help discriminate between compact and extended
low frequency radio components.

6 of the TGSS detections also show extended emission in their e-MERLIN images,
which is consistent with their nature as more evolved radio sources (Section
4.3.2). The two rQSOs with extended structure that remain undetected in TGSS
(1122+3124 and 1535+2434) are also the most core-dominated, and their limits
suggest a typical flat-spectrum core.

###  3.4 The mid-infrared – radio plane

Figure 10: L6μm vs. L1.4 for rQSOs (left panel) and cQSOs (middle panel) from
the parent sample (small coloured points) in the redshift range $1.0<z<1.55$
used in this study. The e-MERLIN targets are shown as large coloured points in
the respective panels. Diagonal lines in all three panels show lines of
constant ‘radio-loudness’ $\mathcal{R}$, as defined in Section 3.4. The solid
diagonal line marks the approximate transition between ‘radio-loud’ and
‘radio-quiet’ sources. In the right panel, we plot the relative enhancement in
the radio detection rate of rQSOs vs. cQSOs in the indicated bins of
$\mathcal{R}$, as measured from the very same populations of QSOs plotted in
the left and middle panels. The detection rate enhancement increases towards
low values of $\mathcal{R}$ (see also Klindt et al. 2019). The points plotted
in the right panel are the e-MERLIN targets of this study, and the sources
with visually extended emission are distinguished as red star points (five
rQSOs) and cyan star points (two cQSOs).

In Figure 10, we plot the MIR luminosity (L6μm) against the FIRST-based rest-
frame 1.4 GHz luminosity (L1.4) of colour-selected QSOs from the parent sample
in our working redshift interval. rQSOs and cQSOs are plotted in the left and
middle panels respectively. As noted in our earlier works, there is no clear
relationship between MIR and radio luminosities, with both spanning orders of
magnitude within the parent sample (Klindt et al. 2019; Rosario et al. 2020;
Fawcett et al. 2020). However, there is a clear difference between cQSOs and
rQSOs in the distribution of radio luminosities in this plane. This is evident
if we compare the fraction of cQSOs and rQSOs across the L1.4–L6μm ratio, a
quantity, when converted into $\log_{10}$ units, that we define as the ‘radio-
loudness’ $\mathcal{R}$. We refer the reader to Klindt et al. (2019) and
Rosario et al. (2020) for a detailed discussion of the $\mathcal{R}$ parameter
in relation to traditional radio-loudness measures, but highlight here that
the value of $\mathcal{R}=-4.2$ corresponds to the typical radio-loud/-quiet
divide, such that more radio-loud systems have a higher value of
$\mathcal{R}$.

In all three panels of Figure 10, we plot diagonal lines which mark constant
values of $\mathcal{R}$. The solid diagonal line corresponds to the
characteristic threshold value of $\mathcal{R}=-4.2$. Earlier work from our
team (Klindt et al. 2019; Rosario et al. 2020) has shown that radio-
intermediate rQSOs have a significantly higher incidence within the QSO
population, i.e., the enhancement in the radio detection rate of rQSOs over
that of cQSOs is highest for systems that have an $\mathcal{R}$ value around
the solid line in Figure 10. We can demonstrate this visually by splitting the
rQSOs and cQSOs in the left and middle panels into bins of $\mathcal{R}$ and
plotting their relative numbers, normalised by the size of the respective
parent sub-samples to account for the larger number of cQSOs drawn from the
parent sample. This is shown in the right panel of Figure 10. Among the most
radio-loud QSOs, towards the top left of the panel, the relative incidence of
rQSOs and cQSOs are similar, but moving towards the bottom right and
decreasing in $\mathcal{R}$, rQSOs become significantly more numerous with
respect to cQSOs until the radio detection limit of FIRST cuts in. Around the
radio-loud/-quiet boundary, there are $\approx 5$ times more rQSOs detected in
the radio than cQSOs if one considers equally populated subsets of the parent
sample.

We can now examine the trends shown by our e-MERLIN targets on the MIR-radio
plane within the context of the co-eval parent QSO population. The targets are
shown as large circular points in their respective panels on Figure 10. The
narrow range in radio luminosity used to select our targets ($25.5<\log L_{\rm
1.4}<26.5$ W Hz-1) is evident, as well as the fact that they are matched in
L6μm.

The targets are all plotted together in the right panel of Figure 10, where we
have additionally highlighted those sources with extended emission as large
coloured star points. Interestingly, the sources seem to cluster differently
on this plane depending on their classification. The two extended cQSOs lie to
the upper left of the range shown by our targets, in the domain of
$\mathcal{R}$ that mark them as being quite radio-loud. On the other hand, the
five rQSOs with extended emission lie to the right and bottom right,
increasingly close to the radio-intermediate regime where rQSOs are most over-
represented in the overall QSO population.

###  3.5 Physical sizes

Figure 11: Maximum projected radio source diameters of the QSOs in our sample,
measured from gaussian fits to the e-MERLIN images and converted to physical
units. Resolved sources are shown using filled histograms and the limits on
the core sizes of the unresolved sources are shown using open histograms.

Even a cursory examination of Figure 6 reveals qualitative differences in the
appearance of the visually extended rQSOs and cQSOs. All five rQSOs show
complex, knotty structure, often on small scales, while the two cQSOs display
single unresolved cores and larger hotspots or lobes. This can be
quantitatively assessed through a comparison of the physical sizes of the
rQSOs and cQSOs.

We define the maximum size of our sources as either the largest separation
between any two Gaussian sub-components or the major-axis width of the largest
single component, whichever is larger. In the case of sources that only have a
single core component, its major-axis width is adopted as a limit on the
source size. We transcribe the measured angular sizes to physical sizes using
the angular diameter distances for the redshifts of our targets. In Figure 11,
we show histograms of the physical sizes of the ensemble of cQSOs and rQSOs,
and use solid histograms to show the sizes of the extended subset.

The two visually extended cQSOs are the largest systems in our sample, both
with sizes $\gtrsim 20$ kpc. Two of the extended rQSOs have similar sizes:
0946+2548 and 1153+5651. The three remaining extended rQSOs are only a few kpc
in size, well within the scale of their host galaxies.

While these differences are interesting, it is important to highlight that the
majority of the colour-selected QSOs that we have imaged with e-MERLINremain
unresolved at scales of $\lesssim 2$ kpc. We interpret this and other results
from this work in the following discussion.

##  4 Discussion

Our studies of the SDSS QSO population (Klindt et al. 2019; Rosario et al.
2020; Fawcett et al. 2020) have conclusively demonstrated that red QSOs
(rQSOs) harbour a significantly larger fraction of compact radio sources of
moderate radio-loudness in comparison to normal blue QSOs (cQSOs). Using
e-MERLIN, we have obtained 1.4 GHz (L-band) images of sets of MIR luminosity-
and redshift-matched rQSOs and cQSOs in a small redshift interval
($1.0<z<1.55$) with compact morphologies in the FIRST survey. The new e-MERLIN
images achieve angular resolutions of $\approx 0\aas@@fstack{\prime\prime}2$,
an improvement of more than an order of magnitude over FIRST, which allows a
detailed search for resolved radio structure among the very subpopulation of
radio quasars in which rQSOs and cQSOs differ the most.

We undertake Gaussian single- or multi-component decomposition of the radio
images of our targets, and apply a battery of tests to search for extended
structure: visual assessment, core/beam comparisons, and the examination of
positional offsets of the radio core with respect to the optical GAIA
positions of the QSOs. We also search for differences in the amount of
resolved 1.4 GHz emission by comparing FIRST and e-MERLIN fluxes. Our analysis
only identifies 7 visually extended sources (5 rQSOs and 2 cQSOs) from the
final colour-selected subsets; the remaining 32 QSOs are unresolved with
e-MERLIN.

In the rest of this discussion, we collate the evidence for morphological
differences in the radio structures of red and normal QSOs, and present a
plausible scenario that connects the dust that reddens the rQSOs and their
radio properties. We also comment broadly on the nature of compact radio
sources in QSOs near cosmic noon, as revealed by this e-MERLIN study.

###  4.1 Kiloparsec-scale radio structures are more common in red QSOs

In terms of the radio structures of the ensemble of QSOs from our study, the
clearest result is that the majority of our targets are unresolved and
therefore exhibit pure core radio morphologies.

32/40 ($82^{+5}_{-8}$%) of the QSOs remain unresolved at the physical
resolution of the e-MERLIN images ($1.2$–$2.5$ kpc). Comparisons of the
e-MERLIN and FIRST 1.4 GHz fluxes of our targets (Section 3.2) do not indicate
the presence of much emission on scales of 10s of kpc that may be missed by
e-MERLIN.

Of the individual subsamples, 5/19 ($26^{+12}_{-7}$%) of the rQSOs and 2/20
($10^{+11}_{-3}$%) of the cQSOs are clearly extended. As it stands, our
results imply a $\approx 2\sigma$ difference in the incidence of extended
structure between the two populations, which we consider to be statistically
significant.

Since only a small fraction of the cQSOs show extended structure, our
interpretation of the cQSO 1511+3428 is important. For the purposes of
baseline statistics, we treat it as a single multi-component radio source with
a nuclear core coincident with the QSO. However, based on the discussion from
Section 3.1.7, it is possible that the offset hotspot seen in the image is an
independent radio source associated with a neighbouring galaxy. If this were
indeed the case, the fraction of cQSOs with extended structure drops to
$5^{+9}_{-2}$%, differing from rQSOs at the $\approx 3\sigma$ level.

At face value, the low incidence of extended radio structures on scales of a
few arcseconds among the cQSOs is unexpected. There is no a priori reason that
so many QSOs, selected only to be unresolved at $>5$”, should not display
detectable radio structures between FIRST and e-MERLIN resolutions. For an
example of a contrasting result, an early MERLIN survey of Jy-level radio
quasars (Reid et al. 1995) only finds one source that remains unresolved at
sub-arcsecond scales, out of a subset of 19 at the same range of redshifts as
our e-MERLIN targets.

However, we are unable to identify work in the current literature that offers
an unbiased perspective on the high-resolution radio morphologies of QSOs of
similar radio luminosities as shown by our targets. The study of Reid et al.
(1995) mentioned above, by virtue of its bright radio flux cut, images quasars
that are at least two orders of magnitude more luminous than our sample. A
high incidence of bright large-scale lobes is perhaps not surprising in these
very powerful systems. Several studies have targeted interesting subsamples,
such as those with known large radio jets or steep radio spectra (e.g. Akujor
et al. 1991; Lonsdale, Barthel & Miley 1993; Mullin, Riley & Hardcastle 2008)
but these have extended radio structure by construction. There have been some
high resolution studies of low-redshift and/or radio-quiet QSOs (e.g., Kukula
et al. 1998; Jarvis et al. 2019), which typically find extended structures in
50-90% of their sample. However, the targets in these studies are often pre-
selected by properties that may be connected to extended radio jets, such as
high-velocity outflows in narrow forbidden lines like [O III]$\lambda 5007$
(e.g., Jarvis et al. 2019).

In this sense, our observations offer a valuable reference for the incidence
of extended cm-wave radio structures in typical QSOs hosting low-power radio
sources at $z\sim 1$.

###  4.2 The incidence of radio sources of different sizes among red and
normal QSOs

Figure 12: The incidence of radio sources in the L1.4 range of our targets
with different maximum projected sizes, expressed as a fraction of the
respective colour-selected QSO subpopulations from the SDSS DR7 with
comparable redshifts. Fractions for the rQSOs (red points) and cQSOs (blue
points) are shown separately. See the associated text in Section 4.2 for
details.

Our e-MERLIN targets were selected as compact or unresolved sources based on
images from the FIRST survey. The 5” angular resolution of FIRST translates to
projected sizes of $41$–$44$ kpc at the redshifts of our targets, much larger
than the typical sizes of even the massive galaxies that are the likely hosts
of these QSOs. As noted above, it is surprising to find that only a few of our
QSOs show resolved radio structure in the e-MERLIN images, despite our ability
to resolve such structure down to $\approx 2$ kpc and with surface-brightness
contrasts of $10$–$100$s. This implies that radio QSOs show a dearth of
emission on scales of several kpc, approximately in the size range of their
host galaxies (e.g., van der Wel et al. 2014).

We investigate this notion further by examining the incidence of radio sources
of different (projected) sizes among QSOs in the redshift and radio luminosity
ranges of our e-MERLIN targets ($1.0<z<1.55$; $10^{25.5}\leq$L1.4$\leq
10^{26.7}$ W Hz-1). We consider four characteristic physical scales: $<2$ kpc
(‘nuclear’), 2–10 kpc (‘galactic’)222The choice of a threshold of 10 kpc to
separate galactic and circumgalactic scales is based on the optical sizes of
massive galaxies at $z\sim 1.3$, the majority of which are found to be smaller
than 10 kpc, with a median effective radius of $\approx 5$ kpc (e.g., van der
Wel et al. 2014)., 10–42 kpc (‘circumgalactic’), and $>42$ kpc
(‘supergalactic’)333The choice of 42 kpc as a threshold between the
circumgalactic and supergalactic scales is set purely by the resolution limit
of FIRST projected to our redshifts of interest..

Our approach is to combine statistics from the FIRST survey and our e-MERLIN
programme to evaluate, or place limits on, the fraction of colour-selected
QSOs that have radio source sizes within the four ranges defined above. An
important detail is that these fractions are evaluated with respect to the
entire parent population of co-eval colour-selected SDSS QSOs, not just
against the radio-detected subsets. This approach normalises for the key
differences in the FIRST radio properties between rQSOs and cQSOs, viz. the
significantly higher incidence of compact radio sources among rQSOs.

As an illustration, consider the fraction of cQSOs with supergalactic radio
sizes. To arrive at this number, we first count cQSOs from the parent sample
satisfying our redshift and L1.4 cuts that are also resolved by FIRST. We then
divide this total by the number of all cQSOs in that redshift range
irrespective of radio properties. For the three smaller size bins (nuclear,
galactic, circumgalactic), we bring in constraints from e-MERLIN, which,
though limited in statistical size, push well below the FIRST resolution
limit. In these cases, we multiply the fraction of cQSOs that are compact in
FIRST by the fraction of e-MERLIN targets that have maximum measured sizes at
the respective physical scales, propagating uncertainties using binomial
statistics (Cameron 2011). Similar calculations are performed in each bin
separately for rQSOs and cQSOs, and the results are shown in Figure 12.

We first consider the trend shown among cQSOs, which should be representative
of normal QSOs of similar redshift and accretion luminosity. Based on the
statistics of e-MERLIN targets that remain unresolved, $\approx 2$% of cQSOs
contain nuclear low-power core-dominated radio sources. We do not find any
cQSOs that have measured e-MERLIN sizes in the 2–10 kpc range, which sets a
2$\sigma$ upper limit of $<0.4$% on the fraction on galactic scales. The 2
e-MERLIN cQSOs that are resolved both have sizes between 10 and 42 kpc
yielding a circumgalactic fraction of 0.1–0.5%. Using the better statistics
for the sources resolved by FIRST, the supergalactic fraction settles to 0.5%,
comprising of radio galaxies of intermediate radio-loudness with traditional
FR I/II classifications, as well as more complex extended morphologies (Klindt
et al. 2019).

The trend among the rQSOs reveals important differences when contrasted to
that of the cQSOs. Klindt et al. (2019) demonstrated that the incidence of
FIRST-resolved radio sources among rQSOs is indistinguishable from cQSOs
across a broad range of redshifts. Among the QSOs within our working redshift
range, the supergalactic fractions for both classes are identical within the
statistical errors, confirming this result. However, proceeding towards
progressively smaller scales, the fraction of rQSOs rises steadily and
deviates strongly from the trends shown by cQSOs. At galactic scales, the 3
rQSOs that are extended in our e-MERLIN images determine an estimated fraction
of $\approx 1$%, more than $\times 2$ higher than the conservative upper limit
placed on the cQSO fraction. In the nuclear bin, the rQSO incidence is
$\approx 4.5$%, again more than $\times 2$ the rate found among cQSOs. The
significant excess of unresolved radio sources seen among rQSOs from lower
resolution surveys (Klindt et al. 2019; Rosario et al. 2020; Fawcett et al.
2020) can be attributed to a truly compact population that lies mostly within
the inner few kpc of their host galaxies. This indicates that the likely
location of the dust that reddens red QSOs is in the central environment of
their AGN.

What can we deduce about the connection between the radio emission and the
rQSO phenomenon from these differences in the fractional radio size
distributions? The clearest excess among rQSOs is found among resolved and
unresolved radio sources at scales $<10$ kpc. From this, we can conclude that
the differences cannot be purely associated with the synchrotron population in
the immediate vicinity (inner few pc) of the accretion disc, such as a jet
base or corona. At least some of these differences must be driven by a radio-
emitting structure that extends beyond the scope of the central engine to
explain the differences we find on galactic scales.

###  4.3 What is responsible for the excess radio emission in red QSOs?

Bringing together various threads from the literature and our own analyses, we
explore three potential explanations for the excess radio emission in rQSOs:
star-formation differences, a higher incidence of small-scale low-power
classical radio jets, or widespread nuclear dusty winds.

####  4.3.1 Star-Formation

In a popular evolutionary model connecting red and normal QSOs, rQSOs are
caught in a special stage during, or shortly after, a powerful merger-
sustained starburst event, when an explosive AGN feedback episode is clearing
out the gas-rich centre of the host galaxy (e.g., Glikman et al. 2012). Strong
differences in the star-formation rate (SFR), particularly within the central
kpcs, are a natural prediction of this model. Since supernova remnants
associated with star-formation can produce synchrotron emission at GHz
frequencies, could the root of the differences we see in our e-MERLIN images
stem from fundamental differences in the SFR and the spatial distribution of
star-forming regions in rQSOs?

The compact radio source components in our e-MERLIN images account for almost
all of the integrated radio emission in our targets. Even the faintest
components that we measure from our images have L-band flux densities $>0.3$
mJy (Table 3), which, at their redshifts, imply L1.4 $>5\times 10^{24}$ W
Hz-1, or SFRs greater than a few 1000 M⊙ yr-1, taking well-used calibrations
between SFR and L1.4 (Murphy et al. 2011; Kennicutt & Evans 2012). Estimates
of the SFR from integrated L1.4 can be much higher. These derived SFRs are 1-2
orders of magnitude larger than the SFRs of typical QSOs at $z\sim 1$ (Rosario
et al. 2013; Stanley et al. 2017; Calistro Rivera et al. 2021). Quite simply,
the radio luminosities of our sample are too large for star-formation to be an
important contributor to the emission we detect with FIRST or e-MERLIN. Even
among co-eval ‘radio-quiet’ QSOs, with L1.4 fainter than our targets by an
order of magnitude, star-formation is not found to dominate the integrated 1.4
GHz radio emission (e.g., White et al. 2017). Therefore, we can confidently
continue with the notion that the radio differences we see are due to AGN-
powered processes.

####  4.3.2 Jet-powered radio sources

Figure 13: Maximum radio source size vs. 1.4 GHz radio power (L1.4) for our
rQSOs (red points) and cQSOs (cyan points). Filled circles and left-pointing
arrows show extended sources and unresolved sources respectively. The dashed
vertical lines mark the typical physical resolution of the FIRST survey and
the VLBA at L-band at a characteristic redshift of $z=1.3$. The dotted
horizontal line marks a rough transition between low-power and high-power
radio sources. The coloured bands spanning the FIRST resolution limit
graphically show the relative fractions of radio rQSOs and cQSOs that are
determined to be compact or resolved by FIRST. Note that compact sources are
more commons among rQSOs compared to cQSOs at low radio luminosities, but they
are found equally among more luminous systems (e.g., Klindt et al. 2019). We
mark using shaded bands the approximate size ranges of the CSS, GPS, and CSO
categories of jetted radio sources. The largest extended radio sources, those
that are well-resolved by FIRST, are the classical double-lobed FRI/II
systems.

Jet-driven radio galaxies present a plethora of morphologies, and have sizes
spanning from nuclear scales to some of the largest coherent structures in the
Universe (Miley 1980). Given the long-standing association between radio
galaxies and QSOs (Urry & Padovani 1995), it is reasonable to interpret the
sources we have characterised with e-MERLIN in the context of the population
of classical radio galaxies at intermediate redshifts.

The e-MERLIN morphologies of the extended small-scale radio sources in our
sample are typically bipolar, but they do not all sport the core/jet or
core/lobe structure reminiscent of classical double radio galaxies. However,
it is also well-known that powerful radio sources that are confined within
their hosts often show quite disturbed morphologies on similar size scales
(O’Dea 1998, and references therein). Therefore, morphological information
alone is not sufficient to assess their nature.

Additional insight and context comes by examining our sources on the space of
1.4 GHz radio luminosity (L1.4) vs. the maximum physical size in kpc (Figure
13). Similar diagrams have been employed by earlier studies to explore the
dynamical evolution of radio sources (e.g. O’Dea & Baum 1997; Kunert-
Bajraszewska et al. 2010; An & Baan 2012; Jarvis et al. 2019).

As jet-powered radio sources evolve, their primary energy loss mechanisms
change as they expand and interact with the ambient medium of their host
galaxies (An & Baan 2012, and references therein). Within the dense,
approximately constant density interstellar medium of the central few 100s of
pcs of a galaxy, adiabatic losses dominate over synchrotron losses, leading to
a low radiative conversion efficiency and a steep radio spectrum. Such sources
are called Compact Symmetric Objects (CSOs). As they expand beyond the inner
galaxy, the confining gas develops a density gradient decreasing outward and
synchrotron losses catch up to adiabatic losses. A prominent spectral break at
cm wavelengths develops and the term Gigahertz-Peaked Spectrum (GPS) is used
to describe such sources. As they burst out of their host galaxies,
synchrotron losses take over; jets and lobe expand out into their galactic
environment as the spectral break moves to lower frequencies in the form of
Compact Steep Spectrum (CSS) sources and eventually the classical doubles of
FR I/FR II morphologies.

In Figure 13, we delineate the ranges of sizes observed in radio galaxies of
the various categories outlined above. All these categories can span orders of
magnitude in L1.4, so we only use their sizes to distinguish them in our
diagram, using various shaded regions which nonetheless have substantial
overlap.

The e-MERLIN QSOs that are resolved (circle points) are in the range of sizes
shown by CSS sources. This is consistent with their moderately steep meter-
wave spectral indices found in our FIRST-TGSS analysis (Figure 9). The
unresolved sources have upper limits to their sizes (left arrow points) that
place them in the GPS and CSO regime. If their actual sizes are at the order
of hundreds of pc, we expect these objects to predominantly display
synchrotron spectra with strong curvature at 100s of MHz to GHz frequencies
(O’Dea & Baum 1997). Unfortunately, from our analysis in Section 3.3, we
cannot clearly ascertain whether the meter-wave spectral indices, most of
which are limits, suggest a turn-over or not, but it is unlikely that the
unresolved e-MERLIN sources all show flat or inverted spectra between TGSS and
FIRST bands.

####  4.3.3 Wind-powered radio sources

Dusty AGN-driven winds (e.g., Hönig 2019) can also offer an explanation for
the small-scale radio emission that we observe. Recently, Calistro Rivera et
al. (2021) presented a comparative multi-wavelength and spectral analysis of
rQSOs and cQSOs selected using the same approach as our earlier works. They
report a correlation between the presence of excess hot dust emission in the
MIR and strong outflow signatures among rQSOs, which is evidence that dusty
winds are responsible for their red colours.

Shocks from fast winds in AGN have been invoked in earlier studies to explain
enhanced radio emission in luminous AGN that also show emission-line outflows
(e.g., Zakamska & Greene 2014). The low radio-loudness of the excess radio
sources in rQSOs is consistent with a possible origin in shocks from AGN-
driven winds that also carry enough dust to mildly redden the nuclear spectra
in these objects (Rosario et al. 2020).

The radio morphologies produced by such winds are still unclear. They are
likely to be bipolar, reflecting the collimation of a wind towards the polar
axis of the accretion structure (Williamson, Hönig & Venanzi 2020), but
whether they retain their shape over kpcs in the gas-rich environment
surrounding the nucleus is subject to debate (Wagner, Umemura & Bicknell
2013). For e.g., radio-quiet QSOs with strong kpc-scale outflows, systems in
which wind shocks are expected to be commonplace, appear to show radio
structures that look like classical radio galaxies (Jarvis et al. 2019).

We stress here that it is the excess compact radio emission found in rQSOs
that we seek to understand. Nuclear radio sources are seen in our cQSOs as
well, and these could very well arise from jets or coronal emission since
cQSOs are not expected to harbour widespread dusty winds. Since nuclear radio
sources are about twice as common among rQSOs as cQSOs (Figure 12), roughly
half of them may arise from standard jet-powered processes. It is the other
half, powered by dusty winds, which accounts for the overall enhancement of
radio emission in rQSOs in this scenario.

Very long baseline interferometry (VLBI) has the capacity to resolve the
small-scale structure of our sources ($<100$ pc). For e.g., the Very Long
Baseline Array (VLBA) has a resolution at 1.4 GHz of 5 mas, probing well into
the domain of physical sizes that separate GPS and CSO sources (Figure 13).
Future multi-frequency studies with this or complementary facilities may allow
us to explore whether the nuclear radio structures in the majority of our
targets could be described as the early evolution of bipolar jets.

Another potential test to distinguish between jet-powered or shock-powered
explanations is through the use of radio spectral curvature constraints. Jet-
driven double radio sources show strong correlations between their spectral
turnover frequencies and their source sizes (O’Dea & Baum 1997), a consequence
of the dynamic changes that such radio sources undergo as they expand within
their host galaxies. Radio structures from wind shocks are not expected to
evolve in a similar fashion, and therefore may not lie along such trends.

With multi-band Giant Metre-Wave Radio Telescope (GMRT) observations which
have recently been taken for all 40 e-MERLIN targets (Principal Investigator:
V. Fawcett), future work from our team will present a comparative radio
spectral and morphological analysis, seeking further insight into the
phenomena that fundamentally distinguish red and normal QSOs.

##  5 Conclusions

We present e-MERLIN L-band images of a sample of 19 red QSOs (rQSOs) and 20
normal QSOs (cQSOs) at redshifts of $1.0<z<1.55$. Our targets are matched in
redshift and rest-frame 6 $\mu$m luminosity (L6μm), a measure of their nuclear
bolometric power, and selected to have moderate 1.4 GHz luminosities
($10^{25.5}\leq$L1.4$\leq 10^{26.7}$ W Hz-1) and compact morphologies in the
FIRST survey (angular resolution of 5”; $>40$ kpc at the QSO redshifts). The
e-MERLIN images resolve radio structures down to $\approx
0\aas@@fstack{\prime\prime}2$, probing host galaxy scales in these QSOs
($2$–$10$ kpc).

Following a morphological assessment of the e-MERLIN images, both visually and
by means of gaussian decomposition, we assessed the incidence and distribution
of radio sources in our targets across a range of projected size scales. Our
main conclusions are as follows:

  * •

The majority of both cQSOs and rQSOs have nuclear radio cores that remain
unresolved with e-MERLIN (Figure 3 and Section 4.1).

  * •

We find a statistically significant excess in the incidence of small-scale
radio sources (sizes $<10$ kpc) among rQSOs, while confirming that larger
radio sources are as common in rQSOs as in cQSOs in the redshift and L1.4
range of interest (Section 4.2). We report a very low incidence ($<0.4$%) of
sources with galactic-scale sizes ($2$–$10$ kpc) among typical QSOs (cQSOs).

  * •

Incorporating TGSS constraints, most of the sources with extended e-MERLIN
structure also show typical steep radio spectral indices (Section 3.3).

  * •

Unlike the cQSOs, rQSOs with extended e-MERLIN emission tend to be of
intermediate radio-loudness (Section 3.4).

  * •

We consider various scenarios to explain the excess in kpc-scale radio
structures we find among rQSOs. Current constraints from radio morphologies
and spectral indices imply that the differences cannot arise purely from the
accretion structure (the accretion disc and/or corona), but must entail
differences in components that partially extend out into the host galaxy.
These could either be classical jet-powered radio sources, or those powered by
winds. Since the key feature that defines rQSOs is the presence of moderate
dust extinction towards their nuclei, we postulate that dusty winds are
widespread among rQSOs, and the shocks that these winds drive into the
interstellar medium of their host galaxies are responsible for the particular
radio properties of red QSOs.

## Acknowledgements

We thank the anonymous referee for input that has improved the material and
message of this work. DJR and DMA acknowledge support from STFC
(ST/T000244/1). JM acknowledges financial support from the State Agency for
Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa”
award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709) and from
the grant RTI2018-096228-B-C31 (MICIU/FEDER, EU) e-MERLIN is a National
Facility operated by the University of Manchester at Jodrell Bank Observatory
on behalf of STFC, part of UK Research and Innovation. Funding for the SDSS
and SDSS-II has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, the U.S.
Department of Energy, the National Aeronautics and Space Administration, the
Japanese Monbukagakusho, the Max Planck Society, and the Higher Education
Funding Council for England. This work has made use of data from the European
Space Agency (ESA) mission Gaia processed by the Gaia Data Processing and
Analysis Consortium (DPAC, Funding for the DPAC has been provided by national
institutions, in particular the institutions participating in the Gaia
Multilateral Agreement.

## Data Availability

The e-MERLIN data used in this work is available from the corresponding author
by reasonable request. All other data are in the public domain and accessible
through the corresponding data archives. All measurements required to
replicate our results are made available in this paper in the form of figures
and tables.

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