# Kpc-scale Radio Structure in $z\sim 0.25$ Radio-Quiet QSOs

Trevor V McCaffrey Department of Physics, Drexel University
32 S. 32nd Street
Philadelphia, PA 19104, USA  National Radio Astronomy Observatory
1003 Lopezville Rd
Socorro, NM 87801, USA  Amy E Kimball National Radio Astronomy Observatory
1003 Lopezville Rd
Socorro, NM 87801, USA  Emmanuel Momjian National Radio Astronomy Observatory
1003 Lopezville Rd
Socorro, NM 87801, USA  Gordon T Richards Department of Physics, Drexel
University
32 S. 32nd Street
Philadelphia, PA 19104, USA

(Received April 11, 2022; Revised July 5, 2022; Accepted July 27, 2022)

###### Abstract

We present analysis of a homogeneous, optically selected, volume-limited
($0.2<z<0.3$) sample of 128 radio-quiet quasi-stellar objects (QSOs) recently
observed at 6 GHz with the Very Large Array (VLA) in A-configuration ($\sim
0\farcs 33$ resolution). We compare these new results to earlier (2010–2011)
6-GHz observations with the VLA in C-configuration ($\sim 3\farcs 5$). While
all of these radio-quiet QSOs (RQQs) were unresolved on a $3\farcs 5$ scale
($\sim$14 kpc at $z=0.25$), we resolve notable complex sub-galactic structures
in about half of the RQQs at $0\farcs 33$ resolution ($\sim$1.3 kpc at
$z=0.25$). By comparison of flux density measurements between the two sets of
observations, we demonstrate that significant sub-galactic-scale radio
structure is present in at least 70% of the RQQ population, and that the
central component accounts for an average of $\approx$65% of the total
detected radio power. One RQQ, J0935+4819, shows striking symmetric, double-
lobed morphology, and appears to be the first identified example of a radio-
quiet QSO with FR II type morphology on $\sim$arcsec scale (projected size of
$\gtrsim 6\mathrm{kpc}$). In addition to revealing RQQ sub-galactic
morphology, we employ counterparts from legacy (FIRST at 1.4 GHz) and recent
(VLA Sky Survey at 3 GHz) VLA surveys to investigate radio spectral indices
and potential variability over decades-long timescales for a subset of the
RQQs, and for the cores of radio-intermediate and -loud sources in the parent
sample of 178 QSOs. These results support the growing notion that the RQQ
population is not a monolithic phenomenon, but instead consists of a mixture
of mainly starburst-powered and jet-powered galaxies.

††journal: AJ

##  1 Introduction

While the first quasi-stellar objects (QSOs) were discovered upon the basis of
their radio properties (Burbidge, 1967; Burbidge & Burbidge, 1967; Schmidt,
1969), our understanding of their radio emission remains incomplete. Emission
from radio-loud QSOs (RLQs) is known to be powered by the jets of their active
galactic nuclei (AGNs) because of, among other lines of reasoning: extended
morphologies (large-scale radio components extending beyond the host galaxy),
observations of apparent superluminal motion (Chi et al., 2013; Maini et al.,
2016; Herrera Ruiz et al., 2016, 2017), or the presence of high brightness
temperature component(s) (non-thermal emission with $T_{\mathrm{B}}>4\times
10^{4}$ K at 6 GHz; Condon, 1992). The dominant source of radio emission in
radio-quiet111For the purposes of this paper, we define radio-quiet QSOs to be
QSOs with $L_{\mathrm{6\,GHz}}<10^{23}\;\mathrm{W\,Hz}^{-1}$. QSOs (RQQs),
however, remains a subject of much controversy. Some arguments assert that
star formation processes are the likely dominant contributor (Kimball et al.,
2011b; Condon et al., 2013; Padovani et al., 2015; Kellermann et al., 2016),
while others have argued that star formation simply is not powerful enough,
and instead mechanisms such as AGN-driven winds (Zakamska & Greene, 2014;
Zakamska et al., 2016) or scaled down jets (e.g., Ulvestad et al., 2005) are
primarily responsible.

The advent of the Karl G. Jansky Very Large Array (VLA; Perley et al., 2011)
allowed Kimball et al. (2011b), followed by Kellermann et al. (2016), to
determine the faint end of the QSO radio luminosity function (RLF) for the
first time, using a volume-complete, homogeneous QSO sample, albeit at
relatively low redshift ($0.2<z<0.3$). Their sample is optically selected and
thus is not subject to selection bias towards any radio properties. The
authors concluded that the RLF is consistent with two independent components
contributing to the radio emission in QSOs: a likely AGN-driven component
dominating at $L_{\mathrm{6\,GHz}}\gtrsim 10^{24}$ W Hz-1 (the RLQs), whereas
a bump in the RLF at $\sim 10^{23}$ W Hz-1 (similar in radio luminosity to
that of nearby starburst galaxies; Condon et al., 2002, 2013) could be due to
an additional, independent, star-formation component dominating in the lower-
luminosity RQQs.

An obstacle to answering the question “what is the dominant source of radio
emission in RQQs?” is that the most sensitive wide-area imaging campaigns have
not been undertaken at a sufficient spatial resolution to reveal the sub-
galaxy-scale radio morphologies across a large fraction of the RQQ population.
Indeed, the conclusions of Kimball et al. (2011b) were based on the shape of
the RLF, as their observations were designed as a detection experiment to
investigate radio luminosity rather than morphology. Moreover, while the
images of their targets show no sign of large-scale jets, they do reveal that
the radio emission in RQQs is confined to the dimensions of the host galaxy
[$\sim$14 kpc at $z=0.25$ (e.g., Lerner, 2018)]. Having radio emission
constrained to that scale is also consistent with AGN-driven winds (Zakamska &
Greene, 2014; Zakamska et al., 2016) or small-scale jets (Ulvestad et al.,
2005; Herrera Ruiz et al., 2016, 2017). To date, the largest and most
sensitive radio survey capable of resolving such galaxy-confined emission is
that of Hodge et al. (2011); however, its area of sky (Stripe 82, $\sim
300\,\mathrm{deg}^{2}$) is too small to probe much of the RQQ population. We
note that none of the 178 QSOs from Kimball et al. (2011b) were observed by
Hodge et al. (2011). Progress is being made on this front; Morabito et al.
(2022) presented a calibration strategy to overcome lasting ionospheric and
computational difficulties of sub-arcsecond ($\sim$0$\farcs$25) imaging with
the international LOw-Frequency Array (LOFAR; van Haarlem et al., 2013). While
their methods so far have been applied to small fields (e.g., the Lockman
Hole; Sweijen et al., 2022), such high-resolution imaging will soon be applied
across the entire northern sky as a complement to the LOFAR Two-metre Sky
Survey (Shimwell et al., 2019, 2022), reaching 1$\sigma$ sensitivities as low
as $\approx$18 $\mu$Jy beam-1 at 1.4 GHz for sources with a radio spectral
index $\alpha=-0.7$.

In this paper, we take the investigations of Kimball et al. (2011b) and
Kellermann et al. (2016) a step further, obtaining high-resolution ($\sim
0\farcs 33$; $\sim 1.3$ kpc at $z=0.25$) follow-up observations of the 128 RQ
sources from their volume-limited sample of 178 QSOs. All 128 were unresolved
in the original observations with resolution $\sim 3\farcs 5$ ($\sim 14$ kpc
at $z=0.25$); we now aim to resolve emission structures on size scales 1.3–14
kpc within the host galaxies across the sample of 128 RQQs. Following Kimball
et al. (2011b), we define “radio-quiet” as having radio luminosity
$L_{\mathrm{6GHz}}<10^{23}$ W Hz-1, where the purported star-formation
component dominates the RLF of QSOs.

While we use a specific limit on radio luminosity to define radio-quiet/radio-
loud categories for our analysis, it is important to acknowledge that various
definitions and diagnostics are used throughout the literature, potentially
leading to different conclusions as to the properties of RQ/RL sources.
Kellermann et al. (1989) first reported a potential bimodality in the Bright
Quasar Survey (Schmidt & Green, 1983) based on $R_{\mathrm{O}}$, the ratio
between 5-GHz radio luminosity and 4400-Å optical luminosity. This criterion
remains a useful radio-loudness diagnostic (e.g., Baloković et al., 2012),
along with $q$—the ratio between radio and far-infrared luminosities—as well
as $R_{X}$—a ratio of radio to X-ray luminosities (e.g., Terashima & Wilson,
2003). Such ratios are particularly useful for comparing sources across large
redshift ranges, because QSOs’ radio and optical luminosities show evolution
with redshift (Padovani et al., 2011); defining RQ/RL classes based on a
luminosity ratio serves somewhat to mitigate these evolutionary effects.
Condon et al. (2013) probed evolution of the 1.4-GHz RLF using optically
selected QSOs, and found that the luminosity-based demarcation between RQ/RL
populations increases in luminosity from low redshift ($0.2<z<0.45$) to high
redshift ($1.8<z<2.5$). For the sample presented here, drawn from Kimball et
al. (2011b) and Kellermann et al. (2016), the narrow redshift range
($0.2<z<0.3$) mitigates effects from evolution; furthermore, for the typical
$i$-band magnitude of 17.0 in this population (optical luminosity of $10^{23}$
W Hz-1 for $z=0.25$), the radio luminosity of $10^{23}$ W Hz-1 corresponds to
a radio-to-optical ratio of 1. Therefore, our definition of radio-quiet/radio-
loud is similar to a definition based on radio-to-optical ratio over this
redshift range.

As an additional step in our investigation, we use counterparts from the
literature [the Faint Images of the Radio Sky at Twenty-cm (FIRST) survey
(Becker et al., 1995; Helfand et al., 2015) and the VLA Sky Survey (VLASS;
Lacy et al., 2020)] to investigate spectral indices and potential variability
of the RQ targets, as well as radio-loud (RL) and radio-intermediate222We
define “radio-intermediate” to be the luminosity range $10^{23}$–$10^{24}$ W
Hz-1 between RQ and RL QSOs. (RI) sources from the parent sample of 178 QSOs.
Cores of RLQs are known to exhibit multi-wavelength variability on timescales
of years, months, and even days (Hovatta et al., 2007; Thyagarajan et al.,
2011). Barvainis et al. (2005) further showed that RQQs are capable of
mirroring this behavior in the radio, suggesting that the underlying
mechanisms that drive radio emission in RQQs may ultimately be similar to
those of their radio-loud counterparts. In a recent study, Nyland et al.
(2020) examined a sample of 26 quasars that were determined to be radio-quiet
based on upper limits in the FIRST survey (1993–2003; Becker et al., 1995),
but recent detections in Epoch 1 of the VLA Sky Survey (observed 2017–2019;
Lacy et al., 2020) and further VLA follow-up observations indicate that they
have now transitioned into a clear radio-loud state. Such results indicate
that RQ and RL populations overlap, and that at least in some cases the
difference between the two classes may simply be related to the duty cycle of
jet activity.

In summary, we present new targeted VLA observations—combined with previous
targeted VLA observations, legacy VLA survey data, and new VLA survey data—to
probe the radio emission in RQQs with unprecedented (for this sample) angular
resolution and years-long timescales, using an established volume-complete RQQ
population. The paper is organized as follows. Section 2 introduces the target
sample. In Section 3, we describe our observation and data reduction
techniques. We discuss the morphologies present across our sample in Section
4, with images provided in the Appendix. Section 5 presents our spectral index
and variability analysis, and we summarize our findings in Section 6.
Throughout, we assume a concordance cosmology with $H_{0}=70\ \mathrm{km\
s}^{-1}\ \mathrm{Mpc}^{-1}$ and $\Omega_{\Lambda}=0.7$.

##  2 Target selection

Table 1: Target Quasar Radio Properties

Name | $S_{\mathrm{p}}$ | $S_{\mathrm{core}}$ | $S_{\mathrm{tot}}$ | $\sigma_{\mathrm{rms}}$ | $S_{\mathrm{core}}/S_{\mathrm{tot}}$ | $S_{\mathrm{A}}/S_{\mathrm{C}}$ | $\log L_{\mathrm{6GHz}}$ | Morph. | $\theta_{\mathrm{maj}}\times\theta_{\mathrm{min}}$
---|---|---|---|---|---|---|---|---|---
(SDSSJ) | ($\mu$Jy beam-1) | ($\mu$Jy) | ($\mu$Jy) | ($\mu$Jy beam-1) |  |  | ($\log$[W Hz-1]) |  | (mas $\times$ mas)
080829.17+440754.1 | 36.3$\pm$8.3 | 36.3$\pm$8.3 | 36.3$\pm$8.3 | 7.0 | 1.00 | 0.60 | 21.90 | U |  $<$472$\times$237
081652.24+425829.4 | 178.5$\pm$7.4 | 189.2$\pm$7.6 | 199.0$\pm$14.0 | 7.6 | 0.90 | 0.90 | 22.49 | SR | 153$\times$105
082205.24+455349.1 | 425.0$\pm$10.0 | 425.0$\pm$10.0 | 531.0$\pm$33.0 | 6.8 | 0.80 | 2.40 | 23.15 | M | 150$\times$89
083443.80+382632.8 | 116.8$\pm$7.1 | 116.8$\pm$7.1 | 116.8$\pm$7.1 | 6.7 | 1.00 | 0.90 | 22.45 | U |  $<$238$\times$39
084313.41+535718.8 | 122.8$\pm$8.2 | 238.0$\pm$11.0 | 349.0$\pm$31.0 | 6.8 | 0.35 | 0.90 | 22.66 | E | 838$\times$168
084755.63+263147.6 | 27.0$\pm$2.7 | 27.0$\pm$2.7 | 41.0$\pm$6.3 | 3.6 | 0.66 | 2.40 | 21.98 | SR | 312$\times$271
085640.78+105755.8 | 305.0$\pm$7.1 | 467.7$\pm$8.9 | 509.0$\pm$101.0 | 6.9 | 0.60 | 1.82 | 23.04 | SR | 510$\times$237
085828.69+342343.8 | 103.8$\pm$8.8 | 103.8$\pm$8.8 | 189.0$\pm$24.1 | 7.0 | 0.55 | 0.90 | 22.55 | M | 370$\times$140
090151.13+103020.4 | 46.5$\pm$6.2 | 46.5$\pm$6.2 | 46.5$\pm$6.2 | 6.5 | 1.00 | 0.69 | 21.71 | U |  $\cdots$
090454.99+511444.5 | 18.4$\pm$6.0 | 18.4$\pm$6.0 | 18.4$\pm$6.0 | 7.1 | 1.00 | 0.40 | 21.41 | U |  $<$1500$\times$180

Note. — Column 1: Full name of QSO in SDSSJ format; Columns 2, 3, and 4: Peak,
core, and total 6-GHz flux densities from the VLA at $\sim 0\farcs 33$
resolution with uncertainties computed by the imfit task in CASA; for
Unresolved sources and Resolved sources whose core component is Unresolved and
clearly separated from its extended emission, columns 2 and 3 are equal.
Column 5: RMS noise of radio image. Column 6: Ratio between the core flux
density measured in column 3 and the total measured in column 4. Column 7:
Ratio between our measured total 6-GHz flux density at $0\farcs 33$ and that
measured at $3\farcs 5$ in Kellermann et al. (2016). Column 8: Base-10
logarithm of 6-GHz luminosity, computed with total flux densities given in
column 3. Column 9: Targets’ radio morphology at $0\farcs 33$ determined by
eye (see Section 4 for a description of morphologies). Column 10: Targets’
angular size deconvolved with the beam using the imfit task in CASA; upper
limits are given for unresolved sources and no estimate is available for
sources too faint to derive an accurate size. A subset of the table is shown
here for brevity; a machine-readable version of the full table is available in
the electronic journal.

Our radio-quiet sources (defined by their 6-GHz radio luminosity, as discussed
further on in this section) are from the volume-complete QSO sample defined in
Kimball et al. (2011b) and Kellermann et al. (2016). Their population was
drawn from the Schneider et al. (2010) quasar catalog in the seventh data
release of the Sloan Digital Sky Survey (Abazajian et al., 2009), with a
narrow redshift range so as to minimize evolutionary effects. Their selection
criteria, repeated below, ensure that the parent sample is volume-complete and
homogeneously selected; the selection purely on optical properties avoids any
bias toward radio-loud objects. Selection criteria for the parent sample were:

  1. 1.

object targeted for SDSS spectroscopy according to “low $z$” color criteria
(see below);

  2. 2.

$M_{i}<-23$, the historical definition for QSOs (Schmidt & Green, 1983);

  3. 3.

SDSS $i$-band magnitude $14<i<19$, after correction for extinction by Galactic
dust (Schlegel et al., 1998);

  4. 4.

$0.2<z<0.3$;

  5. 5.

Galactic latitude $b>30$°.

For SDSS spectroscopic targeting, the “low $z$” criterion refers to
photometric sources whose colors are non-stellar (i.e., inconsistent with the
stellar locus) in a color cube defined by the SDSS $ugri$ bands; this
selection ensures that sources in this sample were targeted for spectroscopy
only by their optical properties. From the SDSS spectroscopic data, QSOs are
identified by having at least one emission line with $\mathrm{FWHM}>1000\
\mathrm{km\ s}^{-1}$ (Richards et al., 2002).

Of 179 sources satisfying the above criteria, one QSO was later removed from
the sample by Kellermann et al. (2016) because it happens to lie along the
line of sight to a nearby strong radio galaxy, which is likely to confuse any
radio follow-up.

From Kellermann et al. (2016)’s final sample of 178 QSOs, we selected 128
sources qualifying as “radio-quiet” for the high-resolution follow-up
observations that are presented in this paper. The criterion we used to
classify sources as “radio-quiet” is
$L_{\mathrm{6GHz}}<10^{23}\mathrm{\,W\,Hz}^{-1}$, where $L_{\mathrm{6GHz}}$ is
the 6-GHz radio luminosity calculated from the Kimball et al. (2011b)
observations.

Table 2: Target Quasar Optical Properties

Name | $z$ | $\Delta$ | $M_{i}$ | $m_{i}$ | log $R_{i}$
---|---|---|---|---|---
(SDSSJ) |  | $(^{\prime\prime})$ |  |  |
080829.17+440754.1 | 0.275 | 0.150 | $-23.61$ | 17.13 | $-1.15$
081652.24+425829.4 | 0.234 | 0.150 | $-23.98$ | 16.36 | $-0.72$
082205.24+455349.1 | 0.300 | 0.067 | $-23.69$ | 17.27 | $0.07$
083443.80+382632.8 | 0.288 | 0.078 | $-23.80$ | 17.05 | $-0.67$
084313.41+535718.8 | 0.218 | 0.153 | $-23.91$ | 16.25 | $-0.52$
084755.63+263147.6 | 0.282 | 0.100 | $-23.61$ | 17.20 | $-1.07$
085640.78+105755.8 | 0.274 | 0.030 | $-24.32$ | 16.41 | $-0.29$
085828.69+342343.8 | 0.257 | 0.222 | $-24.82$ | 15.75 | $-0.98$
090151.13+103020.4 | 0.201 | 0.170 | $-24.20$ | 15.77 | $-1.59$
090454.99+511444.5 | 0.225 | 0.071 | $-23.82$ | 16.42 | $-1.73$

Note. — Column 1: Full name of QSO in SDSSJ format; Column 2: Redshift from
the SDSS-DR7 catalog (Schneider et al., 2010); Column 3: Angular offset of the
QSO’s closest detected radio component from its optical position; typical
uncertainties in the optical positions of SDSS quasars are $\approx 0\farcs
1$; Column 4: Absolute $i$-band magnitude from the SDSS-DR7 catalog; Column 5:
Apparent $i$-band magnitude from the SDSS-DR7 catalog; Column 6: Base-10
logarithm of $R_{i}$, the ratio between the measured total 6-GHz flux density
at $0\farcs 33$ and the optical flux density in the $i$ band6. A subset of the
table is shown here for brevity; a machine-readable version of the full table
is available in the electronic journal.

We note that in the 2010–2011 C-configuration observations—with angular
resolution of 3$\farcs$5 ($\sim$14 kpc)—127 of the 128 RQQs showed no sign of
extended radio morphology. Just one target (J1458+4555) showed any possibility
of having extended structure, with a second radio counterpart separated by a
distance of 5″; however, inspection of the optical SDSS image reveals a
neighboring galaxy that coincides with the second radio component. This galaxy
may in fact be a physical companion to the QSO; its photometric redshift
reported from SDSS is $0.310\pm 0.0751$ (Beck et al., 2016) whereas J1458+4555
has a spectroscopic redshift of 0.285738.

##  3 Observations and Data Reduction

Analyses presented in this paper are based primarily on the 128 RQQs that were
observed in VLA’s A-configuration from 2019 August 3 to 2019 September 20 via
observing program VLA/19A-343. We compare these results to earlier
observations of the same RQQs that were observed in C-configuration as part of
program VLA/10B-104. The C-configuration observations targeted the parent
sample of 178 QSOs, whereas the new A-configuration observations targeted just
the 128 RQQs from the parent sample. The C-configuration observations,
performed from 2010 October 17 to 2011 January 17, have been presented in
detail in Kimball et al. (2011b) and Kellermann et al. (2016). In this
section, we discuss the 2019 follow-up observations (presented here for the
first time) and where relevant we provide additional details of the earlier
observations.

###  3.1 Observations

Both sets of observations were performed in the radio astronomy “C-band” which
comprises the frequency range 4–8 GHz. The 2010–2011 observations were
performed during the commissioning and verification phase of the upgrade from
the legacy VLA hardware and software to the new Karl G. Jansky VLA. As only 2
GHz of bandwidth was available for C-band observations at that time, the
original set of observations covered the frequency range 5–7 GHz. The 2019
observations used the full 4–8 GHz range of the C-band receiver by utilizing
two pairs of the VLA’s 3-bit samplers in each antenna. Each sampler pair
delivered 2 GHz of bandwidth in both right and left circular polarizations.
The correlator was set up to split each 2 GHz of bandwidth into 16 subbands,
each 128 MHz wide with $64\times 2$ MHz spectral channels.

The 2010–2011 observations were performed in the VLA’s C-configuration,
whereas the 2019 observations used the more extended A-configuration. At a
reference frequency of 6 GHz, the typical angular resolution for
C-configuration is $\sim$3$\farcs$5 ($\sim$14 kpc for $z=0.25$), and the
typical angular resolution for A-configuration is $\sim$0$\farcs$33 ($\sim$1.3
kpc for $z=0.25$). Baseline lengths in the C-configuration range from a
minimum of 350 m to a maximum of 3.4 km; baseline lengths in the
A-configuration range from a minimum of 0.68 km to a maximum of 36.4 km. The
largest angular scale of emission detectable at 6 GHz is 4′ in C-configuration
and $\sim 4\farcs 5$ in A-configuration.

The A-configuration observations were designed to reach signal-to-noise (S/N)
levels of at least five, for peak flux densities equal to those calculated
from the original 2010–2011 observations (including two RQQs with marginal
detections). Required on-source observing times were determined using the VLA
Exposure Calculator Tool333https://obs.vla.nrao.edu/ect/; we assumed 15% loss
of bandwidth due to known radio frequency interference (RFI), leaving an
expected useful bandwidth of 3.4 GHz. The faintest detection in the 2010–2011
observations was J0847+2631 with peak flux density of 16.8 $\mu$Jy beam-1,
which for the new observations required 40 minutes on-source to reach a target
1-$\sigma_{\mathrm{rms}}$ sensitivity of 3.36 $\mu$Jy beam-1 (where
$\sigma_{\mathrm{rms}}$ refers to the rms noise of the image). The next 12
most-faint ($\lesssim 33.5\mu$Jy beam-1) targets required on-source times of
15–35 minutes to reach target sensitivities in the range of 3.6–5.5 $\mu$Jy
beam-1. The remaining 116 targets ($>33.5\mu$Jy beam-1) were observed for 10
minutes each, split into two 5-minute scans separated by about an hour in
order to obtain improved $uv$-coverage.

All of the 2019 observations used the radio source 3C 286 as both the primary
flux density scale calibrator and bandpass calibrator, with complex gain
calibrators selected individually for each science target. We incorporate a
systematic uncertainty of 3% in the flux density values we determine from
these observations, following NRAO
guidelines444https://science.nrao.edu/facilities/vla/docs/manuals/oss/performance/fdscale
based on the fundamental accuracy of the flux density scale for 3C 286 (Perley
& Butler, 2017). The error values reported in Table 1 comprise this 3%
uncertainty added in quadrature with the statistical errors reported for the
flux density measurements from CASA (see below).

###  3.2 Data Reduction

We used the Common Astronomy Software Applications package (CASA; McMullin et
al., 2007) (versions 5.6.2 and 5.6.3) to reduce our VLA data and perform all
imaging in this analysis555Images and flux density measurements in Kellermann
et al. (2016) were performed in AIPS.. We used the standard VLA calibration
pipeline to automatically flag and calibrate each data set. We experimented
with further flagging manually, but deemed such manual intervention to be
unnecessary (possibly even counterproductive), because the data directly
output from the the VLA pipeline had been efficiently flagged and weighted;
further manual flagging had a tendency to actually increase the image noise.
We therefore chose to proceed with imaging analysis directly after the
successful pipeline run.

While the imaging process is largely tunable and several small details may
differ from target to target, we outline our general process for imaging here.
The CASA task tclean was used with the natural weighting scheme to deconvolve
all images. We used a pixel size of $0\farcs 06$ in order to adequately sample
the synthesized beam (FWHM $\sim 0\farcs 33$). Image cutouts for sources
showing any structure are presented in Appendix A, along with optical cutouts
from SDSS and the corresponding image cutouts from the 2010–2011 observations
(Kellermann et al., 2016).

For each target, we have imaged the full field-of-view, i.e., the FWHM of the
antenna primary beam ($\sim$7$\farcm$3$\times$7$\farcm$3 at 6 GHz), in order
to include any potential bright sources that—if not properly deconvolved—could
result in imaging artifacts and increase the image noise at the location of
the science target; when such cases appeared we employed phase-only self-
calibration to improve the image. If remaining noise or artifacts appeared to
affect the target location, we would try one or more of the following with
CASA in an attempt to achieve the sensitivity goal (typically $\approx 7$
$\mu$Jy beam-1): a conservative round of amplitude self-calibration, multi-
term multi-frequency synthesis (MT-MFS; Rau & Cornwell, 2011), or aw-
projection (Cornwell et al., 2005; Jagannathan et al., 2018). Nevertheless,
some images containing nearby bright sources remain dynamic-range limited with
sensitivities as poor as $\sim 30~{}\mu\mathrm{Jy~{}beam}^{-1}$. Almost all
(122 of 128) targets have a detected radio component associated with their
known SDSS optical position; radio-optical offsets are shown in Figure 1.

Compilations of radio and optical properties of the RQQ sample are provided in
Tables 1 and 2, respectively. Notes on individual sources can be found in
Appendix A. Distributions of integrated 6-GHz flux density and luminosity, as
well as the ratio between 6-GHz and optical $i$-band flux density666The
$i$-band flux densities are computed from SDSS apparent magnitude as:
$S_{i}=10^{(9.56-i/2.5)}\mu$Jy (Oke & Gunn, 1983; Abazajian et al., 2009).,
$R_{i}$, are shown in Figure 2.

Figure 1: Angular offsets between radio and optical positions of our targets.
Typical SDSS positional uncertainties are $\approx 0\farcs 1$, indicated by
the circle centered at the origin. Not pictured is J1102$+$0844, which has an
angular offset of 0$\farcs$81. Figure 2: Distributions of the radio properties
of the RQQ targets observed at $\sim 0\farcs 33$ resolution. Top: total 6-GHz
flux density measured with the VLA. Middle: 6-GHz luminosity. Bottom: base-10
logarithm of $R_{i}$, where $R_{i}$ represents the ratio between our measured
6-GHz flux density and the source’s optical $i$-band flux density (Schneider
et al., 2010).

##  4 Radio Morphology of RQQs

In this section, we introduce morphology classifications of RQQs based on our
new observations, then compare morphologies and flux densities to the lower-
resolution observations from 2010–2011. Corresponding VLA images for the new
observations can be found in Appendix A for all sources showing structure
(“Resolved” classification; see next sub-section)777A tar.gz file containing
image cutouts of all sources is available at
https://github.com/trevormccaffrey/RQQs/blob/main/RQQs_15arcsec_cutouts.tar.gz..

###  4.1 Morphology Classification

These new A-configuration observations allow us to investigate kpc-scale radio
structure in the population of $z\sim 0.25$ RQQs. Upon visual inspection, we
find that RQQs present a range of radio morphology on sub-galactic scales (1.3
kpc $\lesssim\Delta\lesssim$ 14 kpc); for the purposes of analysis, we
introduce the following classes and subclasses to categorize the range of
observed morphology:

Figure 3: Example images of sources with “Resolved” morphology; one source
from each sub-class is shown. Column 1 shows each object’s arcminute-wide SDSS
color image. Column 2 shows the corresponding $\sim 3\farcs 5$-resolution
6-GHz image from Kellermann et al. (2016), where all sources appeared
unresolved. Column 3 shows the source’s higher-resolution ($\sim 0\farcs 33$)
A-configuration image, where the size of the image relative to the lower-
resolution is indicated by the green inset region from Column 2; each source’s
A-configuration morphology sub-classification is noted in the upper left
corner of this panel. Column 4 further displays contour maps of the
A-configuration images to highlight extended features; the number in the upper
left of each contour map indicates the base contour value (typically
equivalent to a detection with signal-to-noise $\approx$3.5–4; consecutive
contours are spaced by multiples of $\sqrt{2}$; see Column 4 of Table 1 for
exact $\sigma_{\mathrm{rms}}$ values). An approximate linear size scale is
given in each contour map. The SDSS location of each QSO is indicated by the
magenta cross in the contour maps. The approximate FWHM of the synthesized
beam (resolution element) for each radio observation is indicated by the
ellipse in the lower left corner of each image. Image cutouts and individual
notes for _all_ Resolved sources in the sample are included in Appendix A.

  * •

U—Unresolved: the source remains unresolved on A-configuration scales ($\sim
0\farcs 33$, corresponding to $1.3$ kpc at $z=0.25$). A total of 67/128 of our
sources are Unresolved.

  * •

R—Resolved: we observe resolved structure and/or extended radio emission in
55/128 RQQs, revealing a variety of appearances. We adopt the sub-classes
below to describe this diversity. A representative image from each of the
different sub-classes is presented in Figure 3; images of all Resolved sources
appear in Appendix A.

    * –

R-SR—Slightly Resolved: a formal Gaussian fit to the emission component in the
image888Source fitting was performed using the imfit task in CASA. indicates
that the source is resolved (i.e., the integrated source flux density is
significantly greater than the peak flux density) and the source appears
visually to have slight extended structure beyond the $\sim 1.3$ kpc
synthesized beam. There are 31/128 sources in this category.

    * –

R-E—Extended: the source has a dominant radio component coinciding with the
QSO’s optical position, and also has obvious widespread emission extending
well beyond the resolution of the synthesized beam. We identify 7/128 of our
sources with clear extended morphology.

    * –

R-M—Multi-component: the source has a radio component coincident with the
optical SDSS position of the QSO, and also has one or more emission
components—well separated from the core—contributing to the source’s total
radio emission. We utilize the source-finding tool PyBDSF (Mohan & Rafferty,
2015) with a S/N cutoff of 3 to distinguish faint emission components from
unrelated noise peaks. There are 16/128 sources in this category.

    * –

R-D—Double: the source shows two apparent radio “lobes” symmetric about the
central QSO position. There is only one RQQ in our sample that has a Double
morphology: J0935+4819 (shown in the fourth panel of Figure 3).

  * •

ND—Non-detection: no potential radio component from the source is detected.
Typically, 3-$\sigma_{\mathrm{rms}}$ point-source upper limits for Non-
detections in our sample are $\sim$21 $\mu\mathrm{Jy}$ (corresponding to $\sim
10^{21.6}$ W Hz-1 at $z=0.25$), but vary slightly depending on sensitivity
reached in each image, with our most sensitive non-detection (J1703+1910)
achieving a 3-$\sigma_{\mathrm{rms}}$ point-source upper limit of 11.4
$\mu\mathrm{Jy}$ ($\sim 10^{21.4}$ W Hz-1). Only 6/128 total sources are Non-
detections in our A-configuration observations; all were robust detections in
the original C-configuration observations (with peak flux densities in the
range from 19.7–81 $\mu$Jy beam-1).

Figure 4: Histogram of projected physical size of RQQ radio emission, computed
as the geometric mean of the major and minor axes (deconvolved). For Multiple-
Component sources, the size corresponds to the component that is co-located
with the optical QSO. For Extended sources (i.e., with emission connected to
the core component), the size corresponds to the extent of the extended
emission. Upper limits are shown for Unresolved sources. A total of 90/128
sources are included in this figure; the remaining 38 are too faint to derive
accurate size estimates (see Table 1).

Figures 4, 5, and 6 characterize the RQQs in terms of the physical size
and—for the Resolved sources—central concentration of their radio emission.
Figure 4 shows the projected physical size for all sources (based on the
geometric mean of the axis sizes after deconvolution). The bulk of the
detected radio emission for roughly 80% of the sample is constrained within a
$\sim 2$ kpc region. Figure 5 shows total 6-GHz flux density detected in 2019,
$S_{\mathrm{total}}$, plotted against flux density $S_{\mathrm{core}}$
associated with the core component (i.e., the radio component coincident with
the QSO optical position)—both taken from the $0\farcs 33$ observations—for
all detections. For sources without a core clearly separated from the source’s
extended structure, we take $S_{\mathrm{core}}$ to be the peak of the Gaussian
fit to the radio source; for the single source with Double morphology, this
corresponds to the peak of the southwest lobe partially coincident with the
QSO optical position. Figure 6 shows the distribution of
$S_{\mathrm{core}}/S_{\mathrm{total}}$, effectively displaying what fraction
of overall radio emission in these 55 resolved sources is confined within a
single $\sim 0\farcs 33$ resolution element of these observations.

Figure 5: Total 6-GHz flux density in A-configuration versus that associated
with the SDSS optical counterpart for all detections. The core is the dominant
radio component for all RQQs except for J0935$+$4819, J1118$+$3103,
J1146$+$3715, and J1233$+$6443 (marked by star symbols)—all of which exhibit
edge-brightened, extended morphology.

Luminosity distributions from the three main morphology classes are shown in
Figure 7. Resolved sources are typically found among the higher-luminosity
range of our sample ($L_{\mathrm{6GHz}}\simeq 10^{22.2}$–$10^{23.0}$ W Hz-1),
whereas the less-luminous range ($L_{\mathrm{6GHz}}\simeq
10^{21.4}$–$10^{22.2}$ W Hz-1) is populated primarily by Unresolved sources.
Implications of this result, in the context of how a visual morphology
classification depends on an interferometer’s sensitivity as a function of
angular scale, are discussed in Section 4.3.

Figure 6: Histogram showing ratio of core- to total-6-GHz emission detected in
A configuration for the 55 Resolved sources. For sources without a core
clearly separated from more extended structure, $S_{\mathrm{core}}$ is the
peak flux density (determined by Gaussian fit) of the source. The 67
Unresolved sources are not included in this figure; core-to-total ratio for
unresolved sources is by definition equal to unity. Figure 7: Luminosity
distributions at 6 GHz for the different morphology classes of our sample. The
open histogram with arrows emphasizes that the Non-detections are plotted as
3-$\sigma_{\mathrm{rms}}$ upper limits. See Section 4 for descriptions of
morphology classes.

###  4.2 Image constraints on the origin of radio emission in RQQs

These new VLA observations are the first to probe kpc-scale radio emission
across a volume-complete sample of homogeneously selected RQQs. We see that
extended (but sub-galactic) radio emission is visible in a large fraction of
the population: 55 of 128 RQQs are Resolved. Unresolved central components
(i.e., coincident with the optical position) could be dominated by AGN-related
radio emission—small-scale jets, shocks, or winds (Zakamska & Greene, 2014;
Zakamska et al., 2016)—or nuclear starburst emission (e.g., Condon et al.,
1992; Colina & Perez-Olea, 1993; Anantharamaiah et al., 2000; Lonsdale et al.,
2006), whereas emission outside the central component may arise from diffuse
or clumpy star-formation, or could indicate AGN-driven features such as jet or
wind interactions with the intragalactic medium (e.g., Klindt et al., 2019;
Rosario et al., 2021). Note that some sources may have faint diffuse emission
that we fail to detect due to sensitivity limits of these high-resolution
observations (discussed further in §4.3).

Among the 16 Multi-component sources, a separate component is typically found
within a projected distance of about 10 kpc (3″ at $z=0.2$), potentially
indicating a star-forming region near the outskirts of the host galaxy.
However, it is possible that one or more of these additional components
correspond to an unrelated background source. To estimate this likelihood, we
look to Smolčić et al. (2017), who performed a sensitive high-resolution
($\sim 0\farcs 75$) survey of the $\sim$2.6 deg2 COSMOS field; the authors
found an overall source density of $\sim 4200$ deg-2 above about $11.5$
$\mu\mathrm{Jy}$ beam-1. Using their result, the expectation value of the
number of background interlopers with flux density $\gtrsim 11.5$
$\mu\mathrm{Jy}$ beam-1 within 3″ of any of the 128 RQQs is about equal to 1.
We therefore expect that it is likely that one among the Multi-Component class
may be mis-classified due to an unassociated background source, but it is safe
to assume that nearly all of the detected components are physically associated
with the RQQs.

Convincing visual evidence for an AGN as the dominant origin of RQQ radio
emission might manifest as a morphology that is distinctly associated with
powerful QSOs and radio galaxies, albeit scaled down, such as small-scale jets
or lobes analogous to the classical picture of powerful RLQs as double-lobed
or triple sources (e.g., see Figure 1 of Kimball et al., 2011a). In fact,
J0935+4819—the source classified as a “Double” and shown in Figure 3—does have
a morphology that is strikingly similar to that classical picture: two round,
similarly bright lobes appear on either side of the central black hole (whose
position is determined by the optical QSO position). The southwest lobe of
J0935+4819 source has a slight extension toward the northeast that clearly
coincides with the optical position, suggesting possible radio emission from a
core in addition to the two lobes. This source’s appearance is similar to that
of Gigahertz-Peaked Spectrum (GPS) and Compact Steep Spectrum (CSS) sources
with symmetric-double morphology. The GPS and CSS labels indicate two classes
of powerful radio objects, with the main differences being that GPS sources
are more compact ($\lesssim 1$ kpc) whereas CSS sources are larger ($\lesssim
15$ kpc) and with steep spectra. As discussed in reviews by O’Dea (1998),
Sadler (2016), and O’Dea & Saikia (2021), there are two main theories
explaining GPS and CSS sources: (1) in the “frustrated” scenario, GPS/CSS
sources consist of jets that are confined by dense gas in the host galaxy,
preventing them from evolving into large radio galaxies; (2) in the
“evolutionary” scenario, newly formed jets manifest as GPS sources, later
becoming CSS sources as they grow and age, eventually evolving into large
classical radio galaxies. The projected physical extent of J0935+4819’s lobes
is $\gtrsim 6$ kpc and its spectral index is $\alpha\sim-0.7$ (for
$f_{\nu}\propto\nu^{\alpha}$) between 1.4 and 6 GHz.999Spectral indices of the
entire sample are discussed in §5. The visual appearance of J0935+4819 is
therefore consistent with classification as a low-power CSS. RQQ J0935+4819
appears to be the first example of a radio-quiet QSO that shows kpc-scale FR
II-like morphology (Fanaroff & Riley, 1974) at a radio luminosity as low as
1022.9 W Hz-1. Other radio AGNs of this size and luminosity tend to manifest
as FR I sources (viz. Figure 1 of An & Baan, 2012), which may indicate that
they are “frustrated” sources with a jet interrupted by the dense
interstellar-medium101010There also exists a large population of compact “FR
0” sources (Baldi et al., 2015, 2018), some of which may host radio jets on
much smaller size scales. O’Dea & Saikia (2021) suggest that many of these are
in fact low-power CSS or GPS sources.. In contrast, J0935+4819 may be an
example of an RQQ that could properly evolve into FR II radio galaxy as it
grows. Regardless, the symmetric-double morphology of J0935+4819 is strongly
suggestive that AGN activity dominates its radio emission, given the analogous
appearance with classical double radio galaxies and QSOs.

Other intriguing images that may indicate the presence of radio jets are those
with apparent linear or widespread flocculent emission extending outward from
the core in just one direction, or symmetrically in two directions. Among the
Extended RQQs: J0843+5357, J1235+4104, J1304+0205, and J1727+6322 appear to
have widespread two-sided emission; J1408+4303 and J1444+0633 appear to have
linear emission extending out in one direction. Among the Multi-component
RQQs: J1146+3715 has two additional components along the same (projected)
direction, while J1118+3103 has two symmetrically located components (along
with a third), and J1004+1510 has an extension of the central component that
extends directly toward an additional emission component. Such morphology does
not prove the presence of a radio jet, but—similar to J0935+4819—is the type
of morphology that small-scale jets may manifest if present. Images of these
sources are all presented and described in detail in Appendix A.

Further investigation of scaled-down jets as a possible origin of radio
emission in the RQQs likely requires deeper follow-up observations with the
VLA or observations with Very Long Baseline Interferometry (VLBI), which
detects only high brightness temperatures (although deep VLBI observations may
still be sensitive to extreme starburst activity, e.g., Arp 220; Lonsdale et
al., 2006). Ulvestad et al. (2005), Chi et al. (2013), and Maini et al. (2016)
have used VLBI to detect jets in small numbers of purported RQQs, but many
detections in their samples qualify as either radio-intermediate or -loud by
the definition used in this paper—so we would expect a significant jet
contribution in those objects—or fail to meet the historical $M<-23$ optical
criterion of bona fide QSOs (Schmidt & Green, 1983). Similarly, Herrera Ruiz
et al. (2016, 2017) detect a jet in 3/18 $M<-23$ QSOs in the COSMOS field, but
these targets are not RQ by our 6-GHz luminosity criterion111111These three
sources are all brighter than $10^{24}$ W/Hz at 1.4 GHz; assuming a spectral
index of $\alpha=-0.7$, the faintest would have 6-GHz luminosity of
$10^{23.9}$ W/Hz..

###  4.3 Comparison of A-configuration and C-configuration Flux Densities

To further investigate the intrinsic radio structure of RQQs and their host
galaxies, we employ the advantage that this sample has been observed at the
same frequency with different angular-resolution scales. Comparison of flux
density measured from observations made at low-resolution (VLA’s
C-configuration) versus high-resolution (VLA’s A-configuration) allows us to
probe their radio morphology using a quantitative method. Such an approach has
previously been used successfully for automated morphology classification of
large catalogs made from wide-field sky surveys performed with the VLA
(Kimball & Ivezić, 2008).

Recall that these follow-up observations were designed to achieve $\geq
5\sigma$ point-source sensitivity based on the Kellermann et al. flux
densities measured in C-configuration. However, if the radio emission is not
centrally concentrated but instead is spread throughout the host galaxy, then
emission in the higher-resolution image will be distributed across multiple
resolution elements, yielding lower surface-brightness per beam, i.e., a lower
point-source flux density. Therefore, at higher resolution the emission from
extended sub-galactic structures may be hidden within the image noise, leaving
us sensitive only to the brightest emission, such as a bright core
component.121212We note that the largest angular scale of these
A-configuration observations is 4$\farcs$5 or larger (see
http://go.nrao.edu/vla-res) whereas Kellermann et al. (2016) determined that
the radio emission of each of these RQQs is unresolved on a 3$\farcs$5 scale.
Therefore, we should not miss any emission due to interferometric spatial
filtering. If we had observed for a longer amount of time to reach lower image
noise (equivalent to better surface-brightness sensitivity), such extended
emission may have become apparent above the noise level (e.g., Blundell &
Rawlings, 2001). Therefore, a decrease in flux density between the two epochs
cannot be attributed simply to variability, because detection in the
A-configuration images depends strongly on how radio emission is distributed
throughout the host galaxy.

Figure 8: Top: Distribution of $\log(S_{\mathrm{A}}/S_{\mathrm{C}}$) (see
text) for the RQQ sample. Magenta dotted lines mark $\pm$1-$\sigma$ offsets
from 0 (where $\sigma$ is the standard deviation of the sigma-clipped main
distribution). As discussed in §4.3, the excess of sources $<-\sigma$ compared
to those $>+\sigma$ suggests the presence of radio emission below the surface-
brightness sensitivity of our follow-up observations. Bottom: Marginal
distributions of $\log(S_{\mathrm{A}}/S_{\mathrm{C}})$ for sources that appear
unresolved in our 0$\farcs$33-scale images [solid blue; median
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})\approx-0.15$)] and those that have been
resolved [dash orange; median $\log(S_{\mathrm{A}}/S_{\mathrm{C}})\approx
0.0043$)], plotted as the fractional total from each class. Median error bars
of $\log(S_{\mathrm{A}}/S_{\mathrm{C}})$ for each class of object are shown
for reference.

To compare the flux density values measured in the high- and low-resolution
observations, we use the ratio $S_{\mathrm{A}}/S_{\mathrm{C}}$, where
$S_{\mathrm{A}}$ is the source’s total A-configuration 6-GHz flux
density131313The variable $S_{\mathrm{A}}$ is equal to $S_{\mathrm{total}}$
from §4.1, but for clarity is labeled here with subscript “A” to distinguish
from the measurements made in C-configuration. ($0\farcs 33$ scale) measured
from our 2019 observation, and $S_{\mathrm{C}}$ is the C-configuration 6-GHz
flux density ($3\farcs 5$ scale) from 2010–2011. The upper panel of Figure 8
shows the distribution of $\log(S_{\mathrm{A}}/S_{\mathrm{C}})$ for our
complete RQQ population. If we were sensitive to all radio emission at all
angular scales, then our measured flux densities for non-variable sources
would be equivalent to those measured in 2010–2011, and the distribution
should cluster (within measurement errors) around
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})\sim 0$. However, the sample instead
manifests a range of $\log(S_{\mathrm{A}}/S_{\mathrm{C}})$, with a median
value $\approx-0.07\pm 0.03$ and a skew with negative values of
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})$. The lower panel of Figure 8 shows the
marginal distributions for the Unresolved and Resolved classes, and
demonstrates that the skew is due entirely to the Unresolved class (median
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})\approx-0.15\pm 0.04$), whereas the
distribution for Resolved sources is roughly symmetric around
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})=0$, with a median
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})\approx 0.01\pm 0.03$; implications are
discussed in §4.3.1.

For any given source, we consider that flux density values $S_{\mathrm{A}}$
and $S_{\mathrm{C}}$ are consistent if $\log(S_{\mathrm{A}}/S_{\mathrm{C}})$
lies within $3\sigma$ of 0 (where $\sigma$ has been calculated for each source
individually via propagation of errors). By that definition, out of 55
Resolved (67 Unresolved) sources, there are 46 (37) with consistent values of
$S_{\mathrm{A}}$ and $S_{\mathrm{C}}$. The remaining 9 Resolved (30
Unresolved) sources have inconsistent flux density measurements, due either to
variability and/or to the difference in angular resolution discussed earlier.
The 39 sources with a significant change between $S_{\mathrm{A}}$ and
$S_{\mathrm{C}}$ are listed in Table 4. Of the 9 Resolved sources listed, 6
have $\log(S_{\mathrm{A}}/S_{\mathrm{C}})>0$ and 3 have
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})<0$. Among the Unresolved sources, only 4
have $\log(S_{\mathrm{A}}/S_{\mathrm{C}})>0$, while the remaining 26 have
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})<0$. Additionally, all six Non-detections
have $\log(S_{\mathrm{A}}/S_{\mathrm{C}})<0$; they have 3$\sigma$ upper limits
in the range from 11.4–22.2 $\mu$Jy beam-1, whereas all were detected in the
original C-configuration observations with flux density values in the range
19.7–81 $\mu$Jy. We calculate upper limits for their
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})$ ratios to be about $-0.2$ to $-0.3$ for
five of the six sources, and $-0.6$ for the sixth.

In the absence of variability or resolution effects, we would expect the
distribution of flux density ratios to be centered on unity with a spread
determined by measurement errors. Variability could yield a flux density
change in either direction, whereas the difference in angular resolution would
result in $S_{\mathrm{A}}<S_{\mathrm{C}}$ due to missing emission in the high-
resolution A-configuration images.

####  4.3.1 Implications for Morphology

For RQQs whose radio emission is truly compact (i.e. $<0\farcs 33$), they
would appear as Unresolved regardless of observation depth. In contrast, the
visual classification of RQQs with extended emission depends strongly on the
sensitivity of the observations in comparison to the surface brightness of the
extended emission. Therefore, we expect to find more Resolved RQQs at the
bright end of the population. That expectation is confirmed in Figure 9, which
shows $\log(S_{\mathrm{A}}/S_{\mathrm{C}})$ as a function of $S_{\mathrm{C}}$.
In this figure, we see that not only do the majority of Resolved sources
populate the brighter end of the $S_{\mathrm{C}}$ distribution, but also that
the Resolved sources with $S_{\mathrm{C}}>100\mu$Jy are distributed fairly
symmetrically around $\log(S_{\mathrm{A}}/S_{\mathrm{C}})=0$. Similarly,
Unresolved sources with $S_{\mathrm{C}}>100\mu$Jy are also distributed
somewhat symmetrically around $\log(S_{\mathrm{A}}/S_{\mathrm{C}})=0$. Based
on these observations, we conclude that the A-configuration images of RQQs
with $S_{\mathrm{C}}\gtrsim 100\mu$Jy are not systematically missing emission
due to angular resolution effects. Thus the morphology we observe for these
RQQs is a good representation of their actual radio emission.

In contrast, the RQQs with $S_{\mathrm{C}}<100\mu$Jy show clearly different
behavior in Figure 9. Virtually no Resolved RQQs populate the lower-left
quadrant of the main panel. Furthermore, of the Unresolved RQQs with
$S_{\mathrm{C}}<100\mu$Jy, nearly all have ratios
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})\leq 0$. This behavior is precisely the
pattern we expect to see due to the change in angular resolution between the
two sets of observations; when present, the effect will always yield a
decrease of $S_{\mathrm{A}}$ compared to $S_{\mathrm{C}}$. We therefore
conclude that in the A-configuration images, we have “missed” the presence of
extended sub-galactic emission among many of the $S_{\mathrm{C}}<100\mu$Jy
RQQs.

While it is possible that some of the discrepancy between $S_{\mathrm{A}}$ and
$S_{\mathrm{C}}$ may be due to variability (see discussion in §4.3.2), for the
moment we apply the assumption that all Unresolved sources with
$S_{\mathrm{C}}<100\mu$Jy and $\log(S_{\mathrm{A}}/S_{\mathrm{C}})<0$
($>3\sigma$ significance) have additional extended sub-galactic emission that
we did not detect in the A-configuration images. We can then estimate the
fraction of missing emission based on the values of
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})$. There are 15 such sources meeting these
criteria, and their median value of $\log(S_{\mathrm{A}}/S_{\mathrm{C}})$ is
$-0.44$, suggesting that on average we fail to detect almost two-thirds of the
total radio emission in these sources, using the A-configuration images. In
comparison, the sources we identified as Resolved have a typical core-to-total
flux density ratio of 0.65. If we had performed deeper, much more sensitive
observations, these faint RQQs with $S_{\mathrm{C}}<100\,\mu$Jy and
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})<0$ at $3\sigma$ significance that are
currently classified as _Unresolved_ would likely have been classified as
_Resolved_ instead.

Because all 6 Non-detections have upper limits of
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})<0$, we interpret them similarly to the
detected Unresolved sources that also have
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})<0$: it is likely that their emission
detected in C-configuration is spread throughout the host galaxy with a lower
A-configuration peak flux density that falls below the noise limit of these
new observations.

Conversely, we assume that the Unresolved RQQs with
$\log(S_{\mathrm{A}}/S_{\mathrm{C}})\gtrsim 0$ (i.e., for which we do not have
evidence for undetected extended emission) are those which are truly
intrinsically compact. There are only 41 such sources, indicating that up to
$\sim 70$% (the other 87 of 128) of the RQQs in our target population have
significant sub-galactic-scale radio emission (i.e., that contributed to the
C-configuration detections); these complex sources comprise the 55 correctly
identified Resolved sources, as well as the 26 Unresolved sources and 6 Non-
detections with $\log(S_{\mathrm{A}}/S_{\mathrm{C}})<0$. We emphasize that it
would be difficult to reach such a conclusion without both low- and high-
resolution VLA observations, yielding the ability to compare flux densities
measured at different angular resolution.

Figure 9: $\mathrm{Log}(S_{\mathrm{A}}/S_{\mathrm{C}})$ as a function of
$S_{\mathrm{C}}$. The lower-left quadrant exclusively contains Unresolved
RQQs, consistent with an interpretation that these sources have sub-galactic
radio emission that is too faint to be detected in our A-config observations
(see text of §4.3). Marginal distributions for Unresolved and Resolved sources
are shown on the top and right axes (blue solid: Unresolved; orange dashed:
Resolved; black dotted: Non-detections).

####  4.3.2 Implications for Variability

A significant decrease in detected radio emission may be due to either
variability or to resolution effects, as just discussed, but a significant
increase in detected radio emission can only be attributed to source
variability. We use the count of RQQs whose radio emission _increased_ to
roughly estimate how many variable RQQs with _decreased_ radio emission exist
within both the Resolved and Unresolved groups.

If all sources have the same variability duty cycle (i.e., are just as likely
to increase as to decrease during the same time range), then to first order we
expect the same number of sources to _decrease_ due to variability as to
_increase_. Intermittent AGN jets that turn on and off would be an example of
such a variability cycle (O’Dea et al., 2008; Blandford et al., 2019). Because
6 Resolved sources have $S_{\mathrm{A}}>S_{\mathrm{C}}$ ($>3\sigma$), which
must be due to variability, we would similarly expect $\sim 6$ sources with
$S_{\mathrm{A}}<S_{\mathrm{C}}$ ($>3\sigma$) due to variability. We find only
3 with this decrease in flux density, and the discrepancy could be attributed
to resolution/sensitivity effects discussed above, combined with Eddington
(1913) bias: an RQQ with extended structure near the sensitivity limit will
appear to be Unresolved rather than Resolved if negative fluctuations in the
extended emission cause it to appear too faint to rise above the image noise;
fluctuations in the opposite direction will simply cause the source to remain
Resolved. Therefore there may be $\sim 3$ additional variable sources with
$S_{\mathrm{A}}<S_{\mathrm{C}}$ that have undetected sub-galactic structure,
and were thus classified as Unresolved rather than Resolved. This adjustment
amounts to $\sim 12$ variable RQQs with extended subgalactic structure.

The Unresolved class contains 4 RQQs with increased radio emission at
$>3\sigma$ significance, while 26 decreased. As discussed earlier, many of
these sources which decreased are due to resolution differences between
observations, but applying the same assumption regarding RQQ variability duty
cycles as before, we expect the decrease for $\sim 4$ of these to be due to
intrinsic variability. Combining the estimate of 8 variable Unresolved sources
with the above estimate of 12 variable Resolved sources, we conclude that
there are $\sim 20$ RQQs (in the sample of 128) with a variable component as a
dominant source of radio emission.

Table 3: RQQs with $\log(S_{\mathrm{A}}/S_{\mathrm{C}})\neq 0$ ($>3\sigma$ significance) |  | Name | $\log{(S_{A}/S_{C})}$ | $S_{C}$ | Morph.
---|---|---|---|---|---
|  | (J2000) |  | ($\mu$Jy) | (see §4.1)
R | Inc. | J1146+3715 | $0.30\pm 0.06$ | 90 | R-M
J1425+0803 | $0.20\pm 0.04$ | 138 | R-SR
J1045+2933 | $0.26\pm 0.03$ | 179 | R-M
J0822+4553 | $0.38\pm 0.03$ | 222 | R-M
J1444+0633 | $0.15\pm 0.04$ | 255 | R-E
J1235+4104 | $0.32\pm 0.06$ | 266 | R-E
Dec. | J0948+4335 | $-0.44\pm 0.13$ | 260 | R-SR
J1004+1510 | $-0.24\pm 0.05$ | 420 | R-M
J1129+5120 | $-0.48\pm 0.07$ | 501 | R-SR
U | Inc. | J0952+2051 | $0.42\pm 0.13$ | 18 | U
J1000+1047 | $0.37\pm 0.03$ | 233 | U
J1617+0638 | $0.24\pm 0.02$ | 266 | U
J1627+4736 | $0.29\pm 0.04$ | 299 | U
Dec. | J1631+4048 | $-0.27\pm 0.09$ | 49 | U
J1502+0645 | $-0.46\pm 0.11$ | 50 | U
J1233+3101 | $-0.35\pm 0.08$ | 61 | U
J1524+3032 | $-0.33\pm 0.09$ | 63 | U
J1630+4711 | $-0.28\pm 0.08$ | 64 | U
J1206+2814 | $-0.38\pm 0.07$ | 64 | U
J1534+4658 | $-0.55\pm 0.10$ | 66 | U
J1102+0844 | $-0.41\pm 0.08$ | 68 | U
J0934+0306 | $-0.35\pm 0.03$ | 71 | U
J1443+4045 | $-0.57\pm 0.06$ | 78 | U
J1605+4834 | $-0.49\pm 0.13$ | 79 | U
J1125+2513 | $-0.49\pm 0.08$ | 93 | U
J0939+1710 | $-0.21\pm 0.06$ | 94 | U
J1458+4555 | $-0.46\pm 0.10$ | 95 | U
J1007+5007 | $-0.51\pm 0.08$ | 99 | U
J1334+1711 | $-0.51\pm 0.10$ | 104 | U
J1426+1955 | $-0.55\pm 0.08$ | 110 | U
J1005+4230 | $-0.68\pm 0.07$ | 114 | U
J1631+2953 | $-0.27\pm 0.05$ | 125 | U
J0929+4644 | $-0.22\pm 0.05$ | 127 | U
J0942+3451 | $-0.17\pm 0.04$ | 155 | U
J1321+0459 | $-0.47\pm 0.05$ | 163 | U
J1253+1227 | $-0.45\pm 0.04$ | 221 | U
J1252+1402 | $-0.33\pm 0.04$ | 236 | U
J1220+0641 | $-0.09\pm 0.02$ | 392 | U
J1218+3522 | $-0.12\pm 0.02$ | 586 | U

It is not currently thought that starburst emission can contribute significant
variability over the $\sim$1.3-kpc synthesized beam of these A-configuration
observations (Terlevich et al., 1992; Barvainis et al., 2005; Barcos-Muñoz et
al., 2015) within the 8 years between the set of observations, although it is
possible that a mixture of AGN and starburst activity are contributing to the
total radio luminosity (Kimball et al., 2011b; Condon et al., 2013; Kellermann
et al., 2016; Macfarlane et al., 2021). However, fractional increases in flux
density of $\gtrsim 100$% in J0822$+$4553, J1000$+$1047, J1617$+$0638, and
J1627$+$4736 suggest that a starburst would only be contributing slightly (if
at all) to the observed radio, at least in those RQQs. Future joint
investigations monitoring the optical/UV properties of RQQs in parallel with
their observed radio variability would help shed light on the question as to
whether the origin of this radio activity is intrinsic to the AGN (e.g., due
to enhancements of accretion activity; Kunert-Bajraszewska et al., 2020) or
extrinsic (e.g., from tidal disruption events; Komossa, 2015).

An alternative possibility may be that newly formed jets in RQQs represent the
beginning of evolution into RLQs (e.g., Nyland et al., 2020), in which case
there is no particular reason to expect a decrease in radio flux density of
RQQs over decadal timescales. The best way to investigate these possibilities
would be to obtain repeated follow-up observations of the RQQ population at
matching angular resolution, in order to measure the true variability
structure function.

We discuss potential variability of the sample further in Section 5.

##  5 Spectral Index and Variability Analysis

In this section, we incorporate ancillary data from past and ongoing radio
surveys at other frequencies to determine spectral index properties across the
full radio luminosity range of the Kimball et al. (2011b) parent sample.
Because the observations for the ancillary data were taken at different epochs
over a couple of decades, this analysis must necessarily incorporate the
consideration of potential variability.

We reintroduce for this analysis the 27 RIQs and 14 RLQs from Kimball et al.
(2011b) and Kellermann et al. (2016), where we define “radio-intermediate” as
the luminosity range $10^{23}$–$10^{24}$ W Hz-1 between RQ and RL QSOs. We
only consider the unresolved core components (3$\farcs$5 scale) of the
extended RIQs and RLQs in order to probe emission within their host galaxies;
this consideration allows a more direct comparison to their RQ counterparts,
which do not have large-scale emission extending beyond the host galaxy.
Furthermore, we note that Condon et al. (2013) concluded that beaming does not
significantly contribute to the overall luminosity function of these
populations, owing partly to the fact that the most luminous extended sources
are not compact or one-sided (as would be expected for beamed relativistic
jets), and also that the majority of them do not appear compact in FIRST.
Although we did not include RIQs or RLQs in our 2019 A-configuration follow-up
campaign, it is sufficient to use the lower-resolution (C-configuration)
2010–2011 observations of the entire QSO sample because the following analysis
is based on the total radio emission from within the host galaxies, which is
fully probed by the lower-resolution images. The luminosity boundaries we use
in defining RQ/RI/RL classes are reiterated in Table 4.

It is well known that the cores of RLQs exhibit variability on timescales of
years, months, and even days (Barvainis et al., 2005; Hovatta et al., 2007;
Thyagarajan et al., 2011), due presumably to the source of radio emission in
such objects being an optically opaque, compact engine closely associated with
an AGN (e.g., Rees, 1984). To see if the same effects were spread throughout
quasars across the full range of radio loudness, Barvainis et al. (2005)
simultaneously studied samples of 8 RLQs, 11 RIQs, and 11 RQQs over $\sim 2$
total years of observing with the legacy VLA. They concluded that similarities
in the radio light curves between all three classes of objects—coupled with
the presence of flat and inverted spectral indices ($\alpha>-0.5$) throughout
the RQ sources—indicated that the underlying mechanism(s) driving the radio
emission in the cores of RQQs may ultimately be similar to what drives radio
emission in the cores of RLQs.

In stark contrast with the spectral index findings of Barvainis et al. (2005),
Condon et al. (2013) found, through a statistical analysis of data from the
NRAO VLA Sky Survey (NVSS; Condon et al., 1998), that the typical radio
spectral index for low-redshift ($0.2<z<0.45$) RQQs is $\alpha\approx-0.7$
(steep spectrum), whereas for RLQs it is typically $\alpha\sim 0$ (flat
spectrum). For synchrotron radiation, steep spectra are expected from
optically thin emission—typical for star formation processes, or optically
thin radio jets—whereas flat spectra are expected from optically thick
emission, i.e., compact jets and jet cores (e.g., Kellermann & Pauliny-Toth,
1981). Differing spectral indices in RQQs vs. RLQs are thus consistent with
the notion that different physical origins of radio emission dominate in the
two types of sources, as concluded by Kimball et al. (2011b) and Condon et al.
(2013).

In the following subsections, we more thoroughly describe the survey data used
(§ 5.1), present our spectral index measurements (§ 5.2) along with a
complementary time-domain analysis (§ 5.3), then discuss a few individual
sources with particularly interesting spectral properties (§ 5.4).

Table 4: Sample for Spectral Index, Time Domain Analysis

Panel A: Observational Details
---
Observation | $\nu_{\mathrm{obs}}$ | VLA Config. | LAS
| (GHz) | ($\theta$) |
FIRST | 1.4 | B ($5^{\prime\prime}$) | $60^{\prime\prime}$
Kimball+2011 | 6 | C ($3\farcs 5$) | $\geq 120^{\prime\prime}$
VLASS | 3 | B/BnA ($2\farcs 5$) | $30^{\prime\prime}$
This Paper | 6 | A ($0\farcs 33$) | $\geq 4\farcs 5$

Panel B: Source Classification
---
Category | $L_{\mathrm{6GHz}}$ | N
| (W Hz-1) |
Radio-loud | $>10^{24}$ | 14
Radio-intermediate | $10^{23}<L<10^{24}$ | 27
Radio-quiet | $<10^{23}$ | 29

###  5.1 Survey data and subsample selection

To investigate the spectral indices of our targets, we obtained comparison
data at other radio frequencies from the FIRST catalog (Helfand et al., 2015)
and from “QuickLook” images from Epoch 1 of the VLA Sky Survey (VLASS; Lacy et
al., 2020). FIRST, performed with the legacy (pre-upgrade) VLA, was a 1.4-GHz
survey with a 3$\sigma$ sensitivity of $\sim 0.45$ mJy beam-1 and resolution
of $\sim 5^{\prime\prime}$. VLASS is a 3-GHz survey currently being undertaken
with the upgraded VLA, with a 3$\sigma$ sensitivity of $\sim 0.36$ mJy beam-1
per Epoch and a resolution of $\sim 2\farcs 5$.

For counterparts from FIRST, we use the catalogued peak flux density when
available. For sources too faint to have a catalogued FIRST detection, but
which appear to have an identifiable counterpart upon visual inspection, we
determine a peak flux density using CASA’s _imfit_ task, and add an additional
0.25 mJy beam-1 due to “CLEAN bias” affecting the FIRST images (see §7.2 of
Becker et al., 1995). For VLASS, we use peak flux densities obtained from
_imfit_ when we identify a visible counterpart. When a counterpart was not
identified in either survey, we use 3$\sigma$ sensitivity values as upper
limits for our analysis; this is a typical S/N ratio used to estimate possible
counterpart emission at known source positions.

A known issue for early VLASS data is that Epoch 1.1 and 1.2 QuickLook images
yield flux densities that are systematically low by 15% and 8% respectively,
with scatter up to $\sim
8\%$141414https://library.nrao.edu/public/memos/vla/vlass/VLASS_013.pdf. We
have accounted for these discrepancies by adjusting the measured flux
densities accordingly; we have incorporated the scatter by including an
additional 8% error added in quadrature with the flux density errors reported
by CASA’s _imfit_ task.

Figure 10: Spectral indices between 3 and 6 GHz compared to spectral indices
between 1.4 and 3 GHz for the RL, RI, and RQ classes of QSOs. The dashed line
illustrates where the two spectral indices are equal, i.e., a constant power
law across 1.4–6 GHz. Data at 6 GHz are from targeted VLA observations
presented in Kimball et al. (2011b), 3-GHz data are from VLASS, and 1.4-GHz
data are from FIRST. Several RQ and RI sources are not detected in FIRST or
VLASS, as shown by the lower/upper-limit symbols (rightward-pointing for FIRST
non-detections; upward- and leftward-pointing for VLASS non-detections). Two
RQQs (J1425$+$0803 and J1617$+$0638) are omitted from this figure as they are
non-detections in both FIRST and VLASS, so we cannot obtain meaningful
estimates of spectral indices at this frequency range. Median error bars for
each radio loudness class are shown; the large errors primarily result from
the high flux density uncertainties in the early QuickLook images from VLASS
(see discussion in §5.1 and Lacy et al., 2020). Star symbols denote three RIQs
and two RQQs that are highlighted in the discussion of §5.4.

As the A-configuration observations presented in this paper are $\approx
20\times$ deeper than FIRST and VLASS (and with many sources still being only
marginally detected at $\mathrm{S/N}\approx 3$–5), inclusion of the entire
sample of 128 RQQs in this analysis would be dominated by upper limits of
FIRST and VLASS flux densities. Because our goal is to obtain meaningful
estimates of spectral indices across all three radio loudness classes of QSOs
(RQ/RI/RL), we limit our selection of QSOs for this analysis to those whose
measured 6-GHz flux densities in C-configuration are $>200\,\mu\mathrm{Jy}$,
which would correspond to a $>3\sigma_{\mathrm{rms}}$ detection in FIRST for a
source with spectral index $\alpha=-0.7$ from 1.4–6 GHz (and no variability).
All RLQs and all RIQs are brighter than this value; of the 128 RQQs, 29
satisfy this criterion.

The surveys and sample selection for this analysis are summarized in Table 4;
the data for all sources in this analysis are provided in Table B of Appendix
B.

###  5.2 Spectral indices

In Figure 10 we show the 1.4–3 GHz and 3–6 GHz spectral indices of the RL, RI,
and RQ sources included in this analysis; note that calculation for these
values implicitly assumes no variability between the different observing
epochs. The three radio loudness classes generally occupy separate regions of
this parameter space; a two-sample Kolmogorov-Smirnov test (Massey, 1951) on
the RQ/RL populations yields a $p$-value of $6.5\times 10^{-7}$, strongly
indicating that the RQ/RL spectral indices follow two separate distributions.
The bulk of the RQQs have spectral indices $\alpha<0$ across the full
frequency range; the RIQs largely overlap the RQ sources but with a tendency
toward flatter spectral indices. In contrast, the RLQs all manifest flat
($\alpha>-0.5$) or even inverted ($\alpha>0.5$) spectral index on at least one
axis. Note that the bottom-right quadrant is populated with sources that have
a spectral peak between 1.4 and 6 GHz.

The behavior of the different radio loudness classes in Figure 10 is
consistent with typically observed spectral indices for QSOs: RLQs exhibit
flat-spectrum emission indicative of an optically thick, i.e., synchrotron-
self-absorbed jet core (Cotton et al., 1980), while RQQs show steeper spectra
generally associated with optically thin synchrotron emission consistent with
a star formation origin (e.g., Condon et al., 2013), but also consistent with
optically thin jets or shocks from winds. The RIQs appear to have spectral
indices in a range that bridges the RL and RQ classes. Some sources lie far
from the constant power law line in Figure 10. This spectral curvature may be
explained by those sources containing both a significant steep-spectrum
component related to star formation and flat-spectrum component from the
central AGN (Kimball et al., 2011b; Condon et al., 2013; Kellermann et al.,
2016; Macfarlane et al., 2021). The relative contributions of each component
are frequency-dependent, meaning that a combination of the two will produce
scatter from a constant power law across 1.4–6 GHz in Figure 10. We note that,
of the 70 sources in this sub-sample, 7/29 RQQs, 1/27 RIQs, and 5/14 RLQs are
inconsistent with a constant power law beyond $1\sigma$ measurement errors.

Also evident are three obviously outlying RIQs; a possible explanation is that
these three sources are variable, such that their radio emission changed
between the different observing epochs of the 1.4, 3, and 6 GHz data. It is
interesting that these extreme outliers are found primarily in the RIQ class,
and could suggest that radio-loudness is a transient phenomenon, with QSOs
shifting between the two main radio-loudness classes (e.g., Nyland et al.,
2020). The possible presence of variability, particularly in these outlier
sources, is discussed below in §5.4.

###  5.3 Time domain with spectral index analysis

Figure 11: Left panels: Estimated 6-GHz luminosity over decades-long
timescales of all QSOs considered in our time-domain analysis. The top row
shows the curves of the 14 RLQs examined, the middle row shows the 27 RIQs,
and the bottom the 29 RQQs. The left column shows the resultant curves
assuming a steep spectral index ($\alpha=-0.7$) in converting FIRST and VLASS
flux densities to our 6-GHz observing frequency, while the right-hand column
shows the resultant curves assuming a flat spectral index ($\alpha=0.0$).
FIRST observations span 1993–2004; all 2010–2011 points reflect data from
Kellermann et al. (2016); for the RQQs, the 2019 data points represent flux
densities from this paper; the 2017–2019 data points for the RIQs and RLQs
reflect data from preliminary “Quick Look” images from Epoch 1 of VLASS, and
the 2019 data points for the RQQs are from the A-configuration observations in
this paper. Right panels: Preferred results selected on their best-fit
spectral index from the $\chi^{2}$ analysis. Sources not well-suited by either
choice of spectral index are shown with thick lines (two in Panel C and 3 in
Panel E), and discussed further in §5.4.

The data we are using to investigate radio spectral indices of our targets are
based on observations taken over multiple decades: FIRST observed the sky from
1993–2004; the Kimball et al. (2011b) C-configuration observations of our
targets were performed in 2010–2011; VLASS Epoch 1 observations were obtained
in 2017–2019; A-configuration observations of the RQQs (presented in this
paper) were obtained in 2019. We can therefore use these data to additionally
probe variability within the sample over decade timescales. Note that we
employ the Kellermann et al. (2016) 6-GHz measurements for the 2010-2011
C-configuration data points, which for the handful of extended RIQs/RLQs
include emission only from the core components. This choice is reasonable as
the extended features of RLQs/RIQs are not expected to significantly vary on
decadal timescales (Blandford et al., 2019), and it allows an appropriate
comparison with the RQQs, which have no such large-scale emission.

We opt to convert all flux densities (FIRST at 1.4 GHz and VLASS at 3 GHz) to
the 6-GHz frequency of our new observations presented here. However, such a
conversion requires assuming a specific value for radio spectral index. As
demonstrated in the previous section, the spectral indices vary across the
sample, and in fact the possibility of variability of individual sources
(which is supported by the spread seen in Figure 8) means that some calculated
spectral indices may be incorrect. Furthermore, flux density variation of a
source could also coincide with spectral index variability; this would
certainly be the case, for example, for a QSO whose radio emission is a
combination of steep-spectrum star-formation processes along with a varying
flat-spectrum jet component.

To convert the 1.4 GHz and 3 GHz data to 6 GHz, we choose to adopt a steep
($\alpha=-0.7$) or flat ($\alpha=0$) radio spectral index corresponding to the
typical observed spectral slopes for optically thin and optically thick
synchrotron emission, respectively. Given the conflicting results in the
literature regarding spectral indices in different-power QSOs (e.g., Barvainis
et al., 2005; Condon et al., 2013), we recognize that employing one choice of
$\alpha$ for all sources would yield dubious results. We instead try both of
the two values for every QSO, and compare the two results to determine which
value of spectral index yields a more physically credible variability pattern
for each source individually. The distinction between the two values of
$\alpha$ corresponds to a difference in 6-GHz flux density of roughly 0.37 dex
for conversions from 1.4 GHz, and 0.14 dex for conversions from 3 GHz. We note
that, for any given source, it is possible that neither choice of spectral
index is correct.

The resulting luminosity-vs-time values are shown in Figure 11, distinguished
by class (RL, RI, RQ from top to bottom). In both the left and right sets of
panels, panels A–C correspond to the assumption of $\alpha=-0.7$ while panels
D–F correspond to the assumption of $\alpha=0$. The left-hand set of panels
includes the two possible light curves (corresponding to different $\alpha$
value) for each QSO. These left panels display some obviously unphysical
patterns of luminosity variation. For example, panel A shows that when
assuming $\alpha=-0.7$, nearly the entire population of RLQs displays a rising
luminosity to 2010–2011 which then decreases to 2017–2019; conversely, panel F
shows that when assuming $\alpha=0$, the majority of RQQs display a sharp
decrease in luminosity from the first to the second epoch. We would not expect
such coordinated behavior in QSOs that are spread across the sky and are
clearly physically unassociated. Therefore these left-hand panels clearly
indicate that $\alpha=-0.7$ is not a reasonable spectral index to assume for
all RLQs, while $\alpha=0$ is not a reasonable spectral index to assume for
all RQQs.

The right-hand set of panels is effectively a subset of the left-hand-side
that displays only the chosen “best” value of $\alpha$ (of $0$ or $-0.7$) for
each source. To determine quantitatively which $\alpha$ value is the better
match, we employ an assumption that the radio luminosity of each QSO should
monotonically increase or decrease over the multiple epochs of observation,
and therefore we attempt to fit each variation pattern to a power-law over
time (with slope as a free variable). We note that variability may produce a
flux density variation pattern that does not follow this assumption; however,
with just three data points, minimizing the degrees of freedom in this
analysis prevents us from achieving overly spurious results. We use a
reduced-$\chi^{2}$ goodness-of-fit test to determine which of the two values
provides a better match to a power-law variability model. We find that 22/29
($76\pm 8\%$) RQQs and 19/27 ($70\pm 9\%$) RIQs are better represented with a
steep spectral index ($\alpha=-0.7$), whereas 12/14 ($86\pm 9\%$) of the RLQs
are better represented with a flat spectral index ($\alpha=0$). The spectral
index results for the different QSO classes are consistent with the results
presented earlier in Figure 10, but here we have added the opportunity to
probe variability. While a handful of sources show some evidence of
variability, the majority are consistent with a non-variable light curve for
the chosen choice of $\alpha$.

An initially surprising observation from Figure 11 is that the radio-loudness
class showing the most discrepancies from flat light curves is the RQQ
population. In particular, panel F on the right seems to suggest that there is
a population of flat-spectrum RQQs whose radio luminosity all decreased
similarly over about two decades. However, we recall to the reader’s attention
the possibility of missing flux in the higher-resolution 6-GHz observations
from 2019 compared to those from 2010-2011 (see discussion in §4.3), and a
symptom of such missing flux would indeed result in apparently decreasing
light curves for $\alpha=0$, thus populating this panel F. We calculate that
an increase of $\sim 23\%$ of radio emission in the 2019 observations for
these 7 RQQs would alter their results in such a way as to match best to
invariable luminosity with $\alpha=-0.7$, and suggest this value of 23% as a
rough estimate for the amount of undetected emission in the new observations
for those 7 RQQs. We find this conclusion to be more reasonable than the idea
that we coincidentally observed a group of unrelated flat-spectrum RQQs that
all decrease in luminosity over a similar time period, especially given the _a
priori_ knowledge that RQQs tend to have steep radio spectra.

Figure 12: The two outlier RQ sources discussed in §5.4. Column 1 shows the
FIRST image (Becker et al., 1995; Helfand et al., 2015); Column 2 shows the
source in the VLA’s C-configuration (Kimball et al., 2011b; Kellermann et al.,
2016); Column 3 displays the source’s “Quick Look” image from the VLA Sky
Survey (Lacy et al., 2020); Column 4 contains the A-configuration images from
the observations presented in this paper. The resolution element (synthesized
beam) is shown in the lower left corner for each image. Note that images in
the different columns were observed at different times and frequencies. The
colorbar maps the source flux density at 6-GHz for each image assuming
$\alpha=-0.7$; the choice of spectral index is discussed in the text in
§§5.2–5.4. See Panel A of Table 4 for a summary of each of the contributing
surveys.  Figure 13: The three RIQs discussed in §5.4. The panel layout
follows that of the first three columns of Figure 12. All images are on the
same color scale. Assumption of spectral index $\alpha=-0.7$ or 0 yields a
conclusion that all three sources increased then decreased in flux density
over a similar timescale; we suggest the likelier explanation is that these
QSOs have radio spectra peaked at $>3$ GHz.

Finally, we call attention to two RQQs and three RIQs (the five sources marked
as stars in Figure 10, bold linestyles in the right-hand panels of Figure 11),
which are ill-suited for either choice of spectral index resulting from this
analysis. The three RI sources are the outliers in Figure 10; we discuss all
five of these sources in more detail in the following subsection.

###  5.4 Outlier Sources

As just discussed, some of the QSOs studied in this section appear to be
poorly represented by either choice of spectral index ($\alpha=0$ or $-0.7$).
In Figure 11, the thick linestyle in the right set of panels highlights two
RQQs (J0856$+$1057, marked in green in panel C; J1000$+$1047, marked in
purple) and three RIQs (J1017$+$1516, marked in brown in panel E;
J1511$+$1009, marked in orange; J1513$+$2623, marked in blue), each of whose
evolution of flux density deviates strongly from the power-law variability
assumption that appears to be sufficient for most QSOs. These five QSOs are
either extremely variable, and/or they have unusual radio spectral indices
such that we erred in converting FIRST/VLASS flux densities to the fiducial
6-GHz observing frequency. They are also the five sources marked as stars in
Figure 10. We show images of the two RQQs in Figure 12 and the three RIQs in
Figure 13.

The two RQQs—J1000+1047 and J0856+1057—demonstrate similar behavior in their
light curves when assuming a spectral index of $\alpha=-0.7$: each shows a
decrease in luminosity from 2000 (detected at 1.4 GHz in FIRST) to 2011
(detected in 6 GHz by Kimball et al., 2011b), then an increase to 2019. Note
that each of these sources has a counterpart in VLASS, with corresponding
values (from 2017) included in Figure 11. Converting each one’s 2017 VLASS
3-GHz observation to 6-GHz assuming $\alpha=-0.7$ yields a value that is
consistent with a straightforward interpolation between the two epochs of
6-GHz observations (see Panel C on the righthand-side of Figure 11). For
further investigation of these two sources, we performed spectral index
analysis similar to that in §5.1 but leaving $\alpha$ as a free parameter
rather than requiring a value of 0 or $-0.7$. The constant spectral index
values that would lead to a power-law variation of luminosity for each target,
over all four epochs of observations, are $\alpha=-1.6$ for J1000$+$1047 and
$\alpha=-1.2$ for J0856+1057, and the corresponding light curves are shown in
Figure 14. Regardless of spectral index value, the fact that each source
increased between the two epochs of 6-GHz observations proves that they are
variable; the angular resolution difference could not cause such an increase.
Thus the behavior of these objects is similar to that of radio transients
highlighted recently by Nyland et al. (2020), suggesting that these two RQQs
could be additional examples of newly launched radio jets. We note that
J1000+1047 appears compact in our 0$\farcs$33-resolution observations, while
J0856+1057 is slightly resolved, with some extended emission that is apparent
above the 3.5-$\sigma$ level.

Figure 14: The five sources in this figure are those whose observations over
multiple epochs clearly suggest that they are variable rather than having
spectral index values of $\alpha\sim-0.7,0$ that are suitable for the bulk of
the QSO population analyzed in this section. Instead, we solved for $\alpha$
as a free-parameter while attempting to fit the light curves to a constant
power-law. The results shown here correspond to the “best” $\alpha$ value for
each source; see text of Section 5.4.

The three outlier RIQs show the apparent opposite behavior in Figure 11 as the
two outlier RQQs. Assuming a flat ($\alpha=0$) spectral index, all three were
faint in the 1990s (two were non-detections in FIRST), had brightened by 2011,
then decreased again by the time of the VLASS observations in 2017–2019. We
suspect that rather than all three sources manifesting this similar
variability pattern, it is instead likely that these RIQs possess inverted
radio spectra ($\alpha>0$) from 1.4–6 GHz. We performed a similar analysis as
for the two outlier RQQs, wherein we leave $\alpha$ as a free parameter to
identify the “best” spectral index to yield a power-law variation in
luminosity with time. The resulting best-fit spectral index values are
$\alpha=2.0$ for J1017+1516; $\alpha=1.1$ for J1511+1009; and $\alpha=2.3$ for
J1513+2623. Such high values are common in the radio spectra of active stars
(due to the gyro-synchroton emission mechanisms present during Solar flares;
Ramaty, 1969; Melrose, 1980; Bastian et al., 1998), and may even be prevalent
below the spectral peak of optically thick sources of emission at lower radio
frequencies (e.g., Raginski & Laor, 2016). However, to our knowledge no
research to-date has reported $\sim$GHz-regime power-law spectral indices as
high as these for any QSOs. We suggest the more plausible scenario is that
these three RIQs are examples of Gigahertz-Peaked Spectrum (GPS) sources
(O’Dea, 1998), which is a categorization describing compact QSOs with radio
SEDs that peak in the few-GHz range; the peak would have to be above 3 GHz in
order to be consistent with the observation that these sources were brighter
at 6 GHz than at 3 GHz. Values of $\alpha>2$ are commonly observed below the
peaks of emission in GPS sources (e.g., Sotnikova et al., 2019, Fig. 4). It is
also possible that these sources are variable in luminosity or spectral index
or both.

##  6 Summary

We have obtained new high-resolution VLA data for a low-redshift ($0.2<z<0.3$)
radio-quiet QSO population (128 RQQs; $L_{\mathrm{6\,GHz}}<10^{23}$ W Hz-1)
drawn from a homogeneous optically selected, volume-limited sample of 178
QSOs. These 6-GHz observations yield $\sim 0\farcs 33$-resolution images
($\sim 1.3$ kpc at $z=0.25$), and a typical 1-$\sigma$ image sensitivity level
of $\sim 7\mu$Jy beam-1. Until now, the sub-galactic morphologies across a
homogeneous volume-limited population of RQQs have been unknown. Examination
of the images yields the following.

  * •

The detected sources can be classified as “Unresolved” (67 of 128) or
“Resolved” (55 of 128) based on their appearance in the $\sim 0\farcs
33$-resolution images at 6-GHz. Six of the RQQs were undetected in these new
observations.

  * •

Extended sub-galactic emission (i.e., within the host galaxy but outside the
region of peak radio emission) is visible in $\geq 45\%$ of the population.

  * •

A handful of the RQQs have sub-galactic radio morphology that seems to
strongly indicate $\sim$kpc-scale jets or AGN-driven shocks as the power
source of the radio emission. In particular, J0935+4819 has a symmetric
double-lobe morphology; several other sources manifest apparent linear
emission extended outward from the core, or widespread flocculent emission
that extends symmetrically outward from the core.

Through comparison of the new data with lower-resolution ($3\farcs 5$) 6-GHz
observations from the literature, we concluded the following.

  * •

Although not always directly visible in the images, extended sub-galactic
emission is present within $\gtrapprox$70% of RQQs in this population.

  * •

The bulk of sub-galactic radio emission— about 65% on average— is dominated by
an unresolved core component coincident with the QSO’s optical position.

  * •

There is direct evidence of variability in the sample: six Resolved RQQs and
four Unresolved RQQs increased in 6-GHz flux density from 2010 to 2019. We
expect that a similar number decreased in 6-GHz emission, but the latter
cannot be definitively identified due to the change in angular resolution
between the two sets of observations.

We additionally utilized 1.4-GHz FIRST data (Becker et al., 1995; Helfand et
al., 2015) and “Quick Look” images from Epoch 1 of the 3-GHz VLA Sky Survey
(Lacy et al., 2020) to investigate the 1.4–3–6 GHz spectral indices for the
subset of the full QSO sample (178 QSOs, $0.2<z<0.3$) that is brighter than
200 $\mu$Jy beam-1 at 6 GHz (3$\farcs$5 resolution), comprising 29 RQQs, 27
RIQs, and 14 RLQs (core-component only). We make the following observations.

  * •

RQQs generally have steep spectral indices ($\alpha\approx-0.7$), while RLQs
have spectral indices that are flat or even inverted ($\alpha\gtrsim 0$).
These calculated spectral indices are consistent with other observations in
the literature.

  * •

RIQs have spectral indices that span between the RQ and RL populations. This
may indicate that RIQs are a transitional population.

  * •

Three RIQs are clear outliers from the rest of the population; we conclude
that they are likely to be GPS sources, which may indeed be undergoing this
hypothesized transitional phase.

While we have achieved an important step forward in the analysis of origins of
radio emission from RQQs, further observational data are needed in order to
form more concrete conclusions. For example, follow-up observations at this
same frequency and resolution would probe possible variability— both in radio
power and morphology— while observations at different frequencies would
provide more concrete conclusions regarding the spectral slopes/curvature of
individual sources. Far-infrared data could yield estimates of the star-
formation contribution in individual sources, while X-ray data may do the same
in terms of a potential coronal or jet component. Much higher-resolution radio
observations (achievable with Very Long Baseline Interferometry) would put
limits on the brightness temperatures of individual features, and allow for
direct separation between starburst/jet contributions in individual sources. A
more detailed analysis of optical/UV spectra of this sample may also help
interpret the role that AGN-related mechanisms play in shaping the RQQ
population.

We thank Pedro Beaklini, Kristina Nyland, Ken Kellermann, and James Condon for
helpful comments that improved the manuscript. We thank the referee for
suggestions that improved the clarity of this paper. Trevor McCaffrey is a
student at the National Radio Astronomy Observatory. The National Radio
Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc. This
project was partially funded by the NSF through the REU program at NRAO. This
research has made use of NASA’s Astrophysics Data System Bibliographic
Services, Ned Wright’s online Javascript Cosmology Calculator (Wright, 2006),
AstroPy (Astropy Collaboration et al., 2013; Price-Whelan et al., 2018),
Matplotlib (Hunter, 2007), NumPy (Harris et al., 2020), SciPy (Virtanen et
al., 2020), Pandas (pandas development team, 2020), and the CIRADA cutout
service at URL cutouts.cirada.ca, operated by the Canadian Initiative for
Radio Astronomy Data Analysis (CIRADA). CIRADA is funded by a grant from the
Canada Foundation for Innovation 2017 Innovation Fund (Project 35999), as well
as by the Provinces of Ontario, British Columbia, Alberta, Manitoba and
Quebec, in collaboration with the National Research Council of Canada, the US
National Radio Astronomy Observatory and Australia’s Commonwealth Scientific
and Industrial Research Organisation.

## References

  * Abazajian et al. (2009) Abazajian, K. N., Adelman-McCarthy, J. K., Agüeros, M. A., et al. 2009, ApJS, 182, 543, doi: 10.1088/0067-0049/182/2/543
  * An & Baan (2012) An, T., & Baan, W. A. 2012, ApJ, 760, 77, doi: 10.1088/0004-637X/760/1/77
  * Anantharamaiah et al. (2000) Anantharamaiah, K. R., Viallefond, F., Mohan, N. R., Goss, W. M., & Zhao, J. H. 2000, ApJ, 537, 613, doi: 10.1086/309063
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Baldi et al. (2015) Baldi, R. D., Capetti, A., & Giovannini, G. 2015, A&A, 576, A38, doi: 10.1051/0004-6361/201425426
  * Baldi et al. (2018) Baldi, R. D., Capetti, A., & Massaro, F. 2018, A&A, 609, A1, doi: 10.1051/0004-6361/201731333
  * Baloković et al. (2012) Baloković, M., Smolčić, V., Ivezić, Ž., et al. 2012, ApJ, 759, 30, doi: 10.1088/0004-637X/759/1/30
  * Barcos-Muñoz et al. (2015) Barcos-Muñoz, L., Leroy, A. K., Evans, A. S., et al. 2015, ApJ, 799, 10, doi: 10.1088/0004-637X/799/1/10
  * Barvainis et al. (2005) Barvainis, R., Lehár, J., Birkinshaw, M., Falcke, H., & Blundell, K. M. 2005, ApJ, 618, 108, doi: 10.1086/425859
  * Bastian et al. (1998) Bastian, T. S., Benz, A. O., & Gary, D. E. 1998, ARA&A, 36, 131, doi: 10.1146/annurev.astro.36.1.131
  * Beck et al. (2016) Beck, R., Dobos, L., Budavári, T., Szalay, A. S., & Csabai, I. 2016, MNRAS, 460, 1371, doi: 10.1093/mnras/stw1009
  * Becker et al. (1995) Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ, 450, 559, doi: 10.1086/176166
  * Blandford et al. (2019) Blandford, R., Meier, D., & Readhead, A. 2019, ARA&A, 57, 467, doi: 10.1146/annurev-astro-081817-051948
  * Blundell & Rawlings (2001) Blundell, K. M., & Rawlings, S. 2001, ApJ, 562, L5, doi: 10.1086/337970
  * Burbidge (1967) Burbidge, E. M. 1967, ARA&A, 5, 399, doi: 10.1146/annurev.aa.05.090167.002151
  * Burbidge & Burbidge (1967) Burbidge, G. R., & Burbidge, E. M. 1967, Quasi-stellar objects
  * Chi et al. (2013) Chi, S., Barthel, P. D., & Garrett, M. A. 2013, A&A, 550, A68, doi: 10.1051/0004-6361/201220783
  * Colina & Perez-Olea (1993) Colina, L., & Perez-Olea, D. 1993, Ap&SS, 205, 99, doi: 10.1007/BF00657963
  * Condon (1992) Condon, J. J. 1992, ARA&A, 30, 575, doi: 10.1146/annurev.aa.30.090192.003043
  * Condon et al. (2002) Condon, J. J., Cotton, W. D., & Broderick, J. J. 2002, AJ, 124, 675, doi: 10.1086/341650
  * Condon et al. (1998) Condon, J. J., Cotton, W. D., Greisen, E. W., et al. 1998, AJ, 115, 1693, doi: 10.1086/300337
  * Condon et al. (1992) Condon, J. J., Huang, Z. P., Yin, Q. F., & Thuan, T. X. 1992, in Astronomical Society of the Pacific Conference Series, Vol. 31, Relationships Between Active Galactic Nuclei and Starburst Galaxies, ed. A. V. Filippenko, 79
  * Condon et al. (2013) Condon, J. J., Kellermann, K. I., Kimball, A. E., Ivezić, Ž., & Perley, R. A. 2013, ApJ, 768, 37, doi: 10.1088/0004-637X/768/1/37
  * Cornwell et al. (2005) Cornwell, T. J., Golap, K., & Bhatnagar, S. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 347, Astronomical Data Analysis Software and Systems XIV, ed. P. Shopbell, M. Britton, & R. Ebert, 86
  * Cotton et al. (1980) Cotton, W. D., Wittels, J. J., Shapiro, I. I., et al. 1980, ApJ, 238, L123, doi: 10.1086/183271
  * Eddington (1913) Eddington, A. S. 1913, MNRAS, 73, 359, doi: 10.1093/mnras/73.5.359
  * Fanaroff & Riley (1974) Fanaroff, B. L., & Riley, J. M. 1974, MNRAS, 167, 31P, doi: 10.1093/mnras/167.1.31P
  * Harris et al. (2020) Harris, C. R., Jarrod Millman, K., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2
  * Helfand et al. (2015) Helfand, D. J., White, R. L., & Becker, R. H. 2015, ApJ, 801, 26, doi: 10.1088/0004-637X/801/1/26
  * Herrera Ruiz et al. (2016) Herrera Ruiz, N., Middelberg, E., Norris, R. P., & Maini, A. 2016, A&A, 589, L2, doi: 10.1051/0004-6361/201628302
  * Herrera Ruiz et al. (2017) Herrera Ruiz, N., Middelberg, E., Deller, A., et al. 2017, A&A, 607, A132, doi: 10.1051/0004-6361/201731163
  * Hodge et al. (2011) Hodge, J. A., Becker, R. H., White, R. L., Richards, G. T., & Zeimann, G. R. 2011, AJ, 142, 3, doi: 10.1088/0004-6256/142/1/3
  * Hovatta et al. (2007) Hovatta, T., Tornikoski, M., Lainela, M., et al. 2007, A&A, 469, 899, doi: 10.1051/0004-6361:20077529
  * Hunter (2007) Hunter, J. D. 2007, Computing In Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
  * Jagannathan et al. (2018) Jagannathan, P., Bhatnagar, S., Brisken, W., & Taylor, A. R. 2018, AJ, 155, 3, doi: 10.3847/1538-3881/aa989f
  * Kellermann et al. (2016) Kellermann, K. I., Condon, J. J., Kimball, A. E., Perley, R. A., & Ivezić, Ž. 2016, ApJ, 831, 168, doi: 10.3847/0004-637X/831/2/168
  * Kellermann & Pauliny-Toth (1981) Kellermann, K. I., & Pauliny-Toth, I. I. K. 1981, ARA&A, 19, 373, doi: 10.1146/annurev.aa.19.090181.002105
  * Kellermann et al. (1989) Kellermann, K. I., Sramek, R., Schmidt, M., Shaffer, D. B., & Green, R. 1989, AJ, 98, 1195, doi: 10.1086/115207
  * Kimball & Ivezić (2008) Kimball, A. E., & Ivezić, Ž. 2008, AJ, 136, 684, doi: 10.1088/0004-6256/136/2/684
  * Kimball et al. (2011a) Kimball, A. E., Ivezić, Ž., Wiita, P. J., & Schneider, D. P. 2011a, AJ, 141, 182, doi: 10.1088/0004-6256/141/6/182
  * Kimball et al. (2011b) Kimball, A. E., Kellermann, K. I., Condon, J. J., Ivezić, Ž., & Perley, R. A. 2011b, ApJ, 739, L29, doi: 10.1088/2041-8205/739/1/L29
  * Klindt et al. (2019) Klindt, L., Alexander, D. M., Rosario, D. J., Lusso, E., & Fotopoulou, S. 2019, MNRAS, 488, 3109, doi: 10.1093/mnras/stz1771
  * Komossa (2015) Komossa, S. 2015, Journal of High Energy Astrophysics, 7, 148, doi: 10.1016/j.jheap.2015.04.006
  * Kunert-Bajraszewska et al. (2020) Kunert-Bajraszewska, M., Wołowska, A., Mooley, K., Kharb, P., & Hallinan, G. 2020, ApJ, 897, 128, doi: 10.3847/1538-4357/ab9598
  * Lacy et al. (2020) Lacy, M., Baum, S. A., Chandler, C. J., et al. 2020, PASP, 132, 035001, doi: 10.1088/1538-3873/ab63eb
  * Lerner (2018) Lerner, E. J. 2018, MNRAS, 477, 3185, doi: 10.1093/mnras/sty728
  * Lonsdale et al. (2006) Lonsdale, C. J., Diamond, P. J., Thrall, H., Smith, H. E., & Lonsdale, C. J. 2006, ApJ, 647, 185, doi: 10.1086/505193
  * Macfarlane et al. (2021) Macfarlane, C., Best, P. N., Sabater, J., et al. 2021, MNRAS, 506, 5888, doi: 10.1093/mnras/stab1998
  * Maini et al. (2016) Maini, A., Prandoni, I., Norris, R. P., Giovannini, G., & Spitler, L. R. 2016, A&A, 589, L3, doi: 10.1051/0004-6361/201628305
  * Massey (1951) Massey, F. J. 1951, Journal of the American Statistical Association, 46, 68.  http://www.jstor.org/stable/2280095
  * McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell, 127
  * Melrose (1980) Melrose, D. B. 1980, Space Sci. Rev., 26, 3, doi: 10.1007/BF00212597
  * Mohan & Rafferty (2015) Mohan, N., & Rafferty, D. 2015, PyBDSF: Python Blob Detection and Source Finder.  http://ascl.net/1502.007
  * Morabito et al. (2022) Morabito, L. K., Jackson, N. J., Mooney, S., et al. 2022, A&A, 658, A1, doi: 10.1051/0004-6361/202140649
  * Nyland et al. (2020) Nyland, K., Dong, D., Patil, P., et al. 2020, arXiv e-prints, arXiv:2005.04734.  https://arxiv.org/abs/2005.04734
  * O’Dea (1998) O’Dea, C. P. 1998, PASP, 110, 493, doi: 10.1086/316162
  * O’Dea & Saikia (2021) O’Dea, C. P., & Saikia, D. J. 2021, A&A Rev., 29, 3, doi: 10.1007/s00159-021-00131-w
  * O’Dea et al. (2008) O’Dea, C. P., Baum, S. A., Privon, G., et al. 2008, ApJ, 681, 1035, doi: 10.1086/588212
  * Oke & Gunn (1983) Oke, J. B., & Gunn, J. E. 1983, ApJ, 266, 713, doi: 10.1086/160817
  * Padovani et al. (2015) Padovani, P., Bonzini, M., Kellermann, K. I., et al. 2015, MNRAS, 452, 1263, doi: 10.1093/mnras/stv1375
  * Padovani et al. (2011) Padovani, P., Miller, N., Kellermann, K. I., et al. 2011, ApJ, 740, 20, doi: 10.1088/0004-637X/740/1/20
  * pandas development team (2020) pandas development team, T. 2020, pandas-dev/pandas: Pandas, latest, Zenodo, doi: 10.5281/zenodo.3509134
  * Perley & Butler (2017) Perley, R. A., & Butler, B. J. 2017, ApJS, 230, 7, doi: 10.3847/1538-4365/aa6df9
  * Perley et al. (2011) Perley, R. A., Chandler, C. J., Butler, B. J., & Wrobel, J. M. 2011, ApJ, 739, L1, doi: 10.1088/2041-8205/739/1/L1
  * Price-Whelan et al. (2018) Price-Whelan, A. M., Sipőcz, B. M., Günther, H. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Raginski & Laor (2016) Raginski, I., & Laor, A. 2016, MNRAS, 459, 2082, doi: 10.1093/mnras/stw772
  * Ramaty (1969) Ramaty, R. 1969, ApJ, 158, 753, doi: 10.1086/150235
  * Rau & Cornwell (2011) Rau, U., & Cornwell, T. J. 2011, A&A, 532, A71, doi: 10.1051/0004-6361/201117104
  * Rees (1984) Rees, M. J. 1984, ARA&A, 22, 471, doi: 10.1146/annurev.aa.22.090184.002351
  * Richards et al. (2002) Richards, G. T., Fan, X., Newberg, H. J., et al. 2002, AJ, 123, 2945, doi: 10.1086/340187
  * Rosario et al. (2021) Rosario, D. J., Alexander, D. M., Moldon, J., et al. 2021, MNRAS, 505, 5283, doi: 10.1093/mnras/stab1653
  * Sadler (2016) Sadler, E. M. 2016, Astronomische Nachrichten, 337, 105, doi: 10.1002/asna.201512274
  * Schlegel et al. (1998) Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525, doi: 10.1086/305772
  * Schmidt (1969) Schmidt, M. 1969, ARA&A, 7, 527, doi: 10.1146/annurev.aa.07.090169.002523
  * Schmidt & Green (1983) Schmidt, M., & Green, R. F. 1983, ApJ, 269, 352, doi: 10.1086/161048
  * Schneider et al. (2010) Schneider, D. P., Richards, G. T., Hall, P. B., et al. 2010, AJ, 139, 2360, doi: 10.1088/0004-6256/139/6/2360
  * Shimwell et al. (2019) Shimwell, T. W., Tasse, C., Hardcastle, M. J., et al. 2019, A&A, 622, A1, doi: 10.1051/0004-6361/201833559
  * Shimwell et al. (2022) Shimwell, T. W., Hardcastle, M. J., Tasse, C., et al. 2022, A&A, 659, A1, doi: 10.1051/0004-6361/202142484
  * Smolčić et al. (2017) Smolčić, V., Novak, M., Bondi, M., et al. 2017, A&A, 602, A1, doi: 10.1051/0004-6361/201628704
  * Sotnikova et al. (2019) Sotnikova, Y. V., Mufakharov, T. V., Majorova, E. K., et al. 2019, Astrophysical Bulletin, 74, 348, doi: 10.1134/S1990341319040023
  * Sweijen et al. (2022) Sweijen, F., van Weeren, R. J., Röttgering, H. J. A., et al. 2022, Nature Astronomy, 6, 350, doi: 10.1038/s41550-021-01573-z
  * Terashima & Wilson (2003) Terashima, Y., & Wilson, A. S. 2003, ApJ, 583, 145, doi: 10.1086/345339
  * Terlevich et al. (1992) Terlevich, R., Tenorio-Tagle, G., Franco, J., & Melnick, J. 1992, MNRAS, 255, 713, doi: 10.1093/mnras/255.4.713
  * Thyagarajan et al. (2011) Thyagarajan, N., Helfand, D. J., White, R. L., & Becker, R. H. 2011, ApJ, 742, 49, doi: 10.1088/0004-637X/742/1/49
  * Ulvestad et al. (2005) Ulvestad, J. S., Antonucci, R. R. J., & Barvainis, R. 2005, ApJ, 621, 123, doi: 10.1086/427426
  * van Haarlem et al. (2013) van Haarlem, M. P., Wise, M. W., Gunst, A. W., et al. 2013, A&A, 556, A2, doi: 10.1051/0004-6361/201220873
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2
  * Wright (2006) Wright, E. L. 2006, PASP, 118, 1711, doi: 10.1086/510102
  * Zakamska & Greene (2014) Zakamska, N. L., & Greene, J. E. 2014, MNRAS, 442, 784, doi: 10.1093/mnras/stu842
  * Zakamska et al. (2016) Zakamska, N. L., Lampayan, K., Petric, A., et al. 2016, MNRAS, 455, 4191, doi: 10.1093/mnras/stv2571

##  Appendix A Images and notes for individual sources

In Figure 15, we present images of the Resolved (Extended, Multi-component,
Slightly-resolved) sources. Base-level contours correspond to signal-to-noise
detections of 3.5–4 (see caption of Figure 3). Per the analysis in Section
4.2, we estimate that the expectation value of the number of unassociated
faint background sources in the Multi-Component class is $\sim 0.125$.

Figure 15: Images of resolved sources with complex radio morphologies in our
sample. The panel layout follows that of Figure 3. See §4 for a discussion on
morphology classification. Individual notes on each of these sources are
available in Appendix A.

Figure 15 (Continued):

Figure 15 (Continued):

Figure 15 (Continued):

Figure 15 (Continued):

Figure 15 (Continued):

Figure 16: Sources classified as “Slightly Resolved”. The panel layouts follow
that of Figure 3. See §4 for a discussion on morphology classification.

Figure 16 (Continued):

Figure 16 (Continued):

Figure 16 (Continued):

Figure 16 (Continued):

Figure 16 (Continued):

Figure 16 (Continued):

Figure 16 (Continued):

We separate notes into two main subsections to highlight sources with
especially interesting radio morphologies and sources with large
increases/decreases in flux density from 2010–2011 observations separately; a
third subsection discusses images with remaining image artifacts or other
issues.

###  A.1 Sources with Interesting Morphological Features

####  A.1.1 J0843+5357

A clear asymmetric, broad extended structure stretches $\sim 4$ kpc southeast
and traverses roughly half the distance in the opposite direction. Both
extensions appear to abruptly terminate and curve inward southwest.

####  A.1.2 J0935+4819

A well-resolved double-lobed source (see top panel of the first page of Figure
15) that must be powered predominantly by AGN activity. The southwest lobe has
an extension toward the northeast that coincides with the SDSS optical
position, suggesting radio emission from a core that is blended with the
southwest lobe. The linear extent of the two lobes is 1$\farcs$5,
corresponding to a physical extent of $\gtrsim 6$ kpc with unknown line-of-
sight orientation. With radio spectral index of $\alpha\sim-0.7$ from 1.4 to 6
GHz, this appears to be the first example of a Compact Steep Spectrum source
in a radio-_quiet_ QSO.

####  A.1.3 J0944+3608

A $\sim 50\,\mu$Jy core slightly resolved in two directions that also has two
$\sim 30\,\mu$Jy compact components oriented in the directions that the core
exhibits resolution $\sim 8\,\mathrm{kpc}$ from the optical position of the
QSO.

####  A.1.4 J1004+1510

Note that the structure that we see in the C-configuration image appears to be
a calibration error, with a corresponding negative feature just above it; the
only real structure is the unresolved core. Source has an interesting three-
component morphology that stands alone from the rest of the sample (see the
top panel of the third part of Figure 15). There is a fairly strong $\sim
150\,\mu$Jy compact source coinciding with the SDSS optical location, while
two other $\sim 40\,\mu$Jy compact radio sources produce the added-component
radio emission. The two sources offset $\sim 1^{\prime\prime}$ from the core
are both on the southwest side of the bright compact emission. Source’s total
flux density has decreased $\sim$50% from previous $3\farcs 5$ observation.

####  A.1.5 J1045+2933

A slightly resolved $\sim 280\,\mu$Jy component lies at the exact optical
location of the QSO while there is another fainter $\sim 40\,\mu$Jy compact
component $\sim 10$ kpc north of the core component—the opposite direction
from which the central source exhibits its resolution.

####  A.1.6 J1102+0844

There is no clear point of emission overlapping with the optical location of
the QSO, which we typically see in most of these detected targets—however,
there is a faint 22 $\mu$Jy source offset $\approx 0\farcs 81$ from the SDSS
optical location, which we take to be associated with our main target.

####  A.1.7 J1118+3103

The $\sim 30\,\mu$Jy core may be symmetrically emitting a pair of equally
bright ($\sim 20\,\mu$Jy) lobes $\sim 6$ kpc from the detected core; there may
be another slightly elongated component curved away from the rightward offset
component.

####  A.1.8 J1125+2513

The previous $\sim 3\farcs 5$ image of this source hinted at this RQQ being
slightly resolved in the southwest direction and we have confirmed that
suspicion by resolving it into two clear compact components: a core $\sim
30\,\mu$Jy source overlapping with the optical position of the QSO, and
another source of comparable flux density $\sim 16$ kpc southwest of the core.
Inspection of the SDSS image around the area of this target reveals no clear
presence of background sources, so the extended nature of this source is most
certainly real and associated with the QSO.

####  A.1.9 J1146+3715

A faint, odd V-shaped radio source is at the exact location of the SDSS QSO
and two other compact components are present along a line southeast of the QSO
component (see the bottom panel of part 4 of Figure 15 for the image). One of
the offset sources is of comparable flux density ($\sim 35\,\mu\mathrm{Jy}$)
to the V-shaped source and just $\sim 3$ kpc away, while the more distant
($\sim 15\,\mathrm{kpc}$) component is much brighter ($\sim
70\,\mu\mathrm{Jy}$) and appears to be slightly resolved in the opposite
direction from which the V-shaped source is oriented.

####  A.1.10 J1155+5021

There is a faint $\sim 35\,\mu\mathrm{Jy}$ source coincident with the QSO’s
optical position that exhibits some resolution beyond the synthesized beam.
The elongated component extends $\gtrsim 2\,\mathrm{kpc}$ west, and another
compact radio source of comparable flux density resides $\sim
15\,\mathrm{kpc}$ from the component coinciding with the QSO in the same
direction.

####  A.1.11 1210+0154

A two-component source where the main component coincides with the QSO’s SDSS
position as well as another second compact source extending $\sim
19\,\mathrm{kpc}$ from the first. This is the farthest distance from the QSO
that we detect radio emission in any of the RQQs studied herein.

####  A.1.12 J1233+6443

Source potentially appeared to be slightly resolved in C-configuration
observations, but has now been clearly resolved into two components: one faint
$\sim 40\,\mu\mathrm{Jy}$ compact radio source at the exact optical location
of the QSO, and one much brighter $\sim 160\,\mu\mathrm{Jy}$ component offset
$\sim 12\,\mathrm{kpc}$ northeast from the fainter component. Further
assessment of the SDSS optical image at the location of this source is
ambiguous as to discerning whether or not the brighter source could
potentially be another separate galaxy interacting/interfering with our
target, or if it is the edge-brightened extended QSO that it appears to be
(see the second panel of the final part of Figure 15 for the produced VLA
image of this source).

####  A.1.13 J1235+4104

A source that is clearly extended at our $0\farcs 33$ resolution. A well-
defined $\sim 135\,\mu\mathrm{Jy}$ core coincides with the optical position of
the QSO while the asymmetric extended emission contributes $\sim
220\,\mu\mathrm{Jy}$ to the source’s total radio luminosity (see the third
panel of the first part of Figure 15 for image). Interestingly, the source
(with total 6 GHz flux density $S_{\rm 6GHz}=406\pm 36\,\mu\mathrm{Jy}$) does
not appear even as a faint marginal detection in FIRST. Even if the core were
to completely “shut off”, and the extended emission was all that was
contributing at the time of the FIRST observation, assuming a steep spectral
index $\alpha=-0.7$ (typical for synchrotron emisson; Condon, 1992), this
implies a 1.4 GHz spectral flux density of $S_{\rm 1.4GHz}=609\pm
75\,\mu\mathrm{Jy}$—roughly 35% above the typical 450-$\mu\mathrm{Jy}$
3-$\sigma_{\rm rms}$ FIRST detection threshold. This result indicates that the
high resolution image of J1235+4104 either reveals the presence of nascent
jets associated with a variable core, or the extended emission has a flat
spectrum. The 6-GHz observation of this source by Kimball et al. (2011b)
($S_{\rm 6GHz}=266\pm 16.1\,\mu\mathrm{Jy}$) perhaps supports the scenario of
the extended emission being due to some sort of enrichment of AGN
activity—whether it be the emergence of young jets (Nyland et al., 2020) or an
enhancement of accretion activity (Kunert-Bajraszewska et al., 2020).

####  A.1.14 J1304+0205

Source exhibits clear extended emission—apparently in only one direction (see
the lower panel of the first part of Figure 15). The width of the extended
component appears to increase with distance from the core.

####  A.1.15 J1408+4303

Source has a faint $\sim 30\,\mu$Jy core component as well as some apparent
narrow extended emission oriented in only one direction, bringing its total
flux density up to $52.9\pm 8.6\,\mu$Jy, agreeable with its C-configuration
flux density of 52.3 $\mu$Jy.

####  A.1.16 J1444+0633

The relatively strong ($255.8\pm 7.2\,\mu\mathrm{Jy}$) core may have an
associated narrow strip of emission detected in A-configuration contributing
$\sim 100\,\mu\mathrm{Jy}$ to the source’s total flux density.

####  A.1.17 J1458+4555

This is the only RQQ from Kellermann et al. (2016) that was observed to appear
resolved on $\sim$14 kpc scales; our A-configuration observation clearly
resolves the extended radio structure into two compact points of emission of
roughly equal flux density ($\sim 35\,\mu$Jy). Investigation of the SDSS
optical image reveals an overlapping source with the potential added radio
component, so this is probably not a core-lobe structure—rather, it reinforces
the sentiment of all RQQs in this sample being unresolved on host galaxy
scales as even the one RQQ that may have had extended emission was really only
producing compact radio emission.

####  A.1.18 J1529+0216

There is clear emission extending beyond the $\sim 0\farcs 33$ synthesized
beam in what appears to be in four different directions, forming something of
an X-shaped radio morphology (see the second panel of part two of Figure 15).

####  A.1.19 J1727+6322

Source has strong, diffuse extended emission emerging from opposite sides of
the core, reaching distances of $\sim 3.5\,\mathrm{kpc}$ in each of the north
and south directions (see the third panel of the second part of Figure 15).

###  A.2 Notably Variable Sources

####  A.2.1 J0822+4553

Source has a strong $\sim 430\,\mu$Jy radio core coinciding with its optical
position and another $\sim 100\,\mu$Jy slightly elongated component $\sim
16\,\mathrm{kpc}$ from the core. This source’s flux density was only $222\pm
11.2\,\mu$Jy in Kimball et al. (2011b), indicating significant variability
($+140\%$) over decadal timescales. Each of these characteristics are strong
indicators of an AGN being a dominant contributor to the radio in this QSO.

####  A.2.2 J1000+1047

Source remains compact on A-configuration scales and shows strong signs of
variability; flux density has increased from $\sim 223\,\mu$Jy at $\sim
3\farcs 5$ to $\sim 558\,\mu$Jy at $\sim 0\farcs 33$.

####  A.2.3 J1129+5120

Our observation reveals a lone slightly resolved source at the optical
location of this QSO that has decreased $\sim 67\%$ from $501\pm
44.6\,\mu\mathrm{Jy}$ at $3\farcs 5$ resolution to $161\pm 21\,\mu\mathrm{Jy}$
at $\sim 0\farcs 33$.

####  A.2.4 J1617+0638

Source remains unresolved on A-configuration scales, but shows strong
variability in the positive direction—nearing fractional flux density changes
of 80%, increasing from $\sim 265\,\mu\mathrm{Jy}$ at $3\farcs 5$ to $\sim
465\,\mu\mathrm{Jy}$ at $0\farcs 33$.

####  A.2.5 J1627+4736

Source stays unresolved at our higher resolution and doubles in flux density
from $\sim 300\,\mu\mathrm{Jy}$ at $3\farcs 5$ to $\sim 600\,\mu\mathrm{Jy}$
at $0\farcs 33$.

###  A.3 Sources with Image Defects

####  A.3.1 J0934+0306

A bright $\sim 80\,\mathrm{mJy}$ FIRST source at 093430.71+030545.43 $\sim
1\farcm 5$ from the target significantly propagates its individual errors
through to our central target. Although we detect faint $\sim
50\,\mu\mathrm{Jy}$ radio emission at the QSO’s optical position, such errors
make it difficult to untangle any possible extended morphologies present, so
we take it as being a simple point source.

####  A.3.2 J1034+6053

Image has both a complex jetted source at 103436.05+605252.60 offset $\sim
1^{\prime}$ from our source, as well as a strong $\sim 170\,\mathrm{mJy}$
source at 103351.43+605107.32 along the edge of the VLA’s primary beam. A
confusing extended structure overlaps with our central target, making accurate
determination of the source’s morphology difficult. However, this source was
one of the few RQQs not detected by Kimball et al. (2011b) (3-$\sigma_{\rm
rms}$ upper limit of $20.7\,\mu\mathrm{Jy}$), and the total flux of the core
component alone sums to $27.6\pm 7.3\,\mu\mathrm{Jy}$. The total flux density
of the core component plus the possible extended structure on the other hand
sums to $\sim 220\,\mu\mathrm{Jy}$. While variability does play a role in
shaping our results, extended jetted/lobed sources are not capable are being
variable to this degree over these distances (Blandford et al., 2019), so we
take J1034+6053 to be limited to the $27.6\,\mu\mathrm{Jy}$ confined to its
core component.

####  A.3.3 J1443+4045

Image is severely dynamic-range-limited, with a powerful 260mJy source at
144259.34+404429.12 offset $\sim 1^{\prime}$ from the pointing center,
degrading the image sensitivity by a factor of $\approx 5$.

##  Appendix B Multi-frequency Data

Here we provide the multi-frequency data used throughout §5; a full machine-
readable version of this table is available in the online journal. Data stored
in Table B are listed as follows:

  * •

Column 1: Full name of the QSO in SDSSJ format

  * •

Column 2: Redshift from the SDSS-DR7 catalog (Schneider et al., 2010)

  * •

Column 3: Measured total 1.4-GHz flux density of each source as it appeared in
FIRST (Becker et al., 1995).

  * •

Column 4: Date of source’s observation in FIRST in YYYY-MM-DD format.

  * •

Column 5: Total 6-GHz flux density measured by Kellermann et al. (2016) in the
VLA’s C configuration ($\sim 3\farcs 5$ at a 6-GHz reference frequency).

  * •

Column 6: Date of source’s C-configuration VLA observation in YYYY-MM format
(Kimball et al., 2011b).

  * •

Column 7: Measured total 3-GHz flux density in Epoch 1 of VLASS (Lacy et al.,
2020).

  * •

Column 8: Date of source’s observation in VLASS in YYYY-MM-DD format; Epoch
1.1 observations span 2017 September–2018 February while Epoch 1.2 was
undergone from March through July of 2019. We discuss the reliability and
resulting corrections of VLASS flux densities in §5.1.

  * •

Column 9: Measured total 6-GHz flux density of source in the VLA’s A
configuration ($\sim 0\farcs 33$ at a 6-GHz reference frequency).

  * •

Column 10: Date of source’s A-configuration VLA observation in YYYY-MM format.

  * •

Column 11: Source’s radio-loud/-intermediate/-quiet classification based on
6-GHz luminosities measured by Kellermann et al. (2016). See Section 2 for how
“radio-quietness” is defined.

  * •

Column 12: Source’s spectral index determination obtained through the time-
domain analysis explained in § 5.3.

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
---|---|---|---|---|---|---|---|---|---|---|---
Name | $z$ | $S_{\rm 1.4GHz,FIRST}$ |  DATEFIRST | $S_{\rm 6GHz,VLAC}$ |  DATEVLAC | $S_{\rm 3GHz,VLASS}$ |  DATEVLASS | $S_{\rm 6GHz,VLAA}$ |  DATEVLAA | CLASS | $\alpha$
(SDSSJ) |  | (mJy) | (Y-M-D) | (mJy) | (Y-M) | (mJy) | (Y-M-D) | (mJy) | (Y-M) |  |
122011.88+020342.2 | 0.240 | $323.80\pm 1.50$ | 1998-07-15 | $322.00\pm 9.66$ | 2011-01-17 | $393.98\pm 84.91$ | 2019-05-14 |  $\cdots$ |  $\cdots$ | RL | 0.0
083353.88+422401.8 | 0.249 | $229.57\pm 0.42$ | 1995-12-19 | $209.00\pm 6.27$ | 2010-11-15 | $199.80\pm 43.04$ | 2019-05-24 |  $\cdots$ |  $\cdots$ | RL | 0.0
154743.53+205216.6 | 0.265 | $35.20\pm 0.19$ | 1998-10-15 | $51.41\pm 1.56$ | 2010-11-30 | $38.76\pm 8.52$ | 2017-09-26 |  $\cdots$ |  $\cdots$ | RL | 0.0
095407.02+212235.9 | 0.295 | $22.58\pm 0.41$ | 1998-09-15 | $36.08\pm 0.79$ | 2010-12-1 | $30.51\pm 6.57$ | 2019-04-19 |  $\cdots$ |  $\cdots$ | RL | 0.0
085632.99+595746.8 | 0.283 | $24.79\pm 0.18$ | 2002-07-15 | $35.61\pm 1.07$ | 2010-11-30 | $65.00\pm 14.02$ | 2017-09-25 |  $\cdots$ |  $\cdots$ | RL | 0.0
140336.43+174136.1 | 0.222 | $20.57\pm 0.16$ | 1999-11-15 | $17.89\pm 0.54$ | 2011-1-3 | $28.41\pm 6.13$ | 2019-04-01 |  $\cdots$ |  $\cdots$ | RL | 0.0
112952.99+221520.0 | 0.291 | $33.22\pm 0.19$ | 1996-01-15 | $17.01\pm 0.51$ | 2010-12-17 | $15.65\pm 3.37$ | 2019-04-19 |  $\cdots$ |  $\cdots$ | RL | 0.0
100726.10+124856.2 | 0.241 | $13.03\pm 0.96$ | 1999-12-15 | $14.24\pm 0.43$ | 2010-12-15 | $24.81\pm 6.65$ | 2017-10-06 |  $\cdots$ |  $\cdots$ | RL | 0.0
122539.55+245836.3 | 0.268 | $6.48\pm 0.18$ | 1995-12-05 | $9.49\pm 0.29$ | 2011-1-2 | $6.58\pm 1.42$ | 2017-11-24 |  $\cdots$ |  $\cdots$ | RL | 0.0
092837.98+602521.0 | 0.295 | $11.50\pm 1.90$ | 2002-07-15 | $8.94\pm 0.27$ | 2010-10-15 | $8.99\pm 2.03$ | 2017-09-18 |  $\cdots$ |  $\cdots$ | RL | 0.0
111121.71+482045.9 | 0.281 | $14.55\pm 0.28$ | 1997-04-10 | $8.13\pm 0.25$ | 2010-12-16 | $15.10\pm 3.26$ | 2019-05-10 |  $\cdots$ |  $\cdots$ | RL | $-0.7$
145331.47+264946.7 | 0.279 | $13.98\pm 0.17$ | 1995-11-10 | $6.05\pm 0.25$ | 2011-1-4 | $8.59\pm 1.86$ | 2017-11-12 |  $\cdots$ |  $\cdots$ | RL | $-0.7$
084347.84+203752.4 | 0.227 | $2.87\pm 0.14$ | 1998-10-15 | $5.36\pm 0.16$ | 2010-11-15 | $3.43\pm 0.75$ | 2019-04-13 |  $\cdots$ |  $\cdots$ | RL | 0.0
093200.07+553347.4 | 0.266 | $4.95\pm 0.29$ | 1997-05-15 | $5.15\pm 0.16$ | 2010-10-31 | $5.39\pm 1.18$ | 2017-09-23 |  $\cdots$ |  $\cdots$ | RL | 0.0
151351.50+262358.1 | 0.203 | $<0.47$ | 1995-11-13 | $5.04\pm 0.15$ | 2010-12-4 | $1.51\pm 0.36$ | 2017-10-02 |  $\cdots$ |  $\cdots$ | RI | 0.0
091702.11+212337.5 | 0.202 | $4.19\pm 0.13$ | 1998-09-15 | $4.79\pm 0.14$ | 2011-1-15 | $4.53\pm 0.99$ | 2019-04-22 |  $\cdots$ |  $\cdots$ | RI | 0.0
151132.53+100953.1 | 0.282 | $1.14\pm 0.13$ | 2000-01-15 | $3.05\pm 0.09$ | 2010-12-3 | $2.06\pm 0.46$ | 2019-03-12 |  $\cdots$ |  $\cdots$ | RI | 0.0
125807.45+232921.6 | 0.258 | $3.91\pm 0.16$ | 1995-12-23 | $2.96\pm 0.09$ | 2010-11-1 | $3.40\pm 0.75$ | 2020-07-15 |  $\cdots$ |  $\cdots$ | RI | 0.0
075403.60+481428.0 | 0.276 | $7.91\pm 0.16$ | 1997-04-10 | $2.63\pm 0.08$ | 2011-1-15 | $4.40\pm 0.95$ | 2019-05-10 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
083658.90+442602.2 | 0.254 | $9.15\pm 0.12$ | 1997-02-28 | $2.60\pm 0.08$ | 2011-1-15 | $4.25\pm 0.93$ | 2019-05-24 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
094603.94+013923.6 | 0.220 | $7.33\pm 0.15$ | 1998-07-24 | $2.47\pm 0.08$ | 2011-1-15 | $4.38\pm 0.96$ | 2018-01-02 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
134113.93-005315.0 | 0.237 | $5.13\pm 0.16$ | 1998-08-15 | $1.93\pm 0.06$ | 2010-11-2 | $2.43\pm 0.56$ | 2019-03-24 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
140407.17+213321.6 | 0.261 | $3.89\pm 0.15$ | 1998-10-15 | $1.70\pm 0.05$ | 2010-11-4 | $2.60\pm 0.59$ | 2017-09-21 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
161217.97+073145.4 | 0.207 | $4.92\pm 0.11$ | 2000-02-15 | $1.65\pm 0.07$ | 2010-12-16 | $3.06\pm 0.68$ | 2019-03-18 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
134206.56+050523.8 | 0.266 | $3.55\pm 0.14$ | 2000-02-15 | $1.62\pm 0.08$ | 2010-11-3 | $1.92\pm 0.25$ | 2019-04-22 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
144930.49-004746.3 | 0.253 | $2.21\pm 0.15$ | 1998-08-15 | $1.56\pm 0.05$ | 2010-12-1 | $1.85\pm 0.42$ | 2019-04-23 |  $\cdots$ |  $\cdots$ | RI | 0.0
101719.02+151620.8 | 0.245 | $<0.45$ | 1999-11-15 | $1.51\pm 0.05$ | 2010-10-15 | $<0.33$ | 2017-10-06 |  $\cdots$ |  $\cdots$ | RI | 0.0
171013.42+334402.5 | 0.208 | $3.80\pm 0.15$ | 1994-06-19 | $1.24\pm 0.04$ | 2010-12-19 | $2.25\pm 0.50$ | 2017-12-10 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
145005.13+463521.3 | 0.293 | $4.49\pm 0.13$ | 1997-03-25 | $1.19\pm 0.04$ | 2010-12-2 | $2.02\pm 0.46$ | 2019-04-14 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
162607.24+335915.3 | 0.205 | $3.11\pm 0.14$ | 1994-06-25 | $1.18\pm 0.04$ | 2010-12-18 | $1.51\pm 0.35$ | 2017-10-06 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
094215.12+090015.8 | 0.213 | $1.69\pm 0.13$ | 2000-01-15 | $1.16\pm 0.04$ | 2011-1-15 | $1.50\pm 0.34$ | 2017-10-02 |  $\cdots$ |  $\cdots$ | RI | 0.0
133636.65+420934.1 | 0.223 | $2.69\pm 0.10$ | 1995-10-23 | $0.99\pm 0.03$ | 2010-11-1 | $2.05\pm 0.20$ | 2019-03-19 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
144012.74+615633.0 | 0.275 | $3.21\pm 0.18$ | 2003-12-28 | $0.94\pm 0.03$ | 2010-11-6 | $2.17\pm 0.49$ | 2017-11-27 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
113109.24+263207.8 | 0.244 | $1.85\pm 0.13$ | 1995-11-13 | $0.89\pm 0.03$ | 2010-10-18 | $1.11\pm 0.28$ | 2019-04-12 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
110704.52+320630.0 | 0.243 | $2.79\pm 0.14$ | 1994-06-11 | $0.80\pm 0.03$ | 2010-10-17 | $1.16\pm 0.28$ | 2019-06-04 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
141116.72+194440.0 | 0.238 | $1.08\pm 0.10$ | 1999-11-15 | $0.76\pm 0.03$ | 2010-11-5 | $1.08\pm 0.26$ | 2019-04-01 |  $\cdots$ |  $\cdots$ | RI | 0.0
154307.77+193751.7 | 0.229 | $1.21\pm 0.12$ | 1999-01-15 | $0.72\pm 0.03$ | 2010-12-15 | $1.36\pm 0.33$ | 2019-03-21 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
115523.74+150756.9 | 0.287 | $1.40\pm 0.11$ | 1999-11-15 | $0.60\pm 0.02$ | 2010-10-20 | $0.98\pm 0.26$ | 2017-10-28 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
151936.14+283827.6 | 0.269 | $1.83\pm 0.12$ | 1993-04-29 | $0.58\pm 0.02$ | 2010-12-5 | $0.83\pm 0.20$ | 2017-10-03 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
114954.98+044812.8 | 0.270 | $1.36\pm 0.15$ | 2000-02-15 | $0.52\pm 0.02$ | 2010-10-19 | $0.98\pm 0.24$ | 2020-07-22 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
105607.79+134443.6 | 0.284 | $1.63\pm 0.12$ | 1999-12-15 | $0.51\pm 0.02$ | 2010-10-16 | $1.11\pm 0.27$ | 2017-12-28 |  $\cdots$ |  $\cdots$ | RI | $-0.7$
172711.80+632242.1 | 0.217 | $1.09\pm 0.13$ | 2002-08-15 | $0.73\pm 0.03$ | 2010-12-13 | $0.62\pm 0.17$ | 2017-09-11 | $0.67\pm 0.08$ | 2019-09-20 | RQ | 0.0
093509.48+481910.2 | 0.224 | $1.58\pm 0.11$ | 1997-04-10 | $0.60\pm 0.03$ | 2010-12-8 | $0.87\pm 0.19$ | 2019-04-18 | $0.53\pm 0.05$ | 2019-08-13 | RQ | $-0.7$
115753.20-031537.1 | 0.215 | $2.58\pm 0.14$ | 1998-09-16 | $0.60\pm 0.02$ | 2010-12-3 | $1.09\pm 0.21$ | 2018-01-12 | $0.64\pm 0.02$ | 2019-08-20 | RQ | $-0.7$
121832.68+352255.8 | 0.240 | $2.04\pm 0.12$ | 1994-07-05 | $0.59\pm 0.02$ | 2010-12-2 | $1.06\pm 0.20$ | 2017-12-02 | $0.44\pm 0.01$ | 2019-08-04 | RQ | $-0.7$
112941.94+512050.5 | 0.234 | $0.88\pm 0.12$ | 1997-04-29 | $0.50\pm 0.04$ | 2010-12-14 | $<0.39$ | 2019-05-10 | $0.17\pm 0.02$ | 2019-08-04 | RQ | 0.0
101000.68+300321.5 | 0.256 | $1.31\pm 0.07$ | 1993-04-13 | $0.49\pm 0.02$ | 2010-12-6 | $1.03\pm 0.20$ | 2019-04-22 | $0.50\pm 0.02$ | 2019-08-04 | RQ | $-0.7$
161940.56+254323.0 | 0.269 | $1.43\pm 0.11$ | 1995-11-22 | $0.47\pm 0.02$ | 2010-12-4 | $0.75\pm 0.18$ | 2017-11-24 | $0.41\pm 0.02$ | 2019-08-27 | RQ | $-0.7$
100438.82+151057.3 | 0.219 | $1.17\pm 0.06$ | 1999-11-15 | $0.42\pm 0.03$ | 2010-12-11 | $0.50\pm 0.16$ | 2017-10-06 | $0.24\pm 0.02$ | 2019-08-04 | RQ | 0.0
084313.41+535718.8 | 0.218 | $0.52\pm 0.15$ | 1997-05-07 | $0.41\pm 0.01$ | 2010-12-26 | $<0.45$ | 2017-09-26 | $0.35\pm 0.03$ | 2019-08-13 | RQ | 0.0
122018.43+064119.6 | 0.286 | $0.55\pm 0.08$ | 2000-02-07 | $0.39\pm 0.01$ | 2010-12-15 | $<0.49$ | 2019-05-01 | $0.32\pm 0.01$ | 2019-08-20 | RQ | 0.0
135326.12+362049.4 | 0.285 | $1.45\pm 0.14$ | 1994-07-10 | $0.39\pm 0.03$ | 2010-12-1 | $0.62\pm 0.17$ | 2017-10-14 | $0.55\pm 0.02$ | 2019-08-17 | RQ | $-0.7$
161723.67+085414.7 | 0.206 | $<0.45$ | 2000-01-15 | $0.38\pm 0.02$ | 2010-12-28 | $0.62\pm 0.16$ | 2019-03-18 | $0.39\pm 0.02$ | 2019-08-20 | RQ | 0.0
101325.43+221229.4 | 0.274 | $0.83\pm 0.08$ | 1998-09-15 | $0.36\pm 0.02$ | 2010-12-9 | $0.68\pm 0.17$ | 2019-04-18 | $0.40\pm 0.02$ | 2019-08-17 | RQ | $-0.7$