# How does the radio enhancement of broad absorption line quasars relate to
colour and accretion rate?

J. W. Petley1, L. K. Morabito1, A. L. Rankine2, G. T. Richards3, N. L.
Thomas1,4, D. M. Alexander1, V. A. Fawcett5, G. Calistro Rivera6, I.
Prandoni7, P. N. Best2, S. Kolwa8

1Centre for Extragalactic Astronomy, Department of Physics, Durham University,
Durham, DH1 3LE, UK
2Institute for Astronomy, University of Edinburgh, Royal Observatory,
Blackford Hill, Edinburgh EH9 3HJ, UK
3Department of Physics, Drexel University, 32 S. 32nd Street, Philadelphia, PA
19104, USA
4Institute for Computational Cosmology, Department of Physics, Durham
University, South Road, Durham, DH1 3LE, UK
5 School of Mathematics, Statistics and Physics, Newcastle University,
Newcastle upon Tyne, NE1 7RU, UK
6 European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei
München, Germany
7INAF-IRA, Via P. Gobetti 101, 40129 Bologna, Italy
8Physics Department, University of Johannesburg, 5 Kingsway Ave, Rossmore,
Johannesburg, 2092, South Africa
E-mail<EMAIL_ADDRESS>0000-0002-4496-0754 0000-0003-0487-6651
0000-0002-2091-1966 0000-0002-1061-1804 0000-0003-4315-4555
0000-0002-5896-6313 0000-0003-1251-532X 0000-0003-0085-6346
0000-0001-9680-7092 0000-0001-9821-4987

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The origin of radio emission in different populations of radio-quiet quasars
is relatively unknown, but recent work has uncovered various drivers of
increased radio-detection fraction. In this work, we pull together three known
factors: optical colour ($g-i$), C iv Distance (a proxy for $L/L_{Edd}$) and
whether or not the quasar contains broad absorption lines (BALQSOs) which
signify an outflow. We use SDSS DR14 spectra along with the LOFAR Two Metre
Sky Survey Data Release 2 and find that each of these properties have an
independent effect. BALQSOs are marginally more likely to be radio-detected
than non-BALQSOs at similar colours and $L/L_{Edd}$, moderate reddening
significantly increases the radio-detection fraction and the radio-detection
increases with $L/L_{Edd}$ above a threshold for all populations. We test a
widely used simple model for radio wind shock emission and calculate energetic
efficiencies that would be required to reproduce the observed radio
properties. We discuss interpretations of these results concerning radio-quiet
quasars more generally. We suggest that radio emission in BALQSOs is connected
to a different physical origin than the general quasar population since they
show different radio properties independent of colour and C iv distance.

###### keywords:

quasars: general – galaxies: evolution – radio continuum: galaxies

††pubyear: 2023††pagerange: How does the radio enhancement of broad absorption
line quasars relate to colour and accretion rate?–References

##  1 Introduction

Black holes are now key to our understanding of the complex evolution of
galaxies, despite being fundamentally simple to characterise (e.g. mass and
spin - Kerr, 1963). Nearly all galaxies contain a super-massive black hole
(SMBHs) and, during rapid growth, black hole systems can stimulate
electromagnetic radiation in their surroundings. These black holes are
considered to be "active" and referred to as Active Galactic Nuclei (AGN).
Combined with the knowledge that SMBHs grow with their galaxies (see Kormendy
et al., 2013), AGN have become objects of great interest in many different
areas of astronomy today.

Quasars (also known as QSOs) are the brightest of all AGN and are some of the
most luminous objects at optical wavelengths in the observable universe
(Schmidt et al., 1968). The massive amount of luminosity ($>10^{44}$ erg/s)
that quasars radiate could impact the future evolution of their host galaxies
since, at least for a time when we observe them, they have a much greater
energetic output than all the stars in their galaxy. However, it is often
difficult to predict what will be observed across the full spectral energy
distribution of a quasar even if some wavelength regions or physical
properties (eg. accretion rate and black hole mass) are well understood or
measured. Since different wavelength ranges offer information about different
physical scales and processes, we cannot build a full picture of quasar
behaviour without appreciating the longest, as well as the shortest,
wavelengths.

Radio emission at low frequencies ($\lesssim 10$ GHz) in quasars is largely
dominated by the synchrotron radiation process. Emission is released through
the acceleration of electrons moving at relativistic speeds through a magnetic
field (Condon et al., 1992). Radio emission is largely unaffected by sources
of obscuration which significantly modulate what is observed at shorter
wavelengths. For example, we avoid the effects of dust that impact optical and
ultra-violet (UV) emission. Radio observations could therefore play a key role
in understanding energetic interactions between a black hole and its galaxy.
The most widely recognisable sources of synchrotron emission are famous radio-
jet type galaxies with complex jet and filament type structures which extend
well beyond the size of the host galaxy (Fanaroff & Riley, 1974). The
mechanism which extracts energy into these jets from accretion around the
black hole is thought to be the Blandford-Znajek process (Blandford & Znajek,
1977). The formation of such jets likely has a significant connection with the
spin of a black hole (Blandford, 1990; Wilson & Colbert, 1995), a property
currently not measurable at significant redshift. These jets are increasingly
incorporated into both single galaxy or cluster simulations (Huško et al.,
2022) and cosmological simulations with AGN feedback (Davé et al., 2019;
Thomas et al., 2021).

When studying the radio population, observers have typically made a
distinction into two types of source based on the apparent bi-modality in the
radio-to-optical luminosity ratio distribution. Radio-loud sources have higher
radio to optical luminosity ratios than radio-quiet sources (Kellermann et
al., 1989). Although this can be a useful distinction, often splitting into
these two groups can cause confusion amongst astronomers as it has sometimes
been implied that radio-loud sources are jets and that radio-quiet sources are
not. To be clear, many radio-quiet jetted AGN have been observed (Kukula et
al., 1998; Leipski et al., 2006; Jarvis et al., 2019; Macfarlane et al., 2021;
Girdhar et al., 2022) i.e. radio-quiet $\neq$ no jet. Consequently, while we
are confident that the vast majority of radio-loud sources have jets, we lack
the required information to make the contrary statement for radio-quiet
sources.

The origin of radio emission in a given radio-quiet system is therefore a more
complicated matter given there are essentially four emission mechanisms with
the potential to be detected by modern radio surveys. These are: jets, star
formation, disk winds and corona (see Panessa et al., 2019; Kimball et al.,
2011). Coronal emission is unlikely to be the dominant radio emission
mechanism at the low frequencies which we study in this paper (Raginski &
Laor, 2016; Behar et al., 2018; Baldi et al., 2022). Coronal emission is
highly compact, optically thick and has a flat spectrum which is not observed
for the populations we study. Therefore, we do not include a detailed
discussion of this emission mechanism. Distinguishing between the remaining
possible components with current large radio surveys is not a simple task
since the vast majority of sources are unresolved by most large-scale survey
instruments, which means we cannot determine the source of the radio emission
directly without higher resolution information (Morabito et al., 2022).

Radio emission from jets in radio-quiet and radio-loud sources is likely very
similar but jets can be frustrated in size and lifetime, by high-density
environments of gas and/or dust (White et al., 2015; Sadler, 2016; Calistro
Rivera et al., 2023), or simply lower power (Hardcastle, 2018; Hardcastle et
al., 2019). Star formation rate correlations with radio luminosity have now
been calibrated at several frequencies, including low frequency (Calistro
Rivera et al., 2017; Gürkan et al., 2018), based on the clear correlation
between infrared thermal emission and non-thermal radio-emission (Helou et
al., 1985; Bell, 2003). Although there is a scatter and a strong dependence on
the stellar mass of a galaxy (Delvecchio et al., 2021), the fact that this
correlation exists means that radio is regularly used as a measure for star
formation in non-AGN sources. Radio emission from disk winds is probably the
most poorly understood of the potential mechanisms. Quasars are known to
possess various types or phases of outflows (e.g. Broad Absorption Line
Quasars - Weymann et al. 1991, [O iii] outflows - Weedman et al. 1970, Ultra-
Fast Outflows (UFOs) - Pounds et al. 2003) and that these outflow phases can
also couple to each other (eg. Feruglio et al., 2015; Girdhar et al., 2022).
These high-velocity outflows have the ability to generate shock fronts which
could emit synchrotron radiation although currently, only a few simple models
of these shocks exist with limited prediction power (Ostriker et al., 2010;
Faucher-Giguère et al., 2012; Nims et al., 2015).

The presence of radio emission has been found to connect to several other
quasar properties. The investigation of the interaction between these
properties is the focus of this work. A brief introduction to each of these
follows.

###  1.1 Optical Reddening

The distribution of rest frame optical colours of quasars is resolved in the
Sloan Digital Sky Survey (SDSS) photometry and shows a normal distribution
with a longer tail of quasars with excess red colours (Richards et al., 2003).
These red colours in this tail of the distribution are most likely caused by
the effect of dust (Webster et al., 1995; Glikman et al., 2007; Krawczyk et
al., 2015; Calistro Rivera et al., 2021; Fawcett et al., 2022). Quasars that
show excess red colours are defined in various ways, usually by their
particular percentile of the colour distribution, as red quasars. The link
between radio emission and red quasars was firmly established by Klindt et al.
(2019) who found that red quasars were $\sim 3\times$ more likely to be radio
detected than blue or control quasars using the Faint Images of the Radio Sky
at Twenty centimetres (FIRST; Becker et al., 1995).

This result has prompted further research to expand to other wavelengths and
look at different morphologies and powers. Klindt et al. (2019) and Fawcett et
al. (2020) found that the radio enhancement is likely due to emission on
compact scales and from the radio-quiet or and radio-intermediate population.
Rosario et al. (2020) used the LOFAR Two Metre Sky Survey Data Release 1
(LoTSS DR1; Shimwell et al., 2019) to show that the red quasar radio
enhancement exists at low frequencies and at a similar level to Klindt et al.
(2019). High-resolution e-MERLIN data on a small sub-sample of red and blue
quasars revealed a statistically significant difference in the incidence of
kpc scale emission between the two samples with the red sample having a
greater fraction of extended sources at scales $\leq 2$ kpc (Rosario et al.,
2021).

The interpretation of these results is that red quasars are inconsistent with
a simple orientation model for the dusty torus surrounding the black hole but
are broadly consistent as a transition phase where red quasars transition to
blue quasars. Some propose that this may fit into larger evolution models such
as the one proposed in Hopkins et al. (2008). Furthermore, through modelling
of the radio-UV spectral energy distribution and optical spectra of quasars,
Calistro Rivera et al. (2021) found that the reddening may originate from
dusty polar winds. The increased radio emission could then be due to shocks
from AGN winds, or due to shocks from the interactions between compact AGN
jets and dusty gas-dense regions (Fawcett et al., 2023; Calistro Rivera et
al., 2023), or alternatively increased star formation during this earlier
stage of evolution, although the latter has been excluded based on
multiwavelength SED fitting by Calistro Rivera et al. (2023) and the high-
resolution study of Rosario et al. (2021).

###  1.2 Broad Absorption Line Quasars

Around 10-20% of quasars selected by optical magnitude show broad absorption
features bluewards of the C iv emission line, although the intrinsic fraction
of quasars with these features is expected to be higher (up to 40%, e.g Dai et
al., 2007; Allen et al., 2010; Dai et al., 2012). These quasars are known as
Broad Absorption Line Quasars (BALQSOs) and have often been characterised
using the Balnicity Index (BI) measure of Weymann et al. (1991). BI is
calculated as an integral of a region bluewards of the C iv emission line when
absorption is more than 10% of the continuum level. Radio studies of BALQSOs
have shown that they are more likely to be radio-quiet than non-BALQSOs
(Stocke et al., 1992; Becker et al., 2000) and, similar to the red quasars,
they are significantly more likely to be radio-detected (Urrutia et al., 2009;
Morabito et al., 2019; Petley et al., 2022). Petley et al. (2022) found that
radio-detected BALQSOs have different absorption profiles compared to non-
radio-detected BALQSOs implying an intrinsic connection between the wind and
the radio emission, with radio-emission coming from the wind itself (wind
shocks) as the most likely explanation for this connection.

The true fraction of BALQSOs in the quasar population is hard to ascertain. In
a purely geometric understanding (e.g. Weymann et al., 1991; Ghosh & Punsly,
2007), the observed BALQSO fraction is equal to the mean fractional solid
angle that the BAL wind subtends of the quasar. However, BAL troughs are known
to appear and disappear (e.g. Ak et al., 2012; Mishra et al., 2021) and (as
noted in Gregg et al., 2006) if they are predominantly an evolutionary feature
then their lifetime is likely on the order of $\sim$ 10 Myr based on a $\sim
10\%$ fraction of quasars accreting for $\sim 10^{8}$Yrs (Hopkins et al.,
2005). If indeed the lifetime of a BAL wind is shorter than the lifetime of
the average quasar, the BAL wind must have a much larger covering angle than
simply the observed fraction in order to maintain that fraction, or
alternatively, many quasars go through several BAL phases. However, it is not
clear whether this BAL lifetime is a feature of the wind turning on and off or
a feature of a particular geometry such as a rotating clumpy wind. Whatever
the scenario, their radio-detection enhancement is potentially an indicator
that they can interact strongly with their environment even in a relatively
short time. In addition, many quasars identified as non-BALQSOs may in fact be
hosting BAL winds which are not currently in our line of sight, creating some
level of contamination within the non-BALQSO population.

###  1.3 C iv Distance

The C iv emission line ($\lambda~{}1549$) is readily observable in the UV
spectra of most quasars. The anti-correlation between the C iv equivalent
width (EW) and UV continuum luminosity, known as the Baldwin Effect (Baldwin,
1977), was evidence that this line could probe some of the accretion
properties of the SMBH. Subsequently, the informational content of this line
has been explored further and specifically the blueshift of the line was found
to be a feature of importance (Gaskell, 1982; Wilkes & J., 1984; Richards et
al., 2002; Sulentic et al., 2003, 2007). Richards et al. (2011) investigated
radio-quiet and radio-loud quasars in a 2D space of C iv EW and blueshift and
found that the distributions observed could best be understood through a
"disk" vs "wind" model with disk dominated systems having high C iv EW and low
blueshifts and wind dominated systems having low C iv EW and high blueshifts.

Recent work on this 2D C iv space has found further evidence of its diagnostic
power. Rankine et al. (2020) found that BALQSOs comprise a higher fraction of
moderate EW, high blueshift sources but crucially that they can still be found
in all regions of the space. This suggests that BALQSOs are simply QSOs with a
probability of observation based on a particular line of sight or at a
particular time such that a BAL wind is observed. This probability, and also
the average absorption profile of the BALQSOs, changes across the C iv space.
Richards et al. (2021) converted the position in 2D space into a single C iv
distance value (low C iv distance: high EW and low blueshift; high C iv
distance: low EW and high blueshift) and found that the Very Large Array (VLA)
radio detection fraction of quasars varied non-linearly with this parameter,
hinting at multiple radio emission mechanisms at play, a result also suggested
in Rankine et al. (2021). Physical drivers of the changing C iv properties
have been suggested. For example, a link between accretion rate and C iv
blueshift was found in Wang et al. (2011) and Sulentic et al. (2017). Most
recently Temple et al. (2023) connected this space to Spectral Energy
Distribution (SED) models of accretion and showed that changes in the
properties of quasars in this space could be connected to accretion rate and a
likely change in the accretion geometry around an Eddington Ratio of
$\lambda_{\rm Edd}\approx 0.2$, a transition suggested in Giustini & Proga
(2019). We therefore use C iv distance in this work as a proxy for the
accretion rate in our quasars as it is measured for all of our sources and
does not have any additional conversions or assumptions.

This work aims to explore each of these quasar properties - C iv distance,
optical colour and BAL winds - in combination and attempt to understand their
intrinsic connection to radio emission. Each of these properties show overall
changes in detection fraction of a similar magnitude and previous work has not
incorporated all of them simultaneously. With an improved picture of the
connection between these properties, we can re-think the underlying physical
scenarios that govern radio emission in quasars.

##  2 Data and Methods

To create our sample of quasars we begin with the SDSS DR14 quasar catalogue
of Pâris et al. (2018). This catalogue summarises the properties of 526,356
quasars including redshifts and whether a BAL wind is present, although this
is the first of the SDSS releases not to visually inspect all spectra for BAL
signatures. To improve the quality of the spectral data and also extract
several important parameters for this study we use spectral reconstructions of
SDSS DR14 quasars created through mean-field independent component analysis
and described by Rankine et al. (2020). The process improves the redshift
measurements and redefines parameters such as the BI in comparison to the SDSS
release. We therefore use these values to define our BALQSO sample.

Reconstructed spectra are used to obtain the C iv EWs and blueshifts and to
parameterise the C iv EW-blueshift space (hereafter "C iv space") with a
single value, the C iv distance. The method for this process is described in
Rivera et al. (2020) and also improved in Rivera et al. (2022). Strictly, we
use the parallel C iv distance (C iv $\parallel$) described within Rivera et
al. (2022) but simply refer to it as the C iv distance. In summary, the
distance is formed through a piece-wise polynomial fitting of all quasars in
the C iv space which is then scaled using a MinMaxScaler algorithm to place
all values between 0 and 1 with an equal weighting to both axes. Code to
calculate C iv distance is available from McCaffrey & Richards (2021).

We use a slightly different technique to characterise red and blue quasars in
our sample compared to recent radio studies of red and blue quasars such as
Klindt et al. (2019); Fawcett et al. (2020); Rosario et al. (2020). It is not
only the most red sources that show radio enhancement and we aim to study the
overall effect of changing colour. We attempt to capture the variation in
colour of quasars independent of redshift and keep all of the quasars in our
working sample. By obtaining the redshift-independent optical colour
distribution, we can then assign some quasars as being excess red due to some
extra component, most likely dust and the rest as normal variation captured by
a Gaussian. This is more similar to the reddening studies of Richards et al.
(2003) and Glikman et al. (2022).

To accurately determine the colours of our quasars using SDSS photometry, we
restrict our sample to $1.7<z<2.5$. The lower limit of $z=1.7$ is imposed by
the observable range of the C iv emission and absorption region in all of the
SDSS quasars. The upper limit of $z=2.5$ is imposed by the contamination of
the Lyman break in the SDSS $g$ band photometry at higher redshifts.

We split the sample into 20 equally spaced redshift bins and calculate the
galaxy extinction corrected $g-i$ band colour for each quasar in that bin. We
then shift the entire distribution within that bin so that the median is at 0.
We do this for every bin so that in the end we have a stacked distribution of
all the quasars with a median of 0. We then fit two distributions to the data
using the `scipy` Python package. First, a normal distribution with a $\mu=0$
to capture the majority of the colour variation and then another distribution
to capture the excess red quasars. We found that a log-normal distribution
worked best to capture this tail (see Figure 1).

Figure 1: The probability density of redshift corrected quasar optical colour.
We define different optical colours by splitting the quasars into redshift
bins and then shifting the $g-i$ colour distribution in that bin to a median
of zero. We then fit the stacked distribution with a normal (blue) and
lognormal curve (pink). Excess red quasars are defined in the region beyond
the peak of the lognormal, blue quasars are defined with a shifted colour
below zero and red quasars are in between.

We define all quasars with their colour bluer than the median within their bin
as blue quasars (shown in blue in all figures), quasars with their colour more
red than the peak of the log-normal distribution as excess red quasars (shown
in red in all figures) and those in between these two points as "red" quasars
(shown in black in all figures).

We aim to observe how C iv distance relates to an independent measure of the
AGN luminosity, the 6 micron luminosity ($L_{6\mu m}$). Therefore we require
that our sample has detections in the first three bands of the Wide-field
Infrared Survey Explorer (WISE). We perform a log-linear interpolation between
the bands to estimate a rest-frame 6 micron luminosity which should capture
the re-processed disk emission and be free from other extinction.

To understand the radio properties of the quasars, we use the LOFAR Two Metre
Sky Survey (LoTSS) Data Release 2 described in Shimwell et al. (2022b). This
is a radio survey of the Northern sky with over 4 million radio sources
detected with a resolution of 6 arcseconds with a frequency range centred at
144MHz (wavelength of two metres). Specifically, we use the latest catalogue
with optical counterparts identified using a combination of likelihood ratio
matching (Kondapally et al., 2021), machine learning (Alegre et al., 2022) and
citizen scientists (Hardcastle et al., 2023). LoTSS operates in a unique
sensitivity and frequency range and is the best-suited survey for
understanding large radio-quiet populations as it is around an order of
magnitude deeper than FIRST (Becker et al., 1995), an example of an earlier
widely used radio survey.

We restrict our quasar spectra sample to the LoTSS DR2 region and cross-match
with a radius of 2 arcseconds to the LoTSS DR2 optical ID source catalogue.
The overall population split for radio detection and colour is shown in Table
1.

| Radio Detected | Non-radio detected |
---|---|---|---
BALQSOs | 1463 | 3935 |
Non-BALQSOs | 6565 | 31175 |
| Blue | Red | Excess Red
BALQSOs | 903 | 2389 | 2106
Non-BALQSOs | 16959 | 15325 | 5456
Table 1: We present the population numbers for BALQSOs and non-BALQSOs with
respect to their radio detection and colour classification.

##  3 Results

###  3.1 Populations in C iv Space

To understand the behaviour of different populations on their own with respect
to C iv emission, we investigate the distribution of different populations of
quasars in the C iv EW and blueshift space.

Figure 2: Density plots for different populations in the C iv EW and blueshift
space. The white tracks indicate the value of the C iv distance at that point.
A negative value for C iv blueshift indicates redshift. In each plot, we
require a minimum of 10 sources in each bin. Upper left: The median value of
$g-i$ colour in each bin. The distribution is relatively uniform apart from
the most extreme red sources having low C iv blueshift and EW. Upper right:
The fraction of BALQSOs in each bin. This distribution peaks at moderate C iv
EW and higher blueshifts as previously shown in Rankine et al. (2020). Lower
left: The LoTSS radio-detection fraction (RDF) in each bin. This fraction
increases with C iv distance. Lower right: The median six-micron luminosity in
each bin. This is a measure of the quasar luminosity which increases with C iv
distance.

We find that excess red quasars are mostly uniformly spread around the C iv
space (upper left - Figure 2) apart from the most extreme red sources being at
low C iv blueshift and C iv EW. This suggests that the C iv wind and the
origin of the most red colours are not strongly coupled.

BALQSOs are preferentially found towards higher blueshifts and lower
equivalent widths (upper right - Figure 2), although the densest BALQSO region
in C iv space is at a moderate value for both. This result is not unexpected
as the distribution of BALQSOs in C iv space was studied extensively in
Rankine et al. (2020). As well as the BALQSO fraction they also look at the
strength and velocity of the BALQSO winds and find that both increase at
higher C iv distance. Even though the BAL fraction change may not be large
across the whole space, the average properties of the BAL winds do change
quite significantly. There is also a tentative increase in BAL prevalence at
low EW and blueshift, potentially connecting to the more red population.

The radio-detection fraction in C iv space was also studied in Rankine et al.
(2021), but with the smaller LoTSS DR1. We find the same result here with a
much larger sample (lower left - Figure 2). Radio-detection fraction increases
with C iv distance.

We investigate an alternative measure of the accretion power of the black
hole, the $6\mu$m luminosity (lower right - Figure 2). This should probe the
warm dust heated by the quasar and provide a measure of the overall AGN
luminosity, $L_{\mathrm{AGN}}$ (Richards et al., 2006; Gallagher et al., 2007;
Klindt et al., 2019; Calistro Rivera et al., 2021). We find that it correlates
with the C iv distance quite well. If the black hole mass is constant along
the space then it would track the accretion rate. In general, we favour the
use of C iv distance as a measure of the accretion state as the line is driven
closer to the black hole and is less contaminated by other infrared radiation.

###  3.2 Radio Properties and C iv Distance

Quasar Pop. | 0<C iv Dist.<0.2 | 0.2<C iv Dist.<0.4 | 0.4<C iv Dist.<0.5
---|---|---|---
B | R | ER | B | R | ER | B | R | ER
BALQSOs | 26 / 6 | 11 / 4 | 7 / 6 | 99 / 23 | 210 / 72 | 105 / 73 | 149 / 16 | 346 / 81 | 227 / 79
Non-BALQSOs | 242 / 45 | 132 / 30 | 39 / 20 | 3028 / 397 | 2166 / 470 | 538 / 236 | 3423 / 352 | 3605 / 713 | 880 / 317
| 0.5<C iv Dist.<0.6 | 0.6<C iv Dist.<0.8 | 0.8<C iv Dist.<1
B | R | ER | B | R | ER | B | R | ER
BALQSOs | 272 / 35 | 835 / 201 | 536 / 228 | 190 / 64 | 581 / 250 | 417 / 268 | 13 / 9 | 45 / 55 | 57 / 80
Non-BALQSOs | 4612 / 475 | 5183 / 1078 | 1156 / 486 | 3363 / 662 | 4127 / 1342 | 881 / 539 | 235 / 115 | 444 / 285 | 157 / 129
Table 2: We present the populations in each C iv distance bin for BALQSOs and
non-BALQSOs. Radio non-detections are in normal font, radio detections are in
bold and colour classifications are: B - blue, R - red, ER - excess red.

We hypothesise that different processes dominate radio emission at different
ends of the C iv distance space with low C iv distance objects having a
greater jet component and high C iv distance having a greater wind component.
We therefore split into C iv distance bins and measure the radio-detection
fraction for different populations. The bins were selected to ensure a similar
number in each bin in the moderate C iv distance range where most sources
reside and to have reasonable statistics at the low and high C iv distance
end. The populations within our chosen bins are listed in Table 2 along with
the bin definitions.

Figure 3: Radio-detection fraction for six C iv distance bins split into
populations based on colour and whether a BAL wind is present. The spread
around each C iv distance value is just to aid the eye. The colour represents
the colour of the quasar: blue for blue, black for red and red for excess red
quasars. Non-BALQSOs are represented by diamonds and BALQSOs are represented
by crosses. In the lower panel, the ratio of radio-detection fraction for BALs
and non-BALs is displayed as a clearer quantification of the BAL effect in
each bin.

In Figure 3 we show these radio-detection fractions. The error bars in these
figures indicate the standard deviation within each bin. We find that all 3 of
the parameters, C iv distance, colour and the presence of a BAL wind, have
their own effects as expected but we also find different behaviour at each end
of the C iv emission space. Radio detection fraction increases from blue to
excess red quasars. The change in radio-detection fraction from blue to red is
of a similar magnitude, around 5%, to that of the change from red to excess
red quasars. This is consistent with the recent work of Fawcett et al. (2023)
which analysed the connection between dust extinction and radio emission using
quasars identified with the Dark Energy Spectroscopic Instrument (DESI: DESI
Collaboration et al., 2016) and LoTSS, finding a strong positive correlation
between the two properties.

Overall the radio detection fractions decrease with C iv distance to 0.5 and
then increase with increasing C iv distances, with the largest change, both in
overall percentage and percentage per unit C iv distance (the gradient),
coming between the two highest bins. This behaviour is similar for all
populations, suggesting that different accretion properties are not the
driving force behind the radio differences between BALQSOs and non-BALQSOs or
behind reddening in quasars.

Figure 4: In all plots non-BALQSOs are represented with diamonds and BALQSOs
are represented with crosses. Left: The radio loudness as a function of C iv
distance shows a decrease for all populations. We suggest that the trend
observed is largely due to the changing SED of the quasar as the accretion
rate increases. The classical radio-loud threshold would be $\log(R)>2.5$.
Centre: The median radio luminosity as a function of C iv distance, assuming a
spectral index of $\alpha=-0.7$, of different quasar populations in C iv
distance bins. We find that radio luminosity remains constant at moderate C iv
distance which accounts for the majority of most quasars. We only see a
definitive increase in the highest bin at the highest accretion rates. Right:
$g$-band optical luminosity as a function of C iv distance for radio-detected
quasars. The optical luminosity is increasing, driving down the radio-loudness
suggesting that radio-loudness is not a useful measure in determining radio-
emission mechanisms without controlling for accretion rate.

In Figure 4 we also look at the median radio luminosity, median $g$-band
optical luminosity and the radio loudness parameter (the ratio of radio to
optical luminosity) as a function of C iv distance for sources that are radio
detected in the same bins as Figure 3 and for the same populations. We find
again that the largest changes for the whole population of quasars occur at
the low and high C iv distance extremes although it should be noted that the
uncertainty is much more considerable at low C iv distance.

Firstly, it should be noted that the overall range in median radio luminosity
for the whole sample is less than one dex. The radio luminosity results
generally indicate that, when detected, BALQSOs have similar radio
luminosities compared to non-BALQSOs despite their higher radio detection
fractions. For non-BALQSOs, the increase in radio luminosity from blue to red
and from red to excess red quasars is similar and only $\sim 0.05$ dex.

The radio loudness parameter is typically used to identify excess radio
emission in sources relative to their optical emission. In quasars, the
optical luminosity is thought to be a good measure of the power of the quasar
since it is assumed we are obtaining a largely unobscured view of the
accretion disk. In Figure 4 we use the $g$-band luminosity to calculate the
radio-optical radio-loudness. The classical divide from radio-quiet to radio-
loud populations would occur at $\log(R)>2.5$ at the LoTSS 144MHz frequency.
Clearly, our sample is dominated by radio-quiet sources.

We observe a decrease in the radio loudness parameter as C iv distance
increases. This was similarly observed when only looking at C iv blueshift in
Rankine et al. (2021). However, we show that this change in radio loudness is
largely driven by an increase in the $g$-band optical luminosity. The radio
luminosity for all populations across C iv distance changes by less than 1
dex. Therefore it is the increase in optical luminosity with C iv distance
that is driving this behaviour. This shows some of the limits of radio-
loudness as an idealistic measure of "jettedness" as two sources with similar
radio power, accretion rate and radio emission mechanism can have different
radio-loudness measures based on different optical continuum spectral slopes
(Balokovic et al., 2012).

##  4 Discussion

We consider the following different interpretations of these results with
regard to the main potential radio emission mechanisms in radio-quiet quasars:
star formation, jets and wind shocks. We provide a brief introduction to each
mechanism here but for a detailed review see Kimball et al. (2011); Panessa et
al. (2019).

Synchrotron emission from star-forming regions occurs due to the presence of
free electrons and magnetic fields in supernova remnants. The radio flux from
star-forming galaxies has been found to correlate extremely well with the far
infrared emission, a presumed indicator of the star formation rate (Sopp et
al., 1991; Appleton et al., 2004; Sargent et al., 2010; Calistro Rivera et
al., 2017; Smith et al., 2021). This correlation has been shown to hold for
low radio luminosity quasars to moderate redshifts (Bonzini et al., 2015;
Gürkan et al., 2018). However, many studies find radio-quiet AGN with a
compact core that lie on this correlation (Maini et al., 2016; Herrera Ruiz et
al., 2016; McCaffrey et al., 2022), suggesting an AGN origin for at least some
of the radio-quiet emission. A multi-resolution radio study of sources can
allow for a better characterisation of star formation and AGN components
(Morabito et al., 2022).

Radio jets dominate the radio-loud population, but whether their contribution
extends to many of the radio-quiet sources is a topic of much research. It is
possible to model the radio emission and attempt to split contributions from
star formation and AGN components (eg. Mancuso et al., 2017). Specifically for
LOFAR, Macfarlane et al. (2021) fit a two-component, star formation and jets,
model to the radio-quiet LoTSS population. They find that jets could
contribute the majority of radio emission in 10-20% of all quasars across
redshift and optical luminosity. Yue et al. (submitted) extend this analysis
through a Bayesian framework and apply their models to quasar reddening,
showing that the radio enhancement of reddened quasars is due to the AGN
component and not star formation. This is also shown by Fawcett et al. (2020)
and Rosario et al. (2020) for radio-faint quasars. High-resolution studies of
radio-quiet quasars have uncovered systems with compact core regions implying
the presence of small-scale jets (Kukula et al., 1998; Leipski et al., 2006;
Herrera Ruiz et al., 2016; Jarvis et al., 2019).

AGN outflows have been observed at many different scales and in different
phases. When a wind interacts with the intragalactic medium, if it has
sufficient velocity it will generate a shock. These shocks can generate
relativistic electrons and corresponding synchrotron emission. If the wind is
generated from the accretion disk, then we expect an anti-correlation between
the jet and wind prevalence since jets are typically formed at lower accretion
rates when the disk truncates at a greater distance from the black hole and
can generate larger magnetic fields. This is indeed observed in Mehdipour &
Costantini (2019) who found an inverse correlation between radio loudness and
the column density of the ionising wind in radio-loud AGN.

With this wind-jet inverse correlation in mind, the hypothesis for radio
emission mechanisms across C iv distance space is that jets dominate the radio
emission at low C iv distance (low Eddington ratio) and that winds contribute
more and more as the C iv distance increases (higher Eddington ratios).

###  4.1 Does radio emission in radio-quiet quasars connect to accretion?

From Figure 3 we observe all populations to increase in radio-detection
fraction with increasing C iv distance above a C iv distance of 0.5 and
decreasing with increasing C iv distance below that point. Therefore, it is
clear that in some way radio emission across the whole quasar radio-quiet
population responds to the accretion properties of the quasar. Even though the
changes may not be consistent for each group at all points in C iv distance,
the fact that they all do couple to accretion is illuminating. For example, if
one is to assume that star formation is the dominant factor in the radio-
emission of radio-quiet quasars, then an increase in radio-detection fraction
for quasars with potentially high accretion rates implies that the same gas is
fuelling both star formation and accretion or that a significant positive
feedback effect can occur on the timescale at which a quasar exists with a
high C iv distance.

In general, the radio luminosity changes are minimal across moderate C iv
distance from 0.3-0.6. This is the region in which the system is neither jet
nor wind-dominated. Richards et al. (2021) also found this was the region of
lowest radio detection fraction for VLA quasars. Since we are tracing the
behaviour of radio detection fraction with a proxy for accretion rate, could
this be the area where AGN contributions are minimal and the radio emission is
dominated by star formation? Under that assumption, we would conclude that
BALQSOs and red/excess red quasars in this range have higher star formation
rates (SFRs) than blue non-BALQSOs. The SFR-radio luminosity correlation for
LOFAR is studied in Smith et al. (2021) and is roughly linear in the radio
luminosity region our sample covers. The fact that when they are radio-
detected, BALQSOs and red/excess red quasars do not have significantly
different radio luminosities to the rest of the population at moderate C iv
distances, Figure 4, suggests that SFR alone cannot explain the increase for
both BALQSOs and red/excess red quasars.

Increased SFRs for red quasars and BALQSOs is a key prediction of the
hypothesis that both these populations are linked to earlier stages in the
evolution of galaxies than typical quasars if the timescale of the red phase
is long enough to observe a decrease in SFR. However, several studies have
tried to test this connection and have not found any link between red quasars
and enhanced SFRs (Fawcett et al., 2020; Calistro Rivera et al., 2021; Andonie
et al., 2022). It could also be that star formation contributions are similar
to AGN in this region (moderate C iv distance), emphasising differences in the
connection between black holes and radio emission between the various
populations. We hope to explore this further in the future through extensive
SED fitting of sources in the LoTSS Deep-Fields (Tasse et al., 2020; Best et
al., 2023).

It has been noted in previous work that the radio-detection fraction could
have a significant correlation with the luminosity of the AGN itself. To
investigate the effect that this has, previous red quasar studies have used a
redshift and six-micron luminosity-matched sample to study the radio
properties independently of the AGN luminosity (Klindt et al., 2019; Fawcett
et al., 2020). When performing any luminosity matching we have to be cautious
as we are explicitly looking to test correlations with the C iv distance which
we are claiming is a proxy for the accretion rate and will therefore correlate
strongly with the six-micron luminosity. Indeed it is clear from Figure 2 that
this correlation does exist and trying to create a matched sample across six
different populations (BALQSOs vs non-BALQSO $\times$ three colour bins) would
remove a lot of sources and some of these trends we are interested in seeing.

We checked the luminosity and redshift distributions within each C iv distance
bin of Figure 3 and did indeed find some differences between populations. We
verify our key result by performing a 2d-rejection sampling method to match
all populations to the redshift-six-micron distribution of the red quasars. We
then repeat our previous analyses.

Figure 5: The radio detection fraction with C iv distance for samples matched
in redshift and six-micron luminosity space. We use four bins of 0-0.25,
0.25-0.5, 0.5-0.75 and 0.75-1 in C iv distance. The radio enhancement of red
quasars is still apparent and also the moderate enhancement of BALQSOs
remains. The enhancement of low C iv distance samples appears to be somewhat
diminished. Below is a panel displaying the ratio of radio detection fraction
between BALs and non-BALs.

The results from the matched sample are presented in Figure 5 which is an
equivalent plot to Figure 3 but with fewer bins to maintain similar
uncertainties. The same key features are present with this matching. The
increase in radio-detection fraction from blue to excess red quasars and
moderate enhancement of BALQSOs remains, demonstrating the robustness of our
results to luminosity effects.

###  4.2 Are BALQSOs a distinct class of quasars?

Rankine et al. (2020) studied in detail the 2D C iv space properties of
BALQSOs and non-BALQSOs and concluded that, since you can find a non-BALQSO
with the same C iv position and SED hardness as any BALQSO, they must both
originate from the same parent sample. Temple et al. (2021) found that the hot
dust emission is also similar between BALQSOs and non-BALQSOs at the same C iv
position. This supports a geometric interpretation for the BALQSO phenomena at
a given position in C iv space. However, the recent radio studies of BALQSOs
suggested that the more we explore the properties of BALQSOs at longer
wavelengths the more they appear to differentiate themselves from non-BALQSOs.
Morabito et al. (2019) highlighted the increasing radio-detection fraction
with BI, well over 50% of quasars with the strongest winds being detected with
LOFAR. In Petley et al. (2022) we showed further that this radio emission
connects to the absorption profiles of the BALQSO and that this radio emission
is extremely difficult to explain with an angular interpretation of BALQSOs
with a standard equatorial wind. How then can we reconcile this apparent
contrast between the UV and radio nature of BALQSOs?

In this work, we show that much of the BALQSO radio enhancement found in
previous papers can be explained by their connection to optical colour. The
enhancement is still present in the radio-detection fraction of BALQSOs
compared to non-BALQSOs of the same colour classification and contributes
around 5-10% in each bin. The effect is more easily seen as a ratio between
BALQSO and non-BALQSO detection fraction in Figure 3. The median ratio across
the bins is 1.29, 1.46 and 1.17 for blue, red and excess red quasars
respectively. The ratios are a much smaller enhancement than that observed
when not accounting for optical colour such as the detection fractions
presented in Morabito et al. (2019) and Petley et al. (2022). The difference
in these studies opens many further questions about the connection between
these two samples as in the reddest colour bins the BALQSO fraction can be
well over 25%. This feature has been observed in other samples such as in
Vejlgaard et al. (2024). They create a red quasar sample that would not be
selected in SDSS and find that it does not have a higher radio-detection
fraction than a comparative SDSS blue sample using FIRST. The red sample had a
much higher BAL fraction than in SDSS and they suggest this may be the reason
that they do not observe a radio difference. To test this we looked at the
BALQSO and non-BALQSO radio-detection fraction relationship with colour alone.

Figure 6: Radio-detection fraction against corrected colour for BALQSOs
(orange) and non-BALQSOs (green). Each bin was defined by having an equal
number of BALQSOs and the points are separated slightly horizontally to aid
the eye. The BALQSO contribution to the radio-detection fraction is most
prominent for bluer colours.

In Figure 6 one can see that the BALQSO radio-detection contribution within
SDSS occurs primarily within the normal distribution of quasar colours and not
in the most excess red systems. This figure is somewhat similar to those found
in Fawcett et al. (2023) and Calistro Rivera et al. (2023) but with a focus on
the BALQSO effect as colour increases. We find a similar behaviour of
increasing detection-fraction with colour for both populations. We, therefore,
conclude that the BALQSOs fraction is unlikely to be the origin of the
difference in radio emission for red and blue populations of quasars as in
Vejlgaard et al. (2024). The differences could reside in the use of LoTSS
which is deeper than FIRST and also the selection of the two samples. There
are some non-optically spectroscopic surveys (WEAVE-LOFAR - radio-selected
Smith et al. 2016; 4G-PAQS - astrometrically-selected Krogager et al. 2023)
upcoming which may provide samples with much higher BALQSO fractions than
SDSS. These will allow us to study the BALQSO-radio connection in even greater
detail.

If one considers the idea that increasing C iv distance relates to
increasingly wind-dominated systems, one could interpret the radio-detection
fraction of blue non-BALQSOs at a low or moderate C iv distance to be a
measure of the fraction from the combined effect of small-scale jets and star
formation. If we then make the assumption that the contribution to the radio
from star formation and jets does not increase with C iv distance, then the
increasing radio detection fraction with increasing C iv distance could be
related to shocks. With regards to jets, the motivation that their
contribution does not increase with C iv distance is supported by jets being
largely stochastic sources and also radio loudness having an anti-correlation
with accretion rate (Sikora et al., 2007). For star formation, our assumption
that it has no correlation with C iv distance finds some support from Stanley
et al. (2015) which found that the relationship between star formation rate
and AGN luminosity was remarkably flat. They argue that the AGN luminosity
varies much more rapidly than the star formation rate, washing out any
underlying correlations. If a BALQSO wind is observed then it means conditions
around the SMBH are suitable for the creation of the BALQSO wind. Are these
conditions stable for a sufficient period of time for us to both observe the
BAL wind and any resultant radio emission (see subsection 4.4)? Presumably,
BALQSO winds transport gas and dust from a more central region out into the
ISM adding another uncertain timescale to pair with any proposed connection
between BALQSOs, reddening and radio emission.

In Choi et al. (2022) a large sample of BALQSOs with lower ionisation and iron
absorption troughs, FeLoBALs, was studied using the spectral analysis code
SimBAL (Leighly et al., 2018). This represents the most detailed analysis of
the physics of BALQSO outflows although admittedly for a highly extreme sub-
sample. They found that nearly 18% of the FeLoBALs contained multiple BAL
components and that the objects with the highest kinetic energy fractions were
found closer to the SMBH in the vicinity of the torus. Dust could have a key
part to play in the expansion of a wind (Everett & Churchwell, 2010) and a
recent study of the interaction between a torus-like dusty structure and
quasar radiation found that dust is the key to generating high-velocity winds
without over-ionising the gas (Soliman & Hopkins, 2023). This could be a key
connection between BALQSOs and their increased fraction in reddened samples.
Since BALQSOs likely require some amount of shielding, and LoBALs even more
so, dust could be a key factor in launching the BALQSOs winds in the first
place.

###  4.3 Importance of Colour

The fact that in Figure 3 and Figure 5 we see clear changes in the radio
detection fraction even for the red population, suggests that colour, which is
likely connected to dust, couples very strongly to radio emission. Klindt et
al. (2019) showed the radio-detection fraction for SDSS quasars as a function
of $g-i$ colour for different redshift cuts. They found the 1.4GHz FIRST
detection fraction increases steeply around the 80th percentile. We use a
different definition for our red quasar population in this study, which means
our red quasars are not as red as in that study, but we do find that even the
quasars with these intermediate colours have a clear increase in radio-
detection fraction. FIRST is a less sensitive survey than LoTSS and operates
at a higher frequency. This makes it harder to observe detection fraction
differences between blue and moderately reddened systems since FIRST observes
a greater radio-loud fraction thereby potentially missing lower luminosity
emission.

To make use of the high number of sources at moderate C iv distance and the
fact that we resolve the colour distribution with SDSS photometry, we look
again at the radio-detection fraction of quasars but with a focus on the
colour in Figure 7. This is similar to Figure 3 but this time we take the
excess red population of quasars and split it into two colour bins of equal
number and then for the rest of the population, the "blue" and "red" quasars
within the normal distribution of Figure 1, we split into five colour bins of
equal number. We use fewer C iv distance bins to keep the uncertainties lower
and focus on the central region which contains the vast majority of quasars.

Figure 7: Radio-detection fraction for a smaller number of C iv distance bins
with different colour splits for blue/red quasars and excess red quasars. We
use 5 colour bins with an equal number of quasars in each bin for the blue and
red groups. From left to right within each shaded region at each C iv bin the
colour is increasing. The BALQSOs are in orange and the quasars are in green
with the shaded region representing $1\sigma$ uncertainties. We use 2 equal
number bins for the excess red quasars with circles indicating BALQSOs and
triangles for quasars. The darker shade is the most reddened bin. Colour
increases enhance the radio detection fraction even at the blue end and the
difference between BALQSOs and red quasars is minimal in the most red colour
bins.

The reddened quasars show an enhanced radio-detection fraction at all C iv
distances. This is also seen when comparing blue to red BALQSOs. Hence, dust
content could be important for radio emission even when a system is not
overwhelmingly disk-dominated and producing high C iv blueshifts. In fact, the
change in the ratio between the red quasar detection fraction and the blue
quasar detection fraction is relatively constant across C iv distance. One
hypothesis for red quasars is that they exist as a brief intermediate phase
between a dusty star-forming source and a blue quasar (Sanders et al., 1988;
Hopkins et al., 2008). It has recently been shown that the more extreme
counterparts of red quasars, known as obscured quasars, have potentially 3
times the star formation rate at the same mass as unobscured quasars and also
enhanced radio emission (Andonie et al., 2022). However, the work of Rosario
et al. (2021) showed that the physical scale on which the majority of the
radio enhancement of red quasars exists is on a scale $\leq 2$ kpc implying an
AGN origin for a significant fraction of the radio emission in red quasars. An
alternative explanation could be that the radio emission comes from increased
circumnuclear star formation rates and that as the C iv distance increases we
are heightening the effect of positive feedback from the winds that trigger
nuclear starbursts (e.g. Silk, 2003). But, as discussed in subsection 4.1,
this appears to be unlikely, at least for the non-BALQSO colour connection to
radio emission.

###  4.4 Timescale Issues

One aspect of radio emission that we have not discussed to this point is the
timescale over which radio-emitting sources need to be powered to reach
luminosities that we can observe. Radio jets originating from the SMBH
typically reach peak luminosities around 10-100Myrs after they are first
powered (Hardcastle, 2018). If the power stops then the synchrotron luminosity
is expected to decrease rapidly. In the models of Hardcastle (2018) the
luminosity drops around 3 orders of magnitude in around 10Myrs after the jet
stops being powered (see Figure 6 of that paper). The light travel time for a
jet of size 100kpc is 326,000 years which is much lower than this decrease.
Since these are radio-quiet AGN and are largely unresolved at 6 arcseconds, we
know that they cannot have powerful jets that have been active for 100s of
Myrs.

The lifetime of BAL winds themselves is also largely uncertain. The most
recent estimates are that BAL troughs exist for around 100 years but that a
BAL phase lifetime is much harder to estimate as BAL troughs could also appear
during that time frame (De Cicco et al., 2018; Mishra et al., 2021). This
variability is generally thought to arise due to changes in the gas shielding
the BAL from the quasar and hence changing the ionising flux incident upon the
wind. The scale on which the overall BAL wind varies or whether winds are
always present and just the ionisation state changes is uncertain.

The timescale over which a wind shock can generate significant luminosity is
expected to be much shorter than the time scale of a radio jet. Supernova
shocks create radio emission and this has been observed and modelled for
decades. Typically supernova shock radio emission quickly reaches a peak
($\sim$0.1 years) before decaying more slowly (Chevalier et al., 1982; Weiler
et al., 1986). Presumably this time is much longer due to the larger size of
an AGN outflow but perhaps this is a way to constrain the connection between a
BALQSO lifetime and its radio emission. If we can definitively show that the
radio emission is triggered by the BALQSO wind itself then this would allow us
to connect the lifetime of the BALQSO to the lifetime of the radio emission by
looking at the ratio of radio-detected and non-detected BALQSOs. The radio-
detection fraction for a population is modulated by the overlap in the
lifetime of that population and the lifetime at which the radio emission is
luminous enough to be detected. The likely short lifetime of a BALQSO compared
to a quasar in general therefore also implies that the radio emission exists
over a similarly short timescale so that the difference in radio detection
fraction between BALQSOs and non-BALQSOs can be observed.

###  4.5 Testing a wind shock emission model

Nims et al. (2015) provide a model for wind shocks from AGN winds and has been
widely cited in the field. The model makes some simple assumptions for an
energy-conserving wind. They first show that for a wind travelling at 10% the
speed of light through a typical ambient medium over a quasar lifetime, the
wind can achieve $>1$ kpc scales. They then analyse both the thermal and non-
thermal emission processes that would be associated. Important to low-
frequency radio observations is the synchrotron emission for which a formula
is provided in Equation 32 of Nims et al. (2015):

$\nu
L_{\nu}=10^{-5}\xi_{-2}L_{\mathrm{AGN}}\left(\frac{L_{kin}}{0.05L_{\mathrm{AGN}}}\right)$

Here the $\xi_{-2}$ parameter represents the percentage of the shock kinetic
energy which is converted into relativistic electrons (i.e. if we assume 5% of
the energy goes into relativistic electrons, $\xi_{-2}=5$).

We attempt to test whether this model can account for all of the observed
emission given the large number of quasars we have that are both radio-
detected and have an estimate for their overall luminosity. We are also
claiming that the C iv distance traces the influence of winds, hence we can
test whether the wind-dominated systems adhere to the Nims et al. (2015) model
more than the whole quasar population.

To construct the predicted wind shock radio-luminosity at 144MHz from the Nims
et al. (2015) model we need to obtain the overall AGN luminosity,
$L_{\mathrm{AGN}}$, and then pick appropriate values for the fraction of AGN
energy in the wind and the fraction of wind energy that goes into relativistic
electrons, $\xi_{-2}$. To obtain AGN luminosities we convert our interpolated
six-micron luminosities from WISE and use the bolometric corrections from
Richards et al. (2006). We apply the same correction to all quasars,
$L_{\mathrm{AGN}}=8\times L_{6\mu m}$, and then assume that
$L_{kin}=0.05L_{\mathrm{AGN}}$.

We compute models for the expected wind shock radio luminosities at 144MHz for
all of our quasars with a C iv distance above 0.25, which should increase the
prevalence of winds compared to jets. We create three models for the wind
shock luminosity as follows:

  1. 1.

Fixed conversion rate to relativistic electrons of $\xi_{-2}=5$

  2. 2.

Varying the conversion rate $\xi_{-2}$ to minimise the Kolmogorov-Smirnov
(K-S) test statistic between the observed radio luminosities and the model

  3. 3.

Giving the conversion rate a linear dependence on the AGN luminosity such that
$\xi_{-2}=\frac{L_{\mathrm{AGN}}\alpha}{\max(L_{\mathrm{AGN}})}$ and fitting
for $\alpha$ to minimise the K-S test statistic

Figure 8: Three models of the wind shock radio flux as predicted by the
prescription of Nims et al. (2015) using the AGN luminosity of radio-detected
quasars. The observed radio flux is shown in pink, a constant 5% of shock
energy in relativistic electrons in blue, model (i), a best fit constant
conversion of 1.36% in green, model (ii), and a best fit functional form with
a linear dependence on the AGN luminosity in red, model (iii).

The results of these different models along with the observed radio flux
distribution are shown in Figure 8. We find that a similar assumption to the
AGN to kinetic luminosity conversion of 5%, model (i), largely over-predicts
the observed flux for our quasar sample. The value for this conversion factor
that minimises the difference between the observed and model distributions is
a more modest 1.36%, model (ii). The fit here is quite good, especially
between the LoTSS flux limit and 10mJy. The fact that the shape is similar is
not so surprising since the six-micron luminosity is roughly normal
distribution and we are mostly shifting this distribution with some dependence
on the redshift to obtain the fluxes.

These models perform poorly for higher flux sources, which are a small
fraction of the overall population, which suggests that wind shocks cannot
explain all of the sources. We introduced the third model, model (iii), as a
way to allow for potentially higher flux sources. This model includes a linear
dependence of the efficiency on the AGN luminosity. Physically this would mean
that higher luminosity AGN can convert more of their outflow energy to
relativistic electrons. We do not have a specific assumption for how this
would work but one example could be that a more powerful AGN creates a wider
covering angle for outflows which allows for a larger shock front and more
relativistic electrons. This model allows for the distribution to spread out
in both directions. We do not recover the correct shape for the distribution
and still cannot obtain the highest flux sources with just a linear connection
between AGN luminosity and efficiency. Presumably, jets also contribute in
some fraction of the sources so including some model for the jet flux could be
an alternative way to fit the higher flux sources.

##  5 Conclusions

We have studied a sample of SDSS quasars within the LoTSS footprint. We have
cut to a redshift range of $1.7<z<2.5$ to allow for BALQSO and quasar colour
classification. We use spectral reconstructions as described in Rankine et al.
(2020) to de-noise the spectra, improve the redshift estimates and
characterise the C iv emission more accurately. We look at trends for
different quasar populations as a function of their C iv distance, a tracer of
the accretion rate. We focus on the radio properties of these sources as the
origin of radio emission for most quasars is an open question.

Our main findings are:

  1. 1.

Radio-detection fraction has a strong correlation with C iv distance for all
populations. Radio-detection fraction decreases with increasing C iv distance
up to 0.5 and then begins to increase. In the lowest C iv distance bin the
difference in radio properties for all groups narrows but this is also where
we have the most uncertainty due to lack of sources. This narrowing could
potentially be linked to the work of Temple et al. (2023) where trends with
accretion rate and black hole mass become apparent above some threshold;

  2. 2.

Radio luminosity does not change significantly with increasing C iv distance
while the radio-loudness of the populations decreases with increasing C iv
distance. This shows that g-band luminosity is increasing due to the changing
shape of the SED of quasars across the C iv distance space. This is further
evidence that radio-loudness is not a suitable parameter to split radio
populations without controlling for at least accretion rate.

  3. 3.

The colour of quasars is linked to their radio-detection fraction independent
of C iv distance and whether a BAL wind is present. The most reddened quasars
have slightly higher radio luminosities than blue quasars when detected. The
difference between moderately reddened and the most reddened quasars is less
significant for BALQSOs;

  4. 4.

BALQSOs have a marginally higher radio-detection fraction than non-BALQSOs but
overall the difference in detection fraction between these two populations is
largely explained by their colour. This is further evidence that the BAL wind
itself is connected to dust;

  5. 5.

The Nims et al. (2015) wind shock model works well in modelling the observed
radio-flux for radio-detected quasars. This is mainly just an appropriate
scaling of the distribution of AGN luminosities, but the best fit relativistic
electron coupling of 1.36% is quite modest, giving wind shocks the potential
to account for the radio emission of many sources;

Are BALQSOs and red quasars distinct from the general population when it comes
to their accretion and radio properties? For BALQSOs, their radio properties
appear to be largely explained by their relation to optical colour. Although
they have a preference for a particular region of the C iv space, it is still
true that BALQSOs exist with a wide range of C iv EWs and blueshifts. It
therefore appears that some combination of accretion rate, dust and
orientation with respect to the observer is the origin of BALQSO winds. Red
quasars have a similar connection between radio-detection fraction and
accretion as blue quasars but then show different radio properties compared to
the BALQSOs/non-BALQSOs. Their radio-detection enhancement is observable
across C iv space while detection fraction differences between red non-BALQSOs
and red BALQSOs are narrower, indicating that the emission mechanism linked to
colour could dominate over the BALQSO contribution.

Two key steps are needed to advance the studies of these populations with
respect to their radio emission; one is observational and the other is
theoretical. First, we need a statistically significant population of these
populations to be studied at sub-galaxy scale resolution in the radio across
the C iv distance/accretion rate and optical colour space. This population
will allow us to separate star formation and AGN components of the radio
emission and then isolate the behaviour of the AGN component with an accretion
state. Therefore, we should be able to distinguish between jets and wind
shocks, a current limitation of our work. Secondly, we need more detailed
theory and/or simulations of the behaviour and radiative transfer of wind
shocks, which currently has the freedom to fit the entire population with the
right energetic scaling, and the interaction of both wind shocks and jets with
dust. Timescales are still a great uncertainty in this field and new
simulations could be vital in constraining likely timescales for the presence
of a BAL wind and the overlap with the radio emission it may be linked to or
produce itself.

## Acknowledgements

JP acknowledges support for their PhD studentship from grants ST/T506047/1 and
ST/V506643/1.

NLT and LKM acknowledge support from the Medical Research Council
MR/T042842/1.

DMA acknowledges support from the STFC consolidated grant ST/T000244/1 and
ST/X001075/1.

VAF acknowledges funding from a United Kingdom Research and Innovation grant
MR/V022830/1.

PNB is grateful for support from the UK STFC via grant ST/V000594/1.

ALR acknowledges support from UKRI grant code MR/T020989/1.

IP acknowledges support from INAF under the Large Grant 2022 funding scheme
(project “MeerKAT and LOFAR Team up: a Unique Radio Window on Galaxy/AGN co-
Evolution”)

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions.

SDSS-IV acknowledges support and resources from the Center for High
Performance Computing at the University of Utah. The SDSS website is
www.sdss.org.

SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics | Harvard & Smithsonian, the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

LOFAR data products were provided by the LOFAR Surveys Key Science project
(LSKSP; https://lofar-surveys.org/) and were derived from observations with
the International LOFAR Telescope (ILT). LOFAR (van Haarlem et al., 2013) is
the Low Frequency Array designed and constructed by ASTRON. It has observing,
data processing, and data storage facilities in several countries, which are
owned by various parties (each with their own funding sources), and which are
collectively operated by the ILT foundation under a joint scientific policy.
The efforts of the LSKSP have benefited from funding from the European
Research Council, NOVA, NWO, CNRS-INSU, the SURF Co-operative, the UK Science
and Technology Funding Council and the Jülich Supercomputing Centre.

The Jülich LOFAR Long Term Archive and the German LOFAR network are both
coordinated and operated by the Jülich Supercomputing Centre (JSC), and
computing resources on the supercomputer JUWELS at JSC were provided by the
Gauss Centre for Supercomputing e.V. (grant CHTB00) through the John von
Neumann Institute for Computing (NIC).

This research made use of Astropy,111https://www.astropy.org a community-
developed core Python package for Astronomy (Astropy Collaboration et al.,
2013, 2018).

For the purpose of open access, the author has applied a Creative Commons
Attribution (CC BY) licence to any Author Accepted Manuscript version arising
from this submission.

## Data Availability

The LoTSS DR2 radio data and catalogue used in this work are described in
Shimwell et al. (2022a) and can be found at the following page -
https://lofar-surveys.org/dr2_release.html

The SDSS DR14 quasar catalogue used in this work is described in Pâris et al.
(2018) is located at the following URL -
https://data.sdss.org/sas/dr14/eboss/qso/DR14Q/DR14Q_v4_4.fits

The SDSS spectra used as a basis for the ICA reconstructions can be downloaded
through various means described on this page -
https://www.sdss.org/dr17/spectro/.

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