11institutetext: Cosmic Dawn Center (DAWN),
11email<EMAIL_ADDRESS>22institutetext: Niels Bohr Institute,
University of Copenhagen, Jagtvej 155, 2200 Copenhagen N, Denmark
33institutetext: Centre de Recherche Astrophysique de Lyon, Univ. Claude
Bernard Lyon 1, 9 Av. Charles Andre, 69230 St Genis Laval, France
44institutetext: European Southern Observatory, Karl-Schwarzschild-Straße 2,
D-85748 Garching bei München, Germany and Instituto de Astrofísica de
Canarias, Vía Láctea, s/n, 38205, La Laguna, Tenerife, Spain 55institutetext:
Gran Telescopio Canarias (GRANTECAN), Cuesta de San José s/n, E-38712, Breña
Baja, La Palma, Spain

# Absence of radio-bright dominance in a near-infrared selected sample of red
quasars††thanks: Table A1 is only available in electronic form at the CDS via
anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/

S. Vejlgaard 1122 J. P. U. Fynbo 1122 K. E. Heintz 1122 J. K. Krogager 33 P.
Møller 4422 S. J. Geier 5566 L. Christensen 1122 G. Ma 1122

(Received –; accepted –)

###### Abstract

Context. The dichotomy between red and blue quasars is still an open question.
It is debated whether red quasars are simply blue quasars that are observed at
certain inclination angles or if they provide insight into a transitional
phase in the evolution of quasars.

Aims. We investigate the relation between quasar colors and radio-detected
fraction because radio observations of quasars provide a powerful tool in
distinguishing between quasar models.

Methods. We present the eHAQ+GAIA23 sample, which contains quasars from the
High A(V) Quasar (HAQ) Survey, the Extended High A(V) Quasar (eHAQ) Survey,
and the Gaia quasar survey. All quasars in this sample have been found using a
near-infrared color selection of target candidates that have otherwise been
missed by the Sloan Digital Sky Survey (SDSS). We implemented a redshift-
dependent color cut in $g^{*}-i^{*}$ to select red quasars in the sample and
divided them into redshift bins, while using a nearest-neighbors algorithm to
control for luminosity and redshift differences between our red quasar sample
and a selected blue sample from the SDSS. Within each bin, we cross-matched
the quasars to the Faint Images of the Radio Sky at Twenty centimeters (FIRST)
survey and determined the radio-detection fraction.

Results. For redshifts 0.8 $<$ z $\leq$ 1.5, the red and blue quasars have a
radio-detection fraction of 0.153${}^{+0.037}_{-0.032}$ and
0.132${}^{+0.034}_{-0.030}$, respectively. The red and blue quasars with
redshifts 1.5 $<$ z $\leq$ 2.4 have radio-detection fractions of
0.059${}^{+0.019}_{-0.016}$ and 0.060${}^{+0.019}_{-0.016}$, respectively, and
the red and blue quasars with redshifts z $>$ 2.4 have radio-detection
fractions of 0.029${}^{+0.017}_{-0.012}$ and 0.058${}^{+0.024}_{-0.019}$,
respectively. For the WISE color-selected red quasars, we find a radio-
detection fraction of 0.160${}^{+0.038}_{-0.034}$ for redshifts 0.8 $<$ z
$\leq$1.5, 0.063${}^{+0.020}_{-0.017}$ for redshifts 1.5 $<$ z $\leq$ 2.4, and
0.051${}^{+0.030}_{-0.022}$ for redshifts z $>$ 2.4. In other words, we find
similar radio-detection fractions for red and blue quasars within $<1\sigma$
uncertainty, independent of redshift. This disagrees with what has been found
in the literature for red quasars in SDSS. It should be noted that the
fraction of broad absorption line (BAL) quasars in red SDSS quasars is about
five times lower. BAL quasars have been observed to be more frequently radio
quiet than other quasars, therefore the difference in BAL fractions could
explain the difference in radio-detection fraction.

Conclusions. The dusty torus of a quasar is transparent to radio emission.
When we do not observe a difference between red and blue quasars, it leads us
to argue that orientation is the main cause of quasar redness. Moreover, the
observed higher proportion of BAL quasars in our dataset relative to the SDSS
sample, along with the higher rate of radio detections, indicates an
association of the redness of quasars and the inherent BAL fraction within the
overall quasar population. This correlation suggests that the redness of
quasars is intertwined with the inherent occurrence of BAL quasars within the
entire population of quasars. In other words, the question why some quasars
appear red or exhibit BAL characteristics might not be isolated; it could be
directly related to the overall prevalence of BAL quasars in the quasar
population. This finding highlights the need to explore the underlying factors
contributing to both the redness and the frequency of BAL quasars, as they
appear to be interconnected phenomena.

###### Key Words.:

quasars: general – quasars: supermassive black holes – galaxies: active –
radio-continuum: galaxies

##  1 Introduction

Even though the study of quasi-stellar objects (QSOs, or quasars) began more
than half a century ago (Schmidt, 1963; Greenstein & Schmidt, 1964; Sandage,
1965), it remains a field in development. With extremely high bolometric
luminosities (up to $\sim 10^{47}$ erg s-1; see, e.g., Onken et al. 2022),
quasars are not only the most powerful class of active galactic nuclei (AGN),
but also some of the most luminous and distant objects known in the observable
Universe (Wu et al., 2015; Wang et al., 2021). Quasars are powered by the
rapid accretion of matter onto a supermassive black hole (SMBH) with a
possible mass ranging up to $10^{10}$ M⊙ (see also Rees, 1984). According to
the unified model for AGN and quasars presented, for instance, by Antonucci
(1993) and Urry & Padovani (1995), a dust torus absorbs and reemits photons
from the accretion disk with a dependence on the observed viewing angle. In
addition to the broad- and narrow-line regions producing the emission lines
used to classify the quasar, the unified model also describes quasar outflows.
These outflows can take the form of relativistic and collimated radio jets or
more extended winds originating from the accretion disk. In a subset of
quasars called broad absorption line (BAL) quasars, the strong winds create
broad blueshifted absorption lines in the UV part of the quasar spectrum
(Foltz et al., 1987; Weymann et al., 1991).
A typical quasar spectrum is characterized by a rest-frame blue or UV power-
law continuum on which broad emission lines are superimposed. However, a
number of studies have already confirmed the existence of a quasar population
with a much redder continuum, which is simply referred to as ”red” quasars
(Webster et al., 1995; Benn et al., 1998; Warren et al., 2000; Gregg et al.,
2002; Hopkins et al., 2004; Glikman et al., 2007; Fynbo et al., 2013). Our
understanding of this particular subset of quasars is still far from complete.
While many studies attribute the red optical and infrared (IR) colors to dust
obscuration (Sanders et al., 1988a, b), other plausible explanations include
starlight contamination from the quasar host galaxy (Serjeant, 1996) and
differences in the accretion rates (Young et al., 2008). From the attempts to
explain the observational differences, two main quasar redness paradigms have
emerged: The orientation model, and the evolutionary model. The orientation
model claims that any observed differences between red and blue quasars are
due to the observer’s viewing angle with respect to the dusty torus, such that
inclinations closer to the equatorial plane of the torus correspond to a
redder quasar classification (Antonucci, 1993). According to the orientation
model, the differentiation between red and blue quasars is thus not grounded
in physical circumstance, but solely a consequence of relative positioning
with respect to either of these objects. The evolutionary model claims that an
intrinsic physical evolution is the origin of the quasar redness, such that
the red quasar population represents a transitional phase between an early
highly dust-obscured star-forming stage and the blue quasar stage (Sanders et
al., 1988a, b; Hopkins et al., 2006, 2008; Alexander & Hickox, 2012; Glikman
et al., 2012). Within this framework, the host galaxies of red quasars are
thought to have undergone a major galaxy merger, which induces either strong
winds or jets in the central red quasar, with the ability to dissolve their
surrounding dust cocoons. This quenches the host galaxy star formation, and
the underlying unobscured blue quasar is revealed.

The fact that the optical colors of dust-reddened quasars resemble those of
low-mass stars (Richards et al., 2002, 2003) motivated the use of radio
selection to build red quasar samples without stellar contamination (Webster
et al., 1995; White et al., 2003). Based on their findings, Webster et al.
(1995) and White et al. (2003) suggested that up to $\sim$80% of the total
quasar population could be made up of red quasars that were missed by previous
optical selection methods. To investigate whether large numbers of dust
obscured quasars are indeed missed, Glikman et al. (2007) combined the VLA
Faint Images of the Radio Sky at Twenty centimeters (FIRST; Becker et al.
1995) radio survey and the 2 Micron All Sky Survey (2MASS; Skrutskie et al.
2006) in an attempt to counteract the dust bias. However, this introduced a
bias toward the radio-bright red quasar population, as pointed out, for
example, by Heintz et al. (2016) and Glikman et al. (2018). Combining the
Wide-Field Infrared Space Explorer (WISE; Wright et al. 2010) with the Sloan
Digital Sky Survey (SDSS; York et al. 2000) and its extension from the Baryon
Oscillation Spectroscopic Survey (BOSS; Dawson et al. 2013), Glikman et al.
(2022) found it more likely that the red quasars comprise $\sim$40% of the
total quasar population.

Using the SDSS DR7 Quasar catalog (Shen et al., 2011), Klindt et al. (2019)
investigated the fundamental differences between red and blue quasars seen in
radio wavelengths. Searching for mid-IR (MIR) counterparts and checking for
luminosity and redshift effects, they cross-matched the SDSS DR7 Quasar
catalog with sources in the FIRST survey and found a fraction of the radio
detection among the red quasars that was about a factor of 3 higher than that
of the blue quasars. Klindt et al. (2019) claimed that this provided evidence
against the orientation-dependent model because radio emission is not affected
by dust, and hence, orientation alone cannot explain the observed differences.
In a follow-up study, Fawcett et al. (2020) found that the radio excess
decreased toward the radio-quiet part of the red quasar population, but
concluded that the excess is still significant. Furthermore, Fawcett et al.
(2023) found an intrinsic relation between dust reddening and the production
of radio emission in quasars when studying MIR and optical-color selected
quasars in the Dark Energy Spectroscopic Instrument (DESI) survey. This
relation is such that low-powered jets, winds, or outflows are thought to
cause shocks in the dusty quasar environment, which then powers radio
emission. However, clues pointing toward a lack of radio detection excess have
also been presented previously (see, e.g., Krogager et al. (2016a)). When
Krogager et al. (2016a) compared their red quasar radio detection fraction to
the radio detection fraction of the red quasars overlapping in SDSS+BOSS, the
overlapping quasars showed a significantly higher radio detection fraction,
which demonstrates that the radio excess might be a selection artifact.

In this paper, we examine the entire sample of quasars found by Fynbo et al.
(2013), Krogager et al. (2015, 2016a), and Heintz et al. (2020). This sample
contains quasars that have been missed by classic quasar selection methods,
such as those used to build the SDSS DR7 Quasar catalog. Fynbo et al. (2013)
showed that these quasars differ from the classically selected quasars by an
increased dust reddening. Furthermore, the dust-reddening was not found to be
caused by intervening absorbers, but was instead shown to be primarily a
consequence of the quasar host galaxy. In Section 2, we outline how we
gathered the sample, and in Section 3, we describe how we ensured that color
was the only observed difference between our red quasar sample and the blue
SDSS DR7 quasars with which we compared our sample. We present the results of
our investigation in Section 4. Throughout Section 4, we also compare our
results to the blue SDSS DR7 quasars in order to search for fundamental
differences between red and blue quasars. The comparison of our results to the
orientation and evolution model is presented in Section 5, where we also
discuss the other parameters that might influence our findings. Following the
Planck Collaboration et al. (2020), we assume a flat $\Lambda$CDM cosmology
with $H_{0}=67.4$ km s-1 Mpc-1, $\Omega_{\Lambda}=0.685$, and
$\Omega_{M}=0.315$ throughout the paper. We use Vega magnitudes throughout the
paper, except for Section 3.3, where we convert into AB magnitudes to
calculate the rest-frame 6 $\mu$m luminosity.

##  2 Sample

We built our sample of quasars from the catalog of quasar candidates provided
in Fynbo et al. (2013, hereafter F13), Krogager et al. (2015, hereafter K15),
Krogager et al. (2016a, hereafter K16), and Heintz et al. (2020, hereafter
H20). For each candidate, we have broadband photometry from the $u$ (3543 Å),
$g$ (4770 Å), $r$ (6231 Å), $i$ (7625 Å), and $z$ (9134 Å) bands from SDSS and
the $J$, $H$, $K$ bands from UKIRT Infrared Deep Sky Survey (UKIDSS; Lawrence
et al. 2007). UKIDSS uses the Wide Field Camera (WFCAM) on the 3.8 m United
Kingdom Infra-red Telescope (UKIRT). In some cases ($\sim 10\%$ of the
objects), the NIR band was instead taken from the VISTA (Emerson et al., 2006;
Dalton et al., 2006) Kilo-degree Infrared Galaxy (VIKING; Edge et al. 2013)
survey. The candidates from F13 all have $0.8<g^{*}-r^{*}<1.5$ and
$r^{*}-i^{*}>0.2$, while the candidates from K15 and K16 have
$0.5<g^{*}-r^{*}<1.0$ and $g^{*}-r^{*}>0.5$, respectively. H20 have relied
purely on an astrometric selection of quasars as stationary sources in the
Gaia survey.

The sample also contains quasars that have not been published previously, and
a few that have been published in single-object studies (Fynbo et al., 2017;
Heintz et al., 2018; Geier et al., 2019; Fynbo et al., 2020). These quasars
were selected with a combination of optical colors as in K16 and astrometric
exclusion of stellar sources as in H20. We refer to Heintz et al. (2018) and
Geier et al. (2019) for further details on the selection of these quasars. The
unpublished parts of the survey make up $\sim$50% of the total survey.

None of the papers claim to provide an unbiased selection method. On the
contrary, they specifically searched for reddened quasars with the main
motivation of finding foreground dusty damped Lyman-$\alpha$ absorbers (DLAs).
Radio emission has not been part of the selection criteria for any of the
quasar candidates. It should also be noted that the quasars were selected
specifically to not appear in SDSS spectroscopic database. In total, 550 of
the 578 quasar candidates turned out to be quasars after follow-up
spectroscopy.

In order for the quasars to be included in our sample, we also introduced the
requirement of a spectroscopic redshift. These redshifts are obtained as part
of dedicated spectroscopic observations with visually inspected redshift
determinations for all objects. We refer to the list of references for the
surveys in the appendix for further details. Five hundred and forty-three of
the total 550 quasars fulfill this requirement. In addition to the broadband
photometric data and spectroscopic redshifts, we also searched for MIR
counterparts of the quasars using WISE (Wright et al., 2010) and radio
counterparts using FIRST (Becker et al., 1995, 2012; Helfand et al., 2015).
FIRST operates at a frequency of 1.4 GHz (20 cm wavelength) and offers a high
sensitivity of typically about 1 mJy for point sources. With an angular
resolution as fine as 5 arcsec, FIRST covers over 10,000 deg2 of the northern
sky in a region that is largely coincident with SDSS. For the detections, we
adopted a 10 arcsec cross-matching radius. We took the closest-distance match
within the 10 arcsec to be the radio counterpart. It should be noted that the
largest match distance we found is 1.2 arcsec. In the case of multiple sources
within the 10 arcsec search radius, we also checked SDSS for the existence of
multiple optical sources. This was only the case for one of the quasars:
CQ0155+0438. Hence, we did not include CQ0155+0438 in the sample. We find that
534 of the redshift-confirmed quasars have MIR counterparts, while a small
subset of 33 quasars have radio counterparts detected in FIRST. We consider
the 534 MIR counterpart quasars to be the parent sample for our study here and
call this sample the eHAQ+GAIA23 sample. We chose this name because the sample
contains sources from the HAQ Survey, the eHAQ Survey, and the Gaia quasar
survey. The number 23 represents the year 2023, in which this project was
carried out. See the appendix for details on accessing the published data.

##  3 Methods

In order to facilitate a direct comparison to the blue SDSS DR7 quasars, we
followed the method in Klindt et al. (2019). Their method consists of two
steps taken to reduce the differences that are not related to color between
the red and blue SDSS DR7 quasar population. First, they used $g^{*}-i^{*}$
color quantile cuts to define a red and a blue quasar population. Then, they
used an unsupervised nearest-neighbor algorithm in the rest-frame 6 $\mu$m
luminosity-redshift space to match every red quasar with a blue one. These
steps are performed to ensure that the populations are similar in all other
parameters apart from color, which means that any differences can be
attributed to the color of the quasars. Redshift and 6 $\mu$m luminosity are
chosen above other dependences because they have a potentially high impact on
the quasar color. When we do not take redshift into account, a high-redshift
blue quasar might seem red. The 6 $\mu$m rest-frame luminosity is a measure of
the thermal emission from warm–hot dust in the quasar torus. It is heated by
the accretion disk emission and indicates the central black hole accretion
level, which is correlated to the bolometric luminosity of the quasar (Hickox
& Alexander, 2018). By matching this luminosity distribution for the two
different color populations, we ensure that the quasar activity levels are
similar.

###  3.1 Redshift dependence

One of the keystones in exploring the differences between red and blue quasars
is to ensure that the only observed difference in the sample is the color. To
do this, we applied several cuts on the sample redshift. We divided the
eHAQ+GAIA23 sample into two redshift bins: $z_{1}$, including quasars with
$0.8<z\leq 1.5$, and $z_{2}$, including those with $1.5<z\leq 2.4$. However,
we also decided to study $z_{3}$, including those with $2.4<z\leq 4.25$. The
resulting number of quasars within each redshift bin is presented in Table 1.

Sample |  N${}_{\text{all}}$ |  Nz1 |  Nz2 |  Nz3
---|---|---|---|---
Redshift |  [0.09;4.25] |  (0.8;1.5] |  (1.5;2.4] |  (2.4;4.25]
eHAQ+GAIA23 |  534 |  118 |  183 |  202
BAL |  179 |  10 |  84 |  83
rQSO |  423 |  107 |  179 |  110
BAL rQSO |  163 |  10 |  84 |  67
not-red QSO |  111 |  11 |  4 |  92
FrQSO |  33 |  16 |  10 |  3
BAL FrQSO |  3 |  0 |  1 |  2

Table 1: Number of quasars in the eHAQ+GAIA23 catalog. Column 2 presents the
total sample, and columns 3, 4, and 5 present different redshift ranges. We
define red quasars (rQSO) as those with a $g^{*}-i^{*}$ color value in the
upper 10th percentile of the SDSS DR7 Quasar Catalog $g^{*}-i^{*}$ color
values, while all BAL quasars were inspected visually. All quasars between the
upper and lower 10 percentiles are defined as not-red quasars.

###  3.2 Color dependence

We also ensured that we defined a red and a blue quasar in the same manner as
Klindt et al. (2019). They defined a red quasar as a quasar with a
$g^{*}-i^{*}$ color value in the upper 10th percentile of the SDSS DR7 quasar
catalog $g^{*}-i^{*}$ color values, while a blue quasar should belong to the
lower 10th percentile of the SDSS DR7 QC $g^{*}-i^{*}$ color values. All
quasars in between these percentiles are defined as not-red control quasars.
Klindt et al. (2019) already noted that this might lead to issues in the
$z_{3}$ bin, where the $g^{*}$ band is affected by the Lyman-$\alpha$ break.
For this reason, we conducted our analysis with and without the $z_{3}$ bin.
In Figure 1, we show the color selection as a black line on top of the
$g^{*}-i^{*}$ color versus redshift distribution of each quasar in the
eHAQ+GAIA23 sample. The number of red quasars (rQSO) and red quasars with a
radio detection (FrQSO) can be found in Table 1. It is evident from this table
that 423 of the eHAQ+GAIA23 quasars are red, and the remaining 111 are not
red. Upon inspecting the distribution of these two quasar classes across the
three redshift bins, we observe that the red quasars are predominantly
concentrated in the middle redshift bin, where $\sim$40% of them are found.
The not-red quasars in eHAQ+GAIA23 are primarily located in the highest
redshift bin, where $\sim$80% of them are found. One explanation for this
could be that SDSS contains a smaller fraction of red quasars at higher
redshifts, and hence the quantile cut is pushed toward higher $g^{*}-i^{*}$
values.

Figure 1: Distribution of the $g^{*}-i^{*}$ color as a function of redshift
for the quasars in the new quasar catalog. Every cross represents a quasar.
The black line shows the red quasar selection criteria from Klindt et al.
(2019), such that quasars with a higher color value are labeled rQSO and are
shown in red in this figure, while those with a lower color value are labeled
not-red QSO and are shown in gray in this figure. The categorization of the
BAL quasars, marked with black circles, relied on visual assessment without
the application of rigid standards (see F13, K15, K16, H20).

As can be seen from Table 1, 179 of the eHAQ+GAIA23 quasars qualify as BAL,
meaning that this new catalgo contains $\sim 34\%$ BAL quasars. For the red
quasars alone, we find 163 red BAL quasars out of 423 red quasars. For the red
quasars, the BAL percentage therefore increases to $\sim 39\%$ BAL quasars.
For comparison, we include the BAL number statistics from the SDSS DR7 quasar
catalog (Shen et al., 2011) in Table 2.

Sample |  Num. BAL | BAL Percentage (%)
---|---|---
Parent |  179 |  34
rQSO |  163 |  39
rQSO $\in z_{1}\cup z_{2}$ |  94 |  33
SDSS DR7 |  6214 |  5.9
Table 2: Statistics of the quasar distribution with respect to the number of
BALs. For comparison, we include information from the SDSS DR7 quasar catalog
(Shen et al., 2011).

###  3.3 Luminosity dependence

To ensure that any difference between the red and blue quasars cannot be
explained by differences in the rest-frame luminosities, we determined the
rest-frame 6 $\mu$m luminosity of the red quasars in our sample and compared
them to the rest-frame 6 $\mu$m luminosities of the red and blue SDSS quasars.
We used the MIR-magnitude data from WISE. First, we converted from the WISE
Vega-system into AB magnitudes using $m_{\text{AB}}=m_{\text{Vega}}+\Delta m$,
where $\Delta m=3.339$ for the W2 band and $\Delta m=5.174$ for the W3 band
(Tokunaga & Vacca, 2005). Under the assumption that the magnitudes are
monochromatic at the effective filter wavelength, we converted from AB
magnitudes into flux densities following the definition given by Tokunaga &
Vacca (2005). We performed a log-linear fit between the W2 and W3 effective
filter wavelength flux densities, which we used to either interpolate or
extrapolate the rest-frame 6 $\mu$m flux density, depending on the quasar
redshift. It should be noted that for the highest-redshift quasar, we
extrapolated up to $\sim$ 30 $\mu$m. At this wavelength, the extrapolation is
not necessarily reliable. The rest-frame 6 $\mu$m luminosity
$L_{6\mu\text{m}}$ distribution as a function of redshift is shown in Figure
2(a).

With respect to ensuring that the only observed difference between our red
quasars and the SDSS blue quasars is the color, we need to correct this
difference in the luminosity distributions. Without any form of correction,
the difference prohibits us from excluding that any other difference observed
between the two populations is more than the mere result of a correlation with
the rest-frame 6 $\mu$m luminosity.

(a) Before the nearest-neighbour matching

(b) After the nearest-neighbour matching

Figure 2:  The red kernel density estimate plot represents the red eHAQ+GAIA23
quasar distribution, and each purple dot represents a radio-detected red
quasar. The black circles represent red BAL quasars. In addition to these
markers, the blue kernel density estimate plot shows the blue SDSS DR7
quasars. Center: Logarithm of the rest-frame 6 $\mu$m luminosity of either all
the blue SDSS quasars (a) or the redshift-luminosity matched blue SDSS quasars
(b) in blue curves and the red eHAQ+GAIA23 quasars in red curves as a function
of redshift, assuming a continuous probability density curve. Top: Density
histogram of the redshift for the two different populations. Right: Density
histogram of the rest-frame 6 $\mu$m luminosity for the two different
populations.

Even though the redshift distributions of the blue SDSS population and the red
eHAQ+GAIA23 population look similar, the top histogram in Figure 2(a) shows a
shift toward higher redshifts for our red quasars. The right histogram in
Figure 2(a) reveals a clear difference in the two luminosity distributions.
While the red eHAQ+GAIA23 quasar sample has a luminosity median of
$\log(\overline{L}_{6\mu\text{m}})=46.0^{+0.3}_{-0.4}$, the blue SDSS
population has a lower and visibly broader luminosity distribution with median
$\log(\overline{L}_{6\mu\text{m}})=45.4^{+0.6}_{-0.7}$. In order to remove
this difference and be able to report differences related solely to quasar
color, we followed an approach similar to the one taken by Klindt et al.
(2019): We ran the red eHAQ+GAIA23 quasars through a scikit-learn (Pedregosa
et al., 2011), unsupervised nearest-neighbor algorithm in the rest-frame 6
$\mu$m luminosity-redshift space. For each of our red sample quasars, the
algorithm found an SDSS blue quasar within a fixed tolerance of 0.1 dex in
luminosity space and 0.1 in redshift space. After using the nearest-neighbor
algorithm, the redshift-luminosity matched blue quasars show a rest-frame 6
$\mu$m luminosity distribution with median
$\log(\overline{L}_{6\mu\text{m}})=46.0^{+0.3}_{-0.4}$.

Figure 2(b) shows the kernel density estimate plot after using the nearest-
neighbor algorithm. This served mainly as a sanity check and revealed that the
approach has the intended effect. The redshift-luminosity matched blue quasars
show a rest-frame 6 $\mu$m luminosity distribution with median
$\log(\overline{L}_{6\mu\text{m}})=46.0^{+0.3}_{-0.4}$.

Figure 3: Red quasar distribution in the WISE $(W2-W3$,$W1-W2)$ color space.
Each cross is a red quasar, each dot is a radio quasar, and each black circle
indicates whether the red quasar is a BAL quasar. The color of the markers
depends on the quasar redshifts.

###  3.4 Host galaxy dependence

In Figure 3, the distribution of the red quasars in the eHAQ+GAIA23 sample is
shown in the $W2-W3$ vs. $W1-W2$ color space alongside the AGN wedge from
Mateos et al. (2012). Each cross represents a red quasar, while the color of
the cross is determined by the quasar redshift. The dots show the distribution
of the red quasars with radio detection, and a black circle marks which of the
red quasars are BAL quasars. Table 3 shows that 59 of the 423 red quasars lie
outside the AGN wedge. The highest percentage is found in the $z>2.4$ sample.
Even though the AGN torus is expected to dominate the emission at MIR
wavelengths, emission from star formation in the host galaxy might still
contaminate the spectrum. If the MIR fluxes are indeed contaminated by the
host galaxy, this would bias our rest-frame 6 $\mu$m luminosity calculations.
The AGN wedge systematically deselects spectra for which the host galaxy star-
formation contributes more than 10% to the MIR luminosity emitted by the AGN.
Spectra with a contamination from star formation luminosity $>10\%$ end on the
lower right side of the wedge (Mateos et al., 2012). This explains that the
highest percentage of quasars outside the AGN wedge is found in the highest-
redshift sample, which is a more active part of the star formation history
(Madau & Dickinson, 2014). The red BAL quasars show a similar pattern, with an
outside percentage peaking at $z_{3}$. Only the small subcategory of red
quasars with a radio detection have no outliers with respect to the AGN wedge.

Sample | Num. outside |  Percentage outside (%), $z$ $\in$
---|---|---
|  | $(0.8;1.5]$ | $(1.5;2.4]$ | $(2.4;4.25]$
rQSO | 59 | 3.7 | 6.7 | 36
bQSO${}^{L6\mu m}_{z}$ | 74 | 1.8 | 6.8 | 51
BAL rQSO | 32 | 0 | 10 | 34
FrQSO | 0 | 0 | 0 | 0
FbQSO${}^{L6\mu m}_{z}$ | 4 | 0 | 0 | 66

Table 3: Statistics of the red and redshift-luminosity matched blue quasar
distribution with respect to the AGN wedge in WISE colors as defined by Mateos
et al. (2012). Information of the subcategories of red BAL quasars (BAL rQSO),
radio-detected red quasars (FrQSO), and the FIRST-detected percentage of the
redshift-luminosity matched blue SDSS quasar population (FbQSO${}^{L6\mu
m}_{z}$) is also included.

The statistics presented in Table 3 generally have a higher number of quasars
outside the AGN wedge compared to the SDSS population of blue quasars, but not
compared to the redshift-luminosity matched subpopulation. The redshift-
luminosity matched subpopulation has a higher percentage of quasars outside
the AGN wedge at redshifts $z>1.5$. The comparison between red and blue
quasars was to be as unaffected by other physical parameters as possible.
Therefore, we proceeded to run the unsupervised nearest-neighbor algorithm on
the red quasars within the AGN wedge and drew neighbors from the full blue
SDSS quasar population. This yielded a rest-frame 6 $\mu$m luminosity
distribution with median
$\log(\overline{L}_{6\mu\text{m}})=46.0^{+0.3}_{-0.4}$. This is similar to
what we found when we included quasars outside the AGN wedge.

##  4 Results: Radio-detection rates

In Table 4, we report the FIRST-detected percentage in each of the three
redshifts bins for the two different subsamples of red eHAQ+GAIA23 quasars
described in Section 3.2 and 3.4. We also report the FIRST-detected percentage
for the luminosity-redshift matched SDSS sample of blue quasars described in
Section 3.3. All values were calculated using the Bayesian binomial confidence
interval (CI) method described in Cameron (2011), such that the reported value
is the 50% CI and the lower and upper uncertainty are the 15.87% and 84.13% CI
($\pm$ 1$\sigma$), respectively. The leftmost column displays the FIRST-
detected percentage of the red quasars (rQSO) selected as described in Section
3.2, while the center column displays the FIRST-detected percentage of the red
quasars within the AGN wedge (AGN-w rQSO). As shown in Figure 2(a), these
percentages should not be compared directly to the blue quasar FIRST-detected
percentages reported by Klindt et al. (2019) because of the differences in the
rest-frame 6 $\mu$m luminosity distributions. Instead, we report the FIRST-
detected percentage of the redshift-luminosity matched blue quasar population
in the rightmost column of Table 4.

Redshift | FIRST-detected percentage (%)
---|---
|  rQSO | AGN-w rQSO | bQSO${}^{L6\mu m}_{z}$
$0.8<z\leq$1.5 | 15.3${}^{+3.7}_{-3.2}$ | 16.0${}^{+3.8}_{-3.4}$ |  13.2${}^{+3.4}_{-3.0}$
$1.5<z\leq 2.4$ | 5.9${}^{+1.9}_{-1.6}$ | 6.3${}^{+2.0}_{-1.7}$ |  6.0${}^{+1.9}_{-1.6}$
$z>2.4$ | 2.9${}^{+1.7}_{-1.2}$ | 5.1${}^{+3.0}_{-2.2}$ |  5.8${}^{+2.4}_{-1.9}$
Table 4: FIRST-detected percentage in each of the redshift bins for two
subsamples of the new catalog: The red quasars (rQSO), and the red quasars
within the AGN wedge (AGN-w rQSO). The rightmost column shows the FIRST-
detected percentage of the redshift-luminosity matched blue SDSS quasar
population.

The values reported in Table 4 are plotted in Figure 4. In this figure, the
dark red dots with error bars represent the fraction of FIRST-detected red
quasars and their 1$\sigma$ upper and lower limits. The orange diamonds and
error bars represent the fraction of FIRST-detected red quasars with observed
colors within the AGN wedge and their limits. The area shown by the blue
hashed region highlight the area corresponding to the fraction of FIRST-
detected redshift-luminosity matched blue SDSS quasars $\pm 1\sigma$ errors.
Similarly, the shaded purple region highlight the area corresponding to the
fraction of FIRST-detected blue SDSS quasars matched with redshift-luminosity
to our red quasars within the AGN wedge.

Figure 4: FIRST-detected fraction as a function of redshift for the two
different subsamples of our new catalog: The red quasars (rQSO) shown in dark
red, and the red quasars within the AGN wedge (AGN-w rQSO) shown in orange.
The luminosity-redshift matched blue quasars from SDSS are also included. The
area highlighted by blue diagonal stripes corresponds to their detection
fraction $\pm 1\sigma$ confidence intervals. The shaded purple area highlights
the area corresponding to the blue SDSS quasars matched with redshift-
luminosity to our red quasars within the AGN wedge. The two dashed lines show
the median of the luminosity-redshift matched blue quasars from SDSS and the
blue SDSS quasars matched with redshift-luminosity to our red quasars within
the AGN wedge.

Figure 4 illustrates that the red quasars in the eHAQ+GAIA23 sample do not
show a higher radio detection rate within $1\sigma$ than the blue quasar
sample for any redshifts. Even when we exclude the red quasars outside the AGN
wedge, the detection fraction of radio emission is the same within the
$1\sigma$ confidence intervals compared to the blue quasar sample in all
redshift bins. Even though it is not statistically significant, we note that
the red quasar values are at the top part of the blue quasar distribution in
the lowest-redshift bin. In the highest-redshift bin, the red quasar values
lie in the lower part of the blue quasar distribution, even though this is not
statistically significant either.

##  5 Discussion and conclusions

We have presented an analysis of the radio-detection fraction of the red
quasars in eHAQ+GAIA23. Using a color-cut criterion in the $g^{*}-i^{*}$ color
space, we selected only quasars that would belong to the upper 10th
$g^{*}-i^{*}$ color percentile of quasars in the SDSS quasar catalog. Neither
of the redshift bins show an excess of sources with radio emission detected in
FIRST compared to redshift-luminosity matched SDSS blue quasars.

###  5.1 Quasar redness models

Orientation-dependent models claim that the redness of quasars can be
explained by the viewing angle with respect to the dusty torus (Antonucci,
1993; Urry & Padovani, 1995; Netzer, 2015). In this framework, red quasars are
simply observed with an inclination angle and hence through the dusty torus,
while blue quasars are observed face-on. While the intervening dusty torus
will change the optical colors, the radio emission remains unaffected. Under
the assumption that the dusty torus is the only cause of the observed redness,
there should thus be no difference in the radio emission from red and blue
quasars. In this manner, our findings support the orientation model for quasar
redness.

On the other hand, the evolutionary models attribute the redness of quasars to
different phases in the life of quasars. A red quasar evolves from an early-
phase blue quasar that has developed strong winds in order to drive its
initial layers of dust and gas away and reveal the hidden accretion disk
within. Thus, these models suggest that red quasars have stronger winds than
blue quasars. Strong winds have been associated with weak radio emission
(Mehdipour & Costantini, 2019), which suggests that red quasars should have
fewer detected sources at a constant detection sensitivity. This is not what
we observe for our sample, and hence our findings only provide evidence for
the orientation-dependent model for quasar redness.

###  5.2 The BAL Effect

The strong winds of the evolutionary model framework are a well-known
characteristic of BAL quasars. Following the results of Mehdipour & Costantini
(2019), it is expected that BAL quasars are more frequently radio quiet than
other quasars. In the context of explaining why the red eHAQ+GAIA23 quasars
have a similar radio detection fraction compared to their luminosity-redshift
matched blue SDSS quasars, we recall from Table 2 that our red quasar sample
has a high BAL fraction even at redshifts $z<2.4$. With a higher fraction of
radio-quiet quasars, it is expected that the radio-detection fraction
decreases. In other words, it is possible that the radio-detection fraction of
the red eHAQ+GAIA23 quasars is lower solely because of the higher BAL quasar
fraction. This links the question of whether the radio detection fraction
depends on quasar color to the question of the intrinsic BAL quasar fraction
in the total quasar population. The BAL quasar fraction remains an open
question, but the recent study by Bischetti et al. (2023) estimated it to
increase with redshift from $\sim 20\%$ at redshift $z\sim 2-4$ to $\sim 50\%$
at redshift $z\sim 6$. An exploration of the BAL fraction of the total red
quasar population would require a selection cut that is unbiased against BAL
and red quasars.

###  5.3 Selection effects

The quasars in eHAQ+GAIA23 are not selected to be unbiased. Instead, the
selection criteria aim to target red quasars, in particular, to explore how
frequently quasars are reddened by dusty foreground absorbers at redshifts
$z\gtrsim 2$ (Krogager et al., 2016b; Geier et al., 2019). Hence, the chosen
selection cuts are also expected to play a role in the results presented in
this work. The HAQ Survey presented by F13 led the later surveys and
particularly the eHAQ Survey to an increased focus on targeting fewer quasars
at redshifts $z<2$ with high dust reddening as well as fewer unobscured
quasars at redshifts $z>3.5$. This resulted in a decrease of intrinsically red
quasars at lower redshifts, especially at redshifts $z\lesssim 1.5$. One of
the main reasons for doing so is to ensure the ability to detect Ly-$\alpha$
in absorption in the observed spectra from the surveys, which had posed a
problem for the HAQ Survey (see K16).

Even though the original purpose of the survey was aided by this, the intended
bias subtly compromises our results for red quasars with redshifts $0.8<z\leq
1.5$. In addition to explaining why the combined surveys have fewer quasars in
this redshift bin, the focus might also explain why this population behaves
more similar to the red SDSS quasars with radio-detection fractions in the
upper part of the luminosity-redshift matched blue SDSS quasar distribution.

The DESI survey quasars studied, for example, by Fawcett et al. (2023) also
behave more similar to the SDSS quasars. These quasars are selected based on
MIR and optical color and display an intrinsic relation between dust reddening
and the production of radio emission. In contrast to the eHAQ+GAIA23 quasars,
the DESI survey quasars might not be selected completely independently from
the SDSS quasars. In addition to color cuts in the MIR and optical colors,
Chaussidon et al. (2023) used a random forest machine-learning algorithm to
improve the success rate for DESI with respect to quasars. This algorithm is
trained on quasars known from the SDSS Stripe 82, which opens the possibility
for a correlation between the SDSS and the DESI quasars. Hence, the need for a
color-unbiased quasar sample remains.

###  5.4 Conclusion and future work

Our analysis of the radio-detection fraction of red quasars in the eHAQ+GAIA23
sample, when compared to the SDSS blue quasars, provides significant insights
into the nature of quasar redness. Our findings predominantly support the
orientation-dependent model, suggesting that the redness of quasars is
primarily a result of the viewing angle relative to the dusty torus. This
conclusion is drawn from the observation that there is no significant
difference in the radio emission between red and blue quasars. This aligns
with the expectation that the dusty torus affects optical colors without
influencing radio emission. In contrast, the evolutionary model, which links
quasar redness to different developmental phases and associates strong winds
with weak radio emission, finds less support in our data. The lack of a
statistically discernible decrease in radio detection fraction in red quasars,
as predicted by the evolutionary model, suggests that the red quasar redness
is less likely to be due to this phase-based evolution. Furthermore, the
intricacies of our sample selection in eHAQ+GAIA23, with a particular focus on
red quasars and the exclusion of certain quasar populations due to survey
biases, have implications for our results. While these biases were essential
for the previous survey’s objectives, they also limit the generalizability of
our conclusions, particularly in the context of the broader quasar population.

In future works, we will analyze the red quasar spectra further to provide
more details on the emission and absorption lines of this quasar population.
On larger timescales, a hope for a future disentanglement of the selection
biases discussed here has been presented with the 4-meter Multi-Object
Spectroscopic Telescope (4MOST) Gaia purely astrometric quasar survey
(4G-PAQS, Krogager et al., 2023). With its wide-field, high-multiplex, optical
spectroscopic survey facility (de Jong et al., 2019), 4MOST will provide a
unique opportunity to build the first color-unbiased quasar survey based
solely on astrometry from Gaia without an assumption on the spectral shape.
However, it should be noted that the 4G-PAQS will still be limited in
magnitude due to its selection of Gaia-detected sources. The 4G-PAQS community
survey will target a total of approximately 300,000 quasar candidates. In
addition to studying quasar feedback through BAL outflows at redshifts
$0.8<z<4$, 4G-PAQS will also aim to quantify the dust bias in quasar
absorption systems at redshifts $2<z<3$. This will provide a larger unbiased
sample of both red and not-red quasars to determine the origin of the
differences between red and blue quasars.

###### Acknowledgements.

The Cosmic Dawn Center (DAWN) is funded by the Danish National Research
Foundation under grant DNRF140. SV and JPUF is supported by the Independent
Research Fund Denmark (DFF–4090-00079) and thanks the Carlsberg Foundation for
support. LC and GM are supported by the Independent Research Fund Denmark (DFF
2032-00071). KEH acknowledges support from the Carlsberg Foundation
Reintegration Fellowship Grant CF21-0103. This publication makes use of data
products from the Wide-field Infrared Survey Explorer, which is a joint
project of the University of California, Los Angeles, and the Jet Propulsion
Laboratory/California Institute of Technology, funded by the National
Aeronautics and Space Administration. This publication makes use of data
products from the Two Micron All Sky Survey, which is a joint project of the
University of Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National Aeronautics
and Space Administration and the National Science Foundation. Funding for
SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research
Consortium for the Participating Institutions of the SDSS-III Collaboration
including the University of Arizona, the Brazilian Participation Group,
Brookhaven National Laboratory, Carnegie Mellon University, University of
Florida, the French Participation Group, the German Participation Group,
Harvard University, the Instituto de Astrofisica de Canarias, the Michigan
State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence
Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max
Planck Institute for Extraterrestrial Physics, New Mexico State University,
New York University, Ohio State University, Pennsylvania State University,
University of Portsmouth, Princeton University, the Spanish Participation
Group, University of Tokyo, University of Utah, Vanderbilt University,
University of Virginia, University of Washington, and Yale University. When
(some of) the data reported here were obtained, UKIRT was supported by NASA
and operated under an agreement among the University of Hawaii, the University
of Arizona, and Lockheed Martin Advanced Technology Center; operations were
enabled through the cooperation of the East Asian Observatory.

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## Appendix

Name | RA | DEC | QSO | BAL | RED | FIRST | Int. Flux [mJy] | Redshift | u | g | r | i | z | W1 | W2 | W3 | W4 | Ref.
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
CQ0354-0030 | $58.69183$ | $-0.50819$ | $1$ | $0$ | $1$ | $0$ | $0$ | $1.0$ | $22.0\pm 0.2$ | $21.32\pm 0.04$ | $20.33\pm 0.03$ | $20.03\pm 0.03$ | $19.59\pm 0.07$ | $15\pm 4$ | $14\pm 4$ | $11.0\pm 1.0$ | $9\pm 4$ | F13p
cq0206+0624 | $31.5611$ | $6.415122$ | $1$ | $0$ | $1$ | $1$ | $1.57$ | $1.2$ | $21.24\pm 0.08$ | $19.89\pm 0.03$ | $19.02\pm 0.02$ | $18.75\pm 0.02$ | $18.59\pm 0.03$ | $15\pm 4$ | $13\pm 3$ | $11.0\pm 0.7$ | $9\pm 3$ | F13u
eHAQ0940+0532 | $145.214$ | $5.537025$ | $1$ | $0$ | $1$ | $0$ | $0$ | $2.32$ | $20.44\pm 0.06$ | $19.32\pm 0.02$ | $18.49\pm 0.01$ | $18.15\pm 0.03$ | $17.87\pm 0.03$ | $15\pm 4$ | $14\pm 5$ | $11.0\pm 1.0$ | $8.0\pm 2.0$ | K16p
HAQ2349+0620 | $357.26$ | $6.349694$ | $1$ | $0$ | $1$ | $0$ | $0$ | $2.15$ | $20.28\pm 0.04$ | $19.6\pm 0.02$ | $18.81\pm 0.01$ | $18.53\pm 0.02$ | $18.13\pm 0.02$ | $15\pm 4$ | $14\pm 5$ | $11.0\pm 0.9$ | $8.0\pm 2.0$ | K15p
Q564 | $17.1135$ | $28.03839$ | $1$ | $0$ | $0$ | $0$ | $0$ | $3.57$ | $21.1\pm 0.1$ | $19.21\pm 0.02$ | $18.03\pm 0.01$ | $17.91\pm 0.02$ | $17.66\pm 0.02$ | $14\pm 3$ | $14\pm 4$ | $10.33\pm 0.05$ | $8.0\pm 2.0$ | u
eHAQ2300+0409 | $345.143202$ | $4.16287468$ | $1$ | $0$ | $0$ | $0$ | $0$ | $3.42$ | $25.0\pm 1.0$ | $21.0\pm 5.0$ | $20.0\pm 3.0$ | $20.0\pm 3.0$ | $19\pm 8$ | $15\pm 5$ | $15.0\pm 1.30$ | $12.0\pm 1.0$ | $8.8\pm 1.0$ | K16u
GQ1250+2827 | $192.681029$ | $28.454141$ | $1$ | $0$ | $1$ | $0$ | $0$ | $1.48$ | $22.2\pm 0.2$ | $20.08\pm 0.02$ | $19.03\pm 0.01$ | $18.41\pm 0.01$ | $18.01\pm 0.02$ | $14.27\pm 0.03$ | $13.24\pm 0.03$ | $10.45\pm 0.06$ | $8.0\pm 2.0$ | H20u
GaiaQSp1218+0832 | $184.6254$ | $8.537633$ | $1$ | $0$ | $1$ | $0$ | $0$ | $2.6$ | $23.0\pm 0.4$ | $21.09\pm 0.04$ | $20.33\pm 0.03$ | $20.06\pm 0.03$ | $19.55\pm 0.06$ | $16.0\pm 0.7$ | $15.0\pm 0.9$ | $11.5\pm 0.2$ | $8\pm 3$ | G19p
GaiaQSp1309+2904 | $197.3497$ | $29.08106$ | $1$ | $1$ | $1$ | $0$ | $0$ | $2.66$ | $22.7\pm 0.3$ | $21.12\pm 0.04$ | $19.88\pm 0.02$ | $19.24\pm 0.02$ | $18.92\pm 0.05$ | $15\pm 4$ | $14\pm 5$ | $11.0\pm 0.8$ | $9.0\pm 2.0$ | F20p
GQ124958+273317 | $192.4921$ | $27.95103$ | $1$ | $0$ | $1$ | $0$ | $0$ | $1.95$ | $19.81\pm 0.04$ | $19.58\pm 0.02$ | $19.41\pm 0.02$ | $19.17\pm 0.03$ | $19.03\pm 0.04$ | $16.0\pm 0.7$ | $15.0\pm 0.8$ | $12.0\pm 2.0$ | $8.5\pm 0.3$ | H20p

Table A1: Spectroscopic redshift and astrometric and photometric data of 10 of
the 534 total quasars in the eHAQ-GAIA23 sample. The reference column displays
both the original sample paper and whether (p) or not (u) the quasar has been
published before.