# Strange Quasar Candidates with Abnormal Astrometric Characteristics from
Gaia EDR3 and SDSS (SQUAB-II): Optical Identifications

Xiang Ji1, Zhen-Ya Zheng1,2, Qiqi Wu1,2, Ruqiu Lin1,2, P.T. Rahna1, Yingkang
Zhang1, Shuairu Zhu1,2, Shilong Liao1,2, Zhaoxiang Qi1,2, Tao An1,2,3
1Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan
Road, Shanghai 200030, China
2School of Astronomy and Space Sciences, University of Chinese Academy of
Sciences, No. 19A Yuquan Road, Beijing 100049, People’s Republic of China
3 Key Laboratory of Radio Astronomy and Technology, Chinese Academy of
Sciences, A20 Datun Road, Chaoyang District, Beijing, 100101, P. R. China
jixiang<EMAIL_ADDRESS>
###### Abstract

There are some strange quasars with multiple Gaia detections or observed with
abnormal astrometric characteristics, such as with large proper motions or
significant astrometric noises. Those strange quasars could be potential
candidates of quasar-star pairs, dual quasars (DQs), or lensed quasars (LQs).
Searching for both DQs and LQs is of great importance in many fields of
astrophysics. Here in this work, we select 143 SDSS spectroscopically
confirmed quasars that have multiple Gaia EDR3 detections within 1 arcsec of
the SDSS quasar’s position. We apply several optical identification methods to
classify this sample. We firstly exclude 65 quasar-star pairs via their
stellar features including their parallaxes and proper motions, stellar
features in the SDSS spectra, or via the colour-colour diagram. Based on the
spectral-fitting results, we find 2 DQ candidates, one of which presents a
double-peaked [O III] emission line feature and the other shows a broad
$H_{\beta}$ velocity offset ($\sim$ 870 km s-1) relative to the [O III]
$\lambda$5007 line. Via the colour difference method, we further find 56 LQ
candidates with similar colours in their multiple images. We also cross-match
143 objects with the HST archive and find 19 targets with archival HST images.
Our classification results of those 19 targets are mainly consistent with
previous works.

###### keywords:

quasars: general - methods: observational - gravitational lensing: strong

††pagerange: Strange Quasar Candidates with Abnormal Astrometric
Characteristics from Gaia EDR3 and SDSS (SQUAB-II): Optical
Identifications–References

##  1 Introduction

Quasars are regarded as point-like and distant sources with nearly zero proper
motions, thus they could be used to establish a fundamental celestial
reference frame and characterize the properties of Gaia astrometric solution
(Gaia Collaboration et al., 2018b; Liao et al., 2019, 2021a, 2021b; Gaia
Collaboration et al., 2022). However, there are some strange quasars with
multiple Gaia counterparts or observed with strange astrometric behaviours.
For example, some strange quasars have been observed with large proper motions
or significant astrometric noises, making them unsuitable for establishing
celestial reference frames (e.g., Wu et al., 2021, 2022; Souchay et al.,
2022). These strange quasars are interesting targets to reveal their
structures and figure out the underlying physical mechanisms. The anomaly
could be explained by quasar-star pairs, dual quasars (DQs), or lensed quasars
(LQs), of which the latter two are of great importance in many astrophysical
fields.

Supermassive black hole binaries (SMBHBs) are expected to be abundant in the
centers of many massive galaxies (e.g., Volonteri et al., 2003; Chen, Yu & Lu,
2020) according to the hierarchical evolution models (e.g., Begelman et al.,
1980; Yu, 2002). Searching for SMBHBs at different separations is important
for our understanding of the merging process of galaxies, the formation and
evolution of SMBHBs, and the origin of subsequent gravitational wave radiation
(e.g., Sesana et al., 2009; Chen, Yu & Lu, 2020). Quasar pairs are progenitors
of the SMBHB mergers. In particular, dedicated efforts have been put into
searching for dual quasar candidates at a few kpc scales with double-peaked
features of [O III] (e.g., Liu et al., 2011; Fu et al., 2018), although it has
been proved only a small fraction of double-peaked targets are genuine dual
quasars (e.g. Shen et al., 2011; Comerford et al., 2015). However, there are a
number of quasar pairs with separations from pc to kpc scales reported in the
past few decades (e.g., Liu et al., 2010b; Comerford et al., 2009; Shen et
al., 2011; Ge et al., 2012; Koss et al., 2012; Comerford et al., 2015; Liu et
al., 2018). Among those pairs, there is only one SMBHB with a separation
smaller than 10 pc discovered by the Very Long Baseline Array (VLBA)
(Rodriguez et al., 2006), which indicates that Very Long Baseline
Interferometry (VLBI) can be a powerful tool for confirming pc-scale SMBHBs
(An et al., 2018). Along with the process of merger, quasar pairs would
further become sub-parsec SMBHBs (e.g., Yu et al., 2011). However, sub-pc
scale SMBHBs remain difficult to confirm. This is caused not only by the fact
that these systems are too close to being spatially resolved (e.g., Yu, 2002;
Burke-Spolaor, 2011), but also by the lack of distinct and unique features of
these systems that can be used to confirm their duality (e.g., Popović, 2012;
Graham, 2004). Nevertheless, more than one hundred sub-pc SMBHB candidates
have been found by using indirect signatures such as the periodical variation
of the continuum or broad emission lines (BELs) (e.g., Graham et al., 2015a,
b; Charisi et al., 2016; Li et al., 2016), the optical/UV deficit in the
continuum spectrum of a quasar (e.g., Yan et al., 2015; Zheng et al., 2016),
or double-peaked/asymmetric profiles of BELs (e.g., Tsalmantza et al., 2011;
Eracleous et al., 2012; Shen et al., 2011; Liu et al., 2014; Li et al., 2016;
Ji et al., 2021).

Gravitational lensed quasars are another type of typical strange quasars.
Generally, they are useful tools to probe many important features in both
quasars and lensing galaxies (e.g., Ding et al., 2017; Stacey et al., 2018),
for example, revealing the geometry and kinematics of accretion disks (e.g.,
Blackburne et al., 2011, 2015) or the broad line region of quasars (e.g.,
Sluse et al., 2011), inferring properties of the dark matter halos (e.g.,
Oguri & Keeton, 2004), and even measuring the Hubble constant (e.g., Suyu et
al., 2017).

Thanks to Gaia, there are several works on searching for DQs and LQs from
their astrometric properties. With the release of Gaia data release 2 (Gaia
DR2)(Gaia Collaboration et al., 2018a), over one hundred newly detected LQs
have been reported (e.g. Lemon et al., 2017, 2018, 2019, 2022). Besides, the
technique of machine learning has also been applied to discover the LQs (e.g.
Krone-Martins et al., 2018; Ducourant et al., 2018; Delchambre et al., 2019)
from Gaia DR2. In addition, several new methods have also been proposed to
search for DQs and LQs from Gaia. For example, Shen et al. (2019) and Hwang et
al. (2020) have proposed a new method of varstrometry, i.e., the astrometric
jitter caused by flux variations from the multiple components in one system.
Via this method, they have discovered several double quasars from the
varstrometry selection (Shen et al., 2021; Chen et al., 2022). Another method
is called the Gaia Multi Peak (GMP), i.e., the multiple peaks leading to
another peak in the Gaia point-spread function (Mannucci et al., 2022). It has
been proved with high efficiency in finding compact systems with separations
between the multiple, point-like components in the range of $\sim$ 0.1″to
0.7″. Makarov & Secrest (2022) also provide a list of 44 candidate double or
multiple AGNs with excess proper motions from Gaia EDR3. As a consequence, the
high-quality astrometric measurements from Gaia provide us with a good
opportunity to search for DQs and LQs systematically.

However, there is no systematic search for strange quasars from their
astrometric behavior. The high-quality astrometric measurements from Gaia have
not been carefully considered for those strange quasars. In SQUAB-I (Wu et
al., 2022), we have compiled a sample of strange quasars based on Gaia EDR3
and SDSS DR16Q datasets. Those targets can be divided mainly into two
categories. The first category consists of targets with more than one matched
detection from Gaia within a 1″radius of the SDSS’s position. The second
category consists of SDSS quasars with abnormal astrometric properties
measured from Gaia, for example, with significant astrometric noises. The
present work (SQUAB-II) further examines their structures and makes
classifications of those strange quasars in the first category. We have
developed several methods to get rid of contamination of the quasar-star pairs
and select DQ candidates and LQ candidates for further spectroscopic
confirmation.

The paper is organized as follows. In Section 2, we briefly introduce the data
used and the target selection strategy. Methods to select the potential
quasar-star pairs, LQ candidates, and DQ candidates are described in Section
3. In Section 4, we present optical confirmation of our selected LQ or DQ
candidates with the help of the Pan-STARRS images. In Section 5, we first give
brief discussions about our target selection methods, describe the possibility
of quasar-star superpositions, and judge the extra photometric effects from
nearby objects. We further check the HST archival for available high-
resolution HST images, and also make comparisons with previous works. Finally,
the main conclusions from this work are summarized in Section 6.

Figure 1: Distributions of the redshift and the SDSS g magnitude for all the
targets in our sample. The top and the right histograms show the number
density of the distributions for the redshift and the SDSS g magnitude,
respectively.

##  2 Data and sample

Gaia is an all-sky space astrometric mission (Gaia Collaboration et al., 2016)
with the most precise detection ability currently. It provides high-quality
astrometric measurements including the proper motion and parallax
measurements, and the colour information of three passbands, i.e. G, $\rm
G_{BP}$, and $\rm G_{RP}$. For a target at G=20 mag, the photometric
uncertainties for G, $\rm G_{BP}$ and $\rm G_{RP}$ are about 6, 108, and 52
mmag, respectively. The G band magnitude limit is about 20.7 mag and the
highest angular resolution is $\sim$ 0$\aas@@fstack{\prime\prime}$18\. As a
consequence, the high-quality astrometric measurements from Gaia allow us to
exclude stellar contaminates and identify candidates of both LQs and DQs.

Table 1: Basic properties of the known LQs and DQs (candidates). The columns
$\rm N_{image}$ and $\rm N_{Gaia}$ represent the number of the cores in one
system and that detected by Gaia, respectively.

name | redshift | SDSS $g$ | ra${}_{\textrm{Gaia}}$ | dec${}_{\textrm{Gaia}}$ | $G$ | $G_{\textrm{BP}}$ | $G_{\textrm{RP}}$ | $\rm N_{image}$ | $\rm N_{Gaia}$ | class | reference
---|---|---|---|---|---|---|---|---|---|---|---
081331.28+254503.0 | 1.512 | 16.092 $\pm$ 0.003 | 123.38030149239 | 25.75086321438 | 16.338 $\pm$ 0.012 | 16.211 $\pm$ 0.010 | 15.174 $\pm$ 0.008 | 4 | 2 | LQs | [1][2]
|  |  | 123.38054144472 | 25.75079410426 | 17.940 $\pm$ 0.007 |  |  |  |  |  |
111816.94+074558.2 | 1.736 | 16.252 $\pm$ 0.004 | 169.57066749217 | 7.7662504694 | 17.086 $\pm$ 0.011 | 16.481 $\pm$ 0.031 | 15.853 $\pm$ 0.021 | 4 | 4 | LQs | [3][4]
|  |  | 169.57062595971 | 7.76612498888 | 17.211 $\pm$ 0.009 | 16.611 $\pm$ 0.043 | 15.966 $\pm$ 0.033 |  |  |  |
|  |  | 169.57025416162 | 7.7666884210447 | 18.528 $\pm$ 0.006 | 18.574 $\pm$ 0.074 | 17.979 $\pm$ 0.096 |  |  |  |
|  |  | 169.570157868845 | 7.7661434790373 | 18.866 $\pm$ 0.008 |  |  |  |  |  |
091301.02+525928.8 | 1.380 | 16.868 $\pm$ 0.004 | 138.25417691679 | 52.99138630842 | 16.484 $\pm$ 0.005 | 16.470 $\pm$ 0.016 | 15.552 $\pm$ 0.018 | 2 | 2 | LQs | [5]
|  |  | 138.25463214963 | 52.99124835768 | 17.068 $\pm$ 0.005 | 16.687 $\pm$ 0.270 | 15.753 $\pm$ 0.294 |  |  |  |
141546.24+112943.4 | 2.551 | 17.293 $\pm$ 0.004 | 213.94261159532 | 11.49531201636 | 17.569 $\pm$ 0.015 | 16.788 $\pm$ 0.037 | 16.022 $\pm$ 0.025 | 4 | 3 | LQs | [6]
|  |  | 213.94281909923 | 11.49536505201 | 17.574 $\pm$ 0.016 | 17.002 $\pm$ 0.109 | 16.057 $\pm$ 0.114 |  |  |  |
|  |  | 213.9425258972 | 11.4955317232 | 17.638 $\pm$ 0.019 |  |  |  |  |  |
163348.98+313411.9 | 1.523 | 17.371 $\pm$ 0.005 | 248.4540730856 | 31.5700034202 | 17.432 $\pm$ 0.004 | 17.432 $\pm$ 0.011 | 16.795 $\pm$ 0.010 | 2 | 2 | LQs | [7]
|  |  | 248.45424348917 | 31.56989117914 | 19.132 $\pm$ 0.006 |  |  |  |  |  |
095122.57+263513.9 | 1.249 | 17.729 $\pm$ 0.005 | 147.84403947441 | 26.58723286072 | 17.490 $\pm$ 0.006 | 17.522 $\pm$ 0.019 | 16.855 $\pm$ 0.015 | 2 | 2 | LQs | [8]
|  |  | 147.84431797953 | 26.5870561662 | 19.199 $\pm$ 0.009 |  |  |  |  |  |
091127.61+055054.1 | 2.798 | 18.028 $\pm$ 0.006 | 137.86513574363 | 5.84841020213 | 18.870 $\pm$ 0.014 | 18.397 $\pm$ 0.028 | 17.762 $\pm$ 0.016 | 4 | 4 | LQs | [9]
|  |  | 137.86423192750 | 5.848517226935 | 19.875 $\pm$ 0.008 | 20.073 $\pm 0.092$ | 19.423 $\pm 0.111$ |  |  |  |
|  |  | 137.86505887342 | 5.84829857367 | 19.508 $\pm$ 0.020 |  |  |  |  |  |
|  |  | 137.86505738812 | 5.848563639185 | 19.745 $\pm$ 0.016 |  |  |  |  |  |
024634.09-082536.1 | 1.686 | 18.162 $\pm$ 0.007 | 41.64211559961 | -8.42672188068 | 16.929 $\pm$ 0.014 | 16.959 $\pm$0.044 | 16.502 $\pm$ 0.032 | 2 | 2 | LQs | [10]
|  |  | 41.64186218579 | -8.42654907382 | 18.861 $\pm$ 0.011 |  |  |  |  |  |
133222.62+034739.9 | 1.447 | 19.171 $\pm$ 0.008 | 203.0945132929 | 3.79432898831 | 19.934 $\pm$ 0.010 | 19.437 $\pm$ 0.130 | 18.205 $\pm$ 0.076 | 2 | 2 | LQs | [11]
|  |  | 203.09423472652 | 3.79446633063 | 20.295 $\pm$ 0.023 | 19.331 $\pm$ 0.044 | 18.015 $\pm$ 0.023 |  |  |  |
074653.04+440351.3 | 2.006 | 19.102 $\pm$ 0.008 | 116.72118927293 | 44.06422019002 | 19.472$\pm$ 0.009 | 19.019 $\pm$ 0.065 | 18.287$\pm$ 0.032 | 2 | 2 | LQs | [12]
|  |  | 116.72082301636 | 44.06436462402 | 19.624 $\pm$ 0.010 | 19.203 $\pm$ 0.098 | 18.369 $\pm$ 0.043 |  |  |  |
102111.01+491330.3 | 1.721 | 19.431 $\pm$ 0.014 | 155.29599915159 | 49.22503654914 | 19.525 $\pm$ 0.009 | 19.423 $\pm$0.036 | 18.522 $\pm$ 0.026 | 2 | 2 | LQs | [13]
|  |  | 155.2956378427 | 49.22525313164 | 20.998 $\pm$ 0.025 |  |  |  |  |  |
112818.49+240217.4 | 1.608 | 18.295 $\pm$ 0.007 | 172.07698911386 | 24.03815267311 | 18.531$\pm$ 0.008 | 18.383 $\pm$ 0.034 | 17.598 $\pm$ 0.031 | 2 | 2 | LQs | [14][15]
|  |  | 172.07717757309 | 24.03828375358 | 19.317 $\pm$ 0.008 |  |  |  |  |  |
234330.58+043557.9 | 1.605 | 18.732 $\pm$ 0.006 | 355.87759501346 | 4.5993938917 | 18.635 $\pm$ 0.011 | 18.654 $\pm$ 0.046 | 17.489 $\pm$ 0.034 | 2 | 2 | LQs | [18]
|  |  | 355.87727347014 | 4.59951311798 | 18.961 $\pm$ 0.008 |  |  |  |  |  |
133401.39+331534.3 | 2.419 | 18.752 $\pm$ 0.007 | 203.50578096139 | 33.25947865395 | 19.597$\pm$ 0.006 | 19.115 $\pm$ 0.03 | 18.622 $\pm$ 0.046 | 2 | 2 | LQs | [16]
|  |  | 203.50594425795 | 33.25966704236 | 19.793 $\pm$ 0.007 | 19.047 $\pm$ 0.044 | 18.628 $\pm$ 0.053 |  |  |  |
132128.67+541855.5 | 2.259 | 19.974 $\pm$ 0.019 | 200.36940900851 | 54.31544057296 | 20.265 $\pm$0.013 | 20.185 $\pm$ 0.097 | 19.477 $\pm$ 0.070 | 2 | 2 | LQ candidate | [16]
|  |  | 200.36978382582 | 54.31540192645 | 20.943 $\pm$ 0.033 |  |  |  |  |  |
162501.98+430931.6 | 1.657 | 18.978 $\pm$ 0.009 | 246.25829345634 | 43.15872055958 | 19.233 $\pm$ 0.011 | 19.007 $\pm$ 0.034 | 18.369 $\pm$ 0.042 | 2 | 2 | LQ candidate | [16]
|  |  | 246.25818775771 | 43.15885994875 | 20.016 $\pm$ 0.010 |  |  |  |  |  |
105926.43+062227.4 | 2.199 | 17.633 $\pm$0.005 | 164.86015095584 | 6.37420498672 | 17.462 $\pm$ 0.015 | 17.205 $\pm$ 0.024 | 16.538 $\pm$0.017 | 2 | 2 | LQ candidate | [16][17]
|  |  | 164.86009996452 | 6.37436131019 | 17.946 $\pm$ 0.020 |  |  |  |  |  |
212243.01-002653.6 | 1.975 | 19.025 $\pm$ 0.010 | 320.67921837391 | -0.44828161549 | 19.270 $\pm$ 0.006 | 19.078 $\pm$ 0.043 | 18.243 $\pm$ 0.038 | 2 | 2 | LQ candidate | [19]
|  |  | 320.67912428067 | -0.44816230327 | 19.860 $\pm$ 0.009 |  |  |  |  |  |
205752.47+000635.2 | 1.135 | 18.943 $\pm$ 0.009 | 314.46863940567 | 0.10978924318 | 18.718 $\pm$ 0.004 | 18.744 $\pm$ 0.016 | 18.201 $\pm$0.031 | 2 | 2 | LQ candidate | [19]
|  |  | 314.46874170038 | 0.11004439111 | 20.407 $\pm$ 0.007 |  |  |  |  |  |
084129.77+482548.3 | 2.948 | 19.283 $\pm$ 0.010 | 130.37404617611 | 48.43013479612 | 19.478 $\pm$ 0.011 | 19.19 $\pm$ 0.038 | 18.454 $\pm$ 0.038 | 2 | 2 | DQs | [20][21]
|  |  | 130.37417633919 | 48.43005444844 | 19.78 $\pm$ 0.037 | 19.345$\pm$ 0.091 | 18.267$\pm$ 0.115 |  |  |  |
084710.40-001302.6 | 0.628 | 19.333 $\pm$ 0.010 | 131.79334744852 | -0.21735281015 | 19.713 $\pm$ 0.009 | 19.245 $\pm$ 0.037 | 18.157 $\pm$ 0.027 | 2 | 2 | DQs | [22][23]
|  |  | 131.79349676225 | -0.21757556956 | 20.304 $\pm$ 0.012 |  |  |  |  |  |
123915.40+531414.6 | 0.200 | 19.206 $\pm$ 0.007 | 189.8143793831 | 53.2374973296 | 20.399 $\pm$ 0.023 | 18.719 $\pm$ 0.045 | 17.053 $\pm$ 0.019 | 2 | 2 | DQ candidate | [24]
|  |  | 189.81404358851 | 53.23722292116 | 21.414 $\pm$ 0.041 | 18.615 $\pm$0.090 | 17.018 $\pm$0.048 |  |  |  |

  * •

References: [1] Reimers et al. (2002); [2]Jackson et al. (2015); [3] Young et
al. (1981); [4] Chiba et al. (2005); [5] Lehár et al. (2000); [6] Magain et
al. (1988); [7] Morgan et al. (2001); [8] Schechter et al. (1998); [9] Burud
et al. (1998); [10] Inada et al. (2005); [11] Morokuma et al. (2007); [12]
Inada et al. (2007); [13] Pindor et al. (2006); [14] Inada et al. (2014); [15]
Agnello et al. (2018); [16] Lemon et al. (2017); [17] Ducourant et al. (2018);
[18] Krone-Martins et al. (2019) [19] Lacki et al. (2009); [20]Shen et al.
(2021); [21] Mannucci et al. (2022); [22]Inada et al. (2008); [23] Silverman
et al. (2020); [24]Smith et al. (2010);

Our target sample consists of sources from Gaia EDR3 (Gaia Collaboration et
al., 2021) and our parent quasar sample are spectroscopic identified quasars
from SDSS DR16 (Jönsson et al., 2020; Lyke et al., 2020). In this work, we
focus on the sources identified as one quasar in SDSS but with two or more
Gaia detections within 1″ 111Given the fiber diameter of 3″ for the SDSS
spectra, we require separation radius of 1″ to search for more close pairs. of
the SDSS quasar’s position. Our sample consists of 143222In our paper I, there
are 155 targets fulfilling the criteria. However, we find 12 of them labeled
as ’stars’ according to the SDSS spectra, although they are still in the SDSS
DR16q catalog. We get rid of those targets in this work. SDSS quasars in
total. The sample selection method has been described in SQUAB-I in detail.

The distributions of the SDSS g magnitudes and the spectroscopic redshifts
from SDSS for all these strange SDSS quasars are shown in Figure 1.
Furthermore, among the 143 SDSS quasars, there are 22 SDSS quasars reported by
previous works, of which 14 are known LQs, 5 are LQ candidates, 2 are known
DQs, and 1 is a DQ candidate (see Table 1 for details). Those known LQs/DQs
would serve as a reference when carrying out the colour difference analysis in
the following section.

##  3 Method

In this section, we mainly describe our procedures to classify the strange
SDSS quasars in detail. Generally, our procedures can be divided into three
steps. Firstly, we get rid of quasar-star pairs with distinct stellar features
in Section 3.1. Then in Section 3.2, we further deal with the SDSS spectra and
search for double-peaked or offset emission line profiles, which could be
indirect features of the existence of DQs. Finally, we search for LQ
candidates with similar colour differences between their multiple detections
from Gaia in Section 3.3.

###  3.1 Stellar Features

We regard targets as quasar-star pairs once it fulfills one of the following
three conditions. Firstly, we select targets of which one or more detections
from Gaia in one system have proper motions or parallaxes greater than
5$\sigma$ significance, i.e.,

$|\varpi/\sigma_{\varpi}|>5\ or\ |\mu/\sigma_{\mu}|>5,$ (1)

where $\varpi$, $\sigma_{\varpi}$, $\mu$ and $\sigma_{\mu}$ represent the
parallax, parallax error, the total proper motion, and the total proper motion
error, respectively. Secondly, their SDSS spectra could be well explained by
quasar-star superpositions as suggested by Shen et al. (2022), using a method
called the principal component analysis (PCA). Thirdly, we use the colour-
colour diagram as proposed in (Bailer-Jones et al., 2019; Gaia Collaboration
et al., 2022) to select objects with similar colors as stars. Considering that
only a small portion of those targets have measurements for both detections of
$\rm G_{BP}$ and $\rm G_{RP}$ passbands from Gaia in one system, we divide
them into two sub-samples. Those targets with both detections of $\rm G_{BP}$
and $\rm G_{RP}$ passbands are labeled as sub-sample A. Those with only one
detection are labeled as sub-sample B. We further pick out targets of which
one or more Gaia detections have a larger confidence level to be a star than
to be a quasar or galaxy in the colour-colour diagram. See Section 4.1 for
more details. With the above three criteria, we have identified 65 quasar-star
pairs, which are excluded in the following analysis.

###  3.2 Emission line features

Generally, the double-peaked narrow emission line of [O III] could be an
indirect signature of the presence of DQs and a series of efforts have been
put into searching for DQs through this way (e.g. Comerford et al., 2012; Liu
et al., 2010a; Smith et al., 2010). On the other aspect, the offset line
properties could also be a possible signature of galaxy merger and hence imply
the existence of offset active galactic nuclei (AGNs) or DQs (e.g. Comerford
et al., 2013). Usually, the offset could be manifested as the difference
between the broad/narrow emission lines and the quasar rest frame (the host
galaxy) (e.g. Eracleous et al., 2012; Comerford & Greene, 2014; Tsalmantza et
al., 2011) or the broad emission line in respect to the narrow emission line
(e.g. Shen et al., 2013).

Considering the different redshifts for the targets in our sample, we search
for the potential double-peaked features of broad $\rm H_{\beta}$, $\rm
H_{\alpha}$, $\rm Mg\ II$, and $\rm C\ IV$ emission lines as well as the
narrow [O III] emission line. We first visually inspect the spectra and try to
find the potential double-peaked features. In particular, there are 17 targets
in total in our sample with broad $\rm H_{\beta}$ emission lines and [O III]
narrow emission lines due to redshift restriction. Then we use one or two
Gaussians to fit both the broad and narrow emission lines (Ge et al., 2012;
Feng et al., 2021). Then the line offset between the broad $\rm H_{\beta}$
line relative to the [O III] $\lambda$5007 line can be figured out based on
the spectra fitting results.

###  3.3 Colour difference

Generally, the colour difference between lensed images in the same LQ system
is usually very small. For the remaining targets in sub-sample A, we derive
the colour difference of $\rm(G_{BP}-G_{RP})_{d1}-(G_{BP}-G_{RP})_{d2}$ for
them, where $\rm(G_{BP}-G_{RP})_{d1}$ and $\rm(G_{BP}-G_{RP})_{d2}$ represent
the colour for the brighter detection and the dimmer detection in the same
system, respectively. Due to the lack of the $\rm G_{BP}$ and $\rm G_{RP}$
measurements for the dimmer detection for the remaining targets in sub-sample
B, we thus combine the $\rm G_{BP}$, and $\rm G_{RP}$ of the brighter
detection together with the SDSS g and i magnitudes to obtain the colour
difference, i.e., $\rm(G_{BP}-G_{RP})_{d1}-(g-i)_{tot}$. The colour
information $\rm(g-i)_{tot}$ from SDSS could represent the color of the system
as a whole.

Figure 2: Flowchart of the classification procedures of the targets in our
sample. Firstly we compile a sample of SDSS quasars with multiple detections
from Gaia EDR3. The details of each classification criteria are described in
Section 3. We also mark the numbers of the selected targets in each step.

The above classification procedures are shown in Figure 2. Based on these
steps, we select 65 quasar-star pairs, 2 DQ candidates (1 previously
reported), and 56 LQ candidates (18 previously known LQs including 5
candidates). However, there are 20 targets that can not be specified or
classified based on the available data via our methods. We present the
detailed analysis and results in section 4.

Figure 3: Colour-colour diagram for all the Gaia detections with measurements
of magnitudes of G, $\rm G_{BP}$, and $\rm G_{RP}$ passbands in our sample.
The red and green circles represent for the Gaia detections from sub-sample A
and sub-sample B, respectively. For comparison, we have shown the colour-
colour diagram from Gaia Collaboration et al. (2022) as the translucent
background in the above figure. The blue, black, and yellow parts in the
background represent the quasars, stars, and galaxies, respectively. We also
mark the Gaia detections from the known LQs, LQ candidates, DQs, and DQ
candidates in our sample with green pluses, blue pluses, cyan crosses, and
blue crosses, respectively.

##  4 Results

In this section, we present the main classification results of our sample.
Firstly, we get rid of the quasar-star pairs based on the method described in
Section 3. Secondly, we show the spectra fitting results of the discovered 2
DQ candidates. In the following, we single out 56 LQ candidates and show the
optical confirmation with the help of the Pan-STARRS images of those
candidates. Finally, we show the distributions of the separations as a
function of the redshift for the quasars in our sample.

###  4.1 Quasar-star pairs

Based on the high-quality astrometric measurements from Gaia, we first get rid
of targets in our sample of which one or more detections from Gaia have large
proper motion/parallax measurements. We find 55 systems in total. Those
systems are more likely to be quasar-star pairs. In a recent paper (Shen et
al., 2022), they used a PCA method to get rid of quasar-star superpositions.
After cross-matched with our 143 targets, we find 8 targets in common, which
have already been selected by the proper motion/parallax criteria.

According to the colour-colour diagram as proposed in Bailer-Jones et al.
(2019) and Gaia Collaboration et al. (2022), stars, quasars and galaxies are
located in the different regions in the $\rm(G-G_{RP})$ versus $\rm(G_{BP}-G)$
colour-colour diagram, which could help us to distinguish different types of
the targets in our sample. As shown in Figure 3, most of our targets locate in
the region of quasars and extend to the region of galaxies, which takes on
similar features of the distributions for the LQs identified in the
literature. Still, there are a small fraction of detections from Gaia with
higher probabilities of being stars than that being quasars or galaxies. We
further select 10 systems according to the colour-colour diagram. Based on all
the above analyses, we identified 65 quasar-star pairs. We exclude those
systems in the following analysis.

Figure 4: Spectra fitting results and the optical identifications of the two
DQ candidates we selected from our sample. The top and bottom panels are for
the target SDSS J123915.40+531414.6 and SDSS J221130.31+291949.0,
respectively. Left panels: the black, red, and blue lines are for the
observational data, model, and Gaussians of the broad/narrow components. The
values of the reduced $\chi$-square and the best-fitting parameters are marked
in the upper left and right, respectively. Right panels: Pan-STARRS composite
colour images (Pan-STARRS i band in red, Pan-STARRS r band in green, and Pan-
STARRS g band in blue. We invert the colormap for the sake of presentation.)
for the selected DQ candidates. For each image, the size is 10″ $\times$ 10″ ,
with the source id and the redshift marked in the upper left and upper right
corners, respectively. The center of the green circle in each panel is from
the SDSS coordinates, with a radius of 1$\aas@@fstack{\prime\prime}$5\. In
addition, we also mark the detections from Gaia in red dots in each panel.
Figure 5: Left panel: colour differences of the
$\rm(G_{BP}-G_{RP})_{d1}-(G_{BP}-G_{RP})_{d2}$ as a relationship of the
separations for the remaining targets in sub-sample A. The red empty circles,
cyan stars, blue stars and green triangles are for the targets, the known DQs,
the DQ candidates, and the known LQs, respectively. We also display the error
bars for the reported DQs, DQ candidates, and LQs. The red dotted lines are
the reference lines that indicate the range we select for the LQ candidates.
Middle panel: colour differences of $\rm(G_{BP}-G_{RP})_{d1}-(g-i)_{tot}$ as a
relationship of the separations for the remaining targets in sub-sample A.
Legend are similar to that in the left panel. Right panel: similar to that in
the middle panel but for the remaining targets in sub-sample B. The black
empty circles, cyan stars, green triangles, and blue triangles are for the
targets, the known DQs, known LQs and LQ candidates in sub-sample B,
respectively. The red dotted lines are the reference lines that indicate the
range we select for the LQ candidates in this sub-sample.

###  4.2 DQ candidates

We select DQ candidates mainly via their spectral properties. There is one
target, SDSS J123915.40+531414.6, with a distinct double-peaked emission line
feature which has already been reported by Smith et al. (2010). We use one
Gaussian and two Gaussians to fit the broad and narrow components,
respectively. The best fitting results are shown in the top left panel of
Figure 4. We further make optical confirmations via the Pan-STARRS composite
colour image with the Gaia detections superimposed, which has not been
considered before. However, due to the limited resolution of the Pan-STARRS
image, the structure of this target is still elusive.

We also find one target, SDSS J221130.31+291949.0, with a distinct line offset
of the broad $H_{\beta}$ emission line with respect to the narrow [O III]
$\lambda$5007 emission line. We use one Gaussian to fit both the broad and
narrow emission lines and obtain the positions of the peaks for the emission
lines. The best-fitting results and the optical confirmation are shown in the
bottom left and right panels of Figure 4, respectively. Via the fitting
results, we estimate the velocity offset to be about $\sim$ 870 km s-1.
Considering the line offset property as well as the two detections from Gaia,
this target is a potential DQ candidate. Although, we can’t exclude the
possibility of alternative explanations, like a recoiling black hole
(Eracleous et al., 2012). We are carrying up follow-up observations to reveal
its nature.

Table 2: Basic properties of the LQ candidates from sub-sample A. The known LQs have been labeled with stars in the upper right of their source ids. name | redshift | SDSS $g$ | ra${}_{\textrm{Gaia}}$ | dec${}_{\textrm{Gaia}}$ | $G$ | $\rm G_{\textrm{BP}}$ | $\rm G_{\textrm{RP}}$
---|---|---|---|---|---|---|---
111816.94+074558.2∗ | 1.736 | 16.252 $\pm$ 0.004 | 169.57066749217 | 7.7662504694 | 17.086 $\pm$ 0.011 | 16.481 $\pm$ 0.031 | 15.853 $\pm$ 0.021
|  |  | 169.57062595971 | 7.76612498888 | 17.211 $\pm$ 0.009 | 16.611 $\pm$ 0.043 | 15.966 $\pm$ 0.033
|  |  | 169.57025416162 | 7.7666884210447 | 18.528 $\pm$ 0.006 | 18.574 $\pm$ 0.074 | 17.979 $\pm$ 0.096
|  |  | 169.570157868845 | 7.7661434790373 | 18.866 $\pm$ 0.008 |  |
091301.02+525928.8∗ | 1.380 | 16.868 $\pm$ 0.004 | 138.25417691679 | 52.99138630842 | 16.484 $\pm$ 0.005 | 16.470 $\pm$ 0.016 | 15.552 $\pm$ 0.018
|  |  | 138.25463214963 | 52.99124835768 | 17.068 $\pm$ 0.005 | 16.687 $\pm$ 0.270 | 15.753 $\pm$ 0.294
141546.24+112943.4∗ | 2.551 | 17.293 $\pm$ 0.004 | 213.94261159532 | 11.49531201636 | 17.569 $\pm$ 0.015 | 16.788 $\pm$ 0.037 | 16.022 $\pm$ 0.025
|  |  | 213.94281909923 | 11.49536505201 | 17.574 $\pm$ 0.016 | 17.002 $\pm$ 0.109 | 16.057 $\pm$ 0.114
|  |  | 213.9425258972 | 11.4955317232 | 17.638 $\pm$ 0.019 |  |
133222.62+034739.9∗ | 1.447 | 19.171 $\pm$ 0.008 | 203.0945132929 | 3.79432898831 | 19.934 $\pm$ 0.010 | 19.437 $\pm$ 0.130 | 18.205 $\pm$ 0.076
|  |  | 203.09423472652 | 3.79446633063 | 20.295 $\pm$ 0.023 | 19.331 $\pm$ 0.044 | 18.015 $\pm$ 0.023
074653.04+440351.3∗ | 2.006 | 19.102 $\pm$ 0.008 | 116.72118927293 | 44.06422019002 | 19.472 $\pm$ 0.009 | 19.019 $\pm$ 0.065 | 18.287 $\pm$ 0.032
|  |  | 116.72082301636 | 44.06436462402 | 19.624 $\pm$ 0.010 | 19.203 $\pm$ 0.098 | 18.369 $\pm$ 0.043
133401.39+331534.3∗ | 2.419 | 18.752 $\pm$ 0.007 | 203.50578096139 | 33.25947865395 | 19.597 $\pm$ 0.006 | 19.115 $\pm$ 0.030 | 18.622 $\pm$ 0.046
|  |  | 203.50594425795 | 33.25966704236 | 19.793 $\pm$ 0.007 | 19.047 $\pm$ 0.044 | 18.628 $\pm$ 0.053
081246.41+200729.9 | 1.480 | 19.638 $\pm$ 0.013 | 123.19338721538 | 20.12504974558 | 20.166 $\pm$ 0.014 | 19.753 $\pm$ 0.080 | 19.119 $\pm$ 0.070
|  |  | 123.19339549084 | 20.12490340453 | 20.436 $\pm$ 0.018 | 19.962 $\pm$ 0.093 | 18.965 $\pm$ 0.237
080009.98+165509.4 | 0.709 | 17.883 $\pm$ 0.006 | 120.04153952266 | 16.91934178839 | 18.304 $\pm$ 0.015 | 17.996 $\pm$ 0.033 | 17.448 $\pm$ 0.024
|  |  | 120.04170900144 | 16.91920386557 | 18.709 $\pm$ 0.005 | 18.153 $\pm$ 0.004 | 17.533 $\pm$ 0.067
074800.55+314647.7 | 1.408 | 19.803 $\pm$ 0.015 | 117.00230747636 | 31.77985563261 | 20.033 $\pm$ 0.007 | 19.797 $\pm$ 0.062 | 18.811 $\pm$ 0.051
|  |  | 117.00227692679 | 31.77999820592 | 20.319 $\pm$ 0.014 | 19.864 $\pm$ 0.190 | 18.833 $\pm$ 0.041
092011.82+373223.7 | 0.385 | 19.680 $\pm$ 0.026 | 140.049490253 | 37.53993026155 | 21.228 $\pm$ 0.023 | 20.012 $\pm$ 0.161 | 18.177 $\pm$ 0.040
|  |  | 140.04912272088 | 37.53992137658 | 21.530 $\pm$ 0.031 | 19.923 $\pm$ 0.023 | 18.170 $\pm$ 0.117
091150.63+240545.7 | 2.479 | 19.274 $\pm$ 0.011 | 137.96108613064 | 24.09605291507 | 19.799 $\pm$ 0.010 | 19.378 $\pm$ 0.042 | 18.764 $\pm$ 0.050
|  |  | 137.96091707746 | 24.09603443454 | 19.892 $\pm$ 0.014 | 19.498 $\pm$ 0.467 | 18.738 $\pm$ 0.175
100229.47+444942.8 | 2.048 | 18.425 $\pm$ 0.007 | 150.62297307375 | 44.82851082314 | 18.940 $\pm$ 0.010 | 18.511 $\pm$ 0.038 | 17.888 $\pm$ 0.028
|  |  | 150.62269763487 | 44.82856564947 | 19.012 $\pm$ 0.006 | 18.519 $\pm$ 0.030 | 17.903 $\pm$ 0.032
122518.66+483116.3 | 3.082 | 18.131 $\pm$ 0.006 | 186.32777588616 | 48.5211465442 | 18.008 $\pm$ 0.004 | 18.100 $\pm$ 0.014 | 17.253 $\pm$ 0.012
|  |  | 186.32778403906 | 48.5213967025 | 19.258 $\pm$ 0.004 | 18.151 $\pm$ 0.135 | 17.338 $\pm$ 0.105
161320.01+170839.2 | 1.547 | 18.889 $\pm$ 0.009 | 243.33351087171 | 17.14416276643 | 19.453 $\pm$ 0.005 | 19.021 $\pm$ 0.093 | 18.506 $\pm$ 0.071
|  |  | 243.3333279996 | 17.14427796005 | 19.486 $\pm$ 0.011 | 18.907 $\pm$ 0.050 | 18.468 $\pm$ 0.032
Table 3: Basic properties of the LQ candidates from sub-sample B. The known LQs and the reported LQ candidates have been labeled with stars and pluses in the upper right of their source ids, respectively. name | redshift | SDSS $g$ | ra${}_{\textrm{Gaia}}$ | dec${}_{\textrm{Gaia}}$ | $G$ | $\rm G_{\textrm{BP}}$ | $\rm G_{\textrm{RP}}$
---|---|---|---|---|---|---|---
081331.28+254503.0∗ | 1.512 | 16.092 $\pm$ 0.003 | 123.38030149239 | 25.75086321438 | 16.338 $\pm$ 0.012 | 16.211 $\pm$ 0.010 | 15.174 $\pm$ 0.008
|  |  | 123.38054144472 | 25.75079410426 | 17.940 $\pm$ 0.007 |  |
091127.61+055054.1∗ | 2.798 | 18.028 $\pm$ 0.006 | 137.86513574363 | 5.84841020213 | 18.870 $\pm$ 0.014 | 18.397 $\pm$ 0.028 | 17.762 $\pm$ 0.016
|  |  | 137.86423192750 | 5.848517226935 | 19.875 $\pm$ 0.008 | 20.073 $\pm$ 0.092 | 19.423 $\pm$ 0.111
|  |  | 137.86505887342 | 5.84829857367 | 19.508 $\pm$ 0.020 |  |
|  |  | 137.86505738812 | 5.848563639185 | 19.745 $\pm$ 0.016 |  |
163348.98+313411.9∗ | 1.523 | 17.371 $\pm$ 0.004 | 248.4540730856 | 31.5700034202 | 17.432 $\pm$ 0.004 | 17.432 $\pm$ 0.011 | 16.795 $\pm$ 0.010
|  |  | 248.45424348917 | 31.56989117914 | 19.132 $\pm$ 0.006 |  |
095122.57+263513.9∗ | 1.249 | 17.729 $\pm$ 0.005 | 147.84403947441 | 26.58723286072 | 17.490 $\pm$ 0.006 | 17.522 $\pm$ 0.019 | 16.855 $\pm$ 0.015
|  |  | 147.84431797953 | 26.5870561662 | 19.199 $\pm$ 0.009 |  |
102111.01+491330.3∗ | 1.721 | 19.431 $\pm$ 0.011 | 155.29599915159 | 49.22503654914 | 19.525 $\pm$ 0.009 | 19.423 $\pm$ 0.036 | 18.522 $\pm$ 0.026
|  |  | 155.2956378427 | 49.22525313164 | 20.998 $\pm$ 0.025 |  |
112818.49+240217.4∗ | 1.608 | 18.295 $\pm$ 0.007 | 172.07698911386 | 24.03815267311 | 18.531 $\pm$ 0.008 | 18.383 $\pm$ 0.034 | 17.598 $\pm$ 0.031
|  |  | 172.07717757309 | 24.03828375358 | 19.317 $\pm$ 0.008 |  |
234330.58+043557.9∗ | 1.605 | 18.732 $\pm$ 0.006 | 355.87759501346 | 4.5993938917 | 18.635 $\pm$ 0.011 | 18.654 $\pm$ 0.046 | 17.489 $\pm$ 0.034
|  |  | 355.87727347014 | 4.59951311798 | 18.961 $\pm$ 0.008 |  |
105926.43+062227.4+ | 2.199 | 17.633 $\pm$ 0.005 | 164.86015095584 | 6.37420498672 | 17.462 $\pm$ 0.015 | 17.205 $\pm$ 0.024 | 16.538 $\pm$ 0.017
|  |  | 164.86009996452 | 6.37436131019 | 17.946 $\pm$ 0.020 |  |
132128.67+541855.5+ | 2.259 | 19.974 $\pm$ 0.019 | 200.36940900851 | 54.31544057296 | 20.265 $\pm$ 0.013 | 20.185 $\pm$ 0.097 | 19.477 $\pm$ 0.070
|  |  | 200.36978382582 | 54.31540192645 | 20.943 $\pm$ 0.033 |  |
212243.01-002653.6+ | 1.975 | 19.025 $\pm$ 0.009 | 320.67921837391 | -0.44828161549 | 19.270 $\pm$ 0.006 | 19.078 $\pm$ 0.043 | 18.243 $\pm$ 0.038
|  |  | 320.67912428067 | -0.44816230327 | 19.860 $\pm$ 0.009 |  |
205752.47+000635.2+ | 1.135 | 18.943 $\pm$ 0.009 | 314.46863940567 | 0.10978924318 | 18.718 $\pm$ 0.004 | 18.744 $\pm$ 0.016 | 18.201 $\pm$ 0.031
|  |  | 314.46874170038 | 0.11004439111 | 20.407 $\pm$ 0.007 |  |
162501.98+430931.6+ | 1.657 | 18.978 $\pm$ 0.009 | 246.25829345634 | 43.15872055958 | 19.233 $\pm$ 0.011 | 19.007 $\pm$ 0.034 | 18.369 $\pm$ 0.042
|  |  | 246.25818775771 | 43.15885994875 | 20.016 $\pm$ 0.010 |  |
003715.87+205825.6 | 2.049 | 19.658 $\pm$ 0.017 | 9.31620407013 | 20.9737723715 | 19.458 $\pm$ 0.011 | 19.358 $\pm$ 0.061 | 18.617 $\pm$ 0.037
|  |  | 9.31590244232 | 20.97379245651 | 20.460 $\pm$ 0.020 |  |
014613.39+291548.7 | 1.095 | 18.385 $\pm$ 0.007 | 26.55577686969 | 29.26353639033 | 18.437 $\pm$ 0.006 | 18.571 $\pm$ 0.026 | 17.776 $\pm$ 0.026
|  |  | 26.55596783268 | 29.2636809947 | 20.349 $\pm$ 0.014 |  |
074942.51+171512.1 | 2.165 | 19.212 $\pm$ 0.011 | 117.42710879551 | 17.25336133864 | 19.017 $\pm$ 0.007 | 19.070 $\pm$ 0.031 | 18.266 $\pm$ 0.031
|  |  | 117.42738076567 | 17.25340257501 | 20.500 $\pm$ 0.012 |  |
082341.07+241805.4 | 1.814 | 17.490 $\pm$ 0.005 | 125.92116891379 | 24.30157031702 | 17.915 $\pm$ 0.006 | 17.711 $\pm$ 0.020 | 16.721 $\pm$ 0.022
|  |  | 125.92115552747 | 24.30139480146 | 18.253 $\pm$ 0.007 |  |
094046.85+471421.1 | 1.394 | 19.419 $\pm$ 0.012 | 145.19521322175 | 47.23919254429 | 19.475 $\pm$ 0.007 | 19.376 $\pm$ 0.048 | 18.622 $\pm$ 0.029
|  |  | 145.19524563209 | 47.23939009799 | 20.715 $\pm$ 0.013 |  |
093801.86+421603.3 | 1.708 | 19.059 $\pm$ 0.010 | 144.50770088391 | 42.26761835091 | 19.723 $\pm$ 0.009 | 19.410 $\pm$ 0.044 | 18.770 $\pm$ 0.032
|  |  | 144.50793689869 | 42.26748578136 | 20.055 $\pm$ 0.009 |  |
091704.23+312810.7 | 1.168 | 17.801 $\pm$ 0.005 | 139.26763531237 | 31.46963605502 | 17.682 $\pm$ 0.009 | 17.759 $\pm$ 0.028 | 17.242 $\pm$ 0.022
|  |  | 139.26738611027 | 31.46968976471 | 19.894 $\pm$ 0.009 |  |
103451.36+361331.4 | 0.510 | 18.312 $\pm$ 0.007 | 158.71403496132 | 36.22533464576 | 18.774 $\pm$ 0.008 | 18.575 $\pm$ 0.034 | 17.987 $\pm$ 0.040
|  |  | 158.71406359898 | 36.22557455555 | 20.374 $\pm$ 0.013 |  |
101504.76+123022.2 | 1.705 | 17.625 $\pm$ 0.005 | 153.76982886867 | 12.50619163833 | 17.359 $\pm$ 0.006 | 17.455 $\pm$ 0.015 | 16.92 $\pm$ 0.009
|  |  | 153.76965447866 | 12.50611075649 | 19.716 $\pm$ 0.014 |  |
101329.41+443829.8 | 3.011 | 19.132 $\pm$ 0.011 | 153.37259938695 | 44.64159607963 | 18.931 $\pm$ 0.005 | 19.098 $\pm$ 0.025 | 18.356 $\pm$ 0.023
|  |  | 153.3723606294 | 44.64181558952 | 20.937 $\pm$ 0.035 |  |
095636.42+690028.3 | 1.975 | 18.266 $\pm$ 0.007 | 149.15203897788 | 69.0078790747 | 18.165 $\pm$ 0.004 | 18.161 $\pm$ 0.016 | 17.335 $\pm$ 0.017
|  |  | 149.15154197643 | 69.00778738764 | 19.548 $\pm$ 0.009 |  |
111853.50+074946.0 | 2.042 | 18.935 $\pm$ 0.009 | 169.72295455365 | 7.82939200109 | 18.842 $\pm$ 0.006 | 18.768 $\pm$ 0.032 | 18.143 $\pm$ 0.026
|  |  | 169.72292312097 | 7.82953941198 | 19.952 $\pm$ 0.014 |  |
120012.26+160724.5 | 2.137 | 18.804 $\pm$ 0.008 | 180.05111651692 | 16.12351965363 | 18.819 $\pm$ 0.006 | 18.897 $\pm$ 0.027 | 18.314 $\pm$ 0.026
|  |  | 180.05112084092 | 16.1232566556 | 20.842 $\pm$ 0.021 |  |
130505.67-023219.0 | 1.374 | 18.983 $\pm$ 0.010 | 196.27367026925 | -2.53866483065 | 18.903 $\pm$ 0.007 | 18.883 $\pm$ 0.035 | 18.199 $\pm$ 0.046
|  |  | 196.27366189289 | -2.53843594023 | 20.299 $\pm$ 0.011 |  |
125640.55+105742.5 | 0.773 | 18.419 $\pm$ 0.007 | 194.16891486138 | 10.96185898762 | 18.744 $\pm$ 0.006 | 18.638 $\pm$ 0.032 | 18.297 $\pm$ 0.021
|  |  | 194.16912055423 | 10.96190030544 | 20.627 $\pm$ 0.012 |  |
123846.68+644836.6 | 1.560 | 17.968 $\pm$ 0.006 | 189.69441220471 | 64.81015615149 | 18.502 $\pm$ 0.006 | 18.382 $\pm$ 0.021 | 17.509 $\pm$ 0.022
|  |  | 189.69506922748 | 64.81025202878 | 21.115 $\pm$ 0.026 |  |
151109.85+335701.6 | 0.799 | 18.707 $\pm$ 0.008 | 227.79107461147 | 33.95044311403 | 19.004 $\pm$ 0.005 | 18.845 $\pm$ 0.031 | 18.282 $\pm$ 0.025
|  |  | 227.7910201002 | 33.95074072852 | 20.087 $\pm$ 0.006 |  |
142322.93+154437.5 | 1.325 | 19.440 $\pm$ 0.012 | 215.84552422351 | 15.74377030263 | 19.531 $\pm$ 0.01 | 19.477 $\pm$ 0.058 | 18.714 $\pm$ 0.044
---|---|---|---|---|---|---|---
|  |  | 215.84575905158 | 15.74379606868 | 20.753 $\pm$ 0.018 |  |
142341.94+204001.5 | 0.842 | 18.970 $\pm$ 0.009 | 215.92477238695 | 20.66712154342 | 19.12 $\pm$ 0.01 | 19.153 $\pm$ 0.041 | 18.559 $\pm$ 0.034
|  |  | 215.92463966802 | 20.66685847755 | 20.903 $\pm$ 0.029 |  |
141742.28+243723.4 | 0.692 | 18.739 $\pm$ 0.008 | 214.42621742001 | 24.62319243904 | 18.676 $\pm$ 0.005 | 18.594 $\pm$ 0.021 | 18.113 $\pm$ 0.017
|  |  | 214.42606048912 | 24.62300673577 | 20.523 $\pm$ 0.011 |  |
161153.19+054947.9 | 1.318 | 18.720 $\pm$ 0.008 | 242.97162386769 | 5.82998682859 | 18.994 $\pm$ 0.004 | 19.162 $\pm$ 0.036 | 18.315 $\pm$ 0.021
|  |  | 242.97153951361 | 5.82978515317 | 21.097 $\pm$ 0.03 |  |
212315.32+095050.6 | 0.437 | 19.321 $\pm$ 0.013 | 320.81394284429 | 9.84747613285 | 19.729 $\pm$ 0.011 | 19.171 $\pm$ 0.066 | 18.340 $\pm$ 0.035
|  |  | 320.81378526283 | 9.84730546774 | 19.994 $\pm$ 0.008 |  |
211731.94+090237.1 | 0.960 | 19.410 $\pm$ 0.012 | 319.38306783267 | 9.04364377762 | 19.343 $\pm$ 0.013 | 19.197 $\pm$ 0.042 | 18.596 $\pm$ 0.038
|  |  | 319.38321747176 | 9.04364517363 | 20.193 $\pm$ 0.018 |  |
170256.01+252444.9 | 2.177 | 19.057 $\pm$ 0.011 | 255.73339296378 | 25.41257027385 | 19.233 $\pm$ 0.005 | 19.183 $\pm$ 0.041 | 18.512 $\pm$ 0.028
|  |  | 255.73328397873 | 25.4122801499 | 20.122 $\pm$ 0.007 |  |
223512.90+314611.6 | 2.248 | 19.069 $\pm$ 0.010 | 338.80379947433 | 31.76989519099 | 18.989 $\pm$ 0.004 | 19.136 $\pm$ 0.027 | 18.416$\pm$ 0.021
|  |  | 338.80345519001 | 31.76996483494 | 20.974 $\pm$ 0.017 |  |
222819.72+173255.7 | 2.125 | 18.898 $\pm$ 0.009 | 337.08219088284 | 17.54880244878 | 18.855 $\pm$ 0.008 | 18.949 $\pm$ 0.033 | 18.278 $\pm$ 0.033
|  |  | 337.08196086552 | 17.54895879448 | 20.564 $\pm$ 0.011 |  |
221217.12+035040.5 | 0.214 | 17.411 $\pm$ 0.005 | 333.07131876628 | 3.8445960753 | 18.037 $\pm$ 0.025 | 17.932 $\pm$ 0.078 | 17.130 $\pm$ 0.043
|  |  | 333.0711619343 | 3.84480172068 | 20.785 $\pm$ 0.023 |  |
220531.24+232339.5 | 1.169 | 19.138 $\pm$ 0.010 | 331.38020828903 | 23.39432374363 | 19.009 $\pm$ 0.004 | 19.098 $\pm$ 0.031 | 18.322 $\pm$ 0.023
|  |  | 331.37996426152 | 23.3941929473 | 20.693 $\pm$ 0.011 |  |
233522.51+320109.1 | 0.904 | 19.683 $\pm$ 0.013 | 353.8438295556 | 32.01918772811 | 19.458 $\pm$ 0.005 | 19.370 $\pm$ 0.036 | 18.699 $\pm$ 0.028
|  |  | 353.84384120973 | 32.01935785875 | 20.547 $\pm$ 0.019 |  |
233348.78+285412.8 | 1.671 | 18.407 $\pm$ 0.007 | 353.45329231124 | 28.90360063212 | 18.191 $\pm$ 0.004 | 18.312 $\pm$ 0.019 | 17.618 $\pm$ 0.015
|  |  | 353.45328903418 | 28.90338416532 | 20.301 $\pm$ 0.01 |  |
Figure 6: Pan-STARRS composite colour images of the selected LQ candidates
from the sub-sample A, which are listed in Table 2. The legends are similar to
that in the right panels of Figure 4.

###  4.3 LQ candidates

We use the colour difference method to select LQ candidates, which is based on
the fact that the colour difference between the multiple lensed images is
usually very small for one LQ system. For the remaining 17 targets in sub-
sample A, we show the colour difference of
$\rm(G_{BP}-G_{RP})_{d1}-(G_{BP}-G_{RP})_{d2}$ as a relationship of the
separations as indicated in the left panel of Figure 5. The separations are
calculated from the coordinates measured from Gaia in one system. If the
system has multiple Gaia detections, we choose the detections with
measurements of $\rm G_{BP}$, and $\rm G_{RP}$ bands preferentially to carry
out the color difference analysis. Also, we have shown the results of the
known LQs, known DQs, and DQ candidates in this sub-sample for comparison.
Finally, we set the value of $\pm$ 0.4 of the colour difference to select the
LQ candidates in sub-sample A, which is consistent with that in Delchambre et
al. (2019). By applying this criteria, We have selected 14 LQ candidates
including all the 6 known ones from sub-sample A.

For the remaining 61 targets in sub-sample B, we use Gaia $\rm G_{BP}$ and
$\rm G_{RP}$ magnitudes as well as SDSS g and i bands to obtain the colour
difference as described in section 3. To set the limit of the selection
criteria, we use the targets in sub-sample A as a reference as shown in the
middle panel of Figure 5. Based on the distributions for the known LQs, we set
the following criteria to select the LQ candidates for those targets in sub-
sample B, ie, 0.2<$\rm(G_{BP}-G_{RP})_{d1}-(g-i)_{tot}$ <0.6. The right panel
of Figure 5 shows the result of the colour difference for the remaining 61
targets in sub-sample B. Also, we have labeled the reported LQs, LQ
candidates, reported DQs, and DQ candidates from previous works for
comparison. Via this criteria, we have identified most of the known LQs
quasars or candidates (7 out of 8 known LQs and all the reported LQ
candidates) in sub-sample B as LQ candidates.

Figure 7: Legends similar to that in Figure 6 but for the LQ candidates from
sub-sample B which are listed in Table LABEL:table:tb3.

Based on the above analysis, we finally select 14 LQ candidates (including 6
known LQs) in sub-sample A and 42 LQ candidates (including 7 known LQs and 5
reported LQ candidates) in sub-sample B. The selected LQ candidates from sub-
sample A and B are summarized in Table 2 and LABEL:table:tb3, respectively.
Furthermore, we show the optical Pan-STARRS composite colour images of the
selected LQ candidates in Figure 6 and Figure 7. However, their structures are
still elusive, and further high spatial-resolved spectroscopic confirmation is
needed to finally pin them down from alternatives.

###  4.4 Distributions of the Separations as a Function of Redshift

Figure 8: Distributions of the redshift verse the angular separation in arcsec
(left panel) and the physical separation in kpc scale (right panel) for the
targets in our sample, respectively. The red dots represent the targets in our
sample and we mark the sources with HST observations in blue stars. For
comparison, we also include the DQs or LQs from Anguita et al. (2018),
Silverman et al. (2020), Chen et al. (2022), Inada et al. (2008) and More et
al. (2016) in purple pluses, green triangles, cyan triangles, black triangles,
and green stars, respectively. The resolution of SDSS and HST are marked in
green dotted lines for reference.  Figure 9:  Colour-colour diagram for the
Gaia detections with measurements of magnitudes of G, $\rm G_{BP}$, and $\rm
G_{RP}$ passbands for the remaining targets in the fake samples A and B in the
left and right panels, respectively. The background is similar to that in
Figure 3.

Since there are at least two detections from Gaia for the sources in our
sample when cross-matched with SDSS DR16Q, thus the angular and the physical
separations can be calculated accordingly. The distributions of the angular
and projected separations for individual remaining targets after Step One as a
function of the redshift are shown in the left and right panels of Figure 8,
respectively. For the sources with more than two Gaia detections, we show the
smallest separations between the multiple detections from Gaia in one system.
We also show the resolution of SDSS and HST in blue and green dotted lines in
both panels in Figure 8 for reference.

From Figure 8, we could see that the angular separations of the sources are
about 1″ more or less, corresponding to projected separations in the range
from 1 to 10 kpc at the redshift range of z = 0 $\sim$ 3.5. And all the
angular or physical separations of the sources in our sample are beyond the
limit of the HST resolution, with only the separations of five sources larger
than the limit resolution of SDSS. We also show the known DQs or LQs with
multiple detections from Gaia for comparison. Generally, the separations of
our sample are typically larger than those in Chen et al. (2022) but smaller
than those in More et al. (2016) and Inada et al. (2008).

##  5 Discussions

###  5.1 Discussion of our selection methods

To improve the accuracy and help us better constrain the types of those
abnormal quasars, we have introduced a succession of different methods. Here
we discuss briefly about our current classification strategy:

  * •

Stellar features: we have introduced a method to pick out the quasar-star
pairs via their stellar features, including the proper motion or parallax
criteria, stellar features in the SDSS spectra, and via the colour-colour
diagram. We should note that the proper motion or parallax criteria would mis-
identify quasar-star pairs. This has been pointed out by Makarov & Secrest
(2022) that a small portion of quasars with excess proper motions turn out to
be either dual quasars or lensed quasars. Furthermore, we consider the effects
of quasar-star superposition and estimate the probability in section 5.2. For
the quasar-star pairs selected via the stellar features in the SDSS spectra,
they all have been picked out by the proper motion or the parallax criteria.
As for the colour-colour diagram proposed by Bailer-Jones et al. (2019), which
uses a machine learning method to classify the objects from Gaia DR2 into
stars, quasars, and galaxies. The spectroscopic classifications cross-matched
with Gaia is served as the training sets for their justifications. Hence the
colour-colour diagram is based on the statistical distributions of a large
sample. However, there are still some uncertainties around the boundaries
between the three types, which may lead to bias when applied to our sample.

  * •

Emission line features: we have found a promising way to find the DQ
candidates by combining the line offset or the double-peaked properties of the
emission lines as well as the multiple detections from Gaia. However, the
double-peaked or offset properties can also be explained by different physical
interpretations. Future high-resolution spectra are still needed to pin them
down from alternatives.

  * •

Colour difference: there are still some uncertainties based on our current
colour selection strategy. Firstly, we set the limits of the colour difference
according to the known LQs and DQs in our sample. As a consequence, there are
still some uncertainties due to the small sample of the confirmed LQs or DQs
in our sample. While including the known LQs with larger separations would
bring in a mis-match of other nearby objects when carrying out the colour
analysis. Secondly, the colour difference may also be contaminated by the
lensing galaxies. Thirdly, it’s hard to separate the DQs from the LQs without
follow-up spectroscopic confirmations. The reported DQ SDSS
J084129.77+482548.3 is also classified as LQ candidates via our colour
difference method. Since some DQs may also take on similar colors while some
not as determined by the redshifts of the quasars. We could not exclude the
possibility that the selected LQ candidates maybe turn out to be DQs. We tend
to regard those targets with similar color differences as LQ candidates in
this work.

###  5.2 Quasar-star superposition

Although we have excluded the quasar-star pairs by searching for their stellar
features, there are still some possibilities that these systems are DQs or LQs
with a superpositioned star. We find that two reported LQs, SDSS
081331.28+254503.0 (Reimers et al., 2002; Jackson et al., 2015) and SDSS
J234330.58+043557.9 (Krone-Martins et al., 2019), are classified as quasar-
star pairs according to our proper motion/parallax criteria. Both of these two
LQs have two Gaia detections. We think that Gaia only detected one of the
lensed images and the other Gaia detection came from a superpositioned star
with large proper motion or parallax. The HST archival images of the known LQ
SDSS 081331.28+254503.0 clearly showed the lensed quasar system and Gaia only
detected the brightest lensed image and a superpositioned star. The situation
is also similar for some DQs. For our selected dual quasar candidate SDSS
J221130.31+291949.0, we also find that one Gaia detection was observed with
large proper motion. However, we still propose it as a dual quasar candidate
in this work considering its line offset properties as well as the two
detections from Gaia. We are carrying up follow-up spectroscopic confirmation
to pin it down from alternatives.

We also test the quasar-star superposition by using the method proposed by
Chen et al. (2022). For the SDSS DR16q quasars, we offset their decl. by $+$
or $-$ $1^{\prime}$ and search for nearby Gaia DR3 sources at the offset
positions within 1" radius. We require that the G-band magnitude $\leq$ 20.7
mag for the cross-matched targets. We find 655 and 653 targets fulfilling the
above conditions, which are labeled as fake sample A and fake sample B,
respectively. We use the proper motion/parallax criteria and the colour-colour
diagram method in Step one to classify quasar-star pairs in both samples. We
find that 584 and 572 targets could be selected by the proper motion/parallax
criteria in fake samples A and B, respectively. For the remaining targets, 37
and 41 targets could be further selected by the colour-colour diagram method
as shown in the left and right panels of Figure 9. Therefore, it indicates
that $\sim$ 95 percent of the targets in fake sample A and $\sim$ 94 percent
in fake sample B could be selected as quasar-star pairs by the proper
motion/parallax criteria and the colour-colour diagram method. As for our
sample, it indicates that $\sim$ 4 targets in the remaining 78 targets after
Step One are quasar-star pairs.

###  5.3 Extra Photometric Errors from Nearby Objects

As suggested by the referee, here we discuss the reliability of colours for
compact double sources. Gaia’s $\rm G_{BP}$ and $\rm G_{RP}$ photometric
magnitudes are integrated low-resolution spectro-photometry in two different
passbands. According to measurement details of low-resolution BP/RP spectra
from Gaia in section 2.2 from De Angeli et al. (2022), only the measurements
of the brightest source are recorded and transmitted fully to the ground for
the overlapping sources in crowded regions. In other words, if the source in
our sample has BP/RP measurements for both detections from Gaia in the same
system, it should be well-resolved and measured. Otherwise, only the brighter
detection has BP/RP detections. Generally, a series of procedures have been
developed to deblend the low-resolution spectra in crowded regions for $\rm
G_{BP}$ and $\rm G_{RP}$ passbands with Gaia. However, the deblending details
will not be pubic until the release of Gaia DR4.

We then use the measurement errors from Gaia to judge the extra photometric
errors from nearby objects when measuring $\rm G_{BP}$ and $\rm G_{RP}$. We
have divided our targets into two groups with the G band magnitude differences
larger or smaller than 1 mag between the two detections in the same system. We
also consider different separations between the two detections in the same
system in each group. The results of the photometric measurements as a
relationship of measurement errors from Gaia for the two groups, as well as
isolated Quasars, are shown in Figure 10. From this figure, we could see that
the dimmer counterpart would certainly bring extra uncertainties when
measuring the G, $\rm G_{BP}$, and $\rm G_{RP}$ magnitudes, especially for
those targets with smaller magnitude differences between the two detections in
the same system. The relationship is consistent with that from isolated QSOs
as a whole with slightly larger deviations. We also find that there are no
distinct differences for the targets with different separations in both sub-
samples. Overall, the compact nearby sources would bring in extra errors no
more than 0.02, 0.1, and 0.1 for sources brighter than 20 mag in G, $\rm
G_{BP}$, and $\rm G_{RP}$ bands, respectively.

Figure 10:  G, $G_{BP}$, and $G_{RP}$ magnitude measurements as a relationship
with their errors for the double quasars in our sample. The left and right
panels are for the targets which the G band magnitude differences are larger
or smaller than 1 mag between the two detections in the same system ,
respectively. In each separate panel, we mark the targets with the separations
larger than 1.5 ″, between 1 ″and 1.5 ″and smaller than 1 ″in green, blue and
red dots, respectively. For comparison, we also plot the results from the
isolated QSOs from SDSS DR16 cross-matched with Gaia with only one Gaia
detection in small black dots in each panel.

###  5.4 HST coverage

Considering the advantages of HST’s high-resolution imaging in resolving the
physical structures of those strange quasars, we have searched the HST archive
and found 19 objects with available HST observations in our sample. The basic
properties of all those targets with HST observations are summarised in Table
4, with the available archival HST images shown in Figure 11. We have also
compared our classification results with previous works for those targets in
each panel. Our classification results are mainly consistent with previous
works, except for the DQ SDSS J084129.77+482548.3. The reason has been
discussed in section 5.1.

As shown in Figure 11, the coordinates measured from Gaia match well with that
from the HST images for most targets, with only a few of them like SDSS
J081603.83+ 430521.1, showing minor offsets. This misalignment may be caused
by the coordinates offset from the HST observations. On the other aspect, the
observations from HST clearly reveal multiple cores for those objects. This
proves that the high-quality astrometric measurement from Gaia could be used
as a powerful tool when searching for the LQs or DQs. There are 8 targets
without spectroscopic confirmations and we are planning the follow-up
spectroscopic observations to reveal their nature.

###  5.5 Comparison with related works

In this work, we mainly focus on the classification of the spectroscopic
quasars identified from SDSS DR16q with multiple Gaia detections within a
radius of 1″ from SDSS positions. We introduce our classification methods with
the help of the known LQs and DQs in our sample as a reference. There are only
a small portion of targets with available HST observations and our
classification results for those targets are mainly consistent with previous
works.

As described in the introduction, there are also two different methods
searching for DQs/LQs with the Gaia data. The method of varstrometry has been
proved to be very efficient for DQs/LQs with substantial variability. Also,
they have found the efficiency of 53 % and 22 % for both spectroscopic and
non-spectroscopic targets (Chen et al., 2022). As for the method of GMP, they
show the advantages of selecting DQs/LQs at the separations of 0.1″to 0.7 ″.
The above two methods are applicable for both Gaia-resolved and Gaia-
unresolved targets. After cross-matched, we find 8 sources in common with Shen
et al. (2021) and Chen et al. (2022), and 4 sources in common with Mannucci et
al. (2022). Although all the selection methods could have different selection
functions, all these prove that the high-resolution measurements from Gaia
could be an efficient method in searching for DQs or LQs when cross-matched
with available quasar catalogs.

Table 4: Basic properties of the targets in our sample with HST observations.

name | redshift | SDSS g | ra${}_{\textrm{Gaia}}$ | dec${}_{\textrm{Gaia}}$ | G | $\rm G_{BP}$ | $\rm G_{RP}$ | camera | class | ref
---|---|---|---|---|---|---|---|---|---|---
081331.28+254503.0 | 1.512 | 16.092 $\pm$ 0.003 | 123.38030149239 | 25.75086321438 | 16.338 $\pm$ 0.012 | 16.211 $\pm$ 0.010 | 15.174 $\pm$ 0.008 | WFC3 | LQs | [1][2]
|  |  | 123.38054144472 | 25.75079410426 | 17.940 $\pm$ 0.007 |  |  |  |  |
111816.94+074558.2 | 1.736 | 16.252 $\pm$ 0.004 | 169.57066749217 | 7.7662504694 | 17.086 $\pm$ 0.011 | 16.481 $\pm$ 0.031 | 15.853 $\pm$ 0.021 | WFPC2 | LQs | [3][4]
|  |  | 169.57062595971 | 7.76612498888 | 17.211 $\pm$ 0.009 | 16.611 $\pm$ 0.043 | 15.966 $\pm$ 0.033 |  |  |
|  |  | 169.57025416162 | 7.7666884210447 | 18.528 $\pm$ 0.006 | 18.574 $\pm$ 0.074 | 17.979 $\pm$ 0.096 |  |  |
|  |  | 169.570157868845 | 7.7661434790373 | 18.866 $\pm$ 0.008 |  |  |  |  |
091301.02+525928.8 | 1.380 | 16.868 $\pm$ 0.004 | 138.25417691679 | 52.99138630842 | 16.484 $\pm$0.005 | 16.470 $\pm$ 0.016 | 15.552 $\pm$ 0.018 | NICMOS | LQs | [5]
|  |  | 138.25463214963 | 52.99124835768 | 17.068 $\pm$ 0.005 | 16.687 $\pm$ 0.270 | 15.753 $\pm$ 0.294 |  |  |
141546.24+112943.4 | 2.551 | 17.293 $\pm$ 0.004 | 213.94261159532 | 11.49531201636 | 17.569 $\pm$ 0.015 | 16.788 $\pm$ 0.037 | 16.022 $\pm$ 0.025 | WFPC2 | LQs | [6]
|  |  | 213.94281909923 | 11.49536505201 | 17.574 $\pm$ 0.016 | 17.002 $\pm$ 0.109 | 16.057 $\pm$ 0.114 |  |  |
|  |  | 213.9425258972 | 11.4955317232 | 17.638 $\pm$ 0.019 |  |  |  |  |
163348.98+313411.9 | 1.523 | 17.371 $\pm$ 0.004 | 248.4540730856 | 31.5700034202 | 17.432 $\pm$ 0.004 | 17.432 $\pm$ 0.011 | 16.795 $\pm$ 0.010 | WFPC2 | LQs | [7]
|  |  | 248.45424348917 | 31.56989117914 | 19.132 $\pm$ 0.006 |  |  |  |  |
095122.57+263513.9 | 1.249 | 17.729 $\pm$ 0.005 | 147.84403947441 | 26.58723286072 | 17.49 $\pm$ 0.006 | 17.522 $\pm$ 0.019 | 16.855 $\pm$0.015 | WFPC2 | LQs | [8]
|  |  | 147.84431797953 | 26.5870561662 | 19.199 $\pm$ 0.009 |  |  |  |  |
091127.61+055054.1 | 2.798 | 18.028 $\pm$ 0.006 | 137.86513574363 | 5.84841020213 | 18.870 $\pm$ 0.014 | 18.397 $\pm$ 0.028 | 17.762 $\pm$ 0.016 | WFC3 | LQs | [9]
|  |  | 137.86505887342 | 5.84829857367 | 19.508 $\pm$ 0.020 |  |  |  |  |
|  |  | 137.86505738812 | 5.848563639185 | 19.745 $\pm$ 0.016 |  |  |  |  |
|  |  | 137.86423192750 | 5.848517226935 | 19.875 $\pm$ 0.008 | 20.073 $\pm$ 0.092 | 19.423 $\pm$ 0.111 |  |  |
024634.09-082536.1 | 1.686 | 18.162 $\pm$ 0.006 | 41.64211559961 | -8.42672188068 | 16.929 $\pm$ 0.014 | 16.959$\pm$ 0.044 | 16.502 $\pm$ 0.032 | WFC3 | LQs | [10]
|  |  | 41.64186218579 | -8.42654907382 | 18.861 $\pm$ 0.011 |  |  |  |  |
074653.04+440351.3 | 2.006 | 19.102 $\pm$ 0.008 | 116.72118927293 | 44.06422019002 | 19.472 $\pm$ 0.009 | 19.019 $\pm$ 0.065 | 18.287 $\pm$ 0.032 | WFPC2 | LQs | [11]
|  |  | 116.72082301636 | 44.06436462402 | 19.624 $\pm$ 0.010 | 19.203 $\pm$ 0.098 | 18.369 $\pm$ 0.043 |  |  |
102111.01+491330.3 | 1.721 | 19.431 $\pm$ 0.011 | 155.29599915159 | 49.22503654914 | 19.525 $\pm$ 0.009 | 19.423 $\pm$ 0.036 | 18.522 $\pm$ 0.026 | WFPC2 | LQs | [12]
|  |  | 155.2956378427 | 49.22525313164 | 20.998 $\pm$ 0.025 |  |  |  |  |
084129.77+482548.3 | 2.948 | 19.283 $\pm$ 0.010 | 130.37404617611 | 48.43013479612 | 19.478 $\pm$ 0.011 | 19.19 $\pm$ 0.038 | 18.454 $\pm$ 0.038 | WFC3 | DQs | [13][14]
|  |  | 130.37417633919 | 48.43005444844 | 19.780 $\pm$ 0.037 | 19.345 $\pm$ 0.091 | 18.267 $\pm$ 0.115 |  |  |
212243.01-002653.6 | 1.975 | 19.025 $\pm$ 0.009 | 320.67921837391 | -0.44828161549 | 19.27 $\pm$ 0.006 | 19.078 $\pm$ 0.043 | 18.243 $\pm$ 0.038 | WFC3 | LQ candidate | [15]
|  |  | 320.67912428067 | -0.44816230327 | 19.86 $\pm$ 0.009 |  |  |  |  |
123915.40+531414.6 | 0.200 | 19.206 $\pm$ 0.007 | 189.8143793831 | 53.2374973296 | 20.399 $\pm$ 0.023 | 18.719 $\pm$ 0.045 | 17.053 $\pm$ 0.019 | WFC3 | DQ candidate | [16]
|  |  | 189.81404358851 | 53.23722292116 | 21.414 $\pm$ 0.041 | 18.615 $\pm$0.090 | 17.018 $\pm$ 0.048 |  |  |
081603.83+430521.1 | 0.587 | 20.693 $\pm$ 0.017 | 124.01580245472 | 43.08921103297 | 20.624 $\pm$ 0.016 | 21.003 $\pm$ 0.212 | 19.148 $\pm$ 0.081 | WFC3 |  |
|  |  | 124.01606562402 | 43.08920154678 | 20.823 $\pm$ 0.034 | 20.193 $\pm$0.013 | 18.975 $\pm$ 0.061 |  |  |
074800.55+314647.7 | 1.408 | 19.985 $\pm$ 0.015 | 117.00230747636 | 31.77985563261 | 20.033 $\pm$ 0.007 | 19.797 $\pm$ 0.062 | 18.811 $\pm$ 0.051 | WFC3 |  |
|  |  | 117.00227692679 | 31.77999820592 | 20.319 $\pm$ 0.014 | 19.864 $\pm$ 0.190 | 18.833 $\pm$ 0.041 |  |  |
094007.38+334609.6 | 1.786 | 19.849 $\pm$ 0.014 | 145.0309042995 | 33.76931645031 | 19.591 $\pm$ 0.008 | 19.446 $\pm$ 0.037 | 18.215 $\pm$ 0.031 | WFC3 |  |
|  |  | 145.03068493606 | 33.76923979991 | 19.711 $\pm$ 0.006 | 19.451 $\pm$ 0.119 | 18.316 $\pm$ 0.053 |  |  |
091938.92+621951.1 | 1.270 | 19.378 $\pm$ 0.011 | 139.9122152145 | 62.33088639396 | 18.763 $\pm$ 0.003 | 18.937 $\pm$ 0.017 | 17.974 $\pm$ 0.013 | WFC3 |  |
|  |  | 139.91201908388 | 62.33106405635 | 20.494 $\pm$ 0.008 |  |  |  |  |
215444.04+285635.0 | 0.723 | 20.002 $\pm$ 0.017 | 328.68353178311 | 28.94315441283 | 19.608 $\pm$ 0.019 | 19.288 $\pm$ 0.040 | 18.712 $\pm$ 0.063 | WFC3 |  |
|  |  | 328.68348587194 | 28.94297732821 | 20.348 $\pm$ 0.026 | 18.573 $\pm$ 1.295 | 18.776 $\pm$ 0.156 |  |  |
082341.07+241805.4 | 1.814 | 17.602 $\pm$ 0.005 | 125.92116891379 | 24.30157031702 | 17.915 $\pm$ 0.006 | 17.711 $\pm$ 0.020 | 16.721 $\pm$ 0.022 | WFC3 |  |
|  |  | 125.92115552747 | 24.30139480146 | 18.253 $\pm$ 0.007 |  |  |  |  |

  * •

References: [1]Reimers et al. (2002); [2]Jackson et al. (2015); [3] Young et
al. (1981); [4] Chiba et al. (2005); [5] Lehár et al. (2000); [6] Magain et
al. (1988); [7] Morgan et al. (2001); [8] Schechter et al. (1998); [9] Burud
et al. (1998); [10] Inada et al. (2005); [11] Inada et al. (2007); [12] Pindor
et al. (2006); [13]Shen et al. (2021); [14]Mannucci et al. (2022); [15] Lacki
et al. (2009); [16]Smith et al. (2010)

Figure 11: Archival HST images of the targets listed in Table 4. The
resolution for each separate panel is 10″ $\times$ 10 ″. In each separate
panel, the coordinates from Gaia are represented in red points and the green
circle indicates a radius of 1.5 ″. The source id, the redshift, the
reference, and the classification results are labeled in the top left, top
right, bottom left and bottom right, respectively. We also indicate the camera
used below the source id in each panel. Previously known LQs, LQ candidates,
DQs, and DQ candidates are labeled as ’LQs’, ’LQ candidate’, ’DQs’ and ’DQ
candidate’, respectively.

##  6 Conclusions

In this paper, we present the optical confirmations of the 143 strange quasars
with multiple detections from the Gaia EDR3. Our sample mainly consists of
spectroscopically identified quasars from SDSS DR16 which have multiple
detections from Gaia within a radius of 1″. The angular separations of the
targets are $\sim$ 1 arcsec more or less, corresponding to physical
separations of several kpc scales.

Based on the stellar features including proper motion/parallax, stellar-like
spectra from SDSS, and colour-colour diagram, we find 65 quasar-star pairs. We
also discover 2 DQ candidates, one of which presents a double-peaked [O III]
emission line feature and the other shows an obvious broad $H_{\beta}$
velocity offset relative to the [O III] $\lambda$ 5007 line. In addition, we
further find 56 LQ candidates with similar colour differences, including 13
known LQs and 5 reported LQ candidates. Although, the resolution of the
available Pan-STARRS images is not high enough. With more high-resolution
observations in the future, we would certainly reveal their structures and
clarify their basic properties. We also check the HST archive for available
high-resolution observations and find 19 targets with archival HST
observations, of which 10 are reported LQs and 1 reported DQ. Our
classification results for those 19 targets are mainly consistent with
previous works.

We also see the advantage of the higher resolution of HST compared with Pan-
STARRS in resolving the basic structure of those strange quasars. Similarly,
the Multiple Channel Imager (MCI) on board the Chinese Space Station Telescope
(CSST) has many desirable features including high resolution, deep field of
view, and multiple filters. With its broad wavelength coverage and high
angular resolution, CSST offers scientific opportunities and a great legacy
value that complement other forthcoming space-based and ground-based surveys.
CSST is ideally suited for astrometric studies of objects fainter than 20 mag,
it will extend Gaia’s mapping of the sky to fainter magnitudes, adding precise
positions, parallaxes, distance estimates, and extinction estimates. With the
operation of CSST in the future, we will endeavor to advance our research and
identify more DQs and LQs.

## Acknowledgments

We would like to thank the referee for very helpful comments, especially the
suggestion to check the reliability of colours for compact double sources.
Z.Y.Z. acknowledges the supports by National Key R&D Program of China
No.2022YFF0503402 and the National Science Foundation of China (12022303). We
acknowledge the science research grants from the China Manned Space Project
with No.CMS-CSST-2021-A07, No.CMS-CSST-2021-A04, No.CMS-CSST-2021-B04, NO.CMS-
CSST-2021-A12 and NO.CMS-CSST-2021-B10. This work has also been supported by
the Youth Innovation Promotion Association CAS, the grants from the Natural
Science Foundation of Shanghai through grant 21ZR1474100, and National Natural
Science Foundation of China (NSFC) through grants 12173069, and 11703065.

## Data Availability

The data sets underlying this article are publicly available. They can be
accessed from the Gaia archive (https://gea.esac.esa.int/archive/) and the
SDSS SkyServer (https://skyserver.sdss.org/dr16/en/tools/search/). The
Archival HST images are available via MAST
(https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html).

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