© The Authors 2024

1 Introduction

Supermassive black hole binaries (SMBHBs) are crucial for our understanding of the evolutionary process of the massive objects in the Universe (e.g., Dosopoulou & Antonini 2017), the verification of gravitational theories (e.g., Healy et al. 2012), and the origin of the gravitational waves (e.g., Belczynski et al. 2014). Rodriguez et al. (2006) discovered a SMBHB with a projected separation of 7.3 pc using the Very Long Baseline Array (VLBA), finding it to be the closest known black hole pair at the time. Many SMBHB candidates have been reported over the years (e.g., Ju et al. 2013; Graham et al. 2015a,b; Wang et al. 2017; Liu et al. 2019). However, it is difficult to identify them because the components of the systems are too close to one another to be distinguished using telescopes.

Dual active galactic nuclei (AGNs) at kiloparsec (kpc) separations are the precursors of SMBHBs, but have more easily observable separations, and so it is important to carry out systematic investigations and observations of them. In the past decade, a large number of AGN pairs (dual and lensed AGNs) with different separations have been discovered. In particular, with the release of high-resolution data from Gaia Data Release 2 (DR2) (Gaia Collaboration 2018) and Data Release 3 (DR3) (Gaia Collaboration 2021, 2023b), many authors have developed effective and systematic methods to search for AGN pairs using Gaia data (e.g., Ji et al. 2023). Shen et al. (2019) proposed that AGN pair candidates can be selected using the varstrometry method, which is a strong testament to the effectiveness of the Gaia data in the search for dual AGNs (e.g., Chen et al. 2022; Li et al. 2023).

Recently, Mannucci et al. (2022) proposed the Gaia multipeak (GMP) method for effectively selecting dual AGN candidates. The GMP method selects AGN pair candidates using the Gaia multi-peak parameter ipd_ f rac_multi_ peak (FMP). The basic principle is that when Gaia is observing pairs with angular separations of between 0.15″ and 0.8″, if the telescope cannot resolve them effectively, a secondary peak might be detected in the profile. The FMP parameter reports the percentage (from 0 to 100) of Gaia scans showing the presence of multiple peaks. Mannucci et al. (2023) showed that for sources with G < 20.5 mag and δ (separation) > 0.15″, the cut of FMP ≥ 8 ensures a low contamination and high efficiency. Based on this method and high-precision spectroscopic observations, many AGN pairs have been identified (e.g., Ciurlo et al. 2023; Scialpi et al. 2024).

The purity of the AGN pair candidates selected using varstrometry, GMP, or other astrometric methods (e.g., Wu et al. 2022) can be improved by considering the quasars that have already been spectroscopically identified by different telescopes, such as the Sloan Digital Sky Survey quasar catalog (SDSS, Lyke et al. 2020), the LAMOST quasar survey (Dong et al. 2018), the DESI spectroscopic survey (Chaussidon et al. 2023), and so on. The Million Quasars (Milliquas) catalog (Flesch 2023) collects almost all the quasars currently identified for which large-sample spectroscopy has been cataloged, with a total number of 0.9 million. The benefits of using these catalogs as input catalogs are obvious, as all quasars are spectroscopically identified. However, these catalogs are incomplete for most of the sky region (see Flesch 2023, for the sky coverage of these catalogs). Therefore, in order to expand the sample of AGN pair candidates, it is necessary to select reliable quasar candidates from the sources without spectroscopic observations.

Over the past decade, many outstanding projects aiming to select quasar candidates have been completed (e.g., Secrest et al. 2015; Bailer-Jones et al. 2019). Various groups have obtained large numbers of quasar candidates based on different methods, bringing the number of quasar candidates to several million. After the publication of the Gaia DR3, with its high-precision astrometric data with multi-color magnitudes, Gaia Collaboration (2023a) obtained a high-completeness but low-purity sample of quasar candidates numbering 6.6 million using multiple methods. Based on this catalog, some pure quasar candidate catalogs have been constructed. For example, Storey-Fisher et al. (2024) built a pure QUAIA catalog of 1.3 million quasar candidates based on the Gaia proper motions and unWISE color (Lang 2014), while Fu et al. (2024) constructed the CatNorth catalog of 1.5 million quasar candidates (>90% purity) with data from Gaia, Pan-STARRS1 (Flewelling et al. 2020), and CatWISE2020 (Marocco et al. 2021). An important objective in the creation of these substantial collections of quasar candidates was the establishment of the Gaia optical celestial reference frame (Klioner et al. 2022). Therefore, the principal characteristics of these catalogs are their high purity and the almost zero parallax and proper motion of their sources. When selecting AGN pair candidates using these catalogs, the high purity may result in a significant loss of completeness, because AGN pairs are different from normal quasars in various ways:

1. Proper motions and parallaxes: as quasars are extremely distant, it is generally accepted that their parallaxes and proper motions should be consistent with zero. Therefore, most quasar candidate-selection techniques use cut-off parallaxes and proper motions (e.g., Lindegren et al. 2018; Klioner et al. 2022; Wu et al. 2023). However, AGN pairs may show observable parallaxes and proper motions due to apparent movements of their optical centers caused by the variability of the two AGNs (Makarov & Secrest 2022).

2. Optical color and infrared (IR) color: Gaia photometry is optimized for point sources, and this can lead to shifts in the photometry of some dual and lensed AGNs. Also, as the blue and red photometry is derived from extended spectra (De Angeli et al. 2023), the bp − ɡ and ɡ − rp, which are commonly used in the selection of quasar candidates, may not be reliable for sources with components. Regarding the IR color, there are no known differences that exist between AGN pairs and normal AGNs when z > 0.5, and so we explore and discuss this aspect in the present paper.

This paper is organized as follows. In Sect. 2 we introduce the data we used and analyze their characteristics. In Sect. 3 we explore the differences in astrometry and colors between GMP AGN pair candidates and normal AGNs and determine our final selection criteria. In this section, we also describe the construction of our dual and lensed AGN candidate catalog (DULAG) in detail. The properties of the catalog are demonstrated in Sect. 4. In Sect. 5 we provide conclusion and discuss some future prospects in terms of selection.

2 Data

In this section we present our input catalog for AGN pair selection, which is composed of the Gaia quasar candidate catalog and the Milliquas catalog. We also introduce an AGN pair candidate catalog confirmed by observations, which provides an important basis for our selection.

2.1 The Gaia quasar candidate catalog

As mentioned above, a lot of work has been carried out on quasar selection. However, many such works use strict astrometric, IR, and/or optical color criteria to improve the purity of the samples. Gaia has released a catalog of 6.6 million quasar candidates (the qso_candidates table) (Gaia Collaboration 2023a), which is an exception. This catalog is composed of multiple samples that are selected based on Gaia spectra, colors, astrometric parameters, photometric light curves, surface brightness, and so on. In the process of generating this catalog, the authors aim to provide a sample that is as complete as possible. As a major contributor to the catalog, the Discrete Source Classifier (DSC) module (Delchambre et al. 2023) provides about 5.5 million sources. The DSC module contains three classifiers: Specmod, Allosmod, and Combmod. Specmod and Allosmod provide the classification probabilities of the sources using BP/RP spectra and other data of the objects, respectively. Combmod gives the classification probabilities by combining the above two classifiers. The online documentation shows that when sources with a Combmod quasar probability of greater than 0.5 are selected, about 5.2 million sources are available, corresponding to a completeness of about 90%. In addition to these sources, the qso_candidates table contains an additional 0.3 million sources filtered by Specmod and Allosmod, and 1.1 million sources filtered by other modules (e.g., Variability module, Gaia-CRF3 module, etc., all modules that offer a purity of higher than 90%). Therefore, using this table as a major input catalog when performing AGN pair candidate selection could ensure a very high degree of completeness.

The qso_candidates table covers the whole sky, including crowded regions such as the Galactic Plane and Large and Small Magellanic Clouds (LMC and SMC). However, crowded foreground stars are very serious contaminants when selecting GMP AGN pair candidates. The reasons for this are described below.

1. Excessive stellar density in these regions can lead to serious errors when matching with other catalogs (Klioner et al. 2022), and matching errors will reduce the reliability of the selection procedure.

2. These regions will suffer more severe interstellar extinction than others, which will make the color of the extragalactic sources very different from other regions (high Galactic latitude) (Fu et al. 2021).

3. For the AGN pairs selected using the GMP method, the most important parameter is FMP, which, as described above, characterises the probability that a secondary peak is detected in the source light profile. In these crowded regions, the angular separation between objects is very small, resulting in a large percentage of sources with a large FMP. This can lead to contamination of the GMP AGN pair samples by stellar pairs or star-quasar pairs, which we want to avoid. Figure 1 shows the sky density of sources meeting the GMP method cut; the total number is 83 116 497, and the LMC, SMC, and Galactic plane show significantly high density. We also estimate the probability of these sources using the method named SubsampleSelectionFunction presented by Castro-Ginard et al. (2023). The SubsampleSelectionFunction calculates the posterior probability of a source satisfying user-defined criteria. We use this method to calculate the probability of sources that have FMP ≥ 8 in the sample of sources brighter than 20.5 mag; see Fig. 2. The results also show that sources in these crowded regions are more likely to have high FMP values.

Therefore, we remove these regions as follows: we remove circular regions of radius of 9° and 6° around the LMC and SMC, respectively, using the method recommended in Gaia Collaboration (2023a), which is WHERE 1!=CONTAINS (POINT(‘ICRS’, 81.3, -68.7), CIRCLE(‘ICRS’,ra, dec, 9)) AND 1!=CONTAINS(POINT(‘ICRS’, 16.0, -72.8), CIRCLE(‘ICRS’, ra, dec, 6)). We also exclude the regions around the Galactic plane by setting |b| > 11.54°, as in Delchambre et al. (2023). This results in a total of 3,479,889 sources in our major input catalog.

Fig. 1 Density distribution of Gaia sources with FMP ≥ 8 and G < 20.5 mag, using the Hammer Aitoff projection in Galactic coordinates. One cell of this map is approximately 0.84 deg2, and the color coding shows the number of the sources in each cell.

Fig. 2 Probability map at HEALPix level 71 for the same sources as in Fig. 1. The probability is calculated as k/n × 100%, where k is the number of sources meeting the FMP cut (≥ 8) and G cut (< 20.5) in each pixel, and n is the number of sources with G < 20.5 in each pixel.

2.2 The Milliquas catalog

The Milliquas catalog is an ambitious project that aims to collect all the quasars that have been identified in the literature and is constantly updated with the latest publications. The project started in 2009 and released its final version (version 8) in 2023 (Flesch 2023). The NASA HEASARC provides a detailed version log for this catalog.

The Milliquas version 8 (v8 hereafter) includes almost all quasars published as of June 2023, as well as a number of high- confidence quasar candidates, and is therefore an ideal input catalog for selecting GMP AGN pairs. Table 1 displays the variation in the number of sources between different versions of the Milliquas catalog (only some of the versions with detailed publications are shown). Both version 5.2 (v5.2, Flesch 2017) and version 6.3 (v6.3, Flesch 2019) contain approximately two million sources, and more than 65% of them are quasar candidates. In version 7.2 (v7.2, Flesch 2021), about 0.57 million candidates were removed because they did not have any radio, X-ray, or WISE associations and are unlikely to be targeted within a decade. The final version (v8) removes some sources with parallaxes or proper motions detected in Gaia, and retains only those candidates with probability of quasar >99%, thus dramatically reducing the number of candidates. We combined the v7.2 and v8 catalogs, removing non-quasar sources already confirmed in them (e.g., accurately identified as stars in Milliquas), to complement our input catalog. This ensures that our input catalog contains the most recent quasars, while retaining as many reliable candidates as possible.

The combined sample contains many duplicate sources. To address this, we cross-matched the supplemental sample with Gaia DR3 using a 3″ radius and removed the duplicates using the unique source_id of Gaia. Additionally, we excluded sources fainter than 20.5 mag due to the difficulty of resolving them in high-resolution spectroscopic observations. Our final input catalog comprises 2 336 841 sources, of which 408 594 are spectroscopic quasars and 1 928 247 are quasar candidates.

2.3 The GMP quasar catalog-I

The GMP quasar catalog-I comprises a sample of spectroscopic multiple quasars selected using the GMP technique. As described in Section 1, the Gaia satellite is revolutionizing the field with the GMP method, which identifies multiple sources with separations of between 0.15″ and 0.8″ thanks to the presence of multiple peaks in the light profile of Gaia sources.

In the Gaia catalog, some AGNs have been spectroscopically confirmed and thus possess spectroscopic redshifts obtained from surveys such as SDSS, LAMOST, 2QZ (Croom et al. 2009), and the catalog by Lemon et al. (2020), among others. However, another portion of the sample is photometrically selected and lacks known redshifts. These have been observed using the ESO Faint Object Spectrograph and Camera (v.2, EFOSC2) at the New Technology Telescope (NTT) or the DOLORES spectrograph on the Telescopio Nazionale Galileo (TNG). Results from these spectroscopic campaigns will be presented in a forthcoming publication.

Currently, the catalog contains approximately five hundred systems with known redshifts, and they could represent physically associated dual AGNs, gravitationally lensed systems, or AGNs projected close to a foreground Galactic star.

Each source in this catalog includes at least one quasar/AGN and displays multi-component features. This catalog serves as a valuable reference, allowing us to identify similar sources from the vast number of spectroscopically unobserved objects. This significantly facilitates future follow-up observations and identifications of dual AGN and lensed systems.

3 The selection method

3.1 The criteria of selection

The GMP quasar catalog-I and Milliquas provide a large number of quasars with reliable redshifts, and based on these we can study the photometric and astrometric properties of AGN pair candidates (sources with FMP ≥ 8), and in turn search for many similar candidates among the unidentified quasar candidates. The GMP method is excellent for searching for AGN pairs at z > 0.5 (Mannucci et al. 2022, 2023), which are the objects we are most interested in. At the same time, the FMP parameter is only reliable for G < 20.5 mag, and therefore sources with redshifts of lower than 0.5 or fainter than 20.5 mag have been removed from all samples below.

We divided quasars (spectroscopically identified) from Milli-quas into two samples based on the FMP value (cut = 8) of the sources. We then compared the redshift distributions and astrometric properties of the Milliquas and Observed QSOs (the GMP quasar catalog-I; we made follow-up observations); see Fig. 3. These samples, designated Observed QSOs and Milli- quas FMP ≥ 8, contain 482 and 415 sources, respectively. A total of 194 sources are common to the two samples. In order to accurately reflect the overall characteristics of each sample, no additional operations were performed on the common sources. After removing sources with redshifts lower than 0.5, the three samples exhibit similar redshift distributions. However, compared to the Milliquas FMP < 8 sample, the other two samples show a greater dispersion in both normalized parallax and proper motion. To select only the quasars, many catalogs have been filtered using either strict parallax or proper motion criteria (e.g., Guo et al. 2018; Klioner et al. 2022; Storey-Fisher et al. 2024; Fu et al. 2024). This is valid for most quasars and AGNs, but if the goal is to select a sample of AGN pair candidates with GMP ≥ 8, the previous criterion may mistakenly remove a large percentage of valuable sources. The best condition of parallax is | Parallax_over_error| < 6, as in Fig. 3. To determine the optimal proper motion condition, we randomly selected 300 000 reliable SDSS stars, and the cumulative normalized proper motion ratios for the different samples were plotted as in Fig. 4. We find that setting Proper motion_over_error < 10 introduces only 17% of the stars while retaining 83% of the GMP AGN candidates. When the normalized proper motion is greater than 10, the cumulative number of GMP AGN candidates increases at a slow rate, while the number of stars increases rapidly, resulting in a significant increase in stellar contamination. Additionally, we investigated 15 AGNs with Proper motion_over_error > 30, and found that the primary reason for the observed excess proper motion is the presence of neighboring bright stars and the extended structures of sources. For this project, we chose | Proper motion_over_error| ≤ 10 as our proper motion filter².

In general, AGNs will be redder than stars and galaxies in the mid-infrared (MIR) band as their accretion disk heats the surrounding dust. Therefore, the color in the MIR space becomes an important criterion for effectively distinguishing AGNs from other sources (e.g., Stern et al. 2012; Mateos et al. 2012; Secrest et al. 2015; Shu et al. 2019; Storey-Fisher et al. 2024). We note that Type II dual AGN would be bluer at the MIR band (Zhang et al. 2021), which may be linked to the observation that Type II AGN are more susceptible to significant obscuration or contamination from host galaxies (Mateos et al. 2013). For the lensed quasars, we collected lensed quasars with accurate redshift and WISE colors from the SIMBAD database (Wenger et al. 2000). We then compared these sources with normal AGNs (FMP < 8) in Milliquas, as in Fig. 5. Most of the lensed quasars are below the average IR color of normal AGNs, suggesting that the lensed quasars are bluer. The reason for this could be contamination from the foreground lensing galaxies or the limited resolution of WISE observations. In summary, it is anticipated that AGN pairs will exhibit bluer IR colors than normal AGNs. To further probe the MIR color distribution of GMP AGN pair candidates, we randomly selected 300 000 stars and 300 000 galaxies from the clean spectroscopy of SDSS DR18 (Almeida et al. 2023) and matched all the samples with CatWISE within a radius of 3″. Figure 6 shows the distribution of the MIR color for five samples. The W1-W2 color criterion can still be used to effectively distinguish AGNs from stars and galaxies. However, the Observed QSOs and Milliquas FMP ≥ 8 samples have lower W1-W2 values than the Milliquas FMP < 8 sample. Therefore, if we were to use an extreme criterion (e.g.,Wl-W2 > 0.8 mag), we would obtain a pure sample while losing more than 30% of the AGN pair candidates. As a result, in order to preserve as many AGN pair candidates as possible without significantly increasing the contamination, we chose W1-W2 ≥ 0.4 mag as the MIR color criterion, which is similar to what was already done for the QUAIA catalog (Storey-Fisher et al. 2024).

In addition to astrometric data, Gaia DR3 also offers the BP and RP colors, which cover 400–500 nm and 600–750 nm, respectively. Although the gap between these two bands is not large, the difference between these two colors has been proven to be a valid criterion for selecting AGNs (e.g., Bailer-Jones et al. 2019; Storey-Fisher et al. 2024). Figure 7 shows the color–color diagrams of Gaia BP-G and G-RP. The stars and galaxies are the same as the samples in Fig. 6. We find that both Observed QSOs and Milliquas GMP ≥ 8 have different color distributions from the Milliquas GMP < 8 sample, and some AGN pair candidates even fall into the region of galaxies. This result essentially corroborates the hypothesis that GMP AGN pair candidates are not as red as typical single AGNs, as previously suggested based on the WISE colors. We adopt the following criteria: $$\begin{array}{l}G-RP-1.10(BP-G)>0.23;\\ G-RP+1.22(BP-G)>0.35;\\ G-RP+0.98(BP-G)<\mathrm{1.69.}\end{array}$$(1)

As illustrated in Fig. 7, the majority of AGN pair candidates have been retained, while a significant proportion of the stars, some single quasars, and galaxies have been removed. These criteria would vastly reduce stellar contamination in our sample, but would introduce a large number of galaxies. Fortunately, as shown in Fig. 6, the contamination of galaxies will be almost eliminated when W1-W2 ≥ 0.4 mag, which is the MIR color criterion we used.

Fig. 3 Histograms of the characteristics for Observed QSOs and Milli- quas. Top: the spectral redshift. Middle: the parallax_over_error, which is obtained by dividing parallax by parallax_error in Gaia. Bottom: the proper motion_over_error, similar to the parallax_over_error.

Fig. 4 Cumulative rate of normalized proper motion for different samples.

Fig. 5 Comparison of MIR colors of normal AGN (FMP < 8) with SIMBAD lensed quasars at different redshifts. The red line indicates the mean IR color of the normal AGN in each bin.

Fig. 6 Distribution of MIR colors for different samples.

Fig. 7 Color–color diagrams of Gaia colors for different samples. The distributions at the edges are only plotted for Observed QSOs and Milli- quas. The black lines present the cut we used.

Fig. 8 Venn diagram of parameters available for 35 939 candidates.

3.2 Selection process

In the selection process, we first apply the GMP technique by selecting sources with FMP ≥ 8. The test on stellar pairs demonstrates that for pairs with G < 20.5 and δ > 0.15″ (the projected separation), almost all of them can be detected using the FMP ≥ 8 criterion with a very low level of contamination (below 2 × 10⁻³) (Mannucci et al. 2023). After this step, we obtained 36 386 sources, which are made up of 447 spectroscopic quasars and 35 939 candidates. In order to further purify these candidates, it is necessary to apply the criteria set out in Sect. 3.1. However, not all candidates have comprehensive color and astrometric parameters. Figure 8 shows the availability of parameters for these sources, with only 24,151 (67.3%) candidates having complete parameters.

To minimize misjudgments and retain as many candidates as possible, while still providing a reliable and valuable catalog to observe, we divide the selection process into two main steps (STEP1 and STEP2); see Fig. 9. First, we sequentially removed the sources that did not meet the criteria set out in Sect. 3.1. During this process, we also removed 14 galaxies and stars that have been spectroscopically identified in SDSS DR16 (Ahumada et al. 2020). The characteristics of these removed sources are significantly different from those of the quasar sample. This process resulted in the creation of a relatively comprehensive superset comprising 5286 sources. Due to the fact that many sources have missing colors or astrometric parameters but cannot be removed by the method in STEP1, some contamination may remain in the superset. In order to minimize telescope time spent on quasar– star associations, it is essential to select a sample that is as pure as possible.

In STEP2, the sources that lacked colors or astrometric parameters were first removed, as were those with low signal-to- noise ratios (SNRs) in the IR band. This process removed 3355 sources, of which 1493, 3016, and 82 were found to be lacking in astrometry, WISE colors, and Gaia colors, respectively, and 92 exhibited IR magnitude SNR of below 3. Subsequently, the remaining sources were cross-matched with the SIMBAD database (Wenger et al. 2000), resulting in the identification of 64 sources with a MAIN TYPE of star or galaxy. The MAIN TYPE was identified by a variety of methods in the previous literature, but no valid spectroscopic data are available. We consider these sources to be low-confidence quasars or quasar–star pairs, which are of no interest to us and were therefore removed.

3.3 Gaia spectrum and variability

The above selection concerns color and astrometry, and does not encompass detailed spectral or variability data. This is due to the dearth of useful spectral and optical variation information for these sources, rendering identification impossible. While Gaia’s low-resolution spectra offer some assistance, they cannot be considered a valid identification tool. Delchambre et al. (2023) provide classification probabilities (Specmod) for quasars obtained from Gaia spectral information using machine learning. However, the online documentation indicates that even when a threshold of quasar probability of greater than 0.9 is applied, the resulting purity is only about 60%, while 100% completeness is only achieved when the probability is very close to zero. Verification of the Milliquas reveals that approximately 12% of the spectroscopically identified quasars exhibit quasar probability values of below 0.001 in Gaia. Consequently, we did not remove any sources in this step; rather, 345 unreliable quasars with probabilities of below 0.001 and 230 high-confidence quasars with probabilities of above 0.9 were flagged. With regard to the classification of quasars using Gaia light-variation information, Carnerero et al. (2023) and Rimoldini et al. (2023) obtained 95% purity in their respective classifications. However, only 208 sources in our sample have light-variation information, and 199 of them are identified as AGNs in Rimoldini et al. (2023). The remaining 9 sources are more likely to be galaxies or eclipsing binaries. Therefore, we also annotate these high-confidence or low-confidence sources in our catalogs. Finally, we were able to obtain a sample of 1867 sources, of which 447 were spectroscopically identified quasars and 1420 were highly reliable GMP AGN pair candidates.

4 Properties of the catalogs

We provide two catalogs, one is a superset containing 5286 sources, with high completeness but low purity. The other is the Golden sample, a catalog of 1867 GMP AGN pair candidates with high purity. In order to select sources with different priorities for follow-up observations, we performed a more detailed feature exploration of the sources in the Golden sample.

Fig. 9 Flowchart of the catalog selection process.

Fig. 10 The Gaia G mag distribution of Golden sample sources.

4.1 The neighbors and identified pairs

Fig. 10 shows the magnitude distribution of the quasars and candidates in the Golden sample, with only one quasar brighter than 15.5 mag, IGR J18249-3243, a Seyfert 1 AGN (Masetti et al. 2009). About 90% of the sources are in the magnitude range of 18.5–20.5 mag, and these faint sources may have a high value of FMP due to nearby random stars, and so we examined the number of nearby stars within 5″ of the sources in the sample. The results indicate that 984 sources have no other Gaia sources within 5″, 704 sources have one neighbor within 5″, 107 sources have two neighbors, and 72 sources have more than two neighbors. Subsequently, an in-depth analysis was conducted to identify the underlying causes of these multiple neighboring sources, as shown in Table 2. For sources with three neighbors, five of them have been identified as lensed systems, and three are lensed quasar candidates, which further demonstrates the high efficiency of the GMP method for the selection of AGN pair candidates. For sources with more than three neighbors, the majority are located in dense star fields, including the SMC, LMC, the Galactic plane, and Seyfert galaxies. While these sources could be AGN pairs, the presence of dense star fields may hinder the identification, suggesting that these sources should be given a lower priority for follow-up observations.

Furthermore, we labeled the AGN pairs of the Golden sample that have been identified by consulting the relevant literature (e.g., Takahashi & Inoue 2014; Agnello et al. 2018; Lemon et al. 2018; Shen et al. 2021). The Golden sample comprises 39 sources that have been identified. More precisely, 2, 7, and 26 out of 477 quasars have been identified as AGN–star pairs, dual AGNs, and lensed systems, and 4 out of 1420 quasar candidates have been identified as lensed systems. This is readily comprehensible, given that the majority of the previous literature on the identified AGN pairs involved the selection of pair candidates among already identified quasars, with quasar candidates being rarely considered. Consequently, the discovery rate of pairs in the Golden sample quasars is considerably higher than in the candidates, which is a selection effect. In addition, the relationship between these identified pairs and the neighbors of Gaia sources was investigated; see Table 3. The distinct distribution patterns between dual AGN and lensed systems indicate that researchers studying dual AGNs should focus on Gaia sources with ≤1 neighbors, while those investigating lensed systems may find it more effective to target sources with between 1 and 3 neighbors.

4.2 The redshift

Milliquas provides high-precision spectroscopic redshifts for the majority of the quasars listed within our sample. However, there are still more than 1000 sources in the Golden sample that do not have valid spectroscopic redshifts. Gaia provides redshifts derived from low-resolution BP/RP spectra, which are subject to large errors and systematic offsets (Delchambre et al. 2023). Recently, Storey-Fisher et al. (2024) (quaia) and Fu et al. (2024) (CatNorth) improved the redshifts of some Gaia sources with photometric data from other telescopes, thereby substantially reducing the systematic errors. Although the error is significant, photometric redshift can provide a reference redshift for a large number of sources without spectroscopic observations. Moreover, many researchers have demonstrated that machine learning is highly effective in inferring photometric redshifts (e.g. Curran et al. 2021; Razim et al. 2021; Hong et al. 2023). Kunsági-Máté et al. (2022) inferred photometric redshifts of 4.8 million quasar (and candidates) using the colors of Pan-STARRS (PS1, Chambers et al. 2016) and WISE (Wright et al. 2010), with a mean squared error of ∼0.2.

The majority of the redshifts of our Golden sample are derived from the above literature, with the highest priority given to Milliquas. For sources there is no redshift in Milliquas, we obtained a redshift from QUAIA and CatNorth. The remaining sources that still did not have redshift data were supplemented with information from Gaia and PS1-WISE. The sources of redshifts for all sources are shown in Table 4. A total of 298 sources in the Golden sample lack redshift. The majority of these sources lack spectroscopic information from Gaia as well as multi-band photometric information with which to infer the redshift. We note that the redshifts given by references other than Milliquas are derived wholly or partially from photometric information, and are therefore less precise. In some cases, these may even be far from the true redshift. Nevertheless, these redshift data can serve as a valuable reference for researchers, enabling them to identify and filter sources within their desired redshift range.

It is relatively straightforward to identify pairs of sources within the Golden sample. For instance, by setting a radius of 3″ and examining the results, we find three pairs of sources that have similar redshifts. This is illustrated in Fig. 11. The largest difference in redshift among these three pairs reaches 0.23, as shown in the left panel of Fig. 11. However, the component with a redshift of 0.9756 is labeled as a poorer spectroscopic observation in Gaia, which could result in significant errors in the obtained redshift. We consider all three pairs to be high-probability dual or lensed AGNs. It is noteworthy that these three pairs exhibit disparate separations, which are 2.47, 1.72, and 0.76 arcsec. This illustrates the efficacy of the GMP method in screening pairs with varying separations. Upon cross-matching with previous literature, the second pair (RA_center=241.5007, Dec_center=−23.5561) was identified as a lensed AGN by Lemon et al. (2018). Furthermore, it is important to acknowledge that the redshift from Gaia BP and RP may not be entirely reliable, particularly when the two sources are close. In such cases, the other two pairs (see left and right panel of Fig. 11) may necessitate more detailed observations to determine their natural characteristics.

5 Conclusions and the future

As a new approach to select AGN pairs at sub-arcsecond separations, the GMP method employs the parameter ipd_frac_multi_peak provided in Gaia DR3. A series of previous studies demonstrated the efficacy of this method in selecting pairs with separations of 0.15″–0.8″. However, the sources utilized for selecting GMP systems are predominantly drawn from AGN that have been spectroscopically identified by large surveys (e.g., SDSS, LAMOST), with a limited number of exceptions. The aims of the present study are to investigate the differences between single AGN and AGN pairs in astrometric, multi-band colors based on the Milliquas and GMP quasar catalog-I. By analyzing these differences, we were able to develop a more accurate method for selecting reliable AGN pair candidates from over 6 million quasar candidates, significantly expanding the sample size. The main conclusions of this study are as follows:

1. In cases where the redshift distributions are identical, GMP AGNs show more significant parallaxes and proper motions than non-GMP AGNs. Concurrently, the mean value of the color in the IR band of GMP AGNs is also bluer than that of normal AGNs. Furthermore, the optical band color observed by Gaia exhibits a markedly disparate distribution between the two types of samples.

2. We conducted a study to identify the best criteria for selecting AGN pair candidates. The majority of sources in our input catalog lacked spectroscopic information, and so we employed astrometric and color information screening to obtain a complete superset containing 5286 sources. We then proceeded to obtain a pure Golden sample of 1867 sources through further rigorous selection and a match of the previous literature. These two tables are only available in electronic form at the CDS.

3. In order to prioritise candidate sources for the follow-up observations, some sources were marked as high reliability or low reliability in the Golden sample. This classification is based on information regarding light variations as well as low-resolution spectra obtained from Gaia. Some Golden sources with excessive numbers of neighboring sources were examined, and AGN pairs identified in the previous literature were labeled. We found 2, 7, and 30 sources identified as AGN-Star, dual AGN, and lensed AGN, respectively.

4. The majority of sources in the Golden sample have been provided with redshift information through the integration of multiple catalogs. We found three pairs of sources in the Golden sample have separations of less than 3″ and similar redshifts between components. One of the pairs has been identified as a lensed AGN, while the other two lack valid spectroscopic observations. Concurrently, the angular distances between these three pairs are 2.47, 1.72, and 0.76 arcsec, respectively. This indicates that the GMP method can be employed to effectively select not only close pairs (0.15″–0.8″), but also pairs with larger separation.

This is the first attempt to select GMP pair candidates from over six million sources, and we ultimately identify about 1800 high- value sources, of which over 1500 provide reference redshifts. Furthermore, spectroscopic observations of some AGN candidates in the Golden sample have recently been conducted, with the preliminary results presented in Table 5. On the basis of the spectral data, it was established that the 12 primary sources are AGN, while one source with a low SNR is likely to be a star. The decomposition of these sources is currently underway, and the final results will be presented in subsequent papers.

It is anticipated that comprehensive observations of this catalog will yield a substantial number of AGN pairs for the community. In the process of selection, in order to avoid excessive contamination, we removed a number of sources located in the dense star fields, which otherwise would have directly led to noticeable deficiencies in our sample. It is also important to note that hundreds of sources in our Golden sample have been labeled as unreliable quasars. These sources may exhibit characteristics that differ from the AGN population due to poor data quality. Nevertheless, we maintain the view that a significant proportion of these sources are still real AGN pairs, the identification of which will require data of higher precision.

In addition, a potential application of our catalog could be in the area of celestial reference frames; indeed approximately 800 sources from our the Golden sample were used to construct the Gaia-CRF3 (Klioner et al. 2022). Given the potential multipeak structure of these sources, it is recommended that they be used with caution when constructing reference frames.

Fig. 11 PS1 composite color images of three pairs in the Golden sample. The images were obtained by overlaying the i, r, and g bands of PS1, which were set to red, green, and blue, respectively. The size of each cutout is 10″ × 10″. The coordinates of the image centers, the projection separations of the components, and the reference redshift of each component are indicated in the images. The red dots represent the coordinates of the components in Gaia, and the green circles have a radius of 3″.

Data availability

The two catalogs are available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/692/A154.

Acknowledgements

This work has made use of data from the European Space Agency (ESA) mission Gaia, Wide-field Infrared Survey Explorer (WISE) and Sloan Digital Sky Survey (SDSS). We are also very grateful to the developers of the TOPCAT (Taylor 2005) software, the SIMBAD astronomical database and HEALPix. This work has been supported by the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No.XDA0350205, the National Natural Science Foundation of China (NSFC) through grants 12173069, the Youth Innovation Promotion Association CAS with Certificate Number 2022259, the Talent Plan of Shanghai Branch, Chinese Academy of Sciences with No.CASSHB-QNPD-2023-016. Part of this work was supported by the German Deutsche Forschungsgemeinschaft, DFG project number Ts 17/2– 1. We acknowledge the science research grants from the China Manned Space Project with NO. CMS-CSST-2021-A12 and NO.CMS-CSST-2021-B10. This publication was produced as part of the PhD program in Space Science and Technology at the University of Trento, Cycle XXXIX, with the support of a scholarship financed by the Ministerial Decree no. 118 of 2nd march 2023, based on the NRRP - funded by the European Union - NextGenerationEU - Mission 4 “Education and Research”, Component 1 “Enhancement of the offer of educational services: from nurseries to universities” - Investment 4.1 “Extension of the number of research doctorates and innovative doctorates for public administration and cultural heritage”.

Appendix A The details of our catalogs

In Section 3, we obtained two catalogs. For the superset, we provide the right ascension, declination, other astrometric parameters and color parameters (if available). For the Golden sample, we provide additional columns, including reliability flags as mentioned in Section 3.2, and neighboring sources and redshift information as mentioned in Section 4. The details of each column in the Golden sample are shown in Table A.1. These two catalogs will be available to the public at the time of the publication of this paper.

The distribution of the 1,867 sources in the Golden sample is illustrated in Fig. A.1. The ideal distribution of dual AGN or lensed quasar on the celestial sphere would be uniform. However, the regions of Galactic center and the LMC in Fig. A.1 exhibit an excess of these sources. The quasars near the LMC are almost from a study dedicated to investigating quasars behind the Magellanic Clouds (Kozłowski et al. 2013). The high stellar density of the Galactic center and LMC would suggest that these sources are more likely to have a higher FMP (see Fig. 2). These sources have a high probability of being AGN-Star pairs, so we have labeled them in the Golden sample. People may choose to eliminate these sources using the condition

select * from Golden sample
WHERE neighbor_source_comment  !=  ‘near Galactic plane’
& neighbor_source_comment  !=  ‘near LMC’
& neighbor_source_comment  !=  ‘near SMC’.

This would result in a catalog of 1,769 sources distributed almost uniformly on the celestial sphere, see Fig. A.1.

Fig. A.1 The sky distribution of Golden sample sources before (left) and after (right) filter, using the Hammer Aitoff projection in Galactic coordinate.

References

All Tables

All Figures

	Fig. 1 Density distribution of Gaia sources with FMP ≥ 8 and G < 20.5 mag, using the Hammer Aitoff projection in Galactic coordinates. One cell of this map is approximately 0.84 deg2, and the color coding shows the number of the sources in each cell.
In the text

	Fig. 2 Probability map at HEALPix level 71 for the same sources as in Fig. 1. The probability is calculated as k/n × 100%, where k is the number of sources meeting the FMP cut (≥ 8) and G cut (< 20.5) in each pixel, and n is the number of sources with G < 20.5 in each pixel.
In the text

	Fig. 3 Histograms of the characteristics for Observed QSOs and Milli- quas. Top: the spectral redshift. Middle: the parallax_over_error, which is obtained by dividing parallax by parallax_error in Gaia. Bottom: the proper motion_over_error, similar to the parallax_over_error.
In the text

	Fig. 4 Cumulative rate of normalized proper motion for different samples.
In the text

	Fig. 5 Comparison of MIR colors of normal AGN (FMP < 8) with SIMBAD lensed quasars at different redshifts. The red line indicates the mean IR color of the normal AGN in each bin.
In the text

	Fig. 6 Distribution of MIR colors for different samples.
In the text

	Fig. 7 Color–color diagrams of Gaia colors for different samples. The distributions at the edges are only plotted for Observed QSOs and Milli- quas. The black lines present the cut we used.
In the text

	Fig. 8 Venn diagram of parameters available for 35 939 candidates.
In the text

	Fig. 9 Flowchart of the catalog selection process.
In the text

	Fig. 10 The Gaia G mag distribution of Golden sample sources.
In the text

Fig. 11 PS1 composite color images of three pairs in the Golden sample. The images were obtained by overlaying the i, r, and g bands of PS1, which were set to red, green, and blue, respectively. The size of each cutout is 10″ × 10″. The coordinates of the image centers, the projection separations of the components, and the reference redshift of each component are indicated in the images. The red dots represent the coordinates of the components in Gaia, and the green circles have a radius of 3″.

In the text

	Fig. A.1 The sky distribution of Golden sample sources before (left) and after (right) filter, using the Hammer Aitoff projection in Galactic coordinate.
In the text