High energy gamma-ray sources in the VVV survey - II. The AGN counterparts

We identiﬁed Active Galactic Nuclei (AGN) candidates as counterparts to unidentiﬁed gamma-ray sources (UGS) from the Fermi -LAT Fourth Source Catalogue at lower Galactic latitudes. Our methodology is based on the use of near-and mid-infrared photometric data from the VISTA Variables in the V ´ıa L ´actea (VVV) and Wide-ﬁeld Infrared Surv e y Explorer (WISE) surv e ys. The AGN candidates associated with the UGS occupy very different regions from the stars and extragalactic sources in the colour space deﬁned by the VVV and WISE infrared colours. We found 27 near-infrared AGN candidates possibly associated with 14 Fermi -LAT sources using the VVV surv e y. We also found 2 blazar candidates in the regions of 2 Fermi -LAT sources using WISE data. There is no match between VVV and WISE candidates. We have also examined the K s light curves of the VVV candidates and applied the fractional variability amplitude ( σ rms ) and the slope of variation in the K s passband to characterise the near-infrared variability. This analysis shows that more than 85 per cent of the candidates have slopes in the K s passband > 10 − 4 mag/day and present σ rms values consistent with a moderate variability. This is in good agreement with typical results seen from type-1 AGN. The combination of YJHK s colours and K s variability criteria was useful for AGN selection, including its use in identifying counterparts to Fermi γ -ray sources.


INTRODUCTION
Since its launch in June 2008, the Fermi Large Area Telescope (Atwood 2009, Fermi-LAT) has revolutionised our view of the -ray sky above 100 MeV.The Fermi-LAT offers a significant increase in sensitivity, improved angular resolution and nearly uniform sky coverage, making it a powerful tool for the detection and characterisation of large numbers of -ray sources.The Fermi Fourth Source Catalogue (Abdollahi et al. 2020, 4FGL), based on the first 8 years of data from the mission, lists 5064 sources in the energy range 50 MeV to 1 TeV.Out of these sources, 1336 (26.4%) sources do not have even a reliable association with sources detected at other wavelengths; we will henceforth label them as Unassociated Gamma-ray Sources (UGS).More than 3130 of the identified or associated sources are active galaxies of the blazar class, and 239 are pulsars.
The positions of -ray sources listed in the Fermi-LAT catalogues are reported with their associated uncertainty represented by an elliptical region.The Fermi-LAT -ray catalogues provide the semi-major and semi-minor axes of the ellipses together with the positional angle at 68% and 95% level of confidence.The princi-pal reason for the difficulty of finding counterparts to high-energy -ray sources has been the large positional errors in their measured locations, a result of the limited photon statistics and angular resolution of the -ray observations and the bright diffuse -ray emission from the Milky Way (MW).Therefore, the UGS represent one of the biggest challenges in -ray astrophysics (e.g., Thompson 2008).The key to finding plausible counterparts to the unidentified Fermi-LAT sources is the cross-check with observations at one or more wavelengths, such as radio observations (e.g., Hovatta et al. 2014;Schinzel et al. 2015), infrared observations (e.g., Raiteri et al. 2014) and in the sub-millimeter range (e.g., León-Tavares et al. 2012;López-Caniego et al. 2013).Additional X-ray studies have also been carried out with Chandra and Suzaku have been useful in particular when performed in the crowded region of the Galactic plane (e.g., Maeda et al. 2011;Cheung et al. 2012).Optical spectroscopic identification of Fermi sources has been addressed previously to search for counterparts (e.g., Paggi et al. 2014;Peña-Herazo et al. 2021;García-Pérez et al. 2023).In addition, the properties of the ray sources can be used as a statistical set to perform a multivariate analysis.This is a classification strategy to find plausible counterparts at other wavelengths for sources that remain unassociated (e.g., Hassan et al. 2013;Doert & Errando 2014).
Active Galactic Nuclei (AGN) represent an astronomical phenomenon that emit extremely high-energy radiation, as demostrated by Urry & Padovani (1995) and Padovani et al. (2017).Since their discovery many decades ago, research has been conducted at various frequencies unveiling the diverse manifestations of AGN phenomena, observed from radio to -rays.This has resulted in an extensive and captivating assortment of classifications.Among the distinct classes of AGN are type-1 and type-2 AGN, blazars subdivided in BL Lacertae and Flat Spectrum Radio Quasars (FSQR), alongside other classifications (see, Stickel et al. 1991;Stocke et al. 1991).The AGN unification scheme, as proposed by Antonucci (1993), offers a comprehensive representation of AGN phenomena, including elements such as black holes, discs, torus, clouds, and jets.This model explains how orientation effects, different accretion powers, and black hole spin parameters can account for the wide array of AGN types.Furthermore, AGN typically exhibit variations in their emissions (Edelson et al. 2002;Sandrinelli et al. 2014;Husemann et al. 2022).The extent of this variability differs according to the type of AGN and is generally more pronounced, with higher amplitudes in blazars compared to type-1 AGN (e.g., Ulrich et al. 1997;Mao & Yi 2021;Baravalle et al. 2023).
In recent years, the population of known AGN has substantially grown thanks to new surveys and catalogues (e.g., Véron-Cetty & Véron 2010; Rembold et al. 2017;do Nascimento et al. 2019).Nevertheless, the number of AGN observed at lower Galactic latitudes, obscured by dense regions belonging to our Galaxy, remains limited (e.g., Edelson & Malkan 2012;Pichel et al. 2020).Recently, Fu et al. (2021Fu et al. ( , 2022) )  Extragalactic objects located behind the Milky Way are difficult to identify and detect due to the significant amount of gas, dust, and stars present at low Galactic latitudes (e.g., Kraan-Korteweg 2000; Baravalle et al. 2018Baravalle et al. , 2021)).In this context, observations carried out at near-infrared wavelengths minimise the effects of interstellar extinction in these regions in comparison with optical passbands.Although the density of foreground sources is greater in the near-infrared, the reduced foreground extinction can reveal different physical processes.Studying these unknown MW regions at low Galactic latitudes, which are usually obscured at visible wavelengths, presents a challenging task.The first near-infrared survey in these regions was the Two Micron All Sky Survey (Skrutskie et al. 2006, 2MASS).Later, the ESO Public Surveys, the VISTA Variables in the Vía Láctea (Minniti et al. 2010, VVV) and its extension, the VVVX have been mapping the K s -passband variability of stars in the entire MW bulge and disc.The main scientific goal was to gain more insight into the inner MW's origin, structure, and evolution.The VVV survey included the acquisition of ZYJHK s images whereas VVVX was restricted to the JHK s passbands, increasing significantly the coverage area (see Table 1 in Daza-Perilla et al. 2023).Thousands of new galaxies and galaxy associations have been discovered using the photometric data from VVV and VVVX surveys (e.g., Amôres et al. 2012;Baravalle et al. 2019;Coldwell et al. 2014;Galdeano et al. 2021;Soto et al. 2022;Daza-Perilla et al. 2023).The VVV near-infrared galaxy catalogue (Baravalle et al. 2021, VVV NIRGC) is the final catalogue of part of the Southern Galactic disc using the colour criteria and the visual inspection to identify 5554 galaxies.Only 45 of these galaxies were previously known.Pichel et al. (2020) studied for the first time the active galaxies in these regions using a combination of near-infrared (NIR) and mid-infrared (MIR) data.The Wide-field Infrared Survey Explorer (Wright et al. 2010, WISE) is an ideal mission for identifying a very large number of AGN across the full sky.Additionally, Baravalle et al. (2023) reported four AGN candidates at very low Galactic latitudes (| b |< 2 • ) using this combination of VVV and WISE surveys.Also, these sources presented variability in the K s light curves reported in the VIVACE catalogue (Molnar et al. 2022).
The infrared (IR) emission of AGN can be of thermal and nonthermal origin.In the case of radio-loud AGN, specifically blazar subtypes, the non-thermal character of the IR radiation is produced by the synchrotron emission of relativistic electrons within the jet.Radio continuum emission is also associated with these jets.On the other hand, in radio-quiet objects such as Seyfert galaxies, most of the radiated energy is dominated by thermal emission from the accretion disc, which is formed around the central black hole (e.g., Shakura & Sunyaev 1973).The light of the accretion disc is absorbed by the "dust torus" (see, Netzer 2015) and re-emitted in the infrared.The emission of torus and accretion disc dominate the AGN spectral energy distribution (SED) at wavelengths longer than ∼1 m up to a few tens of microns, giving the AGN distinctive red mid-IR colours (e.g.Stern et al. 2005;Richards et al. 2006;Assef et al. 2010).Therefore, IR passbands are well suited to identify AGN, as their SEDs are very different from those of stars and inactive galaxies.Chen et al. (2005) studied the colour distribution of a sample of blazars and normal galaxies using the 2MASS archival data.The main results from these observations are as follows: (1) the distribution of colours of blazars, in the J-H-K s colour-colour diagram, occupy a region centered at the position (0.7; 0. The main goal in this study is to identify, at lower Galactic latitudes, unidentified 4FGL sources with NIR and MIR counterparts using the VVV and WISE surveys, respectively.The paper is organised as follows.Section 2 presents the data which includes the different samples of high energy sources together with the NIR and MIR photometry used in this study.The applied methodology to detect the counterparts is also discussed including colour-magnitude and colour-colour diagrams using VVV and WISE surveys, and the VVV K s light curves of the near-IR sources and the variability analysis.Section 3 shows the diagrams for the Fermi-LAT source regions with VVV candidates and the analysis of the light curves using the near-IR data.Diagrams with the WISE candidates using mid-IR data are also shown.Section 4 presents a summary of the main results.

The samples of high energy gamma-ray sources
At lower Galactic latitudes, we have found 221 4FGL sources in the bulge and disc regions covered by the VVV survey without any previous source associations at any wavelengths.Figure 1 shows the distributions of interstellar K s extinctions (A Ks ) in magnitudes and uncertainties in the positions of the Fermi-LAT sources as the semi-major axis (a) in arcmin of the error ellipse at 95% confidence level for the 221 UGS.The median values are A Ks = 0.74 ± 3.79 mag and a = 4.25 ± 3.04 arcmin.
According to the distributions of the interstellar extinctions and semi-major axis of the Fermi-LAT uncertainties, we choose to analyse sources in regions with lower interstellar extinctions (A Ks < 1.2 mag).Taking this into account, our sample comprises 78 UGS.We defined three subsamples: the A subsample which contains 13 UGS with a < 2.5 arcmin; the B subsample that contains 12 sources with 2.5 ⩽ a < 3.0 arcmin and the C subsample that contains 53 sources with 3.0 ⩽ a < 5.0 arcmin.Tables 1, 2 and 3 show the positions of the UGS for the three subsamples, respectively.
Figure 2 shows the distribution in Galactic coordinates of the 78 UGS over the region covered by the VVV survey.The samples studied are highlighted as yellow squares (A subsample), green diamonds (B subsample) and orange stars (C subsample).Also the coloured UGS are over plotted on the spatial distribution of A  interstellar extinction derived from the extinction map of Schlafly & Finkbeiner (2011).The contours of the different levels correspond to 5, 10, 15, 20, 25 mag.There are 14 UGS located in the Southern disc and 64 in the bulge.The disc (bulge) UGS are 6, 3 and 5 (7, 9 and 48) in the A, B and C subsamples, respectively.

Near-and mid-IR photometry
Our main goal is to identify the selected UGS with near-and mid-IR photometry counterparts using the VVV and WISE photometry, respectively.Pichel et al. (2020) analysed the four blazars located in the VVV region that were identified in the Multi-frequency Catalogue of Blazars (Massaro et al. 2015) as counterparts to 3FGL sources.They defined a specific region with a radius twice the positional uncertainties associated with the high-energy sources and performed a search for all infrared sources within this area.The photometry was conducted in the five VVV passbands: Z, Y, J, H and K s using the combination of SExtractor (Source-Extractor) + PSFEx (PSF Extractor) (Bertin 2011) to assess all the sources in the region as described in Baravalle et al. (2018).The blazars were characterised by their near-and mid-IR properties from VVV and WISE surveys, respectively showing different colours in the infrared diagrams.The photometric results of the blazar 5BZQJ1802-3940 (Pichel et al. 2020) obtained with SExtractor+PSFEx were also compared in Donoso (2020) with the data product provided by Cambridge Astronomical Survey Unit (CASU; Emerson et al. 2006).Both approaches produce comparable results and the studied blazar occupied a similar position in the colour-colour diagrams.
In this work, we analysed all the VVV sources with CASU photometry lying within the positional uncertainty region of the UGS.For this purpose, for each 4FGL sources, we defined a search area centred on the UGS, with radius defined by the semi-major axis of the ellipse (values reported in Table 1-3).We used the positions of the NIR sources, the object classification and the aperture magnitudes within an aperture of radius of 3 pixels, which correspond to ∼1 arcsec (Minniti et al. 2010;Saito et al. 2010).In this way all the Fermi-LAT sources were surveyed in an homogeneous way.

Near-IR: VVV survey
In this section, we use NIR magnitudes and colours of all the VVV objects in the regions of the 4FGL sources.The magnitudes were corrected by interstellar extinction along the line-of-sight, using the dust maps of Schlafly & Finkbeiner (2011) and the VVV NIR relative extinction coefficients of Catelan et al. (2011).Then, we obtained the colours for all the sources.Baravalle et al. (2018) defined extragalactic sources using the colour criteria 0.5 < (J-K s ) < 2.0 mag; 0.0 < (J-H) < 1.0 mag; and 0.0 < (H-K s ) < 2.0 mag with the colour constraint (J-H) + 0.9 (H-K s ) > 0.44 mag to minimise false detections.The main result of this work is the VVV NIRGC, the catalogue of galaxies in part of the Southern Galactic disc.Massaro & D'Abrusco (2016) examined the regions in the colour-colour diagrams using the J, H and K s magnitudes from the 2MASS catalogue, specifically those occupied by Fermi-LAT blazars.The infrared colours of the -ray blazars cover a distinct region, clearly separated from the other extragalactic sources.Also, Cioni et al. (2013) performed an AGN selection using the VISTA Magellanic Survey (Cioni et al. 2011, VMC).In their Figure 2, they divided the JHK s colour-colour space  Based on the results of Baravalle et al. (2023); Massaro & D'Abrusco (2016) and Cioni et al. (2011), we improved the colour cuts and we selected sources that satisfy simultaneously: 0.5 < (J-K s ) < 2.5 mag; 0.4 < (J-H) < 2.0 mag; 0.5 < (H-K s ) < 2.0 mag and 0.2 < (Y-J) < 2.0 mag.This selection define the possible candidates to be related to UGS.In addition to the colour selection, a visual inspection of the candidates in the five passbands of the survey was performed.In case of doubts, we created the false-colour red-greenblue (RGB) images using the K s , H and J passbands.Figure 3 shows some examples of these sources as 1 ′ × 1 ′ VVV colour composed images.We eliminated objects with strong contamination by bright nearby stars and those sources that have fainter K s magnitudes.

Mid-IR: WISE
We applied the methodology used in Pichel et al. (2020) andD'Abrusco et al. (2019) to all the Fermi-LAT sources.For the analysis, unless stated otherwise, we considered only WISE sources detected with a minimum signal-to-noise ratio of 7 in at least one passband.Using the WGS and the WISE locus method described in D' Abrusco et al. (2019), we applied the criterion that blazars lie in a distinctive region in the 3-dimensional MIR CCD using photometry at [3.4], [4.6], [12] and [22] m.The identification of WISE blazar candidates involved a selection process based on 2-dimensional projections within the CCD using the WISE locus method, as described previously.This technique may offer multi-Table 1. Fermi-LAT sources of our sample with low positional uncertainties (the A subsample).Column (1) lists the internal identification used in this work; columns (2) to (5), the 4FGL identification, the J2000 coordinates and the semi-major axis of Fermi-LAT error ellipse, a, at 95% confidence level in arcmin taken from 4FGL, and columns ( 6) and ( 7), the VVV tile identification and the interstellar extinction in the K s passband at the source position, respectively.ple possibilities depending on the number of identified candidates.When there is just one candidate, it is assumed to be directly associated with the Fermi-LAT source.Nevertheless, in cases with more candidates it is difficult to determine which one is associated, making further studies essential.In addition, to improve our selection of WISE candidates, we included AGN candidates using the criteria outlined in studies by Stern et al. (2012) and Assef et al. (2018).All identified WISE blazar candidates are also considered to be WISE AGN candidates, so all WISE candidates.

Variability analysis with the VVV photometry
Here, we performed the variability analysis for the objects associated to the Fermi-LAT sources.We have obtained the K s passband light curves using the second version of VVV Infrared Astrometric Catalogue (VIRAC2; see Smith et al. 2018 and Smith et al. in prep.)This is photometry based on PSF.We selected the measurements with photometric flags equal to 0 (see the catalogue) in order to obtain reliable light curves.Their coordinates were cross-matched with the VIRAC2 assuming differences in their positions of 1 arcsec.Twenty seven good light curves have a five astrometric parameter solution (a de-facto 10 epoch selection), not flagged as a probable duplicate, detected in more than 20% of the observations that cover the source, and with a unit weight error less than 1.8.On the con-trary, the rejected objects have not met the above criteria because they are highly contaminated with nearby stars or they are too faint to have reliable magnitudes.
In order to investigate the variability of these objects, we applied the methodology used in Pichel et al. (2020).We examined the fractional variability amplitude,  rms (Nandra et al. 1997;Edelson et al. 2002;Sandrinelli et al. 2014;Pichel et al. 2020) defined as where N represents the number of flux values F i with their uncertainties  i , and  denotes the average flux.This parameter represents the excess variability that cannot be solely attributed to flux errors.Also, we investigated the slope of the light curves, taking into consideration the results of Cioni et al. (2013) that more than 75% of QSO in the VCM survey exhibit a slope variation in the K s passband larger than 10 −4 mag/day.They defined the slope of the overall K s variation in the light curves that were sampled over a range of 300-600 days, 40-80 days, or shorter.In this analysis we followed the same procedure as Baravalle et al. (2023), we performed a linear fit of the K s light curves, considering a range of days defined by the highest and lowest variations observed in the light curve.In all light curves, the range of days considered for this analysis varies from 1200 to ∼ 2300 days (Baravalle et al. 2023)..7-3420 18:14:45.75 -34:20:28.33.564 b234 0.0652 C49 4FGLJ1816.4-27274.698 b266 0.1222 C50 4FGLJ1817.9-3334 18:17:55.17 -33:34:21.7 3.846 b221 0.0635 C51 4FGLJ1819.9-2926 18:19:57.58 -29:26:20.84.992 b252 0.0920 C52 4FGLJ1820.7-3217 18:20:45.81 -32:17:26.54.944 b222 0.0726 C53 4FGLJ1828.2-3252 18:28:13.49 -32:52:10.64.998 b208 0.0599

RESULTS
On the basis of the methodology detailed above, here, the VVV ZYJHK s magnitudes, colours and K s light curves of the AGN candidates are presented.As explained in subsection 2.2.1, we have constructed colour-magnitude and colour-colour diagrams for each 4FGL.For those 4FGL sources with candidate counterparts, the (J-K s )-K s , colour-magnitude diagram and (H-K s )-(J-H) and (Y-J)-(J-K s ) colour-colour diagrams are shown in the Figures 4 to 17. There, grey-scale contours correspond to density of all the CASU objects found in 4FGL regions with size defined by the positional uncertainty of the Fermi-LAT source, including stellar and extragalactic sources.The regions preferentially populated for AGN candidates are: 0.5 < (J-K s ) < 2.5 mag; 0.5 < (H-K s ) < 2.0 mag; 0.4 < (J-H) < 2.0 mag and 0.2 < (Y-J) < 2.0 mag.The candidates were highlighted and represented by red circles for extended sources and as blue circles for objects with point-like morphology.Those AGN candidates that present variability are indicated by triangles, the colour depending on the origin of the sources: red for galaxy-like sources and blue for stellar-like objects.Full triangles are objects that have slope in K s passband higher than 10 −4 mag/day and empty triangles have slopes lower than this value.Also, the regions limited with lines as defined by Cioni et al. (2013) are shown.
After careful visual inspection, we eliminated faint and contaminated sources, leaving only those that were considered VVV candidates.Thus, 7 Fermi-LAT sources have only one VVV candidate: A13, B6, B12, C40, C46, C47 and C51.Some UGS have more than one VVV candidate: the Fermi-LAT source C53 presents 5 candidates; A9, 4 candidates; A12, 3 candidates; and C44, C48, C50 and C52, 2 candidates each one.These VVV candidates are not located in the Southern disc and therefore, there are no sources in common with the VVV NIRGC.
In Figure 19, we present the differential K s light curves of the VVV sources.These curves represent the K s magnitudes with the median subtracted, sampled over a period covering more than 2500 days.We noted that the overall shape of light curves is irregular, lacking any discernible periodic pattern.In some cases, we observe prominent fluctuations in brightness that resemble peaks, exhibiting statistical significance well above the value of the associated uncertainties.Table 4 presents the main results of the K s variability of these sources, showing the mean magnitude,  rms and the slope of the linear fits with the range of days used.Also some comments of the visual inspection of the objects are included.Most of them are early-type galaxies or the bulges of galaxies, because the near-infrared is sensitive to detecting the oldest stellar population in the galaxy.We did not include in the analysis those objects with strong crowding contamination or faint magnitudes as mentioned above.In general, most of the studied objects exhibit moderate variability, characterised by  rms values ranging from 12.5 to 32.1.These results are in agreement with previous studies on type-1 AGN, such as those by Nandra et al. (1997); Edelson et al. (2002); Baravalle et al. (2023).However, these values are lower than those reported for blazars (e.g., Sandrinelli et al. 2014;Pichel et al. 2020).Since type-1 AGN typically present lower variability amplitudes than blazars (e.g., Ulrich et al. 1997;Mao & Yi 2021), our results suggest that these objects are potential type-1 AGN, such as quasars or Seyfert 1 galaxies.Moreover, the observed light curve slopes are ⩾ 10 −4 mag/day, comfortably lying within the limit established by Cioni et al. (2013) for quasars.On the other hand, there are four objects that present negligible variability, with very low values of  rms .These objects are VVV-J181300.69-314505.6,VVV-J173934.82-283746.5, VVV-J180027.63-291007.4 and VVV-J181803.69-333215.7 in the regions of the Fermi-LAT sources A12, B6, C40 and C50, respectively (see Fig. 19 and Table 4).As expected, these objects also exhibit significantly lower slope values, typically below 10 −5 mag/day.(J-H) and (Y-J)-(J-K s ) CCD using near-IR data from the VVV survey, respectively.The targets in red are those showing extended morphology in the images.The objects marked with circles do not have reliable variability curves; thus, the variability analysis was not performed on these targets.The objects indicated by filled triangles are those for which the variability analysis demonstrates their nature as variable sources.Grey lines defined by Cioni et al. (2013) are drawn on the YJK s CCD and labels of regions defined by those authors are also indicated.Grey-scale contours correspond to density of the NIR objects, lying within the positional uncertainty region of the UGS.Although luminosity variability is a common feature of active galactic nuclei, the absence of variability does not necessarily rule out the possibility of an object being an AGN.It is important to note that not all AGN exhibit the same degree of variability, and certain AGN may display very low or nearly negligible levels of variability (e.g., Ilić et al. 2017;Li et al. 2022;Pennock et al. 2022).Beyond this, more than 85% of the objects studied here show a moderate variability, and as mentioned above, these results suggest that these sources are type-1 AGN candidates.It has to be noted that this analysis is based only with photometric data.A spectroscopic study is necessary in order to investigate the nature and type of AGN.
We also searched for WISE candidates coincident with the position of the VVV candidates found before.We could not get any match between the VVV and WISE candidates with the exception   of the source VVV-J173934.82-283746.5 in the Fermi-LAT B6 region.This object has a source at an angular distance of 0.64 arcsec classified as the OH/IR star 359.54+01.29 (Sevenster et al. 1997).
The WISE results are not as clear as those in Pichel et al. (2020) and Baravalle et al. (2023).All 4 sources explored in Pichel et al. (2020) had VVV candidate counterparts, but only two of them had WISE ones.In Baravalle et al. (2023), the 4 active galaxies had VVV and WISE counterparts.The main difference between these two studies and the present one is that the VVV candidates were brighter in the K s passband.Here, all the VVV candidates are in the range of 14.5 to 18 mag with the exception of the candidate in the Fermi-LAT B12 region.Another difference is the high interstellar extinction towards the fields studied here and in some cases, strong stellar contamination.In the mid-IR, the results here are more noisy in general.Based on these results, we present candidates in the Fermi-LAT source regions both in the NIR and MIR using VVV and WISE surveys, respectively.However, inside the Fermi-LAT source A8 appears a WISE source (J173612.07-342204.7) that satisfies all the criteria to be a blazar candidate using the WGS method.This region has a high interstellar extinction (A Ks = 0.9297 mag) and the NIR CMD shows bright magnitudes without candi-    (Jarrett et al. 2011).These WISE candidates do not have VVV counterparts; thus, no other analysis and cross-match can be done in this paper.Further analysis with IR spectroscopy is needed in order to establish the nature of the WISE sources.
We might note that most of the VVV candidates are found in the B region of the colour-colour diagram defined by Cioni et al. (2013).
Our sample of VVV candidates are centered at the position (0.6; 0.7) in the CCD (J-H) vs (H-K s ) according to Chen et al. (2005).For the 27 candidates listed in Table 4, we then searched for the closest object in a circle of 30 arcsec radius using the SIMBAD database1 and we have not found any catalogued source, with the exception of the object in the region of the Fermi-Lat source B6 mentioned above.There have been no previous photometry or spectroscopy studies performed in these regions.Lefaucheur & Pita (2017) obtained a sample of 595 blazar can-   didates from the unassociated sources within the 3FGL catalogue (Acero & Ackermann 2015).They proceeded to train multivariate classifiers on samples derived from the Fermi-LAT catalogue, carefully selecting discriminant parameters.Within their blazar candidates, there are 30 objects in the region of the VVV survey, of which A5, B3, B4, C10, C27 and C49 in our subsamples.They classified the Fermi-LAT source A5 as BL Lac, however, there are no VVV candidates in this region because of the high interstellar extinction (A Ks = 0.9213 mag).The Fermi-LAT C10 was also classified as BL Lac and the near-IR CMD and CCD show that there are a pointlike and a galaxy-like objects in the region that we have defined as possible VVV candidates.This is a region of strong crowding contamination and the K s light curves of these two objects were noisy and did not satisfy our criteria.For these reasons there are no other VVV nor WISE candidates in common with these authors.
All the Fermi-LAT sources in the A subsample with AGN candidates are found in regions with smaller interstellar extinctions (A Ks < 0.15 mag).In the B subsample, there are only two Fermi-LAT sources associated with VVV AGN candidates: B12 has interstellar extinction lower than 0.10 mag and B6 is in a region with high interstellar extinction.Hence, an interesting feature of B6 source's colour-magnitude diagram is that the K s magnitudes are brightest compared to the other diagrams (Figure 7).In the C subsample most of the cases have A Ks < 0.10 mag with the exception  of C40, C46 and C47 with values from 0.17 to 0.28 mag approximately.For the other Fermi-LAT sources lying at higher interstellar extinction regions, we did not find any NIR nor MIR candidates.
Considering that some UGS have multiple candidates, it is crucial to establish criteria for prioritising the selection of the objects for follow-up observations.This selection process is based on additional criteria that includes magnitude, distance to the Fermi source, variability, interstellar extinction and visual inspection.As a result, the priority candidate for the Fermi-LAT source A9 is VVV-J175851.46-411016.0, which is the brightest, closest, the most variable source and lowest interstellar extinction.For the Fermi-LAT source A12, the priority candidate is VVV-J181258.71-314346.7, using the same criteria mentioned above.Within the C subsample, the priority candidates are VVV-J180826.32-352214.7 for C44, VVV-J181440.95-341915.4 for C48, VVV-J181751.39-333117.3 for C50, VVV-J182052.11-322058.3 for C52 and VVV-J182807.31-325038.0 for C53.

SUMMARY
In this work we present criteria for selecting AGN candidates as counterparts to Fermi-LAT sources, based on NIR and MIR photometry from the VVV and WISE surveys.We analysed a sample of 78 high energy -ray sources located at low Galactic latitudes without any previous source associations at any wavelength and lying in the footprint of the VVV survey.To start with, we divided the sample in three subsamples, considering the interstellar extinctions and semi-major axis of the Fermi-LAT uncertainties.
We analysed photometric data from the VVV and WISE surveys, following the methodology reported by Pichel et al. (2020) to search for blazars and Baravalle et al. (2023) to identify AGN candidates.The following colour cuts were used to identify VVV AGN candidates associated to the UGS sample in the near-IR data: 0.5 < (J-K s ) < 2.5 mag; 0.5 < (H-K s ) < 2.0 mag; 0.4 < (J-H) < 2.0 mag and 0.2 < (Y-J) < 2.0 mag.These sources are located in specific regions in the NIR CCD, clearly separated from stars and other extragalactic sources.Upon visual inspection, we removed the contaminated sources such as those with nearby bright stars or stellar associations.
We then selected 27 VVV AGN candidates within 14 Fermi-LAT positional uncertainties ellipses using the VVV survey.These objects satisfy the colour cuts and also visually look as a galaxy or have point-like morphology.We have also explored the light curves of all sources reported in Table 4 and applied the fractional variability amplitude and the slope of variation in the K s passband.In general, most of the candidates show variability  rms > 12 and slopes in agreement with the limits defined by Cioni et al. (2011).These results suggest the presence of type-1 AGN.However, there are four objects with low variability  rms < 8.0 and smaller slopes that might not be ruled out.We also found 2 blazar candidates in the regions of 2 Fermi-LAT sources using WISE data.There is no match between VVV and WISE candidates.
The combination of YJHK s colours and K s variability criteria have been useful for AGN selection, including its use in identifying counterparts to Fermi-LAT -ray sources.Finally, we aim to perform NIR spectroscopic observations to confirm the extragalactic nature of the AGN candidates reported here.Particularly useful explored the Galactic bulge regions in search for quasars (QSO) at lower latitudes.Employing machine learning techniques, they identified and confirmed 204 QSO candidates at (| b |< 20 • ) based on spectroscopic measurements.Ackermann et al. (2012) reported a significant excess of unassociated sources at | b |< 10 • , where catalogues of AGN are incomplete.Hence the fraction of sources associated with AGN decreases in this sky area.
7), and (2) about 30% of the blazars show NIR colours indicating a possible influence from the host galaxy.Such contamination is not present at MIR wavelengths.Using WISE magnitudes, D'Abrusco et al. (2012) discovered that blazars emitting in -rays were clearly distinguished from other classes of galaxies and/or AGN and/or Galactic sources.Fermi-LAT blazars inhabit different regions in the colour-colour diagrams (CCD) because they are dominated by non-thermal emission in the mid-IR.This two-dimensional region in the MIR CCD [3.4]-[4.6]-[12]-[22]m was originally indicated as the WISE Gamma-ray Strip (D'Abrusco et al. 2012, WGS), and the method was improved in the WISE locus of gamma-ray blazars in D'Abrusco et al. (2013, 2014).Massaro & D'Abrusco (2016) also showed that the Fermi-LAT blazars are located in specific regions both in NIR and MIR CCD, clearly separated from other extragalactic sources.Stern et al. (2012) investigated the power of WISE to identify AGN based solely on the [3.4] and [4.6] magnitudes.The selection criteria of [3.4]-[4.6]> 0.8 mag and [4.6] < 15.05 mag produced an AGN sample with a contamination of only 5%.Following this, Assef et al. (2018) presented two additional colour criteria in their AGN sample: [3.4]-[4.6]> 0.5 mag and [3.4]-[4.6]> 0.77 mag, with a 90% and 75% completeness.

Figure 1 .
Figure 1.Plot resuming the interstellar extinctions in the K s passband and uncertainties in the positions of the 4FGL sources in the VVV region.

Figure 2 .
Figure 2. The distribution of the 78 UGS in the VVV region using different symbols for A, B and C subsamples.The A V iso-contours at 5, 10, 15, 20, 25 mag derived from the extinction maps of Schlafly & Finkbeiner (2011) are superposed.

Figure 3 .
Figure 3. 1 ′ × 1 ′ VVV colour composed images of some cases belonging to our sample of sources.The orientation is shown in the bottom-right panel.

Figure 4 .
Figure 4. CMD and CCD for the field of Fermi-LAT source A9.Left, central and right panels report (J-K s )-K s CMD, (H-K s )-(J-H) and (Y-J)-(J-K s ) CCD using near-IR data from the VVV survey, respectively.The targets in red are those showing extended morphology in the images.The objects marked with circles do not have reliable variability curves; thus, the variability analysis was not performed on these targets.The objects indicated by filled triangles are those for which the variability analysis demonstrates their nature as variable sources.Grey lines defined byCioni et al. (2013) are drawn on the YJK s CCD and labels of regions defined by those authors are also indicated.Grey-scale contours correspond to density of the NIR objects, lying within the positional uncertainty region of the UGS.

Figure 5 .
Figure 5.As Fig. 4, but for Fermi source A12.Empty blue triangle represents an object with low or negligible variability and the blue colour indicates a point-like appearance.

Figure 7 .
Figure 7.As Fig. 4, but for Fermi source B6.Empty blue triangle represents the candidate with low or negligible variability and the blue colour indicates a point-like morphology.

Figure 8 .
Figure 8.As Fig. 4, but for Fermi source B12.The candidate with point-like morphology is indicated by blue circle.

Figure 9 .
Figure 9.As Fig. 4, but for Fermi source C40.Empty blue triangle represents an object with low or negligible variability and the blue colour indicates a point-like appearance.

Figure 14 .
Figure 14.As Fig. 4, but for Fermi source C50.Empty red triangle represents an object with low or negligible variability and the red colour indicates a extended appearance.

Figure 18 .
Figure 18.Mid-IR colour-colour diagrams for the Fermi-LAT sources A8 (top) and B10 (bottom) using WISE data (black dots).The two blazar classes of BZB (BL Lac) and BZQ (FSRQ) are shown in dash-and dot-black lines, respectively.The dotted and dashed red horizontal lines represent the limits for AGN from Stern et al. (2012) and Assef et al. (2018), respectively.The solid red box denotes the defined region of QSO/AGN from Jarrett et al. (2011).

Figure 19 .
Figure 19.K s differential light curves of the VVV sources for the A, B and C subsamples.

Table 2 .
Fermi-LAT sources of our sample with intermediate positional uncertainties (the B subsample).The column description is the same of Table1.

Table 3 .
Fermi-LAT sources of our sample with large positional uncertainties (the C subsample).The column description is the same as in Table1.