The QUEST-La Silla AGN Variability Survey: Selection of AGN Candidates through Optical Variability

Between 2010 and 2015, we carried out "The QUEST-La Silla AGN variability survey" (hereafter QUEST-La Silla), using the wide-field QUEST camera mounted on the 1 m ESO-Schmidt telescope at La Silla Observatory (Cartier et al. 2015, 2016). The survey used a broadband filter, the Q band, similar to the union of the g and r SDSS filters. Our survey includes the COSMOS, ECDF-S, ELAIS-S1, XMM-LSS, and Stripe 82 fields. These are some the most intensively observed regions in the southern sky. Our QUEST fields are much larger than the nominal fields, but we will still adopt the same names, with a surveyed area of ∼14 deg² per field, with the exception of the XMM-LSS field, which covers an area of ∼38 deg². One of the advantages of our survey over other surveys is the intense monitoring used, observing the fields every possible night (but see the binning strategy described below). Individual images reached a limiting magnitude between r ∼ 20.5 and r ∼ 21.5 mag for an exposure time of 60 s or 180 s, respectively.

The aims of our survey are (1) to test and improve variability selection methods of AGNs, and find AGN populations missed by other optical selection techniques (Schmidt et al. 2010; Butler & Bloom 2011; Palanque-Delabrouille et al. 2011), (2) to obtain a large number of well-sampled light curves, covering timescales ranging from days to years, and (3) to study the link between the variability properties (e.g., characteristic timescales and amplitudes of variation) with physical parameters of the system (e.g., black hole mass, luminosity, and Eddington ratio).

Cartier et al. (2015) presented the technical description of the survey, the full characterization of the QUEST camera, and a study of the relation of variability to multiwavelength properties of X-ray-selected AGNs in the COSMOS field. In Sánchez-Sáez et al. (2018), we performed a statistical analysis of the connection between AGN variability and physical properties of the central SMBH, where we found that the amplitude of variability at one-year timescales (A) depends primarily on the rest-frame emission wavelength (λ_rest) and the Eddington ratio, where A is anticorrelated with both λ_rest and L/L_Edd.

We reduced the data from QUEST-La Silla using our own customized pipeline, following the same procedure described by Cartier et al. (2015), which includes dark subtraction, flat-fielding, and astrometric and photometric calibration. To calibrate the photometry, we used public photometric SDSS catalogs (Gunn et al. 1998; Doi et al. 2010) for the COSMOS, Stripe 82, and XMM-LSS fields, and public catalogs from the first year of DES (Abbott et al. 2018) for the ELAIS-S1 and ECDF-S fields. We performed aperture photometry using SExtractor (Bertin & Arnouts 1996), with the same optimal aperture found by Cartier et al. (2015) for the QUEST camera (∼618). We then constructed light curves for all sources from the SDSS and DES catalogs with detections in the QUEST-La Silla data, using the same methodology as in Cartier et al. (2015). In summary, we constructed light curves by cross-matching the SDSS and DES catalogs with every QUEST-La Silla catalog, which we generated for each observation, for which we knew their associated Julian dates, using a radius of 1''. We then constructed light curves for each source, keeping only those epochs where the SExtractor FLAG parameter was equal to zero, to prevent false detection of variability due to bad photometry. Finally, we only saved those light curves with more than three epochs. From the SDSS catalog, we could obtain single-epoch photometry of every source in the COSMOS, XMM-LSS, and Stripe 82 fields in the u, g, r, i, and z bands, and from the DES catalog, we obtained single-epoch photometry in the g, r, i, and z bands for the ELAIS-S1 and ECDF-S fields.

We decided to bin our light curves using three-day bins, in order to reduce the noise in our light curves produced by several factors, including changes in atmospheric conditions and the relatively low cosmetic quality of the QUEST CCD camera chips. This might affect the detection of variability of sources with short timescale variations, like some variable stars (e.g., RR Lyrae or Cepheid stars), however, we do not expect to detect many variable stars in the QUEST-La Silla fields (e.g., Medina et al. 2018). Moreover, in this work we are focused on the detection of sources with long timescale variations (with timescales of months or years), and thus the three-day binning does not affect our detection of AGNs.

In this work, we excluded the Stripe 82 field, because it is a crowded field and requires point-spread function (PSF) photometry. We generated a total of 277,629 light curves for sources located in the COSMOS, ECDF-S, ELAIS-S1, and XMM-LSS fields. In order to have statistically significant variability features of the sources, we decided to include in our analysis only those light curves with at least 40 epochs and a length greater than or equal to 200 days, after the three-day binning was applied (hereafter "well-sampled" light curves). There are 208,583 well-sampled light curves in the four fields. The median, mean, and standard deviation of the number of epochs of each light curve are 118, 119.3, and 47.2, respectively; and the median, mean, and standard deviation of the total length of each light curve are 1283.7, 1306.4, and 254.3, respectively. In Table 1, we summarize the total number of light curves and the number of well-sampled light curves in each field.

A decision tree is a hierarchical structure that performs successive partitions on the data, each of them according to a certain criteria, such as a cutoff value in one of the descriptors or features. In this way, the data are divided into smaller and smaller subsets as the tree goes deeper, until it reaches the leaves of the tree. Each of the leaves is associated with a single class. A given class, however, may be associated with several leaves. Thus, the elements that fall on any of the leaves corresponding to a particular class will be classified as belonging to that class.

An RF algorithm consists of a collection of single decision trees, where each tree is trained using a random subset of sources, sampled with repetition, from a training set (a set of objects with known classification, selected from a labeled set), and a random selection of features. The final classification function of the algorithm weighs each of these results according to the size of the subset used by each tree and generates an average score, which can then be interpreted as the probability that the input element belongs to a certain class (predicted class probability, P_RF). Then, the classifier is validated using a subset of the labeled set that was not used for training (the test set). Finally, a prediction is made on the unlabeled data. RF has several advantages—it can handle thousands of features, it provides a ranking of feature importance during the classification, it does not need to scale the feature values to the same "units," it handles numerous objects, and it is easily parallelizable.

For the selection of AGN candidates, we used the scikit-learn¹³ Python package implementation of RF. We performed a hyperparameter selection procedure in order to obtain the optimal values for the RF classifier by means of a K-Fold Cross-Validation procedure¹⁴ (with k = 5 folds) and using the "accuracy" (see its definition in Section 3.4) as the target score to optimize. This hyperparameter selection procedure was executed as part of the model training phase (i.e., on the training set). In this procedure, the training set is divided into k folds, using k − 1 of them to compute the RF model, and testing it in the remaining data (the validation set). This is done k times, using every time a different fold as the validation set. The parameters considered in this cross-validated search include the number of trees in the forest and the number of features to consider when looking for the best split in a tree. In order to take into account the class imbalance in the classification process, we initialized the class weight hyperparameter as "balanced_subsample."

The variability features used by the RF classifier are described in Section 3.2, and are listed in Table 2. We trained the RF classifier using a labeled set of type 1 AGNs and stars with spectroscopic classification from SDSS and with well-sampled light curves from the QUEST-La Silla survey (see Section 3.3). During the RF classifier training, we used 70% of the labeled set as a training set, and then we tested the performance of the classifier using the remaining 30% of the labeled set (the test set), as normally done during supervised learning procedures. We then applied the trained RF classifier to our unlabeled set, composed of our 208,583 sources with well-sampled QUEST-La Silla light curves, to classify them as either AGN or non-AGN. As a result, we obtain a predicted class and the predicted class probability (P_RF) associated with each source of the unlabeled set.

Table 2.  List of Features

Feature	Description	Reference
Pvar	Probability that the source is intrinsically variable	McLaughlin et al. (1996)
σrms	Measure of the intrinsic variability amplitude.	Allevato et al. (2013)
ASF	Amplitude of the variability at 1 yr, derived from the SF	Schmidt et al. (2010)
γSF	Logarithmic gradient of the change in magnitude, derived from the SF	Schmidt et al. (2010)
Stda	Standard deviation of the light curve (σLC)	Nun et al. (2015)
Meanvariancea	Ratio of the standard deviation to the mean magnitude (${\sigma }_{\mathrm{LC}}/\overline{m}$)	Nun et al. (2015)
MedianBRPa	Fraction of photometric points within amplitude/10 of the median magnitude	Richards et al. (2011)
Autocor-lengtha	Lag value where the autocorrelation becomes smaller than e−1	Kim et al. (2011)
StetsonKa	A robust kurtosis measure	Kim et al. (2011)
ηe a	Ratio of the mean of the square of successive differences to the variance of data points	Kim et al. (2014)
PercentAmpa	Largest percentage difference between either the maximum or minimum magnitude and the median	Richards et al. (2011)
Cona	Number of three consecutive data points that are brighter or fainter than 2σLC	Kim et al. (2011)
LinearTrenda	Slope of a linear fit to the light curve	Richards et al. (2011)
Beyond1Stda	Percentage of points beyond one σLC from the mean	Richards et al. (2011)
Q31a	Difference between the third quartile and the first quartile of a light curve	Kim et al. (2014)
PeriodLS	Period from the Lomb–Scargle periodogram	VanderPlas (2018)

Note.

^aFeatures from FATS.

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In order to have a complete description of the variability of our sources, we used several variability features. Following the same approach of Sánchez et al. (2017) and Sánchez-Sáez et al. (2018), we used two parameters related to the amplitude of the variability, P_var, and the excess variance (σ_rms), and one parameter that describes the shape of the variability between two observations separated by a given time, the SF.

In particular, P_var (see Sánchez et al. 2017 and references therein) corresponds to the probability that the source is intrinsically variable; it considers the χ² of the light curve and calculates the probability P_var = P(χ²) that a χ² lower than or equal to the observed value could occur by chance for an intrinsically nonvariable source.

σ_rms is a measure of the intrinsic variability amplitude (see Sánchez et al. 2017 and references therein), and it is calculated as ${\sigma }_{\mathrm{rms}}^{2}=({\sigma }_{\mathrm{LC}}^{2}-{\overline{\sigma }}_{m}^{2})/{\overline{m}}^{2}$, where σ_LC is the standard deviation of the light curve, ${\overline{\sigma }}_{m}$ is the mean photometric error, and $\overline{m}$ is the mean magnitude.

The SF (e.g., Schmidt et al. 2010) is the average variability amplitude between two observations separated by a given time (τ), and it can be modeled as a power law: $\mathrm{SF}(\tau )\,={A}_{\mathrm{SF}}{\left(\tfrac{\tau }{1\mathrm{yr}}\right)}^{{\gamma }_{\mathrm{SF}}}$, where A_SF corresponds to the amplitude of the variability at 1 yr timescales, and γ_SF is the logarithmic gradient of this change in magnitude.

We also used some variability features from the Feature Analysis for Time Series (Nun et al. 2015) Python package, related to the amplitude of the variability (e.g., the mean variance and the percent amplitude) and the structure of the light curve (e.g., the linear trend and the autocorrelation function length), as well as the period of the Lomb–Scargle periodogram (VanderPlas 2018), derived by using the AstroML module for Python (VanderPlas et al. 2012). A list of all the variability features used in this work is shown in Table 2, together with a brief description of each feature and its reference.

To train our RF classifier, we need a labeled set, which has to be representative of the populations that we want to classify. Because in this analysis we only include extragalactic fields, we do not expect to detect a high fraction of variable stars, because of their low density at high Galactic latitudes (e.g., RR Lyrae or Cepheid stars; see Medina et al. 2018 and references therein). Moreover, because we implemented three-day binning for our light curves, the detection of variable signals with short timescales is not possible. Therefore, any variable star with a short period will have a light curve that will not be very different from a nonvariable star. Only variable stars with long periods would be detectable using our QUEST-La Silla light curves. We cross-matched the positions of the 208,583 sources with well-sampled light curves with the General Catalog of Variable Stars (Version GCVS 5.1; Samus' et al. 2017), which provides a detailed compilation of catalogs of variable stars in the Galaxy. We found that only three known variable stars are present in our data, one RR Lyrae and two cataclysmic variables. Therefore, we did not include variable stars in our RF classifiers.

In this analysis, galaxies are not included in the labeled set, because in general their variability and color properties will be similar to those of stars, unless they host an AGN (which might not have been previously detected). Therefore, we constructed a labeled set composed of stars and type 1 AGNs (i.e., AGNs with broad permitted emission lines). We decided to include only type 1 AGNs because we want to characterize properly the variability of the optical continuum emission, which cannot be detected in most type 2 or obscured AGNs.

Three of our fields (COSMOS, Stripe 82, and XMM-LSS) have spectroscopic information from SDSS. We constructed light curves for sources with spectral classification from the SDSS-DR14 database (Abolfathi et al. 2018). There are 3313 type 1 AGNs and 3332 stars with at least three epochs in the QUEST-La Silla light curves, and 2405 type 1 AGNs and 2608 stars with well-sampled light curves. We considered the sources with well-sampled light curves to define a labeled set for the RF classifier training. As mentioned in Section 3.1, 30% of the labeled set was used as a test set and 70% as a training set for the RF modeling. Figure 1 provides examples of QUEST-La Silla light curves for four sources of the labeled set.

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It is well-known that a fraction of AGNs are misclassified in the SDSS databases; therefore, we cross-match our labeled sample with the Million Quasars Catalog (MILLIQUAS v5.7 update,¹⁵ 2019 January 7, Flesch 2015; see Section 4.1 for further details), in order to estimate the fraction of AGNs in the labeled set that are not, in fact, AGNs. There are 57 AGNs in the labeled set, with well-sampled light curves, that are not present in MILLIQUAS, which correspond to the 2.4% of the AGNs in the labeled set. Of these 57 sources, 21 are classified as variable according to their variability features, and thus we can estimate that less than 2% of the AGNs in the labeled set are misclassified as AGN.

In Figure 2, we show three color–color diagrams of the labeled set: u − g versus g − r, g − r versus r − i, and r − i versus i − z. As a reference, we mark the regions of the u − g versus g − r color–color diagram dominated by a particular type of source, from Sesar et al. (2007). We can see that a high fraction of the AGNs in the labeled set are located in a region of the u − g versus g − r diagram where low-redshift, luminous AGNs (II) are the dominant population, which corresponds to 78.8% of the AGNs in the labeled set. This corresponds to the classical color–color selection of "blue" AGNs. Moreover, we can see in the figure that several high-redshift (z_spec > 2.5) AGNs in the labeled sample are located in the region where high-redshift luminous AGNs are the dominant component (VI), as expected, but a non-negligible fraction is located in other regions, where binary stars or cool dwarf stars (III), RR Lyrae stars, and main-sequence stars or the "stellar locus" (V) are the dominant population.

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On the other hand, we can see in the right panel of Figure 2 that most of the AGNs in the labeled set are located in a region where r − i ≲ 0.7 and i − z ≲ 0.8, cleanly isolating a subpopulation of cool dwarf stars. This can be understood considering that stellar colors become monotonically redder as the effective temperature decreases (Covey et al. 2007), thus we normally observe a high concentration of cool dwarf stars in a region around g − r ∼ 1.5, with r − i ≳ 0.8. Besides, extragalactic sources (i.e., galaxies and AGNs) are normally located in regions of color–color space with r − i ≲ 1.0 (e.g., Rahman et al. 2016), because their integrated emission typically has a low contribution from cool dwarf stars. Therefore, we can use r − i and r − z colors to separate AGNs from cool dwarf stars. The separation of AGNs and stars from the general "stellar locus" is more complicated if we only use optical colors, because there is a high overlap between these two populations in the different color–color diagrams, particularly in the u − g versus g − r diagram, as already discussed. Thus, including variability information in the selection of AGN candidates will be extremely useful to improve AGN selection.

We tested three different RF classifiers. The first one includes only variability features (hereafter RF1), the second one includes variability features and the r − i and i − z colors (hereafter RF2), and the third classifier includes variability features and the g − r, r − i, and i − z optical colors (hereafter RF3). We exclude u − g because we do not have photometry in the u band for the Elais-S1 and ECDF-S fields, and because our labeled set does not cover properly the u − g space, compared to the unlabeled set; thus, including it might produce poor results. For this reason, we did not test a pure color selection, as the u band is highly discriminating for selecting AGNs (e.g., Richards et al. 2002, 2009; Ross et al. 2012).

As can be seen, the difference between RF2 and RF3 is the exclusion of the color g − r in RF2. As mentioned in the previous section, the r − i and i − z colors can easily separate cool dwarf stars and AGNs. However, separating AGNs and stars from the stellar locus is difficult when we use optical colors, particularly for the case of u − g and g − r. Thus, with RF2, we can test whether avoiding the use of g − r can improve the detection of redder AGN populations. On the other hand, RF1 excludes optical colors, and thus the amount of information used by this classifier is lower compared to RF2 and RF3. Optical colors have been exhaustively used in the literature for the selection of AGN candidates (e.g., Fan 1999; Richards et al. 2002, 2004, 2009; Smith et al. 2005; Bovy et al. 2011; Kirkpatrick et al. 2011; Ross et al. 2012), and thus with RF1, we can test whether single-band variability-based techniques can provide results as competitive as the ones obtained using optical colors.

As mentioned in Section 3.1, we trained each classifier using 70% of the labeled set as a training set and the remaining 30% of the labeled set as a test set. The selection of the training and test sets is done randomly, using the "train_test_split" procedure of scikit-learn. The labeled set, by definition, has the same limiting magnitude as the QUEST-La Silla images (r ∼ 21); therefore, the training and test sets have limiting magnitudes of r ∼ 21.

As we are interested in selecting only AGN candidates, for the rest of the analysis, we will refer to stars, and any source that is not an AGN, as non-AGN.

3.4.1. RF1: Selection of AGNs Based Solely on Variability

Our first RF classifier (RF1) includes only variability features. We show the results from this classifier using a confusion matrix, which is shown in Figure 3 (see its RF1 results). It can be seen that AGNs (true positives) are in general well classified, and also that the fraction of non-AGNs classified as AGNs (false positives) is very low.

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We also computed the following scores to assess our classifiers: accuracy (A), precision (P), recall (R), and F1. These scores are defined by means of the True Positives (TPs; known AGNs classified as AGNs by the RF classifier), the False Positives (FPs; known non-AGNs classified as AGNs), the True Negatives (TNs; known non-AGNs classified as non-AGNs), and the False Negatives (FNs; known AGNs classified as non-AGNs):

$$\begin{eqnarray}\begin{array}{rcl}A & = & \displaystyle \frac{\mathrm{TPs}+\mathrm{TNs}}{\mathrm{Total}\ \mathrm{Sample}}\\ P & = & \displaystyle \frac{\mathrm{TPs}}{\mathrm{TPs}+\mathrm{FPs}}\\ R & = & \displaystyle \frac{\mathrm{TPs}}{\mathrm{TPs}+\mathrm{FNs}}\\ {\rm{F}}1 & = & 2\times \displaystyle \frac{P\times R}{P+R}.\end{array}\end{eqnarray} \tag{ 1 }$$

Table 3 shows the computed scores for the RF1 classifier. From these scores, and from the confusion matrix, we can say that RF1 presents a low fraction of FPs; thus, the sample of predicted AGNs has low contamination from non-AGNs. However, we tend to miss a fraction of real AGNs (∼10%). This results from the difficulty of detecting a variable signal from AGNs with low amplitude variability, and because we are only considering variability properties for the classification, they could be classified as non-AGNs.

Table 3.  Scores Measured in the Test Set for Each Classifier

Score	RF1	RF2	RF3
Accuracy	0.916	0.923	0.931
Precision	0.909	0.909	0.921
Recall	0.933	0.950	0.951
F1	0.921	0.930	0.936

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It is important to consider that we are testing the RF1 classifier in a sample of AGNs selected mostly by means of their optical colors, and because we are only considering variability features in our selection, the confusion matrix and the different scores, obtained from our labeled sample, might not necessarily be an optimal prediction of the performance of our method in the unlabeled sample.

One of the advantages of the RF classification is that we can easily know the feature importance, because it provides a ranking score for each feature, or how well every feature separates the two classes. In the first columns of Table 4, we provide the list of features, ordered by importance (rank value), for the RF1 classifier. It can be seen that the four most important features are the amplitude of the SF, the excess variance, the Meanvariance, and Q31. In Figure 4, we show the distribution of the A_SF and Q31 features for the labeled set. We highlight using black dots those AGNs classified as variable, according to the definition proposed by Sánchez et al. (2017), where a source is classified as variable when its light curve satisfies P_var ≥ 0.95 and (${\sigma }_{\mathrm{rms}}^{2}$ − err(${\sigma }_{\mathrm{rms}}^{2}$)) > 0. From the figure, it can be seen that AGNs and non-AGNs are separated by these two features, with A_SF providing a much stronger division than Q31, as there is substantial source overlap between the two classes with the latter indicator. It can be also seen that the majority of AGNs with low variability amplitude are classified as nonvariable.

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Table 4.  Feature Importance for Each Classifier

RF1		RF2		RF3
Feature	Rank	Feature	Rank	Feature	Rank
ASF	0.197	ASF	0.209	ASF	0.189
σrms	0.139	σrms	0.149	σrms	0.142
Meanvariance	0.127	Q31	0.102	Q31	0.113
Q31	0.111	Pvar	0.093	Meanvariance	0.099
Pvar	0.095	Std	0.088	Pvar	0.095
Std	0.090	Meanvariance	0.086	Std	0.074
PercentAmp	0.040	PercentAmp	0.045	Autocor-length	0.042
γSF	0.036	Autocor-length	0.035	PercentAmp	0.039
Autocor-length	0.033	γSF	0.031	g − r	0.031
MedianBRP	0.025	r − i	0.028	γSF	0.029
LinearTrend	0.023	MedianBRP	0.021	r − i	0.023
PeriodLS	0.023	PeriodLS	0.020	MedianBRP	0.020
ηe	0.023	ηe	0.019	ηe	0.020
Beyond1Std	0.019	Beyond1Std	0.019	i − z	0.019
StetsonK	0.018	LinearTrend	0.019	LinearTrend	0.018
Con	0.002	i − z	0.019	PeriodLS	0.017
		StetsonK	0.014	Beyond1Std	0.017
		Con	0.002	StetsonK	0.012
				Con	0.002

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3.4.2. RF2: Selection of AGNs Based on Variability and r − i, and i − z Optical Colors

3.4.3. RF3: Selection of AGNs Based on Variability and g − r, r − i, and i − z Optical Colors

We applied the trained RF1, RF2, and RF3 classifiers to our unlabeled well-sampled set of 208,583 light curves. In order to improve the purity of our selection, we considered the predicted class probability P_RF (computed as the mean predicted class probabilities of the trees in the forest) to select the final set of AGN candidates. We defined two samples of AGN candidates: (a) the full-AGN sample, consisting of all sources classified as AGNs by the RF classifier (P_RF ≥ 0.5), and (b) the hp-AGN sample, consisting of sources that have a high probability (P_RF ≥ 0.8) of being an AGN based on the RF classifier. In Table 5, we provide a summary with the number of sources classified as AGNs in both samples, for each classifier. For the case of the RF1 classifier, there are 17,120 sources in the full-AGN sample, and 5941 sources in the hp-AGN sample. For the RF2 classifier, there are 15,100 sources in the full-AGN sample, and 5252 sources in the hp-AGN sample. Finally, for RF3, there are 13,810 sources in the full-AGN sample, and 4482 sources in the hp-AGN sample. There are 4054 candidates in common among the RF1, RF2, and RF3 hp-AGN samples. For the rest of the analysis, we will only consider the hp-AGN samples of each classifier.

Figure 5 shows the g − r versus r − i color–color diagram of the unlabeled set, and the hp-AGN samples for the RF1, RF2, and RF3. Comparing with Figure 2, we can see that several of our AGN candidates are located in regions of color–color space where AGNs are not normally found, particularly for the case of RF1. The main difference between the candidates of RF1 and the rest of the classifiers is the exclusion of sources in the color–color region where we normally find cool stars. For example, there are 4890 candidates in common between RF1 and RF2, and 1051 RF1 candidates that are not candidates for RF2. Regarding the former ones, 54.1% have r − i > 0.7, where we expect to find mostly cool stars. The main difference between the candidates of RF2 and RF3 is the exclusion of redder candidates in the case of RF3 (g − r ≳ 1.0). There are 4178 candidates in common between RF2 and RF3, and 1074 candidates in RF2 that are not candidates for RF3, with 70.5% of these having g − r > 1.0.

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In the top panel of Figure 5, we also show a selection of AGN candidates observed during spectroscopic follow-up (see Section 4.2). In the middle and bottom panels of the figure, we show the position in the g − r versus r − i diagram of four candidates located in different positions of the stellar locus, marked with letters (ABCD), and in Figure 6, we show their light curves, where it can be seen that they are clearly variable. These four sources are selected as candidates by RF1, two are selected as candidates by RF2 (A and B), and none of them is selected as a candidate by RF3.

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MILLIQUAS (v5.7 update, 2019 January 7; Flesch 2015) provides a very complete compendium of known AGNs (both type 1 and type 2) from the literature, including the last data release of SDSS (SDSS-DR15), and several recent XMM-Newton, Swift, and Chandra catalogs (e.g., Evans et al. 2014; Marchesi et al. 2016; Maitra et al. 2019). It also includes a list of high-confidence AGN candidates from different sources like AllWISE (Secrest et al. 2015).

We used MILLIQUAS to confirm the nature of our candidates. We cross-matched MILLIQUAS with the coordinates of our well-sampled light curves, using a radius of 1''. There are 3524 sources in the well-sampled sample with identifications in MILLIQUAS. For the case of the RF1 classifier, there are 2358 (66.9%) of these sources in the hp-AGN sample, 2757 (78.2%) in the full-AGN sample, and 767 (21.8%) sources classified as non-AGNs. For the RF2 classifier, there are 2366 (67.1%) sources in the hp-AGN sample, 2775 (78.7%) in the full-AGN sample, and 749 (21.3%) sources classified as non-AGNs. Finally, for the RF3 classifier, there are 2348 (66.7%) sources in the hp-AGN sample, 2769 sources in the full-AGN sample (78.6%), and 755 (21.4%) sources classified as non-AGNs. From these results, we can say that ∼21% of the sources are misclassified as non-AGNs when we include variability features in the selection. Thus, we can conclude that when we include variability features in our selection, we obtain a completeness of ∼79%.

We plot in the top panel of Figure 7 the distribution of the A_SF variability feature for sources in MILLIQUAS and QUEST-La Silla belonging to the RF1 hp-AGN sample, the RF1 full-ANG sample, and sources classified as non-AGNs by RF1 (but classified as AGNs by MILLIQUAS). It can be seen that the main difference between the sources classified as AGNs and non-AGNs is the value of the variability amplitude at one year, i.e., we are not detecting variability for the sources classified as non-AGNs.

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In the middle panel of Figure 7, we compare the distribution of the mean Q magnitude (determined from their light curves) of sources from the RF1 hp-AGN sample that have and do not have detection in MILLIQUAS, and in the bottom panel, we compare their A_SF distributions. It can be seen that the sources with detection in MILLIQUAS are in general brighter than the sources without detection in MILLIQUAS; however, the amplitude of the variability is lower for the sources without detection in MILLIQUAS. It is important to note that only a small fraction (≲3%) of the AGNs in MILLIQUAS are classified as host dominated (i.e., they appear extended in imaging). This demonstrates that variability can be used to augment AGN selection to include objects that are extended as well as point sources.

In Table 6, we show the number of hp-AGN candidates confirmed using MILLIQUAS, dividing the hp-AGN samples into red and blue subsamples, as already described. It can be seen that most of the confirmed sources are in the blue subsample, with 52% of the candidates in this sample confirmed for RF1, 52.4% for RF2, and 52.1% for RF3. For the case of the red subsample, 5.3% of the candidates from RF1 are confirmed using MILLIQUAS, 7.1% for RF2, and 12% for RF3. Further, there are 354 AGNs listed as candidates in MILLIQUAS for RF1, 356 for RF2, and 345 for RF3. Most of them are candidates from WISE (Secrest et al. 2015). This lack of confirmed red candidates can be understood if we consider that most of the AGNs presented in MILLIQUAS come from samples that applied morphological cuts to target point sources, and thus, they tend to exclude sources whose emission is dominated by their host galaxies.

4.1.1. Candidates with X-Ray Detections

Because most of the AGNs confirmed with ancillary data have blue colors (g − r ≤ 0.6), we performed spectroscopic follow-up to confirm the nature of sources located in different regions of the color–color space. We used the Goodman, at SOAR (Clemens et al. 2004), and EFOSC2, at the New Technology Telescope (NTT; Buzzoni et al. 1984), instruments to observe 54 candidates (for details, see Appendix B).

To select the candidates for follow-up campaign, we divided the hp-AGN sample of the RF1 classifier into blue and red subsamples. Then, we randomly selected 100 candidates from each subsample, excluding sources with r > 20.5 for which it would be hard to obtain a good-quality spectrum with 4 m class telescopes. We visually inspected the light curves of the selected candidates in order to exclude sources with evidence of bad photometry (produced by the relatively low cosmetic quality of the QUEST CCD camera chips). During the follow-up campaign, we observed as much of the selected candidates as we could, observing in total 54 targets. We gave priority to sources from the red subsample. Of the 54 candidates observed, 38 have g − r > 0.6, which represents 70% of the sample.

In the top panel of Figure 8, we show the r-band magnitude distribution of hp-AGN candidates of the RF1 classifier and the observed candidates. We can see that the distributions are different. This is produced by the limitations of observing faint targets with 4 m class telescopes. During the follow-up campaign, we gave priority to sources with r < 20, for which we expected to obtain spectra with signal to noise higher than 10. In the bottom panel of Figure 8, we show the distribution of the predicted class probability (P_RF) for the hp-AGN candidates of the RF1 classifier and the observed candidates. It can be seen that in general, we observed sources with higher probabilities, compared with the total sample of candidates. This is produced by visual inspection of the light curves and the selection of brighter sources for the follow-up campaign.

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We used the spectra to classify our targets and to estimate their redshifts. For details about the spectroscopic analysis, see Appendix B. The full list of observed candidates can be found in Appendix A We provide the position of the observed sources, their redshift, their g − r and r − i colors, their r magnitude, and their spectroscopic classification. In Table 7, we provide a summary of the follow-up campaign. We divided the classified sources into blue and red subsamples, and we also separate them according to their spectroscopic classes: AGN1 (type 1 AGNs), BAL–QSO, galaxy, and star.

In the top-left panel of Figure 5, we show the color–color diagram of the observed candidates, with colors and shapes depending on their spectral classification. In the top-right and bottom-left panels of Figure 5, we mark with letters some candidates located in the stellar locus. Sources A and B are classified as type 1 AGNs, and sources C and D are classified as type M stars. From the light curves of sources C and D (see Figure 6) and from their spectra, we propose that these candidates are irregular variable stars.

In the bottom panel of Figure 8, we show the normalized redshift distribution of AGNs from the labeled sample and observed candidates classified as AGNs or BAL–QSOs. We can see that we have a much larger fraction of low-redshift sources observed during the follow-up campaign. Further, the fraction of observed AGNs with z > 3.0 is slightly higher compared with the AGNs from the labeled sample.

There are seven targets with redshift higher than 2.5. These types of AGNs are harder to detect than lower-redshift AGNs in magnitude-limited, optical color–color selections (because their colors resemble those of stars, particularly near the magnitude limit of surveys where the stellar locus is wider), and clearly benefit from the variability criteria (Butler & Bloom 2011; Palanque-Delabrouille et al. 2011, 2016). In addition, we found four BAL–QSOs, with three having g − r > 0.6. There are 22 AGNs with z_spec < 0.7, of which 20 have g − r > 0.6, and eight of these are LLAGNs, whose continua are significantly dominated by the host galaxy, but with clearly distinguishable broad emission lines.

The case of the eight LLAGNs is particularly interesting, because the continuum of their spectra is dominated by the host galaxy, but we still detect its optical variable component, which is associated with the accretion disk. This component is revealed by subtracting the galactic continuum of each spectrum following the simple procedure of Greene & Ho (2005) and Kim et al. (2006). As an example, in Figure 9 we show the spectra of two LLAGN sources—in red we show the original observed spectra, and in blue we show the AGN component. It can be seen that in both cases the continuum is dominated by the host galaxy, but after its subtraction, the power-law AGN continuum appears, which is the one that produces the optical variations. It is important to remark that without including variability features in the selection of our candidates, these types of sources would be classified as non-AGNs according to their optical colors. This reflects the importance of including variability in the selection of LLAGNs.

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We define the efficiency of a classifier as the number of confirmed AGNs divided by the total number of observed candidates. Considering all the observed candidates, the efficiency is 100% for the blue subsample and 73.7% for the red subsample. In Table 8, we show from which classifier comes every observed candidate. As we mentioned previously, the 54 observed candidates belong to the RF1 hp-AGN sample; therefore, the efficiency of the follow-up for the RF1 classifier is 100% for the blue subsample and 73.7% for the red subsample. For the case of RF2, there are 50 observed candidates, with an efficiency of 100% for the blue subsample and 79.4% for the red subsample. There are three stars and one type 1 AGN excluded by RF2. For the case of RF3, there are 43 observed candidates. The efficiency of the RF3 blue subsample is 100%, and for the red subsample it is 85.2%. There are four type 1 AGNs, one BAL–QSO, three galaxies, and three stars excluded by RF3.

From these results, we can conclude that RF2 has a higher efficiency compared to RF1 and RF3, because it has a high efficiency for both the blue and red subsamples, and excludes most of the observed stars and only one type 1 AGN. RF3 also provides good results; however, it excluded one BAL–QSO and four type 1 AGNs, one of which has z_spec = 3.5852 and two are LLAGNs. In Appendix C, we provide the list of hp-AGN candidates from the RF2 classifier.

4.2.1. Non-AGN Observed Sources