A REFINED QSO SELECTION METHOD USING DIAGNOSTICS TESTS: 663 QSO CANDIDATES IN THE LARGE MAGELLANIC CLOUD

Active galactic nuclei (AGNs) are very energetic extragalactic objects that have been studied in many astronomical fields such as galaxy formation and evolution (e.g., Heckman et al. 2004; Bower et al. 2006; Trichas et al. 2009, 2010), large-scale structure (e.g., Ross et al. 2009), dark matter substructure (e.g., Miranda & Macciò 2007), and black hole growth (e.g., Kollmeier et al. 2006).

It is known that QSOs show strong variability over a wide range of wavelengths on a timescale from a few days to several years (Hook et al. 1994; Hawkins 2002). It is widely believed that the variability is associated with accretion disk instability (Rees 1984; Kawaguchi et al. 1998). Recently, interesting studies on QSO variability have been published (Kelly et al. 2009; MacLeod et al. 2010), which confirmed a correlation between the timescale of QSO variability and the physical parameters of QSOs such as black hole mass. Although these studies confirmed the correlation, different studies showed a discrepancy at the timescales of QSO variability (Kelly et al. 2009; Kozłowski et al. 2010; MacLeod et al. 2010). Possible reasons for the discrepancy are (1) poorly sampled light curves and/or short observational periods, (2) false positives such as stellar contaminations in their QSO candidates, and (3) biased QSO samples in luminosity or black hole mass. Thus, having a well-sampled set of QSO light curves with a long baseline and small number of false positives is critical for the comprehensive analysis of this correlation. Note that there are only a few hundred well-sampled QSO light curves, and a large portion of them are around the Large Magellanic Cloud (LMC) fields where the MACHO survey monitored for several years (e.g., see Geha et al. 2003; Kelly et al. 2009; Kozłowski et al. 2012).

The MACHO survey observed the sky around the LMC for 7.4 years with relatively regular sampling of a few days. The majority of the MACHO light curves have more than several hundred data points and therefore the MACHO light curves are suitable for the QSO variability studies. Nevertheless, there are only 59 confirmed MACHO QSOs in the 40 deg² areas around the LMC (Geha et al. 2003). The main reasons for the relatively small number of QSOs are (1) the crowdedness of the fields, which makes it difficult to select QSO candidates among the dense stellar sources and thus yields a high false positive rate (e.g., see Geha et al. 2003; Dobrzycki et al. 2005), and (2) the high cost of spectroscopic or X-ray observations, which are the best methods for confirming QSOs. Thus a novel QSO selection algorithm with a high efficiency and a low false positive rate is essential to make the best use of the expensive spectroscopic telescope time and increase the collection of QSOs.

In our previous work (Kim et al. 2011), we developed a QSO selection method using a supervised classification model trained on a set of variability features extracted from the MACHO light curves including a variety of variable stars, non-variable stars, and QSOs. The trained model showed a high efficiency of 80% and a low false positive rate of 25%. Using this method, we first selected 2566 QSO candidates from the light curve database. We then developed and employed a decision procedure on the basis of diagnostics using (1) mid-IR colors, (2) photometric redshifts, and (3) X-ray luminosities on these candidates in order to separate high-confidence QSO candidates (hereinafter hc-QSOs). As a result, we chose in total 663 hc-QSOs out of 2566. These 663 candidates are likely QSOs; if confirmed this will increase the previous collection of QSOs in the MACHO LMC database by a factor of ∼12. Note that most of the hc-QSO light curves are well sampled for 7.4 years (i.e., several hundred data points with relatively regular sampling) and are chosen in such a way to exclude any potential false positives. Therefore, the light curve collection of hc-QSOs is a valuable set for QSO variability studies and can be used as a target set for spectroscopic observations.

In Section 2, we briefly introduce the MACHO database and the QSO selection algorithm that we developed to select the initial set of QSO candidates. We then present multiple diagnostics that we applied on the set of QSO candidates in Section 3. Section 4 presents a classification model trained on the diagnostics features in order to choose hc-QSOs. In Section 5, we crossmatch our candidates with newly discovered QSOs in the LMC fields. A summary is given in Section 6.

We first selected QSO candidates from the MACHO light curve database using the QSO selection method developed by Kim et al. (2011; hereinafter K-method). In this paper, we used a 10% QSO probability product cut to select the QSO candidates rather than a 25% cut which Kim et al. (2011) used because we will employ other diagnostics (see Section 3) that are able to effectively remove false positives.⁷ Here probability product is the product of the probabilities derived independently from MACHO B- and R-band light curves using Support Vector Machine (SVM; Boser et al. 1992) and Platt's probability estimation (Platt 1999). By definition, QSO candidates with higher probabilities are more likely to be QSOs. With the probability cut of 10%, we found 2566 QSO candidates.

In the following subsections, we will introduce the diagnostics performed and the consequent results.

3.1. Spitzer Mid-IR Properties

It is known that mid-IR color selection is an efficient discriminator for AGNs and stars/galaxies resulting from the fact that the spectral energy distributions (SEDs) of these sources are substantially different from each other (Laurent et al. 2000; Lacy et al. 2004). Lacy et al. (2004) introduced a mid-IR color cut to separate AGNs using Spitzer SAGE (Surveying the Agents of a Galaxy's Evolution; Meixner et al. 2006) catalog. Kozłowski & Kochanek (2009) employed a similar mid-IR color cut and selected about 5000 AGN candidates from the Spitzer SAGE catalog.

We used these mid-IR color selections as the first diagnostic. We crossmatched our candidates with the Spitzer SAGE LMC catalog containing 6 million mid-IR objects in order to check whether our candidates are inside the mid-IR selection cuts. We searched for the nearest SAGE source from each candidate within a 1'' search radius. In order to minimize false crossmatchings, we defined a source as a counterpart only if there are no other Spitzer sources within a 3'' radius from the candidate.

We found about 700 Spitzer counterparts shown in Figure 1 (dots). The sources inside region B could be either AGNs or stars, while the sources inside region A are likely AGNs. The YSO region is thought to be dominated by young stellar objects (YSOs) while the QSO region is thought to be dominated by AGNs. Nevertheless, all the sources inside these four regions are potential QSOs.⁸ Almost all of the confirmed MACHO QSOs are inside these four regions as shown in Figure 1 (boxes).⁹ The candidates inside these regions are most likely broad emission line QSOs (i.e., Type I AGNs; Stern et al. 2005). Among these counterparts, the sources inside both the QSO and the A regions are likely to be QSOs. We found that 469 QSO candidates are inside both QSO and A regions.

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Figure 2 shows the estimated K-method QSO probability products of these 469 candidates. As the histogram shows, there are more QSO candidates at higher probability than lower probability, which implies that the mid-IR diagnostic is in line with the K-method.¹⁰ In addition, the histogram shows a bimodal distribution of the probabilities. We will address this bimodality in the following section.

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3.2. Photometric Redshift Using Template Fitting

We first crossmatched the 2566 QSO candidates with the UBVI catalog for the LMC (Zaritsky et al. 2004) and the Two Micron All Sky Survey (2MASS) catalog (Skrutskie et al. 2006) to extract UBVI and JHK magnitudes. We searched the nearest source from each of the candidates within a 3'' search radius. In the case of the UBVI catalog, we found in total 2375 counterparts. Among them, 84% (93%) UBVI counterparts are within a 1'' (15) distance from the candidates. In addition, only 0.3% (2% or 17%) of the candidates have another counterpart within a 1'' (15 or 3'') distance from the candidates. Thus the portion of the false crossmatching is not significant. In the case of the 2MASS catalog, we found in total 846 counterparts. From those, 74% (83%) are within a 1'' (15) distance from the candidates while 0% (0.1% or 0.5%) of the candidates have another counterpart within a 1'' (15 or 3'') distance from the candidates. Again the portion of the false crossmatching is negligible.

We then separated stars from "galaxies and AGNs" (i.e., extragalactic sources) using a criterion proposed by Eisenhardt et al. (2004) and Rowan-Robinson et al. (2005). Figure 3 shows the criterion (the solid line) we applied. There were 686 extragalactic sources (above the cut) and 1274 stars (below the cut).¹¹ These 686 extragalactic sources were then fitted with galaxy templates in order to derive photometric redshifts (Rowan-Robinson et al. 2008). The templates contained three QSOs, one starburst, and ten galaxy templates. For details about the photometric redshift estimations and the SED template fitting, see Rowan-Robinson et al. (2008).

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Among the extragalactic sources, 602 were fitted with AGN templates (i.e., QSOs) while the remaining 84 were fitted with the galaxy templates (i.e., galaxies). These 602 candidates are likely QSOs. Figure 4 shows the photometric redshifts of these QSOs and galaxies. As the figure shows, the QSOs (top panel) have relatively higher redshifts than the galaxies (bottom panel). QSOs are much more luminous than galaxies and thus are detectable at higher redshifts than galaxies. In Figure 5, we show the comparison between the photometric redshifts and the spectroscopic redshifts of the confirmed MACHO QSOs (Geha et al. 2003). Out of the 58 confirmed MACHO QSOs,¹² 40 are fitted with the photometric redshift code. The remaining 18 were not fitted due to the lack of data (i.e., UBVI magnitudes). Among these 40 confirmed MACHO QSOs, only one was best fitted with galaxy templates while the other 39 were fitted with AGN templates. The QSO best fitted with the galaxy templates is confirmed to be a QSO from the work done by Schmidtke et al. (1999) and Geha et al. (2003). Out of the 40 QSOs, 28 (70%) are inside the ±0.1 dex accuracy (the dashed line in the figure).

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Figure 6 shows the K-method probability of QSOs, galaxies, and stars discriminated during the photometric redshift estimation. As the figure shows, the majority of QSOs have higher probabilities than galaxies and stars, which implies that galaxies and stars have different and most likely weaker variability characteristics from/than QSOs. Note that the probabilities are from the K-method which mainly used variability features of light curves to select QSO candidates.

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The left panel of Figure 6 also shows similar bimodality as seen in Figure 2. In order to check if there exists (1) different variability characteristics between QSOs, galaxies, and stars, and (2) different variability characteristics between the high- and low-probability QSO candidates, we show histograms of two variability features defined in Kim et al. (2011) in Figure 7. The left 2 × 2 sub-panels (left panels A, B, C, and D) show the histogram of $\sigma /\bar{m}$, where σ is the standard deviation and $\bar{m}$ is the mean magnitude. In general, $\sigma /\bar{m}$ is large when a light curve has strong variability. The x-axis is scaled to be between 0 and 1. To check if differences exist between high- and low-probability QSOs (A and B), we selected two subsets: one of high (⩾80%) and the other of low (⩽40%) probability QSOs. We included all galaxies (C) and stars (D) regardless of their probabilities. As the left panels display, galaxies and stars show different distributions from the distribution of QSOs that has a peak around ∼0.3. Nevertheless, high- and low-probability QSOs do not show different distribution. The right 2 × 2 sub-panels (right panels A, B, C, and D) show a different time variability index, Stetson K_AC, which is the observation of the distribution of data points between the maximum and minimum values of the autocorrelation function of a light curve (Kim et al. 2011). As the panels show, high-probability QSOs (A) show a peak around 0.6 while low-probability QSOs (B) show a peak around 0.4. Galaxies (C) and stars (D) show peaks around 0.7. Thus, it seems that the bimodality shown in the left panel of Figure 6 and the different distributions between QSOs, galaxies, and stars in Figure 6 is correlated with the different variability characteristics of the light curves. Further analysis of this bimodality, requiring careful investigation of many variability characteristics and understanding of the selection biases, is beyond the scope of this paper.

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In addition, Figure 8 shows the mid-IR colors of QSOs, galaxies, and stars. As the figure shows, almost all of the QSOs (dots) are inside the four regions while most of the stars (triangles) are outside the regions. Galaxies (squares) are either inside or outside the regions.

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3.3. X-Ray Luminosity

In order to estimate the X-ray luminosity, we crossmatched the 2566 QSO candidates with two X-ray point-source catalogs: the Chandra X-ray source catalog (Evans et al. 2010) and the XMM-Newton 2nd Incremental Source catalog (Watson et al. 2009). We searched for the nearest source within a 5'' search radius from each candidate. The majority of the crossmatched counterparts were within a 3'' distance from the candidates and there were no additional counterparts within a 5'' distance from the candidates. We found 88 counterparts from either the XMM or Chandra catalogs.

Among the 88 counterparts, 64 were fitted with the SED templates mentioned in Section 3.2 and therefore had estimated photometric redshifts. We used the photometric redshifts and X-ray fluxes from the catalogs to calculate the X-ray luminosity of each counterpart. Figure 9 shows the photometric redshifts (x-axis) and the estimated X-ray luminosity, logL_X (y-axis). In the left panel, we show the 61 XMM counterparts including eight confirmed MACHO QSOs. The right panel shows 14 Chandra counterparts including three confirmed MACHO QSOs. Almost all of the candidates (60) have higher logL_X than 42. In addition, six confirmed MACHO QSOs and 26 candidates show logL_X higher than 44. The candidates showing higher logL_X than 44 (42) are likely to be QSOs (AGNs; Elvis et al. 1994; Persic et al. 2004). The remaining candidates that show lower logL_X than 42 are likely to be galaxies.

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We show the mid-IR colors of these X-ray counterparts in Figure 10. The classification of QSOs (dots), AGNs ("×"s), and galaxies (squares) is based on the X-ray luminosity of the counterparts.

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4.1. Support Vector Machine

SVM (Boser et al. 1992) is a supervised machine learning algorithm that trains a two-class classification model using samples of two known classes (i.e., training set). SVM is currently one of the best classification methods in machine learning. The classifier of an SVM defines a linear hyperplane that separates two classes in training data. To select a unique hyperplane among the set of possible hyperplanes that separate the data, SVM chooses the hyperplane which maximizes the margin between the two classes, and is therefore often called the maximum margin separator. SVM is also able to separate nonlinearly separable classes by using a kernel function (e.g., a polynomial kernel or a radial basis kernel), transforming nonlinear feature spaces into linear feature spaces. The hypothesis of SVM has the form

$$\begin{equation} {\rm Class}(z) = \mbox{sign}\left(\sum _i \alpha _i y_i K(z,x_i) - b\right), \end{equation} \tag{ 1 }$$

where i are the indices for training set examples, x_i are the examples, y_i are the labels, z is the example that we are predicting the label for, K(z, x_i) is a kernel function, and b is a threshold. The α_i are the parameters learned by the training procedure. Despite the mapping to a potentially high dimensional space using a kernel function, the maximum margin criterion leads to automatic capacity control and thus avoids overfitting.

Compared to neural networks, SVMs provide a flexible classification model, avoid the problems of local minima, and reduce the need for parameter tuning. For an overview, discussion, and practical details, see Cristianini & Shawe-Taylor (2000), Bennett & Campbell (2000), Hsu et al. (2003), Kim et al. (2011), and references therein. Because the standard SVM can only solve a two-class problem, Schölkopf et al. (2001) proposed a method to solve one-class classification problems using the SVM. In brief, they define the origin as the second class and separate the one class from the origin using the SVM. For details about the method, see Schölkopf et al. (2001) and Manevitz & Yousef (2002).

4.2. Training a One-class SVM to Select High-confidence QSO Candidates

We employed the one-class SVM classification method to select high-confidence QSO candidates because we do not have negative examples (i.e., non-QSO training set). We used a linear kernel rather than a polynomial kernel or a radial basis kernel because we empirically found that using other kernels did not improve classification results. To train a model, we first defined the diagnostics results as feature vectors. Table 1 summarizes the feature vectors. When we could not determine a feature value due to the nonexistence of counterpart with either the Spitzer SAGE, UBVI, or X-ray catalogs, we assigned zero to the corresponding feature. Figure 11 outlines the calculation of the diagnostics and the number of candidates for which the diagnostics are available. As mentioned above, we started with the 2566 QSO candidates selected using the K-method ("Data Preparation" panel in the figure). The diagnostics applied to these candidates are shown in the "High Confidence QSO Selection" panel. We also show the number of QSO candidates after the diagnostics (double-lined rectangles).

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Table 1. Feature Vectors

Mid-IR	Extragalactic Sources/Stars	SED Fitting	χ2	Chandra	XMM
No CPa : 0	No CP: 0	No CP: 0	No CP: 0	No CP: 0	No CP: 0
Inside any of the four regions: 1	Stars: 1	Galaxies: 1	χ2 valueb	Galaxies: 1	Galaxies: 1
Inside both the QSO and A region: 2	Extragalactic sources: 2	AGNs: 2		AGNs: 2	AGNs: 2
				QSOs: 3	QSOs: 3

Notes. ^aNo counterpart. ^bχ² is from the SED fitting.

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We trained a one-class SVM model using these features.¹³ We then tuned the model by adjusting the threshold, b, in order to (1) obtain the highest efficiency based on the confirmed 58 MACHO QSOs, and (2) minimize the number of selected QSO candidates, which reduces the number of false positives as well. Figure 12 shows the efficiency and the number of candidates as a function of b. The black square shows the threshold we finally adopted. Using the determined threshold, the trained model showed 74% efficiency. We applied the tuned model to the 2566 QSO candidates and selected 663 QSO candidates (i.e., hc-QSOs).

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Table 2 shows a few important parameters for some of the QSO candidates. The entire parameters of the 2566 QSO candidates are published in the online Journal. We also provide catalogs and light curves of all the candidates at http://timemachine.iic.harvard.edu/coati/QSOs.

Table 2. Several Important Parameters of the QSO Candidates

MACHO ID	R.A.	Decl.	V	hc-QSOa
	(deg)	(deg)	(mag)
11.8747.1083	83.52708	−70.62689	18.98	1
11.8753.346	83.66207	−70.20544	18.72
11.8984.29	83.89623	−70.89459	18.16
11.8989.258	84.04636	−70.61672	18.67
11.8994.1323	83.91927	−70.25463	19.27	1
11.9349.1074	84.53299	−70.81329	20.26	1
11.9353.1217	84.52798	−70.50399	19.52
12.10679.528	86.51372	−70.85550	18.99
13.5834.232	79.19451	−71.16704	19.57
13.6446.758	80.00723	−70.74329	20.32
13.6448.3756	80.03121	−70.59326	19.04
13.6560.555	80.25070	−71.21474	19.68

Note. ^a1: high-confidence QSO candidate.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Recently, Kozłowski et al. (2012) selected QSO candidates using mid-IR colors, X-ray emission, and/or optical variability in the OGLE light curve database (Udalski et al. 2008). For the variability selection, they used the Damped Random Walk (DRW) model of light curves (Kelly et al. 2009; Kozłowski et al. 2010) and then applied several cuts including magnitude, model fitting accuracy,¹⁴ slope of a structure function, amplitude, and timescale of light curve variations. They then visually examined all the light curves of the candidates and removed about 96% of light curves (∼23,000) from the final list. Most of false positives were the "ghost" variable objects caused by photometric defects. They finally observed 845 QSO candidates using AAT/AAOmega¹⁵ and confirmed 169 QSOs including 25 previously known QSOs¹⁶ (i.e., 144 newly discovered QSOs) in the four ∼3 deg² fields near the LMC center. They also provided the list of remaining 676 objects. Among these 676 objects, they confirmed that 275 are non-QSOs, including YSOs, red stars, blue stars, Be stars, and planetary nebulae.¹⁷

To estimate the efficiency and the false positive rate of our selection method, we first crossmatched the 151 discovered QSOs¹⁸ and 275 confirmed non-QSOs (i.e., false positives) with the entire MACHO LMC light curve database. We searched the nearest MACHO LMC source within a 3'' search radius. Out of 151 QSOs and 275 non-QSOs, 64 and 122 were crossmatched with the MACHO sources, respectively. Note that only 46 out of 64 were selected using variability characteristics in the OGLE-III light curves (Kozłowski et al. 2012).

Among these 46 QSOs, 20 are in the hc-QSO list (hereinafter c-QSOs) and 26 are not in the hc-QSO list (hereinafter cn-QSOs), which gives us 43% efficiency. It is worth mentioning that the yield of QSO candidates from Kozłowski et al. (2012) selected using only variability based on the DRW model was 7%.

Despite the fact that these 46 QSOs were determined to be variable objects based on the optical OGLE-III light curves, some of them do not show strong variability in the MACHO light curves because of (1) the difference of the limiting magnitudes of the two surveys, and (2) the photometric uncertainty of the MACHO light curves. For instance, we found that 11 of cn-QSOs are fainter than 19 MACHO R magnitude (m_R) while only two of c-QSOs are fainter than 19 m_R, which is around a limiting magnitude of MACHO survey (Figure 13). Thus, it is likely that the K-method using variability was not able to detect some of the QSOs due to the large photometric uncertainty and thus weak variability. Figure 14 shows the histogram of the ratio between the average photometric uncertainty and standard deviation (i.e., amplitude), σ/, of the light curves of c-QSOs and cn-QSOs. Small σ/ means that the photometric uncertainty is relatively larger than the amplitude of the light curve, which implies that it is rather hard to detect its variability. As the figure shows, c-QSOs have relatively larger σ/ than cn-QSOs, which means c-QSOs are more detectable than cn-QSOs using their variability. σ is one of the time variability features that the K-method used.

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In Figure 15, we show an alternative way of seeing variability characteristic of a light curve by borrowing one example of the time series features, R_cs (Ellaway 1978), used in the K-method. R_cs, the range of a cumulative sum, is typically large for the variables showing non-periodic and strong variability, and is small for periodic variables or non-variables. As the figure shows, the histogram of c-QSOs (top panel) has a peak around 6 while the histograms of cn-QSOs shows a peak around 3 (bottom panel).

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In addition, we show the MACHO light curves of the 20 c-QSOs and 26 cn-QSOs in Figures 16 and 17. As Figure 16 shows, most of the c-QSOs show strong variability. On the other hand, Figure 17 shows that most of the cn-QSOs fainter than 19 m_R show relatively weaker variability than the variability of c-QSOs. Only cn-QSOs brighter than 19 m_R show strong variability comparable to that of c-QSOs.

According to Figures 14, 15, 16, and 17, it seems that the main reason for the non-detection of QSOs is the relatively weaker variability. Thus, if we ignore some of the QSOs showing weak variability, our efficiency would be higher than 43%. For instance, if we ignore the 11 cn-QSOs fainter than 19 m_R, our efficiency increases to 57%.

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In the case of the false positives, only 2 out of 122 confirmed non-QSOs are inside the hc-QSO list, which gives 0.3% false positive rate. The two false positives are YSOs. We examined their MACHO light curves and confirmed that they show strong variability. Note that Kozłowski et al. (2012) monitored 12 deg² fields around the LMC that are mostly inside the 40 deg² MACHO LMC fields. Given that our QSO candidates are uniformly distributed around the LMC, we would have about one-third of the number of the hc-QSOs (12/40) inside the fields that Kozłowski et al. (2012) monitored. In such a case, the false positive rate is about 1%. However, the true false positive rate would be higher than 1% because Kozłowski et al. (2012) did not monitor all the sources in the fields, which means that some of our QSO candidates are not in their list. Nevertheless, these 122 non-QSOs were selected not only by variability but also by mid-IR colors and X-ray emission. Thus, it seems that our method is successful in excluding any type of false positives, which is crucial for the selection of QSO candidates from massive astronomical databases such as Pan-STARRS (Kaiser 2004) and LSST (Ivezic et al. 2008) due to (1) the enormous amount of data, which thus could yield huge number of false positives, and (2) the high cost of spectroscopic observations for such deep and wide field surveys.

In this paper, we presented 663 high-confidence QSO candidates in the LMC fields. We first selected 2566 QSO candidates based on the time variability of MACHO B- and R-band light curves in the MACHO LMC light curve database using the method of Kim et al. (2011). We then applied multiple diagnostics such as mid-IR color, photometric redshift, and X-ray luminosity to these QSO candidates. Using the diagnostics outputs, we trained a one-class SVM model to discriminate high-confidence QSO candidates. We finally applied the trained model to the original candidates and selected 663 QSO candidates.

To estimate the yield and false positive rate of the final list, we crossmatched them with recently confirmed QSOs and non-QSOs in the LMC field (Kozłowski et al. 2012). As a result, we found that the yield is higher than 43%. It is worth mentioning that the yield of the QSO candidates selected using the "DRW" model (Kelly et al. 2009) is 7% (Kozłowski et al. 2012). In the case of the false positive rate, we found that there are only a few confirmed non-QSOs in our list, which is a less than 1% false positive rate. Thus, this set could be used as a target set potential for spectroscopic survey to maximize the yield. This is important because the spectroscopic observations for relatively faint objects such as the QSO candidates in the dense- and wide-field area around the LMC is extremely expensive. We are planning to use the confirmed QSOs and confirmed non-QSOs to improve our QSO selection method. This work will be separately published in the near future.

We will apply our method to the MACHO SMC/bulge database and the Pan-STARRS MDF (Medium Deep Field) time series database to further select QSO candidates and thus increase the collection of QSO light curves.

We thank L. Mylonadis for helpful comments. The analysis in this paper has been done using the Odyssey cluster supported by the FAS Research Computing Group at Harvard. This work has been supported by NSF grant IIS-0803409. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.