An Automated Tool to Detect Variable Sources in the Vista Variables in the Vía Láctea Survey: The VVV Variables (V⁴) Catalog of Tiles d001 and d002

The PSF photometry was obtained using the ${\mathtt{Dophot}}$ software (Schechter et al. 1993; Alonso-García et al. 2012) in all available tile images in the field of view (FoV). We based this procedure on the method explained in Navarro Molina et al. (2016). We assessed the reliability of the photometry using the ${\mathtt{Dophot}}$ parameter chi, which quantifies the PSF quality. The sources with $\mathrm{chi}\gt 3$ were rejected due to the large associated uncertainty. The calibration process to the VISTA system was done using the aperture photometry catalogs produced by the Cambridge Astronomical Survey Unit¹² (CASU). We selected sources with stellar ("−1") or borderline stellar ("−2") morphological classification to perform the cross-match using ${\mathtt{STILTS}}$ (Taylor 2006), using the catalog of the first epoch as reference with a 034 tolerance (VIRCAM pixel size). The conversion factors and uncertainties were estimated via a 2σ clipping linear fit to the ${\mathtt{Dophot}}$ PSF photometry versus the CASU isolated selected sources. By following this procedure, we have found 624,983 sources in d001 and 683,643 sources in d002 in common in the K_s band. The photometry in the J and H bands was performed using ${\mathtt{Dophot}}$ in a similar manner, i.e., using the CASU catalogs to calibrate the PSF photometry.

As has been pointed out, tiles d001 and d002 accumulate up to 55 and 41 epochs observed between 2010 and 2015, respectively. The left panel of Figure 1 shows the gaps, baseline, and maximum size of the time step between epochs. The right panel of Figure 1 shows the distribution of the difference of consecutive observations ΔMJD, zoomed up to ${\rm{\Delta }}\mathrm{MJD}\gt 12$ days. The minimum time interval between the observation is ∼0.35 days, with distribution maximum between 0.35 and 2 days. Thus, from the time cadence of the observations, we can expect to detect variability related to timescale accretion variations, star spots, episodic accretion events, rotational modulation, and variable extinction in the YSOs (Rebull et al. 2014; Contreras Peña et al. 2017a). On the other hand, VVV produces unevenly spaced light curves, which provides its challenges, but we still expect to identify different types of periodic variability in a wide range of timescales (see, for example, Elorrieta et al. 2016; Gran et al. 2016; Minniti et al. 2017).

The K_s-band time series of the sources were constructed by cross-correlation of all the catalogs for all available epochs. We filtered our initial sets of time series with some ad hoc quality and robustness criteria: (1) a minimum of 25 photometric measurements; (2) a total amplitude ${\rm{\Delta }}{K}_{s}\gt 0.2$ mag, where ${\rm{\Delta }}{K}_{s}\,=({K}_{s}^{\max }-{K}_{s}^{\min })$; and (3) an upper limit in flux of ${K}_{s}\gt 11$ mag (to avoid objects that may suffer from saturation in some VVV epochs). The first restriction represents the minimum number of epochs that allows us to search for reliable periods. The second is motivated by a conservative estimation of the errors of photometry and transformation to the standard system. These initial filters reduced the source numbers obtained from photometry by approximately 30% (for example, from 669,825 to 433,102 for d001). Moreover, the photometric measurements are prone to be affected by systematic errors that are hard to clarify and quantify, given atmospheric or instrumental problems. For example, Alonso-García et al. (2015) reported a problem related to highly variable PSFs in the tile images due to different geometric distortions in the combination process of the paw-print images. Thus, to remove outliers in the time series, we implement the modified Thompson τ technique, which is based on the definition shown in Thompson (1985). The modified Thompson τ statistic is defined as

$$\begin{eqnarray}&&\tau =\displaystyle \frac{{t}_{\alpha /2}(n-1)}{\sqrt{n}\sqrt{n-2+{t}_{\alpha /2}^{2}}},\end{eqnarray} \tag{ 1 }$$

where $n$ is the number of data points, and ${t}_{\alpha /2}$ is the critical value of Student's t-distribution given a confidence parameter α. For each photometric data point K_s in a time series, the standard deviation of the time series ${\sigma }_{\mathrm{ts}}$ and the absolute deviation ${\delta }_{i}=| {{Ks}}_{i}-\overline{K}s|$ is calculated, where $\overline{K}s$ is the mean Ks magnitude. Individual photometric measurements were removed from time series when ${\delta }_{i}\gt \tau {\sigma }_{\mathrm{ts}}$ using a confidence level of 95% (i.e., $\alpha =0.05$). One of the consequences of this approach is that we will remove poorly sampled transients event from our time series. Figure 2 shows the performance of this method acting on a time series.

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Eruptive pre-main-sequence (PMS) stars are traditionally classified as FU Orionis (FUors; Herbig 1966) and EX Lupi (EXors; Herbig 1989) types. Their variations occasionally have high amplitudes (up to 2–6 mag in the optical bands) in a short timescale. Different physical processes have been proposed to explain the variations of these objects, among them accretion or variable extinction induced by their circumstellar disks. These high-amplitude variables are potential tracers of a new generation of stars, so we expect to detect them within and close to the SFR of the Galaxy.

As an example, in Contreras Peña et al. (2017a), the total amplitude ${\rm{\Delta }}{K}_{s}$ was used as a discriminant to identify variable sources with ${\rm{\Delta }}{K}_{s}\gt 1$ mag. This method was very useful to help identify likely YSOs among irregular and periodic variable stars projected against SFRs. The "amplitude index" also performs satisfactorily in identifying sources with a large-amplitude ΔK_s, like some eclipsing binary (EB) systems and likely pulsating asymptotic giant branch (AGB) stars, as Miras and semi-regular sources, which have periods longer than $P\geqslant 100$ days and are frequently grouped under the name "long-period variables" (LPVs).

Following the same idea, we made a nonparametric fit on our photometric catalogs of d001 and d002. In order to quantify the behavior of ΔK_s as a function of mean magnitude ${\overline{K}}_{s}$, we measured the dispersion in bins and selected those above $4\sigma$. This allowed us to define dynamical thresholds, taking into account that the estimated σ depends on the stellar population projected on the different tiles (for example, a tile containing a projected SFR will have a different threshold assigned than a tile with Population II stars). The left panel of Figure 4 shows the amplitude ΔK_s selection for the sources found in tile d001.

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To complement the previously described criterion, we performed an additional selection using the η index (von Neumann 1941; Shin et al. 2009; Sokolovsky et al. 2017). This statistic is defined as the squared addition of successive differences between adjacent observations in a time series,

$$\begin{eqnarray}&&\eta =\displaystyle \frac{1}{(N-1){\sigma }_{\mathrm{ts}}^{2}}\displaystyle \sum _{i=1}^{N-1}{({m}_{i+1}-{m}_{i})}^{2},\end{eqnarray} \tag{ 2 }$$

where ${m}_{i}$ are magnitude measurements, and N is the available number of epochs. The properties of the η index are well known for a stationary Gaussian distribution but not for astronomical time series, because they usually have an unequal sampling. For time series with uncorrelated photometric measurements (i.e., time series with uncorrelated normally distributed measurements), the η index would have a value of ∼2 and extreme values for series with long time variability trends. Given the aforementioned properties and the volume of the data, we expect that index η has a Gaussian distribution centered in $\eta \approx 2$. We separated ${\overline{K}}_{s}$ into 0.5 mag bins and considered $3.5\sigma$ confidence intervals on every bin to identify variable sources. The right panel of Figure 4 shows the η selection and the fit of the Gaussian functions in each histogram generated by separating the distribution in bins of 0.5 mag.

Each irregular variable should satisfy both ${\rm{\Delta }}{K}_{s},\eta$ criteria in order to be included in the paper as an irregular variable. All selected candidates have visual confirmation on the corresponding images; the candidates with close (less than 04) companions are removed.

One of the main goals of the VVV Survey is to obtain a complete census of pulsating stars, such as RR Lyrae, Cepheids, semi-regular, and Mira variables across the Milky Way. These sources provide useful information from their quality as standard candles (using the developed period–luminosity relations in the near-IR) to determine the structure of our Galaxy. These stars are also useful to map the extinction affecting the projected areas. Another potential set of targets to be identified are the EB systems, which are known to provide the most robust/model free estimates of the fundamental stellar parameters.

In this study, we have implemented two methods to identify periodic sources within VVV data.

• 1.  
  The generalized Lomb–Scargle periodogram (GLS; Zechmeister & Kürster 2009): a least-squares spectral analysis method based on the classical Lomb–Scargle periodogram (Lomb 1976; Scargle 1982). In particular, we used its implementation in the ${\mathtt{astroML}}$ ¹³ python library (Vanderplas & Ivezić 2007).
• 2.  
  The informatic potential metric Q_m (IP metric; Huijse et al. 2011): a discriminant designed to identify the fundamental period of a time series using information theory. Within this framework, different sets of time series $\{{x}_{n}\}$ are assumed to be realizations of a continuous random variable X. The IP is defined as follows:

  $$\begin{eqnarray}&&{\mathrm{IP}}_{X}(\{{x}_{n}\})=\displaystyle \frac{1}{{N}^{2}}\displaystyle \frac{1}{\sqrt{2\pi }\sigma }\displaystyle \sum _{i=1}^{N}\displaystyle \sum _{j=1}^{N}\exp \left(-\displaystyle \frac{\parallel {x}_{i}-{x}_{j}{\parallel }^{2}}{2{\sigma }^{2}}\right).\end{eqnarray} \tag{ 3 }$$

  We used a grid of trial periods ${P}_{t}$ to fold the time series into phase space. The folded light curves are then segmented in $H$ bins, and IP is computed for every bin ($h$). The IP metric Q_m is computed as the squared differences between the information potential of each bin and the global IP:

  $$\begin{eqnarray}&&{Q}_{m}({P}_{t})=\displaystyle \frac{1}{H}\displaystyle \sum _{h=1}^{H}{[{\mathrm{IP}}_{X}(\{{x}_{n}\})-{\mathrm{IP}}_{X}({\{{x}_{n}\}}_{n\in h})]}^{2}.\end{eqnarray} \tag{ 4 }$$

To estimate the reliability of the periods found with both approaches, we calculated the statistical significance for the spectral power peaks in the GLS and the IP metric. Only objects with peak significance greater that 99.9% were considered for further analysis and characterization. We note that this formal peak significance assumes that the uncertainties are described by uncorrelated Gaussian noise.

To determine the variability type of the identified periodic stars, we consider the shape of the light curve and the period P determined by the methods previously described. A common tool to quantify the shape of a light curve is using templates, where the light curves of periodic sources are compared with templates to assign a well-defined variability class using one or a set of statistics to rely on this classification. These templates could be collected from public archives, literature, and other databases in order to create "training sets" that point to an automated classification. In this context, a significant (and still increasing) number of infrared light-curve templates have been assembled in the VVV Templates Project (Angeloni et al. 2014), where the main goal is to develop and test machine-learning algorithms for the automatic classification of VVV light curves. Nevertheless, we need to consider that in the NIR, RR Lyrae stars are a special case, given that the amplitudes of light curves decrease from optical to infrared wavelengths. This leads to it being more difficult to differentiate between RR Lyraes in the fundamental-mode (RRab) and first-overtone (RRc) subtypes using only templates. In this context, we used two criteria to classify these periodic sources.

3.3.1. Using the VVV Template Project

We expect low accuracies in the period estimation due to the relatively small number of epochs, as we pointed out in Section 2.2. With this in mind, we have used templates of those variables that we expected to find in this galactic longitude, such as classic Cepheids and eclipsing variables. The δ Scuti stars were not considered in this analysis, given that just two light-curve templates are available in the K_s band. Nevertheless, their periods are less than 0.2 days and may have similar characteristics to EBs (Dong et al. 2017). Several δ Scuti sources were identified around open clusters in the K_s band (Palma et al. 2016), so we need more information for a good characterization of this type of variable.

We used templates of classic Cepheids (103 templates in K_s with $0.97\lt P\lt 133.90$) and EBs (76 templates in K_s with $0.305\lt P\lt 16.092$) to compare with the light curves of our objects when the period P is contained in the indicated period range of the templates. To quantify these comparisons, we performed a Fourier fit of N harmonics into the phase space for each template and variable, given its period P and average magnitude $\langle m\rangle$ (see Figure 5). The amplitude ${A}_{k}$ and phase ϕ_k for each k harmonic were determined. The Fourier series f(t) at time t is given by

$$\begin{eqnarray}&&f(t)=\langle m\rangle +\displaystyle \sum _{k=1}^{N}{A}_{k}\sin \left(\displaystyle \frac{2\pi {kt}}{P}+{\phi }_{k}\right).\end{eqnarray} \tag{ 5 }$$

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Each "synthesized" template was then normalized by subtracting the integral of the obtained Fourier series. The harmonic number N used to fit the model to periodic sources is $N=4$. The periodic stars are classified using the template that had the best goodness of fit, using the reduced ${\chi }_{\mathrm{red}}^{2}$ statistics as the criterion. If a source has ${\chi }_{\mathrm{red}}^{2}\gt 1$, it will remain as not classified.

3.3.2. Classifying RR Lyrae Stars

We had identified 72 variable sources that fulfill both the ${\rm{\Delta }}{K}_{s}$ and η criteria. If a source presents periodicity, it is removed from the sample and added to the periodic sample. This was the case for two sources (d001-79 and d002-103) that present a large amplitude and period, typical signatures of dust-enshrouded AGB stars, invisible in the optical range, due to its thick circumstellar-envelope product of its high mass-loss rate.

Finally, we identified 70 irregular variable sources, 45 of them belonging to d001 and 25 to d002. Almost two-thirds of them (64.28%) are projected in the d001 tile and follow the cold gas/dust distribution as traced by the W3 (${\lambda }_{\mathrm{eff}}=12\,\mu {\rm{m}}$) band WISE image (the background of Figure 6). The highest overdensity is observed at the borders of the SFR, where the nebulosity is overwhelming, thus suggesting active star formation. All objects in the sample are, to the best of our knowledge, reported here for the first time. Some of these sources are shown in Figure 7.

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The sample can be separated in two groups.

• 1.  
  Short-term irregular sources. As discussed in Section 2.2, the cadence of VVV can reveal objects with large changes in their magnitudes in short periods of time, often associated with YSOs or PMS stars. Examples of such time series are shown in Figure 7. As noted previously, intrinsic changes in the sources can be explained by variable accretion (see, e.g., Meyer et al. 1997; Cody et al. 2014; Rebull et al. 2014) referred to as bursts if there is a brief, well-defined event and then a return to quiescence. Variable extinction is also possible. The individual characterization of the objects is beyond the scope of this paper, and they will be analyzed in an upcoming work, once the follow-up spectroscopic analysis is completed.
• 2.  
  Long-term irregular variables. These kinds of sources have a slow change of their magnitudes over the time series, reaching large amplitudes ΔK_s in longer time intervals. In general, the sources do not exhibit large-amplitude changes in short time intervals but increase/decrease their luminosities monotonically and then, in certain cases, return to their mean magnitude. Possible mechanisms here are the eruptive episodes or long-term extinction events, followed by quiescent periods. These time series can also reveal stellar sources such as supernovae, microlensing events (Minniti et al. 2015), LPVs, aperiodic long-term variability objects, and even extragalactic variable sources such as quasars. Examples of long-term irregular time series can be seen in the right panels of Figure 7.

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In order to analyze the morphological behavior of VVV irregular variable sources, Contreras Peña et al. (2017a), influenced by previous works such as Findeisen et al. (2013), proposed the following classifications for their sample of high-amplitude variables (${\rm{\Delta }}{K}_{s}\gt 1$ mag): faders, dippers, short-timescale variables (STVs), and eruptives. However, half of our irregular variable sample has an amplitude ${\rm{\Delta }}{K}_{s}\lt 1$ mag (right panel of Figure 9). Similar variable sources with low amplitude have been reported in the literature (see, for example, Carpenter et al. 2001; Wolk et al. 2013) with light curves similar to those reported in this work. Therefore, given that the classification for irregular variables is defined mainly by the shape of the time series, we extended the classification proposed in Contreras Peña et al. (2017a) for low-amplitude sources (${\rm{\Delta }}{K}_{s}\lt 1$ mag), making an exception with the eruptive classification, which describes sources with eruptions on timescales of hours to days. Sources that present eruptive long-timescale variability ($t\gt 1$ yr) and ${\rm{\Delta }}{K}_{s}\lt 1$ mag will be classified as "low-amplitude eruptive" (LAE). We used this classification to characterize our sources when applicable. In Table 2, the main characteristics of the different proposed classes are explained.

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Our automated tool detected 22 periodic variable sources with the GLS analysis in both the d001 and d002 tiles, with a range of periods of $4.03\lt P\lt 1400$ days. Given the cadence of our data and the limitations of the GLS, we cannot obtain reliable periods shorter than 2 days. The IP metric, on the other hand, shows a great performance identifying periodic sources over the entire range of periods. Several stars have been detected by both methods, showing practically identical periods within the uncertainties. Thus, taking into account that the IP metric is computationally expensive, we used this method to search for shorter periods, creating a grid of periods between 0.05 and 5 days. The IP metric identified 108 sources with $0.2\lt P\lt 3.1$ days.

Figure 5 shows examples of the periodic variables, while in Figure 8, we show the period–amplitude diagram. As can be seen, most of the stars have short periods, typical for RR Lyrae stars.

In some cases, it was not possible to distinguish between different variability types—for example, LPVs and YSOs (Figure 5)—so we put a mixed classification, LPV-YSO, and are working on additional (spectroscopic) data to clarify.

Figure 9 shows the ΔK_s distribution of the selected sources as a function of the mean ${\overline{K}}_{s}$ magnitude. The amplitude interval is in the range $0.5\,\mathrm{mag}\lt {\rm{\Delta }}{K}_{s}\lt 3.2$ mag, with an average value of $\langle {\rm{\Delta }}{K}_{s}\rangle =1.1$ mag. The histogram is influenced mainly by the periodic sources.

Figure 10 shows the position of the variable stars in the color–magnitude and color–color diagrams. To plot the nonvariable stars, we used the first epoch of $J$- and H-band tile images taken in 2010. To analyze this, we followed the method described in Ojha et al. (2004). Three regions are defined. The "F" region is located between the reddening vectors of the giant and dwarf stars. The "T" region is between the reddening vector of the giant stars and the classical T Tauri star (CTT) locus, where Class II YSOs and Herbig Ae/Be stars (Hillenbrand et al. 1992) can be identified. In the so-called "P" region, located below the reddening vector of the CTTs, the likely protostellar objects are situated. Thus, the corresponding variability types are assigned. Row 32 of Table 5 contains information on the region in the color–color diagram for each source.

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The catalog is limited to sources brighter than ${K}_{s}=11$ mag, given the saturation of the limit of VVV. We are only sensitive to the stars fainter than this magnitude limit. In the International Variable Star Index Catalog¹⁴ (VSX) are listed 57 variables in d001 and 46 in d002 fainter than ${K}_{s}=11$ mag. From these, 30 sources in d001 and 36 in d002 are identified in the photometry catalog, but all of them have a typical ΔK_s around 0.2–0.3 mag, which is close to our conservative amplitude limit described in Section 2.3. This range of amplitudes is relatively low in comparison to the average amplitude, $\langle {\rm{\Delta }}{K}_{s}\rangle =1.1$ mag, of the selected variable sources (see Figure 11). Taking into account that these variables are detected in the optical wavelengths, the amplitudes are too low to be detected in the K_s band with our searching method. Four sources from the VSX are recovered in our catalog, namely d001-20, d001-81, d002-8, and d002-60; the rest of the stars with amplitudes greater than 0.3 have less than 25 measurements. Thus, in the magnitude interval $11\,\mathrm{mag}\lt {K}_{s}\lt 15.5$ mag, we recovered only 6% of the known optical variable stars, and more than 90% of our discoveries are new. In the context of previous K_s-band studies, Minniti et al. (2017) and S. Eyheramendy et al. (2018, private communication) reported 1 and 13 RRab stars in d001 and d002, respectively. The Minniti et al. (2017) RR Lyrae star, d002-0143595, has been rediscovered in our catalog as source d002-20, with practically the same period P = 0.456794 (with a discrepancy lower than 0.01%). Twelve of the 13 RR Lyrae stars from the Eyheramendy et al. list are rediscovered in our catalog. The only source missed by our procedure has ${\rm{\Delta }}{K}_{s}=0.195$ mag and is rejected from our initial conditions. Thus, the completeness of the catalog $11\,\mathrm{mag}\lt {K}_{s}\lt 15.5$ mag is very close to 90%. We are expecting drops of the completeness for the fainter than ${K}_{s}\gt 15.5$ mag objects, but it is hard to estimate due to a lack of literature data.

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Figure 12 presents the main features η (top row) and ΔK_s (bottom row) as a function of different variability indices used in this article (see Table 1). The distribution of all detected sources in tile d001 is shown in the background. The red stars represent the periodic sources, and the blue crosses are the irregular ones. As can be seen from the figure, the irregular variable sources are well separated from the distribution and follow different trends in the plots. The source d001-75 is an exceptional case, having an amplitude of ${\rm{\Delta }}{K}_{s}=1.151$ mag, $\eta =3.193$, and a low number of observations (26 epochs). Excluding d001-75, the irregular sources fulfill ${J}_{\mathrm{stet}}\gt 0.95$, which agrees with the limit used in Rebull et al. (2014). In the case of the periodic sources with short periods, in general, they are located in the place where the main distribution is contained given the apparently uncorrelated shape of its time series, produced by the lack of observations.

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Nine open-cluster candidates are projected in the FoV of d001 and d002, namely VVV CL005, 007, 008, and 009 (Borissova et al. 2011) and La Serena 001, 002, 003, 009, and 015 (Barbá et al. 2015). The coordinates of the clusters are listed in Table 3, and the VVV color images of the clusters in d001 are shown in Figure 13 for illustration. Little is known about their properties, except for VVV CL009, which has been investigated in Chené et al. (2013) and Hervé et al. (2016). According to these papers, VVV CL009 is a young (4–6 Myr), moderately massive stellar cluster (total mass greater than 1000 ${M}_{\odot }$) containing at least an OIf/WN7 and two O8-9V stars. The cluster distance of 5 kpc is estimated by Chené et al. (2013) using spectroscopic parallaxes. In the context of this paper, we search for variable YSOs around these clusters that could be cluster members. To do this, we use the shape of the light curves, their position on the color–magnitude diagrams, the projection within the visual diameter of the clusters, and proper-motion diagrams taken from Smith et al. (2018).

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Table 3.  Basic Information on the Star Cluster Candidates in the Region

Tile ID	Name	R.A.2000	Decl.2000	ℓ	b	Radius	$E(J-K)$
		(h:m:s)	(d:m:s)	(deg)	(deg)	(arcmin)	(mag)
d001	VVV CL005	11:38:59	−63:28:42	294.9481	−1.7353	0.50 ± 0.15	1.4 ± 0.3
	La Serena 001	11:39:13	−63:29:04	294.9726	−1.7292	0.52 ± 0.10	2.8 ± 0.6
	La Serena 002	11:39:22	−63:28:11	294.9896	−1.7188	0.52 ± 0.17	3.1 ± 0.4
	La Serena 003	11:40:28	−63:27:58	295.1026	−1.6779	0.48 ± 0.09	3.2 ± 0.5
	La Serena 009	11:45:04	−63:17:44	295.5571	−1.3788	0.72 ± 0.10	2.2 ± 0.3
d002	VVV CL007	11:53:50	−64:20:28	296.7463	−2.1629	0.33 ± 0.08	2.2 ± 0.2
	VVV CL008	11:55:29	−63:56:24	296.7611	−1.7328	0.42 ± 0.10	1.4 ± 0.2
	VVV CL009	11:56:03	−63:19:00	296.8331	−1.1105	0.60 ± 0.20	1.0 ± 0.1a
	La Serena 015	11:55:23	−63:25:30	296.7131	−1.2336	0.33 ± 0.07	1.4 ± 0.2

Note.

^aChené et al. (2013).

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To estimate the projected cluster radius, we combined the existing VVV K_s-band images (55 in the case of d001 and 41 for d002) using the standard ${\mathtt{IRAF}}$ procedures, and then the PSF photometry with ${\mathtt{Daophot}}$ in ${\mathtt{IRAF}}$ was performed. The obtained magnitudes were transformed to the 2MASS system using common stars. The details of these procedures can be seen in Borissova et al. (2011, 2014). These photometric catalogs were used to construct the stellar surface-density maps by performing direct star counting in the K_s band with a $5^{\prime\prime}$ bin radius, assuming spherical symmetry. The maps are normalized by the area of the rings to determine the stellar density. The resulting spatial distribution maps of the stellar surface density are shown in Figure 14.

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As can be seen from Figure 14, the overdensity of the stars is clearly visible, and the density peaks are at least 3 times higher that the surface density of the surrounding fields, thus confirming the cluster/group nature of the candidates. The cluster boundary was determined by fitting the theoretical profile presented in Elson et al. (1987). The obtained visual radii of the clusters are listed in Table 3, where the errors correspond to uncertainties from the model fit.

The procedure employed for determining fundamental cluster parameters such as age, reddening, and distance is described in Borissova et al. (2011, 2014) and Chené et al. (2012, 2013). Briefly, to construct the color–magnitude diagram, we perform PSF photometry of the 5' × 5' $J$, $H$, and K_s fields surrounding the selected candidate using the ${\mathtt{Dophot}}$ pipeline. Data for saturated stars (usually ${K}_{s}\leqslant 11.5$ mag, depending on the crowding) were replaced by data from the 2 MASS Point Source Catalog (Skrutskie et al. 2006). Since 2MASS has a much lower angular resolution than VVV, when replacing stars, we carefully examined each cluster to avoid the contamination effects of crowding using the Point Source Catalog quality flags available in the 2MASS catalog.

To separate the field stars from probable cluster members, we used the field-star decontamination algorithm of Bonatto & Bica (2010). The algorithm divides the K_s, ($H-{K}_{s}$), and ($J-{K}_{s}$) quantities into a grid of cells. For each cell, the algorithm estimated the expected number density of member stars by subtracting the respective field-star number density. Thus, each grid setup produced a total number of member stars N_mem. Repeating the above procedure for different setups, we obtained the average number of member stars. Each star was ranked according to the number of times it survived after all runs (survival frequency), and only the N_mem highest-ranked stars were taken as cluster members. For the present cases, we obtained survival frequencies higher than 85%. To additionally clean up the diagrams, we used the relative proper-motion catalog recently constructed by Smith et al. (2018). In general, the cluster members should form a clearly visible overdensity with respect to field stars in the proper-motion diagram. In our case (see Figure 15), it is impossible to separate the cluster members from the field stars, because the cluster members closely follow the motion of the Galactic disk. Nevertheless, they mark compact groups slightly shifted from the disk population. To calculate the radius of the group, we started from the photometrically decontaminated candidates, calculated the mean proper motion and its error (quadratically adding to this error the mean of the individual proper-motion errors), and drew the circle with 3σ radius (blue circle in Figure 15). Thus, the stars with motions projected farther than 3σ from the circle are rejected.

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Taking into account that our candidates are classified as young clusters in the discovery papers of Borissova et al. (2011) and Barbá et al. (2015), the photometry/astrometry alone cannot give accurate distance and age determinations. Usually, spectroscopic parallaxes from follow-up observations of selected members are needed. Here only VVV CL005 has one follow-up object observed, thus it was impossible to obtain accurate basic parameters of the clusters. Instead, we use the PARSEC isochrones compilation for solar metallicity and ages of 5 and 400 Myr (Bressan et al. 2012; Marigo et al. 2017) to illustrate the position of the most probable cluster members and estimate their mean reddening (last column in Table 3).

4.5.1. Notes on Individual Clusters: VVV CL005

The cluster VVV CL005 is a young star cluster candidate, defined in Borissova et al. (2011) as a small group of 24 stars; it is projected close to the IC 2944 H ii region and to the IC 2948 cluster (38), on the part of the cloud [SMN83] Lam Cen 1. The brightest star within the cluster radius, namely HD 308829, is classified as a Be star of B8 spectral type and is suggested to be a member of the IC 2944 cluster (Cl* IC 2944 THA 51). The star is found to be a periodic variable star with P = 0.8709 days (Pojmanski 1998), but we cannot follow its variability with VVV, because the star is saturated in our images ($K=9.68$ mag). The published distance to the IC 2944 H ii region varies from 1.8 kpc (McSwain & Gies 2005) to 2 kpc (Sana et al. 2011) in the literature. The color–magnitude diagram of VVV CL005 (Figure 16) shows a poorly populated main sequence and some reddened stars, suggesting indeed a very young stellar group. With regard to the distance, it is impossible to estimate it from comparison with the theoretical isochrones, because the isochrones for ages younger than 5 Myr in this mass interval in the near-infrared bands are vertical and practically identical. Then, the spectroscopic distance is calculated using the spectral classification of Obj1 (R.A. = 11:38:57.73 and decl. = −63:28:22.4). The object is observed with the Astronomy Research Cornell Infra Red Imaging Spectrograph (ARCoIRIS). This is a cross-dispersed, single-object, long-slit, infrared imaging spectrograph mounted on the Blanco 4 m telescope, CTIO. The wavelength range is from 0.80 to 2.47 μm, with a spectral resolving power of about 3500 Å. The comparison with different spectral templates taken from VOSA (Bayo et al. 2008) gives the most probable spectral type as F4-F6V, used to estimate the spectroscopic parallax. We calculated a reddening and distance modulus of $E(J-{K}_{s})=1.4\pm 0.3$ and ${(M-m)}_{0}=10.45\pm 0.43$ mag (1.23 ± 0.24 kpc), respectively. The distance is comparable with the distance estimates of 1 kpc as measured from interstellar silicon monoxide (SiO) sources (Harju et al. 1998). Five variables (d001-25, 27, 28, 29, and 30; see Table 5) are probable cluster members, taking into account their projected position radius from the cluster center and the position in the proper-motion and color–magnitude diagrams (Figures 15, 16). All of them show irregular variability with relatively large amplitudes ($0.63\,\mathrm{mag}\lt {\rm{\Delta }}{K}_{s}\lt 0.88$ mag) and thus can be classified as YSOs.

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4.5.2. La Serena 001

4.5.3. La Serena 002

4.5.4. La Serena 003 and La Serena 009

The star cluster candidates La Serena 003 and 009 (LS003 and LS009) are groups of stars in formation that are deeply embedded in dust and gas. No stars with variations in the magnitude above our sensitivity limit of ${\rm{\Delta }}{K}_{s}\gt 0.2$ mag are found in the vicinities of clusters. One YSO candidate, IRAS 11426–6301, in the field of LS009 is reported by Kwok et al. (1997). Later on, Mottram et al. (2011) and Lumsden et al. (2013) resolved the source to a YSO (G295.5570-01.3787A) and H ii region (G295.5570-01.3787B, separated by 5'') on the basis of far-infrared MSX measurements. They determined the radial velocity of 37.2 km s⁻¹ and kinematic distance to both sources of 10.4 kpc. The bolometric luminosity of the YSO is calculated as 5980 ${L}_{\odot }$, while the H ii region has 63,570 ${L}_{\odot }$, and the log mass of the whole clump is estimated to be 3.106 ${M}_{\odot }$ according to the same authors. Navarete et al. (2015) reported an extended H ii emission associated with the region. Our K_s-band light curve (Figure 17) shows low-amplitude variability of 0.27 mag during the 2010–2015 time interval, with ${\overline{K}}_{s}=11.365$ mag. Note, however, that the 2MASS magnitude (taken from the 2MASS Extended Sources Catalog; Skrutskie et al. 2006)) is $K=8.94$ mag, and thus the star most probably shows long-term variability.

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IRAS 11426–6301 was observed in 2017 May with the ARCoIRIS spectrograph with 480 s integration time at 1.28 average airmass. We reduced the spectrum using the ${\mathtt{Spextool}}$ IDL package (version 4.1; Cushing et al. 2004), which is a data reduction algorithm specifically designed for the data format and characteristics of ARCoIRIS by Dr. Katelyn Allers. Telluric correction and flux calibration of the post-extraction spectra are achieved through the ${\mathtt{xtellcorr}}$ IDL package (Vacca et al. 2003). Figure 17 shows the spectrum normalized at 2.293 μm. As can be seen from the figure, the continuum level is flat to slightly rising. The overall spectral energy distribution is peaking at around 2.5 μm. The H i and He i lines are clearly visible in absorption, and some Ti lines and an Na i doublet (2.21 μm) in absorption also can be identified. The Ca i triplet (2.26 μm) and ¹²CO bands (2.29 μm) are missing. While H i and He i generally represent early-type stars, the Ti and Na features are typical of low-mass YSOs. The absence of the CO band means the absence of a circumstellar disk. A possible explanation for this contradiction could be related to the photodissociation of the CO molecule. This phenomenon (where one even detects CI but no CO, or a much lower abundance than expected) has been observed around young A-type stars in deep searches for molecular gas in debris disks (Higuchi et al. 2017). Thus, the spectrum shows mixed features arising from both high- and low-mass young stars. Taking into account the kinematic distance of 10 kpc, this object could be an unresolved compact cluster or group of young stars.

4.5.5. VVV CL007

4.5.6. VVV CL008, VVV CL009, and La Serena 015

The clusters in tile d001 are very young, still in formation, and are surrounded by dust and gas; thus, we can use the photometric catalogs from the VPHAS+ survey  (Drew et al. 2014) in order to search for additional YSOs and ${\rm{H}}\alpha$ emission candidates. The VPHAS+ catalog contains magnitudes in five filters: $u\ ({\lambda }_{\mathrm{eff}}=354\,\mathrm{nm})$, $g\ ({\lambda }_{\mathrm{eff}}=475\,\mathrm{nm})$, $r\ ({\lambda }_{\mathrm{eff}}=622\,\mathrm{nm})$, $i\ ({\lambda }_{\mathrm{eff}}=763\,\mathrm{nm})$, and ${{\rm{H}}}_{\alpha }\ ({\lambda }_{\mathrm{eff}}=659\,\mathrm{nm})$. Following Kalari et al. (2015), we construct the $(r-i,r-{\rm{H}}\alpha )$ color–color diagrams using the DR2 of the VPHAS+ catalog. The main-sequence stars do not show any ${\rm{H}}\alpha$ emission with respect to the r-band photospheric continuum. We use the VST/OmegaCAM synthetic colors for main-sequence and giant stars in the $(r-{\rm{H}}\alpha ,r-i)$ plane (Drew et al. 2014) and select the stars with more than $5\sigma$ deviation from these synthetic sequences, corrected for the corresponding reddening (dashed lines in Figure 18). The 73 selected sources are shown in Figure 18 and summarized in Table 4.

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Table 4.  VPHAS+ r, $(r-i)$, and $(r-{{\rm{H}}}_{\alpha })$ Magnitudes and Colors of the YSO Candidates

ID	R.A.2000	Decl.2000	r	r − i	$r-{{\rm{H}}}_{\alpha }$
	(deg)	(deg)	(mag)	(mag)	(mag)
CL005 C1	174.71433	−63.48757	17.98 ± 0.02	1.08 ± 0.011	1.04 ± 0.01
CL005 C2	174.71582	−63.46827	19.39 ± 0.04	0.97 ± 0.025	1.08 ± 0.03
CL005 C3	174.71664	−63.48768	20.29 ± 0.10	1.53 ± 0.054	0.95 ± 0.09
CL005 C4	174.71783	−63.48682	18.37 ± 0.02	1.05 ± 0.011	0.99 ± 0.02
CL005 C5	174.71942	−63.4668	19.67 ± 0.05	1.37 ± 0.032	0.99 ± 0.04

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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Table 5.  Information of content of V⁴ Catalog

Column	Units	Description
ID	...	Identification given by the catalog
R.A.2000	Degrees	Right Ascension of VVV source
Decl.2000	Degrees	Declination of VVV source
GLon	Degrees	Galactic longitude of VVV source
GLat	Degrees	Galactic latitude of VVV source
${\overline{{K}}}_{{s}}$	mag	Photometric mean value of Ks-band
${\overline{{K}}}_{{s}}^{\mathrm{err}}$	mag	Estimation of ${\overline{{K}}}_{{\rm{s}}}$ error using bootstrap technique
Epochs	...	Observation number of the source in their Ks time serie
ΔKs	mag	Photometric total amplitude of Ks-band
J	mag	Photometric J band
Jerr	mag	Photometric J-band error
H	mag	Photometric H band
Herr	mag	Photometric H-band error
u	mag	Photometric u band
uerr	mag	Photometric u-band error
g	mag	Photometric g band
gerr	mag	Photometric g-band error
r	mag	Photometric r band
rerr	mag	Photometric r-band error
r2	mag	Photometric r2 band
r2err	mag	Photometric r2-band error
i	mag	Photometric i band
ierr	mag	Photometric i-band error
Hα	mag	Photometric Hα band
Hα err	mag	Photometric Hα-band error
η	...	Value of the variability index η
Class	...	Classification via VVV templates light curve or shape of the time serie
Tile ID	...	VVV tile where the source is located
Period	days	Identified period for a VVV source
${{A}}_{{{K}}_{{s}}}$	mag	Extinction measured using Nishiyama et al. (2009)
Distance	Kpc	Distance measured from PL relations of RRab sources
CCD	...	Position in (H − Ks, J − H) color–color diagram
Reference	...	Reference to catalog of a documented source

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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The cross-identification of these sources with the K_s variability catalogs shows that the peak of the amplitudes is around 0.3 mag (Figure 19). As we stated in Section 2.3, we set our detection limit on the spread of the magnitude measurements with time to be greater than 0.2 mag. For sources below this threshold, we treat these objects as constant at our sensitivity level. Thus, only a few of the infrared variable YSOs (d001-25 and d001-32) are emission-line object candidates.

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