Variable stars in the VVV globular clusters. I. 2MASS-GC02 and Terzan 10

There are observations in $K_{s}$ in 43 different epochs for 2MASS-GC02 during the period 2010-2013 of the VVV survey (see Table 2), although we only considered 42 in our following analysis since tracking problems during the observations of one set produced very elongated stars that were unusable for our variability study. We more than triple the number of epochs in the only previous variability study of this cluster, performed by Borissova et al. (2007), with only 13 epochs. They found 5 RR Lyrae variable candidates, but our improved photometry and temporal coverage shows that none of them is a true variable star¹¹1Although our NV2 and their V3 RR Lyrae could be in principle cross-matched, they are already $3.1\arcsec$ away, i.e., separated by more than 9 pixels in the VVV images, and the reported periods and average magnitudes are quite different.. Fortunately, after performing the variability analysis described in Section 3, we were able to find 32 new variable candidates inside the tidal radius. Among them, we identified 13 RR Lyrae variables, 3 Cepheids, 4 eclipsing binaries, and 3 LPVs. Their positions, periods, amplitudes, magnitudes and colors are shown in Table 3 (NV1 to NV32), their light curves are plotted in Figure 2, their positions on the sky can be observed in Figure 3, and their positions in the CMD can be observed in the left panel of Figure 1.

All of the RR Lyrae candidates found (NV1 to NV10, NV13, NV24 and NV26) seem to be RRab’s according to their periods and light curves. From their position in the CMD and on the sky, it is immediately clear that the RR Lyrae candidates towards the north of the cluster center (NV4, NV7, NV9 and NV13) have redder colors, and therefore seem to be more severely affected by extinction, than the RRab candidates in the south (NV1, NV2, NV5, NV6, NV8). This feature points towards significant differential extinction across the face of the cluster. From their position in the different available CMDs, all the RRab candidates seem to belong to the cluster except NV26 – we will further confirm this point in Section 4.3. NV26 is approximately half a magnitude dimmer than the other RRab variables with similar colors, which implies that the increase in magnitude is not due to higher reddening. This feature, clearly observable in Figure 4, along with being the one farthest away from the cluster center and having a period significantly shorter than most of the other RRab candidates, suggest it is a background field RR Lyrae.

The Cepheid candidates NV11, NV28, and NV31 show periods between $\approx 1$ and $\approx 10$ days, and light curves with a sawtooth shape, characteristic of these stars in $K_{s}$ (Angeloni et al., 2014). Unfortunately, none of them seem to have high chances to belong to the cluster. NV11 and NV28 are too dim to be Type II Cepheids belonging to 2MASS-GC02. According to the period-luminosity relations by Matsunaga et al. (2013), their apparent distance moduli are $\mu_{\rm NV11}=17.80$ and $\mu_{\rm NV28}=16.76$, which differ significantly from those of the RR Lyrae shown in Figure 4 – the method to obtain those is explained in Section 4.3. Their position in the CMD suggest they are background bulge field Cepheids. On the other hand, NV31 has $\mu_{\rm NV31}=15.57$, according to the period-luminosity relations by Matsunaga et al. (2013) for Type II Cepheids. This apparent distance modulus is in the range shown by the RR Lyrae in the GC (see Figure 4), but as shown in the CMD in Figure 1, its color is too blue for NV31 to belong to the cluster or bulge.

The eclipsing binary candidates NV12, NV20, NV22, and NV32 have light curve characteristics of Algol-type binaries (EA). NV32 is too blue to be a cluster member based on its position in the CMD, but the remaining EA candidates cannot be disregarded as cluster members from the CMD examination since they lie in regions where there are cluster stars.

At the present time, there is not much we can say about the 3 LPVs discovered, NV16, NV19 and NV27. Their long periods have not allowed us yet to sample their light curves with enough phase coverage for an accurate period determination. Also their red colors seem to be the reason NV16 has been detected only in $K_{s}$, NV27 in $H$ and $K_{s}$, and NV19 in $J$, $H$ and $K_{s}$.

Almost all of the remaining 9 unclassified variables seem to be disk field stars based on their position in the CMD. The only one that could be a cluster member is NV29.

As previously mentioned in Section 2, we performed a search for variables out to a radius of $10\arcmin$ from the cluster center. This allowed us to look for variables in the field surrounding the GC, in an area approximately 3 times the size of the cluster. We found a total of 70 new variable candidates in this surrounding region. Their positions, periods, amplitudes, magnitudes and colors are shown in Table 3 (NV33 to NV102), their light curves are plotted in Figure 2, their positions on the sky can be observed in Figure 3, and their positions in the CMD can be observed in the right panel of Figure 1.

We found 6 extra-tidal RR Lyrae (NV70, NV72, NV76, NV77, NV85, and NV99) in the region studied outside the tidal radius. From the shape of their light curve and their periods they are RRab’s. From their position in the CMD all of them are clearly in the background of the GC, except NV85 and NV99 –we will further confirm this point in Section 4.3–. The high angular separations from the center of the cluster (see Table 3) and the positions in the sky (see Figure 3) of NV85 and NV99 suggest that, instead of being variables in a hypothetical GC tidal tail, they have a higher chance of being field stars located at a distance similar to that of the cluster. Most of the found field RR Lyrae being in the background of the cluster, points towards 2MASS-GC02 being in front –or in the near-side– of the Galactic bulge.

In addition to these 6 RR Lyrae, we also identified 6 Cepheids, 4 eclipsing binaries, and 19 LPV candidates. From a purely statistical point of view, being the surrounding area 3 times bigger than the region inside the tidal radius, we should expect 2 field RR Lyrae, 2 field Cepheids, 1 field eclipsing binaries, and 6 field LPV candidates inside the cluster radius. These numbers of variables are within the range of these objects found in Section 4.1, given that we are dealing with small number statistics, except for the case of RR Lyrae, where we find many more (however, it agrees with the number of field RR Lyrae found in Section 4.1). Therefore, this strengthens our assumption that most of the inner RR Lyrae candidates found in Section 4.1 are cluster members, and most, if not all, of the inner Cepheids, eclipsing binaries, and LPV candidates are field stars.

The reddening values and distances of every individual RRab star can be accurately calculated using their tight period-luminosity-metallicity relations in the near-infrared (Longmore et al., 1986, 1990; Bono et al., 2001; Cassisi et al., 2004; Catelan et al., 2004). Following the steps detailed in Dékány et al. (2013), we adapted the Catelan et al. (2004) period-luminosity relations to be used with the VIRCAM/VISTA filter system:

where $P$ is the period of the RRab and $Z$ its metallicity.

The only spectroscopic determination of the iron content for the stars in 2MASS-GC02 we have found in the literature is by Borissova et al. (2007). They found a value of ${\rm[Fe/H]}=-1.08$, using low-resolution infrared spectroscopy of secondary lines in a set of 12 cluster stars, selected by their photometry and radial velocities²²2Peñaloza et al. (in preparation) also report a value of ${\rm[Fe/H]}=-1.08$ from high-resolution spectra of a few cluster giants.. Although photometric estimations are a little higher, with values between ${\rm[Fe/H]}=-0.66$ (Borissova et al., 2002) to ${\rm[Fe/H]}=-0.98$ (Borissova et al., 2007), we decided to stick to the spectroscopic value, which is also the one provided by the Harris (1996) catalog (see Table 1). Using a canonical helium fraction $Y=0.245$, and an alpha-element enhancement $[{\alpha}/Fe]=0.3$, common among Galactic GCs (Pritzl et al., 2005), we translate the iron content ${\rm[Fe/H]}=-1.08$ to the metallicity $Z=0.0025$ that we will assume for all the RRab stars in the cluster.

It is straightforward to calculate the apparent distance modulus of the RRab candidates in $K_{s}$ (see Figure 4), using the calculated period and average apparent magnitudes in Table 3. But to calculate the absolute distance modulus we need to carry out some further calculations and adopt some further assumptions in order to obtain the extinction first. Ideally to calculate the extinction, we should also have the light curve in some other near-infrared filter in addition to $K_{s}$, but VVV only provides single-epoch observations in $Z$, $Y$, $J$, and $H$. What is worse, the $Z$ and $Y$ magnitudes of the RR Lyrae candidates in 2MASS-GC02 are in most cases below the detection limit (see Table 3). For our analysis, we assume that $J-K_{s}$ (or $H-K_{s}$) at the phase position when the $J$ (or $H$) image was taken is equal to the average $J-K_{s}$ (or $H-K_{s}$) color of the RR Lyrae candidate. We obtain the $K_{s}$ value at the desired phase from our Fourier fits to the light curves for the RRab candidates (see Section 3), calculate this way the apparent colors of these RR Lyrae candidates, shown in Table 3, and using equations 3 to 5 obtain their color excesses $E(J-K_{s})$ and $E(H-K_{s})$, shown in Figure 4.

Now, in order to obtain the absolute distance modulus to 2MASS-GC02 we should transform those color excesses to extinctions using the total-to-selective extinction ratios. But these ratios have been shown to differ from the values obtained from the standard Cardelli et al. (1989) extinction law, when observing towards the Galactic center and bulge (e.g. Nishiyama et al., 2006, 2009). Therefore, instead of adopting a ratio from the literature, the highly differential reddening inside the cluster’s area enables us to simultaneously obtain the absolute distance modulus and the total-to-selective extinction ratio (and hence the extinction) by doing a linear fit between the two parameters we already had, the apparent distance modulus $K_{s}-M_{K_{s}}$ and the color excess ($E(J-K_{s})$ and $E(H-K_{s})$). Since there are errors associated with both variables, the fit is performed using the ordinary least square bisector method, which has been proven to outperform other approaches in such cases (Isobe et al., 1990; Kunder et al., 2008). The fits are shown in Figure 4. As we can expect, most RR Lyrae outside the tidal radius are obvious outliers in the fit, and can be clearly located in the background of the cluster (see Section 4.2). From the RR Lyrae inside the tidal radius, only NV26 has been also considered to be an outlier, due to its considerable residuals, and was discarded from the fitted sample (see discussion and explanations for these cases in Section 4.1). From the final fit, we obtain the ratios $R_{K_{s},J-K_{s}}\equiv{\cal A}_{K_{s}}/(E(J-K_{s})$ and $R_{K_{s},H-K_{s}}\equiv{\cal A}_{K_{s}}/(E(H-K_{s})$ shown in Table 4. These ratios are a little lower than those obtained by Nishiyama et al. (2009), and are certainly smaller than suggested by Cardelli et al. (1989) or Rieke & Lebofsky (1985). The absolute distance modulus, calculated as the average of the zero-points of the fits, is $\mu_{0}=14.26\pm 0.14\pm 0.3$, where the first ${\sigma}$ is obtained from the statistical errors in the fit, and the second one comes from omitting some of the fitted stars, as we explained in the following paragraph. This value for the absolute distance modulus yields the cluster’s distances to the Sun and to the Galactic center shown in Table 5, putting the object farther away from us and more than 1 kpc closer to the Galactic center than shown in the Harris (1996) catalog. For the sake of comparison, we chose as a good reference value for the extinction towards 2MASS-GC02 $E(J-K_{s})=3.1\pm 0.5$, the mean of the cluster RRab candidates, but we would like to remark that extinction towards this cluster is highly variable, with almost 50% changes over small regions, and with significant deviations from the standard extinction law.

The assumption of ${\cal A}_{\lambda}/{\cal A}_{K_{s}}=1$ that we have done by using only one epoch in J and H in order to obtain the colors of the RR Lyrae, does not add significantly to the error budget of the different calculated magnitudes. Using the relations from Appendix B1.3 in Feast et al. (2008), we observed that the ratios between the amplitudes of the RR Lyrae in the near-infrared change according to the amplitudes of the RR Lyrae, and for the amplitudes of the detected RR Lyrae (see Table 3), the values³³3A similar value for ${\cal A}_{J}/{\cal A}_{K_{s}}$ is obtained by Navarrete et al. (in preparation) when studying the RR Lyrae light curves in the near-infrared in OmegaCen. should be in the ranges $0.9<{\cal A}_{H}/{\cal A}_{K}<1.1$ and $0.8<{\cal A}_{J}/{\cal A}_{K}<1.9$, and the errors in the RR Lyrae colors due to our assumption could be, at most, of one tenth of a magnitude in $J-K_{s}$, and one hundredth of a magnitude in $H-K_{s}$. Note however that these would be the extreme cases when the measurements were taken at a phase corresponding to a maximum or a minimum; generally the error should be smaller, and their effect on the elevated color excesses that we obtained (see Figure 4) almost negligible. What is more, any effects from our assumption of ${\cal A}_{\lambda}/{\cal A}_{K_{s}}=1$ would cancel out to some extent in the fit we have done to obtain the absolute distance modulus and the reddening law, since the measurements of $J$ and $H$ were done at random phase times, which means that errors in color excesses should have similar chances of being positive and negative, and the only observable effect would be a small increase in the dispersion of the points around the fit. More important for the error budget of the extinction ratios $R$ and the absolute distance modulus $\mu_{0}$ would be if one of the fitted RR Lyrae with a higher extinction (NV4 or NV7) resulted not to be a member of the cluster. Since they present the highest deviations from the fit, and they are also important to extend the extinction baseline, we decided to show the effects of omitting one of them as the variations shown by the second term in the error of the extinction ratios $R$ and the absolute distance modulus $\mu_{0}$.

The average period of the cluster RRab candidates used in the fit (NV1-NV10, NV13 and NV24) is $\langle P_{ab}\rangle=0.59\pm 0.06$ days, which puts 2MASS-GC02 in the Oosterhoff gap, as we can see in Figure 5. Based on the absence of Galactic GCs in this gap, and their high incidence in nearby extragalactic systems (see Figure 5), this feature could suggest an extragalactic origin for 2MASS-GC02. However, we should note that we are dealing with small number statistics here, since only 12 RRab’s are considered.

Observations in $K_{s}$ were taken in 101 different epochs for Terzan 10 during the period 2010-2013 of the VVV survey (see Table 2), making this region one of the most sampled in the VVV so far. No previous search for variable stars in this cluster has been ever done⁴⁴4During the revision process of our article, Soszyński et al. (2014) published their results on the RR Lyrae in the OGLE Galactic Bulge fields. Since Terzan 10 falls on one of the fields covered by OGLE-IV, we matched their results with ours, and found that most of the RRab’s in the field of Terzan 10 and in its surroundings appear in both works. There are only 3 RRab candidates inside the cluster radius of Terzan10 (OGLE_BLG_RRLYR-33521, OGLE_BLG_RRLYR-33518, and OGLE_BLG_RRLYR-33525), and 1 RRab candidate in the surrounding region (OGLE_BLG_RRLYR-33508) that Soszyński et al. (2014) find, and we do not. The reason for this is that these stars lie very close to stars of similar or higher magnitude, and the image subtraction technique they use is better suited than our PSF photometry technique in this case. On the other hand, there are 1 RRab candidate inside the tidal radius of Terzan 10 (NV5) and 1 in the surrounding region (NV140) that we identify and they do not. The reason for this is their dimmer magnitudes in $I$, close to the magnitude limit where the completeness of the OGLE detection is small. We should also note that we are not able to recover any of the 7 RRc candidates that Soszyński et al. (2014) find in Terzan 10 and its surroundings, due to the smaller amplitudes of these variable stars in the near-infrared wavelengths., so this high amount of available epochs puts us in a superb position to find for the first time highly significant variable candidates in this GC. Our analysis resulted in 48 variable candidates inside $r_{t}=5.06\arcmin$, the tidal radius extracted from the Harris (1996) catalog. Among the 48 candidates, we identified 8 RR Lyrae variables, 8 Cepheids, 7 eclipsing binaries, and 1 LPV. Their positions, periods, amplitudes, magnitudes and colors are shown in Table 6 (NV1 to NV48), their light curves are plotted in Figure 7, their positions in the sky can be observed in Figure 8, and their positions in the CMD can be observed in the left panel of Figure 6.

All of the RR Lyrae candidates found (NV2, NV3, NV5, NV6, NV7, NV12, NV22 and NV24) seem to be RRab’s, according to their periods and light curves. From their position in the CMD and in the sky, the RR Lyrae are located along the reddening vector, suggesting the presence of differential extinction in this GC, with the candidates towards the north of the cluster center (NV3 and NV5) with redder colors, and therefore more heavily affected by extinction, than the RRab candidates in the south (NV2, NV6, NV7 and NV12). On the CMD, we can observe that all RR Lyrae show a behavior consistent with their belonging to the cluster and following the same, but again non-standard, reddening law, except NV12 – we will further confirm this point in Section 5.3. NV12 is a little brighter than the other RR Lyrae with similar colors, which suggests that it is a foreground RR Lyrae star.

None of the Cepheid candidates found (NV14, NV16, NV17, NV18, NV19, NV31, NV39 and NV47) could be a Cepheid that belongs to the cluster according to the Matsunaga et al. (2013) period-luminosity relations. While most of them are too dim to even belong to the Galactic bulge, NV16 and NV17 have apparent distance moduli consistent with being bulge Type II Cepheids (${\mu}_{\rm NV16}=15.98$ and ${\mu}_{\rm NV17}=14.98$), along with positions in the CMD accordant with it. But they do not seem to belong to Terzan 10 either. A quick visual comparison with the RR Lyrae apparent distance moduli and extinctions shown in Figure 9 – the method to obtain them is explained in Section 5.3 – strongly points towards NV16 being a Type II Cepheid in the background of the cluster, and NV17 being in its foreground.

All the eclipsing binary candidates (NV1, NV4, NV20, NV23, NV32, NV41, and NV45) lie in a region of the CMD compatible with being cluster members, except NV4 and NV23, which are located among the disk field stars. Based on their light curves most of them appear to be EA stars.

Only 1 LPV was found inside the tidal radius of the cluster, NV48. Its long period precludes us from having a well-sampled light curve.

The vast majority of the remaining 23 unclassified variables, seems to be comprised of disk field variables, based on their positions in the CMD (see Figure 6).

For Terzan 10, we also performed a search for variables in the immediate surrounding of the cluster, out to a radius of $10\arcmin$ from its center. This encircles an area approximately 3 times the size of the cluster out to its tidal radius. In this region we found 112 more variable candidates. Their positions, periods, amplitudes, magnitudes and colors are shown in Table 6 (NV49 to NV160), their light curves are plotted in Figure 7, and their positions in the CMD can be observed in the right panel of Figure 6.

We found 12 RR Lyrae candidates in the surveyed region, significantly more than the RR Lyrae found in the surrounding of 2MASS-GC02. But extinction in that region was higher, as we can guess just by looking at the redder colors of the stars there, and the angular separation from the Galactic center was also higher, meaning that less of the projected bulge was sampled. In general, RR Lyrae found in the surroundings of Terzan 10 are a little brighter than the ones found inside its tidal radius, and their colors are similar, which suggests similar reddenings. These two facts imply that they are field RR Lyrae in the foreground of the cluster, suggesting that the cluster is on the far side of the bulge, farther away than the Galactic center. We will confirm this result and further discuss it in Section 5.3. From the CMD and from the further analysis in Section 5.3, only one of the RR Lyrae, NV140, is behind the cluster, and other two, NV105 and NV136, lie at a distance consistent with being cluster members, although their high angular distances from the cluster center make more probable that they are field stars at the cluster’s distance. From a statistical point of view, the expected number of field RR Lyrae inside the cluster radius should be $\approx 4$, since the surrounding region is 3 times the area occupied by the cluster. Although we only found 1 (see Section 5.1), we should note that we are dealing with small number statistics here.

We also identified 15 Cepheids, 27 eclipsing binaries, and 2 LPVs. Therefore, we should expect in the area inside the cluster tidal radius close to 5 field Cepheids, 9 field eclipsing binaries and 1 field LPV, given the bigger size of the surrounding region (3:1). The amounts of these kinds of variables found in Section 5.1 (8 Cepheids, 7 eclipsing binaries and 1 LPV) are of the same order, suggesting that most, if not all, of the variables of these types found in Section 5.1 belong to the field population, and not to the cluster.

The number of LPVs seems odd when compared with 2MASS-GC02. There we found 19 LPVs, while in the surrounding of Terzan 10 we found only 2.

To calculate the distance and the extinction to Terzan 10 we follow the same steps as in Section 4.3. We use equations 1 to 5 to obtain the absolute magnitudes of our RR Lyrae candidates in the different available filters. Unfortunately, we found no spectroscopic metallicity measurements of individual stars in Terzan 10, and we have to rely on only photometric and integrated spectroscopic values. Metallicity estimations vary between ${\rm[Fe/H]}=-0.7$ in the photometric studies by Liu et al. (1994) to ${\rm[Fe/H]}=-1.2$ ($[Z/Z_{\odot}]=-1.35$) in the integrated spectroscopic studied by Bica et al. (1998). We adopt ${\rm[Fe/H]}=-1.00$, from the Harris (1996) catalog, and assuming the same $Y$ and $\alpha$-enhancement as in Section 4.3, we obtain a value of $Z=0.003$ for the cluster’s metallicity, that we used as input for equations 1 to 5, along with our measured periods. The mean RR Lyrae apparent $K_{s}$ magnitude is obtained as mentioned in Section 3, and the apparent colors from the $K_{s}$ measurements obtained by interpolating in our Fourier fit to the $K_{s}$ light curve at the same phase as the single-epoch images in $Z$, $Y$, $J$, and $H$ were taken.

As in Section 4.3, we did not assume an a priori extinction law to relate color excess with apparent distance modulus of the RRab candidates. Instead, using the ordinary least square bisector method, we got a linear fit between both parameters, which provide us with values for the extinction ratios $R_{K_{s},\lambda-K_{s}}$, as the slope of the fit, and an absolute distance modulus, as the zero-point of the fit (see Figure 9). In our analysis, the only clear outlier among the RR Lyrae inside the tidal radii, and therefore excluded from the fit, was NV12 (see discussion in Section 5.1). Some of the RR Lyrae in the surrounding field outside the tidal radius could belong to the cluster according to their distances, although this is not very plausible (see discussion in Section 5.2). Again, the ratios $R_{K_{s},\lambda-K_{s}}$ derived from the fit differ from those of the standard Cardelli et al. (1989) law, and agree better with those derived by Nishiyama et al. (2009), as we can see in Table 4. The fact that the zero-point of the fits, i.e., the absolute distance modulus, show a much smaller spread among the values derived from using the different filter-combinations, than if we just use the Cardelli et al. (1989) law (see Figure 9), reinforces our confidence in the fitted values. We adopt the weighted average of the zero-points from the different color-excess fits, as the absolute distance modulus of Terzan 10. We obtain a value $\mu_{0}=15.06\pm 0.03\pm 0.03$, where again the first ${\sigma}$ is obtained from the statistical errors in the fit, while the second one comes from omitting two of the fitted stars, NV22 and NV5, which have the smallest and biggest extintion values. This value of $\mu_{0}$ implies the cluster is much farther away from us than previously thought, almost by a factor of 2 (see Table 5). This also implies that Terzan 10 is beyond the Galactic center, in the far side of the Galactic bulge. Until now it was believed that all the inner Galactic GCs found so far were located in the near side of the bulge (Barbuy et al., 1998). For the sake of comparison, a good reference value for the extinction towards Terzan 10 is $E(J-K_{s})=0.86\pm 0.16$, the mean of the cluster RRab candidates that made our fit, but we emphasize that extinction towards this cluster is also highly variable, with almost 50% changes over small regions, and with significant deviations from the standard extinction law.

The average period of Terzan 10 RRab variable candidates used in the fit (NV2, NV3, NV5, NV6, NV7, NV22 and NV24) is $\langle P_{ab}\rangle=0.66\pm 0.06$ days, which makes Terzan 10 an Oosterhoff II cluster. However, its iron-content is significantly higher than the ones of the other Galactic (and even extragalactic) Oosterhoff II GCs (see Figure 5). But we should remember here that the metallicity value adopted in this work is the average of two previous works (${\rm[Fe/H]}=-0.7$ by Liu et al. (1994), and ${\rm[Fe/H]}=-1.2$ by Bica et al. (1998)), as we mentioned in the beginning of this section. If ${\rm[Fe/H]}=-0.7$ is closer to the true value, this will put Terzan 10 closer to NGC 6388 and NGC 6441, in the scarcely populated Oosterhoff III group of metal-rich clusters with RR Lyrae. If, on the other hand, ${\rm[Fe/H]}=-1.2$ is closer to reality, Terzan 10 would still be the most metal-rich cluster in the Oosterhoff II group, and would still stand out significantly from the locus of Galactic GCs. This uncertainty makes a strong case to obtain spectroscopic metallicity measurements from individual stars in this GC.