The VMC Survey – XIII. Type II Cepheids in the Large Magellanic Cloud^★

Abstract

The VISTA (Visible and Infrared Survey Telescope for Astronomy) survey of the Magellanic Clouds System (VMC) is collecting deep K_s-band time-series photometry of the pulsating variable stars hosted in the system formed by the two Magellanic Clouds and the Bridge connecting them. In this paper, we have analysed a sample of 130 Large Magellanic Cloud (LMC) Type II Cepheids (T2CEPs) found in tiles with complete or near-complete VMC observations for which identification and optical magnitudes were obtained from the OGLE III (Optical Gravitational Lensing Experiment) survey. We present J and K_s light curves for all 130 pulsators, including 41 BL Her, 62 W Vir (12 pW Vir) and 27 RV Tau variables. We complement our near-infrared photometry with the V magnitudes from the OGLE III survey, allowing us to build a variety of period–luminosity (PL), period–luminosity–colour (PLC) and period–Wesenheit (PW) relationships, including any combination of the V, J, K_s filters and valid for BL Her and W Vir classes. These relationships were calibrated in terms of the LMC distance modulus, while an independent absolute calibration of the PL(K_s) and the PW(K_s, V) was derived on the basis of distances obtained from Hubble Space Telescope parallaxes and Baade–Wesselink technique. When applied to the LMC and to the Galactic globular clusters hosting T2CEPs, these relations seem to show that (1) the two Population II standard candles RR Lyrae and T2CEPs give results in excellent agreement with each other; (2) there is a discrepancy of ∼0.1 mag between Population II standard candles and classical Cepheids when the distances are gauged in a similar way for all the quoted pulsators. However, given the uncertainties, this discrepancy is within the formal 1σ uncertainties.

1 INTRODUCTION

The Magellanic Clouds (MCs) are fundamental benchmarks in the framework of stellar populations and galactic evolution investigations (see e.g. Harris & Zaritsky 2004, 2009; Ripepi et al. 2014b). The ongoing interaction with the Milky Way also allows us to study in detail the complex mechanisms that rule the interaction among galaxies (see e.g. Putman et al. 1998; Muller et al. 2004; Stanimirović, Staveley-Smith & Jones 2004; Bekki & Chiba 2007; Venzmer, Kerp & Kalberla 2012; For, Staveley-Smith & McClure-Griffiths 2013). Additionally, the MCs are more metal poor than our Galaxy and host a large population of young populous clusters; thus, they are useful to test the physical and numerical assumptions at the basis of stellar evolution codes (see e.g. Matteucci et al. 2002; Brocato et al. 2004; Neilson & Langer 2012).

The Large Magellanic Cloud (LMC) is also fundamental in the context of the extragalactic distance scale. Indeed, it represents the first critical step on which the calibration of classical Cepheid (CC) period–luminosity (PL) relations and in turn of secondary distance indicators relies (see e.g. Freedman et al. 2001; Riess et al. 2011; Walker 2012, and references therein). At the same time, the LMC hosts several thousand of RR Lyrae variables, which represent the most important Population II standard candles through the well-known M_V(RR)–[Fe/H] and near-infrared (NIR) metal-dependent PL relations. Moreover, the LMC contains tens of thousands of intermediate-age red clump stars, which can profitably be used as accurate distance indicators (see e.g. Laney, Joner & Pietrzyński 2012; Subramanian & Subramaniam 2013). Hence, the LMC is the ideal place to compare the distance scales derived from Population I and II indicators (see e.g. Clementini et al. 2003; Walker 2012; de Grijs, Wicker & Bono 2014, and references therein). In particular, NIR observations of pulsating stars (see e.g. Ripepi et al. 2012a, 2014a; Moretti et al. 2014, and references therein) provide stringent constraints to the calibration of their distance scale thanks to the existence of well-defined PL, period–luminosity–colour (PLC) and period–Wesenheit (PW) relations at these wavelengths (see Madore 1982; Madore & Freedman 1991, for the definition of Wesenheit functions).

The VISTA¹ near-infrared YJK_s survey of the Magellanic Clouds system (VMC; Cioni et al. 2011) aims at observing a wide area across the Magellanic system, including the relatively unexplored Bridge connecting the two Clouds. This European Southern Observatory (ESO) public survey relies on the VISTA InfraRed CAMera (VIRCAM) (Dalton et al. 2006) of the ESO VISTA telescope (Emerson, McPherson & Sutherland 2006) to obtain deep NIR photometric data in the Y, J and K_s filters. The main aims are (i) to reconstruct the spatially resolved star formation history and (ii) to infer an accurate 3D map of the whole Magellanic system. The properties of pulsating stars observed by VMC and adopted as tracers of three different stellar populations, namely CCs (younger than few hundred Myr), RR Lyrae stars (older than 9–10 Gyr) and anomalous Cepheids (traditionally associated with an intermediate-age population with few Gyr), have been discussed in recent papers by our team (Ripepi et al. 2012a,b, 2014a; Moretti et al. 2014). In these papers, relevant results on the calibration of the distance scales for all these important standard candles have been provided.

An additional class of Population II pulsating stars is represented by the so-called Type II Cepheids (T2CEPs; see e.g. Caputo 1998; Sandage & Tammann 2006). These objects show periods from ∼1 to ∼20 d and are observed in Galactic globular clusters (GGCs) with few RR Lyrae stars and blue horizontal branch morphology. They are brighter but less massive than RR Lyrae stars for similar metal content (see e.g. Caputo et al. 2004). T2CEPs are often separated into BL Herculis stars (BL Her; periods between 1 and 4 d) and W Virginis stars (W Vir; periods between 4 and 20 d) and, as discussed by several authors (e.g. Wallerstein & Cox 1984; Gingold 1985; Harris 1985; Bono, Caputo & Santolamazza 1997b; Wallerstein 2002), originate from hot, low-mass stellar structures, starting their central He burning on the blue side of the RR Lyrae gap. Moreover, according to several authors (see e.g. Feast et al. 2008; Feast 2010, and references therein) RV Tauri stars, with periods from about 20 to 150 d and often irregular light curves, are considered as an additional subgroup of the T2CEP class. Their evolutionary phase corresponds to the post-asymptotic giant branch phase path towards planetary nebula status. This feature corresponds to the latest evolution of intermediate mass stellar structures and for this reason the claimed link with the low-mass W Vir stars should be considered with caution.

In addition to the three quoted groups, Soszyński et al. (2008) suggested the existence of a new sub-class of T2CEPs, the so-called peculiar W Vir (pW Vir) stars. These objects show peculiar light curves and, at constant period, are usually brighter than normal T2CEPs. It is likely that pW Vir belong to binary systems; however, the true nature of these variables remains uncertain.

Nemec, Nemec & Lutz (1994) derived metal-dependent PL relations in various optical photometric bands both in the fundamental and in the first overtone modes but subsequently Kubiak & Udalski (2003) found that all the observed T2CEPs in the OGLE II (Optical Gravitational Lensing Experiment; Udalski et al. 1992) sample, with periods in the range ∼0.7 to about 10 d, satisfy the same PL relation. This result was then confirmed by Pritzl et al. (2003) and Matsunaga et al. (2006) for GGCs, by Groenewegen, Udalski & Bono (2008) for the Galactic bulge and again by Soszyński et al. (2008) on the basis of OGLE III data.

From the theoretical point of view, Di Criscienzo et al. (2007) and Marconi & Di Criscienzo (2007) have investigated the properties of BL Her stars, by adopting an updated evolutionary and pulsational scenario for metallicities in the range of Z = 0.0001–0.004. The predicted PL and PW relations derived on the basis of these models were found to be in good agreement with the slopes determined by the variables observed in GGCs. Moreover, the distances obtained from the theoretical relations for T2CEPs agree within the errors with the RR Lyrae-based values.

In the NIR bands, a tight PL for 46 T2CEPs hosted in GGCs was found by Matsunaga et al. (2006). Such relations were calibrated by Feast et al. (2008) by means of pulsation parallaxes of nearby T2CEPs and used to estimate the distances of the LMC and the Galactic Centre. Subsequent investigations (Matsunaga, Feast & Menzies 2009; Matsunaga, Feast & Soszyński 2011) confirmed the existence of such tight PL relations in the J, H, K_s bands for the T2CEPs belonging to the LMC and Small Magellanic Cloud found by the OGLE III collaboration (Soszyński et al. 2008). However, the NIR observations at the base of these studies consist of only two epochs for each variable light curve obtained with the Infrared Survey Facility (IRSF) 1.4 m telescope in South Africa. The average magnitudes of the T2CEPs analysed in that paper were derived by comparison with the OGLE III I-band photometry.

In the context of the VMC survey, we present here the NIR results for a significant sample of T2CEPs in the LMC, based on high precision and well-sampled K_s-band light curves.

The VMC data for the T2CEPs are presented in Section 2. The PL, PLC and PW relations involving the J and K_s bands are calculated in Section 3. Section 4 includes the absolute calibration of such relations and a comparison with the literature. In Sections 5, we discuss the results; a concise summary (Section 6) concludes the paper.

2 T2CEPs IN THE VMC SURVEY

T2CEPs in the LMC were identified and studied in the V, I optical bands by Soszyński et al. (2008) in the context of the OGLE III project.² We have also considered the recent early release of the OGLE IV survey (Soszyński et al. 2012), including the South Ecliptic Pole which, in turn, lies within our tile LMC 8_8. In these surveys, a total of 207 T2CEPs were found (203 by OGLE III and 4 by OGLE IV³), of which 65 are BL Her, 98 are W Vir and 44 are RV Tau pulsators.

In this paper, we present results for the T2CEPs included on 13 ‘tiles’ (1.5 deg²) completely or nearly completely observed, processed and catalogued by the VMC survey as of 2013 March (and overlapping with the area investigated by OGLE III), namely the tiles LMC 4_6, 4_8, 5_3, 5_5, 5_7, 6_4, 6_5, 6_6, 6_8, 7_3, 7_5, 7_7 and 8_8 (see Fig. 1 and Table 1). Tile LMC 6_6 is centred on the well-known 30 Dor star-forming region; tiles LMC 5_5, 6_4 and 6_5 are placed on the bar of the LMC. The remaining tiles lie in less crowded regions of the galaxy.

A detailed description of the general observing strategy of the VMC survey can be found in Cioni et al. (2011). As for the variable stars, the specific procedures adopted to study these objects were discussed in Moretti et al. (2014). Here, we only briefly recall that the VMC K_s-band time-series observations were scheduled in 12 separate epochs distributed over several consecutive months. This strategy allows us to obtain well-sampled light curves for a variety of variable types (including RR Lyrae variables and Cepheids of all types). Concerning the J and Y bands, the average number of epochs is 3, as a result of the observing strategy in these bands (i.e. monitoring was not planned). Hence, some epochs could occur in the same night and even one after the other. We note that in this paper, we did not consider the Y-band data for several reasons: (i) this filter is very rarely used in the context of distance scale; (ii) its photometric zero-point (ZP) is difficult to calibrate (no 2MASS measures); (iii) because the Y band is bluer than the typical NIR bands, and the PL, PLC and PW relations in this filter are expected to be more dispersed (see e.g. Madore & Freedman 2012) and of lesser utility with respect to those in J and K_s.

The VMC data, processed through the pipeline (Irwin et al. 2004) of the VISTA Data Flow System (VDFS; Emerson et al. 2004) are in the VISTA photometric system (Vegamag = 0). The time-series photometry used in this paper was retrieved from the VISTA Science Archive⁴ (VSA; Cross et al. 2012). For details about the data reduction, we refer the reader to the aforementioned papers. Nevertheless, we underline two characteristics of the data reduction which we think may have importance in the subsequent discussion. First, the pipeline is able to correct the photometry of stars close to the saturation limit (Irwin 2009). This is relevant in the context of this paper because the RV Tau variables discussed here are very bright objects K_s ∼ 12–13 mag, close to the saturation limits of the VMC survey. The photometry of these stars takes advantage of the VDFS ability to treat saturated images; however, as we will see below, the corrections applied are not always sufficient to fully recover the data. Secondly, the data retrieved from VSA include quality flags which are very useful to understand if the images have problems. We shall use this information later in this paper.

According to OGLE III/IV, 130 T2CEPs are expected to lie in the 13 tiles analysed in this paper. Note that no T2CEP from OGLE III or OGLE IV falls inside our tiles 6_8 or 8_8, respectively. Hence, in the following we only use OGLE III data. Fig. 1 and Table 1 show the distribution of such stars through the VMC tiles.

Table 2 lists the 130 T2CEPs analysed here, together with their main properties as measured by OGLE III and the information about the VMC tile they belong to, as well as the number of epochs of observations in the J and K_s bands. In total, our sample is composed of 41 BL Her, 62 W Vir (12 pW Vir) and 27 RV Tau variables, corresponding to 63, 63 (75 per cent) and 61 per cent of the known LMC populations of the three different variable classes, respectively.

The OGLE III catalogues of T2CEP variables were cross-correlated against the VMC catalogue to obtain the J and K_s light curves for these variables. All the 130 T2CEPs were found to have a counterpart in the VMC catalogue within 2 arcsec from the OGLE III positions. The great majority of the objects showed separation in position with respect to OGLE III less than 0.1 arcsec. However, eight stars (OGLE-LMC-T2CEP-020, 030, 069, 084, 123, 142, 144, 173) present separations significantly larger than average (> 0.5 arcsec). Fig. 2 shows the OGLE III and VMC finding charts of 29 stars with some kind of identification or data problem, within which we included the eight objects quoted above. It can be seen that all the stars lie in crowded regions or are clearly blended by other stars or diffuse objects (e.g. OGLE-LMC-T2CEP-142). We will discuss these objects further in the following sections.

2.1 T2CEP light curves

The VMC time-series J and K_s photometry for the 130 objects is provided in Table 3, which is published in its entirety in the online version of the paper.

Periods and epochs of maximum light available from the OGLE III catalogue were used to fold the J- and K_s-band light curves produced by the VMC observations. Given the larger number of epochs in K_s with respect to J, we discuss first the K_s-band data.

The K_s-band light curves for a sample of 120 T2CEPs with useful light curves are shown in Fig. A1. Apart from a few cases, these light curves are generally well sampled and nicely shaped. Some clearly discrepant data points (open circles in Fig. A1) in the light curves were excluded from the fit but were plotted in the figure for completeness. Note that most of these ‘bad’ data points belong to observations collected during nights that did not strictly meet the VMC observing constraints (see table 2 in Cioni et al. 2011). The final spline fit to the data is shown by a solid line in Fig. A1. Intensity-averaged 〈K_s〉 magnitudes were derived from the light curves using custom software written in c, which performs a spline interpolation to the data with no need of using templates. The numerical model of the light curve is thus obtained and then integrated in intensity to obtain the mean intensity which is eventually transformed to mean magnitude.

10 objects in our sample showed unusable light curves, namely OGLE-LMC-T2CEP-014, 030, 043, 051, 065, 084, 095, 108, 142 and 200. Their light curves are displayed in Fig. A2, whereas their finding charts are shown in Fig. 2. A quick analysis of the finding charts reveals that all these stars have significant problems of crowding/blending. Three of the aforementioned objects (OGLE-LMC-T2CEP-030, 084 and 142) have centroids significantly shifted with respect to OGLE's, thus confirming the presence of strong blending.

As for the J-band data, Fig. A3 shows the light curves for the 34 stars that have sufficiently good data to allow an independent spline fit (solid line in the figure). Figs A4 and A5 show the light curves for the remaining 86 and 10 objects with small number of epochs (∼4–5 on average) and dispersed light curves, respectively. The latter variables show the same problems reported for the K_s band. To estimate the intensity-averaged J magnitude for the 86 stars possessing only few epochs of observation, we decided to use the spline-fit curves in the K_s band as templates.⁵ To this aim, for each star we performed the following steps: (1) subtracted the average 〈K_s〉 magnitude from the K_s spline-fit curve; (2) adjusted by eye the data obtained in this way to fit the J light curve by (i) adding a ZP, (ii) multiplying the amplitude by a proper factor and (iii) shifting the light curve in phase. The factor needed for point (ii) is the ratio Amp(J)/Amp(K_s). To estimate this number, we used the 34 stars with independent J-band spline fit, obtaining a value of 1.1±0.2. The uncertainty of ∼20 per cent may appear large, but it does not actually represent a problem since its contribution to the error on the intensity-averaged J is of the order of 0.5 per cent. In some favourable cases, the few data points covered both maximum and minimum of the light curve and it was then possible to constrain directly the amplitude ratio. The shift in phase (point iii above) varied from case to case, but was on average close to 0.05–0.06. The final error on the intensity-averaged J magnitude was calculated by summing in quadrature the error on the K_s magnitude, the uncertainty on the J magnitude caused by the error on the amplitude ratio and an additional 1 per cent to take into account the uncertainty on the phase shift. The goodness of this procedure can be appreciated in Fig. 3, where we show in different colours the PL and PW relations (see the next section for a detailed description of these relations) for the stars with intensity-averaged J photometry obtained directly from spline fits (black points) and with the template fits (grey points). The figure clearly shows that the results obtained on the basis of the K_s templates are usable for scientific purposes. The final 〈J〉,〈K_s〉 magnitudes with relative uncertainties, as well as pulsational amplitudes and adopted reddening values (see Section 3), are provided in Table 4.

We recall that the J and K_s photometry presented in this paper is set in the VISTA system. A consistent comparison between our results and those in the widely used 2MASS system (Two Micron All Sky Survey; Skrutskie et al. 1996) can be performed after applying proper system transformations as for instance those provided by the Cambridge Astronomy Survey Unit (CASU):⁶ (J − K_s)(2MASS) = 1.081(J − K_s)(VISTA), J(2MASS) = J(VISTA) + 0.07(J − K_s)(VISTA) and K_s(2MASS) = K_s(VISTA)−0.011(J − K_s)(VISTA).

Since the 〈J〉 − 〈K_s〉 colour of our T2CEP sample typically ranges from 0.1 to 0.6 mag, the VISTA and 2MASS K_s can be considered equivalent for T2CEPs (see Fig. 4) and for CCs (see Ripepi et al. 2012b), to a very good approximation (better than ∼5 mmag).

3 J-, K_s-BAND PL, PLC AND PW RELATIONS

The data reported in Table 4 allow us to calculate different useful relationships adopting various combinations of magnitudes and colours. In particular, we derived PL relations in J and K_s as well as PW and PLC relations for the following combinations: (J, V − J), (K_s,V − K_s) and (K_s,J − K_s).

We first corrected magnitudes and colours for reddening using the recent extinction maps by Haschke, Grebel & Duffau (2011). Individual E(V − I) reddening values for the 120 T2CEPs with useful VMC data are reported in column 10 of Table 4. The reliability of this reddening correction can be questioned by observing that it has been derived from the analysis of the red clump stars, which trace the intermediate-age population (2–9 Gyr) instead of the old one to whom BL Her and W Vir belong. However, we recall that in the NIR bands the interstellar absorption is very low: A_J ∼ 0.25A_V and |$A_{K_\mathrm{s}} \sim 0.1 A_{\rm V}$|⁠, where A_V is the absorption in the visible. Hence, even in the unlikely case of a 10 per cent large error in our A_V estimates, this would introduce an amount of uncertainties of only ∼2.5 per cent and ∼1 per cent in J and K_s, respectively. An a posteriori indication about the global correctness of the adopted reddening correction is represented by the concordance of results provided by the PL (reddening-dependent) and PW (reddening-independent) relations (see Sections 4 and 5). The reddening values were converted using the following equations: E(V − J) = 1.80E(V − I), E(V − K_s) = 2.24E(V − I) and E(J − K_s) = 0.43E(V − I) (Cardelli, Clayton & Mathis 1989; Gao et al. 2013).⁷ The coefficients of the PW relations were calculated in a similar way.

In principle, an additional preliminary step would be required, i.e. the correction for the inclination of the LMC disc-like structure by de-projecting each T2CEP with respect to the LMC centre. To do this, we followed the procedure suggested in van der Marel & Cioni (2001) and adopted their values of the LMC centre, inclination and position angle of the line of nodes. However, we have a posteriori verified that the introduction of this correction leads to worse results, i.e. larger dispersion in the various relationships mentioned above. To verify if different choices about the inclined disc parameters could improve the results, we have carried out the de-projection using several results present in the literature (see Haschke et al. 2012; Rubele et al. 2012; Subramanian & Subramaniam 2013, and references therein). Under no circumstances, the dispersion of the PWs decreased (we used PWs as reference because they are reddening-free). To explain this occurrence, we can reasonably hypothesize that the T2CEPs (actually BL Her and W Vir), being old (age> 10 Gyr) objects, are not preferentially distributed along the main disc-like structure of the LMC. Alternatively, the adopted parameters for the de-projection are not accurate enough, although this conclusion may be influenced by the relatively small number of objects. Subsequent studies using a larger number of objects observed in the VMC context sampling different populations (CCs, T2CEPs and RR Lyrae stars) will clarify the issue. In any case, in the following analysis we did not apply any magnitude correction accounting for the LMC disc structure.

Figs 5 –8 show all the relationships investigated here. An inspection of these figures confirms the findings by Matsunaga et al. (2009) that BL Her and W Vir star follow a common PL relation, whereas RV Tau show a different and more dispersed relation (the dispersion is less severe in the J than in the K_s band). In our case, the dispersion among RV Tau stars can in part be due to the proximity of several bright variables to the saturation limit. As a consequence, we decided to exclude these stars from the calculation of the PL, PW and PLC relations. To check if BL Her and W Vir stars can actually be fitted with a unique relation, we performed an independent test by fitting separately the PL(K_s, J) and PW(K_s, V) relations for each class of variables. The result of this exercise is shown in Fig. 9: for both relations, the two variable classes seem to show results that agree with each other well within 1σ, thus confirming that we can use BL Her and W Vir variables together.

For each combination of periods, magnitudes and colours, we performed independent least-squares fits to the data, adopting equations of the form reported in Table 5. The results of the fitting procedure are shown in the same table as well as in Figs 5–8 with a solid line. Note that the equations listed in Table 5 are given in terms of absolute magnitudes since we subtracted the dereddened distance modulus (DM_{0, LMC}) of the LMC from each equation. Thus, the absolute ZP of the relations in Table 5 can be simply obtained by using the preferred value for the DM_{0, LMC} value.

In deriving the equations of Table 5, we have implicitly neglected any dependence of both PL and PW relations on the metallicity of the pulsators. This is in agreement with Matsunaga et al. (2006), who found a hardly significant dependence of the PL relations on metallicity (0.1±0.06 mag dex⁻¹), whereas the theoretical models by Di Criscienzo et al. (2007) predict a very mild metallicity dependence ΔMag/Δ [Fe/H]∼0.04–0.06 mag dex⁻¹ for both the PL and PW relations in the magnitudes and colours of interest. In any case, the very low dispersions of our PL and PW relations listed in Table 5 seem to suggest that the metallicity dependence, if any, should be very small. Alternatively, a small dispersion in metallicity among our sample could explain the results as well. However, since the low-metallicity dependence found by Matsunaga et al. (2006) is based on T2CEPs spanning a wide range of [Fe/H], the latter explanation is less likely.

In each figure, a number of stars are shown with grey symbols. They significantly deviate from almost all relationships discussed above. The crosses represent the stars classified by Soszyński et al. (2008) as peculiar W Vir (see column 4 in Table 2), i.e. suspected binaries that do not follow the optical PL and PW relations. We note that three of these peculiar W Vir stars, namely OGLE-LMC-T2CEP-021, 052 and 083, do not show any difference with respect to the normal W Vir stars in our PL, PW and PLC planes, and were hence included in the calculations. As for BL Her and W Vir, 15 and 4 stars of the two classes were not used in the least-squares fits because, with few exceptions, they show large scattering in almost all the relationships calculated here, and, in particular in the most reliable ones, namely the PWs and PLCs based on the K_s-band photometry. The finding charts for all these stars are displayed in Fig. 2, whereas the notes in Table 2 explain in detail the causes that led us to exclude these objects, with blending by close companions being the most common cause.

Table 5 deserves some discussion: (i) the dispersion of the PL(J) relation is, as expected, larger than for the PL(K_s); (ii) for any combination of magnitude and colour, the dispersions of PW and PLC are equal (this reflects the correctness of the reddening correction applied in this paper); (iii) the PW(J, V) and PLC(J, V) are significantly more dispersed than the PW(K_s, V)–PLC(K_s, V) and PW(K_s, J)–PLC(K_s, J) couples; (iv) the best combination of magnitude and colour (lower dispersion) appears to be the K_s,V; (v) the colour coefficients of the PW(K_s, V) and PLC(K_s, V) relations are very similar and the two relations are coincident. Similarly, for PW(J, V) and PLC(J, V), the colour coefficients are the same within the errors, whereas this is not true for the couple PW(K_s, J) – PLC(K_s, J).

4 ABSOLUTE CALIBRATION OF PL, PLC AND PW RELATIONS

In Table 5, we provided the absolute ZP for the relevant PL, PLC and PW relations as a function of the DM_{0, LMC}. However, it is of considerable astrophysical interest to obtain an independent absolute calibration for at least some of these relations. Indeed, this would allow us to obtain an independent measure of the distance to the LMC and to the GGCs hosting T2CEP variables. To this aim, we can only rely on calibrators located close enough to the Sun to have a measurable parallax or whose distances have been estimated by Baade–Wesselink (BW) techniques (see Gautschy 1987, for a review on this method). There are only two T2CEPs whose parallaxes were measured with reasonable accuracy with the Hubble Space Telescope (HST; Benedict et al. 2011), namely κ Pav (W Vir) and VY Pyx (BL Her). For two additional BL Her variables, SW Tau and V533 Cen, as well as for κ Pav, a BW-based distance is also available (Feast et al. 2008). However, VY Pyx turned out to be a peculiar star, unusable as calibrator (see discussion in Benedict et al. 2011). As for κ Pav, the pulsational parallax estimated by Feast et al. (2008) through BW analysis is about 2σ smaller than the trigonometric parallax measured by HST and adopted here (Δπ = 0.67 ± 0.33 mas). Feast et al. (2008) investigated the possible causes of the discrepancy with respect to the Hipparcos parallax (van Leeuwen 2007), which was even larger than the HST one, but did not find any definitive explanation. A well-known potential problem related with the application of the BW technique is the uncertainty on the projection factor p (see e.g. Molinaro et al. 2012; Nardetto et al. 2014, and references therein). In their analysis, Feast et al. (2008) derived and adopted a fixed p-factor = 1.23 ± 0.03. However, several researchers suggested that the p-factor actually does depend on the period of the pulsator (see e.g. Barnes 2009; Laney & Joner 2009; Storm et al. 2011a; Nardetto et al. 2014, and references therein); hence, for example, different p-factor values should be used for BL Her and W Wir stars. Given the uncertainties on the projection factor discussed above, in the following, we will adopt the HST-based distance for κ Pav, and the ZP of the different PL, PW and PLC relations will be estimated including or not the BW-based distances for SW Tau and V533 Cen. Finally, we note that [Fe/H](κ Pav) ≈ +0.0 dex (Feast et al. 2008), i.e. at least 1 dex more metal rich than expected for typical T2CEPs. Hence, some additional uncertainty when using this object as a distance indicator can be caused by a possible metallicity effect. However, as discussed in Section 3, the metal dependence of the T2CEP PLs, if any, should be very small, and we do not expect the high metallicity of κ Pav to be an issue for our purposes. To enlarge the number of reliable calibrators, a possibility is to use the five RR Lyrae stars whose parallaxes were measured with HST by Benedict et al. (2011). Indeed, as already hypothesized by Sollima, Cacciari & Valenti (2006) and Feast et al. (2008), RR Lyrae and T2CEPs follow the same PL(K_s) relation (Caputo et al. 2004 found similar results in the optical bands). To further test this possibility, we draw in Fig. 10 the PL(K_s) and PW(K_s) relations for the T2CEPs analysed in this paper, in comparison with the location occupied in the same planes by the RR Lyrae stars in the LMC (light blue filled circles, after Borissova et al. 2009). The periods of c-type RR Lyrae stars were fundamentalized by adding δlogP = 0.127 (Bono et al. 1997a) and the magnitudes have been corrected for the metallicity term devised by Sollima et al. (2006), using the individual metallicity measurement compiled by Borissova et al. (2009). It can be seen that both the PL(K_s) and PW(K_s) relations (red lines) derived for T2CEPs in Section 5 tightly match the location of the RR Lyrae stars. On this basis, we decided to proceed using also the RR Lyrae with HST parallax to anchor the ZP of the PL(K_s) and PW(K_s, V) relations for T2CEPs. To this aim, we simply adopted the slopes of the quoted relations from Table 5, corrected for metallicity the ZP for the five RR Lyrae stars with HST parallaxes and calculated the weighted average of the results in two cases: (i) including only stars with HST parallax, namely, κ Pav and the five RR Lyrae stars; (ii) using the stars at point (i) plus the two T2CEPs with BW analysis, namely SW Tau and V533 Cen.⁸ The results of these procedures are outlined in Table 6 (columns 3 and 4) and in Fig. 11. For comparison, column (2) of Table 6 shows the ZPs obtained assuming DM_{0, LMC} = 18.46 ± 0.03 mag, as derived by Ripepi et al. (2012b) from LMC CC stars. We choose the work by Ripepi et al. (2012b) as reference for CCs because (i) these authors adopted a procedure similar to the one adopted in this work; (ii) their results are in excellent agreement with the most recent and accurate literature findings (see e.g. Storm et al. 2011b; Joner & Laney 2012; Laney et al. 2012; Walker 2012; Pietrzyński et al. 2013; de Grijs et al. 2014, and references therein). An analysis of Table 6 reveals that (i) the inclusion of the two stars with BW-based distances does not change significantly the ZPs and (ii) there is a difference of at least ∼0.1 mag between the ZPs calibrated on the basis of CCs and of Galactic T2CEPs (see Section 5).

4.1 Comparison with the literature

The relationships presented in Tables 5 and 6 can now be compared to those available in the literature. As mentioned in the introduction, Matsunaga et al. (2006, 2009) published the PL relations in the JHK_s bands for BL Her and W Vir variables hosted by GGCs and the LMC, respectively. These results can be compared with ours, provided that we first transform all the J and K_s magnitudes into the VISTA system. With this aim, we transformed the Matsunaga et al. (2006) photometry from 2MASS to VISTA using the equations reported in Section 2.1. The results of Matsunaga et al. (2009) are in the IRSF system, whose J and K_s can in principle be transformed to the 2MASS system (Kato et al. 2007), and in turn, into the VISTA system. However, this is not possible for the J band, because we lack H-band photometry (see table 10 in Kato et al. 2007). We can safely overcome this problem by noting that the (J − H) colour for BL Her and W Vir stars spans a very narrow range (0.25 < (J − H) < 0.4 mag; see e.g. Matsunaga et al. 2011) so that, according to Kato et al. (2007), we can assume J(IRSF) = J(2MASS) + (0.005 ± 0.005). Finally, since our targets span the range 0.25 < (J − K_s) < 0.6 mag, we obtained J(IRSF) = J(VISTA) + (0.035 ± 0.015). As for the K_s, the transformation is straightforward: K_s(IRSF) = K_s(VISTA) + (0.014 ± 0.001).

The PL relations by Matsunaga et al. (2006, 2009), corrected as discussed above, are presented in the first four rows of Table 7. We can compare directly the PL(J) and PL(K_s) relations for the LMC (lines 2 and 4 in Table 7) with our results (lines 1 and 2 in Table 5). There is very good agreement within 1σ errors for the PL(J), whereas for the PL(K_s), the comparison is slightly worse, especially concerning the slope of the relation which is discrepant at the 1.5σ level. It is also worth mentioning that the dispersion of our relations is significantly smaller, as a result of the much better light-curve sampling of the VMC data.

As for the PL(J) and PL(K_s) derived for GGCs by Matsunaga et al. (2006), their slopes are in very good agreement with ours, which suggest a ‘universal slope’ in the NIR filters, independent of the galactic environment. As for the ZPs, we can only compare them for the PL(K_s) relations (see Table 6). We found excellent agreement when the ZP is calibrated through the Galactic calibrators (irrespectively of whether stars with BW measures are included or not), whereas there is a 0.12 mag discrepancy if the ZP is calibrated by means of the LMC DM coming from CCs. This occurrence is not surprising, since Matsunaga et al. (2006) used the M_V versus [Fe/H] relation for RR Lyrae variables by Gratton et al. (2003) to estimate the distances of the GGCs hosting T2CEPs and derive their PL(K_s). Hence, the two Population II calibrators, RR Lyrae and T2CEPs, give distance scales in agreement with each other.

A similar comparison can be performed with the theoretical predictions by Di Criscienzo et al. (2007), who in addition calculated the PWs for all the combinations of magnitudes and colours of interest in this work. Again, we converted the Di Criscienzo et al. (2007) results from Bessell & Brett (1988, BB) to the VISTA system. To do this, we used the transformations BB-2MASS from Carpenter (2001) and 2MASS-VISTA (see Section 2.1) and the same procedure as above to derive J(BB) = J(VISTA) + (0.04 ± 0.010) and K_s(BB) = K_s(VISTA) + (0.030 ± 0.015). Secondly, since the predicted PL and PW relations mildly depend on metallicity and adopted a mixing length parameter (α⁹), we have to make a choice for these parameters. We decided to evaluate the relations for α = 1.5 ± 0.5 (to encompass reasonable values for α) and [Fe/H] = −1.5 ± 0.3 dex as an average value for the LMC old population (see e.g. Borissova et al. 2004, 2006; Gratton et al. 2004; Haschke et al. 2012). The uncertainties on these parameters were taken into account in re-deriving the ZP of the predicted PL and PW relations in the VISTA system. The result of this procedure is shown in the second part of Table 7. A comparison with Table 6 shows that both for the PL(K_s) and PW(K_s, V) relations, there is excellent agreement between ours and theoretical results if the quoted relationships are calibrated with the Galactic T2CEPs and RR Lyrae, whereas there is an ∼0.1 mag discrepancy if we adopt the CC-based DM by Ripepi et al. (2012b) for the LMC to define the ZP. However, if we take into account the uncertainties, this discrepancy results formally not significant within 1σ.

5 DISCUSSION

The results reported in Section 4 allow us to discuss the distance of the LMC as estimated from NIR observation of the T2CEPs hosted in this galaxy. Table 8 (columns 3 and 4) lists the DM_{0, LMC} calculated using the different ZP estimates for the PL(K_s) and PW(K_s, V) relations listed in Table 6. An inspection of the table reveals that the DM_{0, LMC} calculated by means of CCs (column 2 in Table 8) and by means of the T2CEPs differ by more than ∼0.1 mag, even if, formally, there is agreement within 1σ. Since both the Ripepi et al. (2012b) calibration for CCs and that presented here for T2CEPs are based on a weighted mix of HST parallaxes and BW analysis, this discrepancy, albeit only partially significant, seems to suggest that the distance scales calibrated on pulsating stars belonging to Population I and Population II give different results (for a recent comprehensive review of the literature and a discussion about this argument, see de Grijs et al. 2014).

An additional application of the absolute PL(K_s) relation for T2CEPs concerns the distance estimate of GGCs hosting such kind of pulsators. Homogeneous K_s photometry, as well as period of pulsation for most of the known T2CEPs in GGCs, was published by Matsunaga et al. (2006, see their table 2). We simply inserted the period of these variables in the PL(K_s) of Table 6, and by difference with the observed magnitudes, we derived the DM for each GGC. When more than one T2CEP was present in a cluster, we averaged the resulting DMs (we excluded from the calculations the variables with periods longer than about 35 d because they are likely neither BL Her nor W Vir variables). The result of such a procedure is shown in Fig. 12 where for each GGC analysed here, we show (as a function of the metal content of the clusters) the difference between the DMs estimated on the basis of the three different calibration of the PL(K_s) listed in Table 6 and the DMs reported by Harris (1996) in his catalogue of GGC parameters. In Fig. 12, the average discrepancy in DMs decreases from top to bottom, suggesting that, even if the statistical significance is low (due to the large dispersion in ΔDM values ∼ 0.14 mag), the distance scale of GGCs, if estimated on the basis of the T2CEPs hosted in this system, is more consistent with Population II rather than Population I standard candles. This is not particularly surprising since most of the distances of GGCs in the Harris catalogue are based on RR Lyrae stars.

6 SUMMARY

In the context of the VMC survey, this paper shows the first results concerning T2CEPs in the LMC. We presented J and K_s light curves for 130 pulsators, including 41 BL Her, 62 W Vir (12 pW Vir) and 27 RV Tau variables, corresponding to 63, 63 (75 per cent) and 61 per cent of the known LMC populations of the three variable classes, respectively. The K_s-band light curves are almost always well sampled, allowing us to obtain accurate spline fits to the data and, in turn, precise intensity-averaged 〈K_s〉 magnitudes for 120 variables in our sample. As for the J band, only about 1/3 of the J light curves were sufficiently sampled to allow a satisfactory spline fit to the data, and for the remaining 2/3 of pulsators, the intensity-averaged 〈J〉 magnitudes were derived using the K_s-band spline fits as templates. On the basis of this data set for BL Her and W Vir, complemented by the 〈V〉 magnitudes from the OGLE survey, we have built for the first time (apart from PL(J) and PL(K_s)) a variety of empirical PL, PLC and PW relationships, for any combination of the V, J, K_s filters. Several outliers were removed from the calculation of these relations, and we provided an explanation for the presence of these divergent objects. All the quoted PL, PLC and PW relationships were calibrated in terms of the LMC distance. However, the availability of absolute M_V and |$M_{K_\mathrm{s}}$| for a small sample of RR Lyrae and T2CEPs variables based on HST parallaxes allowed us to obtain an independent absolute calibration of the PL(K_s) and PW(K_s, V) relationships [the PLC(K_s, V) is identical to the PW(K_s, V)]. If applied to the LMC and to the GGCs hosting T2CEPs, these relations give DMs which are around 0.1 mag longer than those estimated for CCs by means of HST parallaxes and BW techniques. However, if we take into account the uncertainties at their face value, the quoted discrepancy is formally not significant within 1σ.

We wish to thank our referee, Dr C. D. Laney, for his helpful and competent review of the manuscript. VR warmly thanks Roberto Molinaro for providing the program for the spline interpolation of the light curves.

Partial financial support for this work was provided by PRIN-INAF 2011 (PI: Marcella Marconi) and PRIN MIUR 2011 (PI: F. Matteucci). We thank the UK's VISTA Data Flow System comprising the VISTA pipeline at the Cambridge Astronomy Survey Unit (CASU) and the VISTA Science Archive at Wide Field Astronomy Unit (Edinburgh) (WFAU) for providing calibrated data products supported by the STFC. This work was partially supported by the Gaia Research for European Astronomy Training (GREAT-ITN) Marie Curie network, funded through the European Union Seventh Framework Programme ([FP7/2007- 1312 2013] under grant agreement no. 264895). RdG acknowledges research support from the National Natural Science Foundation of China (NSFC) through grant 11373010. This work was partially supported by the Argentinian institutions CONICET and Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT).

REFERENCES

APPENDIX A: LIGHT CURVES

SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Table 3.J and K_s time-series photometry for the T2CEPs investigated in this paper (Supplementary Data).

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