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The VISTA survey of the Magellanic Clouds System (VMC) is collecting deep $K_mathrm{s}$--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 pap er 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 survey. We present $J$ and $K_mathrm{s}$ 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 $V, J, K_mathrm{s}$ 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 $PL(K_mathrm{s})$ and the $PW(K_mathrm{s},V)$ 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 $sim$0.1 mag between population II standard candles and Classical Cepheids when the distances are gauged in a similar way for all the quoted pulsators. However, given the uncertainties, this discrepancy is within the formal 1$sigma$ uncertainties.
The VMC survey is obtaining multi-epoch photometry in the Ks band of the Magellanic System down to a limiting magnitude of Ks ~ 19.3 for individual epoch data. The observations are spaced in time such as to provide optimal sampling of the light curve s for RR Lyrae stars and for Cepheids with periods up to 20-30 days. We present examples of the Ks-band light curves of Classical Cepheids and RR Lyrae stars we are obtaining from the VMC data and outline the strategy we put in place to measure distances and infer the System three-dimensional geometry from the variable stars. For this purpose the near-infrared Period-Luminosity, Period-Wesenheit, and Period-Luminosity-Colour relations of the system RR Lyrae stars and Cepheids are used. We extensively exploit the catalogues of the Magellanic Clouds variable stars provided by the EROS-2 and OGLE III/IV microlensing surveys. By combining these surveys we present the currently widest-area view of the Large Magellanic Cloud as captured by the galaxy Cepheids, RR Lyrae stars and binaries. This reveals the full extent of the main structures (bar/s - spiral arms) that have only been vaguely guessed before. Our work strengthens the case for a detailed study of the Large Magellanic Cloud three-dimensional geometry.
The VISTA near-infrared $YJK_mathrm{s}$ survey of the Magellanic Clouds System (VMC, PI M.-R. L. Cioni) is collecting deep $K_mathrm{s}$-band time-series photometry of the pulsating variable stars hosted in the system formed by the two Magellanic Clo uds and the Bridge connecting them. In this paper we present for the first time $K_mathrm{s}$-band light curves for Anomalous Cepheid (AC) variables. In particular, we have analysed a sample of 48 Large Magellanic Cloud ACs, for which identification and optical magnitudes were obtained from the OGLE III and IV catalogues. The VMC $K_mathrm{s}$-band light curves for ACs are well sampled, with the number of epochs ranging from 8 to 16, and allowing us to obtain very precise mean $K_mathrm{s}$ magnitudes with errors on average of the order of 0.01 mag. The $langle K_mathrm{s} rangle$ values were used to build the first Period-Luminosity and Period-Wesenheit relations in the near-infrared for fundamental-mode and first overtone ACs. At the same time we exploited the optical ($V,I$) OGLE data to build accurate Period-Luminosity, Period-Luminosity-Colour and Period-Wesenheit relations both for fundamental-mode and first overtone ACs. For the first time these relations were derived from a sample of pulsators which uniformly cover the whole AC instability strip. The application of the optical Period-Wesenheit relation to a sample of dwarf galaxies hosting a significant population of ACs revealed that this relation is a valuable tool for deriving distances within the Local Group. Due to its lower dispersion, we expect the $K_mathrm{s}$ Period-Wesenheit relations first derived in this paper to represent a valuable tool for measuring accurate distances to galaxies hosting ACs when more data in near-infrared filters become available.
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