The VMC survey: L. Type II Cepheids in the Magellanic Clouds: Period–luminosity relations in the near-infrared bands.

Context. Type II Cepheids (T2Cs) are the less frequently used counterparts of classical or type I Cepheids (CCs) which provide the primary calibration of the distance ladder for measuring the Hubble constant in the local Universe. In the era of the "Hubble tension", T2C variables together with the RR Lyrae stars and the tip of the red giant branch (TRGB) can potentially provide non-CC-dependent calibration of the cosmic distance ladder. Aims. Our goal is to provide an absolute calibration of the period–luminosity, period–luminosity–colour, and period–Wesenheit relations (PL, PLC, and PW, respectively) of T2Cs in the Large Magellanic Cloud (LMC), which traditionally serves as a crucial first anchor of the extragalactic distance ladder. Methods. We exploited time-series photometry in the near-infrared (NIR) Y,  J, and Ks bands for a sample of approximately 320 T2Cs in the Magellanic Clouds (MCs). These observations were acquired during 2009–2018 in the context of the VISTA survey of the Magellanic Clouds system (VMC), an ESO public survey. We supplemented the NIR photometry from the VMC survey with well-sampled optical light curves and accurate pulsation periods from the Optical Gravitational Lensing Experiment (OGLE) IV survey and the Gaia mission. We used the best-quality NIR light curves to generate custom templates for modelling sparsely sampled light curves in YJKs bands. Results. The best-fitting YJKs template light curves were used to derive accurate and precise intensity-averaged mean magnitudes and pulsation amplitudes of 277 and 62 T2Cs in the LMC and SMC, respectively. We used optical and NIR mean magnitudes for different T2C subclasses (BLHer, WVir, and RVTau) to derive PL/PLC/PW relations in multiple bands, which were calibrated with the geometric distance to the LMC as derived from eclipsing binaries and with the Gaia parallaxes. We used our new empirical calibrations of PL and PW relations to obtain distances to 22 T2C-host Galactic globular clusters, which were found to be systematically smaller by ∼0.1 mag and 0.03−0.06 mag than in the literature when the zero points are calibrated with the distance of the LMC or Gaia parallaxes, respectively. Better agreement is found between our distances and those based on RR Lyrae stars in globular clusters, providing strong support for using these population II stars together with the TRGB for future distance scale studies. [ABSTRACT FROM AUTHOR]