The VMC Survey

Context. Anomalous Cepheids (ACs) are pulsating variable stars, and are less studied compared to the well-known Classical Cepheids (CCs) and RR Lyrae stars. The ACs are metal poor ([Fe/H] < 1.5) and follow distinct period-luminosity (PL) and period-Wesenheit (PW) relations that can be used for distance measurements, and they can pulsate in the fundamental (F) and first overtone (1O) modes. Aims. Our goal is to evaluate the precision and accuracy of distances obtained via PL and PW relations of ACs and thus to assess if they could be used to establish a cosmic distance scale independent from CCs. To this aim, we derived new, precise PL and PW relations for the F mode, the 1O mode, and, for the first time, the combined F+1O mode ACs in the Magellanic Clouds. We investigated the wavelength dependence of these relations and applied them to calculate the distances of various stellar systems in the Local Group hosting ACs, as well as to confirm the classification of these variable stars. Methods. We analyzed near-infrared (NIR) time series photometry in the Y , J , and K s bands for about 200 ACs in the Magellanic Clouds acquired during 2009–2018 in the context of the VISTA survey of the Magellanic Clouds system (VMC), a European Southern Observatory public survey. The VMC NIR photometry was complemented with optical data from Gaia DR3 and the Optical Gravitational Lensing Experiment IV survey, which also provided the identification, periods, and pulsation mode for the investigated ACs. Custom templates generated from our best light curves were used to derive precise intensity-averaged mean magnitudes for 118 and 75 ACs in the Large (LMC) and Small Magellanic Clouds (SMC), respectively. Results. Optical and NIR mean magnitudes were used to derive multiband PL and PW relations, which were calibrated with the geometric distance modulus to the LMC based on eclipsing binaries. We investigated the dependence of PL relations on wavelength, finding that slopes increase and dispersion decreases when going from optical to NIR bands. We calculated the LMC distance modulus through calibrated AC PW relations in the Milky Way using Gaia parallaxes, the LMC-SMC relative distance modulus, and we confirmed the AC nature of a few new pulsators in Galactic globular clusters. We derived a distance modulus for the Draco dwarf spheroidal galaxy of 19.425 ± 0.048 mag, which is in agreement with recent literature determinations, but a discrepancy of 0.1 mag with RR Lyrae-based distance hints at possible metallicity effects on the AC PL and PW relations. Future spectroscopic surveys and Gaia DR4 will refine the AC distance scale and assess metallicity effects on PLRs and PWRs.