Period-Luminosity Relations, projection factor and radii of Anomalous Cepheids

Anomalous Cepheids are radially pulsating stars observed in dwarf galaxies, the Galactic bulge and halo, and globular clusters. Similarly to other radially pulsating stars, they can be used as distance indicators through their Period-Luminosity Relations (PLRs) and the geometrical Baade-Wesselink (BW) method. We aim to calibrate the zero-point of the distance scale of Anomalous Cepheids using nearby representatives of this class of pulsating stars. We collected optical and near-infrared photometry and spectra for a sample of nearby Anomalous Cepheids with twotelescopes located at the Rolf Chini Cerro Murphy Observatory and optical telescopes offered by the Las Cumbres Observatory, and with instruments hosted and operated by the European Southern Observatory. Using parallaxesmeasured by the Gaia space mission and mean magnitudes from our new photometry, we calibrate the zero-point of the PLRs in Johnson B, V, 2MASS J, H, KS , and Pan-STARRS g, r, i passbands and selected Wesenheit indices. Using the surface brightness-colour relation version of the BW technique, we also determined the projection factors and mean radii of three nearby Anomalous Cepheids. Precision of the measured zero-points is at the level of 0.04-0.05mag and their systematic uncertainty is estimated to about 0.1mag. We used our zero-points and literature photometry of the Large Magellanic Cloud Anomalous Cepheids to measure the distance modulus of this galaxy and obtained a value of 18.454$\pm$0.045(statistical) mag, in a very good agreement with the most accurate value from eclipsing binaries. The obtained projection factors are 1.38$\pm$0.13, 1.59$\pm$0.21 and 1.35$\pm$0.14 for V716 Oph, XX Vir and UY Eri, respectively. The radii measured for V716 Oph and UY Eri are in agreement with the period-radius relation obtained from the Large Magellanic Cloud Anomalous Cepheids.