Anomalous Cepheids (ACEPs) 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 ACEPs using nearby representatives of this class of pulsating stars. We collected optical/near-infrared photometry and spectra for a sample of nearby ACEPs with two telescopes located at the Rolf Chini Cerro Murphy Observatory (formerly Observatory Cerro Armazones) and optical telescopes offered by the Las Cumbres Observatory, along with instruments hosted and operated by the European Southern Observatory. Using parallaxes measured by the Gaia space mission and mean magnitudes from our new photometry, we calibrated the zero point of the period-luminosity relations (PLRs) in Johnson B, V, 2MASS J, H, KS, and Pan-STARRS g, r, i passbands, as well as select Wesenheit indices. The slopes were adopted from the PLRs of the LMC ACEPs from the literature. Using the surface brightness-color relation version of the BW technique, we were also able to determine the projection factors (p-factors) and mean radii of three nearby ACEPs. The precision of the measured zero points is at the level of 0. 04-0. 05mag and their systematic uncertainty was estimated to be about 0. 1mag. We used our zero point values and literature photometry related to LMC ACEPs to measure the distance modulus of this galaxy. We obtained a value of 18. 454±0. 045 (statistical), mag, which is in very good agreement with the most accurate value from eclipsing binaries. The p-factors were 1. 38±0. 13, 1. 59±0. 21, and 1. 35±0. 14 for V716 Oph, XX Vir, and UY Eri, respectively. We suspect that the very high p-factor of XX Vir results from the underestimated parallax of this star in the Gaia catalog, as its radius and absolute brightness are also higher than expected for ACEPs at this period. Finally, the radii measured for V716 Oph and UY Eri are in agreement with the period-radius relation obtained from LMC ACEPs.
Wielgórski et al. (Wed,) studied this question.