Projection factor and radii of Type II Cepheids

Context. Type II Cepheids are old pulsating stars that can be used to trace the distribution of an old stellar population and to measure distances to globular clusters and galaxies within several megaparsecs, and by extension, they can improve our understanding of the cosmic distance scale. One method that can be used to measure the distances of Type II Cepheids relies on period-luminosity relations, which are quite widely explored in the literature. The semi-geometrical Baade-Wesselink technique is another method that allows distances of radially pulsating stars, such as Type II Cepheids, to be measured if the so-called projection factor is known. However, the literature concerning this parameter for Type II Cepheids is limited to just a few pioneering works. Aims. In determining projection factors for eight nearby short-period Type II Cepheids, also known as BL Her type stars, we aim to calibrate the Baade-Wesselink method for measuring distances for this class of stars. Methods. Using the surface brightness-colour relation version of the Baade-Wesselink technique, we determined the projection factors and radii of eight nearby BL Her type stars. We adopted accurate distances of target stars from Gaia Data Release 3. Time series photometry in the V and K S bands have been collected with two telescopes located at the RolfChini Cerro Murphy Observatory (former Cerro Armazones Observatory), while spectroscopic data have been obtained within dedicated programmes with instruments hosted by the European Southern Observatory. Results. The measured projection factors for the stars with good quality data are in the range between 1.21 and 1.36. The typical uncertainty of projection factors is 0.1. The mean value is 1.330 ± 0.058, which gives the uncertainty of ∼4%. The main sources of uncertainty on the p -factors are statistical errors of the Baade-Wesselink fit (related to the dispersion and coverage of light and radial velocity curves) and parallax. In the case of radii, the biggest contribution to the error budget comes from the K S band photometry's systematic uncertainty and parallax. The determined radii allowed us to construct the period-radius relation for BL Her stars. Our period-radius relation is in good agreement with the previous empirical calibration, while two theoretical calibrations found in the literature agree with our relation within 2 σ . We also confirm that BL Her and RR Lyr stars obey an apparent common period-radius relation.