Calibrating the Galactic Classical Cepheid period-luminosity relation based on photometric and spectroscopic data

We present a realization of the maximum-likelihood technique, which is one of the latest modifications of the Baade--Becker--Wesselink method. It allows one to estimate the key Cepheid parameters, the distance modulus, and the interstellar reddening, combining photometric and spectroscopic data (including the effective temperature data). This method is applied to the sample of 44 Galactic Cepheids, for which multiphase temperature measurements are available. The additional data correction is performed to subtract the impact of the component in binary/multiple systems. We also study the effect of shock waves, whose presence in the stellar atmosphere distorts the observational data and leads to systematic errors in the obtained parameters. As a result, we obtain the following period-luminosity relation: $M_v = - (2.67 \pm 0.16) \cdot (log\,P - 1) - (4.14 \pm 0.05)$. Despite the fact that the final calibration is in reasonable agreement with the relations calculated using trigonometric parallaxes, a slight zero-point offset is found, indicating the brighter Cepheids and therefore the longer distance scale. Thus, the Hubble constant estimate based on our period-luminosity relation has to be lower.