New Version of the Pulsating Photospheres Method: Multiphase Temprature Measurements of Cepheids

Abstract

We propose a new version of the (Baade–Becker–Wesselink) pulsating photospheres method based on direct spectral measurements of the effective temperatures of Cepheids carried out in different pulsation phases. By comparing the effective temperatures calculated using normal color calibrations with real spectroscopic estimates, we were able to not only determine the color excess with an accuracy of the order of $0\mathop .\limits^{\text{m}} 01$ mag, but also use all the measured effective temperature values to derive a new color calibration for the effective temperature of high luminosity stars, also taking into account the differences in metallicity ${\text{[Fe/H}}]$ and surface gravity $\log {\kern 1pt} g$: log T_eff = 3.88 – 0.20(B – V)₀ + 0.026(B –V)$_{0}^{2}$ + 0.009log g – 0.010(B – V)₀log g – 0.051[Fe/H] + 0.051(B – V)₀[Fe/H], the relative accuracy of which is approximately $1.1\%$. In addition, the complete identity of the two main versions of the Baade–Becker–Wesselink method was proved: the surface brightness method (SB), first proposed by Barnes and Evans in 1976, and the maximum likelihood method (or light-curve modeling method) proposed by Balona in 1977 and later improved by Rastorguev and Dambis in 2010. This approach consists of using significantly nonlinear color calibrations for $\log {{T}_{{{\text{eff}}}}}$ and bolometric correction $BC$ and is easily applicable to the surface brightness method. This method is also applicable in studies of other types of pulsating variable stars, e.g., RR Lyrae, Mirae and $\delta$ Sct type variables with known effective temperature estimates.