| Abstract
| - Context. The parallax of pulsation, and its implementations such as the Baade-Wesselink method and the infrared surface brightness technique, is an elegant method to determine distances of pulsating stars in a quasi-geometrical way. However, these classical implementations in general only use a subset of the available observational data. Aims. Freedman & Madore (2010, ApJ, 719, 335) suggested a more physical approach in the implementation of the parallax of pulsation in order to treat all available data. We present a global and model-based parallax-of-pulsation method that enables including any type of observational data in a consistent model fit, the SpectroPhoto-Interferometric modeling of Pulsating Stars (SPIPS). Methods. We implemented a simple model consisting of a pulsating sphere with a varying effective temperature and a combination of atmospheric model grids to globally fit radial velocities, spectroscopic data, and interferometric angular diameters. We also parametrized (and adjusted) the reddening and the contribution of the circumstellar envelopes in the near-infrared photometric and interferometric measurements. Results. We show the successful application of the method to two stars: δ Cep and η Aql. The agreement of all data fitted by a single model confirms the validity of the method. Derived parameters are compatible with publish values, but with a higher level of confidence. Conclusions. The SPIPS algorithm combines all the available observables (radial velocimetry, interferometry, and photometry) to estimate the physical parameters of the star (ratio distance/ p-factor, Teff, presence of infrared excess, color excess, etc). The statistical precision is improved (compared to other methods) thanks to the large number of data taken into account, the accuracy is improved by using consistent physical modeling and the reliability of the derived parameters is strengthened thanks to the redundancy in the data.
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