Confronting Cepheids Models with Interferometric Observations

In the last years, some issues concerning Cepheids have been resolved, based on observations and modeling. However, as usual, new difficulties arise. The link between the dynamical structure of Cepheid atmosphere and the distance scale calibration in the universe is now clearly established. To support observations, we currently need fully consistent hydrodynamical models, including pulsating and evolutionary theories, convective energy transport, adaptive numerical meshes, and a refined calculation of the radiative transfer within the pulsating atmosphere, and also in the expected circumstellar envelope (hereafter CSE). Confronting such models with observations (spectral line profiles, spatial- and spectral- visibility curves), will permit to resolve and/or strengthen subtle questions concerning (1) the limb-darkening, (2) the dynamical structure of Cepheids' atmosphere, (3) the expected interaction between the atmosphere and the CSE, and (4) it will bring new insights in determining the fundamental parameters of Cepheids. All these physical quantities are supposed furthermore to be linked to the pulsation period of Cepheids. From these studies, it will be possible to paint a glowing picture of all Cepheids within the instability strip, allowing an unprecedent calibration of the period-luminosity relation (hereafter PL relation), leading to new insights in the fields of extragalactic distance scales and cosmology