The atmosphere, the p-factor and the bright visible circumstellar environment of the prototype of classical Cepheids δ Cep
Even ≃ 16000 cycles after its discovery by John Goodricke in 1783, δ Cep, the prototype of classical Cepheids, is still studied intensively in order to better understand its atmospheric dynamical structure and its environment. Using HARPS-N spectroscopic measurements, we have measured the atmospheric velocity gradient of δ Cep for the first time and we confirm the decomposition of the projection factor, a subtle physical quantity limiting the Baade-Wesselink (BW) method of distance determination. This decomposition clarifies the physics behind the projection factor and will be useful to interpret the hundreds of p-factors that will come out from the next Gaia release. Besides, VEGA/CHARA interferometric observations of the star revealed a bright visible circumstellar environment contributing to about 7% to the total flux. Better understanding the physics of the pulsation and the environment of Cepheids is necessary to improve the BW method of distance determination, a robust tool to reach Cepheids in the MilkyWay, and beyond, in the Local Group.