High resolution spectroscopy for Cepheids distance determination. II. A period- projection factor relation

摘要

The projection factor is a key quantity for the interferometricBaade-Wesselink (hereafter IBW) and surface-brightness (hereafter SB) methodsof determining the distance of Cepheids. Indeed, it allows a consistentcombination of angular and linear diameters of the star. We aim to determineconsistent projection factors that include the dynamical structure of theCepheids' atmosphere. Methods. Hydrodynamical models of delta Cep and l Carhave been used to validate a spectroscopic method of determining the projectionfactor. This method, based on the amplitude of the radial velocity curve, isapplied to eight stars observed with the HARPS spectrometer. The projectionfactor is divided into three sub-concepts : (1) a geometrical effect, (2) thevelocity gradient within the atmosphere, and (3) the relative motion of the"optical" pulsating photosphere compared to the corresponding mass elements(hereafter fo-g). Both, (1) and (3) are deduced from geometrical andhydrodynamical models, respectively, while (2) is derived directly fromobservations. The Fe I 4896.439 A line is found to be the best one to use inthe context of IBW and SB methods. A coherent and consistent period-projectionfactor relation (hereafter Pp relation) is derived for this specific spectralline: p = [0.064 +- 0.020] log P + [1.376 +- 0.023]. This procedure is thenextended to derive dynamic projection factors for any spectral line of anyCepheid. This Pp relation is an important tool for removing bias in thecalibration of the period-luminosity relation of Cepheids. Moreover, it revealsa new physical quantity fo-g to investigate in the near future.