High-resolution spectroscopy for Cepheids distance determination^*

II. A period-projection factor relation

¹ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany e-mail: nardetto@mpifr-bonn.mpg.de
² Observatoire de la Côte d'Azur, Dpt. Gemini, UMR 6203, 06130 Grasse, France
³ Institute of Astronomy of the Russian Academy of Sciences, 48 Pjatnitskaya Str., Moscow 109017, Russia
⁴ Observatoire de Haute Provence, 04870 Saint-Michel l'Observatoire, France

Received: 1 December 2006
Accepted: 5 May 2007

Abstract

Context.The projection factor is a key quantity for the interferometric Baade-Wesselink (hereafter IBW) and surface-brightness (hereafter SB) methods of determining the distance of Cepheids. Indeed, it allows a consistent combination of angular and linear diameters of the star.

Aims.We aim to determine consistent projection factors that include the dynamical structure of the Cepheids' atmosphere.

Methods.Hydrodynamical models of δ Cep and  Car have been used to validate a spectroscopic method of determining the projection factor. This method, based on the amplitude of the radial velocity curve, is applied to eight stars observed with the HARPS spectrometer. The projection factor is divided into three sub-concepts : (1) a geometrical effect, (2) the velocity gradient within the atmosphere, and (3) the relative motion of the “optical” pulsating photosphere compared to the corresponding mass elements (hereafter ). Both, (1) and (3) are deduced from geometrical and hydrodynamical models, respectively, while (2) is derived directly from observations.

Results.The 4896.439 Å  line is found to be the best one to use in the context of IBW and SB methods. A coherent and consistent period-projection factor relation (hereafter Pp relation) is derived for this specific spectral line: . This procedure is then extended to derive dynamic projection factors for any spectral line of any Cepheid.

Conclusions.This Pp relation is an important tool for removing bias in the calibration of the period-luminosity relation of Cepheids. Moreover, it reveals a new physical quantity to investigate in the near future.