High-resolution spectroscopy for Cepheids distance determination

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 f o−g ). Both, (1) and (3) are deduced from geometrical and hydrodynamical models, respectively, while (2) is derived directly from observations.Results. The Fe i 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: p = [−0.064 ± 0.020] log P + [1.376 ± 0.023]. 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 f o−g to investigate in the near future.

VEGA: Visible spEctroGraph and polArimeter for the CHARA array: principle and performance

“…Compared to interferometric observations in the infrared, the application of the interferometric Baade-Wesselink method will be more efficient using visible angular diameters from VEGA, as the complementary spectroscopic velocimetry is also obtained in the visible. The high spectral resolution will also make it possible to study the atmosphere dynamics in metallic lines (Nardetto et al 2007), as well as the signatures of their envelopes in hydrogen lines (Nardetto et al 2008;Kervella et al 2009). …”

The long-period Galactic Cepheid RS Puppis

“…Gieren et al (1993), namely p = 1.39−0.03 log P, which amounts to 1.341 in the case of RS Pup (log P = 1.6174). Fouqué et al (2007) derived a distance of 1830 pc based on the same data, but using a lower projection factor based on a mean relation derived by Nardetto et al (2007), p = 1.366−0.075 log P (cross-correlation method), which leads to 1.245 in the case of RS Pup. This revision is based on recent hydrodynamical models of RS Pup itself, combined with high-resolution spectroscopic measurements.…”

“…Changes in the pulsation period bear information on the evolutionary stage of the Cepheid (secular period changes) and the physical processes occurring in the pulsating stellar atmosphere (period changes on a time-scale of years). Recent high resolution spectroscopic observations with the HARPS instrument were reported by Nardetto et al (2006Nardetto et al ( , 2007. They show very broad spectral lines at certain phases, indicative of the presence of strong shock waves.…”

The Baade–Becker–Wesselink technique and the fundamental astrophysical parameters of Cepheids

“…There is yet no consensus as to which projection factor (PF) should be used for Cepheid variables (Nardetto et al 2004, Groenewegen 2007, Nardetto et al 2007, Nardetto et al 2009). Different approaches (constant or period-dependent P F values) lead to systematic differences in the inferred Cepheid parameters, first and foremost in the radii.…”

“…In practice, the P F value for measured a given radial velocity should be determined by iteration for known values of S 0 . To compare our results on Cepheids with other calculations, we finally adopted a moderate dependence of P F on the period advocated by Nardetto et al (2007), although we repeated all calculations with other variants of P F dependence on the period and pulsation phase to assure the stability of the calculated colour excess. …”