High resolution spectroscopy for Cepheids distance determination

Abstract

Context. The ratio of pulsation to radial velocity (the projection factor) is currently limiting the accuracy of the Baade-Wesselink method, and in particular of its interferometric version recently applied to several nearby Cepheids. Aims. This work aims at establishing a link between the line asymmetry evolution over the Cepheids' pulsation cycles and their projection factor, with the final objective to improve the accuracy of the Baade-Wesselink method for distance determinations. Methods. We present HARPS high spectral resolution observations (R = 120 000) of nine galactic Cepheids: R Tra, S Cru, Y Sgr, β Dor, ζ Gem, Y Oph, RZ Vel, Car and RS Pup, having a good period sampling (P = 3.39d to P = 41.52d). We fit spectral line profiles by an asymmetric bi-Gaussian to derive radial velocity, Full-Width at Half-Maximum in the line (FWHM) and line asymmetry for all stars. We then extract correlations curves between radial velocity and asymmetry. A geometric model providing synthetic spectral lines, including limb-darkening, a constant FWHM (hereafter σ C ) and the rotation velocity is used to interpret these correlations curves. Results. For all stars, comparison between observations and modelling is satisfactory, and we were able to determine the projected rotation velocities and σ C for all stars. We also find a correlation between the rotation velocity (V rot sin i) and the period of the star: V rot sin i = (−11.5 ± 0.9) log (P) + (19.8 ± 1.0) [km s−1 ]. Moreover, we observe a systematic shift in observational asymmetry curves (noted γ O ), related to the period of the star, which is not explained by our static model: γ O = (−10.7 ± 0.1) log (P) + (9.7 ± 0.2) [in %]. For long-period Cepheids, in which velocity gradients, compression or shock waves seem to be large compared to short-or mediumperiod Cepheids we observe indeed a greater systematic shift in asymmetry curves. Conclusions. This new way of studying line asymmetry seems to be very promising for a better understanding of Cepheids atmosphere and to determine, for each star, a dynamic projection factor.

Extended envelopes around Galactic Cepheids

“…Consequently, this correlation shows that long-period Cepheids have a larger mass-loss than shorterperiod, less massive stars. This behavior might be explained by the stronger velocity fields in longer-period Cepheids, and the presence of shock waves at certain pulsation phases (Nardetto et al 2006(Nardetto et al , 2008. This scenario is consistent with the theoretically predicted range, 10 −10 −10 −7 M yr −1 , of Neilson & Lester (2008), based on a pulsation-driven mass-loss model.…”

“…Cepheids with long periods have higher masses and larger radii, therefore if we assume that the CSE IR brightness is an indicator of the mass-loss rate, this would mean that heavier stars experience higher mass-loss rates. This behavior could be explained by the stronger velocity fields in longer-period Cepheids and shock waves at certain pulsation phases (Nardetto et al 2008(Nardetto et al , 2006. Studying this correlation between the pulsation period and the IR excess is vital for calibrating relations between the Cepheid' fundamental parameters with respect to their pulsation periods.…”

The long-period Galactic Cepheid RS Puppis

“…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.…”

Notes on disentangling of spectra

“…It is used to characterize such profiles quantitatively by bi-Gaussian fits (cf. Nardetto et al 2006), which, however, are not physically substantiated.…”

“…An example of such Lorentzian profiles with the intrinsic semi-halfwidth γ corresponding to 30 km s −1 broadened by Δ 0 with a semi-amplitude of the pulsational velocity K sim equal to 100 km s −1 is presented in the phase) have the highest asymmetry at extremes of the pulsational velocity, the high-velocity wing always being steeper than the wider low-velocity wings reaching the rest wavelength of the line. Qualitatively the same feature also results if the pulsational broadening is applied to non-Lorentzian line profiles and is in agreement with the line-profile variations observed in Cepheids (cf., e.g., Breitfellner & Gillet 1993;Nardetto et al 2006;Gray & Stevenson 2007). It is used to characterize such profiles quantitatively by bi-Gaussian fits (cf.…”