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Register a new userHARPS-N high spectral resolution observations of Cepheids I. The Baade-Wesselink projection factor of {delta} Cep revisited
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The projection factor p is the key quantity used in the Baade-Wesselink (BW) method for distance determination; it converts radial velocities into pulsation velocities. Several methods are used to determine p, such as geometrical and hydrodynamical models or the inverse BW approach when the distance is known. We analyze new HARPS-N spectra of delta Cep to measure its cycle-averaged atmospheric velocity gradient in order to better constrain the projection factor. We first apply the inverse BW method to derive p directly from observations. The projection factor can be divided into three subconcepts: (1) a geometrical effect (p0); (2) the velocity gradient within the atmosphere (fgrad); and (3) the relative motion of the optical pulsating photosphere with respect to the corresponding mass elements (fo-g). We then measure the fgrad value of delta Cep for the first time. When the HARPS-N mean cross-correlated line-profiles are fitted with a Gaussian profile, the projection factor is pcc-g = 1.239 +/- 0.034(stat) +/- 0.023(syst). When we consider the different amplitudes of the radial velocity curves that are associated with 17 selected spectral lines, we measure projection factors ranging from 1.273 to 1.329. We find a relation between fgrad and the line depth measured when the Cepheid is at minimum radius. This relation is consistent with that obtained from our best hydrodynamical model of delta Cep and with our projection factor decomposition. Using the observational values of p and fgrad found for the 17 spectral lines, we derive a semi-theoretical value of fo-g. We alternatively obtain fo-g = 0.975+/-0.002 or 1.006+/-0.002 assuming models using radiative transfer in plane-parallel or spherically symmetric geometries, respectively. The new HARPS-N observations of delta Cep are consistent with our decomposition of the projection factor.
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Aims. The Baade-Wesselink method of distance determination is based on the oscillations of pulsating stars. The key parameter of this method is the projection factor used to convert the radial velocity into the pulsation velocity. Our analysis was aimed at deriving for the first time the projection factor of delta Scuti stars, using high-resolution spectra of the high-amplitude pulsator AI Vel and of the fast rotator beta Cas. Methods. The geometric component of the projection factor (i.e. p0) was calculated using a limb-darkening model of the intensity distribution for AI Vel, and a fast-rotator model for beta Cas. Then, using SOPHIE/OHP data for beta Cas and HARPS/ESO data for AI Vel, we compared the radial velocity curves of several spectral lines forming at different levels in the atmosphere and derived the velocity gradient associated to the spectral-line-forming regions in the atmosphere of the star. This velocity gradient was used to derive a dynamical projection factor p. Results. We find a flat velocity gradient for both stars and finally p = p0 = 1.44 for AI Vel and p = p0 = 1.41 for beta Cas. By comparing Cepheids and delta Scuti stars, these results bring valuable insights into the dynamical structure of pulsating star atmospheres. They suggest that the period-projection factor relation derived for Cepheids is also applicable to delta Scuti stars pulsating in a dominant radial mode.
Cepheids play a key role in astronomy as standard candles for measuring intergalactic distances. Their distance is usually inferred from the Period-Luminosity relationship, calibrated using the semi-empirical Baade-Wesselink method. Using this method, the distance is known to a multiplicative factor, called the projection factor. Presently, this factor is computed using numerical models - it has hitherto never been measured directly. Based on our new interferometric measurements obtained with the CHARA Array and the already published parallax, we present a geometrical measurement of the projection factor of a Cepheid, delta Cep. The value we determined, p = 1.27$pm$0.06, confirms the generally adopted value of p = 1.36 within 1.5 sigmas. Our value is in line with recent theoretical predictions of Nardetto et al. (2004).
The B-W method is used to determine the distance of Cepheids and consists in combining the angular size variations of the star, as derived from infrared surface-brightness relations or interferometry, with its linear size variation, as deduced from visible spectroscopy using the projection factor. While many Cepheids have been intensively observed by infrared beam combiners, only a few have been observed in the visible. This paper is part of a project to observe Cepheids in the visible with interferometry as a counterpart to infrared observations already in hand. Observations of delta Cep itself were secured with the VEGA/CHARA instrument over the full pulsation cycle of the star. These visible interferometric data are consistent in first approximation with a quasi-hydrostatic model of pulsation surrounded by a static circumstellar environment (CSE) with a size of theta_cse=8.9 +/- 3.0 mas and a relative flux contribution of f_cse=0.07+/-0.01. A model of visible nebula (a background source filling the field of view of the interferometer) with the same relative flux contribution is also consistent with our data at small spatial frequencies. However, in both cases, we find discrepancies in the squared visibilities at high spatial frequencies (maximum 2sigma) with two different regimes over the pulsation cycle of the star, phi=0.0-0.8 and phi=0.8-1.0. We provide several hypotheses to explain these discrepancies, but more observations and theoretical investigations are necessary before a firm conclusion can be drawn. For the first time we have been able to detect in the visible domain a resolved structure around delta~Cep. We have also shown that a simple model cannot explain the observations, and more work will be necessary in the future, both on observations and modelling.
We provided accurate estimates of distances, radii and iron abundances for four metal-rich Cepheids, namely V340 Ara, UZ Sct, AV Sgr and VY Sgr. The main aim of this investigation is to constrain their pulsation properties and their location across the Galactic inner disk. We adopted new accurate NIR (J,H,K) light curves and new radial velocity measurements for the target Cepheids to determinate their distances and radii using the Baade-Wesselink technique. In particular, we adopted the most recent calibration of the IR surface brightness relation and of the projection factor. Moreover, we also provided accurate measurements of the iron abundance of the target Cepheids. Current distance estimates agree within one sigma with similar distances based either on empirical or on theoretical NIR Period-Luminosity relations. However, the uncertainties of the Baade-Wesselink distances are on average a factor of 3-4 smaller when compared with errors affecting other distance determinations. Mean Baade-Wesselink radii also agree at one sigma level with Cepheid radii based either on empirical or on theoretical Period-Radius relations. Iron abundances are, within one sigma, similar to the iron contents provided by Andrievsky and collaborators, thus confirming the super metal-rich nature of the target Cepheids. We also found that the luminosity amplitudes of classical Cepheids, at odds with RR Lyrae stars, do not show a clear correlation with the metal-content. This circumstantial evidence appears to be the consequence of the Hertzsprung progression together with the dependence of the topology of the instability strip on metallicity, evolutionary effects and binaries.
We focus on empirically measure the p-factor of a homogeneous sample of 29 LMC and 10 SMC Cepheids for which an accurate average LMC/SMC distance were estimated from eclipsing binary systems. We used the SPIPS algorithm, which is an implementation of the BW method. As opposed to other conventional use, SPIPS combines all observables, i.e. radial velocities, multi-band photometry and interferometry into a consistent physical modeling to estimate the parameters of the stars. The large number and their redundancy insure its robustness and improves the statistical precision. We successfully estimated the p-factor of several MC Cepheids. Combined with our previous Galactic results, we find the following P-p relation: -0.08(log P-1.18)+1.24. We find no evidence of a metallicity dependent p-factor. We also derive a new calibration of the P-R relation, logR=0.684(log P-0.517)+1.489, with an intrinsic dispersion of 0.020. We detect an IR excess for all stars at 3.6 and 4.5um, which might be the signature of circumstellar dust. We measure a mean offset of $Delta m_{3.6}=0.057$mag and $Delta m_{4.5}=0.065$mag. We provide a new P-p relation based on a multi-wavelengths fit, and can be used for the distance scale calibration from the BW method. The dispersion is due to the MCs width we took into account because individual Cepheids distances are unknown. The new P-R relation has a small intrinsic dispersion, i.e. 4.5% in radius. Such precision will allow us to accurately apply the BW method to nearby galaxies. Finally, the IR excesses we detect raise again the issue on using mid-IR wavelengths to derive P-L relation and calibrate the $H_0$. These IR excesses might be the signature of circumstellar dust, and are never taken into account when applying the BW method at those wavelengths. Our measured offsets may give an average bias of 2.8% on the distances derived through mid-IR P-L relations.
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