High resolution spectroscopy for Cepheids distance determination. V. Impact of the cross-correlation method on the p-factor and the gamma-velocities

The cross correlation method (hereafter CC) is widely used to derive the radial velocity curve of Cepheids when the signal to noise of the spectra is low. However, if it is used with the wrong projection factor, it might introduce some biases in the Baade-Wesselink (hereafter BW) methods of determining the distance of Cepheids. In addition, it might affect the average value of the radial velocity curve (or gamma-velocity) important for Galactic structure studies. We aim to derive a period-projection factor relation (hereafter Pp) appropriate to be used together with the CC method. Moreover, we investigate whether the CC method can explain the misunderstood previous calculation of the K-term of Cepheids. We observed eight galactic Cepheids with the HARPS spectrograph. For each star, we derive an interpolated CC radial velocity curve using the HARPS pipeline. The amplitudes of these curves are used to determine the correction to be applied to the semi-theoretical projection factor derived in Nardetto et al. (2007). Their average value (or gamma-velocity) are also compared to the center-of-mass velocities derived in Nardetto et al. (2008). The correction in amplitudes allows us to derive a new Pp relation: p = [-0.08+-0.05] log P +[1.31+-0.06]. We also find a negligible wavelength dependence (over the optical range) of the Pp relation. We finally show that the gamma-velocity derived from the CC method is systematically blue-shifted by about 1.0 +- 0.2km/s compared to the center-of-mass velocity of the star. An additional blue-shift of 1.0km/s is thus needed to totally explain the previous calculation of the K-term of Cepheids (around 2km/s). The new Pp relation we derived is a solid tool for the distance scale calibration (abridged).Comment: Comments : 9 pages, 3 Postscript figures, 5 Tables, accepted for publication in A&

Calibrating the projection factor for Galactic Cepheids

The projection factor (p), which converts the radial velocity to pulsational velocity, is an important parameter in the Baade-Wesselink (BW) type analysis and distance scale work. The p-factor is either adopted as a constant or linearly depending on the logarithmic of pulsating periods. The aim of this work is to calibrate the p-factor if a Cepheid has both the BW distance and an independent distance measurement, and examine the p-factor for delta Cephei -- the prototype of classical Cepheids. We calibrated the p-factor for several Galactic Cepheids that have both the latest BW distances and independent distances either from Hipparcos parallaxes or main-sequence fitting distances to Cepheid-hosted stellar clusters. Based on 25 Cepheids, the calibrated p-factor relation is consistent with latest p-factor relation in literature. The calibrated p-factor relation also indicates that this relation may not be linear and may exhibit an intrinsic scatter. We also examined the discrepancy of empirical p-factors for delta Cephei, and found that the reasons for this discrepancy include the disagreement of angular diameters, the treatment of radial velocity data, and the phase interval adopted during the fitting procedure. Finally, we investigated the impact of the input p-factor in two BW methodologies for delta Cephei, and found that different p-factors can be adopted in these BW methodologies and yet result in the same angular diameters.Comment: 6 pages, 6 figures and 2 tables. A&A accepte

The Baade-Wesselink p-factor applicable to LMC Cepheids

Context. Recent observations of LMC Cepheids bring new constraints on the slope of the period-projection factor relation (hereafter Pp relation) that is currently used in the Baade-Wesselink (hereafter BW) method of distance determination. The discrepancy between observations and theoretical analysis is particularly significant for short period Cepheids Aims. We investigate three physical effects that might possibly explain this discrepancy: (1) the spectroscopic S/N that is systematically lower for LMC Cepheids (around 10) compared to Galactic ones (up to 300), (2) the impact of the metallicity on the dynamical structure of LMC Cepheids, and (3) the combination of infrared photometry/interferometry with optical spectroscopy. Methods. To study the S/N we use a very simple toy model of Cepheids. The impact of metallicity on the projection factor is based on the hydrodynamical model of delta Cep already described in previous studies. This model is also used to derive the position of the optical versus infrared photospheric layers. Results. We find no significant effect of S/N, metallicity, and optical-versus-infrared observations on the Pp relation. Conclusions. The Pp relation of Cepheids in the LMC does not differ from the Galactic relation. This allows its universal application to determine distances to extragalactic Cepheids via BW analysis.Comment: accepted in A&A LETTER

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

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. We aim to determine consistent projection factors that include the dynamical structure of the Cepheids' atmosphere. Methods. Hydrodynamical models of delta Cep and l 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 fo-g). Both, (1) and (3) are deduced from geometrical and hydrodynamical models, respectively, while (2) is derived directly from observations. The Fe I 4896.439 A 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. 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 fo-g to investigate in the near future

Cepheid distances from infrared long-baseline interferometry - I. VINCI/VLTI observations of seven Galactic Cepheids

We report the angular diameter measurements of seven classical Cepheids (X Sgr, eta Aql, W Sgr, zeta Gem, beta Dor, Y Oph and L Car) that we have obtained with the VINCI instrument, installed at ESO's VLT Interferometer (VLTI). We also present reprocessed archive data obtained with the FLUOR/IOTA instrument on zeta Gem, in order to improve the phase coverage of our observations. We obtain average limb darkened angular diameter values of LD(X Sgr) = 1.471 +/- 0.033 mas, LD(eta Aql) = 1.839 +/- 0.028 mas, LD(W Sgr) = 1.312 +/- 0.029 mas, LD(beta Dor) = 1.891 +/- 0.024 mas, LD(zeta Gem) =1.747 +/- 0.061 mas, LD(Y Oph) = 1.437 +/- 0.040 mas and LD(L Car) = 2.988 +/- 0.012 mas. For four of these stars (eta Aql, W Sgr, beta Dor, and L Car) we detect the pulsational variation of their angular diameter. This enables us to compute directly their distances, using a modified version of the Baade-Wesselink method: d(eta Aql) = 276 [+55 -38] pc, d(W Sgr) = 379 [+216 -130] pc, d(beta Dor) = 345 [+175 -80] pc, d(L Car) = 603 [+24 -19] pc. The stated error bars are statistical in nature. Applying a hybrid method, that makes use of the Gieren et al. (1998) Period-Radius relation to estimate the linear diameters, we obtain the following distances (statistical and systematic error bars are mentioned): d(X Sgr) = 324 +/- 7 +/- 17 pc, d(eta Aql) = 264 +/- 4 +/- 14 pc, d(W Sgr) = 386 +/- 9 +/- 21 pc, d(beta Dor) = 326 +/- 4 +/- 19 pc, d(zeta Gem) = 360 +/- 13 +/- 22 pc, d(Y Oph) = 648 +/- 17 +/- 47 pc and d(L Car) = 542 +/- 2 +/- 49 pc.Comment: 16 pages, 12 figures, accepted for publication in Astronomy & Astrophysic

Understanding the dynamical structure of pulsating stars. HARPS spectroscopy of the delta Scuti stars rho Pup and DX Cet

High-resolution spectroscopy is a powerful tool to study the dynamical structure of pulsating stars atmosphere. We aim at comparing the line asymmetry and velocity of the two delta Sct stars rho Pup and DX Cet with previous spectroscopic data obtained on classical Cepheids and beta Cep stars. We obtained, analysed and discuss HARPS high-resolution spectra of rho Pup and DX Cet. We derived the same physical quantities as used in previous studies, which are the first-moment radial velocities and the bi-Gaussian spectral line asymmetries. The identification of f=7.098 (1/d) as a fundamental radial mode and the very accurate Hipparcos parallax promote rho Pup as the best standard candle to test the period-luminosity relations of delta Sct stars. The action of small-amplitude nonradial modes can be seen as well-defined cycle-to-cycle variations in the radial velocity measurements of rho Pup. Using the spectral-line asymmetry method, we also found the centre-of-mass velocities of rho Pup and DX Cet, V_gamma = 47.49 +/- 0.07 km/s and V_gamma = 25.75 +/- 0.06 km/s, respectively. By comparing our results with previous HARPS observations of classical Cepheids and beta Cep stars, we confirm the linear relation between the atmospheric velocity gradient and the amplitude of the radial velocity curve, but only for amplitudes larger than 22.5 km/s. For lower values of the velocity amplitude (i.e., < 22.5 km/s), our data on rho Pup seem to indicate that the velocity gradient is null, but this result needs to be confirmed with additional data. We derived the Baade-Wesselink projection factor p = 1.36 +/- 0.02 for rho Pup and p = 1.39 +/- 0.02 for DX Cet. We successfully extended the period-projection factor relation from classical Cepheids to delta Scuti stars.Comment: Accepted for publication in A&A (in press

Cepheid limb darkening, angular diameter corrections, and projection factor from static spherical model stellar atmospheres

Context. One challenge for measuring the Hubble constant using Classical Cepheids is the calibration of the Leavitt Law or period-luminosity relationship. The Baade-Wesselink method for distance determination to Cepheids relies on the ratio of the measured radial velocity and pulsation velocity, the so-called projection factor and the ability to measure the stellar angular diameters. Aims. We use spherically-symmetric model stellar atmospheres to explore the dependence of the p-factor and angular diameter corrections as a function of pulsation period. Methods. Intensity profiles are computed from a grid of plane-parallel and spherically-symmetric model stellar atmospheres using the SAtlas code. Projection factors and angular diameter corrections are determined from these intensity profiles and compared to previous results. Results. Our predicted geometric period-projection factor relation including previously published state-of-the-art hydrodynamical predictions is not with recent observational constraints. We suggest a number of potential resolutions to this discrepancy. The model atmosphere geometry also affects predictions for angular diameter corrections used to interpret interferometric observations, suggesting corrections used in the past underestimated Cepheid angular diameters by 3 - 5%. Conclusions. While spherically-symmetric hydrostatic model atmospheres cannot resolve differences between projection factors from theory and observations, they do help constrain underlying physics that must be included, including chromospheres and mass loss. The models also predict more physically-based limb-darkening corrections for interferometric observations.Comment: 8 pages, 6 figures, 2 tables, accepted for publication in A&

Interferometric and spectroscopic observations of the BRITE target δ Cep

We used new HARPS-N spectra to revisitate the projection factor of δ Cep and to directly measure the specific contribution of the velocity gradient within the atmosphere

Classical Cepheids: Yet another version of the Baade-Becker-Wesselink method

We propose a new version of the Baade--Becker--Wesselink technique, which allows one to independently determine the colour excess and the intrinsic colour of a radially pulsating star, in addition to its radius, luminosity, and distance. It is considered to be a generalization of the Balona approach. The method also allows the function F(CI) = BC + 10 log (Teff) for the class of pulsating stars considered to be calibrated. We apply this technique to a number of classical Cepheids with very accurate light and radial-velocity curves and with bona fide membership in open clusters (SZ Tau, CF Cas, U Sgr, DL Cas, GY Sge), and find the results to agree well with the reddening estimates of the host open clusters. The new technique can also be applied to other pulsating variables, e.g. RR Lyrae and RV Tauri.Comment: 6 pages, 2 figures, 1 table; Submitted to Astrophysical Bulletin, 201