The aim of this paper is to investigate the metallicity dependence of the $PL$-relation in $V$ and $K$ based on a sample of 68 Galactic Cepheids with individual Baade-Wesselink distances (some of the stars also have an HST-based parallax) and individually determined metallicities from high-resolution spectroscopy. Literature values of the $V$-band, $K$-band and radial velocity data have been collected for a sample of 68 classical cepheids that have their metallicity determined in the literature from high-resolution spectroscopy. Based on a $(V-K)$ surface-brightness relation and a projection factor derived in a previous paper, distances have been derived from a Baade-Wesselink analysis. $PL$- and $PLZ$-relations in $V$ and $K$ are derived. The effect of the adopted dependence of the projection factor on period is investigated. The change from a constant $p$-factor to one recently suggested in the literature with a mild dependence on $\log P$ results in a less steep slope by 0.1 unit, which is about the 1-sigma error bar in the slope itself. The observed slope in the $PL$-relation in $V$ in the LMC agrees with both hypotheses. In $K$ the difference between the Galactic and LMC slope is larger and would favour a mild period dependence of the $p$-factor. The dependence on metallicity in $V$ and $K$ is found to be marginal, and independent of the choice of $p$-factor on period. This result is severely limited by the small range in metallicity covered by the Galactic Cepheids.
We present results based on a Baade-Wesselink analysis of Cepheids in the Small Magellanic Cloud. The Baade-Wesselink analysis provides individual luminosities for these metal-poor Cepheids which combined with recent Baade-Wesselink results from Gieren et al. (1998) on solar metallicity Galactic Cepheids constrain the metallicity effect on the zero-point of the Cepheid P-L relation. A preliminary analysis leads to an effect of dMv / d[Fe/H]= -0.45 +-0.15, metal-rich Cepheids being brighter, in good agreement with several recent independent determinations. An effect of this magnitude reduces si…
By using the same algorithm in the Baade-Wesselink analyses of Galactic RR Lyrae and Cepheid variables, it is shown that, within 0.03 mag (1 sigma) statistical error, they yield the same distance modulus for the Large Magellanic Cloud. By fixing the zero point of the color-temperature calibration to those of the current infrared flux methods and using updated period-luminosity-color relations, we get an average value of 18.55 for the true distance modulus of the LMC.
We derive an analytic solution for the minimization problem in the geometric Baade-Wesselink method. This solution allows deriving the distance and mean radius of a pulsating star by fitting its velocity curve and angular diameter measured interferometrically. The method also provide analytic solutions for the confidence levels of the best fit parameters, and accurate error estimates for the Baade-Wesselink solution. Special care is taken in the analysis of the various error sources in the final solution, among which the uncertainties due to the projection factor, the limb darkening and the ve…
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 projec…
The geometric Baade-Wesselink method is one of the most promising techniques for obtaining a better calibration of the Cepheid period-luminosity relation by means of interferometric measurements of accurate diameters. In this paper we present new wavelength- and phase-dependent limb darkening corrections based on our time-dependent hydrodynamic models of the classical Cepheid zeta Gem. We show that a model simulation of a Cepheid atmosphere, taking into account the hydrodynamic effects associated with the pulsation, shows strong departures from the limb darkening otherwise predicted by a stati…
(ABRIDGED) We have applied the near-IR Barnes-Evans realization of the Baade-Wesselink method as calibrated by Fouque & Gieren (1997) to five metal-poor Cepheids with periods between 13 and 17 days in the Small Magellanic Cloud as well as to a sample of 34 Galactic Cepheids to determine the effect of metallicity on the period-luminosity (P-L) relation. For ten of the Galactic Cepheids we present new accurate and well sampled radial-velocity curves. The Baade-Wesselink analysis provides accurate individual distances and luminosities to the Cepheids in the two samples, allowing us to constrain d…
We have applied the Baade-Wesselink method to two field RR Lyrae stars, i.e. SW And and RR Cet, and derived their distances and physical parameters. With respect to previous B-W analyses we have applied the following improvements: a) use of all sets of available data, after proper comparison for homogeneity and compatibility; b) use of the most recent and accurate model atmospheres, with turbulent velocity V(turb) = 4 km/s and the no-overshooting approximation, and comparison with other treatments of convection; c) use of the instantaneous gravity along the pulsation cycle rather than the mean…
Recent, and older accurate, data on (limb-darkened) angular diameters is compiled for 221 stars, as well as BVRIJK[12][25] magnitudes for those objects, when available. Nine stars (all M-giants or supergiants) showing excess in the [12-25] colour are excluded in the analysis as this may indicate the present of dust influencing the optical and near-infrared colours as well. Based on this large sample, Baade-Wesselink surface-brightness (SB) relations are presented for dwarfs, giants, supergiants and dwarfs in the optical and near-infrared. M-giants are found to follow different SB-relations fro…
We present a new method for determining physical parameters of RRab variables exclusively from multicolour light curves. Our method is an Inverse Photometric Baade-Wesselink analysis which, using a nonlinear least squares algorithm, searches for the effective temperature (T_eff) and pulsational velocity (V_p) curves and other physical parameters that best fit the observed light curves, utilising synthetic colours and bolometric corrections from static atmosphere models. The T_eff and V_p curves are initially derived from empirical relations then they are varied by the fitting algorithm. The me…
The VLTI is the ideal instrument for measuring the distances of nearby Cepheids with the Baade-Wesselink method, allowing an accurate recalibration of the Cepheid Period-Luminosity relation. The high accuracy required by such measurement, however, can only be reached taking into account the effects of limb darkening, and its dependence on the Cepheid pulsations. We present here our new method to compute phase- and wavelength-dependent limb darkening profiles, based on hydrodynamic simulation of Classical Cepheid atmospheres.
We present the results of a comprehensive theoretical investigation on the Period-Radius (PR) relation of classical Cepheids based on new sequences of full amplitude, nonlinear convective models constructed by adopting a wide range of both stellar masses and chemical compositions. For log P in the range 0.9 - 1.8 a very good agreement is found between theoretical predictions and current available data whereas outside this range, both at shorter and at longer periods, nonlinear radii attain intermediate values between empirical relations based on different Baade-Wesselink (BW) methods and photo…
We have undertaken several projects with the purpose of determining accurate distances to nearby galaxies to calibrate the extragalactic distance scale. Specifically, I describe the DIRECT project which aims to derive the distance to M31 and M33 directly, using detached eclipsing binaries and the Baade-Wesselink method for Cepheids. I also present a ``hybrid'' method of discovering Cepheids with ground-based telescopes using image subtraction and then following them up with the HST to derive Cepheid period-luminosity distances.
The ratio of pulsation to radial velocity (the projection factor) is currently limiting the accuracy of the interferometric Baade-Wesselink method. 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. We present HARPS high spectral resolution observations of nine galactic Cepheids having a good period sampling. We fit spectral line profiles by an asymmetric bi-Gaussian to derive radial velocity, Full-W…
Long baseline interferometry is now able to resolve the pulsational change of the angular diameter of a significant number of Cepheids in the solar neighborhood. This allows the application of a new version of the Baade-Wesselink (BW) method to measure their distance, for which we do not need to estimate the star's temperature. Using angular diameter measurements from the VLT Interferometer, we derived the distances to four nearby Cepheids. For three additional stars, we obtained average values of their angular diameters. Based on these new measurements and already existing data, we derived ca…
We develop a formulation of the Baade-Wesselink method which uses the Fourier coefficients of the observables. We derive an explicit, analytic expression to determine the mean radius from each Fourier order. The simplicity of this method allows us to derive the uncertainty in the mean radius due to measurement errors. Using simulations and a recent dataset we demonstrate that the precision of the radius measurement with optical magnitudes is in most cases limited by the accuracy of the measurement of the phase difference between the light and the color index curve. In this case it is advantage…
Cepheids are the primary distance indicators for extragalactic astronomy and therefore are of very high astrophysical interest. Unfortunately, they are rare stars, situated very far from Earth.Though they are supergiants, their typical angular diameter is only a few milliarcseconds, making them very challenging targets even for long-baseline interferometers. We report observations that were obtained in the K prime band (2-2.3 microns), on the Cepheid Zeta Geminorum with the FLUOR beam combiner, installed at the IOTA interferometer. The mean uniform disk angular diameter was measured to be 1.64…
Thanks to HST, there are now many galaxies with Cepheid distances and these provide the main platform for the calibration of the secondary distance indicators. I review recent progress in our understanding of the standard candle properties of Cepheids with particular emphasis on the techniques used in the HST studies. The PL relation defined by Cepheids in the LMC is shown to be excellent, although the distance to the LMC, which determines the zero-point, is still rather controversial. This LMC relation is consistent with the galactic calibrations which use Hipparcos parallaxes or Baade-Wessel…
We present the results of an extensive theoretical investigation on the pulsation behavior of Bump Cepheids. We constructed several sequences of full amplitude, nonlinear, convective models by adopting a chemical composition typical of Large Magellanic Cloud (LMC) Cepheids (Y=0.25, Z=0.008) and stellar masses ranging from 6.55 to 7.45 solar masses. We find that theoretical light and velocity curves reproduce the HP, and indeed close to the blue edge the bump is located along the descending branch, toward longer periods it crosses at first the luminosity/velocity maximum and then it appears alo…
Unbiased angular diameter measurements are required for accurate distances to Cepheids using the interferometric Baade Wesselink method (IBWM). The precision of this technique is currently limited by interferometric measurements at the 1.5% level. At this level, the center-to-limb darkening (CLD) and the presence of circumstellar envelopes (CSE) seem to be the two main sources of bias. The observations we performed aim at improving our knowledge of the interferometric visibility profile of Cepheids. In particular, we assess the systematic presence of CSE around Cepheids in order determine accu…
The universality of the Cepheid Period-Luminosity relations has been under discussion since metallicity effects have been assumed to play a role in the value of the intercept and, more recently, of the slope of these relations. The goal of the present study is to calibrate the Galactic PL relations in various photometric bands (from B to K) and to compare the results to the well-established PL relations in the LMC. We use a set of 59 calibrating stars, the distances of which are measured using five different distance indicators: Hubble Space Telescope and revised Hipparcos parallaxes, infrared…
We undertook a long term project, DIRECT, to obtain the direct distances to two important galaxies in the cosmological distance ladder -- M31 and M33 -- using detached eclipsing binaries (DEBs) and Cepheids. While rare and difficult to detect, DEBs provide us with the potential to determine these distances with an accuracy better than 5%. The extensive photometry obtained in order to detect DEBs provides us with good light curves for the Cepheid variables. These are essential to the parallel project to derive direct Baade-Wesselink distances to Cepheids in M31 and M33. For both Cepheids and ec…
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 ap…
We undertook a long term project, DIRECT, to obtain the direct distances to two important galaxies in the cosmological distance ladder -- M31 and M33, using detached eclipsing binaries (DEBs) and Cepheids. While rare and difficult to detect, detached eclipsing binaries provide us with the potential to determine these distances with an accuracy better than 5%. The massive photometry obtained in order to detect DEBs provides us with good light curves for the Cepheid variables. These are essential to the parallel project to derive direct Baade-Wesselink distances to Cepheids in M31 and M33. For b…
We undertook a long term project, DIRECT, to obtain the direct distances to two important galaxies in the cosmological distance ladder -- M31 and M33 -- using detached eclipsing binaries (DEBs) and Cepheids. While rare and difficult to detect, DEBs provide us with the potential to determine these distances with an accuracy better than 5%. The extensive photometry obtained in order to detect DEBs provides us with good light curves for the Cepheid variables. These are essential to the parallel project to derive direct Baade-Wesselink distances to Cepheids in M31 and M33. For both Cepheids and ec…
We undertook a long term project, DIRECT, to obtain the direct distances to two important galaxies in the cosmological distance ladder -- M31 and M33 -- using detached eclipsing binaries (DEBs) and Cepheids. While rare and difficult to detect, DEBs provide us with the potential to determine these distances with an accuracy better than 5%. The extensive photometry obtained in order to detect DEBs provides us with good light curves for the Cepheid variables. These are essential to the parallel project to derive direct Baade-Wesselink distances to Cepheids in M31 and M33. For both Cepheids and ec…
We undertook a long term project, DIRECT, to obtain the direct distances to two important galaxies in the cosmological distance ladder -- M31 and M33, using detached eclipsing binaries (DEBs) and Cepheids. While rare and difficult to detect, detached eclipsing binaries provide us with the potential to determine these distances with an accuracy better than 5%. The massive photometry obtained in order to detect DEBs provides us with the light curves for the Cepheid variables. These are essential to the parallel project to derive direct Baade-Wesselink distances to Cepheids in M31 and M33. For bo…
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 +/…
Due to their high intrinsic brightness, type II supernovae (SN) can be used as lighthouses to constrain distances in the Universe using variants of the Baade-Wesselink method. Based on a large set of CMFGEN models (Hillier & Miller 1998) covering the photospheric phase of type II SN, we study the various concepts entering one such technique, the Expanding Photosphere Method (EPM). We compute correction factors $ξ$ needed to approximate the synthetic Spectral Energy Distribution (SED) with that of a blackbody at temperature $T$. Our $ξ$, although similar, are systematically greater, by $\sim 0.…
By adopting the same approach outlined in De Santis & Cassisi (1999), we evaluate the absolute bolometric magnitude of the Zero Age Horizontal Branch (ZAHB) at the level of the RR Lyrae variable instability strip in selected galactic globular clusters. This allows us to estimate the ZAHB absolute visual magnitude for these clusters and to investigate its dependence on the cluster metallicity. The derived $M_V(ZAHB) - [Fe/H]$ relation, corrected in order to account for the luminosity difference between the ZAHB and the mean RR Lyrae magnitude, has been compared with some of the most recent empi…
The kinematical parameters of the local field RR Lyrae population and the zero point of the log P--<M_K> relation for these variables are inferred by applying the statistical parallax (maximum-likelihood) technique to a sample of 182 RR Lyraes with known periods, radial-velocities, metallicities, K-band photometry, and absolute proper motions on the ICRS system. The K-band magnitudes were adopted from the list of Fernley et al. (1998) and the 2MASS Second Incremental Data Release. The parameters of the velocity distribution are found to be (U_0,V_0,W_0) = (-10 +/- 10, -51 +/- 8, -14 +/- 5) km/…
Fourier coefficents have been derived for the $V$ and $R$ light curves of 785 overtone RR Lyrae variables in 16 MACHO fields near the bar of the LMC. The $ϕ_{31}$ and $R_{21}$ coefficients have been compared with those of the first overtone RR Lyrae variables in the Galactic globular clusters NGC 6441, M107, M5, M3, M2, $ω$ Centauri and M68. The results indicate that many of the LMC variables have properties similar to the ones in M2, M3, M5 and the Oosterhoff type I variables in $ω$ Cen, but they are different from the Oosterhoff type II variables in $ω$ Cen. Equations derived from hydrodynam…