Les Céphéides et l'échelle des distances galactiques: apport de l'interférométrie à longue base

Cepheids have been used since more than a century as standard candles to estimate distances in the Universe, owing to the relation between their pulsation period and absolute magnitude. The calibration of this relation (also called "Leavitt law", in homage to its discoverer) is based on independent distance estimates, that are generally derived from the parallax-of-pulsation method. This rather simple technique makes a comparison of the angular diameter variation (measured for example through surface brightness relationships) and the linear diameter variation (obtained through an integration of the radial velocity curve). During my PhD I used a very innovative implementation of this method : the SPIPS code developed by Antoine Mérand. This technique allows a simultaneous adjustement of all the available observables (multi-filter and multi-band photometry, radial velocities, interferometric diameters and effective temperatures), which results in a much better statistical precision. The code also incorporates atmospheric models allowing to take into account the Cepheids physics, and to ensure a better control of the systematics (for instance, circumstellar envelops make the stars appear brighter in the infrared bands). Although the method is quite precise and elegant, it only allows to mesure the distance to the projection factor p, a parameter used to convert radial velocities (deduced from the spectroscopy) into velocities of pulsation (actual displacement of the atmosphere). The value of p and its possible dependence on the pulsation period are still widely debated. For the rare Cepheids whose distances are already known precisely enough (for example through a parallax measurement), it is possible to make an invert use of the SPIPS method and track down the value of p, which is what I did during my PhD. Thanks to this method, I could first calculate the p-factor of the type II Cepheid κ Pavonis. This study led to p = 1.26 ± 0.07. I then extended this work to a larger sample of Cepheids whose parallaxes have been measured with the HST, and to the famous long-period Cepheid RS Pup, whose distance has been measured thanks to the light echoes phenomenon. Contrary to the predictions of some authors, the global study points at a rather weak dependence of p on the pulsation period. For the moment we propose to use the constant value of p = 1.326 ± 0.021. In the current state of the art, the precision is not limited anymore by the method itself, but by the distance measurements. The Gaia parallaxes at 1% will help to progress in that whole problematic. This preliminary work already proved the feasibility of the method and led us to very promising results.Les Céphéides sont utilisées depuis plus d’un siècle comme chandelles cosmiques pour estimer des distances dans l’univers, grâce à la relation qui unie leur période de pulsation et leur luminosité absolue. La calibration de cette relation (dite "Loi de Leavitt", en hommage à sa découvreuse) repose sur des estimations indépendantes de distances, qui sont généralement réalisées grâce à la méthode de la parallaxe de pulsation. Cette technique assez simple repose sur la comparaison de la variation de diamètre angulaire (mesurée par exemple via des relations de brillance de surface) et de la variation de diamètre linéaire (obtenue après une simple intégration de la courbe de vitesse radiale). Durant ma thèse j’ai fait usage d’une implémentation novatrice de cette méthode : le code SPIPS développé par Antoine Mérand. Celui-ci permet un ajustement simultané de toutes les observables disponibles (photométrie multi-filtre et multi-bande, vitesses radiales, diamètres interférométriques et températures effectives), se traduisant par une meilleur précision statistique. Le code intègre également des modèles d’atmosphère permettant de prendre en compte la physique des Céphéides, et d’assurer un meilleur contrôle des systématiques (par exemple, la présence d’une enveloppe circumstellaire se traduit par un excès apparent de la magnitude infrarouge). Bien que précise et élégante, cette méthode ne permet de mesurer des distances qu’à un paramètre près, le facteur de projection p utilisé pour convertir la vitesse radiale (déduite de la spectroscopie) en vitesse de pulsation. La valeur de p et sa dépendance avec la période de pulsation sont encore largement débattues. Pour les rares Céphéides dont la distance est connue avec une précision suffisante (par exemple grâce à une mesure de parallaxe), il est possible de faire un usage inverse de la méthode SPIPS et de remonter à la valeur de p, et c’est ce que j’ai fait durant ma thèse. Grâce à cette méthode, j’ai tout d’abord calculé le p-facteur de la Céphéide de type II κ Pavonis, pour laquelle nous aboutissons à p = 1.26 ± 0.07. J’ai ensuite étendu mon étude à un plus grand échantillon de Céphéides galactiques de parallaxe connue, auxquelles j’ai ajouté RS Pup, célèbre pour ses échos de lumière. Contrairement aux prédictions de certains auteurs, l’étude globale de ces étoiles a permis de conclure à une dépendance plutôt faible de p en fonction de la période. De fait, nous proposons pour le moment d’utiliser une valeur constante moyenne de p = 1.326 ± 0.021. Dans l’état de l’art actuel, la précision n’est pas limitée par la méthode, mais par les mesures de distance elles-mêmes. L’arrivée des parallaxes à moins de 1% du satellite Gaia permettra sans doute une avancée rapide dans cette problématique, ce travail préliminaire ayant dores et déjà permis de démontrer la faisabilité de la méthode et d’aboutir à des résultats prometteurs

Observational calibration of the projection factor of Cepheids I. The Type II Cepheid kappa Pavonis

The distances of pulsating stars, in particular Cepheids, are commonly measured using the parallax of pulsation technique. The different versions of this technique combine measurements of the linear diameter variation (from spectroscopy) and the angular diameter variation (from photometry or interferometry) amplitudes, to retrieve the distance in a quasi-geometrical way. However, the linear diameter amplitude is directly proportional to the projection factor (hereafter p-factor), which is used to convert spectroscopic radial velocities (i.e., disk integrated) into pulsating (i.e., photospheric) velocities. The value of the p-factor and its possible dependence on the pulsation period are still widely debated. Our goal is to measure an observational value of the p-factor of the type-II Cepheid kappa Pavonis, whose parallax was measured with an accuracy of 5% using HST/FGS. We used this parallax as a starting point to derive the p-factor of kappa Pav, using the SPIPS technique, which is a robust version of the parallax-of-pulsation method that employs radial velocity, interferometric and photometric data. We applied this technique to a combination of new VLTI/PIONIER optical interferometric angular diameters, new CORALIE and HARPS radial velocities, as well as multi-colour photometry and radial velocities from the literature. We obtain a value of p = 1.26 +/- 0.07 for the p-factor of kappa Pav. This result agrees with several of the recently derived Period-p-factor relationships from the literature, as well as previous observational determinations for Cepheids. Individual estimates of the p-factor are fundamental to calibrating the parallax of pulsation distances of Cepheids. Together with previous observational estimates, the projection factor we obtain points to a weak dependence of the p-factor on period.Comment: 8 pages, 6 figures, accepted in A&

Observational calibration of the projection factor of Cepheids. II. Application to nine Cepheids with HST/FGS parallax measurements

The distance to pulsating stars is classically estimated using the parallax-of-pulsation (PoP) method, which combines spectroscopic radial velocity measurements and angular diameter estimates to derive the distance of the star. An important application of this method is the determination of Cepheid distances, in view of the calibration of their distance scale. However, the conversion of radial to pulsational velocities in the PoP method relies on a poorly calibrated parameter, the projection factor (p-factor). We aim to measure empirically the value of the p-factors of a homogeneous sample of nine Galactic Cepheids for which trigonometric parallaxes were measured with the Hubble Space Telescope Fine Guidance Sensor. We use the SPIPS algorithm, a robust implementation of the PoP method that combines photometry, interferometry, and radial velocity measurements in a global modeling of the pulsation. We obtained new interferometric angular diameters using the PIONIER instrument at the Very Large Telescope Interferometer, completed by data from the literature. Using the known distance as an input, we derive the value of the p-factor and study its dependence with the pulsation period. We find the following p-factors: 1.20 $\pm$ 0.12 for RT Aur, 1.48 $\pm$ 0.18 for T Vul, 1.14 $\pm$ 0.10 for FF Aql, 1.31 $\pm$ 0.19 for Y Sgr, 1.39 $\pm$ 0.09 for X Sgr, 1.35 $\pm$ 0.13 for W Sgr, 1.36 $\pm$ 0.08 for $\beta$ Dor, 1.41 $\pm$ 0.10 for $\zeta$ Gem, and 1.23 $\pm$ 0.12 for $\ell$ Car. These values are consistently close to p = 1.324 $\pm$ 0.024. We observe some dispersion around this average value, but the observed distribution is statistically consistent with a constant value of the p-factor as a function of the pulsation period. The error budget of our determination of the p-factor values is presently dominated by the uncertainty on the parallax, a limitation that will soon be waived by Gaia.Comment: 18 pages, 13 figure

Spectro-Photo-Interferometry of Stellar Pulsation (SPIPS)

We present our implementation of the parallax of pulsation method which integrates all observables and physical modelling of the photosphere to get the best statistical precision and controlled biases. This method has been validated on well known stars and used to estimate observationally the projection factor of the HST-FGS sample. Our future developments include application to the Gaia Cepheids and modelling of the spectrum

Toward a renewed Galactic Cepheid distance scale from Gaia and optical interferometry

Through an innovative combination of multiple observing techniques and mod- eling, we are assembling a comprehensive understanding of the pulsation and close environment of Cepheids. We developed the SPIPS modeling tool that combines all observables (radial velocimetry, photometry, angular diameters from interferometry) to derive the relevant physical parameters of the star (effective temperature, infrared ex- cess, reddening,...) and the ratio of the distance and the projection factor d/p. We present the application of SPIPS to the long-period Cepheid RS Pup, for which we derive p = 1.25 +/- 0.06. The addition of this massive Cepheid consolidates the existing sample of p-factor measurements towards long-period pulsators. This allows us to conclude that p is constant or mildly variable around p = 1.29 +/- 0.04 (+/-3%) as a function of the pulsation period. The forthcoming Gaia DR2 will provide a considerable improvement in quantity and accuracy of the trigonometric parallaxes of Cepheids. From this sample, the SPIPS modeling tool will enable a robust calibration of the Cepheid distance scale.Comment: 5 pages, 4 figures, proceedings of the 22nd Los Alamos Stellar Pulsation Conference "Wide-field variability surveys: a 21st-century perspective" held in San Pedro de Atacama, Chile, Nov. 28-Dec. 2, 201

Cepheid distances from the SpectroPhoto-Interferometry of Pulsating Stars (SPIPS) - Application to the prototypes delta Cep and eta Aql

The parallax of pulsation, and its implementations such as the Baade-Wesselink method and the infrared surface bright- ness technique, is an elegant method to determine distances of pulsating stars in a quasi-geometrical way. However, these classical implementations in general only use a subset of the available observational data. Freedman & Madore (2010) suggested a more physical approach in the implementation of the parallax of pulsation in order to treat all available data. We present a global and model-based parallax-of-pulsation method that enables including any type of observational data in a consistent model fit, the SpectroPhoto-Interferometric modeling of Pulsating Stars (SPIPS). We implemented a simple model consisting of a pulsating sphere with a varying effective temperature and a combina- tion of atmospheric model grids to globally fit radial velocities, spectroscopic data, and interferometric angular diameters. We also parametrized (and adjusted) the reddening and the contribution of the circumstellar envelopes in the near-infrared photometric and interferometric measurements. We show the successful application of the method to two stars: delta Cep and eta Aql. The agreement of all data fitted by a single model confirms the validity of the method. Derived parameters are compatible with publish values, but with a higher level of confidence. The SPIPS algorithm combines all the available observables (radial velocimetry, interferometry, and photometry) to estimate the physical parameters of the star (ratio distance/ p-factor, Teff, presence of infrared excess, color excess, etc). The statistical precision is improved (compared to other methods) thanks to the large number of data taken into account, the accuracy is improved by using consistent physical modeling and the reliability of the derived parameters is strengthened thanks to the redundancy in the data.Comment: 10 pages, 4 figures, A&A in pres

A spectro-interferometric view of ℓ Carinae's modulated pulsations

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Spectro-Photo-Interferometry of Stellar Pulsation (SPIPS)

We present our implementation of the parallax of pulsation method which integrates all observables and physical modelling of the photosphere to get the best statistical precision and controlled biases. This method has been validated on well known stars and used to estimate observationally the projection factor of the HST-FGS sample. Our future developments include application to the Gaia Cepheids and modelling of the spectrum

Spectro-Photo-Interferometry of Stellar Pulsation (SPIPS)

We present our implementation of the parallax of pulsation method which integrates all observables and physical modelling of the photosphere to get the best statistical precision and controlled biases. This method has been validated on well known stars and used to estimate observationally the projection factor of the HST-FGS sample. Our future developments include application to the Gaia Cepheids and modelling of the spectrum