Cepheid distances from infrared long-baseline interferometry - III. Calibration of the surface brightness-color relations

Astronomy & Astrophysics, Dec 2004

The recent VINCI/VLTI observations presented in Paper I have nearly doubled the total number of available angular diameter measurements of Cepheids. Taking advantage of the significantly larger color range covered by these observations, we derive in the present paper high precision calibrations of the surface brightness-color relations using exclusively Cepheid observations. These empirical laws make it possible to determine the distance to Cepheids through a Baade-Wesselink type technique. The least dispersed relations are based on visible-infrared colors, for instance . The convergence of the Cepheid (this work) and dwarf star (Kervella et al. [CITE]) visible-infrared surface brightness-color relations is strikingly good. The astrophysical dispersion of these relations appears to be very small, and below the present detection sensitivity.

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Cepheid distances from infrared long-baseline interferometry - III. Calibration of the surface brightness-color relations

A&A Cepheid distances from infrared long-baseline interferometry P. Kervella 2 3 D. Bersier 1 D. Mourard 0 N. Nardetto 0 P. Fouqué 3 4 V. Coudé du Foresto 2 0 GEMINI, UMR 6203, Observatoire de la Côte d'Azur , Avenue Copernic, 06130 Grasse , France 1 Space Telescope Science Institute , 3700 San Martin Drive, Baltimore, MD 21218 , USA 2 LESIA, UMR 8109, Observatoire de Paris-Meudon , 5 place Jules Janssen, 92195 Meudon Cedex , France 3 European Southern Observatory , Alonso de Cordova 3107, Casilla 19001, Vitacura, Santiago 19 , Chile 4 Observatoire Midi-Pyrénées , UMR 5572, 14, avenue Edouard Belin, 31400 Toulouse , France The recent VINCI/VLTI observations presented in Paper I have nearly doubled the total number of available angular diameter measurements of Cepheids. Taking advantage of the significantly larger color range covered by these observations, we derive in the present paper high precision calibrations of the surface brightness-color relations using exclusively Cepheid observations. These empirical laws make it possible to determine the distance to Cepheids through a BaadeWesselink type technique. The least dispersed relations are based on visible-infrared colors, for instance FV (V − K) = −0.1336±0.0008 (V − K) + 3.9530±0.0006. The convergence of the Cepheid (this work) and dwarf star (Kervella et al. 2004c) visible-infrared surface brightness-color relations is strikingly good. The astrophysical dispersion of these relations appears to be very small, and below the present detection sensitivity. stars; variables; Cepheids - cosmology; distance scale - stars; oscillations - techniques; interferometric 1. Introduction The surface brightness (hereafter SB) relations link the emerging flux per solid angle unit of a light-emitting body to its color, or effective temperature. These relations are of considerable astrophysical interest for Cepheids, as a well-defined relation between a particular color index and the surface brightness can provide accurate predictions of their angular diameters. When combined with the radius curve, integrated from spectroscopic radial velocity measurements, they give access to the distance of the Cepheid (Baade-Wesselink method). This method has been applied recently to Cepheids in the LMC (Gieren et al. 2000) and in the SMC (Storm et al. 2004) The accuracy that can be achieved in the distance estimate is conditioned for a large part by our knowledge of the SB relations. In our first paper (Kervella et al. 2004a, hereafter Paper I) , we presented new interferometric measurements of seven nearby Cepheids. They complement a number of previously published measurements from several optical and infrared interferometers. We used these data in Paper II (Kervella et al. 2004b) to calibrate the Cepheid Period–Radius and Period–Luminosity relations. Nordgren et al. (2002) derived a preliminary calibration of the Cepheid visible-infrared Table 3 is only available in electronic form at http://www.edpsciences.org SB relations, based on the three stars available at that time (δ Cep, η Aql and ζ Gem). In the present Paper III, we take advantage of the nine Cepheids now resolved by interferometry to derive refined calibrations of the visible and infrared SB relations of these stars. 2. Definition of the surface brightness relations By definition, the bolometric surface flux f ∼ L/D2 is linearly proportional to Te4ff, where L is the bolometric flux of the star, D its bolometric diameter and Teff its effective temperature. In consequence, F = log f is a linear function of the stellar color indices, expressed in magnitudes (logarithmic scale), and SB relations can be fitted using for example the following expressions: FB = a0 (B − V )0 + b0 FV = a1 (V − K)0 + b1 FH = a2 (B − H)0 + b2 where Fλ is the surface brightness. When considering a perfect blackbody curve, any color can in principle be used to obtain the SB, but in practice the linearity of the correspondence between log Teff and color depends on the chosen wavelength (1) (2) (3) bands. The index 0 designates the dereddened magnitudes, and will be omitted in the rest of the paper. The ai and bi coefficients represent respectively the slopes and zero points of the different versions of the SB relation. Historically, the first calibration of the SB relation based on the (B − V ) index was obtained by Wesselink (1969) , and the expression FV (V − R) is also known as the Barnes-Evans (B-E) relation (Barnes & Evans 1976) . The relatively large intrinsic dispersion of the visible light B-E relations has led to preferring their infrared counterparts, in particular those based on the K band magnitudes (λ = 2.0−2.4 µm), as the color-Teff relation is less affected by microturbulence and gravity effects (Laney & Stobie 1995) . The surface brightness Fλ is given by the following expression (Fouqué & Gieren 1997) : Fλ = 4.2207 − 0.1 mλ0 − 0.5 log θLD (4) where θLD is the limb darkened angular diameter, i.e. the angular (...truncated)


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P. Kervella, D. Bersier, D. Mourard, N. Nardetto, P. Fouqué, . Cepheid distances from infrared long-baseline interferometry - III. Calibration of the surface brightness-color relations, Astronomy & Astrophysics, 2004, pp. 587-593, Volume 428, Issue 2, DOI: 10.1051/0004-6361:20041416