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)