An Error Analysis of the Geometric Baade-Wesselink Method

Abstract

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 velocity curve. We also discuss the importance of the phase shift between the stellar lightcurve and the velocity curve as a potential error source in the geometric Baade-Wesselink method. We finally discuss the case of the Classical Cepheid zeta Gem, applying our method to the measurements derived with the Palomar Testbed Interferometer. We show how a careful treatment of the measurement errors can be potentially used to discriminate between different models of limb darkening using interferometric techniques.

24 pages, to be published on the Astrophysical Journal, vol. 603 March 2004

References in corpus (5)

• Long baseline interferometric observations of Cepheids
• Theoretical Limb Darkening for Pulsating Cepheids
• Theoretical Limb Darkening for Classical Cepheids: II. Corrections for the Geometric Baade-Wesselink Method
• The angular diameter and distance of the Cepheid Zeta Geminorum
• Radii and Distances of Cepheids, I., Method and Measurement Errors

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• Spherically-symmetric model stellar atmospheres and limb darkening I: limb-darkening laws, gravity-darkening coefficients and angular diameter corrections for red giant stars
• The angular size of the Cepheid L Car: a comparison of the interferometric and surface brightness techniques
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