**AAS Meeting #193 - Austin, Texas, January 1999**

*Session 64. Pulsating Stars*

Display, Friday, January 8, 1999, 9:20am-6:30pm, Exhibit Hall 1
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## [64.06] New Bayesian Results on the Cepheid Distance Scale

*W. H. Jefferys, T. G. Barnes (U. Texas)*

The surface brightness (Baade-Wesselink) technique is one of
the most important methods for establishing the Cepheid
distance scale, but there is disagreement on how best to use
it. The choice of color index for inferring the surface
brightness and the mathematical process for combining the
photometric and radial velocity information are both at
issue. Here we examine the latter issue using Bayesian
methods.

The Baade-Wesselink method infers the varying angular
diameter of the pulsating star from the relation between the
surface brightness and a color index, and the linear
displacement of the stellar atmosphere by integrating the
radial velocity curve. Fitting the angular diameters to the
linear displacements yields the stellar radius and the
distance. We must properly account for the errors in both
photometry and velocities or risk biasing the results. On
this basis Laney & Stobie (1995) have criticized the
distances of Gieren *et. al.* (1993) for 100 Galactic
Cepheids and have asserted that the results are biased.
Moreover, we must convert radial velocities into linear
displacements by integrating a model fitted to the observed
radial velocity data. Neither Laney & Stobie nor Gieren
*et. al.* address the issue of how to choose the
appropriate number of Fourier terms for the fit.

We have applied an approximately Bayesian analysis to the
complete problem and a fully Bayesian analysis to the
errors-in-variables problem, and are developing a fully
Bayesian analysis of the complete problem, including model
selection/averaging. We describe these techniques and
demonstrate their use on a subset of the Gieren *et.
al.* data. Both methods are successful in accounting for
errors in the data and in providing unbiased distance
estimates. The approximately Bayesian analysis also provides
effective model selection and model averaging. Our new
analyses do not show bias in the distances and thus support
that distance scale.

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