Theoretical Limb Darkening for Classical Cepheids. II. Corrections for the Geometric Baade‐Wesselink Method

The geometric Baade-Wesselink method is one of the most promising techniquesfor obtaining a better calibration of the Cepheid period-luminosity relation bymeans of interferometric measurements of accurate diameters. In this paper wepresent new wavelength- and phase-dependent limb darkening corrections based onour time-dependent hydrodynamic models of the classical Cepheid zeta Gem. Weshow that a model simulation of a Cepheid atmosphere, taking into account thehydrodynamic effects associated with the pulsation, shows strong departuresfrom the limb darkening otherwise predicted by a static model. For most of itspulsational cycle the hydrodynamic model predicts a larger limb darkening thenthe equivalent static model. The hydrodynamics affects the limb darkeningmainly at UV and optical wavelengths. Most of these effects evolve slowly asthe star pulsates, but there are phases, associated with shocks propagatinginto the photosphere, in which significant changes in the limb darkening takeplace on time-scales of the order of less than a day. We assess the implicationof our model LD corrections fitting the geometric Baade-Wesselink distance ofzeta Gem for the available near-IR PTI data. We discuss the effects of ourmodel limb darkening on the best fit result, and analyze the requirementsneeded to test the time-dependence of the limb darkening with futureinterferometric measurements.Comment: 22 pages, 5 figures, to be published on the Astrophysical Journal, June 1 2003 issu