Cepheid limb darkening, angular diameter corrections, and projection factor from static spherical model stellar atmospheres

¹ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
e-mail: hneilson@astro.uni-bonn.de
² Laboratoire Lagrange, UMR7293, UNS/CNRS/OCA, 06300 Nice, France
³ Graduate Institute of Astronomy, National Central University, 32001 Jhongli City, Taiwan
⁴ IRAP, Université de Toulouse, CNRS, 14 avenue Édouard Belin, 31400 Toulouse, France
⁵ Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany

Received: 30 November 2011
Accepted: 13 March 2012

Abstract

Context. One challenge for measuring the Hubble constant using classical Cepheids is the calibration of the Leavitt law or period–luminosity relationship. The Baade-Wesselink method for distance determination to Cepheids relies on the ratio of the measured radial velocity and pulsation velocity, the so-called projection factor and the ability to measure the stellar angular diameters.

Aims. We use spherically-symmetric model stellar atmospheres to explore the dependence of the p-factor and angular diameter corrections as a function of pulsation period.

Methods. Intensity profiles are computed from a grid of plane-parallel and spherically-symmetric model stellar atmospheres using the SAtlas code. Projection factors and angular diameter corrections are determined from these intensity profiles and compared to previous results.

Results. Our predicted geometric period–projection factor relation including previously published state-of-the-art hydrodynamical predictions is not with recent observational constraints. We suggest a number of potential resolutions to this discrepancy. The model atmosphere geometry also affects predictions for angular diameter corrections used to interpret interferometric observations, suggesting corrections used in the past underestimated Cepheid angular diameters by 3–5%.

Conclusions. While spherically-symmetric hydrostatic model atmospheres cannot resolve differences between projection factors from theory and observations, they do help constrain underlying physics that must be included, including chromospheres and mass loss. The models also predict more physically-based limb-darkening corrections for interferometric observations.