The radii of Galactic Cepheids

Astronomy and Astrophysics – Astronomy

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Stars: Fundamental Parameters, Cepheids, Infrared: Stars

Scientific paper

Optical photometry, infrared photometry and radial velocity data have been combined to derive Baade-Wesselink radii of 49 Galactic Cepheids. Of the many possible magnitude-colour combinations four are studied in detail, namely (V, B-V), (V, V-I_C), (K, J-K) and (K, V-K). A fundamental assumption in any form of the Baade-Wesselink technique is that the surface brightness variations can be represented by changes in the colour index. The sensitivity of the surface brightness-colour index relation to variations in gravity and microturbulence is examined from model atmosphere calculations. It is shown that the use of infrared photometry in calculating Cepheid radii minimizes the effects of such variations, and that both random and systematic errors in Cepheid radii calculated using optical photometry are much larger. The effects of varying microturbulence on radii determined using optical photometry appear to be even more severe than the effects of variations in surface gravity, but both can cause serious systematic errors. The large number of stars enables a detailed consideration of the factors systematically affecting Baade-Wesselink radii. It is demonstrated that the limiting factor in most of the radii derived from the observations we have used is the accuracy with which the radius displacement curve can be defined from the radial velocity observations. The non-linear effects in determining the radius are significant, and a new method by Balona is used to determine the non-linear maximum likelihood radii. This method appears to be statistically correct, and supersedes the flawed non-linear correction algorithm used by Coulson et al. Comparisons with radii determined by least squares (including the surface brightness method) show that the expected error-dependent systematic errors in least-squares radii are indeed present. We demonstrate that the systematic errors in radii calculated using V-I_C and V-R_J photometry appear to be virtually identical. The most accurate period-radius relation is derived from the combination of the (K, J-K) and (K, V-K) radius solutions:log R=1.821+0.751(log P-1) +/-0.008+/-0.026.This relation differs significantly from many of the earlier determinations of the period-radius relation based on various optical magnitude-colour combinations. The slope is somewhat steeper than in Fernie's mean pre-OPAL theoretical relation, and the zero-point gives radii 12 per cent smaller at log P=1. This deviation is in the expected sense, since pre-OPAL studies predicted Cepheid luminosities greater than those observed.

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