Cepheid Period‐Radius and Period‐Luminosity Relations and the Distance to the Large Magellanic Cloud

Abstract

We have used the infrared Barnes-Evans surface brightness technique to derive the radii and distances of 34 Galactic Cepheid variables. Radius and distance results obtained from both versions of the technique are in excellent agreement. The radii of 28 variables are used to determine the period-radius (PR) relation. This relation is found to have a smaller dispersion than in previous studies, and is identical to the PR relation found by Laney & Stobie from a completely independent method, a fact which provides persuasive evidence that the Cepheid PR relation is now determined at a very high condence level. We use the accurate infrared distances to determine period-luminosity (PL) relations in the V , I, J, H, and K passbands from the Galactic sample of Cepheids. We derive improved slopes of these relations from updated LMC Cepheid samples and adopt these slopes to obtain accurate absolute calibrations of the PL relation. By comparing these relations to the ones dened by the LMC Cepheids, we derive strikingly consistent and precise values for the LMC distance modulus in each of the passbands that yield a mean value of k 0 (LMC) \ 18.46 ^0.02. By analyzing the observed dispersions of the PL relations dened by the LMC and Galactic samples of Cepheids, we disentangle the contributions due to uncertainties in the reddenings, in distance measurement, and due to metallicity e ects, and we estimate the intrinsic dispersion of the PL relation with the Wesenheit function. Assuming that the Galactic Cepheid distances are typically accurate to ^3% (as shown in a previous paper), and assuming an intrinsic spread in [Fe/H] of D0.4 dex among the Cepheids of our sample as obtained by Fry & Carney, the observed dispersion of the Galactic Cepheid PL relation suggests a metallicity dependence of *k/*[Fe/H] B 0.2, about half the value suggested by Sasselov et al. from EROS data. Since this estimate of the metallicity dependence of the PL (V ) relation is rather uncertain, however, we prefer to retain as our best value, but with an k 0 (LMC) \ 18.46 increased uncertainty of ^0.06, most of which is due to the uncertainty in the appropriate metallicity correction.