2000A&A...356..849G

We analyse a sample of 236 Cepheids from the hipparcos catalog, using the method of ``reduced parallaxes'' in V, I, K and the reddening-free ``Wesenheit-index''. We compare our sample to those considered by Feast & Catchpole (19977MNRAS.286L...1F) and Lanoix et al. (1999MNRAS.308..969L), and argue that our sample is the most carefully selected one with respect to completeness, the flagging of overtone pulsators, and the removal of Cepheids that may influence the analyses for various reasons (double-mode Cepheids, unreliable hipparcos solutions, possible contaminated photometry due to binary companions). From numerical simulations, and confirmed by the observed parallax distribution, we derive a (vertical) scale height of Cepheids of 70 pc, as expected for a population of 3-10M_☉ stars. This has consequences for Malmquist- and Lutz-Kelker (Lutz & Kelker, 1973PASP...85..573L, Oudmaijer et al., 1998MNRAS.294L..41O) type corrections which are smaller for a disk population than for a spherical population. The V and I data suggest that the slope of the Galactic PL-relations may be shallower than that observed for LMC Cepheids, either for the whole period range, or that there is a break at short periods (near logP₀∼0.7-0.8). We stress the importance of two systematic effects which influence the distance to the LMC: the slopes of the Galactic PL-relations and metallicity corrections. In order to assess the influence of these various effects, we present 27 distance moduli (DM) to the LMC. These are based on three different colours (V,I,K), three different slopes (the slope observed for Cepheids in the LMC, a shallower slope predicted from one set of theoretical models, and a steeper slope as derived for Galactic Cepheids from the surface-brightness technique), and three different metallicity corrections (no correction as predicted by one set of theoretical models, one implying larger DM as predicted by another set of theoretical models, and one implying shorter DM based on empirical evidence). We derive DM between 18.45±0.18 and 18.86±0.12. The DM based on K are shorter than those based on V and I and range from 18.45±0.18 to 18.62±0.19, but the DM in K could be systematically too low by about 0.1 magnitude because of a bias due to the fact that NIR photometry is available only for a limited number of stars. From the Wesenheit-index we derive a DM of 18.60±0.11, assuming the observed slope of LMC Cepheids and no metallicity correction, for want of more information. The DM to the LMC based on the parallax data can be summarised as follows. Based on the PL-relation in V and I, and the Wesenheit-index, the DM is 18.60±0.11 (±0.08 slope)(^+0.08_–0.15 metallicity), which is our current best estimate. Based on the PL-relation in K the DM is 18.52±0.18 (±0.03 slope) (±0.06 metallicity) (^+0.10_–0 sampling bias). The random error is mostly due to the given accuracy of the hipparcos parallaxes and the number of Cepheids in the respective samples. The terms between parentheses indicate the possible systematic uncertainties due to the slope of the Galactic PL-relations, the metallicity corrections, and in the K-band, due to the limited number of stars. Recent work by Sandage et al. (1999ApJ...522..250S) indicates that the effect of metallicity towards shorter distances may be smaller in V and I than indicated here. From this, we point out the importance of obtaining NIR photometry for more (closeby) Cepheids, as for the moment NIR photometry is only available for 27% of the total sample. This would eliminate the possible bias due to the limited number of stars, and would reduce the random error estimate from 0.18 to about 0.10mag. Furthermore, the sensitivity of the DM to reddening, metallicity correction and slope are smallest in the K-band.