The period–luminosity relation for Cepheids – I. Numerical simulations

Numerical simulations of the empirical determination of the period–luminosity–colour relation for classical Cepheids are presented. In this study we evaluate the quantitative effects of random errors, reddening, sample size and the presence of both colour and period cut-offs (imposed by the finite extent of the instability strip) on the observational re determination of the original relation. Both random errors in the photometry and correlated errors in the reddening corrections are shown to have systematic effects. Especially sensitive to these errors is the colour coefficient in the period–luminosity–colour relation, where the ratio of the error to the width of the instability strip is the determining factor. With present observations only broad confidence limits can be placed on our present knowledge of the intrinsic period–luminosity–colour relation and/or its variations from galaxy to galaxy.