Bias in the Cepheid period-luminosity relation

We show that the Cepheid period-luminosity (PL) relation is affected by a Malmquist-type bias, the so-called population incompleteness bias. Its calculated slope appears shallower than the true one because of the cutoff in apparent magnitude resulting from the instrumental limiting magnitude. Furthermore, the use of the PL relation, even with the correct slope, leads to an underestimation of distances that is not negligible. We confirm this finding by studying simulated PL relations, and we show that this bias may be as large as 0.2 or 0.3 mag on distance modulus. We also test the efficiency of a cutoff in log P and show that it is a good way to minimize this bias. However, a correction of this is difficult as long as the completeness of the sample is not perfectly well established.