Bias in the Cepheid PL relation

We show that the Cepheid 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 underestimation of distances which 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 magnitudes 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.