Bias in the Estimation of Global Luminosity Functions

We discuss a bias present in the calculation of the global luminosity function (LF) which occurs when analysing faint galaxy samples. This effect exists because of the different spectral energy distributions of galaxies, which are in turn quantified by the k-corrections. We demonstrate that this bias occurs because not all galaxy types are visible in the same absolute magnitude range at a given redshift and it mainly arises at high redshift since it is related to large k-corrections. We use realistic simulations with observed LFs to investigate the amplitude of the bias. We also compare our results to the global LFs derived from Hubble Deep Field-North and -South (HDF) surveys. We conclude that, as expected, there is no bias in the global LF measured in the absolute magnitude range where all galaxy types are observable. Beyond this range the faint-end slope of the global LF can be over/under-estimated depending on the adopted LF estimator. The effect is larger when the reference filter in which the global LF is measured, is far from the rest-frame filter in which galaxies are selected. The fact that LF estimators are differently affected by this bias implies that the bias is minimal when the different LF estimators give measurements consistent with one another at the faint-end. For instance, we show that the estimators are discrepant in the same way both in the simulated and HDF LFs. This suggests that the HDF LFs are affected by the presently studied bias. The best solution to avoid this bias is to derive the global LF in the reference filter closest to the rest-frame selection filter.