Avoiding Spurious Breaks in Binned Luminosity Functions

We show that using either the method of Page & Carrera or the well-known $1/V_a$ method to construct the binned luminosity function (LF) of a flux limited sample of Active Galactic Nuclei (AGN) can produce an artificial flattening (or steepening in the case of negative evolution) of the binned LF for bins intersected by the flux cutoff of the sample. This effect is more pronounced for samples with steep and strongly evolving parent LFs but is still present even for non-evolving LFs. As a result of this distortion of the true LF, fitting a model LF to binned data may lead to errors in the estimation of the parameters and may even prompt the erroneous use of broken power law functions. We compute the expected positions of apparent breaks in the binned LF. We show that these spurious breaks in the binned LFs can be avoided if the binning is done in the flux--redshift plane instead of the typically used luminosity--redshift plane. Binning in the flux--redshift plane can be used in conjunction with the binning in the luminosity--redshift plane to test for real breaks in the binned LFs and to identify the features that are the result of binning biases. We illustrate this effect for most typical forms of luminosity dependence and redshift evolution and show how the proposed method helps address this problem. We also apply this method to the MOJAVE AGN sample and show that it eliminates an apparent break in the binned LF.Comment: 7 pages and 7 figures. Accepted for publication in Ap