Rigorous luminosity function determination in the presence of a background: theory and application to two intermediate redshift clusters

this paper we present a rigorous derivation of the luminosity function (LF) in the presence of a background. Our approach is free from the logical contradictions of assigning negative values to positively defined quantities and avoids the use of incorrect estimates for the 68 per cent confidence interval (error bar). It accounts for Poisson fluctuations ignored in previous approaches and does not require binning of the data. The method is extensible to more complex situations, does not require the existence of an environment-independent LF, and clarifies issues common to field LF derivations. We apply the method to two clusters of galaxies at intermediate redshift (z similar to 0.3) with among the deepest and widest K-s observations ever taken. Finally, we point out the shortcomings of flip-flopping magnitudes.