Open AccessRigorous luminosity function determination in the presence of a background: theory and application to two intermediate redshift clusters ★
Author(s) -
Andreon S.,
Punzi G.,
Grado A.
Publication year - 2005
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2005.09063.x
Subject(s) - physics , redshift , galaxy , function (biology) , poisson distribution , luminosity , luminosity function , field (mathematics) , bar (unit) , astrophysics , point (geometry) , theoretical physics , statistical physics , statistics , pure mathematics , geometry , mathematics , evolutionary biology , meteorology , biology
In 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 ∼ 0.3) with among the deepest and widest K s observations ever taken. Finally, we point out the shortcomings of flip‐flopping magnitudes.