Systematic Biases in Galaxy Luminosity Functions
Both the detection of galaxies and the derivation of the luminosity function depend upon isophotal magnitudes, implicitly in the first case, and explicitly in the latter. However, unlike perfect point sources, the fraction of a galaxy's light contained within the limiting isophote is a function of redshift, due to the combined effects of the point spread function and cosmological dimming. This redshift variation in the measured isophotal luminosity can strongly affect the derived luminosity function. Using simulations which include the effects of seeing upon both disk and elliptical galaxies, we explore the size of the systematic biases which can result from ignoring the redshift variation in the fraction of detected light. We show that the biases lead to underestimates in the normalization of the luminosity function, as well as changes in shape. The size of the bias depends upon redshift, and thus can mimic galaxy evolution. Surprisingly, these biases can be extremely large without affecting <V/V_max>. However, these biases can be detected in the full distribution of V/V_max, and in fact may have already been detected in recent surveys. Because the systematic biases result from the redshift variation in the fraction of lost light, the biases are not significant when the fraction of lost light is always small over the entire survey volume, for all galaxy types; however, modern surveys usually violate these conditions. We show that the expected biases are not necessarily eliminated when using aperture magnitudes, FOCAS "total" magnitudes, or Kron magnitudes, but may be reduced if Petrosian magnitudes are used. These considerations may also apply to samples of clusters selected in X-rays.