Systematic Biases in Galaxy Luminosity Functions

Both the detection of galaxies and the derivation of the luminosity functiondepend upon isophotal magnitudes, implicitly in the first case, and explicitlyin the latter. However, unlike perfect point sources, the fraction of agalaxy's light contained within the limiting isophote is a function ofredshift, due to the combined effects of the point spread function andcosmological dimming. This redshift variation in the measured isophotalluminosity can strongly affect the derived luminosity function. Usingsimulations which include the effects of seeing upon both disk and ellipticalgalaxies, we explore the size of the systematic biases which can result fromignoring the redshift variation in the fraction of detected light. We show thatthe biases lead to underestimates in the normalization of the luminosityfunction, as well as changes in shape. The size of the bias depends uponredshift, and thus can mimic galaxy evolution. Surprisingly, these biases canbe extremely large without affecting . However, these biases can bedetected in the full distribution of V/V_max, and in fact may have already beendetected in recent surveys. Because the systematic biases result from theredshift variation in the fraction of lost light, the biases are notsignificant when the fraction of lost light is always small over the entiresurvey volume, for all galaxy types; however, modern surveys usually violatethese conditions. We show that the expected biases are not necessarilyeliminated when using aperture magnitudes, FOCAS "total" magnitudes, or Kronmagnitudes, but may be reduced if Petrosian magnitudes are used. Theseconsiderations may also apply to samples of clusters selected in X-rays.Comment: 31 pages, including 12 pages of figures. LaTex with aaspp4.sty. Accepted to the Astrophysical Journa