Waveband Luminosity Correlations in Flux-Limited Multiwavelength Data

We explore the general question of correlations among multiple different waveband luminosities in a flux-limited multiband observational data set. If such correlations are observed, they may either be intrinsic or induced by similar redshift evolution of the luminosities and/or the selection effects due to the flux limits. We first develop the question analytically, then use simulated observed flux-limited data sets with known luminosity correlations and evolutions to explore how the intrinsic nature of luminosity correlations can be deduced, including exploring the efficacy of partial correlation analysis with redshift binning in determining whether luminosity correlations are intrinsic. We use these techniques to show that the observed correlations between mid-infrared and optical luminosities in quasars are intrinsic to a greater degree than those observed between radio and optical luminosities. We then show that applying methods that we have developed in recent works can recover the true redshift luminosity evolutions, density evolutions, and local luminosity functions of populations observed in multiple flux-limited surveys in different wavebands, whether the luminosities in the wavebands are intrinsically correlated or not.