Institute for Advanced Study/Princeton University Early Universe/Cosmology Lunch Discussion

Abstract: The cosmological impact of current and upcoming photometric galaxy surveys is contingent on our ability to obtain redshift estimates for large numbers of faint galaxies. In the absence of spectroscopically confirmed redshifts, broad-band photometric redshift point estimates (photo-zs) have been superseded by photo-z probability density functions (PDFs) that encapsulate their nontrivial uncertainties. Traditional applications of photo-z PDFs in weak gravitational lensing studies of cosmology have employed computationally straightforward stacking methodologies for obtaining the redshift distribution function N(z) that violate the laws of probability. In response, mathematically self-consistent models, including but not limited to that of Malz & Hogg (2020), have been proposed in an effort to answer the question, "What is the right way to obtain the redshift distribution function N(z) from a catalog of photo-z PDFs?'' In this talk, corresponding to Malz (2021), I motivate adoption of such principled methods by addressing the contrapositive of the more common presentation of such models, answering the question, "Under what conditions do established stacking methods successfully recover the true redshift distribution function N(z)?'' By exploring a series of mathematical thought experiments, I identify two such conditions that were only weakly violated in the past but will be strongly violated by future galaxy surveys.