2000/03/03 by Ryan Scranton, R. Scranton, S. Dodelson +3
Physics and Astronomy · #Astronomy and Astrophysical Research #Astrophysics (astro-ph) #FOS: Physical sciences #Galaxies: Formation, Evolution, Phenomena #Stellar, planetary, and galactic studies #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0003034
5 pages, 4 figures, to be submitted to MNRAS
arxiv created 2000/03/03 · openalex publication_date 2000/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Extracting the three dimensional power spectrum from the 2D distribution of galaxies has become a standard tool of cosmology. This extraction requires some assumptions about the scaling of the power spectrum with redshift; all treatments to date assume a simple power law scaling. In reality, different scales grow at different rates, due to non-linearities. We show that angular surveys are sensitive to a weighted average of the power spectrum over a distribution of redshifts, where the weight function varies with wavenumber. We compute this weight function and show that it is fairly sharply peaked at z, which is a function of k. As long as the extracted power spectrum is understood to be P(k,z), the error introduced by non-linear scaling is quantifiable and small. We study these effects in the context of the APM and SDSS photometric surveys. In general the weight matrix is peaked at larger z and is broader for deeper surveys, leading to larger (but still quantifiable) errors due to non-linear scaling. The tools introduced here -- in particular the weight function and effective redshift z -- can also be profitably applied to plan surveys to study the evolution of the power spectrum.