Abstract
Extreme value statistics is applied to the distribution of galaxy luminosities in the Sloan Digital Sky Survey. We analyze the DR8 Main Galaxy Sample (MGS), as well as the luminous red galaxies (LRGs). Maximal luminosities are sampled from batches consisting of elongated pencil beams in the radial direction of sight. For the MGS, results suggest a small and positive tail index ξ, effectively ruling out the possibility of having a finite maximum cutoff luminosity, and implying that the luminosity distribution function may decay as a power law at the high-luminosity end. Assuming, however, ξ = 0, a non-parametric comparison of the maximal luminosities with the Fisher-Tippett-Gumbel distribution (limit distribution for variables distributed by the Schechter fit) indicates a good agreement provided that uncertainties arising from both the finite batch size and the batch-size distribution are accounted for. For a volume-limited sample of LRGs, results show that they can be described as being the extremes of a luminosity distribution with an exponentially decaying tail, provided that the uncertainties related to batch-size distribution are taken care of.
Author
Taghizadeh-Popp, M.; Ozogány, K.; Rácz, Z.; Regoes, E.; Szalay, A. S.
Journal
Astrophysical Journal
Paper Publication Date
November 2012
Paper Type
Astrostatistics