Distribution of Maximal Luminosity of Galaxies in the Sloan Digital Sky Survey

TL;DR

This study applies extreme value statistics to analyze the distribution of galaxy luminosities in SDSS, revealing insights about the tail behavior and maximum luminosities of different galaxy samples.

Contribution

It introduces a novel application of EVS to SDSS galaxy luminosities, comparing empirical data with theoretical limit distributions and assessing tail behaviors.

Findings

MGS luminosities suggest a power-law decay at the high end.

LRG luminosities are consistent with an exponential tail distribution.

Results rule out a finite maximum luminosity for MGS galaxies.

Abstract

Extreme value statistics (EVS) is applied to the distribution of galaxy luminosities in the Sloan Digital Sky Survey (SDSS). We analyze the DR8 Main Galaxy Sample (MGS), as well as the Luminous Red Galaxies (LRG). 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 $\xi$, 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, $\xi=0$, 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 uncertainties arising both from the finite batch size and from 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 the uncertainties related to batch-size distribution are taken care of.