GRB Variability-Luminosity Correlation Confirmed

Abstract

Recently, Guidorzi et al. (2005) expanded the size of the sample of GRBs for which variabilities and peak luminosities have been measured, from 11 to 32. They confirm the existence of a correlation, but find a dramatically different relationship between L and V than had originally been found. We find that this is the result of improper statistical methodology. When we fit a model to the data that accommodates both statistical variance (in two dimensions) and sample variance, we find that L ~ V^3.4(+0.9,-0.6) with a sample variance of sigma_logV = 0.20(+0.04,-0.04), which is consistent with the original finding of Reichart et al. (2001) -- L ~ V^3.3(+1.1,-0.9) with a sample variance of sigma_logV = 0.18(+0.07,-0.05) -- and inconsistent with the finding of Guidorzi et al. (2005): L ~ V^1.3(+0.8,-0.4) with sample variance assumed to be zero.