Sample variance and Lyman α forest transmission statistics

Abstract

We compare the observed probability distribution function (PDF) of the transmission in the H I Lyman α forest, measured from the Ultraviolet and Visual Echelle Spectrograph (UVES) ‘Large Programme’ sample at redshifts z = [2, 2.5, 3], to results from the GIMIC cosmological simulations. Our measured values for the mean transmission and its PDF are in good agreement with published results. Errors on statistics measured from high-resolution data are typically estimated using bootstrap or jackknife resampling techniques after splitting the spectra into chunks. We demonstrate that these methods tend to underestimate the sample variance unless the chunk size is much larger than is commonly the case. We therefore estimate the sample variance from the simulations. We conclude that observed and simulated transmission statistics are in good agreement; in particular, we do not require the temperature–density relation to be ‘inverted’.