Investigating signatures of cosmological time dilation in duration measures of prompt gamma-ray burst light curves

We study the evolution with redshift of three measures of gamma-ray burst (GRB) duration (T₉₀, T₅₀ and TR₄₅) in a fixed rest-frame energy band for a sample of 232 Swift/Burst Alert Telescope (BAT) detected GRBs. Binning the data in redshift we demonstrate a trend of increasing duration with increasing redshift that can be modelled with a power law for all three measures. Comparing redshift defined subsets of rest-frame duration reveals that the observed distributions of these durations are broadly consistent with cosmological time dilation. To ascertain if this is an instrumental effect, a similar analysis of Fermi/Gamma-ray Burst Monitor data for the 57 bursts detected by both instruments is conducted, but inconclusive due to small number statistics. We then investigate underpopulated regions of the duration redshift parameter space. We propose that the lack of low-redshift, long duration GRBs is a physical effect due to the sample being volume limited at such redshifts. However, we also find that the high-redshift, short duration region of parameter space suffers from censorship as any Swift GRB sample is fundamentally defined by trigger criteria determined in the observer frame energy band of Swift/BAT. As a result, we find that the significance of any evidence for cosmological time dilation in our sample of duration measures typically reduces to <2σ.