We show how the redshift and peak-flux distributions of gamma-ray bursts ( GRBs ) have an observation-time dependence that can be used to discriminate between different burst populations .
We demonstrate how observation-time relations can be derived from the standard integral distributions and that they can differentiate between GRB populations detected by both the BATSE and Swift satellites .
Using Swift data we show that a redshift–observation-time relation ( log Z – log T ) is consistent with both a peak-flux – observation-time relation ( log P – log T ) and a standard log N – log P brightness distribution .
As the method depends only on rarer small- z events , it is invariant to high- z selection effects .
We use the log Z – log T relation to show that sub-luminous GRBs are a distinct population occurring at a higher rate of order 150 ^ { +180 } _ { -90 } \mathrm { Gpc } ^ { -3 } \mathrm { yr } ^ { -1 } .
Our analysis suggests that GRB 060505 – a relatively nearby GRB observed without any associated supernova – is consistent with a sub-luminous population of bursts .
Finally , we show that our relations can be used as a consistency test for some of the proposed GRB spectral energy correlations .