Threshold effects on V/V(max) for gamma-ray bursts

Abstract

The interpretation of the observed gamma-ray burst V/V(max) statistic in terms of spatial distributions is model-dependent. Detection of gamma-ray bursts requires the counting rate in one or more detectors to exceed a threshold C(lim) determined from a time-dependent background rate B(t). The sampling depth of the burst detector is thus time-dependent, and, if burst sources are nonuniform in space, the observed V/V(max) distribution will be affected by B(t). We demonstrate this effect with a simple geometric distribution of standard candles and argue that V/V(max) statistic without information on threshold variations is insufficient for rigorous data analysis. Peak count rates and threshold values must be given separately for all events in order to facilitate a meaningful comparison of observations with theoretical distribution models.