How Sample Completeness Affects Gamma-Ray Burst Classification

Unsupervised pattern-recognition algorithms support the existence of three gamma-ray burst classes: class 1 (long, large-fluence bursts of intermediate spectral hardness), class 2 (short, small-fluence, hard bursts), and class 3 (soft bursts of intermediate durations and fluences). The algorithms surprisingly assign larger membership to class 3 than to either of the other two classes. A known systematic bias has been previously used to explain the existence of class 3 in terms of class 1; this bias allows the fluences and durations of some bursts to be underestimated, as recently shown by Hakkila et al. We show that this bias primarily affects only the longest bursts and cannot explain the bulk of the class 3 properties. We resolve the question of class 3's existence by demonstrating how samples obtained using standard trigger mechanisms fail to preserve the duration characteristics of small-peak flux bursts. Sample incompleteness is thus primarily responsible for the existence of class 3. In order to avoid this incompleteness, we show how a new, dual-timescale peak flux can be defined in terms of peak flux and fluence. The dual-timescale peak flux preserves the duration distribution of faint bursts and correlates better with spectral hardness (and presumably redshift) than either peak flux or fluence. The techniques presented here are generic and have applicability to the studies of other transient events. The results also indicate that pattern recognition algorithms are sensitive to sample completeness; this can influence the study of large astronomical databases, such as those found in a virtual observatory.