Gamma-Ray Bursts: Evidence for a Common Origin of X-Ray Plateaus with Diverse Temporal Decay Index

Abstract A significant fraction of gamma-ray bursts (GRBs) exhibit a plateau in the early X-ray afterglow light curve, whose mechanism remains uncertain. While the postplateau normal decay index ( α 2 ) is commonly used to constrain the afterglow dynamics, the shallow-decay slope of the plateau itself ( α 1 ) has received comparatively little attention. Recent observations, however, reveal substantial dispersion in α 1 , raising the question of whether GRBs with rising, flat, and mildly decaying plateaus represent intrinsically distinct populations. To address this question, we collect a uniform sample of 185 Swift GRBs with a well-defined plateau and divide them into three groups based on α 1 . Using a nonparametric approach, we reconstruct their X-ray luminosity functions, redshift distributions, and event rates. It is found that the three groups exhibit statistically consistent properties across all diagnostics, with no evidence for group-specific features. Monte Carlo perturbation tests further show that these results are insensitive to the adopted classification boundaries of α 1 . Our results indicate that variations in the plateau slope α 1 do not define distinct GRB subclasses, but instead the sample constitutes a statistically uniform population governed by a common framework.