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

TL;DR

This paper tests whether the diversity in X-ray plateau decay slopes $α_1$ of GRBs indicates distinct populations or a single origin. Using a uniform sample of $185$ Swift/XRT plateaus, it divides bursts into Rising, Flat, and Decaying groups by $α_1$, then applies non-parametric methods—the EP method and Lynden-Bell $C^{-}$ method—to reconstruct intrinsic luminosity functions and comoving event rates, correcting for redshift evolution and selection biases. The analysis finds broadly similar luminosity functions, redshift distributions, and rates across the three groups, with Monte Carlo tests showing robustness to the exact $α_1$ boundaries, supporting a unified plateau mechanism. The results imply a common central-engine framework for X-ray plateaus and show that plateau occurrence rates track the cosmic star-formation rate, highlighting the link between GRB plateaus and the death of massive stars.

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 post-plateau 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 $\textit{Swift}$ GRBs with a well-defined plateau and divide them into three groups based on $α_1$. Using a non-parametric 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.

Figures (8)

• Figure 1: Exemplar X-ray afterglow light curves of GRBs 110213A, 250424A, and 250114A, which has a rising, flat, and decaying plateau, respectively. The solid curves show the best-fit results by using Equation (\ref{['func1']}) with the MCMC method.
• Figure 2: Distributions of the temporal indices during ($\alpha_1$) and after ($\alpha_2$) the plateau phase for the three groups. Left:$\alpha_2$ plotted versus $\alpha_1$, where the filled circles, triangles and squares represent the Rising, Flat and Decaying subsamples, respectively. Middle: histogram of $\alpha_1$ for all the plateau GRBs. Right: histograms of $\alpha_2$ for the three groups.
• Figure 3: X-ray plateau luminosity plotted versus redshift for the three subsamples. The solid curves are plotted by assuming a flux limit of $\log(F_{\rm lim}/{\rm 1\ erg\ cm^{-2}\ s^{-1}} )=-11.9$2025ApJ...990...69K, which will be taken as the detection threshold to ensure sample completeness in our subsequent calculations.
• Figure 4: Luminosity functions of the three subsamples. The data points have been calculated by using Equation (\ref{['luminosityFunction']}), where the diamonds, triangles and filled circles represent the rising, flat and decaying subsamples, respectively. The dashed line denote the best-fit Schechter function for each subsample, while the solid curve shows the best-fit SBPL model. The corresponding best-fit parameters are listed in Table \ref{['tab2']}.
• Figure 5: Normalized cumulative redshift distributions of the three subclasses. The dashed, solid, and dash-dotted lines represent the rising, flat, and decaying plateau groups, respectively.