A complete sample of bright Swift Gamma-Ray Bursts: X-ray afterglow luminosity and its correlation with the prompt emission

We investigate wheter there is any correlation between the X-ray afterglow luminosity and the prompt emission properties of a carefully selected sub-sample of bright Swift long Gamma-Ray Bursts (GRBs) nearly complete in redshift (~90%). Being free of selection effects (except flux limit), this sample provides the possibility to compare the rest frame physical properties of GRB prompt and afterglow emission in an unbiased way. The afterglow X-ray luminosities are computed at four different rest frame times (5 min, 1 hr, 11 hr and 24 hr after trigger) and compared with the prompt emission isotropic energy E_iso, the isotropic peak luminosity L_iso and the rest frame peak energy E_peak. We find that the rest frame afterglow X-ray luminosity do correlate with these prompt emission quantities, but the significance of each correlation decreases over time. This result is in agreement with the idea that the GRB X-ray light curve can be described as the result of a combination of different components whose relative contribution and weight change with time, with the prompt and afterglow emission dominating at early and late time, respectively. In particular, we found evidence that the plateau and the shallow decay phase often observed in GRB X-ray light curves are powered by activity from the central engine. The existence of the L_X-E_iso correlation at late times (t_rf > 11 hr) suggests a similar radiative efficiency among different bursts with on average about 6% of the total kinetic energy powering the prompt emission.

💡 Research Summary

The authors present a systematic investigation of the relationship between the X‑ray afterglow luminosity (L_X) and the prompt emission properties of a carefully curated sample of bright, long‑duration Swift Gamma‑Ray Bursts (GRBs). By selecting bursts with a 1‑second peak flux above 2.6 ph cm⁻² s⁻¹ and achieving a redshift completeness of roughly 90 % (58 GRBs in total), they construct a dataset that is essentially free of selection biases except for the imposed flux limit. Prompt‑phase parameters—namely the isotropic equivalent energy (E_iso), the isotropic peak luminosity (L_iso), and the rest‑frame spectral peak energy (E_peak)—are derived from BAT spectra using either the Band function or a cutoff power‑law model.

The X‑ray afterglow is examined at four rest‑frame epochs: 5 minutes, 1 hour, 11 hours, and 24 hours after the trigger. Light curves are K‑corrected, corrected for Galactic absorption, and converted to luminosities in the 0.3–10 keV band. Correlation analyses employing both Pearson and Spearman statistics reveal robust, positive correlations between L_X and each of the prompt quantities at early times (p < 10⁻⁴, correlation coefficients ≈ 0.6–0.7). As the afterglow evolves, the significance and strength of these correlations systematically decline, reaching marginal levels (p ≈ 10⁻², r ≈ 0.3) by 24 hours.

The temporal weakening of the correlations is interpreted as evidence for a changing composition of the X‑ray light curve. At early epochs the emission is dominated by components directly linked to the prompt phase and ongoing central‑engine activity (e.g., internal shocks, prolonged energy injection), whereas at later times the external forward shock—interacting with the circumburst medium—becomes the primary contributor. Notably, GRBs that display a plateau or shallow‑decay phase maintain a strong L_X–E_iso correlation during that interval, supporting the hypothesis that the plateau is powered by sustained central‑engine energy release.

Furthermore, the persistence of an L_X–E_iso correlation beyond ≈ 11 hours suggests a roughly uniform radiative efficiency across the sample, with about 6 % of the total kinetic energy being converted into prompt γ‑ray emission. This efficiency estimate aligns with theoretical expectations for internal‑shock models and provides a valuable constraint for simulations of jet dynamics and energy dissipation.

In summary, the paper delivers a high‑quality, nearly unbiased empirical assessment of how prompt‑phase energetics imprint on the X‑ray afterglow across multiple timescales. The findings reinforce a two‑component picture of GRB X‑ray emission—central‑engine‑driven at early times and external‑shock‑driven later—and furnish quantitative benchmarks for models of energy partition, radiative efficiency, and central‑engine longevity.