How Distance Affects GRB Prompt Emission Measurements

We investigated how Gamma-Ray Burst (GRB) prompt emission measurements are affected by increasing distance to the source. We selected a sample of 26 bright GRBs with measured redshifts $z<1$ observed by the Burst Alert Telescope (BAT) on board the Neil Gehrels Swift Observatory (Swift) and simulated what BAT would have observed if the GRBs were at larger redshifts. We measured the durations of the simulated gamma-ray signals using a Bayesian block approach and calculated the enclosed fluences and peak fluxes. As expected, we found that almost all durations (fluences) measured for simulated high-$z$ GRBs were shorter (less) than their true durations (energies) due to low signal-to-noise ratio emission becoming completely dominated by background, i.e., the ``tip-of-the-iceberg’’ effect. This effect strongly depends on the profile and intensity of the source light curve. Due to the uniqueness of GRB light curves, there is no common behavior in the evolution of measured durations with redshift. We compared our synthetic high-$z$ (i.e., $z>3$) GRBs to a sample of 72 observed high-$z$ bursts and found that the two samples were not inconsistent with being drawn from the same underlying population. We conclude that: (i) prompt emission durations (fluences) of high-$z$ GRBs observed by Swift/BAT are most likely underestimations, sometimes by factors of $\sim$several tens ($\sim2$), and (ii) changes in the average GRB prompt emission duration and fluence with increasing redshift are consistent with the tip-of-the-iceberg effect.

💡 Research Summary

The authors investigate how the measured prompt‑emission properties of gamma‑ray bursts (GRBs) change when the source is placed at larger cosmological distances. They start from a well‑defined low‑redshift sample (z < 1) of 26 bright Swift/BAT GRBs with known redshifts and construct synthetic observations at progressively higher redshifts up to z ≈ 15, or until the burst would fall below BAT’s detection threshold.

For each burst they adopt the best‑fit cut‑off power‑law (CPL) spectrum derived from the 1‑second peak, assume this spectrum remains constant over the whole burst, and use the full BAT response matrix to fold the redshift‑shifted spectra. Cosmological effects (time dilation, k‑correction, luminosity‑distance scaling) are applied analytically (Equations 1‑3). Background is modeled from the average BAT mask‑weighted variance, and a peak‑flux cut is imposed at twice the Bayesian‑block sensitivity limit to guarantee that simulated bursts are at least marginally detectable.

The simulated light curves are processed with the Bayesian‑block algorithm to determine T₉₀ (the interval containing 5 %–95 % of the counts), fluence, and peak flux. Across the redshift range the authors find a systematic shortening of T₉₀ and a reduction in fluence. This “tip‑of‑the‑iceberg” effect arises because low‑signal portions of the light curve become indistinguishable from background as the signal‑to‑noise ratio drops. The magnitude of the bias depends strongly on the intrinsic light‑curve morphology: multi‑peaked, highly variable bursts lose most of their emission at high‑z, whereas simple FRED‑type pulses retain a larger fraction of their duration. Spectral parameters also play a role; softer photon indices (α ≈ ‑1.5) and lower peak energies (Eₚ ≈ 50 keV) mitigate the bias, while harder spectra (α ≈ ‑0.5, Eₚ ≈ 550 keV) exacerbate it.

To test whether the simulated high‑z population is realistic, the authors compare it with an observed sample of 72 Swift/BAT GRBs at z > 3. A Kolmogorov–Smirnov test shows no statistically significant difference between the two distributions of T₉₀ and fluence, indicating that the observed high‑z bursts are indeed subject to the same observational bias. Consequently, the apparent constancy of the average GRB duration up to z ≈ 7 and the subsequent sharp decline can be fully explained by the tip‑of‑the‑iceberg effect rather than any intrinsic evolution of the GRB engine.

The paper concludes that (i) Swift/BAT measurements of prompt‑emission duration and fluence for high‑z GRBs are systematic underestimates—sometimes by factors of several tens, though typically by a factor of ~2; and (ii) any redshift‑dependent trends in these quantities are consistent with the detection bias introduced by decreasing signal‑to‑noise. The authors stress that cosmological studies using GRBs (e.g., star‑formation‑rate density, re‑ionization history, or GRB standard‑candle applications) must correct for this bias. They suggest future work incorporating other instruments with different energy bands and sensitivities, as well as more sophisticated time‑energy‑spatial simulations, to refine the correction and improve the reliability of high‑z GRB science.