How Distance Affects GRB Prompt Emission Measurements

TL;DR

This paper addresses how distance biases GRB prompt-emission measurements by simulating Swift/BAT observations of bright $z<1$ GRBs at higher redshifts and comparing the results to a sample of observed high-$z$ GRBs. Using the simmes package, it accounts for cosmological time dilation, $k$-corrections, BAT response, and realistic backgrounds, and measures $T_{90}$ and fluence with a Bayesian-block approach. The key finding is that the tip-of-the-iceberg effect systematically underestimates GRB durations (often by large factors) and can also underestimate fluence, with the degree of bias depending on light-curve structure; durations often fail to show simple cosmological scaling. The simulated high-$z$ sample is broadly consistent with the observed high-$z$ GRB population, supporting the bias interpretation and suggesting caution when inferring central-engine lifetimes and energetics from Swift/BAT data alone.

Abstract

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.

Figures (14)

• Figure 1: T$_{90}$ measurements of Swift/BAT GRBs as a function of their measured redshifts. The blue and orange points are GRBs with a measured prompt duration of T$_{90}>2$ s and T$_{90}<2$ s, i.e., long and short GRBs, respectively. The lower and upper violet dashed lines are $\propto(1+z) T$ for rest frame durations of T = 25 s and 100 s, respectively. The black line is the weighted mean of the log durations of LGRBs in each sequential redshift bin, i.e., $\mu = \sum x_i\sigma_i^{-2} / \sum \sigma_i^{-2}$, where $x_i = \log_{10}(\text{T}_{90, i})$. The red stars and green triangles indicate GRBs in the low-$z$ and high-$z$ samples of this work, respectively (see Tables \ref{['tab: low-z']} and \ref{['tab: high-z']}).
• Figure 2: Work flow schematic of the simulations and measurements performed in this work.
• Figure 3: Peak flux measurements of Swift/BAT GRBs as a function of their measured redshifts. Blue points are all Swift/BAT GRBs. The red stars and green triangles indicate GRBs in the low-$z$ and high-$z$ samples of this work, respectively (see Tables \ref{['tab: low-z']} and \ref{['tab: high-z']}). The horizontal gray line indicates the theoretical Bayesian block sensitivity limit, the dashed line is twice that limit (see text for details). For reference, the horizontal purple line indicates the BAT flux sensitivity assuming a 1 second exposure 2013ApJS..207...19B2016ApJ...829....7L. The thin black line represents a 1s peak flux value equal to twice Bayesian block sensitivity limit at $z=3$ calculated at other redshifts between $z = 0 - 10$ assuming a spectrum $dN/dE \propto (E/50.\text{ keV})^\alpha e^{-E(2+\alpha) / E_p}$, where the photon index is assumed to be $\alpha = -1.5$ and the peak energy to be $E_p = 50$ keV. The region shaded in yellow defines the same extrapolated flux value but assuming different spectral shapes (see text for details).
• Figure 4: We compiled the 1-second time-bin background variances from the mask-weighted light curves of all Swift/BAT GRBs (blue) and fit a FRED function to the distribution to create a probability distribution function (orange). The background variances were calculated within the 50 second intervals preceding and following the emission of each burst. We sampled this distribution during our simulations to determine the background variance of each simulated light curve.
• Figure 5: Top: The light curve of GRB 140512A, observed at a redshift of $z=0.725$, displays multiple pulses of emission (T$_{100}\sim$154 seconds). Shaded regions indicate the measured T$_{90}$. Center and Bottom: Using our simulation tool, we show what the same light curve looks like when shifted to $z=3$ and $z=6$, respectively. With increasing redshift, the luminosity of the burst is decreased and the signal is stretched due to time dilation. At $z=3$, the early time emission is still visible and could be interpreted as a precursor. At $z=6$, only the main emission period remains significant for Swift/BAT.