The GRB Intrinsic Duration Distribution: Progenitor Insights Across Cosmic Time

TL;DR

The paper investigates whether the intrinsic prompt-duration distribution of gamma-ray bursts (GRBs), $T_{int}=T_{90}/(1+z)$, preserves the plateau diagnostic for collapsar progenitors first identified in observed durations. By constructing $dN/dT_{int}$ from a Swift sample with redshifts and fitting a two-component model (non-collapsars as a log-normal and collapsars with a plateau ending at $T_B$), the authors quantify how the plateau's end shifts to shorter times by roughly $1/(1+z_{av})$ and how its presence depends on redshift and spectral hardness. They find a robust plateau in high-$z$ and in spectrally soft GRBs, but not in low-$z$ or spectrally hard samples, implying a larger non-collapsar contribution at low redshift and a collapsar-dominated high-redshift population. Linking the plateau end to the threshold time for jet breakout, $t_{ m th}$, and employing jet-head propagation physics, the work constrains progenitor radii to be only a few tenths of a solar radius, with implications for envelope structure and density profiles. These results illuminate how GRB progenitor demographics evolve across cosmic time and demonstrate the power of intrinsic-duration statistics for constraining massive-star endpoints and jet physics.

Abstract

We present the distribution of the intrinsic duration of gamma-ray bursts' prompt emission. This expands upon the analysis of Bromberg et al., 2012 and Bromberg et al. 2013 who showed evidence for collapsar progenitors based on the presence of a plateau in the distribution of $T_{90}$, the duration over which 90 % of the prompt emission is observed for any given detector. We confirm the presence of this plateau in the distribution of duration corrected for cosmological time dilation (what we call intrinsic duration, $T_{int}$), but shifted to smaller timescales by a factor of $1/(1+z_{\rm av}) \sim 1/3$, where $z_{\rm av}$ is the average GRB redshift. More significantly, we show this plateau is only present in the sample of GRBs with redshifts greater than $(1+z) \sim 2$, and does not appear in the duration distribution of lower redshift GRBs. This result aligns with suggestions that the low redshift population of GRBs has a significant contribution from non-collapsar progenitors (while the high redshift sample is dominated by collapsars). We also show the difference in this distribution between spectrally hard and soft GRBs, confirming that a plateau is only present for the soft subset of GRBs. However, when we separate the soft GRBs into low and high redshift subsets, we find that only the high redshift soft GRBs show evidence of a plateau, while the low-redshift soft GRBs do not. This suggests there exists a significant subset of spectrally soft non-collapsar progenitors at low redshift. Finally, we use the end time of the plateau to constrain the GRB progenitor density profile and radius, and show the maximum size of a collapsar is a few tenths of a solar radius.

Figures (8)

• Figure 1: $dN/dT$ distribution of both $T_{90}$ (green line) and intrinsic duration $T_{int}$ (magenta line), for our sample of Swift GRBs with redshifts; the distributions are artificially offset by a constant along the y-axis for comparison purposes. The right edge of the lines indicates the end of the plateau. The end of the plateau of the intrinsic duration distribution is shifted to shorter timescales by a factor of $\sim 1/3$. Table \ref{['tab:funcfit']} gives the best-fit parameters of these distributions according to equation \ref{['eq:func']}.
• Figure 2: $dN/dT$ distribution of intrinsic duration, $T_{int}$, broken into "low" redshift (blue lines) and "high" redshift (orange lines), with a redshift delimiter of $(1+z) = 2.2$. There is a clear plateau in the high redshift sample, while no plateau present in the low redshift sample. The fits to these distributions, according to equation \ref{['eq:func']}, are given in Table \ref{['tab:funcfit']}.
• Figure 3: $dN/dT$ distribution of intrinsic duration, $T_{int}$, for Swift GRBs with redshift, broken into "hard" and "soft" sub-samples based on the power-law index and spectral fit model. A plateau is present in the soft sample with an end at around a few seconds, while there is no plateau in the hard sample, confirming the results of Brom13. The fits to these distributions, according to equation \ref{['eq:func']}, are given in Table \ref{['tab:funcfit']}.
• Figure 4: $dN/dT$ distribution of intrinsic duration, $T_{int}$, for the Swift GRB spectrally soft sample broken into "low" redshift (blue lines) and "high" redshift (green lines), with a redshift delimiter of $(1+z) = 2.0$. Even within the soft sample we see a lack of a plateau in the low redshift GRBs, and a clear plateau in the high redshift GRBs, confirmed by our fits to equation \ref{['eq:func']}, shown in Table \ref{['tab:funcfit']}.
• Figure 5: Threshold time as a function of stellar radius (x-axis) and the stellar density profile index (y-axis) for a star of 15 solar masses. The black dotted and solid lines mark a timescale of 5 seconds and 15 seconds, respectively (corresponding to the range of plateau end times in our $dN/dT_{int}$ distributions). The left panel shows the threshold time scale based on equation \ref{['eq:t_th']}, while the right panel applies a correction to this equation based on the numerical simulations of Harr18. We used the average (beaming-corrected) jet luminosity and opening angle of our high redshift sample in these calculations.