Short gamma-ray burst progenitors have short delay times

TL;DR

This work constrains the delay-time distribution of short gamma-ray burst progenitors by applying a hierarchical Bayesian framework to SGRB samples, testing power-law and log-normal DTDs alongside two luminosity-function models (ELF and QUSJ). By carefully modeling selection effects and rate evolution through a convolution of the CSFH with the DTD, the authors find average delays on the order of 10^2 Myr (shorter than previous estimates) and minimum delays well below ~350 Myr, with significant implications for fast binary-merger channels in shaping the SGRB population. The results are broadly consistent across LF models and align with GW-based BNS rate constraints, supporting BNS mergers as the primary SGRB progenitors while highlighting the critical role of flux-complete samples and robust selection modeling. The study also clarifies why earlier works inferred longer delays, demonstrating that biased sampling from flux-incomplete data can drastically distort inferred population timescales. Overall, the paper advances understanding of SGRB formation channels and their connection to cosmic star formation, informing both GRB physics and multi-messenger merger rates.

Abstract

Short gamma-ray bursts (SGRBs) are thought to be primarily associated with binary neutron star (BNS) mergers. The SGRB population can therefore be scrutinized to look for signatures of the delay time between the formation of the progenitor massive star binary and the eventual merger, which could produce an evolution of the cosmic rate density of such events whose shape departs from that of the cosmic star formation history (CSFH). To that purpose, we study a large sample of SGRBs within a hierarchical Bayesian framework, with a particular focus on the delay time distribution (DTD) of the population. Following previous studies, we model the DTD either as a power-law with a minimum time delay or as a log-normal function. We consider two models for the intrinsic SGRB luminosity distribution: an empirical luminosity function (ELF) with a doubly broken power-law shape, and one based on a quasi-universal structured jet (QUSJ) model. Regardless of the chosen parametrization, we find average time delays $10\lesssim \langle τ_\mathrm{d}\mathrm\rangle/\mathrm{Myr}\lesssim 800$ and a minimum delay time $τ_\mathrm{d,min}\lesssim 350\,\mathrm{Myr}$, in contrast with previous studies that found long delay times of few Gyr. We demonstrate that the cause of the longer inferred time delays in past studies most likely resides in an incorrect treatment of selection effects.

Figures (12)

• Figure 1: Rate density distributions as functions of redshift (left panels) and corner plots of the posterior PDFs for the DTD parameters and $\langle \tau_\mathrm{d} \rangle$ (right panels). Top and bottom panels show the results obtained with a power-law and a log-normal DTD, respectively. Rate density distributions are normalized to $1$ at $z=0$. Red and blue curves represent the distributions obtained considering, respectively, the empirical luminosity function and the quasi-universal structured jet models. WP15* results are displayed in yellow.
• Figure 2: Luminosity probability distributions obtained considering either a power-law or a log-normal DTD (left and right panel, respectively). Results obtained with the broken power-law model are shown in red and the ones obtained with the structured jet model in blue, each with the shaded areas representing their $90\%$ credible intervals. Luminosity functions from WP15 are also shown in yellow. The measured luminosity for GRB 170817A is shown in gray as a reference point.
• Figure 3: Comparisons between local rate density probability distributions. Distributions obtained with the broken power-law and the structured jet luminosity models are shown in red and blue, respectively, while results corresponding to power-law and log-normal DTD are displayed respectively with dashed and dotted lines. BNS rate density inferred from GW observations GWTC4_pop is shown in gray ($90\%$ credible intervals).
• Figure 4: Comparison between the detection efficiency in our simulated sample and that used in the inference. The black solid line shows the detection efficiency model $p_\mathrm{det,GBM}$ from grbpop as a function of the SGRB photon flux, assuming $E_\mathrm{p,obs}=100\,\mathrm{keV}$. The thick coloured lines show the hard-threshold detection efficiency models assumed in our inference on the simulated sample described in Section \ref{['subsec:biases_study']}, with different colours indicating different assumed photon flux thresholds as in Figure \ref{['fig:mockdata_dpdlogtd']}. For each of these analyses, only the SGRBs above the assumed threshold were included in the inference.
• Figure 5: Posterior distribution of the average time delay for inference on a simulated SGRB population assuming different photon peak flux cuts. The dashed black line shows the 'true' average time delay value corresponding to the power-law DTD parameters from which the SGRB events have been sampled. The blue curve shows the result obtained with the same flux threshold cut as in our analysis, which ensures flux completeness of the sample. The yellow, green and pink ones are obtained with lower threshold values, as reported in the legend.