[Paper Review] Short gamma-ray burst progenitors have short delay times

M. Pracchia, Om Sharan Salafia|arXiv (Cornell University)|Jan 7, 2026

Gamma-ray bursts and supernovae0 citations

TL;DR

The study uses hierarchical Bayesian analysis of a large SGRB sample to constrain the delay-time distribution of SGRB progenitors, finding shorter average delays (10 Myr to 800 Myr) and a minimum delay < 350 Myr, challenging earlier long-delay inferences due to selection effects.

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 $10\lesssim \langle τ_\mathrm{d}\mathrm angle/\mathrm{Myr}\lesssim 800$ 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.

Motivation & Objective

• Motivate understanding of SGRB progenitor delays and their link to binary neutron star mergers.
• Infer the delay-time distribution (DTD) of SGRBs under different model parametrizations.
• Assess robustness of results to luminosity function models and selection effects.
• Quantify how selection biases can affect inferred delay times in population studies.

Proposed method

• Employ a hierarchical Bayesian framework to infer population hyper-parameters from an SGRB sample.
• Model the DTD with either a power-law with a minimum delay or a log-normal distribution.
• Use two luminosity function models: an empirical doubly-broken power-law (ELF) and a quasi-universal structured jet (QUSJ).
• Incorporate a Poisson likelihood for the observed event counts and explicit selection functions.
• Compute redshift distributions by convolving CSFH with the DTD.
• Implement population inference in the grbpop code and validate with multiple samples.

Experimental results

Research questions

• RQ1 What is the delay-time distribution (DTD) of short gamma-ray burst progenitors when accounting for selection effects?
• RQ2 Do different DTD forms (power-law with a minimum delay vs. log-normal) yield robust conclusions about typical delay times?
• RQ3 How do different luminosity function models (ELF vs. QUSJ) impact inferred delay times and rate evolution?
• RQ4 Is the inferred SGRB rate evolution consistent with a CSFH-convolved progenitor delay scenario?
• RQ5 How do selection effects bias previous inferences of SGRB delay times?

Key findings

• Average delay times are short: 10 Myr to 800 Myr (90% credible) with a minimum delay under 350 Myr.
• For power-law DTDs, inferred mean delay ⟨τd⟩ is typically around 87–160 Myr (depending on the luminosity model).
• For log-normal DTDs, the median-like parameter μτ is constrained to be below ~700 Myr with broad στ, yielding short delays.
• Results are consistent between ELF and QUSJ luminosity models, indicating robustness to luminosity-function choice.
• Compared with some past studies (e.g., W15), the inferred delays are much shorter, largely due to improved treatment of selection effects.
• The study clarifies that longer inferred delays in previous work likely arose from inadequate modeling of selection biases.