Physical origin of the low-redshift excess in the long-gamma-ray-burst formation rate: compact-object mergers versus selection effects, and the non-collapsar fraction of LGRBs

The formation-rate density of long gamma-ray bursts (LGRBs) exceeds the cosmic star-formation rate at redshifts $z<1$–$1.5$, reaching roughly two orders of magnitude at the lowest redshifts in spectroscopic samples. It is not known whether this low-redshift excess signals a second LGRB progenitor channel — a population of compact-object mergers (neutron-star–neutron-star or neutron-star–black-hole binaries) producing long-duration gamma-ray transients, as suggested by the kilonova-associated events GRB 211211A and GRB 230307A — or whether it is an artifact of selection bias, redshift incompleteness, or systematics of machine-learning-estimated redshifts. Resolving the question fixes the redshift-dependent fraction of LGRBs with non-collapsar progenitors and the implied rates of gravitational-wave and kilonova sources, both of which currently span a wide, model-dependent range (roughly 18%–60% of $z<2$ LGRBs across recent analyses).

Background

Gamma-ray bursts (GRBs) are brief, extremely luminous flashes of gamma rays. By their observed duration $T_{90}$ (the time containing 90% of the burst's fluence) they are traditionally divided into short GRBs (SGRBs, $T_{90}\lesssim 2$ s), whose progenitors are compact-object mergers — binary neutron stars (NS–NS) or neutron-star–black-hole pairs (NS–BH) — and long GRBs (LGRBs, $T_{90}\gtrsim 2$ s), produced by collapsars, the collapse of rapidly rotating massive stars that also give rise to core-collapse supernovae. A kilonova is a thermal transient powered by radioactive decay of r-process nuclei synthesized in neutron-rich merger ejecta and is the distinctive electromagnetic counterpart of compact-object mergers; gravitational waves (GWs) from such mergers are detected by the LIGO–Virgo–KAGRA (LVK) interferometer network. Because collapsars follow massive-star death, the LGRB formation rate is expected to trace the cosmic star-formation rate (SFR), whereas the SGRB rate should be a delay-broadened version of it. Reconstructing intrinsic GRB rates from flux-limited catalogs requires correcting for strong observational truncation: the non-parametric, non-binning Efron–Petrosian (EP) method tests the correlation between luminosity $L$ and redshift $z$ in the truncated $L$–$z$ plane via a Kendall-$\tau$-like statistic, and the parameter $k$ of a luminosity-evolution function $g(z)\propto(1+z)^k$ (normalized so $g(1)=1$) is chosen to remove that correlation; the Lynden–Bell $C^-$ method then yields the cumulative luminosity function (LF, the distribution of intrinsic burst luminosities) and the formation-rate evolution. Since only about a third of Swift GRBs have measured redshifts, machine-learning (ML) estimators trained on prompt and afterglow properties now supply predicted redshifts for a much larger sample, at the cost of training-sample covariate-shift systematics. Using these tools, Petrosian, Kitanidis & Kocevski (2015) reported that the LGRB rate rises above the SFR at low redshift (a similar excess was found independently by Yu et al. 2015); Dong et al. (2022) showed a Gaussian-like excess at $z<1$ that persists regardless of sample completeness; and Petrosian & Dainotti (2024) summarized the evidence and conjectured that about 60%±5% of LGRBs at $z<2$ could have compact-star-merger progenitors, which would markedly raise the expected GW and kilonova source rates. The conjecture gained plausibility from two nearby long GRBs with securely detected kilonovae: GRB 211211A (Rastinejad et al. 2022; Mei et al. 2022) and GRB 230307A (Levan et al. 2024; Yang et al. 2024). Champati, Petrosian & Dainotti (2026) re-examined the question with a roughly doubled spectroscopic sample plus an ML-redshift catalog: the density rate still exceeds the SFR by up to two orders of magnitude at the lowest redshifts in the spectroscopic sample, the excess is reduced (not eliminated) when ML-estimated redshifts are added, and the reduction is argued not to be an upward bias of the ML redshifts; the paper's luminosity-evolution estimates carry large uncertainties ($k=3.7^{+4.2}_{-2.9}$ for the non-ML sample), though the excess is stable across the $1\sigma$ range of $k$. The paper leaves the origin of the excess, the non-collapsar fraction, and the GW-rate consequences explicitly open.

Problem Statement

Determine the physical origin of the low-redshift excess in the long-gamma-ray-burst formation rate. Specifically, decompose the observed excess of the LGRB rate density over the cosmic star-formation rate at $z\lesssim 1$–$1.5$ into (a) a possible contribution from an additional progenitor channel — compact-object mergers (NS–NS or NS–BH) producing long-duration gamma-ray transients — and (b) residual artifacts of selection bias, redshift incompleteness, and machine-learning redshift systematics, with quantified uncertainties on each component. As linked parts of the same objective, the answer should establish the redshift-dependent fraction of LGRBs that arise from non-collapsar progenitors, and derive the corresponding implications for gravitational-wave and kilonova source rates. The question is to be answered at the population level, in the generality in which Champati, Petrosian & Dainotti (2026) and Petrosian & Dainotti (2024) pose it — not for a restricted detector, sample cut, or single event.

References

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