Gravitational-wave observations through GWTC-4 infer a binary neutron star (BNS) merger rate of roughly 28-300 Gpc^-3 yr^-1, which sits in simultaneous tension with four independent multimessenger constraints: the beaming-corrected short gamma-ray burst (SGRB) rate (a factor 3.6-18 above the BNS rate at a fiducial 100 Gpc^-3 yr^-1), the merger rate required to supply the Milky Way's heavy r-process inventory (a factor 0.9-4.1 above it), the Galactic double neutron star (DNS) merger rate scaled to the cosmic population (a factor 2.3-5.1 above it), and the poorly sampled populations of low-mass BNSs and electromagnetically bright neutron-star-black-hole (NSBH) mergers. The open problem, posed by Fishbach et al. (ApJL 1006, L49, 2026), is to determine whether a single self-consistent neutron-star-merger rate budget can satisfy all four constraints simultaneously, and if so which physical parameters or channels deliver it (wider jet opening angles, a lower true local SGRB rate, redshift evolution of the merger rate, collapsar contamination, additional non-BNS progenitor channels, non-merger r-process production, or incomplete DNS beaming/completeness corrections).

Background

A binary neutron star (BNS) system is two neutron stars in a decaying orbit that merge within the age of the Universe, emitting gravitational waves (GW) detectable by the LIGO/Virgo/KAGRA interferometers. The GW Transient Catalog 4 (GWTC-4), the fourth catalog of compact-binary detections, currently implies a BNS merger rate of about 28-300 Gpc^-3 yr^-1, with only two confident BNS detections (GW170817 and GW190425). Short gamma-ray bursts (SGRBs) are flashes of gamma-rays lasting less than about two seconds, widely attributed to relativistic jets launched during BNS (or NSBH) mergers. Because such jets are collimated into a narrow cone, the observed SGRB rate must be corrected by a beaming factor set by the jet half-opening angle; for typical afterglow-inferred angles near 6 degrees the intrinsic rate exceeds the observable one by one to two orders of magnitude, and it is precisely this beaming-corrected SGRB rate that appears too large for the GW-inferred BNS rate. The r-process (rapid neutron capture) builds nuclei heavier than iron, including europium and gold. The kilonova — a thermal transient powered by radioactive decay of neutron-rich ejecta — that followed GW170817 confirmed that BNS mergers synthesize r-process material, but whether mergers account for the Milky Way's entire heavy r-process inventory depends on the ejecta mass per event, the Galactic star-formation history, and the delay-time distribution (the time between binary formation and merger, which sets where and when enrichment happens). Double neutron stars (DNS) are also found in the Galaxy as radio pulsars in binary systems; their merger rate is inferred from a small observed sample after correcting for the pulsar beam geometry (beaming) and survey completeness, and can be scaled to a cosmic rate for comparison with GW results. Neutron-star-black-hole (NSBH) mergers are electromagnetically bright ('EM-bright') only when the neutron star is tidally disrupted outside the black hole, and this subpopulation is poorly sampled. Collapsars — the collapse of rapidly rotating massive stars that produce long gamma-ray bursts — are a potential contaminant in SGRB catalogs. Fishbach et al. (ApJL 1006, L49, 2026; arXiv:2604.05059) showed that after GWTC-4 the GW-inferred BNS rate is simultaneously a factor 3.6-18 below the beaming-corrected SGRB rate, a factor 0.9-4.1 below the rate needed for the Galactic heavy r-process inventory, and a factor 2.3-5.1 below the rate implied by the Galactic DNS population, and they stressed that each single-parameter fix is individually under strain: collapsar contamination large enough to absorb the SGRB discrepancy (roughly 70-90%) contradicts observed kilonova fractions and host-galaxy studies, jet opening angles of order 10 degrees or more are wider than most afterglow-inferred values, and strong redshift evolution of the merger rate, while helping the SGRB and r-process comparisons, worsens the DNS comparison. The unresolved target is therefore not any one discrepancy but a joint accounting problem: a single merger-rate budget, with its astrophysical parameters, consistent with all of these observables at once.

Problem Statement

Determine whether a single self-consistent neutron-star-merger rate budget — one consistent accounting of these four rates, with the neutron-star-merger population fixed by one set of physical parameters and not re-tuned per constraint — can simultaneously satisfy (i) the beaming-corrected short gamma-ray burst rate (including the possibility of collapsar contamination of the SGRB sample), (ii) the Milky Way's heavy r-process inventory given the ejecta mass per merger event, the Galactic star-formation history, and the cosmic delay-time distribution, (iii) the Galactic double-neutron-star merger rate after beaming and completeness corrections, and (iv) the inferred rates of low-mass binary neutron star and electromagnetically bright neutron-star-black-hole mergers. For (iv), Fishbach et al. define these subpopulations through GWTC-4 mass bins — BNS component masses between 1 and 2.6 solar masses, and EM-bright NSBHs with black-hole masses between 2.6 and 3.6 solar masses — and bound their rates from above rather than measuring them: a hidden population of very-low-mass BNSs (component masses around 1 solar mass or below) could raise the inferred BNS rate by at most a factor of about 2-3, and the EM-bright NSBH rate is at most about 50% of the BNS rate, so that the joint neutron-star-merger rate including EM-bright NSBHs is at most about 1.5 times the BNS rate. Constraint (iv) therefore requires the budget's low-mass BNS and EM-bright NSBH subpopulations to remain consistent with these GWTC-4-inferred rates and upper limits. If such a budget exists, identify which combination of physical parameters or channels delivers it — typical jet opening angles and jet-launching efficiencies, the true local SGRB rate, redshift evolution of the merger rate, a contaminating collapsar population, additional non-BNS progenitor channels for SGRBs, non-merger r-process production, or revised DNS beaming/completeness corrections — and quantify the allowed ranges of those parameters, including the bounds on any contribution from outside the neutron-star-merger population that the budget invokes. This is the joint reconciliation question posed in the Discussion and Conclusion of Fishbach et al. (ApJL 1006, L49, 2026), for which each single-parameter resolution is already known to be under strain.

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