Constraining Binary Neutron Star Populations using Short Gamma-Ray Burst Observations

Alessio Ludovico De Santis; Filippo Santoliquido; Marica Branchesi; Samuele Ronchini

REVIEW 3 major objections 6 minor 7 cited by

Short gamma-ray bursts rule out low neutron-star merger rates as the sole source.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-02 23:32 UTC pith:DHVHLLQZ

load-bearing objection A careful population study whose rate floor is real but softer than the abstract claims: the low-rate disfavoring depends on an assumed Fermi-GBM efficiency that isn't marginalized. the 3 major comments →

arxiv 2602.13391 v1 pith:DHVHLLQZ submitted 2026-02-13 astro-ph.HE astro-ph.GA

Constraining Binary Neutron Star Populations using Short Gamma-Ray Burst Observations

Alessio Ludovico De Santis , Samuele Ronchini , Filippo Santoliquido , Marica Branchesi This is my paper

classification astro-ph.HE astro-ph.GA

keywords binary neutron star mergersshort gamma-ray burstsjet fractionpopulation synthesismerger rate densitygamma-ray burst jet structuremulti-messenger constraints

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper asks whether binary neutron star mergers alone can account for the population of short gamma-ray bursts observed over 16 years. It tests 64 population-synthesis models of BNS mergers, each predicting a merger rate and its cosmic history, against the observed burst rate and properties. The central result is a rate floor: models with a local merger rate below about 50 Gpc⁻³ yr⁻¹ would require more short bursts than mergers (jet fraction above unity) and are disfavored as sole progenitors. Models with a local rate near 100 Gpc⁻³ yr⁻¹ fit the data with a physically plausible jet fraction of about 0.7–0.8, implying most BNS mergers must launch successful relativistic jets. If right, gamma-ray observations give an independent lower bound on the BNS merger rate that complements gravitational-wave measurements.

Core claim

Under a universal structured jet calibrated to the first detected BNS merger, each of 64 population models is tested by inferring the jet fraction f_j needed to match the observed short-GRB sample. f_j falls below unity only for models with high intrinsic rates: models at R_BNS(0) ≲ 50 Gpc⁻³ yr⁻¹ need f_j > 1, while models near 100 Gpc⁻³ yr⁻¹ fit with f_j ≈ 0.7–0.8. Relaxing jet geometry does not remove this: low-rate models survive only with wide cores (≳15°), whereas afterglow measurements point to cores near 6°. The paper concludes that sGRB observations favor BNS models with local rates around 100 Gpc⁻³ yr⁻¹ and that most BNS mergers must launch jets.

What carries the argument

The central object is the jet fraction f_j = N_sGRB / N_BNS, the fraction of BNS mergers that successfully launch a detectable relativistic jet. The rate-matching equation (Eq. 7) treats f_j as a free parameter in an MCMC fit that requires each synthetic catalog to reproduce the observed burst rate and observable distributions; when the posterior demands f_j > 1, the BNS population is too sparse. A second key object is the minimum characteristic opening angle θ*, the narrowest jet geometry consistent with f_j ≤ 1, used to compare against afterglow-derived core angles.

Load-bearing premise

The result rests on the rate-matching equation's assumption that the entire burst-detection process is captured by a single efficiency factor of about 0.60 and that the typical short-GRB jet resembles the structured jet of the first confirmed BNS merger; if either is off by a factor of about two, the inferred jet fractions and the 50 Gpc⁻³ yr⁻¹ floor shift.

What would settle it

A future gravitational-wave catalog that robustly places the local BNS merger rate below 50 Gpc⁻³ yr⁻¹ while the short-GRB rate remains near 18.6 yr⁻¹ would falsify the paper's central claim, unless the short-GRB jet population turns out to be dominated by very wide cores (θ_c ≳ 15°), which would require a separate reconciliation with afterglow data.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

A lower bound on the local BNS merger rate near 50 Gpc⁻³ yr⁻¹ follows from gamma-ray observations alone, independent of gravitational-wave event counting.
Preferred models favor common-envelope efficiencies α_CE ≥ 1 and moderate natal kicks; low-α_CE and high-kick models are disfavored.
Jet fractions near 0.7–0.8 imply most BNS mergers launch successful jets, disfavoring scenarios in which prompt collapse to a black hole routinely suppresses jet formation.
Low-rate models are only rescued by wide jets (θ_c ≳ 15°), in tension with the narrow cores inferred from afterglows.
Future gravitational-wave constraints below ~50 Gpc⁻³ yr⁻¹ would sharpen the case for alternative sGRB progenitors such as neutron-star–black-hole mergers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the true detector efficiency is lower than the adopted 0.60, the inferred required rates would move upward, strengthening the floor; if higher, the floor could soften. The exact threshold depends on this single calibration factor.
A direct testable extension: if upcoming gravitational-wave runs measure the local BNS rate below ~50 Gpc⁻³ yr⁻¹ while the short-GRB rate stays near its current value, the paper's conclusion would point strongly to an additional progenitor channel or to systematically underestimated jet widths.
The framework could be applied to neutron-star–black-hole mergers as a second channel; adding them to low-rate BNS models would relax the f_j > 1 tension and provide a quantitative prediction for the NSBH jet fraction needed.
The inferred near-unity jet fraction implies a prediction for afterglow statistics: a large fraction of resolved BNS afterglow jets should show core angles near the value of the first detected BNS merger, rather than a broad distribution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

A careful population study whose rate floor is real but softer than the abstract claims: the low-rate disfavoring depends on an assumed Fermi-GBM efficiency that isn't marginalized.

read the letter

Quick take: the paper is worth serious referee time. It does a genuinely useful thing—takes 64 BNS population synthesis models, simulates sGRB catalogs under three jet geometries, and fits them to the Fermi-GBM sample. The conclusion that low local BNS rates (≲50 Gpc−3 yr−1) require f_j > 1 or very wide jets holds up in direction across the models tested. The quantitative floor is less secure than the abstract implies, because the f_j inference is tied to a fixed detector efficiency ε_GBM = 0.60 in Eq. 7. The stress-test note is right: if the true efficiency is 0.85, the floor drops by roughly a factor of two. The paper mentions this in caveats but doesn't propagate it. That said, the posterior for the fiducial model has f_j = 0.78 +0.61/−0.36, so f_j = 1 is inside the credible interval—the 'disfavored' language is doing more work than the posteriors support. And the non-universal models still lean on the afterglow-derived opening angle distribution (RE23) as the external anchor.

What's actually new: the 64-model grid with four α_CE values, the flat and log-normal non-universal jet treatments, and the θ* minimum-opening-angle metric. These go beyond the earlier Ronchini et al. framework, and the code is public. The posterior predictive check for the fiducial model reproduces the observed distributions, which is real evidence the machinery works.

Where it's soft: the central 'lower bound' is a restatement of the rate equation—f_j is fitted to the observed rate, so low-rate models are disfavored largely because f_j must exceed 1. That's circular in the sense that it tests the model's rate against an assumed efficiency and an assumed jet structure. The independent part is the geometric comparison: low-rate models need θ_c ≥ 15°, in tension with the ~6° median inferred from afterglows. That is the part worth defending, and it does seem stable across the three geometries.

My take: this is a solid, transparent population study that will be useful to the BNS/sGRB community, but the authors should soften the 'effectively disfavored' claim and either marginalize over ε_GBM or at least show how the floor shifts with it. As a referee I'd ask for that. As a reader, I'd cite it for the model grid and the geometry comparison, not for the rate floor.

Referee Report

3 major / 6 minor

Summary. The paper presents a Monte Carlo/MCMC framework (MAGGPY) that connects 64 binary neutron star (BNS) population synthesis models from Iorio et al. (2023) to the Fermi-GBM short gamma-ray burst (sGRB) sample accumulated over 16 years. For each BNS population and for three jet geometry scenarios — a universal structured jet calibrated to GW170817, a universal top-hat jet, and non-universal flat/log-normal distributions of core opening angles — the authors infer the jet launching fraction f_j and prompt emission parameters by matching both the observed sGRB rate and the distributions of fluence, peak flux, peak energy, and (for the structured model) T90. The central claim is that BNS populations with local merger rates R_BNS(0) ≲ 50 Gpc⁻³ yr⁻¹ are disfavored as sole sGRB progenitors because they require unphysical f_j > 1 or jet opening angles in tension with afterglow data, while models with R_BNS(0) ≈ 100 Gpc⁻³ yr⁻¹ reproduce the observations with f_j ≈ 0.7–0.8. The paper also compares inferred sGRB local rates and BNS delay-time distributions with recent literature.

Significance. If the central claim holds, the paper provides a purely electromagnetic lower bound on the local BNS merger rate, complementing the gravitational-wave upper limits, and it constrains the jet launching efficiency of BNS mergers. The analysis is unusually systematic for this problem: 64 population synthesis models, three jet geometries, posterior predictive checks (Fig. D.1), and a public code (MAGGPY) are strong assets. The direction of the rate–geometry tension appears robust across jet models. However, the quantitative lower bound (R_BNS(0) ≲ 50 Gpc⁻³ yr⁻¹) is sensitive to a single fixed detector efficiency factor, and the use of f_j > 1 as a disfavored-model diagnostic is partly circular with the rate-matching equation. The external comparison with afterglow opening angles, rather than the f_j > 1 criterion alone, is the most informative independent element.

major comments (3)

[Sec. 2.2, Eq. (7); Sec. 4.3] The predicted rate is directly proportional to the fixed detector/efficiency factor ε_GBM ≈ 0.60, so the inferred f_j is inversely proportional to ε_GBM. No uncertainty on ε_GBM is propagated into the MCMC or into the quoted floor R_BNS(0) ≲ 50 Gpc⁻³ yr⁻¹. For a low-rate model whose median f_j is ~1.5 (Fig. 2), a plausible upward revision of ε_GBM by 40% (0.6→0.85) lowers the median f_j to ~1.06, moving that model across the physicality boundary. The manuscript's own caveat in Sec. 4.3 acknowledges ε_GBM is an approximation, but the effect is load-bearing for the central quantitative claim. I recommend sampling over a prior on ε_GBM (e.g. 0.4–0.85) or presenting the floor as a function of ε_GBM. As written, the lower bound is not robust to a single nuisance parameter.
[Sec. 3.1, Sec. 2.2, Appendix E] The f_j posterior is essentially fixed by matching the observed Fermi-GBM rate through Eq. (7): R_obs = ε_GBM f_j ∫Φ R(z)/(1+z) dV/dz. Thus stating that low-rate models are disfavored because their f_j posterior lies above unity is, to first order, a restatement of the rate equation. The independent informative content comes from (i) the distributional fit (CvM statistics) and (ii) the comparison of the required opening angles θ* with afterglow-based opening angles (Rouco Escorial et al. 2023). The claim 'effectively disfavoring them as sole progenitors' in the abstract and Sec. 3.1 is therefore overreaching unless the rate-normalization dependence is explicitly de-emphasized or the analysis is reframed as conditional on the rate equation and the external geometry anchor. I am not asking to remove the f_j diagnostic, but the paper should state this circularity and present the θ* comparis
[Sec. 3.1, Appendix G, Table D.1] The physicality criterion 'median f_j ≤ 1' (≡ P(f_j≤1) ≥ 0.5) is an ad hoc threshold. The fiducial structured jet posterior, f_j = 0.78 +0.61 −0.36, has a substantial tail above 1, and for low-rate models the classification between 'physical' and 'non-physical' is based on the median crossing unity. This binary classification is sensitive to the prior upper bound (U(0,10)) and to statistical noise in the MCMC chains. The 'conservative lower bound' at R_BNS(0) ≈ 50 Gpc⁻³ yr⁻¹ is not derived from a formal model-selection statistic. I recommend reporting a more robust measure, e.g. the posterior probability P(f_j > 1) or a Bayes factor between physical and unphysical priors, and quoting the uncertainty in the threshold itself. Without this, Table G.1 and the associated summary overstate the precision of the constraint.

minor comments (6)

[Sec. 2.4] Typo: 'thourough' should be 'thorough'.
[Sec. 2.6] Typo: 'All parameters and their priors are are detailed' — duplicate 'are'.
[Appendix C, Table C.1] The row labeled 'LK, LC, LK' appears to contain a typo; the text describes LK, LC, and LX, so the third acronym should likely be 'LX'.
[Sec. 2.5] The MAGGPY code link (https://github.com/LudoDe/gwpop_LudoDe) does not match the repository name MAGGPY; please verify and include the correct URL.
[Eq. (7)–(8)] The symbol R(z) is used in Eq. (7) but R_BNS(z) in Eq. (8); please make the notation consistent.
[Various] Minor wording: 'a non-physical' should be 'a nonphysical' (or 'an unphysical'), and 'comparitively' in Sec. 4.3 should be 'comparatively'.

Circularity Check

0 steps flagged

No significant circularity: the f_j rate-matching is transparent and the afterglow opening-angle comparison is an external anchor.

full rationale

The paper's derivation chain is self-contained rather than circular. It takes externally computed BNS merger-rate histories from Iorio et al. (2023), combines them with explicit jet-emission models, generates synthetic Fermi-GBM catalogs, and then fits the jet fraction f_j (together with spectral/temporal parameters) to the observed sGRB rate and distributions via Eq. (7) and the likelihood in Eq. (17). The central claim that low-rate models require f_j>1 is a direct consequence of solving Eq. (7) for f_j with the observed rate fixed; this is a legitimate physical consistency test, not a hidden re-importation of the conclusion. The later comparison of the required minimum opening angle theta* with the afterglow-based opening-angle distribution of Rouco Escorial et al. (2023) uses an external data set that was not fit in the MCMC, so it provides independent leverage. The self-citations to Ronchini et al. (2022) and to the population-synthesis/cosmoRate infrastructure are methodological and are backed by code and external calibrations (e.g., Ghirlanda et al. 2019), so they are not load-bearing in a circular sense. The paper itself flags the main fragility in Sec. 4.3: epsilon_GBM is an approximation and its uncertainty is not propagated, and the universal structured jet is an assumption. These are genuine systematic-uncertainty limitations that affect the numerical value of the R_BNS floor, but they do not make the derivation circular. The abstract's wording 'predict too few observable sGRBs' is loose, because the model is calibrated to the observed rate through f_j, but the paper consistently defines f_j as a free physical parameter and uses f_j>1 only as a diagnostic for model viability; this is algebra, not circularity. Overall score 0.

Axiom & Free-Parameter Ledger

10 free parameters · 8 axioms · 0 invented entities

The central inference requires the 64 BNS rate histories from Iorio et al. (2023), a fixed Fermi-GBM efficiency factor, and a suite of emission-model parameters fitted to the data; no new physical entities are introduced.

free parameters (10)

f_j (jet launching fraction) = posterior median 0.78 for fiducial structured jet; prior U(0,10)
Free parameter set by matching the observed Fermi-GBM rate; f_j > 1 is used as a non-physical diagnostic.
k (energy/luminosity power-law index) = fiducial structured posterior median 5.23
Shape of the total radiated energy or luminosity distribution; fitted to observed fluence/flux distributions.
log10(E*/erg) (structured jet cutoff) = fiducial posterior median log10(E*/1e49 erg) ≈ -0.75
Characteristic low-energy cutoff of the radiated energy distribution in the structured jet model.
log10(μ_E/keV) = fiducial posterior median 3.48
Median rest-frame peak energy of the νFν spectrum.
σ_E = fiducial posterior median 0.39
Log-normal spread of the peak energy distribution.
log10(μ_t/s) = fiducial posterior median -0.50
Median peak time of the burst in the structured jet model.
σ_t = fiducial posterior median 0.76
Log-normal spread of the peak time distribution.
log10(L*/erg s−1) (top-hat luminosity cutoff) = fiducial top-hat posterior median log10(L*/1e49 erg s−1) ≈ 3.23
Characteristic luminosity cutoff in the top-hat jet models.
θ_c (universal top-hat core opening angle) = fiducial posterior median 2.74° with broad 90% interval
Core opening angle in the universal top-hat model; sampled to explore the degeneracy with f_j.
θ_max^c or θ_med^c (non-universal geometry parameter) = posterior distribution, no single value
Hyperparameter for the flat or log-normal distribution of core opening angles in the non-universal models.

axioms (8)

domain assumption The SEVN population-synthesis catalogs and cosmoRate merger-rate calculations from Iorio et al. (2023) correctly describe BNS formation and merger rate histories.
All 64 BNS rate histories are taken from these catalogs; errors in binary evolution modeling propagate directly into f_j and the R_BNS floor.
domain assumption The Madau & Fragos (2017) star-formation rate and the log-normal metallicity distribution adequately describe the cosmic environment of BNS progenitors.
Used in Eq. (12)–(15) to compute cosmic merger rates; a different SFR/metallicity evolution would shift the rate histories.
domain assumption Fermi-GBM detection efficiency and field-of-view are summarized by the single factor ε_GBM ≈ 0.60.
Eq. (7) uses this factor to convert intrinsic rates to detected rates; the paper does not propagate its uncertainty.
domain assumption In the fiducial scenario, all sGRBs have the universal structured jet profile calibrated to GW170817 (θc = 3.4°, Γc = 500, s1 = s2 = 4).
Section 2.3 fixes these parameters from Ghirlanda et al. (2019); they are not marginalized in the structured-jet results.
domain assumption The prompt spectrum is a Smoothly Broken Power Law with fixed indices α = −2/3, β_s = −2.6, and smoothness n = 2.
Section 2.1 fixes the spectral shape based on Ravasio et al. (2019) and Rudolph et al. (2024); alternative spectral models could affect the derived E_p and flux distributions.
domain assumption The observed sGRB population is produced entirely by BNS mergers, with negligible contribution from NSBH mergers or collapsars.
This is the hypothesis under test, but it is built into Eq. (6)–(7) and is required for interpreting f_j > 1 as evidence against the BNS-only hypothesis.
ad hoc to paper A BNS population is 'physical' if the median of its fitted f_j posterior is ≤ 1.
Section 3.1 defines physical viability via P(f_j ≤ 1) ≥ 0.5; this is a diagnostic choice, not an observational constraint.
ad hoc to paper Non-universal opening-angle distributions: flat U(1°, θ_max^c) and log-normal with fixed σ_log10 = 0.5, truncated to [1°, 45°].
Section 2.3 introduces these population models as representative diversity; the log-normal width is fixed by hand.

pith-pipeline@v1.3.0-alltime-deepseek · 31835 in / 15448 out tokens · 138510 ms · 2026-08-02T23:32:23.452092+00:00 · methodology

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read the original abstract

The landmark multi-messenger observations of the binary neutron star (BNS) merger GW170817 provided firm evidence that such mergers can produce short gamma-ray bursts (sGRBs). However, the limited number of BNS detections by current gravitational-wave (GW) observatories raises the question of whether BNS mergers alone can account for the full observed sGRB population. We analyze a comprehensive set of 64 BNS population synthesis models with a Monte Carlo-based framework to reproduce the properties of sGRBs detected by Fermi-GBM over the past 16 years. We consider three jet geometry scenarios: a universal structured jet calibrated to GW170817, a universal top-hat jet, and a non-universal top-hat jet with distributions of core opening angles. Our results show that models characterized by low local BNS merger rates ($R_{BNS}(0) \lesssim 50$ Gpc$^{-3}$ yr$^{-1}$) predict too few observable sGRBs to reproduce the Fermi-GBM population, effectively disfavoring them as sole progenitors. Even when relaxing assumptions on jet geometry, low-rate models remain viable only for wide jets ($\theta_c \ge 15^\circ$), in tension with the narrow jet cores ($\theta_c \approx 6^\circ$) inferred from sGRB afterglow observations. In contrast, models with local merger rates of order $R_{BNS}(0) \approx 100$ Gpc$^{-3}$ yr$^{-1}$ successfully reproduce the observed sGRB population, assuming a plausible fraction of BNS mergers launch relativistic jets and realistic jet geometries. This analysis highlights the power of combining GW observations of BNS mergers with electromagnetic observations of sGRBs to place robust constraints on the BNS merger population and to assess their role as progenitors of sGRBs.

Figures

Figures reproduced from arXiv: 2602.13391 by Alessio Ludovico De Santis, Filippo Santoliquido, Marica Branchesi, Samuele Ronchini.

**Figure 2.** Figure 2: Jet fraction statistics for the universal structured jet model assuming the GW170817 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 4.** Figure 4: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Same as the bottom row of Fig [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: Two dimensional marginal posterior distribution [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: Minimum characteristic jet opening angle, [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

**Figure 8.** Figure 8: Left: Inferred intrinsic local sGRB rate RsGRB for all those BNS population models that allow physical jet fractions (with median fj ≤ 1), under the assumption of a universal structured jet. Right: Comparison of the inferred fj posterior distributions for the fiducial BNS population across the four analyzed jet structures: universal structured, universal top-hat, non-universal flat, and non-universal log-n… view at source ↗

**Figure 9.** Figure 9: Average delay time ⟨τd⟩ for each of the 64 BNS population models compared to the median and 90% credible intervals inferred in Pracchia & Salafia (2026). The blue and red lines and ranges correspond to two models by Pracchia & Salafia (2026): a quasi-universal structured jet (QUSJ) model and an empirical luminosity function (ELF) model, respectively. To highlight the relationship between delay times and mo… view at source ↗

discussion (0)

Forward citations

Cited by 7 Pith papers

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Reference graph

Works this paper leans on

6 extracted references · 1 linked inside Pith · cited by 6 Pith papers

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Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017a, ApJ, 848, L13 Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017b, Phys. Rev. Lett., 119, 161101 Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017c, Astrophys. J. Lett., 848, L13 Aghanim, N. et al. 2020, A&A, 641, A6, [Erratum: A&A 652, C4 (2021)] Ascenzi, S., Oganesyan, G., Salafia, O. S., et...

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by preventing collisions in eccentric orbits. Notes.All models listed above are combined with four variations of the common envelope efficiency parameter, αCE∈{ 0.5, 1.0, 3.0, 5.0}, resulting in the 64 total populations analyzed in this work. chain length to be at least 50 times greater thanτ, a criterion typi- cally satisfied within 30,000 to 40,000 iter...

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In contrast, models with higher intrinsic rates find their optimal f j well within the physical boundary. Fig. E.1 illustrates this effect for the universal structured jet. With an unbounded prior, the median f j continuously rises as the BNS rate decreases. This allows us to distinguish between a model that requires f j≈ 1 (corresponding to a physical sc...

2023
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Plots with erratic spikes have a very small number of mergers

assuming the universal structured jet compared to the median and 90% credible intervals inferred in Pracchia & Salafia (2026). Plots with erratic spikes have a very small number of mergers. See Table C.1 for a description of each model variation (top right of each plot). See Fig. H.2 for non physical populations. For consistency with Fig. H.2 we keep the ...

2026
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QCBB Alternative Stability Assumes mass transfer from pure-Helium stars is always stable

as giant donors undergo unstable transfer and merge prematurely. QCBB Alternative Stability Assumes mass transfer from pure-Helium stars is always stable. This avoids for some stars a final, often fatal Common Envelope phase where they would otherwise merge prematurely, allowing more systems to survive and eventually merge as BNSs. RBSE Accretion Efficien...

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Universal top-hat Non-univ

Analogously, for both Flat and Log-Normal structures, we fix the median of theθ c distribution at 6.1 deg . Universal top-hat Non-univ. flat Non-univ. log-normal Universal structured αCE 0.5 1.0 3.0 5.0 0.5 1.0 3.0 5.0 0.5 1.0 3.0 5.0 0.5 1.0 3.0 5.0 F ×a ✓ ✓× ×✓ ✓× ✓ ✓ ✓ ✓ ×✓ ✓× K265 ×a × × × a × × × × ✓b ✓ ✓ ✓ b × × × × K150 × ×✓× × × × × ✓ ✓ ✓ ✓ × × × ...

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by preventing collisions in eccentric orbits. Notes.All models listed above are combined with four variations of the common envelope efficiency parameter, αCE∈{ 0.5, 1.0, 3.0, 5.0}, resulting in the 64 total populations analyzed in this work. chain length to be at least 50 times greater thanτ, a criterion typi- cally satisfied within 30,000 to 40,000 iter...

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In contrast, models with higher intrinsic rates find their optimal f j well within the physical boundary. Fig. E.1 illustrates this effect for the universal structured jet. With an unbounded prior, the median f j continuously rises as the BNS rate decreases. This allows us to distinguish between a model that requires f j≈ 1 (corresponding to a physical sc...

2023

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Plots with erratic spikes have a very small number of mergers

assuming the universal structured jet compared to the median and 90% credible intervals inferred in Pracchia & Salafia (2026). Plots with erratic spikes have a very small number of mergers. See Table C.1 for a description of each model variation (top right of each plot). See Fig. H.2 for non physical populations. For consistency with Fig. H.2 we keep the ...

2026

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QCBB Alternative Stability Assumes mass transfer from pure-Helium stars is always stable

as giant donors undergo unstable transfer and merge prematurely. QCBB Alternative Stability Assumes mass transfer from pure-Helium stars is always stable. This avoids for some stars a final, often fatal Common Envelope phase where they would otherwise merge prematurely, allowing more systems to survive and eventually merge as BNSs. RBSE Accretion Efficien...

2010

[6] [2023]

Universal top-hat Non-univ

Analogously, for both Flat and Log-Normal structures, we fix the median of theθ c distribution at 6.1 deg . Universal top-hat Non-univ. flat Non-univ. log-normal Universal structured αCE 0.5 1.0 3.0 5.0 0.5 1.0 3.0 5.0 0.5 1.0 3.0 5.0 0.5 1.0 3.0 5.0 F ×a ✓ ✓× ×✓ ✓× ✓ ✓ ✓ ✓ ×✓ ✓× K265 ×a × × × a × × × × ✓b ✓ ✓ ✓ b × × × × K150 × ×✓× × × × × ✓ ✓ ✓ ✓ × × × ...

2023