🔭 astrophysics

Wide Jets or Low Rates: Reconciling Short GRB and Gravitational-Wave Neutron Star Merger Rates

This paper demonstrates that the observed rates of short gamma-ray bursts and gravitational-wave-detected binary neutron star mergers can be reconciled if a significant fraction of bursts originate from mergers with relatively wide jets ( $\theta_j \geq 10^\circ$ ) or if the local burst rate density is on the lower end of current estimates, while confirming that binary neutron star mergers remain the primary progenitors over neutron star-black hole mergers.

Original authors: Keerthi Kunnumkai, Antonella Palmese, Brendan O'Connor, Amanda Farah, Ignacio Magana Hernandez

Published 2026-04-08

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CC BY 4.0

Original authors: Keerthi Kunnumkai, Antonella Palmese, Brendan O'Connor, Amanda Farah, Ignacio Magana Hernandez

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is a giant, dark ocean, and every now and then, two massive ships crash into each other. When these ships—made of incredibly dense matter like neutron stars or black holes—collide, they sometimes shoot out a massive, high-speed laser beam of energy. We call these flashes Short Gamma-Ray Bursts (sGRBs).

For a long time, scientists have been trying to solve a cosmic mystery: How often do these crashes happen, and how wide are those laser beams?

This paper is like a detective story trying to reconcile two different sets of clues that seem to contradict each other.

The Two Clues

The "Flash" Clue (Gamma-Ray Bursts):
Astronomers look at the sky and count how many of these laser flashes they see. Based on how bright they are, they try to guess how many crashes are happening in the whole universe. Some estimates suggest a wide range, from about 1 to as high as 13 crashes per cubic billion light-years every year.
- The Problem: If there are that many crashes (especially at the high end), but we only see a few flashes, the laser beams must be incredibly narrow (like a tiny needle) so that we only catch them when we are standing directly in front of them.
The "Rumble" Clue (Gravitational Waves):
Recently, we built giant ears (LIGO/Virgo) that can "hear" the ripples in space-time caused by these crashes. In the latest "listening session" (called O4), they heard very few crashes compared to what the "Flash" clues suggested.
- The Problem: If the "Rumble" count is low, but the "Flash" count is high, something doesn't add up. Either we are missing a lot of flashes, or our math about the laser beams is wrong.

The Investigation: What's Going On?

The authors of this paper asked: "Can we make these two clues fit together?"

They tested two main theories:

Theory 1: The "Wide Beam" Hypothesis

Maybe the laser beams aren't thin needles; maybe they are wide floodlights.

The Analogy: Imagine a lighthouse. If it has a narrow beam, you only see it if you are right in front of it. If it has a wide beam, you can see it from far away on the side.
The Result: If the beams are wide (about 10 to 25 degrees wide), then we don't need as many crashes to explain all the flashes we see. This fits the "Rumble" data (low crash count) with the "Flash" data (high flash count).
The Catch: Most previous studies of these bursts suggested the beams are actually quite narrow. For the narrow jet scenario, the key finding is that the beams can be as tight as about 3 degrees. So, this theory requires us to rethink how these lasers work if we want to keep the high crash counts.

Theory 2: The "Low Count" Hypothesis

Maybe we were overestimating how many flashes happen.

The Analogy: Imagine you are counting cars on a highway. If you only count the ones that zoom past your window, you might think there are fewer cars than there actually are. But if you realize you missed a bunch of cars because they were too far away, or if you misread their speed, you might lower your estimate of the total traffic.
The Result: If the actual number of flashes is lower (closer to the bottom of the range, around 1 to 3 per billion light-years), then the "Rumble" data (low crash count) and the "Flash" data match perfectly with the old idea that the beams are narrow.
The Catch: This depends on how we count the flashes. The discrepancy isn't just about one specific event; it's often driven by overestimating the total rate in previous studies. This happens when scientists incorrectly assign distances to the flashes or fail to account for how the rate of crashes changes over time in the universe.

The "Sidekick" Characters: Black Holes and Neutron Stars

The paper also looked at a second type of crash: a Neutron Star hitting a Black Hole.

The Analogy: Think of the main crash (Neutron Star + Neutron Star) as the "Main Course" of the dinner party. The Black Hole crash is the "Appetizer."
The Result: The authors found that while Black Hole crashes can produce flashes, they are rare and usually don't make a big enough splash to solve the mystery. They might make up about 6% to 16% of the flashes, but they cannot resolve the tension regardless of how high or low we assume the total crash rate to be.

The Big Takeaway

The paper concludes that the universe is likely consistent; we just need to choose the right interpretation of our data:

If the laser beams are wide: Then the number of crashes matches the "Rumble" data, but we have to accept that the beams are wider than we thought.
If the laser beams are narrow: Then the number of flashes must be lower than some previous estimates suggested. This happens if we correct for errors in how we count flashes, such as misjudging their distances or how their frequency changes over time.

In simple terms: The universe isn't broken. It's just that our "flash count" and our "rumble count" are speaking different languages. Once we translate them correctly—either by admitting the beams are wider or that the flashes are fewer—we find that neutron star crashes are indeed the main cause of these cosmic fireworks, and everything fits together nicely.

1. Problem Statement

The paper addresses a growing tension between two independent observational datasets regarding compact object mergers:

Gravitational Wave (GW) Constraints: The LIGO/Virgo/KAGRA (LVK) collaboration's fourth observing run (O4) has yielded a significantly lower inferred local binary neutron star (BNS) merger rate ( $R_{BNS}$ ) compared to previous runs (GWTC-3), largely due to the lack of new high-significance BNS detections. The rescaled rate is approximately $39^{+70}_{-29} \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ .
Short Gamma-Ray Burst (sGRB) Rates: Empirical estimates of the local on-axis sGRB rate density ( $R_{sGRB}$ ) vary widely in the literature, ranging from $\sim 1$ to $\sim 13 \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ . The Coward et al. (2012) rate is $8^{+5}_{-3} \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ , where 8 is the median and the upper $1\sigma$ bound reaches $\sim 13$ .

The Core Conflict: If sGRBs are produced by BNS mergers, the observed sGRB rate must be reconciled with the GW-inferred merger rate. This reconciliation depends on two unknown parameters:

Jet Launching Fraction ( $f_s$ ): The fraction of mergers that successfully produce a relativistic jet.
Jet Opening Angle ( $\theta_j$ ): The half-opening angle of the jet, which determines the geometric beaming fraction ( $\eta = 1 - \cos \theta_j$ ).

The authors investigate whether the current LVK rate constraints can explain the observed sGRB population under different assumptions about jet geometry and efficiency, and whether Neutron Star-Black Hole (NSBH) mergers or other channels can resolve discrepancies.

2. Methodology

The authors employ a Bayesian inference framework to relate the observed sGRB rate to intrinsic merger rates.

Data Inputs:
- GW Rates: Utilizes the FullPop-4.0 population model from GWTC-4. The BNS rate is rescaled by a factor $B=0.44$ to account for the null detection of high-significance BNS events during O4, resulting in $R_{BNS} \approx 39^{+70}_{-29} \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ . The NSBH rate is taken directly as $R_{NSBH} \approx 23^{+20}_{-13} \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ .
- sGRB Rates: Tests three distinct local sGRB rate densities ( $\lambda_{sGRB}$ $λ_{s GR B}$ ) representing the literature spread:
  1. Optimistic/High: $8 \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ (based on Coward et al. 2012, including GRB 080905A).
  2. Intermediate: $3 \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ (Coward et al. 2012 excluding GRB 080905A).
  3. Conservative/Low: $1 \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ (based on Ghirlanda et al. 2016; Salafia et al. 2023).
Models:
- Scenario 1 (BNS Only): Assumes all sGRBs originate from BNS mergers.
- Scenario 2 (BNS + NSBH): Assumes sGRBs originate from both BNS and NSBH mergers.
- Jet Physics: Assumes "top-hat" jet geometry. The authors simulate astrophysical populations using GWTC-4 priors to constrain the maximum possible jet-launching fractions ( $f_s$ ) based on remnant outcomes (e.g., prompt collapse vs. long-lived neutron stars).
Inference: Uses nested sampling (dynesty) to derive posterior distributions for jet opening angles ( $\theta_j$ ) and launching fractions ( $f_s$ ) given the observed rates and GW priors.

3. Key Contributions

Updated Rate Constraints: The first analysis to incorporate the specific non-detection of BNS mergers in the full O4 run, significantly tightening the upper bounds on the intrinsic BNS rate compared to GWTC-3 analyses.
Systematic Comparison: A rigorous comparison of how different sGRB rate estimates (ranging from 1 to 13) impact the required jet physics, specifically testing the "Wide Jet" vs. "Low Rate" hypothesis.
NSBH Contribution Quantification: Provides a quantitative assessment of the NSBH contribution to the sGRB population, demonstrating that despite theoretical plausibility, their volumetric rate and tidal disruption constraints limit their impact on the total sGRB budget.
Bias Analysis: Investigates systematic uncertainties, including the selection bias against detecting wide jets in afterglow studies and the impact of redshift misidentification and evolution.

4. Key Results

A. Reconciling High sGRB Rates ( $\lambda \approx 8$ )

Requirement for Wide Jets: To match a high sGRB rate of $8 \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ with the current low GW BNS rate, the model requires very wide jets ( $\theta_{BNS} \sim 25^\circ$ ) and high launching efficiencies ( $f_s \sim 0.73$ ).
Tension: These wide angles are inconsistent with standard afterglow modeling, which typically infers narrow jets ( $\theta \sim 6^\circ - 10^\circ$ ). Even with wide jets, the required BNS merger rate is pushed to the very upper edge of the GWTC-4 credible interval.

B. Reconciling Low sGRB Rates ( $\lambda \approx 1 - 3$ )

Consistency: If the true local sGRB rate is lower ( $\sim 1 - 3 \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ ), the tension disappears.
Narrow Jets Allowed: In this regime, the inferred jet opening angles have a lower limit of $\theta_{BNS} \approx 3^\circ$ (from the $1\sigma$ credible interval), with median values ranging from $\sim 12^\circ$ to $\sim 19^\circ$ . These values are consistent with both the current GW merger rates and standard afterglow constraints.
Implication: The discrepancy is likely driven by an overestimation of the local sGRB rate in some literature, often due to incorrect redshift assignments and not correctly accounting for the redshift evolution of rates, rather than a failure of the merger model.

C. Role of NSBH Mergers

Subdominant Contribution: NSBH mergers contribute only a small fraction to the total sGRB population.
- At $\lambda = 8$ : NSBH contribution $\approx 1.6\%$ .
- At $\lambda = 1$ : NSBH contribution $\approx 16\%$ .
Inability to Resolve Tension: Even with optimistic assumptions for NSBH jet launching ( $f_{s,NSBH} \approx 0.23$ ), NSBH mergers cannot bridge the gap between high sGRB rates ( $>7$ ) and the current GW BNS rate constraints. They cannot replace the need for BNS mergers as the primary progenitors.

D. Systematic Uncertainties

Jet Break Bias: The paper highlights that afterglow studies often miss wide jets because their breaks occur later and at lower fluxes. If the true population includes a significant fraction of wide jets (as suggested by "mock" samples in literature), the GW rate constraints could accommodate sGRB rates up to $\sim 7 \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ .
Redshift Errors: The rate estimate is highly sensitive to the redshift of nearby bursts. The exclusion of GRB 080905A (due to uncertain host association) drops the inferred rate from 8 to 3, significantly altering the physical requirements.

5. Significance and Conclusion

The paper concludes that current GW and sGRB observations remain broadly consistent with BNS mergers being the primary progenitors of short GRBs, provided that:

The true local sGRB rate density is on the lower end of current estimates ( $\sim 1 - 3 \, \text{Gpc}^{-3} \, \text{yr}^{-1}$ ), or
The sGRB population contains a significant fraction of wide jets ( $\theta_j \gtrsim 10^\circ$ ) that are underrepresented in current afterglow samples.

The authors argue that invoking additional progenitor channels (like NSBH or white dwarf mergers) is unnecessary to explain the rates and that NSBH mergers alone cannot resolve the tension regardless of the sGRB rates assumed. The results suggest that the "tension" is likely a result of systematic uncertainties in sGRB rate estimation and jet selection bias rather than a fundamental flaw in the compact merger paradigm. Future multi-messenger detections in upcoming LVK runs will be crucial to definitively constrain the jet opening angle distribution and the NSBH contribution.