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On Bimodality in the Eccentricity Distribution of Galactic Double Neutron Stars

This paper proposes that the observed bimodal eccentricity distribution in Galactic double neutron stars, characterized by a gap at intermediate values, can be naturally explained by a non-monotonic relationship between progenitor and neutron star masses combined with small natal kicks for the second-born neutron star, a scenario successfully reproduced by the COMPAS population synthesis code.

Original authors: Aldana Grichener, Paul Disberg, Ryosuke Hirai, Ilya Mandel

Published 2026-08-04

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CC BY 4.0

Original authors: Aldana Grichener, Paul Disberg, Ryosuke Hirai, Ilya Mandel

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 as a cosmic dance floor where stars are the dancers. Sometimes, two massive stars are born together, locked in a tight embrace, orbiting a shared center of gravity. As they age, they go through dramatic transformations: swelling into giant red monsters, shedding layers of their skin, and eventually, one or both of them might explode in a spectacular supernova, leaving behind a tiny, incredibly dense core called a neutron star. These neutron stars are like cosmic lighthouses, spinning so fast they beam radio waves across the galaxy. When two of them end up orbiting each other, they form a "double neutron star" system.

Scientists have been watching these cosmic couples for decades. They've noticed something strange about how they move. Most of these pairs orbit each other in nearly perfect circles, while others zoom around in very stretched-out, oval-shaped paths. But there's a weird gap in the middle: almost no pairs are found with a "medium" oval shape. It's as if the dance floor has a forbidden zone where no couples are allowed to spin. Understanding why this gap exists is like finding the missing piece of a puzzle that explains how stars live, die, and interact. If we can solve this, we learn more about the violent explosions that create these dense remnants and how gravity shapes the universe.

The Mystery of the Missing Middle

In a new study, a team of astronomers is proposing a clever explanation for this missing middle ground in the dance of double neutron stars. They suggest that the gap isn't random; it's the result of a specific "switch" in how stars turn into neutron stars, combined with a very gentle push during the final explosion.

To understand their idea, picture a factory that builds tiny, heavy weights (neutron stars) from larger blocks of material (progenitor stars). Usually, you'd expect that if you start with a slightly bigger block, you get a slightly heavier weight. It's a smooth, straight line. But this team suggests that for these specific stars, the factory has a glitch. There's a specific size of the starting block where the rules suddenly change. If the block is just a tiny bit smaller than this size, the factory produces a light weight. If it's just a tiny bit bigger, the factory suddenly produces a much heavier weight. There is no "medium" weight produced in between; the machine skips right over it.

The Gentle Push

Now, imagine the second star in the pair is about to explode. When it goes boom, it usually gets a violent kick, like a cannonball firing out of a cannon. This kick, along with the mass lost during the explosion, determines how oval the new orbit becomes.

The authors suggest that in these double neutron star systems, the second star gets a very small, almost non-existent kick. Because the kick is so weak, the shape of the orbit is almost entirely determined by how much mass was lost in the explosion. Here is where the "factory glitch" comes in:

If the star was just below the critical size, it loses a small amount of mass, resulting in a nearly circular orbit (low eccentricity).
If the star was just above the critical size, it loses a huge amount of mass, resulting in a very stretched-out orbit (high eccentricity).
Because the factory skips the "medium" size, it also skips the "medium" amount of mass loss. Consequently, it skips the "medium" oval shape.

This creates a natural gap in the data, perfectly matching the weird pattern astronomers see in the sky.

Testing the Theory

The researchers didn't just guess; they ran a massive computer simulation called COMPAS to see if this idea holds up. They programmed the simulation to use this "broken" factory rule (where the mass of the neutron star jumps suddenly) and gave the second exploding star almost zero kick.

The result? The simulation produced a population of double neutron stars that looked remarkably like the real ones we observe. It created two distinct groups: one with circular orbits and one with highly oval orbits, with a clear empty space in the middle where no systems existed. This matches the real-world data, which shows 21 systems with low eccentricities (less than 0.4) and eight with high eccentricities (greater than 0.58), but almost nothing in between.

What the Paper Says (and Doesn't Say)

The authors are careful to point out that this is a suggestion based on simulations, not a final proof. They explicitly argue against the idea that the gap is caused by a smooth, continuous relationship between star sizes and neutron star masses, which is what most previous models assumed. Those older models naturally produce a smooth range of orbits and cannot explain the gap.

They also note that this "gentle kick" scenario fits well with observations of a famous double pulsar system (J0737-3039), where the spin of the stars suggests the second explosion was very quiet. However, they acknowledge that other systems, like PSR B1534+12, might have had a slightly stronger kick, showing that nature might be a bit more complex than their simple model.

The Bottom Line

This paper suggests that the strange "missing middle" in the orbits of double neutron stars is likely a natural consequence of how massive stars collapse. If the relationship between a star's size and the neutron star it becomes has a sudden jump, and if the second explosion is gentle, the universe naturally sorts these pairs into two distinct groups, leaving the middle empty. While more observations are needed to confirm this, the model offers a beautiful, natural explanation for a cosmic mystery that has puzzled scientists for years. As the authors note, future telescopes and more data will be crucial to see if this "factory glitch" is the real reason behind the gap.

Technical Summary: On Bimodality in the Eccentricity Distribution of Galactic Double Neutron Stars

Problem Statement
Galactic double neutron star (DNS) systems, observed primarily through radio pulsar timing, exhibit an apparent bimodal distribution in orbital eccentricity. Current data indicates a population split between systems with low measured eccentricities ( $e_m \lesssim 0.4$ ) and those with high eccentricities ( $e_m \gtrsim 0.58$ ), with a notable absence of systems in the intermediate range ( $0.4 \lesssim e_m \lesssim 0.58$ ). Existing population synthesis models, which typically assume continuous distributions for progenitor masses and supernova (SN) natal kicks, naturally produce continuous eccentricity distributions and fail to reproduce this observed gap. The origin of this bimodality remains unexplained by standard isolated binary evolution scenarios.

Methodology
The authors propose a physical mechanism where the bimodality arises from two specific conditions:

Non-monotonic Progenitor-Remnant Mass Relation: A discontinuity or "break" in the relationship between the carbon-oxygen (CO) core mass of the second SN progenitor and the resulting neutron star (NS) mass. This is motivated by structural changes in pre-SN cores (e.g., transitions between convective and radiative carbon burning) and discrete composition-shell interfaces that can cause abrupt shifts in the effective mass cut.
Negligible Natal Kicks for the Second NS: The assumption that the second-born NS, formed via ultra-stripped supernovae (USSNe), receives a sufficiently small natal kick, such that the post-SN orbital eccentricity is dominated by the Blaauw kick (resulting from instantaneous mass loss).

To test this hypothesis, the authors utilized the population synthesis code COMPAS. They implemented the SN remnant mass prescription from Mandel & Müller (2020), which features a sharp break in the NS mass function at a CO core mass of $M_{\text{core}} \approx 3 M_\odot$ . They simulated a population of $10^6$ binaries with solar metallicity, drawing initial masses from the Kroupa initial mass function and mass ratios from a flat distribution. Crucially, they modeled the second SN as a USSN with zero natal kick velocity (Model M&M,0) to isolate the effect of the mass break on the Blaauw kick distribution.

Key Results

Reproduction of the Eccentricity Gap: The simulation successfully reproduced the observed bimodal eccentricity distribution. The break in the remnant mass function at $3 M_\odot$ $3 M_{⊙}$ creates two distinct branches of mass loss during the second SN:
- Progenitors just below the threshold ( $\sim 2.99 M_\odot$ ) lose $\lesssim 1.2 M_\odot$ , retaining a mass fraction $\beta \gtrsim 0.72$ , resulting in low eccentricities ( $e_b \lesssim 0.4$ ).
- Progenitors just above the threshold ( $\sim 3.01 M_\odot$ ) lose $\gtrsim 1.5 M_\odot$ , retaining $\beta \lesssim 0.64$ , resulting in high eccentricities ( $e_b \gtrsim 0.55$ ).
- This bifurcation naturally creates a gap in eccentricity space that aligns with the observed lack of systems between $0.4$ and $0.58$.
Orbital Period Distribution: The model also reproduces the observed orbital period–eccentricity distribution, including the scarcity of short-period systems, which the authors attribute to observational selection effects (e.g., difficulty detecting rapidly accelerating pulsars).
Mass Discrepancies: While the model matches the observed mass distribution in some regimes, it predicts a population of high-mass DNSs with short orbital periods that are not currently detected in radio surveys. The authors suggest these systems may merge too rapidly via gravitational wave emission to be observed as pulsars, or that their radio lifetimes are short.
Constraints on Natal Kicks: The study highlights that the system PSR J0737–3039 is consistent with a very small natal kick ( $\lesssim 35$ km s $^{-1}$ perpendicular to the orbit), supporting the USSN hypothesis. However, PSR B1534+12 shows a larger misalignment, suggesting that while kicks may generally be small, they are not universally negligible, and the mapping between kick magnitude and eccentricity can be direction-dependent.

Significance and Claims
The paper claims that the apparent bimodality in Galactic DNS eccentricities can be explained naturally within the framework of isolated binary evolution, without invoking exotic formation channels. The key insight is that a non-monotonic relationship between progenitor mass and NS mass, combined with weak natal kicks in ultra-stripped supernovae, generates a bimodal Blaauw kick distribution.

The authors maintain a modest stance regarding the statistical significance of the observed gap, noting that the current sample size (29 systems) is small and the gap's significance is not yet definitive (as discussed in their Appendix B). Consequently, they frame their work as a testable prediction: future detections of Galactic DNSs will either fill the intermediate eccentricity gap (refuting the model) or strengthen the evidence for bimodality (supporting the model). The study emphasizes that expanding the sample size with facilities like the SKA, improving mass measurements, and refining SN ejecta physics are necessary to robustly constrain the second SN kick distribution and validate this interpretation.

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