🔭 astrophysics

Binary neutron star populations across cosmic time: the impact of binary stellar evolution uncertainties

This study systematically explores 72 binary stellar evolution models to demonstrate that uncertainties in common-envelope efficiency and natal kicks dominate the predicted binary neutron star merger rates and formation efficiencies across cosmic time, creating significant degeneracies that current gravitational-wave observations cannot resolve but future third-generation detectors may help break.

Original authors: Mathieu Venet, Irina Dvorkin

Published 2026-07-31

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Mathieu Venet, Irina Dvorkin

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

The Cosmic Dance of Dead Stars

Imagine the universe as a giant, chaotic ballroom where stars are the dancers. Most stars dance alone, but some are born as pairs, holding hands and spinning around a common center. When these pairs are massive enough, they eventually run out of fuel, collapse, and explode in spectacular supernovas. If they survive the explosion without flying apart, they become neutron stars—city-sized spheres of matter so dense that a teaspoon would weigh a billion tons. Sometimes, these two neutron stars remain locked in a tight orbit, spiraling closer and closer until they crash into each other. This collision is one of the most violent events in the cosmos, sending ripples through space-time called gravitational waves and forging heavy elements like gold and platinum.

For a long time, we only knew about a handful of these "binary neutron star" couples in our own galaxy, and we had just spotted two of them crashing in the entire history of gravitational-wave detection. But the future is about to get much louder. New telescopes and detectors are coming online that will hear thousands of these cosmic crashes every year. The big question for scientists is: How do these pairs form in the first place? It's a complex puzzle involving how stars lose mass, how they interact when they get too close, and how the "kick" from a supernova explosion might fling them apart. To solve this, astronomers use supercomputer simulations that act like a cosmic time machine, running millions of scenarios to see which rules of physics produce the couples we see today.

The Great Cosmic Simulation

In this paper, authors Mathieu Venet and Irina Dvorkin decided to play a massive game of "what if" with these cosmic couples. They used a powerful computer program called COSMIC to simulate the lives of binary stars across the history of the universe. Think of it as running a video game where you can tweak the physics engine to see how the story changes. They didn't just run one game; they ran 72 different versions, changing four specific "knobs" that control the most uncertain parts of the story: how stars decide to swap mass, how efficiently they can shed their outer layers, how hard the newborn neutron stars get kicked, and when exactly those kicks happen.

They ran these simulations across 20 different metallicity bins (a measure of how "heavy" the elements in the stars are, ranging from very primitive, metal-poor stars to modern, metal-rich ones) to see how the environment affects the outcome. Their goal was to figure out if there are any universal signs in the data that tell us exactly how these stars evolve, or if the uncertainties are so huge that we can't tell one scenario from another.

The Two Paths to a Crash

One of the most striking things the team found is that binary neutron stars don't all come from the same recipe. Instead, they found a bimodal distribution, which means the stars fall into two distinct groups with a "desert" in the middle.

Imagine a bakery that makes two very different types of cakes. One type is made from smaller, lighter ingredients that go through a gentle, stable process. The other type uses huge, heavy ingredients that must go through a chaotic, messy phase to shrink down to the right size.

The Low-Mass Group: These stars are lighter (around 6.5 to 9 times the mass of our Sun). They tend to have a smoother evolution, often skipping the messy "common envelope" phase where one star swallows the other. They usually explode as a specific type of supernova that gives a gentle "nudge" rather than a violent kick, helping the pair stay together.
The High-Mass Group: These are the heavyweights (10 to 30 solar masses). To become neutron stars instead of black holes, they must go through a chaotic "common envelope" phase. This is like a cosmic hug where the two stars get tangled, and the outer layers of the giant star are ejected. This process shrinks their orbit dramatically, which is crucial because it helps them survive the violent kicks from their explosions.

The "desert" between them (roughly 7 to 10 solar masses) is a dangerous zone. Stars in this range are too heavy to get the gentle nudge of the low-mass group, but they aren't heavy enough to survive the chaotic shrinkage of the high-mass group. They usually get kicked apart and never become a binary neutron star.

The Uncertainty Knobs

The authors discovered that while the types of stars are consistent, the number of them depends entirely on how you set the physics knobs. The two biggest factors are:

The Kick Prescription (KICKFLAG): This controls how hard the newborn neutron star is kicked when it's born. If the kick is too strong (the standard setting), most pairs fly apart. If the kick is weaker or depends on the mass of the star (a newer setting), many more pairs survive. This single change can alter the number of binary neutron stars by several orders of magnitude.
The Common Envelope Efficiency (ALPHA): This controls how much energy is needed to blow off the outer layers of a star during that chaotic "hug" phase. If the efficiency is high, more pairs survive the hug and stay together. If it's low, they merge and die.

The simulations showed that these uncertainties are so large that they can change the predicted number of binary neutron stars by a factor of 100 or more. This means that right now, we can't be sure which version of the physics is correct just by looking at the few mergers we've seen so far.

The Metallicity Twist

Despite the chaos of the simulations, the authors found some "fingerprints" that appear no matter how they set the knobs. These are specific patterns in how the formation rate changes as the metal content of the universe changes.

The "Skip" Feature: At very low metallicity (in the early universe), there is a sharp drop in formation efficiency. This happens because stars at this stage suddenly start skipping a specific evolutionary phase (the First Giant Branch) due to how their cores ignite. It's like a star taking a shortcut that accidentally makes it harder to form a binary pair.
The Wobble: Between metallicity values of $10^{-3}$ and $7.5 \times 10^{-3}$ , the formation rate doesn't just go up or down; it wiggles in a non-monotonic way. This is a direct result of the complex interplay between how stars lose mass and how they interact.

The Bottom Line

The paper concludes that while we have a good map of how these stars might form, we are currently stuck in a fog of uncertainty. Different combinations of physics rules can produce the exact same number of mergers, making it hard to know which rules are actually true. This is a problem of degeneracy—like having two different keys that open the same lock.

Currently, gravitational-wave detectors can only rule out the very worst-case scenarios where binary neutron stars are extremely rare. To break the tie and figure out the true physics of these cosmic dances, we need to wait for the next generation of detectors (planned for the 2030s) that will hear up to 100,000 mergers a year. Only with that massive dataset, combined with better measurements of how metal content changes over time, will we be able to finally tune the knobs and see the true story of how these heavy couples come together. Until then, the universe keeps its secrets, hiding behind a veil of simulation uncertainties.

Technical Summary: Binary Neutron Star Populations Across Cosmic Time

Problem and Motivation
Direct observations of binary neutron star (BNS) systems remain scarce, with only a limited number of Galactic double neutron stars characterized and two confidently identified BNS mergers in the fifth Gravitational-Wave Transient Catalog (GWTC-5). However, upcoming electromagnetic surveys (e.g., SKA) and gravitational-wave observatories (e.g., LIGO-Virgo-KAGRA, Einstein Telescope, Cosmic Explorer) are expected to detect orders of magnitude more events. To interpret these forthcoming datasets, robust theoretical tools are required to constrain BNS formation and evolution.

Current population-synthesis models rely on numerous analytical prescriptions and empirical models to describe complex stellar and binary evolution processes. Significant uncertainties persist regarding single stellar evolution, common-envelope (CE) evolution, and supernova natal kick prescriptions. These uncertainties lead to large variations in predicted merger rates and formation efficiencies. The authors note that while standard prescriptions may struggle to simultaneously reproduce observed merger rates and compact-object binary properties, a systematic exploration of the parameter space is essential to assess the robustness of theoretical predictions and identify the physical processes most influential to BNS formation.

Methodology
The authors perform a systematic exploration of the parameter space of the population-synthesis code COSMIC (Compact Object Synthesis and Monte Carlo Investigation Code). Recognizing that a full exploration of the code's 50+ adjustable parameters is computationally prohibitive, the study focuses on four key parameters governing binary evolution, varied across 20 metallicity bins (ranging from $Z=10^{-4}$ to $Z=Z_{\odot}$ ) and two Initial Mass Function (IMF) prescriptions (standard Chabrier and a top-heavy IMF for low-metallicity extremes).

The four explored parameters are:

QCFLAG: The critical mass ratio determining the onset of unstable mass transfer and CE evolution during Roche-lobe overflow (RLOF). Three prescriptions (1, 3, and 5) are tested, spanning different stability assumptions for mass transfer from naked helium stars.
ALPHA: The efficiency parameter of CE evolution, quantifying the conversion of orbital energy into envelope ejection. Six values are tested ($0.5, 1.0, 1.5, 3.0, 5.0, 7.0$) to explore scenarios from standard orbital energy usage to those requiring additional energy reservoirs.
KICKFLAG: The natal kick prescription. Two options are compared: a standard bimodal Maxwellian distribution (Flag 1) and a mass-scaled prescription where kicks are reduced by ejecta and remnant mass (Flag 2).
CE_kickflag: The treatment of supernova kicks occurring during a CE phase. This determines whether pre-CE or post-CE stellar masses and orbital separations are used to calculate the kick magnitude and its effect on the binary orbit.

The study simulates 72 distinct population models. To ensure statistical robustness for rare events, a dedicated "tail-convergence" criterion is implemented, ensuring the stabilization of low-probability regions in the distribution before declaring convergence. Cosmological merger rates are calculated using the cosmoRate framework, integrating over redshift and metallicity using three different prescriptions for the cosmic metallicity-redshift relation (linear, MandF2017, and Belczynski et al. analytical).

Key Results

Bimodal Progenitor Mass Distribution: Across all metallicities and model configurations, the BNS population exhibits a bimodal distribution of primary progenitor masses, separated by a sparsely populated gap between approximately $6.8 M_{\odot}$ and $10 M_{\odot}$ .
- Low-mass channel ( $\sim6.5–9 M_{\odot}$ ): These systems typically undergo stable mass transfer without a CE phase and explode as electron-capture supernovae (ECSN), characterized by weak natal kicks.
- High-mass channel ( $\sim10–30 M_{\odot}$ ): These systems typically require a CE phase to strip their envelopes and reduce orbital separation, allowing them to survive the stronger natal kicks associated with core-collapse supernovae (CCSN). The CE phase is crucial for preventing these massive stars from collapsing into black holes.
- The Gap: Systems in the intermediate mass range are too light to survive a CE phase at low separation yet too massive to undergo ECSN. They retain wide separations while undergoing CCSN with strong kicks, leading to a low survival probability.
Dominance of Uncertainty Sources:
- Natal Kicks (KICKFLAG): This is the most impactful parameter. The mass-scaled prescription (KICKFLAG = 2) significantly increases formation rates compared to the standard bimodal distribution (KICKFLAG = 1) by reducing the disruptive effect of kicks, particularly for high-mass progenitors.
- CE Efficiency (ALPHA): Higher ALPHA values increase the formation efficiency, primarily by allowing more high-mass progenitors to successfully eject their envelopes and survive the CE phase without merging.
- Secondary Parameters: The treatment of kicks during CE (CE_kickflag) and the mass transfer stability criterion (QCFLAG) have notable but secondary effects. QCFLAG = 1 (treating naked helium star RLOF as unstable) systematically suppresses formation rates by channeling systems into mergers during a second CE phase.
Metallicity Dependence: While binary evolution uncertainties dominate the absolute formation efficiency (varying by orders of magnitude), characteristic metallicity-dependent features persist across all models:
- A sharp decrease in formation efficiency occurs between $Z=0.00016$ and $Z=0.00019$ . This is linked to the metallicity-dependent onset of non-degenerate core helium ignition, which allows stars to skip the First Giant Branch (FGB).
- A non-monotonic evolution is observed between $Z=10^{-3}$ and $7.5 \times 10^{-3}$ .
- Generally, formation efficiency decreases with increasing metallicity due to stronger stellar winds requiring more massive progenitors, which are less abundant in the IMF.
Degeneracies: The study finds that different combinations of binary-evolution parameters can produce similar merger-rate histories. Current gravitational-wave observations can only rule out the least efficient formation scenarios.

Significance and Conclusions
The paper concludes that while binary stellar evolution introduces large uncertainties in BNS formation efficiency and cosmological merger rates, robust signatures of specific evolutionary processes (such as FGB skipping) can be identified across a broad range of metallicities. The bimodal mass distribution is a robust feature linked to distinct formation channels.

The authors emphasize that breaking the degeneracies among population-synthesis models—where different parameter sets yield similar merger rates—will require larger samples of BNS mergers expected from future third-generation gravitational-wave observatories. Additionally, improved observational constraints on the evolution of metallicity across cosmic time are necessary to fully exploit these future datasets and constrain the physical processes governing binary evolution. The work establishes that current tools are essential for interpreting the unprecedented volume of future data but highlights the need for continued refinement of stellar evolution prescriptions.