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The Kick Velocities of Neutron Stars in Binary Systems

This study utilizes the COMPAS population synthesis code to demonstrate that while standard natal kicks calibrated to isolated pulsars explain many binary neutron star systems, a model incorporating significantly reduced natal kicks for neutron stars formed in high-mass binaries is required to consistently reproduce the observed properties of high-mass X-ray binaries and double neutron stars.

Original authors: Paul Disberg, Ilya Mandel, Ryosuke Hirai

Published 2026-08-21

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CC BY 4.0

Original authors: Paul Disberg, Ilya Mandel, Ryosuke Hirai

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

When a massive star runs out of fuel, it collapses and explodes in a supernova, leaving behind a city-sized ball of ultra-dense matter called a neutron star. These explosions are rarely perfectly symmetrical. Just as a rocket propels itself forward by shooting gas out the back, the uneven blast of a supernova can kick the newborn neutron star in a random direction, sending it careening through space at hundreds of kilometers per second. If this explosion happens while the star is still part of a pair, orbiting a companion, that sudden kick can drastically alter the dance of the two stars, stretching their orbit, changing how long it takes them to circle each other, or even flinging them apart entirely. Astronomers have long known that isolated neutron stars receive these violent kicks, but a lingering question has been whether the rules change when the star is part of a binary system. Does the presence of a companion star soften the blow, or does the kick remain just as fierce?

A team of researchers set out to answer this by comparing the real movements of neutron stars in different types of binary pairs against computer simulations of how these systems should behave. They looked at five distinct groups of neutron star pairs: wide binaries found by the Gaia space telescope, systems where a neutron star feeds on a small companion, pairs with a white dwarf companion, systems with a massive, rapidly spinning companion, and double neutron star pairs. By running thousands of simulations with different assumptions about how hard the stars get kicked, they tried to find the model that best matched the actual orbits and speeds observed in our galaxy.

The researchers found that the answer depends entirely on the type of companion the neutron star has. For neutron stars paired with low-mass companions, such as those found in the Gaia survey or in systems with white dwarfs, the data fits a picture where the neutron star receives a powerful kick, similar in strength to the kicks given to isolated stars. However, to explain the specific shapes of the orbits for the wide Gaia pairs, the simulations also required a secondary, slower push known as a "rocket kick," which occurs as the neutron star spins down over time. This combination of a strong initial kick and a later rocket boost successfully reproduced the observed paths of these systems.

In stark contrast, the story changes completely for neutron stars paired with massive companions or for double neutron star systems. The observed orbits and speeds of these pairs could not be explained by the same powerful kicks. Instead, the data strongly suggests that when a neutron star forms in a binary system with a massive companion, it receives a significantly gentler kick, moving at speeds of less than 10 kilometers per second. This tiny nudge is barely enough to disturb the orbit, allowing the pair to stay close and evolve into the tight, circular orbits seen in many double neutron star systems. The researchers also noted that the massive companions in these systems likely strip away the outer layers of the exploding star before it goes supernova, a process that may be responsible for this dramatic reduction in the kick's force.

While the model worked well for most systems, it struggled to explain a few specific outliers. Some neutron stars with massive companions were found in highly elliptical orbits that the simulations could not easily reproduce, leading the authors to suggest these might have formed through complex interactions in triple-star systems rather than simple pairs. Similarly, a few neutron stars with low-mass companions were found moving on paths that suggest they originated from outside our galaxy's main disk, hinting at a different history of formation. Despite these exceptions, the study provides a coherent picture: the violence of a neutron star's birth is not a fixed rule but a variable outcome, heavily influenced by the company it keeps. Neutron stars born alone or with small partners get a hard shove, while those born with massive partners get a gentle nudge, shaping the diverse population of binary systems we see in the Milky Way today.

Problem Statement
Neutron stars (NSs) receive natal kicks during their formation in supernovae (SNe), a phenomenon likely driven by asymmetric explosions. While the kick velocities of isolated NSs are estimated to have a median magnitude of $\sim 250$ km s $^{-1}$ , the kick magnitudes for NSs formed in binary systems remain uncertain. Binary interactions can alter stellar structure (e.g., carbon-oxygen core mass), potentially modifying kick magnitudes. Furthermore, different binary populations—such as low-mass X-ray binaries (LMXBs), high-mass X-ray binaries (HMXBs), double neutron stars (DNSs), and Gaia-detected NS binaries—exhibit diverse orbital and kinematic properties. The central problem addressed is determining what natal kick prescriptions can consistently explain the observed orbital periods, eccentricities, and systemic velocities across these distinct binary populations.

Methodology
The authors utilize the rapid population synthesis code COMPAS (v3.29.02) to simulate binary stellar evolution at solar metallicity. They apply various kick models to the pre-SN binary parameters derived from these simulations. The post-SN orbital properties and systemic kicks are calculated by extending the analytical framework of Brandt & Podsiadlowski (1995) to include eccentric pre-SN orbits.

The study employs several specific kick prescriptions:

Natal Kick Magnitudes: Based on the model of Mandel & Müller (2020), where kick velocity is a function of the pre-SN CO-core mass. The authors calibrate the standard kick parameter ( $v_{SN}$ ) to match the velocities of young isolated pulsars (Disberg & Mandel 2025). They also test a scenario with significantly reduced kicks for stripped-envelope supernovae ( $v_{SSN} \lesssim 10$ km s $^{-1}$ ), motivated by theories regarding ultra-stripped SNe (USSNe).
Kick Directions: Models test both isotropic kick directions and polar kicks (aligned with the orbital angular momentum).
Rocket Kicks: The authors incorporate "rocket" kicks (post-SN acceleration due to asymmetric spin-down radiation) to test if they can explain specific orbital anomalies, particularly in Gaia binaries.
Systemic Kick Estimation: For dynamically old binaries, the authors infer systemic kicks by integrating Galactic trajectories backward through a simulated potential, correcting for kinematic biases that affect the observability of high-velocity systems.

The simulated results are compared against five observational samples:

Gaia NS binaries (wide binaries with NS candidates).
NS Low-Mass X-ray Binaries (LMXBs).
NS-White Dwarf binaries (NSWDs).
NS High-Mass X-ray Binaries (HMXBs), specifically Be X-ray binaries (BeXBs).
Double Neutron Stars (DNSs).

Key Results
The comparison between models and observations yields a bifurcation in the required natal kick magnitudes depending on the binary companion's mass:

Gaia NSs, LMXBs, and NSWDs: These systems, typically involving low-mass companions, are best reproduced by models with high natal kicks ( $v_{SN} \approx 630$ km s $^{-1}$ ), calibrated to isolated pulsar velocities. However, reproducing the specific eccentricities of Gaia NSs requires the addition of a rocket kick of $\sim 30$ km s $^{-1}$ to reduce post-SN eccentricities. The systemic velocities of these systems are consistent with high natal kicks, provided one excludes halo-like systems and focuses on those formed via common-envelope evolution.
HMXBs (BeXBs) and DNSs: These systems, involving high-mass companions or double NS formation, are best explained by models with significantly reduced natal kicks ( $v_{SSN} \lesssim 10$ $v_{S S N} ≲ 10$ km s $^{-1}$ $^{- 1}$ ).
- For DNSs, low natal kicks allow the observed bimodal eccentricity distribution to be explained primarily by Blaauw kicks (recoil from isotropic mass loss) arising from the non-monotonic relationship between CO-core mass and NS remnant mass. The observed correlation between DNS eccentricity and systemic kick supports a scenario where natal kicks are sub-dominant.
- For BeXBs, low natal kicks successfully reproduce the low-eccentricity population. The high-eccentricity BeXBs, which show a tight period-eccentricity relation, are not well explained by standard kick models; the authors suggest these may originate from pre-SN eccentricities induced by stellar mergers in triple systems.

Significance and Conclusions
The paper concludes that a unified model for NS kicks in binaries is possible if one distinguishes between formation channels based on companion mass. NSs formed with low-mass companions (Gaia NSs, LMXBs, NSWDs) appear to receive natal kicks similar to those of young isolated NSs. In contrast, NSs formed with high-mass companions (HMXBs, DNSs) receive significantly reduced natal kicks.

This reduction is consistent with theoretical expectations that specific SN mechanisms (such as USSNe, electron-capture SNe, or accretion-induced collapse) produce more symmetric explosions. However, the authors note a tension with the COMPAS simulation labels, which do not always map these reduced-kick systems to the expected SN types (e.g., some BeXB progenitors are labeled as core-collapse SNe in the simulation).

The study highlights that while high natal kicks explain the kinematics of low-mass companion systems, the dynamics of high-mass companion systems are dominated by Blaauw kicks and orbital evolution. The authors acknowledge remaining caveats, including uncertainties in common-envelope formalisms, the origin of high-eccentricity BeXBs, and the masses of DNSs, but assert that their proposed bifurcated kick model provides a relatively consistent explanation for the observed NS populations in binary systems.

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