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Reconciling the Systemic Kicks of Observed Millisecond Pulsars, Spider Pulsars, and Low-mass X-ray Binaries

This paper resolves the apparent tension between the lower systemic kicks of observed millisecond pulsars and the higher kicks of their proposed progenitors (spider pulsars and low-mass X-ray binaries) by demonstrating that distance-dependent kinematic biases favor the detection of low-kick millisecond pulsars at short distances, thereby reconciling the observations with a common evolutionary origin.

Original authors: Paul Disberg, Arash Bahramian, Ilya Mandel

Published 2026-03-17

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CC BY 4.0

Original authors: Paul Disberg, Arash Bahramian, 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

The Cosmic Mystery: Why Do Some Pulsars Seem "Slower"?

Imagine the universe as a giant, bustling city. In this city, there are three types of "runaway" objects: Millisecond Pulsars (MSPs), Spider Pulsars, and Low-mass X-ray Binaries (LMXBs).

Scientists have long believed these three groups are related, like a family tree. The theory goes like this:

The Parents (LMXBs): Two stars orbit each other. One is a dense neutron star, and the other is a small companion. They are close and bright.
The Teenagers (Spider Pulsars): The neutron star starts eating its companion, stripping it away. The companion gets smaller and smaller (like a spider eating its mate, hence the name).
The Adults (MSPs): Eventually, the companion is gone completely. The neutron star is left alone, spinning incredibly fast, but now it's an "isolated" wanderer.

The Problem:
When scientists measured how fast these objects were "kicked" away from their birthplaces (their systemic kicks), they found a weird discrepancy.

The LMXBs and Spider Pulsars seemed to have been kicked hard, traveling fast.
The MSPs (the adults) seemed to have been kicked very gently, moving slowly.

This was confusing! If they are all part of the same family, they should have received similar "birth kicks" from the supernova explosion that created them. Why did the adults seem so calm while the teenagers were running wild?

The Solution: It's All About Distance (The "Foggy Window" Analogy)

The authors of this paper, Paul, Arash, and Ilya, realized the problem wasn't that the MSPs had different kicks. The problem was where we were looking for them.

Imagine you are standing in a park on a foggy day.

The Nearby Objects (MSPs): You can only see the people standing right next to you. If someone runs away from you at high speed, they quickly disappear into the fog or leave your field of view. The only people you can see nearby are the ones who are walking slowly or standing still.
The Distant Objects (LMXBs & Spiders): To see people far away in the distance, they usually have to be moving fast enough to get there, or they are just naturally further out.

The "Kinematic Bias":
The paper argues that we are looking at MSPs at short distances (they are our "neighbors"), while we see LMXBs and Spiders at much greater distances.

Because of physics, if a star gets a huge "kick" (a high-speed launch), it travels far away from its birthplace very quickly.

If an MSP got a huge kick, it would have zoomed far away from us long ago. We wouldn't see it in our "neighborhood" (the nearby part of the galaxy).
The only MSPs we can see nearby are the ones that got small kicks and stayed close to home.

So, the data wasn't showing that MSPs are slow; it was showing that we can only see the slow ones because the fast ones have already left the neighborhood.

How They Proved It

The team used a supercomputer simulation (like a cosmic flight simulator) to test this idea.

They created a virtual galaxy with thousands of stars.
They gave them random "kicks" (speeds) at birth.
They watched them move for billions of years.

The Result:
The simulation confirmed the bias. When they looked at the "nearby" stars in the simulation, they mostly saw slow ones. When they looked at the "distant" stars, they saw a mix of fast and slow, but the average speed was higher.

Once they corrected their math to account for this "distance bias," the gap disappeared.

The MSPs were actually moving just as fast as the others; we just couldn't see the fast ones because they were too far away.
The Spider Pulsars seemed to have slightly higher kicks, but the authors suggest this might just be because we are seeing a specific type of them, or because of measurement errors, not because they are a different species.

The Big Picture Conclusion

The paper concludes that MSPs, Spider Pulsars, and LMXBs are indeed a single family.

They all likely started as the same type of binary star system. The reason they looked different before was because we were looking at them through a "distorted lens" caused by how far away they are.

In short:

Old Theory: "MSPs are calm, but their parents were wild. They must be different."
New Theory: "MSPs are just as wild as their parents. We just can't see the wild ones because they ran too far away to be seen from our backyard."

By fixing the math to account for distance, the family tree makes perfect sense again. The "kicks" match up, and the evolutionary story holds together.

1. Problem Statement

Millisecond Pulsars (MSPs), Spider Pulsars (Redbacks and Black Widows), and Low-mass X-ray Binaries (LMXBs) are hypothesized to share a common evolutionary origin: LMXBs evolve into Spider Pulsars, which eventually lose their companions to become isolated MSPs. A critical test of this evolutionary model is the systemic kick velocity (the recoil velocity of the binary system) imparted during the supernova formation of the neutron star (NS).

Recent work by O'Doherty et al. (2023) revealed a significant tension in this model:

Observation: The systemic kicks of observed LMXBs and Spider Pulsars are significantly higher (median $\sim 150$ km s $^{-1}$ ) than those of observed MSPs (median $\sim 100$ km s $^{-1}$ ).
Conflict: If they share a common progenitor population, their systemic kick distributions should be statistically similar. The observed discrepancy suggests either a different formation channel for MSPs or a flaw in the evolutionary model.

2. Methodology

The authors propose that the discrepancy is not physical but rather an observational artifact caused by a distance-dependent kinematic bias. They employ a multi-step methodology to test this hypothesis:

Data Re-analysis: They utilize the catalog of 145 systems (95 MSPs, 31 spiders, 19 LMXBs) from O'Doherty et al. (2023), focusing on systems with measured distances and proper motions. They perform bootstrapping to determine confidence intervals for distance and kick distributions.
Observation of Distance Disparity: They note that observed MSPs are located much closer to the Sun ( $\sim 1$ kpc) compared to Spider Pulsars ( $\sim 2$ kpc) and LMXBs ( $\gtrsim 5$ kpc).
Galactic Trajectory Simulation:
- They utilize simulations from Disberg et al. (2025) where $10^3$ point masses are seeded in the Galactic thin disc with isotropic kicks ranging from 0 to 1000 km s $^{-1}$ .
- Trajectories are integrated for 1 Gyr through the Galactic potential (using GALPY and the McMillan 2017 potential) to reach dynamical equilibrium ( $>40$ Myr).
- They calculate the conditional probability $P(r|v_{kick})$ to determine how kick magnitude influences the distance of an object from the Sun over time.
Bias Correction Model:
- They derive the expected observed kick distribution $P(v_{kick}|r_{min}, r_{max})$ given an intrinsic kick distribution $P(v_{kick})$ and the observed distance range.
- They fit a lognormal intrinsic kick distribution to the observed MSP data, correcting for the fact that nearby objects are biased toward lower kicks because high-kick objects have migrated further away.
Population Synthesis Validation:
- They use the COMPAS binary population synthesis code to simulate $10^6$ binaries.
- They select systems that form an NS, remain bound, have a companion mass $M_c \le 1 M_\odot$ , and a post-supernova orbital period $P_{orb} \le 10$ days.
- They compare the simulated systemic kicks with the bias-corrected observational data.

3. Key Contributions

Identification of Kinematic Bias: The paper establishes that the lower observed systemic kicks of MSPs are a selection effect. High-kick systems migrate to larger galactocentric distances and are less likely to be detected in nearby radio surveys, whereas low-kick systems remain close to the Sun.
Quantitative Reconciliation: The authors demonstrate that applying a distance-dependent kinematic bias correction allows a single intrinsic systemic kick distribution to explain the observed data for both MSPs and LMXBs.
Spider Pulsar Nuance: While MSPs and LMXBs are reconciled by a single distribution, Spider Pulsars appear to require a slightly higher intrinsic kick distribution. The authors argue this may be due to observational biases (e.g., spiders with lower companion masses being easier to detect) rather than a distinct physical origin.
Validation with Binary Evolution: The corrected observational distributions are shown to be consistent with binary population synthesis predictions for progenitor systems with $P_{orb} \le 10$ d and $M_c \le 1 M_\odot$ .

4. Key Results

Distance-Kick Correlation: The simulation confirms that for dynamically old objects ( $>40$ Myr), the median observed kick velocity increases with distance from the Sun (from $\sim 50$ km s $^{-1}$ at 0 kpc to $\sim 200$ km s $^{-1}$ at $>7$ kpc) due to the kinematic bias.
Reconciled Distributions:
- By correcting for the bias, the authors derive an intrinsic systemic kick distribution for MSPs and LMXBs described by a lognormal model with $\mu = 5.1$ and $\sigma = 0.7$ , yielding a median kick of 164 km s $^{-1}$ .
- This single distribution successfully bridges the gap between the observed MSP and LMXB confidence intervals.
Spider Pulsars: Spider pulsars are best fit by a slightly different lognormal distribution ( $\mu = 5.2, \sigma = 0.5$ , median 181 km s $^{-1}$ ). However, the authors suggest this difference is likely not statistically significant given distance uncertainties and potential observational biases toward lower-mass companions (which yield higher kicks).
COMPAS Consistency: The bias-corrected observational distributions align well with COMPAS simulations for binaries that survive the supernova. The intrinsic binary kicks are lower than isolated NS natal kicks because the companion acts as an inertial anchor, reducing the systemic recoil.

5. Significance

This paper resolves a major tension in the evolutionary model of millisecond pulsars. By demonstrating that the observed difference in systemic kicks is an artifact of distance-dependent selection effects rather than a fundamental difference in formation physics, the authors provide strong evidence that:

MSPs, Spider Pulsars, and LMXBs likely share a common progenitor system.
The evolutionary channel from LMXB $\to$ Spider $\to$ Isolated MSP remains a viable and consistent model.
Future studies of pulsar kinematics must rigorously account for the "kinematic bias" introduced by the limited volume of observation relative to the age of the population.

The work underscores the importance of combining observational data with dynamical simulations to correct for selection biases in Galactic archaeology.