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Eccentric millisecond pulsar + subdwarf B star from rotationally delayed accretion-induced-collapse scenario

This paper presents theoretical predictions for the properties and Galactic birth rate of a previously undetected population of eccentric millisecond pulsar + subdwarf B star binaries formed via the rotationally delayed accretion-induced collapse scenario, suggesting they could constitute a significant fraction of such systems and should be targeted in young stellar environments.

Original authors: Xiangcun Meng

Published 2026-04-08

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CC BY 4.0

Original authors: Xiangcun Meng

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 "Slow-Motion" Collapse: A Story of Pulsars, Stars, and Accidents

Imagine the universe as a giant, chaotic dance floor. Most of the time, the dancers (stars) move in predictable patterns. But sometimes, a dancer trips, spins wildly, and ends up in a completely unexpected pose.

This paper is about predicting a very specific, rare, and slightly "messy" dance move that astronomers haven't seen yet, but think must be happening. The dance involves two partners:

A Millisecond Pulsar (MSP): A super-dense, spinning neutron star (the corpse of a massive star) that spins hundreds of times a second. Think of it as a lighthouse beam spinning so fast it blurs.
A Subdwarf B Star (sdB): A hot, helium-burning star that has been stripped of its outer skin. Think of it as a "naked" star, glowing blue and hot.

Usually, these two dance in perfect circles. But this paper asks: What if they dance in a wobbly, oval (eccentric) orbit?

Here is the story of how the author, Meng Xiangcun, predicts these strange couples exist, how many there might be, and where to look for them.

1. The Standard Story vs. The "Glitch"

The Standard Story (The Recycling Plant):
Normally, a pulsar is born, dies, and then gets "reborn" by stealing gas from a partner star. As the gas falls in, it spins the pulsar up to incredible speeds (like a figure skater pulling in their arms). During this process, the two stars get tidally locked, smoothing out their orbit into a perfect circle. This is the "standard recycling" model.

The Glitch (The Eccentric Mystery):
Astronomers have found a few pulsars with partners that are not in perfect circles. They are in wobbly, oval orbits. This breaks the rules of the standard story. How did they get that way?

One popular theory is the RD-AIC Scenario (Rotationally Delayed Accretion-Induced Collapse).

The Setup: Imagine a heavy white dwarf star (a stellar corpse made of oxygen, neon, and magnesium) that is spinning so fast it doesn't collapse, even though it's too heavy to be stable.
The Partner: It has a partner star (the sdB) feeding it gas.
The Crash: Eventually, the white dwarf spins down just enough that it can't hold itself together anymore. It collapses instantly into a neutron star.
The Result: Because the collapse happens so fast and involves losing a bit of mass, the new neutron star gets a "kick." This kick throws the two stars into a wobbly, oval orbit instead of a circle.

2. The Prediction: "The Missing Link"

The author says, "If this theory is true for the wobbly pulsars we have found, then there must be a whole family of wobbly pulsars with Subdwarf B partners that we haven't found yet."

Think of it like finding a few blue birds in a forest. If you know blue birds usually nest in pine trees, you might predict there are more blue birds in pine trees that you just haven't spotted yet.

What do these missing birds look like? (The Predictions)

The Orbit: They will be oval (eccentric), not round.
The Age: They are "young" in cosmic terms. They are only a few hundred million years old. So, we shouldn't look for them in old, dusty neighborhoods (like globular clusters); we should look in the "young suburbs" of our galaxy (the thin disk).
The Weight: The pulsar in these pairs is likely lighter than the heavyweights we usually find (under 1.5 times the mass of our Sun).
The Numbers: The author did a massive computer simulation (like a cosmic lottery) to guess how many exist.
- Birth Rate: About 1 to 1.5 of these systems are born every 10,000 years.
- Total Population: There could be up to 15,000 of them in the Milky Way.
- The Catch: Even though 15,000 sounds like a lot, it's a tiny fraction of all pulsars. The author estimates they might make up 55% of all pulsar-subdwarf pairs, but since pulsar-subdwarf pairs are rare to begin with, finding them is like finding a needle in a haystack.

3. Why Haven't We Found Them Yet?

This is the big question. If there are 15,000 of them, where are they?

The author suggests a few reasons:

They are short-lived: The pulsars in these systems might have strong magnetic fields that make them "die" (stop spinning fast) much faster than normal pulsars. If they only live for a few million years, they disappear before we can spot them.
They are hard to see: Because they are in oval orbits, they might be harder to detect with our current radio telescopes.
The "Kick" was too small: If the collapse didn't give the star a big enough kick, the orbit might look almost circular, and we'd miss the "eccentric" signature.

4. Why Should We Care? (The "So What?")

Finding these systems would be a huge deal for physics. Here's why:

Testing the "Equation of State": Neutron stars are made of matter so dense that a teaspoon weighs a billion tons. We don't fully understand the rules of this matter. By measuring the mass of these specific pulsars and how they collapsed, we can test the laws of physics under extreme pressure.
Proving the Collapse Theory: If we find a wobbly pulsar with a hot subdwarf partner, it would be the "smoking gun" proof that white dwarfs can collapse into neutron stars without a supernova explosion.
Gravitational Waves: These systems might emit faint ripples in space-time (gravitational waves) that future telescopes (like LISA) could detect.

The Bottom Line

The author is essentially saying: "We have a theory that explains some weird, wobbly pulsars. If that theory is right, there should be a whole hidden population of similar systems with hot, stripped stars. They are young, they are light, and they are hiding in the younger parts of our galaxy. We haven't found them yet, but if we keep looking, finding them will unlock secrets about how stars die and what matter is made of."

It's a cosmic treasure hunt where the map is drawn by math, and the treasure is a deeper understanding of the universe's most extreme objects.

1. Problem Statement

Millisecond pulsars (MSPs) are typically formed via the "recycling" process in low-mass X-ray binaries, resulting in systems with nearly circular orbits. However, the discovery of eccentric MSPs (with companions such as main-sequence stars or helium white dwarfs) challenges this standard model. While several formation channels have been proposed (e.g., dynamical perturbations, asymmetric mass ejection), the origin of these systems remains uncertain.

Specifically, while eccentric MSP + Helium White Dwarf (He WD) systems have been observed and linked to the Rotationally Delayed Accretion-Induced Collapse (RD-AIC) scenario, no eccentric MSP + subdwarf B (sdB) systems have been detected. Given the evolutionary similarities between He WDs and sdB stars, the author investigates whether eccentric MSP + sdB binaries exist, what their properties are, and why they have not yet been observed.

2. Methodology

The study employs Binary Population Synthesis (BPS) calculations to model the formation and evolution of these systems.

Progenitor Systems: The initial binaries consist of an Oxygen-Neon-Magnesium (ONeMg) White Dwarf (WD) and a Main Sequence (MS) star. Mass transfer begins when the companion is on the MS or in the Hertzsprung Gap (HG).
RD-AIC Mechanism: The model assumes the ONeMg WD accretes mass, spins up, and eventually undergoes AIC to form a Neutron Star (NS/MSP).
- Rotation Assumption: Unlike previous models (e.g., Freire & Tauris 2014) that assumed rigid rotation (limiting WD mass to $\sim 1.48 M_\odot$ ), this study incorporates differential rotation, allowing pre-AIC WD masses to reach up to $2.6 M_\odot$ .
- Timescales: A pseudo-spin-down timescale ( $\tau_{sp}$ ) of $10^7$ years is defined between the WD reaching $1.378 M_\odot$ and the AIC event.
Collapse Dynamics:
- Symmetric Collapse: Eccentricity is calculated based on mass loss ( $\Delta M$ ) using the formula $e = \Delta M / (M_{NS} + M_2)$ .
- Asymmetric Collapse: The study uses Monte Carlo simulations to model the effects of "kicks" (asymmetric mass ejection) on orbital parameters, varying kick velocities and directions.
Population Synthesis: Two BPS calculations were performed using the code by Hurley et al. (2000, 2002) with $10^8$ sample binaries. Key parameters included the Common Envelope (CE) ejection efficiency ( $\alpha_{CE}$ ), tested at values of 1.0 and 3.0.

3. Key Contributions

Theoretical Prediction: This is the first study to predict the existence and properties of eccentric MSP + sdB binaries specifically arising from the RD-AIC channel.
Differential Rotation Model: By allowing differential rotation in super-Chandrasekhar WDs, the study expands the parameter space for progenitor masses, predicting more massive pre-AIC WDs than previously considered.
Population Constraints: The paper provides the first quantitative estimates for the Galactic birth rate, total population, and characteristic ages of these specific systems.
Observational Guidance: It offers specific constraints on orbital periods, eccentricities, and masses to guide future radio and optical surveys.

4. Key Results

A. System Properties

Masses:
- MSP Mass: Ranges from $1.25 M_\odot$ to $2.2 M_\odot$ . Notably, most systems (approx. 93-98%) have MSP masses below $1.5 M_\odot$ .
- sdB Mass: Ranges from $0.38 M_\odot$ to $0.65 M_\odot$ .
Orbital Parameters:
- Eccentricity ( $e$ ): Under symmetric collapse, $e$ is narrow (0.09–0.17). With asymmetric kicks (even as low as $5 \text{ km s}^{-1}$ ), eccentricity can reach up to 0.3.
- Orbital Period ( $P_{orb}$ ): Significantly longer than MSP+He WD systems, ranging from $\sim 1.6$ days to $\sim 150$ days.
Bimodal Distribution: The systems divide into two distinct branches in the mass plane, corresponding to different evolutionary stages of the companion and mass transfer rates.

B. Galactic Population and Birth Rate

Birth Rate: Estimated at $(0.67 - 1.5) \times 10^{-4} \text{ yr}^{-1}$ .
Total Population:
- Assuming an optimistic lifetime of $10^8$ years for both the MSP and sdB, the total number in the Galaxy is estimated between 6,700 and 15,000.
- This implies that up to 55% of all MSP + sdB systems could be eccentric (a much higher fraction than the ~2% seen in MSP + He WD systems).
Age and Environment:
- The delay time for formation is 160–630 Myr, peaking at $\sim 300$ Myr.
- These systems are relatively young and should be found in young environments (e.g., the Galactic thin disk) rather than old globular clusters.

C. Non-Detection Explanation

Despite the predicted population, no such systems have been detected. The author suggests two primary reasons:

Short Lifetimes: If post-AIC MSPs have strong magnetic fields (magnetar-like), their active lifetimes could be as short as $10^3$ – $10^6$ years, drastically reducing the observable population.
Spin-down Timescale: If the spin-down timescale prior to AIC is significantly longer ( $>10^8$ years), the sdB companion would evolve into a CO WD before the AIC occurs, resulting in eccentric MSP + CO WD systems instead.

5. Significance and Future Applications

Testing the RD-AIC Scenario: The detection (or continued non-detection) of these systems provides a critical test for the RD-AIC formation channel. A future discovery would offer strong indirect evidence for AIC events.
Equation of State (EoS) Constraints: Because the pre-AIC WD mass and post-AIC NS mass are linked, measuring the mass and eccentricity of these systems could constrain the NS EoS and the physics of the collapse.
Gravitational Waves: Asymmetric RD-AIC events could produce continuous gravitational waves (CGWs) detectable by Advanced LIGO/Virgo, especially if the resulting NS has non-axisymmetric distortions.
Evolutionary Pathways: These systems serve as progenitors for older eccentric NS + CO WD binaries. A statistical comparison between the two populations could validate the evolutionary timeline proposed in the paper.

In conclusion, the paper establishes a robust theoretical framework for eccentric MSP + sdB binaries, predicting a significant but elusive population that, if found, would revolutionize our understanding of neutron star formation and binary evolution.