🔭 astrophysics

Can accreting isolated neutron stars be detected?

Through detailed population synthesis modeling of isolated neutron stars in the Milky Way, this study reveals that the detectability of accreting objects in eROSITA data—potentially reaching a few thousand—is critically dependent on uncertain propeller-stage spin-down rates and accretion efficiencies, suggesting that future observations of wide low-mass binaries discovered by Gaia are essential to resolve these uncertainties.

Original authors: Marina Afonina, Anton Biryukov, Sergei Popov

Published 2026-05-21

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CC BY 4.0

Original authors: Marina Afonina, Anton Biryukov, Sergei Popov

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 Milky Way galaxy as a giant, bustling city. Hidden within this city are billions of "ghosts" called neutron stars. These are the incredibly dense, dead cores of massive stars that exploded long ago. While we know they are there, most of them are invisible to our telescopes because they are old, cold, and have stopped spinning fast enough to shine like radio lighthouses.

For decades, astronomers have asked: Can we find these lonely ghosts? The paper suggests a new way to look for them: by watching for the faint glow of gas they might be "eating" as they drift through space.

Here is the story of their research, explained simply:

1. The Hunt for the Invisible

Think of a neutron star as a tiny, super-heavy marble moving through a thick fog (the interstellar medium). As it moves, it might scoop up some of that fog. If it scoops up enough, the gas gets crushed and heated up, glowing in X-rays. This is called accretion.

In the 1990s, scientists were very optimistic. They thought there were millions of these stars eating gas and that we would easily find them. But when they looked, they found almost nothing. Why?

2. The "Propeller" Problem

The main reason we haven't found them is a tricky phase in the life of a neutron star called the Propeller Stage.

Imagine the neutron star is a spinning fan.

The Ejector Phase: When the fan spins very fast, it blows the gas away. It's like a leaf blower pushing leaves off a driveway. The star cannot eat the gas because it's blowing it away too hard.
The Propeller Phase: As the fan slows down, it gets to a point where it's spinning just fast enough to fling the gas away, but not fast enough to let it fall in. It's like a spinning merry-go-round that throws off anyone trying to jump on. The star is still spinning, but it's not eating yet.
The Accretor Phase: Finally, the fan slows down enough that the gas can stick and fall onto the star. Now, the star starts eating, and it glows.

The Big Mystery: The paper says the biggest unknown is how long the "Propeller Phase" lasts.

If the star slows down quickly, it moves past the "throwing" phase and starts eating soon. We might find thousands of them.
If the star spins for a very long time in the "throwing" phase, it might never start eating within the age of the universe. In this case, we might find zero.

3. The Speed Trap

The paper also highlights that speed matters.

Slow Neutron Stars: If a neutron star is moving slowly through the gas, it has more time to scoop up material. It's like a slow-moving truck collecting more rain in a bucket than a speeding car.
Fast Neutron Stars: If the star is zooming through space (which many do, due to the "kick" they get when they are born), it rushes past the gas too quickly to eat much.

The researchers found that the stars we are most likely to see are the "slow movers" living relatively close to our Solar System.

4. The Magnetic Field

Neutron stars have incredibly strong magnetic fields. The paper looked at whether these fields fade away over billions of years.

Constant Field: If the magnetic field stays strong, it acts like a strong shield, keeping the gas away longer.
Decaying Field: If the magnetic field fades, the shield gets weaker, and the gas can get closer.
The study found that while this changes when the star starts eating, it doesn't change the final number of visible stars as much as the "Propeller" speed does.

5. What Did They Find?

The researchers used a supercomputer to simulate the life of millions of neutron stars over 13.6 billion years (the age of the galaxy). They tested different rules for how the "Propeller" works.

The Optimistic Scenario: If the "Propeller" phase is short and stars start eating quickly, the new eROSITA X-ray telescope (which scanned the whole sky) could have found a few thousand of these lonely, eating stars.
The Pessimistic Scenario: If the "Propeller" phase is very long and inefficient, the number of visible stars drops to zero.

6. The Future Clue

Since we aren't sure which scenario is true, the paper suggests looking at a different group of objects: neutron stars in wide binary systems. These are neutron stars that have a partner star but are far enough away that they don't interact violently. They drift through space just like the lonely ones. If we can figure out how these "partnered" stars behave, it will help us understand the lonely ones better.

The Bottom Line

This paper is a reality check. It tells us that finding these invisible, eating neutron stars depends entirely on a specific, unknown rule about how they slow down.

If they slow down fast, we might find thousands of them with current telescopes.
If they slow down slowly, they remain invisible ghosts.

The authors conclude that until we understand the "Propeller" stage better, we can't be sure if we are looking for a needle in a haystack or a needle that doesn't exist at all.

Technical Summary: Detectability of Accreting Isolated Neutron Stars via Population Synthesis

Problem Statement
The Galactic population of neutron stars (NSs) is estimated to be on the order of $10^9$ , yet fewer than $10^4$ isolated NSs have been observed, predominantly young radio pulsars. The fate of older, isolated NSs remains a significant open question. While it has been hypothesized for decades that old NSs could become detectable by accreting interstellar medium (ISM) matter and emitting X-rays, observational efforts (e.g., ROSAT, Chandra, XMM-Newton) have failed to identify a confirmed population of such sources. Previous population synthesis studies yielded optimistic estimates based on assumptions of low NS velocities, high accretion efficiency, and rapid evolution through the "propeller" stage. However, these assumptions were challenged by the discovery of high natal kick velocities and numerical simulations suggesting low accretion efficiencies. This paper aims to resolve these discrepancies by performing a detailed population synthesis of isolated NSs in the Milky Way, incorporating updated models of the ISM, magneto-rotational evolution, and the uncertain physics of the propeller stage.

Methodology
The authors employ a population synthesis approach simulating the evolution of isolated NSs over the lifetime of the Galaxy ($13.6$ Gyr). The methodology integrates several key components:

Initial Parameters and Kinematics: Synthetic NSs are generated with initial spin periods ( $P_0$ ), magnetic fields ( $B_0$ ), and spatial positions based on distributions derived from radio pulsar and magnetar populations. Initial velocities are calculated as the vector sum of circular galactic velocity, residual progenitor velocity, and a natal kick velocity drawn from a bimodal Maxwellian distribution. Trajectories are calculated within a realistic Galactic gravitational potential.
Interstellar Medium (ISM) Models: Two ISM models are compared:
- A one-phase model consisting of a single cold phase (molecular, neutral, and warm ionized gas plus dust).
- A two-phase model distinguishing between a cold phase and a hot phase (coronal/halo gas), utilizing pressure equilibrium to determine the local filling factor of each phase along the NS trajectory.
Magneto-Rotational Evolution: The study tracks the NS through four evolutionary stages: ejector, propeller, accretor, and georotator. Transitions are governed by critical radii (light cylinder, Alfvén radius, Shvartsman radius, corotation radius).
- Spin-down: The Euler equation is used to model spin evolution. Crucially, the study tests four distinct models (A, B, C, D) for the spin-down torque ( $K_P$ ) during the propeller stage, representing a wide range of theoretical efficiencies from highly efficient (Model A) to inefficient (Model D).
- Magnetic Field: Two magnetic field evolution scenarios are tested: a constant field (CF) and an exponentially decaying field (ED) that accounts for Hall cascade effects in magnetars and long-term ohmic dissipation.
Observability Calculation: For NSs reaching the accretor stage, the X-ray luminosity is calculated assuming Bondi-Hoyle-Littleton accretion with 100% efficiency ( $\zeta=1$ ). The spectrum is modeled as a blackbody from the polar caps, corrected for gravitational redshift and time dilation. Interstellar absorption is applied using column density maps consistent with HI4PI data. The detectability by the eROSITA telescope is assessed by calculating the count rate, with a detection threshold set at $0.01$ counts s $^{-1}$ .

Key Contributions and Results

Dominance of Propeller Stage Uncertainty: The primary finding is that the duration of the propeller stage, determined by the choice of the spin-down torque model, is the most critical factor influencing the number of observable accreting NSs.
- Efficient Spin-down (Models A & B): If the propeller stage is short (rapid spin-down), a significant fraction of NSs ( $17-53\%$ ) reach the accretor stage. In the most optimistic scenario (Model A, constant field, one-phase ISM), the study predicts $\sim 13,000$ potentially observable sources. In more realistic scenarios (Model B, two-phase ISM, decaying field), this number drops to $\sim 3,000-4,000$ .
- Inefficient Spin-down (Models C & D): If the spin-down is inefficient (e.g., Model D, based on Davies and Pringle 1981), the propeller stage can last longer than the age of the Galaxy. Consequently, the number of NSs reaching the accretor stage becomes negligible, resulting in effectively zero detectable sources for eROSITA.
Velocity Dependence: The characteristic velocity of the NS relative to the ISM is the second most important parameter. Accretion rates scale as $\dot{M} \propto v^{-3}$ . Consequently, observable sources are almost exclusively low-velocity objects ( $v \lesssim 60-70$ km s $^{-1}$ for Models A/B and $v \lesssim 40$ km s $^{-1}$ for Model C). High-velocity NSs rarely reach the accretor stage or produce sufficient flux to be detected.
Magnetic Field Evolution: While magnetic field decay significantly alters the ratio of NSs in the ejector and propeller stages (by shrinking interaction radii and facilitating transitions), its impact on the total number of accretors is secondary to the propeller spin-down model. However, field decay does lower the effective temperature of observable sources (from $\sim 5 \times 10^6$ K to $\sim 2 \times 10^6$ K) due to the shrinking magnetosphere and polar cap radius.
Spatial Distribution: Potentially observable accretors are predicted to be located relatively close to the Sun (within $\sim 400-550$ pc) and confined to a thin disk near the Galactic plane ( $z < 470$ pc).
ISM Model Impact: The transition from a one-phase to a two-phase ISM model results in a modest reduction (less than a factor of two) in the number of predicted accretors, as NSs spend more time in low-density regions where evolution is slower.

Significance and Claims
The paper claims that the non-detection of accreting isolated NSs to date is likely due to the uncertainties in the physics of the propeller stage rather than a lack of sources or observational sensitivity. The study demonstrates that if the propeller spin-down is sufficiently rapid, eROSITA has the potential to detect a population of thousands of these sources. Conversely, if the spin-down is inefficient, such a population may be virtually non-existent in the observable universe.

The authors emphasize that current theoretical models of the propeller regime remain unconstrained by observation. They suggest that future observations of neutron stars in wide, low-mass binary systems (recently discovered by Gaia) are crucial. These systems, where NSs interact with stellar winds in a manner analogous to the ISM, could provide the necessary empirical data to constrain propeller spin-down torques and accretion efficiencies, thereby clarifying the detectability of isolated accreting neutron stars. The paper concludes modestly, noting that without resolving the uncertainties in the propeller stage and low-rate accretion efficiency, precise predictions of the observable population remain elusive.