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Gravitational waves from primordial black holes passing by neutron stars: observational prospects for the Galactic center

This paper estimates the detection prospects for gravitational waves generated by planetary-mass primordial black holes interacting with neutron stars in the Galactic center, concluding that despite the potential for repeated bursts from bound systems, the probability of observing such signals with LIGO-Virgo-KAGRA over a decade is negligibly small ( $P\lesssim 10^{-8}$ ).

Original authors: Nicolas Esser, Juan García-Bellido, Peter Tinyakov

Published 2026-03-02

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CC BY 4.0

Original authors: Nicolas Esser, Juan García-Bellido, Peter Tinyakov

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 Big Idea: Hunting Invisible Ghosts with Cosmic Whistles

Imagine the universe is filled with invisible "ghosts" called Primordial Black Holes (PBHs). These aren't the massive black holes you hear about in the news; these are tiny, planetary-sized ghosts that formed right after the Big Bang. Scientists think they might make up the "Dark Matter" that holds galaxies together, but we've never actually seen one.

This paper asks a simple question: Can we hear these ghosts?

The authors suggest a new way to listen for them. Instead of waiting for two black holes to crash into each other (which is like waiting for two cars to collide in a dark parking lot), they propose listening for a tiny black hole zooming past a Neutron Star.

The Cast of Characters

The Neutron Star: Think of this as a cosmic lighthouse. It's the dead, super-dense core of a star that collapsed. It's incredibly heavy (a teaspoon weighs a billion tons) and incredibly small (about the size of a city). It's the perfect "target" because it's so dense that if something flies near it, it screams.
The Primordial Black Hole (PBH): Think of this as a tiny, invisible bullet. It's so small and light (planetary mass) that it doesn't emit light, but it has gravity.
The Gravitational Wave (GW): This is the sound of the event. When the bullet (PBH) flies past the lighthouse (Neutron Star), it ripples the fabric of space-time. It's like a stone skipping across a pond, creating waves. Our detectors (LIGO, Virgo, KAGRA) are like super-sensitive ears trying to hear that splash.

The Two Scenarios: The "Flyby" vs. The "Orbit"

The paper looks at two ways these ghosts might interact with the lighthouses in the center of our galaxy (the Galactic Center).

1. The "Flyby" (Unbound Encounters)

Imagine a tiny bullet flying past a lighthouse at high speed. It zooms by, makes a loud whoosh (a gravitational wave burst), and keeps going forever.

The Problem: The galaxy is huge. The chance of a bullet hitting the exact right spot to make a loud enough whoosh for us to hear is incredibly small. It's like trying to hear a pin drop in a hurricane.

2. The "Orbit" (Bound Encounters)

Now, imagine the bullet gets caught by the lighthouse's gravity. It doesn't crash immediately; instead, it gets stuck in a very stretched-out, oval-shaped orbit.

The Analogy: Think of a skier going down a mountain. They swoop down close to the ground (the Neutron Star), whip around, and shoot back up high. Then they come back down, whip around again, and shoot back up.
The Promise: Every time the skier swoops down close to the ground, they make a whoosh. If the skier does this 1,000 times, we have 1,000 chances to hear them, not just one!
The Reality Check: The authors did the math and found that while this "skier" makes many sounds, there are so few of them in the first place that the total number of sounds is still very low. The "Flyby" scenario, even though it only happens once, is actually more common because there are more bullets flying around than there are skiers stuck in orbits.

The "Galactic Center" Challenge

The authors focused on the center of our galaxy because that's where the "crowd" is.

The Crowd: There are billions of Neutron Stars and a huge amount of Dark Matter (the ghosts) packed tightly there.
The Distance: However, the center is very far away (about 26,000 light-years). It's like trying to hear a whisper from the other side of a football stadium.

The Verdict: The Odds Are Against Us

After crunching the numbers for a 10-year observation period (using current detectors like LIGO), the authors found a disappointing but honest conclusion:

The probability of hearing a single one of these events is about 1 in 100 million ( $10^{-8}$ ).

Even if we assume the center of the galaxy is a "super-dense" cluster of these ghosts (which is a very optimistic guess), and even if we wait for future, super-powerful detectors (like the Einstein Telescope), the odds of catching a signal remain very slim.

Why Do This If We Won't Find Anything?

You might ask, "Why write a paper about something that probably won't happen?"

Ruling Out Possibilities: Science is about knowing what doesn't work. By calculating the odds, the authors tell future scientists: "Don't waste your time looking for these specific signals with current tech; the signal is too weak."
Indirect Clues: Since we probably won't "hear" the ghosts directly, the paper suggests we should look for their footprints. Maybe the ghosts destroy some Neutron Stars over millions of years, or maybe they leave a chemical mark on stars. We might not hear the ghost, but we might see the mess it left behind.

Summary in One Sentence

The authors calculated that while tiny, ancient black holes might zoom past neutron stars in the center of our galaxy creating "space ripples," the chances of our current detectors hearing even one of these events in the next decade are virtually zero, making it a very unlikely way to find Dark Matter.

1. Problem Statement

The authors investigate the feasibility of detecting Primordial Black Holes (PBHs) as a component of Dark Matter (DM) through their gravitational wave (GW) interactions with Neutron Stars (NSs) in the Galactic Center.

While previous studies focused on:

Mergers of stellar-mass PBH binaries.
Continuous GW signals from PBHs captured inside NSs (spiraling inward).

This paper addresses a gap in the literature: the detection of burst-like GW signals generated when PBHs pass near or through NSs on eccentric orbits (either unbound hyperbolic encounters or bound elliptical orbits). The specific focus is on planetary-mass PBHs ( $m \ll M_\odot$ ), a mass range difficult to probe with current detectors but potentially accessible via the high-frequency dynamics of PBH-NS encounters.

2. Methodology

The study employs a multi-step analytical and numerical approach to estimate detection probabilities over a 10-year observation window (LIGO-Virgo-KAGRA O4 sensitivity).

A. Signal Characterization (Section II)

Strain Calculation: The authors model the GW strain ( $h_c$ ) for PBHs on highly eccentric orbits ( $e \approx 1$ ). They utilize the power spectrum derived for parabolic limits, as most relevant bound orbits are highly eccentric.
Frequency Scaling: The characteristic GW frequency is determined by the orbital dynamics: $f_{GW} \propto (M/a)^{1/2}$ . For light PBHs, the total mass is dominated by the NS, placing the signal frequency in the $\sim 100-1000$ Hz range, well within the LVK sensitivity band.
Detection Threshold: A signal is considered detectable if the Signal-to-Noise Ratio (SNR) $> 10$ $> 10$ . The authors calculate the required periastron distance ( $r_p$ $r_{p}$ ) as a function of PBH mass ( $m$ $m$ ) and distance ( $d$ $d$ ).
- Key Finding: Detectable signals require $m \gtrsim 10^{-4} M_\odot$ and $r_p \lesssim 1000$ km.

B. Event Rate Estimation (Sections III & IV)

The authors distinguish between two populations of PBH-NS interactions:

Unbound Encounters: Random flybys where the PBH passes the NS once.
Bound Encounters: PBHs captured by NSs via energy loss, leading to repeated periastron passages.

Formation and Evolution of Bound Systems:

Capture Mechanism: PBHs are captured via energy loss during close encounters. Two mechanisms are analyzed:
- Gravitational Wave (GW) Emission: Dominant for grazing encounters ( $r_p > R_{NS}$ ).
- Dynamical Friction (DF): Dominant for trajectories crossing the NS interior ( $r_p < R_{NS}$ ).
Orbital Decay: The authors calculate the inspiral time ( $t_{ins}$ $t_{in s}$ ) by summing the orbital periods as energy is lost.
- For DF-dominated cases, the inspiral is rapid (single burst/merger).
- For GW-dominated cases, the inspiral is slow, allowing for multiple bursts over the observation window.
Stability Constraints: The maximum apastron ( $r_a$ ) for a bound orbit is limited by gravitational perturbations from neighboring stars in the dense Galactic Center. The authors derive a critical distance $r_c \approx 350$ AU; orbits with $r_a > r_c$ are disrupted before they can produce detectable signals.

C. Probability Calculation (Section V)

The total detection probability ( $P$ ) is calculated using Poisson statistics:
$P = 1 - \exp(-\bar{N}) \approx \bar{N}$
where $\bar{N}$ is the mean number of detectable events in 10 years.

$\bar{N}_{DF}$ (Dynamical Friction): Calculated as the rate of direct mergers (single burst per PBH).
$\bar{N}_{GW}$ (Gravitational Waves): Calculated by integrating the injection rate of bound PBHs multiplied by the probability ( $P_S$ ) that at least one periastron passage occurs within the 10-year window. This accounts for the "correlated" nature of repeated bursts from a single system.

3. Key Contributions

Mass Range Focus: The paper specifically targets the planetary-mass PBH window ( $10^{-4} M_\odot \lesssim m \lesssim 10^{-2} M_\odot$ ), which is largely unconstrained by other methods but accessible via the high-frequency GWs of PBH-NS encounters.
Bound vs. Unbound Comparison: It rigorously compares the detection prospects of repeated bursts from bound PBHs against single bursts from unbound flybys.
Stability Analysis: It introduces a critical constraint on the maximum size of bound PBH-NS orbits ( $r_c \approx 350$ AU) due to stellar perturbations in the Galactic Center, a factor often overlooked in capture rate calculations.
SNR Thresholding: The authors apply a conservative SNR $> 10$ threshold, revealing that previous estimates for detectable PBH masses inside NSs were overly optimistic.

4. Results

Detection Probability: The probability of detecting a signal in a 10-year period is extremely low: $P \lesssim 10^{-8}$ .
Dominant Channel: Despite the potential for repeated bursts from bound systems, unbound (hyperbolic) encounters dominate the detection probability.
- Reasoning: While bound systems produce multiple signals, their formation rate is too low to compensate for the sheer volume of random unbound encounters. The enhancement from repeated bursts does not overcome the lower number density of bound systems.
Mass Threshold: Signals are only detectable for PBH masses $m \gtrsim 10^{-4} M_\odot$ . Below this, the strain is too weak for current detectors unless the event is extremely close to Earth (which is statistically unlikely given the low NS density in the solar neighborhood).
Impact of Optimistic Scenarios:
- Even assuming a Dark Matter spike around the Galactic Center supermassive black hole (increasing DM density to $\sim 10^6$ GeV/cm $^3$ ) and improved sensitivity (Einstein Telescope), the detection probability remains below order unity ( $O(1)$ ).
- Clustering of PBHs could enhance rates by $\sim 100\times$ , but this is insufficient to make detection likely with current technology.

5. Significance and Conclusion

Negative Result for Direct Detection: The paper concludes that direct GW detection of planetary-mass PBHs via PBH-NS encounters in the Galactic Center is highly improbable with current or near-future detectors (LVK, Einstein Telescope).
Shift in Strategy: Given the low direct detection probability, the authors suggest that indirect astrophysical consequences are a more viable probe. These include:
- The destruction of the pulsar population in the Galactic Center.
- R-process enhancement in stars due to NS destruction.
Theoretical Value: The work provides a comprehensive framework for calculating GW rates from non-compact object encounters, highlighting the importance of orbital stability and the specific dynamics of high-eccentricity bursts.

In summary, while the physics of PBH-NS interactions is sound and the signals are theoretically within the frequency band of GW detectors, the event rates are too low to expect a detection in the coming decade, rendering indirect methods the more promising avenue for constraining planetary-mass PBHs.