First Constraints on the Ellipticities of Self-Interacting Fermionic Dark Matter Admixed Neutron Stars from Continuous Gravitational-Wave Searches

This paper presents the first constraints on the ellipticities and self-interaction parameters of fermionic dark matter-admixed neutron stars by analyzing LIGO O3 continuous gravitational-wave data, demonstrating that such searches can effectively probe "dark mountains" and exclude specific regions of dark matter parameter space.

The Gist

Imagine the universe is filled with invisible "ghosts" called Dark Matter. Scientists have long wondered: do these ghosts hang out inside heavy, spinning stars called Neutron Stars? If they do, do they change how those stars behave?

This paper is like a detective story. The authors are trying to find out if Dark Matter is hiding inside Neutron Stars by listening for a specific "hum" that only these stars would make if they were carrying a secret cargo.

Here is the breakdown of their investigation using simple analogies:

1. The "Dark Mountain" Analogy

Normally, a spinning Neutron Star is like a perfectly smooth, spinning top. If it's perfectly round, it spins silently. But if it has a bump on it—like a mountain—it wobbles as it spins. This wobble creates ripples in space-time called Gravitational Waves (think of them as ripples in a pond).

The authors propose a new idea: What if the "mountain" isn't made of rock, but of Dark Matter?

• They imagine Dark Matter gathering inside the star.
• Because Dark Matter particles bump into each other (they "self-interact"), they might pile up unevenly, creating a hidden, invisible "Dark Mountain" on the star's equator.
• This mountain makes the star wobble more than a normal star would, creating a stronger signal.

2. The "Heavy Backpack" Effect

The paper explains that adding Dark Matter doesn't just add a bump; it changes the star's weight distribution.

• The Analogy: Imagine a figure skater spinning. If they hold a heavy backpack, they spin differently than if they are empty-handed.
• The Science: The Dark Matter acts like a heavy backpack that changes the star's Moment of Inertia (a measure of how hard it is to spin something). The more Dark Matter and the stronger its internal "bumping" (self-interaction), the heavier the "backpack" feels, and the more gravitational waves the star emits.

3. Borrowing a Silent Search

The authors did not run a new experiment or listen to the data themselves. Instead, they looked at the results of a previous, massive investigation already completed by the LIGO scientific collaboration.

• The Context: LIGO had previously scanned the entire sky during a specific time period (called "O3") looking for continuous gravitational waves from spinning, isolated neutron stars. That search found nothing—no "hum" was detected.
• The Reinterpretation: The authors took those existing "null results" (the fact that nothing was heard) and asked a new question: "What does this silence tell us about Dark Matter?"
• The Deduction: They reasoned that if Dark Matter were creating a large enough "mountain" inside these stars, the previous search would have heard it. Since the previous search heard nothing, the authors used that silence to draw new conclusions about what is not possible.

4. Setting the Rules (The Constraints)

By reinterpreting the existing silent data, the authors drew a line in the sand to say: "Dark Matter cannot be this strong inside these stars."

• They tested different "weights" for the Dark Matter particles and different "stickiness" levels (how much they bump into each other).
• The Finding: They ruled out the possibility that Dark Matter is very "sticky" (strong self-interaction) inside these stars. Specifically, they said that if the Dark Matter particles are too heavy or interact too strongly, the star would have made a noise that the previous LIGO search would have caught. Since that search heard nothing, those specific types of Dark Matter are likely not present in the way they modeled.

5. The Future: Better Ears

The paper concludes that while the existing search didn't find these "Dark Mountains," it set very strict rules.

• The Analogy: It's like trying to hear a whisper in a noisy room. The previous search was a good microphone, but the room was still a bit noisy.
• The Outlook: The authors say that future, super-sensitive detectors (like the "Einstein Telescope" or "Cosmic Explorer") will be like putting on noise-canceling headphones. These new tools will be able to hear much quieter whispers, allowing us to test even weaker types of Dark Matter interactions that the previous search couldn't catch.

Summary

In short, this paper says: "We took the results of a previous search that listened to spinning neutron stars and found no sound of hidden Dark Matter mountains. By reinterpreting that silence, we determined that if Dark Matter is inside these stars, it can't be too 'sticky' or heavy, or the previous search would have heard it. We have now set the first strict rules on how much Dark Matter can hide inside these stars."

Technical Summary

Technical Summary: First Constraints on the Ellipticities of Self-Interacting Fermionic Dark Matter–Admixed Neutron Stars

Problem Statement
While continuous gravitational waves (CWs) from non-axisymmetric rotating neutron stars remain undetected, upper limits on strain amplitude provide a powerful tool to constrain the internal structure of these compact objects. Specifically, these limits can probe the presence of exotic matter, such as dark matter (DM), within neutron stars. Previous theoretical work has established that DM can accumulate in neutron stars, altering their macroscopic properties (mass, radius, stability). However, the implications of self-interacting fermionic DM on CW emission—specifically regarding the generation of "dark mountains" (equatorial deformations) and the modification of the moment of inertia—have remained underexplored. This paper addresses the gap in connecting self-interacting DM parameters to observable CW strain limits.

Methodology
The authors develop a formalism combining a two-fluid model of neutron stars with a self-interacting fermionic DM component.

1. Theoretical Framework: The model assumes a neutron star composed of baryonic matter (described by a relativistic mean-field framework) and a gravitationally bound, self-interacting fermionic DM component. The DM self-interaction is mediated by a Yukawa-type scalar field with coupling strength $g$ and mediator mass $m_\phi$.
2. Structure and Inertia: The total energy density includes kinetic energy and a repulsive Yukawa potential energy term. The authors calculate the principal moment of inertia ($I_{zz}$) as a function of the DM mass ($m_\chi$) and coupling strength ($g$), assuming the DM is distributed within an oblate spheroid.
3. Ellipticity Generation: To generate CWs, the model introduces an anisotropic perturbation in the DM energy density, analogous to a "dark mountain." This anisotropy, parameterized by $\delta$, creates a non-axisymmetric mass distribution, leading to an ellipticity $\epsilon \propto \delta$.
4. Constraint Procedure: The authors utilize null results from the LIGO O3 all-sky CW search (specifically the Frequency Hough pipeline). They compare the theoretically predicted CW strain amplitude ($h_0$) for various $(g, m_\chi)$ pairs against the O3 upper limits ($h_0^{95\%}$).
   • They verify that the predicted spin-down rates ($\dot{f}$) for these models fall within the search range of the O3 data ($|\dot{f}| \in [10^{-8}, 10^{-9}]$ Hz s$^{-1}$).
   • They identify regions in the $(g, m_\chi)$ parameter space where the predicted strain would have exceeded the O3 upper limits, thereby excluding those configurations.

Key Contributions

• Formalism Development: The paper establishes a direct link between the self-interaction strength of fermionic DM and the CW emission amplitude of neutron stars. It quantifies how DM accumulation increases the moment of inertia ($I_{zz}$) and how anisotropic DM distributions generate ellipticity.
• First Constraints: This work presents the first constraints on the ellipticities of DM-admixed neutron stars derived from continuous gravitational-wave searches.
• Parameter Space Exploration: The study systematically explores a discrete grid of DM masses ($m_\chi \in [0.1, 10]$ GeV) and coupling strengths ($g \in [10^{-6}, 10^{-3.5}]$), consistent with astrophysical bounds on self-interaction cross-sections ($\sigma/m_\chi$).

Results

• Dependence on Coupling: The CW strain amplitude is found to be highly sensitive to the coupling strength $g$, with a strong, monotonic increase as $g$ increases. The dependence on DM mass $m_\chi$ is comparatively weak.
• Exclusion Limits: Using LIGO O3 data, the authors exclude portions of the parameter space where DM-admixed neutron stars would have produced detectable signals:
  • For a source at $d=10$ kpc with ellipticity $\epsilon = 10^{-9}$, couplings $g \gtrsim 10^{-4}$ are excluded.
  • For a source at $d=1$ kpc with ellipticity $\epsilon = 10^{-7}$, couplings as low as $g \gtrsim 10^{-5.5}$ are excluded.
  • In the worst-case scenario (distant, low ellipticity), constraints reach $g \gtrsim 10^{-4}$.
• Moment of Inertia Enhancement: The presence of DM significantly enhances $I_{zz}$, which tightens the constraints on the maximum sustainable ellipticity ($\epsilon_{max}$) for a given strain limit by up to several orders of magnitude compared to ordinary neutron stars.
• Future Projections: The authors project that next-generation detectors (Einstein Telescope and Cosmic Explorer) will improve sensitivity by more than an order of magnitude. This would allow the exclusion of couplings as low as $g \gtrsim 10^{-6}$ for sources at $d=10$ kpc with $\epsilon = 10^{-7}$.

Significance
The paper demonstrates that searches for continuous gravitational waves provide a direct probe of "dark mountains" sustained by self-interacting fermionic dark matter. By utilizing null results from LIGO O3, the authors have ruled out specific combinations of DM mass and self-interaction strength that would have produced observable signals. The study highlights that CW observations offer a unique avenue to constrain DM physics on the scale of individual astrophysical objects, probing self-interaction couplings that are over two orders of magnitude smaller than those constrained by previous studies using pulsar timing or binary merger data. The results motivate future CW searches as a critical tool for testing self-interacting dark matter scenarios in regimes inaccessible to laboratory experiments or traditional telescopic observations.