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arxiv: 2606.05082 · v1 · pith:ZONLNT35new · submitted 2026-06-03 · 🌌 astro-ph.CO · astro-ph.SR· gr-qc

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

Premachand Mahapatra , Andrew L. Miller , Prasanta Kumar Das This is my paper

Pith reviewed 2026-06-28 05:01 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.SRgr-qc
keywords continuous gravitational wavesdark matter admixed neutron starsself-interacting fermionic dark matterdark mountainsLIGO O3 searchesneutron star ellipticitygravitational wave constraints
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The pith

LIGO continuous-wave searches exclude self-interacting fermionic dark matter couplings g ≳ 10^{-5.5} for neutron stars with ellipticities of 10^{-7} at 1 kpc.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a model showing how self-interacting fermionic dark matter accumulates inside neutron stars, forms an anisotropic distribution that creates equatorial deformations called dark mountains, and raises the star's moment of inertia enough to produce stronger continuous gravitational-wave emission than ordinary neutron stars. Using published results from all-sky LIGO O3 searches for such waves, it translates non-detections into upper limits on the dark-matter self-interaction coupling strength across a range of dark-matter masses. A reader should care because the work supplies the first direct gravitational-wave bounds on this class of dark-matter models inside compact objects and shows that next-generation detectors will tighten those bounds further.

Core claim

The central claim is that the developed formalism maps dark-matter accumulation and anisotropic distribution inside a rapidly rotating neutron star to an increased ellipticity and gravitational-wave amplitude; when this amplitude is compared with the sensitivity of existing LIGO all-sky continuous-wave searches, large regions of the dark-matter mass versus self-interaction coupling parameter space are excluded, with the strongest limits ruling out couplings g ≳ 10^{-5.5} for ellipticities ε = 10^{-7} at 1 kpc and m_χ between 0.1 and 10 GeV.

What carries the argument

The formalism that converts dark-matter accumulation and anisotropic distribution into dark mountains, an increased moment of inertia, and a calculable continuous gravitational-wave amplitude.

If this is right

  • Couplings g ≳ 10^{-4} are excluded even for the weaker ellipticity of 10^{-9} at 10 kpc.
  • Einstein Telescope and Cosmic Explorer will reach exclusions as strong as g ≳ 10^{-6} for the same ellipticity at 10 kpc.
  • The same data set already rules out detectable signals across the full frequency range analyzed by LIGO for the considered dark-matter masses.
  • Continuous-wave searches thereby become a direct probe of dark mountains sustained by dark-matter-admixed neutron stars.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same modeling approach could be applied to other dark-matter candidates that produce anisotropic distributions inside neutron stars.
  • Joint analysis with radio or X-ray observations of neutron-star rotation rates might further tighten the ellipticity bounds used here.
  • If the dark-matter density profile inside the star deviates strongly from the assumed form, the derived coupling limits would shift by an amount comparable to the difference between the best and worst cases already quoted.

Load-bearing premise

The mapping from dark-matter parameters to the resulting gravitational-wave amplitude is accurate enough that non-detections in LIGO data can be read directly as exclusions on coupling strength without large extra uncertainties from the internal dark-matter density profile.

What would settle it

A confirmed continuous gravitational-wave detection from an isolated neutron star at 1 kpc with frequency in the LIGO band and ellipticity near 10^{-7} that is inconsistent with the excluded coupling values would falsify the reported exclusions.

Figures

Figures reproduced from arXiv: 2606.05082 by Andrew L. Miller, Prasanta Kumar Das, Premachand Mahapatra.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Contribution of DM to the moment of inertia [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: This feature indicates a crossover between two [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Ellipticity as a function of the DM anisotropy [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spin-down [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Spin-down [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Spin-down [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Strain amplitude for DM-admixed neutron stars compared with the LVK O3 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Constraints on the maximum sustainable ellipticity [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: displays the resulting exclusion maps for three chosen ellipticities ε = 10−9 , 10−8 , 10−7 (δ ∼ 10−10 , 10−9 , 10−8 , respectively) for d = 10 kpc (left column) and d = 1 kpc (right column). The colormap represents the GW strain, while the white contours in￾dicate when the calculated strain amplitude equals the upper-limit value. Observationally excluded regions are distinguished by hatch patterns for ea… view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Same as in Fig. 10, but the plot represents projected exclusion regions using the expected sensitivity of CE (left) [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
read the original abstract

We investigate continuous gravitational-wave (CW) emission from rapidly rotating, non-axisymmetric, isolated neutron stars admixed with self-interacting fermionic dark matter (DM) and hosting DM-induced equatorial deformations (``dark mountains''). In particular, we develop a formalism that describes how DM accumulation inside the star changes its structure, how dark mountains arise from an anisotropic distribution of DM inside it, and how the star's moment of inertia and thus the amplitude of its GW emission is increased compared to that of an ordinary neutron star. Moreover, using results from all-sky searches for CWs from non-axisymmetric neutron stars performed with LIGO O3 data, we place the first constraints on the DM-induced ellipticities $\varepsilon$ of DM-admixed neutron stars across the full GW frequency range analyzed by LIGO and for a range of self-interaction strengths. With the same data, we also exclude portions of the DM-mass/self-interaction coupling strength parameter space that would have produced detectable GW signals in LIGO O3 data. We rule out at best (at worst) couplings $g\gtrsim10^{-5.5}$ ($g\gtrsim 10^{-4}$) for DM-admixed neutron stars with ellipticities $\varepsilon=10^{-7}$ ($\varepsilon=10^{-9}$) at distances $d=1$ ($d=10$) kpc away for DM masses of $m_\chi\in[0.1,10]$ GeV. Furthermore, we show that even larger regions of this parameter space will become accessible to next-generation detectors, such as Einstein Telescope and Cosmic Explorer, with exclusions as strong as $g\gtrsim10^{-6}$ for neutron stars located $d=10$ kpc away for $\varepsilon=10^{-7}$. Our results demonstrate that searches for CWs naturally provide a direct probe of dark mountains sustained by DM-admixed neutron stars.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops a formalism describing how self-interacting fermionic dark matter accumulates in rapidly rotating neutron stars, produces anisotropic distributions leading to equatorial deformations ('dark mountains'), and increases the stellar moment of inertia, thereby enhancing continuous gravitational-wave (CW) emission. Using published upper limits from LIGO O3 all-sky CW searches for non-axisymmetric neutron stars, the authors derive the first constraints on the DM-induced ellipticity ε across the analyzed frequency range and exclude regions of the DM particle mass m_χ and self-interaction coupling g parameter space for assumed values of ε and source distance d, with exclusions as strong as g ≳ 10^{-5.5} for ε=10^{-7} at d=1 kpc; prospects for Einstein Telescope and Cosmic Explorer are also discussed.

Significance. If the mapping from (m_χ, g) to ε and GW strain is robust, the work establishes CW searches as a new probe of DM-admixed neutron stars and demonstrates that existing LIGO limits already constrain portions of the fermionic DM parameter space. The efficient reuse of published all-sky search results without requiring new data analysis is a methodological strength.

major comments (2)
  1. [formalism and constraints sections] The central exclusion bounds on g (abstract and § on constraints) rest on a specific mapping from DM self-interaction parameters to ellipticity ε via an assumed anisotropic DM density profile inside the star. The manuscript does not quantify how changes to this profile (e.g., different anisotropy parameters or self-consistent solutions of the fermionic EOS versus an imposed distribution) propagate into the predicted GW amplitude h_0 and the resulting excluded regions in the (m_χ, g) plane.
  2. [GW amplitude derivation] It is unclear whether the increased moment of inertia due to DM is inserted directly into the standard CW strain formula without additional model-dependent factors arising from modifications to the stellar rotation law or selection effects in the LIGO all-sky searches; this directly affects whether the quoted exclusions (e.g., g ≳ 10^{-5.5} for ε=10^{-7}) can be compared one-to-one with the published upper limits.
minor comments (2)
  1. [formalism] Notation for the DM density profile and anisotropy parameter should be defined explicitly at first use to improve readability.
  2. [parameter space] The range of m_χ ∈ [0.1,10] GeV is stated but the motivation for the lower and upper bounds could be clarified with a brief reference to existing DM constraints.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, positive assessment of its significance, and constructive comments. We address each major comment below and will incorporate clarifications and additional discussion in a revised version.

read point-by-point responses

  1. Referee: [formalism and constraints sections] The central exclusion bounds on g (abstract and § on constraints) rest on a specific mapping from DM self-interaction parameters to ellipticity ε via an assumed anisotropic DM density profile inside the star. The manuscript does not quantify how changes to this profile (e.g., different anisotropy parameters or self-consistent solutions of the fermionic EOS versus an imposed distribution) propagate into the predicted GW amplitude h_0 and the resulting excluded regions in the (m_χ, g) plane.

    Authors: We acknowledge that the exclusion bounds rely on the specific anisotropic DM density profile developed in the formalism section. The manuscript does not include a quantitative sensitivity study to variations in this profile. In the revised manuscript we will add a dedicated paragraph in the constraints section that states the adopted profile explicitly, discusses qualitatively how reasonable changes to the anisotropy parameter or EOS solution could shift the ellipticity and thus the excluded regions in the (m_χ, g) plane, and notes that a full parameter exploration lies beyond the scope of the present work. This will make the model assumptions and their implications transparent without altering the central results obtained under the chosen profile. revision: partial

  2. Referee: [GW amplitude derivation] It is unclear whether the increased moment of inertia due to DM is inserted directly into the standard CW strain formula without additional model-dependent factors arising from modifications to the stellar rotation law or selection effects in the LIGO all-sky searches; this directly affects whether the quoted exclusions (e.g., g ≳ 10^{-5.5} for ε=10^{-7}) can be compared one-to-one with the published upper limits.

    Authors: The GW strain is computed from the standard expression h_0 = (4π²G/c⁴)(I_DM ε f²/d), where I_DM is the moment of inertia of the DM-admixed star. The LIGO O3 all-sky CW searches supply upper limits on the emitted strain amplitude h_0 that are independent of the internal stellar model; they do not incorporate assumptions about the rotation law or moment of inertia. Consequently the comparison between our predicted h_0 and the published limits is direct. In the revised manuscript we will insert an explicit statement of the strain formula together with this justification in the constraints section, confirming that no additional model-dependent selection effects are applied. revision: yes

Circularity Check

0 steps flagged

No circularity: external LIGO limits applied to independent model

full rationale

The paper develops a formalism mapping DM parameters (g, m_χ) to ellipticity ε and GW strain h0 via DM accumulation and anisotropic density effects, then applies published LIGO O3 all-sky CW upper limits as external bounds to exclude regions of parameter space. No equation reduces a claimed prediction to a quantity fitted from the same LIGO data, no self-citation chain is load-bearing for the central mapping, and the derivation remains self-contained against the external search results.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 1 invented entities

The central claim rests on standard neutron-star structure assumptions plus a new model for DM-induced deformations; no machine-checked proofs or shipped code are indicated.

free parameters (4)
  • DM self-interaction coupling g
    Parameter whose values are excluded by the LIGO data for given ellipticity and distance.
  • DM particle mass m_χ
    Considered in the range [0.1,10] GeV for the exclusion plots.
  • ellipticity ε
    Values 10^{-7} and 10^{-9} used to quote the coupling exclusions.
  • distance d
    Values 1 kpc and 10 kpc used for the quoted bounds.
axioms (2)
  • domain assumption DM accumulation inside the neutron star changes its structure and produces an anisotropic distribution that creates equatorial deformations.
    Invoked when describing how dark mountains arise.
  • domain assumption The DM-induced deformations increase the star's moment of inertia and thereby the amplitude of its continuous gravitational-wave emission.
    Used to connect the DM model to observable GW signals.
invented entities (1)
  • dark mountains no independent evidence
    purpose: DM-induced equatorial deformations sustained by anisotropic fermionic DM inside the neutron star
    New descriptive term introduced for the deformations that source the GW signal.

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Reference graph

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