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arxiv: 2606.27456 · v1 · pith:N6OTDAETnew · submitted 2026-06-25 · 🌀 gr-qc · astro-ph.HE· hep-ph· nucl-th

The crust of dark-matter admixed neutron stars: bulk properties and torsional oscillations

Jiayi Zhang , Hector O. Silva This is my paper

Pith reviewed 2026-06-29 01:35 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEhep-phnucl-th
keywords dark matter admixed neutron starscrust thicknesstorsional oscillationsdark coreequation of staterelativistic Cowling approximationneutron star oscillations
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The pith

Dark matter reduces neutron star crust thickness by up to 12% when forming a dark core

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

The paper examines how dark matter admixed with neutron stars affects the outer crust and its torsional oscillations. At fixed total mass and dark matter fraction, when dark matter forms a core inside the baryonic surface, the crust becomes thinner by up to 12 percent compared to ordinary neutron stars. This thinning leads to higher frequencies for torsional modes. The authors derive approximate formulas for crust thickness and the mode equation in the relativistic Cowling approximation. They suggest these shifts could help detect dark matter cores if observed.

Core claim

At fixed total gravitational mass and DM mass fraction, DM reduces the crust thickness in comparison to pure baryonic-matter neutron stars. The thinning of the crust is negligible when most of the DM distribution extends beyond the star's baryonic surface. However, the crust thickness can decrease by as much as 12% when the DM distribution is within the star's baryonic surface, i.e., when the star has a dark core. The oscillation frequencies are in general higher than those of a comparable pure baryonic-matter NS, with the largest frequency shifts happening in the same parameter space where the crust thickness decreases the most. Approximate analytical formulas for the crust thickness agree

What carries the argument

Two-fluid equilibrium solutions wherein baryonic and DM interact gravitationally only, adopting a unified nuclear equation of state for baryons and a fermionic equation of state with repulsive self-interaction for DM; the equation for crustal torsional modes in the relativistic Cowling approximation.

If this is right

  • Crust thinning is negligible if most DM lies outside the baryonic surface.
  • Torsional frequencies increase most where crust thinning is largest.
  • Degeneracy between DM effects and baryonic microphysics such as electron screening can be broken in some regions of parameter space.
  • Torsional oscillations could be used to infer the existence of a DM core within massive NSs if measured.

Where Pith is reading between the lines

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

  • The frequency shifts might allow multi-messenger observations to separate DM signals from variations in nuclear crust parameters.
  • The two-fluid gravitational setup could be applied to study mixed compositions in other compact objects.
  • Crust thinning may indirectly affect NS cooling or magnetic field dynamics not calculated in this work.

Load-bearing premise

Baryonic and dark matter interact only gravitationally and the results rely on one specific unified nuclear EOS for baryons plus one fermionic self-interacting EOS for DM.

What would settle it

A measured torsional oscillation frequency in a massive neutron star of known mass and inferred DM fraction that shows no upward shift relative to the pure baryonic prediction, despite parameters indicating a dark core.

Figures

Figures reproduced from arXiv: 2606.27456 by Hector O. Silva, Jiayi Zhang.

Figure 1
Figure 1. Figure 1: Bulk properties of DANSs. We show the total mass, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: The crust thickness of DANSs with Mt = 1.4 M⊙, normalized with respect to the PNS value, ∆RPNS = 1.556 km, as a function of mχ and vanishing dark matter self-interaction. The horizontal dashed line corresponds to the PNS value. The shaded regions indicate the different DANSs configurations, from diffuse halo to dark core. We see that for small values of mχ, the crust thickness of DANSs changes little with … view at source ↗
Figure 6
Figure 6. Figure 6: The baryonic compactness Cb as a function of the dark matter particle mass mχ for DANS models with fixed total mass Mt = 1.4 M⊙ and dark-matter mass fraction fχ = 0.05. The curve shows the numerical results, while the square and triangle denote the diffuse-halo (24) and dark￾core (22) limiting estimates, respectively. Both estimates agree well with the numerical data. As in previous figures, the shaded reg… view at source ↗
Figure 7
Figure 7. Figure 7: The crust thickness fraction as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: The quadrupolar torsional oscillations frequencies for DANS solutions with fixed total mass [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The ratio between fundamental mode (circles) and [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The fundamental torsional oscillation frequencies [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The relative error between the numerical crust [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
read the original abstract

We study how dark matter (DM) impacts the crust and the spectrum of torsional crust oscillations of dark-matter-admixed neutron stars (DANSs). We construct two-fluid equilibrium solutions wherein baryonic and DM interact gravitationally only, adopting a unified nuclear equation of state for the former and a fermionic equation of state with repulsive self-interaction for the latter. At fixed total gravitational mass and DM mass fraction, we find that DM reduces the crust thickness in comparison to pure baryonic-matter neutron stars (NSs). The thinning of the crust is negligible when most of the DM distribution extends beyond the star's baryonic surface. However, the crust thickness can decrease by as much as 12% when the DM distribution is within the star's baryonic surface, i.e., when the star has a "dark core." We support these results by deriving approximate analytical formulas for the crust thickness that agree with our numerical calculations at the sub-percent level in best case scenarios. Next, we derive the equation that describes crustal torsional modes of DANSs in the relativistic Cowling approximation. We find that the oscillation frequencies are in general higher than those of a comparable pure baryonic-matter NS, with the largest frequency shifts happening in the same parameter space where the crust thickness decreases the most. Moreover, we study the degeneracy between DM and baryonic-crustal microphysics effects on these modes. As an example, we study electron screening, which softens the crust's shear modulus, thus decreasing the frequencies. We find that the degeneracy between the competing effects of DM and electron screening can be broken in some regions of the parameter space we explored. Should they be measured, our results suggest that torsional oscillations could be used to infer the existence of a DM core within massive NSs. (Abridged)

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 manuscript constructs two-fluid TOV equilibria for dark-matter-admixed neutron stars using a unified nuclear EOS for baryons and a self-interacting fermionic EOS for DM. At fixed total gravitational mass and DM mass fraction it reports that a dark core thins the baryonic crust by as much as 12 %, derives analytic crust-thickness approximations that match the numerical solutions at the sub-percent level in best cases, and shows that the associated torsional frequencies (computed in the relativistic Cowling approximation) are systematically higher, with the largest shifts occurring in the same dark-core regime. The work also examines the competing effect of electron screening on the shear modulus and finds that the DM-induced frequency up-shift can be distinguished from screening-induced down-shifts in parts of parameter space.

Significance. If the quantitative results survive EOS variation, the paper supplies both a concrete observational signature (elevated torsional frequencies) for the presence of a DM core and a practical analytic tool for estimating crust thickness. The explicit demonstration that DM and electron-screening effects are not fully degenerate in some regions adds value for future mode-based constraints.

major comments (2)
  1. [Abstract and numerical crust results] Abstract and crust-thickness results: the reported maximum thinning of 12 % (and the associated frequency shifts) is obtained with one specific unified nuclear EOS and one specific fermionic DM EOS; the manuscript presents no additional runs that vary the nuclear symmetry-energy slope, high-density stiffness, or DM self-interaction coupling. Because the gravitational compression of the baryonic envelope depends directly on these microphysical choices, the numerical value of the thinning percentage is tied to the adopted EOS pair and its robustness remains untested.
  2. [Analytic approximations section] Analytic crust-thickness formulas: the text states that the approximations agree with the numerical solutions “at the sub-percent level in best case scenarios.” The manuscript should quantify the typical (not just best-case) fractional error across the explored range of DM mass fraction and core radius, and state the conditions under which the analytic expressions remain accurate to the claimed precision.
minor comments (2)
  1. [Methods / equilibrium construction] The definition of the DM mass fraction and the precise radial boundary used to identify a “dark core” should be stated explicitly in the methods section to avoid ambiguity when comparing with other two-fluid studies.
  2. [Figures] Figure captions for the frequency-shift plots would benefit from an explicit statement of the fixed total mass and the range of DM fractions shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and numerical crust results] Abstract and crust-thickness results: the reported maximum thinning of 12 % (and the associated frequency shifts) is obtained with one specific unified nuclear EOS and one specific fermionic DM EOS; the manuscript presents no additional runs that vary the nuclear symmetry-energy slope, high-density stiffness, or DM self-interaction coupling. Because the gravitational compression of the baryonic envelope depends directly on these microphysical choices, the numerical value of the thinning percentage is tied to the adopted EOS pair and its robustness remains untested.

    Authors: We agree that the quoted 12 % maximum thinning (and the associated frequency shifts) is specific to the chosen unified nuclear EOS and fermionic DM EOS; no parameter variations of the symmetry-energy slope, high-density stiffness, or DM self-interaction strength were performed. The gravitational mechanism itself is independent of those details, but the precise percentage is not. In the revised manuscript we will add an explicit caveat in the abstract, results, and discussion sections stating that the numerical value depends on the microphysical inputs and that a broader EOS survey would be required to establish robustness of the percentage. We will also note that the analytic crust-thickness formulas remain applicable regardless of the specific EOS choice. revision: partial

  2. Referee: [Analytic approximations section] Analytic crust-thickness formulas: the text states that the approximations agree with the numerical solutions “at the sub-percent level in best case scenarios.” The manuscript should quantify the typical (not just best-case) fractional error across the explored range of DM mass fraction and core radius, and state the conditions under which the analytic expressions remain accurate to the claimed precision.

    Authors: We will revise the analytic-approximations section to report both the typical (mean and rms) and worst-case fractional errors between the analytic formulas and the numerical solutions over the full grid of DM mass fractions and core radii. We will also add an explicit statement of the conditions (primarily the presence of a DM core with radius exceeding ~0.6 of the baryonic radius) under which sub-percent accuracy is achieved, together with a brief discussion of the regimes where the error grows. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard two-fluid TOV and Cowling derivations are self-contained

full rationale

The paper solves the standard two-fluid Tolman-Oppenheimer-Volkoff equations for equilibrium configurations with a fixed unified nuclear EOS for baryons and a fixed fermionic self-interacting EOS for DM. Crust thickness is obtained directly from the resulting density profiles at fixed total mass and DM fraction. Torsional mode frequencies follow from the relativistic Cowling-approximation wave equation applied to those profiles. Approximate analytic crust-thickness expressions are derived from the same equilibrium structure and validated numerically; they are not fitted to the target observables. No self-citations are invoked as load-bearing uniqueness theorems, no parameters are fitted to a data subset and then relabeled as predictions, and no ansatz is smuggled via prior work. The quantitative 12% figure is therefore an output of the chosen EOS and the standard equations, not a re-expression of the inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the two-fluid gravitational-only interaction, the choice of one nuclear and one fermionic EOS, and the Cowling approximation; these are domain-standard assumptions rather than new postulates, but they introduce parameter dependence that is not independently validated in the abstract.

free parameters (2)
  • DM mass fraction
    Held fixed while comparing models; its value is chosen rather than derived.
  • DM self-interaction coupling
    Parameter inside the fermionic DM EOS that controls the repulsive term.
axioms (2)
  • domain assumption Baryonic and DM fluids interact only through gravity
    Explicitly adopted in the construction of equilibrium solutions.
  • domain assumption Relativistic Cowling approximation for torsional modes
    Used to derive the oscillation equation without metric perturbations.

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Reference graph

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