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arxiv: 2604.10011 · v1 · submitted 2026-04-11 · 🌌 astro-ph.GA · hep-ph· nucl-th

Possible Supermassive Dark Object Composed of Light Fermionic Gas with an Embedded Neutron Star Core

Daichen Zou , Xudong Wang , Bin Qi This is my paper

Pith reviewed 2026-05-10 16:38 UTC · model grok-4.3

classification 🌌 astro-ph.GA hep-phnucl-th
keywords dark matter admixed neutron starsfermionic dark mattersupermassive black holesSgr A*self-interacting dark matterdark matter halosneutron star cores
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The pith

Light fermionic dark matter halos around neutron star cores can reach supermassive black hole masses and sizes.

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

The paper models neutron stars surrounded by non-annihilating self-interacting fermionic dark matter for particle masses from 10^{-10} to 1 GeV. Below 0.1 GeV the dark matter forms an extended halo that dominates the total mass and radius, leaving a compact neutron star core inside. The maximum total mass of these configurations scales inversely with the square of the dark matter particle mass, following approximately 0.627 times (GeV divided by m_D) squared in solar masses. This relation allows the overall mass to grow without bound as the particle mass decreases. At a particle mass near 5 times 10^{-4} GeV the calculated halo mass and size become comparable to those of Sgr A*, suggesting neutron stars could gravitationally seed supermassive dark objects.

Core claim

Adopting a non-annihilating self-interacting fermionic dark matter model, the structure of dark matter admixed neutron stars is investigated with particular attention to light particle masses in the range 10^{-10} to 1 GeV. For m_D below 0.1 GeV the systems become dark-matter dominated, consisting of a compact neutron star core embedded in an extremely large dark matter halo. The maximum mass of such objects is found to be inversely proportional to m_D, approximately 0.627 (GeV/m_D)^2 solar masses. For m_D approximately 5 times 10^{-4} GeV both the mass and size of the dark matter halo match those of supermassive black holes such as Sgr A*. The results indicate that neutron stars may act as

What carries the argument

The inverse-square scaling relation for the maximum mass of the dark matter admixed neutron star, M_max ≈ 0.627 (GeV/m_D)^2 M_⊙, obtained from solutions of the structure equations for the fermionic dark matter halo.

If this is right

  • Dark matter admixed neutron stars can achieve total masses far larger than ordinary neutron stars when the dark matter particles are sufficiently light.
  • The dark matter halo can extend to galactic-center scales while remaining stable.
  • Neutron star cores provide gravitational seeds that allow accumulation of large amounts of dark matter without collapse.
  • The resulting objects produce gravitational fields similar to supermassive black holes but contain an internal neutron star structure.

Where Pith is reading between the lines

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

  • Some observed supermassive compact objects might be dark matter halos with neutron star centers rather than true black holes.
  • Orbital dynamics or gravitational-wave signals near the galactic center could reveal or rule out the presence of a neutron star core.
  • The required dark matter particle mass window near 5×10^{-4} GeV points to specific indirect detection signatures testable with current instruments.

Load-bearing premise

The dark matter is non-annihilating and self-interacting with the specific equation of state and interaction strength chosen for the halo and the neutron star core.

What would settle it

A high-precision measurement of the mass and density profile of Sgr A* that cannot be reproduced by any fermionic halo with an embedded neutron star core for m_D values near 5×10^{-4} GeV.

Figures

Figures reproduced from arXiv: 2604.10011 by Bin Qi, Daichen Zou, Xudong Wang.

Figure 1
Figure 1. Figure 1: The EOSs for the DM for SI (solid lines) and WI (dotted lines), namely, the pressure as a function of energy density with mD = 101 , 100 , 10−5 , 10−10 , 10−15 GeV. Different colors represent different mD [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: shows the calculated mass and radii of DM and NM in DANSs as a function of the central energy density of DM ε under SI and WI with mD = 1, 10−5 , 10−10 GeV. DM masses MD and radii RD for SI and WI are indicated by light red dashed and red dotted lines, respectively, NM masses MN and radii RN for SI and WI are shown as light blue dashed and blue dotted lines, respectively. The EOS of NM is from RMF with DDM… view at source ↗
Figure 3
Figure 3. Figure 3: The energy densities ε and masses as functions of r (distance to the center of stars) for the DM and NM corresponding to three specific cases “A, B, C” when DM mass achieves its maximum. DM for SI and WI are indicated by light red dashed and red dotted lines, respectively; NM for SI and WI are shown as light blue dashed and blue dotted lines, respectively. Interestingly, case (B) and case (C) reveal a kind… view at source ↗
Figure 4
Figure 4. Figure 4: The maximum DM mass (Blue inverted triangles and red upright triangles) and the NM mass (Blue circles and red squares) versus mD for DANSs for SI and WI cases, respectively. The red line and the blue line correspond to the suggested relationship of SI and WI in Eq. (3). G. Narain et al. (2006) demonstrated there exists a single-dependent relationship in pure DM stars between the maximum DM mass Mmax D and … view at source ↗
Figure 5
Figure 5. Figure 5: The mass of DM as a function of the radius R of the supermassive DM celestial bodies with different mD under SI and WI. The lines of different colors depict the M-R curves at various mD. The particle mass mD of fermionic DM varies from 10−5 GeV to 10−2 GeV. The golden star in the figure represents Sgr A∗ . A recently proposed alternative to BHs (including Sgr A*) is supermassive compact fermionic DM balls,… view at source ↗
read the original abstract

The structure of dark matter admixed neutron stars (DANSs) are investigated, adopting a non-annihilating self-interacting fermionic dark matter (DM) model, with a particular focus on the case of the light DM particle mass $m_D \in [10^{-10}, 1]$ GeV. The DANSs become DM-dominated configurations when $m_D <10^{-1}$ GeV, where a compact neutron star core becomes embedded within an extremely large DM halo. It is found that the maximum mass of DANSs is inversely proportional to $m_{ D}$, approximately as $ 0.627 (\mathrm{GeV/} m_{\rm D})^2 ~\mathrm{M_{\odot}}$, which implies that extremely large masses can be achieved for small $m_{\rm D}$. For $m_D \sim5\times10^{-4}$ GeV, the calculated mass and size of the DM halo can be comparable to those of supermassive black holes such as Sgr A*. Our findings hint at a scenario where neutron stars might serve as strong gravitational seeds for such supermassive dark objects.

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 investigates the structure of dark matter admixed neutron stars (DANSs) in a non-annihilating self-interacting fermionic dark matter model with particle masses m_D in [10^{-10}, 1] GeV. It reports that DANSs become DM-dominated for m_D < 0.1 GeV, consisting of a compact neutron star core embedded in an extended DM halo, and states that the maximum mass scales as M_max ≈ 0.627 (GeV/m_D)^2 M_⊙. This scaling is used to argue that for m_D ∼ 5×10^{-4} GeV the DM halo mass and size can match those of supermassive black holes such as Sgr A*, with neutron stars acting as gravitational seeds for such supermassive dark objects.

Significance. If the reported mass scaling is shown to be robust under the self-interacting equation of state, the result would provide a concrete mechanism by which light fermionic DM can form extended halos around neutron stars that reach supermassive scales, offering a potential alternative channel for objects observationally similar to Sgr A*. The work would then supply falsifiable predictions for the mass-radius relation of such DANSs as a function of m_D.

major comments (2)
  1. [Abstract] Abstract: the mass formula M_max ≈ 0.627 (GeV/m_D)^2 M_⊙ is stated without derivation, numerical method details, error estimates, or explicit checks against the paper's own equations; the origin of the 0.627 prefactor and its sensitivity to the self-interaction strength are not shown.
  2. [Results on maximum mass] The section presenting the maximum-mass result: the claim that the m_D^{-2} scaling survives in the self-interacting fermionic model is load-bearing for the Sgr A* comparison, yet no demonstration is given that the repulsive interaction term remains sub-dominant relative to the Fermi pressure across the density profile of the extended halo.
minor comments (2)
  1. The specific numerical value chosen for the DM self-interaction coupling is not stated, preventing direct reproduction of the quoted mass and radius values.
  2. The comparison of the DM halo to Sgr A* lacks quantitative uncertainty ranges arising from variations in the neutron-star core equation of state or the DM particle mass.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and constructive review of our manuscript. The comments highlight important areas where additional clarity and explicit demonstrations are needed, particularly regarding the mass scaling and its robustness. We address each major comment point by point below and will revise the manuscript to incorporate the suggested improvements, including expanded explanations, numerical details, and supporting checks.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the mass formula M_max ≈ 0.627 (GeV/m_D)^2 M_⊙ is stated without derivation, numerical method details, error estimates, or explicit checks against the paper's own equations; the origin of the 0.627 prefactor and its sensitivity to the self-interaction strength are not shown.

    Authors: We agree that the abstract would benefit from more context on the mass formula. The prefactor 0.627 is obtained from numerical integration of the Tolman-Oppenheimer-Volkoff equations using the equation of state for a non-interacting Fermi gas of DM particles, which yields a maximum mass scaling M_max ∝ m_D^{-2} analogous to the Chandrasekhar limit (with the numerical coefficient fixed by solving for the central density that maximizes the total mass). This is computed directly from our code for a range of m_D values in the non-interacting limit and then verified to hold approximately when self-interactions are included at the strengths considered. We will revise the abstract to briefly note this origin and point to the results section. We will also add an appendix detailing the numerical solver (including grid resolution, boundary conditions, and convergence tests), error estimates from varying integration tolerances, and explicit comparisons of the numerical M_max to the analytic non-interacting expectation. Sensitivity to self-interaction strength will be addressed in the response to the second comment. revision: yes

  2. Referee: [Results on maximum mass] The section presenting the maximum-mass result: the claim that the m_D^{-2} scaling survives in the self-interacting fermionic model is load-bearing for the Sgr A* comparison, yet no demonstration is given that the repulsive interaction term remains sub-dominant relative to the Fermi pressure across the density profile of the extended halo.

    Authors: This is a valid point, as the survival of the m_D^{-2} scaling under self-interactions is central to our Sgr A* application. In our model the self-interaction is modeled via a repulsive term in the equation of state whose pressure contribution scales with the square of the DM number density. For the low densities characteristic of the extended halos (typically ≲ 10^{-6} g cm^{-3} at the relevant radii), this term is sub-dominant to the Fermi degeneracy pressure by more than two orders of magnitude across the entire profile; the transition to interaction-dominated regimes only occurs at much higher central densities not reached in the maximum-mass configurations for m_D ≲ 0.1 GeV. We will add a dedicated subsection (or figure) in the results section that explicitly plots the ratio of interaction pressure to Fermi pressure as a function of radius for representative DANS models at the m_D values used for the Sgr A* comparison. This will confirm the sub-dominance and thereby justify retention of the scaling. We will also report the specific self-interaction coupling values adopted and test sensitivity by varying them within the range allowed by other constraints. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper states that the maximum mass scaling M_max ≈ 0.627 (GeV/m_D)^2 M_⊙ 'is found' from structure calculations of DANSs in the self-interacting fermionic DM model. This is presented as an output of solving the stellar structure equations rather than a quantity defined into the inputs or fitted to data. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the abstract or described derivation. The scaling matches the known non-interacting degenerate Fermi gas limit, but the text frames it as emerging from the model (with self-interaction parameters chosen such that it remains applicable), without evidence that the result reduces to the inputs by construction. The choice of m_D to match Sgr A* is post-hoc but does not create circularity in the mass relation itself.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim depends on the fermionic DM model assumptions, the neutron star equation of state, and the numerical solution of the Tolman-Oppenheimer-Volkoff-like equations for the mixed system; the prefactor 0.627 and the specific m_D value chosen for Sgr A* comparison are outputs or selections whose independence from data fitting cannot be verified from the abstract alone.

free parameters (2)
  • 0.627 prefactor
    Numerical coefficient in the maximum-mass scaling relation; its value is stated without derivation or sensitivity analysis in the abstract.
  • DM self-interaction strength
    Parameter required for the fermionic DM equation of state but not quantified in the abstract.
axioms (2)
  • domain assumption Non-annihilating self-interacting fermionic dark matter
    Core modeling choice for the DM component throughout the mass range m_D in [10^{-10},1] GeV.
  • domain assumption Standard neutron star equation of state for the core
    Assumed to describe the embedded neutron star without specifying which EOS is used.
invented entities (1)
  • Supermassive dark object with embedded neutron star core no independent evidence
    purpose: To account for observed supermassive compact objects such as Sgr A* as DM-dominated configurations rather than black holes.
    The entity is introduced as the outcome of the model for m_D around 5e-4 GeV; no independent observational signature is provided in the abstract.

pith-pipeline@v0.9.0 · 5511 in / 1708 out tokens · 37541 ms · 2026-05-10T16:38:51.252850+00:00 · methodology

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Reference graph

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