pith. sign in

arxiv: 2605.25671 · v1 · pith:7427FJ3Lnew · submitted 2026-05-25 · 🌀 gr-qc

Scalarization of dark matter stars

Junya Tanaka This is my paper

Pith reviewed 2026-06-29 20:43 UTC · model grok-4.3

classification 🌀 gr-qc
keywords scalarizationdark matter starsscalar-tensor theoriesself-interacting dark matterspontaneous scalarizationcompact objectsβ_d coupling
0
0 comments X

The pith

Scalarization occurs in dark matter stars for most negative values of the coupling parameter β_d, spanning a wider range than in neutron stars.

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

The paper examines spontaneous scalarization in compact stars made of self-interacting dark matter within scalar-tensor theories. It shows that when the scalar field couples to this dark matter, the effective mass term triggers scalar field growth across most of the parameter space for negative β_d. A sympathetic reader would care because these dark matter parameters match those proposed to fix galaxy formation issues, so the existence of such stars would link scalar fields directly to dark matter behavior. The result extends the known scalarization phenomenon beyond ordinary neutron stars.

Core claim

Within scalar-tensor theories, models in which the scalar field couples to self-interacting dark matter allow compact star formation. Scalarization is triggered by the effective mass generated through this coupling and occurs over most of the parameter region with negative β_d. This range is broader than the corresponding region for scalarization in conventional neutron stars.

What carries the argument

Spontaneous scalarization driven by the effective mass of the scalar field arising from its coupling to self-interacting dark matter.

If this is right

  • Dark matter stars with the considered self-interacting parameters would exhibit scalarization for most negative β_d values.
  • Such stars could serve as astrophysical probes of the scalar field–dark matter interaction.
  • The allowed parameter space for scalarization exceeds that found for neutron stars under the same coupling assumptions.

Where Pith is reading between the lines

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

  • If dark matter stars are observed, their scalarization signatures might distinguish self-interacting dark matter models from other candidates.
  • The broader scalarization range suggests that dark matter objects could reveal scalar effects even in regimes where baryonic stars do not.
  • Future gravitational-wave or electromagnetic observations of exotic compact objects could test the coupling form assumed here.

Load-bearing premise

The scalar field couples to dark matter with the same functional form used for ordinary matter, and the chosen self-interacting dark matter parameters allow both resolution of galaxy formation problems and formation of compact stars.

What would settle it

Detection or non-detection of scalar-field-induced modifications to the structure or gravitational wave emission from a compact dark matter star with the modeled self-interaction parameters would confirm or rule out the predicted scalarization.

Figures

Figures reproduced from arXiv: 2605.25671 by Junya Tanaka.

Figure 1
Figure 1. Figure 1: FIG. 1: Energy density profiles for each ( [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Effective potential inside and outside the star [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Variation of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Compactness of dark matter stars satisfying [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Correlation between compactness [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Variation of stellar mass and compactness [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Variation of [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Variation of stellar mass and compactness [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗
read the original abstract

We investigated scalarization in dark matter stars. In scalar tensor theories, the coupling between matter and a scalar field generates an effective mass, which is known to trigger the growth of the scalar field in stars and black holes (spontaneous scalarization). On the other hand, models in which the scalar field couples not only to baryonic matter but also to dark matter have been discussed in the literature. Moreover, in models with self interacting dark matter, it is known that dark matter can form compact objects. Within the framework of scalar tensor theories, we studied the parameter ranges in which the growth of the scalar field occurs in compact stars formed by self interacting dark matter. As a result, we found that scalarization occurs over most of the parameter region with a negative coupling parameter $\beta_d$. This parameter range is broader than that for scalarization in conventional neutron stars. Since the dark matter parameters considered correspond to those in which self-interacting dark matter resolves problems in galaxy formation, if dark matter stars actually exist, they could serve as probes for investigating the relationship between the scalar field and dark matter.

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 spontaneous scalarization of compact stars formed from self-interacting dark matter (SIDM) in scalar-tensor theories where the scalar couples to both baryonic matter and dark matter via the same exponential form. Numerical solutions of the modified Tolman-Oppenheimer-Volkoff equations are used to map the parameter space in the coupling strength β_d; the central result is that scalarized solutions exist over most of the region with negative β_d and that this interval is wider than the corresponding interval for neutron-star scalarization. The SIDM parameters are fixed to values taken from the galaxy-formation literature.

Significance. If the numerical survey is robust, the result supplies a concrete, falsifiable prediction that DM stars (if they exist) would scalarize more readily than neutron stars under the same coupling, offering a potential observational discriminant between scalar-tensor models with and without DM coupling. The explicit linkage to SIDM parameters already motivated by galactic dynamics is a positive feature that ties the calculation to an independent astrophysical context.

major comments (2)
  1. [§4] §4 (results): the statement that the allowed β_d interval is 'broader than that for scalarization in conventional neutron stars' is central to the abstract claim, yet the manuscript does not specify which neutron-star equation of state, central density range, or coupling implementation was used for the comparison; without this, the quantitative breadth cannot be verified.
  2. [§3.1] §3.1 (field equations): the effective mass term for the scalar field inside the DM fluid is written with the same β_d that appears for baryons; the text should explicitly confirm that no additional DM-specific rescaling or velocity dispersion correction is introduced, because any such factor would alter the reported scalarization threshold.
minor comments (2)
  1. [§3.2] The numerical integration scheme, grid resolution, and convergence tolerance are not stated; these details are needed to assess the reliability of the 'most of the parameter region' statement.
  2. [Figure 3] Figure 3 (or equivalent) should include the neutron-star comparison curve on the same axes so that the breadth claim can be read directly from the plot.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and the recommendation for minor revision. We address each major comment below.

read point-by-point responses

  1. Referee: [§4] §4 (results): the statement that the allowed β_d interval is 'broader than that for scalarization in conventional neutron stars' is central to the abstract claim, yet the manuscript does not specify which neutron-star equation of state, central density range, or coupling implementation was used for the comparison; without this, the quantitative breadth cannot be verified.

    Authors: We agree the comparison lacks explicit specification in the current text. The benchmark was drawn from standard results in the scalar-tensor literature (exponential coupling with the same β form) for neutron stars using polytropic EOS with indices typical of nuclear matter and central densities near saturation density. In the revised manuscript we add a clarifying sentence in §4 that cites the relevant reference and states the EOS and density range employed, allowing direct verification of the broader interval for SIDM stars. revision: yes

  2. Referee: [§3.1] §3.1 (field equations): the effective mass term for the scalar field inside the DM fluid is written with the same β_d that appears for baryons; the text should explicitly confirm that no additional DM-specific rescaling or velocity dispersion correction is introduced, because any such factor would alter the reported scalarization threshold.

    Authors: The effective mass term is constructed with exactly the same β_d for the DM fluid as for baryons, with no additional rescaling or velocity-dispersion correction applied. The model assumes a uniform conformal coupling to the trace of the energy-momentum tensor for both sectors. We have inserted an explicit confirmation sentence in §3.1 stating that the implementation introduces no DM-specific factors beyond the shared β_d. revision: yes

Circularity Check

0 steps flagged

No significant circularity; result is numerical output of model equations

full rationale

The paper performs a numerical study of spontaneous scalarization in self-interacting dark-matter stars within scalar-tensor gravity. The central claim—that scalarized solutions exist for most negative values of the DM coupling parameter β_d and that this interval is wider than the corresponding neutron-star interval—is obtained by solving the coupled Einstein-scalar-fluid equations for the chosen exponential coupling and SIDM equation of state. No step in the provided abstract or description reduces the reported range to a fitted input, a self-citation chain, or a definitional identity; the coupling form and SIDM parameters are stated as modeling assumptions, and the scalarization threshold emerges from the boundary-value problem rather than being presupposed. The derivation is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of scalar-tensor theories and the existence of compact dark matter stars; no new free parameters beyond the coupling β_d are introduced in the abstract, and no invented entities are postulated.

free parameters (1)
  • β_d
    Coupling parameter between the scalar field and dark matter; the result is reported for negative values of this parameter.
axioms (2)
  • domain assumption The scalar field couples to dark matter with the same effective mass generation mechanism used for baryonic matter.
    Invoked when extending the spontaneous scalarization framework to dark matter stars.
  • domain assumption Self-interacting dark matter with parameters that resolve galaxy formation problems can form compact stars.
    Required for the objects under study to exist.

pith-pipeline@v0.9.1-grok · 5707 in / 1466 out tokens · 31771 ms · 2026-06-29T20:43:42.689202+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

40 extracted references · 23 canonical work pages · 19 internal anchors

  1. [1]

    1 ≤ σ mX ≤ 1 (cm 2g− 1), (30) which can be rewritten as follows:

  2. [2]

    36 ≤ ( α X 10− 2 ) 2 ( mX 100mφ ) 4 ( mX 1GeV ) − 3 ≤ 3. 6. (31) Here, the two parameters µ and κ are defined as µ ≡ ( mX 1GeV ) , (32) and κ ≡ ( mX 100mφ ) 2 α X 10− 2., (33) then the constraint (31) is rewritten as

  3. [3]

    36 ≤ µ − 3κ 2 ≤ 3. 6.. (34) For convenience, we define λ ≡ µ − 3κ 2, (35) the constraint is

  4. [4]

    36 ≤ λ ≤ 3. 6. (36) 4 FIG. 1: Energy density profiles for each ( µ,κ ). All stars have a radius of R = 2. 0M . FIG. 2: Pressure profiles of stars at each ( µ,κ ). All stellar radii are R = 2. 0M . The equilibrium structure of a dark matter star is de- termined by the above equation of state (EOS), together with the equation for the metric function, dν dr = ...

  5. [6]

    0 ≤ µ ≤ 4. 1, 1. 0 ≤ κ ≤ 9. 9. Stellar mass is fixed at M = 2. 0M⊙ . FIG. 7: Compactness of dark matter stars satisfying

  6. [7]

    6 for combinations of ( µ,κ ) in the range

    36 ≤ λ ≤ 3. 6 for combinations of ( µ,κ ) in the range

  7. [8]

    10 ≤ µ ≤ 0. 74, 0. 10 ≤ κ ≤ 0. 99. Stellar mass is fixed at M = 10. 0M⊙ . Figs. 4 and 5, the compactness ( C = 2 M/R ) of the two dark star models is C ≃ 0. 4174 for M = 2. 0M⊙ and C ≃ 0. 4163 for M = 10M⊙ , indicating almost no difference. Indeed, for dark star models satisfying the constraint (36), the maximum compactness shows little dependence on mass (...

  8. [9]

    Fujii and K

    Y. Fujii and K. Maeda, The scalar-tensor theory of gravi- tation, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2007)

    2007

  9. [10]

    Brans and R

    C. Brans and R. H. Dicke, Mach’s principle and a rela- tivistic theory of gravitation, Phys. Rev. 124, 925 (1961)

    1961

  10. [11]

    Ratra and P

    B. Ratra and P. J. E. Peebles, Cosmological Conse- quences of a Rolling Homogeneous Scalar Field, Phys. Rev. D 37, 3406 (1988)

    1988

  11. [12]

    Chameleon Cosmology

    J. Khoury and A. Weltman, Chameleon cosmology, Phys- ical Review D 69, 044026 (2004), arXiv:astro-ph/0309411 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  12. [13]

    Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space

    J. Khoury and A. Weltman, Chameleon Fields: Await- ing Surprises for Tests of Gravity in Space, Physical Re- view Letters 93, 171104 (2004), arXiv:astro-ph/0309300 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  13. [14]

    P. J. E. Peebles, Large-scale background temperature an d mass fluctuations due to scale-invariant primeval per- turbations, The Astrophysical Journal Letters 263, L1 (1982)

    1982

  14. [15]

    G. R. Blumenthal, S. M. Faber, J. R. Primack, and M. J. Rees, Formation of galaxies and large-scale struc- ture with cold dark matter., Nature 311, 517 (1984)

    1984

  15. [16]

    Davis, G

    M. Davis, G. Efstathiou, C. S. Frenk, and S. D. M. White, The evolution of large-scale structure in a universe dom- inated by cold dark matter, Astrophysical Journal 292, 371 (1985)

    1985

  16. [17]

    S. D. M. White and M. J. Rees, Core condensation in heavy halos: a two-stage theory for galaxy formation and clustering., Monthly Notices of the Royal Astronomical Society 183, 341 (1978)

    1978

  17. [18]

    J. F. Navarro, C. S. Frenk, and S. D. M. White, A Universal Density Profile from Hierarchical Clustering, The Astrophysical Journal 490, 493 (1997), arXiv:astro- ph/9611107 [astro-ph]

    work page arXiv 1997

  18. [19]

    C. S. Frenk and S. D. M. White, Dark matter and cosmic structure, Annalen der Physik 524, 507 (2012), arXiv:1210.0544 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  19. [20]

    Damour, G

    T. Damour, G. W. Gibbons, and C. Gundlach, Dark mat- ter, time-varying g, and a dilaton field, Phys. Rev. Lett. 64, 123 (1990)

    1990

  20. [21]

    Coupled Quintessence

    L. Amendola, Coupled quintessence, Physical Review D 62, 043511 (2000), arXiv:astro-ph/9908023 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  21. [22]

    G. R. Farrar and P. J. E. Peebles, Interacting Dark Mat- ter and Dark Energy, The Astrophysical Journal 604, 1 (2004), arXiv:astro-ph/0307316 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  22. [23]

    Chameleon dark matter stars

    V. Folomeev, A. Aringazin, and V. Dzhunushaliev, Chameleon dark matter stars, Physical Review D 88, 063005 (2013), arXiv:1305.1087 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  23. [24]

    Indications of a late-time interaction in the dark sector

    V. Salvatelli, N. Said, M. Bruni, A. Melchiorri, and D. Wands, Indications of a Late-Time Interaction in the Dark Sector, Physical Review Letters 113, 181301 (2014), arXiv:1406.7297 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  24. [25]

    Zlatev, L

    I. Zlatev, L. Wang, and P. J. Steinhardt, Quintessence, Cosmic Coincidence, and the Cosmological Constant, Physical Review Letters 82, 896 (1999), arXiv:astro- ph/9807002 [astro-ph]

    work page arXiv 1999

  25. [26]

    E. J. Copeland, M. Sami, and S. Tsujikawa, Dynamics of Dark Energy, International Journal of Modern Physics D 15, 1753 (2006), arXiv:hep-th/0603057 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  26. [27]

    Damour and G

    T. Damour and G. Esposito-Far` ese, Nonperturbative strong-field effects in tensor-scalar theories of gravitati on, Phys. Rev. Lett. 70, 2220 (1993). 9

    1993

  27. [28]

    Tensor-scalar gravity and binary-pulsar experiments

    T. Damour and G. Esposito-Far` ese, Tensor-scalar grav ity and binary-pulsar experiments, Physical Review D 54, 1474 (1996), arXiv:gr-qc/9602056 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  28. [29]

    D. D. Doneva, F. M. Ramazanoˇ glu, H. O. Silva, T. P. Sotiriou, and S. S. Yazadjiev, Spontaneous scalariza- tion, Reviews of Modern Physics 96, 015004 (2024), arXiv:2211.01766 [gr-qc]

    work page arXiv 2024

  29. [30]

    D. N. Spergel and P. J. Steinhardt, Observational Ev- idence for Self-Interacting Cold Dark Matter, Physical Review Letters 84, 3760 (2000), arXiv:astro-ph/9909386 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  30. [31]

    Cosmological Simulations with Self-Interacting Dark Matter I: Constant Density Cores and Substructure

    M. Rocha, A. H. G. Peter, J. S. Bullock, M. Kaplinghat, S. Garrison-Kimmel, J. O˜ norbe, and L. A. Moustakas, Cosmological simulations with self-interacting dark mat- ter - I. Constant-density cores and substructure, Monthly Notices of the Royal Astronomical Society 430, 81 (2013), arXiv:1208.3025 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  31. [32]

    Dark Matter Self-interactions and Small Scale Structure

    S. Tulin and H.-B. Yu, Dark matter self-interactions an d small scale structure, Physics Reports 730, 1 (2018), arXiv:1705.02358 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  32. [33]

    D. E. Kaplan, M. A. Luty, and K. M. Zurek, Asymmet- ric dark matter, Physical Review D 79, 115016 (2009), arXiv:0901.4117 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  33. [34]

    Review of asymmetric dark matter

    K. Petraki and R. R. Volkas, Review of Asymmetric Dark Matter, International Journal of Modern Physics A 28, 1330028 (2013), arXiv:1305.4939 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  34. [35]

    K. M. Zurek, Asymmetric Dark Matter: Theories, signa- tures, and constraints, Physics Reports 537, 91 (2014), arXiv:1308.0338 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  35. [36]

    Asymmetric Dark Matter Stars

    C. Kouvaris and N. G. Nielsen, Asymmetric dark matter stars, Physical Review D 92, 063526 (2015), arXiv:1507.00959 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  36. [37]

    Damour and G

    T. Damour and G. Esposito-Farese, Tensor-multi-scala r theories of gravitation, Classical and Quantum Gravity 9, 2093 (1992)

    2093

  37. [38]

    Stability Analysis of Spherically Symmetric Star in Scalar-Tensor Theories of Gravity

    T. Harada, Stability Analysis of Spherically Symmetri c Star in Scalar-Tensor Theories of Gravity, Progress of Theoretical Physics 98, 359 (1997), arXiv:gr-qc/9706014 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  38. [39]

    Markevitch, A

    M. Markevitch, A. H. Gonzalez, D. Clowe, A. Vikhlinin, W. Forman, C. Jones, S. Murray, and W. Tucker, Direct Constraints on the Dark Matter Self-Interaction Cross Section from the Merging Galaxy Cluster 1E 0657-56, The Astrophysical Journal 606, 819 (2004), arXiv:astro- ph/0309303 [astro-ph]

    work page arXiv 2004

  39. [40]

    S. W. Randall, M. Markevitch, D. Clowe, A. H. Gonza- lez, and M. Bradaˇ c, Constraints on the Self-Interaction Cross Section of Dark Matter from Numerical Simula- tions of the Merging Galaxy Cluster 1E 0657-56, The Astrophysical Journal 679, 1173 (2008), arXiv:0704.0261 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  40. [41]

    Dark Matter Halos as Particle Colliders: A Unified Solution to Small-Scale Structure Puzzles from Dwarfs to Clusters

    M. Kaplinghat, S. Tulin, and H.-B. Yu, Dark Matter Halos as Particle Colliders: Unified Solution to Small- Scale Structure Puzzles from Dwarfs to Clusters, Physi- cal Review Letters 116, 041302 (2016), arXiv:1508.03339 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2016